LMFDB - Embedded newform 135.2.q.a.68.8

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			68.8
Character	$\chi$	$=$	135.68
Dual form			135.2.q.a.2.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264318 + 0.377486i) q^{2} +(-0.938886 + 1.45550i) q^{3} +(0.611409 + 1.67983i) q^{4} +(2.04357 - 0.907638i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-3.26325 + 1.52168i) q^{7} +(-1.68596 - 0.451753i) q^{8} +(-1.23699 - 2.73311i) q^{9} +O(q^{10})$	\(q+(-0.264318 + 0.377486i) q^{2} +(-0.938886 + 1.45550i) q^{3} +(0.611409 + 1.67983i) q^{4} +(2.04357 - 0.907638i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-3.26325 + 1.52168i) q^{7} +(-1.68596 - 0.451753i) q^{8} +(-1.23699 - 2.73311i) q^{9} +(-0.197534 + 1.01132i) q^{10} +(2.85486 + 3.40229i) q^{11} +(-3.01905 - 0.687263i) q^{12} +(-0.323128 + 0.226257i) q^{13} +(0.288125 - 1.63404i) q^{14} +(-0.597612 + 3.82660i) q^{15} +(-2.12266 + 1.78113i) q^{16} +(3.86289 - 1.03506i) q^{17} +(1.35867 + 0.255466i) q^{18} +(-1.05819 + 0.610947i) q^{19} +(2.77414 + 2.87792i) q^{20} +(0.849012 - 6.17836i) q^{21} +(-2.03891 + 0.178381i) q^{22} +(1.66839 - 3.57786i) q^{23} +(2.24046 - 2.02978i) q^{24} +(3.35239 - 3.70965i) q^{25} -0.181780i q^{26} +(5.13944 + 0.765638i) q^{27} +(-4.55135 - 4.55135i) q^{28} +(-0.885233 - 5.02040i) q^{29} +(-1.28653 - 1.23703i) q^{30} +(9.19946 - 3.34833i) q^{31} +(-0.415541 - 4.74965i) q^{32} +(-7.63244 + 0.960899i) q^{33} +(-0.630312 + 1.73177i) q^{34} +(-5.28756 + 6.07152i) q^{35} +(3.83486 - 3.74897i) q^{36} +(2.84615 + 10.6220i) q^{37} +(0.0490755 - 0.560936i) q^{38} +(-0.0259371 - 0.682744i) q^{39} +(-3.85542 + 0.607055i) q^{40} +(-1.80826 - 0.318845i) q^{41} +(2.10783 + 1.95354i) q^{42} +(-2.49969 - 0.218695i) q^{43} +(-3.96979 + 6.87588i) q^{44} +(-5.00854 - 4.46257i) q^{45} +(0.909608 + 1.57549i) q^{46} +(-0.554905 - 1.19000i) q^{47} +(-0.599497 - 4.76182i) q^{48} +(3.83380 - 4.56894i) q^{49} +(0.514242 + 2.24601i) q^{50} +(-2.12028 + 6.59425i) q^{51} +(-0.577637 - 0.404466i) 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} +(0.104285 - 2.11381i) q^{57} +(2.12911 + 0.992822i) q^{58} +(0.467138 + 0.391975i) q^{59} +(-6.79343 + 1.33573i) q^{60} +(-1.87695 - 0.683152i) q^{61} +(-1.16764 + 4.35769i) q^{62} +(8.19551 + 7.03652i) q^{63} +(-2.89665 - 1.67238i) q^{64} +(-0.454977 + 0.755656i) q^{65} +(1.65467 - 3.13512i) q^{66} +(-2.34038 - 3.34241i) q^{67} +(4.10053 + 5.85616i) q^{68} +(3.64117 + 5.78755i) q^{69} +(-0.894311 - 3.60079i) q^{70} +(-10.9258 - 6.30801i) q^{71} +(0.850825 + 5.16673i) q^{72} +(-1.07262 + 4.00309i) q^{73} +(-4.76194 - 1.73320i) q^{74} +(2.25190 + 8.36235i) q^{75} +(-1.67328 - 1.40404i) q^{76} +(-14.4933 - 6.75835i) q^{77} +(0.264582 + 0.170671i) 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} +(2.20663 + 1.54510i) q^{83} +(10.8977 - 2.35131i) q^{84} +(6.95464 - 5.62132i) q^{85} +(0.743269 - 0.885794i) q^{86} +(8.13835 + 3.42513i) q^{87} +(-3.27620 - 7.02584i) q^{88} +(-1.23513 - 2.13931i) q^{89} +(3.00840 - 0.711114i) q^{90} +(0.710159 - 1.23003i) q^{91} +(7.03028 + 0.615070i) q^{92} +(-3.76374 + 16.5336i) q^{93} +(0.595878 + 0.105069i) q^{94} +(-1.60797 + 2.20897i) q^{95} +(7.30328 + 3.85456i) q^{96} +(0.0496393 - 0.567380i) q^{97} +(0.711367 + 2.65486i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.264318	+	0.377486i	−0.186901	+	0.266923i	−0.901657	−	0.432451i	$-0.857649\pi$
$2$	−0.264318	+	0.377486i	−0.186901	+	0.266923i	0.714756	+	0.699374i	$0.246538\pi$
$3$	−0.938886	+	1.45550i	−0.542066	+	0.840336i
$3$	−0.938886	+	1.45550i	−0.542066	+	0.840336i
$4$	0.611409	+	1.67983i	0.305705	+	0.839916i
$5$	2.04357	−	0.907638i	0.913914	−	0.405908i
$5$	2.04357	−	0.907638i	0.913914	−	0.405908i
$6$	−0.301267	−	0.739132i	−0.122992	−	0.301750i
$7$	−3.26325	+	1.52168i	−1.23339	+	0.575141i	−0.926389	−	0.376567i	$-0.877104\pi$
$7$	−3.26325	+	1.52168i	−1.23339	+	0.575141i	−0.307004	+	0.951708i	$0.599327\pi$
$8$	−1.68596	−	0.451753i	−0.596078	−	0.159719i
$9$	−1.23699	−	2.73311i	−0.412328	−	0.911035i
$10$	−0.197534	+	1.01132i	−0.0624656	+	0.319809i
$11$	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	$0.544259\pi$
$12$	−3.01905	−	0.687263i	−0.871524	−	0.198396i
$13$	−0.323128	+	0.226257i	−0.0896196	+	0.0627524i	−0.617527	−	0.786549i	$-0.711866\pi$
$13$	−0.323128	+	0.226257i	−0.0896196	+	0.0627524i	0.527908	+	0.849302i	$0.322977\pi$
$14$	0.288125	−	1.63404i	0.0770047	−	0.436715i
$15$	−0.597612	+	3.82660i	−0.154303	+	0.988024i
$16$	−2.12266	+	1.78113i	−0.530666	+	0.445281i
$17$	3.86289	−	1.03506i	0.936888	−	0.251038i	0.242098	−	0.970252i	$-0.422164\pi$
$17$	3.86289	−	1.03506i	0.936888	−	0.251038i	0.694789	+	0.719213i	$0.255498\pi$
$18$	1.35867	+	0.255466i	0.320241	+	0.0602138i
$19$	−1.05819	+	0.610947i	−0.242766	+	0.140161i	−0.616447	−	0.787396i	$-0.711429\pi$
$19$	−1.05819	+	0.610947i	−0.242766	+	0.140161i	0.373682	+	0.927557i	$0.378095\pi$
$20$	2.77414	+	2.87792i	0.620316	+	0.643523i
$21$	0.849012	−	6.17836i	0.185270	−	1.34823i
$22$	−2.03891	+	0.178381i	−0.434697	+	0.0380310i
$23$	1.66839	−	3.57786i	0.347882	−	0.746036i	−0.652044	−	0.758181i	$-0.726088\pi$
$23$	1.66839	−	3.57786i	0.347882	−	0.746036i	0.999926	+	0.0121450i	$0.00386597\pi$
$24$	2.24046	−	2.02978i	0.457331	−	0.414328i
$25$	3.35239	−	3.70965i	0.670477	−	0.741930i
$26$		−	0.181780i		−	0.0356500i
$27$	5.13944	+	0.765638i	0.989085	+	0.147347i
$28$	−4.55135	−	4.55135i	−0.860124	−	0.860124i
$29$	−0.885233	−	5.02040i	−0.164384	−	0.932266i	−0.949698	−	0.313168i	$-0.898610\pi$
$29$	−0.885233	−	5.02040i	−0.164384	−	0.932266i	0.785314	−	0.619097i	$-0.212501\pi$
$30$	−1.28653	−	1.23703i	−0.234886	−	0.225850i
$31$	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	$0.0469963\pi$
$32$	−0.415541	−	4.74965i	−0.0734579	−	0.839628i
$33$	−7.63244	+	0.960899i	−1.32864	+	0.167271i
$34$	−0.630312	+	1.73177i	−0.108098	+	0.296996i
$35$	−5.28756	+	6.07152i	−0.893761	+	1.02627i
$36$	3.83486	−	3.74897i	0.639143	−	0.624829i
$37$	2.84615	+	10.6220i	0.467905	+	1.74624i	0.647076	+	0.762426i	$0.275992\pi$
$37$	2.84615	+	10.6220i	0.467905	+	1.74624i	−0.179171	+	0.983818i	$0.557342\pi$
$38$	0.0490755	−	0.560936i	0.00796111	−	0.0909958i
$39$	−0.0259371	−	0.682744i	−0.00415327	−	0.109327i
$40$	−3.85542	+	0.607055i	−0.609596	+	0.0959838i
$41$	−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	$0.601353\pi$
$42$	2.10783	+	1.95354i	0.325246	+	0.301438i
$43$	−2.49969	−	0.218695i	−0.381200	−	0.0333507i	−0.105054	−	0.994466i	$-0.533502\pi$
$43$	−2.49969	−	0.218695i	−0.381200	−	0.0333507i	−0.276146	+	0.961116i	$0.589057\pi$
$44$	−3.96979	+	6.87588i	−0.598469	+	1.03658i
$45$	−5.00854	−	4.46257i	−0.746629	−	0.665240i
$46$	0.909608	+	1.57549i	0.134114	+	0.232293i
$47$	−0.554905	−	1.19000i	−0.0809412	−	0.173579i	0.861672	−	0.507465i	$-0.169418\pi$
$47$	−0.554905	−	1.19000i	−0.0809412	−	0.173579i	−0.942613	+	0.333887i	$0.891640\pi$
$48$	−0.599497	−	4.76182i	−0.0865300	−	0.687309i
$49$	3.83380	−	4.56894i	0.547685	−	0.652706i
$50$	0.514242	+	2.24601i	0.0727249	+	0.317633i
$51$	−2.12028	+	6.59425i	−0.296899	+	0.923380i
$52$	−0.577637	−	0.404466i	−0.0801039	−	0.0560893i
$53$	3.53443	−	3.53443i	0.485491	−	0.485491i	−0.421389	−	0.906880i	$-0.638457\pi$
$53$	3.53443	−	3.53443i	0.485491	−	0.485491i	0.906880	+	0.421389i	$0.138457\pi$
$54$	−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
$57$	0.104285	−	2.11381i	0.0138129	−	0.279981i
$58$	2.12911	+	0.992822i	0.279566	+	0.130364i
$59$	0.467138	+	0.391975i	0.0608162	+	0.0510308i	0.672689	−	0.739925i	$-0.265139\pi$
$59$	0.467138	+	0.391975i	0.0608162	+	0.0510308i	−0.611873	+	0.790956i	$0.709584\pi$
$60$	−6.79343	+	1.33573i	−0.877028	+	0.172442i
$61$	−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	$0.651925\pi$
$62$	−1.16764	+	4.35769i	−0.148290	+	0.553427i
$63$	8.19551	+	7.03652i	1.03254	+	0.886518i
$64$	−2.89665	−	1.67238i	−0.362081	−	0.209048i
$65$	−0.454977	+	0.755656i	−0.0564330	+	0.0937276i
$66$	1.65467	−	3.13512i	0.203676	−	0.385907i
$67$	−2.34038	−	3.34241i	−0.285923	−	0.408341i	0.650338	−	0.759645i	$-0.274627\pi$
$67$	−2.34038	−	3.34241i	−0.285923	−	0.408341i	−0.936261	+	0.351304i	$0.885738\pi$
$68$	4.10053	+	5.85616i	0.497262	+	0.710164i
$69$	3.64117	+	5.78755i	0.438346	+	0.696739i
$70$	−0.894311	−	3.60079i	−0.106891	−	0.430377i
$71$	−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	$0.935951\pi$
$72$	0.850825	+	5.16673i	0.100271	+	0.608905i
$73$	−1.07262	+	4.00309i	−0.125541	+	0.468526i	−0.999858	−	0.0168287i	$-0.994643\pi$
$73$	−1.07262	+	4.00309i	−0.125541	+	0.468526i	0.874317	+	0.485355i	$0.161310\pi$
$74$	−4.76194	−	1.73320i	−0.553564	−	0.201481i
$75$	2.25190	+	8.36235i	0.260027	+	0.965601i
$76$	−1.67328	−	1.40404i	−0.191938	−	0.161055i
$77$	−14.4933	−	6.75835i	−1.65167	−	0.770186i
$78$	0.264582	+	0.170671i	0.0299580	+	0.0193247i
$79$	−11.8688	+	2.09278i	−1.33534	+	0.235457i	−0.795317	−	0.606193i	$-0.792696\pi$
$79$	−11.8688	+	2.09278i	−1.33534	+	0.235457i	−0.540023	+	0.841650i	$0.681585\pi$
$80$	−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
$83$	2.20663	+	1.54510i	0.242209	+	0.169597i	0.688378	−	0.725352i	$-0.258323\pi$
$83$	2.20663	+	1.54510i	0.242209	+	0.169597i	−0.446169	+	0.894949i	$0.647212\pi$
$84$	10.8977	−	2.35131i	1.18904	−	0.256549i
$85$	6.95464	−	5.62132i	0.754336	−	0.609718i
$86$	0.743269	−	0.885794i	0.0801488	−	0.0955176i
$87$	8.13835	+	3.42513i	0.872523	+	0.367212i
$88$	−3.27620	−	7.02584i	−0.349244	−	0.748957i
$89$	−1.23513	−	2.13931i	−0.130924	−	0.226766i	0.793109	−	0.609079i	$-0.208461\pi$
$89$	−1.23513	−	2.13931i	−0.130924	−	0.226766i	−0.924033	+	0.382313i	$0.875128\pi$
$90$	3.00840	−	0.711114i	0.317114	−	0.0749580i
$91$	0.710159	−	1.23003i	0.0744449	−	0.128942i
$92$	7.03028	+	0.615070i	0.732957	+	0.0641254i
$93$	−3.76374	+	16.5336i	−0.390281	+	1.71445i
$94$	0.595878	+	0.105069i	0.0614601	+	0.0108371i
$95$	−1.60797	+	2.20897i	−0.164974	+	0.226635i
$96$	7.30328	+	3.85456i	0.745388	+	0.393405i
$97$	0.0496393	−	0.567380i	0.00504011	−	0.0576087i	−0.993258	−	0.115924i	$-0.963017\pi$
$97$	0.0496393	−	0.567380i	0.00504011	−	0.0576087i	0.998298	+	0.0583150i	$0.0185728\pi$
$98$	0.711367	+	2.65486i	0.0718589	+	0.268181i
$99$	5.76740	−	12.0112i	0.579646	−	1.20717i
$100$	8.28127	+	3.36333i	0.828127	+	0.336333i
$101$	−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	$0.851739\pi$
$102$	−1.92881	−	2.54336i	−0.190980	−	0.251830i
$103$	−1.50115	−	17.1583i	−0.147913	−	1.69066i	−0.601048	−	0.799213i	$-0.705250\pi$
$103$	−1.50115	−	17.1583i	−0.147913	−	1.69066i	0.453135	−	0.891442i	$-0.350306\pi$
$104$	0.646995	−	0.235487i	0.0634431	−	0.0230914i
$105$	−3.87270	−	13.3965i	−0.377937	−	1.30737i
$106$	0.399982	+	2.26841i	0.0388497	+	0.220328i
$107$	−4.07639	−	4.07639i	−0.394080	−	0.394080i	0.482059	−	0.876139i	$-0.339889\pi$
$107$	−4.07639	−	4.07639i	−0.394080	−	0.394080i	−0.876139	+	0.482059i	$0.839889\pi$
$108$	1.85615	+	9.10151i	0.178609	+	0.875793i
$109$		−	7.33084i		−	0.702167i	−0.936344	−	0.351084i	$-0.885813\pi$
$109$		−	7.33084i		−	0.702167i	0.936344	−	0.351084i	$-0.114187\pi$
$110$	−4.00475	+	2.21513i	−0.381838	+	0.211204i
$111$	−18.1326	−	5.83025i	−1.72107	−	0.553383i
$112$	4.21648	−	9.04228i	0.398420	−	0.854415i
$113$	7.30233	−	0.638871i	0.686945	−	0.0600999i	0.261661	−	0.965160i	$-0.415730\pi$
$113$	7.30233	−	0.638871i	0.686945	−	0.0600999i	0.425284	+	0.905060i	$0.360174\pi$
$114$	0.770369	+	0.598085i	0.0721516	+	0.0560158i
$115$	0.162063	−	8.82592i	0.0151125	−	0.823021i
$116$	7.89220	−	4.55656i	0.732772	−	0.423066i
$117$	1.01809	+	0.603267i	0.0941223	+	0.0557721i
$118$	−0.271438	+	0.0727316i	−0.0249879	+	0.00669549i
$119$	−11.0305	+	9.25573i	−1.01117	+	0.848471i
$120$	2.73623	−	6.18154i	0.249782	−	0.564295i
$121$	−1.51523	+	8.59327i	−0.137748	+	0.781206i
$122$	0.753991	−	0.527950i	0.0682632	−	0.0477984i
$123$	2.16183	−	2.33257i	0.194926	−	0.210321i
$124$	11.2493	+	13.4064i	1.01021	+	1.20393i
$125$	3.48383	−	10.6237i	0.311603	−	0.950212i
$126$	−4.82241	+	1.23381i	−0.429614	+	0.109916i
$127$	−5.09700	−	1.36574i	−0.452285	−	0.121189i	0.0254832	−	0.999675i	$-0.491888\pi$
$127$	−5.09700	−	1.36574i	−0.452285	−	0.121189i	−0.477769	+	0.878486i	$0.658554\pi$
$128$	10.0391	−	4.68132i	0.887341	−	0.413774i
$129$	2.66524	−	3.43299i	0.234661	−	0.302258i
$130$	−0.164990	−	0.371481i	−0.0144706	−	0.0325810i
$131$	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	$0.879030\pi$
$132$	−6.28069	−	12.2337i	−0.546664	−	1.06481i
$133$	2.52348	−	3.60390i	0.218813	−	0.312498i
$134$	1.88032			0.162435
$135$	11.1977	−	3.10011i	0.963748	−	0.266815i
$136$	−6.98028			−0.598554
$137$	−0.583999	+	0.834037i	−0.0498944	+	0.0712566i	−0.843324	−	0.537405i	$-0.819405\pi$
$137$	−0.583999	+	0.834037i	−0.0498944	+	0.0712566i	0.793430	+	0.608662i	$0.208293\pi$
$138$	−3.14715	−	0.155265i	−0.267903	−	0.0132170i
$139$	7.61336	+	20.9175i	0.645757	+	1.77420i	0.632837	+	0.774285i	$0.281890\pi$
$139$	7.61336	+	20.9175i	0.645757	+	1.77420i	0.0129201	+	0.999917i	$0.495887\pi$
$140$	−13.4320	−	5.17004i	−1.13521	−	0.436948i
$141$	2.25304	+	0.309606i	0.189740	+	0.0260735i
$142$	5.26907	−	2.45701i	0.442170	−	0.206187i
$143$	−1.69228	−	0.453445i	−0.141515	−	0.0379189i
$144$	7.49371	+	3.59824i	0.624476	+	0.299853i
$145$	−6.36575	−	9.45609i	−0.528647	−	0.785286i
$146$	−1.22759	−	1.46299i	−0.101596	−	0.121078i
$147$	3.05061	+	9.86982i	0.251610	+	0.814049i
$148$	−16.1030	+	11.2754i	−1.32366	+	0.926835i
$149$	2.80203	−	15.8911i	0.229551	−	1.30185i	−0.624240	−	0.781233i	$-0.714591\pi$
$149$	2.80203	−	15.8911i	0.229551	−	1.30185i	0.853791	−	0.520616i	$-0.174298\pi$
$150$	−3.75189	−	1.36026i	−0.306340	−	0.111065i
$151$	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	$0.158130\pi$
$152$	2.06007	−	0.551994i	0.167094	−	0.0447726i
$153$	−7.60726	−	9.27733i	−0.615010	−	0.750027i
$154$	6.38204	−	3.68467i	0.514279	−	0.296919i
$155$	15.7607	−	15.1923i	1.26593	−	1.22028i
$156$	1.13104	−	0.461006i	0.0905555	−	0.0369100i
$157$	−1.42921	+	0.125040i	−0.114063	+	0.00997924i	−0.144044	−	0.989571i	$-0.546011\pi$
$157$	−1.42921	+	0.125040i	−0.114063	+	0.00997924i	0.0299812	+	0.999550i	$0.490455\pi$
$158$	2.34714	−	5.03345i	0.186728	−	0.400440i
$159$	1.82595	+	8.46280i	0.144807	+	0.671144i
$160$	−5.16015	−	9.32910i	−0.407946	−	0.737530i
$161$			14.2142i			1.12024i
$162$	−0.982436	−	4.02938i	−0.0771874	−	0.316578i
$163$	6.66882	+	6.66882i	0.522343	+	0.522343i	0.918278	−	0.395936i	$-0.129580\pi$
$163$	6.66882	+	6.66882i	0.522343	+	0.522343i	−0.395936	+	0.918278i	$0.629580\pi$
$164$	−0.569980	−	3.23252i	−0.0445080	−	0.252417i
$165$	−14.7253	+	8.89116i	−1.14636	+	0.692176i
$166$	−1.16651	+	0.424573i	−0.0905384	+	0.0329533i
$167$	1.46130	+	16.7028i	0.113079	+	1.29250i	0.814672	+	0.579922i	$0.196917\pi$
$167$	1.46130	+	16.7028i	0.113079	+	1.29250i	−0.701593	+	0.712578i	$0.747528\pi$
$168$	−4.22250	+	10.0330i	−0.325773	+	0.774059i
$169$	−4.39304	+	12.0698i	−0.337926	+	0.928445i
$170$	0.283729	+	4.11109i	0.0217611	+	0.315306i
$171$	2.97875	+	2.13641i	0.227791	+	0.163376i
$172$	−1.16096	−	4.33278i	−0.0885227	−	0.330371i
$173$	0.666108	−	7.61365i	0.0506432	−	0.578855i	−0.927902	−	0.372824i	$-0.878390\pi$
$173$	0.666108	−	7.61365i	0.0506432	−	0.578855i	0.978545	−	0.206031i	$-0.0660548\pi$
$174$	−3.44405	+	2.16679i	−0.261093	+	0.164264i
$175$	−5.29479	+	17.2068i	−0.400248	+	1.30071i
$176$	−12.1198	−	2.13705i	−0.913566	−	0.161086i
$177$	−1.00911	+	0.311901i	−0.0758494	+	0.0234439i
$178$	1.13403	+	0.0992144i	0.0849988	+	0.00743644i
$179$	−2.10555	+	3.64692i	−0.157376	+	0.272584i	−0.933922	−	0.357477i	$-0.883637\pi$
$179$	−2.10555	+	3.64692i	−0.157376	+	0.272584i	0.776545	+	0.630061i	$0.216970\pi$
$180$	4.43410	−	11.1420i	0.330498	−	0.830473i
$181$	−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	$0.904270\pi$
$182$	0.276611	+	0.593194i	0.0205038	+	0.0439705i
$183$	2.75657	−	2.09050i	0.203772	−	0.154534i
$184$	−4.42915	+	5.27845i	−0.326521	+	0.389133i
$185$	15.4572	+	19.1235i	1.13644	+	1.40599i
$186$	−5.24635	−	5.79088i	−0.384681	−	0.424608i
$187$	14.5496	+	10.1877i	1.06397	+	0.745000i
$188$	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	$0.572767\pi$
$192$	5.15378	−	2.64591i	0.371942	−	0.190952i
$193$	0.557718	+	0.260068i	0.0401454	+	0.0187201i	0.442587	−	0.896725i	$-0.354061\pi$
$193$	0.557718	+	0.260068i	0.0401454	+	0.0187201i	−0.402442	+	0.915446i	$0.631838\pi$
$194$	0.201057	+	0.168707i	0.0144351	+	0.0121124i
$195$	−0.672689	−	1.37170i	−0.0481722	−	0.0982292i
$196$	10.0191	+	3.64664i	0.715648	+	0.260475i
$197$	7.11316	−	26.5467i	0.506791	−	1.89137i	0.0566946	−	0.998392i	$-0.481944\pi$
$197$	7.11316	−	26.5467i	0.506791	−	1.89137i	0.450097	−	0.892980i	$-0.351389\pi$
$198$	3.00964	+	5.35190i	0.213886	+	0.380343i
$199$	−2.40020	−	1.38576i	−0.170146	−	0.0982338i	0.412509	−	0.910954i	$-0.364653\pi$
$199$	−2.40020	−	1.38576i	−0.170146	−	0.0982338i	−0.582655	+	0.812720i	$0.697986\pi$
$200$	−7.32785	+	4.73989i	−0.518157	+	0.335161i
$201$	7.06225	−	0.268292i	0.498132	−	0.0189238i
$202$	−3.86564	−	5.52070i	−0.271985	−	0.388435i
$203$	10.5282	+	15.0358i	0.738934	+	1.05531i
$204$	−12.3736	+	0.470067i	−0.866325	+	0.0329113i
$205$	−3.98471	+	0.989662i	−0.278304	+	0.0691210i
$206$	6.87379	+	3.96858i	0.478919	+	0.276504i
$207$	−11.8424	−	0.134108i	−0.823107	−	0.00932114i
$208$	0.282900	−	1.05580i	0.0196156	−	0.0732065i
$209$	−5.09961	−	1.85611i	−0.352747	−	0.128389i
$210$	6.08062	+	2.07906i	0.419603	+	0.143469i
$211$	−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	$0.994370\pi$
$212$	8.09823	+	3.77627i	0.556189	+	0.259355i
$213$	19.4394	−	9.98004i	1.33197	−	0.683821i
$214$	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
$218$	2.76729	+	1.93768i	0.187424	+	0.131236i
$219$	−4.81944	−	5.31966i	−0.325668	−	0.359469i
$220$	−1.87175	+	17.6545i	−0.126194	+	1.19027i
$221$	−1.01402	+	1.20846i	−0.0682103	+	0.0812899i
$222$	6.99360	−	5.30374i	0.469380	−	0.355964i
$223$	4.71331	+	10.1077i	0.315627	+	0.676863i	0.998562	−	0.0536157i	$-0.0170746\pi$
$223$	4.71331	+	10.1077i	0.315627	+	0.676863i	−0.682935	+	0.730479i	$0.739297\pi$
$224$	8.58346	+	14.8670i	0.573507	+	0.993343i
$225$	−14.2857	−	4.57364i	−0.952381	−	0.304910i
$226$	−1.68897	+	2.92539i	−0.112349	+	0.194594i
$227$	12.7332	+	1.11401i	0.845130	+	0.0739393i	0.501492	−	0.865163i	$-0.332785\pi$
$227$	12.7332	+	1.11401i	0.845130	+	0.0739393i	0.343639	+	0.939102i	$0.388340\pi$
$228$	3.61461	−	1.11722i	0.239383	−	0.0739898i
$229$	14.6486	+	2.58295i	0.968008	+	0.170686i	0.635233	−	0.772320i	$-0.280904\pi$
$229$	14.6486	+	2.58295i	0.968008	+	0.170686i	0.332775	+	0.943006i	$0.392015\pi$
$230$	3.28882	+	2.39403i	0.216858	+	0.157858i
$231$	23.4444	−	14.7498i	1.54253	−	0.970465i
$232$	−0.775511	+	8.86413i	−0.0509148	+	0.581959i
$233$	−1.29026	−	4.81533i	−0.0845279	−	0.315463i	0.910696	−	0.413076i	$-0.135546\pi$
$233$	−1.29026	−	4.81533i	−0.0845279	−	0.315463i	−0.995224	+	0.0976137i	$0.968879\pi$
$234$	−0.496824	+	0.224859i	−0.0324784	+	0.0146995i
$235$	−2.21407	−	1.92819i	−0.144430	−	0.125781i
$236$	−0.372840	+	1.02437i	−0.0242698	+	0.0666808i
$237$	8.09737	−	19.2399i	0.525980	−	1.24977i
$238$	−0.578329	−	6.61033i	−0.0374875	−	0.428484i
$239$	6.83215	−	2.48670i	0.441935	−	0.160851i	−0.111462	−	0.993769i	$-0.535553\pi$
$239$	6.83215	−	2.48670i	0.441935	−	0.160851i	0.553397	+	0.832918i	$0.313331\pi$
$240$	−5.54712	−	9.18700i	−0.358065	−	0.593018i
$241$	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
$243$	−4.26484	−	14.9937i	−0.273590	−	0.961847i
$244$		−	3.57064i		−	0.228587i
$245$	3.68770	−	12.8167i	0.235599	−	0.818827i
$246$	0.309101	+	1.43260i	0.0197075	+	0.0913393i
$247$	0.203700	−	0.436837i	0.0129611	−	0.0277953i
$248$	−17.0226	+	1.48928i	−1.08094	+	0.0945696i
$249$	−4.32067	+	1.76109i	−0.273812	+	0.111604i
$250$	3.08945	+	4.12313i	0.195394	+	0.260770i
$251$	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	$0.153091\pi$
$252$	−6.80937	+	18.0693i	−0.428950	+	1.13826i
$253$	16.9360	−	4.53797i	1.06475	−	0.285300i
$254$	1.86278	−	1.56305i	0.116881	−	0.0980747i
$255$	1.65224	+	15.4003i	0.103467	+	0.964403i
$256$	0.275231	−	1.56091i	0.0172019	−	0.0975570i
$257$	−12.6747	+	8.87491i	−0.790625	+	0.553601i	−0.897678	−	0.440652i	$-0.854747\pi$
$257$	−12.6747	+	8.87491i	−0.790625	+	0.553601i	0.107053	+	0.994253i	$0.465858\pi$
$258$	0.591431	+	1.91349i	0.0368209	+	0.119129i
$259$	−25.4510	−	30.3313i	−1.58145	−	1.88469i
$260$	−1.54755	−	0.302270i	−0.0959751	−	0.0187460i
$261$	−12.6263	+	8.62960i	−0.781547	+	0.534159i
$262$	−0.315537	−	0.0845478i	−0.0194939	−	0.00522338i
$263$	−22.9238	+	10.6896i	−1.41355	+	0.659147i	−0.971324	−	0.237759i	$-0.923587\pi$
$263$	−22.9238	+	10.6896i	−1.41355	+	0.659147i	−0.442221	+	0.896906i	$0.645809\pi$
$264$	13.3021	+	1.82794i	0.818689	+	0.112502i
$265$	4.01488	−	10.4308i	0.246632	−	0.640762i
$266$	0.693419	+	1.90515i	0.0425163	+	0.116812i
$267$	4.27342	+	0.210830i	0.261529	+	0.0129026i
$268$	4.18376	−	5.97503i	0.255564	−	0.364983i
$269$	20.9181			1.27540			0.637698	−	0.770286i	$-0.279887\pi$
$269$	20.9181			1.27540			0.637698	+	0.770286i	$0.279887\pi$
$270$	−1.78952	+	5.04640i	−0.108907	+	0.307114i
$271$	6.02125			0.365765			0.182882	−	0.983135i	$-0.441457\pi$
$271$	6.02125			0.365765			0.182882	+	0.983135i	$0.441457\pi$
$272$	−6.35604	+	9.07736i	−0.385391	+	0.550396i
$273$	1.12356	+	2.18850i	0.0680008	+	0.132454i
$274$	−0.160475	−	0.440902i	−0.00969467	−	0.0266359i
$275$	22.1919	+	0.815260i	1.33822	+	0.0491620i
$276$	−7.49587	+	9.65512i	−0.451198	+	0.581170i
$277$	3.27946	−	1.52924i	0.197044	−	0.0918830i	−0.321592	−	0.946878i	$-0.604218\pi$
$277$	3.27946	−	1.52924i	0.197044	−	0.0918830i	0.518636	+	0.854995i	$0.326440\pi$
$278$	−9.90842	−	2.65495i	−0.594267	−	0.159233i
$279$	−20.5309	−	21.0013i	−1.22916	−	1.25731i
$280$	11.6575	−	7.84769i	0.696667	−	0.468989i
$281$	−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	$-0.467633\pi$
$282$	−0.712391	+	0.768655i	−0.0424223	+	0.0457727i
$283$	−14.2969	+	10.0108i	−0.849863	+	0.595080i	−0.915298	−	0.402776i	$-0.868045\pi$
$283$	−14.2969	+	10.0108i	−0.849863	+	0.595080i	0.0654355	+	0.997857i	$0.479156\pi$
$284$	3.91627	−	22.2103i	0.232388	−	1.31794i
$285$	−1.70546	−	4.41438i	−0.101023	−	0.261485i
$286$	0.618469	−	0.518957i	0.0365708	−	0.0306866i
$287$	6.38599	−	1.71112i	0.376953	−	0.101004i
$288$	−12.4673	+	7.01097i	−0.734642	+	0.413125i
$289$	−0.871882	+	0.503381i	−0.0512872	+	0.0296107i
$290$	5.25212	+	0.0964406i	0.308415	+	0.00566318i
$291$	0.779218	+	0.604955i	0.0456786	+	0.0354631i
$292$	−7.38033	+	0.645696i	−0.431901	+	0.0377865i
$293$	−6.96793	+	14.9428i	−0.407071	+	0.872966i	0.590742	+	0.806861i	$0.298835\pi$
$293$	−6.96793	+	14.9428i	−0.407071	+	0.872966i	−0.997813	+	0.0661055i	$0.978943\pi$
$294$	−4.53205	−	1.45721i	−0.264314	−	0.0849863i
$295$	1.31040	+	0.377038i	0.0762946	+	0.0219520i
$296$		−	19.1940i		−	1.11563i
$297$	12.0675	+	19.6717i	0.700225	+	1.14147i
$298$	5.25803	+	5.25803i	0.304590	+	0.304590i
$299$	0.270414	+	1.53359i	0.0156384	+	0.0886899i
$300$	−12.6705	+	8.89564i	−0.731533	+	0.513590i
$301$	8.48992	−	3.09008i	0.489351	−	0.178109i
$302$	0.362352	+	4.14170i	0.0208510	+	0.238328i
$303$	−15.3066	−	20.1835i	−0.879340	−	1.15951i
$304$	1.15801	−	3.18160i	0.0664164	−	0.182477i
$305$	−4.45573	+	0.307515i	−0.255134	+	0.0176083i
$306$	5.51279	−	0.419463i	0.315145	−	0.0239791i
$307$	−4.98775	−	18.6145i	−0.284666	−	1.06239i	−0.949083	−	0.315026i	$-0.897987\pi$
$307$	−4.98775	−	18.6145i	−0.284666	−	1.06239i	0.664417	−	0.747362i	$-0.268680\pi$
$308$	2.49155	−	28.4785i	0.141969	−	1.62271i
$309$	26.3834	+	13.9247i	1.50090	+	0.792150i
$310$	1.56905	+	9.96505i	0.0891159	+	0.565977i
$311$	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	$0.517799\pi$
$312$	−0.264702	+	1.16280i	−0.0149858	+	0.0658305i
$313$	−4.56966	−	0.399794i	−0.258293	−	0.0225977i	−0.0427260	−	0.999087i	$-0.513604\pi$
$313$	−4.56966	−	0.399794i	−0.258293	−	0.0225977i	−0.215567	+	0.976489i	$0.569160\pi$
$314$	0.330565	−	0.572556i	0.0186549	−	0.0323112i
$315$	23.1347	+	6.94109i	1.30349	+	0.391086i
$316$	−10.7722	−	18.6580i	−0.605983	−	1.04959i
$317$	−9.81902	−	21.0570i	−0.551491	−	1.18268i	−0.962559	−	0.271072i	$-0.912622\pi$
$317$	−9.81902	−	21.0570i	−0.551491	−	1.18268i	0.411068	−	0.911605i	$-0.365156\pi$
$318$	−3.67722	−	1.54760i	−0.206208	−	0.0867853i
$319$	14.5537	−	17.3444i	0.814849	−	0.971099i
$320$	−7.43743	−	0.788525i	−0.415765	−	0.0440799i
$321$	9.76048	−	2.10594i	0.544777	−	0.117542i
$322$	−5.36567	−	3.75708i	−0.299017	−	0.209374i
$323$	−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
$327$	10.6701	+	6.88283i	0.590056	+	0.380621i
$328$	2.90462	+	1.35445i	0.160381	+	0.0747869i
$329$	3.62159	+	3.03887i	0.199665	+	0.167539i
$330$	0.535883	−	7.90869i	0.0294994	−	0.435359i
$331$	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	$0.438399\pi$
$332$	−1.24635	+	4.65146i	−0.0684026	+	0.255282i
$333$	25.5104	−	20.9181i	1.39796	−	1.14630i
$334$	−6.69131	−	3.86323i	−0.366132	−	0.211386i
$335$	−7.81644	−	4.70625i	−0.427058	−	0.257130i
$336$	9.20227	+	14.6268i	0.502025	+	0.797956i
$337$	4.64324	+	6.63124i	0.252934	+	0.361227i	0.925459	−	0.378847i	$-0.123679\pi$
$337$	4.64324	+	6.63124i	0.252934	+	0.361227i	−0.672526	+	0.740074i	$0.734791\pi$
$338$	−3.39501	−	4.84857i	−0.184664	−	0.263728i
$339$	−5.92618	+	11.2284i	−0.321866	+	0.609843i
$340$	13.6950	+	8.24570i	0.742716	+	0.447186i
$341$	37.6552	+	21.7402i	2.03914	+	1.17730i
$342$	−1.59380	+	0.559741i	−0.0861830	+	0.0302673i
$343$	0.965147	−	3.60198i	0.0521130	−	0.194489i
$344$	4.11560	+	1.49796i	0.221898	+	0.0807644i
$345$	12.6940	+	8.52242i	0.683422	+	0.458832i
$346$	2.69798	+	2.26387i	0.145044	+	0.121707i
$347$	−5.19509	−	2.42251i	−0.278887	−	0.130047i	0.278143	−	0.960540i	$-0.410281\pi$
$347$	−5.19509	−	2.42251i	−0.278887	−	0.130047i	−0.557030	+	0.830493i	$0.688059\pi$
$348$	−0.777779	+	15.7652i	−0.0416933	+	0.845105i
$349$	−3.63192	+	0.640405i	−0.194412	+	0.0342801i	−0.270006	−	0.962859i	$-0.587026\pi$
$349$	−3.63192	+	0.640405i	−0.194412	+	0.0342801i	0.0755941	+	0.997139i	$0.475915\pi$
$350$	−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
$353$	14.3970	+	10.0809i	0.766275	+	0.536551i	0.890107	−	0.455752i	$-0.150630\pi$
$353$	14.3970	+	10.0809i	0.766275	+	0.536551i	−0.123832	+	0.992303i	$0.539518\pi$
$354$	0.148988	−	0.463366i	0.00791864	−	0.0246276i
$355$	−28.0531	−	2.97422i	−1.48890	−	0.157855i
$356$	2.83851	−	3.38281i	0.150441	−	0.179288i
$357$	−3.11532	−	24.7451i	−0.164880	−	1.30965i
$358$	−0.820125	−	1.75876i	−0.0433449	−	0.0929535i
$359$	4.06033	+	7.03269i	0.214296	+	0.371171i	0.953055	−	0.302799i	$-0.0979210\pi$
$359$	4.06033	+	7.03269i	0.214296	+	0.371171i	−0.738759	+	0.673970i	$0.764588\pi$
$360$	6.42825	+	9.78635i	0.338798	+	0.515786i
$361$	−8.75349	+	15.1615i	−0.460710	+	0.797973i
$362$	2.73005	+	0.238849i	0.143488	+	0.0125536i
$363$	−11.0849	−	10.2735i	−0.581807	−	0.539220i
$364$	2.50044	+	0.440896i	0.131059	+	0.0231092i
$365$	1.44137	+	9.15417i	0.0754447	+	0.479151i
$366$	0.0605220	+	1.59312i	0.00316354	+	0.0832739i
$367$	1.48573	−	16.9819i	0.0775543	−	0.886450i	−0.853386	−	0.521279i	$-0.825455\pi$
$367$	1.48573	−	16.9819i	0.0775543	−	0.886450i	0.930940	−	0.365171i	$-0.118989\pi$
$368$	2.83121	+	10.5662i	0.147587	+	0.550801i
$369$	1.36535	+	5.33657i	0.0710775	+	0.277811i
$370$	−11.3045	+	0.780186i	−0.587692	+	0.0405599i
$371$	−6.15547	+	16.9120i	−0.319576	+	0.878028i
$372$	−30.0748	+	3.78632i	−1.55931	+	0.196311i
$373$	2.72173	+	31.1095i	0.140926	+	1.61079i	0.656760	+	0.754100i	$0.271927\pi$
$373$	2.72173	+	31.1095i	0.140926	+	1.61079i	−0.515834	+	0.856688i	$0.672518\pi$
$374$	−7.69144	+	2.79945i	−0.397715	+	0.144756i
$375$	12.1919	+	15.0452i	0.629588	+	0.776929i
$376$	0.397965	+	2.25697i	0.0205235	+	0.116394i
$377$	1.42194	+	1.42194i	0.0732339	+	0.0732339i
$378$	2.73188	−	8.17744i	0.140513	−	0.420602i
$379$		−	31.2281i		−	1.60408i	−0.597269	−	0.802041i	$-0.703748\pi$
$379$		−	31.2281i		−	1.60408i	0.597269	−	0.802041i	$-0.296252\pi$
$380$	−4.69383	−	1.35054i	−0.240788	−	0.0692813i
$381$	6.77334	−	6.13643i	0.347008	−	0.314379i
$382$	2.11182	−	4.52881i	0.108050	−	0.231714i
$383$	−33.6778	+	2.94643i	−1.72086	+	0.150555i	−0.904353	−	0.426786i	$-0.859646\pi$
$383$	−33.6778	+	2.94643i	−1.72086	+	0.150555i	−0.816503	+	0.577341i	$0.804090\pi$
$384$	−2.61191	+	19.0072i	−0.133289	+	0.969957i
$385$	−35.7523	−	0.656492i	−1.82211	−	0.0334579i
$386$	−0.245587	+	0.141790i	−0.0125001	+	0.00721691i
$387$	2.49437	+	7.10245i	0.126796	+	0.361038i
$388$	0.983453	−	0.263515i	0.0499272	−	0.0133780i
$389$	−20.9380	+	17.5690i	−1.06160	+	0.890786i	−0.994265	−	0.106945i	$-0.965893\pi$
$389$	−20.9380	+	17.5690i	−1.06160	+	0.890786i	−0.0673324	+	0.997731i	$0.521449\pi$
$390$	0.695599	+	0.108634i	0.0352230	+	0.00550090i
$391$	2.74149	−	15.5478i	0.138643	−	0.786284i
$392$	−8.52768	+	5.97114i	−0.430713	+	0.301588i
$393$	−1.19718	−	0.272529i	−0.0603898	−	0.0137473i
$394$	8.14085	+	9.70188i	0.410130	+	0.488774i
$395$	−22.3552	+	15.0493i	−1.12481	+	0.757212i
$396$	23.7031	+	2.34450i	1.19113	+	0.117815i
$397$	12.3324	+	3.30445i	0.618945	+	0.165846i	0.554648	−	0.832085i	$-0.312853\pi$
$397$	12.3324	+	3.30445i	0.618945	+	0.165846i	0.0642968	+	0.997931i	$0.479520\pi$
$398$	1.15752	−	0.539761i	0.0580213	−	0.0270558i
$399$	2.87623	+	7.05659i	0.143992	+	0.353271i
$400$	−0.508634	+	13.8454i	−0.0254317	+	0.692268i
$401$	−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	$-0.275063\pi$
$402$	−1.76540	+	2.73681i	−0.0880504	+	0.136500i
$403$	−2.21502	+	3.16338i	−0.110338	+	0.157579i
$404$	−26.1441			−1.30072
$405$	−6.00118	+	19.2090i	−0.298201	+	0.954503i
$406$	−8.45859			−0.419793
$407$	−28.0137	+	40.0078i	−1.38859	+	1.98311i
$408$	6.55369	−	10.1598i	0.324456	−	0.502986i
$409$	−0.987380	−	2.71280i	−0.0488228	−	0.134139i	0.912885	−	0.408218i	$-0.133850\pi$
$409$	−0.987380	−	2.71280i	−0.0488228	−	0.134139i	−0.961707	+	0.274078i	$0.911627\pi$
$410$	0.679648	−	1.76576i	0.0335654	−	0.0872045i
$411$	−0.665636	−	1.63308i	−0.0328334	−	0.0805538i
$412$	27.9052	−	13.0124i	1.37479	−	0.641076i
$413$	−2.12085	−	0.568280i	−0.104360	−	0.0279632i
$414$	3.18080	−	4.43491i	0.156328	−	0.217964i
$415$	5.91180	+	1.15470i	0.290199	+	0.0566821i
$416$	1.20891	+	1.44073i	0.0592719	+	0.0706375i
$417$	−37.5936	−	8.55791i	−1.84097	−	0.419082i
$418$	2.04857	−	1.43443i	0.100199	−	0.0701601i
$419$	−3.08760	+	17.5106i	−0.150839	+	0.855451i	0.811653	+	0.584140i	$0.198568\pi$
$419$	−3.08760	+	17.5106i	−0.150839	+	0.855451i	−0.962492	+	0.271310i	$0.912543\pi$
$420$	20.1361	−	14.6962i	0.982543	−	0.717103i
$421$	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	$0.261859\pi$
$422$	9.75758	−	2.61453i	0.474991	−	0.127274i
$423$	−2.56598	+	2.98862i	−0.124762	+	0.145312i
$424$	−7.55561	+	4.36223i	−0.366933	+	0.211849i
$425$	9.11019	−	17.7999i	0.441909	−	0.863421i
$426$	−1.37087	+	9.97600i	−0.0664189	+	0.483339i
$427$	7.16449	−	0.626811i	0.346714	−	0.0303335i
$428$	4.35531	−	9.34000i	0.210522	−	0.451466i
$429$	2.24885	−	2.03739i	0.108575	−	0.0983659i
$430$	0.714945	−	2.48480i	0.0344777	−	0.119828i
$431$		−	19.3828i		−	0.933636i	−0.884353	−	0.466818i	$-0.845400\pi$
$431$		−	19.3828i		−	0.933636i	0.884353	−	0.466818i	$-0.154600\pi$
$432$	−12.2730	+	7.52879i	−0.590484	+	0.362229i
$433$	−2.30954	−	2.30954i	−0.110989	−	0.110989i	0.649431	−	0.760420i	$-0.275007\pi$
$433$	−2.30954	−	2.30954i	−0.110989	−	0.110989i	−0.760420	+	0.649431i	$0.775007\pi$
$434$	−2.82071	−	15.9970i	−0.135398	−	0.767881i
$435$	19.7401	−	0.387176i	0.946465	−	0.0185637i
$436$	12.3146	−	4.48214i	0.589762	−	0.214656i
$437$	0.420414	+	4.80536i	0.0201111	+	0.229871i
$438$	3.28196	−	0.413188i	0.156818	−	0.0197429i
$439$	1.67858	−	4.61187i	0.0801144	−	0.220112i	−0.893168	−	0.449723i	$-0.851523\pi$
$439$	1.67858	−	4.61187i	0.0801144	−	0.220112i	0.973283	+	0.229610i	$0.0737451\pi$
$440$	−13.0721	−	11.3842i	−0.623187	−	0.542721i
$441$	−17.2297	−	4.82646i	−0.820464	−	0.229831i
$442$	−0.188153	−	0.702196i	−0.00894952	−	0.0334000i
$443$	−1.68450	+	19.2540i	−0.0800331	+	0.914783i	0.844968	+	0.534817i	$0.179620\pi$
$443$	−1.68450	+	19.2540i	−0.0800331	+	0.914783i	−0.925001	+	0.379965i	$0.875936\pi$
$444$	−1.29257	−	34.0243i	−0.0613426	−	1.61472i
$445$	−4.46580	−	3.25078i	−0.211699	−	0.154102i
$446$	−5.06133	−	0.892450i	−0.239661	−	0.0422587i
$447$	20.4988	+	18.9983i	0.969558	+	0.898588i
$448$	11.9973	+	1.04963i	0.566820	+	0.0495903i
$449$	1.49368	−	2.58713i	0.0704911	−	0.122094i	−0.828626	−	0.559803i	$-0.810877\pi$
$449$	1.49368	−	2.58713i	0.0704911	−	0.122094i	0.899117	+	0.437709i	$0.144210\pi$
$450$	5.50246	−	4.18376i	0.259389	−	0.197224i
$451$	−4.07753	−	7.06249i	−0.192003	−	0.332560i
$452$	5.53791	+	11.8761i	0.260481	+	0.558604i
$453$	1.95190	+	15.5040i	0.0917085	+	0.728442i
$454$	−3.78613	+	4.51214i	−0.177692	+	0.211765i
$455$	0.334839	−	3.15823i	0.0156975	−	0.148060i
$456$	−1.13074	+	3.51670i	−0.0529518	+	0.164684i
$457$	5.40989	+	3.78805i	0.253064	+	0.177197i	0.693224	−	0.720722i	$-0.256189\pi$
$457$	5.40989	+	3.78805i	0.253064	+	0.177197i	−0.440160	+	0.897919i	$0.645078\pi$
$458$	−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	$0.0220299\pi$
$462$	−0.628952	+	12.7486i	−0.0292615	+	0.593117i
$463$	4.94630	+	2.30650i	0.229874	+	0.107192i	0.534143	−	0.845394i	$-0.320634\pi$
$463$	4.94630	+	2.30650i	0.229874	+	0.107192i	−0.304269	+	0.952586i	$0.598412\pi$
$464$	10.8210	+	9.07991i	0.502353	+	0.421524i
$465$	7.31501	+	37.2037i	0.339225	+	1.72528i
$466$	2.15876	+	0.785723i	0.100002	+	0.0363979i
$467$	−2.61200	+	9.74812i	−0.120869	+	0.451089i	−0.999659	−	0.0261197i	$-0.991685\pi$
$467$	−2.61200	+	9.74812i	−0.120869	+	0.451089i	0.878790	+	0.477209i	$0.158352\pi$
$468$	−0.390919	+	2.07906i	−0.0180702	+	0.0961047i
$469$	12.7233	+	7.34582i	0.587509	+	0.339199i
$470$	1.31309	−	0.326125i	0.0605681	−	0.0150430i
$471$	1.15987	−	2.19762i	0.0534439	−	0.101261i
$472$	−0.610502	−	0.871887i	−0.0281006	−	0.0401319i
$473$	−6.39222	−	9.12904i	−0.293915	−	0.419753i
$474$	5.12251	+	8.14210i	0.235285	+	0.373979i
$475$	−1.28107	+	5.97365i	−0.0587793	+	0.274090i
$476$	−22.2923	−	12.8704i	−1.02176	−	0.589916i
$477$	−14.0320	−	5.28793i	−0.642481	−	0.242118i
$478$	−0.867168	+	3.23632i	−0.0396634	+	0.148026i
$479$	−4.22629	−	1.53824i	−0.193104	−	0.0702841i	0.243658	−	0.969861i	$-0.421653\pi$
$479$	−4.22629	−	1.53824i	−0.193104	−	0.0702841i	−0.436762	+	0.899577i	$0.643875\pi$
$480$	18.4233	+	1.24834i	0.840907	+	0.0569788i
$481$	−3.32297	−	2.78830i	−0.151514	−	0.127136i
$482$	−8.24398	−	3.84423i	−0.375503	−	0.175100i
$483$	−20.6889	−	13.3455i	−0.941376	−	0.607243i
$484$	−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	−0.761439	−	0.648237i	$-0.775507\pi$
$487$	−2.49814	+	2.49814i	−0.113202	+	0.113202i	0.648237	+	0.761439i	$0.275507\pi$
$488$	2.85585	+	1.99969i	0.129278	+	0.0905215i
$489$	−15.9678	+	3.44524i	−0.722088	+	0.155799i
$490$	3.86338	+	4.77973i	0.174530	+	0.215926i
$491$	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	$0.108531\pi$
$492$	5.24009	+	2.20536i	0.236242	+	0.0994253i
$493$	−8.61596	−	18.4770i	−0.388043	−	0.832162i
$494$	0.111058	+	0.192358i	0.00499673	+	0.00865459i
$495$	0.884265	−	29.7805i	0.0397448	−	1.33854i
$496$	−13.5636	+	23.4928i	−0.609022	+	1.05486i
$497$	45.2524	+	3.95907i	2.02985	+	0.177589i
$498$	0.477248	−	2.09648i	0.0213860	−	0.0939455i
$499$	−16.9468	−	2.98818i	−0.758644	−	0.133769i	−0.219072	−	0.975709i	$-0.570303\pi$
$499$	−16.9468	−	2.98818i	−0.758644	−	0.133769i	−0.539572	+	0.841939i	$0.681414\pi$
$500$	19.9761	−	0.643173i	0.893357	−	0.0287636i
$501$	−25.6830	−	13.5551i	−1.14743	−	0.605596i
$502$	−0.682721	+	7.80354i	−0.0304713	+	0.348289i
$503$	−10.3567	−	38.6515i	−0.461780	−	1.72339i	−0.667349	−	0.744745i	$-0.732571\pi$
$503$	−10.3567	−	38.6515i	−0.461780	−	1.72339i	0.205569	−	0.978643i	$-0.434095\pi$
$504$	−10.6386	−	15.5657i	−0.473879	−	0.693350i
$505$	2.25162	+	32.6247i	0.100196	+	1.45178i
$506$	−2.76346	+	7.59255i	−0.122851	+	0.337530i
$507$	−13.4431	−	17.7262i	−0.597027	−	0.787250i
$508$	−0.822142	−	9.39712i	−0.0364766	−	0.416930i
$509$	36.9106	−	13.4344i	1.63604	−	0.595468i	0.649696	−	0.760194i	$-0.274896\pi$
$509$	36.9106	−	13.4344i	1.63604	−	0.595468i	0.986339	+	0.164726i	$0.0526738\pi$
$510$	−6.25010	−	3.44688i	−0.276759	−	0.152630i
$511$	−2.59118	−	14.6953i	−0.114627	−	0.650081i
$512$	16.1816	+	16.1816i	0.715134	+	0.715134i
$513$	−5.90627	+	2.32973i	−0.260768	+	0.102860i
$514$		−	7.13031i		−	0.314504i
$515$	−18.6412	−	33.7017i	−0.821430	−	1.48507i
$516$	7.39639	+	2.37820i	0.325608	+	0.104694i
$517$	2.46454	−	5.28523i	0.108390	−	0.232444i
$518$	18.1768	−	1.59026i	0.798642	−	0.0698721i
$519$	10.4563	+	8.11787i	0.458980	+	0.356335i
$520$	1.10844	−	1.06847i	0.0486085	−	0.0468556i
$521$	−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	$0.567485\pi$
$522$	0.0798049	−	7.04720i	0.00349296	−	0.308447i
$523$	−4.33233	+	1.16084i	−0.189439	+	0.0507602i	−0.352291	−	0.935890i	$-0.614597\pi$
$523$	−4.33233	+	1.16084i	−0.189439	+	0.0507602i	0.162852	+	0.986651i	$0.447931\pi$
$524$	−0.970744	+	0.814551i	−0.0424071	+	0.0355838i
$525$	−20.0733	−	23.8618i	−0.876073	−	1.04141i
$526$	2.02403	−	11.4789i	0.0882521	−	0.500503i
$527$	32.0708	−	22.4562i	1.39702	−	0.978207i
$528$	14.4896	−	15.6340i	0.630580	−	0.680383i
$529$	4.76651	+	5.68051i	0.207240	+	0.246979i
$530$	2.87629	+	4.27263i	0.124938	+	0.185591i
$531$	0.493467	−	1.76160i	0.0214146	−	0.0764471i
$532$	7.59683	+	2.03556i	0.329364	+	0.0882529i
$533$	0.656441	−	0.306103i	0.0284336	−	0.0132588i
$534$	−1.20913	+	1.55743i	−0.0523241	+	0.0673965i
$535$	−12.0303	−	4.63052i	−0.520115	−	0.200195i
$536$	2.43586	+	6.69246i	0.105213	+	0.289070i
$537$	−3.33124	−	6.48868i	−0.143754	−	0.280007i
$538$	−5.52902	+	7.89626i	−0.238373	+	0.340432i
$539$	26.4898			1.14100
$540$	12.0541	+	16.9149i	0.518724	+	0.727901i
$541$	4.96440			0.213436			0.106718	−	0.994289i	$-0.465966\pi$
$541$	4.96440			0.213436			0.106718	+	0.994289i	$0.465966\pi$
$542$	−1.59153	+	2.27293i	−0.0683619	+	0.0976309i
$543$	10.2878	+	0.507551i	0.441493	+	0.0217811i
$544$	−6.52135	−	17.9173i	−0.279601	−	0.768196i
$545$	−6.65375	−	14.9811i	−0.285015	−	0.641720i
$546$	−1.12310	−	0.154333i	−0.0480644	−	0.00660486i
$547$	−13.1847	+	6.14812i	−0.563737	+	0.262875i	−0.683528	−	0.729924i	$-0.739555\pi$
$547$	−13.1847	+	6.14812i	−0.563737	+	0.262875i	0.119791	+	0.992799i	$0.461777\pi$
$548$	−1.75810	−	0.471083i	−0.0751025	−	0.0201237i
$549$	0.454627	+	5.97494i	0.0194030	+	0.255004i
$550$	−6.17348	+	8.16164i	−0.263238	+	0.348014i
$551$	4.00394	+	4.77171i	0.170574	+	0.203282i
$552$	−3.52435	−	11.4025i	−0.150006	−	0.485323i
$553$	35.5462	−	24.8897i	1.51158	−	1.05842i
$554$	−0.289556	+	1.64216i	−0.0123021	+	0.0697685i
$555$	−42.3470	+	4.54326i	−1.79753	+	0.192850i
$556$	−30.4831	+	25.5783i	−1.29277	+	1.08476i
$557$	−29.0814	+	7.79233i	−1.23222	+	0.330171i	−0.815442	−	0.578838i	$-0.803506\pi$
$557$	−29.0814	+	7.79233i	−1.23222	+	0.330171i	−0.416774	+	0.909010i	$0.636840\pi$
$558$	13.3544	−	2.19912i	0.565336	−	0.0930960i
$559$	0.857203	−	0.494906i	0.0362558	−	0.0209323i
$560$	0.409580	−	22.3056i	0.0173079	−	0.942583i
$561$	−28.4887	+	11.6119i	−1.20279	+	0.490253i
$562$	10.7250	−	0.938313i	0.452405	−	0.0395803i
$563$	−9.07139	+	19.4537i	−0.382314	+	0.819874i	0.617141	+	0.786852i	$0.288291\pi$
$563$	−9.07139	+	19.4537i	−0.382314	+	0.819874i	−0.999455	+	0.0330215i	$0.989487\pi$
$564$	0.857442	+	3.97402i	0.0361048	+	0.167337i
$565$	14.3430	−	7.93345i	0.603414	−	0.333763i
$566$		−	8.04291i		−	0.338069i
$567$	9.09383	−	31.1033i	0.381905	−	1.30621i
$568$	15.5708	+	15.5708i	0.653338	+	0.653338i
$569$	2.94509	+	16.7024i	0.123465	+	0.700202i	0.982208	+	0.187796i	$0.0601345\pi$
$569$	2.94509	+	16.7024i	0.123465	+	0.700202i	−0.858743	+	0.512406i	$0.828754\pi$
$570$	2.11715	+	0.523015i	0.0886776	+	0.0219067i
$571$	−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	$0.607152\pi$
$572$	−0.272963	−	3.11998i	−0.0114132	−	0.130453i
$573$	7.28555	−	17.3110i	0.304358	−	0.723177i
$574$	−1.04201	+	2.86290i	−0.0434927	+	0.119495i
$575$	−7.67955	−	18.1835i	−0.320259	−	0.758305i
$576$	−0.987681	+	9.98555i	−0.0411534	+	0.416065i
$577$	7.49741	+	27.9807i	0.312121	+	1.16485i	0.926640	+	0.375950i	$0.122684\pi$
$577$	7.49741	+	27.9807i	0.312121	+	1.16485i	−0.614518	+	0.788903i	$0.710650\pi$
$578$	0.0404352	−	0.462176i	0.00168188	−	0.0192240i
$579$	−0.902164	+	0.567587i	−0.0374927	+	0.0235881i
$580$	11.9926	−	16.4749i	0.497965	−	0.684084i
$581$	−9.55194	−	1.68426i	−0.396281	−	0.0698751i
$582$	−0.434323	+	0.134243i	−0.0180033	+	0.00556454i
$583$	22.1155	+	1.93485i	0.915929	+	0.0801334i
$584$	3.61681	−	6.26451i	0.149665	−	0.259227i
$585$	2.62809	+	0.308765i	0.108658	+	0.0127659i
$586$	−3.79893	−	6.57994i	−0.156932	−	0.271815i
$587$	−2.76499	−	5.92953i	−0.114123	−	0.244738i	0.840947	−	0.541117i	$-0.181999\pi$
$587$	−2.76499	−	5.92953i	−0.114123	−	0.244738i	−0.955070	+	0.296379i	$0.904221\pi$
$588$	−14.7145	+	11.1590i	−0.606815	+	0.460190i
$589$	−7.68913	+	9.16355i	−0.316825	+	0.377578i
$590$	−0.488690	+	0.395000i	−0.0201190	+	0.0162619i
$591$	31.9603	+	35.2775i	1.31467	+	1.45112i
$592$	−24.9605	−	17.4775i	−1.02587	−	0.718322i
$593$	−22.3175	+	22.3175i	−0.916469	+	0.916469i	−0.996771	−	0.0803015i	$-0.974412\pi$
$593$	−22.3175	+	22.3175i	−0.916469	+	0.916469i	0.0803015	+	0.996771i	$0.474412\pi$
$594$	−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
$597$	4.27049	−	2.19244i	0.174780	−	0.0897305i
$598$	−0.650384	−	0.303279i	−0.0265962	−	0.0124020i
$599$	−8.78838	−	7.37433i	−0.359083	−	0.301307i	0.445342	−	0.895361i	$-0.353082\pi$
$599$	−8.78838	−	7.37433i	−0.359083	−	0.301307i	−0.804425	+	0.594054i	$0.797527\pi$
$600$	−0.0189103	−	15.1159i	−0.000772010	−	0.617105i
$601$	−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	$0.829895\pi$
$602$	−1.07758	+	4.02159i	−0.0439189	+	0.163908i
$603$	−6.24015	+	10.5310i	−0.254118	+	0.428857i
$604$	13.9672	+	8.06397i	0.568317	+	0.328118i
$605$	4.70310	+	18.9363i	0.191208	+	0.769868i
$606$	11.6648	−	0.443141i	0.473850	−	0.0180014i
$607$	−8.41759	−	12.0216i	−0.341659	−	0.487940i	0.611148	−	0.791517i	$-0.290708\pi$
$607$	−8.41759	−	12.0216i	−0.341659	−	0.487940i	−0.952807	+	0.303576i	$0.901819\pi$
$608$	3.34151	+	4.77216i	0.135516	+	0.193537i
$609$	−31.7694	+	1.20691i	−1.28736	+	0.0489064i
$610$	1.06165	−	1.76326i	0.0429849	−	0.0713922i
$611$	0.448550	+	0.258971i	0.0181464	+	0.0104768i
$612$	10.9332	−	18.4512i	0.441949	−	0.745844i
$613$	−5.20779	+	19.4357i	−0.210341	+	0.785002i	0.777414	+	0.628989i	$0.216531\pi$
$613$	−5.20779	+	19.4357i	−0.210341	+	0.785002i	−0.987755	+	0.156013i	$0.950136\pi$
$614$	8.34507	+	3.03736i	0.336780	+	0.122578i
$615$	2.30073	−	6.72894i	0.0927744	−	0.271337i
$616$	21.3821	+	17.9418i	0.861511	+	0.722894i
$617$	−2.70196	−	1.25995i	−0.108777	−	0.0507236i	0.367468	−	0.930036i	$-0.380225\pi$
$617$	−2.70196	−	1.25995i	−0.108777	−	0.0507236i	−0.476245	+	0.879313i	$0.658002\pi$
$618$	−12.2300	+	6.27878i	−0.491962	+	0.252569i
$619$	13.1500	−	2.31870i	0.528542	−	0.0931962i	0.0969919	−	0.995285i	$-0.469078\pi$
$619$	13.1500	−	2.31870i	0.528542	−	0.0931962i	0.431550	+	0.902089i	$0.357967\pi$
$620$	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
$623$	7.28589	+	5.10163i	0.291903	+	0.204393i
$624$	1.27111	+	1.40304i	0.0508851	+	0.0561665i
$625$	−2.52301	−	24.8724i	−0.100920	−	0.994895i
$626$	1.35876	−	1.61931i	0.0543070	−	0.0647206i
$627$	7.48952	−	5.67983i	0.299103	−	0.226831i
$628$	−1.08388	−	2.32438i	−0.0432514	−	0.0927529i
$629$	21.9887	+	38.0856i	0.876748	+	1.51857i
$630$	−8.73510	+	6.89837i	−0.348015	+	0.274838i
$631$	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	$0.157874\pi$
$632$	20.9557	+	1.83339i	0.833575	+	0.0729283i
$633$	36.2752	−	11.2121i	1.44181	−	0.445642i
$634$	10.5440	+	1.85920i	0.418758	+	0.0738383i
$635$	−11.6557	+	1.83525i	−0.462542	+	0.0728295i
$636$	−13.0997	+	8.24153i	−0.519437	+	0.326798i
$637$	−0.205054	+	2.34378i	−0.00812453	+	0.0928638i
$638$	2.70046	+	10.0782i	0.106912	+	0.399001i
$639$	−3.72541	+	37.6643i	−0.147375	+	1.48998i
$640$	16.2667	−	18.6785i	0.642999	−	0.738332i
$641$	−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	$0.986051\pi$
$642$	−1.78491	+	4.24108i	−0.0704448	+	0.167382i
$643$	3.60391	+	41.1928i	0.142124	+	1.62449i	0.647833	+	0.761783i	$0.275676\pi$
$643$	3.60391	+	41.1928i	0.142124	+	1.62449i	−0.505708	+	0.862705i	$0.668769\pi$
$644$	−23.8775	+	8.69071i	−0.940906	+	0.342462i
$645$	2.33071	−	9.43463i	0.0917714	−	0.371488i
$646$	−0.391028	−	2.21763i	−0.0153848	−	0.0872514i
$647$	−12.4891	−	12.4891i	−0.490997	−	0.490997i	0.417623	−	0.908620i	$-0.362863\pi$
$647$	−12.4891	−	12.4891i	−0.490997	−	0.490997i	−0.908620	+	0.417623i	$0.862863\pi$
$648$	13.0688	−	8.71657i	0.513389	−	0.342419i
$649$			2.70837i			0.106313i
$650$	−0.674340	−	0.609397i	−0.0264498	−	0.0239025i
$651$	−12.8767	−	59.6804i	−0.504680	−	2.33906i
$652$	−7.12513	+	15.2799i	−0.279042	+	0.598407i
$653$	14.6673	−	1.28323i	0.573977	−	0.0502165i	0.203528	−	0.979069i	$-0.434759\pi$
$653$	14.6673	−	1.28323i	0.573977	−	0.0502165i	0.370449	+	0.928853i	$0.379204\pi$
$654$	−5.41846	+	2.20854i	−0.211879	+	0.0863608i
$655$	1.10007	+	1.14122i	0.0429831	+	0.0445912i
$656$	4.40623	−	2.54394i	0.172034	−	0.0993241i
$657$	12.2677	−	2.02017i	0.478608	−	0.0788142i
$658$	−2.10438	+	0.563868i	−0.0820374	+	0.0219819i
$659$	21.0565	−	17.6685i	0.820245	−	0.688268i	−0.132784	−	0.991145i	$-0.542392\pi$
$659$	21.0565	−	17.6685i	0.820245	−	0.688268i	0.953030	+	0.302877i	$0.0979473\pi$
$660$	−23.9389	−	19.2999i	−0.931819	−	0.751248i
$661$	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	$-0.00664165\pi$
$662$	−7.09243	+	4.96617i	−0.275655	+	0.193016i
$663$	−0.806871	−	2.61052i	−0.0313363	−	0.101384i
$664$	−3.02230	−	3.60183i	−0.117288	−	0.139778i
$665$	1.88588	−	9.65524i	0.0731312	−	0.374414i
$666$	1.15342	+	15.1588i	0.0446941	+	0.587392i
$667$	−19.4392	−	5.20873i	−0.752690	−	0.201683i
$668$	−27.1644	+	12.6670i	−1.05102	+	0.490100i
$669$	−19.1371	−	2.62976i	−0.739883	−	0.101672i
$670$	3.84257	−	1.70665i	0.148451	−	0.0659336i
$671$	−3.03414	−	8.33623i	−0.117132	−	0.321816i
$672$	−29.6979	−	1.46515i	−1.14562	−	0.0565193i
$673$	0.148446	−	0.212002i	0.00572216	−	0.00817209i	−0.816281	−	0.577655i	$-0.803968\pi$
$673$	0.148446	−	0.212002i	0.00572216	−	0.00817209i	0.822003	+	0.569483i	$0.192857\pi$
$674$	−3.73049			−0.143693
$675$	20.0696	−	16.4988i	0.772480	−	0.635039i
$676$	−22.9612			−0.883122
$677$	14.0797	−	20.1079i	0.541128	−	0.772810i	−0.451725	−	0.892157i	$-0.649191\pi$
$677$	14.0797	−	20.1079i	0.541128	−	0.772810i	0.992853	+	0.119347i	$0.0380801\pi$
$678$	−2.67216	−	5.20492i	−0.102624	−	0.199894i
$679$	0.701384	+	1.92704i	0.0269167	+	0.0739529i
$680$	−14.2647	+	6.33557i	−0.547027	+	0.242958i
$681$	−13.5764	+	17.4873i	−0.520251	+	0.670113i
$682$	−18.1596	+	8.46795i	−0.695366	+	0.324255i
$683$	21.4623	+	5.75081i	0.821232	+	0.220048i	0.644885	−	0.764280i	$-0.276905\pi$
$683$	21.4623	+	5.75081i	0.821232	+	0.220048i	0.176347	+	0.984328i	$0.443572\pi$
$684$	−1.76759	+	6.31002i	−0.0675853	+	0.241270i
$685$	−0.436441	+	2.23448i	−0.0166756	+	0.0853749i
$686$	1.10459	+	1.31640i	0.0421734	+	0.0502603i
$687$	−17.5129	+	18.8960i	−0.668158	+	0.720929i
$688$	5.69553	−	3.98805i	0.217140	−	0.152043i
$689$	−0.342385	+	1.94176i	−0.0130438	+	0.0739753i
$690$	−6.57235	+	2.53917i	−0.250205	+	0.0966647i
$691$	−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	$0.279398\pi$
$692$	13.1969	−	3.53610i	0.501672	−	0.134422i
$693$	−0.543249	+	47.9718i	−0.0206363	+	1.82230i
$694$	2.28762	−	1.32076i	0.0868369	−	0.0501353i
$695$	34.5440	+	35.8363i	1.31033	+	1.35935i
$696$	−12.1737	−	9.45117i	−0.461441	−	0.358246i
$697$	−7.31513	+	0.639991i	−0.277080	+	0.0242414i
$698$	0.718239	−	1.54027i	0.0271857	−	0.0583000i
$699$	8.22014	+	2.64306i	0.310914	+	0.0999697i
$700$	−32.1418	+	1.62603i	−1.21485	+	0.0614582i
$701$			38.5968i			1.45778i	0.684630	+	0.728891i	$0.259964\pi$
$701$			38.5968i			1.45778i	−0.684630	+	0.728891i	$0.740036\pi$
$702$	0.139178	−	0.934247i	0.00525292	−	0.0352609i
$703$	−9.50124	−	9.50124i	−0.358346	−	0.358346i
$704$	−2.57960	−	14.6297i	−0.0972225	−	0.551376i
$705$	4.88526	−	1.41224i	0.183989	−	0.0531881i
$706$	−7.61078	+	2.77010i	−0.286435	+	0.104254i
$707$	−4.58950	−	52.4582i	−0.172606	−	1.97289i
$708$	−1.14092	−	1.50444i	−0.0428784	−	0.0565402i
$709$	−16.0622	+	44.1305i	−0.603228	+	1.65735i	0.141463	+	0.989944i	$0.454819\pi$
$709$	−16.0622	+	44.1305i	−0.603228	+	1.65735i	−0.744690	+	0.667410i	$0.767403\pi$
$710$	8.53766	−	9.80348i	0.320413	−	0.367918i
$711$	20.4013	+	29.8499i	0.765108	+	1.11946i
$712$	1.11595	+	4.16477i	0.0418219	+	0.156081i
$713$	3.36838	−	38.5007i	0.126147	−	1.44186i
$714$	10.1644	+	5.36459i	0.380391	+	0.200765i
$715$	−3.86986	+	0.609329i	−0.144725	+	0.0227876i
$716$	−7.41357	−	1.30721i	−0.277058	−	0.0488528i
$717$	−2.79521	+	12.2789i	−0.104389	+	0.458566i
$718$	−3.72796	−	0.326154i	−0.139126	−	0.0121720i
$719$	−0.577250	+	0.999826i	−0.0215278	+	0.0372872i	−0.876589	−	0.481241i	$-0.840186\pi$
$719$	−0.577250	+	0.999826i	−0.0215278	+	0.0372872i	0.855061	+	0.518528i	$0.173520\pi$
$720$	18.5798	+	0.551686i	0.692430	+	0.0205601i
$721$	31.0080	+	53.7075i	1.15480	+	2.00017i
$722$	−3.40954	−	7.31177i	−0.126890	−	0.272116i
$723$	−31.5119	−	13.2622i	−1.17194	−	0.493226i
$724$	6.83343	−	8.14376i	0.253962	−	0.302660i
$725$	−21.5916	−	13.5464i	−0.801891	−	0.503102i
$726$	6.80805	−	1.46892i	0.252671	−	0.0545167i
$727$	32.4399	+	22.7146i	1.20313	+	0.842439i	0.990876	−	0.134776i	$-0.0430313\pi$
$727$	32.4399	+	22.7146i	1.20313	+	0.842439i	0.212252	+	0.977215i	$0.431920\pi$
$728$	−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
$732$	5.19708	+	3.35242i	0.192090	+	0.123909i
$733$	−6.22149	−	2.90113i	−0.229796	−	0.107156i	0.304310	−	0.952573i	$-0.401574\pi$
$733$	−6.22149	−	2.90113i	−0.229796	−	0.107156i	−0.534106	+	0.845417i	$0.679352\pi$
$734$	6.01773	+	5.04948i	0.222119	+	0.186380i
$735$	15.1924	+	17.4009i	0.560379	+	0.641840i
$736$	−17.6869	−	6.43750i	−0.651948	−	0.237290i
$737$	4.69039	−	17.5048i	0.172773	−	0.644797i
$738$	−2.37537	−	0.895152i	−0.0874385	−	0.0329510i
$739$	−28.7899	−	16.6218i	−1.05905	−	0.611444i	−0.133882	−	0.990997i	$-0.542744\pi$
$739$	−28.7899	−	16.6218i	−1.05905	−	0.611444i	−0.925170	+	0.379553i	$0.876078\pi$
$740$	−22.6736	+	37.6579i	−0.833500	+	1.38433i
$741$	0.444567	+	0.706627i	0.0163316	+	0.0259586i
$742$	−4.75704	−	6.79375i	−0.174636	−	0.249406i
$743$	−9.68027	−	13.8249i	−0.355135	−	0.507185i	0.601343	−	0.798991i	$-0.294633\pi$
$743$	−9.68027	−	13.8249i	−0.355135	−	0.507185i	−0.956477	+	0.291806i	$0.905744\pi$
$744$	13.8146	−	26.1747i	0.506468	−	0.959611i
$745$	−8.69721	−	35.0178i	−0.318641	−	1.28295i
$746$	−12.4628	−	7.19539i	−0.456295	−	0.263442i
$747$	1.49335	−	7.94222i	0.0546388	−	0.290591i
$748$	−8.21793	+	30.6697i	−0.300477	+	1.12140i
$749$	19.5053	+	7.09934i	0.712707	+	0.259404i
$750$	−8.90188	+	0.625559i	−0.325051	+	0.0228422i
$751$	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	$0.467745\pi$
$752$	3.29741	+	1.53761i	0.120244	+	0.0560708i
$753$	−1.45078	+	29.4066i	−0.0528692	+	1.07163i
$754$	−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	−0.369036	−	0.929415i	$-0.620312\pi$
$757$	15.4181	−	15.4181i	0.560380	−	0.560380i	0.929415	+	0.369036i	$0.120312\pi$
$758$	11.7882	+	8.25417i	0.428166	+	0.299805i
$759$	−9.29589	+	28.9110i	−0.337419	+	1.04940i
$760$	3.70889	−	2.99784i	0.134536	−	0.108743i
$761$	−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	$0.361131\pi$
$762$	0.526098	+	4.17881i	0.0190585	+	0.151382i
$763$	11.1552	+	23.9224i	0.403845	+	0.866049i
$764$	−9.69221	−	16.7874i	−0.350652	−	0.607347i
$765$	−23.9664	−	12.0543i	−0.866509	−	0.435823i
$766$	7.78943	−	13.4917i	0.281443	−	0.487474i
$767$	−0.239632	−	0.0209651i	−0.00865263	−	0.000757007i
$768$	2.01350	+	1.86612i	0.0726560	+	0.0673377i
$769$	40.5586	+	7.15158i	1.46258	+	0.257893i	0.847594	−	0.530645i	$-0.178050\pi$
$769$	40.5586	+	7.15158i	1.46258	+	0.257893i	0.614987	+	0.788537i	$0.289161\pi$
$770$	9.69781	−	13.3225i	0.349485	−	0.480109i
$771$	−1.01738	−	26.7806i	−0.0366401	−	0.964479i
$772$	−0.0958772	+	1.09588i	−0.00345069	+	0.0394416i
$773$	−3.85511	−	14.3875i	−0.138659	−	0.517481i	−0.999956	−	0.00937966i	$-0.997014\pi$
$773$	−3.85511	−	14.3875i	−0.138659	−	0.517481i	0.861297	−	0.508101i	$-0.169652\pi$
$774$	−3.34038	−	0.935719i	−0.120067	−	0.0336337i
$775$	18.4190	−	45.3517i	0.661631	−	1.62908i
$776$	−0.340005	+	0.934157i	−0.0122055	+	0.0335343i
$777$	68.0429	−	8.56637i	2.44103	−	0.307317i
$778$	−1.09777	−	12.5476i	−0.0393571	−	0.449853i
$779$	2.10828	−	0.767352i	0.0755370	−	0.0274932i
$780$	1.89293	−	1.96867i	0.0677778	−	0.0704898i
$781$	−9.72994	−	55.1812i	−0.348165	−	1.97454i
$782$	5.14443	+	5.14443i	0.183964	+	0.183964i
$783$	−0.705786	−	26.4798i	−0.0252228	−	0.946311i
$784$			16.5268i			0.590243i
$785$	−2.80720	+	1.55273i	−0.100193	+	0.0554194i
$786$	0.419313	−	0.379884i	0.0149564	−	0.0135500i
$787$	6.57073	−	14.0910i	0.234221	−	0.502289i	−0.753705	−	0.657212i	$-0.771735\pi$
$787$	6.57073	−	14.0910i	0.234221	−	0.502289i	0.987926	+	0.154924i	$0.0495132\pi$
$788$	48.9430	−	4.28196i	1.74352	−	0.152538i
$789$	5.96418	−	43.4020i	0.212330	−	1.54515i
$790$	0.227996	−	12.4166i	0.00811172	−	0.441762i
$791$	−22.8572	+	13.1966i	−0.812708	+	0.469217i
$792$	−15.1497	+	17.6451i	−0.538323	+	0.626990i
$793$	0.761062	−	0.203926i	0.0270261	−	0.00724162i
$794$	−4.50706	+	3.78187i	−0.159950	+	0.134214i
$795$	11.4126	+	15.6371i	0.404764	+	0.554589i
$796$	0.860335	−	4.87920i	0.0304938	−	0.172939i
$797$	−24.7774	+	17.3493i	−0.877661	+	0.614545i	−0.923159	−	0.384419i	$-0.874402\pi$
$797$	−24.7774	+	17.3493i	−0.877661	+	0.614545i	0.0454973	+	0.998964i	$0.485513\pi$
$798$	−3.42400	−	0.779448i	−0.121208	−	0.0275922i
$799$	−3.37525	−	4.02246i	−0.119408	−	0.142305i
$800$	−19.0126	−	14.3812i	−0.672197	−	0.508451i
$801$	−4.31912	+	6.02204i	−0.152609	+	0.212778i
$802$	8.78157	+	2.35301i	0.310088	+	0.0830878i
$803$	−16.6819	+	7.77889i	−0.588691	+	0.274511i
$804$	4.76861	+	11.6994i	0.168176	+	0.412604i
$805$	12.9014	+	29.0478i	0.454714	+	1.02380i
$806$	−0.608660	−	1.67228i	−0.0214391	−	0.0589035i
$807$	−19.6397	+	30.4463i	−0.691349	+	1.07176i
$808$	14.6416	−	20.9104i	0.515091	−	0.735627i
$809$	−38.2730			−1.34561			−0.672804	−	0.739821i	$-0.734910\pi$
$809$	−38.2730			−1.34561			−0.672804	+	0.739821i	$0.734910\pi$
$810$	−5.66490	−	7.34265i	−0.199044	−	0.257994i
$811$	46.0127			1.61572			0.807862	−	0.589371i	$-0.200624\pi$
$811$	46.0127			1.61572			0.807862	+	0.589371i	$0.200624\pi$
$812$	−18.8206	+	26.8786i	−0.660474	+	0.943254i
$813$	−5.65327	+	8.76395i	−0.198269	+	0.307365i
$814$	−7.69781	−	21.1496i	−0.269808	−	0.741292i
$815$	19.6811	+	7.57536i	0.689399	+	0.265353i
$816$	−7.24454	−	17.7739i	−0.253610	−	0.622209i
$817$	2.77876	−	1.29576i	0.0972166	−	0.0453329i
$818$	1.28503	+	0.344322i	0.0449299	+	0.0120389i
$819$	−4.24026	−	0.419408i	−0.148167	−	0.0146553i
$820$	−4.09875	−	6.08856i	−0.143135	−	0.212622i
$821$	−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	$-0.527743\pi$
$822$	0.792404	+	0.180385i	0.0276382	+	0.00629164i
$823$	33.1012	−	23.1777i	1.15383	−	0.807923i	0.169726	−	0.985491i	$-0.445712\pi$
$823$	33.1012	−	23.1777i	1.15383	−	0.807923i	0.984109	+	0.177568i	$0.0568230\pi$
$824$	−5.22041	+	29.6064i	−0.181861	+	1.03139i
$825$	−22.0223	+	31.5350i	−0.766718	+	1.09791i
$826$	0.775097	−	0.650383i	0.0269691	−	0.0226297i
$827$	−38.7205	+	10.3751i	−1.34645	+	0.360779i	−0.858821	−	0.512275i	$-0.828803\pi$
$827$	−38.7205	+	10.3751i	−1.34645	+	0.360779i	−0.487624	+	0.873054i	$0.662136\pi$
$828$	−7.01530	−	19.9753i	−0.243799	−	0.694191i
$829$	27.2086	−	15.7089i	0.944994	−	0.545593i	0.0534718	−	0.998569i	$-0.482971\pi$
$829$	27.2086	−	15.7089i	0.944994	−	0.545593i	0.891522	+	0.452977i	$0.149638\pi$
$830$	−1.99848	+	1.92641i	−0.0693683	+	0.0668667i
$831$	−0.853229	+	6.20905i	−0.0295982	+	0.215390i
$832$	1.31438	−	0.114993i	0.0455678	−	0.00398666i
$833$	10.0804	−	21.6175i	0.349265	−	0.749002i
$834$	13.1672	−	11.9290i	0.455942	−	0.413069i
$835$	18.1464	+	32.8070i	0.627980	+	1.13533i
$836$		−	9.70133i		−	0.335527i
$837$	49.8436	−	10.1651i	1.72285	−	0.351356i
$838$	−5.79390	−	5.79390i	−0.200147	−	0.200147i
$839$	−4.95377	−	28.0942i	−0.171023	−	0.969920i	−0.942635	−	0.333826i	$-0.891660\pi$
$839$	−4.95377	−	28.0942i	−0.171023	−	0.969920i	0.771611	−	0.636094i	$-0.219451\pi$
$840$	0.477310	+	24.3356i	0.0164688	+	0.839657i
$841$	2.83027	−	1.03013i	0.0975955	−	0.0355219i
$842$	0.0823932	+	0.941759i	0.00283946	+	0.0324552i
$843$	40.1478	−	5.05447i	1.38276	−	0.174085i
$844$	13.4028	−	36.8238i	0.461342	−	1.26753i
$845$	1.97749	+	28.6528i	0.0680277	+	0.985686i
$846$	−0.449927	−	1.75857i	−0.0154688	−	0.0604608i
$847$	−8.13164	−	30.3477i	−0.279407	−	1.04276i
$848$	−1.20714	+	13.7977i	−0.0414533	+	0.473814i
$849$	−1.14760	−	30.2082i	−0.0393854	−	1.03674i
$850$	4.31121	+	8.14380i	0.147873	+	0.279330i
$851$	42.7525	+	7.53842i	1.46554	+	0.258414i
$852$	28.6502	+	26.5531i	0.981540	+	0.909693i
$853$	−42.9131	−	3.75441i	−1.46932	−	0.128549i	−0.675795	−	0.737090i	$-0.736199\pi$
$853$	−42.9131	−	3.75441i	−1.46932	−	0.128549i	−0.793522	+	0.608541i	$0.791755\pi$
$854$	−1.65709	+	2.87017i	−0.0567045	+	0.0982152i
$855$	8.02638	+	1.66230i	0.274496	+	0.0568493i
$856$	5.03113	+	8.71418i	0.171961	+	0.297844i
$857$	−14.8273	−	31.7973i	−0.506492	−	1.08617i	−0.978814	−	0.204749i	$-0.934362\pi$
$857$	−14.8273	−	31.7973i	−0.506492	−	1.08617i	0.472323	−	0.881426i	$-0.343416\pi$
$858$	0.174672	+	1.38743i	0.00596321	+	0.0473659i
$859$	−20.1815	+	24.0514i	−0.688584	+	0.820622i	−0.991184	−	0.132496i	$-0.957701\pi$
$859$	−20.1815	+	24.0514i	−0.688584	+	0.820622i	0.302600	+	0.953118i	$0.402145\pi$
$860$	−6.30511	−	7.80062i	−0.215003	−	0.265999i
$861$	−3.50517	+	10.9014i	−0.119456	+	0.371518i
$862$	7.31672	+	5.12322i	0.249209	+	0.174498i
$863$	−2.26670	+	2.26670i	−0.0771594	+	0.0771594i	−0.744633	−	0.667474i	$-0.767376\pi$
$863$	−2.26670	+	2.26670i	−0.0771594	+	0.0771594i	0.667474	+	0.744633i	$0.267376\pi$
$864$	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
$867$	0.0859243	−	1.74165i	0.00291814	−	0.0591494i
$868$	−57.1094	−	26.6305i	−1.93842	−	0.903900i
$869$	−41.0040	−	34.4064i	−1.39096	−	1.16716i
$870$	−5.07152	+	7.55394i	−0.171940	+	0.256103i
$871$	1.51249	+	0.550500i	0.0512487	+	0.0186530i
$872$	−3.31173	+	12.3595i	−0.112149	+	0.418547i
$873$	−1.61211	+	0.566171i	−0.0545617	+	0.0191620i
$874$	−1.92508	−	1.11144i	−0.0651167	−	0.0375951i
$875$	4.79725	+	39.9691i	0.162176	+	1.35120i
$876$	5.98948	−	11.3483i	0.202366	−	0.383425i
$877$	−22.6869	−	32.4003i	−0.766084	−	1.09408i	−0.992760	−	0.120111i	$-0.961675\pi$
$877$	−22.6869	−	32.4003i	−0.766084	−	1.09408i	0.226677	−	0.973970i	$-0.427214\pi$
$878$	1.29723	+	1.85264i	0.0437795	+	0.0625236i
$879$	−15.2072	−	24.1714i	−0.512925	−	0.815282i
$880$	−26.7074	+	6.63319i	−0.900307	+	0.223605i
$881$	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	$0.588913\pi$
$882$	6.37606	−	5.22826i	0.214693	−	0.176045i
$883$	11.2477	−	41.9771i	0.378516	−	1.41264i	−0.469623	−	0.882867i	$-0.655610\pi$
$883$	11.2477	−	41.9771i	0.378516	−	1.41264i	0.848139	−	0.529774i	$-0.177723\pi$
$884$	−2.64999	−	0.964518i	−0.0891289	−	0.0324403i
$885$	−1.77910	+	1.55330i	−0.0598038	+	0.0522136i
$886$	−6.82284	−	5.72505i	−0.229218	−	0.192337i
$887$	37.2137	+	17.3530i	1.24951	+	0.582658i	0.930916	−	0.365232i	$-0.119010\pi$
$887$	37.2137	+	17.3530i	1.24951	+	0.582658i	0.318598	+	0.947890i	$0.396788\pi$
$888$	27.9370	+	18.0210i	0.937505	+	0.604746i
$889$	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
$893$	1.31422	+	0.920226i	0.0439787	+	0.0307942i
$894$	−12.5898	+	2.71639i	−0.421065	+	0.0908498i
$895$	−0.992765	+	9.36383i	−0.0331845	+	0.312998i
$896$	−25.6367	+	30.5526i	−0.856462	+	1.02069i
$897$	−2.48604	−	1.04628i	−0.0830064	−	0.0349343i
$898$	0.581797	+	1.24767i	0.0194148	+	0.0416352i
$899$	−24.9536	−	43.2210i	−0.832250	−	1.44150i
$900$	−1.05146	−	26.7940i	−0.0350487	−	0.893133i
$901$	9.99476	−	17.3114i	0.332974	−	0.576728i
$902$	3.74375	+	0.327536i	0.124653	+	0.0109058i
$903$	−3.47345	+	15.2583i	−0.115589	+	0.507766i
$904$	−12.6001	−	2.22173i	−0.419072	−	0.0738938i
$905$	−10.7510	−	7.82593i	−0.357374	−	0.260143i
$906$	−6.36847	−	3.36118i	−0.211578	−	0.111668i
$907$	−1.86792	+	21.3504i	−0.0620232	+	0.708928i	0.899987	+	0.435916i	$0.143576\pi$
$907$	−1.86792	+	21.3504i	−0.0620232	+	0.708928i	−0.962011	+	0.273012i	$0.911980\pi$
$908$	5.91383	+	22.0707i	0.196257	+	0.732442i
$909$	43.7484	−	3.32877i	1.45104	−	0.110408i
$910$	1.10368	+	0.961174i	0.0365867	+	0.0318626i
$911$	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	$-0.0164325\pi$
$912$	3.54360	+	4.67265i	0.117340	+	0.154727i
$913$	1.04275	+	11.9186i	0.0345099	+	0.394450i
$914$	−2.85987	+	1.04091i	−0.0945960	+	0.0344301i
$915$	3.73584	−	6.77406i	0.123503	−	0.223943i
$916$	4.61738	+	26.1865i	0.152563	+	0.865225i
$917$	−1.80481	−	1.80481i	−0.0595999	−	0.0595999i
$918$	−4.56536	+	8.41772i	−0.150679	+	0.277826i
$919$			40.0326i			1.32055i	0.751023	+	0.660277i	$0.229561\pi$
$919$			40.0326i			1.32055i	−0.751023	+	0.660277i	$0.770439\pi$
$920$	−4.26037	+	14.8070i	−0.140460	+	0.488171i
$921$	31.7765	+	10.2172i	1.04707	+	0.336669i
$922$	−8.11585	+	17.4045i	−0.267281	+	0.573187i
$923$	4.95766	−	0.433739i	0.163183	−	0.0142767i
$924$	39.1113	+	30.3645i	1.28667	+	0.998920i
$925$	48.9453	+	25.0508i	1.60931	+	0.823664i
$926$	−2.17807	+	1.25751i	−0.0715757	+	0.0413243i
$927$	−45.0385	+	25.3274i	−1.47926	+	0.831859i
$928$	−23.4773	+	6.29073i	−0.770681	+	0.206503i
$929$	−33.8872	+	28.4347i	−1.11180	+	0.932913i	−0.998162	−	0.0606092i	$-0.980696\pi$
$929$	−33.8872	+	28.4347i	−1.11180	+	0.932913i	−0.113641	+	0.993522i	$0.536251\pi$
$930$	−15.9773	−	7.07230i	−0.523917	−	0.231910i
$931$	−1.26551	+	7.17705i	−0.0414754	+	0.235218i
$932$	7.30007	−	5.11156i	0.239122	−	0.167435i
$933$	−4.91411	+	5.30223i	−0.160881	+	0.173587i
$934$	−2.98938	−	3.56260i	−0.0978154	−	0.116572i
$935$	38.9799	+	7.61362i	1.27478	+	0.248992i
$936$	−1.44393	−	1.47701i	−0.0471965	−	0.0482776i
$937$	−12.1366	−	3.25201i	−0.396487	−	0.106238i	0.0550659	−	0.998483i	$-0.482463\pi$
$937$	−12.1366	−	3.25201i	−0.396487	−	0.106238i	−0.451553	+	0.892244i	$0.649130\pi$
$938$	−6.13595	+	2.86124i	−0.200346	+	0.0934229i
$939$	4.87229	−	6.27580i	0.159001	−	0.204803i
$940$	1.88534	−	4.89819i	0.0614929	−	0.159761i
$941$	−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	$0.937955\pi$
$942$	0.522994	+	1.01870i	0.0170401	+	0.0331912i
$943$	−4.15766	+	5.93775i	−0.135392	+	0.193360i
$944$	−1.68973			−0.0549961
$945$	−31.8237	+	27.1558i	−1.03522	+	0.883379i
$946$	5.13566			0.166975
$947$	−13.6093	+	19.4360i	−0.442241	+	0.631586i	−0.976955	−	0.213447i	$-0.931531\pi$
$947$	−13.6093	+	19.4360i	−0.442241	+	0.631586i	0.534713	+	0.845034i	$0.320420\pi$
$948$	37.2707	+	1.83875i	1.21049	+	0.0597199i
$949$	−0.559131	−	1.53620i	−0.0181502	−	0.0498672i
$950$	−1.91636	−	2.06253i	−0.0621748	−	0.0669172i
$951$	39.8675	+	5.47846i	1.29279	+	0.177651i
$952$	22.7784	−	10.6218i	0.738253	−	0.344253i
$953$	8.49020	+	2.27494i	0.275025	+	0.0736926i	0.393695	−	0.919241i	$-0.371197\pi$
$953$	8.49020	+	2.27494i	0.275025	+	0.0736926i	−0.118671	+	0.992934i	$0.537863\pi$
$954$	5.70503	−	3.89918i	0.184707	−	0.126241i
$955$	−20.1139	+	13.5405i	−0.650872	+	0.438160i
$956$	8.35447	+	9.95647i	0.270203	+	0.322015i
$957$	11.5806	+	37.4673i	0.374347	+	1.21115i
$958$	1.69775	−	1.18878i	0.0548518	−	0.0384076i
$959$	0.636599	−	3.61033i	0.0205569	−	0.116584i
$960$	8.13060	−	10.0849i	0.262414	−	0.325488i
$961$	49.6714	−	41.6793i	1.60230	−	1.34449i
$962$	1.93087	−	0.517374i	0.0622536	−	0.0166808i
$963$	−6.09878	+	16.1837i	−0.196530	+	0.521511i
$964$	−30.5588	+	17.6431i	−0.984233	+	0.568247i
$965$	1.37579	+	0.0252625i	0.0442881	+	0.000813227i
$966$	10.5062	−	4.28228i	0.338031	−	0.137780i
$967$	10.1245	−	0.885782i	0.325583	−	0.0284848i	0.0768074	−	0.997046i	$-0.475527\pi$
$967$	10.1245	−	0.885782i	0.325583	−	0.0284848i	0.248776	+	0.968561i	$0.419972\pi$
$968$	6.43665	−	13.8034i	0.206882	−	0.443659i
$969$	−1.78507	−	8.27335i	−0.0573448	−	0.265778i
$970$	0.564000	+	0.162278i	0.0181089	+	0.00521043i
$971$		−	25.3812i		−	0.814522i	−0.913312	−	0.407261i	$-0.866484\pi$
$971$		−	25.3812i		−	0.814522i	0.913312	−	0.407261i	$-0.133516\pi$
$972$	22.5794	−	16.3315i	0.724233	−	0.523833i
$973$	−56.6741	−	56.6741i	−1.81689	−	1.81689i
$974$	−0.282708	−	1.60332i	−0.00905856	−	0.0513736i
$975$	−2.61969	−	2.19260i	−0.0838973	−	0.0702195i
$976$	5.20090	−	1.89297i	0.166477	−	0.0605926i
$977$	3.96576	+	45.3288i	0.126876	+	1.45020i	0.746545	+	0.665335i	$0.231711\pi$
$977$	3.96576	+	45.3288i	0.126876	+	1.45020i	−0.619669	+	0.784863i	$0.712733\pi$
$978$	2.92005	−	6.93824i	0.0933728	−	0.221861i
$979$	3.75243	−	10.3097i	0.119928	−	0.329500i
$980$	23.7845	−	1.64150i	0.759769	−	0.0524359i
$981$	−20.0360	+	9.06814i	−0.639699	+	0.289524i
$982$	1.84802	+	6.89690i	0.0589727	+	0.220089i
$983$	2.03223	−	23.2285i	0.0648182	−	0.740875i	−0.892350	−	0.451344i	$-0.850945\pi$
$983$	2.03223	−	23.2285i	0.0648182	−	0.740875i	0.957168	−	0.289532i	$-0.0934995\pi$
$984$	−4.69852	+	2.95602i	−0.149783	+	0.0942345i
$985$	−9.55850	−	60.7062i	−0.304559	−	1.93426i
$986$	9.25215	+	1.63140i	0.294649	+	0.0519545i
$987$	−7.82335	+	2.41808i	−0.249020	+	0.0769684i
$988$	0.858357	+	0.0750965i	0.0273080	+	0.00238914i
$989$	−4.95291	+	8.57870i	−0.157494	+	0.272787i
$990$	11.0080	+	8.20534i	0.349857	+	0.260783i
$991$	−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	$-0.340861\pi$
$992$	−19.7262	−	42.3029i	−0.626306	−	1.34312i
$993$	−25.9297	+	19.6643i	−0.822854	+	0.624028i
$994$	−13.4555	+	16.0357i	−0.426783	+	0.508621i
$995$	−6.16276	−	0.653383i	−0.195373	−	0.0207136i
$996$	−5.60003	−	6.18126i	−0.177444	−	0.195861i
$997$	−25.8471	−	18.0983i	−0.818585	−	0.573180i	0.0875535	−	0.996160i	$-0.472095\pi$
$997$	−25.8471	−	18.0983i	−0.818585	−	0.573180i	−0.906139	+	0.422980i	$0.860984\pi$
$998$	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.68.8	yes	192
3.2	odd	2		405.2.r.a.233.9		192
5.2	odd	4	inner	135.2.q.a.122.8	yes	192
5.3	odd	4		675.2.ba.b.257.9		192
5.4	even	2		675.2.ba.b.68.9		192
15.2	even	4		405.2.r.a.152.9		192
27.2	odd	18	inner	135.2.q.a.83.8	yes	192
27.25	even	9		405.2.r.a.8.9		192
135.2	even	36	inner	135.2.q.a.2.8	✓	192
135.29	odd	18		675.2.ba.b.218.9		192
135.52	odd	36		405.2.r.a.332.9		192
135.83	even	36		675.2.ba.b.407.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.8	✓	192	135.2	even	36	inner
135.2.q.a.68.8	yes	192	1.1	even	1	trivial
135.2.q.a.83.8	yes	192	27.2	odd	18	inner
135.2.q.a.122.8	yes	192	5.2	odd	4	inner
405.2.r.a.8.9		192	27.25	even	9
405.2.r.a.152.9		192	15.2	even	4
405.2.r.a.233.9		192	3.2	odd	2
405.2.r.a.332.9		192	135.52	odd	36
675.2.ba.b.68.9		192	5.4	even	2
675.2.ba.b.218.9		192	135.29	odd	18
675.2.ba.b.257.9		192	5.3	odd	4
675.2.ba.b.407.9		192	135.83	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)

\(f(q)\)	\(=\)	\(q+(-0.264318 + 0.377486i) q^{2} +(-0.938886 + 1.45550i) q^{3} +(0.611409 + 1.67983i) q^{4} +(2.04357 - 0.907638i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-3.26325 + 1.52168i) q^{7} +(-1.68596 - 0.451753i) q^{8} +(-1.23699 - 2.73311i) q^{9} +O(q^{10})\)	\(q+(-0.264318 + 0.377486i) q^{2} +(-0.938886 + 1.45550i) q^{3} +(0.611409 + 1.67983i) q^{4} +(2.04357 - 0.907638i) q^{5} +(-0.301267 - 0.739132i) q^{6} +(-3.26325 + 1.52168i) q^{7} +(-1.68596 - 0.451753i) q^{8} +(-1.23699 - 2.73311i) q^{9} +(-0.197534 + 1.01132i) q^{10} +(2.85486 + 3.40229i) q^{11} +(-3.01905 - 0.687263i) q^{12} +(-0.323128 + 0.226257i) q^{13} +(0.288125 - 1.63404i) q^{14} +(-0.597612 + 3.82660i) q^{15} +(-2.12266 + 1.78113i) q^{16} +(3.86289 - 1.03506i) q^{17} +(1.35867 + 0.255466i) q^{18} +(-1.05819 + 0.610947i) q^{19} +(2.77414 + 2.87792i) q^{20} +(0.849012 - 6.17836i) q^{21} +(-2.03891 + 0.178381i) q^{22} +(1.66839 - 3.57786i) q^{23} +(2.24046 - 2.02978i) q^{24} +(3.35239 - 3.70965i) q^{25} -0.181780i q^{26} +(5.13944 + 0.765638i) q^{27} +(-4.55135 - 4.55135i) q^{28} +(-0.885233 - 5.02040i) q^{29} +(-1.28653 - 1.23703i) q^{30} +(9.19946 - 3.34833i) q^{31} +(-0.415541 - 4.74965i) q^{32} +(-7.63244 + 0.960899i) q^{33} +(-0.630312 + 1.73177i) q^{34} +(-5.28756 + 6.07152i) q^{35} +(3.83486 - 3.74897i) q^{36} +(2.84615 + 10.6220i) q^{37} +(0.0490755 - 0.560936i) q^{38} +(-0.0259371 - 0.682744i) q^{39} +(-3.85542 + 0.607055i) q^{40} +(-1.80826 - 0.318845i) q^{41} +(2.10783 + 1.95354i) q^{42} +(-2.49969 - 0.218695i) q^{43} +(-3.96979 + 6.87588i) q^{44} +(-5.00854 - 4.46257i) q^{45} +(0.909608 + 1.57549i) q^{46} +(-0.554905 - 1.19000i) q^{47} +(-0.599497 - 4.76182i) q^{48} +(3.83380 - 4.56894i) q^{49} +(0.514242 + 2.24601i) q^{50} +(-2.12028 + 6.59425i) q^{51} +(-0.577637 - 0.404466i) 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} +(0.104285 - 2.11381i) q^{57} +(2.12911 + 0.992822i) q^{58} +(0.467138 + 0.391975i) q^{59} +(-6.79343 + 1.33573i) q^{60} +(-1.87695 - 0.683152i) q^{61} +(-1.16764 + 4.35769i) q^{62} +(8.19551 + 7.03652i) q^{63} +(-2.89665 - 1.67238i) q^{64} +(-0.454977 + 0.755656i) q^{65} +(1.65467 - 3.13512i) q^{66} +(-2.34038 - 3.34241i) q^{67} +(4.10053 + 5.85616i) q^{68} +(3.64117 + 5.78755i) q^{69} +(-0.894311 - 3.60079i) q^{70} +(-10.9258 - 6.30801i) q^{71} +(0.850825 + 5.16673i) q^{72} +(-1.07262 + 4.00309i) q^{73} +(-4.76194 - 1.73320i) q^{74} +(2.25190 + 8.36235i) q^{75} +(-1.67328 - 1.40404i) q^{76} +(-14.4933 - 6.75835i) q^{77} +(0.264582 + 0.170671i) 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} +(2.20663 + 1.54510i) q^{83} +(10.8977 - 2.35131i) q^{84} +(6.95464 - 5.62132i) q^{85} +(0.743269 - 0.885794i) q^{86} +(8.13835 + 3.42513i) q^{87} +(-3.27620 - 7.02584i) q^{88} +(-1.23513 - 2.13931i) q^{89} +(3.00840 - 0.711114i) q^{90} +(0.710159 - 1.23003i) q^{91} +(7.03028 + 0.615070i) q^{92} +(-3.76374 + 16.5336i) q^{93} +(0.595878 + 0.105069i) q^{94} +(-1.60797 + 2.20897i) q^{95} +(7.30328 + 3.85456i) q^{96} +(0.0496393 - 0.567380i) q^{97} +(0.711367 + 2.65486i) 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

Varieties

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Representations

Groups

Database

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