LMFDB - Embedded newform 111.2.o.a.28.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,2,Mod(4,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("111.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	111.o (of order $18$, degree $6$, 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:	$0.886339462436$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	12.0.15342238784889.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 12x^{10} + 48x^{8} + 77x^{6} + 48x^{4} + 12x^{2} + 1 $ x^12 + 12x^10 + 48x^8 + 77x^6 + 48x^4 + 12*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			28.1
Root			$-0.545983i$ of defining polynomial
Character	$\chi$	$=$	111.28
Dual form			111.2.o.a.4.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.537688 + 0.0948090i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(-1.59927 + 0.582085i) q^{4} +(-1.80373 + 2.14961i) q^{5} -0.545983i q^{6} +(-3.69621 - 3.10149i) q^{7} +(1.75039 - 1.01059i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})$	\(q+(-0.537688 + 0.0948090i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(-1.59927 + 0.582085i) q^{4} +(-1.80373 + 2.14961i) q^{5} -0.545983i q^{6} +(-3.69621 - 3.10149i) q^{7} +(1.75039 - 1.01059i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.766044 - 1.32683i) q^{10} +(2.52952 + 4.38126i) q^{11} +(-0.295532 - 1.67605i) q^{12} +(1.28368 + 3.52688i) q^{13} +(2.28146 + 1.31720i) q^{14} +(-1.80373 - 2.14961i) q^{15} +(1.76211 - 1.47859i) q^{16} +(-1.35792 + 3.73084i) q^{17} +(0.537688 + 0.0948090i) q^{18} +(0.0176348 + 0.00310950i) q^{19} +(1.63339 - 4.48771i) q^{20} +(3.69621 - 3.10149i) q^{21} +(-1.77548 - 2.11593i) q^{22} +(-1.30435 - 0.753069i) q^{23} +(0.691283 + 1.89928i) q^{24} +(-0.499109 - 2.83059i) q^{25} +(-1.02460 - 1.77466i) q^{26} +(0.500000 - 0.866025i) q^{27} +(7.71654 + 2.80859i) q^{28} +(0.267425 - 0.154398i) q^{29} +(1.17365 + 0.984808i) q^{30} +0.389915i q^{31} +(-3.40566 + 4.05871i) q^{32} +(-4.75395 + 1.73030i) q^{33} +(0.376418 - 2.13477i) q^{34} +(13.3339 - 2.35113i) q^{35} +1.70190 q^{36} +(-1.48422 - 5.89891i) q^{37} -0.00977686 q^{38} +(-3.69621 + 0.651741i) q^{39} +(-0.984871 + 5.58548i) q^{40} +(-5.97342 + 2.17415i) q^{41} +(-1.69336 + 2.01807i) q^{42} -2.06301i q^{43} +(-6.59565 - 5.53440i) q^{44} +(2.43016 - 1.40306i) q^{45} +(0.772733 + 0.281252i) q^{46} +(4.05109 - 7.01669i) q^{47} +(1.15014 + 1.99210i) q^{48} +(2.82719 + 16.0338i) q^{49} +(0.536730 + 1.47465i) q^{50} +(-3.43836 - 1.98514i) q^{51} +(-4.10589 - 4.89321i) q^{52} +(-3.48258 + 2.92223i) q^{53} +(-0.186737 + 0.513056i) q^{54} +(-13.9806 - 2.46515i) q^{55} +(-9.60413 - 1.69347i) q^{56} +(-0.00612451 + 0.0168270i) q^{57} +(-0.129153 + 0.108372i) q^{58} +(4.86717 + 5.80047i) q^{59} +(4.13590 + 2.38786i) q^{60} +(4.15675 + 11.4206i) q^{61} +(-0.0369674 - 0.209653i) q^{62} +(2.41253 + 4.17862i) q^{63} +(-0.853895 + 1.47899i) q^{64} +(-9.89681 - 3.60215i) q^{65} +(2.39210 - 1.38108i) q^{66} +(8.23757 + 6.91214i) q^{67} -6.75703i q^{68} +(0.968127 - 1.15377i) q^{69} +(-6.94660 + 2.52835i) q^{70} +(-0.262423 + 1.48827i) q^{71} +(-1.99047 + 0.350974i) q^{72} -4.55321 q^{73} +(1.35732 + 3.03106i) q^{74} +2.87425 q^{75} +(-0.0300128 + 0.00529206i) q^{76} +(4.23878 - 24.0393i) q^{77} +(1.92562 - 0.700867i) q^{78} +(8.84365 - 10.5395i) q^{79} +6.45483i q^{80} +(0.766044 + 0.642788i) q^{81} +(3.00571 - 1.73535i) q^{82} +(-4.41933 - 1.60850i) q^{83} +(-4.10589 + 7.11160i) q^{84} +(-5.57052 - 9.64843i) q^{85} +(0.195592 + 1.10926i) q^{86} +(0.105614 + 0.290173i) q^{87} +(8.85531 + 5.11261i) q^{88} +(7.73007 + 9.21234i) q^{89} +(-1.17365 + 0.984808i) q^{90} +(6.19382 - 17.0174i) q^{91} +(2.52436 + 0.445112i) q^{92} +(-0.383991 - 0.0677080i) q^{93} +(-1.51298 + 4.15687i) q^{94} +(-0.0384927 + 0.0322992i) q^{95} +(-3.40566 - 4.05871i) q^{96} +(-2.23826 - 1.29226i) q^{97} +(-3.04030 - 8.35315i) q^{98} +(-0.878494 - 4.98219i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8}+O(q^{10}) $ 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8	$ 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8} - 6 q^{11} - 6 q^{12} - 6 q^{13} + 27 q^{14} - 3 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 12 q^{19} + 9 q^{20} + 6 q^{21} - 21 q^{22} - 6 q^{24} - 15 q^{25} + 6 q^{27} + 39 q^{28} + 27 q^{29} + 12 q^{30} - 33 q^{32} - 12 q^{33} + 15 q^{34} + 36 q^{35} + 15 q^{37} - 48 q^{38} - 6 q^{39} + 15 q^{40} + 12 q^{41} + 18 q^{42} - 21 q^{44} - 15 q^{46} + 9 q^{47} - 18 q^{49} - 18 q^{50} + 9 q^{51} + 6 q^{52} - 12 q^{53} - 3 q^{54} - 39 q^{55} - 18 q^{56} - 3 q^{57} - 15 q^{58} - 15 q^{61} + 39 q^{62} + 12 q^{63} - 9 q^{64} - 24 q^{65} + 18 q^{66} + 6 q^{67} - 12 q^{69} - 15 q^{70} - 3 q^{71} - 6 q^{72} + 90 q^{73} + 72 q^{74} - 24 q^{75} - 6 q^{76} + 27 q^{77} + 9 q^{78} + 6 q^{79} + 27 q^{82} - 3 q^{83} + 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{87} + 63 q^{88} + 39 q^{89} - 12 q^{90} - 27 q^{91} + 6 q^{92} - 24 q^{93} + 30 q^{94} - 36 q^{95} - 33 q^{96} - 18 q^{97} - 42 q^{98} + 3 q^{99}+O(q^{100}) $ 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8 - 6 * q^11 - 6 * q^12 - 6 * q^13 + 27 * q^14 - 3 * q^15 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 12 * q^19 + 9 * q^20 + 6 * q^21 - 21 * q^22 - 6 * q^24 - 15 * q^25 + 6 * q^27 + 39 * q^28 + 27 * q^29 + 12 * q^30 - 33 * q^32 - 12 * q^33 + 15 * q^34 + 36 * q^35 + 15 * q^37 - 48 * q^38 - 6 * q^39 + 15 * q^40 + 12 * q^41 + 18 * q^42 - 21 * q^44 - 15 * q^46 + 9 * q^47 - 18 * q^49 - 18 * q^50 + 9 * q^51 + 6 * q^52 - 12 * q^53 - 3 * q^54 - 39 * q^55 - 18 * q^56 - 3 * q^57 - 15 * q^58 - 15 * q^61 + 39 * q^62 + 12 * q^63 - 9 * q^64 - 24 * q^65 + 18 * q^66 + 6 * q^67 - 12 * q^69 - 15 * q^70 - 3 * q^71 - 6 * q^72 + 90 * q^73 + 72 * q^74 - 24 * q^75 - 6 * q^76 + 27 * q^77 + 9 * q^78 + 6 * q^79 + 27 * q^82 - 3 * q^83 + 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^87 + 63 * q^88 + 39 * q^89 - 12 * q^90 - 27 * q^91 + 6 * q^92 - 24 * q^93 + 30 * q^94 - 36 * q^95 - 33 * q^96 - 18 * q^97 - 42 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−0.537688	+	0.0948090i	−0.380203	+	0.0670401i	−0.360484	−	0.932765i	$-0.617388\pi$
$2$	−0.537688	+	0.0948090i	−0.380203	+	0.0670401i	−0.0197194	+	0.999806i	$0.506277\pi$
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$3$	−0.173648	+	0.984808i	−0.100256	+	0.568579i
$4$	−1.59927	+	0.582085i	−0.799633	+	0.291042i
$5$	−1.80373	+	2.14961i	−0.806654	+	0.961333i	−0.999803	−	0.0198367i	$-0.993685\pi$
$5$	−1.80373	+	2.14961i	−0.806654	+	0.961333i	0.193149	+	0.981169i	$0.438130\pi$
$6$		−	0.545983i		−	0.222897i
$7$	−3.69621	−	3.10149i	−1.39703	−	1.17225i	−0.962397	−	0.271646i	$-0.912432\pi$
$7$	−3.69621	−	3.10149i	−1.39703	−	1.17225i	−0.434638	−	0.900605i	$-0.643124\pi$
$8$	1.75039	−	1.01059i	0.618856	−	0.357297i
$9$	−0.939693	−	0.342020i	−0.313231	−	0.114007i
$10$	0.766044	−	1.32683i	0.242245	−	0.419580i
$11$	2.52952	+	4.38126i	0.762680	+	1.32100i	0.941464	+	0.337112i	$0.109450\pi$
$11$	2.52952	+	4.38126i	0.762680	+	1.32100i	−0.178784	+	0.983888i	$0.557216\pi$
$12$	−0.295532	−	1.67605i	−0.0853128	−	0.483833i
$13$	1.28368	+	3.52688i	0.356029	+	0.978180i	0.980394	+	0.197048i	$0.0631355\pi$
$13$	1.28368	+	3.52688i	0.356029	+	0.978180i	−0.624365	+	0.781133i	$0.714642\pi$
$14$	2.28146	+	1.31720i	0.609745	+	0.352036i
$15$	−1.80373	−	2.14961i	−0.465722	−	0.555026i
$16$	1.76211	−	1.47859i	0.440529	−	0.369647i
$17$	−1.35792	+	3.73084i	−0.329343	+	0.904862i	0.658935	+	0.752200i	$0.271007\pi$
$17$	−1.35792	+	3.73084i	−0.329343	+	0.904862i	−0.988278	+	0.152663i	$0.951215\pi$
$18$	0.537688	+	0.0948090i	0.126734	+	0.0223467i
$19$	0.0176348	+	0.00310950i	0.00404571	+	0.000713368i	0.175671	−	0.984449i	$-0.443791\pi$
$19$	0.0176348	+	0.00310950i	0.00404571	+	0.000713368i	−0.171625	+	0.985162i	$0.554902\pi$
$20$	1.63339	−	4.48771i	0.365238	−	1.00348i
$21$	3.69621	−	3.10149i	0.806579	−	0.676800i
$22$	−1.77548	−	2.11593i	−0.378533	−	0.451118i
$23$	−1.30435	−	0.753069i	−0.271977	−	0.157026i	0.357809	−	0.933795i	$-0.383524\pi$
$23$	−1.30435	−	0.753069i	−0.271977	−	0.157026i	−0.629786	+	0.776769i	$0.716857\pi$
$24$	0.691283	+	1.89928i	0.141108	+	0.387690i
$25$	−0.499109	−	2.83059i	−0.0998218	−	0.566118i
$26$	−1.02460	−	1.77466i	−0.200940	−	0.348039i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	7.71654	+	2.80859i	1.45829	+	0.530774i
$29$	0.267425	−	0.154398i	0.0496595	−	0.0286709i	−0.474965	−	0.880005i	$-0.657539\pi$
$29$	0.267425	−	0.154398i	0.0496595	−	0.0286709i	0.524624	+	0.851334i	$0.324206\pi$
$30$	1.17365	+	0.984808i	0.214278	+	0.179800i
$31$			0.389915i			0.0700307i	0.999387	+	0.0350154i	$0.0111480\pi$
$31$			0.389915i			0.0700307i	−0.999387	+	0.0350154i	$0.988852\pi$
$32$	−3.40566	+	4.05871i	−0.602041	+	0.717485i
$33$	−4.75395	+	1.73030i	−0.827556	+	0.301206i
$34$	0.376418	−	2.13477i	0.0645552	−	0.366111i
$35$	13.3339	−	2.35113i	2.25385	−	0.397414i
$36$	1.70190			0.283650
$37$	−1.48422	−	5.89891i	−0.244004	−	0.969774i
$37$	−1.48422	−	5.89891i	−0.244004	−	0.969774i
$38$	−0.00977686			−0.00158602
$39$	−3.69621	+	0.651741i	−0.591867	+	0.104362i
$40$	−0.984871	+	5.58548i	−0.155722	+	0.883142i
$41$	−5.97342	+	2.17415i	−0.932892	+	0.339545i	−0.763355	−	0.645979i	$-0.776449\pi$
$41$	−5.97342	+	2.17415i	−0.932892	+	0.339545i	−0.169537	+	0.985524i	$0.554227\pi$
$42$	−1.69336	+	2.01807i	−0.261291	+	0.311394i
$43$		−	2.06301i		−	0.314606i	−0.987550	−	0.157303i	$-0.949720\pi$
$43$		−	2.06301i		−	0.314606i	0.987550	−	0.157303i	$-0.0502799\pi$
$44$	−6.59565	−	5.53440i	−0.994331	−	0.834343i
$45$	2.43016	−	1.40306i	0.362267	−	0.209155i
$46$	0.772733	+	0.281252i	0.113933	+	0.0414683i
$47$	4.05109	−	7.01669i	0.590912	−	1.02349i	−0.403198	−	0.915113i	$-0.632101\pi$
$47$	4.05109	−	7.01669i	0.590912	−	1.02349i	0.994110	−	0.108377i	$-0.0345653\pi$
$48$	1.15014	+	1.99210i	0.166008	+	0.287535i
$49$	2.82719	+	16.0338i	0.403885	+	2.29055i
$50$	0.536730	+	1.47465i	0.0759051	+	0.208548i
$51$	−3.43836	−	1.98514i	−0.481467	−	0.277975i
$52$	−4.10589	−	4.89321i	−0.569384	−	0.678566i
$53$	−3.48258	+	2.92223i	−0.478369	+	0.401399i	−0.849836	−	0.527047i	$-0.823299\pi$
$53$	−3.48258	+	2.92223i	−0.478369	+	0.401399i	0.371467	+	0.928446i	$0.378855\pi$
$54$	−0.186737	+	0.513056i	−0.0254117	+	0.0698181i
$55$	−13.9806	−	2.46515i	−1.88514	−	0.332401i
$56$	−9.60413	−	1.69347i	−1.28341	−	0.226299i
$57$	−0.00612451	+	0.0168270i	−0.000811212	+	0.00222879i
$58$	−0.129153	+	0.108372i	−0.0169586	+	0.0142300i
$59$	4.86717	+	5.80047i	0.633652	+	0.755157i	0.983353	−	0.181704i	$-0.0581614\pi$
$59$	4.86717	+	5.80047i	0.633652	+	0.755157i	−0.349701	+	0.936861i	$0.613717\pi$
$60$	4.13590	+	2.38786i	0.533942	+	0.308272i
$61$	4.15675	+	11.4206i	0.532217	+	1.46225i	0.856426	+	0.516269i	$0.172680\pi$
$61$	4.15675	+	11.4206i	0.532217	+	1.46225i	−0.324209	+	0.945985i	$0.605098\pi$
$62$	−0.0369674	−	0.209653i	−0.00469487	−	0.0266259i
$63$	2.41253	+	4.17862i	0.303950	+	0.526457i
$64$	−0.853895	+	1.47899i	−0.106737	+	0.184874i
$65$	−9.89681	−	3.60215i	−1.22755	−	0.446791i
$66$	2.39210	−	1.38108i	0.294447	−	0.169999i
$67$	8.23757	+	6.91214i	1.00638	+	0.844452i	0.987855	−	0.155376i	$-0.0496589\pi$
$67$	8.23757	+	6.91214i	1.00638	+	0.844452i	0.0185238	+	0.999828i	$0.494103\pi$
$68$		−	6.75703i		−	0.819410i
$69$	0.968127	−	1.15377i	0.116549	−	0.138897i
$70$	−6.94660	+	2.52835i	−0.830277	+	0.302196i
$71$	−0.262423	+	1.48827i	−0.0311439	+	0.176626i	−0.996412	−	0.0846358i	$-0.973027\pi$
$71$	−0.262423	+	1.48827i	−0.0311439	+	0.176626i	0.965268	+	0.261261i	$0.0841384\pi$
$72$	−1.99047	+	0.350974i	−0.234579	+	0.0413626i
$73$	−4.55321			−0.532913			−0.266456	−	0.963847i	$-0.585853\pi$
$73$	−4.55321			−0.532913			−0.266456	+	0.963847i	$0.585853\pi$
$74$	1.35732	+	3.03106i	0.157785	+	0.352353i
$75$	2.87425			0.331890
$76$	−0.0300128	+	0.00529206i	−0.00344270	+	0.000607041i
$77$	4.23878	−	24.0393i	0.483054	−	2.73954i
$78$	1.92562	−	0.700867i	0.218033	−	0.0793576i
$79$	8.84365	−	10.5395i	0.994988	−	1.18578i	0.0124118	−	0.999923i	$-0.496049\pi$
$79$	8.84365	−	10.5395i	0.994988	−	1.18578i	0.982577	−	0.185858i	$-0.0595065\pi$
$80$			6.45483i			0.721672i
$81$	0.766044	+	0.642788i	0.0851160	+	0.0714208i
$82$	3.00571	−	1.73535i	0.331925	−	0.191637i
$83$	−4.41933	−	1.60850i	−0.485084	−	0.176556i	0.0878889	−	0.996130i	$-0.471988\pi$
$83$	−4.41933	−	1.60850i	−0.485084	−	0.176556i	−0.572973	+	0.819574i	$0.694210\pi$
$84$	−4.10589	+	7.11160i	−0.447989	+	0.775940i
$85$	−5.57052	−	9.64843i	−0.604208	−	1.04652i
$86$	0.195592	+	1.10926i	0.0210912	+	0.119614i
$87$	0.105614	+	0.290173i	0.0113230	+	0.0311098i
$88$	8.85531	+	5.11261i	0.943979	+	0.545006i
$89$	7.73007	+	9.21234i	0.819386	+	0.976506i	0.999975	−	0.00705228i	$-0.00224483\pi$
$89$	7.73007	+	9.21234i	0.819386	+	0.976506i	−0.180589	+	0.983559i	$0.557800\pi$
$90$	−1.17365	+	0.984808i	−0.123713	+	0.103808i
$91$	6.19382	−	17.0174i	0.649289	−	1.78391i
$92$	2.52436	+	0.445112i	0.263182	+	0.0464062i
$93$	−0.383991	−	0.0677080i	−0.0398180	−	0.00702099i
$94$	−1.51298	+	4.15687i	−0.156052	+	0.428749i
$95$	−0.0384927	+	0.0322992i	−0.00394927	+	0.00331383i
$96$	−3.40566	−	4.05871i	−0.347589	−	0.414240i
$97$	−2.23826	−	1.29226i	−0.227261	−	0.131209i	0.382047	−	0.924143i	$-0.375219\pi$
$97$	−2.23826	−	1.29226i	−0.227261	−	0.131209i	−0.609308	+	0.792934i	$0.708553\pi$
$98$	−3.04030	−	8.35315i	−0.307117	−	0.843796i
$99$	−0.878494	−	4.98219i	−0.0882920	−	0.500729i
$100$	2.44585	+	4.23634i	0.244585	+	0.423634i
$101$	−6.72005	+	11.6395i	−0.668670	+	1.15817i	0.309607	+	0.950865i	$0.399803\pi$
$101$	−6.72005	+	11.6395i	−0.668670	+	1.15817i	−0.978276	+	0.207305i	$0.933531\pi$
$102$	2.03698	+	0.741399i	0.201691	+	0.0734095i
$103$	7.56016	−	4.36486i	0.744925	−	0.430083i	−0.0789324	−	0.996880i	$-0.525151\pi$
$103$	7.56016	−	4.36486i	0.744925	−	0.430083i	0.823857	+	0.566797i	$0.191818\pi$
$104$	5.81116	+	4.87614i	0.569831	+	0.478145i
$105$			13.5396i			1.32133i
$106$	1.59549	−	1.90143i	0.154968	−	0.184683i
$107$	−9.53039	+	3.46878i	−0.921337	+	0.335339i	−0.758770	−	0.651358i	$-0.774200\pi$
$107$	−9.53039	+	3.46878i	−0.921337	+	0.335339i	−0.162567	+	0.986698i	$0.551977\pi$
$108$	−0.295532	+	1.67605i	−0.0284376	+	0.161278i
$109$	6.72474	−	1.18575i	0.644113	−	0.113575i	0.157956	−	0.987446i	$-0.449509\pi$
$109$	6.72474	−	1.18575i	0.644113	−	0.113575i	0.486157	+	0.873872i	$0.338398\pi$
$110$	7.75091			0.739020
$111$	6.06702	−	0.437334i	0.575856	−	0.0415099i
$112$	−11.0990			−1.04875
$113$	15.4026	−	2.71589i	1.44895	−	0.255489i	0.606854	−	0.794814i	$-0.292431\pi$
$113$	15.4026	−	2.71589i	1.44895	−	0.255489i	0.842098	+	0.539324i	$0.181320\pi$
$114$	0.00169773	−	0.00962832i	0.000159007	−	0.000901775i
$115$	3.97151	−	1.44551i	0.370345	−	0.134795i
$116$	−0.337810	+	0.402587i	−0.0313649	+	0.0373792i
$117$		−	3.75323i		−	0.346986i
$118$	−3.16696	−	2.65739i	−0.291542	−	0.244633i
$119$	16.5903	−	9.57841i	1.52083	−	0.878052i
$120$	−5.32960	−	1.93982i	−0.486524	−	0.177080i
$121$	−7.29698	+	12.6387i	−0.663362	+	1.14898i
$122$	−3.31781	−	5.74661i	−0.300380	−	0.520274i
$123$	−1.10384	−	6.26021i	−0.0995303	−	0.564464i
$124$	−0.226963	−	0.623577i	−0.0203819	−	0.0559989i
$125$	−5.16591	−	2.98254i	−0.462053	−	0.266766i
$126$	−1.69336	−	2.01807i	−0.150856	−	0.179784i
$127$	−9.89933	+	8.30652i	−0.878423	+	0.737085i	−0.965854	−	0.259086i	$-0.916579\pi$
$127$	−9.89933	+	8.30652i	−0.878423	+	0.737085i	0.0874310	+	0.996171i	$0.472134\pi$
$128$	3.94313	−	10.8337i	0.348527	−	0.957570i
$129$	2.03167	+	0.358238i	0.178878	+	0.0315411i
$130$	5.66292	+	0.998525i	0.496671	+	0.0875765i
$131$	1.14152	−	3.13631i	0.0997354	−	0.274021i	−0.879783	−	0.475376i	$-0.842312\pi$
$131$	1.14152	−	3.13631i	0.0997354	−	0.274021i	0.979518	+	0.201355i	$0.0645344\pi$
$132$	6.59565	−	5.53440i	0.574077	−	0.481708i
$133$	−0.0555380	−	0.0661876i	−0.00481575	−	0.00573919i
$134$	−5.08458	−	2.93558i	−0.439241	−	0.253596i
$135$	0.959746	+	2.63688i	0.0826018	+	0.226947i
$136$	1.39346	+	7.90272i	0.119489	+	0.677653i
$137$	0.444187	+	0.769355i	0.0379495	+	0.0657305i	0.884376	−	0.466775i	$-0.154584\pi$
$137$	0.444187	+	0.769355i	0.0379495	+	0.0657305i	−0.846427	+	0.532505i	$0.821251\pi$
$138$	−0.411163	+	0.712155i	−0.0350005	+	0.0606227i
$139$	−7.04348	−	2.56362i	−0.597420	−	0.217443i	0.0255699	−	0.999673i	$-0.491860\pi$
$139$	−7.04348	−	2.56362i	−0.597420	−	0.217443i	−0.622990	+	0.782230i	$0.714082\pi$
$140$	−19.9559	+	11.5216i	−1.68659	+	0.973751i
$141$	6.20663	+	5.20798i	0.522692	+	0.438591i
$142$		−	0.825108i		−	0.0692415i
$143$	−12.2051	+	14.5455i	−1.02064	+	1.21635i
$144$	−2.16155	+	0.786741i	−0.180129	+	0.0655617i
$145$	−0.150469	+	0.853349i	−0.0124957	+	0.0708668i
$146$	2.44821	−	0.431685i	0.202615	−	0.0357265i
$147$	−16.2812			−1.34285
$148$	5.80732	+	8.56998i	0.477359	+	0.704448i
$149$	−0.468601			−0.0383893			−0.0191947	−	0.999816i	$-0.506110\pi$
$149$	−0.468601			−0.0383893			−0.0191947	+	0.999816i	$0.506110\pi$
$150$	−1.54545	+	0.272505i	−0.126186	+	0.0222500i
$151$	2.69837	−	15.3032i	0.219590	−	1.24536i	−0.653171	−	0.757210i	$-0.726562\pi$
$151$	2.69837	−	15.3032i	0.219590	−	1.24536i	0.872761	−	0.488147i	$-0.162327\pi$
$152$	0.0340103	−	0.0123787i	0.00275860	−	0.00100405i
$153$	2.55205	−	3.04141i	0.206321	−	0.245884i
$154$			13.3275i			1.07396i
$155$	−0.838163	−	0.703302i	−0.0673228	−	0.0564906i
$156$	5.53185	−	3.19381i	0.442902	−	0.255710i
$157$	4.38721	+	1.59681i	0.350138	+	0.127440i	0.511101	−	0.859521i	$-0.329238\pi$
$157$	4.38721	+	1.59681i	0.350138	+	0.127440i	−0.160963	+	0.986960i	$0.551460\pi$
$158$	−3.75589	+	6.50540i	−0.298803	+	0.517542i
$159$	−2.27309	−	3.93711i	−0.180268	−	0.312233i
$160$	−2.58172	−	14.6416i	−0.204103	−	1.15752i
$161$	2.48553	+	6.82893i	0.195887	+	0.538195i
$162$	−0.472835	−	0.272992i	−0.0371494	−	0.0214482i
$163$	−8.50206	−	10.1324i	−0.665932	−	0.793627i	0.322292	−	0.946640i	$-0.395547\pi$
$163$	−8.50206	−	10.1324i	−0.665932	−	0.793627i	−0.988224	+	0.153013i	$0.951102\pi$
$164$	8.28755	−	6.95408i	0.647149	−	0.543022i
$165$	4.85540	−	13.3401i	0.377992	−	1.03853i
$166$	2.52872	+	0.445882i	0.196267	+	0.0346072i
$167$	−5.77491	−	1.01827i	−0.446876	−	0.0787963i	−0.0543182	−	0.998524i	$-0.517299\pi$
$167$	−5.77491	−	1.01827i	−0.446876	−	0.0787963i	−0.392558	+	0.919727i	$0.628410\pi$
$168$	3.33548	−	9.16415i	0.257338	−	0.707030i
$169$	−0.832471	+	0.698526i	−0.0640362	+	0.0537328i
$170$	3.90996	+	4.65971i	0.299880	+	0.357384i
$171$	−0.0155078	−	0.00895344i	−0.00118591	−	0.000684687i
$172$	1.20085	+	3.29930i	0.0915637	+	0.251569i
$173$	4.51398	+	25.6001i	0.343192	+	1.94634i	0.322557	+	0.946550i	$0.395458\pi$
$173$	4.51398	+	25.6001i	0.343192	+	1.94634i	0.0206345	+	0.999787i	$0.493431\pi$
$174$	−0.0842985	−	0.146009i	−0.00639065	−	0.0110689i
$175$	−6.93422	+	12.0104i	−0.524178	+	0.907902i
$176$	10.9354	+	3.98016i	0.824287	+	0.300016i
$177$	−6.55752	+	3.78599i	−0.492894	+	0.284572i
$178$	−5.02978	−	4.22049i	−0.376998	−	0.316339i
$179$		−	2.95686i		−	0.221006i	−0.993876	−	0.110503i	$-0.964754\pi$
$179$		−	2.95686i		−	0.221006i	0.993876	−	0.110503i	$-0.0352462\pi$
$180$	−3.06978	+	3.65842i	−0.228808	+	0.272682i
$181$	1.85270	−	0.674326i	0.137710	−	0.0501223i	−0.272246	−	0.962228i	$-0.587766\pi$
$181$	1.85270	−	0.674326i	0.137710	−	0.0501223i	0.409956	+	0.912105i	$0.365544\pi$
$182$	−1.71695	+	9.73729i	−0.127269	+	0.721776i
$183$	−11.9689	+	2.11044i	−0.884765	+	0.156008i
$184$	−3.04417			−0.224419
$185$	15.3575	+	7.44957i	1.12910	+	0.547703i
$186$	0.212887			0.0156096
$187$	−19.7807	+	3.48787i	−1.44651	+	0.255058i
$188$	−2.39445	+	13.5796i	−0.174634	+	0.990396i
$189$	−4.53407	+	1.65027i	−0.329805	+	0.120039i
$190$	0.0176348	−	0.0210164i	0.00127937	−	0.00152469i
$191$			18.6542i			1.34977i	0.737922	+	0.674886i	$0.235807\pi$
$191$			18.6542i			1.34977i	−0.737922	+	0.674886i	$0.764193\pi$
$192$	−1.30824	−	1.09775i	−0.0944143	−	0.0792230i
$193$	3.01275	−	1.73941i	0.216862	−	0.125205i	−0.387634	−	0.921813i	$-0.626708\pi$
$193$	3.01275	−	1.73941i	0.216862	−	0.125205i	0.604497	+	0.796608i	$0.293374\pi$
$194$	1.32600	+	0.482626i	0.0952015	+	0.0346505i
$195$	5.26598	−	9.12095i	0.377105	−	0.653165i
$196$	−13.8545	−	23.9967i	−0.989605	−	1.71405i
$197$	−3.74235	−	21.2239i	−0.266632	−	1.51214i	−0.764348	−	0.644804i	$-0.776939\pi$
$197$	−3.74235	−	21.2239i	−0.266632	−	1.51214i	0.497717	−	0.867340i	$-0.334172\pi$
$198$	0.944712	+	2.59558i	0.0671378	+	0.184460i
$199$	3.29167	+	1.90045i	0.233341	+	0.134719i	0.612112	−	0.790771i	$-0.290320\pi$
$199$	3.29167	+	1.90045i	0.233341	+	0.134719i	−0.378772	+	0.925490i	$0.623653\pi$
$200$	−3.73419	−	4.45024i	−0.264047	−	0.314679i
$201$	−8.23757	+	6.91214i	−0.581033	+	0.487545i
$202$	2.50977	−	6.89553i	0.176587	−	0.485167i
$203$	−1.46732	−	0.258728i	−0.102986	−	0.0181591i
$204$	6.65437	+	1.17335i	0.465899	+	0.0821506i
$205$	6.10090	−	16.7621i	0.426105	−	1.17071i
$206$	−3.65118	+	3.06371i	−0.254390	+	0.213459i
$207$	0.968127	+	1.15377i	0.0672895	+	0.0801924i
$208$	7.47680	+	4.31673i	0.518423	+	0.299311i
$209$	0.0309842	+	0.0851284i	0.00214322	+	0.00588846i
$210$	−1.28368	−	7.28011i	−0.0885823	−	0.502375i
$211$	5.96306	+	10.3283i	0.410514	+	0.711031i	0.994946	−	0.100411i	$-0.0320159\pi$
$211$	5.96306	+	10.3283i	0.410514	+	0.711031i	−0.584432	+	0.811443i	$0.698683\pi$
$212$	3.86858	−	6.70058i	0.265695	−	0.460198i
$213$	−1.42009	−	0.516872i	−0.0973033	−	0.0354155i
$214$	4.79551	−	2.76869i	0.327814	−	0.189264i
$215$	4.43465	+	3.72112i	0.302441	+	0.253778i
$216$		−	2.02118i		−	0.137524i
$217$	1.20931	−	1.44121i	0.0820936	−	0.0978354i
$218$	−3.50339	+	1.27513i	−0.237280	+	0.0863628i
$219$	0.790656	−	4.48403i	0.0534276	−	0.303003i
$220$	23.7936	−	4.19545i	1.60416	−	0.282857i
$221$	−14.9014			−1.00237
$222$	−3.22070	+	0.810357i	−0.216159	+	0.0543876i
$223$	8.84291			0.592165			0.296082	−	0.955162i	$-0.404320\pi$
$223$	8.84291			0.592165			0.296082	+	0.955162i	$0.404320\pi$
$224$	25.1760	−	4.43922i	1.68215	−	0.296608i
$225$	−0.499109	+	2.83059i	−0.0332739	+	0.188706i
$226$	−8.02429	+	2.92060i	−0.533768	+	0.194276i
$227$	13.1207	−	15.6366i	0.870851	−	1.03784i	−0.128086	−	0.991763i	$-0.540884\pi$
$227$	13.1207	−	15.6366i	0.870851	−	1.03784i	0.998938	−	0.0460773i	$-0.0146720\pi$
$228$		−	0.0304758i		−	0.00201831i
$229$	−5.91699	−	4.96495i	−0.391006	−	0.328093i	0.425999	−	0.904724i	$-0.359923\pi$
$229$	−5.91699	−	4.96495i	−0.391006	−	0.328093i	−0.817005	+	0.576631i	$0.804367\pi$
$230$	−1.99839	+	1.15377i	−0.131770	+	0.0760772i
$231$	22.9381	+	8.34877i	1.50921	+	0.549309i
$232$	0.312065	−	0.540512i	0.0204881	−	0.0354864i
$233$	−9.16873	−	15.8807i	−0.600664	−	1.04038i	−0.992721	−	0.120439i	$-0.961570\pi$
$233$	−9.16873	−	15.8807i	−0.600664	−	1.04038i	0.392057	−	0.919941i	$-0.371764\pi$
$234$	0.355840	+	2.01807i	0.0232620	+	0.131925i
$235$	7.77603	+	21.3645i	0.507253	+	1.39366i
$236$	−11.1603	−	6.44338i	−0.726471	−	0.419428i
$237$	8.84365	+	10.5395i	0.574457	+	0.684611i
$238$	−8.01229	+	6.72311i	−0.519360	+	0.435794i
$239$	−8.51014	+	23.3814i	−0.550475	+	1.51242i	0.282588	+	0.959241i	$0.408807\pi$
$239$	−8.51014	+	23.3814i	−0.550475	+	1.51242i	−0.833064	+	0.553177i	$0.813415\pi$
$240$	−6.35677	−	1.12087i	−0.410328	−	0.0723518i
$241$	20.6598	+	3.64289i	1.33082	+	0.234659i	0.793422	−	0.608672i	$-0.208297\pi$
$241$	20.6598	+	3.64289i	1.33082	+	0.234659i	0.537395	+	0.843331i	$0.319409\pi$
$242$	2.72524	−	7.48752i	0.175185	−	0.481316i
$243$	−0.766044	+	0.642788i	−0.0491418	+	0.0412348i
$244$	−13.2955	−	15.8449i	−0.851156	−	1.01437i
$245$	−39.5659	−	22.8434i	−2.52777	−	1.45941i
$246$	1.18705	+	3.26139i	0.0756834	+	0.207939i
$247$	0.0116707	+	0.0661876i	0.000742586	+	0.00421141i
$248$	0.394043	+	0.682503i	0.0250218	+	0.0433390i
$249$	2.35148	−	4.07288i	0.149019	−	0.258108i
$250$	3.06042	+	1.11390i	0.193558	+	0.0704493i
$251$	11.1998	−	6.46621i	0.706926	−	0.408144i	−0.102996	−	0.994682i	$-0.532843\pi$
$251$	11.1998	−	6.46621i	0.706926	−	0.408144i	0.809922	+	0.586538i	$0.199510\pi$
$252$	−6.29058	−	5.27843i	−0.396270	−	0.332510i
$253$		−	7.61962i		−	0.479042i
$254$	4.53522	−	5.40487i	0.284565	−	0.339131i
$255$	10.4692	−	3.81046i	0.655604	−	0.238620i
$256$	−0.499939	+	2.83530i	−0.0312462	+	0.177206i
$257$	16.0179	−	2.82438i	0.999167	−	0.176180i	0.349938	−	0.936773i	$-0.386203\pi$
$257$	16.0179	−	2.82438i	0.999167	−	0.176180i	0.649229	+	0.760593i	$0.275092\pi$
$258$	−1.12637			−0.0701246
$259$	−12.8094	+	26.4069i	−0.795938	+	1.64084i
$260$	17.9244			1.11162
$261$	−0.304104	+	0.0536217i	−0.0188236	+	0.00331910i
$262$	−0.316434	+	1.79458i	−0.0195493	+	0.110870i
$263$	−1.09010	+	0.396764i	−0.0672185	+	0.0244655i	−0.375411	−	0.926859i	$-0.622498\pi$
$263$	−1.09010	+	0.396764i	−0.0672185	+	0.0244655i	0.308192	+	0.951324i	$0.400276\pi$
$264$	−6.57265	+	7.83298i	−0.404519	+	0.482086i
$265$		−	12.7571i		−	0.783662i
$266$	0.0361373	+	0.0303228i	0.00221572	+	0.00185921i
$267$	−10.4147	+	6.01293i	−0.637369	+	0.367985i
$268$	−17.1975	−	6.25938i	−1.05051	−	0.382353i
$269$	−0.430264	+	0.745238i	−0.0262336	+	0.0454380i	−0.878844	−	0.477109i	$-0.841685\pi$
$269$	−0.430264	+	0.745238i	−0.0262336	+	0.0454380i	0.852611	+	0.522547i	$0.175018\pi$
$270$	−0.766044	−	1.32683i	−0.0466200	−	0.0807482i
$271$	1.23006	+	6.97599i	0.0747205	+	0.423761i	0.999105	+	0.0422991i	$0.0134682\pi$
$271$	1.23006	+	6.97599i	0.0747205	+	0.423761i	−0.924384	+	0.381462i	$0.875421\pi$
$272$	3.12358	+	8.58197i	0.189395	+	0.520358i
$273$	15.6833	+	9.05477i	0.949197	+	0.548019i
$274$	−0.311776	−	0.371560i	−0.0188351	−	0.0224468i
$275$	11.1390	−	9.34677i	0.671710	−	0.563631i
$276$	−0.876700	+	2.40871i	−0.0527711	+	0.144988i
$277$	−2.86846	−	0.505786i	−0.172349	−	0.0303898i	0.0868076	−	0.996225i	$-0.472333\pi$
$277$	−2.86846	−	0.505786i	−0.172349	−	0.0303898i	−0.259157	+	0.965835i	$0.583445\pi$
$278$	4.03025	+	0.710642i	0.241718	+	0.0426215i
$279$	0.133359	−	0.366400i	0.00798397	−	0.0219358i
$280$	20.9636	−	17.5905i	1.25281	−	1.05123i
$281$	−5.45547	−	6.50157i	−0.325446	−	0.387851i	0.578369	−	0.815775i	$-0.303690\pi$
$281$	−5.45547	−	6.50157i	−0.325446	−	0.387851i	−0.903815	+	0.427924i	$0.859245\pi$
$282$	−3.83100	−	2.21183i	−0.228132	−	0.131712i
$283$	5.51112	+	15.1417i	0.327602	+	0.900079i	0.988717	+	0.149795i	$0.0478612\pi$
$283$	5.51112	+	15.1417i	0.327602	+	0.900079i	−0.661115	+	0.750284i	$0.729917\pi$
$284$	−0.446618	−	2.53290i	−0.0265019	−	0.150300i
$285$	−0.0251243	−	0.0435166i	−0.00148824	−	0.00257770i
$286$	5.18350	−	8.97808i	0.306507	−	0.530885i
$287$	28.8221	+	10.4904i	1.70132	+	0.619228i
$288$	4.58843	−	2.64913i	0.270376	−	0.156102i
$289$	0.947502	+	0.795049i	0.0557354	+	0.0467676i
$290$		−	0.473102i		−	0.0277815i
$291$	1.66130	−	1.97986i	0.0973870	−	0.116061i
$292$	7.28179	−	2.65035i	0.426134	−	0.155100i
$293$	1.76380	−	10.0030i	0.103042	−	0.584383i	−0.888942	−	0.458020i	$-0.848559\pi$
$293$	1.76380	−	10.0030i	0.103042	−	0.584383i	0.991984	−	0.126362i	$-0.0403302\pi$
$294$	8.75419	−	1.54360i	0.510555	−	0.0900246i
$295$	−21.2478			−1.23709
$296$	−8.55932	−	8.82546i	−0.497501	−	0.512969i
$297$	5.05905			0.293556
$298$	0.251962	−	0.0444276i	0.0145957	−	0.00257362i
$299$	0.981612	−	5.56700i	0.0567681	−	0.321948i
$300$	−4.59670	+	1.67306i	−0.265390	+	0.0965942i
$301$	−6.39839	+	7.62531i	−0.368797	+	0.439515i
$302$			8.48418i			0.488210i
$303$	−10.2957	−	8.63913i	−0.591473	−	0.496305i
$304$	0.0356723	−	0.0205954i	0.00204594	−	0.00118123i
$305$	−32.0474	−	11.6643i	−1.83503	−	0.667896i
$306$	−1.08385	+	1.87729i	−0.0619598	+	0.107317i
$307$	10.0899	+	17.4762i	0.575859	+	0.997417i	0.995948	+	0.0899341i	$0.0286657\pi$
$307$	10.0899	+	17.4762i	0.575859	+	0.997417i	−0.420089	+	0.907483i	$0.638001\pi$
$308$	7.21400	+	40.9126i	0.411056	+	2.33121i
$309$	2.98574	+	8.20326i	0.169853	+	0.466667i
$310$	0.517350	+	0.298692i	0.0293835	+	0.0169646i
$311$	−18.9438	−	22.5763i	−1.07420	−	1.28018i	−0.957941	−	0.286966i	$-0.907353\pi$
$311$	−18.9438	−	22.5763i	−1.07420	−	1.28018i	−0.116262	−	0.993219i	$-0.537091\pi$
$312$	−5.81116	+	4.87614i	−0.328992	+	0.276057i
$313$	−2.10202	+	5.77526i	−0.118813	+	0.326437i	−0.984816	−	0.173603i	$-0.944459\pi$
$313$	−2.10202	+	5.77526i	−0.118813	+	0.326437i	0.866002	+	0.500040i	$0.166681\pi$
$314$	−2.51035	−	0.442642i	−0.141667	−	0.0249797i
$315$	−13.3339	−	2.35113i	−0.751282	−	0.132471i
$316$	−8.00849	+	22.0031i	−0.450513	+	1.23777i
$317$	−2.61361	+	2.19308i	−0.146795	+	0.123176i	−0.713228	−	0.700932i	$-0.752767\pi$
$317$	−2.61361	+	2.19308i	−0.146795	+	0.123176i	0.566433	+	0.824108i	$0.308323\pi$
$318$	1.59549	+	1.90143i	0.0894706	+	0.106627i
$319$	1.35291	+	0.781105i	0.0757486	+	0.0437335i
$320$	−1.63904	−	4.50324i	−0.0916254	−	0.251739i
$321$	−1.76114	−	9.98795i	−0.0982975	−	0.557473i
$322$	−1.98388	−	3.43619i	−0.110558	−	0.191491i
$323$	−0.0355477	+	0.0615704i	−0.00197793	+	0.00342587i
$324$	−1.59927	−	0.582085i	−0.0888481	−	0.0323381i
$325$	9.34245	−	5.39387i	0.518226	−	0.299198i
$326$	5.53210	+	4.64198i	0.306394	+	0.257095i
$327$			6.82848i			0.377616i
$328$	−8.25865	+	9.84228i	−0.456008	+	0.543449i
$329$	−36.7358	+	13.3708i	−2.02531	+	0.737153i
$330$	−1.34593	+	7.63316i	−0.0740911	+	0.420191i
$331$	−4.32525	+	0.762658i	−0.237737	+	0.0419195i	−0.291247	−	0.956648i	$-0.594070\pi$
$331$	−4.32525	+	0.762658i	−0.237737	+	0.0419195i	0.0535101	+	0.998567i	$0.482959\pi$
$332$	8.00397			0.439275
$333$	−0.622837	+	6.05079i	−0.0341313	+	0.331581i
$334$	3.20164			0.175186
$335$	−29.7167	+	5.23986i	−1.62360	+	0.286284i
$336$	1.92731	−	10.9303i	0.105144	−	0.596299i
$337$	−13.6758	+	4.97759i	−0.744969	+	0.271146i	−0.686487	−	0.727142i	$-0.740848\pi$
$337$	−13.6758	+	4.97759i	−0.744969	+	0.271146i	−0.0584816	+	0.998288i	$0.518626\pi$
$338$	0.381384	−	0.454515i	0.0207445	−	0.0247224i
$339$			15.6402i			0.849458i
$340$	14.5249	+	12.1879i	0.787726	+	0.660980i
$341$	−1.70832	+	0.986298i	−0.0925106	+	0.0534110i
$342$	0.00918724	+	0.00334388i	0.000496789	+	0.000180816i
$343$	22.3911	−	38.7825i	1.20900	−	2.09406i
$344$	−2.08485	−	3.61107i	−0.112408	−	0.194696i
$345$	0.733905	+	4.16218i	0.0395121	+	0.224084i
$346$	−4.85423	−	13.3369i	−0.260965	−	0.716996i
$347$	−11.4598	−	6.61633i	−0.615196	−	0.355183i	0.159801	−	0.987149i	$-0.448915\pi$
$347$	−11.4598	−	6.61633i	−0.615196	−	0.355183i	−0.774996	+	0.631966i	$0.782248\pi$
$348$	−0.337810	−	0.402587i	−0.0181085	−	0.0215809i
$349$	13.4498	−	11.2857i	0.719950	−	0.604110i	−0.207421	−	0.978252i	$-0.566507\pi$
$349$	13.4498	−	11.2857i	0.719950	−	0.604110i	0.927372	+	0.374142i	$0.122063\pi$
$350$	2.58975	−	7.11529i	0.138428	−	0.380328i
$351$	3.69621	+	0.651741i	0.197289	+	0.0347874i
$352$	−26.3970	−	4.65450i	−1.40696	−	0.248085i
$353$	−1.36613	+	3.75340i	−0.0727116	+	0.199774i	−0.970724	−	0.240196i	$-0.922788\pi$
$353$	−1.36613	+	3.75340i	−0.0727116	+	0.199774i	0.898013	+	0.439969i	$0.145011\pi$
$354$	3.16696	−	2.65739i	0.168322	−	0.141239i
$355$	−2.72586	−	3.24855i	−0.144674	−	0.172415i
$356$	−17.7248	−	10.2334i	−0.939413	−	0.542370i
$357$	6.55202	+	18.0015i	0.346770	+	0.952742i
$358$	0.280337	+	1.58987i	0.0148163	+	0.0840272i
$359$	−12.3305	−	21.3571i	−0.650781	−	1.12719i	−0.982934	−	0.183960i	$-0.941108\pi$
$359$	−12.3305	−	21.3571i	−0.650781	−	1.12719i	0.332152	−	0.943226i	$-0.392225\pi$
$360$	2.83582	−	4.91179i	0.149461	−	0.258874i
$361$	−17.8539	−	6.49827i	−0.939677	−	0.342014i
$362$	−0.932241	+	0.538230i	−0.0489975	+	0.0282887i
$363$	−11.1796	−	9.38081i	−0.586778	−	0.492365i
$364$			30.8207i			1.61544i
$365$	8.21277	−	9.78760i	0.429876	−	0.512306i
$366$	6.23544	−	2.26951i	0.325932	−	0.118629i
$367$	−6.03467	+	34.2243i	−0.315007	+	1.78650i	0.257171	+	0.966366i	$0.417210\pi$
$367$	−6.03467	+	34.2243i	−0.315007	+	1.78650i	−0.572178	+	0.820129i	$0.693901\pi$
$368$	−3.41190	+	0.601610i	−0.177858	+	0.0313611i
$369$	6.35679			0.330921
$370$	−8.96381	−	2.54952i	−0.466006	−	0.132543i
$371$	21.9356			1.13884
$372$	0.653515	−	0.115232i	0.0338832	−	0.00597452i
$373$	0.481113	−	2.72853i	0.0249111	−	0.141278i	−0.969816	−	0.243840i	$-0.921593\pi$
$373$	0.481113	−	2.72853i	0.0249111	−	0.141278i	0.994727	+	0.102562i	$0.0327040\pi$
$374$	10.3052	−	3.75077i	0.532867	−	0.193948i
$375$	3.83428	−	4.56951i	0.198001	−	0.235969i
$376$		−	16.3759i		−	0.844524i
$377$	0.887829	+	0.744977i	0.0457255	+	0.0383683i
$378$	2.28146	−	1.31720i	0.117345	−	0.0677494i
$379$	−10.9235	−	3.97583i	−0.561103	−	0.204225i	0.0458698	−	0.998947i	$-0.485394\pi$
$379$	−10.9235	−	3.97583i	−0.561103	−	0.204225i	−0.606973	+	0.794723i	$0.707616\pi$
$380$	0.0427592	−	0.0740611i	0.00219350	−	0.00379925i
$381$	−6.46133	−	11.1913i	−0.331024	−	0.573350i
$382$	−1.76859	−	10.0302i	−0.0904888	−	0.513187i
$383$	2.32884	+	6.39843i	0.118998	+	0.326945i	0.984863	−	0.173333i	$-0.0554536\pi$
$383$	2.32884	+	6.39843i	0.118998	+	0.326945i	−0.865865	+	0.500277i	$0.833231\pi$
$384$	9.98437	+	5.76448i	0.509513	+	0.294167i
$385$	44.0295	+	52.4723i	2.24395	+	2.67423i
$386$	−1.45501	+	1.22090i	−0.0740579	+	0.0621420i
$387$	−0.705590	+	1.93859i	−0.0358672	+	0.0985443i
$388$	4.33178	+	0.763809i	0.219913	+	0.0387765i
$389$	31.6918	+	5.58811i	1.60684	+	0.283329i	0.903842	−	0.427866i	$-0.140735\pi$
$389$	31.6918	+	5.58811i	1.60684	+	0.283329i	0.702995	+	0.711195i	$0.251846\pi$
$390$	−1.96671	+	5.40349i	−0.0995883	+	0.273617i
$391$	4.58078	−	3.84373i	0.231660	−	0.194386i
$392$	21.1523	+	25.2083i	1.06835	+	1.27321i
$393$	2.89044	+	1.66880i	0.145803	+	0.0841796i
$394$	4.02444	+	11.0571i	0.202748	+	0.557047i
$395$	6.70408	+	38.0207i	0.337319	+	1.91303i
$396$	4.30500	+	7.45648i	0.216334	+	0.374702i
$397$	5.60714	−	9.71185i	0.281414	−	0.487424i	−0.690319	−	0.723505i	$-0.742530\pi$
$397$	5.60714	−	9.71185i	0.281414	−	0.487424i	0.971733	+	0.236081i	$0.0758631\pi$
$398$	−1.95008	−	0.709769i	−0.0977484	−	0.0355775i
$399$	0.0748261	−	0.0432009i	0.00374599	−	0.00216275i
$400$	−5.06476	−	4.24984i	−0.253238	−	0.212492i
$401$		−	14.9890i		−	0.748517i	−0.927324	−	0.374259i	$-0.877897\pi$
$401$		−	14.9890i		−	0.748517i	0.927324	−	0.374259i	$-0.122103\pi$
$402$	3.77391	−	4.49757i	0.188226	−	0.224319i
$403$	−1.37518	+	0.500525i	−0.0685027	+	0.0249329i
$404$	3.97198	−	22.5262i	0.197613	−	1.12072i
$405$	−2.76348	+	0.487276i	−0.137318	+	0.0242129i
$406$	0.813490			0.0403728
$407$	22.0903	−	21.4242i	1.09498	−	1.06196i
$408$	−8.02464			−0.397279
$409$	4.46537	−	0.787365i	0.220798	−	0.0389327i	−0.0621544	−	0.998067i	$-0.519797\pi$
$409$	4.46537	−	0.787365i	0.220798	−	0.0389327i	0.282953	+	0.959134i	$0.408686\pi$
$410$	−1.69119	+	9.59120i	−0.0835218	+	0.473676i
$411$	−0.834799	+	0.303842i	−0.0411776	+	0.0149874i
$412$	−9.54998	+	11.3812i	−0.470494	+	0.560713i
$413$		−	36.5352i		−	1.79778i
$414$	−0.629938	−	0.528581i	−0.0309598	−	0.0259783i
$415$	11.4289	−	6.59850i	0.561025	−	0.323908i
$416$	−18.6863	−	6.80127i	−0.916173	−	0.333460i
$417$	3.74776	−	6.49130i	0.183528	−	0.317880i
$418$	−0.0247308	−	0.0428350i	−0.00120962	−	0.00209513i
$419$	−0.0342684	−	0.194346i	−0.00167412	−	0.00949441i	0.983959	−	0.178393i	$-0.0570900\pi$
$419$	−0.0342684	−	0.194346i	−0.00167412	−	0.00949441i	−0.985633	+	0.168899i	$0.945979\pi$
$420$	−7.88122	−	21.6535i	−0.384564	−	1.05658i
$421$	5.34175	+	3.08406i	0.260341	+	0.150308i	0.624490	−	0.781033i	$-0.285307\pi$
$421$	5.34175	+	3.08406i	0.260341	+	0.150308i	−0.364149	+	0.931341i	$0.618640\pi$
$422$	−4.18549	−	4.98807i	−0.203746	−	0.242815i
$423$	−6.20663	+	5.20798i	−0.301777	+	0.253221i
$424$	−3.14270	+	8.63450i	−0.152623	+	0.419328i
$425$	11.2382	+	1.98160i	0.545134	+	0.0961219i
$426$	0.812572	+	0.143278i	0.0393693	+	0.00694186i
$427$	20.0565	−	55.1049i	0.970604	−	2.66671i
$428$	13.2225	−	11.0950i	0.639133	−	0.536296i
$429$	−12.2051	−	14.5455i	−0.589267	−	0.702262i
$430$	−2.73726	−	1.58036i	−0.132002	−	0.0762115i
$431$	−2.23904	−	6.15172i	−0.107851	−	0.296318i	0.874014	−	0.485901i	$-0.161509\pi$
$431$	−2.23904	−	6.15172i	−0.107851	−	0.296318i	−0.981865	+	0.189583i	$0.939286\pi$
$432$	−0.399439	−	2.26533i	−0.0192180	−	0.108991i
$433$	12.5170	+	21.6802i	0.601531	+	1.04188i	0.992589	+	0.121516i	$0.0387755\pi$
$433$	12.5170	+	21.6802i	0.601531	+	1.04188i	−0.391059	+	0.920366i	$0.627891\pi$
$434$	−0.513595	+	0.889573i	−0.0246534	+	0.0427009i
$435$	−0.814257	−	0.296365i	−0.0390406	−	0.0142096i
$436$	−10.0644	+	5.81070i	−0.481999	+	0.278282i
$437$	−0.0206604	−	0.0173361i	−0.000988321	−	0.000829300i
$438$			2.48597i			0.118784i
$439$	9.36033	−	11.1552i	0.446744	−	0.532409i	−0.494931	−	0.868932i	$-0.664807\pi$
$439$	9.36033	−	11.1552i	0.446744	−	0.532409i	0.941675	+	0.336523i	$0.109251\pi$
$440$	−26.9627	+	9.81362i	−1.28540	+	0.467846i
$441$	2.82719	−	16.0338i	0.134628	−	0.763515i
$442$	8.01229	−	1.41278i	0.381106	−	0.0671992i
$443$	28.2339			1.34144			0.670718	−	0.741713i	$-0.265986\pi$
$443$	28.2339			1.34144			0.670718	+	0.741713i	$0.265986\pi$
$444$	−9.44821	+	4.23093i	−0.448392	+	0.200791i
$445$	−33.7459			−1.59971
$446$	−4.75473	+	0.838387i	−0.225143	+	0.0396988i
$447$	0.0813718	−	0.461482i	0.00384875	−	0.0218274i
$448$	7.74324	−	2.81831i	0.365834	−	0.133153i
$449$	15.9272	−	18.9814i	0.751653	−	0.895785i	−0.245636	−	0.969362i	$-0.578997\pi$
$449$	15.9272	−	18.9814i	0.751653	−	0.895785i	0.997290	+	0.0735767i	$0.0234414\pi$
$450$		−	1.56929i		−	0.0739773i
$451$	−24.6354	−	20.6716i	−1.16004	−	0.973387i
$452$	−23.0519	+	13.3090i	−1.08427	+	0.626004i
$453$	14.6021	+	5.31475i	0.686069	+	0.249709i
$454$	−5.57235	+	9.65160i	−0.261524	+	0.452972i
$455$	25.4087	+	44.0091i	1.19118	+	2.06318i
$456$	0.00628484	+	0.0356431i	0.000294315	+	0.00166914i
$457$	0.872797	+	2.39799i	0.0408277	+	0.112173i	0.958431	−	0.285324i	$-0.0921011\pi$
$457$	0.872797	+	2.39799i	0.0408277	+	0.112173i	−0.917603	+	0.397497i	$0.869879\pi$
$458$	3.65222	+	2.10861i	0.170657	+	0.0985289i
$459$	2.55205	+	3.04141i	0.119119	+	0.141961i
$460$	−5.51008	+	4.62351i	−0.256909	+	0.215572i
$461$	−10.9280	+	30.0244i	−0.508966	+	1.39837i	0.373338	+	0.927695i	$0.378213\pi$
$461$	−10.9280	+	30.0244i	−0.508966	+	1.39837i	−0.882305	+	0.470678i	$0.844009\pi$
$462$	−13.1251	−	2.31430i	−0.610634	−	0.107671i
$463$	−36.9492	−	6.51514i	−1.71718	−	0.302784i	−0.773534	−	0.633755i	$-0.781513\pi$
$463$	−36.9492	−	6.51514i	−1.71718	−	0.302784i	−0.943641	+	0.330970i	$0.892624\pi$
$464$	0.242942	−	0.667477i	0.0112783	−	0.0309869i
$465$	0.838163	−	0.703302i	0.0388689	−	0.0326148i
$466$	6.43555	+	7.66960i	0.298121	+	0.355287i
$467$	34.7090	+	20.0392i	1.60614	+	0.927305i	0.990223	+	0.139493i	$0.0445473\pi$
$467$	34.7090	+	20.0392i	1.60614	+	0.927305i	0.615916	+	0.787812i	$0.288786\pi$
$468$	2.18470	+	6.00241i	0.100988	+	0.277461i
$469$	−9.00985	−	51.0974i	−0.416036	−	2.35946i
$470$	−6.20663	−	10.7502i	−0.286290	−	0.495870i
$471$	−2.33439	+	4.04328i	−0.107563	+	0.186304i
$472$	14.3813	+	5.23438i	0.661955	+	0.240932i
$473$	9.03858	−	5.21843i	0.415595	−	0.239944i
$474$	−5.75436	−	4.82848i	−0.264307	−	0.221780i
$475$		−	0.0514689i		−	0.00236156i
$476$	−20.9568	+	24.9754i	−0.960555	+	1.14474i
$477$	4.27202	−	1.55489i	0.195602	−	0.0711934i
$478$	2.35904	−	13.3788i	0.107900	−	0.611930i
$479$	−30.9027	+	5.44898i	−1.41198	+	0.248970i	−0.827056	−	0.562119i	$-0.809986\pi$
$479$	−30.9027	+	5.44898i	−1.41198	+	0.248970i	−0.584923	+	0.811089i	$0.698875\pi$
$480$	14.8675			0.678606
$481$	18.8995	−	12.8070i	0.861742	−	0.583947i
$482$	−11.4539			−0.521712
$483$	−7.15679	+	1.26194i	−0.325645	+	0.0574201i
$484$	4.31299	−	24.4602i	0.196045	−	1.11183i
$485$	6.81507	−	2.48048i	0.309456	−	0.112633i
$486$	0.350951	−	0.418247i	0.0159195	−	0.0189721i
$487$			26.8986i			1.21889i	0.792827	+	0.609447i	$0.208608\pi$
$487$			26.8986i			1.21889i	−0.792827	+	0.609447i	$0.791392\pi$
$488$	18.8174	+	15.7897i	0.851825	+	0.714766i
$489$	11.4548	−	6.61343i	0.518004	−	0.299069i
$490$	23.4399	+	8.53142i	1.05891	+	0.385410i
$491$	−0.885584	+	1.53388i	−0.0399658	+	0.0692229i	−0.885316	−	0.464989i	$-0.846058\pi$
$491$	−0.885584	+	1.53388i	−0.0399658	+	0.0692229i	0.845351	+	0.534212i	$0.179392\pi$
$492$	5.40931	+	9.36921i	0.243871	+	0.422396i
$493$	0.212893	+	1.20738i	0.00958823	+	0.0543776i
$494$	−0.0125503	−	0.0344818i	−0.000564667	−	0.00155141i
$495$	12.2943	+	7.09812i	0.552588	+	0.319037i
$496$	0.576524	+	0.687074i	0.0258867	+	0.0308505i
$497$	5.58583	−	4.68707i	0.250559	−	0.210244i
$498$	−0.878216	+	2.41288i	−0.0393538	+	0.108124i
$499$	2.43843	+	0.429962i	0.109159	+	0.0192477i	0.227961	−	0.973670i	$-0.426794\pi$
$499$	2.43843	+	0.429962i	0.109159	+	0.0192477i	−0.118802	+	0.992918i	$0.537905\pi$
$500$	9.99775	+	1.76287i	0.447113	+	0.0788380i
$501$	2.00560	−	5.51035i	0.0896038	−	0.246184i
$502$	−5.40895	+	4.53865i	−0.241413	+	0.202570i
$503$	−4.85194	−	5.78232i	−0.216337	−	0.257821i	0.646951	−	0.762531i	$-0.276044\pi$
$503$	−4.85194	−	5.78232i	−0.216337	−	0.257821i	−0.863289	+	0.504710i	$0.831599\pi$
$504$	8.44573	+	4.87614i	0.376203	+	0.217201i
$505$	−12.8991	−	35.4399i	−0.574002	−	1.57706i
$506$	0.722409	+	4.09698i	0.0321150	+	0.182133i
$507$	−0.543357	−	0.941122i	−0.0241313	−	0.0417967i
$508$	10.9965	−	19.0466i	0.487893	−	0.845055i
$509$	−23.2229	−	8.45244i	−1.02934	−	0.374648i	−0.228508	−	0.973542i	$-0.573385\pi$
$509$	−23.2229	−	8.45244i	−1.02934	−	0.374648i	−0.800828	+	0.598894i	$0.795607\pi$
$510$	−5.26788	+	3.04141i	−0.233266	+	0.134676i
$511$	16.8296	+	14.1217i	0.744498	+	0.624708i
$512$			21.4860i			0.949556i
$513$	0.0115103	−	0.0137175i	0.000508193	−	0.000605641i
$514$	−8.34485	+	3.03728i	−0.368075	+	0.133968i
$515$	−4.25378	+	24.1244i	−0.187444	+	1.06305i
$516$	−3.45770	+	0.609686i	−0.152217	+	0.0268399i
$517$	40.9893			1.80271
$518$	4.38386	−	15.4131i	0.192616	−	0.677213i
$519$	−25.9950			−1.14105
$520$	−20.9636	+	3.69644i	−0.919313	+	0.162100i
$521$	−3.35908	+	19.0503i	−0.147164	+	0.834609i	0.818440	+	0.574592i	$0.194839\pi$
$521$	−3.35908	+	19.0503i	−0.147164	+	0.834609i	−0.965604	+	0.260017i	$0.916272\pi$
$522$	0.158429	−	0.0576636i	0.00693427	−	0.00252387i
$523$	−17.7210	+	21.1191i	−0.774885	+	0.923472i	−0.998690	−	0.0511616i	$-0.983708\pi$
$523$	−17.7210	+	21.1191i	−0.774885	+	0.923472i	0.223805	+	0.974634i	$0.428152\pi$
$524$			5.68026i			0.248143i
$525$	−10.6238	−	8.91446i	−0.463662	−	0.389059i
$526$	0.548518	−	0.316687i	0.0239165	−	0.0138082i
$527$	−1.45471	−	0.529471i	−0.0633682	−	0.0230641i
$528$	−5.81860	+	10.0781i	−0.253222	+	0.438594i
$529$	−10.3658	−	17.9540i	−0.450686	−	0.780611i
$530$	1.20949	+	6.85934i	0.0525368	+	0.297951i
$531$	−2.58977	−	7.11533i	−0.112386	−	0.308779i
$532$	0.127347	+	0.0735236i	0.00552118	+	0.00318765i
$533$	−15.3359	−	18.2766i	−0.664272	−	0.791649i
$534$	5.02978	−	4.22049i	0.217660	−	0.182638i
$535$	9.73377	−	26.7433i	0.420828	−	1.15621i
$536$	21.4043	+	3.77415i	0.924524	+	0.163019i
$537$	2.91194	+	0.513453i	0.125659	+	0.0221571i
$538$	0.160692	−	0.441499i	0.00692794	−	0.0190344i
$539$	−63.0969	+	52.9446i	−2.71778	+	2.28049i
$540$	−3.06978	−	3.65842i	−0.132102	−	0.157433i
$541$	25.5174	+	14.7325i	1.09708	+	0.633399i	0.935453	−	0.353452i	$-0.114992\pi$
$541$	25.5174	+	14.7325i	1.09708	+	0.633399i	0.161628	+	0.986852i	$0.448326\pi$
$542$	−1.32277	−	3.63429i	−0.0568180	−	0.156106i
$543$	0.342364	+	1.94165i	0.0146923	+	0.0833240i
$544$	−10.5178	−	18.2174i	−0.450947	−	0.781063i
$545$	−9.58073	+	16.5943i	−0.410393	+	0.710822i
$546$	−9.29121	−	3.38172i	−0.397627	−	0.144724i
$547$	−29.3899	+	16.9683i	−1.25662	+	0.725510i	−0.972416	−	0.233254i	$-0.925063\pi$
$547$	−29.3899	+	16.9683i	−1.25662	+	0.725510i	−0.284204	+	0.958764i	$0.591729\pi$
$548$	−1.15820	−	0.971848i	−0.0494760	−	0.0415153i
$549$		−	12.1535i		−	0.518700i
$550$	−5.10318	+	6.08173i	−0.217600	+	0.259326i
$551$	0.00519609	−	0.00189122i	0.000221361	−	8.05688e-5i
$552$	0.528615	−	2.99792i	0.0224993	−	0.127600i
$553$	−65.3759	+	11.5275i	−2.78007	+	0.490201i
$554$	1.59029			0.0675649
$555$	−10.0032	+	13.8305i	−0.424612	+	0.587073i
$556$	12.7566			0.541002
$557$	29.4985	−	5.20139i	1.24989	−	0.220390i	0.490743	−	0.871305i	$-0.336726\pi$
$557$	29.4985	−	5.20139i	1.24989	−	0.220390i	0.759151	+	0.650915i	$0.225614\pi$
$558$	−0.0369674	+	0.209653i	−0.00156496	+	0.00887530i
$559$	7.27598	−	2.64824i	0.307741	−	0.112009i
$560$	20.0196	−	23.8584i	0.845981	−	1.00820i
$561$		−	20.0858i		−	0.848025i
$562$	3.54975	+	2.97859i	0.149737	+	0.125644i
$563$	4.63088	−	2.67364i	0.195168	−	0.112680i	−0.399232	−	0.916850i	$-0.630723\pi$
$563$	4.63088	−	2.67364i	0.195168	−	0.112680i	0.594400	+	0.804170i	$0.297390\pi$
$564$	−12.9575	−	4.71616i	−0.545610	−	0.198586i
$565$	−21.9440	+	38.0082i	−0.923192	+	1.59902i
$566$	−4.39883	−	7.61900i	−0.184897	−	0.320250i
$567$	−0.837862	−	4.75175i	−0.0351869	−	0.199555i
$568$	1.04469	+	2.87026i	0.0438342	+	0.120433i
$569$	16.8153	+	9.70829i	0.704932	+	0.406993i	0.809182	−	0.587558i	$-0.199911\pi$
$569$	16.8153	+	9.70829i	0.704932	+	0.406993i	−0.104250	+	0.994551i	$0.533244\pi$
$570$	0.0176348	+	0.0210164i	0.000738642	+	0.000880279i
$571$	1.86227	−	1.56263i	0.0779337	−	0.0653942i	−0.602989	−	0.797750i	$-0.706024\pi$
$571$	1.86227	−	1.56263i	0.0779337	−	0.0653942i	0.680922	+	0.732356i	$0.261579\pi$
$572$	11.0525	−	30.3665i	0.462128	−	1.26969i
$573$	−18.3708	−	3.23927i	−0.767452	−	0.135322i
$574$	−16.4919	−	2.90797i	−0.688358	−	0.121376i
$575$	−1.48061	+	4.06795i	−0.0617458	+	0.169645i
$576$	1.30824	−	1.09775i	0.0545101	−	0.0457394i
$577$	0.545852	+	0.650521i	0.0227241	+	0.0270816i	0.777287	−	0.629146i	$-0.216595\pi$
$577$	0.545852	+	0.650521i	0.0227241	+	0.0270816i	−0.754563	+	0.656228i	$0.772151\pi$
$578$	−0.584839	−	0.337657i	−0.0243261	−	0.0140447i
$579$	1.18983	+	3.26902i	0.0494475	+	0.135856i
$580$	−0.256083	−	1.45232i	−0.0106333	−	0.0603042i
$581$	11.3460	+	19.6519i	0.470712	+	0.815296i
$582$	−0.705552	+	1.22205i	−0.0292461	+	0.0506557i
$583$	−21.6123	−	7.86625i	−0.895092	−	0.325787i
$584$	−7.96989	+	4.60142i	−0.329796	+	0.190408i
$585$	8.06796	+	6.76982i	0.333569	+	0.279898i
$586$			5.54573i			0.229092i
$587$	−2.75119	+	3.27874i	−0.113554	+	0.135328i	−0.819827	−	0.572611i	$-0.805931\pi$
$587$	−2.75119	+	3.27874i	−0.113554	+	0.135328i	0.706273	+	0.707939i	$0.250375\pi$
$588$	26.0379	−	9.47702i	1.07378	−	0.390826i
$589$	−0.00121244	+	0.00687608i	−4.99577e−5	+	0.000283324i
$590$	11.4247	−	2.01448i	0.470347	−	0.0829349i
$591$	21.5514			0.886504
$592$	−11.3374	−	8.20000i	−0.465965	−	0.337018i
$593$	−9.59883			−0.394177			−0.197088	−	0.980386i	$-0.563149\pi$
$593$	−9.59883			−0.394177			−0.197088	+	0.980386i	$0.563149\pi$
$594$	−2.72019	+	0.479643i	−0.111611	+	0.0196800i
$595$	−9.33466	+	52.9395i	−0.382684	+	2.17031i
$596$	0.749418	−	0.272766i	0.0306974	−	0.0111729i
$597$	−2.44317	+	2.91166i	−0.0999923	+	0.119166i
$598$			3.08638i			0.126211i
$599$	−3.24400	−	2.72204i	−0.132546	−	0.111220i	0.574104	−	0.818782i	$-0.305350\pi$
$599$	−3.24400	−	2.72204i	−0.132546	−	0.111220i	−0.706651	+	0.707562i	$0.749795\pi$
$600$	5.03107	−	2.90469i	0.205392	−	0.118583i
$601$	27.7097	+	10.0855i	1.13030	+	0.411397i	0.838402	−	0.545052i	$-0.183490\pi$
$601$	27.7097	+	10.0855i	1.13030	+	0.411397i	0.291901	+	0.956449i	$0.405712\pi$
$602$	2.71739	−	4.70666i	0.110753	−	0.191829i
$603$	−5.37669	−	9.31270i	−0.218956	−	0.379243i
$604$	4.59236	+	26.0446i	0.186860	+	1.05974i
$605$	−14.0065	−	38.4825i	−0.569445	−	1.56454i
$606$	6.35495	+	3.66903i	0.258152	+	0.149044i
$607$	−10.8931	−	12.9819i	−0.442138	−	0.526920i	0.498245	−	0.867036i	$-0.333978\pi$
$607$	−10.8931	−	12.9819i	−0.442138	−	0.526920i	−0.940383	+	0.340116i	$0.889534\pi$
$608$	−0.0726788	+	0.0609847i	−0.00294751	+	0.00247326i
$609$	0.509595	−	1.40010i	0.0206498	−	0.0567349i
$610$	18.3374	+	3.23338i	0.742459	+	0.130916i
$611$	29.9473	+	5.28052i	1.21154	+	0.213627i
$612$	−2.31104	+	6.34953i	−0.0934183	+	0.256665i
$613$	15.1069	−	12.6762i	0.610161	−	0.511986i	−0.284532	−	0.958666i	$-0.591838\pi$
$613$	15.1069	−	12.6762i	0.610161	−	0.511986i	0.894694	+	0.446680i	$0.147394\pi$
$614$	−7.08210	−	8.44012i	−0.285810	−	0.340616i
$615$	15.4480	+	8.91892i	0.622924	+	0.359646i
$616$	−16.8743	−	46.3619i	−0.679887	−	1.86797i
$617$	7.59942	+	43.0984i	0.305941	+	1.73508i	0.619042	+	0.785358i	$0.287521\pi$
$617$	7.59942	+	43.0984i	0.305941	+	1.73508i	−0.313101	+	0.949720i	$0.601368\pi$
$618$	−2.38314	−	4.12772i	−0.0958640	−	0.166041i
$619$	17.9963	−	31.1705i	0.723332	−	1.25285i	−0.236325	−	0.971674i	$-0.575943\pi$
$619$	17.9963	−	31.1705i	0.723332	−	1.25285i	0.959657	−	0.281173i	$-0.0907236\pi$
$620$	1.74983	+	0.636884i	0.0702747	+	0.0255779i
$621$	−1.30435	+	0.753069i	−0.0523419	+	0.0302196i
$622$	12.3263	+	10.3430i	0.494239	+	0.414716i
$623$		−	58.0254i		−	2.32474i
$624$	−5.54948	+	6.61361i	−0.222157	+	0.264756i
$625$	29.2338	−	10.6402i	1.16935	−	0.425609i
$626$	0.582687	−	3.30458i	0.0232888	−	0.132078i
$627$	−0.0892155	+	0.0157311i	−0.00356292	+	0.000628239i
$628$	−7.94580			−0.317072
$629$	24.0233	+	2.47284i	0.957873	+	0.0985986i
$630$	7.39241			0.294521
$631$	30.3889	−	5.35838i	1.20976	−	0.213314i	0.467848	−	0.883809i	$-0.345030\pi$
$631$	30.3889	−	5.35838i	1.20976	−	0.213314i	0.741914	+	0.670496i	$0.233918\pi$
$632$	4.82879	−	27.3854i	0.192079	−	1.08933i
$633$	−11.2069	+	4.07898i	−0.445434	+	0.162125i
$634$	1.19738	−	1.42699i	0.0475542	−	0.0566729i
$635$		−	36.2624i		−	1.43903i
$636$	5.92701	+	4.97335i	0.235021	+	0.197206i
$637$	−52.9201	+	30.5535i	−2.09677	+	1.21057i
$638$	−0.801502	−	0.291723i	−0.0317318	−	0.0115494i
$639$	0.755616	−	1.30877i	0.0298917	−	0.0517740i
$640$	16.1758	+	28.0172i	0.639403	+	1.10748i
$641$	2.23196	+	12.6581i	0.0881571	+	0.499964i	0.996631	+	0.0820212i	$0.0261375\pi$
$641$	2.23196	+	12.6581i	0.0881571	+	0.499964i	−0.908474	+	0.417942i	$0.862751\pi$
$642$	1.89389	+	5.20343i	0.0747460	+	0.205363i
$643$	−1.77411	−	1.02428i	−0.0699641	−	0.0403938i	0.464610	−	0.885515i	$-0.346195\pi$
$643$	−1.77411	−	1.02428i	−0.0699641	−	0.0403938i	−0.534574	+	0.845122i	$0.679528\pi$
$644$	−7.95004	−	9.47449i	−0.313275	−	0.373347i
$645$	−4.43465	+	3.72112i	−0.174614	+	0.146519i
$646$	0.0132761	−	0.0364759i	0.000522343	−	0.00143513i
$647$	−35.7390	−	6.30175i	−1.40504	−	0.247747i	−0.580830	−	0.814025i	$-0.697272\pi$
$647$	−35.7390	−	6.30175i	−1.40504	−	0.247747i	−0.824214	+	0.566278i	$0.808383\pi$
$648$	1.99047	+	0.350974i	0.0781931	+	0.0137875i
$649$	−13.1018	+	35.9968i	−0.514289	+	1.41300i
$650$	−4.51194	+	3.78597i	−0.176973	+	0.148498i
$651$	1.20931	+	1.44121i	0.0473968	+	0.0564853i
$652$	19.4949	+	11.2554i	0.763481	+	0.440796i
$653$	−11.6682	−	32.0582i	−0.456613	−	1.25453i	−0.927991	−	0.372603i	$-0.878465\pi$
$653$	−11.6682	−	32.0582i	−0.456613	−	1.25453i	0.471377	−	0.881932i	$-0.343757\pi$
$654$	−0.647401	−	3.67159i	−0.0253154	−	0.143571i
$655$	4.68282	+	8.11089i	0.182973	+	0.316919i
$656$	−7.31118	+	12.6633i	−0.285454	+	0.494420i
$657$	4.27862	+	1.55729i	0.166925	+	0.0607556i
$658$	18.4848	−	10.6722i	0.720611	−	0.416045i
$659$	−27.3239	−	22.9275i	−1.06439	−	0.893129i	−0.0698571	−	0.997557i	$-0.522254\pi$
$659$	−27.3239	−	22.9275i	−1.06439	−	0.893129i	−0.994532	+	0.104428i	$0.966699\pi$
$660$			24.1606i			0.940451i
$661$	19.4177	−	23.1411i	0.755262	−	0.900086i	−0.242277	−	0.970207i	$-0.577894\pi$
$661$	19.4177	−	23.1411i	0.755262	−	0.900086i	0.997538	+	0.0701211i	$0.0223386\pi$
$662$	2.25333	−	0.820145i	0.0875781	−	0.0318758i
$663$	2.58759	−	14.6750i	0.100494	−	0.569929i
$664$	−9.36109	+	1.65061i	−0.363281	+	0.0640562i
$665$	0.242453			0.00940191
$666$	−0.238777	−	3.31249i	−0.00925241	−	0.128356i
$667$	−0.465088			−0.0180083
$668$	9.82833	−	1.73300i	0.380270	−	0.0670518i
$669$	−1.53555	+	8.70856i	−0.0593680	+	0.336693i
$670$	15.4816	−	5.63483i	0.598105	−	0.217692i
$671$	−39.5219	+	47.1004i	−1.52573	+	1.81829i
$672$			25.5644i			0.986169i
$673$	27.1690	+	22.7975i	1.04729	+	0.878778i	0.992806	−	0.119737i	$-0.0382051\pi$
$673$	27.1690	+	22.7975i	1.04729	+	0.878778i	0.0544812	+	0.998515i	$0.482650\pi$
$674$	6.88140	−	3.97298i	0.265062	−	0.153033i
$675$	−2.70092	−	0.983053i	−0.103958	−	0.0378377i
$676$	0.924740	−	1.60170i	0.0355669	−	0.0616038i
$677$	10.1453	+	17.5722i	0.389917	+	0.675356i	0.992438	−	0.122747i	$-0.0391703\pi$
$677$	10.1453	+	17.5722i	0.389917	+	0.675356i	−0.602521	+	0.798103i	$0.705837\pi$
$678$	−1.48283	−	8.40954i	−0.0569477	−	0.322967i
$679$	4.26515	+	11.7184i	0.163681	+	0.449711i
$680$	−19.5012	−	11.2590i	−0.747836	−	0.431763i
$681$	13.1207	+	15.6366i	0.502786	+	0.599197i
$682$	0.825033	−	0.692285i	0.0315922	−	0.0265090i
$683$	−3.19901	+	8.78921i	−0.122407	+	0.336310i	−0.985728	−	0.168345i	$-0.946158\pi$
$683$	−3.19901	+	8.78921i	−0.122407	+	0.336310i	0.863321	+	0.504654i	$0.168380\pi$
$684$	0.0300128	+	0.00529206i	0.00114757	+	0.000202347i
$685$	−2.45501	−	0.432884i	−0.0938009	−	0.0165396i
$686$	−8.36249	+	22.9758i	−0.319281	+	0.877218i
$687$	5.91699	−	4.96495i	0.225747	−	0.189425i
$688$	−3.05034	−	3.63526i	−0.116293	−	0.138593i
$689$	−14.7769	−	8.53143i	−0.562954	−	0.325022i
$690$	−0.789224	−	2.16838i	−0.0300452	−	0.0825486i
$691$	−1.16242	−	6.59241i	−0.0442206	−	0.250787i	0.954682	−	0.297628i	$-0.0961957\pi$
$691$	−1.16242	−	6.59241i	−0.0442206	−	0.250787i	−0.998902	+	0.0468412i	$0.985085\pi$
$692$	−22.1205	−	38.3138i	−0.840894	−	1.45647i
$693$	−12.2051	+	21.1398i	−0.463633	+	0.803036i
$694$	6.78910	+	2.47103i	0.257711	+	0.0937991i
$695$	18.2153	−	10.5166i	0.690946	−	0.398918i
$696$	0.478111	+	0.401183i	0.0181228	+	0.0152068i
$697$		−	25.2382i		−	0.955966i
$698$	−6.16181	+	7.34336i	−0.233228	+	0.277950i
$699$	17.2316	−	6.27178i	0.651758	−	0.237221i
$700$	4.09857	−	23.2442i	0.154911	−	0.878546i
$701$	34.2514	−	6.03945i	1.29366	−	0.228107i	0.515888	−	0.856656i	$-0.327462\pi$
$701$	34.2514	−	6.03945i	1.29366	−	0.228107i	0.777770	+	0.628549i	$0.216351\pi$
$702$	−2.04920			−0.0773420
$703$	−0.00783128	−	0.108641i	−0.000295362	−	0.00409749i
$704$	−8.63979			−0.325624
$705$	−22.3902	+	3.94800i	−0.843264	+	0.148690i
$706$	0.378694	−	2.14768i	0.0142524	−	0.0808291i
$707$	60.9383	−	22.1797i	2.29182	−	0.834155i
$708$	8.28345	−	9.87183i	0.311311	−	0.371006i
$709$		−	25.4955i		−	0.957505i	−0.877950	−	0.478752i	$-0.841089\pi$
$709$		−	25.4955i		−	0.957505i	0.877950	−	0.478752i	$-0.158911\pi$
$710$	1.77366	+	1.48827i	0.0665641	+	0.0558539i
$711$	−11.9150	+	6.87914i	−0.446848	+	0.257988i
$712$	22.8405	+	8.31327i	0.855985	+	0.311553i
$713$	0.293633	−	0.508587i	0.0109966	−	0.0190467i
$714$	−5.22965	−	9.05802i	−0.195715	−	0.338988i
$715$	−9.25227	−	52.4723i	−0.346015	−	1.96235i
$716$	1.72114	+	4.72880i	0.0643221	+	0.176724i
$717$	−21.5484	−	12.4410i	−0.804741	−	0.464618i
$718$	8.65484	+	10.3144i	0.322996	+	0.384931i
$719$	19.1755	−	16.0901i	0.715125	−	0.600061i	−0.210907	−	0.977506i	$-0.567642\pi$
$719$	19.1755	−	16.0901i	0.715125	−	0.600061i	0.926032	+	0.377445i	$0.123197\pi$
$720$	2.20768	−	6.06556i	0.0822754	−	0.226050i
$721$	−41.4815	−	7.31430i	−1.54485	−	0.272399i
$722$	10.2159	+	1.80134i	0.380197	+	0.0670389i
$723$	−7.17508	+	19.7134i	−0.266844	+	0.733148i
$724$	−2.57044	+	2.15685i	−0.0955296	+	0.0801588i
$725$	−0.570510	−	0.679908i	−0.0211882	−	0.0252511i
$726$	6.90054	+	3.98403i	0.256103	+	0.147861i
$727$	15.6387	+	42.9671i	0.580009	+	1.59356i	0.788164	+	0.615466i	$0.211032\pi$
$727$	15.6387	+	42.9671i	0.580009	+	1.59356i	−0.208155	+	0.978096i	$0.566746\pi$
$728$	−6.35597	−	36.0465i	−0.235568	−	1.33597i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−3.48796	+	6.04132i	−0.129095	+	0.223599i
$731$	7.69676	+	2.80139i	0.284675	+	0.103613i
$732$	17.9130	−	10.3421i	0.662082	−	0.382253i
$733$	14.3273	+	12.0220i	0.529190	+	0.444043i	0.867822	−	0.496876i	$-0.165520\pi$
$733$	14.3273	+	12.0220i	0.529190	+	0.444043i	−0.338631	+	0.940919i	$0.609964\pi$
$734$		−	18.9742i		−	0.700349i
$735$	29.3669	−	34.9981i	1.08321	−	1.29092i
$736$	7.49867	−	2.72929i	0.276405	−	0.100603i
$737$	−9.44678	+	53.5754i	−0.347977	+	1.97347i
$738$	−3.41797	+	0.602680i	−0.125817	+	0.0221850i
$739$	−42.4774			−1.56256			−0.781278	−	0.624183i	$-0.785432\pi$
$739$	−42.4774			−1.56256			−0.781278	+	0.624183i	$0.785432\pi$
$740$	−28.8969	−	2.97450i	−1.06227	−	0.109345i
$741$	−0.0672086			−0.00246897
$742$	−11.7945	+	2.07969i	−0.432990	+	0.0763479i
$743$	−0.680714	+	3.86052i	−0.0249730	+	0.141629i	−0.994745	−	0.102384i	$-0.967353\pi$
$743$	−0.680714	+	3.86052i	−0.0249730	+	0.141629i	0.969772	+	0.244013i	$0.0784640\pi$
$744$	−0.740559	+	0.269541i	−0.0271502	+	0.00988187i
$745$	0.845232	−	1.00731i	0.0309669	−	0.0369049i
$746$			1.51271i			0.0553843i
$747$	3.60267	+	3.02300i	0.131815	+	0.110606i
$748$	29.6043	−	17.0921i	1.08244	−	0.624948i
$749$	45.9846	+	16.7370i	1.68024	+	0.611558i
$750$	−1.62842	+	2.82050i	−0.0594613	+	0.102990i
$751$	5.73560	+	9.93435i	0.209295	+	0.362510i	0.951493	−	0.307671i	$-0.0995498\pi$
$751$	5.73560	+	9.93435i	0.209295	+	0.362510i	−0.742198	+	0.670181i	$0.766216\pi$
$752$	−3.23632	−	18.3541i	−0.118017	−	0.669305i
$753$	4.42315	+	12.1525i	0.161189	+	0.442862i
$754$	−0.548006	−	0.316392i	−0.0199572	−	0.0115223i
$755$	28.0287	+	33.4033i	1.02007	+	1.21567i
$756$	6.29058	−	5.27843i	0.228786	−	0.191975i
$757$	−14.7635	+	40.5625i	−0.536590	+	1.47427i	0.314505	+	0.949256i	$0.398161\pi$
$757$	−14.7635	+	40.5625i	−0.536590	+	1.47427i	−0.851095	+	0.525012i	$0.824061\pi$
$758$	6.25039	+	1.10211i	0.227024	+	0.0400305i
$759$	7.50386	+	1.32313i	0.272373	+	0.0480267i
$760$	−0.0347361	+	0.0954366i	−0.00126001	+	0.00346185i
$761$	−2.25289	+	1.89040i	−0.0816671	+	0.0685269i	−0.682707	−	0.730692i	$-0.739198\pi$
$761$	−2.25289	+	1.89040i	−0.0816671	+	0.0685269i	0.601040	+	0.799219i	$0.294753\pi$
$762$	4.53522	+	5.40487i	0.164294	+	0.195798i
$763$	−28.5336	−	16.4739i	−1.03299	−	0.596395i
$764$	−10.8583	−	29.8330i	−0.392841	−	1.07932i
$765$	1.93462	+	10.9718i	0.0699464	+	0.396686i
$766$	−1.85882	−	3.21957i	−0.0671618	−	0.116328i
$767$	−14.2097	+	24.6119i	−0.513082	+	0.888683i
$768$	−2.70541	−	0.984688i	−0.0976230	−	0.0355319i
$769$	13.5158	−	7.80335i	0.487392	−	0.281396i	−0.236100	−	0.971729i	$-0.575869\pi$
$769$	13.5158	−	7.80335i	0.487392	−	0.281396i	0.723492	+	0.690333i	$0.242536\pi$
$770$	−28.6490	−	24.0393i	−1.03244	−	0.866318i
$771$			16.2650i			0.585769i
$772$	−3.80570	+	4.53545i	−0.136970	+	0.163235i
$773$	22.3091	−	8.11983i	0.802401	−	0.292050i	0.0919199	−	0.995766i	$-0.470700\pi$
$773$	22.3091	−	8.11983i	0.802401	−	0.292050i	0.710481	+	0.703716i	$0.248477\pi$
$774$	0.195592	−	1.10926i	0.00703040	−	0.0398714i
$775$	1.10369	−	0.194610i	0.0396456	−	0.00699060i
$776$	−5.22377			−0.187522
$777$	−23.7813	−	17.2003i	−0.853151	−	0.617057i
$778$	−17.5701			−0.629919
$779$	−0.112101	+	0.0197664i	−0.00401643	+	0.000708205i
$780$	−3.11254	+	17.6521i	−0.111447	+	0.632046i
$781$	−7.18432	+	2.61488i	−0.257075	+	0.0935678i
$782$	−2.09861	+	2.50103i	−0.0750463	+	0.0894367i
$783$		−	0.308795i		−	0.0110354i
$784$	28.6893	+	24.0732i	1.02462	+	0.859755i
$785$	−11.3459	+	6.55055i	−0.404952	+	0.233799i
$786$	−1.71237	−	0.623253i	−0.0610783	−	0.0222307i
$787$	11.7128	−	20.2872i	0.417516	−	0.723160i	−0.578173	−	0.815914i	$-0.696234\pi$
$787$	11.7128	−	20.2872i	0.417516	−	0.723160i	0.995689	+	0.0927549i	$0.0295673\pi$
$788$	18.3392	+	31.7643i	0.653305	+	1.13156i
$789$	−0.201443	−	1.14244i	−0.00717155	−	0.0406719i
$790$	−7.20941	−	19.8077i	−0.256499	−	0.704726i
$791$	−65.3544	−	37.7324i	−2.32373	−	1.34161i
$792$	−6.57265	−	7.83298i	−0.233549	−	0.278333i
$793$	−34.9431	+	29.3207i	−1.24086	+	1.04121i
$794$	−2.09412	+	5.75356i	−0.0743177	+	0.204186i
$795$	12.5633	+	2.21525i	0.445574	+	0.0785667i
$796$	−6.37048	−	1.12329i	−0.225796	−	0.0398139i
$797$	−9.36121	+	25.7197i	−0.331591	+	0.911039i	0.656107	+	0.754668i	$0.272202\pi$
$797$	−9.36121	+	25.7197i	−0.331591	+	0.911039i	−0.987698	+	0.156371i	$0.950020\pi$
$798$	−0.0361373	+	0.0303228i	−0.00127925	+	0.00107341i
$799$	20.6771	+	24.6421i	0.731504	+	0.871773i
$800$	13.1883	+	7.61428i	0.466278	+	0.269205i
$801$	−4.11309	−	11.3006i	−0.145329	−	0.399287i
$802$	1.42110	+	8.05944i	0.0501806	+	0.284589i
$803$	−11.5174	−	19.9488i	−0.406442	−	0.703978i
$804$	9.15060	−	15.8493i	0.322717	−	0.558962i
$805$	−19.1627	−	6.97467i	−0.675398	−	0.245825i
$806$	0.691965	−	0.399506i	0.0243734	−	0.0140720i
$807$	−0.659202	−	0.553136i	−0.0232050	−	0.0194713i
$808$			27.1648i			0.955654i
$809$	−11.1670	+	13.3083i	−0.392612	+	0.467896i	−0.925752	−	0.378130i	$-0.876567\pi$
$809$	−11.1670	+	13.3083i	−0.392612	+	0.467896i	0.533141	+	0.846027i	$0.321012\pi$
$810$	1.43969	−	0.524005i	0.0505856	−	0.0184117i
$811$	6.49093	−	36.8119i	0.227927	−	1.29264i	−0.629082	−	0.777339i	$-0.716569\pi$
$811$	6.49093	−	36.8119i	0.227927	−	1.29264i	0.857009	−	0.515301i	$-0.172320\pi$
$812$	2.49723	−	0.440330i	0.0876357	−	0.0154525i
$813$	−7.08361			−0.248433
$814$	−9.84650	+	13.6139i	−0.345120	+	0.477166i
$815$	37.1160			1.30012
$816$	−8.99400	+	1.58588i	−0.314853	+	0.0555170i
$817$	0.00641492	−	0.0363808i	0.000224430	−	0.00127280i
$818$	−2.32633	+	0.846714i	−0.0813382	+	0.0296047i
$819$	−11.6406	+	13.8727i	−0.406755	+	0.484752i
$820$			30.3583i			1.06016i
$821$	4.53722	+	3.80718i	0.158350	+	0.132872i	0.718520	−	0.695506i	$-0.244820\pi$
$821$	4.53722	+	3.80718i	0.158350	+	0.132872i	−0.560170	+	0.828378i	$0.689264\pi$
$822$	0.420055	−	0.242519i	0.0146511	−	0.00845882i
$823$	−3.13554	−	1.14124i	−0.109298	−	0.0397812i	0.286792	−	0.957993i	$-0.407411\pi$
$823$	−3.13554	−	1.14124i	−0.109298	−	0.0397812i	−0.396090	+	0.918212i	$0.629633\pi$
$824$	8.82215	−	15.2804i	0.307334	−	0.532319i
$825$	7.27049	+	12.5929i	0.253126	+	0.438427i
$826$	3.46387	+	19.6446i	0.120523	+	0.683522i
$827$	−17.2811	−	47.4794i	−0.600923	−	1.65102i	−0.749409	−	0.662107i	$-0.769662\pi$
$827$	−17.2811	−	47.4794i	−0.600923	−	1.65102i	0.148486	−	0.988914i	$-0.452560\pi$
$828$	−2.21988	−	1.28165i	−0.0771462	−	0.0445404i
$829$	−16.4860	−	19.6473i	−0.572584	−	0.682379i	0.399575	−	0.916700i	$-0.369158\pi$
$829$	−16.4860	−	19.6473i	−0.572584	−	0.682379i	−0.972159	+	0.234321i	$0.924713\pi$
$830$	−5.51961	+	4.63150i	−0.191589	+	0.160762i
$831$	0.996205	−	2.73705i	0.0345580	−	0.0949472i
$832$	−6.31235	−	1.11304i	−0.218841	−	0.0385876i
$833$	−63.6587	−	11.2248i	−2.20564	−	0.388915i
$834$	−1.39969	+	3.84562i	−0.0484673	+	0.133163i
$835$	12.6053	−	10.5771i	0.436224	−	0.366035i
$836$	−0.0991039	−	0.118107i	−0.00342758	−	0.00408483i
$837$	0.337676	+	0.194957i	0.0116718	+	0.00673871i
$838$	0.0368514	+	0.101249i	0.00127301	+	0.00349757i
$839$	−4.78951	−	27.1626i	−0.165352	−	0.937758i	−0.948701	−	0.316176i	$-0.897601\pi$
$839$	−4.78951	−	27.1626i	−0.165352	−	0.937758i	0.783349	−	0.621583i	$-0.213510\pi$
$840$	13.6830	+	23.6996i	0.472108	+	0.817716i
$841$	−14.4523	+	25.0322i	−0.498356	+	0.863178i
$842$	−3.16459	−	1.15182i	−0.109059	−	0.0396943i
$843$	7.35013	−	4.24360i	0.253152	−	0.146157i
$844$	−15.5485	−	13.0467i	−0.535201	−	0.449087i
$845$		−	3.04944i		−	0.104904i
$846$	2.84347	−	3.38871i	0.0977605	−	0.116506i
$847$	66.1700	−	24.0839i	2.27363	−	0.827533i
$848$	−1.81592	+	10.2986i	−0.0623591	+	0.353656i
$849$	−15.8686	+	2.79807i	−0.544610	+	0.0960294i
$850$	−6.23054			−0.213706
$851$	−2.50634	+	8.81198i	−0.0859162	+	0.302071i
$852$	2.57197			0.0881143
$853$	8.34586	−	1.47160i	0.285757	−	0.0503866i	−0.0289325	−	0.999581i	$-0.509211\pi$
$853$	8.34586	−	1.47160i	0.285757	−	0.0503866i	0.314689	+	0.949195i	$0.398100\pi$
$854$	−5.55973	+	31.5308i	−0.190250	+	1.07896i
$855$	0.0472183	−	0.0171861i	0.00161483	−	0.000587751i
$856$	−13.1764	+	15.7030i	−0.450360	+	0.536718i
$857$			15.4390i			0.527385i	0.964607	+	0.263693i	$0.0849404\pi$
$857$			15.4390i			0.527385i	−0.964607	+	0.263693i	$0.915060\pi$
$858$	7.94158	+	6.66377i	0.271121	+	0.227498i
$859$	5.04321	−	2.91170i	0.172072	−	0.0993458i	−0.411490	−	0.911414i	$-0.634992\pi$
$859$	5.04321	−	2.91170i	0.172072	−	0.0993458i	0.583562	+	0.812068i	$0.301658\pi$
$860$	−9.25819	−	3.36971i	−0.315702	−	0.114906i
$861$	−15.3359	+	26.5626i	−0.522647	+	0.905251i
$862$	1.78715	+	3.09543i	0.0608704	+	0.105431i
$863$	2.27781	+	12.9181i	0.0775376	+	0.439738i	0.998719	+	0.0506038i	$0.0161146\pi$
$863$	2.27781	+	12.9181i	0.0775376	+	0.439738i	−0.921181	+	0.389134i	$0.872774\pi$
$864$	1.81211	+	4.97874i	0.0616493	+	0.169380i
$865$	−63.1721	−	36.4724i	−2.14791	−	1.24010i
$866$	−8.78574	−	10.4704i	−0.298552	−	0.355800i
$867$	−0.947502	+	0.795049i	−0.0321789	+	0.0270013i
$868$	−1.09511	+	3.00879i	−0.0371705	+	0.102125i
$869$	68.5463	+	12.0866i	2.32528	+	0.410009i
$870$	0.465914	+	0.0821533i	0.0157960	+	0.00278526i
$871$	−13.8039	+	37.9259i	−0.467727	+	1.28507i
$872$	10.5726	−	8.87147i	0.358034	−	0.300426i
$873$	1.66130	+	1.97986i	0.0562264	+	0.0670080i
$874$	0.0127525	+	0.00736265i	0.000431359	+	0.000249045i
$875$	9.84396	+	27.0461i	0.332787	+	0.914324i
$876$	1.34562	+	7.63139i	0.0454643	+	0.257841i
$877$	4.67498	+	8.09730i	0.157863	+	0.273426i	0.934098	−	0.357017i	$-0.116206\pi$
$877$	4.67498	+	8.09730i	0.157863	+	0.273426i	−0.776235	+	0.630444i	$0.782873\pi$
$878$	−3.97533	+	6.88547i	−0.134161	+	0.232373i
$879$	9.54477	+	3.47401i	0.321937	+	0.117176i
$880$	−28.2803	+	16.3276i	−0.953329	+	0.550405i
$881$	−25.2762	−	21.2092i	−0.851575	−	0.714557i	0.108561	−	0.994090i	$-0.465376\pi$
$881$	−25.2762	−	21.2092i	−0.851575	−	0.714557i	−0.960136	+	0.279533i	$0.909820\pi$
$882$			8.88924i			0.299316i
$883$	16.9099	−	20.1525i	0.569065	−	0.678185i	−0.402374	−	0.915475i	$-0.631815\pi$
$883$	16.9099	−	20.1525i	0.569065	−	0.678185i	0.971439	+	0.237290i	$0.0762592\pi$
$884$	23.8312	−	8.67386i	0.801531	−	0.291733i
$885$	3.68964	−	20.9250i	0.124026	−	0.703386i
$886$	−15.1811	+	2.67683i	−0.510018	+	0.0899299i
$887$	−12.0508			−0.404626			−0.202313	−	0.979321i	$-0.564846\pi$
$887$	−12.0508			−0.404626			−0.202313	+	0.979321i	$0.564846\pi$
$888$	10.1777	−	6.89676i	0.341541	−	0.231440i
$889$	62.3525			2.09124
$890$	18.1448	−	3.19941i	0.608214	−	0.107245i
$891$	−0.878494	+	4.98219i	−0.0294307	+	0.166910i
$892$	−14.1422	+	5.14732i	−0.473514	+	0.172345i
$893$	0.0932587	−	0.111141i	0.00312078	−	0.00371920i
$894$			0.255848i			0.00855685i
$895$	6.35608	+	5.33338i	0.212460	+	0.178275i
$896$	−48.1751	+	27.8139i	−1.60942	+	0.929198i
$897$	5.31197	+	1.93340i	0.177361	+	0.0645543i
$898$	−6.76429	+	11.7161i	−0.225727	+	0.390971i
$899$	0.0602019	+	0.104273i	0.00200785	+	0.00347769i
$900$	−0.849435	−	4.81738i	−0.0283145	−	0.160579i
$901$	−6.17334	−	16.9611i	−0.205664	−	0.565056i
$902$	15.2060	+	8.77921i	0.506306	+	0.292316i
$903$	−6.39839	−	7.62531i	−0.212925	−	0.253754i
$904$	24.2159	−	20.3195i	0.805407	−	0.675817i
$905$	−1.89223	+	5.19887i	−0.0629000	+	0.172816i
$906$	−8.35529	−	1.47326i	−0.277586	−	0.0489459i
$907$	55.1023	+	9.71602i	1.82964	+	0.322615i	0.979113	−	0.203315i	$-0.0651715\pi$
$907$	55.1023	+	9.71602i	1.82964	+	0.322615i	0.850528	+	0.525930i	$0.176283\pi$
$908$	−11.8816	+	32.6445i	−0.394306	+	1.08335i
$909$	10.2957	−	8.63913i	0.341487	−	0.286542i
$910$	−17.8344	−	21.2542i	−0.591205	−	0.704570i
$911$	−32.0377	−	18.4970i	−1.06146	−	0.612832i	−0.135621	−	0.990761i	$-0.543303\pi$
$911$	−32.0377	−	18.4970i	−1.06146	−	0.612832i	−0.925834	+	0.377929i	$0.876636\pi$
$912$	0.0140881	+	0.0387067i	0.000466503	+	0.00128171i
$913$	−4.13152	−	23.4310i	−0.136733	−	0.775453i
$914$	−0.696644	−	1.20662i	−0.0230429	−	0.0399115i
$915$	17.0521	−	29.5350i	0.563724	−	0.976398i
$916$	12.3529	+	4.49607i	0.408150	+	0.148554i
$917$	−13.9465	+	8.05203i	−0.460555	+	0.265902i
$918$	−1.66056	−	1.39337i	−0.0548066	−	0.0459882i
$919$			2.60909i			0.0860660i	0.999074	+	0.0430330i	$0.0137021\pi$
$919$			2.60909i			0.0860660i	−0.999074	+	0.0430330i	$0.986298\pi$
$920$	5.49087	−	6.54376i	0.181029	−	0.215741i
$921$	−18.9627	+	6.90188i	−0.624844	+	0.227425i
$922$	3.02927	−	17.1798i	0.0997635	−	0.565787i
$923$	−5.58583	+	0.984932i	−0.183860	+	0.0324194i
$924$	−41.5438			−1.36669
$925$	−15.9566	+	7.14540i	−0.524649	+	0.234939i
$926$	20.4849			0.673174
$927$	−8.59710	+	1.51590i	−0.282366	+	0.0497887i
$928$	−0.284102	+	1.61122i	−0.00932611	+	0.0528910i
$929$	2.59814	−	0.945645i	0.0852421	−	0.0310256i	−0.299047	−	0.954238i	$-0.596669\pi$
$929$	2.59814	−	0.945645i	0.0852421	−	0.0310256i	0.384289	+	0.923213i	$0.374447\pi$
$930$	−0.383991	+	0.457623i	−0.0125916	+	0.0150060i
$931$			0.291545i			0.00955500i
$932$	23.9072	+	20.0605i	0.783105	+	0.657103i
$933$	25.5229	−	14.7356i	0.835581	−	0.482423i
$934$	−20.5625	−	7.48414i	−0.672826	−	0.244889i
$935$	28.1815	−	48.8118i	0.921635	−	1.59632i
$936$	−3.79297	−	6.56961i	−0.123977	−	0.214734i
$937$	−9.48523	−	53.7934i	−0.309869	−	1.75735i	−0.599651	−	0.800261i	$-0.704694\pi$
$937$	−9.48523	−	53.7934i	−0.309869	−	1.75735i	0.289782	−	0.957093i	$-0.406417\pi$
$938$	9.68899	+	26.6203i	0.316357	+	0.869183i
$939$	−5.32251	−	3.07295i	−0.173694	−	0.100282i
$940$	−24.8719	−	29.6412i	−0.811231	−	0.966788i
$941$	−0.505894	+	0.424495i	−0.0164917	+	0.0138382i	−0.650996	−	0.759081i	$-0.725649\pi$
$941$	−0.505894	+	0.424495i	−0.0164917	+	0.0138382i	0.634505	+	0.772919i	$0.281204\pi$
$942$	0.871834	−	2.39534i	0.0284059	−	0.0780445i
$943$	9.42874	+	1.66254i	0.307042	+	0.0541398i
$944$	17.1530	+	3.02454i	0.558283	+	0.0984404i
$945$	4.63083	−	12.7231i	0.150641	−	0.413882i
$946$	−4.36519	+	3.66283i	−0.141925	+	0.119089i
$947$	20.6317	+	24.5879i	0.670441	+	0.799000i	0.988844	−	0.148955i	$-0.0475910\pi$
$947$	20.6317	+	24.5879i	0.670441	+	0.799000i	−0.318403	+	0.947955i	$0.603147\pi$
$948$	−20.2782	−	11.7076i	−0.658605	−	0.380246i
$949$	−5.84486	−	16.0586i	−0.189732	−	0.521285i
$950$	0.00487972	+	0.0276743i	0.000158319	+	0.000897871i
$951$	−1.70591	−	2.95473i	−0.0553180	−	0.0958136i
$952$	19.3597	−	33.5319i	0.627450	−	1.08678i
$953$	19.7971	+	7.20557i	0.641292	+	0.233411i	0.642139	−	0.766588i	$-0.278047\pi$
$953$	19.7971	+	7.20557i	0.641292	+	0.233411i	−0.000846691		1.00000i	$0.500270\pi$
$954$	−2.14960	+	1.24107i	−0.0695958	+	0.0401811i
$955$	−40.0992	−	33.6472i	−1.29758	−	1.08880i
$956$		−	42.3467i		−	1.36959i
$957$	−1.00417	+	1.19672i	−0.0324602	+	0.0386845i
$958$	16.0994	−	5.85970i	0.520148	−	0.189318i
$959$	0.744336	−	4.22134i	0.0240359	−	0.136314i
$960$	4.71944	−	0.832165i	0.152319	−	0.0268580i
$961$	30.8480			0.995096
$962$	−8.94782	+	8.67799i	−0.288489	+	0.279790i
$963$	10.1420			0.326822
$964$	−35.1610	+	6.19983i	−1.13246	+	0.199683i
$965$	−1.69515	+	9.61365i	−0.0545687	+	0.309474i
$966$	3.72848	−	1.35706i	0.119962	−	0.0436626i
$967$	14.5195	−	17.3037i	0.466917	−	0.556450i	−0.480275	−	0.877118i	$-0.659463\pi$
$967$	14.5195	−	17.3037i	0.466917	−	0.556450i	0.947192	+	0.320668i	$0.103907\pi$
$968$			29.4970i			0.948068i
$969$	−0.0544622	−	0.0456992i	−0.00174958	−	0.00146807i
$970$	−3.42921	+	1.97986i	−0.110105	+	0.0635694i
$971$	21.2779	+	7.74451i	0.682839	+	0.248533i	0.660066	−	0.751208i	$-0.270528\pi$
$971$	21.2779	+	7.74451i	0.682839	+	0.248533i	0.0227729	+	0.999741i	$0.492751\pi$
$972$	0.850951	−	1.47389i	0.0272943	−	0.0472751i
$973$	18.0831	+	31.3209i	0.579719	+	1.00410i
$974$	−2.55023	−	14.4631i	−0.0817147	−	0.463427i
$975$	3.68962	+	10.1372i	0.118162	+	0.324649i
$976$	24.2110	+	13.9782i	0.774975	+	0.447432i
$977$	3.28057	+	3.90964i	0.104955	+	0.125080i	0.815965	−	0.578102i	$-0.196206\pi$
$977$	3.28057	+	3.90964i	0.104955	+	0.125080i	−0.711010	+	0.703182i	$0.751762\pi$
$978$	−5.53210	+	4.64198i	−0.176897	+	0.148434i
$979$	−20.8083	+	57.1703i	−0.665036	+	1.82717i
$980$	76.5731	+	13.5019i	2.44604	+	0.431303i
$981$	−6.72474	−	1.18575i	−0.214704	−	0.0378582i
$982$	0.330743	−	0.908709i	0.0105544	−	0.0289981i
$983$	−34.9698	+	29.3431i	−1.11536	+	0.935900i	−0.998361	−	0.0572313i	$-0.981773\pi$
$983$	−34.9698	+	29.3431i	−1.11536	+	0.935900i	−0.117002	+	0.993132i	$0.537328\pi$
$984$	−8.25865	−	9.84228i	−0.263276	−	0.313760i
$985$	52.3733	+	30.2377i	1.66875	+	0.963455i
$986$	−0.228941	−	0.629009i	−0.00729095	−	0.0200317i
$987$	−6.78851	−	38.4995i	−0.216081	−	1.22545i
$988$	−0.0571912	−	0.0990581i	−0.00181950	−	0.00315146i
$989$	−1.55359	+	2.69089i	−0.0494012	+	0.0855654i
$990$	−7.28347	−	2.65097i	−0.231484	−	0.0842533i
$991$	42.1421	−	24.3308i	1.33869	−	0.772892i	0.352076	−	0.935972i	$-0.385476\pi$
$991$	42.1421	−	24.3308i	1.33869	−	0.772892i	0.986613	+	0.163079i	$0.0521426\pi$
$992$	−1.58255	−	1.32792i	−0.0502460	−	0.0421614i
$993$		−	4.39197i		−	0.139375i
$994$	−2.55906	+	3.04977i	−0.0811685	+	0.0967328i
$995$	−10.0225	+	3.64790i	−0.317735	+	0.115646i
$996$	−1.38987	+	7.88237i	−0.0440398	+	0.249762i
$997$	−28.1822	+	4.96928i	−0.892539	+	0.157379i	−0.601065	−	0.799200i	$-0.705257\pi$
$997$	−28.1822	+	4.96928i	−0.892539	+	0.157379i	−0.291474	+	0.956579i	$0.594146\pi$
$998$	−1.35188			−0.0427931
$999$	−5.85071	−	1.66408i	−0.185108	−	0.0526493i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.o.a.28.1	yes	12
3.2	odd	2		333.2.bl.b.28.2		12
37.2	odd	36		4107.2.a.p.1.5		12
37.4	even	18	inner	111.2.o.a.4.1	✓	12
37.35	odd	36		4107.2.a.p.1.8		12
111.41	odd	18		333.2.bl.b.226.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.o.a.4.1	✓	12	37.4	even	18	inner
111.2.o.a.28.1	yes	12	1.1	even	1	trivial
333.2.bl.b.28.2		12	3.2	odd	2
333.2.bl.b.226.2		12	111.41	odd	18
4107.2.a.p.1.5		12	37.2	odd	36
4107.2.a.p.1.8		12	37.35	odd	36

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:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.o (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.537688 + 0.0948090i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(-1.59927 + 0.582085i) q^{4} +(-1.80373 + 2.14961i) q^{5} -0.545983i q^{6} +(-3.69621 - 3.10149i) q^{7} +(1.75039 - 1.01059i) q^{8} +(-0.939693 - 0.342020i) q^{9} +O(q^{10})\)	\(q+(-0.537688 + 0.0948090i) q^{2} +(-0.173648 + 0.984808i) q^{3} +(-1.59927 + 0.582085i) q^{4} +(-1.80373 + 2.14961i) q^{5} -0.545983i q^{6} +(-3.69621 - 3.10149i) q^{7} +(1.75039 - 1.01059i) q^{8} +(-0.939693 - 0.342020i) q^{9} +(0.766044 - 1.32683i) q^{10} +(2.52952 + 4.38126i) q^{11} +(-0.295532 - 1.67605i) q^{12} +(1.28368 + 3.52688i) q^{13} +(2.28146 + 1.31720i) q^{14} +(-1.80373 - 2.14961i) q^{15} +(1.76211 - 1.47859i) q^{16} +(-1.35792 + 3.73084i) q^{17} +(0.537688 + 0.0948090i) q^{18} +(0.0176348 + 0.00310950i) q^{19} +(1.63339 - 4.48771i) q^{20} +(3.69621 - 3.10149i) q^{21} +(-1.77548 - 2.11593i) q^{22} +(-1.30435 - 0.753069i) q^{23} +(0.691283 + 1.89928i) q^{24} +(-0.499109 - 2.83059i) q^{25} +(-1.02460 - 1.77466i) q^{26} +(0.500000 - 0.866025i) q^{27} +(7.71654 + 2.80859i) q^{28} +(0.267425 - 0.154398i) q^{29} +(1.17365 + 0.984808i) q^{30} +0.389915i q^{31} +(-3.40566 + 4.05871i) q^{32} +(-4.75395 + 1.73030i) q^{33} +(0.376418 - 2.13477i) q^{34} +(13.3339 - 2.35113i) q^{35} +1.70190 q^{36} +(-1.48422 - 5.89891i) q^{37} -0.00977686 q^{38} +(-3.69621 + 0.651741i) q^{39} +(-0.984871 + 5.58548i) q^{40} +(-5.97342 + 2.17415i) q^{41} +(-1.69336 + 2.01807i) q^{42} -2.06301i q^{43} +(-6.59565 - 5.53440i) q^{44} +(2.43016 - 1.40306i) q^{45} +(0.772733 + 0.281252i) q^{46} +(4.05109 - 7.01669i) q^{47} +(1.15014 + 1.99210i) q^{48} +(2.82719 + 16.0338i) q^{49} +(0.536730 + 1.47465i) q^{50} +(-3.43836 - 1.98514i) q^{51} +(-4.10589 - 4.89321i) q^{52} +(-3.48258 + 2.92223i) q^{53} +(-0.186737 + 0.513056i) q^{54} +(-13.9806 - 2.46515i) q^{55} +(-9.60413 - 1.69347i) q^{56} +(-0.00612451 + 0.0168270i) q^{57} +(-0.129153 + 0.108372i) q^{58} +(4.86717 + 5.80047i) q^{59} +(4.13590 + 2.38786i) q^{60} +(4.15675 + 11.4206i) q^{61} +(-0.0369674 - 0.209653i) q^{62} +(2.41253 + 4.17862i) q^{63} +(-0.853895 + 1.47899i) q^{64} +(-9.89681 - 3.60215i) q^{65} +(2.39210 - 1.38108i) q^{66} +(8.23757 + 6.91214i) q^{67} -6.75703i q^{68} +(0.968127 - 1.15377i) q^{69} +(-6.94660 + 2.52835i) q^{70} +(-0.262423 + 1.48827i) q^{71} +(-1.99047 + 0.350974i) q^{72} -4.55321 q^{73} +(1.35732 + 3.03106i) q^{74} +2.87425 q^{75} +(-0.0300128 + 0.00529206i) q^{76} +(4.23878 - 24.0393i) q^{77} +(1.92562 - 0.700867i) q^{78} +(8.84365 - 10.5395i) q^{79} +6.45483i q^{80} +(0.766044 + 0.642788i) q^{81} +(3.00571 - 1.73535i) q^{82} +(-4.41933 - 1.60850i) q^{83} +(-4.10589 + 7.11160i) q^{84} +(-5.57052 - 9.64843i) q^{85} +(0.195592 + 1.10926i) q^{86} +(0.105614 + 0.290173i) q^{87} +(8.85531 + 5.11261i) q^{88} +(7.73007 + 9.21234i) q^{89} +(-1.17365 + 0.984808i) q^{90} +(6.19382 - 17.0174i) q^{91} +(2.52436 + 0.445112i) q^{92} +(-0.383991 - 0.0677080i) q^{93} +(-1.51298 + 4.15687i) q^{94} +(-0.0384927 + 0.0322992i) q^{95} +(-3.40566 - 4.05871i) q^{96} +(-2.23826 - 1.29226i) q^{97} +(-3.04030 - 8.35315i) q^{98} +(-0.878494 - 4.98219i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8}+O(q^{10}) \) 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8	\( 12 q + 3 q^{2} - 3 q^{4} - 3 q^{5} - 6 q^{7} - 9 q^{8} - 6 q^{11} - 6 q^{12} - 6 q^{13} + 27 q^{14} - 3 q^{15} + 3 q^{16} - 6 q^{17} - 3 q^{18} - 12 q^{19} + 9 q^{20} + 6 q^{21} - 21 q^{22} - 6 q^{24} - 15 q^{25} + 6 q^{27} + 39 q^{28} + 27 q^{29} + 12 q^{30} - 33 q^{32} - 12 q^{33} + 15 q^{34} + 36 q^{35} + 15 q^{37} - 48 q^{38} - 6 q^{39} + 15 q^{40} + 12 q^{41} + 18 q^{42} - 21 q^{44} - 15 q^{46} + 9 q^{47} - 18 q^{49} - 18 q^{50} + 9 q^{51} + 6 q^{52} - 12 q^{53} - 3 q^{54} - 39 q^{55} - 18 q^{56} - 3 q^{57} - 15 q^{58} - 15 q^{61} + 39 q^{62} + 12 q^{63} - 9 q^{64} - 24 q^{65} + 18 q^{66} + 6 q^{67} - 12 q^{69} - 15 q^{70} - 3 q^{71} - 6 q^{72} + 90 q^{73} + 72 q^{74} - 24 q^{75} - 6 q^{76} + 27 q^{77} + 9 q^{78} + 6 q^{79} + 27 q^{82} - 3 q^{83} + 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{87} + 63 q^{88} + 39 q^{89} - 12 q^{90} - 27 q^{91} + 6 q^{92} - 24 q^{93} + 30 q^{94} - 36 q^{95} - 33 q^{96} - 18 q^{97} - 42 q^{98} + 3 q^{99}+O(q^{100}) \) 12 * q + 3 * q^2 - 3 * q^4 - 3 * q^5 - 6 * q^7 - 9 * q^8 - 6 * q^11 - 6 * q^12 - 6 * q^13 + 27 * q^14 - 3 * q^15 + 3 * q^16 - 6 * q^17 - 3 * q^18 - 12 * q^19 + 9 * q^20 + 6 * q^21 - 21 * q^22 - 6 * q^24 - 15 * q^25 + 6 * q^27 + 39 * q^28 + 27 * q^29 + 12 * q^30 - 33 * q^32 - 12 * q^33 + 15 * q^34 + 36 * q^35 + 15 * q^37 - 48 * q^38 - 6 * q^39 + 15 * q^40 + 12 * q^41 + 18 * q^42 - 21 * q^44 - 15 * q^46 + 9 * q^47 - 18 * q^49 - 18 * q^50 + 9 * q^51 + 6 * q^52 - 12 * q^53 - 3 * q^54 - 39 * q^55 - 18 * q^56 - 3 * q^57 - 15 * q^58 - 15 * q^61 + 39 * q^62 + 12 * q^63 - 9 * q^64 - 24 * q^65 + 18 * q^66 + 6 * q^67 - 12 * q^69 - 15 * q^70 - 3 * q^71 - 6 * q^72 + 90 * q^73 + 72 * q^74 - 24 * q^75 - 6 * q^76 + 27 * q^77 + 9 * q^78 + 6 * q^79 + 27 * q^82 - 3 * q^83 + 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^87 + 63 * q^88 + 39 * q^89 - 12 * q^90 - 27 * q^91 + 6 * q^92 - 24 * q^93 + 30 * q^94 - 36 * q^95 - 33 * q^96 - 18 * q^97 - 42 * q^98 + 3 * q^99

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