LMFDB - Embedded newform 245.2.x.a.108.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(3,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([63, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$26$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			108.11
Character	$\chi$	$=$	245.108
Dual form			245.2.x.a.152.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.571694 + 0.421929i) q^{2} +(0.0466438 - 0.246518i) q^{3} +(-0.440701 + 1.42872i) q^{4} +(2.23493 - 0.0714359i) q^{5} +(0.0773473 + 0.160613i) q^{6} +(0.120661 - 2.64300i) q^{7} +(-0.820220 - 2.34406i) q^{8} +(2.73403 + 1.07303i) q^{9} +(-1.24755 + 0.983821i) q^{10} +(0.529769 + 1.34983i) q^{11} +(0.331649 + 0.175281i) q^{12} +(0.370005 + 3.28389i) q^{13} +(1.04618 + 1.56190i) q^{14} +(0.0866351 - 0.554282i) q^{15} +(-1.01275 - 0.690479i) q^{16} +(0.0235943 + 0.630570i) q^{17} +(-2.01577 + 0.540123i) q^{18} +(1.79095 + 3.10202i) q^{19} +(-0.882872 + 3.22456i) q^{20} +(-0.645919 - 0.153024i) q^{21} +(-0.872398 - 0.548164i) q^{22} +(2.08265 + 0.0779271i) q^{23} +(-0.616111 + 0.0928637i) q^{24} +(4.98979 - 0.319308i) q^{25} +(-1.59710 - 1.72126i) q^{26} +(0.792494 - 1.26125i) q^{27} +(3.72292 + 1.33716i) q^{28} +(0.472800 + 0.107914i) q^{29} +(0.184339 + 0.353434i) q^{30} +(-5.64184 - 3.25732i) q^{31} +(5.83367 - 0.218281i) q^{32} +(0.357468 - 0.0676366i) q^{33} +(-0.279545 - 0.350538i) q^{34} +(0.0808628 - 5.91553i) q^{35} +(-2.73794 + 3.43326i) q^{36} +(3.69909 - 6.99902i) q^{37} +(-2.33271 - 1.01775i) q^{38} +(0.826797 + 0.0619598i) q^{39} +(-2.00058 - 5.18020i) q^{40} +(-4.67387 + 9.70538i) q^{41} +(0.433834 - 0.185049i) q^{42} +(-12.1330 - 4.24553i) q^{43} +(-2.16199 + 0.162019i) q^{44} +(6.18700 + 2.20283i) q^{45} +(-1.22352 + 0.834179i) q^{46} +(-1.13255 - 1.53455i) q^{47} +(-0.217454 + 0.217454i) q^{48} +(-6.97088 - 0.637812i) q^{49} +(-2.71791 + 2.28789i) q^{50} +(0.156548 + 0.0235958i) q^{51} +(-4.85481 - 0.918579i) q^{52} +(0.557654 + 1.05513i) q^{53} +(0.0790931 + 1.05542i) q^{54} +(1.28042 + 2.97893i) q^{55} +(-6.29430 + 1.88501i) q^{56} +(0.848241 - 0.296812i) q^{57} +(-0.315829 + 0.137795i) q^{58} +(0.818329 - 10.9198i) q^{59} +(0.753732 + 0.368050i) q^{60} +(-3.36739 - 10.9168i) q^{61} +(4.59977 - 0.518269i) q^{62} +(3.16590 - 7.09655i) q^{63} +(-1.32635 + 1.05773i) q^{64} +(1.06152 + 7.31282i) q^{65} +(-0.175824 + 0.189494i) q^{66} +(-1.31551 - 4.90956i) q^{67} +(-0.911304 - 0.244183i) q^{68} +(0.116353 - 0.509775i) q^{69} +(2.44971 + 3.41599i) q^{70} +(1.90716 + 8.35583i) q^{71} +(0.272729 - 7.28883i) q^{72} +(0.424040 - 0.574554i) q^{73} +(0.838345 + 5.56205i) q^{74} +(0.154028 - 1.24497i) q^{75} +(-5.22118 + 1.19170i) q^{76} +(3.63152 - 1.23731i) q^{77} +(-0.498817 + 0.313428i) q^{78} +(8.89287 - 5.13430i) q^{79} +(-2.31274 - 1.47082i) q^{80} +(6.18508 + 5.73892i) q^{81} +(-1.42296 - 7.52055i) q^{82} +(-11.1688 - 1.25843i) q^{83} +(0.503286 - 0.855398i) q^{84} +(0.0977768 + 1.40759i) q^{85} +(8.72769 - 2.69214i) q^{86} +(0.0486558 - 0.111520i) q^{87} +(2.72955 - 2.34897i) q^{88} +(-3.16917 + 8.07490i) q^{89} +(-4.46651 + 1.35113i) q^{90} +(8.72395 - 0.581687i) q^{91} +(-1.02916 + 2.94117i) q^{92} +(-1.06615 + 1.23888i) q^{93} +(1.29494 + 0.399437i) q^{94} +(4.22424 + 6.80485i) q^{95} +(0.218294 - 1.44829i) q^{96} +(-6.86573 - 6.86573i) q^{97} +(4.25432 - 2.57659i) q^{98} +4.25892i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) $ 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.571694	+	0.421929i	−0.404249	+	0.298349i	−0.776902	−	0.629622i	$-0.783210\pi$
$2$	−0.571694	+	0.421929i	−0.404249	+	0.298349i	0.372653	+	0.927971i	$0.378448\pi$
$3$	0.0466438	−	0.246518i	0.0269298	−	0.142327i	−0.966521	−	0.256587i	$-0.917402\pi$
$3$	0.0466438	−	0.246518i	0.0269298	−	0.142327i	0.993451	+	0.114260i	$0.0364496\pi$
$4$	−0.440701	+	1.42872i	−0.220350	+	0.714358i
$5$	2.23493	−	0.0714359i	0.999490	−	0.0319471i
$5$	2.23493	−	0.0714359i	0.999490	−	0.0319471i
$6$	0.0773473	+	0.160613i	0.0315769	+	0.0655701i
$7$	0.120661	−	2.64300i	0.0456055	−	0.998960i
$7$	0.120661	−	2.64300i	0.0456055	−	0.998960i
$8$	−0.820220	−	2.34406i	−0.289992	−	0.828749i
$9$	2.73403	+	1.07303i	0.911342	+	0.357675i
$10$	−1.24755	+	0.983821i	−0.394511	+	0.311111i
$11$	0.529769	+	1.34983i	0.159731	+	0.406989i	0.988225	−	0.153010i	$-0.0488967\pi$
$11$	0.529769	+	1.34983i	0.159731	+	0.406989i	−0.828493	+	0.559999i	$0.810801\pi$
$12$	0.331649	+	0.175281i	0.0957387	+	0.0505994i
$13$	0.370005	+	3.28389i	0.102621	+	0.910787i	0.934532	+	0.355878i	$0.115818\pi$
$13$	0.370005	+	3.28389i	0.102621	+	0.910787i	−0.831911	+	0.554908i	$0.812753\pi$
$14$	1.04618	+	1.56190i	0.279603	+	0.417434i
$15$	0.0866351	−	0.554282i	0.0223691	−	0.143115i
$16$	−1.01275	−	0.690479i	−0.253187	−	0.172620i
$17$	0.0235943	+	0.630570i	0.00572245	+	0.152936i	0.999232	+	0.0391863i	$0.0124766\pi$
$17$	0.0235943	+	0.630570i	0.00572245	+	0.152936i	−0.993509	+	0.113749i	$0.963714\pi$
$18$	−2.01577	+	0.540123i	−0.475121	+	0.127308i
$19$	1.79095	+	3.10202i	0.410872	+	0.711652i	0.994985	−	0.100020i	$-0.0318908\pi$
$19$	1.79095	+	3.10202i	0.410872	+	0.711652i	−0.584113	+	0.811672i	$0.698557\pi$
$20$	−0.882872	+	3.22456i	−0.197416	+	0.721033i
$21$	−0.645919	−	0.153024i	−0.140951	−	0.0333927i
$22$	−0.872398	−	0.548164i	−0.185996	−	0.116869i
$23$	2.08265	+	0.0779271i	0.434262	+	0.0162489i	0.253629	−	0.967302i	$-0.418376\pi$
$23$	2.08265	+	0.0779271i	0.434262	+	0.0162489i	0.180633	+	0.983551i	$0.442185\pi$
$24$	−0.616111	+	0.0928637i	−0.125763	+	0.0189557i
$25$	4.98979	−	0.319308i	0.997959	−	0.0638616i
$26$	−1.59710	−	1.72126i	−0.313217	−	0.337567i
$27$	0.792494	−	1.26125i	0.152515	−	0.242727i
$28$	3.72292	+	1.33716i	0.703566	+	0.252700i
$29$	0.472800	+	0.107914i	0.0877968	+	0.0200390i	0.266194	−	0.963920i	$-0.414234\pi$
$29$	0.472800	+	0.107914i	0.0877968	+	0.0200390i	−0.178397	+	0.983959i	$0.557091\pi$
$30$	0.184339	+	0.353434i	0.0336556	+	0.0645279i
$31$	−5.64184	−	3.25732i	−1.01330	−	0.585032i	−0.101147	−	0.994871i	$-0.532251\pi$
$31$	−5.64184	−	3.25732i	−1.01330	−	0.585032i	−0.912158	+	0.409840i	$0.865585\pi$
$32$	5.83367	−	0.218281i	1.03126	−	0.0385869i
$33$	0.357468	−	0.0676366i	0.0622272	−	0.0117740i
$34$	−0.279545	−	0.350538i	−0.0479415	−	0.0601168i
$35$	0.0808628	−	5.91553i	0.0136683	−	0.999907i
$36$	−2.73794	+	3.43326i	−0.456323	+	0.572211i
$37$	3.69909	−	6.99902i	0.608127	−	1.15063i	−0.367257	−	0.930119i	$-0.619703\pi$
$37$	3.69909	−	6.99902i	0.608127	−	1.15063i	0.975384	−	0.220513i	$-0.0707730\pi$
$38$	−2.33271	−	1.01775i	−0.378415	−	0.165101i
$39$	0.826797	+	0.0619598i	0.132393	+	0.00992151i
$40$	−2.00058	−	5.18020i	−0.316320	−	0.819061i
$41$	−4.67387	+	9.70538i	−0.729935	+	1.51573i	0.122258	+	0.992498i	$0.460987\pi$
$41$	−4.67387	+	9.70538i	−0.729935	+	1.51573i	−0.852193	+	0.523228i	$0.824728\pi$
$42$	0.433834	−	0.185049i	0.0669420	−	0.0285537i
$43$	−12.1330	−	4.24553i	−1.85027	−	0.647437i	−0.990637	−	0.136522i	$-0.956408\pi$
$43$	−12.1330	−	4.24553i	−1.85027	−	0.647437i	−0.859631	−	0.510915i	$-0.829307\pi$
$44$	−2.16199	+	0.162019i	−0.325933	+	0.0244253i
$45$	6.18700	+	2.20283i	0.922303	+	0.328378i
$46$	−1.22352	+	0.834179i	−0.180398	+	0.122993i
$47$	−1.13255	−	1.53455i	−0.165199	−	0.223837i	0.714176	−	0.699966i	$-0.246802\pi$
$47$	−1.13255	−	1.53455i	−0.165199	−	0.223837i	−0.879376	+	0.476129i	$0.842040\pi$
$48$	−0.217454	+	0.217454i	−0.0313868	+	0.0313868i
$49$	−6.97088	−	0.637812i	−0.995840	−	0.0911160i
$50$	−2.71791	+	2.28789i	−0.384370	+	0.323556i
$51$	0.156548	+	0.0235958i	0.0219210	+	0.00330407i
$52$	−4.85481	−	0.918579i	−0.673241	−	0.127384i
$53$	0.557654	+	1.05513i	0.0765996	+	0.144934i	0.919440	−	0.393230i	$-0.128642\pi$
$53$	0.557654	+	1.05513i	0.0765996	+	0.144934i	−0.842841	+	0.538163i	$0.819118\pi$
$54$	0.0790931	+	1.05542i	0.0107632	+	0.143625i
$55$	1.28042	+	2.97893i	0.172652	+	0.401678i
$56$	−6.29430	+	1.88501i	−0.841112	+	0.251895i
$57$	0.848241	−	0.296812i	0.112352	−	0.0393138i
$58$	−0.315829	+	0.137795i	−0.0414704	+	0.0180933i
$59$	0.818329	−	10.9198i	0.106537	−	1.42164i	−0.646123	−	0.763233i	$-0.723611\pi$
$59$	0.818329	−	10.9198i	0.106537	−	1.42164i	0.752660	−	0.658409i	$-0.228770\pi$
$60$	0.753732	+	0.368050i	0.0973064	+	0.0475150i
$61$	−3.36739	−	10.9168i	−0.431149	−	1.39775i	−0.867258	−	0.497858i	$-0.834120\pi$
$61$	−3.36739	−	10.9168i	−0.431149	−	1.39775i	0.436109	−	0.899894i	$-0.356356\pi$
$62$	4.59977	−	0.518269i	0.584171	−	0.0658202i
$63$	3.16590	−	7.09655i	0.398865	−	0.894082i
$64$	−1.32635	+	1.05773i	−0.165793	+	0.132216i
$65$	1.06152	+	7.31282i	0.131666	+	0.907043i
$66$	−0.175824	+	0.189494i	−0.0216425	+	0.0233251i
$67$	−1.31551	−	4.90956i	−0.160716	−	0.599799i	−0.998548	−	0.0538711i	$-0.982844\pi$
$67$	−1.31551	−	4.90956i	−0.160716	−	0.599799i	0.837832	−	0.545928i	$-0.183823\pi$
$68$	−0.911304	−	0.244183i	−0.110512	−	0.0296116i
$69$	0.116353	−	0.509775i	0.0140072	−	0.0613697i
$70$	2.44971	+	3.41599i	0.292796	+	0.408289i
$71$	1.90716	+	8.35583i	0.226339	+	0.991654i	0.952598	+	0.304233i	$0.0984002\pi$
$71$	1.90716	+	8.35583i	0.226339	+	0.991654i	−0.726259	+	0.687421i	$0.758743\pi$
$72$	0.272729	−	7.28883i	0.0321414	−	0.858996i
$73$	0.424040	−	0.574554i	0.0496302	−	0.0672465i	−0.779080	−	0.626925i	$-0.784313\pi$
$73$	0.424040	−	0.574554i	0.0496302	−	0.0672465i	0.828710	+	0.559678i	$0.189075\pi$
$74$	0.838345	+	5.56205i	0.0974556	+	0.646576i
$75$	0.154028	−	1.24497i	0.0177856	−	0.143757i
$76$	−5.22118	+	1.19170i	−0.598910	+	0.136697i
$77$	3.63152	−	1.23731i	0.413850	−	0.141004i
$78$	−0.498817	+	0.313428i	−0.0564799	+	0.0354887i
$79$	8.89287	−	5.13430i	1.00053	−	0.577654i	0.0921221	−	0.995748i	$-0.470635\pi$
$79$	8.89287	−	5.13430i	1.00053	−	0.577654i	0.908404	+	0.418094i	$0.137302\pi$
$80$	−2.31274	−	1.47082i	−0.258572	−	0.164443i
$81$	6.18508	+	5.73892i	0.687231	+	0.637657i
$82$	−1.42296	−	7.52055i	−0.157140	−	0.830506i
$83$	−11.1688	−	1.25843i	−1.22594	−	0.138130i	−0.524845	−	0.851198i	$-0.675877\pi$
$83$	−11.1688	−	1.25843i	−1.22594	−	0.138130i	−0.701095	+	0.713068i	$0.747305\pi$
$84$	0.503286	−	0.855398i	0.0549130	−	0.0933315i
$85$	0.0977768	+	1.40759i	0.0106054	+	0.152675i
$86$	8.72769	−	2.69214i	0.941131	−	0.290300i
$87$	0.0486558	−	0.111520i	0.00521645	−	0.0119562i
$88$	2.72955	−	2.34897i	0.290971	−	0.250401i
$89$	−3.16917	+	8.07490i	−0.335931	+	0.855938i	0.658696	+	0.752410i	$0.271109\pi$
$89$	−3.16917	+	8.07490i	−0.335931	+	0.855938i	−0.994626	+	0.103528i	$0.966987\pi$
$90$	−4.46651	+	1.35113i	−0.470811	+	0.142422i
$91$	8.72395	−	0.581687i	0.914519	−	0.0609774i
$92$	−1.02916	+	2.94117i	−0.107297	+	0.306638i
$93$	−1.06615	+	1.23888i	−0.110554	+	0.128466i
$94$	1.29494	+	0.399437i	0.133563	+	0.0411988i
$95$	4.22424	+	6.80485i	0.433398	+	0.698162i
$96$	0.218294	−	1.44829i	0.0222796	−	0.147815i
$97$	−6.86573	−	6.86573i	−0.697110	−	0.697110i	0.266677	−	0.963786i	$-0.414074\pi$
$97$	−6.86573	−	6.86573i	−0.697110	−	0.697110i	−0.963786	+	0.266677i	$0.914074\pi$
$98$	4.25432	−	2.57659i	0.429752	−	0.260275i
$99$			4.25892i			0.428038i
$100$	−1.74281	+	7.26972i	−0.174281	+	0.726972i
$101$	−4.09220	−	6.00215i	−0.407189	−	0.597237i	0.566793	−	0.823860i	$-0.308184\pi$
$101$	−4.09220	−	6.00215i	−0.407189	−	0.597237i	−0.973982	+	0.226623i	$0.927231\pi$
$102$	−0.0994531	+	0.0525625i	−0.00984732	+	0.00520446i
$103$	−1.63050	−	1.40316i	−0.160658	−	0.138257i	0.568285	−	0.822832i	$-0.307607\pi$
$103$	−1.63050	−	1.40316i	−0.160658	−	0.138257i	−0.728943	+	0.684574i	$0.759988\pi$
$104$	7.39413	−	3.56082i	0.725054	−	0.349168i
$105$	−1.45451	−	0.295857i	−0.141946	−	0.0288726i
$106$	−0.763998	−	0.367922i	−0.0742061	−	0.0357358i
$107$	5.27092	+	12.0811i	0.509559	+	1.16792i	0.961233	+	0.275739i	$0.0889225\pi$
$107$	5.27092	+	12.0811i	0.509559	+	1.16792i	−0.451673	+	0.892183i	$0.649173\pi$
$108$	1.45271	+	1.68808i	0.139787	+	0.162436i
$109$	−15.9067	+	6.24294i	−1.52359	+	0.597965i	−0.971756	−	0.235989i	$-0.924167\pi$
$109$	−15.9067	+	6.24294i	−1.52359	+	0.597965i	−0.551834	+	0.833954i	$0.686072\pi$
$110$	−1.98891	−	1.16279i	−0.189635	−	0.110867i
$111$	−1.55285	−	1.23835i	−0.147390	−	0.117539i
$112$	−1.94713	+	2.59337i	−0.183987	+	0.245051i
$113$	0.241364	−	2.14217i	0.0227056	−	0.201518i	−0.977238	−	0.212146i	$-0.931955\pi$
$113$	0.241364	−	2.14217i	0.0227056	−	0.201518i	0.999944	+	0.0106284i	$0.00338318\pi$
$114$	−0.359700	+	0.527584i	−0.0336890	+	0.0494127i
$115$	4.66013	+	0.0253857i	0.434559	+	0.00236723i
$116$	−0.362541	+	0.627940i	−0.0336611	+	0.0583028i
$117$	−2.51209	+	9.37526i	−0.232243	+	0.866743i
$118$	4.13957	+	6.58809i	0.381078	+	0.606483i
$119$	1.66944	+	0.0137254i	0.153038	+	0.00125821i
$120$	−1.37033	+	0.251556i	−0.125093	+	0.0229638i
$121$	6.52219	−	6.05170i	0.592926	−	0.550155i
$122$	6.53123	+	4.82027i	0.591310	+	0.436406i
$123$	2.17455	+	1.60489i	0.196072	+	0.144708i
$124$	7.14015	−	6.62509i	0.641204	−	0.594951i
$125$	11.1290	−	1.07008i	0.995409	−	0.0957109i
$126$	1.18432	+	5.39284i	0.105508	+	0.480432i
$127$	−1.79446	−	2.85586i	−0.159232	−	0.253417i	0.757574	−	0.652750i	$-0.226385\pi$
$127$	−1.79446	−	2.85586i	−0.159232	−	0.253417i	−0.916806	+	0.399333i	$0.869242\pi$
$128$	−2.70987	+	10.1134i	−0.239521	+	0.893903i
$129$	−1.61253	+	2.79298i	−0.141975	+	0.245908i
$130$	−3.69236	−	3.73281i	−0.323841	−	0.327389i
$131$	0.297993	−	0.437076i	0.0260358	−	0.0381875i	−0.813000	−	0.582263i	$-0.802167\pi$
$131$	0.297993	−	0.437076i	0.0260358	−	0.0381875i	0.839036	+	0.544076i	$0.183120\pi$
$132$	−0.0609029	+	0.540528i	−0.00530091	+	0.0470469i
$133$	8.41473	−	4.35919i	0.729650	−	0.377990i
$134$	2.82356	+	2.25171i	0.243918	+	0.194518i
$135$	1.68107	−	2.87541i	0.144683	−	0.247476i
$136$	1.45874	−	0.572513i	0.125086	−	0.0490926i
$137$	13.0959	+	15.2177i	1.11885	+	1.30013i	0.949216	+	0.314626i	$0.101879\pi$
$137$	13.0959	+	15.2177i	1.11885	+	1.30013i	0.169639	+	0.985506i	$0.445740\pi$
$138$	0.148571	+	0.340528i	0.0126472	+	0.0289877i
$139$	5.96657	+	2.87335i	0.506078	+	0.243714i	0.669459	−	0.742849i	$-0.266526\pi$
$139$	5.96657	+	2.87335i	0.506078	+	0.243714i	−0.163381	+	0.986563i	$0.552240\pi$
$140$	8.41598	+	2.72251i	0.711280	+	0.230094i
$141$	−0.431121	+	0.207617i	−0.0363070	+	0.0174845i
$142$	−4.61588	−	3.97229i	−0.387356	−	0.333347i
$143$	−4.23667	+	2.23915i	−0.354288	+	0.187247i
$144$	−2.02797	−	2.97449i	−0.168998	−	0.247874i
$145$	1.06438	+	0.207404i	0.0883922	+	0.0172240i
$146$			0.507384i			0.0419914i
$147$	−0.482380	+	1.68870i	−0.0397861	+	0.139282i
$148$	8.36943	+	8.36943i	0.687963	+	0.687963i
$149$	−1.13796	+	7.54985i	−0.0932250	+	0.618508i	0.892615	+	0.450820i	$0.148868\pi$
$149$	−1.13796	+	7.54985i	−0.0932250	+	0.618508i	−0.985840	+	0.167688i	$0.946370\pi$
$150$	0.437232	+	0.776730i	0.0356999	+	0.0634197i
$151$	−3.42776	−	1.05732i	−0.278947	−	0.0860439i	0.152125	−	0.988361i	$-0.451388\pi$
$151$	−3.42776	−	1.05732i	−0.278947	−	0.0860439i	−0.431072	+	0.902317i	$0.641865\pi$
$152$	5.80233	−	6.74243i	0.470631	−	0.546883i
$153$	−0.612111	+	1.74931i	−0.0494862	+	0.141424i
$154$	−1.55406	+	2.23961i	−0.125230	+	0.180473i
$155$	−12.8418	−	6.87684i	−1.03148	−	0.552361i
$156$	−0.452893	+	1.15395i	−0.0362604	+	0.0923901i
$157$	−15.7777	+	13.5778i	−1.25920	+	1.08363i	−0.266396	+	0.963864i	$0.585833\pi$
$157$	−15.7777	+	13.5778i	−1.25920	+	1.08363i	−0.992802	+	0.119764i	$0.961786\pi$
$158$	−2.91769	+	6.68741i	−0.232119	+	0.532022i
$159$	0.286120	−	0.0882564i	0.0226908	−	0.00699919i
$160$	13.0222	−	0.904575i	1.02950	−	0.0715129i
$161$	0.457255	−	5.49503i	0.0360367	−	0.433069i
$162$	−5.95739	−	0.671237i	−0.468057	−	0.0527373i
$163$	−1.78812	−	9.45046i	−0.140057	−	0.740217i	−0.980224	−	0.197890i	$-0.936591\pi$
$163$	−1.78812	−	9.45046i	−0.140057	−	0.740217i	0.840168	−	0.542327i	$-0.182457\pi$
$164$	−11.8065	−	10.9548i	−0.921930	−	0.855426i
$165$	0.794083	−	0.176699i	0.0618193	−	0.0137560i
$166$	6.91613	−	3.99303i	0.536796	−	0.309919i
$167$	−10.6091	+	6.66613i	−0.820956	+	0.515841i	−0.875811	−	0.482654i	$-0.839673\pi$
$167$	−10.6091	+	6.66613i	−0.820956	+	0.515841i	0.0548556	+	0.998494i	$0.482530\pi$
$168$	0.171098	+	1.63958i	0.0132005	+	0.126497i
$169$	2.02705	−	0.462661i	0.155927	−	0.0355893i
$170$	−0.649803	−	0.763457i	−0.0498376	−	0.0585545i
$171$	1.56796	+	10.4027i	0.119905	+	0.795517i
$172$	11.4127	−	15.4636i	0.870209	−	1.17909i
$173$	−0.103119	+	2.75591i	−0.00784000	+	0.209528i	0.989874	+	0.141949i	$0.0453370\pi$
$173$	−0.103119	+	2.75591i	−0.00784000	+	0.209528i	−0.997714	+	0.0675790i	$0.978473\pi$
$174$	0.0192375	+	0.0842849i	0.00145839	+	0.00638962i
$175$	−0.241859	−	13.2265i	−0.0182828	−	0.999833i
$176$	0.395507	−	1.73283i	0.0298125	−	0.130617i
$177$	−2.65377	−	0.711076i	−0.199470	−	0.0534477i
$178$	−1.59525	−	5.95354i	−0.119569	−	0.446237i
$179$	1.44978	−	1.56249i	0.108361	−	0.116786i	−0.676542	−	0.736404i	$-0.736522\pi$
$179$	1.44978	−	1.56249i	0.108361	−	0.116786i	0.784903	+	0.619619i	$0.212713\pi$
$180$	−5.87383	+	7.86868i	−0.437809	+	0.586497i
$181$	3.26074	−	2.60035i	0.242369	−	0.193283i	−0.494770	−	0.869024i	$-0.664748\pi$
$181$	3.26074	−	2.60035i	0.242369	−	0.193283i	0.737139	+	0.675741i	$0.236176\pi$
$182$	−4.74200	+	4.01344i	−0.351501	+	0.297496i
$183$	−2.84826	+	0.320921i	−0.210549	+	0.0237232i
$184$	−1.52556	−	4.94576i	−0.112466	−	0.364606i
$185$	7.76722	−	15.9065i	0.571057	−	1.16947i
$186$	0.0867876	−	1.15810i	0.00636357	−	0.0849160i
$187$	−0.838663	+	0.365905i	−0.0613291	+	0.0267576i
$188$	2.69155	−	0.941816i	0.196302	−	0.0686890i
$189$	−3.23785	−	2.24674i	−0.235519	−	0.163426i
$190$	−5.28614	−	2.10796i	−0.383497	−	0.152927i
$191$	−1.14428	−	15.2694i	−0.0827974	−	1.10485i	−0.871603	−	0.490212i	$-0.836919\pi$
$191$	−1.14428	−	15.2694i	−0.0827974	−	1.10485i	0.788806	−	0.614642i	$-0.210700\pi$
$192$	0.198883	+	0.376305i	0.0143531	+	0.0271575i
$193$	−18.8456	−	3.56578i	−1.35654	−	0.256670i	−0.543757	−	0.839243i	$-0.682999\pi$
$193$	−18.8456	−	3.56578i	−1.35654	−	0.256670i	−0.812779	+	0.582572i	$0.802046\pi$
$194$	6.82195	+	1.02824i	0.489788	+	0.0738236i
$195$	1.85226	+	0.0794127i	0.132643	+	0.00568686i
$196$	3.98333	−	9.67833i	0.284523	−	0.691309i
$197$	13.1257	−	13.1257i	0.935165	−	0.935165i	−0.0628573	−	0.998023i	$-0.520021\pi$
$197$	13.1257	−	13.1257i	0.935165	−	0.935165i	0.998023	+	0.0628573i	$0.0200213\pi$
$198$	−1.79697	−	2.43480i	−0.127705	−	0.173034i
$199$	−0.478137	+	0.325988i	−0.0338942	+	0.0231087i	−0.580149	−	0.814511i	$-0.697006\pi$
$199$	−0.478137	+	0.325988i	−0.0338942	+	0.0231087i	0.546254	+	0.837619i	$0.316053\pi$
$200$	−4.84121	−	11.4345i	−0.342325	−	0.808538i
$201$	−1.27166	+	0.0952976i	−0.0896958	+	0.00672177i
$202$	4.87197	+	1.70478i	0.342791	+	0.119948i
$203$	0.342264	−	1.23659i	0.0240222	−	0.0867916i
$204$	−0.102702	+	0.213263i	−0.00719060	+	0.0149314i
$205$	−9.75243	+	22.0247i	−0.681139	+	1.53827i
$206$	1.52418	+	0.114222i	0.106195	+	0.00795819i
$207$	5.61039	+	2.44779i	0.389949	+	0.170133i
$208$	1.89273	−	3.58123i	0.131238	−	0.248313i
$209$	−3.23841	+	4.06083i	−0.224005	+	0.280894i
$210$	0.956367	−	0.444562i	0.0659956	−	0.0306777i
$211$	9.60914	+	12.0495i	0.661520	+	0.829520i	0.993508	−	0.113764i	$-0.0362906\pi$
$211$	9.60914	+	12.0495i	0.661520	+	0.829520i	−0.331988	+	0.943284i	$0.607719\pi$
$212$	−1.75324	+	0.331731i	−0.120413	+	0.0227834i
$213$	2.14882	−	0.0804032i	0.147235	−	0.00550914i
$214$	−8.11072	−	4.68272i	−0.554437	−	0.320104i
$215$	−27.4197	−	8.62171i	−1.87001	−	0.587996i
$216$	−3.60645	−	0.823149i	−0.245388	−	0.0560082i
$217$	−9.28984	+	14.5183i	−0.630635	+	0.985570i
$218$	6.45971	−	10.2806i	0.437507	−	0.696288i
$219$	−0.121859	−	0.131333i	−0.00823448	−	0.00887466i
$220$	−4.82032	+	0.516545i	−0.324986	+	0.0348254i
$221$	−2.06199	+	0.310795i	−0.138705	+	0.0209064i
$222$	1.41025	+	0.0527679i	0.0946499	+	0.00354155i
$223$	−2.57069	−	1.61527i	−0.172146	−	0.108167i	0.443203	−	0.896421i	$-0.353842\pi$
$223$	−2.57069	−	1.61527i	−0.172146	−	0.108167i	−0.615349	+	0.788255i	$0.710985\pi$
$224$	0.126980	−	15.4447i	0.00848418	−	1.03194i
$225$	13.9849	+	4.48118i	0.932323	+	0.298745i
$226$	0.765857	+	1.32650i	0.0509440	+	0.0882376i
$227$	−19.8142	+	5.30919i	−1.31511	+	0.352384i	−0.847145	−	0.531362i	$-0.821681\pi$
$227$	−19.8142	+	5.30919i	−1.31511	+	0.352384i	−0.467968	+	0.883745i	$0.655014\pi$
$228$	0.0502403	+	1.34270i	0.00332725	+	0.0889226i
$229$	6.48884	+	4.42401i	0.428794	+	0.292347i	0.758422	−	0.651764i	$-0.225971\pi$
$229$	6.48884	+	4.42401i	0.428794	+	0.292347i	−0.329627	+	0.944111i	$0.606923\pi$
$230$	−2.67488	+	1.95173i	−0.176376	+	0.128693i
$231$	−0.135631	−	0.952948i	−0.00892387	−	0.0626994i
$232$	−0.134845	−	1.19678i	−0.00885301	−	0.0785727i
$233$	−1.76765	−	0.934232i	−0.115803	−	0.0612036i	0.408364	−	0.912819i	$-0.366099\pi$
$233$	−1.76765	−	0.934232i	−0.115803	−	0.0612036i	−0.524167	+	0.851616i	$0.675623\pi$
$234$	−2.51955	−	6.41970i	−0.164708	−	0.419669i
$235$	−2.64079	−	3.34870i	−0.172266	−	0.218445i
$236$	15.2407	+	5.98154i	0.992087	+	0.389365i
$237$	−0.850902	−	2.43174i	−0.0552720	−	0.157958i
$238$	−0.960202	+	0.696540i	−0.0622406	+	0.0451500i
$239$	2.58182	+	5.36120i	0.167004	+	0.346787i	0.967628	−	0.252379i	$-0.0812131\pi$
$239$	2.58182	+	5.36120i	0.167004	+	0.346787i	−0.800625	+	0.599166i	$0.795499\pi$
$240$	−0.470460	+	0.501528i	−0.0303680	+	0.0323735i
$241$	−6.61001	+	21.4291i	−0.425788	+	1.38037i	0.447986	+	0.894041i	$0.352141\pi$
$241$	−6.61001	+	21.4291i	−0.425788	+	1.38037i	−0.873774	+	0.486332i	$0.838335\pi$
$242$	−1.17530	+	6.21163i	−0.0755513	+	0.399298i
$243$	5.29873	−	3.91064i	0.339914	−	0.250868i
$244$	17.0810			1.09350
$245$	−15.6250	−	0.927492i	−0.998243	−	0.0592553i
$246$	−1.92032			−0.122435
$247$	−9.52402	+	7.02905i	−0.605999	+	0.447248i
$248$	−3.00778	+	15.8965i	−0.190994	+	1.00943i
$249$	−0.831182	+	2.69463i	−0.0526740	+	0.170765i
$250$	−5.91089	+	5.30742i	−0.373838	+	0.335670i
$251$	−10.4208	−	21.6390i	−0.657755	−	1.36584i	−0.916554	−	0.399911i	$-0.869041\pi$
$251$	−10.4208	−	21.6390i	−0.657755	−	1.36584i	0.258799	−	0.965931i	$-0.416673\pi$
$252$	8.74375	+	7.65062i	0.550805	+	0.481944i
$253$	0.998133	+	2.85250i	0.0627521	+	0.179335i
$254$	2.23085	+	0.875545i	0.139976	+	0.0549366i
$255$	0.351558	+	0.0415517i	0.0220154	+	0.00260207i
$256$	−3.95748	−	10.0835i	−0.247343	−	0.630219i
$257$	−9.10975	−	4.81464i	−0.568250	−	0.300329i	0.158357	−	0.987382i	$-0.449380\pi$
$257$	−9.10975	−	4.81464i	−0.568250	−	0.300329i	−0.726607	+	0.687053i	$0.758904\pi$
$258$	−0.256568	−	2.27711i	−0.0159732	−	0.141766i
$259$	−18.0521	−	10.6212i	−1.12170	−	0.659969i
$260$	−10.9158	−	1.70615i	−0.676966	−	0.105811i
$261$	1.17685	+	0.802365i	0.0728454	+	0.0496652i
$262$	0.0140542	+	0.375605i	0.000868269	+	0.0232050i
$263$	12.1784	−	3.26318i	0.750950	−	0.201217i	0.137011	−	0.990570i	$-0.456251\pi$
$263$	12.1784	−	3.26318i	0.750950	−	0.201217i	0.613940	+	0.789353i	$0.289584\pi$
$264$	−0.451746	−	0.782448i	−0.0278031	−	0.0481563i
$265$	1.32169	+	2.31831i	0.0811907	+	0.142412i
$266$	−2.97138	+	6.04254i	−0.182187	+	0.370492i
$267$	1.84279	+	1.15790i	0.112777	+	0.0708624i
$268$	7.59412	+	0.284152i	0.463885	+	0.0173573i
$269$	20.0988	−	3.02940i	1.22544	−	0.184706i	0.495741	−	0.868471i	$-0.334897\pi$
$269$	20.0988	−	3.02940i	1.22544	−	0.184706i	0.729702	+	0.683765i	$0.239659\pi$
$270$	0.252162	+	2.35314i	0.0153461	+	0.143208i
$271$	13.9873	+	15.0747i	0.849669	+	0.915725i	0.997309	−	0.0733158i	$-0.0233581\pi$
$271$	13.9873	+	15.0747i	0.849669	+	0.915725i	−0.147640	+	0.989041i	$0.547168\pi$
$272$	0.411501	−	0.654900i	0.0249509	−	0.0397091i
$273$	0.263522	−	2.17775i	0.0159491	−	0.131803i
$274$	−13.9076	−	3.17432i	−0.840189	−	0.191768i
$275$	3.07445	+	6.56621i	0.185396	+	0.395957i
$276$	0.677048	+	0.390894i	0.0407535	+	0.0235290i
$277$	−3.43127	+	0.128389i	−0.206165	+	0.00771416i	−0.140274	−	0.990113i	$-0.544798\pi$
$277$	−3.43127	+	0.128389i	−0.206165	+	0.00771416i	−0.0658909	+	0.997827i	$0.520989\pi$
$278$	−4.62340	+	0.874795i	−0.277293	+	0.0524667i
$279$	−11.9298	−	14.9594i	−0.714216	−	0.895598i
$280$	−13.9326	+	4.66249i	−0.832635	+	0.278637i
$281$	15.1322	−	18.9751i	0.902710	−	1.13196i	−0.0880205	−	0.996119i	$-0.528054\pi$
$281$	15.1322	−	18.9751i	0.902710	−	1.13196i	0.990730	−	0.135844i	$-0.0433745\pi$
$282$	0.158870	−	0.300596i	0.00946055	−	0.0179002i
$283$	18.8383	+	8.21906i	1.11982	+	0.488573i	0.876514	−	0.481377i	$-0.159863\pi$
$283$	18.8383	+	8.21906i	1.11982	+	0.488573i	0.243306	+	0.969949i	$0.421768\pi$
$284$	−12.7786	−	0.957623i	−0.758270	−	0.0568245i
$285$	1.87455	−	0.723949i	0.111039	−	0.0428830i
$286$	1.47732	−	3.06768i	0.0873556	−	0.181396i
$287$	25.0874	+	13.5241i	1.48086	+	0.798301i
$288$	16.1836	+	5.66290i	0.953630	+	0.333690i
$289$	16.5554	−	1.24066i	0.973847	−	0.0729798i
$290$	−0.696011	+	0.330523i	−0.0408712	+	0.0194090i
$291$	−2.01277	+	1.37228i	−0.117991	+	0.0804447i
$292$	0.634000	+	0.859040i	0.0371021	+	0.0502715i
$293$	−3.00346	+	3.00346i	−0.175464	+	0.175464i	−0.789375	−	0.613911i	$-0.789595\pi$
$293$	−3.00346	+	3.00346i	−0.175464	+	0.175464i	0.613911	+	0.789375i	$0.289595\pi$
$294$	−0.436738	−	1.16895i	−0.0254711	−	0.0681745i
$295$	1.04884	−	24.4635i	0.0610656	−	1.42432i
$296$	−19.4402	−	2.93013i	−1.12994	−	0.170311i
$297$	2.12231	+	0.401562i	0.123149	+	0.0233010i
$298$	−2.53494	−	4.79634i	−0.146845	−	0.277844i
$299$	0.514686	+	6.86801i	0.0297651	+	0.397187i
$300$	1.71083	+	0.768720i	0.0987747	+	0.0443821i
$301$	−12.6849	+	31.5553i	−0.731146	+	1.81882i
$302$	2.40575	−	0.841808i	0.138435	−	0.0484406i
$303$	−1.67052	+	0.728839i	−0.0959686	+	0.0418707i
$304$	0.328099	−	4.37817i	0.0188178	−	0.251106i
$305$	−8.30571	−	24.1577i	−0.475584	−	1.38326i
$306$	−0.388146	−	1.25834i	−0.0221888	−	0.0719345i
$307$	−29.2836	+	3.29947i	−1.67130	+	0.188311i	−0.896239	−	0.443572i	$-0.853711\pi$
$307$	−29.2836	+	3.29947i	−1.67130	+	0.188311i	−0.775064	+	0.631882i	$0.782283\pi$
$308$	0.167348	+	5.73369i	0.00953556	+	0.326708i
$309$	−0.421957	+	0.336499i	−0.0240043	+	0.0191428i
$310$	10.2431	−	1.48688i	0.581770	−	0.0844492i
$311$	19.7096	−	21.2419i	1.11763	−	1.20452i	0.140905	−	0.990023i	$-0.454999\pi$
$311$	19.7096	−	21.2419i	1.11763	−	1.20452i	0.976725	−	0.214495i	$-0.0688107\pi$
$312$	−0.532918	−	1.98888i	−0.0301705	−	0.112598i
$313$	−8.11558	−	2.17456i	−0.458720	−	0.122914i	0.0220569	−	0.999757i	$-0.492978\pi$
$313$	−8.11558	−	2.17456i	−0.458720	−	0.122914i	−0.480776	+	0.876843i	$0.659645\pi$
$314$	3.29114	−	14.4194i	0.185730	−	0.813736i
$315$	6.56860	−	16.0864i	0.370098	−	0.906368i
$316$	3.41637	+	14.9681i	0.192186	+	0.842020i
$317$	0.0777747	−	2.07857i	0.00436826	−	0.116744i	−0.995410	−	0.0956995i	$-0.969491\pi$
$317$	0.0777747	−	2.07857i	0.00436826	−	0.116744i	0.999779	−	0.0210448i	$-0.00669925\pi$
$318$	−0.126335	+	0.171178i	−0.00708453	+	0.00959920i
$319$	0.104810	+	0.695369i	0.00586823	+	0.0389332i
$320$	−2.88873	+	2.45869i	−0.161485	+	0.137445i
$321$	3.22406	−	0.735871i	0.179950	−	0.0410723i
$322$	2.05710	+	3.33440i	0.114638	+	0.185819i
$323$	−1.91378	+	1.20251i	−0.106486	+	0.0669095i
$324$	−10.9251	+	6.30758i	−0.606948	+	0.350421i
$325$	2.89482	+	16.2678i	0.160576	+	0.902374i
$326$	5.00968	+	4.64831i	0.277461	+	0.257446i
$327$	0.797047	+	4.21250i	0.0440768	+	0.232952i
$328$	26.5836	+	2.99525i	1.46783	+	0.165385i
$329$	−4.19247	+	2.80817i	−0.231138	+	0.154819i
$330$	−0.379418	+	0.436065i	−0.0208863	+	0.0240046i
$331$	−11.8730	+	3.66234i	−0.652600	+	0.201301i	−0.603338	−	0.797485i	$-0.706163\pi$
$331$	−11.8730	+	3.66234i	−0.652600	+	0.201301i	−0.0492620	+	0.998786i	$0.515687\pi$
$332$	6.72005	−	15.4025i	0.368811	−	0.845323i
$333$	17.6235	−	15.1663i	0.965764	−	0.831107i
$334$	3.25251	−	8.28727i	0.177970	−	0.453459i
$335$	−3.29080	−	10.8785i	−0.179795	−	0.594358i
$336$	0.548493	+	0.600969i	0.0299227	+	0.0327855i
$337$	3.24612	−	9.27688i	0.176827	−	0.505344i	−0.821022	−	0.570897i	$-0.806596\pi$
$337$	3.24612	−	9.27688i	0.176827	−	0.505344i	0.997849	+	0.0655534i	$0.0208813\pi$
$338$	−0.963642	+	1.11977i	−0.0524152	+	0.0609076i
$339$	−0.516825	−	0.159419i	−0.0280701	−	0.00865847i
$340$	−2.05414	−	0.480632i	−0.111401	−	0.0260659i
$341$	1.40795	−	9.34115i	0.0762449	−	0.505852i
$342$	−5.28561	−	5.28561i	−0.285813	−	0.285813i
$343$	−2.52685	+	18.3471i	−0.136437	+	0.990649i
$344$			31.9227i			1.72116i
$345$	0.223624	−	1.14762i	0.0120395	−	0.0617859i
$346$	−1.10385	−	1.61905i	−0.0593433	−	0.0870406i
$347$	−17.4620	+	9.22892i	−0.937408	+	0.495435i	−0.864906	−	0.501934i	$-0.832622\pi$
$347$	−17.4620	+	9.22892i	−0.937408	+	0.495435i	−0.0725019	+	0.997368i	$0.523098\pi$
$348$	0.137888	+	0.118663i	0.00739159	+	0.00636098i
$349$	2.82409	−	1.36001i	0.151170	−	0.0727996i	−0.356769	−	0.934193i	$-0.616122\pi$
$349$	2.82409	−	1.36001i	0.151170	−	0.0727996i	0.507939	+	0.861393i	$0.330407\pi$
$350$	5.71894	+	7.45949i	0.305690	+	0.398726i
$351$	4.43502	+	2.13579i	0.236724	+	0.114000i
$352$	3.38514	+	7.75883i	0.180429	+	0.413547i
$353$	19.7181	+	22.9128i	1.04949	+	1.21953i	0.974977	+	0.222305i	$0.0713582\pi$
$353$	19.7181	+	22.9128i	1.04949	+	1.21953i	0.0745096	+	0.997220i	$0.476261\pi$
$354$	1.81717	−	0.713186i	0.0965814	−	0.0379054i
$355$	4.85928	+	18.5384i	0.257904	+	0.983917i
$356$	−10.1401	−	8.08646i	−0.537424	−	0.428581i
$357$	0.0812527	−	0.410908i	0.00430035	−	0.0217476i
$358$	−0.169569	+	1.50497i	−0.00896200	+	0.0795400i
$359$	12.7737	−	18.7356i	0.674171	−	0.988828i	−0.324900	−	0.945748i	$-0.605331\pi$
$359$	12.7737	−	18.7356i	0.674171	−	0.988828i	0.999072	−	0.0430793i	$-0.0137168\pi$
$360$	0.0888446	−	16.3095i	0.00468252	−	0.859585i
$361$	3.08499	−	5.34335i	0.162368	−	0.281229i
$362$	−0.766980	+	2.86241i	−0.0403116	+	0.150445i
$363$	−1.18764	−	1.89011i	−0.0623347	−	0.0992052i
$364$	−3.01359	+	12.7204i	−0.157955	+	0.666731i
$365$	0.906655	−	1.31438i	0.0474565	−	0.0687977i
$366$	1.49292	−	1.38523i	0.0780364	−	0.0724072i
$367$	24.7375	+	18.2571i	1.29129	+	0.953015i	0.999993	−	0.00361841i	$-0.00115178\pi$
$367$	24.7375	+	18.2571i	1.29129	+	0.953015i	0.291296	+	0.956633i	$0.405914\pi$
$368$	−2.05539	−	1.51694i	−0.107144	−	0.0790762i
$369$	−23.1926	+	21.5196i	−1.20736	+	1.12026i
$370$	2.27097	+	12.3709i	0.118062	+	0.643132i
$371$	2.85600	−	1.34656i	0.148276	−	0.0699101i
$372$	−1.30016	−	2.06920i	−0.0674103	−	0.107283i
$373$	−1.49353	+	5.57392i	−0.0773319	+	0.288607i	−0.993752	−	0.111611i	$-0.964399\pi$
$373$	−1.49353	+	5.57392i	−0.0773319	+	0.288607i	0.916420	+	0.400218i	$0.131066\pi$
$374$	0.325073	−	0.563042i	0.0168091	−	0.0291142i
$375$	0.255305	−	2.79342i	0.0131839	−	0.144251i
$376$	−2.66813	+	3.91343i	−0.137598	+	0.201820i
$377$	−0.179437	+	1.59255i	−0.00924150	+	0.0820206i
$378$	2.79903	−	0.0816947i	0.143966	−	0.00420192i
$379$	4.91963	+	3.92327i	0.252704	+	0.201525i	0.741646	−	0.670791i	$-0.234045\pi$
$379$	4.91963	+	3.92327i	0.252704	+	0.201525i	−0.488942	+	0.872317i	$0.662617\pi$
$380$	−11.5838	+	3.03634i	−0.594238	+	0.155761i
$381$	−0.787722	+	0.309158i	−0.0403562	+	0.0158387i
$382$	7.09678	+	8.24661i	0.363103	+	0.421933i
$383$	9.18104	+	21.0432i	0.469129	+	1.07526i	0.976887	+	0.213756i	$0.0685696\pi$
$383$	9.18104	+	21.0432i	0.469129	+	1.07526i	−0.507758	+	0.861500i	$0.669526\pi$
$384$	2.36673	+	1.13976i	0.120777	+	0.0581630i
$385$	8.02779	−	3.02471i	0.409134	−	0.154154i
$386$	12.2784	−	5.91298i	0.624955	−	0.300963i
$387$	−28.6164	−	24.6264i	−1.45465	−	1.25183i
$388$	12.8349	−	6.78345i	0.651594	−	0.344378i
$389$	16.5604	+	24.2896i	0.839644	+	1.23153i	0.970733	+	0.240161i	$0.0772004\pi$
$389$	16.5604	+	24.2896i	0.839644	+	1.23153i	−0.131089	+	0.991371i	$0.541847\pi$
$390$	−1.09243	+	0.736121i	−0.0553173	+	0.0372750i
$391$			1.31509i			0.0665071i
$392$	4.22259	+	16.8633i	0.213273	+	0.851724i
$393$	−0.0938476	−	0.0938476i	−0.00473398	−	0.00473398i
$394$	−1.96576	+	13.0420i	−0.0990336	+	0.657045i
$395$	19.5081	−	12.1101i	0.981561	−	0.609323i
$396$	−6.08480	−	1.87691i	−0.305773	−	0.0943183i
$397$	10.8892	−	12.6535i	0.546515	−	0.635062i	−0.414997	−	0.909823i	$-0.636218\pi$
$397$	10.8892	−	12.6535i	0.546515	−	0.635062i	0.961513	+	0.274760i	$0.0885985\pi$
$398$	0.135804	−	0.388106i	0.00680724	−	0.0194540i
$399$	−0.682125	−	2.27771i	−0.0341490	−	0.114028i
$400$	−5.27387	−	3.12197i	−0.263694	−	0.156099i
$401$	−3.50009	+	8.91808i	−0.174786	+	0.445348i	−0.991242	−	0.132061i	$-0.957841\pi$
$401$	−3.50009	+	8.91808i	−0.174786	+	0.445348i	0.816456	+	0.577408i	$0.195936\pi$
$402$	0.686790	−	0.591031i	0.0342540	−	0.0294779i
$403$	8.60916	−	19.7324i	0.428853	−	0.982941i
$404$	10.3788	−	3.20144i	0.516365	−	0.159278i
$405$	14.2332	+	12.3842i	0.707252	+	0.615377i
$406$	0.326083	+	0.851362i	0.0161832	+	0.0422524i
$407$	11.4071	+	1.28528i	0.565431	+	0.0637088i
$408$	−0.0730938	−	0.386310i	−0.00361868	−	0.0191252i
$409$	−10.9489	−	10.1591i	−0.541388	−	0.502335i	0.361405	−	0.932409i	$-0.382297\pi$
$409$	−10.9489	−	10.1591i	−0.541388	−	0.502335i	−0.902794	+	0.430074i	$0.858488\pi$
$410$	−3.71746	−	16.7062i	−0.183592	−	0.825062i
$411$	4.36227	−	2.51856i	0.215175	−	0.124231i
$412$	2.72328	−	1.71115i	0.134166	−	0.0843022i
$413$	−28.7624	−	3.48044i	−1.41530	−	0.171261i
$414$	−4.24022	+	0.967803i	−0.208395	+	0.0475649i
$415$	−25.0514	−	2.01463i	−1.22973	−	0.0988945i
$416$	2.87530	+	19.0764i	0.140973	+	0.935296i
$417$	0.986636	−	1.33684i	0.0483158	−	0.0654656i
$418$	0.137993	−	3.68793i	0.00674944	−	0.180383i
$419$	−0.0395290	−	0.173188i	−0.00193112	−	0.00846078i	0.973953	−	0.226749i	$-0.0728098\pi$
$419$	−0.0395290	−	0.173188i	−0.00193112	−	0.00846078i	−0.975884	+	0.218288i	$0.929953\pi$
$420$	1.06370	−	1.94770i	0.0519033	−	0.0950382i
$421$	6.82383	−	29.8971i	0.332573	−	1.45710i	−0.481557	−	0.876415i	$-0.659928\pi$
$421$	6.82383	−	29.8971i	0.332573	−	1.45710i	0.814130	−	0.580683i	$-0.197214\pi$
$422$	−10.5775	−	2.83424i	−0.514905	−	0.137968i
$423$	−1.44981	−	5.41076i	−0.0704921	−	0.263080i
$424$	2.01589	−	2.17261i	0.0979002	−	0.105511i
$425$	0.319077	+	3.13888i	0.0154775	+	0.152258i
$426$	−1.19454	+	0.952617i	−0.0578758	+	0.0461544i
$427$	−29.2594	+	7.58277i	−1.41596	+	0.366956i
$428$	−19.5833	+	2.20651i	−0.946596	+	0.106656i
$429$	0.354376	+	1.14886i	0.0171094	+	0.0554674i
$430$	19.3134	−	6.64019i	0.931376	−	0.320219i
$431$	−2.15854	+	28.8037i	−0.103973	+	1.38742i	0.664378	+	0.747396i	$0.268696\pi$
$431$	−2.15854	+	28.8037i	−0.103973	+	1.38742i	−0.768351	+	0.640028i	$0.778923\pi$
$432$	−1.67346	+	0.730123i	−0.0805144	+	0.0351281i
$433$	2.42599	−	0.848890i	0.116586	−	0.0407950i	−0.271356	−	0.962479i	$-0.587472\pi$
$433$	2.42599	−	0.848890i	0.116586	−	0.0407950i	0.387941	+	0.921684i	$0.373186\pi$
$434$	−0.814774	−	12.2197i	−0.0391104	−	0.586565i
$435$	0.100776	−	0.252716i	0.00483182	−	0.0121168i
$436$	−1.90927	−	25.4775i	−0.0914377	−	1.22015i
$437$	3.48819	+	6.59997i	0.166863	+	0.315719i
$438$	0.125079	+	0.0236663i	0.00597653	+	0.00113082i
$439$	0.425907	+	0.0641951i	0.0203274	+	0.00306386i	0.159198	−	0.987247i	$-0.449109\pi$
$439$	0.425907	+	0.0641951i	0.0203274	+	0.00306386i	−0.138871	+	0.990311i	$0.544347\pi$
$440$	5.93254	−	5.44475i	0.282823	−	0.259568i
$441$	−18.3742	−	9.22373i	−0.874961	−	0.439225i
$442$	1.04769	−	1.04769i	0.0498338	−	0.0498338i
$443$	−14.4548	−	19.5855i	−0.686766	−	0.930535i	0.313050	−	0.949737i	$-0.398649\pi$
$443$	−14.4548	−	19.5855i	−0.686766	−	0.930535i	−0.999816	+	0.0192019i	$0.993887\pi$
$444$	2.45360	−	1.67283i	0.116443	−	0.0793892i
$445$	−6.50602	+	18.2732i	−0.308415	+	0.866233i
$446$	2.15118	−	0.161209i	0.101861	−	0.00763345i
$447$	1.80810	+	0.632680i	0.0855200	+	0.0299247i
$448$	2.63553	+	3.63316i	0.124517	+	0.171651i
$449$	−6.28620	+	13.0534i	−0.296664	+	0.616030i	−0.995015	−	0.0997260i	$-0.968203\pi$
$449$	−6.28620	+	13.0534i	−0.296664	+	0.616030i	0.698351	+	0.715756i	$0.253918\pi$
$450$	−9.88580	+	3.33875i	−0.466021	+	0.157390i
$451$	−15.5767	−	1.16731i	−0.733477	−	0.0549665i
$452$	2.95418	+	1.28890i	0.138953	+	0.0606245i
$453$	−0.420534	+	0.795688i	−0.0197584	+	0.0373847i
$454$	9.08754	−	11.3954i	0.426500	−	0.534814i
$455$	19.4558	−	1.92323i	0.912104	−	0.0901625i
$456$	−1.39149	−	1.74487i	−0.0651624	−	0.0817111i
$457$	37.6181	−	7.11774i	1.75970	−	0.332954i	0.797095	−	0.603854i	$-0.206369\pi$
$457$	37.6181	−	7.11774i	1.75970	−	0.332954i	0.962607	+	0.270900i	$0.0873213\pi$
$458$	−5.57625	+	0.208649i	−0.260561	+	0.00974951i
$459$	0.814003	+	0.469965i	0.0379944	+	0.0219361i
$460$	−2.08999	+	6.64682i	−0.0974463	+	0.309909i
$461$	19.2541	+	4.39463i	0.896755	+	0.204678i	0.645969	−	0.763364i	$-0.276454\pi$
$461$	19.2541	+	4.39463i	0.896755	+	0.204678i	0.250786	+	0.968042i	$0.419311\pi$
$462$	0.479616	+	0.487568i	0.0223138	+	0.0226837i
$463$	0.770658	−	1.22649i	0.0358155	−	0.0570001i	−0.828337	−	0.560231i	$-0.810713\pi$
$463$	0.770658	−	1.22649i	0.0358155	−	0.0570001i	0.864152	+	0.503231i	$0.167855\pi$
$464$	−0.404315	−	0.435748i	−0.0187699	−	0.0202291i
$465$	−2.29426	+	2.84497i	−0.106394	+	0.131932i
$466$	1.40474	−	0.211730i	0.0650732	−	0.00980820i
$467$	−7.65142	−	0.286296i	−0.354066	−	0.0132482i	−0.140233	−	0.990119i	$-0.544785\pi$
$467$	−7.65142	−	0.286296i	−0.354066	−	0.0132482i	−0.213833	+	0.976870i	$0.568595\pi$
$468$	−12.2875	−	7.72075i	−0.567990	−	0.356892i
$469$	−13.1347	+	2.88451i	−0.606504	+	0.133194i
$470$	2.92264	+	0.800208i	0.134811	+	0.0369108i
$471$	2.61125	+	4.52281i	0.120320	+	0.208400i
$472$	−26.2679	+	7.03847i	−1.20908	+	0.323972i
$473$	−0.696960	−	18.6267i	−0.0320463	−	0.856455i
$474$	1.51248	+	1.03119i	0.0694704	+	0.0473641i
$475$	9.92698	+	14.9066i	0.455481	+	0.683960i
$476$	−0.755335	+	2.37911i	−0.0346207	+	0.109046i
$477$	0.392455	+	3.48313i	0.0179693	+	0.159482i
$478$	−3.73806	−	1.97562i	−0.170975	−	0.0903628i
$479$	−2.01517	−	5.13456i	−0.0920753	−	0.234604i	0.877416	−	0.479731i	$-0.159266\pi$
$479$	−2.01517	−	5.13456i	−0.0920753	−	0.234604i	−0.969491	+	0.245127i	$0.921170\pi$
$480$	0.384412	−	3.25241i	0.0175459	−	0.148452i
$481$	24.3527	+	9.55772i	1.11039	+	0.435795i
$482$	−5.26268	−	15.0399i	−0.239708	−	0.685047i
$483$	−1.33330	−	0.369030i	−0.0606671	−	0.0167915i
$484$	5.77184	+	11.9853i	0.262356	+	0.544788i
$485$	−15.8349	−	14.8539i	−0.719024	−	0.674483i
$486$	−1.37924	+	4.47138i	−0.0625635	+	0.202826i
$487$	2.43253	−	12.8562i	0.110228	−	0.582572i	−0.883283	−	0.468840i	$-0.844672\pi$
$487$	2.43253	−	12.8562i	0.110228	−	0.582572i	0.993512	−	0.113731i	$-0.0362803\pi$
$488$	−22.8276	+	16.8475i	−1.03336	+	0.762651i
$489$	−2.41311			−0.109125
$490$	9.32404	−	6.06239i	0.421217	−	0.273871i
$491$	6.16835			0.278374			0.139187	−	0.990266i	$-0.455551\pi$
$491$	6.16835			0.278374			0.139187	+	0.990266i	$0.455551\pi$
$492$	−3.25126	+	2.39954i	−0.146578	+	0.108179i
$493$	−0.0568917	+	0.300680i	−0.00256227	+	0.0135419i
$494$	2.47906	−	8.03693i	0.111538	−	0.361598i
$495$	0.304240	+	9.51838i	0.0136746	+	0.427820i
$496$	3.46465	+	7.19441i	0.155567	+	0.323039i
$497$	22.3146	−	4.03241i	1.00094	−	0.180878i
$498$	−0.661760	−	1.89120i	−0.0296542	−	0.0847468i
$499$	31.2785	+	12.2759i	1.40022	+	0.549544i	0.940887	−	0.338722i	$-0.109995\pi$
$499$	31.2785	+	12.2759i	1.40022	+	0.549544i	0.459329	+	0.888266i	$0.348090\pi$
$500$	−3.37572	+	16.3718i	−0.150967	+	0.732169i
$501$	1.14847	+	2.92627i	0.0513101	+	0.130736i
$502$	15.0876	+	7.97405i	0.673395	+	0.355899i
$503$	−0.0959737	−	0.851790i	−0.00427926	−	0.0379794i	0.991391	−	0.130934i	$-0.0417975\pi$
$503$	−0.0959737	−	0.851790i	−0.00427926	−	0.0379794i	−0.995670	+	0.0929543i	$0.970369\pi$
$504$	−19.2314	−	1.60030i	−0.856637	−	0.0712829i
$505$	−9.57453	−	13.1220i	−0.426061	−	0.583923i
$506$	−1.77418	−	1.20962i	−0.0788719	−	0.0537740i
$507$	−0.0195051	−	0.521285i	−0.000866252	−	0.0231511i
$508$	4.87104	−	1.30519i	0.216117	−	0.0579084i
$509$	9.20457	+	15.9428i	0.407985	+	0.706651i	0.994664	−	0.103169i	$-0.0328982\pi$
$509$	9.20457	+	15.9428i	0.407985	+	0.706651i	−0.586679	+	0.809820i	$0.699565\pi$
$510$	−0.218515	+	0.124578i	−0.00967603	+	0.00551640i
$511$	−1.46738	−	1.19006i	−0.0649131	−	0.0526453i
$512$	−11.2136	−	7.04598i	−0.495576	−	0.311391i
$513$	5.33173	+	0.199499i	0.235402	+	0.00880810i
$514$	7.23943	−	1.09117i	0.319317	−	0.0481293i
$515$	−3.74428	−	3.01948i	−0.164993	−	0.133054i
$516$	−3.27974	−	3.53472i	−0.144382	−	0.155607i
$517$	1.47139	−	2.34171i	0.0647118	−	0.102988i
$518$	14.8017	−	1.54462i	0.650347	−	0.0678668i
$519$	0.674573	+	0.153967i	0.0296105	+	0.00675840i
$520$	16.2710	−	8.48639i	0.713529	−	0.372153i
$521$	−20.7792	−	11.9969i	−0.910353	−	0.525592i	−0.0298081	−	0.999556i	$-0.509490\pi$
$521$	−20.7792	−	11.9969i	−0.910353	−	0.525592i	−0.880545	+	0.473963i	$0.842823\pi$
$522$	−1.01134	+	0.0378417i	−0.0442652	+	0.00165629i
$523$	−28.8196	+	5.45296i	−1.26019	+	0.238441i	−0.772748	−	0.634713i	$-0.781118\pi$
$523$	−28.8196	+	5.45296i	−1.26019	+	0.238441i	−0.487445	+	0.873154i	$0.662071\pi$
$524$	0.493131	+	0.618367i	0.0215425	+	0.0270135i
$525$	−3.27187	−	0.557313i	−0.142796	−	0.0243231i
$526$	−5.58547	+	7.00395i	−0.243538	+	0.305387i
$527$	1.92085	−	3.63443i	0.0836737	−	0.158318i
$528$	−0.408726	−	0.178325i	−0.0177875	−	0.00776062i
$529$	−18.6043	−	1.39420i	−0.808885	−	0.0606175i
$530$	−1.73376	−	0.767702i	−0.0753099	−	0.0333469i
$531$	13.9546	−	28.9770i	0.605579	−	1.25750i
$532$	2.51967	+	13.9434i	0.109242	+	0.604521i
$533$	−33.6007	−	11.7574i	−1.45541	−	0.509270i
$534$	−1.54206	+	0.115562i	−0.0667316	+	0.00500084i
$535$	12.6431	+	26.6238i	0.546611	+	1.15105i
$536$	−10.4293	+	7.11056i	−0.450476	+	0.307130i
$537$	−0.317558	−	0.430276i	−0.0137037	−	0.0185678i
$538$	−10.2121	+	10.2121i	−0.440277	+	0.440277i
$539$	−2.83202	−	9.74739i	−0.121984	−	0.419850i
$540$	3.36729	+	3.66896i	0.144905	+	0.157887i
$541$	−36.0482	−	5.43339i	−1.54983	−	0.233600i	−0.682334	−	0.731040i	$-0.739035\pi$
$541$	−36.0482	−	5.43339i	−1.54983	−	0.233600i	−0.867498	+	0.497441i	$0.834273\pi$
$542$	−14.3569	−	2.71648i	−0.616683	−	0.116683i
$543$	−0.488941	−	0.925122i	−0.0209825	−	0.0397008i
$544$	0.275283	+	3.67339i	0.0118026	+	0.157495i
$545$	−35.1044	+	15.0888i	−1.50371	+	0.646334i
$546$	0.768201	+	1.35619i	0.0328760	+	0.0580396i
$547$	24.4394	−	8.55173i	1.04495	−	0.365645i	0.247414	−	0.968910i	$-0.420419\pi$
$547$	24.4394	−	8.55173i	1.04495	−	0.365645i	0.797541	+	0.603264i	$0.206134\pi$
$548$	−27.5131	+	12.0038i	−1.17530	+	0.512778i
$549$	2.50749	−	33.4601i	0.107017	−	1.42804i
$550$	−4.52812	−	2.45666i	−0.193080	−	0.104752i
$551$	0.512012	+	1.65990i	0.0218125	+	0.0707143i
$552$	−1.29038	+	0.145391i	−0.0549221	+	0.00618823i
$553$	−12.4969	−	24.1233i	−0.531423	−	1.02583i
$554$	1.90747	−	1.52115i	0.0810405	−	0.0646276i
$555$	−3.55896	−	2.65670i	−0.151070	−	0.112771i
$556$	−6.73467	+	7.25825i	−0.285614	+	0.307818i
$557$	−2.39715	−	8.94627i	−0.101570	−	0.379066i	0.896363	−	0.443320i	$-0.146200\pi$
$557$	−2.39715	−	8.94627i	−0.101570	−	0.379066i	−0.997934	+	0.0642548i	$0.979533\pi$
$558$	13.1320	+	3.51871i	0.555922	+	0.148959i
$559$	9.45255	−	41.4143i	0.399800	−	1.75164i
$560$	−4.16644	+	5.93510i	−0.176064	+	0.250804i
$561$	0.0510838	+	0.223813i	0.00215676	+	0.00944939i
$562$	−0.644802	+	17.2327i	−0.0271993	+	0.726917i
$563$	−4.61289	+	6.25024i	−0.194410	+	0.263416i	−0.890950	−	0.454102i	$-0.849960\pi$
$563$	−4.61289	+	6.25024i	−0.194410	+	0.263416i	0.696540	+	0.717518i	$0.254722\pi$
$564$	−0.106630	−	0.707447i	−0.00448995	−	0.0297889i
$565$	0.386404	−	4.80483i	0.0162561	−	0.202141i
$566$	−14.2376	+	3.24964i	−0.598451	+	0.136593i
$567$	15.9142	−	15.6547i	0.668335	−	0.657436i
$568$	18.0222	−	11.3241i	0.756196	−	0.475149i
$569$	34.5187	−	19.9294i	1.44710	−	0.835483i	0.448791	−	0.893637i	$-0.351855\pi$
$569$	34.5187	−	19.9294i	1.44710	−	0.835483i	0.998308	+	0.0581539i	$0.0185214\pi$
$570$	−0.766216	+	1.20481i	−0.0320932	+	0.0504638i
$571$	24.5458	+	22.7752i	1.02721	+	0.953113i	0.998919	−	0.0464864i	$-0.0148024\pi$
$571$	24.5458	+	22.7752i	1.02721	+	0.953113i	0.0282929	+	0.999600i	$0.490993\pi$
$572$	−1.33200	−	7.03980i	−0.0556938	−	0.294349i
$573$	−3.81756	−	0.430135i	−0.159481	−	0.0179692i
$574$	−20.0485	+	2.85346i	−0.836808	+	0.119101i
$575$	10.4169	−	0.276165i	0.434413	−	0.0115169i
$576$	−4.76123	+	1.46865i	−0.198385	+	0.0611936i
$577$	9.58559	−	21.9704i	0.399053	−	0.914640i	−0.594793	−	0.803879i	$-0.702766\pi$
$577$	9.58559	−	21.9704i	0.399053	−	0.914640i	0.993847	−	0.110762i	$-0.0353291\pi$
$578$	−8.94115	+	7.69449i	−0.371903	+	0.320048i
$579$	−1.75806	+	4.47946i	−0.0730624	+	0.186160i
$580$	−0.765396	+	1.42930i	−0.0317813	+	0.0593484i
$581$	−4.67366	+	29.3674i	−0.193896	+	1.21836i
$582$	0.571682	−	1.63377i	0.0236970	−	0.0677221i
$583$	−1.12882	+	1.31171i	−0.0467510	+	0.0543256i
$584$	−1.69459	−	0.522713i	−0.0701228	−	0.0216300i
$585$	−4.94461	+	21.1325i	−0.204435	+	0.873720i
$586$	0.449812	−	2.98430i	0.0185815	−	0.123280i
$587$	−3.90742	−	3.90742i	−0.161276	−	0.161276i	0.621856	−	0.783132i	$-0.286379\pi$
$587$	−3.90742	−	3.90742i	−0.161276	−	0.161276i	−0.783132	+	0.621856i	$0.786379\pi$
$588$	−2.20009	−	1.43340i	−0.0907301	−	0.0591123i
$589$		−	23.3348i		−	0.961494i
$590$	9.72226	+	14.4282i	0.400259	+	0.593999i
$591$	−2.62349	−	3.84795i	−0.107916	−	0.158283i
$592$	−8.57892	+	4.53409i	−0.352592	+	0.186350i
$593$	−7.38882	−	6.35859i	−0.303422	−	0.261116i	0.487377	−	0.873192i	$-0.337954\pi$
$593$	−7.38882	−	6.35859i	−0.303422	−	0.261116i	−0.790799	+	0.612076i	$0.790335\pi$
$594$	−1.38274	+	0.665893i	−0.0567345	+	0.0273219i
$595$	3.73206	−	0.0885829i	0.153000	−	0.00363155i
$596$	−10.2851	−	4.95304i	−0.421294	−	0.202884i
$597$	0.0580599	+	0.133075i	0.00237624	+	0.00544639i
$598$	−3.19206	−	3.70924i	−0.130533	−	0.151682i
$599$	−26.1059	+	10.2458i	−1.06666	+	0.418633i	−0.832764	−	0.553629i	$-0.813243\pi$
$599$	−26.1059	+	10.2458i	−1.06666	+	0.418633i	−0.233896	+	0.972262i	$0.575147\pi$
$600$	−3.04461	+	0.660100i	−0.124296	+	0.0269485i
$601$	−6.08583	−	4.85329i	−0.248246	−	0.197970i	0.491459	−	0.870901i	$-0.336464\pi$
$601$	−6.08583	−	4.85329i	−0.248246	−	0.197970i	−0.739705	+	0.672931i	$0.765035\pi$
$602$	−6.06222	−	23.3921i	−0.247078	−	0.953391i
$603$	1.67144	−	14.8345i	0.0680664	−	0.604106i
$604$	3.02124	−	4.43134i	0.122932	−	0.180309i
$605$	14.1443	−	13.9910i	0.575048	−	0.568816i
$606$	0.647505	−	1.12151i	0.0263031	−	0.0455583i
$607$	5.14246	−	19.1919i	0.208726	−	0.778976i	−0.779555	−	0.626333i	$-0.784555\pi$
$607$	5.14246	−	19.1919i	0.208726	−	0.778976i	0.988281	−	0.152643i	$-0.0487784\pi$
$608$	11.1249	+	17.7052i	0.451176	+	0.718042i
$609$	−0.288877	−	0.142053i	−0.0117059	−	0.00575630i
$610$	14.9412	+	10.3064i	0.604950	+	0.417293i
$611$	4.62024	−	4.28696i	0.186915	−	0.173432i
$612$	−2.22951	−	1.64546i	−0.0901228	−	0.0665136i
$613$	−14.9869	−	11.0609i	−0.605316	−	0.446744i	0.247549	−	0.968875i	$-0.420375\pi$
$613$	−14.9869	−	11.0609i	−0.605316	−	0.446744i	−0.852865	+	0.522132i	$0.825137\pi$
$614$	15.3491	−	14.2419i	0.619440	−	0.574756i
$615$	4.97460	+	3.43147i	0.200595	+	0.138370i
$616$	−5.87896	−	7.49762i	−0.236870	−	0.302088i
$617$	3.51133	+	5.58826i	0.141361	+	0.224975i	0.909899	−	0.414829i	$-0.136159\pi$
$617$	3.51133	+	5.58826i	0.141361	+	0.224975i	−0.768538	+	0.639804i	$0.779016\pi$
$618$	0.0992512	−	0.370410i	0.00399247	−	0.0149001i
$619$	−21.7108	+	37.6042i	−0.872632	+	1.51144i	−0.0133672	+	0.999911i	$0.504255\pi$
$619$	−21.7108	+	37.6042i	−0.872632	+	1.51144i	−0.859264	+	0.511532i	$0.829078\pi$
$620$	15.4844	−	15.3167i	0.621870	−	0.615132i
$621$	1.74877	−	2.56497i	0.0701757	−	0.102929i
$622$	−2.30528	+	20.4599i	−0.0924334	+	0.820369i
$623$	20.9596	+	9.35042i	0.839727	+	0.374617i
$624$	−0.794554	−	0.633635i	−0.0318076	−	0.0253657i
$625$	24.7961	−	3.18656i	0.991843	−	0.127462i
$626$	5.55714	−	2.18102i	0.222108	−	0.0871709i
$627$	0.850018	+	0.987739i	0.0339464	+	0.0394465i
$628$	−12.4456	−	28.5256i	−0.496634	−	1.13830i
$629$	4.50065	+	2.16740i	0.179453	+	0.0864199i
$630$	3.03211	+	11.9680i	0.120802	+	0.476817i
$631$	0.299479	−	0.144221i	0.0119221	−	0.00574136i	−0.427913	−	0.903820i	$-0.640751\pi$
$631$	0.299479	−	0.144221i	0.0119221	−	0.00574136i	0.439835	+	0.898078i	$0.355037\pi$
$632$	−19.3292	−	16.6341i	−0.768874	−	0.661670i
$633$	3.41862	−	1.80679i	0.135878	−	0.0718136i
$634$	0.832547	+	1.22112i	0.0330647	+	0.0484970i
$635$	−4.21449	−	6.25445i	−0.167247	−	0.248200i
$636$			0.447680i			0.0177516i
$637$	−0.484760	−	23.1276i	−0.0192069	−	0.916348i
$638$	−0.353316	−	0.353316i	−0.0139879	−	0.0139879i
$639$	−3.75179	+	24.8915i	−0.148418	+	0.984692i
$640$	−5.33390	+	22.7962i	−0.210841	+	0.901099i
$641$	−10.8966	−	3.36116i	−0.430390	−	0.132758i	0.0719888	−	0.997405i	$-0.477065\pi$
$641$	−10.8966	−	3.36116i	−0.430390	−	0.132758i	−0.502379	+	0.864648i	$0.667542\pi$
$642$	−1.53269	+	1.78102i	−0.0604905	+	0.0702912i
$643$	−3.45663	+	9.87847i	−0.136316	+	0.389569i	−0.991724	−	0.128385i	$-0.959021\pi$
$643$	−3.45663	+	9.87847i	−0.136316	+	0.389569i	0.855408	+	0.517954i	$0.173306\pi$
$644$	7.64933	+	3.07495i	0.301426	+	0.121170i
$645$	−3.40437	+	6.35731i	−0.134047	+	0.250319i
$646$	0.586725	−	1.49495i	0.0230844	−	0.0588180i
$647$	11.5747	−	9.96087i	0.455050	−	0.391602i	−0.394681	−	0.918818i	$-0.629145\pi$
$647$	11.5747	−	9.96087i	0.455050	−	0.391602i	0.849731	+	0.527216i	$0.176764\pi$
$648$	8.37921	−	19.2054i	0.329166	−	0.754457i
$649$	15.1735	−	4.68039i	0.595610	−	0.183721i
$650$	−8.51880	−	8.07878i	−0.334135	−	0.316876i
$651$	3.14572	+	2.96730i	0.123291	+	0.116298i
$652$	14.2900	+	1.61010i	0.559642	+	0.0630565i
$653$	7.49555	+	39.6149i	0.293324	+	1.55025i	0.750497	+	0.660874i	$0.229814\pi$
$653$	7.49555	+	39.6149i	0.293324	+	1.55025i	−0.457173	+	0.889378i	$0.651138\pi$
$654$	−2.23304	−	2.07196i	−0.0873189	−	0.0810201i
$655$	0.634770	−	0.998119i	0.0248025	−	0.0389997i
$656$	11.4348	−	6.60189i	0.446454	−	0.257760i
$657$	1.77585	−	1.11584i	0.0692824	−	0.0435330i
$658$	1.21196	−	3.37434i	0.0472472	−	0.131545i
$659$	−41.0370	+	9.36643i	−1.59857	+	0.364864i	−0.926700	−	0.375801i	$-0.877368\pi$
$659$	−41.0370	+	9.36643i	−1.59857	+	0.364864i	−0.671874	+	0.740665i	$0.734510\pi$
$660$	−0.0975003	+	1.21239i	−0.00379520	+	0.0471923i
$661$	2.50844	+	16.6424i	0.0975672	+	0.647316i	0.983145	+	0.182826i	$0.0585244\pi$
$661$	2.50844	+	16.6424i	0.0975672	+	0.647316i	−0.885578	+	0.464490i	$0.846238\pi$
$662$	5.24249	−	7.10332i	0.203755	−	0.276078i
$663$	−0.0195624	+	0.522815i	−0.000759739	+	0.0203045i
$664$	6.21109	+	27.2126i	0.241037	+	1.05605i
$665$	18.4949	−	10.3436i	0.717201	−	0.401107i
$666$	−3.67617	+	16.1064i	−0.142449	+	0.624109i
$667$	0.976266	+	0.261590i	0.0378012	+	0.0101288i
$668$	−4.84858	−	18.0951i	−0.187597	−	0.700122i
$669$	−0.518101	+	0.558380i	−0.0200309	+	0.0215882i
$670$	6.47130	+	4.83071i	0.250008	+	0.186627i
$671$	12.9519	−	10.3288i	0.500002	−	0.398738i
$672$	−3.80148	−	0.751703i	−0.146645	−	0.0289976i
$673$	−11.7033	+	1.31864i	−0.451128	+	0.0508299i	−0.334606	−	0.942358i	$-0.608603\pi$
$673$	−11.7033	+	1.31864i	−0.451128	+	0.0508299i	−0.116522	+	0.993188i	$0.537175\pi$
$674$	2.05840	+	6.67317i	0.0792866	+	0.257041i
$675$	3.55165	−	6.54641i	0.136703	−	0.251971i
$676$	−0.232311	+	3.09997i	−0.00893504	+	0.119230i
$677$	15.6357	−	6.82178i	0.600928	−	0.262182i	−0.0773304	−	0.997006i	$-0.524640\pi$
$677$	15.6357	−	6.82178i	0.600928	−	0.262182i	0.678259	+	0.734823i	$0.262735\pi$
$678$	0.362729	−	0.126925i	0.0139305	−	0.00487451i
$679$	−18.9745	+	17.3177i	−0.728176	+	0.664592i
$680$	3.21928	−	1.38373i	0.123454	−	0.0530637i
$681$	0.384605	+	5.13220i	0.0147381	+	0.196666i
$682$	3.13639	+	5.93434i	0.120098	+	0.227237i
$683$	19.8299	+	3.75202i	0.758770	+	0.143567i	0.550879	−	0.834585i	$-0.314292\pi$
$683$	19.8299	+	3.75202i	0.758770	+	0.143567i	0.207891	+	0.978152i	$0.433340\pi$
$684$	−15.5536	−	2.34432i	−0.594705	−	0.0896374i
$685$	30.3554	+	33.0748i	1.15982	+	1.26372i
$686$	−6.29658	−	11.5551i	−0.240405	−	0.441174i
$687$	1.39326	−	1.39326i	0.0531563	−	0.0531563i
$688$	9.35623	+	12.6772i	0.356703	+	0.483315i
$689$	−3.25860	+	2.22168i	−0.124143	+	0.0846391i
$690$	0.356371	+	0.750442i	0.0135668	+	0.0285689i
$691$	−39.7898	+	2.98183i	−1.51368	+	0.113434i	−0.805497	−	0.592599i	$-0.798102\pi$
$691$	−39.7898	+	2.98183i	−1.51368	+	0.113434i	−0.708178	+	0.706034i	$0.750483\pi$
$692$	−3.89198	−	1.36186i	−0.147951	−	0.0517702i
$693$	11.2563	+	0.513885i	0.427593	+	0.0195209i
$694$	6.08895	−	12.6438i	0.231133	−	0.479954i
$695$	13.5401	+	5.99550i	0.513606	+	0.227422i
$696$	−0.301318	−	0.0225807i	−0.0114214	−	0.000855919i
$697$	−6.23020	−	2.71821i	−0.235986	−	0.102960i
$698$	−1.04069	+	1.96907i	−0.0393905	+	0.0745305i
$699$	−0.312755	+	0.392183i	−0.0118295	+	0.0148337i
$700$	19.0036	+	5.48340i	0.718268	+	0.207253i
$701$	−5.85049	−	7.33629i	−0.220970	−	0.277088i	0.658973	−	0.752166i	$-0.270991\pi$
$701$	−5.85049	−	7.33629i	−0.220970	−	0.277088i	−0.879943	+	0.475079i	$0.842420\pi$
$702$	−3.43663	+	0.650245i	−0.129707	+	0.0245419i
$703$	28.3360	−	1.06026i	1.06871	−	0.0399884i
$704$	−2.13041	−	1.22999i	−0.0802927	−	0.0463570i
$705$	−0.948693	+	0.494806i	−0.0357298	+	0.0186355i
$706$	−20.9403	−	4.77948i	−0.788098	−	0.179878i
$707$	−16.3575	+	10.0915i	−0.615185	+	0.379528i
$708$	2.18544	−	3.47811i	0.0821340	−	0.130716i
$709$	1.35444	+	1.45974i	0.0508672	+	0.0548218i	0.757973	−	0.652286i	$-0.226190\pi$
$709$	1.35444	+	1.45974i	0.0508672	+	0.0548218i	−0.707106	+	0.707108i	$0.749999\pi$
$710$	−10.5999	−	8.54803i	−0.397808	−	0.320802i
$711$	29.8226	−	4.49503i	1.11843	−	0.168577i
$712$	21.5274	+	0.805500i	0.806775	+	0.0301874i
$713$	−11.4961	−	7.22349i	−0.430533	−	0.270522i
$714$	0.126922	+	0.269197i	0.00474995	+	0.0100744i
$715$	−9.30869	+	5.30698i	−0.348125	+	0.198470i
$716$	1.59343	+	2.75991i	0.0595494	+	0.103143i
$717$	1.44206	−	0.386398i	0.0538547	−	0.0144303i
$718$	0.602444	+	16.1006i	0.0224830	+	0.600871i
$719$	40.7216	+	27.7635i	1.51866	+	1.03540i	0.981398	+	0.191987i	$0.0614930\pi$
$719$	40.7216	+	27.7635i	1.51866	+	1.03540i	0.537260	+	0.843417i	$0.319459\pi$
$720$	−4.74486	−	6.50290i	−0.176830	−	0.242349i
$721$	−3.90528	+	4.14010i	−0.145440	+	0.154185i
$722$	0.490849	+	4.35641i	0.0182675	+	0.162129i
$723$	4.97436	+	2.62902i	0.184998	+	0.0977745i
$724$	2.27816	+	5.80465i	0.0846670	+	0.215728i
$725$	2.39363	+	0.387498i	0.0888973	+	0.0143913i
$726$	1.47646	+	0.579467i	0.0547965	+	0.0215060i
$727$	9.68904	+	27.6897i	0.359347	+	1.02695i	0.971669	+	0.236346i	$0.0759497\pi$
$727$	9.68904	+	27.6897i	0.359347	+	1.02695i	−0.612322	+	0.790608i	$0.709765\pi$
$728$	−8.51907	−	19.9723i	−0.315738	−	0.740224i
$729$	10.2657	+	21.3170i	0.380212	+	0.789517i
$730$	0.0362454	+	1.13397i	0.00134150	+	0.0419700i
$731$	2.39083	−	7.75089i	0.0884282	−	0.286677i
$732$	0.796723	−	4.21078i	0.0294477	−	0.155635i
$733$	27.1202	−	20.0156i	1.00171	−	0.739293i	0.0361126	−	0.999348i	$-0.488502\pi$
$733$	27.1202	−	20.0156i	1.00171	−	0.739293i	0.965594	+	0.260055i	$0.0837406\pi$
$734$	−21.8455			−0.806333
$735$	−0.957451	+	3.80858i	−0.0353161	+	0.140482i
$736$	12.1665			0.448463
$737$	5.93016	−	4.37665i	0.218440	−	0.161216i
$738$	4.17932	−	22.0883i	0.153843	−	0.813080i
$739$	−6.73688	+	21.8404i	−0.247820	+	0.803413i	0.743126	+	0.669152i	$0.233342\pi$
$739$	−6.73688	+	21.8404i	−0.247820	+	0.803413i	−0.990946	+	0.134261i	$0.957134\pi$
$740$	19.3029	+	18.1072i	0.709590	+	0.665633i
$741$	1.28855	+	2.67571i	0.0473361	+	0.0982945i
$742$	−1.06460	+	1.97485i	−0.0390828	+	0.0724991i
$743$	17.6241	+	50.3667i	0.646564	+	1.84777i	0.516538	+	0.856264i	$0.327220\pi$
$743$	17.6241	+	50.3667i	0.646564	+	1.84777i	0.130026	+	0.991511i	$0.458494\pi$
$744$	3.77848	+	1.48295i	0.138526	+	0.0543674i
$745$	−2.00392	+	16.9546i	−0.0734179	+	0.621170i
$746$	−1.49796	−	3.81674i	−0.0548442	−	0.139741i
$747$	−29.1856	−	15.4250i	−1.06784	−	0.564372i
$748$	−0.153175	−	1.35947i	−0.00560063	−	0.0497070i
$749$	32.5663	−	12.4733i	1.18995	−	0.455765i
$750$	1.03267	+	1.70470i	0.0377077	+	0.0622469i
$751$	34.7982	+	23.7250i	1.26980	+	0.865738i	0.995393	−	0.0958748i	$-0.0305648\pi$
$751$	34.7982	+	23.7250i	1.26980	+	0.865738i	0.274411	+	0.961613i	$0.411517\pi$
$752$	0.0874112	+	2.33611i	0.00318756	+	0.0851893i
$753$	−5.82048	+	1.55959i	−0.212110	+	0.0568347i
$754$	−0.569361	−	0.986162i	−0.0207349	−	0.0359139i
$755$	−7.73633	−	2.11818i	−0.281554	−	0.0770884i
$756$	4.63688	−	3.63583i	0.168642	−	0.132234i
$757$	−2.08740	−	1.31160i	−0.0758680	−	0.0476710i	0.493564	−	0.869710i	$-0.335694\pi$
$757$	−2.08740	−	1.31160i	−0.0758680	−	0.0476710i	−0.569432	+	0.822039i	$0.692837\pi$
$758$	−4.46787	−	0.167176i	−0.162280	−	0.00607210i
$759$	0.749750	−	0.113007i	0.0272142	−	0.00410188i
$760$	12.4861	−	15.4833i	0.452919	−	0.561639i
$761$	−28.3842	−	30.5909i	−1.02893	−	1.10892i	−0.993984	−	0.109530i	$-0.965066\pi$
$761$	−28.3842	−	30.5909i	−1.02893	−	1.10892i	−0.0349429	−	0.999389i	$-0.511125\pi$
$762$	0.319893	−	0.509107i	0.0115885	−	0.0184430i
$763$	14.5808	+	42.7948i	0.527859	+	1.54927i
$764$	22.3199	+	5.09437i	0.807506	+	0.184308i
$765$	−1.24306	+	3.95331i	−0.0449429	+	0.142932i
$766$	−14.1275	−	8.15650i	−0.510446	−	0.294706i
$767$	36.1623	−	1.35310i	1.30575	−	0.0488576i
$768$	−2.67036	+	0.505259i	−0.0963583	+	0.0182320i
$769$	7.78494	+	9.76200i	0.280732	+	0.352027i	0.902127	−	0.431471i	$-0.142005\pi$
$769$	7.78494	+	9.76200i	0.280732	+	0.352027i	−0.621395	+	0.783498i	$0.713434\pi$
$770$	−3.31323	+	5.11637i	−0.119400	+	0.184381i
$771$	−1.61181	+	2.02115i	−0.0580479	+	0.0727898i
$772$	13.3998	−	25.3536i	0.482268	−	0.912495i
$773$	−39.6746	−	17.3099i	−1.42700	−	0.622592i	−0.462484	−	0.886628i	$-0.653042\pi$
$773$	−39.6746	−	17.3099i	−1.42700	−	0.622592i	−0.964513	+	0.264036i	$0.914946\pi$
$774$	26.7505	+	2.00467i	0.961525	+	0.0720564i
$775$	−29.1917	−	14.4519i	−1.04860	−	0.519126i
$776$	−10.4622	+	21.7251i	−0.375573	+	0.779885i
$777$	−3.46034	+	3.95475i	−0.124139	+	0.141876i
$778$	−19.7160	−	6.89892i	−0.706852	−	0.247338i
$779$	−38.4769	+	2.88345i	−1.37858	+	0.103310i
$780$	−0.929749	+	2.61135i	−0.0332903	+	0.0935014i
$781$	−10.2686	+	7.00100i	−0.367439	+	0.250516i
$782$	−0.554877	−	0.751831i	−0.0198423	−	0.0268854i
$783$	0.510797	−	0.510797i	0.0182544	−	0.0182544i
$784$	6.61934	+	5.45919i	0.236405	+	0.194971i
$785$	−34.2921	+	31.4725i	−1.22394	+	1.12330i
$786$	0.0932491	+	0.0140550i	0.00332609	+	0.000501327i
$787$	−34.1668	−	6.46470i	−1.21791	−	0.230442i	−0.463055	−	0.886329i	$-0.653247\pi$
$787$	−34.1668	−	6.46470i	−1.21791	−	0.230442i	−0.754859	+	0.655888i	$0.772295\pi$
$788$	12.9684	+	24.5374i	0.461979	+	0.874107i
$789$	−0.236389	−	3.15440i	−0.00841568	−	0.112300i
$790$	−6.04310	+	15.1543i	−0.215004	+	0.539166i
$791$	−5.63262	−	0.896401i	−0.200273	−	0.0318723i
$792$	9.98315	−	3.49326i	0.354736	−	0.124127i
$793$	34.6036	−	15.0974i	1.22881	−	0.536124i
$794$	−0.886419	+	11.8284i	−0.0314578	+	0.419775i
$795$	0.633153	−	0.217686i	0.0224556	−	0.00772052i
$796$	−0.255030	−	0.826786i	−0.00903928	−	0.0293046i
$797$	3.04582	−	0.343182i	0.107889	−	0.0121561i	−0.0578551	−	0.998325i	$-0.518426\pi$
$797$	3.04582	−	0.343182i	0.107889	−	0.0121561i	0.165744	+	0.986169i	$0.446998\pi$
$798$	1.35100	+	1.01435i	0.0478249	+	0.0359075i
$799$	0.940921	−	0.750359i	0.0332874	−	0.0265458i
$800$	29.0391	−	2.95191i	1.02669	−	0.104366i
$801$	−17.3292	+	18.6764i	−0.612296	+	0.659898i
$802$	−1.76182	−	6.57520i	−0.0622120	−	0.232178i
$803$	1.00019	+	0.268001i	0.0352961	+	0.00945755i
$804$	0.424267	−	1.85884i	0.0149627	−	0.0655561i
$805$	0.629389	−	12.3136i	0.0221830	−	0.433999i
$806$	3.40387	+	14.9133i	0.119896	+	0.525300i
$807$	0.190679	−	5.09601i	0.00671223	−	0.179388i
$808$	−10.7129	+	14.5154i	−0.376878	+	0.510651i
$809$	−7.93286	−	52.6311i	−0.278904	−	1.85041i	−0.488426	−	0.872606i	$-0.662429\pi$
$809$	−7.93286	−	52.6311i	−0.278904	−	1.85041i	0.209521	−	0.977804i	$-0.432809\pi$
$810$	−13.3623	−	1.07459i	−0.469503	−	0.0377574i
$811$	−22.0168	+	5.02518i	−0.773113	+	0.176458i	−0.590839	−	0.806790i	$-0.701203\pi$
$811$	−22.0168	+	5.02518i	−0.773113	+	0.176458i	−0.182274	+	0.983248i	$0.558346\pi$
$812$	1.61590	+	1.03396i	0.0567070	+	0.0362850i
$813$	4.36862	−	2.74499i	0.153214	−	0.0962709i
$814$	−7.06369	+	4.07823i	−0.247582	+	0.142942i
$815$	−4.67142	−	20.9933i	−0.163633	−	0.735365i
$816$	−0.142251	−	0.131989i	−0.00497977	−	0.00462055i
$817$	−8.55994	−	45.2404i	−0.299475	−	1.58276i
$818$	10.5458	+	1.18823i	0.368727	+	0.0415455i
$819$	24.4757	+	7.77068i	0.855250	+	0.271530i
$820$	−27.1691	−	23.6398i	−0.948788	−	0.825536i
$821$	44.3634	−	13.6843i	1.54829	−	0.477585i	0.601349	−	0.798986i	$-0.294630\pi$
$821$	44.3634	−	13.6843i	1.54829	−	0.477585i	0.946943	+	0.321401i	$0.104154\pi$
$822$	−1.43123	+	3.28041i	−0.0499199	+	0.114418i
$823$	−29.6372	+	25.5049i	−1.03309	+	0.889045i	−0.993911	−	0.110187i	$-0.964855\pi$
$823$	−29.6372	+	25.5049i	−1.03309	+	0.889045i	−0.0391784	+	0.999232i	$0.512474\pi$
$824$	−1.95171	+	4.97288i	−0.0679911	+	0.173238i
$825$	1.76209	−	0.451635i	0.0613483	−	0.0157239i
$826$	17.9118	−	10.1460i	0.623231	−	0.353023i
$827$	−14.9155	+	42.6259i	−0.518661	+	1.48225i	0.325178	+	0.945653i	$0.394576\pi$
$827$	−14.9155	+	42.6259i	−0.518661	+	1.48225i	−0.843839	+	0.536596i	$0.819710\pi$
$828$	−5.96970	+	6.93692i	−0.207461	+	0.241074i
$829$	−8.17299	−	2.52103i	−0.283860	−	0.0875591i	0.149556	−	0.988753i	$-0.452216\pi$
$829$	−8.17299	−	2.52103i	−0.283860	−	0.0875591i	−0.433416	+	0.901194i	$0.642692\pi$
$830$	15.1718	−	9.41818i	0.526621	−	0.326910i
$831$	−0.128397	+	0.851860i	−0.00445405	+	0.0295507i
$832$	−3.96421	−	3.96421i	−0.137434	−	0.137434i
$833$	0.237712	−	4.41068i	0.00823625	−	0.152821i
$834$			1.18056i			0.0408793i
$835$	−23.2343	+	15.6562i	−0.804057	+	0.541805i
$836$	−4.37461	−	6.41638i	−0.151299	−	0.221915i
$837$	−8.57941	+	4.53435i	−0.296548	+	0.156730i
$838$	0.0956715	+	0.0823320i	0.00330492	+	0.00284411i
$839$	27.2326	−	13.1145i	0.940172	−	0.452763i	0.0999422	−	0.994993i	$-0.468134\pi$
$839$	27.2326	−	13.1145i	0.940172	−	0.452763i	0.840230	+	0.542230i	$0.182420\pi$
$840$	0.499517	+	3.65213i	0.0172350	+	0.126010i
$841$	−25.9162	−	12.4806i	−0.893662	−	0.430365i
$842$	8.71334	+	19.9712i	0.300282	+	0.688253i
$843$	−3.97190	−	4.61543i	−0.136799	−	0.158964i
$844$	−21.4500	+	8.41852i	−0.738341	+	0.289777i
$845$	4.49726	−	1.17882i	0.154710	−	0.0405525i
$846$	3.11180	+	2.48158i	0.106986	+	0.0853185i
$847$	−15.2077	−	17.9683i	−0.522542	−	0.617399i
$848$	0.163785	−	1.45363i	0.00562439	−	0.0499179i
$849$	2.90484	−	4.26061i	0.0996938	−	0.146224i
$850$	−1.50680	−	1.65985i	−0.0516828	−	0.0569325i
$851$	8.24931	−	14.2882i	0.282783	−	0.489794i
$852$	−0.832113	+	3.10549i	−0.0285077	+	0.106392i
$853$	−3.62996	−	5.77705i	−0.124288	−	0.197802i	0.778785	−	0.627292i	$-0.215837\pi$
$853$	−3.62996	−	5.77705i	−0.124288	−	0.197802i	−0.903072	+	0.429489i	$0.858694\pi$
$854$	13.5280	−	16.6804i	0.462919	−	0.570792i
$855$	4.24741	+	23.1373i	0.145258	+	0.791280i
$856$	23.9954	−	22.2645i	0.820146	−	0.760984i
$857$	43.3021	+	31.9584i	1.47917	+	1.09168i	0.973428	+	0.228992i	$0.0735430\pi$
$857$	43.3021	+	31.9584i	1.47917	+	1.09168i	0.505742	+	0.862685i	$0.331219\pi$
$858$	−0.687332	−	0.507274i	−0.0234651	−	0.0173180i
$859$	3.89966	−	3.61836i	0.133055	−	0.123457i	−0.610838	−	0.791755i	$-0.709168\pi$
$859$	3.89966	−	3.61836i	0.133055	−	0.123457i	0.743893	+	0.668298i	$0.232977\pi$
$860$	24.4019	−	35.3754i	0.832096	−	1.20629i
$861$	4.50410	−	5.55368i	0.153499	−	0.189269i
$862$	−10.9191	−	17.3776i	−0.371906	−	0.591885i
$863$	−2.71767	+	10.1425i	−0.0925106	+	0.345254i	−0.996630	−	0.0820252i	$-0.973861\pi$
$863$	−2.71767	+	10.1425i	−0.0925106	+	0.345254i	0.904120	+	0.427279i	$0.140528\pi$
$864$	4.34784	−	7.53069i	0.147917	−	0.256199i
$865$	−0.0335923	+	6.16663i	−0.00114217	+	0.209672i
$866$	−1.02875	+	1.50890i	−0.0349584	+	0.0512745i
$867$	0.466362	−	4.13908i	0.0158385	−	0.140570i
$868$	−16.6486	−	19.6708i	−0.565089	−	0.667670i
$869$	11.6416	+	9.28386i	0.394914	+	0.314933i
$870$	0.0490153	+	0.186996i	0.00166177	+	0.00633977i
$871$	15.6357	−	6.13656i	0.529796	−	0.207930i
$872$	27.6808	+	32.1657i	0.937391	+	1.08927i
$873$	−11.4040	−	26.1382i	−0.385966	−	0.884644i
$874$	−4.77890	−	2.30140i	−0.161649	−	0.0778459i
$875$	−1.48539	−	29.5431i	−0.0502152	−	0.998738i
$876$	0.241341	−	0.116224i	0.00815416	−	0.00392684i
$877$	−17.3509	−	14.9316i	−0.585898	−	0.504206i	0.308652	−	0.951175i	$-0.400122\pi$
$877$	−17.3509	−	14.9316i	−0.585898	−	0.504206i	−0.894549	+	0.446970i	$0.852503\pi$
$878$	−0.270574	+	0.143003i	−0.00913143	+	0.00482610i
$879$	0.600314	+	0.880499i	0.0202481	+	0.0296985i
$880$	0.760143	−	3.90100i	0.0256244	−	0.131503i
$881$			27.1258i			0.913891i	0.889495	+	0.456945i	$0.151057\pi$
$881$			27.1258i			0.913891i	−0.889495	+	0.456945i	$0.848943\pi$
$882$	14.3962	−	2.47945i	0.484744	−	0.0834876i
$883$	−5.27044	−	5.27044i	−0.177364	−	0.177364i	0.612842	−	0.790206i	$-0.290026\pi$
$883$	−5.27044	−	5.27044i	−0.177364	−	0.177364i	−0.790206	+	0.612842i	$0.790026\pi$
$884$	0.464683	−	3.08297i	0.0156290	−	0.103692i
$885$	−5.98178	−	1.39963i	−0.201075	−	0.0470480i
$886$	16.5274	+	5.09802i	0.555248	+	0.171271i
$887$	−8.79598	+	10.2211i	−0.295340	+	0.343192i	−0.885963	−	0.463756i	$-0.846501\pi$
$887$	−8.79598	+	10.2211i	−0.295340	+	0.343192i	0.590623	+	0.806948i	$0.298882\pi$
$888$	−1.62909	+	4.65568i	−0.0546688	+	0.156234i
$889$	−7.76456	+	4.39816i	−0.260415	+	0.147509i
$890$	−3.99055	−	13.1918i	−0.133764	−	0.442189i
$891$	−4.46989	+	11.3891i	−0.149747	+	0.381549i
$892$	3.44067	−	2.96094i	0.115202	−	0.0991395i
$893$	2.73186	−	6.26150i	0.0914183	−	0.209533i
$894$	−1.30062	+	0.401189i	−0.0434994	+	0.0134178i
$895$	3.12852	−	3.59561i	0.104575	−	0.120188i
$896$	26.4026	+	8.38246i	0.882050	+	0.280038i
$897$	1.71710	+	0.193470i	0.0573322	+	0.00645978i
$898$	−1.91384	−	10.1149i	−0.0638658	−	0.337539i
$899$	−2.31596	−	2.14889i	−0.0772414	−	0.0716696i
$900$	−12.5655	+	18.0055i	−0.418849	+	0.600184i
$901$	−0.652177	+	0.376535i	−0.0217272	+	0.0125442i
$902$	9.39762	−	5.90491i	0.312906	−	0.196612i
$903$	7.18728	+	4.59892i	0.239178	+	0.153042i
$904$	−5.21933	+	1.19128i	−0.173592	+	0.0396213i
$905$	7.10175	−	6.04453i	0.236070	−	0.200927i
$906$	−0.0953078	−	0.632326i	−0.00316639	−	0.0210076i
$907$	−3.26777	+	4.42767i	−0.108505	+	0.147018i	−0.855485	−	0.517827i	$-0.826741\pi$
$907$	−3.26777	+	4.42767i	−0.108505	+	0.147018i	0.746981	+	0.664846i	$0.231503\pi$
$908$	1.14679	−	30.6486i	0.0380576	−	1.01711i
$909$	−4.74771	−	20.8011i	−0.157472	−	0.689928i
$910$	−10.3113	+	9.30849i	−0.341817	+	0.308574i
$911$	−7.31005	+	32.0274i	−0.242193	+	1.06112i	0.696823	+	0.717243i	$0.254596\pi$
$911$	−7.31005	+	32.0274i	−0.242193	+	1.06112i	−0.939016	+	0.343873i	$0.888261\pi$
$912$	−1.06400	−	0.285097i	−0.0352324	−	0.00944050i
$913$	−4.21825	−	15.7427i	−0.139604	−	0.521008i
$914$	−18.5029	+	19.9414i	−0.612021	+	0.659602i
$915$	−6.34272	+	0.920704i	−0.209684	+	0.0304375i
$916$	−9.18030	+	7.32104i	−0.303326	+	0.241894i
$917$	−1.11923	−	0.840333i	−0.0369604	−	0.0277502i
$918$	−0.663653	+	0.0747757i	−0.0219038	+	0.00246797i
$919$	−5.68552	−	18.4320i	−0.187548	−	0.608016i	−0.999698	−	0.0245673i	$-0.992179\pi$
$919$	−5.68552	−	18.4320i	−0.187548	−	0.608016i	0.812150	−	0.583448i	$-0.198297\pi$
$920$	−3.76283	−	10.9444i	−0.124057	−	0.360827i
$921$	−0.552518	+	7.37284i	−0.0182061	+	0.242943i
$922$	−12.8617	+	5.61150i	−0.423578	+	0.184805i
$923$	−26.7339	+	9.35461i	−0.879958	+	0.307911i
$924$	1.42127	+	0.226187i	0.0467562	+	0.00744099i
$925$	16.2229	−	36.1048i	0.533404	−	1.18712i
$926$	0.0769138	+	1.02634i	0.00252754	+	0.0337277i
$927$	−2.95220	−	5.58584i	−0.0969630	−	0.183463i
$928$	2.78172	+	0.526330i	0.0913144	+	0.0172776i
$929$	−30.5876	−	4.61034i	−1.00355	−	0.151260i	−0.373346	−	0.927692i	$-0.621789\pi$
$929$	−30.5876	−	4.61034i	−1.00355	−	0.151260i	−0.630201	+	0.776432i	$0.717028\pi$
$930$	0.111234	−	2.59447i	0.00364751	−	0.0850760i
$931$	−10.5060	−	22.7661i	−0.344320	−	0.746129i
$932$	2.11376	−	2.11376i	0.0692385	−	0.0692385i
$933$	−4.31719	−	5.84958i	−0.141338	−	0.191507i
$934$	4.49507	−	3.06469i	0.147083	−	0.100280i
$935$	−1.84821	+	0.877681i	−0.0604430	+	0.0287032i
$936$	24.0366	−	1.80129i	0.785661	−	0.0588771i
$937$	23.0155	+	8.05347i	0.751884	+	0.263095i	0.678893	−	0.734237i	$-0.262460\pi$
$937$	23.0155	+	8.05347i	0.751884	+	0.263095i	0.0729906	+	0.997333i	$0.476746\pi$
$938$	6.29197	−	7.19097i	0.205440	−	0.234794i
$939$	−0.914610	+	1.89921i	−0.0298472	+	0.0619783i
$940$	5.94815	−	2.29716i	0.194007	−	0.0749252i
$941$	−57.8838	−	4.33779i	−1.88696	−	0.141408i	−0.919281	−	0.393602i	$-0.871229\pi$
$941$	−57.8838	−	4.33779i	−1.88696	−	0.141408i	−0.967677	+	0.252195i	$0.918848\pi$
$942$	−3.40114	−	1.48390i	−0.110815	−	0.0483482i
$943$	−10.4903	+	19.8487i	−0.341612	+	0.646361i
$944$	−8.36869	+	10.4940i	−0.272378	+	0.341551i
$945$	−7.39685	−	4.79001i	−0.240620	−	0.155819i
$946$	8.25758	+	10.3547i	0.268477	+	0.336660i
$947$	−34.9133	+	6.60595i	−1.13453	+	0.214665i	−0.719064	−	0.694944i	$-0.755429\pi$
$947$	−34.9133	+	6.60595i	−1.13453	+	0.214665i	−0.415466	+	0.909609i	$0.636381\pi$
$948$	3.84926	−	0.144029i	0.125018	−	0.00467784i
$949$	2.04367	+	1.17991i	0.0663403	+	0.0383016i
$950$	−11.9647	−	4.33351i	−0.388187	−	0.140598i
$951$	−0.508778	−	0.116125i	−0.0164983	−	0.00376562i
$952$	−1.33714	−	3.92453i	−0.0433369	−	0.127195i
$953$	16.1835	−	25.7559i	0.524236	−	0.834316i	−0.474714	−	0.880140i	$-0.657448\pi$
$953$	16.1835	−	25.7559i	0.524236	−	0.834316i	0.998950	+	0.0458240i	$0.0145913\pi$
$954$	−1.69400	−	1.82570i	−0.0548453	−	0.0591092i
$955$	−3.64817	−	34.0442i	−0.118052	−	1.10164i
$956$	−8.79744	+	1.32600i	−0.284530	+	0.0428859i
$957$	0.176310	+	0.00659705i	0.00569929	+	0.000213252i
$958$	3.31848	+	2.08514i	0.107215	+	0.0673678i
$959$	41.8004	−	32.7762i	1.34981	−	1.05840i
$960$	0.471370	+	0.826806i	0.0152134	+	0.0266851i
$961$	5.72025	+	9.90776i	0.184524	+	0.319605i
$962$	−17.9550	+	4.81102i	−0.578891	+	0.155113i
$963$	1.44752	+	38.6858i	0.0466457	+	1.24663i
$964$	−27.7031	−	18.8877i	−0.892258	−	0.608331i
$965$	−42.3733	−	6.62300i	−1.36404	−	0.213202i
$966$	0.917942	−	0.351584i	0.0295343	−	0.0113120i
$967$	2.26942	+	20.1417i	0.0729796	+	0.647712i	0.975948	+	0.218005i	$0.0699548\pi$
$967$	2.26942	+	20.1417i	0.0729796	+	0.647712i	−0.902968	+	0.429708i	$0.858617\pi$
$968$	−19.5352	−	10.3246i	−0.627884	−	0.331846i
$969$	0.207175	+	0.527872i	0.00665541	+	0.0169577i
$970$	15.3200	+	1.81072i	0.491896	+	0.0581386i
$971$	−31.9444	−	12.5372i	−1.02514	−	0.402339i	−0.207604	−	0.978213i	$-0.566567\pi$
$971$	−31.9444	−	12.5372i	−1.02514	−	0.402339i	−0.817539	+	0.575874i	$0.804662\pi$
$972$	3.25205	+	9.29381i	0.104309	+	0.298099i
$973$	8.31419	−	15.4229i	0.266541	−	0.494437i
$974$	4.03376	+	8.37619i	0.129250	+	0.268390i
$975$	4.14533	+	0.0451641i	0.132757	+	0.00144641i
$976$	−4.12751	+	13.3811i	−0.132118	+	0.428317i
$977$	−6.68778	+	35.3457i	−0.213961	+	1.13081i	0.696608	+	0.717452i	$0.254692\pi$
$977$	−6.68778	+	35.3457i	−0.213961	+	1.13081i	−0.910568	+	0.413358i	$0.864356\pi$
$978$	1.37956	−	1.01816i	0.0441136	−	0.0325573i
$979$	−12.5787			−0.402016
$980$	8.21106	−	21.9149i	0.262293	−	0.700046i
$981$	−50.1883			−1.60239
$982$	−3.52641	+	2.60261i	−0.112532	+	0.0830526i
$983$	−3.78423	+	20.0001i	−0.120698	+	0.637905i	0.869009	+	0.494796i	$0.164757\pi$
$983$	−3.78423	+	20.0001i	−0.120698	+	0.637905i	−0.989707	+	0.143108i	$0.954290\pi$
$984$	1.97834	−	6.41362i	0.0630672	−	0.204459i
$985$	28.3973	−	30.2726i	0.904812	−	0.964564i
$986$	−0.0943411	−	0.195901i	−0.00300443	−	0.00623877i
$987$	0.496712	+	1.16450i	0.0158105	+	0.0370666i
$988$	−5.84527	−	16.7048i	−0.185963	−	0.531451i
$989$	−24.9379	−	9.78742i	−0.792981	−	0.311222i
$990$	−4.19002	−	5.31323i	−0.133167	−	0.168866i
$991$	13.3496	+	34.0143i	0.424065	+	1.08050i	0.970093	+	0.242733i	$0.0780438\pi$
$991$	13.3496	+	34.0143i	0.424065	+	1.08050i	−0.546029	+	0.837767i	$0.683861\pi$
$992$	−33.6237	−	17.7706i	−1.06755	−	0.564218i
$993$	0.349032	+	3.09774i	0.0110762	+	0.0983039i
$994$	−11.0557	+	11.7205i	−0.350666	+	0.371751i
$995$	−1.04531	+	0.762716i	−0.0331387	+	0.0241797i
$996$	−3.48355	−	2.37505i	−0.110381	−	0.0752562i
$997$	0.432039	+	11.5465i	0.0136828	+	0.365681i	0.989273	+	0.146080i	$0.0466658\pi$
$997$	0.432039	+	11.5465i	0.0136828	+	0.365681i	−0.975590	+	0.219600i	$0.929525\pi$
$998$	−23.0613	+	6.17925i	−0.729992	+	0.195601i
$999$	−5.89599	−	10.2121i	−0.186541	−	0.323098i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.x.a.108.11	yes	624
5.2	odd	4	inner	245.2.x.a.157.11	yes	624
49.5	odd	42	inner	245.2.x.a.103.11	✓	624
245.152	even	84	inner	245.2.x.a.152.11	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.11	✓	624	49.5	odd	42	inner
245.2.x.a.108.11	yes	624	1.1	even	1	trivial
245.2.x.a.152.11	yes	624	245.152	even	84	inner
245.2.x.a.157.11	yes	624	5.2	odd	4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.571694 + 0.421929i) q^{2} +(0.0466438 - 0.246518i) q^{3} +(-0.440701 + 1.42872i) q^{4} +(2.23493 - 0.0714359i) q^{5} +(0.0773473 + 0.160613i) q^{6} +(0.120661 - 2.64300i) q^{7} +(-0.820220 - 2.34406i) q^{8} +(2.73403 + 1.07303i) q^{9} +(-1.24755 + 0.983821i) q^{10} +(0.529769 + 1.34983i) q^{11} +(0.331649 + 0.175281i) q^{12} +(0.370005 + 3.28389i) q^{13} +(1.04618 + 1.56190i) q^{14} +(0.0866351 - 0.554282i) q^{15} +(-1.01275 - 0.690479i) q^{16} +(0.0235943 + 0.630570i) q^{17} +(-2.01577 + 0.540123i) q^{18} +(1.79095 + 3.10202i) q^{19} +(-0.882872 + 3.22456i) q^{20} +(-0.645919 - 0.153024i) q^{21} +(-0.872398 - 0.548164i) q^{22} +(2.08265 + 0.0779271i) q^{23} +(-0.616111 + 0.0928637i) q^{24} +(4.98979 - 0.319308i) q^{25} +(-1.59710 - 1.72126i) q^{26} +(0.792494 - 1.26125i) q^{27} +(3.72292 + 1.33716i) q^{28} +(0.472800 + 0.107914i) q^{29} +(0.184339 + 0.353434i) q^{30} +(-5.64184 - 3.25732i) q^{31} +(5.83367 - 0.218281i) q^{32} +(0.357468 - 0.0676366i) q^{33} +(-0.279545 - 0.350538i) q^{34} +(0.0808628 - 5.91553i) q^{35} +(-2.73794 + 3.43326i) q^{36} +(3.69909 - 6.99902i) q^{37} +(-2.33271 - 1.01775i) q^{38} +(0.826797 + 0.0619598i) q^{39} +(-2.00058 - 5.18020i) q^{40} +(-4.67387 + 9.70538i) q^{41} +(0.433834 - 0.185049i) q^{42} +(-12.1330 - 4.24553i) q^{43} +(-2.16199 + 0.162019i) q^{44} +(6.18700 + 2.20283i) q^{45} +(-1.22352 + 0.834179i) q^{46} +(-1.13255 - 1.53455i) q^{47} +(-0.217454 + 0.217454i) q^{48} +(-6.97088 - 0.637812i) q^{49} +(-2.71791 + 2.28789i) q^{50} +(0.156548 + 0.0235958i) q^{51} +(-4.85481 - 0.918579i) q^{52} +(0.557654 + 1.05513i) q^{53} +(0.0790931 + 1.05542i) q^{54} +(1.28042 + 2.97893i) q^{55} +(-6.29430 + 1.88501i) q^{56} +(0.848241 - 0.296812i) q^{57} +(-0.315829 + 0.137795i) q^{58} +(0.818329 - 10.9198i) q^{59} +(0.753732 + 0.368050i) q^{60} +(-3.36739 - 10.9168i) q^{61} +(4.59977 - 0.518269i) q^{62} +(3.16590 - 7.09655i) q^{63} +(-1.32635 + 1.05773i) q^{64} +(1.06152 + 7.31282i) q^{65} +(-0.175824 + 0.189494i) q^{66} +(-1.31551 - 4.90956i) q^{67} +(-0.911304 - 0.244183i) q^{68} +(0.116353 - 0.509775i) q^{69} +(2.44971 + 3.41599i) q^{70} +(1.90716 + 8.35583i) q^{71} +(0.272729 - 7.28883i) q^{72} +(0.424040 - 0.574554i) q^{73} +(0.838345 + 5.56205i) q^{74} +(0.154028 - 1.24497i) q^{75} +(-5.22118 + 1.19170i) q^{76} +(3.63152 - 1.23731i) q^{77} +(-0.498817 + 0.313428i) q^{78} +(8.89287 - 5.13430i) q^{79} +(-2.31274 - 1.47082i) q^{80} +(6.18508 + 5.73892i) q^{81} +(-1.42296 - 7.52055i) q^{82} +(-11.1688 - 1.25843i) q^{83} +(0.503286 - 0.855398i) q^{84} +(0.0977768 + 1.40759i) q^{85} +(8.72769 - 2.69214i) q^{86} +(0.0486558 - 0.111520i) q^{87} +(2.72955 - 2.34897i) q^{88} +(-3.16917 + 8.07490i) q^{89} +(-4.46651 + 1.35113i) q^{90} +(8.72395 - 0.581687i) q^{91} +(-1.02916 + 2.94117i) q^{92} +(-1.06615 + 1.23888i) q^{93} +(1.29494 + 0.399437i) q^{94} +(4.22424 + 6.80485i) q^{95} +(0.218294 - 1.44829i) q^{96} +(-6.86573 - 6.86573i) q^{97} +(4.25432 - 2.57659i) q^{98} +4.25892i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) \) 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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