LMFDB - Embedded newform 135.2.p.a.124.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(4,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2, 9]))

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

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

chi := DirichletCharacter("135.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.p (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$16$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			124.14
Character	$\chi$	$=$	135.124
Dual form			135.2.p.a.49.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.43054 - 1.70485i) q^{2} +(1.69316 + 0.364996i) q^{3} +(-0.512771 - 2.90807i) q^{4} +(-1.92292 + 1.14122i) q^{5} +(3.04438 - 2.36443i) q^{6} +(-3.63532 - 0.641005i) q^{7} +(-1.83663 - 1.06038i) q^{8} +(2.73356 + 1.23599i) q^{9} +O(q^{10})$	\(q+(1.43054 - 1.70485i) q^{2} +(1.69316 + 0.364996i) q^{3} +(-0.512771 - 2.90807i) q^{4} +(-1.92292 + 1.14122i) q^{5} +(3.04438 - 2.36443i) q^{6} +(-3.63532 - 0.641005i) q^{7} +(-1.83663 - 1.06038i) q^{8} +(2.73356 + 1.23599i) q^{9} +(-0.805194 + 4.91084i) q^{10} +(0.208643 - 0.0759398i) q^{11} +(0.193233 - 5.11097i) q^{12} +(2.18338 + 2.60206i) q^{13} +(-6.29327 + 5.28068i) q^{14} +(-3.67234 + 1.23041i) q^{15} +(1.11454 - 0.405659i) q^{16} +(-3.20432 + 1.85001i) q^{17} +(6.01762 - 2.89216i) q^{18} +(2.03386 - 3.52275i) q^{19} +(4.30477 + 5.00679i) q^{20} +(-5.92120 - 2.41220i) q^{21} +(0.169005 - 0.464339i) q^{22} +(-8.81046 + 1.55352i) q^{23} +(-2.72267 - 2.46575i) q^{24} +(2.39522 - 4.38895i) q^{25} +7.55951 q^{26} +(4.17720 + 3.09046i) q^{27} +10.9005i q^{28} +(-2.31546 - 1.94290i) q^{29} +(-3.15576 + 8.02092i) q^{30} +(-0.591627 - 3.35529i) q^{31} +(2.35349 - 6.46615i) q^{32} +(0.380983 - 0.0524241i) q^{33} +(-1.42990 + 8.10938i) q^{34} +(7.72195 - 2.91611i) q^{35} +(2.19266 - 8.58314i) q^{36} +(4.98644 - 2.87892i) q^{37} +(-3.09624 - 8.50684i) q^{38} +(2.74707 + 5.20261i) q^{39} +(4.74182 - 0.0569818i) q^{40} +(-1.56627 + 1.31425i) q^{41} +(-12.5829 + 6.64400i) q^{42} +(0.988279 + 2.71527i) q^{43} +(-0.327824 - 0.567808i) q^{44} +(-6.66694 + 0.742883i) q^{45} +(-9.95516 + 17.2428i) q^{46} +(5.41104 + 0.954113i) q^{47} +(2.03515 - 0.280041i) q^{48} +(6.22683 + 2.26638i) q^{49} +(-4.05603 - 10.3620i) q^{50} +(-6.10066 + 1.96280i) q^{51} +(6.44738 - 7.68369i) q^{52} -0.995243i q^{53} +(11.2444 - 2.70047i) q^{54} +(-0.314539 + 0.384134i) q^{55} +(5.99704 + 5.03212i) q^{56} +(4.72944 - 5.22222i) q^{57} +(-6.62468 + 1.16811i) q^{58} +(9.07341 + 3.30245i) q^{59} +(5.46118 + 10.0485i) q^{60} +(-0.770787 + 4.37135i) q^{61} +(-6.56659 - 3.79122i) q^{62} +(-9.14508 - 6.24545i) q^{63} +(-6.47098 - 11.2081i) q^{64} +(-7.16799 - 2.51181i) q^{65} +(0.455635 - 0.724511i) q^{66} +(-9.78823 - 11.6652i) q^{67} +(7.02305 + 8.36974i) q^{68} +(-15.4845 - 0.585432i) q^{69} +(6.07501 - 17.3363i) q^{70} +(-1.34897 - 2.33649i) q^{71} +(-3.70992 - 5.16867i) q^{72} +(1.00694 + 0.581356i) q^{73} +(2.22516 - 12.6195i) q^{74} +(5.65744 - 6.55693i) q^{75} +(-11.2873 - 4.10824i) q^{76} +(-0.807162 + 0.142324i) q^{77} +(12.7994 + 2.75919i) q^{78} +(3.81056 + 3.19744i) q^{79} +(-1.68022 + 2.05198i) q^{80} +(5.94465 + 6.75730i) q^{81} +4.55033i q^{82} +(-2.76861 + 3.29950i) q^{83} +(-3.97863 + 18.4562i) q^{84} +(4.05036 - 7.21426i) q^{85} +(6.04289 + 2.19943i) q^{86} +(-3.21128 - 4.13476i) q^{87} +(-0.463726 - 0.0817674i) q^{88} +(1.93222 - 3.34670i) q^{89} +(-8.27080 + 12.4288i) q^{90} +(-6.26937 - 10.8589i) q^{91} +(9.03550 + 24.8248i) q^{92} +(0.222950 - 5.89697i) q^{93} +(9.36730 - 7.86010i) q^{94} +(0.109294 + 9.09505i) q^{95} +(6.34494 - 10.0892i) q^{96} +(6.14411 + 16.8808i) q^{97} +(12.7715 - 7.37364i) q^{98} +(0.664198 + 0.0502953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	$ 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) $ 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$-1$

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 $

$2$	1.43054	−	1.70485i	1.01154	−	1.20551i	0.0330002	−	0.999455i	$-0.489494\pi$
$2$	1.43054	−	1.70485i	1.01154	−	1.20551i	0.978541	−	0.206053i	$-0.0660618\pi$
$3$	1.69316	+	0.364996i	0.977544	+	0.210731i
$3$	1.69316	+	0.364996i	0.977544	+	0.210731i
$4$	−0.512771	−	2.90807i	−0.256385	−	1.45403i
$5$	−1.92292	+	1.14122i	−0.859955	+	0.510370i
$5$	−1.92292	+	1.14122i	−0.859955	+	0.510370i
$6$	3.04438	−	2.36443i	1.24286	−	0.965274i
$7$	−3.63532	−	0.641005i	−1.37402	−	0.242277i	−0.562596	−	0.826732i	$-0.690197\pi$
$7$	−3.63532	−	0.641005i	−1.37402	−	0.242277i	−0.811426	+	0.584455i	$0.801308\pi$
$8$	−1.83663	−	1.06038i	−0.649348	−	0.374901i
$9$	2.73356	+	1.23599i	0.911185	+	0.411997i
$10$	−0.805194	+	4.91084i	−0.254625	+	1.55294i
$11$	0.208643	−	0.0759398i	0.0629082	−	0.0228967i	−0.310374	−	0.950614i	$-0.600454\pi$
$11$	0.208643	−	0.0759398i	0.0629082	−	0.0228967i	0.373283	+	0.927718i	$0.378232\pi$
$12$	0.193233	−	5.11097i	0.0557816	−	1.47541i
$13$	2.18338	+	2.60206i	0.605562	+	0.721680i	0.978516	−	0.206169i	$-0.0660997\pi$
$13$	2.18338	+	2.60206i	0.605562	+	0.721680i	−0.372955	+	0.927850i	$0.621655\pi$
$14$	−6.29327	+	5.28068i	−1.68195	+	1.41132i
$15$	−3.67234	+	1.23041i	−0.948195	+	0.317690i
$16$	1.11454	−	0.405659i	0.278634	−	0.101415i
$17$	−3.20432	+	1.85001i	−0.777161	+	0.448694i	−0.835423	−	0.549607i	$-0.814777\pi$
$17$	−3.20432	+	1.85001i	−0.777161	+	0.448694i	0.0582621	+	0.998301i	$0.481444\pi$
$18$	6.01762	−	2.89216i	1.41837	−	0.681689i
$19$	2.03386	−	3.52275i	0.466600	−	0.808175i	−0.532672	−	0.846322i	$-0.678812\pi$
$19$	2.03386	−	3.52275i	0.466600	−	0.808175i	0.999272	+	0.0381470i	$0.0121455\pi$
$20$	4.30477	+	5.00679i	0.962575	+	1.11955i
$21$	−5.92120	−	2.41220i	−1.29211	−	0.526386i
$22$	0.169005	−	0.464339i	0.0360321	−	0.0989973i
$23$	−8.81046	+	1.55352i	−1.83711	+	0.323932i	−0.981170	−	0.193146i	$-0.938131\pi$
$23$	−8.81046	+	1.55352i	−1.83711	+	0.323932i	−0.855939	+	0.517077i	$0.827020\pi$
$24$	−2.72267	−	2.46575i	−0.555763	−	0.503320i
$25$	2.39522	−	4.38895i	0.479045	−	0.877790i
$26$	7.55951			1.48254
$27$	4.17720	+	3.09046i	0.803903	+	0.594760i
$28$			10.9005i			2.05999i
$29$	−2.31546	−	1.94290i	−0.429969	−	0.360787i	0.401971	−	0.915653i	$-0.368325\pi$
$29$	−2.31546	−	1.94290i	−0.429969	−	0.360787i	−0.831940	+	0.554865i	$0.812770\pi$
$30$	−3.15576	+	8.02092i	−0.576160	+	1.46441i
$31$	−0.591627	−	3.35529i	−0.106259	−	0.602627i	−0.990710	−	0.135993i	$-0.956578\pi$
$31$	−0.591627	−	3.35529i	−0.106259	−	0.602627i	0.884450	−	0.466634i	$-0.154534\pi$
$32$	2.35349	−	6.46615i	0.416042	−	1.14306i
$33$	0.380983	−	0.0524241i	0.0663206	−	0.00912586i
$34$	−1.42990	+	8.10938i	−0.245226	+	1.39075i
$35$	7.72195	−	2.91611i	1.30525	−	0.492912i
$36$	2.19266	−	8.58314i	0.365443	−	1.43052i
$37$	4.98644	−	2.87892i	0.819765	−	0.473292i	−0.0305703	−	0.999533i	$-0.509732\pi$
$37$	4.98644	−	2.87892i	0.819765	−	0.473292i	0.850335	+	0.526241i	$0.176399\pi$
$38$	−3.09624	−	8.50684i	−0.502276	−	1.37999i
$39$	2.74707	+	5.20261i	0.439883	+	0.833085i
$40$	4.74182	−	0.0569818i	0.749748	−	0.00900961i
$41$	−1.56627	+	1.31425i	−0.244610	+	0.205252i	−0.756847	−	0.653592i	$-0.773261\pi$
$41$	−1.56627	+	1.31425i	−0.244610	+	0.205252i	0.512237	+	0.858844i	$0.328817\pi$
$42$	−12.5829	+	6.64400i	−1.94159	+	1.02519i
$43$	0.988279	+	2.71527i	0.150711	+	0.414075i	0.991957	−	0.126578i	$-0.0403993\pi$
$43$	0.988279	+	2.71527i	0.150711	+	0.414075i	−0.841246	+	0.540653i	$0.818177\pi$
$44$	−0.327824	−	0.567808i	−0.0494214	−	0.0856003i
$45$	−6.66694	+	0.742883i	−0.993849	+	0.110743i
$46$	−9.95516	+	17.2428i	−1.46781	+	2.54232i
$47$	5.41104	+	0.954113i	0.789282	+	0.139172i	0.553737	−	0.832692i	$-0.313201\pi$
$47$	5.41104	+	0.954113i	0.789282	+	0.139172i	0.235545	+	0.971863i	$0.424313\pi$
$48$	2.03515	−	0.280041i	0.293749	−	0.0404204i
$49$	6.22683	+	2.26638i	0.889547	+	0.323769i
$50$	−4.05603	−	10.3620i	−0.573610	−	1.46541i
$51$	−6.10066	+	1.96280i	−0.854263	+	0.274847i
$52$	6.44738	−	7.68369i	0.894091	−	1.06554i
$53$		−	0.995243i		−	0.136707i	−0.997661	−	0.0683536i	$-0.978225\pi$
$53$		−	0.995243i		−	0.136707i	0.997661	−	0.0683536i	$-0.0217746\pi$
$54$	11.2444	−	2.70047i	1.53017	−	0.367487i
$55$	−0.314539	+	0.384134i	−0.0424124	+	0.0517966i
$56$	5.99704	+	5.03212i	0.801389	+	0.672445i
$57$	4.72944	−	5.22222i	0.626429	−	0.691699i
$58$	−6.62468	+	1.16811i	−0.869864	+	0.153380i
$59$	9.07341	+	3.30245i	1.18126	+	0.429943i	0.856646	−	0.515905i	$-0.172544\pi$
$59$	9.07341	+	3.30245i	1.18126	+	0.429943i	0.324612	+	0.945847i	$0.394766\pi$
$60$	5.46118	+	10.0485i	0.705036	+	1.29726i
$61$	−0.770787	+	4.37135i	−0.0986892	+	0.559694i	0.894865	+	0.446337i	$0.147272\pi$
$61$	−0.770787	+	4.37135i	−0.0986892	+	0.559694i	−0.993554	+	0.113357i	$0.963839\pi$
$62$	−6.56659	−	3.79122i	−0.833958	−	0.481486i
$63$	−9.14508	−	6.24545i	−1.15217	−	0.786853i
$64$	−6.47098	−	11.2081i	−0.808872	−	1.40101i
$65$	−7.16799	−	2.51181i	−0.889080	−	0.311552i
$66$	0.455635	−	0.724511i	0.0560847	−	0.0891812i
$67$	−9.78823	−	11.6652i	−1.19582	−	1.42513i	−0.879120	−	0.476600i	$-0.841869\pi$
$67$	−9.78823	−	11.6652i	−1.19582	−	1.42513i	−0.316702	−	0.948525i	$-0.602576\pi$
$68$	7.02305	+	8.36974i	0.851669	+	1.01498i
$69$	−15.4845	−	0.585432i	−1.86412	−	0.0704777i
$70$	6.07501	−	17.3363i	0.726103	−	2.07209i
$71$	−1.34897	−	2.33649i	−0.160093	−	0.277290i	0.774809	−	0.632196i	$-0.217846\pi$
$71$	−1.34897	−	2.33649i	−0.160093	−	0.277290i	−0.934902	+	0.354906i	$0.884513\pi$
$72$	−3.70992	−	5.16867i	−0.437218	−	0.609134i
$73$	1.00694	+	0.581356i	0.117853	+	0.0680426i	0.557768	−	0.829997i	$-0.311658\pi$
$73$	1.00694	+	0.581356i	0.117853	+	0.0680426i	−0.439915	+	0.898040i	$0.644991\pi$
$74$	2.22516	−	12.6195i	0.258669	−	1.46699i
$75$	5.65744	−	6.55693i	0.653265	−	0.757129i
$76$	−11.2873	−	4.10824i	−1.29474	−	0.471248i
$77$	−0.807162	+	0.142324i	−0.0919847	+	0.0162194i
$78$	12.7994	+	2.75919i	1.44925	+	0.312417i
$79$	3.81056	+	3.19744i	0.428721	+	0.359740i	0.831469	−	0.555571i	$-0.187500\pi$
$79$	3.81056	+	3.19744i	0.428721	+	0.359740i	−0.402748	+	0.915311i	$0.631945\pi$
$80$	−1.68022	+	2.05198i	−0.187854	+	0.229419i
$81$	5.94465	+	6.75730i	0.660517	+	0.750812i
$82$			4.55033i			0.502500i
$83$	−2.76861	+	3.29950i	−0.303895	+	0.362168i	−0.896281	−	0.443486i	$-0.853741\pi$
$83$	−2.76861	+	3.29950i	−0.303895	+	0.362168i	0.592386	+	0.805654i	$0.298186\pi$
$84$	−3.97863	+	18.4562i	−0.434104	+	2.01373i
$85$	4.05036	−	7.21426i	0.439323	−	0.782496i
$86$	6.04289	+	2.19943i	0.651622	+	0.237171i
$87$	−3.21128	−	4.13476i	−0.344285	−	0.443293i
$88$	−0.463726	−	0.0817674i	−0.0494333	−	0.00871643i
$89$	1.93222	−	3.34670i	0.204814	−	0.354749i	−0.745259	−	0.666775i	$-0.767674\pi$
$89$	1.93222	−	3.34670i	0.204814	−	0.354749i	0.950074	+	0.312026i	$0.101008\pi$
$90$	−8.27080	+	12.4288i	−0.871818	+	1.31011i
$91$	−6.26937	−	10.8589i	−0.657209	−	1.13832i
$92$	9.03550	+	24.8248i	0.942016	+	2.58817i
$93$	0.222950	−	5.89697i	0.0231188	−	0.611487i
$94$	9.36730	−	7.86010i	0.966163	−	0.810707i
$95$	0.109294	+	9.09505i	0.0112133	+	0.933132i
$96$	6.34494	−	10.0892i	0.647578	−	1.02972i
$97$	6.14411	+	16.8808i	0.623840	+	1.71399i	0.697388	+	0.716694i	$0.254346\pi$
$97$	6.14411	+	16.8808i	0.623840	+	1.71399i	−0.0735479	+	0.997292i	$0.523432\pi$
$98$	12.7715	−	7.37364i	1.29012	−	0.744851i
$99$	0.664198	+	0.0502953i	0.0667544	+	0.00505487i
$100$	−13.9916	−	4.71495i	−1.39916	−	0.471495i
$101$	−3.19612	+	18.1261i	−0.318026	+	1.80362i	0.236699	+	0.971583i	$0.423935\pi$
$101$	−3.19612	+	18.1261i	−0.318026	+	1.80362i	−0.554725	+	0.832034i	$0.687177\pi$
$102$	−5.38094	+	13.2085i	−0.532792	+	1.30784i
$103$	2.27973	−	6.26352i	0.224629	−	0.617163i	−0.775266	−	0.631634i	$-0.782384\pi$
$103$	2.27973	−	6.26352i	0.224629	−	0.617163i	0.999895	+	0.0144715i	$0.00460660\pi$
$104$	−1.25091	−	7.09424i	−0.122661	−	0.695647i
$105$	14.1388	−	2.11894i	1.37981	−	0.206788i
$106$	−1.69674	−	1.42373i	−0.164801	−	0.138285i
$107$		−	4.74187i		−	0.458414i	−0.973378	−	0.229207i	$-0.926387\pi$
$107$		−	4.74187i		−	0.458414i	0.973378	−	0.229207i	$-0.0736132\pi$
$108$	6.84533	−	13.7323i	0.658693	−	1.32139i
$109$	−1.39975			−0.134072			−0.0670360	−	0.997751i	$-0.521354\pi$
$109$	−1.39975			−0.134072			−0.0670360	+	0.997751i	$0.521354\pi$
$110$	0.204930	+	1.08576i	0.0195393	+	0.103523i
$111$	9.49361	−	3.05443i	0.901094	−	0.289914i
$112$	−4.31173	+	0.760275i	−0.407421	+	0.0718392i
$113$	−3.40346	+	9.35092i	−0.320170	+	0.879660i	0.670319	+	0.742073i	$0.266157\pi$
$113$	−3.40346	+	9.35092i	−0.320170	+	0.879660i	−0.990490	+	0.137588i	$0.956065\pi$
$114$	−2.13745	−	15.5335i	−0.200190	−	1.45485i
$115$	15.1689	−	13.0420i	1.41451	−	1.21617i
$116$	−4.46278	+	7.72977i	−0.414359	+	0.717691i
$117$	2.75228	+	9.81151i	0.254448	+	0.907074i
$118$	18.6100	−	10.7445i	1.71319	−	0.989111i
$119$	12.8346	−	4.67141i	1.17655	−	0.428227i
$120$	8.04945	+	1.63427i	0.734811	+	0.149188i
$121$	−8.38872	+	7.03898i	−0.762611	+	0.639907i
$122$	6.34984	+	7.56744i	0.574887	+	0.685124i
$123$	−3.13163	+	1.65356i	−0.282370	+	0.149096i
$124$	−9.45403	+	3.44099i	−0.848997	+	0.309010i
$125$	0.402951	+	11.1731i	0.0360410	+	0.999350i
$126$	−23.7299	+	6.65660i	−2.11403	+	0.593017i
$127$	−3.93543	−	2.27212i	−0.349213	−	0.201618i	0.315126	−	0.949050i	$-0.397953\pi$
$127$	−3.93543	−	2.27212i	−0.349213	−	0.201618i	−0.664338	+	0.747432i	$0.731287\pi$
$128$	−14.8118	−	2.61172i	−1.30919	−	0.230845i
$129$	0.682245	+	4.95810i	0.0600683	+	0.436536i
$130$	−14.5363	+	8.62708i	−1.27492	+	0.756645i
$131$	−2.61615	−	14.8369i	−0.228574	−	1.29631i	−0.855734	−	0.517417i	$-0.826894\pi$
$131$	−2.61615	−	14.8369i	−0.228574	−	1.29631i	0.627160	−	0.778891i	$-0.284217\pi$
$132$	−0.347810	−	1.08104i	−0.0302729	−	0.0940927i
$133$	−9.65184	+	11.5026i	−0.836921	+	0.997404i
$134$	−33.8897			−2.92762
$135$	−11.5593	−	1.17559i	−0.994868	−	0.101179i
$136$	7.84687			0.672864
$137$	6.87941	−	8.19856i	0.587748	−	0.700451i	−0.387424	−	0.921902i	$-0.626635\pi$
$137$	6.87941	−	8.19856i	0.587748	−	0.700451i	0.975171	+	0.221451i	$0.0710794\pi$
$138$	−23.1492	+	25.5612i	−1.97059	+	2.17592i
$139$	3.81927	+	21.6602i	0.323947	+	1.83719i	0.516977	+	0.855999i	$0.327057\pi$
$139$	3.81927	+	21.6602i	0.323947	+	1.83719i	−0.193031	+	0.981193i	$0.561832\pi$
$140$	−12.4398	−	20.9607i	−1.05136	−	1.77150i
$141$	8.81349	+	3.59047i	0.742230	+	0.302372i
$142$	−5.91310	−	1.04264i	−0.496216	−	0.0874963i
$143$	0.653147	+	0.377095i	0.0546189	+	0.0315343i
$144$	3.54804	+	0.268669i	0.295670	+	0.0223891i
$145$	6.66971	+	1.09358i	0.553889	+	0.0908172i
$146$	2.43158	−	0.885023i	0.201239	−	0.0732451i
$147$	9.71577	+	6.11011i	0.801343	+	0.503953i
$148$	−10.9290	−	13.0247i	−0.898358	−	1.07062i
$149$	−4.40797	+	3.69872i	−0.361115	+	0.303011i	−0.805235	−	0.592956i	$-0.797961\pi$
$149$	−4.40797	+	3.69872i	−0.361115	+	0.303011i	0.444120	+	0.895967i	$0.353516\pi$
$150$	−3.08539	−	19.0250i	−0.251921	−	1.55338i
$151$	−2.91632	+	1.06145i	−0.237327	+	0.0863800i	−0.457946	−	0.888980i	$-0.651415\pi$
$151$	−2.91632	+	1.06145i	−0.237327	+	0.0863800i	0.220619	+	0.975360i	$0.429192\pi$
$152$	−7.47092	+	4.31334i	−0.605971	+	0.349858i
$153$	−11.0458	+	1.09660i	−0.892998	+	0.0886552i
$154$	−0.912033	+	1.57969i	−0.0734937	+	0.127295i
$155$	4.96678	+	5.77676i	0.398941	+	0.464001i
$156$	13.7209	−	10.6564i	1.09855	−	0.853196i
$157$	−3.64985	+	10.0279i	−0.291290	+	0.800312i	0.704589	+	0.709616i	$0.251131\pi$
$157$	−3.64985	+	10.0279i	−0.291290	+	0.800312i	−0.995879	+	0.0906962i	$0.971091\pi$
$158$	10.9023	−	1.92237i	0.867339	−	0.152935i
$159$	0.363260	−	1.68510i	0.0288084	−	0.133637i
$160$	2.85375	+	15.1197i	0.225609	+	1.19532i
$161$	33.0247			2.60271
$162$	20.0242	−	0.468146i	1.57325	−	0.0367811i
$163$		−	13.7464i		−	1.07670i	−0.842722	−	0.538349i	$-0.819048\pi$
$163$		−	13.7464i		−	1.07670i	0.842722	−	0.538349i	$-0.180952\pi$
$164$	4.62508	+	3.88090i	0.361158	+	0.303047i
$165$	−0.672771	+	0.535593i	−0.0523752	+	0.0416959i
$166$	1.66455	+	9.44012i	0.129194	+	0.732695i
$167$	2.73339	−	7.50992i	0.211516	−	0.581135i	−0.787882	−	0.615826i	$-0.788822\pi$
$167$	2.73339	−	7.50992i	0.211516	−	0.581135i	0.999398	+	0.0346908i	$0.0110446\pi$
$168$	8.31723	+	10.7091i	0.641688	+	0.826222i
$169$	0.253898	−	1.43993i	0.0195306	−	0.110764i
$170$	−6.50502	−	17.2255i	−0.498912	−	1.32114i
$171$	9.91376	−	7.11580i	0.758125	−	0.544159i
$172$	7.38944	−	4.26630i	0.563440	−	0.325302i
$173$	−1.19945	−	3.29546i	−0.0911925	−	0.250549i	0.885708	−	0.464242i	$-0.153673\pi$
$173$	−1.19945	−	3.29546i	−0.0911925	−	0.250549i	−0.976901	+	0.213693i	$0.931451\pi$
$174$	−11.6430	−	0.440192i	−0.882652	−	0.0333709i
$175$	−11.5208	+	14.4199i	−0.870887	+	1.09004i
$176$	0.201735	−	0.169276i	0.0152063	−	0.0127596i
$177$	14.1573	+	8.90333i	1.06413	+	0.669215i
$178$	−2.94150	−	8.08170i	−0.220475	−	0.605749i
$179$	−4.97626	−	8.61914i	−0.371943	−	0.644225i	0.617921	−	0.786240i	$-0.287975\pi$
$179$	−4.97626	−	8.61914i	−0.371943	−	0.644225i	−0.989864	+	0.142015i	$0.954642\pi$
$180$	5.57897	+	19.0070i	0.415832	+	1.41670i
$181$	5.74961	−	9.95862i	0.427365	−	0.740218i	−0.569273	−	0.822149i	$-0.692775\pi$
$181$	5.74961	−	9.95862i	0.427365	−	0.740218i	0.996638	+	0.0819305i	$0.0261086\pi$
$182$	−27.4813	−	4.84569i	−2.03705	−	0.359186i
$183$	−2.90059	+	7.12004i	−0.214418	+	0.526329i
$184$	17.8289	+	6.48920i	1.31437	+	0.478390i
$185$	−6.30302	+	11.2266i	−0.463407	+	0.825393i
$186$	−9.73448	−	8.81591i	−0.713767	−	0.646414i
$187$	−0.528069	+	0.629328i	−0.0386162	+	0.0460210i
$188$		−	16.2249i		−	1.18332i
$189$	−13.2045	−	13.9124i	−0.960484	−	1.01198i
$190$	15.6620	+	12.8245i	1.13624	+	0.930384i
$191$	2.41135	+	2.02336i	0.174479	+	0.146405i	0.725845	−	0.687858i	$-0.241449\pi$
$191$	2.41135	+	2.02336i	0.174479	+	0.146405i	−0.551366	+	0.834263i	$0.685893\pi$
$192$	−6.86547	−	21.3389i	−0.495473	−	1.54000i
$193$	−1.80412	+	0.318115i	−0.129863	+	0.0228984i	−0.238202	−	0.971216i	$-0.576558\pi$
$193$	−1.80412	+	0.318115i	−0.129863	+	0.0228984i	0.108339	+	0.994114i	$0.465447\pi$
$194$	37.5685	+	13.6738i	2.69726	+	0.981723i
$195$	−11.2197	−	6.86918i	−0.803461	−	0.491912i
$196$	3.39785	−	19.2702i	0.242704	−	1.37644i
$197$	4.63670	+	2.67700i	0.330351	+	0.190728i	0.655997	−	0.754764i	$-0.272248\pi$
$197$	4.63670	+	2.67700i	0.330351	+	0.190728i	−0.325646	+	0.945492i	$0.605582\pi$
$198$	1.03590	−	1.06041i	0.0736185	−	0.0753598i
$199$	−6.61483	−	11.4572i	−0.468913	−	0.812181i	0.530456	−	0.847713i	$-0.322021\pi$
$199$	−6.61483	−	11.4572i	−0.468913	−	0.812181i	−0.999369	+	0.0355320i	$0.988687\pi$
$200$	−9.05311	+	5.52105i	−0.640151	+	0.390397i
$201$	−12.3153	−	23.3236i	−0.868651	−	1.64512i
$202$	26.3301	+	31.3790i	1.85258	+	2.20782i
$203$	7.17202	+	8.54728i	0.503377	+	0.599902i
$204$	8.83619	+	16.7347i	0.618657	+	1.17166i
$205$	1.51195	−	4.31466i	0.105599	−	0.301349i
$206$	−7.41709	−	12.8468i	−0.516773	−	0.895078i
$207$	−26.0040	−	6.64302i	−1.80741	−	0.461722i
$208$	3.48901	+	2.01438i	0.241919	+	0.139672i
$209$	0.156834	−	0.889448i	0.0108484	−	0.0615244i
$210$	16.6136	−	27.1358i	1.14645	−	1.87255i
$211$	10.1203	+	3.68350i	0.696712	+	0.253582i	0.666006	−	0.745946i	$-0.268002\pi$
$211$	10.1203	+	3.68350i	0.696712	+	0.253582i	0.0307055	+	0.999528i	$0.490225\pi$
$212$	−2.89423	+	0.510331i	−0.198777	+	0.0350497i
$213$	−1.43121	−	4.44840i	−0.0980648	−	0.304800i
$214$	−8.08415	−	6.78341i	−0.552621	−	0.463704i
$215$	−4.99911	−	4.09340i	−0.340936	−	0.279168i
$216$	−4.39492	−	10.1055i	−0.299037	−	0.687591i
$217$			12.5768i			0.853768i
$218$	−2.00240	+	2.38636i	−0.135619	+	0.161625i
$219$	1.49271	+	1.35185i	0.100868	+	0.0913499i
$220$	1.27837	+	0.717728i	0.0861880	+	0.0483892i
$221$	−11.8101	−	4.29852i	−0.794433	−	0.289150i
$222$	8.37361	−	20.5546i	0.562000	−	1.37954i
$223$	13.2593	+	2.33798i	0.887912	+	0.156563i	0.598958	−	0.800780i	$-0.295582\pi$
$223$	13.2593	+	2.33798i	0.887912	+	0.156563i	0.288953	+	0.957343i	$0.406693\pi$
$224$	−12.7005	+	21.9979i	−0.848589	+	1.46980i
$225$	11.9722	−	9.03697i	0.798146	−	0.602464i
$226$	11.0731	+	19.1792i	0.736572	+	1.27578i
$227$	−6.37123	−	17.5048i	−0.422873	−	1.16183i	−0.950055	−	0.312082i	$-0.898974\pi$
$227$	−6.37123	−	17.5048i	−0.422873	−	1.16183i	0.527182	−	0.849752i	$-0.323249\pi$
$228$	−17.6117	−	11.0757i	−1.16636	−	0.733508i
$229$	8.12667	−	6.81909i	0.537026	−	0.450618i	−0.333494	−	0.942752i	$-0.608228\pi$
$229$	8.12667	−	6.81909i	0.537026	−	0.450618i	0.870519	+	0.492134i	$0.163783\pi$
$230$	−0.534962	−	44.5176i	−0.0352743	−	2.93541i
$231$	−1.41860	−	0.0536338i	−0.0933370	−	0.00352884i
$232$	2.19243	+	6.02366i	0.143940	+	0.395472i
$233$	10.1012	−	5.83193i	0.661751	−	0.382062i	−0.131193	−	0.991357i	$-0.541881\pi$
$233$	10.1012	−	5.83193i	0.661751	−	0.382062i	0.792944	+	0.609295i	$0.208547\pi$
$234$	20.6643	+	9.34349i	1.35087	+	0.610803i
$235$	−11.4938	+	4.34052i	−0.749776	+	0.283144i
$236$	4.95117	−	28.0795i	0.322294	−	1.82782i
$237$	5.28482	+	6.80460i	0.343286	+	0.442007i
$238$	10.3963	−	28.5636i	0.673892	−	1.85150i
$239$	1.26563	+	7.17776i	0.0818670	+	0.464291i	0.997989	+	0.0633907i	$0.0201914\pi$
$239$	1.26563	+	7.17776i	0.0818670	+	0.464291i	−0.916122	+	0.400900i	$0.868697\pi$
$240$	−3.59384	+	2.86105i	−0.231981	+	0.184680i
$241$	5.47186	+	4.59144i	0.352474	+	0.295761i	0.801783	−	0.597616i	$-0.203885\pi$
$241$	5.47186	+	4.59144i	0.352474	+	0.295761i	−0.449309	+	0.893377i	$0.648330\pi$
$242$			24.3710i			1.56663i
$243$	7.59883	+	13.6109i	0.487465	+	0.873143i
$244$	13.1074			0.839117
$245$	−14.5601	+	2.74813i	−0.930212	+	0.175572i
$246$	−1.66085	+	7.70442i	−0.105892	+	0.491216i
$247$	13.6071	−	2.39930i	0.865799	−	0.152664i
$248$	−2.47128	+	6.78978i	−0.156926	+	0.431152i
$249$	−5.89200	+	4.57604i	−0.373390	+	0.289995i
$250$	19.6248	+	15.2965i	1.24118	+	0.967436i
$251$	−10.1531	+	17.5856i	−0.640855	+	1.10999i	0.344387	+	0.938828i	$0.388087\pi$
$251$	−10.1531	+	17.5856i	−0.640855	+	1.10999i	−0.985242	+	0.171166i	$0.945247\pi$
$252$	−13.4729	+	29.7970i	−0.848711	+	1.87703i
$253$	−1.72027	+	0.993197i	−0.108152	+	0.0624417i
$254$	−9.50338	+	3.45895i	−0.596295	+	0.217034i
$255$	9.49107	−	10.7365i	0.594354	−	0.672346i
$256$	−5.81313	+	4.87780i	−0.363321	+	0.304862i
$257$	−18.8799	−	22.5001i	−1.17769	−	1.40352i	−0.896022	−	0.444009i	$-0.853556\pi$
$257$	−18.8799	−	22.5001i	−1.17769	−	1.40352i	−0.281671	−	0.959511i	$-0.590889\pi$
$258$	9.42877	+	5.92962i	0.587010	+	0.369162i
$259$	−19.9727	+	7.26947i	−1.24104	+	0.451703i
$260$	−3.62898	+	22.1330i	−0.225060	+	1.37263i
$261$	−3.92802	−	8.17291i	−0.243138	−	0.505890i
$262$	−29.0371	−	16.7646i	−1.79392	−	1.03572i
$263$	9.00868	+	1.58847i	0.555499	+	0.0979494i	0.444348	−	0.895854i	$-0.353435\pi$
$263$	9.00868	+	1.58847i	0.555499	+	0.0979494i	0.111151	+	0.993804i	$0.464546\pi$
$264$	−0.755315	−	0.307703i	−0.0464864	−	0.0189378i
$265$	1.13579	+	1.91377i	0.0697712	+	0.117562i
$266$	5.80289	+	32.9098i	0.355798	+	2.01783i
$267$	4.49308	−	4.96123i	0.274972	−	0.303622i
$268$	−28.9039	+	34.4464i	−1.76559	+	2.10415i
$269$	−9.26706			−0.565023			−0.282511	−	0.959264i	$-0.591167\pi$
$269$	−9.26706			−0.565023			−0.282511	+	0.959264i	$0.591167\pi$
$270$	−18.5402	+	18.0251i	−1.12832	+	1.09697i
$271$	−9.66838			−0.587312			−0.293656	−	0.955911i	$-0.594872\pi$
$271$	−9.66838			−0.587312			−0.293656	+	0.955911i	$0.594872\pi$
$272$	−2.82086	+	3.36177i	−0.171040	+	0.203837i
$273$	−6.65158	−	20.6741i	−0.402572	−	1.25125i
$274$	−4.13604	−	23.4567i	−0.249868	−	1.41707i
$275$	0.166450	−	1.09762i	0.0100373	−	0.0661888i
$276$	6.23754	+	45.3302i	0.375456	+	2.72856i
$277$	−29.3876	−	5.18183i	−1.76573	−	0.311346i	−0.805926	−	0.592017i	$-0.798332\pi$
$277$	−29.3876	−	5.18183i	−1.76573	−	0.311346i	−0.959804	+	0.280671i	$0.909443\pi$
$278$	42.3909	+	24.4744i	2.54243	+	1.46788i
$279$	2.52986	−	9.90311i	0.151459	−	0.592884i
$280$	−17.2746	−	2.83239i	−1.03235	−	0.169268i
$281$	−18.8316	+	6.85412i	−1.12340	+	0.408883i	−0.835891	−	0.548896i	$-0.815048\pi$
$281$	−18.8316	+	6.85412i	−1.12340	+	0.408883i	−0.287506	+	0.957779i	$0.592826\pi$
$282$	18.7292	−	9.88934i	1.11531	−	0.588902i
$283$	−10.8947	−	12.9838i	−0.647623	−	0.771807i	0.337931	−	0.941171i	$-0.390273\pi$
$283$	−10.8947	−	12.9838i	−0.647623	−	0.771807i	−0.985554	+	0.169364i	$0.945829\pi$
$284$	−6.10295	+	5.12098i	−0.362143	+	0.303874i
$285$	−3.13461	+	15.4392i	−0.185678	+	0.914541i
$286$	1.57724	−	0.574068i	0.0932641	−	0.0339453i
$287$	6.53633	−	3.77375i	0.385827	−	0.222758i
$288$	14.4255	−	14.7667i	0.850031	−	0.870136i
$289$	−1.65490	+	2.86637i	−0.0973471	+	0.168610i
$290$	11.4056	−	9.80642i	0.669763	−	0.575853i
$291$	4.24150	+	30.8244i	0.248641	+	1.80696i
$292$	1.17429	−	3.22635i	0.0687203	−	0.188808i
$293$	7.14473	−	1.25981i	0.417399	−	0.0735988i	0.0389955	−	0.999239i	$-0.487584\pi$
$293$	7.14473	−	1.25981i	0.417399	−	0.0735988i	0.378404	+	0.925641i	$0.376473\pi$
$294$	24.3155	−	7.82317i	1.41811	−	0.456257i
$295$	−21.2163	+	4.00444i	−1.23526	+	0.233147i
$296$	−12.2110			−0.709750
$297$	1.10623	+	0.327588i	0.0641902	+	0.0190086i
$298$			12.8061i			0.741835i
$299$	−23.2790	−	19.5334i	−1.34626	−	1.12964i
$300$	−21.9690	−	13.0900i	−1.26838	−	0.755752i
$301$	−1.85221	−	10.5044i	−0.106759	−	0.605463i
$302$	−2.36229	+	6.49033i	−0.135934	+	0.373476i
$303$	−12.0275	+	29.5238i	−0.690962	+	1.69610i
$304$	0.837781	−	4.75129i	0.0480500	−	0.272505i
$305$	−3.50652	−	9.28539i	−0.200783	−	0.531680i
$306$	−13.9318	+	20.4001i	−0.796430	+	1.16619i
$307$	−19.2340	+	11.1047i	−1.09774	+	0.633781i	−0.935627	−	0.352991i	$-0.885165\pi$
$307$	−19.2340	+	11.1047i	−1.09774	+	0.633781i	−0.162114	+	0.986772i	$0.551831\pi$
$308$	0.827778	+	2.27430i	0.0471671	+	0.129590i
$309$	6.14611	−	9.77302i	0.349640	−	0.555968i
$310$	16.9536	−	0.203729i	0.962902	−	0.0115710i
$311$	11.2455	−	9.43607i	0.637672	−	0.535070i	−0.265630	−	0.964075i	$-0.585580\pi$
$311$	11.2455	−	9.43607i	0.637672	−	0.535070i	0.903302	+	0.429005i	$0.141136\pi$
$312$	0.471393	−	12.4682i	0.0266874	−	0.705875i
$313$	−4.53554	−	12.4613i	−0.256364	−	0.704355i	−0.999384	−	0.0350857i	$-0.988830\pi$
$313$	−4.53554	−	12.4613i	−0.256364	−	0.704355i	0.743020	−	0.669269i	$-0.233393\pi$
$314$	11.8747	+	20.5677i	0.670131	+	1.16070i
$315$	24.7127	+	1.57293i	1.39240	+	0.0886243i
$316$	7.34443	−	12.7209i	0.413156	−	0.715608i
$317$	22.8526	+	4.02954i	1.28353	+	0.226321i	0.773479	−	0.633822i	$-0.218515\pi$
$317$	22.8526	+	4.02954i	1.28353	+	0.226321i	0.510053	+	0.860143i	$0.329626\pi$
$318$	−2.35318	−	3.02990i	−0.131960	−	0.169908i
$319$	−0.630647	−	0.229537i	−0.0353095	−	0.0128516i
$320$	25.2340	+	14.1674i	1.41063	+	0.791979i
$321$	1.73077	−	8.02873i	0.0966019	−	0.448120i
$322$	47.2430	−	56.3020i	2.63275	−	3.13759i
$323$			15.0507i			0.837442i
$324$	16.6025	−	20.7524i	0.922359	−	1.15291i
$325$	16.6500	−	3.35026i	0.923575	−	0.185839i
$326$	−23.4354	−	19.6646i	−1.29797	−	1.08912i
$327$	−2.37000	−	0.510905i	−0.131061	−	0.0282531i
$328$	4.27027	−	0.752964i	0.235786	−	0.0415755i
$329$	−19.0593	−	6.93701i	−1.05077	−	0.382450i
$330$	−0.0493192	+	1.91316i	−0.00271493	+	0.105316i
$331$	−3.43030	+	19.4542i	−0.188547	+	1.06930i	0.732767	+	0.680480i	$0.238229\pi$
$331$	−3.43030	+	19.4542i	−0.188547	+	1.06930i	−0.921313	+	0.388821i	$0.872883\pi$
$332$	11.0148	+	6.35942i	0.604518	+	0.349019i
$333$	17.1890	−	1.70649i	0.941953	−	0.0935153i
$334$	−8.89305	−	15.4032i	−0.486606	−	0.842826i
$335$	32.1345	+	11.2606i	1.75569	+	0.615232i
$336$	−7.57794	−	0.286503i	−0.413410	−	0.0156300i
$337$	6.07773	+	7.24315i	0.331075	+	0.394560i	0.905743	−	0.423827i	$-0.139313\pi$
$337$	6.07773	+	7.24315i	0.331075	+	0.394560i	−0.574668	+	0.818386i	$0.694869\pi$
$338$	−2.09165	−	2.49273i	−0.113771	−	0.135586i
$339$	−9.17563	+	14.5903i	−0.498352	+	0.792437i
$340$	−23.0565	−	8.07946i	−1.25041	−	0.438170i
$341$	−0.378239	−	0.655129i	−0.0204828	−	0.0354772i
$342$	2.05065	−	27.0808i	0.110886	−	1.46436i
$343$	1.19417	+	0.689456i	0.0644792	+	0.0372271i
$344$	1.06412	−	6.03491i	0.0573734	−	0.325381i
$345$	30.4436	−	16.5455i	1.63903	−	0.890782i
$346$	−7.33411	−	2.66940i	−0.394284	−	0.143508i
$347$	−0.583262	+	0.102845i	−0.0313112	+	0.00552100i	−0.189282	−	0.981923i	$-0.560616\pi$
$347$	−0.583262	+	0.102845i	−0.0313112	+	0.00552100i	0.157971	+	0.987444i	$0.449505\pi$
$348$	−10.3775	+	11.4588i	−0.556294	+	0.614256i
$349$	−12.1040	−	10.1564i	−0.647910	−	0.543661i	0.258526	−	0.966004i	$-0.416763\pi$
$349$	−12.1040	−	10.1564i	−0.647910	−	0.543661i	−0.906436	+	0.422343i	$0.861208\pi$
$350$	8.10286	+	40.2693i	0.433116	+	2.15248i
$351$	1.07888	+	17.6170i	0.0575862	+	0.940325i
$352$		−	1.52784i		−	0.0814342i
$353$	−6.76965	+	8.06775i	−0.360312	+	0.429403i	−0.915498	−	0.402323i	$-0.868203\pi$
$353$	−6.76965	+	8.06775i	−0.360312	+	0.429403i	0.555186	+	0.831726i	$0.312647\pi$
$354$	35.4314	−	11.3995i	1.88316	−	0.605878i
$355$	5.26041	+	2.95339i	0.279193	+	0.156750i
$356$	−10.7232	−	3.90293i	−0.568329	−	0.206855i
$357$	23.4360	−	3.22485i	1.24037	−	0.170677i
$358$	−21.8130	−	3.84622i	−1.15285	−	0.203279i
$359$	13.4867	−	23.3596i	0.711798	−	1.23287i	−0.252383	−	0.967627i	$-0.581214\pi$
$359$	13.4867	−	23.3596i	0.711798	−	1.23287i	0.964181	−	0.265244i	$-0.0854523\pi$
$360$	13.0325	+	5.70509i	0.686871	+	0.300685i
$361$	1.22681	+	2.12491i	0.0645692	+	0.111837i
$362$	−8.75288	−	24.0483i	−0.460041	−	1.26395i
$363$	−16.7726	+	8.85623i	−0.880334	+	0.464832i
$364$	−28.3636	+	23.7999i	−1.48666	+	1.24745i
$365$	−2.59971	+	0.0312404i	−0.136075	+	0.00163520i
$366$	7.98918	+	15.1305i	0.417601	+	0.790886i
$367$	−0.0590232	−	0.162165i	−0.00308099	−	0.00846495i	0.938143	−	0.346249i	$-0.112545\pi$
$367$	−0.0590232	−	0.162165i	−0.00308099	−	0.00846495i	−0.941224	+	0.337784i	$0.890323\pi$
$368$	−9.18940	+	5.30550i	−0.479030	+	0.276568i
$369$	−5.90589	+	1.65669i	−0.307448	+	0.0862440i
$370$	10.1229	+	26.8057i	0.526262	+	1.39356i
$371$	−0.637956	+	3.61803i	−0.0331210	+	0.187839i
$372$	−17.2631	+	2.37544i	−0.895050	+	0.123161i
$373$	−5.28367	+	14.5168i	−0.273578	+	0.751650i	0.724476	+	0.689300i	$0.242082\pi$
$373$	−5.28367	+	14.5168i	−0.273578	+	0.751650i	−0.998054	+	0.0623502i	$0.980140\pi$
$374$	0.317486	+	1.80055i	0.0164168	+	0.0931043i
$375$	−3.39587	+	19.0648i	−0.175362	+	0.984504i
$376$	−8.92638	−	7.49012i	−0.460343	−	0.386273i
$377$		−	10.2670i		−	0.528779i
$378$	−42.6080	+	2.60935i	−2.19152	+	0.134210i
$379$	28.5283			1.46540			0.732699	−	0.680553i	$-0.238260\pi$
$379$	28.5283			1.46540			0.732699	+	0.680553i	$0.238260\pi$
$380$	26.3930	−	4.98151i	1.35393	−	0.255546i
$381$	−5.83397	−	5.28347i	−0.298884	−	0.270680i
$382$	6.89905	−	1.21649i	0.352986	−	0.0622409i
$383$	0.799095	−	2.19550i	0.0408319	−	0.112185i	−0.917601	−	0.397503i	$-0.869877\pi$
$383$	0.799095	−	2.19550i	0.0408319	−	0.112185i	0.958433	+	0.285318i	$0.0920992\pi$
$384$	−24.1254	−	9.82829i	−1.23114	−	0.501548i
$385$	1.38968	−	1.19483i	0.0708248	−	0.0608942i
$386$	−2.03852	+	3.53082i	−0.103758	+	0.179714i
$387$	−0.654541	+	8.64386i	−0.0332722	+	0.439392i
$388$	45.9400	−	26.5235i	2.33225	−	1.34653i
$389$	22.2311	−	8.09147i	1.12716	−	0.410254i	0.289901	−	0.957057i	$-0.406378\pi$
$389$	22.2311	−	8.09147i	1.12716	−	0.410254i	0.837261	+	0.546803i	$0.184155\pi$
$390$	−27.7611	+	9.30129i	−1.40574	+	0.470989i
$391$	25.3575	−	21.2775i	1.28238	−	1.07605i
$392$	−9.03318	−	10.7653i	−0.456244	−	0.543731i
$393$	0.985873	−	26.0761i	0.0497307	−	1.31537i
$394$	11.1968	−	4.07531i	0.564088	−	0.205311i
$395$	−10.9764	−	1.79972i	−0.552282	−	0.0905536i
$396$	−0.194319	−	1.95732i	−0.00976491	−	0.0983592i
$397$	−7.78766	−	4.49621i	−0.390851	−	0.225658i	0.291678	−	0.956517i	$-0.405787\pi$
$397$	−7.78766	−	4.49621i	−0.390851	−	0.225658i	−0.682529	+	0.730859i	$0.739120\pi$
$398$	−28.9955	−	5.11269i	−1.45341	−	0.256276i
$399$	−20.5405	+	15.9528i	−1.02831	+	0.798641i
$400$	0.889152	−	5.86330i	0.0444576	−	0.293165i
$401$	−0.769462	−	4.36384i	−0.0384251	−	0.217920i	0.959549	−	0.281542i	$-0.0908458\pi$
$401$	−0.769462	−	4.36384i	−0.0384251	−	0.217920i	−0.997974	+	0.0636223i	$0.979735\pi$
$402$	−57.3805	−	12.3696i	−2.86188	−	0.616940i
$403$	7.43889	−	8.86533i	0.370558	−	0.441613i
$404$	54.3509			2.70406
$405$	−19.1427	−	6.20957i	−0.951206	−	0.308556i
$406$	24.8316			1.23237
$407$	0.821760	−	0.979336i	0.0407331	−	0.0485439i
$408$	13.2860	+	2.86408i	0.657754	+	0.141793i
$409$	1.20563	+	6.83747i	0.0596146	+	0.338091i	0.999998	−	0.00202520i	$-0.000644642\pi$
$409$	1.20563	+	6.83747i	0.0596146	+	0.338091i	−0.940383	+	0.340116i	$0.889534\pi$
$410$	−5.19294	−	8.74991i	−0.256461	−	0.432127i
$411$	14.6404	−	11.3705i	0.722156	−	0.560865i
$412$	−19.3837	−	3.41787i	−0.954967	−	0.168387i
$413$	−30.8679	−	17.8216i	−1.51891	−	0.876943i
$414$	−48.5250	+	34.8298i	−2.38487	+	1.71179i
$415$	1.55835	−	9.50428i	0.0764963	−	0.466547i
$416$	21.9639	−	7.99419i	1.07687	−	0.391947i
$417$	−1.43926	+	38.0681i	−0.0704809	+	1.86420i
$418$	−1.29202	−	1.53976i	−0.0631946	−	0.0753124i
$419$	9.05746	−	7.60011i	0.442486	−	0.371290i	−0.394153	−	0.919045i	$-0.628962\pi$
$419$	9.05746	−	7.60011i	0.442486	−	0.371290i	0.836639	+	0.547755i	$0.184517\pi$
$420$	−13.4120	−	40.0302i	−0.654439	−	1.95327i
$421$	−5.46428	+	1.98884i	−0.266313	+	0.0969299i	−0.471725	−	0.881746i	$-0.656369\pi$
$421$	−5.46428	+	1.98884i	−0.266313	+	0.0969299i	0.205413	+	0.978675i	$0.434146\pi$
$422$	20.7573	−	11.9842i	1.01045	−	0.583383i
$423$	13.6121	+	9.29612i	0.661843	+	0.451993i
$424$	−1.05534	+	1.82790i	−0.0512517	+	0.0887705i
$425$	0.444562	+	18.4948i	0.0215644	+	0.897129i
$426$	−9.63124	−	3.92361i	−0.466635	−	0.190099i
$427$	5.60412	−	15.3972i	0.271202	−	0.745122i
$428$	−13.7897	+	2.43149i	−0.666549	+	0.117531i
$429$	0.968242	+	0.876877i	0.0467472	+	0.0423360i
$430$	−14.1300	+	2.66695i	−0.681410	+	0.128612i
$431$	−14.0059			−0.674641			−0.337321	−	0.941390i	$-0.609521\pi$
$431$	−14.0059			−0.674641			−0.337321	+	0.941390i	$0.609521\pi$
$432$	5.90933	+	1.74992i	0.284313	+	0.0841932i
$433$			8.84386i			0.425009i	0.977160	+	0.212504i	$0.0681620\pi$
$433$			8.84386i			0.425009i	−0.977160	+	0.212504i	$0.931838\pi$
$434$	21.4415	+	17.9915i	1.02922	+	0.863621i
$435$	10.8937	+	4.28603i	0.522313	+	0.205499i
$436$	0.717752	+	4.07058i	0.0343741	+	0.194945i
$437$	−12.4466	+	34.1967i	−0.595401	+	1.63585i
$438$	4.44008	−	0.610964i	0.212155	−	0.0291930i
$439$	−4.21297	+	23.8929i	−0.201074	+	1.14035i	0.702426	+	0.711757i	$0.252100\pi$
$439$	−4.21297	+	23.8929i	−0.201074	+	1.14035i	−0.903499	+	0.428589i	$0.859011\pi$
$440$	0.985021	−	0.371982i	0.0469590	−	0.0177336i
$441$	14.2202	+	13.8916i	0.677150	+	0.661504i
$442$	−24.2231	+	13.9852i	−1.15217	+	0.665208i
$443$	−7.98968	−	21.9515i	−0.379601	−	1.04295i	−0.971522	−	0.236949i	$-0.923853\pi$
$443$	−7.98968	−	21.9515i	−0.379601	−	1.04295i	0.591921	−	0.805996i	$-0.298370\pi$
$444$	−13.7505	−	26.0418i	−0.652572	−	1.23589i
$445$	0.103832	+	8.64051i	0.00492209	+	0.409599i
$446$	22.9539	−	19.2606i	1.08690	−	0.912015i
$447$	−8.81340	+	4.65362i	−0.416859	+	0.220109i
$448$	16.3397	+	44.8928i	0.771976	+	2.12099i
$449$	4.72074	+	8.17656i	0.222785	+	0.385876i	0.955653	−	0.294496i	$-0.0951518\pi$
$449$	4.72074	+	8.17656i	0.222785	+	0.385876i	−0.732867	+	0.680372i	$0.761818\pi$
$450$	1.72000	−	33.3384i	0.0810818	−	1.57159i
$451$	−0.226986	+	0.393152i	−0.0106884	+	0.0185128i
$452$	28.9383	+	5.10260i	1.36114	+	0.240006i
$453$	−5.32522	+	0.732761i	−0.250201	+	0.0344281i
$454$	−38.9573	−	14.1793i	−1.82835	−	0.665467i
$455$	24.4479	+	13.7260i	1.14613	+	0.643483i
$456$	−14.2238	+	4.57629i	−0.666089	+	0.214305i
$457$	12.8375	−	15.2991i	0.600512	−	0.715662i	−0.377078	−	0.926182i	$-0.623071\pi$
$457$	12.8375	−	15.2991i	0.600512	−	0.715662i	0.977590	+	0.210519i	$0.0675154\pi$
$458$		−	23.6097i		−	1.10321i
$459$	−19.1025	−	2.17495i	−0.891628	−	0.101518i
$460$	−45.7052	−	37.4246i	−2.13101	−	1.74493i
$461$	2.33070	+	1.95569i	0.108552	+	0.0910856i	0.695448	−	0.718576i	$-0.255206\pi$
$461$	2.33070	+	1.95569i	0.108552	+	0.0910856i	−0.586896	+	0.809662i	$0.699650\pi$
$462$	−2.12079	+	2.34177i	−0.0986683	+	0.108949i
$463$	25.2328	−	4.44923i	1.17267	−	0.206773i	0.446818	−	0.894625i	$-0.352557\pi$
$463$	25.2328	−	4.44923i	1.17267	−	0.206773i	0.725851	+	0.687852i	$0.241446\pi$
$464$	−3.36882	−	1.22615i	−0.156393	−	0.0569225i
$465$	6.30103	+	11.5938i	0.292203	+	0.537650i
$466$	4.50758	−	25.5638i	0.208810	−	1.18422i
$467$	−0.648927	−	0.374658i	−0.0300288	−	0.0173371i	0.484910	−	0.874564i	$-0.338852\pi$
$467$	−0.648927	−	0.374658i	−0.0300288	−	0.0173371i	−0.514939	+	0.857227i	$0.672186\pi$
$468$	27.1212	−	13.0349i	1.25368	−	0.602537i
$469$	28.1059	+	48.6809i	1.29781	+	2.24787i
$470$	−9.04243	+	25.8045i	−0.417096	+	1.19027i
$471$	−9.83991	+	15.6466i	−0.453399	+	0.720957i
$472$	−13.1627	−	15.6867i	−0.605861	−	0.722037i
$473$	0.412395	+	0.491473i	0.0189619	+	0.0225980i
$474$	19.1609	+	0.724427i	0.880090	+	0.0332740i
$475$	−10.5896	−	17.3643i	−0.485886	−	0.796729i
$476$	−20.1660	−	34.9285i	−0.924306	−	1.60095i
$477$	1.23011	−	2.72055i	0.0563230	−	0.124565i
$478$	14.0475	+	8.11033i	0.642518	+	0.370958i
$479$	−1.61152	+	9.13941i	−0.0736324	+	0.417590i	0.925603	+	0.378496i	$0.123558\pi$
$479$	−1.61152	+	9.13941i	−0.0736324	+	0.417590i	−0.999236	+	0.0390946i	$0.987553\pi$
$480$	−0.686795	+	26.6417i	−0.0313478	+	1.21602i
$481$	18.3784	+	6.68920i	0.837984	+	0.305001i
$482$	15.6554	−	2.76047i	0.713083	−	0.125736i
$483$	55.9160	+	12.0539i	2.54426	+	0.548471i
$484$	24.7713	+	20.7856i	1.12597	+	0.944800i
$485$	−31.0794	−	25.4486i	−1.41124	−	1.15556i
$486$	34.0749	+	6.51611i	1.54567	+	0.295577i
$487$		−	17.1548i		−	0.777357i	−0.921373	−	0.388678i	$-0.872932\pi$
$487$		−	17.1548i		−	0.777357i	0.921373	−	0.388678i	$-0.127068\pi$
$488$	6.05095	−	7.21124i	0.273914	−	0.326437i
$489$	5.01737	−	23.2747i	0.226893	−	1.05252i
$490$	−16.1436	+	28.7541i	−0.729295	+	1.29898i
$491$	−32.8524	−	11.9573i	−1.48261	−	0.539626i	−0.531117	−	0.847298i	$-0.678228\pi$
$491$	−32.8524	−	11.9573i	−1.48261	−	0.539626i	−0.951492	+	0.307672i	$0.900450\pi$
$492$	6.41446	+	8.25911i	0.289186	+	0.372349i
$493$	11.0138	+	1.94204i	0.496039	+	0.0874650i
$494$	15.3750	−	26.6303i	0.691754	−	1.19815i
$495$	−1.33460	+	0.661284i	−0.0599856	+	0.0297225i
$496$	−2.02049	−	3.49959i	−0.0907228	−	0.157136i
$497$	3.40624	+	9.35857i	0.152791	+	0.419789i
$498$	−0.627270	+	16.5911i	−0.0281086	+	0.743467i
$499$	−16.9596	+	14.2308i	−0.759218	+	0.637059i	−0.937923	−	0.346843i	$-0.887254\pi$
$499$	−16.9596	+	14.2308i	−0.759218	+	0.637059i	0.178706	+	0.983903i	$0.442809\pi$
$500$	32.2854	−	6.90104i	1.44385	−	0.308624i
$501$	7.36915	−	11.7178i	0.329229	−	0.523512i
$502$	15.4564	+	42.4662i	0.689855	+	1.89536i
$503$	8.40481	−	4.85252i	0.374752	−	0.216363i	−0.300781	−	0.953693i	$-0.597247\pi$
$503$	8.40481	−	4.85252i	0.374752	−	0.216363i	0.675532	+	0.737330i	$0.263914\pi$
$504$	10.1736	+	21.1679i	0.453168	+	0.942892i
$505$	−14.5400	−	38.5025i	−0.647024	−	1.71334i
$506$	−0.767656	+	4.35359i	−0.0341265	+	0.193541i
$507$	0.955459	−	2.34535i	0.0424334	−	0.104161i
$508$	−4.58951	+	12.6096i	−0.203626	+	0.559459i
$509$	−6.56150	−	37.2121i	−0.290834	−	1.64940i	−0.683670	−	0.729791i	$-0.739617\pi$
$509$	−6.56150	−	37.2121i	−0.290834	−	1.64940i	0.392837	−	0.919608i	$-0.371494\pi$
$510$	−4.72676	−	31.5398i	−0.209305	−	1.39660i
$511$	−3.28789	−	2.75887i	−0.145448	−	0.122045i
$512$		−	13.1922i		−	0.583019i
$513$	19.3828	−	8.42967i	0.855771	−	0.372179i
$514$	−65.3676			−2.88324
$515$	2.76433	+	14.6459i	0.121811	+	0.645376i
$516$	14.0687	−	4.52639i	0.619338	−	0.199263i
$517$	1.20143	−	0.211845i	0.0528389	−	0.00931692i
$518$	−16.1783	+	44.4496i	−0.710835	+	1.95300i
$519$	−0.828024	−	6.01752i	−0.0363462	−	0.264140i
$520$	10.5015	+	12.2141i	0.460521	+	0.535623i
$521$	6.94254	−	12.0248i	0.304158	−	0.526818i	−0.672915	−	0.739720i	$-0.734958\pi$
$521$	6.94254	−	12.0248i	0.304158	−	0.526818i	0.977074	+	0.212902i	$0.0682915\pi$
$522$	−19.5527	−	4.99496i	−0.855799	−	0.218623i
$523$	−29.5309	+	17.0497i	−1.29129	+	0.745529i	−0.978884	−	0.204417i	$-0.934470\pi$
$523$	−29.5309	+	17.0497i	−1.29129	+	0.745529i	−0.312411	+	0.949947i	$0.601137\pi$
$524$	−41.8053	+	15.2159i	−1.82627	+	0.664709i
$525$	−24.7696	+	20.2101i	−1.08104	+	0.882042i
$526$	15.5953	−	13.0860i	0.679989	−	0.570578i
$527$	8.10309	+	9.65688i	0.352976	+	0.420660i
$528$	0.403354	−	0.212978i	0.0175537	−	0.00926866i
$529$	53.5979	−	19.5080i	2.33034	−	0.848176i
$530$	4.88747	+	0.801364i	0.212298	+	0.0348090i
$531$	20.7209	+	20.2421i	0.899209	+	0.878432i
$532$	38.3996	+	22.1700i	1.66483	+	0.961192i
$533$	−6.83953	−	1.20599i	−0.296253	−	0.0522374i
$534$	−2.03062	−	14.7572i	−0.0878737	−	0.638607i
$535$	5.41153	+	9.11822i	0.233961	+	0.394215i
$536$	5.60788	+	31.8039i	0.242223	+	1.37372i
$537$	−5.27963	−	16.4099i	−0.227833	−	0.708138i
$538$	−13.2569	+	15.7989i	−0.571544	+	0.681139i
$539$	1.47129			0.0633731
$540$	2.50858	+	34.2181i	0.107952	+	1.47251i
$541$	−23.6759			−1.01791			−0.508953	−	0.860795i	$-0.669967\pi$
$541$	−23.6759			−1.01791			−0.508953	+	0.860795i	$0.669967\pi$
$542$	−13.8310	+	16.4831i	−0.594090	+	0.708009i
$543$	13.3698	−	14.7629i	0.573755	−	0.633537i
$544$	4.42115	+	25.0736i	0.189555	+	1.07502i
$545$	2.69161	−	1.59743i	0.115296	−	0.0684263i
$546$	−44.7614	−	18.2351i	−1.91561	−	0.780389i
$547$	−22.0603	−	3.88982i	−0.943229	−	0.166317i	−0.319173	−	0.947696i	$-0.603405\pi$
$547$	−22.0603	−	3.88982i	−0.943229	−	0.166317i	−0.624056	+	0.781380i	$0.714516\pi$
$548$	−27.3695	−	15.8018i	−1.16917	−	0.675020i
$549$	−7.50994	+	10.9966i	−0.320517	+	0.469325i
$550$	−1.63315	−	1.85395i	−0.0696379	−	0.0790528i
$551$	−11.5537	+	4.20519i	−0.492203	+	0.179147i
$552$	27.8186	+	17.4947i	1.18404	+	0.744624i
$553$	−11.8030	−	14.0663i	−0.501916	−	0.598160i
$554$	−50.8742	+	42.6885i	−2.16144	+	1.81366i
$555$	−14.7696	+	16.7077i	−0.626937	+	0.709204i
$556$	61.0308	−	22.2134i	2.58828	−	0.942058i
$557$	−25.3314	+	14.6251i	−1.07332	+	0.619684i	−0.929088	−	0.369859i	$-0.879406\pi$
$557$	−25.3314	+	14.6251i	−1.07332	+	0.619684i	−0.144237	+	0.989543i	$0.546073\pi$
$558$	−13.2642	−	18.4798i	−0.561519	−	0.782311i
$559$	−4.90750	+	8.50004i	−0.207565	+	0.359513i
$560$	7.42347	−	6.38259i	0.313699	−	0.269714i
$561$	−1.12380	+	0.872807i	−0.0474471	+	0.0368499i
$562$	−15.2540	+	41.9100i	−0.643450	+	1.76786i
$563$	32.5704	−	5.74304i	1.37268	−	0.242040i	0.561809	−	0.827267i	$-0.310106\pi$
$563$	32.5704	−	5.74304i	1.37268	−	0.242040i	0.810870	+	0.585227i	$0.198994\pi$
$564$	5.92204	−	27.4713i	0.249363	−	1.15675i
$565$	−4.12691	−	21.8651i	−0.173620	−	0.919873i
$566$	−37.7206			−1.58552
$567$	−17.2792	−	28.3755i	−0.725660	−	1.19166i
$568$			5.72169i			0.240077i
$569$	19.8969	+	16.6955i	0.834121	+	0.699911i	0.956233	−	0.292606i	$-0.0945223\pi$
$569$	19.8969	+	16.6955i	0.834121	+	0.699911i	−0.122112	+	0.992516i	$0.538967\pi$
$570$	21.8373	+	27.4304i	0.914665	+	1.14893i
$571$	−1.96201	−	11.1271i	−0.0821074	−	0.465654i	−0.997943	−	0.0641016i	$-0.979582\pi$
$571$	−1.96201	−	11.1271i	−0.0821074	−	0.465654i	0.915836	−	0.401553i	$-0.131529\pi$
$572$	0.761702	−	2.09276i	0.0318484	−	0.0875027i
$573$	3.34427	+	4.30601i	0.139709	+	0.179886i
$574$	2.91679	−	16.5419i	0.121744	−	0.690446i
$575$	−14.2847	+	42.3897i	−0.595713	+	1.76777i
$576$	−3.83570	−	38.6359i	−0.159821	−	1.60983i
$577$	26.6345	−	15.3774i	1.10881	−	0.640171i	0.170288	−	0.985394i	$-0.445530\pi$
$577$	26.6345	−	15.3774i	1.10881	−	0.640171i	0.938520	+	0.345224i	$0.112197\pi$
$578$	2.51933	+	6.92180i	0.104790	+	0.287909i
$579$	−3.17076	−	0.119879i	−0.131772	−	0.00498199i
$580$	−0.239817	−	19.9567i	−0.00995786	−	0.828658i
$581$	12.1798	−	10.2201i	0.505303	−	0.424000i
$582$	58.6185	+	36.8643i	2.42981	+	1.52807i
$583$	−0.0755786	−	0.207650i	−0.00313014	−	0.00860000i
$584$	−1.23292	−	2.13547i	−0.0510185	−	0.0883666i
$585$	−16.4895	−	15.7258i	−0.681758	−	0.650180i
$586$	8.07300	−	13.9829i	0.333493	−	0.577626i
$587$	−0.937510	−	0.165308i	−0.0386952	−	0.00682300i	0.154267	−	0.988029i	$-0.450698\pi$
$587$	−0.937510	−	0.165308i	−0.0386952	−	0.00682300i	−0.192962	+	0.981206i	$0.561809\pi$
$588$	12.7866	−	31.3872i	0.527312	−	1.29439i
$589$	−13.0231	−	4.74003i	−0.536609	−	0.195310i
$590$	−23.5237	+	41.8989i	−0.968454	+	1.72495i
$591$	6.87356	+	6.22495i	0.282740	+	0.256060i
$592$	4.38971	−	5.23146i	0.180416	−	0.215012i
$593$		−	27.0360i		−	1.11024i	−0.831771	−	0.555119i	$-0.812673\pi$
$593$		−	27.0360i		−	1.11024i	0.831771	−	0.555119i	$-0.187327\pi$
$594$	2.14099	−	1.41733i	0.0878460	−	0.0581538i
$595$	−19.3487	+	23.6299i	−0.793221	+	0.968730i
$596$	13.0164	+	10.9221i	0.533173	+	0.447385i
$597$	−7.01809	−	21.8132i	−0.287231	−	0.892757i
$598$	−66.6028	+	11.7439i	−2.72359	+	0.480243i
$599$	21.7248	+	7.90718i	0.887652	+	0.323079i	0.745294	−	0.666736i	$-0.232309\pi$
$599$	21.7248	+	7.90718i	0.887652	+	0.323079i	0.142358	+	0.989815i	$0.454532\pi$
$600$	−17.3435	+	6.04364i	−0.708045	+	0.246731i
$601$	−2.60952	+	14.7993i	−0.106445	+	0.603677i	0.884189	+	0.467130i	$0.154712\pi$
$601$	−2.60952	+	14.7993i	−0.106445	+	0.603677i	−0.990633	+	0.136548i	$0.956399\pi$
$602$	−20.5580	−	11.8692i	−0.837882	−	0.483751i
$603$	−12.3386	−	43.9855i	−0.502468	−	1.79123i
$604$	4.58219	+	7.93658i	0.186447	+	0.322935i
$605$	8.09779	−	23.1088i	0.329222	−	0.939505i
$606$	33.1277	+	62.7399i	1.34572	+	2.54863i
$607$	−12.3037	−	14.6630i	−0.499392	−	0.595152i	0.456189	−	0.889883i	$-0.349214\pi$
$607$	−12.3037	−	14.6630i	−0.499392	−	0.595152i	−0.955580	+	0.294731i	$0.904770\pi$
$608$	−17.9920	−	21.4420i	−0.729671	−	0.869588i
$609$	9.02362	+	17.0896i	0.365656	+	0.692507i
$610$	−20.8464	−	7.30499i	−0.844044	−	0.295771i
$611$	9.33173	+	16.1630i	0.377521	+	0.653886i
$612$	8.85295	+	31.5596i	0.357859	+	1.27572i
$613$	30.6773	+	17.7116i	1.23905	+	0.715364i	0.968899	−	0.247455i	$-0.0795943\pi$
$613$	30.6773	+	17.7116i	1.23905	+	0.715364i	0.270147	+	0.962819i	$0.412928\pi$
$614$	−8.58301	+	48.6767i	−0.346382	+	1.96443i
$615$	4.13480	−	6.75354i	0.166731	−	0.272329i
$616$	1.63338	+	0.594501i	0.0658107	+	0.0239531i
$617$	8.90389	−	1.57000i	0.358457	−	0.0632057i	0.00848032	−	0.999964i	$-0.497301\pi$
$617$	8.90389	−	1.57000i	0.358457	−	0.0632057i	0.349977	+	0.936758i	$0.386189\pi$
$618$	−7.86927	−	24.4588i	−0.316548	−	0.983878i
$619$	8.15417	+	6.84216i	0.327744	+	0.275010i	0.791780	−	0.610807i	$-0.209155\pi$
$619$	8.15417	+	6.84216i	0.327744	+	0.275010i	−0.464036	+	0.885816i	$0.653599\pi$
$620$	14.2524	−	17.4059i	0.572390	−	0.699037i
$621$	−41.6042	−	20.7391i	−1.66952	−	0.832229i
$622$		−	32.6704i		−	1.30996i
$623$	−9.16948	+	10.9278i	−0.367367	+	0.437811i
$624$	5.17220	+	4.68414i	0.207054	+	0.187516i
$625$	−13.5258	−	21.0250i	−0.541032	−	0.841002i
$626$	−27.7329	−	10.0939i	−1.10843	−	0.403435i
$627$	0.590190	−	1.44873i	0.0235699	−	0.0578568i
$628$	31.0333	+	5.47201i	1.23836	+	0.218357i
$629$	−10.6521	+	18.4500i	−0.424726	+	0.735648i
$630$	38.0339	−	39.8812i	1.51531	−	1.58890i
$631$	−20.2843	−	35.1335i	−0.807507	−	1.39864i	−0.914586	−	0.404392i	$-0.867483\pi$
$631$	−20.2843	−	35.1335i	−0.807507	−	1.39864i	0.107079	−	0.994251i	$-0.465850\pi$
$632$	−3.60810	−	9.91317i	−0.143522	−	0.394325i
$633$	15.7908	+	9.93062i	0.627629	+	0.394707i
$634$	39.5612	−	33.1958i	1.57118	−	1.31837i
$635$	10.1605	−	0.122097i	0.403207	−	0.00484528i
$636$	−5.08666	−	0.192314i	−0.201699	−	0.00762575i
$637$	7.69831	+	21.1509i	0.305018	+	0.838031i
$638$	−1.29349	+	0.746795i	−0.0512097	+	0.0295659i
$639$	−0.799609	−	8.05423i	−0.0316320	−	0.318620i
$640$	31.4624	−	11.8814i	1.24366	−	0.469654i
$641$	−3.45809	+	19.6118i	−0.136586	+	0.774620i	0.837155	+	0.546965i	$0.184217\pi$
$641$	−3.45809	+	19.6118i	−0.136586	+	0.774620i	−0.973742	+	0.227655i	$0.926894\pi$
$642$	−11.2118	−	14.4361i	−0.442495	−	0.569746i
$643$	−12.3572	+	33.9512i	−0.487322	+	1.33891i	0.415775	+	0.909468i	$0.363511\pi$
$643$	−12.3572	+	33.9512i	−0.487322	+	1.33891i	−0.903096	+	0.429438i	$0.858712\pi$
$644$	−16.9341	−	96.0380i	−0.667297	−	3.78443i
$645$	−6.97020	−	8.75543i	−0.274451	−	0.344745i
$646$	25.6591	+	21.5305i	1.00954	+	0.847108i
$647$			36.2828i			1.42642i	0.700949	+	0.713211i	$0.252760\pi$
$647$			36.2828i			1.42642i	−0.700949	+	0.713211i	$0.747240\pi$
$648$	−3.75282	−	18.7143i	−0.147425	−	0.735166i
$649$	2.14389			0.0841551
$650$	18.1067	−	33.1783i	0.710204	−	1.30136i
$651$	−4.59048	+	21.2945i	−0.179915	+	0.834596i
$652$	−39.9753	+	7.04873i	−1.56555	+	0.276049i
$653$	3.72238	−	10.2271i	0.145668	−	0.400219i	−0.845305	−	0.534285i	$-0.820581\pi$
$653$	3.72238	−	10.2271i	0.145668	−	0.400219i	0.990972	+	0.134066i	$0.0428033\pi$
$654$	−4.26138	+	3.30962i	−0.166633	+	0.129416i
$655$	21.9629	+	25.5446i	0.858160	+	0.998108i
$656$	−1.21253	+	2.10016i	−0.0473412	+	0.0819973i
$657$	2.03397	+	2.83374i	0.0793527	+	0.110555i
$658$	−39.0915	+	22.5695i	−1.52395	+	0.879851i
$659$	−2.92228	+	1.06362i	−0.113836	+	0.0414328i	−0.398310	−	0.917251i	$-0.630403\pi$
$659$	−2.92228	+	1.06362i	−0.113836	+	0.0414328i	0.284474	+	0.958684i	$0.408181\pi$
$660$	1.90252	+	1.68183i	0.0740554	+	0.0654651i
$661$	−6.66558	+	5.59308i	−0.259261	+	0.217546i	−0.763148	−	0.646224i	$-0.776347\pi$
$661$	−6.66558	+	5.59308i	−0.259261	+	0.217546i	0.503887	+	0.863770i	$0.331903\pi$
$662$	28.2593	+	33.6781i	1.09833	+	1.30894i
$663$	−18.4274	−	11.5887i	−0.715660	−	0.450068i
$664$	8.58366	−	3.12420i	0.333111	−	0.121242i
$665$	5.43266	−	33.1335i	0.210669	−	1.28486i
$666$	21.6802	−	31.7458i	0.840090	−	1.23013i
$667$	23.4186	+	13.5207i	0.906771	+	0.523525i
$668$	−23.2410	−	4.09801i	−0.899220	−	0.158557i
$669$	21.5968	+	8.79818i	0.834980	+	0.340157i
$670$	65.1671	−	38.6757i	2.51762	−	1.49417i
$671$	0.171140	+	0.970585i	0.00660680	+	0.0374690i
$672$	−29.5331	+	32.6103i	−1.13927	+	1.25797i
$673$	−2.39450	+	2.85366i	−0.0923014	+	0.110000i	−0.810218	−	0.586128i	$-0.800651\pi$
$673$	−2.39450	+	2.85366i	−0.0923014	+	0.110000i	0.717917	+	0.696129i	$0.245096\pi$
$674$	21.0429			0.810540
$675$	23.5692	−	10.9312i	0.907180	−	0.420742i
$676$	−4.31760			−0.166062
$677$	−21.5673	+	25.7029i	−0.828897	+	0.987841i	0.171099	+	0.985254i	$0.445268\pi$
$677$	−21.5673	+	25.7029i	−0.828897	+	0.987841i	−0.999997	+	0.00258744i	$0.999176\pi$
$678$	11.7482	+	36.5150i	0.451186	+	1.40235i
$679$	−11.5151	−	65.3056i	−0.441910	−	2.50620i
$680$	−15.0889	+	8.95503i	−0.578633	+	0.343410i
$681$	−4.39829	−	31.9638i	−0.168543	−	1.22486i
$682$	−1.65798	−	0.292346i	−0.0634872	−	0.0111945i
$683$	6.92360	+	3.99734i	0.264924	+	0.152954i	0.626579	−	0.779358i	$-0.284455\pi$
$683$	6.92360	+	3.99734i	0.264924	+	0.152954i	−0.361655	+	0.932312i	$0.617788\pi$
$684$	−25.7767	−	25.1811i	−0.985597	−	0.962824i
$685$	−3.87216	+	23.6161i	−0.147948	+	0.902325i
$686$	2.88372	−	1.04959i	0.110101	−	0.0400735i
$687$	16.2487	−	8.57957i	0.619925	−	0.327331i
$688$	2.20295	+	2.62537i	0.0839866	+	0.100091i
$689$	2.58968	−	2.17300i	0.0986588	−	0.0827846i
$690$	15.3430	−	75.5706i	0.584098	−	2.87692i
$691$	−36.6703	+	13.3469i	−1.39500	+	0.507740i	−0.926691	−	0.375823i	$-0.877360\pi$
$691$	−36.6703	+	13.3469i	−1.39500	+	0.507740i	−0.468312	+	0.883563i	$0.655138\pi$
$692$	−8.96838	+	5.17790i	−0.340927	+	0.196834i
$693$	−2.38233	−	0.608594i	−0.0904974	−	0.0231186i
$694$	−0.659043	+	1.14150i	−0.0250169	+	0.0433306i
$695$	−32.0632	−	37.2921i	−1.21623	−	1.41457i
$696$	1.51352	+	10.9992i	0.0573697	+	0.416924i
$697$	2.58743	−	7.10890i	0.0980059	−	0.269269i
$698$	−34.6303	+	6.10625i	−1.31078	+	0.231125i
$699$	19.2315	−	6.18746i	0.727403	−	0.234031i
$700$	47.8416	+	26.1090i	1.80824	+	0.986828i
$701$	16.1937			0.611629			0.305814	−	0.952091i	$-0.401071\pi$
$701$	16.1937			0.611629			0.305814	+	0.952091i	$0.401071\pi$
$702$	31.5776	+	23.3624i	1.19182	+	0.881757i
$703$		−	23.4213i		−	0.883351i
$704$	−2.20126	−	1.84708i	−0.0829632	−	0.0696144i
$705$	−21.0451	+	3.15397i	−0.792606	+	0.118785i
$706$	4.07005	+	23.0824i	0.153178	+	0.868718i
$707$	23.2379	−	63.8456i	0.873951	−	2.40116i
$708$	18.6320	−	45.7358i	0.700235	−	1.71886i
$709$	8.61920	−	48.8819i	0.323701	−	1.83580i	−0.194950	−	0.980813i	$-0.562454\pi$
$709$	8.61920	−	48.8819i	0.323701	−	1.83580i	0.518651	−	0.854986i	$-0.326434\pi$
$710$	12.5603	−	4.74325i	0.471379	−	0.178011i
$711$	6.46437	+	13.4502i	0.242433	+	0.504422i
$712$	−7.09754	+	4.09777i	−0.265992	+	0.153570i
$713$	10.4250	+	28.6425i	0.390420	+	1.07267i
$714$	28.0282	−	44.5680i	1.04893	−	1.66792i
$715$	−1.68630	+	0.0202640i	−0.0630639	+	0.000757830i
$716$	−22.5134	+	18.8909i	−0.841364	+	0.705988i
$717$	−0.476943	+	12.6150i	−0.0178118	+	0.471117i
$718$	−20.5313	−	56.4093i	−0.766222	−	2.10518i
$719$	2.68091	+	4.64347i	0.0999811	+	0.173172i	0.911677	−	0.410909i	$-0.134788\pi$
$719$	2.68091	+	4.64347i	0.0999811	+	0.173172i	−0.811695	+	0.584081i	$0.801455\pi$
$720$	−7.12920	+	3.53247i	−0.265690	+	0.131648i
$721$	−12.3025	+	21.3086i	−0.458170	+	0.793573i
$722$	5.37764	+	0.948223i	0.200135	+	0.0352892i
$723$	7.58886	+	9.77123i	0.282233	+	0.363396i
$724$	−31.9086	−	11.6138i	−1.18587	−	0.431622i
$725$	−14.0733	+	5.50875i	−0.522670	+	0.204590i
$726$	−8.89532	+	41.2639i	−0.330136	+	1.53145i
$727$	−11.2837	+	13.4474i	−0.418491	+	0.498738i	−0.933565	−	0.358408i	$-0.883320\pi$
$727$	−11.2837	+	13.4474i	−0.418491	+	0.498738i	0.515075	+	0.857145i	$0.327764\pi$
$728$			26.5917i			0.985553i
$729$	7.89805	+	25.8190i	0.292520	+	0.956259i
$730$	−3.66572	+	4.47680i	−0.135675	+	0.165694i
$731$	−8.19005	−	6.87227i	−0.302920	−	0.254180i
$732$	22.1929	+	4.78416i	0.820273	+	0.176828i
$733$	39.3876	−	6.94510i	1.45482	−	0.256523i	0.610350	−	0.792132i	$-0.291029\pi$
$733$	39.3876	−	6.94510i	1.45482	−	0.256523i	0.844466	+	0.535609i	$0.179918\pi$
$734$	−0.360901	−	0.131357i	−0.0133211	−	0.00484849i
$735$	−25.6556	−	0.661376i	−0.946322	−	0.0243952i
$736$	−10.6900	+	60.6260i	−0.394039	+	2.23470i
$737$	−2.92809	−	1.69054i	−0.107858	−	0.0622717i
$738$	−5.62417	+	12.4386i	−0.207029	+	0.457871i
$739$	11.3584	+	19.6733i	0.417826	+	0.723695i	0.995720	−	0.0924160i	$-0.0294590\pi$
$739$	11.3584	+	19.6733i	0.417826	+	0.723695i	−0.577895	+	0.816111i	$0.696126\pi$
$740$	35.8796	+	12.5730i	1.31896	+	0.462191i
$741$	23.9147	+	0.904155i	0.878527	+	0.0332150i
$742$	5.25556	+	6.26333i	0.192938	+	0.229934i
$743$	3.03340	+	3.61507i	0.111285	+	0.132624i	0.818811	−	0.574063i	$-0.194633\pi$
$743$	3.03340	+	3.61507i	0.111285	+	0.132624i	−0.707527	+	0.706687i	$0.750189\pi$
$744$	−6.66251	+	10.5942i	−0.244259	+	0.388400i
$745$	4.25509	−	12.1428i	0.155895	−	0.444878i
$746$	17.1904	+	29.7746i	0.629385	+	1.09013i
$747$	−11.6463	+	5.59740i	−0.426116	+	0.204798i
$748$	2.10091	+	1.21296i	0.0768167	+	0.0443502i
$749$	−3.03956	+	17.2382i	−0.111063	+	0.629871i
$750$	27.6447	+	33.0624i	1.00944	+	1.20727i
$751$	47.8416	+	17.4129i	1.74577	+	0.635407i	0.999541	−	0.0302882i	$-0.00964252\pi$
$751$	47.8416	+	17.4129i	1.74577	+	0.635407i	0.746224	+	0.665695i	$0.231865\pi$
$752$	6.41786	−	1.13164i	0.234035	−	0.0412667i
$753$	−23.6094	+	26.0693i	−0.860374	+	0.950020i
$754$	−17.5037	−	14.6874i	−0.637448	−	0.534882i
$755$	4.39649	−	5.36926i	0.160005	−	0.195407i
$756$	−33.6875	+	45.5334i	−1.22520	+	1.65603i
$757$			48.3143i			1.75601i	0.478647	+	0.878007i	$0.341127\pi$
$757$			48.3143i			1.75601i	−0.478647	+	0.878007i	$0.658873\pi$
$758$	40.8107	−	48.6363i	1.48231	−	1.76655i
$759$	−3.27519	+	1.05375i	−0.118882	+	0.0382485i
$760$	9.44348	−	16.8202i	0.342551	−	0.610131i
$761$	30.3570	+	11.0490i	1.10044	+	0.400528i	0.827479	−	0.561497i	$-0.189774\pi$
$761$	30.3570	+	11.0490i	1.10044	+	0.400528i	0.272962	+	0.962025i	$0.411997\pi$
$762$	−17.3532	+	2.38784i	−0.628640	+	0.0865022i
$763$	5.08855	+	0.897249i	0.184218	+	0.0324826i
$764$	4.64761	−	8.04989i	0.168145	−	0.291235i
$765$	19.9887	−	14.7144i	0.722691	−	0.531999i
$766$	−2.59985	−	4.50307i	−0.0939363	−	0.162703i
$767$	11.2176	+	30.8200i	0.405043	+	1.11285i
$768$	−11.6229	+	6.13710i	−0.419406	+	0.221454i
$769$	−32.5792	+	27.3372i	−1.17484	+	0.985804i	−0.174836	+	0.984598i	$0.555939\pi$
$769$	−32.5792	+	27.3372i	−1.17484	+	0.985804i	−0.999999	+	0.00120611i	$0.999616\pi$
$770$	−0.0490100	−	4.07844i	−0.00176620	−	0.146977i
$771$	−23.7541	−	44.9873i	−0.855482	−	1.62018i
$772$	1.85020	+	5.08338i	0.0665901	+	0.182955i
$773$	29.1758	−	16.8447i	1.04938	−	0.605861i	0.126906	−	0.991915i	$-0.459495\pi$
$773$	29.1758	−	16.8447i	1.04938	−	0.605861i	0.922476	+	0.386054i	$0.126162\pi$
$774$	13.8001	+	13.4812i	0.496034	+	0.484573i
$775$	−16.1433	−	5.44004i	−0.579883	−	0.195412i
$776$	6.61560	−	37.5189i	0.237486	−	1.34685i
$777$	−36.4702	+	5.01838i	−1.30836	+	0.180033i
$778$	18.0077	−	49.4758i	0.645608	−	1.77379i
$779$	1.44422	+	8.19058i	0.0517446	+	0.293458i
$780$	−14.2229	+	36.1500i	−0.509261	+	1.29438i
$781$	−0.458886	−	0.385051i	−0.0164202	−	0.0137782i
$782$		−	73.6687i		−	2.63439i
$783$	−3.66767	−	15.2717i	−0.131072	−	0.545767i
$784$	7.85941			0.280693
$785$	−4.42568	−	23.4481i	−0.157959	−	0.836898i
$786$	−43.0454	−	38.9835i	−1.53538	−	1.39050i
$787$	−0.894287	+	0.157687i	−0.0318779	+	0.00562093i	−0.189564	−	0.981868i	$-0.560708\pi$
$787$	−0.894287	+	0.157687i	−0.0318779	+	0.00562093i	0.157686	+	0.987489i	$0.449596\pi$
$788$	5.40733	−	14.8565i	0.192628	−	0.529241i
$789$	14.6733	+	5.97767i	0.522384	+	0.212811i
$790$	−18.7703	+	16.1385i	−0.667819	+	0.574181i
$791$	18.3666	−	31.8120i	0.653043	−	1.13110i
$792$	−1.16656	−	0.796677i	−0.0414518	−	0.0283087i
$793$	−13.0574	+	7.53870i	−0.463683	+	0.267707i
$794$	−18.8059	+	6.84477i	−0.667395	+	0.242912i
$795$	1.22456	+	3.65487i	0.0434305	+	0.129625i
$796$	−29.9265	+	25.1113i	−1.06072	+	0.890046i
$797$	−6.79626	−	8.09946i	−0.240736	−	0.286898i	0.632126	−	0.774866i	$-0.282183\pi$
$797$	−6.79626	−	8.09946i	−0.240736	−	0.286898i	−0.872861	+	0.487968i	$0.837738\pi$
$798$	−2.18677	+	57.8395i	−0.0774107	+	2.04750i
$799$	−19.1038	+	6.95322i	−0.675844	+	0.245987i
$800$	−22.7425	−	25.8172i	−0.804069	−	0.912777i
$801$	9.41831	−	6.76018i	0.332780	−	0.238859i
$802$	−8.54041	−	4.93081i	−0.301572	−	0.174113i
$803$	0.254239	+	0.0448291i	0.00897188	+	0.00158199i
$804$	−61.5117	+	47.7733i	−2.16935	+	1.68483i
$805$	−63.5038	+	37.6885i	−2.23821	+	1.32835i
$806$	−4.47241	−	25.3643i	−0.157534	−	0.893420i
$807$	−15.6906	−	3.38244i	−0.552335	−	0.119068i
$808$	25.0907	−	29.9019i	0.882688	−	1.05195i
$809$	23.0588			0.810703			0.405351	−	0.914161i	$-0.367149\pi$
$809$	23.0588			0.810703			0.405351	+	0.914161i	$0.367149\pi$
$810$	−37.9706	+	23.7523i	−1.33415	+	0.834569i
$811$	8.38290			0.294363			0.147182	−	0.989109i	$-0.452980\pi$
$811$	8.38290			0.294363			0.147182	+	0.989109i	$0.452980\pi$
$812$	21.1785	−	25.2395i	0.743219	−	0.885733i
$813$	−16.3701	−	3.52892i	−0.574124	−	0.123765i
$814$	−0.494059	−	2.80195i	−0.0173168	−	0.0982082i
$815$	15.6876	+	26.4331i	0.549514	+	0.925911i
$816$	−6.00319	+	4.66240i	−0.210154	+	0.163217i
$817$	11.5753	+	2.04103i	0.404967	+	0.0714066i
$818$	13.3815	+	7.72583i	0.467874	+	0.270127i
$819$	−3.71620	−	37.4322i	−0.129855	−	1.30799i
$820$	−13.3226	−	2.18441i	−0.465246	−	0.0762830i
$821$	8.15204	−	2.96710i	0.284508	−	0.103553i	−0.195824	−	0.980639i	$-0.562738\pi$
$821$	8.15204	−	2.96710i	0.284508	−	0.103553i	0.480332	+	0.877086i	$0.340516\pi$
$822$	1.55863	−	41.2254i	0.0543635	−	1.43790i
$823$	26.6834	+	31.8001i	0.930125	+	1.10848i	0.993875	+	0.110514i	$0.0352498\pi$
$823$	26.6834	+	31.8001i	0.930125	+	1.10848i	−0.0637492	+	0.997966i	$0.520306\pi$
$824$	−10.8288	+	9.08640i	−0.377237	+	0.316540i
$825$	0.682453	−	1.79768i	0.0237600	−	0.0625873i
$826$	−74.5407	+	27.1306i	−2.59360	+	0.943994i
$827$	−37.2589	+	21.5114i	−1.29562	+	0.748026i	−0.979644	−	0.200742i	$-0.935665\pi$
$827$	−37.2589	+	21.5114i	−1.29562	+	0.748026i	−0.315975	+	0.948768i	$0.602331\pi$
$828$	−5.98425	+	79.0278i	−0.207967	+	2.74641i
$829$	−11.7233	+	20.3053i	−0.407167	+	0.705233i	−0.994571	−	0.104060i	$-0.966816\pi$
$829$	−11.7233	+	20.3053i	−0.407167	+	0.705233i	0.587404	+	0.809294i	$0.300150\pi$
$830$	−13.9741	−	16.2529i	−0.485047	−	0.564148i
$831$	−47.8664	−	19.5000i	−1.66047	−	0.676448i
$832$	15.0354	−	41.3093i	0.521258	−	1.43214i
$833$	−24.1456	+	4.25752i	−0.836594	+	0.147514i
$834$	62.8413	+	56.9114i	2.17602	+	1.97068i
$835$	3.31441	+	17.5604i	0.114700	+	0.607702i
$836$	−2.66700			−0.0922400
$837$	7.89805	−	15.8441i	0.272996	−	0.547653i
$838$		−	26.3138i		−	0.908995i
$839$	13.1738	+	11.0541i	0.454810	+	0.381631i	0.841217	−	0.540697i	$-0.181840\pi$
$839$	13.1738	+	11.0541i	0.454810	+	0.381631i	−0.386407	+	0.922328i	$0.626284\pi$
$840$	−28.2148	−	11.1008i	−0.973502	−	0.383015i
$841$	−3.44931	−	19.5620i	−0.118942	−	0.674553i
$842$	−4.42619	+	12.1609i	−0.152537	+	0.419091i
$843$	−34.3865	+	4.73165i	−1.18433	+	0.162967i
$844$	5.52245	−	31.3194i	0.190091	−	1.07806i
$845$	1.15505	+	3.05862i	0.0397350	+	0.105220i
$846$	35.3211	−	9.90811i	1.21436	−	0.340648i
$847$	35.0077	−	20.2117i	1.20288	−	0.694483i
$848$	−0.403729	−	1.10924i	−0.0138641	−	0.0380913i
$849$	−13.7074	−	25.9601i	−0.470437	−	0.890949i
$850$	32.1667	+	25.6995i	1.10331	+	0.881487i
$851$	−39.4604	+	33.1112i	−1.35268	+	1.13504i
$852$	−12.2024	+	6.44306i	−0.418047	+	0.220736i
$853$	−11.5159	−	31.6398i	−0.394299	−	1.08333i	−0.965019	−	0.262182i	$-0.915558\pi$
$853$	−11.5159	−	31.6398i	−0.394299	−	1.08333i	0.570720	−	0.821145i	$-0.306664\pi$
$854$	−18.2329	−	31.5804i	−0.623918	−	1.08066i
$855$	−10.9426	+	24.9969i	−0.374231	+	0.854876i
$856$	−5.02819	+	8.70908i	−0.171860	+	0.297670i
$857$	37.2310	+	6.56483i	1.27179	+	0.224250i	0.768490	−	0.639862i	$-0.221009\pi$
$857$	37.2310	+	6.56483i	1.27179	+	0.224250i	0.503298	+	0.864113i	$0.332120\pi$
$858$	2.88004	−	0.396300i	0.0983231	−	0.0135295i
$859$	15.6231	+	5.68635i	0.533054	+	0.194016i	0.594502	−	0.804094i	$-0.297349\pi$
$859$	15.6231	+	5.68635i	0.533054	+	0.194016i	−0.0614473	+	0.998110i	$0.519572\pi$
$860$	−9.34049	+	16.6367i	−0.318508	+	0.567308i
$861$	12.4444	−	4.00381i	0.424105	−	0.136450i
$862$	−20.0360	+	23.8779i	−0.682428	+	0.813285i
$863$			40.1307i			1.36607i	0.730388	+	0.683033i	$0.239339\pi$
$863$			40.1307i			1.36607i	−0.730388	+	0.683033i	$0.760661\pi$
$864$	29.8144	−	19.7371i	1.01431	−	0.671468i
$865$	6.06730	+	4.96806i	0.206294	+	0.168919i
$866$	15.0774	+	12.6515i	0.512351	+	0.429914i
$867$	−3.84822	+	4.24918i	−0.130692	+	0.144310i
$868$	36.5741	−	6.44901i	1.24141	−	0.218894i
$869$	1.03786	+	0.377750i	0.0352070	+	0.0128143i
$870$	22.8908	−	12.4408i	0.776072	−	0.421782i
$871$	8.98192	−	50.9390i	0.304341	−	1.72600i
$872$	2.57083	+	1.48427i	0.0870594	+	0.0502637i
$873$	−4.06927	+	53.7387i	−0.137724	+	1.81878i
$874$	40.4948	+	70.1391i	1.36976	+	2.37249i
$875$	5.69715	−	40.8760i	0.192599	−	1.38186i
$876$	3.16587	−	5.03409i	0.106965	−	0.170086i
$877$	−15.7994	−	18.8290i	−0.533509	−	0.635811i	0.430210	−	0.902729i	$-0.358439\pi$
$877$	−15.7994	−	18.8290i	−0.533509	−	0.635811i	−0.963719	+	0.266917i	$0.913995\pi$
$878$	34.7069	+	41.3621i	1.17130	+	1.39590i
$879$	12.5570	+	0.474748i	0.423536	+	0.0160128i
$880$	−0.194738	+	0.555727i	−0.00656463	+	0.0187336i
$881$	27.2101	+	47.1293i	0.916732	+	1.58783i	0.804346	+	0.594162i	$0.202516\pi$
$881$	27.2101	+	47.1293i	0.916732	+	1.58783i	0.112386	+	0.993665i	$0.464151\pi$
$882$	44.0254	−	4.37076i	1.48241	−	0.147171i
$883$	−2.77533	−	1.60234i	−0.0933974	−	0.0539230i	0.452574	−	0.891727i	$-0.350506\pi$
$883$	−2.77533	−	1.60234i	−0.0933974	−	0.0539230i	−0.545971	+	0.837804i	$0.683839\pi$
$884$	−6.44452	+	36.5487i	−0.216753	+	1.22927i
$885$	−37.3840	−	0.963722i	−1.25665	−	0.0323952i
$886$	−48.8534	−	17.7812i	−1.64126	−	0.597370i
$887$	−50.6541	+	8.93168i	−1.70080	+	0.299896i	−0.937973	−	0.346709i	$-0.887299\pi$
$887$	−50.6541	+	8.93168i	−1.70080	+	0.299896i	−0.762824	+	0.646606i	$0.776188\pi$
$888$	−20.6751	−	4.45697i	−0.693812	−	0.149566i
$889$	12.8501	+	10.7825i	0.430978	+	0.361634i
$890$	14.8793	+	12.1835i	0.498754	+	0.408393i
$891$	1.75346	+	0.958428i	0.0587430	+	0.0321086i
$892$		−	39.7579i		−	1.33119i
$893$	14.3664	−	17.1212i	0.480754	−	0.572940i
$894$	−4.67417	+	21.6827i	−0.156327	+	0.725177i
$895$	19.4053	+	10.8949i	0.648647	+	0.364175i
$896$	52.1715	+	18.9889i	1.74293	+	0.634374i
$897$	−32.2853	−	41.5698i	−1.07798	−	1.38798i
$898$	20.6929	+	3.64872i	0.690533	+	0.121760i
$899$	−5.14909	+	8.91849i	−0.171732	+	0.297448i
$900$	−32.4191	−	30.1820i	−1.08064	−	1.00607i
$901$	1.84121	+	3.18907i	0.0613397	+	0.106243i
$902$	0.345551	+	0.949395i	0.0115056	+	0.0316114i
$903$	0.697988	−	18.4616i	0.0232276	−	0.614364i
$904$	16.1664	−	13.5652i	0.537688	−	0.451173i
$905$	0.308967	+	25.7112i	0.0102704	+	0.854669i
$906$	−6.36867	+	10.1269i	−0.211585	+	0.336444i
$907$	−0.804531	−	2.21043i	−0.0267140	−	0.0733961i	0.925619	−	0.378457i	$-0.123545\pi$
$907$	−0.804531	−	2.21043i	−0.0267140	−	0.0733961i	−0.952333	+	0.305061i	$0.901323\pi$
$908$	−47.6382	+	27.5039i	−1.58093	+	0.912749i
$909$	−31.1405	+	45.5984i	−1.03287	+	1.51240i
$910$	58.3742	−	22.0444i	1.93509	−	0.730763i
$911$	6.53209	−	37.0453i	0.216418	−	1.22737i	−0.662011	−	0.749494i	$-0.730297\pi$
$911$	6.53209	−	37.0453i	0.216418	−	1.22737i	0.878429	−	0.477873i	$-0.158592\pi$
$912$	3.15270	−	7.73889i	0.104396	−	0.256260i
$913$	−0.327088	+	0.898666i	−0.0108250	+	0.0297415i
$914$	−7.71816	−	43.7719i	−0.255294	−	1.44784i
$915$	−2.54796	−	17.0015i	−0.0842328	−	0.562051i
$916$	−23.9975	−	20.1363i	−0.792899	−	0.665321i
$917$			55.6139i			1.83653i
$918$	−31.0347	+	29.4554i	−1.02430	+	0.972175i
$919$	−20.8095			−0.686442			−0.343221	−	0.939255i	$-0.611518\pi$
$919$	−20.8095			−0.686442			−0.343221	+	0.939255i	$0.611518\pi$
$920$	−41.6892	+	7.86857i	−1.37445	+	0.259419i
$921$	−36.6193	+	11.7817i	−1.20665	+	0.388221i
$922$	6.66830	−	1.17580i	0.219609	−	0.0387229i
$923$	3.13434	−	8.61154i	0.103168	−	0.283452i
$924$	0.571446	+	4.15289i	0.0187992	+	0.136620i
$925$	−0.691811	−	28.7809i	−0.0227466	−	0.946310i
$926$	28.5112	−	49.3828i	0.936936	−	1.62282i
$927$	13.9734	−	14.3039i	0.458948	−	0.469803i
$928$	−18.0125	+	10.3995i	−0.591288	+	0.341381i
$929$	−8.82224	+	3.21103i	−0.289448	+	0.105351i	−0.482664	−	0.875806i	$-0.660331\pi$
$929$	−8.82224	+	3.21103i	−0.289448	+	0.105351i	0.193215	+	0.981156i	$0.438108\pi$
$930$	28.7795	+	5.84307i	0.943717	+	0.191602i
$931$	20.6484	−	17.3261i	0.676724	−	0.567839i
$932$	−22.1392	−	26.3845i	−0.725195	−	0.864254i
$933$	22.4845	−	11.8722i	0.736108	−	0.388678i
$934$	−1.56705	+	0.570359i	−0.0512754	+	0.0186627i
$935$	0.297230	−	1.81279i	0.00972045	−	0.0592845i
$936$	5.34900	−	20.9386i	0.174838	−	0.684400i
$937$	37.9686	+	21.9212i	1.24038	+	0.716134i	0.969172	−	0.246387i	$-0.0792433\pi$
$937$	37.9686	+	21.9212i	1.24038	+	0.716134i	0.271209	+	0.962521i	$0.412577\pi$
$938$	123.200	+	21.7235i	4.02262	+	0.709296i
$939$	−3.13105	−	22.7544i	−0.102178	−	0.742562i
$940$	18.5162	+	31.1992i	0.603933	+	1.01761i
$941$	1.63809	+	9.29005i	0.0534001	+	0.302847i	0.999797	−	0.0201597i	$-0.00641747\pi$
$941$	1.63809	+	9.29005i	0.0534001	+	0.302847i	−0.946397	+	0.323007i	$0.895306\pi$
$942$	12.5987	+	39.1585i	0.410487	+	1.27585i
$943$	11.7578	−	14.0124i	0.382887	−	0.456307i
$944$	11.4523			0.372742
$945$	41.2683	+	11.6832i	1.34246	+	0.380056i
$946$	1.42783			0.0464228
$947$	11.2463	−	13.4028i	0.365456	−	0.435533i	−0.551712	−	0.834035i	$-0.686025\pi$
$947$	11.2463	−	13.4028i	0.365456	−	0.435533i	0.917168	+	0.398502i	$0.130470\pi$
$948$	17.0783	−	18.8578i	0.554679	−	0.612473i
$949$	0.685812	+	3.88943i	0.0222624	+	0.126256i
$950$	−44.7523	−	6.78655i	−1.45196	−	0.220185i
$951$	37.2223	+	15.1638i	1.20702	+	0.491719i
$952$	−28.5259	−	5.02989i	−0.924530	−	0.163020i
$953$	−7.59175	−	4.38310i	−0.245921	−	0.141982i	0.371974	−	0.928243i	$-0.378681\pi$
$953$	−7.59175	−	4.38310i	−0.245921	−	0.141982i	−0.617895	+	0.786261i	$0.712014\pi$
$954$	−2.87840	−	5.98900i	−0.0931917	−	0.193901i
$955$	−6.94594	−	1.13887i	−0.224765	−	0.0368531i
$956$	20.2244	−	7.36109i	0.654105	−	0.238075i
$957$	−0.984004	−	0.618825i	−0.0318083	−	0.0200038i
$958$	13.2759	+	15.8216i	0.428926	+	0.511174i
$959$	−30.2642	+	25.3947i	−0.977282	+	0.820037i
$960$	37.5541	+	33.1979i	1.21205	+	1.07146i
$961$	18.2225	−	6.63247i	0.587824	−	0.213950i
$962$	37.6950	−	21.7632i	1.21534	−	0.701675i
$963$	5.86091	−	12.9622i	0.188865	−	0.417700i
$964$	10.5464	−	18.2669i	0.339677	−	0.588338i
$965$	3.10613	−	2.67061i	0.0999899	−	0.0859699i
$966$	100.540	−	78.0845i	3.23481	−	2.51233i
$967$	12.8319	−	35.2554i	0.412647	−	1.13374i	−0.543131	−	0.839648i	$-0.682761\pi$
$967$	12.8319	−	35.2554i	0.412647	−	1.13374i	0.955778	−	0.294090i	$-0.0950166\pi$
$968$	22.8710	−	4.03277i	0.735102	−	0.129618i
$969$	−5.49345	+	25.4832i	−0.176475	+	0.818637i
$970$	−87.8460	+	16.5804i	−2.82057	+	0.532364i
$971$	−28.3696			−0.910424			−0.455212	−	0.890383i	$-0.650437\pi$
$971$	−28.3696			−0.910424			−0.455212	+	0.890383i	$0.650437\pi$
$972$	35.6851	−	29.0772i	1.14460	−	0.932652i
$973$		−	81.1899i		−	2.60283i
$974$	−29.2462	−	24.5405i	−0.937110	−	0.786329i
$975$	29.4139	+	0.404672i	0.941998	+	0.0129599i
$976$	0.914205	+	5.18471i	0.0292630	+	0.165959i
$977$	−7.34198	+	20.1719i	−0.234891	+	0.645357i	0.765108	+	0.643902i	$0.222685\pi$
$977$	−7.34198	+	20.1719i	−0.234891	+	0.645357i	−0.999999	+	0.00145531i	$0.999537\pi$
$978$	−32.5023	−	41.8491i	−1.03931	−	1.33819i
$979$	0.148996	−	0.844997i	0.00476192	−	0.0270062i
$980$	15.4578	+	40.9327i	0.493780	+	1.30755i
$981$	−3.82630	−	1.73008i	−0.122164	−	0.0552373i
$982$	−67.3819	+	38.9030i	−2.15024	+	1.24144i
$983$	−5.05959	−	13.9011i	−0.161376	−	0.443377i	0.832480	−	0.554055i	$-0.186920\pi$
$983$	−5.05959	−	13.9011i	−0.161376	−	0.443377i	−0.993856	+	0.110678i	$0.964698\pi$
$984$	7.50506	+	0.283748i	0.239253	+	0.00904555i
$985$	−11.9710	+	0.143854i	−0.381429	+	0.00458357i
$986$	19.0666	−	15.9988i	0.607203	−	0.509504i
$987$	−29.7384	−	18.7020i	−0.946583	−	0.595292i
$988$	−13.9546	−	38.3401i	−0.443956	−	1.21976i
$989$	−12.9254	−	22.3875i	−0.411005	−	0.711881i
$990$	−0.781800	+	3.22127i	−0.0248472	+	0.102379i
$991$	15.3617	−	26.6073i	0.487981	−	0.845208i	−0.511923	−	0.859031i	$-0.671067\pi$
$991$	15.3617	−	26.6073i	0.487981	−	0.845208i	0.999904	+	0.0138231i	$0.00440018\pi$
$992$	−23.0882	−	4.07107i	−0.733050	−	0.129257i
$993$	−12.9088	+	31.6870i	−0.409647	+	1.00556i
$994$	20.8277	+	7.58065i	0.660614	+	0.240444i
$995$	25.7950	+	14.4823i	0.817756	+	0.459120i
$996$	16.3287	+	14.7879i	0.517394	+	0.468572i
$997$	4.71602	−	5.62033i	0.149358	−	0.177998i	−0.686178	−	0.727434i	$-0.740713\pi$
$997$	4.71602	−	5.62033i	0.149358	−	0.177998i	0.835536	+	0.549436i	$0.185157\pi$
$998$			49.2713i			1.55965i
$999$	29.7266	+	3.38457i	0.940507	+	0.107083i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.p.a.124.14	yes	96
3.2	odd	2		405.2.p.a.289.3		96
5.2	odd	4		675.2.l.h.151.14		96
5.3	odd	4		675.2.l.h.151.3		96
5.4	even	2	inner	135.2.p.a.124.3	yes	96
15.14	odd	2		405.2.p.a.289.14		96
27.5	odd	18		405.2.p.a.199.14		96
27.22	even	9	inner	135.2.p.a.49.3	✓	96
135.22	odd	36		675.2.l.h.76.14		96
135.49	even	18	inner	135.2.p.a.49.14	yes	96
135.59	odd	18		405.2.p.a.199.3		96
135.103	odd	36		675.2.l.h.76.3		96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.p.a.49.3	✓	96	27.22	even	9	inner
135.2.p.a.49.14	yes	96	135.49	even	18	inner
135.2.p.a.124.3	yes	96	5.4	even	2	inner
135.2.p.a.124.14	yes	96	1.1	even	1	trivial
405.2.p.a.199.3		96	135.59	odd	18
405.2.p.a.199.14		96	27.5	odd	18
405.2.p.a.289.3		96	3.2	odd	2
405.2.p.a.289.14		96	15.14	odd	2
675.2.l.h.76.3		96	135.103	odd	36
675.2.l.h.76.14		96	135.22	odd	36
675.2.l.h.151.3		96	5.3	odd	4
675.2.l.h.151.14		96	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.p (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.43054 - 1.70485i) q^{2} +(1.69316 + 0.364996i) q^{3} +(-0.512771 - 2.90807i) q^{4} +(-1.92292 + 1.14122i) q^{5} +(3.04438 - 2.36443i) q^{6} +(-3.63532 - 0.641005i) q^{7} +(-1.83663 - 1.06038i) q^{8} +(2.73356 + 1.23599i) q^{9} +O(q^{10})\)	\(q+(1.43054 - 1.70485i) q^{2} +(1.69316 + 0.364996i) q^{3} +(-0.512771 - 2.90807i) q^{4} +(-1.92292 + 1.14122i) q^{5} +(3.04438 - 2.36443i) q^{6} +(-3.63532 - 0.641005i) q^{7} +(-1.83663 - 1.06038i) q^{8} +(2.73356 + 1.23599i) q^{9} +(-0.805194 + 4.91084i) q^{10} +(0.208643 - 0.0759398i) q^{11} +(0.193233 - 5.11097i) q^{12} +(2.18338 + 2.60206i) q^{13} +(-6.29327 + 5.28068i) q^{14} +(-3.67234 + 1.23041i) q^{15} +(1.11454 - 0.405659i) q^{16} +(-3.20432 + 1.85001i) q^{17} +(6.01762 - 2.89216i) q^{18} +(2.03386 - 3.52275i) q^{19} +(4.30477 + 5.00679i) q^{20} +(-5.92120 - 2.41220i) q^{21} +(0.169005 - 0.464339i) q^{22} +(-8.81046 + 1.55352i) q^{23} +(-2.72267 - 2.46575i) q^{24} +(2.39522 - 4.38895i) q^{25} +7.55951 q^{26} +(4.17720 + 3.09046i) q^{27} +10.9005i q^{28} +(-2.31546 - 1.94290i) q^{29} +(-3.15576 + 8.02092i) q^{30} +(-0.591627 - 3.35529i) q^{31} +(2.35349 - 6.46615i) q^{32} +(0.380983 - 0.0524241i) q^{33} +(-1.42990 + 8.10938i) q^{34} +(7.72195 - 2.91611i) q^{35} +(2.19266 - 8.58314i) q^{36} +(4.98644 - 2.87892i) q^{37} +(-3.09624 - 8.50684i) q^{38} +(2.74707 + 5.20261i) q^{39} +(4.74182 - 0.0569818i) q^{40} +(-1.56627 + 1.31425i) q^{41} +(-12.5829 + 6.64400i) q^{42} +(0.988279 + 2.71527i) q^{43} +(-0.327824 - 0.567808i) q^{44} +(-6.66694 + 0.742883i) q^{45} +(-9.95516 + 17.2428i) q^{46} +(5.41104 + 0.954113i) q^{47} +(2.03515 - 0.280041i) q^{48} +(6.22683 + 2.26638i) q^{49} +(-4.05603 - 10.3620i) q^{50} +(-6.10066 + 1.96280i) q^{51} +(6.44738 - 7.68369i) q^{52} -0.995243i q^{53} +(11.2444 - 2.70047i) q^{54} +(-0.314539 + 0.384134i) q^{55} +(5.99704 + 5.03212i) q^{56} +(4.72944 - 5.22222i) q^{57} +(-6.62468 + 1.16811i) q^{58} +(9.07341 + 3.30245i) q^{59} +(5.46118 + 10.0485i) q^{60} +(-0.770787 + 4.37135i) q^{61} +(-6.56659 - 3.79122i) q^{62} +(-9.14508 - 6.24545i) q^{63} +(-6.47098 - 11.2081i) q^{64} +(-7.16799 - 2.51181i) q^{65} +(0.455635 - 0.724511i) q^{66} +(-9.78823 - 11.6652i) q^{67} +(7.02305 + 8.36974i) q^{68} +(-15.4845 - 0.585432i) q^{69} +(6.07501 - 17.3363i) q^{70} +(-1.34897 - 2.33649i) q^{71} +(-3.70992 - 5.16867i) q^{72} +(1.00694 + 0.581356i) q^{73} +(2.22516 - 12.6195i) q^{74} +(5.65744 - 6.55693i) q^{75} +(-11.2873 - 4.10824i) q^{76} +(-0.807162 + 0.142324i) q^{77} +(12.7994 + 2.75919i) q^{78} +(3.81056 + 3.19744i) q^{79} +(-1.68022 + 2.05198i) q^{80} +(5.94465 + 6.75730i) q^{81} +4.55033i q^{82} +(-2.76861 + 3.29950i) q^{83} +(-3.97863 + 18.4562i) q^{84} +(4.05036 - 7.21426i) q^{85} +(6.04289 + 2.19943i) q^{86} +(-3.21128 - 4.13476i) q^{87} +(-0.463726 - 0.0817674i) q^{88} +(1.93222 - 3.34670i) q^{89} +(-8.27080 + 12.4288i) q^{90} +(-6.26937 - 10.8589i) q^{91} +(9.03550 + 24.8248i) q^{92} +(0.222950 - 5.89697i) q^{93} +(9.36730 - 7.86010i) q^{94} +(0.109294 + 9.09505i) q^{95} +(6.34494 - 10.0892i) q^{96} +(6.14411 + 16.8808i) q^{97} +(12.7715 - 7.37364i) q^{98} +(0.664198 + 0.0502953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9}+O(q^{10}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9	\( 96 q - 12 q^{4} - 9 q^{5} - 6 q^{6} - 18 q^{9} - 3 q^{10} - 6 q^{11} - 18 q^{14} - 21 q^{15} - 24 q^{16} - 6 q^{19} - 57 q^{20} + 24 q^{21} - 30 q^{24} + 3 q^{25} + 48 q^{26} - 30 q^{29} - 51 q^{30} - 30 q^{31} - 24 q^{34} - 12 q^{35} + 54 q^{36} - 6 q^{39} - 9 q^{40} - 12 q^{41} + 78 q^{44} + 45 q^{45} - 6 q^{46} - 30 q^{49} + 84 q^{50} - 90 q^{51} + 108 q^{54} - 12 q^{55} - 96 q^{56} + 66 q^{59} + 84 q^{60} + 6 q^{61} + 45 q^{65} - 150 q^{66} + 24 q^{69} - 33 q^{70} - 90 q^{71} + 66 q^{74} + 39 q^{75} + 12 q^{76} + 24 q^{79} + 30 q^{80} - 54 q^{81} + 198 q^{84} - 21 q^{85} + 18 q^{86} + 96 q^{89} + 90 q^{90} - 6 q^{91} + 24 q^{94} + 87 q^{95} + 42 q^{96} + 36 q^{99}+O(q^{100}) \) 96 * q - 12 * q^4 - 9 * q^5 - 6 * q^6 - 18 * q^9 - 3 * q^10 - 6 * q^11 - 18 * q^14 - 21 * q^15 - 24 * q^16 - 6 * q^19 - 57 * q^20 + 24 * q^21 - 30 * q^24 + 3 * q^25 + 48 * q^26 - 30 * q^29 - 51 * q^30 - 30 * q^31 - 24 * q^34 - 12 * q^35 + 54 * q^36 - 6 * q^39 - 9 * q^40 - 12 * q^41 + 78 * q^44 + 45 * q^45 - 6 * q^46 - 30 * q^49 + 84 * q^50 - 90 * q^51 + 108 * q^54 - 12 * q^55 - 96 * q^56 + 66 * q^59 + 84 * q^60 + 6 * q^61 + 45 * q^65 - 150 * q^66 + 24 * q^69 - 33 * q^70 - 90 * q^71 + 66 * q^74 + 39 * q^75 + 12 * q^76 + 24 * q^79 + 30 * q^80 - 54 * q^81 + 198 * q^84 - 21 * q^85 + 18 * q^86 + 96 * q^89 + 90 * q^90 - 6 * q^91 + 24 * q^94 + 87 * q^95 + 42 * q^96 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more