LMFDB - Embedded newform 135.2.q.a.113.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

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("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, 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:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.4
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.75676 - 0.153697i) q^{2} +(0.305576 + 1.70488i) q^{3} +(1.09297 + 0.192720i) q^{4} +(0.131866 - 2.23218i) q^{5} +(-0.274789 - 3.04204i) q^{6} +(2.75943 + 1.93217i) q^{7} +(1.51630 + 0.406292i) q^{8} +(-2.81325 + 1.04194i) q^{9} +O(q^{10})$	\(q+(-1.75676 - 0.153697i) q^{2} +(0.305576 + 1.70488i) q^{3} +(1.09297 + 0.192720i) q^{4} +(0.131866 - 2.23218i) q^{5} +(-0.274789 - 3.04204i) q^{6} +(2.75943 + 1.93217i) q^{7} +(1.51630 + 0.406292i) q^{8} +(-2.81325 + 1.04194i) q^{9} +(-0.574736 + 3.90113i) q^{10} +(-1.11880 + 3.07388i) q^{11} +(0.00542048 + 1.92227i) q^{12} +(0.506571 + 5.79013i) q^{13} +(-4.55068 - 3.81848i) q^{14} +(3.84589 - 0.457283i) q^{15} +(-4.68713 - 1.70598i) q^{16} +(1.11325 - 0.298295i) q^{17} +(5.10234 - 1.39806i) q^{18} +(6.40749 - 3.69937i) q^{19} +(0.574311 - 2.41429i) q^{20} +(-2.45091 + 5.29492i) q^{21} +(2.43791 - 5.22812i) q^{22} +(1.09807 + 1.56820i) q^{23} +(-0.229334 + 2.70927i) q^{24} +(-4.96522 - 0.588699i) q^{25} -10.2497i q^{26} +(-2.63605 - 4.47786i) q^{27} +(2.64360 + 2.64360i) q^{28} +(0.381851 - 0.320411i) q^{29} +(-6.82659 + 0.212236i) q^{30} +(0.573116 - 3.25030i) q^{31} +(5.12653 + 2.39054i) q^{32} +(-5.58249 - 0.968121i) q^{33} +(-2.00157 + 0.352930i) q^{34} +(4.67682 - 5.90474i) q^{35} +(-3.27559 + 0.596642i) q^{36} +(-1.17991 - 4.40348i) q^{37} +(-11.8250 + 5.51409i) q^{38} +(-9.71669 + 2.63297i) q^{39} +(1.10686 - 3.33107i) q^{40} +(-1.39279 + 1.65986i) q^{41} +(5.11947 - 8.92522i) q^{42} +(-1.68889 - 3.62184i) q^{43} +(-1.81521 + 3.14404i) q^{44} +(1.95483 + 6.41706i) q^{45} +(-1.68801 - 2.92372i) q^{46} +(-2.84791 + 4.06724i) q^{47} +(1.47621 - 8.51231i) q^{48} +(1.48701 + 4.08553i) q^{49} +(8.63222 + 1.79734i) q^{50} +(0.848742 + 1.80681i) q^{51} +(-0.562207 + 6.42605i) q^{52} +(1.25033 - 1.25033i) q^{53} +(3.94268 + 8.27168i) q^{54} +(6.71392 + 2.90271i) q^{55} +(3.39910 + 4.05089i) q^{56} +(8.26496 + 9.79358i) q^{57} +(-0.720066 + 0.504196i) q^{58} +(9.92422 - 3.61212i) q^{59} +(4.29157 + 0.241384i) q^{60} +(-1.82504 - 10.3503i) q^{61} +(-1.50639 + 5.62192i) q^{62} +(-9.77616 - 2.56051i) q^{63} +(0.000691655 + 0.000399327i) q^{64} +(12.9914 - 0.367231i) q^{65} +(9.65830 + 2.55877i) q^{66} +(-5.82623 + 0.509729i) q^{67} +(1.27424 - 0.111481i) q^{68} +(-2.33806 + 2.35128i) q^{69} +(-9.12360 + 9.65440i) q^{70} +(-6.62671 - 3.82593i) q^{71} +(-4.68906 + 0.436900i) q^{72} +(-1.84806 + 6.89704i) q^{73} +(1.39602 + 7.91721i) q^{74} +(-0.513592 - 8.64501i) q^{75} +(7.71612 - 2.80844i) q^{76} +(-9.02653 + 6.32044i) q^{77} +(17.4746 - 3.13207i) q^{78} +(-5.08874 - 6.06452i) q^{79} +(-4.42611 + 10.2375i) q^{80} +(6.82871 - 5.86248i) q^{81} +(2.70191 - 2.70191i) q^{82} +(0.544416 - 6.22270i) q^{83} +(-3.69920 + 5.31485i) q^{84} +(-0.519047 - 2.52431i) q^{85} +(2.41031 + 6.62228i) q^{86} +(0.662947 + 0.553100i) q^{87} +(-2.94533 + 4.20637i) q^{88} +(0.260380 + 0.450992i) q^{89} +(-2.44788 - 11.5737i) q^{90} +(-9.78968 + 16.9562i) q^{91} +(0.897929 + 1.92562i) q^{92} +(5.71652 - 0.0161196i) q^{93} +(5.62822 - 6.70745i) q^{94} +(-7.41270 - 14.7905i) q^{95} +(-2.50905 + 9.47063i) q^{96} +(4.27963 - 1.99563i) q^{97} +(-1.98439 - 7.40585i) q^{98} +(-0.0553442 - 9.81332i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	$ 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) $ 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.75676	−	0.153697i	−1.24222	−	0.108680i	−0.552967	−	0.833203i	$-0.686504\pi$
$2$	−1.75676	−	0.153697i	−1.24222	−	0.108680i	−0.689250	+	0.724523i	$0.742060\pi$
$3$	0.305576	+	1.70488i	0.176424	+	0.984314i
$3$	0.305576	+	1.70488i	0.176424	+	0.984314i
$4$	1.09297	+	0.192720i	0.546484	+	0.0963599i
$5$	0.131866	−	2.23218i	0.0589725	−	0.998260i
$5$	0.131866	−	2.23218i	0.0589725	−	0.998260i
$6$	−0.274789	−	3.04204i	−0.112182	−	1.24191i
$7$	2.75943	+	1.93217i	1.04297	+	0.730292i	0.963815	−	0.266570i	$-0.0858904\pi$
$7$	2.75943	+	1.93217i	1.04297	+	0.730292i	0.0791502	+	0.996863i	$0.474779\pi$
$8$	1.51630	+	0.406292i	0.536093	+	0.143646i
$9$	−2.81325	+	1.04194i	−0.937749	+	0.347314i
$10$	−0.574736	+	3.90113i	−0.181747	+	1.23365i
$11$	−1.11880	+	3.07388i	−0.337332	+	0.926811i	0.648817	+	0.760945i	$0.275264\pi$
$11$	−1.11880	+	3.07388i	−0.337332	+	0.926811i	−0.986148	+	0.165866i	$0.946958\pi$
$12$	0.00542048	+	1.92227i	0.00156476	+	0.554912i
$13$	0.506571	+	5.79013i	0.140497	+	1.60589i	0.659893	+	0.751359i	$0.270601\pi$
$13$	0.506571	+	5.79013i	0.140497	+	1.60589i	−0.519396	+	0.854534i	$0.673843\pi$
$14$	−4.55068	−	3.81848i	−1.21622	−	1.02053i
$15$	3.84589	−	0.457283i	0.993005	−	0.118070i
$16$	−4.68713	−	1.70598i	−1.17178	−	0.426494i
$17$	1.11325	−	0.298295i	0.270003	−	0.0723472i	−0.121277	−	0.992619i	$-0.538699\pi$
$17$	1.11325	−	0.298295i	0.270003	−	0.0723472i	0.391280	+	0.920271i	$0.372032\pi$
$18$	5.10234	−	1.39806i	1.20263	−	0.329525i
$19$	6.40749	−	3.69937i	1.46998	−	0.848693i	0.470546	−	0.882375i	$-0.344057\pi$
$19$	6.40749	−	3.69937i	1.46998	−	0.848693i	0.999433	+	0.0336827i	$0.0107236\pi$
$20$	0.574311	−	2.41429i	0.128420	−	0.539851i
$21$	−2.45091	+	5.29492i	−0.534833	+	1.15545i
$22$	2.43791	−	5.22812i	0.519765	−	1.11464i
$23$	1.09807	+	1.56820i	0.228963	+	0.326993i	0.917151	−	0.398539i	$-0.130483\pi$
$23$	1.09807	+	1.56820i	0.228963	+	0.326993i	−0.688189	+	0.725532i	$0.741594\pi$
$24$	−0.229334	+	2.70927i	−0.0468126	+	0.553027i
$25$	−4.96522	−	0.588699i	−0.993044	−	0.117740i
$26$		−	10.2497i		−	2.01014i
$27$	−2.63605	−	4.47786i	−0.507308	−	0.861765i
$28$	2.64360	+	2.64360i	0.499593	+	0.499593i
$29$	0.381851	−	0.320411i	0.0709079	−	0.0594988i	−0.606645	−	0.794973i	$-0.707485\pi$
$29$	0.381851	−	0.320411i	0.0709079	−	0.0594988i	0.677553	+	0.735474i	$0.263041\pi$
$30$	−6.82659	+	0.212236i	−1.24636	+	0.0387488i
$31$	0.573116	−	3.25030i	0.102935	−	0.583772i	−0.889090	−	0.457732i	$-0.848662\pi$
$31$	0.573116	−	3.25030i	0.102935	−	0.583772i	0.992025	−	0.126040i	$-0.0402269\pi$
$32$	5.12653	+	2.39054i	0.906251	+	0.422592i
$33$	−5.58249	−	0.968121i	−0.971787	−	0.168528i
$34$	−2.00157	+	0.352930i	−0.343266	+	0.0605270i
$35$	4.67682	−	5.90474i	0.790528	−	0.998083i
$36$	−3.27559	+	0.596642i	−0.545932	+	0.0994403i
$37$	−1.17991	−	4.40348i	−0.193976	−	0.723928i	−0.992530	−	0.122004i	$-0.961068\pi$
$37$	−1.17991	−	4.40348i	−0.193976	−	0.723928i	0.798554	−	0.601924i	$-0.205599\pi$
$38$	−11.8250	+	5.51409i	−1.91827	+	0.894503i
$39$	−9.71669	+	2.63297i	−1.55592	+	0.421612i
$40$	1.10686	−	3.33107i	0.175011	−	0.526689i
$41$	−1.39279	+	1.65986i	−0.217517	+	0.259226i	−0.863758	−	0.503907i	$-0.831895\pi$
$41$	−1.39279	+	1.65986i	−0.217517	+	0.259226i	0.646241	+	0.763133i	$0.276340\pi$
$42$	5.11947	−	8.92522i	0.789952	−	1.37719i
$43$	−1.68889	−	3.62184i	−0.257554	−	0.552325i	0.734431	−	0.678683i	$-0.237449\pi$
$43$	−1.68889	−	3.62184i	−0.257554	−	0.552325i	−0.991985	+	0.126358i	$0.959671\pi$
$44$	−1.81521	+	3.14404i	−0.273654	+	0.473982i
$45$	1.95483	+	6.41706i	0.291408	+	0.956599i
$46$	−1.68801	−	2.92372i	−0.248884	−	0.431080i
$47$	−2.84791	+	4.06724i	−0.415410	+	0.593268i	−0.971262	−	0.238014i	$-0.923504\pi$
$47$	−2.84791	+	4.06724i	−0.415410	+	0.593268i	0.555851	+	0.831282i	$0.312392\pi$
$48$	1.47621	−	8.51231i	0.213073	−	1.22865i
$49$	1.48701	+	4.08553i	0.212430	+	0.583647i
$50$	8.63222	+	1.79734i	1.22078	+	0.254182i
$51$	0.848742	+	1.80681i	0.118848	+	0.253004i
$52$	−0.562207	+	6.42605i	−0.0779641	+	0.891133i
$53$	1.25033	−	1.25033i	0.171746	−	0.171746i	−0.616000	−	0.787746i	$-0.711248\pi$
$53$	1.25033	−	1.25033i	0.171746	−	0.171746i	0.787746	+	0.616000i	$0.211248\pi$
$54$	3.94268	+	8.27168i	0.536530	+	1.12563i
$55$	6.71392	+	2.90271i	0.905305	+	0.391401i
$56$	3.39910	+	4.05089i	0.454223	+	0.541322i
$57$	8.26496	+	9.79358i	1.09472	+	1.29719i
$58$	−0.720066	+	0.504196i	−0.0945493	+	0.0662041i
$59$	9.92422	−	3.61212i	1.29202	−	0.470258i	0.397633	−	0.917545i	$-0.369832\pi$
$59$	9.92422	−	3.61212i	1.29202	−	0.470258i	0.894391	+	0.447286i	$0.147609\pi$
$60$	4.29157	+	0.241384i	0.554039	+	0.0311625i
$61$	−1.82504	−	10.3503i	−0.233672	−	1.32522i	−0.845392	−	0.534146i	$-0.820633\pi$
$61$	−1.82504	−	10.3503i	−0.233672	−	1.32522i	0.611720	−	0.791074i	$-0.290478\pi$
$62$	−1.50639	+	5.62192i	−0.191312	+	0.713985i
$63$	−9.77616	−	2.56051i	−1.23168	−	0.322594i
$64$	0.000691655	0	0.000399327i	8.64569e−5	0	4.99159e-5i
$65$	12.9914	−	0.367231i	1.61138	−	0.0455494i
$66$	9.65830	+	2.55877i	1.18885	+	0.314962i
$67$	−5.82623	+	0.509729i	−0.711787	+	0.0622733i	−0.437298	−	0.899317i	$-0.644064\pi$
$67$	−5.82623	+	0.509729i	−0.711787	+	0.0622733i	−0.274490	+	0.961590i	$0.588509\pi$
$68$	1.27424	−	0.111481i	0.154524	−	0.0135191i
$69$	−2.33806	+	2.35128i	−0.281469	+	0.283061i
$70$	−9.12360	+	9.65440i	−1.09048	+	1.15392i
$71$	−6.62671	−	3.82593i	−0.786446	−	0.454055i	0.0522640	−	0.998633i	$-0.483356\pi$
$71$	−6.62671	−	3.82593i	−0.786446	−	0.454055i	−0.838710	+	0.544579i	$0.816690\pi$
$72$	−4.68906	+	0.436900i	−0.552611	+	0.0514892i
$73$	−1.84806	+	6.89704i	−0.216299	+	0.807238i	0.769407	+	0.638759i	$0.220552\pi$
$73$	−1.84806	+	6.89704i	−0.216299	+	0.807238i	−0.985705	+	0.168478i	$0.946115\pi$
$74$	1.39602	+	7.91721i	0.162284	+	0.920357i
$75$	−0.513592	−	8.64501i	−0.0593045	−	0.998240i
$76$	7.71612	−	2.80844i	0.885100	−	0.322150i
$77$	−9.02653	+	6.32044i	−1.02867	+	0.720281i
$78$	17.4746	−	3.13207i	1.97861	−	0.354637i
$79$	−5.08874	−	6.06452i	−0.572528	−	0.682312i	0.399620	−	0.916681i	$-0.369142\pi$
$79$	−5.08874	−	6.06452i	−0.572528	−	0.682312i	−0.972148	+	0.234369i	$0.924698\pi$
$80$	−4.42611	+	10.2375i	−0.494854	+	1.14459i
$81$	6.82871	−	5.86248i	0.758746	−	0.651387i
$82$	2.70191	−	2.70191i	0.298375	−	0.298375i
$83$	0.544416	−	6.22270i	0.0597574	−	0.683031i	−0.905948	−	0.423389i	$-0.860840\pi$
$83$	0.544416	−	6.22270i	0.0597574	−	0.683031i	0.965705	−	0.259641i	$-0.0836042\pi$
$84$	−3.69920	+	5.31485i	−0.403616	+	0.579897i
$85$	−0.519047	−	2.52431i	−0.0562985	−	0.273800i
$86$	2.41031	+	6.62228i	0.259911	+	0.714099i
$87$	0.662947	+	0.553100i	0.0710754	+	0.0592986i
$88$	−2.94533	+	4.20637i	−0.313974	+	0.448401i
$89$	0.260380	+	0.450992i	0.0276002	+	0.0478050i	0.879496	−	0.475907i	$-0.157880\pi$
$89$	0.260380	+	0.450992i	0.0276002	+	0.0478050i	−0.851895	+	0.523712i	$0.824547\pi$
$90$	−2.44788	−	11.5737i	−0.258029	−	1.21997i
$91$	−9.78968	+	16.9562i	−1.02624	+	1.77750i
$92$	0.897929	+	1.92562i	0.0936156	+	0.200759i
$93$	5.71652	−	0.0161196i	0.592775	−	0.00167153i
$94$	5.62822	−	6.70745i	0.580506	−	0.691820i
$95$	−7.41270	−	14.7905i	−0.760527	−	1.51747i
$96$	−2.50905	+	9.47063i	−0.256078	+	0.966592i
$97$	4.27963	−	1.99563i	0.434531	−	0.202625i	−0.193029	−	0.981193i	$-0.561831\pi$
$97$	4.27963	−	1.99563i	0.434531	−	0.202625i	0.627560	+	0.778568i	$0.284054\pi$
$98$	−1.98439	−	7.40585i	−0.200454	−	0.748103i
$99$	−0.0553442	−	9.81332i	−0.00556230	−	0.986276i
$100$	−5.31338	−	1.60033i	−0.531338	−	0.160033i
$101$	−6.92843	+	1.22167i	−0.689404	+	0.121561i	−0.507366	−	0.861731i	$-0.669381\pi$
$101$	−6.92843	+	1.22167i	−0.689404	+	0.121561i	−0.182038	+	0.983291i	$0.558270\pi$
$102$	−1.21333	−	3.30459i	−0.120138	−	0.327203i
$103$	6.34471	+	2.95859i	0.625163	+	0.291518i	0.709268	−	0.704938i	$-0.249025\pi$
$103$	6.34471	+	2.95859i	0.625163	+	0.291518i	−0.0841052	+	0.996457i	$0.526803\pi$
$104$	−1.58437	+	8.98539i	−0.155360	+	0.881090i
$105$	11.4960	+	6.16909i	1.12190	+	0.602041i
$106$	−2.38870	+	2.00436i	−0.232011	+	0.194680i
$107$	−3.17818	−	3.17818i	−0.307247	−	0.307247i	0.536594	−	0.843841i	$-0.319711\pi$
$107$	−3.17818	−	3.17818i	−0.307247	−	0.307247i	−0.843841	+	0.536594i	$0.819711\pi$
$108$	−2.01815	−	5.40218i	−0.194196	−	0.519825i
$109$			3.14715i			0.301442i	0.988576	+	0.150721i	$0.0481595\pi$
$109$			3.14715i			0.301442i	−0.988576	+	0.150721i	$0.951840\pi$
$110$	−11.3486	−	6.13127i	−1.08205	−	0.584593i
$111$	7.14687	−	3.35721i	0.678351	−	0.318652i
$112$	−9.63755	−	13.7639i	−0.910663	−	1.30056i
$113$	0.190621	−	0.408788i	0.0179321	−	0.0384556i	−0.897138	−	0.441751i	$-0.854357\pi$
$113$	0.190621	−	0.408788i	0.0179321	−	0.0384556i	0.915070	+	0.403295i	$0.132135\pi$
$114$	−13.0143	−	18.4753i	−1.21890	−	1.73037i
$115$	3.64530	−	2.24429i	0.339926	−	0.209281i
$116$	0.479100	−	0.276609i	0.0444833	−	0.0256825i
$117$	−7.45809	−	15.7612i	−0.689501	−	1.45713i
$118$	−17.9897	+	4.82031i	−1.65608	+	0.443746i
$119$	3.64830	+	1.32787i	0.334439	+	0.121726i
$120$	6.01732	+	0.869175i	0.549304	+	0.0793445i
$121$	0.229444	+	0.192526i	0.0208585	+	0.0175024i
$122$	1.61535	+	18.4635i	0.146247	+	1.67161i
$123$	−3.25546	−	1.86732i	−0.293535	−	0.168371i
$124$	1.25280	−	3.44203i	0.112504	−	0.309103i
$125$	−1.96883	+	11.0056i	−0.176097	+	0.984373i
$126$	16.7808	+	6.00077i	1.49496	+	0.534591i
$127$	0.534026	+	0.143092i	0.0473871	+	0.0126973i	0.282435	−	0.959287i	$-0.408858\pi$
$127$	0.534026	+	0.143092i	0.0473871	+	0.0126973i	−0.235048	+	0.971984i	$0.575525\pi$
$128$	−9.26822	−	6.48968i	−0.819203	−	0.573612i
$129$	5.65873	−	3.98611i	0.498223	−	0.350957i
$130$	−22.8792	−	1.35160i	−2.00664	−	0.118543i
$131$	14.1236	+	2.49037i	1.23398	+	0.217585i	0.752336	−	0.658780i	$-0.228927\pi$
$131$	14.1236	+	2.49037i	1.23398	+	0.217585i	0.481648	+	0.876365i	$0.340038\pi$
$132$	−5.91491	−	2.13398i	−0.514827	−	0.185739i
$133$	24.8288	+	2.17224i	2.15293	+	0.188357i
$134$	10.3136			0.890962
$135$	−10.3430	+	5.29365i	−0.890182	+	0.455605i
$136$	1.80922			0.155139
$137$	3.37255	+	0.295060i	0.288136	+	0.0252087i	0.230308	−	0.973118i	$-0.426027\pi$
$137$	3.37255	+	0.295060i	0.288136	+	0.0252087i	0.0578286	+	0.998327i	$0.481582\pi$
$138$	4.46879	−	3.77128i	0.380409	−	0.321033i
$139$	5.42140	+	0.955940i	0.459837	+	0.0810818i	0.398768	−	0.917052i	$-0.369438\pi$
$139$	5.42140	+	0.955940i	0.459837	+	0.0810818i	0.0610693	+	0.998134i	$0.480549\pi$
$140$	6.24958	−	5.55238i	0.528186	−	0.469262i
$141$	−7.80442	−	3.61250i	−0.657250	−	0.304227i
$142$	11.0535	+	7.73975i	0.927590	+	0.649505i
$143$	−18.3649	−	4.92087i	−1.53575	−	0.411504i
$144$	14.9636	−	0.0843901i	1.24696	−	0.00703251i
$145$	−0.664860	−	0.894609i	−0.0552136	−	0.0742933i
$146$	4.30665	−	11.8324i	0.356420	−	0.979257i
$147$	−6.51095	+	3.78362i	−0.537014	+	0.312068i
$148$	−0.440966	−	5.04026i	−0.0362472	−	0.414307i
$149$	−10.1897	−	8.55016i	−0.834771	−	0.700456i	0.121610	−	0.992578i	$-0.461194\pi$
$149$	−10.1897	−	8.55016i	−0.834771	−	0.700456i	−0.956381	+	0.292122i	$0.905639\pi$
$150$	−0.426451	+	15.2662i	−0.0348196	+	1.24648i
$151$	13.7660	+	5.01040i	1.12026	+	0.407741i	0.834747	−	0.550634i	$-0.185614\pi$
$151$	13.7660	+	5.01040i	1.12026	+	0.407741i	0.285512	+	0.958375i	$0.407836\pi$
$152$	11.2187	−	3.00604i	0.909957	−	0.243822i
$153$	−2.82105	+	1.99912i	−0.228068	+	0.161620i
$154$	16.8289	−	9.71616i	1.35611	−	0.782950i
$155$	−7.17968	−	1.70790i	−0.576686	−	0.137182i
$156$	−11.1275	+	1.00515i	−0.890910	+	0.0804766i
$157$	−2.34570	+	5.03036i	−0.187207	+	0.401467i	−0.977402	−	0.211389i	$-0.932201\pi$
$157$	−2.34570	+	5.03036i	−0.187207	+	0.401467i	0.790195	+	0.612855i	$0.209979\pi$
$158$	8.00759	+	11.4360i	0.637050	+	0.909802i
$159$	2.51373	+	1.74959i	0.199352	+	0.138752i
$160$	6.01213	−	11.1281i	0.475300	−	0.879753i
$161$			6.44900i			0.508252i
$162$	−12.8975	+	9.24943i	−1.01332	+	0.726704i
$163$	5.06235	+	5.06235i	0.396514	+	0.396514i	0.877002	−	0.480488i	$-0.159540\pi$
$163$	5.06235	+	5.06235i	0.396514	+	0.396514i	−0.480488	+	0.877002i	$0.659540\pi$
$164$	−1.84216	+	1.54575i	−0.143848	+	0.120703i
$165$	−2.89716	+	12.3334i	−0.225544	+	0.960157i
$166$	−1.91282	+	10.8481i	−0.148463	+	0.841978i
$167$	−12.7047	−	5.92432i	−0.983123	−	0.458438i	−0.136505	−	0.990639i	$-0.543587\pi$
$167$	−12.7047	−	5.92432i	−0.983123	−	0.458438i	−0.846618	+	0.532202i	$0.821365\pi$
$168$	−5.86760	+	7.03291i	−0.452695	+	0.542601i
$169$	−20.4665	+	3.60879i	−1.57434	+	0.277599i
$170$	0.523863	+	4.51439i	0.0401784	+	0.346238i
$171$	−14.1713	+	17.0835i	−1.08371	+	1.30641i
$172$	−1.14791	−	4.28404i	−0.0875269	−	0.326655i
$173$	8.87248	−	4.13731i	0.674563	−	0.314554i	−0.0549816	−	0.998487i	$-0.517510\pi$
$173$	8.87248	−	4.13731i	0.674563	−	0.314554i	0.729544	+	0.683934i	$0.239732\pi$
$174$	−1.07963	−	1.07356i	−0.0818465	−	0.0813862i
$175$	−12.5637	−	11.2181i	−0.949727	−	0.848011i
$176$	10.4879	−	12.4990i	0.790558	−	0.942151i
$177$	9.19085	+	15.8159i	0.690827	+	1.18879i
$178$	−0.388110	−	0.832304i	−0.0290900	−	0.0623838i
$179$	5.82103	−	10.0823i	0.435084	−	0.753588i	−0.562218	−	0.826989i	$-0.690052\pi$
$179$	5.82103	−	10.0823i	0.435084	−	0.753588i	0.997303	+	0.0734009i	$0.0233853\pi$
$180$	0.899869	+	7.39038i	0.0670723	+	0.550846i
$181$	−10.5182	−	18.2180i	−0.781810	−	1.35413i	−0.930886	−	0.365309i	$-0.880963\pi$
$181$	−10.5182	−	18.2180i	−0.781810	−	1.35413i	0.149076	−	0.988826i	$-0.452370\pi$
$182$	19.8042	−	28.2834i	1.46799	−	2.09650i
$183$	17.0884	−	6.27428i	1.26321	−	0.463808i
$184$	1.02785	+	2.82400i	0.0757743	+	0.208188i
$185$	−9.98494	+	2.05309i	−0.734108	+	0.150947i
$186$	−10.0450	−	0.850291i	−0.736537	−	0.0623464i
$187$	−0.328585	+	3.75574i	−0.0240285	+	0.274647i
$188$	−3.89651	+	3.89651i	−0.284182	+	0.284182i
$189$	1.37801	−	17.4496i	0.100235	−	1.26927i
$190$	10.7491	+	27.1226i	0.779822	+	1.96768i
$191$	16.1454	+	19.2414i	1.16824	+	1.39226i	0.903854	+	0.427841i	$0.140726\pi$
$191$	16.1454	+	19.2414i	1.16824	+	1.39226i	0.264388	+	0.964416i	$0.414830\pi$
$192$	−0.000469453		0.00130122i	−3.38798e−5		9.39072e-5i
$193$	−3.27354	+	2.29216i	−0.235635	+	0.164993i	−0.685430	−	0.728138i	$-0.740386\pi$
$193$	−3.27354	+	2.29216i	−0.235635	+	0.164993i	0.449795	+	0.893132i	$0.351497\pi$
$194$	−7.82501	+	2.84807i	−0.561803	+	0.204480i
$195$	4.59594	+	22.0366i	0.329122	+	1.57807i
$196$	0.837894	+	4.75193i	0.0598496	+	0.339424i
$197$	2.68314	−	10.0136i	0.191166	−	0.713441i	−0.802060	−	0.597243i	$-0.796263\pi$
$197$	2.68314	−	10.0136i	0.191166	−	0.713441i	0.993226	−	0.116198i	$-0.0370707\pi$
$198$	−1.41105	+	17.2482i	−0.100279	+	1.22577i
$199$	−10.6933	−	6.17378i	−0.758027	−	0.437647i	0.0705597	−	0.997508i	$-0.477521\pi$
$199$	−10.6933	−	6.17378i	−0.758027	−	0.437647i	−0.828587	+	0.559860i	$0.810855\pi$
$200$	−7.28959	−	2.90997i	−0.515452	−	0.205766i
$201$	−2.64938	−	9.77727i	−0.186873	−	0.689636i
$202$	12.3593	−	1.08130i	0.869601	−	0.0760802i
$203$	1.67278	−	0.146349i	0.117406	−	0.0102717i
$204$	0.579439	+	2.13836i	0.0405689	+	0.149715i
$205$	3.52143	+	3.32782i	0.245948	+	0.232425i
$206$	−10.6914	−	6.17269i	−0.744906	−	0.430072i
$207$	−4.72311	−	3.26762i	−0.328279	−	0.227115i
$208$	7.50345	−	28.0033i	0.520271	−	1.94168i
$209$	4.20271	+	23.8347i	0.290707	+	1.64868i
$210$	−19.2476	−	12.6045i	−1.32821	−	0.869794i
$211$	8.83540	−	3.21582i	0.608254	−	0.221386i	−0.0194850	−	0.999810i	$-0.506203\pi$
$211$	8.83540	−	3.21582i	0.608254	−	0.221386i	0.627739	+	0.778424i	$0.283980\pi$
$212$	1.60753	−	1.12561i	0.110406	−	0.0773070i
$213$	4.49780	−	12.4669i	0.308184	−	0.854216i
$214$	5.09483	+	6.07178i	0.348275	+	0.415058i
$215$	−8.30729	+	3.29230i	−0.566553	+	0.224533i
$216$	−2.17773	−	7.86079i	−0.148176	−	0.534859i
$217$	7.86162	−	7.86162i	0.533682	−	0.533682i
$218$	0.483706	−	5.52878i	0.0327607	−	0.374456i
$219$	−12.3234	−	1.04315i	−0.832736	−	0.0704894i
$220$	6.77869	+	4.46647i	0.457019	+	0.301129i
$221$	2.29111	+	6.29477i	0.154117	+	0.423432i
$222$	−13.0713	+	4.79936i	−0.877290	+	0.322112i
$223$	8.07893	−	11.5379i	0.541005	−	0.772635i	−0.451833	−	0.892102i	$-0.649230\pi$
$223$	8.07893	−	11.5379i	0.541005	−	0.772635i	0.992838	+	0.119467i	$0.0381186\pi$
$224$	9.52736	+	16.5019i	0.636573	+	1.10258i
$225$	14.5818	−	3.51732i	0.972119	−	0.234488i
$226$	−0.397705	+	0.688845i	−0.0264549	+	0.0458213i
$227$	−11.1767	−	23.9686i	−0.741825	−	1.59085i	−0.805301	−	0.592866i	$-0.797996\pi$
$227$	−11.1767	−	23.9686i	−0.741825	−	1.59085i	0.0634761	−	0.997983i	$-0.479781\pi$
$228$	7.14592	+	12.2969i	0.473250	+	0.814382i
$229$	−6.42008	+	7.65115i	−0.424251	+	0.505602i	−0.935254	−	0.353976i	$-0.884829\pi$
$229$	−6.42008	+	7.65115i	−0.424251	+	0.505602i	0.511004	+	0.859579i	$0.329274\pi$
$230$	−6.74886	+	3.38240i	−0.445007	+	0.223029i
$231$	−13.5339	−	13.4578i	−0.890465	−	0.885458i
$232$	0.709181	−	0.330696i	0.0465600	−	0.0217113i
$233$	7.01401	+	26.1766i	0.459503	+	1.71489i	0.674500	+	0.738274i	$0.264359\pi$
$233$	7.01401	+	26.1766i	0.459503	+	1.71489i	−0.214997	+	0.976615i	$0.568974\pi$
$234$	10.6796	+	28.8350i	0.698149	+	1.88500i
$235$	8.70325	+	6.89337i	0.567737	+	0.449674i
$236$	11.5430	−	2.03534i	0.751385	−	0.132489i
$237$	8.78430	−	10.5289i	0.570601	−	0.683924i
$238$	−6.20510	−	2.89348i	−0.402217	−	0.187557i
$239$	4.31982	−	24.4989i	0.279426	−	1.58470i	−0.445117	−	0.895472i	$-0.646838\pi$
$239$	4.31982	−	24.4989i	0.279426	−	1.58470i	0.724543	−	0.689230i	$-0.242051\pi$
$240$	−18.8063	−	4.41765i	−1.21394	−	0.285158i
$241$	−21.8499	+	18.3342i	−1.40747	+	1.18101i	−0.449808	+	0.893125i	$0.648508\pi$
$241$	−21.8499	+	18.3342i	−1.40747	+	1.18101i	−0.957665	+	0.287885i	$0.907048\pi$
$242$	−0.373487	−	0.373487i	−0.0240087	−	0.0240087i
$243$	12.0815	+	9.85071i	0.775031	+	0.631924i
$244$		−	11.6643i		−	0.746728i
$245$	9.31571	−	2.78053i	0.595159	−	0.177641i
$246$	5.43207	+	3.78079i	0.346336	+	0.241054i
$247$	24.6656	+	35.2262i	1.56944	+	2.24139i
$248$	2.18959	−	4.69559i	0.139039	−	0.298170i
$249$	10.7753	−	0.973345i	0.682859	−	0.0616832i
$250$	5.15028	−	19.0316i	0.325732	−	1.20367i
$251$	9.61601	−	5.55181i	0.606957	−	0.350427i	−0.164816	−	0.986324i	$-0.552703\pi$
$251$	9.61601	−	5.55181i	0.606957	−	0.350427i	0.771774	+	0.635897i	$0.219370\pi$
$252$	−10.1916	−	4.68262i	−0.642009	−	0.294977i
$253$	−6.04899	+	1.62082i	−0.380297	+	0.101900i
$254$	−0.916163	−	0.333456i	−0.0574852	−	0.0209229i
$255$	4.14505	−	1.65628i	0.259573	−	0.103720i
$256$	15.2834	+	12.8243i	0.955211	+	0.801518i
$257$	2.45897	+	28.1062i	0.153386	+	1.75321i	0.549941	+	0.835203i	$0.314650\pi$
$257$	2.45897	+	28.1062i	0.153386	+	1.75321i	−0.396555	+	0.918011i	$0.629794\pi$
$258$	−10.5537	+	6.13291i	−0.657043	+	0.381818i
$259$	5.25241	−	14.4309i	0.326369	−	0.896691i
$260$	14.2700	+	2.10233i	0.884985	+	0.130381i
$261$	−0.740390	+	1.29926i	−0.0458290	+	0.0804222i
$262$	−24.4290	−	6.54573i	−1.50923	−	0.404397i
$263$	2.02429	+	1.41742i	0.124823	+	0.0874019i	0.634321	−	0.773070i	$-0.281280\pi$
$263$	2.02429	+	1.41742i	0.124823	+	0.0874019i	−0.509498	+	0.860472i	$0.670169\pi$
$264$	−8.07139	−	3.73608i	−0.496760	−	0.229940i
$265$	−2.62608	−	2.95583i	−0.161319	−	0.181575i
$266$	−43.2844	−	7.63221i	−2.65394	−	0.467961i
$267$	−0.689321	+	0.581730i	−0.0421858	+	0.0356013i
$268$	−6.46612	−	0.565712i	−0.394981	−	0.0345564i
$269$	2.07465			0.126494			0.0632468	−	0.997998i	$-0.479854\pi$
$269$	2.07465			0.126494			0.0632468	+	0.997998i	$0.479854\pi$
$270$	18.9838	−	7.70999i	1.15531	−	0.469215i
$271$	−18.0921			−1.09901			−0.549507	−	0.835489i	$-0.685184\pi$
$271$	−18.0921			−1.09901			−0.549507	+	0.835489i	$0.685184\pi$
$272$	−5.72684	−	0.501034i	−0.347241	−	0.0303796i
$273$	−31.8999	−	11.5088i	−1.93067	−	0.696546i
$274$	−5.87941	−	1.03670i	−0.355188	−	0.0626293i
$275$	7.36469	−	14.6039i	0.444108	−	0.880647i
$276$	−3.00856	+	2.11929i	−0.181094	+	0.127566i
$277$	21.0713	+	14.7543i	1.26605	+	0.886497i	0.997058	−	0.0766456i	$-0.0244210\pi$
$277$	21.0713	+	14.7543i	1.26605	+	0.886497i	0.268991	+	0.963143i	$0.413310\pi$
$278$	−9.37718	−	2.51261i	−0.562406	−	0.150696i
$279$	1.77431	+	9.74106i	0.106225	+	0.583182i
$280$	9.49052	−	7.05321i	0.567167	−	0.421510i
$281$	0.952631	−	2.61733i	0.0568292	−	0.156137i	−0.908029	−	0.418906i	$-0.862414\pi$
$281$	0.952631	−	2.61733i	0.0568292	−	0.156137i	0.964859	+	0.262769i	$0.0846358\pi$
$282$	13.1553	+	7.54581i	0.783384	+	0.449346i
$283$	1.78620	+	20.4164i	0.106179	+	1.21363i	0.843140	+	0.537694i	$0.180704\pi$
$283$	1.78620	+	20.4164i	0.106179	+	1.21363i	−0.736962	+	0.675935i	$0.763740\pi$
$284$	−6.50545	−	5.45872i	−0.386028	−	0.323916i
$285$	22.9509	−	17.1574i	1.35949	−	1.01632i
$286$	31.5065	+	11.4674i	1.86302	+	0.678083i
$287$	−7.05042	+	1.88915i	−0.416173	+	0.111513i
$288$	−16.9130	−	1.38363i	−0.996608	−	0.0815311i
$289$	−13.5721	+	7.83584i	−0.798358	+	0.460932i
$290$	1.03050	+	1.67380i	0.0605131	+	0.0982890i
$291$	4.71006	+	6.68646i	0.276109	+	0.391967i
$292$	−3.34907	+	7.18209i	−0.195989	+	0.420300i
$293$	−17.9864	−	25.6873i	−1.05078	−	1.50067i	−0.854036	−	0.520213i	$-0.825852\pi$
$293$	−17.9864	−	25.6873i	−1.05078	−	1.50067i	−0.196743	−	0.980455i	$-0.563036\pi$
$294$	12.0197	−	5.64620i	0.701004	−	0.329293i
$295$	−6.75422	−	22.6289i	−0.393246	−	1.31751i
$296$		−	7.15639i		−	0.415957i
$297$	16.7136	−	3.09307i	0.969824	−	0.179478i
$298$	16.5867	+	16.5867i	0.960842	+	0.960842i
$299$	−8.52385	+	7.15236i	−0.492947	+	0.413631i
$300$	1.10473	−	9.54770i	0.0637814	−	0.551237i
$301$	2.33764	−	13.2574i	0.134740	−	0.764146i
$302$	−23.4134	−	10.9179i	−1.34729	−	0.628252i
$303$	−4.19996	−	11.4388i	−0.241282	−	0.657144i
$304$	−36.3437	+	6.40838i	−2.08446	+	0.367546i
$305$	−23.3444	+	2.70895i	−1.33669	+	0.155114i
$306$	5.26316	−	3.07840i	0.300875	−	0.175980i
$307$	2.49145	+	9.29823i	0.142195	+	0.530678i	0.999864	+	0.0164767i	$0.00524495\pi$
$307$	2.49145	+	9.29823i	0.142195	+	0.530678i	−0.857669	+	0.514201i	$0.828088\pi$
$308$	−11.0838	+	5.16845i	−0.631557	+	0.294500i
$309$	−3.10525	+	11.7211i	−0.176652	+	0.666788i
$310$	12.3505	+	4.10387i	0.701460	+	0.233084i
$311$	−0.00272616	+	0.00324891i	−0.000154586	+	0.000184229i	−0.766122	−	0.642695i	$-0.777816\pi$
$311$	−0.00272616	+	0.00324891i	−0.000154586	+	0.000184229i	0.765967	+	0.642880i	$0.222260\pi$
$312$	−15.8032	+	0.0445623i	−0.894679	+	0.00252284i
$313$	−10.0379	−	21.5265i	−0.567378	−	1.21675i	−0.955460	−	0.295122i	$-0.904640\pi$
$313$	−10.0379	−	21.5265i	−0.567378	−	1.21675i	0.388081	−	0.921625i	$-0.373138\pi$
$314$	4.89398	−	8.47662i	0.276183	−	0.478363i
$315$	−7.00466	+	21.4845i	−0.394668	+	1.21051i
$316$	−4.39308	−	7.60903i	−0.247130	−	0.428041i
$317$	0.455273	−	0.650197i	0.0255707	−	0.0365187i	−0.806163	−	0.591693i	$-0.798460\pi$
$317$	0.455273	−	0.650197i	0.0255707	−	0.0365187i	0.831734	+	0.555175i	$0.187349\pi$
$318$	−4.14712	−	3.45997i	−0.232559	−	0.194025i
$319$	0.557690	+	1.53224i	0.0312246	+	0.0857890i
$320$	0.000982575	−	0.00149124i	5.49276e−5	−	8.33628e-5i
$321$	4.44725	−	6.38960i	0.248221	−	0.356633i
$322$	0.991189	−	11.3293i	0.0552368	−	0.631359i
$323$	6.02965	−	6.02965i	0.335499	−	0.335499i
$324$	8.59338	−	5.09148i	0.477410	−	0.282860i
$325$	0.893405	−	29.0475i	0.0495572	−	1.61127i
$326$	−8.11527	−	9.67140i	−0.449463	−	0.535649i
$327$	−5.36552	+	0.961693i	−0.296714	+	0.0531817i
$328$	−2.78627	+	1.95097i	−0.153846	+	0.107724i
$329$	−15.7172	+	5.72060i	−0.866518	+	0.315387i
$330$	6.98522	−	21.2216i	0.384524	−	1.16821i
$331$	−0.994980	−	5.64281i	−0.0546891	−	0.310157i	0.945176	−	0.326560i	$-0.105890\pi$
$331$	−0.994980	−	5.64281i	−0.0546891	−	0.310157i	−0.999865	+	0.0164031i	$0.994778\pi$
$332$	1.79427	−	6.69630i	0.0984733	−	0.367507i
$333$	7.90755	+	11.1587i	0.433331	+	0.611492i
$334$	21.4086	+	12.3603i	1.17143	+	0.676325i
$335$	0.369521	+	13.0724i	0.0201891	+	0.714221i
$336$	20.5207	−	20.6368i	1.11950	−	1.12583i
$337$	−25.4396	+	2.22568i	−1.38578	+	0.121240i	−0.755512	−	0.655135i	$-0.772612\pi$
$337$	−25.4396	+	2.22568i	−1.38578	+	0.121240i	−0.630271	+	0.776375i	$0.717056\pi$
$338$	36.5094	−	3.19415i	1.98585	−	0.173739i
$339$	0.755185	+	0.200071i	0.0410160	+	0.0108663i
$340$	−0.0808168	−	2.85902i	−0.00438291	−	0.155052i
$341$	9.34986	+	5.39814i	0.506323	+	0.292326i
$342$	27.5213	−	27.8335i	1.48818	−	1.50506i
$343$	2.31243	−	8.63010i	0.124859	−	0.465982i
$344$	−1.08934	−	6.17798i	−0.0587335	−	0.333094i
$345$	4.94016	+	5.52901i	0.265969	+	0.297672i
$346$	−16.2227	+	5.90459i	−0.872139	+	0.317433i
$347$	9.96940	−	6.98065i	0.535185	−	0.374741i	−0.274516	−	0.961582i	$-0.588518\pi$
$347$	9.96940	−	6.98065i	0.535185	−	0.374741i	0.809702	+	0.586842i	$0.199629\pi$
$348$	0.617987	+	0.732284i	0.0331276	+	0.0392546i
$349$	−0.0762364	−	0.0908550i	−0.00408084	−	0.00486336i	0.764000	−	0.645216i	$-0.223233\pi$
$349$	−0.0762364	−	0.0908550i	−0.00408084	−	0.00486336i	−0.768081	+	0.640353i	$0.778788\pi$
$350$	20.3472	+	21.6386i	1.08761	+	1.15663i
$351$	24.5920	−	17.5314i	1.31263	−	0.935758i
$352$	−13.0838	+	13.0838i	−0.697370	+	0.697370i
$353$	−1.88537	+	21.5499i	−0.100348	+	1.14699i	0.764387	+	0.644758i	$0.223042\pi$
$353$	−1.88537	+	21.5499i	−0.100348	+	1.14699i	−0.864735	+	0.502228i	$0.832514\pi$
$354$	−13.7153	−	29.1973i	−0.728959	−	1.55182i
$355$	−9.41400	+	14.2875i	−0.499643	+	0.758300i
$356$	0.197672	+	0.543100i	0.0104766	+	0.0287842i
$357$	−1.14903	+	6.62569i	−0.0608132	+	0.350668i
$358$	−11.7758	+	16.8175i	−0.622369	+	0.888835i
$359$	15.2804	+	26.4664i	0.806468	+	1.39684i	0.915296	+	0.402782i	$0.131957\pi$
$359$	15.2804	+	26.4664i	0.806468	+	1.39684i	−0.108828	+	0.994061i	$0.534710\pi$
$360$	0.356908	+	10.5244i	0.0188107	+	0.554686i
$361$	17.8706	−	30.9528i	0.940558	−	1.62910i
$362$	15.6779	+	33.6213i	0.824011	+	1.76710i
$363$	−0.258122	+	0.450006i	−0.0135479	+	0.0236192i
$364$	−13.9676	+	16.6460i	−0.732102	+	0.872485i
$365$	15.1517	+	5.03468i	0.793077	+	0.263527i
$366$	−30.9845	+	8.39598i	−1.61958	+	0.438865i
$367$	−13.9364	+	6.49863i	−0.727472	+	0.339226i	−0.750825	−	0.660502i	$-0.770344\pi$
$367$	−13.9364	+	6.49863i	−0.727472	+	0.339226i	0.0233530	+	0.999727i	$0.492566\pi$
$368$	−2.47147	−	9.22364i	−0.128834	−	0.480816i
$369$	2.18877	−	6.12079i	0.113943	−	0.318636i
$370$	17.8567	−	2.07214i	0.928326	−	0.107726i
$371$	5.86604	−	1.03434i	0.304550	−	0.0537003i
$372$	6.25108	+	1.08407i	0.324103	+	0.0562063i
$373$	−25.2501	−	11.7743i	−1.30740	−	0.609651i	−0.360976	−	0.932575i	$-0.617556\pi$
$373$	−25.2501	−	11.7743i	−1.30740	−	0.609651i	−0.946425	+	0.322924i	$0.895334\pi$
$374$	1.15449	−	6.54744i	0.0596973	−	0.338560i
$375$	−19.3649	+	0.00644020i	−1.00000	+	0.000332571i
$376$	−5.97077	+	5.01007i	−0.307919	+	0.258375i
$377$	2.04865	+	2.04865i	0.105511	+	0.105511i
$378$	−5.10278	+	30.4430i	−0.262459	+	1.56582i
$379$			16.6622i			0.855880i	0.903807	+	0.427940i	$0.140760\pi$
$379$			16.6622i			0.855880i	−0.903807	+	0.427940i	$0.859240\pi$
$380$	−5.25143	−	17.5941i	−0.269393	−	0.902558i
$381$	−0.0807691	+	0.954176i	−0.00413793	+	0.0488839i
$382$	−25.4063	−	36.2840i	−1.29990	−	1.85645i
$383$	−13.4360	+	28.8135i	−0.686546	+	1.47230i	0.185381	+	0.982667i	$0.440648\pi$
$383$	−13.4360	+	28.8135i	−0.686546	+	1.47230i	−0.871927	+	0.489636i	$0.837130\pi$
$384$	8.23199	−	17.7843i	0.420087	−	0.907552i
$385$	12.9180	+	20.9823i	0.658365	+	1.06935i
$386$	6.10313	−	3.52364i	0.310641	−	0.179349i
$387$	8.52502	+	8.42940i	0.433351	+	0.428490i
$388$	5.06210	−	1.35639i	0.256989	−	0.0688601i
$389$	−10.3645	−	3.77237i	−0.525501	−	0.191267i	0.0656273	−	0.997844i	$-0.479095\pi$
$389$	−10.3645	−	3.77237i	−0.525501	−	0.191267i	−0.591128	+	0.806577i	$0.701317\pi$
$390$	−4.68703	−	39.4194i	−0.237337	−	1.99608i
$391$	1.69021	+	1.41826i	0.0854778	+	0.0717244i
$392$	0.594840	+	6.79905i	0.0300440	+	0.343404i
$393$	0.0700447	+	24.8401i	0.00353329	+	1.25301i
$394$	−6.25270	+	17.1791i	−0.315006	+	0.865473i
$395$	−14.2081	+	10.5593i	−0.714888	+	0.531294i
$396$	1.83073	−	10.7363i	0.0919978	−	0.539520i
$397$	−15.3279	−	4.10710i	−0.769286	−	0.206129i	−0.147230	−	0.989102i	$-0.547036\pi$
$397$	−15.3279	−	4.10710i	−0.769286	−	0.206129i	−0.622056	+	0.782973i	$0.713702\pi$
$398$	17.8367	+	12.4894i	0.894071	+	0.626035i
$399$	3.88368	+	42.9940i	0.194427	+	2.15239i
$400$	22.2683	+	11.2299i	1.11342	+	0.561493i
$401$	−18.2547	−	3.21880i	−0.911598	−	0.160739i	−0.301869	−	0.953349i	$-0.597611\pi$
$401$	−18.2547	−	3.21880i	−0.911598	−	0.160739i	−0.609729	+	0.792610i	$0.708722\pi$
$402$	3.15160	+	17.5835i	0.157188	+	0.876987i
$403$	19.1100	+	1.67191i	0.951937	+	0.0832837i
$404$	−7.80799			−0.388462
$405$	−12.1856	−	16.0160i	−0.605508	−	0.795839i
$406$	−2.96116			−0.146960
$407$	14.8559	+	1.29972i	0.736379	+	0.0644248i
$408$	0.552855	+	3.08451i	0.0273704	+	0.152706i
$409$	15.3828	+	2.71240i	0.760628	+	0.134119i	0.540491	−	0.841350i	$-0.318238\pi$
$409$	15.3828	+	2.71240i	0.760628	+	0.134119i	0.220137	+	0.975469i	$0.429350\pi$
$410$	−5.67484	−	6.38742i	−0.280260	−	0.315452i
$411$	0.527528	+	5.83996i	0.0260211	+	0.288064i
$412$	6.36439	+	4.45640i	0.313551	+	0.219551i
$413$	34.3644	+	9.20792i	1.69096	+	0.453092i
$414$	7.79515	+	6.46635i	0.383111	+	0.317804i
$415$	−13.8184	−	2.03580i	−0.678318	−	0.0999334i
$416$	−11.2446	+	30.8943i	−0.551311	+	1.51472i
$417$	0.0268870	+	9.53497i	0.00131666	+	0.466929i
$418$	−3.71983	−	42.5179i	−0.181943	−	2.07962i
$419$	8.40402	+	7.05181i	0.410563	+	0.344503i	0.824560	−	0.565775i	$-0.191423\pi$
$419$	8.40402	+	7.05181i	0.410563	+	0.344503i	−0.413996	+	0.910279i	$0.635867\pi$
$420$	11.3759	+	8.95813i	0.555086	+	0.437112i
$421$	−4.13716	−	1.50580i	−0.201633	−	0.0733884i	0.239230	−	0.970963i	$-0.423105\pi$
$421$	−4.13716	−	1.50580i	−0.201633	−	0.0733884i	−0.440863	+	0.897575i	$0.645327\pi$
$422$	−16.0159	+	4.29146i	−0.779644	+	0.208905i
$423$	3.77405	−	14.4095i	0.183500	−	0.700614i
$424$	2.40387	−	1.38788i	0.116742	−	0.0674012i
$425$	−5.70315	+	0.825732i	−0.276644	+	0.0400539i
$426$	−9.81767	+	21.2100i	−0.475668	+	1.02763i
$427$	14.9625	−	32.0872i	0.724086	−	1.55281i
$428$	−2.86115	−	4.08615i	−0.138299	−	0.197512i
$429$	2.77762	−	32.8138i	0.134105	−	1.58426i
$430$	15.0999	−	4.50699i	0.728184	−	0.217346i
$431$			22.9617i			1.10603i	0.833173	+	0.553013i	$0.186522\pi$
$431$			22.9617i			1.10603i	−0.833173	+	0.553013i	$0.813478\pi$
$432$	4.71639	+	25.4853i	0.226917	+	1.22616i
$433$	−11.8168	−	11.8168i	−0.567878	−	0.567878i	0.363655	−	0.931534i	$-0.381529\pi$
$433$	−11.8168	−	11.8168i	−0.567878	−	0.567878i	−0.931534	+	0.363655i	$0.881529\pi$
$434$	−15.0193	+	12.6027i	−0.720949	+	0.604948i
$435$	1.32204	−	1.40688i	0.0633869	−	0.0674547i
$436$	−0.606518	+	3.43973i	−0.0290469	+	0.164733i
$437$	12.8372	+	5.98609i	0.614087	+	0.286353i
$438$	21.4889	+	3.72662i	1.02678	+	0.178065i
$439$	15.4676	−	2.72735i	0.738226	−	0.130169i	0.208124	−	0.978103i	$-0.433264\pi$
$439$	15.4676	−	2.72735i	0.738226	−	0.130169i	0.530103	+	0.847933i	$0.322153\pi$
$440$	9.00098	+	7.12918i	0.429105	+	0.339871i
$441$	−8.44022	−	9.94422i	−0.401915	−	0.473534i
$442$	−3.05744	−	11.4105i	−0.145428	−	0.542744i
$443$	21.0959	−	9.83716i	1.00229	−	0.467378i	0.149017	−	0.988835i	$-0.452389\pi$
$443$	21.0959	−	9.83716i	1.00229	−	0.467378i	0.853278	+	0.521457i	$0.174611\pi$
$444$	8.45830	−	2.29198i	0.401413	−	0.108772i
$445$	1.04103	−	0.521744i	0.0493495	−	0.0247330i
$446$	−15.9661	+	19.0276i	−0.756016	+	0.900984i
$447$	11.4633	−	19.9849i	0.542195	−	0.945255i
$448$	0.00113700	+	0.00243831i	5.37184e−5	+	0.000115199i
$449$	15.4027	−	26.6783i	0.726900	−	1.25903i	−0.231288	−	0.972885i	$-0.574294\pi$
$449$	15.4027	−	26.6783i	0.726900	−	1.25903i	0.958187	−	0.286142i	$-0.0923727\pi$
$450$	−26.1573	+	3.93792i	−1.23307	+	0.185635i
$451$	−3.54396	−	6.13831i	−0.166878	−	0.289042i
$452$	0.287125	−	0.410056i	0.0135052	−	0.0192874i
$453$	−4.33560	+	25.0004i	−0.203704	+	1.17462i
$454$	15.9509	+	43.8248i	0.748615	+	2.05680i
$455$	36.5584	+	24.0883i	1.71388	+	1.12927i
$456$	8.55311	+	18.2080i	0.400536	+	0.852667i
$457$	2.28713	−	26.1420i	0.106988	−	1.22287i	−0.732985	−	0.680245i	$-0.761874\pi$
$457$	2.28713	−	26.1420i	0.106988	−	1.22287i	0.839973	−	0.542629i	$-0.182571\pi$
$458$	12.4545	−	12.4545i	0.581961	−	0.581961i
$459$	−4.27032	−	4.19867i	−0.199321	−	0.195977i
$460$	4.41672	−	1.75041i	0.205931	−	0.0816134i
$461$	−12.6198	−	15.0397i	−0.587761	−	0.700467i	0.387413	−	0.921906i	$-0.373369\pi$
$461$	−12.6198	−	15.0397i	−0.587761	−	0.700467i	−0.975174	+	0.221440i	$0.928924\pi$
$462$	21.7074	+	25.7222i	1.00992	+	1.19671i
$463$	−6.86273	+	4.80533i	−0.318938	+	0.223323i	−0.722072	−	0.691818i	$-0.756810\pi$
$463$	−6.86273	+	4.80533i	−0.318938	+	0.223323i	0.403134	+	0.915141i	$0.367921\pi$
$464$	−2.33640	+	0.850378i	−0.108464	+	0.0394778i
$465$	0.717835	−	12.7624i	0.0332888	−	0.591842i
$466$	−8.29867	−	47.0641i	−0.384429	−	2.18020i
$467$	−0.507459	+	1.89386i	−0.0234824	+	0.0876375i	−0.976673	−	0.214734i	$-0.931112\pi$
$467$	−0.507459	+	1.89386i	−0.0234824	+	0.0876375i	0.953190	+	0.302371i	$0.0977783\pi$
$468$	−5.11395	−	18.6639i	−0.236393	−	0.862737i
$469$	−17.0619	−	9.85072i	−0.787847	−	0.454864i
$470$	−14.2300	−	13.4477i	−0.656382	−	0.620294i
$471$	−9.29296	−	2.46198i	−0.428197	−	0.113442i
$472$	16.5157	−	1.44494i	0.760196	−	0.0665085i
$473$	13.0227	−	1.13933i	0.598782	−	0.0523867i
$474$	−17.0502	+	17.1466i	−0.783140	+	0.787569i
$475$	−33.9924	+	14.5961i	−1.55968	+	0.669715i
$476$	3.73157	+	2.15442i	0.171036	+	0.0987478i
$477$	−2.21471	+	4.82025i	−0.101405	+	0.220704i
$478$	−11.3543	+	42.3747i	−0.519333	+	1.93818i
$479$	−3.17060	−	17.9814i	−0.144868	−	0.821589i	−0.967473	−	0.252975i	$-0.918591\pi$
$479$	−3.17060	−	17.9814i	−0.144868	−	0.821589i	0.822604	−	0.568614i	$-0.192520\pi$
$480$	20.8092	+	6.84949i	0.949808	+	0.312635i
$481$	24.8990	−	9.06251i	1.13530	−	0.413215i
$482$	41.2029	−	28.8506i	1.87674	−	1.31411i
$483$	−10.9948	+	1.97066i	−0.500280	+	0.0896681i
$484$	0.213671	+	0.254643i	0.00971233	+	0.0115747i
$485$	−3.89025	−	9.81605i	−0.176647	−	0.445724i
$486$	−19.7103	−	19.1622i	−0.894079	−	0.869216i
$487$	−23.0616	+	23.0616i	−1.04502	+	1.04502i	−0.0460835	+	0.998938i	$0.514674\pi$
$487$	−23.0616	+	23.0616i	−1.04502	+	1.04502i	−0.998938	+	0.0460835i	$0.985326\pi$
$488$	1.43793	−	16.4357i	0.0650922	−	0.744008i
$489$	−7.08378	+	10.1776i	−0.320339	+	0.460249i
$490$	−16.7928	+	3.45293i	−0.758623	+	0.155987i
$491$	1.13497	+	3.11830i	0.0512204	+	0.140727i	0.962665	−	0.270697i	$-0.0872540\pi$
$491$	1.13497	+	3.11830i	0.0512204	+	0.140727i	−0.911444	+	0.411423i	$0.865032\pi$
$492$	−3.19825	−	2.66832i	−0.144188	−	0.120297i
$493$	0.329519	−	0.470602i	0.0148408	−	0.0211949i
$494$	−37.9175	−	65.6750i	−1.70599	−	2.95486i
$495$	−21.9124	−	1.17051i	−0.984887	−	0.0526105i
$496$	−8.23121	+	14.2569i	−0.369592	+	0.640153i
$497$	−10.8936	−	23.3613i	−0.488643	−	1.04790i
$498$	−19.0793	+	0.0538003i	−0.854963	+	0.00241085i
$499$	4.13042	−	4.92245i	0.184903	−	0.220359i	−0.665628	−	0.746284i	$-0.731836\pi$
$499$	4.13042	−	4.92245i	0.184903	−	0.220359i	0.850531	+	0.525925i	$0.176281\pi$
$500$	−4.27287	+	11.6494i	−0.191088	+	0.520976i
$501$	6.21800	−	23.4704i	0.277800	−	1.04858i
$502$	−17.7463	+	8.27524i	−0.792057	+	0.369342i
$503$	1.67013	+	6.23303i	0.0744676	+	0.277917i	0.993112	−	0.117168i	$-0.0373817\pi$
$503$	1.67013	+	6.23303i	0.0744676	+	0.277917i	−0.918644	+	0.395085i	$0.870715\pi$
$504$	−13.7833	−	7.85448i	−0.613956	−	0.349866i
$505$	1.81335	+	15.6266i	0.0806931	+	0.695373i
$506$	10.8757	−	1.91769i	0.483486	−	0.0852516i
$507$	−12.4066	−	33.7902i	−0.550998	−	1.50067i
$508$	0.556097	+	0.259312i	0.0246728	+	0.0115051i
$509$	−2.35893	+	13.3781i	−0.104558	+	0.592976i	0.886838	+	0.462080i	$0.152897\pi$
$509$	−2.35893	+	13.3781i	−0.104558	+	0.592976i	−0.991396	+	0.130896i	$0.958215\pi$
$510$	−7.53642	+	2.27261i	−0.333718	+	0.100633i
$511$	−18.4259	+	15.4611i	−0.815112	+	0.683960i
$512$	−8.87720	−	8.87720i	−0.392320	−	0.392320i
$513$	−33.4557	−	18.9401i	−1.47711	−	0.836227i
$514$		−	49.7537i		−	2.19454i
$515$	7.44075	−	13.7724i	0.327878	−	0.606884i
$516$	6.95301	−	3.26614i	0.306089	−	0.143784i
$517$	−9.31597	−	13.3046i	−0.409716	−	0.585135i
$518$	−11.4452	+	24.5443i	−0.502874	+	1.07842i
$519$	9.76484	+	13.8623i	0.428629	+	0.608487i
$520$	19.8481	+	4.72146i	0.870395	+	0.207050i
$521$	−26.9126	+	15.5380i	−1.17906	+	0.680731i	−0.955797	−	0.294027i	$-0.905004\pi$
$521$	−26.9126	+	15.5380i	−1.17906	+	0.680731i	−0.223263	+	0.974758i	$0.571671\pi$
$522$	1.50038	−	2.16869i	0.0656699	−	0.0949212i
$523$	3.82198	−	1.02410i	0.167124	−	0.0447807i	−0.174287	−	0.984695i	$-0.555762\pi$
$523$	3.82198	−	1.02410i	0.167124	−	0.0447807i	0.341411	+	0.939914i	$0.389095\pi$
$524$	14.9567	+	5.44379i	0.653386	+	0.237813i
$525$	15.2864	−	24.8476i	0.667155	−	1.08444i
$526$	−3.33833	−	2.80120i	−0.145558	−	0.122138i
$527$	−0.331527	−	3.78937i	−0.0144415	−	0.165068i
$528$	24.5143	+	14.0613i	1.06685	+	0.611939i
$529$	6.61296	−	18.1689i	0.287520	−	0.789954i
$530$	4.15909	+	5.59630i	0.180659	+	0.243088i
$531$	−24.1557	+	20.5023i	−1.04827	+	0.889722i
$532$	26.7185	+	7.15919i	1.15839	+	0.310390i
$533$	−10.3163	−	7.22357i	−0.446850	−	0.312888i
$534$	1.30038	−	0.916013i	0.0562731	−	0.0396398i
$535$	−7.51336	+	6.67517i	−0.324831	+	0.288593i
$536$	−9.04142	−	1.59425i	−0.390530	−	0.0688609i
$537$	18.9679	+	6.84325i	0.818527	+	0.295308i
$538$	−3.64466	−	0.318866i	−0.157132	−	0.0137473i
$539$	−14.2221			−0.612590
$540$	−12.3247	+	3.79249i	−0.530373	+	0.163203i
$541$	43.8935			1.88713			0.943565	−	0.331186i	$-0.107449\pi$
$541$	43.8935			1.88713			0.943565	+	0.331186i	$0.107449\pi$
$542$	31.7834	+	2.78069i	1.36521	+	0.119441i
$543$	27.8455	−	23.4993i	1.19496	−	1.00845i
$544$	6.42021	+	1.13206i	0.275264	+	0.0485365i
$545$	7.02499	+	0.415003i	0.300917	+	0.0177768i
$546$	54.2715	+	25.1212i	2.32261	+	1.07509i
$547$	−19.7055	−	13.7979i	−0.842546	−	0.589957i	0.0706388	−	0.997502i	$-0.477496\pi$
$547$	−19.7055	−	13.7979i	−0.842546	−	0.589957i	−0.913185	+	0.407545i	$0.866385\pi$
$548$	3.62923	+	0.972448i	0.155033	+	0.0415409i
$549$	15.9187	+	27.2164i	0.679393	+	1.16157i
$550$	−15.1826	+	24.5236i	−0.647387	+	1.04569i
$551$	1.26139	−	3.46563i	0.0537369	−	0.147641i
$552$	−4.50050	+	2.61532i	−0.191554	+	0.111315i
$553$	−2.32430	−	26.5669i	−0.0988395	−	1.12974i
$554$	−34.7495	−	29.1583i	−1.47636	−	1.23882i
$555$	−6.55145	−	16.3958i	−0.278093	−	0.695962i
$556$	5.74120	+	2.08962i	0.243481	+	0.0886198i
$557$	−25.5871	+	6.85604i	−1.08416	+	0.290500i	−0.756299	−	0.654226i	$-0.772994\pi$
$557$	−25.5871	+	6.85604i	−1.08416	+	0.290500i	−0.327861	+	0.944726i	$0.606328\pi$
$558$	−1.61987	−	17.3854i	−0.0685748	−	0.735983i
$559$	20.1154	−	11.6136i	0.850790	−	0.491204i
$560$	−31.9942	+	19.6977i	−1.35200	+	0.832381i
$561$	−6.50351	+	0.587467i	−0.274578	+	0.0248029i
$562$	−2.07582	+	4.45161i	−0.0875632	+	0.187780i
$563$	−12.3664	−	17.6610i	−0.521181	−	0.744323i	0.469140	−	0.883124i	$-0.344564\pi$
$563$	−12.3664	−	17.6610i	−0.521181	−	0.744323i	−0.990320	+	0.138801i	$0.955675\pi$
$564$	−7.83378	−	5.45242i	−0.329862	−	0.229588i
$565$	−0.887351	−	0.479406i	−0.0373311	−	0.0201687i
$566$		−	36.1412i		−	1.51913i
$567$	30.1707	−	2.98285i	1.26705	−	0.125268i
$568$	−8.49364	−	8.49364i	−0.356385	−	0.356385i
$569$	8.77990	−	7.36721i	0.368073	−	0.308850i	−0.439926	−	0.898034i	$-0.644995\pi$
$569$	8.77990	−	7.36721i	0.368073	−	0.308850i	0.807999	+	0.589184i	$0.200551\pi$
$570$	−42.9562	+	26.6140i	−1.79924	+	1.11474i
$571$	1.87072	−	10.6094i	0.0782872	−	0.443989i	−0.920317	−	0.391173i	$-0.872069\pi$
$571$	1.87072	−	10.6094i	0.0782872	−	0.443989i	0.998604	−	0.0528155i	$-0.0168195\pi$
$572$	−19.1239	−	8.91764i	−0.799612	−	0.372865i
$573$	−27.8706	+	33.4058i	−1.16431	+	1.39555i
$574$	12.6763	−	2.23517i	0.529097	−	0.0932940i
$575$	−4.52895	−	8.43290i	−0.188870	−	0.351676i
$576$	−0.00236187		0.000402741i	−9.84114e−5		1.67809e-5i
$577$	6.65499	+	24.8368i	0.277051	+	1.03397i	0.954454	+	0.298357i	$0.0964385\pi$
$577$	6.65499	+	24.8368i	0.277051	+	1.03397i	−0.677403	+	0.735612i	$0.736895\pi$
$578$	25.0472	−	11.6797i	1.04183	−	0.485812i
$579$	−4.90818	−	4.88058i	−0.203977	−	0.202830i
$580$	−0.554262	−	1.10591i	−0.0230145	−	0.0459205i
$581$	13.5256	−	16.1192i	0.561137	−	0.668737i
$582$	−7.24676	−	12.4704i	−0.300388	−	0.516916i
$583$	2.44449	+	5.24223i	0.101241	+	0.217111i
$584$	−5.60442	+	9.70714i	−0.231913	+	0.401684i
$585$	−36.1653	+	14.5694i	−1.49525	+	0.602370i
$586$	27.6498	+	47.8909i	1.14220	+	1.97835i
$587$	−21.1711	+	30.2354i	−0.873824	+	1.24795i	0.0938095	+	0.995590i	$0.470096\pi$
$587$	−21.1711	+	30.2354i	−0.873824	+	1.24795i	−0.967633	+	0.252360i	$0.918793\pi$
$588$	−7.84544	+	2.88059i	−0.323541	+	0.118793i
$589$	−8.35183	−	22.9465i	−0.344131	−	0.945492i
$590$	8.38756	+	40.7917i	0.345310	+	1.67937i
$591$	17.8920	+	1.51452i	0.735977	+	0.0622989i
$592$	−1.98184	+	22.6526i	−0.0814533	+	0.931016i
$593$	−21.8217	+	21.8217i	−0.896109	+	0.896109i	−0.995089	−	0.0989808i	$-0.968442\pi$
$593$	−21.8217	+	21.8217i	−0.896109	+	0.896109i	0.0989808	+	0.995089i	$0.468442\pi$
$594$	−29.8373	+	2.86496i	−1.22424	+	0.117551i
$595$	3.44513	−	7.96854i	0.141237	−	0.326678i
$596$	−9.48922	−	11.3088i	−0.388693	−	0.463227i
$597$	7.25794	−	20.1174i	0.297048	−	0.823349i
$598$	16.0736	−	11.2549i	0.657300	−	0.460247i
$599$	16.2128	−	5.90099i	0.662438	−	0.241108i	0.0111496	−	0.999938i	$-0.496451\pi$
$599$	16.2128	−	5.90099i	0.662438	−	0.241108i	0.651289	+	0.758830i	$0.274229\pi$
$600$	2.73364	−	13.3171i	0.111600	−	0.543669i
$601$	7.91812	+	44.9059i	0.322987	+	1.83175i	0.523460	+	0.852050i	$0.324641\pi$
$601$	7.91812	+	44.9059i	0.322987	+	1.83175i	−0.200473	+	0.979699i	$0.564248\pi$
$602$	−6.14430	+	22.9308i	−0.250423	+	0.934592i
$603$	15.8595	−	7.50459i	0.645849	−	0.305611i
$604$	14.0802	+	8.12919i	0.572914	+	0.330772i
$605$	0.460008	−	0.486771i	0.0187020	−	0.0197901i
$606$	5.62022	+	20.7408i	0.228306	+	0.842538i
$607$	47.7085	−	4.17395i	1.93643	−	0.169416i	0.947703	−	0.319153i	$-0.103398\pi$
$607$	47.7085	−	4.17395i	1.93643	−	0.169416i	0.988726	+	0.149737i	$0.0478428\pi$
$608$	41.6917	−	3.64755i	1.69082	−	0.147928i
$609$	0.760669	+	2.80717i	0.0308239	+	0.113752i
$610$	41.4268	−	1.17102i	1.67732	−	0.0474133i
$611$	−24.9925	−	14.4294i	−1.01109	−	0.583752i
$612$	−3.46859	+	1.64131i	−0.140209	+	0.0663459i
$613$	−4.15240	+	15.4970i	−0.167714	+	0.625916i	0.829965	+	0.557816i	$0.188360\pi$
$613$	−4.15240	+	15.4970i	−0.167714	+	0.625916i	−0.997678	+	0.0681004i	$0.978306\pi$
$614$	−2.94778	−	16.7177i	−0.118963	−	0.674671i
$615$	−4.59748	+	7.02053i	−0.185388	+	0.283095i
$616$	−16.2549	+	5.91629i	−0.654927	+	0.238374i
$617$	20.9035	−	14.6368i	0.841541	−	0.589254i	−0.0713522	−	0.997451i	$-0.522731\pi$
$617$	20.9035	−	14.6368i	0.841541	−	0.589254i	0.912894	+	0.408198i	$0.133843\pi$
$618$	7.25667	−	20.1138i	0.291906	−	0.809097i
$619$	27.5321	+	32.8114i	1.10661	+	1.31880i	0.943193	+	0.332245i	$0.107806\pi$
$619$	27.5321	+	32.8114i	1.10661	+	1.31880i	0.163414	+	0.986558i	$0.447749\pi$
$620$	−7.51802	−	3.25035i	−0.301931	−	0.130537i
$621$	4.12763	−	9.05085i	0.165636	−	0.363198i
$622$	0.00528856	−	0.00528856i	0.000212052	−	0.000212052i
$623$	−0.152893	+	1.74758i	−0.00612554	+	0.0700152i
$624$	50.0352	+	4.23537i	2.00301	+	0.169551i
$625$	24.3069	+	5.84604i	0.972275	+	0.233842i
$626$	14.3257	+	39.3596i	0.572571	+	1.57313i
$627$	−39.3512	+	14.4484i	−1.57153	+	0.577015i
$628$	−3.53322	+	5.04597i	−0.140991	+	0.201356i
$629$	−2.62708	−	4.55023i	−0.104748	−	0.181430i
$630$	15.6076	−	36.6665i	0.621822	−	1.46083i
$631$	−6.58555	+	11.4065i	−0.262167	+	0.454086i	−0.966817	−	0.255468i	$-0.917770\pi$
$631$	−6.58555	+	11.4065i	−0.262167	+	0.454086i	0.704651	+	0.709554i	$0.251104\pi$
$632$	−5.25209	−	11.2631i	−0.208917	−	0.448024i
$633$	8.18249	+	14.0806i	0.325225	+	0.559655i
$634$	−0.899738	+	1.07227i	−0.0357332	+	0.0425851i
$635$	0.389826	−	1.17317i	0.0154698	−	0.0465559i
$636$	2.41025	+	2.39670i	0.0955726	+	0.0950351i
$637$	−22.9025	+	10.6796i	−0.907429	+	0.423141i
$638$	−0.744227	−	2.77749i	−0.0294642	−	0.109962i
$639$	22.6290	+	3.85864i	0.895188	+	0.152645i
$640$	−15.7083	+	19.8325i	−0.620924	+	0.783950i
$641$	2.12742	−	0.375121i	0.0840278	−	0.0148164i	−0.131476	−	0.991319i	$-0.541972\pi$
$641$	2.12742	−	0.375121i	0.0840278	−	0.0148164i	0.215504	+	0.976503i	$0.430861\pi$
$642$	−8.79481	+	10.5415i	−0.347104	+	0.416039i
$643$	4.05710	+	1.89186i	0.159996	+	0.0746075i	0.500967	−	0.865466i	$-0.332978\pi$
$643$	4.05710	+	1.89186i	0.159996	+	0.0746075i	−0.340970	+	0.940074i	$0.610756\pi$
$644$	−1.24285	+	7.04855i	−0.0489751	+	0.277752i
$645$	−8.15150	−	13.1569i	−0.320965	−	0.518053i
$646$	−11.5194	+	9.66592i	−0.453224	+	0.380300i
$647$	−35.0743	−	35.0743i	−1.37891	−	1.37891i	−0.846461	−	0.532451i	$-0.821271\pi$
$647$	−35.0743	−	35.0743i	−1.37891	−	1.37891i	−0.532451	−	0.846461i	$-0.678729\pi$
$648$	12.7363	−	6.11484i	0.500327	−	0.240214i
$649$			34.5472i			1.35609i
$650$	−6.03400	+	50.8922i	−0.236673	+	1.99616i
$651$	15.8055	+	11.0008i	0.619465	+	0.431156i
$652$	4.55737	+	6.50860i	0.178481	+	0.254897i
$653$	1.35569	−	2.90729i	0.0530523	−	0.113771i	−0.877995	−	0.478670i	$-0.841119\pi$
$653$	1.35569	−	2.90729i	0.0530523	−	0.113771i	0.931047	+	0.364899i	$0.118897\pi$
$654$	9.57373	−	0.864803i	0.374363	−	0.0338165i
$655$	7.42137	−	31.1979i	0.289977	−	1.21900i
$656$	9.35984	−	5.40391i	0.365440	−	0.210987i
$657$	−1.98728	−	21.3287i	−0.0775313	−	0.832110i
$658$	28.4906	−	7.63403i	1.11068	−	0.297606i
$659$	−16.5503	−	6.02381i	−0.644708	−	0.234654i	−0.00108739	−	0.999999i	$-0.500346\pi$
$659$	−16.5503	−	6.02381i	−0.644708	−	0.234654i	−0.643620	+	0.765345i	$0.722568\pi$
$660$	−5.54340	+	12.9217i	−0.215777	+	0.502977i
$661$	−31.9596	−	26.8173i	−1.24309	−	1.04307i	−0.997276	−	0.0737542i	$-0.976502\pi$
$661$	−31.9596	−	26.8173i	−1.24309	−	1.04307i	−0.245809	−	0.969318i	$-0.579054\pi$
$662$	0.880660	+	10.0660i	0.0342278	+	0.391226i
$663$	−10.0317	+	5.82960i	−0.389600	+	0.226403i
$664$	3.35373	−	9.21430i	0.130150	−	0.357584i
$665$	8.12291	−	55.1358i	0.314993	−	2.13808i
$666$	−12.1766	−	20.8185i	−0.471835	−	0.806701i
$667$	0.921766	+	0.246987i	0.0356909	+	0.00956336i
$668$	−12.7441	−	8.92355i	−0.493086	−	0.345263i
$669$	22.1395	+	10.2479i	0.855962	+	0.396207i
$670$	1.36002	−	23.0218i	0.0525423	−	0.889412i
$671$	33.8575	+	5.96999i	1.30705	+	0.230469i
$672$	−25.2224	+	21.2856i	−0.972975	+	0.821110i
$673$	−7.51557	−	0.657527i	−0.289704	−	0.0253458i	−0.0586226	−	0.998280i	$-0.518671\pi$
$673$	−7.51557	−	0.657527i	−0.289704	−	0.0253458i	−0.231081	+	0.972934i	$0.574226\pi$
$674$	45.0333			1.73462
$675$	10.4525	+	23.7854i	0.402316	+	0.915501i
$676$	−23.0647			−0.887104
$677$	−20.9561	−	1.83342i	−0.805407	−	0.0704639i	−0.322986	−	0.946404i	$-0.604687\pi$
$677$	−20.9561	−	1.83342i	−0.805407	−	0.0704639i	−0.482420	+	0.875940i	$0.660242\pi$
$678$	−1.29593	−	0.467546i	−0.0497699	−	0.0179560i
$679$	15.6652	+	2.76220i	0.601177	+	0.106004i
$680$	0.238576	−	4.03850i	0.00914896	−	0.154869i
$681$	37.4482	−	26.3792i	1.43502	−	1.01085i
$682$	−15.5958	−	10.9203i	−0.597193	−	0.418159i
$683$	4.72063	+	1.26489i	0.180630	+	0.0483997i	0.348000	−	0.937494i	$-0.386861\pi$
$683$	4.72063	+	1.26489i	0.180630	+	0.0483997i	−0.167370	+	0.985894i	$0.553528\pi$
$684$	−18.7811	+	15.9406i	−0.718114	+	0.609504i
$685$	1.10335	−	7.48922i	0.0421569	−	0.286148i
$686$	−5.38880	+	14.8056i	−0.205745	+	0.565281i
$687$	−15.0061	−	8.60747i	−0.572520	−	0.328395i
$688$	1.73728	+	19.8572i	0.0662333	+	0.757050i
$689$	7.87294	+	6.60618i	0.299935	+	0.251676i
$690$	−7.82889	−	10.4724i	−0.298041	−	0.398679i
$691$	39.6616	+	14.4357i	1.50880	+	0.549158i	0.958322	−	0.285692i	$-0.0922233\pi$
$691$	39.6616	+	14.4357i	1.50880	+	0.549158i	0.550478	+	0.834850i	$0.314445\pi$
$692$	10.4947	−	2.81204i	0.398948	−	0.106898i
$693$	18.8083	−	27.1861i	0.714469	−	1.03271i
$694$	−18.5867	+	10.7311i	−0.705543	+	0.407346i
$695$	2.84873	−	11.9755i	0.108058	−	0.454256i
$696$	0.780507	+	1.10802i	0.0295850	+	0.0419993i
$697$	−1.05540	+	2.26330i	−0.0399759	+	0.0857287i
$698$	0.119965	+	0.171328i	0.00454074	+	0.00648485i
$699$	−42.4848	+	19.9570i	−1.60692	+	0.754844i
$700$	−11.5698	−	14.6823i	−0.437296	−	0.554940i
$701$			3.71261i			0.140223i	0.997539	+	0.0701117i	$0.0223356\pi$
$701$			3.71261i			0.140223i	−0.997539	+	0.0701117i	$0.977664\pi$
$702$	−45.8969	+	27.0188i	−1.73226	+	1.01976i
$703$	−23.8504	−	23.8504i	−0.899533	−	0.899533i
$704$	−0.00200131	+	0.00167930i	−7.54273e−5	+	6.32910e-5i
$705$	−9.09288	+	16.9445i	−0.342458	+	0.638165i
$706$	6.62429	−	37.5682i	0.249309	−	1.41390i
$707$	−21.4790	−	10.0158i	−0.807800	−	0.376683i
$708$	6.99728	+	19.0575i	0.262974	+	0.716224i
$709$	−18.4462	+	3.25257i	−0.692763	+	0.122153i	−0.508934	−	0.860805i	$-0.669960\pi$
$709$	−18.4462	+	3.25257i	−0.692763	+	0.122153i	−0.183829	+	0.982958i	$0.558849\pi$
$710$	18.7341	−	23.6528i	0.703077	−	0.887673i
$711$	20.6348	+	11.7588i	0.773864	+	0.440990i
$712$	0.211580	+	0.789629i	0.00792931	+	0.0295926i
$713$	5.72646	−	2.67029i	0.214457	−	0.100003i
$714$	3.03692	−	11.4631i	0.113654	−	0.428997i
$715$	−13.4060	+	40.3449i	−0.501355	+	1.50881i
$716$	8.30527	−	9.89783i	0.310382	−	0.369899i
$717$	43.0878	−	0.121500i	1.60914	−	0.00453751i
$718$	−22.7762	−	48.8436i	−0.849999	−	1.82283i
$719$	−7.23920	+	12.5387i	−0.269977	+	0.467613i	−0.968856	−	0.247627i	$-0.920349\pi$
$719$	−7.23920	+	12.5387i	−0.269977	+	0.467613i	0.698879	+	0.715240i	$0.253683\pi$
$720$	1.78482	−	33.4125i	0.0665163	−	1.24521i
$721$	11.7913	+	20.4231i	0.439130	+	0.760596i
$722$	−36.1517	+	51.6300i	−1.34543	+	1.92147i
$723$	−37.9345	−	31.6489i	−1.41080	−	1.17704i
$724$	−7.98507	−	21.9388i	−0.296763	−	0.815349i
$725$	−2.08460	+	1.36612i	−0.0774200	+	0.0507363i
$726$	0.522623	−	0.750880i	0.0193963	−	0.0278678i
$727$	0.355020	−	4.05790i	0.0131670	−	0.150499i	−0.986765	−	0.162156i	$-0.948155\pi$
$727$	0.355020	−	4.05790i	0.0131670	−	0.150499i	0.999932	+	0.0116572i	$0.00371069\pi$
$728$	−21.7333	+	21.7333i	−0.805489	+	0.805489i
$729$	−13.1025	+	23.6077i	−0.485277	+	0.874361i
$730$	−25.8441	−	11.1735i	−0.956534	−	0.413549i
$731$	−2.96054	−	3.52824i	−0.109500	−	0.130497i
$732$	19.8862	−	3.56432i	0.735015	−	0.131741i
$733$	−0.238710	+	0.167146i	−0.00881695	+	0.00617370i	−0.577977	−	0.816053i	$-0.696158\pi$
$733$	−0.238710	+	0.167146i	−0.00881695	+	0.00617370i	0.569160	+	0.822227i	$0.307269\pi$
$734$	25.4816	−	9.27456i	0.940545	−	0.342330i
$735$	7.58713	+	15.0325i	0.279856	+	0.554483i
$736$	1.88042	+	10.6644i	0.0693133	+	0.393096i
$737$	4.95155	−	18.4794i	0.182393	−	0.680699i
$738$	−4.78589	+	10.4164i	−0.176171	+	0.383431i
$739$	0.493834	+	0.285115i	0.0181660	+	0.0104881i	0.509055	−	0.860734i	$-0.329995\pi$
$739$	0.493834	+	0.285115i	0.0181660	+	0.0104881i	−0.490890	+	0.871222i	$0.663328\pi$
$740$	−11.3089	+	0.319672i	−0.415723	+	0.0117514i
$741$	−52.5193	+	52.8163i	−1.92934	+	1.94026i
$742$	−10.4642	+	0.915499i	−0.384153	+	0.0336090i
$743$	−45.2865	+	3.96205i	−1.66140	+	0.145354i	−0.878806	−	0.477179i	$-0.841659\pi$
$743$	−45.2865	+	3.96205i	−1.66140	+	0.145354i	−0.782594	+	0.622533i	$0.786104\pi$
$744$	8.67451	+	2.29813i	0.318023	+	0.0842536i
$745$	−20.4291	+	21.6177i	−0.748466	+	0.792011i
$746$	42.5487	+	24.5655i	1.55782	+	0.899407i
$747$	4.95212	+	18.0733i	0.181189	+	0.661266i
$748$	−1.08294	+	4.04158i	−0.0395962	+	0.147775i
$749$	−2.62917	−	14.9108i	−0.0960678	−	0.544827i
$750$	34.0205	+	2.96501i	1.24225	+	0.108267i
$751$	21.7741	−	7.92512i	0.794547	−	0.289192i	0.0873224	−	0.996180i	$-0.472169\pi$
$751$	21.7741	−	7.92512i	0.794547	−	0.289192i	0.707225	+	0.706988i	$0.249947\pi$
$752$	20.2871	−	14.2052i	0.739795	−	0.518010i
$753$	12.4036	+	14.6977i	0.452012	+	0.535613i
$754$	−3.28412	−	3.91386i	−0.119601	−	0.142535i
$755$	12.9994	−	30.0674i	0.473096	−	1.09426i
$756$	4.86901	−	18.8063i	0.177084	−	0.683980i
$757$	−8.24491	+	8.24491i	−0.299666	+	0.299666i	−0.840883	−	0.541217i	$-0.817964\pi$
$757$	−8.24491	+	8.24491i	−0.299666	+	0.299666i	0.541217	+	0.840883i	$0.317964\pi$
$758$	2.56092	−	29.2715i	0.0930169	−	1.06319i
$759$	−4.61174	−	9.81753i	−0.167396	−	0.356354i
$760$	−5.23065	−	25.4385i	−0.189735	−	0.922752i
$761$	13.7885	+	37.8835i	0.499832	+	1.37328i	0.891437	+	0.453144i	$0.149698\pi$
$761$	13.7885	+	37.8835i	0.499832	+	1.37328i	−0.391605	+	0.920133i	$0.628080\pi$
$762$	0.288546	−	1.66385i	0.0104529	−	0.0602748i
$763$	−6.08083	+	8.68433i	−0.220141	+	0.314394i
$764$	13.9383	+	24.1418i	0.504268	+	0.873418i
$765$	4.09039	+	6.56069i	0.147889	+	0.237202i
$766$	28.0323	−	48.5534i	1.01285	−	1.75431i
$767$	25.9420	+	55.6327i	0.936710	+	2.00878i
$768$	−17.1937	+	29.9752i	−0.620422	+	1.08164i
$769$	−13.5646	+	16.1656i	−0.489151	+	0.582947i	−0.953001	−	0.302966i	$-0.902023\pi$
$769$	−13.5646	+	16.1656i	−0.489151	+	0.582947i	0.463850	+	0.885914i	$0.346468\pi$
$770$	−19.4690	−	38.8463i	−0.701614	−	1.39992i
$771$	−47.1663	+	12.7808i	−1.69865	+	0.460290i
$772$	−4.01963	+	1.87438i	−0.144669	+	0.0674605i
$773$	6.07695	+	22.6795i	0.218573	+	0.815724i	0.984878	+	0.173248i	$0.0554262\pi$
$773$	6.07695	+	22.6795i	0.218573	+	0.815724i	−0.766306	+	0.642476i	$0.777907\pi$
$774$	−13.6808	−	16.1187i	−0.491748	−	0.579375i
$775$	−4.75910	+	15.8011i	−0.170952	+	0.567592i
$776$	7.30002	−	1.28719i	0.262055	−	0.0462074i
$777$	26.2080	+	4.54501i	0.940206	+	0.163051i
$778$	17.6281	+	8.22014i	0.632000	+	0.294706i
$779$	−2.78384	+	15.7879i	−0.0997414	+	0.565662i
$780$	0.776338	+	24.9710i	0.0277974	+	0.894105i
$781$	19.1745	−	16.0893i	0.686116	−	0.575720i
$782$	−2.75132	−	2.75132i	−0.0983870	−	0.0983870i
$783$	−2.44133	−	0.865255i	−0.0872461	−	0.0309217i
$784$		−	21.6862i		−	0.774507i
$785$	10.9193	+	5.89934i	0.389728	+	0.210557i
$786$	3.69478	−	43.6488i	0.131788	−	1.55690i
$787$	4.65344	+	6.64580i	0.165877	+	0.236897i	0.893482	−	0.449100i	$-0.148255\pi$
$787$	4.65344	+	6.64580i	0.165877	+	0.236897i	−0.727604	+	0.685997i	$0.759366\pi$
$788$	4.86241	−	10.4275i	0.173216	−	0.371464i
$789$	−1.79796	+	3.88430i	−0.0640092	+	0.138285i
$790$	26.5832	−	16.3663i	0.945787	−	0.582288i
$791$	1.31585	−	0.759709i	0.0467864	−	0.0270121i
$792$	3.90315	−	14.9024i	0.138692	−	0.529535i
$793$	59.0051	−	15.8104i	2.09533	−	0.561442i
$794$	26.2962	+	9.57104i	0.933218	+	0.339663i
$795$	4.23687	−	5.38038i	0.150266	−	0.190823i
$796$	−10.4976	−	8.80855i	−0.372078	−	0.312211i
$797$	−1.11177	−	12.7075i	−0.0393807	−	0.450124i	−0.990129	−	0.140160i	$-0.955238\pi$
$797$	−1.11177	−	12.7075i	−0.0393807	−	0.450124i	0.950748	−	0.309964i	$-0.100317\pi$
$798$	−0.214665	−	76.1270i	−0.00759907	−	2.69487i
$799$	−1.95721	+	5.37738i	−0.0692410	+	0.190238i
$800$	−24.0471	−	14.8876i	−0.850192	−	0.526354i
$801$	−1.20242	−	0.997449i	−0.0424854	−	0.0352431i
$802$	31.5745	+	8.46035i	1.11493	+	0.298745i
$803$	−19.1331	−	13.3971i	−0.675192	−	0.472775i
$804$	−1.01142	−	11.1968i	−0.0356700	−	0.394882i
$805$	14.3953	+	0.850406i	0.507368	+	0.0299729i
$806$	−33.3147	−	5.87429i	−1.17346	−	0.206913i
$807$	0.633963	+	3.53703i	0.0223166	+	0.124509i
$808$	−11.0019	−	0.962544i	−0.387047	−	0.0338622i
$809$	37.1510			1.30616			0.653080	−	0.757289i	$-0.273477\pi$
$809$	37.1510			1.30616			0.653080	+	0.757289i	$0.273477\pi$
$810$	18.9456	+	30.0091i	0.665681	+	1.05441i
$811$	−4.94368			−0.173596			−0.0867981	−	0.996226i	$-0.527664\pi$
$811$	−4.94368			−0.173596			−0.0867981	+	0.996226i	$0.527664\pi$
$812$	1.85650	+	0.162423i	0.0651503	+	0.00569991i
$813$	−5.52850	−	30.8448i	−0.193893	−	1.08178i
$814$	−25.8985	−	4.56660i	−0.907741	−	0.160059i
$815$	11.9676	−	10.6325i	0.419207	−	0.372440i
$816$	−0.895783	−	9.91670i	−0.0313587	−	0.347154i
$817$	−24.2201	−	16.9591i	−0.847353	−	0.593323i
$818$	−26.6069	−	7.12931i	−0.930290	−	0.249270i
$819$	9.87337	−	57.9023i	0.345004	−	2.02327i
$820$	3.20748	+	4.31586i	0.112010	+	0.150716i
$821$	11.5751	−	31.8023i	0.403973	−	1.10991i	−0.556333	−	0.830959i	$-0.687792\pi$
$821$	11.5751	−	31.8023i	0.403973	−	1.10991i	0.960306	−	0.278948i	$-0.0899857\pi$
$822$	−0.0291584	−	10.3405i	−0.00101702	−	0.360666i
$823$	1.42916	+	16.3354i	0.0498174	+	0.569416i	0.979553	+	0.201187i	$0.0644800\pi$
$823$	1.42916	+	16.3354i	0.0498174	+	0.569416i	−0.929735	+	0.368229i	$0.879964\pi$
$824$	8.41844	+	7.06391i	0.293270	+	0.246083i
$825$	27.1484	+	8.09334i	0.945185	+	0.281774i
$826$	−58.9548	−	21.4578i	−2.05130	−	0.746612i
$827$	30.9381	−	8.28983i	1.07582	−	0.288266i	0.322939	−	0.946420i	$-0.395329\pi$
$827$	30.9381	−	8.28983i	1.07582	−	0.288266i	0.752883	+	0.658154i	$0.228662\pi$
$828$	−4.53248	−	4.48164i	−0.157514	−	0.155748i
$829$	−2.18006	+	1.25866i	−0.0757168	+	0.0437151i	−0.537380	−	0.843340i	$-0.680586\pi$
$829$	−2.18006	+	1.25866i	−0.0757168	+	0.0437151i	0.461664	+	0.887055i	$0.347253\pi$
$830$	23.9627	+	5.70025i	0.831757	+	0.197859i
$831$	−18.7154	+	40.4326i	−0.649230	+	1.40259i
$832$	−0.00196178	+	0.00420706i	−6.80126e−5	+	0.000145854i
$833$	2.87411	+	4.10466i	0.0995821	+	0.142218i
$834$	1.41826	−	16.7548i	0.0491103	−	0.580171i
$835$	−14.8995	+	27.5780i	−0.515617	+	0.954376i
$836$			26.8606i			0.928992i
$837$	−16.0652	+	6.00163i	−0.555294	+	0.207447i
$838$	−13.6800	−	13.6800i	−0.472568	−	0.472568i
$839$	−37.2023	+	31.2164i	−1.28437	+	1.07771i	−0.291739	+	0.956498i	$0.594234\pi$
$839$	−37.2023	+	31.2164i	−1.28437	+	1.07771i	−0.992627	+	0.121213i	$0.961322\pi$
$840$	14.9250	+	14.0249i	0.514960	+	0.483906i
$841$	−4.99265	+	28.3147i	−0.172160	+	0.976370i
$842$	7.03657	+	3.28121i	0.242496	+	0.113078i
$843$	4.75334	+	0.824329i	0.163714	+	0.0283914i
$844$	10.2766	−	1.81204i	0.353734	−	0.0623729i
$845$	5.35662	+	46.1607i	0.184273	+	1.58798i
$846$	−8.84479	+	24.7340i	−0.304090	+	0.850372i
$847$	0.261140	+	0.974587i	0.00897287	+	0.0334872i
$848$	−7.99348	+	3.72742i	−0.274497	+	0.128000i
$849$	−34.2617	+	9.28403i	−1.17586	+	0.318627i
$850$	10.1460	−	0.574057i	0.348004	−	0.0196900i
$851$	5.60993	−	6.68566i	0.192306	−	0.229181i
$852$	7.31857	−	12.7591i	0.250730	−	0.437119i
$853$	3.95780	+	8.48753i	0.135512	+	0.290607i	0.962340	−	0.271848i	$-0.0876347\pi$
$853$	3.95780	+	8.48753i	0.135512	+	0.290607i	−0.826828	+	0.562455i	$0.809857\pi$
$854$	−31.2172	+	54.0698i	−1.06823	+	1.85023i
$855$	36.2646	+	33.8856i	1.24022	+	1.15886i
$856$	−3.52781	−	6.11035i	−0.120578	−	0.208847i
$857$	31.1992	−	44.5570i	1.06574	−	1.52204i	0.229788	−	0.973241i	$-0.426197\pi$
$857$	31.1992	−	44.5570i	1.06574	−	1.52204i	0.835955	−	0.548798i	$-0.184914\pi$
$858$	−9.92297	+	57.2190i	−0.338765	+	1.95342i
$859$	−10.1859	−	27.9855i	−0.347538	−	0.954853i	−0.983143	−	0.182839i	$-0.941471\pi$
$859$	−10.1859	−	27.9855i	−0.347538	−	0.954853i	0.635605	−	0.772015i	$-0.280751\pi$
$860$	−9.71410	+	1.99741i	−0.331248	+	0.0681110i
$861$	−5.37523	−	11.4429i	−0.183187	−	0.389972i
$862$	3.52913	−	40.3382i	0.120203	−	1.37392i
$863$	19.0658	−	19.0658i	0.649007	−	0.649007i	−0.303746	−	0.952753i	$-0.598237\pi$
$863$	19.0658	−	19.0658i	0.649007	−	0.649007i	0.952753	+	0.303746i	$0.0982373\pi$
$864$	−2.80929	−	29.2575i	−0.0955738	−	0.995360i
$865$	−8.06522	−	20.3505i	−0.274226	−	0.691939i
$866$	18.9430	+	22.5754i	0.643711	+	0.767145i
$867$	−17.5065	−	20.7444i	−0.594552	−	0.704515i
$868$	10.1076	−	7.07741i	0.343074	−	0.240223i
$869$	24.3349	−	8.85719i	0.825506	−	0.300460i
$870$	−2.53874	+	2.26836i	−0.0860712	+	0.0769045i
$871$	−5.90279	−	33.4764i	−0.200009	−	1.13430i
$872$	−1.27866	+	4.77202i	−0.0433009	+	0.161601i
$873$	−9.96034	+	10.0733i	−0.337106	+	0.340930i
$874$	−21.6319	−	12.4892i	−0.731708	−	0.422452i
$875$	−26.6976	+	26.5651i	−0.902543	+	0.898065i
$876$	−13.2680	−	3.51509i	−0.448285	−	0.118764i
$877$	−3.95512	+	0.346028i	−0.133555	+	0.0116845i	−0.153737	−	0.988112i	$-0.549131\pi$
$877$	−3.95512	+	0.346028i	−0.133555	+	0.0116845i	0.0201823	+	0.999796i	$0.493575\pi$
$878$	−27.5920	+	2.41399i	−0.931184	+	0.0814681i
$879$	38.2976	−	38.5142i	1.29175	−	1.29905i
$880$	−26.5171	−	25.0591i	−0.893890	−	0.844743i
$881$	11.0930	+	6.40454i	0.373732	+	0.215774i	0.675088	−	0.737737i	$-0.264106\pi$
$881$	11.0930	+	6.40454i	0.373732	+	0.215774i	−0.301355	+	0.953512i	$0.597439\pi$
$882$	13.2990	+	18.7668i	0.447802	+	0.631913i
$883$	−8.03874	+	30.0010i	−0.270525	+	1.00961i	0.688256	+	0.725468i	$0.258377\pi$
$883$	−8.03874	+	30.0010i	−0.270525	+	1.00961i	−0.958781	+	0.284146i	$0.908290\pi$
$884$	1.29098	+	7.32153i	0.0434205	+	0.246250i
$885$	36.5157	−	18.4300i	1.22746	−	0.619518i
$886$	−38.5723	+	14.0392i	−1.29586	+	0.471655i
$887$	−28.2142	+	19.7558i	−0.947341	+	0.663335i	−0.941630	−	0.336649i	$-0.890707\pi$
$887$	−28.2142	+	19.7558i	−0.947341	+	0.663335i	−0.00571031	+	0.999984i	$0.501818\pi$
$888$	12.2008	−	2.18682i	0.409432	−	0.0733850i
$889$	1.19713	+	1.42668i	0.0401504	+	0.0478493i
$890$	−1.90903	+	0.756576i	−0.0639907	+	0.0253605i
$891$	10.3806	+	27.5496i	0.347764	+	0.922947i
$892$	11.0536	−	11.0536i	0.370102	−	0.370102i
$893$	−3.20176	+	36.5962i	−0.107143	+	1.22465i
$894$	−23.2099	+	33.3469i	−0.776254	+	1.11529i
$895$	−21.7379	−	14.3231i	−0.726618	−	0.478768i
$896$	−13.0358	−	35.8156i	−0.435496	−	1.19652i
$897$	−14.7986	−	12.3466i	−0.494111	−	0.412240i
$898$	−31.1593	+	44.5000i	−1.03980	+	1.48499i
$899$	−0.822588	−	1.42476i	−0.0274348	−	0.0475185i
$900$	16.6153	−	1.03412i	0.553843	−	0.0344708i
$901$	1.01896	−	1.76490i	0.0339466	−	0.0587973i
$902$	5.28245	+	11.3282i	0.175886	+	0.377189i
$903$	23.3167	−	0.0657491i	0.775931	−	0.00218799i
$904$	0.455126	−	0.542398i	0.0151373	−	0.0180399i
$905$	−42.0528	+	21.0761i	−1.39788	+	0.700593i
$906$	11.4591	−	43.2534i	0.380703	−	1.43700i
$907$	28.3482	−	13.2190i	0.941287	−	0.438929i	0.109477	−	0.993989i	$-0.465083\pi$
$907$	28.3482	−	13.2190i	0.941287	−	0.438929i	0.831810	+	0.555060i	$0.187305\pi$
$908$	−7.59659	−	28.3509i	−0.252102	−	0.940856i
$909$	18.2185	−	10.6559i	0.604268	−	0.353433i
$910$	−60.5220	−	47.9362i	−2.00628	−	1.58907i
$911$	−14.8888	+	2.62530i	−0.493288	+	0.0869800i	−0.414758	−	0.909932i	$-0.636134\pi$
$911$	−14.8888	+	2.62530i	−0.493288	+	0.0869800i	−0.0785299	+	0.996912i	$0.525023\pi$
$912$	−22.0313	−	60.0036i	−0.729530	−	1.98692i
$913$	18.5188	+	8.63545i	0.612882	+	0.285792i
$914$	−8.03589	+	45.5738i	−0.265804	+	1.50745i
$915$	−11.7519	−	38.9716i	−0.388506	−	1.28836i
$916$	−8.49147	+	7.12519i	−0.280566	+	0.235423i
$917$	34.1612	+	34.1612i	1.12810	+	1.12810i
$918$	6.85660	+	8.03239i	0.226301	+	0.265108i
$919$		−	1.84099i		−	0.0607286i	−0.999539	−	0.0303643i	$-0.990333\pi$
$919$		−	1.84099i		−	0.0607286i	0.999539	−	0.0303643i	$-0.00966675\pi$
$920$	6.43921	−	1.92196i	0.212294	−	0.0633650i
$921$	−15.0911	+	7.08895i	−0.497267	+	0.233589i
$922$	19.8584	+	28.3607i	0.654001	+	0.934010i
$923$	18.7957	−	40.3076i	0.618670	−	1.32674i
$924$	−12.1985	−	17.3172i	−0.401303	−	0.569694i
$925$	3.26619	+	22.5589i	0.107392	+	0.741732i
$926$	12.7947	−	7.38704i	0.420461	−	0.242753i
$927$	−20.9319	−	1.71241i	−0.687495	−	0.0562430i
$928$	2.72352	−	0.729766i	0.0894041	−	0.0239557i
$929$	−43.8338	−	15.9542i	−1.43814	−	0.523441i	−0.498888	−	0.866666i	$-0.666258\pi$
$929$	−43.8338	−	15.9542i	−1.43814	−	0.523441i	−0.939253	+	0.343226i	$0.888480\pi$
$930$	−3.22260	+	22.3102i	−0.105673	+	0.731579i
$931$	24.6419	+	20.6770i	0.807605	+	0.677661i
$932$	2.62133	+	29.9620i	0.0858647	+	0.981438i
$933$	−0.00637206	−	0.00365499i	−0.000208612	−	0.000119659i
$934$	1.18256	−	3.24907i	0.0386947	−	0.106313i
$935$	8.34015	+	1.22872i	0.272752	+	0.0401833i
$936$	−4.90505	−	26.9289i	−0.160327	−	0.880200i
$937$	−6.41697	−	1.71942i	−0.209633	−	0.0561711i	0.152474	−	0.988307i	$-0.451276\pi$
$937$	−6.41697	−	1.71942i	−0.209633	−	0.0561711i	−0.362107	+	0.932136i	$0.617943\pi$
$938$	28.4597	+	19.9277i	0.929243	+	0.650663i
$939$	33.6327	−	23.6915i	1.09756	−	0.773143i
$940$	8.18389	+	9.21153i	0.266929	+	0.300447i
$941$	−42.6827	−	7.52611i	−1.39142	−	0.245344i	−0.572805	−	0.819692i	$-0.694145\pi$
$941$	−42.6827	−	7.52611i	−1.39142	−	0.245344i	−0.818612	+	0.574347i	$0.805256\pi$
$942$	15.9471	+	5.75340i	0.519585	+	0.187456i
$943$	−4.13236	−	0.361535i	−0.134568	−	0.0117732i
$944$	−52.6783			−1.71453
$945$	−38.7690	−	5.37698i	−1.26115	−	0.174913i
$946$	−23.0528			−0.749511
$947$	50.2480	+	4.39613i	1.63284	+	0.142855i	0.866363	−	0.499415i	$-0.166452\pi$
$947$	50.2480	+	4.39613i	1.63284	+	0.142855i	0.766478	+	0.642270i	$0.222007\pi$
$948$	11.6301	−	9.81481i	0.377727	−	0.318770i
$949$	−40.8709	−	7.20665i	−1.32673	−	0.233938i
$950$	61.9599	−	20.4173i	2.01024	−	0.662425i
$951$	1.24763	+	0.577501i	0.0404571	+	0.0187268i
$952$	4.99241	+	3.49573i	0.161805	+	0.113297i
$953$	30.3800	+	8.14030i	0.984105	+	0.263690i	0.714773	−	0.699357i	$-0.246530\pi$
$953$	30.3800	+	8.14030i	0.984105	+	0.263690i	0.269333	+	0.963047i	$0.413197\pi$
$954$	4.63157	−	8.12763i	0.149953	−	0.263142i
$955$	45.0792	−	33.5022i	1.45873	−	1.08410i
$956$	9.44285	−	25.9440i	0.305404	−	0.839089i
$957$	−2.44187	+	1.41901i	−0.0789345	+	0.0458701i
$958$	2.80631	+	32.0762i	0.0906677	+	1.03634i
$959$	8.73620	+	7.33054i	0.282107	+	0.236716i
$960$	0.00284264	+	0.00121949i	9.17457e−5	+	3.93588e-5i
$961$	18.8945	+	6.87702i	0.609498	+	0.221839i
$962$	−45.1345	+	12.0938i	−1.45519	+	0.389918i
$963$	12.2525	+	5.62953i	0.394831	+	0.181409i
$964$	−27.4146	+	15.8278i	−0.882964	+	0.509780i
$965$	4.68483	+	7.60939i	0.150810	+	0.244955i
$966$	19.6181	−	1.77212i	0.631201	−	0.0570169i
$967$	3.62934	−	7.78315i	0.116712	−	0.250289i	−0.839270	−	0.543715i	$-0.817017\pi$
$967$	3.62934	−	7.78315i	0.116712	−	0.250289i	0.955982	+	0.293425i	$0.0947952\pi$
$968$	0.269684	+	0.385149i	0.00866797	+	0.0123791i
$969$	12.1224	+	8.43733i	0.389426	+	0.271046i
$970$	5.32554	+	17.8424i	0.170993	+	0.572884i
$971$		−	29.8892i		−	0.959189i	−0.877490	−	0.479595i	$-0.840784\pi$
$971$		−	29.8892i		−	0.959189i	0.877490	−	0.479595i	$-0.159216\pi$
$972$	11.3063	+	13.0949i	0.362650	+	0.420018i
$973$	13.1129	+	13.1129i	0.420381	+	0.420381i
$974$	44.0582	−	36.9692i	1.41172	−	1.18457i
$975$	49.7956	−	7.35307i	1.59473	−	0.235487i
$976$	−9.10317	+	51.6266i	−0.291385	+	1.65253i
$977$	−32.5668	−	15.1861i	−1.04190	−	0.485848i	−0.175128	−	0.984546i	$-0.556034\pi$
$977$	−32.5668	−	15.1861i	−1.04190	−	0.485848i	−0.866776	+	0.498698i	$0.833812\pi$
$978$	14.0088	−	16.7909i	0.447951	−	0.536915i
$979$	−1.67761	+	0.295808i	−0.0536166	+	0.00945406i
$980$	10.7176	−	1.24371i	0.342362	−	0.0397287i
$981$	−3.27915	−	8.85370i	−0.104695	−	0.282677i
$982$	−1.51459	−	5.65254i	−0.0483327	−	0.180380i
$983$	−33.2165	+	15.4891i	−1.05944	+	0.494026i	−0.872636	−	0.488371i	$-0.837591\pi$
$983$	−33.2165	+	15.4891i	−1.05944	+	0.494026i	−0.186806	+	0.982397i	$0.559814\pi$
$984$	−4.17758	−	4.15409i	−0.133177	−	0.132428i
$985$	−21.9984	−	7.30971i	−0.700926	−	0.232907i
$986$	−0.651216	+	0.776090i	−0.0207390	+	0.0247157i
$987$	−14.5557	−	25.0479i	−0.463314	−	0.797284i
$988$	20.1700	+	43.2547i	0.641693	+	1.37611i
$989$	3.82526	−	6.62555i	0.121636	−	0.210680i
$990$	38.3149	+	5.42416i	1.21773	+	0.172391i
$991$	−19.5180	−	33.8061i	−0.620009	−	1.07389i	−0.989483	−	0.144647i	$-0.953795\pi$
$991$	−19.5180	−	33.8061i	−0.620009	−	1.07389i	0.369474	−	0.929241i	$-0.379538\pi$
$992$	10.7081	−	15.2927i	0.339982	−	0.485545i
$993$	9.31629	−	3.42063i	0.295644	−	0.108551i
$994$	15.5468	+	42.7146i	0.493115	+	1.35482i
$995$	−15.1910	+	23.0552i	−0.481588	+	0.730899i
$996$	11.9647	+	1.01279i	0.379116	+	0.0320914i
$997$	−3.41553	+	39.0397i	−0.108171	+	1.23640i	0.727088	+	0.686544i	$0.240873\pi$
$997$	−3.41553	+	39.0397i	−0.108171	+	1.23640i	−0.835259	+	0.549856i	$0.814683\pi$
$998$	−8.01273	+	8.01273i	−0.253638	+	0.253638i
$999$	−16.6079	+	16.8913i	−0.525450	+	0.534416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.113.4	yes	192
3.2	odd	2		405.2.r.a.368.13		192
5.2	odd	4	inner	135.2.q.a.32.13	✓	192
5.3	odd	4		675.2.ba.b.32.4		192
5.4	even	2		675.2.ba.b.518.13		192
15.2	even	4		405.2.r.a.287.4		192
27.11	odd	18	inner	135.2.q.a.38.13	yes	192
27.16	even	9		405.2.r.a.278.4		192
135.38	even	36		675.2.ba.b.632.13		192
135.92	even	36	inner	135.2.q.a.92.4	yes	192
135.97	odd	36		405.2.r.a.197.13		192
135.119	odd	18		675.2.ba.b.443.4		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.13	✓	192	5.2	odd	4	inner
135.2.q.a.38.13	yes	192	27.11	odd	18	inner
135.2.q.a.92.4	yes	192	135.92	even	36	inner
135.2.q.a.113.4	yes	192	1.1	even	1	trivial
405.2.r.a.197.13		192	135.97	odd	36
405.2.r.a.278.4		192	27.16	even	9
405.2.r.a.287.4		192	15.2	even	4
405.2.r.a.368.13		192	3.2	odd	2
675.2.ba.b.32.4		192	5.3	odd	4
675.2.ba.b.443.4		192	135.119	odd	18
675.2.ba.b.518.13		192	5.4	even	2
675.2.ba.b.632.13		192	135.38	even	36

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.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.75676 - 0.153697i) q^{2} +(0.305576 + 1.70488i) q^{3} +(1.09297 + 0.192720i) q^{4} +(0.131866 - 2.23218i) q^{5} +(-0.274789 - 3.04204i) q^{6} +(2.75943 + 1.93217i) q^{7} +(1.51630 + 0.406292i) q^{8} +(-2.81325 + 1.04194i) q^{9} +O(q^{10})\)	\(q+(-1.75676 - 0.153697i) q^{2} +(0.305576 + 1.70488i) q^{3} +(1.09297 + 0.192720i) q^{4} +(0.131866 - 2.23218i) q^{5} +(-0.274789 - 3.04204i) q^{6} +(2.75943 + 1.93217i) q^{7} +(1.51630 + 0.406292i) q^{8} +(-2.81325 + 1.04194i) q^{9} +(-0.574736 + 3.90113i) q^{10} +(-1.11880 + 3.07388i) q^{11} +(0.00542048 + 1.92227i) q^{12} +(0.506571 + 5.79013i) q^{13} +(-4.55068 - 3.81848i) q^{14} +(3.84589 - 0.457283i) q^{15} +(-4.68713 - 1.70598i) q^{16} +(1.11325 - 0.298295i) q^{17} +(5.10234 - 1.39806i) q^{18} +(6.40749 - 3.69937i) q^{19} +(0.574311 - 2.41429i) q^{20} +(-2.45091 + 5.29492i) q^{21} +(2.43791 - 5.22812i) q^{22} +(1.09807 + 1.56820i) q^{23} +(-0.229334 + 2.70927i) q^{24} +(-4.96522 - 0.588699i) q^{25} -10.2497i q^{26} +(-2.63605 - 4.47786i) q^{27} +(2.64360 + 2.64360i) q^{28} +(0.381851 - 0.320411i) q^{29} +(-6.82659 + 0.212236i) q^{30} +(0.573116 - 3.25030i) q^{31} +(5.12653 + 2.39054i) q^{32} +(-5.58249 - 0.968121i) q^{33} +(-2.00157 + 0.352930i) q^{34} +(4.67682 - 5.90474i) q^{35} +(-3.27559 + 0.596642i) q^{36} +(-1.17991 - 4.40348i) q^{37} +(-11.8250 + 5.51409i) q^{38} +(-9.71669 + 2.63297i) q^{39} +(1.10686 - 3.33107i) q^{40} +(-1.39279 + 1.65986i) q^{41} +(5.11947 - 8.92522i) q^{42} +(-1.68889 - 3.62184i) q^{43} +(-1.81521 + 3.14404i) q^{44} +(1.95483 + 6.41706i) q^{45} +(-1.68801 - 2.92372i) q^{46} +(-2.84791 + 4.06724i) q^{47} +(1.47621 - 8.51231i) q^{48} +(1.48701 + 4.08553i) q^{49} +(8.63222 + 1.79734i) q^{50} +(0.848742 + 1.80681i) q^{51} +(-0.562207 + 6.42605i) q^{52} +(1.25033 - 1.25033i) q^{53} +(3.94268 + 8.27168i) q^{54} +(6.71392 + 2.90271i) q^{55} +(3.39910 + 4.05089i) q^{56} +(8.26496 + 9.79358i) q^{57} +(-0.720066 + 0.504196i) q^{58} +(9.92422 - 3.61212i) q^{59} +(4.29157 + 0.241384i) q^{60} +(-1.82504 - 10.3503i) q^{61} +(-1.50639 + 5.62192i) q^{62} +(-9.77616 - 2.56051i) q^{63} +(0.000691655 + 0.000399327i) q^{64} +(12.9914 - 0.367231i) q^{65} +(9.65830 + 2.55877i) q^{66} +(-5.82623 + 0.509729i) q^{67} +(1.27424 - 0.111481i) q^{68} +(-2.33806 + 2.35128i) q^{69} +(-9.12360 + 9.65440i) q^{70} +(-6.62671 - 3.82593i) q^{71} +(-4.68906 + 0.436900i) q^{72} +(-1.84806 + 6.89704i) q^{73} +(1.39602 + 7.91721i) q^{74} +(-0.513592 - 8.64501i) q^{75} +(7.71612 - 2.80844i) q^{76} +(-9.02653 + 6.32044i) q^{77} +(17.4746 - 3.13207i) q^{78} +(-5.08874 - 6.06452i) q^{79} +(-4.42611 + 10.2375i) q^{80} +(6.82871 - 5.86248i) q^{81} +(2.70191 - 2.70191i) q^{82} +(0.544416 - 6.22270i) q^{83} +(-3.69920 + 5.31485i) q^{84} +(-0.519047 - 2.52431i) q^{85} +(2.41031 + 6.62228i) q^{86} +(0.662947 + 0.553100i) q^{87} +(-2.94533 + 4.20637i) q^{88} +(0.260380 + 0.450992i) q^{89} +(-2.44788 - 11.5737i) q^{90} +(-9.78968 + 16.9562i) q^{91} +(0.897929 + 1.92562i) q^{92} +(5.71652 - 0.0161196i) q^{93} +(5.62822 - 6.70745i) q^{94} +(-7.41270 - 14.7905i) q^{95} +(-2.50905 + 9.47063i) q^{96} +(4.27963 - 1.99563i) q^{97} +(-1.98439 - 7.40585i) q^{98} +(-0.0553442 - 9.81332i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8}+O(q^{10}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8	\( 192 q - 12 q^{2} - 12 q^{3} - 12 q^{5} - 36 q^{6} - 12 q^{7} - 18 q^{8} - 6 q^{10} - 36 q^{11} - 12 q^{12} - 12 q^{13} - 12 q^{15} - 24 q^{16} - 18 q^{17} - 54 q^{18} + 36 q^{20} - 24 q^{21} - 12 q^{22} - 36 q^{23} - 30 q^{25} - 36 q^{27} - 24 q^{28} + 60 q^{30} - 24 q^{31} - 48 q^{32} - 6 q^{33} + 36 q^{35} + 12 q^{36} - 6 q^{37} + 12 q^{38} - 36 q^{40} + 24 q^{41} - 24 q^{42} - 12 q^{43} + 18 q^{45} - 12 q^{46} - 6 q^{47} + 12 q^{48} + 36 q^{50} + 144 q^{51} + 12 q^{52} - 24 q^{55} + 180 q^{56} - 12 q^{57} - 12 q^{58} - 36 q^{60} - 60 q^{61} - 18 q^{62} - 54 q^{63} - 84 q^{65} + 72 q^{66} + 24 q^{67} - 60 q^{68} - 12 q^{70} - 36 q^{71} + 180 q^{72} - 6 q^{73} - 60 q^{75} - 72 q^{76} + 132 q^{77} + 78 q^{78} + 12 q^{81} - 24 q^{82} + 48 q^{83} - 12 q^{85} + 12 q^{86} + 144 q^{87} - 48 q^{88} + 48 q^{90} - 12 q^{91} + 258 q^{92} + 180 q^{93} + 18 q^{95} - 12 q^{96} + 24 q^{97} + 324 q^{98}+O(q^{100}) \) 192 * q - 12 * q^2 - 12 * q^3 - 12 * q^5 - 36 * q^6 - 12 * q^7 - 18 * q^8 - 6 * q^10 - 36 * q^11 - 12 * q^12 - 12 * q^13 - 12 * q^15 - 24 * q^16 - 18 * q^17 - 54 * q^18 + 36 * q^20 - 24 * q^21 - 12 * q^22 - 36 * q^23 - 30 * q^25 - 36 * q^27 - 24 * q^28 + 60 * q^30 - 24 * q^31 - 48 * q^32 - 6 * q^33 + 36 * q^35 + 12 * q^36 - 6 * q^37 + 12 * q^38 - 36 * q^40 + 24 * q^41 - 24 * q^42 - 12 * q^43 + 18 * q^45 - 12 * q^46 - 6 * q^47 + 12 * q^48 + 36 * q^50 + 144 * q^51 + 12 * q^52 - 24 * q^55 + 180 * q^56 - 12 * q^57 - 12 * q^58 - 36 * q^60 - 60 * q^61 - 18 * q^62 - 54 * q^63 - 84 * q^65 + 72 * q^66 + 24 * q^67 - 60 * q^68 - 12 * q^70 - 36 * q^71 + 180 * q^72 - 6 * q^73 - 60 * q^75 - 72 * q^76 + 132 * q^77 + 78 * q^78 + 12 * q^81 - 24 * q^82 + 48 * q^83 - 12 * q^85 + 12 * q^86 + 144 * q^87 - 48 * q^88 + 48 * q^90 - 12 * q^91 + 258 * q^92 + 180 * q^93 + 18 * q^95 - 12 * q^96 + 24 * q^97 + 324 * q^98

Introduction

L-functions

Modular forms

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