LMFDB - Embedded newform 684.3.t.a.265.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(265,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("684.265");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.t (of order $6$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			265.20
Character	$\chi$	$=$	684.265
Dual form			684.3.t.a.493.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0369083 + 2.99977i) q^{3} +(-0.692448 + 1.19936i) q^{5} +(5.80422 + 10.0532i) q^{7} +(-8.99728 - 0.221433i) q^{9} +O(q^{10})$	\(q+(-0.0369083 + 2.99977i) q^{3} +(-0.692448 + 1.19936i) q^{5} +(5.80422 + 10.0532i) q^{7} +(-8.99728 - 0.221433i) q^{9} +(-8.30905 - 14.3917i) q^{11} +(-15.1803 - 8.76433i) q^{13} +(-3.57224 - 2.12145i) q^{15} -24.3230 q^{17} +(2.37807 - 18.8506i) q^{19} +(-30.3715 + 17.0403i) q^{21} +(-11.2487 + 19.4834i) q^{23} +(11.5410 + 19.9897i) q^{25} +(0.996324 - 26.9816i) q^{27} +(21.3202 - 12.3092i) q^{29} +(37.3636 + 21.5719i) q^{31} +(43.4785 - 24.3941i) q^{33} -16.0765 q^{35} -21.6293i q^{37} +(26.8513 - 45.2139i) q^{39} +(-42.9818 - 24.8156i) q^{41} +(-20.8865 - 36.1764i) q^{43} +(6.49573 - 10.6376i) q^{45} +(9.47080 + 16.4039i) q^{47} +(-42.8779 + 74.2666i) q^{49} +(0.897719 - 72.9633i) q^{51} +37.8432i q^{53} +23.0144 q^{55} +(56.4597 + 7.82941i) q^{57} +(-78.8643 - 45.5323i) q^{59} +(37.9986 + 65.8155i) q^{61} +(-49.9960 - 91.7366i) q^{63} +(21.0231 - 12.1377i) q^{65} +(-62.1854 - 35.9028i) q^{67} +(-58.0305 - 34.4627i) q^{69} -52.3432i q^{71} -92.5575 q^{73} +(-60.3904 + 33.8827i) q^{75} +(96.4551 - 167.065i) q^{77} +(-80.9637 + 46.7444i) q^{79} +(80.9019 + 3.98459i) q^{81} +(24.1457 + 41.8215i) q^{83} +(16.8424 - 29.1719i) q^{85} +(36.1379 + 64.4100i) q^{87} -103.029i q^{89} -203.480i q^{91} +(-66.0898 + 111.286i) q^{93} +(20.9619 + 15.9052i) q^{95} +(34.2072 - 19.7495i) q^{97} +(71.5720 + 131.326i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) $ 80 * q + 2 * q^7 + 4 * q^9	$ 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) $ 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.0369083	+	2.99977i	−0.0123028	+	0.999924i
$3$	−0.0369083	+	2.99977i	−0.0123028	+	0.999924i
$4$		0			0
$5$	−0.692448	+	1.19936i	−0.138490	+	0.239871i	−0.926925	−	0.375246i	$-0.877558\pi$
$5$	−0.692448	+	1.19936i	−0.138490	+	0.239871i	0.788435	+	0.615118i	$0.210891\pi$
$6$		0			0
$7$	5.80422	+	10.0532i	0.829174	+	1.43617i	0.898687	+	0.438590i	$0.144522\pi$
$7$	5.80422	+	10.0532i	0.829174	+	1.43617i	−0.0695133	+	0.997581i	$0.522145\pi$
$8$		0			0
$9$	−8.99728	−	0.221433i	−0.999697	−	0.0246037i
$10$		0			0
$11$	−8.30905	−	14.3917i	−0.755368	−	1.30834i	−0.945191	−	0.326518i	$-0.894125\pi$
$11$	−8.30905	−	14.3917i	−0.755368	−	1.30834i	0.189823	−	0.981818i	$-0.439209\pi$
$12$		0			0
$13$	−15.1803	−	8.76433i	−1.16771	−	0.674179i	−0.214572	−	0.976708i	$-0.568836\pi$
$13$	−15.1803	−	8.76433i	−1.16771	−	0.674179i	−0.953140	+	0.302529i	$0.902169\pi$
$14$		0			0
$15$	−3.57224	−	2.12145i	−0.238149	−	0.141430i
$16$		0			0
$17$	−24.3230			−1.43076			−0.715381	−	0.698735i	$-0.753747\pi$
$17$	−24.3230			−1.43076			−0.715381	+	0.698735i	$0.753747\pi$
$18$		0			0
$19$	2.37807	−	18.8506i	0.125161	−	0.992136i
$19$	2.37807	−	18.8506i	0.125161	−	0.992136i
$20$		0			0
$21$	−30.3715	+	17.0403i	−1.44626	+	0.811442i
$22$		0			0
$23$	−11.2487	+	19.4834i	−0.489075	+	0.847103i	−0.999921	−	0.0125693i	$-0.995999\pi$
$23$	−11.2487	+	19.4834i	−0.489075	+	0.847103i	0.510846	+	0.859672i	$0.329332\pi$
$24$		0			0
$25$	11.5410	+	19.9897i	0.461641	+	0.799586i
$26$		0			0
$27$	0.996324	−	26.9816i	0.0369009	−	0.999319i
$28$		0			0
$29$	21.3202	−	12.3092i	0.735178	−	0.424455i	−0.0851352	−	0.996369i	$-0.527132\pi$
$29$	21.3202	−	12.3092i	0.735178	−	0.424455i	0.820314	+	0.571914i	$0.193799\pi$
$30$		0			0
$31$	37.3636	+	21.5719i	1.20528	+	0.695867i	0.961724	−	0.274021i	$-0.0883537\pi$
$31$	37.3636	+	21.5719i	1.20528	+	0.695867i	0.243553	+	0.969888i	$0.421687\pi$
$32$		0			0
$33$	43.4785	−	24.3941i	1.31753	−	0.739215i
$34$		0			0
$35$	−16.0765			−0.459328
$36$		0			0
$37$		−	21.6293i		−	0.584576i	−0.956330	−	0.292288i	$-0.905583\pi$
$37$		−	21.6293i		−	0.584576i	0.956330	−	0.292288i	$-0.0944166\pi$
$38$		0			0
$39$	26.8513	−	45.2139i	0.688494	−	1.15933i
$40$		0			0
$41$	−42.9818	−	24.8156i	−1.04834	−	0.605258i	−0.126154	−	0.992011i	$-0.540263\pi$
$41$	−42.9818	−	24.8156i	−1.04834	−	0.605258i	−0.922183	+	0.386753i	$0.873597\pi$
$42$		0			0
$43$	−20.8865	−	36.1764i	−0.485732	−	0.841312i	0.514134	−	0.857710i	$-0.328113\pi$
$43$	−20.8865	−	36.1764i	−0.485732	−	0.841312i	−0.999866	+	0.0163980i	$0.994780\pi$
$44$		0			0
$45$	6.49573	−	10.6376i	0.144349	−	0.236391i
$46$		0			0
$47$	9.47080	+	16.4039i	0.201506	+	0.349019i	0.949014	−	0.315234i	$-0.102083\pi$
$47$	9.47080	+	16.4039i	0.201506	+	0.349019i	−0.747508	+	0.664253i	$0.768750\pi$
$48$		0			0
$49$	−42.8779	+	74.2666i	−0.875059	+	1.51565i
$50$		0			0
$51$	0.897719	−	72.9633i	0.0176023	−	1.43065i
$52$		0			0
$53$			37.8432i			0.714023i	0.934100	+	0.357011i	$0.116204\pi$
$53$			37.8432i			0.714023i	−0.934100	+	0.357011i	$0.883796\pi$
$54$		0			0
$55$	23.0144			0.418443
$56$		0			0
$57$	56.4597	+	7.82941i	0.990521	+	0.137358i
$58$		0			0
$59$	−78.8643	−	45.5323i	−1.33668	−	0.771734i	−0.350369	−	0.936612i	$-0.613944\pi$
$59$	−78.8643	−	45.5323i	−1.33668	−	0.771734i	−0.986314	+	0.164877i	$0.947277\pi$
$60$		0			0
$61$	37.9986	+	65.8155i	0.622928	+	1.07894i	0.988938	+	0.148332i	$0.0473904\pi$
$61$	37.9986	+	65.8155i	0.622928	+	1.07894i	−0.366010	+	0.930611i	$0.619276\pi$
$62$		0			0
$63$	−49.9960	−	91.7366i	−0.793588	−	1.45614i
$64$		0			0
$65$	21.0231	−	12.1377i	0.323432	−	0.186734i
$66$		0			0
$67$	−62.1854	−	35.9028i	−0.928140	−	0.535862i	−0.0419173	−	0.999121i	$-0.513347\pi$
$67$	−62.1854	−	35.9028i	−0.928140	−	0.535862i	−0.886223	+	0.463259i	$0.846680\pi$
$68$		0			0
$69$	−58.0305	−	34.4627i	−0.841022	−	0.499460i
$70$		0			0
$71$		−	52.3432i		−	0.737228i	−0.929583	−	0.368614i	$-0.879833\pi$
$71$		−	52.3432i		−	0.737228i	0.929583	−	0.368614i	$-0.120167\pi$
$72$		0			0
$73$	−92.5575			−1.26791			−0.633955	−	0.773370i	$-0.718570\pi$
$73$	−92.5575			−1.26791			−0.633955	+	0.773370i	$0.718570\pi$
$74$		0			0
$75$	−60.3904	+	33.8827i	−0.805205	+	0.451769i
$76$		0			0
$77$	96.4551	−	167.065i	1.25266	−	2.16968i
$78$		0			0
$79$	−80.9637	+	46.7444i	−1.02486	+	0.591701i	−0.915507	−	0.402302i	$-0.868210\pi$
$79$	−80.9637	+	46.7444i	−1.02486	+	0.591701i	−0.109350	+	0.994003i	$0.534877\pi$
$80$		0			0
$81$	80.9019	+	3.98459i	0.998789	+	0.0491925i
$82$		0			0
$83$	24.1457	+	41.8215i	0.290912	+	0.503874i	0.974026	−	0.226438i	$-0.0727081\pi$
$83$	24.1457	+	41.8215i	0.290912	+	0.503874i	−0.683114	+	0.730312i	$0.739375\pi$
$84$		0			0
$85$	16.8424	−	29.1719i	0.198146	−	0.343198i
$86$		0			0
$87$	36.1379	+	64.4100i	0.415379	+	0.740345i
$88$		0			0
$89$		−	103.029i		−	1.15763i	−0.815458	−	0.578816i	$-0.803515\pi$
$89$		−	103.029i		−	1.15763i	0.815458	−	0.578816i	$-0.196485\pi$
$90$		0			0
$91$		−	203.480i		−	2.23605i
$92$		0			0
$93$	−66.0898	+	111.286i	−0.710642	+	1.19662i
$94$		0			0
$95$	20.9619	+	15.9052i	0.220651	+	0.167423i
$96$		0			0
$97$	34.2072	−	19.7495i	0.352651	−	0.203603i	−0.313201	−	0.949687i	$-0.601401\pi$
$97$	34.2072	−	19.7495i	0.352651	−	0.203603i	0.665852	+	0.746084i	$0.268068\pi$
$98$		0			0
$99$	71.5720	+	131.326i	0.722950	+	1.32653i
$100$		0			0
$101$	−44.5250	−	77.1195i	−0.440841	−	0.763559i	0.556911	−	0.830572i	$-0.311986\pi$
$101$	−44.5250	−	77.1195i	−0.440841	−	0.763559i	−0.997752	+	0.0670129i	$0.978653\pi$
$102$		0			0
$103$	67.8257	+	39.1592i	0.658502	+	0.380186i	0.791706	−	0.610902i	$-0.209193\pi$
$103$	67.8257	+	39.1592i	0.658502	+	0.380186i	−0.133204	+	0.991089i	$0.542527\pi$
$104$		0			0
$105$	0.593356	−	48.2258i	0.00565101	−	0.459293i
$106$		0			0
$107$			61.1111i			0.571132i	0.958359	+	0.285566i	$0.0921815\pi$
$107$			61.1111i			0.571132i	−0.958359	+	0.285566i	$0.907819\pi$
$108$		0			0
$109$			62.6258i			0.574549i	0.957848	+	0.287274i	$0.0927491\pi$
$109$			62.6258i			0.574549i	−0.957848	+	0.287274i	$0.907251\pi$
$110$		0			0
$111$	64.8830	+	0.798302i	0.584532	+	0.00719191i
$112$		0			0
$113$	83.9331	+	48.4588i	0.742770	+	0.428839i	0.823076	−	0.567932i	$-0.192256\pi$
$113$	83.9331	+	48.4588i	0.742770	+	0.428839i	−0.0803053	+	0.996770i	$0.525590\pi$
$114$		0			0
$115$	−15.5783	−	26.9825i	−0.135464	−	0.234630i
$116$		0			0
$117$	134.640	+	82.2165i	1.15077	+	0.702705i
$118$		0			0
$119$	−141.176	−	244.523i	−1.18635	−	2.05482i
$120$		0			0
$121$	−77.5807	+	134.374i	−0.641163	+	1.11053i
$122$		0			0
$123$	76.0274	−	128.020i	0.618109	−	1.04081i
$124$		0			0
$125$	−66.5887			−0.532710
$126$		0			0
$127$			96.4520i			0.759465i	0.925096	+	0.379732i	$0.123984\pi$
$127$			96.4520i			0.759465i	−0.925096	+	0.379732i	$0.876016\pi$
$128$		0			0
$129$	109.292	−	61.3194i	0.847224	−	0.475344i
$130$		0			0
$131$	−110.854	+	192.005i	−0.846214	+	1.46569i	0.0383486	+	0.999264i	$0.487790\pi$
$131$	−110.854	+	192.005i	−0.846214	+	1.46569i	−0.884563	+	0.466421i	$0.845543\pi$
$132$		0			0
$133$	203.312	−	85.5057i	1.52866	−	0.642900i
$134$		0			0
$135$	31.6706	+	19.8783i	0.234597	+	0.147247i
$136$		0			0
$137$	−23.7177	−	41.0803i	−0.173122	−	0.299856i	0.766388	−	0.642378i	$-0.222052\pi$
$137$	−23.7177	−	41.0803i	−0.173122	−	0.299856i	−0.939510	+	0.342522i	$0.888719\pi$
$138$		0			0
$139$	98.8598	−	171.230i	0.711222	−	1.23187i	−0.253177	−	0.967420i	$-0.581476\pi$
$139$	98.8598	−	171.230i	0.711222	−	1.23187i	0.964399	−	0.264452i	$-0.0851910\pi$
$140$		0			0
$141$	−49.5575	+	27.8048i	−0.351472	+	0.197197i
$142$		0			0
$143$			291.293i			2.03701i
$144$		0			0
$145$			34.0940i			0.235131i
$146$		0			0
$147$	−221.201	−	131.365i	−1.50477	−	0.893639i
$148$		0			0
$149$	−28.5488	+	49.4479i	−0.191603	+	0.331865i	−0.945781	−	0.324804i	$-0.894702\pi$
$149$	−28.5488	+	49.4479i	−0.191603	+	0.331865i	0.754179	+	0.656669i	$0.228035\pi$
$150$		0			0
$151$	−195.507	+	112.876i	−1.29475	+	0.747525i	−0.979492	−	0.201481i	$-0.935425\pi$
$151$	−195.507	+	112.876i	−1.29475	+	0.747525i	−0.315259	+	0.949006i	$0.602091\pi$
$152$		0			0
$153$	218.840	+	5.38591i	1.43033	+	0.0352020i
$154$		0			0
$155$	−51.7447	+	29.8748i	−0.333837	+	0.192741i
$156$		0			0
$157$	−116.518	+	201.815i	−0.742153	+	1.28545i	0.209360	+	0.977839i	$0.432862\pi$
$157$	−116.518	+	201.815i	−0.742153	+	1.28545i	−0.951513	+	0.307608i	$0.900472\pi$
$158$		0			0
$159$	−113.521	−	1.39673i	−0.713969	−	0.00878446i
$160$		0			0
$161$	−261.160			−1.62211
$162$		0			0
$163$	−64.6880			−0.396859			−0.198430	−	0.980115i	$-0.563584\pi$
$163$	−64.6880			−0.396859			−0.198430	+	0.980115i	$0.563584\pi$
$164$		0			0
$165$	−0.849421	+	69.0378i	−0.00514801	+	0.418411i
$166$		0			0
$167$	−176.830	−	102.093i	−1.05886	−	0.611333i	−0.133743	−	0.991016i	$-0.542700\pi$
$167$	−176.830	−	102.093i	−1.05886	−	0.611333i	−0.925117	+	0.379683i	$0.876033\pi$
$168$		0			0
$169$	69.1270	+	119.731i	0.409035	+	0.708470i
$170$		0			0
$171$	−25.5703	+	169.077i	−0.149534	+	0.988757i
$172$		0			0
$173$	22.9678	−	13.2604i	0.132762	−	0.0766499i	−0.432148	−	0.901803i	$-0.642244\pi$
$173$	22.9678	−	13.2604i	0.132762	−	0.0766499i	0.564910	+	0.825153i	$0.308911\pi$
$174$		0			0
$175$	−133.973	+	232.049i	−0.765562	+	1.32599i
$176$		0			0
$177$	139.497	−	234.894i	0.788121	−	1.32709i
$178$		0			0
$179$		−	302.350i		−	1.68911i	−0.535471	−	0.844554i	$-0.679866\pi$
$179$		−	302.350i		−	1.68911i	0.535471	−	0.844554i	$-0.320134\pi$
$180$		0			0
$181$			4.65695i			0.0257290i	0.999917	+	0.0128645i	$0.00409501\pi$
$181$			4.65695i			0.0257290i	−0.999917	+	0.0128645i	$0.995905\pi$
$182$		0			0
$183$	−198.834	+	111.558i	−1.08652	+	0.609607i
$184$		0			0
$185$	25.9412	+	14.9772i	0.140223	+	0.0809577i
$186$		0			0
$187$	202.101	+	350.049i	1.08075	+	1.87192i
$188$		0			0
$189$	277.034	−	146.591i	1.46579	−	0.775613i
$190$		0			0
$191$	−108.895	−	188.612i	−0.570133	−	0.987499i	−0.996552	−	0.0829732i	$-0.973558\pi$
$191$	−108.895	−	188.612i	−0.570133	−	0.987499i	0.426419	−	0.904526i	$-0.359775\pi$
$192$		0			0
$193$	96.2160	+	55.5504i	0.498529	+	0.287826i	0.728106	−	0.685465i	$-0.240401\pi$
$193$	96.2160	+	55.5504i	0.498529	+	0.287826i	−0.229577	+	0.973290i	$0.573734\pi$
$194$		0			0
$195$	35.6344	+	63.5125i	0.182740	+	0.325705i
$196$		0			0
$197$	−151.689			−0.769997			−0.384998	−	0.922917i	$-0.625798\pi$
$197$	−151.689			−0.769997			−0.384998	+	0.922917i	$0.625798\pi$
$198$		0			0
$199$	100.632			0.505689			0.252845	−	0.967507i	$-0.418634\pi$
$199$	100.632			0.505689			0.252845	+	0.967507i	$0.418634\pi$
$200$		0			0
$201$	109.995	−	185.217i	0.547240	−	0.921477i
$202$		0			0
$203$	247.494	+	142.891i	1.21918	+	0.703895i
$204$		0			0
$205$	59.5254	−	34.3670i	0.290368	−	0.167644i
$206$		0			0
$207$	105.522	−	172.806i	0.509769	−	0.834814i
$208$		0			0
$209$	−291.052	+	122.406i	−1.39259	+	0.585675i
$210$		0			0
$211$	74.0101	+	42.7298i	0.350759	+	0.202511i	0.665019	−	0.746826i	$-0.268423\pi$
$211$	74.0101	+	42.7298i	0.350759	+	0.202511i	−0.314261	+	0.949337i	$0.601757\pi$
$212$		0			0
$213$	157.018	+	1.93190i	0.737172	+	0.00906994i
$214$		0			0
$215$	57.8512			0.269075
$216$		0			0
$217$			500.831i			2.30798i
$218$		0			0
$219$	3.41614	−	277.651i	0.0155988	−	1.26781i
$220$		0			0
$221$	369.229	+	213.174i	1.67072	+	0.964590i
$222$		0			0
$223$	−19.0130	+	10.9771i	−0.0852600	+	0.0492249i	−0.542024	−	0.840363i	$-0.682342\pi$
$223$	−19.0130	+	10.9771i	−0.0852600	+	0.0492249i	0.456764	+	0.889588i	$0.349008\pi$
$224$		0			0
$225$	−99.4115	−	182.408i	−0.441829	−	0.810702i
$226$		0			0
$227$	−269.513	+	155.603i	−1.18728	+	0.685477i	−0.957688	−	0.287809i	$-0.907073\pi$
$227$	−269.513	+	155.603i	−1.18728	+	0.685477i	−0.229594	+	0.973286i	$0.573740\pi$
$228$		0			0
$229$	16.1360	−	27.9484i	0.0704629	−	0.122045i	−0.828641	−	0.559780i	$-0.810886\pi$
$229$	16.1360	−	27.9484i	0.0704629	−	0.122045i	0.899104	+	0.437735i	$0.144219\pi$
$230$		0			0
$231$	497.597	+	295.509i	2.15410	+	1.27926i
$232$		0			0
$233$	−55.0046			−0.236071			−0.118036	−	0.993009i	$-0.537660\pi$
$233$	−55.0046			−0.236071			−0.118036	+	0.993009i	$0.537660\pi$
$234$		0			0
$235$	−26.2322			−0.111626
$236$		0			0
$237$	−137.234	−	244.598i	−0.579048	−	1.03206i
$238$		0			0
$239$	9.67357	−	16.7551i	0.0404752	−	0.0701051i	−0.845078	−	0.534643i	$-0.820446\pi$
$239$	9.67357	−	16.7551i	0.0404752	−	0.0701051i	0.885553	+	0.464538i	$0.153779\pi$
$240$		0			0
$241$	156.782	−	90.5179i	0.650546	−	0.375593i	−0.138120	−	0.990416i	$-0.544106\pi$
$241$	156.782	−	90.5179i	0.650546	−	0.375593i	0.788665	+	0.614823i	$0.210772\pi$
$242$		0			0
$243$	−14.9388	+	242.540i	−0.0614766	+	0.998109i
$244$		0			0
$245$	−59.3814	−	102.852i	−0.242373	−	0.419803i
$246$		0			0
$247$	−201.312	+	265.315i	−0.815030	+	1.07415i
$248$		0			0
$249$	−126.346	+	70.8880i	−0.507415	+	0.284691i
$250$		0			0
$251$	9.34226			0.0372202			0.0186101	−	0.999827i	$-0.494076\pi$
$251$	9.34226			0.0372202			0.0186101	+	0.999827i	$0.494076\pi$
$252$		0			0
$253$	373.865			1.47773
$254$		0			0
$255$	86.8874	+	51.6000i	0.340735	+	0.202353i
$256$		0			0
$257$	378.610	+	218.591i	1.47319	+	0.850548i	0.999545	−	0.0301663i	$-0.00960369\pi$
$257$	378.610	+	218.591i	1.47319	+	0.850548i	0.473648	+	0.880714i	$0.342937\pi$
$258$		0			0
$259$	217.444	−	125.541i	0.839551	−	0.484715i
$260$		0			0
$261$	−194.549	+	106.028i	−0.745399	+	0.406239i
$262$		0			0
$263$	129.008	+	223.448i	0.490524	+	0.849612i	0.999941	−	0.0109081i	$-0.00347222\pi$
$263$	129.008	+	223.448i	0.490524	+	0.849612i	−0.509417	+	0.860520i	$0.670139\pi$
$264$		0			0
$265$	−45.3875	−	26.2045i	−0.171274	−	0.0988848i
$266$		0			0
$267$	309.065	+	3.80264i	1.15755	+	0.0142421i
$268$		0			0
$269$		−	2.59527i		−	0.00964786i	−0.999988	−	0.00482393i	$-0.998464\pi$
$269$		−	2.59527i		−	0.00964786i	0.999988	−	0.00482393i	$-0.00153551\pi$
$270$		0			0
$271$	−422.228			−1.55804			−0.779018	−	0.627001i	$-0.784282\pi$
$271$	−422.228			−1.55804			−0.779018	+	0.627001i	$0.784282\pi$
$272$		0			0
$273$	610.395	+	7.51012i	2.23588	+	0.0275096i
$274$		0			0
$275$	191.790	−	332.190i	0.697418	−	1.20796i
$276$		0			0
$277$	67.1788	+	116.357i	0.242523	+	0.420061i	0.961432	−	0.275042i	$-0.0886918\pi$
$277$	67.1788	+	116.357i	0.242523	+	0.420061i	−0.718910	+	0.695104i	$0.755358\pi$
$278$		0			0
$279$	−331.394	−	202.362i	−1.18779	−	0.725310i
$280$		0			0
$281$	−446.841	+	257.984i	−1.59018	+	0.918092i	−0.596908	+	0.802309i	$0.703604\pi$
$281$	−446.841	+	257.984i	−1.59018	+	0.918092i	−0.993275	+	0.115783i	$0.963062\pi$
$282$		0			0
$283$	−149.316	+	258.623i	−0.527618	+	0.913861i	0.471864	+	0.881671i	$0.343581\pi$
$283$	−149.316	+	258.623i	−0.527618	+	0.913861i	−0.999482	+	0.0321898i	$0.989752\pi$
$284$		0			0
$285$	−48.4857	+	62.2938i	−0.170125	+	0.218575i
$286$		0			0
$287$		−	576.140i		−	2.00745i
$288$		0			0
$289$	302.606			1.04708
$290$		0			0
$291$	57.9815	+	103.343i	0.199249	+	0.355129i
$292$		0			0
$293$	253.427	+	146.316i	0.864938	+	0.499372i	0.865663	−	0.500628i	$-0.166897\pi$
$293$	253.427	+	146.316i	0.864938	+	0.499372i	−0.000724815		1.00000i	$0.500231\pi$
$294$		0			0
$295$	109.219	−	63.0576i	0.370234	−	0.213754i
$296$		0			0
$297$	−396.590	+	209.853i	−1.33532	+	0.706575i
$298$		0			0
$299$	341.517	−	197.175i	1.14220	−	0.659449i
$300$		0			0
$301$	242.459	−	419.952i	0.805512	−	1.39519i
$302$		0			0
$303$	232.984	−	130.718i	0.768925	−	0.431414i
$304$		0			0
$305$	−105.248			−0.345076
$306$		0			0
$307$			230.156i			0.749693i	0.927087	+	0.374846i	$0.122305\pi$
$307$			230.156i			0.749693i	−0.927087	+	0.374846i	$0.877695\pi$
$308$		0			0
$309$	−119.972	+	202.016i	−0.388259	+	0.653775i
$310$		0			0
$311$	217.809	−	377.256i	0.700350	−	1.21304i	−0.267994	−	0.963421i	$-0.586361\pi$
$311$	217.809	−	377.256i	0.700350	−	1.21304i	0.968344	−	0.249621i	$-0.0803059\pi$
$312$		0			0
$313$	−145.383	−	251.811i	−0.464484	−	0.804509i	0.534695	−	0.845045i	$-0.320427\pi$
$313$	−145.383	−	251.811i	−0.464484	−	0.804509i	−0.999178	+	0.0405363i	$0.987093\pi$
$314$		0			0
$315$	144.645	+	3.55987i	0.459189	+	0.0113012i
$316$		0			0
$317$	−262.611	+	151.618i	−0.828425	+	0.478291i	−0.853313	−	0.521399i	$-0.825410\pi$
$317$	−262.611	+	151.618i	−0.828425	+	0.478291i	0.0248882	+	0.999690i	$0.492077\pi$
$318$		0			0
$319$	−354.301	−	204.556i	−1.11066	−	0.641240i
$320$		0			0
$321$	−183.319	−	2.25551i	−0.571088	−	0.00702650i
$322$		0			0
$323$	−57.8416	+	458.502i	−0.179076	+	1.41951i
$324$		0			0
$325$		−	404.598i		−	1.24492i
$326$		0			0
$327$	−187.863	−	2.31141i	−0.574505	−	0.00706854i
$328$		0			0
$329$	−109.941	+	190.424i	−0.334168	+	0.578795i
$330$		0			0
$331$	−538.607	+	310.965i	−1.62721	+	0.939471i	−0.642291	+	0.766461i	$0.722016\pi$
$331$	−538.607	+	310.965i	−1.62721	+	0.939471i	−0.984920	+	0.173010i	$0.944651\pi$
$332$		0			0
$333$	−4.78945	+	194.605i	−0.0143827	+	0.584399i
$334$		0			0
$335$	86.1203	−	49.7216i	0.257076	−	0.148423i
$336$		0			0
$337$	23.4116	+	13.5167i	0.0694707	+	0.0401089i	0.534333	−	0.845274i	$-0.320563\pi$
$337$	23.4116	+	13.5167i	0.0694707	+	0.0401089i	−0.464862	+	0.885383i	$0.653896\pi$
$338$		0			0
$339$	−148.463	+	249.992i	−0.437944	+	0.737438i
$340$		0			0
$341$		−	716.967i		−	2.10254i
$342$		0			0
$343$	−426.677			−1.24395
$344$		0			0
$345$	81.5162	−	45.7356i	0.236279	−	0.132567i
$346$		0			0
$347$	70.4925	−	122.097i	0.203148	−	0.351864i	−0.746393	−	0.665506i	$-0.768216\pi$
$347$	70.4925	−	122.097i	0.203148	−	0.351864i	0.949541	+	0.313642i	$0.101549\pi$
$348$		0			0
$349$	5.68571	+	9.84794i	0.0162914	+	0.0282176i	0.874056	−	0.485825i	$-0.161481\pi$
$349$	5.68571	+	9.84794i	0.0162914	+	0.0282176i	−0.857765	+	0.514042i	$0.828147\pi$
$350$		0			0
$351$	−251.600	+	400.856i	−0.716810	+	1.14204i
$352$		0			0
$353$	−61.5296	−	106.572i	−0.174305	−	0.301905i	0.765616	−	0.643298i	$-0.222434\pi$
$353$	−61.5296	−	106.572i	−0.174305	−	0.301905i	−0.939920	+	0.341394i	$0.889101\pi$
$354$		0			0
$355$	62.7781	+	36.2449i	0.176840	+	0.102098i
$356$		0			0
$357$	738.725	−	414.470i	2.06926	−	1.16098i
$358$		0			0
$359$	257.247			0.716566			0.358283	−	0.933613i	$-0.383362\pi$
$359$	257.247			0.716566			0.358283	+	0.933613i	$0.383362\pi$
$360$		0			0
$361$	−349.690	−	89.6560i	−0.968669	−	0.248354i
$362$		0			0
$363$	−400.227	−	237.684i	−1.10255	−	0.654777i
$364$		0			0
$365$	64.0913	−	111.009i	0.175593	−	0.304135i
$366$		0			0
$367$	−7.37211	−	12.7689i	−0.0200875	−	0.0347926i	0.855807	−	0.517295i	$-0.173061\pi$
$367$	−7.37211	−	12.7689i	−0.0200875	−	0.0347926i	−0.875894	+	0.482503i	$0.839728\pi$
$368$		0			0
$369$	381.224	+	232.790i	1.03313	+	0.630867i
$370$		0			0
$371$	−380.445	+	219.650i	−1.02546	+	0.592049i
$372$		0			0
$373$	596.411	+	344.338i	1.59896	+	0.923158i	0.991689	+	0.128660i	$0.0410676\pi$
$373$	596.411	+	344.338i	1.59896	+	0.923158i	0.607267	+	0.794498i	$0.292266\pi$
$374$		0			0
$375$	2.45768	−	199.751i	0.00655380	−	0.532669i
$376$		0			0
$377$	−431.528			−1.14464
$378$		0			0
$379$		−	244.342i		−	0.644702i	−0.946620	−	0.322351i	$-0.895527\pi$
$379$		−	244.342i		−	0.644702i	0.946620	−	0.322351i	$-0.104473\pi$
$380$		0			0
$381$	−289.334	−	3.55988i	−0.759407	−	0.00934352i
$382$		0			0
$383$	−578.360	−	333.917i	−1.51008	−	0.871845i	−0.999931	−	0.0117584i	$-0.996257\pi$
$383$	−578.360	−	333.917i	−1.51008	−	0.871845i	−0.510149	−	0.860086i	$-0.670410\pi$
$384$		0			0
$385$	133.580	+	231.368i	0.346962	+	0.600956i
$386$		0			0
$387$	179.911	+	330.114i	0.464885	+	0.853008i
$388$		0			0
$389$	146.481	+	253.713i	0.376558	+	0.652218i	0.990559	−	0.137088i	$-0.0437742\pi$
$389$	146.481	+	253.713i	0.376558	+	0.652218i	−0.614001	+	0.789305i	$0.710441\pi$
$390$		0			0
$391$	273.602	−	473.893i	0.699750	−	1.21200i
$392$		0			0
$393$	−571.879	−	339.624i	−1.45516	−	0.864182i
$394$		0			0
$395$		−	129.472i		−	0.327778i
$396$		0			0
$397$	296.001			0.745593			0.372797	−	0.927913i	$-0.378399\pi$
$397$	296.001			0.745593			0.372797	+	0.927913i	$0.378399\pi$
$398$		0			0
$399$	248.994	+	613.044i	0.624045	+	1.53645i
$400$		0			0
$401$	363.704	+	209.984i	0.906992	+	0.523652i	0.879462	−	0.475969i	$-0.157903\pi$
$401$	363.704	+	209.984i	0.906992	+	0.523652i	0.0275298	+	0.999621i	$0.491236\pi$
$402$		0			0
$403$	−378.126	−	654.933i	−0.938278	−	1.62515i
$404$		0			0
$405$	−60.7994	+	94.2711i	−0.150122	+	0.232768i
$406$		0			0
$407$	−311.283	+	179.719i	−0.764822	+	0.441570i
$408$		0			0
$409$	−169.833	−	98.0530i	−0.415239	−	0.239738i	0.277799	−	0.960639i	$-0.410395\pi$
$409$	−169.833	−	98.0530i	−0.415239	−	0.239738i	−0.693038	+	0.720901i	$0.743728\pi$
$410$		0			0
$411$	124.107	−	69.6316i	0.301963	−	0.169420i
$412$		0			0
$413$		−	1057.12i		−	2.55961i
$414$		0			0
$415$	−66.8785			−0.161153
$416$		0			0
$417$	510.003	+	302.877i	1.22303	+	0.726323i
$418$		0			0
$419$	34.9728	−	60.5746i	0.0834672	−	0.144569i	−0.821270	−	0.570540i	$-0.806734\pi$
$419$	34.9728	−	60.5746i	0.0834672	−	0.144569i	0.904737	+	0.425971i	$0.140067\pi$
$420$		0			0
$421$	−352.880	+	203.735i	−0.838195	+	0.483932i	−0.856650	−	0.515898i	$-0.827458\pi$
$421$	−352.880	+	203.735i	−0.838195	+	0.483932i	0.0184555	+	0.999830i	$0.494125\pi$
$422$		0			0
$423$	−81.5790	−	149.688i	−0.192858	−	0.353871i
$424$		0			0
$425$	−280.712	−	486.207i	−0.660499	−	1.14402i
$426$		0			0
$427$	−441.104	+	764.015i	−1.03303	+	1.78926i
$428$		0			0
$429$	−873.813	−	10.7511i	−2.03686	−	0.0250609i
$430$		0			0
$431$			285.246i			0.661824i	0.943662	+	0.330912i	$0.107356\pi$
$431$			285.246i			0.661824i	−0.943662	+	0.330912i	$0.892644\pi$
$432$		0			0
$433$		−	492.003i		−	1.13627i	−0.822937	−	0.568133i	$-0.807666\pi$
$433$		−	492.003i		−	1.13627i	0.822937	−	0.568133i	$-0.192334\pi$
$434$		0			0
$435$	−102.274	−	1.25835i	−0.235113	−	0.00289276i
$436$		0			0
$437$	340.523	+	258.378i	0.779228	+	0.591254i
$438$		0			0
$439$	137.637	−	79.4645i	0.313523	−	0.181013i	−0.334979	−	0.942226i	$-0.608729\pi$
$439$	137.637	−	79.4645i	0.313523	−	0.181013i	0.648502	+	0.761213i	$0.275396\pi$
$440$		0			0
$441$	402.229	−	658.703i	0.912084	−	1.49366i
$442$		0			0
$443$	357.264	+	618.799i	0.806465	+	1.39684i	0.915298	+	0.402778i	$0.131955\pi$
$443$	357.264	+	618.799i	0.806465	+	1.39684i	−0.108833	+	0.994060i	$0.534711\pi$
$444$		0			0
$445$	123.569	+	71.3425i	0.277683	+	0.160320i
$446$		0			0
$447$	−147.279	−	87.4649i	−0.329483	−	0.195671i
$448$		0			0
$449$			158.209i			0.352360i	0.984358	+	0.176180i	$0.0563740\pi$
$449$			158.209i			0.352360i	−0.984358	+	0.176180i	$0.943626\pi$
$450$		0			0
$451$			824.775i			1.82877i
$452$		0			0
$453$	−331.387	−	590.644i	−0.731539	−	1.30385i
$454$		0			0
$455$	244.045	+	140.900i	0.536363	+	0.309669i
$456$		0			0
$457$	399.852	+	692.564i	0.874949	+	1.51546i	0.856817	+	0.515621i	$0.172439\pi$
$457$	399.852	+	692.564i	0.874949	+	1.51546i	0.0181326	+	0.999836i	$0.494228\pi$
$458$		0			0
$459$	−24.2335	+	656.272i	−0.0527964	+	1.42979i
$460$		0			0
$461$	329.149	+	570.102i	0.713988	+	1.23666i	0.963348	+	0.268253i	$0.0864463\pi$
$461$	329.149	+	570.102i	0.713988	+	1.23666i	−0.249360	+	0.968411i	$0.580220\pi$
$462$		0			0
$463$	310.681	−	538.116i	0.671018	−	1.16224i	−0.306598	−	0.951839i	$-0.599191\pi$
$463$	310.681	−	538.116i	0.671018	−	1.16224i	0.977616	−	0.210398i	$-0.0674761\pi$
$464$		0			0
$465$	−87.7079	−	156.325i	−0.188619	−	0.336183i
$466$		0			0
$467$	302.546			0.647850			0.323925	−	0.946083i	$-0.394997\pi$
$467$	302.546			0.647850			0.323925	+	0.946083i	$0.394997\pi$
$468$		0			0
$469$		−	833.549i		−	1.77729i
$470$		0			0
$471$	−601.099	−	356.976i	−1.27622	−	0.757911i
$472$		0			0
$473$	−347.093	+	601.183i	−0.733813	+	1.27100i
$474$		0			0
$475$	404.262	−	170.019i	0.851078	−	0.357934i
$476$		0			0
$477$	8.37974	−	340.486i	0.0175676	−	0.713807i
$478$		0			0
$479$	−51.3598	−	88.9577i	−0.107223	−	0.185715i	0.807421	−	0.589975i	$-0.200863\pi$
$479$	−51.3598	−	88.9577i	−0.107223	−	0.185715i	−0.914644	+	0.404260i	$0.867529\pi$
$480$		0			0
$481$	−189.566	+	328.339i	−0.394109	+	0.682617i
$482$		0			0
$483$	9.63899	−	783.421i	0.0199565	−	1.62199i
$484$		0			0
$485$			54.7021i			0.112788i
$486$		0			0
$487$		−	369.083i		−	0.757870i	−0.925423	−	0.378935i	$-0.876290\pi$
$487$		−	369.083i		−	0.757870i	0.925423	−	0.378935i	$-0.123710\pi$
$488$		0			0
$489$	2.38753	−	194.049i	0.00488247	−	0.396829i
$490$		0			0
$491$	−139.855	+	242.235i	−0.284836	+	0.493351i	−0.972569	−	0.232613i	$-0.925273\pi$
$491$	−139.855	+	242.235i	−0.284836	+	0.493351i	0.687733	+	0.725964i	$0.258606\pi$
$492$		0			0
$493$	−518.570	+	299.396i	−1.05187	+	0.607295i
$494$		0			0
$495$	−207.067	−	5.09614i	−0.418316	−	0.0102952i
$496$		0			0
$497$	526.216	−	303.811i	1.05878	−	0.611290i
$498$		0			0
$499$	100.570	−	174.193i	0.201544	−	0.349084i	−0.747482	−	0.664282i	$-0.768737\pi$
$499$	100.570	−	174.193i	0.201544	−	0.349084i	0.949026	+	0.315198i	$0.102071\pi$
$500$		0			0
$501$	312.781	−	526.680i	0.624313	−	1.05126i
$502$		0			0
$503$	−850.812			−1.69148			−0.845738	−	0.533599i	$-0.820839\pi$
$503$	−850.812			−1.69148			−0.845738	+	0.533599i	$0.820839\pi$
$504$		0			0
$505$	123.325			0.244208
$506$		0			0
$507$	−361.718	+	202.946i	−0.713448	+	0.400288i
$508$		0			0
$509$	−301.727	−	174.202i	−0.592783	−	0.342244i	0.173414	−	0.984849i	$-0.444520\pi$
$509$	−301.727	−	174.202i	−0.592783	−	0.342244i	−0.766197	+	0.642605i	$0.777853\pi$
$510$		0			0
$511$	−537.224	−	930.499i	−1.05132	−	1.82094i
$512$		0			0
$513$	−506.250	−	82.9454i	−0.986842	−	0.161687i
$514$		0			0
$515$	−93.9316	+	54.2314i	−0.182391	+	0.105304i
$516$		0			0
$517$	157.387	−	272.602i	0.304423	−	0.527276i
$518$		0			0
$519$	38.9306	+	69.3875i	0.0750108	+	0.133695i
$520$		0			0
$521$		−	725.985i		−	1.39345i	−0.717340	−	0.696723i	$-0.754641\pi$
$521$		−	725.985i		−	1.39345i	0.717340	−	0.696723i	$-0.245359\pi$
$522$		0			0
$523$		−	838.779i		−	1.60378i	−0.597469	−	0.801892i	$-0.703827\pi$
$523$		−	838.779i		−	1.60378i	0.597469	−	0.801892i	$-0.296173\pi$
$524$		0			0
$525$	−691.148	−	410.454i	−1.31647	−	0.781817i
$526$		0			0
$527$	−908.793	−	524.692i	−1.72446	−	0.995620i
$528$		0			0
$529$	11.4322	+	19.8011i	0.0216110	+	0.0374313i
$530$		0			0
$531$	699.481	+	427.130i	1.31729	+	0.804388i
$532$		0			0
$533$	434.984	+	753.414i	0.816104	+	1.41353i
$534$		0			0
$535$	−73.2939	−	42.3163i	−0.136998	−	0.0790958i
$536$		0			0
$537$	906.982	+	11.1592i	1.68898	+	0.0207807i
$538$		0			0
$539$	1425.10			2.64397
$540$		0			0
$541$	−320.683			−0.592759			−0.296380	−	0.955070i	$-0.595779\pi$
$541$	−320.683			−0.592759			−0.296380	+	0.955070i	$0.595779\pi$
$542$		0			0
$543$	−13.9698	−	0.171880i	−0.0257270	−	0.000316538i
$544$		0			0
$545$	−75.1106	−	43.3651i	−0.137818	−	0.0795690i
$546$		0			0
$547$	89.6166	−	51.7402i	0.163833	−	0.0945890i	−0.415842	−	0.909437i	$-0.636513\pi$
$547$	89.6166	−	51.7402i	0.163833	−	0.0945890i	0.579675	+	0.814848i	$0.303180\pi$
$548$		0			0
$549$	−327.310	−	600.574i	−0.596193	−	1.09394i
$550$		0			0
$551$	−181.335	−	431.170i	−0.329102	−	0.782523i
$552$		0			0
$553$	−939.862	−	542.629i	−1.69957	−	0.981247i
$554$		0			0
$555$	−45.8856	+	77.2651i	−0.0826768	+	0.139216i
$556$		0			0
$557$	299.314			0.537367			0.268684	−	0.963228i	$-0.413411\pi$
$557$	299.314			0.537367			0.268684	+	0.963228i	$0.413411\pi$
$558$		0			0
$559$			732.223i			1.30988i
$560$		0			0
$561$	−1057.53	+	593.336i	−1.88507	+	1.05764i
$562$		0			0
$563$	687.954	+	397.190i	1.22194	+	0.705489i	0.965332	−	0.261026i	$-0.0840607\pi$
$563$	687.954	+	397.190i	1.22194	+	0.705489i	0.256611	+	0.966515i	$0.417394\pi$
$564$		0			0
$565$	−116.239	+	67.1104i	−0.205732	+	0.118779i
$566$		0			0
$567$	429.514	+	836.451i	0.757521	+	1.47522i
$568$		0			0
$569$	−579.312	+	334.466i	−1.01812	+	0.587813i	−0.913560	−	0.406705i	$-0.866678\pi$
$569$	−579.312	+	334.466i	−1.01812	+	0.587813i	−0.104563	+	0.994518i	$0.533344\pi$
$570$		0			0
$571$	273.051	−	472.937i	0.478197	−	0.828262i	−0.521490	−	0.853257i	$-0.674624\pi$
$571$	273.051	−	472.937i	0.478197	−	0.828262i	0.999688	+	0.0249954i	$0.00795710\pi$
$572$		0			0
$573$	569.813	−	319.700i	0.994438	−	0.557941i
$574$		0			0
$575$	−519.288			−0.903109
$576$		0			0
$577$	817.312			1.41648			0.708242	−	0.705969i	$-0.249488\pi$
$577$	817.312			1.41648			0.708242	+	0.705969i	$0.249488\pi$
$578$		0			0
$579$	−170.190	+	286.576i	−0.293937	+	0.494950i
$580$		0			0
$581$	−280.293	+	485.482i	−0.482433	+	0.835598i
$582$		0			0
$583$	544.628	−	314.441i	0.934182	−	0.539350i
$584$		0			0
$585$	−191.838	+	104.551i	−0.327929	+	0.178720i
$586$		0			0
$587$	−269.046	−	466.002i	−0.458341	−	0.793870i	0.540532	−	0.841323i	$-0.318223\pi$
$587$	−269.046	−	466.002i	−0.458341	−	0.793870i	−0.998873	+	0.0474530i	$0.984890\pi$
$588$		0			0
$589$	495.496	−	653.026i	0.841249	−	1.10870i
$590$		0			0
$591$	5.59860	−	455.034i	0.00947309	−	0.769938i
$592$		0			0
$593$	757.500			1.27740			0.638702	−	0.769454i	$-0.279472\pi$
$593$	757.500			1.27740			0.638702	+	0.769454i	$0.279472\pi$
$594$		0			0
$595$	391.027			0.657189
$596$		0			0
$597$	−3.71416	+	301.874i	−0.00622138	+	0.505651i
$598$		0			0
$599$	731.576	+	422.375i	1.22133	+	0.705134i	0.965201	−	0.261509i	$-0.0842201\pi$
$599$	731.576	+	422.375i	1.22133	+	0.705134i	0.256127	+	0.966643i	$0.417553\pi$
$600$		0			0
$601$	−470.627	+	271.717i	−0.783074	+	0.452108i	−0.837519	−	0.546409i	$-0.815994\pi$
$601$	−470.627	+	271.717i	−0.783074	+	0.452108i	0.0544448	+	0.998517i	$0.482661\pi$
$602$		0			0
$603$	551.549	+	336.797i	0.914675	+	0.558535i
$604$		0			0
$605$	−107.441	−	186.094i	−0.177589	−	0.307593i
$606$		0			0
$607$	−1049.45	−	605.901i	−1.72891	−	0.998189i	−0.894537	−	0.446994i	$-0.852494\pi$
$607$	−1049.45	−	605.901i	−1.72891	−	0.998189i	−0.834377	−	0.551194i	$-0.814172\pi$
$608$		0			0
$609$	−437.774	+	737.151i	−0.718841	+	1.21043i
$610$		0			0
$611$		−	332.021i		−	0.543406i
$612$		0			0
$613$	288.397			0.470469			0.235234	−	0.971939i	$-0.424414\pi$
$613$	288.397			0.470469			0.235234	+	0.971939i	$0.424414\pi$
$614$		0			0
$615$	100.896	+	179.831i	0.164059	+	0.292408i
$616$		0			0
$617$	−570.931	+	988.882i	−0.925334	+	1.60273i	−0.134311	+	0.990939i	$0.542882\pi$
$617$	−570.931	+	988.882i	−0.925334	+	1.60273i	−0.791023	+	0.611786i	$0.790451\pi$
$618$		0			0
$619$	17.8454	+	30.9092i	0.0288295	+	0.0499341i	0.880080	−	0.474825i	$-0.157489\pi$
$619$	17.8454	+	30.9092i	0.0288295	+	0.0499341i	−0.851251	+	0.524759i	$0.824155\pi$
$620$		0			0
$621$	514.485	+	322.921i	0.828479	+	0.520001i
$622$		0			0
$623$	1035.77	−	598.005i	1.66256	−	0.959879i
$624$		0			0
$625$	−242.417	+	419.878i	−0.387866	+	0.671804i
$626$		0			0
$627$	−356.448	−	877.606i	−0.568498	−	1.39969i
$628$		0			0
$629$			526.089i			0.836389i
$630$		0			0
$631$	585.019			0.927130			0.463565	−	0.886063i	$-0.346570\pi$
$631$	585.019			0.927130			0.463565	+	0.886063i	$0.346570\pi$
$632$		0			0
$633$	−130.911	+	220.437i	−0.206811	+	0.348241i
$634$		0			0
$635$	−115.680	−	66.7881i	−0.182174	−	0.105178i
$636$		0			0
$637$	1301.79	−	751.592i	2.04363	−	1.17989i
$638$		0			0
$639$	−11.5905	+	470.946i	−0.0181385	+	0.737004i
$640$		0			0
$641$	−365.748	+	211.165i	−0.570590	+	0.329430i	−0.757385	−	0.652968i	$-0.773523\pi$
$641$	−365.748	+	211.165i	−0.570590	+	0.329430i	0.186795	+	0.982399i	$0.440190\pi$
$642$		0			0
$643$	633.830	−	1097.83i	0.985738	−	1.70735i	0.347128	−	0.937818i	$-0.387157\pi$
$643$	633.830	−	1097.83i	0.985738	−	1.70735i	0.638610	−	0.769531i	$-0.279510\pi$
$644$		0			0
$645$	−2.13519	+	173.540i	−0.00331037	+	0.269055i
$646$		0			0
$647$	559.785			0.865202			0.432601	−	0.901586i	$-0.357596\pi$
$647$	559.785			0.865202			0.432601	+	0.901586i	$0.357596\pi$
$648$		0			0
$649$			1513.32i			2.33177i
$650$		0			0
$651$	−1502.38	−	18.4848i	−2.30780	−	0.0283945i
$652$		0			0
$653$	38.3296	−	66.3888i	0.0586977	−	0.101667i	−0.835183	−	0.549972i	$-0.814639\pi$
$653$	38.3296	−	66.3888i	0.0586977	−	0.101667i	0.893881	+	0.448304i	$0.147972\pi$
$654$		0			0
$655$	−153.521	−	265.907i	−0.234384	−	0.405965i
$656$		0			0
$657$	832.765	+	20.4953i	1.26753	+	0.0311953i
$658$		0			0
$659$	−195.964	+	113.140i	−0.297365	+	0.171684i	−0.641259	−	0.767325i	$-0.721587\pi$
$659$	−195.964	+	113.140i	−0.297365	+	0.171684i	0.343893	+	0.939009i	$0.388254\pi$
$660$		0			0
$661$	−250.200	−	144.453i	−0.378518	−	0.218537i	0.298655	−	0.954361i	$-0.403462\pi$
$661$	−250.200	−	144.453i	−0.378518	−	0.218537i	−0.677173	+	0.735824i	$0.736795\pi$
$662$		0			0
$663$	−653.102	+	1099.73i	−0.985071	+	1.65873i
$664$		0			0
$665$	−38.2310	+	303.051i	−0.0574902	+	0.455716i
$666$		0			0
$667$			553.852i			0.830363i
$668$		0			0
$669$	−32.2272	−	57.4398i	−0.0481722	−	0.0858592i
$670$		0			0
$671$	631.465	−	1093.73i	0.941080	−	1.63000i
$672$		0			0
$673$	447.003	−	258.077i	0.664194	−	0.383473i	−0.129679	−	0.991556i	$-0.541395\pi$
$673$	447.003	−	258.077i	0.664194	−	0.383473i	0.793873	+	0.608083i	$0.208061\pi$
$674$		0			0
$675$	550.852	−	291.479i	0.816076	−	0.431821i
$676$		0			0
$677$	−34.7280	+	20.0502i	−0.0512969	+	0.0296163i	−0.525429	−	0.850837i	$-0.676095\pi$
$677$	−34.7280	+	20.0502i	−0.0512969	+	0.0296163i	0.474132	+	0.880454i	$0.342762\pi$
$678$		0			0
$679$	397.092	+	229.261i	0.584818	+	0.337645i
$680$		0			0
$681$	−456.828	−	814.221i	−0.670819	−	1.19563i
$682$		0			0
$683$		−	1191.71i		−	1.74482i	−0.488773	−	0.872411i	$-0.662555\pi$
$683$		−	1191.71i		−	1.74482i	0.488773	−	0.872411i	$-0.337445\pi$
$684$		0			0
$685$	65.6932			0.0959024
$686$		0			0
$687$	83.2432	+	49.4359i	0.121169	+	0.0719590i
$688$		0			0
$689$	331.670	−	574.470i	0.481379	−	0.833774i
$690$		0			0
$691$	−209.055	−	362.093i	−0.302539	−	0.524014i	0.674171	−	0.738575i	$-0.264501\pi$
$691$	−209.055	−	362.093i	−0.302539	−	0.524014i	−0.976710	+	0.214562i	$0.931168\pi$
$692$		0			0
$693$	−904.827	+	1481.77i	−1.30567	+	2.13820i
$694$		0			0
$695$	136.911	+	237.136i	0.196994	+	0.341203i
$696$		0			0
$697$	1045.44	+	603.588i	1.49992	+	0.865979i
$698$		0			0
$699$	2.03013	−	165.001i	0.00290433	−	0.236053i
$700$		0			0
$701$	−26.9057			−0.0383819			−0.0191909	−	0.999816i	$-0.506109\pi$
$701$	−26.9057			−0.0383819			−0.0191909	+	0.999816i	$0.506109\pi$
$702$		0			0
$703$	−407.725	−	51.4360i	−0.579979	−	0.0731664i
$704$		0			0
$705$	0.968185	−	78.6905i	0.00137331	−	0.111618i
$706$		0			0
$707$	516.865	−	895.237i	0.731068	−	1.26625i
$708$		0			0
$709$	−208.914	−	361.850i	−0.294661	−	0.510367i	0.680245	−	0.732985i	$-0.261873\pi$
$709$	−208.914	−	361.850i	−0.294661	−	0.510367i	−0.974906	+	0.222617i	$0.928540\pi$
$710$		0			0
$711$	738.804	−	402.644i	1.03910	−	0.566307i
$712$		0			0
$713$	−840.586	+	485.312i	−1.17894	+	0.680662i
$714$		0			0
$715$	−349.364	−	201.705i	−0.488621	−	0.282105i
$716$		0			0
$717$	49.9045	+	29.6369i	0.0696018	+	0.0413346i
$718$		0			0
$719$	1424.53			1.98127			0.990636	−	0.136531i	$-0.0435955\pi$
$719$	1424.53			1.98127			0.990636	+	0.136531i	$0.0435955\pi$
$720$		0			0
$721$			909.154i			1.26096i
$722$		0			0
$723$	265.746	+	473.650i	0.367561	+	0.655117i
$724$		0			0
$725$	492.114	+	284.122i	0.678777	+	0.391892i
$726$		0			0
$727$	−523.530	−	906.780i	−0.720123	−	1.24729i	−0.960950	−	0.276722i	$-0.910752\pi$
$727$	−523.530	−	906.780i	−0.720123	−	1.24729i	0.240826	−	0.970568i	$-0.422582\pi$
$728$		0			0
$729$	−727.015	−	53.7648i	−0.997277	−	0.0737515i
$730$		0			0
$731$	508.020	+	879.917i	0.694966	+	1.20372i
$732$		0			0
$733$	−304.357	+	527.161i	−0.415221	+	0.719183i	−0.995452	−	0.0952687i	$-0.969629\pi$
$733$	−304.357	+	527.161i	−0.415221	+	0.719183i	0.580231	+	0.814452i	$0.302962\pi$
$734$		0			0
$735$	310.723	−	174.335i	0.422753	−	0.237190i
$736$		0			0
$737$			1193.27i			1.61909i
$738$		0			0
$739$	−339.844			−0.459871			−0.229935	−	0.973206i	$-0.573851\pi$
$739$	−339.844			−0.459871			−0.229935	+	0.973206i	$0.573851\pi$
$740$		0			0
$741$	−788.454	−	613.684i	−1.06404	−	0.828184i
$742$		0			0
$743$	212.029	+	122.415i	0.285369	+	0.164758i	0.635851	−	0.771811i	$-0.280649\pi$
$743$	212.029	+	122.415i	0.285369	+	0.164758i	−0.350483	+	0.936569i	$0.613982\pi$
$744$		0			0
$745$	−39.5371	−	68.4803i	−0.0530699	−	0.0919198i
$746$		0			0
$747$	−207.985	−	381.626i	−0.278426	−	0.510879i
$748$		0			0
$749$	−614.362	+	354.702i	−0.820243	+	0.473567i
$750$		0			0
$751$	679.161	+	392.114i	0.904342	+	0.522122i	0.878606	−	0.477547i	$-0.158474\pi$
$751$	679.161	+	392.114i	0.904342	+	0.522122i	0.0257356	+	0.999669i	$0.491807\pi$
$752$		0			0
$753$	−0.344807	+	28.0247i	−0.000457911	+	0.0372174i
$754$		0			0
$755$		−	312.644i		−	0.414098i
$756$		0			0
$757$	−1376.93			−1.81894			−0.909468	−	0.415774i	$-0.863511\pi$
$757$	−1376.93			−1.81894			−0.909468	+	0.415774i	$0.863511\pi$
$758$		0			0
$759$	−13.7987	+	1121.51i	−0.0181801	+	1.47762i
$760$		0			0
$761$	−452.401	+	783.582i	−0.594482	+	1.02967i	0.399137	+	0.916891i	$0.369310\pi$
$761$	−452.401	+	783.582i	−0.594482	+	1.02967i	−0.993620	+	0.112782i	$0.964024\pi$
$762$		0			0
$763$	−629.590	+	363.494i	−0.825150	+	0.476401i
$764$		0			0
$765$	−157.995	+	258.738i	−0.206530	+	0.338219i
$766$		0			0
$767$	798.121	+	1382.39i	1.04057	+	1.80233i
$768$		0			0
$769$	71.7529	−	124.280i	0.0933068	−	0.161612i	−0.815594	−	0.578625i	$-0.803590\pi$
$769$	71.7529	−	124.280i	0.0933068	−	0.161612i	0.908901	+	0.417013i	$0.136923\pi$
$770$		0			0
$771$	−669.697	+	1127.68i	−0.868608	+	1.46262i
$772$		0			0
$773$		−	838.859i		−	1.08520i	−0.839991	−	0.542600i	$-0.817440\pi$
$773$		−	838.859i		−	1.08520i	0.839991	−	0.542600i	$-0.182560\pi$
$774$		0			0
$775$			995.847i			1.28496i
$776$		0			0
$777$	368.570	+	656.916i	0.474350	+	0.845451i
$778$		0			0
$779$	−570.002	+	751.219i	−0.731709	+	0.964338i
$780$		0			0
$781$	−753.307	+	434.922i	−0.964542	+	0.556878i
$782$		0			0
$783$	−310.880	−	587.517i	−0.397038	−	0.750341i
$784$		0			0
$785$	−161.365	−	279.493i	−0.205561	−	0.356042i
$786$		0			0
$787$	−410.315	−	236.896i	−0.521366	−	0.301011i	0.216127	−	0.976365i	$-0.430657\pi$
$787$	−410.315	−	236.896i	−0.521366	−	0.301011i	−0.737493	+	0.675354i	$0.763991\pi$
$788$		0			0
$789$	−675.054	+	378.747i	−0.855582	+	0.480034i
$790$		0			0
$791$			1125.06i			1.42233i
$792$		0			0
$793$		−	1332.13i		−	1.67986i
$794$		0			0
$795$	80.2826	−	135.185i	0.100984	−	0.170044i
$796$		0			0
$797$	−648.789	−	374.578i	−0.814039	−	0.469985i	0.0343177	−	0.999411i	$-0.489074\pi$
$797$	−648.789	−	374.578i	−0.814039	−	0.469985i	−0.848356	+	0.529426i	$0.822408\pi$
$798$		0			0
$799$	−230.358	−	398.991i	−0.288308	−	0.499363i
$800$		0			0
$801$	−22.8141	+	926.983i	−0.0284820	+	1.15728i
$802$		0			0
$803$	769.065	+	1332.06i	0.957739	+	1.65885i
$804$		0			0
$805$	180.840	−	313.224i	0.224646	−	0.389098i
$806$		0			0
$807$	7.78523	+	0.0957872i	0.00964713	+	0.000118695i
$808$		0			0
$809$	−91.9456			−0.113653			−0.0568267	−	0.998384i	$-0.518098\pi$
$809$	−91.9456			−0.113653			−0.0568267	+	0.998384i	$0.518098\pi$
$810$		0			0
$811$		−	396.070i		−	0.488372i	−0.969728	−	0.244186i	$-0.921479\pi$
$811$		−	396.070i		−	0.488372i	0.969728	−	0.244186i	$-0.0785207\pi$
$812$		0			0
$813$	15.5837	−	1266.59i	0.0191682	−	1.55792i
$814$		0			0
$815$	44.7931	−	77.5840i	0.0549609	−	0.0951950i
$816$		0			0
$817$	−731.616	+	307.692i	−0.895491	+	0.376612i
$818$		0			0
$819$	−45.0573	+	1830.77i	−0.0550150	+	2.23537i
$820$		0			0
$821$	517.675	+	896.639i	0.630542	+	1.09213i	0.987441	+	0.157988i	$0.0505006\pi$
$821$	517.675	+	896.639i	0.630542	+	1.09213i	−0.356899	+	0.934143i	$0.616166\pi$
$822$		0			0
$823$	371.250	−	643.024i	0.451094	−	0.781317i	−0.547361	−	0.836897i	$-0.684367\pi$
$823$	371.250	−	643.024i	0.451094	−	0.781317i	0.998454	+	0.0555799i	$0.0177008\pi$
$824$		0			0
$825$	989.416	+	587.587i	1.19929	+	0.712227i
$826$		0			0
$827$		−	339.525i		−	0.410551i	−0.978704	−	0.205275i	$-0.934191\pi$
$827$		−	339.525i		−	0.410551i	0.978704	−	0.205275i	$-0.0658090\pi$
$828$		0			0
$829$		−	185.006i		−	0.223168i	−0.993755	−	0.111584i	$-0.964408\pi$
$829$		−	185.006i		−	0.223168i	0.993755	−	0.111584i	$-0.0355924\pi$
$830$		0			0
$831$	−351.524	+	197.226i	−0.423013	+	0.237336i
$832$		0			0
$833$	1042.92	−	1806.38i	1.25200	−	2.16853i
$834$		0			0
$835$	244.891	−	141.388i	0.293282	−	0.169327i
$836$		0			0
$837$	619.270	−	986.637i	0.739869	−	1.17878i
$838$		0			0
$839$	126.605	−	73.0951i	0.150899	−	0.0871217i	−0.422649	−	0.906293i	$-0.638900\pi$
$839$	126.605	−	73.0951i	0.150899	−	0.0871217i	0.573548	+	0.819172i	$0.305566\pi$
$840$		0			0
$841$	−117.467	+	203.458i	−0.139675	+	0.241924i
$842$		0			0
$843$	−757.401	−	1349.94i	−0.898459	−	1.60136i
$844$		0			0
$845$	−191.467			−0.226589
$846$		0			0
$847$	−1801.18			−2.12654
$848$		0			0
$849$	−770.299	−	457.459i	−0.907301	−	0.538821i
$850$		0			0
$851$	421.412	+	243.302i	0.495196	+	0.285902i
$852$		0			0
$853$	−327.952	−	568.030i	−0.384469	−	0.665921i	0.607226	−	0.794529i	$-0.292282\pi$
$853$	−327.952	−	568.030i	−0.384469	−	0.665921i	−0.991695	+	0.128609i	$0.958949\pi$
$854$		0			0
$855$	−185.078	−	147.745i	−0.216465	−	0.172801i
$856$		0			0
$857$	987.653	−	570.222i	1.15245	−	0.665370i	0.202970	−	0.979185i	$-0.434941\pi$
$857$	987.653	−	570.222i	1.15245	−	0.665370i	0.949484	+	0.313815i	$0.101607\pi$
$858$		0			0
$859$	−6.31737	+	10.9420i	−0.00735433	+	0.0127381i	−0.869679	−	0.493617i	$-0.835674\pi$
$859$	−6.31737	+	10.9420i	−0.00735433	+	0.0127381i	0.862325	+	0.506356i	$0.169008\pi$
$860$		0			0
$861$	1728.29	+	21.2643i	2.00730	+	0.0246973i
$862$		0			0
$863$			916.444i			1.06193i	0.847394	+	0.530964i	$0.178170\pi$
$863$			916.444i			1.06193i	−0.847394	+	0.530964i	$0.821830\pi$
$864$		0			0
$865$			36.7287i			0.0424609i
$866$		0			0
$867$	−11.1687	+	907.749i	−0.0128820	+	1.04700i
$868$		0			0
$869$	1345.46	+	776.803i	1.54829	+	0.893905i
$870$		0			0
$871$	629.327	+	1090.03i	0.722534	+	1.25147i
$872$		0			0
$873$	−312.144	+	170.117i	−0.357554	+	0.194865i
$874$		0			0
$875$	−386.495	−	669.429i	−0.441709	−	0.765062i
$876$		0			0
$877$	−228.241	−	131.775i	−0.260252	−	0.150256i	0.364198	−	0.931322i	$-0.381343\pi$
$877$	−228.241	−	131.775i	−0.260252	−	0.150256i	−0.624449	+	0.781065i	$0.714677\pi$
$878$		0			0
$879$	−448.268	+	754.823i	−0.509976	+	0.858729i
$880$		0			0
$881$	−410.026			−0.465410			−0.232705	−	0.972547i	$-0.574758\pi$
$881$	−410.026			−0.465410			−0.232705	+	0.972547i	$0.574758\pi$
$882$		0			0
$883$	−427.306			−0.483925			−0.241963	−	0.970286i	$-0.577791\pi$
$883$	−427.306			−0.483925			−0.241963	+	0.970286i	$0.577791\pi$
$884$		0			0
$885$	185.127	+	329.959i	0.209183	+	0.372835i
$886$		0			0
$887$	1349.01	+	778.853i	1.52087	+	0.878075i	0.999697	+	0.0246250i	$0.00783916\pi$
$887$	1349.01	+	778.853i	1.52087	+	0.878075i	0.521174	+	0.853450i	$0.325494\pi$
$888$		0			0
$889$	−969.651	+	559.829i	−1.09072	+	0.629728i
$890$		0			0
$891$	−614.873	−	1197.42i	−0.690093	−	1.34391i
$892$		0			0
$893$	331.745	−	139.521i	0.371496	−	0.156238i
$894$		0			0
$895$	362.626	+	209.362i	0.405168	+	0.233924i
$896$		0			0
$897$	578.876	+	1031.75i	0.645347	+	1.15023i
$898$		0			0
$899$	1062.13			1.18146
$900$		0			0
$901$		−	920.459i		−	1.02160i
$902$		0			0
$903$	1250.81	+	742.822i	1.38517	+	0.822616i
$904$		0			0
$905$	−5.58534	−	3.22470i	−0.00617164	−	0.00356320i
$906$		0			0
$907$	−23.8638	+	13.7778i	−0.0263107	+	0.0151905i	−0.513098	−	0.858330i	$-0.671502\pi$
$907$	−23.8638	+	13.7778i	−0.0263107	+	0.0151905i	0.486787	+	0.873521i	$0.338169\pi$
$908$		0			0
$909$	383.527	+	703.725i	0.421921	+	0.774174i
$910$		0			0
$911$	288.403	−	166.509i	0.316578	−	0.182776i	−0.333288	−	0.942825i	$-0.608158\pi$
$911$	288.403	−	166.509i	0.316578	−	0.182776i	0.649866	+	0.760049i	$0.274825\pi$
$912$		0			0
$913$	401.255	−	694.994i	0.439491	−	0.761221i
$914$		0			0
$915$	3.88454	−	315.721i	0.00424540	−	0.345050i
$916$		0			0
$917$	−2573.68			−2.80663
$918$		0			0
$919$	1465.05			1.59418			0.797090	−	0.603861i	$-0.206372\pi$
$919$	1465.05			1.59418			0.797090	+	0.603861i	$0.206372\pi$
$920$		0			0
$921$	−690.415	−	8.49466i	−0.749636	−	0.00922330i
$922$		0			0
$923$	−458.753	+	794.583i	−0.497023	+	0.860870i
$924$		0			0
$925$	432.362	−	249.625i	0.467419	−	0.269864i
$926$		0			0
$927$	−601.576	−	367.345i	−0.648949	−	0.396273i
$928$		0			0
$929$	−163.249	−	282.756i	−0.175726	−	0.304366i	0.764686	−	0.644403i	$-0.222894\pi$
$929$	−163.249	−	282.756i	−0.175726	−	0.304366i	−0.940412	+	0.340037i	$0.889561\pi$
$930$		0			0
$931$	1298.00	+	984.884i	1.39420	+	1.05788i
$932$		0			0
$933$	1123.64	+	667.301i	1.20433	+	0.715220i
$934$		0			0
$935$	−559.777			−0.598692
$936$		0			0
$937$	1365.54			1.45735			0.728674	−	0.684861i	$-0.240137\pi$
$937$	1365.54			1.45735			0.728674	+	0.684861i	$0.240137\pi$
$938$		0			0
$939$	760.743	−	426.823i	0.810163	−	0.454551i
$940$		0			0
$941$	24.6577	+	14.2361i	0.0262037	+	0.0151287i	0.513045	−	0.858362i	$-0.328518\pi$
$941$	24.6577	+	14.2361i	0.0262037	+	0.0151287i	−0.486841	+	0.873491i	$0.661851\pi$
$942$		0			0
$943$	966.981	−	558.287i	1.02543	−	0.592033i
$944$		0			0
$945$	−16.0174	+	433.769i	−0.0169496	+	0.459015i
$946$		0			0
$947$	−138.753	−	240.327i	−0.146519	−	0.253778i	0.783420	−	0.621493i	$-0.213473\pi$
$947$	−138.753	−	240.327i	−0.146519	−	0.253778i	−0.929938	+	0.367715i	$0.880140\pi$
$948$		0			0
$949$	1405.05	+	811.204i	1.48056	+	0.854799i
$950$		0			0
$951$	−445.128	−	793.368i	−0.468063	−	0.834246i
$952$		0			0
$953$		−	1524.01i		−	1.59917i	−0.600555	−	0.799584i	$-0.705054\pi$
$953$		−	1524.01i		−	1.59917i	0.600555	−	0.799584i	$-0.294946\pi$
$954$		0			0
$955$	301.618			0.315830
$956$		0			0
$957$	626.697	−	1055.27i	0.654856	−	1.10269i
$958$		0			0
$959$	275.326	−	476.878i	0.287096	−	0.497266i
$960$		0			0
$961$	450.191	+	779.754i	0.468461	+	0.811399i
$962$		0			0
$963$	13.5320	−	549.833i	0.0140519	−	0.570959i
$964$		0			0
$965$	−133.249	+	76.9315i	−0.138082	+	0.0797218i
$966$		0			0
$967$	−375.207	+	649.878i	−0.388012	+	0.672056i	−0.992182	−	0.124799i	$-0.960171\pi$
$967$	−375.207	+	649.878i	−0.388012	+	0.672056i	0.604170	+	0.796855i	$0.293505\pi$
$968$		0			0
$969$	−1373.27	−	190.434i	−1.41720	−	0.196527i
$970$		0			0
$971$		−	853.154i		−	0.878634i	−0.898332	−	0.439317i	$-0.855220\pi$
$971$		−	853.154i		−	0.878634i	0.898332	−	0.439317i	$-0.144780\pi$
$972$		0			0
$973$	2295.21			2.35891
$974$		0			0
$975$	1213.70	+	14.9330i	1.24482	+	0.0153159i
$976$		0			0
$977$	97.3379	+	56.1980i	0.0996293	+	0.0575210i	0.548987	−	0.835831i	$-0.315014\pi$
$977$	97.3379	+	56.1980i	0.0996293	+	0.0575210i	−0.449357	+	0.893352i	$0.648347\pi$
$978$		0			0
$979$	−1482.77	+	856.076i	−1.51457	+	0.874439i
$980$		0			0
$981$	13.8674	−	563.462i	0.0141360	−	0.574375i
$982$		0			0
$983$	−1214.69	+	701.303i	−1.23570	+	0.713432i	−0.968212	−	0.250129i	$-0.919527\pi$
$983$	−1214.69	+	701.303i	−1.23570	+	0.713432i	−0.267488	+	0.963561i	$0.586193\pi$
$984$		0			0
$985$	105.037	−	181.929i	0.106637	−	0.184700i
$986$		0			0
$987$	−567.170	−	336.827i	−0.574640	−	0.341263i
$988$		0			0
$989$	939.785			0.950237
$990$		0			0
$991$		−	969.615i		−	0.978421i	−0.872166	−	0.489210i	$-0.837285\pi$
$991$		−	969.615i		−	0.978421i	0.872166	−	0.489210i	$-0.162715\pi$
$992$		0			0
$993$	−912.945	−	1627.18i	−0.919380	−	1.63865i
$994$		0			0
$995$	−69.6825	+	120.694i	−0.0700327	+	0.121300i
$996$		0			0
$997$	506.470	+	877.231i	0.507994	+	0.879871i	0.999957	+	0.00925517i	$0.00294605\pi$
$997$	506.470	+	877.231i	0.507994	+	0.879871i	−0.491963	+	0.870616i	$0.663721\pi$
$998$		0			0
$999$	−583.594	−	21.5498i	−0.584178	−	0.0215714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.t.a.265.20	✓	80
3.2	odd	2		2052.3.t.a.37.22		80
9.2	odd	6		2052.3.t.a.721.21		80
9.7	even	3	inner	684.3.t.a.493.21	yes	80
19.18	odd	2	inner	684.3.t.a.265.21	yes	80
57.56	even	2		2052.3.t.a.37.21		80
171.56	even	6		2052.3.t.a.721.22		80
171.151	odd	6	inner	684.3.t.a.493.20	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.t.a.265.20	✓	80	1.1	even	1	trivial
684.3.t.a.265.21	yes	80	19.18	odd	2	inner
684.3.t.a.493.20	yes	80	171.151	odd	6	inner
684.3.t.a.493.21	yes	80	9.7	even	3	inner
2052.3.t.a.37.21		80	57.56	even	2
2052.3.t.a.37.22		80	3.2	odd	2
2052.3.t.a.721.21		80	9.2	odd	6
2052.3.t.a.721.22		80	171.56	even	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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.t (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0369083 + 2.99977i) q^{3} +(-0.692448 + 1.19936i) q^{5} +(5.80422 + 10.0532i) q^{7} +(-8.99728 - 0.221433i) q^{9} +O(q^{10})\)	\(q+(-0.0369083 + 2.99977i) q^{3} +(-0.692448 + 1.19936i) q^{5} +(5.80422 + 10.0532i) q^{7} +(-8.99728 - 0.221433i) q^{9} +(-8.30905 - 14.3917i) q^{11} +(-15.1803 - 8.76433i) q^{13} +(-3.57224 - 2.12145i) q^{15} -24.3230 q^{17} +(2.37807 - 18.8506i) q^{19} +(-30.3715 + 17.0403i) q^{21} +(-11.2487 + 19.4834i) q^{23} +(11.5410 + 19.9897i) q^{25} +(0.996324 - 26.9816i) q^{27} +(21.3202 - 12.3092i) q^{29} +(37.3636 + 21.5719i) q^{31} +(43.4785 - 24.3941i) q^{33} -16.0765 q^{35} -21.6293i q^{37} +(26.8513 - 45.2139i) q^{39} +(-42.9818 - 24.8156i) q^{41} +(-20.8865 - 36.1764i) q^{43} +(6.49573 - 10.6376i) q^{45} +(9.47080 + 16.4039i) q^{47} +(-42.8779 + 74.2666i) q^{49} +(0.897719 - 72.9633i) q^{51} +37.8432i q^{53} +23.0144 q^{55} +(56.4597 + 7.82941i) q^{57} +(-78.8643 - 45.5323i) q^{59} +(37.9986 + 65.8155i) q^{61} +(-49.9960 - 91.7366i) q^{63} +(21.0231 - 12.1377i) q^{65} +(-62.1854 - 35.9028i) q^{67} +(-58.0305 - 34.4627i) q^{69} -52.3432i q^{71} -92.5575 q^{73} +(-60.3904 + 33.8827i) q^{75} +(96.4551 - 167.065i) q^{77} +(-80.9637 + 46.7444i) q^{79} +(80.9019 + 3.98459i) q^{81} +(24.1457 + 41.8215i) q^{83} +(16.8424 - 29.1719i) q^{85} +(36.1379 + 64.4100i) q^{87} -103.029i q^{89} -203.480i q^{91} +(-66.0898 + 111.286i) q^{93} +(20.9619 + 15.9052i) q^{95} +(34.2072 - 19.7495i) q^{97} +(71.5720 + 131.326i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 2 q^{7} + 4 q^{9}+O(q^{10}) \) 80 * q + 2 * q^7 + 4 * q^9	\( 80 q + 2 q^{7} + 4 q^{9} + 12 q^{11} - 12 q^{17} - 2 q^{19} - 48 q^{23} - 200 q^{25} - 216 q^{35} + 102 q^{39} + 28 q^{43} + 2 q^{45} - 174 q^{47} - 306 q^{49} + 213 q^{57} + 14 q^{61} + 62 q^{63} + 220 q^{73} - 60 q^{77} + 340 q^{81} + 150 q^{83} - 252 q^{87} - 252 q^{93} + 360 q^{95} + 542 q^{99}+O(q^{100}) \) 80 * q + 2 * q^7 + 4 * q^9 + 12 * q^11 - 12 * q^17 - 2 * q^19 - 48 * q^23 - 200 * q^25 - 216 * q^35 + 102 * q^39 + 28 * q^43 + 2 * q^45 - 174 * q^47 - 306 * q^49 + 213 * q^57 + 14 * q^61 + 62 * q^63 + 220 * q^73 - 60 * q^77 + 340 * q^81 + 150 * q^83 - 252 * q^87 - 252 * q^93 + 360 * q^95 + 542 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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