LMFDB - Embedded newform 135.2.q.a.113.15

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			113.15
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.08671 + 0.182563i) q^{2} +(-0.507262 + 1.65611i) q^{3} +(2.35140 + 0.414615i) q^{4} +(-1.98370 - 1.03196i) q^{5} +(-1.36085 + 3.36320i) q^{6} +(3.38127 + 2.36759i) q^{7} +(0.784385 + 0.210175i) q^{8} +(-2.48537 - 1.68016i) q^{9} +O(q^{10})$	\(q+(2.08671 + 0.182563i) q^{2} +(-0.507262 + 1.65611i) q^{3} +(2.35140 + 0.414615i) q^{4} +(-1.98370 - 1.03196i) q^{5} +(-1.36085 + 3.36320i) q^{6} +(3.38127 + 2.36759i) q^{7} +(0.784385 + 0.210175i) q^{8} +(-2.48537 - 1.68016i) q^{9} +(-3.95100 - 2.51554i) q^{10} +(1.66957 - 4.58710i) q^{11} +(-1.87942 + 3.68385i) q^{12} +(-0.223275 - 2.55204i) q^{13} +(6.62348 + 5.55776i) q^{14} +(2.71529 - 2.76174i) q^{15} +(-2.88895 - 1.05149i) q^{16} +(-2.36120 + 0.632683i) q^{17} +(-4.87950 - 3.95974i) q^{18} +(-4.05431 + 2.34076i) q^{19} +(-4.23661 - 3.24902i) q^{20} +(-5.63616 + 4.39875i) q^{21} +(4.32134 - 9.26714i) q^{22} +(2.13442 + 3.04827i) q^{23} +(-0.745961 + 1.19241i) q^{24} +(2.87013 + 4.09419i) q^{25} -5.36612i q^{26} +(4.04325 - 3.26375i) q^{27} +(6.96907 + 6.96907i) q^{28} +(2.44490 - 2.05152i) q^{29} +(6.17020 - 5.26724i) q^{30} +(-0.272295 + 1.54426i) q^{31} +(-7.30837 - 3.40795i) q^{32} +(6.74982 + 5.09185i) q^{33} +(-5.04264 + 0.889154i) q^{34} +(-4.26417 - 8.18590i) q^{35} +(-5.14748 - 4.98120i) q^{36} +(0.592937 + 2.21287i) q^{37} +(-8.88750 + 4.14431i) q^{38} +(4.33971 + 0.924787i) q^{39} +(-1.33909 - 1.22638i) q^{40} +(-4.38733 + 5.22862i) q^{41} +(-12.5641 + 8.14994i) q^{42} +(0.553045 + 1.18601i) q^{43} +(5.82771 - 10.0939i) q^{44} +(3.19638 + 5.89773i) q^{45} +(3.89741 + 6.75051i) q^{46} +(-0.220307 + 0.314631i) q^{47} +(3.20684 - 4.25102i) q^{48} +(3.43334 + 9.43304i) q^{49} +(5.24167 + 9.06735i) q^{50} +(0.149960 - 4.23134i) q^{51} +(0.533107 - 6.09344i) q^{52} +(0.177802 - 0.177802i) q^{53} +(9.03293 - 6.07235i) q^{54} +(-8.04562 + 7.37651i) q^{55} +(2.15461 + 2.56776i) q^{56} +(-1.81994 - 7.90174i) q^{57} +(5.47633 - 3.83457i) q^{58} +(-0.797126 + 0.290130i) q^{59} +(7.52979 - 5.36817i) q^{60} +(1.38646 + 7.86300i) q^{61} +(-0.850126 + 3.17272i) q^{62} +(-4.42577 - 11.5654i) q^{63} +(-9.30332 - 5.37128i) q^{64} +(-2.19069 + 5.29289i) q^{65} +(13.1553 + 11.8575i) q^{66} +(8.09911 - 0.708580i) q^{67} +(-5.81446 + 0.508699i) q^{68} +(-6.13097 + 1.98856i) q^{69} +(-7.40362 - 17.8601i) q^{70} +(-7.83146 - 4.52149i) q^{71} +(-1.59636 - 1.84025i) q^{72} +(3.19228 - 11.9138i) q^{73} +(0.833296 + 4.72586i) q^{74} +(-8.23631 + 2.67641i) q^{75} +(-10.5038 + 3.82308i) q^{76} +(16.5056 - 11.5574i) q^{77} +(8.88686 + 2.72203i) q^{78} +(-6.94728 - 8.27944i) q^{79} +(4.64572 + 5.06712i) q^{80} +(3.35413 + 8.35163i) q^{81} +(-10.1096 + 10.1096i) q^{82} +(0.325084 - 3.71573i) q^{83} +(-15.0767 + 8.00637i) q^{84} +(5.33682 + 1.18161i) q^{85} +(0.937521 + 2.57582i) q^{86} +(2.15732 + 5.08968i) q^{87} +(2.27368 - 3.24715i) q^{88} +(7.58469 + 13.1371i) q^{89} +(5.59319 + 12.8904i) q^{90} +(5.28723 - 9.15775i) q^{91} +(3.75502 + 8.05267i) q^{92} +(-2.41934 - 1.23430i) q^{93} +(-0.517156 + 0.616322i) q^{94} +(10.4581 - 0.459486i) q^{95} +(9.35119 - 10.3747i) q^{96} +(-1.25036 + 0.583050i) q^{97} +(5.44226 + 20.3108i) q^{98} +(-11.8566 + 8.59551i) 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 $

$2$	2.08671	+	0.182563i	1.47552	+	0.129092i	0.796328	−	0.604865i	$-0.206773\pi$
$2$	2.08671	+	0.182563i	1.47552	+	0.129092i	0.679196	+	0.733956i	$0.262328\pi$
$3$	−0.507262	+	1.65611i	−0.292868	+	0.956153i
$3$	−0.507262	+	1.65611i	−0.292868	+	0.956153i
$4$	2.35140	+	0.414615i	1.17570	+	0.207308i
$5$	−1.98370	−	1.03196i	−0.887138	−	0.461505i
$5$	−1.98370	−	1.03196i	−0.887138	−	0.461505i
$6$	−1.36085	+	3.36320i	−0.555565	+	1.37302i
$7$	3.38127	+	2.36759i	1.27800	+	0.894864i	0.997879	−	0.0651011i	$-0.0207370\pi$
$7$	3.38127	+	2.36759i	1.27800	+	0.894864i	0.280120	+	0.959965i	$0.409626\pi$
$8$	0.784385	+	0.210175i	0.277322	+	0.0743082i
$9$	−2.48537	−	1.68016i	−0.828457	−	0.560053i
$10$	−3.95100	−	2.51554i	−1.24942	−	0.795484i
$11$	1.66957	−	4.58710i	0.503394	−	1.38306i	−0.384546	−	0.923106i	$-0.625642\pi$
$11$	1.66957	−	4.58710i	0.503394	−	1.38306i	0.887940	−	0.459958i	$-0.152136\pi$
$12$	−1.87942	+	3.68385i	−0.542543	+	1.06344i
$13$	−0.223275	−	2.55204i	−0.0619252	−	0.707809i	−0.962175	−	0.272434i	$-0.912171\pi$
$13$	−0.223275	−	2.55204i	−0.0619252	−	0.707809i	0.900249	−	0.435375i	$-0.143384\pi$
$14$	6.62348	+	5.55776i	1.77020	+	1.48537i
$15$	2.71529	−	2.76174i	0.701084	−	0.713079i
$16$	−2.88895	−	1.05149i	−0.722238	−	0.262873i
$17$	−2.36120	+	0.632683i	−0.572676	+	0.153448i	−0.533524	−	0.845785i	$-0.679132\pi$
$17$	−2.36120	+	0.632683i	−0.572676	+	0.153448i	−0.0391524	+	0.999233i	$0.512466\pi$
$18$	−4.87950	−	3.95974i	−1.15011	−	0.933319i
$19$	−4.05431	+	2.34076i	−0.930123	+	0.537007i	−0.886850	−	0.462057i	$-0.847112\pi$
$19$	−4.05431	+	2.34076i	−0.930123	+	0.537007i	−0.0432724	+	0.999063i	$0.513778\pi$
$20$	−4.23661	−	3.24902i	−0.947335	−	0.726502i
$21$	−5.63616	+	4.39875i	−1.22991	+	0.959885i
$22$	4.32134	−	9.26714i	0.921313	−	1.97576i
$23$	2.13442	+	3.04827i	0.445058	+	0.635608i	0.977519	−	0.210846i	$-0.0676219\pi$
$23$	2.13442	+	3.04827i	0.445058	+	0.635608i	−0.532462	+	0.846454i	$0.678733\pi$
$24$	−0.745961	+	1.19241i	−0.152269	+	0.243400i
$25$	2.87013	+	4.09419i	0.574026	+	0.818837i
$26$		−	5.36612i		−	1.05238i
$27$	4.04325	−	3.26375i	0.778125	−	0.628110i
$28$	6.96907	+	6.96907i	1.31703	+	1.31703i
$29$	2.44490	−	2.05152i	0.454007	−	0.380957i	−0.386913	−	0.922116i	$-0.626459\pi$
$29$	2.44490	−	2.05152i	0.454007	−	0.380957i	0.840920	+	0.541159i	$0.182014\pi$
$30$	6.17020	−	5.26724i	1.12652	−	0.961662i
$31$	−0.272295	+	1.54426i	−0.0489057	+	0.277358i	−0.999447	−	0.0332389i	$-0.989418\pi$
$31$	−0.272295	+	1.54426i	−0.0489057	+	0.277358i	0.950542	+	0.310597i	$0.100529\pi$
$32$	−7.30837	−	3.40795i	−1.29195	−	0.602446i
$33$	6.74982	+	5.09185i	1.17499	+	0.886377i
$34$	−5.04264	+	0.889154i	−0.864806	+	0.152489i
$35$	−4.26417	−	8.18590i	−0.720776	−	1.38367i
$36$	−5.14748	−	4.98120i	−0.857914	−	0.830200i
$37$	0.592937	+	2.21287i	0.0974782	+	0.363793i	0.997384	−	0.0722918i	$-0.0230313\pi$
$37$	0.592937	+	2.21287i	0.0974782	+	0.363793i	−0.899905	+	0.436085i	$0.856365\pi$
$38$	−8.88750	+	4.14431i	−1.44174	+	0.672295i
$39$	4.33971	+	0.924787i	0.694909	+	0.148084i
$40$	−1.33909	−	1.22638i	−0.211729	−	0.193907i
$41$	−4.38733	+	5.22862i	−0.685186	+	0.816573i	−0.990764	−	0.135594i	$-0.956706\pi$
$41$	−4.38733	+	5.22862i	−0.685186	+	0.816573i	0.305579	+	0.952167i	$0.401150\pi$
$42$	−12.5641	+	8.14994i	−1.93868	+	1.25756i
$43$	0.553045	+	1.18601i	0.0843385	+	0.180865i	0.943954	−	0.330077i	$-0.107075\pi$
$43$	0.553045	+	1.18601i	0.0843385	+	0.180865i	−0.859616	+	0.510941i	$0.829297\pi$
$44$	5.82771	−	10.0939i	0.878561	−	1.52171i
$45$	3.19638	+	5.89773i	0.476488	+	0.879181i
$46$	3.89741	+	6.75051i	0.574642	+	0.995309i
$47$	−0.220307	+	0.314631i	−0.0321351	+	0.0458936i	−0.834898	−	0.550405i	$-0.814473\pi$
$47$	−0.220307	+	0.314631i	−0.0321351	+	0.0458936i	0.802763	+	0.596298i	$0.203362\pi$
$48$	3.20684	−	4.25102i	0.462867	−	0.613583i
$49$	3.43334	+	9.43304i	0.490478	+	1.34758i
$50$	5.24167	+	9.06735i	0.741284	+	1.28232i
$51$	0.149960	−	4.23134i	0.0209986	−	0.592506i
$52$	0.533107	−	6.09344i	0.0739287	−	0.845009i
$53$	0.177802	−	0.177802i	0.0244229	−	0.0244229i	−0.694790	−	0.719213i	$-0.744503\pi$
$53$	0.177802	−	0.177802i	0.0244229	−	0.0244229i	0.719213	+	0.694790i	$0.244503\pi$
$54$	9.03293	−	6.07235i	1.22923	−	0.826342i
$55$	−8.04562	+	7.37651i	−1.08487	+	0.994649i
$56$	2.15461	+	2.56776i	0.287921	+	0.343131i
$57$	−1.81994	−	7.90174i	−0.241057	−	1.04661i
$58$	5.47633	−	3.83457i	0.719077	−	0.503503i
$59$	−0.797126	+	0.290130i	−0.103777	+	0.0377717i	−0.393387	−	0.919373i	$-0.628697\pi$
$59$	−0.797126	+	0.290130i	−0.103777	+	0.0377717i	0.289610	+	0.957145i	$0.406474\pi$
$60$	7.52979	−	5.36817i	0.972091	−	0.693027i
$61$	1.38646	+	7.86300i	0.177518	+	1.00675i	0.935197	+	0.354127i	$0.115222\pi$
$61$	1.38646	+	7.86300i	0.177518	+	1.00675i	−0.757679	+	0.652627i	$0.773667\pi$
$62$	−0.850126	+	3.17272i	−0.107966	+	0.402935i
$63$	−4.42577	−	11.5654i	−0.557595	−	1.45710i
$64$	−9.30332	−	5.37128i	−1.16292	−	0.671410i
$65$	−2.19069	+	5.29289i	−0.271721	+	0.656502i
$66$	13.1553	+	11.8575i	1.61931	+	1.45955i
$67$	8.09911	−	0.708580i	0.989463	−	0.0865668i	0.419083	−	0.907948i	$-0.362351\pi$
$67$	8.09911	−	0.708580i	0.989463	−	0.0865668i	0.570380	+	0.821381i	$0.306796\pi$
$68$	−5.81446	+	0.508699i	−0.705106	+	0.0616888i
$69$	−6.13097	+	1.98856i	−0.738082	+	0.239394i
$70$	−7.40362	−	17.8601i	−0.884902	−	2.13469i
$71$	−7.83146	−	4.52149i	−0.929423	−	0.536603i	−0.0427939	−	0.999084i	$-0.513626\pi$
$71$	−7.83146	−	4.52149i	−0.929423	−	0.536603i	−0.886629	+	0.462481i	$0.846959\pi$
$72$	−1.59636	−	1.84025i	−0.188133	−	0.216876i
$73$	3.19228	−	11.9138i	0.373628	−	1.39440i	−0.481710	−	0.876330i	$-0.659984\pi$
$73$	3.19228	−	11.9138i	0.373628	−	1.39440i	0.855339	−	0.518069i	$-0.173349\pi$
$74$	0.833296	+	4.72586i	0.0968687	+	0.549370i
$75$	−8.23631	+	2.67641i	−0.951047	+	0.309045i
$76$	−10.5038	+	3.82308i	−1.20487	+	0.438537i
$77$	16.5056	−	11.5574i	1.88099	−	1.31708i
$78$	8.88686	+	2.72203i	1.00624	+	0.308209i
$79$	−6.94728	−	8.27944i	−0.781630	−	0.931510i	0.217376	−	0.976088i	$-0.430250\pi$
$79$	−6.94728	−	8.27944i	−0.781630	−	0.931510i	−0.999006	+	0.0445777i	$0.985806\pi$
$80$	4.64572	+	5.06712i	0.519407	+	0.566521i
$81$	3.35413	+	8.35163i	0.372681	+	0.927959i
$82$	−10.1096	+	10.1096i	−1.11642	+	1.11642i
$83$	0.325084	−	3.71573i	0.0356826	−	0.407854i	−0.957257	−	0.289237i	$-0.906598\pi$
$83$	0.325084	−	3.71573i	0.0356826	−	0.407854i	0.992940	−	0.118617i	$-0.0378461\pi$
$84$	−15.0767	+	8.00637i	−1.64500	+	0.873567i
$85$	5.33682	+	1.18161i	0.578859	+	0.128163i
$86$	0.937521	+	2.57582i	0.101095	+	0.277758i
$87$	2.15732	+	5.08968i	0.231289	+	0.545671i
$88$	2.27368	−	3.24715i	0.242375	−	0.346148i
$89$	7.58469	+	13.1371i	0.803975	+	1.39253i	0.916981	+	0.398932i	$0.130619\pi$
$89$	7.58469	+	13.1371i	0.803975	+	1.39253i	−0.113006	+	0.993594i	$0.536048\pi$
$90$	5.59319	+	12.8904i	0.589574	+	1.35876i
$91$	5.28723	−	9.15775i	0.554252	−	0.959993i
$92$	3.75502	+	8.05267i	0.391488	+	0.839549i
$93$	−2.41934	−	1.23430i	−0.250874	−	0.127991i
$94$	−0.517156	+	0.616322i	−0.0533406	+	0.0635688i
$95$	10.4581	−	0.459486i	1.07298	−	0.0471422i
$96$	9.35119	−	10.3747i	0.954401	−	1.05886i
$97$	−1.25036	+	0.583050i	−0.126954	+	0.0591998i	−0.485058	−	0.874482i	$-0.661201\pi$
$97$	−1.25036	+	0.583050i	−0.126954	+	0.0591998i	0.358103	+	0.933682i	$0.383424\pi$
$98$	5.44226	+	20.3108i	0.549751	+	2.05170i
$99$	−11.8566	+	8.59551i	−1.19163	+	0.863882i
$100$	5.05131	+	10.8171i	0.505131	+	1.08171i
$101$	0.515416	−	0.0908818i	0.0512858	−	0.00904308i	−0.147946	−	0.988995i	$-0.547266\pi$
$101$	0.515416	−	0.0908818i	0.0512858	−	0.00904308i	0.199232	+	0.979952i	$0.436155\pi$
$102$	1.08541	−	8.80219i	0.107471	−	0.871546i
$103$	3.14419	+	1.46616i	0.309806	+	0.144465i	0.571303	−	0.820739i	$-0.306438\pi$
$103$	3.14419	+	1.46616i	0.309806	+	0.144465i	−0.261496	+	0.965204i	$0.584216\pi$
$104$	0.361243	−	2.04871i	0.0354228	−	0.200892i
$105$	15.7198	−	2.90951i	1.53409	−	0.283939i
$106$	0.403480	−	0.338560i	0.0391894	−	0.0328838i
$107$	−4.07064	−	4.07064i	−0.393524	−	0.393524i	0.482418	−	0.875941i	$-0.339759\pi$
$107$	−4.07064	−	4.07064i	−0.393524	−	0.393524i	−0.875941	+	0.482418i	$0.839759\pi$
$108$	10.8605	−	5.99800i	1.04505	−	0.577158i
$109$		−	10.3288i		−	0.989319i	−0.869087	−	0.494660i	$-0.835293\pi$
$109$		−	10.3288i		−	0.989319i	0.869087	−	0.494660i	$-0.164707\pi$
$110$	−18.1355	+	13.9238i	−1.72916	+	1.32758i
$111$	−3.96552	−	0.140539i	−0.376390	−	0.0133394i
$112$	−7.27881	−	10.3952i	−0.687783	−	0.982256i
$113$	−2.31072	+	4.95536i	−0.217375	+	0.466161i	−0.984511	−	0.175323i	$-0.943903\pi$
$113$	−2.31072	+	4.95536i	−0.217375	+	0.466161i	0.767136	+	0.641484i	$0.221681\pi$
$114$	−2.35512	−	16.8209i	−0.220577	−	1.57542i
$115$	−1.08837	−	8.24948i	−0.101491	−	0.769268i
$116$	6.59954	−	3.81025i	0.612752	−	0.353773i
$117$	−3.73291	+	6.71790i	−0.345108	+	0.621070i
$118$	−1.71634	+	0.459891i	−0.158001	+	0.0423364i
$119$	−9.48179	−	3.45109i	−0.869194	−	0.316361i
$120$	2.71028	−	1.59558i	0.247413	−	0.145656i
$121$	−9.82758	−	8.24632i	−0.893416	−	0.749665i
$122$	1.45764	+	16.6609i	0.131968	+	1.50841i
$123$	−6.43361	−	9.91816i	−0.580099	−	0.894290i
$124$	−1.28055	+	3.51829i	−0.114997	+	0.315951i
$125$	−1.46845	−	11.0835i	−0.131342	−	0.991337i
$126$	−7.12388	−	24.9416i	−0.634646	−	2.22197i
$127$	6.98435	+	1.87145i	0.619760	+	0.166064i	0.555019	−	0.831838i	$-0.312711\pi$
$127$	6.98435	+	1.87145i	0.619760	+	0.166064i	0.0647416	+	0.997902i	$0.479378\pi$
$128$	−5.22160	−	3.65620i	−0.461528	−	0.323166i
$129$	−2.24469	+	0.314283i	−0.197634	+	0.0276711i
$130$	−5.53761	+	10.6448i	−0.485680	+	0.933608i
$131$	7.48308	+	1.31947i	0.653800	+	0.115283i	0.490702	−	0.871327i	$-0.336740\pi$
$131$	7.48308	+	1.31947i	0.653800	+	0.115283i	0.163098	+	0.986610i	$0.447851\pi$
$132$	13.7604	+	14.7716i	1.19769	+	1.28570i
$133$	−19.2507	−	1.68421i	−1.66924	−	0.146040i
$134$	17.0298			1.47115
$135$	−11.3887	+	2.30184i	−0.980180	+	0.198111i
$136$	−1.98507			−0.170218
$137$	8.77434	+	0.767656i	0.749643	+	0.0655852i	0.455573	−	0.890199i	$-0.349435\pi$
$137$	8.77434	+	0.767656i	0.749643	+	0.0655852i	0.294070	+	0.955784i	$0.404990\pi$
$138$	−13.1566	+	3.03024i	−1.11996	+	0.257951i
$139$	0.637180	+	0.112352i	0.0540449	+	0.00952958i	0.200605	−	0.979672i	$-0.435709\pi$
$139$	0.637180	+	0.112352i	0.0540449	+	0.00952958i	−0.146560	+	0.989202i	$0.546820\pi$
$140$	−6.63277	−	21.0163i	−0.560571	−	1.77620i
$141$	−0.409308	−	0.524452i	−0.0344700	−	0.0441668i
$142$	−15.5165	−	10.8648i	−1.30212	−	0.911751i
$143$	−12.0792	−	3.23662i	−1.01012	−	0.270660i
$144$	5.41344	+	7.46724i	0.451120	+	0.622270i
$145$	−6.96703	+	1.54656i	−0.578581	+	0.128435i
$146$	8.83637	−	24.2777i	0.731303	−	2.00924i
$147$	−17.3637	+	0.900959i	−1.43213	+	0.0743099i
$148$	0.476742	+	5.44918i	0.0391879	+	0.447920i
$149$	−14.2896	−	11.9904i	−1.17065	−	0.982290i	−0.170652	−	0.985331i	$-0.554587\pi$
$149$	−14.2896	−	11.9904i	−1.17065	−	0.982290i	−0.999995	+	0.00304137i	$0.999032\pi$
$150$	−17.6754	+	4.08124i	−1.44319	+	0.333232i
$151$	11.1465	+	4.05701i	0.907092	+	0.330155i	0.753091	−	0.657916i	$-0.228562\pi$
$151$	11.1465	+	4.05701i	0.907092	+	0.330155i	0.154001	+	0.988071i	$0.450784\pi$
$152$	−3.67211	+	0.983939i	−0.297847	+	0.0798080i
$153$	6.93147	+	2.39475i	0.560376	+	0.193604i
$154$	36.5524	−	21.1035i	2.94547	−	1.70057i
$155$	2.13377	−	2.78236i	0.171388	−	0.223484i
$156$	9.82096	+	3.97385i	0.786306	+	0.318163i
$157$	0.402710	−	0.863615i	0.0321398	−	0.0689240i	−0.889582	−	0.456775i	$-0.849005\pi$
$157$	0.402710	−	0.863615i	0.0321398	−	0.0689240i	0.921722	+	0.387851i	$0.126782\pi$
$158$	−12.9854	−	18.5451i	−1.03306	−	1.47537i
$159$	0.204266	+	0.384650i	0.0161994	+	0.0305048i
$160$	10.9808	+	14.3023i	0.868105	+	1.13069i
$161$			15.3604i			1.21057i
$162$	5.47439	+	18.0398i	0.430109	+	1.41734i
$163$	12.1885	+	12.1885i	0.954673	+	0.954673i	0.999016	−	0.0443429i	$-0.0141194\pi$
$163$	12.1885	+	12.1885i	0.954673	+	0.954673i	−0.0443429	+	0.999016i	$0.514119\pi$
$164$	−12.4842	+	10.4755i	−0.974855	+	0.818001i
$165$	−8.13505	−	17.0662i	−0.633313	−	1.32860i
$166$	1.35671	−	7.69429i	0.105301	−	0.597193i
$167$	−4.59936	−	2.14472i	−0.355909	−	0.165963i	0.236437	−	0.971647i	$-0.424020\pi$
$167$	−4.59936	−	2.14472i	−0.355909	−	0.165963i	−0.592346	+	0.805684i	$0.701798\pi$
$168$	−5.34543	+	2.26573i	−0.412409	+	0.174805i
$169$	6.33944	−	1.11781i	0.487649	−	0.0859858i
$170$	10.9207	+	3.43998i	0.837577	+	0.263834i
$171$	14.0093	+	0.994237i	1.07132	+	0.0760312i
$172$	0.808693	+	3.01808i	0.0616622	+	0.230127i
$173$	−1.51516	+	0.706530i	−0.115195	+	0.0537164i	−0.479362	−	0.877617i	$-0.659132\pi$
$173$	−1.51516	+	0.706530i	−0.115195	+	0.0537164i	0.364166	+	0.931334i	$0.381354\pi$
$174$	3.57251	+	11.0145i	0.270832	+	0.835008i
$175$	0.0113268	+	20.6388i	0.000856228	+	1.56015i
$176$	−9.64661	+	11.4964i	−0.727140	+	0.866572i
$177$	−0.0761343	−	1.46730i	−0.00572261	−	0.110289i
$178$	13.4287	+	28.7979i	1.00652	+	2.15849i
$179$	7.16939	−	12.4178i	0.535866	−	0.928147i	−0.463255	−	0.886225i	$-0.653319\pi$
$179$	7.16939	−	12.4178i	0.535866	−	0.928147i	0.999121	−	0.0419217i	$-0.0133480\pi$
$180$	5.07068	+	15.1932i	0.377946	+	1.13243i
$181$	−10.7361	−	18.5955i	−0.798011	−	1.38220i	−0.920910	−	0.389776i	$-0.872552\pi$
$181$	−10.7361	−	18.5955i	−0.798011	−	1.38220i	0.122899	−	0.992419i	$-0.460781\pi$
$182$	12.7048	−	18.1443i	0.941740	−	1.34494i
$183$	−13.7253	−	1.69248i	−1.01460	−	0.125112i
$184$	1.03354	+	2.83962i	0.0761933	+	0.209339i
$185$	1.10738	−	5.00155i	0.0814160	−	0.367722i
$186$	−4.82311	−	3.01730i	−0.353648	−	0.221239i
$187$	−1.04001	+	11.8874i	−0.0760532	+	0.869292i
$188$	−0.648481	+	0.648481i	−0.0472953	+	0.0472953i
$189$	21.3985	−	1.46286i	1.55651	−	0.106408i
$190$	21.9069	+	0.950452i	1.58929	+	0.0689530i
$191$	−7.60498	−	9.06326i	−0.550277	−	0.655794i	0.417182	−	0.908823i	$-0.363018\pi$
$191$	−7.60498	−	9.06326i	−0.550277	−	0.655794i	−0.967459	+	0.253029i	$0.918573\pi$
$192$	13.6146	−	12.6826i	0.982551	−	0.915291i
$193$	−13.1725	+	9.22349i	−0.948178	+	0.663922i	−0.941841	−	0.336058i	$-0.890906\pi$
$193$	−13.1725	+	9.22349i	−0.948178	+	0.663922i	−0.00633721	+	0.999980i	$0.502017\pi$
$194$	−2.71557	+	0.988386i	−0.194967	+	0.0709620i
$195$	−7.65433	−	6.31289i	−0.548138	−	0.452075i
$196$	4.16209	+	23.6044i	0.297292	+	1.68603i
$197$	−7.15409	+	26.6994i	−0.509708	+	1.90225i	−0.0864206	+	0.996259i	$0.527543\pi$
$197$	−7.15409	+	26.6994i	−0.509708	+	1.90225i	−0.423287	+	0.905996i	$0.639124\pi$
$198$	−26.3104	+	15.7717i	−1.86980	+	1.12085i
$199$	−17.2147	−	9.93892i	−1.22032	−	0.704551i	−0.255332	−	0.966853i	$-0.582185\pi$
$199$	−17.2147	−	9.93892i	−1.22032	−	0.704551i	−0.964986	+	0.262302i	$0.915518\pi$
$200$	1.39079	+	3.81465i	0.0983437	+	0.269736i
$201$	−2.93489	+	13.7724i	−0.207011	+	0.971431i
$202$	1.09211	−	0.0955476i	0.0768409	−	0.00672271i
$203$	13.1240	−	1.14820i	0.921126	−	0.0805881i
$204$	2.10699	−	9.88740i	0.147519	−	0.692256i
$205$	14.0988	−	5.84447i	0.984706	−	0.408195i
$206$	6.29334	+	3.63346i	0.438478	+	0.253155i
$207$	−0.183251	−	11.1622i	−0.0127368	−	0.775830i
$208$	−2.03842	+	7.60749i	−0.141339	+	0.527484i
$209$	3.96835	+	22.5056i	0.274496	+	1.55675i
$210$	33.3337	−	3.20145i	2.30025	−	0.220921i
$211$	21.2772	−	7.74427i	1.46478	−	0.533137i	0.518105	−	0.855317i	$-0.326638\pi$
$211$	21.2772	−	7.74427i	1.46478	−	0.533137i	0.946678	+	0.322180i	$0.104416\pi$
$212$	0.491802	−	0.344364i	0.0337771	−	0.0236510i
$213$	11.4607	−	10.6761i	0.785272	−	0.731517i
$214$	−7.75108	−	9.23738i	−0.529853	−	0.631454i
$215$	0.126835	−	2.92340i	0.00865006	−	0.199374i
$216$	3.85743	−	1.71025i	0.262465	−	0.116368i
$217$	−4.57688	+	4.57688i	−0.310699	+	0.310699i
$218$	1.88566	−	21.5532i	0.127713	−	1.45976i
$219$	18.1111	+	11.3302i	1.22384	+	0.765621i
$220$	−21.9769	+	14.0093i	−1.48168	+	0.944507i
$221$	2.14183	+	5.88462i	0.144075	+	0.395843i
$222$	−8.24922	−	1.01722i	−0.553651	−	0.0682715i
$223$	5.78878	−	8.26723i	0.387645	−	0.553615i	−0.577143	−	0.816643i	$-0.695832\pi$
$223$	5.78878	−	8.26723i	0.387645	−	0.553615i	0.964788	+	0.263029i	$0.0847213\pi$
$224$	−16.6429	−	28.8264i	−1.11200	−	1.92604i
$225$	−0.254453	−	14.9978i	−0.0169635	−	0.999856i
$226$	−5.72647	+	9.91853i	−0.380919	+	0.659771i
$227$	10.3017	+	22.0920i	0.683745	+	1.46630i	0.874684	+	0.484694i	$0.161069\pi$
$227$	10.3017	+	22.0920i	0.683745	+	1.46630i	−0.190939	+	0.981602i	$0.561153\pi$
$228$	−1.00323	−	19.3347i	−0.0664406	−	1.28048i
$229$	−5.75242	+	6.85547i	−0.380131	+	0.453022i	−0.921855	−	0.387534i	$-0.873327\pi$
$229$	−5.75242	+	6.85547i	−0.380131	+	0.453022i	0.541725	+	0.840556i	$0.317771\pi$
$230$	−0.765053	−	17.4129i	−0.0504461	−	1.14818i
$231$	10.7675	+	33.1977i	0.708452	+	2.18425i
$232$	2.34892	−	1.09532i	0.154214	−	0.0719114i
$233$	4.94285	+	18.4470i	0.323817	+	1.20850i	0.915496	+	0.402328i	$0.131799\pi$
$233$	4.94285	+	18.4470i	0.323817	+	1.20850i	−0.591679	+	0.806174i	$0.701535\pi$
$234$	−9.01594	+	13.3368i	−0.589390	+	0.871854i
$235$	0.761708	−	0.396786i	0.0496884	−	0.0258835i
$236$	−1.99466	+	0.351712i	−0.129841	+	0.0228945i
$237$	17.2357	−	7.30558i	1.11958	−	0.474548i
$238$	−19.1557	−	8.93244i	−1.24168	−	0.579004i
$239$	−0.434105	+	2.46193i	−0.0280799	+	0.159249i	−0.995623	−	0.0934552i	$-0.970209\pi$
$239$	−0.434105	+	2.46193i	−0.0280799	+	0.159249i	0.967544	+	0.252704i	$0.0813199\pi$
$240$	−10.7483	+	5.12344i	−0.693798	+	0.330717i
$241$	16.4029	−	13.7637i	1.05660	−	0.886595i	0.0628307	−	0.998024i	$-0.479987\pi$
$241$	16.4029	−	13.7637i	1.05660	−	0.886595i	0.993772	+	0.111429i	$0.0355428\pi$
$242$	−19.0018	−	19.0018i	−1.22148	−	1.22148i
$243$	−15.5326	+	1.31833i	−0.996417	+	0.0845709i
$244$			19.0639i			1.22044i
$245$	2.92376	−	22.2554i	0.186792	−	1.42184i
$246$	−11.6144	−	21.8708i	−0.740505	−	1.39443i
$247$	6.87893	+	9.82413i	0.437696	+	0.625095i
$248$	−0.538151	+	1.15407i	−0.0341726	+	0.0732834i
$249$	5.98874	+	2.42322i	0.379521	+	0.153565i
$250$	−1.04079	−	23.3961i	−0.0658255	−	1.47970i
$251$	13.6587	−	7.88585i	0.862129	−	0.497751i	−0.00259539	−	0.999997i	$-0.500826\pi$
$251$	13.6587	−	7.88585i	0.862129	−	0.497751i	0.864725	+	0.502246i	$0.167493\pi$
$252$	−5.61158	−	29.0299i	−0.353496	−	1.82871i
$253$	17.5463	−	4.70152i	1.10313	−	0.295582i
$254$	14.2326	+	5.18025i	0.893034	+	0.325038i
$255$	−4.66403	+	8.23895i	−0.292073	+	0.515943i
$256$	6.23009	+	5.22767i	0.389381	+	0.326729i
$257$	−0.121306	−	1.38654i	−0.00756687	−	0.0864897i	0.991472	−	0.130318i	$-0.0416000\pi$
$257$	−0.121306	−	1.38654i	−0.00756687	−	0.0864897i	−0.999039	+	0.0438287i	$0.986044\pi$
$258$	−4.74139	+	0.246019i	−0.295186	+	0.0153165i
$259$	−3.23429	+	8.88613i	−0.200969	+	0.552157i
$260$	−7.34570	+	11.5374i	−0.455561	+	0.715520i
$261$	−9.52337	+	0.990955i	−0.589482	+	0.0613386i
$262$	15.3741	+	4.11948i	0.949816	+	0.254502i
$263$	20.2750	+	14.1967i	1.25021	+	0.875405i	0.995788	−	0.0916894i	$-0.0292267\pi$
$263$	20.2750	+	14.1967i	1.25021	+	0.875405i	0.254420	+	0.967094i	$0.418116\pi$
$264$	4.22428	+	5.41261i	0.259986	+	0.333123i
$265$	−0.536189	+	0.169221i	−0.0329378	+	0.0103952i
$266$	−39.8630	−	7.02892i	−2.44416	−	0.430971i
$267$	−25.6038	+	5.89711i	−1.56693	+	0.360897i
$268$	19.3380	+	1.69186i	1.18126	+	0.103347i
$269$	−30.2129			−1.84212			−0.921058	−	0.389426i	$-0.872673\pi$
$269$	−30.2129			−1.84212			−0.921058	+	0.389426i	$0.872673\pi$
$270$	−24.1850	+	2.72413i	−1.47185	+	0.165785i
$271$	−30.1849			−1.83360			−0.916802	−	0.399341i	$-0.869239\pi$
$271$	−30.1849			−1.83360			−0.916802	+	0.399341i	$0.869239\pi$
$272$	7.48666	+	0.654998i	0.453946	+	0.0397151i
$273$	12.4842	+	13.4016i	0.755577	+	0.811101i
$274$	18.1693	+	3.20374i	1.09765	+	0.193545i
$275$	23.5723	−	6.33006i	1.42147	−	0.381717i
$276$	−15.2408	+	2.13390i	−0.917391	+	0.128446i
$277$	−4.74942	−	3.32558i	−0.285365	−	0.199815i	0.422126	−	0.906537i	$-0.361284\pi$
$277$	−4.74942	−	3.32558i	−0.285365	−	0.199815i	−0.707491	+	0.706723i	$0.750173\pi$
$278$	1.30910	+	0.350772i	0.0785144	+	0.0210379i
$279$	3.27136	−	3.38057i	0.195851	−	0.202389i
$280$	−1.62427	−	7.31712i	−0.0970689	−	0.437282i
$281$	−5.21843	+	14.3375i	−0.311305	+	0.855304i	0.681089	+	0.732201i	$0.261507\pi$
$281$	−5.21843	+	14.3375i	−0.311305	+	0.855304i	−0.992394	+	0.123103i	$0.960715\pi$
$282$	−0.758361	−	1.16910i	−0.0451598	−	0.0696190i
$283$	−2.06765	−	23.6334i	−0.122909	−	1.40486i	−0.767852	−	0.640627i	$-0.778674\pi$
$283$	−2.06765	−	23.6334i	−0.122909	−	1.40486i	0.644943	−	0.764231i	$-0.276881\pi$
$284$	−16.5402	−	13.8789i	−0.981481	−	0.823561i
$285$	−4.54404	+	17.5528i	−0.269166	+	1.03974i
$286$	−24.6150	−	8.95911i	−1.45551	−	0.529764i
$287$	−27.2139	+	7.29195i	−1.60639	+	0.430430i
$288$	12.4381	+	20.7492i	0.732923	+	1.22266i
$289$	−9.54744	+	5.51222i	−0.561614	+	0.324248i
$290$	−14.8205	+	1.95529i	−0.870290	+	0.114819i
$291$	−0.331335	−	2.36648i	−0.0194232	−	0.138726i
$292$	12.4460	−	26.6905i	0.728345	−	1.56194i
$293$	4.78492	+	6.83357i	0.279538	+	0.399221i	0.934228	−	0.356676i	$-0.116090\pi$
$293$	4.78492	+	6.83357i	0.279538	+	0.399221i	−0.654690	+	0.755897i	$0.727201\pi$
$294$	−36.3975	−	1.28994i	−2.12274	−	0.0752306i
$295$	1.88066	+	0.247069i	0.109496	+	0.0143849i
$296$			1.86036i			0.108131i
$297$	−8.22069	−	23.9959i	−0.477013	−	1.39238i
$298$	−27.6292	−	27.6292i	−1.60051	−	1.60051i
$299$	7.30274	−	6.12773i	0.422329	−	0.354376i
$300$	−20.4766	+	2.87842i	−1.18221	+	0.166185i
$301$	−0.937987	+	5.31959i	−0.0540647	+	0.306616i
$302$	22.5189	+	10.5007i	1.29582	+	0.604249i
$303$	−0.110941	+	0.899685i	−0.00637341	+	0.0516855i
$304$	14.1740	−	2.49926i	0.812934	−	0.143342i
$305$	5.36396	−	17.0286i	0.307139	−	0.975055i
$306$	14.0268	+	6.26257i	0.801856	+	0.358007i
$307$	−5.72891	−	21.3806i	−0.326966	−	1.22025i	−0.912321	−	0.409476i	$-0.865711\pi$
$307$	−5.72891	−	21.3806i	−0.326966	−	1.22025i	0.585355	−	0.810777i	$-0.300955\pi$
$308$	43.6032	−	20.3325i	2.48452	−	1.15855i
$309$	−4.02305	+	4.46338i	−0.228863	+	0.253913i
$310$	4.96050	−	5.41642i	0.281738	−	0.307632i
$311$	17.1260	−	20.4100i	0.971128	−	1.15735i	−0.0163937	−	0.999866i	$-0.505219\pi$
$311$	17.1260	−	20.4100i	0.971128	−	1.15735i	0.987522	−	0.157480i	$-0.0503370\pi$
$312$	3.20963	+	1.63749i	0.181710	+	0.0927045i
$313$	−0.188967	−	0.405241i	−0.0106810	−	0.0229056i	0.900895	−	0.434037i	$-0.142911\pi$
$313$	−0.188967	−	0.405241i	−0.0106810	−	0.0229056i	−0.911576	+	0.411132i	$0.865134\pi$
$314$	0.998003	−	1.72859i	0.0563206	−	0.0975501i
$315$	−3.15558	+	27.5095i	−0.177797	+	1.54998i
$316$	−12.9031	−	22.3487i	−0.725853	−	1.25722i
$317$	0.491526	−	0.701972i	0.0276069	−	0.0394267i	−0.805111	−	0.593124i	$-0.797895\pi$
$317$	0.491526	−	0.701972i	0.0276069	−	0.0394267i	0.832718	+	0.553697i	$0.186783\pi$
$318$	0.356021	+	0.839944i	0.0199647	+	0.0471017i
$319$	−5.32859	−	14.6402i	−0.298344	−	0.819693i
$320$	12.9121	+	20.2556i	0.721807	+	1.13232i
$321$	8.80629	−	4.67653i	0.491519	−	0.261018i
$322$	−2.80425	+	32.0527i	−0.156275	+	1.78623i
$323$	8.09210	−	8.09210i	0.450256	−	0.450256i
$324$	4.42419	+	21.0287i	0.245789	+	1.16826i
$325$	9.80770	−	8.23881i	0.544033	−	0.457007i
$326$	23.2086	+	27.6589i	1.28540	+	1.53188i
$327$	17.1056	+	5.23941i	0.945940	+	0.289740i
$328$	−4.54028	+	3.17914i	−0.250695	+	0.175539i
$329$	−1.48983	+	0.542255i	−0.0821371	+	0.0298955i
$330$	−13.8598	−	37.0974i	−0.762957	−	2.04214i
$331$	4.97884	+	28.2364i	0.273662	+	1.55201i	0.743181	+	0.669091i	$0.233316\pi$
$331$	4.97884	+	28.2364i	0.273662	+	1.55201i	−0.469519	+	0.882922i	$0.655573\pi$
$332$	2.30500	−	8.60238i	0.126503	−	0.472117i
$333$	2.24431	−	6.49603i	0.122987	−	0.355980i
$334$	−9.20598	−	5.31507i	−0.503729	−	0.290828i
$335$	−16.7974	−	6.95232i	−0.917741	−	0.379846i
$336$	20.9078	−	6.78138i	1.14062	−	0.369954i
$337$	−7.49834	+	0.656020i	−0.408461	+	0.0357357i	−0.289535	−	0.957167i	$-0.593501\pi$
$337$	−7.49834	+	0.656020i	−0.408461	+	0.0357357i	−0.118926	+	0.992903i	$0.537945\pi$
$338$	13.4326	−	1.17520i	0.730639	−	0.0639226i
$339$	−7.03446	−	6.34047i	−0.382059	−	0.344367i
$340$	12.0591	+	4.99116i	0.653996	+	0.270684i
$341$	6.62908	+	3.82730i	0.358985	+	0.207260i
$342$	29.0518	+	4.63227i	1.57094	+	0.250484i
$343$	−3.24609	+	12.1146i	−0.175272	+	0.654125i
$344$	0.184530	+	1.04652i	0.00994921	+	0.0564248i
$345$	14.2141	+	2.38220i	0.765261	+	0.128253i
$346$	−3.29068	+	1.19771i	−0.176908	+	0.0643892i
$347$	−21.2589	+	14.8856i	−1.14124	+	0.799103i	−0.982138	−	0.188160i	$-0.939748\pi$
$347$	−21.2589	+	14.8856i	−1.14124	+	0.799103i	−0.159099	+	0.987263i	$0.550859\pi$
$348$	2.96247	+	12.8623i	0.158805	+	0.689493i
$349$	11.2260	+	13.3786i	0.600915	+	0.716143i	0.977664	−	0.210173i	$-0.0674026\pi$
$349$	11.2260	+	13.3786i	0.600915	+	0.716143i	−0.376749	+	0.926315i	$0.622958\pi$
$350$	−3.74425	+	43.0692i	−0.200139	+	2.30215i
$351$	−9.23199	−	9.58983i	−0.492767	−	0.511867i
$352$	−27.8345	+	27.8345i	−1.48358	+	1.48358i
$353$	−0.785720	+	8.98082i	−0.0418196	+	0.478001i	0.946190	+	0.323611i	$0.104897\pi$
$353$	−0.785720	+	8.98082i	−0.0418196	+	0.478001i	−0.988010	+	0.154390i	$0.950659\pi$
$354$	0.109004	−	3.07572i	0.00579351	−	0.163473i
$355$	10.8693	+	17.0510i	0.576881	+	0.904974i
$356$	12.3878	+	34.0352i	0.656553	+	1.80386i
$357$	10.5251	−	13.9522i	0.557048	−	0.738431i
$358$	17.2275	−	24.6033i	0.910499	−	1.30033i
$359$	7.90716	+	13.6956i	0.417324	+	0.722827i	0.995669	−	0.0929655i	$-0.0296346\pi$
$359$	7.90716	+	13.6956i	0.417324	+	0.722827i	−0.578345	+	0.815792i	$0.696301\pi$
$360$	1.26763	+	5.29789i	0.0668102	+	0.279223i
$361$	1.45829	−	2.52584i	0.0767523	−	0.132939i
$362$	−19.0083	−	40.7635i	−0.999055	−	2.14248i
$363$	18.6419	−	12.0925i	0.978448	−	0.634690i
$364$	16.2293	−	19.3414i	0.850648	−	1.01376i
$365$	−18.6270	+	20.3390i	−0.974982	+	1.06459i
$366$	−28.3316	−	6.03744i	−1.48092	−	0.315582i
$367$	19.6260	−	9.15174i	1.02447	−	0.477717i	0.163589	−	0.986529i	$-0.447693\pi$
$367$	19.6260	−	9.15174i	1.02447	−	0.477717i	0.860878	+	0.508812i	$0.169915\pi$
$368$	−2.96101	−	11.0506i	−0.154353	−	0.576054i
$369$	19.6890	−	5.62364i	1.02497	−	0.292755i
$370$	3.22387	−	10.2346i	0.167601	−	0.532072i
$371$	1.02216	−	0.180234i	0.0530677	−	0.00935726i
$372$	−5.17708	−	3.90542i	−0.268419	−	0.202487i
$373$	−22.0287	−	10.2722i	−1.14060	−	0.531873i	−0.241845	−	0.970315i	$-0.577753\pi$
$373$	−22.0287	−	10.2722i	−1.14060	−	0.531873i	−0.898760	+	0.438442i	$0.855530\pi$
$374$	−4.34040	+	24.6156i	−0.224437	+	1.27284i
$375$	19.1003	+	3.19032i	0.986336	+	0.164747i
$376$	−0.238933	+	0.200489i	−0.0123220	+	0.0103394i
$377$	−5.78144	−	5.78144i	−0.297759	−	0.297759i
$378$	44.9196	+	0.854021i	2.31041	+	0.0439261i
$379$		−	18.5170i		−	0.951157i	−0.879673	−	0.475578i	$-0.842239\pi$
$379$		−	18.5170i		−	0.951157i	0.879673	−	0.475578i	$-0.157761\pi$
$380$	24.7817	+	3.25565i	1.27127	+	0.167012i
$381$	−6.64221	+	10.6175i	−0.340291	+	0.543951i
$382$	−14.2147	−	20.3008i	−0.727289	−	1.03868i
$383$	−0.998023	+	2.14027i	−0.0509966	+	0.109363i	−0.930155	−	0.367167i	$-0.880328\pi$
$383$	−0.998023	+	2.14027i	−0.0509966	+	0.109363i	0.879158	+	0.476530i	$0.158105\pi$
$384$	8.70378	−	6.79286i	0.444163	−	0.346647i
$385$	−44.6689	+	5.89325i	−2.27654	+	0.300348i
$386$	−29.1711	+	16.8419i	−1.48477	+	0.857231i
$387$	0.618161	−	3.87687i	0.0314229	−	0.197073i
$388$	−3.18183	+	0.852569i	−0.161533	+	0.0432826i
$389$	9.90399	+	3.60476i	0.502152	+	0.182768i	0.580662	−	0.814145i	$-0.302794\pi$
$389$	9.90399	+	3.60476i	0.502152	+	0.182768i	−0.0785096	+	0.996913i	$0.525016\pi$
$390$	−14.8199	−	14.5706i	−0.750432	−	0.737809i
$391$	−6.96839	−	5.84717i	−0.352407	−	0.295704i
$392$	0.710472	+	8.12074i	0.0358843	+	0.410159i
$393$	−5.98107	+	11.7235i	−0.301705	+	0.591370i
$394$	−19.8028	+	54.4078i	−0.997651	+	2.74102i
$395$	5.23728	+	23.5932i	0.263516	+	1.18710i
$396$	−31.4434	+	15.2956i	−1.58009	+	0.768632i
$397$	−7.52877	−	2.01733i	−0.377858	−	0.101247i	0.0648910	−	0.997892i	$-0.479330\pi$
$397$	−7.52877	−	2.01733i	−0.377858	−	0.101247i	−0.442749	+	0.896646i	$0.645997\pi$
$398$	−34.1076	−	23.8824i	−1.70966	−	1.19712i
$399$	12.5544	−	31.0268i	0.628504	−	1.55328i
$400$	−3.98666	−	14.8458i	−0.199333	−	0.742291i
$401$	−28.6980	−	5.06024i	−1.43311	−	0.252696i	−0.597434	−	0.801918i	$-0.703813\pi$
$401$	−28.6980	−	5.06024i	−1.43311	−	0.252696i	−0.835677	+	0.549222i	$0.814924\pi$
$402$	−8.63858	+	28.2032i	−0.430853	+	1.40665i
$403$	4.00182	+	0.350114i	0.199345	+	0.0174404i
$404$	1.24963			0.0621715
$405$	1.96494	−	20.0285i	0.0976384	−	0.995222i
$406$	27.5956			1.36955
$407$	11.1406	+	0.974677i	0.552220	+	0.0483130i
$408$	1.00695	−	3.28748i	0.0498514	−	0.162755i
$409$	−10.1037	−	1.78155i	−0.499594	−	0.0880918i	−0.0818277	−	0.996646i	$-0.526076\pi$
$409$	−10.1037	−	1.78155i	−0.499594	−	0.0880918i	−0.417766	+	0.908555i	$0.637187\pi$
$410$	30.4872	−	9.62176i	1.50565	−	0.475185i
$411$	−5.72221	+	14.1418i	−0.282256	+	0.697565i
$412$	6.78536	+	4.75116i	0.334291	+	0.234073i
$413$	−3.38220	−	0.906258i	−0.166427	−	0.0445941i
$414$	1.65543	−	23.3258i	0.0813597	−	1.14640i
$415$	−4.47934	+	7.03542i	−0.219882	+	0.345355i
$416$	−7.06545	+	19.4122i	−0.346412	+	0.951760i
$417$	−0.509284	+	0.998246i	−0.0249398	+	0.0488843i
$418$	4.17208	+	47.6871i	0.204063	+	2.33245i
$419$	−14.0240	−	11.7675i	−0.685117	−	0.574881i	0.232380	−	0.972625i	$-0.425349\pi$
$419$	−14.0240	−	11.7675i	−0.685117	−	0.574881i	−0.917496	+	0.397744i	$0.869793\pi$
$420$	38.1698	−	0.323771i	1.86250	−	0.0157984i
$421$	−28.8617	−	10.5048i	−1.40664	−	0.511973i	−0.476495	−	0.879177i	$-0.658093\pi$
$421$	−28.8617	−	10.5048i	−1.40664	−	0.511973i	−0.930140	+	0.367204i	$0.880315\pi$
$422$	45.8131	−	12.2756i	2.23015	−	0.597566i
$423$	1.07617	−	0.411824i	0.0523254	−	0.0200235i
$424$	0.176834	−	0.102095i	0.00858784	−	0.00495819i
$425$	−9.36728	−	7.85132i	−0.454380	−	0.380845i
$426$	25.8641	−	20.1857i	1.25312	−	0.977999i
$427$	−13.9284	+	29.8695i	−0.674040	+	1.44548i
$428$	−7.88396	−	11.2595i	−0.381085	−	0.544246i
$429$	11.4875	−	18.3627i	0.554623	−	0.886559i
$430$	0.798373	−	6.07713i	0.0385010	−	0.293065i
$431$		−	13.0253i		−	0.627407i	−0.949521	−	0.313703i	$-0.898430\pi$
$431$		−	13.0253i		−	0.627407i	0.949521	−	0.313703i	$-0.101570\pi$
$432$	−15.1126	+	5.17738i	−0.727104	+	0.249097i
$433$	24.3815	+	24.3815i	1.17170	+	1.17170i	0.981804	+	0.189896i	$0.0608150\pi$
$433$	24.3815	+	24.3815i	1.17170	+	1.17170i	0.189896	+	0.981804i	$0.439185\pi$
$434$	−10.3862	+	8.71504i	−0.498553	+	0.418335i
$435$	0.972845	−	12.3227i	0.0466444	−	0.590826i
$436$	4.28248	−	24.2871i	0.205093	−	1.16314i
$437$	−15.7889	−	7.36247i	−0.755284	−	0.352195i
$438$	35.7241	+	26.9491i	1.70696	+	1.28768i
$439$	21.0657	−	3.71446i	1.00541	−	0.177281i	0.353386	−	0.935477i	$-0.385030\pi$
$439$	21.0657	−	3.71446i	1.00541	−	0.177281i	0.652027	+	0.758196i	$0.273919\pi$
$440$	−7.86122	+	4.09504i	−0.374769	+	0.195223i
$441$	7.31587	−	29.2132i	0.348375	−	1.39110i
$442$	3.39505	+	12.6705i	0.161486	+	0.602674i
$443$	−24.5747	+	11.4594i	−1.16758	+	0.544452i	−0.907054	−	0.421014i	$-0.861674\pi$
$443$	−24.5747	+	11.4594i	−1.16758	+	0.544452i	−0.260527	+	0.965466i	$0.583896\pi$
$444$	−9.26626	−	1.97463i	−0.439757	−	0.0937118i
$445$	−1.48886	−	33.8871i	−0.0705786	−	1.60640i
$446$	13.5888	−	16.1945i	0.643447	−	0.766830i
$447$	27.1059	−	17.5828i	1.28206	−	0.831637i
$448$	−18.7400	−	40.1882i	−0.885384	−	1.89871i
$449$	1.17379	−	2.03306i	0.0553944	−	0.0959459i	−0.836998	−	0.547205i	$-0.815692\pi$
$449$	1.17379	−	2.03306i	0.0553944	−	0.0959459i	0.892393	+	0.451259i	$0.149025\pi$
$450$	2.20709	−	31.3426i	0.104043	−	1.47750i
$451$	16.6593	+	28.8547i	0.784454	+	1.35871i
$452$	−7.48801	+	10.6940i	−0.352206	+	0.503003i
$453$	−12.3730	+	16.4019i	−0.581336	+	0.770627i
$454$	17.4634	+	47.9802i	0.819596	+	2.25182i
$455$	−19.9387	+	12.7100i	−0.934740	+	0.595855i
$456$	0.233215	−	6.58052i	0.0109213	−	0.308161i
$457$	0.0458303	−	0.523843i	0.00214385	−	0.0245043i	−0.995047	−	0.0994013i	$-0.968307\pi$
$457$	0.0458303	−	0.523843i	0.00214385	−	0.0245043i	0.997191	+	0.0748970i	$0.0238628\pi$
$458$	−13.2552	+	13.2552i	−0.619374	+	0.619374i
$459$	−7.48203	+	10.2645i	−0.349231	+	0.479105i
$460$	0.861173	−	19.8491i	0.0401524	−	0.925469i
$461$	−5.97585	−	7.12174i	−0.278323	−	0.331693i	0.608715	−	0.793389i	$-0.291685\pi$
$461$	−5.97585	−	7.12174i	−0.278323	−	0.331693i	−0.887038	+	0.461696i	$0.847241\pi$
$462$	16.4080	+	71.2396i	0.763370	+	3.31437i
$463$	−18.1131	+	12.6829i	−0.841787	+	0.589426i	−0.912965	−	0.408038i	$-0.866213\pi$
$463$	−18.1131	+	12.6829i	−0.841787	+	0.589426i	0.0711780	+	0.997464i	$0.477324\pi$
$464$	−9.22036	+	3.35594i	−0.428045	+	0.155795i
$465$	3.52550	+	4.94513i	0.163491	+	0.229325i
$466$	6.94655	+	39.3958i	0.321793	+	1.82498i
$467$	6.61375	−	24.6828i	0.306048	−	1.14219i	−0.625992	−	0.779830i	$-0.715306\pi$
$467$	6.61375	−	24.6828i	0.306048	−	1.14219i	0.932040	−	0.362356i	$-0.118028\pi$
$468$	−11.5629	+	14.2488i	−0.534496	+	0.658649i
$469$	29.0629	+	16.7794i	1.34200	+	0.774803i
$470$	1.66190	−	0.688916i	0.0766577	−	0.0317773i
$471$	1.22596	+	1.10501i	0.0564892	+	0.0509162i
$472$	−0.686232	+	0.0600375i	−0.0315864	+	0.00276345i
$473$	6.36369	−	0.556751i	0.292603	−	0.0255994i
$474$	37.2996	−	12.0980i	1.71323	−	0.555679i
$475$	−21.2199	−	9.88083i	−0.973636	−	0.453363i
$476$	−20.8646	−	12.0462i	−0.956328	−	0.552136i
$477$	−0.740638	+	0.143168i	−0.0339115	+	0.00655521i
$478$	−1.35531	+	5.05807i	−0.0619903	+	0.231351i
$479$	2.14579	+	12.1694i	0.0980435	+	0.556032i	0.993772	+	0.111431i	$0.0355434\pi$
$479$	2.14579	+	12.1694i	0.0980435	+	0.556032i	−0.895729	+	0.444601i	$0.853345\pi$
$480$	−29.2562	+	10.9303i	−1.33536	+	0.498897i
$481$	5.51494	−	2.00728i	0.251460	−	0.0915239i
$482$	36.7408	−	25.7262i	1.67350	−	1.17179i
$483$	−25.4385	−	7.79177i	−1.15749	−	0.354538i
$484$	−19.6895	−	23.4651i	−0.894979	−	1.06659i
$485$	3.08201	+	0.133716i	0.139947	+	0.00607174i
$486$	−32.6527	−	0.0847152i	−1.48116	−	0.00384276i
$487$	16.4134	−	16.4134i	0.743762	−	0.743762i	−0.229538	−	0.973300i	$-0.573722\pi$
$487$	16.4134	−	16.4134i	0.743762	−	0.743762i	0.973300	+	0.229538i	$0.0737215\pi$
$488$	−0.565091	+	6.45902i	−0.0255805	+	0.292386i
$489$	−26.3681	+	14.0026i	−1.19241	+	0.633221i
$490$	10.1641	−	45.9067i	0.459165	−	2.07385i
$491$	3.53191	+	9.70384i	0.159393	+	0.437928i	0.993522	−	0.113641i	$-0.0362515\pi$
$491$	3.53191	+	9.70384i	0.159393	+	0.437928i	−0.834129	+	0.551569i	$0.814029\pi$
$492$	−11.0158	−	25.9890i	−0.496630	−	1.17168i
$493$	−4.47496	+	6.39090i	−0.201542	+	0.287832i
$494$	12.5608	+	21.7559i	0.565137	+	0.978846i
$495$	32.3901	−	4.81545i	1.45583	−	0.216438i
$496$	2.41043	−	4.17499i	0.108231	−	0.187462i
$497$	−15.7752	−	33.8300i	−0.707615	−	1.51748i
$498$	12.0543	+	6.14988i	0.540168	+	0.275583i
$499$	−21.3906	+	25.4924i	−0.957576	+	1.14119i	0.0323314	+	0.999477i	$0.489707\pi$
$499$	−21.3906	+	25.4924i	−0.957576	+	1.14119i	−0.989907	+	0.141717i	$0.954738\pi$
$500$	1.14247	−	26.6706i	0.0510926	−	1.19274i
$501$	5.88496	−	6.52910i	0.262921	−	0.291698i
$502$	29.9414	−	13.9619i	1.33635	−	0.623150i
$503$	−7.47831	−	27.9094i	−0.333441	−	1.24442i	−0.905549	−	0.424241i	$-0.860541\pi$
$503$	−7.47831	−	27.9094i	−0.333441	−	1.24442i	0.572108	−	0.820178i	$-0.306126\pi$
$504$	−1.04075	−	10.0019i	−0.0463587	−	0.445521i
$505$	−1.11622	−	0.351605i	−0.0496710	−	0.0156462i
$506$	37.4723	−	6.60738i	1.66585	−	0.293734i
$507$	−1.36454	+	11.0658i	−0.0606013	+	0.491450i
$508$	15.6471	+	7.29635i	0.694226	+	0.323723i
$509$	2.41068	−	13.6717i	0.106852	−	0.605986i	−0.883613	−	0.468218i	$-0.844896\pi$
$509$	2.41068	−	13.6717i	0.106852	−	0.605986i	0.990465	−	0.137768i	$-0.0439928\pi$
$510$	−11.2366	+	16.3408i	−0.497565	+	0.723583i
$511$	39.0008	−	32.7256i	1.72529	−	1.44769i
$512$	21.0607	+	21.0607i	0.930762	+	0.930762i
$513$	−8.75295	+	22.6966i	−0.386452	+	1.00208i
$514$		−	2.91544i		−	0.128594i
$515$	−4.72412	−	6.15309i	−0.208169	−	0.271138i
$516$	−5.40848	−	0.191678i	−0.238095	−	0.00843816i
$517$	1.07543	+	1.53587i	0.0472972	+	0.0675474i
$518$	−8.37129	+	17.9523i	−0.367813	+	0.788778i
$519$	−0.401506	−	2.86766i	−0.0176241	−	0.125876i
$520$	−2.83078	+	3.69124i	−0.124138	+	0.161871i
$521$	4.10889	−	2.37227i	0.180014	−	0.103931i	−0.407285	−	0.913301i	$-0.633525\pi$
$521$	4.10889	−	2.37227i	0.180014	−	0.103931i	0.587299	+	0.809370i	$0.300191\pi$
$522$	−20.0534	+	0.329217i	−0.877713	+	0.0144094i
$523$	−39.4721	+	10.5765i	−1.72599	+	0.462478i	−0.979254	−	0.202638i	$-0.935048\pi$
$523$	−39.4721	+	10.5765i	−1.72599	+	0.462478i	−0.746739	+	0.665117i	$0.768382\pi$
$524$	17.0487	+	6.20521i	0.744774	+	0.271076i
$525$	−34.1858	−	10.4505i	−1.49199	−	0.456098i
$526$	39.7161	+	33.3258i	1.73170	+	1.45307i
$527$	−0.334084	−	3.81860i	−0.0145529	−	0.166341i
$528$	−14.1459	−	21.8075i	−0.615620	−	0.949049i
$529$	3.13027	−	8.60035i	0.136099	−	0.373928i
$530$	−1.14976	+	0.255227i	−0.0499425	+	0.0110864i
$531$	2.46862	+	0.618217i	0.107129	+	0.0268283i
$532$	−44.5677	−	11.9419i	−1.93226	−	0.517746i
$533$	14.3232	+	10.0292i	0.620407	+	0.434414i
$534$	−54.5042	+	7.63123i	−2.35863	+	0.330235i
$535$	3.87420	+	12.2757i	0.167496	+	0.530723i
$536$	6.50174	+	1.14643i	0.280833	+	0.0495184i
$537$	16.9284	+	18.1723i	0.730512	+	0.784194i
$538$	−63.0456	−	5.51577i	−2.71809	−	0.237802i
$539$	49.0025			2.11069
$540$	−27.7337	+	0.690647i	−1.19347	+	0.0297207i
$541$	−14.7870			−0.635743			−0.317871	−	0.948134i	$-0.602968\pi$
$541$	−14.7870			−0.635743			−0.317871	+	0.948134i	$0.602968\pi$
$542$	−62.9871	−	5.51066i	−2.70553	−	0.236703i
$543$	36.2422	−	8.34737i	1.55530	−	0.358220i
$544$	19.4127	+	3.42298i	0.832313	+	0.146759i
$545$	−10.6589	+	20.4892i	−0.456576	+	0.877662i
$546$	23.6042	+	30.2443i	1.01017	+	1.29434i
$547$	19.2746	+	13.4962i	0.824123	+	0.577057i	0.907784	−	0.419437i	$-0.137773\pi$
$547$	19.2746	+	13.4962i	0.824123	+	0.577057i	−0.0836614	+	0.996494i	$0.526661\pi$
$548$	20.3137	+	5.44304i	0.867759	+	0.232515i
$549$	9.76523	−	21.8719i	0.416770	−	0.933472i
$550$	50.3442	−	8.90553i	2.14668	−	0.379733i
$551$	−5.11030	+	14.0404i	−0.217706	+	0.598142i
$552$	−5.22698	+	0.271215i	−0.222475	+	0.0115437i
$553$	−3.88828	−	44.4433i	−0.165347	−	1.88992i
$554$	−9.30352	−	7.80658i	−0.395269	−	0.331670i
$555$	7.72137	+	4.37103i	0.327754	+	0.185540i
$556$	1.45168	+	0.528370i	0.0615651	+	0.0224079i
$557$	−23.7629	+	6.36725i	−1.00687	+	0.269789i	−0.724320	−	0.689464i	$-0.757846\pi$
$557$	−23.7629	+	6.36725i	−1.00687	+	0.269789i	−0.282547	+	0.959253i	$0.591179\pi$
$558$	7.44354	−	6.45702i	0.315110	−	0.273348i
$559$	2.90326	−	1.67620i	0.122795	−	0.0708956i
$560$	3.71156	+	28.1324i	0.156842	+	1.18881i
$561$	−19.1592	−	7.75239i	−0.808903	−	0.327306i
$562$	−13.5068	+	28.9655i	−0.569751	+	1.22184i
$563$	−7.57539	−	10.8188i	−0.319265	−	0.455957i	0.627156	−	0.778894i	$-0.284219\pi$
$563$	−7.57539	−	10.8188i	−0.319265	−	0.455957i	−0.946421	+	0.322936i	$0.895330\pi$
$564$	−0.745003	−	1.40290i	−0.0313703	−	0.0590728i
$565$	9.69750	−	7.44538i	0.407977	−	0.313230i
$566$		−	49.6934i		−	2.08877i
$567$	−8.43201	+	36.1803i	−0.354111	+	1.51943i
$568$	−5.19257	−	5.19257i	−0.217875	−	0.217875i
$569$	9.80603	−	8.22824i	0.411090	−	0.344946i	−0.413671	−	0.910426i	$-0.635754\pi$
$569$	9.80603	−	8.22824i	0.411090	−	0.344946i	0.824762	+	0.565481i	$0.191309\pi$
$570$	−12.6866	+	35.7980i	−0.531382	+	1.49941i
$571$	1.27813	−	7.24862i	0.0534879	−	0.303345i	−0.946314	−	0.323249i	$-0.895225\pi$
$571$	1.27813	−	7.24862i	0.0534879	−	0.303345i	0.999802	+	0.0199038i	$0.00633599\pi$
$572$	−27.0612	−	12.6188i	−1.13149	−	0.527620i
$573$	18.8674	−	7.99720i	0.788198	−	0.334088i
$574$	−58.1187	+	10.2479i	−2.42583	+	0.427739i
$575$	−6.35412	+	17.4876i	−0.264985	+	0.729285i
$576$	14.0976	+	28.9807i	0.587400	+	1.20753i
$577$	6.02067	+	22.4695i	0.250644	+	0.935416i	0.970462	+	0.241253i	$0.0775585\pi$
$577$	6.02067	+	22.4695i	0.250644	+	0.935416i	−0.719818	+	0.694163i	$0.755775\pi$
$578$	−20.9290	+	9.75937i	−0.870533	+	0.405936i
$579$	−8.59316	−	26.4938i	−0.357120	−	1.10104i
$580$	−17.0235	+	0.747943i	−0.706863	+	0.0310567i
$581$	9.89651	−	11.7942i	0.410576	−	0.489306i
$582$	−0.259367	−	4.99864i	−0.0107511	−	0.207200i
$583$	−0.518743	−	1.11245i	−0.0214841	−	0.0460729i
$584$	5.00795	−	8.67403i	0.207231	−	0.358934i
$585$	14.3376	−	9.47409i	0.592785	−	0.391706i
$586$	8.73716	+	15.1332i	0.360929	+	0.625147i
$587$	−6.11631	+	8.73500i	−0.252447	+	0.360532i	−0.925294	−	0.379249i	$-0.876182\pi$
$587$	−6.11631	+	8.73500i	−0.252447	+	0.360532i	0.672847	+	0.739781i	$0.265071\pi$
$588$	−41.2026	−	5.08075i	−1.69917	−	0.209526i
$589$	−2.51078	−	6.89830i	−0.103455	−	0.284240i
$590$	3.87928	+	0.858899i	0.159707	+	0.0353603i
$591$	−40.5880	−	25.3915i	−1.66957	−	1.04447i
$592$	0.613850	−	7.01634i	0.0252291	−	0.288370i
$593$	30.2299	−	30.2299i	1.24139	−	1.24139i	0.281969	−	0.959424i	$-0.409013\pi$
$593$	30.2299	−	30.2299i	1.24139	−	1.24139i	0.959424	−	0.281969i	$-0.0909874\pi$
$594$	−12.7734	−	51.5732i	−0.524099	−	2.11607i
$595$	15.2476	+	16.6307i	0.625093	+	0.681793i
$596$	−28.6291	−	34.1189i	−1.17269	−	1.39756i
$597$	25.1923	−	23.4677i	1.03105	−	0.960470i
$598$	16.3574	−	11.4536i	0.668903	−	0.468371i
$599$	18.4157	−	6.70275i	0.752444	−	0.273867i	0.0628100	−	0.998026i	$-0.479994\pi$
$599$	18.4157	−	6.70275i	0.752444	−	0.273867i	0.689634	+	0.724158i	$0.257772\pi$
$600$	−7.02295	+	0.368268i	−0.286711	+	0.0150345i
$601$	−5.44723	−	30.8927i	−0.222197	−	1.26014i	−0.867972	−	0.496614i	$-0.834577\pi$
$601$	−5.44723	−	30.8927i	−0.222197	−	1.26014i	0.645775	−	0.763528i	$-0.276534\pi$
$602$	−2.92847	+	10.9292i	−0.119355	+	0.445440i
$603$	−21.3198	−	11.8467i	−0.868210	−	0.482435i
$604$	24.5279	+	14.1612i	0.998025	+	0.576210i
$605$	10.9851	+	26.4999i	0.446609	+	1.07737i
$606$	−0.395751	+	1.85712i	−0.0160763	+	0.0754405i
$607$	−14.5354	+	1.27168i	−0.589972	+	0.0516159i	−0.378233	−	0.925710i	$-0.623468\pi$
$607$	−14.5354	+	1.27168i	−0.589972	+	0.0516159i	−0.211739	+	0.977326i	$0.567913\pi$
$608$	37.6076	−	3.29024i	1.52519	−	0.133437i
$609$	−4.75577	+	22.3172i	−0.192714	+	0.904339i
$610$	14.3018	−	34.5544i	0.579063	−	1.39907i
$611$	0.852139	+	0.491983i	0.0344739	+	0.0199035i
$612$	15.3058	+	8.50491i	0.618699	+	0.343790i
$613$	3.72795	−	13.9129i	0.150571	−	0.561937i	−0.848873	−	0.528596i	$-0.822719\pi$
$613$	3.72795	−	13.9129i	0.150571	−	0.561937i	0.999444	−	0.0333409i	$-0.0106147\pi$
$614$	−8.05124	−	45.6609i	−0.324922	−	1.84272i
$615$	2.52724	+	26.3139i	0.101908	+	1.06108i
$616$	15.3758	−	5.59635i	0.619510	−	0.225483i
$617$	−2.15631	+	1.50986i	−0.0868096	+	0.0607847i	−0.616175	−	0.787609i	$-0.711319\pi$
$617$	−2.15631	+	1.50986i	−0.0868096	+	0.0607847i	0.529366	+	0.848394i	$0.322430\pi$
$618$	−9.20977	+	8.57932i	−0.370471	+	0.345111i
$619$	−14.0882	−	16.7897i	−0.566254	−	0.674836i	0.404603	−	0.914492i	$-0.367410\pi$
$619$	−14.0882	−	16.7897i	−0.566254	−	0.674836i	−0.970858	+	0.239657i	$0.922965\pi$
$620$	6.17095	−	5.65775i	0.247831	−	0.227221i
$621$	18.5788	+	5.35870i	0.745542	+	0.215037i
$622$	39.4631	−	39.4631i	1.58233	−	1.58233i
$623$	−5.45731	+	62.3773i	−0.218642	+	2.49909i
$624$	−11.5648	−	7.23483i	−0.462962	−	0.289625i
$625$	−8.52471	+	23.5017i	−0.340989	+	0.940067i
$626$	−0.320337	−	0.880118i	−0.0128032	−	0.0351766i
$627$	−39.2847	−	4.84424i	−1.56888	−	0.193460i
$628$	1.30500	−	1.86374i	0.0520753	−	0.0743712i
$629$	−2.80009	−	4.84989i	−0.111647	−	0.193378i
$630$	−11.6070	+	56.8281i	−0.462434	+	2.26409i
$631$	−12.3536	+	21.3971i	−0.491790	+	0.851805i	−0.999955	−	0.00945434i	$-0.996991\pi$
$631$	−12.3536	+	21.3971i	−0.491790	+	0.851805i	0.508165	+	0.861260i	$0.330324\pi$
$632$	−3.70921	−	7.95442i	−0.147544	−	0.316410i
$633$	2.03221	+	39.1657i	0.0807730	+	1.55670i
$634$	1.15383	−	1.37508i	0.0458243	−	0.0546112i
$635$	−11.9236	−	10.9199i	−0.473173	−	0.433345i
$636$	0.320830	+	0.989159i	0.0127217	+	0.0392227i
$637$	23.3069	−	10.8682i	0.923453	−	0.430613i
$638$	−8.44645	−	31.5226i	−0.334398	−	1.24799i
$639$	11.8672	+	24.3957i	0.469461	+	0.965078i
$640$	6.58504	+	12.6413i	0.260297	+	0.499690i
$641$	−1.07217	+	0.189053i	−0.0423482	+	0.00746712i	−0.194782	−	0.980847i	$-0.562400\pi$
$641$	−1.07217	+	0.189053i	−0.0423482	+	0.00746712i	0.152434	+	0.988314i	$0.451289\pi$
$642$	19.2299	−	8.15084i	0.758944	−	0.321688i
$643$	38.6292	+	18.0131i	1.52339	+	0.710367i	0.990715	−	0.135954i	$-0.0434099\pi$
$643$	38.6292	+	18.0131i	1.52339	+	0.710367i	0.532673	+	0.846321i	$0.321188\pi$
$644$	−6.36868	+	36.1186i	−0.250961	+	1.42327i
$645$	4.77712	+	1.69298i	0.188099	+	0.0666611i
$646$	18.3632	−	15.4085i	0.722489	−	0.606240i
$647$	8.11871	+	8.11871i	0.319179	+	0.319179i	0.848452	−	0.529273i	$-0.177535\pi$
$647$	8.11871	+	8.11871i	0.319179	+	0.319179i	−0.529273	+	0.848452i	$0.677535\pi$
$648$	0.875624	+	7.25585i	0.0343977	+	0.285037i
$649$			4.14089i			0.162544i
$650$	21.9699	−	15.4015i	0.861730	−	0.604095i
$651$	−5.25812	−	9.90148i	−0.206082	−	0.388070i
$652$	23.6064	+	33.7135i	0.924499	+	1.32032i
$653$	20.7963	−	44.5979i	0.813823	−	1.74525i	0.162125	−	0.986770i	$-0.448165\pi$
$653$	20.7963	−	44.5979i	0.813823	−	1.74525i	0.651698	−	0.758479i	$-0.274057\pi$
$654$	34.7378	+	14.0560i	1.35836	+	0.549631i
$655$	−13.4826	−	10.3397i	−0.526807	−	0.404004i
$656$	18.1726	−	10.4920i	0.709522	−	0.409643i
$657$	−27.9510	+	24.2466i	−1.09047	+	0.945948i
$658$	−3.20784	+	0.859538i	−0.125055	+	0.0335083i
$659$	−15.4676	−	5.62976i	−0.602534	−	0.219304i	0.0226995	−	0.999742i	$-0.492774\pi$
$659$	−15.4676	−	5.62976i	−0.602534	−	0.219304i	−0.625233	+	0.780438i	$0.714996\pi$
$660$	−12.0528	−	43.5024i	−0.469156	−	1.69333i
$661$	5.35212	+	4.49096i	0.208173	+	0.174678i	0.740913	−	0.671601i	$-0.234393\pi$
$661$	5.35212	+	4.49096i	0.208173	+	0.174678i	−0.532740	+	0.846279i	$0.678838\pi$
$662$	5.23445	+	59.8301i	0.203443	+	2.32536i
$663$	−10.8320	+	0.562047i	−0.420681	+	0.0218281i
$664$	1.03595	−	2.84624i	0.0402025	−	0.110455i
$665$	36.4495	+	23.2068i	1.41345	+	0.899922i
$666$	5.86914	−	13.1456i	0.227425	−	0.509381i
$667$	11.4720	+	3.07392i	0.444199	+	0.119023i
$668$	−9.92571	−	6.95006i	−0.384037	−	0.268906i
$669$	10.7550	+	13.7805i	0.415811	+	0.532784i
$670$	−33.7821	−	17.5740i	−1.30511	−	0.678945i
$671$	38.3832	+	6.76799i	1.48177	+	0.261276i
$672$	56.1819	−	12.9399i	2.16726	−	0.499168i
$673$	−6.71205	−	0.587229i	−0.258731	−	0.0226360i	−0.0429476	−	0.999077i	$-0.513675\pi$
$673$	−6.71205	−	0.587229i	−0.258731	−	0.0226360i	−0.215783	+	0.976441i	$0.569230\pi$
$674$	−15.7666			−0.607307
$675$	24.9671	+	7.18644i	0.960983	+	0.276606i
$676$	15.3700			0.591155
$677$	5.61594	+	0.491331i	0.215838	+	0.0188834i	0.194562	−	0.980890i	$-0.437672\pi$
$677$	5.61594	+	0.491331i	0.215838	+	0.0188834i	0.0212762	+	0.999774i	$0.493227\pi$
$678$	−13.5213	−	14.5149i	−0.519283	−	0.557443i
$679$	−5.60821	−	0.988878i	−0.215223	−	0.0379497i
$680$	3.93778	+	2.04850i	0.151007	+	0.0785565i
$681$	−41.8123	+	5.85421i	−1.60225	+	0.224334i
$682$	13.1342	+	9.19669i	0.502936	+	0.352159i
$683$	−17.2898	−	4.63280i	−0.661577	−	0.177269i	−0.0876196	−	0.996154i	$-0.527926\pi$
$683$	−17.2898	−	4.63280i	−0.661577	−	0.177269i	−0.573958	+	0.818885i	$0.694593\pi$
$684$	32.5293	+	8.14633i	1.24379	+	0.311483i
$685$	−16.6135	−	10.5775i	−0.634768	−	0.404147i
$686$	−8.98530	+	24.6869i	−0.343060	+	0.942551i
$687$	−8.43539	−	13.0041i	−0.321830	−	0.496139i
$688$	−0.350641	−	4.00784i	−0.0133681	−	0.152798i
$689$	−0.493456	−	0.414058i	−0.0187992	−	0.0157744i
$690$	29.2258	+	7.56592i	1.11261	+	0.288030i
$691$	−27.1342	−	9.87603i	−1.03223	−	0.375702i	−0.230302	−	0.973119i	$-0.573971\pi$
$691$	−27.1342	−	9.87603i	−1.03223	−	0.375702i	−0.801930	+	0.597417i	$0.796194\pi$
$692$	−3.85568	+	1.03313i	−0.146571	+	0.0392736i
$693$	−60.4408	+	0.992257i	−2.29596	+	0.0376927i
$694$	−47.0786	+	27.1809i	−1.78708	+	1.03177i
$695$	−1.14803	−	0.880416i	−0.0435473	−	0.0333961i
$696$	0.622448	+	4.44568i	0.0235938	+	0.168513i
$697$	7.05132	−	15.1216i	0.267088	−	0.572772i
$698$	20.9830	+	29.9668i	0.794217	+	1.13426i
$699$	−33.0575	−	1.17157i	−1.25035	−	0.0443127i
$700$	−8.53054	+	48.5348i	−0.322424	+	1.83444i
$701$			20.6819i			0.781145i	0.920572	+	0.390573i	$0.127723\pi$
$701$			20.6819i			0.781145i	−0.920572	+	0.390573i	$0.872277\pi$
$702$	−17.5137	−	21.6966i	−0.661012	−	0.818885i
$703$	−7.58374	−	7.58374i	−0.286026	−	0.286026i
$704$	−40.1712	+	33.7076i	−1.51401	+	1.27040i
$705$	0.270734	+	1.46274i	0.0101964	+	0.0550901i
$706$	−3.27913	+	18.5969i	−0.123412	+	0.699903i
$707$	1.95793	+	0.912998i	0.0736355	+	0.0343368i
$708$	0.429341	−	3.48177i	0.0161356	−	0.130853i
$709$	−18.9529	+	3.34191i	−0.711791	+	0.125508i	−0.517808	−	0.855497i	$-0.673252\pi$
$709$	−18.9529	+	3.34191i	−0.711791	+	0.125508i	−0.193983	+	0.981005i	$0.562141\pi$
$710$	19.5681	+	37.5648i	0.734378	+	1.40978i
$711$	3.35578	+	32.2500i	0.125852	+	1.20947i
$712$	3.18823	+	11.8986i	0.119484	+	0.445920i
$713$	−5.28853	+	2.46608i	−0.198057	+	0.0923554i
$714$	24.5100	−	27.1927i	0.917264	−	1.01766i
$715$	20.6215	+	18.8858i	0.771202	+	0.706287i
$716$	22.0067	−	26.2266i	0.822430	−	0.980133i
$717$	−3.85701	−	1.96777i	−0.144043	−	0.0734876i
$718$	13.9996	+	30.0223i	0.522461	+	1.12042i
$719$	−4.55209	+	7.88446i	−0.169764	+	0.294041i	−0.938337	−	0.345722i	$-0.887634\pi$
$719$	−4.55209	+	7.88446i	−0.169764	+	0.294041i	0.768573	+	0.639763i	$0.220967\pi$
$720$	−3.03276	−	20.3992i	−0.113024	−	0.760233i
$721$	7.16008	+	12.4016i	0.266655	+	0.461861i
$722$	3.50416	−	5.00446i	0.130411	−	0.186247i
$723$	14.4735	+	34.1467i	0.538276	+	1.26993i
$724$	−17.5350	−	48.1769i	−0.651682	−	1.79048i
$725$	15.4165	+	4.12177i	0.572554	+	0.153079i
$726$	41.1079	−	21.8301i	1.52566	−	0.810191i
$727$	−1.02733	+	11.7425i	−0.0381017	+	0.435505i	0.953054	+	0.302801i	$0.0979216\pi$
$727$	−1.02733	+	11.7425i	−0.0381017	+	0.435505i	−0.991156	+	0.132704i	$0.957634\pi$
$728$	6.07195	−	6.07195i	0.225042	−	0.225042i
$729$	5.69581	−	26.3924i	0.210956	−	0.977496i
$730$	−42.5823	+	39.0410i	−1.57604	+	1.44497i
$731$	−2.05622	−	2.45051i	−0.0760520	−	0.0906352i
$732$	−31.5719	−	9.67040i	−1.16693	−	0.357428i
$733$	37.0503	−	25.9429i	1.36848	−	0.958222i	0.368896	−	0.929471i	$-0.379736\pi$
$733$	37.0503	−	25.9429i	1.36848	−	0.958222i	0.999587	−	0.0287512i	$-0.00915305\pi$
$734$	42.6244	−	15.5140i	1.57330	−	0.572633i
$735$	35.3741	+	16.1314i	1.30479	+	0.595015i
$736$	−5.21080	−	29.5519i	−0.192072	−	1.08930i
$737$	10.2717	−	38.3345i	0.378363	−	1.41207i
$738$	42.1119	−	8.14039i	1.55016	−	0.299652i
$739$	36.6974	+	21.1872i	1.34994	+	0.779385i	0.988240	−	0.152911i	$-0.0488648\pi$
$739$	36.6974	+	21.1872i	1.34994	+	0.779385i	0.361695	+	0.932296i	$0.382198\pi$
$740$	4.67761	−	11.3015i	0.171952	−	0.415452i
$741$	−19.7592	+	6.40883i	−0.725873	+	0.235434i
$742$	2.16584	−	0.189487i	0.0795106	−	0.00695628i
$743$	11.6932	−	1.02302i	0.428982	−	0.0375311i	0.129379	−	0.991595i	$-0.458701\pi$
$743$	11.6932	−	1.02302i	0.428982	−	0.0375311i	0.299603	+	0.954064i	$0.403146\pi$
$744$	−1.63827	−	1.47665i	−0.0600620	−	0.0541366i
$745$	15.9727	+	38.5315i	0.585193	+	1.41169i
$746$	−44.0922	−	25.4566i	−1.61433	−	0.932034i
$747$	−7.05097	+	8.68877i	−0.257981	+	0.317905i
$748$	−7.37418	+	27.5208i	−0.269627	+	1.00626i
$749$	−4.12632	−	23.4015i	−0.150772	−	0.855073i
$750$	39.2743	+	10.1443i	1.43410	+	0.370417i
$751$	31.3803	−	11.4215i	1.14509	−	0.416777i	0.301338	−	0.953517i	$-0.402567\pi$
$751$	31.3803	−	11.4215i	1.14509	−	0.416777i	0.843747	+	0.536741i	$0.180345\pi$
$752$	0.967287	−	0.677302i	0.0352733	−	0.0246987i
$753$	6.13127	+	26.6204i	0.223436	+	0.970103i
$754$	−11.0087	−	13.1197i	−0.400913	−	0.477790i
$755$	−17.9247	−	19.5506i	−0.652348	−	0.711520i
$756$	50.9231	+	5.43239i	1.85205	+	0.197574i
$757$	16.3480	−	16.3480i	0.594177	−	0.594177i	−0.344580	−	0.938757i	$-0.611979\pi$
$757$	16.3480	−	16.3480i	0.594177	−	0.594177i	0.938757	+	0.344580i	$0.111979\pi$
$758$	3.38053	−	38.6396i	0.122786	−	1.40345i
$759$	−1.11436	+	31.4434i	−0.0404488	+	1.14132i
$760$	8.29975	+	1.83762i	0.301063	+	0.0666575i
$761$	5.25702	+	14.4435i	0.190567	+	0.523578i	0.997774	−	0.0666905i	$-0.0212440\pi$
$761$	5.25702	+	14.4435i	0.190567	+	0.523578i	−0.807207	+	0.590269i	$0.799022\pi$
$762$	−15.7987	+	20.9430i	−0.572327	+	0.758684i
$763$	24.4543	−	34.9244i	0.885306	−	1.26435i
$764$	−14.1246	−	24.4645i	−0.511010	−	0.885095i
$765$	−11.2787	−	11.9034i	−0.407782	−	0.430370i
$766$	−2.47331	+	4.28391i	−0.0893645	+	0.154784i
$767$	0.918402	+	1.96952i	0.0331616	+	0.0711152i
$768$	−11.8179	+	7.66589i	−0.426440	+	0.276619i
$769$	18.6937	−	22.2783i	0.674112	−	0.803376i	−0.315225	−	0.949017i	$-0.602080\pi$
$769$	18.6937	−	22.2783i	0.674112	−	0.803376i	0.989337	+	0.145641i	$0.0465246\pi$
$770$	−94.2868	+	4.14257i	−3.39786	+	0.149288i
$771$	2.35778	+	0.502441i	0.0849135	+	0.0180950i
$772$	−34.7981	+	16.2266i	−1.25241	+	0.584008i
$773$	2.50707	+	9.35650i	0.0901729	+	0.336530i	0.996243	−	0.0865969i	$-0.0275992\pi$
$773$	2.50707	+	9.35650i	0.0901729	+	0.336530i	−0.906071	+	0.423127i	$0.860933\pi$
$774$	1.99770	−	7.97704i	0.0718057	−	0.286729i
$775$	−7.10403	+	3.31741i	−0.255184	+	0.119165i
$776$	−1.10330	+	0.194542i	−0.0396063	+	0.00698365i
$777$	−13.0757	−	9.86391i	−0.469089	−	0.353866i
$778$	20.0086	+	9.33018i	0.717344	+	0.334503i
$779$	5.54868	−	31.4681i	0.198802	−	1.12746i
$780$	−15.3810	−	18.0177i	−0.550728	−	0.645139i
$781$	−33.8157	+	28.3748i	−1.21002	+	1.01533i
$782$	−13.4735	−	13.4735i	−0.481812	−	0.481812i
$783$	3.18972	−	16.2744i	0.113991	−	0.581599i
$784$		−	30.8617i		−	1.10220i
$785$	−1.69007	+	1.29757i	−0.0603212	+	0.0463124i
$786$	−14.6210	+	23.3715i	−0.521514	+	0.833634i
$787$	−10.8021	−	15.4269i	−0.385052	−	0.549911i	0.579102	−	0.815255i	$-0.303403\pi$
$787$	−10.8021	−	15.4269i	−0.385052	−	0.549911i	−0.964154	+	0.265344i	$0.914514\pi$
$788$	−27.8921	+	59.8148i	−0.993616	+	2.13082i
$789$	−33.7959	+	26.3760i	−1.20317	+	0.939011i
$790$	6.62142	+	50.1883i	0.235580	+	1.78562i
$791$	−19.5454	+	11.2846i	−0.694955	+	0.401233i
$792$	−11.1067	+	4.25023i	−0.394658	+	0.151025i
$793$	19.7571	−	5.29391i	0.701596	−	0.187992i
$794$	−15.3420	−	5.58405i	−0.544469	−	0.198170i
$795$	−0.00826034	−	0.973825i	−0.000292964	−	0.0345380i
$796$	−36.3579	−	30.5079i	−1.28867	−	1.08132i
$797$	4.63317	+	52.9574i	0.164115	+	1.87585i	0.417772	+	0.908552i	$0.362811\pi$
$797$	4.63317	+	52.9574i	0.164115	+	1.87585i	−0.253657	+	0.967294i	$0.581633\pi$
$798$	31.8616	−	62.4518i	1.12789	−	2.21077i
$799$	0.321128	−	0.882292i	0.0113607	−	0.0312132i
$800$	−7.02320	−	39.7031i	−0.248307	−	1.40372i
$801$	3.22160	−	45.3939i	0.113830	−	1.60392i
$802$	−58.9606	−	15.7984i	−2.08197	−	0.557862i
$803$	−49.3199	−	34.5342i	−1.74046	−	1.21868i
$804$	−12.6114	+	31.1676i	−0.444768	+	1.09920i
$805$	15.8513	−	30.4705i	0.558685	−	1.07394i
$806$	8.28671	+	1.46117i	0.291887	+	0.0514675i
$807$	15.3259	−	50.0358i	0.539496	−	1.76134i
$808$	0.423386	+	0.0370415i	0.0148947	+	0.00130311i
$809$	−14.5795			−0.512589			−0.256295	−	0.966599i	$-0.582502\pi$
$809$	−14.5795			−0.512589			−0.256295	+	0.966599i	$0.582502\pi$
$810$	7.75670	−	41.4348i	0.272543	−	1.45587i
$811$	−13.7931			−0.484342			−0.242171	−	0.970234i	$-0.577860\pi$
$811$	−13.7931			−0.484342			−0.242171	+	0.970234i	$0.577860\pi$
$812$	31.3359	+	2.74154i	1.09967	+	0.0962091i
$813$	15.3117	−	49.9895i	0.537004	−	1.75321i
$814$	23.0693	+	4.06773i	0.808577	+	0.142574i
$815$	−11.6003	−	36.7562i	−0.406340	−	1.28751i
$816$	−4.88244	+	12.0664i	−0.170920	+	0.422410i
$817$	−5.01837	−	3.51390i	−0.175571	−	0.122936i
$818$	−20.7581	−	5.56212i	−0.725791	−	0.194475i
$819$	−28.5272	+	13.8770i	−0.996821	+	0.484902i
$820$	35.5753	−	7.89709i	1.24234	−	0.275778i
$821$	3.83252	−	10.5298i	0.133756	−	0.367491i	−0.854675	−	0.519164i	$-0.826244\pi$
$821$	3.83252	−	10.5298i	0.133756	−	0.367491i	0.988431	+	0.151672i	$0.0484658\pi$
$822$	−14.5224	+	28.4652i	−0.506525	+	0.992838i
$823$	2.19759	+	25.1186i	0.0766031	+	0.875578i	0.933145	+	0.359500i	$0.117053\pi$
$823$	2.19759	+	25.1186i	0.0766031	+	0.875578i	−0.856542	+	0.516078i	$0.827392\pi$
$824$	2.15811	+	1.81087i	0.0751812	+	0.0630845i
$825$	−1.47411	+	42.2493i	−0.0513220	+	1.47093i
$826$	−6.89222	−	2.50856i	−0.239811	−	0.0872840i
$827$	50.0696	−	13.4161i	1.74109	−	0.466524i	0.758401	−	0.651788i	$-0.225981\pi$
$827$	50.0696	−	13.4161i	1.74109	−	0.466524i	0.982689	+	0.185265i	$0.0593142\pi$
$828$	4.19714	−	26.3229i	0.145861	−	0.914784i
$829$	−41.4108	+	23.9085i	−1.43826	+	0.830377i	−0.997729	−	0.0673619i	$-0.978542\pi$
$829$	−41.4108	+	23.9085i	−1.43826	+	0.830377i	−0.440527	+	0.897739i	$0.645208\pi$
$830$	−10.6315	+	13.8631i	−0.369024	+	0.481195i
$831$	7.91671	−	6.17860i	0.274628	−	0.214333i
$832$	−11.6305	+	24.9417i	−0.403216	+	0.864699i
$833$	−14.0749	−	20.1011i	−0.487668	−	0.696462i
$834$	−1.24497	+	1.99007i	−0.0431098	+	0.0689105i
$835$	6.91050	+	9.00082i	0.239148	+	0.311486i
$836$			54.5651i			1.88717i
$837$	3.93914	+	7.13256i	0.136157	+	0.246537i
$838$	−27.1156	−	27.1156i	−0.936694	−	0.936694i
$839$	16.8615	−	14.1485i	0.582124	−	0.488460i	−0.303520	−	0.952825i	$-0.598162\pi$
$839$	16.8615	−	14.1485i	0.582124	−	0.488460i	0.885644	+	0.464365i	$0.153717\pi$
$840$	12.9419	+	1.02173i	0.446537	+	0.0352530i
$841$	−3.26697	+	18.5279i	−0.112654	+	0.638893i
$842$	−58.3082	−	27.1896i	−2.00943	−	0.937014i
$843$	−21.0973	−	15.9151i	−0.726630	−	0.548146i
$844$	53.2421	−	9.38803i	1.83267	−	0.323149i
$845$	−13.7291	−	4.32462i	−0.472295	−	0.148772i
$846$	2.32084	−	0.662885i	0.0797922	−	0.0227905i
$847$	−13.7058	−	51.1506i	−0.470936	−	1.75756i
$848$	−0.700617	+	0.326703i	−0.0240593	+	0.0112190i
$849$	40.1882	+	8.56406i	1.37926	+	0.293918i
$850$	−18.1134	−	18.0935i	−0.621285	−	0.620603i
$851$	−5.47985	+	6.53063i	−0.187847	+	0.223867i
$852$	31.3751	−	20.3521i	1.07489	−	0.697252i
$853$	8.91361	+	19.1153i	0.305196	+	0.654496i	0.997762	−	0.0668587i	$-0.0212977\pi$
$853$	8.91361	+	19.1153i	0.305196	+	0.654496i	−0.692566	+	0.721354i	$0.743520\pi$
$854$	−34.5175	+	59.7860i	−1.18116	+	2.04583i
$855$	−26.7643	−	16.4293i	−0.915318	−	0.561869i
$856$	−2.33740	−	4.04850i	−0.0798907	−	0.138375i
$857$	1.13985	−	1.62788i	0.0389366	−	0.0556073i	−0.799212	−	0.601050i	$-0.794749\pi$
$857$	1.13985	−	1.62788i	0.0389366	−	0.0556073i	0.838148	+	0.545442i	$0.183638\pi$
$858$	27.3235	−	36.2204i	0.932808	−	1.23654i
$859$	13.1045	+	36.0043i	0.447119	+	1.22845i	0.934720	+	0.355384i	$0.115650\pi$
$859$	13.1045	+	36.0043i	0.447119	+	1.22845i	−0.487601	+	0.873067i	$0.662128\pi$
$860$	1.51033	−	6.82151i	0.0515017	−	0.232611i
$861$	1.72835	−	48.7681i	0.0589022	−	1.66201i
$862$	2.37794	−	27.1800i	0.0809930	−	0.925754i
$863$	−32.1207	+	32.1207i	−1.09340	+	1.09340i	−0.0982389	+	0.995163i	$0.531321\pi$
$863$	−32.1207	+	32.1207i	−1.09340	+	1.09340i	−0.995163	+	0.0982389i	$0.968679\pi$
$864$	−40.6723	+	10.0735i	−1.38370	+	0.342708i
$865$	3.73473	+	0.162035i	0.126984	+	0.00550935i
$866$	46.4259	+	55.3282i	1.57762	+	1.88013i
$867$	−4.28576	−	18.6077i	−0.145552	−	0.631951i
$868$	−12.6597	+	8.86444i	−0.429699	+	0.300879i
$869$	−49.5776	+	18.0448i	−1.68181	+	0.612127i
$870$	4.27971	−	25.5362i	0.145096	−	0.865757i
$871$	−3.61665	−	20.5110i	−0.122545	−	0.694990i
$872$	2.17086	−	8.10175i	0.0735145	−	0.274360i
$873$	4.08721	+	0.651700i	0.138331	+	0.0220567i
$874$	−31.6026	−	18.2458i	−1.06897	−	0.617173i
$875$	21.2759	−	40.9529i	0.719257	−	1.38446i
$876$	37.8888	+	34.1509i	1.28015	+	1.15385i
$877$	−33.1858	+	2.90338i	−1.12061	+	0.0980403i	−0.632366	−	0.774670i	$-0.717916\pi$
$877$	−33.1858	+	2.90338i	−1.12061	+	0.0980403i	−0.488239	+	0.872710i	$0.662361\pi$
$878$	44.6362	−	3.90516i	1.50640	−	0.131793i
$879$	−13.7443	+	4.45792i	−0.463584	+	0.150362i
$880$	30.9997	−	12.8505i	1.04500	−	0.433190i
$881$	17.9159	+	10.3438i	0.603603	+	0.348491i	0.770458	−	0.637491i	$-0.220028\pi$
$881$	17.9159	+	10.3438i	0.603603	+	0.348491i	−0.166854	+	0.985982i	$0.553361\pi$
$882$	20.5993	−	59.6237i	0.693615	−	2.00763i
$883$	−0.164791	+	0.615007i	−0.00554565	+	0.0206966i	−0.968643	−	0.248456i	$-0.920077\pi$
$883$	−0.164791	+	0.615007i	−0.00554565	+	0.0206966i	0.963098	+	0.269153i	$0.0867436\pi$
$884$	2.59644	+	14.7251i	0.0873278	+	0.495260i
$885$	−1.36316	+	2.98924i	−0.0458221	+	0.100482i
$886$	−53.3723	+	19.4259i	−1.79308	+	0.652627i
$887$	−27.1183	+	18.9884i	−0.910542	+	0.637569i	−0.932101	−	0.362199i	$-0.882026\pi$
$887$	−27.1183	+	18.9884i	−0.910542	+	0.637569i	0.0215585	+	0.999768i	$0.493137\pi$
$888$	−3.08096	−	0.943691i	−0.103390	−	0.0316682i
$889$	19.1851	+	22.8639i	0.643448	+	0.766831i
$890$	3.07972	−	70.9842i	0.103232	−	2.37939i
$891$	43.9098	−	1.44212i	1.47103	−	0.0483129i
$892$	17.0395	−	17.0395i	0.570523	−	0.570523i
$893$	0.156718	−	1.79130i	0.00524437	−	0.0599434i
$894$	59.7720	−	31.7416i	1.99908	−	1.06160i
$895$	−27.0365	+	17.2346i	−0.903731	+	0.576089i
$896$	−8.99923	−	24.7252i	−0.300643	−	0.826010i
$897$	6.44376	+	15.2025i	0.215151	+	0.507596i
$898$	2.82051	−	4.02811i	0.0941216	−	0.134420i
$899$	2.50235	+	4.33420i	0.0834580	+	0.144554i
$900$	5.62002	−	35.3714i	0.187334	−	1.17905i
$901$	−0.307334	+	0.532318i	−0.0102388	+	0.0177341i
$902$	29.4952	+	63.2526i	0.982082	+	2.10608i
$903$	−8.33400	−	4.25183i	−0.277338	−	0.141492i
$904$	−2.85399	+	3.40125i	−0.0949223	+	0.113124i
$905$	2.10748	+	47.9672i	0.0700550	+	1.59448i
$906$	−28.8133	+	31.9670i	−0.957258	+	1.06203i
$907$	−30.9556	+	14.4348i	−1.02786	+	0.479301i	−0.862032	−	0.506853i	$-0.830809\pi$
$907$	−30.9556	+	14.4348i	−1.02786	+	0.479301i	−0.165832	+	0.986154i	$0.553031\pi$
$908$	15.0637	+	56.2183i	0.499905	+	1.86567i
$909$	−1.43370	−	0.640106i	−0.0475527	−	0.0212310i
$910$	−43.9266	+	22.8820i	−1.45615	+	0.758532i
$911$	35.5788	−	6.27351i	1.17878	−	0.207851i	0.450274	−	0.892890i	$-0.351326\pi$
$911$	35.5788	−	6.27351i	1.17878	−	0.207851i	0.728506	+	0.685040i	$0.240215\pi$
$912$	−3.05090	+	24.7414i	−0.101025	+	0.819270i
$913$	−16.5017	−	7.69486i	−0.546126	−	0.254663i
$914$	0.191269	−	1.08474i	0.00632661	−	0.0358800i
$915$	25.4802	+	17.5212i	0.842350	+	0.579235i
$916$	−16.3686	+	13.7349i	−0.540835	+	0.453814i
$917$	22.1783	+	22.1783i	0.732393	+	0.732393i
$918$	−17.4867	+	20.0530i	−0.577148	+	0.661849i
$919$		−	17.3619i		−	0.572717i	−0.958123	−	0.286358i	$-0.907555\pi$
$919$		−	17.3619i		−	0.572717i	0.958123	−	0.286358i	$-0.0924448\pi$
$920$	0.880138	−	6.69952i	0.0290173	−	0.220877i
$921$	38.3145	+	1.35788i	1.26251	+	0.0447436i
$922$	−11.1697	−	15.9520i	−0.367854	−	0.525350i
$923$	−9.79047	+	20.9957i	−0.322257	+	0.691083i
$924$	11.5545	+	82.5255i	0.380116	+	2.71489i
$925$	−7.35809	+	8.77881i	−0.241933	+	0.288646i
$926$	−40.1122	+	23.1588i	−1.31817	+	0.761044i
$927$	−5.35110	−	8.92669i	−0.175753	−	0.293191i
$928$	−24.8597	+	6.66115i	−0.816061	+	0.218663i
$929$	29.3701	+	10.6898i	0.963602	+	0.350722i	0.775444	−	0.631416i	$-0.217526\pi$
$929$	29.3701	+	10.6898i	0.963602	+	0.350722i	0.188158	+	0.982139i	$0.439748\pi$
$930$	6.45389	+	10.9627i	0.211631	+	0.359480i
$931$	−36.0003	−	30.2078i	−1.17986	−	0.990022i
$932$	3.97423	+	45.4256i	0.130180	+	1.48797i
$933$	25.1137	+	38.7157i	0.822187	+	1.26750i
$934$	18.3071	−	50.2984i	0.599028	−	1.64581i
$935$	14.3304	−	22.5078i	0.468653	−	0.736083i
$936$	−4.33998	+	4.48485i	−0.141857	+	0.146592i
$937$	26.3075	+	7.04907i	0.859428	+	0.230283i	0.661511	−	0.749936i	$-0.269916\pi$
$937$	26.3075	+	7.04907i	0.859428	+	0.230283i	0.197917	+	0.980219i	$0.436582\pi$
$938$	57.5824	+	40.3196i	1.88013	+	1.31648i
$939$	0.766978	−	0.107386i	0.0250294	−	0.00350441i
$940$	1.95559	−	0.617187i	0.0637845	−	0.0201304i
$941$	21.7163	+	3.82917i	0.707931	+	0.124827i	0.516009	−	0.856583i	$-0.327417\pi$
$941$	21.7163	+	3.82917i	0.707931	+	0.124827i	0.191922	+	0.981410i	$0.438528\pi$
$942$	2.35648	+	2.52965i	0.0767783	+	0.0824204i
$943$	−25.3026	−	2.21369i	−0.823967	−	0.0720878i
$944$	2.60793			0.0848808
$945$	−43.9579	−	19.1805i	−1.42995	−	0.623942i
$946$	13.3808			0.435047
$947$	25.7079	+	2.24915i	0.835395	+	0.0730876i	0.496822	−	0.867853i	$-0.334500\pi$
$947$	25.7079	+	2.24915i	0.835395	+	0.0730876i	0.338573	+	0.940940i	$0.390056\pi$
$948$	43.5571	−	10.0321i	1.41467	−	0.325829i
$949$	−31.1171	−	5.48679i	−1.01011	−	0.178109i
$950$	−42.4758	−	24.4924i	−1.37810	−	0.794637i
$951$	0.913207	+	1.17010i	0.0296128	+	0.0379432i
$952$	−6.71204	−	4.69982i	−0.217538	−	0.152322i
$953$	48.8773	+	13.0966i	1.58329	+	0.424241i	0.939943	−	0.341333i	$-0.110878\pi$
$953$	48.8773	+	13.0966i	1.58329	+	0.424241i	0.643348	+	0.765574i	$0.277545\pi$
$954$	−1.57163	+	0.163536i	−0.0508835	+	0.00529468i
$955$	5.73310	+	25.8268i	0.185519	+	0.835735i
$956$	−2.04151	+	5.60900i	−0.0660271	+	0.181408i
$957$	26.9487	−	1.39830i	0.871127	−	0.0452006i
$958$	2.25595	+	25.7856i	0.0728864	+	0.833096i
$959$	27.8509	+	23.3697i	0.899352	+	0.754646i
$960$	−40.0953	+	11.1088i	−1.29407	+	0.358536i
$961$	26.8199	+	9.76163i	0.865157	+	0.314891i
$962$	11.8745	−	3.18177i	0.382850	−	0.102584i
$963$	3.27773	+	16.9564i	0.105623	+	0.546411i
$964$	44.2764	−	25.5630i	1.42605	−	0.823329i
$965$	35.6486	−	4.70317i	1.14757	−	0.151401i
$966$	−51.6602	−	20.9033i	−1.66214	−	0.672552i
$967$	15.4305	−	33.0909i	0.496212	−	1.06413i	−0.485583	−	0.874190i	$-0.661393\pi$
$967$	15.4305	−	33.0909i	0.496212	−	1.06413i	0.981796	−	0.189940i	$-0.0608294\pi$
$968$	−5.97543	−	8.53380i	−0.192058	−	0.274287i
$969$	9.29655	+	17.5062i	0.298648	+	0.562380i
$970$	6.40685	+	0.841689i	0.205711	+	0.0270250i
$971$			15.4364i			0.495377i	0.968840	+	0.247689i	$0.0796710\pi$
$971$			15.4364i			0.495377i	−0.968840	+	0.247689i	$0.920329\pi$
$972$	−37.0700	−	3.34014i	−1.18902	−	0.107135i
$973$	1.88847	+	1.88847i	0.0605417	+	0.0605417i
$974$	37.2464	−	31.2535i	1.19345	−	1.00143i
$975$	8.66927	+	20.4218i	0.277639	+	0.654022i
$976$	4.26247	−	24.1737i	0.136438	−	0.773780i
$977$	−10.4307	−	4.86392i	−0.333708	−	0.155611i	0.248540	−	0.968622i	$-0.420049\pi$
$977$	−10.4307	−	4.86392i	−0.333708	−	0.155611i	−0.582248	+	0.813011i	$0.697827\pi$
$978$	−57.5789	+	24.4055i	−1.84117	+	0.780403i
$979$	72.9242	−	12.8585i	2.33067	−	0.410960i
$980$	16.1024	−	51.1191i	0.514371	−	1.63294i
$981$	−17.3540	+	25.6709i	−0.554071	+	0.819608i
$982$	5.59849	+	20.8939i	0.178655	+	0.666750i
$983$	−2.51666	+	1.17354i	−0.0802690	+	0.0374301i	−0.462338	−	0.886704i	$-0.652989\pi$
$983$	−2.51666	+	1.17354i	−0.0802690	+	0.0374301i	0.382069	+	0.924134i	$0.375212\pi$
$984$	−2.96188	−	9.13184i	−0.0944212	−	0.291112i
$985$	41.7442	−	45.5809i	1.33008	−	1.45233i
$986$	−10.5047	+	12.5190i	−0.334537	+	0.398685i
$987$	−0.142295	−	2.74238i	−0.00452931	−	0.0872910i
$988$	12.1019	+	25.9526i	0.385012	+	0.825662i
$989$	−2.43484	+	4.21727i	−0.0774235	+	0.134101i
$990$	68.4677	−	4.13520i	2.17605	−	0.131425i
$991$	−7.70220	−	13.3406i	−0.244668	−	0.423778i	0.717370	−	0.696693i	$-0.245346\pi$
$991$	−7.70220	−	13.3406i	−0.244668	−	0.423778i	−0.962038	+	0.272914i	$0.912012\pi$
$992$	7.25281	−	10.3581i	0.230277	−	0.328870i
$993$	−49.2880	−	6.07777i	−1.56411	−	0.192872i
$994$	−26.7421	−	73.4733i	−0.848208	−	2.33043i
$995$	23.8923	+	37.4807i	0.757436	+	1.18822i
$996$	13.0772	+	8.18099i	0.414367	+	0.259225i
$997$	−4.47315	+	51.1283i	−0.141666	+	1.61925i	0.509608	+	0.860407i	$0.329791\pi$
$997$	−4.47315	+	51.1283i	−0.141666	+	1.61925i	−0.651274	+	0.758843i	$0.725765\pi$
$998$	−49.2899	+	49.2899i	−1.56025	+	1.56025i
$999$	9.61966	+	7.01199i	0.304352	+	0.221850i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.113.15	yes	192
3.2	odd	2		405.2.r.a.368.2		192
5.2	odd	4	inner	135.2.q.a.32.2	✓	192
5.3	odd	4		675.2.ba.b.32.15		192
5.4	even	2		675.2.ba.b.518.2		192
15.2	even	4		405.2.r.a.287.15		192
27.11	odd	18	inner	135.2.q.a.38.2	yes	192
27.16	even	9		405.2.r.a.278.15		192
135.38	even	36		675.2.ba.b.632.2		192
135.92	even	36	inner	135.2.q.a.92.15	yes	192
135.97	odd	36		405.2.r.a.197.2		192
135.119	odd	18		675.2.ba.b.443.15		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.2	✓	192	5.2	odd	4	inner
135.2.q.a.38.2	yes	192	27.11	odd	18	inner
135.2.q.a.92.15	yes	192	135.92	even	36	inner
135.2.q.a.113.15	yes	192	1.1	even	1	trivial
405.2.r.a.197.2		192	135.97	odd	36
405.2.r.a.278.15		192	27.16	even	9
405.2.r.a.287.15		192	15.2	even	4
405.2.r.a.368.2		192	3.2	odd	2
675.2.ba.b.32.15		192	5.3	odd	4
675.2.ba.b.443.15		192	135.119	odd	18
675.2.ba.b.518.2		192	5.4	even	2
675.2.ba.b.632.2		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)

\(f(q)\)	\(=\)	\(q+(2.08671 + 0.182563i) q^{2} +(-0.507262 + 1.65611i) q^{3} +(2.35140 + 0.414615i) q^{4} +(-1.98370 - 1.03196i) q^{5} +(-1.36085 + 3.36320i) q^{6} +(3.38127 + 2.36759i) q^{7} +(0.784385 + 0.210175i) q^{8} +(-2.48537 - 1.68016i) q^{9} +O(q^{10})\)	\(q+(2.08671 + 0.182563i) q^{2} +(-0.507262 + 1.65611i) q^{3} +(2.35140 + 0.414615i) q^{4} +(-1.98370 - 1.03196i) q^{5} +(-1.36085 + 3.36320i) q^{6} +(3.38127 + 2.36759i) q^{7} +(0.784385 + 0.210175i) q^{8} +(-2.48537 - 1.68016i) q^{9} +(-3.95100 - 2.51554i) q^{10} +(1.66957 - 4.58710i) q^{11} +(-1.87942 + 3.68385i) q^{12} +(-0.223275 - 2.55204i) q^{13} +(6.62348 + 5.55776i) q^{14} +(2.71529 - 2.76174i) q^{15} +(-2.88895 - 1.05149i) q^{16} +(-2.36120 + 0.632683i) q^{17} +(-4.87950 - 3.95974i) q^{18} +(-4.05431 + 2.34076i) q^{19} +(-4.23661 - 3.24902i) q^{20} +(-5.63616 + 4.39875i) q^{21} +(4.32134 - 9.26714i) q^{22} +(2.13442 + 3.04827i) q^{23} +(-0.745961 + 1.19241i) q^{24} +(2.87013 + 4.09419i) q^{25} -5.36612i q^{26} +(4.04325 - 3.26375i) q^{27} +(6.96907 + 6.96907i) q^{28} +(2.44490 - 2.05152i) q^{29} +(6.17020 - 5.26724i) q^{30} +(-0.272295 + 1.54426i) q^{31} +(-7.30837 - 3.40795i) q^{32} +(6.74982 + 5.09185i) q^{33} +(-5.04264 + 0.889154i) q^{34} +(-4.26417 - 8.18590i) q^{35} +(-5.14748 - 4.98120i) q^{36} +(0.592937 + 2.21287i) q^{37} +(-8.88750 + 4.14431i) q^{38} +(4.33971 + 0.924787i) q^{39} +(-1.33909 - 1.22638i) q^{40} +(-4.38733 + 5.22862i) q^{41} +(-12.5641 + 8.14994i) q^{42} +(0.553045 + 1.18601i) q^{43} +(5.82771 - 10.0939i) q^{44} +(3.19638 + 5.89773i) q^{45} +(3.89741 + 6.75051i) q^{46} +(-0.220307 + 0.314631i) q^{47} +(3.20684 - 4.25102i) q^{48} +(3.43334 + 9.43304i) q^{49} +(5.24167 + 9.06735i) q^{50} +(0.149960 - 4.23134i) q^{51} +(0.533107 - 6.09344i) q^{52} +(0.177802 - 0.177802i) q^{53} +(9.03293 - 6.07235i) q^{54} +(-8.04562 + 7.37651i) q^{55} +(2.15461 + 2.56776i) q^{56} +(-1.81994 - 7.90174i) q^{57} +(5.47633 - 3.83457i) q^{58} +(-0.797126 + 0.290130i) q^{59} +(7.52979 - 5.36817i) q^{60} +(1.38646 + 7.86300i) q^{61} +(-0.850126 + 3.17272i) q^{62} +(-4.42577 - 11.5654i) q^{63} +(-9.30332 - 5.37128i) q^{64} +(-2.19069 + 5.29289i) q^{65} +(13.1553 + 11.8575i) q^{66} +(8.09911 - 0.708580i) q^{67} +(-5.81446 + 0.508699i) q^{68} +(-6.13097 + 1.98856i) q^{69} +(-7.40362 - 17.8601i) q^{70} +(-7.83146 - 4.52149i) q^{71} +(-1.59636 - 1.84025i) q^{72} +(3.19228 - 11.9138i) q^{73} +(0.833296 + 4.72586i) q^{74} +(-8.23631 + 2.67641i) q^{75} +(-10.5038 + 3.82308i) q^{76} +(16.5056 - 11.5574i) q^{77} +(8.88686 + 2.72203i) q^{78} +(-6.94728 - 8.27944i) q^{79} +(4.64572 + 5.06712i) q^{80} +(3.35413 + 8.35163i) q^{81} +(-10.1096 + 10.1096i) q^{82} +(0.325084 - 3.71573i) q^{83} +(-15.0767 + 8.00637i) q^{84} +(5.33682 + 1.18161i) q^{85} +(0.937521 + 2.57582i) q^{86} +(2.15732 + 5.08968i) q^{87} +(2.27368 - 3.24715i) q^{88} +(7.58469 + 13.1371i) q^{89} +(5.59319 + 12.8904i) q^{90} +(5.28723 - 9.15775i) q^{91} +(3.75502 + 8.05267i) q^{92} +(-2.41934 - 1.23430i) q^{93} +(-0.517156 + 0.616322i) q^{94} +(10.4581 - 0.459486i) q^{95} +(9.35119 - 10.3747i) q^{96} +(-1.25036 + 0.583050i) q^{97} +(5.44226 + 20.3108i) q^{98} +(-11.8566 + 8.59551i) 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

Varieties

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