LMFDB - Embedded newform 1155.2.i.d.76.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(76,1155)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 1, 1]))

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

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

chi := DirichletCharacter("1155.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.i (of order $2$, degree $1$, 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:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			76.12
Character	$\chi$	$=$	1155.76
Dual form			1155.2.i.d.76.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.29033i q^{2} +1.00000i q^{3} +0.335051 q^{4} +1.00000i q^{5} -1.29033 q^{6} +(2.23077 - 1.42256i) q^{7} +3.01298i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.29033i q^{2} +1.00000i q^{3} +0.335051 q^{4} +1.00000i q^{5} -1.29033 q^{6} +(2.23077 - 1.42256i) q^{7} +3.01298i q^{8} -1.00000 q^{9} -1.29033 q^{10} +(0.810680 - 3.21602i) q^{11} +0.335051i q^{12} +3.24076 q^{13} +(1.83557 + 2.87843i) q^{14} -1.00000 q^{15} -3.21764 q^{16} +7.53431 q^{17} -1.29033i q^{18} +2.10854 q^{19} +0.335051i q^{20} +(1.42256 + 2.23077i) q^{21} +(4.14973 + 1.04604i) q^{22} -1.54754 q^{23} -3.01298 q^{24} -1.00000 q^{25} +4.18165i q^{26} -1.00000i q^{27} +(0.747420 - 0.476629i) q^{28} +7.87403i q^{29} -1.29033i q^{30} -2.42925i q^{31} +1.87415i q^{32} +(3.21602 + 0.810680i) q^{33} +9.72174i q^{34} +(1.42256 + 2.23077i) q^{35} -0.335051 q^{36} -8.46051 q^{37} +2.72071i q^{38} +3.24076i q^{39} -3.01298 q^{40} -6.82769 q^{41} +(-2.87843 + 1.83557i) q^{42} -8.43887i q^{43} +(0.271619 - 1.07753i) q^{44} -1.00000i q^{45} -1.99683i q^{46} -2.05061i q^{47} -3.21764i q^{48} +(2.95266 - 6.34679i) q^{49} -1.29033i q^{50} +7.53431i q^{51} +1.08582 q^{52} +11.0999 q^{53} +1.29033 q^{54} +(3.21602 + 0.810680i) q^{55} +(4.28614 + 6.72127i) q^{56} +2.10854i q^{57} -10.1601 q^{58} +9.43543i q^{59} -0.335051 q^{60} +8.80831 q^{61} +3.13453 q^{62} +(-2.23077 + 1.42256i) q^{63} -8.85355 q^{64} +3.24076i q^{65} +(-1.04604 + 4.14973i) q^{66} -11.0082 q^{67} +2.52437 q^{68} -1.54754i q^{69} +(-2.87843 + 1.83557i) q^{70} -11.2669 q^{71} -3.01298i q^{72} -3.80935 q^{73} -10.9168i q^{74} -1.00000i q^{75} +0.706466 q^{76} +(-2.76654 - 8.32744i) q^{77} -4.18165 q^{78} -5.78548i q^{79} -3.21764i q^{80} +1.00000 q^{81} -8.80996i q^{82} -9.24036 q^{83} +(0.476629 + 0.747420i) q^{84} +7.53431i q^{85} +10.8889 q^{86} -7.87403 q^{87} +(9.68982 + 2.44257i) q^{88} +13.1967i q^{89} +1.29033 q^{90} +(7.22938 - 4.61017i) q^{91} -0.518504 q^{92} +2.42925 q^{93} +2.64596 q^{94} +2.10854i q^{95} -1.87415 q^{96} +2.85810i q^{97} +(8.18945 + 3.80990i) q^{98} +(-0.810680 + 3.21602i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) $ 32 * q - 36 * q^4 - 32 * q^9	$ 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) $ 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$-1$	$1$	$1$	$-1$

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 $

$2$			1.29033i			0.912401i	0.889877	+	0.456200i	$0.150790\pi$
$2$			1.29033i			0.912401i	−0.889877	+	0.456200i	$0.849210\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.335051			0.167525
$5$			1.00000i			0.447214i
$5$			1.00000i			0.447214i
$6$	−1.29033			−0.526775
$7$	2.23077	−	1.42256i	0.843151	−	0.537676i
$7$	2.23077	−	1.42256i	0.843151	−	0.537676i
$8$			3.01298i			1.06525i
$9$	−1.00000			−0.333333
$10$	−1.29033			−0.408038
$11$	0.810680	−	3.21602i	0.244429	−	0.969667i
$11$	0.810680	−	3.21602i	0.244429	−	0.969667i
$12$			0.335051i			0.0967208i
$13$	3.24076			0.898825			0.449412	−	0.893324i	$-0.351633\pi$
$13$	3.24076			0.898825			0.449412	+	0.893324i	$0.351633\pi$
$14$	1.83557	+	2.87843i	0.490576	+	0.769292i
$15$	−1.00000			−0.258199
$16$	−3.21764			−0.804410
$17$	7.53431			1.82734			0.913669	−	0.406458i	$-0.133236\pi$
$17$	7.53431			1.82734			0.913669	+	0.406458i	$0.133236\pi$
$18$		−	1.29033i		−	0.304134i
$19$	2.10854			0.483732			0.241866	−	0.970310i	$-0.422241\pi$
$19$	2.10854			0.483732			0.241866	+	0.970310i	$0.422241\pi$
$20$			0.335051i			0.0749196i
$21$	1.42256	+	2.23077i	0.310428	+	0.486794i
$22$	4.14973	+	1.04604i	0.884725	+	0.223017i
$23$	−1.54754			−0.322684			−0.161342	−	0.986899i	$-0.551582\pi$
$23$	−1.54754			−0.322684			−0.161342	+	0.986899i	$0.551582\pi$
$24$	−3.01298			−0.615023
$25$	−1.00000			−0.200000
$26$			4.18165i			0.820088i
$27$		−	1.00000i		−	0.192450i
$28$	0.747420	−	0.476629i	0.141249	−	0.0900743i
$29$			7.87403i			1.46217i	0.682286	+	0.731085i	$0.260986\pi$
$29$			7.87403i			1.46217i	−0.682286	+	0.731085i	$0.739014\pi$
$30$		−	1.29033i		−	0.235581i
$31$		−	2.42925i		−	0.436305i	−0.975915	−	0.218153i	$-0.929997\pi$
$31$		−	2.42925i		−	0.436305i	0.975915	−	0.218153i	$-0.0700031\pi$
$32$			1.87415i			0.331307i
$33$	3.21602	+	0.810680i	0.559838	+	0.141121i
$34$			9.72174i			1.66726i
$35$	1.42256	+	2.23077i	0.240456	+	0.377069i
$36$	−0.335051			−0.0558418
$37$	−8.46051			−1.39090			−0.695450	−	0.718575i	$-0.744795\pi$
$37$	−8.46051			−1.39090			−0.695450	+	0.718575i	$0.744795\pi$
$38$			2.72071i			0.441357i
$39$			3.24076i			0.518937i
$40$	−3.01298			−0.476395
$41$	−6.82769			−1.06631			−0.533153	−	0.846019i	$-0.678993\pi$
$41$	−6.82769			−1.06631			−0.533153	+	0.846019i	$0.678993\pi$
$42$	−2.87843	+	1.83557i	−0.444151	+	0.283234i
$43$		−	8.43887i		−	1.28692i	−0.765481	−	0.643458i	$-0.777499\pi$
$43$		−	8.43887i		−	1.28692i	0.765481	−	0.643458i	$-0.222501\pi$
$44$	0.271619	−	1.07753i	0.0409481	−	0.162444i
$45$		−	1.00000i		−	0.149071i
$46$		−	1.99683i		−	0.294417i
$47$		−	2.05061i		−	0.299112i	−0.988753	−	0.149556i	$-0.952216\pi$
$47$		−	2.05061i		−	0.299112i	0.988753	−	0.149556i	$-0.0477844\pi$
$48$		−	3.21764i		−	0.464426i
$49$	2.95266	−	6.34679i	0.421809	−	0.906685i
$50$		−	1.29033i		−	0.182480i
$51$			7.53431i			1.05501i
$52$	1.08582			0.150576
$53$	11.0999			1.52469			0.762344	−	0.647172i	$-0.224048\pi$
$53$	11.0999			1.52469			0.762344	+	0.647172i	$0.224048\pi$
$54$	1.29033			0.175592
$55$	3.21602	+	0.810680i	0.433648	+	0.109312i
$56$	4.28614	+	6.72127i	0.572760	+	0.898168i
$57$			2.10854i			0.279283i
$58$	−10.1601			−1.33408
$59$			9.43543i			1.22839i	0.789155	+	0.614194i	$0.210519\pi$
$59$			9.43543i			1.22839i	−0.789155	+	0.614194i	$0.789481\pi$
$60$	−0.335051			−0.0432548
$61$	8.80831			1.12779			0.563894	−	0.825847i	$-0.309303\pi$
$61$	8.80831			1.12779			0.563894	+	0.825847i	$0.309303\pi$
$62$	3.13453			0.398085
$63$	−2.23077	+	1.42256i	−0.281050	+	0.179225i
$64$	−8.85355			−1.10669
$65$			3.24076i			0.401967i
$66$	−1.04604	+	4.14973i	−0.128759	+	0.510796i
$67$	−11.0082			−1.34487			−0.672433	−	0.740158i	$-0.734751\pi$
$67$	−11.0082			−1.34487			−0.672433	+	0.740158i	$0.734751\pi$
$68$	2.52437			0.306125
$69$		−	1.54754i		−	0.186302i
$70$	−2.87843	+	1.83557i	−0.344038	+	0.219392i
$71$	−11.2669			−1.33714			−0.668569	−	0.743650i	$-0.733093\pi$
$71$	−11.2669			−1.33714			−0.668569	+	0.743650i	$0.733093\pi$
$72$		−	3.01298i		−	0.355084i
$73$	−3.80935			−0.445851			−0.222925	−	0.974836i	$-0.571561\pi$
$73$	−3.80935			−0.445851			−0.222925	+	0.974836i	$0.571561\pi$
$74$		−	10.9168i		−	1.26906i
$75$		−	1.00000i		−	0.115470i
$76$	0.706466			0.0810373
$77$	−2.76654	−	8.32744i	−0.315276	−	0.949000i
$78$	−4.18165			−0.473478
$79$		−	5.78548i		−	0.650918i	−0.945556	−	0.325459i	$-0.894481\pi$
$79$		−	5.78548i		−	0.650918i	0.945556	−	0.325459i	$-0.105519\pi$
$80$		−	3.21764i		−	0.359743i
$81$	1.00000			0.111111
$82$		−	8.80996i		−	0.972898i
$83$	−9.24036			−1.01426			−0.507131	−	0.861869i	$-0.669294\pi$
$83$	−9.24036			−1.01426			−0.507131	+	0.861869i	$0.669294\pi$
$84$	0.476629	+	0.747420i	0.0520044	+	0.0815502i
$85$			7.53431i			0.817211i
$86$	10.8889			1.17418
$87$	−7.87403			−0.844184
$88$	9.68982	+	2.44257i	1.03294	+	0.260378i
$89$			13.1967i			1.39884i	0.714710	+	0.699421i	$0.246559\pi$
$89$			13.1967i			1.39884i	−0.714710	+	0.699421i	$0.753441\pi$
$90$	1.29033			0.136013
$91$	7.22938	−	4.61017i	0.757845	−	0.483277i
$92$	−0.518504			−0.0540578
$93$	2.42925			0.251901
$94$	2.64596			0.272910
$95$			2.10854i			0.216331i
$96$	−1.87415			−0.191280
$97$			2.85810i			0.290196i	0.989417	+	0.145098i	$0.0463497\pi$
$97$			2.85810i			0.290196i	−0.989417	+	0.145098i	$0.953650\pi$
$98$	8.18945	+	3.80990i	0.827260	+	0.384858i
$99$	−0.810680	+	3.21602i	−0.0814764	+	0.323222i
$100$	−0.335051			−0.0335051
$101$	−7.67234			−0.763427			−0.381713	−	0.924281i	$-0.624666\pi$
$101$	−7.67234			−0.763427			−0.381713	+	0.924281i	$0.624666\pi$
$102$	−9.72174			−0.962596
$103$			5.83595i			0.575033i	0.957776	+	0.287517i	$0.0928297\pi$
$103$			5.83595i			0.575033i	−0.957776	+	0.287517i	$0.907170\pi$
$104$			9.76435i			0.957474i
$105$	−2.23077	+	1.42256i	−0.217701	+	0.138827i
$106$			14.3225i			1.39113i
$107$		−	8.10169i		−	0.783219i	−0.920131	−	0.391610i	$-0.871918\pi$
$107$		−	8.10169i		−	0.783219i	0.920131	−	0.391610i	$-0.128082\pi$
$108$		−	0.335051i		−	0.0322403i
$109$		−	3.24745i		−	0.311049i	−0.987832	−	0.155524i	$-0.950293\pi$
$109$		−	3.24745i		−	0.311049i	0.987832	−	0.155524i	$-0.0497067\pi$
$110$	−1.04604	+	4.14973i	−0.0997364	+	0.395661i
$111$		−	8.46051i		−	0.803036i
$112$	−7.17781	+	4.57728i	−0.678239	+	0.432512i
$113$	−3.16140			−0.297399			−0.148700	−	0.988882i	$-0.547509\pi$
$113$	−3.16140			−0.297399			−0.148700	+	0.988882i	$0.547509\pi$
$114$	−2.72071			−0.254818
$115$		−	1.54754i		−	0.144309i
$116$			2.63820i			0.244950i
$117$	−3.24076			−0.299608
$118$	−12.1748			−1.12078
$119$	16.8073	−	10.7180i	1.54072	−	0.982517i
$120$		−	3.01298i		−	0.275047i
$121$	−9.68560	−	5.21433i	−0.880509	−	0.474030i
$122$			11.3656i			1.02899i
$123$		−	6.82769i		−	0.615632i
$124$		−	0.813920i		−	0.0730922i
$125$		−	1.00000i		−	0.0894427i
$126$	−1.83557	−	2.87843i	−0.163525	−	0.256431i
$127$		−	4.65573i		−	0.413130i	−0.978433	−	0.206565i	$-0.933772\pi$
$127$		−	4.65573i		−	0.413130i	0.978433	−	0.206565i	$-0.0662284\pi$
$128$		−	7.67569i		−	0.678442i
$129$	8.43887			0.743001
$130$	−4.18165			−0.366755
$131$	−16.7450			−1.46301			−0.731507	−	0.681834i	$-0.761182\pi$
$131$	−16.7450			−1.46301			−0.731507	+	0.681834i	$0.761182\pi$
$132$	1.07753	+	0.271619i	0.0937869	+	0.0236414i
$133$	4.70366	−	2.99952i	0.407859	−	0.260091i
$134$		−	14.2042i		−	1.22706i
$135$	1.00000			0.0860663
$136$			22.7008i			1.94657i
$137$	−5.45865			−0.466364			−0.233182	−	0.972433i	$-0.574914\pi$
$137$	−5.45865			−0.466364			−0.233182	+	0.972433i	$0.574914\pi$
$138$	1.99683			0.169982
$139$	12.7584			1.08215			0.541077	−	0.840973i	$-0.318017\pi$
$139$	12.7584			1.08215			0.541077	+	0.840973i	$0.318017\pi$
$140$	0.476629	+	0.747420i	0.0402825	+	0.0631685i
$141$	2.05061			0.172692
$142$		−	14.5380i		−	1.22001i
$143$	2.62722	−	10.4224i	0.219699	−	0.871561i
$144$	3.21764			0.268137
$145$	−7.87403			−0.653902
$146$		−	4.91532i		−	0.406794i
$147$	6.34679	+	2.95266i	0.523475	+	0.243531i
$148$	−2.83470			−0.233011
$149$		−	13.2298i		−	1.08383i	−0.840435	−	0.541913i	$-0.817700\pi$
$149$		−	13.2298i		−	1.08383i	0.840435	−	0.541913i	$-0.182300\pi$
$150$	1.29033			0.105355
$151$			3.45527i			0.281186i	0.990068	+	0.140593i	$0.0449008\pi$
$151$			3.45527i			0.281186i	−0.990068	+	0.140593i	$0.955099\pi$
$152$			6.35299i			0.515295i
$153$	−7.53431			−0.609113
$154$	10.7451	−	3.56974i	0.865868	−	0.287658i
$155$	2.42925			0.195122
$156$			1.08582i			0.0869350i
$157$		−	5.55181i		−	0.443082i	−0.975151	−	0.221541i	$-0.928891\pi$
$157$		−	5.55181i		−	0.443082i	0.975151	−	0.221541i	$-0.0711087\pi$
$158$	7.46518			0.593898
$159$			11.0999i			0.880279i
$160$	−1.87415			−0.148165
$161$	−3.45220	+	2.20146i	−0.272072	+	0.173500i
$162$			1.29033i			0.101378i
$163$	8.55799			0.670314			0.335157	−	0.942162i	$-0.391211\pi$
$163$	8.55799			0.670314			0.335157	+	0.942162i	$0.391211\pi$
$164$	−2.28762			−0.178633
$165$	−0.810680	+	3.21602i	−0.0631114	+	0.250367i
$166$		−	11.9231i		−	0.925413i
$167$	−11.1447			−0.862405			−0.431203	−	0.902255i	$-0.641911\pi$
$167$	−11.1447			−0.862405			−0.431203	+	0.902255i	$0.641911\pi$
$168$	−6.72127	+	4.28614i	−0.518557	+	0.330683i
$169$	−2.49748			−0.192114
$170$	−9.72174			−0.745624
$171$	−2.10854			−0.161244
$172$		−	2.82745i		−	0.215591i
$173$	24.0649			1.82962			0.914811	−	0.403883i	$-0.132340\pi$
$173$	24.0649			1.82962			0.914811	+	0.403883i	$0.132340\pi$
$174$		−	10.1601i		−	0.770234i
$175$	−2.23077	+	1.42256i	−0.168630	+	0.107535i
$176$	−2.60848	+	10.3480i	−0.196621	+	0.780010i
$177$	−9.43543			−0.709210
$178$	−17.0280			−1.27630
$179$	7.81636			0.584223			0.292111	−	0.956384i	$-0.405642\pi$
$179$	7.81636			0.584223			0.292111	+	0.956384i	$0.405642\pi$
$180$		−	0.335051i		−	0.0249732i
$181$			16.7489i			1.24494i	0.782645	+	0.622469i	$0.213870\pi$
$181$			16.7489i			1.24494i	−0.782645	+	0.622469i	$0.786130\pi$
$182$	5.94863	+	9.32829i	0.440942	+	0.691459i
$183$			8.80831i			0.651129i
$184$		−	4.66271i		−	0.343740i
$185$		−	8.46051i		−	0.622029i
$186$			3.13453i			0.229835i
$187$	6.10792	−	24.2305i	0.446655	−	1.77191i
$188$		−	0.687057i		−	0.0501088i
$189$	−1.42256	−	2.23077i	−0.103476	−	0.162265i
$190$	−2.72071			−0.197381
$191$	23.2532			1.68254			0.841272	−	0.540611i	$-0.181807\pi$
$191$	23.2532			1.68254			0.841272	+	0.540611i	$0.181807\pi$
$192$		−	8.85355i		−	0.638950i
$193$		−	4.14238i		−	0.298175i	−0.988824	−	0.149087i	$-0.952366\pi$
$193$		−	4.14238i		−	0.298175i	0.988824	−	0.149087i	$-0.0476336\pi$
$194$	−3.68789			−0.264775
$195$	−3.24076			−0.232076
$196$	0.989290	−	2.12650i	0.0706636	−	0.151893i
$197$			2.74227i			0.195379i	0.995217	+	0.0976894i	$0.0311452\pi$
$197$			2.74227i			0.195379i	−0.995217	+	0.0976894i	$0.968855\pi$
$198$	−4.14973	−	1.04604i	−0.294908	−	0.0743391i
$199$		−	3.96323i		−	0.280946i	−0.990085	−	0.140473i	$-0.955138\pi$
$199$		−	3.96323i		−	0.280946i	0.990085	−	0.140473i	$-0.0448623\pi$
$200$		−	3.01298i		−	0.213050i
$201$		−	11.0082i		−	0.776459i
$202$		−	9.89985i		−	0.696551i
$203$	11.2013	+	17.5651i	0.786174	+	1.23283i
$204$			2.52437i			0.176742i
$205$		−	6.82769i		−	0.476866i
$206$	−7.53030			−0.524661
$207$	1.54754			0.107561
$208$	−10.4276			−0.723024
$209$	1.70935	−	6.78110i	0.118238	−	0.469059i
$210$	−1.83557	−	2.87843i	−0.126666	−	0.198630i
$211$			20.2200i			1.39200i	0.718041	+	0.696000i	$0.245039\pi$
$211$			20.2200i			1.39200i	−0.718041	+	0.696000i	$0.754961\pi$
$212$	3.71903			0.255424
$213$		−	11.2669i		−	0.771997i
$214$	10.4538			0.714610
$215$	8.43887			0.575526
$216$	3.01298			0.205008
$217$	−3.45574	−	5.41909i	−0.234591	−	0.367872i
$218$	4.19027			0.283801
$219$		−	3.80935i		−	0.257412i
$220$	1.07753	+	0.271619i	0.0726470	+	0.0183125i
$221$	24.4169			1.64246
$222$	10.9168			0.732691
$223$		−	17.8967i		−	1.19845i	−0.800580	−	0.599226i	$-0.795475\pi$
$223$		−	17.8967i		−	1.19845i	0.800580	−	0.599226i	$-0.204525\pi$
$224$	2.66609	+	4.18080i	0.178136	+	0.279342i
$225$	1.00000			0.0666667
$226$		−	4.07924i		−	0.271347i
$227$	0.765307			0.0507952			0.0253976	−	0.999677i	$-0.491915\pi$
$227$	0.765307			0.0507952			0.0253976	+	0.999677i	$0.491915\pi$
$228$			0.706466i			0.0467869i
$229$			6.39956i			0.422895i	0.977389	+	0.211447i	$0.0678177\pi$
$229$			6.39956i			0.422895i	−0.977389	+	0.211447i	$0.932182\pi$
$230$	1.99683			0.131667
$231$	8.32744	−	2.76654i	0.547905	−	0.182025i
$232$	−23.7243			−1.55758
$233$		−	4.42667i		−	0.290000i	−0.989432	−	0.145000i	$-0.953682\pi$
$233$		−	4.42667i		−	0.290000i	0.989432	−	0.145000i	$-0.0463183\pi$
$234$		−	4.18165i		−	0.273363i
$235$	2.05061			0.133767
$236$			3.16135i			0.205786i
$237$	5.78548			0.375808
$238$	13.8297	+	21.6870i	0.896449	+	1.40576i
$239$			20.2965i			1.31287i	0.754383	+	0.656434i	$0.227936\pi$
$239$			20.2965i			1.31287i	−0.754383	+	0.656434i	$0.772064\pi$
$240$	3.21764			0.207698
$241$	5.89463			0.379706			0.189853	−	0.981812i	$-0.439199\pi$
$241$	5.89463			0.379706			0.189853	+	0.981812i	$0.439199\pi$
$242$	6.72820	−	12.4976i	0.432505	−	0.803377i
$243$			1.00000i			0.0641500i
$244$	2.95123			0.188933
$245$	6.34679	+	2.95266i	0.405482	+	0.188639i
$246$	8.80996			0.561703
$247$	6.83326			0.434790
$248$	7.31928			0.464775
$249$		−	9.24036i		−	0.585584i
$250$	1.29033			0.0816076
$251$		−	7.01197i		−	0.442592i	−0.975207	−	0.221296i	$-0.928971\pi$
$251$		−	7.01197i		−	0.442592i	0.975207	−	0.221296i	$-0.0710287\pi$
$252$	−0.747420	+	0.476629i	−0.0470831	+	0.0300248i
$253$	−1.25456	+	4.97692i	−0.0788735	+	0.312896i
$254$	6.00743			0.376940
$255$	−7.53431			−0.471817
$256$	−7.80294			−0.487683
$257$		−	29.5080i		−	1.84066i	−0.391144	−	0.920329i	$-0.627921\pi$
$257$		−	29.5080i		−	1.84066i	0.391144	−	0.920329i	$-0.372079\pi$
$258$			10.8889i			0.677915i
$259$	−18.8734	+	12.0356i	−1.17274	+	0.747854i
$260$			1.08582i			0.0673396i
$261$		−	7.87403i		−	0.487390i
$262$		−	21.6065i		−	1.33485i
$263$			3.52655i			0.217456i	0.994072	+	0.108728i	$0.0346778\pi$
$263$			3.52655i			0.217456i	−0.994072	+	0.108728i	$0.965322\pi$
$264$	−2.44257	+	9.68982i	−0.150330	+	0.596367i
$265$			11.0999i			0.681861i
$266$	3.87036	+	6.06927i	0.237307	+	0.372131i
$267$	−13.1967			−0.807622
$268$	−3.68830			−0.225299
$269$		−	6.40717i		−	0.390652i	−0.980738	−	0.195326i	$-0.937424\pi$
$269$		−	6.40717i		−	0.390652i	0.980738	−	0.195326i	$-0.0625765\pi$
$270$			1.29033i			0.0785269i
$271$	7.93034			0.481734			0.240867	−	0.970558i	$-0.422568\pi$
$271$	7.93034			0.481734			0.240867	+	0.970558i	$0.422568\pi$
$272$	−24.2427			−1.46993
$273$	4.61017	+	7.22938i	0.279020	+	0.437542i
$274$		−	7.04345i		−	0.425510i
$275$	−0.810680	+	3.21602i	−0.0488858	+	0.193933i
$276$		−	0.518504i		−	0.0312103i
$277$		−	17.2769i		−	1.03807i	−0.854753	−	0.519034i	$-0.826292\pi$
$277$		−	17.2769i		−	1.03807i	0.854753	−	0.519034i	$-0.173708\pi$
$278$			16.4625i			0.987357i
$279$			2.42925i			0.145435i
$280$	−6.72127	+	4.28614i	−0.401673	+	0.256146i
$281$			8.40629i			0.501477i	0.968055	+	0.250739i	$0.0806735\pi$
$281$			8.40629i			0.501477i	−0.968055	+	0.250739i	$0.919327\pi$
$282$			2.64596i			0.157564i
$283$	0.434262			0.0258142			0.0129071	−	0.999917i	$-0.495891\pi$
$283$	0.434262			0.0258142			0.0129071	+	0.999917i	$0.495891\pi$
$284$	−3.77499			−0.224004
$285$	−2.10854			−0.124899
$286$	13.4483	+	3.38998i	0.795213	+	0.200454i
$287$	−15.2310	+	9.71278i	−0.899057	+	0.573327i
$288$		−	1.87415i		−	0.110436i
$289$	39.7658			2.33917
$290$		−	10.1601i		−	0.596621i
$291$	−2.85810			−0.167545
$292$	−1.27632			−0.0746913
$293$	26.8651			1.56947			0.784737	−	0.619829i	$-0.212798\pi$
$293$	26.8651			1.56947			0.784737	+	0.619829i	$0.212798\pi$
$294$	−3.80990	+	8.18945i	−0.222198	+	0.477619i
$295$	−9.43543			−0.549352
$296$		−	25.4914i		−	1.48166i
$297$	−3.21602	−	0.810680i	−0.186613	−	0.0470404i
$298$	17.0708			0.988883
$299$	−5.01520			−0.290037
$300$		−	0.335051i		−	0.0193442i
$301$	−12.0048	−	18.8252i	−0.691944	−	1.08507i
$302$	−4.45843			−0.256554
$303$		−	7.67234i		−	0.440765i
$304$	−6.78451			−0.389119
$305$			8.80831i			0.504362i
$306$		−	9.72174i		−	0.555755i
$307$	10.6341			0.606920			0.303460	−	0.952844i	$-0.401858\pi$
$307$	10.6341			0.606920			0.303460	+	0.952844i	$0.401858\pi$
$308$	−0.926929	−	2.79011i	−0.0528167	−	0.158981i
$309$	−5.83595			−0.331996
$310$			3.13453i			0.178029i
$311$		−	14.9940i		−	0.850234i	−0.905138	−	0.425117i	$-0.860233\pi$
$311$		−	14.9940i		−	0.850234i	0.905138	−	0.425117i	$-0.139767\pi$
$312$	−9.76435			−0.552798
$313$			11.6551i			0.658785i	0.944193	+	0.329392i	$0.106844\pi$
$313$			11.6551i			0.658785i	−0.944193	+	0.329392i	$0.893156\pi$
$314$	7.16366			0.404269
$315$	−1.42256	−	2.23077i	−0.0801520	−	0.125690i
$316$		−	1.93843i		−	0.109045i
$317$	−27.6631			−1.55372			−0.776858	−	0.629675i	$-0.783188\pi$
$317$	−27.6631			−1.55372			−0.776858	+	0.629675i	$0.783188\pi$
$318$	−14.3225			−0.803167
$319$	25.3230	+	6.38332i	1.41782	+	0.357397i
$320$		−	8.85355i		−	0.494929i
$321$	8.10169			0.452192
$322$	−2.84061	−	4.45448i	−0.158301	−	0.248238i
$323$	15.8864			0.883941
$324$	0.335051			0.0186139
$325$	−3.24076			−0.179765
$326$			11.0426i			0.611595i
$327$	3.24745			0.179584
$328$		−	20.5717i		−	1.13588i
$329$	−2.91711	−	4.57443i	−0.160825	−	0.252196i
$330$	−4.14973	−	1.04604i	−0.228435	−	0.0575828i
$331$	−9.71214			−0.533827			−0.266914	−	0.963720i	$-0.586004\pi$
$331$	−9.71214			−0.533827			−0.266914	+	0.963720i	$0.586004\pi$
$332$	−3.09599			−0.169914
$333$	8.46051			0.463633
$334$		−	14.3804i		−	0.786859i
$335$		−	11.0082i		−	0.601442i
$336$	−4.57728	−	7.17781i	−0.249711	−	0.391582i
$337$			22.0452i			1.20088i	0.799669	+	0.600441i	$0.205008\pi$
$337$			22.0452i			1.20088i	−0.799669	+	0.600441i	$0.794992\pi$
$338$		−	3.22257i		−	0.175285i
$339$		−	3.16140i		−	0.171704i
$340$			2.52437i			0.136903i
$341$	−7.81251	−	1.96934i	−0.423071	−	0.106646i
$342$		−	2.72071i		−	0.147119i
$343$	−2.44198	−	18.3586i	−0.131854	−	0.991269i
$344$	25.4262			1.37089
$345$	1.54754			0.0833167
$346$			31.0517i			1.66935i
$347$		−	31.0772i		−	1.66831i	−0.551528	−	0.834156i	$-0.685955\pi$
$347$		−	31.0772i		−	1.66831i	0.551528	−	0.834156i	$-0.314045\pi$
$348$	−2.63820			−0.141422
$349$	−13.0393			−0.697976			−0.348988	−	0.937127i	$-0.613475\pi$
$349$	−13.0393			−0.697976			−0.348988	+	0.937127i	$0.613475\pi$
$350$	−1.83557	−	2.87843i	−0.0981152	−	0.153858i
$351$		−	3.24076i		−	0.172979i
$352$	6.02732	+	1.51934i	0.321257	+	0.0809810i
$353$			1.42738i			0.0759718i	0.999278	+	0.0379859i	$0.0120942\pi$
$353$			1.42738i			0.0759718i	−0.999278	+	0.0379859i	$0.987906\pi$
$354$		−	12.1748i		−	0.647084i
$355$		−	11.2669i		−	0.597987i
$356$			4.42155i			0.234341i
$357$	10.7180	+	16.8073i	0.567256	+	0.889537i
$358$			10.0857i			0.533045i
$359$			16.6331i			0.877863i	0.898521	+	0.438931i	$0.144643\pi$
$359$			16.6331i			0.877863i	−0.898521	+	0.438931i	$0.855357\pi$
$360$	3.01298			0.158798
$361$	−14.5541			−0.766004
$362$	−21.6116			−1.13588
$363$	5.21433	−	9.68560i	0.273681	−	0.508362i
$364$	2.42221	−	1.54464i	0.126958	−	0.0809611i
$365$		−	3.80935i		−	0.199391i
$366$	−11.3656			−0.594090
$367$		−	10.3033i		−	0.537828i	−0.963164	−	0.268914i	$-0.913335\pi$
$367$		−	10.3033i		−	0.537828i	0.963164	−	0.268914i	$-0.0866648\pi$
$368$	4.97942			0.259570
$369$	6.82769			0.355435
$370$	10.9168			0.567540
$371$	24.7613	−	15.7902i	1.28554	−	0.819788i
$372$	0.813920			0.0421998
$373$		−	22.9352i		−	1.18754i	−0.804635	−	0.593770i	$-0.797639\pi$
$373$		−	22.9352i		−	1.18754i	0.804635	−	0.593770i	$-0.202361\pi$
$374$	31.2653	+	7.88122i	1.61669	+	0.407528i
$375$	1.00000			0.0516398
$376$	6.17844			0.318629
$377$			25.5178i			1.31423i
$378$	2.87843	−	1.83557i	0.148050	−	0.0944114i
$379$	8.73449			0.448661			0.224330	−	0.974513i	$-0.427981\pi$
$379$	8.73449			0.448661			0.224330	+	0.974513i	$0.427981\pi$
$380$			0.706466i			0.0362410i
$381$	4.65573			0.238520
$382$			30.0043i			1.53515i
$383$		−	15.5916i		−	0.796692i	−0.917235	−	0.398346i	$-0.869584\pi$
$383$		−	15.5916i		−	0.796692i	0.917235	−	0.398346i	$-0.130416\pi$
$384$	7.67569			0.391699
$385$	8.32744	−	2.76654i	0.424406	−	0.140996i
$386$	5.34503			0.272055
$387$			8.43887i			0.428972i
$388$			0.957607i			0.0486151i
$389$	−27.6283			−1.40081			−0.700405	−	0.713745i	$-0.746997\pi$
$389$	−27.6283			−1.40081			−0.700405	+	0.713745i	$0.746997\pi$
$390$		−	4.18165i		−	0.211746i
$391$	−11.6596			−0.589653
$392$	19.1228	+	8.89632i	0.965847	+	0.449332i
$393$		−	16.7450i		−	0.844671i
$394$	−3.53843			−0.178264
$395$	5.78548			0.291099
$396$	−0.271619	+	1.07753i	−0.0136494	+	0.0541479i
$397$		−	17.6315i		−	0.884902i	−0.896793	−	0.442451i	$-0.854109\pi$
$397$		−	17.6315i		−	0.884902i	0.896793	−	0.442451i	$-0.145891\pi$
$398$	5.11387			0.256335
$399$	2.99952	+	4.70366i	0.150164	+	0.235477i
$400$	3.21764			0.160882
$401$	−36.5809			−1.82676			−0.913382	−	0.407103i	$-0.866539\pi$
$401$	−36.5809			−1.82676			−0.913382	+	0.407103i	$0.866539\pi$
$402$	14.2042			0.708441
$403$		−	7.87260i		−	0.392162i
$404$	−2.57062			−0.127893
$405$			1.00000i			0.0496904i
$406$	−22.6648	+	14.4533i	−1.12484	+	0.717306i
$407$	−6.85877	+	27.2092i	−0.339977	+	1.34871i
$408$	−22.7008			−1.12385
$409$	11.1695			0.552294			0.276147	−	0.961115i	$-0.410942\pi$
$409$	11.1695			0.552294			0.276147	+	0.961115i	$0.410942\pi$
$410$	8.80996			0.435093
$411$		−	5.45865i		−	0.269255i
$412$			1.95534i			0.0963326i
$413$	13.4224	+	21.0483i	0.660475	+	1.03572i
$414$			1.99683i			0.0981391i
$415$		−	9.24036i		−	0.453591i
$416$			6.07368i			0.297787i
$417$			12.7584i			0.624782i
$418$	8.74985	+	2.20562i	0.427969	+	0.107881i
$419$		−	2.69603i		−	0.131709i	−0.997829	−	0.0658547i	$-0.979023\pi$
$419$		−	2.69603i		−	0.131709i	0.997829	−	0.0658547i	$-0.0209774\pi$
$420$	−0.747420	+	0.476629i	−0.0364704	+	0.0232571i
$421$	11.8615			0.578096			0.289048	−	0.957315i	$-0.406661\pi$
$421$	11.8615			0.578096			0.289048	+	0.957315i	$0.406661\pi$
$422$	−26.0904			−1.27006
$423$			2.05061i			0.0997039i
$424$			33.4438i			1.62417i
$425$	−7.53431			−0.365468
$426$	14.5380			0.704371
$427$	19.6493	−	12.5303i	0.950896	−	0.606385i
$428$		−	2.71447i		−	0.131209i
$429$	10.4224	+	2.62722i	0.503196	+	0.126843i
$430$			10.8889i			0.525111i
$431$		−	39.1098i		−	1.88385i	−0.335819	−	0.941926i	$-0.609013\pi$
$431$		−	39.1098i		−	1.88385i	0.335819	−	0.941926i	$-0.390987\pi$
$432$			3.21764i			0.154809i
$433$			28.2462i			1.35742i	0.734404	+	0.678712i	$0.237462\pi$
$433$			28.2462i			1.35742i	−0.734404	+	0.678712i	$0.762538\pi$
$434$	6.99241	−	4.45904i	0.335646	−	0.214041i
$435$		−	7.87403i		−	0.377531i
$436$		−	1.08806i		−	0.0521086i
$437$	−3.26304			−0.156093
$438$	4.91532			0.234863
$439$	−32.9581			−1.57300			−0.786502	−	0.617587i	$-0.788110\pi$
$439$	−32.9581			−1.57300			−0.786502	+	0.617587i	$0.788110\pi$
$440$	−2.44257	+	9.68982i	−0.116445	+	0.461944i
$441$	−2.95266	+	6.34679i	−0.140603	+	0.302228i
$442$			31.5058i			1.49858i
$443$	16.9942			0.807420			0.403710	−	0.914887i	$-0.367720\pi$
$443$	16.9942			0.807420			0.403710	+	0.914887i	$0.367720\pi$
$444$		−	2.83470i		−	0.134529i
$445$	−13.1967			−0.625581
$446$	23.0927			1.09347
$447$	13.2298			0.625747
$448$	−19.7502	+	12.5947i	−0.933111	+	0.595043i
$449$	11.0171			0.519929			0.259964	−	0.965618i	$-0.416289\pi$
$449$	11.0171			0.519929			0.259964	+	0.965618i	$0.416289\pi$
$450$			1.29033i			0.0608267i
$451$	−5.53507	+	21.9580i	−0.260636	+	1.03396i
$452$	−1.05923			−0.0498219
$453$	−3.45527			−0.162343
$454$			0.987498i			0.0463456i
$455$	4.61017	+	7.22938i	0.216128	+	0.338919i
$456$	−6.35299			−0.297506
$457$			5.85432i			0.273853i	0.990581	+	0.136927i	$0.0437225\pi$
$457$			5.85432i			0.273853i	−0.990581	+	0.136927i	$0.956278\pi$
$458$	−8.25754			−0.385850
$459$		−	7.53431i		−	0.351672i
$460$		−	0.518504i		−	0.0241754i
$461$	−31.2160			−1.45387			−0.726936	−	0.686705i	$-0.759057\pi$
$461$	−31.2160			−1.45387			−0.726936	+	0.686705i	$0.759057\pi$
$462$	3.56974	+	10.7451i	0.166079	+	0.499909i
$463$	11.0802			0.514940			0.257470	−	0.966286i	$-0.417111\pi$
$463$	11.0802			0.514940			0.257470	+	0.966286i	$0.417111\pi$
$464$		−	25.3358i		−	1.17618i
$465$			2.42925i			0.112654i
$466$	5.71186			0.264597
$467$		−	16.2356i		−	0.751295i	−0.926763	−	0.375647i	$-0.877420\pi$
$467$		−	16.2356i		−	0.751295i	0.926763	−	0.375647i	$-0.122580\pi$
$468$	−1.08582			−0.0501919
$469$	−24.5568	+	15.6598i	−1.13393	+	0.723102i
$470$			2.64596i			0.122049i
$471$	5.55181			0.255814
$472$	−28.4288			−1.30854
$473$	−27.1396	−	6.84123i	−1.24788	−	0.314560i
$474$			7.46518i			0.342887i
$475$	−2.10854			−0.0967463
$476$	5.63130	−	3.59107i	0.258110	−	0.164596i
$477$	−11.0999			−0.508229
$478$	−26.1891			−1.19786
$479$	18.1711			0.830259			0.415130	−	0.909762i	$-0.363736\pi$
$479$	18.1711			0.830259			0.415130	+	0.909762i	$0.363736\pi$
$480$		−	1.87415i		−	0.0855430i
$481$	−27.4185			−1.25017
$482$			7.60601i			0.346444i
$483$	−2.20146	−	3.45220i	−0.100170	−	0.157081i
$484$	−3.24516	−	1.74706i	−0.147507	−	0.0794120i
$485$	−2.85810			−0.129780
$486$	−1.29033			−0.0585305
$487$	21.9493			0.994617			0.497309	−	0.867574i	$-0.334322\pi$
$487$	21.9493			0.994617			0.497309	+	0.867574i	$0.334322\pi$
$488$			26.5393i			1.20138i
$489$			8.55799i			0.387006i
$490$	−3.80990	+	8.18945i	−0.172114	+	0.369962i
$491$		−	22.1227i		−	0.998382i	−0.866492	−	0.499191i	$-0.833631\pi$
$491$		−	22.1227i		−	0.998382i	0.866492	−	0.499191i	$-0.166369\pi$
$492$		−	2.28762i		−	0.103134i
$493$			59.3254i			2.67188i
$494$			8.81716i			0.396703i
$495$	−3.21602	−	0.810680i	−0.144549	−	0.0364374i
$496$			7.81644i			0.350968i
$497$	−25.1339	+	16.0279i	−1.12741	+	0.718948i
$498$	11.9231			0.534287
$499$	−23.0195			−1.03049			−0.515247	−	0.857042i	$-0.672300\pi$
$499$	−23.0195			−1.03049			−0.515247	+	0.857042i	$0.672300\pi$
$500$		−	0.335051i		−	0.0149839i
$501$		−	11.1447i		−	0.497910i
$502$	9.04775			0.403821
$503$	−40.8160			−1.81990			−0.909948	−	0.414723i	$-0.863879\pi$
$503$	−40.8160			−1.81990			−0.909948	+	0.414723i	$0.863879\pi$
$504$	−4.28614	−	6.72127i	−0.190920	−	0.299389i
$505$		−	7.67234i		−	0.341415i
$506$	−6.42187	−	1.61879i	−0.285487	−	0.0719642i
$507$		−	2.49748i		−	0.110917i
$508$		−	1.55991i		−	0.0692096i
$509$			26.3468i			1.16780i	0.811826	+	0.583900i	$0.198474\pi$
$509$			26.3468i			1.16780i	−0.811826	+	0.583900i	$0.801526\pi$
$510$		−	9.72174i		−	0.430486i
$511$	−8.49778	+	5.41902i	−0.375920	+	0.239723i
$512$		−	25.4197i		−	1.12340i
$513$		−	2.10854i		−	0.0930942i
$514$	38.0750			1.67942
$515$	−5.83595			−0.257163
$516$	2.82745			0.124472
$517$	−6.59479	−	1.66239i	−0.290039	−	0.0731116i
$518$	−15.5298	−	24.3530i	−0.682342	−	1.07001i
$519$			24.0649i			1.05633i
$520$	−9.76435			−0.428195
$521$		−	26.3925i		−	1.15627i	−0.815939	−	0.578137i	$-0.803780\pi$
$521$		−	26.3925i		−	1.15627i	0.815939	−	0.578137i	$-0.196220\pi$
$522$	10.1601			0.444695
$523$	28.5651			1.24906			0.624532	−	0.780999i	$-0.285290\pi$
$523$	28.5651			1.24906			0.624532	+	0.780999i	$0.285290\pi$
$524$	−5.61040			−0.245092
$525$	−1.42256	−	2.23077i	−0.0620855	−	0.0973587i
$526$	−4.55041			−0.198407
$527$		−	18.3027i		−	0.797278i
$528$	−10.3480	−	2.60848i	−0.450339	−	0.113519i
$529$	−20.6051			−0.895875
$530$	−14.3225			−0.622131
$531$		−	9.43543i		−	0.409463i
$532$	1.57596	−	1.00499i	0.0683267	−	0.0435718i
$533$	−22.1269			−0.958422
$534$		−	17.0280i		−	0.736875i
$535$	8.10169			0.350266
$536$		−	33.1675i		−	1.43262i
$537$			7.81636i			0.337301i
$538$	8.26735			0.356431
$539$	−18.0178	−	14.6410i	−0.776080	−	0.630634i
$540$	0.335051			0.0144183
$541$		−	12.4100i		−	0.533547i	−0.963759	−	0.266774i	$-0.914042\pi$
$541$		−	12.4100i		−	0.533547i	0.963759	−	0.266774i	$-0.0859576\pi$
$542$			10.2328i			0.439534i
$543$	−16.7489			−0.718765
$544$			14.1204i			0.605409i
$545$	3.24745			0.139105
$546$	−9.32829	+	5.94863i	−0.399214	+	0.254578i
$547$			35.9413i			1.53674i	0.640005	+	0.768371i	$0.278932\pi$
$547$			35.9413i			1.53674i	−0.640005	+	0.768371i	$0.721068\pi$
$548$	−1.82892			−0.0781277
$549$	−8.80831			−0.375929
$550$	−4.14973	−	1.04604i	−0.176945	−	0.0446035i
$551$			16.6027i			0.707298i
$552$	4.66271			0.198458
$553$	−8.23018	−	12.9061i	−0.349983	−	0.548822i
$554$	22.2929			0.947134
$555$	8.46051			0.359129
$556$	4.27471			0.181288
$557$			37.6530i			1.59541i	0.603049	+	0.797704i	$0.293952\pi$
$557$			37.6530i			1.59541i	−0.603049	+	0.797704i	$0.706048\pi$
$558$	−3.13453			−0.132695
$559$		−	27.3484i		−	1.15671i
$560$	−4.57728	−	7.17781i	−0.193425	−	0.303318i
$561$	24.2305	+	6.10792i	1.02301	+	0.257876i
$562$	−10.8469			−0.457548
$563$	13.2558			0.558663			0.279332	−	0.960195i	$-0.409887\pi$
$563$	13.2558			0.558663			0.279332	+	0.960195i	$0.409887\pi$
$564$	0.687057			0.0289303
$565$		−	3.16140i		−	0.133001i
$566$			0.560340i			0.0235529i
$567$	2.23077	−	1.42256i	0.0936835	−	0.0597418i
$568$		−	33.9471i		−	1.42439i
$569$		−	18.2679i		−	0.765828i	−0.923784	−	0.382914i	$-0.874920\pi$
$569$		−	18.2679i		−	0.765828i	0.923784	−	0.382914i	$-0.125080\pi$
$570$		−	2.72071i		−	0.113958i
$571$		−	26.9402i		−	1.12741i	−0.825975	−	0.563707i	$-0.809375\pi$
$571$		−	26.9402i		−	1.12741i	0.825975	−	0.563707i	$-0.190625\pi$
$572$	0.880251	−	3.49201i	0.0368051	−	0.146008i
$573$			23.2532i			0.971418i
$574$	−12.5327	−	19.6530i	−0.523104	−	0.820300i
$575$	1.54754			0.0645368
$576$	8.85355			0.368898
$577$			38.1940i			1.59004i	0.606585	+	0.795019i	$0.292539\pi$
$577$			38.1940i			1.59004i	−0.606585	+	0.795019i	$0.707461\pi$
$578$			51.3110i			2.13426i
$579$	4.14238			0.172151
$580$	−2.63820			−0.109545
$581$	−20.6131	+	13.1449i	−0.855176	+	0.545344i
$582$		−	3.68789i		−	0.152868i
$583$	8.99847	−	35.6975i	0.372678	−	1.47844i
$584$		−	11.4775i		−	0.474943i
$585$		−	3.24076i		−	0.133989i
$586$			34.6648i			1.43199i
$587$			34.1079i			1.40778i	0.710307	+	0.703892i	$0.248556\pi$
$587$			34.1079i			1.40778i	−0.710307	+	0.703892i	$0.751444\pi$
$588$	2.12650	+	0.989290i	0.0876952	+	0.0407976i
$589$		−	5.12215i		−	0.211055i
$590$		−	12.1748i		−	0.501229i
$591$	−2.74227			−0.112802
$592$	27.2229			1.11885
$593$	−11.2669			−0.462675			−0.231337	−	0.972874i	$-0.574310\pi$
$593$	−11.2669			−0.462675			−0.231337	+	0.972874i	$0.574310\pi$
$594$	1.04604	−	4.14973i	0.0429197	−	0.170265i
$595$	10.7180	+	16.8073i	0.439395	+	0.689032i
$596$		−	4.43264i		−	0.181568i
$597$	3.96323			0.162204
$598$		−	6.47126i		−	0.264630i
$599$	−42.1747			−1.72321			−0.861605	−	0.507579i	$-0.830541\pi$
$599$	−42.1747			−1.72321			−0.861605	+	0.507579i	$0.830541\pi$
$600$	3.01298			0.123005
$601$	46.5214			1.89765			0.948824	−	0.315805i	$-0.102275\pi$
$601$	46.5214			1.89765			0.948824	+	0.315805i	$0.102275\pi$
$602$	24.2907	−	15.4901i	0.990014	−	0.631330i
$603$	11.0082			0.448289
$604$			1.15769i			0.0471057i
$605$	5.21433	−	9.68560i	0.211993	−	0.393775i
$606$	9.89985			0.402154
$607$	−15.5959			−0.633019			−0.316509	−	0.948589i	$-0.602511\pi$
$607$	−15.5959			−0.633019			−0.316509	+	0.948589i	$0.602511\pi$
$608$			3.95172i			0.160263i
$609$	−17.5651	+	11.2013i	−0.711775	+	0.453898i
$610$	−11.3656			−0.460180
$611$		−	6.64552i		−	0.268849i
$612$	−2.52437			−0.102042
$613$			18.9582i			0.765713i	0.923808	+	0.382856i	$0.125060\pi$
$613$			18.9582i			0.765713i	−0.923808	+	0.382856i	$0.874940\pi$
$614$			13.7215i			0.553754i
$615$	6.82769			0.275319
$616$	25.0904	−	8.33553i	1.01092	−	0.335848i
$617$	0.578277			0.0232806			0.0116403	−	0.999932i	$-0.496295\pi$
$617$	0.578277			0.0232806			0.0116403	+	0.999932i	$0.496295\pi$
$618$		−	7.53030i		−	0.302913i
$619$			15.1762i			0.609985i	0.952355	+	0.304992i	$0.0986539\pi$
$619$			15.1762i			0.609985i	−0.952355	+	0.304992i	$0.901346\pi$
$620$	0.813920			0.0326878
$621$			1.54754i			0.0621006i
$622$	19.3473			0.775754
$623$	18.7730	+	29.4387i	0.752124	+	1.17944i
$624$		−	10.4276i		−	0.417438i
$625$	1.00000			0.0400000
$626$	−15.0389			−0.601075
$627$	6.78110	+	1.70935i	0.270811	+	0.0682648i
$628$		−	1.86014i		−	0.0742275i
$629$	−63.7441			−2.54164
$630$	2.87843	−	1.83557i	0.114679	−	0.0731308i
$631$	17.6744			0.703606			0.351803	−	0.936074i	$-0.385569\pi$
$631$	17.6744			0.703606			0.351803	+	0.936074i	$0.385569\pi$
$632$	17.4316			0.693391
$633$	−20.2200			−0.803672
$634$		−	35.6946i		−	1.41761i
$635$	4.65573			0.184757
$636$			3.71903i			0.147469i
$637$	9.56886	−	20.5684i	0.379132	−	0.814951i
$638$	−8.23658	+	32.6751i	−0.326089	+	1.29362i
$639$	11.2669			0.445713
$640$	7.67569			0.303408
$641$	−45.0543			−1.77954			−0.889768	−	0.456413i	$-0.849134\pi$
$641$	−45.0543			−1.77954			−0.889768	+	0.456413i	$0.849134\pi$
$642$			10.4538i			0.412580i
$643$		−	22.7223i		−	0.896081i	−0.894013	−	0.448040i	$-0.852122\pi$
$643$		−	22.7223i		−	0.896081i	0.894013	−	0.448040i	$-0.147878\pi$
$644$	−1.15666	+	0.737601i	−0.0455789	+	0.0290656i
$645$			8.43887i			0.332280i
$646$			20.4987i			0.806509i
$647$		−	14.9728i		−	0.588643i	−0.955706	−	0.294321i	$-0.904906\pi$
$647$		−	14.9728i		−	0.588643i	0.955706	−	0.294321i	$-0.0950936\pi$
$648$			3.01298i			0.118361i
$649$	30.3446	+	7.64912i	1.19113	+	0.300254i
$650$		−	4.18165i		−	0.164018i
$651$	5.41909	−	3.45574i	0.212391	−	0.135441i
$652$	2.86736			0.112294
$653$	21.6224			0.846148			0.423074	−	0.906095i	$-0.360951\pi$
$653$	21.6224			0.846148			0.423074	+	0.906095i	$0.360951\pi$
$654$			4.19027i			0.163853i
$655$		−	16.7450i		−	0.654279i
$656$	21.9690			0.857747
$657$	3.80935			0.148617
$658$	5.90252	−	3.76403i	0.230104	−	0.146737i
$659$			21.9397i			0.854650i	0.904098	+	0.427325i	$0.140544\pi$
$659$			21.9397i			0.854650i	−0.904098	+	0.427325i	$0.859456\pi$
$660$	−0.271619	+	1.07753i	−0.0105727	+	0.0419428i
$661$			20.3773i			0.792585i	0.918124	+	0.396292i	$0.129703\pi$
$661$			20.3773i			0.792585i	−0.918124	+	0.396292i	$0.870297\pi$
$662$		−	12.5319i		−	0.487064i
$663$			24.4169i			0.948273i
$664$		−	27.8411i		−	1.08044i
$665$	2.99952	+	4.70366i	0.116316	+	0.182400i
$666$			10.9168i			0.423019i
$667$		−	12.1854i		−	0.471819i
$668$	−3.73405			−0.144475
$669$	17.8967			0.691927
$670$	14.2042			0.548756
$671$	7.14072	−	28.3277i	0.275664	−	1.09358i
$672$	−4.18080	+	2.66609i	−0.161278	+	0.102847i
$673$			5.51059i			0.212418i	0.994344	+	0.106209i	$0.0338712\pi$
$673$			5.51059i			0.212418i	−0.994344	+	0.106209i	$0.966129\pi$
$674$	−28.4456			−1.09568
$675$			1.00000i			0.0384900i
$676$	−0.836783			−0.0321840
$677$	−37.7218			−1.44977			−0.724883	−	0.688872i	$-0.758106\pi$
$677$	−37.7218			−1.44977			−0.724883	+	0.688872i	$0.758106\pi$
$678$	4.07924			0.156662
$679$	4.06581	+	6.37576i	0.156031	+	0.244679i
$680$	−22.7008			−0.870534
$681$			0.765307i			0.0293266i
$682$	2.54110	−	10.0807i	0.0973037	−	0.386010i
$683$	−17.7057			−0.677488			−0.338744	−	0.940879i	$-0.610002\pi$
$683$	−17.7057			−0.677488			−0.338744	+	0.940879i	$0.610002\pi$
$684$	−0.706466			−0.0270124
$685$		−	5.45865i		−	0.208564i
$686$	23.6886	−	3.15096i	0.904434	−	0.120304i
$687$	−6.39956			−0.244159
$688$			27.1533i			1.03521i
$689$	35.9721			1.37043
$690$			1.99683i			0.0760182i
$691$			32.3104i			1.22914i	0.788861	+	0.614572i	$0.210671\pi$
$691$			32.3104i			1.22914i	−0.788861	+	0.614572i	$0.789329\pi$
$692$	8.06296			0.306508
$693$	2.76654	+	8.32744i	0.105092	+	0.316333i
$694$	40.0999			1.52217
$695$			12.7584i			0.483954i
$696$		−	23.7243i		−	0.899268i
$697$	−51.4419			−1.94850
$698$		−	16.8250i		−	0.636834i
$699$	4.42667			0.167432
$700$	−0.747420	+	0.476629i	−0.0282498	+	0.0180149i
$701$			39.6471i			1.49745i	0.662880	+	0.748726i	$0.269334\pi$
$701$			39.6471i			1.49745i	−0.662880	+	0.748726i	$0.730666\pi$
$702$	4.18165			0.157826
$703$	−17.8393			−0.672822
$704$	−7.17740	+	28.4732i	−0.270508	+	1.07313i
$705$			2.05061i			0.0772303i
$706$	−1.84179			−0.0693167
$707$	−17.1152	+	10.9143i	−0.643684	+	0.410476i
$708$	−3.16135			−0.118811
$709$	36.2481			1.36133			0.680664	−	0.732596i	$-0.261691\pi$
$709$	36.2481			1.36133			0.680664	+	0.732596i	$0.261691\pi$
$710$	14.5380			0.545603
$711$			5.78548i			0.216973i
$712$	−39.7613			−1.49012
$713$			3.75935i			0.140789i
$714$	−21.6870	+	13.8297i	−0.811614	+	0.517565i
$715$	10.4224	+	2.62722i	0.389774	+	0.0982524i
$716$	2.61888			0.0978720
$717$	−20.2965			−0.757985
$718$	−21.4622			−0.800963
$719$			43.1678i			1.60989i	0.593351	+	0.804944i	$0.297804\pi$
$719$			43.1678i			1.60989i	−0.593351	+	0.804944i	$0.702196\pi$
$720$			3.21764i			0.119914i
$721$	8.30198	+	13.0187i	0.309182	+	0.484840i
$722$		−	18.7795i		−	0.698902i
$723$			5.89463i			0.219224i
$724$			5.61174i			0.208559i
$725$		−	7.87403i		−	0.292434i
$726$	12.4976	+	6.72820i	0.463830	+	0.249707i
$727$		−	5.15755i		−	0.191283i	−0.995416	−	0.0956414i	$-0.969510\pi$
$727$		−	5.15755i		−	0.191283i	0.995416	−	0.0956414i	$-0.0304902\pi$
$728$	13.8904	+	21.7820i	0.514811	+	0.807295i
$729$	−1.00000			−0.0370370
$730$	4.91532			0.181924
$731$		−	63.5811i		−	2.35163i
$732$			2.95123i			0.109081i
$733$	19.8648			0.733723			0.366862	−	0.930276i	$-0.380432\pi$
$733$	19.8648			0.733723			0.366862	+	0.930276i	$0.380432\pi$
$734$	13.2947			0.490715
$735$	−2.95266	+	6.34679i	−0.108911	+	0.234105i
$736$		−	2.90032i		−	0.106907i
$737$	−8.92413	+	35.4026i	−0.328725	+	1.30407i
$738$			8.80996i			0.324299i
$739$		−	34.8337i		−	1.28138i	−0.767801	−	0.640689i	$-0.778649\pi$
$739$		−	34.8337i		−	1.28138i	0.767801	−	0.640689i	$-0.221351\pi$
$740$		−	2.83470i		−	0.104206i
$741$			6.83326i			0.251026i
$742$	20.3746	+	31.9502i	0.747975	+	1.17293i
$743$		−	20.3324i		−	0.745925i	−0.927847	−	0.372962i	$-0.878342\pi$
$743$		−	20.3324i		−	0.745925i	0.927847	−	0.372962i	$-0.121658\pi$
$744$			7.31928i			0.268338i
$745$	13.2298			0.484702
$746$	29.5940			1.08351
$747$	9.24036			0.338087
$748$	2.04646	−	8.11844i	0.0748260	−	0.296840i
$749$	−11.5251	−	18.0730i	−0.421118	−	0.660373i
$750$			1.29033i			0.0471162i
$751$	−52.3490			−1.91024			−0.955122	−	0.296214i	$-0.904276\pi$
$751$	−52.3490			−1.91024			−0.955122	+	0.296214i	$0.904276\pi$
$752$			6.59811i			0.240608i
$753$	7.01197			0.255531
$754$	−32.9264			−1.19911
$755$	−3.45527			−0.125750
$756$	−0.476629	−	0.747420i	−0.0173348	−	0.0271834i
$757$	22.2650			0.809234			0.404617	−	0.914486i	$-0.367405\pi$
$757$	22.2650			0.809234			0.404617	+	0.914486i	$0.367405\pi$
$758$			11.2704i			0.409358i
$759$	−4.97692	−	1.25456i	−0.180651	−	0.0455376i
$760$	−6.35299			−0.230447
$761$	1.03316			0.0374519			0.0187259	−	0.999825i	$-0.494039\pi$
$761$	1.03316			0.0374519			0.0187259	+	0.999825i	$0.494039\pi$
$762$			6.00743i			0.217626i
$763$	−4.61968	−	7.24430i	−0.167244	−	0.262261i
$764$	7.79101			0.281869
$765$		−	7.53431i		−	0.272404i
$766$	20.1183			0.726902
$767$			30.5780i			1.10411i
$768$		−	7.80294i		−	0.281564i
$769$	−1.24342			−0.0448388			−0.0224194	−	0.999749i	$-0.507137\pi$
$769$	−1.24342			−0.0448388			−0.0224194	+	0.999749i	$0.507137\pi$
$770$	3.56974	+	10.7451i	0.128645	+	0.387228i
$771$	29.5080			1.06270
$772$		−	1.38791i		−	0.0499518i
$773$		−	14.4812i		−	0.520851i	−0.965494	−	0.260426i	$-0.916137\pi$
$773$		−	14.4812i		−	0.520851i	0.965494	−	0.260426i	$-0.0838628\pi$
$774$	−10.8889			−0.391394
$775$			2.42925i			0.0872611i
$776$	−8.61140			−0.309131
$777$	−12.0356	−	18.8734i	−0.431773	−	0.677081i
$778$		−	35.6496i		−	1.27810i
$779$	−14.3964			−0.515806
$780$	−1.08582			−0.0388785
$781$	−9.13388	+	36.2347i	−0.326836	+	1.29658i
$782$		−	15.0448i		−	0.538000i
$783$	7.87403			0.281395
$784$	−9.50060	+	20.4217i	−0.339307	+	0.729346i
$785$	5.55181			0.198153
$786$	21.6065			0.770678
$787$	1.64402			0.0586030			0.0293015	−	0.999571i	$-0.490672\pi$
$787$	1.64402			0.0586030			0.0293015	+	0.999571i	$0.490672\pi$
$788$			0.918799i			0.0327309i
$789$	−3.52655			−0.125548
$790$			7.46518i			0.265599i
$791$	−7.05235	+	4.49727i	−0.250753	+	0.159905i
$792$	−9.68982	−	2.44257i	−0.344313	−	0.0867928i
$793$	28.5456			1.01368
$794$	22.7505			0.807385
$795$	−11.0999			−0.393673
$796$		−	1.32788i		−	0.0470656i
$797$		−	0.0492857i		−	0.00174579i	−1.00000		0.000872894i	$-0.999722\pi$
$797$		−	0.0492857i		−	0.00174579i	1.00000		0.000872894i	$-0.000277851\pi$
$798$	−6.06927	+	3.87036i	−0.214850	+	0.137009i
$799$		−	15.4499i		−	0.546578i
$800$		−	1.87415i		−	0.0662613i
$801$		−	13.1967i		−	0.466281i
$802$		−	47.2014i		−	1.66674i
$803$	−3.08816	+	12.2510i	−0.108979	+	0.432327i
$804$		−	3.68830i		−	0.130076i
$805$	−2.20146	−	3.45220i	−0.0775914	−	0.121674i
$806$	10.1582			0.357809
$807$	6.40717			0.225543
$808$		−	23.1166i		−	0.813241i
$809$			33.3068i			1.17100i	0.810671	+	0.585502i	$0.199102\pi$
$809$			33.3068i			1.17100i	−0.810671	+	0.585502i	$0.800898\pi$
$810$	−1.29033			−0.0453375
$811$	27.7727			0.975233			0.487616	−	0.873058i	$-0.337866\pi$
$811$	27.7727			0.975233			0.487616	+	0.873058i	$0.337866\pi$
$812$	3.75299	+	5.88521i	0.131704	+	0.206530i
$813$			7.93034i			0.278129i
$814$	−35.1088	−	8.85007i	−1.23056	−	0.310195i
$815$			8.55799i			0.299773i
$816$		−	24.2427i		−	0.848664i
$817$		−	17.7937i		−	0.622522i
$818$			14.4123i			0.503914i
$819$	−7.22938	+	4.61017i	−0.252615	+	0.161092i
$820$		−	2.28762i		−	0.0798872i
$821$			18.1506i			0.633462i	0.948515	+	0.316731i	$0.102585\pi$
$821$			18.1506i			0.633462i	−0.948515	+	0.316731i	$0.897415\pi$
$822$	7.04345			0.245669
$823$	−23.0784			−0.804464			−0.402232	−	0.915538i	$-0.631765\pi$
$823$	−23.0784			−0.804464			−0.402232	+	0.915538i	$0.631765\pi$
$824$	−17.5836			−0.612555
$825$	−3.21602	−	0.810680i	−0.111968	−	0.0282243i
$826$	−27.1592	+	17.3194i	−0.944989	+	0.602618i
$827$		−	9.11996i		−	0.317132i	−0.987348	−	0.158566i	$-0.949313\pi$
$827$		−	9.11996i		−	0.317132i	0.987348	−	0.158566i	$-0.0506871\pi$
$828$	0.518504			0.0180193
$829$			30.8418i			1.07118i	0.844478	+	0.535590i	$0.179911\pi$
$829$			30.8418i			1.07118i	−0.844478	+	0.535590i	$0.820089\pi$
$830$	11.9231			0.413857
$831$	17.2769			0.599329
$832$	−28.6922			−0.994724
$833$	22.2463	−	47.8187i	0.770787	−	1.65682i
$834$	−16.4625			−0.570051
$835$		−	11.1447i		−	0.385679i
$836$	0.572718	−	2.27201i	0.0198079	−	0.0785792i
$837$	−2.42925			−0.0839670
$838$	3.47876			0.120172
$839$		−	33.7976i		−	1.16682i	−0.812176	−	0.583412i	$-0.801717\pi$
$839$		−	33.7976i		−	1.16682i	0.812176	−	0.583412i	$-0.198283\pi$
$840$	−4.28614	−	6.72127i	−0.147886	−	0.231906i
$841$	−33.0003			−1.13794
$842$			15.3053i			0.527455i
$843$	−8.40629			−0.289528
$844$			6.77471i			0.233195i
$845$		−	2.49748i		−	0.0859160i
$846$	−2.64596			−0.0909699
$847$	−29.0240	+	2.14635i	−0.997277	+	0.0737495i
$848$	−35.7155			−1.22647
$849$			0.434262i			0.0149038i
$850$		−	9.72174i		−	0.333453i
$851$	13.0930			0.448821
$852$		−	3.77499i		−	0.129329i
$853$	−29.4311			−1.00770			−0.503851	−	0.863791i	$-0.668084\pi$
$853$	−29.4311			−1.00770			−0.503851	+	0.863791i	$0.668084\pi$
$854$	16.1682	+	25.3541i	0.553266	+	0.867598i
$855$		−	2.10854i		−	0.0721104i
$856$	24.4102			0.834325
$857$	26.5683			0.907556			0.453778	−	0.891115i	$-0.350076\pi$
$857$	26.5683			0.907556			0.453778	+	0.891115i	$0.350076\pi$
$858$	−3.38998	+	13.4483i	−0.115732	+	0.459116i
$859$		−	45.1307i		−	1.53984i	−0.638141	−	0.769919i	$-0.720296\pi$
$859$		−	45.1307i		−	1.53984i	0.638141	−	0.769919i	$-0.279704\pi$
$860$	2.82745			0.0964152
$861$	−9.71278	−	15.2310i	−0.331011	−	0.519071i
$862$	50.4645			1.71883
$863$	12.8064			0.435936			0.217968	−	0.975956i	$-0.430057\pi$
$863$	12.8064			0.435936			0.217968	+	0.975956i	$0.430057\pi$
$864$	1.87415			0.0637600
$865$			24.0649i			0.818232i
$866$	−36.4469			−1.23852
$867$			39.7658i			1.35052i
$868$	−1.15785	−	1.81567i	−0.0392999	−	0.0616278i
$869$	−18.6062	−	4.69018i	−0.631174	−	0.159103i
$870$	10.1601			0.344459
$871$	−35.6749			−1.20880
$872$	9.78450			0.331345
$873$		−	2.85810i		−	0.0967320i
$874$		−	4.21040i		−	0.142419i
$875$	−1.42256	−	2.23077i	−0.0480912	−	0.0754138i
$876$		−	1.27632i		−	0.0431230i
$877$		−	51.7279i		−	1.74673i	−0.487069	−	0.873363i	$-0.661934\pi$
$877$		−	51.7279i		−	1.74673i	0.487069	−	0.873363i	$-0.338066\pi$
$878$		−	42.5268i		−	1.43521i
$879$			26.8651i			0.906137i
$880$	−10.3480	−	2.60848i	−0.348831	−	0.0879317i
$881$			40.2889i			1.35737i	0.734430	+	0.678684i	$0.237449\pi$
$881$			40.2889i			1.35737i	−0.734430	+	0.678684i	$0.762551\pi$
$882$	−8.18945	−	3.80990i	−0.275753	−	0.128286i
$883$	33.6375			1.13199			0.565996	−	0.824408i	$-0.308492\pi$
$883$	33.6375			1.13199			0.565996	+	0.824408i	$0.308492\pi$
$884$	8.18089			0.275153
$885$		−	9.43543i		−	0.317169i
$886$			21.9282i			0.736691i
$887$	27.9520			0.938535			0.469268	−	0.883056i	$-0.344518\pi$
$887$	27.9520			0.938535			0.469268	+	0.883056i	$0.344518\pi$
$888$	25.4914			0.855435
$889$	−6.62305	−	10.3859i	−0.222130	−	0.348331i
$890$		−	17.0280i		−	0.570781i
$891$	0.810680	−	3.21602i	0.0271588	−	0.107741i
$892$		−	5.99630i		−	0.200771i
$893$		−	4.32378i		−	0.144690i
$894$			17.0708i			0.570932i
$895$			7.81636i			0.261272i
$896$	−10.9191	−	17.1227i	−0.364782	−	0.572029i
$897$		−	5.01520i		−	0.167453i
$898$			14.2157i			0.474383i
$899$	19.1279			0.637953
$900$	0.335051			0.0111684
$901$	83.6301			2.78612
$902$	−28.3330	−	7.14206i	−0.943387	−	0.237805i
$903$	18.8252	−	12.0048i	0.626463	−	0.399494i
$904$		−	9.52524i		−	0.316805i
$905$	−16.7489			−0.556753
$906$		−	4.45843i		−	0.148121i
$907$	43.8934			1.45746			0.728728	−	0.684804i	$-0.240112\pi$
$907$	43.8934			1.45746			0.728728	+	0.684804i	$0.240112\pi$
$908$	0.256417			0.00850948
$909$	7.67234			0.254476
$910$	−9.32829	+	5.94863i	−0.309230	+	0.197195i
$911$	−52.1840			−1.72893			−0.864466	−	0.502690i	$-0.832344\pi$
$911$	−52.1840			−1.72893			−0.864466	+	0.502690i	$0.832344\pi$
$912$		−	6.78451i		−	0.224658i
$913$	−7.49098	+	29.7172i	−0.247915	+	0.983496i
$914$	−7.55400			−0.249864
$915$	−8.80831			−0.291194
$916$			2.14418i			0.0708456i
$917$	−37.3541	+	23.8207i	−1.23354	+	0.786627i
$918$	9.72174			0.320865
$919$			41.1464i			1.35730i	0.734464	+	0.678648i	$0.237434\pi$
$919$			41.1464i			1.35730i	−0.734464	+	0.678648i	$0.762566\pi$
$920$	4.66271			0.153725
$921$			10.6341i			0.350405i
$922$		−	40.2789i		−	1.32651i
$923$	−36.5134			−1.20185
$924$	2.79011	−	0.926929i	0.0917880	−	0.0304937i
$925$	8.46051			0.278180
$926$			14.2971i			0.469832i
$927$		−	5.83595i		−	0.191678i
$928$	−14.7571			−0.484427
$929$			12.6292i			0.414352i	0.978304	+	0.207176i	$0.0664272\pi$
$929$			12.6292i			0.414352i	−0.978304	+	0.207176i	$0.933573\pi$
$930$	−3.13453			−0.102785
$931$	6.22579	−	13.3825i	0.204042	−	0.438592i
$932$		−	1.48316i		−	0.0485824i
$933$	14.9940			0.490883
$934$	20.9493			0.685482
$935$	24.2305	+	6.10792i	0.792422	+	0.199750i
$936$		−	9.76435i		−	0.319158i
$937$	−14.8853			−0.486282			−0.243141	−	0.969991i	$-0.578178\pi$
$937$	−14.8853			−0.486282			−0.243141	+	0.969991i	$0.578178\pi$
$938$	−20.2063	−	31.6863i	−0.659759	−	1.03459i
$939$	−11.6551			−0.380349
$940$	0.687057			0.0224093
$941$	30.1981			0.984431			0.492216	−	0.870473i	$-0.336187\pi$
$941$	30.1981			0.984431			0.492216	+	0.870473i	$0.336187\pi$
$942$			7.16366i			0.233405i
$943$	10.5661			0.344080
$944$		−	30.3598i		−	0.988128i
$945$	2.23077	−	1.42256i	0.0725669	−	0.0462758i
$946$	8.82744	−	35.0190i	0.287005	−	1.13857i
$947$	30.6695			0.996623			0.498312	−	0.866998i	$-0.333954\pi$
$947$	30.6695			0.996623			0.498312	+	0.866998i	$0.333954\pi$
$948$	1.93843			0.0629573
$949$	−12.3452			−0.400742
$950$		−	2.72071i		−	0.0882714i
$951$		−	27.6631i		−	0.897039i
$952$	32.2931	+	50.6401i	1.04663	+	1.64126i
$953$			21.4562i			0.695035i	0.937673	+	0.347518i	$0.112975\pi$
$953$			21.4562i			0.695035i	−0.937673	+	0.347518i	$0.887025\pi$
$954$		−	14.3225i		−	0.463709i
$955$			23.2532i			0.752457i
$956$			6.80034i			0.219939i
$957$	−6.38332	+	25.3230i	−0.206343	+	0.818578i
$958$			23.4467i			0.757529i
$959$	−12.1770	+	7.76524i	−0.393215	+	0.250753i
$960$	8.85355			0.285747
$961$	25.0988			0.809638
$962$		−	35.3789i		−	1.14066i
$963$			8.10169i			0.261073i
$964$	1.97500			0.0636104
$965$	4.14238			0.133348
$966$	4.45448	−	2.84061i	0.143320	−	0.0913952i
$967$		−	7.65175i		−	0.246064i	−0.992403	−	0.123032i	$-0.960738\pi$
$967$		−	7.65175i		−	0.246064i	0.992403	−	0.123032i	$-0.0392617\pi$
$968$	15.7107	−	29.1825i	0.504961	−	0.937962i
$969$			15.8864i			0.510344i
$970$		−	3.68789i		−	0.118411i
$971$		−	33.7929i		−	1.08447i	−0.840228	−	0.542233i	$-0.817579\pi$
$971$		−	33.7929i		−	1.08447i	0.840228	−	0.542233i	$-0.182421\pi$
$972$			0.335051i			0.0107468i
$973$	28.4610	−	18.1496i	0.912419	−	0.581848i
$974$			28.3218i			0.907489i
$975$		−	3.24076i		−	0.103787i
$976$	−28.3420			−0.907204
$977$	−61.1856			−1.95750			−0.978751	−	0.205052i	$-0.934264\pi$
$977$	−61.1856			−1.95750			−0.978751	+	0.205052i	$0.934264\pi$
$978$	−11.0426			−0.353104
$979$	42.4407	+	10.6983i	1.35641	+	0.341918i
$980$	2.12650	+	0.989290i	0.0679284	+	0.0316017i
$981$			3.24745i			0.103683i
$982$	28.5455			0.910924
$983$			29.7824i			0.949910i	0.880010	+	0.474955i	$0.157536\pi$
$983$			29.7824i			0.949910i	−0.880010	+	0.474955i	$0.842464\pi$
$984$	20.5717			0.655802
$985$	−2.74227			−0.0873760
$986$	−76.5493			−2.43783
$987$	4.57443	−	2.91711i	0.145606	−	0.0928525i
$988$	2.28949			0.0728383
$989$			13.0595i			0.415268i
$990$	1.04604	−	4.14973i	0.0332455	−	0.131887i
$991$	−15.6237			−0.496303			−0.248151	−	0.968721i	$-0.579823\pi$
$991$	−15.6237			−0.496303			−0.248151	+	0.968721i	$0.579823\pi$
$992$	4.55278			0.144551
$993$		−	9.71214i		−	0.308205i
$994$	−20.6812	−	32.4310i	−0.655968	−	1.02865i
$995$	3.96323			0.125643
$996$		−	3.09599i		−	0.0981001i
$997$	56.0089			1.77382			0.886909	−	0.461943i	$-0.152848\pi$
$997$	56.0089			1.77382			0.886909	+	0.461943i	$0.152848\pi$
$998$		−	29.7027i		−	0.940224i
$999$			8.46051i			0.267679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.i.d.76.12	yes	32
7.6	odd	2	inner	1155.2.i.d.76.22	yes	32
11.10	odd	2	inner	1155.2.i.d.76.21	yes	32
77.76	even	2	inner	1155.2.i.d.76.11	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.i.d.76.11	✓	32	77.76	even	2	inner
1155.2.i.d.76.12	yes	32	1.1	even	1	trivial
1155.2.i.d.76.21	yes	32	11.10	odd	2	inner
1155.2.i.d.76.22	yes	32	7.6	odd	2	inner

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:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.i (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.29033i q^{2} +1.00000i q^{3} +0.335051 q^{4} +1.00000i q^{5} -1.29033 q^{6} +(2.23077 - 1.42256i) q^{7} +3.01298i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.29033i q^{2} +1.00000i q^{3} +0.335051 q^{4} +1.00000i q^{5} -1.29033 q^{6} +(2.23077 - 1.42256i) q^{7} +3.01298i q^{8} -1.00000 q^{9} -1.29033 q^{10} +(0.810680 - 3.21602i) q^{11} +0.335051i q^{12} +3.24076 q^{13} +(1.83557 + 2.87843i) q^{14} -1.00000 q^{15} -3.21764 q^{16} +7.53431 q^{17} -1.29033i q^{18} +2.10854 q^{19} +0.335051i q^{20} +(1.42256 + 2.23077i) q^{21} +(4.14973 + 1.04604i) q^{22} -1.54754 q^{23} -3.01298 q^{24} -1.00000 q^{25} +4.18165i q^{26} -1.00000i q^{27} +(0.747420 - 0.476629i) q^{28} +7.87403i q^{29} -1.29033i q^{30} -2.42925i q^{31} +1.87415i q^{32} +(3.21602 + 0.810680i) q^{33} +9.72174i q^{34} +(1.42256 + 2.23077i) q^{35} -0.335051 q^{36} -8.46051 q^{37} +2.72071i q^{38} +3.24076i q^{39} -3.01298 q^{40} -6.82769 q^{41} +(-2.87843 + 1.83557i) q^{42} -8.43887i q^{43} +(0.271619 - 1.07753i) q^{44} -1.00000i q^{45} -1.99683i q^{46} -2.05061i q^{47} -3.21764i q^{48} +(2.95266 - 6.34679i) q^{49} -1.29033i q^{50} +7.53431i q^{51} +1.08582 q^{52} +11.0999 q^{53} +1.29033 q^{54} +(3.21602 + 0.810680i) q^{55} +(4.28614 + 6.72127i) q^{56} +2.10854i q^{57} -10.1601 q^{58} +9.43543i q^{59} -0.335051 q^{60} +8.80831 q^{61} +3.13453 q^{62} +(-2.23077 + 1.42256i) q^{63} -8.85355 q^{64} +3.24076i q^{65} +(-1.04604 + 4.14973i) q^{66} -11.0082 q^{67} +2.52437 q^{68} -1.54754i q^{69} +(-2.87843 + 1.83557i) q^{70} -11.2669 q^{71} -3.01298i q^{72} -3.80935 q^{73} -10.9168i q^{74} -1.00000i q^{75} +0.706466 q^{76} +(-2.76654 - 8.32744i) q^{77} -4.18165 q^{78} -5.78548i q^{79} -3.21764i q^{80} +1.00000 q^{81} -8.80996i q^{82} -9.24036 q^{83} +(0.476629 + 0.747420i) q^{84} +7.53431i q^{85} +10.8889 q^{86} -7.87403 q^{87} +(9.68982 + 2.44257i) q^{88} +13.1967i q^{89} +1.29033 q^{90} +(7.22938 - 4.61017i) q^{91} -0.518504 q^{92} +2.42925 q^{93} +2.64596 q^{94} +2.10854i q^{95} -1.87415 q^{96} +2.85810i q^{97} +(8.18945 + 3.80990i) q^{98} +(-0.810680 + 3.21602i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 36 q^{4} - 32 q^{9}+O(q^{10}) \) 32 * q - 36 * q^4 - 32 * q^9	\( 32 q - 36 q^{4} - 32 q^{9} - 8 q^{11} - 28 q^{14} - 32 q^{15} + 44 q^{16} - 12 q^{22} + 4 q^{23} - 32 q^{25} + 36 q^{36} - 16 q^{37} + 8 q^{42} + 56 q^{44} + 16 q^{49} - 20 q^{53} + 52 q^{56} - 48 q^{58} + 36 q^{60} - 156 q^{64} - 72 q^{67} + 8 q^{70} + 48 q^{71} - 20 q^{77} - 8 q^{78} + 32 q^{81} + 56 q^{86} + 4 q^{88} - 80 q^{91} + 64 q^{92} + 32 q^{93} + 8 q^{99}+O(q^{100}) \) 32 * q - 36 * q^4 - 32 * q^9 - 8 * q^11 - 28 * q^14 - 32 * q^15 + 44 * q^16 - 12 * q^22 + 4 * q^23 - 32 * q^25 + 36 * q^36 - 16 * q^37 + 8 * q^42 + 56 * q^44 + 16 * q^49 - 20 * q^53 + 52 * q^56 - 48 * q^58 + 36 * q^60 - 156 * q^64 - 72 * q^67 + 8 * q^70 + 48 * q^71 - 20 * q^77 - 8 * q^78 + 32 * q^81 + 56 * q^86 + 4 * q^88 - 80 * q^91 + 64 * q^92 + 32 * q^93 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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