LMFDB - Embedded newform 430.2.k.b.231.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(11,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 10]))

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

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

chi := DirichletCharacter("430.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.k (of order $7$, degree $6$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{17} + 17 x^{16} - 43 x^{15} + 90 x^{14} - 114 x^{13} + 135 x^{12} + 2 x^{11} + 313 x^{10} + \cdots + 169 $ x^18 - 5x^17 + 17x^16 - 43x^15 + 90x^14 - 114x^13 + 135x^12 + 2x^11 + 313x^10 - 632x^9 + 2382x^8 - 1755x^7 + 2203x^6 - 3817x^5 + 4882x^4 - 4217x^3 + 2612x^2 - 871*x + 169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			231.1
Root			$2.39969 + 1.15563i$ of defining polynomial
Character	$\chi$	$=$	430.231
Dual form			430.2.k.b.121.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 - 0.974928i) q^{2} +(-0.592674 + 2.59667i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-0.623490 - 0.781831i) q^{5} +2.66345 q^{6} +2.84700 q^{7} +(0.623490 + 0.781831i) q^{8} +(-3.68855 - 1.77631i) q^{9} +O(q^{10})$	\(q+(-0.222521 - 0.974928i) q^{2} +(-0.592674 + 2.59667i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-0.623490 - 0.781831i) q^{5} +2.66345 q^{6} +2.84700 q^{7} +(0.623490 + 0.781831i) q^{8} +(-3.68855 - 1.77631i) q^{9} +(-0.623490 + 0.781831i) q^{10} +(-0.409042 - 0.196984i) q^{11} +(-0.592674 - 2.59667i) q^{12} +(4.34337 + 5.44641i) q^{13} +(-0.633517 - 2.77562i) q^{14} +(2.39969 - 1.15563i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-1.58028 + 1.98161i) q^{17} +(-0.910996 + 3.99133i) q^{18} +(-4.04065 + 1.94587i) q^{19} +(0.900969 + 0.433884i) q^{20} +(-1.68734 + 7.39273i) q^{21} +(-0.101025 + 0.442620i) q^{22} +(-6.04296 - 2.91014i) q^{23} +(-2.39969 + 1.15563i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(4.34337 - 5.44641i) q^{26} +(1.81670 - 2.27807i) q^{27} +(-2.56506 + 1.23527i) q^{28} +(1.65596 + 7.25523i) q^{29} +(-1.66064 - 2.08237i) q^{30} +(1.47079 + 6.44395i) q^{31} +(-0.900969 - 0.433884i) q^{32} +(0.753933 - 0.945402i) q^{33} +(2.28357 + 1.09971i) q^{34} +(-1.77507 - 2.22587i) q^{35} +4.09398 q^{36} +4.48684 q^{37} +(2.79622 + 3.50634i) q^{38} +(-16.7167 + 8.05036i) q^{39} +(0.222521 - 0.974928i) q^{40} +(1.22117 + 5.35028i) q^{41} +7.58284 q^{42} +(1.35824 - 6.41523i) q^{43} +0.454003 q^{44} +(0.910996 + 3.99133i) q^{45} +(-1.49249 + 6.53902i) q^{46} +(-2.45184 + 1.18074i) q^{47} +(1.66064 + 2.08237i) q^{48} +1.10540 q^{49} +1.00000 q^{50} +(-4.20900 - 5.27792i) q^{51} +(-6.27635 - 3.02253i) q^{52} +(6.60895 - 8.28736i) q^{53} +(-2.62521 - 1.26423i) q^{54} +(0.101025 + 0.442620i) q^{55} +(1.77507 + 2.22587i) q^{56} +(-2.65801 - 11.6455i) q^{57} +(6.70484 - 3.22888i) q^{58} +(6.35474 - 7.96860i) q^{59} +(-1.66064 + 2.08237i) q^{60} +(0.455793 - 1.99696i) q^{61} +(5.95510 - 2.86783i) q^{62} +(-10.5013 - 5.05715i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(1.55013 - 6.79156i) q^{65} +(-1.08946 - 0.524658i) q^{66} +(12.4790 - 6.00955i) q^{67} +(0.563996 - 2.47103i) q^{68} +(11.1382 - 13.9668i) q^{69} +(-1.77507 + 2.22587i) q^{70} +(-1.44528 + 0.696008i) q^{71} +(-0.910996 - 3.99133i) q^{72} +(2.28028 + 2.85938i) q^{73} +(-0.998415 - 4.37434i) q^{74} +(-2.39969 - 1.15563i) q^{75} +(2.79622 - 3.50634i) q^{76} +(-1.16454 - 0.560814i) q^{77} +(11.5683 + 14.5063i) q^{78} -10.2254 q^{79} -1.00000 q^{80} +(-2.81897 - 3.53488i) q^{81} +(4.94440 - 2.38110i) q^{82} +(-2.12605 + 9.31482i) q^{83} +(-1.68734 - 7.39273i) q^{84} +2.53457 q^{85} +(-6.55662 + 0.103336i) q^{86} -19.8209 q^{87} +(-0.101025 - 0.442620i) q^{88} +(-0.353005 + 1.54662i) q^{89} +(3.68855 - 1.77631i) q^{90} +(12.3656 + 15.5059i) q^{91} +6.70718 q^{92} -17.6045 q^{93} +(1.69673 + 2.12763i) q^{94} +(4.04065 + 1.94587i) q^{95} +(1.66064 - 2.08237i) q^{96} +(8.39580 + 4.04320i) q^{97} +(-0.245975 - 1.07769i) q^{98} +(1.15887 + 1.45317i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) $ 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9	\( 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9} + 3 q^{10} + 9 q^{11} + 2 q^{12} + 4 q^{13} + 13 q^{14} + 5 q^{15} - 3 q^{16} - q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 2 q^{21} - 12 q^{22} - 19 q^{23} - 5 q^{24} - 3 q^{25} + 4 q^{26} + 17 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 13 q^{31} - 3 q^{32} - 42 q^{33} - 8 q^{34} + 15 q^{35} + 2 q^{37} + 12 q^{38} - 39 q^{39} + 3 q^{40} - 4 q^{41} - 2 q^{42} - 13 q^{43} - 12 q^{44} - 7 q^{45} + 16 q^{46} + 16 q^{47} + 2 q^{48} + 4 q^{49} + 18 q^{50} + 7 q^{51} - 10 q^{52} + 14 q^{53} - 4 q^{54} + 12 q^{55} - 15 q^{56} + 45 q^{57} + 24 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} + 50 q^{62} - 33 q^{63} - 3 q^{64} - 4 q^{65} + 5 q^{67} + 13 q^{68} + 4 q^{69} + 15 q^{70} - 3 q^{71} + 7 q^{72} - 22 q^{73} - 12 q^{74} - 5 q^{75} + 12 q^{76} - 24 q^{77} + 31 q^{78} - 38 q^{79} - 18 q^{80} + 22 q^{81} - 11 q^{82} - 26 q^{83} - 2 q^{84} + 8 q^{85} - 41 q^{86} - 22 q^{87} - 12 q^{88} + 52 q^{89} + 7 q^{90} - 14 q^{91} + 2 q^{92} - 6 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 27 q^{97} + 32 q^{98} + 36 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9 + 3 * q^10 + 9 * q^11 + 2 * q^12 + 4 * q^13 + 13 * q^14 + 5 * q^15 - 3 * q^16 - q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 2 * q^21 - 12 * q^22 - 19 * q^23 - 5 * q^24 - 3 * q^25 + 4 * q^26 + 17 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 13 * q^31 - 3 * q^32 - 42 * q^33 - 8 * q^34 + 15 * q^35 + 2 * q^37 + 12 * q^38 - 39 * q^39 + 3 * q^40 - 4 * q^41 - 2 * q^42 - 13 * q^43 - 12 * q^44 - 7 * q^45 + 16 * q^46 + 16 * q^47 + 2 * q^48 + 4 * q^49 + 18 * q^50 + 7 * q^51 - 10 * q^52 + 14 * q^53 - 4 * q^54 + 12 * q^55 - 15 * q^56 + 45 * q^57 + 24 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 + 50 * q^62 - 33 * q^63 - 3 * q^64 - 4 * q^65 + 5 * q^67 + 13 * q^68 + 4 * q^69 + 15 * q^70 - 3 * q^71 + 7 * q^72 - 22 * q^73 - 12 * q^74 - 5 * q^75 + 12 * q^76 - 24 * q^77 + 31 * q^78 - 38 * q^79 - 18 * q^80 + 22 * q^81 - 11 * q^82 - 26 * q^83 - 2 * q^84 + 8 * q^85 - 41 * q^86 - 22 * q^87 - 12 * q^88 + 52 * q^89 + 7 * q^90 - 14 * q^91 + 2 * q^92 - 6 * q^93 + 2 * q^94 + 2 * q^95 + 2 * q^96 + 27 * q^97 + 32 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{4}{7}\right)$

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 $

$2$	−0.222521	−	0.974928i	−0.157346	−	0.689378i
$2$	−0.222521	−	0.974928i	−0.157346	−	0.689378i
$3$	−0.592674	+	2.59667i	−0.342180	+	1.49919i	0.452281	+	0.891876i	$0.350610\pi$
$3$	−0.592674	+	2.59667i	−0.342180	+	1.49919i	−0.794461	+	0.607315i	$0.792247\pi$
$4$	−0.900969	+	0.433884i	−0.450484	+	0.216942i
$5$	−0.623490	−	0.781831i	−0.278833	−	0.349646i
$5$	−0.623490	−	0.781831i	−0.278833	−	0.349646i
$6$	2.66345			1.08735
$7$	2.84700			1.07606			0.538032	−	0.842924i	$-0.319168\pi$
$7$	2.84700			1.07606			0.538032	+	0.842924i	$0.319168\pi$
$8$	0.623490	+	0.781831i	0.220437	+	0.276419i
$9$	−3.68855	−	1.77631i	−1.22952	−	0.592104i
$10$	−0.623490	+	0.781831i	−0.197165	+	0.247237i
$11$	−0.409042	−	0.196984i	−0.123331	−	0.0593930i	0.371201	−	0.928553i	$-0.378946\pi$
$11$	−0.409042	−	0.196984i	−0.123331	−	0.0593930i	−0.494532	+	0.869160i	$0.664660\pi$
$12$	−0.592674	−	2.59667i	−0.171090	−	0.749595i
$13$	4.34337	+	5.44641i	1.20463	+	1.51056i	0.804334	+	0.594178i	$0.202522\pi$
$13$	4.34337	+	5.44641i	1.20463	+	1.51056i	0.400299	+	0.916384i	$0.368906\pi$
$14$	−0.633517	−	2.77562i	−0.169314	−	0.741815i
$15$	2.39969	−	1.15563i	0.619597	−	0.298382i
$16$	0.623490	−	0.781831i	0.155872	−	0.195458i
$17$	−1.58028	+	1.98161i	−0.383275	+	0.480611i	−0.935622	−	0.353003i	$-0.885161\pi$
$17$	−1.58028	+	1.98161i	−0.383275	+	0.480611i	0.552348	+	0.833614i	$0.313732\pi$
$18$	−0.910996	+	3.99133i	−0.214724	+	0.940766i
$19$	−4.04065	+	1.94587i	−0.926989	+	0.446414i	−0.835561	−	0.549398i	$-0.814857\pi$
$19$	−4.04065	+	1.94587i	−0.926989	+	0.446414i	−0.0914275	+	0.995812i	$0.529143\pi$
$20$	0.900969	+	0.433884i	0.201463	+	0.0970194i
$21$	−1.68734	+	7.39273i	−0.368208	+	1.61323i
$22$	−0.101025	+	0.442620i	−0.0215386	+	0.0943669i
$23$	−6.04296	−	2.91014i	−1.26004	−	0.606805i	−0.319858	−	0.947465i	$-0.603635\pi$
$23$	−6.04296	−	2.91014i	−1.26004	−	0.606805i	−0.940187	+	0.340660i	$0.889350\pi$
$24$	−2.39969	+	1.15563i	−0.489834	+	0.235892i
$25$	−0.222521	+	0.974928i	−0.0445042	+	0.194986i
$26$	4.34337	−	5.44641i	0.851804	−	1.06813i
$27$	1.81670	−	2.27807i	0.349624	−	0.438414i
$28$	−2.56506	+	1.23527i	−0.484750	+	0.233443i
$29$	1.65596	+	7.25523i	0.307504	+	1.34726i	0.858525	+	0.512771i	$0.171381\pi$
$29$	1.65596	+	7.25523i	0.307504	+	1.34726i	−0.551022	+	0.834491i	$0.685762\pi$
$30$	−1.66064	−	2.08237i	−0.303189	−	0.380187i
$31$	1.47079	+	6.44395i	0.264161	+	1.15737i	0.916689	+	0.399602i	$0.130852\pi$
$31$	1.47079	+	6.44395i	0.264161	+	1.15737i	−0.652527	+	0.757765i	$0.726291\pi$
$32$	−0.900969	−	0.433884i	−0.159270	−	0.0767005i
$33$	0.753933	−	0.945402i	0.131243	−	0.164573i
$34$	2.28357	+	1.09971i	0.391630	+	0.188599i
$35$	−1.77507	−	2.22587i	−0.300042	−	0.376241i
$36$	4.09398			0.682330
$37$	4.48684			0.737632			0.368816	−	0.929503i	$-0.379763\pi$
$37$	4.48684			0.737632			0.368816	+	0.929503i	$0.379763\pi$
$38$	2.79622	+	3.50634i	0.453606	+	0.568804i
$39$	−16.7167	+	8.05036i	−2.67682	+	1.28909i
$40$	0.222521	−	0.974928i	0.0351836	−	0.154150i
$41$	1.22117	+	5.35028i	0.190714	+	0.835573i	0.976231	+	0.216733i	$0.0695400\pi$
$41$	1.22117	+	5.35028i	0.190714	+	0.835573i	−0.785517	+	0.618840i	$0.787603\pi$
$42$	7.58284			1.17006
$43$	1.35824	−	6.41523i	0.207130	−	0.978313i
$43$	1.35824	−	6.41523i	0.207130	−	0.978313i
$44$	0.454003			0.0684435
$45$	0.910996	+	3.99133i	0.135803	+	0.594993i
$46$	−1.49249	+	6.53902i	−0.220055	+	0.964126i
$47$	−2.45184	+	1.18074i	−0.357638	+	0.172229i	−0.604071	−	0.796930i	$-0.706456\pi$
$47$	−2.45184	+	1.18074i	−0.357638	+	0.172229i	0.246433	+	0.969160i	$0.420741\pi$
$48$	1.66064	+	2.08237i	0.239692	+	0.300564i
$49$	1.10540			0.157914
$50$	1.00000			0.141421
$51$	−4.20900	−	5.27792i	−0.589378	−	0.739057i
$52$	−6.27635	−	3.02253i	−0.870373	−	0.419149i
$53$	6.60895	−	8.28736i	0.907809	−	1.13836i	−0.0820959	−	0.996624i	$-0.526161\pi$
$53$	6.60895	−	8.28736i	0.907809	−	1.13836i	0.989905	−	0.141732i	$-0.0452672\pi$
$54$	−2.62521	−	1.26423i	−0.357245	−	0.172040i
$55$	0.101025	+	0.442620i	0.0136222	+	0.0596828i
$56$	1.77507	+	2.22587i	0.237204	+	0.297445i
$57$	−2.65801	−	11.6455i	−0.352063	−	1.54249i
$58$	6.70484	−	3.22888i	0.880388	−	0.423973i
$59$	6.35474	−	7.96860i	0.827317	−	1.03742i	−0.171319	−	0.985216i	$-0.554803\pi$
$59$	6.35474	−	7.96860i	0.827317	−	1.03742i	0.998636	−	0.0522074i	$-0.0166257\pi$
$60$	−1.66064	+	2.08237i	−0.214387	+	0.268833i
$61$	0.455793	−	1.99696i	0.0583583	−	0.255685i	−0.937330	−	0.348442i	$-0.886711\pi$
$61$	0.455793	−	1.99696i	0.0583583	−	0.255685i	0.995689	+	0.0927572i	$0.0295680\pi$
$62$	5.95510	−	2.86783i	0.756299	−	0.364214i
$63$	−10.5013	−	5.05715i	−1.32304	−	0.637141i
$64$	−0.222521	+	0.974928i	−0.0278151	+	0.121866i
$65$	1.55013	−	6.79156i	0.192270	−	0.842390i
$66$	−1.08946	−	0.524658i	−0.134104	−	0.0645810i
$67$	12.4790	−	6.00955i	1.52455	−	0.734184i	0.530976	−	0.847387i	$-0.321825\pi$
$67$	12.4790	−	6.00955i	1.52455	−	0.734184i	0.993572	+	0.113203i	$0.0361111\pi$
$68$	0.563996	−	2.47103i	0.0683946	−	0.299656i
$69$	11.1382	−	13.9668i	1.34088	−	1.68141i
$70$	−1.77507	+	2.22587i	−0.212162	+	0.266043i
$71$	−1.44528	+	0.696008i	−0.171523	+	0.0826009i	−0.517675	−	0.855577i	$-0.673202\pi$
$71$	−1.44528	+	0.696008i	−0.171523	+	0.0826009i	0.346152	+	0.938178i	$0.387488\pi$
$72$	−0.910996	−	3.99133i	−0.107362	−	0.470383i
$73$	2.28028	+	2.85938i	0.266887	+	0.334665i	0.897158	−	0.441710i	$-0.145628\pi$
$73$	2.28028	+	2.85938i	0.266887	+	0.334665i	−0.630272	+	0.776375i	$0.717056\pi$
$74$	−0.998415	−	4.37434i	−0.116063	−	0.508507i
$75$	−2.39969	−	1.15563i	−0.277092	−	0.133441i
$76$	2.79622	−	3.50634i	0.320748	−	0.402205i
$77$	−1.16454	−	0.560814i	−0.132712	−	0.0639107i
$78$	11.5683	+	14.5063i	1.30986	+	1.64251i
$79$	−10.2254			−1.15044			−0.575221	−	0.817998i	$-0.695084\pi$
$79$	−10.2254			−1.15044			−0.575221	+	0.817998i	$0.695084\pi$
$80$	−1.00000			−0.111803
$81$	−2.81897	−	3.53488i	−0.313219	−	0.392764i
$82$	4.94440	−	2.38110i	0.546018	−	0.262948i
$83$	−2.12605	+	9.31482i	−0.233364	+	1.02243i	0.713463	+	0.700693i	$0.247126\pi$
$83$	−2.12605	+	9.31482i	−0.233364	+	1.02243i	−0.946827	+	0.321742i	$0.895732\pi$
$84$	−1.68734	−	7.39273i	−0.184104	−	0.806613i
$85$	2.53457			0.274913
$86$	−6.55662	+	0.103336i	−0.707019	+	0.0111430i
$87$	−19.8209			−2.12502
$88$	−0.101025	−	0.442620i	−0.0107693	−	0.0471834i
$89$	−0.353005	+	1.54662i	−0.0374185	+	0.163941i	−0.990185	−	0.139763i	$-0.955366\pi$
$89$	−0.353005	+	1.54662i	−0.0374185	+	0.163941i	0.952767	+	0.303704i	$0.0982232\pi$
$90$	3.68855	−	1.77631i	0.388807	−	0.187240i
$91$	12.3656	+	15.5059i	1.29626	+	1.62546i
$92$	6.70718			0.699272
$93$	−17.6045			−1.82550
$94$	1.69673	+	2.12763i	0.175004	+	0.219448i
$95$	4.04065	+	1.94587i	0.414562	+	0.199642i
$96$	1.66064	−	2.08237i	0.169488	−	0.212531i
$97$	8.39580	+	4.04320i	0.852464	+	0.410525i	0.808492	−	0.588508i	$-0.200284\pi$
$97$	8.39580	+	4.04320i	0.852464	+	0.410525i	0.0439724	+	0.999033i	$0.485999\pi$
$98$	−0.245975	−	1.07769i	−0.0248472	−	0.108863i
$99$	1.15887	+	1.45317i	0.116470	+	0.146049i
$100$	−0.222521	−	0.974928i	−0.0222521	−	0.0974928i
$101$	−1.94252	+	0.935466i	−0.193287	+	0.0930823i	−0.528024	−	0.849229i	$-0.677067\pi$
$101$	−1.94252	+	0.935466i	−0.193287	+	0.0930823i	0.334737	+	0.942312i	$0.391353\pi$
$102$	−4.20900	+	5.27792i	−0.416754	+	0.522592i
$103$	5.42253	−	6.79963i	0.534297	−	0.669988i	−0.439279	−	0.898351i	$-0.644766\pi$
$103$	5.42253	−	6.79963i	0.534297	−	0.669988i	0.973576	+	0.228363i	$0.0733373\pi$
$104$	−1.55013	+	6.79156i	−0.152003	+	0.665967i
$105$	6.83191	−	3.29007i	0.666726	−	0.321078i
$106$	−9.55021	−	4.59914i	−0.927598	−	0.446708i
$107$	−0.185294	+	0.811824i	−0.0179130	+	0.0784820i	−0.983094	−	0.183100i	$-0.941387\pi$
$107$	−0.185294	+	0.811824i	−0.0179130	+	0.0784820i	0.965181	+	0.261582i	$0.0842441\pi$
$108$	−0.648372	+	2.84070i	−0.0623897	+	0.273347i
$109$	5.85361	+	2.81895i	0.560674	+	0.270006i	0.692683	−	0.721242i	$-0.256429\pi$
$109$	5.85361	+	2.81895i	0.560674	+	0.270006i	−0.132009	+	0.991249i	$0.542143\pi$
$110$	0.409042	−	0.196984i	0.0390006	−	0.0187817i
$111$	−2.65923	+	11.6509i	−0.252403	+	1.10585i
$112$	1.77507	−	2.22587i	0.167729	−	0.210325i
$113$	7.47982	−	9.37940i	0.703642	−	0.882339i	−0.293648	−	0.955914i	$-0.594869\pi$
$113$	7.47982	−	9.37940i	0.703642	−	0.882339i	0.997290	+	0.0735744i	$0.0234406\pi$
$114$	−10.7621	+	5.18274i	−1.00796	+	0.485408i
$115$	1.49249	+	6.53902i	0.139175	+	0.609767i
$116$	−4.63989	−	5.81824i	−0.430803	−	0.540210i
$117$	−6.34620	−	27.8045i	−0.586706	−	2.57053i
$118$	−9.18287	−	4.42224i	−0.845352	−	0.407100i
$119$	−4.49906	+	5.64164i	−0.412428	+	0.517168i
$120$	2.39969	+	1.15563i	0.219061	+	0.105494i
$121$	−6.72988	−	8.43900i	−0.611807	−	0.767181i
$122$	−2.04832			−0.185446
$123$	−14.6167			−1.31794
$124$	−4.12106	−	5.16764i	−0.370082	−	0.464068i
$125$	0.900969	−	0.433884i	0.0805851	−	0.0388077i
$126$	−2.59360	+	11.3633i	−0.231057	+	1.01233i
$127$	2.71425	+	11.8919i	0.240851	+	1.05524i	0.940244	+	0.340501i	$0.110597\pi$
$127$	2.71425	+	11.8919i	0.240851	+	1.05524i	−0.699393	+	0.714737i	$0.746546\pi$
$128$	1.00000			0.0883883
$129$	15.8533	+	7.32905i	1.39580	+	0.645287i
$130$	−6.96622			−0.610978
$131$	−4.43786	−	19.4435i	−0.387738	−	1.69879i	−0.672421	−	0.740169i	$-0.734745\pi$
$131$	−4.43786	−	19.4435i	−0.387738	−	1.69879i	0.284683	−	0.958622i	$-0.408112\pi$
$132$	−0.269075	+	1.17890i	−0.0234200	+	0.102610i
$133$	−11.5037	+	5.53990i	−0.997499	+	0.480370i
$134$	−8.63571	−	10.8288i	−0.746012	−	0.935469i
$135$	−2.91376			−0.250776
$136$	−2.53457			−0.217338
$137$	−7.93792	−	9.95384i	−0.678182	−	0.850414i	0.317003	−	0.948424i	$-0.397323\pi$
$137$	−7.93792	−	9.95384i	−0.678182	−	0.850414i	−0.995185	+	0.0980109i	$0.968752\pi$
$138$	−16.0951	−	7.75101i	−1.37011	−	0.659810i
$139$	−8.98532	+	11.2672i	−0.762125	+	0.955674i	−0.999878	−	0.0156517i	$-0.995018\pi$
$139$	−8.98532	+	11.2672i	−0.762125	+	0.955674i	0.237753	+	0.971326i	$0.423589\pi$
$140$	2.56506	+	1.23527i	0.216787	+	0.104399i
$141$	−1.61287	−	7.06643i	−0.135828	−	0.595101i
$142$	1.00016	+	1.25416i	0.0839317	+	0.105247i
$143$	−0.703763	−	3.08339i	−0.0588516	−	0.257846i
$144$	−3.68855	+	1.77631i	−0.307379	+	0.148026i
$145$	4.63989	−	5.81824i	0.385322	−	0.483179i
$146$	2.28028	−	2.85938i	0.188717	−	0.236644i
$147$	−0.655142	+	2.87037i	−0.0540352	+	0.236744i
$148$	−4.04250	+	1.94677i	−0.332292	+	0.160023i
$149$	18.2269	+	8.77759i	1.49320	+	0.719088i	0.989466	−	0.144769i	$-0.0462439\pi$
$149$	18.2269	+	8.77759i	1.49320	+	0.719088i	0.503737	+	0.863857i	$0.331958\pi$
$150$	−0.592674	+	2.59667i	−0.0483916	+	0.212018i
$151$	2.84654	−	12.4715i	0.231648	−	1.01492i	−0.716625	−	0.697459i	$-0.754314\pi$
$151$	2.84654	−	12.4715i	0.231648	−	1.01492i	0.948273	−	0.317457i	$-0.102829\pi$
$152$	−4.04065	−	1.94587i	−0.327740	−	0.157831i
$153$	9.34890	−	4.50219i	0.755814	−	0.363981i
$154$	−0.287618	+	1.26014i	−0.0231769	+	0.101545i
$155$	4.12106	−	5.16764i	0.331011	−	0.415075i
$156$	11.5683	−	14.5063i	0.926209	−	1.16143i
$157$	9.51027	−	4.57990i	0.759002	−	0.365516i	−0.0140146	−	0.999902i	$-0.504461\pi$
$157$	9.51027	−	4.57990i	0.759002	−	0.365516i	0.773017	+	0.634386i	$0.218747\pi$
$158$	2.27536	+	9.96899i	0.181018	+	0.793090i
$159$	17.6026	+	22.0730i	1.39598	+	1.75050i
$160$	0.222521	+	0.974928i	0.0175918	+	0.0770748i
$161$	−17.2043	−	8.28516i	−1.35589	−	0.652962i
$162$	−2.81897	+	3.53488i	−0.221479	+	0.277726i
$163$	−4.50714	−	2.17052i	−0.353026	−	0.170008i	0.248962	−	0.968513i	$-0.419910\pi$
$163$	−4.50714	−	2.17052i	−0.353026	−	0.170008i	−0.601989	+	0.798505i	$0.705625\pi$
$164$	−3.42163	−	4.29059i	−0.267185	−	0.335039i
$165$	−1.20921			−0.0941372
$166$	9.55437			0.741563
$167$	−0.805687	−	1.01030i	−0.0623459	−	0.0781793i	0.749681	−	0.661800i	$-0.230207\pi$
$167$	−0.805687	−	1.01030i	−0.0623459	−	0.0781793i	−0.812027	+	0.583620i	$0.801636\pi$
$168$	−6.83191	+	3.29007i	−0.527093	+	0.253835i
$169$	−7.90577	+	34.6374i	−0.608136	+	2.66442i
$170$	−0.563996	−	2.47103i	−0.0432565	−	0.189519i
$171$	18.3606			1.40407
$172$	1.55973	+	6.36924i	0.118928	+	0.485650i
$173$	0.629413			0.0478534			0.0239267	−	0.999714i	$-0.492383\pi$
$173$	0.629413			0.0478534			0.0239267	+	0.999714i	$0.492383\pi$
$174$	4.41057	+	19.3240i	0.334364	+	1.46494i
$175$	−0.633517	+	2.77562i	−0.0478894	+	0.209817i
$176$	−0.409042	+	0.196984i	−0.0308327	+	0.0148483i
$177$	16.9256	+	21.2240i	1.27220	+	1.59529i
$178$	1.58639			0.118905
$179$	2.54048			0.189884			0.0949422	−	0.995483i	$-0.469733\pi$
$179$	2.54048			0.189884			0.0949422	+	0.995483i	$0.469733\pi$
$180$	−2.55255	−	3.20080i	−0.190256	−	0.238574i
$181$	−14.5628	−	7.01309i	−1.08245	−	0.521279i	−0.194349	−	0.980932i	$-0.562259\pi$
$181$	−14.5628	−	7.01309i	−1.08245	−	0.521279i	−0.888098	+	0.459653i	$0.847974\pi$
$182$	12.3656	−	15.5059i	0.916596	−	1.14938i
$183$	4.91532	+	2.36709i	0.363351	+	0.174981i
$184$	−1.49249	−	6.53902i	−0.110028	−	0.482063i
$185$	−2.79750	−	3.50795i	−0.205676	−	0.257910i
$186$	3.91738	+	17.1631i	0.287236	+	1.25846i
$187$	1.03675	−	0.499272i	0.0758145	−	0.0365103i
$188$	1.69673	−	2.12763i	0.123747	−	0.155173i
$189$	5.17214	−	6.48566i	0.376218	−	0.471762i
$190$	0.997958	−	4.37234i	0.0723995	−	0.317203i
$191$	−9.10544	+	4.38495i	−0.658847	+	0.317284i	−0.733265	−	0.679943i	$-0.762004\pi$
$191$	−9.10544	+	4.38495i	−0.658847	+	0.317284i	0.0744181	+	0.997227i	$0.476290\pi$
$192$	−2.39969	−	1.15563i	−0.173183	−	0.0834003i
$193$	−1.55742	+	6.82352i	−0.112106	+	0.491168i	0.887437	+	0.460929i	$0.152484\pi$
$193$	−1.55742	+	6.82352i	−0.112106	+	0.491168i	−0.999543	+	0.0302384i	$0.990373\pi$
$194$	2.07359	−	9.08499i	0.148875	−	0.652264i
$195$	16.7167	+	8.05036i	1.19711	+	0.576498i
$196$	−0.995932	+	0.479615i	−0.0711380	+	0.0342582i
$197$	5.15051	−	22.5659i	0.366959	−	1.60775i	−0.368126	−	0.929776i	$-0.620000\pi$
$197$	5.15051	−	22.5659i	0.366959	−	1.60775i	0.735085	−	0.677975i	$-0.237142\pi$
$198$	1.15887	−	1.45317i	0.0823570	−	0.103272i
$199$	16.3991	−	20.5638i	1.16250	−	1.45773i	0.298376	−	0.954449i	$-0.403555\pi$
$199$	16.3991	−	20.5638i	1.16250	−	1.45773i	0.864124	−	0.503279i	$-0.167873\pi$
$200$	−0.900969	+	0.433884i	−0.0637081	+	0.0306802i
$201$	8.20889	+	35.9655i	0.579011	+	2.53681i
$202$	1.34426	+	1.68565i	0.0945820	+	0.118602i
$203$	4.71451	+	20.6556i	0.330894	+	1.44974i
$204$	6.08219	+	2.92903i	0.425838	+	0.205073i
$205$	3.42163	−	4.29059i	0.238977	−	0.299668i
$206$	−7.83578	−	3.77351i	−0.545944	−	0.262913i
$207$	17.1204	+	21.4684i	1.18995	+	1.49215i
$208$	6.96622			0.483020
$209$	2.03610			0.140840
$210$	−4.72783	−	5.92851i	−0.326251	−	0.409106i
$211$	1.06294	−	0.511885i	0.0731757	−	0.0352396i	−0.396938	−	0.917845i	$-0.629927\pi$
$211$	1.06294	−	0.511885i	0.0731757	−	0.0352396i	0.470114	+	0.882606i	$0.344213\pi$
$212$	−2.35871	+	10.3342i	−0.161997	+	0.709754i
$213$	−0.950729	−	4.16541i	−0.0651429	−	0.285410i
$214$	0.832702			0.0569223
$215$	−5.86248	+	2.93791i	−0.399818	+	0.200364i
$216$	2.91376			0.198256
$217$	4.18733	+	18.3459i	0.284255	+	1.24540i
$218$	1.44572	−	6.33412i	0.0979166	−	0.429001i
$219$	−8.77634	+	4.22646i	−0.593050	+	0.285598i
$220$	−0.283066	−	0.354954i	−0.0190843	−	0.0239310i
$221$	−17.6564			−1.18770
$222$	11.9505			0.802064
$223$	−7.52098	−	9.43101i	−0.503642	−	0.631547i	0.463405	−	0.886147i	$-0.346628\pi$
$223$	−7.52098	−	9.43101i	−0.503642	−	0.631547i	−0.967047	+	0.254600i	$0.918056\pi$
$224$	−2.56506	−	1.23527i	−0.171385	−	0.0825347i
$225$	2.55255	−	3.20080i	0.170170	−	0.213387i
$226$	−10.8087	−	5.20517i	−0.718981	−	0.346243i
$227$	3.48085	+	15.2506i	0.231032	+	1.01222i	0.948786	+	0.315920i	$0.102313\pi$
$227$	3.48085	+	15.2506i	0.231032	+	1.01222i	−0.717754	+	0.696297i	$0.754830\pi$
$228$	7.44759	+	9.33898i	0.493229	+	0.618489i
$229$	4.22691	+	18.5193i	0.279322	+	1.22379i	0.898653	+	0.438660i	$0.144547\pi$
$229$	4.22691	+	18.5193i	0.279322	+	1.22379i	−0.619331	+	0.785130i	$0.712596\pi$
$230$	6.04296	−	2.91014i	0.398461	−	0.191889i
$231$	2.14645	−	2.69156i	0.141226	−	0.177091i
$232$	−4.63989	+	5.81824i	−0.304624	+	0.381986i
$233$	3.42674	−	15.0135i	0.224493	−	0.983568i	−0.729557	−	0.683920i	$-0.760274\pi$
$233$	3.42674	−	15.0135i	0.224493	−	0.983568i	0.954050	−	0.299648i	$-0.0968691\pi$
$234$	−25.6952	+	12.3742i	−1.67975	+	0.808925i
$235$	2.45184	+	1.18074i	0.159940	+	0.0770233i
$236$	−2.26798	+	9.93668i	−0.147633	+	0.646823i
$237$	6.06030	−	26.5519i	0.393659	−	1.72473i
$238$	6.50133	+	3.13087i	0.421419	+	0.202944i
$239$	18.9132	−	9.10812i	1.22339	−	0.589155i	0.293139	−	0.956070i	$-0.405300\pi$
$239$	18.9132	−	9.10812i	1.22339	−	0.589155i	0.930255	+	0.366915i	$0.119586\pi$
$240$	0.592674	−	2.59667i	0.0382569	−	0.167615i
$241$	9.98132	−	12.5162i	0.642954	−	0.806238i	−0.348415	−	0.937340i	$-0.613280\pi$
$241$	9.98132	−	12.5162i	0.642954	−	0.806238i	0.991369	+	0.131102i	$0.0418516\pi$
$242$	−6.72988	+	8.43900i	−0.432613	+	0.542479i
$243$	18.7253	−	9.01762i	1.20123	−	0.578480i
$244$	0.455793	+	1.99696i	0.0291792	+	0.127842i
$245$	−0.689206	−	0.864237i	−0.0440318	−	0.0552141i
$246$	3.25252	+	14.2502i	0.207373	+	0.908560i
$247$	−28.1481	−	13.5554i	−1.79102	−	0.862509i
$248$	−4.12106	+	5.16764i	−0.261687	+	0.328146i
$249$	−22.9275	−	11.0413i	−1.45297	−	0.699714i
$250$	−0.623490	−	0.781831i	−0.0394330	−	0.0494474i
$251$	16.4095			1.03576			0.517881	−	0.855453i	$-0.326721\pi$
$251$	16.4095			1.03576			0.517881	+	0.855453i	$0.326721\pi$
$252$	11.6556			0.734231
$253$	1.89857	+	2.38074i	0.119362	+	0.149676i
$254$	10.9898	−	5.29241i	0.689561	−	0.332075i
$255$	−1.50218	+	6.58146i	−0.0940699	+	0.412147i
$256$	−0.222521	−	0.974928i	−0.0139076	−	0.0609330i
$257$	21.9614			1.36991			0.684956	−	0.728584i	$-0.259821\pi$
$257$	21.9614			1.36991			0.684956	+	0.728584i	$0.259821\pi$
$258$	3.61761	−	17.0867i	0.225223	−	1.06377i
$259$	12.7740			0.793739
$260$	1.55013	+	6.79156i	0.0961350	+	0.421195i
$261$	6.77946	−	29.7027i	0.419638	−	1.83855i
$262$	−17.9685	+	8.65319i	−1.11010	+	0.534596i
$263$	−7.35837	−	9.22710i	−0.453736	−	0.568968i	0.501369	−	0.865234i	$-0.332830\pi$
$263$	−7.35837	−	9.22710i	−0.453736	−	0.568968i	−0.955105	+	0.296266i	$0.904258\pi$
$264$	1.20921			0.0744220
$265$	−10.5999			−0.651149
$266$	7.96082	+	9.98256i	0.488109	+	0.612070i
$267$	−3.80684	−	1.83328i	−0.232975	−	0.112195i
$268$	−8.63571	+	10.8288i	−0.527510	+	0.661477i
$269$	−10.2080	−	4.91592i	−0.622394	−	0.299729i	0.0959833	−	0.995383i	$-0.469400\pi$
$269$	−10.2080	−	4.91592i	−0.622394	−	0.299729i	−0.718377	+	0.695654i	$0.755115\pi$
$270$	0.648372	+	2.84070i	0.0394587	+	0.172880i
$271$	−8.19766	−	10.2795i	−0.497972	−	0.624438i	0.467798	−	0.883835i	$-0.345047\pi$
$271$	−8.19766	−	10.2795i	−0.497972	−	0.624438i	−0.965771	+	0.259398i	$0.916476\pi$
$272$	0.563996	+	2.47103i	0.0341973	+	0.149828i
$273$	−47.5926	+	22.9194i	−2.88043	+	1.38714i
$274$	−7.93792	+	9.95384i	−0.479547	+	0.601333i
$275$	0.283066	−	0.354954i	0.0170695	−	0.0214045i
$276$	−3.97517	+	17.4164i	−0.239277	+	1.04834i
$277$	−0.402647	+	0.193905i	−0.0241927	+	0.0116506i	−0.445941	−	0.895062i	$-0.647131\pi$
$277$	−0.402647	+	0.193905i	−0.0241927	+	0.0116506i	0.421748	+	0.906713i	$0.361417\pi$
$278$	12.9842	+	6.25284i	0.778738	+	0.375020i
$279$	6.02138	−	26.3814i	0.360490	−	1.57941i
$280$	0.633517	−	2.77562i	0.0378599	−	0.165875i
$281$	3.16345	+	1.52344i	0.188715	+	0.0908806i	0.525855	−	0.850574i	$-0.323745\pi$
$281$	3.16345	+	1.52344i	0.188715	+	0.0908806i	−0.337140	+	0.941455i	$0.609460\pi$
$282$	−6.53036	+	3.14486i	−0.388877	+	0.187273i
$283$	−5.47428	+	23.9844i	−0.325412	+	1.42572i	0.502360	+	0.864659i	$0.332465\pi$
$283$	−5.47428	+	23.9844i	−0.325412	+	1.42572i	−0.827772	+	0.561065i	$0.810392\pi$
$284$	1.00016	−	1.25416i	0.0593487	−	0.0744209i
$285$	−7.44759	+	9.33898i	−0.441157	+	0.553194i
$286$	−2.84948	+	1.37224i	−0.168493	+	0.0811420i
$287$	3.47666	+	15.2322i	0.205221	+	0.899130i
$288$	2.55255	+	3.20080i	0.150411	+	0.188609i
$289$	2.35337	+	10.3108i	0.138433	+	0.606516i
$290$	−6.70484	−	3.22888i	−0.393722	−	0.189606i
$291$	−15.4748	+	19.4048i	−0.907152	+	1.13753i
$292$	−3.29510	−	1.58684i	−0.192831	−	0.0928626i
$293$	9.77941	+	12.2630i	0.571319	+	0.716412i	0.980605	−	0.195995i	$-0.0627935\pi$
$293$	9.77941	+	12.2630i	0.571319	+	0.716412i	−0.409286	+	0.912406i	$0.634222\pi$
$294$	2.94418			0.171708
$295$	−10.1922			−0.593414
$296$	2.79750	+	3.50795i	0.162601	+	0.203896i
$297$	−1.19185	+	0.573965i	−0.0691582	+	0.0333048i
$298$	4.50166	−	19.7231i	0.260774	−	1.14253i
$299$	−10.3970	−	45.5522i	−0.601274	−	2.63435i
$300$	2.66345			0.153774
$301$	3.86691	−	18.2642i	0.222885	−	1.05273i
$302$	−12.7922			−0.736110
$303$	−1.27782	−	5.59850i	−0.0734090	−	0.321626i
$304$	−0.997958	+	4.37234i	−0.0572368	+	0.250771i
$305$	−1.84547	+	0.888731i	−0.105671	+	0.0508886i
$306$	−6.46964	−	8.11267i	−0.369845	−	0.463770i
$307$	−1.20277			−0.0686459			−0.0343230	−	0.999411i	$-0.510927\pi$
$307$	−1.20277			−0.0686459			−0.0343230	+	0.999411i	$0.510927\pi$
$308$	1.29254			0.0736496
$309$	14.4426	+	18.1105i	0.821613	+	1.03027i
$310$	−5.95510	−	2.86783i	−0.338227	−	0.162882i
$311$	−13.1516	+	16.4915i	−0.745757	+	0.935150i	−0.999484	−	0.0321263i	$-0.989772\pi$
$311$	−13.1516	+	16.4915i	−0.745757	+	0.935150i	0.253727	+	0.967276i	$0.418344\pi$
$312$	−16.7167	−	8.05036i	−0.946400	−	0.455762i
$313$	4.25209	+	18.6296i	0.240342	+	1.05301i	0.940706	+	0.339223i	$0.110164\pi$
$313$	4.25209	+	18.6296i	0.240342	+	1.05301i	−0.700364	+	0.713786i	$0.746979\pi$
$314$	−6.58131	−	8.25270i	−0.371405	−	0.465727i
$315$	2.59360	+	11.3633i	0.146133	+	0.640251i
$316$	9.21273	−	4.43662i	0.518256	−	0.249579i
$317$	3.85650	−	4.83589i	0.216602	−	0.271611i	−0.661645	−	0.749817i	$-0.730141\pi$
$317$	3.85650	−	4.83589i	0.216602	−	0.271611i	0.878248	+	0.478206i	$0.158713\pi$
$318$	17.6026	−	22.0730i	0.987106	−	1.23779i
$319$	0.751809	−	3.29389i	0.0420932	−	0.184423i
$320$	0.900969	−	0.433884i	0.0503657	−	0.0242548i
$321$	−1.99822	−	0.962294i	−0.111530	−	0.0537100i
$322$	−4.24911	+	18.6166i	−0.236794	+	1.03746i
$323$	2.52940	−	11.0820i	0.140740	−	0.616620i
$324$	4.07353	+	1.96171i	0.226307	+	0.108984i
$325$	−6.27635	+	3.02253i	−0.348149	+	0.167660i
$326$	−1.11317	+	4.87712i	−0.0616528	+	0.270119i
$327$	−10.7892	+	13.5292i	−0.596643	+	0.748166i
$328$	−3.42163	+	4.29059i	−0.188928	+	0.236908i
$329$	−6.98039	+	3.36158i	−0.384841	+	0.185330i
$330$	0.269075	+	1.17890i	0.0148121	+	0.0648961i
$331$	−11.9571	−	14.9937i	−0.657219	−	0.824127i	0.335818	−	0.941927i	$-0.390987\pi$
$331$	−11.9571	−	14.9937i	−0.657219	−	0.824127i	−0.993037	+	0.117800i	$0.962416\pi$
$332$	−2.12605	−	9.31482i	−0.116682	−	0.511217i
$333$	−16.5499	−	7.97002i	−0.906930	−	0.436754i
$334$	−0.805687	+	1.01030i	−0.0440852	+	0.0552811i
$335$	−12.4790	−	6.00955i	−0.681799	−	0.328337i
$336$	4.72783	+	5.92851i	0.257924	+	0.323427i
$337$	−7.57321			−0.412539			−0.206269	−	0.978495i	$-0.566132\pi$
$337$	−7.57321			−0.412539			−0.206269	+	0.978495i	$0.566132\pi$
$338$	35.5282			1.93248
$339$	19.9221	+	24.9816i	1.08202	+	1.35681i
$340$	−2.28357	+	1.09971i	−0.123844	+	0.0596402i
$341$	0.667742	−	2.92557i	0.0361603	−	0.158428i
$342$	−4.08562	−	17.9003i	−0.220925	−	0.967935i
$343$	−16.7819			−0.906138
$344$	5.86248	−	2.93791i	0.316084	−	0.158402i
$345$	−17.8643			−0.961779
$346$	−0.140058	−	0.613632i	−0.00752954	−	0.0329891i
$347$	−1.86574	+	8.17433i	−0.100158	+	0.438821i	0.899839	+	0.436223i	$0.143684\pi$
$347$	−1.86574	+	8.17433i	−0.100158	+	0.438821i	−0.999997	+	0.00259815i	$0.999173\pi$
$348$	17.8580	−	8.59997i	0.957290	−	0.461007i
$349$	−20.4274	−	25.6152i	−1.09346	−	1.37115i	−0.922557	−	0.385861i	$-0.873905\pi$
$349$	−20.4274	−	25.6152i	−1.09346	−	1.37115i	−0.170898	−	0.985289i	$-0.554667\pi$
$350$	2.84700			0.152178
$351$	20.2979			1.08342
$352$	0.283066	+	0.354954i	0.0150875	+	0.0189191i
$353$	1.99014	+	0.958401i	0.105924	+	0.0510105i	0.486096	−	0.873906i	$-0.338421\pi$
$353$	1.99014	+	0.958401i	0.105924	+	0.0510105i	−0.380171	+	0.924916i	$0.624135\pi$
$354$	16.9256	−	21.2240i	0.899583	−	1.12804i
$355$	1.44528	+	0.696008i	0.0767073	+	0.0369403i
$356$	−0.353005	−	1.54662i	−0.0187092	−	0.0819705i
$357$	−11.9830	−	15.0262i	−0.634209	−	0.795273i
$358$	−0.565310	−	2.47679i	−0.0298776	−	0.130902i
$359$	−10.4965	+	5.05487i	−0.553986	+	0.266786i	−0.689863	−	0.723940i	$-0.742329\pi$
$359$	−10.4965	+	5.05487i	−0.553986	+	0.266786i	0.135877	+	0.990726i	$0.456615\pi$
$360$	−2.55255	+	3.20080i	−0.134531	+	0.168697i
$361$	0.694117	−	0.870396i	0.0365325	−	0.0458103i
$362$	−3.59672	+	15.7583i	−0.189040	+	0.828237i
$363$	25.9019	−	12.4737i	1.35950	−	0.654700i
$364$	−17.8687	−	8.60514i	−0.936577	−	0.451032i
$365$	0.813822	−	3.56559i	0.0425974	−	0.186631i
$366$	1.21398	−	5.31881i	0.0634559	−	0.278019i
$367$	24.6927	+	11.8914i	1.28895	+	0.620725i	0.947674	−	0.319239i	$-0.103427\pi$
$367$	24.6927	+	11.8914i	1.28895	+	0.620725i	0.341274	+	0.939964i	$0.389142\pi$
$368$	−6.04296	+	2.91014i	−0.315011	+	0.151701i
$369$	4.99943	−	21.9039i	0.260260	−	1.14027i
$370$	−2.79750	+	3.50795i	−0.145435	+	0.182370i
$371$	18.8157	−	23.5941i	0.976861	−	1.22494i
$372$	15.8611	−	7.63832i	0.822361	−	0.396028i
$373$	2.38436	+	10.4466i	0.123458	+	0.540904i	0.998393	+	0.0566642i	$0.0180465\pi$
$373$	2.38436	+	10.4466i	0.123458	+	0.540904i	−0.874936	+	0.484239i	$0.839096\pi$
$374$	−0.717452	−	0.899656i	−0.0370986	−	0.0465201i
$375$	0.592674	+	2.59667i	0.0306055	+	0.134092i
$376$	−2.45184	−	1.18074i	−0.126444	−	0.0608922i
$377$	−32.3225	+	40.5311i	−1.66469	+	2.08746i
$378$	−7.47396	−	3.59927i	−0.384419	−	0.185126i
$379$	−1.41155	−	1.77002i	−0.0725062	−	0.0909199i	0.744256	−	0.667895i	$-0.232804\pi$
$379$	−1.41155	−	1.77002i	−0.0725062	−	0.0909199i	−0.816762	+	0.576975i	$0.804233\pi$
$380$	−4.48478			−0.230065
$381$	−32.4881			−1.66442
$382$	6.30116	+	7.90141i	0.322395	+	0.404271i
$383$	−33.5237	+	16.1442i	−1.71298	+	0.824929i	−0.721850	+	0.692050i	$0.756708\pi$
$383$	−33.5237	+	16.1442i	−1.71298	+	0.824929i	−0.991132	+	0.132879i	$0.957578\pi$
$384$	−0.592674	+	2.59667i	−0.0302448	+	0.132511i
$385$	0.287618	+	1.26014i	0.0146584	+	0.0642226i
$386$	6.99900			0.356240
$387$	−16.4054	+	21.2502i	−0.833932	+	1.08021i
$388$	−9.31863			−0.473082
$389$	−1.76128	−	7.71668i	−0.0893005	−	0.391251i	0.910449	−	0.413621i	$-0.135736\pi$
$389$	−1.76128	−	7.71668i	−0.0893005	−	0.391251i	−0.999750	+	0.0223697i	$0.992879\pi$
$390$	4.12870	−	18.0890i	0.209065	−	0.915972i
$391$	15.3163	−	7.37596i	0.774580	−	0.373018i
$392$	0.689206	+	0.864237i	0.0348102	+	0.0436506i
$393$	53.1188			2.67949
$394$	−23.1462			−1.16609
$395$	6.37541	+	7.99451i	0.320781	+	0.402247i
$396$	−1.67461	−	0.806450i	−0.0841523	−	0.0405256i
$397$	22.0019	−	27.5895i	1.10424	−	1.38468i	0.188900	−	0.981996i	$-0.439508\pi$
$397$	22.0019	−	27.5895i	1.10424	−	1.38468i	0.915341	−	0.402679i	$-0.131921\pi$
$398$	−23.6973	−	11.4120i	−1.18784	−	0.572034i
$399$	−7.56736	−	33.1548i	−0.378842	−	1.65981i
$400$	0.623490	+	0.781831i	0.0311745	+	0.0390916i
$401$	−0.877317	−	3.84378i	−0.0438111	−	0.191949i	0.948287	−	0.317415i	$-0.102815\pi$
$401$	−0.877317	−	3.84378i	−0.0438111	−	0.191949i	−0.992098	+	0.125466i	$0.959958\pi$
$402$	33.2371	−	16.0062i	1.65772	−	0.798314i
$403$	−28.7082	+	35.9989i	−1.43006	+	1.79323i
$404$	1.34426	−	1.68565i	0.0668795	−	0.0838643i
$405$	−1.00608	+	4.40792i	−0.0499925	+	0.219031i
$406$	19.0887	−	9.19262i	0.947354	−	0.456222i
$407$	−1.83531	−	0.883837i	−0.0909727	−	0.0438102i
$408$	1.50218	−	6.58146i	0.0743688	−	0.325831i
$409$	−5.48978	+	24.0523i	−0.271452	+	1.18931i	0.636848	+	0.770989i	$0.280238\pi$
$409$	−5.48978	+	24.0523i	−0.271452	+	1.18931i	−0.908300	+	0.418319i	$0.862619\pi$
$410$	−4.94440	−	2.38110i	−0.244187	−	0.117594i
$411$	30.5515	−	14.7128i	1.50699	−	0.725729i
$412$	−1.93528	+	8.47900i	−0.0953443	+	0.417731i
$413$	18.0919	−	22.6866i	0.890247	−	1.11633i
$414$	17.1204	−	21.4684i	0.841424	−	1.05511i
$415$	8.60819	−	4.14549i	0.422559	−	0.203494i
$416$	−1.55013	−	6.79156i	−0.0760014	−	0.332984i
$417$	−23.9320	−	30.0097i	−1.17195	−	1.46958i
$418$	−0.453076	−	1.98505i	−0.0221606	−	0.0970922i
$419$	−32.2445	−	15.5281i	−1.57525	−	0.758598i	−0.576940	−	0.816786i	$-0.695753\pi$
$419$	−32.2445	−	15.5281i	−1.57525	−	0.758598i	−0.998306	+	0.0581878i	$0.981468\pi$
$420$	−4.72783	+	5.92851i	−0.230694	+	0.289282i
$421$	14.9879	+	7.21778i	0.730464	+	0.351773i	0.761867	−	0.647734i	$-0.224283\pi$
$421$	14.9879	+	7.21778i	0.730464	+	0.351773i	−0.0314025	+	0.999507i	$0.509997\pi$
$422$	−0.735577	−	0.922384i	−0.0358073	−	0.0449010i
$423$	11.1411			0.541699
$424$	10.5999			0.514778
$425$	−1.58028	−	1.98161i	−0.0766549	−	0.0961222i
$426$	−3.84942	+	1.85378i	−0.186505	+	0.0898161i
$427$	1.29764	−	5.68534i	0.0627973	−	0.275133i
$428$	−0.185294	−	0.811824i	−0.00895651	−	0.0392410i
$429$	8.42365			0.406698
$430$	4.16878	+	5.06175i	0.201036	+	0.244099i
$431$	−4.87263			−0.234706			−0.117353	−	0.993090i	$-0.537441\pi$
$431$	−4.87263			−0.234706			−0.117353	+	0.993090i	$0.537441\pi$
$432$	−0.648372	−	2.84070i	−0.0311948	−	0.136673i
$433$	9.14778	−	40.0790i	0.439614	−	1.92608i	0.0680075	−	0.997685i	$-0.478336\pi$
$433$	9.14778	−	40.0790i	0.439614	−	1.92608i	0.371607	−	0.928390i	$-0.378807\pi$
$434$	16.9542	−	8.16470i	0.813826	−	0.391918i
$435$	12.3581	+	15.4966i	0.592527	+	0.743005i
$436$	−6.49701			−0.311151
$437$	30.0803			1.43893
$438$	6.07342	+	7.61582i	0.290199	+	0.363898i
$439$	−9.92872	−	4.78142i	−0.473872	−	0.228205i	0.181676	−	0.983359i	$-0.441848\pi$
$439$	−9.92872	−	4.78142i	−0.473872	−	0.228205i	−0.655548	+	0.755154i	$0.727562\pi$
$440$	−0.283066	+	0.354954i	−0.0134946	+	0.0169217i
$441$	−4.07732	−	1.96354i	−0.194158	−	0.0935017i
$442$	3.92892	+	17.2137i	0.186880	+	0.818773i
$443$	17.3349	+	21.7373i	0.823606	+	1.03277i	0.998836	+	0.0482420i	$0.0153619\pi$
$443$	17.3349	+	21.7373i	0.823606	+	1.03277i	−0.175229	+	0.984528i	$0.556067\pi$
$444$	−2.65923	−	11.6509i	−0.126202	−	0.552925i
$445$	1.42929	−	0.688309i	0.0677548	−	0.0326290i
$446$	−7.52098	+	9.43101i	−0.356129	+	0.446571i
$447$	−33.5951	+	42.1270i	−1.58899	+	1.99254i
$448$	−0.633517	+	2.77562i	−0.0299309	+	0.131136i
$449$	−5.36278	+	2.58258i	−0.253085	+	0.121879i	−0.556125	−	0.831098i	$-0.687713\pi$
$449$	−5.36278	+	2.58258i	−0.253085	+	0.121879i	0.303040	+	0.952978i	$0.401998\pi$
$450$	−3.68855	−	1.77631i	−0.173880	−	0.0837361i
$451$	0.554413	−	2.42904i	0.0261063	−	0.114379i
$452$	−2.66952	+	11.6959i	−0.125563	+	0.550130i
$453$	30.6973	+	14.7831i	1.44229	+	0.694569i
$454$	14.0937	−	6.78715i	0.661449	−	0.318537i
$455$	4.41322	−	19.3356i	0.206895	−	0.906465i
$456$	7.44759	−	9.33898i	0.348765	−	0.437338i
$457$	0.532413	−	0.667625i	0.0249052	−	0.0312302i	−0.769223	−	0.638981i	$-0.779356\pi$
$457$	0.532413	−	0.667625i	0.0249052	−	0.0312302i	0.794128	+	0.607750i	$0.207928\pi$
$458$	17.1144	−	8.24186i	0.799704	−	0.385117i
$459$	1.64335	+	7.19998i	0.0767049	+	0.336066i
$460$	−4.18186	−	5.24389i	−0.194980	−	0.244497i
$461$	−0.679709	−	2.97800i	−0.0316572	−	0.138699i	0.956630	−	0.291307i	$-0.0940901\pi$
$461$	−0.679709	−	2.97800i	−0.0316572	−	0.138699i	−0.988287	+	0.152608i	$0.951233\pi$
$462$	−3.10170	−	1.49370i	−0.144304	−	0.0694933i
$463$	9.05240	−	11.3513i	0.420701	−	0.527542i	−0.525642	−	0.850706i	$-0.676175\pi$
$463$	9.05240	−	11.3513i	0.420701	−	0.527542i	0.946343	+	0.323164i	$0.104746\pi$
$464$	6.70484	+	3.22888i	0.311264	+	0.149897i
$465$	10.9762	+	13.7638i	0.509011	+	0.638280i
$466$	−15.3996			−0.713373
$467$	16.1158			0.745752			0.372876	−	0.927881i	$-0.378372\pi$
$467$	16.1158			0.745752			0.372876	+	0.927881i	$0.378372\pi$
$468$	17.7816	+	22.2975i	0.821957	+	1.03070i
$469$	35.5276	−	17.1092i	1.64051	−	0.790029i
$470$	0.605555	−	2.65311i	0.0279322	−	0.122379i
$471$	6.25603	+	27.4095i	0.288263	+	1.26296i
$472$	10.1922			0.469135
$473$	−1.81928	+	2.35655i	−0.0836505	+	0.108354i
$474$	−27.2347			−1.25093
$475$	−0.997958	−	4.37234i	−0.0457895	−	0.200617i
$476$	1.60570	−	7.03501i	0.0735969	−	0.322449i
$477$	−39.0983	+	18.8288i	−1.79019	+	0.862110i
$478$	−13.0883	−	16.4123i	−0.598647	−	0.750679i
$479$	−11.4126			−0.521455			−0.260728	−	0.965412i	$-0.583962\pi$
$479$	−11.4126			−0.521455			−0.260728	+	0.965412i	$0.583962\pi$
$480$	−2.66345			−0.121569
$481$	19.4880	+	24.4372i	0.888575	+	1.11424i
$482$	−14.4234	−	6.94596i	−0.656969	−	0.316380i
$483$	31.7104	−	39.7636i	1.44287	−	1.80931i
$484$	9.72495	+	4.68329i	0.442043	+	0.212877i
$485$	−2.07359	−	9.08499i	−0.0941569	−	0.412528i
$486$	−12.9583	−	16.2492i	−0.587800	−	0.737078i
$487$	−3.15094	−	13.8052i	−0.142783	−	0.625572i	−0.994781	−	0.102028i	$-0.967467\pi$
$487$	−3.15094	−	13.8052i	−0.142783	−	0.625572i	0.851999	−	0.523544i	$-0.175390\pi$
$488$	1.84547	−	0.888731i	0.0835405	−	0.0402310i
$489$	8.30740	−	10.4172i	0.375674	−	0.471080i
$490$	−0.689206	+	0.864237i	−0.0311352	+	0.0390423i
$491$	−0.0703170	+	0.308079i	−0.00317336	+	0.0139034i	−0.976490	−	0.215564i	$-0.930841\pi$
$491$	−0.0703170	+	0.308079i	−0.00317336	+	0.0139034i	0.973316	+	0.229467i	$0.0736983\pi$
$492$	13.1692	−	6.34194i	0.593712	−	0.285917i
$493$	−16.9939	−	8.18384i	−0.765367	−	0.368581i
$494$	−6.95199	+	30.4587i	−0.312785	+	1.37040i
$495$	0.413594	−	1.81208i	0.0185897	−	0.0814468i
$496$	5.95510	+	2.86783i	0.267392	+	0.128769i
$497$	−4.11470	+	1.98153i	−0.184569	+	0.0888839i
$498$	−5.66263	+	24.8096i	−0.253748	+	1.11174i
$499$	−4.64845	+	5.82897i	−0.208093	+	0.260940i	−0.874915	−	0.484277i	$-0.839083\pi$
$499$	−4.64845	+	5.82897i	−0.208093	+	0.260940i	0.666822	+	0.745217i	$0.267654\pi$
$500$	−0.623490	+	0.781831i	−0.0278833	+	0.0349646i
$501$	3.10093	−	1.49333i	0.138539	−	0.0667170i
$502$	−3.65147	−	15.9981i	−0.162973	−	0.714031i
$503$	−7.02870	−	8.81371i	−0.313394	−	0.392984i	0.600040	−	0.799970i	$-0.295151\pi$
$503$	−7.02870	−	8.81371i	−0.313394	−	0.392984i	−0.913434	+	0.406986i	$0.866580\pi$
$504$	−2.59360	−	11.3633i	−0.115528	−	0.506163i
$505$	1.94252	+	0.935466i	0.0864408	+	0.0416277i
$506$	1.89857	−	2.38074i	0.0844019	−	0.105837i
$507$	−85.2566	−	41.0574i	−3.78638	−	1.82342i
$508$	−7.60517	−	9.53659i	−0.337425	−	0.423118i
$509$	12.3895			0.549157			0.274578	−	0.961565i	$-0.411462\pi$
$509$	12.3895			0.549157			0.274578	+	0.961565i	$0.411462\pi$
$510$	6.75072			0.298927
$511$	6.49195	+	8.14065i	0.287187	+	0.360121i
$512$	−0.900969	+	0.433884i	−0.0398176	+	0.0191751i
$513$	−2.90781	+	12.7399i	−0.128383	+	0.562482i
$514$	−4.88686	−	21.4107i	−0.215550	−	0.944388i
$515$	−8.69706			−0.383238
$516$	−17.4633	+	0.275229i	−0.768777	+	0.0121163i
$517$	1.23549			0.0543370
$518$	−2.84249	−	12.4537i	−0.124892	−	0.547186i
$519$	−0.373037	+	1.63438i	−0.0163745	+	0.0717413i
$520$	6.27635	−	3.02253i	0.275236	−	0.132547i
$521$	18.6154	+	23.3430i	0.815556	+	1.02268i	0.999212	+	0.0396845i	$0.0126353\pi$
$521$	18.6154	+	23.3430i	0.815556	+	1.02268i	−0.183656	+	0.982991i	$0.558793\pi$
$522$	−30.4666			−1.33349
$523$	13.7490			0.601201			0.300600	−	0.953750i	$-0.402813\pi$
$523$	13.7490			0.601201			0.300600	+	0.953750i	$0.402813\pi$
$524$	12.4346	+	15.5925i	0.543209	+	0.681162i
$525$	−6.83191	−	3.29007i	−0.298169	−	0.143591i
$526$	−7.35837	+	9.22710i	−0.320840	+	0.402321i
$527$	−15.0937	−	7.26872i	−0.657490	−	0.316630i
$528$	−0.269075	−	1.17890i	−0.0117100	−	0.0513049i
$529$	13.7082	+	17.1896i	0.596010	+	0.747372i
$530$	2.35871	+	10.3342i	0.102456	+	0.448888i
$531$	−37.5945	+	18.1045i	−1.63146	+	0.785670i
$532$	7.96082	−	9.98256i	0.345145	−	0.432799i
$533$	−23.8358	+	29.8892i	−1.03244	+	1.29464i
$534$	−0.940212	+	4.11934i	−0.0406870	+	0.178261i
$535$	0.750239	−	0.361296i	0.0324356	−	0.0156202i
$536$	12.4790	+	6.00955i	0.539009	+	0.259573i
$537$	−1.50568	+	6.59680i	−0.0649747	+	0.284673i
$538$	−2.52117	+	11.0460i	−0.108695	+	0.476226i
$539$	−0.452156	−	0.217747i	−0.0194757	−	0.00937901i
$540$	2.62521	−	1.26423i	0.112971	−	0.0544039i
$541$	−8.36942	+	36.6688i	−0.359830	+	1.57652i	0.393787	+	0.919202i	$0.371165\pi$
$541$	−8.36942	+	36.6688i	−0.359830	+	1.57652i	−0.753617	+	0.657314i	$0.771692\pi$
$542$	−8.19766	+	10.2795i	−0.352120	+	0.441544i
$543$	26.8417	−	33.6585i	1.15189	−	1.44442i
$544$	2.28357	−	1.09971i	0.0979074	−	0.0471497i
$545$	−1.44572	−	6.33412i	−0.0619279	−	0.271324i
$546$	32.9351	+	41.2993i	1.40949	+	1.76745i
$547$	7.55939	+	33.1199i	0.323216	+	1.41610i	0.831793	+	0.555086i	$0.187315\pi$
$547$	7.55939	+	33.1199i	0.323216	+	1.41610i	−0.508577	+	0.861017i	$0.669828\pi$
$548$	11.4706	+	5.52396i	0.490001	+	0.235972i
$549$	−5.22844	+	6.55625i	−0.223144	+	0.279814i
$550$	−0.409042	−	0.196984i	−0.0174416	−	0.00839944i
$551$	−20.8089	−	26.0935i	−0.886489	−	1.11162i
$552$	17.8643			0.760353
$553$	−29.1116			−1.23795
$554$	0.278640	+	0.349404i	0.0118383	+	0.0148448i
$555$	10.7670	−	5.18512i	0.457034	−	0.220096i
$556$	3.20682	−	14.0500i	0.136000	−	0.595853i
$557$	5.25576	+	23.0270i	0.222694	+	0.975685i	0.955441	+	0.295184i	$0.0953808\pi$
$557$	5.25576	+	23.0270i	0.222694	+	0.975685i	−0.732747	+	0.680501i	$0.761762\pi$
$558$	−27.0598			−1.14553
$559$	40.8393	−	20.4662i	1.72732	−	0.865626i
$560$	−2.84700			−0.120308
$561$	0.681992	+	2.98800i	0.0287937	+	0.126154i
$562$	0.781307	−	3.42313i	0.0329574	−	0.144396i
$563$	−8.07293	+	3.88772i	−0.340233	+	0.163848i	−0.596196	−	0.802839i	$-0.703322\pi$
$563$	−8.07293	+	3.88772i	−0.340233	+	0.163848i	0.255963	+	0.966687i	$0.417608\pi$
$564$	4.51915	+	5.66684i	0.190291	+	0.238617i
$565$	−11.9967			−0.504705
$566$	24.6012			1.03406
$567$	−8.02560	−	10.0638i	−0.337044	−	0.422639i
$568$	−1.44528	−	0.696008i	−0.0606424	−	0.0292038i
$569$	−9.40358	+	11.7917i	−0.394218	+	0.494334i	−0.938843	−	0.344346i	$-0.888101\pi$
$569$	−9.40358	+	11.7917i	−0.394218	+	0.494334i	0.544624	+	0.838680i	$0.316672\pi$
$570$	10.7621	+	5.18274i	0.450774	+	0.217081i
$571$	−4.53288	−	19.8598i	−0.189695	−	0.831108i	−0.976777	−	0.214259i	$-0.931266\pi$
$571$	−4.53288	−	19.8598i	−0.189695	−	0.831108i	0.787082	−	0.616849i	$-0.211591\pi$
$572$	1.97190	+	2.47268i	0.0824493	+	0.103388i
$573$	−5.98973	−	26.2427i	−0.250224	−	1.09630i
$574$	14.0767	−	6.77898i	0.587550	−	0.282949i
$575$	4.18186	−	5.24389i	0.174396	−	0.218685i
$576$	2.55255	−	3.20080i	0.106356	−	0.133367i
$577$	5.67653	−	24.8705i	0.236317	−	1.03537i	−0.707968	−	0.706244i	$-0.750388\pi$
$577$	5.67653	−	24.8705i	0.236317	−	1.03537i	0.944285	−	0.329128i	$-0.106755\pi$
$578$	9.52858	−	4.58872i	0.396337	−	0.190866i
$579$	−16.7954	−	8.08824i	−0.697993	−	0.336136i
$580$	−1.65596	+	7.25523i	−0.0687599	+	0.301257i
$581$	−6.05285	+	26.5193i	−0.251115	+	1.10021i
$582$	22.3618	+	10.7689i	0.926927	+	0.446384i
$583$	−4.33582	+	2.08802i	−0.179571	+	0.0864770i
$584$	−0.813822	+	3.56559i	−0.0336762	+	0.147545i
$585$	−17.7816	+	22.2975i	−0.735181	+	0.921887i
$586$	9.77941	−	12.2630i	0.403984	−	0.506580i
$587$	10.4616	−	5.03803i	0.431795	−	0.207942i	−0.205345	−	0.978690i	$-0.565832\pi$
$587$	10.4616	−	5.03803i	0.431795	−	0.207942i	0.637140	+	0.770748i	$0.280117\pi$
$588$	−0.655142	−	2.87037i	−0.0270176	−	0.118372i
$589$	−18.4821	−	23.1758i	−0.761540	−	0.954941i
$590$	2.26798	+	9.93668i	0.0933713	+	0.409087i
$591$	55.5436	+	26.7484i	2.28476	+	1.10028i
$592$	2.79750	−	3.50795i	0.114976	−	0.144176i
$593$	25.6718	+	12.3629i	1.05421	+	0.507682i	0.878987	−	0.476846i	$-0.158220\pi$
$593$	25.6718	+	12.3629i	1.05421	+	0.507682i	0.175226	+	0.984528i	$0.443934\pi$
$594$	0.824786	+	1.03425i	0.0338414	+	0.0424357i
$595$	7.21593			0.295824
$596$	−20.2303			−0.828665
$597$	43.6781	+	54.7707i	1.78763	+	2.24161i
$598$	−42.0966	+	20.2727i	−1.72146	+	0.829010i
$599$	−5.50983	+	24.1402i	−0.225126	+	0.986340i	0.728429	+	0.685121i	$0.240251\pi$
$599$	−5.50983	+	24.1402i	−0.225126	+	0.986340i	−0.953555	+	0.301219i	$0.902606\pi$
$600$	−0.592674	−	2.59667i	−0.0241958	−	0.106009i
$601$	9.72742			0.396790			0.198395	−	0.980122i	$-0.436427\pi$
$601$	9.72742			0.396790			0.198395	+	0.980122i	$0.436427\pi$
$602$	−18.6667	+	0.294196i	−0.760798	+	0.0119905i
$603$	−56.7041			−2.30917
$604$	2.84654	+	12.4715i	0.115824	+	0.507458i
$605$	−2.40186	+	10.5233i	−0.0976497	+	0.427831i
$606$	−5.17380	+	2.49157i	−0.210171	+	0.101213i
$607$	−0.228167	−	0.286112i	−0.00926100	−	0.0116129i	0.777179	−	0.629279i	$-0.216650\pi$
$607$	−0.228167	−	0.286112i	−0.00926100	−	0.0116129i	−0.786440	+	0.617666i	$0.788078\pi$
$608$	4.48478			0.181882
$609$	−56.4301			−2.28666
$610$	1.27710	+	1.60144i	0.0517084	+	0.0648403i
$611$	−17.0801	−	8.22532i	−0.690985	−	0.332761i
$612$	−6.46964	+	8.11267i	−0.261520	+	0.327935i
$613$	−17.2992	−	8.33084i	−0.698707	−	0.336479i	0.0505848	−	0.998720i	$-0.483891\pi$
$613$	−17.2992	−	8.33084i	−0.698707	−	0.336479i	−0.749291	+	0.662240i	$0.769606\pi$
$614$	0.267642	+	1.17262i	0.0108012	+	0.0473230i
$615$	9.11335	+	11.4278i	0.367486	+	0.460813i
$616$	−0.287618	−	1.26014i	−0.0115885	−	0.0507724i
$617$	−4.27670	+	2.05955i	−0.172174	+	0.0829144i	−0.517985	−	0.855389i	$-0.673318\pi$
$617$	−4.27670	+	2.05955i	−0.172174	+	0.0829144i	0.345812	+	0.938304i	$0.387604\pi$
$618$	14.4426	−	18.1105i	0.580968	−	0.728511i
$619$	5.78293	−	7.25157i	0.232436	−	0.291465i	−0.651911	−	0.758295i	$-0.726033\pi$
$619$	5.78293	−	7.25157i	0.232436	−	0.291465i	0.884347	+	0.466830i	$0.154604\pi$
$620$	−1.47079	+	6.44395i	−0.0590683	+	0.258795i
$621$	−17.6077	+	8.47944i	−0.706574	+	0.340268i
$622$	19.0046	+	9.15212i	0.762014	+	0.366966i
$623$	−1.00500	+	4.40321i	−0.0402647	+	0.176411i
$624$	−4.12870	+	18.0890i	−0.165280	+	0.724140i
$625$	−0.900969	−	0.433884i	−0.0360388	−	0.0173553i
$626$	17.2164	−	8.29096i	0.688104	−	0.331374i
$627$	−1.20675	+	5.28710i	−0.0481928	+	0.211146i
$628$	−6.58131	+	8.25270i	−0.262623	+	0.329319i
$629$	−7.09047	+	8.89116i	−0.282715	+	0.354514i
$630$	10.5013	−	5.05715i	0.418381	−	0.201482i
$631$	−1.79552	−	7.86667i	−0.0714784	−	0.313167i	0.926532	−	0.376216i	$-0.122775\pi$
$631$	−1.79552	−	7.86667i	−0.0714784	−	0.313167i	−0.998010	+	0.0630485i	$0.979918\pi$
$632$	−6.37541	−	7.99451i	−0.253600	−	0.318004i
$633$	0.699221	+	3.06349i	0.0277915	+	0.121763i
$634$	−5.57280	−	2.68372i	−0.221324	−	0.106584i
$635$	7.60517	−	9.53659i	0.301802	−	0.378448i
$636$	−25.4365	−	12.2496i	−1.00862	−	0.485728i
$637$	4.80116	+	6.02047i	0.190229	+	0.238540i
$638$	−3.37860			−0.133760
$639$	6.56729			0.259798
$640$	−0.623490	−	0.781831i	−0.0246456	−	0.0309046i
$641$	−37.6788	+	18.1451i	−1.48822	+	0.716690i	−0.988741	−	0.149636i	$-0.952190\pi$
$641$	−37.6788	+	18.1451i	−1.48822	+	0.716690i	−0.499480	+	0.866325i	$0.666476\pi$
$642$	−0.493521	+	2.16226i	−0.0194777	+	0.0853374i
$643$	−10.5818	−	46.3618i	−0.417305	−	1.82833i	−0.547453	−	0.836836i	$-0.684403\pi$
$643$	−10.5818	−	46.3618i	−0.417305	−	1.82833i	0.130149	−	0.991494i	$-0.458454\pi$
$644$	19.0953			0.752462
$645$	−4.15427	−	16.9642i	−0.163574	−	0.667964i
$646$	−11.3670			−0.447229
$647$	−7.45786	−	32.6750i	−0.293199	−	1.28459i	−0.880046	−	0.474889i	$-0.842488\pi$
$647$	−7.45786	−	32.6750i	−0.293199	−	1.28459i	0.586847	−	0.809698i	$-0.300369\pi$
$648$	1.00608	−	4.40792i	0.0395225	−	0.173159i
$649$	−4.16905	+	2.00771i	−0.163649	+	0.0788094i
$650$	4.34337	+	5.44641i	0.170361	+	0.213626i
$651$	−50.1201			−1.96436
$652$	5.00254			0.195915
$653$	24.0070	+	30.1039i	0.939468	+	1.17806i	0.983842	+	0.179040i	$0.0572992\pi$
$653$	24.0070	+	30.1039i	0.939468	+	1.17806i	−0.0443741	+	0.999015i	$0.514129\pi$
$654$	15.5908	+	7.50814i	0.609649	+	0.293591i
$655$	−12.4346	+	15.5925i	−0.485861	+	0.609250i
$656$	4.94440	+	2.38110i	0.193046	+	0.0929662i
$657$	−3.33177	−	14.5974i	−0.129985	−	0.569501i
$658$	4.83058	+	6.05735i	0.188316	+	0.236140i
$659$	8.98812	+	39.3795i	0.350128	+	1.53401i	0.776885	+	0.629643i	$0.216799\pi$
$659$	8.98812	+	39.3795i	0.350128	+	1.53401i	−0.426757	+	0.904366i	$0.640344\pi$
$660$	1.08946	−	0.524658i	0.0424073	−	0.0204223i
$661$	−3.31097	+	4.15182i	−0.128782	+	0.161487i	−0.842042	−	0.539412i	$-0.818646\pi$
$661$	−3.31097	+	4.15182i	−0.128782	+	0.161487i	0.713260	+	0.700899i	$0.247218\pi$
$662$	−11.9571	+	14.9937i	−0.464724	+	0.582746i
$663$	10.4645	−	45.8479i	0.406407	−	1.78059i
$664$	−8.60819	+	4.14549i	−0.334063	+	0.160876i
$665$	11.5037	+	5.53990i	0.446095	+	0.214828i
$666$	−4.08749	+	17.9085i	−0.158387	+	0.693939i
$667$	11.1068	−	48.6621i	0.430057	−	1.88420i
$668$	1.16425	+	0.560674i	0.0450462	+	0.0216931i
$669$	28.9467	−	13.9400i	1.11915	−	0.538952i
$670$	−3.08205	+	13.5033i	−0.119070	+	0.521680i
$671$	−0.579809	+	0.727057i	−0.0223833	+	0.0280677i
$672$	4.72783	−	5.92851i	0.182380	−	0.228697i
$673$	−13.9842	+	6.73442i	−0.539050	+	0.259593i	−0.683539	−	0.729914i	$-0.739560\pi$
$673$	−13.9842	+	6.73442i	−0.539050	+	0.259593i	0.144490	+	0.989506i	$0.453846\pi$
$674$	1.68520	+	7.38333i	0.0649114	+	0.284395i
$675$	1.81670	+	2.27807i	0.0699248	+	0.0876829i
$676$	−7.90577	−	34.6374i	−0.304068	−	1.33221i
$677$	27.4525	+	13.2204i	1.05508	+	0.508102i	0.879271	−	0.476321i	$-0.158030\pi$
$677$	27.4525	+	13.2204i	1.05508	+	0.508102i	0.175814	+	0.984423i	$0.443744\pi$
$678$	19.9221	−	24.9816i	0.765105	−	0.959412i
$679$	23.9028	+	11.5110i	0.917306	+	0.441751i
$680$	1.58028	+	1.98161i	0.0606010	+	0.0759913i
$681$	−41.6638			−1.59656
$682$	−3.00080			−0.114907
$683$	10.4692	+	13.1280i	0.400593	+	0.502328i	0.940686	−	0.339277i	$-0.110182\pi$
$683$	10.4692	+	13.1280i	0.400593	+	0.502328i	−0.540093	+	0.841605i	$0.681611\pi$
$684$	−16.5423	+	7.96637i	−0.632512	+	0.304602i
$685$	−2.83301	+	12.4122i	−0.108244	+	0.474247i
$686$	3.73433	+	16.3612i	0.142577	+	0.624672i
$687$	−50.5938			−1.93027
$688$	−4.16878	−	5.06175i	−0.158933	−	0.192977i
$689$	73.8415			2.81314
$690$	3.97517	+	17.4164i	0.151332	+	0.663030i
$691$	8.48232	−	37.1635i	0.322683	−	1.41376i	−0.510076	−	0.860129i	$-0.670383\pi$
$691$	8.48232	−	37.1635i	0.322683	−	1.41376i	0.832759	−	0.553636i	$-0.186760\pi$
$692$	−0.567081	+	0.273092i	−0.0215572	+	0.0103814i
$693$	3.29929	+	4.13718i	0.125330	+	0.157158i
$694$	8.38455			0.318273
$695$	14.4113			0.546653
$696$	−12.3581	−	15.4966i	−0.468434	−	0.587397i
$697$	−12.5320	−	6.03507i	−0.474682	−	0.228595i
$698$	−20.4274	+	25.6152i	−0.773189	+	0.969549i
$699$	36.9542	+	17.7962i	1.39774	+	0.673115i
$700$	−0.633517	−	2.77562i	−0.0239447	−	0.104909i
$701$	11.5570	+	14.4921i	0.436503	+	0.547357i	0.950618	−	0.310364i	$-0.100451\pi$
$701$	11.5570	+	14.4921i	0.436503	+	0.547357i	−0.514115	+	0.857721i	$0.671879\pi$
$702$	−4.51670	−	19.7890i	−0.170472	−	0.746887i
$703$	−18.1297	+	8.73082i	−0.683776	+	0.329289i
$704$	0.283066	−	0.354954i	0.0106685	−	0.0133778i
$705$	−4.51915	+	5.66684i	−0.170201	+	0.213425i
$706$	0.491524	−	2.15351i	0.0184988	−	0.0810483i
$707$	−5.53034	+	2.66327i	−0.207990	+	0.100163i
$708$	−24.4581	−	11.7784i	−0.919193	−	0.442660i
$709$	8.82883	−	38.6816i	0.331574	−	1.45272i	−0.484510	−	0.874786i	$-0.661002\pi$
$709$	8.82883	−	38.6816i	0.331574	−	1.45272i	0.816084	−	0.577934i	$-0.196141\pi$
$710$	0.356954	−	1.56392i	0.0133962	−	0.0586927i
$711$	37.7167	+	18.1634i	1.41449	+	0.681181i
$712$	−1.42929	+	0.688309i	−0.0535648	+	0.0257955i
$713$	9.86485	−	43.2207i	0.369441	−	1.61863i
$714$	−11.9830	+	15.0262i	−0.448454	+	0.562343i
$715$	−1.97190	+	2.47268i	−0.0737449	+	0.0924731i
$716$	−2.28889	+	1.10227i	−0.0855400	+	0.0411939i
$717$	12.4415	+	54.5096i	0.464635	+	2.03570i
$718$	7.26383	+	9.10855i	0.271084	+	0.339928i
$719$	0.891278	+	3.90494i	0.0332391	+	0.145630i	0.988824	−	0.149085i	$-0.0476326\pi$
$719$	0.891278	+	3.90494i	0.0332391	+	0.145630i	−0.955585	+	0.294714i	$0.904776\pi$
$720$	3.68855	+	1.77631i	0.137464	+	0.0661992i
$721$	15.4379	−	19.3585i	0.574938	−	0.720950i
$722$	−1.00303	−	0.483033i	−0.0373289	−	0.0179766i
$723$	26.5848	+	33.3363i	0.988698	+	1.23979i
$724$	16.1635			0.600713
$725$	−7.44181			−0.276382
$726$	−17.9247	−	22.4769i	−0.665248	−	0.834195i
$727$	1.89052	−	0.910424i	0.0701153	−	0.0337658i	−0.398497	−	0.917169i	$-0.630468\pi$
$727$	1.89052	−	0.910424i	0.0701153	−	0.0337658i	0.468613	+	0.883404i	$0.344754\pi$
$728$	−4.41322	+	19.3356i	−0.163565	+	0.716624i
$729$	9.29959	+	40.7442i	0.344429	+	1.50904i
$730$	−3.65728			−0.135362
$731$	10.5661	+	12.8294i	0.390801	+	0.474512i
$732$	−5.45559			−0.201645
$733$	−2.09974	−	9.19956i	−0.0775556	−	0.339793i	0.921232	−	0.389013i	$-0.127184\pi$
$733$	−2.09974	−	9.19956i	−0.0775556	−	0.339793i	−0.998788	+	0.0492194i	$0.984327\pi$
$734$	6.09859	−	26.7197i	0.225103	−	0.986241i
$735$	2.65262	−	1.27743i	0.0978432	−	0.0471188i
$736$	4.18186	+	5.24389i	0.154145	+	0.193292i
$737$	−6.28821			−0.231629
$738$	−22.4672			−0.827030
$739$	4.03798	+	5.06347i	0.148539	+	0.186263i	0.850535	−	0.525919i	$-0.176279\pi$
$739$	4.03798	+	5.06347i	0.148539	+	0.186263i	−0.701995	+	0.712182i	$0.747707\pi$
$740$	4.04250	+	1.94677i	0.148605	+	0.0715645i
$741$	51.8815	−	65.0574i	1.90592	−	2.38994i
$742$	−27.1894	−	13.0937i	−0.998155	−	0.480686i
$743$	−0.655300	−	2.87106i	−0.0240406	−	0.105329i	0.961484	−	0.274860i	$-0.0886317\pi$
$743$	−0.655300	−	2.87106i	−0.0240406	−	0.105329i	−0.985525	+	0.169532i	$0.945775\pi$
$744$	−10.9762	−	13.7638i	−0.402409	−	0.504604i
$745$	−4.50166	−	19.7231i	−0.164928	−	0.722597i
$746$	9.65409	−	4.64917i	0.353462	−	0.170218i
$747$	24.3880	−	30.5816i	0.892312	−	1.11892i
$748$	−0.717452	+	0.899656i	−0.0262326	+	0.0328947i
$749$	−0.527531	+	2.31126i	−0.0192756	+	0.0844517i
$750$	2.39969	−	1.15563i	0.0876242	−	0.0421976i
$751$	42.2339	+	20.3388i	1.54114	+	0.742172i	0.995402	−	0.0957855i	$-0.0305363\pi$
$751$	42.2339	+	20.3388i	1.54114	+	0.742172i	0.545735	+	0.837958i	$0.316251\pi$
$752$	−0.605555	+	2.65311i	−0.0220823	+	0.0967489i
$753$	−9.72551	+	42.6103i	−0.354417	+	1.55280i
$754$	46.7074	+	22.4931i	1.70098	+	0.819150i
$755$	−11.5254	+	5.55034i	−0.419452	+	0.201997i
$756$	−1.84592	+	8.08748i	−0.0671353	+	0.294139i
$757$	5.60696	−	7.03090i	0.203788	−	0.255542i	−0.669426	−	0.742879i	$-0.733460\pi$
$757$	5.60696	−	7.03090i	0.203788	−	0.255542i	0.873214	+	0.487336i	$0.162031\pi$
$758$	−1.41155	+	1.77002i	−0.0512696	+	0.0642901i
$759$	−7.30724	+	3.51898i	−0.265236	+	0.127731i
$760$	0.997958	+	4.37234i	0.0361997	+	0.158601i
$761$	−30.3166	−	38.0158i	−1.09898	−	1.37807i	−0.918933	−	0.394414i	$-0.870948\pi$
$761$	−30.3166	−	38.0158i	−1.09898	−	1.37807i	−0.180044	−	0.983659i	$-0.557624\pi$
$762$	7.22929	+	31.6736i	0.261889	+	1.14741i
$763$	16.6652	+	8.02554i	0.603321	+	0.290544i
$764$	6.30116	−	7.90141i	0.227968	−	0.285863i
$765$	−9.34890	−	4.50219i	−0.338010	−	0.162777i
$766$	23.1991	+	29.0908i	0.838219	+	1.05109i
$767$	71.0012			2.56371
$768$	2.66345			0.0961091
$769$	15.0106	+	18.8228i	0.541298	+	0.678766i	0.974978	−	0.222301i	$-0.0713567\pi$
$769$	15.0106	+	18.8228i	0.541298	+	0.678766i	−0.433680	+	0.901067i	$0.642785\pi$
$770$	1.16454	−	0.560814i	0.0419672	−	0.0202103i
$771$	−13.0159	+	57.0265i	−0.468757	+	2.05376i
$772$	−1.55742	−	6.82352i	−0.0560529	−	0.245584i
$773$	−11.3067			−0.406674			−0.203337	−	0.979109i	$-0.565179\pi$
$773$	−11.3067			−0.406674			−0.203337	+	0.979109i	$0.565179\pi$
$774$	24.3680	+	11.2654i	0.875889	+	0.404928i
$775$	−6.60966			−0.237426
$776$	2.07359	+	9.08499i	0.0744376	+	0.326132i
$777$	−7.57083	+	33.1700i	−0.271602	+	1.18997i
$778$	−7.13128	+	3.43424i	−0.255669	+	0.123124i
$779$	−15.3453	−	19.2424i	−0.549801	−	0.689429i
$780$	−18.5542			−0.664347
$781$	0.728281			0.0260600
$782$	−10.5992	−	13.2910i	−0.379028	−	0.475286i
$783$	19.5363	+	9.40818i	0.698170	+	0.336221i
$784$	0.689206	−	0.864237i	0.0246145	−	0.0308656i
$785$	−9.51027	−	4.57990i	−0.339436	−	0.163464i
$786$	−11.8200	−	51.7870i	−0.421607	−	1.84718i
$787$	15.9131	+	19.9544i	0.567242	+	0.711298i	0.979878	−	0.199597i	$-0.0639634\pi$
$787$	15.9131	+	19.9544i	0.567242	+	0.711298i	−0.412636	+	0.910896i	$0.635392\pi$
$788$	5.15051	+	22.5659i	0.183479	+	0.803876i
$789$	28.3209	−	13.6386i	1.00825	−	0.485548i
$790$	6.37541	−	7.99451i	0.226827	−	0.284432i
$791$	21.2950	−	26.7031i	0.757164	−	0.949454i
$792$	−0.413594	+	1.81208i	−0.0146964	+	0.0643893i
$793$	12.8559	−	6.19110i	0.456528	−	0.219852i
$794$	−31.7936	−	15.3110i	−1.12831	−	0.543367i
$795$	6.28230	−	27.5246i	0.222810	−	0.976196i
$796$	−5.85276	+	25.6426i	−0.207446	+	0.908879i
$797$	−39.8550	−	19.1932i	−1.41174	−	0.679857i	−0.436232	−	0.899834i	$-0.643687\pi$
$797$	−39.8550	−	19.1932i	−1.41174	−	0.679857i	−0.975505	+	0.219977i	$0.929402\pi$
$798$	−30.6396	+	14.7553i	−1.08463	+	0.522331i
$799$	1.53482	−	6.72450i	0.0542982	−	0.237896i
$800$	0.623490	−	0.781831i	0.0220437	−	0.0276419i
$801$	4.04935	−	5.07772i	0.143077	−	0.179412i
$802$	−3.55219	+	1.71064i	−0.125432	+	0.0604049i
$803$	−0.369477	−	1.61879i	−0.0130386	−	0.0571257i
$804$	−23.0008	−	28.8421i	−0.811176	−	1.01718i
$805$	4.24911	+	18.6166i	0.149762	+	0.656148i
$806$	41.4845	+	19.9779i	1.46123	+	0.703692i
$807$	18.8151	−	23.5934i	0.662322	−	0.830525i
$808$	−1.94252	−	0.935466i	−0.0683374	−	0.0329096i
$809$	−13.5277	−	16.9633i	−0.475610	−	0.596396i	0.484925	−	0.874556i	$-0.338847\pi$
$809$	−13.5277	−	16.9633i	−0.475610	−	0.596396i	−0.960535	+	0.278160i	$0.910276\pi$
$810$	4.52128			0.158861
$811$	28.3915			0.996961			0.498481	−	0.866901i	$-0.333891\pi$
$811$	28.3915			0.996961			0.498481	+	0.866901i	$0.333891\pi$
$812$	−13.2098	−	16.5645i	−0.463572	−	0.581301i
$813$	31.5512	−	15.1942i	1.10655	−	0.532885i
$814$	−0.453283	+	1.98596i	−0.0158876	+	0.0696080i
$815$	1.11317	+	4.87712i	0.0389927	+	0.170838i
$816$	−6.75072			−0.236322
$817$	6.99505	+	28.5647i	0.244726	+	0.999351i
$818$	24.6708			0.862595
$819$	−18.0676	−	79.1594i	−0.631333	−	2.76605i
$820$	−1.22117	+	5.35028i	−0.0426450	+	0.186840i
$821$	−37.6370	+	18.1250i	−1.31354	+	0.632568i	−0.953788	−	0.300480i	$-0.902853\pi$
$821$	−37.6370	+	18.1250i	−1.31354	+	0.632568i	−0.359753	+	0.933048i	$0.617139\pi$
$822$	−21.1423	−	26.5116i	−0.737421	−	0.924697i
$823$	−15.2750			−0.532452			−0.266226	−	0.963911i	$-0.585777\pi$
$823$	−15.2750			−0.532452			−0.266226	+	0.963911i	$0.585777\pi$
$824$	8.69706			0.302976
$825$	0.753933	+	0.945402i	0.0262486	+	0.0329147i
$826$	−26.1436	−	12.5901i	−0.909653	−	0.438066i
$827$	−2.19887	+	2.75730i	−0.0764622	+	0.0958806i	−0.818591	−	0.574376i	$-0.805245\pi$
$827$	−2.19887	+	2.75730i	−0.0764622	+	0.0958806i	0.742129	+	0.670257i	$0.233816\pi$
$828$	−24.7398	−	11.9140i	−0.859766	−	0.414041i
$829$	−7.01852	−	30.7501i	−0.243763	−	1.06800i	−0.937560	−	0.347825i	$-0.886920\pi$
$829$	−7.01852	−	30.7501i	−0.243763	−	1.06800i	0.693796	−	0.720171i	$-0.255937\pi$
$830$	−5.95705	−	7.46991i	−0.206772	−	0.259284i
$831$	−0.264869	−	1.16047i	−0.00918819	−	0.0402561i
$832$	−6.27635	+	3.02253i	−0.217593	+	0.104787i
$833$	−1.74684	+	2.19047i	−0.0605246	+	0.0758954i
$834$	−23.9320	+	30.0097i	−0.828696	+	1.03915i
$835$	−0.287546	+	1.25982i	−0.00995095	+	0.0435980i
$836$	−1.83447	+	0.883432i	−0.0634463	+	0.0305541i
$837$	17.3517	+	8.35615i	0.599764	+	0.288831i
$838$	−7.96373	+	34.8914i	−0.275102	+	1.20530i
$839$	−2.61690	+	11.4654i	−0.0903454	+	0.395829i	−0.999801	−	0.0199730i	$-0.993642\pi$
$839$	−2.61690	+	11.4654i	−0.0903454	+	0.395829i	0.909455	+	0.415802i	$0.136499\pi$
$840$	6.83191	+	3.29007i	0.235723	+	0.113518i
$841$	−23.7680	+	11.4461i	−0.819587	+	0.394692i
$842$	3.70170	−	16.2182i	0.127569	−	0.558916i
$843$	−5.83076	+	7.31154i	−0.200822	+	0.251823i
$844$	−0.735577	+	0.922384i	−0.0253196	+	0.0317498i
$845$	32.0098	−	15.4151i	1.10117	−	0.530296i
$846$	−2.47913	−	10.8618i	−0.0852342	−	0.373435i
$847$	−19.1599	−	24.0258i	−0.658343	−	0.825537i
$848$	−2.35871	−	10.3342i	−0.0809983	−	0.354877i
$849$	−59.0351	−	28.4298i	−2.02608	−	0.975709i
$850$	−1.58028	+	1.98161i	−0.0542032	+	0.0679687i
$851$	−27.1138	−	13.0573i	−0.929449	−	0.447599i
$852$	2.66388	+	3.34040i	0.0912631	+	0.114440i
$853$	−28.1304			−0.963168			−0.481584	−	0.876400i	$-0.659938\pi$
$853$	−28.1304			−0.963168			−0.481584	+	0.876400i	$0.659938\pi$
$854$	−5.83155			−0.199552
$855$	−11.4476	−	14.3549i	−0.391501	−	0.490927i
$856$	−0.750239	+	0.361296i	−0.0256426	+	0.0123488i
$857$	−1.65598	+	7.25532i	−0.0565672	+	0.247837i	−0.995304	−	0.0967976i	$-0.969140\pi$
$857$	−1.65598	+	7.25532i	−0.0565672	+	0.247837i	0.938737	+	0.344635i	$0.111997\pi$
$858$	−1.87444	−	8.21245i	−0.0639923	−	0.280369i
$859$	−35.1375			−1.19887			−0.599437	−	0.800422i	$-0.704609\pi$
$859$	−35.1375			−1.19887			−0.599437	+	0.800422i	$0.704609\pi$
$860$	4.00720	−	5.19060i	0.136644	−	0.176998i
$861$	−41.6137			−1.41819
$862$	1.08426	+	4.75046i	0.0369301	+	0.161801i
$863$	0.276457	−	1.21124i	0.00941070	−	0.0412310i	−0.970005	−	0.243087i	$-0.921840\pi$
$863$	0.276457	−	1.21124i	0.00941070	−	0.0412310i	0.979415	+	0.201856i	$0.0646972\pi$
$864$	−2.62521	+	1.26423i	−0.0893113	+	0.0430101i
$865$	−0.392433	−	0.492095i	−0.0133431	−	0.0167317i
$866$	−41.1097			−1.39697
$867$	−28.1685			−0.956652
$868$	−11.7326	−	14.7123i	−0.398232	−	0.499367i
$869$	4.18260	+	2.01424i	0.141885	+	0.0683282i
$870$	12.3581	−	15.4966i	0.418980	−	0.525384i
$871$	86.9312	+	41.8639i	2.94555	+	1.41850i
$872$	1.44572	+	6.33412i	0.0489583	+	0.214500i
$873$	−23.7863	−	29.8271i	−0.805044	−	1.00949i
$874$	−6.69349	−	29.3261i	−0.226411	−	0.991969i
$875$	2.56506	−	1.23527i	0.0867148	−	0.0417596i
$876$	6.07342	−	7.61582i	0.205202	−	0.257315i
$877$	−21.6242	+	27.1158i	−0.730196	+	0.915637i	−0.998867	−	0.0475953i	$-0.984844\pi$
$877$	−21.6242	+	27.1158i	−0.730196	+	0.915637i	0.268671	+	0.963232i	$0.413416\pi$
$878$	−2.45219	+	10.7438i	−0.0827575	+	0.362584i
$879$	−37.6390	+	18.1260i	−1.26953	+	0.611374i
$880$	0.409042	+	0.196984i	0.0137888	+	0.00664034i
$881$	10.0398	−	43.9871i	0.338249	−	1.48196i	−0.464461	−	0.885594i	$-0.653752\pi$
$881$	10.0398	−	43.9871i	0.338249	−	1.48196i	0.802710	−	0.596370i	$-0.203391\pi$
$882$	−1.00702	+	4.41202i	−0.0339080	+	0.148561i
$883$	50.6946	+	24.4132i	1.70601	+	0.821570i	0.992685	+	0.120735i	$0.0385252\pi$
$883$	50.6946	+	24.4132i	1.70601	+	0.821570i	0.713324	+	0.700835i	$0.247189\pi$
$884$	15.9079	−	7.66083i	0.535040	−	0.257661i
$885$	6.04066	−	26.4659i	0.203055	−	0.889640i
$886$	17.3349	−	21.7373i	0.582378	−	0.730278i
$887$	−31.7638	+	39.8305i	−1.06652	+	1.33738i	−0.128150	+	0.991755i	$0.540904\pi$
$887$	−31.7638	+	39.8305i	−1.06652	+	1.33738i	−0.938373	+	0.345623i	$0.887668\pi$
$888$	−10.7670	+	5.18512i	−0.361317	+	0.174001i
$889$	7.72748	+	33.8563i	0.259171	+	1.13550i
$890$	−0.989098	−	1.24029i	−0.0331546	−	0.0415746i
$891$	0.456762	+	2.00121i	0.0153021	+	0.0670429i
$892$	10.8681	+	5.23381i	0.363892	+	0.175241i
$893$	7.60945	−	9.54195i	0.254641	−	0.319309i
$894$	48.5464	+	23.3787i	1.62363	+	0.781901i
$895$	−1.58396	−	1.98623i	−0.0529461	−	0.0663923i
$896$	2.84700			0.0951115
$897$	124.446			4.15514
$898$	3.71116	+	4.65364i	0.123843	+	0.155294i
$899$	−44.3167	+	21.3418i	−1.47805	+	0.711789i
$900$	−0.910996	+	3.99133i	−0.0303665	+	0.133044i
$901$	5.97832	+	26.1927i	0.199167	+	0.872606i
$902$	−2.49151			−0.0829581
$903$	45.1342	+	20.8658i	1.50197	+	0.694370i
$904$	11.9967			0.399004
$905$	3.59672	+	15.7583i	0.119559	+	0.523823i
$906$	7.58162	−	33.2172i	0.251882	−	1.10357i
$907$	36.0475	−	17.3595i	1.19694	−	0.576414i	0.274136	−	0.961691i	$-0.411608\pi$
$907$	36.0475	−	17.3595i	1.19694	−	0.576414i	0.922801	+	0.385277i	$0.125894\pi$
$908$	−9.75312	−	12.2300i	−0.323669	−	0.405868i
$909$	8.82674			0.292764
$910$	−19.8328			−0.657451
$911$	0.559132	+	0.701130i	0.0185249	+	0.0232295i	0.791008	−	0.611806i	$-0.209557\pi$
$911$	0.559132	+	0.701130i	0.0185249	+	0.0232295i	−0.772483	+	0.635036i	$0.780985\pi$
$912$	−10.7621	−	5.18274i	−0.356368	−	0.171618i
$913$	2.70452	−	3.39136i	0.0895065	−	0.112238i
$914$	−0.769359	−	0.370504i	−0.0254481	−	0.0122552i
$915$	−1.21398	−	5.31881i	−0.0401331	−	0.175834i
$916$	−11.8435	−	14.8513i	−0.391321	−	0.490702i
$917$	−12.6346	−	55.3558i	−0.417231	−	1.82801i
$918$	6.65378	−	3.20429i	0.219607	−	0.105757i
$919$	−9.09252	+	11.4017i	−0.299934	+	0.376106i	−0.908846	−	0.417132i	$-0.863035\pi$
$919$	−9.09252	+	11.4017i	−0.299934	+	0.376106i	0.608911	+	0.793238i	$0.291607\pi$
$920$	−4.18186	+	5.24389i	−0.137872	+	0.172886i
$921$	0.712853	−	3.12321i	0.0234893	−	0.102913i
$922$	−2.75208	+	1.32533i	−0.0906351	+	0.0436475i
$923$	−10.0681	−	4.84854i	−0.331396	−	0.159592i
$924$	−0.766058	+	3.35632i	−0.0252014	+	0.110415i
$925$	−0.998415	+	4.37434i	−0.0328277	+	0.143828i
$926$	−13.0811	−	6.29952i	−0.429871	−	0.207015i
$927$	−32.0795	+	15.4487i	−1.05363	+	0.507401i
$928$	1.65596	−	7.25523i	0.0543595	−	0.238164i
$929$	−7.98391	+	10.0115i	−0.261943	+	0.328467i	−0.895359	−	0.445345i	$-0.853081\pi$
$929$	−7.98391	+	10.0115i	−0.261943	+	0.328467i	0.633416	+	0.773812i	$0.281652\pi$
$930$	10.9762	−	13.7638i	0.359925	−	0.451332i
$931$	−4.46654	+	2.15097i	−0.146385	+	0.0704952i
$932$	3.42674	+	15.0135i	0.112246	+	0.491784i
$933$	−35.0286	−	43.9244i	−1.14678	−	1.43802i
$934$	−3.58611	−	15.7118i	−0.117341	−	0.514105i
$935$	−1.03675	−	0.499272i	−0.0339053	−	0.0163279i
$936$	17.7816	−	22.2975i	0.581211	−	0.728816i
$937$	15.2332	+	7.33590i	0.497646	+	0.239654i	0.665832	−	0.746102i	$-0.268077\pi$
$937$	15.2332	+	7.33590i	0.497646	+	0.239654i	−0.168186	+	0.985755i	$0.553791\pi$
$938$	−24.5859	−	30.8297i	−0.802757	−	1.00663i
$939$	−50.8952			−1.66090
$940$	−2.72134			−0.0887603
$941$	29.4471	+	36.9255i	0.959948	+	1.20374i	0.978988	+	0.203918i	$0.0653677\pi$
$941$	29.4471	+	36.9255i	0.959948	+	1.20374i	−0.0190396	+	0.999819i	$0.506061\pi$
$942$	25.3301	−	12.1984i	0.825301	−	0.397444i
$943$	8.19058	−	35.8853i	0.266722	−	1.16859i
$944$	−2.26798	−	9.93668i	−0.0738165	−	0.323411i
$945$	−8.29547			−0.269852
$946$	2.70229	+	1.24928i	0.0878591	+	0.0406177i
$947$	52.2996			1.69951			0.849754	−	0.527179i	$-0.176750\pi$
$947$	52.2996			1.69951			0.849754	+	0.527179i	$0.176750\pi$
$948$	6.06030	+	26.5519i	0.196829	+	0.862366i
$949$	−5.66927	+	24.8387i	−0.184032	+	0.806297i
$950$	−4.04065	+	1.94587i	−0.131096	+	0.0631325i
$951$	10.2716	+	12.8802i	0.333079	+	0.417668i
$952$	−7.21593			−0.233870
$953$	−29.1537			−0.944381			−0.472191	−	0.881496i	$-0.656537\pi$
$953$	−29.1537			−0.944381			−0.472191	+	0.881496i	$0.656537\pi$
$954$	27.0569	+	33.9283i	0.875999	+	1.09847i
$955$	9.10544	+	4.38495i	0.294645	+	0.141894i
$956$	−13.0883	+	16.4123i	−0.423307	+	0.530811i
$957$	8.10759	+	3.90441i	0.262081	+	0.126212i
$958$	2.53954	+	11.1265i	0.0820489	+	0.359480i
$959$	−22.5992	−	28.3386i	−0.729768	−	0.915100i
$960$	0.592674	+	2.59667i	0.0191285	+	0.0838073i
$961$	−11.4312	+	5.50497i	−0.368748	+	0.177580i
$962$	19.4880	−	24.4372i	0.628318	−	0.787886i
$963$	2.12552	−	2.66531i	0.0684938	−	0.0858885i
$964$	−3.56229	+	15.6074i	−0.114734	+	0.502681i
$965$	6.30588	−	3.03675i	0.202993	−	0.0977565i
$966$	−45.8228	−	22.0671i	−1.47433	−	0.709998i
$967$	10.6728	−	46.7606i	0.343214	−	1.50372i	−0.449030	−	0.893517i	$-0.648230\pi$
$967$	10.6728	−	46.7606i	0.343214	−	1.50372i	0.792244	−	0.610204i	$-0.208913\pi$
$968$	2.40186	−	10.5233i	0.0771989	−	0.338230i
$969$	27.2773	+	13.1361i	0.876273	+	0.421991i
$970$	−8.39580	+	4.04320i	−0.269573	+	0.129819i
$971$	−9.65975	+	42.3221i	−0.309996	+	1.35818i	0.544516	+	0.838751i	$0.316713\pi$
$971$	−9.65975	+	42.3221i	−0.309996	+	1.35818i	−0.854512	+	0.519431i	$0.826144\pi$
$972$	−12.9583	+	16.2492i	−0.415637	+	0.521193i
$973$	−25.5812	+	32.0778i	−0.820095	+	1.02837i
$974$	−12.7579	+	6.14388i	−0.408790	+	0.196863i
$975$	−4.12870	−	18.0890i	−0.132224	−	0.579312i
$976$	−1.27710	−	1.60144i	−0.0408791	−	0.0512608i
$977$	10.0069	+	43.8433i	0.320150	+	1.40267i	0.837285	+	0.546767i	$0.184142\pi$
$977$	10.0069	+	43.8433i	0.320150	+	1.40267i	−0.517134	+	0.855904i	$0.673001\pi$
$978$	−12.0045	−	5.78108i	−0.383863	−	0.184859i
$979$	0.449053	−	0.563095i	0.0143518	−	0.0179966i
$980$	0.995932	+	0.479615i	0.0318139	+	0.0153208i
$981$	−16.5840	−	20.7956i	−0.529486	−	0.663954i
$982$	0.316002			0.0100840
$983$	13.3763			0.426636			0.213318	−	0.976983i	$-0.431573\pi$
$983$	13.3763			0.426636			0.213318	+	0.976983i	$0.431573\pi$
$984$	−9.11335	−	11.4278i	−0.290523	−	0.364304i
$985$	−20.8540	+	10.0428i	−0.664464	+	0.319989i
$986$	−4.19715	+	18.3889i	−0.133664	+	0.585622i
$987$	−4.59183	−	20.1181i	−0.146159	−	0.640367i
$988$	31.2420			0.993940
$989$	−26.8770	+	34.8143i	−0.854639	+	1.10703i
$990$	−1.85868			−0.0590726
$991$	−13.4170	−	58.7838i	−0.426206	−	1.86733i	−0.493737	−	0.869611i	$-0.664369\pi$
$991$	−13.4170	−	58.7838i	−0.426206	−	1.86733i	0.0675315	−	0.997717i	$-0.478488\pi$
$992$	1.47079	−	6.44395i	0.0466976	−	0.204596i
$993$	46.0203	−	22.1622i	1.46041	−	0.703297i
$994$	2.84746	+	3.57060i	0.0903159	+	0.113253i
$995$	−26.3021			−0.833832
$996$	25.4476			0.806338
$997$	−27.2211	−	34.1342i	−0.862101	−	1.08104i	−0.995938	−	0.0900371i	$-0.971301\pi$
$997$	−27.2211	−	34.1342i	−0.862101	−	1.08104i	0.133838	−	0.991003i	$-0.457270\pi$
$998$	6.71720	+	3.23483i	0.212629	+	0.102397i
$999$	8.15123	−	10.2213i	0.257894	−	0.323388i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.k.b.231.1	yes	18
43.35	even	7	inner	430.2.k.b.121.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.k.b.121.1	✓	18	43.35	even	7	inner
430.2.k.b.231.1	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 - 0.974928i) q^{2} +(-0.592674 + 2.59667i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-0.623490 - 0.781831i) q^{5} +2.66345 q^{6} +2.84700 q^{7} +(0.623490 + 0.781831i) q^{8} +(-3.68855 - 1.77631i) q^{9} +O(q^{10})\)	\(q+(-0.222521 - 0.974928i) q^{2} +(-0.592674 + 2.59667i) q^{3} +(-0.900969 + 0.433884i) q^{4} +(-0.623490 - 0.781831i) q^{5} +2.66345 q^{6} +2.84700 q^{7} +(0.623490 + 0.781831i) q^{8} +(-3.68855 - 1.77631i) q^{9} +(-0.623490 + 0.781831i) q^{10} +(-0.409042 - 0.196984i) q^{11} +(-0.592674 - 2.59667i) q^{12} +(4.34337 + 5.44641i) q^{13} +(-0.633517 - 2.77562i) q^{14} +(2.39969 - 1.15563i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-1.58028 + 1.98161i) q^{17} +(-0.910996 + 3.99133i) q^{18} +(-4.04065 + 1.94587i) q^{19} +(0.900969 + 0.433884i) q^{20} +(-1.68734 + 7.39273i) q^{21} +(-0.101025 + 0.442620i) q^{22} +(-6.04296 - 2.91014i) q^{23} +(-2.39969 + 1.15563i) q^{24} +(-0.222521 + 0.974928i) q^{25} +(4.34337 - 5.44641i) q^{26} +(1.81670 - 2.27807i) q^{27} +(-2.56506 + 1.23527i) q^{28} +(1.65596 + 7.25523i) q^{29} +(-1.66064 - 2.08237i) q^{30} +(1.47079 + 6.44395i) q^{31} +(-0.900969 - 0.433884i) q^{32} +(0.753933 - 0.945402i) q^{33} +(2.28357 + 1.09971i) q^{34} +(-1.77507 - 2.22587i) q^{35} +4.09398 q^{36} +4.48684 q^{37} +(2.79622 + 3.50634i) q^{38} +(-16.7167 + 8.05036i) q^{39} +(0.222521 - 0.974928i) q^{40} +(1.22117 + 5.35028i) q^{41} +7.58284 q^{42} +(1.35824 - 6.41523i) q^{43} +0.454003 q^{44} +(0.910996 + 3.99133i) q^{45} +(-1.49249 + 6.53902i) q^{46} +(-2.45184 + 1.18074i) q^{47} +(1.66064 + 2.08237i) q^{48} +1.10540 q^{49} +1.00000 q^{50} +(-4.20900 - 5.27792i) q^{51} +(-6.27635 - 3.02253i) q^{52} +(6.60895 - 8.28736i) q^{53} +(-2.62521 - 1.26423i) q^{54} +(0.101025 + 0.442620i) q^{55} +(1.77507 + 2.22587i) q^{56} +(-2.65801 - 11.6455i) q^{57} +(6.70484 - 3.22888i) q^{58} +(6.35474 - 7.96860i) q^{59} +(-1.66064 + 2.08237i) q^{60} +(0.455793 - 1.99696i) q^{61} +(5.95510 - 2.86783i) q^{62} +(-10.5013 - 5.05715i) q^{63} +(-0.222521 + 0.974928i) q^{64} +(1.55013 - 6.79156i) q^{65} +(-1.08946 - 0.524658i) q^{66} +(12.4790 - 6.00955i) q^{67} +(0.563996 - 2.47103i) q^{68} +(11.1382 - 13.9668i) q^{69} +(-1.77507 + 2.22587i) q^{70} +(-1.44528 + 0.696008i) q^{71} +(-0.910996 - 3.99133i) q^{72} +(2.28028 + 2.85938i) q^{73} +(-0.998415 - 4.37434i) q^{74} +(-2.39969 - 1.15563i) q^{75} +(2.79622 - 3.50634i) q^{76} +(-1.16454 - 0.560814i) q^{77} +(11.5683 + 14.5063i) q^{78} -10.2254 q^{79} -1.00000 q^{80} +(-2.81897 - 3.53488i) q^{81} +(4.94440 - 2.38110i) q^{82} +(-2.12605 + 9.31482i) q^{83} +(-1.68734 - 7.39273i) q^{84} +2.53457 q^{85} +(-6.55662 + 0.103336i) q^{86} -19.8209 q^{87} +(-0.101025 - 0.442620i) q^{88} +(-0.353005 + 1.54662i) q^{89} +(3.68855 - 1.77631i) q^{90} +(12.3656 + 15.5059i) q^{91} +6.70718 q^{92} -17.6045 q^{93} +(1.69673 + 2.12763i) q^{94} +(4.04065 + 1.94587i) q^{95} +(1.66064 - 2.08237i) q^{96} +(8.39580 + 4.04320i) q^{97} +(-0.245975 - 1.07769i) q^{98} +(1.15887 + 1.45317i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9}+O(q^{10}) \) 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9	\( 18 q - 3 q^{2} + 2 q^{3} - 3 q^{4} + 3 q^{5} + 2 q^{6} + 6 q^{7} - 3 q^{8} - 7 q^{9} + 3 q^{10} + 9 q^{11} + 2 q^{12} + 4 q^{13} + 13 q^{14} + 5 q^{15} - 3 q^{16} - q^{17} + 7 q^{18} - 2 q^{19} + 3 q^{20} - 2 q^{21} - 12 q^{22} - 19 q^{23} - 5 q^{24} - 3 q^{25} + 4 q^{26} + 17 q^{27} - q^{28} - 4 q^{29} - 2 q^{30} - 13 q^{31} - 3 q^{32} - 42 q^{33} - 8 q^{34} + 15 q^{35} + 2 q^{37} + 12 q^{38} - 39 q^{39} + 3 q^{40} - 4 q^{41} - 2 q^{42} - 13 q^{43} - 12 q^{44} - 7 q^{45} + 16 q^{46} + 16 q^{47} + 2 q^{48} + 4 q^{49} + 18 q^{50} + 7 q^{51} - 10 q^{52} + 14 q^{53} - 4 q^{54} + 12 q^{55} - 15 q^{56} + 45 q^{57} + 24 q^{58} - 16 q^{59} - 2 q^{60} + 24 q^{61} + 50 q^{62} - 33 q^{63} - 3 q^{64} - 4 q^{65} + 5 q^{67} + 13 q^{68} + 4 q^{69} + 15 q^{70} - 3 q^{71} + 7 q^{72} - 22 q^{73} - 12 q^{74} - 5 q^{75} + 12 q^{76} - 24 q^{77} + 31 q^{78} - 38 q^{79} - 18 q^{80} + 22 q^{81} - 11 q^{82} - 26 q^{83} - 2 q^{84} + 8 q^{85} - 41 q^{86} - 22 q^{87} - 12 q^{88} + 52 q^{89} + 7 q^{90} - 14 q^{91} + 2 q^{92} - 6 q^{93} + 2 q^{94} + 2 q^{95} + 2 q^{96} + 27 q^{97} + 32 q^{98} + 36 q^{99}+O(q^{100}) \) 18 * q - 3 * q^2 + 2 * q^3 - 3 * q^4 + 3 * q^5 + 2 * q^6 + 6 * q^7 - 3 * q^8 - 7 * q^9 + 3 * q^10 + 9 * q^11 + 2 * q^12 + 4 * q^13 + 13 * q^14 + 5 * q^15 - 3 * q^16 - q^17 + 7 * q^18 - 2 * q^19 + 3 * q^20 - 2 * q^21 - 12 * q^22 - 19 * q^23 - 5 * q^24 - 3 * q^25 + 4 * q^26 + 17 * q^27 - q^28 - 4 * q^29 - 2 * q^30 - 13 * q^31 - 3 * q^32 - 42 * q^33 - 8 * q^34 + 15 * q^35 + 2 * q^37 + 12 * q^38 - 39 * q^39 + 3 * q^40 - 4 * q^41 - 2 * q^42 - 13 * q^43 - 12 * q^44 - 7 * q^45 + 16 * q^46 + 16 * q^47 + 2 * q^48 + 4 * q^49 + 18 * q^50 + 7 * q^51 - 10 * q^52 + 14 * q^53 - 4 * q^54 + 12 * q^55 - 15 * q^56 + 45 * q^57 + 24 * q^58 - 16 * q^59 - 2 * q^60 + 24 * q^61 + 50 * q^62 - 33 * q^63 - 3 * q^64 - 4 * q^65 + 5 * q^67 + 13 * q^68 + 4 * q^69 + 15 * q^70 - 3 * q^71 + 7 * q^72 - 22 * q^73 - 12 * q^74 - 5 * q^75 + 12 * q^76 - 24 * q^77 + 31 * q^78 - 38 * q^79 - 18 * q^80 + 22 * q^81 - 11 * q^82 - 26 * q^83 - 2 * q^84 + 8 * q^85 - 41 * q^86 - 22 * q^87 - 12 * q^88 + 52 * q^89 + 7 * q^90 - 14 * q^91 + 2 * q^92 - 6 * q^93 + 2 * q^94 + 2 * q^95 + 2 * q^96 + 27 * q^97 + 32 * q^98 + 36 * q^99

Introduction

L-functions

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