LMFDB - Embedded newform 378.3.o.a.181.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [378,3,Mod(181,378)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(378, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 3])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("378.181"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	378.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$10.2997539928$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			181.14
Character	$\chi$	$=$	378.181
Dual form			378.3.o.a.307.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(2.08306 - 1.20266i) q^{5} +(-3.78272 + 5.88991i) q^{7} -2.82843 q^{8} -3.40163i q^{10} +(6.79936 - 11.7768i) q^{11} +(11.7604 - 6.78989i) q^{13} +(4.53884 + 8.79766i) q^{14} +(-2.00000 + 3.46410i) q^{16} -19.8181i q^{17} -34.4974i q^{19} +(-4.16613 - 2.40532i) q^{20} +(-9.61574 - 16.6550i) q^{22} +(-4.33552 - 7.50935i) q^{23} +(-9.60723 + 16.6402i) q^{25} -19.2047i q^{26} +(13.9843 + 0.661961i) q^{28} +(-12.9761 + 22.4752i) q^{29} +(21.6671 - 12.5095i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-24.2721 - 14.0135i) q^{34} +(-0.796113 + 16.8184i) q^{35} +39.6839 q^{37} +(-42.2505 - 24.3933i) q^{38} +(-5.89179 + 3.40163i) q^{40} +(-41.8941 + 24.1876i) q^{41} +(13.1169 - 22.7192i) q^{43} -27.1974 q^{44} -12.2627 q^{46} +(-14.5673 - 8.41045i) q^{47} +(-20.3820 - 44.5598i) q^{49} +(13.5867 + 23.5328i) q^{50} +(-23.5209 - 13.5798i) q^{52} -35.6774 q^{53} -32.7092i q^{55} +(10.6992 - 16.6592i) q^{56} +(18.3509 + 31.7848i) q^{58} +(63.9153 - 36.9015i) q^{59} +(78.5405 + 45.3454i) q^{61} -35.3823i q^{62} +8.00000 q^{64} +(16.3318 - 28.2875i) q^{65} +(-10.3681 - 17.9581i) q^{67} +(-34.3259 + 19.8181i) q^{68} +(20.0353 + 12.8674i) q^{70} +38.1972 q^{71} +12.0702i q^{73} +(28.0607 - 48.6026i) q^{74} +(-59.7512 + 34.4974i) q^{76} +(43.6444 + 84.5961i) q^{77} +(-65.4244 + 113.318i) q^{79} +9.62126i q^{80} +68.4128i q^{82} +(-27.6580 - 15.9683i) q^{83} +(-23.8343 - 41.2823i) q^{85} +(-18.5501 - 32.1298i) q^{86} +(-19.2315 + 33.3099i) q^{88} +118.790i q^{89} +(-4.49464 + 94.9521i) q^{91} +(-8.67105 + 15.0187i) q^{92} +(-20.6013 + 11.8942i) q^{94} +(-41.4885 - 71.8602i) q^{95} +(-99.4807 - 57.4352i) q^{97} +(-68.9866 - 6.54575i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) $ 32 * q - 32 * q^4 - 2 * q^7 + 12 * q^11 + 12 * q^14 - 64 * q^16 - 12 * q^23 + 80 * q^25 + 8 * q^28 + 48 * q^29 - 348 * q^35 - 88 * q^37 + 32 * q^43 - 48 * q^44 + 48 * q^46 + 50 * q^49 - 48 * q^50 + 864 * q^53 + 24 * q^56 + 48 * q^58 + 256 * q^64 - 120 * q^65 - 140 * q^67 - 108 * q^70 - 552 * q^71 - 144 * q^74 + 258 * q^77 - 176 * q^79 - 60 * q^85 - 96 * q^86 + 372 * q^91 - 24 * q^92 - 528 * q^95 - 624 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$2$	0.707107	−	1.22474i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	−	1.73205i	−0.250000	−	0.433013i
$5$	2.08306	−	1.20266i	0.416613	−	0.240532i	−0.277014	−	0.960866i	$-0.589345\pi$
$5$	2.08306	−	1.20266i	0.416613	−	0.240532i	0.693627	+	0.720334i	$0.256012\pi$
$6$		0			0
$7$	−3.78272	+	5.88991i	−0.540389	+	0.841415i
$7$	−3.78272	+	5.88991i	−0.540389	+	0.841415i
$8$	−2.82843			−0.353553
$9$		0			0
$10$		−	3.40163i		−	0.340163i
$11$	6.79936	−	11.7768i	0.618123	−	1.07062i	−0.371705	−	0.928351i	$-0.621227\pi$
$11$	6.79936	−	11.7768i	0.618123	−	1.07062i	0.989828	−	0.142270i	$-0.0454401\pi$
$12$		0			0
$13$	11.7604	−	6.78989i	0.904648	−	0.522299i	0.0259430	−	0.999663i	$-0.491741\pi$
$13$	11.7604	−	6.78989i	0.904648	−	0.522299i	0.878705	+	0.477364i	$0.158408\pi$
$14$	4.53884	+	8.79766i	0.324203	+	0.628405i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$		−	19.8181i		−	1.16577i	−0.812555	−	0.582884i	$-0.801924\pi$
$17$		−	19.8181i		−	1.16577i	0.812555	−	0.582884i	$-0.198076\pi$
$18$		0			0
$19$		−	34.4974i		−	1.81565i	−0.419348	−	0.907826i	$-0.637741\pi$
$19$		−	34.4974i		−	1.81565i	0.419348	−	0.907826i	$-0.362259\pi$
$20$	−4.16613	−	2.40532i	−0.208306	−	0.120266i
$21$		0			0
$22$	−9.61574	−	16.6550i	−0.437079	−	0.757043i
$23$	−4.33552	−	7.50935i	−0.188501	−	0.326493i	0.756250	−	0.654283i	$-0.227030\pi$
$23$	−4.33552	−	7.50935i	−0.188501	−	0.326493i	−0.944751	+	0.327790i	$0.893696\pi$
$24$		0			0
$25$	−9.60723	+	16.6402i	−0.384289	+	0.665608i
$26$		−	19.2047i		−	0.738642i
$27$		0			0
$28$	13.9843	+	0.661961i	0.499441	+	0.0236415i
$29$	−12.9761	+	22.4752i	−0.447451	+	0.775008i	−0.998219	−	0.0596503i	$-0.981001\pi$
$29$	−12.9761	+	22.4752i	−0.447451	+	0.775008i	0.550768	+	0.834658i	$0.314335\pi$
$30$		0			0
$31$	21.6671	−	12.5095i	0.698939	−	0.403533i	−0.108013	−	0.994149i	$-0.534449\pi$
$31$	21.6671	−	12.5095i	0.698939	−	0.403533i	0.806952	+	0.590617i	$0.201115\pi$
$32$	2.82843	+	4.89898i	0.0883883	+	0.153093i
$33$		0			0
$34$	−24.2721	−	14.0135i	−0.713884	−	0.412161i
$35$	−0.796113	+	16.8184i	−0.0227461	+	0.480525i
$36$		0			0
$37$	39.6839			1.07254			0.536268	−	0.844047i	$-0.319833\pi$
$37$	39.6839			1.07254			0.536268	+	0.844047i	$0.319833\pi$
$38$	−42.2505	−	24.3933i	−1.11185	−	0.641930i
$39$		0			0
$40$	−5.89179	+	3.40163i	−0.147295	+	0.0850407i
$41$	−41.8941	+	24.1876i	−1.02181	+	0.589941i	−0.914627	−	0.404299i	$-0.867516\pi$
$41$	−41.8941	+	24.1876i	−1.02181	+	0.589941i	−0.107180	+	0.994240i	$0.534182\pi$
$42$		0			0
$43$	13.1169	−	22.7192i	0.305045	−	0.528353i	−0.672226	−	0.740346i	$-0.734662\pi$
$43$	13.1169	−	22.7192i	0.305045	−	0.528353i	0.977271	+	0.211992i	$0.0679952\pi$
$44$	−27.1974			−0.618123
$45$		0			0
$46$	−12.2627			−0.266581
$47$	−14.5673	−	8.41045i	−0.309943	−	0.178946i	0.336958	−	0.941520i	$-0.390602\pi$
$47$	−14.5673	−	8.41045i	−0.309943	−	0.178946i	−0.646901	+	0.762574i	$0.723935\pi$
$48$		0			0
$49$	−20.3820	−	44.5598i	−0.415959	−	0.909383i
$50$	13.5867	+	23.5328i	0.271733	+	0.470656i
$51$		0			0
$52$	−23.5209	−	13.5798i	−0.452324	−	0.261150i
$53$	−35.6774			−0.673159			−0.336579	−	0.941655i	$-0.609270\pi$
$53$	−35.6774			−0.673159			−0.336579	+	0.941655i	$0.609270\pi$
$54$		0			0
$55$		−	32.7092i		−	0.594712i
$56$	10.6992	−	16.6592i	0.191056	−	0.297485i
$57$		0			0
$58$	18.3509	+	31.7848i	0.316396	+	0.548013i
$59$	63.9153	−	36.9015i	1.08331	−	0.625449i	0.151522	−	0.988454i	$-0.451582\pi$
$59$	63.9153	−	36.9015i	1.08331	−	0.625449i	0.931787	+	0.363005i	$0.118249\pi$
$60$		0			0
$61$	78.5405	+	45.3454i	1.28755	+	0.743367i	0.978217	−	0.207587i	$-0.0665611\pi$
$61$	78.5405	+	45.3454i	1.28755	+	0.743367i	0.309332	+	0.950954i	$0.399894\pi$
$62$		−	35.3823i		−	0.570682i
$63$		0			0
$64$	8.00000			0.125000
$65$	16.3318	−	28.2875i	0.251259	−	0.435193i
$66$		0			0
$67$	−10.3681	−	17.9581i	−0.154748	−	0.268031i	0.778219	−	0.627992i	$-0.216123\pi$
$67$	−10.3681	−	17.9581i	−0.154748	−	0.268031i	−0.932967	+	0.359962i	$0.882790\pi$
$68$	−34.3259	+	19.8181i	−0.504792	+	0.291442i
$69$		0			0
$70$	20.0353	+	12.8674i	0.286218	+	0.183820i
$71$	38.1972			0.537989			0.268995	−	0.963142i	$-0.413309\pi$
$71$	38.1972			0.537989			0.268995	+	0.963142i	$0.413309\pi$
$72$		0			0
$73$			12.0702i			0.165345i	0.996577	+	0.0826726i	$0.0263456\pi$
$73$			12.0702i			0.165345i	−0.996577	+	0.0826726i	$0.973654\pi$
$74$	28.0607	−	48.6026i	0.379199	−	0.656792i
$75$		0			0
$76$	−59.7512	+	34.4974i	−0.786200	+	0.453913i
$77$	43.6444	+	84.5961i	0.566810	+	1.09865i
$78$		0			0
$79$	−65.4244	+	113.318i	−0.828157	+	1.43441i	0.0713263	+	0.997453i	$0.477277\pi$
$79$	−65.4244	+	113.318i	−0.828157	+	1.43441i	−0.899483	+	0.436956i	$0.856056\pi$
$80$			9.62126i			0.120266i
$81$		0			0
$82$			68.4128i			0.834302i
$83$	−27.6580	−	15.9683i	−0.333229	−	0.192390i	0.324045	−	0.946042i	$-0.394957\pi$
$83$	−27.6580	−	15.9683i	−0.333229	−	0.192390i	−0.657274	+	0.753652i	$0.728290\pi$
$84$		0			0
$85$	−23.8343	−	41.2823i	−0.280404	−	0.485674i
$86$	−18.5501	−	32.1298i	−0.215699	−	0.373602i
$87$		0			0
$88$	−19.2315	+	33.3099i	−0.218540	+	0.378522i
$89$			118.790i			1.33472i	0.744737	+	0.667358i	$0.232575\pi$
$89$			118.790i			1.33472i	−0.744737	+	0.667358i	$0.767425\pi$
$90$		0			0
$91$	−4.49464	+	94.9521i	−0.0493917	+	1.04343i
$92$	−8.67105	+	15.0187i	−0.0942505	+	0.163247i
$93$		0			0
$94$	−20.6013	+	11.8942i	−0.219163	+	0.126534i
$95$	−41.4885	−	71.8602i	−0.436721	−	0.756423i
$96$		0			0
$97$	−99.4807	−	57.4352i	−1.02557	−	0.592116i	−0.109861	−	0.993947i	$-0.535040\pi$
$97$	−99.4807	−	57.4352i	−1.02557	−	0.592116i	−0.915714	+	0.401831i	$0.868374\pi$
$98$	−68.9866	−	6.54575i	−0.703945	−	0.0667934i
$99$		0			0
$100$	38.4289			0.384289
$101$	149.663	+	86.4081i	1.48181	+	0.855526i	0.999787	−	0.0206305i	$-0.00656734\pi$
$101$	149.663	+	86.4081i	1.48181	+	0.855526i	0.482027	+	0.876156i	$0.339901\pi$
$102$		0			0
$103$	40.4444	−	23.3506i	0.392664	−	0.226705i	−0.290650	−	0.956830i	$-0.593871\pi$
$103$	40.4444	−	23.3506i	0.392664	−	0.226705i	0.683314	+	0.730125i	$0.260538\pi$
$104$	−33.2635	+	19.2047i	−0.319842	+	0.184661i
$105$		0			0
$106$	−25.2277	+	43.6957i	−0.237998	+	0.412224i
$107$	69.5084			0.649611			0.324806	−	0.945781i	$-0.394701\pi$
$107$	69.5084			0.649611			0.324806	+	0.945781i	$0.394701\pi$
$108$		0			0
$109$	135.887			1.24667			0.623334	−	0.781956i	$-0.285778\pi$
$109$	135.887			1.24667			0.623334	+	0.781956i	$0.285778\pi$
$110$	−40.0604	−	23.1289i	−0.364186	−	0.210263i
$111$		0			0
$112$	−12.8378	−	24.8836i	−0.114623	−	0.222175i
$113$	2.05580	+	3.56076i	0.0181930	+	0.0315111i	0.874979	−	0.484162i	$-0.160875\pi$
$113$	2.05580	+	3.56076i	0.0181930	+	0.0315111i	−0.856786	+	0.515673i	$0.827542\pi$
$114$		0			0
$115$	−18.0623	−	10.4283i	−0.157064	−	0.0906809i
$116$	51.9043			0.447451
$117$		0			0
$118$		−	104.373i		−	0.884519i
$119$	116.727	+	74.9662i	0.980895	+	0.629968i
$120$		0			0
$121$	−31.9625	−	55.3606i	−0.264153	−	0.457526i
$122$	111.073	−	64.1280i	0.910435	−	0.525640i
$123$		0			0
$124$	−43.3342	−	25.0190i	−0.349470	−	0.201766i
$125$			106.350i			0.850798i
$126$		0			0
$127$	12.0291			0.0947171			0.0473585	−	0.998878i	$-0.484920\pi$
$127$	12.0291			0.0947171			0.0473585	+	0.998878i	$0.484920\pi$
$128$	5.65685	−	9.79796i	0.0441942	−	0.0765466i
$129$		0			0
$130$	−23.0967	−	40.0046i	−0.177667	−	0.307728i
$131$	72.6514	−	41.9453i	0.554591	−	0.320193i	−0.196381	−	0.980528i	$-0.562919\pi$
$131$	72.6514	−	41.9453i	0.554591	−	0.320193i	0.750971	+	0.660335i	$0.229586\pi$
$132$		0			0
$133$	203.186	+	130.494i	1.52772	+	0.981158i
$134$	−29.3254			−0.218846
$135$		0			0
$136$			56.0539i			0.412161i
$137$	−99.9694	+	173.152i	−0.729703	+	1.26388i	0.227305	+	0.973824i	$0.427008\pi$
$137$	−99.9694	+	173.152i	−0.729703	+	1.26388i	−0.957009	+	0.290060i	$0.906325\pi$
$138$		0			0
$139$	−127.666	+	73.7083i	−0.918464	+	0.530275i	−0.883145	−	0.469101i	$-0.844578\pi$
$139$	−127.666	+	73.7083i	−0.918464	+	0.530275i	−0.0353192	+	0.999376i	$0.511245\pi$
$140$	29.9264	−	15.4395i	0.213760	−	0.110282i
$141$		0			0
$142$	27.0095	−	46.7819i	0.190208	−	0.329450i
$143$		−	184.667i		−	1.29138i
$144$		0			0
$145$			62.4231i			0.430504i
$146$	14.7829	+	8.53492i	0.101253	+	0.0584584i
$147$		0			0
$148$	−39.6839	−	68.7345i	−0.268134	−	0.464422i
$149$	−105.785	−	183.225i	−0.709967	−	1.22970i	−0.964869	−	0.262731i	$-0.915377\pi$
$149$	−105.785	−	183.225i	−0.709967	−	1.22970i	0.254902	−	0.966967i	$-0.417957\pi$
$150$		0			0
$151$	−9.48372	+	16.4263i	−0.0628061	+	0.108783i	−0.895719	−	0.444621i	$-0.853338\pi$
$151$	−9.48372	+	16.4263i	−0.0628061	+	0.108783i	0.832913	+	0.553405i	$0.186672\pi$
$152$			97.5733i			0.641930i
$153$		0			0
$154$	134.470	+	6.36525i	0.873181	+	0.0413328i
$155$	30.0893	−	52.1163i	0.194125	−	0.336234i
$156$		0			0
$157$	−6.98156	+	4.03081i	−0.0444685	+	0.0256739i	−0.522069	−	0.852903i	$-0.674840\pi$
$157$	−6.98156	+	4.03081i	−0.0444685	+	0.0256739i	0.477601	+	0.878577i	$0.341506\pi$
$158$	92.5240	+	160.256i	0.585595	+	1.01428i
$159$		0			0
$160$	11.7836	+	6.80326i	0.0736474	+	0.0425204i
$161$	60.6294	+	2.86995i	0.376580	+	0.0178258i
$162$		0			0
$163$	49.1196			0.301347			0.150673	−	0.988584i	$-0.451856\pi$
$163$	49.1196			0.301347			0.150673	+	0.988584i	$0.451856\pi$
$164$	83.7882	+	48.3751i	0.510904	+	0.294970i
$165$		0			0
$166$	−39.1143	+	22.5826i	−0.235628	+	0.136040i
$167$	−168.024	+	97.0088i	−1.00613	+	0.580891i	−0.910057	−	0.414483i	$-0.863962\pi$
$167$	−168.024	+	97.0088i	−1.00613	+	0.580891i	−0.0960758	+	0.995374i	$0.530629\pi$
$168$		0			0
$169$	7.70514	−	13.3457i	0.0455926	−	0.0789686i
$170$	−67.4137			−0.396551
$171$		0			0
$172$	−52.4677			−0.305045
$173$	65.2186	+	37.6540i	0.376986	+	0.217653i	0.676506	−	0.736437i	$-0.263493\pi$
$173$	65.2186	+	37.6540i	0.376986	+	0.217653i	−0.299520	+	0.954090i	$0.596827\pi$
$174$		0			0
$175$	−61.6678	−	119.531i	−0.352387	−	0.683034i
$176$	27.1974	+	47.1073i	0.154531	+	0.267655i
$177$		0			0
$178$	145.487	+	83.9970i	0.817343	+	0.471893i
$179$	97.4357			0.544334			0.272167	−	0.962250i	$-0.412260\pi$
$179$	97.4357			0.544334			0.272167	+	0.962250i	$0.412260\pi$
$180$		0			0
$181$		−	83.1541i		−	0.459415i	−0.973260	−	0.229707i	$-0.926223\pi$
$181$		−	83.1541i		−	0.459415i	0.973260	−	0.229707i	$-0.0737769\pi$
$182$	113.114	+	72.6461i	0.621505	+	0.399154i
$183$		0			0
$184$	12.2627	+	21.2396i	0.0666452	+	0.115433i
$185$	82.6640	−	47.7261i	0.446833	−	0.257979i
$186$		0			0
$187$	−233.394	−	134.750i	−1.24810	−	0.720588i
$188$			33.6418i			0.178946i
$189$		0			0
$190$	−117.347			−0.617617
$191$	−109.890	+	190.335i	−0.575341	+	0.996520i	0.420664	+	0.907217i	$0.361797\pi$
$191$	−109.890	+	190.335i	−0.575341	+	0.996520i	−0.996005	+	0.0893029i	$0.971536\pi$
$192$		0			0
$193$	57.6084	+	99.7807i	0.298489	+	0.516998i	0.975790	−	0.218707i	$-0.0701840\pi$
$193$	57.6084	+	99.7807i	0.298489	+	0.516998i	−0.677301	+	0.735706i	$0.736851\pi$
$194$	−140.687	+	81.2257i	−0.725190	+	0.418689i
$195$		0			0
$196$	−56.7978	+	79.8625i	−0.289785	+	0.407462i
$197$	−44.1864			−0.224297			−0.112148	−	0.993691i	$-0.535773\pi$
$197$	−44.1864			−0.224297			−0.112148	+	0.993691i	$0.535773\pi$
$198$		0			0
$199$			14.5566i			0.0731488i	0.999331	+	0.0365744i	$0.0116446\pi$
$199$			14.5566i			0.0731488i	−0.999331	+	0.0365744i	$0.988355\pi$
$200$	27.1733	−	47.0656i	0.135867	−	0.235328i
$201$		0			0
$202$	211.656	−	122.200i	1.04780	−	0.604948i
$203$	−83.2921	−	161.445i	−0.410306	−	0.795298i
$204$		0			0
$205$	−58.1787	+	100.769i	−0.283799	+	0.491554i
$206$		−	66.0455i		−	0.320609i
$207$		0			0
$208$			54.3191i			0.261150i
$209$	−406.270	−	234.560i	−1.94387	−	1.12230i
$210$		0			0
$211$	175.108	+	303.296i	0.829896	+	1.43742i	0.898119	+	0.439752i	$0.144934\pi$
$211$	175.108	+	303.296i	0.829896	+	1.43742i	−0.0682235	+	0.997670i	$0.521733\pi$
$212$	35.6774	+	61.7951i	0.168290	+	0.291486i
$213$		0			0
$214$	49.1499	−	85.1300i	0.229672	−	0.397804i
$215$		−	63.1007i		−	0.293492i
$216$		0			0
$217$	−8.28082	+	174.937i	−0.0381604	+	0.806163i
$218$	96.0864	−	166.427i	0.440763	−	0.763425i
$219$		0			0
$220$	−56.6540	+	32.7092i	−0.257518	+	0.148678i
$221$	−134.562	−	233.069i	−0.608880	−	1.05461i
$222$		0			0
$223$	−277.642	−	160.297i	−1.24503	−	0.718820i	−0.274918	−	0.961468i	$-0.588651\pi$
$223$	−277.642	−	160.297i	−1.24503	−	0.718820i	−0.970114	+	0.242648i	$0.921984\pi$
$224$	−39.5537	−	1.87231i	−0.176579	−	0.00835852i
$225$		0			0
$226$	5.81469			0.0257287
$227$	−242.920	−	140.250i	−1.07013	−	0.617841i	−0.141915	−	0.989879i	$-0.545326\pi$
$227$	−242.920	−	140.250i	−1.07013	−	0.617841i	−0.928218	+	0.372037i	$0.878659\pi$
$228$		0			0
$229$	−31.1962	+	18.0111i	−0.136228	+	0.0786512i	−0.566565	−	0.824017i	$-0.691728\pi$
$229$	−31.1962	+	18.0111i	−0.136228	+	0.0786512i	0.430337	+	0.902668i	$0.358395\pi$
$230$	−25.5440	+	14.7478i	−0.111061	+	0.0641211i
$231$		0			0
$232$	36.7019	−	63.5695i	0.158198	−	0.274007i
$233$	418.773			1.79731			0.898654	−	0.438658i	$-0.144546\pi$
$233$	418.773			1.79731			0.898654	+	0.438658i	$0.144546\pi$
$234$		0			0
$235$	−40.4596			−0.172168
$236$	−127.831	−	73.8030i	−0.541655	−	0.312725i
$237$		0			0
$238$	174.353	−	89.9511i	0.732574	−	0.377946i
$239$	25.6058	+	44.3506i	0.107137	+	0.185567i	0.914609	−	0.404338i	$-0.132498\pi$
$239$	25.6058	+	44.3506i	0.107137	+	0.185567i	−0.807472	+	0.589906i	$0.799165\pi$
$240$		0			0
$241$	227.784	+	131.511i	0.945161	+	0.545689i	0.891574	−	0.452874i	$-0.149601\pi$
$241$	227.784	+	131.511i	0.945161	+	0.545689i	0.0535868	+	0.998563i	$0.482935\pi$
$242$	−90.4035			−0.373568
$243$		0			0
$244$		−	181.381i		−	0.743367i
$245$	−96.0472	−	68.3083i	−0.392029	−	0.278809i
$246$		0			0
$247$	−234.233	−	405.704i	−0.948313	−	1.64253i
$248$	−61.2839	+	35.3823i	−0.247112	+	0.142670i
$249$		0			0
$250$	130.251	+	75.2006i	0.521005	+	0.300802i
$251$		−	244.001i		−	0.972115i	−0.873927	−	0.486058i	$-0.838435\pi$
$251$		−	244.001i		−	0.972115i	0.873927	−	0.486058i	$-0.161565\pi$
$252$		0			0
$253$	−117.915			−0.466067
$254$	8.50584	−	14.7325i	0.0334875	−	0.0580021i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−185.090	+	106.862i	−0.720193	+	0.415804i	−0.814824	−	0.579709i	$-0.803166\pi$
$257$	−185.090	+	106.862i	−0.720193	+	0.415804i	0.0946307	+	0.995512i	$0.469833\pi$
$258$		0			0
$259$	−150.113	+	233.734i	−0.579587	+	0.902449i
$260$	−65.3273			−0.251259
$261$		0			0
$262$		−	118.639i		−	0.452821i
$263$	−77.6298	+	134.459i	−0.295170	+	0.511250i	−0.975025	−	0.222097i	$-0.928710\pi$
$263$	−77.6298	+	134.459i	−0.295170	+	0.511250i	0.679854	+	0.733347i	$0.262043\pi$
$264$		0			0
$265$	−74.3184	+	42.9077i	−0.280447	+	0.161916i
$266$	303.496	−	156.578i	1.14096	−	0.588640i
$267$		0			0
$268$	−20.7362	+	35.9161i	−0.0773739	+	0.134015i
$269$			128.394i			0.477302i	0.971105	+	0.238651i	$0.0767052\pi$
$269$			128.394i			0.477302i	−0.971105	+	0.238651i	$0.923295\pi$
$270$		0			0
$271$		−	520.915i		−	1.92219i	−0.276210	−	0.961097i	$-0.589079\pi$
$271$		−	520.915i		−	1.92219i	0.276210	−	0.961097i	$-0.410921\pi$
$272$	68.6518	+	39.6361i	0.252396	+	0.145721i
$273$		0			0
$274$	141.378	+	244.874i	0.515978	+	0.893700i
$275$	130.646	+	226.285i	0.475076	+	0.822856i
$276$		0			0
$277$	191.963	−	332.489i	0.693007	−	1.20032i	−0.277841	−	0.960627i	$-0.589619\pi$
$277$	191.963	−	332.489i	0.693007	−	1.20032i	0.970848	−	0.239696i	$-0.0770477\pi$
$278$			208.478i			0.749923i
$279$		0			0
$280$	2.25175	−	47.5695i	0.00804195	−	0.169891i
$281$	45.4795	−	78.7728i	0.161849	−	0.280330i	−0.773683	−	0.633573i	$-0.781588\pi$
$281$	45.4795	−	78.7728i	0.161849	−	0.280330i	0.935532	+	0.353243i	$0.114921\pi$
$282$		0			0
$283$	86.2442	−	49.7931i	0.304750	−	0.175947i	−0.339825	−	0.940489i	$-0.610368\pi$
$283$	86.2442	−	49.7931i	0.304750	−	0.175947i	0.644575	+	0.764541i	$0.277034\pi$
$284$	−38.1972	−	66.1595i	−0.134497	−	0.232956i
$285$		0			0
$286$	−226.170	−	130.580i	−0.790806	−	0.456572i
$287$	16.0112	−	338.247i	0.0557883	−	1.17856i
$288$		0			0
$289$	−103.755			−0.359015
$290$	76.4524	+	44.1398i	0.263629	+	0.152206i
$291$		0			0
$292$	20.9062	−	12.0702i	0.0715966	−	0.0413363i
$293$	−493.237	+	284.771i	−1.68340	+	0.971914i	−0.724033	+	0.689765i	$0.757714\pi$
$293$	−493.237	+	284.771i	−1.68340	+	0.971914i	−0.959371	+	0.282149i	$0.908953\pi$
$294$		0			0
$295$	88.7597	−	153.736i	0.300880	−	0.521140i
$296$	−112.243			−0.379199
$297$		0			0
$298$	−299.205			−1.00404
$299$	−101.975	−	58.8754i	−0.341054	−	0.196908i
$300$		0			0
$301$	84.1962	+	163.198i	0.279722	+	0.542186i
$302$	13.4120	+	23.2303i	0.0444106	+	0.0769215i
$303$		0			0
$304$	119.502	+	68.9947i	0.393100	+	0.226956i
$305$	218.140			0.715213
$306$		0			0
$307$		−	235.830i		−	0.768176i	−0.923296	−	0.384088i	$-0.874516\pi$
$307$		−	235.830i		−	0.768176i	0.923296	−	0.384088i	$-0.125484\pi$
$308$	102.880	−	160.190i	0.334027	−	0.520098i
$309$		0			0
$310$	−42.5527	−	73.7035i	−0.137267	−	0.237753i
$311$	525.110	−	303.172i	1.68846	−	0.974831i	0.732756	−	0.680492i	$-0.238234\pi$
$311$	525.110	−	303.172i	1.68846	−	0.974831i	0.955701	−	0.294339i	$-0.0950996\pi$
$312$		0			0
$313$	−21.4543	−	12.3867i	−0.0685442	−	0.0395740i	0.465336	−	0.885134i	$-0.345933\pi$
$313$	−21.4543	−	12.3867i	−0.0685442	−	0.0395740i	−0.533880	+	0.845560i	$0.679267\pi$
$314$			11.4008i			0.0363084i
$315$		0			0
$316$	261.697			0.828157
$317$	−219.173	+	379.619i	−0.691398	+	1.19754i	0.279982	+	0.960005i	$0.409672\pi$
$317$	−219.173	+	379.619i	−0.691398	+	1.19754i	−0.971380	+	0.237531i	$0.923662\pi$
$318$		0			0
$319$	176.458	+	305.634i	0.553160	+	0.958101i
$320$	16.6645	−	9.62126i	0.0520766	−	0.0300664i
$321$		0			0
$322$	46.3864	−	72.2262i	0.144057	−	0.224305i
$323$	−683.671			−2.11663
$324$		0			0
$325$			260.928i			0.802855i
$326$	34.7328	−	60.1589i	0.106542	−	0.184537i
$327$		0			0
$328$	118.494	−	68.4128i	0.361263	−	0.208576i
$329$	104.641	−	53.9858i	0.318058	−	0.164091i
$330$		0			0
$331$	301.074	−	521.476i	0.909590	−	1.57546i	0.0949566	−	0.995481i	$-0.469729\pi$
$331$	301.074	−	521.476i	0.909590	−	1.57546i	0.814634	−	0.579976i	$-0.196938\pi$
$332$			63.8733i			0.192390i
$333$		0			0
$334$			274.382i			0.821504i
$335$	−43.1948	−	24.9385i	−0.128940	−	0.0744434i
$336$		0			0
$337$	−58.8515	−	101.934i	−0.174634	−	0.302474i	0.765401	−	0.643554i	$-0.222541\pi$
$337$	−58.8515	−	101.934i	−0.174634	−	0.302474i	−0.940034	+	0.341080i	$0.889207\pi$
$338$	−10.8967	−	18.8737i	−0.0322388	−	0.0558393i
$339$		0			0
$340$	−47.6687	+	82.5646i	−0.140202	+	0.242837i
$341$		−	340.227i		−	0.997732i
$342$		0			0
$343$	339.552	+	48.5091i	0.989949	+	0.141426i
$344$	−37.1003	+	64.2596i	−0.107850	+	0.186801i
$345$		0			0
$346$	92.2331	−	53.2508i	0.266570	−	0.153904i
$347$	136.895	+	237.110i	0.394511	+	0.683313i	0.993039	−	0.117789i	$-0.0375807\pi$
$347$	136.895	+	237.110i	0.394511	+	0.683313i	−0.598528	+	0.801102i	$0.704247\pi$
$348$		0			0
$349$	−184.692	−	106.632i	−0.529203	−	0.305535i	0.211489	−	0.977380i	$-0.432169\pi$
$349$	−184.692	−	106.632i	−0.529203	−	0.305535i	−0.740692	+	0.671845i	$0.765502\pi$
$350$	−190.001	−	8.99385i	−0.542859	−	0.0256967i
$351$		0			0
$352$	76.9259			0.218540
$353$	497.182	+	287.048i	1.40845	+	0.813168i	0.995239	−	0.0974679i	$-0.0310743\pi$
$353$	497.182	+	287.048i	1.40845	+	0.813168i	0.413210	+	0.910636i	$0.364408\pi$
$354$		0			0
$355$	79.5673	−	45.9382i	0.224133	−	0.129403i
$356$	205.750	−	118.790i	0.577949	−	0.333679i
$357$		0			0
$358$	68.8975	−	119.334i	0.192451	−	0.333335i
$359$	−34.8283			−0.0970149			−0.0485074	−	0.998823i	$-0.515446\pi$
$359$	−34.8283			−0.0970149			−0.0485074	+	0.998823i	$0.515446\pi$
$360$		0			0
$361$	−829.069			−2.29659
$362$	−101.843	−	58.7988i	−0.281333	−	0.162428i
$363$		0			0
$364$	168.957	−	87.1672i	0.464166	−	0.239470i
$365$	14.5163	+	25.1430i	0.0397708	+	0.0688850i
$366$		0			0
$367$	12.0980	+	6.98480i	0.0329646	+	0.0190321i	0.516392	−	0.856352i	$-0.327275\pi$
$367$	12.0980	+	6.98480i	0.0329646	+	0.0190321i	−0.483427	+	0.875385i	$0.660608\pi$
$368$	34.6842			0.0942505
$369$		0			0
$370$		−	134.990i		−	0.364837i
$371$	134.958	−	210.137i	0.363768	−	0.566406i
$372$		0			0
$373$	285.616	+	494.702i	0.765727	+	1.32628i	0.939861	+	0.341556i	$0.110954\pi$
$373$	285.616	+	494.702i	0.765727	+	1.32628i	−0.174135	+	0.984722i	$0.555713\pi$
$374$	−330.069	+	190.565i	−0.882537	+	0.509533i
$375$		0			0
$376$	41.2026	+	23.7883i	0.109581	+	0.0632669i
$377$			352.424i			0.934813i
$378$		0			0
$379$	−387.493			−1.02241			−0.511205	−	0.859459i	$-0.670801\pi$
$379$	−387.493			−1.02241			−0.511205	+	0.859459i	$0.670801\pi$
$380$	−82.9770	+	143.720i	−0.218361	+	0.378212i
$381$		0			0
$382$	155.408	+	269.175i	0.406827	+	0.704646i
$383$	499.981	−	288.664i	1.30543	−	0.753693i	0.324104	−	0.946022i	$-0.394937\pi$
$383$	499.981	−	288.664i	1.30543	−	0.753693i	0.981331	+	0.192329i	$0.0616039\pi$
$384$		0			0
$385$	192.654	+	123.730i	0.500400	+	0.321376i
$386$	162.941			0.422127
$387$		0			0
$388$			229.741i			0.592116i
$389$	166.634	−	288.618i	0.428364	−	0.741948i	−0.568364	−	0.822777i	$-0.692423\pi$
$389$	166.634	−	288.618i	0.428364	−	0.741948i	0.996728	+	0.0808291i	$0.0257568\pi$
$390$		0			0
$391$	−148.821	+	85.9217i	−0.380616	+	0.219748i
$392$	57.6490	+	126.034i	0.147064	+	0.321515i
$393$		0			0
$394$	−31.2445	+	54.1171i	−0.0793009	+	0.137353i
$395$			314.732i			0.796791i
$396$		0			0
$397$		−	279.218i		−	0.703321i	−0.936128	−	0.351661i	$-0.885617\pi$
$397$		−	279.218i		−	0.703321i	0.936128	−	0.351661i	$-0.114383\pi$
$398$	17.8281	+	10.2931i	0.0447943	+	0.0258620i
$399$		0			0
$400$	−38.4289	−	66.5608i	−0.0960723	−	0.166402i
$401$	−110.631	−	191.619i	−0.275888	−	0.477852i	0.694471	−	0.719521i	$-0.255639\pi$
$401$	−110.631	−	191.619i	−0.275888	−	0.477852i	−0.970359	+	0.241669i	$0.922305\pi$
$402$		0			0
$403$	169.876	−	294.235i	0.421530	−	0.730111i
$404$		−	345.632i		−	0.855526i
$405$		0			0
$406$	−256.626	−	12.1476i	−0.632084	−	0.0299202i
$407$	269.825	−	467.350i	0.662960	−	1.14828i
$408$		0			0
$409$	261.910	−	151.214i	0.640366	−	0.369715i	−0.144390	−	0.989521i	$-0.546122\pi$
$409$	261.910	−	151.214i	0.640366	−	0.369715i	0.784755	+	0.619806i	$0.212789\pi$
$410$	82.2771	+	142.508i	0.200676	+	0.347581i
$411$		0			0
$412$	−80.8889	−	46.7012i	−0.196332	−	0.113352i
$413$	−24.4274	+	516.043i	−0.0591461	+	1.24950i
$414$		0			0
$415$	−76.8178			−0.185103
$416$	66.5270	+	38.4094i	0.159921	+	0.0923303i
$417$		0			0
$418$	−574.552	+	331.718i	−1.37453	+	0.793583i
$419$	−437.785	+	252.755i	−1.04483	+	0.603234i	−0.921198	−	0.389093i	$-0.872788\pi$
$419$	−437.785	+	252.755i	−1.04483	+	0.603234i	−0.123634	+	0.992328i	$0.539455\pi$
$420$		0			0
$421$	22.8490	−	39.5757i	0.0542733	−	0.0940040i	−0.837612	−	0.546265i	$-0.816049\pi$
$421$	22.8490	−	39.5757i	0.0542733	−	0.0940040i	0.891886	+	0.452261i	$0.149382\pi$
$422$	495.280			1.17365
$423$		0			0
$424$	100.911			0.237998
$425$	329.777	+	190.397i	0.775945	+	0.447992i
$426$		0			0
$427$	−564.177	+	291.067i	−1.32126	+	0.681656i
$428$	−69.5084	−	120.392i	−0.162403	−	0.281290i
$429$		0			0
$430$	−77.2822	−	44.6189i	−0.179726	−	0.103765i
$431$	−252.544			−0.585948			−0.292974	−	0.956120i	$-0.594645\pi$
$431$	−252.544			−0.585948			−0.292974	+	0.956120i	$0.594645\pi$
$432$		0			0
$433$			830.225i			1.91738i	0.284454	+	0.958690i	$0.408188\pi$
$433$			830.225i			1.91738i	−0.284454	+	0.958690i	$0.591812\pi$
$434$	208.398	+	133.841i	0.480180	+	0.308390i
$435$		0			0
$436$	−135.887	−	235.363i	−0.311667	−	0.539823i
$437$	−259.053	+	149.564i	−0.592798	+	0.342252i
$438$		0			0
$439$	−193.141	−	111.510i	−0.439956	−	0.254009i	0.263623	−	0.964626i	$-0.415083\pi$
$439$	−193.141	−	111.510i	−0.439956	−	0.254009i	−0.703579	+	0.710617i	$0.748416\pi$
$440$			92.5155i			0.210263i
$441$		0			0
$442$	−380.600			−0.861086
$443$	102.606	−	177.719i	0.231616	−	0.401171i	−0.726668	−	0.686989i	$-0.758932\pi$
$443$	102.606	−	177.719i	0.231616	−	0.401171i	0.958284	+	0.285818i	$0.0922654\pi$
$444$		0			0
$445$	142.863	+	247.447i	0.321041	+	0.556060i
$446$	−392.645	+	226.694i	−0.880371	+	0.508282i
$447$		0			0
$448$	−30.2618	+	47.1193i	−0.0675486	+	0.105177i
$449$	441.157			0.982532			0.491266	−	0.871010i	$-0.336534\pi$
$449$	441.157			0.982532			0.491266	+	0.871010i	$0.336534\pi$
$450$		0			0
$451$			657.839i			1.45862i
$452$	4.11161	−	7.12151i	0.00909648	−	0.0157556i
$453$		0			0
$454$	−343.541	+	198.343i	−0.756698	+	0.436880i
$455$	104.832	+	203.197i	0.230401	+	0.446586i
$456$		0			0
$457$	−337.214	+	584.071i	−0.737886	+	1.27806i	0.215560	+	0.976491i	$0.430842\pi$
$457$	−337.214	+	584.071i	−0.737886	+	1.27806i	−0.953446	+	0.301565i	$0.902491\pi$
$458$			50.9432i			0.111230i
$459$		0			0
$460$			41.7132i			0.0906809i
$461$	82.1484	+	47.4284i	0.178196	+	0.102882i	0.586445	−	0.809989i	$-0.300527\pi$
$461$	82.1484	+	47.4284i	0.178196	+	0.102882i	−0.408249	+	0.912871i	$0.633860\pi$
$462$		0			0
$463$	195.201	+	338.099i	0.421601	+	0.730235i	0.996096	−	0.0882733i	$-0.0281349\pi$
$463$	195.201	+	338.099i	0.421601	+	0.730235i	−0.574495	+	0.818508i	$0.694802\pi$
$464$	−51.9043	−	89.9009i	−0.111863	−	0.193752i
$465$		0			0
$466$	296.117	−	512.890i	0.635445	−	1.10062i
$467$		−	135.589i		−	0.290341i	−0.989407	−	0.145170i	$-0.953627\pi$
$467$		−	135.589i		−	0.290341i	0.989407	−	0.145170i	$-0.0463731\pi$
$468$		0			0
$469$	144.991	+	6.86328i	0.309149	+	0.0146339i
$470$	−28.6092	+	49.5527i	−0.0608707	+	0.105431i
$471$		0			0
$472$	−180.780	+	104.373i	−0.383008	+	0.221130i
$473$	−178.373	−	308.952i	−0.377111	−	0.653175i
$474$		0			0
$475$	574.043	+	331.424i	1.20851	+	0.697735i
$476$	13.1188	−	277.143i	0.0275605	−	0.582232i
$477$		0			0
$478$	72.4242			0.151515
$479$	176.072	+	101.655i	0.367583	+	0.212224i	0.672402	−	0.740186i	$-0.265263\pi$
$479$	176.072	+	101.655i	0.367583	+	0.212224i	−0.304819	+	0.952410i	$0.598596\pi$
$480$		0			0
$481$	466.699	−	269.449i	0.970269	−	0.560185i
$482$	322.135	−	185.985i	0.668330	−	0.385860i
$483$		0			0
$484$	−63.9249	+	110.721i	−0.132076	+	0.228763i
$485$	−276.300			−0.569690
$486$		0			0
$487$	−237.902			−0.488504			−0.244252	−	0.969712i	$-0.578542\pi$
$487$	−237.902			−0.488504			−0.244252	+	0.969712i	$0.578542\pi$
$488$	−222.146	−	128.256i	−0.455217	−	0.262820i
$489$		0			0
$490$	−151.576	+	69.3321i	−0.309338	+	0.141494i
$491$	283.247	+	490.597i	0.576877	+	0.999180i	0.995835	+	0.0911744i	$0.0290621\pi$
$491$	283.247	+	490.597i	0.576877	+	0.999180i	−0.418958	+	0.908006i	$0.637605\pi$
$492$		0			0
$493$	445.415	+	257.161i	0.903480	+	0.521624i
$494$	−662.512			−1.34112
$495$		0			0
$496$			100.076i			0.201766i
$497$	−144.490	+	224.978i	−0.290723	+	0.452672i
$498$		0			0
$499$	−118.082	−	204.523i	−0.236636	−	0.409866i	0.723111	−	0.690732i	$-0.242712\pi$
$499$	−118.082	−	204.523i	−0.236636	−	0.409866i	−0.959747	+	0.280866i	$0.909378\pi$
$500$	184.203	−	106.350i	0.368406	−	0.212699i
$501$		0			0
$502$	−298.839	−	172.535i	−0.595297	−	0.343695i
$503$			711.182i			1.41388i	0.707273	+	0.706941i	$0.249925\pi$
$503$			711.182i			1.41388i	−0.707273	+	0.706941i	$0.750075\pi$
$504$		0			0
$505$	415.677			0.823124
$506$	−83.3785	+	144.416i	−0.164780	+	0.285407i
$507$		0			0
$508$	−12.0291	−	20.8350i	−0.0236793	−	0.0410137i
$509$	454.930	−	262.654i	0.893772	−	0.516019i	0.0185973	−	0.999827i	$-0.494080\pi$
$509$	454.930	−	262.654i	0.893772	−	0.516019i	0.875174	+	0.483808i	$0.160747\pi$
$510$		0			0
$511$	−71.0924	−	45.6582i	−0.139124	−	0.0893508i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$			302.250i			0.588035i
$515$	56.1656	−	97.2816i	0.109059	−	0.188896i
$516$		0			0
$517$	−198.097	+	114.371i	−0.383166	+	0.221221i
$518$	180.119	+	349.125i	0.347720	+	0.673987i
$519$		0			0
$520$	−46.1934	+	80.0092i	−0.0888334	+	0.153864i
$521$			58.8034i			0.112866i	0.998406	+	0.0564332i	$0.0179728\pi$
$521$			58.8034i			0.112866i	−0.998406	+	0.0564332i	$0.982027\pi$
$522$		0			0
$523$			49.8806i			0.0953740i	0.998862	+	0.0476870i	$0.0151850\pi$
$523$			49.8806i			0.0953740i	−0.998862	+	0.0476870i	$0.984815\pi$
$524$	−145.303	−	83.8906i	−0.277295	−	0.160097i
$525$		0			0
$526$	109.785	+	190.153i	0.208717	+	0.361509i
$527$	−247.914	−	429.400i	−0.470426	−	0.814801i
$528$		0			0
$529$	226.906	−	393.014i	0.428935	−	0.742937i
$530$			121.361i			0.228984i
$531$		0			0
$532$	22.8359	−	482.423i	0.0429247	−	0.906810i
$533$	−328.462	+	568.912i	−0.616251	+	1.06738i
$534$		0			0
$535$	144.790	−	83.5948i	0.270636	−	0.156252i
$536$	29.3254	+	50.7931i	0.0547116	+	0.0947632i
$537$		0			0
$538$	157.250	+	90.7884i	0.292287	+	0.168752i
$539$	−663.357	−	62.9423i	−1.23072	−	0.116776i
$540$		0			0
$541$	943.506			1.74400			0.872002	−	0.489503i	$-0.162822\pi$
$541$	943.506			1.74400			0.872002	+	0.489503i	$0.162822\pi$
$542$	−637.988	−	368.342i	−1.17710	−	0.679598i
$543$		0			0
$544$	97.0883	−	56.0539i	0.178471	−	0.103040i
$545$	283.061	−	163.425i	0.519377	−	0.299863i
$546$		0			0
$547$	−115.302	+	199.709i	−0.210790	+	0.365100i	−0.951962	−	0.306216i	$-0.900937\pi$
$547$	−115.302	+	199.709i	−0.210790	+	0.365100i	0.741172	+	0.671315i	$0.234270\pi$
$548$	399.877			0.729703
$549$		0			0
$550$	369.523			0.671859
$551$	775.336	+	447.641i	1.40714	+	0.812415i
$552$		0			0
$553$	−419.952	−	813.995i	−0.759407	−	1.47196i
$554$	−271.476	−	470.211i	−0.490030	−	0.848756i
$555$		0			0
$556$	255.333	+	147.417i	0.459232	+	0.265138i
$557$	484.872			0.870506			0.435253	−	0.900308i	$-0.356659\pi$
$557$	484.872			0.870506			0.435253	+	0.900308i	$0.356659\pi$
$558$		0			0
$559$		−	356.250i		−	0.637298i
$560$	−56.6683	−	36.3946i	−0.101193	−	0.0649903i
$561$		0			0
$562$	−64.3178	−	111.402i	−0.114444	−	0.198224i
$563$	−565.382	+	326.423i	−1.00423	+	0.579793i	−0.909497	−	0.415710i	$-0.863533\pi$
$563$	−565.382	+	326.423i	−1.00423	+	0.579793i	−0.0947335	+	0.995503i	$0.530200\pi$
$564$		0			0
$565$	8.56474	+	4.94486i	0.0151588	+	0.00875196i
$566$		−	140.836i		−	0.248827i
$567$		0			0
$568$	−108.038			−0.190208
$569$	203.792	−	352.977i	0.358157	−	0.620347i	−0.629496	−	0.777004i	$-0.716738\pi$
$569$	203.792	−	352.977i	0.358157	−	0.620347i	0.987653	+	0.156657i	$0.0500718\pi$
$570$		0			0
$571$	174.770	+	302.710i	0.306076	+	0.530140i	0.977500	−	0.210934i	$-0.0676504\pi$
$571$	174.770	+	302.710i	0.306076	+	0.530140i	−0.671424	+	0.741073i	$0.734317\pi$
$572$	−319.853	+	184.667i	−0.559184	+	0.322845i
$573$		0			0
$574$	−402.945	−	258.787i	−0.701995	−	0.450848i
$575$	166.609			0.289756
$576$		0			0
$577$		−	695.947i		−	1.20615i	−0.797686	−	0.603073i	$-0.793943\pi$
$577$		−	695.947i		−	1.20615i	0.797686	−	0.603073i	$-0.206057\pi$
$578$	−73.3662	+	127.074i	−0.126931	+	0.219851i
$579$		0			0
$580$	108.120	−	62.4231i	0.186414	−	0.107626i
$581$	198.674	−	102.499i	0.341953	−	0.176418i
$582$		0			0
$583$	−242.583	+	420.167i	−0.416095	+	0.720698i
$584$		−	34.1397i		−	0.0584584i
$585$		0			0
$586$			805.453i			1.37449i
$587$	−45.3007	−	26.1544i	−0.0771732	−	0.0445560i	0.460917	−	0.887443i	$-0.347521\pi$
$587$	−45.3007	−	26.1544i	−0.0771732	−	0.0445560i	−0.538090	+	0.842887i	$0.680854\pi$
$588$		0			0
$589$	−431.546	−	747.459i	−0.732675	−	1.26903i
$590$	−125.525	−	217.416i	−0.212755	−	0.368502i
$591$		0			0
$592$	−79.3677	+	137.469i	−0.134067	+	0.232211i
$593$		−	21.8727i		−	0.0368848i	−0.999830	−	0.0184424i	$-0.994129\pi$
$593$		−	21.8727i		−	0.0368848i	0.999830	−	0.0184424i	$-0.00587072\pi$
$594$		0			0
$595$	333.308	+	15.7774i	0.560181	+	0.0265166i
$596$	−211.570	+	366.450i	−0.354983	+	0.614849i
$597$		0			0
$598$	−144.215	+	83.2624i	−0.241162	+	0.139235i
$599$	350.512	+	607.105i	0.585162	+	1.01353i	0.994855	+	0.101307i	$0.0323025\pi$
$599$	350.512	+	607.105i	0.585162	+	1.01353i	−0.409693	+	0.912224i	$0.634364\pi$
$600$		0			0
$601$	34.2071	+	19.7495i	0.0569170	+	0.0328611i	0.528188	−	0.849127i	$-0.322871\pi$
$601$	34.2071	+	19.7495i	0.0569170	+	0.0328611i	−0.471271	+	0.881988i	$0.656205\pi$
$602$	259.411	+	12.2795i	0.430916	+	0.0203978i
$603$		0			0
$604$	37.9349			0.0628061
$605$	−133.160	−	76.8798i	−0.220099	−	0.127074i
$606$		0			0
$607$	323.783	−	186.936i	0.533415	−	0.307968i	−0.208991	−	0.977918i	$-0.567018\pi$
$607$	323.783	−	186.936i	0.533415	−	0.307968i	0.742406	+	0.669950i	$0.233685\pi$
$608$	169.002	−	97.5733i	0.277964	−	0.160482i
$609$		0			0
$610$	154.248	−	267.166i	0.252866	−	0.437976i
$611$	−228.424			−0.373853
$612$		0			0
$613$	−672.296			−1.09673			−0.548366	−	0.836239i	$-0.684750\pi$
$613$	−672.296			−1.09673			−0.548366	+	0.836239i	$0.684750\pi$
$614$	−288.832	−	166.757i	−0.470410	−	0.271591i
$615$		0			0
$616$	−123.445	−	239.274i	−0.200398	−	0.388431i
$617$	231.200	+	400.450i	0.374716	+	0.649028i	0.990285	−	0.139056i	$-0.0444067\pi$
$617$	231.200	+	400.450i	0.374716	+	0.649028i	−0.615568	+	0.788084i	$0.711073\pi$
$618$		0			0
$619$	−692.305	−	399.702i	−1.11842	−	0.645723i	−0.177426	−	0.984134i	$-0.556777\pi$
$619$	−692.305	−	399.702i	−1.11842	−	0.645723i	−0.940998	+	0.338411i	$0.890110\pi$
$620$	−120.357			−0.194125
$621$		0			0
$622$		−	857.501i		−	1.37862i
$623$	−699.660	−	449.348i	−1.12305	−	0.721266i
$624$		0			0
$625$	−112.278	−	194.472i	−0.179646	−	0.311155i
$626$	−30.3410	+	17.5174i	−0.0484680	+	0.0279830i
$627$		0			0
$628$	13.9631	+	8.06161i	0.0222343	+	0.0128370i
$629$		−	786.457i		−	1.25033i
$630$		0			0
$631$	−410.154			−0.650006			−0.325003	−	0.945713i	$-0.605365\pi$
$631$	−410.154			−0.650006			−0.325003	+	0.945713i	$0.605365\pi$
$632$	185.048	−	320.513i	0.292798	−	0.507140i
$633$		0			0
$634$	309.958	+	536.863i	0.488892	+	0.846786i
$635$	25.0573	−	14.4668i	0.0394603	−	0.0227824i
$636$		0			0
$637$	−542.257	−	385.651i	−0.851267	−	0.605417i
$638$	499.098			0.782286
$639$		0			0
$640$		−	27.2130i		−	0.0425204i
$641$	−543.226	+	940.895i	−0.847466	+	1.46785i	0.0359962	+	0.999352i	$0.488540\pi$
$641$	−543.226	+	940.895i	−0.847466	+	1.46785i	−0.883462	+	0.468502i	$0.844794\pi$
$642$		0			0
$643$	612.173	−	353.438i	0.952057	−	0.549671i	0.0583379	−	0.998297i	$-0.481420\pi$
$643$	612.173	−	353.438i	0.952057	−	0.549671i	0.893719	+	0.448626i	$0.148087\pi$
$644$	−55.6585	−	107.883i	−0.0864263	−	0.167521i
$645$		0			0
$646$	−483.428	+	837.322i	−0.748341	+	1.29616i
$647$		−	422.816i		−	0.653502i	−0.945110	−	0.326751i	$-0.894046\pi$
$647$		−	422.816i		−	0.653502i	0.945110	−	0.326751i	$-0.105954\pi$
$648$		0			0
$649$		−	1003.63i		−	1.54642i
$650$	319.570	+	184.504i	0.491647	+	0.283852i
$651$		0			0
$652$	−49.1196	−	85.0776i	−0.0753367	−	0.130487i
$653$	−394.425	−	683.164i	−0.604019	−	1.04619i	−0.992206	−	0.124611i	$-0.960232\pi$
$653$	−394.425	−	683.164i	−0.604019	−	1.04619i	0.388186	−	0.921581i	$-0.373102\pi$
$654$		0			0
$655$	100.892	−	174.749i	0.154033	−	0.266793i
$656$		−	193.501i		−	0.294970i
$657$		0			0
$658$	7.87348	−	166.332i	0.0119658	−	0.252784i
$659$	548.183	−	949.480i	0.831840	−	1.44079i	−0.0647375	−	0.997902i	$-0.520621\pi$
$659$	548.183	−	949.480i	0.831840	−	1.44079i	0.896578	−	0.442887i	$-0.146046\pi$
$660$		0			0
$661$	213.700	−	123.380i	0.323298	−	0.186656i	−0.329563	−	0.944133i	$-0.606902\pi$
$661$	213.700	−	123.380i	0.323298	−	0.186656i	0.652862	+	0.757477i	$0.273568\pi$
$662$	−425.784	−	737.479i	−0.643178	−	1.11402i
$663$		0			0
$664$	78.2286	+	45.1653i	0.117814	+	0.0680200i
$665$	580.190	+	27.4638i	0.872466	+	0.0412989i
$666$		0			0
$667$	225.032			0.337380
$668$	336.048	+	194.018i	0.503066	+	0.290446i
$669$		0			0
$670$	−61.0867	+	35.2684i	−0.0911742	+	0.0526394i
$671$	1068.05	−	616.639i	1.59173	−	0.918985i
$672$		0			0
$673$	155.614	−	269.532i	0.231225	−	0.400493i	−0.726944	−	0.686697i	$-0.759060\pi$
$673$	155.614	−	269.532i	0.231225	−	0.400493i	0.958169	+	0.286204i	$0.0923935\pi$
$674$	−166.457			−0.246969
$675$		0			0
$676$	−30.8206			−0.0455926
$677$	−467.683	−	270.017i	−0.690817	−	0.398843i	0.113101	−	0.993583i	$-0.463922\pi$
$677$	−467.683	−	270.017i	−0.690817	−	0.398843i	−0.803918	+	0.594740i	$0.797255\pi$
$678$		0			0
$679$	714.596	−	368.671i	1.05242	−	0.542961i
$680$	67.4137	+	116.764i	0.0991378	+	0.171712i
$681$		0			0
$682$	−416.691	−	240.577i	−0.610984	−	0.352752i
$683$	694.411			1.01671			0.508353	−	0.861149i	$-0.330254\pi$
$683$	694.411			1.01671			0.508353	+	0.861149i	$0.330254\pi$
$684$		0			0
$685$			480.916i			0.702067i
$686$	299.511	−	381.564i	0.436605	−	0.556216i
$687$		0			0
$688$	52.4677	+	90.8767i	0.0762612	+	0.132088i
$689$	−419.582	+	242.246i	−0.608972	+	0.351590i
$690$		0			0
$691$	803.725	+	464.031i	1.16313	+	0.671535i	0.952053	−	0.305933i	$-0.0989685\pi$
$691$	803.725	+	464.031i	1.16313	+	0.671535i	0.211080	+	0.977469i	$0.432302\pi$
$692$		−	150.616i		−	0.217653i
$693$		0			0
$694$	387.198			0.557923
$695$	−177.292	+	307.078i	−0.255096	+	0.441839i
$696$		0			0
$697$	479.351	+	830.260i	0.687734	+	1.19119i
$698$	−261.194	+	150.800i	−0.374203	+	0.216046i
$699$		0			0
$700$	−145.366	+	226.343i	−0.207666	+	0.323347i
$701$	−717.659			−1.02376			−0.511882	−	0.859056i	$-0.671052\pi$
$701$	−717.659			−1.02376			−0.511882	+	0.859056i	$0.671052\pi$
$702$		0			0
$703$		−	1368.99i		−	1.94735i
$704$	54.3948	−	94.2146i	0.0772654	−	0.133828i
$705$		0			0
$706$	703.122	−	405.948i	0.995923	−	0.574997i
$707$	−1075.07	+	554.645i	−1.52061	+	0.784504i
$708$		0			0
$709$	−273.064	+	472.960i	−0.385139	+	0.667081i	−0.991789	−	0.127889i	$-0.959180\pi$
$709$	−273.064	+	472.960i	−0.385139	+	0.667081i	0.606649	+	0.794970i	$0.292513\pi$
$710$		−	129.933i		−	0.183004i
$711$		0			0
$712$		−	335.988i		−	0.471893i
$713$	−187.877	−	108.471i	−0.263502	−	0.152133i
$714$		0			0
$715$	−222.092	−	384.674i	−0.310618	−	0.538006i
$716$	−97.4357	−	168.764i	−0.136083	−	0.235703i
$717$		0			0
$718$	−24.6274	+	42.6558i	−0.0342999	+	0.0594092i
$719$			23.4875i			0.0326669i	0.999867	+	0.0163335i	$0.00519934\pi$
$719$			23.4875i			0.0326669i	−0.999867	+	0.0163335i	$0.994801\pi$
$720$		0			0
$721$	−15.4572	+	326.543i	−0.0214385	+	0.452903i
$722$	−586.240	+	1015.40i	−0.811967	+	1.40637i
$723$		0			0
$724$	−144.027	+	83.1541i	−0.198932	+	0.114854i
$725$	−249.328	−	431.849i	−0.343901	−	0.595654i
$726$		0			0
$727$	656.448	+	379.000i	0.902955	+	0.521321i	0.878158	−	0.478371i	$-0.158773\pi$
$727$	656.448	+	379.000i	0.902955	+	0.521321i	0.0247971	+	0.999693i	$0.492106\pi$
$728$	12.7128	−	268.565i	0.0174626	−	0.368908i
$729$		0			0
$730$	41.0584			0.0562443
$731$	−450.250	−	259.952i	−0.615937	−	0.355612i
$732$		0			0
$733$	−436.380	+	251.944i	−0.595334	+	0.343716i	−0.767204	−	0.641404i	$-0.778352\pi$
$733$	−436.380	+	251.944i	−0.595334	+	0.343716i	0.171870	+	0.985120i	$0.445019\pi$
$734$	17.1092	−	9.87800i	0.0233095	−	0.0134578i
$735$		0			0
$736$	24.5254	−	42.4793i	0.0333226	−	0.0577164i
$737$	−281.986			−0.382613
$738$		0			0
$739$	−735.218			−0.994882			−0.497441	−	0.867498i	$-0.665727\pi$
$739$	−735.218			−0.994882			−0.497441	+	0.867498i	$0.665727\pi$
$740$	−165.328	−	95.4522i	−0.223416	−	0.128989i
$741$		0			0
$742$	−161.934	−	313.878i	−0.218240	−	0.423016i
$743$	−121.895	−	211.129i	−0.164058	−	0.284157i	0.772262	−	0.635304i	$-0.219125\pi$
$743$	−121.895	−	211.129i	−0.164058	−	0.284157i	−0.936320	+	0.351147i	$0.885792\pi$
$744$		0			0
$745$	−440.714	−	254.446i	−0.591562	−	0.341539i
$746$	807.844			1.08290
$747$		0			0
$748$			539.000i			0.720588i
$749$	−262.931	+	409.398i	−0.351043	+	0.546593i
$750$		0			0
$751$	−69.2575	−	119.958i	−0.0922204	−	0.159730i	0.816225	−	0.577735i	$-0.196063\pi$
$751$	−69.2575	−	119.958i	−0.0922204	−	0.159730i	−0.908445	+	0.418004i	$0.862730\pi$
$752$	58.2693	−	33.6418i	0.0774858	−	0.0447364i
$753$		0			0
$754$	431.630	+	249.202i	0.572454	+	0.330506i
$755$			45.6227i			0.0604274i
$756$		0			0
$757$	448.741			0.592788			0.296394	−	0.955066i	$-0.404216\pi$
$757$	448.741			0.592788			0.296394	+	0.955066i	$0.404216\pi$
$758$	−273.999	+	474.581i	−0.361477	+	0.626096i
$759$		0			0
$760$	117.347	+	203.251i	0.154404	+	0.267436i
$761$	334.945	−	193.380i	0.440137	−	0.254113i	−0.263519	−	0.964654i	$-0.584883\pi$
$761$	334.945	−	193.380i	0.440137	−	0.254113i	0.703656	+	0.710541i	$0.251550\pi$
$762$		0			0
$763$	−514.022	+	800.360i	−0.673685	+	1.04896i
$764$	439.560			0.575341
$765$		0			0
$766$		−	816.466i		−	1.06588i
$767$	501.114	−	867.955i	0.653343	−	1.13162i
$768$		0			0
$769$	−531.659	+	306.953i	−0.691364	+	0.399159i	−0.804123	−	0.594463i	$-0.797365\pi$
$769$	−531.659	+	306.953i	−0.691364	+	0.399159i	0.112759	+	0.993622i	$0.464031\pi$
$770$	287.764	−	148.462i	0.373720	−	0.192808i
$771$		0			0
$772$	115.217	−	199.561i	0.149245	−	0.258499i
$773$		−	244.996i		−	0.316942i	−0.987364	−	0.158471i	$-0.949344\pi$
$773$		−	244.996i		−	0.316942i	0.987364	−	0.158471i	$-0.0506564\pi$
$774$		0			0
$775$			480.727i			0.620293i
$776$	281.374	+	162.451i	0.362595	+	0.209344i
$777$		0			0
$778$	−235.655	−	408.167i	−0.302899	−	0.524637i
$779$	834.407	+	1445.24i	1.07113	+	1.85525i
$780$		0			0
$781$	259.717	−	449.842i	0.332544	−	0.575982i
$782$			243.023i			0.310771i
$783$		0			0
$784$	195.124	+	18.5142i	0.248882	+	0.0236150i
$785$	−9.69536	+	16.7929i	−0.0123508	+	0.0213922i
$786$		0			0
$787$	−1224.89	+	707.189i	−1.55640	+	0.898589i	−0.558805	+	0.829299i	$0.688740\pi$
$787$	−1224.89	+	707.189i	−1.55640	+	0.898589i	−0.997597	+	0.0692898i	$0.977927\pi$
$788$	44.1864	+	76.5332i	0.0560742	+	0.0971233i
$789$		0			0
$790$	385.467	+	222.549i	0.487933	+	0.281708i
$791$	−28.7491	−	1.36086i	−0.0363452	−	0.00172043i
$792$		0			0
$793$	1231.56			1.55304
$794$	−341.971	−	197.437i	−0.430694	−	0.248662i
$795$		0			0
$796$	25.2128	−	14.5566i	0.0316743	−	0.0182872i
$797$	10.1025	−	5.83266i	0.0126756	−	0.00731827i	−0.493649	−	0.869661i	$-0.664337\pi$
$797$	10.1025	−	5.83266i	0.0126756	−	0.00731827i	0.506324	+	0.862343i	$0.331004\pi$
$798$		0			0
$799$	−166.679	+	288.696i	−0.208609	+	0.361322i
$800$	−108.693			−0.135867
$801$		0			0
$802$	−312.912			−0.390164
$803$	142.149	+	82.0696i	0.177022	+	0.102204i
$804$		0			0
$805$	129.747	−	66.9382i	0.161176	−	0.0831530i
$806$	−240.242	−	416.111i	−0.298066	−	0.516266i
$807$		0			0
$808$	−423.312	−	244.399i	−0.523900	−	0.302474i
$809$	−315.185			−0.389599			−0.194799	−	0.980843i	$-0.562406\pi$
$809$	−315.185			−0.389599			−0.194799	+	0.980843i	$0.562406\pi$
$810$		0			0
$811$			1499.13i			1.84849i	0.381800	+	0.924245i	$0.375304\pi$
$811$			1499.13i			1.84849i	−0.381800	+	0.924245i	$0.624696\pi$
$812$	−196.340	+	305.712i	−0.241798	+	0.376492i
$813$		0			0
$814$	−381.590	−	660.933i	−0.468783	−	0.811957i
$815$	102.319	−	59.0740i	0.125545	−	0.0724834i
$816$		0			0
$817$	−783.752	−	452.500i	−0.959305	−	0.553855i
$818$		−	427.696i		−	0.522856i
$819$		0			0
$820$	232.715			0.283799
$821$	638.518	−	1105.95i	0.777732	−	1.34707i	−0.155515	−	0.987834i	$-0.549704\pi$
$821$	638.518	−	1105.95i	0.777732	−	1.34707i	0.933246	−	0.359237i	$-0.116963\pi$
$822$		0			0
$823$	−456.846	−	791.280i	−0.555098	−	0.961458i	−0.997896	−	0.0648368i	$-0.979347\pi$
$823$	−456.846	−	791.280i	−0.555098	−	0.961458i	0.442798	−	0.896622i	$-0.353986\pi$
$824$	−114.394	+	66.0455i	−0.138828	+	0.0801523i
$825$		0			0
$826$	614.748	+	394.815i	0.744247	+	0.477984i
$827$	−1239.04			−1.49823			−0.749116	−	0.662438i	$-0.769522\pi$
$827$	−1239.04			−1.49823			−0.749116	+	0.662438i	$0.769522\pi$
$828$		0			0
$829$		−	555.123i		−	0.669629i	−0.942284	−	0.334815i	$-0.891326\pi$
$829$		−	555.123i		−	0.669629i	0.942284	−	0.334815i	$-0.108674\pi$
$830$	−54.3184	+	94.0822i	−0.0654438	+	0.113352i
$831$		0			0
$832$	94.0834	−	54.3191i	0.113081	−	0.0652874i
$833$	−883.088	+	403.932i	−1.06013	+	0.484912i
$834$		0			0
$835$	−233.337	+	404.151i	−0.279445	+	0.484013i
$836$			938.240i			1.12230i
$837$		0			0
$838$			714.900i			0.853102i
$839$	955.955	+	551.921i	1.13940	+	0.657832i	0.946281	−	0.323344i	$-0.104807\pi$
$839$	955.955	+	551.921i	1.13940	+	0.657832i	0.193117	+	0.981176i	$0.438140\pi$
$840$		0			0
$841$	83.7427	+	145.047i	0.0995752	+	0.172469i
$842$	−32.3134	−	55.9685i	−0.0383770	−	0.0664709i
$843$		0			0
$844$	350.216	−	606.592i	0.414948	−	0.718711i
$845$		−	37.0666i		−	0.0438658i
$846$		0			0
$847$	446.974	+	21.1579i	0.527714	+	0.0249798i
$848$	71.3548	−	123.590i	0.0841449	−	0.145743i
$849$		0			0
$850$	466.375	−	269.262i	0.548676	−	0.316778i
$851$	−172.050	−	298.000i	−0.202174	−	0.350176i
$852$		0			0
$853$	−38.6408	−	22.3093i	−0.0452999	−	0.0261539i	0.477179	−	0.878806i	$-0.341659\pi$
$853$	−38.6408	−	22.3093i	−0.0452999	−	0.0261539i	−0.522479	+	0.852652i	$0.674993\pi$
$854$	−42.4503	+	896.788i	−0.0497076	+	1.05010i
$855$		0			0
$856$	−196.599			−0.229672
$857$	−680.850	−	393.089i	−0.794458	−	0.458680i	0.0470717	−	0.998892i	$-0.485011\pi$
$857$	−680.850	−	393.089i	−0.794458	−	0.458680i	−0.841530	+	0.540211i	$0.818344\pi$
$858$		0			0
$859$	−286.832	+	165.602i	−0.333914	+	0.192785i	−0.657577	−	0.753387i	$-0.728419\pi$
$859$	−286.832	+	165.602i	−0.333914	+	0.192785i	0.323664	+	0.946172i	$0.395085\pi$
$860$	−109.294	+	63.1007i	−0.127086	+	0.0733729i
$861$		0			0
$862$	−178.575	+	309.301i	−0.207164	+	0.358818i
$863$	−183.153			−0.212228			−0.106114	−	0.994354i	$-0.533841\pi$
$863$	−183.153			−0.212228			−0.106114	+	0.994354i	$0.533841\pi$
$864$		0			0
$865$	181.139			0.209410
$866$	1016.81	+	587.058i	1.17415	+	0.677896i
$867$		0			0
$868$	311.281	−	160.595i	0.358619	−	0.185017i
$869$	889.687	+	1540.98i	1.02381	+	1.77328i
$870$		0			0
$871$	−243.867	−	140.796i	−0.279985	−	0.161649i
$872$	−384.346			−0.440763
$873$		0			0
$874$			423.031i			0.484018i
$875$	−626.390	−	402.291i	−0.715874	−	0.459762i
$876$		0			0
$877$	−560.581	−	970.954i	−0.639203	−	1.10713i	−0.985608	−	0.169047i	$-0.945931\pi$
$877$	−560.581	−	970.954i	−0.639203	−	1.10713i	0.346405	−	0.938085i	$-0.387402\pi$
$878$	−273.142	+	157.699i	−0.311096	+	0.179611i
$879$		0			0
$880$	113.308	+	65.4184i	0.128759	+	0.0743391i
$881$		−	1389.25i		−	1.57690i	−0.615098	−	0.788450i	$-0.710884\pi$
$881$		−	1389.25i		−	1.57690i	0.615098	−	0.788450i	$-0.289116\pi$
$882$		0			0
$883$	1358.53			1.53854			0.769268	−	0.638926i	$-0.220621\pi$
$883$	1358.53			1.53854			0.769268	+	0.638926i	$0.220621\pi$
$884$	−269.125	+	466.138i	−0.304440	+	0.527305i
$885$		0			0
$886$	−145.107	−	251.332i	−0.163777	−	0.283671i
$887$	−908.326	+	524.422i	−1.02404	+	0.591231i	−0.915272	−	0.402836i	$-0.868025\pi$
$887$	−908.326	+	524.422i	−1.02404	+	0.591231i	−0.108770	+	0.994067i	$0.534691\pi$
$888$		0			0
$889$	−45.5026	+	70.8501i	−0.0511841	+	0.0796964i
$890$	404.078			0.454021
$891$		0			0
$892$			641.187i			0.718820i
$893$	−290.138	+	502.535i	−0.324903	+	0.562749i
$894$		0			0
$895$	202.965	−	117.182i	0.226776	−	0.130929i
$896$	36.3108	+	70.3813i	0.0405254	+	0.0785506i
$897$		0			0
$898$	311.945	−	540.305i	0.347378	−	0.601676i
$899$			649.298i			0.722245i
$900$		0			0
$901$			707.057i			0.784747i
$902$	805.686	+	465.163i	0.893221	+	0.515702i
$903$		0			0
$904$	−5.81469	−	10.0713i	−0.00643218	−	0.0111409i
$905$	−100.006	−	173.215i	−0.110504	−	0.191398i
$906$		0			0
$907$	−325.502	+	563.785i	−0.358877	+	0.621593i	−0.987774	−	0.155896i	$-0.950174\pi$
$907$	−325.502	+	563.785i	−0.358877	+	0.621593i	0.628896	+	0.777489i	$0.283507\pi$
$908$			561.000i			0.617841i
$909$		0			0
$910$	322.992	+	15.2891i	0.354936	+	0.0168012i
$911$	371.140	−	642.834i	0.407399	−	0.705636i	−0.587198	−	0.809443i	$-0.699769\pi$
$911$	371.140	−	642.834i	0.407399	−	0.705636i	0.994597	+	0.103807i	$0.0331025\pi$
$912$		0			0
$913$	−376.113	+	217.149i	−0.411953	+	0.237841i
$914$	476.892	+	826.002i	0.521764	+	0.903722i
$915$		0			0
$916$	62.3924	+	36.0223i	0.0681140	+	0.0393256i
$917$	−27.7662	+	586.577i	−0.0302793	+	0.639670i
$918$		0			0
$919$	630.519			0.686093			0.343046	−	0.939319i	$-0.388541\pi$
$919$	630.519			0.686093			0.343046	+	0.939319i	$0.388541\pi$
$920$	51.0880	+	29.4957i	0.0555305	+	0.0320605i
$921$		0			0
$922$	116.175	−	67.0739i	0.126004	−	0.0727483i
$923$	449.216	−	259.355i	0.486691	−	0.280991i
$924$		0			0
$925$	−381.252	+	660.348i	−0.412164	+	0.713890i
$926$	552.113			0.596234
$927$		0			0
$928$	−146.808			−0.158198
$929$	−164.909	−	95.2100i	−0.177512	−	0.102487i	0.408611	−	0.912709i	$-0.366013\pi$
$929$	−164.909	−	95.2100i	−0.177512	−	0.102487i	−0.586123	+	0.810222i	$0.699347\pi$
$930$		0			0
$931$	−1537.20	+	703.126i	−1.65112	+	0.755237i
$932$	−418.773	−	725.336i	−0.449327	−	0.778257i
$933$		0			0
$934$	−166.062	−	95.8760i	−0.177797	−	0.102651i
$935$	−648.233			−0.693297
$936$		0			0
$937$			173.230i			0.184877i	0.995718	+	0.0924384i	$0.0294661\pi$
$937$			173.230i			0.184877i	−0.995718	+	0.0924384i	$0.970534\pi$
$938$	110.930	−	172.724i	0.118262	−	0.184141i
$939$		0			0
$940$	40.4596	+	70.0780i	0.0430421	+	0.0745511i
$941$	1132.98	−	654.124i	1.20401	−	0.695137i	0.242568	−	0.970134i	$-0.422010\pi$
$941$	1132.98	−	654.124i	1.20401	−	0.695137i	0.961445	+	0.274997i	$0.0886770\pi$
$942$		0			0
$943$	363.266	+	209.732i	0.385223	+	0.222409i
$944$			295.212i			0.312725i
$945$		0			0
$946$	−504.516			−0.533315
$947$	−101.101	+	175.112i	−0.106759	+	0.184912i	−0.914456	−	0.404686i	$-0.867381\pi$
$947$	−101.101	+	175.112i	−0.106759	+	0.184912i	0.807696	+	0.589599i	$0.200714\pi$
$948$		0			0
$949$	81.9553	+	141.951i	0.0863597	+	0.149579i
$950$	811.820	−	468.705i	0.854547	−	0.493373i
$951$		0			0
$952$	−330.152	−	212.037i	−0.346799	−	0.222727i
$953$	123.695			0.129796			0.0648978	−	0.997892i	$-0.479328\pi$
$953$	123.695			0.129796			0.0648978	+	0.997892i	$0.479328\pi$
$954$		0			0
$955$			528.641i			0.553550i
$956$	51.2117	−	88.7012i	0.0535687	−	0.0927837i
$957$		0			0
$958$	249.004	−	143.762i	0.259920	−	0.150065i
$959$	−641.693	−	1243.80i	−0.669127	−	1.29697i
$960$		0			0
$961$	−167.524	+	290.160i	−0.174322	+	0.301935i
$962$		−	762.117i		−	0.792221i
$963$		0			0
$964$		−	526.044i		−	0.545689i
$965$	240.004	+	138.566i	0.248709	+	0.143592i
$966$		0			0
$967$	640.089	+	1108.67i	0.661933	+	1.14650i	0.980107	+	0.198469i	$0.0635971\pi$
$967$	640.089	+	1108.67i	0.661933	+	1.14650i	−0.318174	+	0.948032i	$0.603070\pi$
$968$	90.4035	+	156.584i	0.0933921	+	0.161760i
$969$		0			0
$970$	−195.373	+	338.396i	−0.201416	+	0.348862i
$971$			1011.08i			1.04127i	0.853778	+	0.520637i	$0.174305\pi$
$971$			1011.08i			1.04127i	−0.853778	+	0.520637i	$0.825695\pi$
$972$		0			0
$973$	48.7920	−	1030.76i	0.0501460	−	1.05936i
$974$	−168.222	+	291.369i	−0.172712	+	0.299147i
$975$		0			0
$976$	−314.162	+	181.381i	−0.321887	+	0.185842i
$977$	−359.962	−	623.473i	−0.368436	−	0.638150i	0.620885	−	0.783902i	$-0.286773\pi$
$977$	−359.962	−	623.473i	−0.368436	−	0.638150i	−0.989321	+	0.145751i	$0.953440\pi$
$978$		0			0
$979$	1398.97	+	807.693i	1.42897	+	0.825019i
$980$	−22.2662	+	234.667i	−0.0227206	+	0.239456i
$981$		0			0
$982$	801.142			0.815827
$983$	−203.077	−	117.247i	−0.206589	−	0.119274i	0.393136	−	0.919480i	$-0.371390\pi$
$983$	−203.077	−	117.247i	−0.206589	−	0.119274i	−0.599725	+	0.800206i	$0.704724\pi$
$984$		0			0
$985$	−92.0432	+	53.1412i	−0.0934449	+	0.0539504i
$986$	629.913	−	363.680i	0.638857	−	0.368844i
$987$		0			0
$988$	−468.467	+	811.408i	−0.474156	+	0.821263i
$989$	−227.475			−0.230005
$990$		0			0
$991$	57.3158			0.0578363			0.0289181	−	0.999582i	$-0.490794\pi$
$991$	57.3158			0.0578363			0.0289181	+	0.999582i	$0.490794\pi$
$992$	122.568	+	70.7645i	0.123556	+	0.0713352i
$993$		0			0
$994$	173.371	+	336.046i	0.174418	+	0.338075i
$995$	17.5066	+	30.3223i	0.0175946	+	0.0304747i
$996$		0			0
$997$	−763.810	−	440.986i	−0.766108	−	0.442313i	0.0653764	−	0.997861i	$-0.479175\pi$
$997$	−763.810	−	440.986i	−0.766108	−	0.442313i	−0.831484	+	0.555548i	$0.812509\pi$
$998$	−333.985			−0.334654
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.3.o.a.181.14		32
3.2	odd	2		126.3.o.a.97.7	yes	32
7.6	odd	2	inner	378.3.o.a.181.11		32
9.2	odd	6		1134.3.c.e.811.11		16
9.4	even	3	inner	378.3.o.a.307.11		32
9.5	odd	6		126.3.o.a.13.2	✓	32
9.7	even	3		1134.3.c.d.811.6		16
21.20	even	2		126.3.o.a.97.2	yes	32
63.13	odd	6	inner	378.3.o.a.307.14		32
63.20	even	6		1134.3.c.e.811.14		16
63.34	odd	6		1134.3.c.d.811.3		16
63.41	even	6		126.3.o.a.13.7	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.o.a.13.2	✓	32	9.5	odd	6
126.3.o.a.13.7	yes	32	63.41	even	6
126.3.o.a.97.2	yes	32	21.20	even	2
126.3.o.a.97.7	yes	32	3.2	odd	2
378.3.o.a.181.11		32	7.6	odd	2	inner
378.3.o.a.181.14		32	1.1	even	1	trivial
378.3.o.a.307.11		32	9.4	even	3	inner
378.3.o.a.307.14		32	63.13	odd	6	inner
1134.3.c.d.811.3		16	63.34	odd	6
1134.3.c.d.811.6		16	9.7	even	3
1134.3.c.e.811.11		16	9.2	odd	6
1134.3.c.e.811.14		16	63.20	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	378.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(2.08306 - 1.20266i) q^{5} +(-3.78272 + 5.88991i) q^{7} -2.82843 q^{8} -3.40163i q^{10} +(6.79936 - 11.7768i) q^{11} +(11.7604 - 6.78989i) q^{13} +(4.53884 + 8.79766i) q^{14} +(-2.00000 + 3.46410i) q^{16} -19.8181i q^{17} -34.4974i q^{19} +(-4.16613 - 2.40532i) q^{20} +(-9.61574 - 16.6550i) q^{22} +(-4.33552 - 7.50935i) q^{23} +(-9.60723 + 16.6402i) q^{25} -19.2047i q^{26} +(13.9843 + 0.661961i) q^{28} +(-12.9761 + 22.4752i) q^{29} +(21.6671 - 12.5095i) q^{31} +(2.82843 + 4.89898i) q^{32} +(-24.2721 - 14.0135i) q^{34} +(-0.796113 + 16.8184i) q^{35} +39.6839 q^{37} +(-42.2505 - 24.3933i) q^{38} +(-5.89179 + 3.40163i) q^{40} +(-41.8941 + 24.1876i) q^{41} +(13.1169 - 22.7192i) q^{43} -27.1974 q^{44} -12.2627 q^{46} +(-14.5673 - 8.41045i) q^{47} +(-20.3820 - 44.5598i) q^{49} +(13.5867 + 23.5328i) q^{50} +(-23.5209 - 13.5798i) q^{52} -35.6774 q^{53} -32.7092i q^{55} +(10.6992 - 16.6592i) q^{56} +(18.3509 + 31.7848i) q^{58} +(63.9153 - 36.9015i) q^{59} +(78.5405 + 45.3454i) q^{61} -35.3823i q^{62} +8.00000 q^{64} +(16.3318 - 28.2875i) q^{65} +(-10.3681 - 17.9581i) q^{67} +(-34.3259 + 19.8181i) q^{68} +(20.0353 + 12.8674i) q^{70} +38.1972 q^{71} +12.0702i q^{73} +(28.0607 - 48.6026i) q^{74} +(-59.7512 + 34.4974i) q^{76} +(43.6444 + 84.5961i) q^{77} +(-65.4244 + 113.318i) q^{79} +9.62126i q^{80} +68.4128i q^{82} +(-27.6580 - 15.9683i) q^{83} +(-23.8343 - 41.2823i) q^{85} +(-18.5501 - 32.1298i) q^{86} +(-19.2315 + 33.3099i) q^{88} +118.790i q^{89} +(-4.49464 + 94.9521i) q^{91} +(-8.67105 + 15.0187i) q^{92} +(-20.6013 + 11.8942i) q^{94} +(-41.4885 - 71.8602i) q^{95} +(-99.4807 - 57.4352i) q^{97} +(-68.9866 - 6.54575i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) \) 32 * q - 32 * q^4 - 2 * q^7 + 12 * q^11 + 12 * q^14 - 64 * q^16 - 12 * q^23 + 80 * q^25 + 8 * q^28 + 48 * q^29 - 348 * q^35 - 88 * q^37 + 32 * q^43 - 48 * q^44 + 48 * q^46 + 50 * q^49 - 48 * q^50 + 864 * q^53 + 24 * q^56 + 48 * q^58 + 256 * q^64 - 120 * q^65 - 140 * q^67 - 108 * q^70 - 552 * q^71 - 144 * q^74 + 258 * q^77 - 176 * q^79 - 60 * q^85 - 96 * q^86 + 372 * q^91 - 24 * q^92 - 528 * q^95 - 624 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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