LMFDB - Embedded newform 135.2.q.a.2.8

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

$q$-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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.264318	−	0.377486i	−0.186901	−	0.266923i	0.714756	−	0.699374i	$-0.246538\pi$
$2$	−0.264318	−	0.377486i	−0.186901	−	0.266923i	−0.901657	+	0.432451i	$0.857649\pi$
$3$	−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	−0.307004	−	0.951708i	$-0.599327\pi$
$7$	−3.26325	−	1.52168i	−1.23339	−	0.575141i	−0.926389	+	0.376567i	$0.877104\pi$
$8$	−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	−0.138597	−	0.990349i	$-0.544259\pi$
$11$	2.85486	−	3.40229i	0.860773	−	1.02583i	0.999370	−	0.0354810i	$-0.0112963\pi$
$12$	−3.01905	+	0.687263i	−0.871524	+	0.198396i
$13$	−0.323128	−	0.226257i	−0.0896196	−	0.0627524i	0.527908	−	0.849302i	$-0.322977\pi$
$13$	−0.323128	−	0.226257i	−0.0896196	−	0.0627524i	−0.617527	+	0.786549i	$0.711866\pi$
$14$	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	0.694789	−	0.719213i	$-0.255498\pi$
$17$	3.86289	+	1.03506i	0.936888	+	0.251038i	0.242098	+	0.970252i	$0.422164\pi$
$18$	1.35867	−	0.255466i	0.320241	−	0.0602138i
$19$	−1.05819	−	0.610947i	−0.242766	−	0.140161i	0.373682	−	0.927557i	$-0.378095\pi$
$19$	−1.05819	−	0.610947i	−0.242766	−	0.140161i	−0.616447	+	0.787396i	$0.711429\pi$
$20$	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	0.999926	−	0.0121450i	$-0.00386597\pi$
$23$	1.66839	+	3.57786i	0.347882	+	0.746036i	−0.652044	+	0.758181i	$0.726088\pi$
$24$	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	0.785314	+	0.619097i	$0.212501\pi$
$29$	−0.885233	+	5.02040i	−0.164384	+	0.932266i	−0.949698	+	0.313168i	$0.898610\pi$
$30$	−1.28653	+	1.23703i	−0.234886	+	0.225850i
$31$	9.19946	+	3.34833i	1.65227	+	0.601378i	0.989121	−	0.147107i	$-0.0469963\pi$
$31$	9.19946	+	3.34833i	1.65227	+	0.601378i	0.663152	+	0.748485i	$0.269219\pi$
$32$	−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	−0.179171	−	0.983818i	$-0.557342\pi$
$37$	2.84615	−	10.6220i	0.467905	−	1.74624i	0.647076	−	0.762426i	$-0.275992\pi$
$38$	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	−0.313055	−	0.949735i	$-0.601353\pi$
$41$	−1.80826	+	0.318845i	−0.282403	+	0.0497952i	0.0306526	+	0.999530i	$0.490241\pi$
$42$	2.10783	−	1.95354i	0.325246	−	0.301438i
$43$	−2.49969	+	0.218695i	−0.381200	+	0.0333507i	−0.276146	−	0.961116i	$-0.589057\pi$
$43$	−2.49969	+	0.218695i	−0.381200	+	0.0333507i	−0.105054	+	0.994466i	$0.533502\pi$
$44$	−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	−0.942613	−	0.333887i	$-0.891640\pi$
$47$	−0.554905	+	1.19000i	−0.0809412	+	0.173579i	0.861672	+	0.507465i	$0.169418\pi$
$48$	−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	0.906880	−	0.421389i	$-0.138457\pi$
$53$	3.53443	+	3.53443i	0.485491	+	0.485491i	−0.421389	+	0.906880i	$0.638457\pi$
$54$	−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	−0.611873	−	0.790956i	$-0.709584\pi$
$59$	0.467138	−	0.391975i	0.0608162	−	0.0510308i	0.672689	+	0.739925i	$0.265139\pi$
$60$	−6.79343	−	1.33573i	−0.877028	−	0.172442i
$61$	−1.87695	+	0.683152i	−0.240318	+	0.0874687i	−0.459372	−	0.888244i	$-0.651925\pi$
$61$	−1.87695	+	0.683152i	−0.240318	+	0.0874687i	0.219053	+	0.975713i	$0.429703\pi$
$62$	−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	−0.936261	−	0.351304i	$-0.885738\pi$
$67$	−2.34038	+	3.34241i	−0.285923	+	0.408341i	0.650338	+	0.759645i	$0.274627\pi$
$68$	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	−0.979824	−	0.199860i	$-0.935951\pi$
$71$	−10.9258	+	6.30801i	−1.29665	+	0.748623i	−0.316829	+	0.948483i	$0.602618\pi$
$72$	0.850825	−	5.16673i	0.100271	−	0.608905i
$73$	−1.07262	−	4.00309i	−0.125541	−	0.468526i	0.874317	−	0.485355i	$-0.161310\pi$
$73$	−1.07262	−	4.00309i	−0.125541	−	0.468526i	−0.999858	+	0.0168287i	$0.994643\pi$
$74$	−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	−0.540023	−	0.841650i	$-0.681585\pi$
$79$	−11.8688	−	2.09278i	−1.33534	−	0.235457i	−0.795317	+	0.606193i	$0.792696\pi$
$80$	−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	−0.446169	−	0.894949i	$-0.647212\pi$
$83$	2.20663	−	1.54510i	0.242209	−	0.169597i	0.688378	+	0.725352i	$0.258323\pi$
$84$	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	−0.924033	−	0.382313i	$-0.875128\pi$
$89$	−1.23513	+	2.13931i	−0.130924	+	0.226766i	0.793109	+	0.609079i	$0.208461\pi$
$90$	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	0.998298	−	0.0583150i	$-0.0185728\pi$
$97$	0.0496393	+	0.567380i	0.00504011	+	0.0576087i	−0.993258	+	0.115924i	$0.963017\pi$
$98$	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	−0.893473	−	0.449117i	$-0.851739\pi$
$101$	−5.00202	−	13.7429i	−0.497720	−	1.36747i	0.395753	−	0.918357i	$-0.370484\pi$
$102$	−1.92881	+	2.54336i	−0.190980	+	0.251830i
$103$	−1.50115	+	17.1583i	−0.147913	+	1.69066i	0.453135	+	0.891442i	$0.350306\pi$
$103$	−1.50115	+	17.1583i	−0.147913	+	1.69066i	−0.601048	+	0.799213i	$0.705250\pi$
$104$	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	−0.876139	−	0.482059i	$-0.839889\pi$
$107$	−4.07639	+	4.07639i	−0.394080	+	0.394080i	0.482059	+	0.876139i	$0.339889\pi$
$108$	1.85615	−	9.10151i	0.178609	−	0.875793i
$109$			7.33084i			0.702167i	0.936344	+	0.351084i	$0.114187\pi$
$109$			7.33084i			0.702167i	−0.936344	+	0.351084i	$0.885813\pi$
$110$	−4.00475	−	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	0.425284	−	0.905060i	$-0.360174\pi$
$113$	7.30233	+	0.638871i	0.686945	+	0.0600999i	0.261661	+	0.965160i	$0.415730\pi$
$114$	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	−0.477769	−	0.878486i	$-0.658554\pi$
$127$	−5.09700	+	1.36574i	−0.452285	+	0.121189i	0.0254832	+	0.999675i	$0.491888\pi$
$128$	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	−0.928650	−	0.370956i	$-0.879030\pi$
$131$	0.242450	−	0.666126i	0.0211829	−	0.0581997i	0.949833	+	0.312756i	$0.101252\pi$
$132$	−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	0.793430	−	0.608662i	$-0.208293\pi$
$137$	−0.583999	−	0.834037i	−0.0498944	−	0.0712566i	−0.843324	+	0.537405i	$0.819405\pi$
$138$	−3.14715	+	0.155265i	−0.267903	+	0.0132170i
$139$	7.61336	−	20.9175i	0.645757	−	1.77420i	0.0129201	−	0.999917i	$-0.495887\pi$
$139$	7.61336	−	20.9175i	0.645757	−	1.77420i	0.632837	−	0.774285i	$-0.281890\pi$
$140$	−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	0.853791	+	0.520616i	$0.174298\pi$
$149$	2.80203	+	15.8911i	0.229551	+	1.30185i	−0.624240	+	0.781233i	$0.714591\pi$
$150$	−3.75189	+	1.36026i	−0.306340	+	0.111065i
$151$	6.91118	+	5.79917i	0.562424	+	0.471930i	0.879122	−	0.476597i	$-0.158130\pi$
$151$	6.91118	+	5.79917i	0.562424	+	0.471930i	−0.316698	+	0.948526i	$0.602574\pi$
$152$	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	0.0299812	−	0.999550i	$-0.490455\pi$
$157$	−1.42921	−	0.125040i	−0.114063	−	0.00997924i	−0.144044	+	0.989571i	$0.546011\pi$
$158$	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	−0.395936	−	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
$165$	−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	−0.701593	−	0.712578i	$-0.747528\pi$
$167$	1.46130	−	16.7028i	0.113079	−	1.29250i	0.814672	−	0.579922i	$-0.196917\pi$
$168$	−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	0.978545	+	0.206031i	$0.0660548\pi$
$173$	0.666108	+	7.61365i	0.0506432	+	0.578855i	−0.927902	+	0.372824i	$0.878390\pi$
$174$	−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	0.776545	−	0.630061i	$-0.216970\pi$
$179$	−2.10555	−	3.64692i	−0.157376	−	0.272584i	−0.933922	+	0.357477i	$0.883637\pi$
$180$	4.43410	+	11.1420i	0.330498	+	0.830473i
$181$	−2.97345	+	5.15017i	−0.221015	+	0.382809i	−0.955116	−	0.296231i	$-0.904270\pi$
$181$	−2.97345	+	5.15017i	−0.221015	+	0.382809i	0.734102	+	0.679040i	$0.237604\pi$
$182$	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	−0.226619	−	0.973983i	$-0.572767\pi$
$191$	−10.6788	−	1.88297i	−0.772694	−	0.136247i	−0.546074	+	0.837737i	$0.683878\pi$
$192$	5.15378	+	2.64591i	0.371942	+	0.190952i
$193$	0.557718	−	0.260068i	0.0401454	−	0.0187201i	−0.402442	−	0.915446i	$-0.631838\pi$
$193$	0.557718	−	0.260068i	0.0401454	−	0.0187201i	0.442587	+	0.896725i	$0.354061\pi$
$194$	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	0.450097	+	0.892980i	$0.351389\pi$
$197$	7.11316	+	26.5467i	0.506791	+	1.89137i	0.0566946	+	0.998392i	$0.481944\pi$
$198$	3.00964	−	5.35190i	0.213886	−	0.380343i
$199$	−2.40020	+	1.38576i	−0.170146	+	0.0982338i	−0.582655	−	0.812720i	$-0.697986\pi$
$199$	−2.40020	+	1.38576i	−0.170146	+	0.0982338i	0.412509	+	0.910954i	$0.364653\pi$
$200$	−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	−0.999844	−	0.0176876i	$-0.994370\pi$
$211$	−16.7925	+	14.0906i	−1.15605	+	0.970038i	−0.156202	+	0.987725i	$0.549925\pi$
$212$	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	−0.682935	−	0.730479i	$-0.739297\pi$
$223$	4.71331	−	10.1077i	0.315627	−	0.676863i	0.998562	+	0.0536157i	$0.0170746\pi$
$224$	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	0.343639	−	0.939102i	$-0.388340\pi$
$227$	12.7332	−	1.11401i	0.845130	−	0.0739393i	0.501492	+	0.865163i	$0.332785\pi$
$228$	3.61461	+	1.11722i	0.239383	+	0.0739898i
$229$	14.6486	−	2.58295i	0.968008	−	0.170686i	0.332775	−	0.943006i	$-0.392015\pi$
$229$	14.6486	−	2.58295i	0.968008	−	0.170686i	0.635233	+	0.772320i	$0.280904\pi$
$230$	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	−0.995224	−	0.0976137i	$-0.968879\pi$
$233$	−1.29026	+	4.81533i	−0.0845279	+	0.315463i	0.910696	+	0.413076i	$0.135546\pi$
$234$	−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	0.553397	−	0.832918i	$-0.313331\pi$
$239$	6.83215	+	2.48670i	0.441935	+	0.160851i	−0.111462	+	0.993769i	$0.535553\pi$
$240$	−5.54712	+	9.18700i	−0.358065	+	0.593018i
$241$	3.42764	−	19.4391i	0.220794	−	1.25219i	−0.649770	−	0.760131i	$-0.725135\pi$
$241$	3.42764	−	19.4391i	0.220794	−	1.25219i	0.870564	−	0.492055i	$-0.163754\pi$
$242$	−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	0.886556	−	0.462622i	$-0.153091\pi$
$251$	14.7212	+	8.49927i	0.929191	+	0.536469i	0.0426356	+	0.999091i	$0.486425\pi$
$252$	−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	0.107053	−	0.994253i	$-0.465858\pi$
$257$	−12.6747	−	8.87491i	−0.790625	−	0.553601i	−0.897678	+	0.440652i	$0.854747\pi$
$258$	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	−0.442221	−	0.896906i	$-0.645809\pi$
$263$	−22.9238	−	10.6896i	−1.41355	−	0.659147i	−0.971324	+	0.237759i	$0.923587\pi$
$264$	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	0.518636	−	0.854995i	$-0.326440\pi$
$277$	3.27946	+	1.52924i	0.197044	+	0.0918830i	−0.321592	+	0.946878i	$0.604218\pi$
$278$	−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	0.101508	+	0.994835i	$0.467633\pi$
$281$	−15.0170	+	17.8966i	−0.895839	+	1.06762i	−0.997348	+	0.0727851i	$0.976811\pi$
$282$	−0.712391	−	0.768655i	−0.0424223	−	0.0457727i
$283$	−14.2969	−	10.0108i	−0.849863	−	0.595080i	0.0654355	−	0.997857i	$-0.479156\pi$
$283$	−14.2969	−	10.0108i	−0.849863	−	0.595080i	−0.915298	+	0.402776i	$0.868045\pi$
$284$	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	−0.997813	−	0.0661055i	$-0.978943\pi$
$293$	−6.96793	−	14.9428i	−0.407071	−	0.872966i	0.590742	−	0.806861i	$-0.298835\pi$
$294$	−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	0.664417	+	0.747362i	$0.268680\pi$
$307$	−4.98775	+	18.6145i	−0.284666	+	1.06239i	−0.949083	+	0.315026i	$0.897987\pi$
$308$	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	−0.0558883	−	0.998437i	$-0.517799\pi$
$311$	4.11040	−	0.724775i	0.233079	−	0.0410982i	0.288968	+	0.957339i	$0.406688\pi$
$312$	−0.264702	−	1.16280i	−0.0149858	−	0.0658305i
$313$	−4.56966	+	0.399794i	−0.258293	+	0.0225977i	−0.215567	−	0.976489i	$-0.569160\pi$
$313$	−4.56966	+	0.399794i	−0.258293	+	0.0225977i	−0.0427260	+	0.999087i	$0.513604\pi$
$314$	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	0.411068	+	0.911605i	$0.365156\pi$
$317$	−9.81902	+	21.0570i	−0.551491	+	1.18268i	−0.962559	+	0.271072i	$0.912622\pi$
$318$	−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	0.192320	−	0.981332i	$-0.438399\pi$
$331$	17.6555	−	6.42608i	0.970434	−	0.353209i	0.778114	+	0.628123i	$0.216177\pi$
$332$	−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	−0.672526	−	0.740074i	$-0.734791\pi$
$337$	4.64324	−	6.63124i	0.252934	−	0.361227i	0.925459	+	0.378847i	$0.123679\pi$
$338$	−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	−0.557030	−	0.830493i	$-0.688059\pi$
$347$	−5.19509	+	2.42251i	−0.278887	+	0.130047i	0.278143	+	0.960540i	$0.410281\pi$
$348$	−0.777779	−	15.7652i	−0.0416933	−	0.845105i
$349$	−3.63192	−	0.640405i	−0.194412	−	0.0342801i	0.0755941	−	0.997139i	$-0.475915\pi$
$349$	−3.63192	−	0.640405i	−0.194412	−	0.0342801i	−0.270006	+	0.962859i	$0.587026\pi$
$350$	−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	−0.123832	−	0.992303i	$-0.539518\pi$
$353$	14.3970	−	10.0809i	0.766275	−	0.536551i	0.890107	+	0.455752i	$0.150630\pi$
$354$	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	−0.738759	−	0.673970i	$-0.764588\pi$
$359$	4.06033	−	7.03269i	0.214296	−	0.371171i	0.953055	+	0.302799i	$0.0979210\pi$
$360$	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	0.930940	+	0.365171i	$0.118989\pi$
$367$	1.48573	+	16.9819i	0.0775543	+	0.886450i	−0.853386	+	0.521279i	$0.825455\pi$
$368$	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	−0.515834	−	0.856688i	$-0.672518\pi$
$373$	2.72173	−	31.1095i	0.140926	−	1.61079i	0.656760	−	0.754100i	$-0.271927\pi$
$374$	−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	$0.296252\pi$
$379$			31.2281i			1.60408i	−0.597269	+	0.802041i	$0.703748\pi$
$380$	−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	−0.816503	−	0.577341i	$-0.804090\pi$
$383$	−33.6778	−	2.94643i	−1.72086	−	0.150555i	−0.904353	+	0.426786i	$0.859646\pi$
$384$	−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	−0.0673324	−	0.997731i	$-0.521449\pi$
$389$	−20.9380	−	17.5690i	−1.06160	−	0.890786i	−0.994265	+	0.106945i	$0.965893\pi$
$390$	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	0.0642968	−	0.997931i	$-0.479520\pi$
$397$	12.3324	−	3.30445i	0.618945	−	0.165846i	0.554648	+	0.832085i	$0.312853\pi$
$398$	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	0.649298	+	0.760534i	$0.275063\pi$
$401$	−6.74752	+	18.5387i	−0.336955	+	0.925776i	−0.986253	+	0.165242i	$0.947159\pi$
$402$	−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	−0.961707	−	0.274078i	$-0.911627\pi$
$409$	−0.987380	+	2.71280i	−0.0488228	+	0.134139i	0.912885	+	0.408218i	$0.133850\pi$
$410$	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	−0.962492	−	0.271310i	$-0.912543\pi$
$419$	−3.08760	−	17.5106i	−0.150839	−	0.855451i	0.811653	−	0.584140i	$-0.198568\pi$
$420$	20.1361	+	14.6962i	0.982543	+	0.717103i
$421$	1.57150	+	1.31864i	0.0765901	+	0.0642667i	0.680279	−	0.732953i	$-0.261859\pi$
$421$	1.57150	+	1.31864i	0.0765901	+	0.0642667i	−0.603689	+	0.797220i	$0.706303\pi$
$422$	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	$0.154600\pi$
$431$			19.3828i			0.933636i	−0.884353	+	0.466818i	$0.845400\pi$
$432$	−12.2730	−	7.52879i	−0.590484	−	0.362229i
$433$	−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
$435$	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	0.973283	−	0.229610i	$-0.0737451\pi$
$439$	1.67858	+	4.61187i	0.0801144	+	0.220112i	−0.893168	+	0.449723i	$0.851523\pi$
$440$	−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	−0.925001	−	0.379965i	$-0.875936\pi$
$443$	−1.68450	−	19.2540i	−0.0800331	−	0.914783i	0.844968	−	0.534817i	$-0.179620\pi$
$444$	−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	0.899117	−	0.437709i	$-0.144210\pi$
$449$	1.49368	+	2.58713i	0.0704911	+	0.122094i	−0.828626	+	0.559803i	$0.810877\pi$
$450$	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	−0.440160	−	0.897919i	$-0.645078\pi$
$457$	5.40989	−	3.78805i	0.253064	−	0.177197i	0.693224	+	0.720722i	$0.256189\pi$
$458$	−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	0.997606	−	0.0691537i	$-0.0220299\pi$
$461$	41.0394	+	7.23636i	1.91140	+	0.337031i	0.913791	+	0.406185i	$0.133141\pi$
$462$	−0.628952	−	12.7486i	−0.0292615	−	0.593117i
$463$	4.94630	−	2.30650i	0.229874	−	0.107192i	−0.304269	−	0.952586i	$-0.598412\pi$
$463$	4.94630	−	2.30650i	0.229874	−	0.107192i	0.534143	+	0.845394i	$0.320634\pi$
$464$	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	0.878790	−	0.477209i	$-0.158352\pi$
$467$	−2.61200	−	9.74812i	−0.120869	−	0.451089i	−0.999659	+	0.0261197i	$0.991685\pi$
$468$	−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	−0.436762	−	0.899577i	$-0.643875\pi$
$479$	−4.22629	+	1.53824i	−0.193104	+	0.0702841i	0.243658	+	0.969861i	$0.421653\pi$
$480$	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	0.648237	−	0.761439i	$-0.275507\pi$
$487$	−2.49814	−	2.49814i	−0.113202	−	0.113202i	−0.761439	+	0.648237i	$0.775507\pi$
$488$	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	0.942434	−	0.334392i	$-0.108531\pi$
$491$	9.95960	+	11.8694i	0.449471	+	0.535658i	−0.492964	+	0.870050i	$0.664086\pi$
$492$	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	−0.539572	−	0.841939i	$-0.681414\pi$
$499$	−16.9468	+	2.98818i	−0.758644	+	0.133769i	−0.219072	+	0.975709i	$0.570303\pi$
$500$	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	0.205569	+	0.978643i	$0.434095\pi$
$503$	−10.3567	+	38.6515i	−0.461780	+	1.72339i	−0.667349	+	0.744745i	$0.732571\pi$
$504$	−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	0.986339	−	0.164726i	$-0.0526738\pi$
$509$	36.9106	+	13.4344i	1.63604	+	0.595468i	0.649696	+	0.760194i	$0.274896\pi$
$510$	−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	−0.210426	−	0.977610i	$-0.567485\pi$
$521$	−26.5294	−	15.3168i	−1.16227	−	0.671039i	−0.951848	+	0.306571i	$0.900818\pi$
$522$	0.0798049	+	7.04720i	0.00349296	+	0.308447i
$523$	−4.33233	−	1.16084i	−0.189439	−	0.0507602i	0.162852	−	0.986651i	$-0.447931\pi$
$523$	−4.33233	−	1.16084i	−0.189439	−	0.0507602i	−0.352291	+	0.935890i	$0.614597\pi$
$524$	−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	0.119791	−	0.992799i	$-0.461777\pi$
$547$	−13.1847	−	6.14812i	−0.563737	−	0.262875i	−0.683528	+	0.729924i	$0.739555\pi$
$548$	−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	−0.416774	−	0.909010i	$-0.636840\pi$
$557$	−29.0814	−	7.79233i	−1.23222	−	0.330171i	−0.815442	+	0.578838i	$0.803506\pi$
$558$	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	−0.999455	−	0.0330215i	$-0.989487\pi$
$563$	−9.07139	−	19.4537i	−0.382314	−	0.819874i	0.617141	−	0.786852i	$-0.288291\pi$
$564$	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	−0.858743	−	0.512406i	$-0.828754\pi$
$569$	2.94509	−	16.7024i	0.123465	−	0.700202i	0.982208	−	0.187796i	$-0.0601345\pi$
$570$	2.11715	−	0.523015i	0.0886776	−	0.0219067i
$571$	−28.4369	−	10.3502i	−1.19005	−	0.433142i	−0.330307	−	0.943873i	$-0.607152\pi$
$571$	−28.4369	−	10.3502i	−1.19005	−	0.433142i	−0.859740	+	0.510732i	$0.829375\pi$
$572$	−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	−0.614518	−	0.788903i	$-0.710650\pi$
$577$	7.49741	−	27.9807i	0.312121	−	1.16485i	0.926640	−	0.375950i	$-0.122684\pi$
$578$	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	−0.955070	−	0.296379i	$-0.904221\pi$
$587$	−2.76499	+	5.92953i	−0.114123	+	0.244738i	0.840947	+	0.541117i	$0.181999\pi$
$588$	−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	0.0803015	−	0.996771i	$-0.474412\pi$
$593$	−22.3175	−	22.3175i	−0.916469	−	0.916469i	−0.996771	+	0.0803015i	$0.974412\pi$
$594$	−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	−0.804425	−	0.594054i	$-0.797527\pi$
$599$	−8.78838	+	7.37433i	−0.359083	+	0.301307i	0.445342	+	0.895361i	$0.353082\pi$
$600$	−0.0189103	+	15.1159i	−0.000772010	+	0.617105i
$601$	−29.2326	+	10.6398i	−1.19242	+	0.434007i	−0.860574	−	0.509326i	$-0.829895\pi$
$601$	−29.2326	+	10.6398i	−1.19242	+	0.434007i	−0.331850	+	0.943332i	$0.607673\pi$
$602$	−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	−0.952807	−	0.303576i	$-0.901819\pi$
$607$	−8.41759	+	12.0216i	−0.341659	+	0.487940i	0.611148	+	0.791517i	$0.290708\pi$
$608$	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	−0.987755	−	0.156013i	$-0.950136\pi$
$613$	−5.20779	−	19.4357i	−0.210341	−	0.785002i	0.777414	−	0.628989i	$-0.216531\pi$
$614$	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	−0.476245	−	0.879313i	$-0.658002\pi$
$617$	−2.70196	+	1.25995i	−0.108777	+	0.0507236i	0.367468	+	0.930036i	$0.380225\pi$
$618$	−12.2300	−	6.27878i	−0.491962	−	0.252569i
$619$	13.1500	+	2.31870i	0.528542	+	0.0931962i	0.431550	−	0.902089i	$-0.357967\pi$
$619$	13.1500	+	2.31870i	0.528542	+	0.0931962i	0.0969919	+	0.995285i	$0.469078\pi$
$620$	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	0.879504	−	0.475891i	$-0.157874\pi$
$631$	0.693777	+	1.20166i	0.0276188	+	0.0478372i	−0.851886	+	0.523728i	$0.824541\pi$
$632$	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	−0.999040	−	0.0438070i	$-0.986051\pi$
$641$	−6.63051	−	18.2172i	−0.261890	−	0.719536i	0.737150	−	0.675729i	$-0.236171\pi$
$642$	−1.78491	−	4.24108i	−0.0704448	−	0.167382i
$643$	3.60391	−	41.1928i	0.142124	−	1.62449i	−0.505708	−	0.862705i	$-0.668769\pi$
$643$	3.60391	−	41.1928i	0.142124	−	1.62449i	0.647833	−	0.761783i	$-0.275676\pi$
$644$	−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	−0.908620	−	0.417623i	$-0.862863\pi$
$647$	−12.4891	+	12.4891i	−0.490997	+	0.490997i	0.417623	+	0.908620i	$0.362863\pi$
$648$	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	0.370449	−	0.928853i	$-0.379204\pi$
$653$	14.6673	+	1.28323i	0.573977	+	0.0502165i	0.203528	+	0.979069i	$0.434759\pi$
$654$	−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	0.953030	−	0.302877i	$-0.0979473\pi$
$659$	21.0565	+	17.6685i	0.820245	+	0.688268i	−0.132784	+	0.991145i	$0.542392\pi$
$660$	−23.9389	+	19.2999i	−0.931819	+	0.751248i
$661$	1.73362	+	9.83186i	0.0674301	+	0.382415i	0.999782	+	0.0208639i	$0.00664165\pi$
$661$	1.73362	+	9.83186i	0.0674301	+	0.382415i	−0.932352	+	0.361551i	$0.882247\pi$
$662$	−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	0.822003	−	0.569483i	$-0.192857\pi$
$673$	0.148446	+	0.212002i	0.00572216	+	0.00817209i	−0.816281	+	0.577655i	$0.803968\pi$
$674$	−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	0.992853	−	0.119347i	$-0.0380801\pi$
$677$	14.0797	+	20.1079i	0.541128	+	0.772810i	−0.451725	+	0.892157i	$0.649191\pi$
$678$	−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	0.176347	−	0.984328i	$-0.443572\pi$
$683$	21.4623	−	5.75081i	0.821232	−	0.220048i	0.644885	+	0.764280i	$0.276905\pi$
$684$	−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	0.638879	−	0.769307i	$-0.279398\pi$
$691$	−0.205042	−	0.172050i	−0.00780016	−	0.00654511i	−0.646679	+	0.762762i	$0.723843\pi$
$692$	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	$-0.740036\pi$
$701$		−	38.5968i		−	1.45778i	0.684630	−	0.728891i	$-0.259964\pi$
$702$	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	−0.744690	−	0.667410i	$-0.767403\pi$
$709$	−16.0622	−	44.1305i	−0.603228	−	1.65735i	0.141463	−	0.989944i	$-0.454819\pi$
$710$	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	0.855061	−	0.518528i	$-0.173520\pi$
$719$	−0.577250	−	0.999826i	−0.0215278	−	0.0372872i	−0.876589	+	0.481241i	$0.840186\pi$
$720$	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	0.212252	−	0.977215i	$-0.431920\pi$
$727$	32.4399	−	22.7146i	1.20313	−	0.842439i	0.990876	+	0.134776i	$0.0430313\pi$
$728$	−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	−0.534106	−	0.845417i	$-0.679352\pi$
$733$	−6.22149	+	2.90113i	−0.229796	+	0.107156i	0.304310	+	0.952573i	$0.401574\pi$
$734$	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	−0.925170	−	0.379553i	$-0.876078\pi$
$739$	−28.7899	+	16.6218i	−1.05905	+	0.611444i	−0.133882	+	0.990997i	$0.542744\pi$
$740$	−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	−0.956477	−	0.291806i	$-0.905744\pi$
$743$	−9.68027	+	13.8249i	−0.355135	+	0.507185i	0.601343	+	0.798991i	$0.294633\pi$
$744$	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	0.101158	−	0.994870i	$-0.467745\pi$
$751$	30.1032	−	25.2596i	1.09848	−	0.921734i	0.997322	+	0.0731359i	$0.0233007\pi$
$752$	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	0.929415	−	0.369036i	$-0.120312\pi$
$757$	15.4181	+	15.4181i	0.560380	+	0.560380i	−0.369036	+	0.929415i	$0.620312\pi$
$758$	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	0.422560	−	0.906335i	$-0.361131\pi$
$761$	−14.9899	−	17.8642i	−0.543382	−	0.647577i	−0.965942	+	0.258757i	$0.916687\pi$
$762$	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	0.614987	−	0.788537i	$-0.289161\pi$
$769$	40.5586	−	7.15158i	1.46258	−	0.257893i	0.847594	+	0.530645i	$0.178050\pi$
$770$	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	0.861297	+	0.508101i	$0.169652\pi$
$773$	−3.85511	+	14.3875i	−0.138659	+	0.517481i	−0.999956	+	0.00937966i	$0.997014\pi$
$774$	−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	0.987926	−	0.154924i	$-0.0495132\pi$
$787$	6.57073	+	14.0910i	0.234221	+	0.502289i	−0.753705	+	0.657212i	$0.771735\pi$
$788$	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	0.0454973	−	0.998964i	$-0.485513\pi$
$797$	−24.7774	−	17.3493i	−0.877661	−	0.614545i	−0.923159	+	0.384419i	$0.874402\pi$
$798$	−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	−0.0870458	+	0.996204i	$0.527743\pi$
$821$	−30.1717	+	35.9573i	−1.05300	+	1.25492i	−0.965954	+	0.258712i	$0.916702\pi$
$822$	0.792404	−	0.180385i	0.0276382	−	0.00629164i
$823$	33.1012	+	23.1777i	1.15383	+	0.807923i	0.984109	−	0.177568i	$-0.0568230\pi$
$823$	33.1012	+	23.1777i	1.15383	+	0.807923i	0.169726	+	0.985491i	$0.445712\pi$
$824$	−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	−0.487624	−	0.873054i	$-0.662136\pi$
$827$	−38.7205	−	10.3751i	−1.34645	−	0.360779i	−0.858821	+	0.512275i	$0.828803\pi$
$828$	−7.01530	+	19.9753i	−0.243799	+	0.694191i
$829$	27.2086	+	15.7089i	0.944994	+	0.545593i	0.891522	−	0.452977i	$-0.149638\pi$
$829$	27.2086	+	15.7089i	0.944994	+	0.545593i	0.0534718	+	0.998569i	$0.482971\pi$
$830$	−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	0.771611	+	0.636094i	$0.219451\pi$
$839$	−4.95377	+	28.0942i	−0.171023	+	0.969920i	−0.942635	+	0.333826i	$0.891660\pi$
$840$	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	−0.793522	−	0.608541i	$-0.791755\pi$
$853$	−42.9131	+	3.75441i	−1.46932	+	0.128549i	−0.675795	+	0.737090i	$0.736199\pi$
$854$	−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	0.472323	+	0.881426i	$0.343416\pi$
$857$	−14.8273	+	31.7973i	−0.506492	+	1.08617i	−0.978814	+	0.204749i	$0.934362\pi$
$858$	0.174672	−	1.38743i	0.00596321	−	0.0473659i
$859$	−20.1815	−	24.0514i	−0.688584	−	0.820622i	0.302600	−	0.953118i	$-0.402145\pi$
$859$	−20.1815	−	24.0514i	−0.688584	−	0.820622i	−0.991184	+	0.132496i	$0.957701\pi$
$860$	−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	0.667474	−	0.744633i	$-0.267376\pi$
$863$	−2.26670	−	2.26670i	−0.0771594	−	0.0771594i	−0.744633	+	0.667474i	$0.767376\pi$
$864$	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	0.226677	+	0.973970i	$0.427214\pi$
$877$	−22.6869	+	32.4003i	−0.766084	+	1.09408i	−0.992760	+	0.120111i	$0.961675\pi$
$878$	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	−0.275710	−	0.961241i	$-0.588913\pi$
$881$	12.4335	−	7.17846i	0.418894	−	0.241848i	0.694604	+	0.719392i	$0.255580\pi$
$882$	6.37606	+	5.22826i	0.214693	+	0.176045i
$883$	11.2477	+	41.9771i	0.378516	+	1.41264i	0.848139	+	0.529774i	$0.177723\pi$
$883$	11.2477	+	41.9771i	0.378516	+	1.41264i	−0.469623	+	0.882867i	$0.655610\pi$
$884$	−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	0.318598	−	0.947890i	$-0.396788\pi$
$887$	37.2137	−	17.3530i	1.24951	−	0.582658i	0.930916	+	0.365232i	$0.119010\pi$
$888$	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	−0.962011	−	0.273012i	$-0.911980\pi$
$907$	−1.86792	−	21.3504i	−0.0620232	−	0.708928i	0.899987	−	0.435916i	$-0.143576\pi$
$908$	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	0.998668	+	0.0516013i	$0.0164325\pi$
$911$	8.05314	+	22.1258i	0.266813	+	0.733061i	−0.731855	+	0.681460i	$0.761345\pi$
$912$	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	$-0.770439\pi$
$919$		−	40.0326i		−	1.32055i	0.751023	−	0.660277i	$-0.229561\pi$
$920$	−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	−0.113641	−	0.993522i	$-0.536251\pi$
$929$	−33.8872	−	28.4347i	−1.11180	−	0.932913i	−0.998162	+	0.0606092i	$0.980696\pi$
$930$	−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	−0.451553	−	0.892244i	$-0.649130\pi$
$937$	−12.1366	+	3.25201i	−0.396487	+	0.106238i	0.0550659	+	0.998483i	$0.482463\pi$
$938$	−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	−0.981063	−	0.193688i	$-0.937955\pi$
$941$	−3.22172	+	8.85160i	−0.105025	+	0.288554i	0.876038	+	0.482242i	$0.160177\pi$
$942$	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	0.534713	−	0.845034i	$-0.320420\pi$
$947$	−13.6093	−	19.4360i	−0.442241	−	0.631586i	−0.976955	+	0.213447i	$0.931531\pi$
$948$	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	−0.118671	−	0.992934i	$-0.537863\pi$
$953$	8.49020	−	2.27494i	0.275025	−	0.0736926i	0.393695	+	0.919241i	$0.371197\pi$
$954$	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	0.248776	−	0.968561i	$-0.419972\pi$
$967$	10.1245	+	0.885782i	0.325583	+	0.0284848i	0.0768074	+	0.997046i	$0.475527\pi$
$968$	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	$0.133516\pi$
$971$			25.3812i			0.814522i	−0.913312	+	0.407261i	$0.866484\pi$
$972$	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	−0.619669	−	0.784863i	$-0.712733\pi$
$977$	3.96576	−	45.3288i	0.126876	−	1.45020i	0.746545	−	0.665335i	$-0.231711\pi$
$978$	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	0.957168	+	0.289532i	$0.0934995\pi$
$983$	2.03223	+	23.2285i	0.0648182	+	0.740875i	−0.892350	+	0.451344i	$0.850945\pi$
$984$	−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	0.479381	+	0.877607i	$0.340861\pi$
$991$	−16.3804	+	28.3716i	−0.520339	+	0.901254i	−0.999720	+	0.0236474i	$0.992472\pi$
$992$	−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	−0.906139	−	0.422980i	$-0.860984\pi$
$997$	−25.8471	+	18.0983i	−0.818585	+	0.573180i	0.0875535	+	0.996160i	$0.472095\pi$
$998$	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.2.8	✓	192
3.2	odd	2		405.2.r.a.332.9		192
5.2	odd	4		675.2.ba.b.218.9		192
5.3	odd	4	inner	135.2.q.a.83.8	yes	192
5.4	even	2		675.2.ba.b.407.9		192
15.8	even	4		405.2.r.a.8.9		192
27.13	even	9		405.2.r.a.152.9		192
27.14	odd	18	inner	135.2.q.a.122.8	yes	192
135.13	odd	36		405.2.r.a.233.9		192
135.14	odd	18		675.2.ba.b.257.9		192
135.68	even	36	inner	135.2.q.a.68.8	yes	192
135.122	even	36		675.2.ba.b.68.9		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.2.8	✓	192	1.1	even	1	trivial
135.2.q.a.68.8	yes	192	135.68	even	36	inner
135.2.q.a.83.8	yes	192	5.3	odd	4	inner
135.2.q.a.122.8	yes	192	27.14	odd	18	inner
405.2.r.a.8.9		192	15.8	even	4
405.2.r.a.152.9		192	27.13	even	9
405.2.r.a.233.9		192	135.13	odd	36
405.2.r.a.332.9		192	3.2	odd	2
675.2.ba.b.68.9		192	135.122	even	36
675.2.ba.b.218.9		192	5.2	odd	4
675.2.ba.b.257.9		192	135.14	odd	18
675.2.ba.b.407.9		192	5.4	even	2

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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