LMFDB - Embedded newform 552.2.bb.a.85.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [552,2,Mod(13,552)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(552, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 0, 14]))

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

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

chi := DirichletCharacter("552.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 552 = 2^{3} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	552.bb (of order $22$, degree $10$, 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:	$4.40774219157$
Analytic rank:	$0$
Dimension:	$480$
Relative dimension:	$48$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			85.18
Character	$\chi$	$=$	552.85
Dual form			552.2.bb.a.13.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.507861 + 1.31988i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-1.48415 - 1.34063i) q^{4} +(-0.282332 + 0.128937i) q^{5} +(1.38492 - 0.286340i) q^{6} +(-2.03550 + 0.597678i) q^{7} +(2.52321 - 1.27805i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.507861 + 1.31988i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-1.48415 - 1.34063i) q^{4} +(-0.282332 + 0.128937i) q^{5} +(1.38492 - 0.286340i) q^{6} +(-2.03550 + 0.597678i) q^{7} +(2.52321 - 1.27805i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-0.0267952 - 0.438126i) q^{10} +(2.44920 - 2.12224i) q^{11} +(-0.325415 + 1.97335i) q^{12} +(-0.746025 + 2.54073i) q^{13} +(0.244892 - 2.99015i) q^{14} +(0.261109 + 0.167804i) q^{15} +(0.405427 + 3.97940i) q^{16} +(-0.439560 + 3.05721i) q^{17} +(-0.989630 - 1.01026i) q^{18} +(5.09241 - 0.732178i) q^{19} +(0.591881 + 0.187141i) q^{20} +(1.60327 + 1.38925i) q^{21} +(1.55725 + 4.31044i) q^{22} +(-2.97624 + 3.76059i) q^{23} +(-2.43931 - 1.43169i) q^{24} +(-3.21122 + 3.70594i) q^{25} +(-2.97457 - 2.27500i) q^{26} +(0.989821 - 0.142315i) q^{27} +(3.82226 + 1.84181i) q^{28} +(-3.10286 - 0.446125i) q^{29} +(-0.354088 + 0.259410i) q^{30} +(7.94222 + 5.10415i) q^{31} +(-5.45822 - 1.48587i) q^{32} +(-3.10948 - 0.913025i) q^{33} +(-3.81191 - 2.13280i) q^{34} +(0.497625 - 0.431195i) q^{35} +(1.83602 - 0.793117i) q^{36} +(4.16590 + 1.90250i) q^{37} +(-1.61985 + 7.09321i) q^{38} +(2.54073 - 0.746025i) q^{39} +(-0.547596 + 0.686169i) q^{40} +(2.96470 + 6.49179i) q^{41} +(-2.64787 + 1.41058i) q^{42} +(6.68988 + 10.4097i) q^{43} +(-6.48012 - 0.133732i) q^{44} -0.310381i q^{45} +(-3.45200 - 5.83813i) q^{46} -9.79663 q^{47} +(3.12849 - 2.49249i) q^{48} +(-2.10272 + 1.35134i) q^{49} +(-3.26054 - 6.12052i) q^{50} +(2.80953 - 1.28307i) q^{51} +(4.51339 - 2.77069i) q^{52} +(0.793158 + 2.70125i) q^{53} +(-0.314854 + 1.37872i) q^{54} +(-0.417852 + 0.914968i) q^{55} +(-4.37214 + 4.10954i) q^{56} +(-3.36911 - 3.88816i) q^{57} +(2.16465 - 3.86883i) q^{58} +(3.65887 - 12.4610i) q^{59} +(-0.162562 - 0.599098i) q^{60} +(-4.26144 + 6.63092i) q^{61} +(-10.7704 + 7.89055i) q^{62} +(0.301912 - 2.09984i) q^{63} +(4.73319 - 6.44957i) q^{64} +(-0.116966 - 0.813519i) q^{65} +(2.78426 - 3.64044i) q^{66} +(-2.86686 - 2.48415i) q^{67} +(4.75096 - 3.94808i) q^{68} +(4.77268 + 0.470644i) q^{69} +(0.316400 + 0.875792i) q^{70} +(4.09465 - 4.72548i) q^{71} +(0.114374 + 2.82611i) q^{72} +(-1.30557 - 9.08045i) q^{73} +(-4.62677 + 4.53227i) q^{74} +(4.85375 + 0.697864i) q^{75} +(-8.53950 - 5.74037i) q^{76} +(-3.71693 + 5.78366i) q^{77} +(-0.305675 + 3.73233i) q^{78} +(1.58653 + 0.465846i) q^{79} +(-0.627556 - 1.07124i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-10.0740 + 0.616115i) q^{82} +(-3.67870 - 1.68001i) q^{83} +(-0.517044 - 4.21125i) q^{84} +(-0.270085 - 0.919824i) q^{85} +(-17.1370 + 3.54316i) q^{86} +(1.30223 + 2.85149i) q^{87} +(3.46751 - 8.48505i) q^{88} +(2.05200 - 1.31874i) q^{89} +(0.409664 + 0.157630i) q^{90} -5.61754i q^{91} +(9.45875 - 1.59126i) q^{92} -9.44093i q^{93} +(4.97533 - 12.9304i) q^{94} +(-1.34335 + 0.863317i) q^{95} +(1.70094 + 5.39507i) q^{96} +(5.20118 + 11.3890i) q^{97} +(-0.715709 - 3.46162i) q^{98} +(0.913025 + 3.10948i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	$ 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) $ 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/552\mathbb{Z}\right)^\times$.

$n$	$97$	$185$	$277$	$415$
$\chi(n)$	$e\left(\frac{4}{11}\right)$	$1$	$-1$	$1$

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 $

$2$	−0.507861	+	1.31988i	−0.359112	+	0.933294i
$2$	−0.507861	+	1.31988i	−0.359112	+	0.933294i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$3$	−0.540641	−	0.841254i	−0.312139	−	0.485698i
$4$	−1.48415	−	1.34063i	−0.742077	−	0.670315i
$5$	−0.282332	+	0.128937i	−0.126263	+	0.0576623i	−0.477545	−	0.878607i	$-0.658473\pi$
$5$	−0.282332	+	0.128937i	−0.126263	+	0.0576623i	0.351282	+	0.936270i	$0.385746\pi$
$6$	1.38492	−	0.286340i	0.565392	−	0.116898i
$7$	−2.03550	+	0.597678i	−0.769348	+	0.225901i	−0.642774	−	0.766056i	$-0.722216\pi$
$7$	−2.03550	+	0.597678i	−0.769348	+	0.225901i	−0.126574	+	0.991957i	$0.540398\pi$
$8$	2.52321	−	1.27805i	0.892090	−	0.451858i
$9$	−0.415415	+	0.909632i	−0.138472	+	0.303211i
$10$	−0.0267952	−	0.438126i	−0.00847340	−	0.138548i
$11$	2.44920	−	2.12224i	0.738461	−	0.639880i	−0.202155	−	0.979354i	$-0.564794\pi$
$11$	2.44920	−	2.12224i	0.738461	−	0.639880i	0.940615	+	0.339474i	$0.110249\pi$
$12$	−0.325415	+	1.97335i	−0.0939392	+	0.569657i
$13$	−0.746025	+	2.54073i	−0.206910	+	0.704671i	0.789006	+	0.614386i	$0.210596\pi$
$13$	−0.746025	+	2.54073i	−0.206910	+	0.704671i	−0.995916	+	0.0902853i	$0.971222\pi$
$14$	0.244892	−	2.99015i	0.0654500	−	0.799152i
$15$	0.261109	+	0.167804i	0.0674180	+	0.0433269i
$16$	0.405427	+	3.97940i	0.101357	+	0.994850i
$17$	−0.439560	+	3.05721i	−0.106609	+	0.741482i	0.864463	+	0.502696i	$0.167659\pi$
$17$	−0.439560	+	3.05721i	−0.106609	+	0.741482i	−0.971072	+	0.238786i	$0.923251\pi$
$18$	−0.989630	−	1.01026i	−0.233258	−	0.238121i
$19$	5.09241	−	0.732178i	1.16828	−	0.167973i	0.469250	−	0.883066i	$-0.344524\pi$
$19$	5.09241	−	0.732178i	1.16828	−	0.167973i	0.699030	+	0.715092i	$0.253615\pi$
$20$	0.591881	+	0.187141i	0.132349	+	0.0418459i
$21$	1.60327	+	1.38925i	0.349863	+	0.303158i
$22$	1.55725	+	4.31044i	0.332006	+	0.918990i
$23$	−2.97624	+	3.76059i	−0.620588	+	0.784136i
$23$	−2.97624	+	3.76059i	−0.620588	+	0.784136i
$24$	−2.43931	−	1.43169i	−0.497923	−	0.292244i
$25$	−3.21122	+	3.70594i	−0.642243	+	0.741188i
$26$	−2.97457	−	2.27500i	−0.583362	−	0.446164i
$27$	0.989821	−	0.142315i	0.190491	−	0.0273885i
$28$	3.82226	+	1.84181i	0.722340	+	0.348069i
$29$	−3.10286	−	0.446125i	−0.576188	−	0.0828433i	−0.151940	−	0.988390i	$-0.548552\pi$
$29$	−3.10286	−	0.446125i	−0.576188	−	0.0828433i	−0.424247	+	0.905546i	$0.639461\pi$
$30$	−0.354088	+	0.259410i	−0.0646474	+	0.0473616i
$31$	7.94222	+	5.10415i	1.42646	+	0.916733i	0.999925	+	0.0122642i	$0.00390390\pi$
$31$	7.94222	+	5.10415i	1.42646	+	0.916733i	0.426540	+	0.904469i	$0.359732\pi$
$32$	−5.45822	−	1.48587i	−0.964887	−	0.262667i
$33$	−3.10948	−	0.913025i	−0.541291	−	0.158937i
$34$	−3.81191	−	2.13280i	−0.653737	−	0.365773i
$35$	0.497625	−	0.431195i	0.0841140	−	0.0728852i
$36$	1.83602	−	0.793117i	0.306003	−	0.132186i
$37$	4.16590	+	1.90250i	0.684869	+	0.312769i	0.727290	−	0.686331i	$-0.240780\pi$
$37$	4.16590	+	1.90250i	0.684869	+	0.312769i	−0.0424206	+	0.999100i	$0.513507\pi$
$38$	−1.61985	+	7.09321i	−0.262775	+	1.15067i
$39$	2.54073	−	0.746025i	0.406842	−	0.119460i
$40$	−0.547596	+	0.686169i	−0.0865826	+	0.108493i
$41$	2.96470	+	6.49179i	0.463009	+	1.01385i	0.986791	+	0.161996i	$0.0517930\pi$
$41$	2.96470	+	6.49179i	0.463009	+	1.01385i	−0.523783	+	0.851852i	$0.675480\pi$
$42$	−2.64787	+	1.41058i	−0.408576	+	0.217658i
$43$	6.68988	+	10.4097i	1.02020	+	1.58746i	0.788849	+	0.614587i	$0.210677\pi$
$43$	6.68988	+	10.4097i	1.02020	+	1.58746i	0.231348	+	0.972871i	$0.425686\pi$
$44$	−6.48012	−	0.133732i	−0.976915	−	0.0201609i
$45$		−	0.310381i		−	0.0462688i
$46$	−3.45200	−	5.83813i	−0.508969	−	0.860785i
$47$	−9.79663			−1.42899			−0.714493	−	0.699643i	$-0.753342\pi$
$47$	−9.79663			−1.42899			−0.714493	+	0.699643i	$0.753342\pi$
$48$	3.12849	−	2.49249i	0.451559	−	0.359760i
$49$	−2.10272	+	1.35134i	−0.300389	+	0.193048i
$50$	−3.26054	−	6.12052i	−0.461110	−	0.865572i
$51$	2.80953	−	1.28307i	0.393413	−	0.179666i
$52$	4.51339	−	2.77069i	0.625894	−	0.384225i
$53$	0.793158	+	2.70125i	0.108949	+	0.371045i	0.995861	−	0.0908935i	$-0.0289723\pi$
$53$	0.793158	+	2.70125i	0.108949	+	0.371045i	−0.886912	+	0.461938i	$0.847154\pi$
$54$	−0.314854	+	1.37872i	−0.0428462	+	0.187620i
$55$	−0.417852	+	0.914968i	−0.0563432	+	0.123374i
$56$	−4.37214	+	4.10954i	−0.584252	+	0.549160i
$57$	−3.36911	−	3.88816i	−0.446250	−	0.515000i
$58$	2.16465	−	3.86883i	0.284233	−	0.508003i
$59$	3.65887	−	12.4610i	0.476344	−	1.62228i	−0.274350	−	0.961630i	$-0.588463\pi$
$59$	3.65887	−	12.4610i	0.476344	−	1.62228i	0.750695	−	0.660649i	$-0.229719\pi$
$60$	−0.162562	−	0.599098i	−0.0209867	−	0.0773432i
$61$	−4.26144	+	6.63092i	−0.545621	+	0.849003i	−0.999107	−	0.0422608i	$-0.986544\pi$
$61$	−4.26144	+	6.63092i	−0.545621	+	0.849003i	0.453486	+	0.891264i	$0.350180\pi$
$62$	−10.7704	+	7.89055i	−1.36784	+	1.00210i
$63$	0.301912	−	2.09984i	0.0380373	−	0.264555i
$64$	4.73319	−	6.44957i	0.591648	−	0.806196i
$65$	−0.116966	−	0.813519i	−0.0145079	−	0.100905i
$66$	2.78426	−	3.64044i	0.342719	−	0.448107i
$67$	−2.86686	−	2.48415i	−0.350243	−	0.303487i	0.461916	−	0.886924i	$-0.347162\pi$
$67$	−2.86686	−	2.48415i	−0.350243	−	0.303487i	−0.812159	+	0.583437i	$0.801708\pi$
$68$	4.75096	−	3.94808i	0.576139	−	0.478775i
$69$	4.77268	+	0.470644i	0.574563	+	0.0566589i
$70$	0.316400	+	0.875792i	0.0378170	+	0.104677i
$71$	4.09465	−	4.72548i	0.485946	−	0.560811i	−0.458832	−	0.888523i	$-0.651732\pi$
$71$	4.09465	−	4.72548i	0.485946	−	0.560811i	0.944778	+	0.327712i	$0.106278\pi$
$72$	0.114374	+	2.82611i	0.0134791	+	0.333061i
$73$	−1.30557	−	9.08045i	−0.152806	−	1.06279i	−0.911488	−	0.411326i	$-0.865066\pi$
$73$	−1.30557	−	9.08045i	−0.152806	−	1.06279i	0.758683	−	0.651460i	$-0.225843\pi$
$74$	−4.62677	+	4.53227i	−0.537851	+	0.526865i
$75$	4.85375	+	0.697864i	0.560463	+	0.0805824i
$76$	−8.53950	−	5.74037i	−0.979548	−	0.658466i
$77$	−3.71693	+	5.78366i	−0.423584	+	0.659109i
$78$	−0.305675	+	3.73233i	−0.0346109	+	0.422603i
$79$	1.58653	+	0.465846i	0.178498	+	0.0524118i	0.369760	−	0.929127i	$-0.379440\pi$
$79$	1.58653	+	0.465846i	0.178498	+	0.0524118i	−0.191262	+	0.981539i	$0.561258\pi$
$80$	−0.627556	−	1.07124i	−0.0701629	−	0.119768i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−10.0740	+	0.616115i	−1.11249	+	0.0680385i
$83$	−3.67870	−	1.68001i	−0.403790	−	0.184405i	0.203159	−	0.979146i	$-0.434879\pi$
$83$	−3.67870	−	1.68001i	−0.403790	−	0.184405i	−0.606948	+	0.794741i	$0.707607\pi$
$84$	−0.517044	−	4.21125i	−0.0564141	−	0.459485i
$85$	−0.270085	−	0.919824i	−0.0292948	−	0.0997689i
$86$	−17.1370	+	3.54316i	−1.84793	+	0.382069i
$87$	1.30223	+	2.85149i	0.139614	+	0.305712i
$88$	3.46751	−	8.48505i	0.369638	−	0.904510i
$89$	2.05200	−	1.31874i	0.217512	−	0.139786i	−0.427348	−	0.904087i	$-0.640552\pi$
$89$	2.05200	−	1.31874i	0.217512	−	0.139786i	0.644860	+	0.764301i	$0.276916\pi$
$90$	0.409664	+	0.157630i	0.0431824	+	0.0166157i
$91$		−	5.61754i		−	0.588878i
$92$	9.45875	−	1.59126i	0.986143	−	0.165900i
$93$		−	9.44093i		−	0.978979i
$94$	4.97533	−	12.9304i	0.513166	−	1.33366i
$95$	−1.34335	+	0.863317i	−0.137825	+	0.0885744i
$96$	1.70094	+	5.39507i	0.173602	+	0.550632i
$97$	5.20118	+	11.3890i	0.528099	+	1.15638i	0.966281	+	0.257490i	$0.0828954\pi$
$97$	5.20118	+	11.3890i	0.528099	+	1.15638i	−0.438182	+	0.898886i	$0.644377\pi$
$98$	−0.715709	−	3.46162i	−0.0722975	−	0.349677i
$99$	0.913025	+	3.10948i	0.0917625	+	0.312514i
$100$	9.73423	−	1.19514i	0.973423	−	0.119514i
$101$	3.56977	+	1.63026i	0.355206	+	0.162217i	0.585023	−	0.811017i	$-0.301086\pi$
$101$	3.56977	+	1.63026i	0.355206	+	0.162217i	−0.229817	+	0.973234i	$0.573813\pi$
$102$	0.266644	+	4.35986i	0.0264017	+	0.431691i
$103$	−1.71994	−	1.98492i	−0.169471	−	0.195580i	0.664661	−	0.747145i	$-0.268576\pi$
$103$	−1.71994	−	1.98492i	−0.169471	−	0.195580i	−0.834132	+	0.551566i	$0.814031\pi$
$104$	1.36479	+	7.36425i	0.133829	+	0.722124i
$105$	−0.631781	−	0.185508i	−0.0616555	−	0.0181037i
$106$	−3.96813	−	0.324987i	−0.385419	−	0.0315656i
$107$	3.82103	−	5.94564i	0.369393	−	0.574787i	−0.605944	−	0.795507i	$-0.707204\pi$
$107$	3.82103	−	5.94564i	0.369393	−	0.574787i	0.975337	+	0.220720i	$0.0708408\pi$
$108$	−1.65984	−	1.11577i	−0.159718	−	0.107365i
$109$	−6.31166	−	0.907480i	−0.604548	−	0.0869208i	−0.166757	−	0.985998i	$-0.553330\pi$
$109$	−6.31166	−	0.907480i	−0.604548	−	0.0869208i	−0.437790	+	0.899077i	$0.644239\pi$
$110$	−0.995436	−	1.01619i	−0.0949111	−	0.0968900i
$111$	−0.651768	−	4.53314i	−0.0618631	−	0.430267i
$112$	−3.20365	−	7.85777i	−0.302716	−	0.742489i
$113$	8.79321	−	10.1479i	0.827196	−	0.954635i	−0.172342	−	0.985037i	$-0.555133\pi$
$113$	8.79321	−	10.1479i	0.827196	−	0.954635i	0.999538	+	0.0304024i	$0.00967886\pi$
$114$	6.84294	−	2.47217i	0.640900	−	0.231540i
$115$	0.355410	−	1.44548i	0.0331421	−	0.134792i
$116$	4.00704	+	4.82191i	0.372044	+	0.447703i
$117$	−2.00122	−	1.73406i	−0.185013	−	0.160314i
$118$	14.5887	+	11.1577i	1.34300	+	1.02715i
$119$	−0.932499	−	6.48568i	−0.0854821	−	0.594541i
$120$	0.873295	+	0.0896963i	0.0797205	+	0.00818812i
$121$	−0.0708058	+	0.492465i	−0.00643689	+	0.0447696i
$122$	−6.58779	−	8.99216i	−0.596431	−	0.814112i
$123$	3.85840	−	6.00379i	0.347901	−	0.541344i
$124$	−4.94470	−	18.2229i	−0.444047	−	1.63647i
$125$	0.866019	−	2.94939i	0.0774591	−	0.263802i
$126$	2.61821	+	1.46492i	0.233248	+	0.130505i
$127$	12.9567	+	14.9528i	1.14972	+	1.32685i	0.936834	+	0.349773i	$0.113741\pi$
$127$	12.9567	+	14.9528i	1.14972	+	1.32685i	0.212887	+	0.977077i	$0.431713\pi$
$128$	6.10884	+	9.52271i	0.539951	+	0.841697i
$129$	5.14034	−	11.2558i	0.452582	−	0.991015i
$130$	1.13315	+	0.258773i	0.0993837	+	0.0226959i
$131$	1.82660	+	6.22083i	0.159591	+	0.543516i	0.999999	+	0.00156190i	$0.000497168\pi$
$131$	1.82660	+	6.22083i	0.159591	+	0.543516i	−0.840408	+	0.541954i	$0.817685\pi$
$132$	3.39092	+	5.52373i	0.295141	+	0.480779i
$133$	−9.92802	+	4.53397i	−0.860868	+	0.393145i
$134$	4.73474	−	2.52230i	0.409019	−	0.217894i
$135$	−0.261109	+	0.167804i	−0.0224727	+	0.0144423i
$136$	2.79816	+	8.27576i	0.239940	+	0.709641i
$137$	−9.47639			−0.809623			−0.404811	−	0.914400i	$-0.632663\pi$
$137$	−9.47639			−0.809623			−0.404811	+	0.914400i	$0.632663\pi$
$138$	−3.04505	+	6.06033i	−0.259212	+	0.515890i
$139$		−	8.33370i		−	0.706855i	−0.935462	−	0.353427i	$-0.885016\pi$
$139$		−	8.33370i		−	0.706855i	0.935462	−	0.353427i	$-0.114984\pi$
$140$	−1.31663	−	0.0271715i	−0.111275	−	0.00229641i
$141$	5.29646	+	8.24145i	0.446042	+	0.694055i
$142$	4.15754	+	7.80432i	0.348893	+	0.654924i
$143$	3.56487	+	7.80599i	0.298110	+	0.652769i
$144$	−3.78821	−	1.28431i	−0.315684	−	0.107026i
$145$	0.933560	−	0.274118i	0.0775280	−	0.0227643i
$146$	12.6481	+	2.88841i	1.04677	+	0.239047i
$147$	2.27363	+	1.03833i	0.187526	+	0.0856403i
$148$	−3.63228	−	8.40853i	−0.298572	−	0.691177i
$149$	−16.7180	+	14.4862i	−1.36959	+	1.18676i	−0.407772	+	0.913084i	$0.633694\pi$
$149$	−16.7180	+	14.4862i	−1.36959	+	1.18676i	−0.961822	+	0.273676i	$0.911760\pi$
$150$	−3.38613	+	6.05194i	−0.276476	+	0.494139i
$151$	22.6227	+	6.64263i	1.84101	+	0.540570i	1.00000		0.000446619i	$-0.000142163\pi$
$151$	22.6227	+	6.64263i	1.84101	+	0.540570i	0.841012	+	0.541016i	$0.181960\pi$
$152$	11.9135	−	8.35579i	0.966310	−	0.677744i
$153$	−2.59834	−	1.66985i	−0.210063	−	0.134999i
$154$	−5.74604	−	7.84319i	−0.463029	−	0.632022i
$155$	−2.90046	−	0.417023i	−0.232970	−	0.0334961i
$156$	−4.77097	−	2.29896i	−0.381984	−	0.184064i
$157$	−2.42589	+	0.348791i	−0.193607	+	0.0278365i	−0.238436	−	0.971158i	$-0.576635\pi$
$157$	−2.42589	+	0.348791i	−0.193607	+	0.0278365i	0.0448290	+	0.998995i	$0.485726\pi$
$158$	−1.42059	+	1.85744i	−0.113016	+	0.147770i
$159$	1.84362	−	2.12765i	0.146209	−	0.168734i
$160$	1.73262	−	0.284257i	0.136975	−	0.0224725i
$161$	3.81052	−	9.43352i	0.300311	−	0.743465i
$162$	1.33008	−	0.480520i	0.104501	−	0.0377532i
$163$	−13.7415	−	11.9070i	−1.07631	−	0.932631i	−0.0783825	−	0.996923i	$-0.524976\pi$
$163$	−13.7415	−	11.9070i	−1.07631	−	0.932631i	−0.997931	+	0.0642923i	$0.979521\pi$
$164$	4.30301	−	13.6094i	0.336009	−	1.06271i
$165$	0.995628	−	0.143150i	0.0775096	−	0.0111442i
$166$	4.08567	−	4.00222i	0.317109	−	0.310633i
$167$	−0.763769	+	5.31213i	−0.0591022	+	0.411065i	0.938696	+	0.344745i	$0.112035\pi$
$167$	−0.763769	+	5.31213i	−0.0591022	+	0.411065i	−0.997798	+	0.0663195i	$0.978874\pi$
$168$	5.82092	+	1.45630i	0.449094	+	0.112356i
$169$	5.03755	+	3.23744i	0.387504	+	0.249034i
$170$	1.35122	+	0.110664i	0.103634	+	0.00848755i
$171$	−1.44945	+	4.93638i	−0.110842	+	0.377494i
$172$	4.02668	−	24.4182i	0.307031	−	1.86187i
$173$	−0.491897	+	0.426231i	−0.0373982	+	0.0324058i	−0.673359	−	0.739315i	$-0.735149\pi$
$173$	−0.491897	+	0.426231i	−0.0373982	+	0.0324058i	0.635961	+	0.771721i	$0.280604\pi$
$174$	−4.42497	+	0.270626i	−0.335456	+	0.0205161i
$175$	4.32148	−	9.46273i	0.326673	−	0.715315i
$176$	9.43822	+	8.88592i	0.711432	+	0.669802i
$177$	−12.4610	+	3.65887i	−0.936623	+	0.275017i
$178$	0.698446	+	3.37813i	0.0523507	+	0.253202i
$179$	8.62260	−	3.93781i	0.644483	−	0.294326i	−0.0662333	−	0.997804i	$-0.521098\pi$
$179$	8.62260	−	3.93781i	0.644483	−	0.294326i	0.710717	+	0.703479i	$0.248371\pi$
$180$	−0.416105	+	0.460653i	−0.0310147	+	0.0343350i
$181$	−2.03281	−	3.16311i	−0.151097	−	0.235112i	0.757451	−	0.652892i	$-0.226445\pi$
$181$	−2.03281	−	3.16311i	−0.151097	−	0.235112i	−0.908548	+	0.417780i	$0.862808\pi$
$182$	7.41447	+	2.85293i	0.549597	+	0.211473i
$183$	7.88219			0.582669
$184$	−2.70346	+	13.2925i	−0.199302	+	0.979938i
$185$	−1.42147			−0.104508
$186$	12.4609	+	4.79468i	0.913676	+	0.351563i
$187$	5.41157	+	8.42056i	0.395733	+	0.615772i
$188$	14.5397	+	13.1337i	1.06042	+	0.957870i
$189$	−1.92973	+	0.881276i	−0.140367	+	0.0641034i
$190$	−0.457239	−	2.21150i	−0.0331716	−	0.160439i
$191$	−17.9601	+	5.27356i	−1.29955	+	0.381581i	−0.857071	−	0.515199i	$-0.827718\pi$
$191$	−17.9601	+	5.27356i	−1.29955	+	0.381581i	−0.442476	+	0.896780i	$0.645900\pi$
$192$	−7.98468	−	0.494908i	−0.576244	−	0.0357169i
$193$	1.09583	−	2.39952i	0.0788792	−	0.172721i	−0.866084	−	0.499899i	$-0.833370\pi$
$193$	1.09583	−	2.39952i	0.0788792	−	0.172721i	0.944963	+	0.327178i	$0.106098\pi$
$194$	−17.6735	+	1.08089i	−1.26889	+	0.0776035i
$195$	−0.621139	+	0.538220i	−0.0444807	+	0.0385427i
$196$	4.93240	+	0.813377i	0.352314	+	0.0580984i
$197$	2.65182	−	9.03127i	0.188934	−	0.643451i	−0.809479	−	0.587148i	$-0.800251\pi$
$197$	2.65182	−	9.03127i	0.188934	−	0.643451i	0.998414	−	0.0563031i	$-0.0179313\pi$
$198$	−4.56782	−	0.374102i	−0.324621	−	0.0265863i
$199$	−10.7606	−	6.91539i	−0.762796	−	0.490219i	0.100488	−	0.994938i	$-0.467960\pi$
$199$	−10.7606	−	6.91539i	−0.762796	−	0.490219i	−0.863283	+	0.504719i	$0.831596\pi$
$200$	−3.36620	+	13.4550i	−0.238027	+	0.951410i
$201$	−0.539857	+	3.75479i	−0.0380786	+	0.264842i
$202$	−3.96469	+	3.88372i	−0.278955	+	0.273257i
$203$	6.58253	−	0.946425i	0.462003	−	0.0664260i
$204$	−5.88990	−	1.86227i	−0.412376	−	0.130385i
$205$	−1.67406	−	1.45058i	−0.116922	−	0.101313i
$206$	3.49334	−	1.26205i	0.243392	−	0.0879311i
$207$	−2.18438	−	4.26949i	−0.151825	−	0.296750i
$208$	−10.4130	−	1.93865i	−0.722014	−	0.134421i
$209$	10.9185	−	12.6006i	0.755246	−	0.871600i
$210$	0.565704	−	0.739661i	0.0390373	−	0.0510415i
$211$	−22.1431	+	3.18369i	−1.52439	+	0.219175i	−0.852994	−	0.521921i	$-0.825215\pi$
$211$	−22.1431	+	3.18369i	−1.52439	+	0.219175i	−0.671399	+	0.741096i	$0.734306\pi$
$212$	2.44420	−	5.07240i	0.167869	−	0.348374i
$213$	−6.18906	−	0.889853i	−0.424067	−	0.0609717i
$214$	5.90697	+	8.06286i	0.403792	+	0.551166i
$215$	−3.23096	−	2.07641i	−0.220349	−	0.141610i
$216$	2.31564	−	1.62413i	0.157560	−	0.110508i
$217$	−19.2170	−	5.64263i	−1.30454	−	0.383047i
$218$	4.40321	−	7.86975i	0.298223	−	0.533007i
$219$	−6.93311	+	6.00758i	−0.468496	+	0.405954i
$220$	1.84679	−	0.797769i	0.124511	−	0.0537856i
$221$	−7.43961	−	3.39756i	−0.500443	−	0.228544i
$222$	6.31420	+	1.44195i	0.423782	+	0.0967776i
$223$	−12.2796	+	3.60562i	−0.822303	+	0.241450i	−0.665707	−	0.746213i	$-0.731870\pi$
$223$	−12.2796	+	3.60562i	−0.822303	+	0.241450i	−0.156596	+	0.987663i	$0.550052\pi$
$224$	11.9983	−	0.237765i	0.801670	−	0.0158864i
$225$	−2.03706	−	4.46053i	−0.135804	−	0.297369i
$226$	8.92827	+	16.7597i	0.593899	+	1.11484i
$227$	−9.00232	−	14.0079i	−0.597505	−	0.929736i	−0.999898	−	0.0142690i	$-0.995458\pi$
$227$	−9.00232	−	14.0079i	−0.597505	−	0.929736i	0.402393	−	0.915467i	$-0.368178\pi$
$228$	−0.212303	+	10.2874i	−0.0140601	+	0.681298i
$229$		−	9.55860i		−	0.631650i	−0.948817	−	0.315825i	$-0.897719\pi$
$229$		−	9.55860i		−	0.631650i	0.948817	−	0.315825i	$-0.102281\pi$
$230$	1.72736	+	1.20320i	0.113899	+	0.0793367i
$231$	6.87505			0.452345
$232$	−8.39935	+	2.83994i	−0.551444	+	0.186452i
$233$	−0.768576	+	0.493934i	−0.0503511	+	0.0323587i	−0.565574	−	0.824697i	$-0.691345\pi$
$233$	−0.768576	+	0.493934i	−0.0503511	+	0.0323587i	0.515223	+	0.857056i	$0.327709\pi$
$234$	3.30509	−	1.76070i	0.216061	−	0.115100i
$235$	2.76590	−	1.26315i	0.180428	−	0.0823986i
$236$	−22.1359	+	13.5888i	−1.44092	+	0.884556i
$237$	−0.465846	−	1.58653i	−0.0302600	−	0.103056i
$238$	9.03388	+	2.06304i	0.585579	+	0.133727i
$239$	9.22254	−	20.1945i	0.596556	−	1.30628i	−0.334842	−	0.942274i	$-0.608683\pi$
$239$	9.22254	−	20.1945i	0.596556	−	1.30628i	0.931398	−	0.364002i	$-0.118590\pi$
$240$	−0.561901	+	1.10709i	−0.0362705	+	0.0714623i
$241$	−12.4181	−	14.3313i	−0.799921	−	0.923158i	0.198456	−	0.980110i	$-0.436407\pi$
$241$	−12.4181	−	14.3313i	−0.799921	−	0.923158i	−0.998377	+	0.0569516i	$0.981862\pi$
$242$	−0.614034	−	0.343559i	−0.0394716	−	0.0220848i
$243$	−0.281733	+	0.959493i	−0.0180732	+	0.0615515i
$244$	15.2142	−	4.12831i	0.973992	−	0.264288i
$245$	0.419429	−	0.652644i	0.0267963	−	0.0416959i
$246$	5.96474	+	8.14171i	0.380298	+	0.519097i
$247$	−1.93880	+	13.4847i	−0.123363	+	0.858008i
$248$	26.5632	+	2.72832i	1.68677	+	0.173248i
$249$	0.575544	+	4.00300i	0.0364736	+	0.253680i
$250$	3.45302	+	2.64092i	0.218388	+	0.167026i
$251$	3.17575	+	2.75180i	0.200451	+	0.173692i	0.749302	−	0.662228i	$-0.230389\pi$
$251$	3.17575	+	2.75180i	0.200451	+	0.173692i	−0.548851	+	0.835920i	$0.684934\pi$
$252$	−3.26319	+	2.71174i	−0.205562	+	0.170823i
$253$	0.691479	+	15.5267i	0.0434729	+	0.976156i
$254$	−26.3161	+	9.50730i	−1.65122	+	0.596541i
$255$	−0.627787	+	0.724504i	−0.0393135	+	0.0453702i
$256$	−15.6713	+	3.22671i	−0.979454	+	0.201669i
$257$	0.0190142	+	0.132247i	0.00118607	+	0.00824933i	0.990406	−	0.138189i	$-0.0441281\pi$
$257$	0.0190142	+	0.132247i	0.00118607	+	0.00824933i	−0.989220	+	0.146438i	$0.953219\pi$
$258$	12.2457	+	12.5010i	0.762382	+	0.778278i
$259$	−9.61678	−	1.38268i	−0.597557	−	0.0859158i
$260$	−0.917031	+	1.36420i	−0.0568719	+	0.0846039i
$261$	1.69479	−	2.63714i	0.104905	−	0.163235i
$262$	−9.13839	−	0.748428i	−0.564571	−	0.0462380i
$263$	−21.2656	−	6.24415i	−1.31129	−	0.385031i	−0.449951	−	0.893053i	$-0.648558\pi$
$263$	−21.2656	−	6.24415i	−1.31129	−	0.385031i	−0.861344	+	0.508023i	$0.830377\pi$
$264$	−9.01276	+	1.67031i	−0.554697	+	0.102800i
$265$	−0.572224	−	0.660382i	−0.0351514	−	0.0405669i
$266$	−0.942236	−	15.4064i	−0.0577722	−	0.944627i
$267$	−2.21879	−	1.01329i	−0.135788	−	0.0620123i
$268$	0.924541	+	7.53026i	0.0564753	+	0.459984i
$269$	2.75651	+	9.38781i	0.168067	+	0.572385i	0.999851	+	0.0172843i	$0.00550205\pi$
$269$	2.75651	+	9.38781i	0.168067	+	0.572385i	−0.831783	+	0.555101i	$0.812680\pi$
$270$	−0.0888743	−	0.429853i	−0.00540872	−	0.0261600i
$271$	−2.04849	−	4.48556i	−0.124437	−	0.272478i	0.837153	−	0.546968i	$-0.184218\pi$
$271$	−2.04849	−	4.48556i	−0.124437	−	0.272478i	−0.961590	+	0.274490i	$0.911491\pi$
$272$	−12.3441	−	0.509713i	−0.748469	−	0.0309059i
$273$	−4.72578	+	3.03707i	−0.286017	+	0.183812i
$274$	4.81269	−	12.5077i	0.290745	−	0.755616i
$275$			15.8916i			0.958297i
$276$	−6.45244	−	7.09691i	−0.388391	−	0.427183i
$277$			11.8332i			0.710987i	0.934679	+	0.355494i	$0.115687\pi$
$277$			11.8332i			0.710987i	−0.934679	+	0.355494i	$0.884313\pi$
$278$	10.9995	+	4.23236i	0.659704	+	0.253840i
$279$	−7.94222	+	5.10415i	−0.475488	+	0.305578i
$280$	0.704526	−	1.72398i	0.0421035	−	0.103028i
$281$	13.3432	+	29.2175i	0.795986	+	1.74297i	0.658659	+	0.752442i	$0.271124\pi$
$281$	13.3432	+	29.2175i	0.795986	+	1.74297i	0.137327	+	0.990526i	$0.456149\pi$
$282$	−13.5676	+	2.80516i	−0.807937	+	0.167045i
$283$	6.37463	+	21.7100i	0.378933	+	1.29053i	0.899581	+	0.436755i	$0.143872\pi$
$283$	6.37463	+	21.7100i	0.378933	+	1.29053i	−0.520648	+	0.853771i	$0.674310\pi$
$284$	−12.4122	+	1.52393i	−0.736529	+	0.0904286i
$285$	1.45254	+	0.663351i	0.0860408	+	0.0392935i
$286$	−12.1134	+	0.740841i	−0.716281	+	0.0438068i
$287$	−9.91466	−	11.4421i	−0.585244	−	0.675407i
$288$	3.61902	−	4.34772i	0.213253	−	0.256192i
$289$	7.15806	+	2.10180i	0.421062	+	0.123635i
$290$	−0.112317	+	1.37140i	−0.00659547	+	0.0805314i
$291$	6.76906	−	10.5329i	0.396809	−	0.617447i
$292$	−10.2358	+	15.2271i	−0.599008	+	0.891097i
$293$	7.26497	+	1.04455i	0.424424	+	0.0610230i	0.351218	−	0.936294i	$-0.385768\pi$
$293$	7.26497	+	1.04455i	0.424424	+	0.0610230i	0.0732066	+	0.997317i	$0.476677\pi$
$294$	−2.52516	+	2.47359i	−0.147270	+	0.144263i
$295$	0.573660	+	3.98989i	0.0333998	+	0.232301i
$296$	12.9429	−	0.523805i	0.752292	−	0.0304456i
$297$	2.12224	−	2.44920i	0.123145	−	0.142117i
$298$	−10.6296	−	29.4227i	−0.615759	−	1.70441i
$299$	−7.33428	−	10.3673i	−0.424152	−	0.599556i
$300$	−6.26814	−	7.54282i	−0.361891	−	0.435485i
$301$	−19.8389	−	17.1905i	−1.14349	−	0.990844i
$302$	−20.2567	+	26.4857i	−1.16564	+	1.52408i
$303$	−0.558503	−	3.88447i	−0.0320851	−	0.223157i
$304$	4.97823	+	19.9679i	0.285521	+	1.14524i
$305$	0.348171	−	2.42158i	0.0199362	−	0.138659i
$306$	3.52359	−	2.58143i	0.201430	−	0.147571i
$307$	−9.32588	+	14.5113i	−0.532256	+	0.828206i	−0.998403	−	0.0565012i	$-0.982006\pi$
$307$	−9.32588	+	14.5113i	−0.532256	+	0.828206i	0.466147	+	0.884707i	$0.345642\pi$
$308$	13.2702	−	3.60081i	0.756142	−	0.205175i
$309$	−0.739949	+	2.52003i	−0.0420942	+	0.143360i
$310$	2.02345	−	3.61646i	0.114924	−	0.205401i
$311$	−5.10731	−	5.89415i	−0.289609	−	0.334227i	0.592237	−	0.805764i	$-0.298245\pi$
$311$	−5.10731	−	5.89415i	−0.289609	−	0.334227i	−0.881846	+	0.471537i	$0.843699\pi$
$312$	5.45734	−	5.12955i	0.308961	−	0.290404i
$313$	−9.64947	+	21.1294i	−0.545421	+	1.19430i	0.413467	+	0.910519i	$0.364318\pi$
$313$	−9.64947	+	21.1294i	−0.545421	+	1.19430i	−0.958888	+	0.283785i	$0.908410\pi$
$314$	0.771655	−	3.37902i	0.0435470	−	0.190689i
$315$	0.185508	+	0.631781i	0.0104522	+	0.0355968i
$316$	−1.73012	−	2.81833i	−0.0973270	−	0.158544i
$317$	16.7062	−	7.62945i	0.938312	−	0.428513i	0.113257	−	0.993566i	$-0.463872\pi$
$317$	16.7062	−	7.62945i	0.938312	−	0.428513i	0.825055	+	0.565053i	$0.191144\pi$
$318$	1.87194	+	3.51390i	0.104973	+	0.197050i
$319$	−8.54631	+	5.49238i	−0.478502	+	0.307514i
$320$	−0.504744	+	2.43120i	−0.0282160	+	0.135908i
$321$	−7.06760			−0.394475
$322$	10.5159	+	9.82034i	0.586027	+	0.547266i
$323$			15.8904i			0.884166i
$324$	−0.0412657	+	1.99957i	−0.00229254	+	0.111087i
$325$	−7.02014	−	10.9236i	−0.389407	−	0.605930i
$326$	22.6946	−	12.0899i	1.25694	−	0.669598i
$327$	2.64892	+	5.80033i	0.146486	+	0.320759i
$328$	15.7774	+	12.5911i	0.871161	+	0.695229i
$329$	19.9411	−	5.85523i	1.09939	−	0.322809i
$330$	−0.316701	+	1.38681i	−0.0174338	+	0.0763413i
$331$	5.21621	+	2.38217i	0.286709	+	0.130936i	0.553578	−	0.832797i	$-0.313262\pi$
$331$	5.21621	+	2.38217i	0.286709	+	0.130936i	−0.266869	+	0.963733i	$0.585989\pi$
$332$	3.20749	+	7.42516i	0.176034	+	0.407508i
$333$	−3.46115	+	2.99910i	−0.189670	+	0.164350i
$334$	−6.62347	−	3.70591i	−0.362420	−	0.202778i
$335$	1.12971	+	0.331711i	0.0617224	+	0.0181233i
$336$	−4.87835	+	6.94331i	−0.266136	+	0.378789i
$337$	6.14780	+	3.95095i	0.334892	+	0.215222i	0.697269	−	0.716810i	$-0.254398\pi$
$337$	6.14780	+	3.95095i	0.334892	+	0.215222i	−0.362377	+	0.932032i	$0.618035\pi$
$338$	−6.83140	+	5.00478i	−0.371579	+	0.272224i
$339$	−13.2909	−	1.91095i	−0.721864	−	0.103788i
$340$	−0.832296	+	1.72724i	−0.0451376	+	0.0936730i
$341$	30.2843	−	4.35422i	1.63999	−	0.235794i
$342$	−5.77930	−	4.42009i	−0.312509	−	0.239011i
$343$	13.1971	−	15.2303i	0.712579	−	0.822360i
$344$	30.1840	+	17.7158i	1.62741	+	0.955170i
$345$	−1.40817	+	0.482496i	−0.0758131	+	0.0259767i
$346$	−0.312758	−	0.865710i	−0.0168140	−	0.0465409i
$347$	2.40912	+	2.08752i	0.129329	+	0.112064i	0.717123	−	0.696946i	$-0.245458\pi$
$347$	2.40912	+	2.08752i	0.129329	+	0.112064i	−0.587795	+	0.809010i	$0.700004\pi$
$348$	1.89008	−	5.97786i	0.101319	−	0.320447i
$349$	−1.53362	+	0.220502i	−0.0820929	+	0.0118032i	−0.183239	−	0.983068i	$-0.558658\pi$
$349$	−1.53362	+	0.220502i	−0.0820929	+	0.0118032i	0.101146	+	0.994872i	$0.467749\pi$
$350$	10.2949	+	10.5096i	0.550287	+	0.561761i
$351$	−0.376848	+	2.62104i	−0.0201147	+	0.139901i
$352$	−16.5216	+	7.94448i	−0.880606	+	0.423442i
$353$	2.30810	+	1.48333i	0.122848	+	0.0789495i	0.600622	−	0.799533i	$-0.294920\pi$
$353$	2.30810	+	1.48333i	0.122848	+	0.0789495i	−0.477774	+	0.878483i	$0.658556\pi$
$354$	1.49918	−	18.3051i	0.0796805	−	0.972907i
$355$	−0.546764	+	1.86211i	−0.0290192	+	0.0988303i
$356$	−4.81343	−	0.793758i	−0.255111	−	0.0420691i
$357$	−4.95195	+	4.29089i	−0.262085	+	0.227098i
$358$	0.818343	+	13.3806i	0.0432508	+	0.707189i
$359$	−5.93818	+	13.0028i	−0.313405	+	0.686261i	−0.999135	−	0.0415953i	$-0.986756\pi$
$359$	−5.93818	+	13.0028i	−0.313405	+	0.686261i	0.685730	+	0.727856i	$0.259483\pi$
$360$	−0.396681	−	0.783156i	−0.0209069	−	0.0412759i
$361$	7.16622	−	2.10419i	0.377169	−	0.110747i
$362$	5.20730	−	1.07664i	0.273689	−	0.0565867i
$363$	0.452569	−	0.206681i	0.0237537	−	0.0108479i
$364$	−7.53104	+	8.33730i	−0.394734	+	0.436993i
$365$	1.53941	+	2.39537i	0.0805763	+	0.125379i
$366$	−4.00306	+	10.4035i	−0.209243	+	0.543801i
$367$	12.3509			0.644714			0.322357	−	0.946618i	$-0.395525\pi$
$367$	12.3509			0.644714			0.322357	+	0.946618i	$0.395525\pi$
$368$	−16.1715	−	10.3190i	−0.842999	−	0.537915i
$369$	−7.13672			−0.371523
$370$	0.721909	−	1.87617i	0.0375303	−	0.0975372i
$371$	−3.22895	−	5.02434i	−0.167639	−	0.260851i
$372$	−12.6568	+	14.0118i	−0.656224	+	0.726478i
$373$	30.0708	−	13.7329i	1.55701	−	0.711062i	0.563639	−	0.826021i	$-0.309401\pi$
$373$	30.0708	−	13.7329i	1.55701	−	0.711062i	0.993370	+	0.114959i	$0.0366736\pi$
$374$	−13.8624	+	2.86613i	−0.716809	+	0.148204i
$375$	−2.94939	+	0.866019i	−0.152306	+	0.0447210i
$376$	−24.7190	+	12.5206i	−1.27478	+	0.645699i
$377$	3.44830	−	7.55071i	0.177596	−	0.388882i
$378$	−0.183144	−	2.99457i	−0.00941991	−	0.154024i
$379$	15.2385	−	13.2042i	0.782749	−	0.678256i	−0.168835	−	0.985644i	$-0.554001\pi$
$379$	15.2385	−	13.2042i	0.782749	−	0.678256i	0.951584	+	0.307388i	$0.0994551\pi$
$380$	3.15112	+	0.519635i	0.161649	+	0.0266567i
$381$	5.57420	−	18.9840i	0.285575	−	0.972579i
$382$	2.16078	−	26.3834i	0.110555	−	1.34989i
$383$	−10.2315	−	6.57539i	−0.522806	−	0.335987i	0.252475	−	0.967603i	$-0.418755\pi$
$383$	−10.2315	−	6.57539i	−0.522806	−	0.335987i	−0.775281	+	0.631617i	$0.782392\pi$
$384$	4.70833	−	10.2875i	0.240271	−	0.524979i
$385$	0.303683	−	2.11216i	0.0154771	−	0.107646i
$386$	2.61055	+	2.66498i	0.132873	+	0.135644i
$387$	−12.2480	+	1.76100i	−0.622603	+	0.0895167i
$388$	7.54906	−	23.8759i	0.383246	−	1.21211i
$389$	0.438711	+	0.380145i	0.0222435	+	0.0192741i	0.665912	−	0.746031i	$-0.268043\pi$
$389$	0.438711	+	0.380145i	0.0222435	+	0.0192741i	−0.643668	+	0.765305i	$0.722588\pi$
$390$	−0.394932	−	1.09317i	−0.0199982	−	0.0553547i
$391$	−10.1887	−	10.7520i	−0.515263	−	0.543751i
$392$	−3.57853	+	6.09708i	−0.180743	+	0.307949i
$393$	4.24576	−	4.89986i	0.214170	−	0.247165i
$394$	10.5734	+	8.08671i	0.532681	+	0.407403i
$395$	−0.507992	+	0.0730382i	−0.0255599	+	0.00367495i
$396$	2.81359	−	5.83897i	0.141388	−	0.293419i
$397$	17.7178	+	2.54744i	0.889232	+	0.127852i	0.571766	−	0.820417i	$-0.306259\pi$
$397$	17.7178	+	2.54744i	0.889232	+	0.127852i	0.317467	+	0.948269i	$0.397168\pi$
$398$	14.5923	−	10.6906i	0.731448	−	0.535869i
$399$	9.18171	+	5.90073i	0.459660	+	0.295406i
$400$	−16.0493	−	11.2762i	−0.802467	−	0.563812i
$401$	0.732222	+	0.215000i	0.0365654	+	0.0107366i	0.299964	−	0.953950i	$-0.403025\pi$
$401$	0.732222	+	0.215000i	0.0365654	+	0.0107366i	−0.263399	+	0.964687i	$0.584843\pi$
$402$	−4.68169	−	2.61946i	−0.233502	−	0.130647i
$403$	−18.8934	+	16.3712i	−0.941145	+	0.815507i
$404$	−3.11252	−	7.20530i	−0.154854	−	0.358477i
$405$	0.282332	+	0.128937i	0.0140292	+	0.00640692i
$406$	−2.09385	+	9.16879i	−0.103916	+	0.455039i
$407$	14.2407	−	4.18144i	0.705884	−	0.207266i
$408$	5.44922	−	6.82818i	0.269776	−	0.338045i
$409$	1.67560	+	3.66906i	0.0828532	+	0.181423i	0.946524	−	0.322633i	$-0.104568\pi$
$409$	1.67560	+	3.66906i	0.0828532	+	0.181423i	−0.863671	+	0.504056i	$0.831841\pi$
$410$	2.76478	−	1.47286i	0.136543	−	0.0727395i
$411$	5.12332	+	7.97205i	0.252715	+	0.393232i
$412$	−0.108381	+	5.25173i	−0.00533956	+	0.258734i
$413$			27.5512i			1.35570i
$414$	6.74456	−	0.714803i	0.331477	−	0.0351307i
$415$	1.25523			0.0616168
$416$	7.84716	−	12.7594i	0.384739	−	0.625579i
$417$	−7.01075	+	4.50554i	−0.343318	+	0.220637i
$418$	11.0862	+	20.8104i	0.542242	+	1.01787i
$419$	−31.4574	+	14.3661i	−1.53680	+	0.701831i	−0.990722	−	0.135906i	$-0.956605\pi$
$419$	−31.4574	+	14.3661i	−1.53680	+	0.701831i	−0.546074	+	0.837737i	$0.683878\pi$
$420$	0.688963	+	1.12231i	0.0336180	+	0.0547629i
$421$	−3.52357	−	12.0002i	−0.171728	−	0.584853i	−0.999710	−	0.0240970i	$-0.992329\pi$
$421$	−3.52357	−	12.0002i	−0.171728	−	0.584853i	0.827981	−	0.560756i	$-0.189489\pi$
$422$	7.04352	−	30.8430i	0.342873	−	1.50142i
$423$	4.06967	−	8.91133i	0.197874	−	0.433284i
$424$	5.45363	+	5.80212i	0.264852	+	0.281776i
$425$	−9.91832	−	11.4463i	−0.481109	−	0.555229i
$426$	4.31768	−	7.71688i	0.209192	−	0.373884i
$427$	4.71101	−	16.0442i	0.227982	−	0.776435i
$428$	−13.6419	+	3.70166i	−0.659406	+	0.178927i
$429$	4.63950	−	7.21920i	0.223997	−	0.348546i
$430$	4.38148	−	3.20994i	0.211294	−	0.154797i
$431$	4.10694	−	28.5644i	0.197824	−	1.37590i	−0.612757	−	0.790272i	$-0.709939\pi$
$431$	4.10694	−	28.5644i	0.197824	−	1.37590i	0.810581	−	0.585627i	$-0.199152\pi$
$432$	0.967628	+	3.88120i	0.0465550	+	0.186734i
$433$	2.53923	+	17.6607i	0.122028	+	0.848721i	0.955254	+	0.295788i	$0.0955823\pi$
$433$	2.53923	+	17.6607i	0.122028	+	0.848721i	−0.833226	+	0.552933i	$0.813509\pi$
$434$	17.2072	−	22.4985i	0.825971	−	1.07996i
$435$	−0.735324	−	0.637162i	−0.0352561	−	0.0305496i
$436$	8.15089	+	9.80844i	0.390357	+	0.469739i
$437$	−12.4028	+	21.3296i	−0.593307	+	1.02033i
$438$	−4.40821	−	12.2019i	−0.210632	−	0.583028i
$439$	20.6780	−	23.8637i	0.986907	−	1.13895i	−0.00339139	−	0.999994i	$-0.501080\pi$
$439$	20.6780	−	23.8637i	0.986907	−	1.13895i	0.990298	−	0.138957i	$-0.0443750\pi$
$440$	0.115045	+	2.84269i	0.00548455	+	0.135520i
$441$	−0.355717	−	2.47407i	−0.0169389	−	0.117813i
$442$	8.26265	−	8.09389i	0.393014	−	0.384987i
$443$	35.1878	+	5.05925i	1.67182	+	0.240372i	0.912128	−	0.409906i	$-0.134438\pi$
$443$	35.1878	+	5.05925i	1.67182	+	0.240372i	0.759697	+	0.650278i	$0.225347\pi$
$444$	−5.10994	+	7.60166i	−0.242507	+	0.360759i
$445$	−0.409312	+	0.636902i	−0.0194032	+	0.0301920i
$446$	1.47736	−	18.0387i	0.0699551	−	0.854159i
$447$	21.2251	+	6.23224i	1.00391	+	0.294775i
$448$	−5.77965	+	15.9570i	−0.273063	+	0.753899i
$449$	2.46783	+	2.84802i	0.116464	+	0.134407i	0.810988	−	0.585063i	$-0.198930\pi$
$449$	2.46783	+	2.84802i	0.116464	+	0.134407i	−0.694524	+	0.719470i	$0.744385\pi$
$450$	6.92189	−	0.423334i	0.326301	−	0.0199562i
$451$	21.0383	+	9.60786i	0.990654	+	0.452417i
$452$	−26.6551	+	3.27262i	−1.25375	+	0.153931i
$453$	−6.64263	−	22.6227i	−0.312098	−	1.06291i
$454$	23.0606	−	4.76790i	1.08229	−	0.223769i
$455$	0.724308	+	1.58601i	0.0339561	+	0.0743534i
$456$	−13.4702	−	5.50477i	−0.630802	−	0.257784i
$457$	0.806402	−	0.518243i	0.0377219	−	0.0242424i	−0.521644	−	0.853163i	$-0.674681\pi$
$457$	0.806402	−	0.518243i	0.0377219	−	0.0242424i	0.559366	+	0.828921i	$0.311045\pi$
$458$	12.6162	+	4.85444i	0.589515	+	0.226833i
$459$			3.08865i			0.144166i
$460$	−2.46534	+	1.66884i	−0.114947	+	0.0778102i
$461$		−	23.2407i		−	1.08243i	−0.840886	−	0.541213i	$-0.817965\pi$
$461$		−	23.2407i		−	1.08243i	0.840886	−	0.541213i	$-0.182035\pi$
$462$	−3.49157	+	9.07422i	−0.162443	+	0.422171i
$463$	3.28629	−	2.11197i	0.152727	−	0.0981516i	−0.462045	−	0.886856i	$-0.652884\pi$
$463$	3.28629	−	2.11197i	0.152727	−	0.0981516i	0.614772	+	0.788705i	$0.289248\pi$
$464$	0.517325	−	12.5284i	0.0240162	−	0.581617i
$465$	1.21728	+	2.66548i	0.0564502	+	0.123609i
$466$	−0.261602	−	1.26528i	−0.0121185	−	0.0586128i
$467$	−0.758983	−	2.58486i	−0.0351215	−	0.119613i	0.940066	−	0.340991i	$-0.110763\pi$
$467$	−0.758983	−	2.58486i	−0.0351215	−	0.119613i	−0.975188	+	0.221378i	$0.928944\pi$
$468$	0.645377	+	5.25651i	0.0298326	+	0.242982i
$469$	7.32023	+	3.34304i	0.338017	+	0.154367i
$470$	0.262503	+	4.29216i	0.0121084	+	0.197983i
$471$	1.60496	+	1.85222i	0.0739525	+	0.0853458i
$472$	−6.69361	−	36.1178i	−0.308099	−	1.66246i
$473$	38.4766	+	11.2978i	1.76916	+	0.519472i
$474$	2.33061	+	0.190875i	0.107048	+	0.00876719i
$475$	−13.6394	+	21.2234i	−0.625820	+	0.973795i
$476$	−7.31091	+	10.8759i	−0.335095	+	0.498495i
$477$	−2.78663	−	0.400657i	−0.127591	−	0.0183448i
$478$	21.9706	+	22.4286i	1.00491	+	1.02586i
$479$	−0.231990	−	1.61352i	−0.0105999	−	0.0737238i	0.983835	−	0.179078i	$-0.0573114\pi$
$479$	−0.231990	−	1.61352i	−0.0105999	−	0.0737238i	−0.994435	+	0.105354i	$0.966402\pi$
$480$	−1.17585	−	1.30389i	−0.0536702	−	0.0595141i
$481$	−7.94160	+	9.16509i	−0.362106	+	0.417892i
$482$	25.2222	−	9.11210i	1.14884	−	0.415045i
$483$	−9.99610	+	1.89453i	−0.454838	+	0.0862040i
$484$	0.765300	−	0.635970i	0.0347864	−	0.0289077i
$485$	−2.93692	−	2.54485i	−0.133359	−	0.115556i
$486$	−1.12333	−	0.859142i	−0.0509554	−	0.0389715i
$487$	2.21012	+	15.3717i	0.100150	+	0.696558i	0.976600	+	0.215065i	$0.0689963\pi$
$487$	2.21012	+	15.3717i	0.100150	+	0.696558i	−0.876450	+	0.481493i	$0.840095\pi$
$488$	−2.27786	+	22.1775i	−0.103114	+	1.00393i
$489$	−2.58765	+	17.9975i	−0.117017	+	0.813874i
$490$	0.648398	+	0.885047i	0.0292917	+	0.0399823i
$491$	22.2407	−	34.6072i	1.00371	−	1.56180i	0.188958	−	0.981985i	$-0.439489\pi$
$491$	22.2407	−	34.6072i	1.00371	−	1.56180i	0.814749	−	0.579814i	$-0.196875\pi$
$492$	−13.7753	+	3.73787i	−0.621040	+	0.168516i
$493$	2.72779	−	9.29001i	0.122854	−	0.418401i
$494$	−16.8135	−	9.40731i	−0.756473	−	0.423255i
$495$	−0.658703	−	0.760183i	−0.0296065	−	0.0341677i
$496$	−17.0915	+	33.6746i	−0.767430	+	1.51204i
$497$	−5.51036	+	12.0660i	−0.247173	+	0.541234i
$498$	−5.57576	−	1.27332i	−0.249856	−	0.0570588i
$499$	2.78804	+	9.49519i	0.124810	+	0.425063i	0.998064	−	0.0622027i	$-0.0198125\pi$
$499$	2.78804	+	9.49519i	0.124810	+	0.425063i	−0.873254	+	0.487266i	$0.837994\pi$
$500$	−5.23935	+	3.21634i	−0.234311	+	0.143839i
$501$	4.88177	−	2.22943i	0.218101	−	0.0996036i
$502$	−5.24488	+	2.79407i	−0.234090	+	0.124705i
$503$	−33.4972	+	21.5274i	−1.49357	+	0.959857i	−0.497864	+	0.867255i	$0.665882\pi$
$503$	−33.4972	+	21.5274i	−1.49357	+	0.959857i	−0.995703	+	0.0926025i	$0.970481\pi$
$504$	−1.92191	−	5.68420i	−0.0856088	−	0.253195i
$505$	−1.21806			−0.0542031
$506$	−20.8445	−	6.97274i	−0.926652	−	0.309976i
$507$		−	5.98815i		−	0.265943i
$508$	0.816461	−	39.5625i	0.0362246	−	1.75530i
$509$	−19.1176	−	29.7475i	−0.847371	−	1.31853i	−0.946250	−	0.323435i	$-0.895162\pi$
$509$	−19.1176	−	29.7475i	−0.847371	−	1.31853i	0.0988794	−	0.995099i	$-0.468474\pi$
$510$	−0.637429	−	1.19655i	−0.0282258	−	0.0529841i
$511$	8.08468	+	17.7030i	0.357645	+	0.783133i
$512$	3.69996	−	22.3229i	0.163517	−	0.986541i
$513$	4.93638	−	1.44945i	0.217946	−	0.0639949i
$514$	−0.184206	−	0.0420666i	−0.00812499	−	0.00185548i
$515$	0.741523	+	0.338642i	0.0326754	+	0.0149224i
$516$	−22.7189	+	9.81401i	−1.00014	+	0.432038i
$517$	−23.9939	+	20.7908i	−1.05525	+	0.914379i
$518$	6.70896	−	11.9908i	0.294775	−	0.526844i
$519$	0.624508	+	0.183372i	0.0274129	+	0.00804914i
$520$	−1.33485	−	1.90319i	−0.0585369	−	0.0834605i
$521$	27.2574	+	17.5173i	1.19417	+	0.767445i	0.977938	−	0.208897i	$-0.0669873\pi$
$521$	27.2574	+	17.5173i	1.19417	+	0.767445i	0.216231	+	0.976342i	$0.430624\pi$
$522$	2.61998	+	3.57621i	0.114674	+	0.156526i
$523$	−37.6411	−	5.41197i	−1.64593	−	0.236649i	−0.743890	−	0.668302i	$-0.767021\pi$
$523$	−37.6411	−	5.41197i	−1.64593	−	0.236649i	−0.902040	+	0.431653i	$0.857930\pi$
$524$	5.62887	−	11.6815i	0.245898	−	0.510307i
$525$	−10.2969	+	1.48047i	−0.449395	+	0.0646132i
$526$	19.0415	−	24.8969i	0.830249	−	1.08555i
$527$	−19.0956	+	22.0374i	−0.831815	+	0.959966i
$528$	2.37263	−	12.7440i	0.103255	−	0.554612i
$529$	−5.28402	−	22.3848i	−0.229740	−	0.973252i
$530$	1.16223	−	0.419884i	0.0504842	−	0.0182386i
$531$	9.81494	+	8.50470i	0.425932	+	0.369072i
$532$	20.8131	+	6.58067i	0.902361	+	0.285308i
$533$	−18.7056	+	2.68946i	−0.810230	+	0.116493i
$534$	2.46426	−	2.41392i	0.106639	−	0.104461i
$535$	−0.312188	+	2.17132i	−0.0134971	+	0.0938743i
$536$	−10.4086	−	2.60405i	−0.449581	−	0.112478i
$537$	−7.97442	−	5.12485i	−0.344122	−	0.221154i
$538$	−13.7907	−	1.12945i	−0.594559	−	0.0486940i
$539$	−2.28211	+	7.77217i	−0.0982976	+	0.334771i
$540$	0.612489	+	0.101002i	0.0263573	+	0.00434645i
$541$	33.9718	−	29.4368i	1.46056	−	1.26559i	0.561711	−	0.827334i	$-0.310143\pi$
$541$	33.9718	−	29.4368i	1.46056	−	1.26559i	0.898852	−	0.438252i	$-0.144402\pi$
$542$	6.96073	−	0.425710i	0.298989	−	0.0182858i
$543$	−1.56196	+	3.42021i	−0.0670300	+	0.146775i
$544$	6.94183	−	16.0338i	0.297629	−	0.687444i
$545$	1.89899	−	0.557595i	0.0813439	−	0.0238847i
$546$	−1.60853	−	7.77986i	−0.0688385	−	0.332947i
$547$	0.869522	−	0.397098i	0.0371781	−	0.0169787i	−0.396739	−	0.917931i	$-0.629858\pi$
$547$	0.869522	−	0.397098i	0.0371781	−	0.0169787i	0.433917	+	0.900953i	$0.357131\pi$
$548$	14.0644	+	12.7043i	0.600802	+	0.542702i
$549$	−4.26144	−	6.63092i	−0.181874	−	0.283001i
$550$	−20.9749	−	8.07070i	−0.894373	−	0.344136i
$551$	−16.1277			−0.687064
$552$	12.6440	−	4.91218i	0.538164	−	0.209076i
$553$	−3.50780			−0.149167
$554$	−15.6184	−	6.00962i	−0.663560	−	0.255324i
$555$	0.768504	+	1.19582i	0.0326212	+	0.0507596i
$556$	−11.1724	+	12.3685i	−0.473815	+	0.524541i
$557$	38.6047	−	17.6302i	1.63573	−	0.747015i	0.636038	−	0.771658i	$-0.280572\pi$
$557$	38.6047	−	17.6302i	1.63573	−	0.747015i	0.999696	+	0.0246433i	$0.00784500\pi$
$558$	−2.70331	−	13.0750i	−0.114440	−	0.553507i
$559$	−31.4389	+	9.23130i	−1.32972	+	0.390442i
$560$	1.91765	+	1.80543i	0.0810354	+	0.0762935i
$561$	4.15811	−	9.10500i	0.175556	−	0.384413i
$562$	−45.3399	+	2.77293i	−1.91255	+	0.116969i
$563$	−32.6901	+	28.3261i	−1.37772	+	1.19380i	−0.419509	+	0.907751i	$0.637798\pi$
$563$	−32.6901	+	28.3261i	−1.37772	+	1.19380i	−0.958214	+	0.286053i	$0.907657\pi$
$564$	3.18797	−	19.3322i	0.134238	−	0.814031i
$565$	−1.17417	+	3.99885i	−0.0493976	+	0.168233i
$566$	−31.8920	−	2.61193i	−1.34052	−	0.109788i
$567$	1.78467	+	1.14693i	0.0749489	+	0.0481667i
$568$	4.29228	−	17.1565i	0.180100	−	0.719872i
$569$	1.64264	−	11.4248i	0.0688633	−	0.478954i	−0.925983	−	0.377564i	$-0.876762\pi$
$569$	1.64264	−	11.4248i	0.0688633	−	0.478954i	0.994847	−	0.101390i	$-0.0323291\pi$
$570$	−1.61323	+	1.58028i	−0.0675707	+	0.0661907i
$571$	38.4841	−	5.53318i	1.61051	−	0.231557i	0.722497	−	0.691374i	$-0.242994\pi$
$571$	38.4841	−	5.53318i	1.61051	−	0.231557i	0.888014	+	0.459817i	$0.152085\pi$
$572$	5.17411	−	16.3645i	0.216340	−	0.684232i
$573$	14.1464	+	12.2579i	0.590973	+	0.512081i
$574$	20.1375	−	7.27512i	0.840522	−	0.303658i
$575$	−4.37917	−	23.1058i	−0.182624	−	0.963579i
$576$	3.90050	+	6.98471i	0.162521	+	0.291029i
$577$	2.83881	−	3.27616i	0.118181	−	0.136388i	−0.693576	−	0.720384i	$-0.743966\pi$
$577$	2.83881	−	3.27616i	0.118181	−	0.136388i	0.811757	+	0.583995i	$0.198511\pi$
$578$	−6.40942	+	8.38035i	−0.266597	+	0.348576i
$579$	−2.61106	+	0.375413i	−0.108512	+	0.0156016i
$580$	−1.75304	−	0.844725i	−0.0727910	−	0.0350753i
$581$	8.49210	+	1.22098i	0.352312	+	0.0506548i
$582$	10.4643	+	14.2836i	0.433761	+	0.592072i
$583$	7.67530	+	4.93261i	0.317878	+	0.204288i
$584$	−14.8995	−	21.2433i	−0.616545	−	0.879054i
$585$	0.788593	+	0.231552i	0.0326043	+	0.00957348i
$586$	−5.06827	+	9.05839i	−0.209368	+	0.374199i
$587$	10.2663	−	8.89577i	0.423734	−	0.367168i	−0.416734	−	0.909028i	$-0.636825\pi$
$587$	10.2663	−	8.89577i	0.423734	−	0.367168i	0.840468	+	0.541861i	$0.182280\pi$
$588$	−1.98240	−	4.58915i	−0.0817529	−	0.189253i
$589$	44.1822	+	20.1773i	1.82050	+	0.831393i
$590$	−5.55751	−	1.26915i	−0.228799	−	0.0522501i
$591$	−9.03127	+	2.65182i	−0.371497	+	0.109081i
$592$	−5.88185	+	17.3491i	−0.241742	+	0.713043i
$593$	10.3159	+	22.5886i	0.423622	+	0.927602i	0.994319	+	0.106441i	$0.0339457\pi$
$593$	10.3159	+	22.5886i	0.423622	+	0.927602i	−0.570697	+	0.821160i	$0.693327\pi$
$594$	2.15484	+	4.04495i	0.0884140	+	0.165966i
$595$	1.09952	+	1.71088i	0.0450758	+	0.0701393i
$596$	44.2328	+	0.912844i	1.81185	+	0.0373916i
$597$			12.7911i			0.523505i
$598$	17.4084	−	4.41520i	0.711881	−	0.180551i
$599$	41.7860			1.70733			0.853665	−	0.520822i	$-0.174375\pi$
$599$	41.7860			1.70733			0.853665	+	0.520822i	$0.174375\pi$
$600$	13.1389	−	4.44247i	0.536395	−	0.181363i
$601$	−11.2430	+	7.22546i	−0.458613	+	0.294733i	−0.749475	−	0.662032i	$-0.769694\pi$
$601$	−11.2430	+	7.22546i	−0.458613	+	0.294733i	0.290862	+	0.956765i	$0.406058\pi$
$602$	32.7648	−	17.4545i	1.33539	−	0.711393i
$603$	3.45060	−	1.57584i	0.140519	−	0.0641730i
$604$	−24.6703	−	40.1874i	−1.00382	−	1.63520i
$605$	−0.0435061	−	0.148168i	−0.00176878	−	0.00602390i
$606$	5.41067	+	1.23562i	0.219793	+	0.0501935i
$607$	5.05949	−	11.0787i	0.205358	−	0.449672i	−0.778728	−	0.627361i	$-0.784135\pi$
$607$	5.05949	−	11.0787i	0.205358	−	0.449672i	0.984087	+	0.177689i	$0.0568622\pi$
$608$	−28.8834	−	3.57027i	−1.17138	−	0.144794i
$609$	−4.35497	−	5.02590i	−0.176472	−	0.203660i
$610$	3.01937	+	1.68937i	0.122251	+	0.0684005i
$611$	7.30853	−	24.8906i	0.295672	−	1.00696i
$612$	1.61768	+	5.96172i	0.0653909	+	0.240988i
$613$	22.1321	−	34.4383i	0.893908	−	1.39095i	−0.0263573	−	0.999653i	$-0.508391\pi$
$613$	22.1321	−	34.4383i	0.893908	−	1.39095i	0.920265	−	0.391295i	$-0.127973\pi$
$614$	−14.4170	−	19.6788i	−0.581821	−	0.794170i
$615$	−0.315242	+	2.19255i	−0.0127118	+	0.0884123i
$616$	−1.98681	+	19.3438i	−0.0800507	+	0.779384i
$617$	2.58789	+	17.9992i	0.104185	+	0.724620i	0.973221	+	0.229872i	$0.0738307\pi$
$617$	2.58789	+	17.9992i	0.104185	+	0.724620i	−0.869036	+	0.494748i	$0.835260\pi$
$618$	−2.95034	−	2.25647i	−0.118680	−	0.0907685i
$619$	−21.4873	−	18.6189i	−0.863649	−	0.748356i	0.105608	−	0.994408i	$-0.466321\pi$
$619$	−21.4873	−	18.6189i	−0.863649	−	0.748356i	−0.969257	+	0.246052i	$0.920867\pi$
$620$	3.74565	+	4.50736i	0.150429	+	0.181020i
$621$	−2.41076	+	4.14587i	−0.0967403	+	0.166368i
$622$	10.3734	−	3.74762i	0.415934	−	0.150266i
$623$	−3.38867	+	3.91074i	−0.135764	+	0.156680i
$624$	3.99881	+	9.80811i	0.160081	+	0.392639i
$625$	−3.35354	−	23.3244i	−0.134142	−	0.932976i
$626$	−22.9876	−	23.4669i	−0.918771	−	0.937927i
$627$	−16.5032	−	2.37281i	−0.659076	−	0.0947608i
$628$	4.06800	+	2.73456i	0.162331	+	0.109121i
$629$	−7.64751	+	11.8998i	−0.304926	+	0.474474i
$630$	−0.928085	−	0.0760096i	−0.0369758	−	0.00302830i
$631$	−35.5369	−	10.4346i	−1.41470	−	0.415394i	−0.516996	−	0.855988i	$-0.672950\pi$
$631$	−35.5369	−	10.4346i	−1.41470	−	0.415394i	−0.897707	+	0.440594i	$0.854768\pi$
$632$	4.59851	−	0.852229i	0.182919	−	0.0338999i
$633$	14.6497	+	16.9067i	0.582275	+	0.671981i
$634$	1.58553	+	25.9248i	0.0629694	+	1.02961i
$635$	−5.58607	−	2.55107i	−0.221676	−	0.101236i
$636$	−5.58861	+	0.686151i	−0.221603	+	0.0272077i
$637$	−1.86470	−	6.35057i	−0.0738819	−	0.251619i
$638$	−2.90893	−	14.0695i	−0.115166	−	0.557015i
$639$	2.59747	+	5.68766i	0.102754	+	0.225000i
$640$	−2.95255	−	1.90091i	−0.116710	−	0.0751402i
$641$	−6.61573	+	4.25167i	−0.261305	+	0.167931i	−0.664734	−	0.747081i	$-0.731455\pi$
$641$	−6.61573	+	4.25167i	−0.261305	+	0.167931i	0.403428	+	0.915011i	$0.367819\pi$
$642$	3.58936	−	9.32837i	0.141661	−	0.368161i
$643$		−	8.68477i		−	0.342494i	−0.985228	−	0.171247i	$-0.945220\pi$
$643$		−	8.68477i		−	0.342494i	0.985228	−	0.171247i	$-0.0547796\pi$
$644$	−18.3022	+	8.89229i	−0.721210	+	0.350405i
$645$			3.84065i			0.151225i
$646$	−20.9734	−	8.07012i	−0.825187	−	0.317515i
$647$	−5.45157	+	3.50351i	−0.214323	+	0.137737i	−0.643398	−	0.765532i	$-0.722476\pi$
$647$	−5.45157	+	3.50351i	−0.214323	+	0.137737i	0.429075	+	0.903269i	$0.358840\pi$
$648$	−2.61824	−	1.06997i	−0.102854	−	0.0420325i
$649$	−17.4839	−	38.2844i	−0.686302	−	1.50279i
$650$	17.9830	−	3.71808i	0.705352	−	0.145835i
$651$	5.64263	+	19.2170i	0.221152	+	0.753175i
$652$	4.43151	+	36.0941i	0.173551	+	1.41355i
$653$	28.6347	+	13.0770i	1.12056	+	0.511744i	0.887542	−	0.460727i	$-0.152411\pi$
$653$	28.6347	+	13.0770i	1.12056	+	0.511744i	0.233022	+	0.972471i	$0.425139\pi$
$654$	−9.00101	+	0.550490i	−0.351967	+	0.0215259i
$655$	−1.31780	−	1.52082i	−0.0514907	−	0.0594235i
$656$	−24.6315	+	14.4297i	−0.961697	+	0.563384i
$657$	8.80222	+	2.58457i	0.343407	+	0.100833i
$658$	−2.39911	+	29.2934i	−0.0935272	+	1.14198i
$659$	−4.53648	+	7.05890i	−0.176716	+	0.274976i	−0.918301	−	0.395884i	$-0.870438\pi$
$659$	−4.53648	+	7.05890i	−0.176716	+	0.274976i	0.741584	+	0.670860i	$0.234075\pi$
$660$	−1.66958	−	1.12231i	−0.0649882	−	0.0436859i
$661$	−3.27143	−	0.470361i	−0.127244	−	0.0182949i	0.0783985	−	0.996922i	$-0.475019\pi$
$661$	−3.27143	−	0.470361i	−0.127244	−	0.0182949i	−0.205643	+	0.978627i	$0.565928\pi$
$662$	−5.79328	+	5.67495i	−0.225162	+	0.220563i
$663$	1.16395	+	8.09546i	0.0452041	+	0.314402i
$664$	−11.4293	+	0.462547i	−0.443541	+	0.0179503i
$665$	2.21840	−	2.56017i	0.0860260	−	0.0992792i
$666$	−2.20067	−	6.09143i	−0.0852741	−	0.236038i
$667$	10.9126	−	10.3408i	0.422536	−	0.400398i
$668$	8.25515	−	6.86009i	0.319401	−	0.265425i
$669$	9.67209	+	8.38092i	0.373945	+	0.324025i
$670$	−1.01155	+	1.32261i	−0.0390797	+	0.0510969i
$671$	3.63532	+	25.2842i	0.140340	+	0.976087i
$672$	−6.68679	−	9.96507i	−0.257949	−	0.384411i
$673$	1.27214	−	8.84790i	0.0490373	−	0.341062i	−0.950502	−	0.310718i	$-0.899431\pi$
$673$	1.27214	−	8.84790i	0.0490373	−	0.341062i	0.999540	−	0.0303440i	$-0.00966027\pi$
$674$	−8.33700	+	6.10781i	−0.321129	+	0.235264i
$675$	−2.65112	+	4.12522i	−0.102042	+	0.158780i
$676$	−3.13630	−	11.5583i	−0.120627	−	0.444552i
$677$	11.0367	−	37.5876i	0.424175	−	1.44461i	−0.419501	−	0.907755i	$-0.637795\pi$
$677$	11.0367	−	37.5876i	0.424175	−	1.44461i	0.843676	−	0.536853i	$-0.180387\pi$
$678$	9.27217	−	16.5719i	0.356095	−	0.636440i
$679$	−17.3940	−	20.0737i	−0.667519	−	0.770357i
$680$	−1.85706	−	1.97573i	−0.0712150	−	0.0757657i
$681$	−6.91716	+	15.1465i	−0.265066	+	0.580414i
$682$	−9.63317	+	42.1829i	−0.368873	+	1.61527i
$683$	10.7177	+	36.5012i	0.410102	+	1.39668i	0.863039	+	0.505138i	$0.168558\pi$
$683$	10.7177	+	36.5012i	0.410102	+	1.39668i	−0.452937	+	0.891543i	$0.649624\pi$
$684$	8.76906	−	5.38317i	0.335294	−	0.205831i
$685$	2.67549	−	1.22186i	0.102225	−	0.0466847i
$686$	13.3998	+	25.1535i	0.511608	+	0.960365i
$687$	−8.04120	+	5.16777i	−0.306791	+	0.197163i
$688$	−38.7119	+	30.8421i	−1.47588	+	1.17584i
$689$	−7.45485			−0.284007
$690$	0.0783162	−	2.10365i	0.00298145	−	0.0800845i
$691$			21.6997i			0.825496i	0.910845	+	0.412748i	$0.135431\pi$
$691$			21.6997i			0.825496i	−0.910845	+	0.412748i	$0.864569\pi$
$692$	1.30147	+	0.0268588i	0.0494744	+	0.00102102i
$693$	−3.71693	−	5.78366i	−0.141195	−	0.219703i
$694$	−3.97877	+	2.11958i	−0.151032	+	0.0804582i
$695$	1.07452	+	2.35287i	0.0407589	+	0.0892495i
$696$	6.93015	+	5.53059i	0.262686	+	0.209637i
$697$	−21.1499	+	6.21018i	−0.801111	+	0.235227i
$698$	0.487832	−	2.13618i	0.0184647	−	0.0808555i
$699$	0.831047	+	0.379527i	0.0314331	+	0.0143550i
$700$	−19.0998	+	8.25064i	−0.721903	+	0.311845i
$701$	−6.30080	+	5.45967i	−0.237978	+	0.206209i	−0.765682	−	0.643219i	$-0.777598\pi$
$701$	−6.30080	+	5.45967i	−0.237978	+	0.206209i	0.527704	+	0.849428i	$0.323053\pi$
$702$	−3.26806	−	1.82852i	−0.123345	−	0.0690129i
$703$	22.6074	+	6.63814i	0.852655	+	0.250362i
$704$	−2.09504	−	25.8412i	−0.0789598	−	0.973928i
$705$	−2.55799	−	1.64392i	−0.0963394	−	0.0619136i
$706$	−3.13000	+	2.29309i	−0.117799	+	0.0863014i
$707$	−8.24066	−	1.18483i	−0.309922	−	0.0445600i
$708$	23.3992	+	11.2752i	0.879395	+	0.423748i
$709$	−6.65030	+	0.956168i	−0.249757	+	0.0359097i	−0.266056	−	0.963958i	$-0.585721\pi$
$709$	−6.65030	+	0.956168i	−0.249757	+	0.0359097i	0.0162991	+	0.999867i	$0.494812\pi$
$710$	−2.18007	−	1.66735i	−0.0818166	−	0.0625746i
$711$	−1.08282	+	1.24964i	−0.0406087	+	0.0468650i
$712$	3.49222	−	5.95002i	0.130876	−	0.222986i
$713$	−42.8325	+	14.6762i	−1.60409	+	0.549629i
$714$	−3.14855	−	8.71514i	−0.117831	−	0.326156i
$715$	−2.01296	−	1.74424i	−0.0752803	−	0.0652308i
$716$	−18.0764	−	5.71539i	−0.675547	−	0.213594i
$717$	−21.9748	+	3.15950i	−0.820664	+	0.117994i
$718$	−14.1463	−	14.4413i	−0.527936	−	0.538944i
$719$	−1.42587	+	9.91714i	−0.0531760	+	0.369847i	0.945806	+	0.324733i	$0.105274\pi$
$719$	−1.42587	+	9.91714i	−0.0531760	+	0.369847i	−0.998982	+	0.0451144i	$0.985635\pi$
$720$	1.23513	−	0.125837i	0.0460305	−	0.00468965i
$721$	4.68729	+	3.01234i	0.174564	+	0.112185i
$722$	−0.862168	+	10.5272i	−0.0320866	+	0.391780i
$723$	−5.34249	+	18.1949i	−0.198689	+	0.676674i
$724$	−1.22356	+	7.41978i	−0.0454731	+	0.275754i
$725$	11.6173	−	10.0664i	0.431455	−	0.373858i
$726$	0.0429518	+	0.702301i	0.00159409	+	0.0260648i
$727$	6.96948	−	15.2610i	0.258484	−	0.566000i	−0.735247	−	0.677799i	$-0.762934\pi$
$727$	6.96948	−	15.2610i	0.258484	−	0.566000i	0.993731	+	0.111799i	$0.0356612\pi$
$728$	−7.17949	−	14.1742i	−0.266090	−	0.525332i
$729$	0.959493	−	0.281733i	0.0355368	−	0.0104345i
$730$	−3.94340	+	0.815317i	−0.145952	+	0.0301763i
$731$	−34.7651	+	15.8767i	−1.28583	+	0.587221i
$732$	−11.6984	−	10.5671i	−0.432385	−	0.390571i
$733$	8.18962	+	12.7433i	0.302491	+	0.470684i	0.958910	−	0.283712i	$-0.0915660\pi$
$733$	8.18962	+	12.7433i	0.302491	+	0.470684i	−0.656419	+	0.754397i	$0.727930\pi$
$734$	−6.27256	+	16.3017i	−0.231525	+	0.601708i
$735$	−0.775799			−0.0286158
$736$	21.8327	−	16.1038i	0.804764	−	0.593595i
$737$	−12.2935			−0.452836
$738$	3.62446	−	9.41960i	0.133418	−	0.346740i
$739$	1.48235	+	2.30658i	0.0545292	+	0.0848490i	0.867448	−	0.497528i	$-0.165759\pi$
$739$	1.48235	+	2.30658i	0.0545292	+	0.0848490i	−0.812919	+	0.582377i	$0.802123\pi$
$740$	2.10968	+	1.90566i	0.0775533	+	0.0700536i
$741$	12.3922	−	5.65933i	0.455239	−	0.207901i
$742$	8.27138	−	1.71015i	0.303652	−	0.0627816i
$743$	21.3307	−	6.26325i	0.782546	−	0.229776i	0.134030	−	0.990977i	$-0.457208\pi$
$743$	21.3307	−	6.26325i	0.782546	−	0.229776i	0.648516	+	0.761201i	$0.275390\pi$
$744$	−12.0660	−	23.8215i	−0.442360	−	0.873337i
$745$	2.85223	−	6.24550i	0.104497	−	0.228818i
$746$	2.85393	+	46.6642i	0.104490	+	1.70850i
$747$	3.05637	−	2.64836i	0.111827	−	0.0968985i
$748$	3.25725	−	19.7523i	0.119097	−	0.722216i
$749$	−4.22415	+	14.3861i	−0.154347	+	0.525657i
$750$	0.354842	−	4.33265i	0.0129570	−	0.158206i
$751$	25.7966	+	16.5785i	0.941331	+	0.604957i	0.918772	−	0.394789i	$-0.129182\pi$
$751$	25.7966	+	16.5785i	0.941331	+	0.604957i	0.0225589	+	0.999746i	$0.492819\pi$
$752$	−3.97181	−	38.9847i	−0.144837	−	1.42163i
$753$	0.598024	−	4.15935i	0.0217932	−	0.151575i
$754$	8.21476	+	8.38604i	0.299164	+	0.305402i
$755$	−7.24361	+	1.04147i	−0.263622	+	0.0379031i
$756$	4.04548	+	1.27910i	0.147133	+	0.0465203i
$757$	10.6196	+	9.20197i	0.385977	+	0.334451i	0.826138	−	0.563468i	$-0.190533\pi$
$757$	10.6196	+	9.20197i	0.385977	+	0.334451i	−0.440161	+	0.897919i	$0.645079\pi$
$758$	9.68893	+	26.8189i	0.351918	+	0.974105i
$759$	12.6881	−	8.97608i	0.460547	−	0.325811i
$760$	−2.28619	+	3.89519i	−0.0829287	+	0.141294i
$761$	18.3628	−	21.1918i	0.665652	−	0.768203i	−0.318038	−	0.948078i	$-0.603024\pi$
$761$	18.3628	−	21.1918i	0.665652	−	0.768203i	0.983689	+	0.179875i	$0.0575693\pi$
$762$	22.2256	+	16.9985i	0.805149	+	0.615791i
$763$	13.3898	−	1.92516i	0.484743	−	0.0696955i
$764$	33.7254	+	16.2511i	1.22014	+	0.587942i
$765$	0.948899	+	0.136431i	0.0343075	+	0.00493267i
$766$	13.8749	−	10.1650i	0.501320	−	0.367275i
$767$	28.9303	+	18.5924i	1.04461	+	0.671332i
$768$	11.1870	+	11.4390i	0.403676	+	0.412770i
$769$	36.6921	+	10.7738i	1.32315	+	0.388512i	0.865629	−	0.500686i	$-0.166919\pi$
$769$	36.6921	+	10.7738i	1.32315	+	0.388512i	0.457522	+	0.889198i	$0.348737\pi$
$770$	2.63357	+	1.47351i	0.0949072	+	0.0531016i
$771$	0.100973	−	0.0874938i	0.00363646	−	0.00315101i
$772$	−4.84324	+	2.09217i	−0.174312	+	0.0752987i
$773$	−29.5349	−	13.4881i	−1.06230	−	0.485134i	−0.193907	−	0.981020i	$-0.562116\pi$
$773$	−29.5349	−	13.4881i	−1.06230	−	0.485134i	−0.868388	+	0.495886i	$0.834843\pi$
$774$	3.89599	−	17.0603i	0.140039	−	0.613218i
$775$	−44.4199	+	13.0429i	−1.59561	+	0.468513i
$776$	27.6793	+	22.0895i	0.993630	+	0.792965i
$777$	4.03603	+	8.83768i	0.144792	+	0.317050i
$778$	−0.724549	+	0.385984i	−0.0259763	+	0.0138382i
$779$	19.8506	+	30.8882i	0.711223	+	1.10668i
$780$	1.64342	+	0.0339157i	0.0588439	+	0.00121438i
$781$		−	20.2635i		−	0.725084i
$782$	19.3657	−	7.98727i	0.692517	−	0.285624i
$783$	−3.13477			−0.112028
$784$	−6.23001	−	7.81970i	−0.222500	−	0.279275i
$785$	0.639935	−	0.411262i	0.0228403	−	0.0146786i
$786$	4.31097	+	8.09233i	0.153767	+	0.288644i
$787$	20.3986	−	9.31571i	0.727130	−	0.332069i	−0.0172262	−	0.999852i	$-0.505484\pi$
$787$	20.3986	−	9.31571i	0.727130	−	0.332069i	0.744357	+	0.667782i	$0.232756\pi$
$788$	−16.0433	+	9.84869i	−0.571519	+	0.350845i
$789$	6.24415	+	21.2656i	0.222298	+	0.757076i
$790$	0.161588	−	0.707581i	0.00574904	−	0.0251746i
$791$	−11.8334	+	25.9116i	−0.420748	+	0.921311i
$792$	6.27782	+	6.67898i	0.223073	+	0.237327i
$793$	−13.6682	−	15.7740i	−0.485373	−	0.560151i
$794$	−12.3605	+	22.0916i	−0.438658	+	0.784002i
$795$	−0.246181	+	0.838415i	−0.00873113	+	0.0297355i
$796$	6.69935	+	24.6894i	0.237452	+	0.875093i
$797$	−19.5711	+	30.4532i	−0.693243	+	1.07871i	0.298983	+	0.954258i	$0.403353\pi$
$797$	−19.5711	+	30.4532i	−0.693243	+	1.07871i	−0.992226	+	0.124449i	$0.960284\pi$
$798$	−12.4513	+	9.12198i	−0.440770	+	0.322915i
$799$	4.30621	−	29.9504i	0.152343	−	1.05957i
$800$	23.0341	−	15.4564i	0.814378	−	0.546466i
$801$	0.347137	+	2.41439i	0.0122655	+	0.0853083i
$802$	−0.655641	+	0.857254i	−0.0231515	+	0.0302707i
$803$	−22.4685	−	19.4691i	−0.792896	−	0.687048i
$804$	5.83501	−	4.84894i	0.205785	−	0.171009i
$805$	0.140494	+	3.15470i	0.00495176	+	0.111189i
$806$	−12.0128	−	33.2512i	−0.423131	−	1.17122i
$807$	6.40725	−	7.39436i	0.225546	−	0.260294i
$808$	11.0908	−	0.448851i	0.390175	−	0.0157905i
$809$	1.28827	+	8.96009i	0.0452930	+	0.315020i	0.999855	+	0.0170086i	$0.00541426\pi$
$809$	1.28827	+	8.96009i	0.0452930	+	0.315020i	−0.954562	+	0.298011i	$0.903677\pi$
$810$	−0.313566	+	0.307162i	−0.0110176	+	0.0107926i
$811$	47.2423	+	6.79242i	1.65890	+	0.238514i	0.907112	−	0.420890i	$-0.138282\pi$
$811$	47.2423	+	6.79242i	1.65890	+	0.238514i	0.751789	+	0.659404i	$0.229191\pi$
$812$	−11.0383	−	7.42009i	−0.387368	−	0.260394i
$813$	−2.66600	+	4.14837i	−0.0935006	+	0.145490i
$814$	−1.71330	+	20.9195i	−0.0600510	+	0.733229i
$815$	5.41491	+	1.58996i	0.189676	+	0.0556939i
$816$	6.24491	+	10.6601i	0.218616	+	0.373177i
$817$	41.6894	+	48.1121i	1.45853	+	1.68323i
$818$	−5.69368	+	0.348218i	−0.199075	+	0.0121752i
$819$	5.10990	+	2.33361i	0.178554	+	0.0815430i
$820$	0.539872	+	4.39718i	0.0188531	+	0.153556i
$821$	7.72567	+	26.3112i	0.269628	+	0.918267i	0.977324	+	0.211750i	$0.0679164\pi$
$821$	7.72567	+	26.3112i	0.269628	+	0.918267i	−0.707696	+	0.706517i	$0.750265\pi$
$822$	−13.1241	+	2.71347i	−0.457754	+	0.0946430i
$823$	−7.08624	−	15.5167i	−0.247011	−	0.540878i	0.744995	−	0.667070i	$-0.232452\pi$
$823$	−7.08624	−	15.5167i	−0.247011	−	0.540878i	−0.992006	+	0.126192i	$0.959725\pi$
$824$	−6.87659	−	2.81020i	−0.239557	−	0.0978979i
$825$	13.3688	−	8.59162i	0.465443	−	0.299122i
$826$	−36.3642	−	13.9922i	−1.26527	−	0.486850i
$827$		−	27.7789i		−	0.965967i	−0.875629	−	0.482983i	$-0.839553\pi$
$827$		−	27.7789i		−	0.965967i	0.875629	−	0.482983i	$-0.160447\pi$
$828$	−2.48185	+	9.26501i	−0.0862501	+	0.321981i
$829$		−	20.0837i		−	0.697536i	−0.937209	−	0.348768i	$-0.886600\pi$
$829$		−	20.0837i		−	0.697536i	0.937209	−	0.348768i	$-0.113400\pi$
$830$	−0.637482	+	1.65675i	−0.0221273	+	0.0575066i
$831$	9.95471	−	6.39750i	0.345325	−	0.221927i
$832$	12.8555	+	16.8373i	0.445685	+	0.583727i
$833$	−3.20705	−	7.02245i	−0.111118	−	0.243314i
$834$	−2.38627	−	11.5415i	−0.0826297	−	0.399650i
$835$	−0.469292	−	1.59826i	−0.0162405	−	0.0553102i
$836$	−33.0974	+	4.06359i	−1.14470	+	0.140542i
$837$	8.58777	+	3.92191i	0.296837	+	0.135561i
$838$	−2.98552	−	48.8159i	−0.103133	−	1.68632i
$839$	4.86031	+	5.60910i	0.167797	+	0.193648i	0.833420	−	0.552640i	$-0.186380\pi$
$839$	4.86031	+	5.60910i	0.167797	+	0.193648i	−0.665623	+	0.746288i	$0.731834\pi$
$840$	−1.83120	+	0.339372i	−0.0631825	+	0.0117094i
$841$	−18.3966	−	5.40172i	−0.634364	−	0.186266i
$842$	17.6282	+	1.44374i	0.607509	+	0.0497546i
$843$	17.3654	−	27.0211i	0.598097	−	0.930657i
$844$	37.1319	+	24.9606i	1.27813	+	0.859178i
$845$	−1.83969	−	0.264507i	−0.0632872	−	0.00909933i
$846$	9.69504	+	9.89718i	0.333322	+	0.340272i
$847$	−0.150210	−	1.04473i	−0.00516128	−	0.0358975i
$848$	−10.4278	+	4.25145i	−0.358091	+	0.145995i
$849$	14.8172	−	17.1000i	0.508526	−	0.586870i
$850$	20.1449	−	7.27781i	0.690965	−	0.249627i
$851$	−19.5532	+	10.0039i	−0.670276	+	0.342930i
$852$	7.99256	+	9.61791i	0.273821	+	0.329504i
$853$	−16.4917	−	14.2901i	−0.564664	−	0.489284i	0.325116	−	0.945674i	$-0.394597\pi$
$853$	−16.4917	−	14.2901i	−0.564664	−	0.489284i	−0.889780	+	0.456390i	$0.849142\pi$
$854$	18.7839	+	14.3662i	0.642771	+	0.491601i
$855$	−0.227254	−	1.58059i	−0.00777192	−	0.0540549i
$856$	2.04245	−	19.8856i	0.0698096	−	0.679675i
$857$	4.38019	−	30.4649i	0.149624	−	1.04066i	−0.767211	−	0.641395i	$-0.778356\pi$
$857$	4.38019	−	30.4649i	0.149624	−	1.04066i	0.916835	−	0.399266i	$-0.130735\pi$
$858$	7.17224	+	9.78992i	0.244856	+	0.334222i
$859$	20.5223	−	31.9333i	0.700212	−	1.08955i	−0.290930	−	0.956744i	$-0.593965\pi$
$859$	20.5223	−	31.9333i	0.700212	−	1.08955i	0.991142	−	0.132807i	$-0.0423990\pi$
$860$	2.01154	+	7.41323i	0.0685930	+	0.252789i
$861$	−4.26546	+	14.5268i	−0.145366	+	0.495073i
$862$	35.6157	+	19.9274i	1.21308	+	0.678730i
$863$	−6.54483	−	7.55314i	−0.222789	−	0.257112i	0.633341	−	0.773873i	$-0.281683\pi$
$863$	−6.54483	−	7.55314i	−0.222789	−	0.257112i	−0.856130	+	0.516761i	$0.827138\pi$
$864$	−5.61413	−	0.693960i	−0.190996	−	0.0236090i
$865$	0.0839215	−	0.183762i	0.00285342	−	0.00624811i
$866$	−24.5996	−	5.61773i	−0.835928	−	0.190898i
$867$	−2.10180	−	7.15806i	−0.0713808	−	0.243101i
$868$	20.9564	+	34.1375i	0.711306	+	1.15870i
$869$	4.87435	−	2.22604i	0.165351	−	0.0755133i
$870$	1.21442	−	0.646948i	0.0411726	−	0.0219336i
$871$	8.45030	−	5.43068i	0.286327	−	0.184011i
$872$	−17.0855	+	5.77685i	−0.578587	+	0.195629i
$873$	−12.5204			−0.423752
$874$	−21.8535	−	27.2027i	−0.739207	−	0.920144i
$875$			6.52109i			0.220453i
$876$	18.3437	+	0.378565i	0.619778	+	0.0127905i
$877$	0.211861	+	0.329663i	0.00715405	+	0.0111319i	0.844812	−	0.535063i	$-0.179712\pi$
$877$	0.211861	+	0.329663i	0.00715405	+	0.0111319i	−0.837658	+	0.546195i	$0.816076\pi$
$878$	20.9956	+	39.4119i	0.708567	+	1.33009i
$879$	−3.04901	−	6.67641i	−0.102841	−	0.225190i
$880$	−3.81043	−	1.29185i	−0.128450	−	0.0435482i
$881$	−13.5757	+	3.98619i	−0.457377	+	0.134298i	−0.502302	−	0.864692i	$-0.667513\pi$
$881$	−13.5757	+	3.98619i	−0.457377	+	0.134298i	0.0449247	+	0.998990i	$0.485695\pi$
$882$	3.44612	+	0.786979i	0.116037	+	0.0264990i
$883$	−11.3136	−	5.16675i	−0.380733	−	0.173875i	0.215850	−	0.976427i	$-0.430748\pi$
$883$	−11.3136	−	5.16675i	−0.380733	−	0.173875i	−0.596583	+	0.802552i	$0.703475\pi$
$884$	6.48667	+	15.0163i	0.218170	+	0.505052i
$885$	3.04637	−	2.63969i	0.102403	−	0.0887323i
$886$	−24.5481	+	43.8742i	−0.824710	+	1.47398i
$887$	19.7058	+	5.78613i	0.661655	+	0.194279i	0.595284	−	0.803516i	$-0.297040\pi$
$887$	19.7058	+	5.78613i	0.661655	+	0.194279i	0.0663710	+	0.997795i	$0.478858\pi$
$888$	−7.43813	−	10.6051i	−0.249607	−	0.355883i
$889$	−35.3104	−	22.6926i	−1.18427	−	0.761086i
$890$	−0.632759	−	0.863699i	−0.0212101	−	0.0289513i
$891$	−3.20777	−	0.461207i	−0.107464	−	0.0154510i
$892$	23.0586	+	11.1111i	0.772060	+	0.372027i
$893$	−49.8885	+	7.17288i	−1.66945	+	0.240031i
$894$	−19.0052	+	24.8494i	−0.635628	+	0.831087i
$895$	−1.92671	+	2.22354i	−0.0644028	+	0.0743247i
$896$	−18.1261	−	15.7324i	−0.605550	−	0.525582i
$897$	−4.75632	+	11.7750i	−0.158809	+	0.393155i
$898$	−5.01236	+	1.81083i	−0.167265	+	0.0604282i
$899$	−22.3665	−	19.3807i	−0.745966	−	0.646383i
$900$	−2.95661	+	9.35105i	−0.0985537	+	0.311702i
$901$	−8.60692	+	1.23749i	−0.286738	+	0.0412267i
$902$	−23.3657	+	22.8885i	−0.777994	+	0.762104i
$903$	−3.73585	+	25.9834i	−0.124321	+	0.864674i
$904$	9.21761	−	36.8435i	0.306573	−	1.22540i
$905$	0.981767	+	0.630943i	0.0326350	+	0.0209733i
$906$	33.2328	+	2.72174i	1.10409	+	0.0904239i
$907$	7.12442	−	24.2635i	0.236562	−	0.805658i	−0.752555	−	0.658529i	$-0.771179\pi$
$907$	7.12442	−	24.2635i	0.236562	−	0.805658i	0.989117	−	0.147128i	$-0.0470030\pi$
$908$	−5.41855	+	32.8586i	−0.179821	+	1.09045i
$909$	−2.96588	+	2.56995i	−0.0983719	+	0.0852397i
$910$	−2.46119	+	0.150523i	−0.0815877	+	0.00498980i
$911$	−12.9600	+	28.3784i	−0.429384	+	0.940219i	0.564042	+	0.825746i	$0.309245\pi$
$911$	−12.9600	+	28.3784i	−0.429384	+	0.940219i	−0.993426	+	0.114474i	$0.963482\pi$
$912$	14.1066	−	14.9834i	0.467117	−	0.496151i
$913$	−12.5752	+	3.69242i	−0.416179	+	0.122201i
$914$	0.274477	+	1.32755i	0.00907890	+	0.0439114i
$915$	−2.22540	+	1.01630i	−0.0735694	+	0.0335980i
$916$	−12.8145	+	14.1864i	−0.423404	+	0.468733i
$917$	−7.43610	−	11.5708i	−0.245562	−	0.382101i
$918$	−4.07664	−	1.56860i	−0.134549	−	0.0517717i
$919$	−19.2826			−0.636075			−0.318037	−	0.948078i	$-0.603024\pi$
$919$	−19.2826			−0.636075			−0.318037	+	0.948078i	$0.603024\pi$
$920$	−0.950621	−	4.10148i	−0.0313410	−	0.135222i
$921$	17.2497			0.568396
$922$	30.6748	+	11.8030i	1.01022	+	0.388712i
$923$	8.95144	+	13.9287i	0.294640	+	0.458469i
$924$	−10.2036	−	9.21689i	−0.335675	−	0.303213i
$925$	−20.4282	+	9.32923i	−0.671674	+	0.306743i
$926$	1.11856	+	5.41009i	0.0367583	+	0.177787i
$927$	2.52003	−	0.739949i	0.0827688	−	0.0243031i
$928$	16.2732	+	7.04550i	0.534195	+	0.231280i
$929$	−11.4315	+	25.0315i	−0.375056	+	0.821258i	0.624146	+	0.781308i	$0.285447\pi$
$929$	−11.4315	+	25.0315i	−0.375056	+	0.821258i	−0.999202	+	0.0399499i	$0.987280\pi$
$930$	−4.13632	+	0.252972i	−0.135635	+	0.00829528i
$931$	−9.71850	+	8.42113i	−0.318511	+	0.275991i
$932$	1.80287	+	0.297302i	0.0590549	+	0.00973844i
$933$	−2.19726	+	7.48316i	−0.0719349	+	0.244988i
$934$	3.79715	+	0.310985i	0.124247	+	0.0101757i
$935$	−2.61358	−	1.67965i	−0.0854732	−	0.0549303i
$936$	−7.26571	−	1.81776i	−0.237487	−	0.0594153i
$937$	8.57495	−	59.6401i	0.280131	−	1.94836i	−0.0352165	−	0.999380i	$-0.511212\pi$
$937$	8.57495	−	59.6401i	0.280131	−	1.94836i	0.315348	−	0.948976i	$-0.397879\pi$
$938$	−8.13006	+	7.96401i	−0.265456	+	0.260034i
$939$	22.9921	−	3.30576i	0.750318	−	0.107879i
$940$	−5.79844	−	1.83335i	−0.189124	−	0.0597972i
$941$	25.3299	+	21.9485i	0.825730	+	0.715499i	0.961370	−	0.275259i	$-0.0887636\pi$
$941$	25.3299	+	21.9485i	0.825730	+	0.715499i	−0.135640	+	0.990758i	$0.543309\pi$
$942$	−3.25980	+	1.17768i	−0.106210	+	0.0383708i
$943$	−33.2366	−	8.17210i	−1.08233	−	0.266120i
$944$	51.0706	+	9.50810i	1.66221	+	0.309462i
$945$	0.431195	−	0.497625i	0.0140268	−	0.0161878i
$946$	−34.4525	+	45.0468i	−1.12015	+	1.46460i
$947$	−17.3778	+	2.49855i	−0.564703	+	0.0811921i	−0.418754	−	0.908100i	$-0.637533\pi$
$947$	−17.3778	+	2.49855i	−0.564703	+	0.0811921i	−0.145950	+	0.989292i	$0.546624\pi$
$948$	−1.43556	+	2.97918i	−0.0466247	+	0.0967591i
$949$	24.0449	+	3.45714i	0.780532	+	0.112223i
$950$	−21.0853	−	28.7809i	−0.684098	−	0.933776i
$951$	−15.4503	−	9.92933i	−0.501012	−	0.321981i
$952$	−10.6419	−	15.1729i	−0.344906	−	0.491758i
$953$	−42.6541	−	12.5244i	−1.38170	−	0.405705i	−0.495342	−	0.868698i	$-0.664957\pi$
$953$	−42.6541	−	12.5244i	−1.38170	−	0.405705i	−0.886362	+	0.462994i	$0.846775\pi$
$954$	1.94404	−	3.47453i	0.0629406	−	0.112492i
$955$	4.39076	−	3.80461i	0.142082	−	0.123114i
$956$	−40.7611	+	17.6078i	−1.31831	+	0.569477i
$957$	9.24097	+	4.22021i	0.298718	+	0.136420i
$958$	2.24747	+	0.513248i	0.0726125	+	0.0165823i
$959$	19.2892	−	5.66383i	0.622881	−	0.182894i
$960$	2.31814	−	0.889790i	0.0748177	−	0.0287179i
$961$	24.1486	+	52.8780i	0.778986	+	1.70574i
$962$	−8.06357	−	15.1365i	−0.259980	−	0.488021i
$963$	3.82103	+	5.94564i	0.123131	+	0.191596i
$964$	−0.782522	+	37.9179i	−0.0252033	+	1.22125i
$965$			0.818755i			0.0263566i
$966$	2.57609	−	14.1558i	0.0828842	−	0.455455i
$967$	25.1623			0.809165			0.404582	−	0.914502i	$-0.367417\pi$
$967$	25.1623			0.809165			0.404582	+	0.914502i	$0.367417\pi$
$968$	0.450736	+	1.33309i	0.0144872	+	0.0428470i
$969$	13.3679	−	8.59100i	0.429438	−	0.275983i
$970$	4.85044	−	2.58394i	0.155738	−	0.0829653i
$971$	−1.49710	+	0.683704i	−0.0480443	+	0.0219411i	−0.439292	−	0.898344i	$-0.644771\pi$
$971$	−1.49710	+	0.683704i	−0.0480443	+	0.0219411i	0.391248	+	0.920285i	$0.372043\pi$
$972$	1.70446	−	1.04634i	0.0546705	−	0.0335613i
$973$	4.98086	+	16.9633i	0.159679	+	0.543817i
$974$	−21.4112	−	4.88961i	−0.686059	−	0.156673i
$975$	−5.39410	+	11.8114i	−0.172750	+	0.378269i
$976$	−28.1148	−	14.2696i	−0.899933	−	0.456759i
$977$	1.65205	+	1.90656i	0.0528536	+	0.0609963i	0.781561	−	0.623829i	$-0.214424\pi$
$977$	1.65205	+	1.90656i	0.0528536	+	0.0609963i	−0.728707	+	0.684825i	$0.759878\pi$
$978$	−22.4403	−	12.5556i	−0.717562	−	0.401484i
$979$	2.22707	−	7.58470i	0.0711774	−	0.242408i
$980$	−1.49745	+	0.406326i	−0.0478343	+	0.0129796i
$981$	3.44743	−	5.36431i	0.110068	−	0.171269i
$982$	34.3820	+	46.9306i	1.09717	+	1.49762i
$983$	4.49978	−	31.2967i	0.143521	−	0.998208i	−0.783015	−	0.622002i	$-0.786319\pi$
$983$	4.49978	−	31.2967i	0.143521	−	0.998208i	0.926536	−	0.376206i	$-0.122772\pi$
$984$	2.06243	−	20.0801i	0.0657478	−	0.640129i
$985$	0.415769	+	2.89174i	0.0132475	+	0.0921384i
$986$	10.8763	+	8.31839i	0.346373	+	0.264911i
$987$	−15.7067	−	13.6099i	−0.499949	−	0.433209i
$988$	20.9554	−	17.4141i	0.666680	−	0.554016i
$989$	−59.0571	−	5.82374i	−1.87791	−	0.185184i
$990$	1.33788	−	0.483339i	0.0425206	−	0.0153615i
$991$	−13.3854	+	15.4476i	−0.425201	+	0.490708i	−0.927414	−	0.374036i	$-0.877974\pi$
$991$	−13.3854	+	15.4476i	−0.425201	+	0.490708i	0.502214	+	0.864744i	$0.332519\pi$
$992$	−35.7663	−	39.6607i	−1.13558	−	1.25923i
$993$	−0.816093	−	5.67605i	−0.0258979	−	0.180124i
$994$	−13.1272	−	13.4009i	−0.416368	−	0.425049i
$995$	3.92970	+	0.565005i	0.124580	+	0.0179119i
$996$	4.51234	−	6.71266i	0.142979	−	0.212699i
$997$	−27.1780	+	42.2898i	−0.860736	+	1.33933i	0.0788033	+	0.996890i	$0.474890\pi$
$997$	−27.1780	+	42.2898i	−0.860736	+	1.33933i	−0.939539	+	0.342441i	$0.888746\pi$
$998$	−13.9484	−	1.14237i	−0.441530	−	0.0361610i
$999$	4.39425	+	1.29027i	0.139028	+	0.0408223i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	552.2.bb.a.85.18	yes	480
8.5	even	2	inner	552.2.bb.a.85.9	yes	480
23.13	even	11	inner	552.2.bb.a.13.9	✓	480
184.13	even	22	inner	552.2.bb.a.13.18	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
552.2.bb.a.13.9	✓	480	23.13	even	11	inner
552.2.bb.a.13.18	yes	480	184.13	even	22	inner
552.2.bb.a.85.9	yes	480	8.5	even	2	inner
552.2.bb.a.85.18	yes	480	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 552 = 2^{3} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	552.bb (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.507861 + 1.31988i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-1.48415 - 1.34063i) q^{4} +(-0.282332 + 0.128937i) q^{5} +(1.38492 - 0.286340i) q^{6} +(-2.03550 + 0.597678i) q^{7} +(2.52321 - 1.27805i) q^{8} +(-0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.507861 + 1.31988i) q^{2} +(-0.540641 - 0.841254i) q^{3} +(-1.48415 - 1.34063i) q^{4} +(-0.282332 + 0.128937i) q^{5} +(1.38492 - 0.286340i) q^{6} +(-2.03550 + 0.597678i) q^{7} +(2.52321 - 1.27805i) q^{8} +(-0.415415 + 0.909632i) q^{9} +(-0.0267952 - 0.438126i) q^{10} +(2.44920 - 2.12224i) q^{11} +(-0.325415 + 1.97335i) q^{12} +(-0.746025 + 2.54073i) q^{13} +(0.244892 - 2.99015i) q^{14} +(0.261109 + 0.167804i) q^{15} +(0.405427 + 3.97940i) q^{16} +(-0.439560 + 3.05721i) q^{17} +(-0.989630 - 1.01026i) q^{18} +(5.09241 - 0.732178i) q^{19} +(0.591881 + 0.187141i) q^{20} +(1.60327 + 1.38925i) q^{21} +(1.55725 + 4.31044i) q^{22} +(-2.97624 + 3.76059i) q^{23} +(-2.43931 - 1.43169i) q^{24} +(-3.21122 + 3.70594i) q^{25} +(-2.97457 - 2.27500i) q^{26} +(0.989821 - 0.142315i) q^{27} +(3.82226 + 1.84181i) q^{28} +(-3.10286 - 0.446125i) q^{29} +(-0.354088 + 0.259410i) q^{30} +(7.94222 + 5.10415i) q^{31} +(-5.45822 - 1.48587i) q^{32} +(-3.10948 - 0.913025i) q^{33} +(-3.81191 - 2.13280i) q^{34} +(0.497625 - 0.431195i) q^{35} +(1.83602 - 0.793117i) q^{36} +(4.16590 + 1.90250i) q^{37} +(-1.61985 + 7.09321i) q^{38} +(2.54073 - 0.746025i) q^{39} +(-0.547596 + 0.686169i) q^{40} +(2.96470 + 6.49179i) q^{41} +(-2.64787 + 1.41058i) q^{42} +(6.68988 + 10.4097i) q^{43} +(-6.48012 - 0.133732i) q^{44} -0.310381i q^{45} +(-3.45200 - 5.83813i) q^{46} -9.79663 q^{47} +(3.12849 - 2.49249i) q^{48} +(-2.10272 + 1.35134i) q^{49} +(-3.26054 - 6.12052i) q^{50} +(2.80953 - 1.28307i) q^{51} +(4.51339 - 2.77069i) q^{52} +(0.793158 + 2.70125i) q^{53} +(-0.314854 + 1.37872i) q^{54} +(-0.417852 + 0.914968i) q^{55} +(-4.37214 + 4.10954i) q^{56} +(-3.36911 - 3.88816i) q^{57} +(2.16465 - 3.86883i) q^{58} +(3.65887 - 12.4610i) q^{59} +(-0.162562 - 0.599098i) q^{60} +(-4.26144 + 6.63092i) q^{61} +(-10.7704 + 7.89055i) q^{62} +(0.301912 - 2.09984i) q^{63} +(4.73319 - 6.44957i) q^{64} +(-0.116966 - 0.813519i) q^{65} +(2.78426 - 3.64044i) q^{66} +(-2.86686 - 2.48415i) q^{67} +(4.75096 - 3.94808i) q^{68} +(4.77268 + 0.470644i) q^{69} +(0.316400 + 0.875792i) q^{70} +(4.09465 - 4.72548i) q^{71} +(0.114374 + 2.82611i) q^{72} +(-1.30557 - 9.08045i) q^{73} +(-4.62677 + 4.53227i) q^{74} +(4.85375 + 0.697864i) q^{75} +(-8.53950 - 5.74037i) q^{76} +(-3.71693 + 5.78366i) q^{77} +(-0.305675 + 3.73233i) q^{78} +(1.58653 + 0.465846i) q^{79} +(-0.627556 - 1.07124i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-10.0740 + 0.616115i) q^{82} +(-3.67870 - 1.68001i) q^{83} +(-0.517044 - 4.21125i) q^{84} +(-0.270085 - 0.919824i) q^{85} +(-17.1370 + 3.54316i) q^{86} +(1.30223 + 2.85149i) q^{87} +(3.46751 - 8.48505i) q^{88} +(2.05200 - 1.31874i) q^{89} +(0.409664 + 0.157630i) q^{90} -5.61754i q^{91} +(9.45875 - 1.59126i) q^{92} -9.44093i q^{93} +(4.97533 - 12.9304i) q^{94} +(-1.34335 + 0.863317i) q^{95} +(1.70094 + 5.39507i) q^{96} +(5.20118 + 11.3890i) q^{97} +(-0.715709 - 3.46162i) q^{98} +(0.913025 + 3.10948i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9}+O(q^{10}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9	\( 480 q + 4 q^{2} + 4 q^{6} + 8 q^{7} + 4 q^{8} + 48 q^{9} - 4 q^{10} - 4 q^{14} - 8 q^{15} - 8 q^{16} - 4 q^{18} + 20 q^{20} + 20 q^{22} - 8 q^{23} - 4 q^{24} + 48 q^{25} + 16 q^{30} + 16 q^{31} + 4 q^{32} + 6 q^{34} - 22 q^{36} + 90 q^{38} - 74 q^{40} + 90 q^{42} - 130 q^{44} + 96 q^{46} - 88 q^{48} - 48 q^{49} + 142 q^{50} - 142 q^{52} + 18 q^{54} - 82 q^{56} + 22 q^{58} + 2 q^{60} - 40 q^{62} - 8 q^{63} + 16 q^{66} - 44 q^{68} + 16 q^{71} - 4 q^{72} + 10 q^{74} - 138 q^{76} - 40 q^{79} - 170 q^{80} - 48 q^{81} - 124 q^{82} - 8 q^{84} - 216 q^{86} - 108 q^{88} + 4 q^{90} - 198 q^{92} - 238 q^{94} + 80 q^{95} + 4 q^{96} - 132 q^{98}+O(q^{100}) \) 480 * q + 4 * q^2 + 4 * q^6 + 8 * q^7 + 4 * q^8 + 48 * q^9 - 4 * q^10 - 4 * q^14 - 8 * q^15 - 8 * q^16 - 4 * q^18 + 20 * q^20 + 20 * q^22 - 8 * q^23 - 4 * q^24 + 48 * q^25 + 16 * q^30 + 16 * q^31 + 4 * q^32 + 6 * q^34 - 22 * q^36 + 90 * q^38 - 74 * q^40 + 90 * q^42 - 130 * q^44 + 96 * q^46 - 88 * q^48 - 48 * q^49 + 142 * q^50 - 142 * q^52 + 18 * q^54 - 82 * q^56 + 22 * q^58 + 2 * q^60 - 40 * q^62 - 8 * q^63 + 16 * q^66 - 44 * q^68 + 16 * q^71 - 4 * q^72 + 10 * q^74 - 138 * q^76 - 40 * q^79 - 170 * q^80 - 48 * q^81 - 124 * q^82 - 8 * q^84 - 216 * q^86 - 108 * q^88 + 4 * q^90 - 198 * q^92 - 238 * q^94 + 80 * q^95 + 4 * q^96 - 132 * q^98

Introduction

L-functions

Modular forms

Varieties

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