LMFDB - Embedded newform 121.3.d.a.40.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,3,Mod(40,121)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("121.40"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	121.d (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-5,-5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.29701119876$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 11)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			40.1
Root			$-0.309017 - 0.951057i$ of defining polynomial
Character	$\chi$	$=$	121.40
Dual form			121.3.d.a.118.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.427051 - 0.587785i) q^{2} +(0.427051 - 1.31433i) q^{3} +(1.07295 + 3.30220i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(-0.590170 - 0.812299i) q^{6} +(9.47214 - 3.07768i) q^{7} +(5.16312 + 1.67760i) q^{8} +(5.73607 + 4.16750i) q^{9} +2.90617i q^{10} +4.79837 q^{12} +(3.09017 - 4.25325i) q^{13} +(2.23607 - 6.88191i) q^{14} +(1.70820 + 5.25731i) q^{15} +(-8.04508 + 5.84510i) q^{16} +(-8.98278 - 12.3637i) q^{17} +(4.89919 - 1.59184i) q^{18} +(1.97214 + 0.640786i) q^{19} +(-11.2361 - 8.16348i) q^{20} -13.7638i q^{21} -2.76393 q^{23} +(4.40983 - 6.06961i) q^{24} +(-2.78115 + 8.55951i) q^{25} +(-1.18034 - 3.63271i) q^{26} +(17.9894 - 13.0700i) q^{27} +(20.3262 + 27.9767i) q^{28} +(-27.0344 + 8.78402i) q^{29} +(3.81966 + 1.24108i) q^{30} +(5.76393 + 4.18774i) q^{31} +28.9402i q^{32} -11.1033 q^{34} +(-23.4164 + 32.2299i) q^{35} +(-7.60739 + 23.4131i) q^{36} +(-12.4377 - 38.2793i) q^{37} +(1.21885 - 0.885544i) q^{38} +(-4.27051 - 5.87785i) q^{39} +(-20.6525 + 6.71040i) q^{40} +(-66.7320 - 21.6825i) q^{41} +(-8.09017 - 5.87785i) q^{42} -23.0624i q^{43} -28.3607 q^{45} +(-1.18034 + 1.62460i) q^{46} +(8.41641 - 25.9030i) q^{47} +(4.24671 + 13.0700i) q^{48} +(40.6074 - 29.5030i) q^{49} +(3.84346 + 5.29007i) q^{50} +(-20.0861 + 6.52637i) q^{51} +(17.3607 + 5.64083i) q^{52} +(9.27051 + 6.73542i) q^{53} -16.1554i q^{54} +54.0689 q^{56} +(1.68441 - 2.31838i) q^{57} +(-6.38197 + 19.6417i) q^{58} +(-0.701626 - 2.15938i) q^{59} +(-15.5279 + 11.2817i) q^{60} +(-13.2918 - 18.2946i) q^{61} +(4.92299 - 1.59958i) q^{62} +(67.1591 + 21.8213i) q^{63} +(-15.1697 - 11.0214i) q^{64} +21.0292i q^{65} -38.4934 q^{67} +(31.1894 - 42.9286i) q^{68} +(-1.18034 + 3.63271i) q^{69} +(8.94427 + 27.5276i) q^{70} +(-61.7426 + 44.8587i) q^{71} +(22.6246 + 31.1401i) q^{72} +(97.8353 - 31.7886i) q^{73} +(-27.8115 - 9.03651i) q^{74} +(10.0623 + 7.31069i) q^{75} +7.19991i q^{76} -5.27864 q^{78} +(2.31308 - 3.18368i) q^{79} +(12.2918 - 37.8303i) q^{80} +(10.2229 + 31.4629i) q^{81} +(-41.2426 + 29.9645i) q^{82} +(-48.9296 - 67.3458i) q^{83} +(45.4508 - 14.7679i) q^{84} +(58.1378 + 18.8901i) q^{85} +(-13.5557 - 9.84881i) q^{86} +39.2833i q^{87} +123.297 q^{89} +(-12.1115 + 16.6700i) q^{90} +(16.1803 - 49.7980i) q^{91} +(-2.96556 - 9.12705i) q^{92} +(7.96556 - 5.78732i) q^{93} +(-11.6312 - 16.0090i) q^{94} +(-7.88854 + 2.56314i) q^{95} +(38.0370 + 12.3590i) q^{96} +(62.6246 + 45.4994i) q^{97} -36.4677i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 5 q^{2} - 5 q^{3} + 11 q^{4} - 4 q^{5} + 20 q^{6} + 20 q^{7} + 5 q^{8} + 14 q^{9} - 30 q^{12} - 10 q^{13} - 20 q^{15} - 21 q^{16} - 65 q^{17} - 5 q^{18} - 10 q^{19} - 36 q^{20} - 20 q^{23} + 40 q^{24}+ \cdots + 170 q^{97}+O(q^{100}) $ 4 * q - 5 * q^2 - 5 * q^3 + 11 * q^4 - 4 * q^5 + 20 * q^6 + 20 * q^7 + 5 * q^8 + 14 * q^9 - 30 * q^12 - 10 * q^13 - 20 * q^15 - 21 * q^16 - 65 * q^17 - 5 * q^18 - 10 * q^19 - 36 * q^20 - 20 * q^23 + 40 * q^24 + 9 * q^25 + 40 * q^26 + 25 * q^27 + 50 * q^28 - 50 * q^29 + 60 * q^30 + 32 * q^31 + 130 * q^34 - 40 * q^35 + 21 * q^36 - 90 * q^37 + 25 * q^38 + 50 * q^39 - 20 * q^40 - 135 * q^41 - 10 * q^42 - 24 * q^45 + 40 * q^46 - 20 * q^47 + 55 * q^48 + 111 * q^49 - 45 * q^50 + 65 * q^51 - 20 * q^52 - 30 * q^53 + 100 * q^56 + 85 * q^57 - 30 * q^58 - 52 * q^59 - 80 * q^60 - 80 * q^61 - 110 * q^62 + 130 * q^63 + 31 * q^64 - 230 * q^67 - 195 * q^68 + 40 * q^69 - 162 * q^71 + 10 * q^72 + 85 * q^73 + 90 * q^74 - 200 * q^78 + 130 * q^79 + 76 * q^80 + 184 * q^81 - 80 * q^82 + 10 * q^83 + 70 * q^84 - 90 * q^86 + 122 * q^89 - 120 * q^90 + 20 * q^91 - 70 * q^92 + 90 * q^93 + 110 * q^94 + 40 * q^95 - 105 * q^96 + 170 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	0.427051	−	0.587785i	0.213525	−	0.293893i	−0.688797	−	0.724954i	$-0.741861\pi$
$2$	0.427051	−	0.587785i	0.213525	−	0.293893i	0.902322	+	0.431062i	$0.141861\pi$
$3$	0.427051	−	1.31433i	0.142350	−	0.438109i	−0.854310	−	0.519763i	$-0.826020\pi$
$3$	0.427051	−	1.31433i	0.142350	−	0.438109i	0.996661	+	0.0816539i	$0.0260202\pi$
$4$	1.07295	+	3.30220i	0.268237	+	0.825549i
$5$	−3.23607	+	2.35114i	−0.647214	+	0.470228i	−0.862321	−	0.506362i	$-0.830990\pi$
$5$	−3.23607	+	2.35114i	−0.647214	+	0.470228i	0.215107	+	0.976590i	$0.430990\pi$
$6$	−0.590170	−	0.812299i	−0.0983617	−	0.135383i
$7$	9.47214	−	3.07768i	1.35316	−	0.439669i	0.459408	−	0.888225i	$-0.348062\pi$
$7$	9.47214	−	3.07768i	1.35316	−	0.439669i	0.893755	+	0.448556i	$0.148062\pi$
$8$	5.16312	+	1.67760i	0.645390	+	0.209700i
$9$	5.73607	+	4.16750i	0.637341	+	0.463055i
$10$			2.90617i			0.290617i
$11$		0			0
$11$		0			0
$12$	4.79837			0.399864
$13$	3.09017	−	4.25325i	0.237705	−	0.327173i	−0.673453	−	0.739230i	$-0.735190\pi$
$13$	3.09017	−	4.25325i	0.237705	−	0.327173i	0.911158	+	0.412057i	$0.135190\pi$
$14$	2.23607	−	6.88191i	0.159719	−	0.491565i
$15$	1.70820	+	5.25731i	0.113880	+	0.350487i
$16$	−8.04508	+	5.84510i	−0.502818	+	0.365319i
$17$	−8.98278	−	12.3637i	−0.528399	−	0.727279i	0.458487	−	0.888701i	$-0.348392\pi$
$17$	−8.98278	−	12.3637i	−0.528399	−	0.727279i	−0.986885	+	0.161423i	$0.948392\pi$
$18$	4.89919	−	1.59184i	0.272177	−	0.0884357i
$19$	1.97214	+	0.640786i	0.103797	+	0.0337256i	0.360455	−	0.932777i	$-0.382621\pi$
$19$	1.97214	+	0.640786i	0.103797	+	0.0337256i	−0.256658	+	0.966502i	$0.582621\pi$
$20$	−11.2361	−	8.16348i	−0.561803	−	0.408174i
$21$		−	13.7638i		−	0.655420i
$22$		0			0
$23$	−2.76393			−0.120171			−0.0600855	−	0.998193i	$-0.519137\pi$
$23$	−2.76393			−0.120171			−0.0600855	+	0.998193i	$0.519137\pi$
$24$	4.40983	−	6.06961i	0.183743	−	0.252900i
$25$	−2.78115	+	8.55951i	−0.111246	+	0.342380i
$26$	−1.18034	−	3.63271i	−0.0453977	−	0.139720i
$27$	17.9894	−	13.0700i	0.666272	−	0.484075i
$28$	20.3262	+	27.9767i	0.725937	+	0.999167i
$29$	−27.0344	+	8.78402i	−0.932222	+	0.302897i	−0.735471	−	0.677556i	$-0.763039\pi$
$29$	−27.0344	+	8.78402i	−0.932222	+	0.302897i	−0.196751	+	0.980453i	$0.563039\pi$
$30$	3.81966	+	1.24108i	0.127322	+	0.0413694i
$31$	5.76393	+	4.18774i	0.185933	+	0.135088i	0.676858	−	0.736113i	$-0.263341\pi$
$31$	5.76393	+	4.18774i	0.185933	+	0.135088i	−0.490925	+	0.871202i	$0.663341\pi$
$32$			28.9402i			0.904382i
$33$		0			0
$34$	−11.1033			−0.326568
$35$	−23.4164	+	32.2299i	−0.669040	+	0.920855i
$36$	−7.60739	+	23.4131i	−0.211316	+	0.650365i
$37$	−12.4377	−	38.2793i	−0.336154	−	1.03458i	−0.966151	−	0.257978i	$-0.916944\pi$
$37$	−12.4377	−	38.2793i	−0.336154	−	1.03458i	0.629997	−	0.776598i	$-0.283056\pi$
$38$	1.21885	−	0.885544i	0.0320749	−	0.0233038i
$39$	−4.27051	−	5.87785i	−0.109500	−	0.150714i
$40$	−20.6525	+	6.71040i	−0.516312	+	0.167760i
$41$	−66.7320	−	21.6825i	−1.62761	−	0.528842i	−0.653890	−	0.756590i	$-0.726864\pi$
$41$	−66.7320	−	21.6825i	−1.62761	−	0.528842i	−0.973720	+	0.227747i	$0.926864\pi$
$42$	−8.09017	−	5.87785i	−0.192623	−	0.139949i
$43$		−	23.0624i		−	0.536334i	−0.963372	−	0.268167i	$-0.913582\pi$
$43$		−	23.0624i		−	0.536334i	0.963372	−	0.268167i	$-0.0864180\pi$
$44$		0			0
$45$	−28.3607			−0.630237
$46$	−1.18034	+	1.62460i	−0.0256596	+	0.0353174i
$47$	8.41641	−	25.9030i	0.179073	−	0.551129i	−0.820724	−	0.571326i	$-0.806429\pi$
$47$	8.41641	−	25.9030i	0.179073	−	0.551129i	0.999796	+	0.0201971i	$0.00642936\pi$
$48$	4.24671	+	13.0700i	0.0884731	+	0.272292i
$49$	40.6074	−	29.5030i	0.828722	−	0.602102i
$50$	3.84346	+	5.29007i	0.0768692	+	0.105801i
$51$	−20.0861	+	6.52637i	−0.393845	+	0.127968i
$52$	17.3607	+	5.64083i	0.333859	+	0.108477i
$53$	9.27051	+	6.73542i	0.174915	+	0.127083i	0.671798	−	0.740734i	$-0.265522\pi$
$53$	9.27051	+	6.73542i	0.174915	+	0.127083i	−0.496883	+	0.867818i	$0.665522\pi$
$54$		−	16.1554i		−	0.299175i
$55$		0			0
$56$	54.0689			0.965516
$57$	1.68441	−	2.31838i	0.0295510	−	0.0406734i
$58$	−6.38197	+	19.6417i	−0.110034	+	0.338650i
$59$	−0.701626	−	2.15938i	−0.0118920	−	0.0365997i	0.944934	−	0.327260i	$-0.106125\pi$
$59$	−0.701626	−	2.15938i	−0.0118920	−	0.0365997i	−0.956826	+	0.290660i	$0.906125\pi$
$60$	−15.5279	+	11.2817i	−0.258798	+	0.188028i
$61$	−13.2918	−	18.2946i	−0.217898	−	0.299911i	0.686049	−	0.727555i	$-0.259344\pi$
$61$	−13.2918	−	18.2946i	−0.217898	−	0.299911i	−0.903947	+	0.427644i	$0.859344\pi$
$62$	4.92299	−	1.59958i	0.0794030	−	0.0257996i
$63$	67.1591	+	21.8213i	1.06602	+	0.346370i
$64$	−15.1697	−	11.0214i	−0.237027	−	0.172210i
$65$			21.0292i			0.323527i
$66$		0			0
$67$	−38.4934			−0.574529			−0.287264	−	0.957851i	$-0.592746\pi$
$67$	−38.4934			−0.574529			−0.287264	+	0.957851i	$0.592746\pi$
$68$	31.1894	−	42.9286i	0.458668	−	0.631302i
$69$	−1.18034	+	3.63271i	−0.0171064	+	0.0526480i
$70$	8.94427	+	27.5276i	0.127775	+	0.393252i
$71$	−61.7426	+	44.8587i	−0.869615	+	0.631812i	−0.930484	−	0.366334i	$-0.880613\pi$
$71$	−61.7426	+	44.8587i	−0.869615	+	0.631812i	0.0608688	+	0.998146i	$0.480613\pi$
$72$	22.6246	+	31.1401i	0.314231	+	0.432501i
$73$	97.8353	−	31.7886i	1.34021	−	0.435461i	0.450822	−	0.892614i	$-0.351131\pi$
$73$	97.8353	−	31.7886i	1.34021	−	0.435461i	0.889388	+	0.457153i	$0.151131\pi$
$74$	−27.8115	−	9.03651i	−0.375831	−	0.122115i
$75$	10.0623	+	7.31069i	0.134164	+	0.0974759i
$76$			7.19991i			0.0947357i
$77$		0			0
$78$	−5.27864			−0.0676749
$79$	2.31308	−	3.18368i	0.0292795	−	0.0402998i	−0.794126	−	0.607753i	$-0.792071\pi$
$79$	2.31308	−	3.18368i	0.0292795	−	0.0402998i	0.823406	+	0.567453i	$0.192071\pi$
$80$	12.2918	−	37.8303i	0.153647	−	0.472878i
$81$	10.2229	+	31.4629i	0.126209	+	0.388431i
$82$	−41.2426	+	29.9645i	−0.502959	+	0.365421i
$83$	−48.9296	−	67.3458i	−0.589513	−	0.811395i	0.405185	−	0.914235i	$-0.367207\pi$
$83$	−48.9296	−	67.3458i	−0.589513	−	0.811395i	−0.994698	+	0.102840i	$0.967207\pi$
$84$	45.4508	−	14.7679i	0.541082	−	0.175808i
$85$	58.1378	+	18.8901i	0.683974	+	0.222237i
$86$	−13.5557	−	9.84881i	−0.157625	−	0.114521i
$87$			39.2833i			0.451533i
$88$		0			0
$89$	123.297			1.38536			0.692679	−	0.721246i	$-0.256430\pi$
$89$	123.297			1.38536			0.692679	+	0.721246i	$0.256430\pi$
$90$	−12.1115	+	16.6700i	−0.134572	+	0.185222i
$91$	16.1803	−	49.7980i	0.177806	−	0.547230i
$92$	−2.96556	−	9.12705i	−0.0322343	−	0.0992071i
$93$	7.96556	−	5.78732i	0.0856512	−	0.0622292i
$94$	−11.6312	−	16.0090i	−0.123736	−	0.170308i
$95$	−7.88854	+	2.56314i	−0.0830373	+	0.0269805i
$96$	38.0370	+	12.3590i	0.396218	+	0.128739i
$97$	62.6246	+	45.4994i	0.645615	+	0.469066i	0.861775	−	0.507292i	$-0.169353\pi$
$97$	62.6246	+	45.4994i	0.645615	+	0.469066i	−0.216160	+	0.976358i	$0.569353\pi$
$98$		−	36.4677i		−	0.372119i
$99$		0			0
$100$	−31.2492			−0.312492
$101$	66.2279	−	91.1549i	0.655722	−	0.902524i	−0.343608	−	0.939113i	$-0.611649\pi$
$101$	66.2279	−	91.1549i	0.655722	−	0.902524i	0.999330	+	0.0365890i	$0.0116492\pi$
$102$	−4.74169	+	14.5934i	−0.0464871	+	0.143073i
$103$	28.6180	+	88.0773i	0.277845	+	0.855119i	0.988453	+	0.151530i	$0.0484201\pi$
$103$	28.6180	+	88.0773i	0.277845	+	0.855119i	−0.710608	+	0.703589i	$0.751580\pi$
$104$	23.0902	−	16.7760i	0.222021	−	0.161308i
$105$	32.3607	+	44.5407i	0.308197	+	0.424197i
$106$	7.91796	−	2.57270i	0.0746977	−	0.0242708i
$107$	−80.6763	−	26.2133i	−0.753984	−	0.244984i	−0.0932893	−	0.995639i	$-0.529738\pi$
$107$	−80.6763	−	26.2133i	−0.753984	−	0.244984i	−0.660695	+	0.750655i	$0.729738\pi$
$108$	62.4615	+	45.3809i	0.578347	+	0.420194i
$109$		−	94.0766i		−	0.863088i	−0.902092	−	0.431544i	$-0.857969\pi$
$109$		−	94.0766i		−	0.863088i	0.902092	−	0.431544i	$-0.142031\pi$
$110$		0			0
$111$	−55.6231			−0.501109
$112$	−58.2148	+	80.1258i	−0.519775	+	0.715409i
$113$	−2.62461	+	8.07772i	−0.0232267	+	0.0714843i	−0.961998	−	0.273057i	$-0.911965\pi$
$113$	−2.62461	+	8.07772i	−0.0232267	+	0.0714843i	0.938771	+	0.344541i	$0.111965\pi$
$114$	−0.643386	−	1.98014i	−0.00564373	−	0.0173696i
$115$	8.94427	−	6.49839i	0.0777763	−	0.0565078i
$116$	−58.0132	−	79.8483i	−0.500113	−	0.688347i
$117$	35.4508	−	11.5187i	0.302999	−	0.0984503i
$118$	−1.56888	−	0.509761i	−0.0132956	−	0.00432001i
$119$	−123.138	−	89.4648i	−1.03477	−	0.751805i
$120$			30.0098i			0.250082i
$121$		0			0
$122$	−16.4296			−0.134669
$123$	−56.9959	+	78.4482i	−0.463382	+	0.637790i
$124$	−7.64435	+	23.5269i	−0.0616479	+	0.189733i
$125$	−42.0263	−	129.344i	−0.336210	−	1.03475i
$126$	41.5066	−	30.1563i	0.329417	−	0.239336i
$127$	110.652	+	152.300i	0.871279	+	1.19921i	0.978761	+	0.205006i	$0.0657214\pi$
$127$	110.652	+	152.300i	0.871279	+	1.19921i	−0.107481	+	0.994207i	$0.534279\pi$
$128$	−123.052	+	39.9819i	−0.961341	+	0.312359i
$129$	−30.3115	−	9.84881i	−0.234973	−	0.0763474i
$130$	12.3607	+	8.98056i	0.0950822	+	0.0690812i
$131$			141.932i			1.08345i	0.840556	+	0.541725i	$0.182229\pi$
$131$			141.932i			1.08345i	−0.840556	+	0.541725i	$0.817771\pi$
$132$		0			0
$133$	20.6525			0.155282
$134$	−16.4387	+	22.6259i	−0.122677	+	0.168850i
$135$	−27.4853	+	84.5910i	−0.203595	+	0.626600i
$136$	−25.6378	−	78.9049i	−0.188513	−	0.580183i
$137$	−13.1525	+	9.55583i	−0.0960035	+	0.0697506i	−0.634751	−	0.772716i	$-0.718898\pi$
$137$	−13.1525	+	9.55583i	−0.0960035	+	0.0697506i	0.538748	+	0.842467i	$0.318898\pi$
$138$	1.63119	+	2.24514i	0.0118202	+	0.0162691i
$139$	−215.374	+	69.9792i	−1.54945	+	0.503447i	−0.953965	−	0.299918i	$-0.903041\pi$
$139$	−215.374	+	69.9792i	−1.54945	+	0.503447i	−0.595487	+	0.803365i	$0.703041\pi$
$140$	−131.554	−	42.7445i	−0.939673	−	0.305318i
$141$	−30.4508	−	22.1238i	−0.215963	−	0.156907i
$142$			55.4484i			0.390481i
$143$		0			0
$144$	−70.5066			−0.489629
$145$	66.8328	−	91.9875i	0.460916	−	0.634396i
$146$	23.0958	−	71.0815i	0.158190	−	0.486860i
$147$	−21.4352	−	65.9707i	−0.145818	−	0.448780i
$148$	113.061	−	82.1434i	0.763924	−	0.555023i
$149$	39.4903	+	54.3538i	0.265036	+	0.364790i	0.920706	−	0.390257i	$-0.127614\pi$
$149$	39.4903	+	54.3538i	0.265036	+	0.364790i	−0.655670	+	0.755047i	$0.727614\pi$
$150$	8.59424	−	2.79244i	0.0572949	−	0.0186162i
$151$	95.6049	+	31.0639i	0.633145	+	0.205721i	0.607968	−	0.793962i	$-0.291985\pi$
$151$	95.6049	+	31.0639i	0.633145	+	0.205721i	0.0251772	+	0.999683i	$0.491985\pi$
$152$	9.10739	+	6.61691i	0.0599170	+	0.0435323i
$153$		−	108.355i		−	0.708202i
$154$		0			0
$155$	−28.4984			−0.183861
$156$	14.8278	−	20.4087i	0.0950499	−	0.130825i
$157$	−76.2098	+	234.550i	−0.485412	+	1.49395i	0.345970	+	0.938246i	$0.387550\pi$
$157$	−76.2098	+	234.550i	−0.485412	+	1.49395i	−0.831383	+	0.555700i	$0.812450\pi$
$158$	−0.883519	−	2.71919i	−0.00559189	−	0.0172101i
$159$	12.8115	−	9.30812i	0.0805757	−	0.0585416i
$160$	−68.0426	−	93.6526i	−0.425266	−	0.585329i
$161$	−26.1803	+	8.50651i	−0.162611	+	0.0528355i
$162$	22.8591	+	7.42738i	0.141106	+	0.0458480i
$163$	−141.065	−	102.490i	−0.865428	−	0.628770i	0.0639280	−	0.997955i	$-0.479637\pi$
$163$	−141.065	−	102.490i	−0.865428	−	0.628770i	−0.929356	+	0.369184i	$0.879637\pi$
$164$		−	243.627i		−	1.48553i
$165$		0			0
$166$	−60.4803			−0.364339
$167$	−145.154	+	199.787i	−0.869186	+	1.19633i	0.110115	+	0.993919i	$0.464878\pi$
$167$	−145.154	+	199.787i	−0.869186	+	1.19633i	−0.979300	+	0.202413i	$0.935122\pi$
$168$	23.0902	−	71.0642i	0.137441	−	0.423001i
$169$	43.6829	+	134.442i	0.258478	+	0.795515i
$170$	35.9311	−	26.1055i	0.211360	−	0.153562i
$171$	8.64183	+	11.8945i	0.0505370	+	0.0695583i
$172$	76.1565	−	24.7448i	0.442771	−	0.143865i
$173$	−47.3131	−	15.3730i	−0.273486	−	0.0888610i	0.169063	−	0.985605i	$-0.445926\pi$
$173$	−47.3131	−	15.3730i	−0.273486	−	0.0888610i	−0.442549	+	0.896744i	$0.645926\pi$
$174$	23.0902	+	16.7760i	0.132702	+	0.0964137i
$175$			89.6363i			0.512208i
$176$		0			0
$177$	−3.13777			−0.0177275
$178$	52.6540	−	72.4721i	0.295809	−	0.407146i
$179$	67.6591	−	208.233i	0.377984	−	1.16331i	−0.563460	−	0.826143i	$-0.690530\pi$
$179$	67.6591	−	208.233i	0.377984	−	1.16331i	0.941444	−	0.337170i	$-0.109470\pi$
$180$	−30.4296	−	93.6526i	−0.169053	−	0.520292i
$181$	−31.4721	+	22.8658i	−0.173879	+	0.126331i	−0.671321	−	0.741167i	$-0.734273\pi$
$181$	−31.4721	+	22.8658i	−0.173879	+	0.126331i	0.497442	+	0.867497i	$0.334273\pi$
$182$	−22.3607	−	30.7768i	−0.122861	−	0.169103i
$183$	−29.7214	+	9.65706i	−0.162412	+	0.0527708i
$184$	−14.2705	−	4.63677i	−0.0775571	−	0.0251998i
$185$	130.249	+	94.6316i	0.704050	+	0.511522i
$186$		−	7.15352i		−	0.0384598i
$187$		0			0
$188$	94.5673			0.503018
$189$	130.172	−	179.167i	0.688742	−	0.947972i
$190$	−1.86223	+	5.73136i	−0.00980122	+	0.0301651i
$191$	37.0213	+	113.940i	0.193829	+	0.596543i	0.999988	+	0.00484524i	$0.00154229\pi$
$191$	37.0213	+	113.940i	0.193829	+	0.596543i	−0.806160	+	0.591698i	$0.798458\pi$
$192$	−20.9640	+	15.2312i	−0.109188	+	0.0793294i
$193$	−17.1772	−	23.6424i	−0.0890012	−	0.122500i	0.762194	−	0.647348i	$-0.224122\pi$
$193$	−17.1772	−	23.6424i	−0.0890012	−	0.122500i	−0.851196	+	0.524848i	$0.824122\pi$
$194$	53.4878	−	17.3792i	0.275710	−	0.0895837i
$195$	27.6393	+	8.98056i	0.141740	+	0.0460542i
$196$	140.994	+	102.438i	0.719359	+	0.522645i
$197$			282.037i			1.43166i	0.698275	+	0.715830i	$0.253951\pi$
$197$			282.037i			1.43166i	−0.698275	+	0.715830i	$0.746049\pi$
$198$		0			0
$199$	177.469			0.891804			0.445902	−	0.895082i	$-0.352883\pi$
$199$	177.469			0.891804			0.445902	+	0.895082i	$0.352883\pi$
$200$	−28.7188	+	39.5281i	−0.143594	+	0.197641i
$201$	−16.4387	+	50.5930i	−0.0817843	+	0.251706i
$202$	−25.2968	−	77.8556i	−0.125232	−	0.385424i
$203$	−229.039	+	166.407i	−1.12827	+	0.819738i
$204$	−43.1027	−	59.3258i	−0.211288	−	0.290813i
$205$	266.928	−	86.7302i	1.30209	−	0.423074i
$206$	63.9919	+	20.7922i	0.310640	+	0.100933i
$207$	−15.8541	−	11.5187i	−0.0765899	−	0.0556458i
$208$			52.2801i			0.251347i
$209$		0			0
$210$	40.0000			0.190476
$211$	−57.8081	+	79.5660i	−0.273972	+	0.377090i	−0.923726	−	0.383055i	$-0.874872\pi$
$211$	−57.8081	+	79.5660i	−0.273972	+	0.377090i	0.649754	+	0.760145i	$0.274872\pi$
$212$	−12.2949	+	37.8398i	−0.0579948	+	0.178490i
$213$	32.5917	+	100.307i	0.153013	+	0.470925i
$214$	−49.8607	+	36.2259i	−0.232994	+	0.169280i
$215$	54.2229	+	74.6314i	0.252200	+	0.347123i
$216$	114.807	−	37.3032i	0.531516	−	0.172700i
$217$	67.4853	+	21.9273i	0.310992	+	0.101047i
$218$	−55.2968	−	40.1755i	−0.253655	−	0.184291i
$219$		−	142.163i		−	0.649146i
$220$		0			0
$221$	−80.3444			−0.363549
$222$	−23.7539	+	32.6944i	−0.106999	+	0.147272i
$223$	82.2067	−	253.006i	0.368640	−	1.13456i	−0.579031	−	0.815306i	$-0.696569\pi$
$223$	82.2067	−	253.006i	0.368640	−	1.13456i	0.947670	−	0.319251i	$-0.103431\pi$
$224$	89.0689	+	274.126i	0.397629	+	1.22378i
$225$	−51.6246	+	37.5075i	−0.229443	+	0.166700i
$226$	3.62712	+	4.99231i	0.0160492	+	0.0220899i
$227$	242.067	−	78.6524i	1.06638	−	0.346487i	0.277301	−	0.960783i	$-0.410560\pi$
$227$	242.067	−	78.6524i	1.06638	−	0.346487i	0.789075	+	0.614297i	$0.210560\pi$
$228$	9.46305	+	3.07473i	0.0415046	+	0.0134857i
$229$	32.5279	+	23.6329i	0.142043	+	0.103200i	0.656537	−	0.754293i	$-0.272020\pi$
$229$	32.5279	+	23.6329i	0.142043	+	0.103200i	−0.514494	+	0.857494i	$0.672020\pi$
$230$		−	8.03246i		−	0.0349237i
$231$		0			0
$232$	−154.318			−0.665164
$233$	135.744	−	186.836i	0.582593	−	0.801871i	−0.411384	−	0.911462i	$-0.634954\pi$
$233$	135.744	−	186.836i	0.582593	−	0.801871i	0.993977	+	0.109592i	$0.0349543\pi$
$234$	8.36881	−	25.7565i	0.0357641	−	0.110071i
$235$	33.6656	+	103.612i	0.143258	+	0.440903i
$236$	6.37790	−	4.63382i	0.0270250	−	0.0196348i
$237$	−3.19660	−	4.39974i	−0.0134878	−	0.0185643i
$238$	−105.172	+	34.1725i	−0.441900	+	0.143582i
$239$	299.740	+	97.3913i	1.25414	+	0.407495i	0.859403	−	0.511299i	$-0.170836\pi$
$239$	299.740	+	97.3913i	1.25414	+	0.407495i	0.394737	+	0.918794i	$0.370836\pi$
$240$	−44.4721	−	32.3109i	−0.185301	−	0.134629i
$241$		−	270.933i		−	1.12420i	−0.827069	−	0.562101i	$-0.809993\pi$
$241$		−	270.933i		−	1.12420i	0.827069	−	0.562101i	$-0.190007\pi$
$242$		0			0
$243$	245.843			1.01170
$244$	46.1509	−	63.5213i	0.189143	−	0.260333i
$245$	−62.0426	+	190.947i	−0.253235	+	0.779377i
$246$	21.7705	+	67.0027i	0.0884980	+	0.272369i
$247$	8.81966	−	6.40786i	0.0357071	−	0.0259427i
$248$	22.7345	+	31.2914i	0.0916714	+	0.126175i
$249$	−109.410	+	35.5494i	−0.439397	+	0.142769i
$250$	−93.9737	−	30.5339i	−0.375895	−	0.122136i
$251$	−9.00813	−	6.54479i	−0.0358890	−	0.0260749i	0.569696	−	0.821855i	$-0.307061\pi$
$251$	−9.00813	−	6.54479i	−0.0358890	−	0.0260749i	−0.605585	+	0.795781i	$0.707061\pi$
$252$			245.186i			0.972959i
$253$		0			0
$254$	136.774			0.538480
$255$	49.6556	−	68.3450i	0.194728	−	0.268020i
$256$	−5.87132	+	18.0701i	−0.0229349	+	0.0705862i
$257$	−124.621	−	383.543i	−0.484905	−	1.49238i	−0.832119	−	0.554598i	$-0.812872\pi$
$257$	−124.621	−	383.543i	−0.484905	−	1.49238i	0.347214	−	0.937786i	$-0.387128\pi$
$258$	−18.7336	+	13.6107i	−0.0726107	+	0.0527547i
$259$	−235.623	−	324.307i	−0.909742	−	1.25215i
$260$	−69.4427	+	22.5633i	−0.267087	+	0.0867820i
$261$	−191.679	−	62.2802i	−0.734401	−	0.238622i
$262$	83.4255	+	60.6122i	0.318418	+	0.231344i
$263$		−	42.6636i		−	0.162219i	−0.996705	−	0.0811094i	$-0.974154\pi$
$263$		−	42.6636i		−	0.162219i	0.996705	−	0.0811094i	$-0.0258463\pi$
$264$		0			0
$265$	−45.8359			−0.172966
$266$	8.81966	−	12.1392i	0.0331566	−	0.0456362i
$267$	52.6540	−	162.052i	0.197206	−	0.606938i
$268$	−41.3015	−	127.113i	−0.154110	−	0.474302i
$269$	331.692	−	240.988i	1.23306	−	0.895867i	0.235940	−	0.971768i	$-0.424183\pi$
$269$	331.692	−	240.988i	1.23306	−	0.895867i	0.997115	+	0.0759003i	$0.0241831\pi$
$270$	37.9837	+	52.2801i	0.140681	+	0.193630i
$271$	−220.700	+	71.7098i	−0.814391	+	0.264612i	−0.686457	−	0.727171i	$-0.740835\pi$
$271$	−220.700	+	71.7098i	−0.814391	+	0.264612i	−0.127935	+	0.991783i	$0.540835\pi$
$272$	144.534	+	46.9621i	0.531377	+	0.172655i
$273$	−58.5410	−	42.5325i	−0.214436	−	0.155797i
$274$			11.8117i			0.0431082i
$275$		0			0
$276$	−13.2624			−0.0480521
$277$	−180.036	+	247.799i	−0.649951	+	0.894580i	−0.999097	−	0.0424878i	$-0.986472\pi$
$277$	−180.036	+	247.799i	−0.649951	+	0.894580i	0.349146	+	0.937068i	$0.386472\pi$
$278$	−50.8429	+	156.478i	−0.182888	+	0.562871i
$279$	15.6099	+	48.0423i	0.0559495	+	0.172195i
$280$	−174.971	+	127.124i	−0.624895	+	0.454013i
$281$	76.0886	+	104.727i	0.270778	+	0.372694i	0.922652	−	0.385633i	$-0.126017\pi$
$281$	76.0886	+	104.727i	0.270778	+	0.372694i	−0.651874	+	0.758327i	$0.726017\pi$
$282$	−26.0081	+	8.45055i	−0.0922274	+	0.0299665i
$283$	−401.246	−	130.373i	−1.41783	−	0.460681i	−0.502919	−	0.864334i	$-0.667740\pi$
$283$	−401.246	−	130.373i	−1.41783	−	0.460681i	−0.914912	+	0.403653i	$0.867740\pi$
$284$	−214.379	−	155.755i	−0.754855	−	0.548434i
$285$			11.4627i			0.0402201i
$286$		0			0
$287$	−698.827			−2.43494
$288$	−120.608	+	166.003i	−0.418779	+	0.576400i
$289$	17.1343	−	52.7339i	0.0592882	−	0.182470i
$290$	−25.5279	−	78.5667i	−0.0880271	−	0.270920i
$291$	86.5451	−	62.8787i	0.297406	−	0.216078i
$292$	209.945	+	288.964i	0.718988	+	0.989603i
$293$	−61.3231	+	19.9251i	−0.209294	+	0.0680037i	−0.411788	−	0.911280i	$-0.635095\pi$
$293$	−61.3231	+	19.9251i	−0.209294	+	0.0680037i	0.202494	+	0.979284i	$0.435095\pi$
$294$	−47.9305	−	15.5736i	−0.163029	−	0.0529713i
$295$	7.34752	+	5.33829i	0.0249069	+	0.0180959i
$296$		−	218.506i		−	0.738196i
$297$		0			0
$298$	48.8127			0.163801
$299$	−8.54102	+	11.7557i	−0.0285653	+	0.0393167i
$300$	−13.3450	+	41.0717i	−0.0444834	+	0.136906i
$301$	−70.9787	−	218.450i	−0.235810	−	0.725748i
$302$	59.0871	−	42.9293i	0.195653	−	0.142150i
$303$	−91.5248	−	125.973i	−0.302062	−	0.415753i
$304$	−19.6115	+	6.37215i	−0.0645114	+	0.0209610i
$305$	86.0263	+	27.9516i	0.282053	+	0.0916447i
$306$	−63.6894	−	46.2731i	−0.208135	−	0.151219i
$307$			356.512i			1.16128i	0.814161	+	0.580639i	$0.197197\pi$
$307$			356.512i			1.16128i	−0.814161	+	0.580639i	$0.802803\pi$
$308$		0			0
$309$	127.984			0.414187
$310$	−12.1703	+	16.7510i	−0.0392590	+	0.0540354i
$311$	−171.570	+	528.040i	−0.551673	+	1.69788i	0.152897	+	0.988242i	$0.451140\pi$
$311$	−171.570	+	528.040i	−0.551673	+	1.69788i	−0.704570	+	0.709634i	$0.748860\pi$
$312$	−12.1885	−	37.5123i	−0.0390656	−	0.120232i
$313$	268.099	−	194.786i	0.856547	−	0.622318i	−0.0703963	−	0.997519i	$-0.522426\pi$
$313$	268.099	−	194.786i	0.856547	−	0.622318i	0.926943	+	0.375201i	$0.122426\pi$
$314$	105.319	+	144.960i	0.335412	+	0.461655i
$315$	−268.636	+	87.2852i	−0.852813	+	0.277096i
$316$	12.9950	+	4.22232i	0.0411233	+	0.0133618i
$317$	418.204	+	303.843i	1.31925	+	0.958494i	0.999941	+	0.0108449i	$0.00345209\pi$
$317$	418.204	+	303.843i	1.31925	+	0.958494i	0.319313	+	0.947649i	$0.396548\pi$
$318$		−	11.5055i		−	0.0361807i
$319$		0			0
$320$	75.0031			0.234385
$321$	−68.9058	+	94.8406i	−0.214660	+	0.295454i
$322$	−6.18034	+	19.0211i	−0.0191936	+	0.0590718i
$323$	−9.79276	−	30.1390i	−0.0303181	−	0.0933096i
$324$	−92.9280	+	67.5162i	−0.286815	+	0.208383i
$325$	27.8115	+	38.2793i	0.0855739	+	0.117782i
$326$	−120.484	+	39.1475i	−0.369582	+	0.120084i
$327$	−123.647	−	40.1755i	−0.378127	−	0.122861i
$328$	−308.171	−	223.899i	−0.939545	−	0.682619i
$329$		−	271.260i		−	0.824499i
$330$		0			0
$331$	208.884			0.631068			0.315534	−	0.948914i	$-0.397816\pi$
$331$	208.884			0.631068			0.315534	+	0.948914i	$0.397816\pi$
$332$	169.890	−	233.834i	0.511717	−	0.704318i
$333$	88.1854	−	271.407i	0.264821	−	0.815035i
$334$	55.4439	+	170.639i	0.166000	+	0.510895i
$335$	124.567	−	90.5035i	0.371843	−	0.270160i
$336$	80.4508	+	110.731i	0.239437	+	0.329557i
$337$	−128.325	+	41.6952i	−0.380785	+	0.123725i	−0.493154	−	0.869942i	$-0.664156\pi$
$337$	−128.325	+	41.6952i	−0.380785	+	0.123725i	0.112369	+	0.993667i	$0.464156\pi$
$338$	97.6778	+	31.7375i	0.288988	+	0.0938978i
$339$	9.49593	+	6.89920i	0.0280116	+	0.0203516i
$340$			212.251i			0.624266i
$341$		0			0
$342$	10.6819			0.0312336
$343$	6.98684	−	9.61657i	0.0203698	−	0.0280366i
$344$	38.6894	−	119.074i	0.112469	−	0.346145i
$345$	−4.72136	−	14.5309i	−0.0136851	−	0.0421184i
$346$	−29.2411	+	21.2449i	−0.0845118	+	0.0614014i
$347$	55.7092	+	76.6771i	0.160545	+	0.220971i	0.881710	−	0.471792i	$-0.156393\pi$
$347$	55.7092	+	76.6771i	0.160545	+	0.220971i	−0.721165	+	0.692764i	$0.756393\pi$
$348$	−129.721	+	42.1490i	−0.372763	+	0.121118i
$349$	−163.416	−	53.0972i	−0.468242	−	0.152141i	0.0653866	−	0.997860i	$-0.479172\pi$
$349$	−163.416	−	53.0972i	−0.468242	−	0.152141i	−0.533628	+	0.845719i	$0.679172\pi$
$350$	52.6869	+	38.2793i	0.150534	+	0.109369i
$351$		−	116.902i		−	0.333054i
$352$		0			0
$353$	−119.644			−0.338936			−0.169468	−	0.985536i	$-0.554205\pi$
$353$	−119.644			−0.338936			−0.169468	+	0.985536i	$0.554205\pi$
$354$	−1.33999	+	1.84433i	−0.00378527	+	0.00520998i
$355$	94.3344	−	290.331i	0.265731	−	0.817835i
$356$	132.291	+	407.150i	0.371605	+	1.14368i
$357$	−170.172	+	123.637i	−0.476673	+	0.346323i
$358$	−93.5025	−	128.695i	−0.261180	−	0.359484i
$359$	444.443	−	144.408i	1.23800	−	0.402251i	0.384395	−	0.923169i	$-0.374410\pi$
$359$	444.443	−	144.408i	1.23800	−	0.402251i	0.853607	+	0.520917i	$0.174410\pi$
$360$	−146.430	−	47.5778i	−0.406749	−	0.132161i
$361$	−288.576	−	209.663i	−0.799381	−	0.580784i
$362$			28.2637i			0.0780766i
$363$		0			0
$364$	181.803			0.499460
$365$	−241.862	+	332.895i	−0.662636	+	0.912041i
$366$	−7.01626	+	21.5938i	−0.0191701	+	0.0589995i
$367$	−101.613	−	312.733i	−0.276875	−	0.852133i	−0.988717	−	0.149794i	$-0.952139\pi$
$367$	−101.613	−	312.733i	−0.276875	−	0.852133i	0.711843	−	0.702339i	$-0.247861\pi$
$368$	22.2361	−	16.1554i	0.0604241	−	0.0439007i
$369$	−292.417	−	402.478i	−0.792459	−	1.09073i
$370$	111.246	−	36.1461i	0.300665	−	0.0976920i
$371$	108.541	+	35.2671i	0.292563	+	0.0950596i
$372$	27.6575	+	20.0944i	0.0743481	+	0.0540171i
$373$		−	214.135i		−	0.574088i	−0.957917	−	0.287044i	$-0.907327\pi$
$373$		−	214.135i		−	0.574088i	0.957917	−	0.287044i	$-0.0926726\pi$
$374$		0			0
$375$	−187.947			−0.501193
$376$	86.9098	−	119.621i	0.231143	−	0.318141i
$377$	−46.1803	+	142.128i	−0.122494	+	0.376999i
$378$	−49.7214	−	153.027i	−0.131538	−	0.404832i
$379$	−259.089	+	188.239i	−0.683611	+	0.496673i	−0.874554	−	0.484929i	$-0.838846\pi$
$379$	−259.089	+	188.239i	−0.683611	+	0.496673i	0.190943	+	0.981601i	$0.438846\pi$
$380$	−16.9280	−	23.2994i	−0.0445474	−	0.0613142i
$381$	247.426	−	80.3937i	0.649413	−	0.211007i
$382$	82.7821	+	26.8975i	0.216707	+	0.0704124i
$383$	442.984	+	321.847i	1.15662	+	0.840330i	0.989346	−	0.145581i	$-0.0465051\pi$
$383$	442.984	+	321.847i	1.15662	+	0.840330i	0.167269	+	0.985911i	$0.446505\pi$
$384$			178.805i			0.465637i
$385$		0			0
$386$	−21.2322			−0.0550058
$387$	96.1124	−	132.287i	0.248352	−	0.341828i
$388$	−83.0551	+	255.617i	−0.214060	+	0.658808i
$389$	103.994	+	320.060i	0.267336	+	0.822776i	0.991146	+	0.132777i	$0.0423893\pi$
$389$	103.994	+	320.060i	0.267336	+	0.822776i	−0.723810	+	0.690000i	$0.757611\pi$
$390$	17.0820	−	12.4108i	0.0438001	−	0.0318226i
$391$	24.8278	+	34.1725i	0.0634982	+	0.0873978i
$392$	259.155	−	84.2046i	0.661110	−	0.214808i
$393$	186.545	+	60.6122i	0.474669	+	0.154229i
$394$	165.777	+	120.444i	0.420754	+	0.305696i
$395$			15.7410i			0.0398506i
$396$		0			0
$397$	115.374			0.290614			0.145307	−	0.989387i	$-0.453583\pi$
$397$	115.374			0.290614			0.145307	+	0.989387i	$0.453583\pi$
$398$	75.7883	−	104.314i	0.190423	−	0.262095i
$399$	8.81966	−	27.1441i	0.0221044	−	0.0680304i
$400$	−27.6565	−	85.1181i	−0.0691414	−	0.212795i
$401$	−51.6115	+	37.4979i	−0.128707	+	0.0935110i	−0.650276	−	0.759698i	$-0.725347\pi$
$401$	−51.6115	+	37.4979i	−0.128707	+	0.0935110i	0.521569	+	0.853209i	$0.325347\pi$
$402$	22.7177	+	31.2682i	0.0565116	+	0.0777815i
$403$	35.6231	−	11.5746i	0.0883947	−	0.0287212i
$404$	372.071	+	120.893i	0.920967	+	0.299240i
$405$	−107.056	−	77.7805i	−0.264335	−	0.192051i
$406$			205.690i			0.506626i
$407$		0			0
$408$	−114.656			−0.281019
$409$	359.538	−	494.861i	0.879066	−	1.20993i	−0.0976130	−	0.995224i	$-0.531121\pi$
$409$	359.538	−	494.861i	0.879066	−	1.20993i	0.976679	−	0.214706i	$-0.0688793\pi$
$410$	63.0132	−	193.935i	0.153691	−	0.473011i
$411$	6.94272	+	21.3675i	0.0168923	+	0.0519890i
$412$	−260.143	+	189.005i	−0.631415	+	0.458750i
$413$	−13.2918	−	18.2946i	−0.0321835	−	0.0442968i
$414$	−13.5410	+	4.39974i	−0.0327078	+	0.0106274i
$415$	316.679	+	102.895i	0.763081	+	0.247940i
$416$	123.090	+	89.4302i	0.295890	+	0.214977i
$417$			312.957i			0.750495i
$418$		0			0
$419$	146.156			0.348821			0.174410	−	0.984673i	$-0.444198\pi$
$419$	146.156			0.348821			0.174410	+	0.984673i	$0.444198\pi$
$420$	−112.361	+	154.651i	−0.267525	+	0.368217i
$421$	183.374	−	564.367i	0.435567	−	1.34054i	−0.456937	−	0.889499i	$-0.651053\pi$
$421$	183.374	−	564.367i	0.435567	−	1.34054i	0.892504	−	0.451039i	$-0.148947\pi$
$422$	22.0807	+	67.9574i	0.0523240	+	0.161037i
$423$	156.228	−	113.506i	0.369333	−	0.268336i
$424$	36.5654	+	50.3280i	0.0862392	+	0.118698i
$425$	130.810	−	42.5027i	0.307788	−	0.100006i
$426$	72.8773	+	23.6793i	0.171073	+	0.0555851i
$427$	−182.207	−	132.381i	−0.426713	−	0.310025i
$428$		−	294.535i		−	0.688165i
$429$		0			0
$430$	67.0232			0.155868
$431$	−102.474	+	141.043i	−0.237759	+	0.327247i	−0.911177	−	0.412015i	$-0.864825\pi$
$431$	−102.474	+	141.043i	−0.237759	+	0.327247i	0.673418	+	0.739262i	$0.264825\pi$
$432$	−68.3303	+	210.299i	−0.158172	+	0.486803i
$433$	191.789	+	590.265i	0.442930	+	1.36320i	0.884738	+	0.466089i	$0.154337\pi$
$433$	191.789	+	590.265i	0.442930	+	1.36320i	−0.441808	+	0.897110i	$0.645663\pi$
$434$	41.7082	−	30.3028i	0.0961019	−	0.0698221i
$435$	−92.3607	−	127.124i	−0.212323	−	0.292238i
$436$	310.659	−	100.939i	0.712522	−	0.231512i
$437$	−5.45085	−	1.77109i	−0.0124733	−	0.00405283i
$438$	−83.5613	−	60.7109i	−0.190779	−	0.138609i
$439$		−	676.778i		−	1.54164i	−0.637055	−	0.770818i	$-0.719848\pi$
$439$		−	676.778i		−	1.54164i	0.637055	−	0.770818i	$-0.280152\pi$
$440$		0			0
$441$	355.880			0.806985
$442$	−34.3112	+	47.2253i	−0.0776271	+	0.106844i
$443$	−80.1302	+	246.615i	−0.180881	+	0.556694i	−0.999853	−	0.0171390i	$-0.994544\pi$
$443$	−80.1302	+	246.615i	−0.180881	+	0.556694i	0.818972	+	0.573833i	$0.194544\pi$
$444$	−59.6807	−	183.678i	−0.134416	−	0.413690i
$445$	−398.997	+	289.888i	−0.896622	+	0.651434i
$446$	−113.607	−	156.366i	−0.254724	−	0.350597i
$447$	88.3030	−	28.6914i	0.197546	−	0.0641866i
$448$	−177.610	−	57.7090i	−0.396451	−	0.128815i
$449$	−325.550	−	236.526i	−0.725056	−	0.526784i	0.162940	−	0.986636i	$-0.447902\pi$
$449$	−325.550	−	236.526i	−0.725056	−	0.526784i	−0.887996	+	0.459852i	$0.847902\pi$
$450$			46.3618i			0.103026i
$451$		0			0
$452$	−29.4903			−0.0652441
$453$	81.6563	−	112.390i	0.180257	−	0.248102i
$454$	57.1443	−	175.872i	0.125869	−	0.387384i
$455$	64.7214	+	199.192i	0.142245	+	0.437784i
$456$	12.5861	−	9.14434i	0.0276011	−	0.0200534i
$457$	−150.312	−	206.886i	−0.328909	−	0.452705i	0.612252	−	0.790663i	$-0.290264\pi$
$457$	−150.312	−	206.886i	−0.328909	−	0.452705i	−0.941161	+	0.337958i	$0.890264\pi$
$458$	27.7821	−	9.02696i	0.0606596	−	0.0197095i
$459$	−323.189	−	105.010i	−0.704115	−	0.228781i
$460$	31.0557	+	22.5633i	0.0675125	+	0.0490507i
$461$			446.274i			0.968056i	0.875053	+	0.484028i	$0.160827\pi$
$461$			446.274i			0.968056i	−0.875053	+	0.484028i	$0.839173\pi$
$462$		0			0
$463$	73.1308			0.157950			0.0789750	−	0.996877i	$-0.474835\pi$
$463$	73.1308			0.157950			0.0789750	+	0.996877i	$0.474835\pi$
$464$	166.151	−	228.687i	0.358084	−	0.492860i
$465$	−12.1703	+	37.4563i	−0.0261727	+	0.0805512i
$466$	−51.8497	−	159.577i	−0.111265	−	0.342440i
$467$	−8.99187	+	6.53298i	−0.0192545	+	0.0139892i	−0.597371	−	0.801965i	$-0.703788\pi$
$467$	−8.99187	+	6.53298i	−0.0192545	+	0.0139892i	0.578116	+	0.815954i	$0.303788\pi$
$468$	76.0739	+	104.707i	0.162551	+	0.223732i
$469$	−364.615	+	118.471i	−0.777431	+	0.252602i
$470$	75.2786	+	24.4595i	0.160167	+	0.0520415i
$471$	275.729	+	200.329i	0.585413	+	0.425327i
$472$		−	12.3262i		−	0.0261148i
$473$		0			0
$474$	−3.95122			−0.00833590
$475$	−10.9696	+	15.0984i	−0.0230939	+	0.0317861i
$476$	163.310	−	502.616i	0.343088	−	1.05592i
$477$	25.1064	+	77.2696i	0.0526340	+	0.161991i
$478$	185.249	−	134.591i	0.387551	−	0.281572i
$479$	337.166	+	464.069i	0.703896	+	0.968829i	0.999907	+	0.0136448i	$0.00434339\pi$
$479$	337.166	+	464.069i	0.703896	+	0.968829i	−0.296011	+	0.955184i	$0.595657\pi$
$480$	−152.148	+	49.4358i	−0.316975	+	0.102991i
$481$	−201.246	−	65.3888i	−0.418391	−	0.135944i
$482$	−159.250	−	115.702i	−0.330395	−	0.240046i
$483$			38.0423i			0.0787624i
$484$		0			0
$485$	−309.633			−0.638419
$486$	104.987	−	144.503i	0.216024	−	0.297331i
$487$	−194.941	+	599.967i	−0.400290	+	1.23197i	0.524475	+	0.851426i	$0.324262\pi$
$487$	−194.941	+	599.967i	−0.400290	+	1.23197i	−0.924765	+	0.380540i	$0.875738\pi$
$488$	−37.9361	−	116.755i	−0.0777380	−	0.239253i
$489$	−194.947	+	141.637i	−0.398664	+	0.289646i
$490$	85.7407	+	118.012i	0.174981	+	0.240841i
$491$	−414.698	+	134.743i	−0.844598	+	0.274426i	−0.699182	−	0.714944i	$-0.746452\pi$
$491$	−414.698	+	134.743i	−0.844598	+	0.274426i	−0.145416	+	0.989371i	$0.546452\pi$
$492$	−320.205	−	104.041i	−0.650823	−	0.211465i
$493$	351.448	+	255.342i	0.712876	+	0.517935i
$494$		−	7.92055i		−	0.0160335i
$495$		0			0
$496$	−70.8491			−0.142841
$497$	−446.774	+	614.932i	−0.898942	+	1.23729i
$498$	−25.8282	+	79.4909i	−0.0518638	+	0.159620i
$499$	−143.790	−	442.539i	−0.288156	−	0.886852i	−0.985435	−	0.170052i	$-0.945606\pi$
$499$	−143.790	−	442.539i	−0.288156	−	0.886852i	0.697279	−	0.716799i	$-0.254394\pi$
$500$	382.026	−	277.558i	0.764053	−	0.555117i
$501$	200.598	+	276.099i	0.400395	+	0.551097i
$502$	−7.69386	+	2.49989i	−0.0153264	+	0.00497986i
$503$	436.964	+	141.978i	0.868716	+	0.282263i	0.709264	−	0.704943i	$-0.249027\pi$
$503$	436.964	+	141.978i	0.868716	+	0.282263i	0.159452	+	0.987206i	$0.449027\pi$
$504$	310.143	+	225.332i	0.615363	+	0.447087i
$505$			450.695i			0.892465i
$506$		0			0
$507$	195.356			0.385317
$508$	−384.200	+	528.807i	−0.756300	+	1.04096i
$509$	−74.3707	+	228.890i	−0.146111	+	0.449685i	−0.997152	−	0.0754148i	$-0.975972\pi$
$509$	−74.3707	+	228.890i	−0.146111	+	0.449685i	0.851041	+	0.525100i	$0.175972\pi$
$510$	−18.9667	−	58.3736i	−0.0371897	−	0.114458i
$511$	828.874	−	602.212i	1.62206	−	1.17850i
$512$	−296.086	−	407.528i	−0.578294	−	0.795953i
$513$	43.8525	−	14.2486i	0.0854826	−	0.0277750i
$514$	−278.660	−	90.5421i	−0.542140	−	0.176152i
$515$	−299.692	−	217.739i	−0.581926	−	0.422794i
$516$		−	110.662i		−	0.214461i
$517$		0			0
$518$	−291.246			−0.562251
$519$	−40.4102	+	55.6199i	−0.0778617	+	0.107167i
$520$	−35.2786	+	108.576i	−0.0678435	+	0.208801i
$521$	−215.622	−	663.615i	−0.413861	−	1.27373i	−0.913266	−	0.407364i	$-0.866448\pi$
$521$	−215.622	−	663.615i	−0.413861	−	1.27373i	0.499405	−	0.866369i	$-0.333552\pi$
$522$	−118.464	+	86.0691i	−0.226943	+	0.164883i
$523$	218.491	+	300.727i	0.417765	+	0.575005i	0.965091	−	0.261915i	$-0.0843540\pi$
$523$	218.491	+	300.727i	0.417765	+	0.575005i	−0.547326	+	0.836920i	$0.684354\pi$
$524$	−468.687	+	152.286i	−0.894441	+	0.290622i
$525$	117.812	+	38.2793i	0.224403	+	0.0729129i
$526$	−25.0770	−	18.2195i	−0.0476749	−	0.0346379i
$527$		−	108.881i		−	0.206606i
$528$		0			0
$529$	−521.361			−0.985559
$530$	−19.5743	+	26.9417i	−0.0369326	+	0.0508334i
$531$	4.97465	−	15.3104i	0.00936845	−	0.0288331i
$532$	22.1591	+	68.1986i	0.0416524	+	0.128193i
$533$	−298.435	+	216.825i	−0.559915	+	0.406802i
$534$	−72.7661	−	100.154i	−0.136266	−	0.187554i
$535$	322.705	−	104.853i	0.603187	−	0.195987i
$536$	−198.746	−	64.5765i	−0.370795	−	0.120479i
$537$	−244.793	−	177.852i	−0.455852	−	0.331196i
$538$		−	297.878i		−	0.553676i
$539$		0			0
$540$	−308.827			−0.571901
$541$	39.7802	−	54.7527i	0.0735309	−	0.101207i	−0.770667	−	0.637238i	$-0.780077\pi$
$541$	39.7802	−	54.7527i	0.0735309	−	0.101207i	0.844198	+	0.536031i	$0.180077\pi$
$542$	−52.1002	+	160.348i	−0.0961259	+	0.295845i
$543$	16.6130	+	51.1296i	0.0305949	+	0.0941613i
$544$	357.809	−	259.964i	0.657738	−	0.477875i
$545$	221.187	+	304.438i	0.405848	+	0.558602i
$546$	−50.0000	+	16.2460i	−0.0915751	+	0.0297546i
$547$	−706.077	−	229.418i	−1.29082	−	0.419412i	−0.418440	−	0.908244i	$-0.637423\pi$
$547$	−706.077	−	229.418i	−1.29082	−	0.419412i	−0.872378	+	0.488832i	$0.837423\pi$
$548$	−45.6672	−	33.1792i	−0.0833343	−	0.0605459i
$549$		−	160.333i		−	0.292045i
$550$		0			0
$551$	−58.9443			−0.106977
$552$	−12.1885	+	16.7760i	−0.0220806	+	0.0303913i
$553$	12.1115	−	37.2752i	0.0219014	−	0.0674055i
$554$	68.7678	+	211.645i	0.124130	+	0.382031i
$555$	180.000	−	130.778i	0.324324	−	0.235635i
$556$	−462.170	−	636.123i	−0.831242	−	1.14411i
$557$	−714.076	+	232.017i	−1.28200	+	0.416548i	−0.869285	−	0.494311i	$-0.835421\pi$
$557$	−714.076	+	232.017i	−1.28200	+	0.416548i	−0.412718	+	0.910859i	$0.635421\pi$
$558$	34.9048	+	11.3413i	0.0625534	+	0.0203248i
$559$	−98.0902	−	71.2667i	−0.175474	−	0.127490i
$560$		−	396.164i		−	0.707435i
$561$		0			0
$562$	94.0507			0.167350
$563$	612.888	−	843.568i	1.08861	−	1.49834i	0.238937	−	0.971035i	$-0.423201\pi$
$563$	612.888	−	843.568i	1.08861	−	1.49834i	0.849674	−	0.527309i	$-0.176799\pi$
$564$	40.3851	−	124.292i	0.0716047	−	0.220377i
$565$	−10.4984	−	32.3109i	−0.0185813	−	0.0571874i
$566$	−247.984	+	180.171i	−0.438134	+	0.318323i
$567$	193.666	+	266.558i	0.341562	+	0.470120i
$568$	−394.039	+	128.031i	−0.693731	+	0.225407i
$569$	−221.616	−	72.0076i	−0.389484	−	0.126551i	0.107727	−	0.994180i	$-0.465643\pi$
$569$	−221.616	−	72.0076i	−0.389484	−	0.126551i	−0.497211	+	0.867629i	$0.665643\pi$
$570$	6.73762	+	4.89517i	0.0118204	+	0.00858801i
$571$			196.324i			0.343825i	0.985112	+	0.171912i	$0.0549946\pi$
$571$			196.324i			0.343825i	−0.985112	+	0.171912i	$0.945005\pi$
$572$		0			0
$573$	165.564			0.288943
$574$	−298.435	+	410.760i	−0.519921	+	0.715610i
$575$	7.68692	−	23.6579i	0.0133686	−	0.0411442i
$576$	−41.0826	−	126.439i	−0.0713240	−	0.219513i
$577$	−115.163	+	83.6709i	−0.199589	+	0.145010i	−0.683091	−	0.730333i	$-0.739365\pi$
$577$	−115.163	+	83.6709i	−0.199589	+	0.145010i	0.483502	+	0.875344i	$0.339365\pi$
$578$	−23.6790	−	32.5914i	−0.0409672	−	0.0563864i
$579$	−38.4095	+	12.4800i	−0.0663376	+	0.0215544i
$580$	375.469	+	121.997i	0.647360	+	0.210340i
$581$	−670.736	−	487.319i	−1.15445	−	0.838758i
$582$		−	77.7223i		−	0.133544i
$583$		0			0
$584$	558.464			0.956274
$585$	−87.6393	+	120.625i	−0.149811	+	0.206197i
$586$	−14.4764	+	44.5539i	−0.0247038	+	0.0760305i
$587$	−74.0429	−	227.881i	−0.126138	−	0.388212i	0.867969	−	0.496619i	$-0.165425\pi$
$587$	−74.0429	−	227.881i	−0.126138	−	0.388212i	−0.994107	+	0.108406i	$0.965425\pi$
$588$	194.849	−	141.566i	0.331377	−	0.240759i
$589$	8.68381	+	11.9522i	0.0147433	+	0.0202924i
$590$	6.27553	−	2.03904i	0.0106365	−	0.00345601i
$591$	370.689	+	120.444i	0.627223	+	0.203797i
$592$	323.808	+	235.261i	0.546974	+	0.397400i
$593$			598.782i			1.00975i	0.863192	+	0.504875i	$0.168462\pi$
$593$			598.782i			1.00975i	−0.863192	+	0.504875i	$0.831538\pi$
$594$		0			0
$595$	608.827			1.02324
$596$	−137.116	+	188.724i	−0.230060	+	0.316650i
$597$	75.7883	−	233.252i	0.126949	−	0.390708i
$598$	3.26238	+	10.0406i	0.00545548	+	0.0167903i
$599$	−245.666	+	178.487i	−0.410126	+	0.297974i	−0.773653	−	0.633610i	$-0.781573\pi$
$599$	−245.666	+	178.487i	−0.410126	+	0.297974i	0.363527	+	0.931584i	$0.381573\pi$
$600$	39.6885	+	54.6265i	0.0661475	+	0.0910442i
$601$	−173.803	+	56.4720i	−0.289189	+	0.0939633i	−0.450019	−	0.893019i	$-0.648583\pi$
$601$	−173.803	+	56.4720i	−0.289189	+	0.0939633i	0.160830	+	0.986982i	$0.448583\pi$
$602$	−158.713	−	51.5691i	−0.263643	−	0.0856629i
$603$	−220.801	−	160.421i	−0.366171	−	0.266039i
$604$			349.036i			0.577874i
$605$		0			0
$606$	−113.131			−0.186685
$607$	475.414	−	654.352i	0.783220	−	1.07801i	−0.211699	−	0.977335i	$-0.567900\pi$
$607$	475.414	−	654.352i	0.783220	−	1.07801i	0.994919	−	0.100675i	$-0.0321002\pi$
$608$	−18.5445	+	57.0741i	−0.0305008	+	0.0938718i
$609$	120.902	+	372.097i	0.198525	+	0.610997i
$610$	53.1672	−	38.6282i	0.0871593	−	0.0633250i
$611$	−84.1641	−	115.842i	−0.137748	−	0.189594i
$612$	357.809	−	116.259i	0.584656	−	0.189966i
$613$	1135.21	+	368.852i	1.85189	+	0.601716i	0.996487	+	0.0837533i	$0.0266908\pi$
$613$	1135.21	+	368.852i	1.85189	+	0.601716i	0.855403	+	0.517962i	$0.173309\pi$
$614$	209.553	+	152.249i	0.341291	+	0.247962i
$615$		−	387.869i		−	0.630681i
$616$		0			0
$617$	107.900			0.174878			0.0874390	−	0.996170i	$-0.472132\pi$
$617$	107.900			0.174878			0.0874390	+	0.996170i	$0.472132\pi$
$618$	54.6556	−	75.2270i	0.0884395	−	0.121726i
$619$	−174.833	+	538.081i	−0.282445	+	0.869275i	0.704708	+	0.709497i	$0.251078\pi$
$619$	−174.833	+	538.081i	−0.282445	+	0.869275i	−0.987153	+	0.159778i	$0.948922\pi$
$620$	−30.5774	−	94.1075i	−0.0493184	−	0.151786i
$621$	−49.7214	+	36.1247i	−0.0800666	+	0.0581718i
$622$	237.105	+	326.346i	0.381197	+	0.524673i
$623$	1167.88	−	379.469i	1.87461	−	0.609099i
$624$	68.7132	+	22.3263i	0.110117	+	0.0357793i
$625$	258.076	+	187.503i	0.412922	+	0.300006i
$626$		−	240.768i		−	0.384614i
$627$		0			0
$628$	−856.298			−1.36353
$629$	−361.550	+	497.631i	−0.574801	+	0.791146i
$630$	−63.4164	+	195.176i	−0.100661	+	0.309803i
$631$	213.470	+	656.994i	0.338305	+	1.04119i	0.965071	+	0.261988i	$0.0843779\pi$
$631$	213.470	+	656.994i	0.338305	+	1.04119i	−0.626767	+	0.779207i	$0.715622\pi$
$632$	17.2837	−	12.5573i	0.0273476	−	0.0198692i
$633$	79.8888	+	109.957i	0.126207	+	0.173708i
$634$	357.188	−	116.058i	0.563389	−	0.183056i
$635$	−716.158	−	232.694i	−1.12781	−	0.366447i
$636$	44.4834	+	32.3191i	0.0699424	+	0.0508161i
$637$		−	263.883i		−	0.414259i
$638$		0			0
$639$	−541.108			−0.846805
$640$	304.200	−	418.696i	0.475313	−	0.654212i
$641$	238.636	−	734.445i	0.372286	−	1.14578i	−0.573005	−	0.819552i	$-0.694222\pi$
$641$	238.636	−	734.445i	0.372286	−	1.14578i	0.945291	−	0.326228i	$-0.105778\pi$
$642$	26.3197	+	81.0036i	0.0409964	+	0.126174i
$643$	−764.109	+	555.157i	−1.18835	+	0.863386i	−0.993089	−	0.117365i	$-0.962555\pi$
$643$	−764.109	+	555.157i	−1.18835	+	0.863386i	−0.195261	+	0.980751i	$0.562555\pi$
$644$	−56.1803	−	77.3256i	−0.0872366	−	0.120071i
$645$	121.246	−	39.3953i	0.187978	−	0.0610779i
$646$	−21.8973	−	7.11485i	−0.0338967	−	0.0110137i
$647$	789.076	+	573.297i	1.21959	+	0.886085i	0.996066	−	0.0886128i	$-0.0282434\pi$
$647$	789.076	+	573.297i	1.21959	+	0.886085i	0.223526	+	0.974698i	$0.428243\pi$
$648$			179.597i			0.277155i
$649$		0			0
$650$	34.3769			0.0528876
$651$	57.6393	−	79.3337i	0.0885397	−	0.121864i
$652$	187.086	−	575.790i	0.286941	−	0.883113i
$653$	74.3363	+	228.784i	0.113838	+	0.350358i	0.991703	−	0.128551i	$-0.0410326\pi$
$653$	74.3363	+	228.784i	0.113838	+	0.350358i	−0.877865	+	0.478909i	$0.841033\pi$
$654$	−76.4183	+	55.5212i	−0.116848	+	0.0848947i
$655$	−333.702	−	459.301i	−0.509469	−	0.701223i
$656$	663.601	−	215.617i	1.01159	−	0.328685i
$657$	693.669	+	225.387i	1.05581	+	0.343054i
$658$	−159.443	−	115.842i	−0.242314	−	0.176052i
$659$			937.713i			1.42293i	0.702720	+	0.711467i	$0.251969\pi$
$659$			937.713i			1.42293i	−0.702720	+	0.711467i	$0.748031\pi$
$660$		0			0
$661$	133.305			0.201672			0.100836	−	0.994903i	$-0.467848\pi$
$661$	133.305			0.201672			0.100836	+	0.994903i	$0.467848\pi$
$662$	89.2039	−	122.779i	0.134749	−	0.185466i
$663$	−34.3112	+	105.599i	−0.0517514	+	0.159274i
$664$	−139.650	−	429.798i	−0.210316	−	0.647287i
$665$	−66.8328	+	48.5569i	−0.100500	+	0.0730179i
$666$	−121.869	−	167.739i	−0.182987	−	0.251860i
$667$	74.7214	−	24.2784i	0.112026	−	0.0363995i
$668$	−815.480	−	264.966i	−1.22078	−	0.396655i
$669$	−297.426	−	216.093i	−0.444584	−	0.323009i
$670$		−	111.868i		−	0.166968i
$671$		0			0
$672$	398.328			0.592750
$673$	−531.652	+	731.756i	−0.789973	+	1.08730i	0.204139	+	0.978942i	$0.434561\pi$
$673$	−531.652	+	731.756i	−0.789973	+	1.08730i	−0.994112	+	0.108362i	$0.965439\pi$
$674$	−30.2933	+	93.2333i	−0.0449456	+	0.138328i
$675$	61.8419	+	190.330i	0.0916176	+	0.281970i
$676$	−397.085	+	288.499i	−0.587403	+	0.426773i
$677$	−355.245	−	488.953i	−0.524734	−	0.722234i	0.461582	−	0.887097i	$-0.347282\pi$
$677$	−355.245	−	488.953i	−0.524734	−	0.722234i	−0.986316	+	0.164863i	$0.947282\pi$
$678$	8.11050	−	2.63526i	0.0119624	−	0.00388681i
$679$	733.222	+	238.238i	1.07986	+	0.350866i
$680$	268.482	+	195.064i	0.394827	+	0.286858i
$681$		−	351.744i		−	0.516512i
$682$		0			0
$683$	1261.32			1.84673			0.923367	−	0.383919i	$-0.125426\pi$
$683$	1261.32			1.84673			0.923367	+	0.383919i	$0.125426\pi$
$684$	−30.0056	+	41.2992i	−0.0438679	+	0.0603789i
$685$	20.0952	−	61.8467i	0.0293361	−	0.0902871i
$686$	−2.66874	−	8.21353i	−0.00389029	−	0.0119731i
$687$	44.9524	−	32.6598i	0.0654329	−	0.0475398i
$688$	134.802	+	185.539i	0.195933	+	0.269679i
$689$	57.2949	−	18.6162i	0.0831566	−	0.0270192i
$690$	−10.5573	−	3.43027i	−0.0153004	−	0.00497140i
$691$	347.977	+	252.820i	0.503584	+	0.365875i	0.810384	−	0.585899i	$-0.199258\pi$
$691$	347.977	+	252.820i	0.503584	+	0.365875i	−0.306800	+	0.951774i	$0.599258\pi$
$692$		−	172.732i		−	0.249612i
$693$		0			0
$694$	68.8603			0.0992224
$695$	532.433	−	732.832i	0.766091	−	1.05443i
$696$	−65.9017	+	202.825i	−0.0946863	+	0.291415i
$697$	331.362	+	1019.83i	0.475411	+	1.46317i
$698$	−100.997	+	73.3785i	−0.144695	+	0.105127i
$699$	−187.594	−	258.201i	−0.268375	−	0.369386i
$700$	−295.997	+	96.1752i	−0.422853	+	0.137393i
$701$	−483.951	−	157.245i	−0.690373	−	0.224316i	−0.0572417	−	0.998360i	$-0.518231\pi$
$701$	−483.951	−	157.245i	−0.690373	−	0.224316i	−0.633131	+	0.774045i	$0.718231\pi$
$702$	−68.7132	−	49.9231i	−0.0978821	−	0.0711155i
$703$		−	83.4619i		−	0.118722i
$704$		0			0
$705$	150.557			0.213556
$706$	−51.0942	+	70.3252i	−0.0723714	+	0.0996107i
$707$	346.774	−	1067.26i	0.490487	−	1.50956i
$708$	−3.36666	−	10.3615i	−0.00475518	−	0.0146349i
$709$	596.797	−	433.599i	0.841745	−	0.611564i	−0.0811126	−	0.996705i	$-0.525847\pi$
$709$	596.797	−	433.599i	0.841745	−	0.611564i	0.922858	+	0.385141i	$0.125847\pi$
$710$	−130.367	−	179.435i	−0.183615	−	0.252725i
$711$	26.5360	−	8.62207i	0.0373221	−	0.0121267i
$712$	636.596	+	206.843i	0.894096	+	0.290509i
$713$	−15.9311	−	11.5746i	−0.0223438	−	0.0162337i
$714$			152.824i			0.214039i
$715$		0			0
$716$	760.222			1.06176
$717$	256.008	−	352.365i	0.357055	−	0.491443i
$718$	104.919	−	322.907i	0.146126	−	0.449731i
$719$	−162.634	−	500.537i	−0.226195	−	0.696157i	−0.998168	−	0.0605017i	$-0.980730\pi$
$719$	−162.634	−	500.537i	−0.226195	−	0.696157i	0.771973	−	0.635655i	$-0.219270\pi$
$720$	228.164	−	165.771i	0.316895	−	0.230237i
$721$	542.148	+	746.202i	0.751939	+	1.03495i
$722$	−246.474	+	80.0842i	−0.341376	+	0.110920i
$723$	−356.094	−	115.702i	−0.492523	−	0.160030i
$724$	−109.276	−	79.3933i	−0.150933	−	0.109659i
$725$		−	255.831i		−	0.352871i
$726$		0			0
$727$	−756.122			−1.04006			−0.520029	−	0.854149i	$-0.674079\pi$
$727$	−756.122			−1.04006			−0.520029	+	0.854149i	$0.674079\pi$
$728$	167.082	−	229.969i	0.229508	−	0.315891i
$729$	12.9812	−	39.9521i	0.0178069	−	0.0548040i
$730$	92.3832	+	284.326i	0.126552	+	0.389488i
$731$	−285.137	+	207.164i	−0.390065	+	0.283398i
$732$	−63.7790	−	87.7843i	−0.0871298	−	0.119924i
$733$	405.125	−	131.633i	0.552694	−	0.179581i	−0.0193373	−	0.999813i	$-0.506156\pi$
$733$	405.125	−	131.633i	0.552694	−	0.179581i	0.572031	+	0.820232i	$0.306156\pi$
$734$	−227.214	−	73.8262i	−0.309555	−	0.100581i
$735$	224.472	+	163.089i	0.305404	+	0.221889i
$736$		−	79.9888i		−	0.108680i
$737$		0			0
$738$	−361.448			−0.489767
$739$	−114.100	+	157.046i	−0.154398	+	0.212511i	−0.879208	−	0.476438i	$-0.841928\pi$
$739$	−114.100	+	157.046i	−0.154398	+	0.212511i	0.724810	+	0.688949i	$0.241928\pi$
$740$	−172.741	+	531.644i	−0.233434	+	0.718437i
$741$	−4.65558	−	14.3284i	−0.00628284	−	0.0193366i
$742$	67.0820	−	48.7380i	0.0904071	−	0.0656846i
$743$	−130.766	−	179.984i	−0.175997	−	0.242239i	0.711901	−	0.702280i	$-0.247835\pi$
$743$	−130.766	−	179.984i	−0.175997	−	0.242239i	−0.887898	+	0.460041i	$0.847835\pi$
$744$	50.8359	−	16.5176i	0.0683279	−	0.0222011i
$745$	−255.587	−	83.0452i	−0.343069	−	0.111470i
$746$	−125.865	−	91.4465i	−0.168720	−	0.122582i
$747$		−	590.214i		−	0.790112i
$748$		0			0
$749$	−844.853			−1.12797
$750$	−80.2631	+	110.473i	−0.107017	+	0.147297i
$751$	−453.197	+	1394.80i	−0.603459	+	1.85725i	−0.0964000	+	0.995343i	$0.530733\pi$
$751$	−453.197	+	1394.80i	−0.603459	+	1.85725i	−0.507059	+	0.861912i	$0.669267\pi$
$752$	83.6950	+	257.587i	0.111297	+	0.342536i
$753$	−12.4489	+	9.04468i	−0.0165324	+	0.0120115i
$754$	63.8197	+	87.8402i	0.0846415	+	0.116499i
$755$	−382.420	+	124.256i	−0.506516	+	0.164577i
$756$	731.312	+	237.618i	0.967344	+	0.314309i
$757$	−1075.57	−	781.448i	−1.42083	−	1.03230i	−0.991633	−	0.129087i	$-0.958795\pi$
$757$	−1075.57	−	781.448i	−1.42083	−	1.03230i	−0.429200	−	0.903209i	$-0.641205\pi$
$758$			232.676i			0.306961i
$759$		0			0
$760$	−45.0294			−0.0592492
$761$	−404.642	+	556.942i	−0.531724	+	0.731856i	−0.987392	−	0.158294i	$-0.949401\pi$
$761$	−404.642	+	556.942i	−0.531724	+	0.731856i	0.455668	+	0.890150i	$0.349401\pi$
$762$	58.4095	−	179.766i	0.0766528	−	0.235913i
$763$	−289.538	−	891.106i	−0.379473	−	1.16790i
$764$	−336.530	+	244.503i	−0.440484	+	0.320030i
$765$	254.758	+	350.644i	0.333017	+	0.458358i
$766$	378.353	−	122.934i	0.493934	−	0.160489i
$767$	−11.3525	−	3.68867i	−0.0148012	−	0.00480921i
$768$	21.2426	+	15.4337i	0.0276597	+	0.0200959i
$769$			695.838i			0.904860i	0.891800	+	0.452430i	$0.149443\pi$
$769$			695.838i			0.904860i	−0.891800	+	0.452430i	$0.850557\pi$
$770$		0			0
$771$	−557.320			−0.722853
$772$	59.6417	−	82.0897i	0.0772561	−	0.106334i
$773$	25.6525	−	78.9502i	0.0331856	−	0.102135i	−0.933092	−	0.359639i	$-0.882900\pi$
$773$	25.6525	−	78.9502i	0.0331856	−	0.102135i	0.966277	+	0.257504i	$0.0829000\pi$
$774$	−36.7117	−	112.987i	−0.0474311	−	0.145978i
$775$	−51.8754	+	37.6897i	−0.0669360	+	0.0486318i
$776$	247.008	+	339.978i	0.318310	+	0.438116i
$777$	−526.869	+	171.190i	−0.678081	+	0.220322i
$778$	232.537	+	75.5559i	0.298891	+	0.0971156i
$779$	−117.711	−	85.5218i	−0.151105	−	0.109784i
$780$			100.906i			0.129367i
$781$		0			0
$782$	30.6888			0.0392440
$783$	−371.525	+	511.360i	−0.474489	+	0.653078i
$784$	−154.242	+	474.708i	−0.196737	+	0.605495i
$785$	−304.839	−	938.198i	−0.388330	−	1.19516i
$786$	115.291	−	83.7640i	0.146681	−	0.106570i
$787$	−63.7560	−	87.7526i	−0.0810115	−	0.111503i	0.766588	−	0.642139i	$-0.221953\pi$
$787$	−63.7560	−	87.7526i	−0.0810115	−	0.111503i	−0.847599	+	0.530637i	$0.821953\pi$
$788$	−931.341	+	302.611i	−1.18191	+	0.384024i
$789$	−56.0739	−	18.2195i	−0.0710696	−	0.0230919i
$790$	9.25233	+	6.72221i	0.0117118	+	0.00850913i
$791$			84.5910i			0.106942i
$792$		0			0
$793$	−118.885			−0.149919
$794$	49.2705	−	67.8150i	0.0620535	−	0.0854094i
$795$	−19.5743	+	60.2434i	−0.0246217	+	0.0757779i
$796$	190.415	+	586.038i	0.239215	+	0.736228i
$797$	807.914	−	586.984i	1.01369	−	0.736491i	0.0487129	−	0.998813i	$-0.484488\pi$
$797$	807.914	−	586.984i	1.01369	−	0.736491i	0.964981	+	0.262321i	$0.0844881\pi$
$798$	−12.1885	−	16.7760i	−0.0152738	−	0.0210225i
$799$	−395.861	+	128.623i	−0.495446	+	0.160980i
$800$	−247.714	−	80.4872i	−0.309643	−	0.100609i
$801$	707.239	+	513.839i	0.882945	+	0.641497i
$802$			46.3500i			0.0577930i
$803$		0			0
$804$	−184.706			−0.229734
$805$	64.7214	−	89.0813i	0.0803992	−	0.110660i
$806$	8.40946	−	25.8817i	0.0104336	−	0.0321112i
$807$	−175.088	−	538.866i	−0.216962	−	0.667740i
$808$	494.864	−	359.540i	0.612456	−	0.444975i
$809$	−44.3021	−	60.9766i	−0.0547615	−	0.0753728i	0.780758	−	0.624834i	$-0.214833\pi$
$809$	−44.3021	−	60.9766i	−0.0547615	−	0.0753728i	−0.835520	+	0.549461i	$0.814833\pi$
$810$	−91.4365	+	29.7095i	−0.112885	+	0.0366784i
$811$	−943.964	−	306.712i	−1.16395	−	0.378190i	−0.337569	−	0.941301i	$-0.609605\pi$
$811$	−943.964	−	306.712i	−1.16395	−	0.378190i	−0.826382	+	0.563110i	$0.809605\pi$
$812$	−795.256	−	577.787i	−0.979380	−	0.711561i
$813$			320.696i			0.394460i
$814$		0			0
$815$	697.463			0.855783
$816$	123.447	−	169.910i	0.151283	−	0.208224i
$817$	14.7780	−	45.4822i	0.0180882	−	0.0556697i
$818$	−137.331	−	422.662i	−0.167887	−	0.516702i
$819$	300.344	−	218.213i	0.366721	−	0.266438i
$820$	572.800	+	788.392i	0.698537	+	0.961454i
$821$	−1186.15	+	385.402i	−1.44476	+	0.469430i	−0.923377	−	0.383894i	$-0.874583\pi$
$821$	−1186.15	+	385.402i	−1.44476	+	0.469430i	−0.521381	+	0.853324i	$0.674583\pi$
$822$	15.5244	+	5.04418i	0.0188861	+	0.00613647i
$823$	432.812	+	314.456i	0.525895	+	0.382085i	0.818820	−	0.574050i	$-0.194629\pi$
$823$	432.812	+	314.456i	0.525895	+	0.382085i	−0.292925	+	0.956135i	$0.594629\pi$
$824$			502.763i			0.610149i
$825$		0			0
$826$	−16.4296			−0.0198905
$827$	−33.0629	+	45.5072i	−0.0399793	+	0.0550268i	−0.828539	−	0.559932i	$-0.810827\pi$
$827$	−33.0629	+	45.5072i	−0.0399793	+	0.0550268i	0.788559	+	0.614959i	$0.210827\pi$
$828$	21.0263	−	64.7123i	0.0253941	−	0.0781550i
$829$	−252.220	−	776.253i	−0.304246	−	0.936372i	−0.979958	−	0.199206i	$-0.936164\pi$
$829$	−252.220	−	776.253i	−0.304246	−	0.936372i	0.675712	−	0.737166i	$-0.263836\pi$
$830$	195.718	−	142.198i	0.235805	−	0.171322i
$831$	248.804	+	342.450i	0.299403	+	0.412093i
$832$	−93.7539	+	30.4625i	−0.112685	+	0.0366136i
$833$	−729.534	−	237.040i	−0.875792	−	0.284562i
$834$	183.951	+	133.648i	0.220565	+	0.160250i
$835$		−	987.803i		−	1.18300i
$836$		0			0
$837$	158.423			0.189275
$838$	62.4160	−	85.9083i	0.0744821	−	0.102516i
$839$	19.0301	−	58.5688i	0.0226819	−	0.0698078i	−0.939075	−	0.343713i	$-0.888315\pi$
$839$	19.0301	−	58.5688i	0.0226819	−	0.0698078i	0.961757	+	0.273905i	$0.0883154\pi$
$840$	92.3607	+	284.257i	0.109953	+	0.338401i
$841$	−26.6813	+	19.3851i	−0.0317257	+	0.0230501i
$842$	−253.416	−	348.798i	−0.300970	−	0.414249i
$843$	170.139	−	55.2816i	0.201826	−	0.0655772i
$844$	−324.768	−	105.523i	−0.384796	−	0.125028i
$845$	−457.453	−	332.359i	−0.541364	−	0.393324i
$846$		−	140.301i		−	0.165841i
$847$		0			0
$848$	−113.951			−0.134376
$849$	−342.705	+	471.693i	−0.403657	+	0.555587i
$850$	30.8800	−	95.0390i	0.0363295	−	0.111811i
$851$	34.3769	+	105.801i	0.0403959	+	0.124326i
$852$	−296.264	+	215.249i	−0.347728	+	0.252639i
$853$	−832.642	−	1146.03i	−0.976134	−	1.34353i	−0.938887	−	0.344227i	$-0.888141\pi$
$853$	−832.642	−	1146.03i	−0.976134	−	1.34353i	−0.0372470	−	0.999306i	$-0.511859\pi$
$854$	−155.623	+	50.5650i	−0.182228	+	0.0592096i
$855$	−55.9311	−	18.1731i	−0.0654165	−	0.0212551i
$856$	−372.566	−	270.685i	−0.435240	−	0.316221i
$857$		−	1249.64i		−	1.45815i	−0.684432	−	0.729077i	$-0.739950\pi$
$857$		−	1249.64i		−	1.45815i	0.684432	−	0.729077i	$-0.260050\pi$
$858$		0			0
$859$	−345.229			−0.401896			−0.200948	−	0.979602i	$-0.564402\pi$
$859$	−345.229			−0.401896			−0.200948	+	0.979602i	$0.564402\pi$
$860$	−188.269	+	259.130i	−0.218918	+	0.301315i
$861$	−298.435	+	918.487i	−0.346614	+	1.06677i
$862$	39.1416	+	120.465i	0.0454079	+	0.139751i
$863$	327.889	−	238.225i	0.379940	−	0.276043i	−0.381380	−	0.924418i	$-0.624551\pi$
$863$	327.889	−	238.225i	0.379940	−	0.276043i	0.761321	+	0.648375i	$0.224551\pi$
$864$	378.250	+	520.616i	0.437789	+	0.602565i
$865$	189.252	−	61.4918i	0.218789	−	0.0710888i
$866$	428.853	+	139.343i	0.495211	+	0.160904i
$867$	−61.9925	−	45.0402i	−0.0715023	−	0.0519494i
$868$			246.377i			0.283844i
$869$		0			0
$870$	−114.164			−0.131223
$871$	−118.951	+	163.722i	−0.136569	+	0.187970i
$872$	157.823	−	485.729i	0.180989	−	0.557028i
$873$	169.600	+	521.976i	0.194273	+	0.597910i
$874$	−3.36881	+	2.44758i	−0.00385447	+	0.00280044i
$875$	−796.158	−	1095.82i	−0.909895	−	1.25236i
$876$	469.450	−	152.534i	0.535902	−	0.174125i
$877$	338.281	+	109.914i	0.385725	+	0.125330i	0.495459	−	0.868631i	$-0.335000\pi$
$877$	338.281	+	109.914i	0.385725	+	0.125330i	−0.109734	+	0.993961i	$0.535000\pi$
$878$	−397.800	−	289.019i	−0.453076	−	0.329179i
$879$			89.1077i			0.101374i
$880$		0			0
$881$	−883.370			−1.00269			−0.501345	−	0.865248i	$-0.667161\pi$
$881$	−883.370			−1.00269			−0.501345	+	0.865248i	$0.667161\pi$
$882$	151.979	−	209.181i	0.172312	−	0.237167i
$883$	257.641	−	792.936i	0.291779	−	0.898003i	−0.692506	−	0.721412i	$-0.743493\pi$
$883$	257.641	−	792.936i	0.291779	−	0.898003i	0.984284	−	0.176590i	$-0.0565068\pi$
$884$	−86.2055	−	265.313i	−0.0975175	−	0.300128i
$885$	10.1540	−	7.37733i	0.0114735	−	0.00833597i
$886$	110.737	+	152.417i	0.124986	+	0.172028i
$887$	87.9249	−	28.5685i	0.0991262	−	0.0322080i	−0.259034	−	0.965868i	$-0.583404\pi$
$887$	87.9249	−	28.5685i	0.0991262	−	0.0322080i	0.358160	+	0.933660i	$0.383404\pi$
$888$	−287.188	−	93.3132i	−0.323410	−	0.105082i
$889$	1516.85	+	1102.05i	1.70624	+	1.23966i
$890$			358.322i			0.402608i
$891$		0			0
$892$	923.680			1.03552
$893$	33.1966	−	45.6912i	0.0371742	−	0.0511660i
$894$	20.8455	−	64.1559i	0.0233171	−	0.0717628i
$895$	270.636	+	832.933i	0.302387	+	0.930651i
$896$	−1042.51	+	757.428i	−1.16352	+	0.845344i
$897$	11.8034	+	16.2460i	0.0131588	+	0.0181115i
$898$	−278.053	+	90.3449i	−0.309636	+	0.100607i
$899$	−192.610	−	62.5828i	−0.214249	−	0.0696137i
$900$	−179.248	−	130.231i	−0.199164	−	0.144701i
$901$		−	175.121i		−	0.194363i
$902$		0			0
$903$	−317.426			−0.351524
$904$	−27.1024	+	37.3032i	−0.0299805	+	0.0412646i
$905$	48.0851	−	147.991i	0.0531328	−	0.163526i
$906$	−31.1899	−	95.9928i	−0.0344260	−	0.105952i
$907$	1190.64	−	865.050i	1.31272	−	0.953749i	0.312730	−	0.949842i	$-0.398757\pi$
$907$	1190.64	−	865.050i	1.31272	−	0.953749i	0.999992	−	0.00390645i	$-0.00124347\pi$
$908$	519.452	+	714.964i	0.572083	+	0.787405i
$909$	759.776	−	246.866i	0.835837	−	0.271580i
$910$	144.721	+	47.0228i	0.159034	+	0.0516734i
$911$	−142.297	−	103.385i	−0.156198	−	0.113485i	0.506941	−	0.861981i	$-0.330776\pi$
$911$	−142.297	−	103.385i	−0.156198	−	0.113485i	−0.663139	+	0.748496i	$0.730776\pi$
$912$			28.4971i			0.0312468i
$913$		0			0
$914$	−185.795			−0.203277
$915$	73.4752	−	101.130i	0.0803008	−	0.110525i
$916$	−43.1397	+	132.770i	−0.0470957	+	0.144946i
$917$	436.822	+	1344.40i	0.476359	+	1.46608i
$918$	−199.742	+	145.121i	−0.217584	+	0.158084i
$919$	1011.18	+	1391.77i	1.10031	+	1.51444i	0.834979	+	0.550281i	$0.185479\pi$
$919$	1011.18	+	1391.77i	1.10031	+	1.51444i	0.265326	+	0.964159i	$0.414521\pi$
$920$	57.0820	−	18.5471i	0.0620457	−	0.0201599i
$921$	468.574	+	152.249i	0.508766	+	0.165308i
$922$	262.313	+	190.582i	0.284504	+	0.206705i
$923$			401.228i			0.434700i
$924$		0			0
$925$	362.243			0.391614
$926$	31.2306	−	42.9852i	0.0337263	−	0.0464203i
$927$	−202.907	+	624.483i	−0.218885	+	0.673660i
$928$	−254.212	−	782.383i	−0.273935	−	0.843085i
$929$	−756.498	+	549.628i	−0.814315	+	0.591634i	−0.915078	−	0.403276i	$-0.867871\pi$
$929$	−756.498	+	549.628i	−0.814315	+	0.591634i	0.100764	+	0.994910i	$0.467871\pi$
$930$	16.8189	+	23.1493i	0.0180849	+	0.0248917i
$931$	98.9884	−	32.1633i	0.106325	−	0.0345470i
$932$	762.616	+	247.789i	0.818257	+	0.265868i
$933$	620.748	+	451.000i	0.665324	+	0.483386i
$934$			8.07520i			0.00864583i
$935$		0			0
$936$	202.361			0.216197
$937$	527.520	−	726.068i	0.562988	−	0.774886i	−0.428715	−	0.903440i	$-0.641033\pi$
$937$	527.520	−	726.068i	0.562988	−	0.774886i	0.991703	+	0.128554i	$0.0410335\pi$
$938$	−86.0739	+	264.908i	−0.0917632	+	0.282418i
$939$	−141.520	−	435.554i	−0.150713	−	0.463848i
$940$	−306.026	+	222.341i	−0.325560	+	0.236533i
$941$	−270.575	−	372.415i	−0.287540	−	0.395765i	0.640673	−	0.767814i	$-0.278655\pi$
$941$	−270.575	−	372.415i	−0.287540	−	0.395765i	−0.928213	+	0.372049i	$0.878655\pi$
$942$	235.501	−	76.5189i	0.250001	−	0.0812303i
$943$	184.443	+	59.9291i	0.195591	+	0.0635515i
$944$	18.2664	+	13.2713i	0.0193500	+	0.0140586i
$945$			885.849i			0.937406i
$946$		0			0
$947$	1781.44			1.88114			0.940570	−	0.339600i	$-0.110292\pi$
$947$	1781.44			1.88114			0.940570	+	0.339600i	$0.110292\pi$
$948$	11.0990	−	15.2765i	0.0117078	−	0.0161145i
$949$	167.123	−	514.351i	0.176104	−	0.541992i
$950$	4.19002	+	12.8956i	0.00441055	+	0.0135743i
$951$	577.943	−	419.900i	0.607721	−	0.441535i
$952$	−485.689	−	668.493i	−0.510177	−	0.702199i
$953$	764.349	−	248.352i	0.802045	−	0.260600i	0.120820	−	0.992674i	$-0.461448\pi$
$953$	764.349	−	248.352i	0.802045	−	0.260600i	0.681225	+	0.732074i	$0.261448\pi$
$954$	56.1397	+	18.2409i	0.0588466	+	0.0191204i
$955$	−387.692	−	281.675i	−0.405960	−	0.294947i
$956$			1094.30i			1.14466i
$957$		0			0
$958$	416.760			0.435031
$959$	−95.1722	+	130.993i	−0.0992411	+	0.136594i
$960$	32.0301	−	98.5787i	0.0333647	−	0.102686i
$961$	−281.280	−	865.690i	−0.292695	−	0.900822i
$962$	−124.377	+	90.3651i	−0.129290	+	0.0939347i
$963$	−353.521	−	486.579i	−0.367104	−	0.505275i
$964$	894.673	−	290.697i	0.928084	−	0.301553i
$965$	111.173	+	36.1224i	0.115206	+	0.0374326i
$966$	22.3607	+	16.2460i	0.0231477	+	0.0168178i
$967$		−	915.454i		−	0.946695i	−0.880876	−	0.473347i	$-0.843046\pi$
$967$		−	915.454i		−	0.946695i	0.880876	−	0.473347i	$-0.156954\pi$
$968$		0			0
$969$	−43.7945			−0.0451956
$970$	−132.229	+	181.998i	−0.136319	+	0.187627i
$971$	227.791	−	701.070i	0.234595	−	0.722008i	−0.762580	−	0.646894i	$-0.776068\pi$
$971$	227.791	−	701.070i	0.234595	−	0.722008i	0.997175	−	0.0751145i	$-0.0239322\pi$
$972$	263.777	+	811.822i	0.271375	+	0.835208i
$973$	−1824.68	+	1325.71i	−1.87531	+	1.36249i
$974$	269.402	+	370.800i	0.276593	+	0.380698i
$975$	62.1885	−	20.2063i	0.0637830	−	0.0207244i
$976$	213.867	+	69.4897i	0.219126	+	0.0711984i
$977$	−154.769	−	112.446i	−0.158412	−	0.115093i	0.505755	−	0.862677i	$-0.331214\pi$
$977$	−154.769	−	112.446i	−0.158412	−	0.115093i	−0.664168	+	0.747584i	$0.731214\pi$
$978$			175.073i			0.179011i
$979$		0			0
$980$	−697.115			−0.711341
$981$	392.064	−	539.630i	0.399657	−	0.550081i
$982$	−97.8968	+	301.295i	−0.0996913	+	0.306818i
$983$	295.070	+	908.132i	0.300173	+	0.923838i	0.981435	+	0.191797i	$0.0614317\pi$
$983$	295.070	+	908.132i	0.300173	+	0.923838i	−0.681262	+	0.732040i	$0.738568\pi$
$984$	−425.881	+	309.421i	−0.432806	+	0.314452i
$985$	−663.108	−	912.690i	−0.673206	−	0.926589i
$986$	300.172	−	97.5319i	0.304434	−	0.0989167i
$987$	−356.525	−	115.842i	−0.361221	−	0.117368i
$988$	30.6231	+	22.2490i	0.0309950	+	0.0225192i
$989$			63.7429i			0.0644518i
$990$		0			0
$991$	−1076.02			−1.08580			−0.542898	−	0.839799i	$-0.682673\pi$
$991$	−1076.02			−1.08580			−0.542898	+	0.839799i	$0.682673\pi$
$992$	−121.194	+	166.810i	−0.122172	+	0.168155i
$993$	89.2039	−	274.541i	0.0898327	−	0.276477i
$994$	170.652	+	525.214i	0.171683	+	0.528385i
$995$	−574.302	+	417.255i	−0.577188	+	0.419351i
$996$	−234.782	−	323.150i	−0.235725	−	0.324448i
$997$	458.614	−	149.013i	0.459994	−	0.149461i	−0.0698479	−	0.997558i	$-0.522251\pi$
$997$	458.614	−	149.013i	0.459994	−	0.149461i	0.529842	+	0.848097i	$0.322251\pi$
$998$	−321.523	−	104.469i	−0.322168	−	0.104679i
$999$	−724.058	−	526.059i	−0.724782	−	0.526585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.3.d.a.40.1		4
11.2	odd	10		121.3.d.d.94.1		4
11.3	even	5		121.3.d.c.118.1		4
11.4	even	5		121.3.d.d.112.1		4
11.5	even	5		121.3.b.b.120.3		4
11.6	odd	10		121.3.b.b.120.2		4
11.7	odd	10		11.3.d.a.2.1	✓	4
11.8	odd	10	inner	121.3.d.a.118.1		4
11.9	even	5		11.3.d.a.6.1	yes	4
11.10	odd	2		121.3.d.c.40.1		4
33.5	odd	10		1089.3.c.e.604.2		4
33.17	even	10		1089.3.c.e.604.3		4
33.20	odd	10		99.3.k.a.28.1		4
33.29	even	10		99.3.k.a.46.1		4
44.7	even	10		176.3.n.a.145.1		4
44.31	odd	10		176.3.n.a.17.1		4
55.7	even	20		275.3.q.d.24.2		8
55.9	even	10		275.3.x.e.226.1		4
55.18	even	20		275.3.q.d.24.1		8
55.29	odd	10		275.3.x.e.101.1		4
55.42	odd	20		275.3.q.d.149.1		8
55.53	odd	20		275.3.q.d.149.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.3.d.a.2.1	✓	4	11.7	odd	10
11.3.d.a.6.1	yes	4	11.9	even	5
99.3.k.a.28.1		4	33.20	odd	10
99.3.k.a.46.1		4	33.29	even	10
121.3.b.b.120.2		4	11.6	odd	10
121.3.b.b.120.3		4	11.5	even	5
121.3.d.a.40.1		4	1.1	even	1	trivial
121.3.d.a.118.1		4	11.8	odd	10	inner
121.3.d.c.40.1		4	11.10	odd	2
121.3.d.c.118.1		4	11.3	even	5
121.3.d.d.94.1		4	11.2	odd	10
121.3.d.d.112.1		4	11.4	even	5
176.3.n.a.17.1		4	44.31	odd	10
176.3.n.a.145.1		4	44.7	even	10
275.3.q.d.24.1		8	55.18	even	20
275.3.q.d.24.2		8	55.7	even	20
275.3.q.d.149.1		8	55.42	odd	20
275.3.q.d.149.2		8	55.53	odd	20
275.3.x.e.101.1		4	55.29	odd	10
275.3.x.e.226.1		4	55.9	even	10
1089.3.c.e.604.2		4	33.5	odd	10
1089.3.c.e.604.3		4	33.17	even	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	121.d (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.427051 - 0.587785i) q^{2} +(0.427051 - 1.31433i) q^{3} +(1.07295 + 3.30220i) q^{4} +(-3.23607 + 2.35114i) q^{5} +(-0.590170 - 0.812299i) q^{6} +(9.47214 - 3.07768i) q^{7} +(5.16312 + 1.67760i) q^{8} +(5.73607 + 4.16750i) q^{9} +2.90617i q^{10} +4.79837 q^{12} +(3.09017 - 4.25325i) q^{13} +(2.23607 - 6.88191i) q^{14} +(1.70820 + 5.25731i) q^{15} +(-8.04508 + 5.84510i) q^{16} +(-8.98278 - 12.3637i) q^{17} +(4.89919 - 1.59184i) q^{18} +(1.97214 + 0.640786i) q^{19} +(-11.2361 - 8.16348i) q^{20} -13.7638i q^{21} -2.76393 q^{23} +(4.40983 - 6.06961i) q^{24} +(-2.78115 + 8.55951i) q^{25} +(-1.18034 - 3.63271i) q^{26} +(17.9894 - 13.0700i) q^{27} +(20.3262 + 27.9767i) q^{28} +(-27.0344 + 8.78402i) q^{29} +(3.81966 + 1.24108i) q^{30} +(5.76393 + 4.18774i) q^{31} +28.9402i q^{32} -11.1033 q^{34} +(-23.4164 + 32.2299i) q^{35} +(-7.60739 + 23.4131i) q^{36} +(-12.4377 - 38.2793i) q^{37} +(1.21885 - 0.885544i) q^{38} +(-4.27051 - 5.87785i) q^{39} +(-20.6525 + 6.71040i) q^{40} +(-66.7320 - 21.6825i) q^{41} +(-8.09017 - 5.87785i) q^{42} -23.0624i q^{43} -28.3607 q^{45} +(-1.18034 + 1.62460i) q^{46} +(8.41641 - 25.9030i) q^{47} +(4.24671 + 13.0700i) q^{48} +(40.6074 - 29.5030i) q^{49} +(3.84346 + 5.29007i) q^{50} +(-20.0861 + 6.52637i) q^{51} +(17.3607 + 5.64083i) q^{52} +(9.27051 + 6.73542i) q^{53} -16.1554i q^{54} +54.0689 q^{56} +(1.68441 - 2.31838i) q^{57} +(-6.38197 + 19.6417i) q^{58} +(-0.701626 - 2.15938i) q^{59} +(-15.5279 + 11.2817i) q^{60} +(-13.2918 - 18.2946i) q^{61} +(4.92299 - 1.59958i) q^{62} +(67.1591 + 21.8213i) q^{63} +(-15.1697 - 11.0214i) q^{64} +21.0292i q^{65} -38.4934 q^{67} +(31.1894 - 42.9286i) q^{68} +(-1.18034 + 3.63271i) q^{69} +(8.94427 + 27.5276i) q^{70} +(-61.7426 + 44.8587i) q^{71} +(22.6246 + 31.1401i) q^{72} +(97.8353 - 31.7886i) q^{73} +(-27.8115 - 9.03651i) q^{74} +(10.0623 + 7.31069i) q^{75} +7.19991i q^{76} -5.27864 q^{78} +(2.31308 - 3.18368i) q^{79} +(12.2918 - 37.8303i) q^{80} +(10.2229 + 31.4629i) q^{81} +(-41.2426 + 29.9645i) q^{82} +(-48.9296 - 67.3458i) q^{83} +(45.4508 - 14.7679i) q^{84} +(58.1378 + 18.8901i) q^{85} +(-13.5557 - 9.84881i) q^{86} +39.2833i q^{87} +123.297 q^{89} +(-12.1115 + 16.6700i) q^{90} +(16.1803 - 49.7980i) q^{91} +(-2.96556 - 9.12705i) q^{92} +(7.96556 - 5.78732i) q^{93} +(-11.6312 - 16.0090i) q^{94} +(-7.88854 + 2.56314i) q^{95} +(38.0370 + 12.3590i) q^{96} +(62.6246 + 45.4994i) q^{97} -36.4677i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 5 q^{2} - 5 q^{3} + 11 q^{4} - 4 q^{5} + 20 q^{6} + 20 q^{7} + 5 q^{8} + 14 q^{9} - 30 q^{12} - 10 q^{13} - 20 q^{15} - 21 q^{16} - 65 q^{17} - 5 q^{18} - 10 q^{19} - 36 q^{20} - 20 q^{23} + 40 q^{24}+ \cdots + 170 q^{97}+O(q^{100}) \) 4 * q - 5 * q^2 - 5 * q^3 + 11 * q^4 - 4 * q^5 + 20 * q^6 + 20 * q^7 + 5 * q^8 + 14 * q^9 - 30 * q^12 - 10 * q^13 - 20 * q^15 - 21 * q^16 - 65 * q^17 - 5 * q^18 - 10 * q^19 - 36 * q^20 - 20 * q^23 + 40 * q^24 + 9 * q^25 + 40 * q^26 + 25 * q^27 + 50 * q^28 - 50 * q^29 + 60 * q^30 + 32 * q^31 + 130 * q^34 - 40 * q^35 + 21 * q^36 - 90 * q^37 + 25 * q^38 + 50 * q^39 - 20 * q^40 - 135 * q^41 - 10 * q^42 - 24 * q^45 + 40 * q^46 - 20 * q^47 + 55 * q^48 + 111 * q^49 - 45 * q^50 + 65 * q^51 - 20 * q^52 - 30 * q^53 + 100 * q^56 + 85 * q^57 - 30 * q^58 - 52 * q^59 - 80 * q^60 - 80 * q^61 - 110 * q^62 + 130 * q^63 + 31 * q^64 - 230 * q^67 - 195 * q^68 + 40 * q^69 - 162 * q^71 + 10 * q^72 + 85 * q^73 + 90 * q^74 - 200 * q^78 + 130 * q^79 + 76 * q^80 + 184 * q^81 - 80 * q^82 + 10 * q^83 + 70 * q^84 - 90 * q^86 + 122 * q^89 - 120 * q^90 + 20 * q^91 - 70 * q^92 + 90 * q^93 + 110 * q^94 + 40 * q^95 - 105 * q^96 + 170 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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