LMFDB - Embedded newform 216.4.q.a.49.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,4,Mod(25,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 10]))

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

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

chi := DirichletCharacter("216.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	216.q (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$12.7444125612$
Analytic rank:	$0$
Dimension:	$78$
Relative dimension:	$13$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			49.2
Character	$\chi$	$=$	216.49
Dual form			216.4.q.a.97.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.98381 + 1.47026i) q^{3} +(-5.94819 + 2.16496i) q^{5} +(5.30186 + 30.0684i) q^{7} +(22.6767 - 14.6550i) q^{9} +O(q^{10})$	\(q+(-4.98381 + 1.47026i) q^{3} +(-5.94819 + 2.16496i) q^{5} +(5.30186 + 30.0684i) q^{7} +(22.6767 - 14.6550i) q^{9} +(35.9740 + 13.0935i) q^{11} +(-39.8879 - 33.4700i) q^{13} +(26.4616 - 19.5352i) q^{15} +(-49.3543 + 85.4842i) q^{17} +(-70.7605 - 122.561i) q^{19} +(-70.6318 - 142.060i) q^{21} +(14.3133 - 81.1748i) q^{23} +(-65.0616 + 54.5932i) q^{25} +(-91.4695 + 106.378i) q^{27} +(-181.676 + 152.444i) q^{29} +(14.1800 - 80.4185i) q^{31} +(-198.538 - 12.3641i) q^{33} +(-96.6334 - 167.374i) q^{35} +(215.386 - 373.060i) q^{37} +(248.003 + 108.162i) q^{39} +(-370.779 - 311.121i) q^{41} +(219.192 + 79.7795i) q^{43} +(-103.158 + 136.265i) q^{45} +(4.86872 + 27.6119i) q^{47} +(-553.681 + 201.524i) q^{49} +(120.288 - 498.600i) q^{51} +124.874 q^{53} -242.327 q^{55} +(532.853 + 506.783i) q^{57} +(-199.436 + 72.5888i) q^{59} +(-130.212 - 738.470i) q^{61} +(560.880 + 604.151i) q^{63} +(309.722 + 112.730i) q^{65} +(112.474 + 94.3771i) q^{67} +(48.0134 + 425.604i) q^{69} +(-350.941 + 607.847i) q^{71} +(107.438 + 186.088i) q^{73} +(243.988 - 367.740i) q^{75} +(-202.970 + 1151.10i) q^{77} +(-311.546 + 261.418i) q^{79} +(299.462 - 664.653i) q^{81} +(-161.884 + 135.837i) q^{83} +(108.499 - 615.327i) q^{85} +(681.305 - 1026.86i) q^{87} +(370.390 + 641.534i) q^{89} +(794.906 - 1376.82i) q^{91} +(47.5661 + 421.639i) q^{93} +(686.236 + 575.821i) q^{95} +(-411.819 - 149.890i) q^{97} +(1007.65 - 230.282i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 33 q^{7} + 6 q^{9}+O(q^{10}) $ 78 * q + 33 * q^7 + 6 * q^9	$ 78 q + 33 q^{7} + 6 q^{9} + 51 q^{11} - 60 q^{13} - 183 q^{15} - 102 q^{17} + 171 q^{19} + 342 q^{21} + 456 q^{23} + 480 q^{25} + 189 q^{27} - 63 q^{29} + 621 q^{31} + 732 q^{33} + 630 q^{35} + 555 q^{37} + 597 q^{39} - 987 q^{41} + 552 q^{43} - 1311 q^{45} - 216 q^{47} - 1131 q^{49} - 288 q^{51} + 954 q^{53} - 54 q^{55} + 702 q^{57} + 1752 q^{59} - 654 q^{61} - 144 q^{63} + 126 q^{65} + 2277 q^{67} - 165 q^{69} + 684 q^{73} - 1167 q^{75} + 192 q^{77} - 2745 q^{79} - 3330 q^{81} - 3567 q^{83} - 3981 q^{85} - 108 q^{87} - 1314 q^{89} + 147 q^{91} - 2406 q^{93} + 1167 q^{95} + 2046 q^{97} - 5640 q^{99}+O(q^{100}) $ 78 * q + 33 * q^7 + 6 * q^9 + 51 * q^11 - 60 * q^13 - 183 * q^15 - 102 * q^17 + 171 * q^19 + 342 * q^21 + 456 * q^23 + 480 * q^25 + 189 * q^27 - 63 * q^29 + 621 * q^31 + 732 * q^33 + 630 * q^35 + 555 * q^37 + 597 * q^39 - 987 * q^41 + 552 * q^43 - 1311 * q^45 - 216 * q^47 - 1131 * q^49 - 288 * q^51 + 954 * q^53 - 54 * q^55 + 702 * q^57 + 1752 * q^59 - 654 * q^61 - 144 * q^63 + 126 * q^65 + 2277 * q^67 - 165 * q^69 + 684 * q^73 - 1167 * q^75 + 192 * q^77 - 2745 * q^79 - 3330 * q^81 - 3567 * q^83 - 3981 * q^85 - 108 * q^87 - 1314 * q^89 + 147 * q^91 - 2406 * q^93 + 1167 * q^95 + 2046 * q^97 - 5640 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.98381	+	1.47026i	−0.959134	+	0.282952i
$3$	−4.98381	+	1.47026i	−0.959134	+	0.282952i
$4$		0			0
$5$	−5.94819	+	2.16496i	−0.532022	+	0.193640i	−0.594041	−	0.804435i	$-0.702468\pi$
$5$	−5.94819	+	2.16496i	−0.532022	+	0.193640i	0.0620187	+	0.998075i	$0.480246\pi$
$6$		0			0
$7$	5.30186	+	30.0684i	0.286274	+	1.62354i	0.700700	+	0.713456i	$0.252871\pi$
$7$	5.30186	+	30.0684i	0.286274	+	1.62354i	−0.414427	+	0.910083i	$0.636018\pi$
$8$		0			0
$9$	22.6767	−	14.6550i	0.839877	−	0.542778i
$10$		0			0
$11$	35.9740	+	13.0935i	0.986051	+	0.358893i	0.784190	−	0.620521i	$-0.213079\pi$
$11$	35.9740	+	13.0935i	0.986051	+	0.358893i	0.201861	+	0.979414i	$0.435301\pi$
$12$		0			0
$13$	−39.8879	−	33.4700i	−0.850994	−	0.714069i	0.109014	−	0.994040i	$-0.465231\pi$
$13$	−39.8879	−	33.4700i	−0.850994	−	0.714069i	−0.960008	+	0.279971i	$0.909675\pi$
$14$		0			0
$15$	26.4616	−	19.5352i	0.455490	−	0.336264i
$16$		0			0
$17$	−49.3543	+	85.4842i	−0.704128	+	1.21959i	0.262877	+	0.964829i	$0.415329\pi$
$17$	−49.3543	+	85.4842i	−0.704128	+	1.21959i	−0.967005	+	0.254756i	$0.918005\pi$
$18$		0			0
$19$	−70.7605	−	122.561i	−0.854398	−	1.47986i	−0.877202	−	0.480121i	$-0.840593\pi$
$19$	−70.7605	−	122.561i	−0.854398	−	1.47986i	0.0228041	−	0.999740i	$-0.492741\pi$
$20$		0			0
$21$	−70.6318	−	142.060i	−0.733958	−	1.47619i
$22$		0			0
$23$	14.3133	−	81.1748i	0.129762	−	0.735918i	−0.848602	−	0.529031i	$-0.822556\pi$
$23$	14.3133	−	81.1748i	0.129762	−	0.735918i	0.978365	−	0.206887i	$-0.0663334\pi$
$24$		0			0
$25$	−65.0616	+	54.5932i	−0.520493	+	0.436746i
$26$		0			0
$27$	−91.4695	+	106.378i	−0.651974	+	0.758241i
$28$		0			0
$29$	−181.676	+	152.444i	−1.16332	+	0.976145i	−0.999946	−	0.0104190i	$-0.996683\pi$
$29$	−181.676	+	152.444i	−1.16332	+	0.976145i	−0.163378	+	0.986564i	$0.552239\pi$
$30$		0			0
$31$	14.1800	−	80.4185i	0.0821547	−	0.465922i	−0.915780	−	0.401681i	$-0.868426\pi$
$31$	14.1800	−	80.4185i	0.0821547	−	0.465922i	0.997934	−	0.0642415i	$-0.0204628\pi$
$32$		0			0
$33$	−198.538	−	12.3641i	−1.04730	−	0.0652218i
$34$		0			0
$35$	−96.6334	−	167.374i	−0.466686	−	0.808325i
$36$		0			0
$37$	215.386	−	373.060i	0.957007	−	1.65758i	0.227299	−	0.973825i	$-0.427010\pi$
$37$	215.386	−	373.060i	0.957007	−	1.65758i	0.729707	−	0.683759i	$-0.239656\pi$
$38$		0			0
$39$	248.003	+	108.162i	1.01826	+	0.444097i
$40$		0			0
$41$	−370.779	−	311.121i	−1.41234	−	1.18509i	−0.955296	−	0.295650i	$-0.904464\pi$
$41$	−370.779	−	311.121i	−1.41234	−	1.18509i	−0.457044	−	0.889444i	$-0.651092\pi$
$42$		0			0
$43$	219.192	+	79.7795i	0.777361	+	0.282936i	0.700072	−	0.714073i	$-0.253151\pi$
$43$	219.192	+	79.7795i	0.777361	+	0.282936i	0.0772890	+	0.997009i	$0.475374\pi$
$44$		0			0
$45$	−103.158	+	136.265i	−0.341730	+	0.451404i
$46$		0			0
$47$	4.86872	+	27.6119i	0.0151101	+	0.0856938i	0.991430	−	0.130637i	$-0.0417022\pi$
$47$	4.86872	+	27.6119i	0.0151101	+	0.0856938i	−0.976320	+	0.216331i	$0.930591\pi$
$48$		0			0
$49$	−553.681	+	201.524i	−1.61423	+	0.587532i
$50$		0			0
$51$	120.288	−	498.600i	0.330269	−	1.36898i
$52$		0			0
$53$	124.874			0.323638			0.161819	−	0.986820i	$-0.448264\pi$
$53$	124.874			0.323638			0.161819	+	0.986820i	$0.448264\pi$
$54$		0			0
$55$	−242.327			−0.594097
$56$		0			0
$57$	532.853	+	506.783i	1.23821	+	1.17763i
$58$		0			0
$59$	−199.436	+	72.5888i	−0.440074	+	0.160174i	−0.552548	−	0.833481i	$-0.686345\pi$
$59$	−199.436	+	72.5888i	−0.440074	+	0.160174i	0.112475	+	0.993655i	$0.464122\pi$
$60$		0			0
$61$	−130.212	−	738.470i	−0.273311	−	1.55002i	−0.744277	−	0.667871i	$-0.767206\pi$
$61$	−130.212	−	738.470i	−0.273311	−	1.55002i	0.470966	−	0.882151i	$-0.343905\pi$
$62$		0			0
$63$	560.880	+	604.151i	1.12165	+	1.20819i
$64$		0			0
$65$	309.722	+	112.730i	0.591021	+	0.215114i
$66$		0			0
$67$	112.474	+	94.3771i	0.205088	+	0.172090i	0.739547	−	0.673105i	$-0.235040\pi$
$67$	112.474	+	94.3771i	0.205088	+	0.172090i	−0.534458	+	0.845195i	$0.679484\pi$
$68$		0			0
$69$	48.0134	+	425.604i	0.0837700	+	0.742561i
$70$		0			0
$71$	−350.941	+	607.847i	−0.586606	+	1.01603i	0.408068	+	0.912952i	$0.366203\pi$
$71$	−350.941	+	607.847i	−0.586606	+	1.01603i	−0.994673	+	0.103079i	$0.967131\pi$
$72$		0			0
$73$	107.438	+	186.088i	0.172255	+	0.298355i	0.939208	−	0.343349i	$-0.111561\pi$
$73$	107.438	+	186.088i	0.172255	+	0.298355i	−0.766953	+	0.641704i	$0.778228\pi$
$74$		0			0
$75$	243.988	−	367.740i	0.375645	−	0.566172i
$76$		0			0
$77$	−202.970	+	1151.10i	−0.300396	+	1.70363i
$78$		0			0
$79$	−311.546	+	261.418i	−0.443692	+	0.372301i	−0.837089	−	0.547067i	$-0.815744\pi$
$79$	−311.546	+	261.418i	−0.443692	+	0.372301i	0.393397	+	0.919369i	$0.371300\pi$
$80$		0			0
$81$	299.462	−	664.653i	0.410785	−	0.911732i
$82$		0			0
$83$	−161.884	+	135.837i	−0.214086	+	0.179639i	−0.743524	−	0.668709i	$-0.766847\pi$
$83$	−161.884	+	135.837i	−0.214086	+	0.179639i	0.529438	+	0.848348i	$0.322403\pi$
$84$		0			0
$85$	108.499	−	615.327i	0.138451	−	0.785195i
$86$		0			0
$87$	681.305	−	1026.86i	0.839582	−	1.26542i
$88$		0			0
$89$	370.390	+	641.534i	0.441138	+	0.764073i	0.997774	−	0.0666832i	$-0.0212417\pi$
$89$	370.390	+	641.534i	0.441138	+	0.764073i	−0.556636	+	0.830756i	$0.687908\pi$
$90$		0			0
$91$	794.906	−	1376.82i	0.915701	−	1.58604i
$92$		0			0
$93$	47.5661	+	421.639i	0.0530362	+	0.470128i
$94$		0			0
$95$	686.236	+	575.821i	0.741120	+	0.621873i
$96$		0			0
$97$	−411.819	−	149.890i	−0.431071	−	0.156897i	0.117366	−	0.993089i	$-0.462555\pi$
$97$	−411.819	−	149.890i	−0.431071	−	0.156897i	−0.548437	+	0.836192i	$0.684777\pi$
$98$		0			0
$99$	1007.65	−	230.282i	1.02296	−	0.233780i
$100$		0			0
$101$	−27.8678	−	158.046i	−0.0274549	−	0.155705i	0.967998	−	0.250957i	$-0.0807453\pi$
$101$	−27.8678	−	158.046i	−0.0274549	−	0.155705i	−0.995453	+	0.0952524i	$0.969634\pi$
$102$		0			0
$103$	557.460	−	202.899i	0.533283	−	0.194099i	−0.0613207	−	0.998118i	$-0.519531\pi$
$103$	557.460	−	202.899i	0.533283	−	0.194099i	0.594604	+	0.804019i	$0.297309\pi$
$104$		0			0
$105$	727.686	+	692.083i	0.676332	+	0.643242i
$106$		0			0
$107$	430.679			0.389115			0.194557	−	0.980891i	$-0.437673\pi$
$107$	430.679			0.389115			0.194557	+	0.980891i	$0.437673\pi$
$108$		0			0
$109$	−1416.53			−1.24476			−0.622379	−	0.782716i	$-0.713834\pi$
$109$	−1416.53			−1.24476			−0.622379	+	0.782716i	$0.713834\pi$
$110$		0			0
$111$	−524.948	+	2175.93i	−0.448881	+	1.86063i
$112$		0			0
$113$	−576.001	+	209.647i	−0.479519	+	0.174530i	−0.570459	−	0.821326i	$-0.693235\pi$
$113$	−576.001	+	209.647i	−0.479519	+	0.174530i	0.0909408	+	0.995856i	$0.471013\pi$
$114$		0			0
$115$	90.6023	+	513.831i	0.0734670	+	0.416652i
$116$		0			0
$117$	−1395.03	−	174.430i	−1.10231	−	0.137829i
$118$		0			0
$119$	−2832.04	−	1030.78i	−2.18162	−	0.794044i
$120$		0			0
$121$	103.083	+	86.4967i	0.0774476	+	0.0649862i
$122$		0			0
$123$	2305.32	+	1005.42i	1.68995	+	0.737040i
$124$		0			0
$125$	664.428	−	1150.82i	0.475426	−	0.823461i
$126$		0			0
$127$	365.572	+	633.189i	0.255427	+	0.442413i	0.965011	−	0.262208i	$-0.0844505\pi$
$127$	365.572	+	633.189i	0.255427	+	0.442413i	−0.709584	+	0.704621i	$0.751117\pi$
$128$		0			0
$129$	−1209.71	−	75.3356i	−0.825650	−	0.0514181i
$130$		0			0
$131$	−302.276	+	1714.29i	−0.201603	+	1.14335i	0.701093	+	0.713070i	$0.252696\pi$
$131$	−302.276	+	1714.29i	−0.201603	+	1.14335i	−0.902696	+	0.430278i	$0.858415\pi$
$132$		0			0
$133$	3310.04	−	2777.45i	2.15802	−	1.81079i
$134$		0			0
$135$	313.773	−	830.787i	0.200039	−	0.529650i
$136$		0			0
$137$	−1529.93	+	1283.76i	−0.954092	+	0.800578i	−0.979982	−	0.199087i	$-0.936202\pi$
$137$	−1529.93	+	1283.76i	−0.954092	+	0.800578i	0.0258900	+	0.999665i	$0.491758\pi$
$138$		0			0
$139$	−178.581	+	1012.78i	−0.108972	+	0.618009i	0.880588	+	0.473883i	$0.157148\pi$
$139$	−178.581	+	1012.78i	−0.108972	+	0.618009i	−0.989559	+	0.144126i	$0.953963\pi$
$140$		0			0
$141$	−64.8614	−	130.454i	−0.0387398	−	0.0779164i
$142$		0			0
$143$	−996.690	−	1726.32i	−0.582849	−	1.00952i
$144$		0			0
$145$	750.607	−	1300.09i	0.429893	−	0.744597i
$146$		0			0
$147$	2463.15	−	1818.41i	1.38202	−	1.02027i
$148$		0			0
$149$	1384.57	+	1161.79i	0.761263	+	0.638775i	0.938455	−	0.345401i	$-0.112257\pi$
$149$	1384.57	+	1161.79i	0.761263	+	0.638775i	−0.177193	+	0.984176i	$0.556702\pi$
$150$		0			0
$151$	628.902	+	228.902i	0.338936	+	0.123363i	0.505880	−	0.862604i	$-0.331168\pi$
$151$	628.902	+	228.902i	0.338936	+	0.123363i	−0.166944	+	0.985966i	$0.553390\pi$
$152$		0			0
$153$	133.579	+	2661.78i	0.0705830	+	1.40649i
$154$		0			0
$155$	89.7582	+	509.044i	0.0465132	+	0.263790i
$156$		0			0
$157$	−785.085	+	285.748i	−0.399087	+	0.145256i	−0.533763	−	0.845634i	$-0.679223\pi$
$157$	−785.085	+	285.748i	−0.399087	+	0.145256i	0.134677	+	0.990890i	$0.457000\pi$
$158$		0			0
$159$	−622.349	+	183.598i	−0.310412	+	0.0915739i
$160$		0			0
$161$	2516.68			1.23194
$162$		0			0
$163$	−3737.80			−1.79612			−0.898058	−	0.439876i	$-0.855022\pi$
$163$	−3737.80			−1.79612			−0.898058	+	0.439876i	$0.855022\pi$
$164$		0			0
$165$	1207.71	−	356.284i	0.569819	−	0.168101i
$166$		0			0
$167$	−1016.64	+	370.028i	−0.471079	+	0.171459i	−0.566641	−	0.823965i	$-0.691757\pi$
$167$	−1016.64	+	370.028i	−0.471079	+	0.171459i	0.0955620	+	0.995423i	$0.469535\pi$
$168$		0			0
$169$	89.3048	+	506.473i	0.0406485	+	0.230529i
$170$		0			0
$171$	−3400.74	−	1742.27i	−1.52082	−	0.779152i
$172$		0			0
$173$	−1378.82	−	501.848i	−0.605951	−	0.220548i	0.0207796	−	0.999784i	$-0.493385\pi$
$173$	−1378.82	−	501.848i	−0.605951	−	0.220548i	−0.626731	+	0.779236i	$0.715607\pi$
$174$		0			0
$175$	−1986.48	−	1666.85i	−0.858077	−	0.720012i
$176$		0			0
$177$	887.226	−	654.991i	0.376768	−	0.278148i
$178$		0			0
$179$	533.697	−	924.390i	0.222851	−	0.385990i	−0.732821	−	0.680421i	$-0.761797\pi$
$179$	533.697	−	924.390i	0.222851	−	0.385990i	0.955673	+	0.294431i	$0.0951302\pi$
$180$		0			0
$181$	−1223.35	−	2118.90i	−0.502380	−	0.870149i	−0.999996	−	0.00275094i	$-0.999124\pi$
$181$	−1223.35	−	2118.90i	−0.502380	−	0.870149i	0.497616	−	0.867398i	$-0.334209\pi$
$182$		0			0
$183$	1734.70	+	3488.94i	0.700723	+	1.40935i
$184$		0			0
$185$	−473.497	+	2685.33i	−0.188174	+	1.06719i
$186$		0			0
$187$	−2894.75	+	2428.99i	−1.13201	+	0.949867i
$188$		0			0
$189$	−3683.58	−	2186.33i	−1.41768	−	0.841441i
$190$		0			0
$191$	2526.33	−	2119.84i	0.957061	−	0.803069i	−0.0234116	−	0.999726i	$-0.507453\pi$
$191$	2526.33	−	2119.84i	0.957061	−	0.803069i	0.980472	+	0.196657i	$0.0630084\pi$
$192$		0			0
$193$	−137.192	+	778.057i	−0.0511675	+	0.290185i	−0.999645	−	0.0266606i	$-0.991513\pi$
$193$	−137.192	+	778.057i	−0.0511675	+	0.290185i	0.948477	+	0.316846i	$0.102624\pi$
$194$		0			0
$195$	−1709.34	−	106.451i	−0.627735	−	0.0390927i
$196$		0			0
$197$	1490.67	+	2581.92i	0.539117	+	0.933777i	0.998952	+	0.0457730i	$0.0145751\pi$
$197$	1490.67	+	2581.92i	0.539117	+	0.933777i	−0.459835	+	0.888004i	$0.652092\pi$
$198$		0			0
$199$	203.833	−	353.048i	0.0726096	−	0.125763i	−0.827435	−	0.561562i	$-0.810201\pi$
$199$	203.833	−	353.048i	0.0726096	−	0.125763i	0.900044	+	0.435798i	$0.143534\pi$
$200$		0			0
$201$	−699.309	−	304.991i	−0.245400	−	0.107027i
$202$		0			0
$203$	−5546.97	−	4654.46i	−1.91784	−	1.60926i
$204$		0			0
$205$	2879.03	+	1047.88i	0.980879	+	0.357011i
$206$		0			0
$207$	−865.038	−	2050.54i	−0.290456	−	0.688513i
$208$		0			0
$209$	−940.792	−	5335.49i	−0.311368	−	1.76586i
$210$		0			0
$211$	−3119.72	+	1135.49i	−1.01787	+	0.370474i	−0.796450	−	0.604704i	$-0.793291\pi$
$211$	−3119.72	+	1135.49i	−1.01787	+	0.370474i	−0.221420	+	0.975179i	$0.571069\pi$
$212$		0			0
$213$	855.327	−	3545.37i	0.275146	−	1.14049i
$214$		0			0
$215$	−1476.52			−0.468361
$216$		0			0
$217$	2493.23			0.779962
$218$		0			0
$219$	−809.047	−	769.464i	−0.249636	−	0.237423i
$220$		0			0
$221$	4829.79	−	1757.90i	1.47008	−	0.535064i
$222$		0			0
$223$	1.08567	+	6.15712i	0.000326016	+	0.00184893i	0.984970	−	0.172724i	$-0.0552567\pi$
$223$	1.08567	+	6.15712i	0.000326016	+	0.00184893i	−0.984644	+	0.174573i	$0.944146\pi$
$224$		0			0
$225$	−675.318	+	2191.47i	−0.200094	+	0.649324i
$226$		0			0
$227$	−1304.05	−	474.635i	−0.381290	−	0.138778i	0.144262	−	0.989539i	$-0.453919\pi$
$227$	−1304.05	−	474.635i	−0.381290	−	0.138778i	−0.525552	+	0.850761i	$0.676141\pi$
$228$		0			0
$229$	−3467.60	−	2909.67i	−1.00064	−	0.839634i	−0.0135638	−	0.999908i	$-0.504318\pi$
$229$	−3467.60	−	2909.67i	−1.00064	−	0.839634i	−0.987072	+	0.160274i	$0.948762\pi$
$230$		0			0
$231$	−680.853	−	6035.27i	−0.193926	−	1.71901i
$232$		0			0
$233$	−564.114	+	977.074i	−0.158611	+	0.274722i	−0.934368	−	0.356309i	$-0.884035\pi$
$233$	−564.114	+	977.074i	−0.158611	+	0.274722i	0.775757	+	0.631032i	$0.217368\pi$
$234$		0			0
$235$	−88.7388	−	153.700i	−0.0246327	−	0.0426651i
$236$		0			0
$237$	1168.33	−	1760.91i	0.320216	−	0.482630i
$238$		0			0
$239$	−488.677	+	2771.43i	−0.132259	+	0.750078i	0.844470	+	0.535602i	$0.179915\pi$
$239$	−488.677	+	2771.43i	−0.132259	+	0.750078i	−0.976729	+	0.214476i	$0.931196\pi$
$240$		0			0
$241$	−1836.34	+	1540.87i	−0.490825	+	0.411851i	−0.854322	−	0.519745i	$-0.826027\pi$
$241$	−1836.34	+	1540.87i	−0.490825	+	0.411851i	0.363497	+	0.931595i	$0.381583\pi$
$242$		0			0
$243$	−515.250	+	3752.79i	−0.136022	+	0.990706i
$244$		0			0
$245$	2857.11	−	2397.40i	0.745038	−	0.625161i
$246$		0			0
$247$	−1279.61	+	7257.05i	−0.329635	+	1.86945i
$248$		0			0
$249$	607.084	−	914.997i	0.154508	−	0.232874i
$250$		0			0
$251$	438.346	+	759.238i	0.110232	+	0.190927i	0.915864	−	0.401489i	$-0.131507\pi$
$251$	438.346	+	759.238i	0.110232	+	0.190927i	−0.805632	+	0.592416i	$0.798174\pi$
$252$		0			0
$253$	1577.77	−	2732.77i	0.392068	−	0.679082i
$254$		0			0
$255$	363.954	+	3226.19i	0.0893792	+	0.792282i
$256$		0			0
$257$	5571.74	+	4675.24i	1.35236	+	1.13476i	0.978263	+	0.207370i	$0.0664904\pi$
$257$	5571.74	+	4675.24i	1.35236	+	1.13476i	0.374093	+	0.927391i	$0.377954\pi$
$258$		0			0
$259$	12359.2	+	4498.39i	2.96512	+	1.07921i
$260$		0			0
$261$	−1885.74	+	6119.39i	−0.447219	+	1.45127i
$262$		0			0
$263$	45.4066	+	257.514i	0.0106460	+	0.0603764i	0.989668	−	0.143378i	$-0.0457966\pi$
$263$	45.4066	+	257.514i	0.0106460	+	0.0603764i	−0.979022	+	0.203755i	$0.934685\pi$
$264$		0			0
$265$	−742.776	+	270.348i	−0.172183	+	0.0626693i
$266$		0			0
$267$	−2789.18	−	2652.71i	−0.639306	−	0.608028i
$268$		0			0
$269$	−2412.58			−0.546832			−0.273416	−	0.961896i	$-0.588154\pi$
$269$	−2412.58			−0.546832			−0.273416	+	0.961896i	$0.588154\pi$
$270$		0			0
$271$	4788.99			1.07347			0.536735	−	0.843751i	$-0.319657\pi$
$271$	4788.99			1.07347			0.536735	+	0.843751i	$0.319657\pi$
$272$		0			0
$273$	−1937.38	+	8030.51i	−0.429507	+	1.78033i
$274$		0			0
$275$	−3055.34	+	1112.05i	−0.669978	+	0.243852i
$276$		0			0
$277$	126.242	+	715.955i	0.0273832	+	0.155298i	0.995433	−	0.0954586i	$-0.0304317\pi$
$277$	126.242	+	715.955i	0.0273832	+	0.155298i	−0.968050	+	0.250757i	$0.919321\pi$
$278$		0			0
$279$	−856.979	−	2031.43i	−0.183892	−	0.435909i
$280$		0			0
$281$	3839.90	+	1397.61i	0.815193	+	0.296706i	0.715767	−	0.698339i	$-0.246077\pi$
$281$	3839.90	+	1397.61i	0.815193	+	0.296706i	0.0994258	+	0.995045i	$0.468299\pi$
$282$		0			0
$283$	6988.51	+	5864.06i	1.46793	+	1.23174i	0.918032	+	0.396505i	$0.129777\pi$
$283$	6988.51	+	5864.06i	1.46793	+	1.23174i	0.549896	+	0.835233i	$0.314667\pi$
$284$		0			0
$285$	−4266.68	−	1860.83i	−0.886793	−	0.386759i
$286$		0			0
$287$	7389.06	−	12798.2i	1.51973	−	2.63225i
$288$		0			0
$289$	−2415.20	−	4183.24i	−0.491593	−	0.851464i
$290$		0			0
$291$	2272.80	+	141.541i	0.457849	+	0.0285129i
$292$		0			0
$293$	774.775	−	4393.97i	0.154481	−	0.876103i	−0.804778	−	0.593575i	$-0.797716\pi$
$293$	774.775	−	4393.97i	0.154481	−	0.876103i	0.959259	−	0.282528i	$-0.0911730\pi$
$294$		0			0
$295$	1029.13	−	863.544i	0.203113	−	0.170432i
$296$		0			0
$297$	−4683.38	+	2629.20i	−0.915007	+	0.513675i
$298$		0			0
$299$	−3287.85	+	2758.83i	−0.635923	+	0.533603i
$300$		0			0
$301$	−1236.71	+	7013.73i	−0.236820	+	1.34307i
$302$		0			0
$303$	371.257	+	746.698i	0.0703899	+	0.141573i
$304$		0			0
$305$	2373.29	+	4110.65i	0.445554	+	0.771723i
$306$		0			0
$307$	1035.59	−	1793.69i	0.192522	−	0.333457i	−0.753564	−	0.657375i	$-0.771667\pi$
$307$	1035.59	−	1793.69i	0.192522	−	0.333457i	0.946085	+	0.323918i	$0.105000\pi$
$308$		0			0
$309$	−2479.96	+	1830.82i	−0.456569	+	0.337060i
$310$		0			0
$311$	3612.26	+	3031.05i	0.658625	+	0.552652i	0.909674	−	0.415322i	$-0.136331\pi$
$311$	3612.26	+	3031.05i	0.658625	+	0.552652i	−0.251049	+	0.967974i	$0.580776\pi$
$312$		0			0
$313$	9140.90	+	3327.02i	1.65072	+	0.600812i	0.988864	−	0.148823i	$-0.0475484\pi$
$313$	9140.90	+	3327.02i	1.65072	+	0.600812i	0.661852	+	0.749634i	$0.269771\pi$
$314$		0			0
$315$	−4644.19	−	2379.32i	−0.830700	−	0.425586i
$316$		0			0
$317$	−1418.23	−	8043.20i	−0.251281	−	1.42508i	−0.805443	−	0.592674i	$-0.798072\pi$
$317$	−1418.23	−	8043.20i	−0.251281	−	1.42508i	0.554162	−	0.832409i	$-0.313039\pi$
$318$		0			0
$319$	−8531.63	+	3105.26i	−1.49743	+	0.545019i
$320$		0			0
$321$	−2146.42	+	633.210i	−0.373213	+	0.110101i
$322$		0			0
$323$	13969.3			2.40642
$324$		0			0
$325$	4422.41			0.754803
$326$		0			0
$327$	7059.69	−	2082.66i	1.19389	−	0.352207i
$328$		0			0
$329$	−804.430	+	292.789i	−0.134801	+	0.0490637i
$330$		0			0
$331$	1045.09	+	5926.98i	0.173544	+	0.984218i	0.939811	+	0.341695i	$0.111001\pi$
$331$	1045.09	+	5926.98i	0.173544	+	0.984218i	−0.766266	+	0.642523i	$0.777888\pi$
$332$		0			0
$333$	−582.948	−	11616.2i	−0.0959320	−	1.91161i
$334$		0			0
$335$	−873.342	−	317.870i	−0.142435	−	0.0518421i
$336$		0			0
$337$	504.072	+	422.966i	0.0814793	+	0.0683693i	0.682618	−	0.730776i	$-0.260841\pi$
$337$	504.072	+	422.966i	0.0814793	+	0.0683693i	−0.601138	+	0.799145i	$0.705286\pi$
$338$		0			0
$339$	2562.44	−	1891.71i	0.410539	−	0.303079i
$340$		0			0
$341$	1563.07	−	2707.31i	0.248225	−	0.429938i
$342$		0			0
$343$	−3758.75	−	6510.35i	−0.591701	−	1.02486i
$344$		0			0
$345$	−1207.01	−	2427.63i	−0.188357	−	0.378838i
$346$		0			0
$347$	−1075.87	+	6101.55i	−0.166443	+	0.943944i	0.781122	+	0.624379i	$0.214648\pi$
$347$	−1075.87	+	6101.55i	−0.166443	+	0.943944i	−0.947564	+	0.319565i	$0.896463\pi$
$348$		0			0
$349$	−2802.25	+	2351.37i	−0.429802	+	0.360647i	−0.831877	−	0.554960i	$-0.812734\pi$
$349$	−2802.25	+	2351.37i	−0.429802	+	0.360647i	0.402075	+	0.915607i	$0.368289\pi$
$350$		0			0
$351$	7209.01	−	1181.73i	1.09626	−	0.179704i
$352$		0			0
$353$	−9332.17	+	7830.62i	−1.40709	+	1.18068i	−0.449236	+	0.893413i	$0.648304\pi$
$353$	−9332.17	+	7830.62i	−1.40709	+	1.18068i	−0.957849	+	0.287272i	$0.907252\pi$
$354$		0			0
$355$	771.495	−	4375.36i	0.115343	−	0.654142i
$356$		0			0
$357$	15629.8	+	973.362i	2.31714	+	0.144302i
$358$		0			0
$359$	−2032.19	−	3519.86i	−0.298760	−	0.517468i	0.677092	−	0.735898i	$-0.263240\pi$
$359$	−2032.19	−	3519.86i	−0.298760	−	0.517468i	−0.975853	+	0.218430i	$0.929906\pi$
$360$		0			0
$361$	−6584.59	+	11404.8i	−0.959992	+	1.66276i
$362$		0			0
$363$	−640.917	−	279.524i	−0.0926706	−	0.0404166i
$364$		0			0
$365$	−1041.93	−	874.286i	−0.149417	−	0.125376i
$366$		0			0
$367$	−10215.7	−	3718.20i	−1.45301	−	0.528851i	−0.509577	−	0.860425i	$-0.670198\pi$
$367$	−10215.7	−	3718.20i	−1.45301	−	0.528851i	−0.943429	+	0.331575i	$0.892420\pi$
$368$		0			0
$369$	−12967.5	−	1621.41i	−1.82943	−	0.228746i
$370$		0			0
$371$	662.066	+	3754.76i	0.0926490	+	0.525438i
$372$		0			0
$373$	−5781.81	+	2104.41i	−0.802602	+	0.292123i	−0.710564	−	0.703632i	$-0.751560\pi$
$373$	−5781.81	+	2104.41i	−0.802602	+	0.292123i	−0.0920378	+	0.995756i	$0.529338\pi$
$374$		0			0
$375$	−1619.37	+	6712.36i	−0.222997	+	0.924333i
$376$		0			0
$377$	12349.0			1.68702
$378$		0			0
$379$	−7142.96			−0.968098			−0.484049	−	0.875041i	$-0.660834\pi$
$379$	−7142.96			−0.968098			−0.484049	+	0.875041i	$0.660834\pi$
$380$		0			0
$381$	−2752.89	−	2618.21i	−0.370171	−	0.352060i
$382$		0			0
$383$	15.1989	−	5.53196i	0.00202775	−	0.000738041i	−0.341006	−	0.940061i	$-0.610768\pi$
$383$	15.1989	−	5.53196i	0.00202775	−	0.000738041i	0.343034	+	0.939323i	$0.388545\pi$
$384$		0			0
$385$	−1284.78	−	7286.37i	−0.170074	−	0.964540i
$386$		0			0
$387$	6139.72	−	1403.13i	0.806458	−	0.184302i
$388$		0			0
$389$	−7725.80	−	2811.96i	−1.00698	−	0.366509i	−0.214705	−	0.976679i	$-0.568879\pi$
$389$	−7725.80	−	2811.96i	−1.00698	−	0.366509i	−0.792271	+	0.610170i	$0.791101\pi$
$390$		0			0
$391$	6232.74	+	5229.89i	0.806146	+	0.676437i
$392$		0			0
$393$	−1013.97	−	8988.14i	−0.130148	−	1.15367i
$394$		0			0
$395$	1287.17	−	2229.45i	0.163961	−	0.283989i
$396$		0			0
$397$	1165.43	+	2018.59i	0.147333	+	0.255189i	0.930241	−	0.366949i	$-0.119598\pi$
$397$	1165.43	+	2018.59i	0.147333	+	0.255189i	−0.782908	+	0.622138i	$0.786264\pi$
$398$		0			0
$399$	−12413.0	+	18708.9i	−1.55746	+	2.34741i
$400$		0			0
$401$	−108.214	+	613.710i	−0.0134761	+	0.0764270i	−0.990804	−	0.135304i	$-0.956799\pi$
$401$	−108.214	+	613.710i	−0.0134761	+	0.0764270i	0.977328	+	0.211731i	$0.0679100\pi$
$402$		0			0
$403$	−3257.21	+	2733.13i	−0.402614	+	0.337833i
$404$		0			0
$405$	−342.310	+	4601.81i	−0.0419988	+	0.564607i
$406$		0			0
$407$	12632.9	−	10600.3i	1.53855	−	1.29100i
$408$		0			0
$409$	134.284	−	761.561i	0.0162345	−	0.0920703i	−0.975614	−	0.219493i	$-0.929560\pi$
$409$	134.284	−	761.561i	0.0162345	−	0.0920703i	0.991848	+	0.127423i	$0.0406706\pi$
$410$		0			0
$411$	5737.40	−	8647.42i	0.688577	−	1.03782i
$412$		0			0
$413$	−3240.01	−	5611.86i	−0.386030	−	0.668623i
$414$		0			0
$415$	668.836	−	1158.46i	0.0791129	−	0.137028i
$416$		0			0
$417$	−599.043	−	5310.08i	−0.0703483	−	0.623587i
$418$		0			0
$419$	−1420.62	−	1192.04i	−0.165636	−	0.138985i	0.556202	−	0.831047i	$-0.312258\pi$
$419$	−1420.62	−	1192.04i	−0.165636	−	0.138985i	−0.721838	+	0.692062i	$0.756703\pi$
$420$		0			0
$421$	4049.32	+	1473.83i	0.468769	+	0.170618i	0.565595	−	0.824683i	$-0.308647\pi$
$421$	4049.32	+	1473.83i	0.468769	+	0.170618i	−0.0968254	+	0.995301i	$0.530869\pi$
$422$		0			0
$423$	515.058	+	554.794i	0.0592033	+	0.0637707i
$424$		0			0
$425$	−1455.78	−	8256.15i	−0.166155	−	0.942311i
$426$		0			0
$427$	21514.2	−	7830.53i	2.43828	−	0.887461i
$428$		0			0
$429$	7505.45	+	7138.24i	0.844677	+	0.803351i
$430$		0			0
$431$	−382.068			−0.0426997			−0.0213499	−	0.999772i	$-0.506796\pi$
$431$	−382.068			−0.0426997			−0.0213499	+	0.999772i	$0.506796\pi$
$432$		0			0
$433$	11989.0			1.33061			0.665306	−	0.746570i	$-0.268301\pi$
$433$	11989.0			1.33061			0.665306	+	0.746570i	$0.268301\pi$
$434$		0			0
$435$	−1829.41	+	7582.99i	−0.201640	+	0.835808i
$436$		0			0
$437$	−10961.7	+	3989.72i	−1.19993	+	0.436737i
$438$		0			0
$439$	−242.166	−	1373.39i	−0.0263279	−	0.149313i	0.968810	−	0.247805i	$-0.0797092\pi$
$439$	−242.166	−	1373.39i	−0.0263279	−	0.149313i	−0.995138	+	0.0984921i	$0.968598\pi$
$440$		0			0
$441$	−9602.32	+	12684.1i	−1.03686	+	1.36962i
$442$		0			0
$443$	−10417.9	−	3791.81i	−1.11731	−	0.406669i	−0.283642	−	0.958930i	$-0.591543\pi$
$443$	−10417.9	−	3791.81i	−1.11731	−	0.406669i	−0.833671	+	0.552262i	$0.813765\pi$
$444$		0			0
$445$	−3592.05	−	3014.09i	−0.382651	−	0.321082i
$446$		0			0
$447$	−8608.55	−	3754.46i	−0.910895	−	0.397270i
$448$		0			0
$449$	−4999.43	+	8659.27i	−0.525474	+	0.910147i	0.474086	+	0.880478i	$0.342779\pi$
$449$	−4999.43	+	8659.27i	−0.525474	+	0.910147i	−0.999560	+	0.0296686i	$0.990555\pi$
$450$		0			0
$451$	−9264.75	−	16047.0i	−0.967317	−	1.67544i
$452$		0			0
$453$	−3470.87	−	216.151i	−0.359991	−	0.0224187i
$454$		0			0
$455$	−1747.49	+	9910.52i	−0.180052	+	1.02113i
$456$		0			0
$457$	2791.54	−	2342.38i	0.285739	−	0.239764i	−0.488640	−	0.872486i	$-0.662507\pi$
$457$	2791.54	−	2342.38i	0.285739	−	0.239764i	0.774379	+	0.632722i	$0.218062\pi$
$458$		0			0
$459$	−4579.25	−	13069.4i	−0.465667	−	1.32904i
$460$		0			0
$461$	−4558.83	+	3825.31i	−0.460576	+	0.386469i	−0.843343	−	0.537376i	$-0.819416\pi$
$461$	−4558.83	+	3825.31i	−0.460576	+	0.386469i	0.382767	+	0.923845i	$0.374971\pi$
$462$		0			0
$463$	525.995	−	2983.07i	0.0527971	−	0.299427i	−0.946963	−	0.321344i	$-0.895866\pi$
$463$	525.995	−	2983.07i	0.0527971	−	0.299427i	0.999760	+	0.0219162i	$0.00697669\pi$
$464$		0			0
$465$	−1195.76	−	2405.01i	−0.119252	−	0.239849i
$466$		0			0
$467$	1788.04	+	3096.97i	0.177174	+	0.306875i	0.940912	−	0.338652i	$-0.109971\pi$
$467$	1788.04	+	3096.97i	0.177174	+	0.306875i	−0.763737	+	0.645527i	$0.776638\pi$
$468$		0			0
$469$	−2241.44	+	3882.29i	−0.220683	+	0.382234i
$470$		0			0
$471$	3492.59	−	2578.39i	0.341677	−	0.252242i
$472$		0			0
$473$	6840.63	+	5739.97i	0.664973	+	0.557979i
$474$		0			0
$475$	11294.8	+	4110.96i	1.09103	+	0.397103i
$476$		0			0
$477$	2831.73	−	1830.03i	0.271816	−	0.175663i
$478$		0			0
$479$	−1180.11	−	6692.71i	−0.112569	−	0.638409i	−0.987925	−	0.154931i	$-0.950484\pi$
$479$	−1180.11	−	6692.71i	−0.112569	−	0.638409i	0.875357	−	0.483478i	$-0.160627\pi$
$480$		0			0
$481$	−21077.6	+	7671.62i	−1.99804	+	0.727226i
$482$		0			0
$483$	−12542.7	+	3700.18i	−1.18160	+	0.348579i
$484$		0			0
$485$	2774.08			0.259721
$486$		0			0
$487$	−5961.90			−0.554743			−0.277371	−	0.960763i	$-0.589463\pi$
$487$	−5961.90			−0.554743			−0.277371	+	0.960763i	$0.589463\pi$
$488$		0			0
$489$	18628.5	−	5495.54i	1.72272	−	0.508215i
$490$		0			0
$491$	−6366.64	+	2317.27i	−0.585178	+	0.212987i	−0.617607	−	0.786487i	$-0.711898\pi$
$491$	−6366.64	+	2317.27i	−0.585178	+	0.212987i	0.0324295	+	0.999474i	$0.489676\pi$
$492$		0			0
$493$	−4065.08	−	23054.2i	−0.371363	−	2.10610i
$494$		0			0
$495$	−5495.17	+	3551.30i	−0.498968	+	0.322463i
$496$		0			0
$497$	−20137.6	−	7329.49i	−1.81749	−	0.661514i
$498$		0			0
$499$	−4308.65	−	3615.39i	−0.386537	−	0.324343i	0.428725	−	0.903435i	$-0.358963\pi$
$499$	−4308.65	−	3615.39i	−0.386537	−	0.324343i	−0.815262	+	0.579092i	$0.803407\pi$
$500$		0			0
$501$	4522.72	−	3338.88i	0.403313	−	0.297745i
$502$		0			0
$503$	−5750.68	+	9960.47i	−0.509762	+	0.882933i	0.490175	+	0.871624i	$0.336933\pi$
$503$	−5750.68	+	9960.47i	−0.509762	+	0.882933i	−0.999936	+	0.0113086i	$0.996400\pi$
$504$		0			0
$505$	507.927	+	879.756i	0.0447574	+	0.0775220i
$506$		0			0
$507$	−1189.73	−	2392.86i	−0.104216	−	0.209607i
$508$		0			0
$509$	1331.02	−	7548.62i	0.115907	−	0.657341i	−0.870390	−	0.492363i	$-0.836133\pi$
$509$	1331.02	−	7548.62i	0.115907	−	0.657341i	0.986297	−	0.164978i	$-0.0527555\pi$
$510$		0			0
$511$	−5025.73	+	4217.09i	−0.435079	+	0.365074i
$512$		0			0
$513$	19510.2	+	3683.19i	1.67914	+	0.316992i
$514$		0			0
$515$	−2876.61	+	2413.76i	−0.246133	+	0.206530i
$516$		0			0
$517$	−186.388	+	1057.06i	−0.0158556	+	0.0899213i
$518$		0			0
$519$	7609.61	+	473.895i	0.643593	+	0.0400803i
$520$		0			0
$521$	−8590.50	−	14879.2i	−0.722373	−	1.25119i	−0.960046	−	0.279842i	$-0.909718\pi$
$521$	−8590.50	−	14879.2i	−0.722373	−	1.25119i	0.237673	−	0.971345i	$-0.423615\pi$
$522$		0			0
$523$	4925.61	−	8531.40i	0.411820	−	0.713293i	−0.583269	−	0.812279i	$-0.698227\pi$
$523$	4925.61	−	8531.40i	0.411820	−	0.713293i	0.995089	+	0.0989863i	$0.0315600\pi$
$524$		0			0
$525$	12350.9	+	5386.63i	1.02674	+	0.447794i
$526$		0			0
$527$	6174.67	+	5181.16i	0.510385	+	0.428264i
$528$		0			0
$529$	5048.76	+	1837.60i	0.414955	+	0.151031i
$530$		0			0
$531$	−3458.76	+	4568.80i	−0.282669	+	0.373388i
$532$		0			0
$533$	4376.42	+	24819.9i	0.355655	+	2.01702i
$534$		0			0
$535$	−2561.76	+	932.404i	−0.207018	+	0.0753483i
$536$		0			0
$537$	−1300.75	+	5391.66i	−0.104528	+	0.433272i
$538$		0			0
$539$	−22556.8			−1.80258
$540$		0			0
$541$	−4013.68			−0.318968			−0.159484	−	0.987201i	$-0.550983\pi$
$541$	−4013.68			−0.318968			−0.159484	+	0.987201i	$0.550983\pi$
$542$		0			0
$543$	9212.28	+	8761.57i	0.728060	+	0.692440i
$544$		0			0
$545$	8425.77	−	3066.73i	0.662239	−	0.241035i
$546$		0			0
$547$	−1033.24	−	5859.80i	−0.0807645	−	0.458038i	−0.998190	−	0.0601318i	$-0.980848\pi$
$547$	−1033.24	−	5859.80i	−0.0807645	−	0.458038i	0.917426	−	0.397907i	$-0.130263\pi$
$548$		0			0
$549$	−13775.0	−	14837.8i	−1.07086	−	1.15348i
$550$		0			0
$551$	31539.2	+	11479.3i	2.43850	+	0.887541i
$552$		0			0
$553$	−9512.18	−	7981.66i	−0.731463	−	0.613770i
$554$		0			0
$555$	−1588.32	−	14079.3i	−0.121479	−	1.07682i
$556$		0			0
$557$	−2991.77	+	5181.89i	−0.227586	+	0.394190i	−0.957092	−	0.289784i	$-0.906417\pi$
$557$	−2991.77	+	5181.89i	−0.227586	+	0.394190i	0.729506	+	0.683974i	$0.239750\pi$
$558$		0			0
$559$	−6072.91	−	10518.6i	−0.459494	−	0.795866i
$560$		0			0
$561$	10855.7	−	16361.6i	0.816980	−	1.23135i
$562$		0			0
$563$	−211.184	+	1197.69i	−0.0158088	+	0.0896563i	−0.991691	−	0.128640i	$-0.958939\pi$
$563$	−211.184	+	1197.69i	−0.0158088	+	0.0896563i	0.975883	+	0.218296i	$0.0700499\pi$
$564$		0			0
$565$	2972.28	−	2494.04i	0.221318	−	0.185708i
$566$		0			0
$567$	21572.7	+	5480.44i	1.59783	+	0.405921i
$568$		0			0
$569$	13773.9	−	11557.7i	1.01482	−	0.851534i	0.0258510	−	0.999666i	$-0.491770\pi$
$569$	13773.9	−	11557.7i	1.01482	−	0.851534i	0.988968	+	0.148132i	$0.0473260\pi$
$570$		0			0
$571$	1129.06	−	6403.21i	0.0827489	−	0.469292i	−0.915071	−	0.403293i	$-0.867865\pi$
$571$	1129.06	−	6403.21i	0.0827489	−	0.469292i	0.997820	−	0.0659990i	$-0.0210234\pi$
$572$		0			0
$573$	−9474.01	+	14279.2i	−0.690720	+	1.04105i
$574$		0			0
$575$	3500.35	+	6062.78i	0.253869	+	0.439714i
$576$		0			0
$577$	1240.33	−	2148.31i	0.0894896	−	0.155001i	−0.817806	−	0.575494i	$-0.804810\pi$
$577$	1240.33	−	2148.31i	0.0894896	−	0.155001i	0.907296	+	0.420494i	$0.138143\pi$
$578$		0			0
$579$	−460.206	−	4079.39i	−0.0330320	−	0.292804i
$580$		0			0
$581$	−4942.68	−	4147.40i	−0.352938	−	0.296150i
$582$		0			0
$583$	4492.22	+	1635.04i	0.319123	+	0.116151i
$584$		0			0
$585$	8675.52	−	1982.65i	0.613143	−	0.140124i
$586$		0			0
$587$	4249.70	+	24101.3i	0.298814	+	1.69466i	0.651282	+	0.758836i	$0.274232\pi$
$587$	4249.70	+	24101.3i	0.298814	+	1.69466i	−0.352468	+	0.935824i	$0.614657\pi$
$588$		0			0
$589$	−10859.5	+	3952.55i	−0.759693	+	0.276506i
$590$		0			0
$591$	−11225.3	−	10676.1i	−0.781299	−	0.743074i
$592$		0			0
$593$	−21133.4			−1.46348			−0.731742	−	0.681581i	$-0.761293\pi$
$593$	−21133.4			−1.46348			−0.731742	+	0.681581i	$0.761293\pi$
$594$		0			0
$595$	19077.1			1.31443
$596$		0			0
$597$	−496.789	+	2059.21i	−0.0340573	+	0.141169i
$598$		0			0
$599$	−12839.7	+	4673.28i	−0.875822	+	0.318773i	−0.740522	−	0.672032i	$-0.765422\pi$
$599$	−12839.7	+	4673.28i	−0.875822	+	0.318773i	−0.135300	+	0.990805i	$0.543200\pi$
$600$		0			0
$601$	258.554	+	1466.33i	0.0175485	+	0.0995225i	0.992324	−	0.123665i	$-0.0394649\pi$
$601$	258.554	+	1466.33i	0.0175485	+	0.0995225i	−0.974776	+	0.223188i	$0.928354\pi$
$602$		0			0
$603$	3933.64	+	491.849i	0.265655	+	0.0332166i
$604$		0			0
$605$	−800.418	−	291.328i	−0.0537878	−	0.0195772i
$606$		0			0
$607$	−18473.7	−	15501.3i	−1.23529	−	1.03654i	−0.997877	−	0.0651278i	$-0.979254\pi$
$607$	−18473.7	−	15501.3i	−1.23529	−	1.03654i	−0.237418	−	0.971408i	$-0.576301\pi$
$608$		0			0
$609$	34488.3	+	15041.4i	2.29480	+	1.00084i
$610$		0			0
$611$	729.965	−	1264.34i	0.0483326	−	0.0837146i
$612$		0			0
$613$	12370.5	+	21426.4i	0.815074	+	1.41175i	0.909275	+	0.416197i	$0.136637\pi$
$613$	12370.5	+	21426.4i	0.815074	+	1.41175i	−0.0942003	+	0.995553i	$0.530029\pi$
$614$		0			0
$615$	−15889.2	−	989.513i	−1.04181	−	0.0648797i
$616$		0			0
$617$	376.525	−	2135.38i	0.0245678	−	0.139331i	−0.970057	−	0.242879i	$-0.921908\pi$
$617$	376.525	−	2135.38i	0.0245678	−	0.139331i	0.994624	+	0.103548i	$0.0330195\pi$
$618$		0			0
$619$	−21407.8	+	17963.3i	−1.39007	+	1.16641i	−0.424760	+	0.905306i	$0.639641\pi$
$619$	−21407.8	+	17963.3i	−1.39007	+	1.16641i	−0.965311	+	0.261102i	$0.915914\pi$
$620$		0			0
$621$	7326.01	+	8947.64i	0.473402	+	0.578191i
$622$		0			0
$623$	−17326.1	+	14538.3i	−1.11422	+	0.934938i
$624$		0			0
$625$	382.882	−	2171.43i	0.0245044	−	0.138972i
$626$		0			0
$627$	12533.3	+	25207.9i	0.798296	+	1.60559i
$628$		0			0
$629$	21260.5	+	36824.2i	1.34771	+	2.33430i
$630$		0			0
$631$	10153.7	−	17586.8i	0.640591	−	1.10954i	−0.344710	−	0.938709i	$-0.612023\pi$
$631$	10153.7	−	17586.8i	0.640591	−	1.10954i	0.985301	−	0.170827i	$-0.0546440\pi$
$632$		0			0
$633$	13878.6	−	10245.8i	0.871447	−	0.643343i
$634$		0			0
$635$	−3545.32	−	2974.88i	−0.221562	−	0.185913i
$636$		0			0
$637$	28830.2	+	10493.3i	1.79324	+	0.652686i
$638$		0			0
$639$	949.830	+	18927.0i	0.0588023	+	1.17174i
$640$		0			0
$641$	−5092.95	−	28883.6i	−0.313821	−	1.77977i	−0.578753	−	0.815503i	$-0.696461\pi$
$641$	−5092.95	−	28883.6i	−0.313821	−	1.77977i	0.264932	−	0.964267i	$-0.414650\pi$
$642$		0			0
$643$	17570.0	−	6394.95i	1.07759	−	0.392212i	0.258582	−	0.965989i	$-0.416745\pi$
$643$	17570.0	−	6394.95i	1.07759	−	0.392212i	0.819011	+	0.573777i	$0.194523\pi$
$644$		0			0
$645$	7358.68	−	2170.87i	0.449221	−	0.132524i
$646$		0			0
$647$	18551.2			1.12724			0.563619	−	0.826035i	$-0.309408\pi$
$647$	18551.2			1.12724			0.563619	+	0.826035i	$0.309408\pi$
$648$		0			0
$649$	−8124.94			−0.491420
$650$		0			0
$651$	−12425.8	+	3665.70i	−0.748088	+	0.220692i
$652$		0			0
$653$	9873.40	−	3593.62i	0.591693	−	0.215359i	−0.0287806	−	0.999586i	$-0.509162\pi$
$653$	9873.40	−	3593.62i	0.591693	−	0.215359i	0.620474	+	0.784227i	$0.286940\pi$
$654$		0			0
$655$	−1913.39	−	10851.4i	−0.114141	−	0.647325i
$656$		0			0
$657$	5163.45	+	2645.35i	0.306614	+	0.157085i
$658$		0			0
$659$	24870.1	+	9051.96i	1.47011	+	0.535075i	0.948129	−	0.317884i	$-0.102972\pi$
$659$	24870.1	+	9051.96i	1.47011	+	0.535075i	0.521977	+	0.852960i	$0.325195\pi$
$660$		0			0
$661$	9498.41	+	7970.11i	0.558919	+	0.468988i	0.877948	−	0.478756i	$-0.158912\pi$
$661$	9498.41	+	7970.11i	0.558919	+	0.468988i	−0.319029	+	0.947745i	$0.603357\pi$
$662$		0			0
$663$	−21486.2	+	15862.1i	−1.25860	+	0.929160i
$664$		0			0
$665$	−13675.7	+	23686.9i	−0.797472	+	1.38126i
$666$		0			0
$667$	9774.25	+	16929.5i	0.567407	+	0.982778i
$668$		0			0
$669$	−14.4633	−	29.0897i	−0.000835851	−	0.00168112i
$670$		0			0
$671$	4984.87	−	28270.6i	0.286794	−	1.62649i
$672$		0			0
$673$	−14187.2	+	11904.5i	−0.812595	+	0.681848i	−0.951226	−	0.308496i	$-0.900174\pi$
$673$	−14187.2	+	11904.5i	−0.812595	+	0.681848i	0.138631	+	0.990344i	$0.455730\pi$
$674$		0			0
$675$	143.623	−	11914.8i	0.00818973	−	0.679406i
$676$		0			0
$677$	2161.98	−	1814.11i	0.122735	−	0.102987i	−0.579354	−	0.815076i	$-0.696695\pi$
$677$	2161.98	−	1814.11i	0.122735	−	0.102987i	0.702089	+	0.712089i	$0.252251\pi$
$678$		0			0
$679$	2323.53	−	13177.4i	0.131324	−	0.744776i
$680$		0			0
$681$	7196.97	+	448.197i	0.404976	+	0.0252202i
$682$		0			0
$683$	−12739.5	−	22065.5i	−0.713709	−	1.23618i	−0.963455	−	0.267869i	$-0.913680\pi$
$683$	−12739.5	−	22065.5i	−0.713709	−	1.23618i	0.249746	−	0.968311i	$-0.419653\pi$
$684$		0			0
$685$	6321.01	−	10948.3i	0.352574	−	0.610676i
$686$		0			0
$687$	21559.8	+	9402.93i	1.19732	+	0.522189i
$688$		0			0
$689$	−4980.98	−	4179.54i	−0.275414	−	0.231100i
$690$		0			0
$691$	3373.15	+	1227.73i	0.185703	+	0.0675903i	0.433198	−	0.901299i	$-0.357385\pi$
$691$	3373.15	+	1227.73i	0.185703	+	0.0675903i	−0.247495	+	0.968889i	$0.579607\pi$
$692$		0			0
$693$	12266.7	+	29077.6i	0.672398	+	1.59389i
$694$		0			0
$695$	−1130.41	−	6410.85i	−0.0616961	−	0.349896i
$696$		0			0
$697$	44895.4	−	16340.6i	2.43979	−	0.888012i
$698$		0			0
$699$	1374.88	−	5698.94i	0.0743960	−	0.308375i
$700$		0			0
$701$	−26994.7			−1.45446			−0.727229	−	0.686395i	$-0.759192\pi$
$701$	−26994.7			−1.45446			−0.727229	+	0.686395i	$0.759192\pi$
$702$		0			0
$703$	−60963.3			−3.27066
$704$		0			0
$705$	668.237	+	635.543i	0.0356982	+	0.0339517i
$706$		0			0
$707$	4604.44	−	1675.88i	0.244933	−	0.0891483i
$708$		0			0
$709$	−5163.42	−	29283.2i	−0.273507	−	1.55114i	−0.743665	−	0.668553i	$-0.766914\pi$
$709$	−5163.42	−	29283.2i	−0.273507	−	1.55114i	0.470158	−	0.882582i	$-0.344197\pi$
$710$		0			0
$711$	−3233.74	+	10493.8i	−0.170569	+	0.553513i
$712$		0			0
$713$	−6325.00	−	2302.11i	−0.332220	−	0.120918i
$714$		0			0
$715$	9665.92	+	8110.67i	0.505573	+	0.424226i
$716$		0			0
$717$	−1639.25	−	14530.7i	−0.0853818	−	0.756848i
$718$		0			0
$719$	7115.08	−	12323.7i	0.369051	−	0.639215i	−0.620366	−	0.784312i	$-0.713016\pi$
$719$	7115.08	−	12323.7i	0.369051	−	0.639215i	0.989417	+	0.145097i	$0.0463494\pi$
$720$		0			0
$721$	9056.40	+	15686.2i	0.467792	+	0.810240i
$722$		0			0
$723$	6886.46	−	10379.3i	0.354233	−	0.533900i
$724$		0			0
$725$	3497.72	−	19836.6i	0.179175	−	1.01615i
$726$		0			0
$727$	−20941.8	+	17572.3i	−1.06835	+	0.896449i	−0.994902	−	0.100850i	$-0.967844\pi$
$727$	−20941.8	+	17572.3i	−1.06835	+	0.896449i	−0.0734451	+	0.997299i	$0.523399\pi$
$728$		0			0
$729$	−2949.67	−	19460.7i	−0.149859	−	0.988707i
$730$		0			0
$731$	−17638.0	+	14800.0i	−0.892427	+	0.748835i
$732$		0			0
$733$	−2428.66	+	13773.6i	−0.122380	+	0.694053i	0.860449	+	0.509536i	$0.170183\pi$
$733$	−2428.66	+	13773.6i	−0.122380	+	0.694053i	−0.982829	+	0.184517i	$0.940928\pi$
$734$		0			0
$735$	−10714.5	+	16148.9i	−0.537701	+	0.810423i
$736$		0			0
$737$	2810.42	+	4867.80i	0.140466	+	0.243294i
$738$		0			0
$739$	−2156.39	+	3734.98i	−0.107340	+	0.185918i	−0.914692	−	0.404152i	$-0.867567\pi$
$739$	−2156.39	+	3734.98i	−0.107340	+	0.185918i	0.807352	+	0.590070i	$0.200900\pi$
$740$		0			0
$741$	−4292.41	−	38049.1i	−0.212801	−	1.88633i
$742$		0			0
$743$	−14086.7	−	11820.1i	−0.695544	−	0.583631i	0.224958	−	0.974369i	$-0.427776\pi$
$743$	−14086.7	−	11820.1i	−0.695544	−	0.583631i	−0.920502	+	0.390737i	$0.872220\pi$
$744$		0			0
$745$	−10750.9	−	3913.01i	−0.528701	−	0.192432i
$746$		0			0
$747$	−1680.30	+	5452.74i	−0.0823013	+	0.267075i
$748$		0			0
$749$	2283.40	+	12949.8i	0.111393	+	0.631743i
$750$		0			0
$751$	27871.3	−	10144.3i	1.35424	−	0.492905i	0.439974	−	0.898010i	$-0.354988\pi$
$751$	27871.3	−	10144.3i	1.35424	−	0.492905i	0.914270	+	0.405106i	$0.132765\pi$
$752$		0			0
$753$	−3300.91	−	3139.41i	−0.159750	−	0.151934i
$754$		0			0
$755$	−4236.39			−0.204209
$756$		0			0
$757$	−4834.80			−0.232132			−0.116066	−	0.993242i	$-0.537028\pi$
$757$	−4834.80			−0.232132			−0.116066	+	0.993242i	$0.537028\pi$
$758$		0			0
$759$	−3845.39	+	15939.3i	−0.183899	+	0.762267i
$760$		0			0
$761$	−11367.7	+	4137.51i	−0.541498	+	0.197089i	−0.598265	−	0.801298i	$-0.704143\pi$
$761$	−11367.7	+	4137.51i	−0.541498	+	0.197089i	0.0567672	+	0.998387i	$0.481921\pi$
$762$		0			0
$763$	−7510.23	−	42592.6i	−0.356341	−	2.02091i
$764$		0			0
$765$	−6557.22	−	15543.6i	−0.309904	−	0.734615i
$766$		0			0
$767$	10384.6	+	3779.70i	0.488875	+	0.177936i
$768$		0			0
$769$	4302.41	+	3610.15i	0.201754	+	0.169292i	0.738067	−	0.674728i	$-0.235739\pi$
$769$	4302.41	+	3610.15i	0.201754	+	0.169292i	−0.536313	+	0.844019i	$0.680183\pi$
$770$		0			0
$771$	−34642.3	−	15108.6i	−1.61817	−	0.705737i
$772$		0			0
$773$	13221.1	−	22899.6i	0.615174	−	1.06551i	−0.375180	−	0.926952i	$-0.622419\pi$
$773$	13221.1	−	22899.6i	0.615174	−	1.06551i	0.990354	−	0.138561i	$-0.0442477\pi$
$774$		0			0
$775$	3467.73	+	6006.29i	0.160729	+	0.278390i
$776$		0			0
$777$	−68209.9	−	4247.83i	−3.14931	−	0.196126i
$778$		0			0
$779$	−11894.7	+	67458.0i	−0.547074	+	3.10261i
$780$		0			0
$781$	−20583.5	+	17271.6i	−0.943069	+	0.791329i
$782$		0			0
$783$	401.049	−	33270.4i	0.0183044	−	1.51850i
$784$		0			0
$785$	4051.20	−	3399.36i	0.184196	−	0.154559i
$786$		0			0
$787$	−363.427	+	2061.10i	−0.0164609	+	0.0933547i	−0.991931	−	0.126776i	$-0.959537\pi$
$787$	−363.427	+	2061.10i	−0.0164609	+	0.0933547i	0.975470	+	0.220130i	$0.0706483\pi$
$788$		0			0
$789$	−604.911	−	1216.64i	−0.0272945	−	0.0548967i
$790$		0			0
$791$	−9357.62	−	16207.9i	−0.420630	−	0.728553i
$792$		0			0
$793$	−19522.7	+	33814.2i	−0.874237	+	1.51422i
$794$		0			0
$795$	3304.37	−	2439.44i	0.147414	−	0.108828i
$796$		0			0
$797$	29017.1	+	24348.2i	1.28963	+	1.08213i	0.991839	+	0.127500i	$0.0406951\pi$
$797$	29017.1	+	24348.2i	1.28963	+	1.08213i	0.297794	+	0.954630i	$0.403749\pi$
$798$		0			0
$799$	−2600.67	−	946.567i	−0.115150	−	0.0419113i
$800$		0			0
$801$	17800.9	+	9119.80i	0.785223	+	0.402287i
$802$		0			0
$803$	1428.43	+	8101.05i	0.0627750	+	0.356015i
$804$		0			0
$805$	−14969.7	+	5448.52i	−0.655419	+	0.238553i
$806$		0			0
$807$	12023.9	−	3547.13i	0.524485	−	0.154727i
$808$		0			0
$809$	16406.9			0.713023			0.356511	−	0.934291i	$-0.383966\pi$
$809$	16406.9			0.713023			0.356511	+	0.934291i	$0.383966\pi$
$810$		0			0
$811$	28461.1			1.23231			0.616156	−	0.787624i	$-0.288689\pi$
$811$	28461.1			1.23231			0.616156	+	0.787624i	$0.288689\pi$
$812$		0			0
$813$	−23867.4	+	7041.07i	−1.02960	+	0.303740i
$814$		0			0
$815$	22233.1	−	8092.20i	0.955574	−	0.347801i
$816$		0			0
$817$	−5732.32	−	32509.6i	−0.245469	−	1.39213i
$818$		0			0
$819$	−2151.43	−	42871.0i	−0.0917914	−	1.82910i
$820$		0			0
$821$	−16734.0	−	6090.66i	−0.711351	−	0.258910i	−0.0391013	−	0.999235i	$-0.512450\pi$
$821$	−16734.0	−	6090.66i	−0.711351	−	0.258910i	−0.672249	+	0.740325i	$0.734672\pi$
$822$		0			0
$823$	7097.34	+	5955.37i	0.300605	+	0.252237i	0.780596	−	0.625036i	$-0.214916\pi$
$823$	7097.34	+	5955.37i	0.300605	+	0.252237i	−0.479991	+	0.877273i	$0.659360\pi$
$824$		0			0
$825$	13592.2	−	10034.4i	0.573600	−	0.423458i
$826$		0			0
$827$	−366.919	+	635.522i	−0.0154281	+	0.0267222i	−0.873636	−	0.486579i	$-0.838244\pi$
$827$	−366.919	+	635.522i	−0.0154281	+	0.0267222i	0.858208	+	0.513302i	$0.171578\pi$
$828$		0			0
$829$	17779.6	+	30795.1i	0.744886	+	1.29018i	0.950248	+	0.311494i	$0.100829\pi$
$829$	17779.6	+	30795.1i	0.744886	+	1.29018i	−0.205363	+	0.978686i	$0.565837\pi$
$830$		0			0
$831$	−1681.81	−	3382.57i	−0.0702060	−	0.141203i
$832$		0			0
$833$	10099.5	−	57277.1i	0.420080	−	2.38239i
$834$		0			0
$835$	5246.09	−	4401.99i	0.217423	−	0.182440i
$836$		0			0
$837$	7257.75	+	8864.28i	0.299719	+	0.366063i
$838$		0			0
$839$	18947.4	−	15898.7i	0.779661	−	0.654213i	−0.163502	−	0.986543i	$-0.552279\pi$
$839$	18947.4	−	15898.7i	0.779661	−	0.654213i	0.943163	+	0.332330i	$0.107835\pi$
$840$		0			0
$841$	5531.81	−	31372.5i	0.226816	−	1.28634i
$842$		0			0
$843$	−21192.2	−	1319.76i	−0.865833	−	0.0539205i
$844$		0			0
$845$	−1627.70	−	2819.26i	−0.0662657	−	0.114776i
$846$		0			0
$847$	−2054.28	+	3558.12i	−0.0833365	+	0.144343i
$848$		0			0
$849$	−43451.1	−	18950.4i	−1.75646	−	0.766049i
$850$		0			0
$851$	−27200.2	−	22823.6i	−1.09566	−	0.919371i
$852$		0			0
$853$	−27889.1	−	10150.8i	−1.11947	−	0.407452i	−0.285008	−	0.958525i	$-0.591996\pi$
$853$	−27889.1	−	10150.8i	−1.11947	−	0.407452i	−0.834457	+	0.551073i	$0.814219\pi$
$854$		0			0
$855$	24000.2	+	3000.90i	0.959988	+	0.120034i
$856$		0			0
$857$	1286.89	+	7298.31i	0.0512944	+	0.290905i	0.999654	−	0.0262914i	$-0.00836976\pi$
$857$	1286.89	+	7298.31i	0.0512944	+	0.290905i	−0.948360	+	0.317196i	$0.897259\pi$
$858$		0			0
$859$	−32662.6	+	11888.2i	−1.29736	+	0.472200i	−0.896136	−	0.443780i	$-0.853637\pi$
$859$	−32662.6	+	11888.2i	−1.29736	+	0.472200i	−0.401224	+	0.915980i	$0.631415\pi$
$860$		0			0
$861$	−18008.9	+	74647.8i	−0.712825	+	2.95469i
$862$		0			0
$863$	17300.6			0.682410			0.341205	−	0.939989i	$-0.389165\pi$
$863$	17300.6			0.682410			0.341205	+	0.939989i	$0.389165\pi$
$864$		0			0
$865$	9287.95			0.365087
$866$		0			0
$867$	18187.3	+	17297.5i	0.712427	+	0.677571i
$868$		0			0
$869$	−14630.4	+	5325.03i	−0.571119	+	0.207870i
$870$		0			0
$871$	−1327.57	−	7529.02i	−0.0516452	−	0.292895i
$872$		0			0
$873$	−11535.3	+	2636.20i	−0.447206	+	0.102201i
$874$		0			0
$875$	38126.0	+	13876.7i	1.47302	+	0.536137i
$876$		0			0
$877$	−1853.57	−	1555.33i	−0.0713690	−	0.0598857i	0.606405	−	0.795156i	$-0.292611\pi$
$877$	−1853.57	−	1555.33i	−0.0713690	−	0.0598857i	−0.677774	+	0.735270i	$0.737055\pi$
$878$		0			0
$879$	2598.95	+	23037.8i	0.0997273	+	0.884011i
$880$		0			0
$881$	−10449.6	+	18099.2i	−0.399609	+	0.692143i	−0.993678	−	0.112271i	$-0.964187\pi$
$881$	−10449.6	+	18099.2i	−0.399609	+	0.692143i	0.594069	+	0.804414i	$0.297521\pi$
$882$		0			0
$883$	20574.0	+	35635.3i	0.784113	+	1.35812i	0.929528	+	0.368752i	$0.120215\pi$
$883$	20574.0	+	35635.3i	0.784113	+	1.35812i	−0.145415	+	0.989371i	$0.546452\pi$
$884$		0			0
$885$	−3859.36	+	5816.83i	−0.146589	+	0.220938i
$886$		0			0
$887$	7502.83	−	42550.7i	0.284014	−	1.61072i	−0.424773	−	0.905300i	$-0.639646\pi$
$887$	7502.83	−	42550.7i	0.284014	−	1.61072i	0.708787	−	0.705423i	$-0.249243\pi$
$888$		0			0
$889$	−17100.7	+	14349.2i	−0.645152	+	0.541347i
$890$		0			0
$891$	19475.5	−	19989.2i	0.732270	−	0.751586i
$892$		0			0
$893$	3039.62	−	2550.54i	0.113905	−	0.0955775i
$894$		0			0
$895$	−1173.26	+	6653.88i	−0.0438187	+	0.248508i
$896$		0			0
$897$	12329.8	−	18583.5i	0.458952	−	0.691733i
$898$		0			0
$899$	9683.19	+	16771.8i	0.359235	+	0.622213i
$900$		0			0
$901$	−6163.08	+	10674.8i	−0.227882	+	0.394704i
$902$		0			0
$903$	−4148.49	−	36773.4i	−0.152883	−	1.35519i
$904$		0			0
$905$	11864.1	+	9955.14i	0.435774	+	0.365657i
$906$		0			0
$907$	−15691.1	−	5711.09i	−0.574437	−	0.209078i	0.0384336	−	0.999261i	$-0.487763\pi$
$907$	−15691.1	−	5711.09i	−0.574437	−	0.209078i	−0.612871	+	0.790183i	$0.709985\pi$
$908$		0			0
$909$	−2948.11	−	3175.56i	−0.107572	−	0.115871i
$910$		0			0
$911$	4285.11	+	24302.1i	0.155842	+	0.883824i	0.958012	+	0.286728i	$0.0925676\pi$
$911$	4285.11	+	24302.1i	0.155842	+	0.883824i	−0.802170	+	0.597096i	$0.796321\pi$
$912$		0			0
$913$	−7602.19	+	2766.97i	−0.275570	+	0.100299i
$914$		0			0
$915$	−17871.7	−	16997.4i	−0.645707	−	0.614115i
$916$		0			0
$917$	−53148.6			−1.91398
$918$		0			0
$919$	29277.8			1.05091			0.525455	−	0.850821i	$-0.323895\pi$
$919$	29277.8			1.05091			0.525455	+	0.850821i	$0.323895\pi$
$920$		0			0
$921$	−2523.98	+	10462.0i	−0.0903017	+	0.374304i
$922$		0			0
$923$	34342.9	−	12499.8i	1.22471	−	0.445759i
$924$		0			0
$925$	6353.15	+	36030.5i	0.225827	+	1.28073i
$926$		0			0
$927$	9667.85	−	12770.6i	0.342539	−	0.452473i
$928$		0			0
$929$	−11416.7	−	4155.34i	−0.403197	−	0.146752i	0.132458	−	0.991189i	$-0.457713\pi$
$929$	−11416.7	−	4155.34i	−0.403197	−	0.146752i	−0.535655	+	0.844437i	$0.679935\pi$
$930$		0			0
$931$	63877.6	+	53599.7i	2.24866	+	1.88685i
$932$		0			0
$933$	−22459.2	−	9795.18i	−0.788084	−	0.343708i
$934$		0			0
$935$	11959.9	−	20715.1i	0.418321	−	0.724553i
$936$		0			0
$937$	−10654.1	−	18453.5i	−0.371457	−	0.643382i	0.618333	−	0.785916i	$-0.287808\pi$
$937$	−10654.1	−	18453.5i	−0.371457	−	0.643382i	−0.989790	+	0.142534i	$0.954475\pi$
$938$		0			0
$939$	−50448.1	−	3141.70i	−1.75326	−	0.109186i
$940$		0			0
$941$	649.886	−	3685.69i	0.0225140	−	0.127683i	−0.971479	−	0.237125i	$-0.923795\pi$
$941$	649.886	−	3685.69i	0.0225140	−	0.127683i	0.993993	+	0.109441i	$0.0349061\pi$
$942$		0			0
$943$	−30562.2	+	25644.8i	−1.05540	+	0.885587i
$944$		0			0
$945$	26644.0	+	5029.91i	0.917173	+	0.173146i
$946$		0			0
$947$	2488.09	−	2087.76i	0.0853771	−	0.0716399i	−0.599100	−	0.800674i	$-0.704475\pi$
$947$	2488.09	−	2087.76i	0.0853771	−	0.0716399i	0.684477	+	0.729034i	$0.260030\pi$
$948$		0			0
$949$	1942.88	−	11018.6i	0.0664578	−	0.376901i
$950$		0			0
$951$	18893.8	+	38000.6i	0.644241	+	1.29575i
$952$		0			0
$953$	−14268.4	−	24713.6i	−0.484993	−	0.840033i	0.514858	−	0.857275i	$-0.327845\pi$
$953$	−14268.4	−	24713.6i	−0.484993	−	0.840033i	−0.999851	+	0.0172426i	$0.994511\pi$
$954$		0			0
$955$	−10437.7	+	18078.6i	−0.353671	+	0.612577i
$956$		0			0
$957$	37954.5	−	28019.7i	1.28202	−	0.946447i
$958$		0			0
$959$	−46712.1	−	39196.1i	−1.57290	−	1.31982i
$960$		0			0
$961$	21728.3	+	7908.46i	0.729358	+	0.265465i
$962$		0			0
$963$	9766.36	−	6311.59i	0.326808	−	0.211203i
$964$		0			0
$965$	−868.419	−	4925.05i	−0.0289693	−	0.164293i
$966$		0			0
$967$	36140.3	−	13154.0i	1.20185	−	0.437439i	0.337984	−	0.941152i	$-0.390255\pi$
$967$	36140.3	−	13154.0i	1.20185	−	0.437439i	0.863871	+	0.503713i	$0.168033\pi$
$968$		0			0
$969$	−69620.5	+	20538.6i	−2.30808	+	0.680902i
$970$		0			0
$971$	−48761.8			−1.61158			−0.805788	−	0.592204i	$-0.798258\pi$
$971$	−48761.8			−1.61158			−0.805788	+	0.592204i	$0.798258\pi$
$972$		0			0
$973$	−31399.6			−1.03456
$974$		0			0
$975$	−22040.4	+	6502.09i	−0.723957	+	0.213573i
$976$		0			0
$977$	43731.3	−	15916.9i	1.43203	−	0.521215i	0.494515	−	0.869169i	$-0.335346\pi$
$977$	43731.3	−	15916.9i	1.43203	−	0.521215i	0.937511	+	0.347954i	$0.113124\pi$
$978$		0			0
$979$	4924.50	+	27928.2i	0.160764	+	0.911736i
$980$		0			0
$981$	−32122.1	+	20759.2i	−1.04544	+	0.675627i
$982$		0			0
$983$	−40.1606	−	14.6173i	−0.00130308	−	0.000474281i	0.341369	−	0.939930i	$-0.389110\pi$
$983$	−40.1606	−	14.6173i	−0.00130308	−	0.000474281i	−0.342672	+	0.939455i	$0.611332\pi$
$984$		0			0
$985$	−14456.6	−	12130.5i	−0.467639	−	0.392396i
$986$		0			0
$987$	3578.65	−	2641.93i	0.115410	−	0.0852010i
$988$		0			0
$989$	9613.45	−	16651.0i	0.309090	−	0.535360i
$990$		0			0
$991$	−2479.47	−	4294.57i	−0.0794782	−	0.137660i	0.823547	−	0.567248i	$-0.191992\pi$
$991$	−2479.47	−	4294.57i	−0.0794782	−	0.137660i	−0.903025	+	0.429588i	$0.858659\pi$
$992$		0			0
$993$	−13922.7	−	28002.4i	−0.444939	−	0.894893i
$994$		0			0
$995$	−448.098	+	2541.29i	−0.0142770	+	0.0809691i
$996$		0			0
$997$	21974.8	−	18439.1i	0.698043	−	0.585728i	−0.223173	−	0.974779i	$-0.571641\pi$
$997$	21974.8	−	18439.1i	0.698043	−	0.585728i	0.921216	+	0.389051i	$0.127197\pi$
$998$		0			0
$999$	19984.2	+	57036.0i	0.632905	+	1.80634i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.4.q.a.49.2	✓	78
27.16	even	9	inner	216.4.q.a.97.2	yes	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.4.q.a.49.2	✓	78	1.1	even	1	trivial
216.4.q.a.97.2	yes	78	27.16	even	9	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	216.q (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.98381 + 1.47026i) q^{3} +(-5.94819 + 2.16496i) q^{5} +(5.30186 + 30.0684i) q^{7} +(22.6767 - 14.6550i) q^{9} +O(q^{10})\)	\(q+(-4.98381 + 1.47026i) q^{3} +(-5.94819 + 2.16496i) q^{5} +(5.30186 + 30.0684i) q^{7} +(22.6767 - 14.6550i) q^{9} +(35.9740 + 13.0935i) q^{11} +(-39.8879 - 33.4700i) q^{13} +(26.4616 - 19.5352i) q^{15} +(-49.3543 + 85.4842i) q^{17} +(-70.7605 - 122.561i) q^{19} +(-70.6318 - 142.060i) q^{21} +(14.3133 - 81.1748i) q^{23} +(-65.0616 + 54.5932i) q^{25} +(-91.4695 + 106.378i) q^{27} +(-181.676 + 152.444i) q^{29} +(14.1800 - 80.4185i) q^{31} +(-198.538 - 12.3641i) q^{33} +(-96.6334 - 167.374i) q^{35} +(215.386 - 373.060i) q^{37} +(248.003 + 108.162i) q^{39} +(-370.779 - 311.121i) q^{41} +(219.192 + 79.7795i) q^{43} +(-103.158 + 136.265i) q^{45} +(4.86872 + 27.6119i) q^{47} +(-553.681 + 201.524i) q^{49} +(120.288 - 498.600i) q^{51} +124.874 q^{53} -242.327 q^{55} +(532.853 + 506.783i) q^{57} +(-199.436 + 72.5888i) q^{59} +(-130.212 - 738.470i) q^{61} +(560.880 + 604.151i) q^{63} +(309.722 + 112.730i) q^{65} +(112.474 + 94.3771i) q^{67} +(48.0134 + 425.604i) q^{69} +(-350.941 + 607.847i) q^{71} +(107.438 + 186.088i) q^{73} +(243.988 - 367.740i) q^{75} +(-202.970 + 1151.10i) q^{77} +(-311.546 + 261.418i) q^{79} +(299.462 - 664.653i) q^{81} +(-161.884 + 135.837i) q^{83} +(108.499 - 615.327i) q^{85} +(681.305 - 1026.86i) q^{87} +(370.390 + 641.534i) q^{89} +(794.906 - 1376.82i) q^{91} +(47.5661 + 421.639i) q^{93} +(686.236 + 575.821i) q^{95} +(-411.819 - 149.890i) q^{97} +(1007.65 - 230.282i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 33 q^{7} + 6 q^{9}+O(q^{10}) \) 78 * q + 33 * q^7 + 6 * q^9	\( 78 q + 33 q^{7} + 6 q^{9} + 51 q^{11} - 60 q^{13} - 183 q^{15} - 102 q^{17} + 171 q^{19} + 342 q^{21} + 456 q^{23} + 480 q^{25} + 189 q^{27} - 63 q^{29} + 621 q^{31} + 732 q^{33} + 630 q^{35} + 555 q^{37} + 597 q^{39} - 987 q^{41} + 552 q^{43} - 1311 q^{45} - 216 q^{47} - 1131 q^{49} - 288 q^{51} + 954 q^{53} - 54 q^{55} + 702 q^{57} + 1752 q^{59} - 654 q^{61} - 144 q^{63} + 126 q^{65} + 2277 q^{67} - 165 q^{69} + 684 q^{73} - 1167 q^{75} + 192 q^{77} - 2745 q^{79} - 3330 q^{81} - 3567 q^{83} - 3981 q^{85} - 108 q^{87} - 1314 q^{89} + 147 q^{91} - 2406 q^{93} + 1167 q^{95} + 2046 q^{97} - 5640 q^{99}+O(q^{100}) \) 78 * q + 33 * q^7 + 6 * q^9 + 51 * q^11 - 60 * q^13 - 183 * q^15 - 102 * q^17 + 171 * q^19 + 342 * q^21 + 456 * q^23 + 480 * q^25 + 189 * q^27 - 63 * q^29 + 621 * q^31 + 732 * q^33 + 630 * q^35 + 555 * q^37 + 597 * q^39 - 987 * q^41 + 552 * q^43 - 1311 * q^45 - 216 * q^47 - 1131 * q^49 - 288 * q^51 + 954 * q^53 - 54 * q^55 + 702 * q^57 + 1752 * q^59 - 654 * q^61 - 144 * q^63 + 126 * q^65 + 2277 * q^67 - 165 * q^69 + 684 * q^73 - 1167 * q^75 + 192 * q^77 - 2745 * q^79 - 3330 * q^81 - 3567 * q^83 - 3981 * q^85 - 108 * q^87 - 1314 * q^89 + 147 * q^91 - 2406 * q^93 + 1167 * q^95 + 2046 * q^97 - 5640 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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