LMFDB - Embedded newform 150.2.l.a.53.8

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			53.8
Character	$\chi$	$=$	150.53
Dual form			150.2.l.a.17.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.891007 - 0.453990i) q^{2} +(0.368756 - 1.69234i) q^{3} +(0.587785 - 0.809017i) q^{4} +(2.21391 + 0.314018i) q^{5} +(-0.439743 - 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.72804 - 1.24812i) q^{9} +O(q^{10})$	\(q+(0.891007 - 0.453990i) q^{2} +(0.368756 - 1.69234i) q^{3} +(0.587785 - 0.809017i) q^{4} +(2.21391 + 0.314018i) q^{5} +(-0.439743 - 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.72804 - 1.24812i) q^{9} +(2.11517 - 0.725301i) q^{10} +(-0.335657 - 0.109061i) q^{11} +(-1.15238 - 1.29306i) q^{12} +(-1.12512 + 2.20817i) q^{13} +(-1.19166 + 3.66754i) q^{14} +(1.34782 - 3.63089i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.49819 + 0.554059i) q^{17} +(-2.99734 + 0.126420i) q^{18} +(-3.84926 - 5.29805i) q^{19} +(1.55535 - 1.60651i) q^{20} +(3.60915 + 5.62020i) 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} +(-3.11823 + 4.15652i) q^{27} +(0.603255 + 3.80880i) q^{28} +(-5.05137 - 3.67003i) q^{29} +(-0.447477 - 3.84705i) q^{30} +(-3.39184 + 2.46432i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.308344 + 0.527829i) q^{33} +(3.36845 - 1.09448i) q^{34} +(-6.89315 + 5.18062i) q^{35} +(-2.61325 + 1.47340i) q^{36} +(4.33521 + 2.20890i) q^{37} +(-5.83498 - 2.97307i) q^{38} +(3.32209 + 2.71836i) q^{39} +(0.656484 - 2.13753i) q^{40} +(8.06531 - 2.62058i) q^{41} +(5.76730 + 3.36911i) q^{42} +(-5.16349 - 5.16349i) q^{43} +(-0.285527 + 0.207447i) q^{44} +(-5.64770 - 3.61988i) q^{45} +(6.34085 + 4.60690i) q^{46} +(-0.668895 - 4.22323i) q^{47} +(-1.72346 + 0.172255i) 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} +(-0.891339 + 5.11913i) q^{54} +(-0.708866 - 0.346854i) q^{55} +(2.26666 + 3.11979i) q^{56} +(-10.3855 + 4.56057i) q^{57} +(-6.16696 - 0.976751i) q^{58} +(0.713107 + 2.19472i) q^{59} +(-2.14523 - 3.22459i) q^{60} +(0.0451729 - 0.139028i) q^{61} +(-1.90338 + 3.73559i) q^{62} +(10.8422 - 4.03544i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-3.18432 + 4.53538i) q^{65} +(-0.0351078 + 0.610284i) q^{66} +(1.18445 - 7.47829i) q^{67} +(2.50443 - 2.50443i) q^{68} +(13.1305 - 3.44659i) q^{69} +(-3.78989 + 7.74539i) q^{70} +(3.62303 - 4.98667i) q^{71} +(-1.65951 + 2.49920i) q^{72} +(-9.30362 + 4.74043i) q^{73} +4.86552 q^{74} +(4.12411 - 7.61523i) q^{75} -6.54875 q^{76} +(1.21266 - 0.617880i) q^{77} +(4.19411 + 0.913883i) q^{78} +(0.803169 - 1.10547i) q^{79} +(-0.385487 - 2.20259i) q^{80} +(5.88439 + 6.80984i) q^{81} +(5.99652 - 5.99652i) q^{82} +(0.915181 - 5.77823i) q^{83} +(6.66824 + 0.383604i) q^{84} +(7.57069 + 2.32513i) q^{85} +(-6.94488 - 2.25653i) q^{86} +(-8.07367 + 7.19529i) q^{87} +(-0.160227 + 0.314463i) q^{88} +(0.633239 - 1.94891i) q^{89} +(-6.67553 - 0.661335i) q^{90} +(-2.95327 - 9.08922i) q^{91} +(7.74123 + 1.22609i) q^{92} +(2.91971 + 6.64888i) q^{93} +(-2.51330 - 3.45926i) q^{94} +(-6.85822 - 12.9381i) q^{95} +(-1.45742 + 0.935916i) 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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$-1$	$e\left(\frac{7}{20}\right)$

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
$3$	0.368756	−	1.69234i	0.212901	−	0.977074i
$3$	0.368756	−	1.69234i	0.212901	−	0.977074i
$4$	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
$6$	−0.439743	−	1.67530i	−0.179524	−	0.683938i
$7$	−2.72680	+	2.72680i	−1.03063	+	1.03063i	−0.0311178	+	0.999516i	$0.509907\pi$
$7$	−2.72680	+	2.72680i	−1.03063	+	1.03063i	−0.999516	+	0.0311178i	$0.990093\pi$
$8$	0.156434	−	0.987688i	0.0553079	−	0.349201i
$9$	−2.72804	−	1.24812i	−0.909346	−	0.416040i
$10$	2.11517	−	0.725301i	0.668875	−	0.229360i
$11$	−0.335657	−	0.109061i	−0.101204	−	0.0328833i	0.257977	−	0.966151i	$-0.416944\pi$
$11$	−0.335657	−	0.109061i	−0.101204	−	0.0328833i	−0.359181	+	0.933268i	$0.616944\pi$
$12$	−1.15238	−	1.29306i	−0.332665	−	0.373275i
$13$	−1.12512	+	2.20817i	−0.312052	+	0.612437i	−0.992760	−	0.120119i	$-0.961673\pi$
$13$	−1.12512	+	2.20817i	−0.312052	+	0.612437i	0.680707	+	0.732555i	$0.261673\pi$
$14$	−1.19166	+	3.66754i	−0.318483	+	0.980191i
$15$	1.34782	−	3.63089i	0.348005	−	0.937493i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	3.49819	+	0.554059i	0.848436	+	0.134379i	0.565488	−	0.824756i	$-0.308688\pi$
$17$	3.49819	+	0.554059i	0.848436	+	0.134379i	0.282948	+	0.959135i	$0.408688\pi$
$18$	−2.99734	+	0.126420i	−0.706479	+	0.0297975i
$19$	−3.84926	−	5.29805i	−0.883080	−	1.21546i	−0.975558	−	0.219741i	$-0.929479\pi$
$19$	−3.84926	−	5.29805i	−0.883080	−	1.21546i	0.0924780	−	0.995715i	$-0.470521\pi$
$20$	1.55535	−	1.60651i	0.347787	−	0.359228i
$21$	3.60915	+	5.62020i	0.787582	+	1.22643i
$22$	−0.348585	+	0.0552105i	−0.0743186	+	0.0117709i
$23$	3.55825	+	6.98347i	0.741947	+	1.45615i	0.884585	+	0.466378i	$0.154441\pi$
$23$	3.55825	+	6.98347i	0.741947	+	1.45615i	−0.142638	+	0.989775i	$0.545559\pi$
$24$	−1.61382	−	0.628956i	−0.329420	−	0.128385i
$25$	4.80279	+	1.39041i	0.960557	+	0.278083i
$26$			2.47829i			0.486033i
$27$	−3.11823	+	4.15652i	−0.600103	+	0.799923i
$28$	0.603255	+	3.80880i	0.114004	+	0.719796i
$29$	−5.05137	−	3.67003i	−0.938015	−	0.681508i	0.00992666	−	0.999951i	$-0.496840\pi$
$29$	−5.05137	−	3.67003i	−0.938015	−	0.681508i	−0.947942	+	0.318443i	$0.896840\pi$
$30$	−0.447477	−	3.84705i	−0.0816978	−	0.702371i
$31$	−3.39184	+	2.46432i	−0.609193	+	0.442604i	−0.849130	−	0.528184i	$-0.822873\pi$
$31$	−3.39184	+	2.46432i	−0.609193	+	0.442604i	0.239937	+	0.970788i	$0.422873\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.308344	+	0.527829i	−0.0536759	+	0.0918832i
$34$	3.36845	−	1.09448i	0.577684	−	0.187701i
$35$	−6.89315	+	5.18062i	−1.16516	+	0.875685i
$36$	−2.61325	+	1.47340i	−0.435542	+	0.245567i
$37$	4.33521	+	2.20890i	0.712704	+	0.363141i	0.772452	−	0.635073i	$-0.219030\pi$
$37$	4.33521	+	2.20890i	0.712704	+	0.363141i	−0.0597483	+	0.998213i	$0.519030\pi$
$38$	−5.83498	−	2.97307i	−0.946558	−	0.482296i
$39$	3.32209	+	2.71836i	0.531960	+	0.435286i
$40$	0.656484	−	2.13753i	0.103799	−	0.337973i
$41$	8.06531	−	2.62058i	1.25959	−	0.409265i	0.398241	−	0.917281i	$-0.369621\pi$
$41$	8.06531	−	2.62058i	1.25959	−	0.409265i	0.861348	+	0.508015i	$0.169621\pi$
$42$	5.76730	+	3.36911i	0.889913	+	0.519865i
$43$	−5.16349	−	5.16349i	−0.787425	−	0.787425i	0.193647	−	0.981071i	$-0.437969\pi$
$43$	−5.16349	−	5.16349i	−0.787425	−	0.787425i	−0.981071	+	0.193647i	$0.937969\pi$
$44$	−0.285527	+	0.207447i	−0.0430448	+	0.0312738i
$45$	−5.64770	−	3.61988i	−0.841909	−	0.539620i
$46$	6.34085	+	4.60690i	0.934908	+	0.679250i
$47$	−0.668895	−	4.22323i	−0.0975683	−	0.616022i	−0.987218	−	0.159378i	$-0.949051\pi$
$47$	−0.668895	−	4.22323i	−0.0975683	−	0.616022i	0.889649	−	0.456644i	$-0.150949\pi$
$48$	−1.72346	+	0.172255i	−0.248761	+	0.0248628i
$49$		−	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	$-0.647745\pi$
$53$	−4.34698	+	0.688494i	−0.597103	+	0.0945719i	−0.149435	+	0.988772i	$0.547745\pi$
$54$	−0.891339	+	5.11913i	−0.121296	+	0.696626i
$55$	−0.708866	−	0.346854i	−0.0955835	−	0.0467698i
$56$	2.26666	+	3.11979i	0.302896	+	0.416900i
$57$	−10.3855	+	4.56057i	−1.37560	+	0.604063i
$58$	−6.16696	−	0.976751i	−0.809762	−	0.128254i
$59$	0.713107	+	2.19472i	0.0928386	+	0.285728i	0.986684	−	0.162647i	$-0.0520031\pi$
$59$	0.713107	+	2.19472i	0.0928386	+	0.285728i	−0.893846	+	0.448375i	$0.852003\pi$
$60$	−2.14523	−	3.22459i	−0.276948	−	0.416293i
$61$	0.0451729	−	0.139028i	0.00578380	−	0.0178007i	−0.948123	−	0.317904i	$-0.897021\pi$
$61$	0.0451729	−	0.139028i	0.00578380	−	0.0178007i	0.953907	+	0.300103i	$0.0970211\pi$
$62$	−1.90338	+	3.73559i	−0.241729	+	0.474420i
$63$	10.8422	−	4.03544i	1.36599	−	0.508418i
$64$	−0.951057	−	0.309017i	−0.118882	−	0.0386271i
$65$	−3.18432	+	4.53538i	−0.394966	+	0.562545i
$66$	−0.0351078	+	0.610284i	−0.00432147	+	0.0751208i
$67$	1.18445	−	7.47829i	0.144703	−	0.913619i	−0.803350	−	0.595507i	$-0.796951\pi$
$67$	1.18445	−	7.47829i	0.144703	−	0.913619i	0.948053	−	0.318112i	$-0.103049\pi$
$68$	2.50443	−	2.50443i	0.303707	−	0.303707i
$69$	13.1305	−	3.44659i	1.58073	−	0.414920i
$70$	−3.78989	+	7.74539i	−0.452978	+	0.925752i
$71$	3.62303	−	4.98667i	0.429974	−	0.591809i	−0.537973	−	0.842962i	$-0.680810\pi$
$71$	3.62303	−	4.98667i	0.429974	−	0.591809i	0.967947	+	0.251153i	$0.0808098\pi$
$72$	−1.65951	+	2.49920i	−0.195576	+	0.294534i
$73$	−9.30362	+	4.74043i	−1.08891	+	0.554825i	−0.903827	−	0.427898i	$-0.859254\pi$
$73$	−9.30362	+	4.74043i	−1.08891	+	0.554825i	−0.185079	+	0.982724i	$0.559254\pi$
$74$	4.86552			0.565605
$75$	4.12411	−	7.61523i	0.476211	−	0.879331i
$76$	−6.54875			−0.751193
$77$	1.21266	−	0.617880i	0.138195	−	0.0704139i
$78$	4.19411	+	0.913883i	0.474890	+	0.103477i
$79$	0.803169	−	1.10547i	0.0903636	−	0.124375i	−0.761442	−	0.648234i	$-0.775508\pi$
$79$	0.803169	−	1.10547i	0.0903636	−	0.124375i	0.851805	+	0.523859i	$0.175508\pi$
$80$	−0.385487	−	2.20259i	−0.0430987	−	0.246257i
$81$	5.88439	+	6.80984i	0.653821	+	0.756649i
$82$	5.99652	−	5.99652i	0.662205	−	0.662205i
$83$	0.915181	−	5.77823i	0.100454	−	0.634243i	−0.885167	−	0.465273i	$-0.845956\pi$
$83$	0.915181	−	5.77823i	0.100454	−	0.634243i	0.985621	−	0.168969i	$-0.0540439\pi$
$84$	6.66824	+	0.383604i	0.727565	+	0.0418546i
$85$	7.57069	+	2.32513i	0.821157	+	0.252196i
$86$	−6.94488	−	2.25653i	−0.748886	−	0.243328i
$87$	−8.07367	+	7.19529i	−0.865588	+	0.771416i
$88$	−0.160227	+	0.314463i	−0.0170803	+	0.0335219i
$89$	0.633239	−	1.94891i	0.0671232	−	0.206584i	−0.911869	−	0.410481i	$-0.865361\pi$
$89$	0.633239	−	1.94891i	0.0671232	−	0.206584i	0.978992	+	0.203897i	$0.0653608\pi$
$90$	−6.67553	−	0.661335i	−0.703662	−	0.0697109i
$91$	−2.95327	−	9.08922i	−0.309587	−	0.952809i
$92$	7.74123	+	1.22609i	0.807079	+	0.127829i
$93$	2.91971	+	6.64888i	0.302759	+	0.689457i
$94$	−2.51330	−	3.45926i	−0.259227	−	0.356795i
$95$	−6.85822	−	12.9381i	−0.703639	−	1.32742i
$96$	−1.45742	+	0.935916i	−0.148747	+	0.0955216i
$97$	6.93926	−	1.09907i	0.704575	−	0.111594i	0.206142	−	0.978522i	$-0.433909\pi$
$97$	6.93926	−	1.09907i	0.704575	−	0.111594i	0.498433	+	0.866928i	$0.333909\pi$
$98$	−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	$-0.158262\pi$
$102$	−0.610091	−	6.10416i	−0.0604081	−	0.604402i
$103$	1.04075	+	6.57102i	0.102548	+	0.647462i	0.984401	+	0.175938i	$0.0562959\pi$
$103$	1.04075	+	6.57102i	0.102548	+	0.647462i	−0.881853	+	0.471524i	$0.843704\pi$
$104$	2.00498	+	1.45670i	0.196604	+	0.142841i
$105$	6.22549	+	13.5759i	0.607546	+	1.32488i
$106$	−3.56062	+	2.58694i	−0.345838	+	0.251266i
$107$	−10.4337	−	10.4337i	−1.00866	−	1.00866i	−0.999962	−	0.00870186i	$-0.997230\pi$
$107$	−10.4337	−	10.4337i	−1.00866	−	1.00866i	−0.00870186	−	0.999962i	$-0.502770\pi$
$108$	1.52985	+	4.96584i	0.147210	+	0.477838i
$109$	−10.5722	+	3.43511i	−1.01263	+	0.329024i	−0.767902	−	0.640568i	$-0.778699\pi$
$109$	−10.5722	+	3.43511i	−1.01263	+	0.329024i	−0.244729	+	0.969592i	$0.578699\pi$
$110$	−0.789073	+	0.0127689i	−0.0752351	+	0.00121747i
$111$	5.33685	−	6.52211i	0.506551	−	0.619051i
$112$	3.43597	+	1.75071i	0.324668	+	0.165427i
$113$	−1.56816	−	0.799015i	−0.147520	−	0.0751650i	0.378672	−	0.925531i	$-0.376381\pi$
$113$	−1.56816	−	0.799015i	−0.147520	−	0.0751650i	−0.526192	+	0.850366i	$0.676381\pi$
$114$	−7.18313	+	8.77844i	−0.672762	+	0.822176i
$115$	5.68471	+	16.5781i	0.530102	+	1.54592i
$116$	−5.93824	+	1.92945i	−0.551352	+	0.179145i
$117$	5.82544	−	4.61969i	0.538562	−	0.427091i
$118$	1.63176	+	1.63176i	0.150216	+	0.150216i
$119$	−11.0497	+	8.02806i	−1.01292	+	0.735931i
$120$	−3.37535	−	1.89922i	−0.308126	−	0.173374i
$121$	−8.79842	−	6.39242i	−0.799856	−	0.581129i
$122$	−0.0228680	−	0.144383i	−0.00207037	−	0.0130718i
$123$	−1.46078	−	14.6156i	−0.131714	−	1.31784i
$124$			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	0.973762	−	0.227571i	$-0.0730782\pi$
$127$	2.44874	+	4.80592i	0.217290	+	0.426457i	−0.756471	+	0.654027i	$0.773078\pi$
$128$	−0.987688	+	0.156434i	−0.0873001	+	0.0138270i
$129$	−10.6425	+	6.83432i	−0.937016	+	0.601728i
$130$	−0.778228	+	5.48671i	−0.0682551	+	0.481216i
$131$	10.2354	+	14.0878i	0.894273	+	1.23086i	0.972259	+	0.233906i	$0.0751509\pi$
$131$	10.2354	+	14.0878i	0.894273	+	1.23086i	−0.0779865	+	0.996954i	$0.524849\pi$
$132$	0.245782	+	0.559706i	0.0213926	+	0.0487161i
$133$	24.9429	+	3.95056i	2.16282	+	0.342557i
$134$	−2.33973	−	7.20094i	−0.202122	−	0.622066i
$135$	−8.20869	+	8.22298i	−0.706492	+	0.707721i
$136$	1.09448	−	3.36845i	0.0938505	−	0.288842i
$137$	−8.13848	+	15.9727i	−0.695317	+	1.36464i	0.225346	+	0.974279i	$0.427649\pi$
$137$	−8.13848	+	15.9727i	−0.695317	+	1.36464i	−0.920663	+	0.390358i	$0.872351\pi$
$138$	10.1347	−	9.03207i	0.862721	−	0.768861i
$139$	17.1405	+	5.56927i	1.45383	+	0.472379i	0.926181	−	0.377080i	$-0.123072\pi$
$139$	17.1405	+	5.56927i	1.45383	+	0.472379i	0.527654	+	0.849459i	$0.323072\pi$
$140$	0.139519	+	8.62177i	0.0117915	+	0.728673i
$141$	−7.39381	−	0.425343i	−0.622671	−	0.0358204i
$142$	0.964240	−	6.08797i	0.0809172	−	0.510891i
$143$	0.618480	−	0.618480i	0.0517199	−	0.0517199i
$144$	−0.344023	+	2.98021i	−0.0286686	+	0.248351i
$145$	−10.0308	−	9.71134i	−0.833014	−	0.806483i
$146$	−6.13747	+	8.44751i	−0.507941	+	0.699121i
$147$	−13.3202	−	2.90243i	−1.09863	−	0.239388i
$148$	4.33521	−	2.20890i	0.356352	−	0.181570i
$149$	4.64891			0.380854			0.190427	−	0.981701i	$-0.439013\pi$
$149$	4.64891			0.380854			0.190427	+	0.981701i	$0.439013\pi$
$150$	0.217368	−	8.65753i	0.0177480	−	0.706884i
$151$	−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
$153$	−8.85167	−	5.87766i	−0.715615	−	0.475181i
$154$	0.799974	−	1.10107i	0.0644637	−	0.0887267i
$155$	−8.28307	+	4.39067i	−0.665312	+	0.352667i
$156$	4.15188	−	1.08981i	0.332416	−	0.0872547i
$157$	3.17235	−	3.17235i	0.253181	−	0.253181i	−0.569093	−	0.822273i	$-0.692705\pi$
$157$	3.17235	−	3.17235i	0.253181	−	0.253181i	0.822273	+	0.569093i	$0.192705\pi$
$158$	0.213757	−	1.34961i	0.0170056	−	0.107369i
$159$	−0.437806	+	7.61046i	−0.0347203	+	0.603548i
$160$	−1.34343	−	1.78751i	−0.106207	−	0.141315i
$161$	−28.7452	−	9.33987i	−2.26544	−	0.736085i
$162$	8.33463	+	3.39616i	0.654831	+	0.266827i
$163$	−4.91227	+	9.64088i	−0.384759	+	0.755132i	−0.999434	−	0.0336487i	$-0.989287\pi$
$163$	−4.91227	+	9.64088i	−0.384759	+	0.755132i	0.614675	+	0.788781i	$0.289287\pi$
$164$	2.62058	−	8.06531i	0.204633	−	0.629795i
$165$	−0.848394	+	1.07174i	−0.0660474	+	0.0834347i
$166$	−1.80783	−	5.56392i	−0.140315	−	0.431844i
$167$	16.5871	+	2.62714i	1.28355	+	0.203295i	0.760686	−	0.649120i	$-0.224863\pi$
$167$	16.5871	+	2.62714i	1.28355	+	0.203295i	0.522866	+	0.852415i	$0.324863\pi$
$168$	6.11560	−	2.68553i	0.471829	−	0.207193i
$169$	4.03108	+	5.54830i	0.310083	+	0.426793i
$170$	7.80112	−	1.36531i	0.598319	−	0.104715i
$171$	3.88832	+	19.2576i	0.297347	+	1.47267i
$172$	−7.21237	+	1.14233i	−0.549938	+	0.0871017i
$173$	7.90821	+	15.5207i	0.601250	+	1.18002i	0.968293	+	0.249816i	$0.0803702\pi$
$173$	7.90821	+	15.5207i	0.601250	+	1.18002i	−0.367043	+	0.930204i	$0.619630\pi$
$174$	−3.92710	+	10.0764i	−0.297713	+	0.763892i
$175$	−16.8876	+	9.30485i	−1.27658	+	0.703381i
$176$			0.352930i			0.0266031i
$177$	3.97717	−	0.397506i	0.298943	−	0.0298784i
$178$	−0.320566	−	2.02397i	−0.0240274	−	0.151703i
$179$	5.94519	+	4.31943i	0.444364	+	0.322849i	0.787367	−	0.616485i	$-0.211444\pi$
$179$	5.94519	+	4.31943i	0.444364	+	0.322849i	−0.343002	+	0.939334i	$0.611444\pi$
$180$	−6.24818	+	2.44137i	−0.465712	+	0.181969i
$181$	−0.543117	+	0.394597i	−0.0403695	+	0.0293302i	−0.607787	−	0.794100i	$-0.707943\pi$
$181$	−0.543117	+	0.394597i	−0.0403695	+	0.0293302i	0.567418	+	0.823430i	$0.307943\pi$
$182$	−6.75780	−	6.75780i	−0.500922	−	0.500922i
$183$	−0.218625	−	0.127715i	−0.0161612	−	0.00944098i
$184$	7.45412	−	2.42199i	0.549525	−	0.178552i
$185$	8.90413	+	6.25164i	0.654644	+	0.459630i
$186$	5.62001	+	4.59868i	0.412079	+	0.337192i
$187$	−1.11376	−	0.567491i	−0.0814465	−	0.0414991i
$188$	−3.80983	−	1.94121i	−0.277861	−	0.141577i
$189$	−2.83122	−	19.8368i	−0.205941	−	1.44291i
$190$	−11.9845	−	8.41439i	−0.869448	−	0.610444i
$191$	13.4008	−	4.35419i	0.969650	−	0.315058i	0.218975	−	0.975730i	$-0.429729\pi$
$191$	13.4008	−	4.35419i	0.969650	−	0.315058i	0.750675	+	0.660672i	$0.229729\pi$
$192$	−0.873670	+	1.49556i	−0.0630517	+	0.107933i
$193$	−2.89340	−	2.89340i	−0.208271	−	0.208271i	0.595261	−	0.803532i	$-0.297049\pi$
$193$	−2.89340	−	2.89340i	−0.208271	−	0.208271i	−0.803532	+	0.595261i	$0.797049\pi$
$194$	5.68396	−	4.12964i	0.408085	−	0.296491i
$195$	6.50118	+	7.06140i	0.465559	+	0.505678i
$196$	−6.36767	−	4.62638i	−0.454834	−	0.330456i
$197$	−3.55739	−	22.4605i	−0.253454	−	1.60024i	−0.705806	−	0.708405i	$-0.749415\pi$
$197$	−3.55739	−	22.4605i	−0.253454	−	1.60024i	0.452353	−	0.891839i	$-0.350585\pi$
$198$	1.01986	+	0.284460i	0.0724785	+	0.0202157i
$199$			6.31867i			0.447919i	0.974598	+	0.223959i	$0.0718983\pi$
$199$			6.31867i			0.447919i	−0.974598	+	0.223959i	$0.928102\pi$
$200$	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
$204$	−3.31483	−	5.16187i	−0.232084	−	0.361403i
$205$	18.6788	−	3.26907i	1.30458	−	0.228321i
$206$	3.91049	+	5.38233i	0.272457	+	0.375005i
$207$	−0.990845	−	23.4923i	−0.0688685	−	1.63283i
$208$	2.44778	+	0.387690i	0.169723	+	0.0268815i
$209$	0.714216	+	2.19813i	0.0494033	+	0.152048i
$210$	11.7103	+	9.26994i	0.808088	+	0.639687i
$211$	−1.28435	+	3.95283i	−0.0884185	+	0.272124i	−0.985483	−	0.169776i	$-0.945696\pi$
$211$	−1.28435	+	3.95283i	−0.0884185	+	0.272124i	0.897064	+	0.441900i	$0.145696\pi$
$212$	−1.99809	+	3.92147i	−0.137229	+	0.269327i
$213$	−7.10313	−	7.97026i	−0.486699	−	0.546113i
$214$	−14.0333	−	4.55969i	−0.959296	−	0.311694i
$215$	−9.81007	−	13.0529i	−0.669041	−	0.890202i
$216$	3.61755	+	3.73006i	0.246143	+	0.253798i
$217$	2.52917	−	15.9686i	0.171691	−	1.08402i
$218$	−7.86037	+	7.86037i	−0.532371	+	0.532371i
$219$	4.59166	+	17.4930i	0.310276	+	1.18206i
$220$	−0.697272	+	0.369609i	−0.0470101	+	0.0249190i
$221$	−5.15934	+	7.10123i	−0.347055	+	0.477680i
$222$	1.79419	−	8.23412i	0.120418	−	0.552638i
$223$	13.6942	−	6.97753i	0.917030	−	0.467250i	0.0692509	−	0.997599i	$-0.477939\pi$
$223$	13.6942	−	6.97753i	0.917030	−	0.467250i	0.847779	+	0.530349i	$0.177939\pi$
$224$	3.85628			0.257658
$225$	−11.3668	−	9.78756i	−0.757785	−	0.652504i
$226$	−1.75998			−0.117072
$227$	12.4969	−	6.36747i	0.829445	−	0.422624i	0.0129084	−	0.999917i	$-0.495891\pi$
$227$	12.4969	−	6.36747i	0.829445	−	0.422624i	0.816537	+	0.577293i	$0.195891\pi$
$228$	−2.41489	+	11.0827i	−0.159930	+	0.733971i
$229$	10.1878	−	14.0224i	0.673232	−	0.926624i	−0.326596	−	0.945164i	$-0.605902\pi$
$229$	10.1878	−	14.0224i	0.673232	−	0.926624i	0.999828	+	0.0185396i	$0.00590167\pi$
$230$	12.5914	+	12.1904i	0.830254	+	0.803811i
$231$	−0.598489	−	2.28008i	−0.0393777	−	0.150018i
$232$	−4.41506	+	4.41506i	−0.289863	+	0.289863i
$233$	−0.384884	+	2.43006i	−0.0252146	+	0.159199i	−0.997083	−	0.0763263i	$-0.975681\pi$
$233$	−0.384884	+	2.43006i	−0.0252146	+	0.159199i	0.971868	+	0.235525i	$0.0756809\pi$
$234$	3.09320	−	6.76087i	0.202209	−	0.441972i
$235$	−0.154700	−	9.55990i	−0.0100915	−	0.623619i
$236$	2.19472	+	0.713107i	0.142864	+	0.0464193i
$237$	−1.57466	−	1.76688i	−0.102285	−	0.114771i
$238$	−6.20067	+	12.1695i	−0.401930	+	0.788831i
$239$	0.751883	−	2.31406i	0.0486352	−	0.149684i	−0.923790	−	0.382901i	$-0.874925\pi$
$239$	0.751883	−	2.31406i	0.0486352	−	0.149684i	0.972425	+	0.233217i	$0.0749252\pi$
$240$	−3.86968	−	0.159842i	−0.249787	−	0.0103178i
$241$	0.500207	+	1.53948i	0.0322212	+	0.0991666i	0.965874	−	0.259013i	$-0.0833974\pi$
$241$	0.500207	+	1.53948i	0.0322212	+	0.0991666i	−0.933653	+	0.358180i	$0.883397\pi$
$242$	−10.7415	−	1.70129i	−0.690493	−	0.109363i
$243$	13.6945	−	7.44723i	0.878501	−	0.477740i
$244$	−0.0859239	−	0.118264i	−0.00550072	−	0.00757109i
$245$	2.47160	−	17.4254i	0.157905	−	1.11327i
$246$	−7.93691	−	12.3594i	−0.506039	−	0.788008i
$247$	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	$0.715038\pi$
$252$	3.10814	−	11.1435i	0.195794	−	0.701974i
$253$	−0.432724	−	2.73211i	−0.0272052	−	0.171767i
$254$	4.36369	+	3.17040i	0.273802	+	0.198929i
$255$	6.72665	−	11.9548i	0.421239	−	0.748638i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	20.2470	+	20.2470i	1.26297	+	1.26297i	0.949646	+	0.313326i	$0.101443\pi$
$257$	20.2470	+	20.2470i	1.26297	+	1.26297i	0.313326	+	0.949646i	$0.398557\pi$
$258$	−6.37978	+	10.9210i	−0.397188	+	0.679912i
$259$	−17.8445	+	5.79802i	−1.10880	+	0.360272i
$260$	1.79751	+	5.24200i	0.111477	+	0.325095i
$261$	9.19968	+	16.3167i	0.569446	+	1.00998i
$262$	15.5156	+	7.90558i	0.958555	+	0.488408i
$263$	2.68232	+	1.36671i	0.165399	+	0.0842750i	0.534730	−	0.845023i	$-0.320413\pi$
$263$	2.68232	+	1.36671i	0.165399	+	0.0842750i	−0.369331	+	0.929298i	$0.620413\pi$
$264$	0.473094	+	0.387119i	0.0291169	+	0.0238255i
$265$	−9.84001	+	0.159232i	−0.604467	+	0.00978157i
$266$	24.0178	−	7.80385i	1.47262	−	0.478485i
$267$	−3.06471	−	1.79033i	−0.187557	−	0.109566i
$268$	−5.35387	−	5.35387i	−0.327039	−	0.327039i
$269$	10.4918	−	7.62274i	0.639697	−	0.464767i	−0.220049	−	0.975489i	$-0.570622\pi$
$269$	10.4918	−	7.62274i	0.639697	−	0.464767i	0.859746	+	0.510722i	$0.170622\pi$
$270$	−3.58084	+	11.0534i	−0.217923	+	0.672688i
$271$	13.7784	+	10.0106i	0.836981	+	0.608102i	0.921526	−	0.388317i	$-0.126944\pi$
$271$	13.7784	+	10.0106i	0.836981	+	0.608102i	−0.0845447	+	0.996420i	$0.526944\pi$
$272$	−0.554059	−	3.49819i	−0.0335948	−	0.212109i
$273$	−16.4711	+	1.64623i	−0.996876	+	0.0996347i
$274$			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	0.699454	−	0.714677i	$-0.253427\pi$
$277$	−4.82425	−	9.46812i	−0.289861	−	0.568884i	−0.989315	+	0.145793i	$0.953427\pi$
$278$	17.8007	−	2.81935i	1.06761	−	0.169093i
$279$	12.3288	−	2.48932i	0.738108	−	0.149032i
$280$	4.03851	+	7.61871i	0.241347	+	0.455305i
$281$	−16.4932	−	22.7009i	−0.983902	−	1.35422i	−0.934701	−	0.355436i	$-0.884332\pi$
$281$	−16.4932	−	22.7009i	−0.983902	−	1.35422i	−0.0492011	−	0.998789i	$-0.515668\pi$
$282$	−6.78104	+	2.97774i	−0.403805	+	0.177322i
$283$	−25.3567	−	4.01611i	−1.50730	−	0.238733i	−0.652539	−	0.757755i	$-0.726296\pi$
$283$	−25.3567	−	4.01611i	−1.50730	−	0.238733i	−0.854761	+	0.519022i	$0.826296\pi$
$284$	−1.90474	−	5.86218i	−0.113025	−	0.347856i
$285$	−24.4247	+	6.83544i	−1.44680	+	0.404897i
$286$	0.270286	−	0.831854i	0.0159823	−	0.0491886i
$287$	−14.8467	+	29.1383i	−0.876372	+	1.71998i
$288$	1.04646	+	2.81157i	0.0616632	+	0.165673i
$289$	−4.23760	−	1.37688i	−0.249271	−	0.0809930i
$290$	−13.3464	−	4.09898i	−0.783726	−	0.240700i
$291$	0.698888	−	12.1489i	0.0409696	−	0.712181i
$292$	−1.63344	+	10.3131i	−0.0955899	+	0.603531i
$293$	−24.1559	+	24.1559i	−1.41120	+	1.41120i	−0.659495	+	0.751709i	$0.729230\pi$
$293$	−24.1559	+	24.1559i	−1.41120	+	1.41120i	−0.751709	+	0.659495i	$0.770770\pi$
$294$	−13.1861	+	3.46116i	−0.769027	+	0.201859i
$295$	0.889572	+	5.08283i	0.0517929	+	0.295934i
$296$	2.85988	−	3.93629i	0.166227	−	0.228792i
$297$	1.49997	−	1.05509i	0.0870370	−	0.0612223i
$298$	4.14221	−	2.11056i	0.239952	−	0.122262i
$299$	−19.4242			−1.12333
$300$	−3.73676	−	7.81259i	−0.215742	−	0.451060i
$301$	28.1596			1.62309
$302$	−13.0575	+	6.65314i	−0.751376	+	0.382845i
$303$	−16.2241	−	3.53518i	−0.932051	−	0.203091i
$304$	−3.84926	+	5.29805i	−0.220770	+	0.303864i
$305$	0.143666	−	0.293610i	0.00822629	−	0.0168121i
$306$	−10.5553	−	1.21846i	−0.603406	−	0.0696547i
$307$	−12.8970	+	12.8970i	−0.736071	+	0.736071i	−0.971815	−	0.235744i	$-0.924247\pi$
$307$	−12.8970	+	12.8970i	−0.736071	+	0.736071i	0.235744	+	0.971815i	$0.424247\pi$
$308$	0.212907	−	1.34424i	0.0121315	−	0.0765952i
$309$	11.5042	+	0.661801i	0.654451	+	0.0376485i
$310$	−5.38694	+	7.67255i	−0.305958	+	0.435772i
$311$	−15.4255	−	5.01205i	−0.874699	−	0.284207i	−0.162945	−	0.986635i	$-0.552099\pi$
$311$	−15.4255	−	5.01205i	−0.874699	−	0.284207i	−0.711755	+	0.702428i	$0.752099\pi$
$312$	3.20458	−	2.85594i	0.181424	−	0.161686i
$313$	2.45198	−	4.81228i	0.138594	−	0.272006i	−0.811269	−	0.584674i	$-0.801223\pi$
$313$	2.45198	−	4.81228i	0.138594	−	0.272006i	0.949863	+	0.312668i	$0.101223\pi$
$314$	1.38637	−	4.26680i	0.0782372	−	0.240789i
$315$	25.2708	−	5.52945i	1.42385	−	0.311549i
$316$	−0.422251	−	1.29956i	−0.0237535	−	0.0731057i
$317$	8.47316	+	1.34202i	0.475900	+	0.0753752i	0.389777	−	0.920909i	$-0.372552\pi$
$317$	8.47316	+	1.34202i	0.475900	+	0.0753752i	0.0861233	+	0.996284i	$0.472552\pi$
$318$	3.06499	+	6.97973i	0.171876	+	0.391404i
$319$	1.29527	+	1.78278i	0.0725210	+	0.0998166i
$320$	−2.00852	−	0.982784i	−0.112279	−	0.0549393i
$321$	−21.5049	+	13.8099i	−1.20028	+	0.770793i
$322$	−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
$327$	1.91483	+	19.1584i	0.105890	+	1.05946i
$328$	−1.32662	−	8.37596i	−0.0732504	−	0.462485i
$329$	13.3399	+	9.69197i	0.735450	+	0.534336i
$330$	−0.269366	+	1.34009i	−0.0148281	+	0.0737695i
$331$	22.9895	−	16.7029i	1.26362	−	0.918073i	0.264690	−	0.964334i	$-0.414731\pi$
$331$	22.9895	−	16.7029i	1.26362	−	0.918073i	0.998929	+	0.0462607i	$0.0147305\pi$
$332$	−4.13675	−	4.13675i	−0.227034	−	0.227034i
$333$	−9.06965	−	11.4368i	−0.497014	−	0.626734i
$334$	15.9719	−	5.18960i	0.873946	−	0.283962i
$335$	4.97057	−	16.1843i	0.271571	−	0.884244i
$336$	4.22984	−	5.16925i	0.230757	−	0.282005i
$337$	−4.22871	−	2.15464i	−0.230353	−	0.117371i	0.335005	−	0.942216i	$-0.391262\pi$
$337$	−4.22871	−	2.15464i	−0.230353	−	0.117371i	−0.565358	+	0.824846i	$0.691262\pi$
$338$	6.11059	+	3.11350i	0.332372	+	0.169352i
$339$	−1.93047	+	2.35921i	−0.104849	+	0.128135i
$340$	6.33101	−	4.75814i	0.343347	−	0.258046i
$341$	1.40726	−	0.457245i	0.0762072	−	0.0247612i
$342$	12.2073	+	15.3934i	0.660095	+	0.832380i
$343$	2.37470	+	2.37470i	0.128222	+	0.128222i
$344$	−5.90767	+	4.29217i	−0.318520	+	0.231418i
$345$	30.1521	−	3.50721i	1.62333	−	0.188822i
$346$	14.0925	+	10.2388i	0.757620	+	0.550443i
$347$	1.25574	+	7.92843i	0.0674116	+	0.425620i	0.998195	+	0.0600500i	$0.0191260\pi$
$347$	1.25574	+	7.92843i	0.0674116	+	0.425620i	−0.930784	+	0.365570i	$0.880874\pi$
$348$	1.07553	+	10.7610i	0.0576545	+	0.576851i
$349$		−	18.9234i		−	1.01295i	−0.862256	−	0.506474i	$-0.830949\pi$
$349$		−	18.9234i		−	1.01295i	0.862256	−	0.506474i	$-0.169051\pi$
$350$	−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	$-0.590126\pi$
$353$	−4.66620	+	0.739053i	−0.248357	+	0.0393358i	0.0310149	+	0.999519i	$0.490126\pi$
$354$	3.36322	−	2.15978i	0.178753	−	0.114791i
$355$	9.58695	−	9.90233i	0.508823	−	0.525561i
$356$	−1.20449	−	1.65784i	−0.0638379	−	0.0878654i
$357$	9.51159	+	21.6602i	0.503406	+	1.14638i
$358$	7.25818	+	1.14958i	0.383607	+	0.0607573i
$359$	4.67561	+	14.3900i	0.246769	+	0.759478i	0.995340	+	0.0964232i	$0.0307402\pi$
$359$	4.67561	+	14.3900i	0.246769	+	0.759478i	−0.748571	+	0.663054i	$0.769260\pi$
$360$	−4.45881	+	5.01189i	−0.235000	+	0.264150i
$361$	−7.38121	+	22.7170i	−0.388485	+	1.19563i
$362$	−0.304777	+	0.598158i	−0.0160187	+	0.0314385i
$363$	−14.0626	+	12.5327i	−0.738097	+	0.657795i
$364$	−9.08922	−	2.95327i	−0.476405	−	0.154793i
$365$	−22.0859	+	7.57338i	−1.15603	+	0.396409i
$366$	−0.252778	−	0.0145415i	−0.0132129	−	0.000760098i
$367$	−5.73021	+	36.1791i	−0.299114	+	1.88853i	0.140078	+	0.990140i	$0.455265\pi$
$367$	−5.73021	+	36.1791i	−0.299114	+	1.88853i	−0.439193	+	0.898393i	$0.644735\pi$
$368$	5.54211	−	5.54211i	0.288902	−	0.288902i
$369$	−25.2733	−	2.91744i	−1.31567	−	0.151876i
$370$	10.7718	+	1.52786i	0.560000	+	0.0794297i
$371$	9.97595	−	13.7307i	0.517926	−	0.712864i
$372$	7.09522	+	1.54603i	0.367870	+	0.0801577i
$373$	−1.97517	+	1.00640i	−0.102270	+	0.0521093i	−0.504377	−	0.863483i	$-0.668278\pi$
$373$	−1.97517	+	1.00640i	−0.102270	+	0.0521093i	0.402107	+	0.915593i	$0.368278\pi$
$374$	−1.25001			−0.0646363
$375$	11.5217	−	15.5644i	0.594979	−	0.803741i
$376$	−4.27588			−0.220512
$377$	13.7875	−	7.02506i	0.710090	−	0.361809i
$378$	−11.5283	−	16.3894i	−0.592954	−	0.842977i
$379$	4.15559	−	5.71968i	0.213458	−	0.293800i	−0.688839	−	0.724914i	$-0.741879\pi$
$379$	4.15559	−	5.71968i	0.213458	−	0.293800i	0.902297	+	0.431114i	$0.141879\pi$
$380$	−14.4983	−	2.05643i	−0.743749	−	0.105492i
$381$	9.03625	−	2.37189i	0.462941	−	0.121516i
$382$	9.96347	−	9.96347i	0.509775	−	0.509775i
$383$	2.17700	−	13.7450i	0.111240	−	0.702339i	−0.867532	−	0.497382i	$-0.834295\pi$
$383$	2.17700	−	13.7450i	0.111240	−	0.702339i	0.978771	−	0.204957i	$-0.0657053\pi$
$384$	−0.0994751	+	1.72919i	−0.00507632	+	0.0882425i
$385$	2.87874	−	0.987133i	0.146714	−	0.0503090i
$386$	−3.89161	−	1.26446i	−0.198078	−	0.0643593i
$387$	7.64154	+	20.5309i	0.388441	+	1.04364i
$388$	3.18963	−	6.26000i	0.161929	−	0.317803i
$389$	−4.65972	+	14.3411i	−0.236257	+	0.727125i	0.760695	+	0.649110i	$0.224858\pi$
$389$	−4.65972	+	14.3411i	−0.236257	+	0.727125i	−0.996952	+	0.0780155i	$0.975142\pi$
$390$	8.99841	+	3.34028i	0.455652	+	0.169142i
$391$	8.57820	+	26.4010i	0.433818	+	1.33515i
$392$	−7.77397	−	1.23128i	−0.392645	−	0.0621888i
$393$	27.6158	−	12.1268i	1.39303	−	0.611719i
$394$	−13.3665	−	18.3974i	−0.673395	−	0.926849i
$395$	2.12528	−	2.19519i	0.106934	−	0.110452i
$396$	1.03785	−	0.209552i	0.0521538	−	0.0105304i
$397$	−13.6256	+	2.15808i	−0.683849	+	0.108311i	−0.488686	−	0.872460i	$-0.662524\pi$
$397$	−13.6256	+	2.15808i	−0.683849	+	0.108311i	−0.195163	+	0.980771i	$0.562524\pi$
$398$	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	$-0.129254\pi$
$402$	−13.0492	+	1.30423i	−0.650836	+	0.0650490i
$403$	−1.62541	−	10.2624i	−0.0809674	−	0.511208i
$404$	−7.75588	−	5.63497i	−0.385869	−	0.280350i
$405$	10.8891	+	16.9242i	0.541083	+	0.840969i
$406$	19.4795	−	14.1527i	0.966750	−	0.702385i
$407$	−1.21424	−	1.21424i	−0.0601875	−	0.0601875i
$408$	−5.29697	−	3.09436i	−0.262239	−	0.153194i
$409$	−5.65867	+	1.83861i	−0.279803	+	0.0909136i	−0.445557	−	0.895254i	$-0.646994\pi$
$409$	−5.65867	+	1.83861i	−0.279803	+	0.0909136i	0.165754	+	0.986167i	$0.446994\pi$
$410$	15.1588	−	11.3927i	0.748638	−	0.562647i
$411$	24.0301	+	19.6631i	1.18532	+	0.969909i
$412$	5.92780	+	3.02037i	0.292042	+	0.148803i
$413$	−7.92905	−	4.04005i	−0.390163	−	0.198798i
$414$	−11.5481	−	20.4820i	−0.567559	−	1.00663i
$415$	3.84060	−	12.5051i	0.188527	−	0.613850i
$416$	2.35699	−	0.765834i	0.115561	−	0.0375481i
$417$	15.7457	−	26.9538i	0.771073	−	1.31993i
$418$	1.63430	+	1.63430i	0.0799363	+	0.0799363i
$419$	−3.49605	+	2.54003i	−0.170793	+	0.124088i	−0.669898	−	0.742453i	$-0.733662\pi$
$419$	−3.49605	+	2.54003i	−0.170793	+	0.124088i	0.499105	+	0.866542i	$0.333662\pi$
$420$	14.6424	+	2.94321i	0.714477	+	0.143614i
$421$	−20.2471	−	14.7103i	−0.986781	−	0.716939i	−0.0275674	−	0.999620i	$-0.508776\pi$
$421$	−20.2471	−	14.7103i	−0.986781	−	0.716939i	−0.959214	+	0.282681i	$0.908776\pi$
$422$	0.650182	+	4.10508i	0.0316503	+	0.199832i
$423$	−3.44634	+	12.3560i	−0.167567	+	0.600770i
$424$			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
$429$	−0.818612	−	1.27475i	−0.0395230	−	0.0615454i
$430$	−14.6667	−	7.17656i	−0.707293	−	0.346085i
$431$	4.11469	+	5.66339i	0.198198	+	0.272796i	0.896535	−	0.442973i	$-0.146076\pi$
$431$	4.11469	+	5.66339i	0.198198	+	0.272796i	−0.698337	+	0.715769i	$0.746076\pi$
$432$	4.91667	+	1.68117i	0.236553	+	0.0808855i
$433$	−9.74698	−	1.54377i	−0.468410	−	0.0741889i	−0.0822322	−	0.996613i	$-0.526205\pi$
$433$	−9.74698	−	1.54377i	−0.468410	−	0.0741889i	−0.386178	+	0.922424i	$0.626205\pi$
$434$	−4.99607	−	15.3763i	−0.239819	−	0.738087i
$435$	−20.1338	+	13.3944i	−0.965343	+	0.642215i
$436$	−3.43511	+	10.5722i	−0.164512	+	0.506315i
$437$	23.3021	−	45.7330i	1.11469	−	2.18770i
$438$	12.0328	+	13.5018i	0.574951	+	0.645139i
$439$	−0.555271	−	0.180419i	−0.0265016	−	0.00861091i	0.295736	−	0.955270i	$-0.404435\pi$
$439$	−0.555271	−	0.180419i	−0.0265016	−	0.00861091i	−0.322238	+	0.946659i	$0.604435\pi$
$440$	−0.453475	+	0.645879i	−0.0216186	+	0.0307911i
$441$	−9.82380	+	21.4721i	−0.467800	+	1.02248i
$442$	−1.37312	+	8.66953i	−0.0653126	+	0.412368i
$443$	6.33032	−	6.33032i	0.300763	−	0.300763i	−0.540549	−	0.841312i	$-0.681784\pi$
$443$	6.33032	−	6.33032i	0.300763	−	0.300763i	0.841312	+	0.540549i	$0.181784\pi$
$444$	−2.13958	−	8.15120i	−0.101540	−	0.386839i
$445$	2.01393	−	4.11586i	0.0954692	−	0.195110i
$446$	9.03387	−	12.4341i	0.427766	−	0.588770i
$447$	1.71431	−	7.86754i	0.0810842	−	0.372122i
$448$	3.43597	−	1.75071i	0.162334	−	0.0827134i
$449$	−18.3782			−0.867322			−0.433661	−	0.901076i	$-0.642779\pi$
$449$	−18.3782			−0.867322			−0.433661	+	0.901076i	$0.642779\pi$
$450$	−14.5713	−	3.56037i	−0.686899	−	0.167838i
$451$	−2.99298			−0.140934
$452$	−1.56816	+	0.799015i	−0.0737598	+	0.0375825i
$453$	−5.40404	+	24.8009i	−0.253904	+	1.16525i
$454$	8.24401	−	11.3469i	0.386911	−	0.532537i
$455$	−3.68408	−	21.0501i	−0.172713	−	0.986843i
$456$	2.87977	+	10.9711i	0.134857	+	0.513769i
$457$	−24.7918	+	24.7918i	−1.15971	+	1.15971i	−0.175174	+	0.984537i	$0.556049\pi$
$457$	−24.7918	+	24.7918i	−1.15971	+	1.15971i	−0.984537	+	0.175174i	$0.943951\pi$
$458$	2.71142	−	17.1192i	0.126696	−	0.799928i
$459$	−13.2111	+	12.8126i	−0.616642	+	0.598042i
$460$	16.7534	+	5.14534i	0.781130	+	0.239903i
$461$	0.133994	+	0.0435374i	0.00624074	+	0.00202774i	0.312136	−	0.950038i	$-0.398956\pi$
$461$	0.133994	+	0.0435374i	0.00624074	+	0.00202774i	−0.305895	+	0.952065i	$0.598956\pi$
$462$	−1.56839	−	1.75985i	−0.0729681	−	0.0818758i
$463$	−4.02806	+	7.90552i	−0.187200	+	0.367401i	−0.965464	−	0.260537i	$-0.916101\pi$
$463$	−4.02806	+	7.90552i	−0.187200	+	0.367401i	0.778264	+	0.627937i	$0.216101\pi$
$464$	−1.92945	+	5.93824i	−0.0895725	+	0.275676i
$465$	4.37609	+	15.6369i	0.202936	+	0.725142i
$466$	0.760291	+	2.33993i	0.0352198	+	0.108395i
$467$	−4.81480	−	0.762590i	−0.222803	−	0.0352885i	0.0440349	−	0.999030i	$-0.485979\pi$
$467$	−4.81480	−	0.762590i	−0.222803	−	0.0352885i	−0.266838	+	0.963742i	$0.585979\pi$
$468$	−0.313305	−	7.42827i	−0.0144825	−	0.343372i
$469$	17.1621	+	23.6216i	0.792470	+	1.09074i
$470$	−4.47794	−	8.44770i	−0.206552	−	0.389663i
$471$	−4.19887	−	6.53851i	−0.193474	−	0.301279i
$472$	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
$477$	12.7180	+	3.54732i	0.582319	+	0.162420i
$478$	−0.380627	−	2.40319i	−0.0174095	−	0.109919i
$479$	−11.5308	−	8.37759i	−0.526854	−	0.382782i	0.292326	−	0.956319i	$-0.405571\pi$
$479$	−11.5308	−	8.37759i	−0.526854	−	0.382782i	−0.819180	+	0.573537i	$0.805571\pi$
$480$	−3.52048	+	1.61438i	−0.160687	+	0.0736860i
$481$	−9.75526	+	7.08761i	−0.444802	+	0.323167i
$482$	1.14460	+	1.14460i	0.0521349	+	0.0521349i
$483$	−26.4062	+	45.2025i	−1.20152	+	2.05678i
$484$	−10.3432	+	3.36070i	−0.470144	+	0.152759i
$485$	15.7080	−	0.254189i	0.713265	−	0.0115421i
$486$	8.82090	−	12.8527i	0.400124	−	0.583010i
$487$	−31.0777	−	15.8349i	−1.40827	−	0.717547i	−0.425945	−	0.904749i	$-0.640058\pi$
$487$	−31.0777	−	15.8349i	−1.40827	−	0.717547i	−0.982321	+	0.187202i	$0.940058\pi$
$488$	−0.130250	−	0.0663655i	−0.00589612	−	0.00300422i
$489$	14.5042	+	11.8684i	0.655904	+	0.536706i
$490$	−5.70876	−	16.6482i	−0.257895	−	0.752090i
$491$	−5.09165	+	1.65438i	−0.229783	+	0.0746610i	−0.421645	−	0.906761i	$-0.638547\pi$
$491$	−5.09165	+	1.65438i	−0.229783	+	0.0746610i	0.191862	+	0.981422i	$0.438547\pi$
$492$	−12.6829	−	7.40904i	−0.571789	−	0.334025i
$493$	−15.6372	−	15.6372i	−0.704266	−	0.704266i
$494$	13.1301	−	9.53958i	0.590751	−	0.429206i
$495$	1.50090	+	1.83098i	0.0674603	+	0.0822965i
$496$	3.39184	+	2.46432i	0.152298	+	0.110651i
$497$	3.71838	+	23.4769i	0.166792	+	1.05308i
$498$	−10.0827	+	1.00773i	−0.451817	+	0.0451576i
$499$			8.93736i			0.400091i	0.979787	+	0.200046i	$0.0641090\pi$
$499$			8.93736i			0.400091i	−0.979787	+	0.200046i	$0.935891\pi$
$500$	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	$-0.529264\pi$
$503$	2.88408	−	0.456793i	0.128595	−	0.0203674i	0.220400	+	0.975410i	$0.429264\pi$
$504$	−2.28966	−	11.3400i	−0.101990	−	0.505123i
$505$	3.01043	−	21.2243i	0.133962	−	0.944468i
$506$	−1.62591	−	2.23788i	−0.0722807	−	0.0994859i
$507$	10.8761	−	4.77599i	0.483025	−	0.212109i
$508$	5.32741	+	0.843778i	0.236365	+	0.0374366i
$509$	−3.24395	−	9.98385i	−0.143786	−	0.442527i	0.853067	−	0.521801i	$-0.174740\pi$
$509$	−3.24395	−	9.98385i	−0.143786	−	0.442527i	−0.996853	+	0.0792745i	$0.974740\pi$
$510$	0.566129	−	13.7056i	0.0250686	−	0.606895i
$511$	12.4429	−	38.2953i	0.550441	−	1.69408i
$512$	−0.453990	+	0.891007i	−0.0200637	+	0.0393773i
$513$	34.0243	+	0.520992i	1.50221	+	0.0230023i
$514$	27.2321	+	8.84825i	1.20116	+	0.390280i
$515$	0.240701	+	14.8745i	0.0106065	+	0.655447i
$516$	−0.726395	+	12.6270i	−0.0319777	+	0.555874i
$517$	−0.236073	+	1.49051i	−0.0103825	+	0.0655524i
$518$	−13.2673	+	13.2673i	−0.582932	+	0.582932i
$519$	29.1826	−	7.66004i	1.28097	−	0.336238i
$520$	3.98141	+	3.85461i	0.174596	+	0.169036i
$521$	11.1471	−	15.3427i	0.488364	−	0.672175i	−0.491722	−	0.870753i	$-0.663632\pi$
$521$	11.1471	−	15.3427i	0.488364	−	0.672175i	0.980085	+	0.198578i	$0.0636322\pi$
$522$	15.6046	+	10.3617i	0.682995	+	0.453520i
$523$	21.7058	−	11.0596i	0.949127	−	0.483604i	0.0903250	−	0.995912i	$-0.471209\pi$
$523$	21.7058	−	11.0596i	0.949127	−	0.483604i	0.858802	+	0.512308i	$0.171209\pi$
$524$	17.4135			0.760714
$525$	9.51958	+	32.0108i	0.415469	+	1.39707i
$526$	3.01044			0.131261
$527$	−13.2307	+	6.74137i	−0.576338	+	0.293659i
$528$	0.597278	+	0.130145i	0.0259932	+	0.00566383i
$529$	−22.5886	+	31.0905i	−0.982111	+	1.35176i
$530$	−8.69523	+	4.60915i	−0.377696	+	0.200209i
$531$	0.793889	−	6.87732i	0.0344518	−	0.298450i
$532$	17.8571	−	17.8571i	0.774205	−	0.774205i
$533$	−3.28775	+	20.7580i	−0.142408	+	0.899131i
$534$	−3.54347	−	0.203845i	−0.153341	−	0.00882122i
$535$	−19.8229	−	26.3756i	−0.857018	−	1.14032i
$536$	−7.20094	−	2.33973i	−0.311033	−	0.101061i
$537$	9.50227	−	8.46847i	0.410053	−	0.365441i
$538$	5.88761	−	11.5551i	0.253833	−	0.498175i
$539$	−0.858409	+	2.64191i	−0.0369743	+	0.113795i
$540$	1.82758	+	11.4743i	0.0786466	+	0.493776i
$541$	8.94591	+	27.5327i	0.384615	+	1.18372i	0.936759	+	0.349974i	$0.113810\pi$
$541$	8.94591	+	27.5327i	0.384615	+	1.18372i	−0.552144	+	0.833749i	$0.686190\pi$
$542$	16.8214	+	2.66425i	0.722542	+	0.114439i
$543$	0.467516	+	1.06465i	0.0200630	+	0.0456884i
$544$	−2.08182	−	2.86537i	−0.0892571	−	0.122852i
$545$	−24.4845	+	4.28516i	−1.04880	+	0.183556i
$546$	−13.9285	+	8.94453i	−0.596084	+	0.382790i
$547$	12.9801	−	2.05584i	0.554988	−	0.0879014i	0.127360	−	0.991857i	$-0.459350\pi$
$547$	12.9801	−	2.05584i	0.554988	−	0.0879014i	0.427627	+	0.903955i	$0.359350\pi$
$548$	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
$552$	−1.35009	−	13.5080i	−0.0574635	−	0.574940i
$553$	0.824307	+	5.20447i	0.0350531	+	0.221317i
$554$	−8.59687	−	6.24599i	−0.365246	−	0.265367i
$555$	13.8634	−	12.7635i	0.588466	−	0.541780i
$556$	14.5805	−	10.5934i	0.618353	−	0.449260i
$557$	−24.6270	−	24.6270i	−1.04348	−	1.04348i	−0.999011	−	0.0444707i	$-0.985840\pi$
$557$	−24.6270	−	24.6270i	−1.04348	−	1.04348i	−0.0444707	−	0.999011i	$-0.514160\pi$
$558$	9.85495	−	7.81518i	0.417193	−	0.330843i
$559$	17.2114	−	5.59233i	0.727966	−	0.236530i
$560$	7.05717	+	4.95488i	0.298220	+	0.209382i
$561$	−1.37110	+	1.67560i	−0.0578877	+	0.0707441i
$562$	−25.0016	−	12.7389i	−1.05463	−	0.537359i
$563$	−8.71723	−	4.44165i	−0.367388	−	0.187193i	0.260544	−	0.965462i	$-0.416098\pi$
$563$	−8.71723	−	4.44165i	−0.367388	−	0.187193i	−0.627931	+	0.778269i	$0.716098\pi$
$564$	−4.69008	+	5.73171i	−0.197488	+	0.241348i
$565$	−3.22085	−	2.26138i	−0.135502	−	0.0951368i
$566$	−24.4163	+	7.93332i	−1.02629	+	0.333462i
$567$	−34.6146	−	2.52353i	−1.45368	−	0.105978i
$568$	−4.35851	−	4.35851i	−0.182879	−	0.182879i
$569$	8.66014	−	6.29196i	0.363052	−	0.263773i	−0.391272	−	0.920275i	$-0.627965\pi$
$569$	8.66014	−	6.29196i	0.363052	−	0.263773i	0.754324	+	0.656502i	$0.227965\pi$
$570$	−18.6594	+	17.1790i	−0.781555	+	0.719550i
$571$	12.5798	+	9.13980i	0.526450	+	0.382489i	0.819028	−	0.573753i	$-0.194513\pi$
$571$	12.5798	+	9.13980i	0.526450	+	0.382489i	−0.292578	+	0.956242i	$0.594513\pi$
$572$	−0.136828	−	0.863895i	−0.00572105	−	0.0361213i
$573$	−2.42715	−	24.2844i	−0.101396	−	1.01450i
$574$			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	0.706350	−	0.707863i	$-0.250341\pi$
$577$	−6.76199	−	13.2712i	−0.281505	−	0.552485i	−0.987855	+	0.155378i	$0.950341\pi$
$578$	−4.40082	+	0.697022i	−0.183050	+	0.0289923i
$579$	−5.96357	+	3.82966i	−0.247837	+	0.159155i
$580$	−13.7526	+	2.40691i	−0.571046	+	0.0999417i
$581$	13.2606	+	18.2516i	0.550140	+	0.757203i
$582$	−4.89277	−	11.1420i	−0.202812	−	0.461852i
$583$	1.53418	+	0.242990i	0.0635392	+	0.0100636i
$584$	3.22666	+	9.93064i	0.133520	+	0.410933i
$585$	14.3477	−	8.39829i	0.593202	−	0.347227i
$586$	−10.5565	+	32.4896i	−0.436086	+	1.34213i
$587$	11.6079	−	22.7817i	0.479108	−	0.940302i	−0.517315	−	0.855795i	$-0.673068\pi$
$587$	11.6079	−	22.7817i	0.479108	−	0.940302i	0.996423	−	0.0845070i	$-0.0269315\pi$
$588$	−10.1775	+	9.07027i	−0.419715	+	0.374052i
$589$	26.1121	+	8.48435i	1.07593	+	0.349592i
$590$	3.10017	+	4.12498i	0.127632	+	0.169823i
$591$	−39.3226	−	2.26211i	−1.61752	−	0.0930508i
$592$	0.761135	−	4.80562i	0.0312825	−	0.197510i
$593$	−5.46116	+	5.46116i	−0.224263	+	0.224263i	−0.810291	−	0.586028i	$-0.800691\pi$
$593$	−5.46116	+	5.46116i	−0.224263	+	0.224263i	0.586028	+	0.810291i	$0.300691\pi$
$594$	0.857484	−	1.62106i	0.0351830	−	0.0665129i
$595$	−26.9839	+	14.3036i	−1.10623	+	0.586390i
$596$	2.73256	−	3.76105i	0.111930	−	0.154058i
$597$	10.6933	+	2.33005i	0.437650	+	0.0953624i
$598$	−17.3071	+	8.81838i	−0.707738	+	0.360611i
$599$	−20.6409			−0.843363			−0.421681	−	0.906744i	$-0.638560\pi$
$599$	−20.6409			−0.843363			−0.421681	+	0.906744i	$0.638560\pi$
$600$	−6.87632	−	5.26462i	−0.280725	−	0.214927i
$601$	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
$603$	−12.5650	+	18.9227i	−0.511687	+	0.770594i
$604$	−8.61387	+	11.8560i	−0.350494	+	0.482413i
$605$	−17.4716	−	16.9151i	−0.710320	−	0.687697i
$606$	−16.0607	+	4.21573i	−0.652423	+	0.171252i
$607$	5.54524	−	5.54524i	0.225074	−	0.225074i	−0.585557	−	0.810631i	$-0.699124\pi$
$607$	5.54524	−	5.54524i	0.225074	−	0.225074i	0.810631	+	0.585557i	$0.199124\pi$
$608$	−1.02445	+	6.46812i	−0.0415469	+	0.262317i
$609$	2.39516	−	41.6354i	0.0970567	−	1.68715i
$610$	−0.00528883	−	0.326831i	−0.000214138	−	0.0132330i
$611$	10.0782	+	3.27461i	0.407721	+	0.132477i
$612$	−9.95800	+	3.70635i	−0.402528	+	0.149820i
$613$	−2.13588	+	4.19191i	−0.0862676	+	0.169310i	−0.930110	−	0.367282i	$-0.880288\pi$
$613$	−2.13588	+	4.19191i	−0.0862676	+	0.169310i	0.843842	+	0.536592i	$0.180288\pi$
$614$	−5.63620	+	17.3464i	−0.227459	+	0.700045i
$615$	1.35552	−	32.8163i	0.0546599	−	1.32328i
$616$	−0.420571	−	1.29439i	−0.0169453	−	0.0521523i
$617$	−40.5328	−	6.41977i	−1.63179	−	0.258450i	−0.727733	−	0.685861i	$-0.759426\pi$
$617$	−40.5328	−	6.41977i	−1.63179	−	0.258450i	−0.904058	+	0.427410i	$0.859426\pi$
$618$	10.5508	−	4.63313i	0.424414	−	0.186372i
$619$	−10.1486	−	13.9684i	−0.407908	−	0.561438i	0.554798	−	0.831985i	$-0.312795\pi$
$619$	−10.1486	−	13.9684i	−0.407908	−	0.561438i	−0.962707	+	0.270547i	$0.912795\pi$
$620$	−1.31654	+	9.28192i	−0.0528733	+	0.372771i
$621$	−40.1224	−	6.98607i	−1.61005	−	0.280341i
$622$	−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
$627$	3.98336	−	0.398124i	0.159080	−	0.0158995i
$628$	−0.701824	−	4.43114i	−0.0280058	−	0.176822i
$629$	13.9415	+	10.1291i	0.555885	+	0.403874i
$630$	20.0062	−	16.3995i	0.797064	−	0.653371i
$631$	−29.4746	+	21.4146i	−1.17337	+	0.852501i	−0.991408	−	0.130805i	$-0.958244\pi$
$631$	−29.4746	+	21.4146i	−1.17337	+	0.852501i	−0.181959	+	0.983306i	$0.558244\pi$
$632$	−0.966214	−	0.966214i	−0.0384339	−	0.0384339i
$633$	6.21593	+	3.63119i	0.247061	+	0.144327i
$634$	8.15891	−	2.65099i	0.324032	−	0.105284i
$635$	3.91214	+	11.4088i	0.155249	+	0.452745i
$636$	5.89965	+	4.82751i	0.233936	+	0.191423i
$637$	17.3803	+	8.85568i	0.688631	+	0.350875i
$638$	1.96346	+	1.00043i	0.0777340	+	0.0396074i
$639$	−16.1077	+	9.08185i	−0.637212	+	0.359272i
$640$	−2.23578	+	0.0361796i	−0.0883768	+	0.00143013i
$641$	28.1775	−	9.15543i	1.11294	−	0.361618i	0.305874	−	0.952072i	$-0.401051\pi$
$641$	28.1775	−	9.15543i	1.11294	−	0.361618i	0.807071	+	0.590454i	$0.201051\pi$
$642$	−12.8914	+	22.0677i	−0.508784	+	0.870943i
$643$	16.2471	+	16.2471i	0.640721	+	0.640721i	0.950733	−	0.310012i	$-0.100333\pi$
$643$	16.2471	+	16.2471i	0.640721	+	0.640721i	−0.310012	+	0.950733i	$0.600333\pi$
$644$	−24.4521	+	17.7655i	−0.963547	+	0.700058i
$645$	−25.7075	+	11.7886i	−1.01223	+	0.464177i
$646$	−18.7646	−	13.6333i	−0.738284	−	0.536394i
$647$	0.280589	+	1.77157i	0.0110311	+	0.0696477i	0.992590	−	0.121513i	$-0.0387747\pi$
$647$	0.280589	+	1.77157i	0.0110311	+	0.0696477i	−0.981559	+	0.191161i	$0.938775\pi$
$648$	7.64652	−	4.74665i	0.300384	−	0.186466i
$649$		−	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	$-0.375437\pi$
$653$	26.3159	−	4.16803i	1.02982	−	0.163107i	0.648404	+	0.761296i	$0.275437\pi$
$654$	10.4039	+	16.2010i	0.406824	+	0.633509i
$655$	18.2364	+	34.4033i	0.712557	+	1.34425i
$656$	−4.98463	−	6.86076i	−0.194617	−	0.267868i
$657$	31.2973	−	1.32004i	1.22102	−	0.0514996i
$658$	16.2860	+	2.57944i	0.634893	+	0.100557i
$659$	−2.02081	−	6.21940i	−0.0787195	−	0.242274i	0.903951	−	0.427637i	$-0.140654\pi$
$659$	−2.02081	−	6.21940i	−0.0787195	−	0.242274i	−0.982670	+	0.185363i	$0.940654\pi$
$660$	0.368381	+	1.31632i	0.0143392	+	0.0512376i
$661$	5.97584	−	18.3917i	0.232433	−	0.715356i	−0.765018	−	0.644008i	$-0.777270\pi$
$661$	5.97584	−	18.3917i	0.232433	−	0.715356i	0.997452	−	0.0713473i	$-0.0227299\pi$
$662$	12.9009	−	25.3194i	0.501407	−	0.984066i
$663$	10.1152	+	11.3500i	0.392840	+	0.440797i
$664$	−5.56392	−	1.80783i	−0.215922	−	0.0701573i
$665$	53.9807	+	16.5787i	2.09328	+	0.642894i
$666$	−13.2733	−	6.07276i	−0.514331	−	0.235315i
$667$	7.65551	−	48.3350i	0.296422	−	1.87154i
$668$	11.8751	−	11.8751i	0.459461	−	0.459461i
$669$	−6.75856	−	25.7482i	−0.261301	−	0.995484i
$670$	−2.91872	−	16.6769i	−0.112760	−	0.644286i
$671$	−0.0303252	+	0.0417390i	−0.00117069	+	0.00161132i
$672$	1.42202	−	6.52614i	0.0548558	−	0.251751i
$673$	39.1978	−	19.9723i	1.51096	−	0.769874i	0.514793	−	0.857315i	$-0.327869\pi$
$673$	39.1978	−	19.9723i	1.51096	−	0.769874i	0.996170	+	0.0874407i	$0.0278688\pi$
$674$	−4.74599			−0.182809
$675$	−20.7555	+	15.6273i	−0.798878	+	0.601493i
$676$	6.85808			0.263772
$677$	−33.3683	+	17.0020i	−1.28245	+	0.653440i	−0.956441	−	0.291927i	$-0.905704\pi$
$677$	−33.3683	+	17.0020i	−1.28245	+	0.653440i	−0.326008	+	0.945367i	$0.605704\pi$
$678$	−0.649003	+	2.97849i	−0.0249248	+	0.114388i
$679$	−15.9250	+	21.9189i	−0.611147	+	0.841171i
$680$	3.48082	−	7.11375i	0.133483	−	0.272800i
$681$	−6.16764	−	23.4970i	−0.236344	−	0.900406i
$682$	1.04629	−	1.04629i	0.0400645	−	0.0400645i
$683$	5.33840	−	33.7054i	0.204268	−	1.28970i	−0.645995	−	0.763342i	$-0.723557\pi$
$683$	5.33840	−	33.7054i	0.204268	−	1.28970i	0.850263	−	0.526358i	$-0.176443\pi$
$684$	17.8652	+	8.17363i	0.683094	+	0.312526i
$685$	−23.0336	+	32.8064i	−0.880067	+	1.25347i
$686$	3.19397	+	1.03778i	0.121946	+	0.0396228i
$687$	−19.9738	−	22.4121i	−0.762049	−	0.855077i
$688$	−3.31516	+	6.50638i	−0.126389	+	0.248053i
$689$	3.37056	−	10.3735i	0.128408	−	0.395199i
$690$	25.2735	−	16.8137i	0.962145	−	0.640087i
$691$	−9.75674	−	30.0282i	−0.371164	−	1.14232i	−0.946030	−	0.324078i	$-0.894946\pi$
$691$	−9.75674	−	30.0282i	−0.371164	−	1.14232i	0.574867	−	0.818247i	$-0.305054\pi$
$692$	17.2049	+	2.72498i	0.654031	+	0.103588i
$693$	−4.07936	+	0.172057i	−0.154962	+	0.00653591i
$694$	4.71830	+	6.49419i	0.179104	+	0.246516i
$695$	36.1986	+	17.7123i	1.37309	+	0.671865i
$696$	5.84371	+	9.09986i	0.221505	+	0.344929i
$697$	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	$0.716830\pi$
$702$	−10.3011	−	7.72787i	−0.388789	−	0.291670i
$703$	−4.98448	−	31.4708i	−0.187993	−	1.18694i
$704$	0.285527	+	0.207447i	0.0107612	+	0.00781846i
$705$	−16.2357	−	3.26346i	−0.611470	−	0.122909i
$706$	−3.82209	+	2.77691i	−0.143846	+	0.104510i
$707$	26.1413	+	26.1413i	0.983143	+	0.983143i
$708$	2.01613	−	3.45125i	0.0757710	−	0.129706i
$709$	−48.5191	+	15.7648i	−1.82217	+	0.592060i	−0.822443	+	0.568848i	$0.807389\pi$
$709$	−48.5191	+	15.7648i	−1.82217	+	0.592060i	−0.999731	+	0.0232123i	$0.992611\pi$
$710$	4.04647	−	13.1754i	0.151861	−	0.494465i
$711$	−3.57083	+	2.01331i	−0.133917	+	0.0755049i
$712$	−1.82585	−	0.930319i	−0.0684268	−	0.0348652i
$713$	−29.2785	−	14.9181i	−1.09649	−	0.558689i
$714$	18.3084	+	14.9812i	0.685175	+	0.560658i
$715$	1.56347	−	1.17505i	0.0584706	−	0.0439442i
$716$	6.98899	−	2.27086i	0.261191	−	0.0848660i
$717$	−3.63891	−	2.12576i	−0.135898	−	0.0793881i
$718$	10.6989	+	10.6989i	0.399281	+	0.399281i
$719$	29.8994	−	21.7232i	1.11506	−	0.810138i	0.131606	−	0.991302i	$-0.457987\pi$
$719$	29.8994	−	21.7232i	1.11506	−	0.810138i	0.983453	+	0.181164i	$0.0579866\pi$
$720$	−1.69748	+	6.48988i	−0.0632612	+	0.241864i
$721$	−20.7558	−	15.0800i	−0.772985	−	0.561607i
$722$	3.73661	+	23.5920i	0.139062	+	0.878004i
$723$	2.78978	−	0.278830i	0.103753	−	0.0103698i
$724$			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	0.993458	−	0.114198i	$-0.0364299\pi$
$727$	8.55075	+	16.7818i	0.317130	+	0.622402i	−0.676328	+	0.736600i	$0.736430\pi$
$728$	−9.43931	+	1.49504i	−0.349844	+	0.0554099i
$729$	−7.55333	−	25.9219i	−0.279753	−	0.960072i
$730$	−16.2405	+	16.7747i	−0.601087	+	0.620861i
$731$	−15.2020	−	20.9238i	−0.562266	−	0.773893i
$732$	−0.231828	+	0.101802i	−0.00856862	+	0.00376271i
$733$	34.3095	+	5.43410i	1.26725	+	0.200713i	0.753627	−	0.657302i	$-0.228302\pi$
$733$	34.3095	+	5.43410i	1.26725	+	0.200713i	0.513625	+	0.858015i	$0.328302\pi$
$734$	11.3193	+	34.8373i	0.417804	+	1.28587i
$735$	−28.5783	−	10.6085i	−1.05413	−	0.391300i
$736$	2.42199	−	7.45412i	0.0892758	−	0.274763i
$737$	−1.21316	+	2.38096i	−0.0446873	+	0.0877038i
$738$	−23.8431	+	8.87436i	−0.877678	+	0.326670i
$739$	2.70309	+	0.878288i	0.0994348	+	0.0323083i	0.358312	−	0.933602i	$-0.383352\pi$
$739$	2.70309	+	0.878288i	0.0994348	+	0.0323083i	−0.258877	+	0.965910i	$0.583352\pi$
$740$	10.2914	−	3.52897i	0.378319	−	0.129727i
$741$	1.61445	−	28.0643i	0.0593083	−	1.03097i
$742$	2.65502	−	16.7632i	0.0974689	−	0.615395i
$743$	19.3245	−	19.3245i	0.708947	−	0.708947i	−0.257367	−	0.966314i	$-0.582855\pi$
$743$	19.3245	−	19.3245i	0.708947	−	0.708947i	0.966314	+	0.257367i	$0.0828549\pi$
$744$	7.02377	−	1.84364i	0.257504	−	0.0675913i
$745$	10.2923	+	1.45984i	0.377079	+	0.0534845i
$746$	−1.30299	+	1.79341i	−0.0477059	+	0.0656615i
$747$	−9.70857	+	14.6210i	−0.355218	+	0.534953i
$748$	−1.11376	+	0.567491i	−0.0407233	+	0.0207495i
$749$	56.9012			2.07913
$750$	3.19985	−	19.0987i	0.116842	−	0.697386i
$751$	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
$753$	41.8454	+	9.11798i	1.52493	+	0.332278i
$754$	9.09541	−	12.5188i	0.331235	−	0.455906i
$755$	−32.4444	−	4.60187i	−1.18077	−	0.167479i
$756$	−17.7124	−	9.36926i	−0.644195	−	0.340757i
$757$	−11.1659	+	11.1659i	−0.405833	+	0.405833i	−0.880283	−	0.474450i	$-0.842647\pi$
$757$	−11.1659	+	11.1659i	−0.405833	+	0.405833i	0.474450	+	0.880283i	$0.342647\pi$
$758$	1.10598	−	6.98287i	0.0401710	−	0.253629i
$759$	−4.78324	−	0.275165i	−0.173621	−	0.00998786i
$760$	−13.8517	+	4.74982i	−0.502454	+	0.172294i
$761$	−13.3455	−	4.33621i	−0.483774	−	0.157188i	0.0569686	−	0.998376i	$-0.481857\pi$
$761$	−13.3455	−	4.33621i	−0.483774	−	0.157188i	−0.540742	+	0.841188i	$0.681857\pi$
$762$	6.97454	−	6.21574i	0.252661	−	0.225173i
$763$	19.4614	−	38.1951i	0.704548	−	1.38275i
$764$	4.35419	−	13.4008i	0.157529	−	0.484825i
$765$	−17.7511	−	15.7922i	−0.641792	−	0.570968i
$766$	−4.30040	−	13.2353i	−0.155380	−	0.478209i
$767$	−5.64864	−	0.894657i	−0.203961	−	0.0323042i
$768$	0.696404	+	1.58588i	0.0251293	+	0.0572256i
$769$	13.0082	+	17.9042i	0.469087	+	0.645643i	0.976362	−	0.216141i	$-0.0693471\pi$
$769$	13.0082	+	17.9042i	0.469087	+	0.645643i	−0.507275	+	0.861784i	$0.669347\pi$
$770$	2.11683	−	2.18646i	0.0762851	−	0.0787946i
$771$	41.7310	−	26.7986i	1.50290	−	0.965128i
$772$	−4.04150	+	0.640111i	−0.145457	+	0.0230381i
$773$	19.2486	+	37.7774i	0.692323	+	1.35876i	0.922647	+	0.385646i	$0.126021\pi$
$773$	19.2486	+	37.7774i	0.692323	+	1.35876i	−0.230324	+	0.973114i	$0.573979\pi$
$774$	16.1295	+	14.8239i	0.579762	+	0.532836i
$775$	−19.7167	+	7.11952i	−0.708245	+	0.255741i
$776$		−	7.02576i		−	0.252210i
$777$	3.23198	+	32.3370i	0.115947	+	1.16008i
$778$	2.35890	+	14.8935i	0.0845708	+	0.533959i
$779$	−44.9294	−	32.6431i	−1.60976	−	1.16956i
$780$	9.53410	−	1.10898i	0.341375	−	0.0397078i
$781$	−1.75995	+	1.27868i	−0.0629758	+	0.0457546i
$782$	19.6290	+	19.6290i	0.701932	+	0.701932i
$783$	31.0059	−	9.55212i	1.10806	−	0.341365i
$784$	−7.48565	+	2.43223i	−0.267345	+	0.0868655i
$785$	8.01946	−	6.02711i	0.286227	−	0.215117i
$786$	19.1004	−	23.3424i	0.681288	−	0.832596i
$787$	−25.7904	−	13.1408i	−0.919327	−	0.468420i	−0.0707509	−	0.997494i	$-0.522540\pi$
$787$	−25.7904	−	13.1408i	−0.919327	−	0.468420i	−0.848576	+	0.529074i	$0.822540\pi$
$788$	−20.2619	−	10.3240i	−0.721800	−	0.367776i
$789$	3.30206	−	4.03542i	0.117557	−	0.143665i
$790$	0.897041	−	2.92079i	0.0319153	−	0.103917i
$791$	6.45480	−	2.09729i	0.229506	−	0.0745711i
$792$	0.829593	−	0.657885i	0.0294783	−	0.0233769i
$793$	0.256173	+	0.256173i	0.00909695	+	0.00909695i
$794$	−11.1607	+	8.10876i	−0.396080	+	0.287769i
$795$	−3.35908	+	16.7114i	−0.119134	+	0.592691i
$796$	5.11191	+	3.71402i	0.181187	+	0.131640i
$797$	2.70297	+	17.0659i	0.0957441	+	0.604505i	0.988176	+	0.153323i	$0.0489974\pi$
$797$	2.70297	+	17.0659i	0.0957441	+	0.604505i	−0.892432	+	0.451182i	$0.851003\pi$
$798$	−4.35009	−	43.5240i	−0.153991	−	1.54073i
$799$		−	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
$804$	−11.0348	+	7.08630i	−0.389169	+	0.249915i
$805$	−60.7063	−	29.7041i	−2.13962	−	1.04693i
$806$	−6.10729	−	8.40597i	−0.215120	−	0.296088i
$807$	−9.03137	−	20.5666i	−0.317919	−	0.723980i
$808$	−9.46876	−	1.49970i	−0.333110	−	0.0527594i
$809$	14.1884	+	43.6674i	0.498837	+	1.53526i	0.810891	+	0.585198i	$0.198983\pi$
$809$	14.1884	+	43.6674i	0.498837	+	1.53526i	−0.312054	+	0.950064i	$0.601017\pi$
$810$	17.3857	+	10.1360i	0.610870	+	0.356143i
$811$	14.2314	−	43.7999i	0.499733	−	1.53802i	−0.309714	−	0.950830i	$-0.600233\pi$
$811$	14.2314	−	43.7999i	0.499733	−	1.53802i	0.809448	−	0.587192i	$-0.199767\pi$
$812$	10.9312	−	21.4536i	0.383609	−	0.752874i
$813$	22.0223	−	19.6264i	0.772355	−	0.688326i
$814$	−1.63314	−	0.530641i	−0.0572417	−	0.0185989i
$815$	−13.9027	+	19.8015i	−0.486992	+	0.693616i
$816$	−6.12445	−	0.352321i	−0.214398	−	0.0123337i
$817$	−7.48082	+	47.2320i	−0.261721	+	1.65244i
$818$	−4.20720	+	4.20720i	−0.147101	+	0.147101i
$819$	−3.28782	+	28.4818i	−0.114886	+	0.995234i
$820$	8.33437	−	17.0329i	0.291049	−	0.594816i
$821$	13.3733	−	18.4068i	0.466731	−	0.642400i	−0.509156	−	0.860674i	$-0.670043\pi$
$821$	13.3733	−	18.4068i	0.466731	−	0.642400i	0.975888	+	0.218274i	$0.0700425\pi$
$822$	30.3378	+	6.61051i	1.05815	+	0.230568i
$823$	−33.1249	+	16.8780i	−1.15466	+	0.588330i	−0.923127	−	0.384496i	$-0.874375\pi$
$823$	−33.1249	+	16.8780i	−1.15466	+	0.588330i	−0.231536	+	0.972826i	$0.574375\pi$
$824$	6.65293			0.231766
$825$	−2.21481	+	2.10632i	−0.0771099	+	0.0733327i
$826$	−8.89898			−0.309635
$827$	9.39702	−	4.78802i	0.326766	−	0.166496i	−0.282910	−	0.959147i	$-0.591300\pi$
$827$	9.39702	−	4.78802i	0.326766	−	0.166496i	0.609676	+	0.792651i	$0.291300\pi$
$828$	−19.5881	−	13.0068i	−0.680732	−	0.452018i
$829$	7.78028	−	10.7086i	0.270220	−	0.371926i	−0.652244	−	0.758009i	$-0.726172\pi$
$829$	7.78028	−	10.7086i	0.270220	−	0.371926i	0.922464	+	0.386083i	$0.126172\pi$
$830$	−2.25519	−	12.8857i	−0.0782789	−	0.447269i
$831$	−17.8023	+	4.67285i	−0.617553	+	0.162099i
$832$	1.75242	−	1.75242i	0.0607541	−	0.0607541i
$833$	4.36093	−	27.5338i	0.151097	−	0.953990i
$834$	1.79279	−	31.1644i	0.0620794	−	1.07914i
$835$	35.8974	+	11.0249i	1.24228	+	0.381533i
$836$	2.19813	+	0.714216i	0.0760239	+	0.0247017i
$837$	0.333542	−	21.7826i	0.0115289	−	0.752915i
$838$	−1.96185	+	3.85035i	−0.0677711	+	0.133008i
$839$	−0.944989	+	2.90838i	−0.0326247	+	0.100408i	−0.966043	−	0.258382i	$-0.916811\pi$
$839$	−0.944989	+	2.90838i	−0.0326247	+	0.100408i	0.933418	+	0.358790i	$0.116811\pi$
$840$	14.3827	−	4.02510i	0.496250	−	0.138879i
$841$	3.08568	+	9.49674i	0.106403	+	0.327474i
$842$	−24.7186	−	3.91504i	−0.851860	−	0.134921i
$843$	−44.4997	+	19.5410i	−1.53265	+	0.673029i
$844$	2.44299	+	3.36248i	0.0840910	+	0.115741i
$845$	7.18217	+	13.5493i	0.247074	+	0.466109i
$846$	2.53880	+	12.5739i	0.0872858	+	0.432299i
$847$	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
$852$	−10.6232	+	1.06175i	−0.363945	+	0.0363751i
$853$	5.89808	+	37.2390i	0.201946	+	1.27504i	0.855358	+	0.518037i	$0.173337\pi$
$853$	5.89808	+	37.2390i	0.201946	+	1.27504i	−0.653412	+	0.757003i	$0.726663\pi$
$854$	0.456059	+	0.331347i	0.0156060	+	0.0113384i
$855$	2.56114	+	43.8556i	0.0875892	+	1.49983i
$856$	−11.9374	+	8.67305i	−0.408013	+	0.296439i
$857$	−3.57064	−	3.57064i	−0.121971	−	0.121971i	0.643487	−	0.765457i	$-0.277487\pi$
$857$	−3.57064	−	3.57064i	−0.121971	−	0.121971i	−0.765457	+	0.643487i	$0.777487\pi$
$858$	−1.30811	−	0.764167i	−0.0446582	−	0.0260882i
$859$	33.5736	−	10.9087i	1.14552	−	0.372201i	0.326064	−	0.945348i	$-0.394278\pi$
$859$	33.5736	−	10.9087i	1.14552	−	0.372201i	0.819453	+	0.573147i	$0.194278\pi$
$860$	−16.3263	+	0.264194i	−0.556721	+	0.00900893i
$861$	43.8371	+	35.8706i	1.49396	+	1.22247i
$862$	6.23735	+	3.17809i	0.212445	+	0.108246i
$863$	−17.9383	−	9.14003i	−0.610628	−	0.311130i	0.121191	−	0.992629i	$-0.461328\pi$
$863$	−17.9383	−	9.14003i	−0.610628	−	0.311130i	−0.731819	+	0.681499i	$0.761328\pi$
$864$	5.14402	−	0.734186i	0.175003	−	0.0249775i
$865$	12.6343	+	36.8448i	0.429578	+	1.25276i
$866$	−9.38548	+	3.04953i	−0.318932	+	0.103627i
$867$	−3.89279	+	6.66374i	−0.132206	+	0.226312i
$868$	−11.4322	−	11.4322i	−0.388035	−	0.388035i
$869$	−0.390153	+	0.283463i	−0.0132350	+	0.00961581i
$870$	−11.8584	+	21.0751i	−0.402038	+	0.714513i
$871$	15.1807	+	11.0294i	0.514379	+	0.373718i
$872$	1.73896	+	10.9794i	0.0588887	+	0.371809i
$873$	−20.3024	−	5.66273i	−0.687131	−	0.191654i
$874$		−	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	−0.948834	−	0.315774i	$-0.897736\pi$
$877$	−19.1482	−	37.5805i	−0.646590	−	1.26900i	0.302244	−	0.953230i	$-0.402264\pi$
$878$	−0.576659	+	0.0913337i	−0.0194613	+	0.00308236i
$879$	31.9724	+	49.7877i	1.07840	+	1.67930i
$880$	−0.110826	+	0.781355i	−0.00373596	+	0.0263395i
$881$	−22.4775	−	30.9376i	−0.757285	−	1.04231i	−0.997435	−	0.0715779i	$-0.977197\pi$
$881$	−22.4775	−	30.9376i	−0.757285	−	1.04231i	0.240150	−	0.970736i	$-0.422803\pi$
$882$	0.995035	+	23.5917i	0.0335046	+	0.794372i
$883$	−13.8121	−	2.18763i	−0.464816	−	0.0736196i	−0.0803657	−	0.996765i	$-0.525609\pi$
$883$	−13.8121	−	2.18763i	−0.464816	−	0.0736196i	−0.384450	+	0.923146i	$0.625609\pi$
$884$	2.71243	+	8.34799i	0.0912288	+	0.280773i
$885$	8.92992	+	0.368862i	0.300176	+	0.0123992i
$886$	2.76645	−	8.51427i	0.0929408	−	0.286042i
$887$	9.40690	−	18.4621i	0.315853	−	0.619896i	−0.677433	−	0.735585i	$-0.736908\pi$
$887$	9.40690	−	18.4621i	0.315853	−	0.619896i	0.993285	+	0.115689i	$0.0369076\pi$
$888$	−5.60695	−	6.29142i	−0.188157	−	0.211126i
$889$	−19.7820	−	6.42756i	−0.663467	−	0.215574i
$890$	−0.0741394	−	4.58156i	−0.00248516	−	0.153574i
$891$	−1.23244	−	2.92753i	−0.0412884	−	0.0980759i
$892$	2.40429	−	15.1801i	0.0805017	−	0.508268i
$893$	−19.8002	+	19.8002i	−0.662587	+	0.662587i
$894$	−2.04433	−	7.78831i	−0.0683725	−	0.260480i
$895$	11.8057	+	11.4297i	0.394622	+	0.382053i
$896$	2.26666	−	3.11979i	0.0757239	−	0.104225i
$897$	−7.16277	+	32.8723i	−0.239158	+	1.09757i
$898$	−16.3751	+	8.34354i	−0.546445	+	0.278428i
$899$	26.1776			0.873071
$900$	−14.5995	+	3.44293i	−0.486651	+	0.114764i
$901$	−15.5880			−0.519312
$902$	−2.66676	+	1.35878i	−0.0887935	+	0.0452425i
$903$	10.3840	−	47.6557i	0.345558	−	1.58588i
$904$	−1.03449	+	1.42386i	−0.0344067	+	0.0473567i
$905$	−1.32632	+	0.703054i	−0.0440884	+	0.0233703i
$906$	6.44435	+	24.5512i	0.214099	+	0.815658i
$907$	8.19678	−	8.19678i	0.272170	−	0.272170i	−0.557803	−	0.829973i	$-0.688356\pi$
$907$	8.19678	−	8.19678i	0.272170	−	0.272170i	0.829973	+	0.557803i	$0.188356\pi$
$908$	2.19408	−	13.8529i	0.0728131	−	0.459724i
$909$	−11.9655	+	26.1531i	−0.396870	+	0.867445i
$910$	−12.8391	−	17.0832i	−0.425611	−	0.566303i
$911$	4.38290	+	1.42409i	0.145212	+	0.0471822i	0.380721	−	0.924690i	$-0.375676\pi$
$911$	4.38290	+	1.42409i	0.145212	+	0.0471822i	−0.235509	+	0.971872i	$0.575676\pi$
$912$	7.54667	+	8.46794i	0.249895	+	0.280402i
$913$	−0.937368	+	1.83969i	−0.0310224	+	0.0608848i
$914$	−10.8344	+	33.3449i	−0.358371	+	1.10295i
$915$	−0.443911	−	0.351402i	−0.0146752	−	0.0116170i
$916$	−5.35607	−	16.4843i	−0.176970	−	0.544656i
$917$	−66.3247	−	10.5048i	−2.19023	−	0.346899i
$918$	−5.95437	+	17.4138i	−0.196524	+	0.574743i
$919$	1.33595	+	1.83878i	0.0440689	+	0.0606557i	0.830483	−	0.557044i	$-0.188065\pi$
$919$	1.33595	+	1.83878i	0.0440689	+	0.0606557i	−0.786414	+	0.617700i	$0.788065\pi$
$920$	17.2633	−	3.02134i	0.569154	−	0.0996106i
$921$	17.0703	+	26.5820i	0.562485	+	0.875906i
$922$	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
$927$	5.36223	−	19.2250i	0.176119	−	0.631431i
$928$	0.976751	+	6.16696i	0.0320634	+	0.202440i
$929$	−12.0105	−	8.72617i	−0.394053	−	0.286296i	0.373061	−	0.927807i	$-0.378308\pi$
$929$	−12.0105	−	8.72617i	−0.394053	−	0.286296i	−0.767114	+	0.641510i	$0.778308\pi$
$930$	10.9981	+	11.9458i	0.360642	+	0.391720i
$931$	−41.7003	+	30.2970i	−1.36667	+	0.992945i
$932$	1.73973	+	1.73973i	0.0569868	+	0.0569868i
$933$	−14.1703	+	24.2570i	−0.463916	+	0.794138i
$934$	−4.63623	+	1.50640i	−0.151702	+	0.0492910i
$935$	−2.28757	−	1.60612i	−0.0748116	−	0.0525256i
$936$	−3.65152	−	6.47640i	−0.119354	−	0.211688i
$937$	13.2746	+	6.76373i	0.433661	+	0.220961i	0.657173	−	0.753740i	$-0.271752\pi$
$937$	13.2746	+	6.76373i	0.433661	+	0.220961i	−0.223512	+	0.974701i	$0.571752\pi$
$938$	26.0155	+	13.2555i	0.849435	+	0.432809i
$939$	−7.23984	−	5.92414i	−0.236263	−	0.193327i
$940$	−7.82505	−	5.49401i	−0.255225	−	0.179195i
$941$	−29.4117	+	9.55645i	−0.958795	+	0.311531i	−0.746284	−	0.665627i	$-0.768164\pi$
$941$	−29.4117	+	9.55645i	−0.958795	+	0.311531i	−0.212511	+	0.977159i	$0.568164\pi$
$942$	−6.70965	−	3.91961i	−0.218612	−	0.127708i
$943$	46.9991	+	46.9991i	1.53050	+	1.53050i
$944$	1.86694	−	1.35641i	0.0607636	−	0.0441474i
$945$	−0.0389623	−	44.8059i	−0.00126744	−	1.45754i
$946$	2.08499	+	1.51484i	0.0677890	+	0.0492516i
$947$	−1.42242	−	8.98080i	−0.0462224	−	0.291837i	0.953739	−	0.300636i	$-0.0971990\pi$
$947$	−1.42242	−	8.98080i	−0.0462224	−	0.291837i	−0.999961	+	0.00879948i	$0.997199\pi$
$948$	−2.35500	+	0.235375i	−0.0764868	+	0.00764461i
$949$		−	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	$-0.449650\pi$
$953$	18.9081	−	2.99474i	0.612493	−	0.0970093i	0.454971	+	0.890506i	$0.349650\pi$
$954$	12.9423	−	2.61319i	0.419023	−	0.0846052i
$955$	31.0355	−	5.43168i	1.00429	−	0.175765i
$956$	−1.43017	−	1.96845i	−0.0462549	−	0.0636644i
$957$	3.49471	−	1.53462i	0.112968	−	0.0496073i
$958$	−14.0773	−	2.22963i	−0.454818	−	0.0720361i
$959$	−21.3623	−	65.7463i	−0.689823	−	2.12306i
$960$	−2.40386	+	3.03669i	−0.0775842	+	0.0980086i
$961$	−4.14780	+	12.7656i	−0.133800	+	0.411794i
$962$	−5.47429	+	10.7439i	−0.176498	+	0.346397i
$963$	15.4410	+	41.4861i	0.497580	+	1.33687i
$964$	1.53948	+	0.500207i	0.0495833	+	0.0161106i
$965$	−5.49714	−	7.31429i	−0.176959	−	0.235455i
$966$	−3.00658	+	52.2639i	−0.0967351	+	1.68156i
$967$	−6.88343	+	43.4603i	−0.221356	+	1.39759i	0.587330	+	0.809347i	$0.300179\pi$
$967$	−6.88343	+	43.4603i	−0.221356	+	1.39759i	−0.808686	+	0.588240i	$0.799821\pi$
$968$	−7.69010	+	7.69010i	−0.247169	+	0.247169i
$969$	−38.8574	+	10.1995i	−1.24828	+	0.327657i
$970$	13.8806	−	7.35778i	0.445678	−	0.236244i
$971$	18.1657	−	25.0030i	0.582965	−	0.802383i	−0.411051	−	0.911612i	$-0.634838\pi$
$971$	18.1657	−	25.0030i	0.582965	−	0.802383i	0.994017	+	0.109229i	$0.0348383\pi$
$972$	2.02448	−	15.4564i	0.0649352	−	0.495765i
$973$	−61.9249	+	31.5523i	−1.98522	+	1.01152i
$974$	−34.8793			−1.11761
$975$	12.1756	+	17.6748i	0.389932	+	0.566046i
$976$	−0.146183			−0.00467919
$977$	−42.2813	+	21.5434i	−1.35270	+	0.689235i	−0.971894	−	0.235420i	$-0.924354\pi$
$977$	−42.2813	+	21.5434i	−1.35270	+	0.689235i	−0.380806	+	0.924655i	$0.624354\pi$
$978$	18.3115	+	3.99001i	0.585537	+	0.127587i
$979$	−0.425102	+	0.585102i	−0.0135863	+	0.0186999i
$980$	−12.6447	−	12.2420i	−0.403919	−	0.391055i
$981$	33.1287	+	3.82424i	1.05772	+	0.122099i
$982$	−3.78562	+	3.78562i	−0.120804	+	0.120804i
$983$	−5.45227	+	34.4243i	−0.173900	+	1.09796i	0.734114	+	0.679026i	$0.237598\pi$
$983$	−5.45227	+	34.4243i	−0.173900	+	1.09796i	−0.908015	+	0.418938i	$0.862402\pi$
$984$	−14.6642	−	0.843585i	−0.467477	−	0.0268925i
$985$	−0.822742	−	50.8426i	−0.0262147	−	1.61998i
$986$	−21.0320	−	6.83372i	−0.669796	−	0.217630i
$987$	21.3213	−	19.0016i	0.678664	−	0.604828i
$988$	7.36813	−	14.4608i	0.234411	−	0.460058i
$989$	17.6860	−	54.4321i	0.562384	−	1.73084i
$990$	2.16856	+	0.950024i	0.0689213	+	0.0301937i
$991$	1.45449	+	4.47645i	0.0462033	+	0.142199i	0.971497	−	0.237053i	$-0.0761814\pi$
$991$	1.45449	+	4.47645i	0.0462033	+	0.142199i	−0.925293	+	0.379252i	$0.876181\pi$
$992$	4.14093	+	0.655859i	0.131475	+	0.0208235i
$993$	−19.7894	−	45.0654i	−0.627999	−	1.43011i
$994$	13.9714	+	19.2300i	0.443146	+	0.609938i
$995$	−1.98418	+	13.9890i	−0.0629027	+	0.443480i
$996$	−8.52625	+	5.47535i	−0.270165	+	0.173493i
$997$	−20.4803	+	3.24377i	−0.648619	+	0.102731i	−0.472070	−	0.881561i	$-0.656493\pi$
$997$	−20.4803	+	3.24377i	−0.648619	+	0.102731i	−0.176548	+	0.984292i	$0.556493\pi$
$998$	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.53.8	yes	80
3.2	odd	2	inner	150.2.l.a.53.2	yes	80
5.2	odd	4		750.2.l.c.257.6		80
5.3	odd	4		750.2.l.a.257.5		80
5.4	even	2		750.2.l.b.743.3		80
15.2	even	4		750.2.l.c.257.1		80
15.8	even	4		750.2.l.a.257.10		80
15.14	odd	2		750.2.l.b.743.9		80
25.6	even	5		750.2.l.c.143.1		80
25.8	odd	20		750.2.l.b.107.9		80
25.17	odd	20	inner	150.2.l.a.17.2	✓	80
25.19	even	10		750.2.l.a.143.10		80
75.8	even	20		750.2.l.b.107.3		80
75.17	even	20	inner	150.2.l.a.17.8	yes	80
75.44	odd	10		750.2.l.a.143.5		80
75.56	odd	10		750.2.l.c.143.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.2.l.a.17.2	✓	80	25.17	odd	20	inner
150.2.l.a.17.8	yes	80	75.17	even	20	inner
150.2.l.a.53.2	yes	80	3.2	odd	2	inner
150.2.l.a.53.8	yes	80	1.1	even	1	trivial
750.2.l.a.143.5		80	75.44	odd	10
750.2.l.a.143.10		80	25.19	even	10
750.2.l.a.257.5		80	5.3	odd	4
750.2.l.a.257.10		80	15.8	even	4
750.2.l.b.107.3		80	75.8	even	20
750.2.l.b.107.9		80	25.8	odd	20
750.2.l.b.743.3		80	5.4	even	2
750.2.l.b.743.9		80	15.14	odd	2
750.2.l.c.143.1		80	25.6	even	5
750.2.l.c.143.6		80	75.56	odd	10
750.2.l.c.257.1		80	15.2	even	4
750.2.l.c.257.6		80	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+(0.891007 - 0.453990i) q^{2} +(0.368756 - 1.69234i) q^{3} +(0.587785 - 0.809017i) q^{4} +(2.21391 + 0.314018i) q^{5} +(-0.439743 - 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.72804 - 1.24812i) q^{9} +O(q^{10})\)	\(q+(0.891007 - 0.453990i) q^{2} +(0.368756 - 1.69234i) q^{3} +(0.587785 - 0.809017i) q^{4} +(2.21391 + 0.314018i) q^{5} +(-0.439743 - 1.67530i) q^{6} +(-2.72680 + 2.72680i) q^{7} +(0.156434 - 0.987688i) q^{8} +(-2.72804 - 1.24812i) q^{9} +(2.11517 - 0.725301i) q^{10} +(-0.335657 - 0.109061i) q^{11} +(-1.15238 - 1.29306i) q^{12} +(-1.12512 + 2.20817i) q^{13} +(-1.19166 + 3.66754i) q^{14} +(1.34782 - 3.63089i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(3.49819 + 0.554059i) q^{17} +(-2.99734 + 0.126420i) q^{18} +(-3.84926 - 5.29805i) q^{19} +(1.55535 - 1.60651i) q^{20} +(3.60915 + 5.62020i) 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} +(-3.11823 + 4.15652i) q^{27} +(0.603255 + 3.80880i) q^{28} +(-5.05137 - 3.67003i) q^{29} +(-0.447477 - 3.84705i) q^{30} +(-3.39184 + 2.46432i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.308344 + 0.527829i) q^{33} +(3.36845 - 1.09448i) q^{34} +(-6.89315 + 5.18062i) q^{35} +(-2.61325 + 1.47340i) q^{36} +(4.33521 + 2.20890i) q^{37} +(-5.83498 - 2.97307i) q^{38} +(3.32209 + 2.71836i) q^{39} +(0.656484 - 2.13753i) q^{40} +(8.06531 - 2.62058i) q^{41} +(5.76730 + 3.36911i) q^{42} +(-5.16349 - 5.16349i) q^{43} +(-0.285527 + 0.207447i) q^{44} +(-5.64770 - 3.61988i) q^{45} +(6.34085 + 4.60690i) q^{46} +(-0.668895 - 4.22323i) q^{47} +(-1.72346 + 0.172255i) 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} +(-0.891339 + 5.11913i) q^{54} +(-0.708866 - 0.346854i) q^{55} +(2.26666 + 3.11979i) q^{56} +(-10.3855 + 4.56057i) q^{57} +(-6.16696 - 0.976751i) q^{58} +(0.713107 + 2.19472i) q^{59} +(-2.14523 - 3.22459i) q^{60} +(0.0451729 - 0.139028i) q^{61} +(-1.90338 + 3.73559i) q^{62} +(10.8422 - 4.03544i) q^{63} +(-0.951057 - 0.309017i) q^{64} +(-3.18432 + 4.53538i) q^{65} +(-0.0351078 + 0.610284i) q^{66} +(1.18445 - 7.47829i) q^{67} +(2.50443 - 2.50443i) q^{68} +(13.1305 - 3.44659i) q^{69} +(-3.78989 + 7.74539i) q^{70} +(3.62303 - 4.98667i) q^{71} +(-1.65951 + 2.49920i) q^{72} +(-9.30362 + 4.74043i) q^{73} +4.86552 q^{74} +(4.12411 - 7.61523i) q^{75} -6.54875 q^{76} +(1.21266 - 0.617880i) q^{77} +(4.19411 + 0.913883i) q^{78} +(0.803169 - 1.10547i) q^{79} +(-0.385487 - 2.20259i) q^{80} +(5.88439 + 6.80984i) q^{81} +(5.99652 - 5.99652i) q^{82} +(0.915181 - 5.77823i) q^{83} +(6.66824 + 0.383604i) q^{84} +(7.57069 + 2.32513i) q^{85} +(-6.94488 - 2.25653i) q^{86} +(-8.07367 + 7.19529i) q^{87} +(-0.160227 + 0.314463i) q^{88} +(0.633239 - 1.94891i) q^{89} +(-6.67553 - 0.661335i) q^{90} +(-2.95327 - 9.08922i) q^{91} +(7.74123 + 1.22609i) q^{92} +(2.91971 + 6.64888i) q^{93} +(-2.51330 - 3.45926i) q^{94} +(-6.85822 - 12.9381i) q^{95} +(-1.45742 + 0.935916i) 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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