LMFDB - Embedded newform 164.2.o.b.15.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [164,2,Mod(7,164)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(164, base_ring=CyclotomicField(40))

chi = DirichletCharacter(H, H._module([20, 39]))

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

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

chi := DirichletCharacter("164.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 164 = 2^{2} \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	164.o (of order $40$, degree $16$, 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:	$1.30954659315$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{40})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{40}]$

Embedding invariants

Embedding label			15.17
Character	$\chi$	$=$	164.15
Dual form			164.2.o.b.11.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29014 + 0.579249i) q^{2} +(-0.756584 - 1.82656i) q^{3} +(1.32894 + 1.49463i) q^{4} +(-1.28598 - 2.52388i) q^{5} +(0.0819284 - 2.79477i) q^{6} +(0.634663 - 2.64356i) q^{7} +(0.848763 + 2.69807i) q^{8} +(-0.642564 + 0.642564i) q^{9} +O(q^{10})$	\(q+(1.29014 + 0.579249i) q^{2} +(-0.756584 - 1.82656i) q^{3} +(1.32894 + 1.49463i) q^{4} +(-1.28598 - 2.52388i) q^{5} +(0.0819284 - 2.79477i) q^{6} +(0.634663 - 2.64356i) q^{7} +(0.848763 + 2.69807i) q^{8} +(-0.642564 + 0.642564i) q^{9} +(-0.197145 - 4.00108i) q^{10} +(3.28267 + 3.84351i) q^{11} +(1.72457 - 3.55820i) q^{12} +(-2.94163 + 4.80031i) q^{13} +(2.35009 - 3.04295i) q^{14} +(-3.63706 + 4.25845i) q^{15} +(-0.467831 + 3.97255i) q^{16} +(0.0571608 - 0.726296i) q^{17} +(-1.20120 + 0.456795i) q^{18} +(0.531502 - 0.325705i) q^{19} +(2.06327 - 5.27616i) q^{20} +(-5.30879 + 0.840829i) q^{21} +(2.00877 + 6.86017i) q^{22} +(0.882818 - 0.641405i) q^{23} +(4.28602 - 3.59163i) q^{24} +(-1.77731 + 2.44625i) q^{25} +(-6.57571 + 4.48915i) q^{26} +(-3.81983 - 1.58223i) q^{27} +(4.79457 - 2.56455i) q^{28} +(-0.452928 - 5.75499i) q^{29} +(-7.15903 + 3.38725i) q^{30} +(2.23549 + 6.88014i) q^{31} +(-2.90466 + 4.85417i) q^{32} +(4.53677 - 8.90392i) q^{33} +(0.494452 - 0.903916i) q^{34} +(-7.48820 + 1.79776i) q^{35} +(-1.81432 - 0.106465i) q^{36} +(-1.79487 + 5.52404i) q^{37} +(0.874378 - 0.112334i) q^{38} +(10.9936 + 1.74122i) q^{39} +(5.71813 - 5.61185i) q^{40} +(4.55866 + 4.49651i) q^{41} +(-7.33615 - 1.99032i) q^{42} +(-0.642081 + 4.05394i) q^{43} +(-1.38215 + 10.0142i) q^{44} +(2.44808 + 0.795430i) q^{45} +(1.51050 - 0.316133i) q^{46} +(-2.91790 - 12.1539i) q^{47} +(7.61003 - 2.15105i) q^{48} +(-0.348572 - 0.177606i) q^{49} +(-3.70997 + 2.12651i) q^{50} +(-1.36987 + 0.445097i) q^{51} +(-11.0839 + 1.98268i) q^{52} +(-7.02659 + 0.553004i) q^{53} +(-4.01163 - 4.25393i) q^{54} +(5.47912 - 13.2278i) q^{55} +(7.67120 - 0.531388i) q^{56} +(-0.997043 - 0.724394i) q^{57} +(2.74923 - 7.68713i) q^{58} +(-2.32978 - 3.20667i) q^{59} +(-11.1982 + 0.223174i) q^{60} +(-0.330485 - 2.08660i) q^{61} +(-1.10121 + 10.1713i) q^{62} +(1.29085 + 2.10647i) q^{63} +(-6.55920 + 4.58005i) q^{64} +(15.8983 + 1.25122i) q^{65} +(11.0107 - 8.85941i) q^{66} +(-2.50427 - 2.13885i) q^{67} +(1.16151 - 0.879771i) q^{68} +(-1.83949 - 1.12724i) q^{69} +(-10.7022 - 2.01817i) q^{70} +(9.35782 - 7.99233i) q^{71} +(-2.27907 - 1.18830i) q^{72} +(3.14718 + 3.14718i) q^{73} +(-5.51544 + 6.08713i) q^{74} +(5.81290 + 1.39555i) q^{75} +(1.19314 + 0.361555i) q^{76} +(12.2440 - 6.23860i) q^{77} +(13.1748 + 8.61447i) q^{78} +(-14.9861 + 6.20746i) q^{79} +(10.6279 - 3.92788i) q^{80} +10.9004i q^{81} +(3.27673 + 8.44175i) q^{82} +6.63164i q^{83} +(-8.31179 - 6.81725i) q^{84} +(-1.90659 + 0.789737i) q^{85} +(-3.17662 + 4.85824i) q^{86} +(-10.1691 + 5.18143i) q^{87} +(-7.58388 + 12.1191i) q^{88} +(7.99728 + 1.91998i) q^{89} +(2.69763 + 2.44427i) q^{90} +(10.8230 + 10.8230i) q^{91} +(2.13188 + 0.467096i) q^{92} +(10.8756 - 9.28865i) q^{93} +(3.27564 - 17.3705i) q^{94} +(-1.50554 - 0.922597i) q^{95} +(11.0640 + 1.63294i) q^{96} +(-8.34861 - 7.13039i) q^{97} +(-0.346829 - 0.431047i) q^{98} +(-4.57903 - 0.360378i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	$ 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) $ 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/164\mathbb{Z}\right)^\times$.

$n$	$83$	$129$
$\chi(n)$	$-1$	$e\left(\frac{37}{40}\right)$

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 $

$2$	1.29014	+	0.579249i	0.912269	+	0.409591i
$2$	1.29014	+	0.579249i	0.912269	+	0.409591i
$3$	−0.756584	−	1.82656i	−0.436814	−	1.05456i	−0.977043	−	0.213044i	$-0.931662\pi$
$3$	−0.756584	−	1.82656i	−0.436814	−	1.05456i	0.540229	−	0.841518i	$-0.318338\pi$
$4$	1.32894	+	1.49463i	0.664471	+	0.747314i
$5$	−1.28598	−	2.52388i	−0.575109	−	1.12871i	−0.977042	−	0.213046i	$-0.931662\pi$
$5$	−1.28598	−	2.52388i	−0.575109	−	1.12871i	0.401933	−	0.915669i	$-0.368338\pi$
$6$	0.0819284	−	2.79477i	0.0334471	−	1.14096i
$7$	0.634663	−	2.64356i	0.239880	−	0.999172i	−0.714276	−	0.699864i	$-0.753244\pi$
$7$	0.634663	−	2.64356i	0.239880	−	0.999172i	0.954156	−	0.299308i	$-0.0967559\pi$
$8$	0.848763	+	2.69807i	0.300083	+	0.953913i
$9$	−0.642564	+	0.642564i	−0.214188	+	0.214188i
$10$	−0.197145	−	4.00108i	−0.0623429	−	1.26525i
$11$	3.28267	+	3.84351i	0.989762	+	1.15886i	0.987300	+	0.158866i	$0.0507838\pi$
$11$	3.28267	+	3.84351i	0.989762	+	1.15886i	0.00246234	+	0.999997i	$0.499216\pi$
$12$	1.72457	−	3.55820i	0.497840	−	1.02716i
$13$	−2.94163	+	4.80031i	−0.815862	+	1.33137i	0.124855	+	0.992175i	$0.460153\pi$
$13$	−2.94163	+	4.80031i	−0.815862	+	1.33137i	−0.940717	+	0.339191i	$0.889847\pi$
$14$	2.35009	−	3.04295i	0.628087	−	0.813261i
$15$	−3.63706	+	4.25845i	−0.939084	+	1.09953i
$16$	−0.467831	+	3.97255i	−0.116958	+	0.993137i
$17$	0.0571608	−	0.726296i	0.0138635	−	0.176153i	−0.986087	−	0.166229i	$-0.946841\pi$
$17$	0.0571608	−	0.726296i	0.0138635	−	0.176153i	0.999951	−	0.00992409i	$-0.00315899\pi$
$18$	−1.20120	+	0.456795i	−0.283127	+	0.107668i
$19$	0.531502	−	0.325705i	0.121935	−	0.0747218i	−0.460194	−	0.887819i	$-0.652220\pi$
$19$	0.531502	−	0.325705i	0.121935	−	0.0747218i	0.582129	+	0.813097i	$0.302220\pi$
$20$	2.06327	−	5.27616i	0.461362	−	1.17978i
$21$	−5.30879	+	0.840829i	−1.15847	+	0.183484i
$22$	2.00877	+	6.86017i	0.428270	+	1.46259i
$23$	0.882818	−	0.641405i	0.184080	−	0.133742i	−0.491929	−	0.870635i	$-0.663708\pi$
$23$	0.882818	−	0.641405i	0.184080	−	0.133742i	0.676009	+	0.736893i	$0.263708\pi$
$24$	4.28602	−	3.59163i	0.874880	−	0.733139i
$25$	−1.77731	+	2.44625i	−0.355461	+	0.489251i
$26$	−6.57571	+	4.48915i	−1.28960	+	0.880395i
$27$	−3.81983	−	1.58223i	−0.735127	−	0.304500i
$28$	4.79457	−	2.56455i	0.906089	−	0.484655i
$29$	−0.452928	−	5.75499i	−0.0841066	−	1.06868i	−0.883675	−	0.468101i	$-0.844938\pi$
$29$	−0.452928	−	5.75499i	−0.0841066	−	1.06868i	0.799569	−	0.600575i	$-0.205062\pi$
$30$	−7.15903	+	3.38725i	−1.30705	+	0.618424i
$31$	2.23549	+	6.88014i	0.401506	+	1.23571i	0.923777	+	0.382930i	$0.125085\pi$
$31$	2.23549	+	6.88014i	0.401506	+	1.23571i	−0.522271	+	0.852780i	$0.674915\pi$
$32$	−2.90466	+	4.85417i	−0.513477	+	0.858103i
$33$	4.53677	−	8.90392i	0.789751	−	1.54997i
$34$	0.494452	−	0.903916i	0.0847978	−	0.155020i
$35$	−7.48820	+	1.79776i	−1.26574	+	0.303877i
$36$	−1.81432	−	0.106465i	−0.302387	−	0.0177442i
$37$	−1.79487	+	5.52404i	−0.295075	+	0.908147i	0.688121	+	0.725596i	$0.258436\pi$
$37$	−1.79487	+	5.52404i	−0.295075	+	0.908147i	−0.983196	+	0.182552i	$0.941564\pi$
$38$	0.874378	−	0.112334i	0.141843	−	0.0182230i
$39$	10.9936	+	1.74122i	1.76039	+	0.278818i
$40$	5.71813	−	5.61185i	0.904115	−	0.887312i
$41$	4.55866	+	4.49651i	0.711943	+	0.702237i
$41$	4.55866	+	4.49651i	0.711943	+	0.702237i
$42$	−7.33615	−	1.99032i	−1.13199	−	0.307113i
$43$	−0.642081	+	4.05394i	−0.0979164	+	0.618220i	0.889114	+	0.457686i	$0.151322\pi$
$43$	−0.642081	+	4.05394i	−0.0979164	+	0.618220i	−0.987030	+	0.160534i	$0.948678\pi$
$44$	−1.38215	+	10.0142i	−0.208367	+	1.50969i
$45$	2.44808	+	0.795430i	0.364939	+	0.118576i
$46$	1.51050	−	0.316133i	0.222710	−	0.0466113i
$47$	−2.91790	−	12.1539i	−0.425619	−	1.77283i	−0.612522	−	0.790454i	$-0.709845\pi$
$47$	−2.91790	−	12.1539i	−0.425619	−	1.77283i	0.186903	−	0.982378i	$-0.440155\pi$
$48$	7.61003	−	2.15105i	1.09841	−	0.310477i
$49$	−0.348572	−	0.177606i	−0.0497960	−	0.0253723i
$50$	−3.70997	+	2.12651i	−0.524669	+	0.300735i
$51$	−1.36987	+	0.445097i	−0.191820	+	0.0623260i
$52$	−11.0839	+	1.98268i	−1.53707	+	0.274948i
$53$	−7.02659	+	0.553004i	−0.965176	+	0.0759610i	−0.551242	−	0.834346i	$-0.685846\pi$
$53$	−7.02659	+	0.553004i	−0.965176	+	0.0759610i	−0.413934	+	0.910307i	$0.635846\pi$
$54$	−4.01163	−	4.25393i	−0.545914	−	0.578887i
$55$	5.47912	−	13.2278i	0.738805	−	1.78363i
$56$	7.67120	−	0.531388i	1.02511	−	0.0710097i
$57$	−0.997043	−	0.724394i	−0.132062	−	0.0959484i
$58$	2.74923	−	7.68713i	0.360992	−	1.00937i
$59$	−2.32978	−	3.20667i	−0.303312	−	0.417473i	0.629969	−	0.776620i	$-0.283068\pi$
$59$	−2.32978	−	3.20667i	−0.303312	−	0.417473i	−0.933281	+	0.359147i	$0.883068\pi$
$60$	−11.1982	+	0.223174i	−1.44569	+	0.0288117i
$61$	−0.330485	−	2.08660i	−0.0423142	−	0.267162i	0.957456	−	0.288578i	$-0.0931824\pi$
$61$	−0.330485	−	2.08660i	−0.0423142	−	0.267162i	−0.999771	+	0.0214164i	$0.993182\pi$
$62$	−1.10121	+	10.1713i	−0.139853	+	1.29175i
$63$	1.29085	+	2.10647i	0.162631	+	0.265390i
$64$	−6.55920	+	4.58005i	−0.819901	+	0.572506i
$65$	15.8983	+	1.25122i	1.97194	+	0.155195i
$66$	11.0107	−	8.85941i	1.35532	−	1.09052i
$67$	−2.50427	−	2.13885i	−0.305945	−	0.261302i	0.483198	−	0.875511i	$-0.339475\pi$
$67$	−2.50427	−	2.13885i	−0.305945	−	0.261302i	−0.789143	+	0.614209i	$0.789475\pi$
$68$	1.16151	−	0.879771i	0.140853	−	0.106688i
$69$	−1.83949	−	1.12724i	−0.221448	−	0.135704i
$70$	−10.7022	−	2.01817i	−1.27916	−	0.241217i
$71$	9.35782	−	7.99233i	1.11057	−	0.948515i	0.111592	−	0.993754i	$-0.464405\pi$
$71$	9.35782	−	7.99233i	1.11057	−	0.948515i	0.998976	+	0.0452390i	$0.0144049\pi$
$72$	−2.27907	−	1.18830i	−0.268591	−	0.140043i
$73$	3.14718	+	3.14718i	0.368349	+	0.368349i	0.866875	−	0.498526i	$-0.166125\pi$
$73$	3.14718	+	3.14718i	0.368349	+	0.368349i	−0.498526	+	0.866875i	$0.666125\pi$
$74$	−5.51544	+	6.08713i	−0.641157	+	0.707615i
$75$	5.81290	+	1.39555i	0.671216	+	0.161145i
$76$	1.19314	+	0.361555i	0.136863	+	0.0414733i
$77$	12.2440	−	6.23860i	1.39533	−	0.710955i
$78$	13.1748	+	8.61447i	1.49175	+	0.975396i
$79$	−14.9861	+	6.20746i	−1.68607	+	0.698394i	−0.999587	−	0.0287504i	$-0.990847\pi$
$79$	−14.9861	+	6.20746i	−1.68607	+	0.698394i	−0.686485	+	0.727144i	$0.740847\pi$
$80$	10.6279	−	3.92788i	1.18823	−	0.439150i
$81$			10.9004i			1.21115i
$82$	3.27673	+	8.44175i	0.361854	+	0.932235i
$83$			6.63164i			0.727917i	0.931415	+	0.363958i	$0.118575\pi$
$83$			6.63164i			0.727917i	−0.931415	+	0.363958i	$0.881425\pi$
$84$	−8.31179	−	6.81725i	−0.906891	−	0.743823i
$85$	−1.90659	+	0.789737i	−0.206799	+	0.0856591i
$86$	−3.17662	+	4.85824i	−0.342543	+	0.523877i
$87$	−10.1691	+	5.18143i	−1.09025	+	0.555508i
$88$	−7.58388	+	12.1191i	−0.808444	+	1.29190i
$89$	7.99728	+	1.91998i	0.847710	+	0.203517i	0.633955	−	0.773370i	$-0.281430\pi$
$89$	7.99728	+	1.91998i	0.847710	+	0.203517i	0.213755	+	0.976887i	$0.431430\pi$
$90$	2.69763	+	2.44427i	0.284355	+	0.257649i
$91$	10.8230	+	10.8230i	1.13456	+	1.13456i
$92$	2.13188	+	0.467096i	0.222263	+	0.0486981i
$93$	10.8756	−	9.28865i	1.12775	−	0.963189i
$94$	3.27564	−	17.3705i	0.337856	−	1.79163i
$95$	−1.50554	−	0.922597i	−0.154465	−	0.0946565i
$96$	11.0640	+	1.63294i	1.12922	+	0.166662i
$97$	−8.34861	−	7.13039i	−0.847673	−	0.723981i	0.115372	−	0.993322i	$-0.463194\pi$
$97$	−8.34861	−	7.13039i	−0.847673	−	0.723981i	−0.963045	+	0.269341i	$0.913194\pi$
$98$	−0.346829	−	0.431047i	−0.0350351	−	0.0435423i
$99$	−4.57903	−	0.360378i	−0.460210	−	0.0362193i
$100$	−6.01818	+	0.594512i	−0.601818	+	0.0594512i
$101$	−5.80846	−	9.47855i	−0.577963	−	0.943151i	−0.999342	−	0.0362659i	$-0.988454\pi$
$101$	−5.80846	−	9.47855i	−0.577963	−	0.943151i	0.421379	−	0.906885i	$-0.361546\pi$
$102$	−2.02515	−	0.219255i	−0.200519	−	0.0217095i
$103$	−0.586386	−	3.70230i	−0.0577784	−	0.364798i	−0.999589	−	0.0286553i	$-0.990877\pi$
$103$	−0.586386	−	3.70230i	−0.0577784	−	0.364798i	0.941811	−	0.336143i	$-0.109123\pi$
$104$	−15.4483	−	3.86242i	−1.51483	−	0.378742i
$105$	8.94916	+	12.3175i	0.873349	+	1.20206i
$106$	−9.38563	−	3.35669i	−0.911613	−	0.326030i
$107$	−4.95050	−	3.59675i	−0.478583	−	0.347711i	0.322194	−	0.946674i	$-0.395580\pi$
$107$	−4.95050	−	3.59675i	−0.478583	−	0.347711i	−0.800777	+	0.598963i	$0.795580\pi$
$108$	−2.71149	−	7.81192i	−0.260913	−	0.751702i
$109$	2.08867	−	5.04249i	0.200058	−	0.482983i	−0.791731	−	0.610870i	$-0.790820\pi$
$109$	2.08867	−	5.04249i	0.200058	−	0.482983i	0.991789	+	0.127888i	$0.0408196\pi$
$110$	14.7310	−	13.8919i	1.40455	−	1.32454i
$111$	11.4479	−	0.900972i	1.08659	−	0.0855165i
$112$	10.2048	+	3.75797i	0.964259	+	0.355095i
$113$	3.65621	−	1.18798i	0.343947	−	0.111755i	−0.131949	−	0.991256i	$-0.542124\pi$
$113$	3.65621	−	1.18798i	0.343947	−	0.111755i	0.475897	+	0.879501i	$0.342124\pi$
$114$	−0.866724	−	1.51211i	−0.0811761	−	0.141622i
$115$	−2.75412	−	1.40329i	−0.256823	−	0.130858i
$116$	7.99967	−	8.32501i	0.742750	−	0.772957i
$117$	−1.19432	−	4.97470i	−0.110415	−	0.459911i
$118$	−1.14829	−	5.48659i	−0.105709	−	0.505082i
$119$	−1.88373	−	0.612061i	−0.172681	−	0.0561076i
$120$	−14.5766	−	6.19864i	−1.33066	−	0.565856i
$121$	−2.27589	+	14.3694i	−0.206899	+	1.30631i
$122$	0.782287	−	2.88344i	0.0708250	−	0.261055i
$123$	4.76412	−	11.7286i	0.429566	−	1.05754i
$124$	−7.31242	+	12.4845i	−0.656674	+	1.12114i
$125$	−5.52908	−	0.875721i	−0.494536	−	0.0783269i
$126$	0.445206	+	3.46537i	0.0396621	+	0.308720i
$127$	2.62707	−	8.08529i	0.233115	−	0.717453i	−0.764251	−	0.644919i	$-0.776891\pi$
$127$	2.62707	−	8.08529i	0.233115	−	0.717453i	0.997366	−	0.0725347i	$-0.0231088\pi$
$128$	−11.1153	+	2.10951i	−0.982463	+	0.186456i
$129$	7.89053	−	1.89435i	0.694722	−	0.166788i
$130$	19.7863	+	10.8233i	1.73538	+	0.949270i
$131$	−1.26693	+	2.48649i	−0.110692	+	0.217246i	−0.939707	−	0.341981i	$-0.888902\pi$
$131$	−1.26693	+	2.48649i	−0.110692	+	0.217246i	0.829015	+	0.559227i	$0.188902\pi$
$132$	19.3372	−	5.05199i	1.68308	−	0.439719i
$133$	−0.523696	−	1.61177i	−0.0454102	−	0.139758i
$134$	−1.99194	−	4.21001i	−0.172077	−	0.363690i
$135$	0.918884	+	11.6755i	0.0790849	+	1.00487i
$136$	2.00812	−	0.462229i	0.172195	−	0.0396358i
$137$	−19.8790	−	8.23413i	−1.69837	−	0.703489i	−0.698448	−	0.715661i	$-0.746126\pi$
$137$	−19.8790	−	8.23413i	−1.69837	−	0.703489i	−0.999926	+	0.0121718i	$0.996126\pi$
$138$	−1.72025	−	2.51982i	−0.146437	−	0.214501i
$139$	1.29283	−	1.77942i	0.109656	−	0.150929i	−0.750662	−	0.660687i	$-0.770265\pi$
$139$	1.29283	−	1.77942i	0.109656	−	0.150929i	0.860318	+	0.509758i	$0.170265\pi$
$140$	−12.6384	−	8.80297i	−1.06814	−	0.743987i
$141$	−19.9922	+	14.5252i	−1.68365	+	1.22324i
$142$	16.7025	−	4.89075i	1.40164	−	0.410422i
$143$	−28.1065	+	4.45163i	−2.35038	+	0.372264i
$144$	−2.25200	−	2.85323i	−0.187667	−	0.237769i
$145$	−13.9425	+	8.54396i	−1.15786	+	0.709537i
$146$	2.23731	+	5.88331i	0.185161	+	0.486906i
$147$	−0.0606837	+	0.771059i	−0.00500511	+	0.0635959i
$148$	−10.6417	+	4.65846i	−0.874740	+	0.382923i
$149$	7.79130	−	9.12244i	0.638288	−	0.747339i	−0.343116	−	0.939293i	$-0.611482\pi$
$149$	7.79130	−	9.12244i	0.638288	−	0.747339i	0.981404	+	0.191954i	$0.0614824\pi$
$150$	6.69110	+	5.16758i	0.546326	+	0.421931i
$151$	−3.89605	+	6.35778i	−0.317056	+	0.517388i	−0.970977	−	0.239175i	$-0.923123\pi$
$151$	−3.89605	+	6.35778i	−0.317056	+	0.517388i	0.653920	+	0.756563i	$0.273123\pi$
$152$	1.32989	+	1.15758i	0.107869	+	0.0938925i
$153$	0.429963	+	0.503421i	0.0347604	+	0.0406992i
$154$	19.4102	−	0.956399i	1.56412	−	0.0770688i
$155$	14.4899	−	14.4899i	1.16385	−	1.16385i
$156$	12.0074	+	18.7454i	0.961362	+	1.50083i
$157$	−4.46047	+	18.5792i	−0.355984	+	1.48278i	0.451169	+	0.892439i	$0.351007\pi$
$157$	−4.46047	+	18.5792i	−0.355984	+	1.48278i	−0.807153	+	0.590342i	$0.798993\pi$
$158$	−22.9299	−	0.672189i	−1.82421	−	0.0534765i
$159$	6.32630	+	12.4161i	0.501708	+	0.984657i
$160$	15.9867	+	1.08866i	1.26386	+	0.0860660i
$161$	−1.13530	−	2.74086i	−0.0894743	−	0.216010i
$162$	−6.31404	+	14.0631i	−0.496078	+	1.10490i
$163$	24.4302			1.91352			0.956760	−	0.290880i	$-0.0939481\pi$
$163$	24.4302			1.91352			0.956760	+	0.290880i	$0.0939481\pi$
$164$	−0.662425	+	12.7891i	−0.0517267	+	0.998661i
$165$	−28.3067			−2.20367
$166$	−3.84137	+	8.55576i	−0.298148	+	0.664056i
$167$	7.00002	+	16.8995i	0.541678	+	1.30773i	0.923539	+	0.383506i	$0.125283\pi$
$167$	7.00002	+	16.8995i	0.541678	+	1.30773i	−0.381861	+	0.924220i	$0.624717\pi$
$168$	−6.77452	−	13.6098i	−0.522665	−	1.05002i
$169$	−8.48789	−	16.6584i	−0.652915	−	1.28142i
$170$	−2.91724	−	0.0855185i	−0.223742	−	0.00655897i
$171$	−0.132238	+	0.550810i	−0.0101125	+	0.0421215i
$172$	−6.91242	+	4.42777i	−0.527067	+	0.337614i
$173$	−2.96217	+	2.96217i	−0.225210	+	0.225210i	−0.810688	−	0.585478i	$-0.800907\pi$
$173$	−2.96217	+	2.96217i	−0.225210	+	0.225210i	0.585478	+	0.810688i	$0.300907\pi$
$174$	−16.1210	+	0.794331i	−1.22213	+	0.0602181i
$175$	5.33883	+	6.25097i	0.403578	+	0.472529i
$176$	−16.8043	+	11.2425i	−1.26667	+	0.847432i
$177$	−4.09449	+	6.68159i	−0.307760	+	0.502219i
$178$	9.20550	+	7.10946i	0.689981	+	0.532877i
$179$	−7.74208	+	9.06482i	−0.578671	+	0.677536i	−0.970109	−	0.242668i	$-0.921977\pi$
$179$	−7.74208	+	9.06482i	−0.578671	+	0.677536i	0.391439	+	0.920204i	$0.371977\pi$
$180$	2.06448	+	4.71606i	0.153878	+	0.351514i
$181$	−0.507298	+	6.44584i	−0.0377072	+	0.479115i	0.948853	+	0.315718i	$0.102245\pi$
$181$	−0.507298	+	6.44584i	−0.0377072	+	0.479115i	−0.986560	+	0.163397i	$0.947755\pi$
$182$	7.69399	+	20.2324i	0.570316	+	1.49972i
$183$	−3.56125	+	2.18234i	−0.263255	+	0.161323i
$184$	2.47986	+	1.83751i	0.182818	+	0.135463i
$185$	16.2502	−	2.57378i	1.19474	−	0.189228i
$186$	19.4116	−	5.68401i	1.42332	−	0.416772i
$187$	2.97917	−	2.16449i	0.217859	−	0.158283i
$188$	14.2879	−	20.5130i	1.04205	−	1.49607i
$189$	−6.60702	+	9.09378i	−0.480590	+	0.661475i
$190$	−1.40795	−	2.06237i	−0.102144	−	0.149620i
$191$	−2.82698	−	1.17097i	−0.204553	−	0.0847287i	0.278055	−	0.960565i	$-0.410310\pi$
$191$	−2.82698	−	1.17097i	−0.204553	−	0.0847287i	−0.482608	+	0.875837i	$0.660310\pi$
$192$	13.3283	+	8.51556i	0.961887	+	0.614557i
$193$	−0.690746	−	8.77676i	−0.0497210	−	0.631765i	−0.970409	−	0.241466i	$-0.922372\pi$
$193$	−0.690746	−	8.77676i	−0.0497210	−	0.631765i	0.920688	−	0.390299i	$-0.127628\pi$
$194$	−6.64064	−	14.0352i	−0.476770	−	1.00767i
$195$	−9.74298	−	29.9858i	−0.697709	−	2.14733i
$196$	−0.197776	−	0.757013i	−0.0141269	−	0.0540724i
$197$	9.01440	−	17.6918i	0.642249	−	1.26049i	−0.308706	−	0.951158i	$-0.599896\pi$
$197$	9.01440	−	17.6918i	0.642249	−	1.26049i	0.950955	−	0.309328i	$-0.100104\pi$
$198$	−5.69886	−	3.11734i	−0.405000	−	0.221540i
$199$	−4.66888	+	1.12090i	−0.330968	+	0.0794585i	−0.395524	−	0.918456i	$-0.629437\pi$
$199$	−4.66888	+	1.12090i	−0.330968	+	0.0794585i	0.0645557	+	0.997914i	$0.479437\pi$
$200$	−8.10868	−	2.71902i	−0.573371	−	0.192264i
$201$	−2.01203	+	6.19240i	−0.141918	+	0.436778i
$202$	−2.00331	−	15.5932i	−0.140952	−	1.09714i
$203$	−15.5011	−	2.45514i	−1.08797	−	0.172317i
$204$	−2.48573	−	1.45594i	−0.174036	−	0.101936i
$205$	5.48631	−	17.2880i	0.383181	−	1.20744i
$206$	1.38803	−	5.11616i	0.0967086	−	0.356460i
$207$	−0.155123	+	0.979411i	−0.0107818	+	0.0680738i
$208$	−17.6933	−	13.9315i	−1.22681	−	0.965977i
$209$	2.99660	+	0.973653i	0.207279	+	0.0673490i
$210$	4.41082	+	21.0751i	0.304376	+	1.45432i
$211$	1.07793	+	4.48989i	0.0742076	+	0.309097i	0.997113	−	0.0759294i	$-0.0241924\pi$
$211$	1.07793	+	4.48989i	0.0742076	+	0.309097i	−0.922906	+	0.385026i	$0.874192\pi$
$212$	−10.1645	−	9.76723i	−0.698098	−	0.670816i
$213$	−21.6784	−	11.0457i	−1.48538	−	0.756839i
$214$	−4.30344	−	7.50790i	−0.294177	−	0.513229i
$215$	11.0574	−	3.59276i	0.754106	−	0.245024i
$216$	1.02683	−	11.6491i	0.0698671	−	0.792623i
$217$	19.6069	−	1.54309i	1.33100	−	0.104752i
$218$	5.61554	−	5.29568i	0.380332	−	0.358668i
$219$	3.36739	−	8.12959i	0.227547	−	0.549347i
$220$	27.0520	−	9.38967i	1.82385	−	0.633052i
$221$	3.31830	+	2.41089i	0.223213	+	0.162174i
$222$	15.2914	+	5.46882i	1.02629	+	0.367043i
$223$	−0.321267	−	0.442186i	−0.0215136	−	0.0296110i	0.798125	−	0.602492i	$-0.205826\pi$
$223$	−0.321267	−	0.442186i	−0.0215136	−	0.0296110i	−0.819638	+	0.572881i	$0.805826\pi$
$224$	10.9888	+	10.7594i	0.734220	+	0.718894i
$225$	−0.429841	−	2.71391i	−0.0286561	−	0.180927i
$226$	5.40517	+	0.585199i	0.359547	+	0.0389268i
$227$	6.99372	+	11.4127i	0.464189	+	0.757488i	0.995998	−	0.0893763i	$-0.0284874\pi$
$227$	6.99372	+	11.4127i	0.464189	+	0.757488i	−0.531808	+	0.846865i	$0.678487\pi$
$228$	−0.242311	−	2.45289i	−0.0160474	−	0.162446i
$229$	−6.15178	−	0.484155i	−0.406521	−	0.0319939i	−0.126449	−	0.991973i	$-0.540358\pi$
$229$	−6.15178	−	0.484155i	−0.406521	−	0.0319939i	−0.280071	+	0.959979i	$0.590358\pi$
$230$	−2.74035	−	3.40577i	−0.180694	−	0.224570i
$231$	−20.6587	−	17.6442i	−1.35924	−	1.16090i
$232$	15.1430	−	6.10666i	0.994185	−	0.400922i
$233$	13.6270	+	8.35062i	0.892733	+	0.547067i	0.891545	−	0.452932i	$-0.149622\pi$
$233$	13.6270	+	8.35062i	0.892733	+	0.547067i	0.00118778	+	0.999999i	$0.499622\pi$
$234$	1.34074	−	7.10988i	0.0876472	−	0.464787i
$235$	−26.9227	+	22.9942i	−1.75624	+	1.49997i
$236$	1.69664	−	7.74364i	0.110442	−	0.504068i
$237$	22.6765	+	22.6765i	1.47300	+	1.47300i
$238$	−2.07575	−	1.88080i	−0.134551	−	0.121914i
$239$	10.2595	+	2.46308i	0.663630	+	0.159324i	0.551248	−	0.834342i	$-0.314152\pi$
$239$	10.2595	+	2.46308i	0.663630	+	0.159324i	0.112382	+	0.993665i	$0.464152\pi$
$240$	−15.2154	−	16.4406i	−0.982147	−	1.06124i
$241$	−18.0033	+	9.17316i	−1.15970	+	0.590895i	−0.924548	−	0.381064i	$-0.875558\pi$
$241$	−18.0033	+	9.17316i	−1.15970	+	0.590895i	−0.235148	+	0.971959i	$0.575558\pi$
$242$	−11.2597	+	17.2203i	−0.723800	+	1.10696i
$243$	8.45067	−	3.50038i	0.542111	−	0.224550i
$244$	2.67950	−	3.26692i	0.171537	−	0.209143i
$245$			1.10815i			0.0707973i
$246$	12.9402	−	12.3720i	0.825037	−	0.788811i
$247$			3.50948i			0.223303i
$248$	−16.6657	+	11.8711i	−1.05827	+	0.753817i
$249$	12.1130	−	5.01739i	0.767633	−	0.317964i
$250$	−6.62605	−	4.33252i	−0.419068	−	0.274013i
$251$	15.4993	−	7.89729i	0.978308	−	0.498473i	0.109696	−	0.993965i	$-0.465012\pi$
$251$	15.4993	−	7.89729i	0.978308	−	0.498473i	0.868612	+	0.495493i	$0.165012\pi$
$252$	−1.43293	+	4.72871i	−0.0902662	+	0.297881i
$253$	5.36325	+	1.28760i	0.337185	+	0.0809509i
$254$	8.07269	−	8.90946i	0.506526	−	0.559029i
$255$	2.88500	+	2.88500i	0.180666	+	0.180666i
$256$	−15.5623	−	3.71696i	−0.972642	−	0.232310i
$257$	4.29097	−	3.66483i	0.267663	−	0.228606i	−0.505479	−	0.862839i	$-0.668684\pi$
$257$	4.29097	−	3.66483i	0.267663	−	0.228606i	0.773142	+	0.634233i	$0.218684\pi$
$258$	11.2772	+	2.12660i	0.702089	+	0.132396i
$259$	13.4640	+	8.25075i	0.836613	+	0.512677i
$260$	19.2578	+	25.4249i	1.19432	+	1.57678i
$261$	3.98899	+	3.40692i	0.246912	+	0.210883i
$262$	−3.07482	+	2.47406i	−0.189963	+	0.152848i
$263$	11.8015	+	0.928800i	0.727713	+	0.0572723i	0.436903	−	0.899509i	$-0.356075\pi$
$263$	11.8015	+	0.928800i	0.727713	+	0.0572723i	0.290810	+	0.956781i	$0.406075\pi$
$264$	27.8741	+	4.68324i	1.71553	+	0.288233i
$265$	10.4318	+	17.0231i	0.640820	+	1.04572i
$266$	0.257973	−	2.38276i	0.0158174	−	0.146097i
$267$	−2.54367	−	16.0601i	−0.155670	−	0.982862i
$268$	−0.131242	−	6.58535i	−0.00801689	−	0.402264i
$269$	2.08329	+	2.86741i	0.127021	+	0.174829i	0.867791	−	0.496930i	$-0.165539\pi$
$269$	2.08329	+	2.86741i	0.127021	+	0.174829i	−0.740770	+	0.671759i	$0.765539\pi$
$270$	−5.57755	+	15.5954i	−0.339439	+	0.949104i
$271$	−21.9850	−	15.9731i	−1.33550	−	0.970294i	−0.999597	−	0.0283965i	$-0.990960\pi$
$271$	−21.9850	−	15.9731i	−1.33550	−	0.970294i	−0.335899	−	0.941898i	$-0.609040\pi$
$272$	2.85851	+	0.566858i	0.173322	+	0.0343708i
$273$	11.5803	−	27.9572i	0.700869	−	1.69205i
$274$	−20.8771	−	22.1381i	−1.26123	−	1.33741i
$275$	−15.2365	+	1.19914i	−0.918797	+	0.0723109i
$276$	−0.759766	−	4.24739i	−0.0457325	−	0.255663i
$277$	8.05122	−	2.61600i	0.483751	−	0.157180i	−0.0569809	−	0.998375i	$-0.518147\pi$
$277$	8.05122	−	2.61600i	0.483751	−	0.157180i	0.540732	+	0.841195i	$0.318147\pi$
$278$	2.69866	−	1.54684i	0.161855	−	0.0927735i
$279$	−5.85738	−	2.98448i	−0.350672	−	0.178676i
$280$	−11.2062	−	18.6779i	−0.669698	−	1.11622i
$281$	2.66467	+	11.0991i	0.158961	+	0.662119i	0.993758	+	0.111561i	$0.0355850\pi$
$281$	2.66467	+	11.0991i	0.158961	+	0.662119i	−0.834797	+	0.550558i	$0.814415\pi$
$282$	−34.2065	+	7.15910i	−2.03697	+	0.426318i
$283$	5.11521	+	1.66203i	0.304068	+	0.0987976i	0.457077	−	0.889427i	$-0.348896\pi$
$283$	5.11521	+	1.66203i	0.304068	+	0.0987976i	−0.153009	+	0.988225i	$0.548896\pi$
$284$	24.3816	+	3.36513i	1.44678	+	0.199684i
$285$	−0.546106	+	3.44798i	−0.0323485	+	0.204241i
$286$	−38.8400	−	10.5374i	−2.29666	−	0.623090i
$287$	14.7800	−	9.19733i	0.872437	−	0.542901i
$288$	−1.25268	−	4.98555i	−0.0738149	−	0.293776i
$289$	16.2665	+	2.57635i	0.956851	+	0.151550i
$290$	−22.9369	+	2.94677i	−1.34690	+	0.173040i
$291$	−6.70762	+	20.6439i	−0.393208	+	1.21017i
$292$	−0.521449	+	8.88627i	−0.0305155	+	0.520030i
$293$	5.38474	−	1.29276i	0.314580	−	0.0755240i	−0.0730809	−	0.997326i	$-0.523283\pi$
$293$	5.38474	−	1.29276i	0.314580	−	0.0755240i	0.387661	+	0.921802i	$0.373283\pi$
$294$	−0.524926	+	0.959626i	−0.0306143	+	0.0559665i
$295$	−5.09720	+	10.0038i	−0.296771	+	0.582445i
$296$	−16.4277	−	0.154092i	−0.954840	−	0.00895642i
$297$	−6.45794	−	19.8755i	−0.374728	−	1.15329i
$298$	15.3361	−	7.25615i	0.888394	−	0.420338i
$299$	0.482015	+	6.12458i	0.0278756	+	0.354194i
$300$	5.63917	+	10.5427i	0.325577	+	0.608685i
$301$	10.3093	+	4.27026i	0.594220	+	0.246134i
$302$	−8.70920	+	5.94566i	−0.501158	+	0.342134i
$303$	−12.9185	+	17.7808i	−0.742148	+	1.02148i
$304$	1.04522	+	2.26379i	0.0599477	+	0.129837i
$305$	−4.84133	+	3.51743i	−0.277214	+	0.201408i
$306$	0.263107	+	0.898541i	0.0150408	+	0.0513662i
$307$	12.5849	−	1.99325i	0.718259	−	0.113761i	0.213402	−	0.976964i	$-0.431545\pi$
$307$	12.5849	−	1.99325i	0.718259	−	0.113761i	0.504856	+	0.863203i	$0.331545\pi$
$308$	25.5959	+	10.0094i	1.45846	+	0.570340i
$309$	−6.31880	+	3.87217i	−0.359464	+	0.220280i
$310$	27.0872	−	10.3008i	1.53845	−	0.585044i
$311$	1.10426	−	14.0309i	0.0626166	−	0.795620i	−0.882799	−	0.469752i	$-0.844343\pi$
$311$	1.10426	−	14.0309i	0.0626166	−	0.795620i	0.945415	−	0.325868i	$-0.105657\pi$
$312$	4.63304	+	31.1395i	0.262294	+	1.76293i
$313$	20.7317	−	24.2736i	1.17182	−	1.37203i	0.257883	−	0.966176i	$-0.416975\pi$
$313$	20.7317	−	24.2736i	1.17182	−	1.37203i	0.913939	−	0.405851i	$-0.133025\pi$
$314$	−16.5166	+	21.3861i	−0.932087	+	1.20689i
$315$	3.65648	−	5.96683i	0.206019	−	0.336193i
$316$	−29.1935	−	14.1494i	−1.64226	−	0.795964i
$317$	−12.3631	−	14.4753i	−0.694379	−	0.813013i	0.295438	−	0.955362i	$-0.404534\pi$
$317$	−12.3631	−	14.4753i	−0.694379	−	0.813013i	−0.989817	+	0.142349i	$0.954534\pi$
$318$	0.969842	+	19.6830i	0.0543861	+	1.10377i
$319$	20.6326	−	20.6326i	1.15520	−	1.15520i
$320$	19.9945	+	10.6648i	1.11773	+	0.596181i
$321$	−2.82419	+	11.7636i	−0.157631	+	0.656581i
$322$	0.122939	−	4.19372i	0.00685110	−	0.233707i
$323$	−0.206177	−	0.404645i	−0.0114720	−	0.0225151i
$324$	−16.2920	+	14.4860i	−0.905113	+	0.804777i
$325$	−6.51459	−	15.7276i	−0.361364	−	0.872411i
$326$	31.5184	+	14.1512i	1.74564	+	0.783760i
$327$	−10.7906			−0.596724
$328$	−8.26270	+	16.1161i	−0.456231	+	0.889861i
$329$	−33.9815			−1.87346
$330$	−36.5197	−	16.3966i	−2.01034	−	0.902604i
$331$	−4.30582	−	10.3952i	−0.236669	−	0.571371i	0.760265	−	0.649613i	$-0.225069\pi$
$331$	−4.30582	−	10.3952i	−0.236669	−	0.571371i	−0.996934	+	0.0782425i	$0.975069\pi$
$332$	−9.91183	+	8.81305i	−0.543983	+	0.483679i
$333$	−2.39623	−	4.70287i	−0.131313	−	0.257716i
$334$	−0.758013	+	25.8576i	−0.0414766	+	1.41486i
$335$	−2.17775	+	9.07099i	−0.118983	+	0.495601i
$336$	−0.856618	−	21.4828i	−0.0467323	−	1.17198i
$337$	7.28737	−	7.28737i	0.396968	−	0.396968i	−0.480194	−	0.877162i	$-0.659434\pi$
$337$	7.28737	−	7.28737i	0.396968	−	0.396968i	0.877162	+	0.480194i	$0.159434\pi$
$338$	−1.30122	−	26.4084i	−0.0707772	−	1.43643i
$339$	−4.93613	−	5.77947i	−0.268094	−	0.313898i
$340$	−3.71412	−	1.80014i	−0.201426	−	0.0976261i
$341$	−19.1055	+	31.1774i	−1.03462	+	1.68835i
$342$	−0.489662	+	0.634025i	−0.0264779	+	0.0342842i
$343$	11.6687	−	13.6623i	0.630053	−	0.737697i
$344$	−11.4828	+	1.70845i	−0.619111	+	0.0921134i
$345$	−0.479471	+	6.09226i	−0.0258139	+	0.327996i
$346$	−5.53746	+	2.10579i	−0.297696	+	0.113208i
$347$	12.8925	−	7.90055i	0.692107	−	0.424124i	−0.131476	−	0.991319i	$-0.541972\pi$
$347$	12.8925	−	7.90055i	0.692107	−	0.424124i	0.823583	+	0.567196i	$0.191972\pi$
$348$	−21.2585	−	8.31326i	−1.13958	−	0.445638i
$349$	18.8446	−	2.98470i	1.00873	−	0.159767i	0.369865	−	0.929085i	$-0.379404\pi$
$349$	18.8446	−	2.98470i	1.00873	−	0.159767i	0.638866	+	0.769318i	$0.279404\pi$
$350$	3.26699	+	11.1572i	0.174628	+	0.596375i
$351$	18.8317	−	13.6821i	1.00516	−	0.730294i
$352$	−28.1921	+	4.77051i	−1.50264	+	0.254269i
$353$	−11.5751	+	15.9318i	−0.616081	+	0.847963i	−0.997060	−	0.0766208i	$-0.975587\pi$
$353$	−11.5751	+	15.9318i	−0.616081	+	0.847963i	0.380979	+	0.924584i	$0.375587\pi$
$354$	−9.15278	+	6.24849i	−0.486465	+	0.332103i
$355$	−32.2057	−	13.3400i	−1.70930	−	0.708016i
$356$	7.75826	+	14.5045i	0.411187	+	0.768737i
$357$	0.307237	+	3.90381i	0.0162607	+	0.206612i
$358$	−15.2392	+	7.21032i	−0.805416	+	0.381077i
$359$	2.00210	+	6.16183i	0.105667	+	0.325209i	0.989886	−	0.141862i	$-0.0453091\pi$
$359$	2.00210	+	6.16183i	0.105667	+	0.325209i	−0.884220	+	0.467071i	$0.845309\pi$
$360$	−0.0682888	+	7.28024i	−0.00359914	+	0.383702i
$361$	−8.44941	+	16.5829i	−0.444706	+	0.872784i
$362$	−4.38823	+	8.02220i	−0.230640	+	0.421638i
$363$	27.9684	−	6.71462i	1.46796	−	0.352426i
$364$	−1.79323	+	30.5594i	−0.0939910	+	1.60175i
$365$	3.89589	−	11.9903i	0.203920	−	0.627602i
$366$	−5.85864	+	0.752677i	−0.306236	+	0.0393430i
$367$	−4.12337	−	0.653077i	−0.215238	−	0.0340903i	0.0478841	−	0.998853i	$-0.484752\pi$
$367$	−4.12337	−	0.653077i	−0.215238	−	0.0340903i	−0.263122	+	0.964763i	$0.584752\pi$
$368$	2.13500	+	3.80711i	0.111295	+	0.198459i
$369$	−5.81853	+	0.0399347i	−0.302900	+	0.00207892i
$370$	22.4560	+	6.09237i	1.16743	+	0.316727i
$371$	−2.99761	+	18.9262i	−0.155628	+	0.982598i
$372$	28.3361	+	3.91094i	1.46916	+	0.202773i
$373$	28.3511	+	9.21184i	1.46797	+	0.476971i	0.930493	−	0.366310i	$-0.119379\pi$
$373$	28.3511	+	9.21184i	1.46797	+	0.476971i	0.537473	+	0.843281i	$0.319379\pi$
$374$	5.09734	−	1.06683i	0.263577	−	0.0551643i
$375$	2.58366	+	10.7617i	0.133420	+	0.555734i
$376$	30.3156	−	18.1885i	1.56341	−	0.938000i
$377$	28.9581	+	14.7549i	1.49142	+	0.759916i
$378$	−13.7916	+	7.90517i	−0.709362	+	0.406598i
$379$	−7.77898	+	2.52754i	−0.399579	+	0.129831i	−0.501911	−	0.864919i	$-0.667370\pi$
$379$	−7.77898	+	2.52754i	−0.399579	+	0.129831i	0.102332	+	0.994750i	$0.467370\pi$
$380$	−0.621836	−	3.47630i	−0.0318995	−	0.178331i
$381$	−16.7558	+	1.31871i	−0.858427	+	0.0675597i
$382$	−2.96893	−	3.14825i	−0.151903	−	0.161079i
$383$	−10.2389	+	24.7188i	−0.523182	+	1.26307i	0.412735	+	0.910851i	$0.364574\pi$
$383$	−10.2389	+	24.7188i	−0.523182	+	1.26307i	−0.935917	+	0.352222i	$0.885426\pi$
$384$	12.2628	+	18.7067i	0.625783	+	0.954622i
$385$	−31.4910	−	22.8796i	−1.60493	−	1.16605i
$386$	4.19277	−	11.7234i	0.213406	−	0.596705i
$387$	−2.19234	−	3.01749i	−0.111443	−	0.153388i
$388$	−0.437529	−	21.9539i	−0.0222122	−	1.11454i
$389$	−2.79246	−	17.6309i	−0.141583	−	0.893923i	−0.951561	−	0.307461i	$-0.900521\pi$
$389$	−2.79246	−	17.6309i	−0.141583	−	0.893923i	0.809977	−	0.586461i	$-0.199479\pi$
$390$	4.79941	−	44.3296i	0.243027	−	2.24472i
$391$	−0.415388	−	0.677851i	−0.0210071	−	0.0342804i
$392$	0.183340	−	1.09122i	0.00926006	−	0.0551148i
$393$	5.50025	+	0.432879i	0.277451	+	0.0218359i
$394$	21.8778	−	17.6033i	1.10219	−	0.886843i
$395$	34.9388	+	29.8406i	1.75796	+	1.50144i
$396$	−5.54663	−	7.32287i	−0.278729	−	0.367988i
$397$	0.556106	+	0.340782i	0.0279102	+	0.0171034i	0.536384	−	0.843974i	$-0.319790\pi$
$397$	0.556106	+	0.340782i	0.0279102	+	0.0171034i	−0.508473	+	0.861078i	$0.669790\pi$
$398$	−6.67281	−	1.25832i	−0.334478	−	0.0630741i
$399$	−2.54777	+	2.17600i	−0.127548	+	0.108936i
$400$	−8.88638	−	8.20487i	−0.444319	−	0.410244i
$401$	−9.35216	−	9.35216i	−0.467024	−	0.467024i	0.433925	−	0.900949i	$-0.357128\pi$
$401$	−9.35216	−	9.35216i	−0.467024	−	0.467024i	−0.900949	+	0.433925i	$0.857128\pi$
$402$	−6.18275	+	6.82361i	−0.308368	+	0.340331i
$403$	−39.6028	−	9.50779i	−1.97276	−	0.473617i
$404$	6.44781	−	21.2779i	0.320790	−	1.05862i
$405$	27.5113	−	14.0177i	1.36705	−	0.696546i
$406$	−18.5766	−	12.1465i	−0.921939	−	0.602821i
$407$	−27.1237	+	11.2350i	−1.34447	+	0.556899i
$408$	−2.36360	−	3.31822i	−0.117015	−	0.164276i
$409$			13.3975i			0.662465i	0.943549	+	0.331233i	$0.107465\pi$
$409$			13.3975i			0.662465i	−0.943549	+	0.331233i	$0.892535\pi$
$410$	17.0922	−	19.1260i	0.844122	−	0.944566i
$411$			42.5398i			2.09833i
$412$	4.75429	−	5.79656i	0.234227	−	0.285576i
$413$	−9.95566	+	4.12377i	−0.489886	+	0.202917i
$414$	−0.767454	+	1.17373i	−0.0377183	+	0.0576855i
$415$	16.7375	−	8.52817i	0.821610	−	0.418631i
$416$	−14.7570	−	28.2225i	−0.723524	−	1.38372i
$417$	−4.22835	−	1.01514i	−0.207063	−	0.0497114i
$418$	3.30205	+	2.99193i	0.161509	+	0.146340i
$419$	−9.87852	−	9.87852i	−0.482597	−	0.482597i	0.423363	−	0.905960i	$-0.360850\pi$
$419$	−9.87852	−	9.87852i	−0.482597	−	0.482597i	−0.905960	+	0.423363i	$0.860850\pi$
$420$	−6.51713	+	29.7449i	−0.318003	+	1.45140i
$421$	−7.93410	+	6.77636i	−0.386684	+	0.330260i	−0.821446	−	0.570286i	$-0.806832\pi$
$421$	−7.93410	+	6.77636i	−0.386684	+	0.330260i	0.434762	+	0.900545i	$0.356832\pi$
$422$	−1.21008	+	6.41700i	−0.0589060	+	0.312374i
$423$	9.68461	+	5.93474i	0.470882	+	0.288557i
$424$	−7.45595	−	18.4889i	−0.362093	−	0.897899i
$425$	1.67511	+	1.43068i	0.0812549	+	0.0693983i
$426$	−21.5700	−	26.8077i	−1.04507	−	1.29884i
$427$	−5.72580	−	0.450630i	−0.277091	−	0.0218075i
$428$	−1.20312	−	12.1790i	−0.0581549	−	0.588696i
$429$	29.3960	+	47.9700i	1.41925	+	2.31601i
$430$	16.3467	+	1.76980i	0.788308	+	0.0853472i
$431$	−1.99028	−	12.5661i	−0.0958684	−	0.605289i	−0.988112	−	0.153735i	$-0.950870\pi$
$431$	−1.99028	−	12.5661i	−0.0958684	−	0.605289i	0.892244	−	0.451554i	$-0.149130\pi$
$432$	8.07251	−	14.4343i	0.388389	−	0.694468i
$433$	−14.8987	−	20.5062i	−0.715984	−	0.985467i	−0.999648	−	0.0265431i	$-0.991550\pi$
$433$	−14.8987	−	20.5062i	−0.715984	−	0.985467i	0.283664	−	0.958924i	$-0.408450\pi$
$434$	26.1895	+	9.36644i	1.25714	+	0.449603i
$435$	26.1547	+	19.0025i	1.25402	+	0.911099i
$436$	10.3124	−	3.57939i	0.493873	−	0.171422i
$437$	0.260311	−	0.628446i	0.0124524	−	0.0300626i
$438$	9.05347	−	8.53779i	0.432592	−	0.407951i
$439$	8.13307	−	0.640087i	0.388170	−	0.0305497i	0.117127	−	0.993117i	$-0.462631\pi$
$439$	8.13307	−	0.640087i	0.388170	−	0.0305497i	0.271043	+	0.962567i	$0.412631\pi$
$440$	40.3400	+	3.55584i	1.92313	+	0.169518i
$441$	0.338103	−	0.109856i	0.0161001	−	0.00523125i
$442$	2.88458	+	5.03251i	0.137206	+	0.239372i
$443$	−36.7216	−	18.7106i	−1.74470	−	0.888968i	−0.964768	−	0.263100i	$-0.915255\pi$
$443$	−36.7216	−	18.7106i	−1.74470	−	0.888968i	−0.779929	−	0.625868i	$-0.784745\pi$
$444$	16.5603	+	15.9131i	0.785915	+	0.755201i
$445$	−5.43857	−	22.6533i	−0.257813	−	1.07387i
$446$	−0.158345	−	0.756577i	−0.00749784	−	0.0358250i
$447$	−22.5574	−	7.32935i	−1.06693	−	0.346666i
$448$	7.94475	+	20.2464i	0.375354	+	0.956554i
$449$	−0.342383	+	2.16172i	−0.0161580	+	0.102018i	−0.994449	−	0.105217i	$-0.966446\pi$
$449$	−0.342383	+	2.16172i	−0.0161580	+	0.102018i	0.978291	+	0.207235i	$0.0664463\pi$
$450$	1.01747	−	3.75032i	0.0479641	−	0.176792i
$451$	−2.31782	+	32.2818i	−0.109142	+	1.52009i
$452$	6.63447	+	3.88593i	0.312059	+	0.182779i
$453$	14.5605	+	2.30616i	0.684113	+	0.108353i
$454$	2.41210	+	18.7751i	0.113205	+	0.881161i
$455$	13.3978	−	41.2340i	0.628096	−	1.93308i
$456$	1.10822	−	3.30493i	0.0518970	−	0.154768i
$457$	13.9523	−	3.34965i	0.652662	−	0.156690i	0.106424	−	0.994321i	$-0.466060\pi$
$457$	13.9523	−	3.34965i	0.652662	−	0.156690i	0.546237	+	0.837631i	$0.316060\pi$
$458$	−7.65623	−	4.18804i	−0.357752	−	0.195694i
$459$	−1.36751	+	2.68389i	−0.0638299	+	0.125273i
$460$	−1.56266	−	5.98128i	−0.0728593	−	0.278879i
$461$	11.1103	+	34.1941i	0.517460	+	1.59258i	0.778760	+	0.627321i	$0.215849\pi$
$461$	11.1103	+	34.1941i	0.517460	+	1.59258i	−0.261300	+	0.965258i	$0.584151\pi$
$462$	−16.4323	−	34.7301i	−0.764501	−	1.61579i
$463$	−0.631098	−	8.01886i	−0.0293296	−	0.372668i	−0.994013	−	0.109258i	$-0.965153\pi$
$463$	−0.631098	−	8.01886i	−0.0293296	−	0.372668i	0.964684	−	0.263411i	$-0.0848474\pi$
$464$	23.0739	+	0.893088i	1.07118	+	0.0414606i
$465$	−37.4293	−	15.5037i	−1.73574	−	0.718968i
$466$	12.7437	+	18.6669i	0.590339	+	0.864728i
$467$	15.2064	−	20.9298i	0.703667	−	0.968514i	−0.296244	−	0.955112i	$-0.595734\pi$
$467$	15.2064	−	20.9298i	0.703667	−	0.968514i	0.999910	−	0.0134017i	$-0.00426601\pi$
$468$	5.84814	−	8.39614i	0.270331	−	0.388112i
$469$	−7.24353	+	5.26273i	−0.334475	+	0.243011i
$470$	−48.0535	+	14.0708i	−2.21654	+	0.649039i
$471$	37.3106	−	5.90942i	1.71918	−	0.272292i
$472$	6.67440	−	9.00763i	0.307214	−	0.414610i
$473$	−17.6891	+	10.8399i	−0.813346	+	0.498419i
$474$	16.1206	+	42.3913i	0.740445	+	1.94710i
$475$	−0.147886	+	1.87907i	−0.00678546	+	0.0862174i
$476$	−1.58856	−	3.62887i	−0.0728117	−	0.166329i
$477$	4.15969	−	4.87037i	0.190459	−	0.222999i
$478$	11.8095	+	9.12052i	0.540152	+	0.417163i
$479$	−1.60696	+	2.62232i	−0.0734238	+	0.119817i	−0.887245	−	0.461299i	$-0.847384\pi$
$479$	−1.60696	+	2.62232i	−0.0734238	+	0.119817i	0.813821	+	0.581116i	$0.197384\pi$
$480$	−10.1068	−	30.0242i	−0.461309	−	1.37041i
$481$	−21.2373	−	24.8656i	−0.968336	−	1.13378i
$482$	−28.5404	+	1.40628i	−1.29998	+	0.0640541i
$483$	−4.14738	+	4.14738i	−0.188712	+	0.188712i
$484$	−24.5015	+	15.6945i	−1.11370	+	0.713386i
$485$	−7.26010	+	30.2405i	−0.329664	+	1.37315i
$486$	12.9302	+	0.379047i	0.586524	+	0.0171939i
$487$	5.28944	+	10.3811i	0.239687	+	0.470413i	0.979245	−	0.202681i	$-0.0649653\pi$
$487$	5.28944	+	10.3811i	0.239687	+	0.470413i	−0.739558	+	0.673093i	$0.764965\pi$
$488$	5.34929	−	2.66270i	0.242151	−	0.120535i
$489$	−18.4835	−	44.6231i	−0.835852	−	2.01792i
$490$	−0.641896	+	1.42968i	−0.0289979	+	0.0645862i
$491$	−20.0584			−0.905222			−0.452611	−	0.891708i	$-0.649507\pi$
$491$	−20.0584			−0.905222			−0.452611	+	0.891708i	$0.649507\pi$
$492$	23.8612	−	8.46608i	1.07575	−	0.381680i
$493$	−4.20572			−0.189416
$494$	−2.03286	+	4.52773i	−0.0914627	+	0.203712i
$495$	4.97900	+	12.0204i	0.223790	+	0.540276i
$496$	−28.3775	+	5.66186i	−1.27419	+	0.254225i
$497$	−15.1892	−	29.8104i	−0.681327	−	1.33718i
$498$	18.5339	+	0.543319i	0.830523	+	0.0243467i
$499$	10.3645	−	43.1711i	0.463977	−	1.93260i	0.123531	−	0.992341i	$-0.460578\pi$
$499$	10.3645	−	43.1711i	0.463977	−	1.93260i	0.340447	−	0.940264i	$-0.389422\pi$
$500$	−6.03895	−	9.42771i	−0.270070	−	0.421620i
$501$	25.5718	−	25.5718i	1.14247	−	1.14247i
$502$	24.5708	−	1.21068i	1.09665	−	0.0540354i
$503$	−4.45713	−	5.21863i	−0.198734	−	0.232687i	0.652086	−	0.758145i	$-0.273894\pi$
$503$	−4.45713	−	5.21863i	−0.198734	−	0.232687i	−0.850820	+	0.525458i	$0.823894\pi$
$504$	−4.58779	+	5.27069i	−0.204356	+	0.234775i
$505$	−16.4532	+	26.8491i	−0.732156	+	1.19477i
$506$	6.17352	+	4.76785i	0.274446	+	0.211957i
$507$	−24.0057	+	28.1071i	−1.06613	+	1.24828i
$508$	15.5757	−	6.81838i	0.691061	−	0.302517i
$509$	−0.905115	+	11.5006i	−0.0401185	+	0.509754i	0.943726	+	0.330729i	$0.107294\pi$
$509$	−0.905115	+	11.5006i	−0.0401185	+	0.509754i	−0.983844	+	0.179025i	$0.942706\pi$
$510$	2.05093	+	5.39319i	0.0908167	+	0.238815i
$511$	10.3171	−	6.32236i	0.456404	−	0.279685i
$512$	−17.9245	−	13.8098i	−0.792159	−	0.610315i
$513$	−2.54559	+	0.403181i	−0.112390	+	0.0178009i
$514$	7.65881	−	2.24262i	0.337816	−	0.0989178i
$515$	−8.59008	+	6.24106i	−0.378524	+	0.275014i
$516$	13.3174	+	9.27593i	0.586266	+	0.408350i
$517$	37.1353	−	51.1123i	1.63321	−	2.24792i
$518$	12.5913	+	18.4437i	0.553228	+	0.810368i
$519$	7.65170	+	3.16944i	0.335872	+	0.139123i
$520$	10.1180	+	43.9568i	0.443703	+	1.92763i
$521$	1.86742	+	23.7279i	0.0818133	+	1.03954i	0.891603	+	0.452817i	$0.149581\pi$
$521$	1.86742	+	23.7279i	0.0818133	+	1.03954i	−0.809790	+	0.586720i	$0.800419\pi$
$522$	3.17291	+	6.70603i	0.138875	+	0.293515i
$523$	0.794080	+	2.44393i	0.0347227	+	0.106865i	0.966916	−	0.255096i	$-0.0821071\pi$
$523$	0.794080	+	2.44393i	0.0347227	+	0.106865i	−0.932193	+	0.361962i	$0.882107\pi$
$524$	−5.40006	+	1.41081i	−0.235903	+	0.0616315i
$525$	7.37846	−	14.4810i	0.322022	−	0.632005i
$526$	14.6877	+	8.03431i	0.640412	+	0.350312i
$527$	5.12480	−	1.23036i	0.223240	−	0.0535952i
$528$	33.2488	+	22.1881i	1.44697	+	0.965612i
$529$	−6.73942	+	20.7418i	−0.293018	+	0.901818i
$530$	3.59787	+	28.0049i	0.156282	+	1.21645i
$531$	3.55753	+	0.563457i	0.154384	+	0.0244520i
$532$	1.71304	−	2.92468i	0.0742696	−	0.126801i
$533$	−34.9946	+	8.65589i	−1.51578	+	0.374928i
$534$	6.02110	−	22.1933i	0.260558	−	0.960396i
$535$	−2.71152	+	17.1198i	−0.117229	+	0.740156i
$536$	3.64524	−	8.57207i	0.157450	−	0.370257i
$537$	22.4149	+	7.28305i	0.967275	+	0.314287i
$538$	1.02681	+	4.90612i	0.0442687	+	0.211518i
$539$	−0.461614	−	1.92276i	−0.0198831	−	0.0828192i
$540$	−16.2294	+	16.8895i	−0.698404	+	0.726807i
$541$	3.81669	+	1.94470i	0.164092	+	0.0836093i	0.534108	−	0.845416i	$-0.320648\pi$
$541$	3.81669	+	1.94470i	0.164092	+	0.0836093i	−0.370015	+	0.929026i	$0.620648\pi$
$542$	−19.1115	−	33.3424i	−0.820908	−	1.43218i
$543$	12.1575	−	3.95021i	0.521728	−	0.169520i
$544$	3.35953	+	2.38711i	0.144039	+	0.102347i
$545$	−15.4126	+	1.21300i	−0.660205	+	0.0519593i
$546$	31.1344	−	29.3610i	1.33243	−	1.25653i
$547$	−7.69475	+	18.5768i	−0.329004	+	0.794285i	0.669663	+	0.742665i	$0.266439\pi$
$547$	−7.69475	+	18.5768i	−0.329004	+	0.794285i	−0.998667	+	0.0516203i	$0.983561\pi$
$548$	−14.1110	−	40.6543i	−0.602791	−	1.73667i
$549$	1.55313	+	1.12842i	0.0662860	+	0.0481596i
$550$	−20.3519	−	7.27868i	−0.867808	−	0.310364i
$551$	−2.11516	−	2.91127i	−0.0901088	−	0.124024i
$552$	1.48009	−	5.91983i	0.0629967	−	0.251965i
$553$	6.89866	+	43.5564i	0.293361	+	1.85221i
$554$	11.9025	+	1.28865i	0.505691	+	0.0547493i
$555$	−16.9958	−	27.7346i	−0.721431	−	1.17727i
$556$	4.37767	−	0.432453i	0.185655	−	0.0183401i
$557$	−13.2413	−	1.04212i	−0.561053	−	0.0441559i	−0.205238	−	0.978712i	$-0.565797\pi$
$557$	−13.2413	−	1.04212i	−0.561053	−	0.0441559i	−0.355815	+	0.934556i	$0.615797\pi$
$558$	−5.82810	−	7.24329i	−0.246723	−	0.306633i
$559$	−17.5714	−	15.0074i	−0.743191	−	0.634745i
$560$	−3.63847	−	30.5883i	−0.153753	−	1.29259i
$561$	−6.20756	−	3.80400i	−0.262083	−	0.160605i
$562$	−2.99136	+	15.8630i	−0.126183	+	0.669139i
$563$	16.3853	−	13.9944i	0.690558	−	0.589792i	−0.233356	−	0.972391i	$-0.574971\pi$
$563$	16.3853	−	13.9944i	0.690558	−	0.589792i	0.923915	+	0.382599i	$0.124971\pi$
$564$	−48.2782	−	10.5778i	−2.03288	−	0.445405i
$565$	−7.70013	−	7.70013i	−0.323947	−	0.323947i
$566$	5.63663	+	5.10724i	0.236925	+	0.214673i
$567$	28.8158	+	6.91807i	1.21015	+	0.290532i
$568$	29.5065	+	18.4645i	1.23806	+	0.774753i
$569$	9.76143	−	4.97370i	0.409220	−	0.208508i	−0.237248	−	0.971449i	$-0.576245\pi$
$569$	9.76143	−	4.97370i	0.409220	−	0.208508i	0.646468	+	0.762941i	$0.276245\pi$
$570$	−2.70179	+	4.13206i	−0.113166	+	0.173073i
$571$	21.0442	−	8.71679i	0.880672	−	0.364786i	0.103915	−	0.994586i	$-0.466863\pi$
$571$	21.0442	−	8.71679i	0.880672	−	0.364786i	0.776757	+	0.629800i	$0.216863\pi$
$572$	−44.0054	−	36.0928i	−1.83996	−	1.50912i
$573$			6.04958i			0.252725i
$574$	24.3959	−	3.30456i	1.01826	−	0.137930i
$575$			3.29957i			0.137602i
$576$	1.27174	−	7.15768i	0.0529890	−	0.298237i
$577$	−37.8164	+	15.6641i	−1.57432	+	0.652104i	−0.987501	−	0.157615i	$-0.949620\pi$
$577$	−37.8164	+	15.6641i	−1.57432	+	0.652104i	−0.586818	+	0.809719i	$0.699620\pi$
$578$	19.4937	+	12.7462i	0.810832	+	0.530172i
$579$	−15.5086	+	7.90204i	−0.644516	+	0.328398i
$580$	−31.2988	−	9.48441i	−1.29961	−	0.393819i
$581$	17.5311	+	4.20885i	0.727314	+	0.174613i
$582$	−20.6118	+	22.7483i	−0.854386	+	0.942946i
$583$	−25.1915	−	25.1915i	−1.04332	−	1.04332i
$584$	−5.82011	+	11.1625i	−0.240838	+	0.461908i
$585$	−11.0197	+	9.41169i	−0.455607	+	0.389126i
$586$	7.69592	+	1.45126i	0.317916	+	0.0599509i
$587$	7.99125	+	4.89704i	0.329834	+	0.202123i	0.677549	−	0.735478i	$-0.263042\pi$
$587$	7.99125	+	4.89704i	0.329834	+	0.202123i	−0.347715	+	0.937600i	$0.613042\pi$
$588$	−1.23309	+	0.933993i	−0.0508519	+	0.0385172i
$589$	3.42906	+	2.92870i	0.141292	+	0.120675i
$590$	−12.3708	+	9.95382i	−0.509299	+	0.409792i
$591$	−39.1351	−	3.08000i	−1.60980	−	0.126694i
$592$	−21.1048	−	9.71453i	−0.867403	−	0.399265i
$593$	−6.44326	−	10.5145i	−0.264593	−	0.431777i	0.692559	−	0.721361i	$-0.256483\pi$
$593$	−6.44326	−	10.5145i	−0.264593	−	0.431777i	−0.957153	+	0.289584i	$0.906483\pi$
$594$	3.18119	−	29.3830i	0.130526	−	1.20560i
$595$	0.877674	+	5.54142i	0.0359811	+	0.227176i
$596$	23.9888	−	0.478083i	0.982621	−	0.0195831i
$597$	5.57979	+	7.67992i	0.228365	+	0.314318i
$598$	−2.92579	+	8.18079i	−0.119644	+	0.334538i
$599$	25.6621	+	18.6446i	1.04852	+	0.761797i	0.971931	−	0.235266i	$-0.0755961\pi$
$599$	25.6621	+	18.6446i	1.04852	+	0.761797i	0.0765920	+	0.997063i	$0.475596\pi$
$600$	1.16846	+	16.8681i	0.0477024	+	0.688638i
$601$	16.2201	−	39.1587i	0.661631	−	1.59732i	−0.133617	−	0.991033i	$-0.542659\pi$
$601$	16.2201	−	39.1587i	0.661631	−	1.59732i	0.795248	−	0.606285i	$-0.207341\pi$
$602$	10.8270	+	11.4809i	0.441274	+	0.467927i
$603$	2.98350	−	0.234806i	0.121497	−	0.00956205i
$604$	−14.6801	+	2.62596i	−0.597326	+	0.106849i
$605$	39.1935	−	12.7347i	1.59344	−	0.517740i
$606$	−26.9662	+	15.4567i	−1.09543	+	0.627887i
$607$	34.0026	+	17.3252i	1.38012	+	0.703207i	0.977258	−	0.212053i	$-0.0680148\pi$
$607$	34.0026	+	17.3252i	1.38012	+	0.703207i	0.402864	+	0.915260i	$0.368015\pi$
$608$	0.0371908	+	3.52606i	0.00150829	+	0.143001i
$609$	7.24346	+	30.1712i	0.293520	+	1.22260i
$610$	−8.28348	+	1.73366i	−0.335388	+	0.0701937i
$611$	66.9260	+	21.7456i	2.70754	+	0.879732i
$612$	−0.181033	+	1.31165i	−0.00731784	+	0.0530204i
$613$	0.878651	−	5.54758i	0.0354884	−	0.224065i	−0.963570	−	0.267457i	$-0.913817\pi$
$613$	0.878651	−	5.54758i	0.0354884	−	0.224065i	0.999058	+	0.0433924i	$0.0138166\pi$
$614$	17.3909	+	4.71821i	0.701841	+	0.190412i
$615$	−35.7283	+	3.05874i	−1.44070	+	0.123340i
$616$	27.2244	+	27.7400i	1.09690	+	1.11768i
$617$	−21.1341	−	3.34731i	−0.850827	−	0.134758i	−0.284233	−	0.958755i	$-0.591739\pi$
$617$	−21.1341	−	3.34731i	−0.850827	−	0.134758i	−0.566593	+	0.823998i	$0.691739\pi$
$618$	−10.3951	+	1.33549i	−0.418153	+	0.0537213i
$619$	−1.59079	+	4.89595i	−0.0639393	+	0.196785i	−0.977923	−	0.208966i	$-0.932990\pi$
$619$	−1.59079	+	4.89595i	−0.0639393	+	0.196785i	0.913984	+	0.405751i	$0.132990\pi$
$620$	40.9131	+	2.40079i	1.64311	+	0.0964182i
$621$	−4.38707	+	1.05324i	−0.176047	+	0.0422651i
$622$	9.55204	−	17.4622i	0.383002	−	0.700172i
$623$	10.1512	−	19.9228i	0.406697	−	0.798189i
$624$	−12.0602	+	42.8581i	−0.482796	+	1.71570i
$625$	9.57202	+	29.4596i	0.382881	+	1.17839i
$626$	40.8073	−	19.3077i	1.63099	−	0.771691i
$627$	−0.488745	−	6.21010i	−0.0195186	−	0.248007i
$628$	−33.6967	+	18.0239i	−1.34464	+	0.719232i
$629$	3.90950	+	1.61937i	0.155882	+	0.0645684i
$630$	8.17366	−	5.58005i	0.325646	−	0.222315i
$631$	−11.5974	+	15.9625i	−0.461687	+	0.635457i	−0.974857	−	0.222829i	$-0.928471\pi$
$631$	−11.5974	+	15.9625i	−0.461687	+	0.635457i	0.513171	+	0.858287i	$0.328471\pi$
$632$	−29.4678	−	35.1650i	−1.17217	−	1.39879i
$633$	7.38549	−	5.36588i	0.293547	−	0.213274i
$634$	−7.56533	−	25.8365i	−0.300458	−	1.02610i
$635$	−23.7847	+	3.76712i	−0.943867	+	0.149494i
$636$	−10.1501	+	25.9557i	−0.402478	+	1.02921i
$637$	1.87793	−	1.15080i	0.0744065	−	0.0455964i
$638$	38.5704	−	14.6676i	1.52702	−	0.580696i
$639$	−0.877412	+	11.1486i	−0.0347099	+	0.441031i
$640$	19.6182	+	25.3409i	0.775479	+	1.00169i
$641$	−1.63876	+	1.91874i	−0.0647271	+	0.0757857i	−0.791825	−	0.610748i	$-0.790869\pi$
$641$	−1.63876	+	1.91874i	−0.0647271	+	0.0757857i	0.727098	+	0.686534i	$0.240869\pi$
$642$	−10.4577	+	13.5408i	−0.412731	+	0.534414i
$643$	−4.45384	+	7.26801i	−0.175642	+	0.286622i	−0.928331	−	0.371754i	$-0.878756\pi$
$643$	−4.45384	+	7.26801i	−0.175642	+	0.286622i	0.752689	+	0.658376i	$0.228756\pi$
$644$	2.58782	−	5.33929i	0.101974	−	0.210398i
$645$	−14.9282	−	17.4787i	−0.587797	−	0.688222i
$646$	−0.0316076	−	0.641478i	−0.00124359	−	0.0252386i
$647$	−33.1653	+	33.1653i	−1.30386	+	1.30386i	−0.378099	+	0.925765i	$0.623422\pi$
$647$	−33.1653	+	33.1653i	−1.30386	+	1.30386i	−0.925765	+	0.378099i	$0.876578\pi$
$648$	−29.4101	+	9.25184i	−1.15534	+	0.363447i
$649$	4.67698	−	19.4810i	0.183587	−	0.764696i
$650$	0.705447	−	24.0644i	0.0276699	−	0.943885i
$651$	−17.6528	−	34.6455i	−0.691867	−	1.35786i
$652$	32.4663	+	36.5140i	1.27148	+	1.43000i
$653$	7.49515	+	18.0949i	0.293308	+	0.708108i	1.00000		0.000586444i	$0.000186671\pi$
$653$	7.49515	+	18.0949i	0.293308	+	0.708108i	−0.706692	+	0.707521i	$0.749813\pi$
$654$	−13.9215	−	6.25047i	−0.544373	−	0.244413i
$655$	7.90486			0.308868
$656$	−19.9953	+	16.0059i	−0.780685	+	0.624925i
$657$	−4.04453			−0.157792
$658$	−43.8410	−	19.6838i	−1.70910	−	0.767353i
$659$	−14.3361	−	34.6103i	−0.558454	−	1.34823i	−0.910990	−	0.412429i	$-0.864680\pi$
$659$	−14.3361	−	34.6103i	−0.558454	−	1.34823i	0.352536	−	0.935798i	$-0.385320\pi$
$660$	−37.6179	−	42.3080i	−1.46427	−	1.64683i
$661$	−17.8575	−	35.0473i	−0.694575	−	1.36318i	−0.921158	−	0.389189i	$-0.872755\pi$
$661$	−17.8575	−	35.0473i	−0.694575	−	1.36318i	0.226582	−	0.973992i	$-0.427245\pi$
$662$	0.466266	−	15.9054i	0.0181219	−	0.618182i
$663$	1.89305	−	7.88510i	0.0735198	−	0.306232i
$664$	−17.8926	+	5.62868i	−0.694369	+	0.218435i
$665$	−3.39445	+	3.39445i	−0.131631	+	0.131631i
$666$	−0.367350	−	7.45539i	−0.0142345	−	0.288891i
$667$	−4.09113	−	4.79010i	−0.158409	−	0.185474i
$668$	−15.9559	+	32.9209i	−0.617353	+	1.27375i
$669$	−0.564612	+	0.921362i	−0.0218291	+	0.0356219i
$670$	−8.06398	+	10.4414i	−0.311539	+	0.403387i
$671$	6.93500	−	8.11984i	0.267723	−	0.313463i
$672$	11.3387	−	28.2121i	0.437400	−	1.08830i
$673$	2.07791	−	26.4024i	0.0800977	−	1.01774i	−0.817212	−	0.576337i	$-0.804482\pi$
$673$	2.07791	−	26.4024i	0.0800977	−	1.01774i	0.897310	−	0.441401i	$-0.145518\pi$
$674$	13.6230	−	5.18055i	0.524737	−	0.199547i
$675$	10.6595	−	6.53218i	0.410286	−	0.251424i
$676$	13.6183	−	34.8243i	0.523779	−	1.33940i
$677$	−26.6632	+	4.22303i	−1.02475	+	0.162304i	−0.646113	−	0.763242i	$-0.723607\pi$
$677$	−26.6632	+	4.22303i	−1.02475	+	0.162304i	−0.378635	+	0.925546i	$0.623607\pi$
$678$	−3.02057	−	10.3156i	−0.116004	−	0.396168i
$679$	−24.1482	+	17.5447i	−0.926722	+	0.673303i
$680$	−3.74902	−	4.47383i	−0.143768	−	0.171564i
$681$	15.5546	−	21.4091i	0.596054	−	0.820398i
$682$	−42.7083	+	29.1564i	−1.63539	+	1.11646i
$683$	−8.77240	−	3.63365i	−0.335666	−	0.139038i	0.208483	−	0.978026i	$-0.433147\pi$
$683$	−8.77240	−	3.63365i	−0.335666	−	0.139038i	−0.544149	+	0.838988i	$0.683147\pi$
$684$	−0.998993	+	0.534348i	−0.0381974	+	0.0204313i
$685$	4.78200	+	60.7611i	0.182711	+	2.32156i
$686$	22.9683	−	10.8673i	0.876932	−	0.414915i
$687$	3.77000	+	11.6029i	0.143834	+	0.442677i
$688$	−15.8041	−	4.44725i	−0.602525	−	0.169550i
$689$	18.0151	−	35.3565i	0.686319	−	1.34698i
$690$	−4.14752	+	7.58216i	−0.157894	+	0.288648i
$691$	4.80124	−	1.15268i	0.182648	−	0.0438499i	−0.141090	−	0.989997i	$-0.545061\pi$
$691$	4.80124	−	1.15268i	0.182648	−	0.0438499i	0.323737	+	0.946147i	$0.395061\pi$
$692$	−8.36389	−	0.490795i	−0.317948	−	0.0186572i
$693$	−3.85882	+	11.8762i	−0.146584	+	0.451141i
$694$	21.2096	−	2.72486i	0.805105	−	0.103434i
$695$	−6.15361	−	0.974636i	−0.233420	−	0.0369700i
$696$	−22.6111	−	23.0393i	−0.857070	−	0.873301i
$697$	3.52638	−	3.05391i	0.133571	−	0.115675i
$698$	26.0412	+	7.06505i	0.985673	+	0.267416i
$699$	4.94292	−	31.2084i	0.186958	−	1.18041i
$700$	−2.24788	+	16.2867i	−0.0849621	+	0.615581i
$701$	17.9627	+	5.83644i	0.678442	+	0.220439i	0.627913	−	0.778283i	$-0.283909\pi$
$701$	17.9627	+	5.83644i	0.678442	+	0.220439i	0.0505289	+	0.998723i	$0.483909\pi$
$702$	32.2209	−	6.74355i	1.21610	−	0.254519i
$703$	0.845230	+	3.52064i	0.0318784	+	0.132783i
$704$	−39.1352	−	10.1756i	−1.47496	−	0.383507i
$705$	62.3694	+	31.7788i	2.34897	+	1.19686i
$706$	−24.1620	+	13.8494i	−0.909350	+	0.521229i
$707$	−28.7435	+	9.33934i	−1.08101	+	0.351242i
$708$	−15.4278	+	2.75971i	−0.579814	+	0.103716i
$709$	22.0561	−	1.73585i	0.828335	−	0.0651914i	0.342800	−	0.939408i	$-0.388625\pi$
$709$	22.0561	−	1.73585i	0.828335	−	0.0651914i	0.485535	+	0.874217i	$0.338625\pi$
$710$	−33.8228	−	35.8657i	−1.26935	−	1.34601i
$711$	5.64086	−	13.6182i	0.211549	−	0.510724i
$712$	1.60755	+	23.2069i	0.0602456	+	0.869714i
$713$	6.38649	+	4.64006i	0.239176	+	0.173771i
$714$	−1.86490	+	5.21445i	−0.0697922	+	0.195146i
$715$	47.3798	+	65.2127i	1.77190	+	2.43882i
$716$	−23.8373	+	0.475064i	−0.890842	+	0.0177540i
$717$	−3.26320	−	20.6030i	−0.121866	−	0.769434i
$718$	−0.986238	+	9.10936i	−0.0368061	+	0.339958i
$719$	18.6415	+	30.4201i	0.695210	+	1.13448i	0.984185	+	0.177143i	$0.0566856\pi$
$719$	18.6415	+	30.4201i	0.695210	+	1.13448i	−0.288975	+	0.957337i	$0.593314\pi$
$720$	−4.30517	+	9.35300i	−0.160444	+	0.348566i
$721$	−10.1594	−	0.799563i	−0.378356	−	0.0297773i
$722$	−20.5066	+	16.5000i	−0.763176	+	0.614067i
$723$	30.3763	+	25.9438i	1.12971	+	0.964861i
$724$	−10.3083	+	7.80791i	−0.383105	+	0.290179i
$725$	14.8832	+	9.12042i	0.552747	+	0.338724i
$726$	39.9727	+	7.53785i	1.48353	+	0.279756i
$727$	8.78570	−	7.50370i	0.325844	−	0.278297i	−0.471444	−	0.881896i	$-0.656267\pi$
$727$	8.78570	−	7.50370i	0.325844	−	0.278297i	0.797288	+	0.603599i	$0.206267\pi$
$728$	−20.0150	+	38.3873i	−0.741807	+	1.42273i
$729$	10.3359	+	10.3359i	0.382813	+	0.382813i
$730$	11.9716	−	13.2125i	0.443090	−	0.489018i
$731$	2.90766	+	0.698067i	0.107544	+	0.0258189i
$732$	−7.99447	−	2.42255i	−0.295484	−	0.0895400i
$733$	4.65376	−	2.37121i	0.171891	−	0.0875827i	−0.365928	−	0.930643i	$-0.619248\pi$
$733$	4.65376	−	2.37121i	0.171891	−	0.0875827i	0.537819	+	0.843060i	$0.319248\pi$
$734$	−4.94144	−	3.23102i	−0.182392	−	0.119259i
$735$	2.02410	−	0.838410i	0.0746601	−	0.0309252i
$736$	0.549196	+	6.14841i	0.0202436	+	0.226633i
$737$		−	16.6463i		−	0.613175i
$738$	−7.52987	−	3.31886i	−0.277178	−	0.122169i
$739$		−	29.2677i		−	1.07663i	−0.842744	−	0.538315i	$-0.819061\pi$
$739$		−	29.2677i		−	1.07663i	0.842744	−	0.538315i	$-0.180939\pi$
$740$	25.4424	+	20.8676i	0.935282	+	0.767109i
$741$	6.41025	−	2.65521i	0.235487	−	0.0975417i
$742$	−14.8303	+	22.6811i	−0.544438	+	0.832650i
$743$	−38.7076	+	19.7225i	−1.42004	+	0.723549i	−0.984297	−	0.176520i	$-0.943516\pi$
$743$	−38.7076	+	19.7225i	−1.42004	+	0.723549i	−0.435747	+	0.900069i	$0.643516\pi$
$744$	34.2923	+	21.4594i	1.25722	+	0.786738i
$745$	−33.0434	−	7.93303i	−1.21062	−	0.290644i
$746$	31.2411	+	28.3070i	1.14382	+	1.03639i
$747$	−4.26125	−	4.26125i	−0.155911	−	0.155911i
$748$	7.19426	+	1.57627i	0.263048	+	0.0576341i
$749$	−12.6501	+	10.8042i	−0.462226	+	0.394778i
$750$	−2.90043	+	15.3808i	−0.105909	+	0.561626i
$751$	−7.37569	−	4.51983i	−0.269143	−	0.164931i	0.381378	−	0.924419i	$-0.375450\pi$
$751$	−7.37569	−	4.51983i	−0.269143	−	0.164931i	−0.650521	+	0.759488i	$0.725450\pi$
$752$	49.6471	−	5.90551i	1.81044	−	0.215352i
$753$	−26.1514	−	22.3354i	−0.953009	−	0.813946i
$754$	28.8134	+	35.8099i	1.04932	+	1.30412i
$755$	21.0565	+	1.65719i	0.766326	+	0.0603111i
$756$	−22.3722	+	2.21006i	−0.813668	+	0.0803790i
$757$	27.2402	+	44.4520i	0.990062	+	1.61564i	0.767843	+	0.640638i	$0.221330\pi$
$757$	27.2402	+	44.4520i	0.990062	+	1.61564i	0.222220	+	0.974997i	$0.428670\pi$
$758$	−11.5001	−	1.24507i	−0.417701	−	0.0452230i
$759$	−1.70587	−	10.7705i	−0.0619192	−	0.390943i
$760$	1.21139	−	4.84513i	0.0439417	−	0.175751i
$761$	−13.1818	−	18.1431i	−0.477839	−	0.657688i	0.500249	−	0.865881i	$-0.333242\pi$
$761$	−13.1818	−	18.1431i	−0.477839	−	0.657688i	−0.978088	+	0.208193i	$0.933242\pi$
$762$	−22.3813	−	8.00447i	−0.810788	−	0.289971i
$763$	−12.0045	−	8.72180i	−0.434593	−	0.315750i
$764$	−2.00672	−	5.78144i	−0.0726006	−	0.209165i
$765$	0.717652	−	1.73257i	0.0259468	−	0.0626411i
$766$	−27.5280	+	25.9600i	−0.994626	+	0.937972i
$767$	22.2464	−	1.75083i	0.803271	−	0.0632188i
$768$	4.98492	+	31.2375i	0.179878	+	1.12719i
$769$	−34.1687	+	11.1021i	−1.23215	+	0.400351i	−0.851494	−	0.524364i	$-0.824303\pi$
$769$	−34.1687	+	11.1021i	−1.23215	+	0.400351i	−0.380660	+	0.924715i	$0.624303\pi$
$770$	−27.3750	−	47.7591i	−0.986525	−	1.72112i
$771$	−9.94049	−	5.06493i	−0.357998	−	0.182409i
$772$	12.2000	−	12.6962i	0.439089	−	0.456946i
$773$	4.89576	+	20.3923i	0.176088	+	0.733460i	0.988606	+	0.150524i	$0.0480961\pi$
$773$	4.89576	+	20.3923i	0.176088	+	0.733460i	−0.812518	+	0.582936i	$0.801904\pi$
$774$	−1.08055	−	5.16291i	−0.0388396	−	0.185577i
$775$	−20.8037	−	6.75954i	−0.747292	−	0.242810i
$776$	12.1523	−	28.5772i	0.436243	−	1.02586i
$777$	4.88381	−	30.8351i	0.175206	−	1.10620i
$778$	6.61001	−	24.3639i	0.236980	−	0.873490i
$779$	3.88747	+	0.905126i	0.139283	+	0.0324295i
$780$	31.8698	−	54.4115i	1.14112	−	1.94824i
$781$	61.4373	+	9.73071i	2.19840	+	0.348192i
$782$	−0.143265	−	1.11514i	−0.00512315	−	0.0398772i
$783$	−7.37560	+	22.6997i	−0.263582	+	0.811223i
$784$	0.868622	−	1.30163i	0.0310222	−	0.0464867i
$785$	52.6278	−	12.6348i	1.87837	−	0.450956i
$786$	6.84537	+	3.74449i	0.244166	+	0.133562i
$787$	21.7189	−	42.6257i	0.774194	−	1.51944i	−0.0784319	−	0.996919i	$-0.524991\pi$
$787$	21.7189	−	42.6257i	0.774194	−	1.51944i	0.852626	−	0.522522i	$-0.175009\pi$
$788$	38.4222	−	10.0381i	1.36873	−	0.357593i
$789$	−7.23234	−	22.2589i	−0.257478	−	0.792436i
$790$	27.7910	+	58.7369i	0.988758	+	2.08976i
$791$	−0.820023	−	10.4194i	−0.0291567	−	0.370471i
$792$	−2.91418	−	12.6604i	−0.103551	−	0.449869i
$793$	10.9885	+	4.55158i	0.390213	+	0.161631i
$794$	0.520059	+	0.761782i	0.0184562	+	0.0270346i
$795$	23.2012	−	31.9337i	0.822860	−	1.13257i
$796$	−7.88000	−	5.48864i	−0.279299	−	0.194540i
$797$	15.1228	−	10.9873i	0.535676	−	0.389191i	−0.286801	−	0.957990i	$-0.592592\pi$
$797$	15.1228	−	10.9873i	0.535676	−	0.389191i	0.822477	+	0.568799i	$0.192592\pi$
$798$	−4.54743	+	1.33156i	−0.160977	+	0.0471367i
$799$	−8.99414	+	1.42453i	−0.318190	+	0.0503963i
$800$	−6.71204	−	15.7329i	−0.237306	−	0.556242i
$801$	−6.37247	+	3.90506i	−0.225160	+	0.137978i
$802$	−6.64840	−	17.4829i	−0.234763	−	0.617341i
$803$	−1.76507	+	22.4274i	−0.0622880	+	0.791444i
$804$	−11.9292	+	5.22209i	−0.420711	+	0.184169i
$805$	−5.45763	+	6.39006i	−0.192356	+	0.225220i
$806$	−45.5859	−	35.2063i	−1.60570	−	1.24009i
$807$	3.66129	−	5.97469i	0.128884	−	0.210319i
$808$	20.6438	−	23.7167i	0.726247	−	0.834350i
$809$	7.20366	+	8.43441i	0.253267	+	0.296538i	0.872444	−	0.488714i	$-0.162534\pi$
$809$	7.20366	+	8.43441i	0.253267	+	0.296538i	−0.619177	+	0.785251i	$0.712534\pi$
$810$	43.6133	−	2.14896i	1.53241	−	0.0755068i
$811$	−15.4961	+	15.4961i	−0.544143	+	0.544143i	−0.924741	−	0.380598i	$-0.875718\pi$
$811$	−15.4961	+	15.4961i	−0.544143	+	0.544143i	0.380598	+	0.924741i	$0.375718\pi$
$812$	−16.9306	−	26.4312i	−0.594147	−	0.927552i
$813$	−12.5422	+	52.2418i	−0.439873	+	1.83220i
$814$	−41.5013	−	1.21661i	−1.45462	−	0.0426421i
$815$	−31.4168	−	61.6589i	−1.10048	−	2.15982i
$816$	−1.12730	−	5.65009i	−0.0394635	−	0.197793i
$817$	0.979119	+	2.36380i	0.0342550	+	0.0826990i
$818$	−7.76051	+	17.2847i	−0.271340	+	0.604347i
$819$	−13.9089			−0.486016
$820$	33.1301	−	14.7747i	1.15695	−	0.515954i
$821$	−20.7056			−0.722631			−0.361316	−	0.932444i	$-0.617672\pi$
$821$	−20.7056			−0.722631			−0.361316	+	0.932444i	$0.617672\pi$
$822$	−24.6411	+	54.8825i	−0.859459	+	1.91425i
$823$	−2.47391	−	5.97256i	−0.0862352	−	0.208190i	0.874879	−	0.484342i	$-0.160941\pi$
$823$	−2.47391	−	5.97256i	−0.0862352	−	0.208190i	−0.961114	+	0.276151i	$0.910941\pi$
$824$	9.49137	−	4.72448i	0.330647	−	0.164585i
$825$	13.7180	+	26.9231i	0.477600	+	0.937342i
$826$	−15.2329	−	0.446552i	−0.530021	−	0.0155375i
$827$	−2.44994	+	10.2048i	−0.0851929	+	0.354854i	−0.998642	−	0.0520992i	$-0.983409\pi$
$827$	−2.44994	+	10.2048i	−0.0851929	+	0.354854i	0.913449	+	0.406953i	$0.133409\pi$
$828$	−1.67001	+	1.06973i	−0.0580367	+	0.0371756i
$829$	15.3889	−	15.3889i	0.534478	−	0.534478i	−0.387424	−	0.921902i	$-0.626635\pi$
$829$	15.3889	−	15.3889i	0.534478	−	0.534478i	0.921902	+	0.387424i	$0.126635\pi$
$830$	26.5337	−	1.30740i	0.920997	−	0.0453804i
$831$	−10.8697	−	12.7268i	−0.377065	−	0.441487i
$832$	−2.69087	−	44.9590i	−0.0932892	−	1.55867i
$833$	−0.148919	+	0.243014i	−0.00515975	+	0.00841995i
$834$	−4.86716	−	3.75894i	−0.168536	−	0.130161i
$835$	33.6505	−	39.3997i	1.16453	−	1.36348i
$836$	2.52705	+	5.77272i	0.0873998	+	0.199654i
$837$	2.34673	−	29.8180i	0.0811149	−	1.03066i
$838$	−7.02259	−	18.4668i	−0.242591	−	0.637926i
$839$	−9.05214	+	5.54716i	−0.312514	+	0.191509i	−0.669907	−	0.742445i	$-0.733666\pi$
$839$	−9.05214	+	5.54716i	−0.312514	+	0.191509i	0.357392	+	0.933954i	$0.383666\pi$
$840$	−25.6377	+	34.6001i	−0.884585	+	1.19382i
$841$	−4.27185	+	0.676594i	−0.147305	+	0.0233308i
$842$	−14.1613	+	4.14666i	−0.488032	+	0.142903i
$843$	18.2571	−	13.2646i	0.628809	−	0.456857i
$844$	−5.27822	+	7.57791i	−0.181684	+	0.260842i
$845$	−31.1286	+	42.8449i	−1.07086	+	1.47391i
$846$	9.05685	+	13.2665i	0.311381	+	0.456111i
$847$	36.5420	+	15.1362i	1.25560	+	0.520085i
$848$	1.09042	−	28.1722i	0.0374452	−	0.967436i
$849$	−0.834292	−	10.6007i	−0.0286328	−	0.363814i
$850$	1.33242	+	2.81609i	0.0457015	+	0.0965912i
$851$	1.95860	+	6.02796i	0.0671401	+	0.206636i
$852$	−12.3001	−	47.0803i	−0.421395	−	1.61294i
$853$	8.84839	−	17.3659i	0.302963	−	0.594599i	−0.688462	−	0.725272i	$-0.741714\pi$
$853$	8.84839	−	17.3659i	0.302963	−	0.594599i	0.991425	+	0.130673i	$0.0417139\pi$
$854$	−7.12607	−	3.89804i	−0.243849	−	0.133388i
$855$	1.56024	−	0.374579i	0.0533589	−	0.0128103i
$856$	5.50250	−	16.4096i	0.188071	−	0.560869i
$857$	6.41597	−	19.7463i	0.219165	−	0.674522i	−0.779666	−	0.626195i	$-0.784611\pi$
$857$	6.41597	−	19.7463i	0.219165	−	0.674522i	0.998832	−	0.0483265i	$-0.0153888\pi$
$858$	10.1386	+	78.9158i	0.346124	+	2.69414i
$859$	−19.1389	−	3.03130i	−0.653009	−	0.103426i	−0.178865	−	0.983874i	$-0.557242\pi$
$859$	−19.1389	−	3.03130i	−0.653009	−	0.103426i	−0.474144	+	0.880447i	$0.657242\pi$
$860$	20.0644	+	11.7521i	0.684191	+	0.400743i
$861$	−27.9817	−	20.0380i	−0.953615	−	0.682892i
$862$	4.71117	−	17.3650i	0.160463	−	0.591453i
$863$	5.66701	−	35.7801i	0.192907	−	1.21797i	−0.681150	−	0.732144i	$-0.738520\pi$
$863$	5.66701	−	35.7801i	0.192907	−	1.21797i	0.874057	−	0.485824i	$-0.161480\pi$
$864$	18.7757	−	13.9463i	0.638763	−	0.474462i
$865$	11.2855	+	3.66687i	0.383717	+	0.124677i
$866$	−7.34318	−	35.0860i	−0.249532	−	1.19227i
$867$	−7.60109	−	31.6608i	−0.258147	−	1.07526i
$868$	28.3627	+	27.2543i	0.962693	+	0.925071i
$869$	−73.0530	−	37.2224i	−2.47815	−	1.26268i
$870$	22.7361	+	39.6660i	0.770826	+	1.34480i
$871$	17.6338	−	5.72955i	0.597497	−	0.194139i
$872$	15.3778	+	1.35550i	0.520758	+	0.0459031i
$873$	9.94625	−	0.782787i	0.336630	−	0.0264933i
$874$	0.699865	−	0.660001i	0.0236733	−	0.0223248i
$875$	−5.82413	+	14.0607i	−0.196891	+	0.475338i
$876$	16.6258	−	5.77076i	0.561733	−	0.194976i
$877$	24.2703	+	17.6334i	0.819551	+	0.595439i	0.916584	−	0.399842i	$-0.130935\pi$
$877$	24.2703	+	17.6334i	0.819551	+	0.595439i	−0.0970325	+	0.995281i	$0.530935\pi$
$878$	10.8636	+	3.88527i	0.366629	+	0.131122i
$879$	−6.43531	−	8.85745i	−0.217058	−	0.298754i
$880$	49.9846	+	27.9544i	1.68498	+	0.942344i
$881$	−0.466405	−	2.94477i	−0.0157136	−	0.0992117i	0.978585	−	0.205843i	$-0.0659936\pi$
$881$	−0.466405	−	2.94477i	−0.0157136	−	0.0992117i	−0.994299	+	0.106631i	$0.965994\pi$
$882$	0.499836	+	0.0541154i	0.0168303	+	0.00182216i
$883$	12.3771	+	20.1977i	0.416524	+	0.679705i	0.990244	−	0.139346i	$-0.0445002\pi$
$883$	12.3771	+	20.1977i	0.416524	+	0.679705i	−0.573720	+	0.819052i	$0.694500\pi$
$884$	0.806446	+	8.16356i	0.0271237	+	0.274570i
$885$	22.1290	+	1.74159i	0.743858	+	0.0585429i
$886$	−36.5381	−	45.4103i	−1.22752	−	1.52559i
$887$	−14.0083	−	11.9642i	−0.470354	−	0.401720i	0.382430	−	0.923985i	$-0.375087\pi$
$887$	−14.0083	−	11.9642i	−0.470354	−	0.401720i	−0.852784	+	0.522265i	$0.825087\pi$
$888$	12.1475	+	30.1227i	0.407642	+	1.01085i
$889$	−19.7067	−	12.0763i	−0.660940	−	0.405025i
$890$	6.10535	−	32.3762i	0.204652	−	1.08525i
$891$	−41.8958	+	35.7824i	−1.40356	+	1.19876i
$892$	0.233959	−	1.06781i	0.00783353	−	0.0357531i
$893$	−5.50946	−	5.50946i	−0.184367	−	0.184367i
$894$	−24.8568	−	22.5223i	−0.831335	−	0.753257i
$895$	32.8347	+	7.88292i	1.09754	+	0.263497i
$896$	−1.47786	+	30.7228i	−0.0493719	+	1.02638i
$897$	10.8222	−	5.51418i	0.361343	−	0.184113i
$898$	−1.69390	+	2.59060i	−0.0565260	+	0.0864495i
$899$	38.5826	−	15.9815i	1.28680	−	0.533011i
$900$	3.48505	−	4.24908i	0.116168	−	0.141636i
$901$			5.13500i			0.171071i
$902$	−21.6895	+	40.3056i	−0.722183	+	1.34203i
$903$		−	22.0614i		−	0.734156i
$904$	6.30850	+	8.85642i	0.209818	+	0.294560i
$905$	16.9209	−	7.00887i	0.562470	−	0.232983i
$906$	17.4493	+	11.4094i	0.579715	+	0.379053i
$907$	−36.7094	+	18.7044i	−1.21891	+	0.621068i	−0.940631	−	0.339431i	$-0.889766\pi$
$907$	−36.7094	+	18.7044i	−1.21891	+	0.621068i	−0.278284	+	0.960499i	$0.589766\pi$
$908$	−7.76353	+	25.6198i	−0.257642	+	0.850224i
$909$	9.82288	+	2.35827i	0.325804	+	0.0782187i
$910$	41.1698	−	45.4372i	1.36477	−	1.50623i
$911$	−0.623160	−	0.623160i	−0.0206462	−	0.0206462i	0.696708	−	0.717355i	$-0.254647\pi$
$911$	−0.623160	−	0.623160i	−0.0206462	−	0.0206462i	−0.717355	+	0.696708i	$0.754647\pi$
$912$	3.34414	−	3.62191i	0.110735	−	0.119933i
$913$	−25.4888	+	21.7695i	−0.843556	+	0.720464i
$914$	19.9408	+	3.76033i	0.659582	+	0.124381i
$915$	10.0877	+	6.18173i	0.333488	+	0.204362i
$916$	−7.45172	−	9.83804i	−0.246212	−	0.325058i
$917$	5.76912	+	4.92729i	0.190513	+	0.162713i
$918$	−3.31893	+	2.67047i	−0.109541	+	0.0881388i
$919$	3.04641	+	0.239758i	0.100492	+	0.00790888i	0.128605	−	0.991696i	$-0.458950\pi$
$919$	3.04641	+	0.239758i	0.100492	+	0.00790888i	−0.0281135	+	0.999605i	$0.508950\pi$
$920$	1.44860	−	8.62188i	0.0477588	−	0.284255i
$921$	−13.1623	−	21.4790i	−0.433714	−	0.707756i
$922$	−5.47297	+	50.5510i	−0.180243	+	1.66481i
$923$	10.8384	+	68.4309i	0.356750	+	2.25243i
$924$	−1.08267	−	54.3253i	−0.0356173	−	1.78717i
$925$	−10.3232	−	14.2086i	−0.339424	−	0.467177i
$926$	3.83071	−	10.7110i	0.125885	−	0.351987i
$927$	2.75575	+	2.00217i	0.0905108	+	0.0657600i
$928$	29.2513	+	14.5177i	0.960221	+	0.476568i
$929$	15.7525	−	38.0299i	0.516822	−	1.24772i	−0.423023	−	0.906119i	$-0.639031\pi$
$929$	15.7525	−	38.0299i	0.516822	−	1.24772i	0.939845	−	0.341601i	$-0.110969\pi$
$930$	−39.3087	−	41.6829i	−1.28898	−	1.36684i
$931$	−0.243114	+	0.0191335i	−0.00796773	+	0.000627074i
$932$	5.62837	+	31.4648i	0.184363	+	1.03066i
$933$	−26.4637	+	8.59857i	−0.866382	+	0.281505i
$934$	31.7419	−	18.1941i	1.03863	−	0.595330i
$935$	−9.29409	−	4.73558i	−0.303949	−	0.154870i
$936$	12.4084	−	7.44469i	0.405581	−	0.243337i
$937$	11.4057	+	47.5082i	0.372608	+	1.55203i	0.772229	+	0.635345i	$0.219142\pi$
$937$	11.4057	+	47.5082i	0.372608	+	1.55203i	−0.399620	+	0.916681i	$0.630858\pi$
$938$	−12.3936	+	2.59387i	−0.404666	+	0.0846930i
$939$	−60.0224	−	19.5025i	−1.95876	−	0.636439i
$940$	−70.1465	−	9.68157i	−2.28792	−	0.315778i
$941$	2.87736	−	18.1670i	0.0937994	−	0.592226i	−0.895356	−	0.445352i	$-0.853079\pi$
$941$	2.87736	−	18.1670i	0.0937994	−	0.592226i	0.989155	−	0.146874i	$-0.0469213\pi$
$942$	51.5591	+	13.9881i	1.67989	+	0.455758i
$943$	6.90855	+	1.04565i	0.224973	+	0.0340512i
$944$	13.8286	−	7.75499i	0.450083	−	0.252404i
$945$	31.4481	+	4.98090i	1.02301	+	0.162029i
$946$	−29.1005	+	3.73863i	−0.946138	+	0.121553i
$947$	−3.53461	+	10.8784i	−0.114859	+	0.353501i	−0.991918	−	0.126883i	$-0.959503\pi$
$947$	−3.53461	+	10.8784i	−0.114859	+	0.353501i	0.877058	+	0.480384i	$0.159503\pi$
$948$	−3.75722	+	64.0288i	−0.122029	+	2.07956i
$949$	−24.3653	+	5.84958i	−0.790930	+	0.189885i
$950$	−1.27924	+	2.33860i	−0.0415040	+	0.0758742i
$951$	−17.0862	+	33.5336i	−0.554058	+	1.08740i
$952$	0.0525463	−	5.60194i	0.00170304	−	0.181560i
$953$	−3.25321	−	10.0123i	−0.105382	−	0.324332i	0.884438	−	0.466658i	$-0.154542\pi$
$953$	−3.25321	−	10.0123i	−0.105382	−	0.324332i	−0.989820	+	0.142326i	$0.954542\pi$
$954$	8.18776	−	3.87398i	0.265088	−	0.125425i
$955$	0.680047	+	8.64082i	0.0220058	+	0.279610i
$956$	9.95284	+	18.6074i	0.321898	+	0.601806i
$957$	−53.2968	−	22.0763i	−1.72284	−	0.713625i
$958$	−3.59218	+	2.45234i	−0.116058	+	0.0792314i
$959$	−34.3839	+	47.3253i	−1.11031	+	1.52821i
$960$	4.35231	−	44.5899i	0.140470	−	1.43913i
$961$	−17.2594	+	12.5397i	−0.556754	+	0.404505i
$962$	−12.9957	−	44.3819i	−0.418999	−	1.43093i
$963$	5.49216	−	0.869872i	0.176982	−	0.0280312i
$964$	−37.6358	−	14.7177i	−1.21217	−	0.474026i
$965$	−21.2632	+	13.0301i	−0.684487	+	0.419454i
$966$	−7.75308	+	2.94835i	−0.249451	+	0.0948616i
$967$	−2.25579	+	28.6626i	−0.0725414	+	0.921726i	0.847726	+	0.530435i	$0.177971\pi$
$967$	−2.25579	+	28.6626i	−0.0725414	+	0.921726i	−0.920267	+	0.391291i	$0.872029\pi$
$968$	−40.7014	+	6.05569i	−1.30819	+	0.194637i
$969$	−0.583117	+	0.682742i	−0.0187324	+	0.0219328i
$970$	−26.8833	+	34.8092i	−0.863172	+	1.11765i
$971$	7.73945	−	12.6296i	0.248371	−	0.405304i	−0.704022	−	0.710178i	$-0.748614\pi$
$971$	7.73945	−	12.6296i	0.248371	−	0.405304i	0.952393	+	0.304874i	$0.0986143\pi$
$972$	16.4622	+	7.97881i	0.528026	+	0.255920i
$973$	−3.88351	−	4.54700i	−0.124499	−	0.145770i
$974$	0.810888	+	16.4570i	0.0259825	+	0.527317i
$975$	−23.7985	+	23.7985i	−0.762162	+	0.762162i
$976$	8.44372	−	0.336691i	0.270277	−	0.0107772i
$977$	−2.35266	+	9.79953i	−0.0752682	+	0.313515i	−0.997285	−	0.0736345i	$-0.976540\pi$
$977$	−2.35266	+	9.79953i	−0.0752682	+	0.313515i	0.922017	+	0.387149i	$0.126540\pi$
$978$	2.00153	−	68.2767i	0.0640017	−	2.18325i
$979$	18.8730	+	37.0403i	0.603183	+	1.18381i
$980$	−1.65628	+	1.47267i	−0.0529078	+	0.0470427i
$981$	1.89802	+	4.58223i	0.0605991	+	0.146299i
$982$	−25.8782	−	11.6188i	−0.825806	−	0.370771i
$983$	43.4797			1.38679			0.693394	−	0.720559i	$-0.256115\pi$
$983$	43.4797			1.38679			0.693394	+	0.720559i	$0.256115\pi$
$984$	35.6883	+	2.89912i	1.13770	+	0.0924204i
$985$	−56.2443			−1.79209
$986$	−5.42598	−	2.43616i	−0.172799	−	0.0775831i
$987$	25.7099	+	62.0691i	0.818354	+	1.97568i
$988$	−5.24537	+	4.66389i	−0.166877	+	0.148378i
$989$	2.03338	+	3.99072i	0.0646576	+	0.126898i
$990$	−0.539163	+	18.3921i	−0.0171357	+	0.584539i
$991$	−6.96145	+	28.9965i	−0.221138	+	0.921105i	0.745816	+	0.666152i	$0.232060\pi$
$991$	−6.96145	+	28.9965i	−0.221138	+	0.921105i	−0.966953	+	0.254953i	$0.917940\pi$
$992$	−39.8907	−	9.13304i	−1.26653	−	0.289974i
$993$	−15.7296	+	15.7296i	−0.499165	+	0.499165i
$994$	−2.32855	−	47.2580i	−0.0738571	−	1.49893i
$995$	8.83312	+	10.3423i	0.280029	+	0.327872i
$996$	23.5967	+	11.4367i	0.747689	+	0.362386i
$997$	1.80751	−	2.94958i	0.0572443	−	0.0934142i	−0.822738	−	0.568421i	$-0.807554\pi$
$997$	1.80751	−	2.94958i	0.0572443	−	0.0934142i	0.879982	+	0.475007i	$0.157554\pi$
$998$	38.3785	−	49.6933i	1.21485	−	1.57301i
$999$	15.5964	−	18.2610i	0.493448	−	0.577753i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	164.2.o.b.15.17	yes	288
4.3	odd	2	inner	164.2.o.b.15.18	yes	288
41.11	odd	40	inner	164.2.o.b.11.18	yes	288
164.11	even	40	inner	164.2.o.b.11.17	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
164.2.o.b.11.17	✓	288	164.11	even	40	inner
164.2.o.b.11.18	yes	288	41.11	odd	40	inner
164.2.o.b.15.17	yes	288	1.1	even	1	trivial
164.2.o.b.15.18	yes	288	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 164 = 2^{2} \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	164.o (of order \(40\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29014 + 0.579249i) q^{2} +(-0.756584 - 1.82656i) q^{3} +(1.32894 + 1.49463i) q^{4} +(-1.28598 - 2.52388i) q^{5} +(0.0819284 - 2.79477i) q^{6} +(0.634663 - 2.64356i) q^{7} +(0.848763 + 2.69807i) q^{8} +(-0.642564 + 0.642564i) q^{9} +O(q^{10})\)	\(q+(1.29014 + 0.579249i) q^{2} +(-0.756584 - 1.82656i) q^{3} +(1.32894 + 1.49463i) q^{4} +(-1.28598 - 2.52388i) q^{5} +(0.0819284 - 2.79477i) q^{6} +(0.634663 - 2.64356i) q^{7} +(0.848763 + 2.69807i) q^{8} +(-0.642564 + 0.642564i) q^{9} +(-0.197145 - 4.00108i) q^{10} +(3.28267 + 3.84351i) q^{11} +(1.72457 - 3.55820i) q^{12} +(-2.94163 + 4.80031i) q^{13} +(2.35009 - 3.04295i) q^{14} +(-3.63706 + 4.25845i) q^{15} +(-0.467831 + 3.97255i) q^{16} +(0.0571608 - 0.726296i) q^{17} +(-1.20120 + 0.456795i) q^{18} +(0.531502 - 0.325705i) q^{19} +(2.06327 - 5.27616i) q^{20} +(-5.30879 + 0.840829i) q^{21} +(2.00877 + 6.86017i) q^{22} +(0.882818 - 0.641405i) q^{23} +(4.28602 - 3.59163i) q^{24} +(-1.77731 + 2.44625i) q^{25} +(-6.57571 + 4.48915i) q^{26} +(-3.81983 - 1.58223i) q^{27} +(4.79457 - 2.56455i) q^{28} +(-0.452928 - 5.75499i) q^{29} +(-7.15903 + 3.38725i) q^{30} +(2.23549 + 6.88014i) q^{31} +(-2.90466 + 4.85417i) q^{32} +(4.53677 - 8.90392i) q^{33} +(0.494452 - 0.903916i) q^{34} +(-7.48820 + 1.79776i) q^{35} +(-1.81432 - 0.106465i) q^{36} +(-1.79487 + 5.52404i) q^{37} +(0.874378 - 0.112334i) q^{38} +(10.9936 + 1.74122i) q^{39} +(5.71813 - 5.61185i) q^{40} +(4.55866 + 4.49651i) q^{41} +(-7.33615 - 1.99032i) q^{42} +(-0.642081 + 4.05394i) q^{43} +(-1.38215 + 10.0142i) q^{44} +(2.44808 + 0.795430i) q^{45} +(1.51050 - 0.316133i) q^{46} +(-2.91790 - 12.1539i) q^{47} +(7.61003 - 2.15105i) q^{48} +(-0.348572 - 0.177606i) q^{49} +(-3.70997 + 2.12651i) q^{50} +(-1.36987 + 0.445097i) q^{51} +(-11.0839 + 1.98268i) q^{52} +(-7.02659 + 0.553004i) q^{53} +(-4.01163 - 4.25393i) q^{54} +(5.47912 - 13.2278i) q^{55} +(7.67120 - 0.531388i) q^{56} +(-0.997043 - 0.724394i) q^{57} +(2.74923 - 7.68713i) q^{58} +(-2.32978 - 3.20667i) q^{59} +(-11.1982 + 0.223174i) q^{60} +(-0.330485 - 2.08660i) q^{61} +(-1.10121 + 10.1713i) q^{62} +(1.29085 + 2.10647i) q^{63} +(-6.55920 + 4.58005i) q^{64} +(15.8983 + 1.25122i) q^{65} +(11.0107 - 8.85941i) q^{66} +(-2.50427 - 2.13885i) q^{67} +(1.16151 - 0.879771i) q^{68} +(-1.83949 - 1.12724i) q^{69} +(-10.7022 - 2.01817i) q^{70} +(9.35782 - 7.99233i) q^{71} +(-2.27907 - 1.18830i) q^{72} +(3.14718 + 3.14718i) q^{73} +(-5.51544 + 6.08713i) q^{74} +(5.81290 + 1.39555i) q^{75} +(1.19314 + 0.361555i) q^{76} +(12.2440 - 6.23860i) q^{77} +(13.1748 + 8.61447i) q^{78} +(-14.9861 + 6.20746i) q^{79} +(10.6279 - 3.92788i) q^{80} +10.9004i q^{81} +(3.27673 + 8.44175i) q^{82} +6.63164i q^{83} +(-8.31179 - 6.81725i) q^{84} +(-1.90659 + 0.789737i) q^{85} +(-3.17662 + 4.85824i) q^{86} +(-10.1691 + 5.18143i) q^{87} +(-7.58388 + 12.1191i) q^{88} +(7.99728 + 1.91998i) q^{89} +(2.69763 + 2.44427i) q^{90} +(10.8230 + 10.8230i) q^{91} +(2.13188 + 0.467096i) q^{92} +(10.8756 - 9.28865i) q^{93} +(3.27564 - 17.3705i) q^{94} +(-1.50554 - 0.922597i) q^{95} +(11.0640 + 1.63294i) q^{96} +(-8.34861 - 7.13039i) q^{97} +(-0.346829 - 0.431047i) q^{98} +(-4.57903 - 0.360378i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9}+O(q^{10}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9	\( 288 q - 12 q^{2} - 20 q^{4} - 32 q^{5} - 28 q^{6} - 24 q^{8} - 40 q^{9} - 12 q^{10} - 8 q^{12} - 24 q^{13} - 4 q^{14} - 28 q^{16} - 12 q^{18} - 44 q^{20} - 32 q^{21} - 40 q^{22} + 8 q^{24} - 40 q^{25} + 4 q^{26} - 48 q^{29} - 44 q^{30} + 108 q^{32} - 72 q^{33} + 12 q^{34} - 20 q^{36} - 24 q^{37} + 56 q^{38} + 8 q^{41} - 112 q^{42} - 40 q^{45} - 48 q^{46} - 68 q^{48} - 16 q^{49} - 60 q^{50} - 124 q^{52} - 64 q^{53} + 64 q^{54} - 84 q^{56} - 24 q^{57} + 40 q^{60} - 8 q^{61} - 44 q^{62} - 20 q^{64} + 64 q^{65} + 60 q^{66} - 28 q^{68} - 8 q^{69} + 128 q^{70} + 160 q^{72} - 32 q^{73} + 80 q^{74} + 288 q^{76} - 32 q^{77} + 116 q^{78} + 176 q^{80} + 212 q^{82} + 152 q^{84} - 56 q^{85} + 180 q^{86} + 144 q^{88} - 72 q^{89} + 224 q^{90} + 36 q^{92} - 8 q^{93} + 52 q^{94} + 136 q^{96} - 88 q^{97} + 104 q^{98}+O(q^{100}) \) 288 * q - 12 * q^2 - 20 * q^4 - 32 * q^5 - 28 * q^6 - 24 * q^8 - 40 * q^9 - 12 * q^10 - 8 * q^12 - 24 * q^13 - 4 * q^14 - 28 * q^16 - 12 * q^18 - 44 * q^20 - 32 * q^21 - 40 * q^22 + 8 * q^24 - 40 * q^25 + 4 * q^26 - 48 * q^29 - 44 * q^30 + 108 * q^32 - 72 * q^33 + 12 * q^34 - 20 * q^36 - 24 * q^37 + 56 * q^38 + 8 * q^41 - 112 * q^42 - 40 * q^45 - 48 * q^46 - 68 * q^48 - 16 * q^49 - 60 * q^50 - 124 * q^52 - 64 * q^53 + 64 * q^54 - 84 * q^56 - 24 * q^57 + 40 * q^60 - 8 * q^61 - 44 * q^62 - 20 * q^64 + 64 * q^65 + 60 * q^66 - 28 * q^68 - 8 * q^69 + 128 * q^70 + 160 * q^72 - 32 * q^73 + 80 * q^74 + 288 * q^76 - 32 * q^77 + 116 * q^78 + 176 * q^80 + 212 * q^82 + 152 * q^84 - 56 * q^85 + 180 * q^86 + 144 * q^88 - 72 * q^89 + 224 * q^90 + 36 * q^92 - 8 * q^93 + 52 * q^94 + 136 * q^96 - 88 * q^97 + 104 * q^98

Introduction

L-functions

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