LMFDB - Embedded newform 1205.2.b.c.724.38

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(724,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1205.724");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.b (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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$46$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			724.38
Character	$\chi$	$=$	1205.724
Dual form			1205.2.b.c.724.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.84209i q^{2} -1.69681i q^{3} -1.39329 q^{4} +(1.66065 - 1.49741i) q^{5} +3.12567 q^{6} -1.54055i q^{7} +1.11761i q^{8} +0.120844 q^{9} +O(q^{10})$	\(q+1.84209i q^{2} -1.69681i q^{3} -1.39329 q^{4} +(1.66065 - 1.49741i) q^{5} +3.12567 q^{6} -1.54055i q^{7} +1.11761i q^{8} +0.120844 q^{9} +(2.75836 + 3.05907i) q^{10} +2.53578 q^{11} +2.36415i q^{12} +6.36889i q^{13} +2.83783 q^{14} +(-2.54081 - 2.81781i) q^{15} -4.84532 q^{16} +3.54355i q^{17} +0.222605i q^{18} -0.713569 q^{19} +(-2.31377 + 2.08633i) q^{20} -2.61402 q^{21} +4.67113i q^{22} +1.66453i q^{23} +1.89637 q^{24} +(0.515535 - 4.97335i) q^{25} -11.7321 q^{26} -5.29547i q^{27} +2.14644i q^{28} +8.23983 q^{29} +(5.19065 - 4.68041i) q^{30} +10.5697 q^{31} -6.69029i q^{32} -4.30273i q^{33} -6.52753 q^{34} +(-2.30683 - 2.55832i) q^{35} -0.168370 q^{36} +0.496832i q^{37} -1.31446i q^{38} +10.8068 q^{39} +(1.67352 + 1.85597i) q^{40} -8.92984 q^{41} -4.81525i q^{42} +1.50676i q^{43} -3.53308 q^{44} +(0.200679 - 0.180952i) q^{45} -3.06622 q^{46} -6.94849i q^{47} +8.22158i q^{48} +4.62670 q^{49} +(9.16135 + 0.949660i) q^{50} +6.01272 q^{51} -8.87372i q^{52} -9.87593i q^{53} +9.75473 q^{54} +(4.21105 - 3.79710i) q^{55} +1.72174 q^{56} +1.21079i q^{57} +15.1785i q^{58} +10.1744 q^{59} +(3.54009 + 3.92603i) q^{60} -9.13781 q^{61} +19.4703i q^{62} -0.186166i q^{63} +2.63346 q^{64} +(9.53684 + 10.5765i) q^{65} +7.92601 q^{66} +1.85057i q^{67} -4.93720i q^{68} +2.82439 q^{69} +(4.71265 - 4.24939i) q^{70} -9.47485 q^{71} +0.135056i q^{72} -8.88186i q^{73} -0.915209 q^{74} +(-8.43882 - 0.874763i) q^{75} +0.994210 q^{76} -3.90650i q^{77} +19.9071i q^{78} +6.12948 q^{79} +(-8.04640 + 7.25543i) q^{80} -8.62287 q^{81} -16.4496i q^{82} -0.835537i q^{83} +3.64209 q^{84} +(5.30614 + 5.88461i) q^{85} -2.77558 q^{86} -13.9814i q^{87} +2.83402i q^{88} -2.27480 q^{89} +(0.333330 + 0.369669i) q^{90} +9.81161 q^{91} -2.31918i q^{92} -17.9348i q^{93} +12.7997 q^{94} +(-1.18499 + 1.06850i) q^{95} -11.3521 q^{96} +7.56572i q^{97} +8.52280i q^{98} +0.306433 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	$ 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) $ 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1205\mathbb{Z}\right)^\times$.

$n$	$242$	$971$
$\chi(n)$	$-1$	$1$

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 $

$2$			1.84209i			1.30255i	0.758840	+	0.651277i	$0.225766\pi$
$2$			1.84209i			1.30255i	−0.758840	+	0.651277i	$0.774234\pi$
$3$		−	1.69681i		−	0.979652i	−0.871820	−	0.489826i	$-0.837060\pi$
$3$		−	1.69681i		−	0.979652i	0.871820	−	0.489826i	$-0.162940\pi$
$4$	−1.39329			−0.696645
$5$	1.66065	−	1.49741i	0.742666	−	0.669662i
$5$	1.66065	−	1.49741i	0.742666	−	0.669662i
$6$	3.12567			1.27605
$7$		−	1.54055i		−	0.582274i	−0.956681	−	0.291137i	$-0.905967\pi$
$7$		−	1.54055i		−	0.582274i	0.956681	−	0.291137i	$-0.0940335\pi$
$8$			1.11761i			0.395136i
$9$	0.120844			0.0402812
$10$	2.75836	+	3.05907i	0.872270	+	0.967363i
$11$	2.53578			0.764566			0.382283	−	0.924045i	$-0.375138\pi$
$11$	2.53578			0.764566			0.382283	+	0.924045i	$0.375138\pi$
$12$			2.36415i			0.682470i
$13$			6.36889i			1.76641i	0.468984	+	0.883207i	$0.344620\pi$
$13$			6.36889i			1.76641i	−0.468984	+	0.883207i	$0.655380\pi$
$14$	2.83783			0.758442
$15$	−2.54081	−	2.81781i	−0.656036	−	0.727555i
$16$	−4.84532			−1.21133
$17$			3.54355i			0.859437i	0.902963	+	0.429719i	$0.141387\pi$
$17$			3.54355i			0.859437i	−0.902963	+	0.429719i	$0.858613\pi$
$18$			0.222605i			0.0524684i
$19$	−0.713569			−0.163704			−0.0818520	−	0.996644i	$-0.526083\pi$
$19$	−0.713569			−0.163704			−0.0818520	+	0.996644i	$0.526083\pi$
$20$	−2.31377	+	2.08633i	−0.517375	+	0.466517i
$21$	−2.61402			−0.570426
$22$			4.67113i			0.995889i
$23$			1.66453i			0.347079i	0.984827	+	0.173540i	$0.0555204\pi$
$23$			1.66453i			0.347079i	−0.984827	+	0.173540i	$0.944480\pi$
$24$	1.89637			0.387095
$25$	0.515535	−	4.97335i	0.103107	−	0.994670i
$26$	−11.7321			−2.30085
$27$		−	5.29547i		−	1.01911i
$28$			2.14644i			0.405638i
$29$	8.23983			1.53010			0.765049	−	0.643972i	$-0.222715\pi$
$29$	8.23983			1.53010			0.765049	+	0.643972i	$0.222715\pi$
$30$	5.19065	−	4.68041i	0.947679	−	0.854521i
$31$	10.5697			1.89838			0.949188	−	0.314711i	$-0.101908\pi$
$31$	10.5697			1.89838			0.949188	+	0.314711i	$0.101908\pi$
$32$		−	6.69029i		−	1.18269i
$33$		−	4.30273i		−	0.749009i
$34$	−6.52753			−1.11946
$35$	−2.30683	−	2.55832i	−0.389926	−	0.432435i
$36$	−0.168370			−0.0280617
$37$			0.496832i			0.0816787i	0.999166	+	0.0408393i	$0.0130032\pi$
$37$			0.496832i			0.0816787i	−0.999166	+	0.0408393i	$0.986997\pi$
$38$		−	1.31446i		−	0.213233i
$39$	10.8068			1.73047
$40$	1.67352	+	1.85597i	0.264607	+	0.293454i
$41$	−8.92984			−1.39461			−0.697303	−	0.716776i	$-0.745617\pi$
$41$	−8.92984			−1.39461			−0.697303	+	0.716776i	$0.745617\pi$
$42$		−	4.81525i		−	0.743010i
$43$			1.50676i			0.229778i	0.993378	+	0.114889i	$0.0366513\pi$
$43$			1.50676i			0.229778i	−0.993378	+	0.114889i	$0.963349\pi$
$44$	−3.53308			−0.532632
$45$	0.200679	−	0.180952i	0.0299155	−	0.0269748i
$46$	−3.06622			−0.452089
$47$		−	6.94849i		−	1.01354i	−0.862081	−	0.506771i	$-0.830839\pi$
$47$		−	6.94849i		−	1.01354i	0.862081	−	0.506771i	$-0.169161\pi$
$48$			8.22158i			1.18668i
$49$	4.62670			0.660958
$50$	9.16135	+	0.949660i	1.29561	+	0.134302i
$51$	6.01272			0.841950
$52$		−	8.87372i		−	1.23056i
$53$		−	9.87593i		−	1.35656i	−0.734802	−	0.678281i	$-0.762725\pi$
$53$		−	9.87593i		−	1.35656i	0.734802	−	0.678281i	$-0.237275\pi$
$54$	9.75473			1.32745
$55$	4.21105	−	3.79710i	0.567818	−	0.512001i
$56$	1.72174			0.230077
$57$			1.21079i			0.160373i
$58$			15.1785i			1.99303i
$59$	10.1744			1.32459			0.662296	−	0.749242i	$-0.269582\pi$
$59$	10.1744			1.32459			0.662296	+	0.749242i	$0.269582\pi$
$60$	3.54009	+	3.92603i	0.457024	+	0.506848i
$61$	−9.13781			−1.16998			−0.584988	−	0.811042i	$-0.698901\pi$
$61$	−9.13781			−1.16998			−0.584988	+	0.811042i	$0.698901\pi$
$62$			19.4703i			2.47273i
$63$		−	0.186166i		−	0.0234547i
$64$	2.63346			0.329183
$65$	9.53684	+	10.5765i	1.18290	+	1.31186i
$66$	7.92601			0.975625
$67$			1.85057i			0.226083i	0.993590	+	0.113041i	$0.0360593\pi$
$67$			1.85057i			0.226083i	−0.993590	+	0.113041i	$0.963941\pi$
$68$		−	4.93720i		−	0.598723i
$69$	2.82439			0.340017
$70$	4.71265	−	4.24939i	0.563270	−	0.507900i
$71$	−9.47485			−1.12446			−0.562229	−	0.826981i	$-0.690056\pi$
$71$	−9.47485			−1.12446			−0.562229	+	0.826981i	$0.690056\pi$
$72$			0.135056i			0.0159165i
$73$		−	8.88186i		−	1.03954i	−0.854305	−	0.519771i	$-0.826017\pi$
$73$		−	8.88186i		−	1.03954i	0.854305	−	0.519771i	$-0.173983\pi$
$74$	−0.915209			−0.106391
$75$	−8.43882	−	0.874763i	−0.974431	−	0.101009i
$76$	0.994210			0.114044
$77$		−	3.90650i		−	0.445187i
$78$			19.9071i			2.25403i
$79$	6.12948			0.689621			0.344810	−	0.938672i	$-0.387943\pi$
$79$	6.12948			0.689621			0.344810	+	0.938672i	$0.387943\pi$
$80$	−8.04640	+	7.25543i	−0.899615	+	0.811181i
$81$	−8.62287			−0.958096
$82$		−	16.4496i		−	1.81655i
$83$		−	0.835537i		−	0.0917122i	−0.998948	−	0.0458561i	$-0.985398\pi$
$83$		−	0.835537i		−	0.0917122i	0.998948	−	0.0458561i	$-0.0146016\pi$
$84$	3.64209			0.397384
$85$	5.30614	+	5.88461i	0.575532	+	0.638275i
$86$	−2.77558			−0.299299
$87$		−	13.9814i		−	1.49896i
$88$			2.83402i			0.302107i
$89$	−2.27480			−0.241129			−0.120564	−	0.992706i	$-0.538470\pi$
$89$	−2.27480			−0.241129			−0.120564	+	0.992706i	$0.538470\pi$
$90$	0.333330	+	0.369669i	0.0351361	+	0.0389665i
$91$	9.81161			1.02854
$92$		−	2.31918i		−	0.241791i
$93$		−	17.9348i		−	1.85975i
$94$	12.7997			1.32019
$95$	−1.18499	+	1.06850i	−0.121577	+	0.109626i
$96$	−11.3521			−1.15862
$97$			7.56572i			0.768182i	0.923295	+	0.384091i	$0.125485\pi$
$97$			7.56572i			0.768182i	−0.923295	+	0.384091i	$0.874515\pi$
$98$			8.52280i			0.860933i
$99$	0.306433			0.0307976
$100$	−0.718290	+	6.92932i	−0.0718290	+	0.692932i
$101$	−16.9324			−1.68483			−0.842417	−	0.538826i	$-0.818868\pi$
$101$	−16.9324			−1.68483			−0.842417	+	0.538826i	$0.818868\pi$
$102$			11.0760i			1.09668i
$103$			2.83252i			0.279096i	0.990215	+	0.139548i	$0.0445650\pi$
$103$			2.83252i			0.279096i	−0.990215	+	0.139548i	$0.955435\pi$
$104$	−7.11795			−0.697973
$105$	−4.34098	+	3.91425i	−0.423636	+	0.381992i
$106$	18.1923			1.76700
$107$		−	4.86488i		−	0.470306i	−0.971958	−	0.235153i	$-0.924441\pi$
$107$		−	4.86488i		−	0.470306i	0.971958	−	0.235153i	$-0.0755591\pi$
$108$			7.37813i			0.709961i
$109$	−10.2870			−0.985317			−0.492658	−	0.870223i	$-0.663975\pi$
$109$	−10.2870			−0.985317			−0.492658	+	0.870223i	$0.663975\pi$
$110$	6.99459	+	7.75713i	0.666908	+	0.739613i
$111$	0.843029			0.0800167
$112$			7.46447i			0.705326i
$113$			12.6981i			1.19454i	0.802041	+	0.597270i	$0.203748\pi$
$113$			12.6981i			1.19454i	−0.802041	+	0.597270i	$0.796252\pi$
$114$	−2.23038			−0.208894
$115$	2.49249	+	2.76421i	0.232426	+	0.257764i
$116$	−11.4805			−1.06594
$117$			0.769640i			0.0711532i
$118$			18.7421i			1.72535i
$119$	5.45902			0.500427
$120$	3.14922	−	2.83965i	0.287483	−	0.259223i
$121$	−4.56982			−0.415438
$122$		−	16.8326i		−	1.52396i
$123$			15.1522i			1.36623i
$124$	−14.7267			−1.32249
$125$	−6.59102	−	9.03098i	−0.589518	−	0.807755i
$126$	0.342934			0.0305510
$127$		−	1.17595i		−	0.104349i	−0.998638	−	0.0521743i	$-0.983385\pi$
$127$		−	1.17595i		−	0.104349i	0.998638	−	0.0521743i	$-0.0166151\pi$
$128$		−	8.52951i		−	0.753909i
$129$	2.55668			0.225103
$130$	−19.4829	+	17.5677i	−1.70876	+	1.54079i
$131$	18.7573			1.63884			0.819418	−	0.573196i	$-0.194297\pi$
$131$	18.7573			1.63884			0.819418	+	0.573196i	$0.194297\pi$
$132$			5.99496i			0.521794i
$133$			1.09929i			0.0953205i
$134$	−3.40891			−0.294485
$135$	−7.92948	−	8.79394i	−0.682461	−	0.756862i
$136$	−3.96031			−0.339594
$137$			5.04016i			0.430610i	0.976547	+	0.215305i	$0.0690746\pi$
$137$			5.04016i			0.430610i	−0.976547	+	0.215305i	$0.930925\pi$
$138$			5.20278i			0.442890i
$139$	0.226430			0.0192056			0.00960278	−	0.999954i	$-0.496943\pi$
$139$	0.226430			0.0192056			0.00960278	+	0.999954i	$0.496943\pi$
$140$	3.21409	+	3.56448i	0.271640	+	0.301254i
$141$	−11.7902			−0.992918
$142$		−	17.4535i		−	1.46467i
$143$			16.1501i			1.35054i
$144$	−0.585526			−0.0487938
$145$	13.6835	−	12.3384i	1.13635	−	1.02465i
$146$	16.3612			1.35406
$147$		−	7.85063i		−	0.647509i
$148$		−	0.692232i		−	0.0569011i
$149$	4.00539			0.328134			0.164067	−	0.986449i	$-0.447539\pi$
$149$	4.00539			0.328134			0.164067	+	0.986449i	$0.447539\pi$
$150$	1.61139	−	15.5451i	0.131570	−	1.26925i
$151$	−5.73080			−0.466366			−0.233183	−	0.972433i	$-0.574914\pi$
$151$	−5.73080			−0.466366			−0.233183	+	0.972433i	$0.574914\pi$
$152$		−	0.797494i		−	0.0646853i
$153$			0.428215i			0.0346191i
$154$	7.19612			0.579880
$155$	17.5526	−	15.8272i	1.40986	−	1.27127i
$156$	−15.0570			−1.20552
$157$		−	4.02238i		−	0.321021i	−0.987034	−	0.160510i	$-0.948686\pi$
$157$		−	4.02238i		−	0.321021i	0.987034	−	0.160510i	$-0.0513140\pi$
$158$			11.2911i			0.898268i
$159$	−16.7575			−1.32896
$160$	−10.0181	−	11.1102i	−0.792000	−	0.878342i
$161$	2.56430			0.202095
$162$		−	15.8841i		−	1.24797i
$163$		−	2.51003i		−	0.196601i	−0.995157	−	0.0983004i	$-0.968659\pi$
$163$		−	2.51003i		−	0.196601i	0.995157	−	0.0983004i	$-0.0313406\pi$
$164$	12.4419			0.971546
$165$	−6.44295	−	7.14534i	−0.501583	−	0.556264i
$166$	1.53913			0.119460
$167$			25.3075i			1.95835i	0.203008	+	0.979177i	$0.434928\pi$
$167$			25.3075i			1.95835i	−0.203008	+	0.979177i	$0.565072\pi$
$168$		−	2.92146i		−	0.225395i
$169$	−27.5628			−2.12022
$170$	−10.8400	+	9.77438i	−0.831387	+	0.749661i
$171$	−0.0862302			−0.00659419
$172$		−	2.09935i		−	0.160074i
$173$			19.0394i			1.44754i	0.690043	+	0.723769i	$0.257592\pi$
$173$			19.0394i			1.44754i	−0.690043	+	0.723769i	$0.742408\pi$
$174$	25.7550			1.95248
$175$	−7.66170	−	0.794207i	−0.579170	−	0.0600364i
$176$	−12.2867			−0.926143
$177$		−	17.2640i		−	1.29764i
$178$		−	4.19039i		−	0.314083i
$179$	−12.3757			−0.925007			−0.462503	−	0.886618i	$-0.653049\pi$
$179$	−12.3757			−0.925007			−0.462503	+	0.886618i	$0.653049\pi$
$180$	−0.279604	+	0.252119i	−0.0208405	+	0.0187918i
$181$	5.62774			0.418307			0.209153	−	0.977883i	$-0.432929\pi$
$181$	5.62774			0.418307			0.209153	+	0.977883i	$0.432929\pi$
$182$			18.0738i			1.33972i
$183$			15.5051i			1.14617i
$184$	−1.86030			−0.137143
$185$	0.743961	+	0.825066i	0.0546971	+	0.0606600i
$186$	33.0374			2.42242
$187$			8.98566i			0.657097i
$188$			9.68127i			0.706079i
$189$	−8.15794			−0.593403
$190$	−1.96828	−	2.18286i	−0.142794	−	0.158361i
$191$	−16.0108			−1.15850			−0.579251	−	0.815149i	$-0.696655\pi$
$191$	−16.0108			−1.15850			−0.579251	+	0.815149i	$0.696655\pi$
$192$		−	4.46848i		−	0.322485i
$193$		−	6.92078i		−	0.498169i	−0.968482	−	0.249084i	$-0.919870\pi$
$193$		−	6.92078i		−	0.498169i	0.968482	−	0.249084i	$-0.0801296\pi$
$194$	−13.9367			−1.00060
$195$	17.9463	−	16.1822i	1.28516	−	1.15883i
$196$	−6.44634			−0.460453
$197$		−	4.08208i		−	0.290836i	−0.989370	−	0.145418i	$-0.953547\pi$
$197$		−	4.08208i		−	0.290836i	0.989370	−	0.145418i	$-0.0464527\pi$
$198$			0.564476i			0.0401156i
$199$	−7.24353			−0.513481			−0.256740	−	0.966480i	$-0.582648\pi$
$199$	−7.24353			−0.513481			−0.256740	+	0.966480i	$0.582648\pi$
$200$	5.55828	+	0.576168i	0.393030	+	0.0407412i
$201$	3.14006			0.221483
$202$		−	31.1909i		−	2.19459i
$203$		−	12.6939i		−	0.890935i
$204$	−8.37747			−0.586540
$205$	−14.8294	+	13.3716i	−1.03573	+	0.933915i
$206$	−5.21775			−0.363538
$207$			0.201148i			0.0139808i
$208$		−	30.8593i		−	2.13971i
$209$	−1.80945			−0.125163
$210$	−7.21040	−	7.99646i	−0.497565	−	0.551809i
$211$	0.0986890			0.00679403			0.00339701	−	0.999994i	$-0.498919\pi$
$211$	0.0986890			0.00679403			0.00339701	+	0.999994i	$0.498919\pi$
$212$			13.7600i			0.945043i
$213$			16.0770i			1.10158i
$214$	8.96154			0.612598
$215$	2.25623	+	2.50220i	0.153874	+	0.170649i
$216$	5.91828			0.402688
$217$		−	16.2832i		−	1.10537i
$218$		−	18.9496i		−	1.28343i
$219$	−15.0708			−1.01839
$220$	−5.86722	+	5.29046i	−0.395568	+	0.356683i
$221$	−22.5685			−1.51812
$222$			1.55293i			0.104226i
$223$		−	15.5911i		−	1.04406i	−0.852928	−	0.522028i	$-0.825176\pi$
$223$		−	15.5911i		−	1.04406i	0.852928	−	0.522028i	$-0.174824\pi$
$224$	−10.3067			−0.688647
$225$	0.0622990	−	0.600997i	0.00415327	−	0.0400665i
$226$	−23.3911			−1.55595
$227$			24.7410i			1.64212i	0.570843	+	0.821059i	$0.306616\pi$
$227$			24.7410i			1.64212i	−0.570843	+	0.821059i	$0.693384\pi$
$228$		−	1.68698i		−	0.111723i
$229$	21.0262			1.38945			0.694725	−	0.719275i	$-0.255526\pi$
$229$	21.0262			1.38945			0.694725	+	0.719275i	$0.255526\pi$
$230$	−5.09192	+	4.59138i	−0.335751	+	0.302747i
$231$	−6.62858			−0.436128
$232$			9.20893i			0.604596i
$233$			8.57165i			0.561548i	0.959774	+	0.280774i	$0.0905911\pi$
$233$			8.57165i			0.561548i	−0.959774	+	0.280774i	$0.909409\pi$
$234$	−1.41774			−0.0926809
$235$	−10.4047	−	11.5390i	−0.678730	−	0.752723i
$236$	−14.1759			−0.922771
$237$		−	10.4006i		−	0.675589i
$238$			10.0560i			0.651833i
$239$	−22.7072			−1.46880			−0.734402	−	0.678715i	$-0.762537\pi$
$239$	−22.7072			−1.46880			−0.734402	+	0.678715i	$0.762537\pi$
$240$	12.3111	+	13.6532i	0.794676	+	0.881310i
$241$	1.00000			0.0644157
$241$	1.00000			0.0644157
$242$		−	8.41801i		−	0.541130i
$243$		−	1.25507i		−	0.0805127i
$244$	12.7316			0.815059
$245$	7.68335	−	6.92807i	0.490871	−	0.442618i
$246$	−27.9117			−1.77959
$247$		−	4.54465i		−	0.289169i
$248$			11.8128i			0.750115i
$249$	−1.41775			−0.0898460
$250$	16.6359	−	12.1412i	1.05214	−	0.767879i
$251$	−12.9356			−0.816489			−0.408244	−	0.912873i	$-0.633859\pi$
$251$	−12.9356			−0.816489			−0.408244	+	0.912873i	$0.633859\pi$
$252$			0.259383i			0.0163396i
$253$			4.22089i			0.265365i
$254$	2.16620			0.135920
$255$	9.98504	−	9.00350i	0.625288	−	0.563821i
$256$	20.9790			1.31119
$257$		−	10.8510i		−	0.676865i	−0.940991	−	0.338432i	$-0.890103\pi$
$257$		−	10.8510i		−	0.676865i	0.940991	−	0.338432i	$-0.109897\pi$
$258$			4.70963i			0.293209i
$259$	0.765395			0.0475593
$260$	−13.2876	−	14.7362i	−0.824061	−	0.913898i
$261$	0.995730			0.0616341
$262$			34.5527i			2.13467i
$263$		−	14.1032i		−	0.869638i	−0.900518	−	0.434819i	$-0.856812\pi$
$263$		−	14.1032i		−	0.869638i	0.900518	−	0.434819i	$-0.143188\pi$
$264$	4.80878			0.295960
$265$	−14.7883	−	16.4005i	−0.908438	−	1.00747i
$266$	−2.02499			−0.124160
$267$			3.85991i			0.236222i
$268$		−	2.57838i		−	0.157500i
$269$	7.55668			0.460739			0.230370	−	0.973103i	$-0.426007\pi$
$269$	7.55668			0.460739			0.230370	+	0.973103i	$0.426007\pi$
$270$	16.1992	−	14.6068i	0.985853	−	0.888942i
$271$	20.9578			1.27309			0.636546	−	0.771238i	$-0.280362\pi$
$271$	20.9578			1.27309			0.636546	+	0.771238i	$0.280362\pi$
$272$		−	17.1696i		−	1.04106i
$273$		−	16.6484i		−	1.00761i
$274$	−9.28443			−0.560893
$275$	1.30728	−	12.6113i	0.0788321	−	0.760492i
$276$	−3.93520			−0.236871
$277$		−	14.9632i		−	0.899052i	−0.893267	−	0.449526i	$-0.851593\pi$
$277$		−	14.9632i		−	0.899052i	0.893267	−	0.449526i	$-0.148407\pi$
$278$			0.417105i			0.0250163i
$279$	1.27728			0.0764688
$280$	2.85921	−	2.57815i	0.170870	−	0.154074i
$281$	30.7490			1.83433			0.917165	−	0.398507i	$-0.130471\pi$
$281$	30.7490			1.83433			0.917165	+	0.398507i	$0.130471\pi$
$282$		−	21.7187i		−	1.29333i
$283$		−	4.06104i		−	0.241404i	−0.992689	−	0.120702i	$-0.961485\pi$
$283$		−	4.06104i		−	0.241404i	0.992689	−	0.120702i	$-0.0385145\pi$
$284$	13.2012			0.783349
$285$	1.81305	+	2.01070i	0.107396	+	0.119104i
$286$	−29.7499			−1.75915
$287$			13.7569i			0.812043i
$288$		−	0.808478i		−	0.0476400i
$289$	4.44326			0.261368
$290$	22.7284	+	25.2062i	1.33466	+	1.48016i
$291$	12.8376			0.752551
$292$			12.3750i			0.724193i
$293$			18.7249i			1.09392i	0.837158	+	0.546961i	$0.184215\pi$
$293$			18.7249i			1.09392i	−0.837158	+	0.546961i	$0.815785\pi$
$294$	14.4615			0.843415
$295$	16.8961	−	15.2352i	0.983730	−	0.887029i
$296$	−0.555266			−0.0322742
$297$		−	13.4282i		−	0.779180i
$298$			7.37828i			0.427412i
$299$	−10.6012			−0.613085
$300$	11.7577	+	1.21880i	0.678833	+	0.0703674i
$301$	2.32124			0.133794
$302$		−	10.5566i		−	0.607467i
$303$			28.7310i			1.65055i
$304$	3.45747			0.198300
$305$	−15.1747	+	13.6830i	−0.868902	+	0.783488i
$306$	−0.788810			−0.0450933
$307$		−	2.41046i		−	0.137572i	−0.997631	−	0.0687860i	$-0.978087\pi$
$307$		−	2.41046i		−	0.137572i	0.997631	−	0.0687860i	$-0.0219126\pi$
$308$			5.44289i			0.310137i
$309$	4.80624			0.273418
$310$	29.1550	+	32.3335i	1.65590	+	1.83642i
$311$	−16.0513			−0.910183			−0.455092	−	0.890445i	$-0.650394\pi$
$311$	−16.0513			−0.910183			−0.455092	+	0.890445i	$0.650394\pi$
$312$			12.0778i			0.683771i
$313$		−	6.01435i		−	0.339951i	−0.985448	−	0.169976i	$-0.945631\pi$
$313$		−	6.01435i		−	0.339951i	0.985448	−	0.169976i	$-0.0543689\pi$
$314$	7.40958			0.418147
$315$	−0.278766	−	0.309156i	−0.0157067	−	0.0174190i
$316$	−8.54015			−0.480421
$317$			27.5411i			1.54686i	0.633881	+	0.773430i	$0.281461\pi$
$317$			27.5411i			1.54686i	−0.633881	+	0.773430i	$0.718539\pi$
$318$		−	30.8689i		−	1.73104i
$319$	20.8944			1.16986
$320$	4.37327	−	3.94337i	0.244473	−	0.220441i
$321$	−8.25476			−0.460736
$322$			4.72366i			0.263240i
$323$		−	2.52857i		−	0.140693i
$324$	12.0142			0.667453
$325$	31.6747	+	3.28338i	1.75700	+	0.182129i
$326$	4.62370			0.256083
$327$			17.4551i			0.965268i
$328$		−	9.98010i		−	0.551059i
$329$	−10.7045			−0.590158
$330$	13.1624	−	11.8685i	0.724564	−	0.653338i
$331$	0.248029			0.0136329			0.00681645	−	0.999977i	$-0.497830\pi$
$331$	0.248029			0.0136329			0.00681645	+	0.999977i	$0.497830\pi$
$332$			1.16415i			0.0638909i
$333$			0.0600390i			0.00329011i
$334$	−46.6187			−2.55086
$335$	2.77106	+	3.07315i	0.151399	+	0.167904i
$336$	12.6658			0.690974
$337$		−	21.1908i		−	1.15433i	−0.816626	−	0.577167i	$-0.804158\pi$
$337$		−	21.1908i		−	1.15433i	0.816626	−	0.577167i	$-0.195842\pi$
$338$		−	50.7731i		−	2.76169i
$339$	21.5463			1.17023
$340$	−7.39300	−	8.19897i	−0.400942	−	0.444651i
$341$	26.8024			1.45143
$342$		−	0.158844i		−	0.00858929i
$343$		−	17.9115i		−	0.967132i
$344$	−1.68397			−0.0907936
$345$	4.69033	−	4.22927i	0.252519	−	0.227696i
$346$	−35.0722			−1.88549
$347$			17.9531i			0.963775i	0.876233	+	0.481887i	$0.160049\pi$
$347$			17.9531i			0.963775i	−0.876233	+	0.481887i	$0.839951\pi$
$348$			19.4802i			1.04425i
$349$	−7.68481			−0.411358			−0.205679	−	0.978619i	$-0.565940\pi$
$349$	−7.68481			−0.411358			−0.205679	+	0.978619i	$0.565940\pi$
$350$	1.46300	−	14.1135i	0.0782006	−	0.754400i
$351$	33.7263			1.80018
$352$		−	16.9651i		−	0.904243i
$353$		−	25.0052i		−	1.33089i	−0.746446	−	0.665446i	$-0.768241\pi$
$353$		−	25.0052i		−	1.33089i	0.746446	−	0.665446i	$-0.231759\pi$
$354$	31.8018			1.69025
$355$	−15.7344	+	14.1877i	−0.835097	+	0.753006i
$356$	3.16946			0.167981
$357$		−	9.26291i		−	0.490245i
$358$		−	22.7972i		−	1.20487i
$359$	−7.21328			−0.380703			−0.190351	−	0.981716i	$-0.560963\pi$
$359$	−7.21328			−0.380703			−0.190351	+	0.981716i	$0.560963\pi$
$360$	0.202234	+	0.224281i	0.0106587	+	0.0118207i
$361$	−18.4908			−0.973201
$362$			10.3668i			0.544867i
$363$			7.75410i			0.406985i
$364$	−13.6704			−0.716525
$365$	−13.2998	−	14.7497i	−0.696142	−	0.772033i
$366$	−28.5618			−1.49295
$367$			10.0531i			0.524767i	0.964964	+	0.262383i	$0.0845085\pi$
$367$			10.0531i			0.524767i	−0.964964	+	0.262383i	$0.915491\pi$
$368$		−	8.06520i		−	0.420428i
$369$	−1.07911			−0.0561764
$370$	−1.51984	+	1.37044i	−0.0790129	+	0.0712459i
$371$	−15.2144			−0.789891
$372$			24.9883i			1.29558i
$373$		−	31.7029i		−	1.64151i	−0.571279	−	0.820756i	$-0.693553\pi$
$373$		−	31.7029i		−	1.64151i	0.571279	−	0.820756i	$-0.306447\pi$
$374$	−16.5524			−0.855904
$375$	−15.3238	+	11.1837i	−0.791319	+	0.577523i
$376$	7.76571			0.400486
$377$			52.4786i			2.70278i
$378$		−	15.0277i		−	0.772939i
$379$	8.44277			0.433676			0.216838	−	0.976208i	$-0.430426\pi$
$379$	8.44277			0.433676			0.216838	+	0.976208i	$0.430426\pi$
$380$	1.65104	−	1.48874i	0.0846964	−	0.0763707i
$381$	−1.99536			−0.102225
$382$		−	29.4933i		−	1.50901i
$383$			9.65154i			0.493171i	0.969121	+	0.246585i	$0.0793086\pi$
$383$			9.65154i			0.493171i	−0.969121	+	0.246585i	$0.920691\pi$
$384$	−14.4729			−0.738569
$385$	−5.84962	−	6.48734i	−0.298124	−	0.330625i
$386$	12.7487			0.648891
$387$			0.182082i			0.00925574i
$388$		−	10.5412i		−	0.535151i
$389$	−23.9535			−1.21449			−0.607246	−	0.794514i	$-0.707726\pi$
$389$	−23.9535			−1.21449			−0.607246	+	0.794514i	$0.707726\pi$
$390$	29.8090	+	33.0587i	1.50944	+	1.67399i
$391$	−5.89836			−0.298293
$392$			5.17086i			0.261168i
$393$		−	31.8276i		−	1.60549i
$394$	7.51955			0.378829
$395$	10.1789	−	9.17834i	0.512158	−	0.461813i
$396$	−0.426950			−0.0214550
$397$		−	26.7766i		−	1.34388i	−0.740606	−	0.671940i	$-0.765461\pi$
$397$		−	26.7766i		−	1.34388i	0.740606	−	0.671940i	$-0.234539\pi$
$398$		−	13.3432i		−	0.668836i
$399$	1.86528			0.0933810
$400$	−2.49793	+	24.0975i	−0.124897	+	1.20487i
$401$	−25.2168			−1.25927			−0.629635	−	0.776891i	$-0.716795\pi$
$401$	−25.2168			−1.25927			−0.629635	+	0.776891i	$0.716795\pi$
$402$			5.78426i			0.288493i
$403$			67.3173i			3.35331i
$404$	23.5917			1.17373
$405$	−14.3196	+	12.9120i	−0.711546	+	0.641600i
$406$	23.3832			1.16049
$407$			1.25986i			0.0624488i
$408$			6.71989i			0.332684i
$409$	13.2389			0.654619			0.327310	−	0.944917i	$-0.393858\pi$
$409$	13.2389			0.654619			0.327310	+	0.944917i	$0.393858\pi$
$410$	−24.6317	−	27.3170i	−1.21647	−	1.34909i
$411$	8.55219			0.421848
$412$		−	3.94652i		−	0.194431i
$413$		−	15.6742i		−	0.771275i
$414$	−0.370533			−0.0182107
$415$	−1.25114	−	1.38754i	−0.0614161	−	0.0681115i
$416$	42.6097			2.08911
$417$		−	0.384209i		−	0.0188148i
$418$		−	3.33318i		−	0.163031i
$419$	18.5429			0.905880			0.452940	−	0.891541i	$-0.350375\pi$
$419$	18.5429			0.905880			0.452940	+	0.891541i	$0.350375\pi$
$420$	6.04824	−	5.45369i	0.295124	−	0.266113i
$421$	−25.9339			−1.26394			−0.631972	−	0.774992i	$-0.717754\pi$
$421$	−25.9339			−1.26394			−0.631972	+	0.774992i	$0.717754\pi$
$422$			0.181794i			0.00884958i
$423$		−	0.839680i		−	0.0408266i
$424$	11.0375			0.536026
$425$	17.6233	+	1.82682i	0.854856	+	0.0886139i
$426$	−29.6153			−1.43486
$427$			14.0773i			0.681246i
$428$			6.77819i			0.327636i
$429$	27.4036			1.32306
$430$	−4.60928	+	4.15618i	−0.222279	+	0.200429i
$431$	22.5328			1.08537			0.542683	−	0.839937i	$-0.317408\pi$
$431$	22.5328			1.08537			0.542683	+	0.839937i	$0.317408\pi$
$432$			25.6583i			1.23448i
$433$			33.5776i			1.61364i	0.590801	+	0.806818i	$0.298812\pi$
$433$			33.5776i			1.61364i	−0.590801	+	0.806818i	$0.701188\pi$
$434$	29.9950			1.43981
$435$	−20.9359	−	23.2183i	−1.00380	−	1.11323i
$436$	14.3328			0.686416
$437$		−	1.18776i		−	0.0568182i
$438$		−	27.7618i		−	1.32651i
$439$	3.64200			0.173823			0.0869116	−	0.996216i	$-0.472300\pi$
$439$	3.64200			0.173823			0.0869116	+	0.996216i	$0.472300\pi$
$440$	4.24368	+	4.70632i	0.202310	+	0.224365i
$441$	0.559107			0.0266242
$442$		−	41.5732i		−	1.97743i
$443$		−	27.0746i		−	1.28635i	−0.765718	−	0.643177i	$-0.777616\pi$
$443$		−	27.0746i		−	1.28635i	0.765718	−	0.643177i	$-0.222384\pi$
$444$	−1.17458			−0.0557433
$445$	−3.77766	+	3.40631i	−0.179078	+	0.161475i
$446$	28.7202			1.35994
$447$		−	6.79637i		−	0.321457i
$448$		−	4.05698i		−	0.191674i
$449$	−40.1427			−1.89445			−0.947224	−	0.320571i	$-0.896125\pi$
$449$	−40.1427			−1.89445			−0.947224	+	0.320571i	$0.896125\pi$
$450$	1.10709	+	0.114760i	0.0521887	+	0.00540985i
$451$	−22.6441			−1.06627
$452$		−	17.6922i		−	0.832170i
$453$			9.72407i			0.456877i
$454$	−45.5751			−2.13895
$455$	16.2937	−	14.6920i	0.763859	−	0.688771i
$456$	−1.35319			−0.0633691
$457$		−	22.3710i		−	1.04647i	−0.852188	−	0.523236i	$-0.824725\pi$
$457$		−	22.3710i		−	1.04647i	0.852188	−	0.523236i	$-0.175275\pi$
$458$			38.7321i			1.80983i
$459$	18.7648			0.875864
$460$	−3.47276	−	3.85135i	−0.161918	−	0.179570i
$461$	−31.3342			−1.45938			−0.729689	−	0.683780i	$-0.760335\pi$
$461$	−31.3342			−1.45938			−0.729689	+	0.683780i	$0.760335\pi$
$462$		−	12.2104i		−	0.568080i
$463$			9.21061i			0.428053i	0.976828	+	0.214027i	$0.0686579\pi$
$463$			9.21061i			0.428053i	−0.976828	+	0.214027i	$0.931342\pi$
$464$	−39.9246			−1.85345
$465$	−26.8557	−	29.7834i	−1.24540	−	1.38117i
$466$	−15.7897			−0.731446
$467$		−	1.38103i		−	0.0639065i	−0.999489	−	0.0319532i	$-0.989827\pi$
$467$		−	1.38103i		−	0.0639065i	0.999489	−	0.0319532i	$-0.0101728\pi$
$468$		−	1.07233i		−	0.0495686i
$469$	2.85089			0.131642
$470$	21.2559	−	19.1664i	0.980462	−	0.884081i
$471$	−6.82520			−0.314489
$472$			11.3710i			0.523394i
$473$			3.82081i			0.175681i
$474$	19.1587			0.879990
$475$	−0.367870	+	3.54883i	−0.0168790	+	0.162832i
$476$	−7.60600			−0.348620
$477$		−	1.19344i		−	0.0546440i
$478$		−	41.8286i		−	1.91320i
$479$	−1.68759			−0.0771080			−0.0385540	−	0.999257i	$-0.512275\pi$
$479$	−1.68759			−0.0771080			−0.0385540	+	0.999257i	$0.512275\pi$
$480$	−18.8520	+	16.9988i	−0.860470	+	0.775885i
$481$	−3.16427			−0.144278
$482$			1.84209i			0.0839048i
$483$		−	4.35112i		−	0.197983i
$484$	6.36709			0.289413
$485$	11.3290	+	12.5640i	0.514422	+	0.570503i
$486$	2.31195			0.104872
$487$		−	32.1394i		−	1.45638i	−0.685377	−	0.728188i	$-0.740363\pi$
$487$		−	32.1394i		−	1.45638i	0.685377	−	0.728188i	$-0.259637\pi$
$488$		−	10.2125i		−	0.462299i
$489$	−4.25904			−0.192600
$490$	12.7621	+	14.1534i	0.576533	+	0.639386i
$491$	−36.6379			−1.65345			−0.826723	−	0.562608i	$-0.809798\pi$
$491$	−36.6379			−1.65345			−0.826723	+	0.562608i	$0.809798\pi$
$492$		−	21.1115i		−	0.951778i
$493$			29.1982i			1.31502i
$494$	8.37164			0.376658
$495$	0.508878	−	0.458855i	0.0228724	−	0.0206240i
$496$	−51.2136			−2.29956
$497$			14.5965i			0.654742i
$498$		−	2.61161i		−	0.117029i
$499$	−38.2943			−1.71429			−0.857145	−	0.515076i	$-0.827764\pi$
$499$	−38.2943			−1.71429			−0.857145	+	0.515076i	$0.827764\pi$
$500$	9.18320	+	12.5828i	0.410685	+	0.562719i
$501$	42.9420			1.91851
$502$		−	23.8285i		−	1.06352i
$503$			36.2174i			1.61485i	0.589967	+	0.807427i	$0.299141\pi$
$503$			36.2174i			1.61485i	−0.589967	+	0.807427i	$0.700859\pi$
$504$	0.208061			0.00926777
$505$	−28.1188	+	25.3547i	−1.25127	+	1.12827i
$506$	−7.77525			−0.345652
$507$			46.7688i			2.07707i
$508$			1.63844i			0.0726940i
$509$	−18.3681			−0.814153			−0.407076	−	0.913394i	$-0.633452\pi$
$509$	−18.3681			−0.814153			−0.407076	+	0.913394i	$0.633452\pi$
$510$	16.5853	+	18.3933i	0.734407	+	0.814471i
$511$	−13.6830			−0.605298
$512$			21.5862i			0.953985i
$513$			3.77869i			0.166833i
$514$	19.9885			0.881653
$515$	4.24144	+	4.70383i	0.186900	+	0.207276i
$516$	−3.56220			−0.156817
$517$		−	17.6198i		−	0.774920i
$518$			1.40993i			0.0619486i
$519$	32.3062			1.41808
$520$	−11.8204	+	10.6585i	−0.518361	+	0.467405i
$521$	−37.0378			−1.62265			−0.811327	−	0.584593i	$-0.801254\pi$
$521$	−37.0378			−1.62265			−0.811327	+	0.584593i	$0.801254\pi$
$522$			1.83422i			0.0802817i
$523$		−	20.9663i		−	0.916791i	−0.888748	−	0.458395i	$-0.848424\pi$
$523$		−	20.9663i		−	0.916791i	0.888748	−	0.458395i	$-0.151576\pi$
$524$	−26.1344			−1.14169
$525$	−1.34762	+	13.0004i	−0.0588148	+	0.567385i
$526$	25.9793			1.13275
$527$			37.4543i			1.63153i
$528$			20.8481i			0.907298i
$529$	20.2293			0.879536
$530$	30.2111	−	27.2414i	1.31229	−	1.18329i
$531$	1.22951			0.0533561
$532$		−	1.53163i		−	0.0664046i
$533$		−	56.8732i		−	2.46345i
$534$	−7.11029			−0.307692
$535$	−7.28471	−	8.07887i	−0.314946	−	0.349280i
$536$	−2.06822			−0.0893334
$537$			20.9993i			0.906185i
$538$			13.9201i			0.600137i
$539$	11.7323			0.505346
$540$	11.0481	+	12.2525i	0.475434	+	0.527264i
$541$	9.75202			0.419272			0.209636	−	0.977779i	$-0.432772\pi$
$541$	9.75202			0.419272			0.209636	+	0.977779i	$0.432772\pi$
$542$			38.6060i			1.65827i
$543$		−	9.54920i		−	0.409795i
$544$	23.7074			1.01645
$545$	−17.0831	+	15.4039i	−0.731762	+	0.659829i
$546$	30.6678			1.31246
$547$			30.8874i			1.32065i	0.750979	+	0.660326i	$0.229582\pi$
$547$			30.8874i			1.32065i	−0.750979	+	0.660326i	$0.770418\pi$
$548$		−	7.02241i		−	0.299983i
$549$	−1.10424			−0.0471280
$550$	23.2312	+	2.40813i	0.990581	+	0.102683i
$551$	−5.87969			−0.250483
$552$			3.15658i			0.134353i
$553$		−	9.44278i		−	0.401548i
$554$	27.5636			1.17106
$555$	1.39998	−	1.26236i	0.0594257	−	0.0535841i
$556$	−0.315483			−0.0133795
$557$			25.1804i			1.06693i	0.845823	+	0.533463i	$0.179110\pi$
$557$			25.1804i			1.06693i	−0.845823	+	0.533463i	$0.820890\pi$
$558$			2.35286i			0.0996047i
$559$	−9.59638			−0.405884
$560$	11.1774	+	12.3959i	0.472329	+	0.523822i
$561$	15.2469			0.643726
$562$			56.6424i			2.38931i
$563$		−	37.8072i		−	1.59338i	−0.604386	−	0.796692i	$-0.706581\pi$
$563$		−	37.8072i		−	1.59338i	0.604386	−	0.796692i	$-0.293419\pi$
$564$	16.4272			0.691712
$565$	19.0143	+	21.0872i	0.799937	+	0.887144i
$566$	7.48080			0.314441
$567$			13.2840i			0.557874i
$568$		−	10.5892i		−	0.444313i
$569$	9.89011			0.414615			0.207307	−	0.978276i	$-0.433530\pi$
$569$	9.89011			0.414615			0.207307	+	0.978276i	$0.433530\pi$
$570$	−3.70389	+	3.33979i	−0.155139	+	0.139889i
$571$	−20.8124			−0.870972			−0.435486	−	0.900196i	$-0.643423\pi$
$571$	−20.8124			−0.870972			−0.435486	+	0.900196i	$0.643423\pi$
$572$		−	22.5018i		−	0.940848i
$573$			27.1673i			1.13493i
$574$	−25.3414			−1.05773
$575$	8.27831	+	0.858124i	0.345229	+	0.0357863i
$576$	0.318237			0.0132599
$577$			22.7214i			0.945906i	0.881088	+	0.472953i	$0.156812\pi$
$577$			22.7214i			0.945906i	−0.881088	+	0.472953i	$0.843188\pi$
$578$			8.18487i			0.340446i
$579$	−11.7432			−0.488032
$580$	−19.0651	+	17.1910i	−0.791634	+	0.713816i
$581$	−1.28719			−0.0534016
$582$			23.6479i			0.980238i
$583$		−	25.0432i		−	1.03718i
$584$	9.92647			0.410760
$585$	1.15247	+	1.27810i	0.0476486	+	0.0528431i
$586$	−34.4930			−1.42489
$587$			26.2568i			1.08373i	0.840465	+	0.541866i	$0.182282\pi$
$587$			26.2568i			1.08373i	−0.840465	+	0.541866i	$0.817718\pi$
$588$			10.9382i			0.451084i
$589$	−7.54222			−0.310772
$590$	28.0646	+	31.1242i	1.15540	+	1.28136i
$591$	−6.92650			−0.284918
$592$		−	2.40731i		−	0.0989399i
$593$			16.3255i			0.670406i	0.942146	+	0.335203i	$0.108805\pi$
$593$			16.3255i			0.670406i	−0.942146	+	0.335203i	$0.891195\pi$
$594$	24.7358			1.01492
$595$	9.06553	−	8.17438i	0.371651	−	0.335117i
$596$	−5.58067			−0.228593
$597$			12.2909i			0.503032i
$598$		−	19.5284i		−	0.798576i
$599$	45.7396			1.86887			0.934436	−	0.356132i	$-0.115905\pi$
$599$	45.7396			1.86887			0.934436	+	0.356132i	$0.115905\pi$
$600$	0.977646	−	9.43133i	0.0399122	−	0.385032i
$601$	−17.3734			−0.708676			−0.354338	−	0.935117i	$-0.615294\pi$
$601$	−17.3734			−0.708676			−0.354338	+	0.935117i	$0.615294\pi$
$602$			4.27592i			0.174274i
$603$			0.223629i			0.00910688i
$604$	7.98467			0.324892
$605$	−7.58888	+	6.84289i	−0.308532	+	0.278203i
$606$	−52.9250			−2.14993
$607$			4.48838i			0.182178i	0.995843	+	0.0910890i	$0.0290348\pi$
$607$			4.48838i			0.182178i	−0.995843	+	0.0910890i	$0.970965\pi$
$608$			4.77399i			0.193611i
$609$	−21.5391			−0.872807
$610$	−25.2054	−	27.9532i	−1.02054	−	1.13179i
$611$	44.2542			1.79033
$612$		−	0.596628i		−	0.0241173i
$613$			29.9448i			1.20946i	0.796430	+	0.604730i	$0.206719\pi$
$613$			29.9448i			1.20946i	−0.796430	+	0.604730i	$0.793281\pi$
$614$	4.44028			0.179195
$615$	22.6891	+	25.1626i	0.914912	+	1.01465i
$616$	4.36595			0.175909
$617$		−	48.0028i		−	1.93252i	−0.257566	−	0.966261i	$-0.582921\pi$
$617$		−	48.0028i		−	1.93252i	0.257566	−	0.966261i	$-0.417079\pi$
$618$			8.85352i			0.356141i
$619$	6.70266			0.269403			0.134701	−	0.990886i	$-0.456992\pi$
$619$	6.70266			0.269403			0.134701	+	0.990886i	$0.456992\pi$
$620$	−24.4559	+	22.0518i	−0.982172	+	0.885624i
$621$	8.81449			0.353713
$622$		−	29.5678i		−	1.18556i
$623$			3.50445i			0.140403i
$624$	−52.3624			−2.09617
$625$	−24.4684	−	5.12787i	−0.978738	−	0.205115i
$626$	11.0790			0.442805
$627$			3.07030i			0.122616i
$628$			5.60434i			0.223638i
$629$	−1.76055			−0.0701977
$630$	0.569494	−	0.513512i	0.0226892	−	0.0204588i
$631$	−7.36072			−0.293025			−0.146513	−	0.989209i	$-0.546805\pi$
$631$	−7.36072			−0.293025			−0.146513	+	0.989209i	$0.546805\pi$
$632$			6.85039i			0.272494i
$633$		−	0.167456i		−	0.00665579i
$634$	−50.7331			−2.01487
$635$	−1.76088	−	1.95284i	−0.0698782	−	0.0774962i
$636$	23.3481			0.925814
$637$			29.4670i			1.16752i
$638$			38.4893i			1.52381i
$639$	−1.14497			−0.0452945
$640$	−12.7722	−	14.1646i	−0.504864	−	0.559903i
$641$	−37.1888			−1.46887			−0.734434	−	0.678680i	$-0.762552\pi$
$641$	−37.1888			−1.46887			−0.734434	+	0.678680i	$0.762552\pi$
$642$		−	15.2060i		−	0.600133i
$643$		−	27.0935i		−	1.06846i	−0.845338	−	0.534232i	$-0.820601\pi$
$643$		−	27.0935i		−	1.06846i	0.845338	−	0.534232i	$-0.179399\pi$
$644$	−3.57281			−0.140789
$645$	4.24575	−	3.82839i	0.167176	−	0.150743i
$646$	4.65785			0.183261
$647$			16.1175i			0.633646i	0.948485	+	0.316823i	$0.102616\pi$
$647$			16.1175i			0.633646i	−0.948485	+	0.316823i	$0.897384\pi$
$648$		−	9.63702i		−	0.378578i
$649$	25.8000			1.01274
$650$	−6.04829	+	58.3477i	−0.237233	+	2.28858i
$651$	−27.6294			−1.08288
$652$			3.49720i			0.136961i
$653$			11.7529i			0.459928i	0.973199	+	0.229964i	$0.0738608\pi$
$653$			11.7529i			0.459928i	−0.973199	+	0.229964i	$0.926139\pi$
$654$	−32.1538			−1.25731
$655$	31.1494	−	28.0874i	1.21711	−	1.09747i
$656$	43.2680			1.68933
$657$		−	1.07331i		−	0.0418740i
$658$		−	19.7186i		−	0.768713i
$659$	12.7347			0.496075			0.248038	−	0.968750i	$-0.420214\pi$
$659$	12.7347			0.496075			0.248038	+	0.968750i	$0.420214\pi$
$660$	8.97690	+	9.95554i	0.349425	+	0.387519i
$661$	−2.32682			−0.0905028			−0.0452514	−	0.998976i	$-0.514409\pi$
$661$	−2.32682			−0.0905028			−0.0452514	+	0.998976i	$0.514409\pi$
$662$			0.456891i			0.0177576i
$663$			38.2944i			1.48723i
$664$	0.933807			0.0362387
$665$	1.64609	+	1.82554i	0.0638325	+	0.0707914i
$666$	−0.110597			−0.00428555
$667$			13.7155i			0.531065i
$668$		−	35.2607i		−	1.36428i
$669$	−26.4551			−1.02281
$670$	−5.66101	+	5.10453i	−0.218704	+	0.197205i
$671$	−23.1715			−0.894525
$672$			17.4885i			0.674635i
$673$		−	21.2017i		−	0.817267i	−0.912699	−	0.408633i	$-0.866005\pi$
$673$		−	21.2017i		−	0.817267i	0.912699	−	0.408633i	$-0.133995\pi$
$674$	39.0353			1.50358
$675$	−26.3362	−	2.73000i	−1.01368	−	0.105078i
$676$	38.4030			1.47704
$677$			51.8603i			1.99315i	0.0826794	+	0.996576i	$0.473652\pi$
$677$			51.8603i			1.99315i	−0.0826794	+	0.996576i	$0.526348\pi$
$678$			39.6902i			1.52429i
$679$	11.6554			0.447292
$680$	−6.57671	+	5.93021i	−0.252205	+	0.227413i
$681$	41.9807			1.60870
$682$			49.3725i			1.89057i
$683$		−	22.4656i		−	0.859621i	−0.902919	−	0.429811i	$-0.858580\pi$
$683$		−	22.4656i		−	0.859621i	0.902919	−	0.429811i	$-0.141420\pi$
$684$	0.120144			0.00459381
$685$	7.54719	+	8.36996i	0.288363	+	0.319800i
$686$	32.9946			1.25974
$687$		−	35.6774i		−	1.36118i
$688$		−	7.30073i		−	0.278338i
$689$	62.8987			2.39625
$690$	7.79069	+	8.64001i	0.296586	+	0.328920i
$691$	51.2504			1.94966			0.974829	−	0.222953i	$-0.0715698\pi$
$691$	51.2504			1.94966			0.974829	+	0.222953i	$0.0715698\pi$
$692$		−	26.5274i		−	1.00842i
$693$		−	0.472075i		−	0.0179327i
$694$	−33.0713			−1.25537
$695$	0.376022	−	0.339059i	0.0142633	−	0.0128612i
$696$	15.6258			0.592294
$697$		−	31.6433i		−	1.19858i
$698$		−	14.1561i		−	0.535816i
$699$	14.5444			0.550121
$700$	10.6750	+	1.10656i	0.403476	+	0.0418241i
$701$	0.425393			0.0160669			0.00803344	−	0.999968i	$-0.497443\pi$
$701$	0.425393			0.0160669			0.00803344	+	0.999968i	$0.497443\pi$
$702$			62.1268i			2.34483i
$703$		−	0.354524i		−	0.0133711i
$704$	6.67788			0.251682
$705$	−19.5795	+	17.6548i	−0.737407	+	0.664919i
$706$	46.0618			1.73356
$707$			26.0852i			0.981035i
$708$			24.0537i			0.903995i
$709$	15.9902			0.600523			0.300261	−	0.953857i	$-0.402926\pi$
$709$	15.9902			0.600523			0.300261	+	0.953857i	$0.402926\pi$
$710$	−26.1351	−	28.9842i	−0.980831	−	1.08776i
$711$	0.740709			0.0277787
$712$		−	2.54235i		−	0.0952785i
$713$			17.5936i			0.658886i
$714$	17.0631			0.638570
$715$	24.1833	+	26.8197i	0.904405	+	1.00300i
$716$	17.2430			0.644402
$717$			38.5297i			1.43892i
$718$		−	13.2875i		−	0.495885i
$719$	26.2235			0.977973			0.488986	−	0.872291i	$-0.337367\pi$
$719$	26.2235			0.977973			0.488986	+	0.872291i	$0.337367\pi$
$720$	−0.972355	+	0.876772i	−0.0362375	+	0.0326753i
$721$	4.36364			0.162510
$722$		−	34.0617i		−	1.26765i
$723$		−	1.69681i		−	0.0631050i
$724$	−7.84108			−0.291412
$725$	4.24791	−	40.9796i	0.157764	−	1.52194i
$726$	−14.2837			−0.530120
$727$		−	25.2570i		−	0.936730i	−0.883535	−	0.468365i	$-0.844843\pi$
$727$		−	25.2570i		−	0.936730i	0.883535	−	0.468365i	$-0.155157\pi$
$728$			10.9656i			0.406411i
$729$	−27.9982			−1.03697
$730$	27.1702	−	24.4994i	1.00561	−	0.906762i
$731$	−5.33927			−0.197480
$732$		−	21.6031i		−	0.798474i
$733$		−	8.92252i		−	0.329561i	−0.986330	−	0.164780i	$-0.947308\pi$
$733$		−	8.92252i		−	0.329561i	0.986330	−	0.164780i	$-0.0526915\pi$
$734$	−18.5187			−0.683537
$735$	−11.7556	−	13.0372i	−0.433612	−	0.480883i
$736$	11.1362			0.410486
$737$			4.69263i			0.172855i
$738$		−	1.98782i		−	0.0731728i
$739$	14.2439			0.523970			0.261985	−	0.965072i	$-0.415623\pi$
$739$	14.2439			0.523970			0.261985	+	0.965072i	$0.415623\pi$
$740$	−1.03655	−	1.14956i	−0.0381045	−	0.0422585i
$741$	−7.71139			−0.283285
$742$		−	28.0262i		−	1.02887i
$743$		−	14.9854i		−	0.549762i	−0.961478	−	0.274881i	$-0.911362\pi$
$743$		−	14.9854i		−	0.549762i	0.961478	−	0.274881i	$-0.0886384\pi$
$744$	20.0441			0.734852
$745$	6.65155	−	5.99770i	0.243694	−	0.219739i
$746$	58.3995			2.13816
$747$		−	0.100969i		−	0.00369427i
$748$		−	12.5196i		−	0.457763i
$749$	−7.49459			−0.273847
$750$	−20.6013	−	28.2279i	−0.752255	−	1.03074i
$751$	−29.1216			−1.06266			−0.531330	−	0.847165i	$-0.678308\pi$
$751$	−29.1216			−1.06266			−0.531330	+	0.847165i	$0.678308\pi$
$752$			33.6677i			1.22773i
$753$			21.9492i			0.799875i
$754$	−96.6702			−3.52052
$755$	−9.51687	+	8.58135i	−0.346354	+	0.312307i
$756$	11.3664			0.413392
$757$		−	29.9865i		−	1.08988i	−0.838475	−	0.544940i	$-0.816553\pi$
$757$		−	29.9865i		−	1.08988i	0.838475	−	0.544940i	$-0.183447\pi$
$758$			15.5523i			0.564886i
$759$	7.16204			0.259966
$760$	−1.19417	−	1.32436i	−0.0433172	−	0.0480396i
$761$	2.01232			0.0729466			0.0364733	−	0.999335i	$-0.488388\pi$
$761$	2.01232			0.0729466			0.0364733	+	0.999335i	$0.488388\pi$
$762$		−	3.67563i		−	0.133154i
$763$			15.8477i			0.573724i
$764$	22.3077			0.807065
$765$	0.641213	+	0.711117i	0.0231831	+	0.0257105i
$766$	−17.7790			−0.642381
$767$			64.7996i			2.33978i
$768$		−	35.5974i		−	1.28451i
$769$	−46.1301			−1.66350			−0.831748	−	0.555154i	$-0.812659\pi$
$769$	−46.1301			−1.66350			−0.831748	+	0.555154i	$0.812659\pi$
$770$	11.9503	−	10.7755i	0.430657	−	0.388323i
$771$	−18.4120			−0.663092
$772$			9.64266i			0.347047i
$773$			48.0505i			1.72826i	0.503272	+	0.864128i	$0.332130\pi$
$773$			48.0505i			1.72826i	−0.503272	+	0.864128i	$0.667870\pi$
$774$	−0.335411			−0.0120561
$775$	5.44905	−	52.5669i	0.195736	−	1.88826i
$776$	−8.45554			−0.303536
$777$		−	1.29873i		−	0.0465916i
$778$		−	44.1245i		−	1.58194i
$779$	6.37206			0.228303
$780$	−25.0044	+	22.5465i	−0.895303	+	0.807294i
$781$	−24.0261			−0.859723
$782$		−	10.8653i		−	0.388542i
$783$		−	43.6338i		−	1.55934i
$784$	−22.4179			−0.800638
$785$	−6.02314	−	6.67977i	−0.214975	−	0.238411i
$786$	58.6292			2.09124
$787$		−	36.3244i		−	1.29482i	−0.762140	−	0.647412i	$-0.775851\pi$
$787$		−	36.3244i		−	1.29482i	0.762140	−	0.647412i	$-0.224149\pi$
$788$			5.68752i			0.202610i
$789$	−23.9303			−0.851943
$790$	16.9073	+	18.7505i	0.601536	+	0.667114i
$791$	19.5621			0.695548
$792$			0.342473i			0.0121692i
$793$		−	58.1977i		−	2.06666i
$794$	49.3249			1.75048
$795$	−27.8285	+	25.0929i	−0.986974	+	0.889953i
$796$	10.0923			0.357714
$797$		−	36.6218i		−	1.29721i	−0.761124	−	0.648606i	$-0.775352\pi$
$797$		−	36.6218i		−	1.29721i	0.761124	−	0.648606i	$-0.224648\pi$
$798$			3.43602i			0.121634i
$799$	24.6223			0.871075
$800$	−33.2732	−	3.44908i	−1.17638	−	0.121943i
$801$	−0.274895			−0.00971295
$802$		−	46.4517i		−	1.64027i
$803$		−	22.5224i		−	0.794799i
$804$	−4.37501			−0.154295
$805$	4.25841	−	3.83980i	0.150089	−	0.135335i
$806$	−124.004			−4.36787
$807$		−	12.8222i		−	0.451364i
$808$		−	18.9238i		−	0.665738i
$809$	34.5599			1.21506			0.607530	−	0.794297i	$-0.292160\pi$
$809$	34.5599			1.21506			0.607530	+	0.794297i	$0.292160\pi$
$810$	−23.7850	−	26.3779i	−0.835719	−	0.926827i
$811$	−17.3270			−0.608435			−0.304217	−	0.952603i	$-0.598395\pi$
$811$	−17.3270			−0.608435			−0.304217	+	0.952603i	$0.598395\pi$
$812$			17.6863i			0.620666i
$813$		−	35.5613i		−	1.24719i
$814$	−2.32077			−0.0813429
$815$	−3.75854	−	4.16829i	−0.131656	−	0.146009i
$816$	−29.1336			−1.01988
$817$		−	1.07518i		−	0.0376156i
$818$			24.3871i			0.852677i
$819$	1.18567			0.0414306
$820$	20.6616	−	18.6306i	0.721535	−	0.650607i
$821$	13.5004			0.471169			0.235584	−	0.971854i	$-0.424300\pi$
$821$	13.5004			0.471169			0.235584	+	0.971854i	$0.424300\pi$
$822$			15.7539i			0.549480i
$823$			46.7783i			1.63059i	0.579046	+	0.815295i	$0.303425\pi$
$823$			46.7783i			1.63059i	−0.579046	+	0.815295i	$0.696575\pi$
$824$	−3.16566			−0.110281
$825$	−21.3990	−	2.21821i	−0.745017	−	0.0772280i
$826$	28.8732			1.00463
$827$		−	44.0656i		−	1.53231i	−0.642656	−	0.766155i	$-0.722167\pi$
$827$		−	44.0656i		−	1.53231i	0.642656	−	0.766155i	$-0.277833\pi$
$828$		−	0.280258i		−	0.00973963i
$829$	4.27440			0.148456			0.0742280	−	0.997241i	$-0.476351\pi$
$829$	4.27440			0.148456			0.0742280	+	0.997241i	$0.476351\pi$
$830$	2.55597	−	2.30471i	0.0887189	−	0.0799977i
$831$	−25.3897			−0.880759
$832$			16.7722i			0.581473i
$833$			16.3950i			0.568051i
$834$	0.707746			0.0245073
$835$	37.8957	+	42.0270i	1.31143	+	1.45440i
$836$	2.52110			0.0871940
$837$		−	55.9716i		−	1.93466i
$838$			34.1577i			1.17996i
$839$	31.6115			1.09135			0.545675	−	0.837997i	$-0.316273\pi$
$839$	31.6115			1.09135			0.545675	+	0.837997i	$0.316273\pi$
$840$	−4.37462	−	4.85153i	−0.150939	−	0.167394i
$841$	38.8947			1.34120
$842$		−	47.7726i		−	1.64635i
$843$		−	52.1751i		−	1.79701i
$844$	−0.137502			−0.00473303
$845$	−45.7723	+	41.2728i	−1.57461	+	1.41983i
$846$	1.54677			0.0531789
$847$			7.04004i			0.241899i
$848$			47.8521i			1.64325i
$849$	−6.89080			−0.236492
$850$	−3.36517	+	32.4637i	−0.115424	+	1.11350i
$851$	−0.826993			−0.0283490
$852$		−	22.3999i		−	0.767409i
$853$			5.03330i			0.172337i	0.996281	+	0.0861684i	$0.0274623\pi$
$853$			5.03330i			0.172337i	−0.996281	+	0.0861684i	$0.972538\pi$
$854$	−25.9316			−0.887359
$855$	−0.143198	+	0.129122i	−0.00489728	+	0.00441588i
$856$	5.43705			0.185834
$857$		−	17.8339i		−	0.609195i	−0.952481	−	0.304598i	$-0.901478\pi$
$857$		−	17.8339i		−	0.609195i	0.952481	−	0.304598i	$-0.0985220\pi$
$858$			50.4799i			1.72336i
$859$	−29.9247			−1.02102			−0.510509	−	0.859873i	$-0.670543\pi$
$859$	−29.9247			−1.02102			−0.510509	+	0.859873i	$0.670543\pi$
$860$	−3.14359	−	3.48629i	−0.107195	−	0.118882i
$861$	23.3428			0.795519
$862$			41.5074i			1.41375i
$863$			21.1041i			0.718392i	0.933262	+	0.359196i	$0.116949\pi$
$863$			21.1041i			0.718392i	−0.933262	+	0.359196i	$0.883051\pi$
$864$	−35.4282			−1.20529
$865$	28.5097	+	31.6178i	0.969360	+	1.07504i
$866$	−61.8529			−2.10185
$867$		−	7.53935i		−	0.256050i
$868$			22.6872i			0.770053i
$869$	15.5430			0.527261
$870$	42.7701	−	38.5657i	1.45004	−	1.30750i
$871$	−11.7861			−0.399356
$872$		−	11.4969i		−	0.389334i
$873$			0.914268i			0.0309433i
$874$	2.18796			0.0740088
$875$	−13.9127	+	10.1538i	−0.470334	+	0.343261i
$876$	20.9980			0.709457
$877$			12.0202i			0.405892i	0.979190	+	0.202946i	$0.0650516\pi$
$877$			12.0202i			0.405892i	−0.979190	+	0.202946i	$0.934948\pi$
$878$			6.70889i			0.226414i
$879$	31.7726			1.07166
$880$	−20.4039	+	18.3982i	−0.687815	+	0.620202i
$881$	−15.0651			−0.507556			−0.253778	−	0.967263i	$-0.581673\pi$
$881$	−15.0651			−0.507556			−0.253778	+	0.967263i	$0.581673\pi$
$882$			1.02993i			0.0346794i
$883$			3.17468i			0.106836i	0.998572	+	0.0534182i	$0.0170116\pi$
$883$			3.17468i			0.106836i	−0.998572	+	0.0534182i	$0.982988\pi$
$884$	31.4445			1.05759
$885$	−25.8512	−	28.6695i	−0.868980	−	0.963714i
$886$	49.8738			1.67554
$887$		−	33.6952i		−	1.13137i	−0.824620	−	0.565687i	$-0.808611\pi$
$887$		−	33.6952i		−	1.13137i	0.824620	−	0.565687i	$-0.191389\pi$
$888$			0.942179i			0.0316175i
$889$	−1.81161			−0.0607594
$890$	−6.27473	−	6.95878i	−0.210329	−	0.233259i
$891$	−21.8657			−0.732528
$892$			21.7229i			0.727337i
$893$			4.95823i			0.165921i
$894$	12.5195			0.418715
$895$	−20.5518	+	18.5315i	−0.686971	+	0.619441i
$896$	−13.1401			−0.438981
$897$			17.9883i			0.600610i
$898$		−	73.9463i		−	2.46762i
$899$	87.0925			2.90470
$900$	−0.0868007	+	0.837364i	−0.00289336	+	0.0279121i
$901$	34.9958			1.16588
$902$		−	41.7125i		−	1.38887i
$903$		−	3.93869i		−	0.131071i
$904$	−14.1916			−0.472005
$905$	9.34573	−	8.42703i	0.310663	−	0.280124i
$906$	−17.9126			−0.595106
$907$			15.5495i			0.516311i	0.966103	+	0.258156i	$0.0831147\pi$
$907$			15.5495i			0.516311i	−0.966103	+	0.258156i	$0.916885\pi$
$908$		−	34.4714i		−	1.14397i
$909$	−2.04617			−0.0678671
$910$	27.0639	+	30.0144i	0.897161	+	0.994967i
$911$	47.4791			1.57305			0.786527	−	0.617556i	$-0.211877\pi$
$911$	47.4791			1.57305			0.786527	+	0.617556i	$0.211877\pi$
$912$		−	5.86667i		−	0.194265i
$913$		−	2.11874i		−	0.0701200i
$914$	41.2094			1.36309
$915$	23.2175	+	25.7486i	0.767546	+	0.851222i
$916$	−29.2956			−0.967954
$917$		−	28.8966i		−	0.954251i
$918$			34.5664i			1.14086i
$919$	43.8093			1.44514			0.722568	−	0.691299i	$-0.242961\pi$
$919$	43.8093			1.44514			0.722568	+	0.691299i	$0.242961\pi$
$920$	−3.08932	+	2.78563i	−0.101852	+	0.0918396i
$921$	−4.09008			−0.134773
$922$		−	57.7203i		−	1.90092i
$923$		−	60.3443i		−	1.98626i
$924$	9.23554			0.303827
$925$	2.47092	+	0.256134i	0.0812434	+	0.00842164i
$926$	−16.9668			−0.557562
$927$			0.342292i			0.0112423i
$928$		−	55.1268i		−	1.80963i
$929$	23.2341			0.762285			0.381143	−	0.924516i	$-0.375531\pi$
$929$	23.2341			0.762285			0.381143	+	0.924516i	$0.375531\pi$
$930$	54.8637	−	49.4705i	1.79905	−	1.62220i
$931$	−3.30147			−0.108201
$932$		−	11.9428i		−	0.391200i
$933$			27.2359i			0.891663i
$934$	2.54398			0.0832416
$935$	13.4552	+	14.9221i	0.440032	+	0.488004i
$936$	−0.860159			−0.0281152
$937$			26.0794i			0.851975i	0.904729	+	0.425988i	$0.140073\pi$
$937$			26.0794i			0.851975i	−0.904729	+	0.425988i	$0.859927\pi$
$938$			5.25160i			0.171471i
$939$	−10.2052			−0.333034
$940$	14.4968	+	16.0772i	0.472834	+	0.524381i
$941$	−23.0611			−0.751771			−0.375885	−	0.926666i	$-0.622661\pi$
$941$	−23.0611			−0.751771			−0.375885	+	0.926666i	$0.622661\pi$
$942$		−	12.5726i		−	0.409638i
$943$		−	14.8640i		−	0.484039i
$944$	−49.2982			−1.60452
$945$	−13.5475	+	12.2158i	−0.440701	+	0.397379i
$946$	−7.03826			−0.228834
$947$		−	37.2266i		−	1.20970i	−0.796339	−	0.604851i	$-0.793233\pi$
$947$		−	37.2266i		−	1.20970i	0.796339	−	0.604851i	$-0.206767\pi$
$948$			14.4910i			0.470646i
$949$	56.5676			1.83626
$950$	−6.53726	−	0.677648i	−0.212097	−	0.0219858i
$951$	46.7319			1.51539
$952$			6.10107i			0.197737i
$953$		−	23.0528i		−	0.746753i	−0.927680	−	0.373377i	$-0.878200\pi$
$953$		−	23.0528i		−	0.746753i	0.927680	−	0.373377i	$-0.121800\pi$
$954$	2.19843			0.0711767
$955$	−26.5884	+	23.9747i	−0.860381	+	0.775804i
$956$	31.6377			1.02324
$957$		−	35.4538i		−	1.14606i
$958$		−	3.10869i		−	0.100437i
$959$	7.76463			0.250733
$960$	−6.69114	−	7.42059i	−0.215956	−	0.239499i
$961$	80.7187			2.60383
$962$		−	5.82887i		−	0.187930i
$963$		−	0.587889i		−	0.0189445i
$964$	−1.39329			−0.0448749
$965$	−10.3632	−	11.4930i	−0.333604	−	0.369973i
$966$	8.01515			0.257883
$967$		−	29.7340i		−	0.956181i	−0.878311	−	0.478090i	$-0.841329\pi$
$967$		−	29.7340i		−	0.956181i	0.878311	−	0.478090i	$-0.158671\pi$
$968$		−	5.10729i		−	0.164154i
$969$	−4.29049			−0.137831
$970$	−23.1441	+	20.8690i	−0.743111	+	0.670062i
$971$	−16.0126			−0.513868			−0.256934	−	0.966429i	$-0.582712\pi$
$971$	−16.0126			−0.513868			−0.256934	+	0.966429i	$0.582712\pi$
$972$			1.74868i			0.0560888i
$973$		−	0.348827i		−	0.0111829i
$974$	59.2037			1.89701
$975$	5.57127	−	53.7460i	0.178424	−	1.72125i
$976$	44.2756			1.41723
$977$		−	16.8004i		−	0.537493i	−0.963211	−	0.268747i	$-0.913391\pi$
$977$		−	16.8004i		−	0.537493i	0.963211	−	0.268747i	$-0.0866095\pi$
$978$		−	7.84553i		−	0.250872i
$979$	−5.76840			−0.184359
$980$	−10.7051	+	9.65281i	−0.341963	+	0.308348i
$981$	−1.24312			−0.0396897
$982$		−	67.4903i		−	2.15370i
$983$		−	19.1223i		−	0.609908i	−0.952367	−	0.304954i	$-0.901359\pi$
$983$		−	19.1223i		−	0.609908i	0.952367	−	0.304954i	$-0.0986411\pi$
$984$	−16.9343			−0.539846
$985$	−6.11254	−	6.77891i	−0.194762	−	0.215994i
$986$	−53.7857			−1.71289
$987$			18.1635i			0.578150i
$988$			6.33202i			0.201448i
$989$	−2.50805			−0.0797513
$990$	0.845251	+	0.937399i	0.0268639	+	0.0297925i
$991$	−10.1892			−0.323670			−0.161835	−	0.986818i	$-0.551741\pi$
$991$	−10.1892			−0.323670			−0.161835	+	0.986818i	$0.551741\pi$
$992$		−	70.7144i		−	2.24518i
$993$		−	0.420857i		−	0.0133555i
$994$	−26.8880			−0.852837
$995$	−12.0290	+	10.8465i	−0.381345	+	0.343858i
$996$	1.97533			0.0625908
$997$			16.0609i			0.508652i	0.967118	+	0.254326i	$0.0818537\pi$
$997$			16.0609i			0.508652i	−0.967118	+	0.254326i	$0.918146\pi$
$998$		−	70.5415i		−	2.23295i
$999$	2.63096			0.0832399

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.b.c.724.38	yes	46
5.2	odd	4		6025.2.a.p.1.9		46
5.3	odd	4		6025.2.a.p.1.38		46
5.4	even	2	inner	1205.2.b.c.724.9	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.b.c.724.9	✓	46	5.4	even	2	inner
1205.2.b.c.724.38	yes	46	1.1	even	1	trivial
6025.2.a.p.1.9		46	5.2	odd	4
6025.2.a.p.1.38		46	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+1.84209i q^{2} -1.69681i q^{3} -1.39329 q^{4} +(1.66065 - 1.49741i) q^{5} +3.12567 q^{6} -1.54055i q^{7} +1.11761i q^{8} +0.120844 q^{9} +O(q^{10})\)	\(q+1.84209i q^{2} -1.69681i q^{3} -1.39329 q^{4} +(1.66065 - 1.49741i) q^{5} +3.12567 q^{6} -1.54055i q^{7} +1.11761i q^{8} +0.120844 q^{9} +(2.75836 + 3.05907i) q^{10} +2.53578 q^{11} +2.36415i q^{12} +6.36889i q^{13} +2.83783 q^{14} +(-2.54081 - 2.81781i) q^{15} -4.84532 q^{16} +3.54355i q^{17} +0.222605i q^{18} -0.713569 q^{19} +(-2.31377 + 2.08633i) q^{20} -2.61402 q^{21} +4.67113i q^{22} +1.66453i q^{23} +1.89637 q^{24} +(0.515535 - 4.97335i) q^{25} -11.7321 q^{26} -5.29547i q^{27} +2.14644i q^{28} +8.23983 q^{29} +(5.19065 - 4.68041i) q^{30} +10.5697 q^{31} -6.69029i q^{32} -4.30273i q^{33} -6.52753 q^{34} +(-2.30683 - 2.55832i) q^{35} -0.168370 q^{36} +0.496832i q^{37} -1.31446i q^{38} +10.8068 q^{39} +(1.67352 + 1.85597i) q^{40} -8.92984 q^{41} -4.81525i q^{42} +1.50676i q^{43} -3.53308 q^{44} +(0.200679 - 0.180952i) q^{45} -3.06622 q^{46} -6.94849i q^{47} +8.22158i q^{48} +4.62670 q^{49} +(9.16135 + 0.949660i) q^{50} +6.01272 q^{51} -8.87372i q^{52} -9.87593i q^{53} +9.75473 q^{54} +(4.21105 - 3.79710i) q^{55} +1.72174 q^{56} +1.21079i q^{57} +15.1785i q^{58} +10.1744 q^{59} +(3.54009 + 3.92603i) q^{60} -9.13781 q^{61} +19.4703i q^{62} -0.186166i q^{63} +2.63346 q^{64} +(9.53684 + 10.5765i) q^{65} +7.92601 q^{66} +1.85057i q^{67} -4.93720i q^{68} +2.82439 q^{69} +(4.71265 - 4.24939i) q^{70} -9.47485 q^{71} +0.135056i q^{72} -8.88186i q^{73} -0.915209 q^{74} +(-8.43882 - 0.874763i) q^{75} +0.994210 q^{76} -3.90650i q^{77} +19.9071i q^{78} +6.12948 q^{79} +(-8.04640 + 7.25543i) q^{80} -8.62287 q^{81} -16.4496i q^{82} -0.835537i q^{83} +3.64209 q^{84} +(5.30614 + 5.88461i) q^{85} -2.77558 q^{86} -13.9814i q^{87} +2.83402i q^{88} -2.27480 q^{89} +(0.333330 + 0.369669i) q^{90} +9.81161 q^{91} -2.31918i q^{92} -17.9348i q^{93} +12.7997 q^{94} +(-1.18499 + 1.06850i) q^{95} -11.3521 q^{96} +7.56572i q^{97} +8.52280i q^{98} +0.306433 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9}+O(q^{10}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9	\( 46 q - 34 q^{4} - 8 q^{5} - 4 q^{6} - 34 q^{9} - 7 q^{10} - 64 q^{11} + 66 q^{14} + 5 q^{15} + 22 q^{16} - 2 q^{20} - 14 q^{21} + 50 q^{24} + 30 q^{25} - 60 q^{26} + 36 q^{29} + 7 q^{30} - 36 q^{31} - 12 q^{34} + 3 q^{35} - 34 q^{36} + 88 q^{39} - 30 q^{40} - 76 q^{41} + 100 q^{44} - 17 q^{45} - 12 q^{46} - 22 q^{49} - 14 q^{50} - 112 q^{51} + 26 q^{54} - 5 q^{55} - 120 q^{56} + 84 q^{59} - 33 q^{60} - 78 q^{61} - 28 q^{64} + 9 q^{65} - 2 q^{66} + 24 q^{69} + 88 q^{70} - 172 q^{71} + 16 q^{74} + 59 q^{75} - 18 q^{76} + 54 q^{79} + 63 q^{80} - 42 q^{81} - 44 q^{84} + 30 q^{85} - 80 q^{86} + 86 q^{89} + 17 q^{90} - 88 q^{91} - 4 q^{94} + q^{95} - 122 q^{96} + 148 q^{99}+O(q^{100}) \) 46 * q - 34 * q^4 - 8 * q^5 - 4 * q^6 - 34 * q^9 - 7 * q^10 - 64 * q^11 + 66 * q^14 + 5 * q^15 + 22 * q^16 - 2 * q^20 - 14 * q^21 + 50 * q^24 + 30 * q^25 - 60 * q^26 + 36 * q^29 + 7 * q^30 - 36 * q^31 - 12 * q^34 + 3 * q^35 - 34 * q^36 + 88 * q^39 - 30 * q^40 - 76 * q^41 + 100 * q^44 - 17 * q^45 - 12 * q^46 - 22 * q^49 - 14 * q^50 - 112 * q^51 + 26 * q^54 - 5 * q^55 - 120 * q^56 + 84 * q^59 - 33 * q^60 - 78 * q^61 - 28 * q^64 + 9 * q^65 - 2 * q^66 + 24 * q^69 + 88 * q^70 - 172 * q^71 + 16 * q^74 + 59 * q^75 - 18 * q^76 + 54 * q^79 + 63 * q^80 - 42 * q^81 - 44 * q^84 + 30 * q^85 - 80 * q^86 + 86 * q^89 + 17 * q^90 - 88 * q^91 - 4 * q^94 + q^95 - 122 * q^96 + 148 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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