LMFDB - Embedded newform 135.2.q.a.38.7

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			38.7
Character	$\chi$	$=$	135.38
Dual form			135.2.q.a.32.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0140240 - 0.160295i) q^{2} +(0.850222 - 1.50901i) q^{3} +(1.94412 - 0.342800i) q^{4} +(-1.03969 + 1.97966i) q^{5} +(-0.253811 - 0.115124i) q^{6} +(1.66092 + 2.37204i) q^{7} +(-0.165506 - 0.617675i) q^{8} +(-1.55424 - 2.56599i) q^{9} +O(q^{10})$	\(q+(-0.0140240 - 0.160295i) q^{2} +(0.850222 - 1.50901i) q^{3} +(1.94412 - 0.342800i) q^{4} +(-1.03969 + 1.97966i) q^{5} +(-0.253811 - 0.115124i) q^{6} +(1.66092 + 2.37204i) q^{7} +(-0.165506 - 0.617675i) q^{8} +(-1.55424 - 2.56599i) q^{9} +(0.331911 + 0.138894i) q^{10} +(-1.48958 - 4.09258i) q^{11} +(1.13564 - 3.22516i) q^{12} +(-4.71104 - 0.412163i) q^{13} +(0.356933 - 0.299503i) q^{14} +(2.10337 + 3.25205i) q^{15} +(3.61342 - 1.31518i) q^{16} +(-1.51857 + 5.66739i) q^{17} +(-0.389520 + 0.285124i) q^{18} +(-0.695229 - 0.401391i) q^{19} +(-1.34264 + 4.20510i) q^{20} +(4.99158 - 0.489589i) q^{21} +(-0.635132 + 0.296167i) q^{22} +(2.18347 + 1.52888i) q^{23} +(-1.07280 - 0.275411i) q^{24} +(-2.83811 - 4.11645i) q^{25} +0.760939i q^{26} +(-5.19357 + 0.163709i) q^{27} +(4.04215 + 4.04215i) q^{28} +(-2.06994 - 1.73689i) q^{29} +(0.491791 - 0.382767i) q^{30} +(1.27517 + 7.23183i) q^{31} +(-0.801990 - 1.71987i) q^{32} +(-7.44223 - 1.23181i) q^{33} +(0.929752 + 0.163940i) q^{34} +(-6.42266 + 0.821878i) q^{35} +(-3.90126 - 4.45580i) q^{36} +(3.14033 + 0.841448i) q^{37} +(-0.0545912 + 0.117071i) q^{38} +(-4.62739 + 6.75860i) q^{39} +(1.39486 + 0.314544i) q^{40} +(2.88706 + 3.44066i) q^{41} +(-0.148481 - 0.793261i) q^{42} +(-6.22917 - 2.90471i) q^{43} +(-4.29885 - 7.44583i) q^{44} +(6.69572 - 0.409045i) q^{45} +(0.214452 - 0.371442i) q^{46} +(4.52886 - 3.17114i) q^{47} +(1.08759 - 6.57090i) q^{48} +(-0.473765 + 1.30166i) q^{49} +(-0.620046 + 0.512664i) q^{50} +(7.26104 + 7.11008i) q^{51} +(-9.30011 + 0.813654i) q^{52} +(1.70331 - 1.70331i) q^{53} +(0.0990765 + 0.830210i) q^{54} +(9.65061 + 1.30614i) q^{55} +(1.19026 - 1.41849i) q^{56} +(-1.19680 + 0.707839i) q^{57} +(-0.249386 + 0.356161i) q^{58} +(4.31439 + 1.57031i) q^{59} +(5.20400 + 5.60134i) q^{60} +(2.10123 - 11.9167i) q^{61} +(1.14135 - 0.305823i) q^{62} +(3.50516 - 7.94862i) q^{63} +(6.39585 - 3.69265i) q^{64} +(5.71395 - 8.89774i) q^{65} +(-0.0930836 + 1.21023i) q^{66} +(-0.582021 + 6.65253i) q^{67} +(-1.00950 + 11.5386i) q^{68} +(4.16355 - 1.99500i) q^{69} +(0.221815 + 1.01800i) q^{70} +(-5.61473 + 3.24167i) q^{71} +(-1.32772 + 1.38470i) q^{72} +(-9.31768 + 2.49666i) q^{73} +(0.0908402 - 0.515180i) q^{74} +(-8.62480 + 0.782842i) q^{75} +(-1.48920 - 0.542026i) q^{76} +(7.23368 - 10.3308i) q^{77} +(1.14827 + 0.646967i) q^{78} +(0.322504 - 0.384345i) q^{79} +(-1.15322 + 8.52072i) q^{80} +(-4.16865 + 7.97636i) q^{81} +(0.511034 - 0.511034i) q^{82} +(8.92110 - 0.780495i) q^{83} +(9.53639 - 2.66293i) q^{84} +(-9.64066 - 8.89856i) q^{85} +(-0.378253 + 1.03924i) q^{86} +(-4.38090 + 1.64683i) q^{87} +(-2.28135 + 1.59742i) q^{88} +(6.84734 - 11.8599i) q^{89} +(-0.159469 - 1.06756i) q^{90} +(-6.84699 - 11.8593i) q^{91} +(4.76903 + 2.22384i) q^{92} +(11.9971 + 4.22442i) q^{93} +(-0.571832 - 0.681483i) q^{94} +(1.51744 - 0.958997i) q^{95} +(-3.27718 - 0.252061i) q^{96} +(3.08067 - 6.60652i) q^{97} +(0.215294 + 0.0576878i) q^{98} +(-8.18637 + 10.1831i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.0140240	−	0.160295i	−0.00991648	−	0.113346i	0.989623	−	0.143688i	$-0.0458960\pi$
$2$	−0.0140240	−	0.160295i	−0.00991648	−	0.113346i	−0.999540	+	0.0303416i	$0.990340\pi$
$3$	0.850222	−	1.50901i	0.490876	−	0.871229i
$3$	0.850222	−	1.50901i	0.490876	−	0.871229i
$4$	1.94412	−	0.342800i	0.972059	−	0.171400i
$5$	−1.03969	+	1.97966i	−0.464962	+	0.885331i
$5$	−1.03969	+	1.97966i	−0.464962	+	0.885331i
$6$	−0.253811	−	0.115124i	−0.103618	−	0.0469993i
$7$	1.66092	+	2.37204i	0.627768	+	0.896545i	0.999494	−	0.0317971i	$-0.0101231\pi$
$7$	1.66092	+	2.37204i	0.627768	+	0.896545i	−0.371727	+	0.928342i	$0.621234\pi$
$8$	−0.165506	−	0.617675i	−0.0585151	−	0.218381i
$9$	−1.55424	−	2.56599i	−0.518081	−	0.855331i
$10$	0.331911	+	0.138894i	0.104959	+	0.0439222i
$11$	−1.48958	−	4.09258i	−0.449125	−	1.23396i	−0.933335	−	0.359008i	$-0.883115\pi$
$11$	−1.48958	−	4.09258i	−0.449125	−	1.23396i	0.484210	−	0.874952i	$-0.339107\pi$
$12$	1.13564	−	3.22516i	0.327832	−	0.931022i
$13$	−4.71104	−	0.412163i	−1.30661	−	0.114313i	−0.587507	−	0.809219i	$-0.699891\pi$
$13$	−4.71104	−	0.412163i	−1.30661	−	0.114313i	−0.719101	+	0.694905i	$0.755446\pi$
$14$	0.356933	−	0.299503i	0.0953945	−	0.0800455i
$15$	2.10337	+	3.25205i	0.543087	+	0.839676i
$16$	3.61342	−	1.31518i	0.903355	−	0.328794i
$17$	−1.51857	+	5.66739i	−0.368308	+	1.37454i	0.494573	+	0.869136i	$0.335324\pi$
$17$	−1.51857	+	5.66739i	−0.368308	+	1.37454i	−0.862881	+	0.505407i	$0.831342\pi$
$18$	−0.389520	+	0.285124i	−0.0918108	+	0.0672043i
$19$	−0.695229	−	0.401391i	−0.159497	−	0.0920854i	0.418127	−	0.908388i	$-0.362687\pi$
$19$	−0.695229	−	0.401391i	−0.159497	−	0.0920854i	−0.577624	+	0.816303i	$0.696020\pi$
$20$	−1.34264	+	4.20510i	−0.300224	+	0.940288i
$21$	4.99158	−	0.489589i	1.08925	−	0.106837i
$22$	−0.635132	+	0.296167i	−0.135411	+	0.0631430i
$23$	2.18347	+	1.52888i	0.455286	+	0.318794i	0.778626	−	0.627488i	$-0.215917\pi$
$23$	2.18347	+	1.52888i	0.455286	+	0.318794i	−0.323340	+	0.946283i	$0.604806\pi$
$24$	−1.07280	−	0.275411i	−0.218984	−	0.0562181i
$25$	−2.83811	−	4.11645i	−0.567621	−	0.823290i
$26$			0.760939i			0.149232i
$27$	−5.19357	+	0.163709i	−0.999504	+	0.0315057i
$28$	4.04215	+	4.04215i	0.763895	+	0.763895i
$29$	−2.06994	−	1.73689i	−0.384379	−	0.322532i	0.430040	−	0.902810i	$-0.358500\pi$
$29$	−2.06994	−	1.73689i	−0.384379	−	0.322532i	−0.814419	+	0.580278i	$0.802944\pi$
$30$	0.491791	−	0.382767i	0.0897883	−	0.0698834i
$31$	1.27517	+	7.23183i	0.229027	+	1.29887i	0.854836	+	0.518899i	$0.173658\pi$
$31$	1.27517	+	7.23183i	0.229027	+	1.29887i	−0.625809	+	0.779976i	$0.715231\pi$
$32$	−0.801990	−	1.71987i	−0.141773	−	0.304034i
$33$	−7.44223	−	1.23181i	−1.29553	−	0.214431i
$34$	0.929752	+	0.163940i	0.159451	+	0.0281155i
$35$	−6.42266	+	0.821878i	−1.08563	+	0.138923i
$36$	−3.90126	−	4.45580i	−0.650209	−	0.742633i
$37$	3.14033	+	0.841448i	0.516266	+	0.138333i	0.507539	−	0.861629i	$-0.330555\pi$
$37$	3.14033	+	0.841448i	0.516266	+	0.138333i	0.00872734	+	0.999962i	$0.497222\pi$
$38$	−0.0545912	+	0.117071i	−0.00885586	+	0.0189914i
$39$	−4.62739	+	6.75860i	−0.740976	+	1.08224i
$40$	1.39486	+	0.314544i	0.220547	+	0.0497337i
$41$	2.88706	+	3.44066i	0.450883	+	0.537341i	0.942826	−	0.333286i	$-0.108158\pi$
$41$	2.88706	+	3.44066i	0.450883	+	0.537341i	−0.491943	+	0.870628i	$0.663713\pi$
$42$	−0.148481	−	0.793261i	−0.0229111	−	0.122403i
$43$	−6.22917	−	2.90471i	−0.949940	−	0.442964i	−0.115037	−	0.993361i	$-0.536699\pi$
$43$	−6.22917	−	2.90471i	−0.949940	−	0.442964i	−0.834903	+	0.550397i	$0.814476\pi$
$44$	−4.29885	−	7.44583i	−0.648076	−	1.12250i
$45$	6.69572	−	0.409045i	0.998139	−	0.0609768i
$46$	0.214452	−	0.371442i	0.0316192	−	0.0547661i
$47$	4.52886	−	3.17114i	0.660602	−	0.462558i	−0.194580	−	0.980887i	$-0.562334\pi$
$47$	4.52886	−	3.17114i	0.660602	−	0.462558i	0.855182	+	0.518328i	$0.173445\pi$
$48$	1.08759	−	6.57090i	0.156980	−	0.948427i
$49$	−0.473765	+	1.30166i	−0.0676807	+	0.185951i
$50$	−0.620046	+	0.512664i	−0.0876878	+	0.0725017i
$51$	7.26104	+	7.11008i	1.01675	+	0.995611i
$52$	−9.30011	+	0.813654i	−1.28969	+	0.112834i
$53$	1.70331	−	1.70331i	0.233968	−	0.233968i	−0.580379	−	0.814347i	$-0.697095\pi$
$53$	1.70331	−	1.70331i	0.233968	−	0.233968i	0.814347	+	0.580379i	$0.197095\pi$
$54$	0.0990765	+	0.830210i	0.0134826	+	0.112977i
$55$	9.65061	+	1.30614i	1.30129	+	0.176120i
$56$	1.19026	−	1.41849i	0.159055	−	0.189554i
$57$	−1.19680	+	0.707839i	−0.158521	+	0.0937556i
$58$	−0.249386	+	0.356161i	−0.0327460	+	0.0467662i
$59$	4.31439	+	1.57031i	0.561686	+	0.204437i	0.607231	−	0.794525i	$-0.292280\pi$
$59$	4.31439	+	1.57031i	0.561686	+	0.204437i	−0.0455453	+	0.998962i	$0.514503\pi$
$60$	5.20400	+	5.60134i	0.671834	+	0.723129i
$61$	2.10123	−	11.9167i	0.269035	−	1.52577i	−0.488259	−	0.872699i	$-0.662368\pi$
$61$	2.10123	−	11.9167i	0.269035	−	1.52577i	0.757294	−	0.653074i	$-0.226521\pi$
$62$	1.14135	−	0.305823i	0.144951	−	0.0388395i
$63$	3.50516	−	7.94862i	0.441609	−	1.00143i
$64$	6.39585	−	3.69265i	0.799482	−	0.461581i
$65$	5.71395	−	8.89774i	0.708728	−	1.10363i
$66$	−0.0930836	+	1.21023i	−0.0114578	+	0.148969i
$67$	−0.582021	+	6.65253i	−0.0711052	+	0.812736i	0.873991	+	0.485943i	$0.161524\pi$
$67$	−0.582021	+	6.65253i	−0.0711052	+	0.812736i	−0.945096	+	0.326793i	$0.894032\pi$
$68$	−1.00950	+	11.5386i	−0.122420	+	1.39926i
$69$	4.16355	−	1.99500i	0.501232	−	0.240170i
$70$	0.221815	+	1.01800i	0.0265119	+	0.121674i
$71$	−5.61473	+	3.24167i	−0.666346	+	0.384715i	−0.794691	−	0.607014i	$-0.792367\pi$
$71$	−5.61473	+	3.24167i	−0.666346	+	0.384715i	0.128345	+	0.991730i	$0.459034\pi$
$72$	−1.32772	+	1.38470i	−0.156473	+	0.163189i
$73$	−9.31768	+	2.49666i	−1.09055	+	0.292212i	−0.758912	−	0.651194i	$-0.774269\pi$
$73$	−9.31768	+	2.49666i	−1.09055	+	0.292212i	−0.331640	+	0.943406i	$0.607602\pi$
$74$	0.0908402	−	0.515180i	0.0105600	−	0.0598885i
$75$	−8.62480	+	0.782842i	−0.995906	+	0.0903948i
$76$	−1.48920	−	0.542026i	−0.170823	−	0.0621747i
$77$	7.23368	−	10.3308i	0.824355	−	1.17730i
$78$	1.14827	+	0.646967i	0.130016	+	0.0732546i
$79$	0.322504	−	0.384345i	0.0362845	−	0.0432422i	−0.747597	−	0.664153i	$-0.768792\pi$
$79$	0.322504	−	0.384345i	0.0362845	−	0.0432422i	0.783882	+	0.620910i	$0.213237\pi$
$80$	−1.15322	+	8.52072i	−0.128934	+	0.952645i
$81$	−4.16865	+	7.97636i	−0.463184	+	0.886262i
$82$	0.511034	−	0.511034i	0.0564343	−	0.0564343i
$83$	8.92110	−	0.780495i	0.979218	−	0.0856704i	0.413706	−	0.910411i	$-0.364234\pi$
$83$	8.92110	−	0.780495i	0.979218	−	0.0856704i	0.565512	+	0.824740i	$0.308679\pi$
$84$	9.53639	−	2.66293i	1.04051	−	0.290550i
$85$	−9.64066	−	8.89856i	−1.04568	−	0.965184i
$86$	−0.378253	+	1.03924i	−0.0407881	+	0.112064i
$87$	−4.38090	+	1.64683i	−0.469682	+	0.176559i
$88$	−2.28135	+	1.59742i	−0.243193	+	0.170286i
$89$	6.84734	−	11.8599i	0.725816	−	1.25715i	−0.232821	−	0.972520i	$-0.574796\pi$
$89$	6.84734	−	11.8599i	0.725816	−	1.25715i	0.958637	−	0.284631i	$-0.0918711\pi$
$90$	−0.159469	−	1.06756i	−0.0168095	−	0.112530i
$91$	−6.84699	−	11.8593i	−0.717759	−	1.24320i
$92$	4.76903	+	2.22384i	0.497206	+	0.231851i
$93$	11.9971	+	4.22442i	1.24404	+	0.438052i
$94$	−0.571832	−	0.681483i	−0.0589800	−	0.0702896i
$95$	1.51744	−	0.958997i	0.155686	−	0.0983910i
$96$	−3.27718	−	0.252061i	−0.334476	−	0.0257259i
$97$	3.08067	−	6.60652i	0.312795	−	0.670790i	−0.685567	−	0.728010i	$-0.740446\pi$
$97$	3.08067	−	6.60652i	0.312795	−	0.670790i	0.998362	+	0.0572192i	$0.0182234\pi$
$98$	0.215294	+	0.0576878i	0.0217480	+	0.00582735i
$99$	−8.18637	+	10.1831i	−0.822762	+	1.02344i
$100$	−6.92873	−	7.02996i	−0.692873	−	0.702996i
$101$	5.17835	+	0.913082i	0.515265	+	0.0908551i	0.425233	−	0.905084i	$-0.360192\pi$
$101$	5.17835	+	0.913082i	0.515265	+	0.0908551i	0.0900315	+	0.995939i	$0.471303\pi$
$102$	1.03788	−	1.26362i	0.102766	−	0.125117i
$103$	−1.58805	−	3.40559i	−0.156475	−	0.335562i	0.812404	−	0.583094i	$-0.198158\pi$
$103$	−1.58805	−	3.40559i	−0.156475	−	0.335562i	−0.968880	+	0.247532i	$0.920380\pi$
$104$	0.525121	+	2.97811i	0.0514924	+	0.292028i
$105$	−4.22046	+	10.3907i	−0.411875	+	1.01402i
$106$	−0.296920	−	0.249146i	−0.0288395	−	0.0241992i
$107$	−5.69179	−	5.69179i	−0.550246	−	0.550246i	0.376266	−	0.926512i	$-0.377208\pi$
$107$	−5.69179	−	5.69179i	−0.550246	−	0.550246i	−0.926512	+	0.376266i	$0.877208\pi$
$108$	−10.0408	+	2.09863i	−0.966176	+	0.201941i
$109$			12.1610i			1.16481i	0.812899	+	0.582405i	$0.197888\pi$
$109$			12.1610i			1.16481i	−0.812899	+	0.582405i	$0.802112\pi$
$110$	0.0740282	−	1.56527i	0.00705831	−	0.149242i
$111$	3.93973	−	4.02338i	0.373943	−	0.381882i
$112$	9.12124	+	6.38676i	0.861876	+	0.603492i
$113$	3.69017	−	1.72075i	0.347142	−	0.161875i	−0.241225	−	0.970469i	$-0.577549\pi$
$113$	3.69017	−	1.72075i	0.347142	−	0.161875i	0.588366	+	0.808594i	$0.299771\pi$
$114$	0.130247	+	0.181915i	0.0121988	+	0.0170379i
$115$	−5.29680	+	2.73297i	−0.493929	+	0.254851i
$116$	−4.61962	−	2.66714i	−0.428921	−	0.247638i
$117$	6.26450	+	12.7291i	0.579153	+	1.17681i
$118$	0.191208	−	0.713599i	0.0176021	−	0.0656921i
$119$	−15.9655	+	5.81095i	−1.46355	+	0.532689i
$120$	1.66059	−	1.83743i	0.151591	−	0.167734i
$121$	−6.10389	+	5.12177i	−0.554899	+	0.465616i
$122$	−1.93965	−	0.169698i	−0.175608	−	0.0153637i
$123$	7.64665	−	1.43128i	0.689475	−	0.129054i
$124$	4.95815	+	13.6224i	0.445255	+	1.22333i
$125$	11.0999	−	1.33867i	0.992806	−	0.119734i
$126$	−1.32328	−	0.450389i	−0.117887	−	0.0401238i
$127$	−0.200655	−	0.748856i	−0.0178053	−	0.0664502i	0.956452	−	0.291891i	$-0.0942844\pi$
$127$	−0.200655	−	0.748856i	−0.0178053	−	0.0664502i	−0.974257	+	0.225441i	$0.927618\pi$
$128$	−2.85853	−	4.08240i	−0.252661	−	0.360837i
$129$	−9.67943	+	6.93025i	−0.852226	+	0.610175i
$130$	−1.50640	−	0.791137i	−0.132120	−	0.0693873i
$131$	−7.46979	+	1.31713i	−0.652639	+	0.115078i	−0.490158	−	0.871634i	$-0.663061\pi$
$131$	−7.46979	+	1.31713i	−0.652639	+	0.115078i	−0.162481	+	0.986712i	$0.551950\pi$
$132$	−14.8908	+	0.156414i	−1.29608	+	0.0136141i
$133$	−0.202605	−	2.31579i	−0.0175681	−	0.200804i
$134$	1.07453			0.0928254
$135$	5.07560	−	10.4517i	0.436838	−	0.899540i
$136$	3.75194			0.321726
$137$	−0.863173	−	9.86611i	−0.0737459	−	0.842919i	−0.939522	−	0.342488i	$-0.888730\pi$
$137$	−0.863173	−	9.86611i	−0.0737459	−	0.842919i	0.865776	−	0.500431i	$-0.166825\pi$
$138$	−0.378179	−	0.639419i	−0.0321927	−	0.0544310i
$139$	−14.8464	+	2.61782i	−1.25926	+	0.222041i	−0.763150	−	0.646222i	$-0.776348\pi$
$139$	−14.8464	+	2.61782i	−1.25926	+	0.222041i	−0.496105	+	0.868262i	$0.665237\pi$
$140$	−12.2047	+	3.79952i	−1.03148	+	0.321118i
$141$	−0.934757	−	9.53029i	−0.0787208	−	0.802595i
$142$	0.598365	+	0.854554i	0.0502137	+	0.0717126i
$143$	5.33066	+	19.8943i	0.445772	+	1.66364i
$144$	−8.99088	−	7.22791i	−0.749240	−	0.602326i
$145$	5.59054	−	2.29197i	0.464269	−	0.190337i
$146$	0.530875	+	1.45857i	0.0439355	+	0.120712i
$147$	1.56142	+	1.82162i	0.128783	+	0.150244i
$148$	6.39361	+	0.559369i	0.525552	+	0.0459798i
$149$	11.3083	−	9.48879i	0.926412	−	0.777352i	−0.0487579	−	0.998811i	$-0.515526\pi$
$149$	11.3083	−	9.48879i	0.926412	−	0.777352i	0.975170	+	0.221459i	$0.0710818\pi$
$150$	0.246440	+	1.37154i	0.0201218	+	0.111985i
$151$	−2.23835	+	0.814693i	−0.182154	+	0.0662987i	−0.431487	−	0.902119i	$-0.642011\pi$
$151$	−2.23835	+	0.814693i	−0.182154	+	0.0662987i	0.249333	+	0.968418i	$0.419789\pi$
$152$	−0.132865	+	0.495858i	−0.0107768	+	0.0402194i
$153$	16.9027	−	4.91185i	1.36650	−	0.397100i
$154$	−1.75742	−	1.01465i	−0.141617	−	0.0817626i
$155$	−15.6423	−	4.99444i	−1.25642	−	0.401163i
$156$	−6.67935	+	14.7258i	−0.534776	+	1.17901i
$157$	7.10700	−	3.31405i	0.567200	−	0.264490i	−0.117794	−	0.993038i	$-0.537582\pi$
$157$	7.10700	−	3.31405i	0.567200	−	0.264490i	0.684995	+	0.728548i	$0.259805\pi$
$158$	−0.0661316	−	0.0463058i	−0.00526114	−	0.00368389i
$159$	−1.12213	−	4.01852i	−0.0889905	−	0.318689i
$160$	4.23858	+	0.200461i	0.335089	+	0.0158478i
$161$			7.71863i			0.608313i
$162$	1.33703	+	0.556355i	0.105047	+	0.0437114i
$163$	10.1968	+	10.1968i	0.798677	+	0.798677i	0.982887	−	0.184210i	$-0.0589726\pi$
$163$	10.1968	+	10.1968i	0.798677	+	0.798677i	−0.184210	+	0.982887i	$0.558973\pi$
$164$	6.79225	+	5.69937i	0.530385	+	0.445046i
$165$	10.1762	−	13.4524i	0.792213	−	1.04727i
$166$	−0.250219	−	1.41906i	−0.0194208	−	0.110141i
$167$	2.74303	+	5.88244i	0.212262	+	0.455197i	0.983395	−	0.181477i	$-0.0580877\pi$
$167$	2.74303	+	5.88244i	0.212262	+	0.455197i	−0.771133	+	0.636673i	$0.780310\pi$
$168$	−1.12854	−	3.00215i	−0.0870689	−	0.231621i
$169$	9.22155	+	1.62601i	0.709350	+	0.125078i
$170$	−1.29120	+	1.67015i	−0.0990303	+	0.128094i
$171$	0.0505891	+	2.40781i	0.00386865	+	0.184130i
$172$	−13.1060	−	3.51174i	−0.999321	−	0.267767i
$173$	−4.90021	+	10.5085i	−0.372556	+	0.798949i	0.627242	+	0.778825i	$0.284184\pi$
$173$	−4.90021	+	10.5085i	−0.372556	+	0.798949i	−0.999797	+	0.0201240i	$0.993594\pi$
$174$	0.325417	+	0.679143i	0.0246698	+	0.0514857i
$175$	5.05051	−	13.5692i	0.381782	−	1.02573i
$176$	−10.7649	−	12.8292i	−0.811438	−	0.967034i
$177$	6.03781	−	5.17536i	0.453829	−	0.389004i
$178$	−1.99712	−	0.931272i	−0.149690	−	0.0698018i
$179$	3.42048	+	5.92444i	0.255658	+	0.442813i	0.965074	−	0.261977i	$-0.0843744\pi$
$179$	3.42048	+	5.92444i	0.255658	+	0.442813i	−0.709416	+	0.704790i	$0.751041\pi$
$180$	12.8770	−	3.09053i	0.959799	−	0.230354i
$181$	−8.12103	+	14.0660i	−0.603631	+	1.04552i	0.388635	+	0.921392i	$0.372947\pi$
$181$	−8.12103	+	14.0660i	−0.603631	+	1.04552i	−0.992266	+	0.124128i	$0.960387\pi$
$182$	−1.80497	+	1.26386i	−0.133794	+	0.0936832i
$183$	−16.1959	−	13.3026i	−1.19724	−	0.983357i
$184$	0.582977	−	1.60172i	0.0429776	−	0.118080i
$185$	−4.93073	+	5.34194i	−0.362515	+	0.392747i
$186$	0.508907	−	1.98232i	0.0373149	−	0.145351i
$187$	25.4563	−	2.22713i	1.86155	−	0.162864i
$188$	7.71757	−	7.71757i	0.562861	−	0.562861i
$189$	−9.01442	−	12.0474i	−0.655702	−	0.876322i
$190$	−0.175003	−	0.229789i	−0.0126961	−	0.0166707i
$191$	−13.1571	+	15.6801i	−0.952017	+	1.13457i	0.0387846	+	0.999248i	$0.487651\pi$
$191$	−13.1571	+	15.6801i	−0.952017	+	1.13457i	−0.990802	+	0.135322i	$0.956793\pi$
$192$	−0.134357	−	12.7910i	−0.00969639	−	0.923111i
$193$	4.46650	−	6.37883i	0.321506	−	0.459158i	−0.625570	−	0.780168i	$-0.715133\pi$
$193$	4.46650	−	6.37883i	0.321506	−	0.459158i	0.947076	+	0.321010i	$0.104022\pi$
$194$	−1.10220	−	0.401167i	−0.0791332	−	0.0288021i
$195$	−8.56869	−	16.1875i	−0.613616	−	1.15921i
$196$	−0.474846	+	2.69298i	−0.0339176	+	0.192356i
$197$	−5.11454	+	1.37044i	−0.364396	+	0.0976395i	−0.436371	−	0.899767i	$-0.643736\pi$
$197$	−5.11454	+	1.37044i	−0.364396	+	0.0976395i	0.0719752	+	0.997406i	$0.477070\pi$
$198$	1.74711	+	1.16943i	0.124162	+	0.0831077i
$199$	24.0896	−	13.9081i	1.70766	−	0.985920i	0.770225	−	0.637773i	$-0.220144\pi$
$199$	24.0896	−	13.9081i	1.70766	−	0.985920i	0.937440	−	0.348148i	$-0.113189\pi$
$200$	−2.07291	+	2.43432i	−0.146577	+	0.172133i
$201$	9.54391	+	6.53441i	0.673176	+	0.460902i
$202$	0.0737416	−	0.842870i	0.00518844	−	0.0593041i
$203$	0.681958	−	7.79481i	0.0478640	−	0.547088i
$204$	16.5537	+	11.3338i	1.15899	+	0.793521i
$205$	−9.81298	+	2.13819i	−0.685368	+	0.149337i
$206$	−0.523629	+	0.302317i	−0.0364829	+	0.0210634i
$207$	0.529459	−	7.97904i	0.0368000	−	0.554582i
$208$	−17.5651	+	4.70654i	−1.21792	+	0.326340i
$209$	−0.607127	+	3.44319i	−0.0419958	+	0.238170i
$210$	1.72476	+	0.530801i	0.119020	+	0.0366288i
$211$	8.85421	+	3.22267i	0.609549	+	0.221858i	0.628306	−	0.777966i	$-0.283749\pi$
$211$	8.85421	+	3.22267i	0.609549	+	0.221858i	−0.0187568	+	0.999824i	$0.505971\pi$
$212$	2.72754	−	3.89534i	0.187328	−	0.267533i
$213$	0.117948	+	11.2288i	0.00808168	+	0.769388i
$214$	−0.832546	+	0.992189i	−0.0569116	+	0.0678247i
$215$	12.2267	−	9.31165i	0.833855	−	0.635049i
$216$	0.960684	+	3.18085i	0.0653663	+	0.216429i
$217$	−15.0362	+	15.0362i	−1.02072	+	1.02072i
$218$	1.94935	−	0.170546i	0.132026	−	0.0115508i
$219$	−4.15460	+	16.1832i	−0.280742	+	1.09356i
$220$	19.2097	−	0.768938i	1.29512	−	0.0518418i
$221$	9.48994	−	26.0734i	0.638363	−	1.75389i
$222$	−0.700179	−	0.575097i	−0.0469930	−	0.0385980i
$223$	−8.50538	+	5.95553i	−0.569562	+	0.398812i	−0.822580	−	0.568650i	$-0.807466\pi$
$223$	−8.50538	+	5.95553i	−0.569562	+	0.398812i	0.253017	+	0.967462i	$0.418577\pi$
$224$	2.74756	−	4.75892i	0.183579	−	0.317969i
$225$	−6.15168	+	13.6805i	−0.410112	+	0.912035i
$226$	−0.327580	−	0.567385i	−0.0217903	−	0.0377419i
$227$	13.6725	+	6.37560i	0.907477	+	0.423164i	0.819579	−	0.572966i	$-0.194207\pi$
$227$	13.6725	+	6.37560i	0.907477	+	0.423164i	0.0878980	+	0.996129i	$0.471985\pi$
$228$	−2.08408	+	1.78639i	−0.138022	+	0.118306i
$229$	−0.604581	−	0.720511i	−0.0399518	−	0.0476127i	0.745699	−	0.666284i	$-0.232116\pi$
$229$	−0.604581	−	0.720511i	−0.0399518	−	0.0476127i	−0.785650	+	0.618671i	$0.787671\pi$
$230$	0.512365	+	0.810725i	0.0337844	+	0.0534576i
$231$	−9.43903	−	19.6992i	−0.621043	−	1.29611i
$232$	−0.730246	+	1.56602i	−0.0479430	+	0.102814i
$233$	−5.42572	−	1.45382i	−0.355451	−	0.0952427i	0.0766749	−	0.997056i	$-0.475570\pi$
$233$	−5.42572	−	1.45382i	−0.355451	−	0.0952427i	−0.432126	+	0.901813i	$0.642236\pi$
$234$	1.95256	−	1.18268i	0.127643	−	0.0773145i
$235$	1.56919	+	12.2626i	0.102363	+	0.799923i
$236$	8.92598	+	1.57389i	0.581032	+	0.102452i
$237$	−0.305782	−	0.813442i	−0.0198627	−	0.0528387i
$238$	1.15537	+	2.47770i	0.0748914	+	0.160605i
$239$	2.69221	+	15.2683i	0.174144	+	0.987622i	0.939127	+	0.343571i	$0.111637\pi$
$239$	2.69221	+	15.2683i	0.174144	+	0.987622i	−0.764982	+	0.644051i	$0.777252\pi$
$240$	11.8774	+	8.98473i	0.766682	+	0.579962i
$241$	14.6302	+	12.2762i	0.942414	+	0.790779i	0.978004	−	0.208587i	$-0.0668865\pi$
$241$	14.6302	+	12.2762i	0.942414	+	0.790779i	−0.0355896	+	0.999366i	$0.511331\pi$
$242$	0.906597	+	0.906597i	0.0582783	+	0.0582783i
$243$	8.49215	+	13.0722i	0.544772	+	0.838584i
$244$		−	23.8877i		−	1.52925i
$245$	−2.08427	−	2.29121i	−0.133159	−	0.146380i
$246$	−0.336665	−	1.20565i	−0.0214650	−	0.0768695i
$247$	3.10982	+	2.17752i	0.197873	+	0.138552i
$248$	4.25587	−	1.98455i	0.270248	−	0.126019i
$249$	6.40714	−	14.1257i	0.406036	−	0.895177i
$250$	−0.370248	−	1.76049i	−0.0234165	−	0.111343i
$251$	−10.8992	−	6.29267i	−0.687953	−	0.397190i	0.114892	−	0.993378i	$-0.463348\pi$
$251$	−10.8992	−	6.29267i	−0.687953	−	0.397190i	−0.802845	+	0.596188i	$0.796681\pi$
$252$	4.08965	−	16.6546i	0.257624	−	1.04914i
$253$	3.00463	−	11.2134i	0.188900	−	0.704983i
$254$	−0.117224	+	0.0426661i	−0.00735529	+	0.00267711i
$255$	−21.6247	+	6.98213i	−1.35419	+	0.437238i
$256$	10.7006	−	8.97889i	0.668789	−	0.561181i
$257$	−29.5115	−	2.58192i	−1.84088	−	0.161056i	−0.887100	−	0.461576i	$-0.847284\pi$
$257$	−29.5115	−	2.58192i	−1.84088	−	0.161056i	−0.953775	+	0.300521i	$0.902840\pi$
$258$	1.24663	+	1.45438i	0.0776119	+	0.0905456i
$259$	3.21988	+	8.84654i	0.200073	+	0.549697i
$260$	8.05844	−	19.2570i	0.499763	−	1.19427i
$261$	−1.23965	+	8.01102i	−0.0767325	+	0.495869i
$262$	0.315886	+	1.17890i	0.0195155	+	0.0728328i
$263$	0.339036	+	0.484194i	0.0209059	+	0.0298567i	0.829469	−	0.558553i	$-0.188643\pi$
$263$	0.339036	+	0.484194i	0.0209059	+	0.0298567i	−0.808563	+	0.588410i	$0.799754\pi$
$264$	0.470872	+	4.80075i	0.0289801	+	0.295466i
$265$	1.60107	+	5.14289i	0.0983529	+	0.315925i
$266$	−0.368368	+	0.0649533i	−0.0225861	+	0.00398254i
$267$	−12.0750	−	20.4163i	−0.738981	−	1.24946i
$268$	1.14897	+	13.1328i	0.0701847	+	0.802215i
$269$	−29.5187			−1.79979			−0.899894	−	0.436108i	$-0.856357\pi$
$269$	−29.5187			−1.79979			−0.899894	+	0.436108i	$0.856357\pi$
$270$	−1.74654	−	0.667020i	−0.106291	−	0.0405935i
$271$	−9.45815			−0.574542			−0.287271	−	0.957849i	$-0.592748\pi$
$271$	−9.45815			−0.574542			−0.287271	+	0.957849i	$0.592748\pi$
$272$	1.96638	+	22.4758i	0.119229	+	1.36280i
$273$	−23.7174	+	0.249128i	−1.43544	+	0.0150779i
$274$	−1.56939	+	0.276725i	−0.0948101	+	0.0167176i
$275$	−12.6193	+	17.7469i	−0.760974	+	1.07018i
$276$	7.41054	−	5.30578i	0.446062	−	0.319370i
$277$	−11.6968	−	16.7047i	−0.702792	−	1.00369i	−0.998823	−	0.0485123i	$-0.984552\pi$
$277$	−11.6968	−	16.7047i	−0.702792	−	1.00369i	0.296031	−	0.955178i	$-0.404337\pi$
$278$	0.627831	+	2.34310i	0.0376548	+	0.140530i
$279$	16.5749	−	14.5121i	0.992314	−	0.868816i
$280$	1.57064	+	3.83109i	0.0938636	+	0.228951i
$281$	7.06656	+	19.4152i	0.421555	+	1.15821i	0.950816	+	0.309755i	$0.100247\pi$
$281$	7.06656	+	19.4152i	0.421555	+	1.15821i	−0.529261	+	0.848459i	$0.677531\pi$
$282$	−1.51455	+	0.283490i	−0.0901902	+	0.0168816i
$283$	12.8473	+	1.12399i	0.763693	+	0.0668145i	0.462345	−	0.886700i	$-0.347008\pi$
$283$	12.8473	+	1.12399i	0.763693	+	0.0668145i	0.301348	+	0.953514i	$0.402564\pi$
$284$	−9.80446	+	8.22692i	−0.581787	+	0.488178i
$285$	−0.156980	−	3.10519i	−0.00929869	−	0.183936i
$286$	3.11420	−	1.13348i	0.184147	−	0.0670239i
$287$	−3.36621	+	12.5629i	−0.198701	+	0.741563i
$288$	−3.16670	+	4.73101i	−0.186599	+	0.278777i
$289$	−15.0908	−	8.71266i	−0.887692	−	0.512509i
$290$	−0.445793	−	0.863996i	−0.0261779	−	0.0507356i
$291$	−7.35007	−	10.2658i	−0.430869	−	0.601791i
$292$	−17.2588	+	8.04791i	−1.01000	+	0.470968i
$293$	−27.6373	−	19.3518i	−1.61459	−	1.13055i	−0.904538	−	0.426392i	$-0.859784\pi$
$293$	−27.6373	−	19.3518i	−1.61459	−	1.13055i	−0.710048	−	0.704153i	$-0.751327\pi$
$294$	0.270099	−	0.275834i	0.0157525	−	0.0160870i
$295$	−7.59429	+	6.90839i	−0.442157	+	0.402222i
$296$		−	2.07897i		−	0.120837i
$297$	8.40622	+	21.0113i	0.487778	+	1.21920i
$298$	−1.67960	−	1.67960i	−0.0972964	−	0.0972964i
$299$	−9.65629	−	8.10259i	−0.558438	−	0.468585i
$300$	−16.4993	+	4.47852i	−0.952586	+	0.258568i
$301$	−3.45606	−	19.6003i	−0.199204	−	1.12974i
$302$	0.161982	+	0.347372i	0.00932102	+	0.0199890i
$303$	5.78060	−	7.03787i	0.332087	−	0.404315i
$304$	−3.04006	−	0.536044i	−0.174359	−	0.0307442i
$305$	21.4063	+	16.5493i	1.22572	+	0.947611i
$306$	−1.02439	−	2.64054i	−0.0585605	−	0.150950i
$307$	−9.73639	−	2.60886i	−0.555685	−	0.148895i	−0.0299620	−	0.999551i	$-0.509539\pi$
$307$	−9.73639	−	2.60886i	−0.555685	−	0.148895i	−0.525723	+	0.850656i	$0.676205\pi$
$308$	10.5217	−	22.5639i	0.599532	−	1.28570i
$309$	−6.48927	−	0.499116i	−0.369162	−	0.0283937i
$310$	−0.581216	+	2.57744i	−0.0330109	+	0.146389i
$311$	16.5976	+	19.7803i	0.941166	+	1.12164i	0.992413	+	0.122952i	$0.0392361\pi$
$311$	16.5976	+	19.7803i	0.941166	+	1.12164i	−0.0512465	+	0.998686i	$0.516319\pi$
$312$	4.94048	+	1.73964i	0.279700	+	0.0984878i
$313$	5.10324	+	2.37968i	0.288452	+	0.134508i	0.561459	−	0.827505i	$-0.310240\pi$
$313$	5.10324	+	2.37968i	0.288452	+	0.134508i	−0.273007	+	0.962012i	$0.588018\pi$
$314$	−0.630895	−	1.09274i	−0.0356035	−	0.0616670i
$315$	12.0913	+	15.2031i	0.681268	+	0.856597i
$316$	0.495232	−	0.857767i	0.0278590	−	0.0482532i
$317$	−1.51852	+	1.06328i	−0.0852886	+	0.0597197i	−0.615443	−	0.788181i	$-0.711023\pi$
$317$	−1.51852	+	1.06328i	−0.0852886	+	0.0597197i	0.530154	+	0.847901i	$0.322134\pi$
$318$	−0.628413	+	0.236228i	−0.0352396	+	0.0132470i
$319$	−4.02502	+	11.0586i	−0.225358	+	0.619165i
$320$	0.660506	+	16.5008i	0.0369234	+	0.922423i
$321$	−13.4283	+	3.74970i	−0.749493	+	0.209288i
$322$	1.23726	−	0.108246i	0.0689498	−	0.00603233i
$323$	3.33059	−	3.33059i	0.185319	−	0.185319i
$324$	−5.37005	+	16.9360i	−0.298336	+	0.940889i
$325$	11.6738	+	20.5625i	0.647545	+	1.14060i
$326$	1.49150	−	1.77750i	0.0826067	−	0.0984469i
$327$	18.3511	+	10.3395i	1.01482	+	0.571777i
$328$	1.64739	−	2.35271i	0.0909618	−	0.129907i
$329$	15.0441	+	5.47561i	0.829409	+	0.301880i
$330$	−2.29907	−	1.44253i	−0.126559	−	0.0794089i
$331$	−3.34434	+	18.9667i	−0.183822	+	1.04251i	0.743638	+	0.668583i	$0.233099\pi$
$331$	−3.34434	+	18.9667i	−0.183822	+	1.04251i	−0.927460	+	0.373923i	$0.878012\pi$
$332$	17.0761	−	4.57553i	0.937173	−	0.251115i
$333$	−2.72168	−	9.36587i	−0.149147	−	0.513247i
$334$	0.904459	−	0.522190i	0.0494898	−	0.0285730i
$335$	−12.5646	−	8.06875i	−0.686479	−	0.440843i
$336$	17.3928	−	8.33391i	0.948855	−	0.454652i
$337$	0.300674	−	3.43672i	0.0163788	−	0.187210i	−0.983598	−	0.180375i	$-0.942269\pi$
$337$	0.300674	−	3.43672i	0.0163788	−	0.187210i	0.999977	−	0.00683487i	$-0.00217562\pi$
$338$	0.131318	−	1.50097i	0.00714277	−	0.0816423i
$339$	0.540823	−	7.03154i	0.0293735	−	0.381901i
$340$	−21.7930	−	13.9950i	−1.18189	−	0.758987i
$341$	27.6974	−	15.9911i	1.49990	−	0.865966i
$342$	0.385252	−	0.0418764i	0.0208320	−	0.00226442i
$343$	15.7049	−	4.20811i	0.847984	−	0.227217i
$344$	−0.763205	+	4.32835i	−0.0411493	+	0.233369i
$345$	−0.379361	+	10.3166i	−0.0204241	+	0.555426i
$346$	1.75319	+	0.638109i	0.0942520	+	0.0343049i
$347$	4.96478	−	7.09044i	0.266523	−	0.380635i	−0.663475	−	0.748198i	$-0.730919\pi$
$347$	4.96478	−	7.09044i	0.266523	−	0.380635i	0.929998	+	0.367564i	$0.119808\pi$
$348$	−7.95246	+	4.70341i	−0.426296	+	0.252129i
$349$	−6.93929	+	8.26992i	−0.371452	+	0.442679i	−0.919097	−	0.394032i	$-0.871080\pi$
$349$	−6.93929	+	8.26992i	−0.371452	+	0.442679i	0.547645	+	0.836711i	$0.315524\pi$
$350$	−2.24590	−	0.619278i	−0.120049	−	0.0331018i
$351$	24.5346	+	1.36936i	1.30956	+	0.0730910i
$352$	−5.84410	+	5.84410i	−0.311491	+	0.311491i
$353$	−26.6492	+	2.33150i	−1.41839	+	0.124093i	−0.770405	−	0.637555i	$-0.779946\pi$
$353$	−26.6492	+	2.33150i	−1.41839	+	0.124093i	−0.647990	+	0.761649i	$0.724390\pi$
$354$	−0.914260	−	0.895253i	−0.0485924	−	0.0475822i
$355$	−0.579839	−	14.4856i	−0.0307746	−	0.768815i
$356$	9.24644	−	25.4044i	0.490060	−	1.34643i
$357$	−4.80539	+	29.0327i	−0.254328	+	1.53657i
$358$	0.901691	−	0.631371i	0.0476559	−	0.0333690i
$359$	6.82588	−	11.8228i	0.360256	−	0.623982i	−0.627747	−	0.778418i	$-0.716023\pi$
$359$	6.82588	−	11.8228i	0.360256	−	0.623982i	0.988003	+	0.154436i	$0.0493560\pi$
$360$	−1.36084	−	4.06808i	−0.0717224	−	0.214407i
$361$	−9.17777	−	15.8964i	−0.483041	−	0.836651i
$362$	2.36861	+	1.10450i	0.124491	+	0.0580513i
$363$	2.53916	+	13.5655i	0.133271	+	0.712004i
$364$	−17.3767	−	20.7088i	−0.910788	−	1.08544i
$365$	4.74491	−	21.0416i	0.248360	−	1.10137i
$366$	−1.90521	+	2.78268i	−0.0995871	+	0.145453i
$367$	5.50814	−	11.8122i	0.287523	−	0.616594i	−0.708498	−	0.705712i	$-0.750627\pi$
$367$	5.50814	−	11.8122i	0.287523	−	0.616594i	0.996021	+	0.0891181i	$0.0284049\pi$
$368$	9.90056	+	2.65285i	0.516103	+	0.138289i
$369$	4.34153	−	12.7558i	0.226011	−	0.664041i
$370$	0.925436	+	0.715458i	0.0481111	+	0.0371949i
$371$	6.86938	+	1.21126i	0.356640	+	0.0628853i
$372$	24.7719	+	4.10016i	1.28436	+	0.212583i
$373$	−0.799956	−	1.71551i	−0.0414201	−	0.0888258i	0.884509	−	0.466523i	$-0.154494\pi$
$373$	−0.799956	−	1.71551i	−0.0414201	−	0.0888258i	−0.925929	+	0.377698i	$0.876716\pi$
$374$	−0.713999	−	4.04929i	−0.0369200	−	0.209384i
$375$	7.41732	−	17.8881i	0.383029	−	0.923736i
$376$	−2.70829	−	2.27252i	−0.139669	−	0.117196i
$377$	9.03572	+	9.03572i	0.465363	+	0.465363i
$378$	−1.80473	+	1.61392i	−0.0928252	+	0.0830112i
$379$		−	8.64900i		−	0.444270i	−0.975016	−	0.222135i	$-0.928698\pi$
$379$		−	8.64900i		−	0.444270i	0.975016	−	0.222135i	$-0.0713025\pi$
$380$	2.62133	−	2.38458i	0.134472	−	0.122326i
$381$	−1.30063	−	0.333902i	−0.0666335	−	0.0171063i
$382$	2.69796	+	1.88913i	0.138040	+	0.0966563i
$383$	−15.4786	+	7.21777i	−0.790917	+	0.368811i	−0.775723	−	0.631074i	$-0.782614\pi$
$383$	−15.4786	+	7.21777i	−0.790917	+	0.368811i	−0.0151943	+	0.999885i	$0.504837\pi$
$384$	−8.59078	+	0.842608i	−0.438397	+	0.0429992i
$385$	12.9306	+	25.0610i	0.659007	+	1.27723i
$386$	−1.08513	−	0.626503i	−0.0552319	−	0.0318881i
$387$	2.22818	+	20.4986i	0.113265	+	1.04200i
$388$	3.72447	−	13.8999i	0.189081	−	0.705661i
$389$	0.823821	−	0.299846i	0.0417694	−	0.0152028i	−0.321051	−	0.947062i	$-0.604036\pi$
$389$	0.823821	−	0.299846i	0.0417694	−	0.0152028i	0.362820	+	0.931859i	$0.381814\pi$
$390$	−2.47461	+	1.60053i	−0.125307	+	0.0810462i
$391$	−11.9805	+	10.0529i	−0.605882	+	0.508395i
$392$	0.882413	+	0.0772012i	0.0445686	+	0.00389925i
$393$	−4.36343	+	12.3919i	−0.220106	+	0.625087i
$394$	0.291401	+	0.800617i	0.0146806	+	0.0403345i
$395$	0.425570	+	1.03805i	0.0214127	+	0.0522298i
$396$	−12.4245	+	22.6035i	−0.624354	+	1.13587i
$397$	−0.598779	−	2.23467i	−0.0300519	−	0.112155i	0.949271	−	0.314460i	$-0.101823\pi$
$397$	−0.598779	−	2.23467i	−0.0300519	−	0.112155i	−0.979323	+	0.202305i	$0.935157\pi$
$398$	−2.56724	−	3.66640i	−0.128684	−	0.183780i
$399$	−3.66681	−	1.66320i	−0.183570	−	0.0832641i
$400$	−15.6691	−	11.1419i	−0.783457	−	0.557093i
$401$	6.34251	−	1.11835i	0.316730	−	0.0558480i	−0.0130235	−	0.999915i	$-0.504146\pi$
$401$	6.34251	−	1.11835i	0.316730	−	0.0558480i	0.329753	+	0.944067i	$0.393035\pi$
$402$	0.913591	−	1.62148i	0.0455658	−	0.0808722i
$403$	−3.02667	−	34.5950i	−0.150769	−	1.72330i
$404$	10.3803			0.516440
$405$	−11.4564	−	16.5454i	−0.569273	−	0.822149i
$406$	−1.25904			−0.0624849
$407$	−1.23407	−	14.1054i	−0.0611704	−	0.699181i
$408$	3.18998	−	5.66172i	0.157928	−	0.280297i
$409$	−27.7142	+	4.88676i	−1.37038	+	0.241635i	−0.809916	−	0.586546i	$-0.800487\pi$
$409$	−27.7142	+	4.88676i	−1.37038	+	0.241635i	−0.560462	+	0.828180i	$0.689376\pi$
$410$	0.480359	+	1.54299i	0.0237232	+	0.0762028i
$411$	−15.6220	−	7.08585i	−0.770576	−	0.349519i
$412$	−4.25479	−	6.07648i	−0.209619	−	0.299367i
$413$	3.44101	+	12.8420i	0.169321	+	0.631915i
$414$	−1.28643	+	0.0270284i	−0.0632245	+	0.00132837i
$415$	−7.73003	+	18.4722i	−0.379452	+	0.906765i
$416$	3.06934	+	8.43295i	0.150487	+	0.413459i
$417$	−8.67242	+	24.6291i	−0.424690	+	1.20609i
$418$	0.560441	+	0.0490322i	0.0274121	+	0.00239824i
$419$	28.5256	−	23.9358i	1.39357	−	1.16934i	0.429693	−	0.902975i	$-0.358622\pi$
$419$	28.5256	−	23.9358i	1.39357	−	1.16934i	0.963872	−	0.266365i	$-0.0858226\pi$
$420$	−4.64315	+	21.6474i	−0.226563	+	1.05629i
$421$	27.5767	−	10.0371i	1.34400	−	0.489178i	0.432933	−	0.901426i	$-0.357479\pi$
$421$	27.5767	−	10.0371i	1.34400	−	0.489178i	0.911071	+	0.412249i	$0.135256\pi$
$422$	0.392407	−	1.46448i	0.0191021	−	0.0712900i
$423$	−15.1761	−	6.69230i	−0.737886	−	0.325391i
$424$	−1.33400	−	0.770186i	−0.0647849	−	0.0374036i
$425$	27.6394	−	9.83352i	1.34071	−	0.476996i
$426$	1.79828	−	0.176380i	0.0871268	−	0.00854565i
$427$	31.7567	−	14.8084i	1.53682	−	0.716629i
$428$	−13.0167	−	9.11436i	−0.629184	−	0.440559i
$429$	34.5530	+	8.87053i	1.66823	+	0.428273i
$430$	−1.66408	−	1.82930i	−0.0802492	−	0.0882167i
$431$		−	0.480686i		−	0.0231538i	−0.999933	−	0.0115769i	$-0.996315\pi$
$431$		−	0.480686i		−	0.0231538i	0.999933	−	0.0115769i	$-0.00368513\pi$
$432$	−18.5513	+	7.42202i	−0.892548	+	0.357092i
$433$	−5.55599	−	5.55599i	−0.267004	−	0.267004i	0.560888	−	0.827892i	$-0.310460\pi$
$433$	−5.55599	−	5.55599i	−0.267004	−	0.267004i	−0.827892	+	0.560888i	$0.810460\pi$
$434$	2.62110	+	2.19937i	0.125817	+	0.105573i
$435$	1.29460	−	10.3849i	0.0620712	−	0.497917i
$436$	4.16878	+	23.6423i	0.199648	+	1.13226i
$437$	−0.904335	−	1.93935i	−0.0432602	−	0.0927718i
$438$	2.65236	+	0.439009i	0.126735	+	0.0209767i
$439$	12.2268	+	2.15591i	0.583551	+	0.102896i	0.457627	−	0.889144i	$-0.348699\pi$
$439$	12.2268	+	2.15591i	0.583551	+	0.102896i	0.125924	+	0.992040i	$0.459810\pi$
$440$	−0.790458	−	6.17712i	−0.0376836	−	0.294483i
$441$	4.07640	−	0.807416i	0.194114	−	0.0384484i
$442$	−4.31253	−	1.15554i	−0.205126	−	0.0549634i
$443$	7.51833	−	16.1231i	0.357207	−	0.766033i	−0.642793	−	0.766040i	$-0.722225\pi$
$443$	7.51833	−	16.1231i	0.357207	−	0.766033i	1.00000		7.21597e-6i	$2.29692e-6\pi$
$444$	6.28009	−	9.17246i	0.298040	−	0.435306i
$445$	16.3596	+	25.8860i	0.775517	+	1.22711i
$446$	1.07392	+	1.27985i	0.0508517	+	0.0606028i
$447$	−4.70414	−	25.1320i	−0.222498	−	1.18870i
$448$	19.3821	+	9.03801i	0.915717	+	0.427006i
$449$	−1.91039	−	3.30889i	−0.0901568	−	0.156156i	0.817420	−	0.576042i	$-0.195403\pi$
$449$	−1.91039	−	3.30889i	−0.0901568	−	0.156156i	−0.907577	+	0.419886i	$0.862070\pi$
$450$	2.27920	+	0.794229i	0.107442	+	0.0374403i
$451$	9.78070	−	16.9407i	0.460555	−	0.797705i
$452$	6.58425	−	4.61034i	0.309697	−	0.216852i
$453$	−0.673713	+	4.07037i	−0.0316538	+	0.191243i
$454$	0.830236	−	2.28105i	0.0389649	−	0.107055i
$455$	30.5962	−	1.22472i	1.43437	−	0.0574160i
$456$	0.635292	+	0.622085i	0.0297503	+	0.0291318i
$457$	−22.0047	+	1.92516i	−1.02934	+	0.0900553i	−0.589292	−	0.807920i	$-0.700593\pi$
$457$	−22.0047	+	1.92516i	−1.02934	+	0.0900553i	−0.440045	+	0.897976i	$0.645038\pi$
$458$	−0.107016	+	0.107016i	−0.00500053	+	0.00500053i
$459$	6.95901	−	29.6826i	0.324819	−	1.38546i
$460$	−9.36073	+	7.12897i	−0.436446	+	0.332390i
$461$	4.15610	−	4.95304i	0.193569	−	0.230686i	−0.660527	−	0.750803i	$-0.729667\pi$
$461$	4.15610	−	4.95304i	0.193569	−	0.230686i	0.854095	+	0.520116i	$0.174111\pi$
$462$	−3.02531	+	1.78929i	−0.140750	+	0.0832455i
$463$	−0.176051	+	0.251426i	−0.00818177	+	0.0116848i	−0.823222	−	0.567719i	$-0.807826\pi$
$463$	−0.176051	+	0.251426i	−0.00818177	+	0.0116848i	0.815040	+	0.579404i	$0.196715\pi$
$464$	−9.76390	−	3.55377i	−0.453278	−	0.164980i
$465$	−20.8361	+	19.3581i	−0.966253	+	0.897711i
$466$	−0.156950	+	0.890106i	−0.00727056	+	0.0412334i
$467$	−41.3450	+	11.0784i	−1.91322	+	0.512645i	−0.920749	+	0.390156i	$0.872421\pi$
$467$	−41.3450	+	11.0784i	−1.91322	+	0.512645i	−0.992470	+	0.122489i	$0.960912\pi$
$468$	16.5425	+	22.5994i	0.764676	+	1.04466i
$469$	−16.7467	+	9.66873i	−0.773292	+	0.446460i
$470$	1.94363	−	0.423505i	0.0896530	−	0.0195348i
$471$	1.04159	−	13.5422i	0.0479938	−	0.623993i
$472$	0.255886	−	2.92479i	0.0117781	−	0.134624i
$473$	−2.60893	+	29.8202i	−0.119959	+	1.37113i
$474$	−0.126103	+	0.0604232i	−0.00579209	+	0.00277533i
$475$	0.320829	+	4.00107i	0.0147206	+	0.183582i
$476$	−29.0467	+	16.7701i	−1.33135	+	0.768658i
$477$	−7.01805	−	1.72333i	−0.321335	−	0.0789058i
$478$	2.40968	−	0.645671i	0.110216	−	0.0295323i
$479$	−7.22789	+	40.9914i	−0.330251	+	1.87295i	0.139612	+	0.990206i	$0.455415\pi$
$479$	−7.22789	+	40.9914i	−0.330251	+	1.87295i	−0.469863	+	0.882740i	$0.655697\pi$
$480$	3.90624	−	6.22564i	0.178295	−	0.284160i
$481$	−14.4474	−	5.25842i	−0.658745	−	0.239763i
$482$	1.76264	−	2.51732i	0.0802862	−	0.114661i
$483$	11.6475	+	6.56255i	0.529980	+	0.298606i
$484$	−10.1109	+	12.0497i	−0.459588	+	0.547716i
$485$	9.87573	+	12.9674i	0.448434	+	0.588819i
$486$	1.97632	−	1.54458i	0.0896479	−	0.0700635i
$487$	16.8595	−	16.8595i	0.763975	−	0.763975i	−0.213064	−	0.977038i	$-0.568344\pi$
$487$	16.8595	−	16.8595i	0.763975	−	0.763975i	0.977038	+	0.213064i	$0.0683442\pi$
$488$	−7.70840	+	0.674397i	−0.348943	+	0.0305285i
$489$	24.0567	−	6.71758i	1.08788	−	0.303779i
$490$	−0.338040	+	0.366232i	−0.0152711	+	0.0165447i
$491$	−5.41828	+	14.8866i	−0.244524	+	0.671823i	0.755340	+	0.655333i	$0.227472\pi$
$491$	−5.41828	+	14.8866i	−0.244524	+	0.671823i	−0.999864	+	0.0164907i	$0.994751\pi$
$492$	14.3753	−	5.40386i	0.648091	−	0.243625i
$493$	12.9870	−	9.09358i	0.584904	−	0.409554i
$494$	0.305434	−	0.529027i	0.0137421	−	0.0238020i
$495$	−11.6478	−	26.7935i	−0.523532	−	1.20428i
$496$	14.1189	+	24.4546i	0.633955	+	1.09804i
$497$	−17.0150	−	7.93420i	−0.763225	−	0.355898i
$498$	−2.35413	−	0.828936i	−0.105491	−	0.0371455i
$499$	0.350248	+	0.417409i	0.0156792	+	0.0186858i	0.773827	−	0.633397i	$-0.218340\pi$
$499$	0.350248	+	0.417409i	0.0156792	+	0.0186858i	−0.758148	+	0.652083i	$0.773895\pi$
$500$	21.1206	−	6.40758i	0.944543	−	0.286556i
$501$	11.2089	+	0.862118i	0.500775	+	0.0385166i
$502$	−0.855835	+	1.83534i	−0.0381978	+	0.0819154i
$503$	−18.7290	−	5.01841i	−0.835083	−	0.223760i	−0.184153	−	0.982898i	$-0.558954\pi$
$503$	−18.7290	−	5.01841i	−0.835083	−	0.223760i	−0.650930	+	0.759138i	$0.725621\pi$
$504$	−5.48979	−	0.849509i	−0.244535	−	0.0378401i
$505$	−7.19145	+	9.30204i	−0.320015	+	0.413936i
$506$	−1.83960	−	0.324371i	−0.0817801	−	0.0144200i
$507$	10.2940	−	12.5330i	0.457174	−	0.556609i
$508$	−0.646805	−	1.38708i	−0.0286974	−	0.0615417i
$509$	4.57685	+	25.9566i	0.202865	+	1.15051i	0.900764	+	0.434310i	$0.143008\pi$
$509$	4.57685	+	25.9566i	0.202865	+	1.15051i	−0.697898	+	0.716197i	$0.745881\pi$
$510$	1.42247	+	3.36843i	0.0629880	+	0.149157i
$511$	−21.3981	−	17.9551i	−0.946595	−	0.794287i
$512$	−8.63735	−	8.63735i	−0.381720	−	0.381720i
$513$	3.67644	+	1.97084i	0.162319	+	0.0870146i
$514$			4.76676i			0.210253i
$515$	8.39298	+	0.396940i	0.369839	+	0.0174913i
$516$	−16.4423	+	16.7913i	−0.723830	+	0.739197i
$517$	−19.7242	−	13.8111i	−0.867471	−	0.607410i
$518$	1.37290	−	0.640195i	0.0603219	−	0.0281286i
$519$	11.6912	+	16.3291i	0.513189	+	0.716767i
$520$	−6.44161	−	2.05674i	−0.282483	−	0.0901940i
$521$	−6.99745	−	4.03998i	−0.306564	−	0.176995i	0.338824	−	0.940850i	$-0.389971\pi$
$521$	−6.99745	−	4.03998i	−0.306564	−	0.176995i	−0.645388	+	0.763855i	$0.723304\pi$
$522$	1.30151	+	0.0863636i	0.0569657	+	0.00378003i
$523$	−9.26181	+	34.5655i	−0.404991	+	1.51145i	0.399083	+	0.916915i	$0.369329\pi$
$523$	−9.26181	+	34.5655i	−0.404991	+	1.51145i	−0.804073	+	0.594530i	$0.797338\pi$
$524$	−14.0706	+	5.12130i	−0.614679	+	0.223725i
$525$	−16.1820	−	19.1581i	−0.706241	−	0.836128i
$526$	0.0728594	−	0.0611363i	0.00317682	−	0.00266567i
$527$	−42.9220	−	3.75519i	−1.86971	−	0.163579i
$528$	−28.5120	+	5.33681i	−1.24082	+	0.232255i
$529$	−5.43640	−	14.9364i	−0.236365	−	0.649408i
$530$	0.801928	−	0.328768i	0.0348335	−	0.0142808i
$531$	−2.67621	−	13.5113i	−0.116137	−	0.586342i
$532$	−1.18774	−	4.43271i	−0.0514951	−	0.192182i
$533$	−12.1830	−	17.3991i	−0.527702	−	0.753637i
$534$	−3.10330	+	2.22189i	−0.134293	+	0.0961507i
$535$	17.1855	−	5.35013i	0.742993	−	0.231306i
$536$	4.20543	−	0.741531i	0.181647	−	0.0320293i
$537$	11.8482	−	0.124454i	0.511289	−	0.00537059i
$538$	0.413971	+	4.73172i	0.0178476	+	0.203999i
$539$	6.03285			0.259853
$540$	6.28471	−	22.0593i	0.270451	−	0.949280i
$541$	−6.99126			−0.300578			−0.150289	−	0.988642i	$-0.548020\pi$
$541$	−6.99126			−0.300578			−0.150289	+	0.988642i	$0.548020\pi$
$542$	0.132641	+	1.51610i	0.00569743	+	0.0651220i
$543$	14.3212	+	24.2140i	0.614580	+	1.03912i
$544$	10.9651	−	1.93344i	0.470123	−	0.0828954i
$545$	−24.0746	−	12.6436i	−1.03124	−	0.541592i
$546$	0.372547	+	3.79829i	0.0159435	+	0.162552i
$547$	6.72270	+	9.60101i	0.287442	+	0.410509i	0.936741	−	0.350024i	$-0.113826\pi$
$547$	6.72270	+	9.60101i	0.287442	+	0.410509i	−0.649299	+	0.760533i	$0.724938\pi$
$548$	−5.06022	−	18.8850i	−0.216162	−	0.806727i
$549$	−33.8439	+	13.1297i	−1.44442	+	0.560360i
$550$	3.02173	+	1.77394i	0.128847	+	0.0756409i
$551$	0.741915	+	2.03839i	0.0316066	+	0.0868385i
$552$	−1.92135	−	2.24154i	−0.0817781	−	0.0954061i
$553$	1.44733	+	0.126625i	0.0615469	+	0.00538465i
$554$	−2.51366	+	2.10921i	−0.106795	+	0.0896117i
$555$	3.86883	+	11.9824i	0.164223	+	0.508624i
$556$	−27.9658	+	10.1787i	−1.18601	+	0.431673i
$557$	−3.09577	+	11.5536i	−0.131172	+	0.489541i	−0.999984	−	0.00560082i	$-0.998217\pi$
$557$	−3.09577	+	11.5536i	−0.131172	+	0.489541i	0.868812	+	0.495142i	$0.164884\pi$
$558$	−2.55867	−	2.45336i	−0.108317	−	0.103859i
$559$	28.1487	+	16.2516i	1.19056	+	0.687371i
$560$	−22.1268	+	11.4167i	−0.935030	+	0.482445i
$561$	18.2827	−	40.3074i	0.771897	−	1.70178i
$562$	3.01306	−	1.40502i	0.127098	−	0.0592670i
$563$	6.90509	+	4.83500i	0.291015	+	0.203771i	0.709962	−	0.704240i	$-0.248712\pi$
$563$	6.90509	+	4.83500i	0.291015	+	0.203771i	−0.418947	+	0.908010i	$0.637601\pi$
$564$	−5.08426	−	18.2076i	−0.214086	−	0.766677i
$565$	−0.430110	+	9.09432i	−0.0180949	+	0.382601i
$566$		−	2.07513i		−	0.0872241i
$567$	−25.8440	+	3.35988i	−1.08535	+	0.141102i
$568$	2.93157	+	2.93157i	0.123006	+	0.123006i
$569$	9.07677	+	7.61631i	0.380518	+	0.319292i	0.812906	−	0.582395i	$-0.197884\pi$
$569$	9.07677	+	7.61631i	0.380518	+	0.319292i	−0.432388	+	0.901688i	$0.642329\pi$
$570$	−0.495547	+	0.0687105i	−0.0207562	+	0.00287797i
$571$	5.84395	+	33.1427i	0.244562	+	1.38698i	0.821508	+	0.570197i	$0.193133\pi$
$571$	5.84395	+	33.1427i	0.244562	+	1.38698i	−0.576946	+	0.816782i	$0.695756\pi$
$572$	17.1832	+	36.8495i	0.718465	+	1.54075i
$573$	12.4749	+	33.1858i	0.521148	+	1.38636i
$574$	2.06098	+	0.363406i	0.0860235	+	0.0151683i
$575$	0.0966484	−	13.3273i	0.00403052	−	0.555787i
$576$	−19.4160	−	10.6725i	−0.809001	−	0.444685i
$577$	28.4975	+	7.63587i	1.18637	+	0.317886i	0.797448	−	0.603387i	$-0.206183\pi$
$577$	28.4975	+	7.63587i	1.18637	+	0.317886i	0.388917	+	0.921273i	$0.372849\pi$
$578$	−1.18497	+	2.54117i	−0.0492881	+	0.105699i
$579$	−5.82821	−	12.1634i	−0.242212	−	0.505495i
$580$	10.0830	−	6.37229i	0.418673	−	0.264595i
$581$	16.6686	+	19.8648i	0.691529	+	0.824132i
$582$	−1.54248	+	1.32215i	−0.0639378	+	0.0548049i
$583$	−9.50816	−	4.43373i	−0.393788	−	0.183626i
$584$	3.08426	+	5.34209i	0.127627	+	0.221057i
$585$	−31.7124	−	0.832700i	−1.31115	−	0.0344279i
$586$	−2.71442	+	4.70152i	−0.112132	+	0.194218i
$587$	18.6182	−	13.0366i	0.768453	−	0.538077i	−0.122338	−	0.992488i	$-0.539039\pi$
$587$	18.6182	−	13.0366i	0.768453	−	0.538077i	0.890792	+	0.454412i	$0.150150\pi$
$588$	3.66003	+	3.00618i	0.150937	+	0.123973i
$589$	2.01626	−	5.53962i	0.0830784	−	0.228256i
$590$	1.21389	+	1.12045i	0.0499749	+	0.0461280i
$591$	−2.28049	+	8.88308i	−0.0938067	+	0.365401i
$592$	12.4540	−	1.08958i	0.511855	−	0.0447815i
$593$	−9.57575	+	9.57575i	−0.393229	+	0.393229i	−0.875837	−	0.482608i	$-0.839690\pi$
$593$	−9.57575	+	9.57575i	−0.393229	+	0.393229i	0.482608	+	0.875837i	$0.339690\pi$
$594$	3.25012	−	1.64214i	0.133354	−	0.0673778i
$595$	5.09536	−	37.6477i	0.208889	−	1.54341i
$596$	18.7319	−	22.3238i	0.767288	−	0.914419i
$597$	−0.506047	−	48.1765i	−0.0207111	−	1.97173i
$598$	−1.16339	+	1.66149i	−0.0475744	+	0.0679433i
$599$	−13.5529	−	4.93284i	−0.553755	−	0.201550i	0.0499591	−	0.998751i	$-0.484091\pi$
$599$	−13.5529	−	4.93284i	−0.553755	−	0.201550i	−0.603714	+	0.797201i	$0.706313\pi$
$600$	1.91099	+	5.19776i	0.0780160	+	0.212198i
$601$	4.30406	−	24.4095i	0.175566	−	0.995686i	−0.761922	−	0.647669i	$-0.775744\pi$
$601$	4.30406	−	24.4095i	0.175566	−	0.995686i	0.937488	−	0.348017i	$-0.113145\pi$
$602$	−3.09337	+	0.828865i	−0.126076	+	0.0337820i
$603$	17.9750	−	8.84619i	0.731997	−	0.360245i
$604$	−4.07234	+	2.35117i	−0.165701	+	0.0956676i
$605$	−3.79324	−	17.4087i	−0.154217	−	0.707763i
$606$	−1.20921	−	0.827904i	−0.0491206	−	0.0336313i
$607$	−2.42989	+	27.7738i	−0.0986264	+	1.12730i	0.772088	+	0.635516i	$0.219212\pi$
$607$	−2.42989	+	27.7738i	−0.0986264	+	1.12730i	−0.870714	+	0.491789i	$0.836343\pi$
$608$	−0.132774	+	1.51762i	−0.00538471	+	0.0615476i
$609$	−11.1827	−	7.65641i	−0.453144	−	0.310253i
$610$	2.35258	−	3.66342i	0.0952530	−	0.148328i
$611$	−22.6427	+	13.0728i	−0.916025	+	0.528867i
$612$	31.1771	−	15.3435i	1.26026	−	0.620223i
$613$	32.4313	−	8.68995i	1.30989	−	0.350984i	0.464708	−	0.885464i	$-0.346159\pi$
$613$	32.4313	−	8.68995i	1.30989	−	0.350984i	0.845181	+	0.534480i	$0.179493\pi$
$614$	−0.281645	+	1.59729i	−0.0113662	+	0.0644612i
$615$	−5.11667	+	16.6259i	−0.206324	+	0.670419i
$616$	−7.57828	−	2.75827i	−0.305337	−	0.111134i
$617$	16.2918	−	23.2671i	0.655884	−	0.936700i	−0.344113	−	0.938928i	$-0.611820\pi$
$617$	16.2918	−	23.2671i	0.655884	−	0.936700i	0.999998	+	0.00222854i	$0.000709368\pi$
$618$	0.0109998	+	1.04720i	0.000442478	+	0.0421246i
$619$	16.2376	−	19.3513i	0.652646	−	0.777793i	−0.333665	−	0.942692i	$-0.608285\pi$
$619$	16.2376	−	19.3513i	0.652646	−	0.777793i	0.986310	+	0.164899i	$0.0527299\pi$
$620$	−32.1226	−	4.34757i	−1.29008	−	0.174603i
$621$	−11.5903	−	7.58292i	−0.465103	−	0.304292i
$622$	2.93792	−	2.93792i	0.117800	−	0.117800i
$623$	39.5050	−	3.45624i	1.58274	−	0.138471i
$624$	−7.83197	+	30.5075i	−0.313530	+	1.22128i
$625$	−8.89031	+	23.3658i	−0.355613	+	0.934633i
$626$	0.309884	−	0.851399i	0.0123854	−	0.0340287i
$627$	4.67962	+	3.84364i	0.186886	+	0.153500i
$628$	12.6808	−	8.87918i	0.506018	−	0.354318i
$629$	−9.53762	+	16.5196i	−0.380290	+	0.658681i
$630$	2.26742	−	2.15139i	0.0903361	−	0.0857134i
$631$	2.76033	+	4.78103i	0.109887	+	0.190330i	0.915724	−	0.401807i	$-0.131618\pi$
$631$	2.76033	+	4.78103i	0.109887	+	0.190330i	−0.805837	+	0.592137i	$0.798284\pi$
$632$	−0.290777	−	0.135591i	−0.0115665	−	0.00539354i
$633$	12.3911	−	10.6211i	0.492502	−	0.422153i
$634$	0.191734	+	0.228500i	0.00761475	+	0.00907490i
$635$	1.69110	+	0.381346i	0.0671092	+	0.0151332i
$636$	−3.55910	−	7.42780i	−0.141127	−	0.294532i
$637$	2.76842	−	5.93690i	0.109689	−	0.235229i
$638$	1.82910	+	0.490105i	0.0724146	+	0.0194034i
$639$	17.0448	+	9.36903i	0.674280	+	0.370633i
$640$	11.0537	−	1.41450i	0.436937	−	0.0559129i
$641$	−45.0144	−	7.93726i	−1.77796	−	0.313503i	−0.814264	−	0.580494i	$-0.802859\pi$
$641$	−45.0144	−	7.93726i	−1.77796	−	0.313503i	−0.963699	+	0.266991i	$0.913971\pi$
$642$	0.789378	+	2.09990i	0.0311543	+	0.0828766i
$643$	6.68798	+	14.3424i	0.263748	+	0.565610i	0.992929	−	0.118711i	$-0.0378763\pi$
$643$	6.68798	+	14.3424i	0.263748	+	0.565610i	−0.729181	+	0.684321i	$0.760099\pi$
$644$	2.64595	+	15.0059i	0.104265	+	0.591316i
$645$	−3.65598	−	26.3673i	−0.143954	−	1.03821i
$646$	−0.580587	−	0.487170i	−0.0228429	−	0.0191675i
$647$	8.27160	+	8.27160i	0.325190	+	0.325190i	0.850754	−	0.525564i	$-0.176146\pi$
$647$	8.27160	+	8.27160i	0.325190	+	0.325190i	−0.525564	+	0.850754i	$0.676146\pi$
$648$	5.61674	+	1.25474i	0.220646	+	0.0492909i
$649$		−	19.9961i		−	0.784915i
$650$	3.13237	−	2.15962i	0.122861	−	0.0847074i
$651$	9.90572	+	35.4740i	0.388236	+	1.39033i
$652$	23.3193	+	16.3284i	0.913255	+	0.639468i
$653$	44.7948	−	20.8882i	1.75296	−	0.817417i	0.768944	−	0.639316i	$-0.220783\pi$
$653$	44.7948	−	20.8882i	1.75296	−	0.817417i	0.984012	−	0.178100i	$-0.0569952\pi$
$654$	1.40002	−	3.08659i	0.0547452	−	0.120695i
$655$	5.15878	−	16.1571i	0.201570	−	0.631308i
$656$	14.9572	+	8.63557i	0.583982	+	0.337162i
$657$	20.8884	+	20.0287i	0.814933	+	0.781393i
$658$	0.666736	−	2.48829i	0.0259921	−	0.0970037i
$659$	25.0705	−	9.12491i	0.976607	−	0.355456i	0.196087	−	0.980586i	$-0.437176\pi$
$659$	25.0705	−	9.12491i	0.976607	−	0.355456i	0.780520	+	0.625130i	$0.214954\pi$
$660$	15.1722	−	29.6414i	0.590575	−	1.15379i
$661$	−33.2465	+	27.8971i	−1.29314	+	1.08507i	−0.301851	+	0.953355i	$0.597604\pi$
$661$	−33.2465	+	27.8971i	−1.29314	+	1.08507i	−0.991287	+	0.131716i	$0.957951\pi$
$662$	3.08718	+	0.270093i	0.119987	+	0.0104975i
$663$	−31.2766	−	36.4886i	−1.21468	−	1.41710i
$664$	−1.95858	−	5.38117i	−0.0760078	−	0.208830i
$665$	4.79511	+	2.00660i	0.185947	+	0.0778127i
$666$	−1.46314	+	0.567620i	−0.0566954	+	0.0219948i
$667$	−1.86416	−	6.95716i	−0.0721808	−	0.269382i
$668$	7.34927	+	10.4958i	0.284352	+	0.406096i
$669$	1.75551	+	17.8983i	0.0678720	+	0.691987i
$670$	−1.11718	+	2.12721i	−0.0431603	+	0.0821812i
$671$	−51.8999	+	9.15135i	−2.00357	+	0.353284i
$672$	−4.84523	−	8.19225i	−0.186909	−	0.316023i
$673$	0.873070	+	9.97924i	0.0336544	+	0.384671i	0.994278	+	0.106820i	$0.0340668\pi$
$673$	0.873070	+	9.97924i	0.0336544	+	0.384671i	−0.960624	+	0.277852i	$0.910378\pi$
$674$	−0.555107			−0.0213819
$675$	15.4138	+	20.9145i	0.593278	+	0.804998i
$676$	18.4852			0.710968
$677$	3.14213	+	35.9148i	0.120762	+	1.38032i	0.778772	+	0.627307i	$0.215843\pi$
$677$	3.14213	+	35.9148i	0.120762	+	1.38032i	−0.658010	+	0.753009i	$0.728602\pi$
$678$	−1.13471	+	0.0119190i	−0.0435782	+	0.000457747i
$679$	20.7876	−	3.66542i	0.797756	−	0.140666i
$680$	−3.90084	+	7.42756i	−0.149590	+	0.284834i
$681$	21.2456	−	15.2113i	0.814131	−	0.582900i
$682$	−2.95173	−	4.21550i	−0.113027	−	0.161420i
$683$	−10.9399	−	40.8281i	−0.418602	−	1.56224i	−0.777510	−	0.628871i	$-0.783517\pi$
$683$	−10.9399	−	40.8281i	−0.418602	−	1.56224i	0.358908	−	0.933373i	$-0.383149\pi$
$684$	0.923751	+	4.66373i	0.0353205	+	0.178322i
$685$	20.4290	+	8.54887i	0.780551	+	0.326636i
$686$	−0.894787	−	2.45841i	−0.0341631	−	0.0938624i
$687$	−1.60129	+	0.299726i	−0.0610930	+	0.0114352i
$688$	−26.3288	−	2.30347i	−1.00378	−	0.0878191i
$689$	−8.72642	+	7.32234i	−0.332450	+	0.278959i
$690$	1.65902	−	0.0838700i	0.0631578	−	0.00319288i
$691$	−5.10153	+	1.85681i	−0.194071	+	0.0706362i	−0.437227	−	0.899351i	$-0.644040\pi$
$691$	−5.10153	+	1.85681i	−0.194071	+	0.0706362i	0.243156	+	0.969987i	$0.421817\pi$
$692$	−5.92425	+	22.1096i	−0.225206	+	0.840481i
$693$	−37.7516	−	2.50506i	−1.43406	−	0.0951592i
$694$	−1.20619	−	0.696395i	−0.0457864	−	0.0264348i
$695$	10.2532	−	32.1125i	0.388926	−	1.21810i
$696$	1.74227	+	2.43342i	0.0660406	+	0.0922384i
$697$	−23.8838	+	11.1372i	−0.904663	+	0.421851i
$698$	1.42295	+	0.996358i	0.0538593	+	0.0377127i
$699$	−6.80690	+	6.95142i	−0.257461	+	0.262927i
$700$	5.16726	−	28.1114i	0.195304	−	1.06251i
$701$		−	8.37641i		−	0.316373i	−0.987409	−	0.158186i	$-0.949435\pi$
$701$		−	8.37641i		−	0.316373i	0.987409	−	0.158186i	$-0.0505647\pi$
$702$	−0.124572	−	3.95199i	−0.00470167	−	0.149158i
$703$	−1.84550	−	1.84550i	−0.0696043	−	0.0696043i
$704$	−24.6396	−	20.6751i	−0.928639	−	0.779221i
$705$	19.8386	+	8.05800i	0.747164	+	0.303482i
$706$	0.747459	+	4.23905i	0.0281310	+	0.159539i
$707$	6.43494	+	13.7998i	0.242011	+	0.518994i
$708$	9.96409	−	12.1313i	0.374474	−	0.455921i
$709$	−27.2222	−	4.80001i	−1.02235	−	0.180268i	−0.362752	−	0.931886i	$-0.618163\pi$
$709$	−27.2222	−	4.80001i	−1.02235	−	0.180268i	−0.659599	+	0.751617i	$0.729274\pi$
$710$	−2.31384	+	0.296092i	−0.0868368	+	0.0111121i
$711$	−1.48748	−	0.230177i	−0.0557848	−	0.00863232i
$712$	−8.45886	−	2.26655i	−0.317009	−	0.0849424i
$713$	−8.27234	+	17.7401i	−0.309802	+	0.664372i
$714$	4.72120	+	0.363126i	0.176686	+	0.0135896i
$715$	−44.9261	−	10.1309i	−1.68014	−	0.378875i
$716$	8.68071	+	10.3453i	0.324413	+	0.386621i
$717$	25.3290	+	8.91885i	0.945929	+	0.333080i
$718$	−1.99086	−	0.928354i	−0.0742983	−	0.0346459i
$719$	−13.4438	−	23.2854i	−0.501371	−	0.868400i	−0.999999	−	0.00158362i	$-0.999496\pi$
$719$	−13.4438	−	23.2854i	−0.501371	−	0.868400i	0.498628	−	0.866816i	$-0.333837\pi$
$720$	23.6565	−	10.2841i	0.881626	−	0.383266i
$721$	5.44055	−	9.42331i	0.202617	−	0.350942i
$722$	−2.41940	+	1.69408i	−0.0900409	+	0.0630473i
$723$	30.9639	−	11.6397i	1.15156	−	0.432884i
$724$	−10.9664	+	30.1299i	−0.407563	+	1.11977i
$725$	−1.27510	+	13.4503i	−0.0473560	+	0.499532i
$726$	2.13888	−	0.597258i	0.0793812	−	0.0221663i
$727$	−19.0908	+	1.67023i	−0.708040	+	0.0619455i	−0.435487	−	0.900195i	$-0.643424\pi$
$727$	−19.0908	+	1.67023i	−0.708040	+	0.0619455i	−0.272553	+	0.962141i	$0.587868\pi$
$728$	−6.19200	+	6.19200i	−0.229491	+	0.229491i
$729$	26.9464	−	1.70047i	0.998015	−	0.0629802i
$730$	−3.43941	−	0.465500i	−0.127298	−	0.0172289i
$731$	25.9216	−	30.8921i	0.958743	−	1.14259i
$732$	−36.0469	−	20.3099i	−1.33233	−	0.750674i
$733$	20.2855	−	28.9707i	0.749261	−	1.07006i	−0.245656	−	0.969357i	$-0.579003\pi$
$733$	20.2855	−	28.9707i	0.749261	−	1.07006i	0.994917	−	0.100699i	$-0.0321079\pi$
$734$	−1.97069	−	0.717274i	−0.0727397	−	0.0264751i
$735$	−5.22956	+	1.19716i	−0.192895	+	0.0441579i
$736$	0.878364	−	4.98145i	0.0323769	−	0.183619i
$737$	28.0930	−	7.52749i	1.03482	−	0.277279i
$738$	−2.10558	−	0.517039i	−0.0775076	−	0.0190325i
$739$	−16.8271	+	9.71511i	−0.618993	+	0.357376i	−0.776477	−	0.630146i	$-0.782995\pi$
$739$	−16.8271	+	9.71511i	−0.618993	+	0.357376i	0.157484	+	0.987522i	$0.449662\pi$
$740$	−7.75471	+	12.0756i	−0.285069	+	0.443908i
$741$	5.92994	−	2.84138i	0.217842	−	0.104381i
$742$	0.0978225	−	1.11812i	0.00359118	−	0.0410473i
$743$	−2.72437	+	31.1397i	−0.0999474	+	1.14240i	0.766195	+	0.642608i	$0.222147\pi$
$743$	−2.72437	+	31.1397i	−0.0999474	+	1.14240i	−0.866143	+	0.499796i	$0.833408\pi$
$744$	0.623732	−	8.10948i	0.0228671	−	0.297308i
$745$	7.02749	+	32.2519i	0.257467	+	1.18162i
$746$	−0.263770	+	0.152288i	−0.00965730	+	0.00557564i
$747$	−15.8683	−	21.6784i	−0.580591	−	0.793171i
$748$	48.7265	−	13.0562i	1.78162	−	0.477383i
$749$	4.04754	−	22.9547i	0.147894	−	0.838747i
$750$	−2.97140	−	0.938100i	−0.108500	−	0.0342546i
$751$	21.6560	+	7.88215i	0.790240	+	0.287624i	0.705436	−	0.708774i	$-0.250751\pi$
$751$	21.6560	+	7.88215i	0.790240	+	0.287624i	0.0848041	+	0.996398i	$0.472974\pi$
$752$	12.1941	−	17.4149i	0.444672	−	0.635057i
$753$	−18.7625	+	11.0969i	−0.683743	+	0.404394i
$754$	1.32167	−	1.57510i	0.0481322	−	0.0573618i
$755$	0.714367	−	5.27819i	0.0259985	−	0.192093i
$756$	−21.6549	−	20.3315i	−0.787583	−	0.739449i
$757$	10.7861	−	10.7861i	0.392029	−	0.392029i	−0.483381	−	0.875410i	$-0.660592\pi$
$757$	10.7861	−	10.7861i	0.392029	−	0.392029i	0.875410	+	0.483381i	$0.160592\pi$
$758$	−1.38640	+	0.121294i	−0.0503561	+	0.00440559i
$759$	−14.3666	−	14.0679i	−0.521475	−	0.510634i
$760$	−0.843493	−	0.778564i	−0.0305967	−	0.0282415i
$761$	3.19211	−	8.77024i	0.115714	−	0.317921i	−0.868293	−	0.496051i	$-0.834783\pi$
$761$	3.19211	−	8.77024i	0.115714	−	0.317921i	0.984007	+	0.178131i	$0.0570049\pi$
$762$	−0.0352829	+	0.213168i	−0.00127816	+	0.00772228i
$763$	−28.8462	+	20.1984i	−1.04430	+	0.731229i
$764$	−20.2039	+	34.9942i	−0.730951	+	1.26604i
$765$	−7.84972	+	38.5684i	−0.283807	+	1.39444i
$766$	1.37405	+	2.37992i	0.0496463	+	0.0859899i
$767$	−19.6781	−	9.17603i	−0.710533	−	0.331327i
$768$	−4.45136	−	23.7814i	−0.160624	−	0.858139i
$769$	7.77292	+	9.26340i	0.280299	+	0.334047i	0.887764	−	0.460300i	$-0.152258\pi$
$769$	7.77292	+	9.26340i	0.280299	+	0.334047i	−0.607465	+	0.794346i	$0.707814\pi$
$770$	3.83582	−	2.42418i	0.138233	−	0.0873613i
$771$	−28.9875	+	42.3380i	−1.04396	+	1.52477i
$772$	6.49674	−	13.9323i	0.233823	−	0.501435i
$773$	−1.78767	−	0.479004i	−0.0642980	−	0.0172286i	0.226527	−	0.974005i	$-0.427263\pi$
$773$	−1.78767	−	0.479004i	−0.0642980	−	0.0172286i	−0.290825	+	0.956776i	$0.593930\pi$
$774$	3.25459	−	0.644640i	0.116984	−	0.0231711i
$775$	26.1504	−	25.7739i	0.939350	−	0.925824i
$776$	−4.59055	−	0.809438i	−0.164791	−	0.0290571i
$777$	16.0872	+	2.66269i	0.577124	+	0.0955234i
$778$	−0.0596173	−	0.127850i	−0.00213738	−	0.00458363i
$779$	−0.626118	−	3.55089i	−0.0224330	−	0.127224i
$780$	−22.2076	−	28.5330i	−0.795160	−	1.02165i
$781$	21.6304	+	18.1500i	0.773996	+	0.649459i
$782$	1.77944	+	1.77944i	0.0636327	+	0.0636327i
$783$	11.0348	+	8.68180i	0.394350	+	0.310262i
$784$			5.32653i			0.190233i
$785$	−0.828361	+	17.5150i	−0.0295655	+	0.625137i
$786$	2.04755	+	0.525653i	0.0730338	+	0.0187494i
$787$	−13.9857	−	9.79291i	−0.498537	−	0.349080i	0.297106	−	0.954844i	$-0.403978\pi$
$787$	−13.9857	−	9.79291i	−0.498537	−	0.349080i	−0.795644	+	0.605765i	$0.792867\pi$
$788$	−9.47347	+	4.41755i	−0.337479	+	0.157369i
$789$	1.01891	−	0.0999377i	0.0362742	−	0.00355788i
$790$	0.160426	−	0.0827745i	0.00570770	−	0.00294498i
$791$	10.2108	+	5.89518i	0.363053	+	0.209609i
$792$	7.64475	+	3.37116i	0.271644	+	0.119789i
$793$	−14.8106	+	55.2739i	−0.525940	+	1.96283i
$794$	−0.349811	+	0.127321i	−0.0124143	+	0.00451844i
$795$	9.12196	+	1.95657i	0.323522	+	0.0693922i
$796$	42.0652	−	35.2969i	1.49096	−	1.25107i
$797$	16.8357	+	1.47293i	0.596350	+	0.0521739i	0.381335	−	0.924437i	$-0.375464\pi$
$797$	16.8357	+	1.47293i	0.596350	+	0.0521739i	0.215015	+	0.976611i	$0.431020\pi$
$798$	−0.215180	+	0.611097i	−0.00761728	+	0.0216326i
$799$	11.0947	+	30.4824i	0.392502	+	1.07839i
$800$	−4.80364	+	8.18254i	−0.169834	+	0.289296i
$801$	−41.0750	+	0.863001i	−1.45131	+	0.0304926i
$802$	−0.268215	−	1.00099i	−0.00947098	−	0.0353462i
$803$	24.0972	+	34.4144i	0.850372	+	1.21446i
$804$	20.7945	+	9.43200i	0.733365	+	0.332641i
$805$	−15.2803	−	8.02495i	−0.538558	−	0.282842i
$806$	−5.50298	+	0.970323i	−0.193834	+	0.0341782i
$807$	−25.0975	+	44.5442i	−0.883473	+	1.56803i
$808$	−0.293057	−	3.34966i	−0.0103097	−	0.117841i
$809$	47.0271			1.65338			0.826692	−	0.562654i	$-0.190220\pi$
$809$	47.0271			1.65338			0.826692	+	0.562654i	$0.190220\pi$
$810$	−2.49149	+	2.06844i	−0.0875420	+	0.0726775i
$811$	−46.5510			−1.63463			−0.817314	−	0.576192i	$-0.804538\pi$
$811$	−46.5510			−1.63463			−0.817314	+	0.576192i	$0.804538\pi$
$812$	−1.34626	−	15.3878i	−0.0472444	−	0.540006i
$813$	−8.04153	+	14.2725i	−0.282029	+	0.500558i
$814$	−2.24373	+	0.395630i	−0.0786427	+	0.0138668i
$815$	−30.7877	+	9.58475i	−1.07845	+	0.335739i
$816$	35.5882	+	16.1422i	1.24584	+	0.565089i
$817$	3.16478	+	4.51977i	0.110722	+	0.158127i
$818$	1.17199	+	4.37392i	0.0409776	+	0.152931i
$819$	−19.7891	+	36.0016i	−0.691487	+	1.25800i
$820$	−18.3446	+	7.52078i	−0.640622	+	0.262637i
$821$	−11.2400	−	30.8817i	−0.392280	−	1.07778i	−0.965958	−	0.258699i	$-0.916706\pi$
$821$	−11.2400	−	30.8817i	−0.392280	−	1.07778i	0.573678	−	0.819081i	$-0.305516\pi$
$822$	−0.916746	+	2.60350i	−0.0319752	+	0.0908076i
$823$	8.92506	+	0.780841i	0.311108	+	0.0272184i	0.241641	−	0.970366i	$-0.422314\pi$
$823$	8.92506	+	0.780841i	0.311108	+	0.0272184i	0.0694673	+	0.997584i	$0.477870\pi$
$824$	−1.84072	+	1.54454i	−0.0641244	+	0.0538067i
$825$	16.0512	+	34.1316i	0.558829	+	1.18831i
$826$	2.01026	−	0.731675i	0.0699460	−	0.0254582i
$827$	13.3446	−	49.8029i	0.464039	−	1.73182i	−0.196018	−	0.980600i	$-0.562801\pi$
$827$	13.3446	−	49.8029i	0.464039	−	1.73182i	0.660057	−	0.751216i	$-0.270532\pi$
$828$	−1.70589	−	15.6937i	−0.0592836	−	0.545393i
$829$	−6.07560	−	3.50775i	−0.211014	−	0.121829i	0.390768	−	0.920489i	$-0.372209\pi$
$829$	−6.07560	−	3.50775i	−0.211014	−	0.121829i	−0.601783	+	0.798660i	$0.705543\pi$
$830$	3.06941	+	0.980033i	0.106541	+	0.0340174i
$831$	−35.1526	+	3.44786i	−1.21943	+	0.119605i
$832$	−31.6531	+	14.7601i	−1.09737	+	0.511714i
$833$	−6.65756	−	4.66167i	−0.230671	−	0.161517i
$834$	4.06956	+	1.04475i	0.140917	+	0.0361767i
$835$	−14.4971	−	0.685631i	−0.501693	−	0.0237273i
$836$			6.90208i			0.238713i
$837$	−7.80658	−	37.3503i	−0.269835	−	1.29101i
$838$	−4.23684	−	4.23684i	−0.146359	−	0.146359i
$839$	2.86722	+	2.40588i	0.0989873	+	0.0830602i	0.690938	−	0.722914i	$-0.257198\pi$
$839$	2.86722	+	2.40588i	0.0989873	+	0.0830602i	−0.591951	+	0.805974i	$0.701642\pi$
$840$	7.11656	+	0.887163i	0.245545	+	0.0306100i
$841$	−3.76791	−	21.3689i	−0.129928	−	0.736858i
$842$	−1.99563	−	4.27965i	−0.0687741	−	0.147487i
$843$	35.3059	+	5.84371i	1.21600	+	0.201268i
$844$	18.3184	+	3.23002i	0.630544	+	0.111182i
$845$	−12.8065	+	16.5650i	−0.440556	+	0.569853i
$846$	−0.859915	+	2.52651i	−0.0295645	+	0.0868631i
$847$	−22.2871	−	5.97181i	−0.765793	−	0.205194i
$848$	3.91463	−	8.39495i	0.134429	−	0.288284i
$849$	12.6192	−	18.4311i	0.433089	−	0.632554i
$850$	−1.96388	−	4.29256i	−0.0673606	−	0.147234i
$851$	5.57034	+	6.63847i	0.190949	+	0.227564i
$852$	4.07856	+	21.7898i	0.139729	+	0.746505i
$853$	−39.4684	−	18.4044i	−1.35137	−	0.630155i	−0.394025	−	0.919100i	$-0.628918\pi$
$853$	−39.4684	−	18.4044i	−1.35137	−	0.630155i	−0.957346	+	0.288945i	$0.906696\pi$
$854$	−2.81908	−	4.88278i	−0.0964668	−	0.167085i
$855$	−4.81925	−	2.40322i	−0.164815	−	0.0821884i
$856$	−2.57365	+	4.45770i	−0.0879657	+	0.152361i
$857$	−39.0125	+	27.3168i	−1.33264	+	0.933125i	−0.999951	−	0.00991152i	$-0.996845\pi$
$857$	−39.0125	+	27.3168i	−1.33264	+	0.933125i	−0.332690	+	0.943036i	$0.607956\pi$
$858$	0.937333	−	5.66308i	0.0320000	−	0.193334i
$859$	14.5712	−	40.0340i	0.497162	−	1.36594i	−0.396844	−	0.917886i	$-0.629895\pi$
$859$	14.5712	−	40.0340i	0.497162	−	1.36594i	0.894006	−	0.448055i	$-0.147883\pi$
$860$	20.5781	−	22.2943i	0.701709	−	0.760228i
$861$	16.0955	+	15.7609i	0.548533	+	0.537130i
$862$	−0.0770518	+	0.00674116i	−0.00262439	+	0.000229605i
$863$	−11.3790	+	11.3790i	−0.387346	+	0.387346i	−0.873740	−	0.486393i	$-0.838312\pi$
$863$	−11.3790	+	11.3790i	−0.387346	+	0.387346i	0.486393	+	0.873740i	$0.338312\pi$
$864$	4.44675	+	8.80100i	0.151282	+	0.299416i
$865$	−15.7086	−	20.6263i	−0.534110	−	0.701316i
$866$	−0.812682	+	0.968517i	−0.0276161	+	0.0329115i
$867$	−25.9780	+	15.3645i	−0.882260	+	0.521805i
$868$	−24.0777	+	34.3866i	−0.817252	+	1.16716i
$869$	−2.05336	−	0.747362i	−0.0696554	−	0.0253525i
$870$	−1.68280	−	0.0618801i	−0.0570524	−	0.00209793i
$871$	5.48385	−	31.1005i	0.185813	−	1.05380i
$872$	7.51153	−	2.01271i	0.254372	−	0.0681589i
$873$	−21.7404	+	2.36316i	−0.735801	+	0.0799807i
$874$	−0.298187	+	0.172158i	−0.0100863	+	0.00582334i
$875$	21.6114	+	24.1060i	0.730598	+	0.814930i
$876$	−2.52941	+	32.8863i	−0.0854610	+	1.11112i
$877$	2.17490	−	24.8592i	0.0734411	−	0.839435i	−0.866740	−	0.498760i	$-0.833789\pi$
$877$	2.17490	−	24.8592i	0.0734411	−	0.839435i	0.940181	−	0.340675i	$-0.110656\pi$
$878$	0.174114	−	1.99013i	0.00587605	−	0.0671635i
$879$	−52.7000	+	25.2517i	−1.77753	+	0.851717i
$880$	36.5895	−	7.97263i	1.23343	−	0.268757i
$881$	19.2496	−	11.1138i	0.648536	−	0.374432i	−0.139359	−	0.990242i	$-0.544504\pi$
$881$	19.2496	−	11.1138i	0.648536	−	0.374432i	0.787895	+	0.615810i	$0.211171\pi$
$882$	−0.186593	−	0.642104i	−0.00628290	−	0.0216208i
$883$	−51.9401	+	13.9173i	−1.74792	+	0.468355i	−0.984181	−	0.177166i	$-0.943307\pi$
$883$	−51.9401	+	13.9173i	−1.74792	+	0.468355i	−0.763743	+	0.645521i	$0.776640\pi$
$884$	9.51159	−	53.9429i	0.319909	−	1.81430i
$885$	3.96803	+	17.3336i	0.133384	+	0.582661i
$886$	−2.68990	−	0.979043i	−0.0903689	−	0.0328916i
$887$	27.3502	−	39.0601i	0.918330	−	1.31151i	−0.0317472	−	0.999496i	$-0.510107\pi$
$887$	27.3502	−	39.0601i	0.918330	−	1.31151i	0.950077	−	0.312015i	$-0.101004\pi$
$888$	−3.13719	−	1.76758i	−0.105277	−	0.0593162i
$889$	1.44304	−	1.71975i	0.0483980	−	0.0576785i
$890$	3.91998	−	2.98539i	0.131398	−	0.100070i
$891$	38.8534	+	5.17915i	1.30164	+	0.173508i
$892$	−14.4939	+	14.4939i	−0.485292	+	0.485292i
$893$	−4.42146	+	0.386828i	−0.147959	+	0.0129447i
$894$	−3.96256	+	1.10650i	−0.132528	+	0.0370070i
$895$	−15.2846	+	0.611823i	−0.510908	+	0.0204510i
$896$	4.93582	−	13.5611i	0.164894	−	0.453043i
$897$	−20.4369	+	7.68247i	−0.682368	+	0.256510i
$898$	−0.503608	+	0.352630i	−0.0168056	+	0.0117674i
$899$	9.92137	−	17.1843i	0.330896	−	0.573129i
$900$	−7.26990	+	28.7054i	−0.242330	+	0.956845i
$901$	7.06673	+	12.2399i	0.235427	+	0.407771i
$902$	−2.85267	−	1.33022i	−0.0949837	−	0.0442916i
$903$	−32.5155	−	11.4494i	−1.08205	−	0.381011i
$904$	−1.67361	−	1.99453i	−0.0556635	−	0.0663371i
$905$	−19.4026	−	30.7011i	−0.644966	−	1.02054i
$906$	0.661909	+	0.0509101i	0.0219905	+	0.00169137i
$907$	−15.2342	+	32.6698i	−0.505842	+	1.08478i	0.473168	+	0.880972i	$0.343110\pi$
$907$	−15.2342	+	32.6698i	−0.505842	+	1.08478i	−0.979010	+	0.203810i	$0.934668\pi$
$908$	28.7666	+	7.70797i	0.954652	+	0.255798i
$909$	−5.70545	−	14.7068i	−0.189238	−	0.487792i
$910$	−0.625399	−	4.88725i	−0.0207318	−	0.162011i
$911$	35.2604	+	6.21737i	1.16823	+	0.205991i	0.723921	−	0.689883i	$-0.242338\pi$
$911$	35.2604	+	6.21737i	1.16823	+	0.205991i	0.444310	+	0.895873i	$0.353449\pi$
$912$	−3.39362	+	4.13173i	−0.112374	+	0.136815i
$913$	−16.4829	−	35.3477i	−0.545505	−	1.16984i
$914$	0.617189	+	3.50025i	0.0204148	+	0.115778i
$915$	43.1733	−	18.2318i	1.42726	−	0.602726i
$916$	−1.42237	−	1.19351i	−0.0469964	−	0.0394346i
$917$	−15.5310	−	15.5310i	−0.512878	−	0.512878i
$918$	−4.85557	−	0.699228i	−0.160258	−	0.0230780i
$919$			10.8922i			0.359301i	0.983730	+	0.179651i	$0.0574967\pi$
$919$			10.8922i			0.359301i	−0.983730	+	0.179651i	$0.942503\pi$
$920$	2.56474	+	2.81938i	0.0845570	+	0.0929522i
$921$	−12.2149	+	12.4742i	−0.402495	+	0.411040i
$922$	−0.852235	−	0.596741i	−0.0280669	−	0.0196526i
$923$	27.7873	−	12.9575i	0.914632	−	0.426500i
$924$	−25.1035	−	35.0618i	−0.825844	−	1.15345i
$925$	−5.44880	−	15.3151i	−0.179155	−	0.503558i
$926$	0.0427714	+	0.0246941i	0.00140556	+	0.000811498i
$927$	−6.27050	+	9.36804i	−0.205950	+	0.307687i
$928$	−1.32716	+	4.95301i	−0.0435660	+	0.162591i
$929$	−0.624723	+	0.227381i	−0.0204965	+	0.00746012i	−0.352248	−	0.935907i	$-0.614583\pi$
$929$	−0.624723	+	0.227381i	−0.0204965	+	0.00746012i	0.331752	+	0.943367i	$0.392360\pi$
$930$	3.39522	+	3.06846i	0.111334	+	0.100619i
$931$	0.851849	−	0.714786i	0.0279182	−	0.0234262i
$932$	−11.0466	−	0.966453i	−0.361844	−	0.0316572i
$933$	43.9604	−	8.22841i	1.43920	−	0.269386i
$934$	2.35563	+	6.47205i	0.0770787	+	0.211772i
$935$	−22.0576	+	52.7103i	−0.721359	+	1.72381i
$936$	6.82565	−	5.97617i	0.223103	−	0.195337i
$937$	8.19227	+	30.5740i	0.267630	+	0.998808i	0.960621	+	0.277862i	$0.0896258\pi$
$937$	8.19227	+	30.5740i	0.267630	+	0.998808i	−0.692991	+	0.720946i	$0.743708\pi$
$938$	1.78471	+	2.54883i	0.0582728	+	0.0832222i
$939$	7.92986	−	5.67760i	0.258781	−	0.185282i
$940$	7.25431	+	23.3020i	0.236609	+	0.760027i
$941$	15.3045	−	2.69859i	0.498911	−	0.0879715i	0.0814707	−	0.996676i	$-0.474038\pi$
$941$	15.3045	−	2.69859i	0.498911	−	0.0879715i	0.417441	+	0.908704i	$0.362927\pi$
$942$	−2.18536	+	0.0229551i	−0.0712030	+	0.000747919i
$943$	1.04344	+	11.9266i	0.0339791	+	0.388383i
$944$	17.6549			0.574619
$945$	33.2220	−	5.31993i	1.08071	−	0.173057i
$946$	4.81662			0.156602
$947$	−2.28059	−	26.0673i	−0.0741093	−	0.847074i	−0.938731	−	0.344650i	$-0.887997\pi$
$947$	−2.28059	−	26.0673i	−0.0741093	−	0.847074i	0.864622	−	0.502423i	$-0.167558\pi$
$948$	−0.873325	−	1.47660i	−0.0283643	−	0.0479579i
$949$	44.9250	−	7.92149i	1.45833	−	0.257143i
$950$	0.636853	−	0.107538i	0.0206622	−	0.00348901i
$951$	0.313423	+	3.19549i	0.0101634	+	0.103621i
$952$	6.23165	+	8.89972i	0.201969	+	0.288442i
$953$	−10.0312	−	37.4368i	−0.324942	−	1.21270i	−0.914371	−	0.404878i	$-0.867314\pi$
$953$	−10.0312	−	37.4368i	−0.324942	−	1.21270i	0.589429	−	0.807820i	$-0.299353\pi$
$954$	−0.177820	+	1.14913i	−0.00575714	+	0.0372044i
$955$	−17.3619	−	42.3490i	−0.561818	−	1.37038i
$956$	10.4679	+	28.7604i	0.338557	+	0.930178i
$957$	13.2655	+	15.4761i	0.428812	+	0.500272i
$958$	6.67210	+	0.583733i	0.215566	+	0.0188596i
$959$	21.9691	−	18.4343i	0.709420	−	0.595274i
$960$	25.4615	+	13.0326i	0.821767	+	0.420627i
$961$	−21.5428	+	7.84095i	−0.694930	+	0.252934i
$962$	−0.640290	+	2.38959i	−0.0206438	+	0.0770436i
$963$	−5.75867	+	23.4515i	−0.185571	+	0.755715i
$964$	32.6511	+	18.8511i	1.05162	+	0.607154i
$965$	7.98414	+	15.4741i	0.257019	+	0.498130i
$966$	0.888601	−	1.95908i	0.0285903	−	0.0630322i
$967$	30.4117	−	14.1812i	0.977973	−	0.456036i	0.133158	−	0.991095i	$-0.457488\pi$
$967$	30.4117	−	14.1812i	0.977973	−	0.456036i	0.844815	+	0.535058i	$0.179710\pi$
$968$	4.17382	+	2.92254i	0.134152	+	0.0939340i
$969$	−2.19416	−	7.85765i	−0.0704867	−	0.252424i
$970$	1.94011	−	1.76489i	0.0622933	−	0.0566671i
$971$			3.53962i			0.113592i	0.998386	+	0.0567959i	$0.0180884\pi$
$971$			3.53962i			0.113592i	−0.998386	+	0.0567959i	$0.981912\pi$
$972$	20.9909	+	22.5028i	0.673284	+	0.721779i
$973$	−30.8682	−	30.8682i	−0.989589	−	0.989589i
$974$	−2.93893	−	2.46605i	−0.0941694	−	0.0790175i
$975$	40.9545	−	0.133179i	1.31159	−	0.00426513i
$976$	−8.07991	−	45.8234i	−0.258632	−	1.46677i
$977$	19.3025	+	41.3945i	0.617543	+	1.32433i	0.927588	+	0.373604i	$0.121878\pi$
$977$	19.3025	+	41.3945i	0.617543	+	1.32433i	−0.310045	+	0.950722i	$0.600344\pi$
$978$	−1.41417	−	3.76197i	−0.0452201	−	0.120295i
$979$	−58.7374	−	10.3570i	−1.87726	−	0.331011i
$980$	−4.83750	−	3.73989i	−0.154528	−	0.119466i
$981$	31.2050	−	18.9011i	0.996298	−	0.603466i
$982$	2.46224	+	0.659756i	0.0785733	+	0.0210536i
$983$	−13.7607	+	29.5099i	−0.438898	+	0.941220i	0.555096	+	0.831786i	$0.312682\pi$
$983$	−13.7607	+	29.5099i	−0.438898	+	0.941220i	−0.993994	+	0.109434i	$0.965096\pi$
$984$	−2.14963	−	4.48626i	−0.0685278	−	0.143017i
$985$	2.60452	−	11.5499i	0.0829868	−	0.368009i
$986$	−1.63979	−	1.95422i	−0.0522215	−	0.0622352i
$987$	21.0536	−	18.0463i	0.670144	−	0.574420i
$988$	6.79230	+	3.16730i	0.216092	+	0.100765i
$989$	−9.16026	−	15.8660i	−0.291279	−	0.504511i
$990$	−4.13152	+	2.24285i	−0.131308	+	0.0712824i
$991$	22.7542	−	39.4115i	0.722812	−	1.25195i	−0.237057	−	0.971496i	$-0.576183\pi$
$991$	22.7542	−	39.4115i	0.722812	−	1.25195i	0.959868	−	0.280451i	$-0.0904839\pi$
$992$	11.4152	−	7.99298i	0.362432	−	0.253777i
$993$	25.7776	+	21.1726i	0.818028	+	0.671892i
$994$	−1.03320	+	2.83869i	−0.0327710	+	0.0900377i
$995$	2.48775	+	62.1492i	0.0788671	+	1.97026i
$996$	7.61395	−	29.6583i	0.241257	−	0.939759i
$997$	8.98411	−	0.786008i	0.284530	−	0.0248931i	0.0560024	−	0.998431i	$-0.482165\pi$
$997$	8.98411	−	0.786008i	0.284530	−	0.0248931i	0.228527	+	0.973538i	$0.426609\pi$
$998$	0.0619968	−	0.0619968i	0.00196248	−	0.00196248i
$999$	−16.4473	−	3.85602i	−0.520368	−	0.121999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.2.q.a.38.7	yes	192
3.2	odd	2		405.2.r.a.278.10		192
5.2	odd	4	inner	135.2.q.a.92.10	yes	192
5.3	odd	4		675.2.ba.b.632.7		192
5.4	even	2		675.2.ba.b.443.10		192
15.2	even	4		405.2.r.a.197.7		192
27.5	odd	18	inner	135.2.q.a.113.10	yes	192
27.22	even	9		405.2.r.a.368.7		192
135.22	odd	36		405.2.r.a.287.10		192
135.32	even	36	inner	135.2.q.a.32.7	✓	192
135.59	odd	18		675.2.ba.b.518.7		192
135.113	even	36		675.2.ba.b.32.10		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.7	✓	192	135.32	even	36	inner
135.2.q.a.38.7	yes	192	1.1	even	1	trivial
135.2.q.a.92.10	yes	192	5.2	odd	4	inner
135.2.q.a.113.10	yes	192	27.5	odd	18	inner
405.2.r.a.197.7		192	15.2	even	4
405.2.r.a.278.10		192	3.2	odd	2
405.2.r.a.287.10		192	135.22	odd	36
405.2.r.a.368.7		192	27.22	even	9
675.2.ba.b.32.10		192	135.113	even	36
675.2.ba.b.443.10		192	5.4	even	2
675.2.ba.b.518.7		192	135.59	odd	18
675.2.ba.b.632.7		192	5.3	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-0.0140240 - 0.160295i) q^{2} +(0.850222 - 1.50901i) q^{3} +(1.94412 - 0.342800i) q^{4} +(-1.03969 + 1.97966i) q^{5} +(-0.253811 - 0.115124i) q^{6} +(1.66092 + 2.37204i) q^{7} +(-0.165506 - 0.617675i) q^{8} +(-1.55424 - 2.56599i) q^{9} +O(q^{10})\)	\(q+(-0.0140240 - 0.160295i) q^{2} +(0.850222 - 1.50901i) q^{3} +(1.94412 - 0.342800i) q^{4} +(-1.03969 + 1.97966i) q^{5} +(-0.253811 - 0.115124i) q^{6} +(1.66092 + 2.37204i) q^{7} +(-0.165506 - 0.617675i) q^{8} +(-1.55424 - 2.56599i) q^{9} +(0.331911 + 0.138894i) q^{10} +(-1.48958 - 4.09258i) q^{11} +(1.13564 - 3.22516i) q^{12} +(-4.71104 - 0.412163i) q^{13} +(0.356933 - 0.299503i) q^{14} +(2.10337 + 3.25205i) q^{15} +(3.61342 - 1.31518i) q^{16} +(-1.51857 + 5.66739i) q^{17} +(-0.389520 + 0.285124i) q^{18} +(-0.695229 - 0.401391i) q^{19} +(-1.34264 + 4.20510i) q^{20} +(4.99158 - 0.489589i) q^{21} +(-0.635132 + 0.296167i) q^{22} +(2.18347 + 1.52888i) q^{23} +(-1.07280 - 0.275411i) q^{24} +(-2.83811 - 4.11645i) q^{25} +0.760939i q^{26} +(-5.19357 + 0.163709i) q^{27} +(4.04215 + 4.04215i) q^{28} +(-2.06994 - 1.73689i) q^{29} +(0.491791 - 0.382767i) q^{30} +(1.27517 + 7.23183i) q^{31} +(-0.801990 - 1.71987i) q^{32} +(-7.44223 - 1.23181i) q^{33} +(0.929752 + 0.163940i) q^{34} +(-6.42266 + 0.821878i) q^{35} +(-3.90126 - 4.45580i) q^{36} +(3.14033 + 0.841448i) q^{37} +(-0.0545912 + 0.117071i) q^{38} +(-4.62739 + 6.75860i) q^{39} +(1.39486 + 0.314544i) q^{40} +(2.88706 + 3.44066i) q^{41} +(-0.148481 - 0.793261i) q^{42} +(-6.22917 - 2.90471i) q^{43} +(-4.29885 - 7.44583i) q^{44} +(6.69572 - 0.409045i) q^{45} +(0.214452 - 0.371442i) q^{46} +(4.52886 - 3.17114i) q^{47} +(1.08759 - 6.57090i) q^{48} +(-0.473765 + 1.30166i) q^{49} +(-0.620046 + 0.512664i) q^{50} +(7.26104 + 7.11008i) q^{51} +(-9.30011 + 0.813654i) q^{52} +(1.70331 - 1.70331i) q^{53} +(0.0990765 + 0.830210i) q^{54} +(9.65061 + 1.30614i) q^{55} +(1.19026 - 1.41849i) q^{56} +(-1.19680 + 0.707839i) q^{57} +(-0.249386 + 0.356161i) q^{58} +(4.31439 + 1.57031i) q^{59} +(5.20400 + 5.60134i) q^{60} +(2.10123 - 11.9167i) q^{61} +(1.14135 - 0.305823i) q^{62} +(3.50516 - 7.94862i) q^{63} +(6.39585 - 3.69265i) q^{64} +(5.71395 - 8.89774i) q^{65} +(-0.0930836 + 1.21023i) q^{66} +(-0.582021 + 6.65253i) q^{67} +(-1.00950 + 11.5386i) q^{68} +(4.16355 - 1.99500i) q^{69} +(0.221815 + 1.01800i) q^{70} +(-5.61473 + 3.24167i) q^{71} +(-1.32772 + 1.38470i) q^{72} +(-9.31768 + 2.49666i) q^{73} +(0.0908402 - 0.515180i) q^{74} +(-8.62480 + 0.782842i) q^{75} +(-1.48920 - 0.542026i) q^{76} +(7.23368 - 10.3308i) q^{77} +(1.14827 + 0.646967i) q^{78} +(0.322504 - 0.384345i) q^{79} +(-1.15322 + 8.52072i) q^{80} +(-4.16865 + 7.97636i) q^{81} +(0.511034 - 0.511034i) q^{82} +(8.92110 - 0.780495i) q^{83} +(9.53639 - 2.66293i) q^{84} +(-9.64066 - 8.89856i) q^{85} +(-0.378253 + 1.03924i) q^{86} +(-4.38090 + 1.64683i) q^{87} +(-2.28135 + 1.59742i) q^{88} +(6.84734 - 11.8599i) q^{89} +(-0.159469 - 1.06756i) q^{90} +(-6.84699 - 11.8593i) q^{91} +(4.76903 + 2.22384i) q^{92} +(11.9971 + 4.22442i) q^{93} +(-0.571832 - 0.681483i) q^{94} +(1.51744 - 0.958997i) q^{95} +(-3.27718 - 0.252061i) q^{96} +(3.08067 - 6.60652i) q^{97} +(0.215294 + 0.0576878i) q^{98} +(-8.18637 + 10.1831i) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more