LMFDB - Embedded newform 135.2.q.a.113.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,2,Mod(2,135)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([2, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("135.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	135.q (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.07798042729$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$16$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			113.10
Character	$\chi$	$=$	135.113
Dual form			135.2.q.a.92.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.160295 + 0.0140240i) q^{2} +(-1.50901 + 0.850222i) q^{3} +(-1.94412 - 0.342800i) q^{4} +(-0.476055 - 2.18480i) q^{5} +(-0.253811 + 0.115124i) q^{6} +(-2.37204 - 1.66092i) q^{7} +(-0.617675 - 0.165506i) q^{8} +(1.55424 - 2.56599i) q^{9} +O(q^{10})$	\(q+(0.160295 + 0.0140240i) q^{2} +(-1.50901 + 0.850222i) q^{3} +(-1.94412 - 0.342800i) q^{4} +(-0.476055 - 2.18480i) q^{5} +(-0.253811 + 0.115124i) q^{6} +(-2.37204 - 1.66092i) q^{7} +(-0.617675 - 0.165506i) q^{8} +(1.55424 - 2.56599i) q^{9} +(-0.0456696 - 0.356890i) q^{10} +(-1.48958 + 4.09258i) q^{11} +(3.22516 - 1.13564i) q^{12} +(-0.412163 - 4.71104i) q^{13} +(-0.356933 - 0.299503i) q^{14} +(2.57594 + 2.89215i) q^{15} +(3.61342 + 1.31518i) q^{16} +(-5.66739 + 1.51857i) q^{17} +(0.285124 - 0.389520i) q^{18} +(0.695229 - 0.401391i) q^{19} +(0.176555 + 4.41071i) q^{20} +(4.99158 + 0.489589i) q^{21} +(-0.296167 + 0.635132i) q^{22} +(1.52888 + 2.18347i) q^{23} +(1.07280 - 0.275411i) q^{24} +(-4.54674 + 2.08017i) q^{25} -0.760939i q^{26} +(-0.163709 + 5.19357i) q^{27} +(4.04215 + 4.04215i) q^{28} +(2.06994 - 1.73689i) q^{29} +(0.372352 + 0.499723i) q^{30} +(1.27517 - 7.23183i) q^{31} +(1.71987 + 0.801990i) q^{32} +(-1.23181 - 7.44223i) q^{33} +(-0.929752 + 0.163940i) q^{34} +(-2.49956 + 5.97312i) q^{35} +(-3.90126 + 4.45580i) q^{36} +(-0.841448 - 3.14033i) q^{37} +(0.117071 - 0.0545912i) q^{38} +(4.62739 + 6.75860i) q^{39} +(-0.0675500 + 1.42829i) q^{40} +(2.88706 - 3.44066i) q^{41} +(0.793261 + 0.148481i) q^{42} +(-2.90471 - 6.22917i) q^{43} +(4.29885 - 7.44583i) q^{44} +(-6.34610 - 2.17416i) q^{45} +(0.214452 + 0.371442i) q^{46} +(3.17114 - 4.52886i) q^{47} +(-6.57090 + 1.08759i) q^{48} +(0.473765 + 1.30166i) q^{49} +(-0.757994 + 0.269679i) q^{50} +(7.26104 - 7.11008i) q^{51} +(-0.813654 + 9.30011i) 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} +(-0.707839 + 1.19680i) q^{57} +(0.356161 - 0.249386i) q^{58} +(-4.31439 + 1.57031i) q^{59} +(-4.01651 - 6.50571i) q^{60} +(2.10123 + 11.9167i) q^{61} +(0.305823 - 1.14135i) q^{62} +(-7.94862 + 3.50516i) q^{63} +(-6.39585 - 3.69265i) q^{64} +(-10.0965 + 3.14321i) q^{65} +(-0.0930836 - 1.21023i) q^{66} +(-6.65253 + 0.582021i) q^{67} +(11.5386 - 1.00950i) q^{68} +(-4.16355 - 1.99500i) q^{69} +(-0.484435 + 0.922410i) q^{70} +(-5.61473 - 3.24167i) q^{71} +(-1.38470 + 1.32772i) q^{72} +(2.49666 - 9.31768i) q^{73} +(-0.0908402 - 0.515180i) q^{74} +(5.09249 - 7.00475i) q^{75} +(-1.48920 + 0.542026i) q^{76} +(10.3308 - 7.23368i) q^{77} +(0.646967 + 1.14827i) 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} +(-0.780495 + 8.92110i) q^{83} +(-9.53639 - 2.66293i) q^{84} +(6.01577 + 11.6592i) q^{85} +(-0.378253 - 1.03924i) q^{86} +(-1.64683 + 4.38090i) q^{87} +(1.59742 - 2.28135i) q^{88} +(-6.84734 - 11.8599i) q^{89} +(-0.986760 - 0.437506i) q^{90} +(-6.84699 + 11.8593i) q^{91} +(-2.22384 - 4.76903i) q^{92} +(4.22442 + 11.9971i) q^{93} +(0.571832 - 0.681483i) q^{94} +(-1.20793 - 1.32786i) q^{95} +(-3.27718 + 0.252061i) q^{96} +(6.60652 - 3.08067i) q^{97} +(0.0576878 + 0.215294i) 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 $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.160295	+	0.0140240i	0.113346	+	0.00991648i	0.143688	−	0.989623i	$-0.454104\pi$
$2$	0.160295	+	0.0140240i	0.113346	+	0.00991648i	−0.0303416	+	0.999540i	$0.509660\pi$
$3$	−1.50901	+	0.850222i	−0.871229	+	0.490876i
$3$	−1.50901	+	0.850222i	−0.871229	+	0.490876i
$4$	−1.94412	−	0.342800i	−0.972059	−	0.171400i
$5$	−0.476055	−	2.18480i	−0.212898	−	0.977074i
$5$	−0.476055	−	2.18480i	−0.212898	−	0.977074i
$6$	−0.253811	+	0.115124i	−0.103618	+	0.0469993i
$7$	−2.37204	−	1.66092i	−0.896545	−	0.627768i	0.0317971	−	0.999494i	$-0.489877\pi$
$7$	−2.37204	−	1.66092i	−0.896545	−	0.627768i	−0.928342	+	0.371727i	$0.878766\pi$
$8$	−0.617675	−	0.165506i	−0.218381	−	0.0585151i
$9$	1.55424	−	2.56599i	0.518081	−	0.855331i
$10$	−0.0456696	−	0.356890i	−0.0144420	−	0.112859i
$11$	−1.48958	+	4.09258i	−0.449125	+	1.23396i	0.484210	+	0.874952i	$0.339107\pi$
$11$	−1.48958	+	4.09258i	−0.449125	+	1.23396i	−0.933335	+	0.359008i	$0.883115\pi$
$12$	3.22516	−	1.13564i	0.931022	−	0.327832i
$13$	−0.412163	−	4.71104i	−0.114313	−	1.30661i	−0.809219	−	0.587507i	$-0.800109\pi$
$13$	−0.412163	−	4.71104i	−0.114313	−	1.30661i	0.694905	−	0.719101i	$-0.255446\pi$
$14$	−0.356933	−	0.299503i	−0.0953945	−	0.0800455i
$15$	2.57594	+	2.89215i	0.665106	+	0.746749i
$16$	3.61342	+	1.31518i	0.903355	+	0.328794i
$17$	−5.66739	+	1.51857i	−1.37454	+	0.368308i	−0.869136	−	0.494573i	$-0.835324\pi$
$17$	−5.66739	+	1.51857i	−1.37454	+	0.368308i	−0.505407	+	0.862881i	$0.668658\pi$
$18$	0.285124	−	0.389520i	0.0672043	−	0.0918108i
$19$	0.695229	−	0.401391i	0.159497	−	0.0920854i	−0.418127	−	0.908388i	$-0.637313\pi$
$19$	0.695229	−	0.401391i	0.159497	−	0.0920854i	0.577624	+	0.816303i	$0.303980\pi$
$20$	0.176555	+	4.41071i	0.0394789	+	0.986265i
$21$	4.99158	+	0.489589i	1.08925	+	0.106837i
$22$	−0.296167	+	0.635132i	−0.0631430	+	0.135411i
$23$	1.52888	+	2.18347i	0.318794	+	0.455286i	0.946283	−	0.323340i	$-0.104806\pi$
$23$	1.52888	+	2.18347i	0.318794	+	0.455286i	−0.627488	+	0.778626i	$0.715917\pi$
$24$	1.07280	−	0.275411i	0.218984	−	0.0562181i
$25$	−4.54674	+	2.08017i	−0.909349	+	0.416035i
$26$		−	0.760939i		−	0.149232i
$27$	−0.163709	+	5.19357i	−0.0315057	+	0.999504i
$28$	4.04215	+	4.04215i	0.763895	+	0.763895i
$29$	2.06994	−	1.73689i	0.384379	−	0.322532i	−0.430040	−	0.902810i	$-0.641500\pi$
$29$	2.06994	−	1.73689i	0.384379	−	0.322532i	0.814419	+	0.580278i	$0.197056\pi$
$30$	0.372352	+	0.499723i	0.0679819	+	0.0912365i
$31$	1.27517	−	7.23183i	0.229027	−	1.29887i	−0.625809	−	0.779976i	$-0.715231\pi$
$31$	1.27517	−	7.23183i	0.229027	−	1.29887i	0.854836	−	0.518899i	$-0.173658\pi$
$32$	1.71987	+	0.801990i	0.304034	+	0.141773i
$33$	−1.23181	−	7.44223i	−0.214431	−	1.29553i
$34$	−0.929752	+	0.163940i	−0.159451	+	0.0281155i
$35$	−2.49956	+	5.97312i	−0.422503	+	1.00964i
$36$	−3.90126	+	4.45580i	−0.650209	+	0.742633i
$37$	−0.841448	−	3.14033i	−0.138333	−	0.516266i	−0.999962	−	0.00872734i	$-0.997222\pi$
$37$	−0.841448	−	3.14033i	−0.138333	−	0.516266i	0.861629	−	0.507539i	$-0.169445\pi$
$38$	0.117071	−	0.0545912i	0.0189914	−	0.00885586i
$39$	4.62739	+	6.75860i	0.740976	+	1.08224i
$40$	−0.0675500	+	1.42829i	−0.0106806	+	0.225832i
$41$	2.88706	−	3.44066i	0.450883	−	0.537341i	−0.491943	−	0.870628i	$-0.663713\pi$
$41$	2.88706	−	3.44066i	0.450883	−	0.537341i	0.942826	+	0.333286i	$0.108158\pi$
$42$	0.793261	+	0.148481i	0.122403	+	0.0229111i
$43$	−2.90471	−	6.22917i	−0.442964	−	0.949940i	−0.993361	−	0.115037i	$-0.963301\pi$
$43$	−2.90471	−	6.22917i	−0.442964	−	0.949940i	0.550397	−	0.834903i	$-0.314476\pi$
$44$	4.29885	−	7.44583i	0.648076	−	1.12250i
$45$	−6.34610	−	2.17416i	−0.946021	−	0.324105i
$46$	0.214452	+	0.371442i	0.0316192	+	0.0547661i
$47$	3.17114	−	4.52886i	0.462558	−	0.660602i	−0.518328	−	0.855182i	$-0.673445\pi$
$47$	3.17114	−	4.52886i	0.462558	−	0.660602i	0.980887	+	0.194580i	$0.0623343\pi$
$48$	−6.57090	+	1.08759i	−0.948427	+	0.156980i
$49$	0.473765	+	1.30166i	0.0676807	+	0.185951i
$50$	−0.757994	+	0.269679i	−0.107197	+	0.0381383i
$51$	7.26104	−	7.11008i	1.01675	−	0.995611i
$52$	−0.813654	+	9.30011i	−0.112834	+	1.28969i
$53$	−1.70331	+	1.70331i	−0.233968	+	0.233968i	−0.814347	−	0.580379i	$-0.802905\pi$
$53$	−1.70331	+	1.70331i	−0.233968	+	0.233968i	0.580379	+	0.814347i	$0.302905\pi$
$54$	−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
$57$	−0.707839	+	1.19680i	−0.0937556	+	0.158521i
$58$	0.356161	−	0.249386i	0.0467662	−	0.0327460i
$59$	−4.31439	+	1.57031i	−0.561686	+	0.204437i	−0.607231	−	0.794525i	$-0.707720\pi$
$59$	−4.31439	+	1.57031i	−0.561686	+	0.204437i	0.0455453	+	0.998962i	$0.485497\pi$
$60$	−4.01651	−	6.50571i	−0.518529	−	0.839883i
$61$	2.10123	+	11.9167i	0.269035	+	1.52577i	0.757294	+	0.653074i	$0.226521\pi$
$61$	2.10123	+	11.9167i	0.269035	+	1.52577i	−0.488259	+	0.872699i	$0.662368\pi$
$62$	0.305823	−	1.14135i	0.0388395	−	0.144951i
$63$	−7.94862	+	3.50516i	−1.00143	+	0.441609i
$64$	−6.39585	−	3.69265i	−0.799482	−	0.461581i
$65$	−10.0965	+	3.14321i	−1.25232	+	0.389867i
$66$	−0.0930836	−	1.21023i	−0.0114578	−	0.148969i
$67$	−6.65253	+	0.582021i	−0.812736	+	0.0711052i	−0.485943	−	0.873991i	$-0.661524\pi$
$67$	−6.65253	+	0.582021i	−0.812736	+	0.0711052i	−0.326793	+	0.945096i	$0.605968\pi$
$68$	11.5386	−	1.00950i	1.39926	−	0.122420i
$69$	−4.16355	−	1.99500i	−0.501232	−	0.240170i
$70$	−0.484435	+	0.922410i	−0.0579011	+	0.110249i
$71$	−5.61473	−	3.24167i	−0.666346	−	0.384715i	0.128345	−	0.991730i	$-0.459034\pi$
$71$	−5.61473	−	3.24167i	−0.666346	−	0.384715i	−0.794691	+	0.607014i	$0.792367\pi$
$72$	−1.38470	+	1.32772i	−0.163189	+	0.156473i
$73$	2.49666	−	9.31768i	0.292212	−	1.09055i	−0.651194	−	0.758912i	$-0.725731\pi$
$73$	2.49666	−	9.31768i	0.292212	−	1.09055i	0.943406	−	0.331640i	$-0.107602\pi$
$74$	−0.0908402	−	0.515180i	−0.0105600	−	0.0598885i
$75$	5.09249	−	7.00475i	0.588030	−	0.808839i
$76$	−1.48920	+	0.542026i	−0.170823	+	0.0621747i
$77$	10.3308	−	7.23368i	1.17730	−	0.824355i
$78$	0.646967	+	1.14827i	0.0732546	+	0.130016i
$79$	−0.322504	−	0.384345i	−0.0362845	−	0.0432422i	0.747597	−	0.664153i	$-0.231208\pi$
$79$	−0.322504	−	0.384345i	−0.0362845	−	0.0432422i	−0.783882	+	0.620910i	$0.786763\pi$
$80$	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
$83$	−0.780495	+	8.92110i	−0.0856704	+	0.979218i	0.824740	+	0.565512i	$0.191321\pi$
$83$	−0.780495	+	8.92110i	−0.0856704	+	0.979218i	−0.910411	+	0.413706i	$0.864234\pi$
$84$	−9.53639	−	2.66293i	−1.04051	−	0.290550i
$85$	6.01577	+	11.6592i	0.652502	+	1.26462i
$86$	−0.378253	−	1.03924i	−0.0407881	−	0.112064i
$87$	−1.64683	+	4.38090i	−0.176559	+	0.469682i
$88$	1.59742	−	2.28135i	0.170286	−	0.243193i
$89$	−6.84734	−	11.8599i	−0.725816	−	1.25715i	−0.958637	−	0.284631i	$-0.908129\pi$
$89$	−6.84734	−	11.8599i	−0.725816	−	1.25715i	0.232821	−	0.972520i	$-0.425204\pi$
$90$	−0.986760	−	0.437506i	−0.104014	−	0.0461172i
$91$	−6.84699	+	11.8593i	−0.717759	+	1.24320i
$92$	−2.22384	−	4.76903i	−0.231851	−	0.497206i
$93$	4.22442	+	11.9971i	0.438052	+	1.24404i
$94$	0.571832	−	0.681483i	0.0589800	−	0.0702896i
$95$	−1.20793	−	1.32786i	−0.123931	−	0.136235i
$96$	−3.27718	+	0.252061i	−0.334476	+	0.0257259i
$97$	6.60652	−	3.08067i	0.670790	−	0.312795i	−0.0572192	−	0.998362i	$-0.518223\pi$
$97$	6.60652	−	3.08067i	0.670790	−	0.312795i	0.728010	+	0.685567i	$0.240446\pi$
$98$	0.0576878	+	0.215294i	0.00582735	+	0.0217480i
$99$	8.18637	+	10.1831i	0.822762	+	1.02344i
$100$	9.55249	−	2.48548i	0.955249	−	0.248548i
$101$	5.17835	−	0.913082i	0.515265	−	0.0908551i	0.0900315	−	0.995939i	$-0.471303\pi$
$101$	5.17835	−	0.913082i	0.515265	−	0.0908551i	0.425233	+	0.905084i	$0.360192\pi$
$102$	1.26362	−	1.03788i	0.125117	−	0.102766i
$103$	−3.40559	−	1.58805i	−0.335562	−	0.156475i	0.247532	−	0.968880i	$-0.420380\pi$
$103$	−3.40559	−	1.58805i	−0.335562	−	0.156475i	−0.583094	+	0.812404i	$0.698158\pi$
$104$	−0.525121	+	2.97811i	−0.0514924	+	0.292028i
$105$	−1.30661	−	11.1387i	−0.127512	−	1.08703i
$106$	−0.296920	+	0.249146i	−0.0288395	+	0.0241992i
$107$	5.69179	+	5.69179i	0.550246	+	0.550246i	0.926512	−	0.376266i	$-0.122792\pi$
$107$	5.69179	+	5.69179i	0.550246	+	0.550246i	−0.376266	+	0.926512i	$0.622792\pi$
$108$	2.09863	−	10.0408i	0.201941	−	0.966176i
$109$			12.1610i			1.16481i	0.812899	+	0.582405i	$0.197888\pi$
$109$			12.1610i			1.16481i	−0.812899	+	0.582405i	$0.802112\pi$
$110$	1.52863	+	0.344709i	0.145749	+	0.0328667i
$111$	3.93973	+	4.02338i	0.373943	+	0.381882i
$112$	−6.38676	−	9.12124i	−0.603492	−	0.861876i
$113$	−1.72075	+	3.69017i	−0.161875	+	0.347142i	−0.970469	−	0.241225i	$-0.922451\pi$
$113$	−1.72075	+	3.69017i	−0.161875	+	0.347142i	0.808594	+	0.588366i	$0.200229\pi$
$114$	−0.130247	+	0.181915i	−0.0121988	+	0.0170379i
$115$	4.04263	−	4.37977i	0.376977	−	0.408415i
$116$	−4.61962	+	2.66714i	−0.428921	+	0.247638i
$117$	−12.7291	−	6.26450i	−1.17681	−	0.579153i
$118$	−0.713599	+	0.191208i	−0.0656921	+	0.0176021i
$119$	15.9655	+	5.81095i	1.46355	+	0.532689i
$120$	−1.11243	−	2.21274i	−0.101551	−	0.201995i
$121$	−6.10389	−	5.12177i	−0.554899	−	0.465616i
$122$	0.169698	+	1.93965i	0.0153637	+	0.175608i
$123$	−1.43128	+	7.64665i	−0.129054	+	0.689475i
$124$	−4.95815	+	13.6224i	−0.445255	+	1.22333i
$125$	6.70927	+	8.94347i	0.600096	+	0.799928i
$126$	−1.32328	+	0.450389i	−0.117887	+	0.0401238i
$127$	0.748856	+	0.200655i	0.0664502	+	0.0178053i	0.291891	−	0.956452i	$-0.405716\pi$
$127$	0.748856	+	0.200655i	0.0664502	+	0.0178053i	−0.225441	+	0.974257i	$0.572382\pi$
$128$	−4.08240	−	2.85853i	−0.360837	−	0.252661i
$129$	9.67943	+	6.93025i	0.852226	+	0.610175i
$130$	−1.66250	+	0.362249i	−0.145811	+	0.0317713i
$131$	−7.46979	−	1.31713i	−0.652639	−	0.115078i	−0.162481	−	0.986712i	$-0.551950\pi$
$131$	−7.46979	−	1.31713i	−0.652639	−	0.115078i	−0.490158	+	0.871634i	$0.663061\pi$
$132$	−0.156414	+	14.8908i	−0.0136141	+	1.29608i
$133$	−2.31579	−	0.202605i	−0.200804	−	0.0175681i
$134$	−1.07453			−0.0928254
$135$	11.4249	−	2.11475i	0.983297	−	0.182009i
$136$	3.75194			0.321726
$137$	9.86611	+	0.863173i	0.842919	+	0.0737459i	0.500431	−	0.865776i	$-0.333175\pi$
$137$	9.86611	+	0.863173i	0.842919	+	0.0737459i	0.342488	+	0.939522i	$0.388730\pi$
$138$	−0.639419	−	0.378179i	−0.0544310	−	0.0321927i
$139$	14.8464	+	2.61782i	1.25926	+	0.222041i	0.763150	−	0.646222i	$-0.223652\pi$
$139$	14.8464	+	2.61782i	1.25926	+	0.222041i	0.496105	+	0.868262i	$0.334763\pi$
$140$	6.90703	−	10.7556i	0.583750	−	0.909014i
$141$	−0.934757	+	9.53029i	−0.0787208	+	0.802595i
$142$	−0.854554	−	0.598365i	−0.0717126	−	0.0502137i
$143$	19.8943	+	5.33066i	1.66364	+	0.445772i
$144$	8.99088	−	7.22791i	0.749240	−	0.602326i
$145$	−4.78017	−	3.69557i	−0.396972	−	0.306900i
$146$	0.530875	−	1.45857i	0.0439355	−	0.120712i
$147$	−1.82162	−	1.56142i	−0.150244	−	0.128783i
$148$	0.559369	+	6.39361i	0.0459798	+	0.525552i
$149$	−11.3083	−	9.48879i	−0.926412	−	0.777352i	0.0487579	−	0.998811i	$-0.484474\pi$
$149$	−11.3083	−	9.48879i	−0.926412	−	0.777352i	−0.975170	+	0.221459i	$0.928918\pi$
$150$	0.914537	−	1.05141i	0.0746716	−	0.0858475i
$151$	−2.23835	−	0.814693i	−0.182154	−	0.0662987i	0.249333	−	0.968418i	$-0.419789\pi$
$151$	−2.23835	−	0.814693i	−0.182154	−	0.0662987i	−0.431487	+	0.902119i	$0.642011\pi$
$152$	−0.495858	+	0.132865i	−0.0402194	+	0.0107768i
$153$	−4.91185	+	16.9027i	−0.397100	+	1.36650i
$154$	1.75742	−	1.01465i	0.141617	−	0.0817626i
$155$	−16.4072	+	0.656758i	−1.31786	+	0.0527521i
$156$	−6.67935	−	14.7258i	−0.534776	−	1.17901i
$157$	3.31405	−	7.10700i	0.264490	−	0.567200i	−0.728548	−	0.684995i	$-0.759805\pi$
$157$	3.31405	−	7.10700i	0.264490	−	0.567200i	0.993038	+	0.117794i	$0.0375824\pi$
$158$	−0.0463058	−	0.0661316i	−0.00368389	−	0.00526114i
$159$	1.12213	−	4.01852i	0.0889905	−	0.318689i
$160$	0.933438	−	4.13938i	0.0737947	−	0.327247i
$161$		−	7.71863i		−	0.608313i
$162$	−0.556355	−	1.33703i	−0.0437114	−	0.105047i
$163$	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
$165$	−15.6734	+	6.23418i	−1.22017	+	0.485330i
$166$	−0.250219	+	1.41906i	−0.0194208	+	0.110141i
$167$	−5.88244	−	2.74303i	−0.455197	−	0.212262i	0.181477	−	0.983395i	$-0.441912\pi$
$167$	−5.88244	−	2.74303i	−0.455197	−	0.212262i	−0.636673	+	0.771133i	$0.719690\pi$
$168$	−3.00215	−	1.12854i	−0.231621	−	0.0870689i
$169$	−9.22155	+	1.62601i	−0.709350	+	0.125078i
$170$	0.800791	+	1.95328i	0.0614178	+	0.149810i
$171$	0.0505891	−	2.40781i	0.00386865	−	0.184130i
$172$	3.51174	+	13.1060i	0.267767	+	0.999321i
$173$	10.5085	−	4.90021i	0.798949	−	0.372556i	0.0201240	−	0.999797i	$-0.493594\pi$
$173$	10.5085	−	4.90021i	0.798949	−	0.372556i	0.778825	+	0.627242i	$0.215816\pi$
$174$	−0.325417	+	0.679143i	−0.0246698	+	0.0514857i
$175$	14.2400	+	2.61752i	1.07645	+	0.197866i
$176$	−10.7649	+	12.8292i	−0.811438	+	0.967034i
$177$	5.17536	−	6.03781i	0.389004	−	0.453829i
$178$	−0.931272	−	1.99712i	−0.0698018	−	0.149690i
$179$	−3.42048	+	5.92444i	−0.255658	+	0.442813i	−0.965074	−	0.261977i	$-0.915626\pi$
$179$	−3.42048	+	5.92444i	−0.255658	+	0.442813i	0.709416	+	0.704790i	$0.248959\pi$
$180$	11.5923	+	6.40228i	0.864036	+	0.477198i
$181$	−8.12103	−	14.0660i	−0.603631	−	1.04552i	−0.992266	−	0.124128i	$-0.960387\pi$
$181$	−8.12103	−	14.0660i	−0.603631	−	1.04552i	0.388635	−	0.921392i	$-0.372947\pi$
$182$	−1.26386	+	1.80497i	−0.0936832	+	0.133794i
$183$	−13.3026	−	16.1959i	−0.983357	−	1.19724i
$184$	−0.582977	−	1.60172i	−0.0429776	−	0.118080i
$185$	−6.46042	+	3.33337i	−0.474980	+	0.245074i
$186$	0.508907	+	1.98232i	0.0373149	+	0.145351i
$187$	2.22713	−	25.4563i	0.162864	−	1.86155i
$188$	−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	−0.990802	−	0.135322i	$-0.956793\pi$
$191$	−13.1571	−	15.6801i	−0.952017	−	1.13457i	0.0387846	−	0.999248i	$-0.487651\pi$
$192$	12.7910	+	0.134357i	0.923111	+	0.00969639i
$193$	−6.37883	+	4.46650i	−0.459158	+	0.321506i	−0.780168	−	0.625570i	$-0.784867\pi$
$193$	−6.37883	+	4.46650i	−0.459158	+	0.321506i	0.321010	+	0.947076i	$0.395978\pi$
$194$	1.10220	−	0.401167i	0.0791332	−	0.0288021i
$195$	12.5633	−	13.3274i	0.899678	−	0.954396i
$196$	−0.474846	−	2.69298i	−0.0339176	−	0.192356i
$197$	−1.37044	+	5.11454i	−0.0976395	+	0.364396i	−0.997406	−	0.0719752i	$-0.977070\pi$
$197$	−1.37044	+	5.11454i	−0.0976395	+	0.364396i	0.899767	+	0.436371i	$0.143736\pi$
$198$	1.16943	+	1.74711i	0.0831077	+	0.124162i
$199$	−24.0896	−	13.9081i	−1.70766	−	0.985920i	−0.937440	−	0.348148i	$-0.886811\pi$
$199$	−24.0896	−	13.9081i	−1.70766	−	0.985920i	−0.770225	−	0.637773i	$-0.779856\pi$
$200$	3.15269	−	0.532361i	0.222929	−	0.0376436i
$201$	9.54391	−	6.53441i	0.673176	−	0.460902i
$202$	0.842870	−	0.0737416i	0.0593041	−	0.00518844i
$203$	−7.79481	+	0.681958i	−0.547088	+	0.0478640i
$204$	−16.5537	+	11.3338i	−1.15899	+	0.793521i
$205$	−8.89158	−	4.66972i	−0.621015	−	0.326147i
$206$	−0.523629	−	0.302317i	−0.0364829	−	0.0210634i
$207$	7.97904	−	0.529459i	0.554582	−	0.0368000i
$208$	4.70654	−	17.5651i	0.326340	−	1.21792i
$209$	0.607127	+	3.44319i	0.0419958	+	0.238170i
$210$	−0.0532344	−	1.80381i	−0.00367352	−	0.124474i
$211$	8.85421	−	3.22267i	0.609549	−	0.221858i	−0.0187568	−	0.999824i	$-0.505971\pi$
$211$	8.85421	−	3.22267i	0.609549	−	0.221858i	0.628306	+	0.777966i	$0.283749\pi$
$212$	3.89534	−	2.72754i	0.267533	−	0.187328i
$213$	11.2288	+	0.117948i	0.769388	+	0.00808168i
$214$	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
$218$	−0.170546	+	1.94935i	−0.0115508	+	0.132026i
$219$	4.15460	+	16.1832i	0.280742	+	1.09356i
$220$	−18.3142	−	5.84753i	−1.23474	−	0.394240i
$221$	9.48994	+	26.0734i	0.638363	+	1.75389i
$222$	0.575097	+	0.700179i	0.0385980	+	0.0469930i
$223$	5.95553	−	8.50538i	0.398812	−	0.569562i	−0.568650	−	0.822580i	$-0.692534\pi$
$223$	5.95553	−	8.50538i	0.398812	−	0.569562i	0.967462	+	0.253017i	$0.0814230\pi$
$224$	−2.74756	−	4.75892i	−0.183579	−	0.317969i
$225$	−1.72903	+	14.9000i	−0.115269	+	0.993334i
$226$	−0.327580	+	0.567385i	−0.0217903	+	0.0377419i
$227$	−6.37560	−	13.6725i	−0.423164	−	0.907477i	−0.996129	−	0.0878980i	$-0.971985\pi$
$227$	−6.37560	−	13.6725i	−0.423164	−	0.907477i	0.572966	−	0.819579i	$-0.305793\pi$
$228$	1.78639	−	2.08408i	0.118306	−	0.138022i
$229$	0.604581	−	0.720511i	0.0399518	−	0.0476127i	−0.745699	−	0.666284i	$-0.767884\pi$
$229$	0.604581	−	0.720511i	0.0399518	−	0.0476127i	0.785650	+	0.618671i	$0.212329\pi$
$230$	0.709437	−	0.645362i	0.0467789	−	0.0425539i
$231$	−9.43903	+	19.6992i	−0.621043	+	1.29611i
$232$	−1.56602	+	0.730246i	−0.102814	+	0.0479430i
$233$	−1.45382	−	5.42572i	−0.0952427	−	0.355451i	0.901813	−	0.432126i	$-0.142236\pi$
$233$	−1.45382	−	5.42572i	−0.0952427	−	0.355451i	−0.997056	+	0.0766749i	$0.975570\pi$
$234$	−1.95256	−	1.18268i	−0.127643	−	0.0773145i
$235$	−11.4043	−	4.77234i	−0.743935	−	0.311313i
$236$	8.92598	−	1.57389i	0.581032	−	0.102452i
$237$	0.813442	+	0.305782i	0.0528387	+	0.0198627i
$238$	2.47770	+	1.15537i	0.160605	+	0.0748914i
$239$	−2.69221	+	15.2683i	−0.174144	+	0.987622i	0.764982	+	0.644051i	$0.222748\pi$
$239$	−2.69221	+	15.2683i	−0.174144	+	0.987622i	−0.939127	+	0.343571i	$0.888363\pi$
$240$	5.50428	+	13.8384i	0.355300	+	0.893263i
$241$	14.6302	−	12.2762i	0.942414	−	0.790779i	−0.0355896	−	0.999366i	$-0.511331\pi$
$241$	14.6302	−	12.2762i	0.942414	−	0.790779i	0.978004	+	0.208587i	$0.0668865\pi$
$242$	−0.906597	−	0.906597i	−0.0582783	−	0.0582783i
$243$	13.0722	+	8.49215i	0.838584	+	0.544772i
$244$		−	23.8877i		−	1.52925i
$245$	2.61833	−	1.65475i	0.167279	−	0.105718i
$246$	−0.336665	+	1.20565i	−0.0214650	+	0.0768695i
$247$	−2.17752	−	3.10982i	−0.138552	−	0.197873i
$248$	−1.98455	+	4.25587i	−0.126019	+	0.270248i
$249$	−6.40714	−	14.1257i	−0.406036	−	0.895177i
$250$	0.950042	+	1.52769i	0.0600859	+	0.0966194i
$251$	−10.8992	+	6.29267i	−0.687953	+	0.397190i	−0.802845	−	0.596188i	$-0.796681\pi$
$251$	−10.8992	+	6.29267i	−0.687953	+	0.397190i	0.114892	+	0.993378i	$0.463348\pi$
$252$	16.6546	−	4.08965i	1.04914	−	0.257624i
$253$	−11.2134	+	3.00463i	−0.704983	+	0.188900i
$254$	0.117224	+	0.0426661i	0.00735529	+	0.00267711i
$255$	−18.9908	−	12.4792i	−1.18925	−	0.781475i
$256$	10.7006	+	8.97889i	0.668789	+	0.561181i
$257$	2.58192	+	29.5115i	0.161056	+	1.84088i	0.461576	+	0.887100i	$0.347284\pi$
$257$	2.58192	+	29.5115i	0.161056	+	1.84088i	−0.300521	+	0.953775i	$0.597160\pi$
$258$	1.45438	+	1.24663i	0.0905456	+	0.0776119i
$259$	−3.21988	+	8.84654i	−0.200073	+	0.549697i
$260$	20.7063	−	2.64969i	1.28415	−	0.164327i
$261$	−1.23965	−	8.01102i	−0.0767325	−	0.495869i
$262$	−1.17890	−	0.315886i	−0.0728328	−	0.0195155i
$263$	0.484194	+	0.339036i	0.0298567	+	0.0209059i	0.588410	−	0.808563i	$-0.299754\pi$
$263$	0.484194	+	0.339036i	0.0298567	+	0.0209059i	−0.558553	+	0.829469i	$0.688643\pi$
$264$	−0.470872	+	4.80075i	−0.0289801	+	0.295466i
$265$	4.53228	+	2.91054i	0.278416	+	0.178793i
$266$	−0.368368	−	0.0649533i	−0.0225861	−	0.00398254i
$267$	20.4163	+	12.0750i	1.24946	+	0.738981i
$268$	13.1328	+	1.14897i	0.802215	+	0.0701847i
$269$	29.5187			1.79979			0.899894	−	0.436108i	$-0.143643\pi$
$269$	29.5187			1.79979			0.899894	+	0.436108i	$0.143643\pi$
$270$	1.86101	−	0.178763i	0.113258	−	0.0108791i
$271$	−9.45815			−0.574542			−0.287271	−	0.957849i	$-0.592748\pi$
$271$	−9.45815			−0.574542			−0.287271	+	0.957849i	$0.592748\pi$
$272$	−22.4758	−	1.96638i	−1.36280	−	0.119229i
$273$	0.249128	−	23.7174i	0.0150779	−	1.43544i
$274$	1.56939	+	0.276725i	0.0948101	+	0.0167176i
$275$	−1.74055	−	21.7065i	−0.104959	−	1.30895i
$276$	7.41054	+	5.30578i	0.446062	+	0.319370i
$277$	16.7047	+	11.6968i	1.00369	+	0.702792i	0.955178	−	0.296031i	$-0.0956631\pi$
$277$	16.7047	+	11.6968i	1.00369	+	0.702792i	0.0485123	+	0.998823i	$0.484552\pi$
$278$	2.34310	+	0.627831i	0.140530	+	0.0376548i
$279$	−16.5749	−	14.5121i	−0.992314	−	0.868816i
$280$	2.53250	−	3.27576i	0.151346	−	0.195764i
$281$	7.06656	−	19.4152i	0.421555	−	1.15821i	−0.529261	−	0.848459i	$-0.677531\pi$
$281$	7.06656	−	19.4152i	0.421555	−	1.15821i	0.950816	−	0.309755i	$-0.100247\pi$
$282$	−0.283490	+	1.51455i	−0.0168816	+	0.0901902i
$283$	1.12399	+	12.8473i	0.0668145	+	0.763693i	0.953514	+	0.301348i	$0.0974364\pi$
$283$	1.12399	+	12.8473i	0.0668145	+	0.763693i	−0.886700	+	0.462345i	$0.847008\pi$
$284$	9.80446	+	8.22692i	0.581787	+	0.488178i
$285$	2.95175	+	0.976746i	0.174847	+	0.0578574i
$286$	3.11420	+	1.13348i	0.184147	+	0.0670239i
$287$	−12.5629	+	3.36621i	−0.741563	+	0.198701i
$288$	4.73101	−	3.16670i	0.278777	−	0.186599i
$289$	15.0908	−	8.71266i	0.887692	−	0.512509i
$290$	−0.714413	−	0.659420i	−0.0419518	−	0.0387225i
$291$	−7.35007	+	10.2658i	−0.430869	+	0.601791i
$292$	−8.04791	+	17.2588i	−0.470968	+	1.01000i
$293$	−19.3518	−	27.6373i	−1.13055	−	1.61459i	−0.704153	−	0.710048i	$-0.748673\pi$
$293$	−19.3518	−	27.6373i	−1.13055	−	1.61459i	−0.426392	−	0.904538i	$-0.640216\pi$
$294$	−0.270099	−	0.275834i	−0.0157525	−	0.0160870i
$295$	5.48471	+	8.67854i	0.319332	+	0.505284i
$296$			2.07897i			0.120837i
$297$	−21.0113	−	8.40622i	−1.21920	−	0.487778i
$298$	−1.67960	−	1.67960i	−0.0972964	−	0.0972964i
$299$	9.65629	−	8.10259i	0.558438	−	0.468585i
$300$	−12.3016	+	11.8724i	−0.710235	+	0.685451i
$301$	−3.45606	+	19.6003i	−0.199204	+	1.12974i
$302$	−0.347372	−	0.161982i	−0.0199890	−	0.00932102i
$303$	−7.03787	+	5.78060i	−0.404315	+	0.332087i
$304$	3.04006	−	0.536044i	0.174359	−	0.0307442i
$305$	25.0353	−	10.2638i	1.43352	−	0.587702i
$306$	−1.02439	+	2.64054i	−0.0585605	+	0.150950i
$307$	2.60886	+	9.73639i	0.148895	+	0.555685i	0.999551	+	0.0299620i	$0.00953863\pi$
$307$	2.60886	+	9.73639i	0.148895	+	0.555685i	−0.850656	+	0.525723i	$0.823795\pi$
$308$	−22.5639	+	10.5217i	−1.28570	+	0.599532i
$309$	6.48927	−	0.499116i	0.369162	−	0.0283937i
$310$	−2.63921	−	0.124819i	−0.149897	−	0.00708927i
$311$	16.5976	−	19.7803i	0.941166	−	1.12164i	−0.0512465	−	0.998686i	$-0.516319\pi$
$311$	16.5976	−	19.7803i	0.941166	−	1.12164i	0.992413	−	0.122952i	$-0.0392361\pi$
$312$	−1.73964	−	4.94048i	−0.0984878	−	0.279700i
$313$	2.37968	+	5.10324i	0.134508	+	0.288452i	0.962012	−	0.273007i	$-0.0880181\pi$
$313$	2.37968	+	5.10324i	0.134508	+	0.288452i	−0.827505	+	0.561459i	$0.810240\pi$
$314$	0.630895	−	1.09274i	0.0356035	−	0.0616670i
$315$	11.4421	+	15.6975i	0.644688	+	0.884456i
$316$	0.495232	+	0.857767i	0.0278590	+	0.0482532i
$317$	−1.06328	+	1.51852i	−0.0597197	+	0.0852886i	−0.847901	−	0.530154i	$-0.822134\pi$
$317$	−1.06328	+	1.51852i	−0.0597197	+	0.0852886i	0.788181	+	0.615443i	$0.211023\pi$
$318$	0.236228	−	0.628413i	0.0132470	−	0.0352396i
$319$	4.02502	+	11.0586i	0.225358	+	0.619165i
$320$	−5.02294	+	15.7316i	−0.280791	+	0.879423i
$321$	−13.4283	−	3.74970i	−0.749493	−	0.209288i
$322$	0.108246	−	1.23726i	0.00603233	−	0.0689498i
$323$	−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
$327$	−10.3395	−	18.3511i	−0.571777	−	1.01482i
$328$	−2.35271	+	1.64739i	−0.129907	+	0.0909618i
$329$	−15.0441	+	5.47561i	−0.829409	+	0.301880i
$330$	−2.59980	+	0.779506i	−0.143114	+	0.0429104i
$331$	−3.34434	−	18.9667i	−0.183822	−	1.04251i	−0.927460	−	0.373923i	$-0.878012\pi$
$331$	−3.34434	−	18.9667i	−0.183822	−	1.04251i	0.743638	−	0.668583i	$-0.233099\pi$
$332$	4.57553	−	17.0761i	0.251115	−	0.937173i
$333$	−9.36587	−	2.72168i	−0.513247	−	0.149147i
$334$	−0.904459	−	0.522190i	−0.0494898	−	0.0285730i
$335$	4.43857	+	14.2574i	0.242505	+	0.778965i
$336$	17.3928	+	8.33391i	0.948855	+	0.454652i
$337$	3.43672	−	0.300674i	0.187210	−	0.0163788i	0.00683487	−	0.999977i	$-0.497824\pi$
$337$	3.43672	−	0.300674i	0.187210	−	0.0163788i	0.180375	+	0.983598i	$0.442269\pi$
$338$	−1.50097	+	0.131318i	−0.0816423	+	0.00714277i
$339$	−0.540823	−	7.03154i	−0.0293735	−	0.381901i
$340$	−7.69858	−	24.7291i	−0.417514	−	1.34112i
$341$	27.6974	+	15.9911i	1.49990	+	0.865966i
$342$	0.0418764	−	0.385252i	0.00226442	−	0.0208320i
$343$	−4.20811	+	15.7049i	−0.227217	+	0.847984i
$344$	0.763205	+	4.32835i	0.0411493	+	0.233369i
$345$	−2.37661	+	10.0463i	−0.127952	+	0.540873i
$346$	1.75319	−	0.638109i	0.0942520	−	0.0343049i
$347$	7.09044	−	4.96478i	0.380635	−	0.266523i	−0.367564	−	0.929998i	$-0.619808\pi$
$347$	7.09044	−	4.96478i	0.380635	−	0.266523i	0.748198	+	0.663475i	$0.230919\pi$
$348$	4.70341	−	7.95246i	0.252129	−	0.426296i
$349$	6.93929	+	8.26992i	0.371452	+	0.442679i	0.919097	−	0.394032i	$-0.128920\pi$
$349$	6.93929	+	8.26992i	0.371452	+	0.442679i	−0.547645	+	0.836711i	$0.684476\pi$
$350$	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
$353$	2.33150	−	26.6492i	0.124093	−	1.41839i	−0.637555	−	0.770405i	$-0.720054\pi$
$353$	2.33150	−	26.6492i	0.124093	−	1.41839i	0.761649	−	0.647990i	$-0.224390\pi$
$354$	0.914260	−	0.895253i	0.0485924	−	0.0475822i
$355$	−4.40949	+	13.8103i	−0.234031	+	0.732975i
$356$	9.24644	+	25.4044i	0.490060	+	1.34643i
$357$	−29.0327	+	4.80539i	−1.53657	+	0.254328i
$358$	−0.631371	+	0.901691i	−0.0333690	+	0.0476559i
$359$	−6.82588	−	11.8228i	−0.360256	−	0.623982i	0.627747	−	0.778418i	$-0.283977\pi$
$359$	−6.82588	−	11.8228i	−0.360256	−	0.623982i	−0.988003	+	0.154436i	$0.950644\pi$
$360$	3.55999	+	2.39324i	0.187628	+	0.126135i
$361$	−9.17777	+	15.8964i	−0.483041	+	0.836651i
$362$	−1.10450	−	2.36861i	−0.0580513	−	0.124491i
$363$	13.5655	+	2.53916i	0.712004	+	0.133271i
$364$	17.3767	−	20.7088i	0.910788	−	1.08544i
$365$	−21.5459	−	1.01900i	−1.12776	−	0.0533367i
$366$	−1.90521	−	2.78268i	−0.0995871	−	0.145453i
$367$	11.8122	−	5.50814i	0.616594	−	0.287523i	−0.0891181	−	0.996021i	$-0.528405\pi$
$367$	11.8122	−	5.50814i	0.616594	−	0.287523i	0.705712	+	0.708498i	$0.250627\pi$
$368$	2.65285	+	9.90056i	0.138289	+	0.516103i
$369$	−4.34153	−	12.7558i	−0.226011	−	0.664041i
$370$	−1.08232	+	0.443722i	−0.0562673	+	0.0230680i
$371$	6.86938	−	1.21126i	0.356640	−	0.0628853i
$372$	−4.10016	−	24.7719i	−0.212583	−	1.28436i
$373$	−1.71551	−	0.799956i	−0.0888258	−	0.0414201i	0.377698	−	0.925929i	$-0.376716\pi$
$373$	−1.71551	−	0.799956i	−0.0888258	−	0.0414201i	−0.466523	+	0.884509i	$0.654494\pi$
$374$	0.713999	−	4.04929i	0.0369200	−	0.209384i
$375$	−17.7283	−	7.79144i	−0.915487	−	0.402348i
$376$	−2.70829	+	2.27252i	−0.139669	+	0.117196i
$377$	−9.03572	−	9.03572i	−0.465363	−	0.465363i
$378$	1.61392	−	1.80473i	0.0830112	−	0.0928252i
$379$		−	8.64900i		−	0.444270i	−0.975016	−	0.222135i	$-0.928698\pi$
$379$		−	8.64900i		−	0.444270i	0.975016	−	0.222135i	$-0.0713025\pi$
$380$	1.89316	+	2.99559i	0.0971173	+	0.153670i
$381$	−1.30063	+	0.333902i	−0.0666335	+	0.0171063i
$382$	−1.88913	−	2.69796i	−0.0966563	−	0.138040i
$383$	7.21777	−	15.4786i	0.368811	−	0.790917i	−0.631074	−	0.775723i	$-0.717386\pi$
$383$	7.21777	−	15.4786i	0.368811	−	0.790917i	0.999885	−	0.0151943i	$-0.00483668\pi$
$384$	8.59078	+	0.842608i	0.438397	+	0.0429992i
$385$	−20.7222	−	19.1271i	−1.05610	−	0.974806i
$386$	−1.08513	+	0.626503i	−0.0552319	+	0.0318881i
$387$	−20.4986	−	2.22818i	−1.04200	−	0.113265i
$388$	−13.8999	+	3.72447i	−0.705661	+	0.189081i
$389$	−0.823821	−	0.299846i	−0.0417694	−	0.0152028i	0.321051	−	0.947062i	$-0.395964\pi$
$389$	−0.823821	−	0.299846i	−0.0417694	−	0.0152028i	−0.362820	+	0.931859i	$0.618186\pi$
$390$	2.20075	−	1.96013i	0.111439	−	0.0992553i
$391$	−11.9805	−	10.0529i	−0.605882	−	0.508395i
$392$	−0.0772012	−	0.882413i	−0.00389925	−	0.0445686i
$393$	12.3919	−	4.36343i	0.625087	−	0.220106i
$394$	−0.291401	+	0.800617i	−0.0146806	+	0.0403345i
$395$	−0.686190	+	0.887578i	−0.0345260	+	0.0446589i
$396$	−12.4245	−	22.6035i	−0.624354	−	1.13587i
$397$	2.23467	+	0.598779i	0.112155	+	0.0300519i	0.314460	−	0.949271i	$-0.398177\pi$
$397$	2.23467	+	0.598779i	0.112155	+	0.0300519i	−0.202305	+	0.979323i	$0.564843\pi$
$398$	−3.66640	−	2.56724i	−0.183780	−	0.128684i
$399$	3.66681	−	1.66320i	0.183570	−	0.0832641i
$400$	−19.1651	+	1.53677i	−0.958255	+	0.0768385i
$401$	6.34251	+	1.11835i	0.316730	+	0.0558480i	0.329753	−	0.944067i	$-0.393035\pi$
$401$	6.34251	+	1.11835i	0.316730	+	0.0558480i	−0.0130235	+	0.999915i	$0.504146\pi$
$402$	1.62148	−	0.913591i	0.0808722	−	0.0455658i
$403$	−34.5950	−	3.02667i	−1.72330	−	0.150769i
$404$	−10.3803			−0.516440
$405$	−15.4423	+	12.9049i	−0.767333	+	0.641249i
$406$	−1.25904			−0.0624849
$407$	14.1054	+	1.23407i	0.699181	+	0.0611704i
$408$	−5.66172	+	3.18998i	−0.280297	+	0.157928i
$409$	27.7142	+	4.88676i	1.37038	+	0.241635i	0.809916	−	0.586546i	$-0.199513\pi$
$409$	27.7142	+	4.88676i	1.37038	+	0.241635i	0.560462	+	0.828180i	$0.310624\pi$
$410$	−1.35979	−	0.873230i	−0.0671553	−	0.0431257i
$411$	−15.6220	+	7.08585i	−0.770576	+	0.349519i
$412$	6.07648	+	4.25479i	0.299367	+	0.209619i
$413$	12.8420	+	3.44101i	0.631915	+	0.169321i
$414$	1.28643	+	0.0270284i	0.0632245	+	0.00132837i
$415$	19.8624	−	2.54170i	0.975008	−	0.124767i
$416$	3.06934	−	8.43295i	0.150487	−	0.413459i
$417$	−24.6291	+	8.67242i	−1.20609	+	0.424690i
$418$	0.0490322	+	0.560441i	0.00239824	+	0.0274121i
$419$	−28.5256	−	23.9358i	−1.39357	−	1.16934i	−0.963872	−	0.266365i	$-0.914177\pi$
$419$	−28.5256	−	23.9358i	−1.39357	−	1.16934i	−0.429693	−	0.902975i	$-0.641378\pi$
$420$	−1.27814	+	22.1029i	−0.0623670	+	1.07851i
$421$	27.5767	+	10.0371i	1.34400	+	0.489178i	0.911071	−	0.412249i	$-0.135256\pi$
$421$	27.5767	+	10.0371i	1.34400	+	0.489178i	0.432933	+	0.901426i	$0.357479\pi$
$422$	1.46448	−	0.392407i	0.0712900	−	0.0191021i
$423$	−6.69230	−	15.1761i	−0.325391	−	0.737886i
$424$	1.33400	−	0.770186i	0.0647849	−	0.0374036i
$425$	22.6093	−	18.6937i	1.09671	−	0.906778i
$426$	1.79828	+	0.176380i	0.0871268	+	0.00854565i
$427$	14.8084	−	31.7567i	0.716629	−	1.53682i
$428$	−9.11436	−	13.0167i	−0.440559	−	0.629184i
$429$	−34.5530	+	8.87053i	−1.66823	+	0.428273i
$430$	−2.09047	+	1.32115i	−0.100812	+	0.0637113i
$431$			0.480686i			0.0231538i	0.999933	+	0.0115769i	$0.00368513\pi$
$431$			0.480686i			0.0231538i	−0.999933	+	0.0115769i	$0.996315\pi$
$432$	−7.42202	+	18.5513i	−0.357092	+	0.892548i
$433$	−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
$435$	10.3554	+	1.51245i	0.496503	+	0.0725167i
$436$	4.16878	−	23.6423i	0.199648	−	1.13226i
$437$	1.93935	+	0.904335i	0.0927718	+	0.0432602i
$438$	0.439009	+	2.65236i	0.0209767	+	0.126735i
$439$	−12.2268	+	2.15591i	−0.583551	+	0.102896i	−0.457627	−	0.889144i	$-0.651301\pi$
$439$	−12.2268	+	2.15591i	−0.583551	+	0.102896i	−0.125924	+	0.992040i	$0.540190\pi$
$440$	−5.74477	−	2.40400i	−0.273871	−	0.114606i
$441$	4.07640	+	0.807416i	0.194114	+	0.0384484i
$442$	1.15554	+	4.31253i	0.0549634	+	0.205126i
$443$	−16.1231	+	7.51833i	−0.766033	+	0.357207i	−0.766040	−	0.642793i	$-0.777775\pi$
$443$	−16.1231	+	7.51833i	−0.766033	+	0.357207i	7.21597e−6		1.00000i	$0.499998\pi$
$444$	−6.28009	−	9.17246i	−0.298040	−	0.435306i
$445$	−22.6519	+	20.6061i	−1.07380	+	0.976822i
$446$	1.07392	−	1.27985i	0.0508517	−	0.0606028i
$447$	25.1320	+	4.70414i	1.18870	+	0.222498i
$448$	9.03801	+	19.3821i	0.427006	+	0.915717i
$449$	1.91039	−	3.30889i	0.0901568	−	0.156156i	−0.817420	−	0.576042i	$-0.804597\pi$
$449$	1.91039	−	3.30889i	0.0901568	−	0.156156i	0.907577	+	0.419886i	$0.137930\pi$
$450$	−0.486114	+	2.36416i	−0.0229156	+	0.111447i
$451$	9.78070	+	16.9407i	0.460555	+	0.797705i
$452$	4.61034	−	6.58425i	0.216852	−	0.309697i
$453$	4.07037	−	0.673713i	0.191243	−	0.0316538i
$454$	−0.830236	−	2.28105i	−0.0389649	−	0.107055i
$455$	29.1699	+	9.31364i	1.36750	+	0.436630i
$456$	0.635292	−	0.622085i	0.0297503	−	0.0291318i
$457$	−1.92516	+	22.0047i	−0.0900553	+	1.02934i	0.807920	+	0.589292i	$0.200593\pi$
$457$	−1.92516	+	22.0047i	−0.0900553	+	1.02934i	−0.897976	+	0.440045i	$0.854962\pi$
$458$	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	0.854095	−	0.520116i	$-0.174111\pi$
$461$	4.15610	+	4.95304i	0.193569	+	0.230686i	−0.660527	+	0.750803i	$0.729667\pi$
$462$	−1.78929	+	3.02531i	−0.0832455	+	0.140750i
$463$	0.251426	−	0.176051i	0.0116848	−	0.00818177i	−0.567719	−	0.823222i	$-0.692174\pi$
$463$	0.251426	−	0.176051i	0.0116848	−	0.00818177i	0.579404	+	0.815040i	$0.303285\pi$
$464$	9.76390	−	3.55377i	0.453278	−	0.164980i
$465$	24.2003	−	14.9408i	1.12226	−	0.692864i
$466$	−0.156950	−	0.890106i	−0.00727056	−	0.0412334i
$467$	−11.0784	+	41.3450i	−0.512645	+	1.91322i	−0.122489	+	0.992470i	$0.539088\pi$
$467$	−11.0784	+	41.3450i	−0.512645	+	1.91322i	−0.390156	+	0.920749i	$0.627579\pi$
$468$	22.5994	+	16.5425i	1.04466	+	0.764676i
$469$	16.7467	+	9.66873i	0.773292	+	0.446460i
$470$	−1.76113	−	0.924918i	−0.0812349	−	0.0426633i
$471$	1.04159	+	13.5422i	0.0479938	+	0.623993i
$472$	2.92479	−	0.255886i	0.134624	−	0.0117781i
$473$	29.8202	−	2.60893i	1.37113	−	0.119959i
$474$	0.126103	+	0.0604232i	0.00579209	+	0.00277533i
$475$	−2.32607	+	3.27122i	−0.106727	+	0.150094i
$476$	−29.0467	−	16.7701i	−1.33135	−	0.768658i
$477$	1.72333	+	7.01805i	0.0789058	+	0.321335i
$478$	−0.645671	+	2.40968i	−0.0295323	+	0.110216i
$479$	7.22789	+	40.9914i	0.330251	+	1.87295i	0.469863	+	0.882740i	$0.344303\pi$
$479$	7.22789	+	40.9914i	0.330251	+	1.87295i	−0.139612	+	0.990206i	$0.544585\pi$
$480$	2.11082	+	7.04001i	0.0963455	+	0.321331i
$481$	−14.4474	+	5.25842i	−0.658745	+	0.239763i
$482$	2.51732	−	1.76264i	0.114661	−	0.0802862i
$483$	6.56255	+	11.6475i	0.298606	+	0.529980i
$484$	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	$0.0683442\pi$
$488$	0.674397	−	7.70840i	0.0305285	−	0.348943i
$489$	−24.0567	−	6.71758i	−1.08788	−	0.303779i
$490$	0.442913	−	0.228528i	0.0200088	−	0.0103239i
$491$	−5.41828	−	14.8866i	−0.244524	−	0.671823i	−0.999864	−	0.0164907i	$-0.994751\pi$
$491$	−5.41828	−	14.8866i	−0.244524	−	0.671823i	0.755340	−	0.655333i	$-0.227472\pi$
$492$	5.40386	−	14.3753i	0.243625	−	0.648091i
$493$	−9.09358	+	12.9870i	−0.409554	+	0.584904i
$494$	−0.305434	−	0.529027i	−0.0137421	−	0.0238020i
$495$	18.3510	−	22.7334i	0.824814	−	1.02179i
$496$	14.1189	−	24.4546i	0.633955	−	1.09804i
$497$	7.93420	+	17.0150i	0.355898	+	0.763225i
$498$	−0.828936	−	2.35413i	−0.0371455	−	0.105491i
$499$	−0.350248	+	0.417409i	−0.0156792	+	0.0186858i	−0.773827	−	0.633397i	$-0.781660\pi$
$499$	−0.350248	+	0.417409i	−0.0156792	+	0.0186858i	0.758148	+	0.652083i	$0.226105\pi$
$500$	−9.97779	−	19.6871i	−0.446220	−	0.880434i
$501$	11.2089	−	0.862118i	0.500775	−	0.0385166i
$502$	−1.83534	+	0.855835i	−0.0819154	+	0.0381978i
$503$	−5.01841	−	18.7290i	−0.223760	−	0.835083i	−0.982898	−	0.184153i	$-0.941046\pi$
$503$	−5.01841	−	18.7290i	−0.223760	−	0.835083i	0.759138	−	0.650930i	$-0.225621\pi$
$504$	5.48979	−	0.849509i	0.244535	−	0.0378401i
$505$	−4.46008	−	10.8790i	−0.198471	−	0.484109i
$506$	−1.83960	+	0.324371i	−0.0817801	+	0.0144200i
$507$	12.5330	−	10.2940i	0.556609	−	0.457174i
$508$	−1.38708	−	0.646805i	−0.0615417	−	0.0286974i
$509$	−4.57685	+	25.9566i	−0.202865	+	1.15051i	0.697898	+	0.716197i	$0.254119\pi$
$509$	−4.57685	+	25.9566i	−0.202865	+	1.15051i	−0.900764	+	0.434310i	$0.856992\pi$
$510$	−2.86913	−	2.26668i	−0.127047	−	0.100370i
$511$	−21.3981	+	17.9551i	−0.946595	+	0.794287i
$512$	8.63735	+	8.63735i	0.381720	+	0.381720i
$513$	1.97084	+	3.67644i	0.0870146	+	0.162319i
$514$			4.76676i			0.210253i
$515$	−1.84834	+	8.19654i	−0.0814474	+	0.361183i
$516$	−16.4423	−	16.7913i	−0.723830	−	0.739197i
$517$	13.8111	+	19.7242i	0.607410	+	0.867471i
$518$	−0.640195	+	1.37290i	−0.0281286	+	0.0603219i
$519$	−11.6912	+	16.3291i	−0.513189	+	0.716767i
$520$	6.75658	−	0.270457i	0.296295	−	0.0118603i
$521$	−6.99745	+	4.03998i	−0.306564	+	0.176995i	−0.645388	−	0.763855i	$-0.723304\pi$
$521$	−6.99745	+	4.03998i	−0.306564	+	0.176995i	0.338824	+	0.940850i	$0.389971\pi$
$522$	−0.0863636	−	1.30151i	−0.00378003	−	0.0569657i
$523$	34.5655	−	9.26181i	1.51145	−	0.404991i	0.594530	−	0.804073i	$-0.297338\pi$
$523$	34.5655	−	9.26181i	1.51145	−	0.404991i	0.916915	+	0.399083i	$0.130671\pi$
$524$	14.0706	+	5.12130i	0.614679	+	0.223725i
$525$	−23.7139	+	8.15733i	−1.03496	+	0.356015i
$526$	0.0728594	+	0.0611363i	0.00317682	+	0.00266567i
$527$	3.75519	+	42.9220i	0.163579	+	1.86971i
$528$	5.33681	−	28.5120i	0.232255	−	1.24082i
$529$	5.43640	−	14.9364i	0.236365	−	0.649408i
$530$	0.685685	+	0.530106i	0.0297843	+	0.0230263i
$531$	−2.67621	+	13.5113i	−0.116137	+	0.586342i
$532$	4.43271	+	1.18774i	0.192182	+	0.0514951i
$533$	−17.3991	−	12.1830i	−0.753637	−	0.527702i
$534$	3.10330	+	2.22189i	0.134293	+	0.0961507i
$535$	9.72584	−	15.1451i	0.420485	−	0.654778i
$536$	4.20543	+	0.741531i	0.181647	+	0.0320293i
$537$	0.124454	−	11.8482i	0.00537059	−	0.511289i
$538$	4.73172	+	0.413971i	0.203999	+	0.0178476i
$539$	−6.03285			−0.259853
$540$	−22.9362	+	0.194880i	−0.987019	+	0.00838630i
$541$	−6.99126			−0.300578			−0.150289	−	0.988642i	$-0.548020\pi$
$541$	−6.99126			−0.300578			−0.150289	+	0.988642i	$0.548020\pi$
$542$	−1.51610	−	0.132641i	−0.0651220	−	0.00569743i
$543$	24.2140	+	14.3212i	1.03912	+	0.614580i
$544$	−10.9651	−	1.93344i	−0.470123	−	0.0828954i
$545$	26.5693	−	5.78929i	1.13811	−	0.247986i
$546$	0.372547	−	3.79829i	0.0159435	−	0.162552i
$547$	−9.60101	−	6.72270i	−0.410509	−	0.287442i	0.350024	−	0.936741i	$-0.386174\pi$
$547$	−9.60101	−	6.72270i	−0.410509	−	0.287442i	−0.760533	+	0.649299i	$0.775062\pi$
$548$	−18.8850	−	5.06022i	−0.806727	−	0.216162i
$549$	33.8439	+	13.1297i	1.44442	+	0.560360i
$550$	0.0254097	−	3.50386i	0.00108347	−	0.149405i
$551$	0.741915	−	2.03839i	0.0316066	−	0.0868385i
$552$	2.24154	+	1.92135i	0.0954061	+	0.0817781i
$553$	0.126625	+	1.44733i	0.00538465	+	0.0615469i
$554$	2.51366	+	2.10921i	0.106795	+	0.0896117i
$555$	6.91476	−	10.5229i	0.293515	−	0.446672i
$556$	−27.9658	−	10.1787i	−1.18601	−	0.431673i
$557$	−11.5536	+	3.09577i	−0.489541	+	0.131172i	−0.495142	−	0.868812i	$-0.664884\pi$
$557$	−11.5536	+	3.09577i	−0.489541	+	0.131172i	0.00560082	+	0.999984i	$0.498217\pi$
$558$	−2.45336	−	2.55867i	−0.103859	−	0.108317i
$559$	−28.1487	+	16.2516i	−1.19056	+	0.687371i
$560$	−16.8877	+	18.2960i	−0.713635	+	0.773149i
$561$	18.2827	+	40.3074i	0.771897	+	1.70178i
$562$	1.40502	−	3.01306i	0.0592670	−	0.127098i
$563$	4.83500	+	6.90509i	0.203771	+	0.291015i	0.908010	−	0.418947i	$-0.137601\pi$
$563$	4.83500	+	6.90509i	0.203771	+	0.291015i	−0.704240	+	0.709962i	$0.748712\pi$
$564$	5.08426	−	18.2076i	0.214086	−	0.766677i
$565$	8.88147	+	2.00279i	0.373646	+	0.0842579i
$566$			2.07513i			0.0872241i
$567$	−3.35988	+	25.8440i	−0.141102	+	1.08535i
$568$	2.93157	+	2.93157i	0.123006	+	0.123006i
$569$	−9.07677	+	7.61631i	−0.380518	+	0.319292i	−0.812906	−	0.582395i	$-0.802116\pi$
$569$	−9.07677	+	7.61631i	−0.380518	+	0.319292i	0.432388	+	0.901688i	$0.357671\pi$
$570$	0.459454	+	0.197963i	0.0192444	+	0.00829177i
$571$	5.84395	−	33.1427i	0.244562	−	1.38698i	−0.576946	−	0.816782i	$-0.695756\pi$
$571$	5.84395	−	33.1427i	0.244562	−	1.38698i	0.821508	−	0.570197i	$-0.193133\pi$
$572$	−36.8495	−	17.1832i	−1.54075	−	0.718465i
$573$	33.1858	+	12.4749i	1.38636	+	0.521148i
$574$	−2.06098	+	0.363406i	−0.0860235	+	0.0151683i
$575$	−11.4935	−	6.74735i	−0.479310	−	0.281384i
$576$	−19.4160	+	10.6725i	−0.809001	+	0.444685i
$577$	−7.63587	−	28.4975i	−0.317886	−	1.18637i	−0.921273	−	0.388917i	$-0.872849\pi$
$577$	−7.63587	−	28.4975i	−0.317886	−	1.18637i	0.603387	−	0.797448i	$-0.293817\pi$
$578$	2.54117	−	1.18497i	0.105699	−	0.0492881i
$579$	5.82821	−	12.1634i	0.242212	−	0.505495i
$580$	8.02637	+	8.82327i	0.333277	+	0.366366i
$581$	16.6686	−	19.8648i	0.691529	−	0.824132i
$582$	−1.32215	+	1.54248i	−0.0548049	+	0.0639378i
$583$	−4.43373	−	9.50816i	−0.183626	−	0.393788i
$584$	−3.08426	+	5.34209i	−0.127627	+	0.221057i
$585$	−7.62696	+	30.7929i	−0.315336	+	1.27313i
$586$	−2.71442	−	4.70152i	−0.112132	−	0.194218i
$587$	13.0366	−	18.6182i	0.538077	−	0.768453i	−0.454412	−	0.890792i	$-0.650150\pi$
$587$	13.0366	−	18.6182i	0.538077	−	0.768453i	0.992488	+	0.122338i	$0.0390393\pi$
$588$	3.00618	+	3.66003i	0.123973	+	0.150937i
$589$	−2.01626	−	5.53962i	−0.0830784	−	0.228256i
$590$	0.757465	+	1.46805i	0.0311843	+	0.0604386i
$591$	−2.28049	−	8.88308i	−0.0938067	−	0.365401i
$592$	1.08958	−	12.4540i	0.0447815	−	0.511855i
$593$	9.57575	−	9.57575i	0.393229	−	0.393229i	−0.482608	−	0.875837i	$-0.660310\pi$
$593$	9.57575	−	9.57575i	0.393229	−	0.393229i	0.875837	+	0.482608i	$0.160310\pi$
$594$	−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
$597$	48.1765	+	0.506047i	1.97173	+	0.0207111i
$598$	1.66149	−	1.16339i	0.0679433	−	0.0475744i
$599$	13.5529	−	4.93284i	0.553755	−	0.201550i	−0.0499591	−	0.998751i	$-0.515909\pi$
$599$	13.5529	−	4.93284i	0.553755	−	0.201550i	0.603714	+	0.797201i	$0.293687\pi$
$600$	−4.30483	+	3.48383i	−0.175744	+	0.142227i
$601$	4.30406	+	24.4095i	0.175566	+	0.995686i	0.937488	+	0.348017i	$0.113145\pi$
$601$	4.30406	+	24.4095i	0.175566	+	0.995686i	−0.761922	+	0.647669i	$0.775744\pi$
$602$	−0.828865	+	3.09337i	−0.0337820	+	0.126076i
$603$	−8.84619	+	17.9750i	−0.360245	+	0.731997i
$604$	4.07234	+	2.35117i	0.165701	+	0.0956676i
$605$	−8.28429	+	15.7741i	−0.336804	+	0.641307i
$606$	−1.20921	+	0.827904i	−0.0491206	+	0.0336313i
$607$	−27.7738	+	2.42989i	−1.12730	+	0.0986264i	−0.635516	−	0.772088i	$-0.719212\pi$
$607$	−27.7738	+	2.42989i	−1.12730	+	0.0986264i	−0.491789	+	0.870714i	$0.663657\pi$
$608$	1.51762	−	0.132774i	0.0615476	−	0.00538471i
$609$	11.1827	−	7.65641i	0.453144	−	0.310253i
$610$	4.15698	−	1.29414i	0.168311	−	0.0523981i
$611$	−22.6427	−	13.0728i	−0.916025	−	0.528867i
$612$	15.3435	−	31.1771i	0.620223	−	1.26026i
$613$	−8.68995	+	32.4313i	−0.350984	+	1.30989i	0.534480	+	0.845181i	$0.320507\pi$
$613$	−8.68995	+	32.4313i	−0.350984	+	1.30989i	−0.885464	+	0.464708i	$0.846159\pi$
$614$	0.281645	+	1.59729i	0.0113662	+	0.0644612i
$615$	17.3878	−	0.513153i	0.701144	−	0.0206923i
$616$	−7.57828	+	2.75827i	−0.305337	+	0.111134i
$617$	23.2671	−	16.2918i	0.936700	−	0.655884i	−0.00222854	−	0.999998i	$-0.500709\pi$
$617$	23.2671	−	16.2918i	0.936700	−	0.655884i	0.938928	+	0.344113i	$0.111820\pi$
$618$	1.04720	+	0.0109998i	0.0421246	+	0.000442478i
$619$	−16.2376	−	19.3513i	−0.652646	−	0.777793i	0.333665	−	0.942692i	$-0.391715\pi$
$619$	−16.2376	−	19.3513i	−0.652646	−	0.777793i	−0.986310	+	0.164899i	$0.947270\pi$
$620$	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
$623$	−3.45624	+	39.5050i	−0.138471	+	1.58274i
$624$	7.83197	+	30.5075i	0.313530	+	1.22128i
$625$	16.3458	−	18.9160i	0.653830	−	0.756641i
$626$	0.309884	+	0.851399i	0.0123854	+	0.0340287i
$627$	−3.84364	−	4.67962i	−0.153500	−	0.186886i
$628$	−8.87918	+	12.6808i	−0.354318	+	0.506018i
$629$	9.53762	+	16.5196i	0.380290	+	0.658681i
$630$	1.61397	+	2.67671i	0.0643020	+	0.106643i
$631$	2.76033	−	4.78103i	0.109887	−	0.190330i	−0.805837	−	0.592137i	$-0.798284\pi$
$631$	2.76033	−	4.78103i	0.109887	−	0.190330i	0.915724	+	0.401807i	$0.131618\pi$
$632$	0.135591	+	0.290777i	0.00539354	+	0.0115665i
$633$	−10.6211	+	12.3911i	−0.422153	+	0.492502i
$634$	−0.191734	+	0.228500i	−0.00761475	+	0.00907490i
$635$	0.0818961	−	1.73163i	0.00324995	−	0.0687175i
$636$	−3.55910	+	7.42780i	−0.141127	+	0.294532i
$637$	5.93690	−	2.76842i	0.235229	−	0.109689i
$638$	0.490105	+	1.82910i	0.0194034	+	0.0724146i
$639$	−17.0448	+	9.36903i	−0.674280	+	0.370633i
$640$	−4.30188	+	10.2801i	−0.170047	+	0.406355i
$641$	−45.0144	+	7.93726i	−1.77796	+	0.313503i	−0.963699	−	0.266991i	$-0.913971\pi$
$641$	−45.0144	+	7.93726i	−1.77796	+	0.313503i	−0.814264	+	0.580494i	$0.802859\pi$
$642$	−2.09990	−	0.789378i	−0.0828766	−	0.0311543i
$643$	14.3424	+	6.68798i	0.565610	+	0.263748i	0.684321	−	0.729181i	$-0.260099\pi$
$643$	14.3424	+	6.68798i	0.565610	+	0.263748i	−0.118711	+	0.992929i	$0.537876\pi$
$644$	−2.64595	+	15.0059i	−0.104265	+	0.591316i
$645$	10.5333	−	24.4468i	0.414749	−	0.962593i
$646$	−0.580587	+	0.487170i	−0.0228429	+	0.0191675i
$647$	−8.27160	−	8.27160i	−0.325190	−	0.325190i	0.525564	−	0.850754i	$-0.323854\pi$
$647$	−8.27160	−	8.27160i	−0.325190	−	0.325190i	−0.850754	+	0.525564i	$0.823854\pi$
$648$	1.25474	+	5.61674i	0.0492909	+	0.220646i
$649$		−	19.9961i		−	0.784915i
$650$	1.58288	+	3.45979i	0.0620858	+	0.135704i
$651$	9.90572	−	35.4740i	0.388236	−	1.39033i
$652$	−16.3284	−	23.3193i	−0.639468	−	0.913255i
$653$	−20.8882	+	44.7948i	−0.817417	+	1.75296i	−0.178100	+	0.984012i	$0.556995\pi$
$653$	−20.8882	+	44.7948i	−0.817417	+	1.75296i	−0.639316	+	0.768944i	$0.720783\pi$
$654$	−1.40002	−	3.08659i	−0.0547452	−	0.120695i
$655$	0.678369	+	16.9471i	0.0265061	+	0.662177i
$656$	14.9572	−	8.63557i	0.583982	−	0.337162i
$657$	−20.0287	−	20.8884i	−0.781393	−	0.814933i
$658$	−2.48829	+	0.666736i	−0.0970037	+	0.0259921i
$659$	−25.0705	−	9.12491i	−0.976607	−	0.355456i	−0.196087	−	0.980586i	$-0.562824\pi$
$659$	−25.0705	−	9.12491i	−0.976607	−	0.355456i	−0.780520	+	0.625130i	$0.785046\pi$
$660$	32.6080	−	6.74713i	1.26927	−	0.262631i
$661$	−33.2465	−	27.8971i	−1.29314	−	1.08507i	−0.991287	−	0.131716i	$-0.957951\pi$
$661$	−33.2465	−	27.8971i	−1.29314	−	1.08507i	−0.301851	−	0.953355i	$-0.597604\pi$
$662$	−0.270093	−	3.08718i	−0.0104975	−	0.119987i
$663$	−36.4886	−	31.2766i	−1.41710	−	1.21468i
$664$	1.95858	−	5.38117i	0.0760078	−	0.208830i
$665$	0.659789	+	5.15599i	0.0255855	+	0.199941i
$666$	−1.46314	−	0.567620i	−0.0566954	−	0.0219948i
$667$	6.95716	+	1.86416i	0.269382	+	0.0721808i
$668$	10.4958	+	7.34927i	0.406096	+	0.284352i
$669$	−1.75551	+	17.8983i	−0.0678720	+	0.691987i
$670$	0.511536	+	2.34764i	0.0197624	+	0.0906974i
$671$	−51.8999	−	9.15135i	−2.00357	−	0.353284i
$672$	8.19225	+	4.84523i	0.316023	+	0.186909i
$673$	9.97924	+	0.873070i	0.384671	+	0.0336544i	0.277852	−	0.960624i	$-0.410378\pi$
$673$	9.97924	+	0.873070i	0.384671	+	0.0336544i	0.106820	+	0.994278i	$0.465933\pi$
$674$	0.555107			0.0213819
$675$	−10.0592	−	23.9544i	−0.387179	−	0.922005i
$676$	18.4852			0.710968
$677$	−35.9148	−	3.14213i	−1.38032	−	0.120762i	−0.627307	−	0.778772i	$-0.715843\pi$
$677$	−35.9148	−	3.14213i	−1.38032	−	0.120762i	−0.753009	+	0.658010i	$0.771398\pi$
$678$	0.0119190	−	1.13471i	0.000457747	−	0.0435782i
$679$	−20.7876	−	3.66542i	−0.797756	−	0.140666i
$680$	−1.78613	−	8.19725i	−0.0684949	−	0.314350i
$681$	21.2456	+	15.2113i	0.814131	+	0.582900i
$682$	4.21550	+	2.95173i	0.161420	+	0.113027i
$683$	−40.8281	−	10.9399i	−1.56224	−	0.418602i	−0.628871	−	0.777510i	$-0.716483\pi$
$683$	−40.8281	−	10.9399i	−1.56224	−	0.418602i	−0.933373	+	0.358908i	$0.883149\pi$
$684$	−0.923751	+	4.66373i	−0.0353205	+	0.178322i
$685$	−2.81095	−	21.9664i	−0.107401	−	0.839295i
$686$	−0.894787	+	2.45841i	−0.0341631	+	0.0938624i
$687$	−0.299726	+	1.60129i	−0.0114352	+	0.0610930i
$688$	−2.30347	−	26.3288i	−0.0878191	−	1.00378i
$689$	8.72642	+	7.32234i	0.332450	+	0.278959i
$690$	−0.521848	+	1.57704i	−0.0198664	+	0.0600369i
$691$	−5.10153	−	1.85681i	−0.194071	−	0.0706362i	0.243156	−	0.969987i	$-0.421817\pi$
$691$	−5.10153	−	1.85681i	−0.194071	−	0.0706362i	−0.437227	+	0.899351i	$0.644040\pi$
$692$	−22.1096	+	5.92425i	−0.840481	+	0.225206i
$693$	−2.50506	−	37.7516i	−0.0951592	−	1.43406i
$694$	1.20619	−	0.696395i	0.0457864	−	0.0264348i
$695$	−1.34827	−	33.6827i	−0.0511430	−	1.27766i
$696$	1.74227	−	2.43342i	0.0660406	−	0.0922384i
$697$	−11.1372	+	23.8838i	−0.421851	+	0.904663i
$698$	0.996358	+	1.42295i	0.0377127	+	0.0538593i
$699$	6.80690	+	6.95142i	0.257461	+	0.262927i
$700$	−26.7870	−	9.97025i	−1.01245	−	0.376840i
$701$			8.37641i			0.316373i	0.987409	+	0.158186i	$0.0505647\pi$
$701$			8.37641i			0.316373i	−0.987409	+	0.158186i	$0.949435\pi$
$702$	3.95199	+	0.124572i	0.149158	+	0.00470167i
$703$	−1.84550	−	1.84550i	−0.0696043	−	0.0696043i
$704$	24.6396	−	20.6751i	0.928639	−	0.779221i
$705$	21.2668	−	2.49468i	0.800954	−	0.0939550i
$706$	0.747459	−	4.23905i	0.0281310	−	0.159539i
$707$	−13.7998	−	6.43494i	−0.518994	−	0.242011i
$708$	−12.1313	+	9.96409i	−0.455921	+	0.374474i
$709$	27.2222	−	4.80001i	1.02235	−	0.180268i	0.362752	−	0.931886i	$-0.381837\pi$
$709$	27.2222	−	4.80001i	1.02235	−	0.180268i	0.659599	+	0.751617i	$0.270726\pi$
$710$	−0.900497	+	2.15189i	−0.0337950	+	0.0807590i
$711$	−1.48748	+	0.230177i	−0.0557848	+	0.00863232i
$712$	2.26655	+	8.45886i	0.0849424	+	0.317009i
$713$	17.7401	−	8.27234i	0.664372	−	0.309802i
$714$	−4.72120	+	0.363126i	−0.176686	+	0.0135896i
$715$	2.17567	−	46.0028i	0.0813655	−	1.72041i
$716$	8.68071	−	10.3453i	0.324413	−	0.386621i
$717$	−8.91885	−	25.3290i	−0.333080	−	0.945929i
$718$	−0.928354	−	1.99086i	−0.0346459	−	0.0742983i
$719$	13.4438	−	23.2854i	0.501371	−	0.868400i	−0.498628	−	0.866816i	$-0.666163\pi$
$719$	13.4438	−	23.2854i	0.501371	−	0.868400i	0.999999	−	0.00158362i	$-0.000504083\pi$
$720$	−20.0717	−	16.2024i	−0.748029	−	0.603829i
$721$	5.44055	+	9.42331i	0.202617	+	0.350942i
$722$	−1.69408	+	2.41940i	−0.0630473	+	0.0900409i
$723$	−11.6397	+	30.9639i	−0.432884	+	1.15156i
$724$	10.9664	+	30.1299i	0.407563	+	1.11977i
$725$	−5.79847	+	12.2030i	−0.215350	+	0.453209i
$726$	2.13888	+	0.597258i	0.0793812	+	0.0221663i
$727$	−1.67023	+	19.0908i	−0.0619455	+	0.708040i	0.900195	+	0.435487i	$0.143424\pi$
$727$	−1.67023	+	19.0908i	−0.0619455	+	0.708040i	−0.962141	+	0.272553i	$0.912132\pi$
$728$	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
$732$	20.3099	+	36.0469i	0.750674	+	1.33233i
$733$	−28.9707	+	20.2855i	−1.07006	+	0.749261i	−0.969357	−	0.245656i	$-0.920997\pi$
$733$	−28.9707	+	20.2855i	−1.07006	+	0.749261i	−0.100699	+	0.994917i	$0.532108\pi$
$734$	1.97069	−	0.717274i	0.0727397	−	0.0264751i
$735$	−2.54420	+	4.72320i	−0.0938441	+	0.174218i
$736$	0.878364	+	4.98145i	0.0323769	+	0.183619i
$737$	7.52749	−	28.0930i	0.277279	−	1.03482i
$738$	−0.517039	−	2.10558i	−0.0190325	−	0.0775076i
$739$	16.8271	+	9.71511i	0.618993	+	0.357376i	0.776477	−	0.630146i	$-0.217005\pi$
$739$	16.8271	+	9.71511i	0.618993	+	0.357376i	−0.157484	+	0.987522i	$0.550338\pi$
$740$	13.7025	−	4.26582i	0.503714	−	0.156815i
$741$	5.92994	+	2.84138i	0.217842	+	0.104381i
$742$	1.11812	−	0.0978225i	0.0410473	−	0.00359118i
$743$	31.1397	−	2.72437i	1.14240	−	0.0999474i	0.499796	−	0.866143i	$-0.333408\pi$
$743$	31.1397	−	2.72437i	1.14240	−	0.0999474i	0.642608	+	0.766195i	$0.277853\pi$
$744$	−0.623732	−	8.10948i	−0.0228671	−	0.297308i
$745$	−15.3478	+	29.2236i	−0.562299	+	1.07067i
$746$	−0.263770	−	0.152288i	−0.00965730	−	0.00557564i
$747$	21.6784	+	15.8683i	0.793171	+	0.580591i
$748$	−13.0562	+	48.7265i	−0.477383	+	1.78162i
$749$	−4.04754	−	22.9547i	−0.147894	−	0.838747i
$750$	−2.73250	−	1.49755i	−0.0997768	−	0.0546829i
$751$	21.6560	−	7.88215i	0.790240	−	0.287624i	0.0848041	−	0.996398i	$-0.472974\pi$
$751$	21.6560	−	7.88215i	0.790240	−	0.287624i	0.705436	+	0.708774i	$0.250751\pi$
$752$	17.4149	−	12.1941i	0.635057	−	0.444672i
$753$	11.0969	−	18.7625i	0.404394	−	0.683743i
$754$	−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	$0.160592\pi$
$758$	0.121294	−	1.38640i	0.00440559	−	0.0503561i
$759$	14.3666	−	14.0679i	0.521475	−	0.510634i
$760$	0.526340	+	1.02010i	0.0190923	+	0.0370030i
$761$	3.19211	+	8.77024i	0.115714	+	0.317921i	0.984007	−	0.178131i	$-0.0570049\pi$
$761$	3.19211	+	8.77024i	0.115714	+	0.317921i	−0.868293	+	0.496051i	$0.834783\pi$
$762$	−0.213168	+	0.0352829i	−0.00772228	+	0.00127816i
$763$	20.1984	−	28.8462i	0.731229	−	1.04430i
$764$	20.2039	+	34.9942i	0.730951	+	1.26604i
$765$	39.2674	+	2.68482i	1.41972	+	0.0970698i
$766$	1.37405	−	2.37992i	0.0496463	−	0.0859899i
$767$	9.17603	+	19.6781i	0.331327	+	0.710533i
$768$	−23.7814	−	4.45136i	−0.858139	−	0.160624i
$769$	−7.77292	+	9.26340i	−0.280299	+	0.334047i	−0.887764	−	0.460300i	$-0.847742\pi$
$769$	−7.77292	+	9.26340i	−0.280299	+	0.334047i	0.607465	+	0.794346i	$0.292186\pi$
$770$	−3.05343	−	3.35659i	−0.110038	−	0.120963i
$771$	−28.9875	−	42.3380i	−1.04396	−	1.52477i
$772$	13.9323	−	6.49674i	0.501435	−	0.233823i
$773$	−0.479004	−	1.78767i	−0.0172286	−	0.0642980i	0.956776	−	0.290825i	$-0.0939296\pi$
$773$	−0.479004	−	1.78767i	−0.0172286	−	0.0642980i	−0.974005	+	0.226527i	$0.927263\pi$
$774$	−3.25459	−	0.644640i	−0.116984	−	0.0231711i
$775$	9.24561	+	35.5338i	0.332112	+	1.27641i
$776$	−4.59055	+	0.809438i	−0.164791	+	0.0290571i
$777$	−2.66269	−	16.0872i	−0.0955234	−	0.577124i
$778$	−0.127850	−	0.0596173i	−0.00458363	−	0.00213738i
$779$	0.626118	−	3.55089i	0.0224330	−	0.127224i
$780$	−28.9932	+	21.6034i	−1.03812	+	0.773524i
$781$	21.6304	−	18.1500i	0.773996	−	0.649459i
$782$	−1.77944	−	1.77944i	−0.0636327	−	0.0636327i
$783$	8.68180	+	11.0348i	0.310262	+	0.394350i
$784$			5.32653i			0.190233i
$785$	−17.1051	−	3.85723i	−0.610506	−	0.137670i
$786$	2.04755	−	0.525653i	0.0730338	−	0.0187494i
$787$	9.79291	+	13.9857i	0.349080	+	0.498537i	0.954844	−	0.297106i	$-0.0960216\pi$
$787$	9.79291	+	13.9857i	0.349080	+	0.498537i	−0.605765	+	0.795644i	$0.707133\pi$
$788$	4.41755	−	9.47347i	0.157369	−	0.337479i
$789$	−1.01891	−	0.0999377i	−0.0362742	−	0.00355788i
$790$	−0.122440	+	0.132651i	−0.00435624	+	0.00471953i
$791$	10.2108	−	5.89518i	0.363053	−	0.209609i
$792$	−3.37116	−	7.64475i	−0.119789	−	0.271644i
$793$	55.2739	−	14.8106i	1.96283	−	0.525940i
$794$	0.349811	+	0.127321i	0.0124143	+	0.00451844i
$795$	−9.31387	−	0.538594i	−0.330329	−	0.0191020i
$796$	42.0652	+	35.2969i	1.49096	+	1.25107i
$797$	−1.47293	−	16.8357i	−0.0521739	−	0.596350i	−0.976611	−	0.215015i	$-0.931020\pi$
$797$	−1.47293	−	16.8357i	−0.0521739	−	0.596350i	0.924437	−	0.381335i	$-0.124536\pi$
$798$	0.611097	−	0.215180i	0.0216326	−	0.00761728i
$799$	−11.0947	+	30.4824i	−0.392502	+	1.07839i
$800$	−9.48810	−	0.0688069i	−0.335455	−	0.00243269i
$801$	−41.0750	−	0.863001i	−1.45131	−	0.0304926i
$802$	1.00099	+	0.268215i	0.0353462	+	0.00947098i
$803$	34.4144	+	24.0972i	1.21446	+	0.850372i
$804$	−20.7945	+	9.43200i	−0.733365	+	0.332641i
$805$	−16.8637	+	3.67449i	−0.594367	+	0.129509i
$806$	−5.50298	−	0.970323i	−0.193834	−	0.0341782i
$807$	−44.5442	+	25.0975i	−1.56803	+	0.883473i
$808$	−3.34966	−	0.293057i	−0.117841	−	0.0103097i
$809$	−47.0271			−1.65338			−0.826692	−	0.562654i	$-0.809780\pi$
$809$	−47.0271			−1.65338			−0.826692	+	0.562654i	$0.809780\pi$
$810$	−2.65630	+	1.85203i	−0.0933330	+	0.0650737i
$811$	−46.5510			−1.63463			−0.817314	−	0.576192i	$-0.804538\pi$
$811$	−46.5510			−1.63463			−0.817314	+	0.576192i	$0.804538\pi$
$812$	15.3878	+	1.34626i	0.540006	+	0.0472444i
$813$	14.2725	−	8.04153i	0.500558	−	0.282029i
$814$	2.24373	+	0.395630i	0.0786427	+	0.0138668i
$815$	17.4238	−	27.1323i	0.610330	−	0.950404i
$816$	35.5882	−	16.1422i	1.24584	−	0.565089i
$817$	−4.51977	−	3.16478i	−0.158127	−	0.110722i
$818$	4.37392	+	1.17199i	0.152931	+	0.0409776i
$819$	19.7891	+	36.0016i	0.691487	+	1.25800i
$820$	15.6855	+	12.1265i	0.547761	+	0.423476i
$821$	−11.2400	+	30.8817i	−0.392280	+	1.07778i	0.573678	+	0.819081i	$0.305516\pi$
$821$	−11.2400	+	30.8817i	−0.392280	+	1.07778i	−0.965958	+	0.258699i	$0.916706\pi$
$822$	−2.60350	+	0.916746i	−0.0908076	+	0.0319752i
$823$	0.780841	+	8.92506i	0.0272184	+	0.311108i	0.997584	+	0.0694673i	$0.0221299\pi$
$823$	0.780841	+	8.92506i	0.0272184	+	0.311108i	−0.970366	+	0.241641i	$0.922314\pi$
$824$	1.84072	+	1.54454i	0.0641244	+	0.0538067i
$825$	21.0819	+	31.2755i	0.733977	+	1.08887i
$826$	2.01026	+	0.731675i	0.0699460	+	0.0254582i
$827$	49.8029	−	13.3446i	1.73182	−	0.464039i	0.751216	−	0.660057i	$-0.229468\pi$
$827$	49.8029	−	13.3446i	1.73182	−	0.464039i	0.980600	+	0.196018i	$0.0628011\pi$
$828$	−15.6937	−	1.70589i	−0.545393	−	0.0592836i
$829$	6.07560	−	3.50775i	0.211014	−	0.121829i	−0.390768	−	0.920489i	$-0.627791\pi$
$829$	6.07560	−	3.50775i	0.211014	−	0.121829i	0.601783	+	0.798660i	$0.294457\pi$
$830$	3.21950	−	0.128872i	0.111750	−	0.00447322i
$831$	−35.1526	−	3.44786i	−1.21943	−	0.119605i
$832$	−14.7601	+	31.6531i	−0.511714	+	1.09737i
$833$	−4.66167	−	6.65756i	−0.161517	−	0.230671i
$834$	−4.06956	+	1.04475i	−0.140917	+	0.0361767i
$835$	−3.19261	+	14.1578i	−0.110485	+	0.489951i
$836$		−	6.90208i		−	0.238713i
$837$	37.3503	+	7.80658i	1.29101	+	0.269835i
$838$	−4.23684	−	4.23684i	−0.146359	−	0.146359i
$839$	−2.86722	+	2.40588i	−0.0989873	+	0.0830602i	−0.690938	−	0.722914i	$-0.742802\pi$
$839$	−2.86722	+	2.40588i	−0.0989873	+	0.0830602i	0.591951	+	0.805974i	$0.298358\pi$
$840$	−1.03646	+	7.09635i	−0.0357611	+	0.244847i
$841$	−3.76791	+	21.3689i	−0.129928	+	0.736858i
$842$	4.27965	+	1.99563i	0.147487	+	0.0687741i
$843$	5.84371	+	35.3059i	0.201268	+	1.21600i
$844$	−18.3184	+	3.23002i	−0.630544	+	0.111182i
$845$	7.94248	+	19.3732i	0.273229	+	0.666459i
$846$	−0.859915	−	2.52651i	−0.0295645	−	0.0868631i
$847$	5.97181	+	22.2871i	0.205194	+	0.765793i
$848$	−8.39495	+	3.91463i	−0.288284	+	0.134429i
$849$	−12.6192	−	18.4311i	−0.433089	−	0.632554i
$850$	3.88632	−	2.67944i	0.133300	−	0.0919041i
$851$	5.57034	−	6.63847i	0.190949	−	0.227564i
$852$	−21.7898	−	4.07856i	−0.746505	−	0.139729i
$853$	−18.4044	−	39.4684i	−0.630155	−	1.35137i	−0.919100	−	0.394025i	$-0.871082\pi$
$853$	−18.4044	−	39.4684i	−0.630155	−	1.35137i	0.288945	−	0.957346i	$-0.406696\pi$
$854$	2.81908	−	4.88278i	0.0964668	−	0.167085i
$855$	−5.28469	+	1.03572i	−0.180732	+	0.0354210i
$856$	−2.57365	−	4.45770i	−0.0879657	−	0.152361i
$857$	−27.3168	+	39.0125i	−0.933125	+	1.33264i	0.00991152	+	0.999951i	$0.496845\pi$
$857$	−27.3168	+	39.0125i	−0.933125	+	1.33264i	−0.943036	+	0.332690i	$0.892044\pi$
$858$	−5.66308	+	0.937333i	−0.193334	+	0.0320000i
$859$	−14.5712	−	40.0340i	−0.497162	−	1.36594i	−0.894006	−	0.448055i	$-0.852117\pi$
$859$	−14.5712	−	40.0340i	−0.497162	−	1.36594i	0.396844	−	0.917886i	$-0.370105\pi$
$860$	26.9622	−	13.9116i	0.919404	−	0.474382i
$861$	16.0955	−	15.7609i	0.548533	−	0.537130i
$862$	−0.00674116	+	0.0770518i	−0.000229605	+	0.00262439i
$863$	11.3790	−	11.3790i	0.387346	−	0.387346i	−0.486393	−	0.873740i	$-0.661688\pi$
$863$	11.3790	−	11.3790i	0.387346	−	0.387346i	0.873740	+	0.486393i	$0.161688\pi$
$864$	−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
$867$	−15.3645	+	25.9780i	−0.521805	+	0.882260i
$868$	34.3866	−	24.0777i	1.16716	−	0.817252i
$869$	2.05336	−	0.747362i	0.0696554	−	0.0253525i
$870$	1.63871	+	0.387664i	0.0555575	+	0.0131430i
$871$	5.48385	+	31.1005i	0.185813	+	1.05380i
$872$	2.01271	−	7.51153i	0.0681589	−	0.254372i
$873$	2.36316	−	21.7404i	0.0799807	−	0.735801i
$874$	0.298187	+	0.172158i	0.0100863	+	0.00582334i
$875$	−1.06028	−	32.3578i	−0.0358439	−	1.09389i
$876$	−2.52941	−	32.8863i	−0.0854610	−	1.11112i
$877$	24.8592	−	2.17490i	0.839435	−	0.0734411i	0.340675	−	0.940181i	$-0.389344\pi$
$877$	24.8592	−	2.17490i	0.839435	−	0.0734411i	0.498760	+	0.866740i	$0.333789\pi$
$878$	−1.99013	+	0.174114i	−0.0671635	+	0.00587605i
$879$	52.7000	+	25.2517i	1.77753	+	0.851717i
$880$	33.1539	+	17.4119i	1.11762	+	0.586956i
$881$	19.2496	+	11.1138i	0.648536	+	0.374432i	0.787895	−	0.615810i	$-0.211171\pi$
$881$	19.2496	+	11.1138i	0.648536	+	0.374432i	−0.139359	+	0.990242i	$0.544504\pi$
$882$	0.642104	+	0.186593i	0.0216208	+	0.00628290i
$883$	13.9173	−	51.9401i	0.468355	−	1.74792i	−0.177166	−	0.984181i	$-0.556693\pi$
$883$	13.9173	−	51.9401i	0.468355	−	1.74792i	0.645521	−	0.763743i	$-0.276640\pi$
$884$	−9.51159	−	53.9429i	−0.319909	−	1.81430i
$885$	−15.6552	−	8.43282i	−0.526243	−	0.283466i
$886$	−2.68990	+	0.979043i	−0.0903689	+	0.0328916i
$887$	39.0601	−	27.3502i	1.31151	−	0.918330i	0.312015	−	0.950077i	$-0.398996\pi$
$887$	39.0601	−	27.3502i	1.31151	−	0.918330i	0.999496	+	0.0317472i	$0.0101071\pi$
$888$	−1.76758	−	3.13719i	−0.0593162	−	0.105277i
$889$	−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
$893$	0.386828	−	4.42146i	0.0129447	−	0.147959i
$894$	3.96256	+	1.10650i	0.132528	+	0.0370070i
$895$	14.5721	+	4.65272i	0.487091	+	0.155523i
$896$	4.93582	+	13.5611i	0.164894	+	0.453043i
$897$	−7.68247	+	20.4369i	−0.256510	+	0.682368i
$898$	0.352630	−	0.503608i	0.0117674	−	0.0168056i
$899$	−9.92137	−	17.1843i	−0.330896	−	0.573129i
$900$	8.46917	−	28.3747i	0.282306	−	0.945822i
$901$	7.06673	−	12.2399i	0.235427	−	0.407771i
$902$	1.33022	+	2.85267i	0.0442916	+	0.0949837i
$903$	−11.4494	−	32.5155i	−0.381011	−	1.08205i
$904$	1.67361	−	1.99453i	0.0556635	−	0.0663371i
$905$	−26.8655	+	24.4391i	−0.893039	+	0.812382i
$906$	0.661909	−	0.0509101i	0.0219905	−	0.00169137i
$907$	−32.6698	+	15.2342i	−1.08478	+	0.505842i	−0.880972	−	0.473168i	$-0.843110\pi$
$907$	−32.6698	+	15.2342i	−1.08478	+	0.505842i	−0.203810	+	0.979010i	$0.565332\pi$
$908$	7.70797	+	28.7666i	0.255798	+	0.954652i
$909$	5.70545	−	14.7068i	0.189238	−	0.487792i
$910$	4.54518	+	1.90201i	0.150671	+	0.0630511i
$911$	35.2604	−	6.21737i	1.16823	−	0.205991i	0.444310	−	0.895873i	$-0.353449\pi$
$911$	35.2604	−	6.21737i	1.16823	−	0.205991i	0.723921	+	0.689883i	$0.242338\pi$
$912$	−4.13173	+	3.39362i	−0.136815	+	0.112374i
$913$	−35.3477	−	16.4829i	−1.16984	−	0.545505i
$914$	−0.617189	+	3.50025i	−0.0204148	+	0.115778i
$915$	−29.0521	+	36.7737i	−0.960433	+	1.21570i
$916$	−1.42237	+	1.19351i	−0.0469964	+	0.0394346i
$917$	15.5310	+	15.5310i	0.512878	+	0.512878i
$918$	−0.699228	−	4.85557i	−0.0230780	−	0.160258i
$919$			10.8922i			0.359301i	0.983730	+	0.179651i	$0.0574967\pi$
$919$			10.8922i			0.359301i	−0.983730	+	0.179651i	$0.942503\pi$
$920$	−3.22191	+	2.03620i	−0.106223	+	0.0671314i
$921$	−12.2149	−	12.4742i	−0.402495	−	0.411040i
$922$	0.596741	+	0.852235i	0.0196526	+	0.0280669i
$923$	−12.9575	+	27.7873i	−0.426500	+	0.914632i
$924$	25.1035	−	35.0618i	0.825844	−	1.15345i
$925$	10.3583	+	12.5279i	0.340578	+	0.411915i
$926$	0.0427714	−	0.0246941i	0.00140556	−	0.000811498i
$927$	−9.36804	+	6.27050i	−0.307687	+	0.205950i
$928$	4.95301	−	1.32716i	0.162591	−	0.0435660i
$929$	0.624723	+	0.227381i	0.0204965	+	0.00746012i	0.352248	−	0.935907i	$-0.385417\pi$
$929$	0.624723	+	0.227381i	0.0204965	+	0.00746012i	−0.331752	+	0.943367i	$0.607640\pi$
$930$	4.08872	−	2.05556i	0.134074	−	0.0674044i
$931$	0.851849	+	0.714786i	0.0279182	+	0.0234262i
$932$	0.966453	+	11.0466i	0.0316572	+	0.361844i
$933$	−8.22841	+	43.9604i	−0.269386	+	1.43920i
$934$	−2.35563	+	6.47205i	−0.0770787	+	0.211772i
$935$	−56.6772	+	7.25273i	−1.85354	+	0.237190i
$936$	6.82565	+	5.97617i	0.223103	+	0.195337i
$937$	−30.5740	−	8.19227i	−0.998808	−	0.267630i	−0.277862	−	0.960621i	$-0.589626\pi$
$937$	−30.5740	−	8.19227i	−0.998808	−	0.267630i	−0.720946	+	0.692991i	$0.756292\pi$
$938$	2.54883	+	1.78471i	0.0832222	+	0.0582728i
$939$	−7.92986	−	5.67760i	−0.258781	−	0.185282i
$940$	20.5354	+	13.1874i	0.669790	+	0.430125i
$941$	15.3045	+	2.69859i	0.498911	+	0.0879715i	0.417441	−	0.908704i	$-0.362927\pi$
$941$	15.3045	+	2.69859i	0.498911	+	0.0879715i	0.0814707	+	0.996676i	$0.474038\pi$
$942$	−0.0229551	+	2.18536i	−0.000747919	+	0.0712030i
$943$	11.9266	+	1.04344i	0.388383	+	0.0339791i
$944$	−17.6549			−0.574619
$945$	−30.6126	−	13.9595i	−0.995829	−	0.454103i
$946$	4.81662			0.156602
$947$	26.0673	+	2.28059i	0.847074	+	0.0741093i	0.502423	−	0.864622i	$-0.332442\pi$
$947$	26.0673	+	2.28059i	0.847074	+	0.0741093i	0.344650	+	0.938731i	$0.387997\pi$
$948$	−1.47660	−	0.873325i	−0.0479579	−	0.0283643i
$949$	−44.9250	−	7.92149i	−1.45833	−	0.257143i
$950$	−0.418733	+	0.491740i	−0.0135855	+	0.0159542i
$951$	0.313423	−	3.19549i	0.0101634	−	0.103621i
$952$	−8.89972	−	6.23165i	−0.288442	−	0.201969i
$953$	−37.4368	−	10.0312i	−1.21270	−	0.324942i	−0.404878	−	0.914371i	$-0.632686\pi$
$953$	−37.4368	−	10.0312i	−1.21270	−	0.324942i	−0.807820	+	0.589429i	$0.799353\pi$
$954$	0.177820	+	1.14913i	0.00575714	+	0.0372044i
$955$	−27.9944	+	36.2103i	−0.905876	+	1.17174i
$956$	10.4679	−	28.7604i	0.338557	−	0.930178i
$957$	−15.4761	−	13.2655i	−0.500272	−	0.428812i
$958$	0.583733	+	6.67210i	0.0188596	+	0.215566i
$959$	−21.9691	−	18.4343i	−0.709420	−	0.595274i
$960$	−5.79568	−	28.0098i	−0.187055	−	0.904012i
$961$	−21.5428	−	7.84095i	−0.694930	−	0.252934i
$962$	−2.38959	+	0.640290i	−0.0770436	+	0.0206438i
$963$	23.4515	−	5.75867i	0.755715	−	0.185571i
$964$	−32.6511	+	18.8511i	−1.05162	+	0.607154i
$965$	12.7951	+	11.8102i	0.411889	+	0.380183i
$966$	0.888601	+	1.95908i	0.0285903	+	0.0630322i
$967$	14.1812	−	30.4117i	0.456036	−	0.977973i	−0.535058	−	0.844815i	$-0.679710\pi$
$967$	14.1812	−	30.4117i	0.456036	−	0.977973i	0.991095	−	0.133158i	$-0.0425118\pi$
$968$	2.92254	+	4.17382i	0.0939340	+	0.134152i
$969$	2.19416	−	7.85765i	0.0704867	−	0.252424i
$970$	−1.40118	−	2.21711i	−0.0449891	−	0.0711871i
$971$		−	3.53962i		−	0.113592i	−0.998386	−	0.0567959i	$-0.981912\pi$
$971$		−	3.53962i		−	0.113592i	0.998386	−	0.0567959i	$-0.0180884\pi$
$972$	−22.5028	−	20.9909i	−0.721779	−	0.673284i
$973$	−30.8682	−	30.8682i	−0.989589	−	0.989589i
$974$	2.93893	−	2.46605i	0.0941694	−	0.0790175i
$975$	−35.0986	−	21.1038i	−1.12406	−	0.675863i
$976$	−8.07991	+	45.8234i	−0.258632	+	1.46677i
$977$	−41.3945	−	19.3025i	−1.32433	−	0.617543i	−0.373604	−	0.927588i	$-0.621878\pi$
$977$	−41.3945	−	19.3025i	−1.32433	−	0.617543i	−0.950722	+	0.310045i	$0.899656\pi$
$978$	−3.76197	−	1.41417i	−0.120295	−	0.0452201i
$979$	58.7374	−	10.3570i	1.87726	−	0.331011i
$980$	−5.65759	+	2.31945i	−0.180725	+	0.0740922i
$981$	31.2050	+	18.9011i	0.996298	+	0.603466i
$982$	−0.659756	−	2.46224i	−0.0210536	−	0.0785733i
$983$	29.5099	−	13.7607i	0.941220	−	0.438898i	0.109434	−	0.993994i	$-0.465096\pi$
$983$	29.5099	−	13.7607i	0.941220	−	0.438898i	0.831786	+	0.555096i	$0.187318\pi$
$984$	2.14963	−	4.48626i	0.0685278	−	0.143017i
$985$	11.8267	+	0.559334i	0.376829	+	0.0178219i
$986$	−1.63979	+	1.95422i	−0.0522215	+	0.0622352i
$987$	18.0463	−	21.0536i	0.574420	−	0.670144i
$988$	3.16730	+	6.79230i	0.100765	+	0.216092i
$989$	9.16026	−	15.8660i	0.291279	−	0.504511i
$990$	3.26039	−	3.38670i	0.103622	−	0.107636i
$991$	22.7542	+	39.4115i	0.722812	+	1.25195i	0.959868	+	0.280451i	$0.0904839\pi$
$991$	22.7542	+	39.4115i	0.722812	+	1.25195i	−0.237057	+	0.971496i	$0.576183\pi$
$992$	7.99298	−	11.4152i	0.253777	−	0.362432i
$993$	21.1726	+	25.7776i	0.671892	+	0.818028i
$994$	1.03320	+	2.83869i	0.0327710	+	0.0900377i
$995$	−18.9186	+	59.2520i	−0.599759	+	1.87842i
$996$	7.61395	+	29.6583i	0.241257	+	0.939759i
$997$	0.786008	−	8.98411i	0.0248931	−	0.284530i	−0.973538	−	0.228527i	$-0.926609\pi$
$997$	0.786008	−	8.98411i	0.0248931	−	0.284530i	0.998431	−	0.0560024i	$-0.0178355\pi$
$998$	−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.113.10	yes	192
3.2	odd	2		405.2.r.a.368.7		192
5.2	odd	4	inner	135.2.q.a.32.7	✓	192
5.3	odd	4		675.2.ba.b.32.10		192
5.4	even	2		675.2.ba.b.518.7		192
15.2	even	4		405.2.r.a.287.10		192
27.11	odd	18	inner	135.2.q.a.38.7	yes	192
27.16	even	9		405.2.r.a.278.10		192
135.38	even	36		675.2.ba.b.632.7		192
135.92	even	36	inner	135.2.q.a.92.10	yes	192
135.97	odd	36		405.2.r.a.197.7		192
135.119	odd	18		675.2.ba.b.443.10		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.2.q.a.32.7	✓	192	5.2	odd	4	inner
135.2.q.a.38.7	yes	192	27.11	odd	18	inner
135.2.q.a.92.10	yes	192	135.92	even	36	inner
135.2.q.a.113.10	yes	192	1.1	even	1	trivial
405.2.r.a.197.7		192	135.97	odd	36
405.2.r.a.278.10		192	27.16	even	9
405.2.r.a.287.10		192	15.2	even	4
405.2.r.a.368.7		192	3.2	odd	2
675.2.ba.b.32.10		192	5.3	odd	4
675.2.ba.b.443.10		192	135.119	odd	18
675.2.ba.b.518.7		192	5.4	even	2
675.2.ba.b.632.7		192	135.38	even	36

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	135.q (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.160295 + 0.0140240i) q^{2} +(-1.50901 + 0.850222i) q^{3} +(-1.94412 - 0.342800i) q^{4} +(-0.476055 - 2.18480i) q^{5} +(-0.253811 + 0.115124i) q^{6} +(-2.37204 - 1.66092i) q^{7} +(-0.617675 - 0.165506i) q^{8} +(1.55424 - 2.56599i) q^{9} +O(q^{10})\)	\(q+(0.160295 + 0.0140240i) q^{2} +(-1.50901 + 0.850222i) q^{3} +(-1.94412 - 0.342800i) q^{4} +(-0.476055 - 2.18480i) q^{5} +(-0.253811 + 0.115124i) q^{6} +(-2.37204 - 1.66092i) q^{7} +(-0.617675 - 0.165506i) q^{8} +(1.55424 - 2.56599i) q^{9} +(-0.0456696 - 0.356890i) q^{10} +(-1.48958 + 4.09258i) q^{11} +(3.22516 - 1.13564i) q^{12} +(-0.412163 - 4.71104i) q^{13} +(-0.356933 - 0.299503i) q^{14} +(2.57594 + 2.89215i) q^{15} +(3.61342 + 1.31518i) q^{16} +(-5.66739 + 1.51857i) q^{17} +(0.285124 - 0.389520i) q^{18} +(0.695229 - 0.401391i) q^{19} +(0.176555 + 4.41071i) q^{20} +(4.99158 + 0.489589i) q^{21} +(-0.296167 + 0.635132i) q^{22} +(1.52888 + 2.18347i) q^{23} +(1.07280 - 0.275411i) q^{24} +(-4.54674 + 2.08017i) q^{25} -0.760939i q^{26} +(-0.163709 + 5.19357i) q^{27} +(4.04215 + 4.04215i) q^{28} +(2.06994 - 1.73689i) q^{29} +(0.372352 + 0.499723i) q^{30} +(1.27517 - 7.23183i) q^{31} +(1.71987 + 0.801990i) q^{32} +(-1.23181 - 7.44223i) q^{33} +(-0.929752 + 0.163940i) q^{34} +(-2.49956 + 5.97312i) q^{35} +(-3.90126 + 4.45580i) q^{36} +(-0.841448 - 3.14033i) q^{37} +(0.117071 - 0.0545912i) q^{38} +(4.62739 + 6.75860i) q^{39} +(-0.0675500 + 1.42829i) q^{40} +(2.88706 - 3.44066i) q^{41} +(0.793261 + 0.148481i) q^{42} +(-2.90471 - 6.22917i) q^{43} +(4.29885 - 7.44583i) q^{44} +(-6.34610 - 2.17416i) q^{45} +(0.214452 + 0.371442i) q^{46} +(3.17114 - 4.52886i) q^{47} +(-6.57090 + 1.08759i) q^{48} +(0.473765 + 1.30166i) q^{49} +(-0.757994 + 0.269679i) q^{50} +(7.26104 - 7.11008i) q^{51} +(-0.813654 + 9.30011i) 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} +(-0.707839 + 1.19680i) q^{57} +(0.356161 - 0.249386i) q^{58} +(-4.31439 + 1.57031i) q^{59} +(-4.01651 - 6.50571i) q^{60} +(2.10123 + 11.9167i) q^{61} +(0.305823 - 1.14135i) q^{62} +(-7.94862 + 3.50516i) q^{63} +(-6.39585 - 3.69265i) q^{64} +(-10.0965 + 3.14321i) q^{65} +(-0.0930836 - 1.21023i) q^{66} +(-6.65253 + 0.582021i) q^{67} +(11.5386 - 1.00950i) q^{68} +(-4.16355 - 1.99500i) q^{69} +(-0.484435 + 0.922410i) q^{70} +(-5.61473 - 3.24167i) q^{71} +(-1.38470 + 1.32772i) q^{72} +(2.49666 - 9.31768i) q^{73} +(-0.0908402 - 0.515180i) q^{74} +(5.09249 - 7.00475i) q^{75} +(-1.48920 + 0.542026i) q^{76} +(10.3308 - 7.23368i) q^{77} +(0.646967 + 1.14827i) 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} +(-0.780495 + 8.92110i) q^{83} +(-9.53639 - 2.66293i) q^{84} +(6.01577 + 11.6592i) q^{85} +(-0.378253 - 1.03924i) q^{86} +(-1.64683 + 4.38090i) q^{87} +(1.59742 - 2.28135i) q^{88} +(-6.84734 - 11.8599i) q^{89} +(-0.986760 - 0.437506i) q^{90} +(-6.84699 + 11.8593i) q^{91} +(-2.22384 - 4.76903i) q^{92} +(4.22442 + 11.9971i) q^{93} +(0.571832 - 0.681483i) q^{94} +(-1.20793 - 1.32786i) q^{95} +(-3.27718 + 0.252061i) q^{96} +(6.60652 - 3.08067i) q^{97} +(0.0576878 + 0.215294i) 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

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