LMFDB - Embedded newform 324.3.o.a.65.3

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			65.3
Character	$\chi$	$=$	324.65
Dual form			324.3.o.a.5.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.78702 - 1.11018i) q^{3} +(2.99904 + 2.23270i) q^{5} +(-3.97531 - 2.61460i) q^{7} +(6.53498 + 6.18822i) q^{9} +O(q^{10})$	\(q+(-2.78702 - 1.11018i) q^{3} +(2.99904 + 2.23270i) q^{5} +(-3.97531 - 2.61460i) q^{7} +(6.53498 + 6.18822i) q^{9} +(-1.24265 - 10.6316i) q^{11} +(-1.49763 + 5.00242i) q^{13} +(-5.87968 - 9.55208i) q^{15} +(5.51128 - 0.971787i) q^{17} +(1.82736 - 10.3635i) q^{19} +(8.17659 + 11.7003i) q^{21} +(-8.74216 - 13.2918i) q^{23} +(-3.16080 - 10.5578i) q^{25} +(-11.3431 - 24.5017i) q^{27} +(-38.1193 - 35.9637i) q^{29} +(-0.509041 - 8.73990i) q^{31} +(-8.33971 + 31.0100i) q^{33} +(-6.08449 - 16.7170i) q^{35} +(-4.52480 - 1.64689i) q^{37} +(9.72752 - 12.2792i) q^{39} +(-3.69981 - 15.6107i) q^{41} +(21.9847 - 50.9663i) q^{43} +(5.78222 + 33.1494i) q^{45} +(-52.3473 - 3.04888i) q^{47} +(-10.4410 - 24.2049i) q^{49} +(-16.4389 - 3.41014i) q^{51} +(-34.3012 + 19.8038i) q^{53} +(20.0104 - 34.6590i) q^{55} +(-16.5983 + 26.8546i) q^{57} +(-3.82736 + 32.7451i) q^{59} +(85.7037 - 43.0420i) q^{61} +(-9.79885 - 41.6865i) q^{63} +(-15.6604 + 11.6587i) q^{65} +(51.3313 + 54.4080i) q^{67} +(9.60823 + 46.7500i) q^{69} +(20.4870 + 24.4154i) q^{71} +(43.6333 + 36.6127i) q^{73} +(-2.91189 + 32.9339i) q^{75} +(-22.8574 + 45.5129i) q^{77} +(31.4164 + 7.44583i) q^{79} +(4.41193 + 80.8798i) q^{81} +(2.97712 - 12.5614i) q^{83} +(18.6983 + 9.39062i) q^{85} +(66.3129 + 142.551i) q^{87} +(45.6637 - 54.4198i) q^{89} +(19.0329 - 15.9705i) q^{91} +(-8.28419 + 24.9234i) q^{93} +(28.6190 - 27.0006i) q^{95} +(113.983 + 153.105i) q^{97} +(57.6698 - 77.1670i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$1$	$e\left(\frac{31}{54}\right)$

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
$3$	−2.78702	−	1.11018i	−0.929007	−	0.370062i
$3$	−2.78702	−	1.11018i	−0.929007	−	0.370062i
$4$		0			0
$5$	2.99904	+	2.23270i	0.599808	+	0.446541i	0.853753	−	0.520678i	$-0.174321\pi$
$5$	2.99904	+	2.23270i	0.599808	+	0.446541i	−0.253945	+	0.967219i	$0.581728\pi$
$6$		0			0
$7$	−3.97531	−	2.61460i	−0.567902	−	0.373515i	0.232849	−	0.972513i	$-0.425195\pi$
$7$	−3.97531	−	2.61460i	−0.567902	−	0.373515i	−0.800750	+	0.598998i	$0.795566\pi$
$8$		0			0
$9$	6.53498	+	6.18822i	0.726109	+	0.687580i
$10$		0			0
$11$	−1.24265	−	10.6316i	−0.112968	−	0.966507i	−0.924233	−	0.381828i	$-0.875295\pi$
$11$	−1.24265	−	10.6316i	−0.112968	−	0.966507i	0.811265	−	0.584679i	$-0.198779\pi$
$12$		0			0
$13$	−1.49763	+	5.00242i	−0.115202	+	0.384801i	−0.996071	−	0.0885588i	$-0.971774\pi$
$13$	−1.49763	+	5.00242i	−0.115202	+	0.384801i	0.880869	+	0.473360i	$0.156959\pi$
$14$		0			0
$15$	−5.87968	−	9.55208i	−0.391979	−	0.636806i
$16$		0			0
$17$	5.51128	−	0.971787i	0.324193	−	0.0571639i	−0.00918342	−	0.999958i	$-0.502923\pi$
$17$	5.51128	−	0.971787i	0.324193	−	0.0571639i	0.333376	+	0.942794i	$0.391812\pi$
$18$		0			0
$19$	1.82736	−	10.3635i	0.0961771	−	0.545447i	−0.898203	−	0.439580i	$-0.855127\pi$
$19$	1.82736	−	10.3635i	0.0961771	−	0.545447i	0.994380	−	0.105867i	$-0.0337617\pi$
$20$		0			0
$21$	8.17659	+	11.7003i	0.389361	+	0.557157i
$22$		0			0
$23$	−8.74216	−	13.2918i	−0.380094	−	0.577905i	0.593883	−	0.804551i	$-0.297594\pi$
$23$	−8.74216	−	13.2918i	−0.380094	−	0.577905i	−0.973977	+	0.226646i	$0.927224\pi$
$24$		0			0
$25$	−3.16080	−	10.5578i	−0.126432	−	0.422312i
$26$		0			0
$27$	−11.3431	−	24.5017i	−0.420114	−	0.907472i
$28$		0			0
$29$	−38.1193	−	35.9637i	−1.31446	−	1.24013i	−0.951251	−	0.308419i	$-0.900200\pi$
$29$	−38.1193	−	35.9637i	−1.31446	−	1.24013i	−0.363208	−	0.931708i	$-0.618318\pi$
$30$		0			0
$31$	−0.509041	−	8.73990i	−0.0164207	−	0.281932i	−0.996516	−	0.0834038i	$-0.973421\pi$
$31$	−0.509041	−	8.73990i	−0.0164207	−	0.281932i	0.980095	−	0.198528i	$-0.0636162\pi$
$32$		0			0
$33$	−8.33971	+	31.0100i	−0.252719	+	0.939697i
$34$		0			0
$35$	−6.08449	−	16.7170i	−0.173843	−	0.477629i
$36$		0			0
$37$	−4.52480	−	1.64689i	−0.122292	−	0.0445106i	0.280149	−	0.959956i	$-0.409616\pi$
$37$	−4.52480	−	1.64689i	−0.122292	−	0.0445106i	−0.402441	+	0.915446i	$0.631838\pi$
$38$		0			0
$39$	9.72752	−	12.2792i	0.249424	−	0.314851i
$40$		0			0
$41$	−3.69981	−	15.6107i	−0.0902392	−	0.380749i	0.909120	−	0.416534i	$-0.136755\pi$
$41$	−3.69981	−	15.6107i	−0.0902392	−	0.380749i	−0.999360	+	0.0357845i	$0.988607\pi$
$42$		0			0
$43$	21.9847	−	50.9663i	0.511273	−	1.18526i	−0.445726	−	0.895170i	$-0.647054\pi$
$43$	21.9847	−	50.9663i	0.511273	−	1.18526i	0.956998	−	0.290094i	$-0.0936865\pi$
$44$		0			0
$45$	5.78222	+	33.1494i	0.128494	+	0.736653i
$46$		0			0
$47$	−52.3473	−	3.04888i	−1.11377	−	0.0648699i	−0.508629	−	0.860986i	$-0.669847\pi$
$47$	−52.3473	−	3.04888i	−1.11377	−	0.0648699i	−0.605144	+	0.796116i	$0.706885\pi$
$48$		0			0
$49$	−10.4410	−	24.2049i	−0.213081	−	0.493977i
$50$		0			0
$51$	−16.4389	−	3.41014i	−0.322332	−	0.0668656i
$52$		0			0
$53$	−34.3012	+	19.8038i	−0.647192	+	0.373656i	−0.787379	−	0.616469i	$-0.788563\pi$
$53$	−34.3012	+	19.8038i	−0.647192	+	0.373656i	0.140188	+	0.990125i	$0.455229\pi$
$54$		0			0
$55$	20.0104	−	34.6590i	0.363825	−	0.630164i
$56$		0			0
$57$	−16.5983	+	26.8546i	−0.291198	+	0.471133i
$58$		0			0
$59$	−3.82736	+	32.7451i	−0.0648704	+	0.555002i	0.921250	+	0.388971i	$0.127169\pi$
$59$	−3.82736	+	32.7451i	−0.0648704	+	0.555002i	−0.986120	+	0.166031i	$0.946905\pi$
$60$		0			0
$61$	85.7037	−	43.0420i	1.40498	−	0.705606i	0.425089	−	0.905151i	$-0.360243\pi$
$61$	85.7037	−	43.0420i	1.40498	−	0.705606i	0.979889	+	0.199545i	$0.0639464\pi$
$62$		0			0
$63$	−9.79885	−	41.6865i	−0.155537	−	0.661690i
$64$		0			0
$65$	−15.6604	+	11.6587i	−0.240929	+	0.179365i
$66$		0			0
$67$	51.3313	+	54.4080i	0.766139	+	0.812059i	0.986569	−	0.163343i	$-0.0522278\pi$
$67$	51.3313	+	54.4080i	0.766139	+	0.812059i	−0.220431	+	0.975403i	$0.570746\pi$
$68$		0			0
$69$	9.60823	+	46.7500i	0.139250	+	0.677536i
$70$		0			0
$71$	20.4870	+	24.4154i	0.288549	+	0.343879i	0.890774	−	0.454447i	$-0.150163\pi$
$71$	20.4870	+	24.4154i	0.288549	+	0.343879i	−0.602224	+	0.798327i	$0.705719\pi$
$72$		0			0
$73$	43.6333	+	36.6127i	0.597716	+	0.501544i	0.890711	−	0.454571i	$-0.150207\pi$
$73$	43.6333	+	36.6127i	0.597716	+	0.501544i	−0.292994	+	0.956114i	$0.594652\pi$
$74$		0			0
$75$	−2.91189	+	32.9339i	−0.0388253	+	0.439118i
$76$		0			0
$77$	−22.8574	+	45.5129i	−0.296850	+	0.591077i
$78$		0			0
$79$	31.4164	+	7.44583i	0.397677	+	0.0942511i	0.424588	−	0.905387i	$-0.360419\pi$
$79$	31.4164	+	7.44583i	0.397677	+	0.0942511i	−0.0269113	+	0.999638i	$0.508567\pi$
$80$		0			0
$81$	4.41193	+	80.8798i	0.0544683	+	0.998516i
$82$		0			0
$83$	2.97712	−	12.5614i	0.0358689	−	0.151343i	−0.952164	−	0.305589i	$-0.901147\pi$
$83$	2.97712	−	12.5614i	0.0358689	−	0.151343i	0.988032	+	0.154246i	$0.0492949\pi$
$84$		0			0
$85$	18.6983	+	9.39062i	0.219979	+	0.110478i
$86$		0			0
$87$	66.3129	+	142.551i	0.762218	+	1.63852i
$88$		0			0
$89$	45.6637	−	54.4198i	0.513075	−	0.611459i	−0.445854	−	0.895106i	$-0.647100\pi$
$89$	45.6637	−	54.4198i	0.513075	−	0.611459i	0.958929	+	0.283647i	$0.0915443\pi$
$90$		0			0
$91$	19.0329	−	15.9705i	0.209152	−	0.175500i
$92$		0			0
$93$	−8.28419	+	24.9234i	−0.0890773	+	0.267994i
$94$		0			0
$95$	28.6190	−	27.0006i	0.301252	−	0.284217i
$96$		0			0
$97$	113.983	+	153.105i	1.17508	+	1.57840i	0.730932	+	0.682450i	$0.239086\pi$
$97$	113.983	+	153.105i	1.17508	+	1.57840i	0.444146	+	0.895954i	$0.353507\pi$
$98$		0			0
$99$	57.6698	−	77.1670i	0.582523	−	0.779464i
$100$		0			0
$101$	−8.04628	−	16.0215i	−0.0796661	−	0.158628i	0.850273	−	0.526342i	$-0.176437\pi$
$101$	−8.04628	−	16.0215i	−0.0796661	−	0.158628i	−0.929939	+	0.367714i	$0.880141\pi$
$102$		0			0
$103$	−105.477	−	12.3285i	−1.02405	−	0.119694i	−0.412547	−	0.910936i	$-0.635361\pi$
$103$	−105.477	−	12.3285i	−1.02405	−	0.119694i	−0.611503	+	0.791242i	$0.709435\pi$
$104$		0			0
$105$	−1.60135	+	53.3456i	−0.0152510	+	0.508053i
$106$		0			0
$107$	−65.0364	−	37.5488i	−0.607817	−	0.350923i	0.164294	−	0.986411i	$-0.447466\pi$
$107$	−65.0364	−	37.5488i	−0.607817	−	0.350923i	−0.772111	+	0.635488i	$0.780799\pi$
$108$		0			0
$109$	−33.1628	−	57.4397i	−0.304246	−	0.526970i	0.672847	−	0.739782i	$-0.265071\pi$
$109$	−33.1628	−	57.4397i	−0.304246	−	0.526970i	−0.977093	+	0.212812i	$0.931738\pi$
$110$		0			0
$111$	10.7824	+	9.61328i	0.0971383	+	0.0866062i
$112$		0			0
$113$	−120.171	+	51.8369i	−1.06346	+	0.458734i	−0.854641	−	0.519220i	$-0.826223\pi$
$113$	−120.171	+	51.8369i	−1.06346	+	0.458734i	−0.208823	+	0.977953i	$0.566963\pi$
$114$		0			0
$115$	3.45857	−	59.3814i	0.0300745	−	0.516360i
$116$		0			0
$117$	−40.7430	+	23.4231i	−0.348231	+	0.200197i
$118$		0			0
$119$	−24.4499	−	10.5466i	−0.205461	−	0.0886273i
$120$		0			0
$121$	6.25217	−	1.48179i	0.0516708	−	0.0122462i
$122$		0			0
$123$	−7.01933	+	47.6149i	−0.0570677	+	0.387113i
$124$		0			0
$125$	46.0624	−	126.555i	0.368499	−	1.01244i
$126$		0			0
$127$	−19.7693	+	7.19543i	−0.155664	+	0.0566569i	−0.418677	−	0.908135i	$-0.637506\pi$
$127$	−19.7693	+	7.19543i	−0.155664	+	0.0566569i	0.263013	+	0.964792i	$0.415284\pi$
$128$		0			0
$129$	−117.854	+	117.637i	−0.913596	+	0.911916i
$130$		0			0
$131$	−72.3880	+	4.21612i	−0.552580	+	0.0321841i	−0.332164	−	0.943222i	$-0.607779\pi$
$131$	−72.3880	+	4.21612i	−0.552580	+	0.0321841i	−0.220416	+	0.975406i	$0.570742\pi$
$132$		0			0
$133$	−34.3608	+	36.4203i	−0.258352	+	0.273837i
$134$		0			0
$135$	20.6868	−	98.8074i	0.153235	−	0.731907i
$136$		0			0
$137$	−127.080	+	38.0453i	−0.927592	+	0.277703i	−0.714747	−	0.699383i	$-0.753458\pi$
$137$	−127.080	+	38.0453i	−0.927592	+	0.277703i	−0.212845	+	0.977086i	$0.568273\pi$
$138$		0			0
$139$	−18.1233	+	11.9199i	−0.130383	+	0.0857545i	−0.613025	−	0.790063i	$-0.710048\pi$
$139$	−18.1233	+	11.9199i	−0.130383	+	0.0857545i	0.482642	+	0.875818i	$0.339677\pi$
$140$		0			0
$141$	142.508	+	66.6125i	1.01070	+	0.472429i
$142$		0			0
$143$	55.0446	+	9.70585i	0.384927	+	0.0678731i
$144$		0			0
$145$	−34.0251	−	192.966i	−0.234656	−	1.33080i
$146$		0			0
$147$	2.22731	+	79.0508i	0.0151518	+	0.537761i
$148$		0			0
$149$	103.319	+	30.9317i	0.693417	+	0.207595i	0.614070	−	0.789252i	$-0.289531\pi$
$149$	103.319	+	30.9317i	0.693417	+	0.207595i	0.0793469	+	0.996847i	$0.474717\pi$
$150$		0			0
$151$	42.6597	−	4.98621i	0.282515	−	0.0330212i	0.0263445	−	0.999653i	$-0.491613\pi$
$151$	42.6597	−	4.98621i	0.282515	−	0.0330212i	0.256170	+	0.966632i	$0.417539\pi$
$152$		0			0
$153$	42.0297	+	27.7544i	0.274704	+	0.181401i
$154$		0			0
$155$	17.9870	−	27.3478i	0.116045	−	0.176438i
$156$		0			0
$157$	−2.82333	+	3.79238i	−0.0179830	+	0.0241553i	−0.811024	−	0.585013i	$-0.801089\pi$
$157$	−2.82333	+	3.79238i	−0.0179830	+	0.0241553i	0.793041	+	0.609169i	$0.208497\pi$
$158$		0			0
$159$	117.584	−	17.1130i	0.739522	−	0.107629i
$160$		0			0
$161$			75.6964i			0.470164i
$162$		0			0
$163$	215.812			1.32400			0.662001	−	0.749503i	$-0.269707\pi$
$163$	215.812			1.32400			0.662001	+	0.749503i	$0.269707\pi$
$164$		0			0
$165$	−94.2473	+	74.3802i	−0.571196	+	0.450789i
$166$		0			0
$167$	68.4444	+	50.9550i	0.409847	+	0.305120i	0.782266	−	0.622945i	$-0.214064\pi$
$167$	68.4444	+	50.9550i	0.409847	+	0.305120i	−0.372419	+	0.928065i	$0.621471\pi$
$168$		0			0
$169$	118.416	+	77.8835i	0.700687	+	0.460849i
$170$		0			0
$171$	76.0734	−	56.4171i	0.444873	−	0.329925i
$172$		0			0
$173$	−5.63109	−	48.1771i	−0.0325497	−	0.278480i	−0.999705	−	0.0242937i	$-0.992266\pi$
$173$	−5.63109	−	48.1771i	−0.0325497	−	0.278480i	0.967155	−	0.254187i	$-0.0818077\pi$
$174$		0			0
$175$	−15.0393	+	50.2348i	−0.0859389	+	0.287056i
$176$		0			0
$177$	47.0201	−	87.0123i	0.265650	−	0.491595i
$178$		0			0
$179$	29.9680	−	5.28417i	0.167419	−	0.0295205i	−0.0893101	−	0.996004i	$-0.528466\pi$
$179$	29.9680	−	5.28417i	0.167419	−	0.0295205i	0.256729	+	0.966483i	$0.417355\pi$
$180$		0			0
$181$	40.4209	−	229.238i	0.223320	−	1.26651i	−0.642552	−	0.766242i	$-0.722124\pi$
$181$	40.4209	−	229.238i	0.223320	−	1.26651i	0.865871	−	0.500267i	$-0.166765\pi$
$182$		0			0
$183$	−286.643	+	24.8121i	−1.56635	+	0.135585i
$184$		0			0
$185$	−9.89303	−	15.0416i	−0.0534759	−	0.0813061i
$186$		0			0
$187$	−17.1802	−	57.3860i	−0.0918729	−	0.306877i
$188$		0			0
$189$	−18.9701	+	127.060i	−0.100371	+	0.672273i
$190$		0			0
$191$	−153.174	−	144.512i	−0.801958	−	0.756608i	0.171571	−	0.985172i	$-0.445116\pi$
$191$	−153.174	−	144.512i	−0.801958	−	0.756608i	−0.973529	+	0.228564i	$0.926597\pi$
$192$		0			0
$193$	18.1666	+	311.908i	0.0941274	+	1.61611i	0.633297	+	0.773908i	$0.281701\pi$
$193$	18.1666	+	311.908i	0.0941274	+	1.61611i	−0.539170	+	0.842197i	$0.681262\pi$
$194$		0			0
$195$	56.5891	−	15.1072i	0.290200	−	0.0774727i
$196$		0			0
$197$	−43.7492	−	120.200i	−0.222077	−	0.610152i	0.777753	−	0.628570i	$-0.216359\pi$
$197$	−43.7492	−	120.200i	−0.222077	−	0.610152i	−0.999830	+	0.0184177i	$0.994137\pi$
$198$		0			0
$199$	−359.858	−	130.978i	−1.80833	−	0.658179i	−0.997321	−	0.0731461i	$-0.976696\pi$
$199$	−359.858	−	130.978i	−1.80833	−	0.658179i	−0.811010	−	0.585033i	$-0.801082\pi$
$200$		0			0
$201$	−82.6585	−	208.623i	−0.411236	−	1.03793i
$202$		0			0
$203$	57.5053	+	242.634i	0.283277	+	1.19524i
$204$		0			0
$205$	23.7582	−	55.0777i	0.115894	−	0.268672i
$206$		0			0
$207$	25.1228	−	140.960i	0.121366	−	0.680967i
$208$		0			0
$209$	−112.451	−	6.54953i	−0.538044	−	0.0313375i
$210$		0			0
$211$	−23.0672	−	53.4759i	−0.109323	−	0.253440i	0.854768	−	0.519010i	$-0.173699\pi$
$211$	−23.0672	−	53.4759i	−0.109323	−	0.253440i	−0.964092	+	0.265570i	$0.914440\pi$
$212$		0			0
$213$	−29.9920	−	90.7907i	−0.140808	−	0.426247i
$214$		0			0
$215$	179.726	−	103.765i	0.835934	−	0.482627i
$216$		0			0
$217$	−20.8278	+	36.0748i	−0.0959805	+	0.166243i
$218$		0			0
$219$	−80.9601	−	150.481i	−0.369681	−	0.687130i
$220$		0			0
$221$	−3.39254	+	29.0251i	−0.0153509	+	0.131335i
$222$		0			0
$223$	−244.819	+	122.953i	−1.09785	+	0.551359i	−0.903072	−	0.429490i	$-0.858693\pi$
$223$	−244.819	+	122.953i	−1.09785	+	0.551359i	−0.194773	+	0.980848i	$0.562397\pi$
$224$		0			0
$225$	44.6782	−	88.5547i	0.198570	−	0.393576i
$226$		0			0
$227$	66.7550	−	49.6973i	0.294075	−	0.218931i	−0.440002	−	0.897997i	$-0.645022\pi$
$227$	66.7550	−	49.6973i	0.294075	−	0.218931i	0.734077	+	0.679066i	$0.237615\pi$
$228$		0			0
$229$	−33.2348	−	35.2269i	−0.145130	−	0.153829i	0.650730	−	0.759309i	$-0.274463\pi$
$229$	−33.2348	−	35.2269i	−0.145130	−	0.153829i	−0.795861	+	0.605480i	$0.792981\pi$
$230$		0			0
$231$	114.232	−	101.469i	0.494510	−	0.439262i
$232$		0			0
$233$	−33.2461	−	39.6212i	−0.142687	−	0.170048i	0.689968	−	0.723840i	$-0.257625\pi$
$233$	−33.2461	−	39.6212i	−0.142687	−	0.170048i	−0.832655	+	0.553792i	$0.813180\pi$
$234$		0			0
$235$	−150.185	−	126.020i	−0.639083	−	0.536255i
$236$		0			0
$237$	−79.2921	−	55.6298i	−0.334566	−	0.234725i
$238$		0			0
$239$	−117.132	+	233.229i	−0.490092	+	0.975854i	0.503624	+	0.863923i	$0.332000\pi$
$239$	−117.132	+	233.229i	−0.490092	+	0.975854i	−0.993716	+	0.111931i	$0.964297\pi$
$240$		0			0
$241$	378.122	+	89.6165i	1.56897	+	0.371853i	0.920922	−	0.389746i	$-0.127437\pi$
$241$	378.122	+	89.6165i	1.56897	+	0.371853i	0.648048	+	0.761599i	$0.275585\pi$
$242$		0			0
$243$	77.4953	−	230.312i	0.318911	−	0.947785i
$244$		0			0
$245$	22.7294	−	95.9029i	0.0927731	−	0.391440i
$246$		0			0
$247$	49.1058	+	24.6619i	0.198809	+	0.0998457i
$248$		0			0
$249$	−22.2428	+	31.7039i	−0.0893285	+	0.127325i
$250$		0			0
$251$	283.465	−	337.821i	1.12934	−	1.34590i	0.198662	−	0.980068i	$-0.436340\pi$
$251$	283.465	−	337.821i	1.12934	−	1.34590i	0.930681	−	0.365831i	$-0.119215\pi$
$252$		0			0
$253$	−130.449	+	109.460i	−0.515611	+	0.432649i
$254$		0			0
$255$	−41.6871	−	46.9304i	−0.163479	−	0.184041i
$256$		0			0
$257$	−5.62529	+	5.30719i	−0.0218883	+	0.0206505i	−0.697108	−	0.716966i	$-0.745530\pi$
$257$	−5.62529	+	5.30719i	−0.0218883	+	0.0206505i	0.675220	+	0.737617i	$0.264049\pi$
$258$		0			0
$259$	13.6815	+	18.3775i	0.0528244	+	0.0709555i
$260$		0			0
$261$	−26.5576	−	470.912i	−0.101753	−	1.80426i
$262$		0			0
$263$	190.163	+	378.647i	0.723055	+	1.43972i	0.891037	+	0.453931i	$0.149979\pi$
$263$	190.163	+	378.647i	0.723055	+	1.43972i	−0.167982	+	0.985790i	$0.553725\pi$
$264$		0			0
$265$	−147.087	−	17.1920i	−0.555044	−	0.0648753i
$266$		0			0
$267$	−187.682	+	100.974i	−0.702928	+	0.378180i
$268$		0			0
$269$	339.417	+	195.963i	1.26177	+	0.728486i	0.973418	−	0.229037i	$-0.0735578\pi$
$269$	339.417	+	195.963i	1.26177	+	0.728486i	0.288357	+	0.957523i	$0.406891\pi$
$270$		0			0
$271$	−57.5950	−	99.7574i	−0.212528	−	0.368109i	0.739977	−	0.672632i	$-0.234836\pi$
$271$	−57.5950	−	99.7574i	−0.212528	−	0.368109i	−0.952505	+	0.304523i	$0.901503\pi$
$272$		0			0
$273$	−70.7752	+	23.3801i	−0.259250	+	0.0856412i
$274$		0			0
$275$	−108.318	+	46.7239i	−0.393885	+	0.169905i
$276$		0			0
$277$	3.24902	−	55.7835i	0.0117293	−	0.201385i	−0.987352	−	0.158541i	$-0.949321\pi$
$277$	3.24902	−	55.7835i	0.0117293	−	0.201385i	0.999082	−	0.0428440i	$-0.0136418\pi$
$278$		0			0
$279$	50.7578	−	60.2651i	0.181928	−	0.216004i
$280$		0			0
$281$	−392.022	−	169.102i	−1.39510	−	0.601786i	−0.439977	−	0.898009i	$-0.645013\pi$
$281$	−392.022	−	169.102i	−1.39510	−	0.601786i	−0.955119	+	0.296223i	$0.904273\pi$
$282$		0			0
$283$	−204.478	+	48.4623i	−0.722539	+	0.171245i	−0.575401	−	0.817871i	$-0.695154\pi$
$283$	−204.478	+	48.4623i	−0.722539	+	0.171245i	−0.147138	+	0.989116i	$0.547006\pi$
$284$		0			0
$285$	−109.737	+	43.4789i	−0.385043	+	0.152558i
$286$		0			0
$287$	−26.1079	+	71.7310i	−0.0909684	+	0.249934i
$288$		0			0
$289$	−242.141	+	88.1323i	−0.837859	+	0.304956i
$290$		0			0
$291$	−147.697	−	553.249i	−0.507550	−	1.90120i
$292$		0			0
$293$	−179.433	+	10.4508i	−0.612398	+	0.0356681i	−0.361541	−	0.932356i	$-0.617749\pi$
$293$	−179.433	+	10.4508i	−0.612398	+	0.0356681i	−0.250857	+	0.968024i	$0.580712\pi$
$294$		0			0
$295$	−84.5886	+	89.6586i	−0.286741	+	0.303928i
$296$		0			0
$297$	−246.397	+	151.042i	−0.829618	+	0.508558i
$298$		0			0
$299$	79.5837	−	23.8258i	0.266166	−	0.0796849i
$300$		0			0
$301$	−220.653	+	145.126i	−0.733066	+	0.482145i
$302$		0			0
$303$	4.63838	+	53.5850i	0.0153082	+	0.176848i
$304$		0			0
$305$	353.129	+	62.2661i	1.15780	+	0.204151i
$306$		0			0
$307$	−58.8444	−	333.723i	−0.191676	−	1.08705i	−0.917074	−	0.398717i	$-0.869455\pi$
$307$	−58.8444	−	333.723i	−0.191676	−	1.08705i	0.725398	−	0.688329i	$-0.241656\pi$
$308$		0			0
$309$	280.280	+	151.459i	0.907056	+	0.490159i
$310$		0			0
$311$	391.993	+	117.355i	1.26043	+	0.377347i	0.846219	−	0.532835i	$-0.178873\pi$
$311$	391.993	+	117.355i	1.26043	+	0.377347i	0.414208	+	0.910182i	$0.364058\pi$
$312$		0			0
$313$	536.791	−	62.7418i	1.71499	−	0.200453i	0.798908	−	0.601453i	$-0.205411\pi$
$313$	536.791	−	62.7418i	1.71499	−	0.200453i	0.916078	+	0.401000i	$0.131337\pi$
$314$		0			0
$315$	63.6864	−	146.897i	0.202179	−	0.466341i
$316$		0			0
$317$	228.446	−	347.335i	0.720649	−	1.09569i	−0.270472	−	0.962728i	$-0.587180\pi$
$317$	228.446	−	347.335i	0.720649	−	1.09569i	0.991121	−	0.132965i	$-0.0424499\pi$
$318$		0			0
$319$	−334.982	+	449.959i	−1.05010	+	1.41053i
$320$		0			0
$321$	139.572	+	176.852i	0.434803	+	0.550940i
$322$		0			0
$323$		−	58.8919i		−	0.182328i
$324$		0			0
$325$	57.5482			0.177071
$326$		0			0
$327$	28.6568	+	196.903i	0.0876356	+	0.602148i
$328$		0			0
$329$	200.125	+	148.988i	0.608284	+	0.452851i
$330$		0			0
$331$	−24.3183	−	15.9944i	−0.0734692	−	0.0483215i	0.512243	−	0.858841i	$-0.328815\pi$
$331$	−24.3183	−	15.9944i	−0.0734692	−	0.0483215i	−0.585712	+	0.810519i	$0.699185\pi$
$332$		0			0
$333$	−19.3781	−	38.7628i	−0.0581926	−	0.116405i
$334$		0			0
$335$	32.4677	+	277.779i	0.0969186	+	0.829192i
$336$		0			0
$337$	−31.2668	+	104.438i	−0.0927798	+	0.309906i	−0.991765	−	0.128074i	$-0.959121\pi$
$337$	−31.2668	+	104.438i	−0.0927798	+	0.309906i	0.898985	+	0.437980i	$0.144306\pi$
$338$		0			0
$339$	392.469	−	11.0581i	1.15773	−	0.0326197i
$340$		0			0
$341$	−92.2863	+	16.2726i	−0.270634	+	0.0477201i
$342$		0			0
$343$	−62.2654	+	353.124i	−0.181532	+	1.02952i
$344$		0			0
$345$	−75.5634	+	161.657i	−0.219024	+	0.468572i
$346$		0			0
$347$	177.792	+	270.320i	0.512369	+	0.779019i	0.995321	−	0.0966281i	$-0.0308058\pi$
$347$	177.792	+	270.320i	0.512369	+	0.779019i	−0.482952	+	0.875647i	$0.660435\pi$
$348$		0			0
$349$	−130.884	−	437.183i	−0.375026	−	1.25267i	−0.912390	−	0.409323i	$-0.865765\pi$
$349$	−130.884	−	437.183i	−0.375026	−	1.25267i	0.537364	−	0.843351i	$-0.319420\pi$
$350$		0			0
$351$	139.556	−	20.0483i	0.397594	−	0.0571178i
$352$		0			0
$353$	−285.540	−	269.393i	−0.808895	−	0.763153i	0.165927	−	0.986138i	$-0.446938\pi$
$353$	−285.540	−	269.393i	−0.808895	−	0.763153i	−0.974822	+	0.222985i	$0.928420\pi$
$354$		0			0
$355$	6.92888	+	118.964i	0.0195180	+	0.335111i
$356$		0			0
$357$	56.4336	+	56.5376i	0.158077	+	0.158369i
$358$		0			0
$359$	56.7575	+	155.940i	0.158099	+	0.434373i	0.993299	−	0.115573i	$-0.0368704\pi$
$359$	56.7575	+	155.940i	0.158099	+	0.434373i	−0.835200	+	0.549946i	$0.814648\pi$
$360$		0			0
$361$	235.166	+	85.5935i	0.651430	+	0.237101i
$362$		0			0
$363$	−19.0700	−	2.81128i	−0.0525344	−	0.00774457i
$364$		0			0
$365$	49.1128	+	207.223i	0.134556	+	0.567735i
$366$		0			0
$367$	−153.014	+	354.727i	−0.416933	+	0.966559i	0.572278	+	0.820060i	$0.306060\pi$
$367$	−153.014	+	354.727i	−0.416933	+	0.966559i	−0.989211	+	0.146499i	$0.953199\pi$
$368$		0			0
$369$	72.4243	−	124.911i	0.196272	−	0.338512i
$370$		0			0
$371$	188.137	+	10.9577i	0.507108	+	0.0295356i
$372$		0			0
$373$	37.3278	+	86.5355i	0.100074	+	0.231999i	0.960897	−	0.276907i	$-0.0893094\pi$
$373$	37.3278	+	86.5355i	0.100074	+	0.231999i	−0.860822	+	0.508906i	$0.830050\pi$
$374$		0			0
$375$	−268.877	+	301.575i	−0.717004	+	0.804199i
$376$		0			0
$377$	236.994	−	136.828i	0.628631	−	0.362940i
$378$		0			0
$379$	−200.722	+	347.660i	−0.529609	+	0.917309i	0.469795	+	0.882776i	$0.344328\pi$
$379$	−200.722	+	347.660i	−0.529609	+	0.917309i	−0.999404	+	0.0345335i	$0.989005\pi$
$380$		0			0
$381$	63.0856	+	1.89373i	0.165579	+	0.00497043i
$382$		0			0
$383$	−61.1247	+	522.955i	−0.159594	+	1.36542i	0.641612	+	0.767029i	$0.278266\pi$
$383$	−61.1247	+	522.955i	−0.159594	+	1.36542i	−0.801206	+	0.598388i	$0.795808\pi$
$384$		0			0
$385$	−170.167	+	85.4612i	−0.441993	+	0.221977i
$386$		0			0
$387$	459.060	−	197.018i	1.18620	−	0.509089i
$388$		0			0
$389$	−444.345	+	330.802i	−1.14227	+	0.850392i	−0.990431	−	0.138012i	$-0.955929\pi$
$389$	−444.345	+	330.802i	−1.14227	+	0.850392i	−0.151844	+	0.988404i	$0.548521\pi$
$390$		0			0
$391$	−61.0973	−	64.7593i	−0.156259	−	0.165625i
$392$		0			0
$393$	206.427	+	68.6136i	0.525261	+	0.174589i
$394$		0			0
$395$	77.5949	+	92.4740i	0.196443	+	0.234111i
$396$		0			0
$397$	76.8496	+	64.4845i	0.193576	+	0.162429i	0.734424	−	0.678691i	$-0.237452\pi$
$397$	76.8496	+	64.4845i	0.193576	+	0.162429i	−0.540848	+	0.841120i	$0.681897\pi$
$398$		0			0
$399$	136.198	−	63.3574i	0.341347	−	0.158790i
$400$		0			0
$401$	188.161	−	374.660i	0.469230	−	0.934314i	−0.527188	−	0.849749i	$-0.676754\pi$
$401$	188.161	−	374.660i	0.469230	−	0.934314i	0.996418	−	0.0845650i	$-0.0269501\pi$
$402$		0			0
$403$	44.4830	+	10.5427i	0.110380	+	0.0261604i
$404$		0			0
$405$	−167.349	+	252.412i	−0.413207	+	0.623240i
$406$		0			0
$407$	−11.8863	+	50.1523i	−0.0292047	+	0.123224i
$408$		0			0
$409$	135.074	+	67.8368i	0.330255	+	0.165860i	0.606198	−	0.795314i	$-0.292694\pi$
$409$	135.074	+	67.8368i	0.330255	+	0.165860i	−0.275943	+	0.961174i	$0.588990\pi$
$410$		0			0
$411$	396.412	+	35.0493i	0.964506	+	0.0852782i
$412$		0			0
$413$	100.830	−	120.165i	0.244142	−	0.290957i
$414$		0			0
$415$	36.9745	−	31.0253i	0.0890951	−	0.0747597i
$416$		0			0
$417$	63.7433	−	13.1008i	0.152862	−	0.0314167i
$418$		0			0
$419$	367.334	−	346.562i	0.876693	−	0.827117i	−0.109282	−	0.994011i	$-0.534855\pi$
$419$	367.334	−	346.562i	0.876693	−	0.827117i	0.985975	+	0.166894i	$0.0533736\pi$
$420$		0			0
$421$	295.389	+	396.776i	0.701636	+	0.942461i	0.999928	−	0.0120140i	$-0.00382426\pi$
$421$	295.389	+	396.776i	0.701636	+	0.942461i	−0.298292	+	0.954475i	$0.596417\pi$
$422$		0			0
$423$	−323.222	−	343.861i	−0.764117	−	0.812910i
$424$		0			0
$425$	−27.6800	−	55.1153i	−0.0651293	−	0.129683i
$426$		0			0
$427$	−453.237	−	52.9758i	−1.06144	−	0.124065i
$428$		0			0
$429$	−142.635	−	88.1601i	−0.332483	−	0.205501i
$430$		0			0
$431$	335.198	+	193.527i	0.777721	+	0.449017i	0.835622	−	0.549305i	$-0.185107\pi$
$431$	335.198	+	193.527i	0.777721	+	0.449017i	−0.0579010	+	0.998322i	$0.518441\pi$
$432$		0			0
$433$	−224.531	−	388.900i	−0.518548	−	0.898152i	−0.999768	−	0.0215515i	$-0.993139\pi$
$433$	−224.531	−	388.900i	−0.518548	−	0.898152i	0.481220	−	0.876600i	$-0.340194\pi$
$434$		0			0
$435$	−119.399	+	575.574i	−0.274480	+	1.32316i
$436$		0			0
$437$	−153.725	+	66.3104i	−0.351773	+	0.151740i
$438$		0			0
$439$	−34.2243	+	587.609i	−0.0779597	+	1.33852i	0.701771	+	0.712402i	$0.252393\pi$
$439$	−34.2243	+	587.609i	−0.0779597	+	1.33852i	−0.779731	+	0.626115i	$0.784644\pi$
$440$		0			0
$441$	81.5535	−	222.789i	0.184928	−	0.505191i
$442$		0			0
$443$	−258.524	−	111.516i	−0.583576	−	0.251730i	0.0837614	−	0.996486i	$-0.473307\pi$
$443$	−258.524	−	111.516i	−0.583576	−	0.251730i	−0.667337	+	0.744756i	$0.732566\pi$
$444$		0			0
$445$	258.451	−	61.2539i	0.580788	−	0.137649i
$446$		0			0
$447$	−253.613	−	200.911i	−0.567366	−	0.449464i
$448$		0			0
$449$	−50.6783	+	139.238i	−0.112869	+	0.310106i	−0.983247	−	0.182279i	$-0.941653\pi$
$449$	−50.6783	+	139.238i	−0.112869	+	0.310106i	0.870377	+	0.492385i	$0.163875\pi$
$450$		0			0
$451$	−161.369	+	58.7335i	−0.357802	+	0.130229i
$452$		0			0
$453$	−124.429	−	33.4635i	−0.274678	−	0.0738709i
$454$		0			0
$455$	92.7377	−	5.40136i	0.203819	−	0.0118711i
$456$		0			0
$457$	558.475	−	591.948i	1.22204	−	1.29529i	0.279923	−	0.960023i	$-0.409691\pi$
$457$	558.475	−	591.948i	1.22204	−	1.29529i	0.942122	−	0.335269i	$-0.108827\pi$
$458$		0			0
$459$	−86.3252	−	124.013i	−0.188072	−	0.270180i
$460$		0			0
$461$	668.129	−	200.025i	1.44930	−	0.433893i	0.537062	−	0.843543i	$-0.319534\pi$
$461$	668.129	−	200.025i	1.44930	−	0.433893i	0.912243	+	0.409650i	$0.134349\pi$
$462$		0			0
$463$	−313.179	+	205.981i	−0.676412	+	0.444883i	−0.840680	−	0.541533i	$-0.817844\pi$
$463$	−313.179	+	205.981i	−0.676412	+	0.444883i	0.164268	+	0.986416i	$0.447474\pi$
$464$		0			0
$465$	−80.4912	+	56.2502i	−0.173099	+	0.120968i
$466$		0			0
$467$	−180.965	−	31.9091i	−0.387506	−	0.0683278i	−0.0234987	−	0.999724i	$-0.507481\pi$
$467$	−180.965	−	31.9091i	−0.387506	−	0.0683278i	−0.364007	+	0.931396i	$0.618592\pi$
$468$		0			0
$469$	−61.8026	−	350.500i	−0.131775	−	0.747334i
$470$		0			0
$471$	12.0789	−	7.43504i	0.0256453	−	0.0157857i
$472$		0			0
$473$	−569.172	−	170.399i	−1.20332	−	0.360251i
$474$		0			0
$475$	−115.192	+	13.4640i	−0.242509	+	0.0283452i
$476$		0			0
$477$	−346.708	−	82.8457i	−0.726850	−	0.173681i
$478$		0			0
$479$	−287.426	+	437.010i	−0.600054	+	0.912338i	−0.999991	−	0.00420485i	$-0.998662\pi$
$479$	−287.426	+	437.010i	−0.600054	+	0.912338i	0.399937	+	0.916543i	$0.369032\pi$
$480$		0			0
$481$	15.0149	−	20.1685i	0.0312160	−	0.0419304i
$482$		0			0
$483$	84.0370	−	210.968i	0.173990	−	0.436786i
$484$		0			0
$485$			713.658i			1.47146i
$486$		0			0
$487$	868.356			1.78307			0.891536	−	0.452949i	$-0.149628\pi$
$487$	868.356			1.78307			0.891536	+	0.452949i	$0.149628\pi$
$488$		0			0
$489$	−601.474	−	239.592i	−1.23001	−	0.489962i
$490$		0			0
$491$	584.290	+	434.987i	1.19000	+	0.885922i	0.995479	−	0.0949771i	$-0.0302778\pi$
$491$	584.290	+	434.987i	1.19000	+	0.885922i	0.194520	+	0.980899i	$0.437685\pi$
$492$		0			0
$493$	−245.035	−	161.162i	−0.497028	−	0.326901i
$494$		0			0
$495$	345.245	−	102.667i	0.697465	−	0.207409i
$496$		0			0
$497$	−17.6055	−	150.624i	−0.0354235	−	0.303067i
$498$		0			0
$499$	168.979	−	564.429i	0.338635	−	1.13112i	−0.603913	−	0.797050i	$-0.706393\pi$
$499$	168.979	−	564.429i	0.338635	−	1.13112i	0.942548	−	0.334070i	$-0.108422\pi$
$500$		0			0
$501$	−134.187	−	217.999i	−0.267838	−	0.435127i
$502$		0			0
$503$	−461.070	+	81.2990i	−0.916640	+	0.161628i	−0.612017	−	0.790845i	$-0.709642\pi$
$503$	−461.070	+	81.2990i	−0.916640	+	0.161628i	−0.304623	+	0.952473i	$0.598530\pi$
$504$		0			0
$505$	11.6400	−	66.0140i	0.0230496	−	0.130721i
$506$		0			0
$507$	−243.563	−	348.527i	−0.480401	−	0.687430i
$508$		0			0
$509$	−216.585	−	329.301i	−0.425510	−	0.646956i	0.557571	−	0.830129i	$-0.311734\pi$
$509$	−216.585	−	329.301i	−0.425510	−	0.646956i	−0.983081	+	0.183173i	$0.941363\pi$
$510$		0			0
$511$	−77.7283	−	259.631i	−0.152110	−	0.508084i
$512$		0			0
$513$	−274.652	+	72.7803i	−0.535383	+	0.141872i
$514$		0			0
$515$	−288.805	−	272.473i	−0.560786	−	0.529074i
$516$		0			0
$517$	32.6351	+	560.323i	0.0631240	+	1.08380i
$518$		0			0
$519$	−37.7915	+	140.522i	−0.0728160	+	0.270756i
$520$		0			0
$521$	−220.120	−	604.775i	−0.422496	−	1.16080i	−0.950274	−	0.311415i	$-0.899197\pi$
$521$	−220.120	−	604.775i	−0.422496	−	1.16080i	0.527778	−	0.849382i	$-0.323025\pi$
$522$		0			0
$523$	129.725	+	47.2159i	0.248040	+	0.0902790i	0.463048	−	0.886333i	$-0.346756\pi$
$523$	129.725	+	47.2159i	0.248040	+	0.0902790i	−0.215009	+	0.976612i	$0.568978\pi$
$524$		0			0
$525$	97.6847	−	123.309i	0.186066	−	0.234874i
$526$		0			0
$527$	−11.2988	−	47.6733i	−0.0214398	−	0.0904617i
$528$		0			0
$529$	109.279	−	253.338i	0.206577	−	0.478900i
$530$		0			0
$531$	−227.646	+	190.304i	−0.428711	+	0.358388i
$532$		0			0
$533$	83.6322	+	4.87102i	0.156908	+	0.00913888i
$534$		0			0
$535$	−111.212	−	257.817i	−0.207872	−	0.481902i
$536$		0			0
$537$	−89.3880	−	18.5430i	−0.166458	−	0.0345306i
$538$		0			0
$539$	−244.361	+	141.082i	−0.453360	+	0.261748i
$540$		0			0
$541$	290.221	−	502.678i	0.536453	−	0.929164i	−0.462638	−	0.886547i	$-0.653097\pi$
$541$	290.221	−	502.678i	0.536453	−	0.929164i	0.999091	−	0.0426171i	$-0.0135695\pi$
$542$		0			0
$543$	−367.150	+	594.017i	−0.676152	+	1.09395i
$544$		0			0
$545$	28.7891	−	246.307i	0.0528241	−	0.451939i
$546$		0			0
$547$	−230.863	+	115.944i	−0.422054	+	0.211963i	−0.647133	−	0.762377i	$-0.724032\pi$
$547$	−230.863	+	115.944i	−0.422054	+	0.211963i	0.225079	+	0.974340i	$0.427736\pi$
$548$		0			0
$549$	826.425	+	249.074i	1.50533	+	0.453687i
$550$		0			0
$551$	−442.367	+	329.330i	−0.802845	+	0.597696i
$552$		0			0
$553$	−105.422	−	111.741i	−0.190637	−	0.202063i
$554$		0			0
$555$	10.8731	+	52.9044i	0.0195912	+	0.0953233i
$556$		0			0
$557$	−530.543	−	632.276i	−0.952501	−	1.13515i	−0.990726	−	0.135877i	$-0.956615\pi$
$557$	−530.543	−	632.276i	−0.952501	−	1.13515i	0.0382252	−	0.999269i	$-0.487830\pi$
$558$		0			0
$559$	222.030	+	186.305i	0.397191	+	0.333283i
$560$		0			0
$561$	−15.8273	+	179.009i	−0.0282127	+	0.319089i
$562$		0			0
$563$	400.146	−	796.756i	0.710739	−	1.41520i	−0.190417	−	0.981703i	$-0.560984\pi$
$563$	400.146	−	796.756i	0.710739	−	1.41520i	0.901156	−	0.433494i	$-0.142720\pi$
$564$		0			0
$565$	−476.135	−	112.846i	−0.842718	−	0.199728i
$566$		0			0
$567$	193.930	−	333.058i	0.342028	−	0.587403i
$568$		0			0
$569$	226.456	−	955.491i	0.397989	−	1.67925i	−0.292787	−	0.956178i	$-0.594583\pi$
$569$	226.456	−	955.491i	0.397989	−	1.67925i	0.690776	−	0.723069i	$-0.257269\pi$
$570$		0			0
$571$	64.1225	+	32.2035i	0.112299	+	0.0563985i	0.504062	−	0.863668i	$-0.331838\pi$
$571$	64.1225	+	32.2035i	0.112299	+	0.0563985i	−0.391763	+	0.920066i	$0.628135\pi$
$572$		0			0
$573$	266.464	+	572.810i	0.465033	+	0.999668i
$574$		0			0
$575$	−112.700	+	134.311i	−0.196000	+	0.233584i
$576$		0			0
$577$	303.996	−	255.083i	0.526856	−	0.442085i	−0.340158	−	0.940368i	$-0.610481\pi$
$577$	303.996	−	255.083i	0.526856	−	0.442085i	0.867014	+	0.498283i	$0.166036\pi$
$578$		0			0
$579$	295.645	−	889.464i	0.510613	−	1.53621i
$580$		0			0
$581$	−44.6782	+	42.1517i	−0.0768987	+	0.0725502i
$582$		0			0
$583$	253.170	+	340.066i	0.434254	+	0.583304i
$584$		0			0
$585$	−174.487	−	20.7203i	−0.298268	−	0.0354193i
$586$		0			0
$587$	184.790	+	367.947i	0.314804	+	0.626827i	0.994272	−	0.106878i	$-0.0340856\pi$
$587$	184.790	+	367.947i	0.314804	+	0.626827i	−0.679468	+	0.733705i	$0.737789\pi$
$588$		0			0
$589$	−91.5061	−	10.6955i	−0.155358	−	0.0181588i
$590$		0			0
$591$	−11.5142	+	383.570i	−0.0194825	+	0.649018i
$592$		0			0
$593$	98.1896	+	56.6898i	0.165581	+	0.0955983i	0.580501	−	0.814260i	$-0.302857\pi$
$593$	98.1896	+	56.6898i	0.165581	+	0.0955983i	−0.414919	+	0.909858i	$0.636190\pi$
$594$		0			0
$595$	−49.7787	−	86.2192i	−0.0836616	−	0.144906i
$596$		0			0
$597$	857.522	+	764.546i	1.43639	+	1.28065i
$598$		0			0
$599$	−767.126	+	330.906i	−1.28068	+	0.552430i	−0.924213	−	0.381878i	$-0.875277\pi$
$599$	−767.126	+	330.906i	−1.28068	+	0.552430i	−0.356465	+	0.934309i	$0.616018\pi$
$600$		0			0
$601$	−5.42209	+	93.0937i	−0.00902178	+	0.154898i	0.990788	+	0.135419i	$0.0432379\pi$
$601$	−5.42209	+	93.0937i	−0.00902178	+	0.154898i	−0.999810	+	0.0194794i	$0.993799\pi$
$602$		0			0
$603$	−1.23951	+	673.204i	−0.00205557	+	1.11642i
$604$		0			0
$605$	22.0589	+	9.51529i	0.0364610	+	0.0157278i
$606$		0			0
$607$	1072.66	−	254.225i	1.76715	−	0.418822i	0.786978	−	0.616982i	$-0.211645\pi$
$607$	1072.66	−	254.225i	1.76715	−	0.418822i	0.980170	+	0.198160i	$0.0634966\pi$
$608$		0			0
$609$	109.100	−	740.067i	0.179146	−	1.21522i
$610$		0			0
$611$	93.6485	−	257.297i	0.153271	−	0.421108i
$612$		0			0
$613$	−1040.43	+	378.687i	−1.69728	+	0.617760i	−0.995511	−	0.0946443i	$-0.969829\pi$
$613$	−1040.43	+	378.687i	−1.69728	+	0.617760i	−0.701770	+	0.712404i	$0.747606\pi$
$614$		0			0
$615$	−127.361	+	127.127i	−0.207091	+	0.206710i
$616$		0			0
$617$	−963.879	+	56.1395i	−1.56220	+	0.0909879i	−0.817311	−	0.576197i	$-0.804536\pi$
$617$	−963.879	+	56.1395i	−1.56220	+	0.0909879i	−0.744892	+	0.667185i	$0.767499\pi$
$618$		0			0
$619$	620.422	−	657.609i	1.00230	−	1.06237i	0.00424496	−	0.999991i	$-0.498649\pi$
$619$	620.422	−	657.609i	1.00230	−	1.06237i	0.998052	−	0.0623821i	$-0.0198697\pi$
$620$		0			0
$621$	−226.509	+	364.968i	−0.364750	+	0.587710i
$622$		0			0
$623$	−323.814	+	96.9435i	−0.519765	+	0.155607i
$624$		0			0
$625$	190.510	−	125.300i	0.304816	−	0.200481i
$626$		0			0
$627$	306.132	+	143.095i	0.488250	+	0.228222i
$628$		0			0
$629$	−26.5378	−	4.67934i	−0.0421905	−	0.00743933i
$630$		0			0
$631$	−86.6647	−	491.500i	−0.137345	−	0.778922i	−0.973198	−	0.229969i	$-0.926138\pi$
$631$	−86.6647	−	491.500i	−0.137345	−	0.778922i	0.835853	−	0.548953i	$-0.184974\pi$
$632$		0			0
$633$	4.92080	+	174.647i	0.00777378	+	0.275904i
$634$		0			0
$635$	−75.3541	−	22.5595i	−0.118668	−	0.0355268i
$636$		0			0
$637$	136.719	−	15.9802i	0.214630	−	0.0250867i
$638$		0			0
$639$	−17.2060	+	286.332i	−0.0269265	+	0.448094i
$640$		0			0
$641$	458.241	−	696.721i	0.714884	−	1.08693i	−0.277134	−	0.960831i	$-0.589384\pi$
$641$	458.241	−	696.721i	0.714884	−	1.08693i	0.992018	−	0.126097i	$-0.0402451\pi$
$642$		0			0
$643$	206.304	−	277.114i	0.320846	−	0.430971i	−0.612214	−	0.790692i	$-0.709721\pi$
$643$	206.304	−	277.114i	0.320846	−	0.430971i	0.933060	+	0.359721i	$0.117128\pi$
$644$		0			0
$645$	−616.098	+	89.6658i	−0.955190	+	0.139017i
$646$		0			0
$647$		−	564.348i		−	0.872253i	−0.899885	−	0.436127i	$-0.856350\pi$
$647$		−	564.348i		−	0.872253i	0.899885	−	0.436127i	$-0.143650\pi$
$648$		0			0
$649$	352.888			0.543742
$650$		0			0
$651$	98.0971	−	77.4185i	0.150687	−	0.118922i
$652$		0			0
$653$	−43.5742	−	32.4398i	−0.0667292	−	0.0496780i	0.563277	−	0.826268i	$-0.309540\pi$
$653$	−43.5742	−	32.4398i	−0.0667292	−	0.0496780i	−0.630006	+	0.776590i	$0.716948\pi$
$654$		0			0
$655$	−226.508	−	148.977i	−0.345814	−	0.227445i
$656$		0			0
$657$	58.5755	+	509.276i	0.0891560	+	0.775153i
$658$		0			0
$659$	110.969	+	949.397i	0.168389	+	1.44066i	0.768040	+	0.640401i	$0.221232\pi$
$659$	110.969	+	949.397i	0.168389	+	1.44066i	−0.599651	+	0.800262i	$0.704694\pi$
$660$		0			0
$661$	178.937	−	597.692i	0.270707	−	0.904223i	−0.709241	−	0.704966i	$-0.750962\pi$
$661$	178.937	−	597.692i	0.270707	−	0.904223i	0.979947	−	0.199257i	$-0.0638528\pi$
$662$		0			0
$663$	41.6783	−	77.1272i	0.0628632	−	0.116331i
$664$		0			0
$665$	−184.365	+	32.5086i	−0.277241	+	0.0488850i
$666$		0			0
$667$	−144.778	+	821.075i	−0.217058	+	1.23100i
$668$		0			0
$669$	818.818	−	70.8778i	1.22394	−	0.105946i
$670$		0			0
$671$	−564.104	−	857.679i	−0.840692	−	1.27821i
$672$		0			0
$673$	39.4371	+	131.729i	0.0585989	+	0.195734i	0.982277	−	0.187436i	$-0.0600176\pi$
$673$	39.4371	+	131.729i	0.0585989	+	0.195734i	−0.923678	+	0.383170i	$0.874832\pi$
$674$		0			0
$675$	−222.831	+	197.203i	−0.330120	+	0.292152i
$676$		0			0
$677$	435.742	+	411.101i	0.643637	+	0.607240i	0.937239	−	0.348688i	$-0.113373\pi$
$677$	435.742	+	411.101i	0.643637	+	0.607240i	−0.293602	+	0.955928i	$0.594854\pi$
$678$		0			0
$679$	−52.8070	−	906.661i	−0.0777717	−	1.33529i
$680$		0			0
$681$	−241.221	+	64.3970i	−0.354216	+	0.0945623i
$682$		0			0
$683$	−164.403	−	451.692i	−0.240706	−	0.661336i	−0.999945	−	0.0105227i	$-0.996650\pi$
$683$	−164.403	−	451.692i	−0.240706	−	0.661336i	0.759238	−	0.650813i	$-0.225572\pi$
$684$		0			0
$685$	−466.062	−	169.633i	−0.680383	−	0.247639i
$686$		0			0
$687$	53.5179	+	135.075i	0.0779009	+	0.196616i
$688$		0			0
$689$	−47.6965	−	201.247i	−0.0692257	−	0.292086i
$690$		0			0
$691$	63.6440	−	147.543i	0.0921041	−	0.213521i	−0.865936	−	0.500154i	$-0.833277\pi$
$691$	63.6440	−	147.543i	0.0921041	−	0.213521i	0.958041	+	0.286633i	$0.0925359\pi$
$692$		0			0
$693$	−431.017	+	155.979i	−0.621957	+	0.225078i
$694$		0			0
$695$	−80.9660	−	4.71573i	−0.116498	−	0.00678523i
$696$		0			0
$697$	−35.5609	−	82.4395i	−0.0510200	−	0.118278i
$698$		0			0
$699$	48.6708	+	147.334i	0.0696292	+	0.210779i
$700$		0			0
$701$	−214.085	+	123.602i	−0.305400	+	0.176323i	−0.644866	−	0.764295i	$-0.723087\pi$
$701$	−214.085	+	123.602i	−0.305400	+	0.176323i	0.339466	+	0.940618i	$0.389754\pi$
$702$		0			0
$703$	−25.3360	+	43.8833i	−0.0360398	+	0.0624228i
$704$		0			0
$705$	278.662	+	517.953i	0.395266	+	0.734684i
$706$		0			0
$707$	−9.90330	+	84.7281i	−0.0140075	+	0.119842i
$708$		0			0
$709$	−140.524	+	70.5738i	−0.198200	+	0.0995399i	−0.545131	−	0.838351i	$-0.683520\pi$
$709$	−140.524	+	70.5738i	−0.198200	+	0.0995399i	0.346931	+	0.937891i	$0.387224\pi$
$710$		0			0
$711$	159.229	+	243.070i	0.223951	+	0.341871i
$712$		0			0
$713$	−111.719	+	83.1717i	−0.156689	+	0.116650i
$714$		0			0
$715$	143.411	+	152.007i	0.200575	+	0.212597i
$716$		0			0
$717$	585.377	−	519.976i	0.816425	−	0.725211i
$718$		0			0
$719$	−660.354	−	786.979i	−0.918434	−	1.09455i	−0.995235	−	0.0975004i	$-0.968915\pi$
$719$	−660.354	−	786.979i	−0.918434	−	1.09455i	0.0768017	−	0.997046i	$-0.475529\pi$
$720$		0			0
$721$	387.071	+	324.791i	0.536852	+	0.450473i
$722$		0			0
$723$	−954.343	−	669.548i	−1.31998	−	0.926070i
$724$		0			0
$725$	−259.210	+	516.130i	−0.357531	+	0.711903i
$726$		0			0
$727$	−794.499	−	188.300i	−1.09285	−	0.259009i	−0.355603	−	0.934637i	$-0.615724\pi$
$727$	−794.499	−	188.300i	−1.09285	−	0.259009i	−0.737243	+	0.675628i	$0.763873\pi$
$728$		0			0
$729$	−471.670	+	555.850i	−0.647009	+	0.762482i
$730$		0			0
$731$	71.6355	−	302.254i	0.0979966	−	0.413480i
$732$		0			0
$733$	644.074	+	323.466i	0.878682	+	0.441291i	0.830156	−	0.557531i	$-0.188251\pi$
$733$	644.074	+	323.466i	0.878682	+	0.441291i	0.0485263	+	0.998822i	$0.484548\pi$
$734$		0			0
$735$	−169.817	+	242.050i	−0.231044	+	0.329319i
$736$		0			0
$737$	514.656	−	613.343i	0.698312	−	0.832215i
$738$		0			0
$739$	−1.82552	+	1.53179i	−0.00247025	+	0.00207279i	−0.644022	−	0.765007i	$-0.722735\pi$
$739$	−1.82552	+	1.53179i	−0.00247025	+	0.00207279i	0.641552	+	0.767080i	$0.278291\pi$
$740$		0			0
$741$	−109.480	−	123.250i	−0.147746	−	0.166329i
$742$		0			0
$743$	905.837	−	854.613i	1.21916	−	1.15022i	0.235179	−	0.971952i	$-0.424432\pi$
$743$	905.837	−	854.613i	1.21916	−	1.15022i	0.983982	−	0.178267i	$-0.0570490\pi$
$744$		0			0
$745$	240.797	+	323.446i	0.323217	+	0.434156i
$746$		0			0
$747$	97.1883	−	63.6657i	0.130105	−	0.0852286i
$748$		0			0
$749$	160.365	+	319.313i	0.214105	+	0.426319i
$750$		0			0
$751$	22.2978	+	2.60624i	0.0296909	+	0.00347037i	0.130925	−	0.991392i	$-0.458205\pi$
$751$	22.2978	+	2.60624i	0.0296909	+	0.00347037i	−0.101235	+	0.994863i	$0.532279\pi$
$752$		0			0
$753$	−1165.07	+	626.815i	−1.54723	+	0.832423i
$754$		0			0
$755$	139.071	+	80.2927i	0.184200	+	0.106348i
$756$		0			0
$757$	100.399	+	173.896i	0.132627	+	0.229717i	0.924688	−	0.380725i	$-0.124325\pi$
$757$	100.399	+	173.896i	0.132627	+	0.229717i	−0.792061	+	0.610441i	$0.790992\pi$
$758$		0			0
$759$	485.086	−	160.245i	0.639113	−	0.211126i
$760$		0			0
$761$	−1163.54	+	501.904i	−1.52897	+	0.659532i	−0.983877	−	0.178846i	$-0.942764\pi$
$761$	−1163.54	+	501.904i	−1.52897	+	0.659532i	−0.545090	+	0.838378i	$0.683505\pi$
$762$		0			0
$763$	−18.3495	+	315.048i	−0.0240491	+	0.412908i
$764$		0			0
$765$	64.0816	+	177.076i	0.0837667	+	0.231472i
$766$		0			0
$767$	−158.073	−	68.1860i	−0.206092	−	0.0888996i
$768$		0			0
$769$	1010.19	−	239.420i	1.31365	−	0.311340i	0.486674	−	0.873584i	$-0.338210\pi$
$769$	1010.19	−	239.420i	1.31365	−	0.311340i	0.826971	+	0.562244i	$0.190062\pi$
$770$		0			0
$771$	21.5698	−	8.54614i	0.0279764	−	0.0110845i
$772$		0			0
$773$	−443.535	+	1218.60i	−0.573785	+	1.57646i	0.224689	+	0.974430i	$0.427863\pi$
$773$	−443.535	+	1218.60i	−0.573785	+	1.57646i	−0.798474	+	0.602030i	$0.794359\pi$
$774$		0			0
$775$	−90.6651	+	32.9994i	−0.116987	+	0.0425799i
$776$		0			0
$777$	−17.7283	−	66.4074i	−0.0228163	−	0.0854664i
$778$		0			0
$779$	−168.542	+	9.81648i	−0.216357	+	0.0126014i
$780$		0			0
$781$	234.116	−	248.149i	0.299765	−	0.317732i
$782$		0			0
$783$	−448.783	+	1341.93i	−0.573158	+	1.71383i
$784$		0			0
$785$	−16.9345	+	5.06987i	−0.0215727	+	0.00645843i
$786$		0			0
$787$	318.724	−	209.628i	0.404986	−	0.266363i	−0.330633	−	0.943760i	$-0.607262\pi$
$787$	318.724	−	209.628i	0.404986	−	0.266363i	0.735618	+	0.677396i	$0.236892\pi$
$788$		0			0
$789$	−109.622	−	1266.41i	−0.138938	−	1.60509i
$790$		0			0
$791$	613.252	+	108.133i	0.775287	+	0.136704i
$792$		0			0
$793$	86.9620	+	493.186i	0.109662	+	0.621925i
$794$		0			0
$795$	390.847	+	211.208i	0.491632	+	0.265670i
$796$		0			0
$797$	323.152	+	96.7455i	0.405461	+	0.121387i	0.483038	−	0.875599i	$-0.339533\pi$
$797$	323.152	+	96.7455i	0.405461	+	0.121387i	−0.0775772	+	0.996986i	$0.524718\pi$
$798$		0			0
$799$	−291.463	+	34.0672i	−0.364785	+	0.0426373i
$800$		0			0
$801$	635.173	−	73.0559i	0.792975	−	0.0912058i
$802$		0			0
$803$	335.030	−	509.388i	0.417222	−	0.634356i
$804$		0			0
$805$	−169.008	+	227.017i	−0.209947	+	0.282008i
$806$		0			0
$807$	−728.409	−	922.968i	−0.902613	−	1.14370i
$808$		0			0
$809$			1449.37i			1.79156i	0.444495	+	0.895781i	$0.353383\pi$
$809$			1449.37i			1.79156i	−0.444495	+	0.895781i	$0.646617\pi$
$810$		0			0
$811$	1215.86			1.49921			0.749603	−	0.661888i	$-0.230244\pi$
$811$	1215.86			1.49921			0.749603	+	0.661888i	$0.230244\pi$
$812$		0			0
$813$	49.7693	+	341.967i	0.0612168	+	0.420624i
$814$		0			0
$815$	647.230	+	481.845i	0.794147	+	0.591221i
$816$		0			0
$817$	−488.015	−	320.973i	−0.597326	−	0.392867i
$818$		0			0
$819$	223.208	+	13.4128i	0.272538	+	0.0163771i
$820$		0			0
$821$	18.5801	+	158.963i	0.0226310	+	0.193621i	0.999825	−	0.0187298i	$-0.00596223\pi$
$821$	18.5801	+	158.963i	0.0226310	+	0.193621i	−0.977194	+	0.212350i	$0.931888\pi$
$822$		0			0
$823$	277.908	−	928.276i	0.337676	−	1.12792i	−0.605561	−	0.795799i	$-0.707051\pi$
$823$	277.908	−	928.276i	0.337676	−	1.12792i	0.943238	−	0.332119i	$-0.107763\pi$
$824$		0			0
$825$	353.758	−	9.96736i	0.428797	−	0.0120816i
$826$		0			0
$827$	−1259.13	+	222.019i	−1.52253	+	0.268463i	−0.871426	−	0.490527i	$-0.836804\pi$
$827$	−1259.13	+	222.019i	−1.52253	+	0.268463i	−0.651103	+	0.758990i	$0.725693\pi$
$828$		0			0
$829$	−35.6634	+	202.257i	−0.0430198	+	0.243978i	−0.998733	−	0.0503220i	$-0.983975\pi$
$829$	−35.6634	+	202.257i	−0.0430198	+	0.243978i	0.955713	+	0.294300i	$0.0950863\pi$
$830$		0			0
$831$	−70.9851	+	151.863i	−0.0854213	+	0.182747i
$832$		0			0
$833$	−81.0649	−	123.253i	−0.0973168	−	0.147963i
$834$		0			0
$835$	91.5003	+	305.632i	0.109581	+	0.366027i
$836$		0			0
$837$	−208.368	+	111.610i	−0.248947	+	0.133345i
$838$		0			0
$839$	−245.053	−	231.195i	−0.292077	−	0.275560i	0.526229	−	0.850343i	$-0.323605\pi$
$839$	−245.053	−	231.195i	−0.292077	−	0.275560i	−0.818306	+	0.574782i	$0.805087\pi$
$840$		0			0
$841$	110.793	+	1902.24i	0.131740	+	2.26188i
$842$		0			0
$843$	904.839	+	906.507i	1.07336	+	1.07533i
$844$		0			0
$845$	181.244	+	497.964i	0.214490	+	0.589307i
$846$		0			0
$847$	−28.7286	−	10.4564i	−0.0339181	−	0.0123452i
$848$		0			0
$849$	623.688	+	91.9434i	0.734615	+	0.108296i
$850$		0			0
$851$	17.6663	+	74.5402i	0.0207595	+	0.0875913i
$852$		0			0
$853$	−234.133	+	542.781i	−0.274482	+	0.636321i	−0.998574	−	0.0533826i	$-0.983000\pi$
$853$	−234.133	+	542.781i	−0.274482	+	0.636321i	0.724092	+	0.689703i	$0.242259\pi$
$854$		0			0
$855$	354.110	+	0.651990i	0.414164	+	0.000762561i
$856$		0			0
$857$	1520.62	+	88.5662i	1.77436	+	0.103345i	0.913839	−	0.406076i	$-0.133103\pi$
$857$	1520.62	+	88.5662i	1.77436	+	0.103345i	0.860517	+	0.509421i	$0.170140\pi$
$858$		0			0
$859$	−314.247	−	728.505i	−0.365828	−	0.848085i	−0.997352	−	0.0727286i	$-0.976829\pi$
$859$	−314.247	−	728.505i	−0.365828	−	0.848085i	0.631523	−	0.775357i	$-0.282430\pi$
$860$		0			0
$861$	152.398	−	170.931i	0.177001	−	0.198526i
$862$		0			0
$863$	−524.230	+	302.664i	−0.607450	+	0.350712i	−0.771967	−	0.635663i	$-0.780727\pi$
$863$	−524.230	+	302.664i	−0.607450	+	0.350712i	0.164517	+	0.986374i	$0.447394\pi$
$864$		0			0
$865$	90.6773	−	157.058i	0.104829	−	0.181570i
$866$		0			0
$867$	772.696	+	23.1951i	0.891230	+	0.0267533i
$868$		0			0
$869$	40.1212	−	343.259i	0.0461694	−	0.395005i
$870$		0			0
$871$	−349.046	+	175.298i	−0.400742	+	0.201260i
$872$		0			0
$873$	−202.574	+	1705.89i	−0.232044	+	1.95405i
$874$		0			0
$875$	−514.004	+	382.662i	−0.587434	+	0.437328i
$876$		0			0
$877$	229.216	+	242.955i	0.261364	+	0.277029i	0.844745	−	0.535169i	$-0.179752\pi$
$877$	229.216	+	242.955i	0.261364	+	0.277029i	−0.583381	+	0.812198i	$0.698271\pi$
$878$		0			0
$879$	511.685	+	170.077i	0.582121	+	0.193489i
$880$		0			0
$881$	91.1162	+	108.588i	0.103424	+	0.123255i	0.815273	−	0.579076i	$-0.196587\pi$
$881$	91.1162	+	108.588i	0.103424	+	0.123255i	−0.711850	+	0.702332i	$0.752142\pi$
$882$		0			0
$883$	982.063	+	824.048i	1.11219	+	0.933237i	0.998184	−	0.0602431i	$-0.0191876\pi$
$883$	982.063	+	824.048i	1.11219	+	0.933237i	0.114005	+	0.993480i	$0.463632\pi$
$884$		0			0
$885$	335.288	−	155.972i	0.378856	−	0.176239i
$886$		0			0
$887$	638.858	−	1272.07i	0.720246	−	1.43413i	−0.173168	−	0.984892i	$-0.555400\pi$
$887$	638.858	−	1272.07i	0.720246	−	1.43413i	0.893414	−	0.449235i	$-0.148303\pi$
$888$		0			0
$889$	97.4022	+	23.0848i	0.109564	+	0.0259671i
$890$		0			0
$891$	854.397	−	147.411i	0.958919	−	0.165445i
$892$		0			0
$893$	−127.255	+	536.930i	−0.142503	+	0.601265i
$894$		0			0
$895$	101.673	+	51.0623i	0.113602	+	0.0570528i
$896$		0			0
$897$	−248.252	−	21.9496i	−0.276759	−	0.0244700i
$898$		0			0
$899$	−294.915	+	351.466i	−0.328047	+	0.390952i
$900$		0			0
$901$	−169.798	+	142.478i	−0.188455	+	0.158133i
$902$		0			0
$903$	776.081	−	159.503i	0.859447	−	0.176637i
$904$		0			0
$905$	633.045	−	597.247i	0.699497	−	0.659941i
$906$		0			0
$907$	−976.076	−	1311.10i	−1.07616	−	1.44553i	−0.885946	−	0.463789i	$-0.846490\pi$
$907$	−976.076	−	1311.10i	−1.07616	−	1.44553i	−0.190213	−	0.981743i	$-0.560918\pi$
$908$		0			0
$909$	46.5620	−	154.492i	0.0512233	−	0.169958i
$910$		0			0
$911$	173.350	+	345.168i	0.190285	+	0.378889i	0.968464	−	0.249154i	$-0.0801525\pi$
$911$	173.350	+	345.168i	0.190285	+	0.378889i	−0.778179	+	0.628043i	$0.783856\pi$
$912$		0			0
$913$	−137.247	−	16.0419i	−0.150326	−	0.0175706i
$914$		0			0
$915$	−915.051	−	565.575i	−1.00006	−	0.618115i
$916$		0			0
$917$	298.788	+	172.505i	0.325832	+	0.188119i
$918$		0			0
$919$	675.858	+	1170.62i	0.735427	+	1.27380i	0.954536	+	0.298097i	$0.0963519\pi$
$919$	675.858	+	1170.62i	0.735427	+	1.27380i	−0.219108	+	0.975701i	$0.570315\pi$
$920$		0			0
$921$	−206.494	+	995.422i	−0.224206	+	1.08081i
$922$		0			0
$923$	−152.818	+	65.9193i	−0.165567	+	0.0714185i
$924$		0			0
$925$	−3.08558	+	52.9774i	−0.00333576	+	0.0572729i
$926$		0			0
$927$	−613.000	−	733.282i	−0.661273	−	0.791027i
$928$		0			0
$929$	597.809	+	257.870i	0.643498	+	0.277578i	0.692716	−	0.721210i	$-0.256414\pi$
$929$	597.809	+	257.870i	0.643498	+	0.277578i	−0.0492186	+	0.998788i	$0.515673\pi$
$930$		0			0
$931$	−269.926	+	63.9737i	−0.289932	+	0.0687151i
$932$		0			0
$933$	−962.207	−	762.256i	−1.03130	−	0.816994i
$934$		0			0
$935$	76.6016	−	210.461i	0.0819269	−	0.225092i
$936$		0			0
$937$	132.631	−	48.2738i	0.141549	−	0.0515195i	−0.270274	−	0.962783i	$-0.587114\pi$
$937$	132.631	−	48.2738i	0.141549	−	0.0515195i	0.411823	+	0.911264i	$0.364892\pi$
$938$		0			0
$939$	−1565.70	−	421.074i	−1.66741	−	0.448428i
$940$		0			0
$941$	−1075.77	+	62.6563i	−1.14322	+	0.0665848i	−0.619278	−	0.785172i	$-0.712575\pi$
$941$	−1075.77	+	62.6563i	−1.14322	+	0.0665848i	−0.523938	+	0.851756i	$0.675538\pi$
$942$		0			0
$943$	−175.150	+	185.649i	−0.185737	+	0.196870i
$944$		0			0
$945$	−340.579	+	338.703i	−0.360401	+	0.358415i
$946$		0			0
$947$	−101.651	+	30.4322i	−0.107340	+	0.0321354i	−0.340023	−	0.940417i	$-0.610435\pi$
$947$	−101.651	+	30.4322i	−0.107340	+	0.0321354i	0.232683	+	0.972553i	$0.425250\pi$
$948$		0			0
$949$	−248.498	+	163.440i	−0.261853	+	0.172223i
$950$		0			0
$951$	−1022.29	+	714.413i	−1.07496	+	0.751223i
$952$		0			0
$953$	−308.415	−	54.3819i	−0.323626	−	0.0570640i	0.00947524	−	0.999955i	$-0.496984\pi$
$953$	−308.415	−	54.3819i	−0.323626	−	0.0570640i	−0.333101	+	0.942891i	$0.608095\pi$
$954$		0			0
$955$	−136.722	−	775.390i	−0.143165	−	0.811927i
$956$		0			0
$957$	1433.14	−	882.153i	1.49753	−	0.921790i
$958$		0			0
$959$	604.656	+	181.022i	0.630507	+	0.188761i
$960$		0			0
$961$	878.375	−	102.667i	0.914022	−	0.106834i
$962$		0			0
$963$	−192.652	−	647.840i	−0.200054	−	0.672731i
$964$		0			0
$965$	−641.917	+	975.987i	−0.665198	+	1.01139i
$966$		0			0
$967$	858.995	−	1153.83i	0.888309	−	1.19321i	−0.0920046	−	0.995759i	$-0.529327\pi$
$967$	858.995	−	1153.83i	0.888309	−	1.19321i	0.980314	−	0.197447i	$-0.0632651\pi$
$968$		0			0
$969$	−65.3809	+	164.133i	−0.0674725	+	0.169384i
$970$		0			0
$971$			47.5473i			0.0489674i	0.999700	+	0.0244837i	$0.00779418\pi$
$971$			47.5473i			0.0489674i	−0.999700	+	0.0244837i	$0.992206\pi$
$972$		0			0
$973$	103.211			0.106076
$974$		0			0
$975$	−160.388	−	63.8891i	−0.164501	−	0.0655273i
$976$		0			0
$977$	834.926	+	621.579i	0.854581	+	0.636212i	0.932669	−	0.360734i	$-0.117474\pi$
$977$	834.926	+	621.579i	0.854581	+	0.636212i	−0.0780872	+	0.996947i	$0.524881\pi$
$978$		0			0
$979$	−635.313	−	417.852i	−0.648941	−	0.426815i
$980$		0			0
$981$	138.731	−	580.586i	0.141418	−	0.591831i
$982$		0			0
$983$	−47.5208	−	406.567i	−0.0483426	−	0.413598i	−0.995643	−	0.0932501i	$-0.970274\pi$
$983$	−47.5208	−	406.567i	−0.0483426	−	0.413598i	0.947300	−	0.320348i	$-0.103800\pi$
$984$		0			0
$985$	137.165	−	458.164i	0.139254	−	0.465141i
$986$		0			0
$987$	−392.350	−	637.408i	−0.397518	−	0.645804i
$988$		0			0
$989$	−869.629	+	153.339i	−0.879301	+	0.155045i
$990$		0			0
$991$	−200.524	+	1137.23i	−0.202345	+	1.14755i	0.699219	+	0.714908i	$0.253531\pi$
$991$	−200.524	+	1137.23i	−0.202345	+	1.14755i	−0.901563	+	0.432647i	$0.857580\pi$
$992$		0			0
$993$	50.0189	+	71.5746i	0.0503715	+	0.0720791i
$994$		0			0
$995$	−786.795	−	1196.26i	−0.790748	−	1.20227i
$996$		0			0
$997$	−263.654	−	880.667i	−0.264448	−	0.883317i	−0.982331	−	0.187153i	$-0.940074\pi$
$997$	−263.654	−	880.667i	−0.264448	−	0.883317i	0.717883	−	0.696164i	$-0.245111\pi$
$998$		0			0
$999$	10.9734	+	129.546i	0.0109844	+	0.129676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.3.o.a.65.3	yes	324
81.5	odd	54	inner	324.3.o.a.5.3	✓	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
324.3.o.a.5.3	✓	324	81.5	odd	54	inner
324.3.o.a.65.3	yes	324	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-2.78702 - 1.11018i) q^{3} +(2.99904 + 2.23270i) q^{5} +(-3.97531 - 2.61460i) q^{7} +(6.53498 + 6.18822i) q^{9} +O(q^{10})\)	\(q+(-2.78702 - 1.11018i) q^{3} +(2.99904 + 2.23270i) q^{5} +(-3.97531 - 2.61460i) q^{7} +(6.53498 + 6.18822i) q^{9} +(-1.24265 - 10.6316i) q^{11} +(-1.49763 + 5.00242i) q^{13} +(-5.87968 - 9.55208i) q^{15} +(5.51128 - 0.971787i) q^{17} +(1.82736 - 10.3635i) q^{19} +(8.17659 + 11.7003i) q^{21} +(-8.74216 - 13.2918i) q^{23} +(-3.16080 - 10.5578i) q^{25} +(-11.3431 - 24.5017i) q^{27} +(-38.1193 - 35.9637i) q^{29} +(-0.509041 - 8.73990i) q^{31} +(-8.33971 + 31.0100i) q^{33} +(-6.08449 - 16.7170i) q^{35} +(-4.52480 - 1.64689i) q^{37} +(9.72752 - 12.2792i) q^{39} +(-3.69981 - 15.6107i) q^{41} +(21.9847 - 50.9663i) q^{43} +(5.78222 + 33.1494i) q^{45} +(-52.3473 - 3.04888i) q^{47} +(-10.4410 - 24.2049i) q^{49} +(-16.4389 - 3.41014i) q^{51} +(-34.3012 + 19.8038i) q^{53} +(20.0104 - 34.6590i) q^{55} +(-16.5983 + 26.8546i) q^{57} +(-3.82736 + 32.7451i) q^{59} +(85.7037 - 43.0420i) q^{61} +(-9.79885 - 41.6865i) q^{63} +(-15.6604 + 11.6587i) q^{65} +(51.3313 + 54.4080i) q^{67} +(9.60823 + 46.7500i) q^{69} +(20.4870 + 24.4154i) q^{71} +(43.6333 + 36.6127i) q^{73} +(-2.91189 + 32.9339i) q^{75} +(-22.8574 + 45.5129i) q^{77} +(31.4164 + 7.44583i) q^{79} +(4.41193 + 80.8798i) q^{81} +(2.97712 - 12.5614i) q^{83} +(18.6983 + 9.39062i) q^{85} +(66.3129 + 142.551i) q^{87} +(45.6637 - 54.4198i) q^{89} +(19.0329 - 15.9705i) q^{91} +(-8.28419 + 24.9234i) q^{93} +(28.6190 - 27.0006i) q^{95} +(113.983 + 153.105i) q^{97} +(57.6698 - 77.1670i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q+O(q^{10}) \) 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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