LMFDB - Embedded newform 1155.3.b.a.736.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,3,Mod(736,1155)]

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, 0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1155.736");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1155.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:	$31.4714705336$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			736.18
Character	$\chi$	$=$	1155.736
Dual form			1155.3.b.a.736.79

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.89693i q^{2} -1.73205 q^{3} -4.39221 q^{4} +2.23607 q^{5} +5.01763i q^{6} +2.64575i q^{7} +1.13621i q^{8} +3.00000 q^{9} +O(q^{10})$	\(q-2.89693i q^{2} -1.73205 q^{3} -4.39221 q^{4} +2.23607 q^{5} +5.01763i q^{6} +2.64575i q^{7} +1.13621i q^{8} +3.00000 q^{9} -6.47774i q^{10} +(10.5908 - 2.97219i) q^{11} +7.60753 q^{12} -0.711740i q^{13} +7.66456 q^{14} -3.87298 q^{15} -14.2773 q^{16} +14.8732i q^{17} -8.69079i q^{18} +8.46103i q^{19} -9.82128 q^{20} -4.58258i q^{21} +(-8.61023 - 30.6810i) q^{22} -11.9912 q^{23} -1.96797i q^{24} +5.00000 q^{25} -2.06186 q^{26} -5.19615 q^{27} -11.6207i q^{28} +46.8706i q^{29} +11.2198i q^{30} +51.2760 q^{31} +45.9053i q^{32} +(-18.3439 + 5.14798i) q^{33} +43.0865 q^{34} +5.91608i q^{35} -13.1766 q^{36} +49.0328 q^{37} +24.5110 q^{38} +1.23277i q^{39} +2.54064i q^{40} +15.4167i q^{41} -13.2754 q^{42} +41.8430i q^{43} +(-46.5173 + 13.0545i) q^{44} +6.70820 q^{45} +34.7376i q^{46} +12.2417 q^{47} +24.7291 q^{48} -7.00000 q^{49} -14.4847i q^{50} -25.7611i q^{51} +3.12611i q^{52} -12.2476 q^{53} +15.0529i q^{54} +(23.6819 - 6.64602i) q^{55} -3.00613 q^{56} -14.6549i q^{57} +135.781 q^{58} +28.8624 q^{59} +17.0110 q^{60} -112.815i q^{61} -148.543i q^{62} +7.93725i q^{63} +75.8751 q^{64} -1.59150i q^{65} +(14.9134 + 53.1410i) q^{66} -91.9069 q^{67} -65.3261i q^{68} +20.7693 q^{69} +17.1385 q^{70} +116.132 q^{71} +3.40863i q^{72} -25.4033i q^{73} -142.045i q^{74} -8.66025 q^{75} -37.1626i q^{76} +(7.86367 + 28.0208i) q^{77} +3.57125 q^{78} -17.1707i q^{79} -31.9251 q^{80} +9.00000 q^{81} +44.6612 q^{82} +145.242i q^{83} +20.1276i q^{84} +33.2574i q^{85} +121.216 q^{86} -81.1823i q^{87} +(3.37703 + 12.0334i) q^{88} +5.32225 q^{89} -19.4332i q^{90} +1.88309 q^{91} +52.6677 q^{92} -88.8127 q^{93} -35.4633i q^{94} +18.9194i q^{95} -79.5103i q^{96} +98.8311 q^{97} +20.2785i q^{98} +(31.7725 - 8.91657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) $ 96 * q - 216 * q^4 + 288 * q^9	$ 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) $ 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * 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 $

$2$		−	2.89693i		−	1.44847i	−0.689555	−	0.724233i	$-0.742194\pi$
$2$		−	2.89693i		−	1.44847i	0.689555	−	0.724233i	$-0.257806\pi$
$3$	−1.73205			−0.577350
$3$	−1.73205			−0.577350
$4$	−4.39221			−1.09805
$5$	2.23607			0.447214
$5$	2.23607			0.447214
$6$			5.01763i			0.836272i
$7$			2.64575i			0.377964i
$7$			2.64575i			0.377964i
$8$			1.13621i			0.142026i
$9$	3.00000			0.333333
$10$		−	6.47774i		−	0.647774i
$11$	10.5908	−	2.97219i	0.962804	−	0.270199i
$11$	10.5908	−	2.97219i	0.962804	−	0.270199i
$12$	7.60753			0.633961
$13$		−	0.711740i		−	0.0547492i	−0.999625	−	0.0273746i	$-0.991285\pi$
$13$		−	0.711740i		−	0.0547492i	0.999625	−	0.0273746i	$-0.00871470\pi$
$14$	7.66456			0.547469
$15$	−3.87298			−0.258199
$16$	−14.2773			−0.892333
$17$			14.8732i			0.874892i	0.899245	+	0.437446i	$0.144117\pi$
$17$			14.8732i			0.874892i	−0.899245	+	0.437446i	$0.855883\pi$
$18$		−	8.69079i		−	0.482822i
$19$			8.46103i			0.445317i	0.974896	+	0.222659i	$0.0714735\pi$
$19$			8.46103i			0.445317i	−0.974896	+	0.222659i	$0.928526\pi$
$20$	−9.82128			−0.491064
$21$		−	4.58258i		−	0.218218i
$22$	−8.61023	−	30.6810i	−0.391374	−	1.39459i
$23$	−11.9912			−0.521355			−0.260677	−	0.965426i	$-0.583946\pi$
$23$	−11.9912			−0.521355			−0.260677	+	0.965426i	$0.583946\pi$
$24$		−	1.96797i		−	0.0819989i
$25$	5.00000			0.200000
$26$	−2.06186			−0.0793024
$27$	−5.19615			−0.192450
$28$		−	11.6207i		−	0.415025i
$29$			46.8706i			1.61623i	0.589026	+	0.808114i	$0.299512\pi$
$29$			46.8706i			1.61623i	−0.589026	+	0.808114i	$0.700488\pi$
$30$			11.2198i			0.373992i
$31$	51.2760			1.65407			0.827033	−	0.562154i	$-0.190027\pi$
$31$	51.2760			1.65407			0.827033	+	0.562154i	$0.190027\pi$
$32$			45.9053i			1.43454i
$33$	−18.3439	+	5.14798i	−0.555875	+	0.155999i
$34$	43.0865			1.26725
$35$			5.91608i			0.169031i
$36$	−13.1766			−0.366018
$37$	49.0328			1.32521			0.662606	−	0.748968i	$-0.269451\pi$
$37$	49.0328			1.32521			0.662606	+	0.748968i	$0.269451\pi$
$38$	24.5110			0.645027
$39$			1.23277i			0.0316095i
$40$			2.54064i			0.0635161i
$41$			15.4167i			0.376018i	0.982167	+	0.188009i	$0.0602034\pi$
$41$			15.4167i			0.376018i	−0.982167	+	0.188009i	$0.939797\pi$
$42$	−13.2754			−0.316081
$43$			41.8430i			0.973092i	0.873655	+	0.486546i	$0.161743\pi$
$43$			41.8430i			0.973092i	−0.873655	+	0.486546i	$0.838257\pi$
$44$	−46.5173	+	13.0545i	−1.05721	+	0.296693i
$45$	6.70820			0.149071
$46$			34.7376i			0.755164i
$47$	12.2417			0.260462			0.130231	−	0.991484i	$-0.458428\pi$
$47$	12.2417			0.260462			0.130231	+	0.991484i	$0.458428\pi$
$48$	24.7291			0.515189
$49$	−7.00000			−0.142857
$50$		−	14.4847i		−	0.289693i
$51$		−	25.7611i		−	0.505119i
$52$			3.12611i			0.0601175i
$53$	−12.2476			−0.231087			−0.115543	−	0.993302i	$-0.536861\pi$
$53$	−12.2476			−0.231087			−0.115543	+	0.993302i	$0.536861\pi$
$54$			15.0529i			0.278757i
$55$	23.6819	−	6.64602i	0.430579	−	0.120837i
$56$	−3.00613			−0.0536809
$57$		−	14.6549i		−	0.257104i
$58$	135.781			2.34105
$59$	28.8624			0.489194			0.244597	−	0.969625i	$-0.421344\pi$
$59$	28.8624			0.489194			0.244597	+	0.969625i	$0.421344\pi$
$60$	17.0110			0.283516
$61$		−	112.815i		−	1.84943i	−0.380659	−	0.924715i	$-0.624303\pi$
$61$		−	112.815i		−	1.84943i	0.380659	−	0.924715i	$-0.375697\pi$
$62$		−	148.543i		−	2.39586i
$63$			7.93725i			0.125988i
$64$	75.8751			1.18555
$65$		−	1.59150i		−	0.0244846i
$66$	14.9134	+	53.1410i	0.225960	+	0.805166i
$67$	−91.9069			−1.37174			−0.685872	−	0.727722i	$-0.740579\pi$
$67$	−91.9069			−1.37174			−0.685872	+	0.727722i	$0.740579\pi$
$68$		−	65.3261i		−	0.960678i
$69$	20.7693			0.301004
$70$	17.1385			0.244835
$71$	116.132			1.63566			0.817830	−	0.575459i	$-0.195177\pi$
$71$	116.132			1.63566			0.817830	+	0.575459i	$0.195177\pi$
$72$			3.40863i			0.0473421i
$73$		−	25.4033i		−	0.347990i	−0.984747	−	0.173995i	$-0.944332\pi$
$73$		−	25.4033i		−	0.347990i	0.984747	−	0.173995i	$-0.0556677\pi$
$74$		−	142.045i		−	1.91952i
$75$	−8.66025			−0.115470
$76$		−	37.1626i		−	0.488982i
$77$	7.86367	+	28.0208i	0.102126	+	0.363906i
$78$	3.57125			0.0457852
$79$		−	17.1707i		−	0.217351i	−0.994077	−	0.108675i	$-0.965339\pi$
$79$		−	17.1707i		−	0.217351i	0.994077	−	0.108675i	$-0.0346609\pi$
$80$	−31.9251			−0.399063
$81$	9.00000			0.111111
$82$	44.6612			0.544649
$83$			145.242i			1.74991i	0.484205	+	0.874954i	$0.339109\pi$
$83$			145.242i			1.74991i	−0.484205	+	0.874954i	$0.660891\pi$
$84$			20.1276i			0.239615i
$85$			33.2574i			0.391264i
$86$	121.216			1.40949
$87$		−	81.1823i		−	0.933130i
$88$	3.37703	+	12.0334i	0.0383753	+	0.136743i
$89$	5.32225			0.0598005			0.0299003	−	0.999553i	$-0.490481\pi$
$89$	5.32225			0.0598005			0.0299003	+	0.999553i	$0.490481\pi$
$90$		−	19.4332i		−	0.215925i
$91$	1.88309			0.0206933
$92$	52.6677			0.572475
$93$	−88.8127			−0.954975
$94$		−	35.4633i		−	0.377270i
$95$			18.9194i			0.199152i
$96$		−	79.5103i		−	0.828232i
$97$	98.8311			1.01888			0.509439	−	0.860507i	$-0.329853\pi$
$97$	98.8311			1.01888			0.509439	+	0.860507i	$0.329853\pi$
$98$			20.2785i			0.206924i
$99$	31.7725	−	8.91657i	0.320935	−	0.0900663i
$100$	−21.9611			−0.219611
$101$		−	153.234i		−	1.51717i	−0.651574	−	0.758585i	$-0.725891\pi$
$101$		−	153.234i		−	1.51717i	0.651574	−	0.758585i	$-0.274109\pi$
$102$	−74.6281			−0.731648
$103$	180.215			1.74966			0.874832	−	0.484427i	$-0.160972\pi$
$103$	180.215			1.74966			0.874832	+	0.484427i	$0.160972\pi$
$104$	0.808686			0.00777582
$105$		−	10.2470i		−	0.0975900i
$106$			35.4805i			0.334722i
$107$		−	113.109i		−	1.05709i	−0.848904	−	0.528547i	$-0.822737\pi$
$107$		−	113.109i		−	1.05709i	0.848904	−	0.528547i	$-0.177263\pi$
$108$	22.8226			0.211320
$109$			181.876i			1.66859i	0.551320	+	0.834294i	$0.314124\pi$
$109$			181.876i			1.66859i	−0.551320	+	0.834294i	$0.685876\pi$
$110$	−19.2531	−	68.6047i	−0.175028	−	0.623679i
$111$	−84.9273			−0.765111
$112$		−	37.7742i		−	0.337270i
$113$	−86.4371			−0.764930			−0.382465	−	0.923970i	$-0.624925\pi$
$113$	−86.4371			−0.764930			−0.382465	+	0.923970i	$0.624925\pi$
$114$	−42.4543			−0.372406
$115$	−26.8130			−0.233157
$116$		−	205.866i		−	1.77470i
$117$		−	2.13522i		−	0.0182497i
$118$		−	83.6124i		−	0.708580i
$119$	−39.3507			−0.330678
$120$		−	4.40052i		−	0.0366710i
$121$	103.332	−	62.9560i	0.853985	−	0.520298i
$122$	−326.818			−2.67884
$123$		−	26.7026i		−	0.217094i
$124$	−225.215			−1.81625
$125$	11.1803			0.0894427
$126$	22.9937			0.182490
$127$		−	151.633i		−	1.19396i	−0.802255	−	0.596982i	$-0.796366\pi$
$127$		−	151.633i		−	1.19396i	0.802255	−	0.596982i	$-0.203634\pi$
$128$		−	36.1839i		−	0.282687i
$129$		−	72.4742i		−	0.561815i
$130$	−4.61046			−0.0354651
$131$			105.053i			0.801934i	0.916093	+	0.400967i	$0.131326\pi$
$131$			105.053i			0.801934i	−0.916093	+	0.400967i	$0.868674\pi$
$132$	80.5702	−	22.6110i	0.610381	−	0.171296i
$133$	−22.3858			−0.168314
$134$			266.248i			1.98692i
$135$	−11.6190			−0.0860663
$136$	−16.8990			−0.124258
$137$	−230.503			−1.68250			−0.841251	−	0.540645i	$-0.818180\pi$
$137$	−230.503			−1.68250			−0.841251	+	0.540645i	$0.818180\pi$
$138$		−	60.1672i		−	0.435994i
$139$			94.7740i			0.681827i	0.940095	+	0.340914i	$0.110736\pi$
$139$			94.7740i			0.681827i	−0.940095	+	0.340914i	$0.889264\pi$
$140$		−	25.9847i		−	0.185605i
$141$	−21.2032			−0.150378
$142$		−	336.426i		−	2.36920i
$143$	−2.11543	−	7.53793i	−0.0147932	−	0.0527128i
$144$	−42.8320			−0.297444
$145$			104.806i			0.722799i
$146$	−73.5915			−0.504052
$147$	12.1244			0.0824786
$148$	−215.363			−1.45515
$149$		−	242.846i		−	1.62984i	−0.579574	−	0.814919i	$-0.696781\pi$
$149$		−	242.846i		−	1.62984i	0.579574	−	0.814919i	$-0.303219\pi$
$150$			25.0882i			0.167254i
$151$			126.564i			0.838172i	0.907947	+	0.419086i	$0.137649\pi$
$151$			126.564i			0.838172i	−0.907947	+	0.419086i	$0.862351\pi$
$152$	−9.61350			−0.0632467
$153$			44.6195i			0.291631i
$154$	81.1742	−	22.7805i	0.527105	−	0.147925i
$155$	114.657			0.739721
$156$		−	5.41458i		−	0.0347089i
$157$	99.0931			0.631166			0.315583	−	0.948898i	$-0.397800\pi$
$157$	99.0931			0.631166			0.315583	+	0.948898i	$0.397800\pi$
$158$	−49.7423			−0.314825
$159$	21.2135			0.133418
$160$			102.647i			0.641546i
$161$		−	31.7256i		−	0.197054i
$162$		−	26.0724i		−	0.160941i
$163$	−166.857			−1.02366			−0.511831	−	0.859086i	$-0.671033\pi$
$163$	−166.857			−1.02366			−0.511831	+	0.859086i	$0.671033\pi$
$164$		−	67.7135i		−	0.412887i
$165$	−41.0182	+	11.5112i	−0.248595	+	0.0697651i
$166$	420.757			2.53468
$167$		−	204.702i		−	1.22576i	−0.790177	−	0.612879i	$-0.790011\pi$
$167$		−	204.702i		−	1.22576i	0.790177	−	0.612879i	$-0.209989\pi$
$168$	5.20677			0.0309927
$169$	168.493			0.997003
$170$	96.3445			0.566732
$171$			25.3831i			0.148439i
$172$		−	183.783i		−	1.06851i
$173$		−	155.004i		−	0.895979i	−0.894039	−	0.447990i	$-0.852140\pi$
$173$		−	155.004i		−	0.895979i	0.894039	−	0.447990i	$-0.147860\pi$
$174$	−235.180			−1.35161
$175$			13.2288i			0.0755929i
$176$	−151.209	+	42.4349i	−0.859142	+	0.241107i
$177$	−49.9912			−0.282436
$178$		−	15.4182i		−	0.0866190i
$179$	44.9185			0.250941			0.125471	−	0.992097i	$-0.459956\pi$
$179$	44.9185			0.250941			0.125471	+	0.992097i	$0.459956\pi$
$180$	−29.4639			−0.163688
$181$	349.101			1.92873			0.964367	−	0.264567i	$-0.0852289\pi$
$181$	349.101			1.92873			0.964367	+	0.264567i	$0.0852289\pi$
$182$		−	5.45517i		−	0.0299735i
$183$			195.402i			1.06777i
$184$		−	13.6245i		−	0.0740460i
$185$	109.641			0.592653
$186$			257.284i			1.38325i
$187$	44.2059	+	157.519i	0.236395	+	0.842350i
$188$	−53.7681			−0.286001
$189$		−	13.7477i		−	0.0727393i
$190$	54.8083			0.288465
$191$	72.8722			0.381530			0.190765	−	0.981636i	$-0.438903\pi$
$191$	72.8722			0.381530			0.190765	+	0.981636i	$0.438903\pi$
$192$	−131.420			−0.684477
$193$			65.7576i			0.340713i	0.985383	+	0.170356i	$0.0544919\pi$
$193$			65.7576i			0.340713i	−0.985383	+	0.170356i	$0.945508\pi$
$194$		−	286.307i		−	1.47581i
$195$			2.75656i			0.0141362i
$196$	30.7455			0.156865
$197$			91.6909i			0.465436i	0.972544	+	0.232718i	$0.0747620\pi$
$197$			91.6909i			0.465436i	−0.972544	+	0.232718i	$0.925238\pi$
$198$	−25.8307	−	92.0429i	−0.130458	−	0.464863i
$199$	−308.023			−1.54786			−0.773928	−	0.633273i	$-0.781711\pi$
$199$	−308.023			−1.54786			−0.773928	+	0.633273i	$0.781711\pi$
$200$			5.68105i			0.0284052i
$201$	159.187			0.791977
$202$	−443.909			−2.19757
$203$	−124.008			−0.610877
$204$			113.148i			0.554648i
$205$			34.4729i			0.168160i
$206$		−	522.071i		−	2.53433i
$207$	−35.9735			−0.173785
$208$			10.1617i			0.0488545i
$209$	25.1478	+	89.6095i	0.120324	+	0.428753i
$210$	−29.6847			−0.141356
$211$		−	24.2083i		−	0.114731i	−0.998353	−	0.0573656i	$-0.981730\pi$
$211$		−	24.2083i		−	0.114731i	0.998353	−	0.0573656i	$-0.0182701\pi$
$212$	53.7941			0.253746
$213$	−201.146			−0.944349
$214$	−327.669			−1.53117
$215$			93.5637i			0.435180i
$216$		−	5.90392i		−	0.0273330i
$217$			135.664i			0.625178i
$218$	526.882			2.41689
$219$			43.9998i			0.200912i
$220$	−104.016	+	29.1907i	−0.472799	+	0.132685i
$221$	10.5858			0.0478997
$222$			246.029i			1.10824i
$223$	−142.571			−0.639334			−0.319667	−	0.947530i	$-0.603571\pi$
$223$	−142.571			−0.639334			−0.319667	+	0.947530i	$0.603571\pi$
$224$	−121.454			−0.542205
$225$	15.0000			0.0666667
$226$			250.402i			1.10797i
$227$		−	104.955i		−	0.462355i	−0.972912	−	0.231178i	$-0.925742\pi$
$227$		−	104.955i		−	0.462355i	0.972912	−	0.231178i	$-0.0742579\pi$
$228$			64.3676i			0.282314i
$229$	303.799			1.32663			0.663316	−	0.748339i	$-0.269148\pi$
$229$	303.799			1.32663			0.663316	+	0.748339i	$0.269148\pi$
$230$			77.6755i			0.337720i
$231$	−13.6203	−	48.5334i	−0.0589623	−	0.210101i
$232$	−53.2549			−0.229547
$233$			336.730i			1.44519i	0.691270	+	0.722596i	$0.257051\pi$
$233$			336.730i			1.44519i	−0.691270	+	0.722596i	$0.742949\pi$
$234$	−6.18558			−0.0264341
$235$	27.3733			0.116482
$236$	−126.770			−0.537160
$237$			29.7405i			0.125487i
$238$			113.996i			0.478976i
$239$			94.1140i			0.393783i	0.980425	+	0.196891i	$0.0630846\pi$
$239$			94.1140i			0.393783i	−0.980425	+	0.196891i	$0.936915\pi$
$240$	55.2958			0.230399
$241$		−	96.7286i		−	0.401363i	−0.979656	−	0.200682i	$-0.935684\pi$
$241$		−	96.7286i		−	0.401363i	0.979656	−	0.200682i	$-0.0643157\pi$
$242$	−182.379	−	299.346i	−0.753633	−	1.23697i
$243$	−15.5885			−0.0641500
$244$			495.509i			2.03077i
$245$	−15.6525			−0.0638877
$246$	−77.3555			−0.314453
$247$	6.02205			0.0243808
$248$			58.2603i			0.234921i
$249$		−	251.567i		−	1.01031i
$250$		−	32.3887i		−	0.129555i
$251$	67.9504			0.270719			0.135359	−	0.990797i	$-0.456781\pi$
$251$	67.9504			0.270719			0.135359	+	0.990797i	$0.456781\pi$
$252$		−	34.8621i		−	0.138342i
$253$	−126.997	+	35.6400i	−0.501963	+	0.140870i
$254$	−439.272			−1.72942
$255$		−	57.6035i		−	0.225896i
$256$	198.678			0.776086
$257$	−324.191			−1.26144			−0.630722	−	0.776009i	$-0.717241\pi$
$257$	−324.191			−1.26144			−0.630722	+	0.776009i	$0.717241\pi$
$258$	−209.953			−0.813770
$259$			129.729i			0.500883i
$260$			6.99020i			0.0268854i
$261$			140.612i			0.538743i
$262$	304.332			1.16157
$263$			273.807i			1.04109i	0.853834	+	0.520546i	$0.174272\pi$
$263$			273.807i			1.04109i	−0.853834	+	0.520546i	$0.825728\pi$
$264$	−5.84919	−	20.8425i	−0.0221560	−	0.0789489i
$265$	−27.3865			−0.103345
$266$			64.8501i			0.243797i
$267$	−9.21840			−0.0345258
$268$	403.674			1.50625
$269$	333.929			1.24137			0.620685	−	0.784060i	$-0.286855\pi$
$269$	333.929			1.24137			0.620685	+	0.784060i	$0.286855\pi$
$270$			33.6593i			0.124664i
$271$			187.556i			0.692090i	0.938218	+	0.346045i	$0.112475\pi$
$271$			187.556i			0.692090i	−0.938218	+	0.346045i	$0.887525\pi$
$272$		−	212.349i		−	0.780695i
$273$	−3.26160			−0.0119473
$274$			667.750i			2.43705i
$275$	52.9542	−	14.8609i	0.192561	−	0.0540398i
$276$	−91.2231			−0.330519
$277$			177.652i			0.641341i	0.947191	+	0.320671i	$0.103908\pi$
$277$			177.652i			0.641341i	−0.947191	+	0.320671i	$0.896092\pi$
$278$	274.554			0.987603
$279$	153.828			0.551355
$280$	−6.72191			−0.0240068
$281$			69.4125i			0.247020i	0.992343	+	0.123510i	$0.0394150\pi$
$281$			69.4125i			0.247020i	−0.992343	+	0.123510i	$0.960585\pi$
$282$			61.4243i			0.217817i
$283$		−	406.335i		−	1.43581i	−0.696140	−	0.717906i	$-0.745101\pi$
$283$		−	406.335i		−	1.43581i	0.696140	−	0.717906i	$-0.254899\pi$
$284$	−510.076			−1.79604
$285$		−	32.7694i		−	0.114980i
$286$	−21.8369	+	6.12824i	−0.0763527	+	0.0214274i
$287$	−40.7888			−0.142121
$288$			137.716i			0.478180i
$289$	67.7889			0.234564
$290$	303.616			1.04695
$291$	−171.180			−0.588249
$292$			111.577i			0.382112i
$293$		−	489.919i		−	1.67208i	−0.548669	−	0.836039i	$-0.684865\pi$
$293$		−	489.919i		−	1.67208i	0.548669	−	0.836039i	$-0.315135\pi$
$294$		−	35.1234i		−	0.119467i
$295$	64.5383			0.218774
$296$			55.7116i			0.188215i
$297$	−55.0317	+	15.4439i	−0.185292	+	0.0519998i
$298$	−703.508			−2.36077
$299$			8.53458i			0.0285438i
$300$	38.0377			0.126792
$301$	−110.706			−0.367794
$302$	366.647			1.21406
$303$			265.409i			0.875939i
$304$		−	120.801i		−	0.397371i
$305$		−	252.263i		−	0.827091i
$306$	129.260			0.422417
$307$			370.346i			1.20634i	0.797613	+	0.603169i	$0.206096\pi$
$307$			370.346i			1.20634i	−0.797613	+	0.603169i	$0.793904\pi$
$308$	−34.5389	−	123.073i	−0.112139	−	0.399588i
$309$	−312.142			−1.01017
$310$		−	332.153i		−	1.07146i
$311$	−143.777			−0.462306			−0.231153	−	0.972917i	$-0.574250\pi$
$311$	−143.777			−0.462306			−0.231153	+	0.972917i	$0.574250\pi$
$312$	−1.40068			−0.00448937
$313$	−146.378			−0.467660			−0.233830	−	0.972277i	$-0.575126\pi$
$313$	−146.378			−0.467660			−0.233830	+	0.972277i	$0.575126\pi$
$314$		−	287.066i		−	0.914223i
$315$			17.7482i			0.0563436i
$316$			75.4174i			0.238663i
$317$	28.3508			0.0894348			0.0447174	−	0.999000i	$-0.485761\pi$
$317$	28.3508			0.0894348			0.0447174	+	0.999000i	$0.485761\pi$
$318$		−	61.4540i		−	0.193252i
$319$	139.308	+	496.400i	0.436703	+	1.55611i
$320$	169.662			0.530193
$321$			195.911i			0.610314i
$322$	−91.9069			−0.285425
$323$	−125.842			−0.389605
$324$	−39.5299			−0.122006
$325$		−	3.55870i		−	0.0109498i
$326$			483.373i			1.48274i
$327$		−	315.018i		−	0.963359i
$328$	−17.5166			−0.0534044
$329$			32.3885i			0.0984452i
$330$	33.3473	+	118.827i	0.101052	+	0.360081i
$331$	602.605			1.82056			0.910279	−	0.413995i	$-0.135867\pi$
$331$	602.605			1.82056			0.910279	+	0.413995i	$0.135867\pi$
$332$		−	637.936i		−	1.92149i
$333$	147.098			0.441737
$334$	−593.007			−1.77547
$335$	−205.510			−0.613463
$336$			65.4269i			0.194723i
$337$			92.5156i			0.274527i	0.990535	+	0.137263i	$0.0438307\pi$
$337$			92.5156i			0.274527i	−0.990535	+	0.137263i	$0.956169\pi$
$338$		−	488.114i		−	1.44412i
$339$	149.713			0.441633
$340$		−	146.074i		−	0.429628i
$341$	543.057	−	152.402i	1.59254	−	0.446927i
$342$	73.5331			0.215009
$343$		−	18.5203i		−	0.0539949i
$344$	−47.5424			−0.138205
$345$	46.4416			0.134613
$346$	−449.037			−1.29780
$347$			142.199i			0.409796i	0.978783	+	0.204898i	$0.0656862\pi$
$347$			142.199i			0.409796i	−0.978783	+	0.204898i	$0.934314\pi$
$348$			356.570i			1.02463i
$349$			102.659i			0.294151i	0.989125	+	0.147076i	$0.0469861\pi$
$349$			102.659i			0.294151i	−0.989125	+	0.147076i	$0.953014\pi$
$350$	38.3228			0.109494
$351$			3.69831i			0.0105365i
$352$	136.439	+	486.176i	0.387611	+	1.38118i
$353$	399.221			1.13094			0.565469	−	0.824769i	$-0.308695\pi$
$353$	399.221			1.13094			0.565469	+	0.824769i	$0.308695\pi$
$354$			144.821i			0.409099i
$355$	259.679			0.731490
$356$	−23.3764			−0.0656641
$357$	68.1574			0.190917
$358$		−	130.126i		−	0.363480i
$359$			556.875i			1.55118i	0.631235	+	0.775592i	$0.282548\pi$
$359$			556.875i			1.55118i	−0.631235	+	0.775592i	$0.717452\pi$
$360$			7.62193i			0.0211720i
$361$	289.411			0.801693
$362$		−	1011.32i		−	2.79371i
$363$	−178.977	+	109.043i	−0.493048	+	0.300394i
$364$	−8.27091			−0.0227223
$365$		−	56.8035i		−	0.155626i
$366$	566.066			1.54663
$367$	73.7263			0.200889			0.100445	−	0.994943i	$-0.467974\pi$
$367$	73.7263			0.200889			0.100445	+	0.994943i	$0.467974\pi$
$368$	171.202			0.465222
$369$			46.2502i			0.125339i
$370$		−	317.622i		−	0.858437i
$371$		−	32.4041i		−	0.0873427i
$372$	390.084			1.04861
$373$			182.813i			0.490114i	0.969509	+	0.245057i	$0.0788067\pi$
$373$			182.813i			0.490114i	−0.969509	+	0.245057i	$0.921193\pi$
$374$	456.323	−	128.061i	1.22012	−	0.342410i
$375$	−19.3649			−0.0516398
$376$			13.9091i			0.0369924i
$377$	33.3597			0.0884872
$378$	−39.8262			−0.105360
$379$	−402.562			−1.06217			−0.531084	−	0.847319i	$-0.678215\pi$
$379$	−402.562			−1.06217			−0.531084	+	0.847319i	$0.678215\pi$
$380$		−	83.0982i		−	0.218679i
$381$			262.637i			0.689335i
$382$		−	211.106i		−	0.552633i
$383$	−17.2465			−0.0450301			−0.0225151	−	0.999747i	$-0.507167\pi$
$383$	−17.2465			−0.0450301			−0.0225151	+	0.999747i	$0.507167\pi$
$384$			62.6724i			0.163209i
$385$	17.5837	+	62.6563i	0.0456720	+	0.162744i
$386$	190.495			0.493511
$387$			125.529i			0.324364i
$388$	−434.087			−1.11878
$389$	−507.474			−1.30456			−0.652281	−	0.757978i	$-0.726188\pi$
$389$	−507.474			−1.30456			−0.652281	+	0.757978i	$0.726188\pi$
$390$	7.98555			0.0204758
$391$		−	178.346i		−	0.456129i
$392$		−	7.95347i		−	0.0202895i
$393$		−	181.958i		−	0.462997i
$394$	265.622			0.674168
$395$		−	38.3949i		−	0.0972022i
$396$	−139.552	+	39.1634i	−0.352403	+	0.0988976i
$397$	42.2426			0.106404			0.0532022	−	0.998584i	$-0.483057\pi$
$397$	42.2426			0.106404			0.0532022	+	0.998584i	$0.483057\pi$
$398$			892.323i			2.24202i
$399$	38.7733			0.0971762
$400$	−71.3866			−0.178467
$401$	−520.772			−1.29868			−0.649342	−	0.760497i	$-0.724955\pi$
$401$	−520.772			−1.29868			−0.649342	+	0.760497i	$0.724955\pi$
$402$		−	461.155i		−	1.14715i
$403$		−	36.4952i		−	0.0905588i
$404$			673.037i			1.66593i
$405$	20.1246			0.0496904
$406$			359.243i			0.884834i
$407$	519.299	−	145.735i	1.27592	−	0.358071i
$408$	29.2700			0.0717402
$409$			52.3323i			0.127952i	0.997951	+	0.0639760i	$0.0203781\pi$
$409$			52.3323i			0.127952i	−0.997951	+	0.0639760i	$0.979622\pi$
$410$	99.8655			0.243574
$411$	399.242			0.971393
$412$	−791.544			−1.92122
$413$			76.3628i			0.184898i
$414$			104.213i			0.251721i
$415$			324.772i			0.782583i
$416$	32.6726			0.0785399
$417$		−	164.153i		−	0.393653i
$418$	259.592	−	72.8514i	0.621035	−	0.174286i
$419$	−576.390			−1.37563			−0.687816	−	0.725885i	$-0.741430\pi$
$419$	−576.390			−1.37563			−0.687816	+	0.725885i	$0.741430\pi$
$420$			45.0068i			0.107159i
$421$	358.171			0.850761			0.425381	−	0.905014i	$-0.360140\pi$
$421$	358.171			0.850761			0.425381	+	0.905014i	$0.360140\pi$
$422$	−70.1297			−0.166184
$423$	36.7251			0.0868205
$424$		−	13.9159i		−	0.0328204i
$425$			74.3658i			0.174978i
$426$			582.707i			1.36786i
$427$	298.481			0.699019
$428$			496.799i			1.16075i
$429$	3.66402	+	13.0561i	0.00854085	+	0.0304337i
$430$	271.048			0.630344
$431$			164.732i			0.382209i	0.981570	+	0.191105i	$0.0612070\pi$
$431$			164.732i			0.382209i	−0.981570	+	0.191105i	$0.938793\pi$
$432$	74.1872			0.171730
$433$	514.038			1.18715			0.593577	−	0.804777i	$-0.297715\pi$
$433$	514.038			1.18715			0.593577	+	0.804777i	$0.297715\pi$
$434$	393.008			0.905549
$435$		−	181.529i		−	0.417308i
$436$		−	798.838i		−	1.83220i
$437$		−	101.458i		−	0.232168i
$438$	127.464			0.291014
$439$			715.735i			1.63038i	0.579196	+	0.815188i	$0.303367\pi$
$439$			715.735i			1.63038i	−0.579196	+	0.815188i	$0.696633\pi$
$440$	7.55127	+	26.9076i	0.0171620	+	0.0611535i
$441$	−21.0000			−0.0476190
$442$		−	30.6664i		−	0.0693810i
$443$	695.369			1.56968			0.784841	−	0.619697i	$-0.212745\pi$
$443$	695.369			1.56968			0.784841	+	0.619697i	$0.212745\pi$
$444$	373.019			0.840133
$445$	11.9009			0.0267436
$446$			413.020i			0.926053i
$447$			420.622i			0.940988i
$448$			200.747i			0.448095i
$449$	468.024			1.04237			0.521185	−	0.853444i	$-0.325490\pi$
$449$	468.024			1.04237			0.521185	+	0.853444i	$0.325490\pi$
$450$		−	43.4540i		−	0.0965644i
$451$	45.8214	+	163.276i	0.101600	+	0.362032i
$452$	379.650			0.839934
$453$		−	219.215i		−	0.483919i
$454$	−304.046			−0.669706
$455$	4.21071			0.00925431
$456$	16.6511			0.0365155
$457$		−	684.861i		−	1.49860i	−0.662229	−	0.749301i	$-0.730389\pi$
$457$		−	684.861i		−	1.49860i	0.662229	−	0.749301i	$-0.269611\pi$
$458$		−	880.084i		−	1.92158i
$459$		−	77.2833i		−	0.168373i
$460$	117.769			0.256019
$461$			529.665i			1.14895i	0.818523	+	0.574474i	$0.194793\pi$
$461$			529.665i			1.14895i	−0.818523	+	0.574474i	$0.805207\pi$
$462$	−140.598	+	39.4570i	−0.304324	+	0.0854048i
$463$	−416.136			−0.898782			−0.449391	−	0.893335i	$-0.648359\pi$
$463$	−416.136			−0.898782			−0.449391	+	0.893335i	$0.648359\pi$
$464$		−	669.187i		−	1.44221i
$465$	−198.591			−0.427078
$466$	975.483			2.09331
$467$	−729.942			−1.56304			−0.781522	−	0.623877i	$-0.785556\pi$
$467$	−729.942			−1.56304			−0.781522	+	0.623877i	$0.785556\pi$
$468$			9.37833i			0.0200392i
$469$		−	243.163i		−	0.518471i
$470$		−	79.2984i		−	0.168720i
$471$	−171.634			−0.364404
$472$			32.7938i			0.0694783i
$473$	124.365	+	443.153i	0.262929	+	0.936898i
$474$	86.1563			0.181764
$475$			42.3051i			0.0890635i
$476$	172.837			0.363102
$477$	−36.7428			−0.0770290
$478$	272.642			0.570381
$479$		−	195.068i		−	0.407239i	−0.979050	−	0.203620i	$-0.934729\pi$
$479$		−	195.068i		−	0.407239i	0.979050	−	0.203620i	$-0.0652706\pi$
$480$		−	177.790i		−	0.370397i
$481$		−	34.8986i		−	0.0725543i
$482$	−280.216			−0.581361
$483$			54.9504i			0.113769i
$484$	−453.857	+	276.516i	−0.937721	+	0.571314i
$485$	220.993			0.455656
$486$			45.1587i			0.0929191i
$487$	−555.859			−1.14139			−0.570697	−	0.821161i	$-0.693327\pi$
$487$	−555.859			−1.14139			−0.570697	+	0.821161i	$0.693327\pi$
$488$	128.182			0.262668
$489$	289.005			0.591012
$490$			45.3441i			0.0925391i
$491$			414.754i			0.844713i	0.906430	+	0.422357i	$0.138797\pi$
$491$			414.754i			0.844713i	−0.906430	+	0.422357i	$0.861203\pi$
$492$			117.283i			0.238381i
$493$	−697.115			−1.41403
$494$		−	17.4455i		−	0.0353147i
$495$	71.0456	−	19.9381i	0.143526	−	0.0402789i
$496$	−732.084			−1.47598
$497$			307.256i			0.618222i
$498$	−728.773			−1.46340
$499$	142.728			0.286027			0.143014	−	0.989721i	$-0.454321\pi$
$499$	142.728			0.286027			0.143014	+	0.989721i	$0.454321\pi$
$500$	−49.1064			−0.0982128
$501$			354.554i			0.707692i
$502$		−	196.848i		−	0.392127i
$503$			133.747i			0.265898i	0.991123	+	0.132949i	$0.0424446\pi$
$503$			133.747i			0.265898i	−0.991123	+	0.132949i	$0.957555\pi$
$504$	−9.01839			−0.0178936
$505$		−	342.642i		−	0.678499i
$506$	103.247	+	367.900i	0.204045	+	0.727076i
$507$	−291.839			−0.575620
$508$			666.006i			1.31104i
$509$	−412.459			−0.810332			−0.405166	−	0.914243i	$-0.632786\pi$
$509$	−412.459			−0.810332			−0.405166	+	0.914243i	$0.632786\pi$
$510$	−166.873			−0.327203
$511$	67.2108			0.131528
$512$		−	720.293i		−	1.40682i
$513$		−	43.9648i		−	0.0857013i
$514$			939.160i			1.82716i
$515$	402.974			0.782473
$516$			318.322i			0.616903i
$517$	129.650	−	36.3846i	0.250774	−	0.0703765i
$518$	375.815			0.725512
$519$			268.475i			0.517294i
$520$	1.80828			0.00347745
$521$	−630.906			−1.21095			−0.605476	−	0.795863i	$-0.707017\pi$
$521$	−630.906			−1.21095			−0.605476	+	0.795863i	$0.707017\pi$
$522$	407.343			0.780351
$523$			2.02836i			0.00387831i	0.999998	+	0.00193915i	$0.000617252\pi$
$523$			2.02836i			0.00387831i	−0.999998	+	0.00193915i	$0.999383\pi$
$524$		−	461.417i		−	0.880566i
$525$		−	22.9129i		−	0.0436436i
$526$	793.201			1.50799
$527$			762.637i			1.44713i
$528$	261.902	−	73.4994i	0.496026	−	0.139203i
$529$	−385.212			−0.728189
$530$			79.3368i			0.149692i
$531$	86.5873			0.163065
$532$	98.3231			0.184818
$533$	10.9727			0.0205867
$534$			26.7051i			0.0500095i
$535$		−	252.920i		−	0.472747i
$536$		−	104.425i		−	0.194824i
$537$	−77.8011			−0.144881
$538$		−	967.368i		−	1.79808i
$539$	−74.1359	+	20.8053i	−0.137543	+	0.0385999i
$540$	51.0329			0.0945053
$541$		−	540.779i		−	0.999592i	−0.866143	−	0.499796i	$-0.833408\pi$
$541$		−	540.779i		−	0.999592i	0.866143	−	0.499796i	$-0.166592\pi$
$542$	543.338			1.00247
$543$	−604.661			−1.11356
$544$	−682.757			−1.25507
$545$			406.687i			0.746215i
$546$			9.44863i			0.0173052i
$547$		−	370.898i		−	0.678059i	−0.940776	−	0.339029i	$-0.889901\pi$
$547$		−	370.898i		−	0.678059i	0.940776	−	0.339029i	$-0.110099\pi$
$548$	1012.42			1.84748
$549$		−	338.446i		−	0.616477i
$550$	−43.0511	−	153.405i	−0.0782748	−	0.278918i
$551$	−396.574			−0.719734
$552$			23.5983i			0.0427505i
$553$	45.4294			0.0821508
$554$	514.644			0.928961
$555$	−189.903			−0.342168
$556$		−	416.267i		−	0.748682i
$557$			263.296i			0.472703i	0.971668	+	0.236351i	$0.0759517\pi$
$557$			263.296i			0.472703i	−0.971668	+	0.236351i	$0.924048\pi$
$558$		−	445.629i		−	0.798619i
$559$	29.7813			0.0532760
$560$		−	84.4658i		−	0.150832i
$561$	−76.5668	−	272.832i	−0.136483	−	0.486331i
$562$	201.083			0.357799
$563$			731.582i			1.29944i	0.760176	+	0.649718i	$0.225113\pi$
$563$			731.582i			1.29944i	−0.760176	+	0.649718i	$0.774887\pi$
$564$	93.1291			0.165122
$565$	−193.279			−0.342087
$566$	−1177.12			−2.07973
$567$			23.8118i			0.0419961i
$568$			131.950i			0.232307i
$569$		−	473.306i		−	0.831821i	−0.909406	−	0.415910i	$-0.863463\pi$
$569$		−	473.306i		−	0.831821i	0.909406	−	0.415910i	$-0.136537\pi$
$570$	−94.9308			−0.166545
$571$			1012.32i			1.77289i	0.462838	+	0.886443i	$0.346831\pi$
$571$			1012.32i			1.77289i	−0.462838	+	0.886443i	$0.653169\pi$
$572$	9.29139	+	33.1082i	0.0162437	+	0.0578814i
$573$	−126.218			−0.220276
$574$			118.162i			0.205858i
$575$	−59.9558			−0.104271
$576$	227.625			0.395183
$577$	372.070			0.644836			0.322418	−	0.946597i	$-0.395504\pi$
$577$	372.070			0.644836			0.322418	+	0.946597i	$0.395504\pi$
$578$		−	196.380i		−	0.339757i
$579$		−	113.895i		−	0.196711i
$580$		−	460.330i		−	0.793672i
$581$	−384.275			−0.661403
$582$			495.898i			0.852059i
$583$	−129.713	+	36.4022i	−0.222492	+	0.0624395i
$584$	28.8635			0.0494237
$585$		−	4.77450i		−	0.00816153i
$586$	−1419.26			−2.42195
$587$	−504.784			−0.859939			−0.429969	−	0.902843i	$-0.641476\pi$
$587$	−504.784			−0.859939			−0.429969	+	0.902843i	$0.641476\pi$
$588$	−53.2527			−0.0905659
$589$			433.848i			0.736584i
$590$		−	186.963i		−	0.316887i
$591$		−	158.813i		−	0.268720i
$592$	−700.057			−1.18253
$593$		−	573.183i		−	0.966582i	−0.875460	−	0.483291i	$-0.839441\pi$
$593$		−	573.183i		−	0.966582i	0.875460	−	0.483291i	$-0.160559\pi$
$594$	44.7401	+	159.423i	0.0753200	+	0.268389i
$595$	−87.9909			−0.147884
$596$			1066.63i			1.78965i
$597$	533.512			0.893655
$598$	24.7241			0.0413446
$599$	−85.7158			−0.143098			−0.0715491	−	0.997437i	$-0.522794\pi$
$599$	−85.7158			−0.143098			−0.0715491	+	0.997437i	$0.522794\pi$
$600$		−	9.83987i		−	0.0163998i
$601$		−	1139.84i		−	1.89657i	−0.317419	−	0.948285i	$-0.602816\pi$
$601$		−	1139.84i		−	1.89657i	0.317419	−	0.948285i	$-0.397184\pi$
$602$			320.708i			0.532738i
$603$	−275.721			−0.457248
$604$		−	555.896i		−	0.920357i
$605$	231.058	−	140.774i	0.381914	−	0.232684i
$606$	768.873			1.26877
$607$			409.695i			0.674950i	0.941334	+	0.337475i	$0.109573\pi$
$607$			409.695i			0.674950i	−0.941334	+	0.337475i	$0.890427\pi$
$608$	−388.406			−0.638825
$609$	214.788			0.352690
$610$	−730.788			−1.19801
$611$		−	8.71290i		−	0.0142601i
$612$		−	195.978i		−	0.320226i
$613$			439.482i			0.716936i	0.933542	+	0.358468i	$0.116701\pi$
$613$			439.482i			0.716936i	−0.933542	+	0.358468i	$0.883299\pi$
$614$	1072.87			1.74734
$615$		−	59.7087i		−	0.0970874i
$616$	−31.8375	+	8.93478i	−0.0516842	+	0.0145045i
$617$	−154.070			−0.249708			−0.124854	−	0.992175i	$-0.539846\pi$
$617$	−154.070			−0.249708			−0.124854	+	0.992175i	$0.539846\pi$
$618$			904.254i			1.46319i
$619$	847.420			1.36901			0.684507	−	0.729006i	$-0.260017\pi$
$619$	847.420			1.36901			0.684507	+	0.729006i	$0.260017\pi$
$620$	−503.596			−0.812252
$621$	62.3079			0.100335
$622$			416.512i			0.669634i
$623$			14.0813i			0.0226025i
$624$		−	17.6006i		−	0.0282062i
$625$	25.0000			0.0400000
$626$			424.046i			0.677390i
$627$	−43.5572	−	155.208i	−0.0694693	−	0.247541i
$628$	−435.238			−0.693054
$629$			729.273i			1.15942i
$630$	51.4154			0.0816118
$631$	−1243.23			−1.97025			−0.985126	−	0.171836i	$-0.945030\pi$
$631$	−1243.23			−1.97025			−0.985126	+	0.171836i	$0.945030\pi$
$632$	19.5095			0.0308695
$633$			41.9300i			0.0662400i
$634$		−	82.1304i		−	0.129543i
$635$		−	339.063i		−	0.533957i
$636$	−93.1741			−0.146500
$637$			4.98218i			0.00782132i
$638$	1438.04	−	403.567i	2.25398	−	0.632550i
$639$	348.396			0.545220
$640$		−	80.9097i		−	0.126421i
$641$	−547.215			−0.853689			−0.426845	−	0.904325i	$-0.640375\pi$
$641$	−547.215			−0.853689			−0.426845	+	0.904325i	$0.640375\pi$
$642$	567.540			0.884019
$643$	−818.702			−1.27325			−0.636627	−	0.771172i	$-0.719671\pi$
$643$	−818.702			−1.27325			−0.636627	+	0.771172i	$0.719671\pi$
$644$			139.346i			0.216375i
$645$		−	162.057i		−	0.251251i
$646$			364.557i			0.564329i
$647$	853.865			1.31973			0.659865	−	0.751384i	$-0.270613\pi$
$647$	853.865			1.31973			0.659865	+	0.751384i	$0.270613\pi$
$648$			10.2259i			0.0157807i
$649$	305.678	−	85.7846i	0.470998	−	0.132180i
$650$	−10.3093			−0.0158605
$651$		−	234.976i		−	0.360947i
$652$	732.871			1.12404
$653$	−973.029			−1.49009			−0.745045	−	0.667014i	$-0.767572\pi$
$653$	−973.029			−1.49009			−0.745045	+	0.667014i	$0.767572\pi$
$654$	−912.587			−1.39539
$655$			234.906i			0.358636i
$656$		−	220.110i		−	0.335533i
$657$		−	76.2098i		−	0.115997i
$658$	93.8272			0.142595
$659$			608.065i			0.922709i	0.887216	+	0.461354i	$0.152636\pi$
$659$			608.065i			0.922709i	−0.887216	+	0.461354i	$0.847364\pi$
$660$	180.161	−	50.5598i	0.272971	−	0.0766058i
$661$	−845.646			−1.27934			−0.639671	−	0.768649i	$-0.720930\pi$
$661$	−845.646			−1.27934			−0.639671	+	0.768649i	$0.720930\pi$
$662$		−	1745.70i		−	2.63702i
$663$	−18.3352			−0.0276549
$664$	−165.026			−0.248533
$665$	−50.0561			−0.0752724
$666$		−	426.134i		−	0.639841i
$667$		−	562.033i		−	0.842628i
$668$			899.093i			1.34595i
$669$	246.941			0.369120
$670$			595.348i			0.888580i
$671$	−335.308	−	1194.81i	−0.499714	−	1.78064i
$672$	210.364			0.313042
$673$		−	1059.94i		−	1.57495i	−0.616343	−	0.787477i	$-0.711387\pi$
$673$		−	1059.94i		−	1.57495i	0.616343	−	0.787477i	$-0.288613\pi$
$674$	268.011			0.397643
$675$	−25.9808			−0.0384900
$676$	−740.059			−1.09476
$677$		−	105.704i		−	0.156135i	−0.996948	−	0.0780676i	$-0.975125\pi$
$677$		−	105.704i		−	0.156135i	0.996948	−	0.0780676i	$-0.0248750\pi$
$678$		−	433.710i		−	0.639690i
$679$			261.482i			0.385099i
$680$	−37.7874			−0.0555697
$681$			181.787i			0.266941i
$682$	−441.498	−	1573.20i	−0.647358	−	2.30674i
$683$	−793.770			−1.16218			−0.581091	−	0.813839i	$-0.697374\pi$
$683$	−793.770			−1.16218			−0.581091	+	0.813839i	$0.697374\pi$
$684$		−	111.488i		−	0.162994i
$685$	−515.420			−0.752437
$686$	−53.6519			−0.0782098
$687$	−526.195			−0.765932
$688$		−	597.406i		−	0.868322i
$689$			8.71711i			0.0126518i
$690$		−	134.538i		−	0.194983i
$691$	−338.653			−0.490091			−0.245045	−	0.969512i	$-0.578803\pi$
$691$	−338.653			−0.490091			−0.245045	+	0.969512i	$0.578803\pi$
$692$			680.812i			0.983832i
$693$	23.5910	+	84.0623i	0.0340419	+	0.121302i
$694$	411.941			0.593575
$695$			211.921i			0.304922i
$696$	92.2401			0.132529
$697$	−229.296			−0.328975
$698$	297.396			0.426068
$699$		−	583.233i		−	0.834382i
$700$		−	58.1035i		−	0.0830050i
$701$			42.6789i			0.0608829i	0.999537	+	0.0304415i	$0.00969132\pi$
$701$			42.6789i			0.0608829i	−0.999537	+	0.0304415i	$0.990309\pi$
$702$	10.7137			0.0152617
$703$			414.868i			0.590140i
$704$	803.582	−	225.515i	1.14145	−	0.320334i
$705$	−47.4119			−0.0672509
$706$		−	1156.52i		−	1.63813i
$707$	405.420			0.573436
$708$	219.572			0.310130
$709$	735.890			1.03793			0.518963	−	0.854797i	$-0.326318\pi$
$709$	735.890			1.03793			0.518963	+	0.854797i	$0.326318\pi$
$710$		−	752.272i		−	1.05954i
$711$		−	51.5121i		−	0.0724502i
$712$			6.04719i			0.00849324i
$713$	−614.859			−0.862355
$714$		−	197.447i		−	0.276537i
$715$	−4.73023	−	16.8553i	−0.00661571	−	0.0235739i
$716$	−197.291			−0.275547
$717$		−	163.010i		−	0.227350i
$718$	1613.23			2.24684
$719$	−613.250			−0.852921			−0.426460	−	0.904506i	$-0.640240\pi$
$719$	−613.250			−0.852921			−0.426460	+	0.904506i	$0.640240\pi$
$720$	−95.7752			−0.133021
$721$			476.805i			0.661311i
$722$		−	838.404i		−	1.16122i
$723$			167.539i			0.231727i
$724$	−1533.33			−2.11785
$725$			234.353i			0.323246i
$726$	315.890	+	518.483i	0.435110	+	0.714164i
$727$	−534.215			−0.734822			−0.367411	−	0.930059i	$-0.619756\pi$
$727$	−534.215			−0.734822			−0.367411	+	0.930059i	$0.619756\pi$
$728$			2.13958i			0.00293899i
$729$	27.0000			0.0370370
$730$	−164.556			−0.225419
$731$	−622.338			−0.851351
$732$		−	858.246i		−	1.17247i
$733$		−	1244.06i		−	1.69721i	−0.529024	−	0.848607i	$-0.677442\pi$
$733$		−	1244.06i		−	1.69721i	0.529024	−	0.848607i	$-0.322558\pi$
$734$		−	213.580i		−	0.290981i
$735$	27.1109			0.0368856
$736$		−	550.457i		−	0.747904i
$737$	−973.372	+	273.165i	−1.32072	+	0.370644i
$738$	133.984			0.181550
$739$		−	101.334i		−	0.137123i	−0.997647	−	0.0685616i	$-0.978159\pi$
$739$		−	101.334i		−	0.137123i	0.997647	−	0.0685616i	$-0.0218410\pi$
$740$	−481.565			−0.650764
$741$	−10.4305			−0.0140762
$742$	−93.8725			−0.126513
$743$			943.645i			1.27005i	0.772493	+	0.635024i	$0.219010\pi$
$743$			943.645i			1.27005i	−0.772493	+	0.635024i	$0.780990\pi$
$744$		−	100.910i		−	0.135632i
$745$		−	543.020i		−	0.728886i
$746$	529.596			0.709914
$747$			435.727i			0.583303i
$748$	−194.162	−	691.859i	−0.259574	−	0.924945i
$749$	299.259			0.399544
$750$			56.0988i			0.0747984i
$751$	731.692			0.974290			0.487145	−	0.873321i	$-0.338038\pi$
$751$	731.692			0.974290			0.487145	+	0.873321i	$0.338038\pi$
$752$	−174.779			−0.232418
$753$	−117.694			−0.156300
$754$		−	96.6407i		−	0.128171i
$755$			283.006i			0.374842i
$756$			60.3829i			0.0798716i
$757$	174.741			0.230834			0.115417	−	0.993317i	$-0.463180\pi$
$757$	174.741			0.230834			0.115417	+	0.993317i	$0.463180\pi$
$758$			1166.19i			1.53852i
$759$	219.964	−	61.7303i	0.289808	−	0.0813310i
$760$	−21.4964			−0.0282848
$761$		−	895.484i		−	1.17672i	−0.808599	−	0.588360i	$-0.799774\pi$
$761$		−	895.484i		−	1.17672i	0.808599	−	0.588360i	$-0.200226\pi$
$762$	760.841			0.998479
$763$	−481.199			−0.630667
$764$	−320.070			−0.418940
$765$			99.7722i			0.130421i
$766$			49.9620i			0.0652246i
$767$		−	20.5425i		−	0.0267830i
$768$	−344.121			−0.448074
$769$		−	866.291i		−	1.12652i	−0.826281	−	0.563258i	$-0.809548\pi$
$769$		−	866.291i		−	1.12652i	0.826281	−	0.563258i	$-0.190452\pi$
$770$	181.511	−	50.9388i	0.235729	−	0.0661543i
$771$	561.516			0.728295
$772$		−	288.821i		−	0.374121i
$773$	26.2361			0.0339406			0.0169703	−	0.999856i	$-0.494598\pi$
$773$	26.2361			0.0339406			0.0169703	+	0.999856i	$0.494598\pi$
$774$	363.649			0.469830
$775$	256.380			0.330813
$776$			112.293i			0.144707i
$777$		−	224.697i		−	0.289185i
$778$			1470.12i			1.88961i
$779$	−130.441			−0.167447
$780$		−	12.1074i		−	0.0155223i
$781$	1229.94	−	345.166i	1.57482	−	0.441954i
$782$	−516.658			−0.660687
$783$		−	243.547i		−	0.311043i
$784$	99.9413			0.127476
$785$	221.579			0.282266
$786$	−527.119			−0.670635
$787$			457.871i			0.581793i	0.956754	+	0.290897i	$0.0939536\pi$
$787$			457.871i			0.581793i	−0.956754	+	0.290897i	$0.906046\pi$
$788$		−	402.726i		−	0.511074i
$789$		−	474.248i		−	0.601075i
$790$	−111.227			−0.140794
$791$		−	228.691i		−	0.289116i
$792$	10.1311	+	36.1003i	0.0127918	+	0.0455812i
$793$	−80.2951			−0.101255
$794$		−	122.374i		−	0.154123i
$795$	47.4348			0.0596664
$796$	1352.90			1.69963
$797$	1074.95			1.34874			0.674372	−	0.738392i	$-0.264415\pi$
$797$	1074.95			1.34874			0.674372	+	0.738392i	$0.264415\pi$
$798$		−	112.324i		−	0.140756i
$799$			182.073i			0.227876i
$800$			229.526i			0.286908i
$801$	15.9667			0.0199335
$802$			1508.64i			1.88110i
$803$	−75.5033	−	269.042i	−0.0940266	−	0.335046i
$804$	−699.185			−0.869633
$805$		−	70.9406i		−	0.0881250i
$806$	−105.724			−0.131171
$807$	−578.381			−0.716705
$808$	174.106			0.215478
$809$			42.4671i			0.0524933i	0.999655	+	0.0262466i	$0.00835552\pi$
$809$			42.4671i			0.0524933i	−0.999655	+	0.0262466i	$0.991644\pi$
$810$		−	58.2996i		−	0.0719748i
$811$			285.790i			0.352392i	0.984355	+	0.176196i	$0.0563792\pi$
$811$			285.790i			0.352392i	−0.984355	+	0.176196i	$0.943621\pi$
$812$	544.669			0.670775
$813$		−	324.857i		−	0.399578i
$814$	−422.184	−	1504.37i	−0.518653	−	1.84813i
$815$	−373.103			−0.457796
$816$			367.799i			0.450734i
$817$	−354.035			−0.433335
$818$	151.603			0.185334
$819$	5.64926			0.00689775
$820$		−	151.412i		−	0.184649i
$821$			56.1359i			0.0683750i	0.999415	+	0.0341875i	$0.0108843\pi$
$821$			56.1359i			0.0683750i	−0.999415	+	0.0341875i	$0.989116\pi$
$822$		−	1156.58i		−	1.40703i
$823$	−729.017			−0.885804			−0.442902	−	0.896570i	$-0.646051\pi$
$823$	−729.017			−0.885804			−0.442902	+	0.896570i	$0.646051\pi$
$824$			204.762i			0.248498i
$825$	−91.7194	+	25.7399i	−0.111175	+	0.0311999i
$826$	221.218			0.267818
$827$		−	126.809i		−	0.153336i	−0.997057	−	0.0766679i	$-0.975572\pi$
$827$		−	126.809i		−	0.153336i	0.997057	−	0.0766679i	$-0.0244281\pi$
$828$	158.003			0.190825
$829$	251.855			0.303806			0.151903	−	0.988395i	$-0.451460\pi$
$829$	251.855			0.303806			0.151903	+	0.988395i	$0.451460\pi$
$830$	940.842			1.13354
$831$		−	307.701i		−	0.370279i
$832$		−	54.0033i		−	0.0649079i
$833$		−	104.112i		−	0.124985i
$834$	−475.541			−0.570193
$835$		−	457.727i		−	0.548176i
$836$	−110.454	−	393.584i	−0.132122	−	0.470794i
$837$	−266.438			−0.318325
$838$			1669.76i			1.99256i
$839$	199.028			0.237220			0.118610	−	0.992941i	$-0.462156\pi$
$839$	199.028			0.237220			0.118610	+	0.992941i	$0.462156\pi$
$840$	11.6427			0.0138603
$841$	−1355.86			−1.61219
$842$		−	1037.60i		−	1.23230i
$843$		−	120.226i		−	0.142617i
$844$			106.328i			0.125981i
$845$	376.763			0.445873
$846$		−	106.390i		−	0.125757i
$847$	166.566	+	273.391i	0.196654	+	0.322776i
$848$	174.863			0.206206
$849$			703.793i			0.828967i
$850$	215.433			0.253450
$851$	−587.960			−0.690905
$852$	883.478			1.03695
$853$			738.707i			0.866011i	0.901391	+	0.433005i	$0.142547\pi$
$853$			738.707i			0.866011i	−0.901391	+	0.433005i	$0.857453\pi$
$854$		−	864.679i		−	1.01251i
$855$			56.7583i			0.0663840i
$856$	128.516			0.150135
$857$		−	574.376i		−	0.670217i	−0.942180	−	0.335109i	$-0.891227\pi$
$857$		−	574.376i		−	0.670217i	0.942180	−	0.335109i	$-0.108773\pi$
$858$	37.8226	−	10.6144i	0.0440822	−	0.0123711i
$859$	1020.80			1.18836			0.594178	−	0.804334i	$-0.297478\pi$
$859$	1020.80			1.18836			0.594178	+	0.804334i	$0.297478\pi$
$860$		−	410.952i		−	0.477851i
$861$	70.6483			0.0820538
$862$	477.218			0.553617
$863$	600.040			0.695295			0.347648	−	0.937625i	$-0.386981\pi$
$863$	600.040			0.695295			0.347648	+	0.937625i	$0.386981\pi$
$864$		−	238.531i		−	0.276077i
$865$		−	346.600i		−	0.400694i
$866$		−	1489.13i		−	1.71955i
$867$	−117.414			−0.135425
$868$		−	595.863i		−	0.686478i
$869$	−51.0346	−	181.852i	−0.0587279	−	0.209266i
$870$	−525.878			−0.604457
$871$			65.4138i			0.0751019i
$872$	−206.649			−0.236983
$873$	296.493			0.339626
$874$	−293.915			−0.336288
$875$			29.5804i			0.0338062i
$876$		−	193.256i		−	0.220612i
$877$			901.224i			1.02762i	0.857904	+	0.513811i	$0.171767\pi$
$877$			901.224i			1.02762i	−0.857904	+	0.513811i	$0.828233\pi$
$878$	2073.44			2.36154
$879$			848.565i			0.965375i
$880$	−338.114	+	94.8873i	−0.384220	+	0.107827i
$881$	−1631.17			−1.85150			−0.925751	−	0.378133i	$-0.876566\pi$
$881$	−1631.17			−1.85150			−0.925751	+	0.378133i	$0.876566\pi$
$882$			60.8356i			0.0689746i
$883$	1371.17			1.55286			0.776430	−	0.630204i	$-0.217029\pi$
$883$	1371.17			1.55286			0.776430	+	0.630204i	$0.217029\pi$
$884$	−46.4952			−0.0525964
$885$	−111.784			−0.126309
$886$		−	2014.44i		−	2.27363i
$887$			54.8712i			0.0618615i	0.999522	+	0.0309308i	$0.00984714\pi$
$887$			54.8712i			0.0618615i	−0.999522	+	0.0309308i	$0.990153\pi$
$888$		−	96.4953i		−	0.108666i
$889$	401.184			0.451276
$890$		−	34.4761i		−	0.0387372i
$891$	95.3176	−	26.7497i	0.106978	−	0.0300221i
$892$	626.204			0.702022
$893$			103.577i			0.115988i
$894$	1218.51			1.36299
$895$	100.441			0.112224
$896$	95.7337			0.106846
$897$		−	14.7823i		−	0.0164797i
$898$		−	1355.83i		−	1.50984i
$899$			2403.34i			2.67335i
$900$	−65.8832			−0.0732035
$901$		−	182.161i		−	0.202176i
$902$	473.000	−	132.742i	0.524390	−	0.147164i
$903$	191.749			0.212346
$904$		−	98.2107i		−	0.108640i
$905$	780.614			0.862556
$906$	−635.051			−0.700940
$907$	216.133			0.238294			0.119147	−	0.992877i	$-0.461984\pi$
$907$	216.133			0.238294			0.119147	+	0.992877i	$0.461984\pi$
$908$			460.983i			0.507691i
$909$		−	459.703i		−	0.505723i
$910$		−	12.1981i		−	0.0134045i
$911$	−991.648			−1.08853			−0.544263	−	0.838915i	$-0.683191\pi$
$911$	−991.648			−1.08853			−0.544263	+	0.838915i	$0.683191\pi$
$912$			209.233i			0.229422i
$913$	431.688	+	1538.24i	0.472824	+	1.68482i
$914$	−1984.00			−2.17067
$915$			436.932i			0.477521i
$916$	−1334.35			−1.45671
$917$	−277.945			−0.303103
$918$	−223.884			−0.243883
$919$			567.429i			0.617442i	0.951153	+	0.308721i	$0.0999009\pi$
$919$			567.429i			0.617442i	−0.951153	+	0.308721i	$0.900099\pi$
$920$		−	30.4652i		−	0.0331144i
$921$		−	641.458i		−	0.696480i
$922$	1534.40			1.66421
$923$		−	82.6557i		−	0.0895511i
$924$	59.8232	+	213.169i	0.0647437	+	0.230702i
$925$	245.164			0.265042
$926$			1205.52i			1.30186i
$927$	540.646			0.583221
$928$	−2151.61			−2.31854
$929$	1317.80			1.41851			0.709257	−	0.704950i	$-0.249031\pi$
$929$	1317.80			1.41851			0.709257	+	0.704950i	$0.249031\pi$
$930$			575.305i			0.618608i
$931$		−	59.2272i		−	0.0636168i
$932$		−	1478.99i		−	1.58690i
$933$	249.029			0.266912
$934$			2114.59i			2.26402i
$935$	98.8473	+	352.224i	0.105719	+	0.376710i
$936$	2.42606			0.00259194
$937$		−	1078.36i		−	1.15086i	−0.817850	−	0.575431i	$-0.804834\pi$
$937$		−	1078.36i		−	1.15086i	0.817850	−	0.575431i	$-0.195166\pi$
$938$	−704.426			−0.750987
$939$	253.534			0.270004
$940$	−120.229			−0.127903
$941$		−	1421.53i		−	1.51066i	−0.655344	−	0.755331i	$-0.727476\pi$
$941$		−	1421.53i		−	1.51066i	0.655344	−	0.755331i	$-0.272524\pi$
$942$			497.213i			0.527827i
$943$		−	184.864i		−	0.196039i
$944$	−412.078			−0.436523
$945$		−	30.7409i		−	0.0325300i
$946$	1283.78	−	360.278i	1.35706	−	0.380843i
$947$	866.866			0.915381			0.457690	−	0.889112i	$-0.348677\pi$
$947$	866.866			0.915381			0.457690	+	0.889112i	$0.348677\pi$
$948$		−	130.627i		−	0.137792i
$949$	−18.0805			−0.0190522
$950$	122.555			0.129005
$951$	−49.1051			−0.0516352
$952$		−	44.7107i		−	0.0469650i
$953$			525.153i			0.551053i	0.961293	+	0.275526i	$0.0888522\pi$
$953$			525.153i			0.551053i	−0.961293	+	0.275526i	$0.911148\pi$
$954$			106.441i			0.111574i
$955$	162.947			0.170625
$956$		−	413.369i		−	0.432394i
$957$	−241.289	−	859.790i	−0.252131	−	0.898422i
$958$	−565.097			−0.589872
$959$		−	609.853i		−	0.635926i
$960$	−293.863			−0.306107
$961$	1668.23			1.73593
$962$	−101.099			−0.105092
$963$		−	339.327i		−	0.352365i
$964$			424.852i			0.440718i
$965$			147.038i			0.152371i
$966$	159.187			0.164790
$967$		−	1703.41i		−	1.76154i	−0.473543	−	0.880771i	$-0.657025\pi$
$967$		−	1703.41i		−	1.76154i	0.473543	−	0.880771i	$-0.342975\pi$
$968$	71.5312	+	117.407i	0.0738959	+	0.121288i
$969$	217.965			0.224938
$970$		−	640.202i		−	0.660002i
$971$	690.121			0.710732			0.355366	−	0.934727i	$-0.384356\pi$
$971$	690.121			0.710732			0.355366	+	0.934727i	$0.384356\pi$
$972$	68.4678			0.0704401
$973$	−250.748			−0.257706
$974$			1610.28i			1.65327i
$975$			6.16385i			0.00632189i
$976$			1610.70i			1.65031i
$977$	−617.192			−0.631721			−0.315861	−	0.948806i	$-0.602293\pi$
$977$	−617.192			−0.631721			−0.315861	+	0.948806i	$0.602293\pi$
$978$		−	837.227i		−	0.856060i
$979$	56.3671	−	15.8187i	0.0575762	−	0.0161580i
$980$	68.7490			0.0701520
$981$			545.628i			0.556196i
$982$	1201.51			1.22354
$983$	371.796			0.378226			0.189113	−	0.981955i	$-0.439439\pi$
$983$	371.796			0.378226			0.189113	+	0.981955i	$0.439439\pi$
$984$	30.3397			0.0308330
$985$			205.027i			0.208149i
$986$			2019.49i			2.04817i
$987$		−	56.0985i		−	0.0568374i
$988$	−26.4501			−0.0267714
$989$		−	501.746i		−	0.507326i
$990$	−57.7592	−	205.814i	−0.0583426	−	0.207893i
$991$	1315.99			1.32794			0.663971	−	0.747759i	$-0.268870\pi$
$991$	1315.99			1.32794			0.663971	+	0.747759i	$0.268870\pi$
$992$			2353.84i			2.37282i
$993$	−1043.74			−1.05110
$994$	890.100			0.895473
$995$	−688.761			−0.692222
$996$			1104.94i			1.10937i
$997$			207.654i			0.208279i	0.994563	+	0.104139i	$0.0332088\pi$
$997$			207.654i			0.208279i	−0.994563	+	0.104139i	$0.966791\pi$
$998$		−	413.472i		−	0.414301i
$999$	−254.782			−0.255037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.3.b.a.736.18	✓	96
11.10	odd	2	inner	1155.3.b.a.736.79	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.3.b.a.736.18	✓	96	1.1	even	1	trivial
1155.3.b.a.736.79	yes	96	11.10	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1155.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.89693i q^{2} -1.73205 q^{3} -4.39221 q^{4} +2.23607 q^{5} +5.01763i q^{6} +2.64575i q^{7} +1.13621i q^{8} +3.00000 q^{9} +O(q^{10})\)	\(q-2.89693i q^{2} -1.73205 q^{3} -4.39221 q^{4} +2.23607 q^{5} +5.01763i q^{6} +2.64575i q^{7} +1.13621i q^{8} +3.00000 q^{9} -6.47774i q^{10} +(10.5908 - 2.97219i) q^{11} +7.60753 q^{12} -0.711740i q^{13} +7.66456 q^{14} -3.87298 q^{15} -14.2773 q^{16} +14.8732i q^{17} -8.69079i q^{18} +8.46103i q^{19} -9.82128 q^{20} -4.58258i q^{21} +(-8.61023 - 30.6810i) q^{22} -11.9912 q^{23} -1.96797i q^{24} +5.00000 q^{25} -2.06186 q^{26} -5.19615 q^{27} -11.6207i q^{28} +46.8706i q^{29} +11.2198i q^{30} +51.2760 q^{31} +45.9053i q^{32} +(-18.3439 + 5.14798i) q^{33} +43.0865 q^{34} +5.91608i q^{35} -13.1766 q^{36} +49.0328 q^{37} +24.5110 q^{38} +1.23277i q^{39} +2.54064i q^{40} +15.4167i q^{41} -13.2754 q^{42} +41.8430i q^{43} +(-46.5173 + 13.0545i) q^{44} +6.70820 q^{45} +34.7376i q^{46} +12.2417 q^{47} +24.7291 q^{48} -7.00000 q^{49} -14.4847i q^{50} -25.7611i q^{51} +3.12611i q^{52} -12.2476 q^{53} +15.0529i q^{54} +(23.6819 - 6.64602i) q^{55} -3.00613 q^{56} -14.6549i q^{57} +135.781 q^{58} +28.8624 q^{59} +17.0110 q^{60} -112.815i q^{61} -148.543i q^{62} +7.93725i q^{63} +75.8751 q^{64} -1.59150i q^{65} +(14.9134 + 53.1410i) q^{66} -91.9069 q^{67} -65.3261i q^{68} +20.7693 q^{69} +17.1385 q^{70} +116.132 q^{71} +3.40863i q^{72} -25.4033i q^{73} -142.045i q^{74} -8.66025 q^{75} -37.1626i q^{76} +(7.86367 + 28.0208i) q^{77} +3.57125 q^{78} -17.1707i q^{79} -31.9251 q^{80} +9.00000 q^{81} +44.6612 q^{82} +145.242i q^{83} +20.1276i q^{84} +33.2574i q^{85} +121.216 q^{86} -81.1823i q^{87} +(3.37703 + 12.0334i) q^{88} +5.32225 q^{89} -19.4332i q^{90} +1.88309 q^{91} +52.6677 q^{92} -88.8127 q^{93} -35.4633i q^{94} +18.9194i q^{95} -79.5103i q^{96} +98.8311 q^{97} +20.2785i q^{98} +(31.7725 - 8.91657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 216 q^{4} + 288 q^{9}+O(q^{10}) \) 96 * q - 216 * q^4 + 288 * q^9	\( 96 q - 216 q^{4} + 288 q^{9} + 40 q^{11} - 56 q^{14} + 488 q^{16} + 56 q^{22} + 16 q^{23} + 480 q^{25} - 64 q^{26} + 192 q^{31} + 24 q^{33} + 176 q^{34} - 648 q^{36} - 112 q^{37} - 272 q^{38} - 520 q^{44} + 416 q^{47} - 192 q^{48} - 672 q^{49} + 112 q^{53} - 80 q^{55} + 280 q^{56} - 352 q^{58} + 512 q^{59} - 1112 q^{64} + 288 q^{66} - 304 q^{67} - 480 q^{71} + 224 q^{77} + 240 q^{78} + 864 q^{81} - 720 q^{82} - 432 q^{86} - 376 q^{88} - 32 q^{89} - 384 q^{92} + 384 q^{93} + 272 q^{97} + 120 q^{99}+O(q^{100}) \) 96 * q - 216 * q^4 + 288 * q^9 + 40 * q^11 - 56 * q^14 + 488 * q^16 + 56 * q^22 + 16 * q^23 + 480 * q^25 - 64 * q^26 + 192 * q^31 + 24 * q^33 + 176 * q^34 - 648 * q^36 - 112 * q^37 - 272 * q^38 - 520 * q^44 + 416 * q^47 - 192 * q^48 - 672 * q^49 + 112 * q^53 - 80 * q^55 + 280 * q^56 - 352 * q^58 + 512 * q^59 - 1112 * q^64 + 288 * q^66 - 304 * q^67 - 480 * q^71 + 224 * q^77 + 240 * q^78 + 864 * q^81 - 720 * q^82 - 432 * q^86 - 376 * q^88 - 32 * q^89 - 384 * q^92 + 384 * q^93 + 272 * q^97 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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