LMFDB - Embedded newform 525.2.bo.a.319.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(4,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 3, 20]))

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

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

chi := DirichletCharacter("525.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bo (of order $30$, degree $8$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$320$
Relative dimension:	$40$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			319.1
Character	$\chi$	$=$	525.319
Dual form			525.2.bo.a.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.06124 - 1.85595i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.595110 + 5.66210i) q^{4} +(-2.11932 - 0.713090i) q^{5} +(2.24395 + 1.63033i) q^{6} +(-1.97794 - 1.75720i) q^{7} +(6.02126 - 8.28755i) q^{8} +(0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-2.06124 - 1.85595i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.595110 + 5.66210i) q^{4} +(-2.11932 - 0.713090i) q^{5} +(2.24395 + 1.63033i) q^{6} +(-1.97794 - 1.75720i) q^{7} +(6.02126 - 8.28755i) q^{8} +(0.978148 - 0.207912i) q^{9} +(3.04497 + 5.40320i) q^{10} +(-5.77814 - 1.22818i) q^{11} +(-1.18370 - 5.56887i) q^{12} +(-1.69479 - 0.550670i) q^{13} +(0.815750 + 7.29298i) q^{14} +(2.18224 + 0.487654i) q^{15} +(-16.6548 + 3.54009i) q^{16} +(-0.431974 - 0.970229i) q^{17} +(-2.40207 - 1.38684i) q^{18} +(-0.320492 + 3.04928i) q^{19} +(2.77636 - 12.4241i) q^{20} +(2.15078 + 1.54082i) q^{21} +(9.63070 + 13.2555i) q^{22} +(0.664866 + 0.598648i) q^{23} +(-5.12199 + 8.87154i) q^{24} +(3.98301 + 3.02253i) q^{25} +(2.47136 + 4.28051i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(8.77232 - 12.2450i) q^{28} +(5.67658 - 4.12428i) q^{29} +(-3.59308 - 5.05532i) q^{30} +(1.21004 - 0.538746i) q^{31} +(23.1568 + 13.3696i) q^{32} +(5.87486 + 0.617473i) q^{33} +(-0.910295 + 2.80160i) q^{34} +(2.93885 + 5.13451i) q^{35} +(1.75932 + 5.41463i) q^{36} +(-0.798924 - 3.75864i) q^{37} +(6.31993 - 5.69049i) q^{38} +(1.74307 + 0.370500i) q^{39} +(-18.6707 + 13.2702i) q^{40} +(-2.22233 + 6.83962i) q^{41} +(-1.57360 - 7.16776i) q^{42} +3.18781i q^{43} +(3.51545 - 33.4473i) q^{44} +(-2.22126 - 0.256876i) q^{45} +(-0.259389 - 2.46792i) q^{46} +(-3.01093 + 6.76267i) q^{47} +(16.1936 - 5.26161i) q^{48} +(0.824518 + 6.95127i) q^{49} +(-2.60028 - 13.6224i) q^{50} +(0.531024 + 0.919760i) q^{51} +(2.10936 - 9.92377i) q^{52} +(2.90991 - 0.305844i) q^{53} +(2.53388 + 1.12816i) q^{54} +(11.3699 + 6.72324i) q^{55} +(-26.4726 + 5.81177i) q^{56} -3.06607i q^{57} +(-19.3553 - 2.03432i) q^{58} +(0.739890 + 0.821731i) q^{59} +(-1.46247 + 12.6463i) q^{60} +(8.98254 - 9.97613i) q^{61} +(-3.49408 - 1.13530i) q^{62} +(-2.30006 - 1.30756i) q^{63} +(-12.3953 - 38.1489i) q^{64} +(3.19912 + 2.37558i) q^{65} +(-10.9635 - 12.1762i) q^{66} +(-2.66268 - 5.98047i) q^{67} +(5.23646 - 3.02327i) q^{68} +(-0.723799 - 0.525871i) q^{69} +(3.47172 - 16.0378i) q^{70} +(2.66243 - 1.93437i) q^{71} +(4.16660 - 9.35834i) q^{72} +(1.43323 - 6.74280i) q^{73} +(-5.32908 + 9.23024i) q^{74} +(-4.27713 - 2.58963i) q^{75} -17.4560 q^{76} +(9.27067 + 12.5826i) q^{77} +(-2.90525 - 3.99874i) q^{78} +(14.3422 + 6.38557i) q^{79} +(37.8213 + 4.37381i) q^{80} +(0.913545 - 0.406737i) q^{81} +(17.2748 - 9.97358i) q^{82} +(0.236448 - 0.325442i) q^{83} +(-7.44431 + 13.0949i) q^{84} +(0.223629 + 2.36426i) q^{85} +(5.91642 - 6.57085i) q^{86} +(-5.21438 + 4.69505i) q^{87} +(-44.9703 + 40.4914i) q^{88} +(-9.16905 + 10.1833i) q^{89} +(4.10182 + 4.65204i) q^{90} +(2.38456 + 4.06727i) q^{91} +(-2.99393 + 4.12079i) q^{92} +(-1.14710 + 0.662278i) q^{93} +(18.7575 - 8.35136i) q^{94} +(2.85363 - 6.23385i) q^{95} +(-24.4275 - 10.8758i) q^{96} +(4.20973 + 5.79420i) q^{97} +(11.2017 - 15.8585i) q^{98} -5.90722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	$ 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) $ 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{9}{10}\right)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.06124	−	1.85595i	−1.45752	−	1.31236i	−0.859779	−	0.510667i	$-0.829399\pi$
$2$	−2.06124	−	1.85595i	−1.45752	−	1.31236i	−0.597741	−	0.801689i	$-0.703935\pi$
$3$	−0.994522	+	0.104528i	−0.574187	+	0.0603495i
$3$	−0.994522	+	0.104528i	−0.574187	+	0.0603495i
$4$	0.595110	+	5.66210i	0.297555	+	2.83105i
$5$	−2.11932	−	0.713090i	−0.947787	−	0.318903i
$5$	−2.11932	−	0.713090i	−0.947787	−	0.318903i
$6$	2.24395	+	1.63033i	0.916089	+	0.665578i
$7$	−1.97794	−	1.75720i	−0.747592	−	0.664158i
$7$	−1.97794	−	1.75720i	−0.747592	−	0.664158i
$8$	6.02126	−	8.28755i	2.12884	−	2.93009i
$9$	0.978148	−	0.207912i	0.326049	−	0.0693039i
$10$	3.04497	+	5.40320i	0.962903	+	1.70864i
$11$	−5.77814	−	1.22818i	−1.74217	−	0.370311i	−0.776510	−	0.630105i	$-0.783012\pi$
$11$	−5.77814	−	1.22818i	−1.74217	−	0.370311i	−0.965664	+	0.259794i	$0.916345\pi$
$12$	−1.18370	−	5.56887i	−0.341705	−	1.60759i
$13$	−1.69479	−	0.550670i	−0.470050	−	0.152729i	0.0644078	−	0.997924i	$-0.479484\pi$
$13$	−1.69479	−	0.550670i	−0.470050	−	0.152729i	−0.534458	+	0.845195i	$0.679484\pi$
$14$	0.815750	+	7.29298i	0.218018	+	1.94913i
$15$	2.18224	+	0.487654i	0.563453	+	0.125912i
$16$	−16.6548	+	3.54009i	−4.16371	+	0.885024i
$17$	−0.431974	−	0.970229i	−0.104769	−	0.235315i	0.853553	−	0.521007i	$-0.174443\pi$
$17$	−0.431974	−	0.970229i	−0.104769	−	0.235315i	−0.958322	+	0.285692i	$0.907777\pi$
$18$	−2.40207	−	1.38684i	−0.566174	−	0.326881i
$19$	−0.320492	+	3.04928i	−0.0735259	+	0.699552i	0.894221	+	0.447627i	$0.147731\pi$
$19$	−0.320492	+	3.04928i	−0.0735259	+	0.699552i	−0.967747	+	0.251926i	$0.918936\pi$
$20$	2.77636	−	12.4241i	0.620812	−	2.77812i
$21$	2.15078	+	1.54082i	0.469340	+	0.336234i
$22$	9.63070	+	13.2555i	2.05327	+	2.82609i
$23$	0.664866	+	0.598648i	0.138634	+	0.124827i	0.735530	−	0.677492i	$-0.236933\pi$
$23$	0.664866	+	0.598648i	0.138634	+	0.124827i	−0.596896	+	0.802318i	$0.703600\pi$
$24$	−5.12199	+	8.87154i	−1.04552	+	1.81090i
$25$	3.98301	+	3.02253i	0.796601	+	0.604505i
$26$	2.47136	+	4.28051i	0.484673	+	0.839478i
$27$	−0.951057	+	0.309017i	−0.183031	+	0.0594703i
$28$	8.77232	−	12.2450i	1.65781	−	2.31409i
$29$	5.67658	−	4.12428i	1.05411	−	0.765859i	0.0811237	−	0.996704i	$-0.474149\pi$
$29$	5.67658	−	4.12428i	1.05411	−	0.765859i	0.972990	+	0.230845i	$0.0741491\pi$
$30$	−3.59308	−	5.05532i	−0.656003	−	0.922970i
$31$	1.21004	−	0.538746i	0.217330	−	0.0967616i	−0.295184	−	0.955440i	$-0.595381\pi$
$31$	1.21004	−	0.538746i	0.217330	−	0.0967616i	0.512514	+	0.858679i	$0.328714\pi$
$32$	23.1568	+	13.3696i	4.09359	+	2.36343i
$33$	5.87486	+	0.617473i	1.02268	+	0.107488i
$34$	−0.910295	+	2.80160i	−0.156114	+	0.480471i
$35$	2.93885	+	5.13451i	0.496756	+	0.867890i
$36$	1.75932	+	5.41463i	0.293220	+	0.902439i
$37$	−0.798924	−	3.75864i	−0.131342	−	0.617917i	−0.993743	−	0.111691i	$-0.964373\pi$
$37$	−0.798924	−	3.75864i	−0.131342	−	0.617917i	0.862401	−	0.506226i	$-0.168960\pi$
$38$	6.31993	−	5.69049i	1.02523	−	0.923119i
$39$	1.74307	+	0.370500i	0.279114	+	0.0593275i
$40$	−18.6707	+	13.2702i	−2.95210	+	2.09821i
$41$	−2.22233	+	6.83962i	−0.347069	+	1.06817i	0.613398	+	0.789774i	$0.289802\pi$
$41$	−2.22233	+	6.83962i	−0.347069	+	1.06817i	−0.960467	+	0.278394i	$0.910198\pi$
$42$	−1.57360	−	7.16776i	−0.242812	−	1.10601i
$43$			3.18781i			0.486136i	0.970009	+	0.243068i	$0.0781538\pi$
$43$			3.18781i			0.486136i	−0.970009	+	0.243068i	$0.921846\pi$
$44$	3.51545	−	33.4473i	0.529974	−	5.04237i
$45$	−2.22126	−	0.256876i	−0.331127	−	0.0382929i
$46$	−0.259389	−	2.46792i	−0.0382448	−	0.363875i
$47$	−3.01093	+	6.76267i	−0.439190	+	0.986437i	0.549366	+	0.835582i	$0.314869\pi$
$47$	−3.01093	+	6.76267i	−0.439190	+	0.986437i	−0.988556	+	0.150855i	$0.951797\pi$
$48$	16.1936	−	5.26161i	2.33734	−	0.759447i
$49$	0.824518	+	6.95127i	0.117788	+	0.993039i
$50$	−2.60028	−	13.6224i	−0.367735	−	1.92650i
$51$	0.531024	+	0.919760i	0.0743582	+	0.128792i
$52$	2.10936	−	9.92377i	0.292516	−	1.37618i
$53$	2.90991	−	0.305844i	0.399707	−	0.0420109i	0.0974571	−	0.995240i	$-0.468929\pi$
$53$	2.90991	−	0.305844i	0.399707	−	0.0420109i	0.302249	+	0.953229i	$0.402262\pi$
$54$	2.53388	+	1.12816i	0.344817	+	0.153523i
$55$	11.3699	+	6.72324i	1.53312	+	0.906561i
$56$	−26.4726	+	5.81177i	−3.53755	+	0.776630i
$57$		−	3.06607i		−	0.406111i
$58$	−19.3553	−	2.03432i	−2.54147	−	0.267119i
$59$	0.739890	+	0.821731i	0.0963255	+	0.106980i	0.789380	−	0.613905i	$-0.210402\pi$
$59$	0.739890	+	0.821731i	0.0963255	+	0.106980i	−0.693055	+	0.720885i	$0.743735\pi$
$60$	−1.46247	+	12.6463i	−0.188804	+	1.63263i
$61$	8.98254	−	9.97613i	1.15010	−	1.27731i	0.195071	−	0.980789i	$-0.437506\pi$
$61$	8.98254	−	9.97613i	1.15010	−	1.27731i	0.955026	−	0.296523i	$-0.0958271\pi$
$62$	−3.49408	−	1.13530i	−0.443749	−	0.144183i
$63$	−2.30006	−	1.30756i	−0.289781	−	0.164737i
$64$	−12.3953	−	38.1489i	−1.54941	−	4.76861i
$65$	3.19912	+	2.37558i	0.396802	+	0.294655i
$66$	−10.9635	−	12.1762i	−1.34952	−	1.49879i
$67$	−2.66268	−	5.98047i	−0.325298	−	0.730631i	0.674674	−	0.738116i	$-0.264284\pi$
$67$	−2.66268	−	5.98047i	−0.325298	−	0.730631i	−0.999972	+	0.00748465i	$0.997618\pi$
$68$	5.23646	−	3.02327i	0.635014	−	0.366625i
$69$	−0.723799	−	0.525871i	−0.0871352	−	0.0633074i
$70$	3.47172	−	16.0378i	0.414950	−	1.91689i
$71$	2.66243	−	1.93437i	0.315973	−	0.229568i	−0.418482	−	0.908225i	$-0.637438\pi$
$71$	2.66243	−	1.93437i	0.315973	−	0.229568i	0.734455	+	0.678657i	$0.237438\pi$
$72$	4.16660	−	9.35834i	0.491039	−	1.10289i
$73$	1.43323	−	6.74280i	0.167747	−	0.789185i	−0.811152	−	0.584836i	$-0.801159\pi$
$73$	1.43323	−	6.74280i	0.167747	−	0.789185i	0.978898	−	0.204349i	$-0.0655078\pi$
$74$	−5.32908	+	9.23024i	−0.619493	+	1.07299i
$75$	−4.27713	−	2.58963i	−0.493880	−	0.299025i
$76$	−17.4560			−2.00234
$77$	9.27067	+	12.5826i	1.05649	+	1.43392i
$78$	−2.90525	−	3.99874i	−0.328955	−	0.452768i
$79$	14.3422	+	6.38557i	1.61363	+	0.718432i	0.997596	−	0.0692909i	$-0.0220737\pi$
$79$	14.3422	+	6.38557i	1.61363	+	0.718432i	0.616029	+	0.787723i	$0.288740\pi$
$80$	37.8213	+	4.37381i	4.22855	+	0.489007i
$81$	0.913545	−	0.406737i	0.101505	−	0.0451930i
$82$	17.2748	−	9.97358i	1.90768	−	1.10140i
$83$	0.236448	−	0.325442i	0.0259535	−	0.0357219i	−0.795843	−	0.605503i	$-0.792972\pi$
$83$	0.236448	−	0.325442i	0.0259535	−	0.0357219i	0.821797	+	0.569781i	$0.192972\pi$
$84$	−7.44431	+	13.0949i	−0.812241	+	1.42877i
$85$	0.223629	+	2.36426i	0.0242560	+	0.256440i
$86$	5.91642	−	6.57085i	0.637984	−	0.708552i
$87$	−5.21438	+	4.69505i	−0.559040	+	0.503362i
$88$	−44.9703	+	40.4914i	−4.79385	+	4.31640i
$89$	−9.16905	+	10.1833i	−0.971917	+	1.07942i	0.0248991	+	0.999690i	$0.492074\pi$
$89$	−9.16905	+	10.1833i	−0.971917	+	1.07942i	−0.996816	+	0.0797334i	$0.974593\pi$
$90$	4.10182	+	4.65204i	0.432369	+	0.490369i
$91$	2.38456	+	4.06727i	0.249970	+	0.426366i
$92$	−2.99393	+	4.12079i	−0.312139	+	0.429622i
$93$	−1.14710	+	0.662278i	−0.118949	+	0.0686751i
$94$	18.7575	−	8.35136i	1.93468	−	0.861377i
$95$	2.85363	−	6.23385i	0.292777	−	0.639579i
$96$	−24.4275	−	10.8758i	−2.49312	−	1.11001i
$97$	4.20973	+	5.79420i	0.427433	+	0.588312i	0.967362	−	0.253399i	$-0.0815487\pi$
$97$	4.20973	+	5.79420i	0.427433	+	0.588312i	−0.539928	+	0.841711i	$0.681549\pi$
$98$	11.2017	−	15.8585i	1.13154	−	1.60195i
$99$	−5.90722			−0.593698
$100$	−14.7435	+	24.3509i	−1.47435	+	2.43509i
$101$	−1.93488	+	3.35132i	−0.192528	+	0.333468i	−0.946087	−	0.323912i	$-0.895002\pi$
$101$	−1.93488	+	3.35132i	−0.192528	+	0.333468i	0.753559	+	0.657380i	$0.228335\pi$
$102$	0.612461	−	2.88140i	0.0606427	−	0.285302i
$103$	−3.34227	+	7.50685i	−0.329323	+	0.739672i	−0.999998	−	0.00207945i	$-0.999338\pi$
$103$	−3.34227	+	7.50685i	−0.329323	+	0.739672i	0.670674	+	0.741752i	$0.266005\pi$
$104$	−14.7685	+	10.7299i	−1.44817	+	1.05216i
$105$	−3.45945	−	4.79919i	−0.337608	−	0.468353i
$106$	−6.56566	−	4.77023i	−0.637713	−	0.463326i
$107$	−4.61144	+	2.66241i	−0.445804	+	0.257385i	−0.706057	−	0.708155i	$-0.749528\pi$
$107$	−4.61144	+	2.66241i	−0.445804	+	0.257385i	0.260252	+	0.965541i	$0.416194\pi$
$108$	−2.31567	−	5.20107i	−0.222825	−	0.500474i
$109$	0.989171	+	1.09859i	0.0947454	+	0.105225i	0.788653	−	0.614839i	$-0.210779\pi$
$109$	0.989171	+	1.09859i	0.0947454	+	0.105225i	−0.693907	+	0.720064i	$0.744112\pi$
$110$	−10.9581	−	34.9602i	−1.04482	−	3.33333i
$111$	1.18743	+	3.65454i	0.112706	+	0.346874i
$112$	39.1630	+	22.2637i	3.70055	+	2.10372i
$113$	0.0380239	+	0.0123547i	0.00357699	+	0.00116223i	0.310805	−	0.950474i	$-0.399401\pi$
$113$	0.0380239	+	0.0123547i	0.00357699	+	0.00116223i	−0.307228	+	0.951636i	$0.599401\pi$
$114$	−5.69049	+	6.31993i	−0.532963	+	0.591915i
$115$	−0.982171	−	1.74283i	−0.0915879	−	0.162520i
$116$	26.7302	+	29.6869i	2.48184	+	2.75636i
$117$	−1.77224	−	0.186270i	−0.163844	−	0.0172207i
$118$		−	3.06699i		−	0.282339i
$119$	−0.850464	+	2.67812i	−0.0779619	+	0.245503i
$120$	17.1813	−	15.1492i	1.56843	−	1.38292i
$121$	21.8294	+	9.71910i	1.98450	+	0.883554i
$122$	−37.0304	+	3.89205i	−3.35258	+	0.352370i
$123$	1.49522	−	7.03444i	0.134819	−	0.634274i
$124$	3.77054	+	6.53077i	0.338604	+	0.586480i
$125$	−6.28592	−	9.24593i	−0.562230	−	0.826981i
$126$	2.31422	+	6.96401i	0.206167	+	0.620403i
$127$	−15.7827	+	5.12811i	−1.40049	+	0.455046i	−0.909349	−	0.416035i	$-0.863419\pi$
$127$	−15.7827	+	5.12811i	−1.40049	+	0.455046i	−0.491139	+	0.871081i	$0.663419\pi$
$128$	−23.5011	+	52.7843i	−2.07722	+	4.66551i
$129$	−0.333216	−	3.17034i	−0.0293381	−	0.279133i
$130$	−2.18520	−	10.8341i	−0.191654	−	0.950210i
$131$	0.388376	−	3.69515i	0.0339325	−	0.322847i	−0.964368	−	0.264566i	$-0.914771\pi$
$131$	0.388376	−	3.69515i	0.0339325	−	0.322847i	0.998300	−	0.0582809i	$-0.0185619\pi$
$132$			33.6315i			2.92725i
$133$	5.99210	−	5.46813i	0.519581	−	0.474147i
$134$	−5.61104	+	17.2690i	−0.484720	+	1.49182i
$135$	2.23595	+	0.0232838i	0.192440	+	0.00200395i
$136$	−10.6418	−	2.26199i	−0.912531	−	0.193964i
$137$	1.79623	−	1.61733i	0.153462	−	0.138178i	−0.588823	−	0.808262i	$-0.700409\pi$
$137$	1.79623	−	1.61733i	0.153462	−	0.138178i	0.742285	+	0.670084i	$0.233742\pi$
$138$	0.515935	+	2.42728i	0.0439193	+	0.206624i
$139$	1.96047	+	6.03372i	0.166285	+	0.511773i	0.999129	−	0.0417352i	$-0.0132886\pi$
$139$	1.96047	+	6.03372i	0.166285	+	0.511773i	−0.832843	+	0.553509i	$0.813289\pi$
$140$	−27.3231	+	19.6956i	−2.30923	+	1.66459i
$141$	2.28755	−	7.04035i	0.192646	−	0.592904i
$142$	−9.07802	−	0.954139i	−0.761811	−	0.0800695i
$143$	9.11640	+	5.26336i	0.762352	+	0.440144i
$144$	−15.5549	+	6.92547i	−1.29624	+	0.577123i
$145$	−14.9714	+	4.69274i	−1.24331	+	0.389711i
$146$	−15.4685	+	11.2386i	−1.28019	+	0.930110i
$147$	−1.54661	−	6.82701i	−0.127562	−	0.563082i
$148$	20.8063	−	6.76039i	1.71027	−	0.555701i
$149$	−2.55241	−	4.42090i	−0.209102	−	0.362175i	0.742330	−	0.670034i	$-0.233721\pi$
$149$	−2.55241	−	4.42090i	−0.209102	−	0.362175i	−0.951432	+	0.307860i	$0.900387\pi$
$150$	4.00997	+	13.2760i	0.327413	+	1.08398i
$151$	1.60032	−	2.77184i	0.130232	−	0.225569i	−0.793534	−	0.608526i	$-0.791761\pi$
$151$	1.60032	−	2.77184i	0.130232	−	0.225569i	0.923766	+	0.382957i	$0.125094\pi$
$152$	23.3413	+	21.0166i	1.89323	+	1.70467i
$153$	−0.624256	−	0.859215i	−0.0504681	−	0.0694634i
$154$	4.24359	−	43.1417i	0.341958	−	3.47646i
$155$	−2.94864	+	0.278904i	−0.236840	+	0.0224021i
$156$	−1.06049	+	10.0899i	−0.0849072	+	0.807838i
$157$	1.62466	+	0.937998i	0.129662	+	0.0748604i	0.563428	−	0.826165i	$-0.309482\pi$
$157$	1.62466	+	0.937998i	0.129662	+	0.0748604i	−0.433766	+	0.901026i	$0.642816\pi$
$158$	−17.7115	−	39.7807i	−1.40905	−	3.16478i
$159$	−2.86200	+	0.608336i	−0.226971	+	0.0482442i
$160$	−39.5429	−	44.8473i	−3.12614	−	3.54549i
$161$	−0.263125	−	2.35239i	−0.0207371	−	0.185394i
$162$	−2.63792	−	0.857113i	−0.207255	−	0.0673412i
$163$	−3.73700	−	17.5812i	−0.292704	−	1.37706i	−0.841115	−	0.540856i	$-0.818100\pi$
$163$	−3.73700	−	17.5812i	−0.292704	−	1.37706i	0.548411	−	0.836209i	$-0.315233\pi$
$164$	−40.0491	−	8.51270i	−3.12731	−	0.664730i
$165$	−12.0104	−	5.49793i	−0.935007	−	0.428013i
$166$	−1.09138	+	0.231980i	−0.0847076	+	0.0180052i
$167$	−12.9156	+	17.7768i	−0.999438	+	1.37561i	−0.0737680	+	0.997275i	$0.523502\pi$
$167$	−12.9156	+	17.7768i	−0.999438	+	1.37561i	−0.925670	+	0.378333i	$0.876498\pi$
$168$	25.7201	−	8.54707i	1.98435	−	0.659421i
$169$	−7.94815	−	5.77467i	−0.611396	−	0.444205i
$170$	3.92700	−	5.28836i	0.301187	−	0.405598i
$171$	0.320492	+	3.04928i	0.0245086	+	0.233184i
$172$	−18.0497	+	1.89710i	−1.37627	+	0.144652i
$173$	5.34131	+	4.80934i	0.406092	+	0.365647i	0.846716	−	0.532045i	$-0.178576\pi$
$173$	5.34131	+	4.80934i	0.406092	+	0.365647i	−0.440624	+	0.897692i	$0.645243\pi$
$174$	19.4619			1.47540
$175$	−2.56699	−	12.9773i	−0.194046	−	0.980992i
$176$	100.582			7.58164
$177$	−0.821731	−	0.739890i	−0.0617651	−	0.0556136i
$178$	37.7993	−	3.97286i	2.83318	−	0.297779i
$179$	−0.501307	−	4.76962i	−0.0374694	−	0.356498i	−0.997152	−	0.0754131i	$-0.975972\pi$
$179$	−0.501307	−	4.76962i	−0.0374694	−	0.356498i	0.959683	−	0.281085i	$-0.0906942\pi$
$180$	0.132561	−	12.7299i	0.00988053	−	0.948829i
$181$	7.38985	+	5.36904i	0.549283	+	0.399078i	0.827521	−	0.561435i	$-0.189750\pi$
$181$	7.38985	+	5.36904i	0.549283	+	0.399078i	−0.278238	+	0.960512i	$0.589750\pi$
$182$	2.63350	−	12.8093i	0.195208	−	0.949486i
$183$	−7.89055	+	10.8604i	−0.583286	+	0.802824i
$184$	8.96465	−	1.90550i	0.660883	−	0.140475i
$185$	−0.987076	+	8.53546i	−0.0725713	+	0.627539i
$186$	3.59361	+	0.763845i	0.263496	+	0.0560079i
$187$	1.30439	+	6.13666i	0.0953862	+	0.448757i
$188$	−40.0827	−	13.0237i	−2.92333	−	0.949848i
$189$	2.42414	+	1.05998i	0.176330	+	0.0771019i
$190$	−17.4518	+	7.55327i	−1.26608	+	0.547972i
$191$	16.7012	−	3.54996i	1.20846	−	0.256866i	0.440729	−	0.897640i	$-0.354720\pi$
$191$	16.7012	−	3.54996i	1.20846	−	0.256866i	0.767729	+	0.640774i	$0.221387\pi$
$192$	16.3151	+	36.6442i	1.17744	+	2.64457i
$193$	20.4596	+	11.8124i	1.47272	+	0.850273i	0.999529	−	0.0306889i	$-0.00977012\pi$
$193$	20.4596	+	11.8124i	1.47272	+	0.850273i	0.473187	+	0.880962i	$0.343103\pi$
$194$	2.07647	−	19.7563i	0.149082	−	1.41842i
$195$	−3.42991	−	2.02817i	−0.245621	−	0.145240i
$196$	−38.8681	+	8.80527i	−2.77629	+	0.628948i
$197$	5.78960	+	7.96870i	0.412492	+	0.567746i	0.963824	−	0.266539i	$-0.0858803\pi$
$197$	5.78960	+	7.96870i	0.412492	+	0.567746i	−0.551332	+	0.834286i	$0.685880\pi$
$198$	12.1762	+	10.9635i	0.865327	+	0.779144i
$199$	−9.91383	+	17.1713i	−0.702773	+	1.21724i	0.264717	+	0.964326i	$0.414721\pi$
$199$	−9.91383	+	17.1713i	−0.702773	+	1.21724i	−0.967489	+	0.252912i	$0.918612\pi$
$200$	49.0320	−	14.8100i	3.46709	−	1.04722i
$201$	3.27322	+	5.66939i	0.230875	+	0.399888i
$202$	10.2081	−	3.31683i	0.718243	−	0.233371i
$203$	−18.4751	−	1.81728i	−1.29670	−	0.127548i
$204$	−4.89175	+	3.55407i	−0.342491	+	0.248834i
$205$	9.58707	−	12.9106i	0.669590	−	0.901715i
$206$	20.8216	−	9.27037i	1.45071	−	0.645897i
$207$	0.774802	+	0.447332i	0.0538525	+	0.0310918i
$208$	30.1759	+	3.17161i	2.09232	+	0.219912i
$209$	5.59691	−	17.2255i	0.387147	−	1.19151i
$210$	−1.77629	+	16.3129i	−0.122576	+	1.12570i
$211$	−3.60631	−	11.0991i	−0.248268	−	0.764092i	−0.995082	−	0.0990579i	$-0.968417\pi$
$211$	−3.60631	−	11.0991i	−0.248268	−	0.764092i	0.746813	−	0.665034i	$-0.231583\pi$
$212$	3.46343	+	16.2942i	0.237869	+	1.11909i
$213$	−2.44565	+	2.20207i	−0.167573	+	0.150884i
$214$	14.4466	+	3.07072i	0.987550	+	0.209910i
$215$	2.27319	−	6.75597i	0.155030	−	0.460753i
$216$	−3.16556	+	9.74260i	−0.215389	+	0.662900i
$217$	−3.34008	−	1.06068i	−0.226739	−	0.0720033i
$218$		−	4.10031i		−	0.277708i
$219$	−0.720561	+	6.85568i	−0.0486910	+	0.463264i
$220$	−31.3013	+	68.3785i	−2.11033	+	4.61008i
$221$	0.197828	+	1.88221i	0.0133074	+	0.126611i
$222$	4.33507	−	9.73672i	0.290951	−	0.653486i
$223$	−20.8405	+	6.77150i	−1.39558	+	0.453453i	−0.907760	−	0.419489i	$-0.862209\pi$
$223$	−20.8405	+	6.77150i	−1.39558	+	0.453453i	−0.487824	+	0.872942i	$0.662209\pi$
$224$	−22.3099	−	67.1354i	−1.49064	−	4.48567i
$225$	4.52439	+	2.12836i	0.301626	+	0.141891i
$226$	−0.0554468	−	0.0960367i	−0.00368827	−	0.00638826i
$227$	2.78873	−	13.1199i	0.185094	−	0.870801i	−0.783352	−	0.621579i	$-0.786492\pi$
$227$	2.78873	−	13.1199i	0.185094	−	0.870801i	0.968446	−	0.249222i	$-0.0801750\pi$
$228$	17.3604	−	1.82465i	1.14972	−	0.120841i
$229$	−27.2140	−	12.1165i	−1.79835	−	0.800679i	−0.971031	−	0.238954i	$-0.923195\pi$
$229$	−27.2140	−	12.1165i	−1.79835	−	0.800679i	−0.827324	−	0.561725i	$-0.810138\pi$
$230$	−1.21012	+	5.41527i	−0.0797929	+	0.357072i
$231$	−10.5351	−	11.5446i	−0.693160	−	0.759580i
$232$		−	71.8783i		−	4.71904i
$233$	−1.05366	−	0.110744i	−0.0690277	−	0.00725510i	0.0699517	−	0.997550i	$-0.477715\pi$
$233$	−1.05366	−	0.110744i	−0.0690277	−	0.00725510i	−0.138979	+	0.990295i	$0.544382\pi$
$234$	3.30732	+	3.67315i	0.216206	+	0.240121i
$235$	11.2035	−	12.1852i	0.730836	−	0.794873i
$236$	−4.21240	+	4.67835i	−0.274204	+	0.304535i
$237$	−14.9311	−	4.85142i	−0.969881	−	0.315133i
$238$	6.72348	−	3.94184i	0.435818	−	0.255511i
$239$	−0.181849	−	0.559674i	−0.0117628	−	0.0362023i	0.945003	−	0.327062i	$-0.106059\pi$
$239$	−0.181849	−	0.559674i	−0.0117628	−	0.0362023i	−0.956766	+	0.290860i	$0.906059\pi$
$240$	−38.0713	−	0.396451i	−2.45749	−	0.0255908i
$241$	1.20549	+	1.33883i	0.0776522	+	0.0862415i	0.780719	−	0.624882i	$-0.214853\pi$
$241$	1.20549	+	1.33883i	0.0776522	+	0.0862415i	−0.703067	+	0.711124i	$0.748186\pi$
$242$	−26.9576	−	60.5478i	−1.73290	−	3.89216i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	61.8314	+	44.9231i	3.95835	+	2.87591i
$245$	3.20946	−	15.3199i	0.205045	−	0.978753i
$246$	−16.1376	+	11.7247i	−1.02890	+	0.747537i
$247$	2.22231	−	4.99140i	0.141402	−	0.317595i
$248$	2.82110	−	13.2722i	0.179140	−	0.842787i
$249$	−0.201134	+	0.348375i	−0.0127464	+	0.0220774i
$250$	−4.20319	+	30.7245i	−0.265833	+	1.94319i
$251$	−2.27594			−0.143656			−0.0718281	−	0.997417i	$-0.522883\pi$
$251$	−2.27594			−0.143656			−0.0718281	+	0.997417i	$0.522883\pi$
$252$	6.03474	−	13.8013i	0.380153	−	0.869401i
$253$	−3.10644	−	4.27564i	−0.195300	−	0.268807i
$254$	42.0495	+	18.7216i	2.63842	+	1.17470i
$255$	−0.469536	−	2.32793i	−0.0294035	−	0.145781i
$256$	73.1181	−	32.5543i	4.56988	−	2.03464i
$257$	−18.5990	+	10.7382i	−1.16018	+	0.669828i	−0.951346	−	0.308124i	$-0.900299\pi$
$257$	−18.5990	+	10.7382i	−1.16018	+	0.669828i	−0.208830	+	0.977952i	$0.566966\pi$
$258$	−5.19716	+	7.15328i	−0.323561	+	0.445344i
$259$	−5.02445	+	8.83825i	−0.312204	+	0.549182i
$260$	−11.5469	+	19.5274i	−0.716111	+	1.21104i
$261$	4.69505	−	5.21438i	0.290616	−	0.322762i
$262$	−7.65855	+	6.89579i	−0.473147	+	0.426024i
$263$	−7.32941	+	6.59943i	−0.451951	+	0.406938i	−0.863420	−	0.504485i	$-0.831682\pi$
$263$	−7.32941	+	6.59943i	−0.451951	+	0.406938i	0.411470	+	0.911423i	$0.365016\pi$
$264$	40.4914	−	44.9703i	2.49207	−	2.76773i
$265$	−6.38511	−	1.42685i	−0.392234	−	0.0876504i
$266$	−22.4998	+	0.150106i	−1.37955	+	0.00920357i
$267$	8.05438	−	11.0859i	0.492920	−	0.678446i
$268$	32.2774	−	18.6354i	1.97166	−	1.13834i
$269$	−27.6877	+	12.3273i	−1.68815	+	0.751611i	−0.688494	+	0.725242i	$0.741728\pi$
$269$	−27.6877	+	12.3273i	−1.68815	+	0.751611i	−0.999652	+	0.0263695i	$0.991605\pi$
$270$	−4.56562	−	4.19780i	−0.277855	−	0.255470i
$271$	−4.07763	−	1.81548i	−0.247698	−	0.110282i	0.279133	−	0.960253i	$-0.409953\pi$
$271$	−4.07763	−	1.81548i	−0.247698	−	0.110282i	−0.526831	+	0.849970i	$0.676620\pi$
$272$	10.6292	+	14.6298i	0.644487	+	0.887060i
$273$	−2.79664	−	3.79574i	−0.169261	−	0.229729i
$274$	−6.70416			−0.405013
$275$	−19.3021	−	22.3564i	−1.16396	−	1.34814i
$276$	2.54679	−	4.41117i	0.153299	−	0.265521i
$277$	−1.58578	+	7.46050i	−0.0952801	+	0.448258i	0.904483	+	0.426509i	$0.140257\pi$
$277$	−1.58578	+	7.46050i	−0.0952801	+	0.448258i	−0.999763	+	0.0217488i	$0.993077\pi$
$278$	7.15728	−	16.0755i	0.429265	−	0.964145i
$279$	1.07159	−	0.778555i	0.0641544	−	0.0466109i
$280$	60.2481	+	6.56034i	3.60051	+	0.392055i
$281$	9.86096	+	7.16441i	0.588256	+	0.427393i	0.841691	−	0.539960i	$-0.181560\pi$
$281$	9.86096	+	7.16441i	0.588256	+	0.427393i	−0.253435	+	0.967352i	$0.581560\pi$
$282$	−17.7817	+	10.2663i	−1.05889	+	0.611349i
$283$	4.10186	+	9.21293i	0.243830	+	0.547652i	0.993457	−	0.114209i	$-0.0364334\pi$
$283$	4.10186	+	9.21293i	0.243830	+	0.547652i	−0.749626	+	0.661861i	$0.769767\pi$
$284$	12.5370	+	13.9238i	0.743936	+	0.826225i
$285$	−2.18639	+	6.49798i	−0.129510	+	0.384907i
$286$	−9.02259	−	27.7687i	−0.533517	−	1.64200i
$287$	16.4142	−	9.62331i	0.968899	−	0.568046i
$288$	25.4305	+	8.26287i	1.49851	+	0.486894i
$289$	10.6205	−	11.7952i	0.624734	−	0.693837i
$290$	39.5693	+	18.1134i	2.32359	+	1.06366i
$291$	−4.79233	−	5.32242i	−0.280931	−	0.312006i
$292$	39.0313	+	4.10236i	2.28414	+	0.240072i
$293$			1.72539i			0.100798i	0.998729	+	0.0503991i	$0.0160493\pi$
$293$			1.72539i			0.100798i	−0.998729	+	0.0503991i	$0.983951\pi$
$294$	−9.48266	+	16.9426i	−0.553040	+	0.988110i
$295$	−0.982093	−	2.26912i	−0.0571797	−	0.132113i
$296$	−35.9605	−	16.0106i	−2.09016	−	0.930599i
$297$	5.87486	−	0.617473i	0.340894	−	0.0358294i
$298$	−2.94385	+	13.8497i	−0.170533	+	0.802292i
$299$	−0.797149	−	1.38070i	−0.0461003	−	0.0798481i
$300$	12.1174	−	25.7586i	0.699597	−	1.48717i
$301$	5.60160	−	6.30530i	0.322871	−	0.363431i
$302$	−8.44305	+	2.74331i	−0.485843	+	0.157860i
$303$	1.57398	−	3.53521i	0.0904225	−	0.203092i
$304$	−5.45699	−	51.9198i	−0.312980	−	2.97780i
$305$	−26.1507	+	14.7372i	−1.49739	+	0.843850i
$306$	−0.307918	+	2.92964i	−0.0176025	+	0.167476i
$307$			8.97272i			0.512100i	0.966664	+	0.256050i	$0.0824212\pi$
$307$			8.97272i			0.512100i	−0.966664	+	0.256050i	$0.917579\pi$
$308$	−65.7268	+	59.9795i	−3.74513	+	3.41765i
$309$	2.53928	−	7.81509i	0.144454	−	0.444585i
$310$	6.59549	+	4.89764i	0.374599	+	0.278167i
$311$	18.5250	+	3.93761i	1.05046	+	0.223281i	0.700623	−	0.713531i	$-0.252905\pi$
$311$	18.5250	+	3.93761i	1.05046	+	0.223281i	0.349832	+	0.936813i	$0.386239\pi$
$312$	13.5660	−	12.2149i	0.768023	−	0.691531i
$313$	−5.88374	−	27.6808i	−0.332569	−	1.56461i	−0.753455	−	0.657500i	$-0.771614\pi$
$313$	−5.88374	−	27.6808i	−0.332569	−	1.56461i	0.420886	−	0.907114i	$-0.361719\pi$
$314$	−1.60794	−	4.94874i	−0.0907414	−	0.279273i
$315$	3.94215	+	4.41129i	0.222115	+	0.248548i
$316$	−27.6205	+	85.0071i	−1.55377	+	4.78202i
$317$	21.8525	+	2.29679i	1.22736	+	0.129001i	0.695935	−	0.718104i	$-0.254990\pi$
$317$	21.8525	+	2.29679i	1.22736	+	0.129001i	0.531425	+	0.847105i	$0.321657\pi$
$318$	7.02832	+	4.05780i	0.394129	+	0.227550i
$319$	−37.8654	+	16.8588i	−2.12006	+	0.943910i
$320$	−0.933961	+	89.6885i	−0.0522100	+	5.01374i
$321$	4.30788	−	3.12986i	0.240442	−	0.174692i
$322$	−3.82356	+	5.33720i	−0.213079	+	0.297430i
$323$	3.09694	−	1.00626i	0.172318	−	0.0559897i
$324$	2.84664	+	4.93053i	0.158147	+	0.273918i
$325$	−5.08594	−	7.31587i	−0.282117	−	0.405811i
$326$	−24.9270	+	43.1748i	−1.38058	+	2.39123i
$327$	−1.09859	−	0.989171i	−0.0607519	−	0.0547013i
$328$	43.3025	+	59.6007i	2.39098	+	3.29090i
$329$	17.8388	−	8.08537i	0.983485	−	0.445761i
$330$	14.5524	+	33.6233i	0.801085	+	1.85090i
$331$	−1.36430	+	12.9805i	−0.0749888	+	0.713471i	0.890845	+	0.454308i	$0.150113\pi$
$331$	−1.36430	+	12.9805i	−0.0749888	+	0.713471i	−0.965834	+	0.259163i	$0.916553\pi$
$332$	1.98340	+	1.14511i	0.108853	+	0.0628463i
$333$	−1.56293	−	3.51040i	−0.0856481	−	0.192369i
$334$	59.6150	−	12.6716i	3.26199	−	0.693357i
$335$	1.37844	+	14.5732i	0.0753125	+	0.796221i
$336$	−41.2756	−	18.0481i	−2.25177	−	0.984605i
$337$	8.52369	+	2.76952i	0.464315	+	0.150865i	0.531826	−	0.846853i	$-0.321506\pi$
$337$	8.52369	+	2.76952i	0.464315	+	0.150865i	−0.0675114	+	0.997719i	$0.521506\pi$
$338$	5.66556	+	26.6544i	0.308166	+	1.44981i
$339$	−0.0391070	−	0.00831246i	−0.00212400	−	0.000451471i
$340$	−13.2536	+	2.67320i	−0.718776	+	0.144975i
$341$	−7.65347	+	1.62680i	−0.414459	+	0.0880959i
$342$	4.99870	−	6.88012i	0.270299	−	0.372034i
$343$	10.5839	−	15.1981i	0.571477	−	0.820618i
$344$	26.4191	+	19.1946i	1.42442	+	1.03490i
$345$	1.15897	+	1.63062i	0.0623966	+	0.0877897i
$346$	−2.08384	−	19.8264i	−0.112028	−	1.06588i
$347$	−10.0277	+	1.05396i	−0.538317	+	0.0565794i	−0.369786	−	0.929117i	$-0.620569\pi$
$347$	−10.0277	+	1.05396i	−0.538317	+	0.0565794i	−0.168531	+	0.985696i	$0.553902\pi$
$348$	−29.6869	−	26.7302i	−1.59139	−	1.43289i
$349$	24.3984			1.30601			0.653007	−	0.757351i	$-0.273507\pi$
$349$	24.3984			1.30601			0.653007	+	0.757351i	$0.273507\pi$
$350$	−18.7941	+	31.5136i	−1.00459	+	1.68447i
$351$	1.78201			0.0951165
$352$	−117.383	−	105.692i	−6.25654	−	5.63341i
$353$	27.6772	−	2.90899i	1.47311	−	0.154830i	0.666319	−	0.745667i	$-0.267869\pi$
$353$	27.6772	−	2.90899i	1.47311	−	0.154830i	0.806791	+	0.590837i	$0.201202\pi$
$354$	0.320588	+	3.05019i	0.0170390	+	0.162116i
$355$	−7.02192	+	2.20099i	−0.372685	+	0.116816i
$356$	−63.1152	−	45.8559i	−3.34510	−	2.43036i
$357$	0.565865	−	2.75235i	0.0299487	−	0.145670i
$358$	−7.81886	+	10.7617i	−0.413240	+	0.568776i
$359$	15.8627	−	3.37172i	0.837201	−	0.177953i	0.230690	−	0.973027i	$-0.425902\pi$
$359$	15.8627	−	3.37172i	0.837201	−	0.177953i	0.606512	+	0.795075i	$0.292568\pi$
$360$	−15.5037	+	16.8621i	−0.817116	+	0.888712i
$361$	9.38942	+	1.99578i	0.494180	+	0.105041i
$362$	−5.26760	−	24.7821i	−0.276859	−	1.30252i
$363$	−22.7258	−	7.38406i	−1.19279	−	0.387562i
$364$	−21.6102	+	15.9221i	−1.13268	+	0.834544i
$365$	−7.84568	+	13.2681i	−0.410662	+	0.694485i
$366$	36.4207	−	7.74147i	1.90374	−	0.404653i
$367$	0.540323	+	1.21359i	0.0282046	+	0.0633487i	0.927099	−	0.374818i	$-0.122295\pi$
$367$	0.540323	+	1.21359i	0.0282046	+	0.0633487i	−0.898894	+	0.438166i	$0.855628\pi$
$368$	−13.1925	−	7.61669i	−0.687706	−	0.397047i
$369$	−0.751727	+	7.15220i	−0.0391333	+	0.372329i
$370$	17.8760	−	15.7617i	0.929329	−	0.819411i
$371$	−6.29306	−	4.50834i	−0.326719	−	0.234061i
$372$	−4.43253	−	6.10086i	−0.229816	−	0.316315i
$373$	17.9820	+	16.1911i	0.931073	+	0.838342i	0.987103	−	0.160087i	$-0.0511775\pi$
$373$	17.9820	+	16.1911i	0.931073	+	0.838342i	−0.0560296	+	0.998429i	$0.517844\pi$
$374$	8.70068	−	15.0700i	0.449902	−	0.779252i
$375$	7.21795	+	8.53822i	0.372733	+	0.440912i
$376$	37.9163	+	65.6730i	1.95539	+	3.38683i
$377$	−11.8917	+	3.86385i	−0.612455	+	0.198999i
$378$	−3.02948	−	6.68395i	−0.155820	−	0.343786i
$379$	−18.4240	+	13.3858i	−0.946378	+	0.687584i	−0.949948	−	0.312410i	$-0.898864\pi$
$379$	−18.4240	+	13.3858i	−0.946378	+	0.687584i	0.00356918	+	0.999994i	$0.498864\pi$
$380$	36.9949	+	12.4477i	1.89780	+	0.638554i
$381$	15.1602	−	6.74976i	0.776681	−	0.345801i
$382$	−41.0139	−	23.6794i	−2.09845	−	1.21154i
$383$	21.4442	+	2.25388i	1.09575	+	0.115168i	0.635111	−	0.772421i	$-0.280954\pi$
$383$	21.4442	+	2.25388i	1.09575	+	0.115168i	0.460637	+	0.887589i	$0.347621\pi$
$384$	17.8549	−	54.9516i	0.911153	−	2.80424i
$385$	−10.6750	−	33.2773i	−0.544047	−	1.69597i
$386$	−20.2491	−	62.3203i	−1.03065	−	3.17202i
$387$	0.662782	+	3.11814i	0.0336911	+	0.158504i
$388$	−30.3020	+	27.2841i	−1.53835	+	1.38514i
$389$	16.0028	+	3.40151i	0.811375	+	0.172463i	0.594874	−	0.803819i	$-0.297202\pi$
$389$	16.0028	+	3.40151i	0.811375	+	0.172463i	0.216502	+	0.976282i	$0.430535\pi$
$390$	3.30569	+	10.5463i	0.167390	+	0.534033i
$391$	0.293621	−	0.903672i	0.0148490	−	0.0457006i
$392$	62.5737	+	35.0222i	3.16045	+	1.76889i
$393$			3.71550i			0.187422i
$394$	2.85575	−	27.1707i	0.143871	−	1.36884i
$395$	−25.8422	−	23.7603i	−1.30026	−	1.19551i
$396$	−3.51545	−	33.4473i	−0.176658	−	1.68079i
$397$	−0.278685	+	0.625938i	−0.0139868	+	0.0314149i	−0.920404	−	0.390969i	$-0.872140\pi$
$397$	−0.278685	+	0.625938i	−0.0139868	+	0.0314149i	0.906417	+	0.422384i	$0.138807\pi$
$398$	52.3038	−	16.9945i	2.62175	−	0.851860i
$399$	−5.38770	+	6.06452i	−0.269722	+	0.303606i
$400$	−77.0363	−	36.2395i	−3.85182	−	1.81197i
$401$	−7.49185	−	12.9763i	−0.374125	−	0.648004i	0.616071	−	0.787691i	$-0.288724\pi$
$401$	−7.49185	−	12.9763i	−0.374125	−	0.648004i	−0.990196	+	0.139687i	$0.955390\pi$
$402$	3.77520	−	17.7609i	0.188290	−	0.885835i
$403$	−2.34744	+	0.246726i	−0.116934	+	0.0122903i
$404$	−20.1269	−	8.96109i	−1.00135	−	0.445831i
$405$	−2.22613	+	0.210564i	−0.110617	+	0.0104630i
$406$	34.7089	+	38.0348i	1.72257	+	1.88764i
$407$			22.6992i			1.12516i
$408$	10.8200	+	1.13723i	0.535669	+	0.0563011i
$409$	5.97022	+	6.63060i	0.295208	+	0.327862i	0.872443	−	0.488717i	$-0.162535\pi$
$409$	5.97022	+	6.63060i	0.295208	+	0.327862i	−0.577234	+	0.816578i	$0.695868\pi$
$410$	−43.7227	+	8.81873i	−2.15931	+	0.435526i
$411$	−1.61733	+	1.79623i	−0.0797772	+	0.0886015i
$412$	−44.4935	−	14.4568i	−2.19204	−	0.712237i
$413$	−0.0195171	−	2.92547i	−0.000960373	−	0.143953i
$414$	−0.766829	−	2.36006i	−0.0376876	−	0.115990i
$415$	−0.733177	+	0.521107i	−0.0359902	+	0.0255801i
$416$	−31.8837	−	35.4104i	−1.56323	−	1.73614i
$417$	−2.58043	−	5.79574i	−0.126364	−	0.283819i
$418$	−43.5064	+	25.1184i	−2.12797	+	1.22858i
$419$	−0.413755	−	0.300611i	−0.0202133	−	0.0146858i	0.577633	−	0.816297i	$-0.303977\pi$
$419$	−0.413755	−	0.300611i	−0.0202133	−	0.0146858i	−0.597846	+	0.801611i	$0.703977\pi$
$420$	25.1147	−	22.4438i	1.22547	−	1.09514i
$421$	23.1072	−	16.7884i	1.12618	−	0.818214i	0.141042	−	0.990004i	$-0.454955\pi$
$421$	23.1072	−	16.7884i	1.12618	−	0.818214i	0.985134	+	0.171789i	$0.0549549\pi$
$422$	−13.1659	+	29.5710i	−0.640905	+	1.43950i
$423$	−1.53910	+	7.24090i	−0.0748336	+	0.352064i
$424$	14.9866	−	25.9576i	0.727814	−	1.26061i
$425$	1.21199	−	5.17008i	0.0587900	−	0.250786i
$426$	9.12803			0.442254
$427$	−35.2970	+	3.94811i	−1.70814	+	0.191063i
$428$	−17.8192	−	24.5260i	−0.861322	−	1.18551i
$429$	−9.61663	−	4.28160i	−0.464295	−	0.206718i
$430$	−17.2244	+	9.70677i	−0.830632	+	0.468102i
$431$	20.4758	−	9.11641i	0.986285	−	0.439122i	0.150757	−	0.988571i	$-0.451829\pi$
$431$	20.4758	−	9.11641i	0.986285	−	0.439122i	0.835528	+	0.549449i	$0.185162\pi$
$432$	14.7457	−	8.51346i	0.709455	−	0.409604i
$433$	16.1763	−	22.2647i	0.777382	−	1.06997i	−0.218184	−	0.975908i	$-0.570013\pi$
$433$	16.1763	−	22.2647i	0.777382	−	1.06997i	0.995566	−	0.0940663i	$-0.0299866\pi$
$434$	4.91615	+	8.38534i	0.235983	+	0.402509i
$435$	14.3989	−	6.23197i	0.690375	−	0.298800i
$436$	−5.63163	+	6.25456i	−0.269706	+	0.299539i
$437$	−2.03853	+	1.83550i	−0.0975160	+	0.0878038i
$438$	14.2091	−	12.7939i	0.678935	−	0.611316i
$439$	−13.2819	+	14.7511i	−0.633913	+	0.704031i	−0.971440	−	0.237284i	$-0.923743\pi$
$439$	−13.2819	+	14.7511i	−0.633913	+	0.704031i	0.337528	+	0.941316i	$0.390409\pi$
$440$	124.180	−	53.7463i	5.92006	−	2.56225i
$441$	2.25175	+	6.62794i	0.107226	+	0.315616i
$442$	3.08552	−	4.24685i	0.146763	−	0.202002i
$443$	−33.1499	+	19.1391i	−1.57500	+	0.909326i	−0.579456	+	0.815003i	$0.696735\pi$
$443$	−33.1499	+	19.1391i	−1.57500	+	0.909326i	−0.995542	+	0.0943223i	$0.969932\pi$
$444$	−19.9857	+	8.89821i	−0.948480	+	0.422290i
$445$	26.6937	−	15.0432i	1.26540	−	0.713116i
$446$	55.5250	+	24.7213i	2.62918	+	1.17059i
$447$	3.00054	+	4.12989i	0.141921	+	0.195337i
$448$	−42.5178	+	97.2373i	−2.00878	+	4.59403i
$449$	4.52594			0.213592			0.106796	−	0.994281i	$-0.465941\pi$
$449$	4.52594			0.213592			0.106796	+	0.994281i	$0.465941\pi$
$450$	−5.37572	−	12.7841i	−0.253414	−	0.602649i
$451$	21.2412	−	36.7908i	1.00021	−	1.73241i
$452$	−0.0473252	+	0.222647i	−0.00222599	+	0.0104725i
$453$	−1.30182	+	2.92393i	−0.0611648	+	0.137378i
$454$	−30.0982	+	21.8676i	−1.41258	+	1.02630i
$455$	−2.15331	−	10.3202i	−0.100949	−	0.483821i
$456$	−25.4102	−	18.4616i	−1.18994	−	0.864545i
$457$	−11.7532	+	6.78574i	−0.549794	+	0.317424i	−0.749039	−	0.662526i	$-0.769484\pi$
$457$	−11.7532	+	6.78574i	−0.549794	+	0.317424i	0.199245	+	0.979950i	$0.436151\pi$
$458$	33.6072	+	75.4830i	1.57036	+	3.52709i
$459$	0.710649	+	0.789255i	0.0331702	+	0.0368393i
$460$	9.28359	−	6.59832i	0.432849	−	0.307648i
$461$	9.65979	+	29.7298i	0.449901	+	1.38465i	0.877018	+	0.480457i	$0.159529\pi$
$461$	9.65979	+	29.7298i	0.449901	+	1.38465i	−0.427117	+	0.904196i	$0.640471\pi$
$462$	0.289200	+	43.3490i	0.0134548	+	2.01678i
$463$	2.61420	+	0.849405i	0.121492	+	0.0394752i	0.369132	−	0.929377i	$-0.379655\pi$
$463$	2.61420	+	0.849405i	0.121492	+	0.0394752i	−0.247640	+	0.968852i	$0.579655\pi$
$464$	−79.9422	+	88.7848i	−3.71122	+	4.12173i
$465$	2.90333	−	0.585593i	0.134639	−	0.0271562i
$466$	1.96632	+	2.18382i	0.0910879	+	0.101163i
$467$	−24.7220	−	2.59838i	−1.14400	−	0.120239i	−0.486488	−	0.873687i	$-0.661722\pi$
$467$	−24.7220	−	2.59838i	−1.14400	−	0.120239i	−0.657507	+	0.753448i	$0.728389\pi$
$468$		−	10.1455i		−	0.468975i
$469$	−5.24224	+	16.5079i	−0.242064	+	0.762263i
$470$	−45.7083	+	4.32342i	−2.10836	+	0.199425i
$471$	−1.71381	−	0.763037i	−0.0789681	−	0.0351589i
$472$	11.2652	−	1.18402i	0.518523	−	0.0544990i
$473$	3.91520	−	18.4196i	0.180021	−	0.846933i
$474$	21.7727	+	37.7114i	1.00005	+	1.73214i
$475$	−10.4930	+	11.1766i	−0.481454	+	0.512817i
$476$	−15.6699	−	3.22163i	−0.718228	−	0.147663i
$477$	2.78273	−	0.904164i	0.127412	−	0.0413988i
$478$	−0.663893	+	1.49113i	−0.0303658	+	0.0682026i
$479$	1.44226	+	13.7222i	0.0658987	+	0.626985i	0.976769	+	0.214293i	$0.0687447\pi$
$479$	1.44226	+	13.7222i	0.0658987	+	0.626985i	−0.910871	+	0.412692i	$0.864589\pi$
$480$	44.0141	+	40.4683i	2.00896	+	1.84712i
$481$	−0.715765	+	6.81005i	−0.0326361	+	0.310512i
$482$		−	4.99698i		−	0.227606i
$483$	0.507575	+	2.31200i	0.0230955	+	0.105200i
$484$	−42.0395	+	129.384i	−1.91089	+	5.88111i
$485$	−4.78997	−	15.2817i	−0.217501	−	0.693904i
$486$	2.71307	+	0.576680i	0.123067	+	0.0261587i
$487$	1.98226	−	1.78483i	0.0898246	−	0.0808784i	−0.622995	−	0.782226i	$-0.714084\pi$
$487$	1.98226	−	1.78483i	0.0898246	−	0.0808784i	0.712820	+	0.701347i	$0.247418\pi$
$488$	−28.5914	−	134.512i	−1.29427	−	6.08908i
$489$	5.55426	+	17.0943i	0.251172	+	0.773029i
$490$	−35.0485	+	25.6214i	−1.58333	+	1.15746i
$491$	−6.77214	+	20.8425i	−0.305622	+	0.940609i	0.673822	+	0.738894i	$0.264651\pi$
$491$	−6.77214	+	20.8425i	−0.305622	+	0.940609i	−0.979444	+	0.201715i	$0.935349\pi$
$492$	40.7195	+	4.27979i	1.83578	+	0.192948i
$493$	−6.45362	−	3.72600i	−0.290657	−	0.167811i
$494$	−13.8445	+	6.16398i	−0.622895	+	0.277331i
$495$	12.5193	+	4.21238i	0.562700	+	0.189332i
$496$	−18.2459	+	13.2564i	−0.819263	+	0.595229i
$497$	−8.66521	−	0.852343i	−0.388688	−	0.0382328i
$498$	1.06115	−	0.344790i	0.0475514	−	0.0154504i
$499$	10.5793	+	18.3239i	0.473596	+	0.820292i	0.999543	−	0.0302253i	$-0.00962246\pi$
$499$	10.5793	+	18.3239i	0.473596	+	0.820292i	−0.525947	+	0.850517i	$0.676289\pi$
$500$	48.6105	−	41.0938i	2.17393	−	1.83777i
$501$	10.9866	−	19.0294i	0.490847	−	0.850172i
$502$	4.69127	+	4.22404i	0.209382	+	0.188528i
$503$	19.5034	+	26.8442i	0.869616	+	1.19692i	0.979190	+	0.202945i	$0.0650512\pi$
$503$	19.5034	+	26.8442i	0.869616	+	1.19692i	−0.109574	+	0.993979i	$0.534949\pi$
$504$	−24.6857	+	11.1887i	−1.09959	+	0.498385i
$505$	6.49042	−	5.72275i	0.288820	−	0.254659i
$506$	−1.53227	+	14.5785i	−0.0681176	+	0.648095i
$507$	8.50822	+	4.91223i	0.377864	+	0.218160i
$508$	−38.4283	−	86.3113i	−1.70498	−	3.82945i
$509$	10.6760	−	2.26925i	0.473205	−	0.100583i	0.0348651	−	0.999392i	$-0.488900\pi$
$509$	10.6760	−	2.26925i	0.473205	−	0.100583i	0.438340	+	0.898809i	$0.355567\pi$
$510$	−3.35270	+	5.66987i	−0.148460	+	0.251066i
$511$	−14.6833	+	10.8184i	−0.649550	+	0.478579i
$512$	−101.230	−	32.8916i	−4.47378	−	1.45362i
$513$	−0.637473	−	2.99907i	−0.0281451	−	0.132412i
$514$	58.2667	+	12.3850i	2.57003	+	0.546277i
$515$	12.4364	−	13.5261i	0.548012	−	0.596030i
$516$	17.7525	−	3.77341i	0.781510	−	0.166115i
$517$	25.7034	−	35.3777i	1.13043	−	1.55591i
$518$	26.7600	−	8.89265i	1.17577	−	0.390720i
$519$	−5.81476	−	4.22467i	−0.255240	−	0.185442i
$520$	38.9505	−	12.2089i	1.70809	−	0.535394i
$521$	−1.25485	−	11.9391i	−0.0549758	−	0.523059i	−0.987007	−	0.160680i	$-0.948631\pi$
$521$	−1.25485	−	11.9391i	−0.0549758	−	0.523059i	0.932031	−	0.362379i	$-0.118035\pi$
$522$	−19.3553	+	2.03432i	−0.847157	+	0.0890398i
$523$	4.87812	+	4.39228i	0.213305	+	0.192061i	0.768856	−	0.639421i	$-0.220826\pi$
$523$	4.87812	+	4.39228i	0.213305	+	0.192061i	−0.555551	+	0.831482i	$0.687493\pi$
$524$	21.1534			0.924091
$525$	3.90942	+	12.6379i	0.170621	+	0.551563i
$526$	27.3559			1.19277
$527$	−1.04541	−	0.941294i	−0.0455389	−	0.0410034i
$528$	−100.031	+	10.5137i	−4.35328	+	0.457548i
$529$	−2.32049	−	22.0780i	−0.100891	−	0.959911i
$530$	10.5131	+	14.7915i	0.456660	+	0.642503i
$531$	0.894569	+	0.649943i	0.0388210	+	0.0282051i
$532$	34.5270	+	30.6737i	1.49694	+	1.32987i
$533$	7.53275	−	10.3679i	0.326280	−	0.449085i
$534$	−37.1769	+	7.90220i	−1.60880	+	0.341962i
$535$	11.6716	−	2.35413i	0.504609	−	0.101778i
$536$	−65.5962	−	13.9429i	−2.83332	−	0.602241i
$537$	0.997121	+	4.69109i	0.0430290	+	0.202435i
$538$	79.9500	+	25.9773i	3.44689	+	1.11996i
$539$	3.77324	−	41.1781i	0.162525	−	1.77366i
$540$	1.19880	+	12.6740i	0.0515881	+	0.545402i
$541$	9.50002	−	2.01929i	0.408438	−	0.0868162i	0.000889158	−	1.00000i	$-0.499717\pi$
$541$	9.50002	−	2.01929i	0.408438	−	0.0868162i	0.407549	+	0.913183i	$0.366384\pi$
$542$	5.03554	+	11.3100i	0.216295	+	0.485807i
$543$	−7.91058	−	4.56718i	−0.339476	−	0.195996i
$544$	2.96843	−	28.2427i	0.127270	−	1.21090i
$545$	−1.31298	−	3.03362i	−0.0562417	−	0.129946i
$546$	−1.28014	+	13.0144i	−0.0547851	+	0.556964i
$547$	−10.0894	−	13.8869i	−0.431392	−	0.593760i	0.536880	−	0.843659i	$-0.319603\pi$
$547$	−10.0894	−	13.8869i	−0.431392	−	0.593760i	−0.968272	+	0.249898i	$0.919603\pi$
$548$	10.2264	+	9.20794i	0.436852	+	0.393344i
$549$	6.71210	−	11.6257i	0.286465	−	0.496173i
$550$	−1.70602	+	81.9059i	−0.0727450	+	3.49248i
$551$	10.7568	+	18.6313i	0.458254	+	0.793719i
$552$	−8.71636	+	2.83212i	−0.370993	+	0.120543i
$553$	−17.1474	−	37.8324i	−0.729181	−	1.60880i
$554$	17.1150	−	12.4348i	0.727146	−	0.528303i
$555$	0.0894705	−	8.59188i	0.00379781	−	0.364705i
$556$	−32.9968	+	14.6911i	−1.39938	+	0.623042i
$557$	30.5138	+	17.6171i	1.29291	+	0.746462i	0.979169	−	0.203046i	$-0.0650841\pi$
$557$	30.5138	+	17.6171i	1.29291	+	0.746462i	0.313742	+	0.949508i	$0.398417\pi$
$558$	−3.65377	−	0.384026i	−0.154676	−	0.0162571i
$559$	1.75543	−	5.40266i	0.0742468	−	0.228508i
$560$	−67.1227	−	75.1106i	−2.83645	−	3.17400i
$561$	−1.93870	−	5.96669i	−0.0818518	−	0.251914i
$562$	−7.02905	−	33.0691i	−0.296502	−	1.39493i
$563$	1.89479	−	1.70607i	0.0798557	−	0.0719024i	−0.628236	−	0.778023i	$-0.716223\pi$
$563$	1.89479	−	1.70607i	0.0798557	−	0.0719024i	0.708092	+	0.706120i	$0.249556\pi$
$564$	41.2245	+	8.76253i	1.73586	+	0.368969i
$565$	−0.0717747	−	0.0532980i	−0.00301958	−	0.00224226i
$566$	8.64383	−	26.6030i	0.363327	−	1.11821i
$567$	−2.52166	−	0.800777i	−0.105900	−	0.0336295i
$568$		−	33.7124i		−	1.41454i
$569$	−0.736526	+	7.00757i	−0.0308768	+	0.293773i	0.968176	+	0.250268i	$0.0805189\pi$
$569$	−0.736526	+	7.00757i	−0.0308768	+	0.293773i	−0.999053	+	0.0435043i	$0.986148\pi$
$570$	16.5666	−	9.33610i	0.693899	−	0.391046i
$571$	3.68954	+	35.1036i	0.154402	+	1.46904i	0.747689	+	0.664050i	$0.231164\pi$
$571$	3.68954	+	35.1036i	0.154402	+	1.46904i	−0.593286	+	0.804992i	$0.702170\pi$
$572$	−24.3764	+	54.7502i	−1.01923	+	2.28922i
$573$	−16.2387	+	5.27626i	−0.678380	+	0.220419i
$574$	−51.6940	−	10.6280i	−2.15767	−	0.443603i
$575$	0.838736	+	4.39399i	0.0349777	+	0.183242i
$576$	−20.0560	−	34.7381i	−0.835669	−	1.44742i
$577$	−4.38609	+	20.6349i	−0.182595	+	0.859044i	0.787499	+	0.616316i	$0.211376\pi$
$577$	−4.38609	+	20.6349i	−0.182595	+	0.859044i	−0.970094	+	0.242728i	$0.921958\pi$
$578$	−43.7828	+	4.60176i	−1.82112	+	0.191408i
$579$	−21.5823	−	9.60905i	−0.896929	−	0.399338i
$580$	−35.4804	−	81.9771i	−1.47324	−	3.40391i
$581$	−1.03955	+	0.228221i	−0.0431276	+	0.00946821i
$582$			19.8651i			0.823436i
$583$	−17.1895	−	1.80669i	−0.711916	−	0.0748253i
$584$	−47.2515	−	52.4781i	−1.95528	−	2.17156i
$585$	3.62312	+	1.65854i	0.149798	+	0.0685720i
$586$	3.20223	−	3.55644i	0.132283	−	0.146915i
$587$	43.4984	+	14.1335i	1.79537	+	0.583351i	0.999748	−	0.0224425i	$-0.00714427\pi$
$587$	43.4984	+	14.1335i	1.79537	+	0.583351i	0.795622	+	0.605794i	$0.207144\pi$
$588$	37.7348	−	12.8199i	1.55616	−	0.528682i
$589$	1.25498	+	3.86242i	0.0517104	+	0.159148i
$590$	−2.18704	+	6.49992i	−0.0900390	+	0.267598i
$591$	−6.59084	−	7.31987i	−0.271111	−	0.301099i
$592$	26.6119	+	59.7713i	1.09374	+	2.45658i
$593$	20.8662	−	12.0471i	0.856873	−	0.494716i	−0.00609089	−	0.999981i	$-0.501939\pi$
$593$	20.8662	−	12.0471i	0.856873	−	0.494716i	0.862964	+	0.505266i	$0.168605\pi$
$594$	−13.2555	−	9.63070i	−0.543881	−	0.395153i
$595$	3.71214	−	5.06933i	0.152183	−	0.207822i
$596$	23.5126	−	17.0829i	0.963114	−	0.699744i
$597$	8.06463	−	18.1135i	0.330063	−	0.741335i
$598$	−0.919400	+	4.32544i	−0.0375971	+	0.176880i
$599$	11.4686	−	19.8641i	0.468593	−	0.811627i	−0.530762	−	0.847521i	$-0.678094\pi$
$599$	11.4686	−	19.8641i	0.468593	−	0.811627i	0.999356	+	0.0358935i	$0.0114277\pi$
$600$	−47.2154	+	19.8541i	−1.92756	+	0.810539i
$601$	−7.20390			−0.293853			−0.146927	−	0.989147i	$-0.546938\pi$
$601$	−7.20390			−0.293853			−0.146927	+	0.989147i	$0.546938\pi$
$602$	−23.2486	+	2.60045i	−0.947542	+	0.105986i
$603$	−3.84790	−	5.29618i	−0.156699	−	0.215677i
$604$	16.6468	+	7.41162i	0.677348	+	0.301575i
$605$	−39.3329	−	36.1642i	−1.59911	−	1.47028i
$606$	−9.80552	+	4.36570i	−0.398322	+	0.177344i
$607$	−18.1985	+	10.5069i	−0.738654	+	0.426462i	−0.821580	−	0.570093i	$-0.806907\pi$
$607$	−18.1985	+	10.5069i	−0.738654	+	0.426462i	0.0829254	+	0.996556i	$0.473574\pi$
$608$	−48.1892	+	66.3268i	−1.95433	+	2.68991i
$609$	18.5639	−	0.123848i	0.752246	−	0.00501856i
$610$	81.2546	+	18.1575i	3.28990	+	0.735177i
$611$	8.82690	−	9.80327i	0.357098	−	0.396598i
$612$	4.49345	−	4.04592i	0.181637	−	0.163547i
$613$	−26.6643	+	24.0087i	−1.07696	+	0.969702i	−0.999627	−	0.0273035i	$-0.991308\pi$
$613$	−26.6643	+	24.0087i	−1.07696	+	0.969702i	−0.0773356	+	0.997005i	$0.524641\pi$
$614$	16.6529	−	18.4950i	0.672058	−	0.746396i
$615$	−8.18503	+	13.8420i	−0.330052	+	0.558163i
$616$	160.100	−	1.06810i	6.45061	−	0.0430349i
$617$	−10.8278	+	14.9031i	−0.435909	+	0.599977i	−0.969297	−	0.245893i	$-0.920919\pi$
$617$	−10.8278	+	14.9031i	−0.435909	+	0.599977i	0.533388	+	0.845871i	$0.320919\pi$
$618$	−19.7385	+	11.3960i	−0.793999	+	0.458416i
$619$	−18.1866	+	8.09720i	−0.730981	+	0.325454i	−0.738257	−	0.674520i	$-0.764351\pi$
$619$	−18.1866	+	8.09720i	−0.730981	+	0.325454i	0.00727564	+	0.999974i	$0.497684\pi$
$620$	−3.33394	−	16.5295i	−0.133894	−	0.663840i
$621$	−0.817317	−	0.363893i	−0.0327978	−	0.0146025i
$622$	−30.8765	−	42.4978i	−1.23803	−	1.70401i
$623$	36.0298	−	4.03009i	1.44351	−	0.161462i
$624$	−30.3421			−1.21466
$625$	6.72867	+	24.0775i	0.269147	+	0.963099i
$626$	−39.2465	+	67.9769i	−1.56860	+	2.71690i
$627$	−3.76569	+	17.7162i	−0.150387	+	0.707517i
$628$	−4.34418	+	9.75720i	−0.173352	+	0.389355i
$629$	−3.30163	+	2.39877i	−0.131645	+	0.0956454i
$630$	0.0613981	−	16.4092i	0.00244616	−	0.653757i
$631$	−31.6753	−	23.0135i	−1.26098	−	0.916152i	−0.262170	−	0.965022i	$-0.584438\pi$
$631$	−31.6753	−	23.0135i	−1.26098	−	0.916152i	−0.998805	+	0.0488694i	$0.984438\pi$
$632$	139.279	−	80.4127i	5.54022	−	3.19865i
$633$	4.74672	+	10.6613i	0.188665	+	0.423749i
$634$	−40.7807	−	45.2915i	−1.61961	−	1.79876i
$635$	37.1053	+	0.386392i	1.47248	+	0.0153335i
$636$	−5.14766	−	15.8429i	−0.204118	−	0.628211i
$637$	2.43047	−	12.2350i	0.0962989	−	0.484767i
$638$	109.339	+	35.5264i	4.32877	+	1.40650i
$639$	2.20207	−	2.44565i	0.0871127	−	0.0967485i
$640$	87.4461	−	95.1082i	3.45661	−	3.75948i
$641$	−7.09829	−	7.88345i	−0.280366	−	0.311378i	0.586471	−	0.809970i	$-0.300517\pi$
$641$	−7.09829	−	7.88345i	−0.280366	−	0.311378i	−0.866836	+	0.498593i	$0.833850\pi$
$642$	−14.6884	−	1.54382i	−0.579707	−	0.0609296i
$643$			13.8928i			0.547880i	0.961747	+	0.273940i	$0.0883270\pi$
$643$			13.8928i			0.547880i	−0.961747	+	0.273940i	$0.911673\pi$
$644$	13.1629	−	2.88977i	0.518690	−	0.113873i
$645$	−1.55455	+	6.95657i	−0.0612103	+	0.273915i
$646$	−8.25112	−	3.67363i	−0.324636	−	0.144537i
$647$	31.5725	−	3.31840i	1.24124	−	0.130460i	0.538943	−	0.842342i	$-0.318824\pi$
$647$	31.5725	−	3.31840i	1.24124	−	0.130460i	0.702299	+	0.711882i	$0.252157\pi$
$648$	2.12984	−	10.0201i	0.0836681	−	0.393628i
$649$	−3.26595	−	5.65680i	−0.128200	−	0.222049i
$650$	−3.09454	+	24.5191i	−0.121378	+	0.961716i
$651$	3.43265	+	0.705731i	0.134536	+	0.0276598i
$652$	97.3224	−	31.6220i	3.81144	−	1.23841i
$653$	−7.06949	+	15.8783i	−0.276651	+	0.621368i	−0.997418	−	0.0718091i	$-0.977123\pi$
$653$	−7.06949	+	15.8783i	−0.276651	+	0.621368i	0.720768	+	0.693177i	$0.243789\pi$
$654$	0.428599	+	4.07784i	0.0167595	+	0.159456i
$655$	−3.45806	+	7.55424i	−0.135118	+	0.295169i
$656$	12.7996	−	121.780i	0.499740	−	4.75471i
$657$		−	6.89344i		−	0.268939i
$658$	−51.7762	−	16.4420i	−2.01844	−	0.640977i
$659$	10.5900	−	32.5927i	0.412528	−	1.26963i	−0.501915	−	0.864917i	$-0.667371\pi$
$659$	10.5900	−	32.5927i	0.412528	−	1.26963i	0.914443	−	0.404714i	$-0.132629\pi$
$660$	23.9823	−	71.2758i	0.933509	−	2.77441i
$661$	−0.963213	−	0.204737i	−0.0374646	−	0.00796335i	0.189141	−	0.981950i	$-0.439430\pi$
$661$	−0.963213	−	0.204737i	−0.0374646	−	0.00796335i	−0.226606	+	0.973987i	$0.572763\pi$
$662$	26.9033	−	24.2238i	1.04563	−	0.941486i
$663$	−0.393489	−	1.85122i	−0.0152818	−	0.0718954i
$664$	−1.27341	−	3.91914i	−0.0494178	−	0.152092i
$665$	−16.5984	+	7.31580i	−0.643659	+	0.283695i
$666$	−3.29355	+	10.1365i	−0.127623	+	0.392782i
$667$	6.24315	+	0.656181i	0.241736	+	0.0254074i
$668$	−108.340	−	62.5501i	−4.19180	−	2.42014i
$669$	20.0185	−	8.91283i	0.773962	−	0.344590i
$670$	24.2059	−	32.5973i	0.935157	−	1.25935i
$671$	−64.1549	+	46.6112i	−2.47667	+	1.79941i
$672$	29.2052	+	64.4356i	1.12662	+	2.48566i
$673$	−17.8880	+	5.81216i	−0.689532	+	0.224042i	−0.632764	−	0.774345i	$-0.718080\pi$
$673$	−17.8880	+	5.81216i	−0.689532	+	0.224042i	−0.0567681	+	0.998387i	$0.518080\pi$
$674$	−12.4293	−	21.5282i	−0.478759	−	0.829236i
$675$	−4.72208	−	1.64378i	−0.181753	−	0.0632690i
$676$	27.9667	−	48.4397i	1.07564	−	1.86307i
$677$	31.4968	+	28.3599i	1.21052	+	1.08996i	0.993505	+	0.113791i	$0.0362995\pi$
$677$	31.4968	+	28.3599i	1.21052	+	1.08996i	0.217017	+	0.976168i	$0.430367\pi$
$678$	0.0651816	+	0.0897148i	0.00250328	+	0.00344548i
$679$	1.85494	−	18.8579i	0.0711860	−	0.723701i
$680$	20.9404	+	12.3825i	0.803029	+	0.474846i
$681$	−1.40205	+	13.3396i	−0.0537265	+	0.511173i
$682$	18.7949	+	10.8513i	0.719695	+	0.415516i
$683$	6.48632	+	14.5685i	0.248192	+	0.557449i	0.994083	−	0.108619i	$-0.0346428\pi$
$683$	6.48632	+	14.5685i	0.248192	+	0.557449i	−0.745891	+	0.666068i	$0.767976\pi$
$684$	−17.0746	+	3.62931i	−0.652863	+	0.138770i
$685$	−4.96008	+	2.14677i	−0.189515	+	0.0820238i
$686$	−50.0229	+	11.6837i	−1.90988	+	0.446085i
$687$	28.3315	+	9.20546i	1.08091	+	0.351210i
$688$	−11.2851	−	53.0924i	−0.430242	−	2.02413i
$689$	−5.10010	−	1.08406i	−0.194298	−	0.0412994i
$690$	0.637441	−	5.51209i	0.0242670	−	0.209842i
$691$	−11.3614	+	2.41495i	−0.432210	+	0.0918690i	−0.418879	−	0.908042i	$-0.637577\pi$
$691$	−11.3614	+	2.41495i	−0.432210	+	0.0918690i	−0.0133309	+	0.999911i	$0.504243\pi$
$692$	−24.0523	+	33.1051i	−0.914330	+	1.25847i
$693$	11.6842	+	10.3802i	0.443844	+	0.394310i
$694$	22.6257	+	16.4385i	0.858860	+	0.623999i
$695$	0.147718	−	14.1854i	0.00560325	−	0.538081i
$696$	7.51333	+	71.4845i	0.284792	+	2.70961i
$697$	7.59598	−	0.798370i	0.287718	−	0.0302404i
$698$	−50.2910	−	45.2822i	−1.90354	−	1.71396i
$699$	1.05947			0.0400727
$700$	71.9511	−	22.2575i	2.71950	−	0.841253i
$701$	−30.7205			−1.16030			−0.580148	−	0.814511i	$-0.697005\pi$
$701$	−30.7205			−1.16030			−0.580148	+	0.814511i	$0.697005\pi$
$702$	−3.67315	−	3.30732i	−0.138634	−	0.124827i
$703$	11.7172	−	1.23153i	0.441922	−	0.0464479i
$704$	24.7681	+	235.653i	0.933484	+	8.88151i
$705$	−9.86844	+	13.2895i	−0.371667	+	0.500512i
$706$	−62.4485	−	45.3715i	−2.35028	−	1.70758i
$707$	9.71601	−	3.22874i	0.365408	−	0.121429i
$708$	3.70031	−	5.09304i	0.139066	−	0.191408i
$709$	−44.4758	+	9.45361i	−1.67032	+	0.355038i	−0.943394	−	0.331675i	$-0.892386\pi$
$709$	−44.4758	+	9.45361i	−1.67032	+	0.355038i	−0.726929	+	0.686713i	$0.759053\pi$
$710$	18.5588	+	8.49557i	0.696500	+	0.318833i
$711$	15.3564	+	3.26411i	0.575912	+	0.122414i
$712$	29.1851	+	137.305i	1.09376	+	5.14572i
$713$	1.12703	+	0.366196i	0.0422078	+	0.0137141i
$714$	−6.27461	+	4.62304i	−0.234821	+	0.173013i
$715$	−15.5673	−	17.6555i	−0.582184	−	0.660280i
$716$	26.7077	−	5.67690i	0.998113	−	0.212156i
$717$	0.239355	+	0.537600i	0.00893887	+	0.0200770i
$718$	−38.9546	−	22.4905i	−1.45377	−	0.839337i
$719$	2.72979	−	25.9722i	0.101804	−	0.968601i	−0.817733	−	0.575598i	$-0.804769\pi$
$719$	2.72979	−	25.9722i	0.101804	−	0.968601i	0.919537	−	0.393004i	$-0.128564\pi$
$720$	37.9042	−	3.58525i	1.41260	−	0.133614i
$721$	19.8018	−	8.97511i	0.737459	−	0.334251i
$722$	−15.6498	−	21.5401i	−0.582426	−	0.801640i
$723$	−1.33883	−	1.20549i	−0.0497916	−	0.0448325i
$724$	−26.0022	+	45.0372i	−0.966366	+	1.67379i
$725$	35.0756	+	0.730591i	1.30267	+	0.0271335i
$726$	33.1389	+	57.3983i	1.22990	+	2.13025i
$727$	18.2676	−	5.93551i	0.677508	−	0.220136i	0.0500040	−	0.998749i	$-0.484077\pi$
$727$	18.2676	−	5.93551i	0.677508	−	0.220136i	0.627504	+	0.778613i	$0.284077\pi$
$728$	48.0658	+	4.72794i	1.78144	+	0.175229i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	40.7969	−	12.7876i	1.50996	−	0.473290i
$731$	3.09290	−	1.37705i	0.114395	−	0.0509320i
$732$	−66.1884	−	38.2139i	−2.44639	−	1.41243i
$733$	−20.5475	−	2.15963i	−0.758941	−	0.0797679i	−0.282850	−	0.959164i	$-0.591280\pi$
$733$	−20.5475	−	2.15963i	−0.758941	−	0.0797679i	−0.476091	+	0.879396i	$0.657947\pi$
$734$	1.13862	−	3.50431i	0.0420272	−	0.129346i
$735$	−1.59052	+	15.5715i	−0.0586671	+	0.574362i
$736$	7.39250	+	22.7518i	0.272491	+	0.838641i
$737$	8.04022	+	37.8263i	0.296165	+	1.39335i
$738$	14.8236	−	13.3473i	0.545666	−	0.491319i
$739$	−36.0039	−	7.65286i	−1.32442	−	0.281515i	−0.509194	−	0.860652i	$-0.670056\pi$
$739$	−36.0039	−	7.65286i	−1.32442	−	0.281515i	−0.815231	+	0.579137i	$0.803390\pi$
$740$	−48.9160	−	0.509381i	−1.79819	−	0.0187252i
$741$	−1.68840	+	5.19635i	−0.0620248	+	0.190893i
$742$	4.60427	+	20.9724i	0.169028	+	0.769921i
$743$		−	0.773807i		−	0.0283882i	−0.999899	−	0.0141941i	$-0.995482\pi$
$743$		−	0.773807i		−	0.0283882i	0.999899	−	0.0141941i	$-0.00451828\pi$
$744$	−1.41832	+	13.4944i	−0.0519981	+	0.494729i
$745$	2.25686	+	11.1894i	0.0826851	+	0.409948i
$746$	−7.01545	−	66.7475i	−0.256854	−	2.44380i
$747$	0.163617	−	0.367491i	0.00598645	−	0.0134458i
$748$	−33.9701	+	11.0376i	−1.24207	+	0.403573i
$749$	13.7995	+	2.83710i	0.504224	+	0.103665i
$750$	0.968585	−	30.9955i	0.0353677	−	1.13180i
$751$	3.29980	+	5.71542i	0.120411	+	0.208559i	0.919930	−	0.392083i	$-0.128245\pi$
$751$	3.29980	+	5.71542i	0.120411	+	0.208559i	−0.799519	+	0.600641i	$0.794912\pi$
$752$	26.2061	−	123.290i	0.955639	−	4.49593i
$753$	2.26347	−	0.237901i	0.0824856	−	0.00866959i
$754$	31.6829	+	14.1061i	1.15382	+	0.513715i
$755$	−5.36816	+	4.73323i	−0.195367	+	0.172260i
$756$	−4.55905	+	14.3565i	−0.165811	+	0.522141i
$757$			32.8389i			1.19355i	0.802409	+	0.596774i	$0.203551\pi$
$757$			32.8389i			1.19355i	−0.802409	+	0.596774i	$0.796449\pi$
$758$	62.8199	+	6.60263i	2.28172	+	0.239818i
$759$	3.53635	+	3.92751i	0.128361	+	0.142560i
$760$	−34.4809	−	61.1852i	−1.25075	−	2.21942i
$761$	−16.0997	+	17.8805i	−0.583613	+	0.648168i	−0.960562	−	0.278066i	$-0.910307\pi$
$761$	−16.0997	+	17.8805i	−0.583613	+	0.648168i	0.376949	+	0.926234i	$0.376973\pi$
$762$	−43.7761	−	14.2237i	−1.58584	−	0.515271i
$763$	−0.0260927	−	3.91111i	−0.000944619	−	0.141592i
$764$	30.0393	+	92.4514i	1.08678	+	3.34477i
$765$	0.710299	+	2.26610i	0.0256809	+	0.0819310i
$766$	−40.0187	−	44.4452i	−1.44593	−	1.60587i
$767$	−0.801455	−	1.80010i	−0.0289389	−	0.0649977i
$768$	−69.3147	+	40.0189i	−2.50118	+	1.44406i
$769$	−30.8364	−	22.4040i	−1.11199	−	0.807908i	−0.129014	−	0.991643i	$-0.541181\pi$
$769$	−30.8364	−	22.4040i	−1.11199	−	0.807908i	−0.982976	+	0.183735i	$0.941181\pi$
$770$	−39.7574	+	88.4049i	−1.43276	+	3.18589i
$771$	17.3747	−	12.6235i	0.625735	−	0.454623i
$772$	−54.7070	+	122.874i	−1.96895	+	4.42233i
$773$	−9.99102	+	47.0041i	−0.359352	+	1.69062i	0.312488	+	0.949922i	$0.398838\pi$
$773$	−9.99102	+	47.0041i	−0.359352	+	1.69062i	−0.671840	+	0.740697i	$0.734496\pi$
$774$	4.42097	−	7.65735i	0.158909	−	0.275238i
$775$	6.44798	+	1.51156i	0.231618	+	0.0542968i
$776$	73.3676			2.63374
$777$	4.07307	−	9.31503i	0.146121	−	0.334175i
$778$	−26.6727	−	36.7118i	−0.956262	−	1.31618i
$779$	−20.1437	−	8.96853i	−0.721721	−	0.321331i
$780$	9.44252	−	20.6275i	0.338096	−	0.738581i
$781$	−17.7597	+	7.90711i	−0.635491	+	0.282939i
$782$	−2.28240	+	1.31774i	−0.0816183	+	0.0471223i
$783$	−4.12428	+	5.67658i	−0.147390	+	0.202864i
$784$	−38.3404	−	112.853i	−1.36930	−	4.03048i
$785$	−2.77429	−	3.14644i	−0.0990188	−	0.112301i
$786$	6.89579	−	7.65855i	0.245965	−	0.273172i
$787$	38.8254	−	34.9585i	1.38398	−	1.24614i	0.448019	−	0.894024i	$-0.352130\pi$
$787$	38.8254	−	34.9585i	1.38398	−	1.24614i	0.935957	−	0.352113i	$-0.114537\pi$
$788$	−41.6741	+	37.5235i	−1.48458	+	1.33672i
$789$	6.59943	−	7.32941i	0.234946	−	0.260934i
$790$	9.16908	+	96.9377i	0.326221	+	3.44889i
$791$	−0.0534995	−	0.0912524i	−0.00190222	−	0.00324456i
$792$	−35.5689	+	48.9564i	−1.26389	+	1.73959i
$793$	−20.7171	+	11.9610i	−0.735685	+	0.424748i
$794$	1.73615	−	0.772983i	0.0616136	−	0.0274322i
$795$	6.49928	+	0.751604i	0.230506	+	0.0266566i
$796$	−103.125	−	45.9142i	−3.65517	−	1.62739i
$797$	−31.1243	−	42.8390i	−1.10248	−	1.51743i	−0.832055	−	0.554693i	$-0.812836\pi$
$797$	−31.1243	−	42.8390i	−1.10248	−	1.51743i	−0.270425	−	0.962741i	$-0.587164\pi$
$798$	22.3608	−	2.50115i	0.791564	−	0.0885397i
$799$	7.86198			0.278137
$800$	51.8238	+	123.243i	1.83225	+	4.35731i
$801$	−6.85146	+	11.8671i	−0.242085	+	0.419303i
$802$	−8.64080	+	40.6518i	−0.305117	+	1.43546i
$803$	−16.5628	+	37.2006i	−0.584487	+	1.31278i
$804$	−30.1527	+	21.9072i	−1.06340	+	0.772608i
$805$	−1.11982	+	5.17309i	−0.0394685	+	0.182328i
$806$	5.29656	+	3.84817i	0.186563	+	0.135546i
$807$	26.2474	−	15.1540i	0.923953	−	0.533445i
$808$	16.1238	+	36.2146i	0.567232	+	1.27402i
$809$	8.49167	+	9.43095i	0.298551	+	0.331575i	0.873692	−	0.486480i	$-0.161719\pi$
$809$	8.49167	+	9.43095i	0.298551	+	0.331575i	−0.575141	+	0.818055i	$0.695053\pi$
$810$	4.97940	+	3.69757i	0.174958	+	0.129919i
$811$	−4.30210	−	13.2405i	−0.151067	−	0.464937i	0.846674	−	0.532112i	$-0.178601\pi$
$811$	−4.30210	−	13.2405i	−0.151067	−	0.464937i	−0.997741	+	0.0671750i	$0.978601\pi$
$812$	−0.705100	−	105.689i	−0.0247442	−	3.70897i
$813$	4.24506	+	1.37930i	0.148881	+	0.0483743i
$814$	42.1286	−	46.7885i	1.47661	−	1.63994i
$815$	−4.61708	+	39.9249i	−0.161729	+	1.39851i
$816$	−12.1002	−	13.4386i	−0.423590	−	0.470444i
$817$	−9.72051	−	1.02167i	−0.340078	−	0.0357436i
$818$		−	24.7477i		−	0.865283i
$819$	3.17809	+	3.48262i	0.111051	+	0.121692i
$820$	78.8064	+	46.5997i	2.75204	+	1.62733i
$821$	−4.80970	−	2.14142i	−0.167860	−	0.0747360i	0.321087	−	0.947050i	$-0.395952\pi$
$821$	−4.80970	−	2.14142i	−0.167860	−	0.0747360i	−0.488946	+	0.872314i	$0.662619\pi$
$822$	6.66744	−	0.700776i	0.232554	−	0.0244424i
$823$	−1.33860	+	6.29764i	−0.0466608	+	0.219522i	−0.995300	−	0.0968376i	$-0.969127\pi$
$823$	−1.33860	+	6.29764i	−0.0466608	+	0.219522i	0.948639	+	0.316359i	$0.102461\pi$
$824$	42.0888	+	72.8999i	1.46623	+	2.53959i
$825$	21.5333	+	20.2163i	0.749693	+	0.703842i
$826$	−5.38930	+	6.06633i	−0.187518	+	0.211075i
$827$	30.2452	−	9.82725i	1.05173	−	0.341727i	0.268381	−	0.963313i	$-0.413511\pi$
$827$	30.2452	−	9.82725i	1.05173	−	0.341727i	0.783346	+	0.621586i	$0.213511\pi$
$828$	−2.07175	+	4.65322i	−0.0719982	+	0.161710i
$829$	−1.84340	−	17.5388i	−0.0640239	−	0.609147i	−0.978748	−	0.205067i	$-0.934259\pi$
$829$	−1.84340	−	17.5388i	−0.0640239	−	0.609147i	0.914724	−	0.404079i	$-0.132408\pi$
$830$	2.47840	+	0.286613i	0.0860267	+	0.00994849i
$831$	0.797256	−	7.58538i	0.0276565	−	0.263134i
$832$			71.4800i			2.47812i
$833$	6.38815	−	3.80274i	0.221336	−	0.131757i
$834$	−5.43772	+	16.7356i	−0.188293	+	0.579506i
$835$	40.0486	−	28.4646i	1.38594	−	0.985060i
$836$	100.863	+	21.4392i	3.48843	+	0.741489i
$837$	−0.984338	+	0.886302i	−0.0340237	+	0.0306351i
$838$	0.294931	+	1.38754i	0.0101882	+	0.0479319i
$839$	14.4676	+	44.5267i	0.499477	+	1.53723i	0.809861	+	0.586622i	$0.199542\pi$
$839$	14.4676	+	44.5267i	0.499477	+	1.53723i	−0.310384	+	0.950611i	$0.600458\pi$
$840$	−60.6038	−	0.226761i	−2.09103	−	0.00782399i
$841$	6.25240	−	19.2429i	0.215600	−	0.663549i
$842$	−78.7879	−	8.28094i	−2.71521	−	0.285380i
$843$	−10.5558	−	6.09441i	−0.363562	−	0.209903i
$844$	60.6979	−	27.0244i	2.08931	−	0.930219i
$845$	12.7268	+	17.9061i	0.437815	+	0.615988i
$846$	16.6112	−	12.0688i	0.571105	−	0.414932i
$847$	−26.0990	−	57.5825i	−0.896774	−	1.97856i
$848$	−47.3813	+	15.3951i	−1.62708	+	0.528671i
$849$	−5.04241	−	8.73370i	−0.173055	−	0.299740i
$850$	−12.0936	+	8.40740i	−0.414808	+	0.288371i
$851$	1.71892	−	2.97727i	0.0589240	−	0.102059i
$852$	−13.9238	−	12.5370i	−0.477021	−	0.429512i
$853$	17.2020	+	23.6765i	0.588984	+	0.810666i	0.994644	−	0.103357i	$-0.0329585\pi$
$853$	17.2020	+	23.6765i	0.588984	+	0.810666i	−0.405661	+	0.914024i	$0.632959\pi$
$854$	80.0832	+	57.3715i	2.74039	+	1.96321i
$855$	1.49518	−	6.69093i	0.0511342	−	0.228825i
$856$	−5.70176	+	54.2486i	−0.194882	+	1.85418i
$857$	21.5081	+	12.4177i	0.734702	+	0.424180i	0.820140	−	0.572163i	$-0.193896\pi$
$857$	21.5081	+	12.4177i	0.734702	+	0.424180i	−0.0854378	+	0.996344i	$0.527229\pi$
$858$	11.8758	+	26.6734i	0.405432	+	0.910616i
$859$	11.1161	−	2.36281i	0.379278	−	0.0806180i	−0.0143277	−	0.999897i	$-0.504561\pi$
$859$	11.1161	−	2.36281i	0.379278	−	0.0806180i	0.393606	+	0.919279i	$0.371227\pi$
$860$	39.6058	+	8.85048i	1.35054	+	0.301799i
$861$	−15.3184	+	11.2863i	−0.522048	+	0.384637i
$862$	−59.1252	−	19.2110i	−2.01381	−	0.654328i
$863$	−3.03711	−	14.2885i	−0.103384	−	0.486385i	−0.999126	−	0.0418095i	$-0.986688\pi$
$863$	−3.03711	−	14.2885i	−0.103384	−	0.486385i	0.895741	−	0.444576i	$-0.146646\pi$
$864$	−26.1549	−	5.55939i	−0.889807	−	0.189134i
$865$	−7.89044	−	14.0013i	−0.268283	−	0.476060i
$866$	−74.6655	+	15.8706i	−2.53724	+	0.539306i
$867$	−9.32936	+	12.8408i	−0.316842	+	0.436095i
$868$	4.01793	−	19.5431i	0.136377	−	0.663335i
$869$	−75.0287	−	54.5115i	−2.54517	−	1.84918i
$870$	−41.2459	−	13.8781i	−1.39837	−	0.470511i
$871$	1.21941	+	11.6019i	0.0413181	+	0.393115i
$872$	15.0606	−	1.58294i	0.510018	−	0.0536050i
$873$	5.32242	+	4.79233i	0.180137	+	0.162196i
$874$	7.60850			0.257361
$875$	−3.81373	+	29.3335i	−0.128928	+	0.991654i
$876$	−39.2463			−1.32601
$877$	39.9956	+	36.0122i	1.35056	+	1.21605i	0.954641	+	0.297760i	$0.0962394\pi$
$877$	39.9956	+	36.0122i	1.35056	+	1.21605i	0.395916	+	0.918287i	$0.370427\pi$
$878$	54.7546	−	5.75494i	1.84788	−	0.194220i
$879$	−0.180352	−	1.71593i	−0.00608312	−	0.0578770i
$880$	−213.165	−	71.7239i	−7.18578	−	2.41781i
$881$	29.9817	+	21.7830i	1.01011	+	0.733888i	0.964232	−	0.265059i	$-0.0853915\pi$
$881$	29.9817	+	21.7830i	1.01011	+	0.733888i	0.0458778	+	0.998947i	$0.485392\pi$
$882$	7.65974	−	17.8409i	0.257917	−	0.600736i
$883$	2.09491	−	2.88340i	0.0704994	−	0.0970342i	−0.772311	−	0.635244i	$-0.780899\pi$
$883$	2.09491	−	2.88340i	0.0704994	−	0.0970342i	0.842811	+	0.538210i	$0.180899\pi$
$884$	−10.5395	+	2.24024i	−0.354482	+	0.0753475i
$885$	1.21390	+	2.15403i	0.0408048	+	0.0724069i
$886$	103.851	+	22.0743i	3.48895	+	0.741599i
$887$	−8.28115	−	38.9598i	−0.278054	−	1.30814i	−0.866327	−	0.499478i	$-0.833525\pi$
$887$	−8.28115	−	38.9598i	−0.278054	−	1.30814i	0.588273	−	0.808663i	$-0.299808\pi$
$888$	37.4370	+	12.1640i	1.25630	+	0.408198i
$889$	40.2284	+	17.5902i	1.34922	+	0.589956i
$890$	−82.9417	−	18.5345i	−2.78021	−	0.621279i
$891$	−5.77814	+	1.22818i	−0.193575	+	0.0411456i
$892$	−50.7433	−	113.971i	−1.69901	−	3.81604i
$893$	−19.6563	−	11.3486i	−0.657772	−	0.379765i
$894$	1.48003	−	14.0816i	0.0494997	−	0.470958i
$895$	−2.33874	+	10.4658i	−0.0781753	+	0.349833i
$896$	139.236	−	63.1083i	4.65155	−	2.10830i
$897$	0.937105	+	1.28981i	0.0312890	+	0.0430657i
$898$	−9.32906	−	8.39992i	−0.311315	−	0.280309i
$899$	4.64697	−	8.04878i	0.154985	−	0.268442i
$900$	−9.35849	+	26.8841i	−0.311950	+	0.896137i
$901$	−1.55374	−	2.69116i	−0.0517626	−	0.0896555i
$902$	−112.065	+	36.4122i	−3.73137	+	1.21239i
$903$	−4.91183	+	6.85629i	−0.163456	+	0.228163i
$904$	0.331342	−	0.240734i	0.0110203	−	0.00800670i
$905$	−11.8328	−	16.6483i	−0.393336	−	0.553409i
$906$	8.11004	−	3.61082i	0.269438	−	0.119962i
$907$	−4.05096	−	2.33882i	−0.134510	−	0.0776593i	0.431235	−	0.902240i	$-0.358078\pi$
$907$	−4.05096	−	2.33882i	−0.134510	−	0.0776593i	−0.565745	+	0.824580i	$0.691411\pi$
$908$	75.9460	+	7.98224i	2.52036	+	0.264900i
$909$	−1.19582	+	3.68037i	−0.0396630	+	0.122070i
$910$	−14.7154	+	25.2690i	−0.487810	+	0.837658i
$911$	10.3322	+	31.7991i	0.342320	+	1.05355i	0.963003	+	0.269491i	$0.0868555\pi$
$911$	10.3322	+	31.7991i	0.342320	+	1.05355i	−0.620683	+	0.784062i	$0.713145\pi$
$912$	10.8542	+	51.0650i	0.359418	+	1.69093i
$913$	−1.76593	+	1.59005i	−0.0584437	+	0.0526229i
$914$	36.8203	+	7.82640i	1.21791	+	0.258874i
$915$	24.4670	−	17.3900i	0.808855	−	0.574895i
$916$	52.4093	−	161.299i	1.73165	−	5.32948i
$917$	−7.26129	+	6.62634i	−0.239789	+	0.218821i
$918$		−	2.94578i		−	0.0972251i
$919$	−1.21955	+	11.6032i	−0.0402291	+	0.382755i	0.955820	+	0.293952i	$0.0949707\pi$
$919$	−1.21955	+	11.6032i	−0.0402291	+	0.382755i	−0.996049	+	0.0888025i	$0.971696\pi$
$920$	−20.3577	−	2.35425i	−0.671174	−	0.0776174i
$921$	−0.937904	−	8.92356i	−0.0309050	−	0.294041i
$922$	35.2659	−	79.2084i	1.16142	−	2.60859i
$923$	−5.57746	+	1.81223i	−0.183584	+	0.0596502i
$924$	59.0972	−	66.5212i	1.94415	−	2.18839i
$925$	8.17847	−	17.3855i	0.268907	−	0.571630i
$926$	−3.81205	−	6.60266i	−0.125272	−	0.216977i
$927$	−1.70847	+	8.03771i	−0.0561134	+	0.263993i
$928$	186.592	−	19.6116i	6.12517	−	0.643781i
$929$	5.09967	+	2.27052i	0.167315	+	0.0744933i	0.488685	−	0.872460i	$-0.337477\pi$
$929$	5.09967	+	2.27052i	0.167315	+	0.0744933i	−0.321370	+	0.946954i	$0.604143\pi$
$930$	−7.07131	−	4.18140i	−0.231877	−	0.137113i
$931$	−21.4606	+	0.286359i	−0.703343	+	0.00938504i
$932$		−	6.03184i		−	0.197579i
$933$	−18.8351	−	1.97965i	−0.616633	−	0.0648107i
$934$	46.1355	+	51.2387i	1.50960	+	1.67658i
$935$	1.61158	−	13.9357i	0.0527043	−	0.455745i
$936$	−12.2149	+	13.5660i	−0.399256	+	0.443418i
$937$	−16.4983	−	5.36061i	−0.538975	−	0.175123i	0.0268646	−	0.999639i	$-0.491448\pi$
$937$	−16.4983	−	5.36061i	−0.538975	−	0.175123i	−0.565839	+	0.824516i	$0.691448\pi$
$938$	41.4434	−	24.2974i	1.35317	−	0.793339i
$939$	8.74495	+	26.9142i	0.285381	+	0.878311i
$940$	75.6609	+	56.1838i	2.46779	+	1.83251i
$941$	−17.1857	−	19.0867i	−0.560238	−	0.622207i	0.394773	−	0.918779i	$-0.370823\pi$
$941$	−17.1857	−	19.0867i	−0.560238	−	0.622207i	−0.955011	+	0.296572i	$0.904157\pi$
$942$	2.11642	+	4.75355i	0.0689566	+	0.154879i
$943$	−5.57207	+	3.21703i	−0.181451	+	0.104761i
$944$	−15.2318	−	11.0665i	−0.495751	−	0.360185i
$945$	−4.38166	−	3.97505i	−0.142535	−	0.129308i
$946$	−42.2561	+	30.7008i	−1.37386	+	0.998170i
$947$	−13.1529	+	29.5419i	−0.427412	+	0.959983i	0.563580	+	0.826062i	$0.309424\pi$
$947$	−13.1529	+	29.5419i	−0.427412	+	0.959983i	−0.990992	+	0.133922i	$0.957243\pi$
$948$	18.5835	−	87.4286i	0.603565	−	2.83955i
$949$	−6.14208	+	10.6384i	−0.199380	+	0.345337i
$950$	42.3720	−	3.56310i	1.37473	−	0.115602i
$951$	−21.9729			−0.712520
$952$	17.0742	+	23.1739i	0.553378	+	0.751071i
$953$	−29.3999	−	40.4654i	−0.952355	−	1.31080i	−0.950473	−	0.310806i	$-0.899401\pi$
$953$	−29.3999	−	40.4654i	−0.952355	−	1.31080i	−0.00188128	−	0.999998i	$-0.500599\pi$
$954$	−7.41397	−	3.30091i	−0.240036	−	0.106871i
$955$	−37.9266	−	4.38600i	−1.22728	−	0.141927i
$956$	3.06071	−	1.36271i	0.0989904	−	0.0440733i
$957$	35.8958	−	20.7244i	1.16035	−	0.669926i
$958$	22.4949	−	30.9616i	0.726778	−	1.00032i
$959$	−6.39481	+	0.0426626i	−0.206499	+	0.00137765i
$960$	−8.44616	−	89.2948i	−0.272599	−	2.88198i
$961$	−19.5691	+	21.7337i	−0.631261	+	0.701086i
$962$	14.1145	−	12.7087i	0.455069	−	0.409746i
$963$	−3.95712	+	3.56301i	−0.127516	+	0.114816i
$964$	−6.86318	+	7.62233i	−0.221048	+	0.245499i
$965$	−34.9371	−	39.6237i	−1.12467	−	1.27553i
$966$	3.24473	−	5.70763i	0.104397	−	0.183640i
$967$	−2.27676	+	3.13369i	−0.0732157	+	0.100773i	−0.844054	−	0.536258i	$-0.819838\pi$
$967$	−2.27676	+	3.13369i	−0.0732157	+	0.100773i	0.770839	+	0.637031i	$0.219838\pi$
$968$	211.988	−	122.391i	6.81356	−	3.93381i
$969$	−2.97479	+	1.32446i	−0.0955641	+	0.0425479i
$970$	−18.4887	+	40.3892i	−0.593637	+	1.29682i
$971$	−40.1885	−	17.8931i	−1.28971	−	0.574216i	−0.356751	−	0.934200i	$-0.616115\pi$
$971$	−40.1885	−	17.8931i	−1.28971	−	0.574216i	−0.932958	+	0.359984i	$0.882782\pi$
$972$	−3.34643	−	4.60596i	−0.107337	−	0.147736i
$973$	6.72473	−	15.3793i	0.215585	−	0.493037i
$974$	−7.39847			−0.237062
$975$	5.82280	+	6.74417i	0.186479	+	0.215986i
$976$	−114.286	+	197.950i	−3.65822	+	6.33622i
$977$	−1.17812	+	5.54260i	−0.0376913	+	0.177324i	−0.992967	−	0.118394i	$-0.962225\pi$
$977$	−1.17812	+	5.54260i	−0.0376913	+	0.177324i	0.955275	+	0.295718i	$0.0955587\pi$
$978$	20.2774	−	45.5439i	0.648401	−	1.45633i
$979$	65.4869	−	47.5790i	2.09297	−	1.52063i
$980$	88.6527	+	9.05527i	2.83191	+	0.289260i
$981$	1.19596	+	0.868919i	0.0381842	+	0.0277424i
$982$	52.6417	−	30.3927i	1.67986	−	0.969870i
$983$	−15.3887	−	34.5637i	−0.490825	−	1.10241i	−0.973930	−	0.226848i	$-0.927158\pi$
$983$	−15.3887	−	34.5637i	−0.490825	−	1.10241i	0.483105	−	0.875562i	$-0.339509\pi$
$984$	−49.2952	−	54.7479i	−1.57147	−	1.74530i
$985$	−6.58760	−	21.0167i	−0.209898	−	0.669648i
$986$	6.38721	+	19.6578i	0.203410	+	0.626032i
$987$	−16.8959	+	9.90574i	−0.537803	+	0.315303i
$988$	29.5843	+	9.61252i	0.941202	+	0.305815i
$989$	−1.90837	+	2.11946i	−0.0606827	+	0.0673950i
$990$	−17.9873	−	31.9179i	−0.571674	−	1.01442i
$991$	8.04681	+	8.93689i	0.255615	+	0.283890i	0.857270	−	0.514866i	$-0.172158\pi$
$991$	8.04681	+	8.93689i	0.255615	+	0.283890i	−0.601655	+	0.798756i	$0.705492\pi$
$992$	35.2236	+	3.70215i	1.11835	+	0.117543i
$993$		−	13.0520i		−	0.414192i
$994$	16.2792	+	17.8391i	0.516345	+	0.565822i
$995$	33.2552	−	29.3219i	1.05426	−	0.929566i
$996$	−2.09223	−	0.931520i	−0.0662948	−	0.0295164i
$997$	−28.7237	+	3.01898i	−0.909687	+	0.0956120i	−0.547800	−	0.836610i	$-0.684534\pi$
$997$	−28.7237	+	3.01898i	−0.909687	+	0.0956120i	−0.361888	+	0.932222i	$0.617868\pi$
$998$	12.2018	−	57.4048i	0.386240	−	1.81712i
$999$	1.92131	+	3.32780i	0.0607874	+	0.105287i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bo.a.319.1	yes	320
7.2	even	3	inner	525.2.bo.a.394.1	yes	320
25.4	even	10	inner	525.2.bo.a.4.1	✓	320
175.79	even	30	inner	525.2.bo.a.79.1	yes	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bo.a.4.1	✓	320	25.4	even	10	inner
525.2.bo.a.79.1	yes	320	175.79	even	30	inner
525.2.bo.a.319.1	yes	320	1.1	even	1	trivial
525.2.bo.a.394.1	yes	320	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bo (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.06124 - 1.85595i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.595110 + 5.66210i) q^{4} +(-2.11932 - 0.713090i) q^{5} +(2.24395 + 1.63033i) q^{6} +(-1.97794 - 1.75720i) q^{7} +(6.02126 - 8.28755i) q^{8} +(0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-2.06124 - 1.85595i) q^{2} +(-0.994522 + 0.104528i) q^{3} +(0.595110 + 5.66210i) q^{4} +(-2.11932 - 0.713090i) q^{5} +(2.24395 + 1.63033i) q^{6} +(-1.97794 - 1.75720i) q^{7} +(6.02126 - 8.28755i) q^{8} +(0.978148 - 0.207912i) q^{9} +(3.04497 + 5.40320i) q^{10} +(-5.77814 - 1.22818i) q^{11} +(-1.18370 - 5.56887i) q^{12} +(-1.69479 - 0.550670i) q^{13} +(0.815750 + 7.29298i) q^{14} +(2.18224 + 0.487654i) q^{15} +(-16.6548 + 3.54009i) q^{16} +(-0.431974 - 0.970229i) q^{17} +(-2.40207 - 1.38684i) q^{18} +(-0.320492 + 3.04928i) q^{19} +(2.77636 - 12.4241i) q^{20} +(2.15078 + 1.54082i) q^{21} +(9.63070 + 13.2555i) q^{22} +(0.664866 + 0.598648i) q^{23} +(-5.12199 + 8.87154i) q^{24} +(3.98301 + 3.02253i) q^{25} +(2.47136 + 4.28051i) q^{26} +(-0.951057 + 0.309017i) q^{27} +(8.77232 - 12.2450i) q^{28} +(5.67658 - 4.12428i) q^{29} +(-3.59308 - 5.05532i) q^{30} +(1.21004 - 0.538746i) q^{31} +(23.1568 + 13.3696i) q^{32} +(5.87486 + 0.617473i) q^{33} +(-0.910295 + 2.80160i) q^{34} +(2.93885 + 5.13451i) q^{35} +(1.75932 + 5.41463i) q^{36} +(-0.798924 - 3.75864i) q^{37} +(6.31993 - 5.69049i) q^{38} +(1.74307 + 0.370500i) q^{39} +(-18.6707 + 13.2702i) q^{40} +(-2.22233 + 6.83962i) q^{41} +(-1.57360 - 7.16776i) q^{42} +3.18781i q^{43} +(3.51545 - 33.4473i) q^{44} +(-2.22126 - 0.256876i) q^{45} +(-0.259389 - 2.46792i) q^{46} +(-3.01093 + 6.76267i) q^{47} +(16.1936 - 5.26161i) q^{48} +(0.824518 + 6.95127i) q^{49} +(-2.60028 - 13.6224i) q^{50} +(0.531024 + 0.919760i) q^{51} +(2.10936 - 9.92377i) q^{52} +(2.90991 - 0.305844i) q^{53} +(2.53388 + 1.12816i) q^{54} +(11.3699 + 6.72324i) q^{55} +(-26.4726 + 5.81177i) q^{56} -3.06607i q^{57} +(-19.3553 - 2.03432i) q^{58} +(0.739890 + 0.821731i) q^{59} +(-1.46247 + 12.6463i) q^{60} +(8.98254 - 9.97613i) q^{61} +(-3.49408 - 1.13530i) q^{62} +(-2.30006 - 1.30756i) q^{63} +(-12.3953 - 38.1489i) q^{64} +(3.19912 + 2.37558i) q^{65} +(-10.9635 - 12.1762i) q^{66} +(-2.66268 - 5.98047i) q^{67} +(5.23646 - 3.02327i) q^{68} +(-0.723799 - 0.525871i) q^{69} +(3.47172 - 16.0378i) q^{70} +(2.66243 - 1.93437i) q^{71} +(4.16660 - 9.35834i) q^{72} +(1.43323 - 6.74280i) q^{73} +(-5.32908 + 9.23024i) q^{74} +(-4.27713 - 2.58963i) q^{75} -17.4560 q^{76} +(9.27067 + 12.5826i) q^{77} +(-2.90525 - 3.99874i) q^{78} +(14.3422 + 6.38557i) q^{79} +(37.8213 + 4.37381i) q^{80} +(0.913545 - 0.406737i) q^{81} +(17.2748 - 9.97358i) q^{82} +(0.236448 - 0.325442i) q^{83} +(-7.44431 + 13.0949i) q^{84} +(0.223629 + 2.36426i) q^{85} +(5.91642 - 6.57085i) q^{86} +(-5.21438 + 4.69505i) q^{87} +(-44.9703 + 40.4914i) q^{88} +(-9.16905 + 10.1833i) q^{89} +(4.10182 + 4.65204i) q^{90} +(2.38456 + 4.06727i) q^{91} +(-2.99393 + 4.12079i) q^{92} +(-1.14710 + 0.662278i) q^{93} +(18.7575 - 8.35136i) q^{94} +(2.85363 - 6.23385i) q^{95} +(-24.4275 - 10.8758i) q^{96} +(4.20973 + 5.79420i) q^{97} +(11.2017 - 15.8585i) q^{98} -5.90722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9}+O(q^{10}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9	\( 320 q - 40 q^{4} - 2 q^{5} + 8 q^{6} + 60 q^{8} - 40 q^{9} + 4 q^{10} - 6 q^{11} + 12 q^{14} + 4 q^{15} + 40 q^{16} - 20 q^{17} + 16 q^{19} + 8 q^{20} + 40 q^{22} - 60 q^{23} - 48 q^{24} + 4 q^{25} - 30 q^{28} + 24 q^{29} - 48 q^{30} - 30 q^{31} - 80 q^{36} + 30 q^{38} - 32 q^{40} + 36 q^{41} + 10 q^{42} - 16 q^{44} + 2 q^{45} + 32 q^{46} + 16 q^{49} - 140 q^{50} + 190 q^{52} - 60 q^{53} + 4 q^{54} - 8 q^{55} + 60 q^{58} + 24 q^{59} - 46 q^{60} - 20 q^{61} + 120 q^{62} + 10 q^{63} - 4 q^{64} - 30 q^{65} - 16 q^{66} - 60 q^{67} - 32 q^{69} - 76 q^{70} + 32 q^{71} - 30 q^{72} - 40 q^{73} - 12 q^{74} - 8 q^{75} - 344 q^{76} + 4 q^{79} - 52 q^{80} + 40 q^{81} - 80 q^{83} + 48 q^{84} - 76 q^{85} + 24 q^{86} - 200 q^{88} - 52 q^{90} + 26 q^{91} + 180 q^{92} + 16 q^{94} - 38 q^{95} - 58 q^{96} - 140 q^{97} + 360 q^{98} + 8 q^{99}+O(q^{100}) \) 320 * q - 40 * q^4 - 2 * q^5 + 8 * q^6 + 60 * q^8 - 40 * q^9 + 4 * q^10 - 6 * q^11 + 12 * q^14 + 4 * q^15 + 40 * q^16 - 20 * q^17 + 16 * q^19 + 8 * q^20 + 40 * q^22 - 60 * q^23 - 48 * q^24 + 4 * q^25 - 30 * q^28 + 24 * q^29 - 48 * q^30 - 30 * q^31 - 80 * q^36 + 30 * q^38 - 32 * q^40 + 36 * q^41 + 10 * q^42 - 16 * q^44 + 2 * q^45 + 32 * q^46 + 16 * q^49 - 140 * q^50 + 190 * q^52 - 60 * q^53 + 4 * q^54 - 8 * q^55 + 60 * q^58 + 24 * q^59 - 46 * q^60 - 20 * q^61 + 120 * q^62 + 10 * q^63 - 4 * q^64 - 30 * q^65 - 16 * q^66 - 60 * q^67 - 32 * q^69 - 76 * q^70 + 32 * q^71 - 30 * q^72 - 40 * q^73 - 12 * q^74 - 8 * q^75 - 344 * q^76 + 4 * q^79 - 52 * q^80 + 40 * q^81 - 80 * q^83 + 48 * q^84 - 76 * q^85 + 24 * q^86 - 200 * q^88 - 52 * q^90 + 26 * q^91 + 180 * q^92 + 16 * q^94 - 38 * q^95 - 58 * q^96 - 140 * q^97 + 360 * q^98 + 8 * q^99

Introduction

L-functions

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