LMFDB - Embedded newform 230.2.g.d.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,2,Mod(31,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(22))

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

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

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

chi := DirichletCharacter("230.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	230.g (of order $11$, degree $10$, 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:	$1.83655924649$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	230.81
Dual form			230.2.g.d.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 - 0.540641i) q^{2} +(0.219067 - 1.52364i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.639452 - 1.40020i) q^{6} +(2.43457 + 2.80964i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(0.604987 + 0.177640i) q^{9} +O(q^{10})$	\(q+(0.841254 - 0.540641i) q^{2} +(0.219067 - 1.52364i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.639452 - 1.40020i) q^{6} +(2.43457 + 2.80964i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(0.604987 + 0.177640i) q^{9} +(0.654861 - 0.755750i) q^{10} +(-4.65177 - 2.98951i) q^{11} +(-1.29495 - 0.832213i) q^{12} +(-1.67820 + 1.93674i) q^{13} +(3.56709 + 1.04739i) q^{14} +(-0.219067 - 1.52364i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-2.39530 - 5.24499i) q^{17} +(0.604987 - 0.177640i) q^{18} +(-1.51918 + 3.32653i) q^{19} +(0.142315 - 0.989821i) q^{20} +(4.81421 - 3.09391i) q^{21} -5.52957 q^{22} +(-2.11449 + 4.30452i) q^{23} -1.53931 q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.364707 + 2.53659i) q^{26} +(2.32155 - 5.08348i) q^{27} +(3.56709 - 1.04739i) q^{28} +(3.55230 + 7.77845i) q^{29} +(-1.00803 - 1.16333i) q^{30} +(1.31556 + 9.14993i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-5.57399 + 6.43273i) q^{33} +(-4.85071 - 3.11736i) q^{34} +(3.12752 + 2.00993i) q^{35} +(0.412908 - 0.476521i) q^{36} +(-0.470298 - 0.138092i) q^{37} +(0.520446 + 3.61978i) q^{38} +(2.58326 + 2.98124i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(10.9326 - 3.21011i) q^{41} +(2.37728 - 5.20552i) q^{42} +(1.28674 - 8.94946i) q^{43} +(-4.65177 + 2.98951i) q^{44} +0.630528 q^{45} +(0.548378 + 4.76438i) q^{46} -9.73542 q^{47} +(-1.29495 + 0.832213i) q^{48} +(-0.970757 + 6.75176i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-8.51621 + 2.50058i) q^{51} +(1.06457 + 2.33109i) q^{52} +(-0.540177 - 0.623397i) q^{53} +(-0.795327 - 5.53162i) q^{54} +(-5.30559 - 1.55786i) q^{55} +(2.43457 - 2.80964i) q^{56} +(4.73564 + 3.04341i) q^{57} +(7.19373 + 4.62313i) q^{58} +(-1.36676 + 1.57733i) q^{59} +(-1.47696 - 0.433673i) q^{60} +(-1.34732 - 9.37080i) q^{61} +(6.05355 + 6.98617i) q^{62} +(0.973776 + 2.13227i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-1.06457 + 2.33109i) q^{65} +(-1.21134 + 8.42508i) q^{66} +(-0.964698 + 0.619974i) q^{67} -5.76605 q^{68} +(6.09534 + 4.16470i) q^{69} +3.71769 q^{70} +(2.41244 - 1.55038i) q^{71} +(0.0897335 - 0.624110i) q^{72} +(-1.33751 + 2.92873i) q^{73} +(-0.470298 + 0.138092i) q^{74} +(-0.639452 - 1.40020i) q^{75} +(2.39483 + 2.76378i) q^{76} +(-2.92560 - 20.3480i) q^{77} +(3.78496 + 1.11136i) q^{78} +(-4.55111 + 5.25227i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(-5.64553 - 3.62816i) q^{81} +(7.46159 - 8.61113i) q^{82} +(-9.46528 - 2.77926i) q^{83} +(-0.814421 - 5.66442i) q^{84} +(-3.77596 - 4.35769i) q^{85} +(-3.75597 - 8.22443i) q^{86} +(12.6298 - 3.70843i) q^{87} +(-2.29707 + 5.02988i) q^{88} +(-0.510160 + 3.54824i) q^{89} +(0.530434 - 0.340889i) q^{90} -9.52722 q^{91} +(3.03714 + 3.71157i) q^{92} +14.2294 q^{93} +(-8.18995 + 5.26336i) q^{94} +(-0.520446 + 3.61978i) q^{95} +(-0.639452 + 1.40020i) q^{96} +(-2.45368 + 0.720465i) q^{97} +(2.83363 + 6.20477i) q^{98} +(-2.28320 - 2.63496i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) $ 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{10}{11}\right)$

Coefficient data

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

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

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

$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$2$	0.841254	−	0.540641i	0.594856	−	0.382291i
$3$	0.219067	−	1.52364i	0.126478	−	0.879675i	−0.823491	−	0.567330i	$-0.807976\pi$
$3$	0.219067	−	1.52364i	0.126478	−	0.879675i	0.949969	−	0.312345i	$-0.101114\pi$
$4$	0.415415	−	0.909632i	0.207708	−	0.454816i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$5$	0.959493	−	0.281733i	0.429098	−	0.125995i
$6$	−0.639452	−	1.40020i	−0.261055	−	0.571631i
$7$	2.43457	+	2.80964i	0.920180	+	1.06194i	0.997887	+	0.0649679i	$0.0206945\pi$
$7$	2.43457	+	2.80964i	0.920180	+	1.06194i	−0.0777076	+	0.996976i	$0.524760\pi$
$8$	−0.142315	−	0.989821i	−0.0503159	−	0.349955i
$9$	0.604987	+	0.177640i	0.201662	+	0.0592134i
$10$	0.654861	−	0.755750i	0.207085	−	0.238989i
$11$	−4.65177	−	2.98951i	−1.40256	−	0.901372i	−0.402660	−	0.915350i	$-0.631914\pi$
$11$	−4.65177	−	2.98951i	−1.40256	−	0.901372i	−0.999902	+	0.0139778i	$0.995551\pi$
$12$	−1.29495	−	0.832213i	−0.373820	−	0.240239i
$13$	−1.67820	+	1.93674i	−0.465448	+	0.537155i	−0.939140	−	0.343535i	$-0.888376\pi$
$13$	−1.67820	+	1.93674i	−0.465448	+	0.537155i	0.473692	+	0.880691i	$0.342921\pi$
$14$	3.56709	+	1.04739i	0.953346	+	0.279928i
$15$	−0.219067	−	1.52364i	−0.0565627	−	0.393402i
$16$	−0.654861	−	0.755750i	−0.163715	−	0.188937i
$17$	−2.39530	−	5.24499i	−0.580947	−	1.27210i	−0.940760	−	0.339072i	$-0.889887\pi$
$17$	−2.39530	−	5.24499i	−0.580947	−	1.27210i	0.359814	−	0.933024i	$-0.382840\pi$
$18$	0.604987	−	0.177640i	0.142597	−	0.0418702i
$19$	−1.51918	+	3.32653i	−0.348523	+	0.763158i	0.651467	+	0.758677i	$0.274154\pi$
$19$	−1.51918	+	3.32653i	−0.348523	+	0.763158i	−0.999990	+	0.00448153i	$0.998573\pi$
$20$	0.142315	−	0.989821i	0.0318226	−	0.221331i
$21$	4.81421	−	3.09391i	1.05055	−	0.675146i
$22$	−5.52957			−1.17891
$23$	−2.11449	+	4.30452i	−0.440902	+	0.897555i
$23$	−2.11449	+	4.30452i	−0.440902	+	0.897555i
$24$	−1.53931			−0.314210
$25$	0.841254	−	0.540641i	0.168251	−	0.108128i
$26$	−0.364707	+	2.53659i	−0.0715249	+	0.497466i
$27$	2.32155	−	5.08348i	0.446782	−	0.978317i
$28$	3.56709	−	1.04739i	0.674117	−	0.197939i
$29$	3.55230	+	7.77845i	0.659645	+	1.44442i	0.882852	+	0.469650i	$0.155620\pi$
$29$	3.55230	+	7.77845i	0.659645	+	1.44442i	−0.223207	+	0.974771i	$0.571653\pi$
$30$	−1.00803	−	1.16333i	−0.184041	−	0.212394i
$31$	1.31556	+	9.14993i	0.236282	+	1.64338i	0.670024	+	0.742339i	$0.266284\pi$
$31$	1.31556	+	9.14993i	0.236282	+	1.64338i	−0.433742	+	0.901037i	$0.642807\pi$
$32$	−0.959493	−	0.281733i	−0.169616	−	0.0498038i
$33$	−5.57399	+	6.43273i	−0.970307	+	1.11979i
$34$	−4.85071	−	3.11736i	−0.831890	−	0.534623i
$35$	3.12752	+	2.00993i	0.528647	+	0.339741i
$36$	0.412908	−	0.476521i	0.0688180	−	0.0794202i
$37$	−0.470298	−	0.138092i	−0.0773164	−	0.0227022i	0.242846	−	0.970065i	$-0.421919\pi$
$37$	−0.470298	−	0.138092i	−0.0773164	−	0.0227022i	−0.320162	+	0.947363i	$0.603737\pi$
$38$	0.520446	+	3.61978i	0.0844275	+	0.587206i
$39$	2.58326	+	2.98124i	0.413653	+	0.477381i
$40$	−0.415415	−	0.909632i	−0.0656829	−	0.143825i
$41$	10.9326	−	3.21011i	1.70739	−	0.501334i	0.725089	−	0.688655i	$-0.241798\pi$
$41$	10.9326	−	3.21011i	1.70739	−	0.501334i	0.982299	+	0.187320i	$0.0599803\pi$
$42$	2.37728	−	5.20552i	0.366823	−	0.803229i
$43$	1.28674	−	8.94946i	0.196226	−	1.36478i	−0.618888	−	0.785479i	$-0.712417\pi$
$43$	1.28674	−	8.94946i	0.196226	−	1.36478i	0.815114	−	0.579301i	$-0.196674\pi$
$44$	−4.65177	+	2.98951i	−0.701281	+	0.450686i
$45$	0.630528			0.0939935
$46$	0.548378	+	4.76438i	0.0808539	+	0.702469i
$47$	−9.73542			−1.42006			−0.710028	−	0.704173i	$-0.751318\pi$
$47$	−9.73542			−1.42006			−0.710028	+	0.704173i	$0.751318\pi$
$48$	−1.29495	+	0.832213i	−0.186910	+	0.120120i
$49$	−0.970757	+	6.75176i	−0.138680	+	0.964537i
$50$	0.415415	−	0.909632i	0.0587486	−	0.128641i
$51$	−8.51621	+	2.50058i	−1.19251	+	0.350152i
$52$	1.06457	+	2.33109i	0.147630	+	0.323264i
$53$	−0.540177	−	0.623397i	−0.0741990	−	0.0856302i	0.717436	−	0.696624i	$-0.245315\pi$
$53$	−0.540177	−	0.623397i	−0.0741990	−	0.0856302i	−0.791635	+	0.610994i	$0.790770\pi$
$54$	−0.795327	−	5.53162i	−0.108230	−	0.752758i
$55$	−5.30559	−	1.55786i	−0.715405	−	0.210062i
$56$	2.43457	−	2.80964i	0.325333	−	0.375454i
$57$	4.73564	+	3.04341i	0.627250	+	0.403109i
$58$	7.19373	+	4.62313i	0.944583	+	0.607047i
$59$	−1.36676	+	1.57733i	−0.177937	+	0.205350i	−0.837711	−	0.546114i	$-0.816107\pi$
$59$	−1.36676	+	1.57733i	−0.177937	+	0.205350i	0.659774	+	0.751464i	$0.270652\pi$
$60$	−1.47696	−	0.433673i	−0.190674	−	0.0559870i
$61$	−1.34732	−	9.37080i	−0.172506	−	1.19981i	−0.873566	−	0.486705i	$-0.838199\pi$
$61$	−1.34732	−	9.37080i	−0.172506	−	1.19981i	0.701060	−	0.713102i	$-0.252711\pi$
$62$	6.05355	+	6.98617i	0.768801	+	0.887244i
$63$	0.973776	+	2.13227i	0.122684	+	0.268641i
$64$	−0.959493	+	0.281733i	−0.119937	+	0.0352166i
$65$	−1.06457	+	2.33109i	−0.132044	+	0.289136i
$66$	−1.21134	+	8.42508i	−0.149106	+	1.03706i
$67$	−0.964698	+	0.619974i	−0.117857	+	0.0757418i	−0.598241	−	0.801316i	$-0.704133\pi$
$67$	−0.964698	+	0.619974i	−0.117857	+	0.0757418i	0.480385	+	0.877058i	$0.340497\pi$
$68$	−5.76605			−0.699237
$69$	6.09534	+	4.16470i	0.733792	+	0.501371i
$70$	3.71769			0.444349
$71$	2.41244	−	1.55038i	0.286304	−	0.183996i	−0.389604	−	0.920983i	$-0.627388\pi$
$71$	2.41244	−	1.55038i	0.286304	−	0.183996i	0.675908	+	0.736986i	$0.263752\pi$
$72$	0.0897335	−	0.624110i	0.0105752	−	0.0735521i
$73$	−1.33751	+	2.92873i	−0.156543	+	0.342782i	−0.971611	−	0.236584i	$-0.923972\pi$
$73$	−1.33751	+	2.92873i	−0.156543	+	0.342782i	0.815068	+	0.579365i	$0.196700\pi$
$74$	−0.470298	+	0.138092i	−0.0546710	+	0.0160528i
$75$	−0.639452	−	1.40020i	−0.0738376	−	0.161682i
$76$	2.39483	+	2.76378i	0.274706	+	0.317027i
$77$	−2.92560	−	20.3480i	−0.333403	−	2.31887i
$78$	3.78496	+	1.11136i	0.428562	+	0.125837i
$79$	−4.55111	+	5.25227i	−0.512040	+	0.590926i	−0.951620	−	0.307278i	$-0.900582\pi$
$79$	−4.55111	+	5.25227i	−0.512040	+	0.590926i	0.439580	+	0.898204i	$0.355127\pi$
$80$	−0.841254	−	0.540641i	−0.0940550	−	0.0604455i
$81$	−5.64553	−	3.62816i	−0.627281	−	0.403129i
$82$	7.46159	−	8.61113i	0.823995	−	0.950941i
$83$	−9.46528	−	2.77926i	−1.03895	−	0.305063i	−0.282605	−	0.959236i	$-0.591199\pi$
$83$	−9.46528	−	2.77926i	−1.03895	−	0.305063i	−0.756345	+	0.654173i	$0.773017\pi$
$84$	−0.814421	−	5.66442i	−0.0888606	−	0.618039i
$85$	−3.77596	−	4.35769i	−0.409561	−	0.472658i
$86$	−3.75597	−	8.22443i	−0.405017	−	0.886863i
$87$	12.6298	−	3.70843i	1.35405	−	0.397585i
$88$	−2.29707	+	5.02988i	−0.244868	+	0.536187i
$89$	−0.510160	+	3.54824i	−0.0540769	+	0.376113i	0.944754	+	0.327779i	$0.106300\pi$
$89$	−0.510160	+	3.54824i	−0.0540769	+	0.376113i	−0.998831	+	0.0483338i	$0.984609\pi$
$90$	0.530434	−	0.340889i	0.0559126	−	0.0359329i
$91$	−9.52722			−0.998724
$92$	3.03714	+	3.71157i	0.316644	+	0.386958i
$93$	14.2294			1.47552
$94$	−8.18995	+	5.26336i	−0.844729	+	0.542874i
$95$	−0.520446	+	3.61978i	−0.0533967	+	0.371382i
$96$	−0.639452	+	1.40020i	−0.0652638	+	0.142908i
$97$	−2.45368	+	0.720465i	−0.249133	+	0.0731522i	−0.403915	−	0.914797i	$-0.632351\pi$
$97$	−2.45368	+	0.720465i	−0.249133	+	0.0731522i	0.154781	+	0.987949i	$0.450533\pi$
$98$	2.83363	+	6.20477i	0.286239	+	0.626777i
$99$	−2.28320	−	2.63496i	−0.229471	−	0.264823i
$100$	−0.142315	−	0.989821i	−0.0142315	−	0.0989821i
$101$	6.71231	+	1.97091i	0.667900	+	0.196113i	0.598068	−	0.801446i	$-0.295935\pi$
$101$	6.71231	+	1.97091i	0.667900	+	0.196113i	0.0698323	+	0.997559i	$0.477754\pi$
$102$	−5.81237	+	6.70783i	−0.575511	+	0.664175i
$103$	−1.46415	−	0.940954i	−0.144267	−	0.0927150i	0.466516	−	0.884513i	$-0.345509\pi$
$103$	−1.46415	−	0.940954i	−0.144267	−	0.0927150i	−0.610783	+	0.791798i	$0.709145\pi$
$104$	2.15586	+	1.38549i	0.211399	+	0.135858i
$105$	3.74755	−	4.32490i	0.365724	−	0.422067i
$106$	−0.791460	−	0.232394i	−0.0768734	−	0.0225721i
$107$	−0.153960	−	1.07081i	−0.0148838	−	0.103519i	0.981025	−	0.193880i	$-0.0621072\pi$
$107$	−0.153960	−	1.07081i	−0.0148838	−	0.103519i	−0.995909	+	0.0903604i	$0.971198\pi$
$108$	−3.65969	−	4.22351i	−0.352154	−	0.406407i
$109$	0.970980	+	2.12615i	0.0930030	+	0.203648i	0.950416	−	0.310980i	$-0.100657\pi$
$109$	0.970980	+	2.12615i	0.0930030	+	0.203648i	−0.857413	+	0.514628i	$0.827930\pi$
$110$	−5.30559	+	1.55786i	−0.505868	+	0.148536i
$111$	−0.313429	+	0.686313i	−0.0297493	+	0.0651420i
$112$	0.529082	−	3.67985i	0.0499935	−	0.347713i
$113$	13.4634	−	8.65243i	1.26653	−	0.813952i	0.277369	−	0.960763i	$-0.410537\pi$
$113$	13.4634	−	8.65243i	1.26653	−	0.813952i	0.989164	+	0.146812i	$0.0469011\pi$
$114$	5.62926			0.527229
$115$	−0.816115	+	4.72588i	−0.0761031	+	0.440691i
$116$	8.55120			0.793959
$117$	−1.35933	+	0.873588i	−0.125670	+	0.0807632i
$118$	−0.297026	+	2.06586i	−0.0273434	+	0.190178i
$119$	8.90499	−	19.4992i	0.816319	−	1.78749i
$120$	−1.47696	+	0.433673i	−0.134827	+	0.0395888i
$121$	8.13223	+	17.8071i	0.739294	+	1.61883i
$122$	−6.19967	−	7.15480i	−0.561292	−	0.647765i
$123$	−2.49608	−	17.3606i	−0.225064	−	1.56535i
$124$	8.86957	+	2.60434i	0.796511	+	0.233877i
$125$	0.654861	−	0.755750i	0.0585725	−	0.0675963i
$126$	1.97199	+	1.26732i	0.175678	+	0.112902i
$127$	−2.07304	−	1.33226i	−0.183953	−	0.118219i	0.445424	−	0.895320i	$-0.353053\pi$
$127$	−2.07304	−	1.33226i	−0.183953	−	0.118219i	−0.629376	+	0.777101i	$0.716689\pi$
$128$	−0.654861	+	0.755750i	−0.0578821	+	0.0667995i
$129$	−13.3539	−	3.92105i	−1.17574	−	0.345230i
$130$	0.364707	+	2.53659i	0.0319869	+	0.222474i
$131$	−14.3341	−	16.5424i	−1.25237	−	1.44532i	−0.847371	−	0.531001i	$-0.821816\pi$
$131$	−14.3341	−	16.5424i	−1.25237	−	1.44532i	−0.405003	−	0.914315i	$-0.632729\pi$
$132$	3.53590	+	7.74253i	0.307760	+	0.673901i
$133$	−13.0449	+	3.83032i	−1.13113	+	0.332131i
$134$	−0.476372	+	1.04311i	−0.0411523	+	0.0901110i
$135$	0.795327	−	5.53162i	0.0684509	−	0.476086i
$136$	−4.85071	+	3.11736i	−0.415945	+	0.267312i
$137$	3.01304			0.257421			0.128711	−	0.991682i	$-0.458916\pi$
$137$	3.01304			0.257421			0.128711	+	0.991682i	$0.458916\pi$
$138$	7.37933	+	0.208184i	0.628170	+	0.0177218i
$139$	−5.93581			−0.503469			−0.251734	−	0.967796i	$-0.581001\pi$
$139$	−5.93581			−0.503469			−0.251734	+	0.967796i	$0.581001\pi$
$140$	3.12752	−	2.00993i	0.264323	−	0.169870i
$141$	−2.13270	+	14.8333i	−0.179606	+	1.24919i
$142$	1.19127	−	2.60853i	0.0999696	−	0.218903i
$143$	13.5965	−	3.99229i	1.13700	−	0.333852i
$144$	−0.261931	−	0.573548i	−0.0218276	−	0.0477957i
$145$	5.59985	+	6.46257i	0.465042	+	0.536687i
$146$	0.458209	+	3.18691i	0.0379217	+	0.263751i
$147$	10.0746	+	2.95817i	0.830939	+	0.243986i
$148$	−0.320981	+	0.370432i	−0.0263845	+	0.0304493i
$149$	1.25623	+	0.807327i	0.102914	+	0.0661388i	0.591085	−	0.806609i	$-0.298700\pi$
$149$	1.25623	+	0.807327i	0.102914	+	0.0661388i	−0.488171	+	0.872748i	$0.662336\pi$
$150$	−1.29495	−	0.832213i	−0.105732	−	0.0679499i
$151$	10.2411	−	11.8189i	0.833410	−	0.961807i	−0.166295	−	0.986076i	$-0.553181\pi$
$151$	10.2411	−	11.8189i	0.833410	−	0.961807i	0.999705	+	0.0242695i	$0.00772596\pi$
$152$	3.50887	+	1.03030i	0.284607	+	0.0835682i
$153$	−0.517408	−	3.59865i	−0.0418299	−	0.290934i
$154$	−13.4621	−	15.5361i	−1.08481	−	1.25194i
$155$	3.84011	+	8.40866i	0.308445	+	0.675400i
$156$	3.78496	−	1.11136i	0.303039	−	0.0889804i
$157$	2.53687	−	5.55497i	0.202464	−	0.443335i	−0.780978	−	0.624559i	$-0.785279\pi$
$157$	2.53687	−	5.55497i	0.202464	−	0.443335i	0.983442	+	0.181224i	$0.0580060\pi$
$158$	−0.989052	+	6.87901i	−0.0786847	+	0.547264i
$159$	−1.06817	+	0.686470i	−0.0847113	+	0.0544406i
$160$	−1.00000			−0.0790569
$161$	−17.2420	+	4.53869i	−1.35886	+	0.357699i
$162$	−6.71085			−0.527254
$163$	13.8010	−	8.86935i	1.08098	−	0.694701i	0.126193	−	0.992006i	$-0.459724\pi$
$163$	13.8010	−	8.86935i	1.08098	−	0.694701i	0.954783	+	0.297305i	$0.0960877\pi$
$164$	1.62156	−	11.2782i	0.126622	−	0.880678i
$165$	−3.53590	+	7.74253i	−0.275269	+	0.602755i
$166$	−9.46528	+	2.77926i	−0.734648	+	0.215712i
$167$	−5.96270	−	13.0565i	−0.461407	−	1.01034i	−0.987165	−	0.159707i	$-0.948945\pi$
$167$	−5.96270	−	13.0565i	−0.461407	−	1.01034i	0.525757	−	0.850635i	$-0.323782\pi$
$168$	−3.74755	−	4.32490i	−0.289130	−	0.333674i
$169$	0.915468	+	6.36722i	0.0704206	+	0.489786i
$170$	−5.53249	−	1.62448i	−0.424322	−	0.124592i
$171$	−1.51001	+	1.74264i	−0.115473	+	0.133263i
$172$	−7.60618	−	4.88820i	−0.579966	−	0.372722i
$173$	−8.75087	−	5.62385i	−0.665317	−	0.427573i	0.163918	−	0.986474i	$-0.447587\pi$
$173$	−8.75087	−	5.62385i	−0.665317	−	0.427573i	−0.829234	+	0.558901i	$0.811223\pi$
$174$	8.61990	−	9.94789i	0.653473	−	0.754148i
$175$	3.56709	+	1.04739i	0.269647	+	0.0791755i
$176$	0.786940	+	5.47329i	0.0593178	+	0.412565i
$177$	2.10387	+	2.42799i	0.158136	+	0.182499i
$178$	1.48915	+	3.26078i	0.111617	+	0.244406i
$179$	12.1351	−	3.56318i	0.907018	−	0.266325i	0.205233	−	0.978713i	$-0.434205\pi$
$179$	12.1351	−	3.56318i	0.907018	−	0.266325i	0.701785	+	0.712389i	$0.252387\pi$
$180$	0.261931	−	0.573548i	0.0195232	−	0.0427498i
$181$	0.579681	−	4.03177i	0.0430873	−	0.299679i	−0.956871	−	0.290514i	$-0.906174\pi$
$181$	0.579681	−	4.03177i	0.0430873	−	0.299679i	0.999958	−	0.00916470i	$-0.00291725\pi$
$182$	−8.01481	+	5.15081i	−0.594097	+	0.381803i
$183$	−14.5729			−1.07726
$184$	4.56163	+	1.48037i	0.336288	+	0.109134i
$185$	−0.490152			−0.0360367
$186$	11.9705	−	7.69300i	0.877722	−	0.564078i
$187$	−4.53754	+	31.5593i	−0.331818	+	2.30784i
$188$	−4.04424	+	8.85565i	−0.294956	+	0.645864i
$189$	19.9347	−	5.85336i	1.45004	−	0.425769i
$190$	1.51918	+	3.32653i	0.110213	+	0.241332i
$191$	4.02232	+	4.64201i	0.291045	+	0.335884i	0.882376	−	0.470545i	$-0.155943\pi$
$191$	4.02232	+	4.64201i	0.291045	+	0.335884i	−0.591331	+	0.806429i	$0.701397\pi$
$192$	0.219067	+	1.52364i	0.0158098	+	0.109959i
$193$	−6.27038	−	1.84115i	−0.451352	−	0.132529i	0.0481530	−	0.998840i	$-0.484666\pi$
$193$	−6.27038	−	1.84115i	−0.451352	−	0.132529i	−0.499505	+	0.866311i	$0.666485\pi$
$194$	−1.67465	+	1.93265i	−0.120233	+	0.138756i
$195$	3.31853	+	2.13269i	0.237645	+	0.152725i
$196$	5.73835	+	3.68781i	0.409882	+	0.263415i
$197$	−2.91774	+	3.36725i	−0.207880	+	0.239907i	−0.850110	−	0.526606i	$-0.823464\pi$
$197$	−2.91774	+	3.36725i	−0.207880	+	0.239907i	0.642229	+	0.766513i	$0.278010\pi$
$198$	−3.34532	−	0.982274i	−0.237741	−	0.0698072i
$199$	2.15082	+	14.9593i	0.152468	+	1.06044i	0.912066	+	0.410044i	$0.134487\pi$
$199$	2.15082	+	14.9593i	0.152468	+	1.06044i	−0.759598	+	0.650393i	$0.774604\pi$
$200$	−0.654861	−	0.755750i	−0.0463056	−	0.0534396i
$201$	0.733284	+	1.60567i	0.0517219	+	0.113255i
$202$	6.71231	−	1.97091i	0.472277	−	0.138673i
$203$	−13.2063	+	28.9178i	−0.926903	+	2.02963i
$204$	−1.26315	+	8.78539i	−0.0884381	+	0.615101i
$205$	9.58538	−	6.16015i	0.669472	−	0.430243i
$206$	−1.74044			−0.121262
$207$	−2.04390	+	2.22856i	−0.142061	+	0.154896i
$208$	2.56268			0.177690
$209$	17.0116	−	10.9327i	1.17671	−	0.756228i
$210$	0.814421	−	5.66442i	0.0562004	−	0.390882i
$211$	−3.57069	+	7.81872i	−0.245816	+	0.538263i	−0.991815	−	0.127685i	$-0.959245\pi$
$211$	−3.57069	+	7.81872i	−0.245816	+	0.538263i	0.745998	+	0.665948i	$0.231973\pi$
$212$	−0.791460	+	0.232394i	−0.0543577	+	0.0159609i
$213$	−1.83374	−	4.01533i	−0.125646	−	0.275126i
$214$	−0.708444	−	0.817588i	−0.0484282	−	0.0558892i
$215$	−1.28674	−	8.94946i	−0.0877548	−	0.610348i
$216$	−5.36213	−	1.57446i	−0.364847	−	0.107129i
$217$	−22.5052	+	25.9724i	−1.52775	+	1.76312i
$218$	1.96632	+	1.26368i	0.133176	+	0.0855872i
$219$	4.16933	+	2.67947i	0.281737	+	0.181062i
$220$	−3.62110	+	4.17897i	−0.244134	+	0.281746i
$221$	14.1780	+	4.16303i	0.953713	+	0.280036i
$222$	0.107376	+	0.746816i	0.00720660	+	0.0501230i
$223$	−0.809622	−	0.934354i	−0.0542163	−	0.0625690i	0.727994	−	0.685584i	$-0.240453\pi$
$223$	−0.809622	−	0.934354i	−0.0542163	−	0.0625690i	−0.782210	+	0.623015i	$0.785908\pi$
$224$	−1.54438	−	3.38173i	−0.103188	−	0.225951i
$225$	0.604987	−	0.177640i	0.0403325	−	0.0118427i
$226$	6.64831	−	14.5578i	0.442239	−	0.968368i
$227$	−3.01319	+	20.9572i	−0.199992	+	1.39098i	0.604307	+	0.796752i	$0.293450\pi$
$227$	−3.01319	+	20.9572i	−0.199992	+	1.39098i	−0.804299	+	0.594225i	$0.797459\pi$
$228$	4.73564	−	3.04341i	0.313625	−	0.201555i
$229$	−11.2218			−0.741557			−0.370779	−	0.928721i	$-0.620909\pi$
$229$	−11.2218			−0.741557			−0.370779	+	0.928721i	$0.620909\pi$
$230$	1.86844	+	4.41689i	0.123202	+	0.291241i
$231$	−31.6439			−2.08202
$232$	7.19373	−	4.62313i	0.472291	−	0.303523i
$233$	−0.204043	+	1.41915i	−0.0133673	+	0.0929716i	−0.995413	−	0.0956720i	$-0.969500\pi$
$233$	−0.204043	+	1.41915i	−0.0133673	+	0.0929716i	0.982046	+	0.188644i	$0.0604091\pi$
$234$	−0.671243	+	1.46982i	−0.0438805	+	0.0960850i
$235$	−9.34106	+	2.74278i	−0.609344	+	0.178919i
$236$	0.867014	+	1.89850i	0.0564378	+	0.123582i
$237$	7.00557	+	8.08486i	0.455061	+	0.525168i
$238$	−3.05071	−	21.2182i	−0.197748	−	1.37537i
$239$	6.63782	+	1.94904i	0.429365	+	0.126073i	0.489272	−	0.872131i	$-0.337262\pi$
$239$	6.63782	+	1.94904i	0.429365	+	0.126073i	−0.0599076	+	0.998204i	$0.519081\pi$
$240$	−1.00803	+	1.16333i	−0.0650683	+	0.0750928i
$241$	−13.8682	−	8.91258i	−0.893332	−	0.574109i	0.0114739	−	0.999934i	$-0.496348\pi$
$241$	−13.8682	−	8.91258i	−0.893332	−	0.574109i	−0.904806	+	0.425825i	$0.859984\pi$
$242$	16.4685	+	10.5837i	1.05864	+	0.680344i
$243$	4.21432	−	4.86358i	0.270348	−	0.311999i
$244$	−9.08368	−	2.66721i	−0.581523	−	0.170750i
$245$	0.970757	+	6.75176i	0.0620194	+	0.431354i
$246$	−11.4857	−	13.2552i	−0.732301	−	0.845120i
$247$	−3.89315	−	8.52482i	−0.247715	−	0.542421i
$248$	8.86957	−	2.60434i	0.563218	−	0.165376i
$249$	−6.30812	+	13.8129i	−0.399761	+	0.875354i
$250$	0.142315	−	0.989821i	0.00900078	−	0.0626018i
$251$	17.8198	−	11.4521i	1.12478	−	0.722850i	0.160314	−	0.987066i	$-0.448749\pi$
$251$	17.8198	−	11.4521i	1.12478	−	0.722850i	0.964464	+	0.264216i	$0.0851131\pi$
$252$	2.34410			0.147665
$253$	22.7046	−	13.7024i	1.42742	−	0.861460i
$254$	−2.46423			−0.154619
$255$	−7.46674	+	4.79859i	−0.467586	+	0.300499i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	0.261558	−	0.572731i	0.0163155	−	0.0357260i	−0.901299	−	0.433198i	$-0.857385\pi$
$257$	0.261558	−	0.572731i	0.0163155	−	0.0357260i	0.917614	+	0.397472i	$0.130112\pi$
$258$	−13.3539	+	3.92105i	−0.831376	+	0.244114i
$259$	−0.756983	−	1.65756i	−0.0470366	−	0.102996i
$260$	1.67820	+	1.93674i	0.104077	+	0.120112i
$261$	0.767329	+	5.33689i	0.0474965	+	0.330345i
$262$	−21.0021	−	6.16677i	−1.29751	−	0.380984i
$263$	−17.2204	+	19.8733i	−1.06185	+	1.22544i	−0.0885128	+	0.996075i	$0.528211\pi$
$263$	−17.2204	+	19.8733i	−1.06185	+	1.22544i	−0.973340	+	0.229368i	$0.926334\pi$
$264$	7.16051	+	4.60178i	0.440699	+	0.283220i
$265$	−0.693927	−	0.445960i	−0.0426276	−	0.0273951i
$266$	−8.90323	+	10.2749i	−0.545892	+	0.629993i
$267$	5.29449	+	1.55460i	0.324017	+	0.0951401i
$268$	0.163198	+	1.13507i	0.00996890	+	0.0693352i
$269$	−17.4282	−	20.1132i	−1.06261	−	1.22632i	−0.973111	−	0.230335i	$-0.926018\pi$
$269$	−17.4282	−	20.1132i	−1.06261	−	1.22632i	−0.0895020	−	0.995987i	$-0.528528\pi$
$270$	−2.32155	−	5.08348i	−0.141285	−	0.309371i
$271$	−9.42841	+	2.76843i	−0.572735	+	0.168170i	−0.555259	−	0.831677i	$-0.687381\pi$
$271$	−9.42841	+	2.76843i	−0.572735	+	0.168170i	−0.0174754	+	0.999847i	$0.505563\pi$
$272$	−2.39530	+	5.24499i	−0.145237	+	0.318024i
$273$	−2.08710	+	14.5161i	−0.126317	+	0.878552i
$274$	2.53473	−	1.62897i	0.153129	−	0.0984098i
$275$	−5.52957			−0.333446
$276$	6.32044	−	3.81443i	0.380446	−	0.229602i
$277$	11.7531			0.706178			0.353089	−	0.935590i	$-0.385131\pi$
$277$	11.7531			0.706178			0.353089	+	0.935590i	$0.385131\pi$
$278$	−4.99352	+	3.20914i	−0.299492	+	0.192472i
$279$	−0.829498	+	5.76928i	−0.0496607	+	0.345398i
$280$	1.54438	−	3.38173i	0.0922945	−	0.202097i
$281$	14.1395	−	4.15174i	0.843493	−	0.247672i	0.168690	−	0.985669i	$-0.446046\pi$
$281$	14.1395	−	4.15174i	0.843493	−	0.247672i	0.674804	+	0.737997i	$0.264228\pi$
$282$	6.22533	+	13.6316i	0.370713	+	0.811748i
$283$	1.35549	+	1.56432i	0.0805755	+	0.0929891i	0.794606	−	0.607126i	$-0.207678\pi$
$283$	1.35549	+	1.56432i	0.0805755	+	0.0929891i	−0.714030	+	0.700115i	$0.753132\pi$
$284$	−0.408113	−	2.83849i	−0.0242170	−	0.168433i
$285$	5.40124	+	1.58595i	0.319942	+	0.0939434i
$286$	9.27970	−	10.7093i	0.548720	−	0.633257i
$287$	35.6354	+	22.9015i	2.10349	+	1.35183i
$288$	−0.530434	−	0.340889i	−0.0312561	−	0.0200871i
$289$	−10.6398	+	12.2789i	−0.625868	+	0.722290i
$290$	8.20482	+	2.40915i	0.481804	+	0.141470i
$291$	0.560212	+	3.89636i	0.0328402	+	0.228409i
$292$	2.10845	+	2.43328i	0.123387	+	0.142397i
$293$	−8.49265	−	18.5963i	−0.496146	−	1.08641i	−0.977703	−	0.209993i	$-0.932656\pi$
$293$	−8.49265	−	18.5963i	−0.496146	−	1.08641i	0.481557	−	0.876415i	$-0.340072\pi$
$294$	10.0746	−	2.95817i	0.587563	−	0.172524i
$295$	−0.867014	+	1.89850i	−0.0504795	+	0.110535i
$296$	−0.0697559	+	0.485163i	−0.00405448	+	0.0281995i
$297$	−25.9964	+	16.7069i	−1.50847	+	0.969433i
$298$	1.49328			0.0865033
$299$	−4.78822	−	11.3191i	−0.276910	−	0.654598i
$300$	−1.53931			−0.0888720
$301$	28.2774	−	18.1728i	1.62988	−	1.04746i
$302$	2.22561	−	15.4794i	0.128069	−	0.890741i
$303$	4.47341	−	9.79539i	0.256990	−	0.562731i
$304$	3.50887	−	1.03030i	0.201248	−	0.0590916i
$305$	−3.93280	−	8.61163i	−0.225192	−	0.493101i
$306$	−2.38085	−	2.74765i	−0.136104	−	0.157072i
$307$	1.33383	+	9.27703i	0.0761260	+	0.529468i	0.991825	+	0.127604i	$0.0407285\pi$
$307$	1.33383	+	9.27703i	0.0761260	+	0.529468i	−0.915699	+	0.401864i	$0.868362\pi$
$308$	−19.7245	−	5.79164i	−1.12391	−	0.330009i
$309$	−1.75442	+	2.02471i	−0.0998057	+	0.115182i
$310$	7.77657	+	4.99770i	0.441679	+	0.283850i
$311$	6.29557	+	4.04592i	0.356989	+	0.229423i	0.706826	−	0.707388i	$-0.250126\pi$
$311$	6.29557	+	4.04592i	0.356989	+	0.229423i	−0.349837	+	0.936811i	$0.613763\pi$
$312$	2.58326	−	2.98124i	0.146248	−	0.168780i
$313$	2.67346	+	0.784999i	0.151113	+	0.0443707i	0.356414	−	0.934328i	$-0.383999\pi$
$313$	2.67346	+	0.784999i	0.151113	+	0.0443707i	−0.205301	+	0.978699i	$0.565817\pi$
$314$	−0.869093	−	6.04467i	−0.0490457	−	0.341121i
$315$	1.53506	+	1.77156i	0.0864909	+	0.0998159i
$316$	2.88703	+	6.32171i	0.162408	+	0.355624i
$317$	−15.2117	+	4.46655i	−0.854372	+	0.250866i	−0.679455	−	0.733717i	$-0.737784\pi$
$317$	−15.2117	+	4.46655i	−0.854372	+	0.250866i	−0.174917	+	0.984583i	$0.555966\pi$
$318$	−0.527467	+	1.15499i	−0.0295789	+	0.0647687i
$319$	6.72929	−	46.8032i	0.376768	−	2.62048i
$320$	−0.841254	+	0.540641i	−0.0470275	+	0.0302227i
$321$	−1.66526			−0.0929458
$322$	−12.0511	+	13.1399i	−0.671583	+	0.732260i
$323$	21.0865			1.17328
$324$	−5.64553	+	3.62816i	−0.313640	+	0.201564i
$325$	−0.364707	+	2.53659i	−0.0202303	+	0.140705i
$326$	6.81499	−	14.9227i	0.377447	−	0.826494i
$327$	3.45220	−	1.01366i	0.190907	−	0.0560554i
$328$	−4.73331	−	10.3645i	−0.261353	−	0.572283i
$329$	−23.7015	−	27.3530i	−1.30671	−	1.50802i
$330$	1.21134	+	8.42508i	0.0666823	+	0.463786i
$331$	10.5463	+	3.09667i	0.579677	+	0.170208i	0.558410	−	0.829565i	$-0.311412\pi$
$331$	10.5463	+	3.09667i	0.579677	+	0.170208i	0.0212671	+	0.999774i	$0.493230\pi$
$332$	−6.46012	+	7.45538i	−0.354545	+	0.409167i
$333$	−0.259993	−	0.167088i	−0.0142475	−	0.00915634i
$334$	−12.0750	−	7.76014i	−0.660715	−	0.424616i
$335$	−0.750954	+	0.866647i	−0.0410290	+	0.0473500i
$336$	−5.49086	−	1.61226i	−0.299551	−	0.0879561i
$337$	−3.47485	−	24.1681i	−0.189287	−	1.31652i	−0.833859	−	0.551978i	$-0.813873\pi$
$337$	−3.47485	−	24.1681i	−0.189287	−	1.31652i	0.644571	−	0.764544i	$-0.277036\pi$
$338$	4.21252	+	4.86151i	0.229131	+	0.264431i
$339$	−10.2338	−	22.4089i	−0.555824	−	1.21708i
$340$	−5.53249	+	1.62448i	−0.300041	+	0.0881001i
$341$	21.2341	−	46.4963i	1.14989	−	2.51791i
$342$	−0.328156	+	2.28237i	−0.0177446	+	0.123417i
$343$	0.559225	−	0.359392i	0.0301953	−	0.0194053i
$344$	−9.04149			−0.487484
$345$	7.02176	+	2.27875i	0.378039	+	0.122684i
$346$	−10.4022			−0.559225
$347$	20.1546	−	12.9526i	1.08196	−	0.695332i	0.126949	−	0.991909i	$-0.459482\pi$
$347$	20.1546	−	12.9526i	1.08196	−	0.695332i	0.955009	+	0.296577i	$0.0958452\pi$
$348$	1.87328	−	13.0290i	0.100418	−	0.698426i
$349$	−2.43181	+	5.32493i	−0.130172	+	0.285037i	−0.963484	−	0.267766i	$-0.913715\pi$
$349$	−2.43181	+	5.32493i	−0.130172	+	0.285037i	0.833312	+	0.552803i	$0.186442\pi$
$350$	3.56709	−	1.04739i	0.190669	−	0.0559855i
$351$	5.94938	+	13.0273i	0.317554	+	0.695347i
$352$	3.62110	+	4.17897i	0.193005	+	0.222740i
$353$	1.97451	+	13.7330i	0.105093	+	0.730935i	0.972427	+	0.233209i	$0.0749226\pi$
$353$	1.97451	+	13.7330i	0.105093	+	0.730935i	−0.867334	+	0.497726i	$0.834168\pi$
$354$	3.08256	+	0.905121i	0.163836	+	0.0481066i
$355$	1.87793	−	2.16724i	0.0996700	−	0.115025i
$356$	3.01567	+	1.93805i	0.159830	+	0.102717i
$357$	−27.7590	−	17.8396i	−1.46916	−	0.944174i
$358$	8.28227	−	9.55825i	0.437732	−	0.505169i
$359$	19.1700	+	5.62882i	1.01175	+	0.297078i	0.745271	−	0.666761i	$-0.232320\pi$
$359$	19.1700	+	5.62882i	1.01175	+	0.297078i	0.266484	+	0.963839i	$0.414138\pi$
$360$	−0.0897335	−	0.624110i	−0.00472937	−	0.0328935i
$361$	3.68445	+	4.25208i	0.193918	+	0.223794i
$362$	−1.69208	−	3.70514i	−0.0889337	−	0.194738i
$363$	28.9131	−	8.48966i	1.51755	−	0.445592i
$364$	−3.95775	+	8.66627i	−0.207443	+	0.454236i
$365$	−0.458209	+	3.18691i	−0.0239838	+	0.166811i
$366$	−12.2595	+	7.87870i	−0.640814	+	0.411826i
$367$	5.43074			0.283482			0.141741	−	0.989904i	$-0.454730\pi$
$367$	5.43074			0.283482			0.141741	+	0.989904i	$0.454730\pi$
$368$	4.63784	−	1.22084i	0.241764	−	0.0636406i
$369$	7.18434			0.374002
$370$	−0.412342	+	0.264996i	−0.0214367	+	0.0137765i
$371$	0.436425	−	3.03541i	0.0226581	−	0.157590i
$372$	5.91111	−	12.9435i	0.306477	−	0.671090i
$373$	29.4435	−	8.64539i	1.52453	−	0.447642i	0.591157	−	0.806557i	$-0.298671\pi$
$373$	29.4435	−	8.64539i	1.52453	−	0.447642i	0.933370	+	0.358915i	$0.116853\pi$
$374$	13.2450	+	29.0025i	0.684883	+	1.49969i
$375$	−1.00803	−	1.16333i	−0.0520546	−	0.0600742i
$376$	1.38549	+	9.63632i	0.0714514	+	0.496955i
$377$	−21.0263	−	6.17388i	−1.08291	−	0.317971i
$378$	13.6056	−	15.7017i	0.699796	−	0.807607i
$379$	9.66578	+	6.21182i	0.496498	+	0.319080i	0.764814	−	0.644251i	$-0.222831\pi$
$379$	9.66578	+	6.21182i	0.496498	+	0.319080i	−0.268316	+	0.963331i	$0.586467\pi$
$380$	3.07647	+	1.97713i	0.157820	+	0.101424i
$381$	−2.48402	+	2.86671i	−0.127260	+	0.146866i
$382$	5.89345	+	1.73047i	0.301535	+	0.0885387i
$383$	1.50940	+	10.4981i	0.0771267	+	0.536428i	0.991353	+	0.131224i	$0.0418906\pi$
$383$	1.50940	+	10.4981i	0.0771267	+	0.536428i	−0.914226	+	0.405205i	$0.867200\pi$
$384$	1.00803	+	1.16333i	0.0514410	+	0.0593660i
$385$	−8.53978	−	18.6995i	−0.435227	−	0.953015i
$386$	−6.27038	+	1.84115i	−0.319154	+	0.0937120i
$387$	2.36824	−	5.18573i	0.120385	−	0.263605i
$388$	−0.363937	+	2.53124i	−0.0184761	+	0.128504i
$389$	−30.8536	+	19.8284i	−1.56434	+	1.00534i	−0.583130	+	0.812379i	$0.698172\pi$
$389$	−30.8536	+	19.8284i	−1.56434	+	1.00534i	−0.981207	+	0.192960i	$0.938191\pi$
$390$	3.94475			0.199750
$391$	27.6420	+	0.779831i	1.39792	+	0.0394378i
$392$	6.82119			0.344522
$393$	−28.3448	+	18.2161i	−1.42981	+	0.918881i
$394$	−0.634086	+	4.41016i	−0.0319448	+	0.222181i
$395$	−2.88703	+	6.32171i	−0.145262	+	0.318080i
$396$	−3.34532	+	0.982274i	−0.168109	+	0.0493611i
$397$	−1.77869	−	3.89479i	−0.0892700	−	0.195474i	0.859731	−	0.510747i	$-0.170631\pi$
$397$	−1.77869	−	3.89479i	−0.0892700	−	0.195474i	−0.949001	+	0.315273i	$0.897904\pi$
$398$	9.89700	+	11.4217i	0.496092	+	0.572520i
$399$	2.97834	+	20.7148i	0.149104	+	1.03704i
$400$	−0.959493	−	0.281733i	−0.0479746	−	0.0140866i
$401$	−17.7027	+	20.4300i	−0.884030	+	1.02022i	0.115608	+	0.993295i	$0.463118\pi$
$401$	−17.7027	+	20.4300i	−0.884030	+	1.02022i	−0.999637	+	0.0269297i	$0.991427\pi$
$402$	1.48497	+	0.954331i	0.0740635	+	0.0475977i
$403$	−19.9288	−	12.8075i	−0.992725	−	0.637986i
$404$	4.58120	−	5.28699i	0.227923	−	0.263037i
$405$	−6.43901	−	1.89067i	−0.319957	−	0.0939479i
$406$	4.52429	+	31.4671i	0.224537	+	1.56169i
$407$	1.77489	+	2.04833i	0.0879780	+	0.101532i
$408$	3.68711	+	8.07365i	0.182539	+	0.399705i
$409$	25.6735	−	7.53841i	1.26947	−	0.372750i	0.423460	−	0.905915i	$-0.360815\pi$
$409$	25.6735	−	7.53841i	1.26947	−	0.372750i	0.846012	+	0.533164i	$0.178997\pi$
$410$	4.73331	−	10.3645i	0.233761	−	0.511866i
$411$	0.660056	−	4.59079i	0.0325582	−	0.226447i
$412$	−1.46415	+	0.940954i	−0.0721337	+	0.0463575i
$413$	−7.75919			−0.381805
$414$	−0.514583	+	2.97980i	−0.0252904	+	0.146449i
$415$	−9.86488			−0.484248
$416$	2.15586	−	1.38549i	0.105700	−	0.0679291i
$417$	−1.30034	+	9.04404i	−0.0636778	+	0.442889i
$418$	8.40039	−	18.3943i	0.410876	−	0.899694i
$419$	4.39604	−	1.29079i	0.214761	−	0.0630594i	−0.172582	−	0.984995i	$-0.555211\pi$
$419$	4.39604	−	1.29079i	0.214761	−	0.0630594i	0.387343	+	0.921936i	$0.373393\pi$
$420$	−2.37728	−	5.20552i	−0.115999	−	0.254003i
$421$	9.53577	+	11.0049i	0.464745	+	0.536345i	0.938943	−	0.344074i	$-0.111807\pi$
$421$	9.53577	+	11.0049i	0.464745	+	0.536345i	−0.474197	+	0.880419i	$0.657262\pi$
$422$	1.22326	+	8.50799i	0.0595475	+	0.414162i
$423$	−5.88980	−	1.72940i	−0.286372	−	0.0840864i
$424$	−0.540177	+	0.623397i	−0.0262333	+	0.0302749i
$425$	−4.85071	−	3.11736i	−0.235294	−	0.151214i
$426$	−3.71349	−	2.38652i	−0.179919	−	0.115627i
$427$	23.0484	−	26.5993i	1.11539	−	1.28723i
$428$	−1.03800	−	0.304785i	−0.0501738	−	0.0147323i
$429$	−3.10428	−	21.5908i	−0.149876	−	1.04241i
$430$	−5.92092	−	6.83310i	−0.285532	−	0.329521i
$431$	−3.40309	−	7.45172i	−0.163921	−	0.358937i	0.809791	−	0.586718i	$-0.199580\pi$
$431$	−3.40309	−	7.45172i	−0.163921	−	0.358937i	−0.973712	+	0.227781i	$0.926853\pi$
$432$	−5.36213	+	1.57446i	−0.257986	+	0.0757514i
$433$	1.70894	−	3.74206i	0.0821265	−	0.179832i	−0.864114	−	0.503296i	$-0.832120\pi$
$433$	1.70894	−	3.74206i	0.0821265	−	0.179832i	0.946240	+	0.323465i	$0.104848\pi$
$434$	−4.89084	+	34.0166i	−0.234768	+	1.63285i
$435$	11.0734	−	7.11642i	0.530928	−	0.341206i
$436$	2.33737			0.111940
$437$	−11.1068	−	13.5732i	−0.531312	−	0.649296i
$438$	4.95609			0.236811
$439$	−6.55451	+	4.21233i	−0.312830	+	0.201044i	−0.687629	−	0.726063i	$-0.741348\pi$
$439$	−6.55451	+	4.21233i	−0.312830	+	0.201044i	0.374799	+	0.927106i	$0.377712\pi$
$440$	−0.786940	+	5.47329i	−0.0375159	+	0.260929i
$441$	−1.78668	+	3.91228i	−0.0850800	+	0.186299i
$442$	14.1780	−	4.16303i	0.674377	−	0.198015i
$443$	15.2135	+	33.3129i	0.722815	+	1.58274i	0.809917	+	0.586544i	$0.199512\pi$
$443$	15.2135	+	33.3129i	0.722815	+	1.58274i	−0.0871027	+	0.996199i	$0.527761\pi$
$444$	0.494090	+	0.570210i	0.0234485	+	0.0270610i
$445$	0.510160	+	3.54824i	0.0241839	+	0.168203i
$446$	−1.18625	−	0.348314i	−0.0561705	−	0.0164931i
$447$	1.50527	−	1.73718i	0.0711970	−	0.0821657i
$448$	−3.12752	−	2.00993i	−0.147761	−	0.0949604i
$449$	2.96571	+	1.90595i	0.139961	+	0.0899472i	0.608747	−	0.793364i	$-0.291672\pi$
$449$	2.96571	+	1.90595i	0.139961	+	0.0899472i	−0.468787	+	0.883311i	$0.655309\pi$
$450$	0.412908	−	0.476521i	0.0194647	−	0.0224634i
$451$	−60.4527	−	17.7505i	−2.84661	−	0.835839i
$452$	−2.27761	−	15.8411i	−0.107130	−	0.745104i
$453$	−15.7642	−	18.1929i	−0.740669	−	0.854777i
$454$	8.79545	+	19.2593i	0.412791	+	0.903886i
$455$	−9.14130	+	2.68413i	−0.428551	+	0.125834i
$456$	2.33848	−	5.12056i	0.109509	−	0.239792i
$457$	−4.34218	+	30.2005i	−0.203119	+	1.41272i	0.591839	+	0.806056i	$0.298402\pi$
$457$	−4.34218	+	30.2005i	−0.203119	+	1.41272i	−0.794958	+	0.606665i	$0.792507\pi$
$458$	−9.44037	+	6.06696i	−0.441120	+	0.283490i
$459$	−32.2236			−1.50407
$460$	3.95979	+	2.70557i	0.184626	+	0.126148i
$461$	−6.50868			−0.303139			−0.151570	−	0.988447i	$-0.548433\pi$
$461$	−6.50868			−0.303139			−0.151570	+	0.988447i	$0.548433\pi$
$462$	−26.6205	+	17.1080i	−1.23850	+	0.795936i
$463$	−0.673091	+	4.68145i	−0.0312812	+	0.217566i	−0.999466	−	0.0326700i	$-0.989599\pi$
$463$	−0.673091	+	4.68145i	−0.0312812	+	0.217566i	0.968185	+	0.250236i	$0.0805081\pi$
$464$	3.55230	−	7.77845i	0.164911	−	0.361105i
$465$	13.6530	−	4.00889i	0.633143	−	0.185908i
$466$	0.595598	+	1.30418i	0.0275906	+	0.0604149i
$467$	−17.4918	−	20.1866i	−0.809422	−	0.934123i	0.189436	−	0.981893i	$-0.439334\pi$
$467$	−17.4918	−	20.1866i	−0.809422	−	0.934123i	−0.998858	+	0.0477699i	$0.984789\pi$
$468$	0.229958	+	1.59939i	0.0106298	+	0.0739319i
$469$	−4.09052	−	1.20109i	−0.188883	−	0.0554610i
$470$	−6.37534	+	7.35754i	−0.294073	+	0.339378i
$471$	−7.90803	−	5.08219i	−0.364383	−	0.234175i
$472$	1.75578	+	1.12837i	0.0808164	+	0.0519376i
$473$	−32.7401	+	37.7841i	−1.50539	+	1.73732i
$474$	10.2645	+	3.01392i	0.471463	+	0.138434i
$475$	0.520446	+	3.61978i	0.0238797	+	0.166087i
$476$	−14.0378	−	16.2005i	−0.643423	−	0.742550i
$477$	−0.216060	−	0.473104i	−0.00989269	−	0.0216620i
$478$	6.63782	−	1.94904i	0.303607	−	0.0891470i
$479$	−3.37649	+	7.39349i	−0.154276	+	0.337817i	−0.970950	−	0.239282i	$-0.923088\pi$
$479$	−3.37649	+	7.39349i	−0.154276	+	0.337817i	0.816674	+	0.577099i	$0.195815\pi$
$480$	−0.219067	+	1.52364i	−0.00999897	+	0.0695444i
$481$	1.05670	−	0.679099i	0.0481813	−	0.0309643i
$482$	−16.4852			−0.750881
$483$	3.13818	+	27.2649i	0.142792	+	1.24060i
$484$	19.5762			0.889826
$485$	−2.15131	+	1.38256i	−0.0976860	+	0.0627790i
$486$	0.915858	−	6.36993i	0.0415442	−	0.288946i
$487$	−3.07442	+	6.73203i	−0.139315	+	0.305058i	−0.966410	−	0.257004i	$-0.917265\pi$
$487$	−3.07442	+	6.73203i	−0.139315	+	0.305058i	0.827095	+	0.562062i	$0.189992\pi$
$488$	−9.08368	+	2.66721i	−0.411199	+	0.120739i
$489$	−10.4904	−	22.9707i	−0.474391	−	1.03877i
$490$	4.46693	+	5.15511i	0.201795	+	0.232884i
$491$	3.69789	+	25.7194i	0.166883	+	1.16070i	0.885277	+	0.465064i	$0.153969\pi$
$491$	3.69789	+	25.7194i	0.166883	+	1.16070i	−0.718394	+	0.695637i	$0.755122\pi$
$492$	−16.8287	−	4.94135i	−0.758695	−	0.222773i
$493$	32.2890	−	37.2635i	1.45422	−	1.67826i
$494$	−7.88399	−	5.06673i	−0.354718	−	0.227963i
$495$	−2.93307	−	1.88497i	−0.131832	−	0.0847231i
$496$	6.05355	−	6.98617i	0.271812	−	0.313688i
$497$	10.2293	+	3.00358i	0.458845	+	0.134729i
$498$	2.16106	+	15.0305i	0.0968396	+	0.673534i
$499$	22.6105	+	26.0939i	1.01218	+	1.16812i	0.985706	+	0.168474i	$0.0538839\pi$
$499$	22.6105	+	26.0939i	1.01218	+	1.16812i	0.0264785	+	0.999649i	$0.491571\pi$
$500$	−0.415415	−	0.909632i	−0.0185779	−	0.0406800i
$501$	−21.1996	+	6.22477i	−0.947130	+	0.278102i
$502$	8.79951	−	19.2682i	0.392741	−	0.859984i
$503$	0.924047	−	6.42689i	0.0412012	−	0.286561i	−0.958796	−	0.284096i	$-0.908306\pi$
$503$	0.924047	−	6.42689i	0.0412012	−	0.286561i	0.999997	−	0.00246444i	$-0.000784455\pi$
$504$	1.97199	−	1.26732i	0.0878392	−	0.0564509i
$505$	6.99569			0.311304
$506$	11.6922	−	23.8022i	0.519783	−	1.05814i
$507$	9.90190			0.439759
$508$	−2.07304	+	1.33226i	−0.0919763	+	0.0591096i
$509$	−4.13303	+	28.7458i	−0.183193	+	1.27414i	0.665959	+	0.745989i	$0.268023\pi$
$509$	−4.13303	+	28.7458i	−0.183193	+	1.27414i	−0.849152	+	0.528149i	$0.822886\pi$
$510$	−3.68711	+	8.07365i	−0.163268	+	0.357507i
$511$	−11.4849	+	3.37228i	−0.508063	+	0.149181i
$512$	0.415415	+	0.909632i	0.0183589	+	0.0402004i
$513$	13.3835	+	15.4454i	0.590897	+	0.681931i
$514$	−0.0896056	−	0.623221i	−0.00395234	−	0.0274891i
$515$	−1.66994	−	0.490339i	−0.0735865	−	0.0216069i
$516$	−9.11412	+	10.5183i	−0.401227	+	0.463040i
$517$	45.2869	+	29.1041i	1.99172	+	1.28000i
$518$	−1.53296	−	0.985173i	−0.0673544	−	0.0432860i
$519$	−10.4857	+	12.1012i	−0.460273	+	0.531184i
$520$	2.45887	+	0.721989i	0.107829	+	0.0316613i
$521$	4.30166	+	29.9187i	0.188459	+	1.31076i	0.835999	+	0.548731i	$0.184889\pi$
$521$	4.30166	+	29.9187i	0.188459	+	1.31076i	−0.647540	+	0.762031i	$0.724202\pi$
$522$	3.53086	+	4.07483i	0.154541	+	0.178350i
$523$	−6.37553	−	13.9605i	−0.278782	−	0.610448i	0.717504	−	0.696555i	$-0.245285\pi$
$523$	−6.37553	−	13.9605i	−0.278782	−	0.610448i	−0.996286	+	0.0861066i	$0.972557\pi$
$524$	−21.0021	+	6.16677i	−0.917481	+	0.269397i
$525$	2.37728	−	5.20552i	0.103753	−	0.227188i
$526$	−3.74234	+	26.0286i	−0.163174	+	1.13490i
$527$	44.8401	−	28.8170i	1.95326	−	1.25529i
$528$	8.51172			0.370425
$529$	−14.0579	−	18.2038i	−0.611211	−	0.791468i
$530$	−0.824873			−0.0358302
$531$	−1.10707	+	0.711470i	−0.0480427	+	0.0308752i
$532$	−1.93486	+	13.4572i	−0.0838866	+	0.583444i
$533$	−12.1299	+	26.5608i	−0.525405	+	1.15048i
$534$	5.29449	−	1.55460i	0.229115	−	0.0672742i
$535$	−0.449406	−	0.984062i	−0.0194295	−	0.0425447i
$536$	0.750954	+	0.866647i	0.0324363	+	0.0374334i
$537$	−2.77062	−	19.2701i	−0.119561	−	0.831565i
$538$	−25.5355	−	7.49790i	−1.10091	−	0.323257i
$539$	24.7002	−	28.5056i	1.06391	−	1.22782i
$540$	−4.70135	−	3.02137i	−0.202314	−	0.130019i
$541$	10.4172	+	6.69475i	0.447872	+	0.287830i	0.745070	−	0.666986i	$-0.232416\pi$
$541$	10.4172	+	6.69475i	0.447872	+	0.287830i	−0.297198	+	0.954816i	$0.596052\pi$
$542$	−6.43495	+	7.42633i	−0.276405	+	0.318988i
$543$	−6.01598	−	1.76645i	−0.258170	−	0.0758056i
$544$	0.820595	+	5.70736i	0.0351827	+	0.244701i
$545$	1.53065	+	1.76647i	0.0655660	+	0.0756672i
$546$	6.09220	+	13.3401i	0.260722	+	0.570902i
$547$	12.7786	−	3.75213i	0.546373	−	0.160430i	0.00311472	−	0.999995i	$-0.499009\pi$
$547$	12.7786	−	3.75213i	0.546373	−	0.160430i	0.543258	+	0.839566i	$0.317190\pi$
$548$	1.25166	−	2.74076i	0.0534684	−	0.117079i
$549$	0.849521	−	5.90855i	0.0362567	−	0.252171i
$550$	−4.65177	+	2.98951i	−0.198352	+	0.127473i
$551$	−31.2718			−1.33222
$552$	3.25486	−	6.62599i	0.138536	−	0.282021i
$553$	−25.8370			−1.09870
$554$	9.88738	−	6.35423i	0.420074	−	0.269965i
$555$	−0.107376	+	0.746816i	−0.00455785	+	0.0317006i
$556$	−2.46582	+	5.39940i	−0.104574	+	0.228986i
$557$	−20.0265	+	5.88032i	−0.848552	+	0.249157i	−0.676968	−	0.736012i	$-0.736707\pi$
$557$	−20.0265	+	5.88032i	−0.848552	+	0.249157i	−0.171583	+	0.985170i	$0.554888\pi$
$558$	2.42129	+	5.30189i	0.102502	+	0.224447i
$559$	15.1734	+	17.5110i	0.641766	+	0.740637i
$560$	−0.529082	−	3.67985i	−0.0223578	−	0.155502i
$561$	47.0910	+	13.8272i	1.98818	+	0.583783i
$562$	9.65033	−	11.1371i	0.407074	−	0.469789i
$563$	2.24841	+	1.44497i	0.0947593	+	0.0608981i	0.587162	−	0.809469i	$-0.300245\pi$
$563$	2.24841	+	1.44497i	0.0947593	+	0.0608981i	−0.492403	+	0.870367i	$0.663881\pi$
$564$	12.6069	+	8.10194i	0.530845	+	0.341153i
$565$	10.4804	−	12.0950i	0.440914	−	0.508842i
$566$	1.98604	+	0.583155i	0.0834797	+	0.0245118i
$567$	−3.55059	−	24.6949i	−0.149111	−	1.03709i
$568$	−1.87793	−	2.16724i	−0.0787961	−	0.0909355i
$569$	−7.14159	−	15.6379i	−0.299391	−	0.655575i	0.698824	−	0.715294i	$-0.253707\pi$
$569$	−7.14159	−	15.6379i	−0.299391	−	0.655575i	−0.998215	+	0.0597184i	$0.980980\pi$
$570$	5.40124	−	1.58595i	0.226233	−	0.0664280i
$571$	−10.9506	+	23.9786i	−0.458270	+	1.00347i	0.529609	+	0.848242i	$0.322339\pi$
$571$	−10.9506	+	23.9786i	−0.458270	+	1.00347i	−0.987879	+	0.155229i	$0.950388\pi$
$572$	2.01667	−	14.0263i	0.0843213	−	0.586468i
$573$	7.95391	−	5.11167i	0.332279	−	0.213543i
$574$	42.3599			1.76807
$575$	0.548378	+	4.76438i	0.0228689	+	0.198688i
$576$	−0.630528			−0.0262720
$577$	12.1869	−	7.83208i	0.507349	−	0.326054i	−0.261801	−	0.965122i	$-0.584316\pi$
$577$	12.1869	−	7.83208i	0.507349	−	0.326054i	0.769150	+	0.639068i	$0.220680\pi$
$578$	−2.31224	+	16.0820i	−0.0961765	+	0.668923i
$579$	−4.17888	+	9.15047i	−0.173668	+	0.380281i
$580$	8.20482	−	2.40915i	0.340687	−	0.100035i
$581$	−15.2351	−	33.3603i	−0.632060	−	1.38402i
$582$	2.57781	+	2.97495i	0.106854	+	0.123316i
$583$	0.649126	+	4.51477i	0.0268840	+	0.186983i
$584$	3.08927	+	0.907091i	0.127835	+	0.0375357i
$585$	−1.05815	+	1.22117i	−0.0437491	+	0.0504891i
$586$	−17.1984	−	11.0527i	−0.710459	−	0.456584i
$587$	8.36209	+	5.37399i	0.345141	+	0.221808i	0.701714	−	0.712459i	$-0.252419\pi$
$587$	8.36209	+	5.37399i	0.345141	+	0.221808i	−0.356573	+	0.934267i	$0.616055\pi$
$588$	6.87599	−	7.93531i	0.283561	−	0.327247i
$589$	−32.4361	−	9.52409i	−1.33651	−	0.392433i
$590$	0.297026	+	2.06586i	0.0122284	+	0.0850501i
$591$	4.49131	+	5.18324i	0.184748	+	0.213210i
$592$	0.203617	+	0.445858i	0.00836859	+	0.0183247i
$593$	−16.5529	+	4.86038i	−0.679748	+	0.199592i	−0.603339	−	0.797485i	$-0.706164\pi$
$593$	−16.5529	+	4.86038i	−0.679748	+	0.199592i	−0.0764086	+	0.997077i	$0.524345\pi$
$594$	−12.8372	+	28.1095i	−0.526715	+	1.15335i
$595$	3.05071	−	21.2182i	0.125067	−	0.869861i
$596$	1.25623	−	0.807327i	0.0514570	−	0.0330694i
$597$	23.2638			0.952123
$598$	−10.1476	−	6.93349i	−0.414968	−	0.283531i
$599$	−7.22276			−0.295114			−0.147557	−	0.989054i	$-0.547141\pi$
$599$	−7.22276			−0.295114			−0.147557	+	0.989054i	$0.547141\pi$
$600$	−1.29495	+	0.832213i	−0.0528661	+	0.0339750i
$601$	3.33498	−	23.1953i	0.136037	−	0.946157i	−0.801432	−	0.598086i	$-0.795928\pi$
$601$	3.33498	−	23.1953i	0.136037	−	0.946157i	0.937468	−	0.348070i	$-0.113163\pi$
$602$	13.9635	−	30.5758i	0.569111	−	1.24618i
$603$	−0.693762	+	0.203707i	−0.0282522	+	0.00829558i
$604$	−6.49652	−	14.2254i	−0.264339	−	0.578823i
$605$	12.8197	+	14.7947i	0.521193	+	0.601489i
$606$	−1.53252	−	10.6589i	−0.0622544	−	0.432989i
$607$	−31.1391	−	9.14327i	−1.26390	−	0.371114i	−0.419954	−	0.907545i	$-0.637954\pi$
$607$	−31.1391	−	9.14327i	−1.26390	−	0.371114i	−0.843944	+	0.536431i	$0.819772\pi$
$608$	2.39483	−	2.76378i	0.0971232	−	0.112086i
$609$	41.1673	+	26.4566i	1.66818	+	1.07208i
$610$	−7.96428	−	5.11833i	−0.322464	−	0.207235i
$611$	16.3379	−	18.8550i	0.660962	−	0.762791i
$612$	−3.48839	−	1.02428i	−0.141010	−	0.0414042i
$613$	0.820567	+	5.70717i	0.0331424	+	0.230510i	0.999660	−	0.0260916i	$-0.00830617\pi$
$613$	0.820567	+	5.70717i	0.0331424	+	0.230510i	−0.966517	+	0.256602i	$0.917397\pi$
$614$	6.13763	+	7.08321i	0.247695	+	0.285855i
$615$	−7.28602	−	15.9542i	−0.293801	−	0.643334i
$616$	−19.7245	+	5.79164i	−0.794723	+	0.233352i
$617$	−0.560682	+	1.22772i	−0.0225722	+	0.0494262i	−0.920582	−	0.390549i	$-0.872285\pi$
$617$	−0.560682	+	1.22772i	−0.0225722	+	0.0494262i	0.898010	+	0.439975i	$0.145013\pi$
$618$	−0.381273	+	2.65181i	−0.0153370	+	0.106671i
$619$	12.4497	−	8.00094i	0.500396	−	0.321585i	−0.265979	−	0.963979i	$-0.585695\pi$
$619$	12.4497	−	8.00094i	0.500396	−	0.321585i	0.766375	+	0.642394i	$0.222059\pi$
$620$	9.24402			0.371249
$621$	16.9731	+	20.7421i	0.681106	+	0.832353i
$622$	7.48356			0.300064
$623$	−11.2113	+	7.20507i	−0.449171	+	0.288665i
$624$	0.561396	−	3.90460i	0.0224738	−	0.156309i
$625$	0.415415	−	0.909632i	0.0166166	−	0.0363853i
$626$	2.67346	−	0.784999i	0.106853	−	0.0313749i
$627$	−12.9308	−	28.3145i	−0.516406	−	1.13077i
$628$	−3.99912	−	4.61523i	−0.159582	−	0.184168i
$629$	0.402216	+	2.79748i	0.0160374	+	0.111543i
$630$	2.24915	+	0.660411i	0.0896083	+	0.0263114i
$631$	10.4041	−	12.0069i	0.414179	−	0.477988i	−0.509876	−	0.860248i	$-0.670309\pi$
$631$	10.4041	−	12.0069i	0.414179	−	0.477988i	0.924055	+	0.382260i	$0.124854\pi$
$632$	5.84650	+	3.75732i	0.232561	+	0.149458i
$633$	11.1307	+	7.15327i	0.442406	+	0.284317i
$634$	−10.3821	+	11.9815i	−0.412325	+	0.475848i
$635$	−2.36441	−	0.694253i	−0.0938287	−	0.0275506i
$636$	0.180702	+	1.25681i	0.00716530	+	0.0498358i
$637$	−11.4473	−	13.2109i	−0.453558	−	0.523434i
$638$	−19.6427	−	43.0115i	−0.777661	−	1.70284i
$639$	1.73491	−	0.509414i	0.0686318	−	0.0201521i
$640$	−0.415415	+	0.909632i	−0.0164207	+	0.0359564i
$641$	2.42865	−	16.8916i	0.0959258	−	0.667179i	−0.883952	−	0.467579i	$-0.845127\pi$
$641$	2.42865	−	16.8916i	0.0959258	−	0.667179i	0.979877	−	0.199600i	$-0.0639644\pi$
$642$	−1.40091	+	0.900308i	−0.0552894	+	0.0355323i
$643$	40.2129			1.58584			0.792920	−	0.609326i	$-0.208560\pi$
$643$	40.2129			1.58584			0.792920	+	0.609326i	$0.208560\pi$
$644$	−3.03406	+	17.5693i	−0.119559	+	0.692329i
$645$	−13.9176			−0.548007
$646$	17.7391	−	11.4002i	0.697935	−	0.448536i
$647$	6.35283	−	44.1849i	0.249755	−	1.73709i	−0.349862	−	0.936801i	$-0.613772\pi$
$647$	6.35283	−	44.1849i	0.249755	−	1.73709i	0.599618	−	0.800286i	$-0.295319\pi$
$648$	−2.78779	+	6.10441i	−0.109515	+	0.239804i
$649$	11.0733	−	3.25141i	0.434665	−	0.127629i
$650$	1.06457	+	2.33109i	0.0417560	+	0.0914329i
$651$	34.6424	+	39.9795i	1.35774	+	1.56692i
$652$	−2.33471	−	16.2383i	−0.0914343	−	0.635940i
$653$	20.2533	+	5.94691i	0.792573	+	0.232721i	0.652867	−	0.757472i	$-0.273566\pi$
$653$	20.2533	+	5.94691i	0.792573	+	0.232721i	0.139706	+	0.990193i	$0.455384\pi$
$654$	2.35615	−	2.71914i	0.0921327	−	0.106327i
$655$	−18.4140	−	11.8339i	−0.719494	−	0.462390i
$656$	−9.58538	−	6.16015i	−0.374246	−	0.240513i
$657$	−1.32943	+	1.53425i	−0.0518662	+	0.0598567i
$658$	−34.7271	−	10.1968i	−1.35380	−	0.397513i
$659$	2.27383	+	15.8148i	0.0885759	+	0.616059i	0.984960	+	0.172781i	$0.0552753\pi$
$659$	2.27383	+	15.8148i	0.0885759	+	0.616059i	−0.896384	+	0.443278i	$0.853816\pi$
$660$	5.57399	+	6.43273i	0.216967	+	0.250394i
$661$	5.58295	+	12.2250i	0.217152	+	0.475496i	0.986589	−	0.163227i	$-0.0521904\pi$
$661$	5.58295	+	12.2250i	0.217152	+	0.475496i	−0.769437	+	0.638723i	$0.779463\pi$
$662$	10.5463	−	3.09667i	0.409893	−	0.120356i
$663$	9.44888	−	20.6902i	0.366964	−	0.803539i
$664$	−1.40392	+	9.76447i	−0.0544826	+	0.378935i
$665$	−11.4373	+	7.35034i	−0.443521	+	0.285034i
$666$	−0.309055			−0.0119756
$667$	−40.9938	−	1.15651i	−1.58729	−	0.0447802i
$668$	−14.3536			−0.555357
$669$	−1.60098	+	1.02889i	−0.0618975	+	0.0397791i
$670$	−0.163198	+	1.13507i	−0.00630488	+	0.0438514i
$671$	−21.7467	+	47.6186i	−0.839522	+	1.83830i
$672$	−5.49086	+	1.61226i	−0.211815	+	0.0621944i
$673$	13.7339	+	30.0731i	0.529403	+	1.15923i	0.965755	+	0.259456i	$0.0835431\pi$
$673$	13.7339	+	30.0731i	0.529403	+	1.15923i	−0.436352	+	0.899776i	$0.643730\pi$
$674$	−15.9895	−	18.4529i	−0.615893	−	0.710778i
$675$	−0.795327	−	5.53162i	−0.0306122	−	0.212912i
$676$	6.17213	+	1.81230i	0.237389	+	0.0697038i
$677$	−19.9218	+	22.9910i	−0.765658	+	0.883616i	−0.995987	−	0.0894963i	$-0.971474\pi$
$677$	−19.9218	+	22.9910i	−0.765658	+	0.883616i	0.230329	+	0.973113i	$0.426020\pi$
$678$	−20.7244	−	13.3188i	−0.795915	−	0.511504i
$679$	−7.99790	−	5.13994i	−0.306931	−	0.197253i
$680$	−3.77596	+	4.35769i	−0.144802	+	0.167110i
$681$	31.2711	+	9.18203i	1.19831	+	0.351856i
$682$	−7.27449	−	50.5952i	−0.278555	−	1.93739i
$683$	30.9532	+	35.7219i	1.18439	+	1.36686i	0.914810	+	0.403884i	$0.132340\pi$
$683$	30.9532	+	35.7219i	1.18439	+	1.36686i	0.269582	+	0.962977i	$0.413114\pi$
$684$	0.957882	+	2.09747i	0.0366255	+	0.0801987i
$685$	2.89099	−	0.848872i	0.110459	−	0.0324337i
$686$	0.276148	−	0.604679i	0.0105434	−	0.0230868i
$687$	−2.45832	+	17.0980i	−0.0937907	+	0.652329i
$688$	−7.60618	+	4.88820i	−0.289983	+	0.186361i
$689$	2.11388			0.0805325
$690$	7.13907	−	1.87925i	0.271780	−	0.0715417i
$691$	−16.7843			−0.638507			−0.319253	−	0.947669i	$-0.603432\pi$
$691$	−16.7843			−0.638507			−0.319253	+	0.947669i	$0.603432\pi$
$692$	−8.75087	+	5.62385i	−0.332658	+	0.213787i
$693$	1.84467	−	12.8300i	0.0700732	−	0.487370i
$694$	9.95246	−	21.7928i	0.377790	−	0.827245i
$695$	−5.69537	+	1.67231i	−0.216038	+	0.0634344i
$696$	−5.46808	−	11.9734i	−0.207267	−	0.453852i
$697$	−43.0239	−	49.6522i	−1.62965	−	1.88071i
$698$	0.833102	+	5.79435i	0.0315334	+	0.219319i
$699$	2.11758	+	0.621776i	0.0800941	+	0.0235177i
$700$	2.43457	−	2.80964i	0.0920180	−	0.106194i
$701$	−10.7701	−	6.92150i	−0.406780	−	0.261421i	0.321212	−	0.947007i	$-0.395910\pi$
$701$	−10.7701	−	6.92150i	−0.406780	−	0.261421i	−0.727992	+	0.685586i	$0.759546\pi$
$702$	12.0480	+	7.74280i	0.454724	+	0.292233i
$703$	1.17383	−	1.35467i	0.0442719	−	0.0510925i
$704$	5.30559	+	1.55786i	0.199962	+	0.0587141i
$705$	2.13270	+	14.8333i	0.0803223	+	0.558654i
$706$	9.08570	+	10.4855i	0.341945	+	0.394625i
$707$	10.8040	+	23.6575i	0.406327	+	0.889732i
$708$	3.08256	−	0.905121i	0.115850	−	0.0340165i
$709$	−10.6527	+	23.3261i	−0.400070	+	0.876030i	0.597194	+	0.802097i	$0.296282\pi$
$709$	−10.6527	+	23.3261i	−0.400070	+	0.876030i	−0.997263	+	0.0739330i	$0.976445\pi$
$710$	0.408113	−	2.83849i	0.0153162	−	0.106526i
$711$	−3.68638	+	2.36909i	−0.138250	+	0.0888479i
$712$	3.58473			0.134343
$713$	−42.1678	−	13.6846i	−1.57920	−	0.512492i
$714$	−32.9972			−1.23489
$715$	11.9210	−	7.66115i	0.445819	−	0.286511i
$716$	1.79991	−	12.5186i	0.0672658	−	0.467844i
$717$	4.42376	−	9.68668i	0.165208	−	0.361756i
$718$	19.1700	−	5.62882i	0.715419	−	0.210066i
$719$	16.1095	+	35.2749i	0.600784	+	1.31553i	0.928702	+	0.370827i	$0.120926\pi$
$719$	16.1095	+	35.2749i	0.600784	+	1.31553i	−0.327919	+	0.944706i	$0.606347\pi$
$720$	−0.412908	−	0.476521i	−0.0153882	−	0.0177589i
$721$	−0.920837	−	6.40456i	−0.0342938	−	0.238518i
$722$	5.39840	+	1.58511i	0.200908	+	0.0589918i
$723$	−16.6176	+	19.1778i	−0.618016	+	0.713229i
$724$	−3.42662	−	2.20215i	−0.127349	−	0.0818424i
$725$	7.19373	+	4.62313i	0.267168	+	0.171699i
$726$	19.7334	−	22.7736i	0.732376	−	0.845207i
$727$	21.3475	+	6.26818i	0.791734	+	0.232474i	0.652503	−	0.757786i	$-0.273719\pi$
$727$	21.3475	+	6.26818i	0.791734	+	0.232474i	0.139231	+	0.990260i	$0.455537\pi$
$728$	1.35587	+	9.43025i	0.0502517	+	0.349508i
$729$	−19.6712	−	22.7017i	−0.728561	−	0.840804i
$730$	1.33751	+	2.92873i	0.0495033	+	0.108397i
$731$	−50.0219	+	14.6878i	−1.85013	+	0.543246i
$732$	−6.05380	+	13.2560i	−0.223755	+	0.489955i
$733$	−0.566725	+	3.94166i	−0.0209325	+	0.145588i	−0.997607	−	0.0691352i	$-0.977976\pi$
$733$	−0.566725	+	3.94166i	−0.0209325	+	0.145588i	0.976675	+	0.214724i	$0.0688851\pi$
$734$	4.56863	−	2.93608i	0.168631	−	0.108373i
$735$	10.4999			0.387295
$736$	3.24156	−	3.53444i	0.119486	−	0.130281i
$737$	6.34097			0.233573
$738$	6.04385	−	3.88414i	0.222477	−	0.142977i
$739$	6.56813	−	45.6824i	0.241613	−	1.68045i	−0.402420	−	0.915455i	$-0.631831\pi$
$739$	6.56813	−	45.6824i	0.241613	−	1.68045i	0.644032	−	0.764998i	$-0.277260\pi$
$740$	−0.203617	+	0.445858i	−0.00748509	+	0.0163901i
$741$	−13.8416	+	4.06427i	−0.508485	+	0.149305i
$742$	−1.27392	−	2.78949i	−0.0467671	−	0.102406i
$743$	−30.2001	−	34.8528i	−1.10793	−	1.27862i	−0.957002	−	0.290080i	$-0.906318\pi$
$743$	−30.2001	−	34.8528i	−1.10793	−	1.27862i	−0.150932	−	0.988544i	$-0.548227\pi$
$744$	−2.02506	−	14.0846i	−0.0742421	−	0.516365i
$745$	1.43279	+	0.420705i	0.0524934	+	0.0154134i
$746$	20.0954	−	23.1913i	0.735745	−	0.849095i
$747$	−5.23266	−	3.36283i	−0.191453	−	0.123039i
$748$	26.8224	+	17.2377i	0.980723	+	0.630272i
$749$	2.63377	−	3.03954i	0.0962360	−	0.111062i
$750$	−1.47696	−	0.433673i	−0.0539308	−	0.0158355i
$751$	−6.85019	−	47.6441i	−0.249967	−	1.73856i	−0.598375	−	0.801216i	$-0.704187\pi$
$751$	−6.85019	−	47.6441i	−0.249967	−	1.73856i	0.348408	−	0.937343i	$-0.386723\pi$
$752$	6.37534	+	7.35754i	0.232485	+	0.268302i
$753$	−13.5452	−	29.6598i	−0.493613	−	1.08086i
$754$	−21.0263	+	6.17388i	−0.765732	+	0.224839i
$755$	6.49652	−	14.2254i	0.236432	−	0.517715i
$756$	2.95678	−	20.5648i	0.107537	−	0.747936i
$757$	14.2466	−	9.15572i	0.517800	−	0.332770i	−0.255501	−	0.966809i	$-0.582240\pi$
$757$	14.2466	−	9.15572i	0.517800	−	0.332770i	0.773301	+	0.634039i	$0.218604\pi$
$758$	11.4897			0.417326
$759$	−15.9037	−	37.5953i	−0.577267	−	1.36462i
$760$	3.65701			0.132654
$761$	16.3004	−	10.4756i	0.590888	−	0.379741i	−0.210759	−	0.977538i	$-0.567594\pi$
$761$	16.3004	−	10.4756i	0.590888	−	0.379741i	0.801647	+	0.597797i	$0.203957\pi$
$762$	−0.539830	+	3.75460i	−0.0195560	+	0.136015i
$763$	−3.60980	+	7.90436i	−0.130684	+	0.286157i
$764$	5.89345	−	1.73047i	0.213218	−	0.0626063i
$765$	−1.51031	−	3.30711i	−0.0546052	−	0.119569i
$766$	6.94549	+	8.01553i	0.250951	+	0.289613i
$767$	−0.761180	−	5.29413i	−0.0274846	−	0.191160i
$768$	1.47696	+	0.433673i	0.0532951	+	0.0156488i
$769$	−23.2957	+	26.8847i	−0.840065	+	0.969487i	−0.999844	−	0.0176659i	$-0.994376\pi$
$769$	−23.2957	+	26.8847i	−0.840065	+	0.969487i	0.159779	+	0.987153i	$0.448922\pi$
$770$	−17.2938	−	11.1141i	−0.623226	−	0.400523i
$771$	−0.815338	−	0.523986i	−0.0293637	−	0.0188709i
$772$	−4.27958	+	4.93890i	−0.154025	+	0.177755i
$773$	10.0230	+	2.94301i	0.360501	+	0.105853i	0.456967	−	0.889484i	$-0.348936\pi$
$773$	10.0230	+	2.94301i	0.360501	+	0.105853i	−0.0964659	+	0.995336i	$0.530754\pi$
$774$	−0.811324	−	5.64288i	−0.0291624	−	0.202829i
$775$	6.05355	+	6.98617i	0.217450	+	0.250950i
$776$	1.06233	+	2.32617i	0.0381353	+	0.0835047i
$777$	−2.69136	+	0.790254i	−0.0965519	+	0.0283502i
$778$	−15.2356	+	33.3614i	−0.546224	+	1.19606i
$779$	−5.93005	+	41.2444i	−0.212466	+	1.47773i
$780$	3.31853	−	2.13269i	0.118823	−	0.0763626i
$781$	−15.8570			−0.567408
$782$	23.6756	−	14.2884i	0.846636	−	0.510951i
$783$	47.7884			1.70782
$784$	5.73835	−	3.68781i	0.204941	−	0.131708i
$785$	0.869093	−	6.04467i	0.0310192	−	0.215744i
$786$	−13.9968	+	30.6487i	−0.499249	+	1.09320i
$787$	−6.74204	+	1.97964i	−0.240328	+	0.0705666i	−0.399678	−	0.916655i	$-0.630878\pi$
$787$	−6.74204	+	1.97964i	−0.240328	+	0.0705666i	0.159351	+	0.987222i	$0.449060\pi$
$788$	1.85089	+	4.05288i	0.0659351	+	0.144378i
$789$	26.5074	+	30.5912i	0.943690	+	1.08908i
$790$	0.989052	+	6.87901i	0.0351889	+	0.244744i
$791$	57.0878	+	16.7625i	2.02981	+	0.596006i
$792$	−2.28320	+	2.63496i	−0.0811301	+	0.0936291i
$793$	20.4099	+	13.1166i	0.724776	+	0.465785i
$794$	−3.60201	−	2.31487i	−0.127831	−	0.0821518i
$795$	−0.831499	+	0.959601i	−0.0294902	+	0.0340335i
$796$	14.5009	+	4.25786i	0.513972	+	0.150916i
$797$	6.70998	+	46.6689i	0.237680	+	1.65310i	0.663415	+	0.748251i	$0.269106\pi$
$797$	6.70998	+	46.6689i	0.237680	+	1.65310i	−0.425736	+	0.904848i	$0.639985\pi$
$798$	13.7048	+	15.8162i	0.485145	+	0.559887i
$799$	23.3193	+	51.0621i	0.824977	+	1.80645i
$800$	−0.959493	+	0.281733i	−0.0339232	+	0.00996075i
$801$	−0.938951	+	2.05602i	−0.0331762	+	0.0726457i
$802$	−3.84716	+	26.7576i	−0.135848	+	0.944843i
$803$	14.9772	−	9.62529i	0.528536	−	0.339669i
$804$	1.76518			0.0622533
$805$	−15.2649	+	9.21248i	−0.538017	+	0.324697i
$806$	−23.6894			−0.834424
$807$	−34.4632	+	22.1481i	−1.21316	+	0.779651i
$808$	0.995590	−	6.92448i	0.0350247	−	0.243602i
$809$	10.1032	−	22.1229i	0.355209	−	0.777799i	−0.644702	−	0.764434i	$-0.723018\pi$
$809$	10.1032	−	22.1229i	0.355209	−	0.777799i	0.999911	−	0.0133649i	$-0.00425429\pi$
$810$	−6.43901	+	1.89067i	−0.226244	+	0.0664312i
$811$	−19.9309	−	43.6426i	−0.699869	−	1.53250i	−0.840130	−	0.542385i	$-0.817521\pi$
$811$	−19.9309	−	43.6426i	−0.699869	−	1.53250i	0.140261	−	0.990115i	$-0.455206\pi$
$812$	20.8185	+	24.0258i	0.730585	+	0.843140i
$813$	2.15265	+	14.9720i	0.0754966	+	0.525090i
$814$	2.60054	+	0.763589i	0.0911490	+	0.0267638i
$815$	10.7432	−	12.3983i	0.376316	−	0.434292i
$816$	7.46674	+	4.79859i	0.261388	+	0.167984i
$817$	27.8159	+	17.8762i	0.973154	+	0.625408i
$818$	17.5223	−	20.2218i	0.612654	−	0.707040i
$819$	−5.76385	−	1.69242i	−0.201405	−	0.0591379i
$820$	−1.62156	−	11.2782i	−0.0566273	−	0.393851i
$821$	−23.5725	−	27.2041i	−0.822684	−	0.949428i	0.176709	−	0.984263i	$-0.443455\pi$
$821$	−23.5725	−	27.2041i	−0.822684	−	0.949428i	−0.999393	+	0.0348348i	$0.988909\pi$
$822$	−1.92669	−	4.21887i	−0.0672012	−	0.147150i
$823$	25.5982	−	7.51631i	0.892297	−	0.262002i	0.196725	−	0.980459i	$-0.436969\pi$
$823$	25.5982	−	7.51631i	0.892297	−	0.262002i	0.695572	+	0.718457i	$0.255151\pi$
$824$	−0.723006	+	1.58316i	−0.0251871	+	0.0551521i
$825$	−1.21134	+	8.42508i	−0.0421736	+	0.293324i
$826$	−6.52745	+	4.19494i	−0.227119	+	0.145960i
$827$	−1.18494			−0.0412043			−0.0206021	−	0.999788i	$-0.506558\pi$
$827$	−1.18494			−0.0412043			−0.0206021	+	0.999788i	$0.506558\pi$
$828$	1.17811	+	2.78497i	0.0409420	+	0.0967844i
$829$	11.1131			0.385974			0.192987	−	0.981201i	$-0.438182\pi$
$829$	11.1131			0.385974			0.192987	+	0.981201i	$0.438182\pi$
$830$	−8.29886	+	5.33336i	−0.288058	+	0.185124i
$831$	2.57472	−	17.9076i	0.0893161	−	0.621207i
$832$	1.06457	−	2.33109i	0.0369075	−	0.0808161i
$833$	37.7382	−	11.0809i	1.30755	−	0.383931i
$834$	3.79567	+	8.31135i	0.131433	+	0.287799i
$835$	−9.39961	−	10.8477i	−0.325287	−	0.375401i
$836$	−2.87785	−	20.0159i	−0.0995324	−	0.692263i
$837$	49.5676	+	14.5544i	1.71331	+	0.503073i
$838$	3.00033	−	3.46256i	0.103645	−	0.119612i
$839$	−20.3005	−	13.0463i	−0.700851	−	0.450410i	0.141078	−	0.989999i	$-0.454943\pi$
$839$	−20.3005	−	13.0463i	−0.700851	−	0.450410i	−0.841929	+	0.539589i	$0.818580\pi$
$840$	−4.81421	−	3.09391i	−0.166106	−	0.106750i
$841$	−28.8945	+	33.3460i	−0.996361	+	1.14986i
$842$	13.9717	+	4.10246i	0.481496	+	0.141380i
$843$	−3.22826	−	22.4531i	−0.111187	−	0.773325i
$844$	5.62884	+	6.49603i	0.193753	+	0.223602i
$845$	2.67224	+	5.85138i	0.0919278	+	0.201294i
$846$	−5.88980	+	1.72940i	−0.202495	+	0.0594580i
$847$	−30.2331	+	66.2012i	−1.03882	+	2.27470i
$848$	−0.117392	+	0.816477i	−0.00403125	+	0.0280379i
$849$	2.68040	−	1.72259i	0.0919912	−	0.0591191i
$850$	−5.76605			−0.197774
$851$	1.58886	−	1.73241i	0.0544654	−	0.0593864i
$852$	−4.41424			−0.151229
$853$	−40.6178	+	26.1035i	−1.39073	+	0.893766i	−0.999646	−	0.0265898i	$-0.991535\pi$
$853$	−40.6178	+	26.1035i	−1.39073	+	0.893766i	−0.391081	+	0.920356i	$0.627899\pi$
$854$	5.00890	−	34.8377i	0.171401	−	1.19212i
$855$	−0.957882	+	2.09747i	−0.0327589	+	0.0717319i
$856$	−1.03800	+	0.304785i	−0.0354782	+	0.0104173i
$857$	−8.83336	−	19.3424i	−0.301742	−	0.660722i	0.696650	−	0.717411i	$-0.254673\pi$
$857$	−8.83336	−	19.3424i	−0.301742	−	0.660722i	−0.998392	+	0.0566887i	$0.981946\pi$
$858$	−14.2843	−	16.4850i	−0.487659	−	0.562789i
$859$	−0.768506	−	5.34508i	−0.0262211	−	0.182372i	0.972502	−	0.232896i	$-0.0748200\pi$
$859$	−0.768506	−	5.34508i	−0.0262211	−	0.182372i	−0.998723	+	0.0505238i	$0.983911\pi$
$860$	−8.67524	−	2.54728i	−0.295823	−	0.0868616i
$861$	42.7002	−	49.2787i	1.45522	−	1.67941i
$862$	−6.89156	−	4.42894i	−0.234728	−	0.150850i
$863$	−35.9868	−	23.1273i	−1.22500	−	0.787262i	−0.241898	−	0.970302i	$-0.577770\pi$
$863$	−35.9868	−	23.1273i	−1.22500	−	0.787262i	−0.983106	+	0.183040i	$0.941406\pi$
$864$	−3.65969	+	4.22351i	−0.124505	+	0.143687i
$865$	−9.98082	−	2.93063i	−0.339358	−	0.0996445i
$866$	−0.585457	−	4.07194i	−0.0198946	−	0.138370i
$867$	16.3779	+	18.9011i	0.556222	+	0.641914i
$868$	14.2763	+	31.2608i	0.484569	+	1.06106i
$869$	36.8725	−	10.8267i	1.25081	−	0.367272i
$870$	5.46808	−	11.9734i	0.185385	−	0.405937i
$871$	0.418223	−	2.90881i	0.0141710	−	0.0985611i
$872$	1.96632	−	1.26368i	0.0665881	−	0.0427936i
$873$	−1.61243			−0.0545724
$874$	−16.6819	−	5.41373i	−0.564274	−	0.183122i
$875$	3.71769			0.125681
$876$	4.16933	−	2.67947i	0.140869	−	0.0905308i
$877$	−2.20561	+	15.3404i	−0.0744782	+	0.518007i	0.918095	+	0.396360i	$0.129727\pi$
$877$	−2.20561	+	15.3404i	−0.0744782	+	0.518007i	−0.992573	+	0.121647i	$0.961182\pi$
$878$	−3.23665	+	7.08728i	−0.109232	+	0.239184i
$879$	−30.1946	+	8.86592i	−1.01844	+	0.299040i
$880$	2.29707	+	5.02988i	0.0774341	+	0.169557i
$881$	4.08664	+	4.71624i	0.137683	+	0.158894i	0.820403	−	0.571785i	$-0.193749\pi$
$881$	4.08664	+	4.71624i	0.137683	+	0.158894i	−0.682721	+	0.730679i	$0.739203\pi$
$882$	0.612089	+	4.25717i	0.0206101	+	0.143346i
$883$	−13.9018	−	4.08192i	−0.467831	−	0.137368i	0.0393164	−	0.999227i	$-0.487482\pi$
$883$	−13.9018	−	4.08192i	−0.467831	−	0.137368i	−0.507148	+	0.861859i	$0.669300\pi$
$884$	9.67656	−	11.1673i	0.325458	−	0.375599i
$885$	2.70269	+	1.73691i	0.0908500	+	0.0583857i
$886$	30.8087	+	19.7996i	1.03504	+	0.665179i
$887$	0.872745	−	1.00720i	0.0293039	−	0.0338185i	−0.740908	−	0.671606i	$-0.765605\pi$
$887$	0.872745	−	1.00720i	0.0293039	−	0.0338185i	0.770212	+	0.637788i	$0.220150\pi$
$888$	0.723933	+	0.212566i	0.0242936	+	0.00713325i
$889$	−1.30378	−	9.06798i	−0.0437273	−	0.304130i
$890$	2.34750	+	2.70916i	0.0786883	+	0.0908112i
$891$	15.4153	+	33.7547i	0.516431	+	1.13083i
$892$	−1.18625	+	0.348314i	−0.0397185	+	0.0116624i
$893$	14.7898	−	32.3851i	0.494922	−	1.08373i
$894$	0.327127	−	2.27522i	0.0109408	−	0.0760947i
$895$	10.6397	−	6.83769i	0.355644	−	0.228559i
$896$	−3.71769			−0.124199
$897$	−18.2951	+	4.81590i	−0.610856	+	0.160798i
$898$	3.52535			0.117642
$899$	−66.4990	+	42.7363i	−2.21787	+	1.42534i
$900$	0.0897335	−	0.624110i	0.00299112	−	0.0208037i
$901$	−1.97582	+	4.32645i	−0.0658242	+	0.144135i
$902$	−60.4527	+	17.7505i	−2.01285	+	0.591028i
$903$	−21.4942	−	47.0657i	−0.715281	−	1.56625i
$904$	−10.4804	−	12.0950i	−0.348573	−	0.402275i
$905$	−0.579681	−	4.03177i	−0.0192692	−	0.134020i
$906$	−23.0975	−	6.78205i	−0.767365	−	0.225319i
$907$	−17.4080	+	20.0899i	−0.578024	+	0.667076i	−0.967179	−	0.254097i	$-0.918222\pi$
$907$	−17.4080	+	20.0899i	−0.578024	+	0.667076i	0.389154	+	0.921173i	$0.372767\pi$
$908$	17.8116	+	11.4468i	0.591098	+	0.379876i
$909$	3.71075	+	2.38475i	0.123078	+	0.0790973i
$910$	−6.23900	+	7.20020i	−0.206821	+	0.238684i
$911$	10.5497	+	3.09766i	0.349526	+	0.102630i	0.451783	−	0.892128i	$-0.350788\pi$
$911$	10.5497	+	3.09766i	0.349526	+	0.102630i	−0.102257	+	0.994758i	$0.532606\pi$
$912$	−0.801128	−	5.57196i	−0.0265280	−	0.184506i
$913$	35.7217	+	41.2251i	1.18222	+	1.36435i
$914$	12.6748	+	27.7539i	0.419244	+	0.918016i
$915$	−13.9826	+	4.10566i	−0.462250	+	0.135729i
$916$	−4.66170	+	10.2077i	−0.154027	+	0.337272i
$917$	11.5809	−	80.5472i	0.382436	−	2.65990i
$918$	−27.1082	+	17.4214i	−0.894705	+	0.574992i
$919$	−29.3494			−0.968148			−0.484074	−	0.875027i	$-0.660844\pi$
$919$	−29.3494			−0.968148			−0.484074	+	0.875027i	$0.660844\pi$
$920$	4.79392	+	0.135245i	0.158051	+	0.00445890i
$921$	14.4271			0.475388
$922$	−5.47545	+	3.51886i	−0.180324	+	0.115887i
$923$	−1.04586	+	7.27412i	−0.0344249	+	0.239430i
$924$	−13.1454	+	28.7843i	−0.432450	+	0.946934i
$925$	−0.470298	+	0.138092i	−0.0154633	+	0.00454043i
$926$	1.96474	+	4.30219i	0.0645655	+	0.141379i
$927$	−0.718643	−	0.829358i	−0.0236033	−	0.0272397i
$928$	−1.21696	−	8.46416i	−0.0399488	−	0.277850i
$929$	−49.0664	−	14.4072i	−1.60982	−	0.472685i	−0.651561	−	0.758596i	$-0.725886\pi$
$929$	−49.0664	−	14.4072i	−1.60982	−	0.472685i	−0.958256	+	0.285911i	$0.907704\pi$
$930$	9.31828	−	10.7539i	0.305558	−	0.352633i
$931$	−20.9852	−	13.4864i	−0.687762	−	0.441998i
$932$	1.20614	+	0.775140i	0.0395085	+	0.0253906i
$933$	7.54368	−	8.70587i	0.246969	−	0.285017i
$934$	−25.6287	−	7.52526i	−0.838596	−	0.246234i
$935$	4.53754	+	31.5593i	0.148393	+	1.03210i
$936$	1.05815	+	1.22117i	0.0345867	+	0.0399152i
$937$	20.6118	+	45.1335i	0.673358	+	1.47445i	0.869531	+	0.493879i	$0.164421\pi$
$937$	20.6118	+	45.1335i	0.673358	+	1.47445i	−0.196173	+	0.980569i	$0.562851\pi$
$938$	−4.09052	+	1.20109i	−0.133560	+	0.0392168i
$939$	1.78172	−	3.90143i	0.0581443	−	0.127318i
$940$	−1.38549	+	9.63632i	−0.0451898	+	0.314302i
$941$	16.4081	−	10.5448i	0.534889	−	0.343752i	−0.245148	−	0.969486i	$-0.578837\pi$
$941$	16.4081	−	10.5448i	0.534889	−	0.343752i	0.780037	+	0.625733i	$0.215200\pi$
$942$	−9.40030			−0.306278
$943$	−9.29895	+	53.8475i	−0.302815	+	1.75351i
$944$	2.08710			0.0679294
$945$	17.4781	−	11.2325i	0.568564	−	0.365394i
$946$	−7.11511	+	49.4867i	−0.231332	+	1.60895i
$947$	16.5532	−	36.2466i	0.537908	−	1.17785i	−0.424295	−	0.905524i	$-0.639478\pi$
$947$	16.5532	−	36.2466i	0.537908	−	1.17785i	0.962204	−	0.272331i	$-0.0877945\pi$
$948$	10.2645	−	3.01392i	0.333374	−	0.0978876i
$949$	−3.42759	−	7.50538i	−0.111264	−	0.243635i
$950$	2.39483	+	2.76378i	0.0776985	+	0.0896689i
$951$	3.47305	+	24.1556i	0.112621	+	0.783299i
$952$	−20.5681	−	6.03932i	−0.666614	−	0.195736i
$953$	22.0955	−	25.4996i	0.715744	−	0.826012i	−0.275045	−	0.961431i	$-0.588693\pi$
$953$	22.0955	−	25.4996i	0.715744	−	0.826012i	0.990788	+	0.135419i	$0.0432381\pi$
$954$	−0.437540	−	0.281190i	−0.0141659	−	0.00910387i
$955$	5.16719	+	3.32075i	0.167206	+	0.107457i
$956$	4.53036	−	5.22831i	0.146522	−	0.169096i
$957$	−69.8371	−	20.5060i	−2.25751	−	0.662866i
$958$	1.15674	+	8.04527i	0.0373724	+	0.259931i
$959$	7.33545	+	8.46556i	0.236874	+	0.273367i
$960$	0.639452	+	1.40020i	0.0206382	+	0.0451914i
$961$	−52.2462	+	15.3409i	−1.68536	+	0.494867i
$962$	0.521803	−	1.14259i	0.0168236	−	0.0368386i
$963$	0.0970758	−	0.675177i	0.00312822	−	0.0217573i
$964$	−13.8682	+	8.91258i	−0.446666	+	0.287055i
$965$	−6.53510			−0.210372
$966$	17.3806	+	21.2401i	0.559210	+	0.683389i
$967$	12.3031			0.395642			0.197821	−	0.980238i	$-0.436614\pi$
$967$	12.3031			0.395642			0.197821	+	0.980238i	$0.436614\pi$
$968$	16.4685	−	10.5837i	0.529318	−	0.340172i
$969$	4.61934	−	32.1282i	0.148395	−	1.03211i
$970$	−1.06233	+	2.32617i	−0.0341093	+	0.0746889i
$971$	17.3680	−	5.09970i	0.557366	−	0.163657i	0.00909553	−	0.999959i	$-0.497105\pi$
$971$	17.3680	−	5.09970i	0.557366	−	0.163657i	0.548270	+	0.836301i	$0.315287\pi$
$972$	−2.67338	−	5.85388i	−0.0857486	−	0.187763i
$973$	−14.4511	−	16.6775i	−0.463282	−	0.534656i
$974$	1.05325	+	7.32550i	0.0337483	+	0.234724i
$975$	3.78496	+	1.11136i	0.121216	+	0.0355921i
$976$	−6.19967	+	7.15480i	−0.198447	+	0.229020i
$977$	34.3603	+	22.0820i	1.09928	+	0.706466i	0.958932	−	0.283636i	$-0.0915409\pi$
$977$	34.3603	+	22.0820i	1.09928	+	0.706466i	0.140350	+	0.990102i	$0.455177\pi$
$978$	−21.2440	−	13.6527i	−0.679307	−	0.436564i
$979$	12.9807	−	14.9805i	0.414864	−	0.478778i
$980$	6.54489	+	1.92175i	0.209069	+	0.0613881i
$981$	0.209741	+	1.45878i	0.00669650	+	0.0465752i
$982$	17.0158	+	19.6373i	0.542997	+	0.626652i
$983$	3.32105	+	7.27208i	0.105925	+	0.231943i	0.955171	−	0.296053i	$-0.0956706\pi$
$983$	3.32105	+	7.27208i	0.105925	+	0.231943i	−0.849246	+	0.527997i	$0.822943\pi$
$984$	−16.8287	+	4.94135i	−0.536479	+	0.157524i
$985$	−1.85089	+	4.05288i	−0.0589742	+	0.129135i
$986$	7.01707	−	48.8048i	0.223469	−	1.55426i
$987$	−46.8684	+	30.1205i	−1.49184	+	0.958745i
$988$	−9.37172			−0.298154
$989$	35.8024	+	24.4624i	1.13845	+	0.777857i
$990$	−3.48655			−0.110810
$991$	5.79182	−	3.72218i	0.183983	−	0.118239i	−0.445407	−	0.895328i	$-0.646941\pi$
$991$	5.79182	−	3.72218i	0.183983	−	0.118239i	0.629390	+	0.777089i	$0.283305\pi$
$992$	1.31556	−	9.14993i	0.0417691	−	0.290511i
$993$	7.02855	−	15.3904i	0.223044	−	0.488399i
$994$	10.2293	−	3.00358i	0.324453	−	0.0952679i
$995$	6.27822	+	13.7474i	0.199033	+	0.435821i
$996$	9.94412	+	11.4761i	0.315092	+	0.363635i
$997$	3.80406	+	26.4578i	0.120476	+	0.837928i	0.957019	+	0.290026i	$0.0936641\pi$
$997$	3.80406	+	26.4578i	0.120476	+	0.837928i	−0.836543	+	0.547902i	$0.815427\pi$
$998$	33.1286	+	9.72743i	1.04867	+	0.307916i
$999$	−1.79381	+	2.07016i	−0.0567535	+	0.0654970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.2.g.d.81.3	yes	30
23.2	even	11	inner	230.2.g.d.71.3	✓	30
23.5	odd	22		5290.2.a.bl.1.4		15
23.18	even	11		5290.2.a.bk.1.4		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.2.g.d.71.3	✓	30	23.2	even	11	inner
230.2.g.d.81.3	yes	30	1.1	even	1	trivial
5290.2.a.bk.1.4		15	23.18	even	11
5290.2.a.bl.1.4		15	23.5	odd	22

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	230.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.219067 - 1.52364i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.639452 - 1.40020i) q^{6} +(2.43457 + 2.80964i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(0.604987 + 0.177640i) q^{9} +O(q^{10})\)	\(q+(0.841254 - 0.540641i) q^{2} +(0.219067 - 1.52364i) q^{3} +(0.415415 - 0.909632i) q^{4} +(0.959493 - 0.281733i) q^{5} +(-0.639452 - 1.40020i) q^{6} +(2.43457 + 2.80964i) q^{7} +(-0.142315 - 0.989821i) q^{8} +(0.604987 + 0.177640i) q^{9} +(0.654861 - 0.755750i) q^{10} +(-4.65177 - 2.98951i) q^{11} +(-1.29495 - 0.832213i) q^{12} +(-1.67820 + 1.93674i) q^{13} +(3.56709 + 1.04739i) q^{14} +(-0.219067 - 1.52364i) q^{15} +(-0.654861 - 0.755750i) q^{16} +(-2.39530 - 5.24499i) q^{17} +(0.604987 - 0.177640i) q^{18} +(-1.51918 + 3.32653i) q^{19} +(0.142315 - 0.989821i) q^{20} +(4.81421 - 3.09391i) q^{21} -5.52957 q^{22} +(-2.11449 + 4.30452i) q^{23} -1.53931 q^{24} +(0.841254 - 0.540641i) q^{25} +(-0.364707 + 2.53659i) q^{26} +(2.32155 - 5.08348i) q^{27} +(3.56709 - 1.04739i) q^{28} +(3.55230 + 7.77845i) q^{29} +(-1.00803 - 1.16333i) q^{30} +(1.31556 + 9.14993i) q^{31} +(-0.959493 - 0.281733i) q^{32} +(-5.57399 + 6.43273i) q^{33} +(-4.85071 - 3.11736i) q^{34} +(3.12752 + 2.00993i) q^{35} +(0.412908 - 0.476521i) q^{36} +(-0.470298 - 0.138092i) q^{37} +(0.520446 + 3.61978i) q^{38} +(2.58326 + 2.98124i) q^{39} +(-0.415415 - 0.909632i) q^{40} +(10.9326 - 3.21011i) q^{41} +(2.37728 - 5.20552i) q^{42} +(1.28674 - 8.94946i) q^{43} +(-4.65177 + 2.98951i) q^{44} +0.630528 q^{45} +(0.548378 + 4.76438i) q^{46} -9.73542 q^{47} +(-1.29495 + 0.832213i) q^{48} +(-0.970757 + 6.75176i) q^{49} +(0.415415 - 0.909632i) q^{50} +(-8.51621 + 2.50058i) q^{51} +(1.06457 + 2.33109i) q^{52} +(-0.540177 - 0.623397i) q^{53} +(-0.795327 - 5.53162i) q^{54} +(-5.30559 - 1.55786i) q^{55} +(2.43457 - 2.80964i) q^{56} +(4.73564 + 3.04341i) q^{57} +(7.19373 + 4.62313i) q^{58} +(-1.36676 + 1.57733i) q^{59} +(-1.47696 - 0.433673i) q^{60} +(-1.34732 - 9.37080i) q^{61} +(6.05355 + 6.98617i) q^{62} +(0.973776 + 2.13227i) q^{63} +(-0.959493 + 0.281733i) q^{64} +(-1.06457 + 2.33109i) q^{65} +(-1.21134 + 8.42508i) q^{66} +(-0.964698 + 0.619974i) q^{67} -5.76605 q^{68} +(6.09534 + 4.16470i) q^{69} +3.71769 q^{70} +(2.41244 - 1.55038i) q^{71} +(0.0897335 - 0.624110i) q^{72} +(-1.33751 + 2.92873i) q^{73} +(-0.470298 + 0.138092i) q^{74} +(-0.639452 - 1.40020i) q^{75} +(2.39483 + 2.76378i) q^{76} +(-2.92560 - 20.3480i) q^{77} +(3.78496 + 1.11136i) q^{78} +(-4.55111 + 5.25227i) q^{79} +(-0.841254 - 0.540641i) q^{80} +(-5.64553 - 3.62816i) q^{81} +(7.46159 - 8.61113i) q^{82} +(-9.46528 - 2.77926i) q^{83} +(-0.814421 - 5.66442i) q^{84} +(-3.77596 - 4.35769i) q^{85} +(-3.75597 - 8.22443i) q^{86} +(12.6298 - 3.70843i) q^{87} +(-2.29707 + 5.02988i) q^{88} +(-0.510160 + 3.54824i) q^{89} +(0.530434 - 0.340889i) q^{90} -9.52722 q^{91} +(3.03714 + 3.71157i) q^{92} +14.2294 q^{93} +(-8.18995 + 5.26336i) q^{94} +(-0.520446 + 3.61978i) q^{95} +(-0.639452 + 1.40020i) q^{96} +(-2.45368 + 0.720465i) q^{97} +(2.83363 + 6.20477i) q^{98} +(-2.28320 - 2.63496i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9}+O(q^{10}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9	\( 30 q - 3 q^{2} - q^{3} - 3 q^{4} + 3 q^{5} - q^{6} + 8 q^{7} - 3 q^{8} + 12 q^{9} + 3 q^{10} - 3 q^{11} - q^{12} + 12 q^{13} - 3 q^{14} + q^{15} - 3 q^{16} - 26 q^{17} + 12 q^{18} - 25 q^{19} + 3 q^{20} - 11 q^{21} - 14 q^{22} + 14 q^{23} + 10 q^{24} - 3 q^{25} - 10 q^{26} - 52 q^{27} - 3 q^{28} + 4 q^{29} + q^{30} + 5 q^{31} - 3 q^{32} + 9 q^{33} + 7 q^{34} + 3 q^{35} + 12 q^{36} - 20 q^{37} + 19 q^{38} + 41 q^{39} + 3 q^{40} + 32 q^{41} + 22 q^{42} - 46 q^{43} - 3 q^{44} - 56 q^{45} + 3 q^{46} + 80 q^{47} - q^{48} - 41 q^{49} - 3 q^{50} - 34 q^{51} - 21 q^{52} + 29 q^{53} + 47 q^{54} + 3 q^{55} + 8 q^{56} - 33 q^{57} - 7 q^{58} - 3 q^{59} + q^{60} - q^{61} - 28 q^{62} - 8 q^{63} - 3 q^{64} + 21 q^{65} - 46 q^{66} - 63 q^{67} - 4 q^{68} + 78 q^{69} - 8 q^{70} + 55 q^{71} - 32 q^{72} - 36 q^{73} - 20 q^{74} - q^{75} - 3 q^{76} - 9 q^{77} - 80 q^{78} - 29 q^{79} + 3 q^{80} + 15 q^{81} - 23 q^{82} - 63 q^{83} + 4 q^{85} + 31 q^{86} + 63 q^{87} - 3 q^{88} - 95 q^{89} + 10 q^{90} - 12 q^{91} + 14 q^{92} + 126 q^{93} + 3 q^{94} - 19 q^{95} - q^{96} + 11 q^{97} + 58 q^{98} + 97 q^{99}+O(q^{100}) \) 30 * q - 3 * q^2 - q^3 - 3 * q^4 + 3 * q^5 - q^6 + 8 * q^7 - 3 * q^8 + 12 * q^9 + 3 * q^10 - 3 * q^11 - q^12 + 12 * q^13 - 3 * q^14 + q^15 - 3 * q^16 - 26 * q^17 + 12 * q^18 - 25 * q^19 + 3 * q^20 - 11 * q^21 - 14 * q^22 + 14 * q^23 + 10 * q^24 - 3 * q^25 - 10 * q^26 - 52 * q^27 - 3 * q^28 + 4 * q^29 + q^30 + 5 * q^31 - 3 * q^32 + 9 * q^33 + 7 * q^34 + 3 * q^35 + 12 * q^36 - 20 * q^37 + 19 * q^38 + 41 * q^39 + 3 * q^40 + 32 * q^41 + 22 * q^42 - 46 * q^43 - 3 * q^44 - 56 * q^45 + 3 * q^46 + 80 * q^47 - q^48 - 41 * q^49 - 3 * q^50 - 34 * q^51 - 21 * q^52 + 29 * q^53 + 47 * q^54 + 3 * q^55 + 8 * q^56 - 33 * q^57 - 7 * q^58 - 3 * q^59 + q^60 - q^61 - 28 * q^62 - 8 * q^63 - 3 * q^64 + 21 * q^65 - 46 * q^66 - 63 * q^67 - 4 * q^68 + 78 * q^69 - 8 * q^70 + 55 * q^71 - 32 * q^72 - 36 * q^73 - 20 * q^74 - q^75 - 3 * q^76 - 9 * q^77 - 80 * q^78 - 29 * q^79 + 3 * q^80 + 15 * q^81 - 23 * q^82 - 63 * q^83 + 4 * q^85 + 31 * q^86 + 63 * q^87 - 3 * q^88 - 95 * q^89 + 10 * q^90 - 12 * q^91 + 14 * q^92 + 126 * q^93 + 3 * q^94 - 19 * q^95 - q^96 + 11 * q^97 + 58 * q^98 + 97 * q^99

Introduction

L-functions

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