LMFDB - Embedded newform 324.3.o.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,3,Mod(5,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([0, 23]))

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

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

chi := DirichletCharacter("324.5");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	324.o (of order $54$, degree $18$, 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:	$8.82836056527$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$18$ over $\Q(\zeta_{54})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{54}]$

Embedding invariants

Embedding label			5.1
Character	$\chi$	$=$	324.5
Dual form			324.3.o.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.85677 + 0.915910i) q^{3} +(-4.55987 + 3.39470i) q^{5} +(9.74231 - 6.40762i) q^{7} +(7.32222 - 5.23308i) q^{9} +O(q^{10})$	\(q+(-2.85677 + 0.915910i) q^{3} +(-4.55987 + 3.39470i) q^{5} +(9.74231 - 6.40762i) q^{7} +(7.32222 - 5.23308i) q^{9} +(0.713033 - 6.10039i) q^{11} +(4.08156 + 13.6334i) q^{13} +(9.91723 - 13.8743i) q^{15} +(-21.2831 - 3.75278i) q^{17} +(6.10801 + 34.6402i) q^{19} +(-21.9627 + 27.2281i) q^{21} +(-11.5087 + 17.4982i) q^{23} +(2.09835 - 7.00898i) q^{25} +(-16.1248 + 21.6562i) q^{27} +(4.94737 - 4.66760i) q^{29} +(-2.02555 + 34.7774i) q^{31} +(3.55044 + 18.0805i) q^{33} +(-22.6717 + 62.2901i) q^{35} +(14.3291 - 5.21535i) q^{37} +(-24.1470 - 35.2090i) q^{39} +(-0.792837 + 3.34524i) q^{41} +(-5.34616 - 12.3938i) q^{43} +(-15.6236 + 48.7188i) q^{45} +(29.6405 - 1.72636i) q^{47} +(34.4471 - 79.8574i) q^{49} +(64.2379 - 8.77257i) q^{51} +(58.2609 + 33.6369i) q^{53} +(17.4576 + 30.2375i) q^{55} +(-49.1765 - 93.3646i) q^{57} +(5.87325 + 50.2489i) q^{59} +(-19.7711 - 9.92944i) q^{61} +(37.8037 - 97.9003i) q^{63} +(-64.8925 - 48.3107i) q^{65} +(-72.8296 + 77.1949i) q^{67} +(16.8510 - 60.5292i) q^{69} +(-63.7955 + 76.0285i) q^{71} +(-40.8467 + 34.2745i) q^{73} +(0.425101 + 21.9449i) q^{75} +(-32.1424 - 64.0007i) q^{77} +(70.7096 - 16.7585i) q^{79} +(26.2297 - 76.6355i) q^{81} +(20.3016 + 85.6592i) q^{83} +(109.787 - 55.1373i) q^{85} +(-9.85837 + 17.8656i) q^{87} +(-17.1945 - 20.4917i) q^{89} +(127.121 + 106.667i) q^{91} +(-26.0664 - 101.206i) q^{93} +(-145.445 - 137.220i) q^{95} +(25.5532 - 34.3239i) q^{97} +(-26.7029 - 48.3997i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q+O(q^{10}) $ 324 * q	$ 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) $ 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{23}{54}\right)$

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
$3$	−2.85677	+	0.915910i	−0.952255	+	0.305303i
$3$	−2.85677	+	0.915910i	−0.952255	+	0.305303i
$4$		0			0
$5$	−4.55987	+	3.39470i	−0.911973	+	0.678939i	−0.947270	−	0.320438i	$-0.896170\pi$
$5$	−4.55987	+	3.39470i	−0.911973	+	0.678939i	0.0352962	+	0.999377i	$0.488763\pi$
$6$		0			0
$7$	9.74231	−	6.40762i	1.39176	−	0.915374i	0.391770	−	0.920063i	$-0.371863\pi$
$7$	9.74231	−	6.40762i	1.39176	−	0.915374i	0.999989	+	0.00468942i	$0.00149269\pi$
$8$		0			0
$9$	7.32222	−	5.23308i	0.813580	−	0.581454i
$10$		0			0
$11$	0.713033	−	6.10039i	0.0648212	−	0.554581i	−0.921336	−	0.388767i	$-0.872901\pi$
$11$	0.713033	−	6.10039i	0.0648212	−	0.554581i	0.986157	−	0.165813i	$-0.0530250\pi$
$12$		0			0
$13$	4.08156	+	13.6334i	0.313966	+	1.04872i	0.958725	+	0.284334i	$0.0917725\pi$
$13$	4.08156	+	13.6334i	0.313966	+	1.04872i	−0.644759	+	0.764386i	$0.723042\pi$
$14$		0			0
$15$	9.91723	−	13.8743i	0.661149	−	0.924952i
$16$		0			0
$17$	−21.2831	−	3.75278i	−1.25194	−	0.220752i	−0.491917	−	0.870642i	$-0.663704\pi$
$17$	−21.2831	−	3.75278i	−1.25194	−	0.220752i	−0.760028	+	0.649891i	$0.774815\pi$
$18$		0			0
$19$	6.10801	+	34.6402i	0.321474	+	1.82317i	0.533375	+	0.845879i	$0.320924\pi$
$19$	6.10801	+	34.6402i	0.321474	+	1.82317i	−0.211901	+	0.977291i	$0.567965\pi$
$20$		0			0
$21$	−21.9627	+	27.2281i	−1.04584	+	1.29658i
$22$		0			0
$23$	−11.5087	+	17.4982i	−0.500380	+	0.760791i	−0.994058	−	0.108854i	$-0.965282\pi$
$23$	−11.5087	+	17.4982i	−0.500380	+	0.760791i	0.493678	+	0.869645i	$0.335652\pi$
$24$		0			0
$25$	2.09835	−	7.00898i	0.0839340	−	0.280359i
$26$		0			0
$27$	−16.1248	+	21.6562i	−0.597216	+	0.802081i
$28$		0			0
$29$	4.94737	−	4.66760i	0.170599	−	0.160952i	−0.596207	−	0.802831i	$-0.703326\pi$
$29$	4.94737	−	4.66760i	0.170599	−	0.160952i	0.766806	+	0.641879i	$0.221845\pi$
$30$		0			0
$31$	−2.02555	+	34.7774i	−0.0653404	+	1.12185i	0.793152	+	0.609024i	$0.208439\pi$
$31$	−2.02555	+	34.7774i	−0.0653404	+	1.12185i	−0.858492	+	0.512827i	$0.828598\pi$
$32$		0			0
$33$	3.55044	+	18.0805i	0.107589	+	0.547893i
$34$		0			0
$35$	−22.6717	+	62.2901i	−0.647764	+	1.77972i
$36$		0			0
$37$	14.3291	−	5.21535i	0.387272	−	0.140955i	−0.141044	−	0.990003i	$-0.545046\pi$
$37$	14.3291	−	5.21535i	0.387272	−	0.140955i	0.528316	+	0.849048i	$0.322824\pi$
$38$		0			0
$39$	−24.1470	−	35.2090i	−0.619154	−	0.902794i
$40$		0			0
$41$	−0.792837	+	3.34524i	−0.0193375	+	0.0815913i	−0.981858	−	0.189617i	$-0.939275\pi$
$41$	−0.792837	+	3.34524i	−0.0193375	+	0.0815913i	0.962521	+	0.271209i	$0.0874234\pi$
$42$		0			0
$43$	−5.34616	−	12.3938i	−0.124329	−	0.288228i	0.844672	−	0.535285i	$-0.179796\pi$
$43$	−5.34616	−	12.3938i	−0.124329	−	0.288228i	−0.969001	+	0.247057i	$0.920536\pi$
$44$		0			0
$45$	−15.6236	+	48.7188i	−0.347191	+	1.08264i
$46$		0			0
$47$	29.6405	−	1.72636i	0.630648	−	0.0367311i	0.260156	−	0.965567i	$-0.416226\pi$
$47$	29.6405	−	1.72636i	0.630648	−	0.0367311i	0.370492	+	0.928836i	$0.379189\pi$
$48$		0			0
$49$	34.4471	−	79.8574i	0.703002	−	1.62974i
$50$		0			0
$51$	64.2379	−	8.77257i	1.25957	−	0.172011i
$52$		0			0
$53$	58.2609	+	33.6369i	1.09926	+	0.634659i	0.936027	−	0.351928i	$-0.114474\pi$
$53$	58.2609	+	33.6369i	1.09926	+	0.634659i	0.163235	+	0.986587i	$0.447807\pi$
$54$		0			0
$55$	17.4576	+	30.2375i	0.317411	+	0.549773i
$56$		0			0
$57$	−49.1765	−	93.3646i	−0.862746	−	1.63798i
$58$		0			0
$59$	5.87325	+	50.2489i	0.0995467	+	0.851676i	0.947094	+	0.320956i	$0.104004\pi$
$59$	5.87325	+	50.2489i	0.0995467	+	0.851676i	−0.847547	+	0.530720i	$0.821922\pi$
$60$		0			0
$61$	−19.7711	−	9.92944i	−0.324117	−	0.162778i	0.279299	−	0.960204i	$-0.409898\pi$
$61$	−19.7711	−	9.92944i	−0.324117	−	0.162778i	−0.603416	+	0.797426i	$0.706194\pi$
$62$		0			0
$63$	37.8037	−	97.9003i	0.600059	−	1.55397i
$64$		0			0
$65$	−64.8925	−	48.3107i	−0.998346	−	0.743241i
$66$		0			0
$67$	−72.8296	+	77.1949i	−1.08701	+	1.15216i	−0.0994298	+	0.995045i	$0.531702\pi$
$67$	−72.8296	+	77.1949i	−1.08701	+	1.15216i	−0.987580	+	0.157118i	$0.949780\pi$
$68$		0			0
$69$	16.8510	−	60.5292i	0.244217	−	0.877235i
$70$		0			0
$71$	−63.7955	+	76.0285i	−0.898528	+	1.07082i	0.0986029	+	0.995127i	$0.468563\pi$
$71$	−63.7955	+	76.0285i	−0.898528	+	1.07082i	−0.997131	+	0.0756971i	$0.975882\pi$
$72$		0			0
$73$	−40.8467	+	34.2745i	−0.559544	+	0.469514i	−0.878158	−	0.478371i	$-0.841227\pi$
$73$	−40.8467	+	34.2745i	−0.559544	+	0.469514i	0.318613	+	0.947885i	$0.396783\pi$
$74$		0			0
$75$	0.425101	+	21.9449i	0.00566802	+	0.292599i
$76$		0			0
$77$	−32.1424	−	64.0007i	−0.417433	−	0.831178i
$78$		0			0
$79$	70.7096	−	16.7585i	0.895059	−	0.212133i	0.242752	−	0.970088i	$-0.421950\pi$
$79$	70.7096	−	16.7585i	0.895059	−	0.212133i	0.652306	+	0.757955i	$0.273802\pi$
$80$		0			0
$81$	26.2297	−	76.6355i	0.323823	−	0.946118i
$82$		0			0
$83$	20.3016	+	85.6592i	0.244598	+	1.03204i	0.947248	+	0.320503i	$0.103852\pi$
$83$	20.3016	+	85.6592i	0.244598	+	1.03204i	−0.702650	+	0.711536i	$0.748000\pi$
$84$		0			0
$85$	109.787	−	55.1373i	1.29162	−	0.648674i
$86$		0			0
$87$	−9.85837	+	17.8656i	−0.113315	+	0.205352i
$88$		0			0
$89$	−17.1945	−	20.4917i	−0.193197	−	0.230243i	0.660746	−	0.750609i	$-0.270240\pi$
$89$	−17.1945	−	20.4917i	−0.193197	−	0.230243i	−0.853943	+	0.520366i	$0.825796\pi$
$90$		0			0
$91$	127.121	+	106.667i	1.39694	+	1.17217i
$92$		0			0
$93$	−26.0664	−	101.206i	−0.280284	−	1.08824i
$94$		0			0
$95$	−145.445	−	137.220i	−1.53100	−	1.44442i
$96$		0			0
$97$	25.5532	−	34.3239i	0.263435	−	0.353855i	−0.650650	−	0.759378i	$-0.725503\pi$
$97$	25.5532	−	34.3239i	0.263435	−	0.353855i	0.914085	+	0.405523i	$0.132911\pi$
$98$		0			0
$99$	−26.7029	−	48.3997i	−0.269726	−	0.488886i
$100$		0			0
$101$	−62.6480	+	124.742i	−0.620277	+	1.23507i	0.335793	+	0.941936i	$0.390996\pi$
$101$	−62.6480	+	124.742i	−0.620277	+	1.23507i	−0.956070	+	0.293138i	$0.905301\pi$
$102$		0			0
$103$	65.2925	−	7.63160i	0.633908	−	0.0740932i	0.206931	−	0.978356i	$-0.433653\pi$
$103$	65.2925	−	7.63160i	0.633908	−	0.0740932i	0.426977	+	0.904262i	$0.359578\pi$
$104$		0			0
$105$	7.71569	−	198.713i	0.0734828	−	1.89251i
$106$		0			0
$107$	181.287	−	104.666i	1.69427	−	0.978189i	0.743280	−	0.668981i	$-0.233269\pi$
$107$	181.287	−	104.666i	1.69427	−	0.978189i	0.950994	−	0.309209i	$-0.100064\pi$
$108$		0			0
$109$	20.8349	−	36.0872i	0.191146	−	0.331075i	−0.754484	−	0.656318i	$-0.772113\pi$
$109$	20.8349	−	36.0872i	0.191146	−	0.331075i	0.945630	+	0.325243i	$0.105446\pi$
$110$		0			0
$111$	−36.1580	+	28.0232i	−0.325747	+	0.252461i
$112$		0			0
$113$	−122.722	−	52.9372i	−1.08604	−	0.468471i	−0.223624	−	0.974676i	$-0.571789\pi$
$113$	−122.722	−	52.9372i	−1.08604	−	0.468471i	−0.862413	+	0.506205i	$0.831048\pi$
$114$		0			0
$115$	−6.92269	−	118.858i	−0.0601973	−	1.03355i
$116$		0			0
$117$	101.231	+	78.4673i	0.865219	+	0.670661i
$118$		0			0
$119$	−231.393	+	99.8130i	−1.94447	+	0.838765i
$120$		0			0
$121$	81.0321	+	19.2050i	0.669687	+	0.158719i
$122$		0			0
$123$	−0.798993	−	10.2827i	−0.00649588	−	0.0835995i
$124$		0			0
$125$	−34.3823	−	94.4646i	−0.275058	−	0.755717i
$126$		0			0
$127$	−94.9637	−	34.5640i	−0.747746	−	0.272157i	−0.0600888	−	0.998193i	$-0.519138\pi$
$127$	−94.9637	−	34.5640i	−0.747746	−	0.272157i	−0.687657	+	0.726036i	$0.741361\pi$
$128$		0			0
$129$	26.6243	+	30.5095i	0.206390	+	0.236508i
$130$		0			0
$131$	252.920	+	14.7309i	1.93068	+	0.112450i	0.980161	−	0.198204i	$-0.0635110\pi$
$131$	252.920	+	14.7309i	1.93068	+	0.112450i	0.950523	+	0.310654i	$0.100548\pi$
$132$		0			0
$133$	281.467	+	298.338i	2.11630	+	2.24314i
$134$		0			0
$135$	0.0108963	−	153.488i	8.07134e−5	−	1.13695i
$136$		0			0
$137$	10.5100	+	3.14647i	0.0767150	+	0.0229670i	0.324931	−	0.945738i	$-0.394659\pi$
$137$	10.5100	+	3.14647i	0.0767150	+	0.0229670i	−0.248216	+	0.968705i	$0.579844\pi$
$138$		0			0
$139$	−147.347	−	96.9117i	−1.06005	−	0.697206i	−0.105248	−	0.994446i	$-0.533564\pi$
$139$	−147.347	−	96.9117i	−1.06005	−	0.697206i	−0.954803	+	0.297240i	$0.903934\pi$
$140$		0			0
$141$	−83.0946	+	32.0798i	−0.589324	+	0.227516i
$142$		0			0
$143$	86.0791	−	15.1781i	0.601952	−	0.106140i
$144$		0			0
$145$	−6.71426	+	38.0785i	−0.0463052	+	0.262610i
$146$		0			0
$147$	−25.2651	+	259.684i	−0.171872	+	1.76656i
$148$		0			0
$149$	−145.353	+	43.5159i	−0.975525	+	0.292053i	−0.734607	−	0.678493i	$-0.762634\pi$
$149$	−145.353	+	43.5159i	−0.975525	+	0.292053i	−0.240918	+	0.970546i	$0.577448\pi$
$150$		0			0
$151$	242.653	+	28.3621i	1.60697	+	0.187828i	0.871734	−	0.489980i	$-0.162996\pi$
$151$	242.653	+	28.3621i	1.60697	+	0.187828i	0.735239	+	0.677808i	$0.237070\pi$
$152$		0			0
$153$	−175.478	+	83.8973i	−1.14691	+	0.548349i
$154$		0			0
$155$	−108.822	−	165.456i	−0.702080	−	1.06746i
$156$		0			0
$157$	−169.034	−	227.051i	−1.07665	−	1.44619i	−0.885508	−	0.464625i	$-0.846189\pi$
$157$	−169.034	−	227.051i	−1.07665	−	1.44619i	−0.191139	−	0.981563i	$-0.561218\pi$
$158$		0			0
$159$	−197.246	−	42.7311i	−1.24054	−	0.268749i
$160$		0			0
$161$			244.216i			1.51687i
$162$		0			0
$163$	−240.338			−1.47447			−0.737234	−	0.675637i	$-0.763869\pi$
$163$	−240.338			−1.47447			−0.737234	+	0.675637i	$0.763869\pi$
$164$		0			0
$165$	−77.5672	−	70.3918i	−0.470104	−	0.426617i
$166$		0			0
$167$	217.785	−	162.135i	1.30410	−	0.970868i	0.304269	−	0.952586i	$-0.401588\pi$
$167$	217.785	−	162.135i	1.30410	−	0.970868i	0.999833	−	0.0182817i	$-0.00581957\pi$
$168$		0			0
$169$	−28.0120	+	18.4238i	−0.165751	+	0.109016i
$170$		0			0
$171$	225.999	+	221.680i	1.32163	+	1.29637i
$172$		0			0
$173$	−32.6034	+	278.939i	−0.188459	+	1.61237i	0.485935	+	0.873995i	$0.338479\pi$
$173$	−32.6034	+	278.939i	−0.188459	+	1.61237i	−0.674394	+	0.738372i	$0.735595\pi$
$174$		0			0
$175$	−24.4681	−	81.7290i	−0.139818	−	0.467023i
$176$		0			0
$177$	−62.8020	−	138.170i	−0.354813	−	0.780621i
$178$		0			0
$179$	123.722	+	21.8155i	0.691183	+	0.121874i	0.508197	−	0.861241i	$-0.330312\pi$
$179$	123.722	+	21.8155i	0.691183	+	0.121874i	0.182987	+	0.983115i	$0.441423\pi$
$180$		0			0
$181$	−17.3397	−	98.3386i	−0.0957997	−	0.543307i	−0.994499	−	0.104743i	$-0.966598\pi$
$181$	−17.3397	−	98.3386i	−0.0957997	−	0.543307i	0.898700	−	0.438565i	$-0.144513\pi$
$182$		0			0
$183$	65.5760	+	10.2575i	0.358339	+	0.0560518i
$184$		0			0
$185$	−47.6341	+	72.4241i	−0.257481	+	0.391481i
$186$		0			0
$187$	−38.0689	+	127.159i	−0.203577	+	0.679995i
$188$		0			0
$189$	−18.3284	+	314.303i	−0.0969759	+	1.66298i
$190$		0			0
$191$	−2.52109	+	2.37852i	−0.0131994	+	0.0124530i	−0.692813	−	0.721117i	$-0.743629\pi$
$191$	−2.52109	+	2.37852i	−0.0131994	+	0.0124530i	0.679614	+	0.733570i	$0.262147\pi$
$192$		0			0
$193$	9.65273	−	165.731i	0.0500142	−	0.858710i	−0.876255	−	0.481848i	$-0.839966\pi$
$193$	9.65273	−	165.731i	0.0500142	−	0.858710i	0.926269	−	0.376862i	$-0.122997\pi$
$194$		0			0
$195$	229.631	+	78.5765i	1.17759	+	0.402957i
$196$		0			0
$197$	35.0480	−	96.2936i	0.177909	−	0.488800i	−0.818399	−	0.574650i	$-0.805138\pi$
$197$	35.0480	−	96.2936i	0.177909	−	0.488800i	0.996308	+	0.0858498i	$0.0273605\pi$
$198$		0			0
$199$	30.5394	−	11.1154i	0.153464	−	0.0558564i	−0.264146	−	0.964483i	$-0.585090\pi$
$199$	30.5394	−	11.1154i	0.153464	−	0.0558564i	0.417610	+	0.908626i	$0.362868\pi$
$200$		0			0
$201$	137.354	−	287.233i	0.683351	−	1.42902i
$202$		0			0
$203$	18.2906	−	77.1741i	0.0901014	−	0.380168i
$204$		0			0
$205$	−7.74085	−	17.9453i	−0.0377602	−	0.0875381i
$206$		0			0
$207$	7.29998	+	188.352i	0.0352656	+	0.909912i
$208$		0			0
$209$	215.674	−	12.5616i	1.03193	−	0.0601033i
$210$		0			0
$211$	−77.0783	+	178.688i	−0.365300	+	0.846861i	0.632106	+	0.774882i	$0.282191\pi$
$211$	−77.0783	+	178.688i	−0.365300	+	0.846861i	−0.997406	+	0.0719788i	$0.977069\pi$
$212$		0			0
$213$	112.613	−	275.627i	0.528702	−	1.29402i
$214$		0			0
$215$	66.4509	+	38.3654i	0.309074	+	0.178444i
$216$		0			0
$217$	203.107	+	351.791i	0.935975	+	1.62116i
$218$		0			0
$219$	85.2972	−	135.326i	0.389485	−	0.617928i
$220$		0			0
$221$	−35.7051	−	305.477i	−0.161562	−	1.38225i
$222$		0			0
$223$	−112.471	−	56.4849i	−0.504353	−	0.253295i	0.178383	−	0.983961i	$-0.442914\pi$
$223$	−112.471	−	56.4849i	−0.504353	−	0.253295i	−0.682735	+	0.730666i	$0.739210\pi$
$224$		0			0
$225$	−21.3140	−	62.3021i	−0.0947288	−	0.276898i
$226$		0			0
$227$	−354.671	−	264.043i	−1.56243	−	1.16319i	−0.916671	−	0.399643i	$-0.869134\pi$
$227$	−354.671	−	264.043i	−1.56243	−	1.16319i	−0.645758	−	0.763542i	$-0.723458\pi$
$228$		0			0
$229$	−69.5855	+	73.7563i	−0.303867	+	0.322080i	−0.861256	−	0.508171i	$-0.830322\pi$
$229$	−69.5855	+	73.7563i	−0.303867	+	0.322080i	0.557389	+	0.830251i	$0.311803\pi$
$230$		0			0
$231$	150.442	+	153.396i	0.651265	+	0.664050i
$232$		0			0
$233$	−63.5879	+	75.7811i	−0.272909	+	0.325241i	−0.885039	−	0.465517i	$-0.845869\pi$
$233$	−63.5879	+	75.7811i	−0.272909	+	0.325241i	0.612130	+	0.790757i	$0.290313\pi$
$234$		0			0
$235$	−129.296	+	108.492i	−0.550196	+	0.461669i
$236$		0			0
$237$	−186.652	+	112.639i	−0.787559	+	0.475269i
$238$		0			0
$239$	6.13576	+	12.2173i	0.0256726	+	0.0511184i	0.906103	−	0.423056i	$-0.139043\pi$
$239$	6.13576	+	12.2173i	0.0256726	+	0.0511184i	−0.880431	+	0.474175i	$0.842746\pi$
$240$		0			0
$241$	96.4899	−	22.8685i	0.400373	−	0.0948902i	−0.0254961	−	0.999675i	$-0.508117\pi$
$241$	96.4899	−	22.8685i	0.400373	−	0.0948902i	0.425869	+	0.904785i	$0.359968\pi$
$242$		0			0
$243$	−4.74084	+	242.954i	−0.0195096	+	0.999810i
$244$		0			0
$245$	114.017	+	481.077i	0.465377	+	1.96358i
$246$		0			0
$247$	−447.333	+	224.659i	−1.81106	+	0.909550i
$248$		0			0
$249$	−136.453	−	226.114i	−0.548004	−	0.908087i
$250$		0			0
$251$	157.220	+	187.368i	0.626375	+	0.746485i	0.982153	−	0.188086i	$-0.0602283\pi$
$251$	157.220	+	187.368i	0.626375	+	0.746485i	−0.355777	+	0.934571i	$0.615784\pi$
$252$		0			0
$253$	98.5397	+	82.6846i	0.389485	+	0.326817i
$254$		0			0
$255$	−263.136	+	258.070i	−1.03191	+	1.01204i
$256$		0			0
$257$	256.249	+	241.758i	0.997076	+	0.940693i	0.998240	−	0.0593067i	$-0.0188890\pi$
$257$	256.249	+	241.758i	0.997076	+	0.940693i	−0.00116387	+	0.999999i	$0.500370\pi$
$258$		0			0
$259$	106.180	−	142.625i	0.409962	−	0.550674i
$260$		0			0
$261$	11.7998	−	60.0672i	0.0452098	−	0.230142i
$262$		0			0
$263$	−196.319	+	390.904i	−0.746461	+	1.48633i	0.123043	+	0.992401i	$0.460735\pi$
$263$	−196.319	+	390.904i	−0.746461	+	1.48633i	−0.869504	+	0.493925i	$0.835562\pi$
$264$		0			0
$265$	−379.849	+	44.3980i	−1.43339	+	0.167540i
$266$		0			0
$267$	67.8893	+	42.7912i	0.254267	+	0.160267i
$268$		0			0
$269$	166.520	−	96.1402i	0.619033	−	0.357399i	−0.157460	−	0.987525i	$-0.550330\pi$
$269$	166.520	−	96.1402i	0.619033	−	0.357399i	0.776492	+	0.630127i	$0.216997\pi$
$270$		0			0
$271$	−60.1759	+	104.228i	−0.222051	+	0.384604i	−0.955431	−	0.295215i	$-0.904609\pi$
$271$	−60.1759	+	104.228i	−0.222051	+	0.384604i	0.733379	+	0.679820i	$0.237942\pi$
$272$		0			0
$273$	−460.853	−	188.292i	−1.68811	−	0.689714i
$274$		0			0
$275$	−41.2613	−	17.7984i	−0.150041	−	0.0647214i
$276$		0			0
$277$	−13.4243	−	230.487i	−0.0484633	−	0.832082i	−0.931717	−	0.363186i	$-0.881689\pi$
$277$	−13.4243	−	230.487i	−0.0484633	−	0.832082i	0.883253	−	0.468896i	$-0.155348\pi$
$278$		0			0
$279$	167.161	+	265.247i	0.599145	+	0.950707i
$280$		0			0
$281$	245.678	−	105.975i	0.874300	−	0.377136i	0.0888383	−	0.996046i	$-0.471685\pi$
$281$	245.678	−	105.975i	0.874300	−	0.377136i	0.785462	+	0.618910i	$0.212425\pi$
$282$		0			0
$283$	−15.5619	−	3.68823i	−0.0549889	−	0.0130326i	0.203029	−	0.979173i	$-0.434921\pi$
$283$	−15.5619	−	3.68823i	−0.0549889	−	0.0130326i	−0.258018	+	0.966140i	$0.583069\pi$
$284$		0			0
$285$	541.183	+	258.791i	1.89889	+	0.908039i
$286$		0			0
$287$	13.7110	+	37.6706i	0.0477734	+	0.131256i
$288$		0			0
$289$	167.314	+	60.8974i	0.578942	+	0.210717i
$290$		0			0
$291$	−41.5619	+	121.460i	−0.142824	+	0.417388i
$292$		0			0
$293$	−509.342	−	29.6658i	−1.73837	−	0.101248i	−0.840584	−	0.541681i	$-0.817788\pi$
$293$	−509.342	−	29.6658i	−1.73837	−	0.101248i	−0.897786	+	0.440433i	$0.854825\pi$
$294$		0			0
$295$	−197.361	−	209.190i	−0.669020	−	0.709120i
$296$		0			0
$297$	120.614	+	113.809i	0.406106	+	0.383196i
$298$		0			0
$299$	−285.533	−	85.4829i	−0.954959	−	0.285896i
$300$		0			0
$301$	−131.499	−	86.4880i	−0.436872	−	0.287335i
$302$		0			0
$303$	64.7177	−	413.740i	0.213590	−	1.36548i
$304$		0			0
$305$	123.861	−	21.8401i	0.406102	−	0.0716068i
$306$		0			0
$307$	−11.0876	+	62.8808i	−0.0361159	+	0.204823i	−0.997526	−	0.0702950i	$-0.977606\pi$
$307$	−11.0876	+	62.8808i	−0.0361159	+	0.204823i	0.961410	+	0.275118i	$0.0887171\pi$
$308$		0			0
$309$	−179.535	+	81.6038i	−0.581021	+	0.264090i
$310$		0			0
$311$	540.937	−	161.946i	1.73935	−	0.520726i	0.749393	−	0.662125i	$-0.230345\pi$
$311$	540.937	−	161.946i	1.73935	−	0.520726i	0.989953	+	0.141399i	$0.0451600\pi$
$312$		0			0
$313$	−127.811	−	14.9390i	−0.408343	−	0.0477285i	−0.0905580	−	0.995891i	$-0.528865\pi$
$313$	−127.811	−	14.9390i	−0.408343	−	0.0477285i	−0.317785	+	0.948163i	$0.602939\pi$
$314$		0			0
$315$	159.962	+	574.744i	0.507815	+	1.82458i
$316$		0			0
$317$	−170.224	−	258.812i	−0.536983	−	0.816443i	0.460477	−	0.887672i	$-0.347678\pi$
$317$	−170.224	−	258.812i	−0.536983	−	0.816443i	−0.997460	+	0.0712288i	$0.977308\pi$
$318$		0			0
$319$	−24.9466	−	33.5090i	−0.0782024	−	0.105044i
$320$		0			0
$321$	−422.030	+	465.050i	−1.31474	+	1.44875i
$322$		0			0
$323$		−	760.172i		−	2.35347i
$324$		0			0
$325$	104.120			0.320371
$326$		0			0
$327$	−26.4679	+	122.175i	−0.0809416	+	0.373625i
$328$		0			0
$329$	277.705	−	206.743i	0.844087	−	0.628399i
$330$		0			0
$331$	208.163	−	136.911i	0.628891	−	0.413628i	−0.194660	−	0.980871i	$-0.562360\pi$
$331$	208.163	−	136.911i	0.628891	−	0.413628i	0.823551	+	0.567243i	$0.191990\pi$
$332$		0			0
$333$	77.6281	−	113.173i	0.233117	−	0.339859i
$334$		0			0
$335$	70.0403	−	599.233i	0.209075	−	1.78876i
$336$		0			0
$337$	−22.4371	−	74.9452i	−0.0665790	−	0.222389i	0.918225	−	0.396059i	$-0.129623\pi$
$337$	−22.4371	−	74.9452i	−0.0665790	−	0.222389i	−0.984804	+	0.173670i	$0.944437\pi$
$338$		0			0
$339$	399.074	+	38.8266i	1.17721	+	0.114533i
$340$		0			0
$341$	210.711	+	37.1541i	0.617922	+	0.108956i
$342$		0			0
$343$	−76.8837	−	436.029i	−0.224151	−	1.27122i
$344$		0			0
$345$	128.640	+	333.209i	0.372869	+	0.965823i
$346$		0			0
$347$	85.9382	−	130.663i	0.247660	−	0.376549i	−0.690168	−	0.723649i	$-0.742463\pi$
$347$	85.9382	−	130.663i	0.247660	−	0.376549i	0.937828	+	0.347100i	$0.112834\pi$
$348$		0			0
$349$	142.642	−	476.457i	0.408716	−	1.36521i	−0.467800	−	0.883834i	$-0.654953\pi$
$349$	142.642	−	476.457i	0.408716	−	1.36521i	0.876516	−	0.481372i	$-0.159861\pi$
$350$		0			0
$351$	−361.061	−	131.444i	−1.02866	−	0.374486i
$352$		0			0
$353$	83.6354	−	78.9059i	0.236927	−	0.223529i	−0.558615	−	0.829427i	$-0.688667\pi$
$353$	83.6354	−	78.9059i	0.236927	−	0.223529i	0.795543	+	0.605897i	$0.207186\pi$
$354$		0			0
$355$	32.8053	−	563.246i	0.0924094	−	1.58661i
$356$		0			0
$357$	569.614	−	497.077i	1.59556	−	1.39237i
$358$		0			0
$359$	−40.0128	+	109.934i	−0.111456	+	0.306224i	−0.982863	−	0.184338i	$-0.940986\pi$
$359$	−40.0128	+	109.934i	−0.111456	+	0.306224i	0.871407	+	0.490561i	$0.163208\pi$
$360$		0			0
$361$	−823.409	+	299.696i	−2.28091	+	0.830184i
$362$		0			0
$363$	−249.080	+	19.3541i	−0.686170	+	0.0533170i
$364$		0			0
$365$	69.9043	−	294.949i	0.191519	−	0.808080i
$366$		0			0
$367$	−84.6431	−	196.225i	−0.230635	−	0.534672i	0.763120	−	0.646257i	$-0.223667\pi$
$367$	−84.6431	−	196.225i	−0.230635	−	0.534672i	−0.993755	+	0.111585i	$0.964407\pi$
$368$		0			0
$369$	11.7006	+	28.6436i	0.0317090	+	0.0776249i
$370$		0			0
$371$	783.128	−	45.6120i	2.11086	−	0.122943i
$372$		0			0
$373$	88.1077	−	204.257i	0.236214	−	0.547605i	−0.758337	−	0.651863i	$-0.773988\pi$
$373$	88.1077	−	204.257i	0.236214	−	0.547605i	0.994550	+	0.104258i	$0.0332469\pi$
$374$		0			0
$375$	184.743	+	238.372i	0.492649	+	0.635659i
$376$		0			0
$377$	83.8281	+	48.3982i	0.222356	+	0.128377i
$378$		0			0
$379$	289.707	+	501.788i	0.764399	+	1.32398i	0.940564	+	0.339618i	$0.110298\pi$
$379$	289.707	+	501.788i	0.764399	+	1.32398i	−0.176164	+	0.984361i	$0.556369\pi$
$380$		0			0
$381$	302.946	+	11.7629i	0.795135	+	0.0308737i
$382$		0			0
$383$	−73.9675	−	632.833i	−0.193127	−	1.65230i	−0.647920	−	0.761708i	$-0.724361\pi$
$383$	−73.9675	−	632.833i	−0.193127	−	1.65230i	0.454794	−	0.890597i	$-0.349713\pi$
$384$		0			0
$385$	363.828	+	182.721i	0.945008	+	0.474601i
$386$		0			0
$387$	−104.003	−	62.7731i	−0.268743	−	0.162204i
$388$		0			0
$389$	−78.9710	−	58.7917i	−0.203010	−	0.151136i	0.490853	−	0.871243i	$-0.336685\pi$
$389$	−78.9710	−	58.7917i	−0.203010	−	0.151136i	−0.693863	+	0.720107i	$0.744093\pi$
$390$		0			0
$391$	310.608	−	329.225i	0.794394	−	0.842008i
$392$		0			0
$393$	−736.024	+	189.569i	−1.87283	+	0.482364i
$394$		0			0
$395$	−265.537	+	316.454i	−0.672244	+	0.801150i
$396$		0			0
$397$	−349.614	+	293.361i	−0.880640	+	0.738945i	−0.966311	−	0.257379i	$-0.917141\pi$
$397$	−349.614	+	293.361i	−0.880640	+	0.738945i	0.0856707	+	0.996324i	$0.472697\pi$
$398$		0			0
$399$	−1077.34	−	594.483i	−2.70009	−	1.48993i
$400$		0			0
$401$	69.8376	+	139.058i	0.174159	+	0.346778i	0.963729	−	0.266881i	$-0.0859931\pi$
$401$	69.8376	+	139.058i	0.174159	+	0.346778i	−0.789571	+	0.613659i	$0.789697\pi$
$402$		0			0
$403$	−482.400	+	114.331i	−1.19702	+	0.283700i
$404$		0			0
$405$	140.550	+	438.490i	0.347038	+	1.08269i
$406$		0			0
$407$	−21.5986	−	91.1315i	−0.0530677	−	0.223910i
$408$		0			0
$409$	415.908	−	208.877i	1.01689	−	0.510701i	0.139370	−	0.990240i	$-0.455492\pi$
$409$	415.908	−	208.877i	1.01689	−	0.510701i	0.877521	+	0.479539i	$0.159196\pi$
$410$		0			0
$411$	−32.9064	+	0.637439i	−0.0800642	+	0.00155095i
$412$		0			0
$413$	379.195	+	451.907i	0.918147	+	1.09421i
$414$		0			0
$415$	−383.359	−	321.677i	−0.923758	−	0.775125i
$416$		0			0
$417$	509.698	+	141.897i	1.22230	+	0.340281i
$418$		0			0
$419$	188.971	+	178.285i	0.451005	+	0.425501i	0.877932	−	0.478785i	$-0.158922\pi$
$419$	188.971	+	178.285i	0.451005	+	0.425501i	−0.426927	+	0.904286i	$0.640404\pi$
$420$		0			0
$421$	102.618	−	137.840i	0.243748	−	0.327410i	−0.663366	−	0.748295i	$-0.730873\pi$
$421$	102.618	−	137.840i	0.243748	−	0.327410i	0.907114	+	0.420885i	$0.138280\pi$
$422$		0			0
$423$	208.000	−	167.752i	0.491725	−	0.396576i
$424$		0			0
$425$	−70.9624	+	141.298i	−0.166970	+	0.332465i
$426$		0			0
$427$	−256.241	+	29.9502i	−0.600095	+	0.0701411i
$428$		0			0
$429$	−232.006	+	122.201i	−0.540807	+	0.284851i
$430$		0			0
$431$	−85.6611	+	49.4564i	−0.198750	+	0.114748i	−0.596072	−	0.802931i	$-0.703273\pi$
$431$	−85.6611	+	49.4564i	−0.198750	+	0.114748i	0.397323	+	0.917679i	$0.369939\pi$
$432$		0			0
$433$	366.778	−	635.278i	0.847062	−	1.46715i	−0.0367569	−	0.999324i	$-0.511703\pi$
$433$	366.778	−	635.278i	0.847062	−	1.46715i	0.883819	−	0.467830i	$-0.154964\pi$
$434$		0			0
$435$	−15.6954	−	114.931i	−0.0360814	−	0.264209i
$436$		0			0
$437$	−676.437	−	291.786i	−1.54791	−	0.667703i
$438$		0			0
$439$	17.3442	+	297.789i	0.0395085	+	0.678335i	0.958682	+	0.284481i	$0.0918214\pi$
$439$	17.3442	+	297.789i	0.0395085	+	0.678335i	−0.919173	+	0.393854i	$0.871142\pi$
$440$		0			0
$441$	−165.671	−	764.998i	−0.375671	−	1.73469i
$442$		0			0
$443$	246.735	−	106.431i	0.556964	−	0.240251i	−0.0989420	−	0.995093i	$-0.531546\pi$
$443$	246.735	−	106.431i	0.556964	−	0.240251i	0.655906	+	0.754842i	$0.272287\pi$
$444$		0			0
$445$	147.968	+	35.0690i	0.332512	+	0.0788068i
$446$		0			0
$447$	375.383	−	257.445i	0.839784	−	0.575940i
$448$		0			0
$449$	116.174	+	319.185i	0.258739	+	0.710881i	0.999246	+	0.0388313i	$0.0123635\pi$
$449$	116.174	+	319.185i	0.258739	+	0.710881i	−0.740506	+	0.672049i	$0.765414\pi$
$450$		0			0
$451$	19.8420	+	7.22189i	0.0439955	+	0.0160131i
$452$		0			0
$453$	−719.179	+	141.225i	−1.58759	+	0.311754i
$454$		0			0
$455$	−941.759	−	54.8512i	−2.06980	−	0.120552i
$456$		0			0
$457$	230.720	+	244.549i	0.504858	+	0.535118i	0.928805	−	0.370569i	$-0.120837\pi$
$457$	230.720	+	244.549i	0.504858	+	0.535118i	−0.423947	+	0.905687i	$0.639356\pi$
$458$		0			0
$459$	424.456	−	400.397i	0.924741	−	0.872324i
$460$		0			0
$461$	−547.795	−	163.999i	−1.18827	−	0.355746i	−0.369154	−	0.929368i	$-0.620353\pi$
$461$	−547.795	−	163.999i	−1.18827	−	0.355746i	−0.819120	+	0.573622i	$0.805538\pi$
$462$		0			0
$463$	−468.978	−	308.451i	−1.01291	−	0.666202i	−0.0694153	−	0.997588i	$-0.522113\pi$
$463$	−468.978	−	308.451i	−1.01291	−	0.666202i	−0.943495	+	0.331386i	$0.892484\pi$
$464$		0			0
$465$	462.423	+	372.998i	0.994458	+	0.802147i
$466$		0			0
$467$	858.425	−	151.363i	1.83817	−	0.324119i	0.856711	−	0.515797i	$-0.172504\pi$
$467$	858.425	−	151.363i	1.83817	−	0.324119i	0.981458	+	0.191678i	$0.0613930\pi$
$468$		0			0
$469$	−214.893	+	1218.72i	−0.458195	+	2.59855i
$470$		0			0
$471$	690.848	+	493.813i	1.46677	+	1.04844i
$472$		0			0
$473$	−79.4189	+	23.7765i	−0.167905	+	0.0502674i
$474$		0			0
$475$	255.609	+	29.8764i	0.538125	+	0.0628978i
$476$		0			0
$477$	602.624	−	58.5871i	1.26336	−	0.122824i
$478$		0			0
$479$	22.1952	+	33.7461i	0.0463365	+	0.0704512i	0.857913	−	0.513795i	$-0.171761\pi$
$479$	22.1952	+	33.7461i	0.0463365	+	0.0704512i	−0.811577	+	0.584246i	$0.801390\pi$
$480$		0			0
$481$	129.588	+	174.066i	0.269413	+	0.361884i
$482$		0			0
$483$	−223.680	−	697.669i	−0.463106	−	1.44445i
$484$		0			0
$485$			243.258i			0.501562i
$486$		0			0
$487$	−31.4352			−0.0645487			−0.0322743	−	0.999479i	$-0.510275\pi$
$487$	−31.4352			−0.0645487			−0.0322743	+	0.999479i	$0.510275\pi$
$488$		0			0
$489$	686.590	−	220.128i	1.40407	−	0.450160i
$490$		0			0
$491$	−331.401	+	246.719i	−0.674951	+	0.502482i	−0.879210	−	0.476434i	$-0.841929\pi$
$491$	−331.401	+	246.719i	−0.674951	+	0.502482i	0.204259	+	0.978917i	$0.434522\pi$
$492$		0			0
$493$	−122.812	+	80.7745i	−0.249111	+	0.163843i
$494$		0			0
$495$	286.064	+	130.048i	0.577907	+	0.262724i
$496$		0			0
$497$	−134.354	+	1149.47i	−0.270330	+	2.31282i
$498$		0			0
$499$	241.974	+	808.249i	0.484917	+	1.61974i	0.754178	+	0.656670i	$0.228035\pi$
$499$	241.974	+	808.249i	0.484917	+	1.61974i	−0.269261	+	0.963067i	$0.586779\pi$
$500$		0			0
$501$	−473.660	+	662.653i	−0.945428	+	1.32266i
$502$		0			0
$503$	−253.898	−	44.7690i	−0.504767	−	0.0890040i	−0.0845346	−	0.996421i	$-0.526940\pi$
$503$	−253.898	−	44.7690i	−0.504767	−	0.0890040i	−0.420232	+	0.907416i	$0.638051\pi$
$504$		0			0
$505$	−137.796	−	781.480i	−0.272863	−	1.54748i
$506$		0			0
$507$	63.1491	−	78.2889i	0.124555	−	0.154416i
$508$		0			0
$509$	−12.7762	+	19.4252i	−0.0251005	+	0.0381634i	−0.847820	−	0.530284i	$-0.822085\pi$
$509$	−12.7762	+	19.4252i	−0.0251005	+	0.0381634i	0.822720	+	0.568447i	$0.192456\pi$
$510$		0			0
$511$	−178.324	+	595.643i	−0.348970	+	1.16564i
$512$		0			0
$513$	−848.666	−	426.291i	−1.65432	−	0.830977i
$514$		0			0
$515$	−271.818	+	256.447i	−0.527802	+	0.497956i
$516$		0			0
$517$	10.6032	−	182.049i	0.0205090	−	0.352126i
$518$		0			0
$519$	−162.343	−	826.726i	−0.312800	−	1.59292i
$520$		0			0
$521$	−62.8514	+	172.683i	−0.120636	+	0.331445i	−0.985282	−	0.170937i	$-0.945321\pi$
$521$	−62.8514	+	172.683i	−0.120636	+	0.331445i	0.864646	+	0.502382i	$0.167543\pi$
$522$		0			0
$523$	−671.395	+	244.368i	−1.28374	+	0.467242i	−0.891667	−	0.452693i	$-0.850463\pi$
$523$	−671.395	+	244.368i	−1.28374	+	0.467242i	−0.392071	+	0.919935i	$0.628241\pi$
$524$		0			0
$525$	144.756	+	211.070i	0.275726	+	0.402038i
$526$		0			0
$527$	173.622	−	732.568i	0.329453	−	1.39007i
$528$		0			0
$529$	35.7907	+	82.9721i	0.0676573	+	0.156847i
$530$		0			0
$531$	305.962	+	337.198i	0.576199	+	0.635025i
$532$		0			0
$533$	−48.8429	+	2.84478i	−0.0916378	+	0.00533729i
$534$		0			0
$535$	−471.336	+	1092.68i	−0.881002	+	2.04239i
$536$		0			0
$537$	−373.425	+	50.9964i	−0.695392	+	0.0949653i
$538$		0			0
$539$	−462.599	−	267.082i	−0.858255	−	0.495514i
$540$		0			0
$541$	225.360	+	390.335i	0.416561	+	0.721506i	0.995591	−	0.0938010i	$-0.0299017\pi$
$541$	225.360	+	390.335i	0.416561	+	0.721506i	−0.579030	+	0.815307i	$0.696568\pi$
$542$		0			0
$543$	139.605	+	265.049i	0.257099	+	0.488119i
$544$		0			0
$545$	27.5004	+	235.281i	0.0504594	+	0.431708i
$546$		0			0
$547$	−733.120	−	368.187i	−1.34026	−	0.673102i	−0.373221	−	0.927743i	$-0.621747\pi$
$547$	−733.120	−	368.187i	−1.34026	−	0.673102i	−0.967036	+	0.254640i	$0.918043\pi$
$548$		0			0
$549$	−196.730	+	30.7585i	−0.358343	+	0.0560264i
$550$		0			0
$551$	191.905	+	142.868i	0.348286	+	0.259289i
$552$		0			0
$553$	581.493	−	616.347i	1.05152	−	1.11455i
$554$		0			0
$555$	69.7454	−	250.527i	0.125667	−	0.451400i
$556$		0			0
$557$	431.034	−	513.686i	0.773848	−	0.922237i	−0.224790	−	0.974407i	$-0.572170\pi$
$557$	431.034	−	513.686i	0.773848	−	0.922237i	0.998638	+	0.0521707i	$0.0166140\pi$
$558$		0			0
$559$	147.148	−	123.472i	0.263235	−	0.220880i
$560$		0			0
$561$	−7.71233	−	398.131i	−0.0137475	−	0.709682i
$562$		0			0
$563$	322.900	+	642.947i	0.573535	+	1.14200i	0.974181	+	0.225769i	$0.0724896\pi$
$563$	322.900	+	642.947i	0.573535	+	1.14200i	−0.400646	+	0.916233i	$0.631214\pi$
$564$		0			0
$565$	739.303	−	175.218i	1.30850	−	0.310120i
$566$		0			0
$567$	−235.513	−	914.677i	−0.415367	−	1.61319i
$568$		0			0
$569$	180.519	+	761.670i	0.317257	+	1.33861i	0.864918	+	0.501912i	$0.167370\pi$
$569$	180.519	+	761.670i	0.317257	+	1.33861i	−0.547661	+	0.836700i	$0.684482\pi$
$570$		0			0
$571$	946.211	−	475.205i	1.65711	−	0.832233i	0.660426	−	0.750891i	$-0.270376\pi$
$571$	946.211	−	475.205i	1.65711	−	0.832233i	0.996686	−	0.0813421i	$-0.0259206\pi$
$572$		0			0
$573$	5.02364	−	9.10398i	0.00876726	−	0.0158883i
$574$		0			0
$575$	98.4950	+	117.382i	0.171296	+	0.204142i
$576$		0			0
$577$	636.586	+	534.159i	1.10327	+	0.925752i	0.997641	−	0.0686535i	$-0.0218703\pi$
$577$	636.586	+	534.159i	1.10327	+	0.925752i	0.105628	+	0.994406i	$0.466315\pi$
$578$		0			0
$579$	124.219	+	482.296i	0.214541	+	0.832981i
$580$		0			0
$581$	746.656	+	704.433i	1.28512	+	1.21245i
$582$		0			0
$583$	246.740	−	331.430i	0.423225	−	0.568490i
$584$		0			0
$585$	−727.970	−	14.1534i	−1.24439	−	0.0241939i
$586$		0			0
$587$	−54.2594	+	108.039i	−0.0924350	+	0.184053i	−0.935099	−	0.354386i	$-0.884690\pi$
$587$	−54.2594	+	108.039i	−0.0924350	+	0.184053i	0.842664	+	0.538440i	$0.180986\pi$
$588$		0			0
$589$	−1217.07	+	142.255i	−2.06633	+	0.241519i
$590$		0			0
$591$	−11.9276	+	307.189i	−0.0201821	+	0.519778i
$592$		0			0
$593$	313.520	−	181.011i	0.528702	−	0.305246i	−0.211786	−	0.977316i	$-0.567928\pi$
$593$	313.520	−	181.011i	0.528702	−	0.305246i	0.740488	+	0.672070i	$0.234595\pi$
$594$		0			0
$595$	716.284	−	1240.64i	1.20384	−	2.08511i
$596$		0			0
$597$	−77.0631	+	59.7255i	−0.129084	+	0.100043i
$598$		0			0
$599$	−356.686	−	153.859i	−0.595469	−	0.256860i	0.0769452	−	0.997035i	$-0.475483\pi$
$599$	−356.686	−	153.859i	−0.595469	−	0.256860i	−0.672414	+	0.740175i	$0.734743\pi$
$600$		0			0
$601$	15.2482	+	261.801i	0.0253714	+	0.435610i	0.986945	+	0.161061i	$0.0514915\pi$
$601$	15.2482	+	261.801i	0.0253714	+	0.435610i	−0.961573	+	0.274549i	$0.911471\pi$
$602$		0			0
$603$	−129.307	+	946.361i	−0.214440	+	1.56942i
$604$		0			0
$605$	−434.690	+	187.507i	−0.718497	+	0.309929i
$606$		0			0
$607$	−83.7301	−	19.8444i	−0.137941	−	0.0326926i	0.161065	−	0.986944i	$-0.448507\pi$
$607$	−83.7301	−	19.8444i	−0.137941	−	0.0326926i	−0.299006	+	0.954251i	$0.596655\pi$
$608$		0			0
$609$	18.4326	+	237.221i	0.0302670	+	0.389525i
$610$		0			0
$611$	144.515	+	397.053i	0.236523	+	0.649841i
$612$		0			0
$613$	12.8212	+	4.66653i	0.0209155	+	0.00761261i	0.352457	−	0.935828i	$-0.385346\pi$
$613$	12.8212	+	4.66653i	0.0209155	+	0.00761261i	−0.331541	+	0.943441i	$0.607569\pi$
$614$		0			0
$615$	38.5501	+	44.1756i	0.0626831	+	0.0718302i
$616$		0			0
$617$	−313.342	−	18.2501i	−0.507847	−	0.0295787i	−0.197691	−	0.980264i	$-0.563344\pi$
$617$	−313.342	−	18.2501i	−0.507847	−	0.0295787i	−0.310156	+	0.950686i	$0.600381\pi$
$618$		0			0
$619$	−102.967	−	109.139i	−0.166344	−	0.176314i	0.638840	−	0.769340i	$-0.279415\pi$
$619$	−102.967	−	109.139i	−0.166344	−	0.176314i	−0.805184	+	0.593026i	$0.797933\pi$
$620$		0			0
$621$	−193.368	−	531.390i	−0.311381	−	0.855701i
$622$		0			0
$623$	−298.817	−	89.4600i	−0.479643	−	0.143596i
$624$		0			0
$625$	630.275	+	414.538i	1.00844	+	0.663261i
$626$		0			0
$627$	−604.625	+	233.424i	−0.964315	+	0.372287i
$628$		0			0
$629$	−324.538	+	57.2248i	−0.515959	+	0.0909775i
$630$		0			0
$631$	147.025	−	833.822i	0.233004	−	1.32143i	−0.613773	−	0.789482i	$-0.710349\pi$
$631$	147.025	−	833.822i	0.233004	−	1.32143i	0.846777	−	0.531948i	$-0.178540\pi$
$632$		0			0
$633$	56.5328	−	581.065i	0.0893093	−	0.917955i
$634$		0			0
$635$	550.356	−	164.766i	0.866702	−	0.259474i
$636$		0			0
$637$	1229.32	+	143.687i	1.92986	+	0.225569i
$638$		0			0
$639$	−69.2610	+	890.544i	−0.108390	+	1.39365i
$640$		0			0
$641$	−433.403	−	658.957i	−0.676136	−	1.02801i	−0.996730	−	0.0807981i	$-0.974253\pi$
$641$	−433.403	−	658.957i	−0.676136	−	1.02801i	0.320595	−	0.947216i	$-0.396117\pi$
$642$		0			0
$643$	435.168	+	584.531i	0.676777	+	0.909069i	0.999297	−	0.0374936i	$-0.0119374\pi$
$643$	435.168	+	584.531i	0.676777	+	0.909069i	−0.322520	+	0.946563i	$0.604530\pi$
$644$		0			0
$645$	−224.974	−	48.7380i	−0.348797	−	0.0755628i
$646$		0			0
$647$		−	540.276i		−	0.835048i	−0.908666	−	0.417524i	$-0.862898\pi$
$647$		−	540.276i		−	0.835048i	0.908666	−	0.417524i	$-0.137102\pi$
$648$		0			0
$649$	310.726			0.478776
$650$		0			0
$651$	−902.437	−	818.957i	−1.38623	−	1.25800i
$652$		0			0
$653$	217.491	−	161.916i	0.333065	−	0.247958i	−0.417614	−	0.908624i	$-0.637134\pi$
$653$	217.491	−	161.916i	0.333065	−	0.247958i	0.750679	+	0.660667i	$0.229726\pi$
$654$		0			0
$655$	−1203.29	+	791.414i	−1.83708	+	1.20827i
$656$		0			0
$657$	−119.727	+	464.720i	−0.182234	+	0.707336i
$658$		0			0
$659$	96.9441	−	829.409i	0.147108	−	1.25859i	−0.694894	−	0.719113i	$-0.744549\pi$
$659$	96.9441	−	829.409i	0.147108	−	1.25859i	0.842001	−	0.539475i	$-0.181377\pi$
$660$		0			0
$661$	138.086	+	461.240i	0.208905	+	0.697792i	0.996650	+	0.0817896i	$0.0260636\pi$
$661$	138.086	+	461.240i	0.208905	+	0.697792i	−0.787744	+	0.616002i	$0.788751\pi$
$662$		0			0
$663$	381.791	+	839.973i	0.575853	+	1.26693i
$664$		0			0
$665$	−2296.22	−	404.886i	−3.45296	−	0.608851i
$666$		0			0
$667$	24.7366	+	140.288i	0.0370863	+	0.210327i
$668$		0			0
$669$	373.037	+	58.3510i	0.557604	+	0.0872213i
$670$		0			0
$671$	−74.6709	+	113.532i	−0.111283	+	0.169198i
$672$		0			0
$673$	−186.905	+	624.307i	−0.277720	+	0.927648i	0.699359	+	0.714770i	$0.253469\pi$
$673$	−186.905	+	624.307i	−0.277720	+	0.927648i	−0.977079	+	0.212878i	$0.931716\pi$
$674$		0			0
$675$	117.952	+	158.461i	0.174744	+	0.234757i
$676$		0			0
$677$	−745.201	+	703.061i	−1.10074	+	1.03849i	−0.101694	+	0.994816i	$0.532426\pi$
$677$	−745.201	+	703.061i	−1.10074	+	1.03849i	−0.999046	+	0.0436787i	$0.986092\pi$
$678$		0			0
$679$	29.0127	−	498.129i	0.0427286	−	0.733622i
$680$		0			0
$681$	1255.05	+	429.462i	1.84296	+	0.630634i
$682$		0			0
$683$	−226.518	+	622.353i	−0.331652	+	0.911205i	0.656031	+	0.754734i	$0.272234\pi$
$683$	−226.518	+	622.353i	−0.331652	+	0.911205i	−0.987683	+	0.156471i	$0.949988\pi$
$684$		0			0
$685$	−58.6053	+	21.3306i	−0.0855552	+	0.0311396i
$686$		0			0
$687$	131.235	−	274.439i	0.191027	−	0.399474i
$688$		0			0
$689$	−220.789	+	931.583i	−0.320449	+	1.35208i
$690$		0			0
$691$	207.987	+	482.167i	0.300994	+	0.697782i	0.999847	−	0.0174831i	$-0.00556532\pi$
$691$	207.987	+	482.167i	0.300994	+	0.697782i	−0.698853	+	0.715265i	$0.746306\pi$
$692$		0			0
$693$	−570.275	−	300.424i	−0.822907	−	0.433512i
$694$		0			0
$695$	1000.87	−	58.2940i	1.44010	−	0.0838762i
$696$		0			0
$697$	29.4280	−	68.2217i	0.0422209	−	0.0978790i
$698$		0			0
$699$	112.247	−	274.730i	0.160582	−	0.393032i
$700$		0			0
$701$	−646.931	−	373.506i	−0.922868	−	0.532818i	−0.0383193	−	0.999266i	$-0.512200\pi$
$701$	−646.931	−	373.506i	−0.922868	−	0.532818i	−0.884549	+	0.466447i	$0.845534\pi$
$702$		0			0
$703$	268.183	+	464.506i	0.381484	+	0.660749i
$704$		0			0
$705$	269.999	−	428.361i	0.382978	−	0.607604i
$706$		0			0
$707$	188.966	+	1616.70i	0.267278	+	2.28671i
$708$		0			0
$709$	−224.708	−	112.853i	−0.316936	−	0.159171i	0.283218	−	0.959055i	$-0.408598\pi$
$709$	−224.708	−	112.853i	−0.316936	−	0.159171i	−0.600154	+	0.799884i	$0.704894\pi$
$710$		0			0
$711$	430.053	−	492.739i	0.604856	−	0.693022i
$712$		0			0
$713$	−585.230	−	435.687i	−0.820799	−	0.611062i
$714$		0			0
$715$	−340.984	+	361.422i	−0.476901	+	0.505486i
$716$		0			0
$717$	−28.7184	−	29.2822i	−0.0400535	−	0.0408398i
$718$		0			0
$719$	76.7779	−	91.5004i	0.106784	−	0.127261i	−0.710005	−	0.704197i	$-0.751307\pi$
$719$	76.7779	−	91.5004i	0.106784	−	0.127261i	0.816789	+	0.576936i	$0.195752\pi$
$720$		0			0
$721$	587.199	−	492.719i	0.814423	−	0.683382i
$722$		0			0
$723$	−254.704	+	153.706i	−0.352287	+	0.212595i
$724$		0			0
$725$	−22.3338	−	44.4703i	−0.0308052	−	0.0613383i
$726$		0			0
$727$	−3.58303	+	0.849193i	−0.00492851	+	0.00116808i	−0.233079	−	0.972458i	$-0.574880\pi$
$727$	−3.58303	+	0.849193i	−0.00492851	+	0.00116808i	0.228151	+	0.973626i	$0.426732\pi$
$728$		0			0
$729$	−208.980	−	698.404i	−0.286667	−	0.958030i
$730$		0			0
$731$	67.2715	+	283.841i	0.0920266	+	0.388291i
$732$		0			0
$733$	−325.858	+	163.652i	−0.444554	+	0.223263i	−0.656971	−	0.753916i	$-0.728163\pi$
$733$	−325.858	+	163.652i	−0.444554	+	0.223263i	0.212417	+	0.977179i	$0.431866\pi$
$734$		0			0
$735$	−766.344	−	1269.89i	−1.04264	−	1.72775i
$736$		0			0
$737$	418.989	+	499.332i	0.568506	+	0.677519i
$738$		0			0
$739$	410.682	+	344.603i	0.555726	+	0.466310i	0.876875	−	0.480719i	$-0.159624\pi$
$739$	410.682	+	344.603i	0.555726	+	0.466310i	−0.321148	+	0.947029i	$0.604069\pi$
$740$		0			0
$741$	1072.16	−	1051.51i	1.44691	−	1.41905i
$742$		0			0
$743$	530.708	+	500.697i	0.714277	+	0.673886i	0.954966	−	0.296716i	$-0.0958916\pi$
$743$	530.708	+	500.697i	0.714277	+	0.673886i	−0.240688	+	0.970603i	$0.577373\pi$
$744$		0			0
$745$	515.068	−	691.857i	0.691367	−	0.928666i
$746$		0			0
$747$	596.914	+	520.975i	0.799082	+	0.697423i
$748$		0			0
$749$	1095.50	−	2181.31i	1.46261	−	2.91230i
$750$		0			0
$751$	572.563	−	66.9230i	0.762400	−	0.0891118i	0.273998	−	0.961730i	$-0.411654\pi$
$751$	572.563	−	66.9230i	0.762400	−	0.0891118i	0.488402	+	0.872619i	$0.337580\pi$
$752$		0			0
$753$	−620.753	−	391.266i	−0.824373	−	0.519610i
$754$		0			0
$755$	−1202.75	+	694.405i	−1.59304	+	0.919742i
$756$		0			0
$757$	76.0153	−	131.662i	0.100416	−	0.173926i	−0.811440	−	0.584436i	$-0.801316\pi$
$757$	76.0153	−	131.662i	0.100416	−	0.173926i	0.911856	+	0.410510i	$0.134649\pi$
$758$		0			0
$759$	−357.236	−	145.957i	−0.470667	−	0.192302i
$760$		0			0
$761$	−18.5423	−	7.99837i	−0.0243657	−	0.0105103i	0.383862	−	0.923390i	$-0.374594\pi$
$761$	−18.5423	−	7.99837i	−0.0243657	−	0.0105103i	−0.408228	+	0.912880i	$0.633853\pi$
$762$		0			0
$763$	−28.2524	−	485.075i	−0.0370280	−	0.635746i
$764$		0			0
$765$	515.349	−	978.254i	0.673659	−	1.27876i
$766$		0			0
$767$	−661.089	+	285.166i	−0.861916	+	0.371794i
$768$		0			0
$769$	−30.1241	−	7.13955i	−0.0391731	−	0.00928420i	0.210983	−	0.977490i	$-0.432334\pi$
$769$	−30.1241	−	7.13955i	−0.0391731	−	0.00928420i	−0.250156	+	0.968206i	$0.580482\pi$
$770$		0			0
$771$	−953.471	−	455.945i	−1.23667	−	0.591369i
$772$		0			0
$773$	−400.057	−	1099.15i	−0.517538	−	1.42192i	−0.873225	−	0.487318i	$-0.837975\pi$
$773$	−400.057	−	1099.15i	−0.517538	−	1.42192i	0.355687	−	0.934605i	$-0.384247\pi$
$774$		0			0
$775$	239.504	+	87.1721i	0.309037	+	0.112480i
$776$		0			0
$777$	−172.700	+	504.697i	−0.222266	+	0.649545i
$778$		0			0
$779$	−120.723	−	7.03130i	−0.154971	−	0.00902605i
$780$		0			0
$781$	418.315	+	443.388i	0.535615	+	0.567719i
$782$		0			0
$783$	21.3070	+	182.405i	0.0272120	+	0.232957i
$784$		0			0
$785$	1541.54	+	461.507i	1.96375	+	0.587907i
$786$		0			0
$787$	928.845	+	610.911i	1.18024	+	0.776253i	0.979114	−	0.203313i	$-0.0651710\pi$
$787$	928.845	+	610.911i	1.18024	+	0.776253i	0.201122	+	0.979566i	$0.435541\pi$
$788$		0			0
$789$	202.805	−	1296.53i	0.257041	−	1.64326i
$790$		0			0
$791$	−1534.80	+	270.626i	−1.94033	+	0.342132i
$792$		0			0
$793$	54.6745	−	310.075i	0.0689465	−	0.391015i
$794$		0			0
$795$	1044.47	−	474.742i	1.31380	−	0.597160i
$796$		0			0
$797$	−459.764	+	137.644i	−0.576868	+	0.172703i	−0.561929	−	0.827185i	$-0.689941\pi$
$797$	−459.764	+	137.644i	−0.576868	+	0.172703i	−0.0149389	+	0.999888i	$0.504755\pi$
$798$		0			0
$799$	−637.318	−	74.4918i	−0.797645	−	0.0932313i
$800$		0			0
$801$	−233.137	−	60.0639i	−0.291057	−	0.0749861i
$802$		0			0
$803$	179.963	+	273.620i	0.224113	+	0.340747i
$804$		0			0
$805$	−829.040	−	1113.59i	−1.02986	−	1.38335i
$806$		0			0
$807$	−387.652	+	427.167i	−0.480362	+	0.529327i
$808$		0			0
$809$		−	1158.10i		−	1.43152i	−0.698345	−	0.715761i	$-0.746080\pi$
$809$		−	1158.10i		−	1.43152i	0.698345	−	0.715761i	$-0.253920\pi$
$810$		0			0
$811$	864.183			1.06558			0.532788	−	0.846249i	$-0.321144\pi$
$811$	864.183			1.06558			0.532788	+	0.846249i	$0.321144\pi$
$812$		0			0
$813$	76.4452	−	352.870i	0.0940285	−	0.434034i
$814$		0			0
$815$	1095.91	−	815.875i	1.34468	−	1.00107i
$816$		0			0
$817$	396.669	−	260.893i	0.485519	−	0.319331i
$818$		0			0
$819$	1489.01	+	115.806i	1.81808	+	0.141399i
$820$		0			0
$821$	37.9038	−	324.287i	0.0461678	−	0.394991i	−0.950321	−	0.311270i	$-0.899246\pi$
$821$	37.9038	−	324.287i	0.0461678	−	0.394991i	0.996489	−	0.0837206i	$-0.0266803\pi$
$822$		0			0
$823$	−62.4058	−	208.450i	−0.0758272	−	0.253281i	0.911668	−	0.410926i	$-0.134795\pi$
$823$	−62.4058	−	208.450i	−0.0758272	−	0.253281i	−0.987496	+	0.157646i	$0.949610\pi$
$824$		0			0
$825$	134.176	+	13.0542i	0.162637	+	0.0158232i
$826$		0			0
$827$	−324.877	−	57.2845i	−0.392838	−	0.0692679i	−0.0262595	−	0.999655i	$-0.508360\pi$
$827$	−324.877	−	57.2845i	−0.392838	−	0.0692679i	−0.366578	+	0.930387i	$0.619471\pi$
$828$		0			0
$829$	44.4297	+	251.973i	0.0535943	+	0.303948i	0.999808	−	0.0195940i	$-0.00623735\pi$
$829$	44.4297	+	251.973i	0.0535943	+	0.303948i	−0.946214	+	0.323542i	$0.895126\pi$
$830$		0			0
$831$	249.455	+	646.151i	0.300187	+	0.777559i
$832$		0			0
$833$	−1032.83	+	1570.34i	−1.23989	+	1.88516i
$834$		0			0
$835$	−442.672	+	1478.63i	−0.530146	+	1.77081i
$836$		0			0
$837$	−720.484	−	604.645i	−0.860793	−	0.722395i
$838$		0			0
$839$	−22.5991	+	21.3211i	−0.0269357	+	0.0254126i	−0.699592	−	0.714543i	$-0.746635\pi$
$839$	−22.5991	+	21.3211i	−0.0269357	+	0.0254126i	0.672656	+	0.739955i	$0.265153\pi$
$840$		0			0
$841$	−46.2098	+	793.392i	−0.0549463	+	0.943392i
$842$		0			0
$843$	−604.782	+	527.766i	−0.717416	+	0.626057i
$844$		0			0
$845$	65.1878	−	179.102i	0.0771454	−	0.211955i
$846$		0			0
$847$	912.498	−	332.122i	1.07733	−	0.392116i
$848$		0			0
$849$	47.8347	−	3.71687i	0.0563424	−	0.00437793i
$850$		0			0
$851$	−73.6502	+	310.755i	−0.0865455	+	0.365164i
$852$		0			0
$853$	−527.754	−	1223.47i	−0.618704	−	1.43432i	−0.882767	−	0.469811i	$-0.844322\pi$
$853$	−527.754	−	1223.47i	−0.618704	−	1.43432i	0.264063	−	0.964505i	$-0.414937\pi$
$854$		0			0
$855$	−1783.06	−	243.631i	−2.08545	−	0.284948i
$856$		0			0
$857$	627.135	−	36.5264i	0.731779	−	0.0426213i	0.311791	−	0.950151i	$-0.399071\pi$
$857$	627.135	−	36.5264i	0.731779	−	0.0426213i	0.419988	+	0.907530i	$0.362034\pi$
$858$		0			0
$859$	−90.4413	+	209.667i	−0.105287	+	0.244082i	−0.962713	−	0.270525i	$-0.912803\pi$
$859$	−90.4413	+	209.667i	−0.105287	+	0.244082i	0.857426	+	0.514607i	$0.172062\pi$
$860$		0			0
$861$	−73.6719	−	95.0580i	−0.0855655	−	0.110404i
$862$		0			0
$863$	1149.54	+	663.686i	1.33203	+	0.769046i	0.985610	−	0.169035i	$-0.0540653\pi$
$863$	1149.54	+	663.686i	1.33203	+	0.769046i	0.346416	+	0.938081i	$0.387399\pi$
$864$		0			0
$865$	−798.248	−	1382.61i	−0.922830	−	1.59839i
$866$		0			0
$867$	−533.754	−	20.7247i	−0.615633	−	0.0239039i
$868$		0			0
$869$	−51.8150	−	443.306i	−0.0596260	−	0.510133i
$870$		0			0
$871$	−1349.68	−	677.837i	−1.54958	−	0.778229i
$872$		0			0
$873$	7.48625	−	385.049i	0.00857531	−	0.441064i
$874$		0			0
$875$	−940.256	−	699.995i	−1.07458	−	0.799994i
$876$		0			0
$877$	−793.797	+	841.376i	−0.905128	+	0.959379i	−0.999346	−	0.0361721i	$-0.988484\pi$
$877$	−793.797	+	841.376i	−0.905128	+	0.959379i	0.0942177	+	0.995552i	$0.469965\pi$
$878$		0			0
$879$	1482.24	−	381.764i	1.68628	−	0.434316i
$880$		0			0
$881$	−284.554	+	339.118i	−0.322989	+	0.384924i	−0.902968	−	0.429708i	$-0.858616\pi$
$881$	−284.554	+	339.118i	−0.322989	+	0.384924i	0.579979	+	0.814632i	$0.303061\pi$
$882$		0			0
$883$	−71.5367	+	60.0264i	−0.0810155	+	0.0679801i	−0.682396	−	0.730983i	$-0.739062\pi$
$883$	−71.5367	+	60.0264i	−0.0810155	+	0.0679801i	0.601381	+	0.798963i	$0.294618\pi$
$884$		0			0
$885$	755.413	+	416.843i	0.853574	+	0.471009i
$886$		0			0
$887$	−3.20988	−	6.39141i	−0.00361881	−	0.00720564i	0.891816	−	0.452398i	$-0.149431\pi$
$887$	−3.20988	−	6.39141i	−0.00361881	−	0.00720564i	−0.895435	+	0.445193i	$0.853135\pi$
$888$		0			0
$889$	−1146.64	+	271.758i	−1.28981	+	0.305690i
$890$		0			0
$891$	−448.804	−	214.655i	−0.503708	−	0.240915i
$892$		0			0
$893$	240.846	+	1016.21i	0.269704	+	1.13797i
$894$		0			0
$895$	−638.212	+	320.522i	−0.713086	+	0.358125i
$896$		0			0
$897$	893.995	−	17.3178i	0.996650	−	0.0193064i
$898$		0			0
$899$	152.306	+	181.511i	0.169417	+	0.201903i
$900$		0			0
$901$	−1113.74	−	934.537i	−1.23611	−	1.03722i
$902$		0			0
$903$	454.876	+	126.635i	0.503738	+	0.140238i
$904$		0			0
$905$	412.896	+	389.548i	0.456239	+	0.430439i
$906$		0			0
$907$	964.376	−	1295.38i	1.06326	−	1.42820i	0.166308	−	0.986074i	$-0.446815\pi$
$907$	964.376	−	1295.38i	1.06326	−	1.42820i	0.896951	−	0.442130i	$-0.145777\pi$
$908$		0			0
$909$	194.065	+	1241.23i	0.213493	+	1.36549i
$910$		0			0
$911$	528.239	−	1051.81i	0.579845	−	1.15457i	−0.392223	−	0.919870i	$-0.628294\pi$
$911$	528.239	−	1051.81i	0.579845	−	1.15457i	0.972069	−	0.234697i	$-0.0754097\pi$
$912$		0			0
$913$	537.030	−	62.7698i	0.588204	−	0.0687512i
$914$		0			0
$915$	−333.839	+	175.838i	−0.364851	+	0.192172i
$916$		0			0
$917$	2558.41	−	1477.10i	2.78998	−	1.61080i
$918$		0			0
$919$	430.121	−	744.992i	0.468032	−	0.810655i	−0.531301	−	0.847183i	$-0.678297\pi$
$919$	430.121	−	744.992i	0.468032	−	0.810655i	0.999333	+	0.0365285i	$0.0116300\pi$
$920$		0			0
$921$	−25.9186	−	189.791i	−0.0281418	−	0.206070i
$922$		0			0
$923$	−1296.91	−	559.432i	−1.40510	−	0.606102i
$924$		0			0
$925$	−6.48689	−	111.376i	−0.00701286	−	0.120406i
$926$		0			0
$927$	438.149	−	397.561i	0.472653	−	0.428869i
$928$		0			0
$929$	−239.868	+	103.469i	−0.258201	+	0.111377i	−0.521246	−	0.853407i	$-0.674532\pi$
$929$	−239.868	+	103.469i	−0.258201	+	0.111377i	0.263045	+	0.964784i	$0.415273\pi$
$930$		0			0
$931$	2976.68	+	705.487i	3.19730	+	0.757773i
$932$		0			0
$933$	−1397.00	+	958.091i	−1.49732	+	1.02689i
$934$		0			0
$935$	−258.077	−	709.061i	−0.276018	−	0.758354i
$936$		0			0
$937$	−682.470	−	248.399i	−0.728357	−	0.265100i	−0.0488877	−	0.998804i	$-0.515568\pi$
$937$	−682.470	−	248.399i	−0.728357	−	0.265100i	−0.679469	+	0.733704i	$0.737790\pi$
$938$		0			0
$939$	378.810	−	74.3866i	0.403419	−	0.0792189i
$940$		0			0
$941$	1305.70	+	76.0484i	1.38757	+	0.0808166i	0.735592	−	0.677424i	$-0.236904\pi$
$941$	1305.70	+	76.0484i	1.38757	+	0.0808166i	0.651974	+	0.758241i	$0.273941\pi$
$942$		0			0
$943$	−49.4111	−	52.3728i	−0.0523978	−	0.0555384i
$944$		0			0
$945$	−983.387	−	1495.40i	−1.04062	−	1.58243i
$946$		0			0
$947$	1330.45	+	398.309i	1.40491	+	0.420601i	0.897465	−	0.441086i	$-0.145407\pi$
$947$	1330.45	+	398.309i	1.40491	+	0.420601i	0.507440	+	0.861687i	$0.330592\pi$
$948$		0			0
$949$	−633.995	−	416.985i	−0.668066	−	0.439394i
$950$		0			0
$951$	723.338	+	583.457i	0.760607	+	0.613519i
$952$		0			0
$953$	260.494	−	45.9321i	0.273341	−	0.0481974i	−0.0352974	−	0.999377i	$-0.511238\pi$
$953$	260.494	−	45.9321i	0.273341	−	0.0481974i	0.308638	+	0.951179i	$0.400127\pi$
$954$		0			0
$955$	3.42146	−	19.4041i	0.00358268	−	0.0203184i
$956$		0			0
$957$	101.958	+	72.8786i	0.106539	+	0.0761532i
$958$		0			0
$959$	122.553	−	36.6899i	0.127792	−	0.0382585i
$960$		0			0
$961$	−250.861	−	29.3215i	−0.261042	−	0.0305114i
$962$		0			0
$963$	779.698	−	1715.08i	0.809655	−	1.78098i
$964$		0			0
$965$	518.591	+	788.480i	0.537400	+	0.817077i
$966$		0			0
$967$	293.433	+	394.149i	0.303446	+	0.407599i	0.927524	−	0.373763i	$-0.121933\pi$
$967$	293.433	+	394.149i	0.303446	+	0.407599i	−0.624078	+	0.781362i	$0.714525\pi$
$968$		0			0
$969$	696.250	+	2171.63i	0.718524	+	2.24111i
$970$		0			0
$971$		−	583.676i		−	0.601108i	−0.953765	−	0.300554i	$-0.902828\pi$
$971$		−	583.676i		−	0.601108i	0.953765	−	0.300554i	$-0.0971716\pi$
$972$		0			0
$973$	−2056.47			−2.11354
$974$		0			0
$975$	−297.448	+	95.3650i	−0.305075	+	0.0978103i
$976$		0			0
$977$	217.977	−	162.278i	0.223109	−	0.166098i	−0.479801	−	0.877377i	$-0.659291\pi$
$977$	217.977	−	162.278i	0.223109	−	0.166098i	0.702910	+	0.711279i	$0.251884\pi$
$978$		0			0
$979$	−137.267	+	90.2822i	−0.140212	+	0.0922188i
$980$		0			0
$981$	−36.2892	−	373.269i	−0.0369920	−	0.380498i
$982$		0			0
$983$	182.305	−	1559.72i	0.185458	−	1.58670i	−0.504868	−	0.863197i	$-0.668459\pi$
$983$	182.305	−	1559.72i	0.185458	−	1.58670i	0.690326	−	0.723499i	$-0.257467\pi$
$984$		0			0
$985$	167.073	+	558.063i	0.169617	+	0.566562i
$986$		0			0
$987$	−603.978	+	844.970i	−0.611934	+	0.856099i
$988$		0			0
$989$	278.396	+	49.0888i	0.281493	+	0.0496348i
$990$		0			0
$991$	−221.108	−	1253.96i	−0.223116	−	1.26535i	−0.866255	−	0.499602i	$-0.833479\pi$
$991$	−221.108	−	1253.96i	−0.223116	−	1.26535i	0.643139	−	0.765749i	$-0.277632\pi$
$992$		0			0
$993$	−469.274	+	581.781i	−0.472582	+	0.585882i
$994$		0			0
$995$	−101.522	+	154.357i	−0.102032	+	0.155132i
$996$		0			0
$997$	−347.481	+	1160.67i	−0.348527	+	1.16416i	0.586609	+	0.809871i	$0.300463\pi$
$997$	−347.481	+	1160.67i	−0.348527	+	1.16416i	−0.935136	+	0.354290i	$0.884722\pi$
$998$		0			0
$999$	−118.109	+	394.409i	−0.118227	+	0.394804i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.5.1	✓	324
81.65	odd	54	inner	324.3.o.a.65.1	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.1	✓	324	1.1	even	1	trivial
324.3.o.a.65.1	yes	324	81.65	odd	54	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	324.o (of order \(54\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.85677 + 0.915910i) q^{3} +(-4.55987 + 3.39470i) q^{5} +(9.74231 - 6.40762i) q^{7} +(7.32222 - 5.23308i) q^{9} +O(q^{10})\)	\(q+(-2.85677 + 0.915910i) q^{3} +(-4.55987 + 3.39470i) q^{5} +(9.74231 - 6.40762i) q^{7} +(7.32222 - 5.23308i) q^{9} +(0.713033 - 6.10039i) q^{11} +(4.08156 + 13.6334i) q^{13} +(9.91723 - 13.8743i) q^{15} +(-21.2831 - 3.75278i) q^{17} +(6.10801 + 34.6402i) q^{19} +(-21.9627 + 27.2281i) q^{21} +(-11.5087 + 17.4982i) q^{23} +(2.09835 - 7.00898i) q^{25} +(-16.1248 + 21.6562i) q^{27} +(4.94737 - 4.66760i) q^{29} +(-2.02555 + 34.7774i) q^{31} +(3.55044 + 18.0805i) q^{33} +(-22.6717 + 62.2901i) q^{35} +(14.3291 - 5.21535i) q^{37} +(-24.1470 - 35.2090i) q^{39} +(-0.792837 + 3.34524i) q^{41} +(-5.34616 - 12.3938i) q^{43} +(-15.6236 + 48.7188i) q^{45} +(29.6405 - 1.72636i) q^{47} +(34.4471 - 79.8574i) q^{49} +(64.2379 - 8.77257i) q^{51} +(58.2609 + 33.6369i) q^{53} +(17.4576 + 30.2375i) q^{55} +(-49.1765 - 93.3646i) q^{57} +(5.87325 + 50.2489i) q^{59} +(-19.7711 - 9.92944i) q^{61} +(37.8037 - 97.9003i) q^{63} +(-64.8925 - 48.3107i) q^{65} +(-72.8296 + 77.1949i) q^{67} +(16.8510 - 60.5292i) q^{69} +(-63.7955 + 76.0285i) q^{71} +(-40.8467 + 34.2745i) q^{73} +(0.425101 + 21.9449i) q^{75} +(-32.1424 - 64.0007i) q^{77} +(70.7096 - 16.7585i) q^{79} +(26.2297 - 76.6355i) q^{81} +(20.3016 + 85.6592i) q^{83} +(109.787 - 55.1373i) q^{85} +(-9.85837 + 17.8656i) q^{87} +(-17.1945 - 20.4917i) q^{89} +(127.121 + 106.667i) q^{91} +(-26.0664 - 101.206i) q^{93} +(-145.445 - 137.220i) q^{95} +(25.5532 - 34.3239i) q^{97} +(-26.7029 - 48.3997i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 324 * q	\( 324 q - 135 q^{21} - 81 q^{23} + 27 q^{27} + 81 q^{29} + 189 q^{33} + 243 q^{35} + 216 q^{41} + 432 q^{45} + 324 q^{47} + 126 q^{51} - 216 q^{57} - 378 q^{59} - 540 q^{63} - 108 q^{65} - 351 q^{67} + 504 q^{69} + 648 q^{71} + 450 q^{75} + 432 q^{77} - 54 q^{79} - 72 q^{81} - 216 q^{83} + 270 q^{85} - 1008 q^{87} - 648 q^{89} - 684 q^{93} - 432 q^{95} + 459 q^{97} - 252 q^{99}+O(q^{100}) \) 324 * q - 135 * q^21 - 81 * q^23 + 27 * q^27 + 81 * q^29 + 189 * q^33 + 243 * q^35 + 216 * q^41 + 432 * q^45 + 324 * q^47 + 126 * q^51 - 216 * q^57 - 378 * q^59 - 540 * q^63 - 108 * q^65 - 351 * q^67 + 504 * q^69 + 648 * q^71 + 450 * q^75 + 432 * q^77 - 54 * q^79 - 72 * q^81 - 216 * q^83 + 270 * q^85 - 1008 * q^87 - 648 * q^89 - 684 * q^93 - 432 * q^95 + 459 * q^97 - 252 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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