LMFDB - Embedded newform 966.2.y.d.121.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			121.6
Character	$\chi$	$=$	966.121
Dual form			966.2.y.d.487.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0802489 + 1.68463i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.50657 + 2.17491i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0802489 + 1.68463i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.50657 + 2.17491i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-1.32571 + 1.04255i) q^{10} +(-3.22478 + 4.52857i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.802447 - 5.58114i) q^{13} +(-0.897733 + 2.48879i) q^{14} +(-1.61822 + 0.475154i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-5.60515 - 1.08030i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(1.95418 - 0.376637i) q^{19} +(-1.61822 - 0.475154i) q^{20} +(-1.75842 + 1.97686i) q^{21} -5.55942 q^{22} +(-0.275959 + 4.78789i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.14582 - 0.204901i) q^{25} +(4.08080 - 3.89103i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.54804 + 0.712368i) q^{28} +(4.92479 - 5.68351i) q^{29} +(-1.32571 - 1.04255i) q^{30} +(6.83229 + 6.51457i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-5.16119 - 2.06623i) q^{33} +(-2.37132 - 5.19246i) q^{34} +(-3.54302 + 2.71255i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(1.53452 - 0.791101i) q^{37} +(1.44033 + 1.37336i) q^{38} +(5.23463 - 2.09563i) q^{39} +(-0.551614 - 1.59378i) q^{40} +(5.76467 - 3.70473i) q^{41} +(-2.63028 - 0.285673i) q^{42} +(-8.51132 - 2.49915i) q^{43} +(-3.22478 - 4.52857i) q^{44} +(-0.843271 - 1.46059i) q^{45} +(-4.06017 + 2.55246i) q^{46} +(-2.74488 + 4.75426i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-2.46048 + 6.55332i) q^{49} +(1.41160 + 1.62908i) q^{50} +(-0.271612 - 5.70184i) q^{51} +(5.53663 + 1.06710i) q^{52} +(-9.59833 + 3.84259i) q^{53} +(0.235759 - 0.971812i) q^{54} +(-7.88775 - 5.06915i) q^{55} +(-2.05829 - 1.66236i) q^{56} +(0.826735 + 1.81030i) q^{57} +(7.48631 + 0.714856i) q^{58} +(7.81457 - 6.14544i) q^{59} +(0.0802489 - 1.68463i) q^{60} +(-2.74484 + 11.3144i) q^{61} +(-1.34350 + 9.34424i) q^{62} +(-2.33570 - 1.24279i) q^{63} +(0.841254 - 0.540641i) q^{64} +(9.33776 - 1.79971i) q^{65} +(-1.31068 - 5.40271i) q^{66} +(-1.09268 + 0.104338i) q^{67} +(2.85415 - 4.94354i) q^{68} +(-4.71798 + 0.860606i) q^{69} +(-4.26473 - 1.31263i) q^{70} +(-1.94744 + 4.26430i) q^{71} +(0.723734 - 0.690079i) q^{72} +(0.979890 - 2.83121i) q^{73} +(1.53452 + 0.791101i) q^{74} +(0.705021 + 2.03702i) q^{75} +(-0.283227 + 1.96989i) q^{76} +(-14.7076 - 0.190993i) q^{77} +(4.74343 + 3.04842i) q^{78} +(-6.48718 - 2.59707i) q^{79} +(0.978290 - 1.37382i) q^{80} +(0.580057 - 0.814576i) q^{81} +(6.36162 + 2.54681i) q^{82} +(5.51404 + 3.54366i) q^{83} +(-1.29301 - 2.30827i) q^{84} +(1.37011 - 9.52931i) q^{85} +(-2.90130 - 8.38276i) q^{86} +(6.68437 + 3.44603i) q^{87} +(1.81831 - 5.25366i) q^{88} +(-9.67856 + 9.22849i) q^{89} +(0.700614 - 1.53413i) q^{90} +(10.9295 - 10.1536i) q^{91} +(-4.43430 - 1.82675i) q^{92} +(-4.72016 + 8.17557i) q^{93} +(-5.46489 + 0.521834i) q^{94} +(0.791315 + 3.26185i) q^{95} +(0.981929 - 0.189251i) q^{96} +(11.0997 - 7.13333i) q^{97} +(-6.76540 + 1.79705i) q^{98} +(0.791188 - 5.50283i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$2$	0.580057	+	0.814576i	0.410162	+	0.575992i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	0.0802489	+	1.68463i	0.0358884	+	0.753390i	0.943059	+	0.332626i	$0.107935\pi$
$5$	0.0802489	+	1.68463i	0.0358884	+	0.753390i	−0.907170	+	0.420764i	$0.861762\pi$
$6$	−0.654861	+	0.755750i	−0.267346	+	0.308533i
$7$	1.50657	+	2.17491i	0.569431	+	0.822039i
$7$	1.50657	+	2.17491i	0.569431	+	0.822039i
$8$	−0.959493	+	0.281733i	−0.339232	+	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−1.32571	+	1.04255i	−0.419227	+	0.329683i
$11$	−3.22478	+	4.52857i	−0.972308	+	1.36542i	−0.0418071	+	0.999126i	$0.513311\pi$
$11$	−3.22478	+	4.52857i	−0.972308	+	1.36542i	−0.930501	+	0.366290i	$0.880628\pi$
$12$	−0.995472	−	0.0950560i	−0.287368	−	0.0274403i
$13$	−0.802447	−	5.58114i	−0.222559	−	1.54793i	−0.728309	−	0.685249i	$-0.759693\pi$
$13$	−0.802447	−	5.58114i	−0.222559	−	1.54793i	0.505750	−	0.862680i	$-0.331216\pi$
$14$	−0.897733	+	2.48879i	−0.239929	+	0.665157i
$15$	−1.61822	+	0.475154i	−0.417824	+	0.122684i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	−5.60515	−	1.08030i	−1.35945	−	0.262012i	−0.543147	−	0.839638i	$-0.682767\pi$
$17$	−5.60515	−	1.08030i	−1.35945	−	0.262012i	−0.816302	+	0.577625i	$0.803980\pi$
$18$	−0.888835	−	0.458227i	−0.209501	−	0.108005i
$19$	1.95418	−	0.376637i	0.448319	−	0.0864065i	0.0399058	−	0.999203i	$-0.487294\pi$
$19$	1.95418	−	0.376637i	0.448319	−	0.0864065i	0.408414	+	0.912797i	$0.366082\pi$
$20$	−1.61822	−	0.475154i	−0.361846	−	0.106248i
$21$	−1.75842	+	1.97686i	−0.383718	+	0.431386i
$22$	−5.55942			−1.18527
$23$	−0.275959	+	4.78789i	−0.0575415	+	0.998343i
$23$	−0.275959	+	4.78789i	−0.0575415	+	0.998343i
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	2.14582	−	0.204901i	0.429164	−	0.0409802i
$26$	4.08080	−	3.89103i	0.800310	−	0.763094i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−2.54804	+	0.712368i	−0.481535	+	0.134625i
$29$	4.92479	−	5.68351i	0.914511	−	1.05540i	−0.0837520	−	0.996487i	$-0.526690\pi$
$29$	4.92479	−	5.68351i	0.914511	−	1.05540i	0.998263	−	0.0589154i	$-0.0187642\pi$
$30$	−1.32571	−	1.04255i	−0.242041	−	0.190343i
$31$	6.83229	+	6.51457i	1.22712	+	1.17005i	0.979554	+	0.201180i	$0.0644775\pi$
$31$	6.83229	+	6.51457i	1.22712	+	1.17005i	0.247561	+	0.968872i	$0.420371\pi$
$32$	0.0475819	−	0.998867i	0.00841137	−	0.176576i
$33$	−5.16119	−	2.06623i	−0.898448	−	0.359684i
$34$	−2.37132	−	5.19246i	−0.406678	−	0.890500i
$35$	−3.54302	+	2.71255i	−0.598880	+	0.458505i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	1.53452	−	0.791101i	0.252274	−	0.130056i	−0.327452	−	0.944868i	$-0.606190\pi$
$37$	1.53452	−	0.791101i	0.252274	−	0.130056i	0.579726	+	0.814812i	$0.303160\pi$
$38$	1.44033	+	1.37336i	0.233653	+	0.222788i
$39$	5.23463	−	2.09563i	0.838212	−	0.335569i
$40$	−0.551614	−	1.59378i	−0.0872178	−	0.251999i
$41$	5.76467	−	3.70473i	0.900291	−	0.578582i	−0.00658587	−	0.999978i	$-0.502096\pi$
$41$	5.76467	−	3.70473i	0.900291	−	0.578582i	0.906876	+	0.421397i	$0.138460\pi$
$42$	−2.63028	−	0.285673i	−0.405862	−	0.0440803i
$43$	−8.51132	−	2.49915i	−1.29796	−	0.381117i	−0.441471	−	0.897275i	$-0.645543\pi$
$43$	−8.51132	−	2.49915i	−1.29796	−	0.381117i	−0.856493	+	0.516159i	$0.827361\pi$
$44$	−3.22478	−	4.52857i	−0.486154	−	0.682708i
$45$	−0.843271	−	1.46059i	−0.125707	−	0.217732i
$46$	−4.06017	+	2.55246i	−0.598639	+	0.376339i
$47$	−2.74488	+	4.75426i	−0.400381	+	0.693481i	−0.993772	−	0.111434i	$-0.964456\pi$
$47$	−2.74488	+	4.75426i	−0.400381	+	0.693481i	0.593391	+	0.804915i	$0.297789\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−2.46048	+	6.55332i	−0.351497	+	0.936189i
$50$	1.41160	+	1.62908i	0.199631	+	0.230386i
$51$	−0.271612	−	5.70184i	−0.0380333	−	0.798418i
$52$	5.53663	+	1.06710i	0.767793	+	0.147980i
$53$	−9.59833	+	3.84259i	−1.31843	+	0.527821i	−0.920911	−	0.389773i	$-0.872554\pi$
$53$	−9.59833	+	3.84259i	−1.31843	+	0.527821i	−0.397521	+	0.917593i	$0.630129\pi$
$54$	0.235759	−	0.971812i	0.0320827	−	0.132247i
$55$	−7.88775	−	5.06915i	−1.06358	−	0.683524i
$56$	−2.05829	−	1.66236i	−0.275050	−	0.222142i
$57$	0.826735	+	1.81030i	0.109504	+	0.239780i
$58$	7.48631	+	0.714856i	0.983001	+	0.0938652i
$59$	7.81457	−	6.14544i	1.01737	−	0.800068i	0.0374173	−	0.999300i	$-0.488087\pi$
$59$	7.81457	−	6.14544i	1.01737	−	0.800068i	0.979953	+	0.199231i	$0.0638445\pi$
$60$	0.0802489	−	1.68463i	0.0103601	−	0.217485i
$61$	−2.74484	+	11.3144i	−0.351440	+	1.44866i	0.472174	+	0.881505i	$0.343469\pi$
$61$	−2.74484	+	11.3144i	−0.351440	+	1.44866i	−0.823614	+	0.567151i	$0.808046\pi$
$62$	−1.34350	+	9.34424i	−0.170625	+	1.18672i
$63$	−2.33570	−	1.24279i	−0.294270	−	0.156576i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	9.33776	−	1.79971i	1.15821	−	0.223226i
$66$	−1.31068	−	5.40271i	−0.161334	−	0.665028i
$67$	−1.09268	+	0.104338i	−0.133492	+	0.0127470i	−0.161588	−	0.986858i	$-0.551662\pi$
$67$	−1.09268	+	0.104338i	−0.133492	+	0.0127470i	0.0280960	+	0.999605i	$0.491056\pi$
$68$	2.85415	−	4.94354i	0.346117	−	0.599492i
$69$	−4.71798	+	0.860606i	−0.567978	+	0.103605i
$70$	−4.26473	−	1.31263i	−0.509733	−	0.156889i
$71$	−1.94744	+	4.26430i	−0.231119	+	0.506079i	−0.989288	−	0.145979i	$-0.953367\pi$
$71$	−1.94744	+	4.26430i	−0.231119	+	0.506079i	0.758169	+	0.652058i	$0.226094\pi$
$72$	0.723734	−	0.690079i	0.0852929	−	0.0813266i
$73$	0.979890	−	2.83121i	0.114687	−	0.331368i	−0.873019	−	0.487686i	$-0.837841\pi$
$73$	0.979890	−	2.83121i	0.114687	−	0.331368i	0.987707	+	0.156318i	$0.0499624\pi$
$74$	1.53452	+	0.791101i	0.178384	+	0.0919636i
$75$	0.705021	+	2.03702i	0.0814088	+	0.235215i
$76$	−0.283227	+	1.96989i	−0.0324884	+	0.225961i
$77$	−14.7076	−	0.190993i	−1.67609	−	0.0217657i
$78$	4.74343	+	3.04842i	0.537088	+	0.345166i
$79$	−6.48718	−	2.59707i	−0.729865	−	0.292194i	−0.0231887	−	0.999731i	$-0.507382\pi$
$79$	−6.48718	−	2.59707i	−0.729865	−	0.292194i	−0.706676	+	0.707537i	$0.749806\pi$
$80$	0.978290	−	1.37382i	0.109376	−	0.153597i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	6.36162	+	2.54681i	0.702524	+	0.281248i
$83$	5.51404	+	3.54366i	0.605244	+	0.388967i	0.807071	−	0.590454i	$-0.201051\pi$
$83$	5.51404	+	3.54366i	0.605244	+	0.388967i	−0.201827	+	0.979421i	$0.564688\pi$
$84$	−1.29301	−	2.30827i	−0.141079	−	0.251853i
$85$	1.37011	−	9.52931i	0.148609	−	1.03360i
$86$	−2.90130	−	8.38276i	−0.312856	−	0.903937i
$87$	6.68437	+	3.44603i	0.716639	+	0.369453i
$88$	1.81831	−	5.25366i	0.193832	−	0.560042i
$89$	−9.67856	+	9.22849i	−1.02593	+	0.978218i	−0.999770	−	0.0214396i	$-0.993175\pi$
$89$	−9.67856	+	9.22849i	−1.02593	+	0.978218i	−0.0261556	+	0.999658i	$0.508327\pi$
$90$	0.700614	−	1.53413i	0.0738513	−	0.161712i
$91$	10.9295	−	10.1536i	1.14573	−	1.06439i
$92$	−4.43430	−	1.82675i	−0.462308	−	0.190451i
$93$	−4.72016	+	8.17557i	−0.489458	+	0.847767i
$94$	−5.46489	+	0.521834i	−0.563661	+	0.0538231i
$95$	0.791315	+	3.26185i	0.0811872	+	0.334658i
$96$	0.981929	−	0.189251i	0.100218	−	0.0193154i
$97$	11.0997	−	7.13333i	1.12700	−	0.724280i	0.162070	−	0.986779i	$-0.448183\pi$
$97$	11.0997	−	7.13333i	1.12700	−	0.724280i	0.964932	+	0.262499i	$0.0845466\pi$
$98$	−6.76540	+	1.79705i	−0.683408	+	0.181530i
$99$	0.791188	−	5.50283i	0.0795174	−	0.553056i
$100$	−0.508197	+	2.09482i	−0.0508197	+	0.209482i
$101$	−0.611109	+	12.8288i	−0.0608076	+	1.27651i	0.737949	+	0.674856i	$0.235794\pi$
$101$	−0.611109	+	12.8288i	−0.0608076	+	1.27651i	−0.798757	+	0.601654i	$0.794509\pi$
$102$	4.48703	−	3.52864i	0.444283	−	0.349388i
$103$	1.92160	+	0.183490i	0.189341	+	0.0180798i	0.189296	−	0.981920i	$-0.439380\pi$
$103$	1.92160	+	0.183490i	0.189341	+	0.0180798i	4.50867e−5		1.00000i	$0.499986\pi$
$104$	2.34233	+	5.12899i	0.229684	+	0.502939i
$105$	−3.47139	−	2.80364i	−0.338773	−	0.273607i
$106$	−8.69766	−	5.58965i	−0.844791	−	0.542914i
$107$	1.90281	−	7.84347i	0.183951	−	0.758257i	−0.802831	−	0.596206i	$-0.796674\pi$
$107$	1.90281	−	7.84347i	0.183951	−	0.758257i	0.986782	−	0.162051i	$-0.0518108\pi$
$108$	0.928368	−	0.371662i	0.0893322	−	0.0357632i
$109$	14.4401	+	2.78310i	1.38311	+	0.266573i	0.825909	−	0.563803i	$-0.190662\pi$
$109$	14.4401	+	2.78310i	1.38311	+	0.266573i	0.557203	+	0.830376i	$0.311874\pi$
$110$	−0.446137	−	9.36557i	−0.0425375	−	0.892972i
$111$	1.13058	+	1.30476i	0.107310	+	0.123842i
$112$	0.160195	−	2.64090i	0.0151370	−	0.249541i
$113$	−1.24261	+	2.72094i	−0.116895	+	0.255965i	−0.959031	−	0.283300i	$-0.908571\pi$
$113$	−1.24261	+	2.72094i	−0.116895	+	0.255965i	0.842136	+	0.539265i	$0.181298\pi$
$114$	−0.995072	+	1.72351i	−0.0931970	+	0.161422i
$115$	−8.08796	−	0.0806671i	−0.754207	−	0.00752225i
$116$	3.76018	+	6.51283i	0.349124	+	0.604701i
$117$	3.27067	+	4.59301i	0.302373	+	0.424624i
$118$	9.53882	+	2.80085i	0.878120	+	0.257839i
$119$	−6.09500	−	13.8183i	−0.558728	−	1.26672i
$120$	1.41881	−	0.911813i	0.129519	−	0.0832368i
$121$	−6.51099	−	18.8123i	−0.591909	−	1.71021i
$122$	−10.8086	+	4.32710i	−0.978562	+	0.391757i
$123$	4.95937	+	4.72875i	0.447172	+	0.426377i
$124$	−8.39090	+	4.32581i	−0.753525	+	0.388469i
$125$	1.71748	+	11.9453i	0.153616	+	1.06842i
$126$	−0.342493	−	2.62349i	−0.0305117	−	0.233719i
$127$	5.48911	+	12.0195i	0.487080	+	1.06656i	0.980456	+	0.196740i	$0.0630355\pi$
$127$	5.48911	+	12.0195i	0.487080	+	1.06656i	−0.493376	+	0.869816i	$0.664237\pi$
$128$	0.928368	+	0.371662i	0.0820569	+	0.0328506i
$129$	0.422082	−	8.86059i	0.0371623	−	0.780132i
$130$	6.88243	+	6.56238i	0.603629	+	0.575559i
$131$	11.4943	+	9.03925i	1.00427	+	0.789763i	0.977726	−	0.209885i	$-0.0673090\pi$
$131$	11.4943	+	9.03925i	1.00427	+	0.789763i	0.0265390	+	0.999648i	$0.491551\pi$
$132$	3.64065	−	4.20153i	0.316878	−	0.365696i
$133$	3.76326	+	3.68274i	0.326316	+	0.319334i
$134$	−0.718809	−	0.829550i	−0.0620956	−	0.0716622i
$135$	1.22061	−	1.16385i	0.105053	−	0.100168i
$136$	5.68246	−	0.542609i	0.487267	−	0.0465284i
$137$	2.82303	+	4.88963i	0.241187	+	0.417749i	0.961053	−	0.276365i	$-0.0891298\pi$
$137$	2.82303	+	4.88963i	0.241187	+	0.417749i	−0.719865	+	0.694114i	$0.755796\pi$
$138$	−3.43773	−	3.34395i	−0.292639	−	0.284656i
$139$	13.9967			1.18718			0.593591	−	0.804767i	$-0.297710\pi$
$139$	13.9967			1.18718			0.593591	+	0.804767i	$0.297710\pi$
$140$	−1.40455	−	4.23535i	−0.118707	−	0.357952i
$141$	−5.26738	−	1.54664i	−0.443593	−	0.130251i
$142$	−4.60322	+	0.887198i	−0.386294	+	0.0744520i
$143$	27.8623	+	14.3640i	2.32996	+	1.20118i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	9.96983	+	7.84036i	0.827949	+	0.651107i
$146$	2.87462	−	0.844066i	0.237906	−	0.0698554i
$147$	−6.94867	−	0.846119i	−0.573117	−	0.0697867i
$148$	0.245698	+	1.70887i	0.0201963	+	0.140468i
$149$	12.5132	+	1.19486i	1.02512	+	0.0978869i	0.594047	−	0.804431i	$-0.297529\pi$
$149$	12.5132	+	1.19486i	1.02512	+	0.0978869i	0.431072	+	0.902318i	$0.358136\pi$
$150$	−1.25036	+	1.75588i	−0.102091	+	0.143367i
$151$	−5.75375	+	4.52480i	−0.468233	+	0.368223i	−0.824221	−	0.566268i	$-0.808387\pi$
$151$	−5.75375	+	4.52480i	−0.468233	+	0.368223i	0.355988	+	0.934491i	$0.384144\pi$
$152$	−1.76891	+	0.911937i	−0.143478	+	0.0739678i
$153$	5.47708	−	1.60822i	0.442796	−	0.130017i
$154$	−8.37567	−	12.0912i	−0.674931	−	0.974341i
$155$	−10.4264	+	12.0327i	−0.837466	+	0.966487i
$156$	0.268292	+	5.63214i	0.0214806	+	0.450932i
$157$	6.19337	−	17.8946i	0.494285	−	1.42814i	−0.371831	−	0.928300i	$-0.621270\pi$
$157$	6.19337	−	17.8946i	0.494285	−	1.42814i	0.866116	−	0.499842i	$-0.166609\pi$
$158$	−1.64742	−	6.79075i	−0.131062	−	0.540243i
$159$	−5.99717	−	8.42184i	−0.475606	−	0.667896i
$160$	1.68654			0.133333
$161$	−10.8290	+	6.61311i	−0.853443	+	0.521186i
$162$	1.00000			0.0785674
$163$	1.89397	+	2.65971i	0.148348	+	0.208325i	0.882062	−	0.471132i	$-0.156155\pi$
$163$	1.89397	+	2.65971i	0.148348	+	0.208325i	−0.733715	+	0.679457i	$0.762215\pi$
$164$	1.61553	+	6.65932i	0.126152	+	0.520005i
$165$	3.06665	−	8.86051i	0.238739	−	0.689790i
$166$	0.311878	+	6.54713i	0.0242064	+	0.508156i
$167$	7.63868	−	8.81550i	0.591099	−	0.682164i	−0.378854	−	0.925456i	$-0.623682\pi$
$167$	7.63868	−	8.81550i	0.591099	−	0.682164i	0.969953	+	0.243292i	$0.0782274\pi$
$168$	1.13024	−	2.39219i	0.0872001	−	0.184561i
$169$	−18.0318	+	5.29461i	−1.38706	+	0.407277i
$170$	8.55708	−	4.41148i	0.656298	−	0.338345i
$171$	−1.56436	+	1.23023i	−0.119629	+	0.0940777i
$172$	5.14548	−	7.22581i	0.392339	−	0.550963i
$173$	6.25407	+	0.597191i	0.475488	+	0.0454036i	0.330049	−	0.943964i	$-0.392935\pi$
$173$	6.25407	+	0.597191i	0.475488	+	0.0454036i	0.145439	+	0.989367i	$0.453541\pi$
$174$	1.07026	+	7.44382i	0.0811362	+	0.564315i
$175$	3.67847	+	4.35827i	0.278066	+	0.329454i
$176$	5.33423	−	1.56627i	0.402082	−	0.118062i
$177$	7.81457	+	6.14544i	0.587379	+	0.461920i
$178$	−13.1314	−	2.53087i	−0.984242	−	0.189697i
$179$	−12.2717	−	6.32648i	−0.917227	−	0.472863i	−0.0660938	−	0.997813i	$-0.521054\pi$
$179$	−12.2717	−	6.32648i	−0.917227	−	0.472863i	−0.851133	+	0.524950i	$0.824084\pi$
$180$	1.65606	−	0.319180i	0.123436	−	0.0237903i
$181$	−13.6968	−	4.02174i	−1.01807	−	0.298933i	−0.270221	−	0.962798i	$-0.587097\pi$
$181$	−13.6968	−	4.02174i	−1.01807	−	0.298933i	−0.747852	+	0.663865i	$0.768915\pi$
$182$	14.6107	+	3.01325i	1.08301	+	0.223357i
$183$	−11.6426			−0.860642
$184$	−1.08412	−	4.67169i	−0.0799226	−	0.344401i
$185$	1.45586	+	2.52162i	0.107037	+	0.185393i
$186$	−9.39758	+	0.897360i	−0.689064	+	0.0657977i
$187$	22.9676	−	21.8996i	1.67956	−	1.60146i
$188$	−3.59502	−	4.14888i	−0.262194	−	0.302588i
$189$	0.657093	−	2.56286i	0.0477965	−	0.186420i
$190$	−2.19801	+	2.53664i	−0.159461	+	0.184027i
$191$	−16.6036	−	13.0572i	−1.20139	−	0.944787i	−0.201994	−	0.979387i	$-0.564742\pi$
$191$	−16.6036	−	13.0572i	−1.20139	−	0.944787i	−0.999401	+	0.0345995i	$0.988984\pi$
$192$	0.723734	+	0.690079i	0.0522310	+	0.0498022i
$193$	−0.981786	+	20.6102i	−0.0706705	+	1.48356i	0.633620	+	0.773644i	$0.281568\pi$
$193$	−0.981786	+	20.6102i	−0.0706705	+	1.48356i	−0.704291	+	0.709912i	$0.748735\pi$
$194$	12.2491	+	4.90380i	0.879434	+	0.352072i
$195$	3.95044	+	8.65025i	0.282897	+	0.619457i
$196$	−5.38815	−	4.46854i	−0.384868	−	0.319181i
$197$	−0.773790	−	5.38183i	−0.0551303	−	0.383440i	−0.998642	−	0.0521000i	$-0.983409\pi$
$197$	−0.773790	−	5.38183i	−0.0551303	−	0.383440i	0.943512	−	0.331340i	$-0.107501\pi$
$198$	4.94141	−	2.54747i	0.351171	−	0.181041i
$199$	−9.62116	−	9.17376i	−0.682026	−	0.650311i	0.267660	−	0.963513i	$-0.413750\pi$
$199$	−9.62116	−	9.17376i	−0.682026	−	0.650311i	−0.949686	+	0.313203i	$0.898598\pi$
$200$	−2.00117	+	0.801148i	−0.141504	+	0.0566497i
$201$	−0.359007	−	1.03728i	−0.0253224	−	0.0731642i
$202$	−10.8045	+	6.94362i	−0.760201	+	0.488551i
$203$	19.7807	+	2.14836i	1.38833	+	0.150786i
$204$	5.47708	+	1.60822i	0.383472	+	0.112598i
$205$	6.70371	+	9.41404i	0.468207	+	0.657505i
$206$	0.965169	+	1.67172i	0.0672465	+	0.116474i
$207$	−1.94865	−	4.38209i	−0.135441	−	0.304577i
$208$	−2.81927	+	4.88311i	−0.195481	+	0.338583i
$209$	−4.59617	+	10.0642i	−0.317924	+	0.696156i
$210$	0.270176	−	4.45398i	0.0186439	−	0.307354i
$211$	4.42004	+	5.10099i	0.304288	+	0.351167i	0.887214	−	0.461358i	$-0.152638\pi$
$211$	4.42004	+	5.10099i	0.304288	+	0.351167i	−0.582926	+	0.812525i	$0.698092\pi$
$212$	−0.491946	−	10.3272i	−0.0337870	−	0.709276i
$213$	−4.60322	−	0.887198i	−0.315408	−	0.0607898i
$214$	7.49284	−	2.99968i	0.512200	−	0.205054i
$215$	3.52712	−	14.5390i	0.240548	−	0.991550i
$216$	0.841254	+	0.540641i	0.0572401	+	0.0367859i
$217$	−3.87529	+	24.6743i	−0.263071	+	1.67500i
$218$	6.10904	+	13.3769i	0.413756	+	0.906000i
$219$	2.98242	+	0.284786i	0.201533	+	0.0192441i
$220$	7.37018	−	5.79598i	0.496898	−	0.390765i
$221$	−1.53149	+	32.1500i	−0.103019	+	2.16264i
$222$	−0.407024	+	1.67777i	−0.0273176	+	0.112605i
$223$	−0.0751460	+	0.522652i	−0.00503215	+	0.0349994i	−0.992183	−	0.124793i	$-0.960173\pi$
$223$	−0.0751460	+	0.522652i	−0.00503215	+	0.0349994i	0.987151	+	0.159792i	$0.0510824\pi$
$224$	2.24413	−	1.40138i	0.149942	−	0.0936336i
$225$	−1.81339	+	1.16539i	−0.120893	+	0.0776929i
$226$	−2.93720	+	0.566099i	−0.195380	+	0.0376564i
$227$	3.70501	+	15.2723i	0.245910	+	1.01366i	0.952138	+	0.305670i	$0.0988804\pi$
$227$	3.70501	+	15.2723i	0.245910	+	1.01366i	−0.706227	+	0.707985i	$0.749604\pi$
$228$	−1.98113	+	0.189175i	−0.131204	+	0.0125284i
$229$	11.2849	−	19.5459i	0.745724	−	1.29163i	−0.204131	−	0.978944i	$-0.565437\pi$
$229$	11.2849	−	19.5459i	0.745724	−	1.29163i	0.949856	−	0.312689i	$-0.101230\pi$
$230$	−4.62577	−	6.63505i	−0.305014	−	0.437502i
$231$	−3.28184	−	14.3380i	−0.215929	−	0.943374i
$232$	−3.12407	+	6.84077i	−0.205105	+	0.449118i
$233$	4.20023	−	4.00491i	0.275166	−	0.262371i	−0.539912	−	0.841722i	$-0.681542\pi$
$233$	4.20023	−	4.00491i	0.275166	−	0.262371i	0.815078	+	0.579351i	$0.196694\pi$
$234$	−1.84418	+	5.32842i	−0.120558	+	0.348329i
$235$	−8.22945	−	4.24258i	−0.536830	−	0.276755i
$236$	3.25155	+	9.39475i	0.211658	+	0.611546i
$237$	0.994457	−	6.91660i	0.0645969	−	0.449281i
$238$	7.72058	−	12.9802i	0.500451	−	0.841383i
$239$	16.1248	+	10.3628i	1.04303	+	0.670313i	0.945734	−	0.324943i	$-0.105345\pi$
$239$	16.1248	+	10.3628i	1.04303	+	0.670313i	0.0972933	+	0.995256i	$0.468982\pi$
$240$	1.56573	+	0.626824i	0.101067	+	0.0404613i
$241$	5.82171	−	8.17545i	0.375009	−	0.526627i	−0.583339	−	0.812229i	$-0.698254\pi$
$241$	5.82171	−	8.17545i	0.375009	−	0.526627i	0.958348	+	0.285602i	$0.0921935\pi$
$242$	11.5473	−	16.2159i	0.742288	−	1.04240i
$243$	0.928368	+	0.371662i	0.0595548	+	0.0238422i
$244$	−9.79434	−	6.29444i	−0.627018	−	0.402960i
$245$	−11.2374	−	3.61910i	−0.717930	−	0.231216i
$246$	−0.975209	+	6.78273i	−0.0621771	+	0.432451i
$247$	−3.67019	−	10.6043i	−0.233528	−	0.674736i
$248$	−8.39090	−	4.32581i	−0.532823	−	0.274689i
$249$	−2.14378	+	6.19406i	−0.135857	+	0.392532i
$250$	−8.73415	+	8.32800i	−0.552396	+	0.526709i
$251$	−4.21495	+	9.22945i	−0.266045	+	0.582558i	−0.994757	−	0.102262i	$-0.967392\pi$
$251$	−4.21495	+	9.22945i	−0.266045	+	0.582558i	0.728712	+	0.684820i	$0.240119\pi$
$252$	1.93837	−	1.80076i	0.122106	−	0.113437i
$253$	−20.7924	−	16.6896i	−1.30721	−	1.04926i
$254$	−6.60678	+	11.4433i	−0.414546	+	0.718015i
$255$	9.58371	−	0.915133i	0.600155	−	0.0573078i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	−0.992612	+	0.191310i	−0.0619174	+	0.0119336i	−0.220116	−	0.975474i	$-0.570644\pi$
$257$	−0.992612	+	0.191310i	−0.0619174	+	0.0119336i	0.158198	+	0.987407i	$0.449431\pi$
$258$	7.46246	−	4.79583i	0.464592	−	0.298575i
$259$	4.03244	+	2.14560i	0.250564	+	0.133321i
$260$	−1.35336	+	9.41282i	−0.0839318	+	0.583758i
$261$	−1.77299	+	7.30838i	−0.109746	+	0.452377i
$262$	−0.695783	+	14.6063i	−0.0429856	+	0.902380i
$263$	3.32709	−	2.61645i	0.205157	−	0.161337i	−0.510294	−	0.860000i	$-0.670463\pi$
$263$	3.32709	−	2.61645i	0.205157	−	0.161337i	0.715451	+	0.698662i	$0.246221\pi$
$264$	5.53425	+	0.528457i	0.340609	+	0.0325243i
$265$	−7.24360	−	15.8613i	−0.444971	−	0.974351i
$266$	−0.816960	+	5.20166i	−0.0500910	+	0.318934i
$267$	−11.2502	−	7.23004i	−0.688499	−	0.442471i
$268$	0.258781	−	1.06671i	0.0158076	−	0.0651597i
$269$	20.0259	−	8.01714i	1.22100	−	0.488814i	0.330502	−	0.943805i	$-0.392782\pi$
$269$	20.0259	−	8.01714i	1.22100	−	0.488814i	0.890496	+	0.454992i	$0.150358\pi$
$270$	1.65606	+	0.319180i	0.100785	+	0.0194247i
$271$	0.214731	+	4.50775i	0.0130440	+	0.273826i	0.995962	+	0.0897804i	$0.0286165\pi$
$271$	0.214731	+	4.50775i	0.0130440	+	0.273826i	−0.982918	+	0.184046i	$0.941080\pi$
$272$	3.73815	+	4.31405i	0.226658	+	0.261578i
$273$	12.4442	+	8.22764i	0.753155	+	0.497959i
$274$	−2.34546	+	5.13583i	−0.141694	+	0.310267i
$275$	−5.99189	+	10.3783i	−0.361324	+	0.625832i
$276$	0.729827	−	4.73997i	0.0439304	−	0.285313i
$277$	−9.08899	−	15.7426i	−0.546104	−	0.945880i	−0.998537	−	0.0540816i	$-0.982777\pi$
$277$	−9.08899	−	15.7426i	−0.546104	−	0.945880i	0.452432	−	0.891799i	$-0.350556\pi$
$278$	8.11887	+	11.4014i	0.486937	+	0.683808i
$279$	−9.05793	−	2.65965i	−0.542284	−	0.159229i
$280$	2.63529	−	3.60086i	0.157489	−	0.215193i
$281$	−12.8811	+	8.27818i	−0.768422	+	0.493835i	−0.865173	−	0.501474i	$-0.832791\pi$
$281$	−12.8811	+	8.27818i	−0.768422	+	0.493835i	0.0967509	+	0.995309i	$0.469155\pi$
$282$	−1.79552	−	5.18782i	−0.106922	−	0.308930i
$283$	4.77128	−	1.91013i	0.283623	−	0.113546i	−0.225489	−	0.974246i	$-0.572398\pi$
$283$	4.77128	−	1.91013i	0.283623	−	0.113546i	0.509112	+	0.860700i	$0.329974\pi$
$284$	−3.39282	−	3.23505i	−0.201327	−	0.191965i
$285$	−2.98334	+	1.53802i	−0.176718	+	0.0911043i
$286$	4.46114	+	31.0279i	0.263793	+	1.83472i
$287$	16.7424	+	6.95621i	0.988270	+	0.410612i
$288$	0.415415	+	0.909632i	0.0244786	+	0.0536006i
$289$	14.4684	+	5.79228i	0.851084	+	0.340723i
$290$	−0.603501	+	12.6690i	−0.0354388	+	0.743952i
$291$	9.54911	+	9.10505i	0.559779	+	0.533748i
$292$	2.35500	+	1.85199i	0.137816	+	0.108380i
$293$	13.6956	−	15.8056i	0.800105	−	0.923371i	−0.198282	−	0.980145i	$-0.563536\pi$
$293$	13.6956	−	15.8056i	0.800105	−	0.923371i	0.998387	+	0.0567742i	$0.0180815\pi$
$294$	−3.34140	−	6.15102i	−0.194874	−	0.358735i
$295$	10.9799	+	12.6715i	0.639275	+	0.737763i
$296$	−1.24948	+	1.19138i	−0.0726247	+	0.0692476i
$297$	5.53425	−	0.528457i	0.321130	−	0.0306642i
$298$	6.28504	+	10.8860i	0.364083	+	0.630610i
$299$	26.9433	−	2.30186i	1.55817	−	0.133120i
$300$	−2.15558			−0.124452
$301$	−7.38749	−	22.2765i	−0.425808	−	1.28400i
$302$	−7.02329	−	2.06222i	−0.404145	−	0.118668i
$303$	−12.6112	+	2.43061i	−0.724495	+	0.139635i
$304$	−1.76891	−	0.911937i	−0.101454	−	0.0523031i
$305$	−19.2808	−	3.71607i	−1.10402	−	0.212782i
$306$	4.48703	+	3.52864i	0.256507	+	0.201719i
$307$	14.8188	−	4.35120i	0.845756	−	0.248336i	0.169984	−	0.985447i	$-0.445629\pi$
$307$	14.8188	−	4.35120i	0.845756	−	0.248336i	0.675772	+	0.737111i	$0.263810\pi$
$308$	4.99088	−	13.8362i	0.284382	−	0.788392i
$309$	0.274716	+	1.91069i	0.0156280	+	0.108695i
$310$	−15.8494	−	1.51344i	−0.900186	−	0.0859573i
$311$	7.56933	−	10.6296i	0.429217	−	0.602751i	−0.542165	−	0.840272i	$-0.682395\pi$
$311$	7.56933	−	10.6296i	0.429217	−	0.602751i	0.971382	+	0.237521i	$0.0763348\pi$
$312$	−4.43218	+	3.48551i	−0.250923	+	0.197328i
$313$	3.55286	−	1.83163i	0.200820	−	0.103530i	−0.354883	−	0.934911i	$-0.615479\pi$
$313$	3.55286	−	1.83163i	0.200820	−	0.103530i	0.555703	+	0.831381i	$0.312449\pi$
$314$	18.1690	−	5.33490i	1.02534	−	0.301066i
$315$	1.90620	−	4.03452i	0.107402	−	0.227319i
$316$	4.57599	−	5.28097i	0.257419	−	0.297078i
$317$	−0.908764	−	19.0773i	−0.0510413	−	1.07149i	−0.868559	−	0.495585i	$-0.834954\pi$
$317$	−0.908764	−	19.0773i	−0.0510413	−	1.07149i	0.817518	−	0.575903i	$-0.195349\pi$
$318$	3.38153	−	9.77030i	0.189627	−	0.547891i
$319$	9.85682	+	40.6304i	0.551876	+	2.27486i
$320$	0.978290	+	1.37382i	0.0546881	+	0.0767986i
$321$	8.07098			0.450478
$322$	−11.6683	−	4.98505i	−0.650249	−	0.277806i
$323$	−11.3604			−0.632107
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	−2.86548	−	11.8117i	−0.158948	−	0.655195i
$326$	−1.06793	+	3.08557i	−0.0591470	+	0.170894i
$327$	0.699734	+	14.6892i	0.0386954	+	0.812315i
$328$	−4.48742	+	5.17876i	−0.247776	+	0.285949i
$329$	−14.4755	+	1.19278i	−0.798058	+	0.0657601i
$330$	8.99639	−	2.64158i	0.495235	−	0.145414i
$331$	26.9493	−	13.8933i	1.48127	−	0.763647i	0.487292	−	0.873239i	$-0.337985\pi$
$331$	26.9493	−	13.8933i	1.48127	−	0.763647i	0.993977	+	0.109592i	$0.0349544\pi$
$332$	−5.15222	+	4.05175i	−0.282765	+	0.222369i
$333$	−1.00143	+	1.40632i	−0.0548782	+	0.0770657i
$334$	11.6118	+	1.10879i	0.635368	+	0.0606702i
$335$	−0.263458	−	1.83239i	−0.0143943	−	0.100114i
$336$	2.60422	−	0.466935i	0.142072	−	0.0254734i
$337$	−26.1566	+	7.68028i	−1.42484	+	0.418371i	−0.901139	−	0.433530i	$-0.857268\pi$
$337$	−26.1566	+	7.68028i	−1.42484	+	0.418371i	−0.523703	+	0.851901i	$0.675450\pi$
$338$	−14.7723	−	11.6171i	−0.803508	−	0.631886i
$339$	−2.93720	−	0.566099i	−0.159527	−	0.0307463i
$340$	8.55708	+	4.41148i	0.464073	+	0.239246i
$341$	−51.5343	+	9.93243i	−2.79074	+	0.537871i
$342$	−1.90953	−	0.560688i	−0.103255	−	0.0303185i
$343$	−17.9598	+	4.52173i	−0.969737	+	0.244150i
$344$	8.87064			0.478273
$345$	−1.82842	−	7.87900i	−0.0984386	−	0.424191i
$346$	3.14126	+	5.44082i	0.168875	+	0.292500i
$347$	−7.07204	+	0.675298i	−0.379647	+	0.0362519i	−0.283135	−	0.959080i	$-0.591375\pi$
$347$	−7.07204	+	0.675298i	−0.379647	+	0.0362519i	−0.0965116	+	0.995332i	$0.530768\pi$
$348$	−5.44275	+	5.18965i	−0.291762	+	0.278194i
$349$	11.5126	+	13.2862i	0.616253	+	0.711194i	0.974991	−	0.222244i	$-0.0713382\pi$
$349$	11.5126	+	13.2862i	0.616253	+	0.711194i	−0.358738	+	0.933438i	$0.616793\pi$
$350$	−1.41642	+	5.52444i	−0.0757107	+	0.295294i
$351$	−3.69245	+	4.26132i	−0.197089	+	0.227452i
$352$	4.37000	+	3.43661i	0.232922	+	0.183172i
$353$	−17.1674	−	16.3691i	−0.913730	−	0.871240i	0.0783402	−	0.996927i	$-0.475038\pi$
$353$	−17.1674	−	16.3691i	−0.913730	−	0.871240i	−0.992070	+	0.125687i	$0.959886\pi$
$354$	−0.473037	+	9.93026i	−0.0251416	+	0.527788i
$355$	−7.34005	−	2.93851i	−0.389569	−	0.155960i
$356$	−5.55538	−	12.1646i	−0.294435	−	0.644722i
$357$	11.9918	−	9.18097i	0.634673	−	0.485909i
$358$	−1.96486	−	13.6659i	−0.103846	−	0.722266i
$359$	20.7391	−	10.6918i	1.09457	−	0.564289i	0.186222	−	0.982508i	$-0.440376\pi$
$359$	20.7391	−	10.6918i	1.09457	−	0.564289i	0.908346	+	0.418219i	$0.137345\pi$
$360$	1.22061	+	1.16385i	0.0643316	+	0.0613401i
$361$	−13.9620	+	5.58955i	−0.734844	+	0.294187i
$362$	−4.66890	−	13.4899i	−0.245392	−	0.709013i
$363$	16.7470	−	10.7626i	0.878988	−	0.564891i
$364$	6.02049	+	13.6494i	0.315560	+	0.715420i
$365$	4.84817	+	1.42355i	0.253765	+	0.0745121i
$366$	−6.75334	−	9.48374i	−0.353003	−	0.495723i
$367$	1.76094	+	3.05005i	0.0919206	+	0.159211i	0.908319	−	0.418278i	$-0.137366\pi$
$367$	1.76094	+	3.05005i	0.0919206	+	0.159211i	−0.816399	+	0.577489i	$0.804033\pi$
$368$	3.17659	−	3.59295i	0.165591	−	0.187295i
$369$	−3.42624	+	5.93442i	−0.178363	+	0.308934i
$370$	−1.20957	+	2.64859i	−0.0628825	+	0.137693i
$371$	−22.8179	−	15.0864i	−1.18464	−	0.783246i
$372$	−6.18210	−	7.13452i	−0.320527	−	0.369908i
$373$	0.0164686	+	0.345718i	0.000852710	+	0.0179006i	0.999254	−	0.0386297i	$-0.0122993\pi$
$373$	0.0164686	+	0.345718i	0.000852710	+	0.0179006i	−0.998401	+	0.0565303i	$0.981996\pi$
$374$	31.1614	+	6.00587i	1.61132	+	0.310556i
$375$	−11.2037	+	4.48529i	−0.578557	+	0.231619i
$376$	1.29426	−	5.33500i	0.0667463	−	0.275132i
$377$	−35.6724	−	22.9252i	−1.83722	−	1.18071i
$378$	2.46879	−	0.951350i	0.126981	−	0.0489321i
$379$	0.566103	+	1.23959i	0.0290788	+	0.0636736i	0.923614	−	0.383324i	$-0.125221\pi$
$379$	0.566103	+	1.23959i	0.0290788	+	0.0636736i	−0.894535	+	0.446997i	$0.852493\pi$
$380$	−3.34126	−	0.319052i	−0.171403	−	0.0163670i
$381$	−10.3866	+	8.16808i	−0.532120	+	0.418464i
$382$	1.00506	−	21.0988i	0.0514234	−	1.07951i
$383$	−1.76874	+	7.29085i	−0.0903784	+	0.372545i	−0.998982	−	0.0451151i	$-0.985635\pi$
$383$	−1.76874	+	7.29085i	−0.0903784	+	0.372545i	0.908603	+	0.417660i	$0.137150\pi$
$384$	−0.142315	+	0.989821i	−0.00726247	+	0.0505116i
$385$	−0.858515	−	24.7922i	−0.0437540	−	1.26353i
$386$	−17.3581	+	11.1554i	−0.883503	+	0.567793i
$387$	8.71034	−	1.67878i	0.442771	−	0.0853372i
$388$	3.11066	+	12.8223i	0.157920	+	0.650953i
$389$	27.3125	−	2.60803i	1.38480	−	0.132232i	0.624104	−	0.781341i	$-0.285464\pi$
$389$	27.3125	−	2.60803i	1.38480	−	0.132232i	0.760696	+	0.649109i	$0.224858\pi$
$390$	−4.75481	+	8.23557i	−0.240769	+	0.417024i
$391$	6.71917	−	26.5387i	0.339803	−	1.34212i
$392$	0.514529	−	6.98106i	0.0259876	−	0.352597i
$393$	−6.07455	+	13.3014i	−0.306421	+	0.670968i
$394$	3.93507	−	3.75208i	0.198246	−	0.189027i
$395$	3.85452	−	11.1369i	0.193942	−	0.560359i
$396$	4.94141	+	2.54747i	0.248315	+	0.128015i
$397$	0.791286	+	2.28627i	0.0397135	+	0.114745i	0.963114	−	0.269092i	$-0.0867237\pi$
$397$	0.791286	+	2.28627i	0.0397135	+	0.114745i	−0.923401	+	0.383837i	$0.874602\pi$
$398$	1.89190	−	13.1585i	0.0948325	−	0.659575i
$399$	−2.69170	+	4.52542i	−0.134754	+	0.226554i
$400$	−1.81339	−	1.16539i	−0.0906694	−	0.0582697i
$401$	−9.45486	−	3.78515i	−0.472153	−	0.189022i	0.123368	−	0.992361i	$-0.460630\pi$
$401$	−9.45486	−	3.78515i	−0.472153	−	0.189022i	−0.595522	+	0.803339i	$0.703055\pi$
$402$	0.636700	−	0.894121i	0.0317557	−	0.0445947i
$403$	30.8762	−	43.3595i	1.53805	−	2.15989i
$404$	−11.9233	−	4.77338i	−0.593207	−	0.237484i
$405$	1.41881	+	0.911813i	0.0705012	+	0.0453084i
$406$	9.72392	+	17.3591i	0.482590	+	0.861515i
$407$	−1.36594	+	9.50031i	−0.0677071	+	0.470913i
$408$	1.86701	+	5.39436i	0.0924305	+	0.267060i
$409$	4.83334	+	2.49176i	0.238993	+	0.123210i	0.573563	−	0.819161i	$-0.305561\pi$
$409$	4.83334	+	2.49176i	0.238993	+	0.123210i	−0.334570	+	0.942371i	$0.608591\pi$
$410$	−3.77992	+	10.9214i	−0.186677	+	0.539368i
$411$	−4.08624	+	3.89622i	−0.201559	+	0.192187i
$412$	−0.801891	+	1.75590i	−0.0395064	+	0.0865068i
$413$	25.1390	+	7.73744i	1.23701	+	0.380734i
$414$	2.43922	−	4.12919i	0.119881	−	0.202939i
$415$	−5.52726	+	9.57349i	−0.271322	+	0.469944i
$416$	−5.61300	+	0.535976i	−0.275200	+	0.0262784i
$417$	3.29984	+	13.6021i	0.161594	+	0.666099i
$418$	−10.8641	+	2.09388i	−0.531381	+	0.102415i
$419$	−16.7776	+	10.7823i	−0.819640	+	0.526750i	−0.881970	−	0.471305i	$-0.843783\pi$
$419$	−16.7776	+	10.7823i	−0.819640	+	0.526750i	0.0623306	+	0.998056i	$0.480147\pi$
$420$	3.78482	−	2.36348i	0.184680	−	0.115326i
$421$	4.98188	−	34.6498i	0.242802	−	1.68873i	−0.395123	−	0.918628i	$-0.629298\pi$
$421$	4.98188	−	34.6498i	0.242802	−	1.68873i	0.637925	−	0.770098i	$-0.279793\pi$
$422$	−1.59127	+	6.55932i	−0.0774620	+	0.319303i
$423$	0.261213	−	5.48353i	0.0127006	−	0.266619i
$424$	8.12695	−	6.39110i	0.394679	−	0.310379i
$425$	−12.2490	−	1.16964i	−0.594164	−	0.0567357i
$426$	−1.94744	−	4.26430i	−0.0943538	−	0.206606i
$427$	−28.7430	+	11.0761i	−1.39097	+	0.536012i
$428$	6.78974	+	4.36350i	0.328194	+	0.210918i
$429$	−7.39033	+	30.4633i	−0.356808	+	1.47078i
$430$	13.8890	−	5.56033i	0.669789	−	0.268143i
$431$	−5.09431	−	0.981849i	−0.245384	−	0.0472940i	0.0650758	−	0.997880i	$-0.479271\pi$
$431$	−5.09431	−	0.981849i	−0.245384	−	0.0472940i	−0.310460	+	0.950586i	$0.600483\pi$
$432$	0.0475819	+	0.998867i	0.00228929	+	0.0480580i
$433$	11.0946	+	12.8039i	0.533174	+	0.615315i	0.956880	−	0.290484i	$-0.0938164\pi$
$433$	11.0946	+	12.8039i	0.533174	+	0.615315i	−0.423706	+	0.905800i	$0.639271\pi$
$434$	−22.3470	+	11.1558i	−1.07269	+	0.535495i
$435$	−5.26888	+	11.5372i	−0.252623	+	0.553168i
$436$	−7.35294	+	12.7357i	−0.352142	+	0.609927i
$437$	1.26402	+	9.46032i	0.0604664	+	0.452549i
$438$	1.49799	+	2.59460i	0.0715768	+	0.123975i
$439$	−4.92989	−	6.92306i	−0.235291	−	0.330420i	0.680001	−	0.733211i	$-0.261979\pi$
$439$	−4.92989	−	6.92306i	−0.235291	−	0.330420i	−0.915292	+	0.402792i	$0.868040\pi$
$440$	8.99639	+	2.64158i	0.428886	+	0.125932i
$441$	−0.815944	−	6.95228i	−0.0388545	−	0.331061i
$442$	−27.0770	+	17.4013i	−1.28792	+	0.827697i
$443$	−5.33533	−	15.4154i	−0.253489	−	0.732410i	−0.997905	−	0.0646932i	$-0.979393\pi$
$443$	−5.33533	−	15.4154i	−0.253489	−	0.732410i	0.744416	−	0.667716i	$-0.232728\pi$
$444$	−1.60277	+	0.641653i	−0.0760642	+	0.0304515i
$445$	−16.3233	−	15.5642i	−0.773798	−	0.737815i
$446$	−0.469329	+	0.241956i	−0.0222234	+	0.0114569i
$447$	1.78891	+	12.4421i	0.0846125	+	0.588493i
$448$	2.44326	+	1.01514i	0.115433	+	0.0479607i
$449$	3.44353	+	7.54027i	0.162510	+	0.355847i	0.973316	−	0.229467i	$-0.0736983\pi$
$449$	3.44353	+	7.54027i	0.162510	+	0.355847i	−0.810806	+	0.585315i	$0.800971\pi$
$450$	−2.00117	−	0.801148i	−0.0943361	−	0.0377665i
$451$	−1.81267	+	38.0527i	−0.0853554	+	1.79183i
$452$	−2.16487	−	2.06420i	−0.101827	−	0.0970920i
$453$	−5.75375	−	4.52480i	−0.270335	−	0.212594i
$454$	−10.2913	+	11.8768i	−0.482994	+	0.557405i
$455$	17.9822	+	17.5974i	0.843019	+	0.824980i
$456$	−1.30327	−	1.50405i	−0.0610311	−	0.0704336i
$457$	−25.7401	+	24.5431i	−1.20407	+	1.14808i	−0.219037	+	0.975717i	$0.570291\pi$
$457$	−25.7401	+	24.5431i	−1.20407	+	1.14808i	−0.985034	+	0.172362i	$0.944860\pi$
$458$	22.4675	−	2.14539i	1.04984	−	0.100247i
$459$	2.85415	+	4.94354i	0.133221	+	0.230745i
$460$	2.72154	−	7.61675i	0.126893	−	0.355133i
$461$	6.53126			0.304191			0.152096	−	0.988366i	$-0.451398\pi$
$461$	6.53126			0.304191			0.152096	+	0.988366i	$0.451398\pi$
$462$	9.77578	−	10.9902i	0.454810	−	0.511310i
$463$	−15.5884	−	4.57716i	−0.724453	−	0.212719i	−0.101342	−	0.994852i	$-0.532314\pi$
$463$	−15.5884	−	4.57716i	−0.724453	−	0.212719i	−0.623111	+	0.782133i	$0.714132\pi$
$464$	−7.38446	+	1.42324i	−0.342815	+	0.0660722i
$465$	−14.1516	−	7.29566i	−0.656265	−	0.338328i
$466$	5.69868	+	1.09833i	0.263986	+	0.0508792i
$467$	−5.55702	−	4.37009i	−0.257148	−	0.202224i	0.481259	−	0.876578i	$-0.340180\pi$
$467$	−5.55702	−	4.37009i	−0.257148	−	0.202224i	−0.738408	+	0.674355i	$0.764422\pi$
$468$	−5.41013	+	1.58856i	−0.250083	+	0.0734311i
$469$	−1.87313	−	2.21929i	−0.0864931	−	0.102477i
$470$	−1.31765	−	9.16445i	−0.0607786	−	0.422725i
$471$	18.8503	+	1.79999i	0.868576	+	0.0829390i
$472$	−5.76665	+	8.09813i	−0.265432	+	0.372746i
$473$	38.7647	−	30.4849i	1.78240	−	1.40170i
$474$	6.21094	−	3.20196i	0.285278	−	0.147071i
$475$	4.11614	−	1.20861i	0.188861	−	0.0554547i
$476$	15.0518	−	1.24027i	0.689896	−	0.0568476i
$477$	6.77056	−	7.81364i	0.310003	−	0.357762i
$478$	0.912031	+	19.1459i	0.0417153	+	0.875712i
$479$	9.45340	−	27.3138i	0.431937	−	1.24800i	−0.493715	−	0.869624i	$-0.664361\pi$
$479$	9.45340	−	27.3138i	0.431937	−	1.24800i	0.925652	−	0.378376i	$-0.123517\pi$
$480$	0.397617	+	1.63900i	0.0181487	+	0.0748098i
$481$	−5.64661	−	7.92956i	−0.257463	−	0.361557i
$482$	10.0364			0.457148
$483$	−8.97972	−	8.96463i	−0.408592	−	0.407905i
$484$	19.9072			0.904871
$485$	12.9078	+	18.1264i	0.586112	+	0.823079i
$486$	0.235759	+	0.971812i	0.0106942	+	0.0440823i
$487$	0.171713	−	0.496132i	0.00778106	−	0.0224819i	−0.941043	−	0.338286i	$-0.890153\pi$
$487$	0.171713	−	0.496132i	0.00778106	−	0.0224819i	0.948824	+	0.315804i	$0.102274\pi$
$488$	−0.553975	−	11.6294i	−0.0250773	−	0.526437i
$489$	−2.13822	+	2.46764i	−0.0966937	+	0.111590i
$490$	−3.57028	−	11.2530i	−0.161289	−	0.508358i
$491$	26.6589	−	7.82777i	1.20310	−	0.353262i	0.382063	−	0.924136i	$-0.375214\pi$
$491$	26.6589	−	7.82777i	1.20310	−	0.353262i	0.821038	+	0.570874i	$0.193396\pi$
$492$	−6.09073	+	3.13999i	−0.274591	+	0.141562i
$493$	−33.7441	+	26.5367i	−1.51976	+	1.19515i
$494$	6.50910	−	9.14075i	0.292858	−	0.411262i
$495$	9.33374	+	0.891264i	0.419520	+	0.0400593i
$496$	−1.34350	−	9.34424i	−0.0603249	−	0.419569i
$497$	−12.2084	+	2.18896i	−0.547623	+	0.0981885i
$498$	−6.28904	+	1.84663i	−0.281819	+	0.0827495i
$499$	7.01522	+	5.51683i	0.314044	+	0.246967i	0.762722	−	0.646726i	$-0.223862\pi$
$499$	7.01522	+	5.51683i	0.314044	+	0.246967i	−0.448678	+	0.893694i	$0.648105\pi$
$500$	−11.8501	−	2.28392i	−0.529952	−	0.102140i
$501$	10.3679	+	5.34502i	0.463203	+	0.238798i
$502$	−9.96300	+	1.92021i	−0.444670	+	0.0857032i
$503$	0.201544	+	0.0591786i	0.00898640	+	0.00263864i	0.286223	−	0.958163i	$-0.407600\pi$
$503$	0.201544	+	0.0591786i	0.00898640	+	0.00263864i	−0.277236	+	0.960802i	$0.589418\pi$
$504$	2.59122	+	0.534404i	0.115422	+	0.0238042i
$505$	−21.6608			−0.963892
$506$	1.53417	−	26.6179i	0.0682023	−	1.18331i
$507$	−9.39651	−	16.2752i	−0.417314	−	0.722809i
$508$	−13.1537	+	1.25603i	−0.583603	+	0.0557273i
$509$	−17.9313	+	17.0975i	−0.794791	+	0.757832i	−0.974138	−	0.225954i	$-0.927450\pi$
$509$	−17.9313	+	17.0975i	−0.794791	+	0.757832i	0.179347	+	0.983786i	$0.442602\pi$
$510$	6.30454	+	7.27583i	0.279170	+	0.322179i
$511$	7.63390	−	2.13424i	0.337704	−	0.0944134i
$512$	−0.654861	+	0.755750i	−0.0289410	+	0.0333997i
$513$	−1.56436	−	1.23023i	−0.0690681	−	0.0543158i
$514$	−0.731608	−	0.697587i	−0.0322699	−	0.0307692i
$515$	−0.154907	+	3.25191i	−0.00682604	+	0.143296i
$516$	8.23522	+	3.29688i	0.362535	+	0.145137i
$517$	−12.6784	−	27.7618i	−0.557595	−	1.22096i
$518$	0.591293	+	4.52930i	0.0259799	+	0.199006i
$519$	0.894095	+	6.21857i	0.0392464	+	0.272965i
$520$	−8.45248	+	4.35756i	−0.370666	+	0.191092i
$521$	27.5440	+	26.2631i	1.20672	+	1.15061i	0.984458	+	0.175622i	$0.0561936\pi$
$521$	27.5440	+	26.2631i	1.20672	+	1.15061i	0.222265	+	0.974986i	$0.428655\pi$
$522$	−6.98167	+	2.79504i	−0.305579	+	0.122335i
$523$	−7.42678	−	21.4583i	−0.324750	−	0.938305i	−0.982694	−	0.185237i	$-0.940695\pi$
$523$	−7.42678	−	21.4583i	−0.324750	−	0.938305i	0.657943	−	0.753067i	$-0.271427\pi$
$524$	−12.3015	+	7.90571i	−0.537395	+	0.345363i
$525$	−3.36818	+	4.60228i	−0.147000	+	0.200860i
$526$	4.06120	+	1.19248i	0.177077	+	0.0519945i
$527$	−31.2583	−	43.8961i	−1.36163	−	1.91215i
$528$	2.77971	+	4.81460i	0.120971	+	0.209529i
$529$	−22.8477	−	2.64252i	−0.993378	−	0.114892i
$530$	8.71851	−	15.1009i	0.378708	−	0.655942i
$531$	−4.12986	+	9.04313i	−0.179221	+	0.392438i
$532$	−4.71103	+	2.35178i	−0.204249	+	0.101963i
$533$	−25.3025	−	29.2006i	−1.09597	−	1.26482i
$534$	−0.636317	−	13.3579i	−0.0275362	−	0.578055i
$535$	13.3661	+	2.57610i	0.577865	+	0.111374i
$536$	1.01902	−	0.407956i	0.0440152	−	0.0176210i
$537$	3.25499	−	13.4173i	0.140463	−	0.578998i
$538$	18.1467	+	11.6622i	0.782360	+	0.502792i
$539$	−21.7427	−	32.2755i	−0.936523	−	1.39020i
$540$	0.700614	+	1.53413i	0.0301496	+	0.0660185i
$541$	−30.4592	−	2.90850i	−1.30954	−	0.125046i	−0.583171	−	0.812349i	$-0.698188\pi$
$541$	−30.4592	−	2.90850i	−1.30954	−	0.125046i	−0.726371	+	0.687303i	$0.758794\pi$
$542$	−3.54735	+	2.78967i	−0.152372	+	0.119826i
$543$	0.679232	−	14.2588i	0.0291487	−	0.611906i
$544$	−1.34578	+	5.54740i	−0.0577001	+	0.237843i
$545$	−3.52970	+	24.5496i	−0.151196	+	1.05159i
$546$	0.516282	+	14.9092i	0.0220949	+	0.638055i
$547$	−15.5029	+	9.96309i	−0.662855	+	0.425991i	−0.828343	−	0.560221i	$-0.810716\pi$
$547$	−15.5029	+	9.96309i	−0.662855	+	0.425991i	0.165488	+	0.986212i	$0.447080\pi$
$548$	−5.54402	+	1.06852i	−0.236829	+	0.0456450i
$549$	−2.74484	−	11.3144i	−0.117147	−	0.482885i
$550$	−11.9295	+	1.13913i	−0.508676	+	0.0485727i
$551$	7.48330	−	12.9615i	0.318799	−	0.552177i
$552$	4.28441	−	2.15495i	0.182357	−	0.0917210i
$553$	−4.12500	−	18.0217i	−0.175413	−	0.766362i
$554$	7.55140	−	16.5353i	0.320828	−	0.702516i
$555$	−2.10730	+	2.00931i	−0.0894501	+	0.0852905i
$556$	−4.57786	+	13.2269i	−0.194145	+	0.560944i
$557$	−26.4299	−	13.6256i	−1.11987	−	0.577334i	−0.204067	−	0.978957i	$-0.565416\pi$
$557$	−26.4299	−	13.6256i	−1.11987	−	0.577334i	−0.915805	+	0.401623i	$0.868446\pi$
$558$	−3.08763	−	8.92112i	−0.130710	−	0.377661i
$559$	−7.11822	+	49.5083i	−0.301068	+	2.09398i
$560$	4.46179	+	0.0579410i	0.188545	+	0.00244845i
$561$	26.6971	+	17.1572i	1.12715	+	0.724377i
$562$	−14.2150	−	5.69082i	−0.599623	−	0.240053i
$563$	−5.98654	+	8.40693i	−0.252303	+	0.354310i	−0.921230	−	0.389018i	$-0.872814\pi$
$563$	−5.98654	+	8.40693i	−0.252303	+	0.354310i	0.668927	+	0.743328i	$0.266754\pi$
$564$	3.18437	−	4.47182i	0.134086	−	0.188298i
$565$	−4.68350	−	1.87499i	−0.197036	−	0.0788815i
$566$	4.32356	+	2.77859i	0.181733	+	0.116793i
$567$	2.64553	+	0.0343549i	0.111102	+	0.00144277i
$568$	0.667163	−	4.64022i	0.0279935	−	0.194699i
$569$	−1.89953	−	5.48832i	−0.0796323	−	0.230082i	0.898156	−	0.439677i	$-0.144907\pi$
$569$	−1.89953	−	5.48832i	−0.0796323	−	0.230082i	−0.977788	+	0.209594i	$0.932786\pi$
$570$	−2.98334	−	1.53802i	−0.124958	−	0.0644205i
$571$	11.5506	−	33.3731i	0.483376	−	1.39662i	−0.395013	−	0.918675i	$-0.629260\pi$
$571$	11.5506	−	33.3731i	0.483376	−	1.39662i	0.878389	−	0.477947i	$-0.158619\pi$
$572$	−22.6869	+	21.6319i	−0.948585	+	0.904474i
$573$	8.77471	−	19.2139i	0.366569	−	0.802674i
$574$	4.04516	+	17.6729i	0.168842	+	0.737653i
$575$	0.388883	+	10.3305i	0.0162176	+	0.430811i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	30.6360	−	2.92538i	1.27539	−	0.121785i	0.564704	−	0.825293i	$-0.308990\pi$
$577$	30.6360	−	2.92538i	1.27539	−	0.121785i	0.710687	+	0.703508i	$0.248384\pi$
$578$	3.67426	+	15.1455i	0.152829	+	0.629969i
$579$	−20.2607	+	3.90493i	−0.842006	+	0.162283i
$580$	−10.6700	+	6.85717i	−0.443046	+	0.284728i
$581$	0.600156	+	17.3313i	0.0248987	+	0.719024i
$582$	−1.87773	+	13.0599i	−0.0778346	+	0.541351i
$583$	13.5511	−	55.8582i	0.561228	−	2.31341i
$584$	−0.142555	+	2.99259i	−0.00589895	+	0.123834i
$585$	−7.47506	+	5.87845i	−0.309056	+	0.243044i
$586$	20.8191	+	1.98798i	0.860027	+	0.0821227i
$587$	−17.2490	−	37.7701i	−0.711943	−	1.55894i	−0.824862	−	0.565334i	$-0.808747\pi$
$587$	−17.2490	−	37.7701i	−0.711943	−	1.55894i	0.112918	−	0.993604i	$-0.463980\pi$
$588$	3.07227	−	6.28977i	0.126698	−	0.259386i
$589$	15.8051	+	10.1573i	0.651240	+	0.418526i
$590$	−3.95292	+	16.2942i	−0.162739	+	0.670820i
$591$	5.04770	−	2.02079i	0.207635	−	0.0831243i
$592$	−1.69524	−	0.326731i	−0.0696740	−	0.0134286i
$593$	0.954904	+	20.0459i	0.0392132	+	0.823186i	0.929731	+	0.368239i	$0.120039\pi$
$593$	0.954904	+	20.0459i	0.0392132	+	0.823186i	−0.890518	+	0.454948i	$0.849658\pi$
$594$	3.64065	+	4.20153i	0.149378	+	0.172391i
$595$	22.7896	−	11.3767i	0.934281	−	0.466400i
$596$	−5.22180	+	11.4341i	−0.213893	+	0.468361i
$597$	6.64689	−	11.5128i	0.272039	−	0.471186i
$598$	17.5037	+	20.6122i	0.715779	+	0.842894i
$599$	−10.2990	−	17.8384i	−0.420806	−	0.728857i	0.575213	−	0.818004i	$-0.304919\pi$
$599$	−10.2990	−	17.8384i	−0.420806	−	0.728857i	−0.996018	+	0.0891471i	$0.971586\pi$
$600$	−1.25036	−	1.75588i	−0.0510457	−	0.0716836i
$601$	3.01881	+	0.886403i	0.123140	+	0.0361571i	0.342722	−	0.939437i	$-0.388651\pi$
$601$	3.01881	+	0.886403i	0.123140	+	0.0361571i	−0.219582	+	0.975594i	$0.570469\pi$
$602$	13.8607	−	18.9393i	0.564922	−	0.771909i
$603$	0.923403	−	0.593435i	0.0376039	−	0.0241666i
$604$	−2.39407	−	6.91721i	−0.0974134	−	0.281457i
$605$	31.1693	−	12.4783i	1.26721	−	0.507314i
$606$	−9.29514	−	8.86290i	−0.377589	−	0.360031i
$607$	−19.2243	+	9.91082i	−0.780291	+	0.402268i	−0.801869	−	0.597499i	$-0.796161\pi$
$607$	−19.2243	+	9.91082i	−0.780291	+	0.402268i	0.0215788	+	0.999767i	$0.493131\pi$
$608$	−0.283227	−	1.96989i	−0.0114864	−	0.0798895i
$609$	2.57567	+	19.7296i	0.104371	+	0.799484i
$610$	−8.15694	−	17.8612i	−0.330265	−	0.723179i
$611$	28.7368	+	11.5045i	1.16257	+	0.465422i
$612$	−0.271612	+	5.70184i	−0.0109793	+	0.230483i
$613$	29.3867	+	28.0202i	1.18692	+	1.13172i	0.988439	+	0.151620i	$0.0484490\pi$
$613$	29.3867	+	28.0202i	1.18692	+	1.13172i	0.198480	+	0.980105i	$0.436400\pi$
$614$	12.1402	+	9.54712i	0.489937	+	0.385291i
$615$	−7.56822	+	8.73419i	−0.305180	+	0.352196i
$616$	14.1657	−	3.96035i	0.570750	−	0.159567i
$617$	−1.65161	−	1.90606i	−0.0664912	−	0.0767350i	0.721529	−	0.692384i	$-0.243439\pi$
$617$	−1.65161	−	1.90606i	−0.0664912	−	0.0767350i	−0.788021	+	0.615649i	$0.788894\pi$
$618$	−1.39705	+	1.33209i	−0.0561976	+	0.0535843i
$619$	−4.65934	+	0.444913i	−0.187275	+	0.0178826i	−0.188272	−	0.982117i	$-0.560289\pi$
$619$	−4.65934	+	0.444913i	−0.187275	+	0.0178826i	0.000997170		1.00000i	$0.499683\pi$
$620$	−7.96075	−	13.7884i	−0.319711	−	0.553757i
$621$	3.79916	−	2.92684i	0.152455	−	0.117450i
$622$	13.0493			0.523228
$623$	−34.6526	−	7.14663i	−1.38833	−	0.286324i
$624$	−5.41013	−	1.58856i	−0.216579	−	0.0635932i
$625$	−9.40254	+	1.81219i	−0.376102	+	0.0724876i
$626$	3.55286	+	1.83163i	0.142001	+	0.0732065i
$627$	−10.8641	−	2.09388i	−0.433871	−	0.0836217i
$628$	14.8847	+	11.7055i	0.593966	+	0.467100i
$629$	−9.45585	+	2.77649i	−0.377030	+	0.110706i
$630$	4.39213	−	0.787506i	0.174987	−	0.0313750i
$631$	4.31029	+	29.9787i	0.171590	+	1.19343i	0.875526	+	0.483170i	$0.160515\pi$
$631$	4.31029	+	29.9787i	0.171590	+	1.19343i	−0.703936	+	0.710263i	$0.748576\pi$
$632$	6.95608	+	0.664225i	0.276698	+	0.0264215i
$633$	−3.91514	+	5.49805i	−0.155613	+	0.218528i
$634$	15.0128	−	11.8062i	0.596234	−	0.468883i
$635$	−19.8079	+	10.2117i	−0.786052	+	0.405238i
$636$	9.92013	−	2.91281i	0.393359	−	0.115501i
$637$	38.5494	+	8.47359i	1.52738	+	0.335736i
$638$	−27.3790	+	31.5970i	−1.08394	+	1.25094i
$639$	−0.223061	−	4.68263i	−0.00882416	−	0.185242i
$640$	−0.551614	+	1.59378i	−0.0218044	+	0.0629998i
$641$	−7.63285	−	31.4630i	−0.301479	−	1.24271i	−0.897956	−	0.440085i	$-0.854948\pi$
$641$	−7.63285	−	31.4630i	−0.301479	−	1.24271i	0.596477	−	0.802630i	$-0.296567\pi$
$642$	4.68163	+	6.57443i	0.184769	+	0.259472i
$643$	−2.52839			−0.0997098			−0.0498549	−	0.998756i	$-0.515876\pi$
$643$	−2.52839			−0.0997098			−0.0498549	+	0.998756i	$0.515876\pi$
$644$	−2.70758	−	12.3963i	−0.106694	−	0.488484i
$645$	14.9607			0.589077
$646$	−6.58965	−	9.25387i	−0.259266	−	0.364089i
$647$	−2.75607	−	11.3607i	−0.108352	−	0.446634i	0.891629	−	0.452767i	$-0.149563\pi$
$647$	−2.75607	−	11.3607i	−0.108352	−	0.446634i	−0.999981	+	0.00613276i	$0.998048\pi$
$648$	−0.327068	+	0.945001i	−0.0128484	+	0.0371231i
$649$	2.62981	+	55.2065i	0.103229	+	2.16705i
$650$	7.95937	−	9.18561i	0.312192	−	0.360289i
$651$	−24.8924	+	2.05114i	−0.975610	+	0.0803905i
$652$	−3.13289	+	0.919900i	−0.122693	+	0.0360261i
$653$	1.16396	−	0.600063i	0.0455493	−	0.0234823i	−0.435301	−	0.900285i	$-0.643358\pi$
$653$	1.16396	−	0.600063i	0.0455493	−	0.0234823i	0.480851	+	0.876802i	$0.340328\pi$
$654$	−11.5596	+	9.09057i	−0.452016	+	0.355469i
$655$	−14.3054	+	20.0891i	−0.558958	+	0.784946i
$656$	−6.82145	−	0.651370i	−0.266333	−	0.0254317i
$657$	0.426373	+	2.96549i	0.0166344	+	0.115695i
$658$	−9.36820	−	11.0995i	−0.365210	−	0.432703i
$659$	7.52363	−	2.20914i	0.293079	−	0.0860558i	−0.131888	−	0.991265i	$-0.542104\pi$
$659$	7.52363	−	2.20914i	0.293079	−	0.0860558i	0.424967	+	0.905209i	$0.360286\pi$
$660$	7.37018	+	5.79598i	0.286884	+	0.225608i
$661$	−23.3218	−	4.49490i	−0.907111	−	0.174831i	−0.285703	−	0.958318i	$-0.592227\pi$
$661$	−23.3218	−	4.49490i	−0.907111	−	0.174831i	−0.621408	+	0.783487i	$0.713439\pi$
$662$	26.9493	+	13.8933i	1.04742	+	0.539980i
$663$	−31.6048	+	6.09133i	−1.22743	+	0.236568i
$664$	−6.28904	−	1.84663i	−0.244062	−	0.0716631i
$665$	−5.90205	+	6.63525i	−0.228872	+	0.257304i
$666$	−1.72644			−0.0668982
$667$	25.8530	+	25.1478i	1.00103	+	0.973725i
$668$	5.83229	+	10.1018i	0.225658	+	0.390851i
$669$	−0.525636	+	0.0501921i	−0.0203223	+	0.00194054i
$670$	1.33980	−	1.27750i	0.0517610	−	0.0493541i
$671$	−42.3864	−	48.9165i	−1.63631	−	1.88840i
$672$	1.89095	+	1.85049i	0.0729450	+	0.0713841i
$673$	12.7725	−	14.7403i	0.492345	−	0.568196i	−0.454146	−	0.890927i	$-0.650056\pi$
$673$	12.7725	−	14.7403i	0.492345	−	0.568196i	0.946491	+	0.322731i	$0.104601\pi$
$674$	−21.4285	−	16.8516i	−0.825395	−	0.649098i
$675$	−1.56007	−	1.48752i	−0.0600470	−	0.0572547i
$676$	0.894208	−	18.7717i	0.0343926	−	0.721990i
$677$	29.8386	+	11.9456i	1.14679	+	0.459105i	0.865693	−	0.500575i	$-0.166878\pi$
$677$	29.8386	+	11.9456i	1.14679	+	0.459105i	0.281095	+	0.959680i	$0.409302\pi$
$678$	−1.24261	−	2.72094i	−0.0477223	−	0.104497i
$679$	32.2368	+	13.3939i	1.23714	+	0.514013i
$680$	1.37011	+	9.52931i	0.0525412	+	0.365432i
$681$	−13.9683	+	7.20114i	−0.535265	+	0.275948i
$682$	−37.9836	−	36.2173i	−1.45447	−	1.38683i
$683$	−34.0249	+	13.6215i	−1.30193	+	0.521213i	−0.915949	−	0.401294i	$-0.868560\pi$
$683$	−34.0249	+	13.6215i	−1.30193	+	0.521213i	−0.385979	+	0.922508i	$0.626136\pi$
$684$	−0.650912	−	1.88069i	−0.0248882	−	0.0719099i
$685$	−8.01067	+	5.14815i	−0.306072	+	0.196701i
$686$	−14.1010	−	12.0068i	−0.538378	−	0.458420i
$687$	21.6555	+	6.35862i	0.826208	+	0.242597i
$688$	5.14548	+	7.22581i	0.196169	+	0.275481i
$689$	29.1482	+	50.4861i	1.11046	+	1.92337i
$690$	5.35745	−	6.05965i	0.203955	−	0.230687i
$691$	−18.8474	+	32.6447i	−0.716990	+	1.24186i	0.245197	+	0.969473i	$0.421147\pi$
$691$	−18.8474	+	32.6447i	−0.716990	+	1.24186i	−0.962187	+	0.272389i	$0.912186\pi$
$692$	−2.60985	+	5.71478i	−0.0992117	+	0.217243i
$693$	13.1602	−	6.56965i	0.499913	−	0.249560i
$694$	−4.65227	−	5.36900i	−0.176598	−	0.203804i
$695$	1.12322	+	23.5792i	0.0426061	+	0.894411i
$696$	−7.38446	−	1.42324i	−0.279907	−	0.0539477i
$697$	−36.3141	+	14.5380i	−1.37549	+	0.550665i
$698$	−4.14468	+	17.0846i	−0.156878	+	0.646662i
$699$	4.88226	+	3.13764i	0.184664	+	0.118676i
$700$	−5.32168	+	2.05071i	−0.201140	+	0.0775095i
$701$	−2.97346	−	6.51096i	−0.112306	−	0.245916i	0.845130	−	0.534560i	$-0.179523\pi$
$701$	−2.97346	−	6.51096i	−0.112306	−	0.245916i	−0.957436	+	0.288645i	$0.906795\pi$
$702$	−5.61300	−	0.535976i	−0.211849	−	0.0202291i
$703$	2.70077	−	2.12391i	0.101861	−	0.0801048i
$704$	−0.264528	+	5.55312i	−0.00996977	+	0.209291i
$705$	2.18282	−	8.99770i	0.0822097	−	0.338873i
$706$	3.37580	−	23.4792i	0.127050	−	0.883651i
$707$	−28.8221	+	17.9984i	−1.08397	+	0.676898i
$708$	−8.36334	+	5.37479i	−0.314314	+	0.201997i
$709$	−1.64871	+	0.317763i	−0.0619186	+	0.0119338i	−0.220116	−	0.975474i	$-0.570644\pi$
$709$	−1.64871	+	0.317763i	−0.0619186	+	0.0119338i	0.158198	+	0.987407i	$0.449432\pi$
$710$	−1.86400	−	7.68353i	−0.0699548	−	0.288358i
$711$	6.95608	−	0.664225i	0.260873	−	0.0249104i
$712$	6.68655	−	11.5814i	0.250589	−	0.434033i
$713$	−33.0765	+	30.9145i	−1.23872	+	1.15776i
$714$	14.4345	+	4.44275i	0.540199	+	0.166266i
$715$	−21.9621	+	48.0904i	−0.821337	+	1.79848i
$716$	9.99219	−	9.52754i	0.373426	−	0.356061i
$717$	−6.26910	+	18.1134i	−0.234124	+	0.676457i
$718$	20.7391	+	10.6918i	0.773976	+	0.399013i
$719$	−17.1950	−	49.6816i	−0.641264	−	1.85281i	−0.507177	−	0.861842i	$-0.669311\pi$
$719$	−17.1950	−	49.6816i	−0.641264	−	1.85281i	−0.134088	−	0.990969i	$-0.542810\pi$
$720$	−0.240020	+	1.66937i	−0.00894501	+	0.0622139i
$721$	2.49595	+	4.45575i	0.0929540	+	0.165941i
$722$	−12.6519	−	8.13088i	−0.470855	−	0.302600i
$723$	9.31752	+	3.73017i	0.346522	+	0.138727i
$724$	8.28032	−	11.6281i	0.307736	−	0.432154i
$725$	9.40315	−	13.2049i	0.349224	−	0.490417i
$726$	18.4812	+	7.39874i	0.685901	+	0.274593i
$727$	15.2237	+	9.78370i	0.564617	+	0.362857i	0.791598	−	0.611042i	$-0.209249\pi$
$727$	15.2237	+	9.78370i	0.564617	+	0.362857i	−0.226981	+	0.973899i	$0.572886\pi$
$728$	−7.62620	+	12.8216i	−0.282646	+	0.475198i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	1.65263	+	4.77495i	0.0611664	+	0.176729i
$731$	45.0074	+	23.2029i	1.66466	+	0.858191i
$732$	3.80791	−	11.0022i	0.140744	−	0.406654i
$733$	17.8671	−	17.0362i	0.659935	−	0.629247i	−0.284216	−	0.958760i	$-0.591733\pi$
$733$	17.8671	−	17.0362i	0.659935	−	0.629247i	0.944151	+	0.329513i	$0.106885\pi$
$734$	−1.46305	+	3.20362i	−0.0540020	+	0.118248i
$735$	0.867774	−	11.7739i	0.0320083	−	0.434285i
$736$	4.76933	+	0.503463i	0.175800	+	0.0185579i
$737$	3.05115	−	5.28475i	0.112391	−	0.194666i
$738$	−6.82145	+	0.651370i	−0.251101	+	0.0239772i
$739$	1.54004	+	6.34813i	0.0566512	+	0.233520i	0.993098	−	0.117291i	$-0.0374211\pi$
$739$	1.54004	+	6.34813i	0.0566512	+	0.233520i	−0.936446	+	0.350811i	$0.885906\pi$
$740$	−2.85909	+	0.551045i	−0.105102	+	0.0202568i
$741$	9.44011	−	6.06679i	0.346791	−	0.222869i
$742$	−0.946666	−	27.3378i	−0.0347532	−	1.00360i
$743$	4.70450	−	32.7205i	0.172591	−	1.20040i	−0.700792	−	0.713366i	$-0.747170\pi$
$743$	4.70450	−	32.7205i	0.172591	−	1.20040i	0.873383	−	0.487034i	$-0.161921\pi$
$744$	2.22564	−	9.17422i	0.0815960	−	0.336343i
$745$	−1.00873	+	21.1759i	−0.0369572	+	0.775827i
$746$	−0.272061	+	0.213951i	−0.00996084	+	0.00783329i
$747$	−6.52487	−	0.623050i	−0.238733	−	0.0227962i
$748$	13.1832	+	28.8671i	0.482024	+	1.05548i
$749$	19.9256	−	7.67832i	0.728064	−	0.280560i
$750$	−10.1524	−	6.52455i	−0.370713	−	0.238243i
$751$	3.21091	−	13.2356i	0.117168	−	0.482972i	−0.882746	−	0.469850i	$-0.844308\pi$
$751$	3.21091	−	13.2356i	0.117168	−	0.482972i	0.999914	−	0.0131219i	$-0.00417695\pi$
$752$	5.09651	−	2.04033i	0.185851	−	0.0744033i
$753$	−9.96300	−	1.92021i	−0.363072	−	0.0699764i
$754$	−2.01765	−	42.3558i	−0.0734787	−	1.54251i
$755$	−8.08434	−	9.32983i	−0.294219	−	0.339547i
$756$	2.20699	+	1.45918i	0.0802673	+	0.0530699i
$757$	1.28410	−	2.81179i	0.0466715	−	0.102196i	−0.884860	−	0.465857i	$-0.845746\pi$
$757$	1.28410	−	2.81179i	0.0466715	−	0.102196i	0.931531	+	0.363661i	$0.118473\pi$
$758$	−0.681371	+	1.18017i	−0.0247485	+	0.0428657i
$759$	11.3171	−	24.1410i	0.410786	−	0.876262i
$760$	−1.67823	−	2.90678i	−0.0608758	−	0.105440i
$761$	−19.0367	−	26.7333i	−0.690079	−	0.969081i	−0.999833	−	0.0182639i	$-0.994186\pi$
$761$	−19.0367	−	26.7333i	−0.690079	−	0.969081i	0.309754	−	0.950817i	$-0.399753\pi$
$762$	−12.6783	−	3.72269i	−0.459287	−	0.134859i
$763$	15.7021	+	35.5989i	0.568453	+	1.28877i
$764$	17.7696	−	11.4198i	0.642881	−	0.413155i
$765$	3.14878	+	9.09780i	0.113844	+	0.328932i
$766$	−6.96492	+	2.78833i	−0.251653	+	0.100747i
$767$	−40.5693	−	38.6828i	−1.46487	−	1.39675i
$768$	−0.888835	+	0.458227i	−0.0320731	+	0.0165348i
$769$	−3.39752	−	23.6303i	−0.122518	−	0.852130i	−0.954688	−	0.297609i	$-0.903811\pi$
$769$	−3.39752	−	23.6303i	−0.122518	−	0.852130i	0.832170	−	0.554520i	$-0.187098\pi$
$770$	19.6972	−	15.0802i	0.709836	−	0.543453i
$771$	−0.419935	−	0.919529i	−0.0151236	−	0.0331160i
$772$	−19.1556	−	7.66873i	−0.689424	−	0.276004i
$773$	0.667973	−	14.0225i	0.0240253	−	0.504354i	−0.954498	−	0.298217i	$-0.903608\pi$
$773$	0.667973	−	14.0225i	0.0240253	−	0.504354i	0.978523	−	0.206136i	$-0.0660890\pi$
$774$	6.41999	+	6.12144i	0.230762	+	0.220031i
$775$	15.9957	+	12.5792i	0.574582	+	0.451856i
$776$	−8.64038	+	9.97153i	−0.310171	+	0.357957i
$777$	−1.13443	+	4.42462i	−0.0406975	+	0.158732i
$778$	17.9673	+	20.7353i	0.644157	+	0.743397i
$779$	9.86986	−	9.41089i	0.353625	−	0.337180i
$780$	−9.46655	+	0.903946i	−0.338957	+	0.0323665i
$781$	−13.0311	−	22.5705i	−0.466290	−	0.807638i
$782$	25.5153	−	9.92069i	0.912425	−	0.354763i
$783$	−7.52037			−0.268756
$784$	5.98506	−	3.63029i	0.213752	−	0.129653i
$785$	30.6428	+	8.99753i	1.09369	+	0.321136i
$786$	−14.3586	+	2.76739i	−0.512154	+	0.0987096i
$787$	19.9926	+	10.3069i	0.712661	+	0.367402i	0.776123	−	0.630582i	$-0.217184\pi$
$787$	19.9926	+	10.3069i	0.712661	+	0.367402i	−0.0634617	+	0.997984i	$0.520214\pi$
$788$	5.33892	+	1.02899i	0.190191	+	0.0366563i
$789$	3.32709	+	2.61645i	0.118448	+	0.0931482i
$790$	11.3077	−	3.32024i	0.402310	−	0.118129i
$791$	−7.78990	+	1.39672i	−0.276977	+	0.0496618i
$792$	0.791188	+	5.50283i	0.0281136	+	0.195535i
$793$	65.3496	+	6.24013i	2.32063	+	0.221594i
$794$	−1.40335	+	1.97073i	−0.0498030	+	0.0699385i
$795$	13.7064	−	10.7789i	0.486117	−	0.382287i
$796$	11.8160	−	6.09156i	0.418807	−	0.215910i
$797$	−3.75446	+	1.10241i	−0.132990	+	0.0390493i	−0.347550	−	0.937661i	$-0.612986\pi$
$797$	−3.75446	+	1.10241i	−0.132990	+	0.0390493i	0.214560	+	0.976711i	$0.431168\pi$
$798$	−5.24764	+	0.432407i	−0.185764	+	0.0153070i
$799$	20.5215	−	23.6831i	0.725999	−	0.837847i
$800$	−0.102567	−	2.15314i	−0.00362628	−	0.0761249i
$801$	4.37391	−	12.6376i	0.154545	−	0.446527i
$802$	−2.40106	−	9.89731i	−0.0847844	−	0.349486i
$803$	9.66139	+	13.5675i	0.340943	+	0.478787i
$804$	1.09765			0.0387112
$805$	−12.0097	−	17.7121i	−0.423285	−	0.624271i
$806$	53.2296			1.87493
$807$	12.5124	+	17.5712i	0.440458	+	0.618537i
$808$	−3.02793	−	12.4813i	−0.106522	−	0.439090i
$809$	−11.4267	+	33.0153i	−0.401742	+	1.16076i	0.544908	+	0.838496i	$0.316564\pi$
$809$	−11.4267	+	33.0153i	−0.401742	+	1.16076i	−0.946650	+	0.322262i	$0.895557\pi$
$810$	0.0802489	+	1.68463i	0.00281966	+	0.0591919i
$811$	8.67346	−	10.0097i	0.304566	−	0.351488i	−0.582748	−	0.812653i	$-0.698023\pi$
$811$	8.67346	−	10.0097i	0.304566	−	0.351488i	0.887315	+	0.461164i	$0.152568\pi$
$812$	−8.49984	+	17.9901i	−0.298286	+	0.631329i
$813$	−4.33006	+	1.27142i	−0.151862	+	0.0445907i
$814$	−8.53105	+	4.39806i	−0.299013	+	0.154152i
$815$	−4.32865	+	3.40409i	−0.151626	+	0.119240i
$816$	−3.31114	+	4.64985i	−0.115913	+	0.162777i
$817$	−17.5739	−	1.67811i	−0.614833	−	0.0587095i
$818$	0.773885	+	5.38249i	0.0270583	+	0.188194i
$819$	−5.06189	+	14.0331i	−0.176877	+	0.490357i
$820$	−11.0888	+	3.25598i	−0.387239	+	0.113704i
$821$	23.1913	+	18.2378i	0.809382	+	0.636505i	0.934630	−	0.355621i	$-0.115730\pi$
$821$	23.1913	+	18.2378i	0.809382	+	0.636505i	−0.125249	+	0.992125i	$0.539973\pi$
$822$	−5.54402	−	1.06852i	−0.193370	−	0.0372690i
$823$	35.2434	+	18.1692i	1.22851	+	0.633339i	0.945451	−	0.325765i	$-0.105622\pi$
$823$	35.2434	+	18.1692i	1.22851	+	0.633339i	0.283055	+	0.959104i	$0.408652\pi$
$824$	−1.89545	+	0.365319i	−0.0660313	+	0.0127265i
$825$	−11.4983	−	3.37622i	−0.400321	−	0.117545i
$826$	8.27932	+	24.9658i	0.288074	+	0.868671i
$827$	−26.7904			−0.931594			−0.465797	−	0.884892i	$-0.654232\pi$
$827$	−26.7904			−0.931594			−0.465797	+	0.884892i	$0.654232\pi$
$828$	4.77842	−	0.408237i	0.166062	−	0.0141872i
$829$	9.33636	+	16.1710i	0.324265	+	0.561643i	0.981363	−	0.192161i	$-0.0615497\pi$
$829$	9.33636	+	16.1710i	0.324265	+	0.561643i	−0.657098	+	0.753805i	$0.728216\pi$
$830$	−11.0045	+	1.05080i	−0.381970	+	0.0364738i
$831$	13.1560	−	12.5442i	0.456377	−	0.435155i
$832$	−3.69245	−	4.26132i	−0.128013	−	0.147735i
$833$	20.8710	−	34.0743i	0.723136	−	1.18060i
$834$	−9.16587	+	10.5780i	−0.317388	+	0.366286i
$835$	15.4639	+	12.1609i	0.535149	+	0.420846i
$836$	−8.00743	−	7.63507i	−0.276943	−	0.264064i
$837$	0.449189	−	9.42964i	0.0155262	−	0.325936i
$838$	−18.5150	−	7.41228i	−0.639589	−	0.256053i
$839$	3.25975	+	7.13786i	0.112539	+	0.246426i	0.957518	−	0.288373i	$-0.0931144\pi$
$839$	3.25975	+	7.13786i	0.112539	+	0.246426i	−0.844979	+	0.534800i	$0.820387\pi$
$840$	4.12065	+	1.71207i	0.142176	+	0.0590721i
$841$	−3.92161	−	27.2754i	−0.135228	−	0.940532i
$842$	31.1146	−	16.0407i	1.07228	−	0.552800i
$843$	−11.0817	−	10.5663i	−0.381673	−	0.363924i
$844$	−6.26610	+	2.50857i	−0.215688	+	0.0863484i
$845$	−10.3665	−	29.9520i	−0.356618	−	1.03038i
$846$	4.61827	−	2.96798i	0.158779	−	0.102041i
$847$	31.1058	−	42.5029i	1.06881	−	1.46042i
$848$	9.92013	+	2.91281i	0.340659	+	0.100026i
$849$	2.98116	+	4.18646i	0.102313	+	0.143679i
$850$	−6.15236	−	10.6562i	−0.211024	−	0.365504i
$851$	3.36423	+	7.56542i	0.115324	+	0.259339i
$852$	2.34397	−	4.05987i	0.0803031	−	0.139089i
$853$	19.1768	−	41.9912i	0.656600	−	1.43775i	−0.229058	−	0.973413i	$-0.573564\pi$
$853$	19.1768	−	41.9912i	0.656600	−	1.43775i	0.885657	−	0.464340i	$-0.153708\pi$
$854$	−25.6950	−	16.9886i	−0.879263	−	0.581338i
$855$	−2.19801	−	2.53664i	−0.0751705	−	0.0867513i
$856$	0.384033	+	8.06184i	0.0131260	+	0.275548i
$857$	−47.9413	−	9.23993i	−1.63764	−	0.315630i	−0.714369	−	0.699769i	$-0.753286\pi$
$857$	−47.9413	−	9.23993i	−1.63764	−	0.315630i	−0.923275	+	0.384139i	$0.874498\pi$
$858$	−29.1015	+	11.6505i	−0.993509	+	0.397741i
$859$	−1.89597	+	7.81529i	−0.0646896	+	0.266654i	−0.994967	−	0.100203i	$-0.968051\pi$
$859$	−1.89597	+	7.81529i	−0.0646896	+	0.266654i	0.930277	+	0.366857i	$0.119566\pi$
$860$	12.5857	+	8.08837i	0.429170	+	0.275811i
$861$	−2.81296	+	17.9104i	−0.0958656	+	0.610385i
$862$	−2.15520	−	4.71923i	−0.0734065	−	0.160738i
$863$	16.5152	+	1.57701i	0.562183	+	0.0536820i	0.372279	−	0.928121i	$-0.378576\pi$
$863$	16.5152	+	1.57701i	0.562183	+	0.0536820i	0.189904	+	0.981803i	$0.439182\pi$
$864$	−0.786053	+	0.618159i	−0.0267421	+	0.0210302i
$865$	−0.504165	+	10.5837i	−0.0171421	+	0.359857i
$866$	−3.99422	+	16.4644i	−0.135729	+	0.559483i
$867$	−2.21795	+	15.4262i	−0.0753255	+	0.523900i
$868$	−22.0497	−	11.7323i	−0.748417	−	0.398221i
$869$	32.6808	−	21.0027i	1.10862	−	0.712466i
$870$	−12.4542	+	2.40035i	−0.422237	+	0.0813795i
$871$	1.45915	+	6.01468i	0.0494413	+	0.203800i
$872$	−14.6393	+	1.39788i	−0.495749	+	0.0473383i
$873$	−6.59711	+	11.4265i	−0.223278	+	0.386729i
$874$	−6.97295	+	6.51717i	−0.235863	+	0.220446i
$875$	−23.3926	+	21.7319i	−0.790813	+	0.734672i
$876$	−1.24458	+	2.72524i	−0.0420503	+	0.0920774i
$877$	−36.1928	+	34.5098i	−1.22215	+	1.16531i	−0.241316	+	0.970447i	$0.577579\pi$
$877$	−36.1928	+	34.5098i	−1.22215	+	1.16531i	−0.980830	+	0.194867i	$0.937573\pi$
$878$	2.77974	−	8.03154i	0.0938118	−	0.271051i
$879$	18.5889	+	9.58324i	0.626988	+	0.323235i
$880$	3.06665	+	8.86051i	0.103377	+	0.298688i
$881$	−3.40257	+	23.6654i	−0.114635	+	0.797307i	0.848674	+	0.528916i	$0.177401\pi$
$881$	−3.40257	+	23.6654i	−0.114635	+	0.797307i	−0.963310	+	0.268392i	$0.913508\pi$
$882$	5.18987	−	4.69737i	0.174752	−	0.158169i
$883$	44.6327	+	28.6837i	1.50201	+	0.965283i	0.994623	+	0.103564i	$0.0330247\pi$
$883$	44.6327	+	28.6837i	1.50201	+	0.965283i	0.507386	+	0.861719i	$0.330612\pi$
$884$	−29.8809	−	11.9625i	−1.00500	−	0.402343i
$885$	−9.72569	+	13.6578i	−0.326926	+	0.459103i
$886$	9.46225	−	13.2879i	0.317890	−	0.446415i
$887$	13.4992	+	5.40425i	0.453257	+	0.181457i	0.587047	−	0.809553i	$-0.300290\pi$
$887$	13.4992	+	5.40425i	0.453257	+	0.181457i	−0.133790	+	0.991010i	$0.542715\pi$
$888$	−1.45237	−	0.933384i	−0.0487385	−	0.0313223i
$889$	−17.8716	+	30.0466i	−0.599393	+	1.00773i
$890$	3.20981	−	22.3247i	0.107593	−	0.748326i
$891$	1.81831	+	5.25366i	0.0609156	+	0.176004i
$892$	−0.469329	−	0.241956i	−0.0157143	−	0.00810128i
$893$	−3.57335	+	10.3245i	−0.119577	+	0.345496i
$894$	−9.09740	+	8.67435i	−0.304262	+	0.290114i
$895$	9.67299	−	21.1809i	0.323333	−	0.708000i
$896$	0.590320	+	2.57905i	0.0197212	+	0.0861602i
$897$	8.58909	+	25.6411i	0.286781	+	0.856132i
$898$	−4.14468	+	7.17880i	−0.138310	+	0.239560i
$899$	70.6733	−	6.74848i	2.35709	−	0.225074i
$900$	−0.508197	−	2.09482i	−0.0169399	−	0.0698272i
$901$	57.9513	−	11.1692i	1.93064	−	0.372100i
$902$	−32.0482	+	20.5962i	−1.06709	+	0.685777i
$903$	19.9069	−	12.4311i	0.662460	−	0.413682i
$904$	0.425700	−	2.96081i	0.0141586	−	0.0984751i
$905$	5.67599	−	23.3967i	0.188676	−	0.777734i
$906$	0.348290	−	7.31150i	0.0115712	−	0.242908i
$907$	1.52382	−	1.19835i	0.0505978	−	0.0397905i	−0.592540	−	0.805541i	$-0.701875\pi$
$907$	1.52382	−	1.19835i	0.0505978	−	0.0397905i	0.643138	+	0.765751i	$0.277632\pi$
$908$	−15.6441	−	1.49383i	−0.519167	−	0.0495744i
$909$	−5.33530	−	11.6827i	−0.176961	−	0.387490i
$910$	−3.90373	+	24.8554i	−0.129407	+	0.823948i
$911$	−2.92491	−	1.87973i	−0.0969066	−	0.0622781i	0.491290	−	0.870996i	$-0.336526\pi$
$911$	−2.92491	−	1.87973i	−0.0969066	−	0.0622781i	−0.588197	+	0.808718i	$0.700162\pi$
$912$	0.469194	−	1.93404i	0.0155366	−	0.0640426i
$913$	−33.8293	+	13.5432i	−1.11959	+	0.448214i
$914$	−34.9230	−	6.73085i	−1.15515	−	0.222637i
$915$	−0.934302	−	19.6134i	−0.0308871	−	0.648399i
$916$	14.7800	+	17.0571i	0.488346	+	0.563581i
$917$	−2.34251	+	38.6174i	−0.0773566	+	1.27526i
$918$	−2.37132	+	5.19246i	−0.0782651	+	0.171377i
$919$	−3.02918	+	5.24670i	−0.0999235	+	0.173073i	−0.911653	−	0.410961i	$-0.865193\pi$
$919$	−3.02918	+	5.24670i	−0.0999235	+	0.173073i	0.811729	+	0.584034i	$0.198526\pi$
$920$	7.78307	−	2.20124i	0.256600	−	0.0725728i
$921$	7.72222	+	13.3753i	0.254456	+	0.440731i
$922$	3.78850	+	5.32021i	0.124768	+	0.175212i
$923$	25.3624	+	7.44706i	0.834812	+	0.245123i
$924$	14.6229	+	1.58818i	0.481057	+	0.0522471i
$925$	3.13071	−	2.01198i	0.102937	−	0.0661536i
$926$	−5.31370	−	15.3529i	−0.174619	−	0.504528i
$927$	−1.79206	+	0.717434i	−0.0588591	+	0.0235636i
$928$	−5.44275	−	5.18965i	−0.178667	−	0.170359i
$929$	25.9411	−	13.3736i	0.851099	−	0.438772i	0.0232547	−	0.999730i	$-0.492597\pi$
$929$	25.9411	−	13.3736i	0.851099	−	0.438772i	0.827845	+	0.560957i	$0.189567\pi$
$930$	−2.26587	−	15.7594i	−0.0743007	−	0.516773i
$931$	−2.33999	+	13.7331i	−0.0766902	+	0.450083i
$932$	2.41088	+	5.27910i	0.0789712	+	0.172923i
$933$	12.1145	+	4.84993i	0.396612	+	0.158780i
$934$	0.336382	−	7.06152i	0.0110067	−	0.231060i
$935$	38.7358	+	36.9346i	1.26680	+	1.20789i
$936$	−4.43218	−	3.48551i	−0.144870	−	0.113927i
$937$	24.4369	−	28.2017i	0.798319	−	0.921310i	−0.199969	−	0.979802i	$-0.564084\pi$
$937$	24.4369	−	28.2017i	0.798319	−	0.921310i	0.998288	+	0.0584927i	$0.0186295\pi$
$938$	0.721260	−	2.81312i	0.0235500	−	0.0918517i
$939$	2.61761	+	3.02089i	0.0854226	+	0.0985830i
$940$	6.70083	−	6.38923i	0.218557	−	0.208394i
$941$	−41.3047	+	3.94412i	−1.34649	+	0.128575i	−0.743267	−	0.668994i	$-0.766725\pi$
$941$	−41.3047	+	3.94412i	−1.34649	+	0.128575i	−0.603228	+	0.797569i	$0.706119\pi$
$942$	9.46802	+	16.3991i	0.308485	+	0.534311i
$943$	16.1470	+	28.6229i	0.525819	+	0.932091i
$944$	−9.94152			−0.323569
$945$	4.37020	+	0.901294i	0.142162	+	0.0293191i
$946$	47.3180	+	13.8938i	1.53844	+	0.451727i
$947$	38.1501	−	7.35283i	1.23971	−	0.238935i	0.473079	−	0.881020i	$-0.343142\pi$
$947$	38.1501	−	7.35283i	1.23971	−	0.238935i	0.766634	+	0.642085i	$0.221930\pi$
$948$	6.21094	+	3.20196i	0.201722	+	0.103995i
$949$	−16.5877	−	3.19701i	−0.538458	−	0.103779i
$950$	3.37210	+	2.65185i	0.109405	+	0.0860373i
$951$	18.3253	−	5.38079i	0.594238	−	0.174484i
$952$	9.74117	+	11.5414i	0.315713	+	0.374058i
$953$	0.0614415	+	0.427335i	0.00199028	+	0.0138427i	0.990792	−	0.135390i	$-0.0432287\pi$
$953$	0.0614415	+	0.427335i	0.00199028	+	0.0138427i	−0.988802	+	0.149233i	$0.952320\pi$
$954$	10.2921	+	0.982778i	0.333219	+	0.0318186i
$955$	20.6642	−	29.0188i	0.668677	−	0.939026i
$956$	−15.0667	+	11.8486i	−0.487293	+	0.383212i
$957$	−37.1612	+	19.1579i	−1.20125	+	0.619288i
$958$	27.7327	−	8.14305i	0.896003	−	0.263090i
$959$	−6.38141	+	13.5064i	−0.206066	+	0.436145i
$960$	−1.10445	+	1.27460i	−0.0356460	+	0.0411376i
$961$	2.76545	+	58.0540i	0.0892081	+	1.87271i
$962$	3.18387	−	9.19919i	0.102652	−	0.296594i
$963$	1.90281	+	7.84347i	0.0613171	+	0.252752i
$964$	5.82171	+	8.17545i	0.187505	+	0.263313i
$965$	−34.7994			−1.12023
$966$	2.09362	−	12.5147i	0.0673611	−	0.402653i
$967$	−49.3995			−1.58858			−0.794290	−	0.607539i	$-0.792157\pi$
$967$	−49.3995			−1.58858			−0.794290	+	0.607539i	$0.792157\pi$
$968$	11.5473	+	16.2159i	0.371144	+	0.521199i
$969$	−2.67831	−	11.0401i	−0.0860396	−	0.354660i
$970$	−7.27811	+	21.0287i	−0.233686	+	0.675192i
$971$	−0.821810	−	17.2519i	−0.0263732	−	0.553641i	−0.972930	−	0.231102i	$-0.925767\pi$
$971$	−0.821810	−	17.2519i	−0.0263732	−	0.553641i	0.946556	−	0.322538i	$-0.104536\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	21.0870	+	30.4415i	0.676018	+	0.975911i
$974$	0.503741	−	0.147912i	0.0161409	−	0.00473939i
$975$	10.8032	−	5.56942i	0.345978	−	0.178364i
$976$	9.15166	−	7.19695i	0.292938	−	0.230369i
$977$	29.8006	−	41.8491i	0.953407	−	1.33887i	0.0126033	−	0.999921i	$-0.495988\pi$
$977$	29.8006	−	41.8491i	0.953407	−	1.33887i	0.940804	−	0.338952i	$-0.110072\pi$
$978$	−3.25037	−	0.310372i	−0.103935	−	0.00992462i
$979$	−10.5806	−	73.5899i	−0.338159	−	2.35194i
$980$	7.09544	−	9.43564i	0.226656	−	0.301410i
$981$	−14.1102	+	4.14312i	−0.450503	+	0.132280i
$982$	21.8400	+	17.1752i	0.696943	+	0.548082i
$983$	3.56181	+	0.686483i	0.113604	+	0.0218954i	0.245736	−	0.969337i	$-0.420970\pi$
$983$	3.56181	+	0.686483i	0.113604	+	0.0218954i	−0.132132	+	0.991232i	$0.542182\pi$
$984$	−6.09073	−	3.13999i	−0.194165	−	0.100099i
$985$	9.00430	−	1.73544i	0.286901	−	0.0552956i
$986$	−41.1897	−	12.0944i	−1.31175	−	0.385163i
$987$	−4.57188	−	13.7862i	−0.145524	−	0.438820i
$988$	11.2215			0.357003
$989$	14.3144	−	40.0616i	0.455172	−	1.27388i
$990$	4.68810	+	8.12002i	0.148997	+	0.258071i
$991$	−45.4387	+	4.33887i	−1.44341	+	0.137829i	−0.787175	−	0.616730i	$-0.788457\pi$
$991$	−45.4387	+	4.33887i	−1.44341	+	0.137829i	−0.656233	+	0.754559i	$0.727851\pi$
$992$	6.83229	−	6.51457i	0.216925	−	0.206838i
$993$	19.8553	+	22.9142i	0.630087	+	0.727160i
$994$	−8.86466	−	8.67497i	−0.281170	−	0.275153i
$995$	14.6823	−	16.9443i	0.465461	−	0.537170i
$996$	−5.15222	−	4.05175i	−0.163254	−	0.128385i
$997$	−27.5679	−	26.2860i	−0.873085	−	0.832485i	0.113867	−	0.993496i	$-0.463676\pi$
$997$	−27.5679	−	26.2860i	−0.873085	−	0.832485i	−0.986953	+	0.161011i	$0.948525\pi$
$998$	−0.424650	+	8.91450i	−0.0134421	+	0.282184i
$999$	−1.60277	−	0.641653i	−0.0507094	−	0.0203010i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.d.121.6	✓	160
7.4	even	3	inner	966.2.y.d.949.3	yes	160
23.4	even	11	inner	966.2.y.d.625.3	yes	160
161.4	even	33	inner	966.2.y.d.487.6	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.d.121.6	✓	160	1.1	even	1	trivial
966.2.y.d.487.6	yes	160	161.4	even	33	inner
966.2.y.d.625.3	yes	160	23.4	even	11	inner
966.2.y.d.949.3	yes	160	7.4	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0802489 + 1.68463i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.50657 + 2.17491i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(0.580057 + 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(0.0802489 + 1.68463i) q^{5} +(-0.654861 + 0.755750i) q^{6} +(1.50657 + 2.17491i) q^{7} +(-0.959493 + 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-1.32571 + 1.04255i) q^{10} +(-3.22478 + 4.52857i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.802447 - 5.58114i) q^{13} +(-0.897733 + 2.48879i) q^{14} +(-1.61822 + 0.475154i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-5.60515 - 1.08030i) q^{17} +(-0.888835 - 0.458227i) q^{18} +(1.95418 - 0.376637i) q^{19} +(-1.61822 - 0.475154i) q^{20} +(-1.75842 + 1.97686i) q^{21} -5.55942 q^{22} +(-0.275959 + 4.78789i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.14582 - 0.204901i) q^{25} +(4.08080 - 3.89103i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-2.54804 + 0.712368i) q^{28} +(4.92479 - 5.68351i) q^{29} +(-1.32571 - 1.04255i) q^{30} +(6.83229 + 6.51457i) q^{31} +(0.0475819 - 0.998867i) q^{32} +(-5.16119 - 2.06623i) q^{33} +(-2.37132 - 5.19246i) q^{34} +(-3.54302 + 2.71255i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(1.53452 - 0.791101i) q^{37} +(1.44033 + 1.37336i) q^{38} +(5.23463 - 2.09563i) q^{39} +(-0.551614 - 1.59378i) q^{40} +(5.76467 - 3.70473i) q^{41} +(-2.63028 - 0.285673i) q^{42} +(-8.51132 - 2.49915i) q^{43} +(-3.22478 - 4.52857i) q^{44} +(-0.843271 - 1.46059i) q^{45} +(-4.06017 + 2.55246i) q^{46} +(-2.74488 + 4.75426i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-2.46048 + 6.55332i) q^{49} +(1.41160 + 1.62908i) q^{50} +(-0.271612 - 5.70184i) q^{51} +(5.53663 + 1.06710i) q^{52} +(-9.59833 + 3.84259i) q^{53} +(0.235759 - 0.971812i) q^{54} +(-7.88775 - 5.06915i) q^{55} +(-2.05829 - 1.66236i) q^{56} +(0.826735 + 1.81030i) q^{57} +(7.48631 + 0.714856i) q^{58} +(7.81457 - 6.14544i) q^{59} +(0.0802489 - 1.68463i) q^{60} +(-2.74484 + 11.3144i) q^{61} +(-1.34350 + 9.34424i) q^{62} +(-2.33570 - 1.24279i) q^{63} +(0.841254 - 0.540641i) q^{64} +(9.33776 - 1.79971i) q^{65} +(-1.31068 - 5.40271i) q^{66} +(-1.09268 + 0.104338i) q^{67} +(2.85415 - 4.94354i) q^{68} +(-4.71798 + 0.860606i) q^{69} +(-4.26473 - 1.31263i) q^{70} +(-1.94744 + 4.26430i) q^{71} +(0.723734 - 0.690079i) q^{72} +(0.979890 - 2.83121i) q^{73} +(1.53452 + 0.791101i) q^{74} +(0.705021 + 2.03702i) q^{75} +(-0.283227 + 1.96989i) q^{76} +(-14.7076 - 0.190993i) q^{77} +(4.74343 + 3.04842i) q^{78} +(-6.48718 - 2.59707i) q^{79} +(0.978290 - 1.37382i) q^{80} +(0.580057 - 0.814576i) q^{81} +(6.36162 + 2.54681i) q^{82} +(5.51404 + 3.54366i) q^{83} +(-1.29301 - 2.30827i) q^{84} +(1.37011 - 9.52931i) q^{85} +(-2.90130 - 8.38276i) q^{86} +(6.68437 + 3.44603i) q^{87} +(1.81831 - 5.25366i) q^{88} +(-9.67856 + 9.22849i) q^{89} +(0.700614 - 1.53413i) q^{90} +(10.9295 - 10.1536i) q^{91} +(-4.43430 - 1.82675i) q^{92} +(-4.72016 + 8.17557i) q^{93} +(-5.46489 + 0.521834i) q^{94} +(0.791315 + 3.26185i) q^{95} +(0.981929 - 0.189251i) q^{96} +(11.0997 - 7.13333i) q^{97} +(-6.76540 + 1.79705i) q^{98} +(0.791188 - 5.50283i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 2 q^{5} - 16 q^{6} + 6 q^{7} - 16 q^{8} + 8 q^{9} - 2 q^{10} - 4 q^{11} + 8 q^{12} - 4 q^{13} + 5 q^{14} + 26 q^{15} + 8 q^{16} - 13 q^{17} + 8 q^{18} + 4 q^{19} + 26 q^{20} + 11 q^{21} - 124 q^{22} + 26 q^{23} - 80 q^{24} + 14 q^{25} + 2 q^{26} - 16 q^{27} - 22 q^{28} + 54 q^{29} - 2 q^{30} + 15 q^{31} + 8 q^{32} - 4 q^{33} + 4 q^{34} - 2 q^{35} - 16 q^{36} + 7 q^{37} - 7 q^{38} + 2 q^{39} + 9 q^{40} - 30 q^{41} + 6 q^{42} + 36 q^{43} - 4 q^{44} + 20 q^{45} + 4 q^{46} - 6 q^{47} - 16 q^{48} + 14 q^{49} - 28 q^{50} + 9 q^{51} + 2 q^{52} - 24 q^{53} + 8 q^{54} - 14 q^{55} + 6 q^{56} - 30 q^{57} - 5 q^{58} + 4 q^{59} - 2 q^{60} + 32 q^{61} - 8 q^{62} - 6 q^{63} - 16 q^{64} + 38 q^{65} - 4 q^{66} + 6 q^{67} + 42 q^{68} - 30 q^{69} - 8 q^{70} - 180 q^{71} + 8 q^{72} - 32 q^{73} + 7 q^{74} + 14 q^{75} - 8 q^{76} + 61 q^{77} + 18 q^{78} - 66 q^{79} - 2 q^{80} + 8 q^{81} - 7 q^{82} + 130 q^{83} + 5 q^{84} - 70 q^{85} - 40 q^{86} + 6 q^{87} - 15 q^{88} - 4 q^{89} + 4 q^{90} - 6 q^{91} + 58 q^{92} - 18 q^{93} + 16 q^{94} + 19 q^{95} + 8 q^{96} + 40 q^{97} + 43 q^{98} + 8 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 2 * q^5 - 16 * q^6 + 6 * q^7 - 16 * q^8 + 8 * q^9 - 2 * q^10 - 4 * q^11 + 8 * q^12 - 4 * q^13 + 5 * q^14 + 26 * q^15 + 8 * q^16 - 13 * q^17 + 8 * q^18 + 4 * q^19 + 26 * q^20 + 11 * q^21 - 124 * q^22 + 26 * q^23 - 80 * q^24 + 14 * q^25 + 2 * q^26 - 16 * q^27 - 22 * q^28 + 54 * q^29 - 2 * q^30 + 15 * q^31 + 8 * q^32 - 4 * q^33 + 4 * q^34 - 2 * q^35 - 16 * q^36 + 7 * q^37 - 7 * q^38 + 2 * q^39 + 9 * q^40 - 30 * q^41 + 6 * q^42 + 36 * q^43 - 4 * q^44 + 20 * q^45 + 4 * q^46 - 6 * q^47 - 16 * q^48 + 14 * q^49 - 28 * q^50 + 9 * q^51 + 2 * q^52 - 24 * q^53 + 8 * q^54 - 14 * q^55 + 6 * q^56 - 30 * q^57 - 5 * q^58 + 4 * q^59 - 2 * q^60 + 32 * q^61 - 8 * q^62 - 6 * q^63 - 16 * q^64 + 38 * q^65 - 4 * q^66 + 6 * q^67 + 42 * q^68 - 30 * q^69 - 8 * q^70 - 180 * q^71 + 8 * q^72 - 32 * q^73 + 7 * q^74 + 14 * q^75 - 8 * q^76 + 61 * q^77 + 18 * q^78 - 66 * q^79 - 2 * q^80 + 8 * q^81 - 7 * q^82 + 130 * q^83 + 5 * q^84 - 70 * q^85 - 40 * q^86 + 6 * q^87 - 15 * q^88 - 4 * q^89 + 4 * q^90 - 6 * q^91 + 58 * q^92 - 18 * q^93 + 16 * q^94 + 19 * q^95 + 8 * q^96 + 40 * q^97 + 43 * q^98 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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