LMFDB - Embedded newform 315.2.bv.a.23.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(23,315)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9, 4]))

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

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

chi := DirichletCharacter("315.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bv (of order $12$, degree $4$, 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:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$176$
Relative dimension:	$44$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.19
Character	$\chi$	$=$	315.23
Dual form			315.2.bv.a.137.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.391477 - 0.391477i) q^{2} +(-1.67401 + 0.444638i) q^{3} -1.69349i q^{4} +(-0.676575 + 2.13125i) q^{5} +(0.829400 + 0.481269i) q^{6} +(2.43542 - 1.03378i) q^{7} +(-1.44592 + 1.44592i) q^{8} +(2.60459 - 1.48865i) q^{9} +O(q^{10})$	\(q+(-0.391477 - 0.391477i) q^{2} +(-1.67401 + 0.444638i) q^{3} -1.69349i q^{4} +(-0.676575 + 2.13125i) q^{5} +(0.829400 + 0.481269i) q^{6} +(2.43542 - 1.03378i) q^{7} +(-1.44592 + 1.44592i) q^{8} +(2.60459 - 1.48865i) q^{9} +(1.09920 - 0.569474i) q^{10} +(-5.11658 - 2.95406i) q^{11} +(0.752991 + 2.83492i) q^{12} +(1.73683 - 0.465382i) q^{13} +(-1.35811 - 0.548710i) q^{14} +(0.184952 - 3.86856i) q^{15} -2.25490 q^{16} +(0.837635 - 3.12610i) q^{17} +(-1.60241 - 0.436864i) q^{18} +(-6.21952 - 3.59084i) q^{19} +(3.60926 + 1.14577i) q^{20} +(-3.61726 + 2.81344i) q^{21} +(0.846577 + 3.15947i) q^{22} +(-1.25716 - 0.336855i) q^{23} +(1.77756 - 3.06338i) q^{24} +(-4.08449 - 2.88391i) q^{25} +(-0.862115 - 0.497742i) q^{26} +(-3.69819 + 3.65012i) q^{27} +(-1.75070 - 4.12437i) q^{28} +(-4.31736 - 7.47789i) q^{29} +(-1.58686 + 1.44205i) q^{30} +2.84474 q^{31} +(3.77457 + 3.77457i) q^{32} +(9.87867 + 2.67008i) q^{33} +(-1.55171 + 0.895880i) q^{34} +(0.555510 + 5.88994i) q^{35} +(-2.52102 - 4.41086i) q^{36} +(-0.172607 - 0.644179i) q^{37} +(1.02907 + 3.84053i) q^{38} +(-2.70054 + 1.55131i) q^{39} +(-2.10335 - 4.05989i) q^{40} +(6.48625 + 3.74484i) q^{41} +(2.51747 + 0.314674i) q^{42} +(0.990460 - 3.69645i) q^{43} +(-5.00267 + 8.66488i) q^{44} +(1.41050 + 6.55824i) q^{45} +(0.360278 + 0.624020i) q^{46} +(-2.61343 - 2.61343i) q^{47} +(3.77471 - 1.00261i) q^{48} +(4.86258 - 5.03540i) q^{49} +(0.470003 + 2.72797i) q^{50} +(-0.0122238 + 5.60555i) q^{51} +(-0.788121 - 2.94131i) q^{52} +(4.01818 + 1.07667i) q^{53} +(2.87669 + 0.0188195i) q^{54} +(9.75759 - 8.90609i) q^{55} +(-2.02666 + 5.01619i) q^{56} +(12.0081 + 3.24565i) q^{57} +(-1.23727 + 4.61757i) q^{58} +1.30367 q^{59} +(-6.55138 - 0.313215i) q^{60} +3.28837 q^{61} +(-1.11365 - 1.11365i) q^{62} +(4.80434 - 6.31809i) q^{63} +1.55448i q^{64} +(-0.183247 + 4.01649i) q^{65} +(-2.82199 - 4.91255i) q^{66} +(-8.83375 + 8.83375i) q^{67} +(-5.29402 - 1.41853i) q^{68} +(2.25427 + 0.00491579i) q^{69} +(2.08831 - 2.52325i) q^{70} -5.48346i q^{71} +(-1.61355 + 5.91850i) q^{72} +(-3.27360 + 12.2172i) q^{73} +(-0.184609 + 0.319753i) q^{74} +(8.11976 + 3.01155i) q^{75} +(-6.08106 + 10.5327i) q^{76} +(-15.5149 - 1.90495i) q^{77} +(1.66450 + 0.449894i) q^{78} -0.161603i q^{79} +(1.52561 - 4.80576i) q^{80} +(4.56781 - 7.75468i) q^{81} +(-1.07320 - 4.00523i) q^{82} +(7.21655 + 1.93367i) q^{83} +(4.76454 + 6.12579i) q^{84} +(6.09579 + 3.90025i) q^{85} +(-1.83482 + 1.05933i) q^{86} +(10.5523 + 10.5984i) q^{87} +(11.6695 - 3.12682i) q^{88} +(-2.57489 + 4.45984i) q^{89} +(2.01522 - 3.11958i) q^{90} +(3.74881 - 2.92891i) q^{91} +(-0.570461 + 2.12899i) q^{92} +(-4.76211 + 1.26488i) q^{93} +2.04620i q^{94} +(11.8610 - 10.8259i) q^{95} +(-7.99698 - 4.64034i) q^{96} +(-7.61525 - 2.04050i) q^{97} +(-3.87483 + 0.0676551i) q^{98} +(-17.7242 - 0.0773010i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	$ 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) $ 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.391477	−	0.391477i	−0.276816	−	0.276816i	0.555021	−	0.831837i	$-0.312710\pi$
$2$	−0.391477	−	0.391477i	−0.276816	−	0.276816i	−0.831837	+	0.555021i	$0.812710\pi$
$3$	−1.67401	+	0.444638i	−0.966488	+	0.256712i
$3$	−1.67401	+	0.444638i	−0.966488	+	0.256712i
$4$		−	1.69349i		−	0.846746i
$5$	−0.676575	+	2.13125i	−0.302573	+	0.953126i
$5$	−0.676575	+	2.13125i	−0.302573	+	0.953126i
$6$	0.829400	+	0.481269i	0.338601	+	0.196477i
$7$	2.43542	−	1.03378i	0.920504	−	0.390733i
$7$	2.43542	−	1.03378i	0.920504	−	0.390733i
$8$	−1.44592	+	1.44592i	−0.511209	+	0.511209i
$9$	2.60459	−	1.48865i	0.868198	−	0.496218i
$10$	1.09920	−	0.569474i	0.347598	−	0.180083i
$11$	−5.11658	−	2.95406i	−1.54271	−	0.890682i	−0.998667	−	0.0516220i	$-0.983561\pi$
$11$	−5.11658	−	2.95406i	−1.54271	−	0.890682i	−0.544039	−	0.839060i	$-0.683106\pi$
$12$	0.752991	+	2.83492i	0.217370	+	0.818370i
$13$	1.73683	−	0.465382i	0.481710	−	0.129074i	−0.00978878	−	0.999952i	$-0.503116\pi$
$13$	1.73683	−	0.465382i	0.481710	−	0.129074i	0.491499	+	0.870878i	$0.336449\pi$
$14$	−1.35811	−	0.548710i	−0.362971	−	0.146649i
$15$	0.184952	−	3.86856i	0.0477545	−	0.998859i
$16$	−2.25490			−0.563724
$17$	0.837635	−	3.12610i	0.203156	−	0.758190i	−0.786847	−	0.617148i	$-0.788288\pi$
$17$	0.837635	−	3.12610i	0.203156	−	0.758190i	0.990004	−	0.141042i	$-0.0450453\pi$
$18$	−1.60241	−	0.436864i	−0.377692	−	0.102970i
$19$	−6.21952	−	3.59084i	−1.42685	−	0.823795i	−0.429983	−	0.902837i	$-0.641481\pi$
$19$	−6.21952	−	3.59084i	−1.42685	−	0.823795i	−0.996871	+	0.0790418i	$0.974814\pi$
$20$	3.60926	+	1.14577i	0.807056	+	0.256203i
$21$	−3.61726	+	2.81344i	−0.789350	+	0.613944i
$22$	0.846577	+	3.15947i	0.180491	+	0.673601i
$23$	−1.25716	−	0.336855i	−0.262136	−	0.0702391i	0.125357	−	0.992112i	$-0.459992\pi$
$23$	−1.25716	−	0.336855i	−0.262136	−	0.0702391i	−0.387493	+	0.921873i	$0.626659\pi$
$24$	1.77756	−	3.06338i	0.362844	−	0.625311i
$25$	−4.08449	−	2.88391i	−0.816899	−	0.576781i
$26$	−0.862115	−	0.497742i	−0.169075	−	0.0976153i
$27$	−3.69819	+	3.65012i	−0.711717	+	0.702466i
$28$	−1.75070	−	4.12437i	−0.330852	−	0.779433i
$29$	−4.31736	−	7.47789i	−0.801714	−	1.38861i	−0.918487	−	0.395451i	$-0.870588\pi$
$29$	−4.31736	−	7.47789i	−0.801714	−	1.38861i	0.116772	−	0.993159i	$-0.462745\pi$
$30$	−1.58686	+	1.44205i	−0.289719	+	0.263281i
$31$	2.84474			0.510930			0.255465	−	0.966818i	$-0.417771\pi$
$31$	2.84474			0.510930			0.255465	+	0.966818i	$0.417771\pi$
$32$	3.77457	+	3.77457i	0.667257	+	0.667257i
$33$	9.87867	+	2.67008i	1.71966	+	0.464802i
$34$	−1.55171	+	0.895880i	−0.266116	+	0.153642i
$35$	0.555510	+	5.88994i	0.0938983	+	0.995582i
$36$	−2.52102	−	4.41086i	−0.420171	−	0.735143i
$37$	−0.172607	−	0.644179i	−0.0283764	−	0.105902i	0.950285	−	0.311381i	$-0.100792\pi$
$37$	−0.172607	−	0.644179i	−0.0283764	−	0.105902i	−0.978662	+	0.205479i	$0.934125\pi$
$38$	1.02907	+	3.84053i	0.166937	+	0.623016i
$39$	−2.70054	+	1.55131i	−0.432432	+	0.248409i
$40$	−2.10335	−	4.05989i	−0.332568	−	0.641925i
$41$	6.48625	+	3.74484i	1.01298	+	0.584845i	0.912063	−	0.410049i	$-0.134488\pi$
$41$	6.48625	+	3.74484i	1.01298	+	0.584845i	0.100919	+	0.994895i	$0.467822\pi$
$42$	2.51747	+	0.314674i	0.388454	+	0.0485553i
$43$	0.990460	−	3.69645i	0.151044	−	0.563703i	−0.848368	−	0.529407i	$-0.822414\pi$
$43$	0.990460	−	3.69645i	0.151044	−	0.563703i	0.999412	−	0.0342958i	$-0.0109188\pi$
$44$	−5.00267	+	8.66488i	−0.754181	+	1.30628i
$45$	1.41050	+	6.55824i	0.210265	+	0.977644i
$46$	0.360278	+	0.624020i	0.0531201	+	0.0920067i
$47$	−2.61343	−	2.61343i	−0.381208	−	0.381208i	0.490329	−	0.871537i	$-0.336877\pi$
$47$	−2.61343	−	2.61343i	−0.381208	−	0.381208i	−0.871537	+	0.490329i	$0.836877\pi$
$48$	3.77471	−	1.00261i	0.544833	−	0.144715i
$49$	4.86258	−	5.03540i	0.694655	−	0.719343i
$50$	0.470003	+	2.72797i	0.0664684	+	0.385793i
$51$	−0.0122238	+	5.60555i	−0.00171167	+	0.784934i
$52$	−0.788121	−	2.94131i	−0.109293	−	0.407886i
$53$	4.01818	+	1.07667i	0.551940	+	0.147892i	0.524001	−	0.851718i	$-0.324439\pi$
$53$	4.01818	+	1.07667i	0.551940	+	0.147892i	0.0279390	+	0.999610i	$0.491106\pi$
$54$	2.87669	+	0.0188195i	0.391469	+	0.00256101i
$55$	9.75759	−	8.90609i	1.31571	−	1.20090i
$56$	−2.02666	+	5.01619i	−0.270823	+	0.670316i
$57$	12.0081	+	3.24565i	1.59052	+	0.429897i
$58$	−1.23727	+	4.61757i	−0.162462	+	0.606317i
$59$	1.30367			0.169723			0.0848614	−	0.996393i	$-0.472955\pi$
$59$	1.30367			0.169723			0.0848614	+	0.996393i	$0.472955\pi$
$60$	−6.55138	−	0.313215i	−0.845780	−	0.0404359i
$61$	3.28837			0.421033			0.210516	−	0.977590i	$-0.432485\pi$
$61$	3.28837			0.421033			0.210516	+	0.977590i	$0.432485\pi$
$62$	−1.11365	−	1.11365i	−0.141434	−	0.141434i
$63$	4.80434	−	6.31809i	0.605290	−	0.796005i
$64$			1.55448i			0.194310i
$65$	−0.183247	+	4.01649i	−0.0227290	+	0.498185i
$66$	−2.82199	−	4.91255i	−0.347364	−	0.604693i
$67$	−8.83375	+	8.83375i	−1.07921	+	1.07921i	−0.0826341	+	0.996580i	$0.526333\pi$
$67$	−8.83375	+	8.83375i	−1.07921	+	1.07921i	−0.996580	+	0.0826341i	$0.973667\pi$
$68$	−5.29402	−	1.41853i	−0.641994	−	0.172022i
$69$	2.25427	+	0.00491579i	0.271382	+	0.000591792i
$70$	2.08831	−	2.52325i	0.249600	−	0.301586i
$71$		−	5.48346i		−	0.650767i	−0.945582	−	0.325384i	$-0.894507\pi$
$71$		−	5.48346i		−	0.650767i	0.945582	−	0.325384i	$-0.105493\pi$
$72$	−1.61355	+	5.91850i	−0.190159	+	0.697501i
$73$	−3.27360	+	12.2172i	−0.383146	+	1.42992i	0.457924	+	0.888991i	$0.348593\pi$
$73$	−3.27360	+	12.2172i	−0.383146	+	1.42992i	−0.841069	+	0.540927i	$0.818073\pi$
$74$	−0.184609	+	0.319753i	−0.0214604	+	0.0371705i
$75$	8.11976	+	3.01155i	0.937589	+	0.347744i
$76$	−6.08106	+	10.5327i	−0.697545	+	1.20818i
$77$	−15.5149	−	1.90495i	−1.76809	−	0.217089i
$78$	1.66450	+	0.449894i	0.188468	+	0.0509405i
$79$		−	0.161603i		−	0.0181817i	−0.999959	−	0.00909086i	$-0.997106\pi$
$79$		−	0.161603i		−	0.0181817i	0.999959	−	0.00909086i	$-0.00289375\pi$
$80$	1.52561	−	4.80576i	0.170568	−	0.537300i
$81$	4.56781	−	7.75468i	0.507535	−	0.861631i
$82$	−1.07320	−	4.00523i	−0.118515	−	0.442304i
$83$	7.21655	+	1.93367i	0.792119	+	0.212248i	0.632121	−	0.774870i	$-0.282185\pi$
$83$	7.21655	+	1.93367i	0.792119	+	0.212248i	0.159998	+	0.987117i	$0.448851\pi$
$84$	4.76454	+	6.12579i	0.519854	+	0.668379i
$85$	6.09579	+	3.90025i	0.661181	+	0.423042i
$86$	−1.83482	+	1.05933i	−0.197853	+	0.114231i
$87$	10.5523	+	10.5984i	1.13132	+	1.13627i
$88$	11.6695	−	3.12682i	1.24397	−	0.333321i
$89$	−2.57489	+	4.45984i	−0.272938	+	0.472742i	−0.969613	−	0.244645i	$-0.921329\pi$
$89$	−2.57489	+	4.45984i	−0.272938	+	0.472742i	0.696675	+	0.717387i	$0.254662\pi$
$90$	2.01522	−	3.11958i	0.212423	−	0.328832i
$91$	3.74881	−	2.92891i	0.392982	−	0.307033i
$92$	−0.570461	+	2.12899i	−0.0594747	+	0.221962i
$93$	−4.76211	+	1.26488i	−0.493808	+	0.131162i
$94$			2.04620i			0.211049i
$95$	11.8610	−	10.8259i	1.21691	−	1.11071i
$96$	−7.99698	−	4.64034i	−0.816188	−	0.473603i
$97$	−7.61525	−	2.04050i	−0.773211	−	0.207181i	−0.149421	−	0.988774i	$-0.547741\pi$
$97$	−7.61525	−	2.04050i	−0.773211	−	0.207181i	−0.623790	+	0.781592i	$0.714408\pi$
$98$	−3.87483	+	0.0676551i	−0.391417	+	0.00683420i
$99$	−17.7242	−	0.0773010i	−1.78135	−	0.00776904i
$100$	−4.88387	+	6.91706i	−0.488387	+	0.691706i
$101$	−3.14032	−	1.81306i	−0.312473	−	0.180407i	0.335559	−	0.942019i	$-0.391075\pi$
$101$	−3.14032	−	1.81306i	−0.312473	−	0.180407i	−0.648033	+	0.761612i	$0.724408\pi$
$102$	2.19923	−	2.18966i	0.217756	−	0.216809i
$103$	2.21829	−	8.27876i	0.218574	−	0.815730i	−0.766303	−	0.642479i	$-0.777906\pi$
$103$	2.21829	−	8.27876i	0.218574	−	0.815730i	0.984878	−	0.173251i	$-0.0554273\pi$
$104$	−1.83841	+	3.18422i	−0.180271	+	0.312238i
$105$	−3.54882	−	9.61280i	−0.346329	−	0.938113i
$106$	−1.15153	−	1.99452i	−0.111847	−	0.193725i
$107$	10.2136	−	2.73672i	0.987382	−	0.264568i	0.271232	−	0.962514i	$-0.412569\pi$
$107$	10.2136	−	2.73672i	0.987382	−	0.264568i	0.716151	+	0.697946i	$0.245902\pi$
$108$	6.18145	+	6.26286i	0.594810	+	0.602644i
$109$	12.0906	−	6.98052i	1.15807	−	0.668613i	0.207230	−	0.978292i	$-0.433555\pi$
$109$	12.0906	−	6.98052i	1.15807	−	0.668613i	0.950841	+	0.309679i	$0.100222\pi$
$110$	−7.30640	−	0.333345i	−0.696638	−	0.0317832i
$111$	0.575372	+	1.00161i	0.0546119	+	0.0950687i
$112$	−5.49163	+	2.33108i	−0.518910	+	0.220266i
$113$	0.384527	+	1.43507i	0.0361733	+	0.135000i	0.981651	−	0.190686i	$-0.0610712\pi$
$113$	0.384527	+	1.43507i	0.0361733	+	0.135000i	−0.945478	+	0.325687i	$0.894405\pi$
$114$	−3.43031	−	5.97150i	−0.321278	−	0.559283i
$115$	1.56849	−	2.45142i	0.146262	−	0.228596i
$116$	−12.6638	+	7.31142i	−1.17580	+	0.678848i
$117$	3.83094	−	3.79767i	0.354171	−	0.351095i
$118$	−0.510355	−	0.510355i	−0.0469820	−	0.0469820i
$119$	−1.19171	−	8.47931i	−0.109244	−	0.777297i
$120$	5.32620	+	5.86105i	0.486213	+	0.535038i
$121$	11.9529	+	20.7030i	1.08663	+	1.88209i
$122$	−1.28732	−	1.28732i	−0.116549	−	0.116549i
$123$	−12.5231	−	3.38485i	−1.12917	−	0.305201i
$124$		−	4.81754i		−	0.432628i
$125$	8.90980	−	6.75392i	0.796917	−	0.604089i
$126$	−4.35418	+	0.592598i	−0.387901	+	0.0527928i
$127$	−2.25939	+	2.25939i	−0.200488	+	0.200488i	−0.800209	−	0.599721i	$-0.795278\pi$
$127$	−2.25939	+	2.25939i	−0.200488	+	0.200488i	0.599721	+	0.800209i	$0.295278\pi$
$128$	8.15769	−	8.15769i	0.721045	−	0.721045i
$129$	−0.0144540	+	6.62827i	−0.00127260	+	0.583587i
$130$	1.64410	−	1.50063i	0.144197	−	0.131614i
$131$	−7.55026	+	4.35914i	−0.659669	+	0.380860i	−0.792151	−	0.610325i	$-0.791039\pi$
$131$	−7.55026	+	4.35914i	−0.659669	+	0.380860i	0.132482	+	0.991185i	$0.457705\pi$
$132$	4.52176	−	16.7294i	0.393569	−	1.45611i
$133$	−18.8593	−	2.31558i	−1.63531	−	0.200787i
$134$	6.91642			0.597487
$135$	−5.27723	−	10.3514i	−0.454192	−	0.890904i
$136$	3.30893	+	5.73123i	0.283738	+	0.491449i
$137$	−1.56786	+	0.420107i	−0.133952	+	0.0358922i	−0.325172	−	0.945655i	$-0.605422\pi$
$137$	−1.56786	+	0.420107i	−0.133952	+	0.0358922i	0.191220	+	0.981547i	$0.438755\pi$
$138$	−0.880571	−	0.884420i	−0.0749592	−	0.0752868i
$139$	−10.4587	−	6.03832i	−0.887093	−	0.512163i	−0.0141025	−	0.999901i	$-0.504489\pi$
$139$	−10.4587	−	6.03832i	−0.887093	−	0.512163i	−0.872991	+	0.487737i	$0.837822\pi$
$140$	9.97457	−	0.940752i	0.843005	−	0.0795080i
$141$	5.53694	+	3.21287i	0.466294	+	0.270573i
$142$	−2.14665	+	2.14665i	−0.180143	+	0.180143i
$143$	−10.2614	−	2.74953i	−0.858100	−	0.229927i
$144$	−5.87309	+	3.35676i	−0.489424	+	0.279730i
$145$	18.8583	−	4.14205i	1.56610	−	0.343979i
$146$	6.06430	−	3.50123i	0.501885	−	0.289764i
$147$	−5.90106	+	10.5914i	−0.486711	+	0.873563i
$148$	−1.09091	+	0.292309i	−0.0896723	+	0.0240276i
$149$	−3.98463	−	6.90158i	−0.326434	−	0.565400i	0.655368	−	0.755310i	$-0.272514\pi$
$149$	−3.98463	−	6.90158i	−0.326434	−	0.565400i	−0.981801	+	0.189910i	$0.939180\pi$
$150$	−1.99975	−	4.35765i	−0.163279	−	0.355801i
$151$	2.64063	−	4.57371i	0.214892	−	0.372203i	−0.738347	−	0.674421i	$-0.764393\pi$
$151$	2.64063	−	4.57371i	0.214892	−	0.372203i	0.953239	+	0.302217i	$0.0977268\pi$
$152$	14.1850	−	3.80085i	1.15055	−	0.308289i
$153$	−2.47198	−	9.38916i	−0.199848	−	0.759069i
$154$	5.32798	+	6.81947i	0.429341	+	0.549528i
$155$	−1.92468	+	6.06287i	−0.154594	+	0.486981i
$156$	2.62714	+	4.57334i	0.210339	+	0.366160i
$157$	−10.2727	+	10.2727i	−0.819849	+	0.819849i	−0.986086	−	0.166237i	$-0.946838\pi$
$157$	−10.2727	+	10.2727i	−0.819849	+	0.819849i	0.166237	+	0.986086i	$0.446838\pi$
$158$	−0.0632637	+	0.0632637i	−0.00503299	+	0.00503299i
$159$	−7.20519	−	0.0157120i	−0.571409	−	0.00124605i
$160$	−10.5984	+	5.49080i	−0.837874	+	0.434086i
$161$	−3.40995	+	0.479246i	−0.268742	+	0.0377699i
$162$	−4.82397	+	1.24758i	−0.379007	+	0.0980195i
$163$	8.52972	−	2.28553i	0.668100	−	0.179017i	0.0912010	−	0.995833i	$-0.470929\pi$
$163$	8.52972	−	2.28553i	0.668100	−	0.179017i	0.576899	+	0.816816i	$0.304263\pi$
$164$	6.34185	−	10.9844i	0.495215	−	0.857738i
$165$	−12.3743	+	19.2474i	−0.963337	+	1.49841i
$166$	−2.06813	−	3.58210i	−0.160518	−	0.278025i
$167$	3.09522	−	0.829362i	0.239515	−	0.0641780i	−0.137064	−	0.990562i	$-0.543767\pi$
$167$	3.09522	−	0.829362i	0.239515	−	0.0641780i	0.376580	+	0.926384i	$0.377100\pi$
$168$	1.16225	−	9.29826i	0.0896692	−	0.717376i
$169$	−8.45833	+	4.88342i	−0.650641	+	0.375648i
$170$	−0.859501	−	3.91322i	−0.0659207	−	0.300130i
$171$	−21.5448	−	0.0939642i	−1.64757	−	0.00718562i
$172$	−6.25990	−	1.67734i	−0.477313	−	0.127896i
$173$	−2.64800	+	2.64800i	−0.201323	+	0.201323i	−0.800567	−	0.599243i	$-0.795468\pi$
$173$	−2.64800	+	2.64800i	−0.201323	+	0.201323i	0.599243	+	0.800567i	$0.295468\pi$
$174$	0.0180558	−	8.27998i	0.00136881	−	0.627704i
$175$	−12.9288	−	2.80105i	−0.977326	−	0.211740i
$176$	11.5374	+	6.66109i	0.869661	+	0.502099i
$177$	−2.18234	+	0.579660i	−0.164035	+	0.0435699i
$178$	2.75394	−	0.737915i	0.206416	−	0.0553090i
$179$	−7.87352	−	13.6373i	−0.588494	−	1.01930i	−0.994430	−	0.105400i	$-0.966388\pi$
$179$	−7.87352	−	13.6373i	−0.588494	−	1.01930i	0.405936	−	0.913902i	$-0.366946\pi$
$180$	11.1063	−	2.38867i	0.827816	−	0.178041i
$181$	12.0853			0.898294			0.449147	−	0.893458i	$-0.351728\pi$
$181$	12.0853			0.898294			0.449147	+	0.893458i	$0.351728\pi$
$182$	−2.61417	−	0.320974i	−0.193775	−	0.0237921i
$183$	−5.50476	+	1.46214i	−0.406923	+	0.108084i
$184$	2.30481	−	1.33068i	0.169913	−	0.0980993i
$185$	1.48969	+	0.0679651i	0.109524	+	0.00499689i
$186$	2.35943	+	1.36909i	0.173002	+	0.100386i
$187$	−13.5205	+	13.5205i	−0.988717	+	0.988717i
$188$	−4.42583	+	4.42583i	−0.322787	+	0.322787i
$189$	−5.23323	+	12.7127i	−0.380662	+	0.924714i
$190$	−8.88138	−	0.405201i	−0.644323	−	0.0293964i
$191$			13.2196i			0.956536i	0.878214	+	0.478268i	$0.158735\pi$
$191$			13.2196i			0.956536i	−0.878214	+	0.478268i	$0.841265\pi$
$192$	−0.691180	−	2.60220i	−0.0498816	−	0.187798i
$193$	16.0543	+	16.0543i	1.15561	+	1.15561i	0.985409	+	0.170203i	$0.0544425\pi$
$193$	16.0543	+	16.0543i	1.15561	+	1.15561i	0.170203	+	0.985409i	$0.445558\pi$
$194$	2.18238	+	3.78000i	0.156686	+	0.271388i
$195$	−1.47913	−	6.80511i	−0.105923	−	0.487324i
$196$	−8.52741	−	8.23474i	−0.609101	−	0.588196i
$197$	−4.71621	−	4.71621i	−0.336016	−	0.336016i	0.518850	−	0.854866i	$-0.326360\pi$
$197$	−4.71621	−	4.71621i	−0.336016	−	0.336016i	−0.854866	+	0.518850i	$0.826360\pi$
$198$	6.90834	+	6.96887i	0.490955	+	0.495256i
$199$	3.47281	−	2.00503i	0.246181	−	0.142133i	−0.371833	−	0.928300i	$-0.621271\pi$
$199$	3.47281	−	2.00503i	0.246181	−	0.142133i	0.618014	+	0.786167i	$0.287937\pi$
$200$	10.0757	−	1.73595i	0.712461	−	0.122750i
$201$	10.8599	−	18.7156i	0.766000	−	1.32009i
$202$	0.519590	+	1.93913i	0.0365582	+	0.136437i
$203$	−18.2451	−	13.7486i	−1.28056	−	0.964964i
$204$	9.49295	+	0.0207009i	0.664640	+	0.00144935i
$205$	−12.3696	+	11.2902i	−0.863933	+	0.788541i
$206$	−4.10935	+	2.37253i	−0.286312	+	0.165302i
$207$	−3.77585	+	0.994106i	−0.262440	+	0.0690952i
$208$	−3.91637	+	1.04939i	−0.271552	+	0.0727620i
$209$	21.2151	+	36.7456i	1.46748	+	2.54175i
$210$	−2.37391	+	5.15247i	−0.163815	+	0.355554i
$211$	8.73996	−	15.1381i	0.601684	−	1.04215i	−0.390883	−	0.920441i	$-0.627830\pi$
$211$	8.73996	−	15.1381i	0.601684	−	1.04215i	0.992566	−	0.121706i	$-0.0388365\pi$
$212$	1.82333	−	6.80476i	0.125227	−	0.467353i
$213$	2.43816	+	9.17935i	0.167060	+	0.628959i
$214$	−5.06974	−	2.92701i	−0.346560	−	0.200087i
$215$	7.20795	+	4.61184i	0.491578	+	0.314525i
$216$	0.0695096	−	10.6250i	0.00472953	−	0.722943i
$217$	6.92815	−	2.94085i	0.470313	−	0.199638i
$218$	−7.46591	−	2.00049i	−0.505655	−	0.135490i
$219$	0.0477722	−	21.9073i	0.00322815	−	1.48036i
$220$	−15.0824	−	16.5244i	−1.01685	−	1.11408i
$221$		−	5.81932i		−	0.391450i
$222$	0.166863	−	0.617352i	0.0111991	−	0.0414340i
$223$	−3.09538	+	11.5521i	−0.207282	+	0.773587i	0.781460	+	0.623956i	$0.214475\pi$
$223$	−3.09538	+	11.5521i	−0.207282	+	0.773587i	−0.988742	+	0.149632i	$0.952191\pi$
$224$	13.0948	+	5.29060i	0.874932	+	0.353493i
$225$	−14.9316	−	1.43100i	−0.995439	−	0.0954000i
$226$	0.411265	−	0.712332i	0.0273570	−	0.0473836i
$227$	12.7688	−	3.42138i	0.847492	−	0.227085i	0.191162	−	0.981559i	$-0.438775\pi$
$227$	12.7688	−	3.42138i	0.847492	−	0.227085i	0.656330	+	0.754474i	$0.272108\pi$
$228$	5.49648	−	20.3357i	0.364014	−	1.34676i
$229$	14.2940	−	8.25265i	0.944574	−	0.545350i	0.0531831	−	0.998585i	$-0.483063\pi$
$229$	14.2940	−	8.25265i	0.944574	−	0.545350i	0.891391	+	0.453234i	$0.149730\pi$
$230$	−1.57370	+	0.345648i	−0.103767	+	0.0227914i
$231$	26.8190	−	3.70962i	1.76456	−	0.244075i
$232$	17.0550	+	4.56986i	1.11971	+	0.300026i
$233$	−2.98975	−	11.1579i	−0.195865	−	0.730977i	−0.992041	−	0.125913i	$-0.959814\pi$
$233$	−2.98975	−	11.1579i	−0.195865	−	0.730977i	0.796177	−	0.605064i	$-0.206853\pi$
$234$	−2.98643	−	0.0130248i	−0.195229	−	0.000851458i
$235$	7.33807	−	3.80171i	0.478683	−	0.247996i
$236$		−	2.20775i		−	0.143712i
$237$	0.0718547	+	0.270524i	0.00466747	+	0.0175724i
$238$	−2.85293	+	3.78598i	−0.184928	+	0.245409i
$239$	9.68398	−	16.7731i	0.626405	−	1.08496i	−0.361863	−	0.932231i	$-0.617859\pi$
$239$	9.68398	−	16.7731i	0.626405	−	1.08496i	0.988267	−	0.152733i	$-0.0488076\pi$
$240$	−0.417049	+	8.72322i	−0.0269204	+	0.563081i
$241$	8.55376	−	14.8155i	0.550996	−	0.954353i	−0.447207	−	0.894431i	$-0.647581\pi$
$241$	8.55376	−	14.8155i	0.550996	−	0.954353i	0.998203	−	0.0599228i	$-0.0190854\pi$
$242$	3.42548	−	12.7841i	0.220198	−	0.821790i
$243$	−4.19852	+	15.0124i	−0.269335	+	0.963046i
$244$		−	5.56883i		−	0.356508i
$245$	7.44183	+	13.7702i	0.475441	+	0.879748i
$246$	3.57742	+	6.22760i	0.228088	+	0.397057i
$247$	−12.4734	−	3.34222i	−0.793660	−	0.212661i
$248$	−4.11326	+	4.11326i	−0.261192	+	0.261192i
$249$	−12.9403	−	0.0282184i	−0.820060	−	0.00178827i
$250$	−6.13199	−	0.843978i	−0.387821	−	0.0533779i
$251$		−	12.0876i		−	0.762961i	−0.924377	−	0.381480i	$-0.875414\pi$
$251$		−	12.0876i		−	0.762961i	0.924377	−	0.381480i	$-0.124586\pi$
$252$	−10.6996	−	8.13612i	−0.674014	−	0.512527i
$253$	5.43726	+	5.43726i	0.341838	+	0.341838i
$254$	1.76900			0.110997
$255$	−11.9386	−	3.81863i	−0.747623	−	0.239132i
$256$	−3.27814			−0.204884
$257$	2.12695	−	7.93789i	0.132676	−	0.495152i	−0.867321	−	0.497749i	$-0.834160\pi$
$257$	2.12695	−	7.93789i	0.132676	−	0.495152i	0.999997	+	0.00259727i	$0.000826737\pi$
$258$	2.60047	−	2.58916i	0.161898	−	0.161194i
$259$	−1.08631	−	1.39041i	−0.0675002	−	0.0863959i
$260$	6.80190	+	0.310327i	0.421836	+	0.0192457i
$261$	−22.3770	−	13.0498i	−1.38510	−	0.807763i
$262$	4.66226	+	1.24925i	0.288035	+	0.0771788i
$263$	−6.87818	−	25.6697i	−0.424127	−	1.58286i	−0.765822	−	0.643052i	$-0.777668\pi$
$263$	−6.87818	−	25.6697i	−0.424127	−	1.58286i	0.341695	−	0.939811i	$-0.388999\pi$
$264$	−18.1445	+	10.4230i	−1.11671	+	0.641492i
$265$	−5.01325	+	7.83532i	−0.307962	+	0.481320i
$266$	6.47649	+	8.28948i	0.397099	+	0.508261i
$267$	2.32737	−	8.61070i	0.142432	−	0.526966i
$268$	14.9599	+	14.9599i	0.913820	+	0.913820i
$269$	16.1889	+	28.0400i	0.987054	+	1.70963i	0.632426	+	0.774621i	$0.282059\pi$
$269$	16.1889	+	28.0400i	0.987054	+	1.70963i	0.354628	+	0.935008i	$0.384608\pi$
$270$	−1.98641	+	6.11824i	−0.120889	+	0.372344i
$271$	−12.7553	+	22.0928i	−0.774829	+	1.34204i	0.160062	+	0.987107i	$0.448831\pi$
$271$	−12.7553	+	22.0928i	−0.774829	+	1.34204i	−0.934891	+	0.354936i	$0.884503\pi$
$272$	−1.88878	+	7.04903i	−0.114524	+	0.427410i
$273$	−4.97323	+	6.56988i	−0.300994	+	0.397627i
$274$	0.778244	+	0.449320i	0.0470155	+	0.0271444i
$275$	12.3794	+	26.8216i	0.746506	+	1.61740i
$276$	0.00832485	−	3.81759i	0.000501097	−	0.229792i
$277$	0.969090	+	3.61669i	0.0582269	+	0.217306i	0.988909	−	0.148523i	$-0.0474520\pi$
$277$	0.969090	+	3.61669i	0.0582269	+	0.217306i	−0.930682	+	0.365829i	$0.880785\pi$
$278$	1.73047	+	6.45819i	0.103787	+	0.387337i
$279$	7.40939	−	4.23484i	0.443589	−	0.253533i
$280$	−9.31959	−	7.71314i	−0.556952	−	0.460948i
$281$	−3.29015	+	1.89957i	−0.196274	+	0.113319i	−0.594916	−	0.803788i	$-0.702815\pi$
$281$	−3.29015	+	1.89957i	−0.196274	+	0.113319i	0.398642	+	0.917106i	$0.369481\pi$
$282$	−0.909818	−	3.42535i	−0.0541789	−	0.203976i
$283$	14.1020	+	14.1020i	0.838274	+	0.838274i	0.988632	−	0.150358i	$-0.0480425\pi$
$283$	14.1020	+	14.1020i	0.838274	+	0.838274i	−0.150358	+	0.988632i	$0.548042\pi$
$284$	−9.28620			−0.551035
$285$	−15.0417	+	23.3965i	−0.890994	+	1.38589i
$286$	2.94072	+	5.09348i	0.173888	+	0.301184i
$287$	19.6681	+	2.41489i	1.16097	+	0.142547i
$288$	15.4503	+	4.21219i	0.910416	+	0.248206i
$289$	5.65158	+	3.26294i	0.332446	+	0.191938i
$290$	−9.00411	−	5.76108i	−0.528740	−	0.338302i
$291$	13.6553	+	0.0297774i	0.800485	+	0.00174558i
$292$	20.6898	+	5.54381i	1.21078	+	0.324427i
$293$	3.52232	+	13.1455i	0.205776	+	0.767967i	0.989212	+	0.146494i	$0.0467989\pi$
$293$	3.52232	+	13.1455i	0.205776	+	0.767967i	−0.783435	+	0.621473i	$0.786534\pi$
$294$	6.45641	−	1.83615i	0.376546	−	0.107087i
$295$	−0.882027	+	2.77844i	−0.0513536	+	0.161767i
$296$	1.18100	+	0.681853i	0.0686445	+	0.0396319i
$297$	29.7047	−	7.75145i	1.72364	−	0.449784i
$298$	−1.14192	+	4.26170i	−0.0661496	+	0.246874i
$299$	−2.34024			−0.135339
$300$	5.10004	−	13.7508i	0.294451	−	0.793900i
$301$	−1.40914	−	10.0263i	−0.0812212	−	0.577908i
$302$	−2.82425	+	0.756755i	−0.162517	+	0.0435464i
$303$	6.06307	+	1.63877i	0.348314	+	0.0941451i
$304$	14.0244	+	8.09697i	0.804353	+	0.464393i
$305$	−2.22483	+	7.00836i	−0.127393	+	0.401298i
$306$	−2.70792	+	4.64336i	−0.154801	+	0.265443i
$307$	−11.6981	+	11.6981i	−0.667647	+	0.667647i	−0.957171	−	0.289524i	$-0.906503\pi$
$307$	−11.6981	+	11.6981i	−0.667647	+	0.667647i	0.289524	+	0.957171i	$0.406503\pi$
$308$	−3.22602	+	26.2743i	−0.183819	+	1.49712i
$309$	−0.0323719	+	14.8450i	−0.00184157	+	0.844504i
$310$	3.12694	−	1.62001i	0.177598	−	0.0920101i
$311$		−	9.52101i		−	0.539887i	−0.962876	−	0.269944i	$-0.912995\pi$
$311$		−	9.52101i		−	0.539887i	0.962876	−	0.269944i	$-0.0870051\pi$
$312$	1.66168	−	6.14782i	0.0940742	−	0.348052i
$313$	−1.28452	−	1.28452i	−0.0726056	−	0.0726056i	0.669871	−	0.742477i	$-0.266349\pi$
$313$	−1.28452	−	1.28452i	−0.0726056	−	0.0726056i	−0.742477	+	0.669871i	$0.766349\pi$
$314$	8.04304			0.453895
$315$	10.2150	+	14.5139i	0.575548	+	0.817768i
$316$	−0.273673			−0.0153953
$317$	−5.24434	−	5.24434i	−0.294551	−	0.294551i	0.544324	−	0.838875i	$-0.316786\pi$
$317$	−5.24434	−	5.24434i	−0.294551	−	0.294551i	−0.838875	+	0.544324i	$0.816786\pi$
$318$	2.81451	+	2.82682i	0.157830	+	0.158520i
$319$			51.0150i			2.85629i
$320$	−3.31299	−	1.05172i	−0.185202	−	0.0587929i
$321$	−15.8807	+	9.12262i	−0.886375	+	0.509175i
$322$	1.52253	+	1.14730i	0.0848473	+	0.0639367i
$323$	−16.4350	+	16.4350i	−0.914468	+	0.914468i
$324$	−13.1325	−	7.73555i	−0.729583	−	0.429753i
$325$	−8.43619	−	3.10800i	−0.467956	−	0.172401i
$326$	−4.23392	−	2.44446i	−0.234495	−	0.135386i
$327$	−17.1360	+	17.0614i	−0.947621	+	0.943497i
$328$	−14.7933	+	3.96385i	−0.816823	+	0.218867i
$329$	−9.06654	−	3.66309i	−0.499855	−	0.201953i
$330$	12.3792	−	2.69069i	0.681451	−	0.148117i
$331$	2.66549			0.146509			0.0732543	−	0.997313i	$-0.476662\pi$
$331$	2.66549			0.146509			0.0732543	+	0.997313i	$0.476662\pi$
$332$	3.27465	−	12.2212i	0.179720	−	0.670724i
$333$	−1.40853	−	1.42087i	−0.0771870	−	0.0778632i
$334$	−1.53638	−	0.887032i	−0.0840672	−	0.0485362i
$335$	−12.8503	−	24.8037i	−0.702086	−	1.35517i
$336$	8.15654	−	6.34402i	0.444976	−	0.346095i
$337$	−8.33786	−	31.1173i	−0.454192	−	1.69507i	−0.690452	−	0.723378i	$-0.742588\pi$
$337$	−8.33786	−	31.1173i	−0.454192	−	1.69507i	0.236260	−	0.971690i	$-0.424078\pi$
$338$	5.22299	+	1.39950i	0.284093	+	0.0761225i
$339$	−1.28179	−	2.23135i	−0.0696173	−	0.121190i
$340$	6.60504	−	10.3232i	0.358209	−	0.559852i
$341$	−14.5553	−	8.40353i	−0.788216	−	0.455076i
$342$	8.39752	+	8.47109i	0.454086	+	0.458064i
$343$	6.63694	−	17.2902i	0.358361	−	0.933583i
$344$	3.91263	+	6.77688i	0.210955	+	0.365385i
$345$	−1.53566	+	4.80110i	−0.0826771	+	0.258483i
$346$	2.07326			0.111459
$347$	−7.23029	−	7.23029i	−0.388142	−	0.388142i	0.485882	−	0.874024i	$-0.338498\pi$
$347$	−7.23029	−	7.23029i	−0.388142	−	0.388142i	−0.874024	+	0.485882i	$0.838498\pi$
$348$	17.9483	−	17.8702i	0.962128	−	0.957941i
$349$	1.74542	−	1.00772i	0.0934304	−	0.0539421i	−0.452557	−	0.891736i	$-0.649488\pi$
$349$	1.74542	−	1.00772i	0.0934304	−	0.0539421i	0.545987	+	0.837793i	$0.316155\pi$
$350$	3.96478	+	6.15788i	0.211927	+	0.329152i
$351$	−4.72443	+	8.06071i	−0.252171	+	0.430249i
$352$	−8.16259	−	30.4632i	−0.435068	−	1.62369i
$353$	−0.242573	−	0.905296i	−0.0129109	−	0.0481840i	0.959170	−	0.282831i	$-0.0912734\pi$
$353$	−0.242573	−	0.905296i	−0.0129109	−	0.0481840i	−0.972081	+	0.234647i	$0.924607\pi$
$354$	1.08126	+	0.627414i	0.0574684	+	0.0333467i
$355$	11.6867	+	3.70997i	0.620263	+	0.196905i
$356$	7.55270	+	4.36056i	0.400292	+	0.231109i
$357$	5.76516	+	13.6645i	0.305124	+	0.723204i
$358$	−2.25640	+	8.42100i	−0.119254	+	0.445064i
$359$	−2.33118	+	4.03773i	−0.123035	+	0.213103i	−0.920963	−	0.389650i	$-0.872596\pi$
$359$	−2.33118	+	4.03773i	−0.123035	+	0.213103i	0.797928	+	0.602753i	$0.205929\pi$
$360$	−11.5221	−	7.44320i	−0.607270	−	0.392291i
$361$	16.2883	+	28.2121i	0.857276	+	1.48485i
$362$	−4.73112	−	4.73112i	−0.248662	−	0.248662i
$363$	−29.2146	−	29.3423i	−1.53337	−	1.54007i
$364$	−4.96008	−	6.34858i	−0.259979	−	0.332756i
$365$	−23.8232	−	15.2427i	−1.24696	−	0.797841i
$366$	2.72738	+	1.58259i	0.142562	+	0.0827234i
$367$	0.529774	+	1.97714i	0.0276540	+	0.103206i	0.978373	−	0.206846i	$-0.0663200\pi$
$367$	0.529774	+	1.97714i	0.0276540	+	0.103206i	−0.950719	+	0.310052i	$0.899653\pi$
$368$	2.83477	+	0.759573i	0.147772	+	0.0395955i
$369$	22.4688	+	0.0979940i	1.16968	+	0.00510136i
$370$	−0.556573	−	0.609786i	−0.0289348	−	0.0317013i
$371$	10.8990	−	1.53179i	0.565849	−	0.0795263i
$372$	2.14207	+	8.06460i	0.111061	+	0.418130i
$373$	2.21404	−	8.26292i	0.114639	−	0.427838i	−0.884621	−	0.466311i	$-0.845583\pi$
$373$	2.21404	−	8.26292i	0.114639	−	0.427838i	0.999260	+	0.0384732i	$0.0122494\pi$
$374$	10.5859			0.547385
$375$	−11.9120	+	15.2677i	−0.615134	+	0.788423i
$376$	7.55761			0.389754
$377$	−10.9786	−	10.9786i	−0.565427	−	0.565427i
$378$	7.02543	−	2.92805i	0.361349	−	0.150602i
$379$			1.82867i			0.0939324i	0.998896	+	0.0469662i	$0.0149553\pi$
$379$			1.82867i			0.0939324i	−0.998896	+	0.0469662i	$0.985045\pi$
$380$	−18.3336	−	20.0864i	−0.940493	−	1.03041i
$381$	2.77762	−	4.78684i	0.142302	−	0.245237i
$382$	5.17517	−	5.17517i	0.264785	−	0.264785i
$383$	4.88077	+	1.30780i	0.249396	+	0.0668254i	0.381351	−	0.924430i	$-0.375459\pi$
$383$	4.88077	+	1.30780i	0.249396	+	0.0668254i	−0.131955	+	0.991256i	$0.542126\pi$
$384$	−10.0288	+	17.2832i	−0.511780	+	0.881982i
$385$	14.5569	−	31.7773i	0.741889	−	1.61952i
$386$		−	12.5698i		−	0.639784i
$387$	−2.92299	−	11.1022i	−0.148584	−	0.564356i
$388$	−3.45557	+	12.8964i	−0.175430	+	0.654713i
$389$	4.75400	−	8.23417i	0.241037	−	0.417489i	−0.719973	−	0.694002i	$-0.755846\pi$
$389$	4.75400	−	8.23417i	0.241037	−	0.417489i	0.961010	+	0.276514i	$0.0891791\pi$
$390$	−2.08500	+	3.24309i	−0.105578	+	0.164220i
$391$	−2.10608	+	3.64784i	−0.106509	+	0.184479i
$392$	0.249884	+	14.3117i	0.0126210	+	0.722848i
$393$	10.7009	−	10.6544i	0.539791	−	0.537442i
$394$			3.69257i			0.186029i
$395$	0.344416	+	0.109336i	0.0173295	+	0.00550130i
$396$	−0.130909	+	30.0157i	−0.00657841	+	1.50835i
$397$	−4.34181	−	16.2039i	−0.217909	−	0.813248i	−0.985122	−	0.171856i	$-0.945024\pi$
$397$	−4.34181	−	16.2039i	−0.217909	−	0.813248i	0.767213	−	0.641392i	$-0.221643\pi$
$398$	−2.14445	−	0.574603i	−0.107491	−	0.0288023i
$399$	32.6002	−	4.50927i	1.63205	−	0.225746i
$400$	9.21011	+	6.50291i	0.460506	+	0.325146i
$401$	−2.63265	+	1.51996i	−0.131468	+	0.0759033i	−0.564292	−	0.825575i	$-0.690851\pi$
$401$	−2.63265	+	1.51996i	−0.131468	+	0.0759033i	0.432823	+	0.901479i	$0.357517\pi$
$402$	−11.5781	+	3.07530i	−0.577464	+	0.153382i
$403$	4.94083	−	1.32389i	0.246120	−	0.0659477i
$404$	−3.07041	+	5.31810i	−0.152758	+	0.264585i
$405$	13.4367	+	14.9818i	0.667677	+	0.744451i
$406$	1.76028	+	12.5248i	0.0873613	+	0.621596i
$407$	−1.01978	+	3.80588i	−0.0505487	+	0.188650i
$408$	−8.08749	−	8.12284i	−0.400390	−	0.402140i
$409$		−	35.0978i		−	1.73547i	−0.497024	−	0.867737i	$-0.665574\pi$
$409$		−	35.0978i		−	1.73547i	0.497024	−	0.867737i	$-0.334426\pi$
$410$	9.26228	+	0.422579i	0.457431	+	0.0208697i
$411$	2.43782	−	1.40039i	0.120249	−	0.0690764i
$412$	−14.0200	−	3.75665i	−0.690716	−	0.185077i
$413$	3.17498	−	1.34771i	0.156231	−	0.0663164i
$414$	1.86733	+	1.08899i	0.0917742	+	0.0535209i
$415$	−9.00367	+	14.0720i	−0.441973	+	0.690769i
$416$	8.31241	+	4.79917i	0.407550	+	0.235299i
$417$	20.1927	+	5.45785i	0.988843	+	0.267272i
$418$	6.07984	−	22.6903i	0.297375	−	1.10982i
$419$	−6.48197	+	11.2271i	−0.316665	+	0.548480i	−0.979790	−	0.200029i	$-0.935896\pi$
$419$	−6.48197	+	11.2271i	−0.316665	+	0.548480i	0.663125	+	0.748509i	$0.269230\pi$
$420$	−16.2792	+	6.00990i	−0.794343	+	0.293253i
$421$	−8.77764	−	15.2033i	−0.427796	−	0.740964i	0.568881	−	0.822420i	$-0.307376\pi$
$421$	−8.77764	−	15.2033i	−0.427796	−	0.740964i	−0.996677	+	0.0814556i	$0.974043\pi$
$422$	−9.34769	+	2.50471i	−0.455039	+	0.121927i
$423$	−10.6974	−	2.91643i	−0.520127	−	0.141802i
$424$	−7.36673	+	4.25318i	−0.357760	+	0.206553i
$425$	−12.4367	+	10.3529i	−0.603268	+	0.502188i
$426$	2.63902	−	4.54799i	0.127861	−	0.220351i
$427$	8.00858	−	3.39947i	0.387562	−	0.164512i
$428$	−4.63461	−	17.2966i	−0.224022	−	0.836062i
$429$	18.4002	+	0.0401245i	0.888369	+	0.00193723i
$430$	−1.01632	−	4.62718i	−0.0490111	−	0.223142i
$431$	3.45619	−	1.99543i	0.166479	−	0.0961166i	−0.414446	−	0.910074i	$-0.636024\pi$
$431$	3.45619	−	1.99543i	0.166479	−	0.0961166i	0.580924	+	0.813957i	$0.302691\pi$
$432$	8.33904	−	8.23064i	0.401212	−	0.395997i
$433$	−26.5859	−	26.5859i	−1.27763	−	1.27763i	−0.941988	−	0.335647i	$-0.891045\pi$
$433$	−26.5859	−	26.5859i	−1.27763	−	1.27763i	−0.335647	−	0.941988i	$-0.608955\pi$
$434$	−3.86348	−	1.56094i	−0.185453	−	0.0749274i
$435$	−29.7272	+	15.3189i	−1.42531	+	0.734487i
$436$	−11.8215	−	20.4754i	−0.566145	−	0.980592i
$437$	6.60933	+	6.60933i	0.316167	+	0.316167i
$438$	−8.59490	+	8.55749i	−0.410680	+	0.408893i
$439$		−	13.0953i		−	0.625003i	−0.949917	−	0.312502i	$-0.898833\pi$
$439$		−	13.0953i		−	0.625003i	0.949917	−	0.312502i	$-0.101167\pi$
$440$	−1.23121	+	26.9861i	−0.0586954	+	1.28651i
$441$	5.16908	−	20.3539i	0.246146	−	0.969233i
$442$	−2.27813	+	2.27813i	−0.108360	+	0.108360i
$443$	26.2476	−	26.2476i	1.24706	−	1.24706i	0.290053	−	0.957011i	$-0.406327\pi$
$443$	26.2476	−	26.2476i	1.24706	−	1.24706i	0.957011	−	0.290053i	$-0.0936729\pi$
$444$	1.69622	−	0.974387i	0.0804990	−	0.0462424i
$445$	−7.76295	−	8.50516i	−0.367999	−	0.403183i
$446$	5.73416	−	3.31062i	0.271520	−	0.156762i
$447$	9.73901	+	9.78158i	0.460639	+	0.462653i
$448$	1.60699	+	3.78581i	0.0759233	+	0.178863i
$449$	−30.6611			−1.44699			−0.723494	−	0.690330i	$-0.757465\pi$
$449$	−30.6611			−1.44699			−0.723494	+	0.690330i	$0.757465\pi$
$450$	5.28517	+	6.40557i	0.249145	+	0.301962i
$451$	−22.1249	−	38.3215i	−1.04182	−	1.80449i
$452$	2.43029	−	0.651194i	0.114311	−	0.0306296i
$453$	−2.38679	+	8.83055i	−0.112141	+	0.414895i
$454$	−6.33806	−	3.65928i	−0.297460	−	0.171739i
$455$	3.70590	+	9.97130i	0.173735	+	0.467462i
$456$	−22.0557	+	12.6698i	−1.03285	+	0.593319i
$457$	12.9734	−	12.9734i	0.606872	−	0.606872i	−0.335255	−	0.942127i	$-0.608823\pi$
$457$	12.9734	−	12.9734i	0.606872	−	0.606872i	0.942127	+	0.335255i	$0.108823\pi$
$458$	−8.82649	−	2.36505i	−0.412435	−	0.110512i
$459$	8.31289	+	14.6184i	0.388013	+	0.682328i
$460$	−4.15146	−	2.65622i	−0.193563	−	0.123847i
$461$	−8.89052	+	5.13295i	−0.414073	+	0.239065i	−0.692538	−	0.721381i	$-0.743508\pi$
$461$	−8.89052	+	5.13295i	−0.414073	+	0.239065i	0.278465	+	0.960446i	$0.410174\pi$
$462$	−11.9513	−	9.04680i	−0.556023	−	0.420895i
$463$	−8.20369	+	2.19817i	−0.381258	+	0.102158i	−0.444358	−	0.895849i	$-0.646568\pi$
$463$	−8.20369	+	2.19817i	−0.381258	+	0.102158i	0.0630997	+	0.998007i	$0.479901\pi$
$464$	9.73521	+	16.8619i	0.451946	+	0.782793i
$465$	0.526141	−	11.0051i	0.0243992	−	0.510348i
$466$	−3.19764	+	5.53847i	−0.148128	+	0.256565i
$467$	−16.8855	+	4.52445i	−0.781366	+	0.209366i	−0.627387	−	0.778708i	$-0.715876\pi$
$467$	−16.8855	+	4.52445i	−0.781366	+	0.209366i	−0.153979	+	0.988074i	$0.549209\pi$
$468$	−6.43132	−	6.48767i	−0.297288	−	0.299893i
$469$	−12.3817	+	30.6461i	−0.571736	+	1.41511i
$470$	−4.36097	−	1.38441i	−0.201156	−	0.0638578i
$471$	12.6289	−	21.7642i	0.581909	−	1.00284i
$472$	−1.88499	+	1.88499i	−0.0867638	+	0.0867638i
$473$	−15.9873	+	15.9873i	−0.735096	+	0.735096i
$474$	0.0777744	−	0.134033i	0.00357229	−	0.00615635i
$475$	15.0479	+	32.6033i	0.690446	+	1.49594i
$476$	−14.3596	+	2.01815i	−0.658173	+	0.0925019i
$477$	12.0685	−	3.17740i	0.552579	−	0.145483i
$478$	−10.3574	+	2.77525i	−0.473734	+	0.126937i
$479$	−1.40309	+	2.43023i	−0.0641090	+	0.111040i	−0.896298	−	0.443451i	$-0.853754\pi$
$479$	−1.40309	+	2.43023i	−0.0641090	+	0.111040i	0.832189	+	0.554491i	$0.187087\pi$
$480$	15.3003	−	13.9041i	0.698360	−	0.634631i
$481$	−0.599578	−	1.03850i	−0.0273384	−	0.0473515i
$482$	−9.14854	+	2.45135i	−0.416705	+	0.111656i
$483$	5.49519	−	2.31846i	0.250040	−	0.105493i
$484$	35.0604	−	20.2421i	1.59366	−	0.920098i
$485$	9.50110	−	14.8495i	0.431423	−	0.674280i
$486$	7.52064	−	4.23339i	0.341143	−	0.192030i
$487$	13.5809	+	3.63898i	0.615408	+	0.164898i	0.553039	−	0.833155i	$-0.313468\pi$
$487$	13.5809	+	3.63898i	0.615408	+	0.164898i	0.0623685	+	0.998053i	$0.480135\pi$
$488$	−4.75471	+	4.75471i	−0.215236	+	0.215236i
$489$	−13.2626	+	7.61864i	−0.599754	+	0.344527i
$490$	2.47742	−	8.30403i	0.111919	−	0.375138i
$491$	11.5144	+	6.64784i	0.519637	+	0.300013i	0.736786	−	0.676126i	$-0.236342\pi$
$491$	11.5144	+	6.64784i	0.519637	+	0.300013i	−0.217149	+	0.976138i	$0.569676\pi$
$492$	−5.73221	+	21.2078i	−0.258428	+	0.956121i
$493$	−26.9930	+	7.23275i	−1.21570	+	0.325747i
$494$	3.57463	+	6.19143i	0.160830	+	0.278566i
$495$	12.1565	−	37.7224i	0.546393	−	1.69550i
$496$	−6.41460			−0.288024
$497$	−5.66871	−	13.3546i	−0.254277	−	0.599034i
$498$	5.05479	+	5.07689i	0.226511	+	0.227501i
$499$	−7.34266	+	4.23928i	−0.328702	+	0.189776i	−0.655265	−	0.755399i	$-0.727443\pi$
$499$	−7.34266	+	4.23928i	−0.328702	+	0.189776i	0.326562	+	0.945176i	$0.394110\pi$
$500$	−11.4377	−	15.0887i	−0.511510	−	0.674786i
$501$	−4.81265	+	2.76461i	−0.215014	+	0.123514i
$502$	−4.73200	+	4.73200i	−0.211200	+	0.211200i
$503$	12.1225	−	12.1225i	0.540516	−	0.540516i	−0.383164	−	0.923680i	$-0.625166\pi$
$503$	12.1225	−	12.1225i	0.540516	−	0.540516i	0.923680	+	0.383164i	$0.125166\pi$
$504$	2.18875	+	16.0821i	0.0974949	+	0.716354i
$505$	5.98876	−	5.46614i	0.266496	−	0.243240i
$506$		−	4.25713i		−	0.189252i
$507$	11.9879	−	11.9358i	0.532403	−	0.530086i
$508$	3.82625	+	3.82625i	0.169763	+	0.169763i
$509$	−19.8514	−	34.3837i	−0.879899	−	1.52403i	−0.851451	−	0.524435i	$-0.824277\pi$
$509$	−19.8514	−	34.3837i	−0.879899	−	1.52403i	−0.0284488	−	0.999595i	$-0.509057\pi$
$510$	3.17878	+	6.16859i	0.140759	+	0.273150i
$511$	4.65737	+	33.1383i	0.206030	+	1.46595i
$512$	−15.0321	−	15.0321i	−0.664330	−	0.664330i
$513$	36.1080	−	9.42236i	1.59421	−	0.416007i
$514$	−3.94015	+	2.27485i	−0.173793	+	0.100339i
$515$	16.1433	+	10.3289i	0.711359	+	0.455147i
$516$	11.2249	+	0.0244777i	0.494150	+	0.00107757i
$517$	5.65160	+	21.0921i	0.248557	+	0.927628i
$518$	−0.119047	+	0.969580i	−0.00523062	+	0.0426009i
$519$	3.25536	−	5.61016i	0.142895	−	0.246259i
$520$	−5.54255	−	6.07247i	−0.243057	−	0.266296i
$521$	−10.3591	+	5.98085i	−0.453842	+	0.262026i	−0.709451	−	0.704754i	$-0.751057\pi$
$521$	−10.3591	+	5.98085i	−0.453842	+	0.262026i	0.255610	+	0.966780i	$0.417724\pi$
$522$	3.65137	+	13.8688i	0.159816	+	0.607020i
$523$	−23.1351	+	6.19902i	−1.01163	+	0.271064i	−0.726309	−	0.687369i	$-0.758766\pi$
$523$	−23.1351	+	6.19902i	−1.01163	+	0.271064i	−0.285317	+	0.958433i	$0.592099\pi$
$524$	7.38217	+	12.7863i	0.322492	+	0.558572i
$525$	22.8884	−	1.05967i	0.998930	−	0.0462477i
$526$	−7.35646	+	12.7418i	−0.320757	+	0.555567i
$527$	2.38286	−	8.89294i	0.103799	−	0.387382i
$528$	−22.2754	−	6.02076i	−0.969412	−	0.262020i
$529$	−18.4516	−	10.6530i	−0.802244	−	0.463176i
$530$	5.02992	−	1.10477i	0.218486	−	0.0479883i
$531$	3.39552	−	1.94071i	0.147353	−	0.0842196i
$532$	−3.92142	+	31.9381i	−0.170015	+	1.38469i
$533$	13.0083	+	3.48556i	0.563452	+	0.150976i
$534$	−4.28200	+	2.45978i	−0.185300	+	0.106445i
$535$	−1.07760	+	23.6193i	−0.0465886	+	1.02115i
$536$		−	25.5457i		−	1.10341i
$537$	19.2440	+	19.3281i	0.830440	+	0.834069i
$538$	4.63943	−	17.3146i	0.200020	−	0.746485i
$539$	−39.7546	+	11.3997i	−1.71235	+	0.491019i
$540$	−17.5300	+	8.93695i	−0.754369	+	0.384585i
$541$	21.5558	−	37.3358i	0.926757	−	1.60519i	0.138046	−	0.990426i	$-0.455918\pi$
$541$	21.5558	−	37.3358i	0.926757	−	1.60519i	0.788711	−	0.614764i	$-0.210749\pi$
$542$	13.6422	−	3.65542i	0.585984	−	0.157014i
$543$	−20.2309	+	5.37359i	−0.868190	+	0.230603i
$544$	14.9614	−	8.63797i	0.641465	−	0.370350i
$545$	6.69707	+	30.4910i	0.286871	+	1.30609i
$546$	4.51886	−	0.625051i	0.193389	−	0.0267497i
$547$	38.8489	+	10.4095i	1.66106	+	0.445079i	0.962678	−	0.270648i	$-0.0872378\pi$
$547$	38.8489	+	10.4095i	1.66106	+	0.445079i	0.698380	+	0.715727i	$0.253905\pi$
$548$	0.711449	+	2.65516i	0.0303916	+	0.113423i
$549$	8.56487	−	4.89525i	0.365540	−	0.208924i
$550$	5.65377	−	15.3463i	0.241077	−	0.654367i
$551$			62.0118i			2.64179i
$552$	−3.26660	+	3.25238i	−0.139036	+	0.138431i
$553$	−0.167062	−	0.393571i	−0.00710421	−	0.0167363i
$554$	1.03648	−	1.79523i	0.0440356	−	0.0762719i
$555$	−2.52397	+	0.548599i	−0.107137	+	0.0232868i
$556$	−10.2258	+	17.7117i	−0.433672	+	0.751142i
$557$	−5.94135	+	22.1734i	−0.251743	+	0.939517i	0.718131	+	0.695908i	$0.244998\pi$
$557$	−5.94135	+	22.1734i	−0.251743	+	0.939517i	−0.969874	+	0.243609i	$0.921669\pi$
$558$	−4.55845	−	1.24277i	−0.192974	−	0.0526105i
$559$		−	6.88104i		−	0.291037i
$560$	−1.25262	−	13.2812i	−0.0529328	−	0.561234i
$561$	16.6217	−	28.6451i	0.701767	−	1.20940i
$562$	2.03165	+	0.544380i	0.0857002	+	0.0229633i
$563$	−3.91623	+	3.91623i	−0.165049	+	0.165049i	−0.784799	−	0.619750i	$-0.787234\pi$
$563$	−3.91623	+	3.91623i	−0.165049	+	0.165049i	0.619750	+	0.784799i	$0.287234\pi$
$564$	5.44097	−	9.37675i	0.229106	−	0.394833i
$565$	−3.31867	−	0.151410i	−0.139618	−	0.00636986i
$566$		−	11.0412i		−	0.464095i
$567$	3.10790	−	23.6081i	0.130520	−	0.991446i
$568$	7.92863	+	7.92863i	0.332678	+	0.332678i
$569$	−18.0227			−0.755549			−0.377775	−	0.925898i	$-0.623311\pi$
$569$	−18.0227			−0.755549			−0.377775	+	0.925898i	$0.623311\pi$
$570$	15.0477	−	3.27069i	0.630277	−	0.136994i
$571$	18.2721			0.764665			0.382333	−	0.924025i	$-0.375121\pi$
$571$	18.2721			0.764665			0.382333	+	0.924025i	$0.375121\pi$
$572$	−4.65631	+	17.3776i	−0.194690	+	0.726593i
$573$	−5.87794	−	22.1297i	−0.245554	−	0.924481i
$574$	−6.75424	−	8.64499i	−0.281917	−	0.360835i
$575$	4.16340	+	5.00141i	0.173626	+	0.208573i
$576$	2.31408	+	4.04878i	0.0964200	+	0.168699i
$577$	−19.6959	−	5.27751i	−0.819952	−	0.219706i	−0.175627	−	0.984457i	$-0.556195\pi$
$577$	−19.6959	−	5.27751i	−0.819952	−	0.219706i	−0.644326	+	0.764751i	$0.722862\pi$
$578$	−0.935097	−	3.48983i	−0.0388949	−	0.145158i
$579$	−34.0133	−	19.7366i	−1.41355	−	0.820226i
$580$	−7.01453	−	31.9364i	−0.291262	−	1.32609i
$581$	19.5744	−	2.75105i	0.812081	−	0.114133i
$582$	−5.33406	−	5.35737i	−0.221104	−	0.222070i
$583$	−17.3788	−	17.3788i	−0.719756	−	0.719756i
$584$	−12.9317	−	22.3984i	−0.535120	−	0.926854i
$585$	5.50189	+	10.7341i	0.227475	+	0.443801i
$586$	3.76725	−	6.52506i	0.155623	−	0.269548i
$587$	3.64279	−	13.5951i	0.150354	−	0.561129i	−0.849104	−	0.528225i	$-0.822858\pi$
$587$	3.64279	−	13.5951i	0.150354	−	0.561129i	0.999459	−	0.0329040i	$-0.0104756\pi$
$588$	17.9364	+	9.99340i	0.739686	+	0.412121i
$589$	−17.6929	−	10.2150i	−0.729024	−	0.420902i
$590$	1.43299	−	0.742403i	0.0589953	−	0.0305643i
$591$	9.99197	+	5.79795i	0.411015	+	0.238496i
$592$	0.389211	+	1.45256i	0.0159965	+	0.0596997i
$593$	9.87835	+	36.8665i	0.405655	+	1.51393i	0.802844	+	0.596189i	$0.203319\pi$
$593$	9.87835	+	36.8665i	0.405655	+	1.51393i	−0.397189	+	0.917737i	$0.630014\pi$
$594$	−14.6632	−	8.59421i	−0.601640	−	0.352625i
$595$	18.8778	+	3.19704i	0.773916	+	0.131066i
$596$	−11.6878	+	6.74794i	−0.478750	+	0.276406i
$597$	−4.92200	+	4.90058i	−0.201444	+	0.200567i
$598$	0.916149	+	0.916149i	0.0374641	+	0.0374641i
$599$	35.3711			1.44522			0.722611	−	0.691255i	$-0.242942\pi$
$599$	35.3711			1.44522			0.722611	+	0.691255i	$0.242942\pi$
$600$	−16.0950	+	7.38605i	−0.657074	+	0.301534i
$601$	−0.0211063	−	0.0365571i	−0.000860943	−	0.00149120i	0.865595	−	0.500745i	$-0.166941\pi$
$601$	−0.0211063	−	0.0365571i	−0.000860943	−	0.00149120i	−0.866456	+	0.499254i	$0.833607\pi$
$602$	−3.37344	+	4.47672i	−0.137491	+	0.182458i
$603$	−9.85792	+	36.1587i	−0.401446	+	1.47250i
$604$	−7.74554	−	4.47189i	−0.315162	−	0.181959i
$605$	−52.2105	+	11.4675i	−2.12266	+	0.466222i
$606$	−1.73201	−	3.01509i	−0.0703581	−	0.122480i
$607$	−18.7964	−	5.03648i	−0.762922	−	0.204424i	−0.143680	−	0.989624i	$-0.545894\pi$
$607$	−18.7964	−	5.03648i	−0.762922	−	0.204424i	−0.619242	+	0.785200i	$0.712560\pi$
$608$	−9.92213	−	37.0299i	−0.402396	−	1.50176i
$609$	36.6556	+	14.9028i	1.48536	+	0.603892i
$610$	3.61458	−	1.87264i	0.146350	−	0.0758211i
$611$	−5.75533	−	3.32284i	−0.232836	−	0.134428i
$612$	−15.9005	+	4.18628i	−0.642738	+	0.169220i
$613$	9.03178	−	33.7070i	0.364790	−	1.36141i	−0.502915	−	0.864336i	$-0.667739\pi$
$613$	9.03178	−	33.7070i	0.364790	−	1.36141i	0.867705	−	0.497079i	$-0.165594\pi$
$614$	9.15909			0.369631
$615$	15.6868	−	24.3999i	0.632553	−	0.983897i
$616$	25.1876	−	19.6788i	1.01484	−	0.792883i
$617$	7.62996	−	2.04444i	0.307171	−	0.0823061i	−0.101941	−	0.994790i	$-0.532505\pi$
$617$	7.62996	−	2.04444i	0.307171	−	0.0823061i	0.409112	+	0.912484i	$0.365839\pi$
$618$	5.82416	−	5.79881i	0.234282	−	0.233262i
$619$	33.3148	+	19.2343i	1.33904	+	0.773093i	0.986664	−	0.162768i	$-0.0520421\pi$
$619$	33.3148	+	19.2343i	1.33904	+	0.773093i	0.352371	+	0.935860i	$0.385375\pi$
$620$	10.2674	+	3.25943i	0.412349	+	0.130902i
$621$	5.87878	−	3.34303i	0.235907	−	0.134151i
$622$	−3.72726	+	3.72726i	−0.149449	+	0.149449i
$623$	−1.66044	+	13.5235i	−0.0665241	+	0.541807i
$624$	6.08943	−	3.49805i	0.243772	−	0.140034i
$625$	8.36618	+	23.5586i	0.334647	+	0.942344i
$626$			1.00572i			0.0401968i
$627$	−51.8527	−	52.0793i	−2.07080	−	2.07985i
$628$	17.3967	+	17.3967i	0.694204	+	0.694204i
$629$	−2.15835			−0.0860589
$630$	1.68295	−	9.68080i	0.0670503	−	0.385692i
$631$	−38.7109			−1.54106			−0.770529	−	0.637405i	$-0.780008\pi$
$631$	−38.7109			−1.54106			−0.770529	+	0.637405i	$0.780008\pi$
$632$	0.233664	+	0.233664i	0.00929465	+	0.00929465i
$633$	−7.89979	+	29.2273i	−0.313988	+	1.16168i
$634$			4.10608i			0.163073i
$635$	−3.28669	−	6.34397i	−0.130428	−	0.251753i
$636$	−0.0266082	+	12.2019i	−0.00105508	+	0.483838i
$637$	6.10209	−	11.0086i	0.241774	−	0.436177i
$638$	19.9712	−	19.9712i	0.790667	−	0.790667i
$639$	−8.16298	−	14.2822i	−0.322923	−	0.564995i
$640$	11.8668	+	22.9054i	0.469078	+	0.905415i
$641$	3.11864	+	1.80054i	0.123179	+	0.0711173i	0.560323	−	0.828274i	$-0.310677\pi$
$641$	3.11864	+	1.80054i	0.123179	+	0.0711173i	−0.437145	+	0.899391i	$0.644010\pi$
$642$	9.78823	+	2.64564i	0.386311	+	0.104415i
$643$	10.6901	−	2.86440i	0.421576	−	0.112961i	−0.0417930	−	0.999126i	$-0.513307\pi$
$643$	10.6901	−	2.86440i	0.421576	−	0.112961i	0.463369	+	0.886165i	$0.346640\pi$
$644$	0.811599	+	5.77472i	0.0319815	+	0.227556i
$645$	−14.1168	−	4.51532i	−0.555847	−	0.177791i
$646$	12.8678			0.506279
$647$	−8.26503	+	30.8455i	−0.324932	+	1.21266i	0.589449	+	0.807806i	$0.299345\pi$
$647$	−8.26503	+	30.8455i	−0.324932	+	1.21266i	−0.914381	+	0.404856i	$0.867322\pi$
$648$	4.60794	+	17.8173i	0.181017	+	0.699930i
$649$	−6.67031	−	3.85110i	−0.261832	−	0.151169i
$650$	2.08586	+	4.51928i	0.0818142	+	0.177261i
$651$	−10.2902	+	8.00352i	−0.403303	+	0.313683i
$652$	−3.87053	−	14.4450i	−0.151582	−	0.565711i
$653$	29.6410	+	7.94228i	1.15994	+	0.310805i	0.786942	−	0.617027i	$-0.211663\pi$
$653$	29.6410	+	7.94228i	1.15994	+	0.310805i	0.372999	+	0.927832i	$0.378330\pi$
$654$	13.3875	+	0.0291935i	0.523492	+	0.00114156i
$655$	−4.18213	−	19.0408i	−0.163409	−	0.743986i
$656$	−14.6258	−	8.44422i	−0.571043	−	0.329692i
$657$	9.66085	+	36.6942i	0.376906	+	1.43158i
$658$	2.11533	+	4.98336i	0.0824640	+	0.194272i
$659$	8.40307	+	14.5545i	0.327337	+	0.566964i	0.981983	−	0.188972i	$-0.0605154\pi$
$659$	8.40307	+	14.5545i	0.327337	+	0.566964i	−0.654645	+	0.755936i	$0.727182\pi$
$660$	32.5954	+	20.9557i	1.26877	+	0.815701i
$661$	30.7279			1.19518			0.597589	−	0.801803i	$-0.296125\pi$
$661$	30.7279			1.19518			0.597589	+	0.801803i	$0.296125\pi$
$662$	−1.04348	−	1.04348i	−0.0405559	−	0.0405559i
$663$	2.58749	+	9.74158i	0.100490	+	0.378332i
$664$	−13.2305	+	7.63860i	−0.513441	+	0.296435i
$665$	17.6948	−	38.6273i	0.686176	−	1.49790i
$666$	−0.00483081	+	1.10765i	−0.000187190	+	0.0429204i
$667$	2.90865	+	10.8552i	0.112623	+	0.420316i
$668$	−1.40452	−	5.24173i	−0.0543424	−	0.202809i
$669$	0.0451715	−	20.7146i	0.00174643	−	0.800874i
$670$	−4.67947	+	14.7406i	−0.180784	+	0.569481i
$671$	−16.8252	−	9.71404i	−0.649530	−	0.375006i
$672$	−24.2731	−	3.03405i	−0.936357	−	0.117041i
$673$	5.70381	−	21.2869i	0.219866	−	0.820550i	−0.764531	−	0.644587i	$-0.777029\pi$
$673$	5.70381	−	21.2869i	0.219866	−	0.820550i	0.984397	−	0.175963i	$-0.0563039\pi$
$674$	−8.91763	+	15.4458i	−0.343494	+	0.594949i
$675$	25.6318	−	4.24365i	0.986570	−	0.163338i
$676$	8.27003	+	14.3241i	0.318078	+	0.550928i
$677$	−22.7286	−	22.7286i	−0.873531	−	0.873531i	0.119325	−	0.992855i	$-0.461927\pi$
$677$	−22.7286	−	22.7286i	−0.873531	−	0.873531i	−0.992855	+	0.119325i	$0.961927\pi$
$678$	−0.371730	+	1.37531i	−0.0142762	+	0.0528186i
$679$	−20.6558	+	2.90304i	−0.792696	+	0.111408i
$680$	−14.4534	+	3.17456i	−0.554264	+	0.121739i
$681$	−19.8537	+	11.4049i	−0.760795	+	0.437036i
$682$	2.40829	+	8.98786i	0.0922182	+	0.344163i
$683$	21.3174	+	5.71198i	0.815687	+	0.218563i	0.642460	−	0.766319i	$-0.277914\pi$
$683$	21.3174	+	5.71198i	0.815687	+	0.218563i	0.173227	+	0.984882i	$0.444580\pi$
$684$	−0.159128	+	36.4860i	−0.00608439	+	1.39508i
$685$	0.165420	−	3.62575i	0.00632037	−	0.138533i
$686$	−9.36692	+	4.17051i	−0.357631	+	0.159231i
$687$	−20.2588	+	20.1706i	−0.772922	+	0.769558i
$688$	−2.23338	+	8.33511i	−0.0851470	+	0.317773i
$689$	7.47996			0.284964
$690$	2.48070	−	1.27834i	0.0944385	−	0.0486658i
$691$	7.72196			0.293757			0.146879	−	0.989155i	$-0.453077\pi$
$691$	7.72196			0.293757			0.146879	+	0.989155i	$0.453077\pi$
$692$	4.48436	+	4.48436i	0.170470	+	0.170470i
$693$	−43.2458	+	18.1347i	−1.64277	+	0.688880i
$694$			5.66098i			0.214888i
$695$	19.9453	−	18.2047i	0.756567	−	0.690545i
$696$	−30.5820	−	0.0666889i	−1.15921	−	0.00252784i
$697$	17.1398	−	17.1398i	0.649218	−	0.649218i
$698$	−1.07779	−	0.288794i	−0.0407951	−	0.0109310i
$699$	9.96608	+	17.3490i	0.376952	+	0.656200i
$700$	−4.74356	+	21.8948i	−0.179290	+	0.827547i
$701$			42.9782i			1.62326i	0.584168	+	0.811632i	$0.301421\pi$
$701$			42.9782i			1.62326i	−0.584168	+	0.811632i	$0.698579\pi$
$702$	5.00509	−	1.30608i	0.188905	−	0.0492947i
$703$	−1.23961	+	4.62628i	−0.0467527	+	0.174484i
$704$	4.59201	−	7.95360i	0.173068	−	0.299763i
$705$	−10.5936	+	9.62687i	−0.398978	+	0.362569i
$706$	−0.259441	+	0.449364i	−0.00976417	+	0.0169120i
$707$	−9.52232	−	1.16917i	−0.358124	−	0.0439711i
$708$	0.981649	+	3.69578i	0.0368926	+	0.138896i
$709$			22.8507i			0.858177i	0.903262	+	0.429088i	$0.141165\pi$
$709$			22.8507i			0.858177i	−0.903262	+	0.429088i	$0.858835\pi$
$710$	−3.12269	−	6.02743i	−0.117192	−	0.226205i
$711$	−0.240571	−	0.420909i	−0.00902210	−	0.0157853i
$712$	−2.72548	−	10.1716i	−0.102142	−	0.381198i
$713$	−3.57629	−	0.958265i	−0.133933	−	0.0358873i
$714$	3.09242	−	7.60628i	0.115731	−	0.284658i
$715$	12.8025	−	20.0094i	0.478788	−	0.748308i
$716$	−23.0947	+	13.3337i	−0.863090	+	0.498305i
$717$	−8.75306	+	32.3842i	−0.326889	+	1.20941i
$718$	2.49328	−	0.668073i	0.0930485	−	0.0249323i
$719$	17.8696	−	30.9511i	0.666424	−	1.15428i	−0.312473	−	0.949927i	$-0.601157\pi$
$719$	17.8696	−	30.9511i	0.666424	−	1.15428i	0.978897	−	0.204354i	$-0.0655093\pi$
$720$	−3.18053	−	14.7882i	−0.118532	−	0.551122i
$721$	−3.15597	−	22.4555i	−0.117535	−	0.836287i
$722$	4.66790	−	17.4209i	0.173721	−	0.648337i
$723$	−7.73149	+	28.6046i	−0.287537	+	1.06382i
$724$		−	20.4664i		−	0.760627i
$725$	−3.93129	+	42.9943i	−0.146005	+	1.59677i
$726$	−0.0499887	+	22.9237i	−0.00185525	+	0.850777i
$727$	−12.5366	−	3.35918i	−0.464958	−	0.124585i	0.0187319	−	0.999825i	$-0.494037\pi$
$727$	−12.5366	−	3.35918i	−0.464958	−	0.124585i	−0.483690	+	0.875239i	$0.660704\pi$
$728$	−1.18551	+	9.65543i	−0.0439380	+	0.357854i
$729$	0.353256	−	26.9977i	0.0130835	−	0.999914i
$730$	3.35905	+	15.2934i	0.124324	+	0.566035i
$731$	−10.7258	−	6.19255i	−0.396708	−	0.229040i
$732$	2.47612	+	9.32226i	0.0915199	+	0.344561i
$733$	−2.02304	+	7.55010i	−0.0747228	+	0.278869i	−0.993170	−	0.116674i	$-0.962777\pi$
$733$	−2.02304	+	7.55010i	−0.0747228	+	0.278869i	0.918447	+	0.395543i	$0.129444\pi$
$734$	0.566612	−	0.981401i	0.0209140	−	0.0362242i
$735$	−18.5804	−	19.7425i	−0.685350	−	0.728214i
$736$	−3.47376	−	6.01672i	−0.128044	−	0.221779i
$737$	71.2939	−	19.1032i	2.62615	−	0.703674i
$738$	−8.75766	−	8.83439i	−0.322374	−	0.325198i
$739$	−9.14078	+	5.27743i	−0.336249	+	0.194133i	−0.658612	−	0.752483i	$-0.728856\pi$
$739$	−9.14078	+	5.27743i	−0.336249	+	0.194133i	0.322363	+	0.946616i	$0.395523\pi$
$740$	0.115098	−	2.52278i	0.00423110	−	0.0927392i
$741$	22.3666	+	0.0487737i	0.821656	+	0.00179175i
$742$	−4.86637	−	3.66706i	−0.178650	−	0.134622i
$743$	9.24373	+	34.4981i	0.339120	+	1.26561i	0.899334	+	0.437263i	$0.144052\pi$
$743$	9.24373	+	34.4981i	0.339120	+	1.26561i	−0.560214	+	0.828348i	$0.689281\pi$
$744$	5.05671	−	8.71453i	0.185388	−	0.319490i
$745$	17.4049	−	3.82283i	0.637667	−	0.140058i
$746$	−4.10149	+	2.36800i	−0.150166	+	0.0866985i
$747$	21.6747	−	5.70653i	0.793037	−	0.208791i
$748$	22.8968	+	22.8968i	0.837192	+	0.837192i
$749$	22.0452	−	17.2237i	0.805514	−	0.629340i
$750$	10.6402	−	1.31369i	0.388527	−	0.0479692i
$751$	−10.1717	−	17.6179i	−0.371170	−	0.642885i	0.618576	−	0.785725i	$-0.287710\pi$
$751$	−10.1717	−	17.6179i	−0.371170	−	0.642885i	−0.989746	+	0.142840i	$0.954377\pi$
$752$	5.89302	+	5.89302i	0.214896	+	0.214896i
$753$	5.37460	+	20.2347i	0.195861	+	0.737392i
$754$			8.59574i			0.313038i
$755$	7.96116	+	8.72232i	0.289736	+	0.317438i
$756$	21.5289	+	8.86244i	0.782998	+	0.322324i
$757$	−36.7503	+	36.7503i	−1.33571	+	1.33571i	−0.435547	+	0.900166i	$0.643445\pi$
$757$	−36.7503	+	36.7503i	−1.33571	+	1.33571i	−0.900166	+	0.435547i	$0.856555\pi$
$758$	0.715881	−	0.715881i	0.0260020	−	0.0260020i
$759$	−11.5196	−	6.68440i	−0.418136	−	0.242628i
$760$	−1.49661	+	32.8033i	−0.0542876	+	1.18990i
$761$	28.0309	−	16.1837i	1.01612	−	0.586658i	0.103143	−	0.994667i	$-0.467110\pi$
$761$	28.0309	−	16.1837i	1.01612	−	0.586658i	0.912978	+	0.408009i	$0.133777\pi$
$762$	−2.96131	+	0.786564i	−0.107277	+	0.0284942i
$763$	22.2294	−	29.4996i	0.804760	−	1.06796i
$764$	22.3873			0.809943
$765$	21.6832	+	1.08405i	0.783957	+	0.0391939i
$766$	−1.39874	−	2.42268i	−0.0505384	−	0.0875351i
$767$	2.26425	−	0.606703i	0.0817572	−	0.0219068i
$768$	5.48763	−	1.45759i	0.198018	−	0.0525961i
$769$	1.66229	+	0.959722i	0.0599436	+	0.0346084i	0.529672	−	0.848202i	$-0.322315\pi$
$769$	1.66229	+	0.959722i	0.0599436	+	0.0346084i	−0.469729	+	0.882811i	$0.655648\pi$
$770$	−18.1388	+	6.74140i	−0.653677	+	0.242943i
$771$	−0.0310390	+	14.2338i	−0.00111784	+	0.512618i
$772$	27.1878	−	27.1878i	0.978510	−	0.978510i
$773$	26.2815	+	7.04212i	0.945282	+	0.253287i	0.698359	−	0.715748i	$-0.253914\pi$
$773$	26.2815	+	7.04212i	0.945282	+	0.253287i	0.246923	+	0.969035i	$0.420581\pi$
$774$	−3.20197	+	5.49053i	−0.115092	+	0.197353i
$775$	−11.6193	−	8.20396i	−0.417378	−	0.294695i
$776$	13.9614	−	8.06062i	0.501185	−	0.289359i
$777$	2.43672	+	1.84454i	0.0874170	+	0.0661724i
$778$	−5.08457	+	1.36241i	−0.182291	+	0.0488446i
$779$	−26.8942	−	46.5822i	−0.963585	−	1.66898i
$780$	−11.5244	+	2.50489i	−0.412640	+	0.0896896i
$781$	−16.1985	+	28.0566i	−0.579627	+	1.00394i
$782$	2.25253	−	0.603563i	0.0805503	−	0.0215834i
$783$	43.2617	+	11.8958i	1.54605	+	0.425121i
$784$	−10.9646	+	11.3543i	−0.391594	+	0.405511i
$785$	−14.9435	−	28.8439i	−0.533355	−	1.02948i
$786$	−8.36011	−	0.0182305i	−0.298195	−	0.000650261i
$787$	4.35392	−	4.35392i	0.155201	−	0.155201i	−0.625236	−	0.780436i	$-0.714997\pi$
$787$	4.35392	−	4.35392i	0.155201	−	0.155201i	0.780436	+	0.625236i	$0.214997\pi$
$788$	−7.98686	+	7.98686i	−0.284520	+	0.284520i
$789$	22.9279	+	39.9130i	0.816254	+	1.42094i
$790$	−0.0920285	−	0.177634i	−0.00327423	−	0.00631992i
$791$	2.42004	+	3.09750i	0.0860468	+	0.110134i
$792$	25.7395	−	25.5159i	0.914612	−	0.906668i
$793$	5.71134	−	1.53035i	0.202816	−	0.0543443i
$794$	−4.64372	+	8.04315i	−0.164799	+	0.285441i
$795$	4.90833	−	15.3455i	0.174081	−	0.544247i
$796$	−3.39550	−	5.88118i	−0.120350	−	0.208453i
$797$	26.6791	−	7.14864i	0.945022	−	0.253218i	0.246773	−	0.969073i	$-0.420630\pi$
$797$	26.6791	−	7.14864i	0.945022	−	0.253218i	0.698248	+	0.715855i	$0.253963\pi$
$798$	−14.5275	−	10.9970i	−0.514268	−	0.389288i
$799$	−10.3590	+	5.98074i	−0.366473	+	0.211583i
$800$	−4.53171	−	26.3027i	−0.160220	−	0.929942i
$801$	−0.0673791	+	15.4492i	−0.00238072	+	0.545870i
$802$	1.62565	+	0.435593i	0.0574038	+	0.0153813i
$803$	52.8400	−	52.8400i	1.86468	−	1.86468i
$804$	−31.6947	−	18.3912i	−1.11778	−	0.648607i
$805$	1.28569	−	7.59172i	0.0453146	−	0.267573i
$806$	−2.45249	−	1.41595i	−0.0863854	−	0.0498746i
$807$	−39.5680	−	39.7409i	−1.39286	−	1.39895i
$808$	7.16218	−	1.91910i	0.251965	−	0.0675137i
$809$	−12.3778	−	21.4389i	−0.435179	−	0.753752i	0.562131	−	0.827048i	$-0.309982\pi$
$809$	−12.3778	−	21.4389i	−0.435179	−	0.753752i	−0.997310	+	0.0732961i	$0.976648\pi$
$810$	0.604856	−	11.1252i	0.0212525	−	0.390900i
$811$	−21.7364			−0.763268			−0.381634	−	0.924313i	$-0.624639\pi$
$811$	−21.7364			−0.763268			−0.381634	+	0.924313i	$0.624639\pi$
$812$	−23.2832	+	30.8980i	−0.817079	+	1.08431i
$813$	11.5291	−	42.6550i	0.404344	−	1.49598i
$814$	1.88914	−	1.09069i	0.0662142	−	0.0382288i
$815$	−0.899942	+	19.7254i	−0.0315236	+	0.690949i
$816$	0.0275634	−	12.6399i	0.000964911	−	0.442486i
$817$	−19.4335	+	19.4335i	−0.679893	+	0.679893i
$818$	−13.7400	+	13.7400i	−0.480407	+	0.480407i
$819$	5.40400	−	13.2093i	0.188831	−	0.461571i
$820$	19.1198	+	20.9479i	0.667694	+	0.731531i
$821$			25.4280i			0.887443i	0.896165	+	0.443722i	$0.146342\pi$
$821$			25.4280i			0.887443i	−0.896165	+	0.443722i	$0.853658\pi$
$822$	−1.50257	−	0.406126i	−0.0524082	−	0.0141653i
$823$	−14.8637	−	14.8637i	−0.518115	−	0.518115i	0.398886	−	0.917001i	$-0.369397\pi$
$823$	−14.8637	−	14.8637i	−0.518115	−	0.518115i	−0.917001	+	0.398886i	$0.869397\pi$
$824$	8.76294	+	15.1779i	0.305271	+	0.528745i
$825$	−32.6491	−	39.3951i	−1.13670	−	1.37156i
$826$	−1.77053	−	0.715334i	−0.0616045	−	0.0248897i
$827$	33.2506	+	33.2506i	1.15624	+	1.15624i	0.985278	+	0.170960i	$0.0546869\pi$
$827$	33.2506	+	33.2506i	1.15624	+	1.15624i	0.170960	+	0.985278i	$0.445313\pi$
$828$	1.68351	+	6.39437i	0.0585060	+	0.222220i
$829$	32.5535	−	18.7948i	1.13063	−	0.652769i	0.186536	−	0.982448i	$-0.440274\pi$
$829$	32.5535	−	18.7948i	1.13063	−	0.652769i	0.944093	+	0.329679i	$0.106940\pi$
$830$	9.03361	−	1.98415i	0.313561	−	0.0688707i
$831$	−3.23038	−	5.62347i	−0.112061	−	0.195076i
$832$	0.723426	+	2.69986i	0.0250803	+	0.0936009i
$833$	−11.6681	−	19.4187i	−0.404275	−	0.672820i
$834$	−5.76837	−	10.0416i	−0.199742	−	0.347713i
$835$	−0.326566	+	7.15783i	−0.0113013	+	0.247707i
$836$	62.2284	−	35.9276i	2.15221	−	1.24258i
$837$	−10.5204	+	10.3836i	−0.363638	+	0.358911i
$838$	6.93269	−	1.85761i	0.239486	−	0.0641700i
$839$	−14.4171	−	24.9712i	−0.497734	−	0.862101i	0.502262	−	0.864715i	$-0.332501\pi$
$839$	−14.4171	−	24.9712i	−0.497734	−	0.862101i	−0.999997	+	0.00261440i	$0.999168\pi$
$840$	19.0306	+	8.76800i	0.656618	+	0.302525i
$841$	−22.7793	+	39.4548i	−0.785492	+	1.36051i
$842$	−2.51550	+	9.38799i	−0.0866900	+	0.323532i
$843$	4.66311	−	4.64282i	0.160606	−	0.159907i
$844$	−25.6362	−	14.8010i	−0.882433	−	0.509473i
$845$	−4.68512	−	21.3309i	−0.161173	−	0.733804i
$846$	3.04608	+	5.32951i	0.104726	+	0.183232i
$847$	50.5129	+	38.0640i	1.73564	+	1.30789i
$848$	−9.06059	−	2.42778i	−0.311142	−	0.0833702i
$849$	−29.8770	−	17.3365i	−1.02538	−	0.594987i
$850$	8.92158	+	0.815768i	0.306008	+	0.0279806i
$851$			0.867979i			0.0297539i
$852$	15.5452	−	4.12900i	0.532568	−	0.141457i
$853$	−14.6092	+	54.5223i	−0.500210	+	1.86681i	−0.00156835	+	0.999999i	$0.500499\pi$
$853$	−14.6092	+	54.5223i	−0.500210	+	1.86681i	−0.498641	+	0.866809i	$0.666167\pi$
$854$	−4.46599	−	1.80436i	−0.152823	−	0.0617440i
$855$	14.7769	−	45.8539i	0.505361	−	1.56817i
$856$	−10.8109	+	18.7250i	−0.369509	+	0.640008i
$857$	−16.4403	+	4.40516i	−0.561589	+	0.150477i	−0.528436	−	0.848973i	$-0.677222\pi$
$857$	−16.4403	+	4.40516i	−0.561589	+	0.150477i	−0.0331530	+	0.999450i	$0.510555\pi$
$858$	−7.18754	−	7.21895i	−0.245378	−	0.246451i
$859$	−15.7475	+	9.09184i	−0.537299	+	0.310210i	−0.743983	−	0.668198i	$-0.767066\pi$
$859$	−15.7475	+	9.09184i	−0.537299	+	0.310210i	0.206685	+	0.978408i	$0.433733\pi$
$860$	7.81012	−	12.2066i	0.266323	−	0.416242i
$861$	−33.9983	+	4.70266i	−1.15866	+	0.160266i
$862$	−2.13419	−	0.571853i	−0.0726906	−	0.0194774i
$863$	7.80966	+	29.1460i	0.265844	+	0.992143i	0.961732	+	0.273993i	$0.0883444\pi$
$863$	7.80966	+	29.1460i	0.265844	+	0.992143i	−0.695888	+	0.718150i	$0.744989\pi$
$864$	−27.7367	−	0.181455i	−0.943623	−	0.00617323i
$865$	−3.85199	−	7.43512i	−0.130972	−	0.252802i
$866$			20.8155i			0.707339i
$867$	−10.9116	−	2.94927i	−0.370578	−	0.100163i
$868$	−4.98030	−	11.7328i	−0.169042	−	0.398236i
$869$	−0.477383	+	0.826852i	−0.0161941	+	0.0280490i
$870$	17.6345	+	5.64051i	0.597867	+	0.191231i
$871$	−11.2316	+	19.4538i	−0.380570	+	0.659166i
$872$	−7.38878	+	27.5753i	−0.250216	+	0.933817i
$873$	−22.8722	+	6.02180i	−0.774107	+	0.203807i
$874$		−	5.17480i		−	0.175040i
$875$	14.7171	−	25.6595i	0.497527	−	0.867448i
$876$	−37.0998	−	0.0809019i	−1.25349	−	0.00273342i
$877$	14.9506	+	4.00601i	0.504847	+	0.135273i	0.502249	−	0.864723i	$-0.332506\pi$
$877$	14.9506	+	4.00601i	0.504847	+	0.135273i	0.00259831	+	0.999997i	$0.499173\pi$
$878$	−5.12650	+	5.12650i	−0.173011	+	0.173011i
$879$	−11.7414	−	20.4395i	−0.396027	−	0.689406i
$880$	−22.0024	+	20.0823i	−0.741700	+	0.676975i
$881$		−	15.5632i		−	0.524339i	−0.965022	−	0.262169i	$-0.915562\pi$
$881$		−	15.5632i		−	0.524339i	0.965022	−	0.262169i	$-0.0844379\pi$
$882$	−9.99165	+	5.94450i	−0.336436	+	0.200162i
$883$	22.3729	+	22.3729i	0.752909	+	0.752909i	0.975021	−	0.222112i	$-0.0712951\pi$
$883$	22.3729	+	22.3729i	0.752909	+	0.752909i	−0.222112	+	0.975021i	$0.571295\pi$
$884$	−9.85497			−0.331459
$885$	0.241116	−	5.04331i	0.00810503	−	0.169529i
$886$	−20.5507			−0.690414
$887$	−12.0527	+	44.9813i	−0.404690	+	1.51033i	0.399936	+	0.916543i	$0.369033\pi$
$887$	−12.0527	+	44.9813i	−0.404690	+	1.51033i	−0.804626	+	0.593782i	$0.797634\pi$
$888$	−2.28019	−	0.616306i	−0.0765180	−	0.0206819i
$889$	−3.16685	+	7.83828i	−0.106213	+	0.262888i
$890$	−0.290558	+	6.36859i	−0.00973953	+	0.213476i
$891$	−46.2793	+	26.1838i	−1.55042	+	0.877192i
$892$	19.5634	+	5.24200i	0.655032	+	0.175515i
$893$	6.86987	+	25.6387i	0.229891	+	0.857967i
$894$	0.0166643	−	7.64186i	0.000557336	−	0.255582i
$895$	34.3916	−	7.55380i	1.14959	−	0.252496i
$896$	11.4341	−	28.3007i	0.381988	−	0.945461i
$897$	3.91757	−	1.04056i	0.130804	−	0.0347433i
$898$	12.0031	+	12.0031i	0.400550	+	0.400550i
$899$	−12.2818	−	21.2727i	−0.409620	−	0.709483i
$900$	−2.42339	+	25.2865i	−0.0807796	+	0.842884i
$901$	6.73154	−	11.6594i	0.224260	−	0.388430i
$902$	−6.34058	+	23.6634i	−0.211118	+	0.787905i
$903$	6.81699	+	16.1576i	0.226855	+	0.537691i
$904$	−2.63099	−	1.51900i	−0.0875055	−	0.0505213i
$905$	−8.17661	+	25.7569i	−0.271800	+	0.856187i
$906$	4.39133	−	2.52258i	0.145892	−	0.0838072i
$907$	−5.98509	−	22.3366i	−0.198732	−	0.741676i	−0.991269	−	0.131853i	$-0.957907\pi$
$907$	−5.98509	−	22.3366i	−0.198732	−	0.741676i	0.792538	−	0.609823i	$-0.208759\pi$
$908$	−5.79407	−	21.6238i	−0.192283	−	0.717610i
$909$	−10.8783	−	0.0474438i	−0.360810	−	0.00157361i
$910$	2.45276	−	5.35431i	0.0813082	−	0.177494i
$911$	20.2276	−	11.6784i	0.670171	−	0.386924i	−0.125970	−	0.992034i	$-0.540204\pi$
$911$	20.2276	−	11.6784i	0.670171	−	0.386924i	0.796142	+	0.605110i	$0.206871\pi$
$912$	−27.0771	−	7.31861i	−0.896612	−	0.242343i
$913$	−31.2119	−	31.2119i	−1.03296	−	1.03296i
$914$	−10.1576			−0.335984
$915$	0.608192	−	12.7213i	0.0201062	−	0.420553i
$916$	−13.9758	−	24.2068i	−0.461773	−	0.799814i
$917$	−13.8817	+	18.4217i	−0.458413	+	0.608338i
$918$	2.46845	−	8.97706i	0.0814711	−	0.296287i
$919$	35.0381	+	20.2293i	1.15580	+	0.667302i	0.950294	−	0.311354i	$-0.100783\pi$
$919$	35.0381	+	20.2293i	1.15580	+	0.667302i	0.205506	+	0.978656i	$0.434116\pi$
$920$	1.27665	+	5.81245i	0.0420899	+	0.191631i
$921$	14.3813	−	24.7842i	0.473880	−	0.816666i
$922$	5.48986	+	1.47100i	0.180799	+	0.0484450i
$923$	−2.55191	−	9.52384i	−0.0839970	−	0.313481i
$924$	−6.28221	−	45.4178i	−0.206670	−	1.49414i
$925$	−1.15274	+	3.12893i	−0.0379018	+	0.102878i
$926$	4.07209	+	2.35102i	0.133817	+	0.0772594i
$927$	−6.54648	−	24.8651i	−0.215015	−	0.816676i
$928$	11.9297	−	44.5221i	0.391610	−	1.46151i
$929$	24.4409			0.801880			0.400940	−	0.916104i	$-0.368684\pi$
$929$	24.4409			0.801880			0.400940	+	0.916104i	$0.368684\pi$
$930$	−4.51420	+	4.10226i	−0.148026	+	0.134518i
$931$	−48.3242	+	13.8570i	−1.58376	+	0.454145i
$932$	−18.8958	+	5.06311i	−0.618952	+	0.165848i
$933$	4.23341	+	15.9382i	0.138596	+	0.521794i
$934$	8.38148	+	4.83905i	0.274251	+	0.158339i
$935$	−19.6680	−	37.9632i	−0.643212	−	1.24153i
$936$	−0.0481070	+	11.0303i	−0.00157243	+	0.360538i
$937$	2.55473	−	2.55473i	0.0834593	−	0.0834593i	−0.664145	−	0.747604i	$-0.731204\pi$
$937$	2.55473	−	2.55473i	0.0834593	−	0.0834593i	0.747604	+	0.664145i	$0.231204\pi$
$938$	16.8444	−	7.15008i	0.549989	−	0.233458i
$939$	2.72145	+	1.57915i	0.0888112	+	0.0515337i
$940$	−6.43816	−	12.4270i	−0.209990	−	0.405323i
$941$			0.882446i			0.0287669i	0.999897	+	0.0143835i	$0.00457855\pi$
$941$			0.882446i			0.0287669i	−0.999897	+	0.0143835i	$0.995421\pi$
$942$	−13.4641	+	3.57624i	−0.438684	+	0.116520i
$943$	−6.89278	−	6.89278i	−0.224460	−	0.224460i
$944$	−2.93963			−0.0956769
$945$	−23.5534	−	19.7545i	−0.766191	−	0.642613i
$946$	12.5173			0.406973
$947$	41.0265	+	41.0265i	1.33318	+	1.33318i	0.902507	+	0.430674i	$0.141724\pi$
$947$	41.0265	+	41.0265i	1.33318	+	1.33318i	0.430674	+	0.902507i	$0.358276\pi$
$948$	0.458130	−	0.121685i	0.0148794	−	0.00395216i
$949$			22.7427i			0.738260i
$950$	6.87250	−	18.6543i	0.222973	−	0.605227i
$951$	11.1109	+	6.44722i	0.360295	+	0.209066i
$952$	13.9835	+	10.5373i	0.453207	+	0.341515i
$953$	16.3179	−	16.3179i	0.528587	−	0.528587i	−0.391564	−	0.920151i	$-0.628066\pi$
$953$	16.3179	−	16.3179i	0.528587	−	0.528587i	0.920151	+	0.391564i	$0.128066\pi$
$954$	−5.96843	−	3.48067i	−0.193235	−	0.112691i
$955$	−28.1743	−	8.94404i	−0.911700	−	0.289422i
$956$	−28.4052	−	16.3997i	−0.918689	−	0.530406i
$957$	−22.6832	−	85.3994i	−0.733244	−	2.76057i
$958$	1.50066	−	0.402100i	0.0484840	−	0.0129913i
$959$	−3.38411	+	2.64397i	−0.109279	+	0.0853783i
$960$	6.01360	+	0.287504i	0.194088	+	0.00927916i
$961$	−22.9075			−0.738950
$962$	−0.171828	+	0.641270i	−0.00553995	+	0.0206754i
$963$	22.5282	−	22.3325i	0.725960	−	0.719655i
$964$	−25.0900	−	14.4857i	−0.808095	−	0.466554i
$965$	−45.0777	+	23.3538i	−1.45110	+	0.751787i
$966$	−3.05886	−	1.24362i	−0.0984173	−	0.0400127i
$967$	−0.776434	−	2.89769i	−0.0249684	−	0.0931834i	0.952317	−	0.305109i	$-0.0986931\pi$
$967$	−0.776434	−	2.89769i	−0.0249684	−	0.0931834i	−0.977286	+	0.211926i	$0.932026\pi$
$968$	−47.2178	−	12.6520i	−1.51764	−	0.406650i
$969$	20.2047	−	34.8199i	0.649067	−	1.11858i
$970$	−9.53269	+	2.09377i	−0.306076	+	0.0672267i
$971$	−31.0297	−	17.9150i	−0.995792	−	0.574920i	−0.0887911	−	0.996050i	$-0.528300\pi$
$971$	−31.0297	−	17.9150i	−0.995792	−	0.574920i	−0.907000	+	0.421130i	$0.861634\pi$
$972$	25.4234	+	7.11016i	0.815456	+	0.228058i
$973$	−31.7136	−	3.89386i	−1.01669	−	0.124831i
$974$	−3.89202	−	6.74117i	−0.124708	−	0.216001i
$975$	15.5042	+	1.45176i	0.496531	+	0.0464936i
$976$	−7.41494			−0.237347
$977$	−29.6107	−	29.6107i	−0.947330	−	0.947330i	0.0513502	−	0.998681i	$-0.483648\pi$
$977$	−29.6107	−	29.6107i	−0.947330	−	0.947330i	−0.998681	+	0.0513502i	$0.983648\pi$
$978$	8.17451	+	2.20947i	0.261392	+	0.0706511i
$979$	26.3492	−	15.2127i	0.842126	−	0.486201i
$980$	23.3198	−	12.6027i	0.744923	−	0.402578i
$981$	21.0996	−	36.1802i	0.673657	−	1.15514i
$982$	−1.90514	−	7.11009i	−0.0607956	−	0.226892i
$983$	4.87747	+	18.2030i	0.155567	+	0.580584i	0.999056	+	0.0434379i	$0.0138310\pi$
$983$	4.87747	+	18.2030i	0.155567	+	0.580584i	−0.843489	+	0.537146i	$0.819502\pi$
$984$	23.0016	−	13.2132i	0.733264	−	0.421221i
$985$	13.2423	−	6.86057i	0.421935	−	0.218596i
$986$	13.3986	+	7.73568i	0.426698	+	0.246354i
$987$	16.8062	+	2.10071i	0.534947	+	0.0668663i
$988$	−5.66003	+	21.1235i	−0.180070	+	0.672029i
$989$	−2.49033	+	4.31338i	−0.0791879	+	0.137158i
$990$	−19.5264	+	10.0085i	−0.620591	+	0.318090i
$991$	−10.4180	−	18.0445i	−0.330938	−	0.573201i	0.651758	−	0.758427i	$-0.274032\pi$
$991$	−10.4180	−	18.0445i	−0.330938	−	0.573201i	−0.982696	+	0.185226i	$0.940698\pi$
$992$	10.7377	+	10.7377i	0.340922	+	0.340922i
$993$	−4.46205	+	1.18518i	−0.141599	+	0.0376105i
$994$	−3.00883	+	7.44717i	−0.0954343	+	0.236210i
$995$	1.92361	+	8.75800i	0.0609826	+	0.277647i
$996$	−0.0477876	+	21.9143i	−0.00151421	+	0.694382i
$997$	−4.18694	−	15.6259i	−0.132602	−	0.494876i	0.867395	−	0.497621i	$-0.165793\pi$
$997$	−4.18694	−	15.6259i	−0.132602	−	0.494876i	−0.999996	+	0.00274486i	$0.999126\pi$
$998$	4.53406	+	1.21490i	0.143523	+	0.0384569i
$999$	2.98966	+	1.75226i	0.0945888	+	0.0554390i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bv.a.23.19	✓	176
3.2	odd	2		945.2.by.a.233.26		176
5.2	odd	4	inner	315.2.bv.a.212.26	yes	176
7.4	even	3		315.2.bx.a.158.26	yes	176
9.2	odd	6		315.2.bx.a.128.26	yes	176
9.7	even	3		945.2.ca.a.548.19		176
15.2	even	4		945.2.by.a.422.19		176
21.11	odd	6		945.2.ca.a.368.19		176
35.32	odd	12		315.2.bx.a.32.26	yes	176
45.2	even	12		315.2.bx.a.2.26	yes	176
45.7	odd	12		945.2.ca.a.737.19		176
63.11	odd	6	inner	315.2.bv.a.263.26	yes	176
63.25	even	3		945.2.by.a.683.19		176
105.32	even	12		945.2.ca.a.557.19		176
315.137	even	12	inner	315.2.bv.a.137.19	yes	176
315.277	odd	12		945.2.by.a.872.26		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bv.a.23.19	✓	176	1.1	even	1	trivial
315.2.bv.a.137.19	yes	176	315.137	even	12	inner
315.2.bv.a.212.26	yes	176	5.2	odd	4	inner
315.2.bv.a.263.26	yes	176	63.11	odd	6	inner
315.2.bx.a.2.26	yes	176	45.2	even	12
315.2.bx.a.32.26	yes	176	35.32	odd	12
315.2.bx.a.128.26	yes	176	9.2	odd	6
315.2.bx.a.158.26	yes	176	7.4	even	3
945.2.by.a.233.26		176	3.2	odd	2
945.2.by.a.422.19		176	15.2	even	4
945.2.by.a.683.19		176	63.25	even	3
945.2.by.a.872.26		176	315.277	odd	12
945.2.ca.a.368.19		176	21.11	odd	6
945.2.ca.a.548.19		176	9.7	even	3
945.2.ca.a.557.19		176	105.32	even	12
945.2.ca.a.737.19		176	45.7	odd	12

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:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bv (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.391477 - 0.391477i) q^{2} +(-1.67401 + 0.444638i) q^{3} -1.69349i q^{4} +(-0.676575 + 2.13125i) q^{5} +(0.829400 + 0.481269i) q^{6} +(2.43542 - 1.03378i) q^{7} +(-1.44592 + 1.44592i) q^{8} +(2.60459 - 1.48865i) q^{9} +O(q^{10})\)	\(q+(-0.391477 - 0.391477i) q^{2} +(-1.67401 + 0.444638i) q^{3} -1.69349i q^{4} +(-0.676575 + 2.13125i) q^{5} +(0.829400 + 0.481269i) q^{6} +(2.43542 - 1.03378i) q^{7} +(-1.44592 + 1.44592i) q^{8} +(2.60459 - 1.48865i) q^{9} +(1.09920 - 0.569474i) q^{10} +(-5.11658 - 2.95406i) q^{11} +(0.752991 + 2.83492i) q^{12} +(1.73683 - 0.465382i) q^{13} +(-1.35811 - 0.548710i) q^{14} +(0.184952 - 3.86856i) q^{15} -2.25490 q^{16} +(0.837635 - 3.12610i) q^{17} +(-1.60241 - 0.436864i) q^{18} +(-6.21952 - 3.59084i) q^{19} +(3.60926 + 1.14577i) q^{20} +(-3.61726 + 2.81344i) q^{21} +(0.846577 + 3.15947i) q^{22} +(-1.25716 - 0.336855i) q^{23} +(1.77756 - 3.06338i) q^{24} +(-4.08449 - 2.88391i) q^{25} +(-0.862115 - 0.497742i) q^{26} +(-3.69819 + 3.65012i) q^{27} +(-1.75070 - 4.12437i) q^{28} +(-4.31736 - 7.47789i) q^{29} +(-1.58686 + 1.44205i) q^{30} +2.84474 q^{31} +(3.77457 + 3.77457i) q^{32} +(9.87867 + 2.67008i) q^{33} +(-1.55171 + 0.895880i) q^{34} +(0.555510 + 5.88994i) q^{35} +(-2.52102 - 4.41086i) q^{36} +(-0.172607 - 0.644179i) q^{37} +(1.02907 + 3.84053i) q^{38} +(-2.70054 + 1.55131i) q^{39} +(-2.10335 - 4.05989i) q^{40} +(6.48625 + 3.74484i) q^{41} +(2.51747 + 0.314674i) q^{42} +(0.990460 - 3.69645i) q^{43} +(-5.00267 + 8.66488i) q^{44} +(1.41050 + 6.55824i) q^{45} +(0.360278 + 0.624020i) q^{46} +(-2.61343 - 2.61343i) q^{47} +(3.77471 - 1.00261i) q^{48} +(4.86258 - 5.03540i) q^{49} +(0.470003 + 2.72797i) q^{50} +(-0.0122238 + 5.60555i) q^{51} +(-0.788121 - 2.94131i) q^{52} +(4.01818 + 1.07667i) q^{53} +(2.87669 + 0.0188195i) q^{54} +(9.75759 - 8.90609i) q^{55} +(-2.02666 + 5.01619i) q^{56} +(12.0081 + 3.24565i) q^{57} +(-1.23727 + 4.61757i) q^{58} +1.30367 q^{59} +(-6.55138 - 0.313215i) q^{60} +3.28837 q^{61} +(-1.11365 - 1.11365i) q^{62} +(4.80434 - 6.31809i) q^{63} +1.55448i q^{64} +(-0.183247 + 4.01649i) q^{65} +(-2.82199 - 4.91255i) q^{66} +(-8.83375 + 8.83375i) q^{67} +(-5.29402 - 1.41853i) q^{68} +(2.25427 + 0.00491579i) q^{69} +(2.08831 - 2.52325i) q^{70} -5.48346i q^{71} +(-1.61355 + 5.91850i) q^{72} +(-3.27360 + 12.2172i) q^{73} +(-0.184609 + 0.319753i) q^{74} +(8.11976 + 3.01155i) q^{75} +(-6.08106 + 10.5327i) q^{76} +(-15.5149 - 1.90495i) q^{77} +(1.66450 + 0.449894i) q^{78} -0.161603i q^{79} +(1.52561 - 4.80576i) q^{80} +(4.56781 - 7.75468i) q^{81} +(-1.07320 - 4.00523i) q^{82} +(7.21655 + 1.93367i) q^{83} +(4.76454 + 6.12579i) q^{84} +(6.09579 + 3.90025i) q^{85} +(-1.83482 + 1.05933i) q^{86} +(10.5523 + 10.5984i) q^{87} +(11.6695 - 3.12682i) q^{88} +(-2.57489 + 4.45984i) q^{89} +(2.01522 - 3.11958i) q^{90} +(3.74881 - 2.92891i) q^{91} +(-0.570461 + 2.12899i) q^{92} +(-4.76211 + 1.26488i) q^{93} +2.04620i q^{94} +(11.8610 - 10.8259i) q^{95} +(-7.99698 - 4.64034i) q^{96} +(-7.61525 - 2.04050i) q^{97} +(-3.87483 + 0.0676551i) q^{98} +(-17.7242 - 0.0773010i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7	\( 176 q - 2 q^{3} - 6 q^{5} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 24 q^{11} + 26 q^{12} - 4 q^{13} - 14 q^{15} - 136 q^{16} + 18 q^{17} - 10 q^{18} - 12 q^{20} - 16 q^{21} + 4 q^{22} - 30 q^{23} + 2 q^{25} - 32 q^{27} - 4 q^{28} + 10 q^{30} - 8 q^{31} - 34 q^{33} + 8 q^{36} - 4 q^{37} - 30 q^{38} + 18 q^{40} - 36 q^{41} + 8 q^{42} - 4 q^{43} + 22 q^{45} + 4 q^{46} + 38 q^{48} + 36 q^{50} - 40 q^{51} + 26 q^{52} + 4 q^{55} + 24 q^{56} + 32 q^{57} + 6 q^{58} + 22 q^{60} + 16 q^{61} + 14 q^{63} + 4 q^{66} - 4 q^{67} + 114 q^{68} + 18 q^{70} - 46 q^{72} - 4 q^{73} + 6 q^{75} - 24 q^{76} - 54 q^{77} + 54 q^{78} - 36 q^{80} - 64 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 120 q^{86} - 28 q^{87} - 6 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} - 38 q^{93} + 192 q^{96} - 4 q^{97} - 12 q^{98}+O(q^{100}) \) 176 * q - 2 * q^3 - 6 * q^5 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 24 * q^11 + 26 * q^12 - 4 * q^13 - 14 * q^15 - 136 * q^16 + 18 * q^17 - 10 * q^18 - 12 * q^20 - 16 * q^21 + 4 * q^22 - 30 * q^23 + 2 * q^25 - 32 * q^27 - 4 * q^28 + 10 * q^30 - 8 * q^31 - 34 * q^33 + 8 * q^36 - 4 * q^37 - 30 * q^38 + 18 * q^40 - 36 * q^41 + 8 * q^42 - 4 * q^43 + 22 * q^45 + 4 * q^46 + 38 * q^48 + 36 * q^50 - 40 * q^51 + 26 * q^52 + 4 * q^55 + 24 * q^56 + 32 * q^57 + 6 * q^58 + 22 * q^60 + 16 * q^61 + 14 * q^63 + 4 * q^66 - 4 * q^67 + 114 * q^68 + 18 * q^70 - 46 * q^72 - 4 * q^73 + 6 * q^75 - 24 * q^76 - 54 * q^77 + 54 * q^78 - 36 * q^80 - 64 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 120 * q^86 - 28 * q^87 - 6 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 - 38 * q^93 + 192 * q^96 - 4 * q^97 - 12 * q^98

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