LMFDB - Embedded newform 111.2.o.a.4.2

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			4.2
Root			$-1.83156i$ of defining polynomial
Character	$\chi$	$=$	111.4
Dual form			111.2.o.a.28.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80373 + 0.318047i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(1.27291 + 0.463303i) q^{4} +(0.537688 + 0.640792i) q^{5} -1.83156i q^{6} +(-0.541619 + 0.454472i) q^{7} +(-1.02371 - 0.591038i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})$	\(q+(1.80373 + 0.318047i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(1.27291 + 0.463303i) q^{4} +(0.537688 + 0.640792i) q^{5} -1.83156i q^{6} +(-0.541619 + 0.454472i) q^{7} +(-1.02371 - 0.591038i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.766044 + 1.32683i) q^{10} +(-1.05774 + 1.83206i) q^{11} +(0.235225 - 1.33403i) q^{12} +(0.188102 - 0.516807i) q^{13} +(-1.12148 + 0.647486i) q^{14} +(0.537688 - 0.640792i) q^{15} +(-3.73390 - 3.13311i) q^{16} +(0.603016 + 1.65677i) q^{17} +(-1.80373 + 0.318047i) q^{18} +(-1.07794 + 0.190070i) q^{19} +(0.387550 + 1.06479i) q^{20} +(0.541619 + 0.454472i) q^{21} +(-2.49057 + 2.96814i) q^{22} +(-3.36336 + 1.94184i) q^{23} +(-0.404294 + 1.11079i) q^{24} +(0.746735 - 4.23495i) q^{25} +(0.503655 - 0.872356i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.899992 + 0.327570i) q^{28} +(6.53071 + 3.77051i) q^{29} +(1.17365 - 0.984808i) q^{30} -5.68394i q^{31} +(-4.21883 - 5.02780i) q^{32} +(1.98790 + 0.723538i) q^{33} +(0.560748 + 3.18016i) q^{34} +(-0.582444 - 0.102701i) q^{35} -1.35461 q^{36} +(4.57661 - 4.00682i) q^{37} -2.00477 q^{38} +(-0.541619 - 0.0955020i) q^{39} +(-0.171703 - 0.973779i) q^{40} +(6.51279 + 2.37046i) q^{41} +(0.832392 + 0.992006i) q^{42} -8.86481i q^{43} +(-2.19521 + 1.84200i) q^{44} +(-0.724426 - 0.418247i) q^{45} +(-6.68421 + 2.43285i) q^{46} +(4.86426 + 8.42514i) q^{47} +(-2.43713 + 4.22123i) q^{48} +(-1.12873 + 6.40135i) q^{49} +(2.69382 - 7.40121i) q^{50} +(1.52689 - 0.881550i) q^{51} +(0.478876 - 0.570702i) q^{52} +(-6.10641 - 5.12389i) q^{53} +(0.626430 + 1.72110i) q^{54} +(-1.74271 + 0.307286i) q^{55} +(0.823070 - 0.145129i) q^{56} +(0.374365 + 1.02856i) q^{57} +(10.5805 + 8.87806i) q^{58} +(-4.86717 + 5.80047i) q^{59} +(0.981311 - 0.566560i) q^{60} +(-1.43734 + 3.94906i) q^{61} +(1.80776 - 10.2523i) q^{62} +(0.353517 - 0.612309i) q^{63} +(-1.13630 - 1.96814i) q^{64} +(0.432306 - 0.157347i) q^{65} +(3.35553 + 1.93732i) q^{66} +(-2.29401 + 1.92490i) q^{67} +2.38831i q^{68} +(2.49638 + 2.97507i) q^{69} +(-1.01791 - 0.370489i) q^{70} +(-2.63791 - 14.9603i) q^{71} +(1.16412 + 0.205265i) q^{72} +10.3607 q^{73} +(9.52934 - 5.77166i) q^{74} -4.30028 q^{75} +(-1.46019 - 0.257470i) q^{76} +(-0.259729 - 1.47299i) q^{77} +(-0.946561 - 0.344520i) q^{78} +(2.66662 + 3.17795i) q^{79} -4.07729i q^{80} +(0.766044 - 0.642788i) q^{81} +(10.9934 + 6.34705i) q^{82} +(-5.23250 + 1.90447i) q^{83} +(0.478876 + 0.829437i) q^{84} +(-0.737412 + 1.27723i) q^{85} +(2.81942 - 15.9897i) q^{86} +(2.57918 - 7.08623i) q^{87} +(2.16564 - 1.25033i) q^{88} +(-1.88396 + 2.24521i) q^{89} +(-1.17365 - 0.984808i) q^{90} +(0.132994 + 0.365399i) q^{91} +(-5.18093 + 0.913538i) q^{92} +(-5.59759 + 0.987006i) q^{93} +(6.09423 + 16.7438i) q^{94} +(-0.701393 - 0.588538i) q^{95} +(-4.21883 + 5.02780i) q^{96} +(-13.2943 + 7.67547i) q^{97} +(-4.07186 + 11.1873i) q^{98} +(0.367350 - 2.08335i) 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 $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.80373	+	0.318047i	1.27543	+	0.224893i	0.770039	−	0.637997i	$-0.220237\pi$
$2$	1.80373	+	0.318047i	1.27543	+	0.224893i	0.505393	+	0.862890i	$0.331348\pi$
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$3$	−0.173648	−	0.984808i	−0.100256	−	0.568579i
$4$	1.27291	+	0.463303i	0.636457	+	0.231651i
$5$	0.537688	+	0.640792i	0.240462	+	0.286571i	0.872755	−	0.488158i	$-0.162331\pi$
$5$	0.537688	+	0.640792i	0.240462	+	0.286571i	−0.632294	+	0.774729i	$0.717886\pi$
$6$		−	1.83156i		−	0.747731i
$7$	−0.541619	+	0.454472i	−0.204713	+	0.171774i	−0.739380	−	0.673288i	$-0.764881\pi$
$7$	−0.541619	+	0.454472i	−0.204713	+	0.171774i	0.534667	+	0.845063i	$0.320437\pi$
$8$	−1.02371	−	0.591038i	−0.361936	−	0.208964i
$9$	−0.939693	+	0.342020i	−0.313231	+	0.114007i
$10$	0.766044	+	1.32683i	0.242245	+	0.419580i
$11$	−1.05774	+	1.83206i	−0.318921	+	0.552388i	−0.980263	−	0.197697i	$-0.936654\pi$
$11$	−1.05774	+	1.83206i	−0.318921	+	0.552388i	0.661342	+	0.750084i	$0.269987\pi$
$12$	0.235225	−	1.33403i	0.0679036	−	0.385100i
$13$	0.188102	−	0.516807i	0.0521702	−	0.143336i	−0.910871	−	0.412692i	$-0.864589\pi$
$13$	0.188102	−	0.516807i	0.0521702	−	0.143336i	0.963041	+	0.269356i	$0.0868108\pi$
$14$	−1.12148	+	0.647486i	−0.299728	+	0.173048i
$15$	0.537688	−	0.640792i	0.138831	−	0.165452i
$16$	−3.73390	−	3.13311i	−0.933474	−	0.783278i
$17$	0.603016	+	1.65677i	0.146253	+	0.401826i	0.991089	−	0.133198i	$-0.0425247\pi$
$17$	0.603016	+	1.65677i	0.146253	+	0.401826i	−0.844837	+	0.535024i	$0.820302\pi$
$18$	−1.80373	+	0.318047i	−0.425144	+	0.0749643i
$19$	−1.07794	+	0.190070i	−0.247297	+	0.0436051i	−0.295922	−	0.955212i	$-0.595627\pi$
$19$	−1.07794	+	0.190070i	−0.247297	+	0.0436051i	0.0486256	+	0.998817i	$0.484516\pi$
$20$	0.387550	+	1.06479i	0.0866588	+	0.238093i
$21$	0.541619	+	0.454472i	0.118191	+	0.0991739i
$22$	−2.49057	+	2.96814i	−0.530990	+	0.632810i
$23$	−3.36336	+	1.94184i	−0.701310	+	0.404902i	−0.807835	−	0.589408i	$-0.799361\pi$
$23$	−3.36336	+	1.94184i	−0.701310	+	0.404902i	0.106525	+	0.994310i	$0.466028\pi$
$24$	−0.404294	+	1.11079i	−0.0825262	+	0.226739i
$25$	0.746735	−	4.23495i	0.149347	−	0.846989i
$26$	0.503655	−	0.872356i	0.0987748	−	0.171083i
$27$	0.500000	+	0.866025i	0.0962250	+	0.166667i
$28$	−0.899992	+	0.327570i	−0.170082	+	0.0619050i
$29$	6.53071	+	3.77051i	1.21272	+	0.700165i	0.963351	−	0.268243i	$-0.0864429\pi$
$29$	6.53071	+	3.77051i	1.21272	+	0.700165i	0.249371	+	0.968408i	$0.419776\pi$
$30$	1.17365	−	0.984808i	0.214278	−	0.179800i
$31$		−	5.68394i		−	1.02087i	−0.859917	−	0.510433i	$-0.829485\pi$
$31$		−	5.68394i		−	1.02087i	0.859917	−	0.510433i	$-0.170515\pi$
$32$	−4.21883	−	5.02780i	−0.745790	−	0.888798i
$33$	1.98790	+	0.723538i	0.346050	+	0.125952i
$34$	0.560748	+	3.18016i	0.0961675	+	0.545393i
$35$	−0.582444	−	0.102701i	−0.0984511	−	0.0173596i
$36$	−1.35461			−0.225768
$37$	4.57661	−	4.00682i	0.752391	−	0.658717i
$37$	4.57661	−	4.00682i	0.752391	−	0.658717i
$38$	−2.00477			−0.325217
$39$	−0.541619	−	0.0955020i	−0.0867284	−	0.0152926i
$40$	−0.171703	−	0.973779i	−0.0271487	−	0.153968i
$41$	6.51279	+	2.37046i	1.01713	+	0.370204i	0.796165	−	0.605079i	$-0.206858\pi$
$41$	6.51279	+	2.37046i	1.01713	+	0.370204i	0.220961	+	0.975283i	$0.429081\pi$
$42$	0.832392	+	0.992006i	0.128441	+	0.153070i
$43$		−	8.86481i		−	1.35187i	−0.736961	−	0.675935i	$-0.763740\pi$
$43$		−	8.86481i		−	1.35187i	0.736961	−	0.675935i	$-0.236260\pi$
$44$	−2.19521	+	1.84200i	−0.330941	+	0.277692i
$45$	−0.724426	−	0.418247i	−0.107991	−	0.0623486i
$46$	−6.68421	+	2.43285i	−0.985533	+	0.358705i
$47$	4.86426	+	8.42514i	0.709525	+	1.22893i	0.965034	+	0.262126i	$0.0844236\pi$
$47$	4.86426	+	8.42514i	0.709525	+	1.22893i	−0.255509	+	0.966807i	$0.582243\pi$
$48$	−2.43713	+	4.22123i	−0.351769	+	0.609282i
$49$	−1.12873	+	6.40135i	−0.161247	+	0.914479i
$50$	2.69382	−	7.40121i	0.380964	−	1.04669i
$51$	1.52689	−	0.881550i	0.213807	−	0.123442i
$52$	0.478876	−	0.570702i	0.0664081	−	0.0791421i
$53$	−6.10641	−	5.12389i	−0.838780	−	0.703820i	0.118509	−	0.992953i	$-0.462189\pi$
$53$	−6.10641	−	5.12389i	−0.838780	−	0.703820i	−0.957289	+	0.289133i	$0.906633\pi$
$54$	0.626430	+	1.72110i	0.0852463	+	0.234212i
$55$	−1.74271	+	0.307286i	−0.234987	+	0.0414345i
$56$	0.823070	−	0.145129i	0.109987	−	0.0193937i
$57$	0.374365	+	1.02856i	0.0495859	+	0.136236i
$58$	10.5805	+	8.87806i	1.38928	+	1.16575i
$59$	−4.86717	+	5.80047i	−0.633652	+	0.755157i	−0.983353	−	0.181704i	$-0.941839\pi$
$59$	−4.86717	+	5.80047i	−0.633652	+	0.755157i	0.349701	+	0.936861i	$0.386283\pi$
$60$	0.981311	−	0.566560i	0.126687	−	0.0731426i
$61$	−1.43734	+	3.94906i	−0.184033	+	0.505626i	−0.997062	−	0.0765969i	$-0.975595\pi$
$61$	−1.43734	+	3.94906i	−0.184033	+	0.505626i	0.813029	+	0.582223i	$0.197817\pi$
$62$	1.80776	−	10.2523i	0.229586	−	1.30205i
$63$	0.353517	−	0.612309i	0.0445389	−	0.0771436i
$64$	−1.13630	−	1.96814i	−0.142038	−	0.246017i
$65$	0.432306	−	0.157347i	0.0536210	−	0.0195164i
$66$	3.35553	+	1.93732i	0.413037	+	0.238467i
$67$	−2.29401	+	1.92490i	−0.280257	+	0.235164i	−0.772070	−	0.635537i	$-0.780779\pi$
$67$	−2.29401	+	1.92490i	−0.280257	+	0.235164i	0.491813	+	0.870701i	$0.336334\pi$
$68$			2.38831i			0.289625i
$69$	2.49638	+	2.97507i	0.300529	+	0.358156i
$70$	−1.01791	−	0.370489i	−0.121664	−	0.0442819i
$71$	−2.63791	−	14.9603i	−0.313062	−	1.77546i	−0.582887	−	0.812553i	$-0.698077\pi$
$71$	−2.63791	−	14.9603i	−0.313062	−	1.77546i	0.269825	−	0.962909i	$-0.413034\pi$
$72$	1.16412	+	0.205265i	0.137193	+	0.0241908i
$73$	10.3607			1.21263			0.606313	−	0.795226i	$-0.292648\pi$
$73$	10.3607			1.21263			0.606313	+	0.795226i	$0.292648\pi$
$74$	9.52934	−	5.77166i	1.10776	−	0.670942i
$75$	−4.30028			−0.496553
$76$	−1.46019	−	0.257470i	−0.167495	−	0.0295339i
$77$	−0.259729	−	1.47299i	−0.0295988	−	0.167863i
$78$	−0.946561	−	0.344520i	−0.107177	−	0.0390092i
$79$	2.66662	+	3.17795i	0.300018	+	0.357547i	0.894901	−	0.446265i	$-0.147246\pi$
$79$	2.66662	+	3.17795i	0.300018	+	0.357547i	−0.594883	+	0.803812i	$0.702802\pi$
$80$		−	4.07729i		−	0.455855i
$81$	0.766044	−	0.642788i	0.0851160	−	0.0714208i
$82$	10.9934	+	6.34705i	1.21402	+	0.700914i
$83$	−5.23250	+	1.90447i	−0.574341	+	0.209043i	−0.612828	−	0.790216i	$-0.709968\pi$
$83$	−5.23250	+	1.90447i	−0.574341	+	0.209043i	0.0384873	+	0.999259i	$0.487746\pi$
$84$	0.478876	+	0.829437i	0.0522496	+	0.0904990i
$85$	−0.737412	+	1.27723i	−0.0799835	+	0.138536i
$86$	2.81942	−	15.9897i	0.304026	−	1.72422i
$87$	2.57918	−	7.08623i	0.276517	−	0.759724i
$88$	2.16564	−	1.25033i	0.230858	−	0.133286i
$89$	−1.88396	+	2.24521i	−0.199699	+	0.237992i	−0.856595	−	0.515989i	$-0.827425\pi$
$89$	−1.88396	+	2.24521i	−0.199699	+	0.237992i	0.656896	+	0.753981i	$0.271869\pi$
$90$	−1.17365	−	0.984808i	−0.123713	−	0.103808i
$91$	0.132994	+	0.365399i	0.0139416	+	0.0383043i
$92$	−5.18093	+	0.913538i	−0.540149	+	0.0952429i
$93$	−5.59759	+	0.987006i	−0.580443	+	0.102348i
$94$	6.09423	+	16.7438i	0.628572	+	1.72699i
$95$	−0.701393	−	0.588538i	−0.0719614	−	0.0603828i
$96$	−4.21883	+	5.02780i	−0.430582	+	0.513148i
$97$	−13.2943	+	7.67547i	−1.34983	+	0.779325i	−0.988225	−	0.153006i	$-0.951105\pi$
$97$	−13.2943	+	7.67547i	−1.34983	+	0.779325i	−0.361606	+	0.932331i	$0.617771\pi$
$98$	−4.07186	+	11.1873i	−0.411320	+	1.13009i
$99$	0.367350	−	2.08335i	0.0369201	−	0.209384i
$100$	2.91259	−	5.04475i	0.291259	−	0.504475i
$101$	−0.174353	−	0.301988i	−0.0173488	−	0.0300489i	0.857221	−	0.514949i	$-0.172189\pi$
$101$	−0.174353	−	0.301988i	−0.0173488	−	0.0300489i	−0.874569	+	0.484900i	$0.838856\pi$
$102$	3.03447	−	1.10446i	0.300458	−	0.109358i
$103$	3.82263	+	2.20700i	0.376655	+	0.217462i	0.676362	−	0.736570i	$-0.263556\pi$
$103$	3.82263	+	2.20700i	0.376655	+	0.217462i	−0.299707	+	0.954031i	$0.596889\pi$
$104$	−0.498014	+	0.417884i	−0.0488343	+	0.0409769i
$105$			0.591429i			0.0577176i
$106$	−9.38470	−	11.1842i	−0.911523	−	1.08631i
$107$	−16.5206	−	6.01300i	−1.59711	−	0.581299i	−0.618273	−	0.785963i	$-0.712167\pi$
$107$	−16.5206	−	6.01300i	−1.59711	−	0.581299i	−0.978832	+	0.204664i	$0.934390\pi$
$108$	0.235225	+	1.33403i	0.0226345	+	0.128367i
$109$	−13.8813	−	2.44765i	−1.32959	−	0.234442i	−0.536682	−	0.843785i	$-0.680322\pi$
$109$	−13.8813	−	2.44765i	−1.32959	−	0.234442i	−0.792907	+	0.609343i	$0.791433\pi$
$110$	−3.24111			−0.309028
$111$	−4.74067	−	3.81131i	−0.449964	−	0.361753i
$112$	3.44626			0.325641
$113$	−1.23573	−	0.217892i	−0.116247	−	0.0204976i	0.115222	−	0.993340i	$-0.463242\pi$
$113$	−1.23573	−	0.217892i	−0.116247	−	0.0204976i	−0.231469	+	0.972842i	$0.574353\pi$
$114$	0.348125	+	1.97431i	0.0326049	+	0.184911i
$115$	−3.05276	−	1.11111i	−0.284671	−	0.103612i
$116$	6.56614	+	7.82522i	0.609651	+	0.726554i
$117$			0.549974i			0.0508451i
$118$	−10.6239	+	8.91451i	−0.978009	+	0.820647i
$119$	−1.07956	−	0.623285i	−0.0989632	−	0.0571364i
$120$	−0.929169	+	0.338190i	−0.0848211	+	0.0308724i
$121$	3.26236	+	5.65058i	0.296579	+	0.513689i
$122$	−3.84857	+	6.66591i	−0.348433	+	0.603503i
$123$	1.20351	−	6.82547i	0.108517	−	0.615432i
$124$	2.63339	−	7.23517i	0.236485	−	0.649737i
$125$	6.73736	−	3.88982i	0.602608	−	0.347916i
$126$	0.832392	−	0.992006i	0.0741554	−	0.0883750i
$127$	−13.2564	−	11.1234i	−1.17631	−	0.987043i	−0.999996	−	0.00270990i	$-0.999137\pi$
$127$	−13.2564	−	11.1234i	−1.17631	−	0.987043i	−0.176316	−	0.984334i	$-0.556418\pi$
$128$	3.06595	+	8.42363i	0.270994	+	0.744551i
$129$	−8.73013	+	1.53936i	−0.768645	+	0.135533i
$130$	0.829808	−	0.146318i	0.0727790	−	0.0128329i
$131$	4.19803	+	11.5340i	0.366784	+	1.00773i	0.976577	+	0.215169i	$0.0690304\pi$
$131$	4.19803	+	11.5340i	0.366784	+	1.00773i	−0.609793	+	0.792561i	$0.708747\pi$
$132$	2.19521	+	1.84200i	0.191069	+	0.160326i
$133$	0.497452	−	0.592840i	0.0431346	−	0.0514058i
$134$	−4.74998	+	2.74240i	−0.410336	+	0.236908i
$135$	−0.286098	+	0.786048i	−0.0246234	+	0.0676522i
$136$	0.361904	−	2.05246i	0.0310330	−	0.175997i
$137$	−1.13625	+	1.96805i	−0.0970767	+	0.168142i	−0.910473	−	0.413568i	$-0.864283\pi$
$137$	−1.13625	+	1.96805i	−0.0970767	+	0.168142i	0.813397	+	0.581709i	$0.197616\pi$
$138$	3.55659	+	6.16020i	0.302757	+	0.524391i
$139$	0.759891	−	0.276578i	0.0644531	−	0.0234590i	−0.309592	−	0.950869i	$-0.600193\pi$
$139$	0.759891	−	0.276578i	0.0644531	−	0.0234590i	0.374046	+	0.927410i	$0.377970\pi$
$140$	−0.693820	−	0.400577i	−0.0586385	−	0.0338549i
$141$	7.45247	−	6.25337i	0.627611	−	0.526628i
$142$		−	27.8234i		−	2.33489i
$143$	0.747859	+	0.891263i	0.0625391	+	0.0745312i
$144$	4.58030	+	1.66709i	0.381692	+	0.138924i
$145$	1.09538	+	6.21218i	0.0909660	+	0.515894i
$146$	18.6879	+	3.29518i	1.54662	+	0.272711i
$147$	6.50010			0.536120
$148$	7.68200	−	2.97998i	0.631457	−	0.244953i
$149$	4.77906			0.391516			0.195758	−	0.980652i	$-0.437283\pi$
$149$	4.77906			0.391516			0.195758	+	0.980652i	$0.437283\pi$
$150$	−7.75655	−	1.36769i	−0.633320	−	0.111671i
$151$	0.258866	+	1.46810i	0.0210662	+	0.119473i	0.993527	−	0.113592i	$-0.0362357\pi$
$151$	0.258866	+	1.46810i	0.0210662	+	0.119473i	−0.972461	+	0.233065i	$0.925125\pi$
$152$	1.21584	+	0.442529i	0.0986174	+	0.0358938i
$153$	−1.13330	−	1.35061i	−0.0916218	−	0.109191i
$154$		−	2.73949i		−	0.220755i
$155$	3.64223	−	3.05619i	0.292551	−	0.245479i
$156$	−0.645187	−	0.372499i	−0.0516563	−	0.0298238i
$157$	14.5320	−	5.28922i	1.15978	−	0.422125i	0.310761	−	0.950488i	$-0.399416\pi$
$157$	14.5320	−	5.28922i	1.15978	−	0.422125i	0.849019	+	0.528363i	$0.177194\pi$
$158$	3.79913	+	6.58028i	0.302242	+	0.523499i
$159$	−3.98568	+	6.90340i	−0.316085	+	0.547475i
$160$	0.953361	−	5.40678i	0.0753698	−	0.427444i
$161$	0.939150	−	2.58029i	0.0740154	−	0.203356i
$162$	1.58618	−	0.915779i	0.124622	−	0.0719504i
$163$	8.81726	−	10.5080i	0.690621	−	0.823051i	−0.300809	−	0.953684i	$-0.597257\pi$
$163$	8.81726	−	10.5080i	0.690621	−	0.823051i	0.991431	+	0.130634i	$0.0417012\pi$
$164$	7.19197	+	6.03478i	0.561599	+	0.471237i
$165$	0.605236	+	1.66287i	0.0471175	+	0.129454i
$166$	−10.0437	+	1.77098i	−0.779545	+	0.137455i
$167$	5.93220	−	1.04601i	0.459047	−	0.0809424i	0.0606575	−	0.998159i	$-0.480680\pi$
$167$	5.93220	−	1.04601i	0.459047	−	0.0809424i	0.398390	+	0.917216i	$0.369569\pi$
$168$	−0.285849	−	0.785364i	−0.0220537	−	0.0605922i
$169$	9.72687	+	8.16181i	0.748221	+	0.627832i
$170$	−1.73631	+	2.06926i	−0.133169	+	0.158705i
$171$	0.947926	−	0.547286i	0.0724897	−	0.0418520i
$172$	4.10709	−	11.2841i	0.313162	−	0.860407i
$173$	1.04292	−	5.91470i	0.0792918	−	0.449686i	−0.919151	−	0.393905i	$-0.871124\pi$
$173$	1.04292	−	5.91470i	0.0792918	−	0.449686i	0.998443	−	0.0557814i	$-0.0177650\pi$
$174$	6.90590	−	11.9614i	0.523535	−	0.906789i
$175$	1.52022	+	2.63310i	0.114918	+	0.199043i
$176$	9.68955	−	3.52671i	0.730378	−	0.265836i
$177$	6.55752	+	3.78599i	0.492894	+	0.284572i
$178$	−4.11224	+	3.45058i	−0.308226	+	0.258632i
$179$			21.1169i			1.57835i	0.614168	+	0.789175i	$0.289492\pi$
$179$			21.1169i			1.57835i	−0.614168	+	0.789175i	$0.710508\pi$
$180$	−0.728356	−	0.868021i	−0.0542885	−	0.0646985i
$181$	−20.9626	−	7.62977i	−1.55814	−	0.567117i	−0.587831	−	0.808984i	$-0.700018\pi$
$181$	−20.9626	−	7.62977i	−1.55814	−	0.567117i	−0.970309	+	0.241867i	$0.922240\pi$
$182$	0.123672	+	0.701381i	0.00916721	+	0.0519898i
$183$	4.13866	+	0.729757i	0.305938	+	0.0539452i
$184$	4.59081			0.338439
$185$	5.02833	+	0.778236i	0.369690	+	0.0572171i
$186$	−10.4105			−0.763333
$187$	−3.67315	−	0.647675i	−0.268607	−	0.0473627i
$188$	2.28839	+	12.9781i	0.166898	+	0.946525i
$189$	−0.664394	−	0.241820i	−0.0483275	−	0.0175898i
$190$	−1.07794	−	1.28464i	−0.0782021	−	0.0931977i
$191$			5.32678i			0.385433i	0.981255	+	0.192716i	$0.0617297\pi$
$191$			5.32678i			0.385433i	−0.981255	+	0.192716i	$0.938270\pi$
$192$	−1.74092	+	1.46081i	−0.125640	+	0.105425i
$193$	18.4352	+	10.6435i	1.32699	+	0.766139i	0.984833	−	0.173504i	$-0.0555088\pi$
$193$	18.4352	+	10.6435i	1.32699	+	0.766139i	0.342158	+	0.939642i	$0.388842\pi$
$194$	−26.4205	+	9.61628i	−1.89688	+	0.690409i
$195$	−0.230025	−	0.398415i	−0.0164724	−	0.0285311i
$196$	−4.40254	+	7.62542i	−0.314467	+	0.544673i
$197$	3.07392	−	17.4331i	0.219008	−	1.24205i	−0.654807	−	0.755796i	$-0.727250\pi$
$197$	3.07392	−	17.4331i	0.219008	−	1.24205i	0.873815	−	0.486259i	$-0.161639\pi$
$198$	1.32520	−	3.64096i	0.0941780	−	0.258752i
$199$	10.5483	−	6.09009i	0.747753	−	0.431715i	−0.0771287	−	0.997021i	$-0.524575\pi$
$199$	10.5483	−	6.09009i	0.747753	−	0.431715i	0.824881	+	0.565306i	$0.191242\pi$
$200$	−3.26745	+	3.89400i	−0.231044	+	0.275347i
$201$	2.29401	+	1.92490i	0.161807	+	0.135772i
$202$	−0.218440	−	0.600158i	−0.0153694	−	0.0422270i
$203$	−5.25074	+	0.925848i	−0.368530	+	0.0649818i
$204$	2.35202	−	0.414725i	0.164674	−	0.0290366i
$205$	1.98288	+	5.44791i	0.138490	+	0.380499i
$206$	6.19307	+	5.19660i	0.431492	+	0.362065i
$207$	2.49638	−	2.97507i	0.173510	−	0.206782i
$208$	−2.32157	+	1.34036i	−0.160972	+	0.0929370i
$209$	0.791964	−	2.17590i	0.0547813	−	0.150510i
$210$	−0.188102	+	1.06678i	−0.0129803	+	0.0736149i
$211$	−5.42757	+	9.40083i	−0.373649	+	0.647180i	−0.990124	−	0.140195i	$-0.955227\pi$
$211$	−5.42757	+	9.40083i	−0.373649	+	0.647180i	0.616475	+	0.787375i	$0.288560\pi$
$212$	−5.39902	−	9.35138i	−0.370806	−	0.642256i
$213$	−14.2750	+	5.19566i	−0.978104	+	0.356001i
$214$	−27.8863	−	16.1002i	−1.90627	−	1.10058i
$215$	5.68050	−	4.76650i	0.387407	−	0.325073i
$216$		−	1.18208i		−	0.0804301i
$217$	2.58319	+	3.07853i	0.175359	+	0.208984i
$218$	−24.2597	−	8.82981i	−1.64308	−	0.598030i
$219$	−1.79911	−	10.2033i	−0.121573	−	0.689473i
$220$	−2.36068	−	0.416252i	−0.159157	−	0.0280637i
$221$	0.969659			0.0652263
$222$	−7.33873	−	8.38233i	−0.492543	−	0.562585i
$223$	18.0124			1.20620			0.603101	−	0.797665i	$-0.293932\pi$
$223$	18.0124			1.20620			0.603101	+	0.797665i	$0.293932\pi$
$224$	4.56999	+	0.805813i	0.305345	+	0.0538406i
$225$	0.746735	+	4.23495i	0.0497823	+	0.282330i
$226$	−2.15962	−	0.786038i	−0.143656	−	0.0522865i
$227$	−9.26195	−	11.0380i	−0.614737	−	0.732616i	0.365419	−	0.930843i	$-0.380926\pi$
$227$	−9.26195	−	11.0380i	−0.614737	−	0.732616i	−0.980156	+	0.198228i	$0.936481\pi$
$228$			1.48271i			0.0981951i
$229$	−19.0480	+	15.9832i	−1.25873	+	1.05620i	−0.262910	+	0.964820i	$0.584682\pi$
$229$	−19.0480	+	15.9832i	−1.25873	+	1.05620i	−0.995816	+	0.0913760i	$0.970873\pi$
$230$	−5.15297	−	2.97507i	−0.339777	−	0.196170i
$231$	−1.40551	+	0.511565i	−0.0924761	+	0.0336585i
$232$	−4.45703	−	7.71980i	−0.292618	−	0.506830i
$233$	0.0126240	−	0.0218654i	0.000827027	−	0.00143245i	−0.865612	−	0.500716i	$-0.833070\pi$
$233$	0.0126240	−	0.0218654i	0.000827027	−	0.00143245i	0.866439	+	0.499284i	$0.166403\pi$
$234$	−0.174917	+	0.992006i	−0.0114347	+	0.0648495i
$235$	−2.78331	+	7.64708i	−0.181563	+	0.498840i
$236$	−8.88286	+	5.12852i	−0.578225	+	0.333838i
$237$	2.66662	−	3.17795i	0.173215	−	0.206430i
$238$	−1.74901	−	1.46759i	−0.113371	−	0.0951298i
$239$	−0.470257	−	1.29202i	−0.0304184	−	0.0835739i	0.923554	−	0.383469i	$-0.125271\pi$
$239$	−0.470257	−	1.29202i	−0.0304184	−	0.0835739i	−0.953972	+	0.299895i	$0.903048\pi$
$240$	−4.01534	+	0.708014i	−0.259189	+	0.0457021i
$241$	−1.62475	+	0.286486i	−0.104659	+	0.0184542i	−0.225732	−	0.974189i	$-0.572477\pi$
$241$	−1.62475	+	0.286486i	−0.104659	+	0.0184542i	0.121073	+	0.992644i	$0.461366\pi$
$242$	4.08728	+	11.2297i	0.262741	+	0.721874i
$243$	−0.766044	−	0.642788i	−0.0491418	−	0.0412348i
$244$	−3.65922	+	4.36089i	−0.234258	+	0.279177i
$245$	−4.70884	+	2.71865i	−0.300837	+	0.173688i
$246$	4.34164	−	11.9285i	0.276813	−	0.760537i
$247$	−0.104534	+	0.592840i	−0.00665132	+	0.0377215i
$248$	−3.35943	+	5.81870i	−0.213324	+	0.369488i
$249$	2.78415	+	4.82230i	0.176439	+	0.305601i
$250$	13.3895	−	4.87339i	0.846829	−	0.308220i
$251$	14.7349	+	8.50719i	0.930058	+	0.536969i	0.886830	−	0.462096i	$-0.152902\pi$
$251$	14.7349	+	8.50719i	0.930058	+	0.536969i	0.0432280	+	0.999065i	$0.486236\pi$
$252$	0.733680	−	0.615631i	0.0462175	−	0.0387811i
$253$		−	8.21586i		−	0.516527i
$254$	−20.3732	−	24.2798i	−1.27833	−	1.52345i
$255$	1.38588	+	0.504419i	0.0867872	+	0.0315880i
$256$	3.64032	+	20.6453i	0.227520	+	1.29033i
$257$	20.4364	+	3.60349i	1.27479	+	0.224780i	0.769766	−	0.638326i	$-0.220373\pi$
$257$	20.4364	+	3.60349i	1.27479	+	0.224780i	0.505023	+	0.863106i	$0.331484\pi$
$258$	−16.2364			−1.01083
$259$	−0.657791	+	4.25011i	−0.0408732	+	0.264089i
$260$	0.623187			0.0386484
$261$	−7.42645	−	1.30948i	−0.459686	−	0.0810550i
$262$	3.90378	+	22.1394i	0.241176	+	1.36778i
$263$	5.65175	+	2.05707i	0.348502	+	0.126844i	0.510339	−	0.859973i	$-0.329520\pi$
$263$	5.65175	+	2.05707i	0.348502	+	0.126844i	−0.161837	+	0.986817i	$0.551742\pi$
$264$	−1.60740	−	1.91562i	−0.0989284	−	0.117898i
$265$		−	6.66800i		−	0.409612i
$266$	1.08582	−	0.911113i	0.0665760	−	0.0558639i
$267$	2.53825	+	1.46546i	0.155338	+	0.0896847i
$268$	−3.81188	+	1.38741i	−0.232848	+	0.0847496i
$269$	−9.89403	−	17.1370i	−0.603250	−	1.04486i	−0.992325	−	0.123653i	$-0.960539\pi$
$269$	−9.89403	−	17.1370i	−0.603250	−	1.04486i	0.389076	−	0.921206i	$-0.372794\pi$
$270$	−0.766044	+	1.32683i	−0.0466200	+	0.0807482i
$271$	−4.87667	+	27.6570i	−0.296236	+	1.68004i	0.365898	+	0.930655i	$0.380762\pi$
$271$	−4.87667	+	27.6570i	−0.296236	+	1.68004i	−0.662134	+	0.749385i	$0.730349\pi$
$272$	2.93925	−	8.07553i	0.178218	−	0.489651i
$273$	0.336754	−	0.194425i	0.0203813	−	0.0117671i
$274$	−2.67543	+	3.18845i	−0.161629	+	0.192622i
$275$	6.96883	+	5.84755i	0.420236	+	0.352620i
$276$	1.79932	+	4.94359i	0.108306	+	0.297569i
$277$	7.00022	−	1.23433i	0.420602	−	0.0741635i	0.0406585	−	0.999173i	$-0.487054\pi$
$277$	7.00022	−	1.23433i	0.420602	−	0.0741635i	0.379944	+	0.925010i	$0.375943\pi$
$278$	1.45861	−	0.257192i	0.0874814	−	0.0154253i
$279$	1.94402	+	5.34116i	0.116386	+	0.319767i
$280$	0.535553	+	0.449382i	0.0320054	+	0.0268557i
$281$	6.66208	−	7.93956i	0.397427	−	0.473634i	−0.529807	−	0.848118i	$-0.677736\pi$
$281$	6.66208	−	7.93956i	0.397427	−	0.473634i	0.927233	+	0.374484i	$0.122180\pi$
$282$	15.4311	−	8.90917i	0.918911	−	0.530533i
$283$	10.1821	−	27.9752i	0.605265	−	1.66295i	−0.135169	−	0.990823i	$-0.543158\pi$
$283$	10.1821	−	27.9752i	0.605265	−	1.66295i	0.740434	−	0.672129i	$-0.234620\pi$
$284$	3.57332	−	20.2653i	0.212038	−	1.20253i
$285$	−0.457802	+	0.792935i	−0.0271178	+	0.0469694i
$286$	1.06547	+	1.84545i	0.0630028	+	0.109124i
$287$	−4.60476	+	1.67599i	−0.271810	+	0.0989308i
$288$	5.68401	+	3.28166i	0.334933	+	0.193374i
$289$	10.6415	−	8.92927i	0.625970	−	0.525251i
$290$			11.5535i			0.678445i
$291$	9.86739	+	11.7595i	0.578437	+	0.689354i
$292$	13.1882	+	4.80013i	0.771783	+	0.280906i
$293$	−4.52944	−	25.6877i	−0.264612	−	1.50069i	−0.770136	−	0.637879i	$-0.779812\pi$
$293$	−4.52944	−	25.6877i	−0.264612	−	1.50069i	0.505524	−	0.862813i	$-0.331299\pi$
$294$	11.7245	+	2.06734i	0.683784	+	0.120570i
$295$	−6.33392			−0.368775
$296$	−7.05330	+	1.39686i	−0.409965	+	0.0811910i
$297$	−2.11548			−0.122753
$298$	8.62015	+	1.51996i	0.499352	+	0.0880492i
$299$	0.370899	+	2.10347i	0.0214497	+	0.121647i
$300$	−5.47388	−	1.99233i	−0.316035	−	0.115027i
$301$	4.02881	+	4.80135i	0.232217	+	0.276745i
$302$			2.73040i			0.157117i
$303$	−0.267124	+	0.224144i	−0.0153459	+	0.0128767i
$304$	4.62043	+	2.66761i	0.265000	+	0.152998i
$305$	−3.30337	+	1.20233i	−0.189150	+	0.0688451i
$306$	−1.61461	−	2.79659i	−0.0923011	−	0.159870i
$307$	3.44609	−	5.96881i	0.196679	−	0.340658i	−0.750771	−	0.660563i	$-0.770318\pi$
$307$	3.44609	−	5.96881i	0.196679	−	0.340658i	0.947450	+	0.319905i	$0.103651\pi$
$308$	0.351830	−	1.99533i	0.0200474	−	0.113694i
$309$	1.50967	−	4.14779i	0.0858823	−	0.235960i
$310$	7.54161	−	4.35415i	0.428335	−	0.247299i
$311$	−6.19738	+	7.38575i	−0.351421	+	0.418807i	−0.912578	−	0.408902i	$-0.865912\pi$
$311$	−6.19738	+	7.38575i	−0.351421	+	0.418807i	0.561157	+	0.827709i	$0.310356\pi$
$312$	0.498014	+	0.417884i	0.0281945	+	0.0236580i
$313$	2.32618	+	6.39112i	0.131483	+	0.361248i	0.987912	−	0.155019i	$-0.0495437\pi$
$313$	2.32618	+	6.39112i	0.131483	+	0.361248i	−0.856428	+	0.516266i	$0.827322\pi$
$314$	27.8941	−	4.91848i	1.57415	−	0.277566i
$315$	0.582444	−	0.102701i	0.0328170	−	0.00578653i
$316$	1.92202	+	5.28070i	0.108122	+	0.297063i
$317$	−20.8782	−	17.5189i	−1.17264	−	0.983961i	−0.172639	−	0.984985i	$-0.555229\pi$
$317$	−20.8782	−	17.5189i	−1.17264	−	0.983961i	−0.999999	+	0.00102436i	$0.999674\pi$
$318$	−9.38470	+	11.1842i	−0.526268	+	0.627182i
$319$	−13.8156	+	7.97645i	−0.773526	+	0.446595i
$320$	0.650189	−	1.78638i	0.0363467	−	0.0998617i
$321$	−3.05288	+	17.3137i	−0.170395	+	0.966359i
$322$	2.51463	−	4.35546i	0.140135	−	0.242721i
$323$	−0.964919	−	1.67129i	−0.0536895	−	0.0929930i
$324$	1.27291	−	0.463303i	0.0707174	−	0.0257390i
$325$	−2.04819	−	1.18252i	−0.113613	−	0.0655944i
$326$	19.2460	−	16.1493i	1.06594	−	0.894429i
$327$			14.0955i			0.779480i
$328$	−5.26616	−	6.27597i	−0.290775	−	0.346532i
$329$	−6.46356	−	2.35254i	−0.356348	−	0.129700i
$330$	0.562813	+	3.19187i	0.0309818	+	0.175707i
$331$	−5.08623	−	0.896839i	−0.279564	−	0.0492947i	0.0321079	−	0.999484i	$-0.489778\pi$
$331$	−5.08623	−	0.896839i	−0.279564	−	0.0492947i	−0.311672	+	0.950190i	$0.600889\pi$
$332$	−7.54286			−0.413968
$333$	−2.93020	+	5.33047i	−0.160574	+	0.292108i
$334$	11.0328			0.603687
$335$	−2.46692	−	0.434985i	−0.134782	−	0.0237657i
$336$	−0.598437	−	3.39390i	−0.0326474	−	0.185153i
$337$	−27.8106	−	10.1222i	−1.51494	−	0.551393i	−0.555061	−	0.831810i	$-0.687305\pi$
$337$	−27.8106	−	10.1222i	−1.51494	−	0.551393i	−0.959878	+	0.280417i	$0.909527\pi$
$338$	14.9488	+	17.8153i	0.813110	+	0.969026i
$339$			1.25479i			0.0681509i
$340$	−1.53041	+	1.28416i	−0.0829980	+	0.0696436i
$341$	10.4133	+	6.01214i	0.563914	+	0.325576i
$342$	1.88387	−	0.685672i	0.101868	−	0.0370769i
$343$	−4.77251	−	8.26623i	−0.257691	−	0.446334i
$344$	−5.23944	+	9.07498i	−0.282492	+	0.489290i
$345$	−0.564127	+	3.19932i	−0.0303716	+	0.172246i
$346$	3.76230	−	10.3368i	0.202263	−	0.555712i
$347$	−9.61921	+	5.55365i	−0.516386	+	0.298136i	−0.735455	−	0.677574i	$-0.763031\pi$
$347$	−9.61921	+	5.55365i	−0.516386	+	0.298136i	0.219069	+	0.975709i	$0.429698\pi$
$348$	6.56614	−	7.82522i	0.351982	−	0.419476i
$349$	−7.79140	−	6.53776i	−0.417064	−	0.349958i	0.409981	−	0.912094i	$-0.365535\pi$
$349$	−7.79140	−	6.53776i	−0.417064	−	0.349958i	−0.827045	+	0.562136i	$0.809980\pi$
$350$	1.90462	+	5.23290i	0.101806	+	0.279710i
$351$	0.541619	−	0.0955020i	0.0289095	−	0.00509752i
$352$	13.6737	−	2.41104i	0.728809	−	0.128509i
$353$	−6.70223	−	18.4142i	−0.356723	−	0.980090i	−0.980159	−	0.198215i	$-0.936486\pi$
$353$	−6.70223	−	18.4142i	−0.356723	−	0.980090i	0.623435	−	0.781875i	$-0.285737\pi$
$354$	10.6239	+	8.91451i	0.564654	+	0.473801i
$355$	8.16808	−	9.73434i	0.433517	−	0.516645i
$356$	−3.43833	+	1.98512i	−0.182231	+	0.105211i
$357$	−0.426352	+	1.17139i	−0.0225649	+	0.0619967i
$358$	−6.71616	+	38.0892i	−0.354960	+	2.01308i
$359$	0.922941	−	1.59858i	0.0487109	−	0.0843698i	−0.840642	−	0.541591i	$-0.817822\pi$
$359$	0.922941	−	1.59858i	0.0487109	−	0.0843698i	0.889353	+	0.457222i	$0.151155\pi$
$360$	0.494400	+	0.856327i	0.0260572	+	0.0451324i
$361$	−16.7283	+	6.08861i	−0.880438	+	0.320453i
$362$	−35.3844	−	20.4292i	−1.85976	−	1.07373i
$363$	4.99823	−	4.19401i	0.262339	−	0.220129i
$364$			0.526738i			0.0276086i
$365$	5.57081	+	6.63904i	0.291590	+	0.347503i
$366$	7.23294	+	2.63257i	0.378072	+	0.137607i
$367$	2.55191	+	14.4726i	0.133209	+	0.755463i	0.976090	+	0.217365i	$0.0697461\pi$
$367$	2.55191	+	14.4726i	0.133209	+	0.755463i	−0.842882	+	0.538099i	$0.819143\pi$
$368$	18.6425	+	3.28717i	0.971805	+	0.171355i
$369$	−6.93076			−0.360801
$370$	8.82225	+	3.00297i	0.458647	+	0.156117i
$371$	5.63601			0.292607
$372$	−7.58253	−	1.33700i	−0.393136	−	0.0693205i
$373$	−2.62758	−	14.9018i	−0.136051	−	0.771584i	−0.974122	−	0.226023i	$-0.927428\pi$
$373$	−2.62758	−	14.9018i	−0.136051	−	0.771584i	0.838071	−	0.545561i	$-0.183683\pi$
$374$	−6.41938	−	2.33646i	−0.331938	−	0.120816i
$375$	−5.00065	−	5.95954i	−0.258233	−	0.307750i
$376$		−	11.4998i		−	0.593059i
$377$	3.17706	−	2.66587i	0.163627	−	0.137299i
$378$	−1.12148	−	0.647486i	−0.0576827	−	0.0333031i
$379$	34.7294	−	12.6405i	1.78393	−	0.649297i	0.784349	−	0.620320i	$-0.212997\pi$
$379$	34.7294	−	12.6405i	1.78393	−	0.649297i	0.999580	−	0.0289765i	$-0.00922481\pi$
$380$	−0.620141	−	1.07412i	−0.0318125	−	0.0551009i
$381$	−8.65248	+	14.9865i	−0.443280	+	0.767784i
$382$	−1.69417	+	9.60809i	−0.0866811	+	0.491593i
$383$	2.69968	−	7.41732i	0.137947	−	0.379007i	−0.851412	−	0.524497i	$-0.824253\pi$
$383$	2.69968	−	7.41732i	0.137947	−	0.379007i	0.989360	+	0.145489i	$0.0464757\pi$
$384$	7.76326	−	4.48212i	0.396167	−	0.228727i
$385$	0.804230	−	0.958444i	0.0409873	−	0.0488468i
$386$	29.8669	+	25.0613i	1.52019	+	1.27559i
$387$	3.03194	+	8.33019i	0.154122	+	0.423448i
$388$	−20.4785	+	3.61092i	−1.03964	+	0.183317i
$389$	−15.7496	+	2.77707i	−0.798534	+	0.140803i	−0.558004	−	0.829839i	$-0.688432\pi$
$389$	−15.7496	+	2.77707i	−0.798534	+	0.140803i	−0.240530	+	0.970642i	$0.577321\pi$
$390$	−0.288189	−	0.791794i	−0.0145930	−	0.0400940i
$391$	−5.24535	−	4.40137i	−0.265269	−	0.222587i
$392$	4.93894	−	5.88600i	0.249454	−	0.297288i
$393$	10.6298	−	6.13711i	0.536202	−	0.309576i
$394$	11.0891	−	30.4669i	0.558659	−	1.53490i
$395$	−0.602596	+	3.41749i	−0.0303199	+	0.171953i
$396$	1.43282	−	2.48172i	0.0720021	−	0.124711i
$397$	−11.3017	−	19.5752i	−0.567218	−	0.982450i	−0.996840	−	0.0794411i	$-0.974686\pi$
$397$	−11.3017	−	19.5752i	−0.567218	−	0.982450i	0.429622	−	0.903009i	$-0.358647\pi$
$398$	20.9633	−	7.63003i	1.05080	−	0.382459i
$399$	−0.670215	−	0.386949i	−0.0335527	−	0.0193717i
$400$	−16.0568	+	13.4732i	−0.802839	+	0.673662i
$401$			17.9585i			0.896806i	0.893832	+	0.448403i	$0.148007\pi$
$401$			17.9585i			0.896806i	−0.893832	+	0.448403i	$0.851993\pi$
$402$	3.52557	+	4.20160i	0.175839	+	0.209557i
$403$	−2.93750	−	1.06916i	−0.146327	−	0.0532588i
$404$	−0.0820243	−	0.465183i	−0.00408086	−	0.0231437i
$405$	0.823786	+	0.145256i	0.0409343	+	0.00721782i
$406$	−9.76540			−0.484649
$407$	2.49987	+	12.6228i	0.123914	+	0.625690i
$408$	−2.08412			−0.103179
$409$	−2.47264	−	0.435994i	−0.122264	−	0.0215585i	0.112181	−	0.993688i	$-0.464216\pi$
$409$	−2.47264	−	0.435994i	−0.122264	−	0.0215585i	−0.234445	+	0.972129i	$0.575327\pi$
$410$	1.84389	+	10.4572i	0.0910633	+	0.516446i
$411$	2.13546	+	0.777244i	0.105334	+	0.0383386i
$412$	3.84337	+	4.58035i	0.189349	+	0.225658i
$413$		−	5.35364i		−	0.263435i
$414$	5.44902	−	4.57227i	0.267805	−	0.224715i
$415$	−4.03382	−	2.32893i	−0.198013	−	0.114323i
$416$	−3.39197	+	1.23458i	−0.166305	+	0.0605301i
$417$	−0.404330	−	0.700320i	−0.0198001	−	0.0342948i
$418$	2.12053	−	3.67287i	0.103719	−	0.179646i
$419$	−4.30885	+	24.4367i	−0.210501	+	1.19381i	0.678043	+	0.735022i	$0.262828\pi$
$419$	−4.30885	+	24.4367i	−0.210501	+	1.19381i	−0.888545	+	0.458790i	$0.848283\pi$
$420$	−0.274011	+	0.752838i	−0.0133704	+	0.0367348i
$421$	10.4391	−	6.02704i	0.508773	−	0.293740i	−0.223556	−	0.974691i	$-0.571767\pi$
$421$	10.4391	−	6.02704i	0.508773	−	0.293740i	0.732329	+	0.680951i	$0.238433\pi$
$422$	−12.7798	+	15.2304i	−0.622110	+	0.741402i
$423$	−7.45247	−	6.25337i	−0.362352	−	0.304049i
$424$	3.22277	+	8.85449i	0.156512	+	0.430012i
$425$	7.46663	−	1.31657i	0.362185	−	0.0638630i
$426$	−27.4007	+	4.83148i	−1.32757	+	0.234086i
$427$	−1.01625	−	2.79212i	−0.0491797	−	0.135120i
$428$	−18.2434	−	15.3081i	−0.881830	−	0.739943i
$429$	0.747859	−	0.891263i	0.0361070	−	0.0430306i
$430$	11.7621	−	6.79084i	0.567217	−	0.327483i
$431$	3.12482	−	8.58538i	0.150517	−	0.413543i	−0.841402	−	0.540409i	$-0.818269\pi$
$431$	3.12482	−	8.58538i	0.150517	−	0.413543i	0.991920	+	0.126866i	$0.0404917\pi$
$432$	0.846405	−	4.80020i	0.0407227	−	0.230950i
$433$	−0.233455	+	0.404357i	−0.0112192	+	0.0194321i	−0.871580	−	0.490252i	$-0.836905\pi$
$433$	−0.233455	+	0.404357i	−0.0112192	+	0.0194321i	0.860361	+	0.509685i	$0.170238\pi$
$434$	3.68027	+	6.37442i	0.176659	+	0.305982i
$435$	5.92760	−	2.15747i	0.284207	−	0.103443i
$436$	−16.5357	−	9.54689i	−0.791917	−	0.457213i
$437$	3.25643	−	2.73247i	0.155776	−	0.130712i
$438$		−	18.9762i		−	0.906717i
$439$	3.05115	+	3.63622i	0.145623	+	0.173547i	0.833926	−	0.551877i	$-0.186088\pi$
$439$	3.05115	+	3.63622i	0.145623	+	0.173547i	−0.688302	+	0.725424i	$0.741644\pi$
$440$	1.96564	+	0.715435i	0.0937083	+	0.0341070i
$441$	−1.12873	−	6.40135i	−0.0537491	−	0.304826i
$442$	1.74901	+	0.308397i	0.0831917	+	0.0146689i
$443$	−19.8884			−0.944927			−0.472463	−	0.881350i	$-0.656635\pi$
$443$	−19.8884			−0.944927			−0.472463	+	0.881350i	$0.656635\pi$
$444$	−4.26867	−	7.04783i	−0.202582	−	0.334475i
$445$	−2.45170			−0.116222
$446$	32.4896	+	5.72880i	1.53843	+	0.271266i
$447$	−0.829875	−	4.70646i	−0.0392518	−	0.222608i
$448$	1.50991	+	0.549561i	0.0713364	+	0.0259643i
$449$	1.06966	+	1.27477i	0.0504802	+	0.0601600i	0.790694	−	0.612212i	$-0.209720\pi$
$449$	1.06966	+	1.27477i	0.0504802	+	0.0601600i	−0.740214	+	0.672372i	$0.765276\pi$
$450$			7.87621i			0.371288i
$451$	−11.2317	+	9.42450i	−0.528879	+	0.443782i
$452$	−1.47202	−	0.849874i	−0.0692382	−	0.0399747i
$453$	1.40085	−	0.509867i	0.0658176	−	0.0239556i
$454$	−13.1955	−	22.8553i	−0.619296	−	1.07265i
$455$	−0.162635	+	0.281693i	−0.00762447	+	0.0132060i
$456$	0.224678	−	1.27421i	0.0105215	−	0.0596704i
$457$	−14.0474	+	38.5949i	−0.657109	+	1.80539i	−0.0674743	+	0.997721i	$0.521494\pi$
$457$	−14.0474	+	38.5949i	−0.657109	+	1.80539i	−0.589634	+	0.807670i	$0.700728\pi$
$458$	−39.4409	+	22.7712i	−1.84295	+	1.06403i
$459$	−1.13330	+	1.35061i	−0.0528979	+	0.0630412i
$460$	−3.37111	−	2.82870i	−0.157179	−	0.131889i
$461$	−7.16267	−	19.6793i	−0.333599	−	0.916555i	−0.987168	−	0.159688i	$-0.948951\pi$
$461$	−7.16267	−	19.6793i	−0.333599	−	0.916555i	0.653569	−	0.756867i	$-0.273271\pi$
$462$	−2.69787	+	0.475708i	−0.125516	+	0.0221319i
$463$	4.21701	−	0.743572i	0.195981	−	0.0345567i	−0.0747960	−	0.997199i	$-0.523831\pi$
$463$	4.21701	−	0.743572i	0.195981	−	0.0345567i	0.270777	+	0.962642i	$0.412719\pi$
$464$	−12.5716	−	34.5401i	−0.583621	−	1.60348i
$465$	−3.64223	−	3.05619i	−0.168904	−	0.141727i
$466$	0.0297246	−	0.0354244i	0.00137696	−	0.00164100i
$467$	−29.2385	+	16.8809i	−1.35300	+	0.781153i	−0.988668	−	0.150117i	$-0.952035\pi$
$467$	−29.2385	+	16.8809i	−1.35300	+	0.781153i	−0.364329	+	0.931270i	$0.618702\pi$
$468$	−0.254804	+	0.700069i	−0.0117783	+	0.0323607i
$469$	0.367663	−	2.08512i	0.0169771	−	0.0962820i
$470$	−7.45247	+	12.9081i	−0.343757	+	0.595404i
$471$	−7.73232	−	13.3928i	−0.356286	−	0.617106i
$472$	8.41087	−	3.06130i	0.387141	−	0.140908i
$473$	16.2409	+	9.37668i	0.746757	+	0.431140i
$474$	5.82060	−	4.88406i	0.267349	−	0.224332i
$475$			4.70696i			0.215970i
$476$	−1.08542	−	1.29355i	−0.0497501	−	0.0592898i
$477$	7.49062	+	2.72636i	0.342972	+	0.124832i
$478$	−0.437295	−	2.48002i	−0.0200014	−	0.113434i
$479$	33.8398	+	5.96688i	1.54618	+	0.272634i	0.880662	−	0.473746i	$-0.157099\pi$
$479$	33.8398	+	5.96688i	1.54618	+	0.272634i	0.665520	+	0.746380i	$0.268210\pi$
$480$	−5.49019			−0.250592
$481$	−1.20988	−	3.11892i	−0.0551658	−	0.142210i
$482$	−3.02172			−0.137636
$483$	−2.70417	−	0.476819i	−0.123044	−	0.0216960i
$484$	1.53478	+	8.70416i	0.0697626	+	0.395644i
$485$	−12.0666	−	4.39187i	−0.547915	−	0.199425i
$486$	−1.17730	−	1.40306i	−0.0534035	−	0.0636439i
$487$			13.1820i			0.597335i	0.954357	+	0.298668i	$0.0965422\pi$
$487$			13.1820i			0.597335i	−0.954357	+	0.298668i	$0.903458\pi$
$488$	3.80547	−	3.19316i	0.172265	−	0.144548i
$489$	−11.8795	−	6.85861i	−0.537208	−	0.310157i
$490$	−9.35815	+	3.40609i	−0.422758	+	0.153871i
$491$	−2.39161	−	4.14238i	−0.107932	−	0.186943i	0.807001	−	0.590551i	$-0.201089\pi$
$491$	−2.39161	−	4.14238i	−0.107932	−	0.186943i	−0.914932	+	0.403608i	$0.867756\pi$
$492$	4.69423	−	8.13064i	0.211632	−	0.366558i
$493$	−2.30875	+	13.0936i	−0.103981	+	0.589705i
$494$	−0.377102	+	1.03608i	−0.0169666	+	0.0466154i
$495$	1.53251	−	0.884796i	0.0688812	−	0.0397686i
$496$	−17.8084	+	21.2232i	−0.799622	+	0.952952i
$497$	8.22779	+	6.90393i	0.369067	+	0.309684i
$498$	3.48815	+	9.58362i	0.156308	+	0.429452i
$499$	38.2589	−	6.74608i	1.71270	−	0.301996i	0.770600	−	0.637319i	$-0.219956\pi$
$499$	38.2589	−	6.74608i	1.71270	−	0.301996i	0.942103	+	0.335323i	$0.108845\pi$
$500$	10.3782	−	1.82996i	0.464129	−	0.0818384i
$501$	−2.06023	−	5.66044i	−0.0920443	−	0.252890i
$502$	23.8721	+	20.0311i	1.06546	+	0.894031i
$503$	24.8555	−	29.6216i	1.10825	−	1.32076i	0.165900	−	0.986143i	$-0.446947\pi$
$503$	24.8555	−	29.6216i	1.10825	−	1.32076i	0.942353	−	0.334621i	$-0.108608\pi$
$504$	−0.723796	+	0.417884i	−0.0322404	+	0.0186140i
$505$	0.0997641	−	0.274100i	0.00443944	−	0.0121973i
$506$	2.61303	−	14.8192i	0.116163	−	0.658795i
$507$	6.34876	−	10.9964i	0.281959	−	0.488366i
$508$	−11.7207	−	20.3009i	−0.520022	−	0.900705i
$509$	−33.2696	+	12.1091i	−1.47465	+	0.536728i	−0.949359	−	0.314195i	$-0.898265\pi$
$509$	−33.2696	+	12.1091i	−1.47465	+	0.536728i	−0.525290	+	0.850923i	$0.676043\pi$
$510$	2.33933	+	1.35061i	0.103587	+	0.0598061i
$511$	−5.61154	+	4.70864i	−0.248240	+	0.208298i
$512$			20.4678i			0.904560i
$513$	−0.703577	−	0.838490i	−0.0310637	−	0.0370202i
$514$	35.7158	+	12.9995i	1.57536	+	0.573382i
$515$	0.641158	+	3.63619i	0.0282528	+	0.160229i
$516$	−11.8259	−	2.08522i	−0.520606	−	0.0917968i
$517$	−20.5805			−0.905130
$518$	−2.53821	+	7.45686i	−0.111523	+	0.327636i
$519$	−6.00594			−0.263632
$520$	−0.535553	−	0.0944325i	−0.0234856	−	0.00414114i
$521$	1.70978	+	9.69667i	0.0749070	+	0.424819i	0.999082	+	0.0428484i	$0.0136432\pi$
$521$	1.70978	+	9.69667i	0.0749070	+	0.424819i	−0.924175	+	0.381970i	$0.875246\pi$
$522$	−12.9789	−	4.72392i	−0.568069	−	0.206760i
$523$	11.3994	+	13.5853i	0.498461	+	0.594042i	0.955348	−	0.295482i	$-0.0954802\pi$
$523$	11.3994	+	13.5853i	0.498461	+	0.594042i	−0.456887	+	0.889525i	$0.651036\pi$
$524$			16.6267i			0.726342i
$525$	2.32911	−	1.95436i	0.101651	−	0.0852951i
$526$	9.54001	+	5.50793i	0.415964	+	0.240157i
$527$	9.41700	−	3.42751i	0.410211	−	0.149305i
$528$	−5.15570	−	8.92994i	−0.224373	−	0.388626i
$529$	−3.95852	+	6.85635i	−0.172109	+	0.298102i
$530$	2.12073	−	12.0273i	0.0921188	−	0.522432i
$531$	2.58977	−	7.11533i	0.112386	−	0.308779i
$532$	0.907878	−	0.524164i	0.0393615	−	0.0227254i
$533$	2.45014	−	2.91996i	0.106127	−	0.126478i
$534$	4.11224	+	3.45058i	0.177954	+	0.149321i
$535$	−5.02984	−	13.8194i	−0.217459	−	0.597464i
$536$	3.48608	−	0.614690i	0.150576	−	0.0265506i
$537$	20.7961	−	3.66691i	0.897417	−	0.158239i
$538$	−12.3958	−	34.0573i	−0.534422	−	1.46831i
$539$	−10.5338	−	8.83889i	−0.453722	−	0.380718i
$540$	−0.728356	+	0.868021i	−0.0313435	+	0.0373537i
$541$	24.3356	−	14.0502i	1.04627	−	0.604064i	0.124667	−	0.992199i	$-0.460214\pi$
$541$	24.3356	−	14.0502i	1.04627	−	0.604064i	0.921603	+	0.388135i	$0.126881\pi$
$542$	−17.5924	+	48.3347i	−0.755659	+	2.07616i
$543$	−3.87374	+	21.9691i	−0.166238	+	0.942783i
$544$	5.78590	−	10.0215i	0.248068	−	0.429667i
$545$	−5.89539	−	10.2111i	−0.252531	−	0.437396i
$546$	0.669250	−	0.243587i	0.0286413	−	0.0104246i
$547$	20.4492	+	11.8063i	0.874343	+	0.504802i	0.868789	−	0.495182i	$-0.164899\pi$
$547$	20.4492	+	11.8063i	0.874343	+	0.504802i	0.00555407	+	0.999985i	$0.498232\pi$
$548$	−2.35816	+	1.97873i	−0.100735	+	0.0845270i
$549$		−	4.20250i		−	0.179358i
$550$	10.7101	+	12.7638i	0.456681	+	0.544251i
$551$	−7.75639	−	2.82309i	−0.330433	−	0.120268i
$552$	−0.797185	−	4.52106i	−0.0339305	−	0.192429i
$553$	−2.88858	−	0.509334i	−0.122835	−	0.0216591i
$554$	13.0191			0.553128
$555$	−0.106747	−	5.08708i	−0.00453118	−	0.215934i
$556$	1.09542			0.0464559
$557$	30.4960	+	5.37728i	1.29216	+	0.227842i	0.777135	−	0.629334i	$-0.216672\pi$
$557$	30.4960	+	5.37728i	1.29216	+	0.227842i	0.515024	+	0.857176i	$0.327783\pi$
$558$	1.80776	+	10.2523i	0.0765286	+	0.434015i
$559$	−4.58139	−	1.66749i	−0.193772	−	0.0705273i
$560$	1.85301	+	2.20834i	0.0783041	+	0.0933192i
$561$			3.72981i			0.157473i
$562$	14.5418	−	12.2020i	0.613408	−	0.514710i
$563$	11.0826	+	6.39854i	0.467076	+	0.269666i	0.715015	−	0.699109i	$-0.246420\pi$
$563$	11.0826	+	6.39854i	0.467076	+	0.269666i	−0.247939	+	0.968776i	$0.579753\pi$
$564$	12.3836	−	4.50724i	0.521442	−	0.189789i
$565$	−0.524813	−	0.909003i	−0.0220790	−	0.0382420i
$566$	27.2633	−	47.2213i	1.14596	−	1.98486i
$567$	−0.122775	+	0.696292i	−0.00515607	+	0.0292415i
$568$	−6.14167	+	16.8741i	−0.257699	+	0.708022i
$569$	4.32905	−	2.49938i	0.181483	−	0.104779i	−0.406506	−	0.913648i	$-0.633253\pi$
$569$	4.32905	−	2.49938i	0.181483	−	0.104779i	0.587989	+	0.808869i	$0.299920\pi$
$570$	−1.07794	+	1.28464i	−0.0451500	+	0.0538077i
$571$	−11.2409	−	9.43227i	−0.470419	−	0.394728i	0.376529	−	0.926405i	$-0.377118\pi$
$571$	−11.2409	−	9.43227i	−0.470419	−	0.394728i	−0.846947	+	0.531677i	$0.821562\pi$
$572$	0.539035	+	1.48099i	0.0225382	+	0.0619231i
$573$	5.24586	−	0.924986i	0.219149	−	0.0386419i
$574$	−8.83879	+	1.55852i	−0.368924	+	0.0650513i
$575$	5.71204	+	15.6937i	0.238209	+	0.654473i
$576$	1.74092	+	1.46081i	0.0725383	+	0.0608669i
$577$	19.5137	−	23.2556i	0.812368	−	0.968142i	−0.187533	−	0.982258i	$-0.560049\pi$
$577$	19.5137	−	23.2556i	0.812368	−	0.968142i	0.999900	+	0.0141163i	$0.00449351\pi$
$578$	22.0343	−	12.7215i	0.916507	−	0.529146i
$579$	7.28061	−	20.0033i	0.302572	−	0.831309i
$580$	−1.48380	+	8.41506i	−0.0616115	+	0.349416i
$581$	1.96849	−	3.40952i	0.0816667	−	0.141451i
$582$	14.0581	+	24.3493i	0.582725	+	1.00931i
$583$	15.8463	−	5.76758i	0.656286	−	0.238869i
$584$	−10.6063	−	6.12356i	−0.438892	−	0.253395i
$585$	−0.352419	+	0.295715i	−0.0145707	+	0.0122263i
$586$		−	47.7743i		−	1.97354i
$587$	22.5336	+	26.8545i	0.930061	+	1.10840i	0.993883	+	0.110442i	$0.0352267\pi$
$587$	22.5336	+	26.8545i	0.930061	+	1.10840i	−0.0638216	+	0.997961i	$0.520329\pi$
$588$	8.27407	+	3.01151i	0.341217	+	0.124193i
$589$	1.08035	+	6.12696i	0.0445150	+	0.252457i
$590$	−11.4247	−	2.01448i	−0.470347	−	0.0829349i
$591$	−17.7020			−0.728163
$592$	−29.6424	+	0.622017i	−1.21830	+	0.0255648i
$593$	−6.41429			−0.263403			−0.131702	−	0.991289i	$-0.542044\pi$
$593$	−6.41429			−0.263403			−0.131702	+	0.991289i	$0.542044\pi$
$594$	−3.81577	−	0.672823i	−0.156563	−	0.0276063i
$595$	−0.181071	−	1.02691i	−0.00742321	−	0.0420991i
$596$	6.08333	+	2.21415i	0.249183	+	0.0906952i
$597$	−7.82927	−	9.33056i	−0.320431	−	0.381874i
$598$			3.91207i			0.159976i
$599$	3.70030	−	3.10492i	0.151190	−	0.126864i	−0.564055	−	0.825737i	$-0.690759\pi$
$599$	3.70030	−	3.10492i	0.151190	−	0.126864i	0.715245	+	0.698873i	$0.246315\pi$
$600$	4.40223	+	2.54163i	0.179720	+	0.103762i
$601$	23.3955	−	8.51528i	0.954324	−	0.347345i	0.182517	−	0.983203i	$-0.441576\pi$
$601$	23.3955	−	8.51528i	0.954324	−	0.347345i	0.771807	+	0.635857i	$0.219353\pi$
$602$	5.73984	+	9.94169i	0.233938	+	0.405193i
$603$	1.49731	−	2.59341i	0.0609750	−	0.105612i
$604$	−0.350662	+	1.98870i	−0.0142682	+	0.0809191i
$605$	−1.86671	+	5.12875i	−0.0758926	+	0.208513i
$606$	−0.553109	+	0.319338i	−0.0224685	+	0.0129722i
$607$	−7.26139	+	8.65379i	−0.294731	+	0.351246i	−0.893006	−	0.450044i	$-0.851408\pi$
$607$	−7.26139	+	8.65379i	−0.294731	+	0.351246i	0.598276	+	0.801290i	$0.295853\pi$
$608$	5.50329	+	4.61781i	0.223188	+	0.187277i
$609$	1.82356	+	5.01020i	0.0738946	+	0.203024i
$610$	−6.34079	+	1.11805i	−0.256731	+	0.0452686i
$611$	5.26914	−	0.929092i	0.213167	−	0.0375871i
$612$	−0.816849	−	2.24427i	−0.0330191	−	0.0907194i
$613$	−10.1542	−	8.52042i	−0.410126	−	0.344136i	0.414266	−	0.910156i	$-0.364038\pi$
$613$	−10.1542	−	8.52042i	−0.410126	−	0.344136i	−0.824392	+	0.566019i	$0.808483\pi$
$614$	8.11419	−	9.67012i	0.327462	−	0.390254i
$615$	5.02082	−	2.89877i	0.202459	−	0.116890i
$616$	−0.604710	+	1.66143i	−0.0243644	+	0.0669408i
$617$	0.657294	−	3.72770i	0.0264617	−	0.150072i	−0.968714	−	0.248179i	$-0.920168\pi$
$617$	0.657294	−	3.72770i	0.0264617	−	0.150072i	0.995176	+	0.0981076i	$0.0312789\pi$
$618$	4.04224	−	7.00137i	0.162603	−	0.281636i
$619$	4.70874	+	8.15577i	0.189260	+	0.327808i	0.945004	−	0.327059i	$-0.106058\pi$
$619$	4.70874	+	8.15577i	0.189260	+	0.327808i	−0.755744	+	0.654868i	$0.772724\pi$
$620$	6.05218	−	2.20281i	0.243061	−	0.0884671i
$621$	−3.36336	−	1.94184i	−0.134967	−	0.0779233i
$622$	−13.5274	+	11.3509i	−0.542401	+	0.455128i
$623$		−	2.07226i		−	0.0830232i
$624$	1.72313	+	2.05355i	0.0689804	+	0.0822076i
$625$	−14.0895	−	5.12817i	−0.563581	−	0.205127i
$626$	2.16313	+	12.2677i	0.0864560	+	0.490316i
$627$	−2.28037	−	0.402091i	−0.0910692	−	0.0160580i
$628$	20.9485			0.835936
$629$	9.39816	+	5.16623i	0.374729	+	0.205991i
$630$	1.08324			0.0431572
$631$	−15.3162	−	2.70066i	−0.609729	−	0.107512i	−0.139746	−	0.990187i	$-0.544629\pi$
$631$	−15.3162	−	2.70066i	−0.609729	−	0.107512i	−0.469983	+	0.882676i	$0.655740\pi$
$632$	−0.851548	−	4.82937i	−0.0338727	−	0.192102i
$633$	10.2005	+	3.71268i	0.405433	+	0.147566i
$634$	−32.0869	−	38.2397i	−1.27433	−	1.51869i
$635$		−	14.4755i		−	0.574443i
$636$	−8.27178	+	6.94085i	−0.327998	+	0.275223i
$637$	3.09594	+	1.78744i	0.122666	+	0.0708211i
$638$	−27.4566	+	9.99337i	−1.08702	+	0.395641i
$639$	7.59555	+	13.1559i	0.300475	+	0.520439i
$640$	−3.74927	+	6.49392i	−0.148203	+	0.256695i
$641$	−4.84231	+	27.4621i	−0.191260	+	1.08469i	0.726386	+	0.687287i	$0.241199\pi$
$641$	−4.84231	+	27.4621i	−0.191260	+	1.08469i	−0.917645	+	0.397400i	$0.869913\pi$
$642$	−11.0132	+	30.2584i	−0.434655	+	1.19420i
$643$	−17.2724	+	9.97220i	−0.681156	+	0.393265i	−0.800290	−	0.599613i	$-0.795321\pi$
$643$	−17.2724	+	9.97220i	−0.681156	+	0.393265i	0.119135	+	0.992878i	$0.461988\pi$
$644$	2.39091	−	2.84938i	0.0942151	−	0.112281i
$645$	−5.68050	−	4.76650i	−0.223669	−	0.187681i
$646$	−1.20891	−	3.32145i	−0.0475639	−	0.130681i
$647$	−35.1901	+	6.20496i	−1.38347	+	0.243942i	−0.815332	−	0.578994i	$-0.803445\pi$
$647$	−35.1901	+	6.20496i	−1.38347	+	0.243942i	−0.568134	+	0.822936i	$0.692334\pi$
$648$	−1.16412	+	0.205265i	−0.0457309	+	0.00806359i
$649$	−5.47861	−	15.0524i	−0.215054	−	0.590857i
$650$	−3.31828	−	2.78437i	−0.130154	−	0.109212i
$651$	2.58319	−	3.07853i	0.101243	−	0.120657i
$652$	16.0920	−	9.29072i	0.630211	−	0.363853i
$653$	−12.2449	+	33.6425i	−0.479179	+	1.31653i	0.431012	+	0.902346i	$0.358157\pi$
$653$	−12.2449	+	33.6425i	−0.479179	+	1.31653i	−0.910191	+	0.414188i	$0.864065\pi$
$654$	−4.48301	+	25.4244i	−0.175300	+	0.994174i
$655$	−5.13366	+	8.89176i	−0.200589	+	0.347430i
$656$	−16.8912	−	29.2563i	−0.659489	−	1.14227i
$657$	−9.73585	+	3.54356i	−0.379832	+	0.138247i
$658$	−10.9103	−	6.29908i	−0.425329	−	0.245564i
$659$	−1.72822	+	1.45015i	−0.0673217	+	0.0564897i	−0.675828	−	0.737060i	$-0.736214\pi$
$659$	−1.72822	+	1.45015i	−0.0673217	+	0.0564897i	0.608506	+	0.793549i	$0.291769\pi$
$660$			2.39710i			0.0933070i
$661$	3.77692	+	4.50116i	0.146905	+	0.175075i	0.834479	−	0.551040i	$-0.185769\pi$
$661$	3.77692	+	4.50116i	0.146905	+	0.175075i	−0.687574	+	0.726115i	$0.741324\pi$
$662$	−8.88896	−	3.23532i	−0.345479	−	0.125744i
$663$	−0.168380	−	0.954928i	−0.00653932	−	0.0370863i
$664$	6.48217	+	1.14298i	0.251557	+	0.0443563i
$665$	0.647362			0.0251036
$666$	−6.98063	+	8.68281i	−0.270494	+	0.336452i
$667$	−29.2869			−1.13399
$668$	8.03579	+	1.41693i	0.310914	+	0.0548225i
$669$	−3.12783	−	17.7388i	−0.120929	−	0.685821i
$670$	−4.31132	−	1.56919i	−0.166561	−	0.0606232i
$671$	−5.71459	−	6.81039i	−0.220609	−	0.262912i
$672$		−	4.64049i		−	0.179011i
$673$	−5.77932	+	4.84942i	−0.222776	+	0.186932i	−0.747344	−	0.664437i	$-0.768671\pi$
$673$	−5.77932	+	4.84942i	−0.222776	+	0.186932i	0.524568	+	0.851369i	$0.324227\pi$
$674$	−46.9435	−	27.1029i	−1.80820	−	1.04396i
$675$	4.04094	−	1.47078i	0.155536	−	0.0566104i
$676$	8.60007	+	14.8958i	0.330772	+	0.572914i
$677$	−8.66598	+	15.0099i	−0.333061	+	0.576878i	−0.983110	−	0.183014i	$-0.941415\pi$
$677$	−8.66598	+	15.0099i	−0.333061	+	0.576878i	0.650050	+	0.759892i	$0.274748\pi$
$678$	−0.399082	+	2.26331i	−0.0153267	+	0.0869218i
$679$	3.71216	−	10.1991i	0.142459	−	0.391404i
$680$	1.50979	−	0.871677i	0.0578978	−	0.0334273i
$681$	−9.26195	+	11.0380i	−0.354919	+	0.422976i
$682$	16.8707	+	14.1562i	0.646014	+	0.542070i
$683$	−13.2061	−	36.2835i	−0.505318	−	1.38835i	−0.886018	−	0.463652i	$-0.846539\pi$
$683$	−13.2061	−	36.2835i	−0.505318	−	1.38835i	0.380699	−	0.924699i	$-0.375683\pi$
$684$	1.46019	−	0.257470i	0.0558316	−	0.00984463i
$685$	−1.87206	+	0.330095i	−0.0715278	+	0.0126123i
$686$	−5.97929	−	16.4280i	−0.228290	−	0.627222i
$687$	19.0480	+	15.9832i	0.726726	+	0.609795i
$688$	−27.7744	+	33.1003i	−1.05889	+	1.26194i
$689$	−3.79669	+	2.19202i	−0.144642	+	0.0835093i
$690$	−2.03507	+	5.59130i	−0.0774737	+	0.212857i
$691$	0.225969	−	1.28154i	0.00859628	−	0.0487519i	−0.980208	−	0.197971i	$-0.936565\pi$
$691$	0.225969	−	1.28154i	0.00859628	−	0.0487519i	0.988804	+	0.149219i	$0.0476759\pi$
$692$	4.06784	−	7.04571i	0.154636	−	0.267838i
$693$	0.747859	+	1.29533i	0.0284088	+	0.0492055i
$694$	−19.1168	+	6.95795i	−0.725664	+	0.264120i
$695$	0.585814	+	0.338220i	0.0222212	+	0.0128294i
$696$	−6.82856	+	5.72984i	−0.258836	+	0.217189i
$697$			12.2196i			0.462851i
$698$	−11.9743	−	14.2704i	−0.453234	−	0.540143i
$699$	−0.0237254	−	0.00863534i	−0.000897377	−	0.000326618i
$700$	0.715187	+	4.05602i	0.0270315	+	0.153303i
$701$	−30.2309	−	5.33053i	−1.14181	−	0.201331i	−0.429411	−	0.903109i	$-0.641279\pi$
$701$	−30.2309	−	5.33053i	−1.14181	−	0.201331i	−0.712396	+	0.701778i	$0.752390\pi$
$702$	1.00731			0.0380185
$703$	−4.17175	+	5.18900i	−0.157340	+	0.195707i
$704$	4.80767			0.181196
$705$	8.01422	+	1.41312i	0.301833	+	0.0532213i
$706$	−6.23244	−	35.3459i	−0.234561	−	1.33026i
$707$	0.231678	+	0.0843239i	0.00871315	+	0.00317133i
$708$	6.59310	+	7.85735i	0.247784	+	0.295297i
$709$			23.6103i			0.886705i	0.896347	+	0.443352i	$0.146211\pi$
$709$			23.6103i			0.886705i	−0.896347	+	0.443352i	$0.853789\pi$
$710$	17.8290	−	14.9603i	0.669111	−	0.561451i
$711$	−3.59272	−	2.07426i	−0.134738	−	0.0777908i
$712$	3.25563	−	1.18495i	0.122010	−	0.0444080i
$713$	11.0373	+	19.1172i	0.413350	+	0.715944i
$714$	−1.14158	+	1.97728i	−0.0427227	+	0.0739978i
$715$	−0.169000	+	0.958444i	−0.00632022	+	0.0358438i
$716$	−9.78351	+	26.8800i	−0.365627	+	1.00455i
$717$	−1.19073	+	0.687470i	−0.0444687	+	0.0256740i
$718$	2.17316	−	2.58987i	0.0811017	−	0.0966532i
$719$	5.64588	+	4.73745i	0.210556	+	0.176677i	0.741966	−	0.670437i	$-0.233893\pi$
$719$	5.64588	+	4.73745i	0.210556	+	0.176677i	−0.531411	+	0.847114i	$0.678338\pi$
$720$	1.39451	+	3.83140i	0.0519705	+	0.142788i
$721$	−3.07342	+	0.541928i	−0.114460	+	0.0201824i
$722$	−32.1099	+	5.66184i	−1.19501	+	0.210712i
$723$	0.564268	+	1.55031i	0.0209854	+	0.0576568i
$724$	−23.1487	−	19.4241i	−0.860315	−	0.721890i
$725$	20.8446	−	24.8416i	0.774149	−	0.922595i
$726$	10.3494	−	5.97521i	0.384101	−	0.221761i
$727$	−3.60191	+	9.89616i	−0.133587	+	0.367028i	−0.988393	−	0.151920i	$-0.951454\pi$
$727$	−3.60191	+	9.89616i	−0.133587	+	0.367028i	0.854805	+	0.518949i	$0.173676\pi$
$728$	0.0798175	−	0.452667i	0.00295823	−	0.0167770i
$729$	−0.500000	+	0.866025i	−0.0185185	+	0.0320750i
$730$	7.93674	+	13.7468i	0.293752	+	0.508793i
$731$	14.6870	−	5.34562i	0.543217	−	0.197715i
$732$	4.93006	+	2.84637i	0.182220	+	0.105205i
$733$	10.7922	−	9.05574i	0.398619	−	0.334481i	−0.421340	−	0.906903i	$-0.638440\pi$
$733$	10.7922	−	9.05574i	0.398619	−	0.334481i	0.819960	+	0.572421i	$0.193996\pi$
$734$			26.9163i			0.993499i
$735$	3.49503	+	4.16522i	0.128916	+	0.153636i
$736$	23.9526	+	8.71805i	0.882906	+	0.321351i
$737$	−1.10007	−	6.23881i	−0.0405216	−	0.229809i
$738$	−12.5012	−	2.20431i	−0.460177	−	0.0811417i
$739$	1.68684			0.0620515			0.0310257	−	0.999519i	$-0.490123\pi$
$739$	1.68684			0.0620515			0.0310257	+	0.999519i	$0.490123\pi$
$740$	6.04007	+	3.32027i	0.222037	+	0.122055i
$741$	0.601986			0.0221145
$742$	10.1659	+	1.79252i	0.373200	+	0.0658053i
$743$	−5.09708	−	28.9070i	−0.186994	−	1.06050i	−0.923367	−	0.383919i	$-0.874574\pi$
$743$	−5.09708	−	28.9070i	−0.186994	−	1.06050i	0.736373	−	0.676576i	$-0.236537\pi$
$744$	6.31366	+	2.29798i	0.231470	+	0.0842482i
$745$	2.56965	+	3.06238i	0.0941445	+	0.112197i
$746$		−	27.7145i		−	1.01470i
$747$	4.26557	−	3.57924i	0.156069	−	0.130957i
$748$	−4.37553	−	2.52621i	−0.159985	−	0.0923674i
$749$	11.6806	−	4.25139i	0.426800	−	0.155342i
$750$	−7.12443	−	12.3399i	−0.260147	−	0.450588i
$751$	23.6197	−	40.9106i	0.861897	−	1.49285i	−0.00819939	−	0.999966i	$-0.502610\pi$
$751$	23.6197	−	40.9106i	0.861897	−	1.49285i	0.870096	−	0.492882i	$-0.164057\pi$
$752$	8.23426	−	46.6988i	0.300273	−	1.70293i
$753$	5.81926	−	15.9883i	0.212066	−	0.582646i
$754$	6.57845	−	3.79807i	0.239573	−	0.138317i
$755$	−0.801559	+	0.955261i	−0.0291717	+	0.0347655i
$756$	−0.733680	−	0.615631i	−0.0266837	−	0.0223903i
$757$	8.80314	+	24.1864i	0.319956	+	0.879071i	0.990538	+	0.137236i	$0.0438219\pi$
$757$	8.80314	+	24.1864i	0.319956	+	0.879071i	−0.670583	+	0.741835i	$0.733956\pi$
$758$	66.6628	−	11.7544i	2.42130	−	0.426941i
$759$	−8.09104	+	1.42667i	−0.293686	+	0.0517848i
$760$	0.370173	+	1.01704i	0.0134276	+	0.0368920i
$761$	−36.3671	−	30.5156i	−1.31831	−	1.10619i	−0.986662	−	0.162785i	$-0.947952\pi$
$761$	−36.3671	−	30.5156i	−1.31831	−	1.10619i	−0.331644	−	0.943405i	$-0.607603\pi$
$762$	−20.3732	+	24.2798i	−0.738043	+	0.879565i
$763$	8.63077	−	4.98298i	0.312455	−	0.180396i
$764$	−2.46791	+	6.78053i	−0.0892859	+	0.245311i
$765$	0.256100	−	1.45242i	0.00925933	−	0.0525123i
$766$	7.22857	−	12.5202i	0.261179	−	0.452375i
$767$	2.08220	+	3.60647i	0.0751837	+	0.130222i
$768$	19.6995	−	7.17002i	0.710844	−	0.258726i
$769$	28.6843	+	16.5609i	1.03438	+	0.597201i	0.918237	−	0.396031i	$-0.129613\pi$
$769$	28.6843	+	16.5609i	1.03438	+	0.597201i	0.116146	+	0.993232i	$0.462946\pi$
$770$	1.75545	−	1.47299i	0.0632619	−	0.0530830i
$771$		−	20.7517i		−	0.747354i
$772$	18.5352	+	22.0894i	0.667095	+	0.795013i
$773$	41.5371	+	15.1183i	1.49399	+	0.543767i	0.954496	−	0.298225i	$-0.0963946\pi$
$773$	41.5371	+	15.1183i	1.49399	+	0.543767i	0.539491	+	0.841992i	$0.318617\pi$
$774$	2.81942	+	15.9897i	0.101342	+	0.574739i
$775$	−24.0712	−	4.24440i	−0.864663	−	0.152463i
$776$	18.1460			0.651403
$777$	4.29977	−	0.0902265i	0.154253	−	0.00323686i
$778$	−29.2912			−1.05014
$779$	−7.47096	−	1.31733i	−0.267675	−	0.0471983i
$780$	−0.108215	−	0.613719i	−0.00387473	−	0.0219747i
$781$	30.1985	+	10.9913i	1.08059	+	0.393301i
$782$	−8.06136	−	9.60716i	−0.288274	−	0.343551i
$783$			7.54101i			0.269494i
$784$	24.2707	−	20.3655i	0.866811	−	0.727341i
$785$	11.2030	+	6.46804i	0.399851	+	0.230854i
$786$	21.1252	−	7.68894i	0.753511	−	0.274255i
$787$	18.7670	+	32.5054i	0.668972	+	1.15869i	0.978192	+	0.207703i	$0.0665988\pi$
$787$	18.7670	+	32.5054i	0.668972	+	1.15869i	−0.309220	+	0.950991i	$0.600068\pi$
$788$	11.9896	−	20.7666i	0.427112	−	0.739781i
$789$	1.04440	−	5.92310i	0.0371817	−	0.210868i
$790$	−2.17385	+	5.97259i	−0.0773420	+	0.212495i
$791$	0.768319	−	0.443589i	0.0273183	−	0.0157722i
$792$	−1.60740	+	1.91562i	−0.0571163	+	0.0680686i
$793$	1.77053	+	1.48565i	0.0628735	+	0.0527571i
$794$	−14.1595	−	38.9029i	−0.502501	−	1.38061i
$795$	−6.56669	+	1.15789i	−0.232897	+	0.0410660i
$796$	16.2487	−	2.86508i	0.575919	−	0.101550i
$797$	10.6981	+	29.3929i	0.378948	+	1.04115i	0.971793	+	0.235834i	$0.0757823\pi$
$797$	10.6981	+	29.3929i	0.378948	+	1.04115i	−0.592845	+	0.805316i	$0.701995\pi$
$798$	−1.08582	−	0.911113i	−0.0384377	−	0.0322530i
$799$	−11.0253	+	13.1395i	−0.390047	+	0.464840i
$800$	−24.4428	+	14.1121i	−0.864184	+	0.498937i
$801$	1.00243	−	2.75416i	0.0354193	−	0.0973136i
$802$	−5.71165	+	32.3924i	−0.201685	+	1.14381i
$803$	−10.9589	+	18.9814i	−0.386732	+	0.669839i
$804$	2.02826	+	3.51305i	0.0715312	+	0.123896i
$805$	2.15840	−	0.785594i	0.0760736	−	0.0276885i
$806$	−4.95842	−	2.86275i	−0.174653	−	0.100836i
$807$	−15.1585	+	12.7195i	−0.533606	+	0.447748i
$808$			0.412197i			0.0145010i
$809$	−1.77138	−	2.11105i	−0.0622785	−	0.0742206i	0.734006	−	0.679143i	$-0.237648\pi$
$809$	−1.77138	−	2.11105i	−0.0622785	−	0.0742206i	−0.796284	+	0.604923i	$0.793204\pi$
$810$	1.43969	+	0.524005i	0.0505856	+	0.0184117i
$811$	−2.48025	−	14.0662i	−0.0870934	−	0.493931i	−0.996885	−	0.0788663i	$-0.974870\pi$
$811$	−2.48025	−	14.0662i	−0.0870934	−	0.493931i	0.909792	−	0.415065i	$-0.136241\pi$
$812$	−7.11269	−	1.25416i	−0.249606	−	0.0440124i
$813$	28.0836			0.984935
$814$	0.494453	+	23.5633i	0.0173306	+	0.825893i
$815$	11.4744			0.401930
$816$	−8.46324	−	1.49230i	−0.296273	−	0.0522409i
$817$	1.68494	+	9.55575i	0.0589485	+	0.334313i
$818$	−4.32132	−	1.57283i	−0.151092	−	0.0549928i
$819$	−0.249948	−	0.297876i	−0.00873389	−	0.0104086i
$820$			7.85339i			0.274252i
$821$	−2.21427	+	1.85800i	−0.0772787	+	0.0648445i	−0.680609	−	0.732647i	$-0.738285\pi$
$821$	−2.21427	+	1.85800i	−0.0772787	+	0.0648445i	0.603330	+	0.797492i	$0.293840\pi$
$822$	3.60460	+	2.08112i	0.125725	+	0.0725872i
$823$	11.4959	−	4.18418i	0.400723	−	0.145851i	−0.133794	−	0.991009i	$-0.542716\pi$
$823$	11.4959	−	4.18418i	0.400723	−	0.145851i	0.534517	+	0.845158i	$0.320494\pi$
$824$	−2.60884	−	4.51864i	−0.0908832	−	0.157414i
$825$	4.54858	−	7.87838i	0.158361	−	0.274290i
$826$	1.70271	−	9.65653i	0.0592448	−	0.335994i
$827$	−4.39436	+	12.0734i	−0.152807	+	0.419833i	−0.992349	−	0.123461i	$-0.960601\pi$
$827$	−4.39436	+	12.0734i	−0.152807	+	0.419833i	0.839543	+	0.543294i	$0.182823\pi$
$828$	4.55603	−	2.63043i	0.158333	−	0.0914137i
$829$	25.1066	−	29.9208i	0.871987	−	1.03919i	−0.126895	−	0.991916i	$-0.540501\pi$
$829$	25.1066	−	29.9208i	0.871987	−	1.03919i	0.998882	−	0.0472770i	$-0.0150543\pi$
$830$	−6.53523	−	5.48371i	−0.226841	−	0.190342i
$831$	−2.43115	−	6.67953i	−0.0843356	−	0.231710i
$832$	−1.23089	+	0.217039i	−0.0426734	+	0.00752447i
$833$	−11.2862	+	1.99007i	−0.391044	+	0.0689517i
$834$	−0.506568	−	1.39179i	−0.0175410	−	0.0481936i
$835$	3.85995	+	3.23888i	0.133579	+	0.112086i
$836$	2.01620	−	2.40282i	0.0697318	−	0.0831032i
$837$	4.92244	−	2.84197i	0.170144	−	0.0982329i
$838$	−15.5440	+	42.7069i	−0.536960	+	1.47529i
$839$	8.25742	−	46.8301i	0.285078	−	1.61676i	−0.419930	−	0.907556i	$-0.637945\pi$
$839$	8.25742	−	46.8301i	0.285078	−	1.61676i	0.705008	−	0.709199i	$-0.250943\pi$
$840$	0.349557	−	0.605451i	0.0120609	−	0.0208901i
$841$	13.9334	+	24.1334i	0.480463	+	0.832187i
$842$	20.7463	−	7.55104i	0.714965	−	0.260226i
$843$	−8.97580	−	5.18218i	−0.309143	−	0.178484i
$844$	−11.2643	+	9.45183i	−0.387732	+	0.325345i
$845$			10.6214i			0.365388i
$846$	−11.4534	−	13.6496i	−0.393776	−	0.469284i
$847$	−4.33499	−	1.57781i	−0.148952	−	0.0542141i
$848$	6.74700	+	38.2641i	0.231693	+	1.31400i
$849$	−29.3183	−	5.16960i	−1.00620	−	0.177420i
$850$	13.8865			0.476304
$851$	−7.61222	+	22.3634i	−0.260943	+	0.766609i
$852$	−20.5780			−0.704989
$853$	−24.8327	−	4.37867i	−0.850254	−	0.149923i	−0.268492	−	0.963282i	$-0.586525\pi$
$853$	−24.8327	−	4.37867i	−0.850254	−	0.149923i	−0.581762	+	0.813359i	$0.697636\pi$
$854$	−0.945015	−	5.35945i	−0.0323378	−	0.183397i
$855$	0.860385	+	0.313155i	0.0294246	+	0.0107097i
$856$	13.3584	+	15.9199i	0.456579	+	0.544130i
$857$			32.2299i			1.10095i	0.834851	+	0.550475i	$0.185554\pi$
$857$			32.2299i			1.10095i	−0.834851	+	0.550475i	$0.814446\pi$
$858$	1.63240	−	1.36975i	0.0557292	−	0.0467624i
$859$	−48.1229	−	27.7838i	−1.64193	−	0.947970i	−0.980146	−	0.198279i	$-0.936465\pi$
$859$	−48.1229	−	27.7838i	−1.64193	−	0.947970i	−0.661787	−	0.749692i	$-0.730202\pi$
$860$	9.43911	−	3.43556i	0.321871	−	0.117152i
$861$	2.45014	+	4.24377i	0.0835005	+	0.144627i
$862$	8.36690	−	14.4919i	0.284978	−	0.493596i
$863$	0.191033	−	1.08340i	0.00650282	−	0.0368794i	−0.981384	−	0.192057i	$-0.938484\pi$
$863$	0.191033	−	1.08340i	0.00650282	−	0.0368794i	0.987887	+	0.155178i	$0.0495951\pi$
$864$	2.24479	−	6.16751i	0.0763693	−	0.209823i
$865$	4.35086	−	2.51197i	0.147934	−	0.0854096i
$866$	−0.549696	+	0.655102i	−0.0186794	+	0.0222613i
$867$	−10.6415	−	8.92927i	−0.361404	−	0.303254i
$868$	1.86189	+	5.11550i	0.0631967	+	0.173631i
$869$	−8.64280	+	1.52396i	−0.293187	+	0.0516967i
$870$	11.3780	−	2.00624i	0.385750	−	0.0680181i
$871$	0.563293	+	1.54764i	0.0190865	+	0.0524396i
$872$	12.7638	+	10.7101i	0.432236	+	0.362689i
$873$	9.86739	−	11.7595i	0.333960	−	0.397999i
$874$	6.74278	−	3.89294i	0.228078	−	0.131681i
$875$	−1.88127	+	5.16874i	−0.0635984	+	0.174735i
$876$	2.43709	−	13.8214i	0.0823416	−	0.466982i
$877$	5.63430	−	9.75890i	0.190257	−	0.329535i	−0.755078	−	0.655634i	$-0.772401\pi$
$877$	5.63430	−	9.75890i	0.190257	−	0.329535i	0.945335	+	0.326100i	$0.105735\pi$
$878$	4.34697	+	7.52917i	0.146703	+	0.254097i
$879$	−24.5109	+	8.92125i	−0.826733	+	0.300906i
$880$	7.46985	+	4.31272i	0.251809	+	0.145382i
$881$	−15.3179	+	12.8532i	−0.516073	+	0.433036i	−0.863260	−	0.504759i	$-0.831581\pi$
$881$	−15.3179	+	12.8532i	−0.516073	+	0.433036i	0.347187	+	0.937796i	$0.387137\pi$
$882$		−	11.9053i		−	0.400873i
$883$	−8.49373	−	10.1224i	−0.285837	−	0.340647i	0.603951	−	0.797021i	$-0.293592\pi$
$883$	−8.49373	−	10.1224i	−0.285837	−	0.340647i	−0.889788	+	0.456375i	$0.849148\pi$
$884$	1.23429	+	0.449246i	0.0415137	+	0.0151098i
$885$	1.09987	+	6.23769i	0.0369718	+	0.209678i
$886$	−35.8734	−	6.32544i	−1.20519	−	0.212507i
$887$	33.7760			1.13409			0.567044	−	0.823688i	$-0.308087\pi$
$887$	33.7760			1.13409			0.567044	+	0.823688i	$0.308087\pi$
$888$	2.60043	+	6.70358i	0.0872649	+	0.224958i
$889$	12.2352			0.410355
$890$	−4.42221	−	0.779755i	−0.148233	−	0.0261374i
$891$	0.367350	+	2.08335i	0.0123067	+	0.0697947i
$892$	22.9283	+	8.34521i	0.767695	+	0.279418i
$893$	−6.84476	−	8.15726i	−0.229051	−	0.272972i
$894$		−	8.75313i		−	0.292748i
$895$	−13.5315	+	11.3543i	−0.452309	+	0.379533i
$896$	−5.48888	−	3.16901i	−0.183371	−	0.105869i
$897$	2.00711	−	0.730529i	0.0670155	−	0.0243916i
$898$	1.52394	+	2.63954i	0.0508545	+	0.0880827i
$899$	21.4313	−	37.1202i	0.714775	−	1.23803i
$900$	−1.01153	+	5.73668i	−0.0337177	+	0.191223i
$901$	4.80685	−	13.2067i	0.160139	−	0.439980i
$902$	−23.2564	+	13.4271i	−0.774353	+	0.447073i
$903$	4.02881	−	4.80135i	0.134070	−	0.159779i
$904$	1.13624	+	0.953420i	0.0377909	+	0.0317103i
$905$	−6.38227	−	17.5351i	−0.212154	−	0.582888i
$906$	2.68892	−	0.474128i	0.0893333	−	0.0157519i
$907$	19.7944	−	3.49030i	0.657264	−	0.115893i	0.164938	−	0.986304i	$-0.447258\pi$
$907$	19.7944	−	3.49030i	0.657264	−	0.115893i	0.492326	+	0.870411i	$0.336147\pi$
$908$	−6.67575	−	18.3415i	−0.221542	−	0.608683i
$909$	0.267124	+	0.224144i	0.00885995	+	0.00743438i
$910$	−0.382942	+	0.456373i	−0.0126944	+	0.0151286i
$911$	13.0282	−	7.52182i	0.431643	−	0.249209i	−0.268404	−	0.963307i	$-0.586496\pi$
$911$	13.0282	−	7.52182i	0.431643	−	0.249209i	0.700046	+	0.714098i	$0.253163\pi$
$912$	1.82475	−	5.01347i	0.0604236	−	0.166012i
$913$	2.04552	−	11.6007i	0.0676967	−	0.383927i
$914$	−37.6127	+	65.1471i	−1.24412	+	2.15487i
$915$	1.75769	+	3.04440i	0.0581073	+	0.100645i
$916$	−31.6515	+	11.5202i	−1.04579	+	0.380638i
$917$	−7.51561	−	4.33914i	−0.248187	−	0.143291i
$918$	−2.47373	+	2.07570i	−0.0816451	+	0.0685084i
$919$			35.3646i			1.16657i	0.812267	+	0.583286i	$0.198233\pi$
$919$			35.3646i			1.16657i	−0.812267	+	0.583286i	$0.801767\pi$
$920$	2.46842	+	2.94175i	0.0813815	+	0.0969867i
$921$	−6.47654	−	2.35727i	−0.213409	−	0.0776746i
$922$	−6.66061	−	37.7742i	−0.219356	−	1.24403i
$923$	−8.22779	−	1.45078i	−0.270821	−	0.0477530i
$924$	−2.02611			−0.0666540
$925$	−13.5512	−	22.3737i	−0.445559	−	0.735644i
$926$	7.84284			0.257732
$927$	−4.34693	−	0.766481i	−0.142772	−	0.0251746i
$928$	−8.59457	−	48.7422i	−0.282131	−	1.60004i
$929$	51.6880	+	18.8129i	1.69583	+	0.617231i	0.995340	−	0.0964312i	$-0.0307428\pi$
$929$	51.6880	+	18.8129i	1.69583	+	0.617231i	0.700490	+	0.713663i	$0.252965\pi$
$930$	−5.59759	−	6.67095i	−0.183552	−	0.218749i
$931$		−	7.11483i		−	0.233179i
$932$	0.0261996	−	0.0219841i	0.000858196	−	0.000720112i
$933$	8.34971	+	4.82071i	0.273357	+	0.157823i
$934$	−58.1074	+	21.1494i	−1.90133	+	0.692028i
$935$	−1.55998	−	2.70197i	−0.0510169	−	0.0883639i
$936$	0.325056	−	0.563013i	0.0106248	−	0.0184027i
$937$	8.10878	−	45.9872i	0.264902	−	1.50234i	−0.504411	−	0.863464i	$-0.668290\pi$
$937$	8.10878	−	45.9872i	0.264902	−	1.50234i	0.769313	−	0.638872i	$-0.220599\pi$
$938$	1.32633	−	3.64407i	0.0433063	−	0.118983i
$939$	5.89009	−	3.40064i	0.192216	−	0.110976i
$940$	−7.08582	+	8.44455i	−0.231114	+	0.275431i
$941$	5.75739	+	4.83102i	0.187686	+	0.157487i	0.731789	−	0.681531i	$-0.238686\pi$
$941$	5.75739	+	4.83102i	0.187686	+	0.157487i	−0.544103	+	0.839018i	$0.683130\pi$
$942$	−9.68751	−	26.6162i	−0.315636	−	0.867203i
$943$	−26.5079	+	4.67406i	−0.863217	+	0.152208i
$944$	36.3470	−	6.40896i	1.18300	−	0.208594i
$945$	−0.202281	−	0.555762i	−0.00658019	−	0.0180789i
$946$	26.3120	+	22.0784i	0.855477	+	0.717830i
$947$	−28.6621	+	34.1581i	−0.931392	+	1.10999i	0.0623241	+	0.998056i	$0.480149\pi$
$947$	−28.6621	+	34.1581i	−0.931392	+	1.10999i	−0.993716	+	0.111933i	$0.964296\pi$
$948$	4.86672	−	2.80980i	0.158064	−	0.0912582i
$949$	1.94887	−	5.35447i	0.0632629	−	0.173813i
$950$	−1.49703	+	8.49010i	−0.0485702	+	0.275455i
$951$	−13.6273	+	23.6032i	−0.441896	+	0.765386i
$952$	0.736771	+	1.27612i	0.0238789	+	0.0413594i
$953$	−53.0611	+	19.3127i	−1.71882	+	0.625599i	−0.997736	−	0.0672509i	$-0.978577\pi$
$953$	−53.0611	+	19.3127i	−1.71882	+	0.625599i	−0.721082	+	0.692850i	$0.756355\pi$
$954$	12.6440	+	7.30000i	0.409364	+	0.236346i
$955$	−3.41336	+	2.86415i	−0.110454	+	0.0926817i
$956$		−	1.86250i		−	0.0602376i
$957$	10.2543	+	12.2206i	0.331475	+	0.395037i
$958$	59.1403	+	21.5253i	1.91074	+	0.695451i
$959$	−0.279007	−	1.58233i	−0.00900961	−	0.0510960i
$960$	−1.87215	−	0.330110i	−0.0604232	−	0.0106542i
$961$	−1.30720			−0.0421678
$962$	−1.19034	−	6.01049i	−0.0383781	−	0.193786i
$963$	17.5808			0.566535
$964$	−2.20089	−	0.388076i	−0.0708859	−	0.0124991i
$965$	3.09207	+	17.5360i	0.0995373	+	0.564504i
$966$	−4.72596	−	1.72011i	−0.152055	−	0.0553435i
$967$	−35.4553	−	42.2539i	−1.14016	−	1.35879i	−0.923979	−	0.382442i	$-0.875083\pi$
$967$	−35.4553	−	42.2539i	−1.14016	−	1.35879i	−0.216185	−	0.976352i	$-0.569361\pi$
$968$		−	7.71273i		−	0.247896i
$969$	−1.47834	+	1.24048i	−0.0474912	+	0.0398498i
$970$	−20.3680	−	11.7595i	−0.653978	−	0.377575i
$971$	−37.9986	+	13.8304i	−1.21943	+	0.443837i	−0.869966	−	0.493111i	$-0.835860\pi$
$971$	−37.9986	+	13.8304i	−1.21943	+	0.443837i	−0.349467	+	0.936949i	$0.613637\pi$
$972$	−0.677303	−	1.17312i	−0.0217245	−	0.0376279i
$973$	−0.285875	+	0.495149i	−0.00916472	+	0.0158738i
$974$	−4.19250	+	23.7769i	−0.134336	+	0.761860i
$975$	−0.808892	+	2.22241i	−0.0259053	+	0.0711741i
$976$	17.7397	−	10.2420i	0.567835	−	0.327840i
$977$	20.3098	−	24.2042i	0.649767	−	0.774362i	−0.336112	−	0.941822i	$-0.609112\pi$
$977$	20.3098	−	24.2042i	0.649767	−	0.774362i	0.985879	+	0.167460i	$0.0535565\pi$
$978$	−19.2460	−	16.1493i	−0.615420	−	0.516399i
$979$	−2.12063	−	5.82639i	−0.0677757	−	0.186212i
$980$	−7.25351	+	1.27899i	−0.231705	+	0.0408558i
$981$	13.8813	−	2.44765i	0.443196	−	0.0781475i
$982$	−2.99635	−	8.23239i	−0.0956172	−	0.262706i
$983$	−21.9187	−	18.3920i	−0.699099	−	0.586614i	0.222418	−	0.974951i	$-0.428605\pi$
$983$	−21.9187	−	18.3920i	−0.699099	−	0.586614i	−0.921517	+	0.388337i	$0.873050\pi$
$984$	−5.26616	+	6.27597i	−0.167879	+	0.200071i
$985$	12.8238	−	7.40382i	0.408600	−	0.235905i
$986$	−8.32873	+	22.8830i	−0.265241	+	0.728744i
$987$	−1.19442	+	6.77388i	−0.0380187	+	0.215615i
$988$	−0.407727	+	0.706204i	−0.0129715	+	0.0224673i
$989$	17.2140	+	29.8156i	0.547374	+	0.948080i
$990$	3.04565	−	1.10852i	0.0967970	−	0.0352312i
$991$	32.6784	+	18.8669i	1.03806	+	0.599325i	0.919284	−	0.393595i	$-0.128769\pi$
$991$	32.6784	+	18.8669i	1.03806	+	0.599325i	0.118778	+	0.992921i	$0.462102\pi$
$992$	−28.5777	+	23.9796i	−0.907344	+	0.761352i
$993$			5.16469i			0.163896i
$994$	12.6450	+	15.0697i	0.401074	+	0.477981i
$995$	9.57421	+	3.48473i	0.303523	+	0.110473i
$996$	1.30980	+	7.42827i	0.0415027	+	0.235374i
$997$	−18.7184	−	3.30057i	−0.592819	−	0.104530i	−0.130813	−	0.991407i	$-0.541759\pi$
$997$	−18.7184	−	3.30057i	−0.592819	−	0.104530i	−0.462005	+	0.886877i	$0.652870\pi$
$998$	71.1544			2.25235
$999$	5.75832	+	1.96005i	0.182185	+	0.0620133i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.o.a.4.2	✓	12
3.2	odd	2		333.2.bl.b.226.1		12
37.18	odd	36		4107.2.a.p.1.2		12
37.19	odd	36		4107.2.a.p.1.11		12
37.28	even	18	inner	111.2.o.a.28.2	yes	12
111.65	odd	18		333.2.bl.b.28.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.o.a.4.2	✓	12	1.1	even	1	trivial
111.2.o.a.28.2	yes	12	37.28	even	18	inner
333.2.bl.b.28.1		12	111.65	odd	18
333.2.bl.b.226.1		12	3.2	odd	2
4107.2.a.p.1.2		12	37.18	odd	36
4107.2.a.p.1.11		12	37.19	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)

\(f(q)\)	\(=\)	\(q+(1.80373 + 0.318047i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(1.27291 + 0.463303i) q^{4} +(0.537688 + 0.640792i) q^{5} -1.83156i q^{6} +(-0.541619 + 0.454472i) q^{7} +(-1.02371 - 0.591038i) q^{8} +(-0.939693 + 0.342020i) q^{9} +O(q^{10})\)	\(q+(1.80373 + 0.318047i) q^{2} +(-0.173648 - 0.984808i) q^{3} +(1.27291 + 0.463303i) q^{4} +(0.537688 + 0.640792i) q^{5} -1.83156i q^{6} +(-0.541619 + 0.454472i) q^{7} +(-1.02371 - 0.591038i) q^{8} +(-0.939693 + 0.342020i) q^{9} +(0.766044 + 1.32683i) q^{10} +(-1.05774 + 1.83206i) q^{11} +(0.235225 - 1.33403i) q^{12} +(0.188102 - 0.516807i) q^{13} +(-1.12148 + 0.647486i) q^{14} +(0.537688 - 0.640792i) q^{15} +(-3.73390 - 3.13311i) q^{16} +(0.603016 + 1.65677i) q^{17} +(-1.80373 + 0.318047i) q^{18} +(-1.07794 + 0.190070i) q^{19} +(0.387550 + 1.06479i) q^{20} +(0.541619 + 0.454472i) q^{21} +(-2.49057 + 2.96814i) q^{22} +(-3.36336 + 1.94184i) q^{23} +(-0.404294 + 1.11079i) q^{24} +(0.746735 - 4.23495i) q^{25} +(0.503655 - 0.872356i) q^{26} +(0.500000 + 0.866025i) q^{27} +(-0.899992 + 0.327570i) q^{28} +(6.53071 + 3.77051i) q^{29} +(1.17365 - 0.984808i) q^{30} -5.68394i q^{31} +(-4.21883 - 5.02780i) q^{32} +(1.98790 + 0.723538i) q^{33} +(0.560748 + 3.18016i) q^{34} +(-0.582444 - 0.102701i) q^{35} -1.35461 q^{36} +(4.57661 - 4.00682i) q^{37} -2.00477 q^{38} +(-0.541619 - 0.0955020i) q^{39} +(-0.171703 - 0.973779i) q^{40} +(6.51279 + 2.37046i) q^{41} +(0.832392 + 0.992006i) q^{42} -8.86481i q^{43} +(-2.19521 + 1.84200i) q^{44} +(-0.724426 - 0.418247i) q^{45} +(-6.68421 + 2.43285i) q^{46} +(4.86426 + 8.42514i) q^{47} +(-2.43713 + 4.22123i) q^{48} +(-1.12873 + 6.40135i) q^{49} +(2.69382 - 7.40121i) q^{50} +(1.52689 - 0.881550i) q^{51} +(0.478876 - 0.570702i) q^{52} +(-6.10641 - 5.12389i) q^{53} +(0.626430 + 1.72110i) q^{54} +(-1.74271 + 0.307286i) q^{55} +(0.823070 - 0.145129i) q^{56} +(0.374365 + 1.02856i) q^{57} +(10.5805 + 8.87806i) q^{58} +(-4.86717 + 5.80047i) q^{59} +(0.981311 - 0.566560i) q^{60} +(-1.43734 + 3.94906i) q^{61} +(1.80776 - 10.2523i) q^{62} +(0.353517 - 0.612309i) q^{63} +(-1.13630 - 1.96814i) q^{64} +(0.432306 - 0.157347i) q^{65} +(3.35553 + 1.93732i) q^{66} +(-2.29401 + 1.92490i) q^{67} +2.38831i q^{68} +(2.49638 + 2.97507i) q^{69} +(-1.01791 - 0.370489i) q^{70} +(-2.63791 - 14.9603i) q^{71} +(1.16412 + 0.205265i) q^{72} +10.3607 q^{73} +(9.52934 - 5.77166i) q^{74} -4.30028 q^{75} +(-1.46019 - 0.257470i) q^{76} +(-0.259729 - 1.47299i) q^{77} +(-0.946561 - 0.344520i) q^{78} +(2.66662 + 3.17795i) q^{79} -4.07729i q^{80} +(0.766044 - 0.642788i) q^{81} +(10.9934 + 6.34705i) q^{82} +(-5.23250 + 1.90447i) q^{83} +(0.478876 + 0.829437i) q^{84} +(-0.737412 + 1.27723i) q^{85} +(2.81942 - 15.9897i) q^{86} +(2.57918 - 7.08623i) q^{87} +(2.16564 - 1.25033i) q^{88} +(-1.88396 + 2.24521i) q^{89} +(-1.17365 - 0.984808i) q^{90} +(0.132994 + 0.365399i) q^{91} +(-5.18093 + 0.913538i) q^{92} +(-5.59759 + 0.987006i) q^{93} +(6.09423 + 16.7438i) q^{94} +(-0.701393 - 0.588538i) q^{95} +(-4.21883 + 5.02780i) q^{96} +(-13.2943 + 7.67547i) q^{97} +(-4.07186 + 11.1873i) q^{98} +(0.367350 - 2.08335i) 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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