LMFDB - Embedded newform 966.2.q.j.463.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$4$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			463.2
Character	$\chi$	$=$	966.463
Dual form			966.2.q.j.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.463708 + 0.535148i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.463708 + 0.535148i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.595693 + 0.382829i) q^{10} +(0.451723 - 3.14180i) q^{11} +(0.142315 - 0.989821i) q^{12} +(-1.29427 - 0.831777i) q^{13} +(0.654861 + 0.755750i) q^{14} +(-0.294156 - 0.644112i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.0911307 - 0.0267584i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(7.28021 - 2.13766i) q^{19} +(0.294156 - 0.644112i) q^{20} +(-0.142315 - 0.989821i) q^{21} -3.17411 q^{22} +(0.668409 + 4.74902i) q^{23} -1.00000 q^{24} +(0.640216 + 4.45280i) q^{25} +(-0.639117 + 1.39947i) q^{26} +(0.959493 - 0.281733i) q^{27} +(0.654861 - 0.755750i) q^{28} +(3.30375 + 0.970069i) q^{29} +(-0.595693 + 0.382829i) q^{30} +(1.18264 + 2.58962i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(2.67023 + 1.71605i) q^{33} +(-0.0135168 + 0.0940112i) q^{34} +(0.100773 - 0.700895i) q^{35} +(0.841254 + 0.540641i) q^{36} +(7.66925 + 8.85078i) q^{37} +(-3.15198 - 6.90188i) q^{38} +(1.29427 - 0.831777i) q^{39} +(-0.679419 - 0.199495i) q^{40} +(-2.14536 + 2.47588i) q^{41} +(-0.959493 + 0.281733i) q^{42} +(-5.39839 + 11.8208i) q^{43} +(0.451723 + 3.14180i) q^{44} +0.708102 q^{45} +(4.60556 - 1.33746i) q^{46} +0.0496167 q^{47} +(0.142315 + 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(4.31637 - 1.26740i) q^{50} +(0.0621973 - 0.0717795i) q^{51} +(1.47618 + 0.433446i) q^{52} +(7.41291 - 4.76399i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(1.47186 + 1.69862i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(-1.07982 + 7.51032i) q^{57} +(0.490022 - 3.40818i) q^{58} +(4.45189 + 2.86106i) q^{59} +(0.463708 + 0.535148i) q^{60} +(-3.10422 - 6.79729i) q^{61} +(2.39496 - 1.53915i) q^{62} +(0.959493 + 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(1.04529 - 0.306924i) q^{65} +(1.31857 - 2.88727i) q^{66} +(-0.391264 - 2.72130i) q^{67} +0.0949780 q^{68} +(-4.59753 - 1.36481i) q^{69} -0.708102 q^{70} +(0.224781 + 1.56339i) q^{71} +(0.415415 - 0.909632i) q^{72} +(2.70365 - 0.793862i) q^{73} +(7.66925 - 8.85078i) q^{74} +(-4.31637 - 1.26740i) q^{75} +(-6.38306 + 4.10214i) q^{76} +(1.31857 + 2.88727i) q^{77} +(-1.00750 - 1.16272i) q^{78} +(7.77320 + 4.99553i) q^{79} +(-0.100773 + 0.700895i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(2.75599 + 1.77117i) q^{82} +(2.82492 + 3.26013i) q^{83} +(0.415415 + 0.909632i) q^{84} +(0.0565777 - 0.0363603i) q^{85} +(12.4688 + 3.66116i) q^{86} +(-2.25483 + 2.60222i) q^{87} +(3.04553 - 0.894250i) q^{88} +(7.43522 - 16.2809i) q^{89} +(-0.100773 - 0.700895i) q^{90} +1.53850 q^{91} +(-1.97929 - 4.36834i) q^{92} -2.84689 q^{93} +(-0.00706120 - 0.0491117i) q^{94} +(-2.23193 + 4.88724i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-1.72578 + 1.99166i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-2.67023 + 1.71605i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) $ 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	−0.463708	+	0.535148i	−0.207377	+	0.239325i	−0.849904	−	0.526937i	$-0.823340\pi$
$5$	−0.463708	+	0.535148i	−0.207377	+	0.239325i	0.642528	+	0.766263i	$0.277886\pi$
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$7$	−0.841254	+	0.540641i	−0.317964	+	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	0.595693	+	0.382829i	0.188375	+	0.121061i
$11$	0.451723	−	3.14180i	0.136200	−	0.947288i	−0.801042	−	0.598608i	$-0.795721\pi$
$11$	0.451723	−	3.14180i	0.136200	−	0.947288i	0.937242	−	0.348680i	$-0.113370\pi$
$12$	0.142315	−	0.989821i	0.0410828	−	0.285737i
$13$	−1.29427	−	0.831777i	−0.358966	−	0.230693i	0.348710	−	0.937231i	$-0.386620\pi$
$13$	−1.29427	−	0.831777i	−0.358966	−	0.230693i	−0.707676	+	0.706537i	$0.750256\pi$
$14$	0.654861	+	0.755750i	0.175019	+	0.201983i
$15$	−0.294156	−	0.644112i	−0.0759508	−	0.166309i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−0.0911307	−	0.0267584i	−0.0221024	−	0.00648986i	0.270663	−	0.962674i	$-0.412757\pi$
$17$	−0.0911307	−	0.0267584i	−0.0221024	−	0.00648986i	−0.292765	+	0.956184i	$0.594575\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	7.28021	−	2.13766i	1.67019	−	0.490413i	0.696363	−	0.717689i	$-0.254800\pi$
$19$	7.28021	−	2.13766i	1.67019	−	0.490413i	0.973830	+	0.227276i	$0.0729820\pi$
$20$	0.294156	−	0.644112i	0.0657753	−	0.144028i
$21$	−0.142315	−	0.989821i	−0.0310556	−	0.215997i
$22$	−3.17411			−0.676722
$23$	0.668409	+	4.74902i	0.139373	+	0.990240i
$23$	0.668409	+	4.74902i	0.139373	+	0.990240i
$24$	−1.00000			−0.204124
$25$	0.640216	+	4.45280i	0.128043	+	0.890560i
$26$	−0.639117	+	1.39947i	−0.125341	+	0.274459i
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$	0.654861	−	0.755750i	0.123757	−	0.142823i
$29$	3.30375	+	0.970069i	0.613491	+	0.180137i	0.573693	−	0.819070i	$-0.305510\pi$
$29$	3.30375	+	0.970069i	0.613491	+	0.180137i	0.0397982	+	0.999208i	$0.487328\pi$
$30$	−0.595693	+	0.382829i	−0.108758	+	0.0698947i
$31$	1.18264	+	2.58962i	0.212409	+	0.465110i	0.985607	−	0.169055i	$-0.0540714\pi$
$31$	1.18264	+	2.58962i	0.212409	+	0.465110i	−0.773198	+	0.634165i	$0.781344\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	2.67023	+	1.71605i	0.464827	+	0.298726i
$34$	−0.0135168	+	0.0940112i	−0.00231811	+	0.0161228i
$35$	0.100773	−	0.700895i	0.0170338	−	0.118473i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	7.66925	+	8.85078i	1.26082	+	1.45506i	0.835000	+	0.550250i	$0.185467\pi$
$37$	7.66925	+	8.85078i	1.26082	+	1.45506i	0.425816	+	0.904810i	$0.359987\pi$
$38$	−3.15198	−	6.90188i	−0.511319	−	1.11963i
$39$	1.29427	−	0.831777i	0.207249	−	0.133191i
$40$	−0.679419	−	0.199495i	−0.107426	−	0.0315430i
$41$	−2.14536	+	2.47588i	−0.335049	+	0.386667i	−0.898127	−	0.439737i	$-0.855072\pi$
$41$	−2.14536	+	2.47588i	−0.335049	+	0.386667i	0.563078	+	0.826404i	$0.309617\pi$
$42$	−0.959493	+	0.281733i	−0.148053	+	0.0434723i
$43$	−5.39839	+	11.8208i	−0.823247	+	1.80266i	−0.289007	+	0.957327i	$0.593325\pi$
$43$	−5.39839	+	11.8208i	−0.823247	+	1.80266i	−0.534241	+	0.845333i	$0.679402\pi$
$44$	0.451723	+	3.14180i	0.0680998	+	0.473644i
$45$	0.708102			0.105558
$46$	4.60556	−	1.33746i	0.679053	−	0.197198i
$47$	0.0496167			0.00723734			0.00361867	−	0.999993i	$-0.498848\pi$
$47$	0.0496167			0.00723734			0.00361867	+	0.999993i	$0.498848\pi$
$48$	0.142315	+	0.989821i	0.0205414	+	0.142868i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	4.31637	−	1.26740i	0.610426	−	0.179237i
$51$	0.0621973	−	0.0717795i	0.00870937	−	0.0100511i
$52$	1.47618	+	0.433446i	0.204710	+	0.0601081i
$53$	7.41291	−	4.76399i	1.01824	−	0.654384i	0.0787286	−	0.996896i	$-0.474914\pi$
$53$	7.41291	−	4.76399i	1.01824	−	0.654384i	0.939514	+	0.342512i	$0.111278\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	1.47186	+	1.69862i	0.198466	+	0.229041i
$56$	−0.841254	−	0.540641i	−0.112417	−	0.0722462i
$57$	−1.07982	+	7.51032i	−0.143026	+	0.994767i
$58$	0.490022	−	3.40818i	0.0643431	−	0.447516i
$59$	4.45189	+	2.86106i	0.579587	+	0.372478i	0.797344	−	0.603525i	$-0.206238\pi$
$59$	4.45189	+	2.86106i	0.579587	+	0.372478i	−0.217757	+	0.976003i	$0.569874\pi$
$60$	0.463708	+	0.535148i	0.0598645	+	0.0690873i
$61$	−3.10422	−	6.79729i	−0.397454	−	0.870303i	−0.997522	−	0.0703542i	$-0.977587\pi$
$61$	−3.10422	−	6.79729i	−0.397454	−	0.870303i	0.600068	−	0.799949i	$-0.295140\pi$
$62$	2.39496	−	1.53915i	0.304160	−	0.195472i
$63$	0.959493	+	0.281733i	0.120885	+	0.0354950i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	1.04529	−	0.306924i	0.129652	−	0.0380692i
$66$	1.31857	−	2.88727i	0.162305	−	0.355398i
$67$	−0.391264	−	2.72130i	−0.0478005	−	0.332460i	−0.999664	−	0.0259365i	$-0.991743\pi$
$67$	−0.391264	−	2.72130i	−0.0478005	−	0.332460i	0.951863	−	0.306524i	$-0.0991659\pi$
$68$	0.0949780			0.0115178
$69$	−4.59753	−	1.36481i	−0.553478	−	0.164304i
$70$	−0.708102			−0.0846344
$71$	0.224781	+	1.56339i	0.0266766	+	0.185540i	0.998803	−	0.0489185i	$-0.0155775\pi$
$71$	0.224781	+	1.56339i	0.0266766	+	0.185540i	−0.972126	+	0.234458i	$0.924668\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	2.70365	−	0.793862i	0.316438	−	0.0929146i	−0.119657	−	0.992815i	$-0.538179\pi$
$73$	2.70365	−	0.793862i	0.316438	−	0.0929146i	0.436095	+	0.899901i	$0.356361\pi$
$74$	7.66925	−	8.85078i	0.891532	−	1.02888i
$75$	−4.31637	−	1.26740i	−0.498411	−	0.146347i
$76$	−6.38306	+	4.10214i	−0.732187	+	0.470548i
$77$	1.31857	+	2.88727i	0.150265	+	0.329035i
$78$	−1.00750	−	1.16272i	−0.114077	−	0.131652i
$79$	7.77320	+	4.99553i	0.874553	+	0.562041i	0.899142	−	0.437656i	$-0.144191\pi$
$79$	7.77320	+	4.99553i	0.874553	+	0.562041i	−0.0245889	+	0.999698i	$0.507828\pi$
$80$	−0.100773	+	0.700895i	−0.0112668	+	0.0783624i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	2.75599	+	1.77117i	0.304349	+	0.195593i
$83$	2.82492	+	3.26013i	0.310075	+	0.357846i	0.889302	−	0.457321i	$-0.151191\pi$
$83$	2.82492	+	3.26013i	0.310075	+	0.357846i	−0.579227	+	0.815166i	$0.696645\pi$
$84$	0.415415	+	0.909632i	0.0453255	+	0.0992490i
$85$	0.0565777	−	0.0363603i	0.00613672	−	0.00394383i
$86$	12.4688	+	3.66116i	1.34454	+	0.394794i
$87$	−2.25483	+	2.60222i	−0.241743	+	0.278987i
$88$	3.04553	−	0.894250i	0.324655	−	0.0953273i
$89$	7.43522	−	16.2809i	0.788132	−	1.72577i	0.106208	−	0.994344i	$-0.466129\pi$
$89$	7.43522	−	16.2809i	0.788132	−	1.72577i	0.681923	−	0.731424i	$-0.261144\pi$
$90$	−0.100773	−	0.700895i	−0.0106225	−	0.0738808i
$91$	1.53850			0.161279
$92$	−1.97929	−	4.36834i	−0.206355	−	0.455431i
$93$	−2.84689			−0.295209
$94$	−0.00706120	−	0.0491117i	−0.000728307	−	0.00506548i
$95$	−2.23193	+	4.88724i	−0.228991	+	0.501420i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	−1.72578	+	1.99166i	−0.175227	+	0.202222i	−0.836569	−	0.547862i	$-0.815442\pi$
$97$	−1.72578	+	1.99166i	−0.175227	+	0.202222i	0.661342	+	0.750085i	$0.269987\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	−2.67023	+	1.71605i	−0.268368	+	0.172470i
$100$	−1.86878	−	4.09206i	−0.186878	−	0.409206i
$101$	−8.16830	−	9.42672i	−0.812776	−	0.937994i	0.186233	−	0.982506i	$-0.440372\pi$
$101$	−8.16830	−	9.42672i	−0.812776	−	0.937994i	−0.999009	+	0.0445120i	$0.985827\pi$
$102$	−0.0799005	−	0.0513490i	−0.00791133	−	0.00508430i
$103$	−1.81815	+	12.6455i	−0.179148	+	1.24600i	0.679594	+	0.733589i	$0.262156\pi$
$103$	−1.81815	+	12.6455i	−0.179148	+	1.24600i	−0.858741	+	0.512410i	$0.828753\pi$
$104$	0.218952	−	1.52284i	0.0214700	−	0.149327i
$105$	0.595693	+	0.382829i	0.0581337	+	0.0373603i
$106$	−5.77047	−	6.65948i	−0.560477	−	0.646825i
$107$	−2.28026	−	4.99308i	−0.220442	−	0.482700i	0.766809	−	0.641876i	$-0.221843\pi$
$107$	−2.28026	−	4.99308i	−0.220442	−	0.482700i	−0.987250	+	0.159176i	$0.949116\pi$
$108$	−0.841254	+	0.540641i	−0.0809497	+	0.0520232i
$109$	6.10904	+	1.79378i	0.585140	+	0.171813i	0.560886	−	0.827893i	$-0.310461\pi$
$109$	6.10904	+	1.79378i	0.585140	+	0.171813i	0.0242543	+	0.999706i	$0.492279\pi$
$110$	1.47186	−	1.69862i	0.140336	−	0.161957i
$111$	−11.2369	+	3.29944i	−1.06656	+	0.313169i
$112$	−0.415415	+	0.909632i	−0.0392530	+	0.0859521i
$113$	−2.82240	−	19.6302i	−0.265509	−	1.84665i	−0.489424	−	0.872046i	$-0.662793\pi$
$113$	−2.82240	−	19.6302i	−0.265509	−	1.84665i	0.223915	−	0.974609i	$-0.428116\pi$
$114$	7.58756			0.710640
$115$	−2.85138	−	1.84446i	−0.265892	−	0.171997i
$116$	−3.44323			−0.319695
$117$	0.218952	+	1.52284i	0.0202421	+	0.140787i
$118$	2.19836	−	4.81375i	0.202376	−	0.443141i
$119$	0.0911307	−	0.0267584i	0.00835394	−	0.00245294i
$120$	0.463708	−	0.535148i	0.0423306	−	0.0488521i
$121$	0.887567	+	0.260613i	0.0806879	+	0.0236921i
$122$	−6.28632	+	4.03997i	−0.569137	+	0.365762i
$123$	−1.36092	−	2.98001i	−0.122710	−	0.268698i
$124$	−1.86432	−	2.15154i	−0.167421	−	0.193214i
$125$	−5.65825	−	3.63634i	−0.506089	−	0.325244i
$126$	0.142315	−	0.989821i	0.0126784	−	0.0881803i
$127$	−2.71854	+	18.9079i	−0.241231	+	1.67780i	0.404735	+	0.914434i	$0.367364\pi$
$127$	−2.71854	+	18.9079i	−0.241231	+	1.67780i	−0.645966	+	0.763366i	$0.723545\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	−8.51003	−	9.82110i	−0.749267	−	0.864700i
$130$	−0.452560	−	0.990968i	−0.0396921	−	0.0869136i
$131$	12.1732	−	7.82326i	1.06358	−	0.683521i	0.112872	−	0.993610i	$-0.463995\pi$
$131$	12.1732	−	7.82326i	1.06358	−	0.683521i	0.950708	+	0.310088i	$0.100359\pi$
$132$	−3.04553	−	0.894250i	−0.265080	−	0.0778344i
$133$	−4.96879	+	5.73429i	−0.430849	+	0.497226i
$134$	−2.63792	+	0.774564i	−0.227882	+	0.0669121i
$135$	−0.294156	+	0.644112i	−0.0253169	+	0.0554364i
$136$	−0.0135168	−	0.0940112i	−0.00115905	−	0.00806140i
$137$	4.88824			0.417631			0.208815	−	0.977955i	$-0.433039\pi$
$137$	4.88824			0.417631			0.208815	+	0.977955i	$0.433039\pi$
$138$	−0.696621	+	4.74497i	−0.0593003	+	0.403918i
$139$	6.29106			0.533601			0.266800	−	0.963752i	$-0.414034\pi$
$139$	6.29106			0.533601			0.266800	+	0.963752i	$0.414034\pi$
$140$	0.100773	+	0.700895i	0.00851691	+	0.0592364i
$141$	−0.0206115	+	0.0451330i	−0.00173580	+	0.00380088i
$142$	1.51548	−	0.444986i	0.127177	−	0.0373424i
$143$	−3.19793	+	3.69060i	−0.267424	+	0.308624i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	−2.05111	+	1.31817i	−0.170335	+	0.109468i
$146$	−1.17055	−	2.56315i	−0.0968755	−	0.212128i
$147$	0.654861	+	0.755750i	0.0540120	+	0.0623332i
$148$	−9.85214	−	6.33159i	−0.809841	−	0.520453i
$149$	−2.84471	+	19.7854i	−0.233048	+	1.62088i	0.451745	+	0.892147i	$0.350802\pi$
$149$	−2.84471	+	19.7854i	−0.233048	+	1.62088i	−0.684793	+	0.728737i	$0.740108\pi$
$150$	−0.640216	+	4.45280i	−0.0522734	+	0.363570i
$151$	−5.34828	−	3.43713i	−0.435237	−	0.279710i	0.304620	−	0.952474i	$-0.401470\pi$
$151$	−5.34828	−	3.43713i	−0.435237	−	0.279710i	−0.739857	+	0.672764i	$0.765107\pi$
$152$	4.96879	+	5.73429i	0.403022	+	0.465112i
$153$	0.0394553	+	0.0863950i	0.00318977	+	0.00698462i
$154$	2.67023	−	1.71605i	0.215173	−	0.138283i
$155$	−1.93423	−	0.567942i	−0.155361	−	0.0456182i
$156$	−1.00750	+	1.16272i	−0.0806649	+	0.0930923i
$157$	11.2821	−	3.31272i	0.900409	−	0.264384i	0.201411	−	0.979507i	$-0.435447\pi$
$157$	11.2821	−	3.31272i	0.900409	−	0.264384i	0.698999	+	0.715123i	$0.253629\pi$
$158$	3.83844	−	8.40502i	0.305370	−	0.668667i
$159$	1.25404	+	8.72206i	0.0994520	+	0.691704i
$160$	0.708102			0.0559804
$161$	−3.12982	−	3.63376i	−0.246664	−	0.286381i
$162$	1.00000			0.0785674
$163$	0.0244670	+	0.170172i	0.00191640	+	0.0133289i	0.990757	−	0.135647i	$-0.0433114\pi$
$163$	0.0244670	+	0.170172i	0.00191640	+	0.0133289i	−0.988841	+	0.148976i	$0.952402\pi$
$164$	1.36092	−	2.98001i	0.106270	−	0.232699i
$165$	−2.15655	+	0.633220i	−0.167887	+	0.0492961i
$166$	2.82492	−	3.26013i	0.219256	−	0.253035i
$167$	−13.2868	−	3.90136i	−1.02816	−	0.301896i	−0.276200	−	0.961100i	$-0.589075\pi$
$167$	−13.2868	−	3.90136i	−1.02816	−	0.301896i	−0.751964	+	0.659204i	$0.770894\pi$
$168$	0.841254	−	0.540641i	0.0649041	−	0.0417113i
$169$	−4.41711	−	9.67213i	−0.339778	−	0.744010i
$170$	−0.0440421	−	0.0508272i	−0.00337787	−	0.00389827i
$171$	−6.38306	−	4.10214i	−0.488125	−	0.313699i
$172$	1.84941	−	12.8629i	0.141016	−	0.980787i
$173$	2.27770	−	15.8417i	0.173170	−	1.20442i	−0.698964	−	0.715157i	$-0.746355\pi$
$173$	2.27770	−	15.8417i	0.173170	−	1.20442i	0.872134	−	0.489267i	$-0.162736\pi$
$174$	2.89663	+	1.86155i	0.219593	+	0.141124i
$175$	−2.94595	−	3.39981i	−0.222693	−	0.257001i
$176$	−1.31857	−	2.88727i	−0.0993911	−	0.217636i
$177$	−4.45189	+	2.86106i	−0.334624	+	0.215050i
$178$	−17.1733	−	5.04253i	−1.28719	−	0.377954i
$179$	1.23255	−	1.42244i	0.0921252	−	0.106318i	−0.707815	−	0.706398i	$-0.750319\pi$
$179$	1.23255	−	1.42244i	0.0921252	−	0.106318i	0.799940	+	0.600080i	$0.204864\pi$
$180$	−0.679419	+	0.199495i	−0.0506409	+	0.0148695i
$181$	−7.24346	+	15.8610i	−0.538402	+	1.17894i	0.423589	+	0.905854i	$0.360770\pi$
$181$	−7.24346	+	15.8610i	−0.538402	+	1.17894i	−0.961991	+	0.273081i	$0.911957\pi$
$182$	−0.218952	−	1.52284i	−0.0162298	−	0.112881i
$183$	7.47257			0.552388
$184$	−4.04220	+	2.58082i	−0.297995	+	0.190261i
$185$	−8.29277			−0.609697
$186$	0.405155	+	2.81791i	0.0297074	+	0.206619i
$187$	−0.125235	+	0.274227i	−0.00915811	+	0.0200535i
$188$	−0.0476069	+	0.0139786i	−0.00347209	+	0.00101950i
$189$	−0.654861	+	0.755750i	−0.0476341	+	0.0549727i
$190$	5.15513	+	1.51368i	0.373992	+	0.109814i
$191$	0.110858	−	0.0712441i	0.00802140	−	0.00515504i	−0.536624	−	0.843821i	$-0.680301\pi$
$191$	0.110858	−	0.0712441i	0.00802140	−	0.00515504i	0.544645	+	0.838666i	$0.316664\pi$
$192$	−0.415415	−	0.909632i	−0.0299800	−	0.0656470i
$193$	2.69530	+	3.11054i	0.194012	+	0.223901i	0.844418	−	0.535685i	$-0.179947\pi$
$193$	2.69530	+	3.11054i	0.194012	+	0.223901i	−0.650406	+	0.759587i	$0.725401\pi$
$194$	2.21699	+	1.42477i	0.159171	+	0.102293i
$195$	−0.155040	+	1.07833i	−0.0111027	+	0.0772206i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	7.73834	+	4.97313i	0.551334	+	0.354321i	0.786457	−	0.617645i	$-0.211913\pi$
$197$	7.73834	+	4.97313i	0.551334	+	0.354321i	−0.235123	+	0.971966i	$0.575549\pi$
$198$	2.07860	+	2.39883i	0.147720	+	0.170477i
$199$	−9.16278	−	20.0637i	−0.649532	−	1.42228i	−0.891963	−	0.452108i	$-0.850672\pi$
$199$	−9.16278	−	20.0637i	−0.649532	−	1.42228i	0.242431	−	0.970169i	$-0.422055\pi$
$200$	−3.78446	+	2.43212i	−0.267601	+	0.171977i
$201$	2.63792	+	0.774564i	0.186065	+	0.0546335i
$202$	−8.16830	+	9.42672i	−0.574720	+	0.663262i
$203$	−3.30375	+	0.970069i	−0.231878	+	0.0680855i
$204$	−0.0394553	+	0.0863950i	−0.00276242	+	0.00604886i
$205$	−0.330139	−	2.29617i	−0.0230579	−	0.160371i
$206$	12.7755			0.890114
$207$	3.15136	−	3.61510i	0.219035	−	0.251267i
$208$	−1.53850			−0.106676
$209$	−3.42747	−	23.8386i	−0.237083	−	1.64895i
$210$	0.294156	−	0.644112i	0.0202987	−	0.0444480i
$211$	−19.1777	+	5.63108i	−1.32025	+	0.387660i	−0.864582	−	0.502491i	$-0.832417\pi$
$211$	−19.1777	+	5.63108i	−1.32025	+	0.387660i	−0.455666	+	0.890151i	$0.650599\pi$
$212$	−5.77047	+	6.65948i	−0.396317	+	0.457375i
$213$	−1.51548	−	0.444986i	−0.103839	−	0.0304899i
$214$	−4.61775	+	2.96764i	−0.315663	+	0.202864i
$215$	−3.82261	−	8.37035i	−0.260700	−	0.570853i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	−2.39496	−	1.53915i	−0.162580	−	0.104484i
$218$	0.906111	−	6.30214i	0.0613696	−	0.426835i
$219$	−0.401013	+	2.78911i	−0.0270979	+	0.188470i
$220$	−1.89080	−	1.21514i	−0.127477	−	0.0819247i
$221$	0.0956907	+	0.110433i	0.00643685	+	0.00742852i
$222$	4.86503	+	10.6529i	0.326520	+	0.714978i
$223$	9.95716	−	6.39908i	0.666781	−	0.428514i	−0.162983	−	0.986629i	$-0.552112\pi$
$223$	9.95716	−	6.39908i	0.666781	−	0.428514i	0.829764	+	0.558115i	$0.188475\pi$
$224$	0.959493	+	0.281733i	0.0641088	+	0.0188240i
$225$	2.94595	−	3.39981i	0.196397	−	0.226654i
$226$	−19.0287	+	5.58734i	−1.26577	+	0.371664i
$227$	−11.2163	+	24.5603i	−0.744454	+	1.63013i	0.0316314	+	0.999500i	$0.489930\pi$
$227$	−11.2163	+	24.5603i	−0.744454	+	1.63013i	−0.776086	+	0.630628i	$0.782798\pi$
$228$	−1.07982	−	7.51032i	−0.0715129	−	0.497383i
$229$	5.78157			0.382057			0.191029	−	0.981584i	$-0.438818\pi$
$229$	5.78157			0.382057			0.191029	+	0.981584i	$0.438818\pi$
$230$	−1.41990	+	3.08485i	−0.0936252	+	0.203409i
$231$	−3.17411			−0.208841
$232$	0.490022	+	3.40818i	0.0321715	+	0.223758i
$233$	10.3926	−	22.7565i	0.680840	−	1.49083i	−0.180911	−	0.983499i	$-0.557905\pi$
$233$	10.3926	−	22.7565i	0.680840	−	1.49083i	0.861751	−	0.507332i	$-0.169368\pi$
$234$	1.47618	−	0.433446i	0.0965010	−	0.0283352i
$235$	−0.0230077	+	0.0265523i	−0.00150086	+	0.00173208i
$236$	−5.07761	−	1.49092i	−0.330524	−	0.0970506i
$237$	−7.77320	+	4.99553i	−0.504924	+	0.324495i
$238$	−0.0394553	−	0.0863950i	−0.00255751	−	0.00560016i
$239$	12.8844	+	14.8694i	0.833424	+	0.961822i	0.999706	−	0.0242558i	$-0.00772163\pi$
$239$	12.8844	+	14.8694i	0.833424	+	0.961822i	−0.166282	+	0.986078i	$0.553176\pi$
$240$	−0.595693	−	0.382829i	−0.0384518	−	0.0247115i
$241$	−3.65669	+	25.4328i	−0.235548	+	1.63827i	0.437890	+	0.899029i	$0.355726\pi$
$241$	−3.65669	+	25.4328i	−0.235548	+	1.63827i	−0.673438	+	0.739244i	$0.735183\pi$
$242$	0.131647	−	0.915622i	0.00846256	−	0.0588584i
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$	4.89349	+	5.64739i	0.313274	+	0.361537i
$245$	0.294156	+	0.644112i	0.0187930	+	0.0411508i
$246$	−2.75599	+	1.77117i	−0.175716	+	0.112926i
$247$	−11.2006	−	3.28880i	−0.712678	−	0.209261i
$248$	−1.86432	+	2.15154i	−0.118384	+	0.136623i
$249$	−4.13903	+	1.21533i	−0.262300	+	0.0770184i
$250$	−2.79407	+	6.11816i	−0.176713	+	0.386946i
$251$	1.99858	+	13.9004i	0.126149	+	0.877387i	0.950371	+	0.311120i	$0.100704\pi$
$251$	1.99858	+	13.9004i	0.126149	+	0.877387i	−0.824221	+	0.566268i	$0.808387\pi$
$252$	−1.00000			−0.0629941
$253$	15.2224	+	0.0452344i	0.957025	+	0.00284386i
$254$	19.1023			1.19858
$255$	0.00957125	+	0.0665695i	0.000599375	+	0.00416875i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−4.16433	+	1.22276i	−0.259764	+	0.0762735i	−0.409021	−	0.912525i	$-0.634130\pi$
$257$	−4.16433	+	1.22276i	−0.259764	+	0.0762735i	0.149258	+	0.988798i	$0.452312\pi$
$258$	−8.51003	+	9.82110i	−0.529811	+	0.611435i
$259$	−11.2369	−	3.29944i	−0.698225	−	0.205017i
$260$	−0.916475	+	0.588983i	−0.0568374	+	0.0365272i
$261$	−1.43037	−	3.13207i	−0.0885375	−	0.193870i
$262$	−9.47606	−	10.9360i	−0.585433	−	0.675626i
$263$	13.9454	+	8.96213i	0.859907	+	0.552629i	0.894650	−	0.446767i	$-0.147425\pi$
$263$	13.9454	+	8.96213i	0.859907	+	0.552629i	−0.0347428	+	0.999396i	$0.511061\pi$
$264$	−0.451723	+	3.14180i	−0.0278016	+	0.193364i
$265$	−0.887990	+	6.17611i	−0.0545488	+	0.379395i
$266$	6.38306	+	4.10214i	0.391370	+	0.251518i
$267$	11.7209	+	13.5266i	0.717307	+	0.827816i
$268$	1.14210	+	2.50084i	0.0697646	+	0.152763i
$269$	−13.3840	+	8.60140i	−0.816040	+	0.524437i	−0.880814	−	0.473463i	$-0.843004\pi$
$269$	−13.3840	+	8.60140i	−0.816040	+	0.524437i	0.0647740	+	0.997900i	$0.479367\pi$
$270$	0.679419	+	0.199495i	0.0413481	+	0.0121409i
$271$	2.05132	−	2.36735i	0.124609	−	0.143806i	−0.690017	−	0.723793i	$-0.742397\pi$
$271$	2.05132	−	2.36735i	0.124609	−	0.143806i	0.814626	+	0.579987i	$0.196942\pi$
$272$	−0.0911307	+	0.0267584i	−0.00552561	+	0.00162247i
$273$	−0.639117	+	1.39947i	−0.0386811	+	0.0846998i
$274$	−0.695669	−	4.83849i	−0.0420269	−	0.292304i
$275$	14.2790			0.861057
$276$	4.79581	+	0.0142511i	0.288674	+	0.000857813i
$277$	28.4463			1.70918			0.854588	−	0.519307i	$-0.173810\pi$
$277$	28.4463			1.70918			0.854588	+	0.519307i	$0.173810\pi$
$278$	−0.895311	−	6.22703i	−0.0536972	−	0.373472i
$279$	1.18264	−	2.58962i	0.0708029	−	0.155037i
$280$	0.679419	−	0.199495i	0.0406031	−	0.0119221i
$281$	−10.1007	+	11.6569i	−0.602559	+	0.695390i	−0.972298	−	0.233745i	$-0.924902\pi$
$281$	−10.1007	+	11.6569i	−0.602559	+	0.695390i	0.369739	+	0.929136i	$0.379447\pi$
$282$	0.0476069	+	0.0139786i	0.00283495	+	0.000832416i
$283$	−24.7912	+	15.9323i	−1.47368	+	0.947077i	−0.475970	+	0.879462i	$0.657903\pi$
$283$	−24.7912	+	15.9323i	−1.47368	+	0.947077i	−0.997711	+	0.0676158i	$0.978461\pi$
$284$	−0.656133	−	1.43673i	−0.0389343	−	0.0852542i
$285$	−3.51841	−	4.06046i	−0.208413	−	0.240521i
$286$	4.10815	+	2.64015i	0.242920	+	0.156115i
$287$	0.466231	−	3.24271i	0.0275208	−	0.191411i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	−14.2937	−	9.18602i	−0.840807	−	0.540354i
$290$	1.59665	+	1.84263i	0.0937586	+	0.108203i
$291$	−1.09476	−	2.39719i	−0.0641760	−	0.140526i
$292$	−2.37047	+	1.52341i	−0.138721	+	0.0891509i
$293$	−21.4744	−	6.30546i	−1.25455	−	0.368369i	−0.414086	−	0.910238i	$-0.635899\pi$
$293$	−21.4744	−	6.30546i	−1.25455	−	0.368369i	−0.840463	+	0.541869i	$0.817717\pi$
$294$	0.654861	−	0.755750i	0.0381923	−	0.0440762i
$295$	−3.59547	+	1.05572i	−0.209336	+	0.0614666i
$296$	−4.86503	+	10.6529i	−0.282774	+	0.619189i
$297$	−0.451723	−	3.14180i	−0.0262116	−	0.182306i
$298$	19.9889			1.15792
$299$	3.08503	−	6.70249i	0.178412	−	0.387615i
$300$	4.49859			0.259726
$301$	−1.84941	−	12.8629i	−0.106598	−	0.741406i
$302$	−2.64100	+	5.78299i	−0.151973	+	0.332774i
$303$	11.9681	−	3.51415i	0.687548	−	0.201882i
$304$	4.96879	−	5.73429i	0.284980	−	0.328884i
$305$	5.07700	+	1.49074i	0.290708	+	0.0853597i
$306$	0.0799005	−	0.0513490i	0.00456761	−	0.00293542i
$307$	−6.46244	−	14.1508i	−0.368831	−	0.807627i	−0.999501	−	0.0315760i	$-0.989947\pi$
$307$	−6.46244	−	14.1508i	−0.368831	−	0.807627i	0.630671	−	0.776051i	$-0.282780\pi$
$308$	−2.07860	−	2.39883i	−0.118439	−	0.136686i
$309$	−10.7475	−	6.90698i	−0.611402	−	0.392924i
$310$	−0.286891	+	1.99537i	−0.0162943	+	0.113329i
$311$	−0.111510	+	0.775568i	−0.00632315	+	0.0439784i	−0.992739	−	0.120290i	$-0.961617\pi$
$311$	−0.111510	+	0.775568i	−0.00632315	+	0.0439784i	0.986416	+	0.164269i	$0.0525265\pi$
$312$	1.29427	+	0.831777i	0.0732736	+	0.0470901i
$313$	−17.4817	−	20.1749i	−0.988121	−	1.14035i	−0.990101	−	0.140355i	$-0.955176\pi$
$313$	−17.4817	−	20.1749i	−0.988121	−	1.14035i	0.00197986	−	0.999998i	$-0.499370\pi$
$314$	−4.88461	−	10.6958i	−0.275655	−	0.603600i
$315$	−0.595693	+	0.382829i	−0.0335635	+	0.0215700i
$316$	−8.86574	−	2.60322i	−0.498737	−	0.146442i
$317$	−16.5545	+	19.1049i	−0.929792	+	1.07304i	0.0673682	+	0.997728i	$0.478540\pi$
$317$	−16.5545	+	19.1049i	−0.929792	+	1.07304i	−0.997160	+	0.0753091i	$0.976006\pi$
$318$	8.45481	−	2.48256i	0.474122	−	0.139215i
$319$	4.54014	−	9.94152i	0.254199	−	0.556618i
$320$	−0.100773	−	0.700895i	−0.00563341	−	0.0391812i
$321$	5.48912			0.306373
$322$	−3.15136	+	3.61510i	−0.175618	+	0.201462i
$323$	−0.720650			−0.0400981
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	2.87512	−	6.29564i	0.159483	−	0.349220i
$326$	0.164958	−	0.0484359i	0.00913616	−	0.00268262i
$327$	−4.16946	+	4.81182i	−0.230572	+	0.266094i
$328$	−3.14335	−	0.922972i	−0.173563	−	0.0509626i
$329$	−0.0417402	+	0.0268248i	−0.00230121	+	0.00147890i
$330$	0.933684	+	2.04448i	0.0513976	+	0.112545i
$331$	4.71546	+	5.44193i	0.259185	+	0.299115i	0.870396	−	0.492352i	$-0.163863\pi$
$331$	4.71546	+	5.44193i	0.259185	+	0.299115i	−0.611211	+	0.791468i	$0.709317\pi$
$332$	−3.62897	−	2.33220i	−0.199166	−	0.127996i
$333$	1.66669	−	11.5921i	0.0913338	−	0.635241i
$334$	−1.97074	+	13.7068i	−0.107834	+	0.750003i
$335$	1.63773	+	1.05251i	0.0894789	+	0.0575046i
$336$	−0.654861	−	0.755750i	−0.0357256	−	0.0412295i
$337$	−0.230934	−	0.505676i	−0.0125798	−	0.0275459i	0.903238	−	0.429140i	$-0.141183\pi$
$337$	−0.230934	−	0.505676i	−0.0125798	−	0.0275459i	−0.915818	+	0.401594i	$0.868456\pi$
$338$	−8.94506	+	5.74864i	−0.486547	+	0.312685i
$339$	19.0287	+	5.58734i	1.03350	+	0.303463i
$340$	−0.0440421	+	0.0508272i	−0.00238852	+	0.00275649i
$341$	8.67030	−	2.54583i	0.469523	−	0.137864i
$342$	−3.15198	+	6.90188i	−0.170440	+	0.373211i
$343$	0.142315	+	0.989821i	0.00768428	+	0.0534453i
$344$	−12.9952			−0.700653
$345$	2.86229	−	1.82749i	0.154100	−	0.0983885i
$346$	−16.0046			−0.860415
$347$	1.83540	+	12.7655i	0.0985297	+	0.685289i	0.977888	+	0.209129i	$0.0670627\pi$
$347$	1.83540	+	12.7655i	0.0985297	+	0.685289i	−0.879358	+	0.476160i	$0.842028\pi$
$348$	1.43037	−	3.13207i	0.0766758	−	0.167896i
$349$	−11.8408	+	3.47678i	−0.633824	+	0.186108i	−0.582834	−	0.812592i	$-0.698056\pi$
$349$	−11.8408	+	3.47678i	−0.633824	+	0.186108i	−0.0509906	+	0.998699i	$0.516238\pi$
$350$	−2.94595	+	3.39981i	−0.157468	+	0.181727i
$351$	−1.47618	−	0.433446i	−0.0787927	−	0.0231356i
$352$	−2.67023	+	1.71605i	−0.142324	+	0.0914659i
$353$	0.828140	+	1.81337i	0.0440774	+	0.0965161i	0.930390	−	0.366572i	$-0.119469\pi$
$353$	0.828140	+	1.81337i	0.0440774	+	0.0965161i	−0.886312	+	0.463088i	$0.846741\pi$
$354$	3.46550	+	3.99940i	0.184189	+	0.212566i
$355$	−0.940876	−	0.604664i	−0.0499365	−	0.0320922i
$356$	−2.54719	+	17.7161i	−0.135001	+	0.938952i
$357$	−0.0135168	+	0.0940112i	−0.000715383	+	0.00497560i
$358$	−1.58337	−	1.01757i	−0.0836838	−	0.0537803i
$359$	6.46702	+	7.46333i	0.341316	+	0.393900i	0.900294	−	0.435283i	$-0.143352\pi$
$359$	6.46702	+	7.46333i	0.341316	+	0.393900i	−0.558978	+	0.829183i	$0.688806\pi$
$360$	0.294156	+	0.644112i	0.0155034	+	0.0339477i
$361$	32.4480	−	20.8531i	1.70779	−	1.09753i
$362$	16.7304	+	4.91248i	0.879329	+	0.258194i
$363$	−0.605771	+	0.699097i	−0.0317947	+	0.0366931i
$364$	−1.47618	+	0.433446i	−0.0773729	+	0.0227187i
$365$	−0.828870	+	1.81497i	−0.0433850	+	0.0950000i
$366$	−1.06346	−	7.39651i	−0.0555878	−	0.386622i
$367$	29.4111			1.53525			0.767624	−	0.640900i	$-0.221439\pi$
$367$	29.4111			1.53525			0.767624	+	0.640900i	$0.221439\pi$
$368$	3.12982	+	3.63376i	0.163153	+	0.189423i
$369$	3.27606			0.170545
$370$	1.18018	+	8.20836i	0.0613549	+	0.426732i
$371$	−3.66053	+	8.01545i	−0.190045	+	0.416141i
$372$	2.73157	−	0.802062i	0.141625	−	0.0415850i
$373$	6.90271	−	7.96615i	0.357409	−	0.412472i	−0.548361	−	0.836242i	$-0.684748\pi$
$373$	6.90271	−	7.96615i	0.357409	−	0.412472i	0.905770	+	0.423770i	$0.139293\pi$
$374$	0.289259	+	0.0849340i	0.0149572	+	0.00439183i
$375$	5.65825	−	3.63634i	0.292191	−	0.187780i
$376$	0.0206115	+	0.0451330i	0.00106296	+	0.00232755i
$377$	−3.46906	−	4.00351i	−0.178666	−	0.206191i
$378$	0.841254	+	0.540641i	0.0432694	+	0.0278076i
$379$	−3.04515	+	21.1795i	−0.156419	+	1.08792i	0.748747	+	0.662856i	$0.230656\pi$
$379$	−3.04515	+	21.1795i	−0.156419	+	1.08792i	−0.905165	+	0.425060i	$0.860253\pi$
$380$	0.764624	−	5.31808i	0.0392244	−	0.272812i
$381$	−16.0699	−	10.3275i	−0.823284	−	0.529093i
$382$	−0.0862957	−	0.0995905i	−0.00441527	−	0.00509549i
$383$	−9.39978	−	20.5827i	−0.480306	−	1.05172i	−0.982379	−	0.186899i	$-0.940156\pi$
$383$	−9.39978	−	20.5827i	−0.480306	−	1.05172i	0.502073	−	0.864825i	$-0.332571\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	−2.15655	−	0.633220i	−0.109908	−	0.0322719i
$386$	2.69530	−	3.11054i	0.137187	−	0.158322i
$387$	12.4688	−	3.66116i	0.633824	−	0.186107i
$388$	1.09476	−	2.39719i	0.0555780	−	0.121699i
$389$	−5.06278	−	35.2124i	−0.256693	−	1.78534i	−0.556000	−	0.831183i	$-0.687664\pi$
$389$	−5.06278	−	35.2124i	−0.256693	−	1.78534i	0.299307	−	0.954157i	$-0.403245\pi$
$390$	1.08942			0.0551647
$391$	0.0661636	−	0.450667i	0.00334604	−	0.0227912i
$392$	1.00000			0.0505076
$393$	2.05935	+	14.3231i	0.103880	+	0.722503i
$394$	3.82123	−	8.36732i	0.192511	−	0.421540i
$395$	−6.27785	+	1.84334i	−0.315873	+	0.0927486i
$396$	2.07860	−	2.39883i	0.104454	−	0.120546i
$397$	22.6700	+	6.65652i	1.13778	+	0.334081i	0.795759	−	0.605613i	$-0.207072\pi$
$397$	22.6700	+	6.65652i	1.13778	+	0.334081i	0.342016	+	0.939694i	$0.388890\pi$
$398$	−18.5555	+	11.9249i	−0.930102	+	0.597740i
$399$	−3.15198	−	6.90188i	−0.157797	−	0.345526i
$400$	2.94595	+	3.39981i	0.147298	+	0.169990i
$401$	−15.8414	−	10.1806i	−0.791082	−	0.508397i	0.0816127	−	0.996664i	$-0.473993\pi$
$401$	−15.8414	−	10.1806i	−0.791082	−	0.508397i	−0.872694	+	0.488267i	$0.837629\pi$
$402$	0.391264	−	2.72130i	0.0195145	−	0.135726i
$403$	0.623331	−	4.33536i	0.0310503	−	0.215960i
$404$	10.4932	+	6.74360i	0.522058	+	0.335506i
$405$	−0.463708	−	0.535148i	−0.0230418	−	0.0265917i
$406$	1.43037	+	3.13207i	0.0709880	+	0.155442i
$407$	31.2718	−	20.0971i	1.55008	−	0.996178i
$408$	0.0911307	+	0.0267584i	0.00451164	+	0.00132474i
$409$	13.2394	−	15.2791i	0.654646	−	0.755502i	−0.327247	−	0.944939i	$-0.606121\pi$
$409$	13.2394	−	15.2791i	0.654646	−	0.755502i	0.981893	+	0.189437i	$0.0606662\pi$
$410$	−2.22581	+	0.653558i	−0.109925	+	0.0322769i
$411$	−2.03065	+	4.44650i	−0.100165	+	0.219330i
$412$	−1.81815	−	12.6455i	−0.0895738	−	0.622999i
$413$	−5.29197			−0.260401
$414$	−4.02679	−	2.60480i	−0.197906	−	0.128019i
$415$	−3.05459			−0.149944
$416$	0.218952	+	1.52284i	0.0107350	+	0.0746635i
$417$	−2.61340	+	5.72255i	−0.127979	+	0.280234i
$418$	−23.1082	+	6.78517i	−1.13026	+	0.331873i
$419$	9.85718	−	11.3758i	0.481555	−	0.555744i	−0.462035	−	0.886862i	$-0.652880\pi$
$419$	9.85718	−	11.3758i	0.481555	−	0.555744i	0.943589	+	0.331118i	$0.107426\pi$
$420$	−0.679419	−	0.199495i	−0.0331523	−	0.00973438i
$421$	−3.61595	+	2.32383i	−0.176230	+	0.113256i	−0.625782	−	0.779998i	$-0.715220\pi$
$421$	−3.61595	+	2.32383i	−0.176230	+	0.113256i	0.449552	+	0.893254i	$0.351584\pi$
$422$	8.30304	+	18.1811i	0.404186	+	0.885043i
$423$	−0.0324920	−	0.0374978i	−0.00157982	−	0.00182321i
$424$	7.41291	+	4.76399i	0.360003	+	0.231360i
$425$	0.0608064	−	0.422918i	0.00294955	−	0.0205145i
$426$	−0.224781	+	1.56339i	−0.0108907	+	0.0757463i
$427$	6.28632	+	4.03997i	0.304216	+	0.195508i
$428$	3.59461	+	4.14840i	0.173752	+	0.200521i
$429$	−2.02863	−	4.44207i	−0.0979430	−	0.214465i
$430$	−7.74114	+	4.97493i	−0.373311	+	0.239912i
$431$	13.7334	+	4.03249i	0.661515	+	0.194238i	0.595221	−	0.803562i	$-0.297064\pi$
$431$	13.7334	+	4.03249i	0.661515	+	0.194238i	0.0662939	+	0.997800i	$0.478883\pi$
$432$	0.654861	−	0.755750i	0.0315070	−	0.0363610i
$433$	9.23454	−	2.71150i	0.443783	−	0.130307i	−0.0522036	−	0.998636i	$-0.516624\pi$
$433$	9.23454	−	2.71150i	0.443783	−	0.130307i	0.495987	+	0.868330i	$0.334806\pi$
$434$	−1.18264	+	2.58962i	−0.0567686	+	0.124306i
$435$	−0.346986	−	2.41334i	−0.0166367	−	0.115711i
$436$	−6.36695			−0.304922
$437$	15.0180	+	33.1450i	0.718406	+	1.58554i
$438$	2.81779			0.134639
$439$	−1.23838	−	8.61313i	−0.0591047	−	0.411082i	−0.997798	−	0.0663284i	$-0.978872\pi$
$439$	−1.23838	−	8.61313i	−0.0591047	−	0.411082i	0.938693	−	0.344754i	$-0.112038\pi$
$440$	−0.933684	+	2.04448i	−0.0445116	+	0.0974669i
$441$	−0.959493	+	0.281733i	−0.0456901	+	0.0134158i
$442$	0.0956907	−	0.110433i	0.00455154	−	0.00525276i
$443$	−18.8756	−	5.54238i	−0.896807	−	0.263326i	−0.199329	−	0.979933i	$-0.563876\pi$
$443$	−18.8756	−	5.54238i	−0.896807	−	0.263326i	−0.697478	+	0.716606i	$0.745695\pi$
$444$	9.85214	−	6.33159i	0.467562	−	0.300484i
$445$	5.26489	+	11.5285i	0.249580	+	0.546504i
$446$	−7.75099	−	8.94512i	−0.367020	−	0.423564i
$447$	−16.8157	−	10.8068i	−0.795356	−	0.511144i
$448$	0.142315	−	0.989821i	0.00672374	−	0.0467647i
$449$	4.26531	−	29.6659i	0.201293	−	1.40002i	−0.599162	−	0.800628i	$-0.704500\pi$
$449$	4.26531	−	29.6659i	0.201293	−	1.40002i	0.800455	−	0.599393i	$-0.204591\pi$
$450$	−3.78446	−	2.43212i	−0.178401	−	0.114651i
$451$	6.80961	+	7.85870i	0.320652	+	0.370052i
$452$	8.23854	+	18.0399i	0.387508	+	0.848525i
$453$	5.34828	−	3.43713i	0.251284	−	0.161490i
$454$	25.9066	+	7.60687i	1.21586	+	0.357008i
$455$	−0.713416	+	0.823326i	−0.0334455	+	0.0385981i
$456$	−7.28021	+	2.13766i	−0.340927	+	0.100105i
$457$	16.2284	−	35.5352i	0.759131	−	1.66226i	0.00990407	−	0.999951i	$-0.496847\pi$
$457$	16.2284	−	35.5352i	0.759131	−	1.66226i	0.749227	−	0.662314i	$-0.230425\pi$
$458$	−0.822804	−	5.72272i	−0.0384471	−	0.267405i
$459$	−0.0949780			−0.00443319
$460$	3.25552	+	0.966425i	0.151789	+	0.0450598i
$461$	−1.62328			−0.0756038			−0.0378019	−	0.999285i	$-0.512036\pi$
$461$	−1.62328			−0.0756038			−0.0378019	+	0.999285i	$0.512036\pi$
$462$	0.451723	+	3.14180i	0.0210160	+	0.146170i
$463$	7.92067	−	17.3439i	0.368105	−	0.806037i	−0.631427	−	0.775436i	$-0.717530\pi$
$463$	7.92067	−	17.3439i	0.368105	−	0.806037i	0.999532	−	0.0306018i	$-0.00974238\pi$
$464$	3.30375	−	0.970069i	0.153373	−	0.0450343i
$465$	1.32013	−	1.52351i	0.0612194	−	0.0706510i
$466$	−24.0039	−	7.04819i	−1.11196	−	0.326501i
$467$	−6.39966	+	4.11281i	−0.296141	+	0.190318i	−0.680271	−	0.732961i	$-0.738138\pi$
$467$	−6.39966	+	4.11281i	−0.296141	+	0.190318i	0.384130	+	0.923279i	$0.374501\pi$
$468$	−0.639117	−	1.39947i	−0.0295432	−	0.0646905i
$469$	1.80040	+	2.07777i	0.0831348	+	0.0959426i
$470$	0.0295564	+	0.0189947i	0.00136333	+	0.000876161i
$471$	−1.67339	+	11.6387i	−0.0771059	+	0.536283i
$472$	−0.753126	+	5.23811i	−0.0346654	+	0.241103i
$473$	34.7001	+	22.3004i	1.59551	+	1.02537i
$474$	6.05093	+	6.98314i	0.277928	+	0.320746i
$475$	14.1795	+	31.0488i	0.650600	+	1.42461i
$476$	−0.0799005	+	0.0513490i	−0.00366224	+	0.00235358i
$477$	−8.45481	−	2.48256i	−0.387119	−	0.113668i
$478$	12.8844	−	14.8694i	0.589320	−	0.680111i
$479$	4.16815	−	1.22388i	0.190447	−	0.0559204i	−0.185118	−	0.982716i	$-0.559267\pi$
$479$	4.16815	−	1.22388i	0.190447	−	0.0559204i	0.375565	+	0.926796i	$0.377449\pi$
$480$	−0.294156	+	0.644112i	−0.0134263	+	0.0293996i
$481$	−2.56420	−	17.8344i	−0.116917	−	0.813179i
$482$	25.6944			1.17035
$483$	4.60556	−	1.33746i	0.209560	−	0.0608566i
$484$	−0.925038			−0.0420472
$485$	−0.265572	−	1.84710i	−0.0120590	−	0.0838723i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	−1.51897	+	0.446009i	−0.0688310	+	0.0202106i	−0.315967	−	0.948770i	$-0.602329\pi$
$487$	−1.51897	+	0.446009i	−0.0688310	+	0.0202106i	0.247136	+	0.968981i	$0.420511\pi$
$488$	4.89349	−	5.64739i	0.221518	−	0.255645i
$489$	−0.164958	−	0.0484359i	−0.00745964	−	0.00219035i
$490$	0.595693	−	0.382829i	0.0269107	−	0.0172944i
$491$	−4.22115	−	9.24304i	−0.190498	−	0.417132i	0.790150	−	0.612914i	$-0.210003\pi$
$491$	−4.22115	−	9.24304i	−0.190498	−	0.417132i	−0.980647	+	0.195782i	$0.937276\pi$
$492$	2.14536	+	2.47588i	0.0967203	+	0.111621i
$493$	−0.275116	−	0.176806i	−0.0123906	−	0.00796294i
$494$	−1.66131	+	11.5546i	−0.0747458	+	0.519868i
$495$	0.319866	−	2.22472i	0.0143769	−	0.0999935i
$496$	2.39496	+	1.53915i	0.107537	+	0.0691097i
$497$	−1.03433	−	1.19368i	−0.0463960	−	0.0535438i
$498$	1.79200	+	3.92394i	0.0803016	+	0.175836i
$499$	−12.5054	+	8.03670i	−0.559816	+	0.359772i	−0.789745	−	0.613435i	$-0.789787\pi$
$499$	−12.5054	+	8.03670i	−0.559816	+	0.359772i	0.229928	+	0.973208i	$0.426151\pi$
$500$	6.45352	+	1.89493i	0.288610	+	0.0847436i
$501$	9.06835	−	10.4654i	0.405144	−	0.467561i
$502$	13.4745	−	3.95647i	0.601397	−	0.176586i
$503$	−7.15486	+	15.6670i	−0.319019	+	0.698555i	−0.999412	−	0.0342930i	$-0.989082\pi$
$503$	−7.15486	+	15.6670i	−0.319019	+	0.698555i	0.680392	+	0.732848i	$0.261809\pi$
$504$	0.142315	+	0.989821i	0.00633921	+	0.0440902i
$505$	8.83240			0.393037
$506$	−2.12160	−	15.0739i	−0.0943167	−	0.670117i
$507$	10.6330			0.472229
$508$	−2.71854	−	18.9079i	−0.120616	−	0.838900i
$509$	−0.973070	+	2.13073i	−0.0431306	+	0.0944427i	−0.929971	−	0.367634i	$-0.880168\pi$
$509$	−0.973070	+	2.13073i	−0.0431306	+	0.0944427i	0.886840	+	0.462076i	$0.152895\pi$
$510$	0.0645298	−	0.0189477i	0.00285743	−	0.000839017i
$511$	−1.84526	+	2.12954i	−0.0816294	+	0.0942054i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	6.38306	−	4.10214i	0.281819	−	0.181114i
$514$	1.80296	+	3.94793i	0.0795250	+	0.174136i
$515$	−5.92412	−	6.83680i	−0.261048	−	0.301266i
$516$	10.9322	+	7.02572i	0.481265	+	0.309290i
$517$	0.0224130	−	0.155886i	0.000985723	−	0.00685585i
$518$	−1.66669	+	11.5921i	−0.0732300	+	0.509326i
$519$	13.4640	+	8.65276i	0.591002	+	0.379814i
$520$	0.713416	+	0.823326i	0.0312854	+	0.0361052i
$521$	−3.22251	−	7.05631i	−0.141181	−	0.309143i	0.825813	−	0.563945i	$-0.190717\pi$
$521$	−3.22251	−	7.05631i	−0.141181	−	0.309143i	−0.966993	+	0.254802i	$0.917990\pi$
$522$	−2.89663	+	1.86155i	−0.126782	+	0.0814778i
$523$	31.4024	+	9.22059i	1.37313	+	0.403188i	0.883374	−	0.468670i	$-0.155267\pi$
$523$	31.4024	+	9.22059i	1.37313	+	0.403188i	0.489759	+	0.871858i	$0.337085\pi$
$524$	−9.47606	+	10.9360i	−0.413964	+	0.477740i
$525$	4.31637	−	1.26740i	0.188382	−	0.0553139i
$526$	6.88628	−	15.0789i	0.300256	−	0.657469i
$527$	−0.0384808	−	0.267640i	−0.00167625	−	0.0116586i
$528$	3.17411			0.138135
$529$	−22.1065	+	6.34858i	−0.961150	+	0.276025i
$530$	6.23962			0.271032
$531$	−0.753126	−	5.23811i	−0.0326829	−	0.227314i
$532$	3.15198	−	6.90188i	0.136656	−	0.299235i
$533$	4.83605	−	1.41999i	0.209473	−	0.0615067i
$534$	11.7209	−	13.5266i	0.507212	−	0.585354i
$535$	3.72942	+	1.09506i	0.161237	+	0.0473434i
$536$	2.31285	−	1.48638i	0.0998998	−	0.0642017i
$537$	0.781876	+	1.71207i	0.0337405	+	0.0738813i
$538$	10.4186	+	12.0237i	0.449178	+	0.518379i
$539$	−2.67023	−	1.71605i	−0.115015	−	0.0739156i
$540$	0.100773	−	0.700895i	0.00433660	−	0.0301617i
$541$	3.91647	−	27.2397i	0.168382	−	1.17112i	−0.713846	−	0.700303i	$-0.753048\pi$
$541$	3.91647	−	27.2397i	0.168382	−	1.17112i	0.882228	−	0.470822i	$-0.156043\pi$
$542$	−2.63518	−	1.69353i	−0.113191	−	0.0727433i
$543$	−11.4186	−	13.1778i	−0.490019	−	0.565512i
$544$	0.0394553	+	0.0863950i	0.00169163	+	0.00370415i
$545$	−3.79275	+	2.43745i	−0.162464	+	0.104409i
$546$	1.47618	+	0.433446i	0.0631747	+	0.0185498i
$547$	−15.4394	+	17.8181i	−0.660143	+	0.761845i	−0.982801	−	0.184670i	$-0.940878\pi$
$547$	−15.4394	+	17.8181i	−0.660143	+	0.761845i	0.322658	+	0.946516i	$0.395424\pi$
$548$	−4.69023	+	1.37718i	−0.200357	+	0.0588301i
$549$	−3.10422	+	6.79729i	−0.132485	+	0.290101i
$550$	−2.03212	−	14.1337i	−0.0866497	−	0.602662i
$551$	26.1257			1.11299
$552$	−0.668409	−	4.74902i	−0.0284494	−	0.202132i
$553$	−9.24002			−0.392926
$554$	−4.04834	−	28.1568i	−0.171997	−	1.19627i
$555$	3.44494	−	7.54337i	0.146230	−	0.320198i
$556$	−6.03623	+	1.77240i	−0.255993	+	0.0751664i
$557$	−21.2090	+	24.4765i	−0.898653	+	1.03710i	0.100458	+	0.994941i	$0.467969\pi$
$557$	−21.2090	+	24.4765i	−0.898653	+	1.03710i	−0.999111	+	0.0421594i	$0.986576\pi$
$558$	−2.73157	−	0.802062i	−0.115637	−	0.0339540i
$559$	16.8193	−	10.8091i	0.711379	−	0.457176i
$560$	−0.294156	−	0.644112i	−0.0124304	−	0.0272187i
$561$	−0.197421	−	0.227836i	−0.00833512	−	0.00961925i
$562$	12.9757	+	8.33898i	0.547347	+	0.351758i
$563$	0.139087	−	0.967368i	0.00586180	−	0.0407697i	−0.986681	−	0.162670i	$-0.947990\pi$
$563$	0.139087	−	0.967368i	0.00586180	−	0.0407697i	0.992542	+	0.121900i	$0.0388987\pi$
$564$	0.00706120	−	0.0491117i	0.000297330	−	0.00206798i
$565$	11.8138	+	7.59229i	0.497012	+	0.319410i
$566$	19.2983	+	22.2714i	0.811168	+	0.936137i
$567$	−0.415415	−	0.909632i	−0.0174458	−	0.0382010i
$568$	−1.32873	+	0.853922i	−0.0557522	+	0.0358298i
$569$	0.0955089	+	0.0280439i	0.00400394	+	0.00117566i	0.283734	−	0.958903i	$-0.408427\pi$
$569$	0.0955089	+	0.0280439i	0.00400394	+	0.00117566i	−0.279730	+	0.960079i	$0.590245\pi$
$570$	−3.51841	+	4.06046i	−0.147370	+	0.170074i
$571$	22.6810	−	6.65973i	0.949169	−	0.278701i	0.229728	−	0.973255i	$-0.426216\pi$
$571$	22.6810	−	6.65973i	0.949169	−	0.278701i	0.719441	+	0.694554i	$0.244398\pi$
$572$	2.02863	−	4.44207i	0.0848211	−	0.185732i
$573$	0.0187538	+	0.130436i	0.000783453	+	0.00544904i
$574$	−3.27606			−0.136740
$575$	−20.7185	+	6.01670i	−0.864023	+	0.250914i
$576$	1.00000			0.0416667
$577$	1.63047	+	11.3402i	0.0678774	+	0.472097i	0.995202	+	0.0978399i	$0.0311933\pi$
$577$	1.63047	+	11.3402i	0.0678774	+	0.472097i	−0.927325	+	0.374258i	$0.877898\pi$
$578$	−7.05831	+	15.4555i	−0.293587	+	0.642866i
$579$	−3.94911	+	1.15956i	−0.164119	+	0.0481898i
$580$	1.59665	−	1.84263i	0.0662974	−	0.0765112i
$581$	−4.13903	−	1.21533i	−0.171716	−	0.0504204i
$582$	−2.21699	+	1.42477i	−0.0918972	+	0.0590587i
$583$	−11.6189	−	25.4419i	−0.481207	−	1.05370i
$584$	1.84526	+	2.12954i	0.0763573	+	0.0881211i
$585$	−0.916475	−	0.588983i	−0.0378916	−	0.0243514i
$586$	−3.18515	+	22.1532i	−0.131577	+	0.915140i
$587$	1.97498	−	13.7363i	0.0815160	−	0.566956i	−0.907602	−	0.419832i	$-0.862089\pi$
$587$	1.97498	−	13.7363i	0.0815160	−	0.566956i	0.989118	−	0.147124i	$-0.0470018\pi$
$588$	−0.841254	−	0.540641i	−0.0346927	−	0.0222957i
$589$	14.1456	+	16.3249i	0.582860	+	0.672656i
$590$	1.55667	+	3.40862i	0.0640869	+	0.140331i
$591$	−7.73834	+	4.97313i	−0.318313	+	0.204567i
$592$	11.2369	+	3.29944i	0.461833	+	0.135606i
$593$	0.774365	−	0.893665i	0.0317994	−	0.0366984i	−0.739627	−	0.673017i	$-0.764998\pi$
$593$	0.774365	−	0.893665i	0.0317994	−	0.0366984i	0.771426	+	0.636318i	$0.219544\pi$
$594$	−3.04553	+	0.894250i	−0.124960	+	0.0366915i
$595$	−0.0279384	+	0.0611765i	−0.00114536	+	0.00250799i
$596$	−2.84471	−	19.7854i	−0.116524	−	0.810442i
$597$	22.0569			0.902730
$598$	−7.07331	−	2.09976i	−0.289249	−	0.0858656i
$599$	6.01642			0.245824			0.122912	−	0.992418i	$-0.460777\pi$
$599$	6.01642			0.245824			0.122912	+	0.992418i	$0.460777\pi$
$600$	−0.640216	−	4.45280i	−0.0261367	−	0.181785i
$601$	12.2033	−	26.7215i	0.497782	−	1.08999i	−0.479402	−	0.877596i	$-0.659146\pi$
$601$	12.2033	−	26.7215i	0.497782	−	1.08999i	0.977184	−	0.212395i	$-0.0681264\pi$
$602$	−12.4688	+	3.66116i	−0.508190	+	0.149218i
$603$	−1.80040	+	2.07777i	−0.0733180	+	0.0846134i
$604$	6.09998	+	1.79112i	0.248205	+	0.0728795i
$605$	−0.551039	+	0.354131i	−0.0224029	+	0.0143975i
$606$	−5.18161	−	11.3461i	−0.210489	−	0.460906i
$607$	1.72657	+	1.99256i	0.0700792	+	0.0808757i	0.789707	−	0.613485i	$-0.210233\pi$
$607$	1.72657	+	1.99256i	0.0700792	+	0.0808757i	−0.719627	+	0.694360i	$0.755687\pi$
$608$	−6.38306	−	4.10214i	−0.258867	−	0.166364i
$609$	0.490022	−	3.40818i	0.0198567	−	0.138106i
$610$	0.753036	−	5.23748i	0.0304895	−	0.212059i
$611$	−0.0642174	−	0.0412700i	−0.00259796	−	0.00166961i
$612$	−0.0621973	−	0.0717795i	−0.00251418	−	0.00290152i
$613$	3.82212	+	8.36927i	0.154374	+	0.338032i	0.970979	−	0.239165i	$-0.0768738\pi$
$613$	3.82212	+	8.36927i	0.154374	+	0.338032i	−0.816605	+	0.577197i	$0.804147\pi$
$614$	−13.0870	+	8.41052i	−0.528149	+	0.339421i
$615$	2.22581	+	0.653558i	0.0897535	+	0.0263540i
$616$	−2.07860	+	2.39883i	−0.0837491	+	0.0966516i
$617$	−27.5712	+	8.09564i	−1.10998	+	0.325918i	−0.784808	−	0.619738i	$-0.787239\pi$
$617$	−27.5712	+	8.09564i	−1.10998	+	0.325918i	−0.325167	+	0.945657i	$0.605421\pi$
$618$	−5.30715	+	11.6210i	−0.213485	+	0.467467i
$619$	−3.99681	−	27.7984i	−0.160645	−	1.11731i	−0.897421	−	0.441176i	$-0.854562\pi$
$619$	−3.99681	−	27.7984i	−0.160645	−	1.11731i	0.736775	−	0.676138i	$-0.236348\pi$
$620$	2.01589			0.0809601
$621$	1.97929	+	4.36834i	0.0794261	+	0.175296i
$622$	0.783544			0.0314172
$623$	2.54719	+	17.7161i	0.102051	+	0.709781i
$624$	0.639117	−	1.39947i	0.0255851	−	0.0560236i
$625$	−17.0121	+	4.99520i	−0.680483	+	0.199808i
$626$	−17.4817	+	20.1749i	−0.698707	+	0.806351i
$627$	23.1082	+	6.78517i	0.922851	+	0.270974i
$628$	−9.89179	+	6.35707i	−0.394725	+	0.253675i
$629$	−0.462071	−	1.01179i	−0.0184240	−	0.0403429i
$630$	0.463708	+	0.535148i	0.0184746	+	0.0213208i
$631$	−7.84273	−	5.04021i	−0.312214	−	0.200648i	0.375144	−	0.926967i	$-0.377593\pi$
$631$	−7.84273	−	5.04021i	−0.312214	−	0.200648i	−0.687358	+	0.726319i	$0.741230\pi$
$632$	−1.31499	+	9.14597i	−0.0523076	+	0.363807i
$633$	2.84449	−	19.7839i	0.113059	−	0.786339i
$634$	21.2664	+	13.6671i	0.844596	+	0.542789i
$635$	−8.85789	−	10.2225i	−0.351515	−	0.405669i
$636$	−3.66053	−	8.01545i	−0.145150	−	0.317833i
$637$	−1.29427	+	0.831777i	−0.0512808	+	0.0329562i
$638$	−10.4865	−	3.07910i	−0.415163	−	0.121903i
$639$	1.03433	−	1.19368i	0.0409174	−	0.0472212i
$640$	−0.679419	+	0.199495i	−0.0268564	+	0.00788575i
$641$	−19.2015	+	42.0454i	−0.758414	+	1.66069i	−0.00778503	+	0.999970i	$0.502478\pi$
$641$	−19.2015	+	42.0454i	−0.758414	+	1.66069i	−0.750629	+	0.660724i	$0.770249\pi$
$642$	−0.781184	−	5.43325i	−0.0308309	−	0.214433i
$643$	−46.5474			−1.83565			−0.917825	−	0.396984i	$-0.870057\pi$
$643$	−46.5474			−1.83565			−0.917825	+	0.396984i	$0.870057\pi$
$644$	4.02679	+	2.60480i	0.158678	+	0.102643i
$645$	9.20191			0.362325
$646$	0.102559	+	0.713315i	0.00403514	+	0.0280650i
$647$	−2.82465	+	6.18513i	−0.111049	+	0.243162i	−0.956994	−	0.290106i	$-0.906309\pi$
$647$	−2.82465	+	6.18513i	−0.111049	+	0.243162i	0.845946	+	0.533269i	$0.179037\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	10.9999	−	12.6945i	0.431783	−	0.498304i
$650$	−6.64074	−	1.94990i	−0.260471	−	0.0764812i
$651$	2.39496	−	1.53915i	0.0938658	−	0.0603239i
$652$	−0.0714188	−	0.156385i	−0.00279698	−	0.00612453i
$653$	31.8511	+	36.7581i	1.24643	+	1.43846i	0.855310	+	0.518117i	$0.173367\pi$
$653$	31.8511	+	36.7581i	1.24643	+	1.43846i	0.391120	+	0.920340i	$0.372088\pi$
$654$	5.35622	+	3.44223i	0.209445	+	0.134602i
$655$	−1.45823	+	10.1422i	−0.0569776	+	0.396288i
$656$	−0.466231	+	3.24271i	−0.0182033	+	0.126607i
$657$	−2.37047	−	1.52341i	−0.0924810	−	0.0594339i
$658$	0.0324920	+	0.0374978i	0.00126667	+	0.00146182i
$659$	13.9674	+	30.5844i	0.544094	+	1.19140i	0.959486	+	0.281757i	$0.0909173\pi$
$659$	13.9674	+	30.5844i	0.544094	+	1.19140i	−0.415392	+	0.909643i	$0.636355\pi$
$660$	1.89080	−	1.21514i	0.0735991	−	0.0472993i
$661$	−18.2186	−	5.34947i	−0.708622	−	0.208070i	−0.0924908	−	0.995714i	$-0.529483\pi$
$661$	−18.2186	−	5.34947i	−0.708622	−	0.208070i	−0.616132	+	0.787643i	$0.711301\pi$
$662$	4.71546	−	5.44193i	0.183271	−	0.211506i
$663$	−0.140205	+	0.0411678i	−0.00544510	+	0.00159883i
$664$	−1.79200	+	3.92394i	−0.0695433	+	0.152279i
$665$	−0.764624	−	5.31808i	−0.0296508	−	0.206226i
$666$	−11.7113			−0.453802
$667$	−2.39862	+	16.3380i	−0.0928751	+	0.632610i
$668$	13.8477			0.535785
$669$	1.68445	+	11.7156i	0.0651247	+	0.452952i
$670$	0.808720	−	1.77085i	0.0312436	−	0.0684139i
$671$	−22.7580	+	6.68234i	−0.878561	+	0.257969i
$672$	−0.654861	+	0.755750i	−0.0252618	+	0.0291537i
$673$	−4.59673	−	1.34972i	−0.177191	−	0.0520279i	0.191934	−	0.981408i	$-0.438524\pi$
$673$	−4.59673	−	1.34972i	−0.177191	−	0.0520279i	−0.369124	+	0.929380i	$0.620342\pi$
$674$	−0.467663	+	0.300549i	−0.0180137	+	0.0115767i
$675$	1.86878	+	4.09206i	0.0719295	+	0.157504i
$676$	6.96314	+	8.03590i	0.267813	+	0.309073i
$677$	−8.68582	−	5.58204i	−0.333823	−	0.214535i	0.362981	−	0.931797i	$-0.381759\pi$
$677$	−8.68582	−	5.58204i	−0.333823	−	0.214535i	−0.696804	+	0.717261i	$0.745395\pi$
$678$	2.82240	−	19.6302i	0.108394	−	0.753894i
$679$	0.375048	−	2.60852i	0.0143930	−	0.100106i
$680$	0.0565777	+	0.0363603i	0.00216966	+	0.00139435i
$681$	−17.6814	−	20.4055i	−0.677554	−	0.781939i
$682$	−3.75383	−	8.21974i	−0.143742	−	0.314750i
$683$	27.9131	−	17.9387i	1.06807	−	0.686405i	0.116296	−	0.993215i	$-0.462898\pi$
$683$	27.9131	−	17.9387i	1.06807	−	0.686405i	0.951771	+	0.306810i	$0.0992616\pi$
$684$	7.28021	+	2.13766i	0.278366	+	0.0817355i
$685$	−2.26672	+	2.61593i	−0.0866068	+	0.0999496i
$686$	0.959493	−	0.281733i	0.0366336	−	0.0107566i
$687$	−2.40175	+	5.25910i	−0.0916326	+	0.200647i
$688$	1.84941	+	12.8629i	0.0705080	+	0.490394i
$689$	−13.5569			−0.516476
$690$	−2.21623	−	2.57308i	−0.0843705	−	0.0979553i
$691$	−24.0469			−0.914785			−0.457393	−	0.889265i	$-0.651217\pi$
$691$	−24.0469			−0.914785			−0.457393	+	0.889265i	$0.651217\pi$
$692$	2.27770	+	15.8417i	0.0865851	+	0.602212i
$693$	1.31857	−	2.88727i	0.0500884	−	0.109678i
$694$	12.3744	−	3.63345i	0.469725	−	0.137924i
$695$	−2.91722	+	3.36665i	−0.110656	+	0.127704i
$696$	−3.30375	−	0.970069i	−0.125228	−	0.0367704i
$697$	0.261759	−	0.168222i	0.00991482	−	0.00637186i
$698$	5.12651	+	11.2255i	0.194041	+	0.424891i
$699$	16.3829	+	18.9068i	0.619657	+	0.715122i
$700$	3.78446	+	2.43212i	0.143039	+	0.0919256i
$701$	−0.309024	+	2.14931i	−0.0116717	+	0.0811782i	−0.994825	−	0.101606i	$-0.967602\pi$
$701$	−0.309024	+	2.14931i	−0.0116717	+	0.0811782i	0.983153	+	0.182784i	$0.0585110\pi$
$702$	−0.218952	+	1.52284i	−0.00826380	+	0.0574760i
$703$	74.7537	+	48.0413i	2.81939	+	1.81191i
$704$	2.07860	+	2.39883i	0.0783401	+	0.0904093i
$705$	−0.0145951	−	0.0319587i	−0.000549682	−	0.00120364i
$706$	1.67706	−	1.07778i	0.0631169	−	0.0405628i
$707$	11.9681	+	3.51415i	0.450106	+	0.132163i
$708$	3.46550	−	3.99940i	0.130242	−	0.150307i
$709$	4.18530	−	1.22892i	0.157182	−	0.0461529i	−0.202195	−	0.979345i	$-0.564807\pi$
$709$	4.18530	−	1.22892i	0.157182	−	0.0461529i	0.359377	+	0.933192i	$0.382989\pi$
$710$	−0.464609	+	1.01735i	−0.0174365	+	0.0381805i
$711$	−1.31499	−	9.14597i	−0.0493161	−	0.343001i
$712$	17.8983			0.670767
$713$	−11.5077	+	7.34732i	−0.430967	+	0.275159i
$714$	0.0949780			0.00355446
$715$	−0.492114	−	3.42273i	−0.0184040	−	0.128003i
$716$	−0.781876	+	1.71207i	−0.0292201	+	0.0639831i
$717$	−18.8781	+	5.54310i	−0.705015	+	0.207011i
$718$	6.46702	−	7.46333i	0.241347	−	0.278529i
$719$	−38.8793	−	11.4160i	−1.44995	−	0.425744i	−0.540426	−	0.841392i	$-0.681737\pi$
$719$	−38.8793	−	11.4160i	−1.44995	−	0.425744i	−0.909526	+	0.415647i	$0.863555\pi$
$720$	0.595693	−	0.382829i	0.0222002	−	0.0142672i
$721$	−5.30715	−	11.6210i	−0.197649	−	0.432790i
$722$	−25.2586	−	29.1500i	−0.940029	−	1.08485i
$723$	−21.6155	−	13.8914i	−0.803888	−	0.516627i
$724$	2.48150	−	17.2592i	0.0922241	−	0.641433i
$725$	−2.20441	+	15.3320i	−0.0818697	+	0.569416i
$726$	0.778191	+	0.500113i	0.0288814	+	0.0185609i
$727$	22.2616	+	25.6913i	0.825638	+	0.952837i	0.999490	−	0.0319348i	$-0.0101669\pi$
$727$	22.2616	+	25.6913i	0.825638	+	0.952837i	−0.173852	+	0.984772i	$0.555621\pi$
$728$	0.639117	+	1.39947i	0.0236872	+	0.0518678i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	1.91446	+	0.562136i	0.0708573	+	0.0208056i
$731$	0.808265	−	0.932788i	0.0298948	−	0.0345004i
$732$	−7.16987	+	2.10527i	−0.265006	+	0.0778128i
$733$	−14.2905	+	31.2918i	−0.527831	+	1.15579i	0.438558	+	0.898703i	$0.355489\pi$
$733$	−14.2905	+	31.2918i	−0.527831	+	1.15579i	−0.966389	+	0.257085i	$0.917238\pi$
$734$	−4.18564	−	29.1118i	−0.154495	−	1.07454i
$735$	−0.708102			−0.0261187
$736$	3.15136	−	3.61510i	0.116161	−	0.133254i
$737$	−8.72653			−0.321446
$738$	−0.466231	−	3.24271i	−0.0171622	−	0.119366i
$739$	10.9023	−	23.8727i	0.401047	−	0.878171i	−0.596116	−	0.802898i	$-0.703290\pi$
$739$	10.9023	−	23.8727i	0.401047	−	0.878171i	0.997163	−	0.0752722i	$-0.0239826\pi$
$740$	7.95685	−	2.33634i	0.292500	−	0.0858857i
$741$	7.64449	−	8.82222i	0.280828	−	0.324092i
$742$	8.45481	+	2.48256i	0.310386	+	0.0911375i
$743$	−17.0691	+	10.9696i	−0.626203	+	0.402436i	−0.814902	−	0.579599i	$-0.803209\pi$
$743$	−17.0691	+	10.9696i	−0.626203	+	0.402436i	0.188699	+	0.982035i	$0.439573\pi$
$744$	−1.18264	−	2.58962i	−0.0433577	−	0.0949402i
$745$	−9.26901	−	10.6970i	−0.339590	−	0.391908i
$746$	−8.86743	−	5.69875i	−0.324660	−	0.208646i
$747$	0.613913	−	4.26986i	0.0224619	−	0.156226i
$748$	0.0429037	−	0.298402i	0.00156871	−	0.0109106i
$749$	4.61775	+	2.96764i	0.168729	+	0.108435i
$750$	−4.40458	−	5.08315i	−0.160832	−	0.185610i
$751$	−13.5160	−	29.5959i	−0.493206	−	1.07997i	−0.978618	−	0.205684i	$-0.934058\pi$
$751$	−13.5160	−	29.5959i	−0.493206	−	1.07997i	0.485413	−	0.874285i	$-0.338669\pi$
$752$	0.0417402	−	0.0268248i	0.00152211	−	0.000978201i
$753$	−13.4745	−	3.95647i	−0.491039	−	0.144182i
$754$	−3.46906	+	4.00351i	−0.126336	+	0.145799i
$755$	4.31941	−	1.26829i	0.157199	−	0.0461579i
$756$	0.415415	−	0.909632i	0.0151085	−	0.0330830i
$757$	1.00816	+	7.01193i	0.0366423	+	0.254853i	0.999906	−	0.0137040i	$-0.00436227\pi$
$757$	1.00816	+	7.01193i	0.0366423	+	0.254853i	−0.963264	+	0.268557i	$0.913453\pi$
$758$	21.3973			0.777183
$759$	−6.36477	+	13.8280i	−0.231026	+	0.501925i
$760$	−5.37276			−0.194891
$761$	−4.93934	−	34.3538i	−0.179051	−	1.24533i	−0.858965	−	0.512034i	$-0.828892\pi$
$761$	−4.93934	−	34.3538i	−0.179051	−	1.24533i	0.679914	−	0.733292i	$-0.262017\pi$
$762$	−7.93538	+	17.3760i	−0.287468	+	0.629468i
$763$	−6.10904	+	1.79378i	−0.221162	+	0.0649391i
$764$	−0.0862957	+	0.0995905i	−0.00312207	+	0.00360306i
$765$	−0.0645298	−	0.0189477i	−0.00233308	−	0.000685054i
$766$	−19.0354	+	12.2333i	−0.687778	+	0.442008i
$767$	−3.38219	−	7.40595i	−0.122124	−	0.267414i
$768$	0.654861	+	0.755750i	0.0236303	+	0.0272708i
$769$	6.96244	+	4.47449i	0.251072	+	0.161354i	0.660123	−	0.751157i	$-0.270504\pi$
$769$	6.96244	+	4.47449i	0.251072	+	0.161354i	−0.409051	+	0.912511i	$0.634140\pi$
$770$	−0.319866	+	2.22472i	−0.0115272	+	0.0801732i
$771$	0.617666	−	4.29596i	0.0222447	−	0.154715i
$772$	−3.46246	−	2.22519i	−0.124617	−	0.0800862i
$773$	12.7792	+	14.7479i	0.459634	+	0.530446i	0.937499	−	0.347987i	$-0.113135\pi$
$773$	12.7792	+	14.7479i	0.459634	+	0.530446i	−0.477865	+	0.878433i	$0.658589\pi$
$774$	−5.39839	−	11.8208i	−0.194041	−	0.424891i
$775$	−10.7739	+	6.92399i	−0.387011	+	0.248717i
$776$	−2.52859	−	0.742461i	−0.0907711	−	0.0266528i
$777$	7.66925	−	8.85078i	0.275133	−	0.317520i
$778$	−34.1335	+	10.0225i	−1.22374	+	0.359324i
$779$	−10.3261	+	22.6110i	−0.369970	+	0.810122i
$780$	−0.155040	−	1.07833i	−0.00555133	−	0.0386103i
$781$	5.01339			0.179393
$782$	−0.455496	−	0.00135354i	−0.0162885	−	4.84024e-5i
$783$	3.44323			0.123051
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	−3.45881	+	7.57373i	−0.123450	+	0.270318i
$786$	13.8842	−	4.07677i	0.495233	−	0.145414i
$787$	−22.6142	+	26.0982i	−0.806110	+	0.930300i	−0.998700	−	0.0509790i	$-0.983766\pi$
$787$	−22.6142	+	26.0982i	−0.806110	+	0.930300i	0.192590	+	0.981279i	$0.438311\pi$
$788$	−8.82597	−	2.59154i	−0.314412	−	0.0923198i
$789$	−13.9454	+	8.96213i	−0.496468	+	0.319060i
$790$	2.71801	+	5.95161i	0.0967025	+	0.211749i
$791$	12.9872	+	14.9881i	0.461773	+	0.532915i
$792$	−2.67023	−	1.71605i	−0.0948825	−	0.0609773i
$793$	−1.63613	+	11.3795i	−0.0581007	+	0.404099i
$794$	3.36248	−	23.3866i	0.119330	−	0.829959i
$795$	−5.24910	−	3.37339i	−0.186166	−	0.119642i
$796$	14.4442	+	16.6695i	0.511962	+	0.590835i
$797$	−21.0446	−	46.0812i	−0.745438	−	1.63228i	−0.774396	−	0.632701i	$-0.781946\pi$
$797$	−21.0446	−	46.0812i	−0.745438	−	1.63228i	0.0289586	−	0.999581i	$-0.490781\pi$
$798$	−6.38306	+	4.10214i	−0.225958	+	0.145214i
$799$	−0.00452161	−	0.00132766i	−0.000159963	−	4.69693e-5i
$800$	2.94595	−	3.39981i	0.104155	−	0.120201i
$801$	−17.1733	+	5.04253i	−0.606788	+	0.178169i
$802$	−7.82256	+	17.1290i	−0.276224	+	0.604847i
$803$	−1.27286	−	8.85293i	−0.0449182	−	0.312413i
$804$	−2.74929			−0.0969599
$805$	3.39592	+	0.0100912i	0.119691	+	0.000355668i
$806$	−4.37995			−0.154277
$807$	−2.26418	−	15.7477i	−0.0797029	−	0.554346i
$808$	5.18161	−	11.3461i	0.182288	−	0.399156i
$809$	−28.4532	+	8.35460i	−1.00036	+	0.293732i	−0.740604	−	0.671942i	$-0.765460\pi$
$809$	−28.4532	+	8.35460i	−1.00036	+	0.293732i	−0.259756	+	0.965674i	$0.583642\pi$
$810$	−0.463708	+	0.535148i	−0.0162930	+	0.0188032i
$811$	1.15325	+	0.338625i	0.0404961	+	0.0118907i	0.301918	−	0.953334i	$-0.402373\pi$
$811$	1.15325	+	0.338625i	0.0404961	+	0.0118907i	−0.261422	+	0.965225i	$0.584191\pi$
$812$	2.89663	−	1.86155i	0.101652	−	0.0653275i
$813$	1.30127	+	2.84938i	0.0456374	+	0.0999320i
$814$	−24.3430	−	28.0933i	−0.853222	−	0.984671i
$815$	−0.102413	−	0.0658166i	−0.00358736	−	0.00230545i
$816$	0.0135168	−	0.0940112i	0.000473182	−	0.00329105i
$817$	−14.0325	+	97.5980i	−0.490934	+	3.41452i
$818$	−17.0077	−	10.9302i	−0.594661	−	0.382166i
$819$	−1.00750	−	1.16272i	−0.0352050	−	0.0406288i
$820$	0.963672	+	2.11015i	0.0336529	+	0.0736896i
$821$	32.8829	−	21.1326i	1.14762	−	0.737532i	0.178458	−	0.983948i	$-0.442889\pi$
$821$	32.8829	−	21.1326i	1.14762	−	0.737532i	0.969164	+	0.246416i	$0.0792528\pi$
$822$	4.69023	+	1.37718i	0.163591	+	0.0480345i
$823$	−21.4666	+	24.7738i	−0.748280	+	0.863561i	−0.994400	−	0.105678i	$-0.966299\pi$
$823$	−21.4666	+	24.7738i	−0.748280	+	0.863561i	0.246121	+	0.969239i	$0.420844\pi$
$824$	−12.2580	+	3.59929i	−0.427029	+	0.125387i
$825$	−5.93172	+	12.9886i	−0.206516	+	0.452207i
$826$	0.753126	+	5.23811i	0.0262046	+	0.182257i
$827$	6.32293			0.219870			0.109935	−	0.993939i	$-0.464936\pi$
$827$	6.32293			0.219870			0.109935	+	0.993939i	$0.464936\pi$
$828$	−2.00521	+	4.35650i	−0.0696860	+	0.151399i
$829$	56.3526			1.95721			0.978603	−	0.205759i	$-0.0659663\pi$
$829$	56.3526			1.95721			0.978603	+	0.205759i	$0.0659663\pi$
$830$	0.434713	+	3.02350i	0.0150891	+	0.104947i
$831$	−11.8170	+	25.8757i	−0.409929	+	0.897618i
$832$	1.47618	−	0.433446i	0.0511774	−	0.0150270i
$833$	−0.0621973	+	0.0717795i	−0.00215501	+	0.00248701i
$834$	6.03623	+	1.77240i	0.209017	+	0.0613731i
$835$	8.24901	−	5.30132i	0.285469	−	0.183460i
$836$	10.0047	+	21.9073i	0.346021	+	0.757681i
$837$	1.86432	+	2.15154i	0.0644402	+	0.0743680i
$838$	−12.6628	−	8.13790i	−0.437430	−	0.281119i
$839$	3.96073	−	27.5475i	0.136739	−	0.951044i	−0.799746	−	0.600338i	$-0.795033\pi$
$839$	3.96073	−	27.5475i	0.136739	−	0.951044i	0.936486	−	0.350706i	$-0.114058\pi$
$840$	−0.100773	+	0.700895i	−0.00347701	+	0.0241832i
$841$	−14.4226	−	9.26885i	−0.497332	−	0.319616i
$842$	2.81478	+	3.24843i	0.0970036	+	0.111948i
$843$	−6.40746	−	14.0304i	−0.220685	−	0.483232i
$844$	16.8144	−	10.8060i	0.578776	−	0.371957i
$845$	7.22427	+	2.12124i	0.248522	+	0.0729728i
$846$	−0.0324920	+	0.0374978i	−0.00111710	+	0.00128920i
$847$	−0.887567	+	0.260613i	−0.0304972	+	0.00895478i
$848$	3.66053	−	8.01545i	0.125703	−	0.275252i
$849$	−4.19392	−	29.1693i	−0.143935	−	1.00109i
$850$	−0.427267			−0.0146551
$851$	−36.9064	+	42.3374i	−1.26513	+	1.45131i
$852$	1.57946			0.0541115
$853$	0.686682	+	4.77598i	0.0235115	+	0.163526i	0.998194	−	0.0600653i	$-0.0191309\pi$
$853$	0.686682	+	4.77598i	0.0235115	+	0.163526i	−0.974683	+	0.223592i	$0.928222\pi$
$854$	3.10422	−	6.79729i	0.106224	−	0.232598i
$855$	5.15513	−	1.51368i	0.176302	−	0.0517668i
$856$	3.59461	−	4.14840i	0.122861	−	0.141790i
$857$	−29.9759	−	8.80171i	−1.02396	−	0.300661i	−0.273705	−	0.961814i	$-0.588249\pi$
$857$	−29.9759	−	8.80171i	−1.02396	−	0.300661i	−0.750251	+	0.661153i	$0.770067\pi$
$858$	−4.10815	+	2.64015i	−0.140250	+	0.0901332i
$859$	−13.4631	−	29.4800i	−0.459354	−	1.00585i	−0.987634	−	0.156775i	$-0.949890\pi$
$859$	−13.4631	−	29.4800i	−0.459354	−	1.00585i	0.528280	−	0.849070i	$-0.322837\pi$
$860$	6.02597	+	6.95434i	0.205484	+	0.237141i
$861$	2.75599	+	1.77117i	0.0939240	+	0.0603613i
$862$	2.03698	−	14.1675i	0.0693798	−	0.482547i
$863$	−0.412917	+	2.87190i	−0.0140559	+	0.0977606i	−0.995642	−	0.0932609i	$-0.970271\pi$
$863$	−0.412917	+	2.87190i	−0.0140559	+	0.0977606i	0.981586	+	0.191022i	$0.0611800\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	7.42148	+	8.56485i	0.252338	+	0.291214i
$866$	−3.99812	−	8.75465i	−0.135862	−	0.297495i
$867$	14.2937	−	9.18602i	0.485440	−	0.311973i
$868$	2.73157	+	0.802062i	0.0927156	+	0.0272238i
$869$	19.2063	−	22.1652i	0.651529	−	0.751905i
$870$	−2.33939	+	0.686908i	−0.0793128	+	0.0232884i
$871$	−1.75712	+	3.84755i	−0.0595376	+	0.130369i
$872$	0.906111	+	6.30214i	0.0306848	+	0.213417i
$873$	2.63534			0.0891928
$874$	30.6704	−	19.5821i	1.03744	−	0.662375i
$875$	6.72597			0.227379
$876$	−0.401013	−	2.78911i	−0.0135490	−	0.0942352i
$877$	11.7665	−	25.7650i	0.397326	−	0.870022i	−0.600209	−	0.799844i	$-0.704916\pi$
$877$	11.7665	−	25.7650i	0.397326	−	0.870022i	0.997534	−	0.0701788i	$-0.0223570\pi$
$878$	−8.34922	+	2.45155i	−0.281772	+	0.0827359i
$879$	14.6564	−	16.9144i	0.494349	−	0.570510i
$880$	2.15655	+	0.633220i	0.0726973	+	0.0213458i
$881$	−0.423229	+	0.271992i	−0.0142589	+	0.00916366i	−0.547751	−	0.836641i	$-0.684516\pi$
$881$	−0.423229	+	0.271992i	−0.0142589	+	0.00916366i	0.533492	+	0.845805i	$0.320879\pi$
$882$	0.415415	+	0.909632i	0.0139878	+	0.0306289i
$883$	−13.5675	−	15.6577i	−0.456581	−	0.526923i	0.480049	−	0.877241i	$-0.340619\pi$
$883$	−13.5675	−	15.6577i	−0.456581	−	0.526923i	−0.936631	+	0.350319i	$0.886073\pi$
$884$	−0.122927	−	0.0790005i	−0.00413449	−	0.00265707i
$885$	0.533290	−	3.70911i	0.0179263	−	0.124680i
$886$	−2.79969	+	19.4722i	−0.0940573	+	0.654183i
$887$	−2.62507	−	1.68703i	−0.0881412	−	0.0566449i	0.495828	−	0.868421i	$-0.334865\pi$
$887$	−2.62507	−	1.68703i	−0.0881412	−	0.0566449i	−0.583969	+	0.811776i	$0.698501\pi$
$888$	−7.66925	−	8.85078i	−0.257363	−	0.297013i
$889$	−7.93538	−	17.3760i	−0.266144	−	0.582774i
$890$	10.6619	−	6.85198i	0.357387	−	0.229679i
$891$	3.04553	+	0.894250i	0.102029	+	0.0299585i
$892$	−7.75099	+	8.94512i	−0.259523	+	0.299505i
$893$	0.361220	−	0.106064i	0.0120878	−	0.00354929i
$894$	−8.30368	+	18.1825i	−0.277717	+	0.608114i
$895$	0.189671	+	1.31919i	0.00634002	+	0.0440958i
$896$	−1.00000			−0.0334077
$897$	4.81523	+	5.59055i	0.160776	+	0.186663i
$898$	−29.9710			−1.00014
$899$	1.39504	+	9.70271i	0.0465272	+	0.323604i
$900$	−1.86878	+	4.09206i	−0.0622927	+	0.136402i
$901$	−0.803021	+	0.235788i	−0.0267525	+	0.00785524i
$902$	6.80961	−	7.85870i	0.226735	−	0.261666i
$903$	12.4688	+	3.66116i	0.414935	+	0.121836i
$904$	16.6838	−	10.7220i	0.554895	−	0.356609i
$905$	−5.12911	−	11.2312i	−0.170497	−	0.373337i
$906$	−4.16328	−	4.80468i	−0.138316	−	0.159625i
$907$	−13.3815	−	8.59977i	−0.444325	−	0.285551i	0.299285	−	0.954164i	$-0.403252\pi$
$907$	−13.3815	−	8.59977i	−0.444325	−	0.285551i	−0.743610	+	0.668613i	$0.766888\pi$
$908$	3.84254	−	26.7255i	0.127519	−	0.886916i
$909$	−1.77514	+	12.3464i	−0.0588777	+	0.409503i
$910$	0.916475	+	0.588983i	0.0303809	+	0.0195246i
$911$	34.8139	+	40.1773i	1.15343	+	1.33113i	0.934736	+	0.355342i	$0.115636\pi$
$911$	34.8139	+	40.1773i	1.15343	+	1.33113i	0.218699	+	0.975792i	$0.429819\pi$
$912$	3.15198	+	6.90188i	0.104373	+	0.228544i
$913$	11.5188	−	7.40265i	0.381215	−	0.244992i
$914$	−37.4830	−	11.0060i	−1.23983	−	0.364046i
$915$	−3.46509	+	3.99893i	−0.114552	+	0.132200i
$916$	−5.54738	+	1.62886i	−0.183291	+	0.0538190i
$917$	−6.01120	+	13.1627i	−0.198507	+	0.434670i
$918$	0.0135168	+	0.0940112i	0.000446120	+	0.00310283i
$919$	−4.34048			−0.143179			−0.0715897	−	0.997434i	$-0.522807\pi$
$919$	−4.34048			−0.143179			−0.0715897	+	0.997434i	$0.522807\pi$
$920$	0.493279	−	3.35992i	0.0162629	−	0.110773i
$921$	15.5566			0.512607
$922$	0.231017	+	1.60676i	0.00760815	+	0.0529158i
$923$	1.00946	−	2.21041i	0.0332268	−	0.0727566i
$924$	3.04553	−	0.894250i	0.100191	−	0.0294187i
$925$	−34.5008	+	39.8160i	−1.13438	+	1.30914i
$926$	−18.2946	−	5.37176i	−0.601196	−	0.176527i
$927$	10.7475	−	6.90698i	0.352993	−	0.226855i
$928$	−1.43037	−	3.13207i	−0.0469541	−	0.102815i
$929$	−21.4733	−	24.7815i	−0.704516	−	0.813055i	0.284839	−	0.958575i	$-0.408060\pi$
$929$	−21.4733	−	24.7815i	−0.704516	−	0.813055i	−0.989355	+	0.145521i	$0.953514\pi$
$930$	−1.69587	−	1.08987i	−0.0556099	−	0.0357383i
$931$	1.07982	−	7.51032i	0.0353897	−	0.246141i
$932$	−3.56033	+	24.7627i	−0.116623	+	0.811128i
$933$	−0.659159	−	0.423616i	−0.0215799	−	0.0138686i
$934$	4.98172	+	5.74921i	0.163007	+	0.188120i
$935$	−0.0886794	−	0.194181i	−0.00290013	−	0.00635039i
$936$	−1.29427	+	0.831777i	−0.0423045	+	0.0271875i
$937$	19.5520	+	5.74099i	0.638737	+	0.187550i	0.585036	−	0.811007i	$-0.301080\pi$
$937$	19.5520	+	5.74099i	0.638737	+	0.187550i	0.0537003	+	0.998557i	$0.482898\pi$
$938$	1.80040	−	2.07777i	0.0587851	−	0.0678417i
$939$	25.6139	−	7.52091i	0.835877	−	0.245436i
$940$	0.0145951	−	0.0319587i	0.000476039	−	0.00104238i
$941$	8.30252	+	57.7453i	0.270654	+	1.88244i	0.441676	+	0.897175i	$0.354384\pi$
$941$	8.30252	+	57.7453i	0.270654	+	1.88244i	−0.171022	+	0.985267i	$0.554707\pi$
$942$	11.7584			0.383109
$943$	−13.1920	−	8.53347i	−0.429590	−	0.277888i
$944$	5.29197			0.172239
$945$	−0.100773	−	0.700895i	−0.00327816	−	0.0228001i
$946$	17.1351	−	37.5206i	0.557110	−	1.21990i
$947$	−4.73082	+	1.38909i	−0.153731	+	0.0451395i	−0.357693	−	0.933839i	$-0.616436\pi$
$947$	−4.73082	+	1.38909i	−0.153731	+	0.0451395i	0.203962	+	0.978979i	$0.434618\pi$
$948$	6.05093	−	6.98314i	0.196525	−	0.226802i
$949$	−4.15957	−	1.22136i	−0.135025	−	0.0396470i
$950$	28.7148	−	18.4539i	0.931630	−	0.598722i
$951$	−10.5014	−	22.9949i	−0.340532	−	0.745662i
$952$	0.0621973	+	0.0717795i	0.00201583	+	0.00232639i
$953$	−16.6105	−	10.6749i	−0.538067	−	0.345795i	0.243215	−	0.969972i	$-0.421798\pi$
$953$	−16.6105	−	10.6749i	−0.538067	−	0.345795i	−0.781283	+	0.624177i	$0.785434\pi$
$954$	−1.25404	+	8.72206i	−0.0406011	+	0.282387i
$955$	−0.0132796	+	0.0923619i	−0.000429719	+	0.00298876i
$956$	−16.5517	−	10.6371i	−0.535321	−	0.344030i
$957$	7.15708	+	8.25972i	0.231356	+	0.266999i
$958$	−1.80461	−	3.95154i	−0.0583043	−	0.127669i
$959$	−4.11225	+	2.64278i	−0.132791	+	0.0853399i
$960$	0.679419	+	0.199495i	0.0219282	+	0.00643869i
$961$	14.9932	−	17.3030i	0.483651	−	0.558163i
$962$	−17.2879	+	5.07620i	−0.557386	+	0.163663i
$963$	−2.28026	+	4.99308i	−0.0734805	+	0.160900i
$964$	−3.65669	−	25.4328i	−0.117774	−	0.819136i
$965$	−2.91443			−0.0938188
$966$	−1.97929	−	4.36834i	−0.0636826	−	0.140549i
$967$	−12.1878			−0.391933			−0.195966	−	0.980611i	$-0.562784\pi$
$967$	−12.1878			−0.391933			−0.195966	+	0.980611i	$0.562784\pi$
$968$	0.131647	+	0.915622i	0.00423128	+	0.0294292i
$969$	0.299369	−	0.655527i	0.00961712	−	0.0210586i
$970$	−1.79050	+	0.525738i	−0.0574895	+	0.0168804i
$971$	−0.990575	+	1.14318i	−0.0317890	+	0.0366865i	−0.771421	−	0.636325i	$-0.780454\pi$
$971$	−0.990575	+	1.14318i	−0.0317890	+	0.0366865i	0.739632	+	0.673011i	$0.234999\pi$
$972$	0.959493	+	0.281733i	0.0307758	+	0.00903658i
$973$	−5.29238	+	3.40120i	−0.169666	+	0.109038i
$974$	0.657641	+	1.44003i	0.0210722	+	0.0461417i
$975$	4.53235	+	5.23061i	0.145151	+	0.167514i
$976$	−6.28632	−	4.03997i	−0.201220	−	0.129316i
$977$	−3.75189	+	26.0950i	−0.120034	+	0.834852i	0.837481	+	0.546467i	$0.184028\pi$
$977$	−3.75189	+	26.0950i	−0.120034	+	0.834852i	−0.957514	+	0.288385i	$0.906882\pi$
$978$	−0.0244670	+	0.170172i	−0.000782368	+	0.00544149i
$979$	−47.7925	−	30.7144i	−1.52746	−	0.981637i
$980$	−0.463708	−	0.535148i	−0.0148126	−	0.0170947i
$981$	−2.64493	−	5.79158i	−0.0844460	−	0.184911i
$982$	−8.54822	+	5.49361i	−0.272785	+	0.175308i
$983$	−8.03568	−	2.35949i	−0.256298	−	0.0752560i	0.151059	−	0.988525i	$-0.451732\pi$
$983$	−8.03568	−	2.35949i	−0.256298	−	0.0752560i	−0.407358	+	0.913269i	$0.633550\pi$
$984$	2.14536	−	2.47588i	0.0683916	−	0.0789281i
$985$	−6.24969	+	1.83507i	−0.199132	+	0.0584703i
$986$	−0.135853	+	0.297477i	−0.00432645	+	0.00947361i
$987$	−0.00706120	−	0.0491117i	−0.000224760	−	0.00156324i
$988$	11.6735			0.371382
$989$	−59.7457	−	17.7359i	−1.89980	−	0.563970i
$990$	−2.24759			−0.0714332
$991$	−4.78636	−	33.2899i	−0.152044	−	1.05749i	−0.912788	−	0.408435i	$-0.866075\pi$
$991$	−4.78636	−	33.2899i	−0.152044	−	1.05749i	0.760744	−	0.649052i	$-0.224834\pi$
$992$	1.18264	−	2.58962i	0.0375489	−	0.0822206i
$993$	−6.90902	+	2.02867i	−0.219251	+	0.0643779i
$994$	−1.03433	+	1.19368i	−0.0328069	+	0.0378612i
$995$	14.9859	+	4.40026i	0.475085	+	0.139498i
$996$	3.62897	−	2.33220i	0.114988	−	0.0738986i
$997$	−12.6593	−	27.7200i	−0.400924	−	0.877902i	−0.997176	−	0.0751041i	$-0.976071\pi$
$997$	−12.6593	−	27.7200i	−0.400924	−	0.877902i	0.596251	−	0.802798i	$-0.296656\pi$
$998$	9.73460	+	11.2343i	0.308143	+	0.355616i
$999$	9.85214	+	6.33159i	0.311708	+	0.200323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.j.463.2	yes	40
23.8	even	11	inner	966.2.q.j.169.2	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.j.169.2	✓	40	23.8	even	11	inner
966.2.q.j.463.2	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.463708 + 0.535148i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-0.463708 + 0.535148i) q^{5} +(0.959493 + 0.281733i) q^{6} +(-0.841254 + 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(0.595693 + 0.382829i) q^{10} +(0.451723 - 3.14180i) q^{11} +(0.142315 - 0.989821i) q^{12} +(-1.29427 - 0.831777i) q^{13} +(0.654861 + 0.755750i) q^{14} +(-0.294156 - 0.644112i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-0.0911307 - 0.0267584i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(7.28021 - 2.13766i) q^{19} +(0.294156 - 0.644112i) q^{20} +(-0.142315 - 0.989821i) q^{21} -3.17411 q^{22} +(0.668409 + 4.74902i) q^{23} -1.00000 q^{24} +(0.640216 + 4.45280i) q^{25} +(-0.639117 + 1.39947i) q^{26} +(0.959493 - 0.281733i) q^{27} +(0.654861 - 0.755750i) q^{28} +(3.30375 + 0.970069i) q^{29} +(-0.595693 + 0.382829i) q^{30} +(1.18264 + 2.58962i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(2.67023 + 1.71605i) q^{33} +(-0.0135168 + 0.0940112i) q^{34} +(0.100773 - 0.700895i) q^{35} +(0.841254 + 0.540641i) q^{36} +(7.66925 + 8.85078i) q^{37} +(-3.15198 - 6.90188i) q^{38} +(1.29427 - 0.831777i) q^{39} +(-0.679419 - 0.199495i) q^{40} +(-2.14536 + 2.47588i) q^{41} +(-0.959493 + 0.281733i) q^{42} +(-5.39839 + 11.8208i) q^{43} +(0.451723 + 3.14180i) q^{44} +0.708102 q^{45} +(4.60556 - 1.33746i) q^{46} +0.0496167 q^{47} +(0.142315 + 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(4.31637 - 1.26740i) q^{50} +(0.0621973 - 0.0717795i) q^{51} +(1.47618 + 0.433446i) q^{52} +(7.41291 - 4.76399i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(1.47186 + 1.69862i) q^{55} +(-0.841254 - 0.540641i) q^{56} +(-1.07982 + 7.51032i) q^{57} +(0.490022 - 3.40818i) q^{58} +(4.45189 + 2.86106i) q^{59} +(0.463708 + 0.535148i) q^{60} +(-3.10422 - 6.79729i) q^{61} +(2.39496 - 1.53915i) q^{62} +(0.959493 + 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(1.04529 - 0.306924i) q^{65} +(1.31857 - 2.88727i) q^{66} +(-0.391264 - 2.72130i) q^{67} +0.0949780 q^{68} +(-4.59753 - 1.36481i) q^{69} -0.708102 q^{70} +(0.224781 + 1.56339i) q^{71} +(0.415415 - 0.909632i) q^{72} +(2.70365 - 0.793862i) q^{73} +(7.66925 - 8.85078i) q^{74} +(-4.31637 - 1.26740i) q^{75} +(-6.38306 + 4.10214i) q^{76} +(1.31857 + 2.88727i) q^{77} +(-1.00750 - 1.16272i) q^{78} +(7.77320 + 4.99553i) q^{79} +(-0.100773 + 0.700895i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(2.75599 + 1.77117i) q^{82} +(2.82492 + 3.26013i) q^{83} +(0.415415 + 0.909632i) q^{84} +(0.0565777 - 0.0363603i) q^{85} +(12.4688 + 3.66116i) q^{86} +(-2.25483 + 2.60222i) q^{87} +(3.04553 - 0.894250i) q^{88} +(7.43522 - 16.2809i) q^{89} +(-0.100773 - 0.700895i) q^{90} +1.53850 q^{91} +(-1.97929 - 4.36834i) q^{92} -2.84689 q^{93} +(-0.00706120 - 0.0491117i) q^{94} +(-2.23193 + 4.88724i) q^{95} +(0.959493 - 0.281733i) q^{96} +(-1.72578 + 1.99166i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-2.67023 + 1.71605i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9}+O(q^{10}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9	\( 40 q - 4 q^{2} + 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 4 q^{7} - 4 q^{8} - 4 q^{9} - 4 q^{10} - 11 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{14} - 7 q^{15} - 4 q^{16} + 5 q^{17} - 4 q^{18} + 44 q^{19} + 7 q^{20} - 4 q^{21} + 22 q^{22} - 6 q^{23} - 40 q^{24} + 2 q^{25} + 24 q^{26} + 4 q^{27} + 4 q^{28} + 35 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 11 q^{33} + 5 q^{34} - 7 q^{35} - 4 q^{36} + 20 q^{37} - 11 q^{38} + 20 q^{39} - 4 q^{40} + 11 q^{41} - 4 q^{42} - 42 q^{43} - 11 q^{44} - 4 q^{45} - 6 q^{46} + 40 q^{47} + 4 q^{48} - 4 q^{49} - 53 q^{50} + 17 q^{51} - 9 q^{52} - 32 q^{53} + 4 q^{54} + 29 q^{55} + 4 q^{56} - 11 q^{57} - 31 q^{58} - 25 q^{59} + 4 q^{60} - 30 q^{61} - 24 q^{62} + 4 q^{63} - 4 q^{64} + 80 q^{65} - 88 q^{67} - 28 q^{68} + 6 q^{69} + 4 q^{70} - 45 q^{71} - 4 q^{72} - 39 q^{73} + 20 q^{74} + 53 q^{75} - 22 q^{76} - 2 q^{78} + 26 q^{79} + 7 q^{80} - 4 q^{81} + 22 q^{83} - 4 q^{84} + 77 q^{85} - 31 q^{86} + 9 q^{87} - 11 q^{88} + 20 q^{89} + 7 q^{90} - 24 q^{91} - 17 q^{92} - 42 q^{93} - 26 q^{94} + 84 q^{95} + 4 q^{96} + 74 q^{97} - 4 q^{98} + 11 q^{99}+O(q^{100}) \) 40 * q - 4 * q^2 + 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 4 * q^7 - 4 * q^8 - 4 * q^9 - 4 * q^10 - 11 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^14 - 7 * q^15 - 4 * q^16 + 5 * q^17 - 4 * q^18 + 44 * q^19 + 7 * q^20 - 4 * q^21 + 22 * q^22 - 6 * q^23 - 40 * q^24 + 2 * q^25 + 24 * q^26 + 4 * q^27 + 4 * q^28 + 35 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 11 * q^33 + 5 * q^34 - 7 * q^35 - 4 * q^36 + 20 * q^37 - 11 * q^38 + 20 * q^39 - 4 * q^40 + 11 * q^41 - 4 * q^42 - 42 * q^43 - 11 * q^44 - 4 * q^45 - 6 * q^46 + 40 * q^47 + 4 * q^48 - 4 * q^49 - 53 * q^50 + 17 * q^51 - 9 * q^52 - 32 * q^53 + 4 * q^54 + 29 * q^55 + 4 * q^56 - 11 * q^57 - 31 * q^58 - 25 * q^59 + 4 * q^60 - 30 * q^61 - 24 * q^62 + 4 * q^63 - 4 * q^64 + 80 * q^65 - 88 * q^67 - 28 * q^68 + 6 * q^69 + 4 * q^70 - 45 * q^71 - 4 * q^72 - 39 * q^73 + 20 * q^74 + 53 * q^75 - 22 * q^76 - 2 * q^78 + 26 * q^79 + 7 * q^80 - 4 * q^81 + 22 * q^83 - 4 * q^84 + 77 * q^85 - 31 * q^86 + 9 * q^87 - 11 * q^88 + 20 * q^89 + 7 * q^90 - 24 * q^91 - 17 * q^92 - 42 * q^93 - 26 * q^94 + 84 * q^95 + 4 * q^96 + 74 * q^97 - 4 * q^98 + 11 * q^99

Introduction

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