LMFDB - Embedded newform 294.2.p.a.101.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [294,2,Mod(5,294)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(294, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 29]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("294.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 294 = 2 \cdot 3 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	294.p (of order $42$, degree $12$, 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:	$2.34760181943$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			101.6
Character	$\chi$	$=$	294.101
Dual form			294.2.p.a.131.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.930874 - 0.365341i) q^{2} +(0.996433 + 1.41673i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.655797 - 0.447115i) q^{5} +(-0.409964 - 1.68283i) q^{6} +(0.217232 + 2.63682i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-1.01424 + 2.82335i) q^{9} +O(q^{10})$	\(q+(-0.930874 - 0.365341i) q^{2} +(0.996433 + 1.41673i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.655797 - 0.447115i) q^{5} +(-0.409964 - 1.68283i) q^{6} +(0.217232 + 2.63682i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-1.01424 + 2.82335i) q^{9} +(0.447115 + 0.655797i) q^{10} +(0.169672 + 1.12570i) q^{11} +(-0.233184 + 1.71628i) q^{12} +(-0.0449563 + 0.0358514i) q^{13} +(0.761122 - 2.53391i) q^{14} +(-0.0200168 - 1.37461i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(1.90714 + 0.588275i) q^{17} +(1.97562 - 2.25764i) q^{18} +(-2.58631 + 1.49321i) q^{19} +(-0.176618 - 0.773813i) q^{20} +(-3.51920 + 2.93517i) q^{21} +(0.253321 - 1.10987i) q^{22} +(1.62062 + 5.25393i) q^{23} +(0.844093 - 1.51245i) q^{24} +(-1.59655 - 4.06794i) q^{25} +(0.0549466 - 0.0169488i) q^{26} +(-5.01055 + 1.37637i) q^{27} +(-1.63425 + 2.08068i) q^{28} +(-0.688874 + 0.157231i) q^{29} +(-0.483567 + 1.28690i) q^{30} +(5.31255 + 3.06720i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-1.42575 + 1.36206i) q^{33} +(-1.56039 - 1.24437i) q^{34} +(1.03650 - 1.82634i) q^{35} +(-2.66386 + 1.37980i) q^{36} +(-2.45744 + 2.28017i) q^{37} +(2.95306 - 0.445101i) q^{38} +(-0.0955877 - 0.0279673i) q^{39} +(-0.118297 + 0.784848i) q^{40} +(8.84115 - 4.25767i) q^{41} +(4.34827 - 1.44656i) q^{42} +(6.62093 + 3.18847i) q^{43} +(-0.641292 + 0.940603i) q^{44} +(1.92750 - 1.39806i) q^{45} +(0.410881 - 5.48282i) q^{46} +(2.56225 - 6.52851i) q^{47} +(-1.33830 + 1.09952i) q^{48} +(-6.90562 + 1.14560i) q^{49} +4.37002i q^{50} +(1.06691 + 3.28808i) q^{51} +(-0.0573405 - 0.00429707i) q^{52} +(0.289787 - 0.312316i) q^{53} +(5.16703 + 0.549333i) q^{54} +(0.392047 - 0.814093i) q^{55} +(2.28144 - 1.33979i) q^{56} +(-4.69255 - 2.17622i) q^{57} +(0.698698 + 0.105312i) q^{58} +(5.09218 - 3.47179i) q^{59} +(0.920296 - 1.02127i) q^{60} +(-7.26602 - 7.83091i) q^{61} +(-3.82474 - 4.79607i) q^{62} +(-7.66499 - 2.06106i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(0.0455119 - 0.00341064i) q^{65} +(1.82481 - 0.747026i) q^{66} +(4.84017 - 8.38342i) q^{67} +(0.997904 + 1.72842i) q^{68} +(-5.82855 + 7.53117i) q^{69} +(-1.63209 + 1.32142i) q^{70} +(-13.9162 - 3.17628i) q^{71} +(2.98382 - 0.311204i) q^{72} +(8.46509 - 3.32230i) q^{73} +(3.12060 - 1.22475i) q^{74} +(4.17231 - 6.31530i) q^{75} +(-2.91154 - 0.664539i) q^{76} +(-2.93141 + 0.691932i) q^{77} +(0.0787625 + 0.0609562i) q^{78} +(-1.41114 - 2.44416i) q^{79} +(0.396857 - 0.687376i) q^{80} +(-6.94262 - 5.72713i) q^{81} +(-9.78549 + 0.733321i) q^{82} +(8.28124 - 10.3843i) q^{83} +(-4.57618 - 0.242032i) q^{84} +(-0.987669 - 1.23850i) q^{85} +(-4.99837 - 5.38696i) q^{86} +(-0.909171 - 0.819278i) q^{87} +(0.940603 - 0.641292i) q^{88} +(-4.00546 - 0.603726i) q^{89} +(-2.30503 + 0.597223i) q^{90} +(-0.104300 - 0.110753i) q^{91} +(-2.38558 + 4.95370i) q^{92} +(0.948204 + 10.5827i) q^{93} +(-4.77026 + 5.14112i) q^{94} +(2.36373 + 0.177137i) q^{95} +(1.64749 - 0.534576i) q^{96} +3.54633i q^{97} +(6.84680 + 1.45649i) q^{98} +(-3.35034 - 0.662691i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	$ 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) $ 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/294\mathbb{Z}\right)^\times$.

$n$	$197$	$199$
$\chi(n)$	$-1$	$e\left(\frac{1}{42}\right)$

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 $

$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$2$	−0.930874	−	0.365341i	−0.658227	−	0.258335i
$3$	0.996433	+	1.41673i	0.575291	+	0.817949i
$3$	0.996433	+	1.41673i	0.575291	+	0.817949i
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	−0.655797	−	0.447115i	−0.293281	−	0.199956i	0.407736	−	0.913100i	$-0.366318\pi$
$5$	−0.655797	−	0.447115i	−0.293281	−	0.199956i	−0.701018	+	0.713144i	$0.747271\pi$
$6$	−0.409964	−	1.68283i	−0.167367	−	0.687014i
$7$	0.217232	+	2.63682i	0.0821060	+	0.996624i
$7$	0.217232	+	2.63682i	0.0821060	+	0.996624i
$8$	−0.433884	−	0.900969i	−0.153401	−	0.318541i
$9$	−1.01424	+	2.82335i	−0.338081	+	0.941117i
$10$	0.447115	+	0.655797i	0.141390	+	0.207381i
$11$	0.169672	+	1.12570i	0.0511580	+	0.339411i	0.999738	+	0.0228748i	$0.00728192\pi$
$11$	0.169672	+	1.12570i	0.0511580	+	0.339411i	−0.948580	+	0.316537i	$0.897480\pi$
$12$	−0.233184	+	1.71628i	−0.0673144	+	0.495448i
$13$	−0.0449563	+	0.0358514i	−0.0124686	+	0.00994340i	−0.629704	−	0.776835i	$-0.716824\pi$
$13$	−0.0449563	+	0.0358514i	−0.0124686	+	0.00994340i	0.617236	+	0.786778i	$0.288253\pi$
$14$	0.761122	−	2.53391i	0.203418	−	0.677216i
$15$	−0.0200168	−	1.37461i	−0.00516832	−	0.354922i
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	1.90714	+	0.588275i	0.462549	+	0.142678i	0.517267	−	0.855824i	$-0.326950\pi$
$17$	1.90714	+	0.588275i	0.462549	+	0.142678i	−0.0547173	+	0.998502i	$0.517426\pi$
$18$	1.97562	−	2.25764i	0.465658	−	0.532130i
$19$	−2.58631	+	1.49321i	−0.593340	+	0.342565i	−0.766417	−	0.642343i	$-0.777962\pi$
$19$	−2.58631	+	1.49321i	−0.593340	+	0.342565i	0.173077	+	0.984908i	$0.444629\pi$
$20$	−0.176618	−	0.773813i	−0.0394929	−	0.173030i
$21$	−3.51920	+	2.93517i	−0.767953	+	0.640507i
$22$	0.253321	−	1.10987i	0.0540083	−	0.236626i
$23$	1.62062	+	5.25393i	0.337923	+	1.09552i	0.951955	+	0.306238i	$0.0990705\pi$
$23$	1.62062	+	5.25393i	0.337923	+	1.09552i	−0.614032	+	0.789281i	$0.710453\pi$
$24$	0.844093	−	1.51245i	0.172300	−	0.308728i
$25$	−1.59655	−	4.06794i	−0.319309	−	0.813587i
$26$	0.0549466	−	0.0169488i	0.0107759	−	0.00332393i
$27$	−5.01055	+	1.37637i	−0.964281	+	0.264882i
$28$	−1.63425	+	2.08068i	−0.308844	+	0.393212i
$29$	−0.688874	+	0.157231i	−0.127921	+	0.0291971i	−0.286002	−	0.958229i	$-0.592326\pi$
$29$	−0.688874	+	0.157231i	−0.127921	+	0.0291971i	0.158081	+	0.987426i	$0.449469\pi$
$30$	−0.483567	+	1.28690i	−0.0882868	+	0.234954i
$31$	5.31255	+	3.06720i	0.954163	+	0.550886i	0.894372	−	0.447325i	$-0.147623\pi$
$31$	5.31255	+	3.06720i	0.954163	+	0.550886i	0.0597913	+	0.998211i	$0.480956\pi$
$32$	0.294755	−	0.955573i	0.0521058	−	0.168923i
$33$	−1.42575	+	1.36206i	−0.248191	+	0.237105i
$34$	−1.56039	−	1.24437i	−0.267604	−	0.213407i
$35$	1.03650	−	1.82634i	0.175200	−	0.308708i
$36$	−2.66386	+	1.37980i	−0.443977	+	0.229967i
$37$	−2.45744	+	2.28017i	−0.404000	+	0.374857i	−0.855839	−	0.517242i	$-0.826959\pi$
$37$	−2.45744	+	2.28017i	−0.404000	+	0.374857i	0.451839	+	0.892099i	$0.350768\pi$
$38$	2.95306	−	0.445101i	0.479049	−	0.0722050i
$39$	−0.0955877	−	0.0279673i	−0.0153063	−	0.00447836i
$40$	−0.118297	+	0.784848i	−0.0187044	+	0.124095i
$41$	8.84115	−	4.25767i	1.38075	−	0.664937i	0.411594	−	0.911367i	$-0.364972\pi$
$41$	8.84115	−	4.25767i	1.38075	−	0.664937i	0.969160	+	0.246431i	$0.0792577\pi$
$42$	4.34827	−	1.44656i	0.670953	−	0.223210i
$43$	6.62093	+	3.18847i	1.00968	+	0.486237i	0.864213	−	0.503126i	$-0.167817\pi$
$43$	6.62093	+	3.18847i	1.00968	+	0.486237i	0.145469	+	0.989363i	$0.453531\pi$
$44$	−0.641292	+	0.940603i	−0.0966785	+	0.141801i
$45$	1.92750	−	1.39806i	0.287335	−	0.208411i
$46$	0.410881	−	5.48282i	0.0605811	−	0.808398i
$47$	2.56225	−	6.52851i	0.373743	−	0.952281i	−0.613014	−	0.790072i	$-0.710043\pi$
$47$	2.56225	−	6.52851i	0.373743	−	0.952281i	0.986756	−	0.162209i	$-0.0518618\pi$
$48$	−1.33830	+	1.09952i	−0.193168	+	0.158702i
$49$	−6.90562	+	1.14560i	−0.986517	+	0.163658i
$50$			4.37002i			0.618014i
$51$	1.06691	+	3.28808i	0.149397	+	0.460423i
$52$	−0.0573405	−	0.00429707i	−0.00795169	−	0.000595897i
$53$	0.289787	−	0.312316i	0.0398053	−	0.0428999i	−0.712835	−	0.701331i	$-0.752589\pi$
$53$	0.289787	−	0.312316i	0.0398053	−	0.0428999i	0.752641	+	0.658432i	$0.228780\pi$
$54$	5.16703	+	0.549333i	0.703144	+	0.0747548i
$55$	0.392047	−	0.814093i	0.0528636	−	0.109772i
$56$	2.28144	−	1.33979i	0.304870	−	0.179037i
$57$	−4.69255	−	2.17622i	−0.621543	−	0.288247i
$58$	0.698698	+	0.105312i	0.0917436	+	0.0138281i
$59$	5.09218	−	3.47179i	0.662946	−	0.451989i	−0.184527	−	0.982827i	$-0.559075\pi$
$59$	5.09218	−	3.47179i	0.662946	−	0.451989i	0.847473	+	0.530839i	$0.178123\pi$
$60$	0.920296	−	1.02127i	0.118810	−	0.131846i
$61$	−7.26602	−	7.83091i	−0.930319	−	1.00265i	−0.999987	−	0.00507533i	$-0.998384\pi$
$61$	−7.26602	−	7.83091i	−0.930319	−	1.00265i	0.0696680	−	0.997570i	$-0.477806\pi$
$62$	−3.82474	−	4.79607i	−0.485743	−	0.609102i
$63$	−7.66499	−	2.06106i	−0.965698	−	0.259669i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	0.0455119	−	0.00341064i	0.00564505	−	0.000423038i
$66$	1.82481	−	0.747026i	0.224618	−	0.0919526i
$67$	4.84017	−	8.38342i	0.591321	−	1.02420i	−0.402734	−	0.915317i	$-0.631940\pi$
$67$	4.84017	−	8.38342i	0.591321	−	1.02420i	0.994055	−	0.108880i	$-0.0347266\pi$
$68$	0.997904	+	1.72842i	0.121014	+	0.209602i
$69$	−5.82855	+	7.53117i	−0.701675	+	0.906646i
$70$	−1.63209	+	1.32142i	−0.195072	+	0.157940i
$71$	−13.9162	−	3.17628i	−1.65155	−	0.376955i	−0.707488	−	0.706725i	$-0.750172\pi$
$71$	−13.9162	−	3.17628i	−1.65155	−	0.376955i	−0.944061	+	0.329770i	$0.893029\pi$
$72$	2.98382	−	0.311204i	0.351646	−	0.0366757i
$73$	8.46509	−	3.32230i	0.990764	−	0.388846i	0.186071	−	0.982536i	$-0.440425\pi$
$73$	8.46509	−	3.32230i	0.990764	−	0.388846i	0.804694	+	0.593690i	$0.202329\pi$
$74$	3.12060	−	1.22475i	0.362762	−	0.142374i
$75$	4.17231	−	6.31530i	0.481777	−	0.729228i
$76$	−2.91154	−	0.664539i	−0.333976	−	0.0762278i
$77$	−2.93141	+	0.691932i	−0.334065	+	0.0788530i
$78$	0.0787625	+	0.0609562i	0.00891809	+	0.00690193i
$79$	−1.41114	−	2.44416i	−0.158765	−	0.274989i	0.775658	−	0.631153i	$-0.217418\pi$
$79$	−1.41114	−	2.44416i	−0.158765	−	0.274989i	−0.934424	+	0.356163i	$0.884085\pi$
$80$	0.396857	−	0.687376i	0.0443699	−	0.0768509i
$81$	−6.94262	−	5.72713i	−0.771402	−	0.636348i
$82$	−9.78549	+	0.733321i	−1.08063	+	0.0809818i
$83$	8.28124	−	10.3843i	0.908984	−	1.13983i	−0.0807250	−	0.996736i	$-0.525724\pi$
$83$	8.28124	−	10.3843i	0.908984	−	1.13983i	0.989709	−	0.143094i	$-0.0457050\pi$
$84$	−4.57618	−	0.242032i	−0.499302	−	0.0264079i
$85$	−0.987669	−	1.23850i	−0.107128	−	0.134334i
$86$	−4.99837	−	5.38696i	−0.538988	−	0.580891i
$87$	−0.909171	−	0.819278i	−0.0974733	−	0.0878359i
$88$	0.940603	−	0.641292i	0.100269	−	0.0683620i
$89$	−4.00546	−	0.603726i	−0.424578	−	0.0639948i	−0.0667220	−	0.997772i	$-0.521254\pi$
$89$	−4.00546	−	0.603726i	−0.424578	−	0.0639948i	−0.357856	+	0.933777i	$0.616492\pi$
$90$	−2.30503	+	0.597223i	−0.242971	+	0.0629529i
$91$	−0.104300	−	0.110753i	−0.0109336	−	0.0116101i
$92$	−2.38558	+	4.95370i	−0.248714	+	0.516459i
$93$	0.948204	+	10.5827i	0.0983241	+	1.09738i
$94$	−4.77026	+	5.14112i	−0.492015	+	0.530266i
$95$	2.36373	+	0.177137i	0.242513	+	0.0181738i
$96$	1.64749	−	0.534576i	0.168146	−	0.0545599i
$97$			3.54633i			0.360076i	0.983660	+	0.180038i	$0.0576220\pi$
$97$			3.54633i			0.360076i	−0.983660	+	0.180038i	$0.942378\pi$
$98$	6.84680	+	1.45649i	0.691631	+	0.147128i
$99$	−3.35034	−	0.662691i	−0.336721	−	0.0666030i
$100$	1.59655	−	4.06794i	0.159655	−	0.406794i
$101$	−0.682345	+	9.10527i	−0.0678959	+	0.906008i	0.854423	+	0.519578i	$0.173911\pi$
$101$	−0.682345	+	9.10527i	−0.0678959	+	0.906008i	−0.922319	+	0.386430i	$0.873708\pi$
$102$	0.208111	−	3.45057i	0.0206060	−	0.341657i
$103$	10.8498	−	15.9137i	1.06906	−	1.56803i	0.273778	−	0.961793i	$-0.411727\pi$
$103$	10.8498	−	15.9137i	1.06906	−	1.56803i	0.795285	−	0.606235i	$-0.207321\pi$
$104$	0.0518068	+	0.0249489i	0.00508008	+	0.00244644i
$105$	3.62024	−	0.351389i	0.353299	−	0.0342921i
$106$	−0.383857	+	0.184856i	−0.0372835	+	0.0179548i
$107$	−0.408321	+	2.70904i	−0.0394739	+	0.261892i	−0.999859	−	0.0167835i	$-0.994657\pi$
$107$	−0.408321	+	2.70904i	−0.0394739	+	0.261892i	0.960385	+	0.278676i	$0.0898955\pi$
$108$	−4.60916	−	2.39909i	−0.443517	−	0.230852i
$109$	−0.100826	+	0.0151971i	−0.00965741	+	0.00145562i	−0.153869	−	0.988091i	$-0.549173\pi$
$109$	−0.100826	+	0.0151971i	−0.00965741	+	0.00145562i	0.144212	+	0.989547i	$0.453935\pi$
$110$	−0.662368	+	0.614587i	−0.0631543	+	0.0585986i
$111$	−5.67905	−	1.20949i	−0.539031	−	0.114800i
$112$	−2.61321	+	0.413674i	−0.246925	+	0.0390885i
$113$	3.18369	+	2.53891i	0.299497	+	0.238841i	0.761695	−	0.647936i	$-0.224368\pi$
$113$	3.18369	+	2.53891i	0.299497	+	0.238841i	−0.462198	+	0.886777i	$0.652939\pi$
$114$	3.57311	+	3.74017i	0.334652	+	0.350299i
$115$	1.28631	−	4.17011i	0.119949	−	0.388865i
$116$	−0.611925	−	0.353295i	−0.0568158	−	0.0328026i
$117$	−0.0556245	−	0.163289i	−0.00514249	−	0.0150961i
$118$	−6.00857	+	1.37142i	−0.553133	+	0.126249i
$119$	−1.13688	+	5.15657i	−0.104218	+	0.472702i
$120$	−1.22979	+	0.614454i	−0.112264	+	0.0560917i
$121$	9.27289	−	2.86031i	0.842990	−	0.260028i
$122$	3.90280	+	9.94417i	0.353343	+	0.900303i
$123$	14.8416	+	8.28303i	1.33822	+	0.746855i
$124$	1.80815	+	5.86187i	0.162377	+	0.526412i
$125$	−1.65491	+	7.25064i	−0.148020	+	0.648517i
$126$	6.38215	+	4.71892i	0.568567	+	0.420395i
$127$	4.97967	+	21.8174i	0.441874	+	1.93598i	0.337049	+	0.941487i	$0.390571\pi$
$127$	4.97967	+	21.8174i	0.441874	+	1.93598i	0.104826	+	0.994491i	$0.466572\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	2.08011	+	12.5572i	0.183143	+	1.10560i
$130$	−0.0436119	−	0.0134525i	−0.00382501	−	0.00117986i
$131$	−0.839679	−	11.2047i	−0.0733631	−	0.978962i	−0.905487	−	0.424373i	$-0.860495\pi$
$131$	−0.839679	−	11.2047i	−0.0733631	−	0.978962i	0.832124	−	0.554589i	$-0.187125\pi$
$132$	−1.97158	+	0.0287099i	−0.171604	+	0.00249888i
$133$	−4.49914	−	6.49525i	−0.390125	−	0.563210i
$134$	−7.56839	+	6.03559i	−0.653809	+	0.521396i
$135$	3.90130	+	1.33767i	0.335770	+	0.115128i
$136$	−0.297460	−	1.97352i	−0.0255070	−	0.169228i
$137$	5.67410	+	8.32237i	0.484771	+	0.711028i	0.988227	−	0.152992i	$-0.0488910\pi$
$137$	5.67410	+	8.32237i	0.484771	+	0.711028i	−0.503457	+	0.864020i	$0.667939\pi$
$138$	8.17709	−	4.88116i	0.696080	−	0.415512i
$139$	5.33555	+	11.0794i	0.452555	+	0.939741i	0.995021	+	0.0996632i	$0.0317765\pi$
$139$	5.33555	+	11.0794i	0.452555	+	0.939741i	−0.542466	+	0.840078i	$0.682509\pi$
$140$	2.00204	−	0.633806i	0.169203	−	0.0535664i
$141$	11.8022	−	2.87520i	0.993928	−	0.242136i
$142$	11.7938	+	8.04088i	0.989714	+	0.674775i
$143$	−0.0479858	−	0.0445243i	−0.00401277	−	0.00372331i
$144$	−2.89125	−	0.800419i	−0.240938	−	0.0667016i
$145$	0.522062	+	0.204894i	0.0433549	+	0.0170155i
$146$	−9.09371			−0.752601
$147$	−8.50399	−	8.64188i	−0.701398	−	0.712770i
$148$	−3.35233			−0.275560
$149$	−11.0780	−	4.34781i	−0.907549	−	0.356187i	−0.134781	−	0.990875i	$-0.543033\pi$
$149$	−11.0780	−	4.34781i	−0.907549	−	0.356187i	−0.772768	+	0.634689i	$0.781128\pi$
$150$	−6.19113	+	4.35443i	−0.505504	+	0.355538i
$151$	10.0790	+	9.35192i	0.820215	+	0.761048i	0.973877	−	0.227075i	$-0.0729163\pi$
$151$	10.0790	+	9.35192i	0.820215	+	0.761048i	−0.153662	+	0.988123i	$0.549107\pi$
$152$	2.46749	+	1.68231i	0.200140	+	0.136453i
$153$	−3.59521	+	4.78787i	−0.290656	+	0.387076i
$154$	2.98156	+	0.426862i	0.240261	+	0.0343975i
$155$	−2.11256	−	4.38678i	−0.169685	−	0.352355i
$156$	−0.0510481	−	0.0855177i	−0.00408712	−	0.00684689i
$157$	−4.03920	−	5.92442i	−0.322364	−	0.472820i	0.630513	−	0.776179i	$-0.282845\pi$
$157$	−4.03920	−	5.92442i	−0.322364	−	0.472820i	−0.952877	+	0.303358i	$0.901892\pi$
$158$	0.420638	+	2.79075i	0.0334641	+	0.222020i
$159$	0.731220	+	0.0993477i	0.0579895	+	0.00787879i
$160$	−0.620550	+	0.494872i	−0.0490588	+	0.0391231i
$161$	−13.5016	+	5.41461i	−1.06408	+	0.426731i
$162$	4.37034	+	7.86766i	0.343367	+	0.618142i
$163$	−0.270552	−	3.61027i	−0.0211913	−	0.282778i	−0.997725	−	0.0674139i	$-0.978525\pi$
$163$	−0.270552	−	3.61027i	−0.0211913	−	0.282778i	0.976534	−	0.215364i	$-0.0690939\pi$
$164$	9.37697	+	2.89241i	0.732218	+	0.225859i
$165$	1.54400	−	0.255765i	0.120200	−	0.0199113i
$166$	−11.5026	+	6.64104i	−0.892776	+	0.515445i
$167$	−3.61536	−	15.8399i	−0.279765	−	1.22573i	−0.898091	−	0.439809i	$-0.855046\pi$
$167$	−3.61536	−	15.8399i	−0.279765	−	1.22573i	0.618326	−	0.785922i	$-0.287811\pi$
$168$	4.17142	+	1.89717i	0.321832	+	0.146370i
$169$	−2.89204	+	12.6708i	−0.222464	+	0.974680i
$170$	0.466921	+	1.51372i	0.0358112	+	0.116097i
$171$	−1.59270	−	8.81653i	−0.121796	−	0.674217i
$172$	2.68477	+	6.84069i	0.204712	+	0.521597i
$173$	−14.7983	+	4.56468i	−1.12510	+	0.347046i	−0.800813	−	0.598914i	$-0.795599\pi$
$173$	−14.7983	+	4.56468i	−1.12510	+	0.347046i	−0.324283	+	0.945960i	$0.605123\pi$
$174$	0.547007	+	1.09480i	0.0414685	+	0.0829967i
$175$	10.3796	−	5.09349i	0.784623	−	0.385032i
$176$	−1.10987	+	0.253321i	−0.0836598	+	0.0190948i
$177$	9.99261	+	3.75484i	0.751090	+	0.282231i
$178$	3.50801	+	2.02535i	0.262937	+	0.151807i
$179$	−6.85736	+	22.2310i	−0.512543	+	1.66162i	0.215821	+	0.976433i	$0.430757\pi$
$179$	−6.85736	+	22.2310i	−0.512543	+	1.66162i	−0.728364	+	0.685190i	$0.759719\pi$
$180$	2.36388	+	0.286181i	0.176193	+	0.0213307i
$181$	0.109282	+	0.0871496i	0.00812288	+	0.00647778i	0.627543	−	0.778582i	$-0.284061\pi$
$181$	0.109282	+	0.0871496i	0.00812288	+	0.00647778i	−0.619420	+	0.785060i	$0.712632\pi$
$182$	0.0566270	+	0.141202i	0.00419748	+	0.0104666i
$183$	3.85418	−	18.0970i	0.284909	−	1.33777i
$184$	4.03046	−	3.73972i	0.297130	−	0.275696i
$185$	2.63107	−	0.396570i	0.193440	−	0.0291564i
$186$	2.98364	−	10.1976i	0.218771	−	0.747723i
$187$	−0.338633	+	2.24668i	−0.0247633	+	0.164294i
$188$	6.31878	−	3.04296i	0.460844	−	0.221931i
$189$	−4.71769	−	12.9129i	−0.343161	−	0.939276i
$190$	−2.13561	−	1.02846i	−0.154934	−	0.0746122i
$191$	−1.10551	+	1.62149i	−0.0799922	+	0.117327i	−0.864150	−	0.503235i	$-0.832143\pi$
$191$	−1.10551	+	1.62149i	−0.0799922	+	0.117327i	0.784157	+	0.620562i	$0.213095\pi$
$192$	−1.72891	−	0.104274i	−0.124773	−	0.00752532i
$193$	0.977596	−	13.0451i	0.0703689	−	0.939008i	−0.844578	−	0.535433i	$-0.820148\pi$
$193$	0.977596	−	13.0451i	0.0703689	−	0.939008i	0.914947	−	0.403575i	$-0.132233\pi$
$194$	1.29562	−	3.30119i	0.0930202	−	0.237011i
$195$	0.0501815	+	0.0610795i	0.00359357	+	0.00437400i
$196$	−5.84139	−	3.85723i	−0.417242	−	0.275516i
$197$			17.5077i			1.24738i	0.781674	+	0.623688i	$0.214366\pi$
$197$			17.5077i			1.24738i	−0.781674	+	0.623688i	$0.785634\pi$
$198$	2.87663	+	1.84090i	0.204433	+	0.130827i
$199$	−5.84093	−	0.437718i	−0.414053	−	0.0310290i	−0.133925	−	0.990992i	$-0.542758\pi$
$199$	−5.84093	−	0.437718i	−0.414053	−	0.0310290i	−0.280128	+	0.959963i	$0.590377\pi$
$200$	−2.97237	+	3.20345i	−0.210178	+	0.226518i
$201$	16.6999	−	1.49630i	1.17792	−	0.105541i
$202$	3.96170	−	8.22656i	0.278745	−	0.578819i
$203$	−0.564235	−	1.78228i	−0.0396016	−	0.125092i
$204$	−1.45436	+	3.13601i	−0.101826	+	0.219565i
$205$	−7.70166	−	1.16084i	−0.537907	−	0.0810765i
$206$	−15.9137	+	10.8498i	−1.10876	+	0.755942i
$207$	−16.4774	−	0.753181i	−1.14526	−	0.0523497i
$208$	−0.0391108	−	0.0421514i	−0.00271184	−	0.00292267i
$209$	−2.11973	−	2.65805i	−0.146625	−	0.183861i
$210$	−3.49836	−	0.995522i	−0.241410	−	0.0686976i
$211$	4.76640	−	5.97688i	0.328133	−	0.411465i	−0.590211	−	0.807249i	$-0.700956\pi$
$211$	4.76640	−	5.97688i	0.328133	−	0.411465i	0.918344	+	0.395784i	$0.129527\pi$
$212$	0.424857	−	0.0318387i	0.0291793	−	0.00218669i
$213$	−9.36662	−	22.8804i	−0.641791	−	1.56774i
$214$	1.36982	−	2.37259i	0.0936388	−	0.162187i
$215$	−2.91637	−	5.05130i	−0.198895	−	0.344496i
$216$	3.41406	+	3.91716i	0.232297	+	0.266529i
$217$	−6.93360	+	14.6745i	−0.470684	+	0.996172i
$218$	0.0994088	+	0.0226894i	0.00673281	+	0.00153672i
$219$	13.1417	+	8.68230i	0.888034	+	0.586695i
$220$	0.841115	−	0.330113i	0.0567079	−	0.0222562i
$221$	−0.106828	+	0.0419271i	−0.00718606	+	0.00282032i
$222$	4.84460	+	3.20067i	0.325148	+	0.214815i
$223$	−0.992692	−	0.226575i	−0.0664756	−	0.0151726i	0.189154	−	0.981947i	$-0.439426\pi$
$223$	−0.992692	−	0.226575i	−0.0664756	−	0.0151726i	−0.255629	+	0.966775i	$0.582283\pi$
$224$	2.58370	+	0.569635i	0.172631	+	0.0380603i
$225$	13.1045	−	0.381733i	0.873633	−	0.0254489i
$226$	−2.03605	−	3.52654i	−0.135436	−	0.234582i
$227$	7.95619	−	13.7805i	0.528071	−	0.914646i	−0.471394	−	0.881923i	$-0.656249\pi$
$227$	7.95619	−	13.7805i	0.528071	−	0.914646i	0.999464	−	0.0327227i	$-0.0104178\pi$
$228$	−1.95968	−	4.78703i	−0.129783	−	0.317029i
$229$	−12.5827	+	0.942946i	−0.831491	+	0.0623116i	−0.483671	−	0.875250i	$-0.660697\pi$
$229$	−12.5827	+	0.942946i	−0.831491	+	0.0623116i	−0.347820	+	0.937561i	$0.613078\pi$
$230$	−2.72090	+	3.41191i	−0.179411	+	0.224974i
$231$	−3.90123	−	3.46355i	−0.256682	−	0.227885i
$232$	0.440552	+	0.552434i	0.0289236	+	0.0362691i
$233$	−4.50367	−	4.85380i	−0.295045	−	0.317983i	0.568080	−	0.822974i	$-0.307687\pi$
$233$	−4.50367	−	4.85380i	−0.295045	−	0.317983i	−0.863125	+	0.504990i	$0.831496\pi$
$234$	−0.00787691	+	0.172324i	−0.000514930	+	0.0112652i
$235$	−4.59931	+	3.13575i	−0.300026	+	0.204554i
$236$	6.09425	+	0.918561i	0.396702	+	0.0597932i
$237$	2.05661	−	4.43464i	0.133591	−	0.288061i
$238$	2.94220	−	4.38477i	0.190715	−	0.284222i
$239$	−5.73781	+	11.9147i	−0.371148	+	0.770697i	−0.999977	−	0.00684683i	$-0.997821\pi$
$239$	−5.73781	+	11.9147i	−0.371148	+	0.770697i	0.628828	+	0.777544i	$0.283535\pi$
$240$	1.36927	−	0.122685i	0.0883858	−	0.00791930i
$241$	−4.61766	+	4.97665i	−0.297450	+	0.320574i	−0.864038	−	0.503426i	$-0.832072\pi$
$241$	−4.61766	+	4.97665i	−0.297450	+	0.320574i	0.566588	+	0.824001i	$0.308263\pi$
$242$	−9.67688	−	0.725182i	−0.622053	−	0.0466164i
$243$	1.19595	−	15.5425i	0.0767200	−	0.997053i
$244$		−	10.6826i		−	0.683884i
$245$	5.04090	+	2.33632i	0.322051	+	0.149262i
$246$	−10.7895	−	13.1327i	−0.687913	−	0.837310i
$247$	0.0627372	−	0.159852i	0.00399187	−	0.0101711i
$248$	0.458425	−	6.11726i	0.0291100	−	0.388446i
$249$	22.9635	+	1.38497i	1.45525	+	0.0877692i
$250$	4.18947	−	6.14483i	0.264965	−	0.388633i
$251$	−9.32309	−	4.48977i	−0.588468	−	0.283391i	0.115860	−	0.993266i	$-0.463038\pi$
$251$	−9.32309	−	4.48977i	−0.588468	−	0.283391i	−0.704329	+	0.709874i	$0.748752\pi$
$252$	−4.21696	−	6.72438i	−0.265644	−	0.423596i
$253$	−5.63937	+	2.71578i	−0.354544	+	0.170740i
$254$	3.33533	−	22.1285i	0.209277	−	1.38846i
$255$	0.770471	−	2.63334i	0.0482488	−	0.164906i
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	−17.1009	+	15.8674i	−1.06673	+	0.989779i	−0.999968	−	0.00799059i	$-0.997456\pi$
$257$	−17.1009	+	15.8674i	−1.06673	+	0.989779i	−0.0667595	+	0.997769i	$0.521266\pi$
$258$	2.65133	−	12.4491i	0.165064	−	0.775046i
$259$	−6.54622	−	5.98448i	−0.406762	−	0.371858i
$260$	0.0356824	+	0.0284558i	0.00221293	+	0.00176475i
$261$	0.254768	−	2.10440i	0.0157698	−	0.130259i
$262$	−3.31191	+	10.7370i	−0.204611	+	0.663332i
$263$	25.6463	+	14.8069i	1.58142	+	0.913034i	0.994652	+	0.103279i	$0.0329335\pi$
$263$	25.6463	+	14.8069i	1.58142	+	0.913034i	0.586769	+	0.809755i	$0.300400\pi$
$264$	1.84579	+	0.693575i	0.113600	+	0.0426866i
$265$	−0.329682	+	0.0752478i	−0.0202522	+	0.00462244i
$266$	1.81515	+	7.68998i	0.111294	+	0.471503i
$267$	−3.13586	−	6.27623i	−0.191911	−	0.384099i
$268$	9.25027	−	2.85333i	0.565050	−	0.174295i
$269$	−4.75769	−	12.1224i	−0.290082	−	0.739116i	−0.999414	−	0.0342415i	$-0.989098\pi$
$269$	−4.75769	−	12.1224i	−0.290082	−	0.739116i	0.709332	−	0.704875i	$-0.248997\pi$
$270$	−3.14291	−	2.67051i	−0.191271	−	0.162522i
$271$	7.12816	+	23.1089i	0.433005	+	1.40377i	0.864946	+	0.501866i	$0.167353\pi$
$271$	7.12816	+	23.1089i	0.433005	+	1.40377i	−0.431940	+	0.901902i	$0.642171\pi$
$272$	−0.444109	+	1.94577i	−0.0269281	+	0.117980i
$273$	0.0529801	−	0.258123i	0.00320650	−	0.0156223i
$274$	−2.24136	−	9.82006i	−0.135406	−	0.593251i
$275$	4.30839	−	2.48745i	0.259806	−	0.149999i
$276$	−9.39513	+	1.55631i	−0.565520	+	0.0936791i
$277$	−27.9645	−	8.62591i	−1.68022	−	0.518281i	−0.699660	−	0.714476i	$-0.746665\pi$
$277$	−27.9645	−	8.62591i	−1.68022	−	0.518281i	−0.980565	+	0.196196i	$0.937141\pi$
$278$	−0.918970	−	12.2628i	−0.0551162	−	0.735474i
$279$	−14.0480	+	11.8883i	−0.841033	+	0.711734i
$280$	−2.09520	−	0.141433i	−0.125212	−	0.00845224i
$281$	23.0231	−	18.3603i	1.37344	−	1.09529i	0.388683	−	0.921372i	$-0.372930\pi$
$281$	23.0231	−	18.3603i	1.37344	−	1.09529i	0.984761	−	0.173913i	$-0.0556413\pi$
$282$	−12.0368	−	1.63539i	−0.716782	−	0.0973861i
$283$	−0.358464	−	2.37825i	−0.0213085	−	0.141372i	0.975647	−	0.219347i	$-0.0703927\pi$
$283$	−0.358464	−	2.37825i	−0.0213085	−	0.141372i	−0.996955	+	0.0779748i	$0.975155\pi$
$284$	−8.04088	−	11.7938i	−0.477138	−	0.699833i
$285$	2.10434	+	3.52526i	0.124650	+	0.208819i
$286$	0.0284022	+	0.0589777i	0.00167946	+	0.00348742i
$287$	13.1473	+	22.3876i	0.776060	+	1.32150i
$288$	2.39896	+	1.80138i	0.141360	+	0.106147i
$289$	−10.7549	−	7.33260i	−0.632644	−	0.431329i
$290$	−0.411117	−	0.381461i	−0.0241416	−	0.0224002i
$291$	−5.02419	+	3.53368i	−0.294523	+	0.207148i
$292$	8.46509	+	3.32230i	0.495382	+	0.194423i
$293$	29.2566			1.70919			0.854594	−	0.519297i	$-0.173806\pi$
$293$	29.2566			1.70919			0.854594	+	0.519297i	$0.173806\pi$
$294$	4.75891	+	11.1514i	0.277545	+	0.650360i
$295$	−4.89172			−0.284807
$296$	3.12060	+	1.22475i	0.181381	+	0.0711869i
$297$	−2.39953	−	5.40685i	−0.139235	−	0.313737i
$298$	8.72383	+	8.09453i	0.505358	+	0.468904i
$299$	−0.261218	−	0.178095i	−0.0151066	−	0.0102995i
$300$	7.35402	−	1.79155i	0.424584	−	0.103435i
$301$	−6.96914	+	18.1508i	−0.401694	+	1.04620i
$302$	−5.96561	−	12.3877i	−0.343282	−	0.712833i
$303$	−13.5796	+	8.10608i	−0.780128	+	0.465682i
$304$	−1.68231	−	2.46749i	−0.0964868	−	0.141520i
$305$	1.26372	+	8.38423i	0.0723604	+	0.480080i
$306$	5.09589	−	3.14342i	0.291313	−	0.179698i
$307$	24.8854	−	19.8454i	1.42028	−	1.13264i	0.449331	−	0.893366i	$-0.351663\pi$
$307$	24.8854	−	19.8454i	1.42028	−	1.13264i	0.970952	−	0.239272i	$-0.0769089\pi$
$308$	−2.61951	−	1.48664i	−0.149260	−	0.0847093i
$309$	33.3566	−	0.485734i	1.89759	−	0.0276324i
$310$	0.363858	+	4.85535i	0.0206657	+	0.275765i
$311$	−0.580318	−	0.179004i	−0.0329068	−	0.0101504i	0.278258	−	0.960506i	$-0.410243\pi$
$311$	−0.580318	−	0.179004i	−0.0329068	−	0.0101504i	−0.311165	+	0.950356i	$0.600719\pi$
$312$	0.0162762	+	0.0982561i	0.000921461	+	0.00556266i
$313$	3.64037	−	2.10177i	0.205766	−	0.118799i	−0.393576	−	0.919292i	$-0.628762\pi$
$313$	3.64037	−	2.10177i	0.205766	−	0.118799i	0.599342	+	0.800493i	$0.295429\pi$
$314$	1.59555	+	6.99058i	0.0900423	+	0.394501i
$315$	4.10515	+	4.77876i	0.231299	+	0.269253i
$316$	0.628015	−	2.75151i	0.0353286	−	0.154785i
$317$	−4.07159	−	13.1998i	−0.228683	−	0.741373i	−0.995086	−	0.0990127i	$-0.968432\pi$
$317$	−4.07159	−	13.1998i	−0.228683	−	0.741373i	0.766403	−	0.642360i	$-0.222045\pi$
$318$	−0.644378	−	0.359625i	−0.0361349	−	0.0201668i
$319$	−0.293878	−	0.748788i	−0.0164540	−	0.0419241i
$320$	0.758451	−	0.233951i	0.0423987	−	0.0130783i
$321$	−4.24484	+	2.12089i	−0.236924	+	0.118377i
$322$	14.5465	−	0.107627i	0.810643	−	0.00599781i
$323$	−5.81086	+	1.32629i	−0.323325	+	0.0737969i
$324$	−1.19386	−	8.92047i	−0.0663255	−	0.495581i
$325$	0.217616	+	0.125641i	0.0120712	+	0.00696930i
$326$	−1.06713	+	3.45955i	−0.0591028	+	0.191607i
$327$	−0.121997	−	0.127701i	−0.00674644	−	0.00706187i
$328$	−7.67206	−	6.11826i	−0.423619	−	0.337825i
$329$	17.7711	+	5.33799i	0.979752	+	0.294293i
$330$	−1.53071	−	0.326001i	−0.0842627	−	0.0179458i
$331$	−23.6897	+	21.9809i	−1.30211	+	1.20818i	−0.338464	+	0.940979i	$0.609908\pi$
$331$	−23.6897	+	21.9809i	−1.30211	+	1.20818i	−0.963641	+	0.267199i	$0.913902\pi$
$332$	13.1337	−	1.97959i	0.720807	−	0.108644i
$333$	−3.94527	−	9.25085i	−0.216200	−	0.506943i
$334$	−2.42153	+	16.0658i	−0.132500	+	0.879082i
$335$	−6.92251	+	3.33371i	−0.378217	+	0.182140i
$336$	−3.18995	−	3.29001i	−0.174026	−	0.179485i
$337$	17.5445	+	8.44898i	0.955709	+	0.460245i	0.845684	−	0.533684i	$-0.179193\pi$
$337$	17.5445	+	8.44898i	0.955709	+	0.460245i	0.110025	+	0.993929i	$0.464907\pi$
$338$	7.32130	−	10.7384i	0.398226	−	0.584090i
$339$	−0.424613	+	7.04029i	−0.0230618	+	0.382376i
$340$	0.118380	−	1.57967i	0.00642005	−	0.0856696i
$341$	−2.55136	+	6.50076i	−0.138164	+	0.352036i
$342$	−1.73844	+	8.78895i	−0.0940041	+	0.475252i
$343$	−4.52087	−	17.9600i	−0.244104	−	0.969749i
$344$		−	7.34867i		−	0.396214i
$345$	7.18964	−	2.33288i	0.387077	−	0.125598i
$346$	15.4430	+	1.15730i	0.830223	+	0.0622166i
$347$	7.56625	−	8.15447i	0.406177	−	0.437755i	−0.496524	−	0.868023i	$-0.665390\pi$
$347$	7.56625	−	8.15447i	0.406177	−	0.437755i	0.902701	+	0.430268i	$0.141581\pi$
$348$	−0.109219	−	1.21897i	−0.00585473	−	0.0653435i
$349$	−0.359580	+	0.746675i	−0.0192479	+	0.0399686i	−0.910371	−	0.413793i	$-0.864204\pi$
$349$	−0.359580	+	0.746675i	−0.0192479	+	0.0399686i	0.891123	+	0.453761i	$0.149918\pi$
$350$	−11.5229	+	0.949308i	−0.615927	+	0.0507427i
$351$	0.175911	−	0.241512i	0.00938943	−	0.0128910i
$352$	1.12570	+	0.169672i	0.0600000	+	0.00904355i
$353$	19.6605	−	13.4043i	1.04642	−	0.713440i	0.0872296	−	0.996188i	$-0.472199\pi$
$353$	19.6605	−	13.4043i	1.04642	−	0.713440i	0.959194	+	0.282749i	$0.0912462\pi$
$354$	−7.93006	−	7.14599i	−0.421478	−	0.379805i
$355$	7.70603	+	8.30513i	0.408994	+	0.440791i
$356$	−2.52557	−	3.16697i	−0.133855	−	0.167849i
$357$	−8.43829	+	3.52752i	−0.446602	+	0.186696i
$358$	14.5052	−	18.1890i	0.766625	−	0.961318i
$359$	−26.5896	+	1.99261i	−1.40334	+	0.105166i	−0.754772	−	0.655987i	$-0.772253\pi$
$359$	−26.5896	+	1.99261i	−1.40334	+	0.105166i	−0.648572	+	0.761153i	$0.724633\pi$
$360$	−2.09592	−	1.13002i	−0.110465	−	0.0595573i
$361$	−5.04068	+	8.73071i	−0.265299	+	0.459511i
$362$	−0.0698885	−	0.121051i	−0.00367326	−	0.00636227i
$363$	13.2921	+	10.2871i	0.697654	+	0.539931i
$364$	−0.00112558	−	0.152130i	−5.89966e−5	−	0.00797377i
$365$	−7.03683	−	1.60611i	−0.368325	−	0.0840677i
$366$	−10.1993	+	15.4379i	−0.533127	+	0.806952i
$367$	−23.6216	+	9.27079i	−1.23304	+	0.483932i	−0.890246	−	0.455480i	$-0.849468\pi$
$367$	−23.6216	+	9.27079i	−1.23304	+	0.483932i	−0.342791	+	0.939412i	$0.611372\pi$
$368$	−5.11813	+	2.00872i	−0.266801	+	0.104712i
$369$	3.05382	+	29.2800i	0.158975	+	1.52425i
$370$	−2.59408	−	0.592082i	−0.134860	−	0.0307809i
$371$	0.886471	+	0.696270i	0.0460233	+	0.0361485i
$372$	−6.50299	+	8.40262i	−0.337164	+	0.435656i
$373$	−7.49835	−	12.9875i	−0.388250	−	0.672469i	0.603964	−	0.797011i	$-0.293587\pi$
$373$	−7.49835	−	12.9875i	−0.388250	−	0.672469i	−0.992214	+	0.124543i	$0.960254\pi$
$374$	1.13603	−	1.96766i	0.0587427	−	0.101745i
$375$	−11.9212	+	4.88022i	−0.615609	+	0.252013i
$376$	−6.99370	+	0.524106i	−0.360673	+	0.0270287i
$377$	0.0253323	−	0.0317657i	0.00130468	−	0.00163602i
$378$	−0.326047	+	13.7439i	−0.0167700	+	0.706908i
$379$	−21.5074	−	26.9695i	−1.10476	−	1.38533i	−0.914978	−	0.403504i	$-0.867792\pi$
$379$	−21.5074	−	26.9695i	−1.10476	−	1.38533i	−0.189785	−	0.981826i	$-0.560779\pi$
$380$	1.61225	+	1.73759i	0.0827067	+	0.0891366i
$381$	−25.9474	+	28.7944i	−1.32933	+	1.47518i
$382$	1.62149	−	1.10551i	0.0829627	−	0.0565630i
$383$	3.36193	+	0.506730i	0.171787	+	0.0258927i	0.234372	−	0.972147i	$-0.424697\pi$
$383$	3.36193	+	0.506730i	0.171787	+	0.0258927i	−0.0625855	+	0.998040i	$0.519935\pi$
$384$	1.57130	+	0.728707i	0.0801851	+	0.0371867i
$385$	2.23178	+	0.856909i	0.113742	+	0.0436721i
$386$	−5.67594	+	11.7862i	−0.288898	+	0.599902i
$387$	−15.7174	+	15.4593i	−0.798960	+	0.785841i
$388$	−2.41212	+	2.59965i	−0.122457	+	0.131977i
$389$	−23.3398	−	1.74908i	−1.18338	−	0.0886818i	−0.531535	−	0.847037i	$-0.678384\pi$
$389$	−23.3398	−	1.74908i	−1.18338	−	0.0886818i	−0.651842	+	0.758355i	$0.726004\pi$
$390$	−0.0243978	−	0.0751907i	−0.00123543	−	0.00380743i
$391$			10.9733i			0.554946i
$392$	4.02839	+	5.72469i	0.203464	+	0.289141i
$393$	15.0374	−	12.3544i	0.758536	−	0.623195i
$394$	6.39630	−	16.2975i	0.322241	−	0.821056i
$395$	−0.167401	+	2.23381i	−0.00842286	+	0.112395i
$396$	−2.00523	−	2.76459i	−0.100766	−	0.138926i
$397$	19.8376	−	29.0965i	0.995622	−	1.46031i	0.111101	−	0.993809i	$-0.464562\pi$
$397$	19.8376	−	29.0965i	0.995622	−	1.46031i	0.884521	−	0.466500i	$-0.154485\pi$
$398$	5.27726	+	2.54139i	0.264525	+	0.127389i
$399$	4.71892	−	12.8461i	0.236242	−	0.643112i
$400$	3.93725	−	1.89608i	0.196863	−	0.0948040i
$401$	5.38358	−	35.7177i	0.268843	−	1.78366i	−0.292693	−	0.956207i	$-0.594551\pi$
$401$	5.38358	−	35.7177i	0.268843	−	1.78366i	0.561536	−	0.827452i	$-0.310211\pi$
$402$	−16.0922	−	4.70830i	−0.802606	−	0.234829i
$403$	−0.348796	+	0.0525726i	−0.0173748	+	0.00261883i
$404$	−6.69335	+	6.21052i	−0.333006	+	0.308985i
$405$	1.99226	+	6.85998i	0.0989962	+	0.340875i
$406$	−0.125908	+	1.86522i	−0.00624873	+	0.0925692i
$407$	−2.98374	−	2.37946i	−0.147899	−	0.117945i
$408$	2.49954	−	2.38790i	0.123746	−	0.118218i
$409$	−0.307208	+	0.995945i	−0.0151905	+	0.0492463i	−0.962851	−	0.270034i	$-0.912965\pi$
$409$	−0.307208	+	0.995945i	−0.0151905	+	0.0492463i	0.947660	+	0.319280i	$0.103441\pi$
$410$	6.74517	+	3.89433i	0.333120	+	0.192327i
$411$	−6.13669	+	16.3313i	−0.302701	+	0.805566i
$412$	18.7776	−	4.28586i	0.925105	−	0.211149i
$413$	10.2607	+	12.6730i	0.504894	+	0.623596i
$414$	15.0632	+	6.72098i	0.740316	+	0.330318i
$415$	−10.0738	+	3.10736i	−0.494503	+	0.152534i
$416$	0.0210076	+	0.0535264i	0.00102998	+	0.00262435i
$417$	−10.3800	+	18.5989i	−0.508309	+	0.910792i
$418$	1.00210	+	3.24873i	0.0490144	+	0.158901i
$419$	−1.96023	+	8.58834i	−0.0957636	+	0.419568i	−0.999972	−	0.00752446i	$-0.997605\pi$
$419$	−1.96023	+	8.58834i	−0.0957636	+	0.419568i	0.904208	+	0.427092i	$0.140462\pi$
$420$	2.89283	+	2.20480i	0.141155	+	0.107583i
$421$	−2.69781	−	11.8199i	−0.131483	−	0.576065i	−0.997150	−	0.0754444i	$-0.975962\pi$
$421$	−2.69781	−	11.8199i	−0.131483	−	0.576065i	0.865667	−	0.500620i	$-0.166895\pi$
$422$	−6.62052	+	3.82236i	−0.322282	+	0.186069i
$423$	15.8335	+	13.8556i	0.769852	+	0.673684i
$424$	−0.407121	−	0.125580i	−0.0197715	−	0.00609871i
$425$	−0.651775	−	8.69733i	−0.0316157	−	0.421882i
$426$	0.359981	+	24.7208i	0.0174411	+	1.19773i
$427$	19.0703	−	20.8603i	0.922875	−	1.00950i
$428$	−2.14193	+	1.70813i	−0.103534	+	0.0825658i
$429$	0.0152643	−	0.112348i	0.000736967	−	0.00542423i
$430$	0.869325	+	5.76759i	0.0419226	+	0.278138i
$431$	−3.98994	−	5.85217i	−0.192189	−	0.281889i	0.718034	−	0.696008i	$-0.245042\pi$
$431$	−3.98994	−	5.85217i	−0.192189	−	0.281889i	−0.910223	+	0.414119i	$0.864090\pi$
$432$	−1.74696	−	4.89368i	−0.0840506	−	0.235447i
$433$	2.57175	+	5.34030i	0.123590	+	0.256638i	0.953579	−	0.301142i	$-0.0973677\pi$
$433$	2.57175	+	5.34030i	0.123590	+	0.256638i	−0.829989	+	0.557780i	$0.811653\pi$
$434$	11.8155	−	11.1270i	0.567163	−	0.534114i
$435$	0.229920	+	0.943783i	0.0110238	+	0.0452510i
$436$	−0.0842476	−	0.0574391i	−0.00403473	−	0.00275083i
$437$	−12.0366	−	11.1684i	−0.575790	−	0.534255i
$438$	−9.06127	−	12.8833i	−0.432964	−	0.615589i
$439$	27.6001	+	10.8322i	1.31728	+	0.516994i	0.916813	−	0.399317i	$-0.130753\pi$
$439$	27.6001	+	10.8322i	1.31728	+	0.516994i	0.400467	+	0.916311i	$0.368848\pi$
$440$	−0.903575			−0.0430763
$441$	3.76955	−	20.6589i	0.179502	−	0.983758i
$442$	0.114761			0.00545864
$443$	26.0439	+	10.2215i	1.23738	+	0.485636i	0.891662	−	0.452702i	$-0.149540\pi$
$443$	26.0439	+	10.2215i	1.23738	+	0.485636i	0.345719	+	0.938338i	$0.387635\pi$
$444$	−3.34038	−	4.74935i	−0.158527	−	0.225394i
$445$	2.35683	+	2.18682i	0.111725	+	0.103665i
$446$	0.841294	+	0.573584i	0.0398364	+	0.0271600i
$447$	−4.87885	−	20.0269i	−0.230762	−	0.947240i
$448$	−2.19699	−	1.47419i	−0.103798	−	0.0696490i
$449$	−5.29779	−	11.0010i	−0.250018	−	0.519168i	0.737754	−	0.675069i	$-0.235886\pi$
$449$	−5.29779	−	11.0010i	−0.250018	−	0.519168i	−0.987773	+	0.155901i	$0.950172\pi$
$450$	−12.3381	−	4.43227i	−0.581623	−	0.208939i
$451$	6.29296	+	9.23007i	0.296324	+	0.434627i
$452$	0.606915	+	4.02661i	0.0285469	+	0.189396i
$453$	−3.20612	+	23.5977i	−0.150637	+	1.10872i
$454$	−12.4408	+	9.92121i	−0.583876	+	0.465625i
$455$	0.0188799	+	0.119266i	0.000885103	+	0.00559126i
$456$	0.0753149	+	5.17207i	0.00352694	+	0.242204i
$457$	1.20150	+	16.0329i	0.0562037	+	0.749986i	0.952112	+	0.305748i	$0.0989065\pi$
$457$	1.20150	+	16.0329i	0.0562037	+	0.749986i	−0.895909	+	0.444238i	$0.853474\pi$
$458$	12.0574	+	3.71923i	0.563407	+	0.173788i
$459$	−10.3655	−	0.322651i	−0.483820	−	0.0150600i
$460$	3.77933	−	2.18200i	0.176212	−	0.101736i
$461$	−1.26100	−	5.52481i	−0.0587307	−	0.257316i	0.937036	−	0.349233i	$-0.113558\pi$
$461$	−1.26100	−	5.52481i	−0.0587307	−	0.257316i	−0.995767	+	0.0919167i	$0.970701\pi$
$462$	2.36618	+	4.64941i	0.110085	+	0.216310i
$463$	0.192036	−	0.841363i	0.00892466	−	0.0391015i	−0.970270	−	0.242027i	$-0.922188\pi$
$463$	0.192036	−	0.841363i	0.00892466	−	0.0391015i	0.979194	+	0.202925i	$0.0650449\pi$
$464$	−0.208271	−	0.675198i	−0.00966874	−	0.0313453i
$465$	4.10986	−	7.36406i	0.190590	−	0.341500i
$466$	2.41906	+	6.16365i	0.112061	+	0.285526i
$467$	−32.7769	+	10.1103i	−1.51674	+	0.467851i	−0.937698	−	0.347450i	$-0.887048\pi$
$467$	−32.7769	+	10.1103i	−1.51674	+	0.467851i	−0.579037	+	0.815301i	$0.696571\pi$
$468$	0.0702894	−	0.157534i	0.00324913	−	0.00728201i
$469$	23.1570	+	10.9415i	1.06929	+	0.505231i
$470$	5.42699	−	1.23868i	0.250329	−	0.0571359i
$471$	4.36851	−	11.6257i	0.201290	−	0.535686i
$472$	−5.33739	−	3.08154i	−0.245673	−	0.141840i
$473$	−2.46588	+	7.99417i	−0.113381	+	0.367572i
$474$	−3.53460	+	3.37672i	−0.162350	+	0.155098i
$475$	10.2034	+	8.13696i	0.468165	+	0.373349i
$476$	−4.34075	+	3.00676i	−0.198958	+	0.137815i
$477$	0.587863	+	1.13493i	0.0269164	+	0.0519651i
$478$	9.69411	−	8.99482i	0.443398	−	0.411413i
$479$	19.5775	−	2.95084i	0.894521	−	0.134827i	0.314335	−	0.949312i	$-0.398218\pi$
$479$	19.5775	−	2.95084i	0.894521	−	0.134827i	0.580185	+	0.814485i	$0.302980\pi$
$480$	−1.31944	−	0.386045i	−0.0602237	−	0.0176204i
$481$	0.0287299	−	0.190610i	0.00130997	−	0.00869109i
$482$	6.11663	−	2.94562i	0.278605	−	0.134169i
$483$	−21.1245	−	13.7328i	−0.961197	−	0.624865i
$484$	8.74301	+	4.21041i	0.397410	+	0.191382i
$485$	1.58562	−	2.32567i	0.0719992	−	0.105603i
$486$	−6.79159	+	14.0312i	−0.308073	+	0.636468i
$487$	−0.709317	+	9.46518i	−0.0321422	+	0.428908i	0.957800	+	0.287436i	$0.0928028\pi$
$487$	−0.709317	+	9.46518i	−0.0321422	+	0.428908i	−0.989942	+	0.141473i	$0.954816\pi$
$488$	−3.90280	+	9.94417i	−0.176671	+	0.450151i
$489$	4.84519	−	3.98069i	0.219107	−	0.180013i
$490$	−3.83889	−	4.01647i	−0.173423	−	0.181445i
$491$			23.9146i			1.07925i	0.841905	+	0.539625i	$0.181434\pi$
$491$			23.9146i			1.07925i	−0.841905	+	0.539625i	$0.818566\pi$
$492$	5.24575	+	16.1667i	0.236497	+	0.728852i
$493$	−1.40627	−	0.105386i	−0.0633354	−	0.00474633i
$494$	−0.116801	+	0.125881i	−0.00525512	+	0.00566367i
$495$	1.90084	+	1.93257i	0.0854364	+	0.0868628i
$496$	−2.66162	+	5.52691i	−0.119510	+	0.248166i
$497$	5.35223	−	37.3845i	0.240080	−	1.67692i
$498$	−20.8701	−	9.67875i	−0.935213	−	0.433715i
$499$	−18.2563	−	2.75170i	−0.817265	−	0.123183i	−0.272912	−	0.962039i	$-0.587987\pi$
$499$	−18.2563	−	2.75170i	−0.817265	−	0.123183i	−0.544353	+	0.838856i	$0.683225\pi$
$500$	−6.14483	+	4.18947i	−0.274805	+	0.187359i
$501$	18.8384	−	20.9054i	0.841639	−	0.933985i
$502$	7.03833	+	7.58551i	0.314136	+	0.338558i
$503$	9.22054	+	11.5622i	0.411123	+	0.515532i	0.943679	−	0.330863i	$-0.107340\pi$
$503$	9.22054	+	11.5622i	0.411123	+	0.515532i	−0.532556	+	0.846395i	$0.678768\pi$
$504$	1.46877	+	7.80017i	0.0654241	+	0.347447i
$505$	4.51858	−	5.66612i	0.201074	−	0.252139i
$506$	6.24173	−	0.467753i	0.277479	−	0.0207942i
$507$	−20.8329	+	8.52840i	−0.925220	+	0.378760i
$508$	−11.1892	+	19.3803i	−0.496441	+	0.859862i
$509$	1.69754	+	2.94022i	0.0752420	+	0.130323i	0.901191	−	0.433421i	$-0.142694\pi$
$509$	1.69754	+	2.94022i	0.0752420	+	0.130323i	−0.825950	+	0.563744i	$0.809360\pi$
$510$	−1.67928	+	2.16982i	−0.0743597	+	0.0960814i
$511$	10.5992	+	21.5992i	0.468881	+	0.955493i
$512$	0.974928	+	0.222521i	0.0430861	+	0.00983413i
$513$	10.9036	−	11.0415i	0.481407	−	0.487494i
$514$	21.7158	−	8.52283i	0.957844	−	0.375926i
$515$	−14.2305	+	5.58507i	−0.627072	+	0.246108i
$516$	−7.01621	+	10.6199i	−0.308871	+	0.467514i
$517$	7.78389	+	1.77662i	0.342335	+	0.0781357i
$518$	3.90733	+	7.96240i	0.171678	+	0.349848i
$519$	−21.2125	−	16.4168i	−0.931123	−	0.720619i
$520$	−0.0228197	−	0.0395250i	−0.00100071	−	0.00173328i
$521$	2.76890	−	4.79588i	0.121308	−	0.210111i	−0.798976	−	0.601363i	$-0.794624\pi$
$521$	2.76890	−	4.79588i	0.121308	−	0.210111i	0.920284	+	0.391252i	$0.127958\pi$
$522$	−1.00598	+	1.86586i	−0.0440307	+	0.0816664i
$523$	−27.4392	+	2.05629i	−1.19983	+	0.0899152i	−0.659612	−	0.751607i	$-0.729279\pi$
$523$	−27.4392	+	2.05629i	−1.19983	+	0.0899152i	−0.540223	+	0.841522i	$0.681660\pi$
$524$	7.00563	−	8.78478i	0.306042	−	0.383765i
$525$	17.5587	+	9.62975i	0.766323	+	0.420277i
$526$	−18.4639	−	23.1530i	−0.805066	−	1.00952i
$527$	8.32742	+	8.97483i	0.362748	+	0.390950i
$528$	−1.46480	−	1.31997i	−0.0637473	−	0.0574444i
$529$	−5.97385	+	4.07290i	−0.259732	+	0.177083i
$530$	0.334384	+	0.0504002i	0.0145247	+	0.00218925i
$531$	4.63737	+	17.8983i	0.201245	+	0.776718i
$532$	1.11979	−	7.82155i	0.0485490	−	0.339107i
$533$	−0.244821	+	0.508377i	−0.0106044	+	0.0220202i
$534$	0.626123	+	6.98803i	0.0270950	+	0.302402i
$535$	1.47903	−	1.59401i	0.0639438	−	0.0689151i
$536$	−9.65327	−	0.723412i	−0.416958	−	0.0312467i
$537$	−38.3282	+	12.4367i	−1.65398	+	0.536682i
$538$			13.0226i			0.561445i
$539$	−2.46130	−	7.57928i	−0.106016	−	0.326463i
$540$	1.95000	+	3.63414i	0.0839148	+	0.156388i
$541$	5.10351	−	13.0035i	0.219417	−	0.559066i	−0.778203	−	0.628013i	$-0.783869\pi$
$541$	5.10351	−	13.0035i	0.219417	−	0.559066i	0.997620	+	0.0689467i	$0.0219638\pi$
$542$	1.80722	−	24.1157i	0.0776269	−	1.03586i
$543$	−0.0145751	+	0.241662i	−0.000625478	+	0.0103707i
$544$	1.12428	−	1.64901i	0.0482030	−	0.0707009i
$545$	0.0729164	+	0.0351147i	0.00312340	+	0.00150415i
$546$	−0.143621	+	0.220924i	−0.00614640	+	0.00945467i
$547$	−10.0419	+	4.83591i	−0.429359	+	0.206769i	−0.636066	−	0.771634i	$-0.719440\pi$
$547$	−10.0419	+	4.83591i	−0.429359	+	0.206769i	0.206707	+	0.978403i	$0.433725\pi$
$548$	−1.50124	+	9.96009i	−0.0641299	+	0.425474i
$549$	29.4789	−	12.5721i	1.25813	−	0.536563i
$550$	−4.91933	+	0.741470i	−0.209761	+	0.0316164i
$551$	1.54686	−	1.43528i	0.0658986	−	0.0611449i
$552$	9.31426	+	1.98369i	0.396441	+	0.0844316i
$553$	6.13826	−	4.25186i	0.261025	−	0.180807i
$554$	22.8800	+	18.2462i	0.972079	+	0.775207i
$555$	3.18352	+	3.33236i	0.135133	+	0.141451i
$556$	−3.62466	+	11.7509i	−0.153720	+	0.498347i
$557$	−27.3461	−	15.7883i	−1.15869	−	0.668970i	−0.207700	−	0.978192i	$-0.566598\pi$
$557$	−27.3461	−	15.7883i	−1.15869	−	0.668970i	−0.950990	+	0.309222i	$0.899931\pi$
$558$	17.4202	−	5.93420i	0.737457	−	0.251215i
$559$	−0.411963	+	0.0940280i	−0.0174242	+	0.00397696i
$560$	1.89869	+	0.897119i	0.0802345	+	0.0379102i
$561$	−3.52036	+	1.75892i	−0.148630	+	0.0742615i
$562$	−28.1394	+	8.67985i	−1.18699	+	0.366138i
$563$	7.69505	+	19.6067i	0.324308	+	0.826323i	0.996314	+	0.0857775i	$0.0273374\pi$
$563$	7.69505	+	19.6067i	0.324308	+	0.826323i	−0.672007	+	0.740545i	$0.734567\pi$
$564$	10.6073	+	5.91989i	0.446647	+	0.249272i
$565$	−0.952671	−	3.08848i	−0.0400792	−	0.129934i
$566$	−0.535188	+	2.34481i	−0.0224956	+	0.0985598i
$567$	13.5933	−	19.5505i	0.570863	−	0.821045i
$568$	3.17628	+	13.9162i	0.133274	+	0.583911i
$569$	31.7135	−	18.3098i	1.32950	−	0.767588i	0.344279	−	0.938868i	$-0.388124\pi$
$569$	31.7135	−	18.3098i	1.32950	−	0.767588i	0.985222	+	0.171280i	$0.0547902\pi$
$570$	−0.670950	−	4.05038i	−0.0281030	−	0.169652i
$571$	28.6200	+	8.82810i	1.19771	+	0.369444i	0.828546	−	0.559920i	$-0.189168\pi$
$571$	28.6200	+	8.82810i	1.19771	+	0.369444i	0.369163	+	0.929365i	$0.379644\pi$
$572$	−0.00489186	−	0.0652773i	−0.000204539	−	0.00272938i
$573$	−3.39878	+	0.0494926i	−0.141986	+	0.00206758i
$574$	−4.05936	−	25.6433i	−0.169434	−	1.07033i
$575$	18.7852	−	14.9807i	0.783399	−	0.624740i
$576$	−1.57501	−	2.55330i	−0.0656256	−	0.106387i
$577$	−3.31136	−	21.9694i	−0.137854	−	0.914599i	−0.945661	−	0.325153i	$-0.894584\pi$
$577$	−3.31136	−	21.9694i	−0.137854	−	0.914599i	0.807808	−	0.589446i	$-0.200654\pi$
$578$	7.33260	+	10.7549i	0.304996	+	0.447347i
$579$	19.4555	−	11.6136i	0.808543	−	0.482644i
$580$	0.243335	+	0.505290i	0.0101039	+	0.0209810i
$581$	29.1806	+	19.5803i	1.21061	+	0.812328i
$582$	5.96789	−	1.45387i	0.247377	−	0.0602647i
$583$	0.400743	+	0.273222i	0.0165971	+	0.0113157i
$584$	−6.66616	−	6.18529i	−0.275848	−	0.255949i
$585$	−0.0365307	+	0.131955i	−0.00151036	+	0.00545568i
$586$	−27.2342	−	10.6886i	−1.12503	−	0.441543i
$587$	2.54324			0.104971			0.0524854	−	0.998622i	$-0.483286\pi$
$587$	2.54324			0.104971			0.0524854	+	0.998622i	$0.483286\pi$
$588$	−0.355898	−	12.1191i	−0.0146770	−	0.499785i
$589$	−18.3199			−0.754857
$590$	4.55358	+	1.78715i	0.187468	+	0.0735757i
$591$	−24.8037	+	17.4453i	−1.02029	+	0.717603i
$592$	−2.45744	−	2.28017i	−0.101000	−	0.0937143i
$593$	8.04366	+	5.48407i	0.330313	+	0.225204i	0.717108	−	0.696962i	$-0.245465\pi$
$593$	8.04366	+	5.48407i	0.330313	+	0.225204i	−0.386795	+	0.922166i	$0.626418\pi$
$594$	0.258316	+	5.90974i	0.0105989	+	0.242479i
$595$	3.05114	−	2.87335i	0.125085	−	0.117796i
$596$	−5.16352	−	10.7222i	−0.211506	−	0.439197i
$597$	−5.19997	−	8.71118i	−0.212821	−	0.356525i
$598$	0.178095	+	0.261218i	0.00728286	+	0.0106820i
$599$	−5.42529	−	35.9944i	−0.221671	−	1.47069i	−0.771935	−	0.635702i	$-0.780711\pi$
$599$	−5.42529	−	35.9944i	−0.221671	−	1.47069i	0.550263	−	0.834991i	$-0.314527\pi$
$600$	−7.50019	−	1.01902i	−0.306194	−	0.0416012i
$601$	−12.2160	+	9.74197i	−0.498303	+	0.397383i	−0.840135	−	0.542378i	$-0.817524\pi$
$601$	−12.2160	+	9.74197i	−0.498303	+	0.397383i	0.341832	+	0.939761i	$0.388953\pi$
$602$	13.1186	−	14.3500i	0.534675	−	0.584863i
$603$	18.7602	+	22.1683i	0.763975	+	0.902764i
$604$	1.02749	+	13.7109i	0.0418079	+	0.557888i
$605$	−7.36001	−	2.27026i	−0.299227	−	0.0922993i
$606$	15.6024	−	2.58455i	0.633804	−	0.104990i
$607$	11.3320	−	6.54252i	0.459951	−	0.265553i	−0.252073	−	0.967708i	$-0.581112\pi$
$607$	11.3320	−	6.54252i	0.459951	−	0.265553i	0.712024	+	0.702155i	$0.247779\pi$
$608$	0.664539	+	2.91154i	0.0269506	+	0.118078i
$609$	1.96279	−	2.57529i	0.0795362	−	0.104356i
$610$	1.88674	−	8.26635i	0.0763919	−	0.334695i
$611$	0.118867	+	0.385358i	0.00480885	+	0.0155899i
$612$	−5.89205	+	1.06439i	−0.238172	+	0.0430255i
$613$	−4.01982	−	10.2423i	−0.162359	−	0.413684i	0.826423	−	0.563050i	$-0.190372\pi$
$613$	−4.01982	−	10.2423i	−0.162359	−	0.413684i	−0.988782	+	0.149366i	$0.952277\pi$
$614$	−30.4155	+	9.38193i	−1.22747	+	0.378624i
$615$	−6.02959	−	12.0679i	−0.243137	−	0.486623i
$616$	1.89530	+	2.34089i	0.0763638	+	0.0943171i
$617$	19.2149	−	4.38566i	0.773561	−	0.176560i	0.182520	−	0.983202i	$-0.441574\pi$
$617$	19.2149	−	4.38566i	0.773561	−	0.176560i	0.591040	+	0.806642i	$0.298717\pi$
$618$	−31.2282	−	11.7344i	−1.25618	−	0.472026i
$619$	−35.2484	−	20.3507i	−1.41675	−	0.817963i	−0.420741	−	0.907181i	$-0.638230\pi$
$619$	−35.2484	−	20.3507i	−1.41675	−	0.817963i	−0.996012	+	0.0892185i	$0.971563\pi$
$620$	1.43515	−	4.65265i	0.0576371	−	0.186855i
$621$	−15.3516	−	24.0945i	−0.616037	−	0.966879i
$622$	0.474805	+	0.378645i	0.0190380	+	0.0151823i
$623$	0.721802	−	10.6928i	0.0289184	−	0.428399i
$624$	0.0207459	−	0.0974104i	0.000830499	−	0.00389954i
$625$	−11.6901	+	10.8468i	−0.467604	+	0.433873i
$626$	−4.15658	+	0.626504i	−0.166130	+	0.0250401i
$627$	1.65358	−	5.65165i	0.0660375	−	0.225705i
$628$	1.06869	−	7.09027i	0.0426452	−	0.282932i
$629$	−6.02804	+	2.90295i	−0.240354	+	0.115748i
$630$	−2.07549	−	5.94820i	−0.0826897	−	0.236982i
$631$	−0.346017	−	0.166633i	−0.0137747	−	0.00663356i	0.426984	−	0.904259i	$-0.359576\pi$
$631$	−0.346017	−	0.166633i	−0.0137747	−	0.00663356i	−0.440758	+	0.897626i	$0.645290\pi$
$632$	−1.58984	+	2.33187i	−0.0632405	+	0.0927568i
$633$	13.2170	+	0.797144i	0.525329	+	0.0316836i
$634$	−1.03228	+	13.7748i	−0.0409971	+	0.547069i
$635$	6.48921	−	16.5342i	0.257516	−	0.656141i
$636$	0.468449	+	0.570183i	0.0185752	+	0.0226092i
$637$	0.269380	−	0.299078i	0.0106732	−	0.0118499i
$638$			0.804393i			0.0318462i
$639$	23.0822	−	36.0688i	0.913117	−	1.42686i
$640$	−0.791494	−	0.0593143i	−0.0312865	−	0.00234460i
$641$	4.35863	−	4.69749i	0.172156	−	0.185540i	−0.641080	−	0.767474i	$-0.721513\pi$
$641$	4.35863	−	4.69749i	0.172156	−	0.185540i	0.813236	+	0.581934i	$0.197704\pi$
$642$	4.72625	−	0.423469i	0.186530	−	0.0167130i
$643$	−1.81905	+	3.77729i	−0.0717362	+	0.148962i	−0.933753	−	0.357918i	$-0.883487\pi$
$643$	−1.81905	+	3.77729i	−0.0717362	+	0.148962i	0.862017	+	0.506880i	$0.169201\pi$
$644$	−13.5802	−	5.21423i	−0.535136	−	0.205470i
$645$	4.25036	−	9.16499i	0.167358	−	0.360871i
$646$	5.89373	+	0.888337i	0.231886	+	0.0349511i
$647$	−14.3190	+	9.76253i	−0.562938	+	0.383804i	−0.811094	−	0.584915i	$-0.801128\pi$
$647$	−14.3190	+	9.76253i	−0.562938	+	0.383804i	0.248156	+	0.968720i	$0.420175\pi$
$648$	−2.14768	+	8.73999i	−0.0843688	+	0.343339i
$649$	4.77220	+	5.14321i	0.187325	+	0.201889i
$650$	−0.156672	−	0.196460i	−0.00614516	−	0.00770579i
$651$	−27.6987	+	4.79914i	−1.08560	+	0.188093i
$652$	2.25728	−	2.83054i	0.0884018	−	0.110852i
$653$	−44.2247	+	3.31418i	−1.73064	+	0.129694i	−0.902464	−	0.430766i	$-0.858243\pi$
$653$	−44.2247	+	3.31418i	−1.73064	+	0.129694i	−0.828181	+	0.560460i	$0.810624\pi$
$654$	0.0669094	+	0.163444i	0.00261636	+	0.00639116i
$655$	−4.45914	+	7.72346i	−0.174233	+	0.301780i
$656$	4.90647	+	8.49825i	0.191565	+	0.331801i
$657$	0.794360	+	27.2696i	0.0309909	+	1.06389i
$658$	−14.5925	−	11.4615i	−0.568873	−	0.446816i
$659$	−44.9871	−	10.2680i	−1.75245	−	0.399985i	−0.778662	−	0.627444i	$-0.784101\pi$
$659$	−44.9871	−	10.2680i	−1.75245	−	0.399985i	−0.973788	+	0.227459i	$0.926958\pi$
$660$	1.30579	+	0.862696i	0.0508280	+	0.0335804i
$661$	−23.2624	+	9.12980i	−0.904801	+	0.355108i	−0.771694	−	0.635993i	$-0.780591\pi$
$661$	−23.2624	+	9.12980i	−0.904801	+	0.355108i	−0.133107	+	0.991102i	$0.542495\pi$
$662$	30.0827	−	11.8066i	1.16920	−	0.458876i
$663$	−0.165847	−	0.109569i	−0.00644095	−	0.00425532i
$664$	−12.9491	−	2.95554i	−0.502521	−	0.114697i
$665$	0.0463995	+	6.27119i	0.00179930	+	0.243186i
$666$	0.292835	+	10.0527i	0.0113471	+	0.389536i
$667$	−1.94249	−	3.36448i	−0.0752133	−	0.130273i
$668$	8.12364	−	14.0706i	0.314313	−	0.544406i
$669$	−0.668155	−	1.63214i	−0.0258324	−	0.0631023i
$670$	7.66193	−	0.574182i	0.296006	−	0.0221826i
$671$	7.58242	−	9.50805i	0.292716	−	0.367054i
$672$	1.76747	+	4.22801i	0.0681815	+	0.163099i
$673$	−16.5285	−	20.7260i	−0.637125	−	0.798930i	0.353515	−	0.935429i	$-0.384986\pi$
$673$	−16.5285	−	20.7260i	−0.637125	−	0.798930i	−0.990640	+	0.136499i	$0.956415\pi$
$674$	−13.2449	−	14.2747i	−0.510176	−	0.549839i
$675$	13.5986	+	18.1852i	0.523409	+	0.699947i
$676$	−10.7384	+	7.32130i	−0.413014	+	0.281588i
$677$	4.67031	+	0.703936i	0.179494	+	0.0270544i	0.238174	−	0.971222i	$-0.423451\pi$
$677$	4.67031	+	0.703936i	0.179494	+	0.0270544i	−0.0586799	+	0.998277i	$0.518689\pi$
$678$	2.96737	−	6.39849i	0.113961	−	0.245732i
$679$	−9.35104	+	0.770377i	−0.358860	+	0.0295644i
$680$	−0.687315	+	1.42722i	−0.0263573	+	0.0547315i
$681$	27.4511	−	2.45960i	1.05193	−	0.0942520i
$682$	4.74999	−	5.11927i	0.181887	−	0.196027i
$683$	29.5558	+	2.21490i	1.13092	+	0.0847509i	0.627015	−	0.779007i	$-0.284276\pi$
$683$	29.5558	+	2.21490i	1.13092	+	0.0847509i	0.503907	+	0.863758i	$0.331895\pi$
$684$	4.82923	−	7.54628i	0.184650	−	0.288539i
$685$		−	7.99475i		−	0.305464i
$686$	−2.35317	+	18.3702i	−0.0898444	+	0.701376i
$687$	−13.8737	−	16.8868i	−0.529317	−	0.644270i
$688$	−2.68477	+	6.84069i	−0.102356	+	0.260799i
$689$	−0.00183076	+	0.0244298i	−6.97465e−5	+	0.000930703i
$690$	−7.54494	−	0.455050i	−0.287231	−	0.0173235i
$691$	10.1176	−	14.8398i	0.384893	−	0.564534i	−0.584082	−	0.811695i	$-0.698545\pi$
$691$	10.1176	−	14.8398i	0.384893	−	0.564534i	0.968974	+	0.247161i	$0.0794976\pi$
$692$	−13.9527	−	6.71927i	−0.530403	−	0.255428i
$693$	1.01960	−	8.97818i	0.0387313	−	0.341053i
$694$	−10.0224	+	4.82653i	−0.380444	+	0.183212i
$695$	1.45472	−	9.65142i	0.0551806	−	0.366099i
$696$	−0.343670	+	1.17461i	−0.0130268	+	0.0445233i
$697$	19.3660	−	2.91895i	0.733539	−	0.110563i
$698$	0.607514	−	0.563691i	0.0229947	−	0.0213360i
$699$	2.38892	−	11.2170i	0.0903572	−	0.424265i
$700$	11.0732	+	3.32612i	0.418529	+	0.125715i
$701$	−2.39846	−	1.91271i	−0.0905887	−	0.0722421i	0.577148	−	0.816639i	$-0.304165\pi$
$701$	−2.39846	−	1.91271i	−0.0905887	−	0.0722421i	−0.667737	+	0.744397i	$0.732737\pi$
$702$	−0.251985	+	0.160550i	−0.00951056	+	0.00605955i
$703$	2.95093	−	9.56667i	0.111296	−	0.360814i
$704$	−0.985897	−	0.569208i	−0.0371574	−	0.0214528i
$705$	−9.02541	−	3.39140i	−0.339917	−	0.127728i
$706$	−23.1986	+	5.29493i	−0.873091	+	0.199277i
$707$	−24.1572	+	0.178735i	−0.908523	+	0.00672201i
$708$	4.77116	+	9.54919i	0.179311	+	0.358881i
$709$	41.2379	−	12.7202i	1.54872	−	0.477717i	0.601654	−	0.798756i	$-0.294508\pi$
$709$	41.2379	−	12.7202i	1.54872	−	0.477717i	0.947066	+	0.321040i	$0.104032\pi$
$710$	−4.13914	−	10.5464i	−0.155339	−	0.395798i
$711$	8.33195	−	1.50516i	0.312473	−	0.0564478i
$712$	1.19397	+	3.87074i	0.0447458	+	0.145062i
$713$	−7.50523	+	32.8826i	−0.281073	+	1.23146i
$714$	9.14373	−	0.200824i	0.342196	−	0.00751566i
$715$	0.0115615	+	0.0506540i	0.000432374	+	0.00189435i
$716$	−20.1477	+	11.6323i	−0.752956	+	0.434719i
$717$	−22.5972	+	3.74326i	−0.843909	+	0.139795i
$718$	25.4795	+	7.85939i	0.950887	+	0.293310i
$719$	−1.41971	−	18.9447i	−0.0529462	−	0.706518i	−0.959009	−	0.283375i	$-0.908546\pi$
$719$	−1.41971	−	18.9447i	−0.0529462	−	0.706518i	0.906063	−	0.423143i	$-0.139073\pi$
$720$	1.53819	+	1.81763i	0.0573251	+	0.0677391i
$721$	44.3186	+	25.1520i	1.65051	+	0.936709i
$722$	7.88192	−	6.28562i	0.293335	−	0.233927i
$723$	−11.6518	−	1.58307i	−0.433334	−	0.0588752i
$724$	0.0208327	+	0.138216i	0.000774241	+	0.00513675i
$725$	1.73943	+	2.55127i	0.0646007	+	0.0947518i
$726$	−8.61497	−	14.4321i	−0.319731	−	0.535626i
$727$	−9.01952	−	18.7292i	−0.334516	−	0.694629i	0.664077	−	0.747664i	$-0.268825\pi$
$727$	−9.01952	−	18.7292i	−0.334516	−	0.694629i	−0.998593	+	0.0530353i	$0.983110\pi$
$728$	−0.0545315	+	0.142025i	−0.00202107	+	0.00526379i
$729$	23.2112	−	13.7927i	0.859675	−	0.510842i
$730$	5.96362	+	4.06593i	0.220724	+	0.150487i
$731$	10.7513	+	9.97578i	0.397652	+	0.368968i
$732$	15.1344	−	10.6445i	0.559383	−	0.393432i
$733$	−14.6161	−	5.73639i	−0.539857	−	0.211878i	0.0797155	−	0.996818i	$-0.474599\pi$
$733$	−14.6161	−	5.73639i	−0.539857	−	0.211878i	−0.619573	+	0.784939i	$0.712694\pi$
$734$	25.3757			0.936635
$735$	1.71298	+	9.46957i	0.0631842	+	0.349290i
$736$	5.49820			0.202666
$737$	10.2585	+	4.02615i	0.377875	+	0.148305i
$738$	7.85445	−	28.3716i	0.289126	−	1.04437i
$739$	3.75260	+	3.48190i	0.138042	+	0.128084i	0.746172	−	0.665753i	$-0.231890\pi$
$739$	3.75260	+	3.48190i	0.138042	+	0.128084i	−0.608130	+	0.793837i	$0.708080\pi$
$740$	2.19845	+	1.49888i	0.0808166	+	0.0550998i
$741$	0.288980	−	0.0703999i	0.0106160	−	0.00258621i
$742$	−0.570817	−	0.972004i	−0.0209553	−	0.0356834i
$743$	2.99195	+	6.21286i	0.109764	+	0.227928i	0.948614	−	0.316435i	$-0.102486\pi$
$743$	2.99195	+	6.21286i	0.109764	+	0.227928i	−0.838850	+	0.544363i	$0.816772\pi$
$744$	9.12329	−	5.44597i	0.334476	−	0.199659i
$745$	5.32097	+	7.80444i	0.194945	+	0.285932i
$746$	2.23514	+	14.8292i	0.0818344	+	0.542936i
$747$	20.9195	+	33.9131i	0.765403	+	1.24082i
$748$	−1.77637	+	1.41661i	−0.0649504	+	0.0517962i
$749$	−7.23194	−	0.488180i	−0.264249	−	0.0178377i
$750$	12.8801	−	0.187558i	0.470314	−	0.00684865i
$751$	1.30820	+	17.4568i	0.0477370	+	0.637006i	0.968840	+	0.247687i	$0.0796706\pi$
$751$	1.30820	+	17.4568i	0.0477370	+	0.637006i	−0.921103	+	0.389319i	$0.872710\pi$
$752$	6.70173	+	2.06721i	0.244387	+	0.0753834i
$753$	−2.92905	−	17.6820i	−0.106741	−	0.644370i
$754$	−0.0351865	+	0.0203149i	−0.00128141	+	0.000739825i
$755$	−2.42838	−	10.6394i	−0.0883776	−	0.387208i
$756$	5.32470	−	12.6747i	0.193658	−	0.460974i
$757$	−8.44784	+	37.0124i	−0.307042	+	1.34524i	0.552218	+	0.833700i	$0.313782\pi$
$757$	−8.44784	+	37.0124i	−0.307042	+	1.34524i	−0.859260	+	0.511539i	$0.829075\pi$
$758$	10.1677	+	32.9627i	0.369306	+	1.19726i
$759$	−9.46678	−	5.28338i	−0.343622	−	0.191774i
$760$	−0.865987	−	2.20650i	−0.0314127	−	0.0800382i
$761$	13.5966	−	4.19399i	0.492876	−	0.152032i	−0.0383464	−	0.999265i	$-0.512209\pi$
$761$	13.5966	−	4.19399i	0.492876	−	0.152032i	0.531222	+	0.847232i	$0.321733\pi$
$762$	34.6735	−	17.3243i	1.25609	−	0.627593i
$763$	−0.0619748	−	0.262559i	−0.00224364	−	0.00950529i
$764$	−1.91329	+	0.436697i	−0.0692205	+	0.0157991i
$765$	4.49845	−	1.53240i	0.162642	−	0.0554039i
$766$	−2.94441	−	1.69995i	−0.106386	−	0.0614218i
$767$	−0.104457	+	0.338641i	−0.00377172	+	0.0122276i
$768$	−1.19646	−	1.25240i	−0.0431734	−	0.0451919i
$769$	18.5915	+	14.8262i	0.670425	+	0.534646i	0.898487	−	0.439000i	$-0.144667\pi$
$769$	18.5915	+	14.8262i	0.670425	+	0.534646i	−0.228061	+	0.973647i	$0.573239\pi$
$770$	−1.76444	−	1.61303i	−0.0635861	−	0.0581297i
$771$	−39.5197	−	8.41666i	−1.42327	−	0.303118i
$772$	9.58956	−	8.89781i	0.345136	−	0.320239i
$773$	−23.1243	+	3.48543i	−0.831725	+	0.125362i	−0.551083	−	0.834450i	$-0.685785\pi$
$773$	−23.1243	+	3.48543i	−0.831725	+	0.125362i	−0.280642	+	0.959813i	$0.590547\pi$
$774$	20.2788	−	8.64845i	0.728908	−	0.310862i
$775$	3.99545	−	26.5081i	0.143521	−	0.952198i
$776$	3.19514	−	1.53870i	0.114699	−	0.0552360i
$777$	1.95553	−	15.2374i	0.0701542	−	0.546637i
$778$	21.0874	+	10.1552i	0.756021	+	0.364081i
$779$	−16.5083	+	24.2133i	−0.591473	+	0.867531i
$780$	−0.00475901	+	0.0789065i	−0.000170400	+	0.00282531i
$781$	1.21435	−	16.2044i	0.0434529	−	0.579839i
$782$	4.00901	−	10.2148i	0.143362	−	0.365280i
$783$	3.23523	−	1.73596i	0.115618	−	0.0620381i
$784$	−1.65846	−	6.80070i	−0.0592306	−	0.242882i
$785$			5.69120i			0.203128i
$786$	−18.5115	+	6.00657i	−0.660282	+	0.214247i
$787$	−16.9283	−	1.26860i	−0.603430	−	0.0452208i	−0.230488	−	0.973075i	$-0.574032\pi$
$787$	−16.9283	−	1.26860i	−0.603430	−	0.0452208i	−0.372943	+	0.927854i	$0.621651\pi$
$788$	−11.9083	+	12.8341i	−0.424215	+	0.457195i
$789$	4.57745	+	51.0880i	0.162962	+	1.81878i
$790$	0.971932	−	2.01824i	0.0345798	−	0.0718057i
$791$	−6.00305	+	8.94635i	−0.213444	+	0.318096i
$792$	0.856592	+	3.30608i	0.0304377	+	0.117476i
$793$	0.607403	+	0.0915513i	0.0215695	+	0.00325108i
$794$	−29.0965	+	19.8376i	−1.03259	+	0.704011i
$795$	−0.435112	−	0.392091i	−0.0154318	−	0.0139060i
$796$	−3.98398	−	4.29371i	−0.141209	−	0.152187i
$797$	17.1308	+	21.4813i	0.606803	+	0.760907i	0.986421	−	0.164236i	$-0.0525160\pi$
$797$	17.1308	+	21.4813i	0.606803	+	0.760907i	−0.379618	+	0.925143i	$0.623945\pi$
$798$	−9.08594	+	10.2341i	−0.321639	+	0.362284i
$799$	8.72713	−	10.9435i	0.308744	−	0.387152i
$800$	−4.35780	+	0.326572i	−0.154071	+	0.0115461i
$801$	5.76705	−	10.6965i	0.203769	−	0.377942i
$802$	−18.0606	+	31.2819i	−0.637742	+	1.10460i
$803$	5.17621	+	8.96546i	0.182664	+	0.316384i
$804$	13.2597	+	10.2620i	0.467632	+	0.361912i
$805$	11.2753	+	2.48588i	0.397400	+	0.0876158i
$806$	0.343892	+	0.0784912i	0.0121131	+	0.00276473i
$807$	12.4334	−	18.8195i	0.437678	−	0.662479i
$808$	8.49962	−	3.33585i	0.299016	−	0.117355i
$809$	−24.0782	+	9.45000i	−0.846545	+	0.332244i	−0.748661	−	0.662954i	$-0.769303\pi$
$809$	−24.0782	+	9.45000i	−0.846545	+	0.332244i	−0.0978841	+	0.995198i	$0.531207\pi$
$810$	0.651689	−	7.11363i	0.0228980	−	0.249947i
$811$	−7.63498	−	1.74263i	−0.268100	−	0.0611921i	0.0863573	−	0.996264i	$-0.472477\pi$
$811$	−7.63498	−	1.74263i	−0.268100	−	0.0611921i	−0.354458	+	0.935072i	$0.615334\pi$
$812$	0.798645	−	1.69028i	0.0280269	−	0.0593173i
$813$	−25.6364	+	33.1252i	−0.899107	+	1.16175i
$814$	1.90817	+	3.30506i	0.0668815	+	0.115842i
$815$	−1.43678	+	2.48857i	−0.0503281	+	0.0871708i
$816$	−3.19915	+	1.30965i	−0.111993	+	0.0458467i
$817$	−21.8848	+	1.64004i	−0.765652	+	0.0573777i
$818$	0.649832	−	0.814863i	0.0227208	−	0.0284910i
$819$	0.418481	−	0.182144i	0.0146229	−	0.00636461i
$820$	−4.85614	−	6.08941i	−0.169584	−	0.212652i
$821$	5.77631	+	6.22539i	0.201595	+	0.217267i	0.825755	−	0.564029i	$-0.190749\pi$
$821$	5.77631	+	6.22539i	0.201595	+	0.217267i	−0.624160	+	0.781296i	$0.714559\pi$
$822$	11.6790	−	12.9604i	0.407352	−	0.452047i
$823$	−15.1393	+	10.3218i	−0.527721	+	0.359794i	−0.797683	−	0.603077i	$-0.793941\pi$
$823$	−15.1393	+	10.3218i	−0.527721	+	0.359794i	0.269962	+	0.962871i	$0.412989\pi$
$824$	−19.0453	−	2.87062i	−0.663476	−	0.100003i
$825$	7.81706	+	3.62524i	0.272155	+	0.126215i
$826$	−4.92143	−	15.5456i	−0.171238	−	0.540900i
$827$	−24.4534	+	50.7780i	−0.850328	+	1.76572i	−0.245444	+	0.969411i	$0.578934\pi$
$827$	−24.4534	+	50.7780i	−0.850328	+	1.76572i	−0.604884	+	0.796314i	$0.706781\pi$
$828$	−11.5665	−	11.7596i	−0.401963	−	0.408674i
$829$	36.3201	−	39.1438i	1.26145	−	1.35952i	0.356331	−	0.934360i	$-0.384027\pi$
$829$	36.3201	−	39.1438i	1.26145	−	1.35952i	0.905118	−	0.425160i	$-0.139782\pi$
$830$	10.5127	+	0.787817i	0.364900	+	0.0273455i
$831$	−15.6442	−	48.2133i	−0.542690	−	1.67250i
$832$		−	0.0575012i		−	0.00199350i
$833$	−13.8439	−	1.87758i	−0.479663	−	0.0650542i
$834$	16.4574	−	13.5210i	0.569873	−	0.468194i
$835$	−4.71132	+	12.0043i	−0.163042	+	0.415424i
$836$	0.254066	−	3.39027i	0.00878704	−	0.117255i
$837$	−30.8404	−	8.05634i	−1.06600	−	0.278468i
$838$	4.96240	−	7.27850i	0.171423	−	0.251432i
$839$	−39.8907	−	19.2104i	−1.37718	−	0.663216i	−0.408785	−	0.912631i	$-0.634047\pi$
$839$	−39.8907	−	19.2104i	−1.37718	−	0.663216i	−0.968397	+	0.249415i	$0.919762\pi$
$840$	−1.88735	−	3.10926i	−0.0651199	−	0.107280i
$841$	−25.6783	+	12.3660i	−0.885458	+	0.426414i
$842$	−1.80696	+	11.9884i	−0.0622721	+	0.413148i
$843$	48.9526	+	14.3227i	1.68602	+	0.493300i
$844$	7.55933	−	1.13939i	0.260203	−	0.0392193i
$845$	7.56190	−	7.01642i	0.260137	−	0.241372i
$846$	−9.67698	−	18.6825i	−0.332701	−	0.642317i
$847$	9.55648	+	23.8296i	0.328364	+	0.818794i
$848$	0.333098	+	0.265637i	0.0114386	+	0.00912202i
$849$	3.01215	−	2.87761i	0.103377	−	0.0987594i
$850$	−2.57077	+	8.33424i	−0.0881767	+	0.285862i
$851$	−15.9624	−	9.21590i	−0.547184	−	0.315917i
$852$	8.69643	−	23.1435i	0.297935	−	0.792882i
$853$	−11.9154	+	2.71961i	−0.407975	+	0.0931176i	−0.421583	−	0.906790i	$-0.638525\pi$
$853$	−11.9154	+	2.71961i	−0.407975	+	0.0931176i	0.0136081	+	0.999907i	$0.495668\pi$
$854$	−25.3731	+	12.4512i	−0.868251	+	0.426070i
$855$	−2.89751	+	6.49397i	−0.0990929	+	0.222089i
$856$	2.61792	−	0.807522i	0.0894787	−	0.0276005i
$857$	18.8196	+	47.9515i	0.642865	+	1.63799i	0.763893	+	0.645343i	$0.223286\pi$
$857$	18.8196	+	47.9515i	0.642865	+	1.63799i	−0.121028	+	0.992649i	$0.538619\pi$
$858$	−0.0552546	+	0.0990055i	−0.00188636	+	0.00337999i
$859$	5.84888	+	18.9616i	0.199561	+	0.646962i	0.998936	+	0.0461282i	$0.0146883\pi$
$859$	5.84888	+	18.9616i	0.199561	+	0.646962i	−0.799374	+	0.600833i	$0.794836\pi$
$860$	1.29791	−	5.68650i	0.0442582	−	0.193908i
$861$	−18.6168	+	40.9339i	−0.634458	+	1.39502i
$862$	1.57609	+	6.90532i	0.0536820	+	0.235196i
$863$	13.6539	−	7.88309i	0.464785	−	0.268344i	−0.249269	−	0.968434i	$-0.580190\pi$
$863$	13.6539	−	7.88309i	0.464785	−	0.268344i	0.714054	+	0.700091i	$0.246857\pi$
$864$	−0.161664	+	5.19364i	−0.00549993	+	0.176691i
$865$	11.7456	+	3.62305i	0.399363	+	0.123187i
$866$	−0.442946	−	5.91071i	−0.0150519	−	0.200854i
$867$	−0.328272	−	22.5433i	−0.0111487	−	0.765610i
$868$	−15.0639	+	6.04115i	−0.511302	+	0.205050i
$869$	2.51196	−	2.00322i	0.0852124	−	0.0679546i
$870$	0.130776	−	0.962542i	0.00443374	−	0.0326332i
$871$	0.0829616	+	0.550414i	0.00281105	+	0.0186501i
$872$	0.0574391	+	0.0842476i	0.00194513	+	0.00285298i
$873$	−10.0125	−	3.59685i	−0.338873	−	0.121735i
$874$	7.12432	+	14.7938i	0.240984	+	0.500408i
$875$	−19.4781	−	2.78863i	−0.658481	−	0.0942729i
$876$	3.72809	+	15.3032i	0.125960	+	0.517047i
$877$	39.6321	+	27.0207i	1.33828	+	0.912424i	0.999594	−	0.0284754i	$-0.00906523\pi$
$877$	39.6321	+	27.0207i	1.33828	+	0.912424i	0.338686	+	0.940900i	$0.390018\pi$
$878$	−21.7347	−	20.1669i	−0.733512	−	0.680599i
$879$	29.1522	+	41.4487i	0.983280	+	1.39803i
$880$	0.841115	+	0.330113i	0.0283540	+	0.0111281i
$881$	−17.5667			−0.591837			−0.295918	−	0.955213i	$-0.595626\pi$
$881$	−17.5667			−0.591837			−0.295918	+	0.955213i	$0.595626\pi$
$882$	−11.0565	+	17.8537i	−0.372292	+	0.601164i
$883$	5.83837			0.196477			0.0982384	−	0.995163i	$-0.468679\pi$
$883$	5.83837			0.196477			0.0982384	+	0.995163i	$0.468679\pi$
$884$	−0.106828	−	0.0419271i	−0.00359303	−	0.00141016i
$885$	−4.87427	−	6.93025i	−0.163847	−	0.232958i
$886$	−20.5092	−	19.0298i	−0.689021	−	0.639318i
$887$	27.2899	+	18.6059i	0.916304	+	0.624726i	0.926937	−	0.375218i	$-0.122432\pi$
$887$	27.2899	+	18.6059i	0.916304	+	0.624726i	−0.0106326	+	0.999943i	$0.503385\pi$
$888$	1.37434	+	5.64142i	0.0461197	+	0.189314i
$889$	−56.4467	+	17.8699i	−1.89316	+	0.599338i
$890$	−1.39498	−	2.89670i	−0.0467598	−	0.0970977i
$891$	5.26907	−	8.78704i	0.176520	−	0.294377i
$892$	−0.573584	−	0.841294i	−0.0192050	−	0.0281686i
$893$	3.12164	+	20.7107i	0.104462	+	0.693057i
$894$	−2.77505	+	20.4250i	−0.0928116	+	0.683113i
$895$	14.4368	−	11.5130i	0.482570	−	0.384837i
$896$	1.50654	+	2.17494i	0.0503299	+	0.0726595i
$897$	−0.00797313	−	0.547535i	−0.000266215	−	0.0182817i
$898$	0.912467	+	12.1760i	0.0304494	+	0.406319i
$899$	−4.14194	−	1.27762i	−0.138142	−	0.0426110i
$900$	9.86592	+	8.63349i	0.328864	+	0.287783i
$901$	0.736391	−	0.425156i	0.0245328	−	0.0141640i
$902$	−2.48582	−	10.8911i	−0.0827689	−	0.362634i
$903$	−32.6591	+	8.21268i	−1.08683	+	0.273301i
$904$	0.906127	−	3.97000i	0.0301373	−	0.132040i
$905$	−0.0327010	−	0.106014i	−0.00108702	−	0.00352403i
$906$	11.6057	−	20.7952i	0.385574	−	0.690874i
$907$	−20.6836	−	52.7009i	−0.686787	−	1.74991i	−0.661173	−	0.750233i	$-0.729941\pi$
$907$	−20.6836	−	52.7009i	−0.686787	−	1.74991i	−0.0256139	−	0.999672i	$-0.508154\pi$
$908$	15.2054	−	4.69026i	0.504610	−	0.155652i
$909$	−25.0153	−	11.1615i	−0.829705	−	0.370202i
$910$	0.0259978	−	0.117919i	0.000861820	−	0.00390897i
$911$	30.3589	−	6.92923i	1.00584	−	0.229576i	0.312289	−	0.949987i	$-0.398904\pi$
$911$	30.3589	−	6.92923i	1.00584	−	0.229576i	0.693547	+	0.720412i	$0.256047\pi$
$912$	1.81946	−	4.84206i	0.0602483	−	0.160337i
$913$	13.0948	+	7.56026i	0.433373	+	0.250208i
$914$	4.73902	−	15.3635i	0.156753	−	0.508181i
$915$	−10.6190	+	10.1447i	−0.351052	+	0.335372i
$916$	−9.86516	−	7.86721i	−0.325954	−	0.259940i
$917$	29.3624	−	4.64811i	0.969633	−	0.153494i
$918$	9.53109	+	4.08729i	0.314573	+	0.134901i
$919$	−7.30518	+	6.77821i	−0.240976	+	0.223593i	−0.791410	−	0.611286i	$-0.790653\pi$
$919$	−7.30518	+	6.77821i	−0.240976	+	0.223593i	0.550434	+	0.834878i	$0.314462\pi$
$920$	−4.31525	+	0.650419i	−0.142270	+	0.0214437i
$921$	52.9122	+	15.4812i	1.74352	+	0.510123i
$922$	−0.844606	+	5.60360i	−0.0278156	+	0.184545i
$923$	0.739495	−	0.356122i	0.0243408	−	0.0117219i
$924$	−0.503994	−	5.19247i	−0.0165802	−	0.170820i
$925$	13.1990	+	6.35630i	0.433980	+	0.208994i
$926$	−0.486146	+	0.713045i	−0.0159757	+	0.0234321i
$927$	33.9257	+	46.7732i	1.11427	+	1.53623i
$928$	−0.0528035	+	0.704614i	−0.00173336	+	0.0231301i
$929$	−9.26240	+	23.6002i	−0.303889	+	0.774298i	0.694602	+	0.719394i	$0.255580\pi$
$929$	−9.26240	+	23.6002i	−0.303889	+	0.774298i	−0.998492	+	0.0549036i	$0.982515\pi$
$930$	−6.51615	+	5.35351i	−0.213673	+	0.175549i
$931$	16.1494	−	13.2744i	0.529276	−	0.435051i
$932$		−	6.62136i		−	0.216890i
$933$	−0.324647	−	1.00052i	−0.0106285	−	0.0327555i
$934$	34.2049	+	2.56330i	1.11922	+	0.0838738i
$935$	1.22660	−	1.32196i	0.0401140	−	0.0432327i
$936$	−0.122984	+	0.120965i	−0.00401986	+	0.00395385i
$937$	15.5497	−	32.2893i	0.507987	−	1.05485i	−0.476466	−	0.879193i	$-0.658082\pi$
$937$	15.5497	−	32.2893i	0.507987	−	1.05485i	0.984452	−	0.175652i	$-0.0562034\pi$
$938$	−17.5589	−	18.6453i	−0.573317	−	0.608792i
$939$	6.60501	+	3.06314i	0.215546	+	0.0999619i
$940$	−5.50438	−	0.829652i	−0.179533	−	0.0270603i
$941$	−25.3899	+	17.3105i	−0.827687	+	0.564307i	−0.901408	−	0.432972i	$-0.857465\pi$
$941$	−25.3899	+	17.3105i	−0.827687	+	0.564307i	0.0737208	+	0.997279i	$0.476513\pi$
$942$	−8.31389	+	9.22611i	−0.270881	+	0.300603i
$943$	36.6976	+	39.5507i	1.19504	+	1.28795i
$944$	3.84262	+	4.81850i	0.125067	+	0.156829i
$945$	−2.67971	+	10.5776i	−0.0871710	+	0.344089i
$946$	5.21602	−	6.54068i	0.169587	−	0.212656i
$947$	10.1319	−	0.759284i	0.329244	−	0.0246734i	0.0909171	−	0.995858i	$-0.471020\pi$
$947$	10.1319	−	0.759284i	0.329244	−	0.0246734i	0.238327	+	0.971185i	$0.423401\pi$
$948$	4.52392	−	1.85197i	0.146930	−	0.0601492i
$949$	−0.261450	+	0.452844i	−0.00848702	+	0.0146999i
$950$	−6.52534	−	11.3022i	−0.211710	−	0.366692i
$951$	14.6434	−	18.9210i	0.474846	−	0.613556i
$952$	5.13919	−	1.21306i	0.166562	−	0.0393154i
$953$	5.54443	+	1.26548i	0.179602	+	0.0409929i	0.311376	−	0.950287i	$-0.399210\pi$
$953$	5.54443	+	1.26548i	0.179602	+	0.0409929i	−0.131774	+	0.991280i	$0.542067\pi$
$954$	−0.132588	−	1.27125i	−0.00429269	−	0.0411583i
$955$	1.44998	−	0.569077i	0.0469204	−	0.0184149i
$956$	−12.3102	+	4.83138i	−0.398139	+	0.156258i
$957$	0.768001	−	1.16246i	0.0248260	−	0.0375771i
$958$	−19.3023	−	4.40562i	−0.623628	−	0.142339i
$959$	−20.7120	+	16.7694i	−0.668825	+	0.541514i
$960$	1.08719	+	0.841403i	0.0350889	+	0.0271562i
$961$	3.31549	+	5.74259i	0.106951	+	0.185245i
$962$	−0.0963817	+	0.166938i	−0.00310747	+	0.00538230i
$963$	−7.23442	−	3.90046i	−0.233126	−	0.125691i
$964$	−6.76997	+	0.507339i	−0.218046	+	0.0163403i
$965$	−6.47377	+	8.11785i	−0.208398	+	0.261323i
$966$	14.6470	+	20.5012i	0.471261	+	0.659614i
$967$	16.6060	+	20.8233i	0.534013	+	0.669631i	0.973518	−	0.228609i	$-0.0734177\pi$
$967$	16.6060	+	20.8233i	0.534013	+	0.669631i	−0.439506	+	0.898240i	$0.644846\pi$
$968$	−6.60040	−	7.11354i	−0.212145	−	0.228638i
$969$	−7.66913	−	6.91086i	−0.246368	−	0.222009i
$970$	−2.32567	+	1.58562i	−0.0746729	+	0.0509111i
$971$	53.4033	+	8.04925i	1.71379	+	0.258313i	0.931275	−	0.364316i	$-0.118697\pi$
$971$	53.4033	+	8.04925i	1.71379	+	0.258313i	0.782517	+	0.622629i	$0.213935\pi$
$972$	11.4483	−	10.5800i	0.367204	−	0.339354i
$973$	−28.0553	+	16.4757i	−0.899411	+	0.528186i
$974$	4.11830	−	8.55175i	0.131959	−	0.274016i
$975$	0.0388409	+	0.433496i	0.00124390	+	0.0138830i
$976$	7.26602	−	7.83091i	0.232580	−	0.250661i
$977$	−14.1742	−	1.06221i	−0.453473	−	0.0339831i	−0.153964	−	0.988076i	$-0.549204\pi$
$977$	−14.1742	−	1.06221i	−0.453473	−	0.0339831i	−0.299509	+	0.954093i	$0.596823\pi$
$978$	−5.96457	+	1.93537i	−0.190726	+	0.0618864i
$979$		−	4.61138i		−	0.147380i
$980$	2.10614	+	5.14133i	0.0672781	+	0.164234i
$981$	0.0593557	−	0.300082i	0.00189508	−	0.00958087i
$982$	8.73698	−	22.2615i	0.278808	−	0.710392i
$983$	−4.03680	+	53.8673i	−0.128754	+	1.71810i	0.442031	+	0.897000i	$0.354258\pi$
$983$	−4.03680	+	53.8673i	−0.128754	+	1.71810i	−0.570784	+	0.821100i	$0.693361\pi$
$984$	1.02323	−	16.9657i	0.0326195	−	0.540846i
$985$	7.82797	−	11.4815i	0.249420	−	0.365832i
$986$	1.27056	+	0.611871i	0.0404629	+	0.0194859i
$987$	10.1452	+	30.4958i	0.322926	+	0.970691i
$988$	0.154716	−	0.0745075i	0.00492219	−	0.00237040i
$989$	−6.02197	+	39.9532i	−0.191488	+	1.27044i
$990$	−1.06339	−	2.49344i	−0.0337969	−	0.0792466i
$991$	42.3170	−	6.37827i	1.34425	−	0.202612i	0.562804	−	0.826591i	$-0.309723\pi$
$991$	42.3170	−	6.37827i	1.34425	−	0.202612i	0.781442	+	0.623978i	$0.214485\pi$
$992$	4.49684	−	4.17246i	0.142775	−	0.132476i
$993$	−54.7462	−	11.6595i	−1.73732	−	0.370003i
$994$	−18.6403	+	32.8448i	−0.591236	+	1.04178i
$995$	3.63475	+	2.89862i	0.115229	+	0.0918924i
$996$	15.8914	+	16.6344i	0.503539	+	0.527081i
$997$	1.71814	−	5.57008i	0.0544141	−	0.176406i	−0.924286	−	0.381700i	$-0.875339\pi$
$997$	1.71814	−	5.57008i	0.0544141	−	0.176406i	0.978700	+	0.205294i	$0.0658150\pi$
$998$	15.9890	+	9.23127i	0.506124	+	0.292211i
$999$	9.17475	−	14.8072i	0.290276	−	0.468480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	294.2.p.a.101.6	✓	216
3.2	odd	2	inner	294.2.p.a.101.16	yes	216
49.33	odd	42	inner	294.2.p.a.131.16	yes	216
147.131	even	42	inner	294.2.p.a.131.6	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
294.2.p.a.101.6	✓	216	1.1	even	1	trivial
294.2.p.a.101.16	yes	216	3.2	odd	2	inner
294.2.p.a.131.6	yes	216	147.131	even	42	inner
294.2.p.a.131.16	yes	216	49.33	odd	42	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:	\( N \)	\(=\)	\( 294 = 2 \cdot 3 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	294.p (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.996433 + 1.41673i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.655797 - 0.447115i) q^{5} +(-0.409964 - 1.68283i) q^{6} +(0.217232 + 2.63682i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-1.01424 + 2.82335i) q^{9} +O(q^{10})\)	\(q+(-0.930874 - 0.365341i) q^{2} +(0.996433 + 1.41673i) q^{3} +(0.733052 + 0.680173i) q^{4} +(-0.655797 - 0.447115i) q^{5} +(-0.409964 - 1.68283i) q^{6} +(0.217232 + 2.63682i) q^{7} +(-0.433884 - 0.900969i) q^{8} +(-1.01424 + 2.82335i) q^{9} +(0.447115 + 0.655797i) q^{10} +(0.169672 + 1.12570i) q^{11} +(-0.233184 + 1.71628i) q^{12} +(-0.0449563 + 0.0358514i) q^{13} +(0.761122 - 2.53391i) q^{14} +(-0.0200168 - 1.37461i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(1.90714 + 0.588275i) q^{17} +(1.97562 - 2.25764i) q^{18} +(-2.58631 + 1.49321i) q^{19} +(-0.176618 - 0.773813i) q^{20} +(-3.51920 + 2.93517i) q^{21} +(0.253321 - 1.10987i) q^{22} +(1.62062 + 5.25393i) q^{23} +(0.844093 - 1.51245i) q^{24} +(-1.59655 - 4.06794i) q^{25} +(0.0549466 - 0.0169488i) q^{26} +(-5.01055 + 1.37637i) q^{27} +(-1.63425 + 2.08068i) q^{28} +(-0.688874 + 0.157231i) q^{29} +(-0.483567 + 1.28690i) q^{30} +(5.31255 + 3.06720i) q^{31} +(0.294755 - 0.955573i) q^{32} +(-1.42575 + 1.36206i) q^{33} +(-1.56039 - 1.24437i) q^{34} +(1.03650 - 1.82634i) q^{35} +(-2.66386 + 1.37980i) q^{36} +(-2.45744 + 2.28017i) q^{37} +(2.95306 - 0.445101i) q^{38} +(-0.0955877 - 0.0279673i) q^{39} +(-0.118297 + 0.784848i) q^{40} +(8.84115 - 4.25767i) q^{41} +(4.34827 - 1.44656i) q^{42} +(6.62093 + 3.18847i) q^{43} +(-0.641292 + 0.940603i) q^{44} +(1.92750 - 1.39806i) q^{45} +(0.410881 - 5.48282i) q^{46} +(2.56225 - 6.52851i) q^{47} +(-1.33830 + 1.09952i) q^{48} +(-6.90562 + 1.14560i) q^{49} +4.37002i q^{50} +(1.06691 + 3.28808i) q^{51} +(-0.0573405 - 0.00429707i) q^{52} +(0.289787 - 0.312316i) q^{53} +(5.16703 + 0.549333i) q^{54} +(0.392047 - 0.814093i) q^{55} +(2.28144 - 1.33979i) q^{56} +(-4.69255 - 2.17622i) q^{57} +(0.698698 + 0.105312i) q^{58} +(5.09218 - 3.47179i) q^{59} +(0.920296 - 1.02127i) q^{60} +(-7.26602 - 7.83091i) q^{61} +(-3.82474 - 4.79607i) q^{62} +(-7.66499 - 2.06106i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(0.0455119 - 0.00341064i) q^{65} +(1.82481 - 0.747026i) q^{66} +(4.84017 - 8.38342i) q^{67} +(0.997904 + 1.72842i) q^{68} +(-5.82855 + 7.53117i) q^{69} +(-1.63209 + 1.32142i) q^{70} +(-13.9162 - 3.17628i) q^{71} +(2.98382 - 0.311204i) q^{72} +(8.46509 - 3.32230i) q^{73} +(3.12060 - 1.22475i) q^{74} +(4.17231 - 6.31530i) q^{75} +(-2.91154 - 0.664539i) q^{76} +(-2.93141 + 0.691932i) q^{77} +(0.0787625 + 0.0609562i) q^{78} +(-1.41114 - 2.44416i) q^{79} +(0.396857 - 0.687376i) q^{80} +(-6.94262 - 5.72713i) q^{81} +(-9.78549 + 0.733321i) q^{82} +(8.28124 - 10.3843i) q^{83} +(-4.57618 - 0.242032i) q^{84} +(-0.987669 - 1.23850i) q^{85} +(-4.99837 - 5.38696i) q^{86} +(-0.909171 - 0.819278i) q^{87} +(0.940603 - 0.641292i) q^{88} +(-4.00546 - 0.603726i) q^{89} +(-2.30503 + 0.597223i) q^{90} +(-0.104300 - 0.110753i) q^{91} +(-2.38558 + 4.95370i) q^{92} +(0.948204 + 10.5827i) q^{93} +(-4.77026 + 5.14112i) q^{94} +(2.36373 + 0.177137i) q^{95} +(1.64749 - 0.534576i) q^{96} +3.54633i q^{97} +(6.84680 + 1.45649i) q^{98} +(-3.35034 - 0.662691i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9}+O(q^{10}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9	\( 216 q - 18 q^{4} + 14 q^{6} + 10 q^{7} + 16 q^{9} + 6 q^{10} - 12 q^{15} + 18 q^{16} - 4 q^{18} - 12 q^{19} + 10 q^{22} - 6 q^{24} + 16 q^{25} - 42 q^{27} + 2 q^{28} + 4 q^{30} + 6 q^{31} + 18 q^{33} - 10 q^{36} - 36 q^{37} + 4 q^{39} - 22 q^{40} + 20 q^{42} + 40 q^{43} - 14 q^{45} - 156 q^{46} - 134 q^{49} - 12 q^{51} + 16 q^{52} - 18 q^{54} - 322 q^{55} - 34 q^{57} - 164 q^{58} - 6 q^{60} + 56 q^{61} - 24 q^{63} + 36 q^{64} - 28 q^{69} - 4 q^{70} + 4 q^{72} - 24 q^{73} + 84 q^{75} + 16 q^{78} + 22 q^{79} - 52 q^{81} + 24 q^{82} + 42 q^{84} + 32 q^{85} - 94 q^{87} - 2 q^{88} + 42 q^{90} - 100 q^{91} - 266 q^{93} - 88 q^{94} - 6 q^{96} + 224 q^{99}+O(q^{100}) \) 216 * q - 18 * q^4 + 14 * q^6 + 10 * q^7 + 16 * q^9 + 6 * q^10 - 12 * q^15 + 18 * q^16 - 4 * q^18 - 12 * q^19 + 10 * q^22 - 6 * q^24 + 16 * q^25 - 42 * q^27 + 2 * q^28 + 4 * q^30 + 6 * q^31 + 18 * q^33 - 10 * q^36 - 36 * q^37 + 4 * q^39 - 22 * q^40 + 20 * q^42 + 40 * q^43 - 14 * q^45 - 156 * q^46 - 134 * q^49 - 12 * q^51 + 16 * q^52 - 18 * q^54 - 322 * q^55 - 34 * q^57 - 164 * q^58 - 6 * q^60 + 56 * q^61 - 24 * q^63 + 36 * q^64 - 28 * q^69 - 4 * q^70 + 4 * q^72 - 24 * q^73 + 84 * q^75 + 16 * q^78 + 22 * q^79 - 52 * q^81 + 24 * q^82 + 42 * q^84 + 32 * q^85 - 94 * q^87 - 2 * q^88 + 42 * q^90 - 100 * q^91 - 266 * q^93 - 88 * q^94 - 6 * q^96 + 224 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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