LMFDB - Embedded newform 150.2.l.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,2,Mod(17,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 13]))

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

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

chi := DirichletCharacter("150.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	150.l (of order $20$, 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:	$1.19775603032$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	150.17
Dual form			150.2.l.a.53.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.891007 - 0.453990i) q^{2} +(-0.873670 + 1.49556i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-2.21391 + 0.314018i) q^{5} +(1.45742 - 0.935916i) q^{6} +(-2.72680 - 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.47340 - 2.61325i) q^{9} +O(q^{10})$	\(q+(-0.891007 - 0.453990i) q^{2} +(-0.873670 + 1.49556i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-2.21391 + 0.314018i) q^{5} +(1.45742 - 0.935916i) q^{6} +(-2.72680 - 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.47340 - 2.61325i) q^{9} +(2.11517 + 0.725301i) q^{10} +(0.335657 - 0.109061i) q^{11} +(-1.72346 + 0.172255i) q^{12} +(-1.12512 - 2.20817i) q^{13} +(1.19166 + 3.66754i) q^{14} +(1.46459 - 3.58538i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-3.49819 + 0.554059i) q^{17} +(0.126420 + 2.99734i) q^{18} +(-3.84926 + 5.29805i) q^{19} +(-1.55535 - 1.60651i) q^{20} +(6.46042 - 1.69577i) q^{21} +(-0.348585 - 0.0552105i) q^{22} +(-3.55825 + 6.98347i) q^{23} +(1.61382 + 0.628956i) q^{24} +(4.80279 - 1.39041i) q^{25} +2.47829i q^{26} +(5.19554 + 0.0795559i) q^{27} +(0.603255 - 3.80880i) q^{28} +(5.05137 - 3.67003i) q^{29} +(-2.93269 + 2.52969i) q^{30} +(-3.39184 - 2.46432i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.130145 + 0.597278i) q^{33} +(3.36845 + 1.09448i) q^{34} +(6.89315 + 5.18062i) q^{35} +(1.24812 - 2.72804i) q^{36} +(4.33521 - 2.20890i) q^{37} +(5.83498 - 2.97307i) q^{38} +(4.28544 + 0.246528i) q^{39} +(0.656484 + 2.13753i) q^{40} +(-8.06531 - 2.62058i) q^{41} +(-6.52614 - 1.42202i) q^{42} +(-5.16349 + 5.16349i) q^{43} +(0.285527 + 0.207447i) q^{44} +(4.08259 + 5.32283i) q^{45} +(6.34085 - 4.60690i) q^{46} +(0.668895 - 4.22323i) q^{47} +(-1.15238 - 1.29306i) q^{48} +7.87088i q^{49} +(-4.91055 - 0.941550i) q^{50} +(2.22763 - 5.71582i) q^{51} +(1.12512 - 2.20817i) q^{52} +(4.34698 + 0.688494i) q^{53} +(-4.59315 - 2.42961i) q^{54} +(-0.708866 + 0.346854i) q^{55} +(-2.26666 + 3.11979i) q^{56} +(-4.56057 - 10.3855i) q^{57} +(-6.16696 + 0.976751i) q^{58} +(-0.713107 + 2.19472i) q^{59} +(3.76150 - 0.922555i) q^{60} +(0.0451729 + 0.139028i) q^{61} +(1.90338 + 3.73559i) q^{62} +(-3.10814 + 11.1435i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(3.18432 + 4.53538i) q^{65} +(0.387119 - 0.473094i) q^{66} +(1.18445 + 7.47829i) q^{67} +(-2.50443 - 2.50443i) q^{68} +(-7.33546 - 11.4228i) q^{69} +(-3.78989 - 7.74539i) q^{70} +(-3.62303 - 4.98667i) q^{71} +(-2.35059 + 1.86407i) q^{72} +(-9.30362 - 4.74043i) q^{73} -4.86552 q^{74} +(-2.11660 + 8.39762i) q^{75} -6.54875 q^{76} +(-1.21266 - 0.617880i) q^{77} +(-3.70643 - 2.16521i) q^{78} +(0.803169 + 1.10547i) q^{79} +(0.385487 - 2.20259i) q^{80} +(-4.65817 + 7.70074i) q^{81} +(5.99652 + 5.99652i) q^{82} +(-0.915181 - 5.77823i) q^{83} +(5.16925 + 4.22984i) q^{84} +(7.57069 - 2.32513i) q^{85} +(6.94488 - 2.25653i) q^{86} +(1.07553 + 10.7610i) q^{87} +(-0.160227 - 0.314463i) q^{88} +(-0.633239 - 1.94891i) q^{89} +(-1.22110 - 6.59613i) q^{90} +(-2.95327 + 9.08922i) q^{91} +(-7.74123 + 1.22609i) q^{92} +(6.64888 - 2.91971i) q^{93} +(-2.51330 + 3.45926i) q^{94} +(6.85822 - 12.9381i) q^{95} +(0.439743 + 1.67530i) q^{96} +(6.93926 + 1.09907i) q^{97} +(3.57330 - 7.01300i) q^{98} +(-0.779562 - 0.716464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) $ 80 * q + 4 * q^3 + 4 * q^7	$ 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) $ 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{13}{20}\right)$

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 $

$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$2$	−0.891007	−	0.453990i	−0.630037	−	0.321020i
$3$	−0.873670	+	1.49556i	−0.504413	+	0.863462i
$3$	−0.873670	+	1.49556i	−0.504413	+	0.863462i
$4$	0.587785	+	0.809017i	0.293893	+	0.404508i
$5$	−2.21391	+	0.314018i	−0.990090	+	0.140433i
$5$	−2.21391	+	0.314018i	−0.990090	+	0.140433i
$6$	1.45742	−	0.935916i	0.594987	−	0.382086i
$7$	−2.72680	−	2.72680i	−1.03063	−	1.03063i	−0.999516	−	0.0311178i	$-0.990093\pi$
$7$	−2.72680	−	2.72680i	−1.03063	−	1.03063i	−0.0311178	−	0.999516i	$-0.509907\pi$
$8$	−0.156434	−	0.987688i	−0.0553079	−	0.349201i
$9$	−1.47340	−	2.61325i	−0.491134	−	0.871084i
$10$	2.11517	+	0.725301i	0.668875	+	0.229360i
$11$	0.335657	−	0.109061i	0.101204	−	0.0328833i	−0.257977	−	0.966151i	$-0.583056\pi$
$11$	0.335657	−	0.109061i	0.101204	−	0.0328833i	0.359181	+	0.933268i	$0.383056\pi$
$12$	−1.72346	+	0.172255i	−0.497521	+	0.0497257i
$13$	−1.12512	−	2.20817i	−0.312052	−	0.612437i	0.680707	−	0.732555i	$-0.261673\pi$
$13$	−1.12512	−	2.20817i	−0.312052	−	0.612437i	−0.992760	+	0.120119i	$0.961673\pi$
$14$	1.19166	+	3.66754i	0.318483	+	0.980191i
$15$	1.46459	−	3.58538i	0.378156	−	0.925742i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	−3.49819	+	0.554059i	−0.848436	+	0.134379i	−0.565488	−	0.824756i	$-0.691312\pi$
$17$	−3.49819	+	0.554059i	−0.848436	+	0.134379i	−0.282948	+	0.959135i	$0.591312\pi$
$18$	0.126420	+	2.99734i	0.0297975	+	0.706479i
$19$	−3.84926	+	5.29805i	−0.883080	+	1.21546i	0.0924780	+	0.995715i	$0.470521\pi$
$19$	−3.84926	+	5.29805i	−0.883080	+	1.21546i	−0.975558	+	0.219741i	$0.929479\pi$
$20$	−1.55535	−	1.60651i	−0.347787	−	0.359228i
$21$	6.46042	−	1.69577i	1.40978	−	0.370048i
$22$	−0.348585	−	0.0552105i	−0.0743186	−	0.0117709i
$23$	−3.55825	+	6.98347i	−0.741947	+	1.45615i	0.142638	+	0.989775i	$0.454441\pi$
$23$	−3.55825	+	6.98347i	−0.741947	+	1.45615i	−0.884585	+	0.466378i	$0.845559\pi$
$24$	1.61382	+	0.628956i	0.329420	+	0.128385i
$25$	4.80279	−	1.39041i	0.960557	−	0.278083i
$26$			2.47829i			0.486033i
$27$	5.19554	+	0.0795559i	0.999883	+	0.0153105i
$28$	0.603255	−	3.80880i	0.114004	−	0.719796i
$29$	5.05137	−	3.67003i	0.938015	−	0.681508i	−0.00992666	−	0.999951i	$-0.503160\pi$
$29$	5.05137	−	3.67003i	0.938015	−	0.681508i	0.947942	+	0.318443i	$0.103160\pi$
$30$	−2.93269	+	2.52969i	−0.535434	+	0.461856i
$31$	−3.39184	−	2.46432i	−0.609193	−	0.442604i	0.239937	−	0.970788i	$-0.422873\pi$
$31$	−3.39184	−	2.46432i	−0.609193	−	0.442604i	−0.849130	+	0.528184i	$0.822873\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.130145	+	0.597278i	−0.0226553	+	0.103973i
$34$	3.36845	+	1.09448i	0.577684	+	0.187701i
$35$	6.89315	+	5.18062i	1.16516	+	0.875685i
$36$	1.24812	−	2.72804i	0.208020	−	0.454673i
$37$	4.33521	−	2.20890i	0.712704	−	0.363141i	−0.0597483	−	0.998213i	$-0.519030\pi$
$37$	4.33521	−	2.20890i	0.712704	−	0.363141i	0.772452	+	0.635073i	$0.219030\pi$
$38$	5.83498	−	2.97307i	0.946558	−	0.482296i
$39$	4.28544	+	0.246528i	0.686219	+	0.0394761i
$40$	0.656484	+	2.13753i	0.103799	+	0.337973i
$41$	−8.06531	−	2.62058i	−1.25959	−	0.409265i	−0.398241	−	0.917281i	$-0.630379\pi$
$41$	−8.06531	−	2.62058i	−1.25959	−	0.409265i	−0.861348	+	0.508015i	$0.830379\pi$
$42$	−6.52614	−	1.42202i	−1.00700	−	0.219423i
$43$	−5.16349	+	5.16349i	−0.787425	+	0.787425i	−0.981071	−	0.193647i	$-0.937969\pi$
$43$	−5.16349	+	5.16349i	−0.787425	+	0.787425i	0.193647	+	0.981071i	$0.437969\pi$
$44$	0.285527	+	0.207447i	0.0430448	+	0.0312738i
$45$	4.08259	+	5.32283i	0.608596	+	0.793480i
$46$	6.34085	−	4.60690i	0.934908	−	0.679250i
$47$	0.668895	−	4.22323i	0.0975683	−	0.616022i	−0.889649	−	0.456644i	$-0.849051\pi$
$47$	0.668895	−	4.22323i	0.0975683	−	0.616022i	0.987218	−	0.159378i	$-0.0509488\pi$
$48$	−1.15238	−	1.29306i	−0.166332	−	0.186638i
$49$			7.87088i			1.12441i
$50$	−4.91055	−	0.941550i	−0.694456	−	0.133155i
$51$	2.22763	−	5.71582i	0.311931	−	0.800375i
$52$	1.12512	−	2.20817i	0.156026	−	0.306218i
$53$	4.34698	+	0.688494i	0.597103	+	0.0945719i	0.447668	−	0.894200i	$-0.352255\pi$
$53$	4.34698	+	0.688494i	0.597103	+	0.0945719i	0.149435	+	0.988772i	$0.452255\pi$
$54$	−4.59315	−	2.42961i	−0.625048	−	0.330628i
$55$	−0.708866	+	0.346854i	−0.0955835	+	0.0467698i
$56$	−2.26666	+	3.11979i	−0.302896	+	0.416900i
$57$	−4.56057	−	10.3855i	−0.604063	−	1.37560i
$58$	−6.16696	+	0.976751i	−0.809762	+	0.128254i
$59$	−0.713107	+	2.19472i	−0.0928386	+	0.285728i	−0.986684	−	0.162647i	$-0.947997\pi$
$59$	−0.713107	+	2.19472i	−0.0928386	+	0.285728i	0.893846	+	0.448375i	$0.147997\pi$
$60$	3.76150	−	0.922555i	0.485608	−	0.119101i
$61$	0.0451729	+	0.139028i	0.00578380	+	0.0178007i	0.953907	−	0.300103i	$-0.0970211\pi$
$61$	0.0451729	+	0.139028i	0.00578380	+	0.0178007i	−0.948123	+	0.317904i	$0.897021\pi$
$62$	1.90338	+	3.73559i	0.241729	+	0.474420i
$63$	−3.10814	+	11.1435i	−0.391589	+	1.40395i
$64$	−0.951057	+	0.309017i	−0.118882	+	0.0386271i
$65$	3.18432	+	4.53538i	0.394966	+	0.562545i
$66$	0.387119	−	0.473094i	0.0476510	−	0.0582339i
$67$	1.18445	+	7.47829i	0.144703	+	0.913619i	0.948053	+	0.318112i	$0.103049\pi$
$67$	1.18445	+	7.47829i	0.144703	+	0.913619i	−0.803350	+	0.595507i	$0.796951\pi$
$68$	−2.50443	−	2.50443i	−0.303707	−	0.303707i
$69$	−7.33546	−	11.4228i	−0.883085	−	1.37515i
$70$	−3.78989	−	7.74539i	−0.452978	−	0.925752i
$71$	−3.62303	−	4.98667i	−0.429974	−	0.591809i	0.537973	−	0.842962i	$-0.319190\pi$
$71$	−3.62303	−	4.98667i	−0.429974	−	0.591809i	−0.967947	+	0.251153i	$0.919190\pi$
$72$	−2.35059	+	1.86407i	−0.277019	+	0.219682i
$73$	−9.30362	−	4.74043i	−1.08891	−	0.554825i	−0.185079	−	0.982724i	$-0.559254\pi$
$73$	−9.30362	−	4.74043i	−1.08891	−	0.554825i	−0.903827	+	0.427898i	$0.859254\pi$
$74$	−4.86552			−0.565605
$75$	−2.11660	+	8.39762i	−0.244404	+	0.969674i
$76$	−6.54875			−0.751193
$77$	−1.21266	−	0.617880i	−0.138195	−	0.0704139i
$78$	−3.70643	−	2.16521i	−0.419671	−	0.245161i
$79$	0.803169	+	1.10547i	0.0903636	+	0.124375i	0.851805	−	0.523859i	$-0.175508\pi$
$79$	0.803169	+	1.10547i	0.0903636	+	0.124375i	−0.761442	+	0.648234i	$0.775508\pi$
$80$	0.385487	−	2.20259i	0.0430987	−	0.246257i
$81$	−4.65817	+	7.70074i	−0.517574	+	0.855638i
$82$	5.99652	+	5.99652i	0.662205	+	0.662205i
$83$	−0.915181	−	5.77823i	−0.100454	−	0.634243i	−0.985621	−	0.168969i	$-0.945956\pi$
$83$	−0.915181	−	5.77823i	−0.100454	−	0.634243i	0.885167	−	0.465273i	$-0.154044\pi$
$84$	5.16925	+	4.22984i	0.564011	+	0.461513i
$85$	7.57069	−	2.32513i	0.821157	−	0.252196i
$86$	6.94488	−	2.25653i	0.748886	−	0.243328i
$87$	1.07553	+	10.7610i	0.115309	+	1.15370i
$88$	−0.160227	−	0.314463i	−0.0170803	−	0.0335219i
$89$	−0.633239	−	1.94891i	−0.0671232	−	0.206584i	0.911869	−	0.410481i	$-0.134639\pi$
$89$	−0.633239	−	1.94891i	−0.0671232	−	0.206584i	−0.978992	+	0.203897i	$0.934639\pi$
$90$	−1.22110	−	6.59613i	−0.128715	−	0.695293i
$91$	−2.95327	+	9.08922i	−0.309587	+	0.952809i
$92$	−7.74123	+	1.22609i	−0.807079	+	0.127829i
$93$	6.64888	−	2.91971i	0.689457	−	0.302759i
$94$	−2.51330	+	3.45926i	−0.259227	+	0.356795i
$95$	6.85822	−	12.9381i	0.703639	−	1.32742i
$96$	0.439743	+	1.67530i	0.0448811	+	0.170984i
$97$	6.93926	+	1.09907i	0.704575	+	0.111594i	0.498433	−	0.866928i	$-0.333909\pi$
$97$	6.93926	+	1.09907i	0.704575	+	0.111594i	0.206142	+	0.978522i	$0.433909\pi$
$98$	3.57330	−	7.01300i	0.360958	−	0.708420i
$99$	−0.779562	−	0.716464i	−0.0783490	−	0.0720073i
$100$	3.94788	+	3.06827i	0.394788	+	0.306827i
$101$		−	9.58679i		−	0.953921i	−0.878925	−	0.476961i	$-0.841738\pi$
$101$		−	9.58679i		−	0.953921i	0.878925	−	0.476961i	$-0.158262\pi$
$102$	−4.57976	+	4.08151i	−0.453464	+	0.404130i
$103$	1.04075	−	6.57102i	0.102548	−	0.647462i	−0.881853	−	0.471524i	$-0.843704\pi$
$103$	1.04075	−	6.57102i	0.102548	−	0.647462i	0.984401	−	0.175938i	$-0.0562959\pi$
$104$	−2.00498	+	1.45670i	−0.196604	+	0.142841i
$105$	−13.7703	+	5.78297i	−1.34384	+	0.564360i
$106$	−3.56062	−	2.58694i	−0.345838	−	0.251266i
$107$	10.4337	−	10.4337i	1.00866	−	1.00866i	0.00870186	−	0.999962i	$-0.497230\pi$
$107$	10.4337	−	10.4337i	1.00866	−	1.00866i	0.999962	−	0.00870186i	$-0.00276992\pi$
$108$	2.98950	+	4.25004i	0.287665	+	0.408961i
$109$	−10.5722	−	3.43511i	−1.01263	−	0.329024i	−0.244729	−	0.969592i	$-0.578699\pi$
$109$	−10.5722	−	3.43511i	−1.01263	−	0.329024i	−0.767902	+	0.640568i	$0.778699\pi$
$110$	0.789073	+	0.0127689i	0.0752351	+	0.00121747i
$111$	−0.483998	+	8.41342i	−0.0459391	+	0.798566i
$112$	3.43597	−	1.75071i	0.324668	−	0.165427i
$113$	1.56816	−	0.799015i	0.147520	−	0.0751650i	−0.378672	−	0.925531i	$-0.623619\pi$
$113$	1.56816	−	0.799015i	0.147520	−	0.0751650i	0.526192	+	0.850366i	$0.323619\pi$
$114$	−0.651437	+	11.3240i	−0.0610127	+	1.06059i
$115$	5.68471	−	16.5781i	0.530102	−	1.54592i
$116$	5.93824	+	1.92945i	0.551352	+	0.179145i
$117$	−4.11276	+	6.19375i	−0.380224	+	0.572612i
$118$	1.63176	−	1.63176i	0.150216	−	0.150216i
$119$	11.0497	+	8.02806i	1.01292	+	0.735931i
$120$	−3.77035	−	0.885683i	−0.344185	−	0.0808514i
$121$	−8.79842	+	6.39242i	−0.799856	+	0.581129i
$122$	0.0228680	−	0.144383i	0.00207037	−	0.0130718i
$123$	10.9656	−	9.77263i	0.988739	−	0.881169i
$124$		−	4.19255i		−	0.376502i
$125$	−10.1963	+	4.58641i	−0.911986	+	0.410221i
$126$	7.82841	−	8.51786i	0.697410	−	0.758831i
$127$	2.44874	−	4.80592i	0.217290	−	0.426457i	−0.756471	−	0.654027i	$-0.773078\pi$
$127$	2.44874	−	4.80592i	0.217290	−	0.426457i	0.973762	+	0.227571i	$0.0730782\pi$
$128$	0.987688	+	0.156434i	0.0873001	+	0.0138270i
$129$	−3.21113	−	12.2335i	−0.282724	−	1.07710i
$130$	−0.778228	−	5.48671i	−0.0682551	−	0.481216i
$131$	−10.2354	+	14.0878i	−0.894273	+	1.23086i	0.0779865	+	0.996954i	$0.475151\pi$
$131$	−10.2354	+	14.0878i	−0.894273	+	1.23086i	−0.972259	+	0.233906i	$0.924849\pi$
$132$	−0.559706	+	0.245782i	−0.0487161	+	0.0213926i
$133$	24.9429	−	3.95056i	2.16282	−	0.342557i
$134$	2.33973	−	7.20094i	0.202122	−	0.622066i
$135$	−11.5274	+	1.45537i	−0.992124	+	0.125258i
$136$	1.09448	+	3.36845i	0.0938505	+	0.288842i
$137$	8.13848	+	15.9727i	0.695317	+	1.36464i	0.920663	+	0.390358i	$0.127649\pi$
$137$	8.13848	+	15.9727i	0.695317	+	1.36464i	−0.225346	+	0.974279i	$0.572351\pi$
$138$	1.35009	+	13.5080i	0.114927	+	1.14988i
$139$	17.1405	−	5.56927i	1.45383	−	0.472379i	0.527654	−	0.849459i	$-0.323072\pi$
$139$	17.1405	−	5.56927i	1.45383	−	0.472379i	0.926181	+	0.377080i	$0.123072\pi$
$140$	−0.139519	+	8.62177i	−0.0117915	+	0.728673i
$141$	5.73171	+	4.69008i	0.482697	+	0.394976i
$142$	0.964240	+	6.08797i	0.0809172	+	0.510891i
$143$	−0.618480	−	0.618480i	−0.0517199	−	0.0517199i
$144$	2.94066	−	0.593750i	0.245055	−	0.0494792i
$145$	−10.0308	+	9.71134i	−0.833014	+	0.806483i
$146$	6.13747	+	8.44751i	0.507941	+	0.699121i
$147$	−11.7714	−	6.87655i	−0.970886	−	0.567168i
$148$	4.33521	+	2.20890i	0.356352	+	0.181570i
$149$	−4.64891			−0.380854			−0.190427	−	0.981701i	$-0.560987\pi$
$149$	−4.64891			−0.380854			−0.190427	+	0.981701i	$0.560987\pi$
$150$	5.69834	−	6.52142i	0.465268	−	0.532472i
$151$	−14.6548			−1.19259			−0.596295	−	0.802765i	$-0.703361\pi$
$151$	−14.6548			−1.19259			−0.596295	+	0.802765i	$0.703361\pi$
$152$	5.83498	+	2.97307i	0.473279	+	0.241148i
$153$	6.60214	+	8.32530i	0.533751	+	0.673061i
$154$	0.799974	+	1.10107i	0.0644637	+	0.0887267i
$155$	8.28307	+	4.39067i	0.665312	+	0.352667i
$156$	2.31947	+	3.61190i	0.185706	+	0.289183i
$157$	3.17235	+	3.17235i	0.253181	+	0.253181i	0.822273	−	0.569093i	$-0.192705\pi$
$157$	3.17235	+	3.17235i	0.253181	+	0.253181i	−0.569093	+	0.822273i	$0.692705\pi$
$158$	−0.213757	−	1.34961i	−0.0170056	−	0.107369i
$159$	−4.82751	+	5.89965i	−0.382846	+	0.467873i
$160$	−1.34343	+	1.78751i	−0.106207	+	0.141315i
$161$	28.7452	−	9.33987i	2.26544	−	0.736085i
$162$	7.64652	−	4.74665i	0.600768	−	0.372932i
$163$	−4.91227	−	9.64088i	−0.384759	−	0.755132i	0.614675	−	0.788781i	$-0.289287\pi$
$163$	−4.91227	−	9.64088i	−0.384759	−	0.755132i	−0.999434	+	0.0336487i	$0.989287\pi$
$164$	−2.62058	−	8.06531i	−0.204633	−	0.629795i
$165$	0.100573	−	1.36319i	0.00782959	−	0.106124i
$166$	−1.80783	+	5.56392i	−0.140315	+	0.431844i
$167$	−16.5871	+	2.62714i	−1.28355	+	0.203295i	−0.760686	−	0.649120i	$-0.775137\pi$
$167$	−16.5871	+	2.62714i	−1.28355	+	0.203295i	−0.522866	+	0.852415i	$0.675137\pi$
$168$	−2.68553	−	6.11560i	−0.207193	−	0.471829i
$169$	4.03108	−	5.54830i	0.310083	−	0.426793i
$170$	−7.80112	−	1.36531i	−0.598319	−	0.104715i
$171$	19.5166	+	2.25292i	1.49247	+	0.172285i
$172$	−7.21237	−	1.14233i	−0.549938	−	0.0871017i
$173$	−7.90821	+	15.5207i	−0.601250	+	1.18002i	0.367043	+	0.930204i	$0.380370\pi$
$173$	−7.90821	+	15.5207i	−0.601250	+	1.18002i	−0.968293	+	0.249816i	$0.919630\pi$
$174$	3.92710	−	10.0764i	0.297713	−	0.763892i
$175$	−16.8876	−	9.30485i	−1.27658	−	0.703381i
$176$			0.352930i			0.0266031i
$177$	−2.65931	−	2.98395i	−0.199886	−	0.224288i
$178$	−0.320566	+	2.02397i	−0.0240274	+	0.151703i
$179$	−5.94519	+	4.31943i	−0.444364	+	0.322849i	−0.787367	−	0.616485i	$-0.788556\pi$
$179$	−5.94519	+	4.31943i	−0.444364	+	0.322849i	0.343002	+	0.939334i	$0.388556\pi$
$180$	−1.90657	+	6.43156i	−0.142107	+	0.479380i
$181$	−0.543117	−	0.394597i	−0.0403695	−	0.0293302i	0.567418	−	0.823430i	$-0.307943\pi$
$181$	−0.543117	−	0.394597i	−0.0403695	−	0.0293302i	−0.607787	+	0.794100i	$0.707943\pi$
$182$	6.75780	−	6.75780i	0.500922	−	0.500922i
$183$	−0.247391	−	0.0539056i	−0.0182877	−	0.00398482i
$184$	7.45412	+	2.42199i	0.549525	+	0.178552i
$185$	−8.90413	+	6.25164i	−0.654644	+	0.459630i
$186$	−7.24972	−	0.417054i	−0.531575	−	0.0305799i
$187$	−1.11376	+	0.567491i	−0.0814465	+	0.0414991i
$188$	3.80983	−	1.94121i	0.277861	−	0.141577i
$189$	−13.9503	−	14.3841i	−1.01473	−	1.04629i
$190$	−11.9845	+	8.41439i	−0.869448	+	0.610444i
$191$	−13.4008	−	4.35419i	−0.969650	−	0.315058i	−0.218975	−	0.975730i	$-0.570271\pi$
$191$	−13.4008	−	4.35419i	−0.969650	−	0.315058i	−0.750675	+	0.660672i	$0.770271\pi$
$192$	0.368756	−	1.69234i	0.0266126	−	0.122134i
$193$	−2.89340	+	2.89340i	−0.208271	+	0.208271i	−0.803532	−	0.595261i	$-0.797049\pi$
$193$	−2.89340	+	2.89340i	−0.208271	+	0.208271i	0.595261	+	0.803532i	$0.297049\pi$
$194$	−5.68396	−	4.12964i	−0.408085	−	0.296491i
$195$	−9.56499	+	0.799915i	−0.684963	+	0.0572831i
$196$	−6.36767	+	4.62638i	−0.454834	+	0.330456i
$197$	3.55739	−	22.4605i	0.253454	−	1.60024i	−0.452353	−	0.891839i	$-0.649415\pi$
$197$	3.55739	−	22.4605i	0.253454	−	1.60024i	0.705806	−	0.708405i	$-0.250585\pi$
$198$	0.369327	+	0.992288i	0.0262470	+	0.0705188i
$199$		−	6.31867i		−	0.447919i	−0.974598	−	0.223959i	$-0.928102\pi$
$199$		−	6.31867i		−	0.447919i	0.974598	−	0.223959i	$-0.0718983\pi$
$200$	−2.12462	−	4.52615i	−0.150233	−	0.320047i
$201$	−12.2191	−	4.76215i	−0.861866	−	0.335896i
$202$	−4.35231	+	8.54189i	−0.306228	+	0.601006i
$203$	−23.7815	−	3.76662i	−1.66914	−	0.264365i
$204$	5.93357	−	1.55748i	0.415433	−	0.109045i
$205$	18.6788	+	3.26907i	1.30458	+	0.228321i
$206$	−3.91049	+	5.38233i	−0.272457	+	0.375005i
$207$	23.4923	−	0.990845i	1.63283	−	0.0688685i
$208$	2.44778	−	0.387690i	0.169723	−	0.0268815i
$209$	−0.714216	+	2.19813i	−0.0494033	+	0.152048i
$210$	14.8948	+	1.09891i	1.02784	+	0.0758317i
$211$	−1.28435	−	3.95283i	−0.0884185	−	0.272124i	0.897064	−	0.441900i	$-0.145696\pi$
$211$	−1.28435	−	3.95283i	−0.0884185	−	0.272124i	−0.985483	+	0.169776i	$0.945696\pi$
$212$	1.99809	+	3.92147i	0.137229	+	0.269327i
$213$	10.6232	−	1.06175i	0.727889	−	0.0727502i
$214$	−14.0333	+	4.55969i	−0.959296	+	0.311694i
$215$	9.81007	−	13.0529i	0.669041	−	0.890202i
$216$	−0.734186	−	5.14402i	−0.0499550	−	0.350006i
$217$	2.52917	+	15.9686i	0.171691	+	1.08402i
$218$	7.86037	+	7.86037i	0.532371	+	0.532371i
$219$	15.2179	−	9.77255i	1.02833	−	0.660368i
$220$	−0.697272	−	0.369609i	−0.0470101	−	0.0249190i
$221$	5.15934	+	7.10123i	0.347055	+	0.477680i
$222$	4.25086	−	7.27668i	0.285299	−	0.488379i
$223$	13.6942	+	6.97753i	0.917030	+	0.467250i	0.847779	−	0.530349i	$-0.177939\pi$
$223$	13.6942	+	6.97753i	0.917030	+	0.467250i	0.0692509	+	0.997599i	$0.477939\pi$
$224$	−3.85628			−0.257658
$225$	−10.7099	−	10.5022i	−0.713996	−	0.700150i
$226$	−1.75998			−0.117072
$227$	−12.4969	−	6.36747i	−0.829445	−	0.422624i	−0.0129084	−	0.999917i	$-0.504109\pi$
$227$	−12.4969	−	6.36747i	−0.829445	−	0.422624i	−0.816537	+	0.577293i	$0.804109\pi$
$228$	5.72144	−	9.79405i	0.378912	−	0.648627i
$229$	10.1878	+	14.0224i	0.673232	+	0.926624i	0.999828	−	0.0185396i	$-0.00590167\pi$
$229$	10.1878	+	14.0224i	0.673232	+	0.926624i	−0.326596	+	0.945164i	$0.605902\pi$
$230$	−12.5914	+	12.1904i	−0.830254	+	0.803811i
$231$	1.98354	−	1.27378i	0.130507	−	0.0838085i
$232$	−4.41506	−	4.41506i	−0.289863	−	0.289863i
$233$	0.384884	+	2.43006i	0.0252146	+	0.159199i	0.997083	−	0.0763263i	$-0.0243191\pi$
$233$	0.384884	+	2.43006i	0.0252146	+	0.159199i	−0.971868	+	0.235525i	$0.924319\pi$
$234$	6.47640	−	3.65152i	0.423375	−	0.238707i
$235$	−0.154700	+	9.55990i	−0.0100915	+	0.623619i
$236$	−2.19472	+	0.713107i	−0.142864	+	0.0464193i
$237$	−2.35500	+	0.235375i	−0.152974	+	0.0152892i
$238$	−6.20067	−	12.1695i	−0.401930	−	0.788831i
$239$	−0.751883	−	2.31406i	−0.0486352	−	0.149684i	0.923790	−	0.382901i	$-0.125075\pi$
$239$	−0.751883	−	2.31406i	−0.0486352	−	0.149684i	−0.972425	+	0.233217i	$0.925075\pi$
$240$	2.95732	+	2.50085i	0.190894	+	0.161429i
$241$	0.500207	−	1.53948i	0.0322212	−	0.0991666i	−0.933653	−	0.358180i	$-0.883397\pi$
$241$	0.500207	−	1.53948i	0.0322212	−	0.0991666i	0.965874	+	0.259013i	$0.0833974\pi$
$242$	10.7415	−	1.70129i	0.690493	−	0.109363i
$243$	−7.44723	−	13.6945i	−0.477740	−	0.878501i
$244$	−0.0859239	+	0.118264i	−0.00550072	+	0.00757109i
$245$	−2.47160	−	17.4254i	−0.157905	−	1.11327i
$246$	−14.2071	+	3.72918i	−0.905814	+	0.237764i
$247$	16.0299	+	2.53888i	1.01996	+	0.161545i
$248$	−1.90338	+	3.73559i	−0.120865	+	0.237210i
$249$	9.44125	+	3.67955i	0.598315	+	0.233182i
$250$	11.1672	+	0.542505i	0.706274	+	0.0343110i
$251$			24.7263i			1.56071i	0.625335	+	0.780357i	$0.284962\pi$
$251$			24.7263i			1.56071i	−0.625335	+	0.780357i	$0.715038\pi$
$252$	−10.8422	+	4.03544i	−0.682994	+	0.254209i
$253$	−0.432724	+	2.73211i	−0.0272052	+	0.171767i
$254$	−4.36369	+	3.17040i	−0.273802	+	0.198929i
$255$	−3.13691	+	13.3538i	−0.196441	+	0.836249i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−20.2470	+	20.2470i	−1.26297	+	1.26297i	−0.313326	+	0.949646i	$0.601443\pi$
$257$	−20.2470	+	20.2470i	−1.26297	+	1.26297i	−0.949646	+	0.313326i	$0.898557\pi$
$258$	−2.69276	+	12.3579i	−0.167644	+	0.769372i
$259$	−17.8445	−	5.79802i	−1.10880	−	0.360272i
$260$	−1.79751	+	5.24200i	−0.111477	+	0.325095i
$261$	−17.0334	−	7.79306i	−1.05434	−	0.482378i
$262$	15.5156	−	7.90558i	0.958555	−	0.488408i
$263$	−2.68232	+	1.36671i	−0.165399	+	0.0842750i	−0.534730	−	0.845023i	$-0.679587\pi$
$263$	−2.68232	+	1.36671i	−0.165399	+	0.0842750i	0.369331	+	0.929298i	$0.379587\pi$
$264$	0.610284	+	0.0351078i	0.0375604	+	0.00216073i
$265$	−9.84001	−	0.159232i	−0.604467	−	0.00978157i
$266$	−24.0178	−	7.80385i	−1.47262	−	0.478485i
$267$	3.46795	+	0.755655i	0.212235	+	0.0462454i
$268$	−5.35387	+	5.35387i	−0.327039	+	0.327039i
$269$	−10.4918	−	7.62274i	−0.639697	−	0.464767i	0.220049	−	0.975489i	$-0.429378\pi$
$269$	−10.4918	−	7.62274i	−0.639697	−	0.464767i	−0.859746	+	0.510722i	$0.829378\pi$
$270$	10.9317	+	3.93661i	0.665285	+	0.239574i
$271$	13.7784	−	10.0106i	0.836981	−	0.608102i	−0.0845447	−	0.996420i	$-0.526944\pi$
$271$	13.7784	−	10.0106i	0.836981	−	0.608102i	0.921526	+	0.388317i	$0.126944\pi$
$272$	0.554059	−	3.49819i	0.0335948	−	0.212109i
$273$	−11.0133	−	12.3578i	−0.666555	−	0.747926i
$274$		−	17.9265i		−	1.08298i
$275$	1.46045	−	0.990501i	0.0880682	−	0.0597294i
$276$	4.92959	−	12.6487i	0.296726	−	0.761361i
$277$	−4.82425	+	9.46812i	−0.289861	+	0.568884i	−0.989315	−	0.145793i	$-0.953427\pi$
$277$	−4.82425	+	9.46812i	−0.289861	+	0.568884i	0.699454	+	0.714677i	$0.253427\pi$
$278$	−17.8007	−	2.81935i	−1.06761	−	0.169093i
$279$	−1.44233	+	12.4947i	−0.0863502	+	0.748036i
$280$	4.03851	−	7.61871i	0.241347	−	0.455305i
$281$	16.4932	−	22.7009i	0.983902	−	1.35422i	0.0492011	−	0.998789i	$-0.484332\pi$
$281$	16.4932	−	22.7009i	0.983902	−	1.35422i	0.934701	−	0.355436i	$-0.115668\pi$
$282$	−2.97774	−	6.78104i	−0.177322	−	0.403805i
$283$	−25.3567	+	4.01611i	−1.50730	+	0.238733i	−0.854761	−	0.519022i	$-0.826296\pi$
$283$	−25.3567	+	4.01611i	−1.50730	+	0.238733i	−0.652539	+	0.757755i	$0.726296\pi$
$284$	1.90474	−	5.86218i	0.113025	−	0.347856i
$285$	13.3579	+	21.5605i	0.791256	+	1.27714i
$286$	0.270286	+	0.831854i	0.0159823	+	0.0491886i
$287$	14.8467	+	29.1383i	0.876372	+	1.71998i
$288$	−2.88970	−	0.805995i	−0.170277	−	0.0474937i
$289$	−4.23760	+	1.37688i	−0.249271	+	0.0809930i
$290$	13.3464	−	4.09898i	0.783726	−	0.240700i
$291$	−7.70635	+	9.41786i	−0.451754	+	0.552085i
$292$	−1.63344	−	10.3131i	−0.0955899	−	0.603531i
$293$	24.1559	+	24.1559i	1.41120	+	1.41120i	0.751709	+	0.659495i	$0.229230\pi$
$293$	24.1559	+	24.1559i	1.41120	+	1.41120i	0.659495	+	0.751709i	$0.270770\pi$
$294$	7.36648	+	11.4711i	0.429622	+	0.669010i
$295$	0.889572	−	5.08283i	0.0517929	−	0.295934i
$296$	−2.85988	−	3.93629i	−0.166227	−	0.228792i
$297$	1.75260	−	0.539930i	0.101696	−	0.0313299i
$298$	4.14221	+	2.11056i	0.239952	+	0.122262i
$299$	19.4242			1.12333
$300$	−8.03792	+	3.22363i	−0.464070	+	0.186117i
$301$	28.1596			1.62309
$302$	13.0575	+	6.65314i	0.751376	+	0.382845i
$303$	14.3376	+	8.37569i	0.823675	+	0.481171i
$304$	−3.84926	−	5.29805i	−0.220770	−	0.303864i
$305$	−0.143666	−	0.293610i	−0.00822629	−	0.0168121i
$306$	−2.10294	−	10.4152i	−0.120217	−	0.595398i
$307$	−12.8970	−	12.8970i	−0.736071	−	0.736071i	0.235744	−	0.971815i	$-0.424247\pi$
$307$	−12.8970	−	12.8970i	−0.736071	−	0.736071i	−0.971815	+	0.235744i	$0.924247\pi$
$308$	−0.212907	−	1.34424i	−0.0121315	−	0.0765952i
$309$	8.91809	+	7.29740i	0.507333	+	0.415135i
$310$	−5.38694	−	7.67255i	−0.305958	−	0.435772i
$311$	15.4255	−	5.01205i	0.874699	−	0.284207i	0.162945	−	0.986635i	$-0.447901\pi$
$311$	15.4255	−	5.01205i	0.874699	−	0.284207i	0.711755	+	0.702428i	$0.247901\pi$
$312$	−0.426897	−	4.27124i	−0.0241683	−	0.241812i
$313$	2.45198	+	4.81228i	0.138594	+	0.272006i	0.949863	−	0.312668i	$-0.101223\pi$
$313$	2.45198	+	4.81228i	0.138594	+	0.272006i	−0.811269	+	0.584674i	$0.801223\pi$
$314$	−1.38637	−	4.26680i	−0.0782372	−	0.240789i
$315$	3.38188	−	25.6467i	0.190547	−	1.44503i
$316$	−0.422251	+	1.29956i	−0.0237535	+	0.0731057i
$317$	−8.47316	+	1.34202i	−0.475900	+	0.0753752i	−0.389777	−	0.920909i	$-0.627448\pi$
$317$	−8.47316	+	1.34202i	−0.475900	+	0.0753752i	−0.0861233	+	0.996284i	$0.527448\pi$
$318$	6.97973	−	3.06499i	0.391404	−	0.171876i
$319$	1.29527	−	1.78278i	0.0725210	−	0.0998166i
$320$	2.00852	−	0.982784i	0.112279	−	0.0549393i
$321$	6.48862	+	24.7198i	0.362160	+	1.37973i
$322$	−29.8523	−	4.72815i	−1.66361	−	0.263489i
$323$	10.5300	−	20.6663i	0.585905	−	1.14990i
$324$	−8.96804	+	0.757846i	−0.498224	+	0.0421025i
$325$	−8.47399	−	9.04099i	−0.470052	−	0.501504i
$326$			10.8202i			0.599276i
$327$	14.3740	−	12.8102i	0.794884	−	0.708404i
$328$	−1.32662	+	8.37596i	−0.0732504	+	0.462485i
$329$	−13.3399	+	9.69197i	−0.735450	+	0.534336i
$330$	−0.708486	+	1.16895i	−0.0390008	+	0.0643486i
$331$	22.9895	+	16.7029i	1.26362	+	0.918073i	0.998929	−	0.0462607i	$-0.0147305\pi$
$331$	22.9895	+	16.7029i	1.26362	+	0.918073i	0.264690	+	0.964334i	$0.414731\pi$
$332$	4.13675	−	4.13675i	0.227034	−	0.227034i
$333$	−12.1599	−	8.07440i	−0.666360	−	0.442474i
$334$	15.9719	+	5.18960i	0.873946	+	0.283962i
$335$	−4.97057	−	16.1843i	−0.271571	−	0.884244i
$336$	−0.383604	+	6.66824i	−0.0209273	+	0.363783i
$337$	−4.22871	+	2.15464i	−0.230353	+	0.117371i	−0.565358	−	0.824846i	$-0.691262\pi$
$337$	−4.22871	+	2.15464i	−0.230353	+	0.117371i	0.335005	+	0.942216i	$0.391262\pi$
$338$	−6.11059	+	3.11350i	−0.332372	+	0.169352i
$339$	−0.175074	+	3.04335i	−0.00950874	+	0.165292i
$340$	6.33101	+	4.75814i	0.343347	+	0.258046i
$341$	−1.40726	−	0.457245i	−0.0762072	−	0.0247612i
$342$	−16.3666	−	10.8677i	−0.885007	−	0.587660i
$343$	2.37470	−	2.37470i	0.128222	−	0.128222i
$344$	5.90767	+	4.29217i	0.318520	+	0.231418i
$345$	19.8270	+	22.9856i	1.06745	+	1.23750i
$346$	14.0925	−	10.2388i	0.757620	−	0.550443i
$347$	−1.25574	+	7.92843i	−0.0674116	+	0.425620i	0.930784	+	0.365570i	$0.119126\pi$
$347$	−1.25574	+	7.92843i	−0.0674116	+	0.425620i	−0.998195	+	0.0600500i	$0.980874\pi$
$348$	−8.07367	+	7.19529i	−0.432794	+	0.385708i
$349$			18.9234i			1.01295i	0.862256	+	0.506474i	$0.169051\pi$
$349$			18.9234i			1.01295i	−0.862256	+	0.506474i	$0.830949\pi$
$350$	10.8227	+	15.9575i	0.578496	+	0.852964i
$351$	−5.66994	−	11.5622i	−0.302639	−	0.617143i
$352$	0.160227	−	0.314463i	0.00854013	−	0.0167609i
$353$	4.66620	+	0.739053i	0.248357	+	0.0393358i	0.279371	−	0.960183i	$-0.409874\pi$
$353$	4.66620	+	0.739053i	0.248357	+	0.0393358i	−0.0310149	+	0.999519i	$0.509874\pi$
$354$	1.01478	+	3.86602i	0.0539349	+	0.205477i
$355$	9.58695	+	9.90233i	0.508823	+	0.525561i
$356$	1.20449	−	1.65784i	0.0638379	−	0.0878654i
$357$	−21.6602	+	9.51159i	−1.14638	+	0.503406i
$358$	7.25818	−	1.14958i	0.383607	−	0.0607573i
$359$	−4.67561	+	14.3900i	−0.246769	+	0.759478i	0.748571	+	0.663054i	$0.230740\pi$
$359$	−4.67561	+	14.3900i	−0.246769	+	0.759478i	−0.995340	+	0.0964232i	$0.969260\pi$
$360$	4.61864	−	4.86500i	0.243423	−	0.256408i
$361$	−7.38121	−	22.7170i	−0.388485	−	1.19563i
$362$	0.304777	+	0.598158i	0.0160187	+	0.0314385i
$363$	−1.87335	−	18.7434i	−0.0983252	−	0.983775i
$364$	−9.08922	+	2.95327i	−0.476405	+	0.154793i
$365$	22.0859	+	7.57338i	1.15603	+	0.396409i
$366$	0.195954	+	0.160343i	0.0102427	+	0.00838128i
$367$	−5.73021	−	36.1791i	−0.299114	−	1.88853i	−0.439193	−	0.898393i	$-0.644735\pi$
$367$	−5.73021	−	36.1791i	−0.299114	−	1.88853i	0.140078	−	0.990140i	$-0.455265\pi$
$368$	−5.54211	−	5.54211i	−0.288902	−	0.288902i
$369$	5.03522	+	24.9378i	0.262123	+	1.29821i
$370$	10.7718	−	1.52786i	0.560000	−	0.0794297i
$371$	−9.97595	−	13.7307i	−0.517926	−	0.712864i
$372$	6.27021	+	3.66290i	0.325095	+	0.189913i
$373$	−1.97517	−	1.00640i	−0.102270	−	0.0521093i	0.402107	−	0.915593i	$-0.368278\pi$
$373$	−1.97517	−	1.00640i	−0.102270	−	0.0521093i	−0.504377	+	0.863483i	$0.668278\pi$
$374$	1.25001			0.0646363
$375$	2.04895	−	19.2562i	0.105807	−	0.994387i
$376$	−4.27588			−0.220512
$377$	−13.7875	−	7.02506i	−0.710090	−	0.361809i
$378$	5.89952	+	19.1497i	0.303439	+	0.984952i
$379$	4.15559	+	5.71968i	0.213458	+	0.293800i	0.902297	−	0.431114i	$-0.141879\pi$
$379$	4.15559	+	5.71968i	0.213458	+	0.293800i	−0.688839	+	0.724914i	$0.741879\pi$
$380$	14.4983	−	2.05643i	0.743749	−	0.105492i
$381$	5.04816	+	7.86103i	0.258625	+	0.402733i
$382$	9.96347	+	9.96347i	0.509775	+	0.509775i
$383$	−2.17700	−	13.7450i	−0.111240	−	0.702339i	−0.978771	−	0.204957i	$-0.934295\pi$
$383$	−2.17700	−	13.7450i	−0.111240	−	0.702339i	0.867532	−	0.497382i	$-0.165705\pi$
$384$	−1.09687	+	1.34048i	−0.0559744	+	0.0684059i
$385$	2.87874	+	0.987133i	0.146714	+	0.0503090i
$386$	3.89161	−	1.26446i	0.198078	−	0.0643593i
$387$	21.1014	+	5.88560i	1.07264	+	0.299182i
$388$	3.18963	+	6.26000i	0.161929	+	0.317803i
$389$	4.65972	+	14.3411i	0.236257	+	0.727125i	0.996952	+	0.0780155i	$0.0248584\pi$
$389$	4.65972	+	14.3411i	0.236257	+	0.727125i	−0.760695	+	0.649110i	$0.775142\pi$
$390$	8.88562	+	3.62968i	0.449941	+	0.183796i
$391$	8.57820	−	26.4010i	0.433818	−	1.33515i
$392$	7.77397	−	1.23128i	0.392645	−	0.0621888i
$393$	−12.1268	−	27.6158i	−0.611719	−	1.39303i
$394$	−13.3665	+	18.3974i	−0.673395	+	0.926849i
$395$	−2.12528	−	2.19519i	−0.106934	−	0.110452i
$396$	0.121416	−	1.05181i	0.00610139	−	0.0528552i
$397$	−13.6256	−	2.15808i	−0.683849	−	0.108311i	−0.195163	−	0.980771i	$-0.562524\pi$
$397$	−13.6256	−	2.15808i	−0.683849	−	0.108311i	−0.488686	+	0.872460i	$0.662524\pi$
$398$	−2.86862	+	5.62998i	−0.143791	+	0.282205i
$399$	−15.8835	+	40.7551i	−0.795171	+	2.04031i
$400$	−0.161779	+	4.99738i	−0.00808895	+	0.249869i
$401$		−	15.8196i		−	0.789991i	−0.918683	−	0.394995i	$-0.870746\pi$
$401$		−	15.8196i		−	0.789991i	0.918683	−	0.394995i	$-0.129254\pi$
$402$	8.72529	+	9.79044i	0.435178	+	0.488303i
$403$	−1.62541	+	10.2624i	−0.0809674	+	0.511208i
$404$	7.75588	−	5.63497i	0.385869	−	0.280350i
$405$	7.89459	−	18.5115i	0.392285	−	0.919844i
$406$	19.4795	+	14.1527i	0.966750	+	0.702385i
$407$	1.21424	−	1.21424i	0.0601875	−	0.0601875i
$408$	−5.99393	−	1.30606i	−0.296744	−	0.0646595i
$409$	−5.65867	−	1.83861i	−0.279803	−	0.0909136i	0.165754	−	0.986167i	$-0.446994\pi$
$409$	−5.65867	−	1.83861i	−0.279803	−	0.0909136i	−0.445557	+	0.895254i	$0.646994\pi$
$410$	−15.1588	−	11.3927i	−0.748638	−	0.562647i
$411$	−30.9984	−	1.78324i	−1.52904	−	0.0879610i
$412$	5.92780	−	3.02037i	0.292042	−	0.148803i
$413$	7.92905	−	4.04005i	0.390163	−	0.198798i
$414$	−21.3816	−	9.78243i	−1.05085	−	0.480780i
$415$	3.84060	+	12.5051i	0.188527	+	0.613850i
$416$	−2.35699	−	0.765834i	−0.115561	−	0.0375481i
$417$	−6.64591	+	30.5003i	−0.325452	+	1.49361i
$418$	1.63430	−	1.63430i	0.0799363	−	0.0799363i
$419$	3.49605	+	2.54003i	0.170793	+	0.124088i	0.669898	−	0.742453i	$-0.266338\pi$
$419$	3.49605	+	2.54003i	0.170793	+	0.124088i	−0.499105	+	0.866542i	$0.666338\pi$
$420$	−12.7725	−	7.74124i	−0.623233	−	0.377734i
$421$	−20.2471	+	14.7103i	−0.986781	+	0.716939i	−0.959214	−	0.282681i	$-0.908776\pi$
$421$	−20.2471	+	14.7103i	−0.986781	+	0.716939i	−0.0275674	+	0.999620i	$0.508776\pi$
$422$	−0.650182	+	4.10508i	−0.0316503	+	0.199832i
$423$	−12.0219	+	4.47453i	−0.584526	+	0.217559i
$424$		−	4.40116i		−	0.213739i
$425$	−16.0307	+	7.52496i	−0.777603	+	0.365014i
$426$	−9.94736	−	3.87680i	−0.481951	−	0.187831i
$427$	0.255924	−	0.502279i	0.0123850	−	0.0243070i
$428$	14.5738	+	2.30827i	0.704452	+	0.111574i
$429$	1.46532	−	0.384627i	0.0707464	−	0.0185700i
$430$	−14.6667	+	7.17656i	−0.707293	+	0.346085i
$431$	−4.11469	+	5.66339i	−0.198198	+	0.272796i	−0.896535	−	0.442973i	$-0.853924\pi$
$431$	−4.11469	+	5.66339i	−0.198198	+	0.272796i	0.698337	+	0.715769i	$0.253924\pi$
$432$	−1.68117	+	4.91667i	−0.0808855	+	0.236553i
$433$	−9.74698	+	1.54377i	−0.468410	+	0.0741889i	−0.386178	−	0.922424i	$-0.626205\pi$
$433$	−9.74698	+	1.54377i	−0.468410	+	0.0741889i	−0.0822322	+	0.996613i	$0.526205\pi$
$434$	4.99607	−	15.3763i	0.239819	−	0.738087i
$435$	−5.76028	−	23.4862i	−0.276184	−	1.12608i
$436$	−3.43511	−	10.5722i	−0.164512	−	0.506315i
$437$	−23.3021	−	45.7330i	−1.11469	−	2.18770i
$438$	−17.9959	+	1.79863i	−0.859877	+	0.0859420i
$439$	−0.555271	+	0.180419i	−0.0265016	+	0.00861091i	−0.322238	−	0.946659i	$-0.604435\pi$
$439$	−0.555271	+	0.180419i	−0.0265016	+	0.00861091i	0.295736	+	0.955270i	$0.404435\pi$
$440$	0.453475	+	0.645879i	0.0216186	+	0.0307911i
$441$	20.5686	−	11.5970i	0.979456	−	0.552237i
$442$	−1.37312	−	8.66953i	−0.0653126	−	0.412368i
$443$	−6.33032	−	6.33032i	−0.300763	−	0.300763i	0.540549	−	0.841312i	$-0.318216\pi$
$443$	−6.33032	−	6.33032i	−0.300763	−	0.300763i	−0.841312	+	0.540549i	$0.818216\pi$
$444$	−7.09108	+	4.55372i	−0.336528	+	0.216110i
$445$	2.01393	+	4.11586i	0.0954692	+	0.195110i
$446$	−9.03387	−	12.4341i	−0.427766	−	0.588770i
$447$	4.06161	−	6.95273i	0.192108	−	0.328853i
$448$	3.43597	+	1.75071i	0.162334	+	0.0827134i
$449$	18.3782			0.867322			0.433661	−	0.901076i	$-0.357221\pi$
$449$	18.3782			0.867322			0.433661	+	0.901076i	$0.357221\pi$
$450$	4.77471	+	14.2198i	0.225082	+	0.670327i
$451$	−2.99298			−0.140934
$452$	1.56816	+	0.799015i	0.0737598	+	0.0375825i
$453$	12.8035	−	21.9171i	0.601559	−	1.02976i
$454$	8.24401	+	11.3469i	0.386911	+	0.532537i
$455$	3.68408	−	21.0501i	0.172713	−	0.986843i
$456$	−9.54425	+	6.12908i	−0.446950	+	0.287021i
$457$	−24.7918	−	24.7918i	−1.15971	−	1.15971i	−0.984537	−	0.175174i	$-0.943951\pi$
$457$	−24.7918	−	24.7918i	−1.15971	−	1.15971i	−0.175174	−	0.984537i	$-0.556049\pi$
$458$	−2.71142	−	17.1192i	−0.126696	−	0.799928i
$459$	−18.2191	+	2.60034i	−0.850394	+	0.121373i
$460$	16.7534	−	5.14534i	0.781130	−	0.239903i
$461$	−0.133994	+	0.0435374i	−0.00624074	+	0.00202774i	−0.312136	−	0.950038i	$-0.601044\pi$
$461$	−0.133994	+	0.0435374i	−0.00624074	+	0.00202774i	0.305895	+	0.952065i	$0.401044\pi$
$462$	−2.34563	+	0.234438i	−0.109129	+	0.0109071i
$463$	−4.02806	−	7.90552i	−0.187200	−	0.367401i	0.778264	−	0.627937i	$-0.216101\pi$
$463$	−4.02806	−	7.90552i	−0.187200	−	0.367401i	−0.965464	+	0.260537i	$0.916101\pi$
$464$	1.92945	+	5.93824i	0.0895725	+	0.275676i
$465$	−13.8032	+	8.55183i	−0.640107	+	0.396582i
$466$	0.760291	−	2.33993i	0.0352198	−	0.108395i
$467$	4.81480	−	0.762590i	0.222803	−	0.0352885i	−0.0440349	−	0.999030i	$-0.514021\pi$
$467$	4.81480	−	0.762590i	0.222803	−	0.0352885i	0.266838	+	0.963742i	$0.414021\pi$
$468$	−7.42827	+	0.313305i	−0.343372	+	0.0144825i
$469$	17.1621	−	23.6216i	0.792470	−	1.09074i
$470$	4.47794	−	8.44770i	0.206552	−	0.389663i
$471$	−7.51602	+	1.97285i	−0.346320	+	0.0909043i
$472$	2.27925	+	0.360998i	0.104911	+	0.0166163i
$473$	−1.17002	+	2.29630i	−0.0537977	+	0.105584i
$474$	2.20518	+	0.859427i	0.101287	+	0.0394748i
$475$	−11.1207	+	30.7975i	−0.510251	+	1.41308i
$476$			13.6581i			0.626020i
$477$	−4.60564	−	12.3742i	−0.210878	−	0.566575i
$478$	−0.380627	+	2.40319i	−0.0174095	+	0.109919i
$479$	11.5308	−	8.37759i	0.526854	−	0.382782i	−0.292326	−	0.956319i	$-0.594429\pi$
$479$	11.5308	−	8.37759i	0.526854	−	0.382782i	0.819180	+	0.573537i	$0.194429\pi$
$480$	−1.49963	−	3.57087i	−0.0684482	−	0.162987i
$481$	−9.75526	−	7.08761i	−0.444802	−	0.323167i
$482$	−1.14460	+	1.14460i	−0.0521349	+	0.0521349i
$483$	−11.1454	+	51.1501i	−0.507135	+	2.32741i
$484$	−10.3432	−	3.36070i	−0.470144	−	0.152759i
$485$	−15.7080	−	0.254189i	−0.713265	−	0.0115421i
$486$	0.418364	+	15.5828i	0.0189774	+	0.706852i
$487$	−31.0777	+	15.8349i	−1.40827	+	0.717547i	−0.982321	−	0.187202i	$-0.940058\pi$
$487$	−31.0777	+	15.8349i	−1.40827	+	0.717547i	−0.425945	+	0.904749i	$0.640058\pi$
$488$	0.130250	−	0.0663655i	0.00589612	−	0.00300422i
$489$	18.7102	+	1.07634i	0.846106	+	0.0486739i
$490$	−5.70876	+	16.6482i	−0.257895	+	0.752090i
$491$	5.09165	+	1.65438i	0.229783	+	0.0746610i	0.421645	−	0.906761i	$-0.361453\pi$
$491$	5.09165	+	1.65438i	0.229783	+	0.0746610i	−0.191862	+	0.981422i	$0.561453\pi$
$492$	14.3517	+	3.12718i	0.647023	+	0.140984i
$493$	−15.6372	+	15.6372i	−0.704266	+	0.704266i
$494$	−13.1301	−	9.53958i	−0.590751	−	0.429206i
$495$	1.95086	+	1.34139i	0.0876848	+	0.0602909i
$496$	3.39184	−	2.46432i	0.152298	−	0.110651i
$497$	−3.71838	+	23.4769i	−0.166792	+	1.05308i
$498$	−6.74174	−	7.56474i	−0.302104	−	0.338984i
$499$		−	8.93736i		−	0.400091i	−0.979787	−	0.200046i	$-0.935891\pi$
$499$		−	8.93736i		−	0.400091i	0.979787	−	0.200046i	$-0.0641090\pi$
$500$	−9.70373	−	5.55316i	−0.433964	−	0.248345i
$501$	10.5626	−	27.1023i	0.471903	−	1.21084i
$502$	11.2255	−	22.0313i	0.501020	−	0.983307i
$503$	−2.88408	−	0.456793i	−0.128595	−	0.0203674i	0.0918053	−	0.995777i	$-0.470736\pi$
$503$	−2.88408	−	0.456793i	−0.128595	−	0.0203674i	−0.220400	+	0.975410i	$0.570736\pi$
$504$	11.4925	+	1.32665i	0.511917	+	0.0590936i
$505$	3.01043	+	21.2243i	0.133962	+	0.944468i
$506$	1.62591	−	2.23788i	0.0722807	−	0.0994859i
$507$	4.77599	+	10.8761i	0.212109	+	0.483025i
$508$	5.32741	−	0.843778i	0.236365	−	0.0374366i
$509$	3.24395	−	9.98385i	0.143786	−	0.442527i	−0.853067	−	0.521801i	$-0.825260\pi$
$509$	3.24395	−	9.98385i	0.143786	−	0.442527i	0.996853	+	0.0792745i	$0.0252604\pi$
$510$	8.85751	−	10.4742i	0.392217	−	0.463806i
$511$	12.4429	+	38.2953i	0.550441	+	1.69408i
$512$	0.453990	+	0.891007i	0.0200637	+	0.0393773i
$513$	−20.4205	+	27.2200i	−0.901586	+	1.20179i
$514$	27.2321	−	8.84825i	1.20116	−	0.390280i
$515$	−0.240701	+	14.8745i	−0.0106065	+	0.655447i
$516$	8.00965	−	9.78853i	0.352605	−	0.430916i
$517$	−0.236073	−	1.49051i	−0.0103825	−	0.0655524i
$518$	13.2673	+	13.2673i	0.582932	+	0.582932i
$519$	−16.3030	−	25.3872i	−0.715624	−	1.11437i
$520$	3.98141	−	3.85461i	0.174596	−	0.169036i
$521$	−11.1471	−	15.3427i	−0.488364	−	0.672175i	0.491722	−	0.870753i	$-0.336368\pi$
$521$	−11.1471	−	15.3427i	−0.488364	−	0.672175i	−0.980085	+	0.198578i	$0.936368\pi$
$522$	11.6389	+	14.6767i	0.509421	+	0.642381i
$523$	21.7058	+	11.0596i	0.949127	+	0.483604i	0.858802	−	0.512308i	$-0.171209\pi$
$523$	21.7058	+	11.0596i	0.949127	+	0.483604i	0.0903250	+	0.995912i	$0.471209\pi$
$524$	−17.4135			−0.760714
$525$	28.6702	−	17.1271i	1.25127	−	0.747487i
$526$	3.01044			0.131261
$527$	13.2307	+	6.74137i	0.576338	+	0.293659i
$528$	−0.527829	−	0.308344i	−0.0229708	−	0.0134190i
$529$	−22.5886	−	31.0905i	−0.982111	−	1.35176i
$530$	8.69523	+	4.60915i	0.377696	+	0.200209i
$531$	6.78604	−	1.37017i	0.294489	−	0.0594605i
$532$	17.8571	+	17.8571i	0.774205	+	0.774205i
$533$	3.28775	+	20.7580i	0.142408	+	0.899131i
$534$	−2.74691	−	2.24771i	−0.118870	−	0.0972680i
$535$	−19.8229	+	26.3756i	−0.857018	+	1.14032i
$536$	7.20094	−	2.33973i	0.311033	−	0.101061i
$537$	−1.26584	−	12.6651i	−0.0546251	−	0.546541i
$538$	5.88761	+	11.5551i	0.253833	+	0.498175i
$539$	0.858409	+	2.64191i	0.0369743	+	0.113795i
$540$	−7.95308	−	8.47045i	−0.342246	−	0.364510i
$541$	8.94591	−	27.5327i	0.384615	−	1.18372i	−0.552144	−	0.833749i	$-0.686190\pi$
$541$	8.94591	−	27.5327i	0.384615	−	1.18372i	0.936759	−	0.349974i	$-0.113810\pi$
$542$	−16.8214	+	2.66425i	−0.722542	+	0.114439i
$543$	1.06465	−	0.467516i	0.0456884	−	0.0200630i
$544$	−2.08182	+	2.86537i	−0.0892571	+	0.122852i
$545$	24.4845	+	4.28516i	1.04880	+	0.183556i
$546$	4.20261	+	16.0108i	0.179855	+	0.685198i
$547$	12.9801	+	2.05584i	0.554988	+	0.0879014i	0.427627	−	0.903955i	$-0.359350\pi$
$547$	12.9801	+	2.05584i	0.554988	+	0.0879014i	0.127360	+	0.991857i	$0.459350\pi$
$548$	−8.13848	+	15.9727i	−0.347659	+	0.682319i
$549$	0.296757	−	0.322892i	0.0126653	−	0.0137807i
$550$	−1.75094	+	0.219514i	−0.0746605	+	0.00936011i
$551$			40.8893i			1.74194i
$552$	−10.1347	+	9.03207i	−0.431360	+	0.384430i
$553$	0.824307	−	5.20447i	0.0350531	−	0.221317i
$554$	8.59687	−	6.24599i	0.365246	−	0.265367i
$555$	−1.57044	−	18.7785i	−0.0666614	−	0.797104i
$556$	14.5805	+	10.5934i	0.618353	+	0.449260i
$557$	24.6270	−	24.6270i	1.04348	−	1.04348i	0.0444707	−	0.999011i	$-0.485840\pi$
$557$	24.6270	−	24.6270i	1.04348	−	1.04348i	0.999011	−	0.0444707i	$-0.0141601\pi$
$558$	6.95759	−	10.4780i	0.294538	−	0.443570i
$559$	17.2114	+	5.59233i	0.727966	+	0.236530i
$560$	−7.05717	+	4.95488i	−0.298220	+	0.209382i
$561$	0.124345	−	2.16150i	0.00524983	−	0.0912587i
$562$	−25.0016	+	12.7389i	−1.05463	+	0.537359i
$563$	8.71723	−	4.44165i	0.367388	−	0.187193i	−0.260544	−	0.965462i	$-0.583902\pi$
$563$	8.71723	−	4.44165i	0.367388	−	0.187193i	0.627931	+	0.778269i	$0.283902\pi$
$564$	−0.425343	+	7.39381i	−0.0179102	+	0.311336i
$565$	−3.22085	+	2.26138i	−0.135502	+	0.0951368i
$566$	24.4163	+	7.93332i	1.02629	+	0.333462i
$567$	33.7003	−	8.29649i	1.41528	−	0.348420i
$568$	−4.35851	+	4.35851i	−0.182879	+	0.182879i
$569$	−8.66014	−	6.29196i	−0.363052	−	0.263773i	0.391272	−	0.920275i	$-0.372035\pi$
$569$	−8.66014	−	6.29196i	−0.363052	−	0.263773i	−0.754324	+	0.656502i	$0.772035\pi$
$570$	−2.11373	−	25.2750i	−0.0885345	−	1.05865i
$571$	12.5798	−	9.13980i	0.526450	−	0.382489i	−0.292578	−	0.956242i	$-0.594513\pi$
$571$	12.5798	−	9.13980i	0.526450	−	0.382489i	0.819028	+	0.573753i	$0.194513\pi$
$572$	0.136828	−	0.863895i	0.00572105	−	0.0361213i
$573$	18.2199	−	16.2376i	0.761146	−	0.678337i
$574$		−	32.7026i		−	1.36498i
$575$	−7.37961	+	38.4875i	−0.307751	+	1.60504i
$576$	2.20883	+	2.03004i	0.0920345	+	0.0845852i
$577$	−6.76199	+	13.2712i	−0.281505	+	0.552485i	−0.987855	−	0.155378i	$-0.950341\pi$
$577$	−6.76199	+	13.2712i	−0.281505	+	0.552485i	0.706350	+	0.707863i	$0.250341\pi$
$578$	4.40082	+	0.697022i	0.183050	+	0.0289923i
$579$	−1.79938	−	6.85512i	−0.0747795	−	0.284889i
$580$	−13.7526	−	2.40691i	−0.571046	−	0.0999417i
$581$	−13.2606	+	18.2516i	−0.550140	+	0.757203i
$582$	11.1420	−	4.89277i	0.461852	−	0.202812i
$583$	1.53418	−	0.242990i	0.0635392	−	0.0100636i
$584$	−3.22666	+	9.93064i	−0.133520	+	0.410933i
$585$	7.16032	−	15.0039i	0.296043	−	0.620334i
$586$	−10.5565	−	32.4896i	−0.436086	−	1.34213i
$587$	−11.6079	−	22.7817i	−0.479108	−	0.940302i	−0.996423	−	0.0845070i	$-0.973068\pi$
$587$	−11.6079	−	22.7817i	−0.479108	−	0.940302i	0.517315	−	0.855795i	$-0.326932\pi$
$588$	−1.35580	−	13.5652i	−0.0559121	−	0.559418i
$589$	26.1121	−	8.48435i	1.07593	−	0.349592i
$590$	−3.10017	+	4.12498i	−0.127632	+	0.169823i
$591$	30.4830	+	24.9433i	1.25390	+	1.02603i
$592$	0.761135	+	4.80562i	0.0312825	+	0.197510i
$593$	5.46116	+	5.46116i	0.224263	+	0.224263i	0.810291	−	0.586028i	$-0.199309\pi$
$593$	5.46116	+	5.46116i	0.224263	+	0.224263i	−0.586028	+	0.810291i	$0.699309\pi$
$594$	−1.80670	−	0.314580i	−0.0741297	−	0.0129074i
$595$	−26.9839	−	14.3036i	−1.10623	−	0.586390i
$596$	−2.73256	−	3.76105i	−0.111930	−	0.154058i
$597$	9.44996	+	5.52043i	0.386761	+	0.225936i
$598$	−17.3071	−	8.81838i	−0.707738	−	0.360611i
$599$	20.6409			0.843363			0.421681	−	0.906744i	$-0.361440\pi$
$599$	20.6409			0.843363			0.421681	+	0.906744i	$0.361440\pi$
$600$	8.62534	+	0.776862i	0.352128	+	0.0317153i
$601$	17.9854			0.733642			0.366821	−	0.930292i	$-0.380446\pi$
$601$	17.9854			0.733642			0.366821	+	0.930292i	$0.380446\pi$
$602$	−25.0904	−	12.7842i	−1.02261	−	0.521045i
$603$	17.7975	−	14.1138i	0.724770	−	0.574758i
$604$	−8.61387	−	11.8560i	−0.350494	−	0.482413i
$605$	17.4716	−	16.9151i	0.710320	−	0.687697i
$606$	−8.97244	−	13.9719i	−0.364480	−	0.567571i
$607$	5.54524	+	5.54524i	0.225074	+	0.225074i	0.810631	−	0.585557i	$-0.199124\pi$
$607$	5.54524	+	5.54524i	0.225074	+	0.225074i	−0.585557	+	0.810631i	$0.699124\pi$
$608$	1.02445	+	6.46812i	0.0415469	+	0.262317i
$609$	26.4104	−	32.2759i	1.07020	−	1.30789i
$610$	−0.00528883	+	0.326831i	−0.000214138	+	0.0132330i
$611$	−10.0782	+	3.27461i	−0.407721	+	0.132477i
$612$	−2.85467	+	10.2347i	−0.115393	+	0.413715i
$613$	−2.13588	−	4.19191i	−0.0862676	−	0.169310i	0.843842	−	0.536592i	$-0.180288\pi$
$613$	−2.13588	−	4.19191i	−0.0862676	−	0.169310i	−0.930110	+	0.367282i	$0.880288\pi$
$614$	5.63620	+	17.3464i	0.227459	+	0.700045i
$615$	−21.2082	+	25.0791i	−0.855195	+	1.01129i
$616$	−0.420571	+	1.29439i	−0.0169453	+	0.0521523i
$617$	40.5328	−	6.41977i	1.63179	−	0.258450i	0.727733	−	0.685861i	$-0.240574\pi$
$617$	40.5328	−	6.41977i	1.63179	−	0.258450i	0.904058	+	0.427410i	$0.140574\pi$
$618$	−4.63313	−	10.5508i	−0.186372	−	0.424414i
$619$	−10.1486	+	13.9684i	−0.407908	+	0.561438i	−0.962707	−	0.270547i	$-0.912795\pi$
$619$	−10.1486	+	13.9684i	−0.407908	+	0.561438i	0.554798	+	0.831985i	$0.312795\pi$
$620$	1.31654	+	9.28192i	0.0528733	+	0.372771i
$621$	−19.0426	+	35.9998i	−0.764155	+	1.44462i
$622$	−16.0196	−	2.53726i	−0.642329	−	0.101735i
$623$	−3.58757	+	7.04100i	−0.143733	+	0.282092i
$624$	−1.55874	+	3.99951i	−0.0623994	+	0.160109i
$625$	21.1335	−	13.3557i	0.845340	−	0.534229i
$626$		−	5.40095i		−	0.215865i
$627$	−2.66345	−	2.98859i	−0.106368	−	0.119353i
$628$	−0.701824	+	4.43114i	−0.0280058	+	0.176822i
$629$	−13.9415	+	10.1291i	−0.555885	+	0.403874i
$630$	−14.6566	+	21.3160i	−0.583934	+	0.849250i
$631$	−29.4746	−	21.4146i	−1.17337	−	0.852501i	−0.181959	−	0.983306i	$-0.558244\pi$
$631$	−29.4746	−	21.4146i	−1.17337	−	0.852501i	−0.991408	+	0.130805i	$0.958244\pi$
$632$	0.966214	−	0.966214i	0.0384339	−	0.0384339i
$633$	7.03380	+	1.53264i	0.279569	+	0.0609171i
$634$	8.15891	+	2.65099i	0.324032	+	0.105284i
$635$	−3.91214	+	11.4088i	−0.155249	+	0.452745i
$636$	−7.61046	−	0.437806i	−0.301774	−	0.0173601i
$637$	17.3803	−	8.85568i	0.688631	−	0.350875i
$638$	−1.96346	+	1.00043i	−0.0777340	+	0.0396074i
$639$	−7.69324	+	16.8152i	−0.304340	+	0.665201i
$640$	−2.23578	−	0.0361796i	−0.0883768	−	0.00143013i
$641$	−28.1775	−	9.15543i	−1.11294	−	0.361618i	−0.305874	−	0.952072i	$-0.598949\pi$
$641$	−28.1775	−	9.15543i	−1.11294	−	0.361618i	−0.807071	+	0.590454i	$0.798949\pi$
$642$	5.44117	−	24.9713i	0.214746	−	0.985539i
$643$	16.2471	−	16.2471i	0.640721	−	0.640721i	−0.310012	−	0.950733i	$-0.600333\pi$
$643$	16.2471	−	16.2471i	0.640721	−	0.640721i	0.950733	+	0.310012i	$0.100333\pi$
$644$	24.4521	+	17.7655i	0.963547	+	0.700058i
$645$	10.9507	+	26.0755i	0.431183	+	1.02672i
$646$	−18.7646	+	13.6333i	−0.738284	+	0.536394i
$647$	−0.280589	+	1.77157i	−0.0110311	+	0.0696477i	−0.992590	−	0.121513i	$-0.961225\pi$
$647$	−0.280589	+	1.77157i	−0.0110311	+	0.0696477i	0.981559	+	0.191161i	$0.0612253\pi$
$648$	8.33463	+	3.39616i	0.327415	+	0.133414i
$649$			0.814444i			0.0319697i
$650$	3.44585	+	11.9027i	0.135157	+	0.466862i
$651$	−26.0916	−	10.1687i	−1.02261	−	0.398544i
$652$	4.91227	−	9.64088i	0.192379	−	0.377566i
$653$	−26.3159	−	4.16803i	−1.02982	−	0.163107i	−0.381416	−	0.924404i	$-0.624563\pi$
$653$	−26.3159	−	4.16803i	−1.02982	−	0.163107i	−0.648404	+	0.761296i	$0.724563\pi$
$654$	−18.6230	+	4.88829i	−0.728218	+	0.191147i
$655$	18.2364	−	34.4033i	0.712557	−	1.34425i
$656$	4.98463	−	6.86076i	0.194617	−	0.267868i
$657$	1.32004	+	31.2973i	0.0514996	+	1.22102i
$658$	16.2860	−	2.57944i	0.634893	−	0.100557i
$659$	2.02081	−	6.21940i	0.0787195	−	0.242274i	−0.903951	−	0.427637i	$-0.859346\pi$
$659$	2.02081	−	6.21940i	0.0787195	−	0.242274i	0.982670	+	0.185363i	$0.0593462\pi$
$660$	1.16196	−	0.719897i	0.0452291	−	0.0280219i
$661$	5.97584	+	18.3917i	0.232433	+	0.715356i	0.997452	+	0.0713473i	$0.0227299\pi$
$661$	5.97584	+	18.3917i	0.232433	+	0.715356i	−0.765018	+	0.644008i	$0.777270\pi$
$662$	−12.9009	−	25.3194i	−0.501407	−	0.984066i
$663$	−15.1279	+	1.51198i	−0.587518	+	0.0587206i
$664$	−5.56392	+	1.80783i	−0.215922	+	0.0701573i
$665$	−53.9807	+	16.5787i	−2.09328	+	0.642894i
$666$	7.16887	+	12.7148i	0.277788	+	0.492690i
$667$	7.65551	+	48.3350i	0.296422	+	1.87154i
$668$	−11.8751	−	11.8751i	−0.459461	−	0.459461i
$669$	−22.3995	+	14.3844i	−0.866015	+	0.556134i
$670$	−2.91872	+	16.6769i	−0.112760	+	0.644286i
$671$	0.0303252	+	0.0417390i	0.00117069	+	0.00161132i
$672$	3.36911	−	5.76730i	0.129966	−	0.222478i
$673$	39.1978	+	19.9723i	1.51096	+	0.769874i	0.996170	−	0.0874407i	$-0.0278688\pi$
$673$	39.1978	+	19.9723i	1.51096	+	0.769874i	0.514793	+	0.857315i	$0.327869\pi$
$674$	4.74599			0.182809
$675$	25.0637	−	6.84187i	0.964702	−	0.263344i
$676$	6.85808			0.263772
$677$	33.3683	+	17.0020i	1.28245	+	0.653440i	0.956441	−	0.291927i	$-0.0942963\pi$
$677$	33.3683	+	17.0020i	1.28245	+	0.653440i	0.326008	+	0.945367i	$0.394296\pi$
$678$	1.53764	−	2.63216i	0.0590528	−	0.101087i
$679$	−15.9250	−	21.9189i	−0.611147	−	0.841171i
$680$	−3.48082	−	7.11375i	−0.133483	−	0.272800i
$681$	20.4411	−	13.1267i	0.783303	−	0.503018i
$682$	1.04629	+	1.04629i	0.0400645	+	0.0400645i
$683$	−5.33840	−	33.7054i	−0.204268	−	1.28970i	−0.850263	−	0.526358i	$-0.823557\pi$
$683$	−5.33840	−	33.7054i	−0.204268	−	1.28970i	0.645995	−	0.763342i	$-0.276443\pi$
$684$	9.64894	+	17.1135i	0.368937	+	0.654352i
$685$	−23.0336	−	32.8064i	−0.880067	−	1.25347i
$686$	−3.19397	+	1.03778i	−0.121946	+	0.0396228i
$687$	−29.8721	+	2.98562i	−1.13969	+	0.113909i
$688$	−3.31516	−	6.50638i	−0.126389	−	0.248053i
$689$	−3.37056	−	10.3735i	−0.128408	−	0.395199i
$690$	−7.23074	−	29.4816i	−0.275269	−	1.12235i
$691$	−9.75674	+	30.0282i	−0.371164	+	1.14232i	0.574867	+	0.818247i	$0.305054\pi$
$691$	−9.75674	+	30.0282i	−0.371164	+	1.14232i	−0.946030	+	0.324078i	$0.894946\pi$
$692$	−17.2049	+	2.72498i	−0.654031	+	0.103588i
$693$	0.172057	+	4.07936i	0.00653591	+	0.154962i
$694$	4.71830	−	6.49419i	0.179104	−	0.246516i
$695$	−36.1986	+	17.7123i	−1.37309	+	0.671865i
$696$	10.4603	−	2.74568i	0.396496	−	0.104075i
$697$	29.6659	+	4.69862i	1.12368	+	0.177973i
$698$	8.59105	−	16.8609i	0.325176	−	0.638194i
$699$	−3.97056	−	1.54745i	−0.150181	−	0.0585301i
$700$	−2.39851	−	19.1316i	−0.0906552	−	0.723107i
$701$			41.1349i			1.55364i	0.629720	+	0.776822i	$0.283170\pi$
$701$			41.1349i			1.55364i	−0.629720	+	0.776822i	$0.716830\pi$
$702$	−0.197163	+	12.8761i	−0.00744143	+	0.485976i
$703$	−4.98448	+	31.4708i	−0.187993	+	1.18694i
$704$	−0.285527	+	0.207447i	−0.0107612	+	0.00781846i
$705$	−14.1623	−	8.58356i	−0.533381	−	0.323275i
$706$	−3.82209	−	2.77691i	−0.143846	−	0.104510i
$707$	−26.1413	+	26.1413i	−0.983143	+	0.983143i
$708$	0.850963	−	3.90535i	0.0319812	−	0.146772i
$709$	−48.5191	−	15.7648i	−1.82217	−	0.592060i	−0.999731	−	0.0232123i	$-0.992611\pi$
$709$	−48.5191	−	15.7648i	−1.82217	−	0.592060i	−0.822443	−	0.568848i	$-0.807389\pi$
$710$	−4.04647	−	13.1754i	−0.151861	−	0.494465i
$711$	1.70547	−	3.72768i	0.0639603	−	0.139799i
$712$	−1.82585	+	0.930319i	−0.0684268	+	0.0348652i
$713$	29.2785	−	14.9181i	1.09649	−	0.558689i
$714$	23.6176	+	1.35865i	0.883865	+	0.0508460i
$715$	1.56347	+	1.17505i	0.0584706	+	0.0439442i
$716$	−6.98899	−	2.27086i	−0.261191	−	0.0848660i
$717$	4.11771	+	0.897235i	0.153779	+	0.0335079i
$718$	10.6989	−	10.6989i	0.399281	−	0.399281i
$719$	−29.8994	−	21.7232i	−1.11506	−	0.810138i	−0.131606	−	0.991302i	$-0.542013\pi$
$719$	−29.8994	−	21.7232i	−1.11506	−	0.810138i	−0.983453	+	0.181164i	$0.942013\pi$
$720$	−6.32390	+	2.23793i	−0.235678	+	0.0834026i
$721$	−20.7558	+	15.0800i	−0.772985	+	0.561607i
$722$	−3.73661	+	23.5920i	−0.139062	+	0.878004i
$723$	1.86537	+	2.09309i	0.0693738	+	0.0778427i
$724$		−	0.671329i		−	0.0249497i
$725$	19.1578	−	24.6499i	0.711502	−	0.915474i
$726$	−6.84017	+	17.5510i	−0.253863	+	0.651379i
$727$	8.55075	−	16.7818i	0.317130	−	0.622402i	−0.676328	−	0.736600i	$-0.736430\pi$
$727$	8.55075	−	16.7818i	0.317130	−	0.622402i	0.993458	+	0.114198i	$0.0364299\pi$
$728$	9.43931	+	1.49504i	0.349844	+	0.0554099i
$729$	26.9873	+	0.826673i	0.999531	+	0.0306175i
$730$	−16.2405	−	16.7747i	−0.601087	−	0.620861i
$731$	15.2020	−	20.9238i	0.562266	−	0.773893i
$732$	−0.101802	−	0.231828i	−0.00376271	−	0.00856862i
$733$	34.3095	−	5.43410i	1.26725	−	0.200713i	0.513625	−	0.858015i	$-0.328302\pi$
$733$	34.3095	−	5.43410i	1.26725	−	0.200713i	0.753627	+	0.657302i	$0.228302\pi$
$734$	−11.3193	+	34.8373i	−0.417804	+	1.28587i
$735$	28.2201	+	11.5276i	1.04091	+	0.425203i
$736$	2.42199	+	7.45412i	0.0892758	+	0.274763i
$737$	1.21316	+	2.38096i	0.0446873	+	0.0877038i
$738$	6.83513	−	24.5057i	0.251605	−	0.902068i
$739$	2.70309	−	0.878288i	0.0994348	−	0.0323083i	−0.258877	−	0.965910i	$-0.583352\pi$
$739$	2.70309	−	0.878288i	0.0994348	−	0.0323083i	0.358312	+	0.933602i	$0.383352\pi$
$740$	−10.2914	−	3.52897i	−0.378319	−	0.129727i
$741$	−17.8019	+	21.7555i	−0.653968	+	0.799209i
$742$	2.65502	+	16.7632i	0.0974689	+	0.615395i
$743$	−19.3245	−	19.3245i	−0.708947	−	0.708947i	0.257367	−	0.966314i	$-0.417145\pi$
$743$	−19.3245	−	19.3245i	−0.708947	−	0.708947i	−0.966314	+	0.257367i	$0.917145\pi$
$744$	−3.92387	−	6.11028i	−0.143856	−	0.224014i
$745$	10.2923	−	1.45984i	0.377079	−	0.0534845i
$746$	1.30299	+	1.79341i	0.0477059	+	0.0656615i
$747$	−13.7515	+	10.9053i	−0.503142	+	0.399002i
$748$	−1.11376	−	0.567491i	−0.0407233	−	0.0207495i
$749$	−56.9012			−2.07913
$750$	−10.5678	+	16.2272i	−0.385880	+	0.592534i
$751$	13.6596			0.498445			0.249222	−	0.968446i	$-0.419825\pi$
$751$	13.6596			0.498445			0.249222	+	0.968446i	$0.419825\pi$
$752$	3.80983	+	1.94121i	0.138930	+	0.0707886i
$753$	−36.9797	−	21.6027i	−1.34762	−	0.787245i
$754$	9.09541	+	12.5188i	0.331235	+	0.455906i
$755$	32.4444	−	4.60187i	1.18077	−	0.167479i
$756$	3.43725	−	19.7408i	0.125012	−	0.717966i
$757$	−11.1659	−	11.1659i	−0.405833	−	0.405833i	0.474450	−	0.880283i	$-0.342647\pi$
$757$	−11.1659	−	11.1659i	−0.405833	−	0.405833i	−0.880283	+	0.474450i	$0.842647\pi$
$758$	−1.10598	−	6.98287i	−0.0401710	−	0.253629i
$759$	−3.70798	−	3.03413i	−0.134591	−	0.110132i
$760$	−13.8517	−	4.74982i	−0.502454	−	0.172294i
$761$	13.3455	−	4.33621i	0.483774	−	0.157188i	−0.0569686	−	0.998376i	$-0.518143\pi$
$761$	13.3455	−	4.33621i	0.483774	−	0.157188i	0.540742	+	0.841188i	$0.318143\pi$
$762$	−0.929110	−	9.29604i	−0.0336581	−	0.336760i
$763$	19.4614	+	38.1951i	0.704548	+	1.38275i
$764$	−4.35419	−	13.4008i	−0.157529	−	0.484825i
$765$	−17.2308	−	16.3583i	−0.622982	−	0.591434i
$766$	−4.30040	+	13.2353i	−0.155380	+	0.478209i
$767$	5.64864	−	0.894657i	0.203961	−	0.0323042i
$768$	1.58588	−	0.696404i	0.0572256	−	0.0251293i
$769$	13.0082	−	17.9042i	0.469087	−	0.645643i	−0.507275	−	0.861784i	$-0.669347\pi$
$769$	13.0082	−	17.9042i	0.469087	−	0.645643i	0.976362	+	0.216141i	$0.0693471\pi$
$770$	−2.11683	−	2.18646i	−0.0762851	−	0.0787946i
$771$	−12.5914	−	47.9697i	−0.453468	−	1.72759i
$772$	−4.04150	−	0.640111i	−0.145457	−	0.0230381i
$773$	−19.2486	+	37.7774i	−0.692323	+	1.35876i	0.230324	+	0.973114i	$0.426021\pi$
$773$	−19.2486	+	37.7774i	−0.692323	+	1.35876i	−0.922647	+	0.385646i	$0.873979\pi$
$774$	−16.1295	−	14.8239i	−0.579762	−	0.532836i
$775$	−19.7167	−	7.11952i	−0.708245	−	0.255741i
$776$		−	7.02576i		−	0.252210i
$777$	24.2615	−	21.6219i	0.870376	−	0.775683i
$778$	2.35890	−	14.8935i	0.0845708	−	0.533959i
$779$	44.9294	−	32.6431i	1.60976	−	1.16956i
$780$	−6.26930	−	7.26806i	−0.224477	−	0.260238i
$781$	−1.75995	−	1.27868i	−0.0629758	−	0.0457546i
$782$	−19.6290	+	19.6290i	−0.701932	+	0.701932i
$783$	26.5366	−	18.6660i	0.948340	−	0.667067i
$784$	−7.48565	−	2.43223i	−0.267345	−	0.0868655i
$785$	−8.01946	−	6.02711i	−0.286227	−	0.215117i
$786$	−1.73221	+	30.1113i	−0.0617860	+	1.07404i
$787$	−25.7904	+	13.1408i	−0.919327	+	0.468420i	−0.848576	−	0.529074i	$-0.822540\pi$
$787$	−25.7904	+	13.1408i	−0.919327	+	0.468420i	−0.0707509	+	0.997494i	$0.522540\pi$
$788$	20.2619	−	10.3240i	0.721800	−	0.367776i
$789$	0.299464	−	5.20563i	0.0106612	−	0.185325i
$790$	0.897041	+	2.92079i	0.0319153	+	0.103917i
$791$	−6.45480	−	2.09729i	−0.229506	−	0.0745711i
$792$	−0.585693	+	0.882044i	−0.0208117	+	0.0313421i
$793$	0.256173	−	0.256173i	0.00909695	−	0.00909695i
$794$	11.1607	+	8.10876i	0.396080	+	0.287769i
$795$	8.83506	−	14.5772i	0.313347	−	0.517001i
$796$	5.11191	−	3.71402i	0.181187	−	0.131640i
$797$	−2.70297	+	17.0659i	−0.0957441	+	0.604505i	0.892432	+	0.451182i	$0.148997\pi$
$797$	−2.70297	+	17.0659i	−0.0957441	+	0.604505i	−0.988176	+	0.153323i	$0.951003\pi$
$798$	32.6547	−	29.1021i	1.15597	−	1.03020i
$799$			15.1443i			0.535766i
$800$	2.41291	−	4.37925i	0.0853093	−	0.154830i
$801$	−4.15997	+	4.52634i	−0.146985	+	0.159930i
$802$	−7.18193	+	14.0953i	−0.253603	+	0.497723i
$803$	−3.63982	−	0.576491i	−0.128446	−	0.0203439i
$804$	−3.32952	−	12.6845i	−0.117423	−	0.447349i
$805$	−60.7063	+	29.7041i	−2.13962	+	1.04693i
$806$	6.10729	−	8.40597i	0.215120	−	0.296088i
$807$	20.5666	−	9.03137i	0.723980	−	0.317919i
$808$	−9.46876	+	1.49970i	−0.333110	+	0.0527594i
$809$	−14.1884	+	43.6674i	−0.498837	+	1.53526i	0.312054	+	0.950064i	$0.398983\pi$
$809$	−14.1884	+	43.6674i	−0.498837	+	1.53526i	−0.810891	+	0.585198i	$0.801017\pi$
$810$	−15.4382	+	12.9098i	−0.542442	+	0.453604i
$811$	14.2314	+	43.7999i	0.499733	+	1.53802i	0.809448	+	0.587192i	$0.199767\pi$
$811$	14.2314	+	43.7999i	0.499733	+	1.53802i	−0.309714	+	0.950830i	$0.600233\pi$
$812$	−10.9312	−	21.4536i	−0.383609	−	0.752874i
$813$	2.93369	+	29.3525i	0.102889	+	1.02944i
$814$	−1.63314	+	0.530641i	−0.0572417	+	0.0185989i
$815$	13.9027	+	19.8015i	0.486992	+	0.693616i
$816$	4.74769	+	3.88489i	0.166202	+	0.135998i
$817$	−7.48082	−	47.2320i	−0.261721	−	1.65244i
$818$	4.20720	+	4.20720i	0.147101	+	0.147101i
$819$	28.1038	−	5.67445i	0.982025	−	0.198281i
$820$	8.33437	+	17.0329i	0.291049	+	0.594816i
$821$	−13.3733	−	18.4068i	−0.466731	−	0.642400i	0.509156	−	0.860674i	$-0.329957\pi$
$821$	−13.3733	−	18.4068i	−0.466731	−	0.642400i	−0.975888	+	0.218274i	$0.929957\pi$
$822$	26.8102	+	15.6619i	0.935114	+	0.546271i
$823$	−33.1249	−	16.8780i	−1.15466	−	0.588330i	−0.231536	−	0.972826i	$-0.574375\pi$
$823$	−33.1249	−	16.8780i	−1.15466	−	0.588330i	−0.923127	+	0.384496i	$0.874375\pi$
$824$	−6.65293			−0.231766
$825$	0.205406	+	3.04956i	0.00715133	+	0.106172i
$826$	−8.89898			−0.309635
$827$	−9.39702	−	4.78802i	−0.326766	−	0.166496i	0.282910	−	0.959147i	$-0.408700\pi$
$827$	−9.39702	−	4.78802i	−0.326766	−	0.166496i	−0.609676	+	0.792651i	$0.708700\pi$
$828$	14.6100	+	18.4233i	0.507734	+	0.640253i
$829$	7.78028	+	10.7086i	0.270220	+	0.371926i	0.922464	−	0.386083i	$-0.126172\pi$
$829$	7.78028	+	10.7086i	0.270220	+	0.371926i	−0.652244	+	0.758009i	$0.726172\pi$
$830$	2.25519	−	12.8857i	0.0782789	−	0.447269i
$831$	−9.94535	−	15.4870i	−0.345000	−	0.537237i
$832$	1.75242	+	1.75242i	0.0607541	+	0.0607541i
$833$	−4.36093	−	27.5338i	−0.151097	−	0.953990i
$834$	19.7684	−	24.1588i	0.684524	−	0.836550i
$835$	35.8974	−	11.0249i	1.24228	−	0.381533i
$836$	−2.19813	+	0.714216i	−0.0760239	+	0.0247017i
$837$	−17.4264	−	13.0733i	−0.602345	−	0.451880i
$838$	−1.96185	−	3.85035i	−0.0677711	−	0.133008i
$839$	0.944989	+	2.90838i	0.0326247	+	0.100408i	0.966043	−	0.258382i	$-0.0831893\pi$
$839$	0.944989	+	2.90838i	0.0326247	+	0.100408i	−0.933418	+	0.358790i	$0.883189\pi$
$840$	7.86592	+	12.6961i	0.271400	+	0.438056i
$841$	3.08568	−	9.49674i	0.106403	−	0.327474i
$842$	24.7186	−	3.91504i	0.851860	−	0.134921i
$843$	19.5410	+	44.4997i	0.673029	+	1.53265i
$844$	2.44299	−	3.36248i	0.0840910	−	0.115741i
$845$	−7.18217	+	13.5493i	−0.247074	+	0.466109i
$846$	12.7430	+	1.47100i	0.438114	+	0.0505740i
$847$	41.4224	+	6.56066i	1.42329	+	0.225427i
$848$	−1.99809	+	3.92147i	−0.0686146	+	0.134664i
$849$	16.1471	−	41.4312i	0.554165	−	1.42192i
$850$	17.6997	+	0.572988i	0.607095	+	0.0196533i
$851$			38.1346i			1.30724i
$852$	7.10313	+	7.97026i	0.243349	+	0.273057i
$853$	5.89808	−	37.2390i	0.201946	−	1.27504i	−0.653412	−	0.757003i	$-0.726663\pi$
$853$	5.89808	−	37.2390i	0.201946	−	1.27504i	0.855358	−	0.518037i	$-0.173337\pi$
$854$	−0.456059	+	0.331347i	−0.0156060	+	0.0113384i
$855$	−43.9155	+	1.14082i	−1.50188	+	0.0390152i
$856$	−11.9374	−	8.67305i	−0.408013	−	0.296439i
$857$	3.57064	−	3.57064i	0.121971	−	0.121971i	−0.643487	−	0.765457i	$-0.722513\pi$
$857$	3.57064	−	3.57064i	0.121971	−	0.121971i	0.765457	+	0.643487i	$0.222513\pi$
$858$	−1.48023	−	0.322537i	−0.0505342	−	0.0110112i
$859$	33.5736	+	10.9087i	1.14552	+	0.372201i	0.819453	−	0.573147i	$-0.194278\pi$
$859$	33.5736	+	10.9087i	1.14552	+	0.372201i	0.326064	+	0.945348i	$0.394278\pi$
$860$	16.3263	+	0.264194i	0.556721	+	0.00900893i
$861$	−56.5491	−	3.25310i	−1.92719	−	0.110865i
$862$	6.23735	−	3.17809i	0.212445	−	0.108246i
$863$	17.9383	−	9.14003i	0.610628	−	0.311130i	−0.121191	−	0.992629i	$-0.538672\pi$
$863$	17.9383	−	9.14003i	0.610628	−	0.311130i	0.731819	+	0.681499i	$0.238672\pi$
$864$	3.73006	−	3.61755i	0.126899	−	0.123072i
$865$	12.6343	−	36.8448i	0.429578	−	1.25276i
$866$	9.38548	+	3.04953i	0.318932	+	0.103627i
$867$	1.64306	−	7.54053i	0.0558011	−	0.256090i
$868$	−11.4322	+	11.4322i	−0.388035	+	0.388035i
$869$	0.390153	+	0.283463i	0.0132350	+	0.00961581i
$870$	−5.53006	+	23.5415i	−0.187487	+	0.798130i
$871$	15.1807	−	11.0294i	0.514379	−	0.373718i
$872$	−1.73896	+	10.9794i	−0.0588887	+	0.371809i
$873$	−7.35218	−	19.7534i	−0.248834	−	0.668552i
$874$			51.3273i			1.73617i
$875$	40.3095	+	15.2971i	1.36271	+	0.517135i
$876$	16.8510	+	6.56737i	0.569343	+	0.221891i
$877$	−19.1482	+	37.5805i	−0.646590	+	1.26900i	0.302244	+	0.953230i	$0.402264\pi$
$877$	−19.1482	+	37.5805i	−0.646590	+	1.26900i	−0.948834	+	0.315774i	$0.897736\pi$
$878$	0.576659	+	0.0913337i	0.0194613	+	0.00308236i
$879$	−57.2309	+	15.0223i	−1.93035	+	0.506691i
$880$	−0.110826	−	0.781355i	−0.00373596	−	0.0263395i
$881$	22.4775	−	30.9376i	0.757285	−	1.04231i	−0.240150	−	0.970736i	$-0.577197\pi$
$881$	22.4775	−	30.9376i	0.757285	−	1.04231i	0.997435	−	0.0715779i	$-0.0228035\pi$
$882$	−23.5917	+	0.995035i	−0.794372	+	0.0335046i
$883$	−13.8121	+	2.18763i	−0.464816	+	0.0736196i	−0.384450	−	0.923146i	$-0.625609\pi$
$883$	−13.8121	+	2.18763i	−0.464816	+	0.0736196i	−0.0803657	+	0.996765i	$0.525609\pi$
$884$	−2.71243	+	8.34799i	−0.0912288	+	0.280773i
$885$	6.82449	+	5.77113i	0.229403	+	0.193994i
$886$	2.76645	+	8.51427i	0.0929408	+	0.286042i
$887$	−9.40690	−	18.4621i	−0.315853	−	0.619896i	0.677433	−	0.735585i	$-0.263092\pi$
$887$	−9.40690	−	18.4621i	−0.315853	−	0.619896i	−0.993285	+	0.115689i	$0.963092\pi$
$888$	8.38555	−	0.838109i	0.281401	−	0.0281251i
$889$	−19.7820	+	6.42756i	−0.663467	+	0.215574i
$890$	0.0741394	−	4.58156i	0.00248516	−	0.153574i
$891$	−0.723691	+	3.09283i	−0.0242446	+	0.103614i
$892$	2.40429	+	15.1801i	0.0805017	+	0.508268i
$893$	19.8002	+	19.8002i	0.662587	+	0.662587i
$894$	−6.77539	+	4.35099i	−0.226603	+	0.145519i
$895$	11.8057	−	11.4297i	0.394622	−	0.382053i
$896$	−2.26666	−	3.11979i	−0.0757239	−	0.104225i
$897$	−16.9703	+	29.0500i	−0.566622	+	0.969951i
$898$	−16.3751	−	8.34354i	−0.546445	−	0.278428i
$899$	−26.1776			−0.873071
$900$	2.20135	−	14.8376i	0.0733783	−	0.494586i
$901$	−15.5880			−0.519312
$902$	2.66676	+	1.35878i	0.0887935	+	0.0452425i
$903$	−24.6022	+	42.1144i	−0.818710	+	1.40148i
$904$	−1.03449	−	1.42386i	−0.0344067	−	0.0473567i
$905$	1.32632	+	0.703054i	0.0440884	+	0.0233703i
$906$	−21.3581	+	13.7157i	−0.709576	+	0.455672i
$907$	8.19678	+	8.19678i	0.272170	+	0.272170i	0.829973	−	0.557803i	$-0.188356\pi$
$907$	8.19678	+	8.19678i	0.272170	+	0.272170i	−0.557803	+	0.829973i	$0.688356\pi$
$908$	−2.19408	−	13.8529i	−0.0728131	−	0.459724i
$909$	−25.0527	+	14.1252i	−0.830946	+	0.468503i
$910$	−12.8391	+	17.0832i	−0.425611	+	0.566303i
$911$	−4.38290	+	1.42409i	−0.145212	+	0.0471822i	−0.380721	−	0.924690i	$-0.624324\pi$
$911$	−4.38290	+	1.42409i	−0.145212	+	0.0471822i	0.235509	+	0.971872i	$0.424324\pi$
$912$	11.2865	−	1.12805i	0.373734	−	0.0373536i
$913$	−0.937368	−	1.83969i	−0.0310224	−	0.0608848i
$914$	10.8344	+	33.3449i	0.358371	+	1.10295i
$915$	0.564628	+	0.0416570i	0.0186660	+	0.00137714i
$916$	−5.35607	+	16.4843i	−0.176970	+	0.544656i
$917$	66.3247	−	10.5048i	2.19023	−	0.346899i
$918$	17.4138	+	5.95437i	0.574743	+	0.196524i
$919$	1.33595	−	1.83878i	0.0440689	−	0.0606557i	−0.786414	−	0.617700i	$-0.788065\pi$
$919$	1.33595	−	1.83878i	0.0440689	−	0.0606557i	0.830483	+	0.557044i	$0.188065\pi$
$920$	−17.2633	−	3.02134i	−0.569154	−	0.0996106i
$921$	30.5560	−	8.02053i	1.00685	−	0.264286i
$922$	0.139155	+	0.0220400i	0.00458284	+	0.000725850i
$923$	−6.93508	+	13.6109i	−0.228271	+	0.448007i
$924$	2.19640	+	0.856007i	0.0722564	+	0.0281606i
$925$	17.7498	−	16.6366i	0.583610	−	0.547008i
$926$			8.87257i			0.291571i
$927$	−18.7052	+	6.96203i	−0.614359	+	0.228663i
$928$	0.976751	−	6.16696i	0.0320634	−	0.202440i
$929$	12.0105	−	8.72617i	0.394053	−	0.286296i	−0.373061	−	0.927807i	$-0.621692\pi$
$929$	12.0105	−	8.72617i	0.394053	−	0.286296i	0.767114	+	0.641510i	$0.221692\pi$
$930$	16.1812	−	1.35322i	0.530602	−	0.0443739i
$931$	−41.7003	−	30.2970i	−1.36667	−	0.992945i
$932$	−1.73973	+	1.73973i	−0.0569868	+	0.0569868i
$933$	−5.98097	+	27.4486i	−0.195808	+	0.898628i
$934$	−4.63623	−	1.50640i	−0.151702	−	0.0492910i
$935$	2.28757	−	1.60612i	0.0748116	−	0.0525256i
$936$	6.76087	+	3.09320i	0.220986	+	0.101105i
$937$	13.2746	−	6.76373i	0.433661	−	0.220961i	−0.223512	−	0.974701i	$-0.571752\pi$
$937$	13.2746	−	6.76373i	0.433661	−	0.220961i	0.657173	+	0.753740i	$0.271752\pi$
$938$	−26.0155	+	13.2555i	−0.849435	+	0.432809i
$939$	−9.33928	−	0.537260i	−0.304776	−	0.0175328i
$940$	−7.82505	+	5.49401i	−0.255225	+	0.179195i
$941$	29.4117	+	9.55645i	0.958795	+	0.311531i	0.746284	−	0.665627i	$-0.231836\pi$
$941$	29.4117	+	9.55645i	0.958795	+	0.311531i	0.212511	+	0.977159i	$0.431836\pi$
$942$	7.59248	+	1.65438i	0.247376	+	0.0539025i
$943$	46.9991	−	46.9991i	1.53050	−	1.53050i
$944$	−1.86694	−	1.35641i	−0.0607636	−	0.0441474i
$945$	35.4015	+	27.4645i	1.15161	+	0.893421i
$946$	2.08499	−	1.51484i	0.0677890	−	0.0492516i
$947$	1.42242	−	8.98080i	0.0462224	−	0.291837i	−0.953739	−	0.300636i	$-0.902801\pi$
$947$	1.42242	−	8.98080i	0.0462224	−	0.291837i	0.999961	+	0.00879948i	$0.00280100\pi$
$948$	−1.57466	−	1.76688i	−0.0511424	−	0.0573857i
$949$			25.8775i			0.840021i
$950$	23.8903	−	22.3921i	0.775105	−	0.726494i
$951$	5.39568	−	13.8446i	0.174967	−	0.448942i
$952$	6.20067	−	12.1695i	0.200965	−	0.394416i
$953$	−18.9081	−	2.99474i	−0.612493	−	0.0970093i	−0.157522	−	0.987516i	$-0.550350\pi$
$953$	−18.9081	−	2.99474i	−0.612493	−	0.0970093i	−0.454971	+	0.890506i	$0.650350\pi$
$954$	−1.51410	+	13.1164i	−0.0490209	+	0.424659i
$955$	31.0355	+	5.43168i	1.00429	+	0.175765i
$956$	1.43017	−	1.96845i	0.0462549	−	0.0636644i
$957$	1.53462	+	3.49471i	0.0496073	+	0.112968i
$958$	−14.0773	+	2.22963i	−0.454818	+	0.0720361i
$959$	21.3623	−	65.7463i	0.689823	−	2.12306i
$960$	−0.284965	+	3.86249i	−0.00919722	+	0.124661i
$961$	−4.14780	−	12.7656i	−0.133800	−	0.411794i
$962$	5.47429	+	10.7439i	0.176498	+	0.346397i
$963$	−42.6389	−	11.8928i	−1.37402	−	0.383242i
$964$	1.53948	−	0.500207i	0.0495833	−	0.0161106i
$965$	5.49714	−	7.31429i	0.176959	−	0.235455i
$966$	33.1523	−	40.5151i	1.06666	−	1.30355i
$967$	−6.88343	−	43.4603i	−0.221356	−	1.39759i	−0.808686	−	0.588240i	$-0.799821\pi$
$967$	−6.88343	−	43.4603i	−0.221356	−	1.39759i	0.587330	−	0.809347i	$-0.300179\pi$
$968$	7.69010	+	7.69010i	0.247169	+	0.247169i
$969$	21.7080	+	33.8038i	0.697360	+	1.08593i
$970$	13.8806	+	7.35778i	0.445678	+	0.236244i
$971$	−18.1657	−	25.0030i	−0.582965	−	0.802383i	0.411051	−	0.911612i	$-0.365162\pi$
$971$	−18.1657	−	25.0030i	−0.582965	−	0.802383i	−0.994017	+	0.109229i	$0.965162\pi$
$972$	6.70170	−	14.0743i	0.214957	−	0.451435i
$973$	−61.9249	−	31.5523i	−1.98522	−	1.01152i
$974$	34.8793			1.11761
$975$	20.9248	−	4.77452i	0.670131	−	0.152907i
$976$	−0.146183			−0.00467919
$977$	42.2813	+	21.5434i	1.35270	+	0.689235i	0.971894	−	0.235420i	$-0.0756465\pi$
$977$	42.2813	+	21.5434i	1.35270	+	0.689235i	0.380806	+	0.924655i	$0.375646\pi$
$978$	−16.1823	−	9.45329i	−0.517452	−	0.302283i
$979$	−0.425102	−	0.585102i	−0.0135863	−	0.0186999i
$980$	12.6447	−	12.2420i	0.403919	−	0.391055i
$981$	6.60027	+	32.6890i	0.210730	+	1.04368i
$982$	−3.78562	−	3.78562i	−0.120804	−	0.120804i
$983$	5.45227	+	34.4243i	0.173900	+	1.09796i	0.908015	+	0.418938i	$0.137598\pi$
$983$	5.45227	+	34.4243i	0.173900	+	1.09796i	−0.734114	+	0.679026i	$0.762402\pi$
$984$	−11.3677	−	9.30186i	−0.362390	−	0.296533i
$985$	−0.822742	+	50.8426i	−0.0262147	+	1.61998i
$986$	21.0320	−	6.83372i	0.669796	−	0.217630i
$987$	−2.84030	−	28.4181i	−0.0904079	−	0.904560i
$988$	7.36813	+	14.4608i	0.234411	+	0.460058i
$989$	−17.6860	−	54.4321i	−0.562384	−	1.73084i
$990$	−1.12925	−	2.08086i	−0.0358900	−	0.0661341i
$991$	1.45449	−	4.47645i	0.0462033	−	0.142199i	−0.925293	−	0.379252i	$-0.876181\pi$
$991$	1.45449	−	4.47645i	0.0462033	−	0.142199i	0.971497	+	0.237053i	$0.0761814\pi$
$992$	−4.14093	+	0.655859i	−0.131475	+	0.0208235i
$993$	−45.0654	+	19.7894i	−1.43011	+	0.627999i
$994$	13.9714	−	19.2300i	0.443146	−	0.609938i
$995$	1.98418	+	13.9890i	0.0629027	+	0.443480i
$996$	2.57261	+	9.80092i	0.0815162	+	0.310554i
$997$	−20.4803	−	3.24377i	−0.648619	−	0.102731i	−0.176548	−	0.984292i	$-0.556493\pi$
$997$	−20.4803	−	3.24377i	−0.648619	−	0.102731i	−0.472070	+	0.881561i	$0.656493\pi$
$998$	−4.05748	+	7.96325i	−0.128437	+	0.252072i
$999$	22.6995	−	11.1315i	0.718180	−	0.352186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.2.l.a.17.2	✓	80
3.2	odd	2	inner	150.2.l.a.17.8	yes	80
5.2	odd	4		750.2.l.a.143.10		80
5.3	odd	4		750.2.l.c.143.1		80
5.4	even	2		750.2.l.b.107.9		80
15.2	even	4		750.2.l.a.143.5		80
15.8	even	4		750.2.l.c.143.6		80
15.14	odd	2		750.2.l.b.107.3		80
25.3	odd	20	inner	150.2.l.a.53.8	yes	80
25.4	even	10		750.2.l.a.257.5		80
25.21	even	5		750.2.l.c.257.6		80
25.22	odd	20		750.2.l.b.743.3		80
75.29	odd	10		750.2.l.a.257.10		80
75.47	even	20		750.2.l.b.743.9		80
75.53	even	20	inner	150.2.l.a.53.2	yes	80
75.71	odd	10		750.2.l.c.257.1		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.2	✓	80	1.1	even	1	trivial
150.2.l.a.17.8	yes	80	3.2	odd	2	inner
150.2.l.a.53.2	yes	80	75.53	even	20	inner
150.2.l.a.53.8	yes	80	25.3	odd	20	inner
750.2.l.a.143.5		80	15.2	even	4
750.2.l.a.143.10		80	5.2	odd	4
750.2.l.a.257.5		80	25.4	even	10
750.2.l.a.257.10		80	75.29	odd	10
750.2.l.b.107.3		80	15.14	odd	2
750.2.l.b.107.9		80	5.4	even	2
750.2.l.b.743.3		80	25.22	odd	20
750.2.l.b.743.9		80	75.47	even	20
750.2.l.c.143.1		80	5.3	odd	4
750.2.l.c.143.6		80	15.8	even	4
750.2.l.c.257.1		80	75.71	odd	10
750.2.l.c.257.6		80	25.21	even	5

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	150.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-0.873670 + 1.49556i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-2.21391 + 0.314018i) q^{5} +(1.45742 - 0.935916i) q^{6} +(-2.72680 - 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.47340 - 2.61325i) q^{9} +O(q^{10})\)	\(q+(-0.891007 - 0.453990i) q^{2} +(-0.873670 + 1.49556i) q^{3} +(0.587785 + 0.809017i) q^{4} +(-2.21391 + 0.314018i) q^{5} +(1.45742 - 0.935916i) q^{6} +(-2.72680 - 2.72680i) q^{7} +(-0.156434 - 0.987688i) q^{8} +(-1.47340 - 2.61325i) q^{9} +(2.11517 + 0.725301i) q^{10} +(0.335657 - 0.109061i) q^{11} +(-1.72346 + 0.172255i) q^{12} +(-1.12512 - 2.20817i) q^{13} +(1.19166 + 3.66754i) q^{14} +(1.46459 - 3.58538i) q^{15} +(-0.309017 + 0.951057i) q^{16} +(-3.49819 + 0.554059i) q^{17} +(0.126420 + 2.99734i) q^{18} +(-3.84926 + 5.29805i) q^{19} +(-1.55535 - 1.60651i) q^{20} +(6.46042 - 1.69577i) q^{21} +(-0.348585 - 0.0552105i) q^{22} +(-3.55825 + 6.98347i) q^{23} +(1.61382 + 0.628956i) q^{24} +(4.80279 - 1.39041i) q^{25} +2.47829i q^{26} +(5.19554 + 0.0795559i) q^{27} +(0.603255 - 3.80880i) q^{28} +(5.05137 - 3.67003i) q^{29} +(-2.93269 + 2.52969i) q^{30} +(-3.39184 - 2.46432i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.130145 + 0.597278i) q^{33} +(3.36845 + 1.09448i) q^{34} +(6.89315 + 5.18062i) q^{35} +(1.24812 - 2.72804i) q^{36} +(4.33521 - 2.20890i) q^{37} +(5.83498 - 2.97307i) q^{38} +(4.28544 + 0.246528i) q^{39} +(0.656484 + 2.13753i) q^{40} +(-8.06531 - 2.62058i) q^{41} +(-6.52614 - 1.42202i) q^{42} +(-5.16349 + 5.16349i) q^{43} +(0.285527 + 0.207447i) q^{44} +(4.08259 + 5.32283i) q^{45} +(6.34085 - 4.60690i) q^{46} +(0.668895 - 4.22323i) q^{47} +(-1.15238 - 1.29306i) q^{48} +7.87088i q^{49} +(-4.91055 - 0.941550i) q^{50} +(2.22763 - 5.71582i) q^{51} +(1.12512 - 2.20817i) q^{52} +(4.34698 + 0.688494i) q^{53} +(-4.59315 - 2.42961i) q^{54} +(-0.708866 + 0.346854i) q^{55} +(-2.26666 + 3.11979i) q^{56} +(-4.56057 - 10.3855i) q^{57} +(-6.16696 + 0.976751i) q^{58} +(-0.713107 + 2.19472i) q^{59} +(3.76150 - 0.922555i) q^{60} +(0.0451729 + 0.139028i) q^{61} +(1.90338 + 3.73559i) q^{62} +(-3.10814 + 11.1435i) q^{63} +(-0.951057 + 0.309017i) q^{64} +(3.18432 + 4.53538i) q^{65} +(0.387119 - 0.473094i) q^{66} +(1.18445 + 7.47829i) q^{67} +(-2.50443 - 2.50443i) q^{68} +(-7.33546 - 11.4228i) q^{69} +(-3.78989 - 7.74539i) q^{70} +(-3.62303 - 4.98667i) q^{71} +(-2.35059 + 1.86407i) q^{72} +(-9.30362 - 4.74043i) q^{73} -4.86552 q^{74} +(-2.11660 + 8.39762i) q^{75} -6.54875 q^{76} +(-1.21266 - 0.617880i) q^{77} +(-3.70643 - 2.16521i) q^{78} +(0.803169 + 1.10547i) q^{79} +(0.385487 - 2.20259i) q^{80} +(-4.65817 + 7.70074i) q^{81} +(5.99652 + 5.99652i) q^{82} +(-0.915181 - 5.77823i) q^{83} +(5.16925 + 4.22984i) q^{84} +(7.57069 - 2.32513i) q^{85} +(6.94488 - 2.25653i) q^{86} +(1.07553 + 10.7610i) q^{87} +(-0.160227 - 0.314463i) q^{88} +(-0.633239 - 1.94891i) q^{89} +(-1.22110 - 6.59613i) q^{90} +(-2.95327 + 9.08922i) q^{91} +(-7.74123 + 1.22609i) q^{92} +(6.64888 - 2.91971i) q^{93} +(-2.51330 + 3.45926i) q^{94} +(6.85822 - 12.9381i) q^{95} +(0.439743 + 1.67530i) q^{96} +(6.93926 + 1.09907i) q^{97} +(3.57330 - 7.01300i) q^{98} +(-0.779562 - 0.716464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{3} + 4 q^{7}+O(q^{10}) \) 80 * q + 4 * q^3 + 4 * q^7	\( 80 q + 4 q^{3} + 4 q^{7} - 4 q^{10} - 4 q^{12} - 8 q^{15} + 20 q^{16} - 8 q^{18} - 40 q^{19} - 36 q^{22} - 104 q^{25} + 4 q^{27} - 16 q^{28} + 12 q^{30} + 4 q^{33} - 40 q^{34} - 24 q^{37} - 40 q^{39} - 8 q^{40} - 4 q^{42} - 24 q^{43} - 72 q^{45} - 4 q^{48} - 12 q^{55} - 64 q^{57} + 20 q^{58} + 24 q^{60} + 64 q^{63} + 96 q^{67} + 140 q^{69} + 76 q^{70} + 8 q^{72} + 100 q^{73} + 132 q^{75} + 100 q^{78} + 80 q^{79} - 40 q^{81} + 96 q^{82} + 60 q^{84} + 32 q^{85} + 80 q^{87} + 4 q^{88} + 52 q^{90} + 12 q^{93} - 32 q^{97}+O(q^{100}) \) 80 * q + 4 * q^3 + 4 * q^7 - 4 * q^10 - 4 * q^12 - 8 * q^15 + 20 * q^16 - 8 * q^18 - 40 * q^19 - 36 * q^22 - 104 * q^25 + 4 * q^27 - 16 * q^28 + 12 * q^30 + 4 * q^33 - 40 * q^34 - 24 * q^37 - 40 * q^39 - 8 * q^40 - 4 * q^42 - 24 * q^43 - 72 * q^45 - 4 * q^48 - 12 * q^55 - 64 * q^57 + 20 * q^58 + 24 * q^60 + 64 * q^63 + 96 * q^67 + 140 * q^69 + 76 * q^70 + 8 * q^72 + 100 * q^73 + 132 * q^75 + 100 * q^78 + 80 * q^79 - 40 * q^81 + 96 * q^82 + 60 * q^84 + 32 * q^85 + 80 * q^87 + 4 * q^88 + 52 * q^90 + 12 * q^93 - 32 * q^97

Introduction

L-functions

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