LMFDB - Embedded newform 294.2.p.a.101.16

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			101.16
Character	$\chi$	$=$	294.101
Dual form			294.2.p.a.131.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.930874 + 0.365341i) q^{2} +(1.19646 - 1.25240i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.655797 + 0.447115i) q^{5} +(1.57130 - 0.728707i) q^{6} +(0.217232 + 2.63682i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-0.136987 - 2.99687i) q^{9} +O(q^{10})$	\(q+(0.930874 + 0.365341i) q^{2} +(1.19646 - 1.25240i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.655797 + 0.447115i) q^{5} +(1.57130 - 0.728707i) q^{6} +(0.217232 + 2.63682i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-0.136987 - 2.99687i) q^{9} +(0.447115 + 0.655797i) q^{10} +(-0.169672 - 1.12570i) q^{11} +(1.72891 - 0.104274i) q^{12} +(-0.0449563 + 0.0358514i) q^{13} +(-0.761122 + 2.53391i) q^{14} +(1.34460 - 0.286364i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-1.90714 - 0.588275i) q^{17} +(0.967362 - 2.83976i) q^{18} +(-2.58631 + 1.49321i) q^{19} +(0.176618 + 0.773813i) q^{20} +(3.56225 + 2.88278i) q^{21} +(0.253321 - 1.10987i) q^{22} +(-1.62062 - 5.25393i) q^{23} +(1.64749 + 0.534576i) q^{24} +(-1.59655 - 4.06794i) q^{25} +(-0.0549466 + 0.0169488i) q^{26} +(-3.91716 - 3.41406i) q^{27} +(-1.63425 + 2.08068i) q^{28} +(0.688874 - 0.157231i) q^{29} +(1.35627 + 0.224668i) q^{30} +(5.31255 + 3.06720i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-1.61283 - 1.13435i) q^{33} +(-1.56039 - 1.24437i) q^{34} +(-1.03650 + 1.82634i) q^{35} +(1.93797 - 2.29004i) q^{36} +(-2.45744 + 2.28017i) q^{37} +(-2.95306 + 0.445101i) q^{38} +(-0.00888804 + 0.0991977i) q^{39} +(-0.118297 + 0.784848i) q^{40} +(-8.84115 + 4.25767i) q^{41} +(2.26281 + 3.98494i) q^{42} +(6.62093 + 3.18847i) q^{43} +(0.641292 - 0.940603i) q^{44} +(1.25011 - 2.02659i) 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} +(-3.01856 + 1.68465i) q^{51} +(-0.0573405 - 0.00429707i) q^{52} +(-0.289787 + 0.312316i) q^{53} +(-2.39909 - 4.60916i) q^{54} +(0.392047 - 0.814093i) q^{55} +(-2.28144 + 1.33979i) q^{56} +(-1.22432 + 5.02563i) q^{57} +(0.698698 + 0.105312i) q^{58} +(-5.09218 + 3.47179i) q^{59} +(1.18044 + 0.704638i) q^{60} +(-7.26602 - 7.83091i) q^{61} +(3.82474 + 4.79607i) q^{62} +(7.87245 - 1.01223i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-0.0455119 + 0.00341064i) q^{65} +(-1.08691 - 1.64517i) q^{66} +(4.84017 - 8.38342i) q^{67} +(-0.997904 - 1.72842i) q^{68} +(-8.51900 - 4.25643i) q^{69} +(-1.63209 + 1.32142i) q^{70} +(13.9162 + 3.17628i) q^{71} +(2.64065 - 1.42371i) q^{72} +(8.46509 - 3.32230i) q^{73} +(-3.12060 + 1.22475i) q^{74} +(-7.00486 - 2.86760i) q^{75} +(-2.91154 - 0.664539i) q^{76} +(2.93141 - 0.691932i) q^{77} +(-0.0445146 + 0.0890934i) q^{78} +(-1.41114 - 2.44416i) q^{79} +(-0.396857 + 0.687376i) q^{80} +(-8.96247 + 0.821064i) q^{81} +(-9.78549 + 0.733321i) q^{82} +(-8.28124 + 10.3843i) q^{83} +(0.650526 + 4.53617i) q^{84} +(-0.987669 - 1.23850i) q^{85} +(4.99837 + 5.38696i) q^{86} +(0.627292 - 1.05086i) q^{87} +(0.940603 - 0.641292i) q^{88} +(4.00546 + 0.603726i) q^{89} +(1.90409 - 1.42978i) q^{90} +(-0.104300 - 0.110753i) q^{91} +(2.38558 - 4.95370i) q^{92} +(10.1976 - 2.98364i) q^{93} +(-4.77026 + 5.14112i) q^{94} +(-2.36373 - 0.177137i) q^{95} +(0.844093 + 1.51245i) 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
$3$	1.19646	−	1.25240i	0.690774	−	0.723071i
$3$	1.19646	−	1.25240i	0.690774	−	0.723071i
$4$	0.733052	+	0.680173i	0.366526	+	0.340086i
$5$	0.655797	+	0.447115i	0.293281	+	0.199956i	0.701018	−	0.713144i	$-0.252729\pi$
$5$	0.655797	+	0.447115i	0.293281	+	0.199956i	−0.407736	+	0.913100i	$0.633682\pi$
$6$	1.57130	−	0.728707i	0.641481	−	0.297494i
$7$	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
$9$	−0.136987	−	2.99687i	−0.0456623	−	0.998957i
$10$	0.447115	+	0.655797i	0.141390	+	0.207381i
$11$	−0.169672	−	1.12570i	−0.0511580	−	0.339411i	−0.999738	−	0.0228748i	$-0.992718\pi$
$11$	−0.169672	−	1.12570i	−0.0511580	−	0.339411i	0.948580	−	0.316537i	$-0.102520\pi$
$12$	1.72891	−	0.104274i	0.499093	−	0.0301013i
$13$	−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
$15$	1.34460	−	0.286364i	0.347173	−	0.0739388i
$16$	0.0747301	+	0.997204i	0.0186825	+	0.249301i
$17$	−1.90714	−	0.588275i	−0.462549	−	0.142678i	0.0547173	−	0.998502i	$-0.482574\pi$
$17$	−1.90714	−	0.588275i	−0.462549	−	0.142678i	−0.517267	+	0.855824i	$0.673050\pi$
$18$	0.967362	−	2.83976i	0.228010	−	0.669337i
$19$	−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
$21$	3.56225	+	2.88278i	0.777346	+	0.629073i
$22$	0.253321	−	1.10987i	0.0540083	−	0.236626i
$23$	−1.62062	−	5.25393i	−0.337923	−	1.09552i	−0.951955	−	0.306238i	$-0.900930\pi$
$23$	−1.62062	−	5.25393i	−0.337923	−	1.09552i	0.614032	−	0.789281i	$-0.289547\pi$
$24$	1.64749	+	0.534576i	0.336293	+	0.109120i
$25$	−1.59655	−	4.06794i	−0.319309	−	0.813587i
$26$	−0.0549466	+	0.0169488i	−0.0107759	+	0.00332393i
$27$	−3.91716	−	3.41406i	−0.753859	−	0.657037i
$28$	−1.63425	+	2.08068i	−0.308844	+	0.393212i
$29$	0.688874	−	0.157231i	0.127921	−	0.0291971i	−0.158081	−	0.987426i	$-0.550531\pi$
$29$	0.688874	−	0.157231i	0.127921	−	0.0291971i	0.286002	+	0.958229i	$0.407674\pi$
$30$	1.35627	+	0.224668i	0.247620	+	0.0410185i
$31$	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
$33$	−1.61283	−	1.13435i	−0.280757	−	0.197466i
$34$	−1.56039	−	1.24437i	−0.267604	−	0.213407i
$35$	−1.03650	+	1.82634i	−0.175200	+	0.308708i
$36$	1.93797	−	2.29004i	0.322995	−	0.381673i
$37$	−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
$39$	−0.00888804	+	0.0991977i	−0.00142323	+	0.0158843i
$40$	−0.118297	+	0.784848i	−0.0187044	+	0.124095i
$41$	−8.84115	+	4.25767i	−1.38075	+	0.664937i	−0.969160	−	0.246431i	$-0.920742\pi$
$41$	−8.84115	+	4.25767i	−1.38075	+	0.664937i	−0.411594	+	0.911367i	$0.635028\pi$
$42$	2.26281	+	3.98494i	0.349158	+	0.614889i
$43$	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
$45$	1.25011	−	2.02659i	0.186355	−	0.302106i
$46$	0.410881	−	5.48282i	0.0605811	−	0.808398i
$47$	−2.56225	+	6.52851i	−0.373743	+	0.952281i	0.613014	+	0.790072i	$0.289957\pi$
$47$	−2.56225	+	6.52851i	−0.373743	+	0.952281i	−0.986756	+	0.162209i	$0.948138\pi$
$48$	1.33830	+	1.09952i	0.193168	+	0.158702i
$49$	−6.90562	+	1.14560i	−0.986517	+	0.163658i
$50$		−	4.37002i		−	0.618014i
$51$	−3.01856	+	1.68465i	−0.422683	+	0.235898i
$52$	−0.0573405	−	0.00429707i	−0.00795169	−	0.000595897i
$53$	−0.289787	+	0.312316i	−0.0398053	+	0.0428999i	−0.752641	−	0.658432i	$-0.771220\pi$
$53$	−0.289787	+	0.312316i	−0.0398053	+	0.0428999i	0.712835	+	0.701331i	$0.247411\pi$
$54$	−2.39909	−	4.60916i	−0.326475	−	0.627227i
$55$	0.392047	−	0.814093i	0.0528636	−	0.109772i
$56$	−2.28144	+	1.33979i	−0.304870	+	0.179037i
$57$	−1.22432	+	5.02563i	−0.162165	+	0.665661i
$58$	0.698698	+	0.105312i	0.0917436	+	0.0138281i
$59$	−5.09218	+	3.47179i	−0.662946	+	0.451989i	−0.847473	−	0.530839i	$-0.821877\pi$
$59$	−5.09218	+	3.47179i	−0.662946	+	0.451989i	0.184527	+	0.982827i	$0.440925\pi$
$60$	1.18044	+	0.704638i	0.152394	+	0.0909684i
$61$	−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
$63$	7.87245	−	1.01223i	0.991835	−	0.127528i
$64$	−0.623490	+	0.781831i	−0.0779362	+	0.0977289i
$65$	−0.0455119	+	0.00341064i	−0.00564505	+	0.000423038i
$66$	−1.08691	−	1.64517i	−0.133790	−	0.202507i
$67$	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
$69$	−8.51900	−	4.25643i	−1.02557	−	0.512414i
$70$	−1.63209	+	1.32142i	−0.195072	+	0.157940i
$71$	13.9162	+	3.17628i	1.65155	+	0.376955i	0.944061	−	0.329770i	$-0.106971\pi$
$71$	13.9162	+	3.17628i	1.65155	+	0.376955i	0.707488	+	0.706725i	$0.249828\pi$
$72$	2.64065	−	1.42371i	0.311204	−	0.167786i
$73$	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
$75$	−7.00486	−	2.86760i	−0.808852	−	0.331122i
$76$	−2.91154	−	0.664539i	−0.333976	−	0.0762278i
$77$	2.93141	−	0.691932i	0.334065	−	0.0788530i
$78$	−0.0445146	+	0.0890934i	−0.00504029	+	0.0100878i
$79$	−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
$81$	−8.96247	+	0.821064i	−0.995830	+	0.0912293i
$82$	−9.78549	+	0.733321i	−1.08063	+	0.0809818i
$83$	−8.28124	+	10.3843i	−0.908984	+	1.13983i	0.0807250	+	0.996736i	$0.474276\pi$
$83$	−8.28124	+	10.3843i	−0.908984	+	1.13983i	−0.989709	+	0.143094i	$0.954295\pi$
$84$	0.650526	+	4.53617i	0.0709782	+	0.494936i
$85$	−0.987669	−	1.23850i	−0.107128	−	0.134334i
$86$	4.99837	+	5.38696i	0.538988	+	0.580891i
$87$	0.627292	−	1.05086i	0.0672528	−	0.112664i
$88$	0.940603	−	0.641292i	0.100269	−	0.0683620i
$89$	4.00546	+	0.603726i	0.424578	+	0.0639948i	0.357856	−	0.933777i	$-0.383508\pi$
$89$	4.00546	+	0.603726i	0.424578	+	0.0639948i	0.0667220	+	0.997772i	$0.478746\pi$
$90$	1.90409	−	1.42978i	0.200709	−	0.150712i
$91$	−0.104300	−	0.110753i	−0.0109336	−	0.0116101i
$92$	2.38558	−	4.95370i	0.248714	−	0.516459i
$93$	10.1976	−	2.98364i	1.05744	−	0.309389i
$94$	−4.77026	+	5.14112i	−0.492015	+	0.530266i
$95$	−2.36373	−	0.177137i	−0.242513	−	0.0181738i
$96$	0.844093	+	1.51245i	0.0861499	+	0.154364i
$97$			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	$-0.826089\pi$
$101$	0.682345	−	9.10527i	0.0678959	−	0.906008i	0.922319	−	0.386430i	$-0.126292\pi$
$102$	−3.42537	+	0.465390i	−0.339162	+	0.0460805i
$103$	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
$105$	1.04718	+	3.48325i	0.102194	+	0.339930i
$106$	−0.383857	+	0.184856i	−0.0372835	+	0.0179548i
$107$	0.408321	−	2.70904i	0.0394739	−	0.261892i	−0.960385	−	0.278676i	$-0.910104\pi$
$107$	0.408321	−	2.70904i	0.0394739	−	0.261892i	0.999859	+	0.0167835i	$0.00534259\pi$
$108$	−0.549333	−	5.16703i	−0.0528596	−	0.497198i
$109$	−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
$111$	−0.0845432	+	5.80580i	−0.00802449	+	0.551062i
$112$	−2.61321	+	0.413674i	−0.246925	+	0.0390885i
$113$	−3.18369	−	2.53891i	−0.299497	−	0.238841i	0.462198	−	0.886777i	$-0.347061\pi$
$113$	−3.18369	−	2.53891i	−0.299497	−	0.238841i	−0.761695	+	0.647936i	$0.775632\pi$
$114$	−2.97576	+	4.23094i	−0.278705	+	0.396263i
$115$	1.28631	−	4.17011i	0.119949	−	0.388865i
$116$	0.611925	+	0.353295i	0.0568158	+	0.0328026i
$117$	0.113601	+	0.129817i	0.0105024	+	0.0120016i
$118$	−6.00857	+	1.37142i	−0.553133	+	0.126249i
$119$	1.13688	−	5.15657i	0.104218	−	0.472702i
$120$	0.841403	+	1.08719i	0.0768092	+	0.0992464i
$121$	9.27289	−	2.86031i	0.842990	−	0.260028i
$122$	−3.90280	−	9.94417i	−0.353343	−	0.900303i
$123$	−5.24575	+	16.1667i	−0.472994	+	1.45770i
$124$	1.80815	+	5.86187i	0.162377	+	0.526412i
$125$	1.65491	−	7.25064i	0.148020	−	0.648517i
$126$	7.69806	+	1.93387i	0.685798	+	0.172283i
$127$	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
$129$	11.9149	−	4.47715i	1.04905	−	0.394191i
$130$	−0.0436119	−	0.0134525i	−0.00382501	−	0.00117986i
$131$	0.839679	+	11.2047i	0.0733631	+	0.978962i	0.905487	+	0.424373i	$0.139505\pi$
$131$	0.839679	+	11.2047i	0.0733631	+	0.978962i	−0.832124	+	0.554589i	$0.812875\pi$
$132$	−0.410729	−	1.92854i	−0.0357493	−	0.167858i
$133$	−4.49914	−	6.49525i	−0.390125	−	0.563210i
$134$	7.56839	−	6.03559i	0.653809	−	0.521396i
$135$	−1.04239	−	3.99035i	−0.0897144	−	0.343435i
$136$	−0.297460	−	1.97352i	−0.0255070	−	0.169228i
$137$	−5.67410	−	8.32237i	−0.484771	−	0.711028i	0.503457	−	0.864020i	$-0.332061\pi$
$137$	−5.67410	−	8.32237i	−0.484771	−	0.711028i	−0.988227	+	0.152992i	$0.951109\pi$
$138$	−6.37506	−	7.07454i	−0.542681	−	0.602225i
$139$	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
$141$	5.11065	+	11.0200i	0.430395	+	0.928053i
$142$	11.7938	+	8.04088i	0.989714	+	0.674775i
$143$	0.0479858	+	0.0445243i	0.00401277	+	0.00372331i
$144$	2.97825	−	0.360560i	0.248188	−	0.0300467i
$145$	0.522062	+	0.204894i	0.0433549	+	0.0170155i
$146$	9.09371			0.752601
$147$	−6.82752	+	10.0192i	−0.563125	+	0.826372i
$148$	−3.35233			−0.275560
$149$	11.0780	+	4.34781i	0.907549	+	0.356187i	0.772768	−	0.634689i	$-0.218872\pi$
$149$	11.0780	+	4.34781i	0.907549	+	0.356187i	0.134781	+	0.990875i	$0.456967\pi$
$150$	−5.47299	−	5.22854i	−0.446868	−	0.426908i
$151$	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
$153$	−1.50173	+	5.79604i	−0.121408	+	0.468582i
$154$	2.98156	+	0.426862i	0.240261	+	0.0343975i
$155$	2.11256	+	4.38678i	0.169685	+	0.352355i
$156$	−0.0739870	+	0.0666717i	−0.00592370	+	0.00533800i
$157$	−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
$159$	0.0444258	+	0.736600i	0.00352319	+	0.0584162i
$160$	−0.620550	+	0.494872i	−0.0490588	+	0.0391231i
$161$	13.5016	−	5.41461i	1.06408	−	0.426731i
$162$	−8.64290	−	2.51005i	−0.679050	−	0.197208i
$163$	−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
$165$	−0.550500	−	1.46502i	−0.0428564	−	0.114052i
$166$	−11.5026	+	6.64104i	−0.892776	+	0.515445i
$167$	3.61536	+	15.8399i	0.279765	+	1.22573i	0.898091	+	0.439809i	$0.144954\pi$
$167$	3.61536	+	15.8399i	0.279765	+	1.22573i	−0.618326	+	0.785922i	$0.712189\pi$
$168$	−1.05169	+	4.46026i	−0.0811397	+	0.344117i
$169$	−2.89204	+	12.6708i	−0.222464	+	0.974680i
$170$	−0.466921	−	1.51372i	−0.0358112	−	0.116097i
$171$	4.82923	+	7.54628i	0.369301	+	0.577078i
$172$	2.68477	+	6.84069i	0.204712	+	0.521597i
$173$	14.7983	−	4.56468i	1.12510	−	0.347046i	0.324283	−	0.945960i	$-0.394877\pi$
$173$	14.7983	−	4.56468i	1.12510	−	0.347046i	0.800813	+	0.598914i	$0.204401\pi$
$174$	0.967853	−	0.749045i	0.0733728	−	0.0567850i
$175$	10.3796	−	5.09349i	0.784623	−	0.385032i
$176$	1.10987	−	0.253321i	0.0836598	−	0.0190948i
$177$	−1.74452	+	10.5313i	−0.131126	+	0.791579i
$178$	3.50801	+	2.02535i	0.262937	+	0.151807i
$179$	6.85736	−	22.2310i	0.512543	−	1.66162i	−0.215821	−	0.976433i	$-0.569243\pi$
$179$	6.85736	−	22.2310i	0.512543	−	1.66162i	0.728364	−	0.685190i	$-0.240281\pi$
$180$	2.29482	−	0.635303i	0.171046	−	0.0473527i
$181$	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
$183$	−18.5009	−	0.269407i	−1.36762	−	0.0199152i
$184$	4.03046	−	3.73972i	0.297130	−	0.275696i
$185$	−2.63107	+	0.396570i	−0.193440	+	0.0291564i
$186$	10.5827	+	0.948204i	0.775962	+	0.0695257i
$187$	−0.338633	+	2.24668i	−0.0247633	+	0.164294i
$188$	−6.31878	+	3.04296i	−0.460844	+	0.221931i
$189$	8.15133	−	11.0705i	0.592922	−	0.805260i
$190$	−2.13561	−	1.02846i	−0.154934	−	0.0746122i
$191$	1.10551	−	1.62149i	0.0799922	−	0.117327i	−0.784157	−	0.620562i	$-0.786905\pi$
$191$	1.10551	−	1.62149i	0.0799922	−	0.117327i	0.864150	+	0.503235i	$0.167857\pi$
$192$	0.233184	+	1.71628i	0.0168286	+	0.123862i
$193$	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	$-0.785634\pi$
$197$		−	17.5077i		−	1.24738i	0.781674	−	0.623688i	$-0.214366\pi$
$198$	−3.36085	−	0.607133i	−0.238845	−	0.0431471i
$199$	−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
$201$	−4.70830	−	16.0922i	−0.332098	−	1.13506i
$202$	3.96170	−	8.22656i	0.278745	−	0.578819i
$203$	0.564235	+	1.78228i	0.0396016	+	0.125092i
$204$	−3.35861	−	0.818208i	−0.235150	−	0.0572861i
$205$	−7.70166	−	1.16084i	−0.537907	−	0.0810765i
$206$	15.9137	−	10.8498i	1.10876	−	0.755942i
$207$	−15.5233	+	5.57651i	−1.07895	+	0.387594i
$208$	−0.0391108	−	0.0421514i	−0.00271184	−	0.00292267i
$209$	2.11973	+	2.65805i	0.146625	+	0.183861i
$210$	−0.297783	+	3.62504i	−0.0205489	+	0.250152i
$211$	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
$213$	20.6281	−	13.6283i	1.41341	−	0.933796i
$214$	1.36982	−	2.37259i	0.0936388	−	0.162187i
$215$	2.91637	+	5.05130i	0.198895	+	0.344496i
$216$	1.37637	−	5.01055i	0.0936501	−	0.340925i
$217$	−6.93360	+	14.6745i	−0.470684	+	0.996172i
$218$	−0.0994088	−	0.0226894i	−0.00673281	−	0.00153672i
$219$	5.96727	−	14.5766i	0.403231	−	0.984998i
$220$	0.841115	−	0.330113i	0.0567079	−	0.0222562i
$221$	0.106828	−	0.0419271i	0.00718606	−	0.00282032i
$222$	−2.19980	+	5.37358i	−0.147641	+	0.360651i
$223$	−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
$225$	−11.9724	+	5.34190i	−0.798158	+	0.356127i
$226$	−2.03605	−	3.52654i	−0.135436	−	0.234582i
$227$	−7.95619	+	13.7805i	−0.528071	+	0.914646i	0.471394	+	0.881923i	$0.343751\pi$
$227$	−7.95619	+	13.7805i	−0.528071	+	0.914646i	−0.999464	+	0.0327227i	$0.989582\pi$
$228$	−4.31579	+	2.85130i	−0.285820	+	0.188832i
$229$	−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
$231$	2.64073	−	4.49915i	0.173747	−	0.296022i
$232$	0.440552	+	0.552434i	0.0289236	+	0.0362691i
$233$	4.50367	+	4.85380i	0.295045	+	0.317983i	0.863125	−	0.504990i	$-0.168504\pi$
$233$	4.50367	+	4.85380i	0.295045	+	0.317983i	−0.568080	+	0.822974i	$0.692313\pi$
$234$	0.0583203	+	0.162346i	0.00381252	+	0.0106129i
$235$	−4.59931	+	3.13575i	−0.300026	+	0.204554i
$236$	−6.09425	−	0.918561i	−0.396702	−	0.0597932i
$237$	−4.74941	−	1.15703i	−0.308508	−	0.0751571i
$238$	2.94220	−	4.38477i	0.190715	−	0.284222i
$239$	5.73781	−	11.9147i	0.371148	−	0.770697i	−0.628828	−	0.777544i	$-0.716465\pi$
$239$	5.73781	−	11.9147i	0.371148	−	0.770697i	0.999977	+	0.00684683i	$0.00217943\pi$
$240$	0.386045	+	1.31944i	0.0249191	+	0.0851692i
$241$	−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
$243$	−9.69490	+	12.2069i	−0.621928	+	0.783074i
$244$		−	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
$249$	3.09717	+	22.7958i	0.196275	+	1.44462i
$250$	4.18947	−	6.14483i	0.264965	−	0.388633i
$251$	9.32309	+	4.48977i	0.588468	+	0.283391i	0.704329	−	0.709874i	$-0.251248\pi$
$251$	9.32309	+	4.48977i	0.588468	+	0.283391i	−0.115860	+	0.993266i	$0.536962\pi$
$252$	6.45940	+	4.61261i	0.406904	+	0.290567i
$253$	−5.63937	+	2.71578i	−0.354544	+	0.170740i
$254$	−3.33533	+	22.1285i	−0.209277	+	1.38846i
$255$	−2.73279	−	0.244856i	−0.171134	−	0.0153335i
$256$	−0.988831	+	0.149042i	−0.0618019	+	0.00931514i
$257$	17.1009	−	15.8674i	1.06673	−	0.989779i	0.0667595	−	0.997769i	$-0.478734\pi$
$257$	17.1009	−	15.8674i	1.06673	−	0.989779i	0.999968	+	0.00799059i	$0.00254351\pi$
$258$	12.7269	+	0.185328i	0.792344	+	0.0115380i
$259$	−6.54622	−	5.98448i	−0.406762	−	0.371858i
$260$	−0.0356824	−	0.0284558i	−0.00221293	−	0.00176475i
$261$	−0.565568	−	2.04293i	−0.0350078	−	0.126454i
$262$	−3.31191	+	10.7370i	−0.204611	+	0.663332i
$263$	−25.6463	−	14.8069i	−1.58142	−	0.913034i	−0.994652	−	0.103279i	$-0.967066\pi$
$263$	−25.6463	−	14.8069i	−1.58142	−	0.913034i	−0.586769	−	0.809755i	$-0.699600\pi$
$264$	0.322239	−	1.94528i	0.0198324	−	0.119724i
$265$	−0.329682	+	0.0752478i	−0.0202522	+	0.00462244i
$266$	−1.81515	−	7.68998i	−0.111294	−	0.471503i
$267$	5.54846	−	4.29409i	0.339560	−	0.262794i
$268$	9.25027	−	2.85333i	0.565050	−	0.174295i
$269$	4.75769	+	12.1224i	0.290082	+	0.739116i	0.999414	+	0.0342415i	$0.0109015\pi$
$269$	4.75769	+	12.1224i	0.290082	+	0.739116i	−0.709332	+	0.704875i	$0.751003\pi$
$270$	0.487509	−	4.09534i	0.0296688	−	0.249234i
$271$	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
$273$	−0.263497	−	0.00188723i	−0.0159476	−	0.000114221i
$274$	−2.24136	−	9.82006i	−0.135406	−	0.593251i
$275$	−4.30839	+	2.48745i	−0.259806	+	0.149999i
$276$	−3.34976	−	8.91457i	−0.201632	−	0.536594i
$277$	−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
$279$	8.46427	−	16.3412i	0.506742	−	0.978322i
$280$	−2.09520	−	0.141433i	−0.125212	−	0.00845224i
$281$	−23.0231	+	18.3603i	−1.37344	+	1.09529i	−0.388683	+	0.921372i	$0.627070\pi$
$281$	−23.0231	+	18.3603i	−1.37344	+	1.09529i	−0.984761	+	0.173913i	$0.944359\pi$
$282$	0.731305	+	12.1254i	0.0435486	+	0.722056i
$283$	−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
$285$	−3.04994	+	2.74838i	−0.180663	+	0.162800i
$286$	0.0284022	+	0.0589777i	0.00167946	+	0.00348742i
$287$	−13.1473	−	22.3876i	−0.776060	−	1.32150i
$288$	2.90411	+	0.752442i	0.171126	+	0.0443381i
$289$	−10.7549	−	7.33260i	−0.632644	−	0.431329i
$290$	0.411117	+	0.381461i	0.0241416	+	0.0224002i
$291$	4.44141	+	4.24303i	0.260360	+	0.248731i
$292$	8.46509	+	3.32230i	0.495382	+	0.194423i
$293$	−29.2566			−1.70919			−0.854594	−	0.519297i	$-0.826194\pi$
$293$	−29.2566			−1.70919			−0.854594	+	0.519297i	$0.826194\pi$
$294$	−10.0160	+	6.83226i	−0.584145	+	0.398466i
$295$	−4.89172			−0.284807
$296$	−3.12060	−	1.22475i	−0.181381	−	0.0711869i
$297$	−3.17858	+	4.98882i	−0.184440	+	0.289481i
$298$	8.72383	+	8.09453i	0.505358	+	0.468904i
$299$	0.261218	+	0.178095i	0.0151066	+	0.0102995i
$300$	−3.18447	−	6.86661i	−0.183855	−	0.396444i
$301$	−6.96914	+	18.1508i	−0.401694	+	1.04620i
$302$	5.96561	+	12.3877i	0.343282	+	0.712833i
$303$	−10.5870	−	11.7486i	−0.608207	−	0.674940i
$304$	−1.68231	−	2.46749i	−0.0964868	−	0.141520i
$305$	−1.26372	−	8.38423i	−0.0723604	−	0.480080i
$306$	−3.51545	+	4.84673i	−0.200965	+	0.277069i
$307$	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
$309$	−6.94898	−	32.6283i	−0.395314	−	1.85616i
$310$	0.363858	+	4.85535i	0.0206657	+	0.275765i
$311$	0.580318	+	0.179004i	0.0329068	+	0.0101504i	0.311165	−	0.950356i	$-0.399281\pi$
$311$	0.580318	+	0.179004i	0.0329068	+	0.0101504i	−0.278258	+	0.960506i	$0.589757\pi$
$312$	−0.0932304	+	0.0350324i	−0.00527813	+	0.00198332i
$313$	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
$315$	5.61530	+	2.85607i	0.316387	+	0.160921i
$316$	0.628015	−	2.75151i	0.0353286	−	0.154785i
$317$	4.07159	+	13.1998i	0.228683	+	0.741373i	0.995086	+	0.0990127i	$0.0315684\pi$
$317$	4.07159	+	13.1998i	0.228683	+	0.741373i	−0.766403	+	0.642360i	$0.777955\pi$
$318$	−0.227755	+	0.701912i	−0.0127719	+	0.0393613i
$319$	−0.293878	−	0.748788i	−0.0164540	−	0.0419241i
$320$	−0.758451	+	0.233951i	−0.0423987	+	0.0130783i
$321$	−2.90424	−	3.75262i	−0.162099	−	0.209451i
$322$	14.5465	−	0.107627i	0.810643	−	0.00599781i
$323$	5.81086	−	1.32629i	0.323325	−	0.0737969i
$324$	−7.12842	−	5.49414i	−0.396023	−	0.305230i
$325$	0.217616	+	0.125641i	0.0120712	+	0.00696930i
$326$	1.06713	−	3.45955i	0.0591028	−	0.191607i
$327$	−0.101601	+	0.144457i	−0.00561857	+	0.00798850i
$328$	−7.67206	−	6.11826i	−0.423619	−	0.337825i
$329$	−17.7711	−	5.33799i	−0.979752	−	0.294293i
$330$	0.0227875	−	1.56487i	0.00125441	−	0.0861434i
$331$	−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
$333$	7.17000	+	7.05226i	0.392914	+	0.386462i
$334$	−2.42153	+	16.0658i	−0.132500	+	0.879082i
$335$	6.92251	−	3.33371i	0.378217	−	0.182140i
$336$	−2.60851	+	3.76772i	−0.142306	+	0.205546i
$337$	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
$339$	−6.98887	+	0.949547i	−0.379583	+	0.0515723i
$340$	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
$345$	−3.68361	−	6.60032i	−0.198319	−	0.355349i
$346$	15.4430	+	1.15730i	0.830223	+	0.0622166i
$347$	−7.56625	+	8.15447i	−0.406177	+	0.437755i	−0.902701	−	0.430268i	$-0.858419\pi$
$347$	−7.56625	+	8.15447i	−0.406177	+	0.437755i	0.496524	+	0.868023i	$0.334610\pi$
$348$	1.17461	−	0.343670i	0.0629655	−	0.0184226i
$349$	−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
$351$	0.298500	+	0.0130475i	0.0159328	+	0.000696426i
$352$	1.12570	+	0.169672i	0.0600000	+	0.00904355i
$353$	−19.6605	+	13.4043i	−1.04642	+	0.713440i	−0.959194	−	0.282749i	$-0.908754\pi$
$353$	−19.6605	+	13.4043i	−1.04642	+	0.713440i	−0.0872296	+	0.996188i	$0.527801\pi$
$354$	−5.47143	+	9.16594i	−0.290803	+	0.487164i
$355$	7.70603	+	8.30513i	0.408994	+	0.440791i
$356$	2.52557	+	3.16697i	0.133855	+	0.167849i
$357$	−5.09784	−	7.59344i	−0.269806	−	0.401887i
$358$	14.5052	−	18.1890i	0.766625	−	0.961318i
$359$	26.5896	−	1.99261i	1.40334	−	0.105166i	0.648572	−	0.761153i	$-0.275367\pi$
$359$	26.5896	−	1.99261i	1.40334	−	0.105166i	0.754772	+	0.655987i	$0.227747\pi$
$360$	2.36829	+	0.247006i	0.124820	+	0.0130184i
$361$	−5.04068	+	8.73071i	−0.265299	+	0.459511i
$362$	0.0698885	+	0.121051i	0.00367326	+	0.00636227i
$363$	7.51237	−	15.0356i	0.394297	−	0.789162i
$364$	−0.00112558	−	0.152130i	−5.89966e−5	−	0.00797377i
$365$	7.03683	+	1.60611i	0.368325	+	0.0840677i
$366$	−17.1236	−	7.00991i	−0.895062	−	0.366414i
$367$	−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
$369$	13.9708	+	25.9125i	0.727291	+	1.34895i
$370$	−2.59408	−	0.592082i	−0.134860	−	0.0307809i
$371$	−0.886471	−	0.696270i	−0.0460233	−	0.0361485i
$372$	9.50475	+	4.74896i	0.492798	+	0.246222i
$373$	−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
$375$	−7.10064	−	10.7477i	−0.366676	−	0.555008i
$376$	−6.99370	+	0.524106i	−0.360673	+	0.0270287i
$377$	−0.0253323	+	0.0317657i	−0.00130468	+	0.00163602i
$378$	11.6324	−	7.32722i	0.598304	−	0.376871i
$379$	−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
$381$	33.2819	+	19.8670i	1.70508	+	1.01782i
$382$	1.62149	−	1.10551i	0.0829627	−	0.0565630i
$383$	−3.36193	−	0.506730i	−0.171787	−	0.0258927i	0.0625855	−	0.998040i	$-0.480065\pi$
$383$	−3.36193	−	0.506730i	−0.171787	−	0.0258927i	−0.234372	+	0.972147i	$0.575303\pi$
$384$	−0.409964	+	1.68283i	−0.0209209	+	0.0858768i
$385$	2.23178	+	0.856909i	0.113742	+	0.0436721i
$386$	5.67594	−	11.7862i	0.288898	−	0.599902i
$387$	8.64845	−	20.2788i	0.439626	−	1.03083i
$388$	−2.41212	+	2.59965i	−0.122457	+	0.131977i
$389$	23.3398	+	1.74908i	1.18338	+	0.0886818i	0.651842	−	0.758355i	$-0.273996\pi$
$389$	23.3398	+	1.74908i	1.18338	+	0.0886818i	0.531535	+	0.847037i	$0.321616\pi$
$390$	−0.0690275	+	0.0385240i	−0.00349534	+	0.00195074i
$391$			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
$396$	−2.90671	−	1.79302i	−0.146068	−	0.0901026i
$397$	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
$399$	−13.5176	−	2.13658i	−0.676729	−	0.106963i
$400$	3.93725	−	1.89608i	0.196863	−	0.0948040i
$401$	−5.38358	+	35.7177i	−0.268843	+	1.78366i	0.292693	+	0.956207i	$0.405449\pi$
$401$	−5.38358	+	35.7177i	−0.268843	+	1.78366i	−0.561536	+	0.827452i	$0.689789\pi$
$402$	1.49630	−	16.6999i	0.0746288	−	0.832917i
$403$	−0.348796	+	0.0525726i	−0.0173748	+	0.00261883i
$404$	6.69335	−	6.21052i	0.333006	−	0.308985i
$405$	−6.24467	−	3.46880i	−0.310300	−	0.172366i
$406$	−0.125908	+	1.86522i	−0.00624873	+	0.0925692i
$407$	2.98374	+	2.37946i	0.147899	+	0.117945i
$408$	−2.82752	−	1.98869i	−0.139983	−	0.0984547i
$409$	−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
$411$	−17.2117	−	2.85114i	−0.848991	−	0.140636i
$412$	18.7776	−	4.28586i	0.925105	−	0.211149i
$413$	−10.2607	−	12.6730i	−0.504894	−	0.623596i
$414$	−16.4876	−	0.480282i	−0.810321	−	0.0236046i
$415$	−10.0738	+	3.10736i	−0.494503	+	0.152534i
$416$	−0.0210076	−	0.0535264i	−0.00102998	−	0.00262435i
$417$	20.2595	+	6.57378i	0.992113	+	0.321919i
$418$	1.00210	+	3.24873i	0.0490144	+	0.158901i
$419$	1.96023	−	8.58834i	0.0957636	−	0.419568i	−0.904208	−	0.427092i	$-0.859538\pi$
$419$	1.96023	−	8.58834i	0.0957636	−	0.419568i	0.999972	+	0.00752446i	$0.00239513\pi$
$420$	−1.60157	+	3.26566i	−0.0781488	+	0.159348i
$421$	−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
$423$	19.9161	+	6.78441i	0.968354	+	0.329870i
$424$	−0.407121	−	0.125580i	−0.0197715	−	0.00609871i
$425$	0.651775	+	8.69733i	0.0316157	+	0.421882i
$426$	24.1811	−	5.14994i	1.17158	−	0.249516i
$427$	19.0703	−	20.8603i	0.922875	−	1.00950i
$428$	2.14193	−	1.70813i	0.103534	−	0.0825658i
$429$	0.113175	−	0.00682580i	0.00546414	−	0.000329553i
$430$	0.869325	+	5.76759i	0.0419226	+	0.278138i
$431$	3.98994	+	5.85217i	0.192189	+	0.281889i	0.910223	−	0.414119i	$-0.135910\pi$
$431$	3.98994	+	5.85217i	0.192189	+	0.281889i	−0.718034	+	0.696008i	$0.754958\pi$
$432$	3.11179	−	4.16134i	0.149716	−	0.200213i
$433$	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
$435$	0.881232	−	0.408681i	0.0422519	−	0.0195947i
$436$	−0.0842476	−	0.0574391i	−0.00403473	−	0.00275083i
$437$	12.0366	+	11.1684i	0.575790	+	0.534255i
$438$	10.8802	−	11.3889i	0.519877	−	0.544183i
$439$	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
$441$	4.37920	+	20.5383i	0.208533	+	0.978015i
$442$	0.114761			0.00545864
$443$	−26.0439	−	10.2215i	−1.23738	−	0.485636i	−0.345719	−	0.938338i	$-0.612365\pi$
$443$	−26.0439	−	10.2215i	−1.23738	−	0.485636i	−0.891662	+	0.452702i	$0.850460\pi$
$444$	−4.01092	+	4.19845i	−0.190350	+	0.199249i
$445$	2.35683	+	2.18682i	0.111725	+	0.103665i
$446$	−0.841294	−	0.573584i	−0.0398364	−	0.0271600i
$447$	18.6996	−	8.67212i	0.884459	−	0.410177i
$448$	−2.19699	−	1.47419i	−0.103798	−	0.0696490i
$449$	5.29779	+	11.0010i	0.250018	+	0.519168i	0.987773	−	0.155901i	$-0.0498280\pi$
$449$	5.29779	+	11.0010i	0.250018	+	0.519168i	−0.737754	+	0.675069i	$0.764114\pi$
$450$	−13.0964	+	0.598635i	−0.617369	+	0.0282199i
$451$	6.29296	+	9.23007i	0.296324	+	0.434627i
$452$	−0.606915	−	4.02661i	−0.0285469	−	0.189396i
$453$	23.7713	−	1.43370i	1.11687	−	0.0673609i
$454$	−12.4408	+	9.92121i	−0.583876	+	0.465625i
$455$	−0.0188799	−	0.119266i	−0.000885103	−	0.00559126i
$456$	−5.05915	+	1.07747i	−0.236916	+	0.0504570i
$457$	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
$459$	5.46217	+	8.81546i	0.254952	+	0.411470i
$460$	3.77933	−	2.18200i	0.176212	−	0.101736i
$461$	1.26100	+	5.52481i	0.0587307	+	0.257316i	0.995767	−	0.0919167i	$-0.0292994\pi$
$461$	1.26100	+	5.52481i	0.0587307	+	0.257316i	−0.937036	+	0.349233i	$0.886442\pi$
$462$	4.10191	−	3.22337i	0.190838	−	0.149965i
$463$	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
$465$	8.02157	+	2.60283i	0.371992	+	0.120703i
$466$	2.41906	+	6.16365i	0.112061	+	0.285526i
$467$	32.7769	−	10.1103i	1.51674	−	0.467851i	0.579037	−	0.815301i	$-0.303429\pi$
$467$	32.7769	−	10.1103i	1.51674	−	0.467851i	0.937698	+	0.347450i	$0.112952\pi$
$468$	−0.00502289	+	0.172431i	−0.000232183	+	0.00797061i
$469$	23.1570	+	10.9415i	1.06929	+	0.505231i
$470$	−5.42699	+	1.23868i	−0.250329	+	0.0571359i
$471$	−12.2524	−	2.02963i	−0.564563	−	0.0935205i
$472$	−5.33739	−	3.08154i	−0.245673	−	0.141840i
$473$	2.46588	−	7.99417i	0.113381	−	0.367572i
$474$	−3.99840	−	2.81220i	−0.183652	−	0.129169i
$475$	10.2034	+	8.13696i	0.468165	+	0.373349i
$476$	4.34075	−	3.00676i	0.198958	−	0.137815i
$477$	0.975667	+	0.825670i	0.0446727	+	0.0378049i
$478$	9.69411	−	8.99482i	0.443398	−	0.411413i
$479$	−19.5775	+	2.95084i	−0.894521	+	0.134827i	−0.580185	−	0.814485i	$-0.697020\pi$
$479$	−19.5775	+	2.95084i	−0.894521	+	0.134827i	−0.314335	+	0.949312i	$0.601782\pi$
$480$	−0.122685	+	1.36927i	−0.00559979	+	0.0624982i
$481$	0.0287299	−	0.190610i	0.00130997	−	0.00869109i
$482$	−6.11663	+	2.94562i	−0.278605	+	0.134169i
$483$	9.37284	−	23.3877i	0.426479	−	1.06418i
$484$	8.74301	+	4.21041i	0.397410	+	0.191382i
$485$	−1.58562	+	2.32567i	−0.0719992	+	0.105603i
$486$	−13.4844	+	7.82115i	−0.611666	+	0.354775i
$487$	−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	$-0.818566\pi$
$491$		−	23.9146i		−	1.07925i	0.841905	−	0.539625i	$-0.181434\pi$
$492$	−14.8416	+	8.28303i	−0.669110	+	0.373428i
$493$	−1.40627	−	0.105386i	−0.0633354	−	0.00474633i
$494$	0.116801	−	0.125881i	0.00525512	−	0.00566367i
$495$	−2.49344	−	1.06339i	−0.112072	−	0.0477960i
$496$	−2.66162	+	5.52691i	−0.119510	+	0.248166i
$497$	−5.35223	+	37.3845i	−0.240080	+	1.67692i
$498$	−5.44517	+	22.3515i	−0.244004	+	1.00160i
$499$	−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
$501$	24.1635	+	14.4239i	1.07954	+	0.644413i
$502$	7.03833	+	7.58551i	0.314136	+	0.338558i
$503$	−9.22054	−	11.5622i	−0.411123	−	0.515532i	0.532556	−	0.846395i	$-0.321232\pi$
$503$	−9.22054	−	11.5622i	−0.411123	−	0.515532i	−0.943679	+	0.330863i	$0.892660\pi$
$504$	4.32771	+	6.65364i	0.192772	+	0.296377i
$505$	4.51858	−	5.66612i	0.201074	−	0.252139i
$506$	−6.24173	+	0.467753i	−0.277479	+	0.0207942i
$507$	12.4087	+	18.7821i	0.551090	+	0.834141i
$508$	−11.1892	+	19.3803i	−0.496441	+	0.859862i
$509$	−1.69754	−	2.94022i	−0.0752420	−	0.130323i	0.825950	−	0.563744i	$-0.190640\pi$
$509$	−1.69754	−	2.94022i	−0.0752420	−	0.130323i	−0.901191	+	0.433421i	$0.857306\pi$
$510$	−2.45443	−	1.22633i	−0.108684	−	0.0543029i
$511$	10.5992	+	21.5992i	0.468881	+	0.955493i
$512$	−0.974928	−	0.222521i	−0.0430861	−	0.00983413i
$513$	15.2289	+	2.98068i	0.672372	+	0.131600i
$514$	21.7158	−	8.52283i	0.957844	−	0.375926i
$515$	14.2305	−	5.58507i	0.627072	−	0.246108i
$516$	11.7795	+	4.82218i	0.518562	+	0.212285i
$517$	7.78389	+	1.77662i	0.342335	+	0.0781357i
$518$	−3.90733	−	7.96240i	−0.171678	−	0.349848i
$519$	11.9888	−	23.9948i	0.526248	−	1.05325i
$520$	−0.0228197	−	0.0395250i	−0.00100071	−	0.00173328i
$521$	−2.76890	+	4.79588i	−0.121308	+	0.210111i	−0.920284	−	0.391252i	$-0.872042\pi$
$521$	−2.76890	+	4.79588i	−0.121308	+	0.210111i	0.798976	+	0.601363i	$0.205376\pi$
$522$	0.219893	−	2.10833i	0.00962447	−	0.0922793i
$523$	−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
$525$	6.03965	−	19.0935i	0.263592	−	0.833308i
$526$	−18.4639	−	23.1530i	−0.805066	−	1.00952i
$527$	−8.32742	−	8.97483i	−0.362748	−	0.390950i
$528$	1.01066	−	1.69309i	0.0439831	−	0.0736822i
$529$	−5.97385	+	4.07290i	−0.259732	+	0.177083i
$530$	−0.334384	−	0.0504002i	−0.0145247	−	0.00218925i
$531$	11.1021	+	14.7850i	0.481789	+	0.641615i
$532$	1.11979	−	7.82155i	0.0485490	−	0.339107i
$533$	0.244821	−	0.508377i	0.0106044	−	0.0220202i
$534$	6.73372	−	1.97017i	0.291397	−	0.0852577i
$535$	1.47903	−	1.59401i	0.0639438	−	0.0689151i
$536$	9.65327	+	0.723412i	0.416958	+	0.0312467i
$537$	−19.6375	−	35.1865i	−0.847420	−	1.51841i
$538$			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
$543$	0.239897	−	0.0325938i	0.0102950	−	0.00139873i
$544$	1.12428	−	1.64901i	0.0482030	−	0.0707009i
$545$	−0.0729164	−	0.0351147i	−0.00312340	−	0.00150415i
$546$	−0.244593	−	0.0980231i	−0.0104676	−	0.00419500i
$547$	−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
$549$	−22.4729	+	22.8481i	−0.959119	+	0.975132i
$550$	−4.91933	+	0.741470i	−0.209761	+	0.0316164i
$551$	−1.54686	+	1.43528i	−0.0658986	+	0.0611449i
$552$	0.138660	−	9.52215i	0.00590177	−	0.405289i
$553$	6.13826	−	4.25186i	0.261025	−	0.180807i
$554$	−22.8800	−	18.2462i	−0.972079	−	0.775207i
$555$	−2.65130	+	3.76962i	−0.112541	+	0.160012i
$556$	−3.62466	+	11.7509i	−0.153720	+	0.498347i
$557$	27.3461	+	15.7883i	1.15869	+	0.668970i	0.950990	−	0.309222i	$-0.100069\pi$
$557$	27.3461	+	15.7883i	1.15869	+	0.668970i	0.207700	+	0.978192i	$0.433402\pi$
$558$	13.8493	−	12.1193i	0.586287	−	0.513049i
$559$	−0.411963	+	0.0940280i	−0.0174242	+	0.00397696i
$560$	−1.89869	−	0.897119i	−0.0802345	−	0.0379102i
$561$	2.40857	+	3.11216i	0.101690	+	0.131395i
$562$	−28.1394	+	8.67985i	−1.18699	+	0.366138i
$563$	−7.69505	−	19.6067i	−0.324308	−	0.826323i	−0.996314	−	0.0857775i	$-0.972663\pi$
$563$	−7.69505	−	19.6067i	−0.324308	−	0.826323i	0.672007	−	0.740545i	$-0.265433\pi$
$564$	−3.74915	+	11.5544i	−0.157868	+	0.486527i
$565$	−0.952671	−	3.08848i	−0.0400792	−	0.129934i
$566$	0.535188	−	2.34481i	0.0224956	−	0.0985598i
$567$	−4.11193	−	23.4540i	−0.172685	−	0.984977i
$568$	3.17628	+	13.9162i	0.133274	+	0.583911i
$569$	−31.7135	+	18.3098i	−1.32950	+	0.767588i	−0.985222	−	0.171280i	$-0.945210\pi$
$569$	−31.7135	+	18.3098i	−1.32950	+	0.767588i	−0.344279	+	0.938868i	$0.611876\pi$
$570$	−3.84320	+	1.44413i	−0.160974	+	0.0604879i
$571$	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
$573$	−0.708049	−	3.32458i	−0.0295792	−	0.138886i
$574$	−4.05936	−	25.6433i	−0.169434	−	1.07033i
$575$	−18.7852	+	14.9807i	−0.783399	+	0.624740i
$576$	2.42846	+	1.76142i	0.101186	+	0.0733924i
$577$	−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
$579$	−15.1680	−	16.8322i	−0.630360	−	0.699524i
$580$	0.243335	+	0.505290i	0.0101039	+	0.0209810i
$581$	−29.1806	−	19.5803i	−1.21061	−	0.812328i
$582$	2.58424	+	5.57236i	0.107120	+	0.230982i
$583$	0.400743	+	0.273222i	0.0165971	+	0.0113157i
$584$	6.66616	+	6.18529i	0.275848	+	0.255949i
$585$	0.0164558	+	0.135926i	0.000680363	+	0.00561985i
$586$	−27.2342	−	10.6886i	−1.12503	−	0.441543i
$587$	−2.54324			−0.104971			−0.0524854	−	0.998622i	$-0.516714\pi$
$587$	−2.54324			−0.104971			−0.0524854	+	0.998622i	$0.516714\pi$
$588$	−11.8197	+	2.70072i	−0.487438	+	0.111376i
$589$	−18.3199			−0.754857
$590$	−4.55358	−	1.78715i	−0.187468	−	0.0735757i
$591$	−21.9266	−	20.9472i	−0.901940	−	0.861655i
$592$	−2.45744	−	2.28017i	−0.101000	−	0.0937143i
$593$	−8.04366	−	5.48407i	−0.330313	−	0.225204i	0.386795	−	0.922166i	$-0.373582\pi$
$593$	−8.04366	−	5.48407i	−0.330313	−	0.225204i	−0.717108	+	0.696962i	$0.754535\pi$
$594$	−4.78148	+	3.48270i	−0.196186	+	0.142897i
$595$	3.05114	−	2.87335i	0.125085	−	0.117796i
$596$	5.16352	+	10.7222i	0.211506	+	0.439197i
$597$	−7.53662	+	6.79145i	−0.308453	+	0.277955i
$598$	0.178095	+	0.261218i	0.00728286	+	0.0106820i
$599$	5.42529	+	35.9944i	0.221671	+	1.47069i	0.771935	+	0.635702i	$0.219289\pi$
$599$	5.42529	+	35.9944i	0.221671	+	1.47069i	−0.550263	+	0.834991i	$0.685473\pi$
$600$	−0.455679	−	7.55537i	−0.0186030	−	0.308447i
$601$	−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
$603$	−25.7871	−	13.3569i	−1.05013	−	0.543937i
$604$	1.02749	+	13.7109i	0.0418079	+	0.557888i
$605$	7.36001	+	2.27026i	0.299227	+	0.0922993i
$606$	−5.56290	−	14.8043i	−0.225978	−	0.601385i
$607$	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
$609$	2.90720	+	1.42577i	0.117806	+	0.0577753i
$610$	1.88674	−	8.26635i	0.0763919	−	0.334695i
$611$	−0.118867	−	0.385358i	−0.00480885	−	0.0155899i
$612$	−5.04315	+	3.22736i	−0.203857	+	0.130458i
$613$	−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
$615$	−10.6685	+	8.25663i	−0.430196	+	0.332939i
$616$	1.89530	+	2.34089i	0.0763638	+	0.0943171i
$617$	−19.2149	+	4.38566i	−0.773561	+	0.176560i	−0.591040	−	0.806642i	$-0.701283\pi$
$617$	−19.2149	+	4.38566i	−0.773561	+	0.176560i	−0.182520	+	0.983202i	$0.558426\pi$
$618$	5.45185	−	32.9116i	0.219306	−	1.32390i
$619$	−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
$621$	−11.5890	+	26.1134i	−0.465050	+	1.04789i
$622$	0.474805	+	0.378645i	0.0190380	+	0.0151823i
$623$	−0.721802	+	10.6928i	−0.0289184	+	0.428399i
$624$	−0.0995845	−	0.00145014i	−0.00398657	−	5.80519e-5i
$625$	−11.6901	+	10.8468i	−0.467604	+	0.433873i
$626$	4.15658	−	0.626504i	0.166130	−	0.0250401i
$627$	5.86509	+	0.525508i	0.234229	+	0.0209868i
$628$	1.06869	−	7.09027i	0.0426452	−	0.282932i
$629$	6.02804	−	2.90295i	0.240354	−	0.115748i
$630$	4.18370	+	4.71014i	0.166683	+	0.187657i
$631$	−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
$633$	−1.78262	−	13.1205i	−0.0708530	−	0.521493i
$634$	−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
$639$	7.61257	−	42.1402i	0.301149	−	1.66704i
$640$	−0.791494	−	0.0593143i	−0.0312865	−	0.00234460i
$641$	−4.35863	+	4.69749i	−0.172156	+	0.185540i	−0.813236	−	0.581934i	$-0.802296\pi$
$641$	−4.35863	+	4.69749i	−0.172156	+	0.185540i	0.641080	+	0.767474i	$0.278487\pi$
$642$	−1.33250	−	4.55426i	−0.0525895	−	0.179742i
$643$	−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
$645$	9.81553	+	2.39121i	0.386486	+	0.0941538i
$646$	5.89373	+	0.888337i	0.231886	+	0.0349511i
$647$	14.3190	−	9.76253i	0.562938	−	0.383804i	−0.248156	−	0.968720i	$-0.579825\pi$
$647$	14.3190	−	9.76253i	0.562938	−	0.383804i	0.811094	+	0.584915i	$0.198872\pi$
$648$	−4.62842	−	7.71866i	−0.181822	−	0.303218i
$649$	4.77220	+	5.14321i	0.187325	+	0.201889i
$650$	0.156672	+	0.196460i	0.00614516	+	0.00770579i
$651$	10.0826	+	26.2410i	0.395167	+	1.02847i
$652$	2.25728	−	2.83054i	0.0884018	−	0.110852i
$653$	44.2247	−	3.31418i	1.73064	−	0.129694i	0.828181	−	0.560460i	$-0.189376\pi$
$653$	44.2247	−	3.31418i	1.73064	−	0.129694i	0.902464	+	0.430766i	$0.141757\pi$
$654$	−0.147354	+	0.0973522i	−0.00576201	+	0.00380677i
$655$	−4.45914	+	7.72346i	−0.174233	+	0.301780i
$656$	−4.90647	−	8.49825i	−0.191565	−	0.331801i
$657$	−11.1161	−	24.9137i	−0.433681	−	0.971975i
$658$	−14.5925	−	11.4615i	−0.568873	−	0.446816i
$659$	44.9871	+	10.2680i	1.75245	+	0.399985i	0.973788	−	0.227459i	$-0.0730418\pi$
$659$	44.9871	+	10.2680i	1.75245	+	0.399985i	0.778662	+	0.627444i	$0.215899\pi$
$660$	0.592924	−	1.44837i	0.0230795	−	0.0563779i
$661$	−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
$663$	0.0753062	−	0.183955i	0.00292465	−	0.00714423i
$664$	−12.9491	−	2.95554i	−0.502521	−	0.114697i
$665$	−0.0463995	−	6.27119i	−0.00179930	−	0.243186i
$666$	4.09788	+	9.18426i	0.158790	+	0.355883i
$667$	−1.94249	−	3.36448i	−0.0752133	−	0.130273i
$668$	−8.12364	+	14.0706i	−0.314313	+	0.544406i
$669$	−1.47147	+	0.972155i	−0.0568905	+	0.0375857i
$670$	7.66193	−	0.574182i	0.296006	−	0.0221826i
$671$	−7.58242	+	9.50805i	−0.292716	+	0.367054i
$672$	−3.80469	+	2.55427i	−0.146769	+	0.0985332i
$673$	−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
$675$	−7.63425	+	21.3855i	−0.293842	+	0.823128i
$676$	−10.7384	+	7.32130i	−0.413014	+	0.281588i
$677$	−4.67031	−	0.703936i	−0.179494	−	0.0270544i	0.0586799	−	0.998277i	$-0.481311\pi$
$677$	−4.67031	−	0.703936i	−0.179494	−	0.0270544i	−0.238174	+	0.971222i	$0.576549\pi$
$678$	−6.85266	−	1.66941i	−0.263175	−	0.0641134i
$679$	−9.35104	+	0.770377i	−0.358860	+	0.0295644i
$680$	0.687315	−	1.42722i	0.0263573	−	0.0547315i
$681$	7.73943	+	26.4521i	0.296576	+	1.01365i
$682$	4.74999	−	5.11927i	0.181887	−	0.196027i
$683$	−29.5558	−	2.21490i	−1.13092	−	0.0847509i	−0.503907	−	0.863758i	$-0.668105\pi$
$683$	−29.5558	−	2.21490i	−1.13092	−	0.0847509i	−0.627015	+	0.779007i	$0.715724\pi$
$684$	−1.59270	+	8.81653i	−0.0608982	+	0.337108i
$685$		−	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
$690$	−1.01761	−	7.48984i	−0.0387398	−	0.285133i
$691$	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
$693$	−2.47520	−	8.69027i	−0.0940249	−	0.330116i
$694$	−10.0224	+	4.82653i	−0.380444	+	0.183212i
$695$	−1.45472	+	9.65142i	−0.0551806	+	0.366099i
$696$	1.21897	+	0.109219i	0.0462048	+	0.00413992i
$697$	19.3660	−	2.91895i	0.733539	−	0.110563i
$698$	−0.607514	+	0.563691i	−0.0229947	+	0.0213360i
$699$	11.4673	+	0.166986i	0.433734	+	0.00631597i
$700$	11.0732	+	3.32612i	0.418529	+	0.125715i
$701$	2.39846	+	1.91271i	0.0905887	+	0.0722421i	0.667737	−	0.744397i	$-0.267263\pi$
$701$	2.39846	+	1.91271i	0.0905887	+	0.0722421i	−0.577148	+	0.816639i	$0.695835\pi$
$702$	0.273099	+	0.121200i	0.0103075	+	0.00457440i
$703$	2.95093	−	9.56667i	0.111296	−	0.360814i
$704$	0.985897	+	0.569208i	0.0371574	+	0.0214528i
$705$	−1.57566	+	9.51194i	−0.0593429	+	0.358240i
$706$	−23.1986	+	5.29493i	−0.873091	+	0.199277i
$707$	24.1572	−	0.178735i	0.908523	−	0.00672201i
$708$	−8.44190	+	6.53339i	−0.317266	+	0.245540i
$709$	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
$711$	−7.13152	+	4.56381i	−0.267453	+	0.171156i
$712$	1.19397	+	3.87074i	0.0447458	+	0.145062i
$713$	7.50523	−	32.8826i	0.281073	−	1.23146i
$714$	−1.97125	−	8.93098i	−0.0737721	−	0.334233i
$715$	0.0115615	+	0.0506540i	0.000432374	+	0.00189435i
$716$	20.1477	−	11.6323i	0.752956	−	0.434719i
$717$	−8.05686	−	21.4414i	−0.300889	−	0.800744i
$718$	25.4795	+	7.85939i	0.950887	+	0.293310i
$719$	1.41971	+	18.9447i	0.0529462	+	0.706518i	0.959009	+	0.283375i	$0.0914541\pi$
$719$	1.41971	+	18.9447i	0.0529462	+	0.706518i	−0.906063	+	0.423143i	$0.860927\pi$
$720$	2.11434	+	1.09517i	0.0787968	+	0.0408144i
$721$	44.3186	+	25.1520i	1.65051	+	0.936709i
$722$	−7.88192	+	6.28562i	−0.293335	+	0.233927i
$723$	0.707910	+	11.7375i	0.0263275	+	0.436522i
$724$	0.0208327	+	0.138216i	0.000774241	+	0.00513675i
$725$	−1.73943	−	2.55127i	−0.0646007	−	0.0947518i
$726$	12.4862	−	11.2516i	0.463405	−	0.417587i
$727$	−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
$729$	3.68836	+	26.7469i	0.136606	+	0.990625i
$730$	5.96362	+	4.06593i	0.220724	+	0.150487i
$731$	−10.7513	−	9.97578i	−0.397652	−	0.368968i
$732$	−13.3789	−	12.7813i	−0.494497	−	0.472410i
$733$	−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
$735$	−8.95721	+	3.51789i	−0.330392	+	0.129759i
$736$	5.49820			0.202666
$737$	−10.2585	−	4.02615i	−0.377875	−	0.148305i
$738$	3.53815	+	29.2254i	0.130241	+	1.07580i
$739$	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
$741$	−0.125135	−	0.269827i	−0.00459696	−	0.00991236i
$742$	−0.570817	−	0.972004i	−0.0209553	−	0.0356834i
$743$	−2.99195	−	6.21286i	−0.109764	−	0.227928i	0.838850	−	0.544363i	$-0.183228\pi$
$743$	−2.99195	−	6.21286i	−0.109764	−	0.227928i	−0.948614	+	0.316435i	$0.897514\pi$
$744$	7.11274	+	7.89316i	0.260766	+	0.289377i
$745$	5.32097	+	7.80444i	0.194945	+	0.285932i
$746$	−2.23514	−	14.8292i	−0.0818344	−	0.542936i
$747$	32.2550	+	23.3953i	1.18015	+	0.855989i
$748$	−1.77637	+	1.41661i	−0.0649504	+	0.0517962i
$749$	7.23194	+	0.488180i	0.264249	+	0.0178377i
$750$	−2.68323	−	12.5989i	−0.0979778	−	0.460046i
$751$	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
$753$	16.7776	−	6.30439i	0.611411	−	0.229745i
$754$	−0.0351865	+	0.0203149i	−0.00128141	+	0.000739825i
$755$	2.42838	+	10.6394i	0.0883776	+	0.387208i
$756$	13.5052	−	2.57094i	0.491179	−	0.0935041i
$757$	−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
$759$	−3.34603	+	10.3120i	−0.121453	+	0.374303i
$760$	−0.865987	−	2.20650i	−0.0314127	−	0.0800382i
$761$	−13.5966	+	4.19399i	−0.492876	+	0.152032i	−0.531222	−	0.847232i	$-0.678267\pi$
$761$	−13.5966	+	4.19399i	−0.492876	+	0.152032i	0.0383464	+	0.999265i	$0.487791\pi$
$762$	23.7230	+	30.6529i	0.859395	+	1.11044i
$763$	−0.0619748	−	0.262559i	−0.00224364	−	0.00950529i
$764$	1.91329	−	0.436697i	0.0692205	−	0.0157991i
$765$	−3.57632	+	3.12958i	−0.129302	+	0.113150i
$766$	−2.94441	−	1.69995i	−0.106386	−	0.0614218i
$767$	0.104457	−	0.338641i	0.00377172	−	0.0122276i
$768$	−0.996433	+	1.41673i	−0.0359557	+	0.0511218i
$769$	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
$771$	0.588324	−	40.4017i	0.0211880	−	1.45503i
$772$	9.58956	−	8.89781i	0.345136	−	0.320239i
$773$	23.1243	−	3.48543i	0.831725	−	0.125362i	0.280642	−	0.959813i	$-0.409453\pi$
$773$	23.1243	−	3.48543i	0.831725	−	0.125362i	0.551083	+	0.834450i	$0.314215\pi$
$774$	15.4593	−	15.7174i	0.555673	−	0.564950i
$775$	3.99545	−	26.5081i	0.143521	−	0.952198i
$776$	−3.19514	+	1.53870i	−0.114699	+	0.0552360i
$777$	−15.3272	+	1.03828i	−0.549860	+	0.0372481i
$778$	21.0874	+	10.1552i	0.756021	+	0.364081i
$779$	16.5083	−	24.2133i	0.591473	−	0.867531i
$780$	−0.0783303	+	0.0106424i	−0.00280467	+	0.000381059i
$781$	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
$786$	9.48436	+	16.9941i	0.338296	+	0.606160i
$787$	−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
$789$	−49.2288	+	14.4035i	−1.75259	+	0.512779i
$790$	0.971932	−	2.01824i	0.0345798	−	0.0718057i
$791$	6.00305	−	8.94635i	0.213444	−	0.318096i
$792$	−2.05072	−	2.73102i	−0.0728692	−	0.0970425i
$793$	0.607403	+	0.0915513i	0.0215695	+	0.00325108i
$794$	29.0965	−	19.8376i	1.03259	−	0.704011i
$795$	−0.300210	+	0.502923i	−0.0106474	+	0.0178368i
$796$	−3.98398	−	4.29371i	−0.141209	−	0.152187i
$797$	−17.1308	−	21.4813i	−0.606803	−	0.760907i	0.379618	−	0.925143i	$-0.376055\pi$
$797$	−17.1308	−	21.4813i	−0.606803	−	0.760907i	−0.986421	+	0.164236i	$0.947484\pi$
$798$	−11.8026	−	6.92744i	−0.417809	−	0.245229i
$799$	8.72713	−	10.9435i	0.308744	−	0.387152i
$800$	4.35780	−	0.326572i	0.154071	−	0.0115461i
$801$	1.26059	−	12.0866i	0.0445409	−	0.427057i
$802$	−18.0606	+	31.2819i	−0.637742	+	1.10460i
$803$	−5.17621	−	8.96546i	−0.182664	−	0.316384i
$804$	7.49404	−	14.9989i	0.264294	−	0.528969i
$805$	11.2753	+	2.48588i	0.397400	+	0.0876158i
$806$	−0.343892	−	0.0784912i	−0.0121131	−	0.00276473i
$807$	20.8744	+	8.54541i	0.734814	+	0.300813i
$808$	8.49962	−	3.33585i	0.299016	−	0.117355i
$809$	24.0782	−	9.45000i	0.846545	−	0.332244i	0.0978841	−	0.995198i	$-0.468793\pi$
$809$	24.0782	−	9.45000i	0.846545	−	0.332244i	0.748661	+	0.662954i	$0.230697\pi$
$810$	−4.54570	−	5.51045i	−0.159720	−	0.193617i
$811$	−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
$813$	37.4700	+	18.7215i	1.31413	+	0.656593i
$814$	1.90817	+	3.30506i	0.0668815	+	0.115842i
$815$	1.43678	−	2.48857i	0.0503281	−	0.0871708i
$816$	−1.90551	−	2.88423i	−0.0667063	−	0.100968i
$817$	−21.8848	+	1.64004i	−0.765652	+	0.0573777i
$818$	−0.649832	+	0.814863i	−0.0227208	+	0.0284910i
$819$	−0.317626	+	0.327744i	−0.0110988	+	0.0114523i
$820$	−4.85614	−	6.08941i	−0.169584	−	0.212652i
$821$	−5.77631	−	6.22539i	−0.201595	−	0.217267i	0.624160	−	0.781296i	$-0.285441\pi$
$821$	−5.77631	−	6.22539i	−0.201595	−	0.217267i	−0.825755	+	0.564029i	$0.809251\pi$
$822$	−14.9803	−	8.94219i	−0.522497	−	0.311895i
$823$	−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
$825$	−2.03953	+	8.37193i	−0.0710072	+	0.291473i
$826$	−4.92143	−	15.5456i	−0.171238	−	0.540900i
$827$	24.4534	−	50.7780i	0.850328	−	1.76572i	0.245444	−	0.969411i	$-0.421066\pi$
$827$	24.4534	−	50.7780i	0.850328	−	1.76572i	0.604884	−	0.796314i	$-0.293219\pi$
$828$	−15.1724	−	6.47068i	−0.527278	−	0.224872i
$829$	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
$831$	−44.2613	+	24.7021i	−1.53541	+	0.856906i
$832$		−	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
$837$	−10.3385	−	30.1521i	−0.357352	−	1.04221i
$838$	4.96240	−	7.27850i	0.171423	−	0.251432i
$839$	39.8907	+	19.2104i	1.37718	+	0.663216i	0.968397	−	0.249415i	$-0.0802384\pi$
$839$	39.8907	+	19.2104i	1.37718	+	0.663216i	0.408785	+	0.912631i	$0.365953\pi$
$840$	−2.68394	+	2.45480i	−0.0926048	+	0.0846986i
$841$	−25.6783	+	12.3660i	−0.885458	+	0.426414i
$842$	1.80696	−	11.9884i	0.0622721	−	0.413148i
$843$	−4.55176	+	50.8014i	−0.156771	+	1.74969i
$844$	7.55933	−	1.13939i	0.260203	−	0.0392193i
$845$	−7.56190	+	7.01642i	−0.260137	+	0.241372i
$846$	16.0607	+	13.5916i	0.552180	+	0.467289i
$847$	9.55648	+	23.8296i	0.328364	+	0.818794i
$848$	−0.333098	−	0.265637i	−0.0114386	−	0.00912202i
$849$	−3.40740	−	2.39653i	−0.116942	−	0.0822488i
$850$	−2.57077	+	8.33424i	−0.0881767	+	0.285862i
$851$	15.9624	+	9.21590i	0.547184	+	0.315917i
$852$	24.3911	+	4.04041i	0.835624	+	0.138422i
$853$	−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
$855$	−0.207057	+	7.10805i	−0.00708119	+	0.243090i
$856$	2.61792	−	0.807522i	0.0894787	−	0.0276005i
$857$	−18.8196	−	47.9515i	−0.642865	−	1.63799i	−0.763893	−	0.645343i	$-0.776714\pi$
$857$	−18.8196	−	47.9515i	−0.642865	−	1.63799i	0.121028	−	0.992649i	$-0.461381\pi$
$858$	0.107845	+	0.0349935i	0.00368178	+	0.00119466i
$859$	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
$861$	−43.7683	−	10.3202i	−1.49162	−	0.351710i
$862$	1.57609	+	6.90532i	0.0536820	+	0.235196i
$863$	−13.6539	+	7.88309i	−0.464785	+	0.268344i	−0.714054	−	0.700091i	$-0.753143\pi$
$863$	−13.6539	+	7.88309i	−0.464785	+	0.268344i	0.249269	+	0.968434i	$0.419810\pi$
$864$	4.41699	−	2.73682i	0.150269	−	0.0931086i
$865$	11.7456	+	3.62305i	0.399363	+	0.123187i
$866$	0.442946	+	5.91071i	0.0150519	+	0.200854i
$867$	−22.0511	+	4.69631i	−0.748896	+	0.159495i
$868$	−15.0639	+	6.04115i	−0.511302	+	0.205050i
$869$	−2.51196	+	2.00322i	−0.0852124	+	0.0679546i
$870$	0.969624	−	0.0584799i	0.0328733	−	0.00198265i
$871$	0.0829616	+	0.550414i	0.00281105	+	0.0186501i
$872$	−0.0574391	−	0.0842476i	−0.00194513	−	0.00285298i
$873$	10.6279	−	0.485801i	0.359700	−	0.0164419i
$874$	7.12432	+	14.7938i	0.240984	+	0.500408i
$875$	19.4781	+	2.78863i	0.658481	+	0.0942729i
$876$	14.2890	−	6.62665i	0.482779	−	0.223894i
$877$	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
$879$	−35.0042	+	36.6408i	−1.18066	+	1.23586i
$880$	0.841115	+	0.330113i	0.0283540	+	0.0111281i
$881$	17.5667			0.591837			0.295918	−	0.955213i	$-0.404374\pi$
$881$	17.5667			0.591837			0.295918	+	0.955213i	$0.404374\pi$
$882$	−3.42701	+	20.7185i	−0.115393	+	0.697628i
$883$	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
$885$	−5.85273	+	6.12637i	−0.196737	+	0.205936i
$886$	−20.5092	−	19.0298i	−0.689021	−	0.639318i
$887$	−27.2899	−	18.6059i	−0.916304	−	0.624726i	0.0106326	−	0.999943i	$-0.496615\pi$
$887$	−27.2899	−	18.6059i	−0.916304	−	0.624726i	−0.926937	+	0.375218i	$0.877568\pi$
$888$	−5.26753	+	2.44287i	−0.176767	+	0.0819774i
$889$	−56.4467	+	17.8699i	−1.89316	+	0.599338i
$890$	1.39498	+	2.89670i	0.0467598	+	0.0970977i
$891$	2.44495	+	9.94974i	0.0819090	+	0.333329i
$892$	−0.573584	−	0.841294i	−0.0192050	−	0.0281686i
$893$	−3.12164	−	20.7107i	−0.104462	−	0.693057i
$894$	20.5752	−	1.24093i	0.688138	−	0.0415030i
$895$	14.4368	−	11.5130i	0.482570	−	0.384837i
$896$	−1.50654	−	2.17494i	−0.0503299	−	0.0726595i
$897$	0.535582	−	0.114065i	0.0178826	−	0.00380851i
$898$	0.912467	+	12.1760i	0.0304494	+	0.406319i
$899$	4.14194	+	1.27762i	0.138142	+	0.0426110i
$900$	−12.4098	−	4.22739i	−0.413660	−	0.140913i
$901$	0.736391	−	0.425156i	0.0245328	−	0.0141640i
$902$	2.48582	+	10.8911i	0.0827689	+	0.362634i
$903$	14.3937	+	30.4448i	0.478993	+	1.01314i
$904$	0.906127	−	3.97000i	0.0301373	−	0.132040i
$905$	0.0327010	+	0.106014i	0.00108702	+	0.00352403i
$906$	22.6519	+	7.35006i	0.752559	+	0.244189i
$907$	−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
$909$	−27.3808	−	0.797599i	−0.908163	−	0.0264547i
$910$	0.0259978	−	0.117919i	0.000861820	−	0.00390897i
$911$	−30.3589	+	6.92923i	−1.00584	+	0.229576i	−0.693547	−	0.720412i	$-0.743953\pi$
$911$	−30.3589	+	6.92923i	−1.00584	+	0.229576i	−0.312289	+	0.949987i	$0.601096\pi$
$912$	−5.10307	−	0.845330i	−0.168980	−	0.0279917i
$913$	13.0948	+	7.56026i	0.433373	+	0.250208i
$914$	−4.73902	+	15.3635i	−0.156753	+	0.508181i
$915$	−12.0124	−	8.44869i	−0.397116	−	0.279305i
$916$	−9.86516	−	7.86721i	−0.325954	−	0.259940i
$917$	−29.3624	+	4.64811i	−0.969633	+	0.153494i
$918$	1.86394	+	10.2016i	0.0615193	+	0.336704i
$919$	−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
$921$	4.91994	−	54.9105i	0.162118	−	1.80936i
$922$	−0.844606	+	5.60360i	−0.0278156	+	0.184545i
$923$	−0.739495	+	0.356122i	−0.0243408	+	0.0117219i
$924$	4.99599	−	1.50196i	0.164356	−	0.0494108i
$925$	13.1990	+	6.35630i	0.433980	+	0.208994i
$926$	0.486146	−	0.713045i	0.0159757	−	0.0234321i
$927$	−49.1777	−	30.3355i	−1.61521	−	0.996349i
$928$	−0.0528035	+	0.704614i	−0.00173336	+	0.0231301i
$929$	9.26240	−	23.6002i	0.303889	−	0.774298i	−0.694602	−	0.719394i	$-0.744420\pi$
$929$	9.26240	−	23.6002i	0.303889	−	0.774298i	0.998492	−	0.0549036i	$-0.0174851\pi$
$930$	6.51615	+	5.35351i	0.213673	+	0.175549i
$931$	16.1494	−	13.2744i	0.529276	−	0.435051i
$932$			6.62136i			0.216890i
$933$	0.918510	−	0.512617i	0.0300707	−	0.0167823i
$934$	34.2049	+	2.56330i	1.11922	+	0.0838738i
$935$	−1.22660	+	1.32196i	−0.0401140	+	0.0432327i
$936$	−0.0676716	+	0.158676i	−0.00221192	+	0.00518649i
$937$	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
$939$	1.72330	−	7.07385i	0.0562376	−	0.230846i
$940$	−5.50438	−	0.829652i	−0.179533	−	0.0270603i
$941$	25.3899	−	17.3105i	0.827687	−	0.564307i	−0.0737208	−	0.997279i	$-0.523487\pi$
$941$	25.3899	−	17.3105i	0.827687	−	0.564307i	0.901408	+	0.432972i	$0.142535\pi$
$942$	−10.6640	−	6.36565i	−0.347451	−	0.207404i
$943$	36.6976	+	39.5507i	1.19504	+	1.28795i
$944$	−3.84262	−	4.81850i	−0.125067	−	0.156829i
$945$	10.2954	−	3.61542i	0.334909	−	0.117609i
$946$	5.21602	−	6.54068i	0.169587	−	0.212656i
$947$	−10.1319	+	0.759284i	−0.329244	+	0.0246734i	−0.238327	−	0.971185i	$-0.576599\pi$
$947$	−10.1319	+	0.759284i	−0.329244	+	0.0246734i	−0.0909171	+	0.995858i	$0.528980\pi$
$948$	−2.69459	−	4.07858i	−0.0875161	−	0.132466i
$949$	−0.261450	+	0.452844i	−0.00848702	+	0.0146999i
$950$	6.52534	+	11.3022i	0.211710	+	0.366692i
$951$	21.4028	+	10.6937i	0.694033	+	0.346767i
$952$	5.13919	−	1.21306i	0.166562	−	0.0393154i
$953$	−5.54443	−	1.26548i	−0.179602	−	0.0409929i	0.131774	−	0.991280i	$-0.457933\pi$
$953$	−5.54443	−	1.26548i	−0.179602	−	0.0409929i	−0.311376	+	0.950287i	$0.600790\pi$
$954$	0.606572	+	1.12505i	0.0196385	+	0.0364247i
$955$	1.44998	−	0.569077i	0.0469204	−	0.0184149i
$956$	12.3102	−	4.83138i	0.398139	−	0.156258i
$957$	−1.28939	−	0.527841i	−0.0416801	−	0.0170627i
$958$	−19.3023	−	4.40562i	−0.623628	−	0.142339i
$959$	20.7120	−	16.7694i	0.668825	−	0.541514i
$960$	−0.614454	+	1.22979i	−0.0198314	+	0.0396914i
$961$	3.31549	+	5.74259i	0.106951	+	0.185245i
$962$	0.0963817	−	0.166938i	0.00310747	−	0.00538230i
$963$	−8.17457	−	0.852584i	−0.263422	−	0.0274741i
$964$	−6.76997	+	0.507339i	−0.218046	+	0.0163403i
$965$	6.47377	−	8.11785i	0.208398	−	0.261323i
$966$	17.2694	−	18.3467i	0.555634	−	0.590295i
$967$	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
$969$	5.29140	−	8.86435i	0.169984	−	0.284764i
$970$	−2.32567	+	1.58562i	−0.0746729	+	0.0509111i
$971$	−53.4033	−	8.04925i	−1.71379	−	0.258313i	−0.782517	−	0.622629i	$-0.786065\pi$
$971$	−53.4033	−	8.04925i	−1.71379	−	0.258313i	−0.931275	+	0.364316i	$0.881303\pi$
$972$	−15.4097	+	2.35410i	−0.494266	+	0.0755077i
$973$	−28.0553	+	16.4757i	−0.899411	+	0.528186i
$974$	−4.11830	+	8.55175i	−0.131959	+	0.274016i
$975$	0.417720	−	0.122218i	0.0133778	−	0.00391410i
$976$	7.26602	−	7.83091i	0.232580	−	0.250661i
$977$	14.1742	+	1.06221i	0.453473	+	0.0339831i	0.299509	−	0.954093i	$-0.403177\pi$
$977$	14.1742	+	1.06221i	0.453473	+	0.0339831i	0.153964	+	0.988076i	$0.450796\pi$
$978$	−3.05595	−	5.47566i	−0.0977185	−	0.175092i
$979$		−	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	$-0.645742\pi$
$983$	4.03680	−	53.8673i	0.128754	−	1.71810i	0.570784	−	0.821100i	$-0.306639\pi$
$984$	−16.8418	+	2.28822i	−0.536896	+	0.0729457i
$985$	7.82797	−	11.4815i	0.249420	−	0.365832i
$986$	−1.27056	−	0.611871i	−0.0404629	−	0.0194859i
$987$	−27.9476	+	15.8698i	−0.889582	+	0.505140i
$988$	0.154716	−	0.0745075i	0.00492219	−	0.00237040i
$989$	6.02197	−	39.9532i	0.191488	−	1.27044i
$990$	−1.93257	−	1.90084i	−0.0614212	−	0.0604127i
$991$	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
$993$	−0.814999	+	55.9681i	−0.0258632	+	1.77609i
$994$	−18.6403	+	32.8448i	−0.591236	+	1.04178i
$995$	−3.63475	−	2.89862i	−0.115229	−	0.0918924i
$996$	−13.2347	+	18.8171i	−0.419357	+	0.596243i
$997$	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
$999$	17.4108	−	0.541953i	0.550854	−	0.0171466i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(0.930874 + 0.365341i) q^{2} +(1.19646 - 1.25240i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.655797 + 0.447115i) q^{5} +(1.57130 - 0.728707i) q^{6} +(0.217232 + 2.63682i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-0.136987 - 2.99687i) q^{9} +O(q^{10})\)	\(q+(0.930874 + 0.365341i) q^{2} +(1.19646 - 1.25240i) q^{3} +(0.733052 + 0.680173i) q^{4} +(0.655797 + 0.447115i) q^{5} +(1.57130 - 0.728707i) q^{6} +(0.217232 + 2.63682i) q^{7} +(0.433884 + 0.900969i) q^{8} +(-0.136987 - 2.99687i) q^{9} +(0.447115 + 0.655797i) q^{10} +(-0.169672 - 1.12570i) q^{11} +(1.72891 - 0.104274i) q^{12} +(-0.0449563 + 0.0358514i) q^{13} +(-0.761122 + 2.53391i) q^{14} +(1.34460 - 0.286364i) q^{15} +(0.0747301 + 0.997204i) q^{16} +(-1.90714 - 0.588275i) q^{17} +(0.967362 - 2.83976i) q^{18} +(-2.58631 + 1.49321i) q^{19} +(0.176618 + 0.773813i) q^{20} +(3.56225 + 2.88278i) q^{21} +(0.253321 - 1.10987i) q^{22} +(-1.62062 - 5.25393i) q^{23} +(1.64749 + 0.534576i) q^{24} +(-1.59655 - 4.06794i) q^{25} +(-0.0549466 + 0.0169488i) q^{26} +(-3.91716 - 3.41406i) q^{27} +(-1.63425 + 2.08068i) q^{28} +(0.688874 - 0.157231i) q^{29} +(1.35627 + 0.224668i) q^{30} +(5.31255 + 3.06720i) q^{31} +(-0.294755 + 0.955573i) q^{32} +(-1.61283 - 1.13435i) q^{33} +(-1.56039 - 1.24437i) q^{34} +(-1.03650 + 1.82634i) q^{35} +(1.93797 - 2.29004i) q^{36} +(-2.45744 + 2.28017i) q^{37} +(-2.95306 + 0.445101i) q^{38} +(-0.00888804 + 0.0991977i) q^{39} +(-0.118297 + 0.784848i) q^{40} +(-8.84115 + 4.25767i) q^{41} +(2.26281 + 3.98494i) q^{42} +(6.62093 + 3.18847i) q^{43} +(0.641292 - 0.940603i) q^{44} +(1.25011 - 2.02659i) 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} +(-3.01856 + 1.68465i) q^{51} +(-0.0573405 - 0.00429707i) q^{52} +(-0.289787 + 0.312316i) q^{53} +(-2.39909 - 4.60916i) q^{54} +(0.392047 - 0.814093i) q^{55} +(-2.28144 + 1.33979i) q^{56} +(-1.22432 + 5.02563i) q^{57} +(0.698698 + 0.105312i) q^{58} +(-5.09218 + 3.47179i) q^{59} +(1.18044 + 0.704638i) q^{60} +(-7.26602 - 7.83091i) q^{61} +(3.82474 + 4.79607i) q^{62} +(7.87245 - 1.01223i) q^{63} +(-0.623490 + 0.781831i) q^{64} +(-0.0455119 + 0.00341064i) q^{65} +(-1.08691 - 1.64517i) q^{66} +(4.84017 - 8.38342i) q^{67} +(-0.997904 - 1.72842i) q^{68} +(-8.51900 - 4.25643i) q^{69} +(-1.63209 + 1.32142i) q^{70} +(13.9162 + 3.17628i) q^{71} +(2.64065 - 1.42371i) q^{72} +(8.46509 - 3.32230i) q^{73} +(-3.12060 + 1.22475i) q^{74} +(-7.00486 - 2.86760i) q^{75} +(-2.91154 - 0.664539i) q^{76} +(2.93141 - 0.691932i) q^{77} +(-0.0445146 + 0.0890934i) q^{78} +(-1.41114 - 2.44416i) q^{79} +(-0.396857 + 0.687376i) q^{80} +(-8.96247 + 0.821064i) q^{81} +(-9.78549 + 0.733321i) q^{82} +(-8.28124 + 10.3843i) q^{83} +(0.650526 + 4.53617i) q^{84} +(-0.987669 - 1.23850i) q^{85} +(4.99837 + 5.38696i) q^{86} +(0.627292 - 1.05086i) q^{87} +(0.940603 - 0.641292i) q^{88} +(4.00546 + 0.603726i) q^{89} +(1.90409 - 1.42978i) q^{90} +(-0.104300 - 0.110753i) q^{91} +(2.38558 - 4.95370i) q^{92} +(10.1976 - 2.98364i) q^{93} +(-4.77026 + 5.14112i) q^{94} +(-2.36373 - 0.177137i) q^{95} +(0.844093 + 1.51245i) 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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