LMFDB - Embedded newform 135.2.q.a.122.8

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			122.8
Character	$\chi$	$=$	135.122
Dual form			135.2.q.a.83.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.377486 - 0.264318i) q^{2} +(1.45550 + 0.938886i) q^{3} +(-0.611409 - 1.67983i) q^{4} +(0.538986 - 2.17014i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-1.52168 - 3.26325i) q^{7} +(-0.451753 + 1.68596i) q^{8} +(1.23699 + 2.73311i) q^{9} +O(q^{10})$	\(q+(-0.377486 - 0.264318i) q^{2} +(1.45550 + 0.938886i) q^{3} +(-0.611409 - 1.67983i) q^{4} +(0.538986 - 2.17014i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-1.52168 - 3.26325i) q^{7} +(-0.451753 + 1.68596i) q^{8} +(1.23699 + 2.73311i) q^{9} +(-0.777066 + 0.676732i) q^{10} +(2.85486 + 3.40229i) q^{11} +(0.687263 - 3.01905i) q^{12} +(0.226257 + 0.323128i) q^{13} +(-0.288125 + 1.63404i) q^{14} +(2.82201 - 2.65260i) q^{15} +(-2.12266 + 1.78113i) q^{16} +(1.03506 + 3.86289i) q^{17} +(0.255466 - 1.35867i) q^{18} +(1.05819 - 0.610947i) q^{19} +(-3.97501 + 0.421435i) q^{20} +(0.849012 - 6.17836i) q^{21} +(-0.178381 - 2.03891i) q^{22} +(-3.57786 - 1.66839i) q^{23} +(-2.24046 + 2.02978i) q^{24} +(-4.41899 - 2.33935i) q^{25} -0.181780i q^{26} +(-0.765638 + 5.13944i) q^{27} +(-4.55135 + 4.55135i) q^{28} +(0.885233 + 5.02040i) q^{29} +(-1.76640 + 0.255409i) q^{30} +(9.19946 - 3.34833i) q^{31} +(4.74965 - 0.415541i) q^{32} +(0.960899 + 7.63244i) q^{33} +(0.630312 - 1.73177i) q^{34} +(-7.90187 + 1.54341i) q^{35} +(3.83486 - 3.74897i) q^{36} +(-10.6220 + 2.84615i) q^{37} +(-0.560936 - 0.0490755i) q^{38} +(0.0259371 + 0.682744i) q^{39} +(3.41529 + 1.88908i) q^{40} +(-1.80826 - 0.318845i) q^{41} +(-1.95354 + 2.10783i) q^{42} +(-0.218695 + 2.49969i) q^{43} +(3.96979 - 6.87588i) q^{44} +(6.59793 - 1.21132i) q^{45} +(0.909608 + 1.57549i) q^{46} +(1.19000 - 0.554905i) q^{47} +(-4.76182 + 0.599497i) q^{48} +(-3.83380 + 4.56894i) q^{49} +(1.04977 + 2.05109i) q^{50} +(-2.12028 + 6.59425i) q^{51} +(0.404466 - 0.577637i) q^{52} +(-3.53443 - 3.53443i) q^{53} +(1.64746 - 1.73769i) q^{54} +(8.92217 - 4.36165i) q^{55} +(6.18915 - 1.09131i) q^{56} +(2.11381 + 0.104285i) q^{57} +(0.992822 - 2.12911i) q^{58} +(-0.467138 - 0.391975i) q^{59} +(-6.18132 - 3.11868i) q^{60} +(-1.87695 - 0.683152i) q^{61} +(-4.35769 - 1.16764i) q^{62} +(7.03652 - 8.19551i) q^{63} +(2.89665 + 1.67238i) q^{64} +(0.823182 - 0.316847i) q^{65} +(1.65467 - 3.13512i) q^{66} +(3.34241 - 2.34038i) q^{67} +(5.85616 - 4.10053i) q^{68} +(-3.64117 - 5.78755i) q^{69} +(3.39079 + 1.50600i) q^{70} +(-10.9258 - 6.30801i) q^{71} +(-5.16673 + 0.850825i) q^{72} +(4.00309 + 1.07262i) q^{73} +(4.76194 + 1.73320i) q^{74} +(-4.23548 - 7.55386i) q^{75} +(-1.67328 - 1.40404i) q^{76} +(6.75835 - 14.4933i) q^{77} +(0.170671 - 0.264582i) q^{78} +(11.8688 - 2.09278i) q^{79} +(2.72120 + 5.56647i) q^{80} +(-5.93973 + 6.76162i) q^{81} +(0.598316 + 0.598316i) q^{82} +(1.54510 - 2.20663i) q^{83} +(-10.8977 + 2.35131i) q^{84} +(8.94087 - 0.164174i) q^{85} +(0.743269 - 0.885794i) q^{86} +(-3.42513 + 8.13835i) q^{87} +(-7.02584 + 3.27620i) q^{88} +(1.23513 + 2.13931i) q^{89} +(-2.81080 - 1.28670i) q^{90} +(0.710159 - 1.23003i) q^{91} +(-0.615070 + 7.03028i) q^{92} +(16.5336 + 3.76374i) q^{93} +(-0.595878 - 0.105069i) q^{94} +(-0.755488 - 2.62571i) q^{95} +(7.30328 + 3.85456i) q^{96} +(0.567380 + 0.0496393i) q^{97} +(2.65486 - 0.711367i) q^{98} +(-5.76740 + 12.0112i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.377486	−	0.264318i	−0.266923	−	0.186901i	0.432451	−	0.901657i	$-0.357649\pi$
$2$	−0.377486	−	0.264318i	−0.266923	−	0.186901i	−0.699374	+	0.714756i	$0.746538\pi$
$3$	1.45550	+	0.938886i	0.840336	+	0.542066i
$3$	1.45550	+	0.938886i	0.840336	+	0.542066i
$4$	−0.611409	−	1.67983i	−0.305705	−	0.839916i
$5$	0.538986	−	2.17014i	0.241042	−	0.970515i
$5$	0.538986	−	2.17014i	0.241042	−	0.970515i
$6$	−0.301267	−	0.739132i	−0.122992	−	0.301750i
$7$	−1.52168	−	3.26325i	−0.575141	−	1.23339i	−0.951708	−	0.307004i	$-0.900673\pi$
$7$	−1.52168	−	3.26325i	−0.575141	−	1.23339i	0.376567	−	0.926389i	$-0.377104\pi$
$8$	−0.451753	+	1.68596i	−0.159719	+	0.596078i
$9$	1.23699	+	2.73311i	0.412328	+	0.911035i
$10$	−0.777066	+	0.676732i	−0.245730	+	0.214001i
$11$	2.85486	+	3.40229i	0.860773	+	1.02583i	0.999370	+	0.0354810i	$0.0112963\pi$
$11$	2.85486	+	3.40229i	0.860773	+	1.02583i	−0.138597	+	0.990349i	$0.544259\pi$
$12$	0.687263	−	3.01905i	0.198396	−	0.871524i
$13$	0.226257	+	0.323128i	0.0627524	+	0.0896196i	0.849302	−	0.527908i	$-0.177023\pi$
$13$	0.226257	+	0.323128i	0.0627524	+	0.0896196i	−0.786549	+	0.617527i	$0.788134\pi$
$14$	−0.288125	+	1.63404i	−0.0770047	+	0.436715i
$15$	2.82201	−	2.65260i	0.728639	−	0.684898i
$16$	−2.12266	+	1.78113i	−0.530666	+	0.445281i
$17$	1.03506	+	3.86289i	0.251038	+	0.936888i	0.970252	+	0.242098i	$0.0778357\pi$
$17$	1.03506	+	3.86289i	0.251038	+	0.936888i	−0.719213	+	0.694789i	$0.755498\pi$
$18$	0.255466	−	1.35867i	0.0602138	−	0.320241i
$19$	1.05819	−	0.610947i	0.242766	−	0.140161i	−0.373682	−	0.927557i	$-0.621905\pi$
$19$	1.05819	−	0.610947i	0.242766	−	0.140161i	0.616447	+	0.787396i	$0.288571\pi$
$20$	−3.97501	+	0.421435i	−0.888839	+	0.0942357i
$21$	0.849012	−	6.17836i	0.185270	−	1.34823i
$22$	−0.178381	−	2.03891i	−0.0380310	−	0.434697i
$23$	−3.57786	−	1.66839i	−0.746036	−	0.347882i	0.0121450	−	0.999926i	$-0.496134\pi$
$23$	−3.57786	−	1.66839i	−0.746036	−	0.347882i	−0.758181	+	0.652044i	$0.773912\pi$
$24$	−2.24046	+	2.02978i	−0.457331	+	0.414328i
$25$	−4.41899	−	2.33935i	−0.883798	−	0.467869i
$26$		−	0.181780i		−	0.0356500i
$27$	−0.765638	+	5.13944i	−0.147347	+	0.989085i
$28$	−4.55135	+	4.55135i	−0.860124	+	0.860124i
$29$	0.885233	+	5.02040i	0.164384	+	0.932266i	0.949698	+	0.313168i	$0.101390\pi$
$29$	0.885233	+	5.02040i	0.164384	+	0.932266i	−0.785314	+	0.619097i	$0.787499\pi$
$30$	−1.76640	+	0.255409i	−0.322499	+	0.0466311i
$31$	9.19946	−	3.34833i	1.65227	−	0.601378i	0.663152	−	0.748485i	$-0.269219\pi$
$31$	9.19946	−	3.34833i	1.65227	−	0.601378i	0.989121	+	0.147107i	$0.0469963\pi$
$32$	4.74965	−	0.415541i	0.839628	−	0.0734579i
$33$	0.960899	+	7.63244i	0.167271	+	1.32864i
$34$	0.630312	−	1.73177i	0.108098	−	0.296996i
$35$	−7.90187	+	1.54341i	−1.33566	+	0.260883i
$36$	3.83486	−	3.74897i	0.639143	−	0.624829i
$37$	−10.6220	+	2.84615i	−1.74624	+	0.467905i	−0.983818	−	0.179171i	$-0.942658\pi$
$37$	−10.6220	+	2.84615i	−1.74624	+	0.467905i	−0.762426	+	0.647076i	$0.775992\pi$
$38$	−0.560936	−	0.0490755i	−0.0909958	−	0.00796111i
$39$	0.0259371	+	0.682744i	0.00415327	+	0.109327i
$40$	3.41529	+	1.88908i	0.540004	+	0.298689i
$41$	−1.80826	−	0.318845i	−0.282403	−	0.0497952i	0.0306526	−	0.999530i	$-0.490241\pi$
$41$	−1.80826	−	0.318845i	−0.282403	−	0.0497952i	−0.313055	+	0.949735i	$0.601353\pi$
$42$	−1.95354	+	2.10783i	−0.301438	+	0.325246i
$43$	−0.218695	+	2.49969i	−0.0333507	+	0.381200i	0.961116	+	0.276146i	$0.0890572\pi$
$43$	−0.218695	+	2.49969i	−0.0333507	+	0.381200i	−0.994466	+	0.105054i	$0.966498\pi$
$44$	3.96979	−	6.87588i	0.598469	−	1.03658i
$45$	6.59793	−	1.21132i	0.983562	−	0.180573i
$46$	0.909608	+	1.57549i	0.134114	+	0.232293i
$47$	1.19000	−	0.554905i	0.173579	−	0.0809412i	−0.333887	−	0.942613i	$-0.608360\pi$
$47$	1.19000	−	0.554905i	0.173579	−	0.0809412i	0.507465	+	0.861672i	$0.330582\pi$
$48$	−4.76182	+	0.599497i	−0.687309	+	0.0865300i
$49$	−3.83380	+	4.56894i	−0.547685	+	0.652706i
$50$	1.04977	+	2.05109i	0.148460	+	0.290068i
$51$	−2.12028	+	6.59425i	−0.296899	+	0.923380i
$52$	0.404466	−	0.577637i	0.0560893	−	0.0801039i
$53$	−3.53443	−	3.53443i	−0.485491	−	0.485491i	0.421389	−	0.906880i	$-0.361543\pi$
$53$	−3.53443	−	3.53443i	−0.485491	−	0.485491i	−0.906880	+	0.421389i	$0.861543\pi$
$54$	1.64746	−	1.73769i	0.224191	−	0.236470i
$55$	8.92217	−	4.36165i	1.20307	−	0.588125i
$56$	6.18915	−	1.09131i	0.827060	−	0.145833i
$57$	2.11381	+	0.104285i	0.279981	+	0.0138129i
$58$	0.992822	−	2.12911i	0.130364	−	0.279566i
$59$	−0.467138	−	0.391975i	−0.0608162	−	0.0510308i	0.611873	−	0.790956i	$-0.290416\pi$
$59$	−0.467138	−	0.391975i	−0.0608162	−	0.0510308i	−0.672689	+	0.739925i	$0.734861\pi$
$60$	−6.18132	−	3.11868i	−0.798005	−	0.402620i
$61$	−1.87695	−	0.683152i	−0.240318	−	0.0874687i	0.219053	−	0.975713i	$-0.429703\pi$
$61$	−1.87695	−	0.683152i	−0.240318	−	0.0874687i	−0.459372	+	0.888244i	$0.651925\pi$
$62$	−4.35769	−	1.16764i	−0.553427	−	0.148290i
$63$	7.03652	−	8.19551i	0.886518	−	1.03254i
$64$	2.89665	+	1.67238i	0.362081	+	0.209048i
$65$	0.823182	−	0.316847i	0.102103	−	0.0393000i
$66$	1.65467	−	3.13512i	0.203676	−	0.385907i
$67$	3.34241	−	2.34038i	0.408341	−	0.285923i	−0.351304	−	0.936261i	$-0.614262\pi$
$67$	3.34241	−	2.34038i	0.408341	−	0.285923i	0.759645	+	0.650338i	$0.225373\pi$
$68$	5.85616	−	4.10053i	0.710164	−	0.497262i
$69$	−3.64117	−	5.78755i	−0.438346	−	0.696739i
$70$	3.39079	+	1.50600i	0.405277	+	0.180001i
$71$	−10.9258	−	6.30801i	−1.29665	−	0.748623i	−0.316829	−	0.948483i	$-0.602618\pi$
$71$	−10.9258	−	6.30801i	−1.29665	−	0.748623i	−0.979824	+	0.199860i	$0.935951\pi$
$72$	−5.16673	+	0.850825i	−0.608905	+	0.100271i
$73$	4.00309	+	1.07262i	0.468526	+	0.125541i	0.485355	−	0.874317i	$-0.338690\pi$
$73$	4.00309	+	1.07262i	0.468526	+	0.125541i	−0.0168287	+	0.999858i	$0.505357\pi$
$74$	4.76194	+	1.73320i	0.553564	+	0.201481i
$75$	−4.23548	−	7.55386i	−0.489071	−	0.872244i
$76$	−1.67328	−	1.40404i	−0.191938	−	0.161055i
$77$	6.75835	−	14.4933i	0.770186	−	1.65167i
$78$	0.170671	−	0.264582i	0.0193247	−	0.0299580i
$79$	11.8688	−	2.09278i	1.33534	−	0.235457i	0.540023	−	0.841650i	$-0.318415\pi$
$79$	11.8688	−	2.09278i	1.33534	−	0.235457i	0.795317	+	0.606193i	$0.207304\pi$
$80$	2.72120	+	5.56647i	0.304239	+	0.622350i
$81$	−5.93973	+	6.76162i	−0.659970	+	0.751292i
$82$	0.598316	+	0.598316i	0.0660729	+	0.0660729i
$83$	1.54510	−	2.20663i	0.169597	−	0.242209i	−0.725352	−	0.688378i	$-0.758323\pi$
$83$	1.54510	−	2.20663i	0.169597	−	0.242209i	0.894949	+	0.446169i	$0.147212\pi$
$84$	−10.8977	+	2.35131i	−1.18904	+	0.256549i
$85$	8.94087	−	0.164174i	0.969774	−	0.0178072i
$86$	0.743269	−	0.885794i	0.0801488	−	0.0955176i
$87$	−3.42513	+	8.13835i	−0.367212	+	0.872523i
$88$	−7.02584	+	3.27620i	−0.748957	+	0.349244i
$89$	1.23513	+	2.13931i	0.130924	+	0.226766i	0.924033	−	0.382313i	$-0.124872\pi$
$89$	1.23513	+	2.13931i	0.130924	+	0.226766i	−0.793109	+	0.609079i	$0.791539\pi$
$90$	−2.81080	−	1.28670i	−0.296284	−	0.135630i
$91$	0.710159	−	1.23003i	0.0744449	−	0.128942i
$92$	−0.615070	+	7.03028i	−0.0641254	+	0.732957i
$93$	16.5336	+	3.76374i	1.71445	+	0.390281i
$94$	−0.595878	−	0.105069i	−0.0614601	−	0.0108371i
$95$	−0.755488	−	2.62571i	−0.0775114	−	0.269392i
$96$	7.30328	+	3.85456i	0.745388	+	0.393405i
$97$	0.567380	+	0.0496393i	0.0576087	+	0.00504011i	0.115924	−	0.993258i	$-0.463017\pi$
$97$	0.567380	+	0.0496393i	0.0576087	+	0.00504011i	−0.0583150	+	0.998298i	$0.518573\pi$
$98$	2.65486	−	0.711367i	0.268181	−	0.0718589i
$99$	−5.76740	+	12.0112i	−0.579646	+	1.20717i
$100$	−1.22790	+	8.85346i	−0.122790	+	0.885346i
$101$	−5.00202	+	13.7429i	−0.497720	+	1.36747i	0.395753	+	0.918357i	$0.370484\pi$
$101$	−5.00202	+	13.7429i	−0.497720	+	1.36747i	−0.893473	+	0.449117i	$0.851739\pi$
$102$	2.54336	−	1.92881i	0.251830	−	0.190980i
$103$	−17.1583	+	1.50115i	−1.69066	+	0.147913i	−0.891442	−	0.453135i	$-0.850306\pi$
$103$	−17.1583	+	1.50115i	−1.69066	+	0.147913i	−0.799213	+	0.601048i	$0.794750\pi$
$104$	−0.646995	+	0.235487i	−0.0634431	+	0.0230914i
$105$	−12.9503	−	5.17252i	−1.26382	−	0.504786i
$106$	0.399982	+	2.26841i	0.0388497	+	0.220328i
$107$	4.07639	−	4.07639i	0.394080	−	0.394080i	−0.482059	−	0.876139i	$-0.660111\pi$
$107$	4.07639	−	4.07639i	0.394080	−	0.394080i	0.876139	+	0.482059i	$0.160111\pi$
$108$	9.10151	−	1.85615i	0.875793	−	0.178609i
$109$			7.33084i			0.702167i	0.936344	+	0.351084i	$0.114187\pi$
$109$			7.33084i			0.702167i	−0.936344	+	0.351084i	$0.885813\pi$
$110$	−4.52086	−	0.711831i	−0.431047	−	0.0678705i
$111$	−18.1326	−	5.83025i	−1.72107	−	0.553383i
$112$	9.04228	+	4.21648i	0.854415	+	0.398420i
$113$	−0.638871	−	7.30233i	−0.0600999	−	0.686945i	−0.965160	−	0.261661i	$-0.915730\pi$
$113$	−0.638871	−	7.30233i	−0.0600999	−	0.686945i	0.905060	−	0.425284i	$-0.139826\pi$
$114$	−0.770369	−	0.598085i	−0.0721516	−	0.0560158i
$115$	−5.54904	+	6.86522i	−0.517451	+	0.640185i
$116$	7.89220	−	4.55656i	0.732772	−	0.423066i
$117$	−0.603267	+	1.01809i	−0.0557721	+	0.0941223i
$118$	0.0727316	+	0.271438i	0.00669549	+	0.0249879i
$119$	11.0305	−	9.25573i	1.01117	−	0.848471i
$120$	3.19733	+	5.95612i	0.291875	+	0.543717i
$121$	−1.51523	+	8.59327i	−0.137748	+	0.781206i
$122$	0.527950	+	0.753991i	0.0477984	+	0.0682632i
$123$	−2.33257	−	2.16183i	−0.210321	−	0.194926i
$124$	−11.2493	−	13.4064i	−1.01021	−	1.20393i
$125$	−7.45848	+	8.32893i	−0.667106	+	0.744962i
$126$	−4.82241	+	1.23381i	−0.429614	+	0.109916i
$127$	1.36574	−	5.09700i	0.121189	−	0.452285i	−0.878486	−	0.477769i	$-0.841446\pi$
$127$	1.36574	−	5.09700i	0.121189	−	0.452285i	0.999675	+	0.0254832i	$0.00811243\pi$
$128$	−4.68132	−	10.0391i	−0.413774	−	0.887341i
$129$	−2.66524	+	3.43299i	−0.234661	+	0.302258i
$130$	−0.394488	−	0.0979769i	−0.0345989	−	0.00859314i
$131$	0.242450	+	0.666126i	0.0211829	+	0.0581997i	0.949833	−	0.312756i	$-0.101252\pi$
$131$	0.242450	+	0.666126i	0.0211829	+	0.0581997i	−0.928650	+	0.370956i	$0.879030\pi$
$132$	12.2337	−	6.28069i	1.06481	−	0.546664i
$133$	−3.60390	−	2.52348i	−0.312498	−	0.218813i
$134$	−1.88032			−0.162435
$135$	10.7406	+	4.43162i	0.924405	+	0.381413i
$136$	−6.98028			−0.598554
$137$	−0.834037	−	0.583999i	−0.0712566	−	0.0498944i	0.537405	−	0.843324i	$-0.319405\pi$
$137$	−0.834037	−	0.583999i	−0.0712566	−	0.0498944i	−0.608662	+	0.793430i	$0.708293\pi$
$138$	−0.155265	+	3.14715i	−0.0132170	+	0.267903i
$139$	−7.61336	−	20.9175i	−0.645757	−	1.77420i	−0.632837	−	0.774285i	$-0.718110\pi$
$139$	−7.61336	−	20.9175i	−0.645757	−	1.77420i	−0.0129201	−	0.999917i	$-0.504113\pi$
$140$	7.42394	+	12.3302i	0.627437	+	1.04209i
$141$	2.25304	+	0.309606i	0.189740	+	0.0260735i
$142$	2.45701	+	5.26907i	0.206187	+	0.442170i
$143$	−0.453445	+	1.69228i	−0.0379189	+	0.141515i
$144$	−7.49371	−	3.59824i	−0.624476	−	0.299853i
$145$	11.3721	+	0.784852i	0.944401	+	0.0651784i
$146$	−1.22759	−	1.46299i	−0.101596	−	0.121078i
$147$	−9.86982	+	3.05061i	−0.814049	+	0.251610i
$148$	11.2754	+	16.1030i	0.926835	+	1.32366i
$149$	−2.80203	+	15.8911i	−0.229551	+	1.30185i	0.624240	+	0.781233i	$0.285409\pi$
$149$	−2.80203	+	15.8911i	−0.229551	+	1.30185i	−0.853791	+	0.520616i	$0.825702\pi$
$150$	−0.397791	+	3.97099i	−0.0324795	+	0.324230i
$151$	6.91118	−	5.79917i	0.562424	−	0.471930i	−0.316698	−	0.948526i	$-0.602574\pi$
$151$	6.91118	−	5.79917i	0.562424	−	0.471930i	0.879122	+	0.476597i	$0.158130\pi$
$152$	0.551994	+	2.06007i	0.0447726	+	0.167094i
$153$	−9.27733	+	7.60726i	−0.750027	+	0.615010i
$154$	−6.38204	+	3.68467i	−0.514279	+	0.296919i
$155$	−2.30795	−	21.7688i	−0.185379	−	1.74851i
$156$	1.13104	−	0.461006i	0.0905555	−	0.0369100i
$157$	−0.125040	−	1.42921i	−0.00997924	−	0.114063i	0.989571	−	0.144044i	$-0.0460108\pi$
$157$	−0.125040	−	1.42921i	−0.00997924	−	0.114063i	−0.999550	+	0.0299812i	$0.990455\pi$
$158$	−5.03345	−	2.34714i	−0.400440	−	0.186728i
$159$	−1.82595	−	8.46280i	−0.144807	−	0.671144i
$160$	1.65822	−	10.5314i	0.131093	−	0.832578i
$161$			14.2142i			1.12024i
$162$	4.02938	−	0.982436i	0.316578	−	0.0771874i
$163$	6.66882	−	6.66882i	0.522343	−	0.522343i	−0.395936	−	0.918278i	$-0.629580\pi$
$163$	6.66882	−	6.66882i	0.522343	−	0.522343i	0.918278	+	0.395936i	$0.129580\pi$
$164$	0.569980	+	3.23252i	0.0445080	+	0.252417i
$165$	17.0814	+	2.02850i	1.32978	+	0.157918i
$166$	−1.16651	+	0.424573i	−0.0905384	+	0.0329533i
$167$	−16.7028	+	1.46130i	−1.29250	+	0.113079i	−0.712578	−	0.701593i	$-0.752472\pi$
$167$	−16.7028	+	1.46130i	−1.29250	+	0.113079i	−0.579922	+	0.814672i	$0.696917\pi$
$168$	10.0330	+	4.22250i	0.774059	+	0.325773i
$169$	4.39304	−	12.0698i	0.337926	−	0.928445i
$170$	−3.41845	−	2.30126i	−0.262183	−	0.176499i
$171$	2.97875	+	2.13641i	0.227791	+	0.163376i
$172$	4.33278	−	1.16096i	0.330371	−	0.0885227i
$173$	−7.61365	−	0.666108i	−0.578855	−	0.0506432i	−0.206031	−	0.978545i	$-0.566055\pi$
$173$	−7.61365	−	0.666108i	−0.578855	−	0.0506432i	−0.372824	+	0.927902i	$0.621610\pi$
$174$	3.44405	−	2.16679i	0.261093	−	0.164264i
$175$	−0.909596	+	17.9800i	−0.0687590	+	1.35916i
$176$	−12.1198	−	2.13705i	−0.913566	−	0.161086i
$177$	−0.311901	−	1.00911i	−0.0234439	−	0.0758494i
$178$	0.0992144	−	1.13403i	0.00743644	−	0.0849988i
$179$	2.10555	−	3.64692i	0.157376	−	0.272584i	−0.776545	−	0.630061i	$-0.783030\pi$
$179$	2.10555	−	3.64692i	0.157376	−	0.272584i	0.933922	+	0.357477i	$0.116363\pi$
$180$	−6.06885	−	10.3428i	−0.452346	−	0.770907i
$181$	−2.97345	−	5.15017i	−0.221015	−	0.382809i	0.734102	−	0.679040i	$-0.237604\pi$
$181$	−2.97345	−	5.15017i	−0.221015	−	0.382809i	−0.955116	+	0.296231i	$0.904270\pi$
$182$	−0.593194	+	0.276611i	−0.0439705	+	0.0205038i
$183$	−2.09050	−	2.75657i	−0.154534	−	0.203772i
$184$	4.42915	−	5.27845i	0.326521	−	0.389133i
$185$	0.451438	+	24.5852i	0.0331904	+	1.80754i
$186$	−5.24635	−	5.79088i	−0.384681	−	0.424608i
$187$	−10.1877	+	14.5496i	−0.745000	+	1.06397i
$188$	−1.65972	−	1.65972i	−0.121048	−	0.121048i
$189$	17.9363	−	5.32211i	1.30468	−	0.387126i
$190$	−0.408837	+	1.19086i	−0.0296602	+	0.0863938i
$191$	−10.6788	+	1.88297i	−0.772694	+	0.136247i	−0.546074	−	0.837737i	$-0.683878\pi$
$191$	−10.6788	+	1.88297i	−0.772694	+	0.136247i	−0.226619	+	0.973983i	$0.572767\pi$
$192$	2.64591	+	5.15378i	0.190952	+	0.371942i
$193$	0.260068	−	0.557718i	0.0187201	−	0.0401454i	−0.896725	−	0.442587i	$-0.854061\pi$
$193$	0.260068	−	0.557718i	0.0187201	−	0.0401454i	0.915446	+	0.402442i	$0.131838\pi$
$194$	−0.201057	−	0.168707i	−0.0144351	−	0.0121124i
$195$	1.49563	+	0.311702i	0.107104	+	0.0223215i
$196$	10.0191	+	3.64664i	0.715648	+	0.260475i
$197$	26.5467	+	7.11316i	1.89137	+	0.506791i	0.998392	+	0.0566946i	$0.0180561\pi$
$197$	26.5467	+	7.11316i	1.89137	+	0.506791i	0.892980	+	0.450097i	$0.148611\pi$
$198$	5.35190	−	3.00964i	0.380343	−	0.213886i
$199$	2.40020	+	1.38576i	0.170146	+	0.0982338i	0.582655	−	0.812720i	$-0.302014\pi$
$199$	2.40020	+	1.38576i	0.170146	+	0.0982338i	−0.412509	+	0.910954i	$0.635347\pi$
$200$	5.94035	−	6.39345i	0.420046	−	0.452085i
$201$	7.06225	−	0.268292i	0.498132	−	0.0189238i
$202$	5.52070	−	3.86564i	0.388435	−	0.271985i
$203$	15.0358	−	10.5282i	1.05531	−	0.738934i
$204$	12.3736	−	0.470067i	0.866325	−	0.0329113i
$205$	−1.66656	+	3.75232i	−0.116398	+	0.262073i
$206$	6.87379	+	3.96858i	0.478919	+	0.276504i
$207$	0.134108	−	11.8424i	0.00932114	−	0.823107i
$208$	−1.05580	−	0.282900i	−0.0732065	−	0.0196156i
$209$	5.09961	+	1.85611i	0.352747	+	0.128389i
$210$	3.52135	+	5.37555i	0.242997	+	0.370948i
$211$	−16.7925	−	14.0906i	−1.15605	−	0.970038i	−0.156202	−	0.987725i	$-0.549925\pi$
$211$	−16.7925	−	14.0906i	−1.15605	−	0.970038i	−0.999844	+	0.0176876i	$0.994370\pi$
$212$	−3.77627	+	8.09823i	−0.259355	+	0.556189i
$213$	−9.98004	−	19.4394i	−0.683821	−	1.33197i
$214$	−2.61625	+	0.461315i	−0.178843	+	0.0315348i
$215$	5.30681	+	1.82190i	0.361921	+	0.124252i
$216$	−8.31903	−	3.61259i	−0.566038	−	0.245806i
$217$	−24.9251	−	24.9251i	−1.69202	−	1.69202i
$218$	1.93768	−	2.76729i	0.131236	−	0.187424i
$219$	4.81944	+	5.31966i	0.325668	+	0.359469i
$220$	−12.7819	−	12.3210i	−0.861759	−	0.830682i
$221$	−1.01402	+	1.20846i	−0.0682103	+	0.0812899i
$222$	5.30374	+	6.99360i	0.355964	+	0.469380i
$223$	10.1077	−	4.71331i	0.676863	−	0.315627i	−0.0536157	−	0.998562i	$-0.517075\pi$
$223$	10.1077	−	4.71331i	0.676863	−	0.315627i	0.730479	+	0.682935i	$0.239297\pi$
$224$	−8.58346	−	14.8670i	−0.573507	−	0.993343i
$225$	0.927458	−	14.9713i	0.0618306	−	0.998087i
$226$	−1.68897	+	2.92539i	−0.112349	+	0.194594i
$227$	−1.11401	+	12.7332i	−0.0739393	+	0.845130i	0.865163	+	0.501492i	$0.167215\pi$
$227$	−1.11401	+	12.7332i	−0.0739393	+	0.845130i	−0.939102	+	0.343639i	$0.888340\pi$
$228$	−1.11722	−	3.61461i	−0.0739898	−	0.239383i
$229$	−14.6486	−	2.58295i	−0.968008	−	0.170686i	−0.332775	−	0.943006i	$-0.607985\pi$
$229$	−14.6486	−	2.58295i	−0.968008	−	0.170686i	−0.635233	+	0.772320i	$0.719096\pi$
$230$	3.90929	−	1.12481i	0.257771	−	0.0741676i
$231$	23.4444	−	14.7498i	1.54253	−	0.970465i
$232$	−8.86413	−	0.775511i	−0.581959	−	0.0509148i
$233$	−4.81533	+	1.29026i	−0.315463	+	0.0845279i	−0.413076	−	0.910696i	$-0.635546\pi$
$233$	−4.81533	+	1.29026i	−0.315463	+	0.0845279i	0.0976137	+	0.995224i	$0.468879\pi$
$234$	0.496824	−	0.224859i	0.0324784	−	0.0146995i
$235$	−0.562827	−	2.88154i	−0.0367148	−	0.187971i
$236$	−0.372840	+	1.02437i	−0.0242698	+	0.0666808i
$237$	19.2399	+	8.09737i	1.24977	+	0.525980i
$238$	−6.61033	+	0.578329i	−0.428484	+	0.0374875i
$239$	−6.83215	+	2.48670i	−0.441935	+	0.160851i	−0.553397	−	0.832918i	$-0.686669\pi$
$239$	−6.83215	+	2.48670i	−0.441935	+	0.160851i	0.111462	+	0.993769i	$0.464447\pi$
$240$	−1.26556	+	10.6569i	−0.0816917	+	0.687901i
$241$	3.42764	+	19.4391i	0.220794	+	1.25219i	0.870564	+	0.492055i	$0.163754\pi$
$241$	3.42764	+	19.4391i	0.220794	+	1.25219i	−0.649770	+	0.760131i	$0.725135\pi$
$242$	2.84333	−	2.84333i	0.182776	−	0.182776i
$243$	−14.9937	+	4.26484i	−0.961847	+	0.273590i
$244$			3.57064i			0.228587i
$245$	7.84886	+	10.7825i	0.501445	+	0.688866i
$246$	0.309101	+	1.43260i	0.0197075	+	0.0913393i
$247$	0.436837	+	0.203700i	0.0277953	+	0.0129611i
$248$	1.48928	+	17.0226i	0.0945696	+	1.08094i
$249$	4.32067	−	1.76109i	0.273812	−	0.111604i
$250$	5.01696	−	1.17264i	0.317300	−	0.0741643i
$251$	14.7212	−	8.49927i	0.929191	−	0.536469i	0.0426356	−	0.999091i	$-0.486425\pi$
$251$	14.7212	−	8.49927i	0.929191	−	0.536469i	0.886556	+	0.462622i	$0.153091\pi$
$252$	−18.0693	−	6.80937i	−1.13826	−	0.428950i
$253$	−4.53797	−	16.9360i	−0.285300	−	1.06475i
$254$	−1.86278	+	1.56305i	−0.116881	+	0.0980747i
$255$	13.1676	+	8.15551i	0.824588	+	0.510718i
$256$	0.275231	−	1.56091i	0.0172019	−	0.0975570i
$257$	−8.87491	−	12.6747i	−0.553601	−	0.790625i	0.440652	−	0.897678i	$-0.354747\pi$
$257$	−8.87491	−	12.6747i	−0.553601	−	0.790625i	−0.994253	+	0.107053i	$0.965858\pi$
$258$	1.91349	−	0.591431i	0.119129	−	0.0368209i
$259$	25.4510	+	30.3313i	1.58145	+	1.88469i
$260$	−1.03555	−	1.18908i	−0.0642221	−	0.0737439i
$261$	−12.6263	+	8.62960i	−0.781547	+	0.534159i
$262$	0.0845478	−	0.315537i	0.00522338	−	0.0194939i
$263$	10.6896	+	22.9238i	0.659147	+	1.41355i	0.896906	+	0.442221i	$0.145809\pi$
$263$	10.6896	+	22.9238i	0.659147	+	1.41355i	−0.237759	+	0.971324i	$0.576413\pi$
$264$	−13.3021	−	1.82794i	−0.818689	−	0.112502i
$265$	−9.57520	+	5.76519i	−0.588200	+	0.354153i
$266$	0.693419	+	1.90515i	0.0425163	+	0.116812i
$267$	−0.210830	+	4.27342i	−0.0129026	+	0.261529i
$268$	−5.97503	−	4.18376i	−0.364983	−	0.255564i
$269$	−20.9181			−1.27540			−0.637698	−	0.770286i	$-0.720113\pi$
$269$	−20.9181			−1.27540			−0.637698	+	0.770286i	$0.720113\pi$
$270$	−2.88307	−	4.51181i	−0.175458	−	0.274580i
$271$	6.02125			0.365765			0.182882	−	0.983135i	$-0.441457\pi$
$271$	6.02125			0.365765			0.182882	+	0.983135i	$0.441457\pi$
$272$	−9.07736	−	6.35604i	−0.550396	−	0.385391i
$273$	2.18850	−	1.12356i	0.132454	−	0.0680008i
$274$	0.160475	+	0.440902i	0.00969467	+	0.0266359i
$275$	−4.65646	−	21.7132i	−0.280795	−	1.30936i
$276$	−7.49587	+	9.65512i	−0.451198	+	0.581170i
$277$	1.52924	+	3.27946i	0.0918830	+	0.197044i	0.946878	−	0.321592i	$-0.104218\pi$
$277$	1.52924	+	3.27946i	0.0918830	+	0.197044i	−0.854995	+	0.518636i	$0.826440\pi$
$278$	−2.65495	+	9.90842i	−0.159233	+	0.594267i
$279$	20.5309	+	21.0013i	1.22916	+	1.25731i
$280$	0.967565	−	14.0195i	0.0578230	−	0.837826i
$281$	−15.0170	−	17.8966i	−0.895839	−	1.06762i	−0.997348	−	0.0727851i	$-0.976811\pi$
$281$	−15.0170	−	17.8966i	−0.895839	−	1.06762i	0.101508	−	0.994835i	$-0.467633\pi$
$282$	−0.768655	−	0.712391i	−0.0457727	−	0.0424223i
$283$	10.0108	+	14.2969i	0.595080	+	0.849863i	0.997857	−	0.0654355i	$-0.0208437\pi$
$283$	10.0108	+	14.2969i	0.595080	+	0.849863i	−0.402776	+	0.915298i	$0.631955\pi$
$284$	−3.91627	+	22.2103i	−0.232388	+	1.31794i
$285$	1.36563	−	4.53105i	0.0808928	−	0.268396i
$286$	0.618469	−	0.518957i	0.0365708	−	0.0306866i
$287$	1.71112	+	6.38599i	0.101004	+	0.376953i
$288$	7.01097	+	12.4673i	0.413125	+	0.734642i
$289$	0.871882	−	0.503381i	0.0512872	−	0.0296107i
$290$	−4.08535	−	3.30212i	−0.239900	−	0.193907i
$291$	0.779218	+	0.604955i	0.0456786	+	0.0354631i
$292$	−0.645696	−	7.38033i	−0.0377865	−	0.431901i
$293$	14.9428	+	6.96793i	0.872966	+	0.407071i	0.806861	−	0.590742i	$-0.201165\pi$
$293$	14.9428	+	6.96793i	0.872966	+	0.407071i	0.0661055	+	0.997813i	$0.478943\pi$
$294$	4.53205	+	1.45721i	0.264314	+	0.0849863i
$295$	−1.10242	+	0.802484i	−0.0641854	+	0.0467224i
$296$		−	19.1940i		−	1.11563i
$297$	−19.6717	+	12.0675i	−1.14147	+	0.700225i
$298$	5.25803	−	5.25803i	0.304590	−	0.304590i
$299$	−0.270414	−	1.53359i	−0.0156384	−	0.0886899i
$300$	−10.0996	+	11.7334i	−0.583101	+	0.677427i
$301$	8.48992	−	3.09008i	0.489351	−	0.178109i
$302$	−4.14170	+	0.362352i	−0.238328	+	0.0208510i
$303$	−20.1835	+	15.3066i	−1.15951	+	0.879340i
$304$	−1.15801	+	3.18160i	−0.0664164	+	0.182477i
$305$	−2.49418	+	3.70502i	−0.142816	+	0.212149i
$306$	5.51279	−	0.419463i	0.315145	−	0.0239791i
$307$	18.6145	−	4.98775i	1.06239	−	0.284666i	0.315026	−	0.949083i	$-0.397987\pi$
$307$	18.6145	−	4.98775i	1.06239	−	0.284666i	0.747362	+	0.664417i	$0.231320\pi$
$308$	−28.4785	−	2.49155i	−1.62271	−	0.141969i
$309$	−26.3834	−	13.9247i	−1.50090	−	0.792150i
$310$	−4.88267	+	8.82744i	−0.277317	+	0.501365i
$311$	4.11040	+	0.724775i	0.233079	+	0.0410982i	0.288968	−	0.957339i	$-0.406688\pi$
$311$	4.11040	+	0.724775i	0.233079	+	0.0410982i	−0.0558883	+	0.998437i	$0.517799\pi$
$312$	−1.16280	−	0.264702i	−0.0658305	−	0.0149858i
$313$	−0.399794	+	4.56966i	−0.0225977	+	0.258293i	0.976489	+	0.215567i	$0.0691598\pi$
$313$	−0.399794	+	4.56966i	−0.0225977	+	0.258293i	−0.999087	+	0.0427260i	$0.986396\pi$
$314$	−0.330565	+	0.572556i	−0.0186549	+	0.0323112i
$315$	−13.9928	−	19.6875i	−0.788404	−	1.10926i
$316$	−10.7722	−	18.6580i	−0.605983	−	1.04959i
$317$	21.0570	−	9.81902i	1.18268	−	0.551491i	0.271072	−	0.962559i	$-0.412622\pi$
$317$	21.0570	−	9.81902i	1.18268	−	0.551491i	0.911605	+	0.411068i	$0.134844\pi$
$318$	−1.54760	+	3.67722i	−0.0867853	+	0.206208i
$319$	−14.5537	+	17.3444i	−0.814849	+	0.971099i
$320$	5.19055	−	5.38473i	0.290160	−	0.301016i
$321$	9.76048	−	2.10594i	0.544777	−	0.117542i
$322$	3.75708	−	5.36567i	0.209374	−	0.299017i
$323$	3.45531	+	3.45531i	0.192258	+	0.192258i
$324$	14.9900	+	5.84364i	0.832778	+	0.324647i
$325$	−0.243917	−	1.95719i	−0.0135301	−	0.108566i
$326$	−4.28008	+	0.754693i	−0.237052	+	0.0417986i
$327$	−6.88283	+	10.6701i	−0.380621	+	0.590056i
$328$	1.35445	−	2.90462i	0.0747869	−	0.160381i
$329$	−3.62159	−	3.03887i	−0.199665	−	0.167539i
$330$	−5.91180	−	5.28064i	−0.325434	−	0.290690i
$331$	17.6555	+	6.42608i	0.970434	+	0.353209i	0.778114	−	0.628123i	$-0.216177\pi$
$331$	17.6555	+	6.42608i	0.970434	+	0.353209i	0.192320	+	0.981332i	$0.438399\pi$
$332$	−4.65146	−	1.24635i	−0.255282	−	0.0684026i
$333$	−20.9181	−	25.5104i	−1.14630	−	1.39796i
$334$	6.69131	+	3.86323i	0.366132	+	0.211386i
$335$	−3.27744	−	8.51492i	−0.179065	−	0.465220i
$336$	9.20227	+	14.6268i	0.502025	+	0.797956i
$337$	−6.63124	+	4.64324i	−0.361227	+	0.252934i	−0.740074	−	0.672526i	$-0.765209\pi$
$337$	−6.63124	+	4.64324i	−0.361227	+	0.252934i	0.378847	+	0.925459i	$0.376321\pi$
$338$	−4.84857	+	3.39501i	−0.263728	+	0.184664i
$339$	5.92618	−	11.2284i	0.321866	−	0.609843i
$340$	−5.74232	−	14.9188i	−0.311421	−	0.809085i
$341$	37.6552	+	21.7402i	2.03914	+	1.17730i
$342$	−0.559741	−	1.59380i	−0.0302673	−	0.0861830i
$343$	−3.60198	−	0.965147i	−0.194489	−	0.0521130i
$344$	−4.11560	−	1.49796i	−0.221898	−	0.0807644i
$345$	−14.5223	+	4.78243i	−0.781855	+	0.257478i
$346$	2.69798	+	2.26387i	0.145044	+	0.121707i
$347$	2.42251	−	5.19509i	0.130047	−	0.278887i	−0.830493	−	0.557030i	$-0.811941\pi$
$347$	2.42251	−	5.19509i	0.130047	−	0.278887i	0.960540	+	0.278143i	$0.0897188\pi$
$348$	15.7652	+	0.777779i	0.845105	+	0.0416933i
$349$	3.63192	−	0.640405i	0.194412	−	0.0342801i	−0.0755941	−	0.997139i	$-0.524085\pi$
$349$	3.63192	−	0.640405i	0.194412	−	0.0342801i	0.270006	+	0.962859i	$0.412974\pi$
$350$	5.09580	−	6.54677i	0.272382	−	0.349940i
$351$	−1.83393	+	0.915433i	−0.0978878	+	0.0488622i
$352$	14.9734	+	14.9734i	0.798085	+	0.798085i
$353$	10.0809	−	14.3970i	0.536551	−	0.766275i	−0.455752	−	0.890107i	$-0.650630\pi$
$353$	10.0809	−	14.3970i	0.536551	−	0.766275i	0.992303	+	0.123832i	$0.0395184\pi$
$354$	−0.148988	+	0.463366i	−0.00791864	+	0.0246276i
$355$	−19.5781	+	20.3105i	−1.03910	+	1.07797i
$356$	2.83851	−	3.38281i	0.150441	−	0.179288i
$357$	24.7451	−	3.11532i	1.30965	−	0.164880i
$358$	−1.75876	+	0.820125i	−0.0929535	+	0.0433449i
$359$	−4.06033	−	7.03269i	−0.214296	−	0.371171i	0.738759	−	0.673970i	$-0.235412\pi$
$359$	−4.06033	−	7.03269i	−0.214296	−	0.371171i	−0.953055	+	0.302799i	$0.902079\pi$
$360$	−0.938388	+	11.6711i	−0.0494574	+	0.615121i
$361$	−8.75349	+	15.1615i	−0.460710	+	0.797973i
$362$	−0.238849	+	2.73005i	−0.0125536	+	0.143488i
$363$	−10.2735	+	11.0849i	−0.539220	+	0.581807i
$364$	−2.50044	−	0.440896i	−0.131059	−	0.0231092i
$365$	4.48535	−	8.10912i	0.234774	−	0.424451i
$366$	0.0605220	+	1.59312i	0.00316354	+	0.0832739i
$367$	16.9819	+	1.48573i	0.886450	+	0.0775543i	0.521279	−	0.853386i	$-0.325455\pi$
$367$	16.9819	+	1.48573i	0.886450	+	0.0775543i	0.365171	+	0.930940i	$0.381011\pi$
$368$	10.5662	−	2.83121i	0.550801	−	0.147587i
$369$	−1.36535	−	5.33657i	−0.0710775	−	0.277811i
$370$	6.32791	−	9.39988i	0.328972	−	0.488677i
$371$	−6.15547	+	16.9120i	−0.319576	+	0.878028i
$372$	−3.78632	−	30.0748i	−0.196311	−	1.55931i
$373$	31.1095	−	2.72173i	1.61079	−	0.140926i	0.754100	−	0.656760i	$-0.228073\pi$
$373$	31.1095	−	2.72173i	1.61079	−	0.140926i	0.856688	+	0.515834i	$0.172518\pi$
$374$	7.69144	−	2.79945i	0.397715	−	0.144756i
$375$	−18.6758	+	5.12014i	−0.964412	+	0.264403i
$376$	0.397965	+	2.25697i	0.0205235	+	0.116394i
$377$	−1.42194	+	1.42194i	−0.0732339	+	0.0732339i
$378$	−8.17744	−	2.73188i	−0.420602	−	0.140513i
$379$			31.2281i			1.60408i	0.597269	+	0.802041i	$0.296252\pi$
$379$			31.2281i			1.60408i	−0.597269	+	0.802041i	$0.703748\pi$
$380$	−3.94884	+	2.87448i	−0.202571	+	0.147458i
$381$	6.77334	−	6.13643i	0.347008	−	0.314379i
$382$	4.52881	+	2.11182i	0.231714	+	0.108050i
$383$	2.94643	+	33.6778i	0.150555	+	1.72086i	0.577341	+	0.816503i	$0.304090\pi$
$383$	2.94643	+	33.6778i	0.150555	+	1.72086i	−0.426786	+	0.904353i	$0.640354\pi$
$384$	2.61191	−	19.0072i	0.133289	−	0.969957i
$385$	−27.8099	−	22.4783i	−1.41732	−	1.14560i
$386$	−0.245587	+	0.141790i	−0.0125001	+	0.00721691i
$387$	−7.10245	+	2.49437i	−0.361038	+	0.126796i
$388$	−0.263515	−	0.983453i	−0.0133780	−	0.0499272i
$389$	20.9380	−	17.5690i	1.06160	−	0.890786i	0.0673324	−	0.997731i	$-0.478551\pi$
$389$	20.9380	−	17.5690i	1.06160	−	0.890786i	0.994265	+	0.106945i	$0.0341068\pi$
$390$	−0.482189	−	0.512985i	−0.0244166	−	0.0259760i
$391$	2.74149	−	15.5478i	0.138643	−	0.786284i
$392$	−5.97114	−	8.52768i	−0.301588	−	0.430713i
$393$	−0.272529	+	1.19718i	−0.0137473	+	0.0603898i
$394$	−8.14085	−	9.70188i	−0.410130	−	0.488774i
$395$	1.85547	−	26.8848i	0.0933589	−	1.35272i
$396$	23.7031	+	2.34450i	1.19113	+	0.117815i
$397$	−3.30445	+	12.3324i	−0.165846	+	0.618945i	0.832085	+	0.554648i	$0.187147\pi$
$397$	−3.30445	+	12.3324i	−0.165846	+	0.618945i	−0.997931	+	0.0642968i	$0.979520\pi$
$398$	−0.539761	−	1.15752i	−0.0270558	−	0.0580213i
$399$	−2.87623	−	7.05659i	−0.143992	−	0.353271i
$400$	13.5467	−	2.90513i	0.677335	−	0.145256i
$401$	−6.74752	−	18.5387i	−0.336955	−	0.925776i	−0.986253	−	0.165242i	$-0.947159\pi$
$401$	−6.74752	−	18.5387i	−0.336955	−	0.925776i	0.649298	−	0.760534i	$-0.275063\pi$
$402$	−2.73681	−	1.76540i	−0.136500	−	0.0880504i
$403$	3.16338	+	2.21502i	0.157579	+	0.110338i
$404$	26.1441			1.30072
$405$	11.4722	+	16.5345i	0.570059	+	0.821604i
$406$	−8.45859			−0.419793
$407$	−40.0078	−	28.0137i	−1.98311	−	1.38859i
$408$	−10.1598	−	6.55369i	−0.502986	−	0.324456i
$409$	0.987380	+	2.71280i	0.0488228	+	0.134139i	0.961707	−	0.274078i	$-0.0883727\pi$
$409$	0.987380	+	2.71280i	0.0488228	+	0.134139i	−0.912885	+	0.408218i	$0.866150\pi$
$410$	1.62091	−	0.975943i	0.0800511	−	0.0481984i
$411$	−0.665636	−	1.63308i	−0.0328334	−	0.0805538i
$412$	13.0124	+	27.9052i	0.641076	+	1.37479i
$413$	−0.568280	+	2.12085i	−0.0279632	+	0.104360i
$414$	−3.18080	+	4.43491i	−0.156328	+	0.217964i
$415$	−3.95590	−	4.54242i	−0.194188	−	0.222979i
$416$	1.20891	+	1.44073i	0.0592719	+	0.0706375i
$417$	8.55791	−	37.5936i	0.419082	−	1.84097i
$418$	−1.43443	−	2.04857i	−0.0701601	−	0.100199i
$419$	3.08760	−	17.5106i	0.150839	−	0.855451i	−0.811653	−	0.584140i	$-0.801432\pi$
$419$	3.08760	−	17.5106i	0.150839	−	0.855451i	0.962492	−	0.271310i	$-0.0874570\pi$
$420$	−0.771049	+	24.9168i	−0.0376233	+	1.21582i
$421$	1.57150	−	1.31864i	0.0765901	−	0.0642667i	−0.603689	−	0.797220i	$-0.706303\pi$
$421$	1.57150	−	1.31864i	0.0765901	−	0.0642667i	0.680279	+	0.732953i	$0.261859\pi$
$422$	2.61453	+	9.75758i	0.127274	+	0.474991i
$423$	2.98862	+	2.56598i	0.145312	+	0.124762i
$424$	7.55561	−	4.36223i	0.366933	−	0.211849i
$425$	4.46273	−	19.4914i	0.216474	−	0.945472i
$426$	−1.37087	+	9.97600i	−0.0664189	+	0.483339i
$427$	0.626811	+	7.16449i	0.0303335	+	0.346714i
$428$	−9.34000	−	4.35531i	−0.451466	−	0.210522i
$429$	−2.24885	+	2.03739i	−0.108575	+	0.0983659i
$430$	−1.52168	−	2.09043i	−0.0733820	−	0.100809i
$431$		−	19.3828i		−	0.933636i	−0.884353	−	0.466818i	$-0.845400\pi$
$431$		−	19.3828i		−	0.933636i	0.884353	−	0.466818i	$-0.154600\pi$
$432$	−7.52879	−	12.2730i	−0.362229	−	0.590484i
$433$	−2.30954	+	2.30954i	−0.110989	+	0.110989i	−0.760420	−	0.649431i	$-0.775007\pi$
$433$	−2.30954	+	2.30954i	−0.110989	+	0.110989i	0.649431	+	0.760420i	$0.275007\pi$
$434$	2.82071	+	15.9970i	0.135398	+	0.767881i
$435$	15.8152	+	11.8195i	0.758283	+	0.566699i
$436$	12.3146	−	4.48214i	0.589762	−	0.214656i
$437$	−4.80536	+	0.420414i	−0.229871	+	0.0201111i
$438$	−0.413188	−	3.28196i	−0.0197429	−	0.156818i
$439$	−1.67858	+	4.61187i	−0.0801144	+	0.220112i	−0.973283	−	0.229610i	$-0.926255\pi$
$439$	−1.67858	+	4.61187i	−0.0801144	+	0.220112i	0.893168	+	0.449723i	$0.148477\pi$
$440$	3.32298	+	17.0129i	0.158417	+	0.811056i
$441$	−17.2297	−	4.82646i	−0.820464	−	0.229831i
$442$	0.702196	−	0.188153i	0.0334000	−	0.00894952i
$443$	19.2540	+	1.68450i	0.914783	+	0.0800331i	0.534817	−	0.844968i	$-0.320380\pi$
$443$	19.2540	+	1.68450i	0.914783	+	0.0800331i	0.379965	+	0.925001i	$0.375936\pi$
$444$	1.29257	+	34.0243i	0.0613426	+	1.61472i
$445$	5.30831	−	1.52734i	0.251638	−	0.0724031i
$446$	−5.06133	−	0.892450i	−0.239661	−	0.0422587i
$447$	−18.9983	+	20.4988i	−0.898588	+	0.969558i
$448$	1.04963	−	11.9973i	0.0495903	−	0.566820i
$449$	−1.49368	+	2.58713i	−0.0704911	+	0.122094i	−0.899117	−	0.437709i	$-0.855790\pi$
$449$	−1.49368	+	2.58713i	−0.0704911	+	0.122094i	0.828626	+	0.559803i	$0.189123\pi$
$450$	−4.30729	+	5.40631i	−0.203048	+	0.254856i
$451$	−4.07753	−	7.06249i	−0.192003	−	0.332560i
$452$	−11.8761	+	5.53791i	−0.558604	+	0.260481i
$453$	15.5040	−	1.95190i	0.728442	−	0.0917085i
$454$	3.78613	−	4.51214i	0.177692	−	0.211765i
$455$	−2.28657	−	2.20411i	−0.107196	−	0.103330i
$456$	−1.13074	+	3.51670i	−0.0529518	+	0.164684i
$457$	−3.78805	+	5.40989i	−0.177197	+	0.253064i	−0.897919	−	0.440160i	$-0.854922\pi$
$457$	−3.78805	+	5.40989i	−0.177197	+	0.253064i	0.720722	+	0.693224i	$0.243811\pi$
$458$	4.84692	+	4.84692i	0.226482	+	0.226482i
$459$	−20.6455	+	2.36204i	−0.963651	+	0.110251i
$460$	14.9252	+	5.12401i	0.695889	+	0.238908i
$461$	41.0394	−	7.23636i	1.91140	−	0.337031i	0.913791	−	0.406185i	$-0.133141\pi$
$461$	41.0394	−	7.23636i	1.91140	−	0.337031i	0.997606	+	0.0691537i	$0.0220299\pi$
$462$	−12.7486	−	0.628952i	−0.593117	−	0.0292615i
$463$	2.30650	−	4.94630i	0.107192	−	0.229874i	−0.845394	−	0.534143i	$-0.820634\pi$
$463$	2.30650	−	4.94630i	0.107192	−	0.229874i	0.952586	+	0.304269i	$0.0984122\pi$
$464$	−10.8210	−	9.07991i	−0.502353	−	0.421524i
$465$	17.0792	−	33.8515i	0.792028	−	1.56982i
$466$	2.15876	+	0.785723i	0.100002	+	0.0363979i
$467$	−9.74812	−	2.61200i	−0.451089	−	0.120869i	0.0261197	−	0.999659i	$-0.491685\pi$
$467$	−9.74812	−	2.61200i	−0.451089	−	0.120869i	−0.477209	+	0.878790i	$0.658352\pi$
$468$	2.07906	+	0.390919i	0.0961047	+	0.0180702i
$469$	−12.7233	−	7.34582i	−0.587509	−	0.339199i
$470$	−0.549185	+	1.23651i	−0.0253320	+	0.0570358i
$471$	1.15987	−	2.19762i	0.0534439	−	0.101261i
$472$	0.871887	−	0.610502i	0.0401319	−	0.0281006i
$473$	−9.12904	+	6.39222i	−0.419753	+	0.293915i
$474$	−5.12251	−	8.14210i	−0.235285	−	0.373979i
$475$	−6.10535	+	0.224291i	−0.280133	+	0.0102912i
$476$	−22.2923	−	12.8704i	−1.02176	−	0.589916i
$477$	5.28793	−	14.0320i	0.242118	−	0.642481i
$478$	3.23632	+	0.867168i	0.148026	+	0.0396634i
$479$	4.22629	+	1.53824i	0.193104	+	0.0702841i	0.436762	−	0.899577i	$-0.356125\pi$
$479$	4.22629	+	1.53824i	0.193104	+	0.0702841i	−0.243658	+	0.969861i	$0.578347\pi$
$480$	12.3013	−	13.7716i	0.561475	−	0.628583i
$481$	−3.32297	−	2.78830i	−0.151514	−	0.127136i
$482$	3.84423	−	8.24398i	0.175100	−	0.375503i
$483$	−13.3455	+	20.6889i	−0.607243	+	0.941376i
$484$	15.3617	−	2.70868i	0.698258	−	0.123122i
$485$	0.413534	−	1.20454i	0.0187776	−	0.0546952i
$486$	6.78718	+	2.35319i	0.307873	+	0.106743i
$487$	−2.49814	−	2.49814i	−0.113202	−	0.113202i	0.648237	−	0.761439i	$-0.275507\pi$
$487$	−2.49814	−	2.49814i	−0.113202	−	0.113202i	−0.761439	+	0.648237i	$0.775507\pi$
$488$	1.99969	−	2.85585i	0.0905215	−	0.129278i
$489$	15.9678	−	3.44524i	0.722088	−	0.155799i
$490$	−0.112832	−	6.14482i	−0.00509725	−	0.277595i
$491$	9.95960	−	11.8694i	0.449471	−	0.535658i	−0.492964	−	0.870050i	$-0.664086\pi$
$491$	9.95960	−	11.8694i	0.449471	−	0.535658i	0.942434	+	0.334392i	$0.108531\pi$
$492$	−2.20536	+	5.24009i	−0.0994253	+	0.236242i
$493$	−18.4770	+	8.61596i	−0.832162	+	0.388043i
$494$	−0.111058	−	0.192358i	−0.00499673	−	0.00865459i
$495$	22.9575	+	18.9899i	1.03186	+	0.853534i
$496$	−13.5636	+	23.4928i	−0.609022	+	1.05486i
$497$	−3.95907	+	45.2524i	−0.177589	+	2.02985i
$498$	−2.09648	−	0.477248i	−0.0939455	−	0.0213860i
$499$	16.9468	+	2.98818i	0.758644	+	0.133769i	0.539572	−	0.841939i	$-0.318586\pi$
$499$	16.9468	+	2.98818i	0.758644	+	0.133769i	0.219072	+	0.975709i	$0.429697\pi$
$500$	18.5514	+	7.43661i	0.829644	+	0.332575i
$501$	−25.6830	−	13.5551i	−1.14743	−	0.605596i
$502$	−7.80354	−	0.682721i	−0.348289	−	0.0304713i
$503$	−38.6515	+	10.3567i	−1.72339	+	0.461780i	−0.978643	−	0.205569i	$-0.934095\pi$
$503$	−38.6515	+	10.3567i	−1.72339	+	0.461780i	−0.744745	+	0.667349i	$0.767429\pi$
$504$	10.6386	+	15.5657i	0.473879	+	0.693350i
$505$	27.1281	+	18.2623i	1.20718	+	0.812663i
$506$	−2.76346	+	7.59255i	−0.122851	+	0.337530i
$507$	17.7262	−	13.4431i	0.787250	−	0.597027i
$508$	−9.39712	+	0.822142i	−0.416930	+	0.0364766i
$509$	−36.9106	+	13.4344i	−1.63604	+	0.595468i	−0.986339	−	0.164726i	$-0.947326\pi$
$509$	−36.9106	+	13.4344i	−1.63604	+	0.595468i	−0.649696	+	0.760194i	$0.725104\pi$
$510$	−2.81494	−	6.55903i	−0.124648	−	0.290439i
$511$	−2.59118	−	14.6953i	−0.114627	−	0.650081i
$512$	−16.1816	+	16.1816i	−0.715134	+	0.715134i
$513$	2.32973	+	5.90627i	0.102860	+	0.260768i
$514$			7.13031i			0.314504i
$515$	−5.99036	+	38.0449i	−0.263967	+	1.67646i
$516$	7.39639	+	2.37820i	0.325608	+	0.104694i
$517$	5.28523	+	2.46454i	0.232444	+	0.108390i
$518$	−1.59026	−	18.1768i	−0.0698721	−	0.798642i
$519$	−10.4563	−	8.11787i	−0.458980	−	0.356335i
$520$	0.162318	+	1.53099i	0.00711810	+	0.0671384i
$521$	−26.5294	+	15.3168i	−1.16227	+	0.671039i	−0.951848	−	0.306571i	$-0.900818\pi$
$521$	−26.5294	+	15.3168i	−1.16227	+	0.671039i	−0.210426	+	0.977610i	$0.567485\pi$
$522$	7.04720	+	0.0798049i	0.308447	+	0.00349296i
$523$	1.16084	+	4.33233i	0.0507602	+	0.189439i	0.986651	−	0.162852i	$-0.0520693\pi$
$523$	1.16084	+	4.33233i	0.0507602	+	0.189439i	−0.935890	+	0.352291i	$0.885403\pi$
$524$	0.970744	−	0.814551i	0.0424071	−	0.0355838i
$525$	−18.2051	+	25.3160i	−0.794536	+	1.10488i
$526$	2.02403	−	11.4789i	0.0882521	−	0.500503i
$527$	22.4562	+	32.0708i	0.978207	+	1.39702i
$528$	−15.6340	−	14.4896i	−0.680383	−	0.630580i
$529$	−4.76651	−	5.68051i	−0.207240	−	0.246979i
$530$	5.13835	+	0.354626i	0.223195	+	0.0154040i
$531$	0.493467	−	1.76160i	0.0214146	−	0.0764471i
$532$	−2.03556	+	7.59683i	−0.0882529	+	0.329364i
$533$	−0.306103	−	0.656441i	−0.0132588	−	0.0284336i
$534$	1.20913	−	1.55743i	0.0523241	−	0.0673965i
$535$	−6.64921	−	11.0435i	−0.287471	−	0.477450i
$536$	2.43586	+	6.69246i	0.105213	+	0.289070i
$537$	6.48868	−	3.33124i	0.280007	−	0.143754i
$538$	7.89626	+	5.52902i	0.340432	+	0.238373i
$539$	−26.4898			−1.14100
$540$	0.877477	−	20.7520i	0.0377606	−	0.893022i
$541$	4.96440			0.213436			0.106718	−	0.994289i	$-0.465966\pi$
$541$	4.96440			0.213436			0.106718	+	0.994289i	$0.465966\pi$
$542$	−2.27293	−	1.59153i	−0.0976309	−	0.0683619i
$543$	0.507551	−	10.2878i	0.0217811	−	0.441493i
$544$	6.52135	+	17.9173i	0.279601	+	0.768196i
$545$	15.9089	+	3.95122i	0.681464	+	0.169252i
$546$	−1.12310	−	0.154333i	−0.0480644	−	0.00660486i
$547$	−6.14812	−	13.1847i	−0.262875	−	0.563737i	0.729924	−	0.683528i	$-0.239555\pi$
$547$	−6.14812	−	13.1847i	−0.262875	−	0.563737i	−0.992799	+	0.119791i	$0.961777\pi$
$548$	−0.471083	+	1.75810i	−0.0201237	+	0.0751025i
$549$	−0.454627	−	5.97494i	−0.0194030	−	0.255004i
$550$	−3.98145	+	9.42721i	−0.169770	+	0.401978i
$551$	4.00394	+	4.77171i	0.170574	+	0.203282i
$552$	11.4025	−	3.52435i	0.485323	−	0.150006i
$553$	−24.8897	−	35.5462i	−1.05842	−	1.51158i
$554$	0.289556	−	1.64216i	0.0123021	−	0.0697685i
$555$	−22.4256	+	36.2077i	−0.951915	+	1.53693i
$556$	−30.4831	+	25.5783i	−1.29277	+	1.08476i
$557$	−7.79233	−	29.0814i	−0.330171	−	1.23222i	−0.909010	−	0.416774i	$-0.863160\pi$
$557$	−7.79233	−	29.0814i	−0.330171	−	1.23222i	0.578838	−	0.815442i	$-0.303506\pi$
$558$	−2.19912	−	13.3544i	−0.0930960	−	0.565336i
$559$	−0.857203	+	0.494906i	−0.0362558	+	0.0209323i
$560$	14.0240	−	17.3504i	0.592622	−	0.733186i
$561$	−28.4887	+	11.6119i	−1.20279	+	0.490253i
$562$	0.938313	+	10.7250i	0.0395803	+	0.452405i
$563$	19.4537	+	9.07139i	0.819874	+	0.382314i	0.786852	−	0.617141i	$-0.211709\pi$
$563$	19.4537	+	9.07139i	0.819874	+	0.382314i	0.0330215	+	0.999455i	$0.489487\pi$
$564$	−0.857442	−	3.97402i	−0.0361048	−	0.167337i
$565$	−16.1914	−	2.54942i	−0.681177	−	0.107255i
$566$		−	8.04291i		−	0.338069i
$567$	31.1033	+	9.09383i	1.30621	+	0.381905i
$568$	15.5708	−	15.5708i	0.653338	−	0.653338i
$569$	−2.94509	−	16.7024i	−0.123465	−	0.700202i	−0.982208	−	0.187796i	$-0.939865\pi$
$569$	−2.94509	−	16.7024i	−0.123465	−	0.700202i	0.858743	−	0.512406i	$-0.171246\pi$
$570$	−1.71314	+	1.34945i	−0.0717557	+	0.0565221i
$571$	−28.4369	+	10.3502i	−1.19005	+	0.433142i	−0.859740	−	0.510732i	$-0.829375\pi$
$571$	−28.4369	+	10.3502i	−1.19005	+	0.433142i	−0.330307	+	0.943873i	$0.607152\pi$
$572$	3.11998	−	0.272963i	0.130453	−	0.0114132i
$573$	−17.3110	−	7.28555i	−0.723177	−	0.304358i
$574$	1.04201	−	2.86290i	0.0434927	−	0.119495i
$575$	11.9076	+	15.7424i	0.496582	+	0.656505i
$576$	−0.987681	+	9.98555i	−0.0411534	+	0.416065i
$577$	−27.9807	+	7.49741i	−1.16485	+	0.312121i	−0.788903	−	0.614518i	$-0.789350\pi$
$577$	−27.9807	+	7.49741i	−1.16485	+	0.312121i	−0.375950	+	0.926640i	$0.622684\pi$
$578$	−0.462176	−	0.0404352i	−0.0192240	−	0.00168188i
$579$	0.902164	−	0.567587i	0.0374927	−	0.0235881i
$580$	−5.63458	−	19.5831i	−0.233963	−	0.813143i
$581$	−9.55194	−	1.68426i	−0.396281	−	0.0698751i
$582$	−0.134243	−	0.434323i	−0.00556454	−	0.0180033i
$583$	1.93485	−	22.1155i	0.0801334	−	0.915929i
$584$	−3.61681	+	6.26451i	−0.149665	+	0.259227i
$585$	1.88424	+	1.85791i	0.0779037	+	0.0768150i
$586$	−3.79893	−	6.57994i	−0.156932	−	0.271815i
$587$	5.92953	−	2.76499i	0.244738	−	0.114123i	−0.296379	−	0.955070i	$-0.595779\pi$
$587$	5.92953	−	2.76499i	0.244738	−	0.114123i	0.541117	+	0.840947i	$0.318001\pi$
$588$	11.1590	+	14.7145i	0.460190	+	0.606815i
$589$	7.68913	−	9.16355i	0.316825	−	0.377578i
$590$	0.628259	−	0.0115362i	0.0258650	−	0.000474939i
$591$	31.9603	+	35.2775i	1.31467	+	1.45112i
$592$	17.4775	−	24.9605i	0.718322	−	1.02587i
$593$	22.3175	+	22.3175i	0.916469	+	0.916469i	0.996771	−	0.0803015i	$-0.0255883\pi$
$593$	22.3175	+	22.3175i	0.916469	+	0.916469i	−0.0803015	+	0.996771i	$0.525588\pi$
$594$	10.6154	+	0.644285i	0.435556	+	0.0264354i
$595$	−14.1409	−	28.9265i	−0.579720	−	1.18587i
$596$	28.4076	−	5.00902i	1.16362	−	0.205177i
$597$	2.19244	+	4.27049i	0.0897305	+	0.174780i
$598$	−0.303279	+	0.650384i	−0.0124020	+	0.0265962i
$599$	8.78838	+	7.37433i	0.359083	+	0.301307i	0.804425	−	0.594054i	$-0.202473\pi$
$599$	8.78838	+	7.37433i	0.359083	+	0.301307i	−0.445342	+	0.895361i	$0.646918\pi$
$600$	14.6489	−	3.72839i	0.598040	−	0.152211i
$601$	−29.2326	−	10.6398i	−1.19242	−	0.434007i	−0.331850	−	0.943332i	$-0.607673\pi$
$601$	−29.2326	−	10.6398i	−1.19242	−	0.434007i	−0.860574	+	0.509326i	$0.829895\pi$
$602$	−4.02159	−	1.07758i	−0.163908	−	0.0439189i
$603$	10.5310	+	6.24015i	0.428857	+	0.254118i
$604$	−13.9672	−	8.06397i	−0.568317	−	0.328118i
$605$	17.8319	+	7.91990i	0.724969	+	0.321990i
$606$	11.6648	−	0.443141i	0.473850	−	0.0180014i
$607$	12.0216	−	8.41759i	0.487940	−	0.341659i	−0.303576	−	0.952807i	$-0.598181\pi$
$607$	12.0216	−	8.41759i	0.487940	−	0.341659i	0.791517	+	0.611148i	$0.209292\pi$
$608$	4.77216	−	3.34151i	0.193537	−	0.135516i
$609$	31.7694	−	1.20691i	1.28736	−	0.0489064i
$610$	1.92082	−	0.739334i	0.0777718	−	0.0299348i
$611$	0.448550	+	0.258971i	0.0181464	+	0.0104768i
$612$	18.4512	+	10.9332i	0.745844	+	0.441949i
$613$	19.4357	+	5.20779i	0.785002	+	0.210341i	0.628989	−	0.777414i	$-0.283469\pi$
$613$	19.4357	+	5.20779i	0.785002	+	0.210341i	0.156013	+	0.987755i	$0.450136\pi$
$614$	−8.34507	−	3.03736i	−0.336780	−	0.122578i
$615$	−5.94869	+	3.89680i	−0.239874	+	0.157134i
$616$	21.3821	+	17.9418i	0.861511	+	0.722894i
$617$	1.25995	−	2.70196i	0.0507236	−	0.108777i	−0.879313	−	0.476245i	$-0.841998\pi$
$617$	1.25995	−	2.70196i	0.0507236	−	0.108777i	0.930036	+	0.367468i	$0.119775\pi$
$618$	6.27878	+	12.2300i	0.252569	+	0.491962i
$619$	−13.1500	+	2.31870i	−0.528542	+	0.0931962i	−0.431550	−	0.902089i	$-0.642033\pi$
$619$	−13.1500	+	2.31870i	−0.528542	+	0.0931962i	−0.0969919	+	0.995285i	$0.530922\pi$
$620$	−35.1568	+	17.1866i	−1.41193	+	0.690231i
$621$	11.3139	−	17.1108i	0.454011	−	0.686634i
$622$	−1.36005	−	1.36005i	−0.0545329	−	0.0545329i
$623$	5.10163	−	7.28589i	0.204393	−	0.291903i
$624$	−1.27111	−	1.40304i	−0.0508851	−	0.0561665i
$625$	14.0549	+	20.6751i	0.562196	+	0.827004i
$626$	1.35876	−	1.61931i	0.0543070	−	0.0647206i
$627$	5.67983	+	7.48952i	0.226831	+	0.299103i
$628$	−2.32438	+	1.08388i	−0.0927529	+	0.0432514i
$629$	−21.9887	−	38.0856i	−0.876748	−	1.51857i
$630$	0.0783172	+	11.1303i	0.00312023	+	0.443441i
$631$	0.693777	−	1.20166i	0.0276188	−	0.0478372i	−0.851886	−	0.523728i	$-0.824541\pi$
$631$	0.693777	−	1.20166i	0.0276188	−	0.0478372i	0.879504	+	0.475891i	$0.157874\pi$
$632$	−1.83339	+	20.9557i	−0.0729283	+	0.833575i
$633$	−11.2121	−	36.2752i	−0.445642	−	1.44181i
$634$	−10.5440	−	1.85920i	−0.418758	−	0.0738383i
$635$	−10.3251	−	5.71104i	−0.409738	−	0.226636i
$636$	−13.0997	+	8.24153i	−0.519437	+	0.326798i
$637$	−2.34378	−	0.205054i	−0.0928638	−	0.00812453i
$638$	10.0782	−	2.70046i	0.399001	−	0.106912i
$639$	3.72541	−	37.6643i	0.147375	−	1.48998i
$640$	−24.3094	+	4.74815i	−0.960914	+	0.187687i
$641$	−6.63051	+	18.2172i	−0.261890	+	0.719536i	0.737150	+	0.675729i	$0.236171\pi$
$641$	−6.63051	+	18.2172i	−0.261890	+	0.719536i	−0.999040	+	0.0438070i	$0.986051\pi$
$642$	−4.24108	−	1.78491i	−0.167382	−	0.0704448i
$643$	41.1928	−	3.60391i	1.62449	−	0.142124i	0.761783	−	0.647833i	$-0.224324\pi$
$643$	41.1928	−	3.60391i	1.62449	−	0.142124i	0.862705	+	0.505708i	$0.168769\pi$
$644$	23.8775	−	8.69071i	0.940906	−	0.342462i
$645$	6.01352	+	7.63427i	0.236782	+	0.300599i
$646$	−0.391028	−	2.21763i	−0.0153848	−	0.0872514i
$647$	12.4891	−	12.4891i	0.490997	−	0.490997i	−0.417623	−	0.908620i	$-0.637137\pi$
$647$	12.4891	−	12.4891i	0.490997	−	0.490997i	0.908620	+	0.417623i	$0.137137\pi$
$648$	−8.71657	−	13.0688i	−0.342419	−	0.513389i
$649$		−	2.70837i		−	0.106313i
$650$	−0.425247	+	0.803284i	−0.0166795	+	0.0315074i
$651$	−12.8767	−	59.6804i	−0.504680	−	2.33906i
$652$	−15.2799	−	7.12513i	−0.598407	−	0.279042i
$653$	−1.28323	−	14.6673i	−0.0502165	−	0.573977i	−0.979069	−	0.203528i	$-0.934759\pi$
$653$	−1.28323	−	14.6673i	−0.0502165	−	0.573977i	0.928853	−	0.370449i	$-0.120796\pi$
$654$	5.41846	−	2.20854i	0.211879	−	0.0863608i
$655$	1.57626	−	0.167117i	0.0615896	−	0.00652980i
$656$	4.40623	−	2.54394i	0.172034	−	0.0993241i
$657$	2.02017	+	12.2677i	0.0788142	+	0.478608i
$658$	0.563868	+	2.10438i	0.0219819	+	0.0820374i
$659$	−21.0565	+	17.6685i	−0.820245	+	0.688268i	−0.953030	−	0.302877i	$-0.902053\pi$
$659$	−21.0565	+	17.6685i	−0.820245	+	0.688268i	0.132784	+	0.991145i	$0.457608\pi$
$660$	−7.03616	−	29.9341i	−0.273882	−	1.16518i
$661$	1.73362	−	9.83186i	0.0674301	−	0.382415i	−0.932352	−	0.361551i	$-0.882247\pi$
$661$	1.73362	−	9.83186i	0.0674301	−	0.382415i	0.999782	−	0.0208639i	$-0.00664165\pi$
$662$	−4.96617	−	7.09243i	−0.193016	−	0.275655i
$663$	−2.61052	+	0.806871i	−0.101384	+	0.0313363i
$664$	3.02230	+	3.60183i	0.117288	+	0.139778i
$665$	−7.41875	+	6.46084i	−0.287687	+	0.250541i
$666$	1.15342	+	15.1588i	0.0446941	+	0.587392i
$667$	5.20873	−	19.4392i	0.201683	−	0.752690i
$668$	12.6670	+	27.1644i	0.490100	+	1.05102i
$669$	19.1371	+	2.62976i	0.739883	+	0.101672i
$670$	−1.01347	+	4.08055i	−0.0391536	+	0.157645i
$671$	−3.03414	−	8.33623i	−0.117132	−	0.321816i
$672$	1.46515	−	29.6979i	0.0565193	−	1.14562i
$673$	−0.212002	−	0.148446i	−0.00817209	−	0.00572216i	0.569483	−	0.822003i	$-0.307143\pi$
$673$	−0.212002	−	0.148446i	−0.00817209	−	0.00572216i	−0.577655	+	0.816281i	$0.696032\pi$
$674$	3.73049			0.143693
$675$	15.4063	−	20.9200i	0.592987	−	0.805212i
$676$	−22.9612			−0.883122
$677$	20.1079	+	14.0797i	0.772810	+	0.541128i	0.892157	−	0.451725i	$-0.149191\pi$
$677$	20.1079	+	14.0797i	0.772810	+	0.541128i	−0.119347	+	0.992853i	$0.538080\pi$
$678$	−5.20492	+	2.67216i	−0.199894	+	0.102624i
$679$	−0.701384	−	1.92704i	−0.0269167	−	0.0739529i
$680$	−3.76227	+	15.1482i	−0.144277	+	0.580906i
$681$	−13.5764	+	17.4873i	−0.520251	+	0.670113i
$682$	−8.46795	−	18.1596i	−0.324255	−	0.695366i
$683$	5.75081	−	21.4623i	0.220048	−	0.821232i	−0.764280	−	0.644885i	$-0.776905\pi$
$683$	5.75081	−	21.4623i	0.220048	−	0.821232i	0.984328	−	0.176347i	$-0.0564281\pi$
$684$	1.76759	−	6.31002i	0.0675853	−	0.241270i
$685$	−1.71689	+	1.49521i	−0.0655991	+	0.0571289i
$686$	1.10459	+	1.31640i	0.0421734	+	0.0502603i
$687$	−18.8960	−	17.5129i	−0.720929	−	0.668158i
$688$	−3.98805	−	5.69553i	−0.152043	−	0.217140i
$689$	0.342385	−	1.94176i	0.0130438	−	0.0739753i
$690$	6.74605	+	2.03321i	0.256818	+	0.0774031i
$691$	−0.205042	+	0.172050i	−0.00780016	+	0.00654511i	−0.646679	−	0.762762i	$-0.723843\pi$
$691$	−0.205042	+	0.172050i	−0.00780016	+	0.00654511i	0.638879	+	0.769307i	$0.279398\pi$
$692$	3.53610	+	13.1969i	0.134422	+	0.501672i
$693$	47.9718	+	0.543249i	1.82230	+	0.0206363i
$694$	−2.28762	+	1.32076i	−0.0868369	+	0.0501353i
$695$	−49.4974	+	5.24777i	−1.87754	+	0.199059i
$696$	−12.1737	−	9.45117i	−0.461441	−	0.358246i
$697$	−0.639991	−	7.31513i	−0.0242414	−	0.277080i
$698$	−1.54027	−	0.718239i	−0.0583000	−	0.0271857i
$699$	−8.22014	−	2.64306i	−0.310914	−	0.0999697i
$700$	30.7595	−	9.46517i	1.16260	−	0.357750i
$701$			38.5968i			1.45778i	0.684630	+	0.728891i	$0.259964\pi$
$701$			38.5968i			1.45778i	−0.684630	+	0.728891i	$0.740036\pi$
$702$	0.934247	+	0.139178i	0.0352609	+	0.00525292i
$703$	−9.50124	+	9.50124i	−0.358346	+	0.358346i
$704$	2.57960	+	14.6297i	0.0972225	+	0.551376i
$705$	1.88624	−	4.72253i	0.0710400	−	0.177861i
$706$	−7.61078	+	2.77010i	−0.286435	+	0.104254i
$707$	52.4582	−	4.58950i	1.97289	−	0.172606i
$708$	−1.50444	+	1.14092i	−0.0565402	+	0.0428784i
$709$	16.0622	−	44.1305i	0.603228	−	1.65735i	−0.141463	−	0.989944i	$-0.545181\pi$
$709$	16.0622	−	44.1305i	0.603228	−	1.65735i	0.744690	−	0.667410i	$-0.232597\pi$
$710$	12.7589	−	2.49209i	0.478833	−	0.0935264i
$711$	20.4013	+	29.8499i	0.765108	+	1.11946i
$712$	−4.16477	+	1.11595i	−0.156081	+	0.0418219i
$713$	−38.5007	−	3.36838i	−1.44186	−	0.126147i
$714$	−10.1644	−	5.36459i	−0.380391	−	0.200765i
$715$	3.42808	+	1.89615i	0.128203	+	0.0709120i
$716$	−7.41357	−	1.30721i	−0.277058	−	0.0488528i
$717$	−12.2789	−	2.79521i	−0.458566	−	0.104389i
$718$	−0.326154	+	3.72796i	−0.0121720	+	0.139126i
$719$	0.577250	−	0.999826i	0.0215278	−	0.0372872i	−0.855061	−	0.518528i	$-0.826480\pi$
$719$	0.577250	−	0.999826i	0.0215278	−	0.0372872i	0.876589	+	0.481241i	$0.159814\pi$
$720$	−11.8477	+	14.3230i	−0.441536	+	0.533786i
$721$	31.0080	+	53.7075i	1.15480	+	2.00017i
$722$	7.31177	−	3.40954i	0.272116	−	0.126890i
$723$	−13.2622	+	31.5119i	−0.493226	+	1.17194i
$724$	−6.83343	+	8.14376i	−0.253962	+	0.302660i
$725$	7.83263	−	24.2560i	0.290897	−	0.900844i
$726$	6.80805	−	1.46892i	0.252671	−	0.0545167i
$727$	−22.7146	+	32.4399i	−0.842439	+	1.20313i	0.134776	+	0.990876i	$0.456969\pi$
$727$	−22.7146	+	32.4399i	−0.842439	+	1.20313i	−0.977215	+	0.212252i	$0.931920\pi$
$728$	1.75297	+	1.75297i	0.0649695	+	0.0649695i
$729$	−25.8276	−	7.86989i	−0.956578	−	0.291477i
$730$	−3.83655	+	1.87552i	−0.141997	+	0.0694160i
$731$	−9.88240	+	1.74253i	−0.365514	+	0.0644499i
$732$	−3.35242	+	5.19708i	−0.123909	+	0.192090i
$733$	−2.90113	+	6.22149i	−0.107156	+	0.229796i	−0.952573	−	0.304310i	$-0.901574\pi$
$733$	−2.90113	+	6.22149i	−0.107156	+	0.229796i	0.845417	+	0.534106i	$0.179352\pi$
$734$	−6.01773	−	5.04948i	−0.222119	−	0.186380i
$735$	1.30055	+	23.0631i	0.0479717	+	0.850695i
$736$	−17.6869	−	6.43750i	−0.651948	−	0.237290i
$737$	17.5048	+	4.69039i	0.644797	+	0.172773i
$738$	−0.895152	+	2.37537i	−0.0329510	+	0.0874385i
$739$	28.7899	+	16.6218i	1.05905	+	0.611444i	0.925170	−	0.379553i	$-0.123922\pi$
$739$	28.7899	+	16.6218i	1.05905	+	0.611444i	0.133882	+	0.990997i	$0.457256\pi$
$740$	41.0230	−	15.7900i	1.50804	−	0.580450i
$741$	0.444567	+	0.706627i	0.0163316	+	0.0259586i
$742$	6.79375	−	4.75704i	0.249406	−	0.174636i
$743$	−13.8249	+	9.68027i	−0.507185	+	0.355135i	−0.798991	−	0.601343i	$-0.794633\pi$
$743$	−13.8249	+	9.68027i	−0.507185	+	0.355135i	0.291806	+	0.956477i	$0.405744\pi$
$744$	−13.8146	+	26.1747i	−0.506468	+	0.959611i
$745$	32.9756	+	14.6459i	1.20813	+	0.536583i
$746$	−12.4628	−	7.19539i	−0.456295	−	0.263442i
$747$	7.94222	+	1.49335i	0.290591	+	0.0546388i
$748$	30.6697	+	8.21793i	1.12140	+	0.300477i
$749$	−19.5053	−	7.09934i	−0.712707	−	0.259404i
$750$	8.40318	+	3.00357i	0.306841	+	0.109675i
$751$	30.1032	+	25.2596i	1.09848	+	0.921734i	0.997322	−	0.0731359i	$-0.0233007\pi$
$751$	30.1032	+	25.2596i	1.09848	+	0.921734i	0.101158	+	0.994870i	$0.467745\pi$
$752$	−1.53761	+	3.29741i	−0.0560708	+	0.120244i
$753$	29.4066	+	1.45078i	1.07163	+	0.0528692i
$754$	0.912609	−	0.160918i	0.0332353	−	0.00586028i
$755$	−8.85996	−	18.1239i	−0.322447	−	0.659596i
$756$	−19.9067	−	26.8761i	−0.723999	−	0.977473i
$757$	15.4181	+	15.4181i	0.560380	+	0.560380i	0.929415	−	0.369036i	$-0.120312\pi$
$757$	15.4181	+	15.4181i	0.560380	+	0.560380i	−0.369036	+	0.929415i	$0.620312\pi$
$758$	8.25417	−	11.7882i	0.299805	−	0.428166i
$759$	9.29589	−	28.9110i	0.337419	−	1.04940i
$760$	4.76815	−	0.0875537i	0.172959	−	0.00317591i
$761$	−14.9899	+	17.8642i	−0.543382	+	0.647577i	−0.965942	−	0.258757i	$-0.916687\pi$
$761$	−14.9899	+	17.8642i	−0.543382	+	0.647577i	0.422560	+	0.906335i	$0.361131\pi$
$762$	−4.17881	+	0.526098i	−0.151382	+	0.0190585i
$763$	23.9224	−	11.1552i	0.866049	−	0.403845i
$764$	9.69221	+	16.7874i	0.350652	+	0.607347i
$765$	11.5084	+	24.2333i	0.416088	+	0.876156i
$766$	7.78943	−	13.4917i	0.281443	−	0.487474i
$767$	0.0209651	−	0.239632i	0.000757007	−	0.00865263i
$768$	1.86612	−	2.01350i	0.0673377	−	0.0726560i
$769$	−40.5586	−	7.15158i	−1.46258	−	0.257893i	−0.614987	−	0.788537i	$-0.710839\pi$
$769$	−40.5586	−	7.15158i	−1.46258	−	0.257893i	−0.847594	+	0.530645i	$0.821950\pi$
$770$	4.55641	+	15.8359i	0.164202	+	0.570685i
$771$	−1.01738	−	26.7806i	−0.0366401	−	0.964479i
$772$	−1.09588	−	0.0958772i	−0.0394416	−	0.00345069i
$773$	−14.3875	+	3.85511i	−0.517481	+	0.138659i	−0.508101	−	0.861297i	$-0.669652\pi$
$773$	−14.3875	+	3.85511i	−0.517481	+	0.138659i	−0.00937966	+	0.999956i	$0.502986\pi$
$774$	3.34038	+	0.935719i	0.120067	+	0.0336337i
$775$	−48.4852	−	6.72450i	−1.74164	−	0.241551i
$776$	−0.340005	+	0.934157i	−0.0122055	+	0.0335343i
$777$	8.56637	+	68.0429i	0.307317	+	2.44103i
$778$	−12.5476	+	1.09777i	−0.449853	+	0.0393571i
$779$	−2.10828	+	0.767352i	−0.0755370	+	0.0274932i
$780$	−0.390833	−	2.70298i	−0.0139941	−	0.0967823i
$781$	−9.72994	−	55.1812i	−0.348165	−	1.97454i
$782$	−5.14443	+	5.14443i	−0.183964	+	0.183964i
$783$	−26.4798	+	0.705786i	−0.946311	+	0.0252228i
$784$		−	16.5268i		−	0.590243i
$785$	−3.16897	−	0.498971i	−0.113105	−	0.0178090i
$786$	0.419313	−	0.379884i	0.0149564	−	0.0135500i
$787$	14.0910	+	6.57073i	0.502289	+	0.234221i	0.657212	−	0.753705i	$-0.271735\pi$
$787$	14.0910	+	6.57073i	0.502289	+	0.234221i	−0.154924	+	0.987926i	$0.549513\pi$
$788$	−4.28196	−	48.9430i	−0.152538	−	1.74352i
$789$	−5.96418	+	43.4020i	−0.212330	+	1.54515i
$790$	−7.80657	+	9.65820i	−0.277745	+	0.343623i
$791$	−22.8572	+	13.1966i	−0.812708	+	0.469217i
$792$	−17.6451	−	15.1497i	−0.626990	−	0.538323i
$793$	−0.203926	−	0.761062i	−0.00724162	−	0.0270261i
$794$	4.50706	−	3.78187i	0.159950	−	0.134214i
$795$	−19.3496	−	0.598771i	−0.686260	−	0.0212362i
$796$	0.860335	−	4.87920i	0.0304938	−	0.172939i
$797$	−17.3493	−	24.7774i	−0.614545	−	0.877661i	0.384419	−	0.923159i	$-0.374402\pi$
$797$	−17.3493	−	24.7774i	−0.614545	−	0.877661i	−0.998964	+	0.0454973i	$0.985513\pi$
$798$	−0.779448	+	3.42400i	−0.0275922	+	0.121208i
$799$	3.37525	+	4.02246i	0.119408	+	0.142305i
$800$	−21.9608	−	9.27482i	−0.776430	−	0.327914i
$801$	−4.31912	+	6.02204i	−0.152609	+	0.212778i
$802$	−2.35301	+	8.78157i	−0.0830878	+	0.310088i
$803$	7.77889	+	16.6819i	0.274511	+	0.588691i
$804$	−4.76861	−	11.6994i	−0.168176	−	0.412604i
$805$	30.8468	+	7.66127i	1.08721	+	0.270024i
$806$	−0.608660	−	1.67228i	−0.0214391	−	0.0589035i
$807$	−30.4463	−	19.6397i	−1.07176	−	0.691349i
$808$	−20.9104	−	14.6416i	−0.735627	−	0.515091i
$809$	38.2730			1.34561			0.672804	−	0.739821i	$-0.265090\pi$
$809$	38.2730			1.34561			0.672804	+	0.739821i	$0.265090\pi$
$810$	0.0397624	−	9.27384i	0.00139711	−	0.325849i
$811$	46.0127			1.61572			0.807862	−	0.589371i	$-0.200624\pi$
$811$	46.0127			1.61572			0.807862	+	0.589371i	$0.200624\pi$
$812$	−26.8786	−	18.8206i	−0.943254	−	0.660474i
$813$	8.76395	+	5.65327i	0.307365	+	0.198269i
$814$	7.69781	+	21.1496i	0.269808	+	0.741292i
$815$	−10.8779	−	18.0667i	−0.381035	−	0.632848i
$816$	−7.24454	−	17.7739i	−0.253610	−	0.622209i
$817$	1.29576	+	2.77876i	0.0453329	+	0.0972166i
$818$	0.344322	−	1.28503i	0.0120389	−	0.0449299i
$819$	4.24026	+	0.419408i	0.148167	+	0.0146553i
$820$	7.32222	+	0.505347i	0.255703	+	0.0176475i
$821$	−30.1717	−	35.9573i	−1.05300	−	1.25492i	−0.965954	−	0.258712i	$-0.916702\pi$
$821$	−30.1717	−	35.9573i	−1.05300	−	1.25492i	−0.0870458	−	0.996204i	$-0.527743\pi$
$822$	−0.180385	+	0.792404i	−0.00629164	+	0.0276382i
$823$	−23.1777	−	33.1012i	−0.807923	−	1.15383i	−0.985491	−	0.169726i	$-0.945712\pi$
$823$	−23.1777	−	33.1012i	−0.807923	−	1.15383i	0.177568	−	0.984109i	$-0.443177\pi$
$824$	5.22041	−	29.6064i	0.181861	−	1.03139i
$825$	13.6087	−	35.9755i	0.473795	−	1.25251i
$826$	0.775097	−	0.650383i	0.0269691	−	0.0226297i
$827$	−10.3751	−	38.7205i	−0.360779	−	1.34645i	−0.873054	−	0.487624i	$-0.837864\pi$
$827$	−10.3751	−	38.7205i	−0.360779	−	1.34645i	0.512275	−	0.858821i	$-0.328803\pi$
$828$	−19.9753	+	7.01530i	−0.694191	+	0.243799i
$829$	−27.2086	+	15.7089i	−0.944994	+	0.545593i	−0.891522	−	0.452977i	$-0.850362\pi$
$829$	−27.2086	+	15.7089i	−0.944994	+	0.545593i	−0.0534718	+	0.998569i	$0.517029\pi$
$830$	0.292652	+	2.76032i	0.0101581	+	0.0958119i
$831$	−0.853229	+	6.20905i	−0.0295982	+	0.215390i
$832$	0.114993	+	1.31438i	0.00398666	+	0.0455678i
$833$	−21.6175	−	10.0804i	−0.749002	−	0.349265i
$834$	−13.1672	+	11.9290i	−0.455942	+	0.413069i
$835$	−5.83133	+	37.0349i	−0.201802	+	1.28165i
$836$		−	9.70133i		−	0.335527i
$837$	10.1651	+	49.8436i	0.351356	+	1.72285i
$838$	−5.79390	+	5.79390i	−0.200147	+	0.200147i
$839$	4.95377	+	28.0942i	0.171023	+	0.969920i	0.942635	+	0.333826i	$0.108340\pi$
$839$	4.95377	+	28.0942i	0.171023	+	0.969920i	−0.771611	+	0.636094i	$0.780549\pi$
$840$	14.5710	−	19.4970i	0.502748	−	0.672711i
$841$	2.83027	−	1.03013i	0.0975955	−	0.0355219i
$842$	−0.941759	+	0.0823932i	−0.0324552	+	0.00283946i
$843$	−5.05447	−	40.1478i	−0.174085	−	1.38276i
$844$	−13.4028	+	36.8238i	−0.461342	+	1.26753i
$845$	−23.8253	−	16.0389i	−0.819615	−	0.551757i
$846$	−0.449927	−	1.75857i	−0.0154688	−	0.0604608i
$847$	30.3477	−	8.13164i	1.04276	−	0.279407i
$848$	13.7977	+	1.20714i	0.473814	+	0.0414533i
$849$	1.14760	+	30.2082i	0.0393854	+	1.03674i
$850$	−6.83655	+	6.17815i	−0.234492	+	0.211909i
$851$	42.7525	+	7.53842i	1.46554	+	0.258414i
$852$	−26.5531	+	28.6502i	−0.909693	+	0.981540i
$853$	−3.75441	+	42.9131i	−0.128549	+	1.46932i	0.608541	+	0.793522i	$0.291755\pi$
$853$	−3.75441	+	42.9131i	−0.128549	+	1.46932i	−0.737090	+	0.675795i	$0.763801\pi$
$854$	1.65709	−	2.87017i	0.0567045	−	0.0982152i
$855$	6.24182	−	5.31279i	0.213466	−	0.181694i
$856$	5.03113	+	8.71418i	0.171961	+	0.297844i
$857$	31.7973	−	14.8273i	1.08617	−	0.506492i	0.204749	−	0.978814i	$-0.434362\pi$
$857$	31.7973	−	14.8273i	1.08617	−	0.506492i	0.881426	+	0.472323i	$0.156584\pi$
$858$	1.38743	−	0.174672i	0.0473659	−	0.00596321i
$859$	20.1815	−	24.0514i	0.688584	−	0.820622i	−0.302600	−	0.953118i	$-0.597855\pi$
$859$	20.1815	−	24.0514i	0.688584	−	0.820622i	0.991184	+	0.132496i	$0.0422991\pi$
$860$	−0.184145	−	10.0285i	−0.00627929	−	0.341968i
$861$	−3.50517	+	10.9014i	−0.119456	+	0.371518i
$862$	−5.12322	+	7.31672i	−0.174498	+	0.249209i
$863$	2.26670	+	2.26670i	0.0771594	+	0.0771594i	0.744633	−	0.667474i	$-0.232624\pi$
$863$	2.26670	+	2.26670i	0.0771594	+	0.0771594i	−0.667474	+	0.744633i	$0.732624\pi$
$864$	−1.50087	+	24.7287i	−0.0510605	+	0.841287i
$865$	−5.54919	+	16.1636i	−0.188678	+	0.549580i
$866$	1.48227	−	0.261364i	0.0503696	−	0.00888152i
$867$	1.74165	+	0.0859243i	0.0591494	+	0.00291814i
$868$	−26.6305	+	57.1094i	−0.903900	+	1.93842i
$869$	41.0040	+	34.4064i	1.39096	+	1.16716i
$870$	−2.84593	−	8.64193i	−0.0964860	−	0.292989i
$871$	1.51249	+	0.550500i	0.0512487	+	0.0186530i
$872$	−12.3595	−	3.31173i	−0.418547	−	0.112149i
$873$	0.566171	+	1.61211i	0.0191620	+	0.0545617i
$874$	1.92508	+	1.11144i	0.0651167	+	0.0375951i
$875$	38.5288	+	11.6649i	1.30251	+	0.394346i
$876$	5.98948	−	11.3483i	0.202366	−	0.383425i
$877$	32.4003	−	22.6869i	1.09408	−	0.766084i	0.120111	−	0.992760i	$-0.461675\pi$
$877$	32.4003	−	22.6869i	1.09408	−	0.766084i	0.973970	+	0.226677i	$0.0727861\pi$
$878$	1.85264	−	1.29723i	0.0625236	−	0.0437795i
$879$	15.2072	+	24.1714i	0.512925	+	0.815282i
$880$	−11.1701	+	25.1498i	−0.376544	+	0.847801i
$881$	12.4335	+	7.17846i	0.418894	+	0.241848i	0.694604	−	0.719392i	$-0.255580\pi$
$881$	12.4335	+	7.17846i	0.418894	+	0.241848i	−0.275710	+	0.961241i	$0.588913\pi$
$882$	5.22826	+	6.37606i	0.176045	+	0.214693i
$883$	−41.9771	−	11.2477i	−1.41264	−	0.378516i	−0.529774	−	0.848139i	$-0.677723\pi$
$883$	−41.9771	−	11.2477i	−1.41264	−	0.378516i	−0.882867	+	0.469623i	$0.844390\pi$
$884$	2.64999	+	0.964518i	0.0891289	+	0.0324403i
$885$	−2.35802	+	0.132971i	−0.0792639	+	0.00446978i
$886$	−6.82284	−	5.72505i	−0.229218	−	0.192337i
$887$	−17.3530	+	37.2137i	−0.582658	+	1.24951i	0.365232	+	0.930916i	$0.380990\pi$
$887$	−17.3530	+	37.2137i	−0.582658	+	1.24951i	−0.947890	+	0.318598i	$0.896788\pi$
$888$	18.0210	−	27.9370i	0.604746	−	0.937505i
$889$	−18.7110	+	3.29925i	−0.627547	+	0.110653i
$890$	−2.40752	−	0.826533i	−0.0807001	−	0.0277055i
$891$	−39.9621	−	0.905206i	−1.33878	−	0.0303255i
$892$	−14.0975	−	14.0975i	−0.472020	−	0.472020i
$893$	0.920226	−	1.31422i	0.0307942	−	0.0439787i
$894$	12.5898	−	2.71639i	0.421065	−	0.0908498i
$895$	−6.77946	−	6.53497i	−0.226612	−	0.218440i
$896$	−25.6367	+	30.5526i	−0.856462	+	1.02069i
$897$	1.04628	−	2.48604i	0.0349343	−	0.0830064i
$898$	1.24767	−	0.581797i	0.0416352	−	0.0194148i
$899$	24.9536	+	43.2210i	0.832250	+	1.44150i
$900$	−25.7163	+	7.59561i	−0.857211	+	0.253187i
$901$	9.99476	−	17.3114i	0.332974	−	0.576728i
$902$	−0.327536	+	3.74375i	−0.0109058	+	0.124653i
$903$	15.2583	+	3.47345i	0.507766	+	0.115589i
$904$	12.6001	+	2.22173i	0.419072	+	0.0738938i
$905$	−12.7792	+	3.67693i	−0.424796	+	0.122225i
$906$	−6.36847	−	3.36118i	−0.211578	−	0.111668i
$907$	−21.3504	−	1.86792i	−0.708928	−	0.0620232i	−0.273012	−	0.962011i	$-0.588020\pi$
$907$	−21.3504	−	1.86792i	−0.708928	−	0.0620232i	−0.435916	+	0.899987i	$0.643576\pi$
$908$	22.0707	−	5.91383i	0.732442	−	0.196257i
$909$	−43.7484	+	3.32877i	−1.45104	+	0.110408i
$910$	0.280560	+	1.43640i	0.00930049	+	0.0476163i
$911$	8.05314	−	22.1258i	0.266813	−	0.733061i	−0.731855	−	0.681460i	$-0.761345\pi$
$911$	8.05314	−	22.1258i	0.266813	−	0.733061i	0.998668	−	0.0516013i	$-0.0164325\pi$
$912$	−4.67265	+	3.54360i	−0.154727	+	0.117340i
$913$	11.9186	−	1.04275i	0.394450	−	0.0345099i
$914$	2.85987	−	1.04091i	0.0945960	−	0.0344301i
$915$	−7.10888	+	3.05092i	−0.235012	+	0.100860i
$916$	4.61738	+	26.1865i	0.152563	+	0.865225i
$917$	1.80481	−	1.80481i	0.0595999	−	0.0595999i
$918$	8.41772	+	4.56536i	0.277826	+	0.150679i
$919$		−	40.0326i		−	1.32055i	−0.751023	−	0.660277i	$-0.770439\pi$
$919$		−	40.0326i		−	1.32055i	0.751023	−	0.660277i	$-0.229561\pi$
$920$	−9.06772	−	12.4569i	−0.298954	−	0.410691i
$921$	31.7765	+	10.2172i	1.04707	+	0.336669i
$922$	−17.4045	−	8.11585i	−0.573187	−	0.267281i
$923$	−0.433739	−	4.95766i	−0.0142767	−	0.163183i
$924$	−39.1113	−	30.3645i	−1.28667	−	0.998920i
$925$	53.5966	+	12.2714i	1.76224	+	0.403481i
$926$	−2.17807	+	1.25751i	−0.0715757	+	0.0413243i
$927$	−25.3274	−	45.0385i	−0.831859	−	1.47926i
$928$	6.29073	+	23.4773i	0.206503	+	0.770681i
$929$	33.8872	−	28.4347i	1.11180	−	0.932913i	0.113641	−	0.993522i	$-0.463749\pi$
$929$	33.8872	−	28.4347i	1.11180	−	0.932913i	0.998162	+	0.0606092i	$0.0193043\pi$
$930$	−15.3947	+	8.26411i	−0.504812	+	0.270991i
$931$	−1.26551	+	7.17705i	−0.0414754	+	0.235218i
$932$	5.11156	+	7.30007i	0.167435	+	0.239122i
$933$	5.30223	+	4.91411i	0.173587	+	0.160881i
$934$	2.98938	+	3.56260i	0.0978154	+	0.116572i
$935$	26.0835	+	29.9508i	0.853023	+	0.979495i
$936$	−1.44393	−	1.47701i	−0.0471965	−	0.0482776i
$937$	3.25201	−	12.1366i	0.106238	−	0.396487i	−0.892244	−	0.451553i	$-0.850870\pi$
$937$	3.25201	−	12.1366i	0.106238	−	0.396487i	0.998483	+	0.0550659i	$0.0175369\pi$
$938$	2.86124	+	6.13595i	0.0934229	+	0.200346i
$939$	−4.87229	+	6.27580i	−0.159001	+	0.204803i
$940$	−4.49639	+	2.70726i	−0.146656	+	0.0883010i
$941$	−3.22172	−	8.85160i	−0.105025	−	0.288554i	0.876038	−	0.482242i	$-0.160177\pi$
$941$	−3.22172	−	8.85160i	−0.105025	−	0.288554i	−0.981063	+	0.193688i	$0.937955\pi$
$942$	−1.01870	+	0.522994i	−0.0331912	+	0.0170401i
$943$	5.93775	+	4.15766i	0.193360	+	0.135392i
$944$	1.68973			0.0549961
$945$	−1.88227	−	41.7928i	−0.0612301	−	1.35952i
$946$	5.13566			0.166975
$947$	−19.4360	−	13.6093i	−0.631586	−	0.442241i	0.213447	−	0.976955i	$-0.431531\pi$
$947$	−19.4360	−	13.6093i	−0.631586	−	0.442241i	−0.845034	+	0.534713i	$0.820420\pi$
$948$	1.83875	−	37.2707i	0.0597199	−	1.21049i
$949$	0.559131	+	1.53620i	0.0181502	+	0.0498672i
$950$	2.36397	+	1.52909i	0.0766972	+	0.0496102i
$951$	39.8675	+	5.47846i	1.29279	+	0.177651i
$952$	10.6218	+	22.7784i	0.344253	+	0.738253i
$953$	2.27494	−	8.49020i	0.0736926	−	0.275025i	−0.919241	−	0.393695i	$-0.871197\pi$
$953$	2.27494	−	8.49020i	0.0736926	−	0.275025i	0.992934	+	0.118671i	$0.0378632\pi$
$954$	−5.70503	+	3.89918i	−0.184707	+	0.126241i
$955$	−1.66945	+	24.1894i	−0.0540221	+	0.782752i
$956$	8.35447	+	9.95647i	0.270203	+	0.322015i
$957$	−37.4673	+	11.5806i	−1.21115	+	0.374347i
$958$	−1.18878	−	1.69775i	−0.0384076	−	0.0548518i
$959$	−0.636599	+	3.61033i	−0.0205569	+	0.116584i
$960$	12.6105	−	2.96417i	0.407003	−	0.0956681i
$961$	49.6714	−	41.6793i	1.60230	−	1.34449i
$962$	0.517374	+	1.93087i	0.0166808	+	0.0622536i
$963$	16.1837	+	6.09878i	0.521511	+	0.196530i
$964$	30.5588	−	17.6431i	0.984233	−	0.568247i
$965$	−1.07015	−	0.864986i	−0.0344494	−	0.0278449i
$966$	10.5062	−	4.28228i	0.338031	−	0.137780i
$967$	0.885782	+	10.1245i	0.0284848	+	0.325583i	0.997046	+	0.0768074i	$0.0244727\pi$
$967$	0.885782	+	10.1245i	0.0284848	+	0.325583i	−0.968561	+	0.248776i	$0.919972\pi$
$968$	−13.8034	−	6.43665i	−0.443659	−	0.206882i
$969$	1.78507	+	8.27335i	0.0573448	+	0.265778i
$970$	−0.474484	+	0.345391i	−0.0152348	+	0.0110898i
$971$		−	25.3812i		−	0.814522i	−0.913312	−	0.407261i	$-0.866484\pi$
$971$		−	25.3812i		−	0.814522i	0.913312	−	0.407261i	$-0.133516\pi$
$972$	16.3315	+	22.5794i	0.523833	+	0.724233i
$973$	−56.6741	+	56.6741i	−1.81689	+	1.81689i
$974$	0.282708	+	1.60332i	0.00905856	+	0.0513736i
$975$	1.48256	−	3.07771i	0.0474799	−	0.0985657i
$976$	5.20090	−	1.89297i	0.166477	−	0.0605926i
$977$	−45.3288	+	3.96576i	−1.45020	+	0.126876i	−0.784863	−	0.619669i	$-0.787267\pi$
$977$	−45.3288	+	3.96576i	−1.45020	+	0.126876i	−0.665335	+	0.746545i	$0.731711\pi$
$978$	−6.93824	−	2.92005i	−0.221861	−	0.0933728i
$979$	−3.75243	+	10.3097i	−0.119928	+	0.329500i
$980$	13.3139	−	19.7773i	0.425296	−	0.631762i
$981$	−20.0360	+	9.06814i	−0.639699	+	0.289524i
$982$	−6.89690	+	1.84802i	−0.220089	+	0.0589727i
$983$	−23.2285	−	2.03223i	−0.740875	−	0.0648182i	−0.289532	−	0.957168i	$-0.593500\pi$
$983$	−23.2285	−	2.03223i	−0.740875	−	0.0648182i	−0.451344	+	0.892350i	$0.649055\pi$
$984$	4.69852	−	2.95602i	0.149783	−	0.0942345i
$985$	29.7448	−	53.7760i	0.947748	−	1.71345i
$986$	9.25215	+	1.63140i	0.294649	+	0.0519545i
$987$	−2.41808	−	7.82335i	−0.0769684	−	0.249020i
$988$	0.0750965	−	0.858357i	0.00238914	−	0.0273080i
$989$	4.95291	−	8.57870i	0.157494	−	0.272787i
$990$	−3.64672	−	13.2365i	−0.115900	−	0.420684i
$991$	−16.3804	−	28.3716i	−0.520339	−	0.901254i	−0.999720	−	0.0236474i	$-0.992472\pi$
$991$	−16.3804	−	28.3716i	−0.520339	−	0.901254i	0.479381	−	0.877607i	$-0.340861\pi$
$992$	42.3029	−	19.7262i	1.34312	−	0.626306i
$993$	19.6643	+	25.9297i	0.624028	+	0.822854i
$994$	13.4555	−	16.0357i	0.426783	−	0.508621i
$995$	4.30096	−	4.46186i	0.136350	−	0.141451i
$996$	−5.60003	−	6.18126i	−0.177444	−	0.195861i
$997$	18.0983	−	25.8471i	0.573180	−	0.818585i	−0.422980	−	0.906139i	$-0.639016\pi$
$997$	18.0983	−	25.8471i	0.573180	−	0.818585i	0.996160	+	0.0875535i	$0.0279049\pi$
$998$	−5.60735	−	5.60735i	−0.177498	−	0.177498i
$999$	−6.49503	−	56.7701i	−0.205494	−	1.79613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.122.8	yes	192
3.2	odd	2		405.2.r.a.152.9		192
5.2	odd	4		675.2.ba.b.68.9		192
5.3	odd	4	inner	135.2.q.a.68.8	yes	192
5.4	even	2		675.2.ba.b.257.9		192
15.8	even	4		405.2.r.a.233.9		192
27.2	odd	18	inner	135.2.q.a.2.8	✓	192
27.25	even	9		405.2.r.a.332.9		192
135.2	even	36		675.2.ba.b.218.9		192
135.29	odd	18		675.2.ba.b.407.9		192
135.83	even	36	inner	135.2.q.a.83.8	yes	192
135.133	odd	36		405.2.r.a.8.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.8	✓	192	27.2	odd	18	inner
135.2.q.a.68.8	yes	192	5.3	odd	4	inner
135.2.q.a.83.8	yes	192	135.83	even	36	inner
135.2.q.a.122.8	yes	192	1.1	even	1	trivial
405.2.r.a.8.9		192	135.133	odd	36
405.2.r.a.152.9		192	3.2	odd	2
405.2.r.a.233.9		192	15.8	even	4
405.2.r.a.332.9		192	27.25	even	9
675.2.ba.b.68.9		192	5.2	odd	4
675.2.ba.b.218.9		192	135.2	even	36
675.2.ba.b.257.9		192	5.4	even	2
675.2.ba.b.407.9		192	135.29	odd	18

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)

\(f(q)\)	\(=\)	\(q+(-0.377486 - 0.264318i) q^{2} +(1.45550 + 0.938886i) q^{3} +(-0.611409 - 1.67983i) q^{4} +(0.538986 - 2.17014i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-1.52168 - 3.26325i) q^{7} +(-0.451753 + 1.68596i) q^{8} +(1.23699 + 2.73311i) q^{9} +O(q^{10})\)	\(q+(-0.377486 - 0.264318i) q^{2} +(1.45550 + 0.938886i) q^{3} +(-0.611409 - 1.67983i) q^{4} +(0.538986 - 2.17014i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-1.52168 - 3.26325i) q^{7} +(-0.451753 + 1.68596i) q^{8} +(1.23699 + 2.73311i) q^{9} +(-0.777066 + 0.676732i) q^{10} +(2.85486 + 3.40229i) q^{11} +(0.687263 - 3.01905i) q^{12} +(0.226257 + 0.323128i) q^{13} +(-0.288125 + 1.63404i) q^{14} +(2.82201 - 2.65260i) q^{15} +(-2.12266 + 1.78113i) q^{16} +(1.03506 + 3.86289i) q^{17} +(0.255466 - 1.35867i) q^{18} +(1.05819 - 0.610947i) q^{19} +(-3.97501 + 0.421435i) q^{20} +(0.849012 - 6.17836i) q^{21} +(-0.178381 - 2.03891i) q^{22} +(-3.57786 - 1.66839i) q^{23} +(-2.24046 + 2.02978i) q^{24} +(-4.41899 - 2.33935i) q^{25} -0.181780i q^{26} +(-0.765638 + 5.13944i) q^{27} +(-4.55135 + 4.55135i) q^{28} +(0.885233 + 5.02040i) q^{29} +(-1.76640 + 0.255409i) q^{30} +(9.19946 - 3.34833i) q^{31} +(4.74965 - 0.415541i) q^{32} +(0.960899 + 7.63244i) q^{33} +(0.630312 - 1.73177i) q^{34} +(-7.90187 + 1.54341i) q^{35} +(3.83486 - 3.74897i) q^{36} +(-10.6220 + 2.84615i) q^{37} +(-0.560936 - 0.0490755i) q^{38} +(0.0259371 + 0.682744i) q^{39} +(3.41529 + 1.88908i) q^{40} +(-1.80826 - 0.318845i) q^{41} +(-1.95354 + 2.10783i) q^{42} +(-0.218695 + 2.49969i) q^{43} +(3.96979 - 6.87588i) q^{44} +(6.59793 - 1.21132i) q^{45} +(0.909608 + 1.57549i) q^{46} +(1.19000 - 0.554905i) q^{47} +(-4.76182 + 0.599497i) q^{48} +(-3.83380 + 4.56894i) q^{49} +(1.04977 + 2.05109i) q^{50} +(-2.12028 + 6.59425i) q^{51} +(0.404466 - 0.577637i) q^{52} +(-3.53443 - 3.53443i) q^{53} +(1.64746 - 1.73769i) q^{54} +(8.92217 - 4.36165i) q^{55} +(6.18915 - 1.09131i) q^{56} +(2.11381 + 0.104285i) q^{57} +(0.992822 - 2.12911i) q^{58} +(-0.467138 - 0.391975i) q^{59} +(-6.18132 - 3.11868i) q^{60} +(-1.87695 - 0.683152i) q^{61} +(-4.35769 - 1.16764i) q^{62} +(7.03652 - 8.19551i) q^{63} +(2.89665 + 1.67238i) q^{64} +(0.823182 - 0.316847i) q^{65} +(1.65467 - 3.13512i) q^{66} +(3.34241 - 2.34038i) q^{67} +(5.85616 - 4.10053i) q^{68} +(-3.64117 - 5.78755i) q^{69} +(3.39079 + 1.50600i) q^{70} +(-10.9258 - 6.30801i) q^{71} +(-5.16673 + 0.850825i) q^{72} +(4.00309 + 1.07262i) q^{73} +(4.76194 + 1.73320i) q^{74} +(-4.23548 - 7.55386i) q^{75} +(-1.67328 - 1.40404i) q^{76} +(6.75835 - 14.4933i) q^{77} +(0.170671 - 0.264582i) q^{78} +(11.8688 - 2.09278i) q^{79} +(2.72120 + 5.56647i) q^{80} +(-5.93973 + 6.76162i) q^{81} +(0.598316 + 0.598316i) q^{82} +(1.54510 - 2.20663i) q^{83} +(-10.8977 + 2.35131i) q^{84} +(8.94087 - 0.164174i) q^{85} +(0.743269 - 0.885794i) q^{86} +(-3.42513 + 8.13835i) q^{87} +(-7.02584 + 3.27620i) q^{88} +(1.23513 + 2.13931i) q^{89} +(-2.81080 - 1.28670i) q^{90} +(0.710159 - 1.23003i) q^{91} +(-0.615070 + 7.03028i) q^{92} +(16.5336 + 3.76374i) q^{93} +(-0.595878 - 0.105069i) q^{94} +(-0.755488 - 2.62571i) q^{95} +(7.30328 + 3.85456i) q^{96} +(0.567380 + 0.0496393i) q^{97} +(2.65486 - 0.711367i) q^{98} +(-5.76740 + 12.0112i) 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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