LMFDB - Embedded newform 378.3.o.a.181.11

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			181.11
Character	$\chi$	$=$	378.181
Dual form			378.3.o.a.307.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-2.08306 + 1.20266i) q^{5} +(-3.20945 + 6.22089i) q^{7} -2.82843 q^{8} +3.40163i q^{10} +(6.79936 - 11.7768i) q^{11} +(-11.7604 + 6.78989i) q^{13} +(5.34958 + 8.32959i) q^{14} +(-2.00000 + 3.46410i) q^{16} +19.8181i q^{17} +34.4974i q^{19} +(4.16613 + 2.40532i) q^{20} +(-9.61574 - 16.6550i) q^{22} +(-4.33552 - 7.50935i) q^{23} +(-9.60723 + 16.6402i) q^{25} +19.2047i q^{26} +(13.9843 - 0.661961i) q^{28} +(-12.9761 + 22.4752i) q^{29} +(-21.6671 + 12.5095i) q^{31} +(2.82843 + 4.89898i) q^{32} +(24.2721 + 14.0135i) q^{34} +(-0.796113 - 16.8184i) q^{35} +39.6839 q^{37} +(42.2505 + 24.3933i) q^{38} +(5.89179 - 3.40163i) q^{40} +(41.8941 - 24.1876i) q^{41} +(13.1169 - 22.7192i) q^{43} -27.1974 q^{44} -12.2627 q^{46} +(14.5673 + 8.41045i) q^{47} +(-28.3989 - 39.9312i) q^{49} +(13.5867 + 23.5328i) q^{50} +(23.5209 + 13.5798i) q^{52} -35.6774 q^{53} +32.7092i q^{55} +(9.07769 - 17.5953i) q^{56} +(18.3509 + 31.7848i) q^{58} +(-63.9153 + 36.9015i) q^{59} +(-78.5405 - 45.3454i) q^{61} +35.3823i q^{62} +8.00000 q^{64} +(16.3318 - 28.2875i) q^{65} +(-10.3681 - 17.9581i) q^{67} +(34.3259 - 19.8181i) q^{68} +(-21.1612 - 10.9174i) q^{70} +38.1972 q^{71} -12.0702i q^{73} +(28.0607 - 48.6026i) q^{74} +(59.7512 - 34.4974i) q^{76} +(51.4402 + 80.0951i) q^{77} +(-65.4244 + 113.318i) q^{79} -9.62126i q^{80} -68.4128i q^{82} +(27.6580 + 15.9683i) q^{83} +(-23.8343 - 41.2823i) q^{85} +(-18.5501 - 32.1298i) q^{86} +(-19.2315 + 33.3099i) q^{88} -118.790i q^{89} +(-4.49464 - 94.9521i) q^{91} +(-8.67105 + 15.0187i) q^{92} +(20.6013 - 11.8942i) q^{94} +(-41.4885 - 71.8602i) q^{95} +(99.4807 + 57.4352i) q^{97} +(-68.9866 + 6.54575i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	−0.693627	−	0.720334i	$-0.743988\pi$
$5$	−2.08306	+	1.20266i	−0.416613	+	0.240532i	0.277014	+	0.960866i	$0.410655\pi$
$6$		0			0
$7$	−3.20945	+	6.22089i	−0.458493	+	0.888698i
$7$	−3.20945	+	6.22089i	−0.458493	+	0.888698i
$8$	−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	−0.878705	−	0.477364i	$-0.841592\pi$
$13$	−11.7604	+	6.78989i	−0.904648	+	0.522299i	−0.0259430	+	0.999663i	$0.508259\pi$
$14$	5.34958	+	8.32959i	0.382113	+	0.594970i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$			19.8181i			1.16577i	0.812555	+	0.582884i	$0.198076\pi$
$17$			19.8181i			1.16577i	−0.812555	+	0.582884i	$0.801924\pi$
$18$		0			0
$19$			34.4974i			1.81565i	0.419348	+	0.907826i	$0.362259\pi$
$19$			34.4974i			1.81565i	−0.419348	+	0.907826i	$0.637741\pi$
$20$	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	−0.806952	−	0.590617i	$-0.798885\pi$
$31$	−21.6671	+	12.5095i	−0.698939	+	0.403533i	0.108013	+	0.994149i	$0.465551\pi$
$32$	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	0.107180	−	0.994240i	$-0.465818\pi$
$41$	41.8941	−	24.1876i	1.02181	−	0.589941i	0.914627	+	0.404299i	$0.132484\pi$
$42$		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	0.646901	−	0.762574i	$-0.276065\pi$
$47$	14.5673	+	8.41045i	0.309943	+	0.178946i	−0.336958	+	0.941520i	$0.609398\pi$
$48$		0			0
$49$	−28.3989	−	39.9312i	−0.579569	−	0.814923i
$50$	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
$56$	9.07769	−	17.5953i	0.162102	−	0.314202i
$57$		0			0
$58$	18.3509	+	31.7848i	0.316396	+	0.548013i
$59$	−63.9153	+	36.9015i	−1.08331	+	0.625449i	−0.931787	−	0.363005i	$-0.881751\pi$
$59$	−63.9153	+	36.9015i	−1.08331	+	0.625449i	−0.151522	+	0.988454i	$0.548418\pi$
$60$		0			0
$61$	−78.5405	−	45.3454i	−1.28755	−	0.743367i	−0.309332	−	0.950954i	$-0.600106\pi$
$61$	−78.5405	−	45.3454i	−1.28755	−	0.743367i	−0.978217	+	0.207587i	$0.933439\pi$
$62$			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
$70$	−21.1612	−	10.9174i	−0.302302	−	0.155962i
$71$	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	$-0.973654\pi$
$73$		−	12.0702i		−	0.165345i	0.996577	−	0.0826726i	$-0.0263456\pi$
$74$	28.0607	−	48.6026i	0.379199	−	0.656792i
$75$		0			0
$76$	59.7512	−	34.4974i	0.786200	−	0.453913i
$77$	51.4402	+	80.0951i	0.668054	+	1.04020i
$78$		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	0.657274	−	0.753652i	$-0.271710\pi$
$83$	27.6580	+	15.9683i	0.333229	+	0.192390i	−0.324045	+	0.946042i	$0.605043\pi$
$84$		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	$-0.767425\pi$
$89$		−	118.790i		−	1.33472i	0.744737	−	0.667358i	$-0.232575\pi$
$90$		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	0.915714	−	0.401831i	$-0.131626\pi$
$97$	99.4807	+	57.4352i	1.02557	+	0.592116i	0.109861	+	0.993947i	$0.464960\pi$
$98$	−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	−0.482027	−	0.876156i	$-0.660099\pi$
$101$	−149.663	−	86.4081i	−1.48181	−	0.855526i	−0.999787	+	0.0206305i	$0.993433\pi$
$102$		0			0
$103$	−40.4444	+	23.3506i	−0.392664	+	0.226705i	−0.683314	−	0.730125i	$-0.739462\pi$
$103$	−40.4444	+	23.3506i	−0.392664	+	0.226705i	0.290650	+	0.956830i	$0.406129\pi$
$104$	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
$112$	−15.1309	−	23.5596i	−0.135097	−	0.210354i
$113$	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
$119$	−123.286	−	63.6050i	−1.03602	−	0.534496i
$120$		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	−0.750971	−	0.660335i	$-0.770414\pi$
$131$	−72.6514	+	41.9453i	−0.554591	+	0.320193i	0.196381	+	0.980528i	$0.437081\pi$
$132$		0			0
$133$	−214.604	−	110.718i	−1.61357	−	0.832462i
$134$	−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	0.0353192	−	0.999376i	$-0.488755\pi$
$139$	127.666	−	73.7083i	0.918464	−	0.530275i	0.883145	+	0.469101i	$0.155422\pi$
$140$	−28.3342	+	18.1973i	−0.202387	+	0.129981i
$141$		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	−0.477601	−	0.878577i	$-0.658494\pi$
$157$	6.98156	−	4.03081i	0.0444685	−	0.0256739i	0.522069	+	0.852903i	$0.325160\pi$
$158$	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	0.0960758	−	0.995374i	$-0.469371\pi$
$167$	168.024	−	97.0088i	1.00613	−	0.580891i	0.910057	+	0.414483i	$0.136038\pi$
$168$		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	0.299520	−	0.954090i	$-0.403173\pi$
$173$	−65.2186	−	37.6540i	−0.376986	−	0.217653i	−0.676506	+	0.736437i	$0.736507\pi$
$174$		0			0
$175$	−72.6830	−	113.171i	−0.415331	−	0.646694i
$176$	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	$0.0737769\pi$
$181$			83.1541i			0.459415i	−0.973260	+	0.229707i	$0.926223\pi$
$182$	−119.470	−	61.6365i	−0.656430	−	0.338662i
$183$		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
$196$	−40.7640	+	89.1195i	−0.207980	+	0.454692i
$197$	−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	$-0.988355\pi$
$199$		−	14.5566i		−	0.0731488i	0.999331	−	0.0365744i	$-0.0116446\pi$
$200$	27.1733	−	47.0656i	0.135867	−	0.235328i
$201$		0			0
$202$	−211.656	+	122.200i	−1.04780	+	0.604948i
$203$	−98.1698	−	152.856i	−0.483595	−	0.752984i
$204$		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	0.970114	−	0.242648i	$-0.0780161\pi$
$223$	277.642	+	160.297i	1.24503	+	0.718820i	0.274918	+	0.961468i	$0.411349\pi$
$224$	−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	0.928218	−	0.372037i	$-0.121341\pi$
$227$	242.920	+	140.250i	1.07013	+	0.617841i	0.141915	+	0.989879i	$0.454674\pi$
$228$		0			0
$229$	31.1962	−	18.0111i	0.136228	−	0.0786512i	−0.430337	−	0.902668i	$-0.641605\pi$
$229$	31.1962	−	18.0111i	0.136228	−	0.0786512i	0.566565	+	0.824017i	$0.308272\pi$
$230$	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
$238$	−165.076	+	106.018i	−0.693598	+	0.445455i
$239$	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	−0.0535868	−	0.998563i	$-0.517065\pi$
$241$	−227.784	−	131.511i	−0.945161	−	0.545689i	−0.891574	+	0.452874i	$0.850399\pi$
$242$	−90.4035			−0.373568
$243$		0			0
$244$			181.381i			0.743367i
$245$	107.180	+	49.0252i	0.437471	+	0.200103i
$246$		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	$0.161565\pi$
$251$			244.001i			0.972115i	−0.873927	+	0.486058i	$0.838435\pi$
$252$		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	−0.0946307	−	0.995512i	$-0.530167\pi$
$257$	185.090	−	106.862i	0.720193	−	0.415804i	0.814824	+	0.579709i	$0.196834\pi$
$258$		0			0
$259$	−127.363	+	246.869i	−0.491750	+	0.953162i
$260$	−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
$266$	−287.349	+	184.546i	−1.08026	+	0.693783i
$267$		0			0
$268$	−20.7362	+	35.9161i	−0.0773739	+	0.134015i
$269$		−	128.394i		−	0.477302i	−0.971105	−	0.238651i	$-0.923295\pi$
$269$		−	128.394i		−	0.477302i	0.971105	−	0.238651i	$-0.0767052\pi$
$270$		0			0
$271$			520.915i			1.92219i	0.276210	+	0.961097i	$0.410921\pi$
$271$			520.915i			1.92219i	−0.276210	+	0.961097i	$0.589079\pi$
$272$	−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	−0.644575	−	0.764541i	$-0.722966\pi$
$283$	−86.2442	+	49.7931i	−0.304750	+	0.175947i	0.339825	+	0.940489i	$0.389632\pi$
$284$	−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	$-0.242286\pi$
$293$	493.237	−	284.771i	1.68340	−	0.971914i	0.959371	−	0.282149i	$-0.0910472\pi$
$294$		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
$301$	99.2354	+	154.515i	0.329686	+	0.513339i
$302$	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	$0.125484\pi$
$307$			235.830i			0.768176i	−0.923296	+	0.384088i	$0.874516\pi$
$308$	87.2887	−	169.192i	0.283405	−	0.549325i
$309$		0			0
$310$	−42.5527	−	73.7035i	−0.137267	−	0.237753i
$311$	−525.110	+	303.172i	−1.68846	+	0.974831i	−0.732756	+	0.680492i	$0.761766\pi$
$311$	−525.110	+	303.172i	−1.68846	+	0.974831i	−0.955701	+	0.294339i	$0.904900\pi$
$312$		0			0
$313$	21.4543	+	12.3867i	0.0685442	+	0.0395740i	0.533880	−	0.845560i	$-0.320733\pi$
$313$	21.4543	+	12.3867i	0.0685442	+	0.0395740i	−0.465336	+	0.885134i	$0.654067\pi$
$314$		−	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
$322$	39.3565	−	76.2850i	0.122225	−	0.236910i
$323$	−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
$329$	−99.0736	+	63.6288i	−0.301135	+	0.193401i
$330$		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	0.740692	−	0.671845i	$-0.234498\pi$
$349$	184.692	+	106.632i	0.529203	+	0.305535i	−0.211489	+	0.977380i	$0.567831\pi$
$350$	−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	−0.413210	−	0.910636i	$-0.635592\pi$
$353$	−497.182	−	287.048i	−1.40845	−	0.813168i	−0.995239	+	0.0974679i	$0.968926\pi$
$354$		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
$364$	−159.967	+	102.737i	−0.439470	+	0.282245i
$365$	14.5163	+	25.1430i	0.0397708	+	0.0688850i
$366$		0			0
$367$	−12.0980	−	6.98480i	−0.0329646	−	0.0190321i	0.483427	−	0.875385i	$-0.339392\pi$
$367$	−12.0980	−	6.98480i	−0.0329646	−	0.0190321i	−0.516392	+	0.856352i	$0.672725\pi$
$368$	34.6842			0.0942505
$369$		0			0
$370$			134.990i			0.364837i
$371$	114.505	−	221.945i	0.308638	−	0.598235i
$372$		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	−0.981331	−	0.192329i	$-0.938396\pi$
$383$	−499.981	+	288.664i	−1.30543	+	0.753693i	−0.324104	+	0.946022i	$0.605063\pi$
$384$		0			0
$385$	−203.480	−	104.978i	−0.528520	−	0.272671i
$386$	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
$392$	80.3242	+	112.943i	0.204909	+	0.288119i
$393$		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	$0.114383\pi$
$397$			279.218i			0.703321i	−0.936128	+	0.351661i	$0.885617\pi$
$398$	−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	−0.784755	−	0.619806i	$-0.787211\pi$
$409$	−261.910	+	151.214i	−0.640366	+	0.369715i	0.144390	+	0.989521i	$0.453878\pi$
$410$	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	0.123634	−	0.992328i	$-0.460545\pi$
$419$	437.785	−	252.755i	1.04483	−	0.603234i	0.921198	+	0.389093i	$0.127212\pi$
$420$		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
$427$	534.160	−	343.058i	1.25096	−	0.803414i
$428$	−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	$-0.591812\pi$
$433$		−	830.225i		−	1.91738i	0.284454	−	0.958690i	$-0.408188\pi$
$434$	−220.109	−	113.558i	−0.507164	−	0.261653i
$435$		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	0.703579	−	0.710617i	$-0.251584\pi$
$439$	193.141	+	111.510i	0.439956	+	0.254009i	−0.263623	+	0.964626i	$0.584917\pi$
$440$		−	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
$448$	−25.6756	+	49.7671i	−0.0573116	+	0.111087i
$449$	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
$455$	123.557	+	192.386i	0.271555	+	0.422826i
$456$		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	0.408249	−	0.912871i	$-0.366140\pi$
$461$	−82.1484	−	47.4284i	−0.178196	−	0.102882i	−0.586445	+	0.809989i	$0.699473\pi$
$462$		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	$0.0463731\pi$
$467$			135.589i			0.290341i	−0.989407	+	0.145170i	$0.953627\pi$
$468$		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	0.304819	−	0.952410i	$-0.401404\pi$
$479$	−176.072	−	101.655i	−0.367583	−	0.212224i	−0.672402	+	0.740186i	$0.734737\pi$
$480$		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
$490$	135.831	−	96.6025i	0.277207	−	0.197148i
$491$	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
$497$	−122.592	+	237.621i	−0.246664	+	0.478110i
$498$		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	$-0.750075\pi$
$503$		−	711.182i		−	1.41388i	0.707273	−	0.706941i	$-0.249925\pi$
$504$		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	−0.875174	−	0.483808i	$-0.839253\pi$
$509$	−454.930	+	262.654i	−0.893772	+	0.516019i	−0.0185973	+	0.999827i	$0.505920\pi$
$510$		0			0
$511$	75.0874	+	38.7387i	0.146942	+	0.0758096i
$512$	−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
$518$	212.292	+	330.550i	0.409830	+	0.638128i
$519$		0			0
$520$	−46.1934	+	80.0092i	−0.0888334	+	0.153864i
$521$		−	58.8034i		−	0.112866i	−0.998406	−	0.0564332i	$-0.982027\pi$
$521$		−	58.8034i		−	0.112866i	0.998406	−	0.0564332i	$-0.0179728\pi$
$522$		0			0
$523$		−	49.8806i		−	0.0953740i	−0.998862	−	0.0476870i	$-0.984815\pi$
$523$		−	49.8806i		−	0.0953740i	0.998862	−	0.0476870i	$-0.0151850\pi$
$524$	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
$553$	−494.964	−	770.687i	−0.895053	−	1.39365i
$554$	−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
$560$	59.8528	+	30.8789i	0.106880	+	0.0551410i
$561$		0			0
$562$	−64.3178	−	111.402i	−0.114444	−	0.198224i
$563$	565.382	−	326.423i	1.00423	−	0.579793i	0.0947335	−	0.995503i	$-0.469800\pi$
$563$	565.382	−	326.423i	1.00423	−	0.579793i	0.909497	+	0.415710i	$0.136467\pi$
$564$		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
$574$	425.588	+	219.567i	0.741443	+	0.382521i
$575$	166.609			0.289756
$576$		0			0
$577$			695.947i			1.20615i	0.797686	+	0.603073i	$0.206057\pi$
$577$			695.947i			1.20615i	−0.797686	+	0.603073i	$0.793943\pi$
$578$	−73.3662	+	127.074i	−0.126931	+	0.219851i
$579$		0			0
$580$	−108.120	+	62.4231i	−0.186414	+	0.107626i
$581$	−188.104	+	120.808i	−0.323759	+	0.207930i
$582$		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	0.538090	−	0.842887i	$-0.319146\pi$
$587$	45.3007	+	26.1544i	0.0771732	+	0.0445560i	−0.460917	+	0.887443i	$0.652479\pi$
$588$		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	$0.00587072\pi$
$593$			21.8727i			0.0368848i	−0.999830	+	0.0184424i	$0.994129\pi$
$594$		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	0.471271	−	0.881988i	$-0.343795\pi$
$601$	−34.2071	−	19.7495i	−0.0569170	−	0.0328611i	−0.528188	+	0.849127i	$0.677129\pi$
$602$	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	−0.742406	−	0.669950i	$-0.766315\pi$
$607$	−323.783	+	186.936i	−0.533415	+	0.307968i	0.208991	+	0.977918i	$0.432982\pi$
$608$	−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
$616$	−145.495	−	226.543i	−0.236193	−	0.367765i
$617$	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	0.940998	−	0.338411i	$-0.109890\pi$
$619$	692.305	+	399.702i	1.11842	+	0.645723i	0.177426	+	0.984134i	$0.443223\pi$
$620$	−120.357			−0.194125
$621$		0			0
$622$			857.501i			1.37862i
$623$	738.977	+	381.249i	1.18616	+	0.611957i
$624$		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
$637$	605.112	+	276.783i	0.949940	+	0.434510i
$638$	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	−0.893719	−	0.448626i	$-0.851913\pi$
$643$	−612.173	+	353.438i	−0.952057	+	0.549671i	−0.0583379	+	0.998297i	$0.518580\pi$
$644$	−65.6003	−	102.143i	−0.101864	−	0.158608i
$645$		0			0
$646$	−483.428	+	837.322i	−0.748341	+	1.29616i
$647$			422.816i			0.653502i	0.945110	+	0.326751i	$0.105954\pi$
$647$			422.816i			0.653502i	−0.945110	+	0.326751i	$0.894046\pi$
$648$		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	−0.652862	−	0.757477i	$-0.726432\pi$
$661$	−213.700	+	123.380i	−0.323298	+	0.186656i	0.329563	+	0.944133i	$0.393098\pi$
$662$	−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	0.803918	−	0.594740i	$-0.202745\pi$
$677$	467.683	+	270.017i	0.690817	+	0.398843i	−0.113101	+	0.993583i	$0.536078\pi$
$678$		0			0
$679$	−676.576	+	434.523i	−0.996430	+	0.639945i
$680$	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
$686$	180.689	−	450.166i	0.263394	−	0.656219i
$687$		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	−0.211080	−	0.977469i	$-0.567698\pi$
$691$	−803.725	−	464.031i	−1.16313	−	0.671535i	−0.952053	+	0.305933i	$0.901032\pi$
$692$			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
$700$	−123.336	+	239.062i	−0.176194	+	0.341517i
$701$	−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
$707$	1017.87	−	653.716i	1.43971	−	0.924634i
$708$		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	$-0.994801\pi$
$719$		−	23.4875i		−	0.0326669i	0.999867	−	0.0163335i	$-0.00519934\pi$
$720$		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	−0.0247971	−	0.999693i	$-0.507894\pi$
$727$	−656.448	−	379.000i	−0.902955	−	0.521321i	−0.878158	+	0.478371i	$0.841227\pi$
$728$	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	−0.171870	−	0.985120i	$-0.554981\pi$
$733$	436.380	−	251.944i	0.595334	−	0.343716i	0.767204	+	0.641404i	$0.221648\pi$
$734$	−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
$742$	−190.859	−	297.178i	−0.257223	−	0.400510i
$743$	−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
$749$	−223.084	+	432.404i	−0.297842	+	0.577308i
$750$		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	−0.703656	−	0.710541i	$-0.748450\pi$
$761$	−334.945	+	193.380i	−0.440137	+	0.254113i	0.263519	+	0.964654i	$0.415117\pi$
$762$		0			0
$763$	−436.121	+	845.336i	−0.571588	+	1.10791i
$764$	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	−0.112759	−	0.993622i	$-0.535969\pi$
$769$	531.659	−	306.953i	0.691364	−	0.399159i	0.804123	+	0.594463i	$0.202635\pi$
$770$	−272.454	+	174.980i	−0.353836	+	0.227247i
$771$		0			0
$772$	115.217	−	199.561i	0.149245	−	0.258499i
$773$			244.996i			0.316942i	0.987364	+	0.158471i	$0.0506564\pi$
$773$			244.996i			0.316942i	−0.987364	+	0.158471i	$0.949344\pi$
$774$		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	$-0.311260\pi$
$787$	1224.89	−	707.189i	1.55640	−	0.898589i	0.997597	−	0.0692898i	$-0.0220733\pi$
$788$	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	−0.506324	−	0.862343i	$-0.668996\pi$
$797$	−10.1025	+	5.83266i	−0.0126756	+	0.00731827i	0.493649	+	0.869661i	$0.335663\pi$
$798$		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
$805$	−122.843	+	78.8947i	−0.152601	+	0.0980059i
$806$	−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	$-0.624696\pi$
$811$		−	1499.13i		−	1.84849i	0.381800	−	0.924245i	$-0.375304\pi$
$812$	−166.584	+	322.891i	−0.205153	+	0.397649i
$813$		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
$826$	−649.294	−	334.980i	−0.786070	−	0.405545i
$827$	−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	$0.108674\pi$
$829$			555.123i			0.669629i	−0.942284	+	0.334815i	$0.891326\pi$
$830$	−54.3184	+	94.0822i	−0.0654438	+	0.113352i
$831$		0			0
$832$	−94.0834	+	54.3191i	−0.113081	+	0.0652874i
$833$	791.359	−	562.811i	0.950011	−	0.675643i
$834$		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	−0.193117	−	0.981176i	$-0.561860\pi$
$839$	−955.955	−	551.921i	−1.13940	−	0.657832i	−0.946281	+	0.323344i	$0.895193\pi$
$840$		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	0.522479	−	0.852652i	$-0.325007\pi$
$853$	38.6408	+	22.3093i	0.0452999	+	0.0261539i	−0.477179	+	0.878806i	$0.658341\pi$
$854$	−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	0.841530	−	0.540211i	$-0.181656\pi$
$857$	680.850	+	393.089i	0.794458	+	0.458680i	−0.0470717	+	0.998892i	$0.514989\pi$
$858$		0			0
$859$	286.832	−	165.602i	0.333914	−	0.192785i	−0.323664	−	0.946172i	$-0.604915\pi$
$859$	286.832	−	165.602i	0.333914	−	0.192785i	0.657577	+	0.753387i	$0.271581\pi$
$860$	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
$868$	−294.720	+	189.280i	−0.339539	+	0.218065i
$869$	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
$875$	661.590	+	341.324i	0.756102	+	0.390084i
$876$		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	$0.289116\pi$
$881$			1389.25i			1.57690i	−0.615098	+	0.788450i	$0.710884\pi$
$882$		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	0.108770	−	0.994067i	$-0.465309\pi$
$887$	908.326	−	524.422i	1.02404	−	0.591231i	0.915272	+	0.402836i	$0.131975\pi$
$888$		0			0
$889$	−38.6067	+	74.8315i	−0.0434271	+	0.0841749i
$890$	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
$896$	42.7966	+	66.6367i	0.0477641	+	0.0743713i
$897$		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	0.586123	−	0.810222i	$-0.300653\pi$
$929$	164.909	+	95.2100i	0.177512	+	0.102487i	−0.408611	+	0.912709i	$0.633987\pi$
$930$		0			0
$931$	1377.52	−	979.687i	1.47962	−	1.05230i
$932$	−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	$-0.970534\pi$
$937$		−	173.230i		−	0.184877i	0.995718	−	0.0924384i	$-0.0294661\pi$
$938$	94.1184	−	182.430i	0.100339	−	0.194488i
$939$		0			0
$940$	40.4596	+	70.0780i	0.0430421	+	0.0745511i
$941$	−1132.98	+	654.124i	−1.20401	+	0.695137i	−0.961445	−	0.274997i	$-0.911323\pi$
$941$	−1132.98	+	654.124i	−1.20401	+	0.695137i	−0.242568	+	0.970134i	$0.577990\pi$
$942$		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
$952$	348.705	+	179.902i	0.366287	+	0.188973i
$953$	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
$959$	−756.313	−	1177.62i	−0.788647	−	1.22797i
$960$		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	$-0.825695\pi$
$971$		−	1011.08i		−	1.04127i	0.853778	−	0.520637i	$-0.174305\pi$
$972$		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	0.599725	−	0.800206i	$-0.295276\pi$
$983$	203.077	+	117.247i	0.206589	+	0.119274i	−0.393136	+	0.919480i	$0.628610\pi$
$984$		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
$994$	204.339	+	318.167i	0.205572	+	0.320088i
$995$	17.5066	+	30.3223i	0.0175946	+	0.0304747i
$996$		0			0
$997$	763.810	+	440.986i	0.766108	+	0.442313i	0.831484	−	0.555548i	$-0.187491\pi$
$997$	763.810	+	440.986i	0.766108	+	0.442313i	−0.0653764	+	0.997861i	$0.520825\pi$
$998$	−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.181.11		32
3.2	odd	2		126.3.o.a.97.2	yes	32
7.6	odd	2	inner	378.3.o.a.181.14		32
9.2	odd	6		1134.3.c.e.811.14		16
9.4	even	3	inner	378.3.o.a.307.14		32
9.5	odd	6		126.3.o.a.13.7	yes	32
9.7	even	3		1134.3.c.d.811.3		16
21.20	even	2		126.3.o.a.97.7	yes	32
63.13	odd	6	inner	378.3.o.a.307.11		32
63.20	even	6		1134.3.c.e.811.11		16
63.34	odd	6		1134.3.c.d.811.6		16
63.41	even	6		126.3.o.a.13.2	✓	32

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

\(f(q)\)	\(=\)	\(q+(0.707107 - 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(-2.08306 + 1.20266i) q^{5} +(-3.20945 + 6.22089i) q^{7} -2.82843 q^{8} +3.40163i q^{10} +(6.79936 - 11.7768i) q^{11} +(-11.7604 + 6.78989i) q^{13} +(5.34958 + 8.32959i) q^{14} +(-2.00000 + 3.46410i) q^{16} +19.8181i q^{17} +34.4974i q^{19} +(4.16613 + 2.40532i) q^{20} +(-9.61574 - 16.6550i) q^{22} +(-4.33552 - 7.50935i) q^{23} +(-9.60723 + 16.6402i) q^{25} +19.2047i q^{26} +(13.9843 - 0.661961i) q^{28} +(-12.9761 + 22.4752i) q^{29} +(-21.6671 + 12.5095i) q^{31} +(2.82843 + 4.89898i) q^{32} +(24.2721 + 14.0135i) q^{34} +(-0.796113 - 16.8184i) q^{35} +39.6839 q^{37} +(42.2505 + 24.3933i) q^{38} +(5.89179 - 3.40163i) q^{40} +(41.8941 - 24.1876i) q^{41} +(13.1169 - 22.7192i) q^{43} -27.1974 q^{44} -12.2627 q^{46} +(14.5673 + 8.41045i) q^{47} +(-28.3989 - 39.9312i) q^{49} +(13.5867 + 23.5328i) q^{50} +(23.5209 + 13.5798i) q^{52} -35.6774 q^{53} +32.7092i q^{55} +(9.07769 - 17.5953i) q^{56} +(18.3509 + 31.7848i) q^{58} +(-63.9153 + 36.9015i) q^{59} +(-78.5405 - 45.3454i) q^{61} +35.3823i q^{62} +8.00000 q^{64} +(16.3318 - 28.2875i) q^{65} +(-10.3681 - 17.9581i) q^{67} +(34.3259 - 19.8181i) q^{68} +(-21.1612 - 10.9174i) q^{70} +38.1972 q^{71} -12.0702i q^{73} +(28.0607 - 48.6026i) q^{74} +(59.7512 - 34.4974i) q^{76} +(51.4402 + 80.0951i) q^{77} +(-65.4244 + 113.318i) q^{79} -9.62126i q^{80} -68.4128i q^{82} +(27.6580 + 15.9683i) q^{83} +(-23.8343 - 41.2823i) q^{85} +(-18.5501 - 32.1298i) q^{86} +(-19.2315 + 33.3099i) q^{88} -118.790i q^{89} +(-4.49464 - 94.9521i) q^{91} +(-8.67105 + 15.0187i) q^{92} +(20.6013 - 11.8942i) q^{94} +(-41.4885 - 71.8602i) q^{95} +(99.4807 + 57.4352i) q^{97} +(-68.9866 + 6.54575i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} - 2 q^{7} + 12 q^{11} + 12 q^{14} - 64 q^{16} - 12 q^{23} + 80 q^{25} + 8 q^{28} + 48 q^{29} - 348 q^{35} - 88 q^{37} + 32 q^{43} - 48 q^{44} + 48 q^{46} + 50 q^{49} - 48 q^{50} + 864 q^{53}+ \cdots - 624 q^{98}+O(q^{100}) \) 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

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Representations

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Database

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