LMFDB - Embedded newform 150.2.l.a.17.8

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			17.8
Character	$\chi$	$=$	150.17
Dual form			150.2.l.a.53.8

$q$-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 $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

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

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
$3$	0.368756	+	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	−0.999516	−	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
$9$	−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	−0.359181	−	0.933268i	$-0.616944\pi$
$11$	−0.335657	+	0.109061i	−0.101204	+	0.0328833i	0.257977	+	0.966151i	$0.416944\pi$
$12$	−1.15238	+	1.29306i	−0.332665	+	0.373275i
$13$	−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
$15$	1.34782	+	3.63089i	0.348005	+	0.937493i
$16$	−0.309017	+	0.951057i	−0.0772542	+	0.237764i
$17$	3.49819	−	0.554059i	0.848436	−	0.134379i	0.282948	−	0.959135i	$-0.408688\pi$
$17$	3.49819	−	0.554059i	0.848436	−	0.134379i	0.565488	+	0.824756i	$0.308688\pi$
$18$	−2.99734	−	0.126420i	−0.706479	−	0.0297975i
$19$	−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
$21$	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	−0.142638	−	0.989775i	$-0.545559\pi$
$23$	3.55825	−	6.98347i	0.741947	−	1.45615i	0.884585	−	0.466378i	$-0.154441\pi$
$24$	−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	−0.947942	−	0.318443i	$-0.896840\pi$
$29$	−5.05137	+	3.67003i	−0.938015	+	0.681508i	0.00992666	+	0.999951i	$0.496840\pi$
$30$	−0.447477	+	3.84705i	−0.0816978	+	0.702371i
$31$	−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
$33$	−0.308344	−	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	−0.0597483	−	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
$39$	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	0.861348	−	0.508015i	$-0.169621\pi$
$41$	8.06531	+	2.62058i	1.25959	+	0.409265i	0.398241	+	0.917281i	$0.369621\pi$
$42$	5.76730	−	3.36911i	0.889913	−	0.519865i
$43$	−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
$45$	−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	0.889649	+	0.456644i	$0.150949\pi$
$47$	−0.668895	+	4.22323i	−0.0975683	+	0.616022i	−0.987218	+	0.159378i	$0.949051\pi$
$48$	−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	−0.149435	−	0.988772i	$-0.547745\pi$
$53$	−4.34698	−	0.688494i	−0.597103	−	0.0945719i	−0.447668	+	0.894200i	$0.647745\pi$
$54$	−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	−0.893846	−	0.448375i	$-0.852003\pi$
$59$	0.713107	−	2.19472i	0.0928386	−	0.285728i	0.986684	+	0.162647i	$0.0520031\pi$
$60$	−2.14523	+	3.22459i	−0.276948	+	0.416293i
$61$	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
$63$	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	0.948053	+	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
$69$	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	0.967947	−	0.251153i	$-0.0808098\pi$
$71$	3.62303	+	4.98667i	0.429974	+	0.591809i	−0.537973	+	0.842962i	$0.680810\pi$
$72$	−1.65951	−	2.49920i	−0.195576	−	0.294534i
$73$	−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
$75$	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	0.851805	−	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
$81$	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	0.985621	+	0.168969i	$0.0540439\pi$
$83$	0.915181	+	5.77823i	0.100454	+	0.634243i	−0.885167	+	0.465273i	$0.845956\pi$
$84$	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	0.978992	−	0.203897i	$-0.0653608\pi$
$89$	0.633239	+	1.94891i	0.0671232	+	0.206584i	−0.911869	+	0.410481i	$0.865361\pi$
$90$	−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	0.498433	−	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	$0.158262\pi$
$101$			9.58679i			0.953921i	−0.878925	+	0.476961i	$0.841738\pi$
$102$	−0.610091	+	6.10416i	−0.0604081	+	0.604402i
$103$	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
$105$	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	−0.00870186	+	0.999962i	$0.502770\pi$
$107$	−10.4337	+	10.4337i	−1.00866	+	1.00866i	−0.999962	+	0.00870186i	$0.997230\pi$
$108$	1.52985	−	4.96584i	0.147210	−	0.477838i
$109$	−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
$111$	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	−0.526192	−	0.850366i	$-0.676381\pi$
$113$	−1.56816	+	0.799015i	−0.147520	+	0.0751650i	0.378672	+	0.925531i	$0.376381\pi$
$114$	−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	−0.756471	−	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
$129$	−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	−0.0779865	−	0.996954i	$-0.524849\pi$
$131$	10.2354	−	14.0878i	0.894273	−	1.23086i	0.972259	−	0.233906i	$-0.0751509\pi$
$132$	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	−0.920663	−	0.390358i	$-0.872351\pi$
$137$	−8.13848	−	15.9727i	−0.695317	−	1.36464i	0.225346	−	0.974279i	$-0.427649\pi$
$138$	10.1347	+	9.03207i	0.862721	+	0.768861i
$139$	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
$141$	−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	0.822273	−	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
$159$	−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	0.614675	−	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
$165$	−0.848394	−	1.07174i	−0.0660474	−	0.0834347i
$166$	−1.80783	+	5.56392i	−0.140315	+	0.431844i
$167$	16.5871	−	2.62714i	1.28355	−	0.203295i	0.522866	−	0.852415i	$-0.324863\pi$
$167$	16.5871	−	2.62714i	1.28355	−	0.203295i	0.760686	+	0.649120i	$0.224863\pi$
$168$	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	−0.367043	−	0.930204i	$-0.619630\pi$
$173$	7.90821	−	15.5207i	0.601250	−	1.18002i	0.968293	−	0.249816i	$-0.0803702\pi$
$174$	−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	−0.343002	−	0.939334i	$-0.611444\pi$
$179$	5.94519	−	4.31943i	0.444364	−	0.322849i	0.787367	+	0.616485i	$0.211444\pi$
$180$	−6.24818	−	2.44137i	−0.465712	−	0.181969i
$181$	−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
$183$	−0.218625	+	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	0.750675	−	0.660672i	$-0.229729\pi$
$191$	13.4008	+	4.35419i	0.969650	+	0.315058i	0.218975	+	0.975730i	$0.429729\pi$
$192$	−0.873670	−	1.49556i	−0.0630517	−	0.107933i
$193$	−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
$195$	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	0.452353	+	0.891839i	$0.350585\pi$
$197$	−3.55739	+	22.4605i	−0.253454	+	1.60024i	−0.705806	+	0.708405i	$0.749415\pi$
$198$	1.01986	−	0.284460i	0.0724785	−	0.0202157i
$199$		−	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
$204$	−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	0.897064	−	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
$213$	−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	0.847779	−	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
$225$	−11.3668	+	9.78756i	−0.757785	+	0.652504i
$226$	−1.75998			−0.117072
$227$	12.4969	+	6.36747i	0.829445	+	0.422624i	0.816537	−	0.577293i	$-0.195891\pi$
$227$	12.4969	+	6.36747i	0.829445	+	0.422624i	0.0129084	+	0.999917i	$0.495891\pi$
$228$	−2.41489	−	11.0827i	−0.159930	−	0.733971i
$229$	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
$231$	−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	0.971868	−	0.235525i	$-0.0756809\pi$
$233$	−0.384884	−	2.43006i	−0.0252146	−	0.159199i	−0.997083	+	0.0763263i	$0.975681\pi$
$234$	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	0.972425	−	0.233217i	$-0.0749252\pi$
$239$	0.751883	+	2.31406i	0.0486352	+	0.149684i	−0.923790	+	0.382901i	$0.874925\pi$
$240$	−3.86968	+	0.159842i	−0.249787	+	0.0103178i
$241$	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
$243$	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	$-0.715038\pi$
$251$		−	24.7263i		−	1.56071i	0.625335	−	0.780357i	$-0.284962\pi$
$252$	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	0.313326	−	0.949646i	$-0.398557\pi$
$257$	20.2470	−	20.2470i	1.26297	−	1.26297i	0.949646	−	0.313326i	$-0.101443\pi$
$258$	−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	−0.369331	−	0.929298i	$-0.620413\pi$
$263$	2.68232	−	1.36671i	0.165399	−	0.0842750i	0.534730	+	0.845023i	$0.320413\pi$
$264$	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	0.859746	−	0.510722i	$-0.170622\pi$
$269$	10.4918	+	7.62274i	0.639697	+	0.464767i	−0.220049	+	0.975489i	$0.570622\pi$
$270$	−3.58084	−	11.0534i	−0.217923	−	0.672688i
$271$	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
$273$	−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	−0.989315	−	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
$279$	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	−0.0492011	+	0.998789i	$0.515668\pi$
$281$	−16.4932	+	22.7009i	−0.983902	+	1.35422i	−0.934701	+	0.355436i	$0.884332\pi$
$282$	−6.78104	−	2.97774i	−0.403805	−	0.177322i
$283$	−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
$285$	−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	−0.751709	−	0.659495i	$-0.770770\pi$
$293$	−24.1559	−	24.1559i	−1.41120	−	1.41120i	−0.659495	−	0.751709i	$-0.729230\pi$
$294$	−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	0.235744	−	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
$309$	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	−0.711755	−	0.702428i	$-0.752099\pi$
$311$	−15.4255	+	5.01205i	−0.874699	+	0.284207i	−0.162945	+	0.986635i	$0.552099\pi$
$312$	3.20458	+	2.85594i	0.181424	+	0.161686i
$313$	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
$315$	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	0.0861233	−	0.996284i	$-0.472552\pi$
$317$	8.47316	−	1.34202i	0.475900	−	0.0753752i	0.389777	+	0.920909i	$0.372552\pi$
$318$	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	0.998929	−	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
$333$	−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	−0.565358	−	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
$339$	−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	−0.930784	−	0.365570i	$-0.880874\pi$
$347$	1.25574	−	7.92843i	0.0674116	−	0.425620i	0.998195	−	0.0600500i	$-0.0191260\pi$
$348$	1.07553	−	10.7610i	0.0576545	−	0.576851i
$349$			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	0.0310149	−	0.999519i	$-0.490126\pi$
$353$	−4.66620	−	0.739053i	−0.248357	−	0.0393358i	−0.279371	+	0.960183i	$0.590126\pi$
$354$	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	−0.748571	−	0.663054i	$-0.769260\pi$
$359$	4.67561	−	14.3900i	0.246769	−	0.759478i	0.995340	−	0.0964232i	$-0.0307402\pi$
$360$	−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	−0.439193	−	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
$369$	−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	0.402107	−	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
$375$	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	0.902297	−	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
$381$	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	0.978771	+	0.204957i	$0.0657053\pi$
$383$	2.17700	+	13.7450i	0.111240	+	0.702339i	−0.867532	+	0.497382i	$0.834295\pi$
$384$	−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	−0.996952	−	0.0780155i	$-0.975142\pi$
$389$	−4.65972	−	14.3411i	−0.236257	−	0.727125i	0.760695	−	0.649110i	$-0.224858\pi$
$390$	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	−0.195163	−	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	$0.129254\pi$
$401$			15.8196i			0.789991i	−0.918683	+	0.394995i	$0.870746\pi$
$402$	−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	0.165754	−	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
$411$	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	0.499105	−	0.866542i	$-0.333662\pi$
$419$	−3.49605	−	2.54003i	−0.170793	−	0.124088i	−0.669898	+	0.742453i	$0.733662\pi$
$420$	14.6424	−	2.94321i	0.714477	−	0.143614i
$421$	−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
$423$	−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	−0.698337	−	0.715769i	$-0.746076\pi$
$431$	4.11469	−	5.66339i	0.198198	−	0.272796i	0.896535	+	0.442973i	$0.146076\pi$
$432$	4.91667	−	1.68117i	0.236553	−	0.0808855i
$433$	−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
$435$	−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	−0.322238	−	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
$441$	−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	0.841312	−	0.540549i	$-0.181784\pi$
$443$	6.33032	+	6.33032i	0.300763	+	0.300763i	−0.540549	+	0.841312i	$0.681784\pi$
$444$	−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	−0.984537	−	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
$459$	−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	−0.305895	−	0.952065i	$-0.598956\pi$
$461$	0.133994	−	0.0435374i	0.00624074	−	0.00202774i	0.312136	+	0.950038i	$0.398956\pi$
$462$	−1.56839	+	1.75985i	−0.0729681	+	0.0818758i
$463$	−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
$465$	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	−0.266838	−	0.963742i	$-0.585979\pi$
$467$	−4.81480	+	0.762590i	−0.222803	+	0.0352885i	0.0440349	+	0.999030i	$0.485979\pi$
$468$	−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	−0.819180	−	0.573537i	$-0.805571\pi$
$479$	−11.5308	+	8.37759i	−0.526854	+	0.382782i	0.292326	+	0.956319i	$0.405571\pi$
$480$	−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	−0.982321	−	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
$489$	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	0.191862	−	0.981422i	$-0.438547\pi$
$491$	−5.09165	−	1.65438i	−0.229783	−	0.0746610i	−0.421645	+	0.906761i	$0.638547\pi$
$492$	−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	$-0.935891\pi$
$499$		−	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	0.220400	−	0.975410i	$-0.429264\pi$
$503$	2.88408	+	0.456793i	0.128595	+	0.0203674i	−0.0918053	+	0.995777i	$0.529264\pi$
$504$	−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	−0.996853	−	0.0792745i	$-0.974740\pi$
$509$	−3.24395	+	9.98385i	−0.143786	+	0.442527i	0.853067	+	0.521801i	$0.174740\pi$
$510$	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	0.980085	−	0.198578i	$-0.0636322\pi$
$521$	11.1471	+	15.3427i	0.488364	+	0.672175i	−0.491722	+	0.870753i	$0.663632\pi$
$522$	15.6046	−	10.3617i	0.682995	−	0.453520i
$523$	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
$525$	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	−0.552144	−	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
$543$	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	0.427627	−	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
$552$	−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	−0.0444707	+	0.999011i	$0.514160\pi$
$557$	−24.6270	+	24.6270i	−1.04348	+	1.04348i	−0.999011	+	0.0444707i	$0.985840\pi$
$558$	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	−0.627931	−	0.778269i	$-0.716098\pi$
$563$	−8.71723	+	4.44165i	−0.367388	+	0.187193i	0.260544	+	0.965462i	$0.416098\pi$
$564$	−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	0.754324	−	0.656502i	$-0.227965\pi$
$569$	8.66014	+	6.29196i	0.363052	+	0.263773i	−0.391272	+	0.920275i	$0.627965\pi$
$570$	−18.6594	−	17.1790i	−0.781555	−	0.719550i
$571$	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
$573$	−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	−0.987855	−	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
$579$	−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	0.996423	+	0.0845070i	$0.0269315\pi$
$587$	11.6079	+	22.7817i	0.479108	+	0.940302i	−0.517315	+	0.855795i	$0.673068\pi$
$588$	−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	0.586028	−	0.810291i	$-0.300691\pi$
$593$	−5.46116	−	5.46116i	−0.224263	−	0.224263i	−0.810291	+	0.586028i	$0.800691\pi$
$594$	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	0.810631	−	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
$609$	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	0.843842	−	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
$615$	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	−0.904058	−	0.427410i	$-0.859426\pi$
$617$	−40.5328	+	6.41977i	−1.63179	+	0.258450i	−0.727733	+	0.685861i	$0.759426\pi$
$618$	10.5508	+	4.63313i	0.424414	+	0.186372i
$619$	−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
$621$	−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	−0.181959	−	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
$633$	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	0.807071	−	0.590454i	$-0.201051\pi$
$641$	28.1775	+	9.15543i	1.11294	+	0.361618i	0.305874	+	0.952072i	$0.401051\pi$
$642$	−12.8914	−	22.0677i	−0.508784	−	0.870943i
$643$	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
$645$	−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	−0.981559	−	0.191161i	$-0.938775\pi$
$647$	0.280589	−	1.77157i	0.0110311	−	0.0696477i	0.992590	+	0.121513i	$0.0387747\pi$
$648$	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	0.648404	−	0.761296i	$-0.275437\pi$
$653$	26.3159	+	4.16803i	1.02982	+	0.163107i	0.381416	+	0.924404i	$0.375437\pi$
$654$	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	−0.982670	−	0.185363i	$-0.940654\pi$
$659$	−2.02081	+	6.21940i	−0.0787195	+	0.242274i	0.903951	+	0.427637i	$0.140654\pi$
$660$	0.368381	−	1.31632i	0.0143392	−	0.0512376i
$661$	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
$663$	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	0.996170	−	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
$675$	−20.7555	−	15.6273i	−0.798878	−	0.601493i
$676$	6.85808			0.263772
$677$	−33.3683	−	17.0020i	−1.28245	−	0.653440i	−0.326008	−	0.945367i	$-0.605704\pi$
$677$	−33.3683	−	17.0020i	−1.28245	−	0.653440i	−0.956441	+	0.291927i	$0.905704\pi$
$678$	−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	0.850263	+	0.526358i	$0.176443\pi$
$683$	5.33840	+	33.7054i	0.204268	+	1.28970i	−0.645995	+	0.763342i	$0.723557\pi$
$684$	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	0.574867	+	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
$693$	−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	$-0.716830\pi$
$701$		−	41.1349i		−	1.55364i	0.629720	−	0.776822i	$-0.283170\pi$
$702$	−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	−0.999731	−	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
$711$	−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	0.983453	−	0.181164i	$-0.0579866\pi$
$719$	29.8994	+	21.7232i	1.11506	+	0.810138i	0.131606	+	0.991302i	$0.457987\pi$
$720$	−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	−0.676328	−	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
$729$	−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	0.513625	−	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
$735$	−28.5783	+	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	−0.258877	−	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
$741$	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	0.966314	−	0.257367i	$-0.0828549\pi$
$743$	19.3245	+	19.3245i	0.708947	+	0.708947i	−0.257367	+	0.966314i	$0.582855\pi$
$744$	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	0.474450	−	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
$759$	−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	−0.540742	−	0.841188i	$-0.681857\pi$
$761$	−13.3455	+	4.33621i	−0.483774	+	0.157188i	0.0569686	+	0.998376i	$0.481857\pi$
$762$	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	−0.507275	−	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
$771$	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	−0.230324	−	0.973114i	$-0.573979\pi$
$773$	19.2486	−	37.7774i	0.692323	−	1.35876i	0.922647	−	0.385646i	$-0.126021\pi$
$774$	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	−0.848576	−	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
$789$	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	−0.892432	−	0.451182i	$-0.851003\pi$
$797$	2.70297	−	17.0659i	0.0957441	−	0.604505i	0.988176	−	0.153323i	$-0.0489974\pi$
$798$	−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	−0.312054	−	0.950064i	$-0.601017\pi$
$809$	14.1884	−	43.6674i	0.498837	−	1.53526i	0.810891	−	0.585198i	$-0.198983\pi$
$810$	17.3857	−	10.1360i	0.610870	−	0.356143i
$811$	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
$813$	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	0.975888	−	0.218274i	$-0.0700425\pi$
$821$	13.3733	+	18.4068i	0.466731	+	0.642400i	−0.509156	+	0.860674i	$0.670043\pi$
$822$	30.3378	−	6.61051i	1.05815	−	0.230568i
$823$	−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
$825$	−2.21481	−	2.10632i	−0.0771099	−	0.0733327i
$826$	−8.89898			−0.309635
$827$	9.39702	+	4.78802i	0.326766	+	0.166496i	0.609676	−	0.792651i	$-0.291300\pi$
$827$	9.39702	+	4.78802i	0.326766	+	0.166496i	−0.282910	+	0.959147i	$0.591300\pi$
$828$	−19.5881	+	13.0068i	−0.680732	+	0.452018i
$829$	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
$831$	−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	0.933418	−	0.358790i	$-0.116811\pi$
$839$	−0.944989	−	2.90838i	−0.0326247	−	0.100408i	−0.966043	+	0.258382i	$0.916811\pi$
$840$	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	−0.653412	−	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
$855$	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	−0.765457	−	0.643487i	$-0.777487\pi$
$857$	−3.57064	+	3.57064i	−0.121971	+	0.121971i	0.643487	+	0.765457i	$0.277487\pi$
$858$	−1.30811	+	0.764167i	−0.0446582	+	0.0260882i
$859$	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
$861$	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	−0.731819	−	0.681499i	$-0.761328\pi$
$863$	−17.9383	+	9.14003i	−0.610628	+	0.311130i	0.121191	+	0.992629i	$0.461328\pi$
$864$	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	0.302244	+	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
$879$	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	0.240150	+	0.970736i	$0.422803\pi$
$881$	−22.4775	+	30.9376i	−0.757285	+	1.04231i	−0.997435	+	0.0715779i	$0.977197\pi$
$882$	0.995035	−	23.5917i	0.0335046	−	0.794372i
$883$	−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
$885$	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	0.993285	−	0.115689i	$-0.0369076\pi$
$887$	9.40690	+	18.4621i	0.315853	+	0.619896i	−0.677433	+	0.735585i	$0.736908\pi$
$888$	−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	0.829973	−	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
$909$	−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	−0.235509	−	0.971872i	$-0.575676\pi$
$911$	4.38290	−	1.42409i	0.145212	−	0.0471822i	0.380721	+	0.924690i	$0.375676\pi$
$912$	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	−0.786414	−	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
$921$	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	−0.767114	−	0.641510i	$-0.778308\pi$
$929$	−12.0105	+	8.72617i	−0.394053	+	0.286296i	0.373061	+	0.927807i	$0.378308\pi$
$930$	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	−0.223512	−	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
$939$	−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	−0.212511	−	0.977159i	$-0.568164\pi$
$941$	−29.4117	−	9.55645i	−0.958795	−	0.311531i	−0.746284	+	0.665627i	$0.768164\pi$
$942$	−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	−0.999961	−	0.00879948i	$-0.997199\pi$
$947$	−1.42242	+	8.98080i	−0.0462224	+	0.291837i	0.953739	+	0.300636i	$0.0971990\pi$
$948$	−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	0.454971	−	0.890506i	$-0.349650\pi$
$953$	18.9081	+	2.99474i	0.612493	+	0.0970093i	0.157522	+	0.987516i	$0.449650\pi$
$954$	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	−0.808686	−	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
$969$	−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	0.994017	−	0.109229i	$-0.0348383\pi$
$971$	18.1657	+	25.0030i	0.582965	+	0.802383i	−0.411051	+	0.911612i	$0.634838\pi$
$972$	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	−0.380806	−	0.924655i	$-0.624354\pi$
$977$	−42.2813	−	21.5434i	−1.35270	−	0.689235i	−0.971894	+	0.235420i	$0.924354\pi$
$978$	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	−0.908015	−	0.418938i	$-0.862402\pi$
$983$	−5.45227	−	34.4243i	−0.173900	−	1.09796i	0.734114	−	0.679026i	$-0.237598\pi$
$984$	−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	−0.925293	−	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
$993$	−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	−0.176548	−	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.17.8	yes	80
3.2	odd	2	inner	150.2.l.a.17.2	✓	80
5.2	odd	4		750.2.l.a.143.5		80
5.3	odd	4		750.2.l.c.143.6		80
5.4	even	2		750.2.l.b.107.3		80
15.2	even	4		750.2.l.a.143.10		80
15.8	even	4		750.2.l.c.143.1		80
15.14	odd	2		750.2.l.b.107.9		80
25.3	odd	20	inner	150.2.l.a.53.2	yes	80
25.4	even	10		750.2.l.a.257.10		80
25.21	even	5		750.2.l.c.257.1		80
25.22	odd	20		750.2.l.b.743.9		80
75.29	odd	10		750.2.l.a.257.5		80
75.47	even	20		750.2.l.b.743.3		80
75.53	even	20	inner	150.2.l.a.53.8	yes	80
75.71	odd	10		750.2.l.c.257.6		80

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

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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