LMFDB - Embedded newform 370.2.q.e.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.q (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:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 $ x^16 - 4x^15 + 12x^14 - 48x^13 + 67x^12 - 24x^11 + 118x^10 - 176x^9 + 351x^8 - 180x^7 + 358x^6 - 336x^5 + 390x^4 - 344x^3 + 164x^2 - 40*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			103.1
Root			$-0.709944 + 0.925217i$ of defining polynomial
Character	$\chi$	$=$	370.103
Dual form			370.2.q.e.97.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.758819 - 2.83195i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61069 + 1.55103i) q^{5} +(-2.07313 + 2.07313i) q^{6} +(0.455091 + 1.69842i) q^{7} +1.00000 q^{8} +(-4.84607 + 2.79788i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.758819 - 2.83195i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61069 + 1.55103i) q^{5} +(-2.07313 + 2.07313i) q^{6} +(0.455091 + 1.69842i) q^{7} +1.00000 q^{8} +(-4.84607 + 2.79788i) q^{9} +(2.14857 + 0.619385i) q^{10} +5.29342i q^{11} +(2.83195 + 0.758819i) q^{12} +(-0.197969 + 0.342893i) q^{13} +(1.24333 - 1.24333i) q^{14} +(5.61465 + 3.38445i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.21090 - 1.85382i) q^{17} +(4.84607 + 2.79788i) q^{18} +(-5.24257 + 1.40474i) q^{19} +(-0.537883 - 2.17041i) q^{20} +(4.46452 - 2.57759i) q^{21} +(4.58424 - 2.64671i) q^{22} -7.28057 q^{23} +(-0.758819 - 2.83195i) q^{24} +(0.188640 - 4.99644i) q^{25} +0.395938 q^{26} +(5.38134 + 5.38134i) q^{27} +(-1.69842 - 0.455091i) q^{28} +(-1.33851 + 1.33851i) q^{29} +(0.123691 - 6.55465i) q^{30} +(3.75473 + 3.75473i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(14.9907 - 4.01675i) q^{33} +(-3.21090 - 1.85382i) q^{34} +(-3.36731 - 2.02977i) q^{35} -5.59575i q^{36} +(2.51884 + 5.53674i) q^{37} +(3.83783 + 3.83783i) q^{38} +(1.12128 + 0.300446i) q^{39} +(-1.61069 + 1.55103i) q^{40} +(-5.24826 - 3.03009i) q^{41} +(-4.46452 - 2.57759i) q^{42} +8.65292 q^{43} +(-4.58424 - 2.64671i) q^{44} +(3.46593 - 12.0229i) q^{45} +(3.64029 + 6.30516i) q^{46} +(-7.10699 + 7.10699i) q^{47} +(-2.07313 + 2.07313i) q^{48} +(3.38465 - 1.95413i) q^{49} +(-4.42136 + 2.33485i) q^{50} +(-7.68641 - 7.68641i) q^{51} +(-0.197969 - 0.342893i) q^{52} +(-2.33073 + 8.69839i) q^{53} +(1.96971 - 7.35105i) q^{54} +(-8.21023 - 8.52606i) q^{55} +(0.455091 + 1.69842i) q^{56} +(7.95632 + 13.7808i) q^{57} +(1.82844 + 0.489930i) q^{58} +(-1.49924 + 5.59523i) q^{59} +(-5.73834 + 3.17021i) q^{60} +(-0.793650 + 0.212658i) q^{61} +(1.37433 - 5.12906i) q^{62} +(-6.95738 - 6.95738i) q^{63} +1.00000 q^{64} +(-0.212968 - 0.859349i) q^{65} +(-10.9740 - 10.9740i) q^{66} +(-3.42259 + 0.917081i) q^{67} +3.70763i q^{68} +(5.52464 + 20.6182i) q^{69} +(-0.0741820 + 3.93106i) q^{70} +(-1.22491 + 2.12161i) q^{71} +(-4.84607 + 2.79788i) q^{72} +(7.76616 - 7.76616i) q^{73} +(3.53553 - 4.94975i) q^{74} +(-14.2928 + 3.25717i) q^{75} +(1.40474 - 5.24257i) q^{76} +(-8.99046 + 2.40899i) q^{77} +(-0.300446 - 1.12128i) q^{78} +(-12.4441 + 3.33439i) q^{79} +(2.14857 + 0.619385i) q^{80} +(2.76260 - 4.78497i) q^{81} +6.06017i q^{82} +(-0.519789 + 1.93988i) q^{83} +5.15518i q^{84} +(-2.29645 + 7.96612i) q^{85} +(-4.32646 - 7.49365i) q^{86} +(4.80629 + 2.77491i) q^{87} +5.29342i q^{88} +(0.441597 + 0.118325i) q^{89} +(-12.1451 + 3.00986i) q^{90} +(-0.672471 - 0.180188i) q^{91} +(3.64029 - 6.30516i) q^{92} +(7.78405 - 13.4824i) q^{93} +(9.70832 + 2.60134i) q^{94} +(6.26536 - 10.3940i) q^{95} +(2.83195 + 0.758819i) q^{96} -10.7641i q^{97} +(-3.38465 - 1.95413i) q^{98} +(-14.8103 - 25.6523i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9}+O(q^{10}) $ 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9	$ 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9} - 4 q^{10} + 16 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 24 q^{18} - 24 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{23} - 8 q^{24} + 32 q^{25} + 8 q^{26} + 16 q^{27} + 16 q^{29} - 4 q^{30} + 24 q^{31} - 8 q^{32} + 12 q^{33} - 20 q^{35} - 4 q^{40} - 36 q^{41} + 12 q^{42} - 16 q^{43} + 4 q^{45} + 4 q^{46} + 32 q^{47} - 8 q^{48} + 24 q^{49} - 16 q^{50} - 16 q^{51} - 4 q^{52} - 48 q^{53} - 8 q^{54} - 24 q^{55} + 20 q^{57} - 8 q^{58} - 8 q^{59} - 4 q^{60} + 8 q^{61} - 12 q^{62} + 16 q^{63} + 16 q^{64} + 24 q^{65} - 24 q^{66} - 8 q^{67} - 8 q^{69} + 28 q^{70} + 4 q^{71} - 24 q^{72} + 48 q^{73} - 36 q^{75} + 24 q^{76} - 60 q^{77} + 20 q^{79} - 4 q^{80} + 16 q^{81} + 24 q^{83} + 8 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{89} - 8 q^{90} - 8 q^{91} + 4 q^{92} + 36 q^{93} - 28 q^{94} + 28 q^{95} + 16 q^{96} - 24 q^{98} + 8 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9 - 4 * q^10 + 16 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 24 * q^18 - 24 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^23 - 8 * q^24 + 32 * q^25 + 8 * q^26 + 16 * q^27 + 16 * q^29 - 4 * q^30 + 24 * q^31 - 8 * q^32 + 12 * q^33 - 20 * q^35 - 4 * q^40 - 36 * q^41 + 12 * q^42 - 16 * q^43 + 4 * q^45 + 4 * q^46 + 32 * q^47 - 8 * q^48 + 24 * q^49 - 16 * q^50 - 16 * q^51 - 4 * q^52 - 48 * q^53 - 8 * q^54 - 24 * q^55 + 20 * q^57 - 8 * q^58 - 8 * q^59 - 4 * q^60 + 8 * q^61 - 12 * q^62 + 16 * q^63 + 16 * q^64 + 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^69 + 28 * q^70 + 4 * q^71 - 24 * q^72 + 48 * q^73 - 36 * q^75 + 24 * q^76 - 60 * q^77 + 20 * q^79 - 4 * q^80 + 16 * q^81 + 24 * q^83 + 8 * q^85 + 8 * q^86 + 12 * q^87 - 8 * q^89 - 8 * q^90 - 8 * q^91 + 4 * q^92 + 36 * q^93 - 28 * q^94 + 28 * q^95 + 16 * q^96 - 24 * q^98 + 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.758819	−	2.83195i	−0.438104	−	1.63503i	−0.733526	−	0.679661i	$-0.762127\pi$
$3$	−0.758819	−	2.83195i	−0.438104	−	1.63503i	0.295422	−	0.955367i	$-0.404540\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.61069	+	1.55103i	−0.720322	+	0.693640i
$5$	−1.61069	+	1.55103i	−0.720322	+	0.693640i
$6$	−2.07313	+	2.07313i	−0.846353	+	0.846353i
$7$	0.455091	+	1.69842i	0.172008	+	0.641943i	0.997042	+	0.0768598i	$0.0244894\pi$
$7$	0.455091	+	1.69842i	0.172008	+	0.641943i	−0.825034	+	0.565083i	$0.808844\pi$
$8$	1.00000			0.353553
$9$	−4.84607	+	2.79788i	−1.61536	+	0.932626i
$10$	2.14857	+	0.619385i	0.679438	+	0.195867i
$11$			5.29342i			1.59603i	0.602640	+	0.798013i	$0.294115\pi$
$11$			5.29342i			1.59603i	−0.602640	+	0.798013i	$0.705885\pi$
$12$	2.83195	+	0.758819i	0.817514	+	0.219052i
$13$	−0.197969	+	0.342893i	−0.0549068	+	0.0951013i	−0.892172	−	0.451695i	$-0.850819\pi$
$13$	−0.197969	+	0.342893i	−0.0549068	+	0.0951013i	0.837266	+	0.546796i	$0.184153\pi$
$14$	1.24333	−	1.24333i	0.332294	−	0.332294i
$15$	5.61465	+	3.38445i	1.44970	+	0.873860i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.21090	−	1.85382i	0.778759	−	0.449617i	−0.0572314	−	0.998361i	$-0.518227\pi$
$17$	3.21090	−	1.85382i	0.778759	−	0.449617i	0.835990	+	0.548744i	$0.184894\pi$
$18$	4.84607	+	2.79788i	1.14223	+	0.659466i
$19$	−5.24257	+	1.40474i	−1.20273	+	0.322270i	−0.803905	−	0.594758i	$-0.797248\pi$
$19$	−5.24257	+	1.40474i	−1.20273	+	0.322270i	−0.398823	+	0.917028i	$0.630581\pi$
$20$	−0.537883	−	2.17041i	−0.120274	−	0.485319i
$21$	4.46452	−	2.57759i	0.974238	−	0.562476i
$22$	4.58424	−	2.64671i	0.977362	−	0.564280i
$23$	−7.28057			−1.51810			−0.759052	−	0.651030i	$-0.774337\pi$
$23$	−7.28057			−1.51810			−0.759052	+	0.651030i	$0.774337\pi$
$24$	−0.758819	−	2.83195i	−0.154893	−	0.578070i
$25$	0.188640	−	4.99644i	0.0377280	−	0.999288i
$26$	0.395938			0.0776499
$27$	5.38134	+	5.38134i	1.03564	+	1.03564i
$28$	−1.69842	−	0.455091i	−0.320972	−	0.0860041i
$29$	−1.33851	+	1.33851i	−0.248556	+	0.248556i	−0.820378	−	0.571822i	$-0.806237\pi$
$29$	−1.33851	+	1.33851i	−0.248556	+	0.248556i	0.571822	+	0.820378i	$0.306237\pi$
$30$	0.123691	−	6.55465i	0.0225828	−	1.19671i
$31$	3.75473	+	3.75473i	0.674369	+	0.674369i	0.958720	−	0.284351i	$-0.0917780\pi$
$31$	3.75473	+	3.75473i	0.674369	+	0.674369i	−0.284351	+	0.958720i	$0.591778\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	14.9907	−	4.01675i	2.60955	−	0.699226i
$34$	−3.21090	−	1.85382i	−0.550666	−	0.317927i
$35$	−3.36731	−	2.02977i	−0.569179	−	0.343094i
$36$		−	5.59575i		−	0.932626i
$37$	2.51884	+	5.53674i	0.414095	+	0.910234i
$37$	2.51884	+	5.53674i	0.414095	+	0.910234i
$38$	3.83783	+	3.83783i	0.622578	+	0.622578i
$39$	1.12128	+	0.300446i	0.179548	+	0.0481098i
$40$	−1.61069	+	1.55103i	−0.254672	+	0.245239i
$41$	−5.24826	−	3.03009i	−0.819641	−	0.473220i	0.0306518	−	0.999530i	$-0.490242\pi$
$41$	−5.24826	−	3.03009i	−0.819641	−	0.473220i	−0.850293	+	0.526310i	$0.823575\pi$
$42$	−4.46452	−	2.57759i	−0.688890	−	0.397731i
$43$	8.65292			1.31956			0.659779	−	0.751459i	$-0.270650\pi$
$43$	8.65292			1.31956			0.659779	+	0.751459i	$0.270650\pi$
$44$	−4.58424	−	2.64671i	−0.691100	−	0.399007i
$45$	3.46593	−	12.0229i	0.516670	−	1.79227i
$46$	3.64029	+	6.30516i	0.536731	+	0.929645i
$47$	−7.10699	+	7.10699i	−1.03666	+	1.03666i	−0.0373585	+	0.999302i	$0.511894\pi$
$47$	−7.10699	+	7.10699i	−1.03666	+	1.03666i	−0.999302	+	0.0373585i	$0.988106\pi$
$48$	−2.07313	+	2.07313i	−0.299231	+	0.299231i
$49$	3.38465	−	1.95413i	0.483521	−	0.279161i
$50$	−4.42136	+	2.33485i	−0.625275	+	0.330198i
$51$	−7.68641	−	7.68641i	−1.07631	−	1.07631i
$52$	−0.197969	−	0.342893i	−0.0274534	−	0.0475507i
$53$	−2.33073	+	8.69839i	−0.320150	+	1.19482i	0.598948	+	0.800788i	$0.295586\pi$
$53$	−2.33073	+	8.69839i	−0.320150	+	1.19482i	−0.919098	+	0.394028i	$0.871081\pi$
$54$	1.96971	−	7.35105i	0.268043	−	1.00035i
$55$	−8.21023	−	8.52606i	−1.10707	−	1.14965i
$56$	0.455091	+	1.69842i	0.0608141	+	0.226961i
$57$	7.95632	+	13.7808i	1.05384	+	1.82531i
$58$	1.82844	+	0.489930i	0.240086	+	0.0643309i
$59$	−1.49924	+	5.59523i	−0.195184	+	0.728437i	0.797035	+	0.603933i	$0.206401\pi$
$59$	−1.49924	+	5.59523i	−0.195184	+	0.728437i	−0.992219	+	0.124504i	$0.960266\pi$
$60$	−5.73834	+	3.17021i	−0.740817	+	0.409272i
$61$	−0.793650	+	0.212658i	−0.101617	+	0.0272281i	−0.309269	−	0.950975i	$-0.600084\pi$
$61$	−0.793650	+	0.212658i	−0.101617	+	0.0272281i	0.207652	+	0.978203i	$0.433418\pi$
$62$	1.37433	−	5.12906i	0.174540	−	0.651391i
$63$	−6.95738	−	6.95738i	−0.876547	−	0.876547i
$64$	1.00000			0.125000
$65$	−0.212968	−	0.859349i	−0.0264155	−	0.106589i
$66$	−10.9740	−	10.9740i	−1.35080	−	1.35080i
$67$	−3.42259	+	0.917081i	−0.418136	+	0.112039i	−0.461752	−	0.887009i	$-0.652779\pi$
$67$	−3.42259	+	0.917081i	−0.418136	+	0.112039i	0.0436155	+	0.999048i	$0.486112\pi$
$68$			3.70763i			0.449617i
$69$	5.52464	+	20.6182i	0.665088	+	2.48214i
$70$	−0.0741820	+	3.93106i	−0.00886644	+	0.469851i
$71$	−1.22491	+	2.12161i	−0.145370	+	0.251788i	−0.929511	−	0.368795i	$-0.879771\pi$
$71$	−1.22491	+	2.12161i	−0.145370	+	0.251788i	0.784141	+	0.620583i	$0.213104\pi$
$72$	−4.84607	+	2.79788i	−0.571114	+	0.329733i
$73$	7.76616	−	7.76616i	0.908961	−	0.908961i	−0.0872276	−	0.996188i	$-0.527801\pi$
$73$	7.76616	−	7.76616i	0.908961	−	0.908961i	0.996188	+	0.0872276i	$0.0278007\pi$
$74$	3.53553	−	4.94975i	0.410997	−	0.575396i
$75$	−14.2928	+	3.25717i	−1.65039	+	0.376106i
$76$	1.40474	−	5.24257i	0.161135	−	0.601364i
$77$	−8.99046	+	2.40899i	−1.02456	+	0.274530i
$78$	−0.300446	−	1.12128i	−0.0340188	−	0.126960i
$79$	−12.4441	+	3.33439i	−1.40007	+	0.375148i	−0.878370	−	0.477981i	$-0.841369\pi$
$79$	−12.4441	+	3.33439i	−1.40007	+	0.375148i	−0.521700	+	0.853129i	$0.674702\pi$
$80$	2.14857	+	0.619385i	0.240218	+	0.0692494i
$81$	2.76260	−	4.78497i	0.306956	−	0.531663i
$82$			6.06017i			0.669234i
$83$	−0.519789	+	1.93988i	−0.0570542	+	0.212929i	−0.988568	−	0.150778i	$-0.951822\pi$
$83$	−0.519789	+	1.93988i	−0.0570542	+	0.212929i	0.931514	+	0.363707i	$0.118489\pi$
$84$			5.15518i			0.562476i
$85$	−2.29645	+	7.96612i	−0.249085	+	0.864047i
$86$	−4.32646	−	7.49365i	−0.466534	−	0.808061i
$87$	4.80629	+	2.77491i	0.515289	+	0.297502i
$88$			5.29342i			0.564280i
$89$	0.441597	+	0.118325i	0.0468091	+	0.0125425i	0.282148	−	0.959371i	$-0.408953\pi$
$89$	0.441597	+	0.118325i	0.0468091	+	0.0125425i	−0.235338	+	0.971913i	$0.575620\pi$
$90$	−12.1451	+	3.00986i	−1.28020	+	0.317267i
$91$	−0.672471	−	0.180188i	−0.0704941	−	0.0188888i
$92$	3.64029	−	6.30516i	0.379526	−	0.657359i
$93$	7.78405	−	13.4824i	0.807169	−	1.39806i
$94$	9.70832	+	2.60134i	1.00134	+	0.268307i
$95$	6.26536	−	10.3940i	0.642812	−	1.06640i
$96$	2.83195	+	0.758819i	0.289035	+	0.0774466i
$97$		−	10.7641i		−	1.09293i	−0.837481	−	0.546466i	$-0.815973\pi$
$97$		−	10.7641i		−	1.09293i	0.837481	−	0.546466i	$-0.184027\pi$
$98$	−3.38465	−	1.95413i	−0.341901	−	0.197397i
$99$	−14.8103	−	25.6523i	−1.48850	−	2.57815i
$100$	4.23272	+	2.66159i	0.423272	+	0.266159i
$101$			1.23852i			0.123237i	0.998100	+	0.0616184i	$0.0196262\pi$
$101$			1.23852i			0.123237i	−0.998100	+	0.0616184i	$0.980374\pi$
$102$	−2.81342	+	10.4998i	−0.278570	+	1.03964i
$103$		−	15.6859i		−	1.54558i	−0.634662	−	0.772790i	$-0.718861\pi$
$103$		−	15.6859i		−	1.54558i	0.634662	−	0.772790i	$-0.281139\pi$
$104$	−0.197969	+	0.342893i	−0.0194125	+	0.0336234i
$105$	−3.19304	+	11.0763i	−0.311609	+	1.08093i
$106$	8.69839	−	2.33073i	0.844863	−	0.226380i
$107$	−0.801309	−	2.99053i	−0.0774655	−	0.289105i	0.916316	−	0.400457i	$-0.131149\pi$
$107$	−0.801309	−	2.99053i	−0.0774655	−	0.289105i	−0.993781	+	0.111352i	$0.964482\pi$
$108$	−7.35105	+	1.96971i	−0.707355	+	0.189535i
$109$	0.513107	−	1.91494i	0.0491468	−	0.183418i	−0.936989	−	0.349359i	$-0.886399\pi$
$109$	0.513107	−	1.91494i	0.0491468	−	0.183418i	0.986136	+	0.165941i	$0.0530660\pi$
$110$	−3.27867	+	11.3733i	−0.312609	+	1.08440i
$111$	13.7684	−	11.3346i	1.30684	−	1.07583i
$112$	1.24333	−	1.24333i	0.117484	−	0.117484i
$113$	−14.5475	+	8.39900i	−1.36851	+	0.790112i	−0.990738	−	0.135786i	$-0.956644\pi$
$113$	−14.5475	+	8.39900i	−1.36851	+	0.790112i	−0.377775	+	0.925897i	$0.623311\pi$
$114$	7.95632	−	13.7808i	0.745178	−	1.29069i
$115$	11.7267	−	11.2924i	1.09352	−	1.05302i
$116$	−0.489930	−	1.82844i	−0.0454888	−	0.169767i
$117$		−	2.21557i		−	0.204830i
$118$	5.59523	−	1.49924i	0.515082	−	0.138016i
$119$	4.60982	+	4.60982i	0.422581	+	0.422581i
$120$	5.61465	+	3.38445i	0.512545	+	0.308956i
$121$	−17.0203			−1.54730
$122$	0.580992	+	0.580992i	0.0526006	+	0.0526006i
$123$	−4.59857	+	17.1621i	−0.414639	+	1.54746i
$124$	−5.12906	+	1.37433i	−0.460603	+	0.123418i
$125$	7.44577	+	8.34030i	0.665969	+	0.745979i
$126$	−2.54658	+	9.50395i	−0.226867	+	0.846679i
$127$	−3.10721	−	0.832573i	−0.275720	−	0.0738789i	0.118309	−	0.992977i	$-0.462253\pi$
$127$	−3.10721	−	0.832573i	−0.275720	−	0.0738789i	−0.394029	+	0.919098i	$0.628919\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−6.56600	−	24.5047i	−0.578104	−	2.15751i
$130$	−0.637734	+	0.614111i	−0.0559329	+	0.0538611i
$131$	1.42519	−	5.31888i	0.124519	−	0.464713i	−0.875303	−	0.483576i	$-0.839338\pi$
$131$	1.42519	−	5.31888i	0.124519	−	0.464713i	0.999822	+	0.0188626i	$0.00600451\pi$
$132$	−4.01675	+	14.9907i	−0.349613	+	1.30477i
$133$	−4.77169	−	8.26481i	−0.413758	−	0.716650i
$134$	2.50551	+	2.50551i	0.216443	+	0.216443i
$135$	−17.0143	−	0.321072i	−1.46435	−	0.0276335i
$136$	3.21090	−	1.85382i	0.275333	−	0.158963i
$137$	14.6294	−	14.6294i	1.24988	−	1.24988i	0.294103	−	0.955774i	$-0.404979\pi$
$137$	14.6294	−	14.6294i	1.24988	−	1.24988i	0.955774	−	0.294103i	$-0.0950210\pi$
$138$	15.0936	−	15.0936i	1.28485	−	1.28485i
$139$	11.1080	+	19.2396i	0.942165	+	1.63188i	0.761330	+	0.648365i	$0.224547\pi$
$139$	11.1080	+	19.2396i	0.942165	+	1.63188i	0.180835	+	0.983513i	$0.442120\pi$
$140$	3.44149	−	1.90129i	0.290859	−	0.160688i
$141$	25.5196	+	14.7337i	2.14913	+	1.24080i
$142$	2.44982			0.205584
$143$	−1.81508	−	1.04793i	−0.151784	−	0.0876327i
$144$	4.84607	+	2.79788i	0.403839	+	0.233156i
$145$	0.0798609	−	4.23200i	0.00663208	−	0.351448i
$146$	−10.6088	−	2.84261i	−0.877989	−	0.235256i
$147$	−8.10233	−	8.10233i	−0.668269	−	0.668269i
$148$	−6.05437	−	0.586988i	−0.497666	−	0.0482502i
$149$			7.99685i			0.655127i	0.944829	+	0.327564i	$0.106228\pi$
$149$			7.99685i			0.655127i	−0.944829	+	0.327564i	$0.893772\pi$
$150$	9.96721	+	10.7494i	0.813819	+	0.877681i
$151$	12.3792	+	7.14715i	1.00741	+	0.581627i	0.910431	−	0.413660i	$-0.135750\pi$
$151$	12.3792	+	7.14715i	1.00741	+	0.581627i	0.0969755	+	0.995287i	$0.469083\pi$
$152$	−5.24257	+	1.40474i	−0.425228	+	0.113940i
$153$	−10.3735	+	17.9674i	−0.838648	+	1.45258i
$154$	6.58148	+	6.58148i	0.530350	+	0.530350i
$155$	−11.8714	−	0.224022i	−0.953533	−	0.0179939i
$156$	−0.820833	+	0.820833i	−0.0657192	+	0.0657192i
$157$	−7.78666	−	2.08643i	−0.621443	−	0.166515i	−0.0656592	−	0.997842i	$-0.520915\pi$
$157$	−7.78666	−	2.08643i	−0.621443	−	0.166515i	−0.555784	+	0.831327i	$0.687582\pi$
$158$	9.10971	+	9.10971i	0.724730	+	0.724730i
$159$	26.4020			2.09382
$160$	−0.537883	−	2.17041i	−0.0425234	−	0.171586i
$161$	−3.31332	−	12.3655i	−0.261126	−	0.974537i
$162$	−5.52520			−0.434101
$163$	−0.520426	+	0.300468i	−0.0407629	+	0.0235345i	−0.520243	−	0.854018i	$-0.674159\pi$
$163$	−0.520426	+	0.300468i	−0.0407629	+	0.0235345i	0.479480	+	0.877553i	$0.340825\pi$
$164$	5.24826	−	3.03009i	0.409820	−	0.236610i
$165$	−17.9153	+	29.7207i	−1.39470	+	2.31375i
$166$	1.93988	−	0.519789i	0.150564	−	0.0403434i
$167$	−14.0365	−	8.10399i	−1.08618	−	0.627106i	−0.153623	−	0.988130i	$-0.549094\pi$
$167$	−14.0365	−	8.10399i	−1.08618	−	0.627106i	−0.932557	+	0.361024i	$0.882427\pi$
$168$	4.46452	−	2.57759i	0.344445	−	0.198865i
$169$	6.42162	+	11.1226i	0.493970	+	0.855582i
$170$	8.04709	−	1.99427i	0.617183	−	0.152954i
$171$	21.4755	−	21.4755i	1.64227	−	1.64227i
$172$	−4.32646	+	7.49365i	−0.329890	+	0.571386i
$173$	12.8789	+	3.45090i	0.979167	+	0.262367i	0.712694	−	0.701475i	$-0.247475\pi$
$173$	12.8789	+	3.45090i	0.979167	+	0.262367i	0.266473	+	0.963842i	$0.414142\pi$
$174$		−	5.54983i		−	0.420731i
$175$	8.57191	−	1.95344i	0.647976	−	0.147666i
$176$	4.58424	−	2.64671i	0.345550	−	0.199503i
$177$	16.9831			1.27653
$178$	−0.118325	−	0.441597i	−0.00886887	−	0.0330991i
$179$	−5.55861	+	5.55861i	−0.415470	+	0.415470i	−0.883639	−	0.468169i	$-0.844914\pi$
$179$	−5.55861	+	5.55861i	−0.415470	+	0.415470i	0.468169	+	0.883639i	$0.344914\pi$
$180$	8.67916	+	9.01302i	0.646906	+	0.671791i
$181$	1.28072	−	2.21827i	0.0951949	−	0.164882i	−0.814495	−	0.580171i	$-0.802986\pi$
$181$	1.28072	−	2.21827i	0.0951949	−	0.164882i	0.909690	+	0.415288i	$0.136319\pi$
$182$	0.180188	+	0.672471i	0.0133564	+	0.0498468i
$183$	1.20447	+	2.08621i	0.0890373	+	0.154217i
$184$	−7.28057			−0.536731
$185$	−12.6447	−	5.01118i	−0.929656	−	0.368429i
$186$	−15.5681			−1.14151
$187$	9.81303	+	16.9967i	0.717600	+	1.24292i
$188$	−2.60134	−	9.70832i	−0.189722	−	0.708052i
$189$	−6.69079	+	11.5888i	−0.486683	+	0.842960i
$190$	−12.1341	−	0.228980i	−0.880301	−	0.0166119i
$191$	−3.22968	+	3.22968i	−0.233691	+	0.233691i	−0.814232	−	0.580540i	$-0.802841\pi$
$191$	−3.22968	+	3.22968i	−0.233691	+	0.233691i	0.580540	+	0.814232i	$0.302841\pi$
$192$	−0.758819	−	2.83195i	−0.0547630	−	0.204378i
$193$	−17.5567			−1.26376			−0.631880	−	0.775066i	$-0.717716\pi$
$193$	−17.5567			−1.26376			−0.631880	+	0.775066i	$0.717716\pi$
$194$	−9.32202	+	5.38207i	−0.669282	+	0.386410i
$195$	−2.27203	+	1.25521i	−0.162703	+	0.0898872i
$196$			3.90825i			0.279161i
$197$	−0.428008	−	0.114684i	−0.0304943	−	0.00817093i	0.243540	−	0.969891i	$-0.421691\pi$
$197$	−0.428008	−	0.114684i	−0.0304943	−	0.00817093i	−0.274034	+	0.961720i	$0.588358\pi$
$198$	−14.8103	+	25.6523i	−1.05252	+	1.82303i
$199$	19.1007	−	19.1007i	1.35401	−	1.35401i	0.472897	−	0.881118i	$-0.343208\pi$
$199$	19.1007	−	19.1007i	1.35401	−	1.35401i	0.881118	−	0.472897i	$-0.156792\pi$
$200$	0.188640	−	4.99644i	0.0133389	−	0.353302i
$201$	5.19426	+	8.99672i	0.366375	+	0.634580i
$202$	1.07259	−	0.619258i	0.0754669	−	0.0435708i
$203$	−2.88251	−	1.66422i	−0.202312	−	0.116805i
$204$	10.4998	−	2.81342i	0.735136	−	0.196979i
$205$	13.1531	−	3.25966i	0.918649	−	0.227665i
$206$	−13.5844	+	7.84296i	−0.946470	+	0.546445i
$207$	35.2821	−	20.3702i	2.45228	−	1.41582i
$208$	0.395938			0.0274534
$209$	−7.43589	−	27.7511i	−0.514351	−	1.91958i
$210$	11.1889	−	2.77288i	0.772105	−	0.191347i
$211$	−27.6353			−1.90250			−0.951248	−	0.308428i	$-0.900197\pi$
$211$	−27.6353			−1.90250			−0.951248	+	0.308428i	$0.900197\pi$
$212$	−6.36767	−	6.36767i	−0.437333	−	0.437333i
$213$	6.93777	+	1.85897i	0.475368	+	0.127374i
$214$	−2.18922	+	2.18922i	−0.149652	+	0.149652i
$215$	−13.9372	+	13.4209i	−0.950507	+	0.915298i
$216$	5.38134	+	5.38134i	0.366154	+	0.366154i
$217$	−4.66837	+	8.08586i	−0.316910	+	0.548904i
$218$	−1.91494	+	0.513107i	−0.129696	+	0.0347520i
$219$	−27.8865	−	16.1003i	−1.88440	−	1.08796i
$220$	11.4889	−	2.84724i	0.774581	−	0.191961i
$221$			1.46799i			0.0987480i
$222$	−16.7003	−	6.25650i	−1.12085	−	0.419909i
$223$	19.6785	+	19.6785i	1.31777	+	1.31777i	0.915539	+	0.402229i	$0.131764\pi$
$223$	19.6785	+	19.6785i	1.31777	+	1.31777i	0.402229	+	0.915539i	$0.368236\pi$
$224$	−1.69842	−	0.455091i	−0.113481	−	0.0304070i
$225$	13.0653	+	24.7409i	0.871018	+	1.64939i
$226$	14.5475	+	8.39900i	0.967685	+	0.558693i
$227$	−14.9254	−	8.61717i	−0.990632	−	0.571941i	−0.0851686	−	0.996367i	$-0.527143\pi$
$227$	−14.9254	−	8.61717i	−0.990632	−	0.571941i	−0.905463	+	0.424425i	$0.860476\pi$
$228$	−15.9126			−1.05384
$229$	6.96524	+	4.02138i	0.460276	+	0.265740i	0.712160	−	0.702017i	$-0.247717\pi$
$229$	6.96524	+	4.02138i	0.460276	+	0.265740i	−0.251884	+	0.967757i	$0.581050\pi$
$230$	−15.6428	−	4.50948i	−1.03146	−	0.297346i
$231$	13.6443	+	23.6326i	0.897727	+	1.55491i
$232$	−1.33851	+	1.33851i	−0.0878777	+	0.0878777i
$233$	15.0559	−	15.0559i	0.986346	−	0.986346i	−0.0135616	−	0.999908i	$-0.504317\pi$
$233$	15.0559	−	15.0559i	0.986346	−	0.986346i	0.999908	+	0.0135616i	$0.00431692\pi$
$234$	−1.91874	+	1.10779i	−0.125432	+	0.0724183i
$235$	0.424030	−	22.4703i	0.0276607	−	1.46580i
$236$	−4.09599	−	4.09599i	−0.266626	−	0.266626i
$237$	18.8856	+	32.7109i	1.22675	+	2.12480i
$238$	1.68731	−	6.29713i	0.109372	−	0.408182i
$239$	2.47074	−	9.22091i	0.159819	−	0.596451i	−0.838826	−	0.544400i	$-0.816757\pi$
$239$	2.47074	−	9.22091i	0.159819	−	0.596451i	0.998644	−	0.0520513i	$-0.0165759\pi$
$240$	0.123691	−	6.55465i	0.00798423	−	0.423101i
$241$	1.03693	+	3.86989i	0.0667947	+	0.249281i	0.991248	−	0.132015i	$-0.0421446\pi$
$241$	1.03693	+	3.86989i	0.0667947	+	0.249281i	−0.924453	+	0.381296i	$0.875478\pi$
$242$	8.51015	+	14.7400i	0.547053	+	0.947524i
$243$	6.40605	+	1.71649i	0.410948	+	0.110113i
$244$	0.212658	−	0.793650i	0.0136140	−	0.0508083i
$245$	−2.42071	+	8.39717i	−0.154654	+	0.536475i
$246$	17.1621	−	4.59857i	1.09422	−	0.293194i
$247$	0.556191	−	2.07573i	0.0353896	−	0.132076i
$248$	3.75473	+	3.75473i	0.238426	+	0.238426i
$249$	5.88806			0.373141
$250$	3.50003	−	10.6184i	0.221361	−	0.671565i
$251$	6.79402	+	6.79402i	0.428834	+	0.428834i	0.888231	−	0.459397i	$-0.151934\pi$
$251$	6.79402	+	6.79402i	0.428834	+	0.428834i	−0.459397	+	0.888231i	$0.651934\pi$
$252$	9.50395	−	2.54658i	0.598693	−	0.160419i
$253$		−	38.5391i		−	2.42293i
$254$	0.832573	+	3.10721i	0.0522403	+	0.194963i
$255$	24.3023	+	0.458601i	1.52187	+	0.0287187i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.89445	−	2.82581i	0.305307	−	0.176269i	−0.339517	−	0.940600i	$-0.610264\pi$
$257$	4.89445	−	2.82581i	0.305307	−	0.176269i	0.644825	+	0.764331i	$0.276930\pi$
$258$	−17.9387	+	17.9387i	−1.11681	+	1.11681i
$259$	−8.25741	+	6.79777i	−0.513091	+	0.422393i
$260$	0.850702	+	0.245238i	0.0527583	+	0.0152090i
$261$	2.74153	−	10.2315i	0.169696	−	0.633315i
$262$	−5.31888	+	1.42519i	−0.328602	+	0.0880486i
$263$	1.82357	+	6.80564i	0.112446	+	0.419654i	0.999083	−	0.0428117i	$-0.0136315\pi$
$263$	1.82357	+	6.80564i	0.112446	+	0.419654i	−0.886637	+	0.462466i	$0.846965\pi$
$264$	14.9907	−	4.01675i	0.922614	−	0.247214i
$265$	−9.73735	−	17.6254i	−0.598161	−	1.08272i
$266$	−4.77169	+	8.26481i	−0.292571	+	0.506748i
$267$		−	1.34037i		−	0.0820291i
$268$	0.917081	−	3.42259i	0.0560197	−	0.209068i
$269$			20.1816i			1.23049i	0.788336	+	0.615246i	$0.210943\pi$
$269$			20.1816i			1.23049i	−0.788336	+	0.615246i	$0.789057\pi$
$270$	8.22908	+	14.8953i	0.500806	+	0.906500i
$271$	5.27948	+	9.14432i	0.320705	+	0.555478i	0.980634	−	0.195851i	$-0.0627468\pi$
$271$	5.27948	+	9.14432i	0.320705	+	0.555478i	−0.659928	+	0.751328i	$0.729413\pi$
$272$	−3.21090	−	1.85382i	−0.194690	−	0.112404i
$273$			2.04113i			0.123535i
$274$	−19.9842	−	5.35474i	−1.20729	−	0.323492i
$275$	26.4483	+	0.998552i	1.59489	+	0.0602149i
$276$	−20.6182	−	5.52464i	−1.24107	−	0.332544i
$277$	11.1864	−	19.3754i	0.672126	−	1.16416i	−0.305174	−	0.952297i	$-0.598715\pi$
$277$	11.1864	−	19.3754i	0.672126	−	1.16416i	0.977300	−	0.211860i	$-0.0679520\pi$
$278$	11.1080	−	19.2396i	0.666211	−	1.15391i
$279$	−28.7009	−	7.69039i	−1.71828	−	0.460412i
$280$	−3.36731	−	2.02977i	−0.201235	−	0.121302i
$281$	12.0535	+	3.22972i	0.719050	+	0.192669i	0.599748	−	0.800189i	$-0.295268\pi$
$281$	12.0535	+	3.22972i	0.719050	+	0.192669i	0.119302	+	0.992858i	$0.461934\pi$
$282$		−	29.4674i		−	1.75476i
$283$	−23.4570	−	13.5429i	−1.39437	−	0.805041i	−0.400576	−	0.916263i	$-0.631190\pi$
$283$	−23.4570	−	13.5429i	−1.39437	−	0.805041i	−0.993796	+	0.111223i	$0.964523\pi$
$284$	−1.22491	−	2.12161i	−0.0726850	−	0.125894i
$285$	−34.1895	−	9.85605i	−2.02521	−	0.583822i
$286$			2.09587i			0.123931i
$287$	2.75793	−	10.2927i	0.162795	−	0.607561i
$288$		−	5.59575i		−	0.329733i
$289$	−1.62673	+	2.81757i	−0.0956898	+	0.165740i
$290$	−3.70495	+	2.04684i	−0.217562	+	0.120194i
$291$	−30.4835	+	8.16803i	−1.78698	+	0.478819i
$292$	2.84261	+	10.6088i	0.166351	+	0.620832i
$293$	20.9501	−	5.61358i	1.22392	−	0.327949i	0.411711	−	0.911314i	$-0.364931\pi$
$293$	20.9501	−	5.61358i	1.22392	−	0.327949i	0.812210	+	0.583366i	$0.198265\pi$
$294$	−2.96566	+	11.0680i	−0.172961	+	0.645498i
$295$	−6.26354	−	11.3375i	−0.364677	−	0.660096i
$296$	2.51884	+	5.53674i	0.146405	+	0.321816i
$297$	−28.4857	+	28.4857i	−1.65291	+	1.65291i
$298$	6.92547	−	3.99842i	0.401182	−	0.231622i
$299$	1.44133	−	2.49646i	0.0833542	−	0.144374i
$300$	4.32561	−	14.0065i	0.249739	−	0.808667i
$301$	3.93787	+	14.6963i	0.226975	+	0.847082i
$302$		−	14.2943i		−	0.822544i
$303$	3.50742	−	0.939809i	0.201496	−	0.0539906i
$304$	3.83783	+	3.83783i	0.220114	+	0.220114i
$305$	0.948486	−	1.57350i	0.0543102	−	0.0900982i
$306$	20.7470			1.18603
$307$	9.50973	+	9.50973i	0.542749	+	0.542749i	0.924334	−	0.381585i	$-0.124622\pi$
$307$	9.50973	+	9.50973i	0.542749	+	0.542749i	−0.381585	+	0.924334i	$0.624622\pi$
$308$	2.40899	−	8.99046i	0.137265	−	0.512279i
$309$	−44.4218	+	11.9028i	−2.52707	+	0.677125i
$310$	5.74168	+	10.3929i	0.326106	+	0.590279i
$311$	2.08579	−	7.78427i	0.118274	−	0.441405i	−0.881237	−	0.472675i	$-0.843288\pi$
$311$	2.08579	−	7.78427i	0.118274	−	0.441405i	0.999511	+	0.0312698i	$0.00995511\pi$
$312$	1.12128	+	0.300446i	0.0634799	+	0.0170094i
$313$	−0.733158	−	1.26987i	−0.0414406	−	0.0717771i	0.844561	−	0.535459i	$-0.179861\pi$
$313$	−0.733158	−	1.26987i	−0.0414406	−	0.0717771i	−0.886002	+	0.463682i	$0.846528\pi$
$314$	2.08643	+	7.78666i	0.117744	+	0.439426i
$315$	21.9972	+	0.415104i	1.23940	+	0.0233885i
$316$	3.33439	−	12.4441i	0.187574	−	0.700035i
$317$	3.21563	−	12.0009i	0.180608	−	0.674037i	−0.814921	−	0.579572i	$-0.803220\pi$
$317$	3.21563	−	12.0009i	0.180608	−	0.674037i	0.995528	−	0.0944641i	$-0.0301138\pi$
$318$	−13.2010	−	22.8648i	−0.740276	−	1.28220i
$319$	−7.08531	−	7.08531i	−0.396701	−	0.396701i
$320$	−1.61069	+	1.55103i	−0.0900403	+	0.0867050i
$321$	−7.86098	+	4.53854i	−0.438757	+	0.253317i
$322$	−9.05217	+	9.05217i	−0.504457	+	0.504457i
$323$	−14.2293	+	14.2293i	−0.791737	+	0.791737i
$324$	2.76260	+	4.78497i	0.153478	+	0.265831i
$325$	1.67590	+	1.05382i	0.0929621	+	0.0584557i
$326$	0.520426	+	0.300468i	0.0288237	+	0.0166414i
$327$	−5.81238			−0.321425
$328$	−5.24826	−	3.03009i	−0.289787	−	0.167308i
$329$	−15.3050	−	8.83634i	−0.843791	−	0.487163i
$330$	34.6965	+	0.654749i	1.90998	+	0.0360427i
$331$	−2.13031	−	0.570816i	−0.117093	−	0.0313749i	0.199797	−	0.979837i	$-0.435972\pi$
$331$	−2.13031	−	0.570816i	−0.117093	−	0.0313749i	−0.316889	+	0.948462i	$0.602638\pi$
$332$	−1.42009	−	1.42009i	−0.0779375	−	0.0779375i
$333$	−27.6976	−	19.7840i	−1.51782	−	1.08416i
$334$			16.2080i			0.886862i
$335$	4.09032	−	6.78566i	0.223478	−	0.370740i
$336$	−4.46452	−	2.57759i	−0.243559	−	0.140619i
$337$	−20.7233	+	5.55278i	−1.12887	+	0.302479i	−0.774467	−	0.632614i	$-0.781982\pi$
$337$	−20.7233	+	5.55278i	−1.12887	+	0.302479i	−0.354401	+	0.935093i	$0.615315\pi$
$338$	6.42162	−	11.1226i	0.349290	−	0.604988i
$339$	34.8245	+	34.8245i	1.89141	+	1.89141i
$340$	−5.75063	−	5.97185i	−0.311872	−	0.323869i
$341$	−19.8754	+	19.8754i	−1.07631	+	1.07631i
$342$	−29.3361	−	7.86059i	−1.58632	−	0.425052i
$343$	13.5626	+	13.5626i	0.732310	+	0.732310i
$344$	8.65292			0.466534
$345$	−40.8779	−	24.6407i	−2.20079	−	1.32661i
$346$	−3.45090	−	12.8789i	−0.185521	−	0.692376i
$347$	−15.3997			−0.826699			−0.413349	−	0.910572i	$-0.635641\pi$
$347$	−15.3997			−0.826699			−0.413349	+	0.910572i	$0.635641\pi$
$348$	−4.80629	+	2.77491i	−0.257644	+	0.148751i
$349$	−10.8175	+	6.24552i	−0.579050	+	0.334315i	−0.760756	−	0.649038i	$-0.775172\pi$
$349$	−10.8175	+	6.24552i	−0.579050	+	0.334315i	0.181706	+	0.983353i	$0.441838\pi$
$350$	−5.97769	−	6.44677i	−0.319521	−	0.344595i
$351$	−2.91056	+	0.779883i	−0.155354	+	0.0416271i
$352$	−4.58424	−	2.64671i	−0.244341	−	0.141070i
$353$	11.9913	−	6.92318i	0.638232	−	0.368484i	−0.145701	−	0.989329i	$-0.546544\pi$
$353$	11.9913	−	6.92318i	0.638232	−	0.368484i	0.783933	+	0.620845i	$0.213210\pi$
$354$	−8.49153	−	14.7078i	−0.451320	−	0.781709i
$355$	−1.31772	−	5.31711i	−0.0699371	−	0.282203i
$356$	−0.323271	+	0.323271i	−0.0171333	+	0.0171333i
$357$	9.55676	−	16.5528i	0.505797	−	0.876067i
$358$	7.59321	+	2.03459i	0.401313	+	0.107532i
$359$		−	25.9408i		−	1.36910i	−0.728964	−	0.684552i	$-0.759998\pi$
$359$		−	25.9408i		−	1.36910i	0.728964	−	0.684552i	$-0.240002\pi$
$360$	3.46593	−	12.0229i	0.182670	−	0.633661i
$361$	9.05673	−	5.22891i	0.476670	−	0.275206i
$362$	−2.56143			−0.134626
$363$	12.9153	+	48.2006i	0.677879	+	2.52988i
$364$	0.492283	−	0.492283i	0.0258026	−	0.0258026i
$365$	−0.463360	+	24.5544i	−0.0242533	+	1.28524i
$366$	1.20447	−	2.08621i	0.0629589	−	0.109048i
$367$	1.20114	+	4.48271i	0.0626990	+	0.233996i	0.990163	−	0.139916i	$-0.0446831\pi$
$367$	1.20114	+	4.48271i	0.0626990	+	0.233996i	−0.927464	+	0.373911i	$0.878016\pi$
$368$	3.64029	+	6.30516i	0.189763	+	0.328679i
$369$	33.9112			1.76535
$370$	1.98254	+	13.4562i	0.103067	+	0.699555i
$371$	−15.8342			−0.822073
$372$	7.78405	+	13.4824i	0.403584	+	0.699029i
$373$	3.75148	+	14.0007i	0.194244	+	0.724929i	0.992461	+	0.122559i	$0.0391101\pi$
$373$	3.75148	+	14.0007i	0.194244	+	0.724929i	−0.798217	+	0.602370i	$0.794223\pi$
$374$	9.81303	−	16.9967i	0.507420	−	0.878877i
$375$	17.9693	−	27.4148i	0.927932	−	1.41570i
$376$	−7.10699	+	7.10699i	−0.366515	+	0.366515i
$377$	−0.193982	−	0.723951i	−0.00999058	−	0.0372854i
$378$	13.3816			0.688274
$379$	−3.28199	+	1.89486i	−0.168585	+	0.0973324i	−0.581918	−	0.813247i	$-0.697698\pi$
$379$	−3.28199	+	1.89486i	−0.168585	+	0.0973324i	0.413334	+	0.910580i	$0.364364\pi$
$380$	5.86875	+	10.6229i	0.301061	+	0.544945i
$381$			9.43123i			0.483176i
$382$	4.41182	+	1.18214i	0.225728	+	0.0604838i
$383$	−15.6875	+	27.1715i	−0.801592	+	1.38840i	0.116976	+	0.993135i	$0.462680\pi$
$383$	−15.6875	+	27.1715i	−0.801592	+	1.38840i	−0.918568	+	0.395263i	$0.870653\pi$
$384$	−2.07313	+	2.07313i	−0.105794	+	0.105794i
$385$	10.7444	−	17.8246i	0.547587	−	0.908424i
$386$	8.77836	+	15.2046i	0.446807	+	0.773892i
$387$	−41.9326	+	24.2098i	−2.13156	+	1.23065i
$388$	9.32202	+	5.38207i	0.473254	+	0.273233i
$389$	10.3766	−	2.78041i	0.526116	−	0.140972i	0.0140217	−	0.999902i	$-0.495537\pi$
$389$	10.3766	−	2.78041i	0.526116	−	0.140972i	0.512094	+	0.858929i	$0.328870\pi$
$390$	2.22306	+	1.34003i	0.112569	+	0.0678552i
$391$	−23.3772	+	13.4968i	−1.18224	+	0.682565i
$392$	3.38465	−	1.95413i	0.170951	−	0.0986983i
$393$	−16.1443			−0.814371
$394$	0.114684	+	0.428008i	0.00577772	+	0.0215627i
$395$	14.8719	−	24.6718i	0.748284	−	1.24137i
$396$	29.6207			1.48850
$397$	1.98688	+	1.98688i	0.0997189	+	0.0997189i	0.755206	−	0.655487i	$-0.227537\pi$
$397$	1.98688	+	1.98688i	0.0997189	+	0.0997189i	−0.655487	+	0.755206i	$0.727537\pi$
$398$	−26.0921	−	6.99135i	−1.30788	−	0.350445i
$399$	−19.7847	+	19.7847i	−0.990473	+	0.990473i
$400$	−4.42136	+	2.33485i	−0.221068	+	0.116743i
$401$	−1.17240	−	1.17240i	−0.0585467	−	0.0585467i	0.677227	−	0.735774i	$-0.263181\pi$
$401$	−1.17240	−	1.17240i	−0.0585467	−	0.0585467i	−0.735774	+	0.677227i	$0.763181\pi$
$402$	5.19426	−	8.99672i	0.259066	−	0.448716i
$403$	−2.03079	+	0.544149i	−0.101161	+	0.0271060i
$404$	−1.07259	−	0.619258i	−0.0533631	−	0.0308092i
$405$	2.97191	+	11.9920i	0.147675	+	0.595885i
$406$			3.32843i			0.165187i
$407$	−29.3083	+	13.3333i	−1.45276	+	0.660906i
$408$	−7.68641	−	7.68641i	−0.380534	−	0.380534i
$409$	30.9004	+	8.27974i	1.52793	+	0.409407i	0.922342	−	0.386373i	$-0.126272\pi$
$409$	30.9004	+	8.27974i	1.52793	+	0.409407i	0.605585	+	0.795780i	$0.292939\pi$
$410$	−9.39948	−	9.76105i	−0.464207	−	0.482064i
$411$	−52.5309	−	30.3288i	−2.59116	−	1.49601i
$412$	13.5844	+	7.84296i	0.669256	+	0.386395i
$413$	−10.1853			−0.501188
$414$	−35.2821	−	20.3702i	−1.73402	−	1.00114i
$415$	−2.17158	−	3.93074i	−0.106599	−	0.192953i
$416$	−0.197969	−	0.342893i	−0.00970624	−	0.0168117i
$417$	46.0566	−	46.0566i	2.25540	−	2.25540i
$418$	−20.3152	+	20.3152i	−0.993650	+	0.993650i
$419$	−3.92076	+	2.26365i	−0.191542	+	0.110587i	−0.592704	−	0.805420i	$-0.701940\pi$
$419$	−3.92076	+	2.26365i	−0.191542	+	0.110587i	0.401162	+	0.916007i	$0.368606\pi$
$420$	−7.99582	−	8.30339i	−0.390156	−	0.405164i
$421$	−16.3796	−	16.3796i	−0.798291	−	0.798291i	0.184535	−	0.982826i	$-0.440922\pi$
$421$	−16.3796	−	16.3796i	−0.798291	−	0.798291i	−0.982826	+	0.184535i	$0.940922\pi$
$422$	13.8177	+	23.9329i	0.672634	+	1.16504i
$423$	14.5564	−	54.3254i	0.707759	−	2.64139i
$424$	−2.33073	+	8.69839i	−0.113190	+	0.422431i
$425$	−8.65678	−	16.3928i	−0.419915	−	0.795168i
$426$	−1.85897	−	6.93777i	−0.0900673	−	0.336136i
$427$	−0.722366	−	1.25117i	−0.0349577	−	0.0605486i
$428$	2.99053	+	0.801309i	0.144553	+	0.0387328i
$429$	−1.59038	+	5.93540i	−0.0767845	+	0.286564i
$430$	18.5914	+	5.35949i	0.896558	+	0.258458i
$431$	7.19885	−	1.92893i	0.346757	−	0.0929131i	−0.0812373	−	0.996695i	$-0.525887\pi$
$431$	7.19885	−	1.92893i	0.346757	−	0.0929131i	0.427994	+	0.903782i	$0.359220\pi$
$432$	1.96971	−	7.35105i	0.0947676	−	0.353678i
$433$	4.98607	+	4.98607i	0.239615	+	0.239615i	0.816691	−	0.577075i	$-0.195806\pi$
$433$	4.98607	+	4.98607i	0.239615	+	0.239615i	−0.577075	+	0.816691i	$0.695806\pi$
$434$	9.33675			0.448178
$435$	−12.0454	+	2.98516i	−0.577533	+	0.143127i
$436$	1.40184	+	1.40184i	0.0671357	+	0.0671357i
$437$	38.1689	−	10.2273i	1.82587	−	0.489239i
$438$			32.2006i			1.53860i
$439$	−0.561343	−	2.09496i	−0.0267914	−	0.0999871i	0.951235	−	0.308466i	$-0.0998155\pi$
$439$	−0.561343	−	2.09496i	−0.0267914	−	0.0999871i	−0.978027	+	0.208479i	$0.933149\pi$
$440$	−8.21023	−	8.52606i	−0.391407	−	0.406464i
$441$	−10.9348	+	18.9397i	−0.520705	+	0.901888i
$442$	1.27132	−	0.733997i	0.0604705	−	0.0349127i
$443$	15.0759	−	15.0759i	0.716279	−	0.716279i	−0.251562	−	0.967841i	$-0.580944\pi$
$443$	15.0759	−	15.0759i	0.716279	−	0.716279i	0.967841	+	0.251562i	$0.0809442\pi$
$444$	2.93185	+	17.5911i	0.139140	+	0.834837i
$445$	−0.894801	+	0.494342i	−0.0424176	+	0.0234341i
$446$	7.20282	−	26.8813i	0.341064	−	1.27287i
$447$	22.6467	−	6.06816i	1.07115	−	0.287014i
$448$	0.455091	+	1.69842i	0.0215010	+	0.0802429i
$449$	29.8192	−	7.99003i	1.40725	−	0.377073i	0.526310	−	0.850293i	$-0.323575\pi$
$449$	29.8192	−	7.99003i	1.40725	−	0.377073i	0.880944	+	0.473220i	$0.156908\pi$
$450$	14.8936	−	23.6853i	0.702090	−	1.11653i
$451$	16.0395	−	27.7813i	0.755271	−	1.30817i
$452$		−	16.7980i		−	0.790112i
$453$	10.8468	−	40.4808i	0.509626	−	1.90195i
$454$			17.2343i			0.808847i
$455$	1.36262	−	0.752792i	0.0638805	−	0.0352914i
$456$	7.95632	+	13.7808i	0.372589	+	0.645343i
$457$	−5.96166	−	3.44196i	−0.278875	−	0.161008i	0.354039	−	0.935231i	$-0.384808\pi$
$457$	−5.96166	−	3.44196i	−0.278875	−	0.161008i	−0.632914	+	0.774222i	$0.718141\pi$
$458$		−	8.04277i		−	0.375814i
$459$	27.2550	+	7.30295i	1.27215	+	0.340873i
$460$	3.91610	+	15.8018i	0.182589	+	0.736764i
$461$	18.2684	+	4.89500i	0.850843	+	0.227983i	0.657786	−	0.753205i	$-0.271493\pi$
$461$	18.2684	+	4.89500i	0.850843	+	0.227983i	0.193057	+	0.981188i	$0.438160\pi$
$462$	13.6443	−	23.6326i	0.634789	−	1.09949i
$463$	−8.21257	+	14.2246i	−0.381670	+	0.661073i	−0.991301	−	0.131613i	$-0.957984\pi$
$463$	−8.21257	+	14.2246i	−0.381670	+	0.661073i	0.609631	+	0.792686i	$0.291318\pi$
$464$	1.82844	+	0.489930i	0.0848833	+	0.0227444i
$465$	8.37382	+	33.7892i	0.388326	+	1.56694i
$466$	−20.5668	−	5.51085i	−0.952738	−	0.255285i
$467$		−	15.6616i		−	0.724732i	−0.932036	−	0.362366i	$-0.881969\pi$
$467$		−	15.6616i		−	0.724732i	0.932036	−	0.362366i	$-0.118031\pi$
$468$	1.91874	+	1.10779i	0.0886939	+	0.0512075i
$469$	−3.11518	−	5.39566i	−0.143846	−	0.249148i
$470$	−19.6718	+	10.8679i	−0.907394	+	0.501299i
$471$			23.6346i			1.08903i
$472$	−1.49924	+	5.59523i	−0.0690080	+	0.257541i
$473$			45.8036i			2.10605i
$474$	18.8856	−	32.7109i	0.867446	−	1.50246i
$475$	6.02975	+	26.4592i	0.276664	+	1.21403i
$476$	−6.29713	+	1.68731i	−0.288628	+	0.0773377i
$477$	−13.0422	−	48.6741i	−0.597160	−	2.22863i
$478$	−9.22091	+	2.47074i	−0.421755	+	0.113009i
$479$	1.58757	−	5.92489i	0.0725379	−	0.270715i	−0.920126	−	0.391623i	$-0.871914\pi$
$479$	1.58757	−	5.92489i	0.0725379	−	0.270715i	0.992664	+	0.120908i	$0.0385805\pi$
$480$	−5.73834	+	3.17021i	−0.261918	+	0.144699i
$481$	−2.39716	−	0.232411i	−0.109301	−	0.0105970i
$482$	2.83295	−	2.83295i	0.129038	−	0.129038i
$483$	−32.5042	+	18.7663i	−1.47899	+	0.853898i
$484$	8.51015	−	14.7400i	0.386825	−	0.670000i
$485$	16.6955	+	17.3377i	0.758102	+	0.787264i
$486$	−1.71649	−	6.40605i	−0.0778618	−	0.290584i
$487$			41.9951i			1.90298i	0.307679	+	0.951490i	$0.400448\pi$
$487$			41.9951i			1.90298i	−0.307679	+	0.951490i	$0.599552\pi$
$488$	−0.793650	+	0.212658i	−0.0359269	+	0.00962657i
$489$	1.24582	+	1.24582i	0.0563379	+	0.0563379i
$490$	8.48252	−	2.10218i	0.383201	−	0.0949669i
$491$	−1.23433			−0.0557047			−0.0278524	−	0.999612i	$-0.508867\pi$
$491$	−1.23433			−0.0557047			−0.0278524	+	0.999612i	$0.508867\pi$
$492$	−12.5635	−	12.5635i	−0.566408	−	0.566408i
$493$	−1.81648	+	6.77920i	−0.0818101	+	0.305320i
$494$	−2.07573	+	0.556191i	−0.0933917	+	0.0250242i
$495$	63.6422	+	18.3466i	2.86050	+	0.824619i
$496$	1.37433	−	5.12906i	0.0617091	−	0.230301i
$497$	−4.16083	−	1.11489i	−0.186639	−	0.0500097i
$498$	−2.94403	−	5.09921i	−0.131925	−	0.228501i
$499$	9.97949	+	37.2439i	0.446743	+	1.66727i	0.711293	+	0.702896i	$0.248110\pi$
$499$	9.97949	+	37.2439i	0.446743	+	1.66727i	−0.264550	+	0.964372i	$0.585223\pi$
$500$	−10.9458	+	2.27807i	−0.489511	+	0.101878i
$501$	−12.2989	+	45.9002i	−0.549476	+	2.05067i
$502$	2.48678	−	9.28080i	0.110991	−	0.414222i
$503$	12.3990	+	21.4757i	0.552844	+	0.957553i	0.998068	+	0.0621341i	$0.0197906\pi$
$503$	12.3990	+	21.4757i	0.552844	+	0.957553i	−0.445224	+	0.895419i	$0.646876\pi$
$504$	−6.95738	−	6.95738i	−0.309906	−	0.309906i
$505$	−1.92097	−	1.99486i	−0.0854820	−	0.0887703i
$506$	−33.3759	+	19.2696i	−1.48374	+	0.856637i
$507$	26.6257	−	26.6257i	1.18249	−	1.18249i
$508$	2.27463	−	2.27463i	0.100920	−	0.100920i
$509$	6.82884	+	11.8279i	0.302683	+	0.524263i	0.976743	−	0.214414i	$-0.0687843\pi$
$509$	6.82884	+	11.8279i	0.302683	+	0.524263i	−0.674060	+	0.738677i	$0.735451\pi$
$510$	−11.7540	−	21.2757i	−0.520474	−	0.942102i
$511$	16.7245	+	9.65592i	0.739850	+	0.427153i
$512$	1.00000			0.0441942
$513$	−35.7714	−	20.6527i	−1.57935	−	0.911837i
$514$	−4.89445	−	2.82581i	−0.215885	−	0.124641i
$515$	24.3293	+	25.2651i	1.07208	+	1.11332i
$516$	24.5047	+	6.56600i	1.07876	+	0.289052i
$517$	−37.6203	−	37.6203i	−1.65454	−	1.65454i
$518$	10.0158	+	3.75224i	0.440067	+	0.164864i
$519$		−	39.0911i		−	1.71591i
$520$	−0.212968	−	0.859349i	−0.00933928	−	0.0376849i
$521$	5.66705	+	3.27187i	0.248278	+	0.143343i	0.618976	−	0.785410i	$-0.287548\pi$
$521$	5.66705	+	3.27187i	0.248278	+	0.143343i	−0.370697	+	0.928754i	$0.620881\pi$
$522$	−10.2315	+	2.74153i	−0.447821	+	0.119993i
$523$	−18.1226	+	31.3893i	−0.792446	+	1.37256i	0.132002	+	0.991249i	$0.457859\pi$
$523$	−18.1226	+	31.3893i	−0.792446	+	1.37256i	−0.924448	+	0.381308i	$0.875474\pi$
$524$	3.89369	+	3.89369i	0.170097	+	0.170097i
$525$	−12.0366	−	22.7929i	−0.525320	−	0.994765i
$526$	4.98208	−	4.98208i	0.217229	−	0.217229i
$527$	19.0167	+	5.09550i	0.828379	+	0.221963i
$528$	−10.9740	−	10.9740i	−0.477580	−	0.477580i
$529$	30.0068			1.30464
$530$	−10.3954	+	17.2455i	−0.451547	+	0.749097i
$531$	−8.38936	−	31.3095i	−0.364067	−	1.35872i
$532$	9.54338			0.413758
$533$	2.07799	−	1.19973i	0.0900077	−	0.0519659i
$534$	−1.16079	+	0.670184i	−0.0502324	+	0.0290017i
$535$	5.92904	+	3.57396i	0.256335	+	0.154516i
$536$	−3.42259	+	0.917081i	−0.147834	+	0.0396119i
$537$	19.9597	+	11.5237i	0.861325	+	0.497286i
$538$	17.4777	−	10.0908i	0.753519	−	0.435044i
$539$	10.3440	+	17.9164i	0.445548	+	0.771712i
$540$	8.78519	−	14.5743i	0.378054	−	0.627176i
$541$	−16.4032	+	16.4032i	−0.705230	+	0.705230i	−0.965528	−	0.260298i	$-0.916179\pi$
$541$	−16.4032	+	16.4032i	−0.705230	+	0.705230i	0.260298	+	0.965528i	$0.416179\pi$
$542$	5.27948	−	9.14432i	0.226773	−	0.392782i
$543$	−7.25385	−	1.94366i	−0.311293	−	0.0834106i
$544$			3.70763i			0.158963i
$545$	2.14367	+	3.88022i	0.0918247	+	0.166210i
$546$	1.76767	−	1.02057i	0.0756495	−	0.0436762i
$547$	−4.82213			−0.206179			−0.103090	−	0.994672i	$-0.532873\pi$
$547$	−4.82213			−0.206179			−0.103090	+	0.994672i	$0.532873\pi$
$548$	5.35474	+	19.9842i	0.228743	+	0.853682i
$549$	3.25109	−	3.25109i	0.138753	−	0.138753i
$550$	−12.3594	−	23.4041i	−0.527005	−	0.997956i
$551$	5.13698	−	8.89751i	0.218843	−	0.379047i
$552$	5.52464	+	20.6182i	0.235144	+	0.877570i
$553$	−11.3264	−	19.6179i	−0.481647	−	0.834237i
$554$	−22.3728			−0.950529
$555$	−4.59638	+	39.6117i	−0.195105	+	1.68142i
$556$	−22.2159			−0.942165
$557$	0.215707	+	0.373616i	0.00913981	+	0.0158306i	0.870559	−	0.492064i	$-0.163757\pi$
$557$	0.215707	+	0.373616i	0.00913981	+	0.0158306i	−0.861419	+	0.507894i	$0.830424\pi$
$558$	7.69039	+	28.7009i	0.325560	+	1.21501i
$559$	−1.71301	+	2.96702i	−0.0724527	+	0.125492i
$560$	−0.0741820	+	3.93106i	−0.00313476	+	0.166118i
$561$	40.6874	−	40.6874i	1.71782	−	1.71782i
$562$	−3.22972	−	12.0535i	−0.136237	−	0.508445i
$563$	−6.79207			−0.286252			−0.143126	−	0.989704i	$-0.545715\pi$
$563$	−6.79207			−0.286252			−0.143126	+	0.989704i	$0.545715\pi$
$564$	−25.5196	+	14.7337i	−1.07457	+	0.620402i
$565$	10.4044	−	36.0917i	0.437718	−	1.51839i
$566$			27.0858i			1.13850i
$567$	9.38413	+	2.51447i	0.394096	+	0.105598i
$568$	−1.22491	+	2.12161i	−0.0513961	+	0.0890206i
$569$	−1.81640	+	1.81640i	−0.0761474	+	0.0761474i	−0.744155	−	0.668007i	$-0.767147\pi$
$569$	−1.81640	+	1.81640i	−0.0761474	+	0.0761474i	0.668007	+	0.744155i	$0.267147\pi$
$570$	8.55914	+	34.5370i	0.358503	+	1.44659i
$571$	11.8321	+	20.4938i	0.495159	+	0.857641i	0.999984	−	0.00558071i	$-0.00177641\pi$
$571$	11.8321	+	20.4938i	0.495159	+	0.857641i	−0.504825	+	0.863222i	$0.668443\pi$
$572$	1.81508	−	1.04793i	0.0758921	−	0.0438163i
$573$	11.5970	+	6.69555i	0.484473	+	0.279711i
$574$	−10.2927	+	2.75793i	−0.429610	+	0.115114i
$575$	−1.37341	+	36.3770i	−0.0572751	+	1.51702i
$576$	−4.84607	+	2.79788i	−0.201919	+	0.116578i
$577$	−17.0150	+	9.82363i	−0.708344	+	0.408963i	−0.810448	−	0.585811i	$-0.800776\pi$
$577$	−17.0150	+	9.82363i	−0.708344	+	0.408963i	0.102103	+	0.994774i	$0.467443\pi$
$578$	3.25345			0.135326
$579$	13.3224	+	49.7198i	0.553659	+	2.06628i
$580$	3.62509	+	2.18516i	0.150523	+	0.0907338i
$581$	−3.53128			−0.146502
$582$	22.3155	+	22.3155i	0.925007	+	0.925007i
$583$	−46.0442	−	12.3375i	−1.90696	−	0.510968i
$584$	7.76616	−	7.76616i	0.321366	−	0.321366i
$585$	3.43641	+	3.56860i	0.142078	+	0.147543i
$586$	−15.3366	−	15.3366i	−0.633548	−	0.633548i
$587$	11.3896	−	19.7273i	0.470098	−	0.814234i	−0.529317	−	0.848424i	$-0.677552\pi$
$587$	11.3896	−	19.7273i	0.470098	−	0.814234i	0.999415	+	0.0341902i	$0.0108852\pi$
$588$	11.0680	−	2.96566i	0.456436	−	0.122302i
$589$	−24.9589	−	14.4100i	−1.02841	−	0.593754i
$590$	−6.68682	+	11.0931i	−0.275292	+	0.456698i
$591$			1.29912i			0.0534388i
$592$	3.53553	−	4.94975i	0.145310	−	0.203433i
$593$	7.46742	+	7.46742i	0.306650	+	0.306650i	0.843609	−	0.536958i	$-0.180427\pi$
$593$	7.46742	+	7.46742i	0.306650	+	0.306650i	−0.536958	+	0.843609i	$0.680427\pi$
$594$	38.9122	+	10.4265i	1.59659	+	0.427804i
$595$	−14.5749	−	0.275040i	−0.597514	−	0.0112755i
$596$	−6.92547	−	3.99842i	−0.283678	−	0.163782i
$597$	−68.5863	−	39.5983i	−2.80705	−	1.62065i
$598$	−2.88266			−0.117881
$599$	−0.384513	−	0.221999i	−0.0157108	−	0.00907062i	0.492124	−	0.870525i	$-0.336221\pi$
$599$	−0.384513	−	0.221999i	−0.0157108	−	0.00907062i	−0.507835	+	0.861454i	$0.669554\pi$
$600$	−14.2928	+	3.25717i	−0.583502	+	0.132974i
$601$	12.2726	+	21.2568i	0.500609	+	0.867081i	1.00000		0.000703826i	$0.000224035\pi$
$601$	12.2726	+	21.2568i	0.500609	+	0.867081i	−0.499390	+	0.866377i	$0.666443\pi$
$602$	10.7585	−	10.7585i	0.438482	−	0.438482i
$603$	14.0202	−	14.0202i	0.570948	−	0.570948i
$604$	−12.3792	+	7.14715i	−0.503703	+	0.290813i
$605$	27.4144	−	26.3989i	1.11455	−	1.07327i
$606$	−2.56761	−	2.56761i	−0.104302	−	0.104302i
$607$	−1.89323	−	3.27917i	−0.0768439	−	0.133098i	0.825043	−	0.565070i	$-0.191151\pi$
$607$	−1.89323	−	3.27917i	−0.0768439	−	0.133098i	−0.901887	+	0.431973i	$0.857818\pi$
$608$	1.40474	−	5.24257i	0.0569698	−	0.212614i
$609$	−2.52568	+	9.42595i	−0.102346	+	0.381959i
$610$	−1.83693	−	0.0346643i	−0.0743752	−	0.00140351i
$611$	−1.02997	−	3.84390i	−0.0416681	−	0.155507i
$612$	−10.3735	−	17.9674i	−0.419324	−	0.726290i
$613$	5.00768	+	1.34180i	0.202258	+	0.0541949i	0.358526	−	0.933520i	$-0.383280\pi$
$613$	5.00768	+	1.34180i	0.202258	+	0.0541949i	−0.156267	+	0.987715i	$0.549946\pi$
$614$	3.48080	−	12.9905i	0.140474	−	0.524255i
$615$	−19.2120	−	34.7753i	−0.774702	−	1.40228i
$616$	−8.99046	+	2.40899i	−0.362236	+	0.0970609i
$617$	−8.27183	+	30.8709i	−0.333011	+	1.24281i	0.572998	+	0.819557i	$0.305780\pi$
$617$	−8.27183	+	30.8709i	−0.333011	+	1.24281i	−0.906009	+	0.423258i	$0.860886\pi$
$618$	32.5190	+	32.5190i	1.30811	+	1.30811i
$619$	−16.9452			−0.681086			−0.340543	−	0.940229i	$-0.610611\pi$
$619$	−16.9452			−0.681086			−0.340543	+	0.940229i	$0.610611\pi$
$620$	6.12970	−	10.1689i	0.246175	−	0.408393i
$621$	−39.1793	−	39.1793i	−1.57221	−	1.57221i
$622$	−7.78427	+	2.08579i	−0.312121	+	0.0836325i
$623$			0.803866i			0.0322062i
$624$	−0.300446	−	1.12128i	−0.0120274	−	0.0448871i
$625$	−24.9288	−	1.88506i	−0.997153	−	0.0754023i
$626$	−0.733158	+	1.26987i	−0.0293029	+	0.0507541i
$627$	−72.9473	+	42.1161i	−2.91323	+	1.68196i
$628$	5.70023	−	5.70023i	0.227464	−	0.227464i
$629$	18.3519	+	13.1085i	0.731736	+	0.522669i
$630$	−10.6391	−	19.2577i	−0.423873	−	0.767246i
$631$	4.85936	−	18.1354i	0.193448	−	0.721958i	−0.799215	−	0.601045i	$-0.794751\pi$
$631$	4.85936	−	18.1354i	0.193448	−	0.721958i	0.992663	−	0.120913i	$-0.0385822\pi$
$632$	−12.4441	+	3.33439i	−0.495000	+	0.132635i
$633$	20.9702	+	78.2619i	0.833492	+	3.11063i
$634$	−12.0009	+	3.21563i	−0.476616	+	0.127709i
$635$	6.29608	−	3.47834i	0.249852	−	0.138034i
$636$	−13.2010	+	22.8648i	−0.523454	+	0.906649i
$637$			1.54743i			0.0613113i
$638$	−2.59340	+	9.67871i	−0.102674	+	0.383184i
$639$		−	13.7086i		−	0.542303i
$640$	2.14857	+	0.619385i	0.0849298	+	0.0244833i
$641$	−21.3524	−	36.9834i	−0.843367	−	1.46076i	−0.887031	−	0.461709i	$-0.847236\pi$
$641$	−21.3524	−	36.9834i	−0.843367	−	1.46076i	0.0436641	−	0.999046i	$-0.486097\pi$
$642$	7.86098	+	4.53854i	0.310248	+	0.179122i
$643$		−	40.4138i		−	1.59376i	−0.604135	−	0.796882i	$-0.706481\pi$
$643$		−	40.4138i		−	1.59376i	0.604135	−	0.796882i	$-0.293519\pi$
$644$	12.3655	+	3.31332i	0.487269	+	0.130563i
$645$	48.5831	+	29.2854i	1.91296	+	1.15311i
$646$	19.4375	+	5.20827i	0.764759	+	0.204917i
$647$	−13.5544	+	23.4770i	−0.532880	+	0.922975i	0.466383	+	0.884583i	$0.345557\pi$
$647$	−13.5544	+	23.4770i	−0.532880	+	0.922975i	−0.999263	+	0.0383921i	$0.987776\pi$
$648$	2.76260	−	4.78497i	0.108525	−	0.187971i
$649$	−29.6179	−	7.93609i	−1.16260	−	0.311519i
$650$	0.0746899	−	1.97828i	0.00292958	−	0.0775946i
$651$	26.4412	+	7.08490i	1.03631	+	0.277679i
$652$		−	0.600936i		−	0.0235345i
$653$	3.69595	+	2.13386i	0.144634	+	0.0835044i	0.570571	−	0.821249i	$-0.306722\pi$
$653$	3.69595	+	2.13386i	0.144634	+	0.0835044i	−0.425937	+	0.904753i	$0.640055\pi$
$654$	2.90619	+	5.03367i	0.113641	+	0.196832i
$655$	5.95418	+	10.7776i	0.232649	+	0.421115i
$656$			6.06017i			0.236610i
$657$	−15.9066	+	59.3641i	−0.620574	+	2.31601i
$658$			17.6727i			0.688953i
$659$	2.86699	−	4.96578i	0.111682	−	0.193439i	−0.804766	−	0.593592i	$-0.797709\pi$
$659$	2.86699	−	4.96578i	0.111682	−	0.193439i	0.916449	+	0.400152i	$0.131043\pi$
$660$	−16.7812	−	30.3755i	−0.653209	−	1.18236i
$661$	26.4406	−	7.08473i	1.02842	−	0.275564i	0.295112	−	0.955463i	$-0.404643\pi$
$661$	26.4406	−	7.08473i	1.02842	−	0.275564i	0.733306	+	0.679899i	$0.237976\pi$
$662$	0.570816	+	2.13031i	0.0221854	+	0.0827970i
$663$	4.15729	−	1.11394i	0.161456	−	0.0432619i
$664$	−0.519789	+	1.93988i	−0.0201717	+	0.0752818i
$665$	20.5046	+	5.91103i	0.795136	+	0.229220i
$666$	−3.28464	+	33.8788i	−0.127277	+	1.31278i
$667$	9.74514	−	9.74514i	0.377333	−	0.377333i
$668$	14.0365	−	8.10399i	0.543090	−	0.313553i
$669$	40.7961	−	70.6609i	1.57727	−	2.73191i
$670$	−7.92172	−	0.149489i	−0.306043	−	0.00577525i
$671$	−1.12569	−	4.20112i	−0.0434567	−	0.162183i
$672$			5.15518i			0.198865i
$673$	9.38545	−	2.51482i	0.361783	−	0.0969393i	−0.0733487	−	0.997306i	$-0.523369\pi$
$673$	9.38545	−	2.51482i	0.361783	−	0.0969393i	0.435131	+	0.900367i	$0.356702\pi$
$674$	15.1705	+	15.1705i	0.584345	+	0.584345i
$675$	27.9027	−	25.8724i	1.07397	−	0.995830i
$676$	−12.8432			−0.493970
$677$	15.7154	+	15.7154i	0.603991	+	0.603991i	0.941369	−	0.337378i	$-0.109540\pi$
$677$	15.7154	+	15.7154i	0.603991	+	0.603991i	−0.337378	+	0.941369i	$0.609540\pi$
$678$	12.7466	−	47.5711i	0.489532	−	1.82696i
$679$	18.2821	−	4.89866i	0.701601	−	0.187993i
$680$	−2.29645	+	7.96612i	−0.0880650	+	0.305487i
$681$	−13.0777	+	48.8068i	−0.501140	+	1.87028i
$682$	27.1503	+	7.27489i	1.03964	+	0.278570i
$683$	20.7880	+	36.0059i	0.795430	+	1.37773i	0.922566	+	0.385840i	$0.126088\pi$
$683$	20.7880	+	36.0059i	0.795430	+	1.37773i	−0.127135	+	0.991885i	$0.540578\pi$
$684$	7.86059	+	29.3361i	0.300557	+	1.12169i
$685$	−0.872849	+	46.2541i	−0.0333498	+	1.76728i
$686$	4.96425	−	18.5268i	0.189536	−	0.707357i
$687$	6.10300	−	22.7767i	0.232844	−	0.868986i
$688$	−4.32646	−	7.49365i	−0.164945	−	0.285693i
$689$	−2.52120	−	2.52120i	−0.0960502	−	0.0960502i
$690$	−0.900542	+	47.7216i	−0.0342831	+	1.81673i
$691$	37.3098	−	21.5408i	1.41933	−	0.819451i	0.423091	−	0.906087i	$-0.360945\pi$
$691$	37.3098	−	21.5408i	1.41933	−	0.819451i	0.996240	+	0.0866365i	$0.0276119\pi$
$692$	−9.42803	+	9.42803i	−0.358400	+	0.358400i
$693$	36.8283	−	36.8283i	1.39899	−	1.39899i
$694$	7.69985	+	13.3365i	0.292282	+	0.506248i
$695$	−47.7325	−	13.7602i	−1.81060	−	0.521955i
$696$	4.80629	+	2.77491i	0.182182	+	0.105183i
$697$	−22.4689			−0.851070
$698$	10.8175	+	6.24552i	0.409450	+	0.236396i
$699$	−54.0624	−	31.2129i	−2.04483	−	1.18058i
$700$	−2.59423	+	8.40022i	−0.0980525	+	0.317498i
$701$	23.0701	+	6.18163i	0.871347	+	0.233477i	0.666670	−	0.745353i	$-0.267719\pi$
$701$	23.0701	+	6.18163i	0.871347	+	0.233477i	0.204677	+	0.978830i	$0.434386\pi$
$702$	2.13068	+	2.13068i	0.0804173	+	0.0804173i
$703$	−20.9829	−	25.4884i	−0.791384	−	0.961313i
$704$			5.29342i			0.199503i
$705$	−63.9564	+	15.8500i	−2.40874	+	0.596947i
$706$	−11.9913	−	6.92318i	−0.451298	−	0.260557i
$707$	−2.10352	+	0.563637i	−0.0791111	+	0.0211978i
$708$	−8.49153	+	14.7078i	−0.319131	+	0.552752i
$709$	−21.5173	−	21.5173i	−0.808098	−	0.808098i	0.176248	−	0.984346i	$-0.443604\pi$
$709$	−21.5173	−	21.5173i	−0.808098	−	0.808098i	−0.984346	+	0.176248i	$0.943604\pi$
$710$	−3.94590	+	3.79973i	−0.148087	+	0.142601i
$711$	50.9757	−	50.9757i	1.91174	−	1.91174i
$712$	0.441597	+	0.118325i	0.0165495	+	0.00443443i
$713$	−27.3366	−	27.3366i	−1.02376	−	1.02376i
$714$	−19.1135			−0.715306
$715$	4.54889	−	1.12733i	0.170119	−	0.0421598i
$716$	−2.03459	−	7.59321i	−0.0760363	−	0.283771i
$717$	−27.9880			−1.04523
$718$	−22.4654	+	12.9704i	−0.838402	+	0.484052i
$719$	18.6677	−	10.7778i	0.696188	−	0.401944i	−0.109738	−	0.993961i	$-0.535001\pi$
$719$	18.6677	−	10.7778i	0.696188	−	0.401944i	0.805926	+	0.592016i	$0.201668\pi$
$720$	−12.1451	+	3.00986i	−0.452621	+	0.112171i
$721$	26.6413	−	7.13852i	0.992174	−	0.265852i
$722$	−9.05673	−	5.22891i	−0.337057	−	0.194600i
$723$	10.1725	−	5.87309i	0.378319	−	0.218423i
$724$	1.28072	+	2.21827i	0.0475974	+	0.0824412i
$725$	6.43530	+	6.94030i	0.239001	+	0.257756i
$726$	35.2853	−	35.2853i	1.30956	−	1.30956i
$727$	13.8287	−	23.9521i	0.512879	−	0.888333i	−0.487009	−	0.873397i	$-0.661912\pi$
$727$	13.8287	−	23.9521i	0.512879	−	0.888333i	0.999888	−	0.0149359i	$-0.00475442\pi$
$728$	−0.672471	−	0.180188i	−0.0249234	−	0.00667821i
$729$		−	36.0197i		−	1.33406i
$730$	21.4964	−	11.8759i	0.795618	−	0.439547i
$731$	27.7837	−	16.0409i	1.02762	−	0.593295i
$732$	−2.40895			−0.0890373
$733$	−11.3795	−	42.4690i	−0.420312	−	1.56863i	−0.773951	−	0.633245i	$-0.781723\pi$
$733$	−11.3795	−	42.4690i	−0.420312	−	1.56863i	0.353639	−	0.935382i	$-0.384944\pi$
$734$	3.28157	−	3.28157i	0.121125	−	0.121125i
$735$	25.6172	+	0.483416i	0.944906	+	0.0178311i
$736$	3.64029	−	6.30516i	0.134183	−	0.232411i
$737$	−4.85450	−	18.1172i	−0.178818	−	0.667357i
$738$	−16.9556	−	29.3680i	−0.624145	−	1.08105i
$739$	33.8211			1.24413			0.622064	−	0.782967i	$-0.286294\pi$
$739$	33.8211			1.24413			0.622064	+	0.782967i	$0.286294\pi$
$740$	10.6621	−	8.44503i	0.391948	−	0.310446i
$741$	−6.30043			−0.231452
$742$	7.91712	+	13.7129i	0.290647	+	0.503415i
$743$	−0.0771256	−	0.287837i	−0.00282946	−	0.0105597i	0.964497	−	0.264095i	$-0.0850733\pi$
$743$	−0.0771256	−	0.287837i	−0.00282946	−	0.0105597i	−0.967326	+	0.253535i	$0.918407\pi$
$744$	7.78405	−	13.4824i	0.285377	−	0.494288i
$745$	−12.4033	−	12.8804i	−0.454422	−	0.471903i
$746$	10.2492	−	10.2492i	0.375251	−	0.375251i
$747$	−2.90861	−	10.8551i	−0.106420	−	0.397166i
$748$	−19.6261			−0.717600
$749$	4.71451	−	2.72192i	0.172264	−	0.0994569i
$750$	−32.7266	−	1.85449i	−1.19501	−	0.0677163i
$751$			42.9846i			1.56853i	0.620426	+	0.784265i	$0.286960\pi$
$751$			42.9846i			1.56853i	−0.620426	+	0.784265i	$0.713040\pi$
$752$	9.70832	+	2.60134i	0.354026	+	0.0948610i
$753$	14.0849	−	24.3958i	0.513282	−	0.889031i
$754$	−0.529969	+	0.529969i	−0.0193003	+	0.0193003i
$755$	−31.0245	+	7.68866i	−1.12910	+	0.279819i
$756$	−6.69079	−	11.5888i	−0.243342	−	0.421480i
$757$	9.93843	−	5.73795i	0.361218	−	0.208549i	−0.308397	−	0.951258i	$-0.599792\pi$
$757$	9.93843	−	5.73795i	0.361218	−	0.208549i	0.669615	+	0.742708i	$0.266459\pi$
$758$	3.28199	+	1.89486i	0.119207	+	0.0688244i
$759$	−109.141	+	29.2442i	−3.96157	+	1.06150i
$760$	6.26536	−	10.3940i	0.227268	−	0.377028i
$761$	−43.7719	+	25.2717i	−1.58673	+	0.916100i	−0.592890	+	0.805283i	$0.702013\pi$
$761$	−43.7719	+	25.2717i	−1.58673	+	0.916100i	−0.993841	+	0.110817i	$0.964653\pi$
$762$	8.16768	−	4.71561i	0.295884	−	0.170829i
$763$	3.48589			0.126198
$764$	−1.18214	−	4.41182i	−0.0427685	−	0.159614i
$765$	−11.1595	−	45.0295i	−0.403471	−	1.62805i
$766$	31.3749			1.13362
$767$	−1.62176	−	1.62176i	−0.0585584	−	0.0585584i
$768$	2.83195	+	0.758819i	0.102189	+	0.0273815i
$769$	20.6641	−	20.6641i	0.745167	−	0.745167i	−0.228400	−	0.973567i	$-0.573349\pi$
$769$	20.6641	−	20.6641i	0.745167	−	0.745167i	0.973567	+	0.228400i	$0.0733495\pi$
$770$	−20.8087	−	0.392676i	−0.749895	−	0.0141511i
$771$	−11.7166	−	11.7166i	−0.421961	−	0.421961i
$772$	8.77836	−	15.2046i	0.315940	−	0.547224i
$773$	−41.3185	+	11.0713i	−1.48612	+	0.398205i	−0.908426	−	0.418046i	$-0.862715\pi$
$773$	−41.3185	+	11.0713i	−1.48612	+	0.398205i	−0.577697	+	0.816252i	$0.696048\pi$
$774$	41.9326	+	24.2098i	1.50724	+	0.870204i
$775$	19.4686	−	18.0520i	0.699332	−	0.648447i
$776$		−	10.7641i		−	0.386410i
$777$	25.5168	+	18.2263i	0.915412	+	0.653865i
$778$	−7.59621	−	7.59621i	−0.272337	−	0.272337i
$779$	31.7709	+	8.51297i	1.13831	+	0.305009i
$780$	0.0489741	−	2.59524i	0.00175355	−	0.0929244i
$781$	−11.2305	−	6.48396i	−0.401861	−	0.232014i
$782$	23.3772	+	13.4968i	0.835968	+	0.482646i
$783$	−14.4060			−0.514828
$784$	−3.38465	−	1.95413i	−0.120880	−	0.0697903i
$785$	15.7780	−	8.71671i	0.563140	−	0.311113i
$786$	8.07214	+	13.9814i	0.287924	+	0.498698i
$787$	24.7659	−	24.7659i	0.882811	−	0.882811i	−0.111009	−	0.993819i	$-0.535408\pi$
$787$	24.7659	−	24.7659i	0.882811	−	0.882811i	0.993819	+	0.111009i	$0.0354082\pi$
$788$	0.313324	−	0.313324i	0.0111617	−	0.0111617i
$789$	17.8895	−	10.3285i	0.636883	−	0.367704i
$790$	−28.8023	−	0.543521i	−1.02474	−	0.0193376i
$791$	−20.8855	−	20.8855i	−0.742602	−	0.742602i
$792$	−14.8103	−	25.6523i	−0.526262	−	0.911513i
$793$	0.0841995	−	0.314237i	0.00299001	−	0.0111589i
$794$	0.727250	−	2.71413i	0.0258091	−	0.0963210i
$795$	−42.5255	+	40.9502i	−1.50822	+	1.45235i
$796$	6.99135	+	26.0921i	0.247802	+	0.924809i
$797$	−0.0523506	−	0.0906740i	−0.00185435	−	0.00321184i	0.865097	−	0.501605i	$-0.167257\pi$
$797$	−0.0523506	−	0.0906740i	−0.00185435	−	0.00321184i	−0.866951	+	0.498393i	$0.833924\pi$
$798$	27.0264	+	7.24170i	0.956724	+	0.256353i
$799$	−9.64481	+	35.9949i	−0.341209	+	1.27341i
$800$	4.23272	+	2.66159i	0.149649	+	0.0941013i
$801$	−2.47107	+	0.662120i	−0.0873108	+	0.0233949i
$802$	−0.429127	+	1.60152i	−0.0151530	+	0.0565518i
$803$	41.1096	+	41.1096i	1.45073	+	1.45073i
$804$	−10.3885			−0.366375
$805$	24.5159	+	14.7779i	0.864073	+	0.520853i
$806$	1.48664	+	1.48664i	0.0523647	+	0.0523647i
$807$	57.1532	−	15.3141i	2.01189	−	0.539084i
$808$			1.23852i			0.0435708i
$809$	−0.335132	−	1.25073i	−0.0117826	−	0.0439732i	0.959784	−	0.280739i	$-0.0905794\pi$
$809$	−0.335132	−	1.25073i	−0.0117826	−	0.0439732i	−0.971567	+	0.236765i	$0.923913\pi$
$810$	8.89938	−	8.56973i	0.312692	−	0.301110i
$811$	12.1384	−	21.0244i	0.426238	−	0.738267i	−0.570297	−	0.821439i	$-0.693172\pi$
$811$	12.1384	−	21.0244i	0.426238	−	0.738267i	0.996535	+	0.0831721i	$0.0265051\pi$
$812$	2.88251	−	1.66422i	0.101156	−	0.0584025i
$813$	21.8901	−	21.8901i	0.767719	−	0.767719i
$814$	26.2011	+	18.7151i	0.918348	+	0.655963i
$815$	0.372211	−	1.29115i	0.0130380	−	0.0452271i
$816$	−2.81342	+	10.4998i	−0.0984895	+	0.367568i
$817$	−45.3635	+	12.1551i	−1.58707	+	0.425254i
$818$	−8.27974	−	30.9004i	−0.289494	−	1.08041i
$819$	3.76298	−	1.00829i	0.131489	−	0.0352324i
$820$	−3.75358	+	13.0207i	−0.131081	+	0.454703i
$821$	−3.54806	+	6.14541i	−0.123828	+	0.214476i	−0.921274	−	0.388914i	$-0.872850\pi$
$821$	−3.54806	+	6.14541i	−0.123828	+	0.214476i	0.797446	+	0.603390i	$0.206184\pi$
$822$			60.6575i			2.11567i
$823$	3.26815	−	12.1969i	0.113921	−	0.425158i	−0.885283	−	0.465052i	$-0.846036\pi$
$823$	3.26815	−	12.1969i	0.113921	−	0.425158i	0.999204	+	0.0398946i	$0.0127022\pi$
$824$		−	15.6859i		−	0.546445i
$825$	−17.2416	−	75.6579i	−0.600275	−	2.63407i
$826$	5.09267	+	8.82077i	0.177197	+	0.306914i
$827$	24.8917	+	14.3712i	0.865570	+	0.499737i	0.865873	−	0.500263i	$-0.166763\pi$
$827$	24.8917	+	14.3712i	0.865570	+	0.499737i	−0.000303909		1.00000i	$0.500097\pi$
$828$			40.7403i			1.41582i
$829$	−9.88765	−	2.64939i	−0.343412	−	0.0920171i	0.0829907	−	0.996550i	$-0.473553\pi$
$829$	−9.88765	−	2.64939i	−0.343412	−	0.0920171i	−0.426403	+	0.904533i	$0.640219\pi$
$830$	−2.31833	+	3.84602i	−0.0804706	+	0.133497i
$831$	−63.3587	−	16.9769i	−2.19789	−	0.588923i
$832$	−0.197969	+	0.342893i	−0.00686335	+	0.0118877i
$833$	7.24519	−	12.5490i	0.251031	−	0.434798i
$834$	−62.9144	−	16.8579i	−2.17855	−	0.583740i
$835$	35.1780	−	8.71800i	1.21738	−	0.301699i
$836$	27.7511	+	7.43589i	0.959792	+	0.257176i
$837$			40.4110i			1.39681i
$838$	3.92076	+	2.26365i	0.135440	+	0.0781965i
$839$	7.06834	+	12.2427i	0.244026	+	0.422666i	0.961857	−	0.273551i	$-0.0881983\pi$
$839$	7.06834	+	12.2427i	0.244026	+	0.422666i	−0.717831	+	0.696217i	$0.754865\pi$
$840$	−3.19304	+	11.0763i	−0.110170	+	0.382168i
$841$			25.4168i			0.876440i
$842$	−5.99534	+	22.3749i	−0.206613	+	0.771090i
$843$		−	36.5856i		−	1.26008i
$844$	13.8177	−	23.9329i	0.475624	−	0.823805i
$845$	−27.5946	−	7.95491i	−0.949283	−	0.273657i
$846$	−54.3254	+	14.5564i	−1.86775	+	0.500461i
$847$	−7.74578	−	28.9076i	−0.266148	−	0.993279i
$848$	8.69839	−	2.33073i	0.298704	−	0.0800375i
$849$	−20.5532	+	76.7056i	−0.705384	+	2.63253i
$850$	−9.86819	+	15.6934i	−0.338476	+	0.538279i
$851$	−18.3386	−	40.3106i	−0.628639	−	1.38183i
$852$	−5.07880	+	5.07880i	−0.173997	+	0.173997i
$853$	−29.7522	+	17.1775i	−1.01870	+	0.588145i	−0.913726	−	0.406330i	$-0.866808\pi$
$853$	−29.7522	+	17.1775i	−1.01870	+	0.588145i	−0.104971	+	0.994475i	$0.533475\pi$
$854$	−0.722366	+	1.25117i	−0.0247189	+	0.0428143i
$855$	−1.28131	+	67.8995i	−0.0438200	+	2.32211i
$856$	−0.801309	−	2.99053i	−0.0273882	−	0.102214i
$857$			42.9846i			1.46833i	0.678973	+	0.734164i	$0.262426\pi$
$857$			42.9846i			1.46833i	−0.678973	+	0.734164i	$0.737574\pi$
$858$	5.93540	−	1.59038i	0.202631	−	0.0542948i
$859$	2.89013	+	2.89013i	0.0986099	+	0.0986099i	0.754691	−	0.656081i	$-0.227787\pi$
$859$	2.89013	+	2.89013i	0.0986099	+	0.0986099i	−0.656081	+	0.754691i	$0.727787\pi$
$860$	−4.65426	−	18.7804i	−0.158709	−	0.640406i
$861$	−31.2413			−1.06470
$862$	−5.26993	−	5.26993i	−0.179494	−	0.179494i
$863$	−3.90885	+	14.5880i	−0.133059	+	0.496582i	−0.999998	−	0.00183104i	$-0.999417\pi$
$863$	−3.90885	+	14.5880i	−0.133059	+	0.496582i	0.866939	+	0.498413i	$0.166084\pi$
$864$	−7.35105	+	1.96971i	−0.250088	+	0.0670108i
$865$	−26.0964	+	14.4172i	−0.887304	+	0.490200i
$866$	1.82503	−	6.81110i	0.0620170	−	0.231451i
$867$	9.21362	+	2.46878i	0.312911	+	0.0838442i
$868$	−4.66837	−	8.08586i	−0.158455	−	0.274452i
$869$	−17.6503	−	65.8718i	−0.598746	−	2.23455i
$870$	8.60792	+	8.93905i	0.291836	+	0.303062i
$871$	0.363108	−	1.35514i	0.0123034	−	0.0459171i
$872$	0.513107	−	1.91494i	0.0173760	−	0.0648481i
$873$	30.1167	+	52.1637i	1.01930	+	1.76547i
$874$	−27.9416	−	27.9416i	−0.945138	−	0.945138i
$875$	−10.7768	+	16.4416i	−0.364324	+	0.555829i
$876$	27.8865	−	16.1003i	0.942198	−	0.543978i
$877$	−22.1626	+	22.1626i	−0.748378	+	0.748378i	−0.974175	−	0.225796i	$-0.927502\pi$
$877$	−22.1626	+	22.1626i	−0.748378	+	0.748378i	0.225796	+	0.974175i	$0.427502\pi$
$878$	−1.53362	+	1.53362i	−0.0517571	+	0.0517571i
$879$	−31.7947	−	55.0701i	−1.07241	−	1.85747i
$880$	−3.27867	+	11.3733i	−0.110524	+	0.383394i
$881$	−24.2620	−	14.0077i	−0.817407	−	0.471930i	0.0321147	−	0.999484i	$-0.489776\pi$
$881$	−24.2620	−	14.0077i	−0.817407	−	0.471930i	−0.849521	+	0.527554i	$0.823109\pi$
$882$	21.8696			0.736389
$883$	−19.6051	−	11.3190i	−0.659764	−	0.380915i	0.132423	−	0.991193i	$-0.457724\pi$
$883$	−19.6051	−	11.3190i	−0.659764	−	0.380915i	−0.792187	+	0.610278i	$0.791058\pi$
$884$	−1.27132	−	0.733997i	−0.0427591	−	0.0246870i
$885$	−27.3544	+	26.3412i	−0.919509	+	0.885448i
$886$	−20.5941	−	5.51818i	−0.691873	−	0.185387i
$887$	31.2178	+	31.2178i	1.04819	+	1.04819i	0.998778	+	0.0494116i	$0.0157346\pi$
$887$	31.2178	+	31.2178i	1.04819	+	1.04819i	0.0494116	+	0.998778i	$0.484265\pi$
$888$	13.7684	−	11.3346i	0.462038	−	0.380365i
$889$		−	5.65624i		−	0.189704i
$890$	0.875513	+	0.527749i	0.0293473	+	0.0176902i
$891$	25.3288	+	14.6236i	0.848548	+	0.489909i
$892$	−26.8813	+	7.20282i	−0.900052	+	0.241168i
$893$	27.2754	−	47.2423i	0.912736	−	1.58090i
$894$	−16.5785	−	16.5785i	−0.554469	−	0.554469i
$895$	0.331648	−	17.5747i	0.0110858	−	0.587459i
$896$	1.24333	−	1.24333i	0.0415368	−	0.0415368i
$897$	−8.16355	−	2.18742i	−0.272573	−	0.0730357i
$898$	−21.8292	−	21.8292i	−0.728449	−	0.728449i
$899$	−10.0515			−0.335237
$900$	−27.9589	−	1.05558i	−0.931962	−	0.0351861i
$901$	8.64148	+	32.2505i	0.287890	+	1.07442i
$902$	−32.0790			−1.06811
$903$	38.6311	−	22.3037i	1.28556	−	0.742220i
$904$	−14.5475	+	8.39900i	−0.483843	+	0.279347i
$905$	1.37775	+	5.55936i	0.0457980	+	0.184799i
$906$	−40.4808	+	10.8468i	−1.34488	+	0.360360i
$907$	−21.0297	−	12.1415i	−0.698280	−	0.403152i	0.108427	−	0.994104i	$-0.465419\pi$
$907$	−21.0297	−	12.1415i	−0.698280	−	0.403152i	−0.806706	+	0.590952i	$0.798752\pi$
$908$	14.9254	−	8.61717i	0.495316	−	0.285971i
$909$	−3.46521	−	6.00193i	−0.114934	−	0.199071i
$910$	−1.33325	−	0.803665i	−0.0441967	−	0.0266412i
$911$	7.00677	−	7.00677i	0.232145	−	0.232145i	−0.581443	−	0.813587i	$-0.697512\pi$
$911$	7.00677	−	7.00677i	0.232145	−	0.232145i	0.813587	+	0.581443i	$0.197512\pi$
$912$	7.95632	−	13.7808i	0.263460	−	0.456326i
$913$	−10.2686	−	2.75146i	−0.339841	−	0.0910600i
$914$			6.88393i			0.227700i
$915$	−5.17580	−	1.49207i	−0.171107	−	0.0493262i
$916$	−6.96524	+	4.02138i	−0.230138	+	0.132870i
$917$	9.68230			0.319738
$918$	−7.30295	−	27.2550i	−0.241033	−	0.899549i
$919$	−7.04314	+	7.04314i	−0.232332	+	0.232332i	−0.813665	−	0.581334i	$-0.802531\pi$
$919$	−7.04314	+	7.04314i	−0.232332	+	0.232332i	0.581334	+	0.813665i	$0.302531\pi$
$920$	11.7267	−	11.2924i	0.386619	−	0.372298i
$921$	19.7149	−	34.1473i	0.649629	−	1.12519i
$922$	−4.89500	−	18.2684i	−0.161208	−	0.601637i
$923$	−0.484989	−	0.840025i	−0.0159636	−	0.0276498i
$924$	−27.2885			−0.897727
$925$	28.1391	−	11.5408i	0.925209	−	0.379459i
$926$	16.4251			0.539764
$927$	43.8873	+	76.0150i	1.44145	+	2.49666i
$928$	−0.489930	−	1.82844i	−0.0160827	−	0.0600216i
$929$	1.73828	−	3.01078i	0.0570310	−	0.0987806i	−0.836100	−	0.548577i	$-0.815170\pi$
$929$	1.73828	−	3.01078i	0.0570310	−	0.0987806i	0.893131	+	0.449796i	$0.148503\pi$
$930$	25.0754	−	24.1465i	0.822254	−	0.791796i
$931$	−14.9992	+	14.9992i	−0.491579	+	0.491579i
$932$	5.51085	+	20.5668i	0.180514	+	0.673687i
$933$	−23.6274			−0.773526
$934$	−13.5633	+	7.83079i	−0.443806	+	0.256231i
$935$	−42.1680	−	12.1561i	−1.37904	−	0.397547i
$936$		−	2.21557i		−	0.0724183i
$937$	−18.0318	−	4.83161i	−0.589074	−	0.157842i	−0.0480439	−	0.998845i	$-0.515299\pi$
$937$	−18.0318	−	4.83161i	−0.589074	−	0.157842i	−0.541030	+	0.841003i	$0.681965\pi$
$938$	−3.11518	+	5.39566i	−0.101714	+	0.176174i
$939$	−3.03987	+	3.03987i	−0.0992023	+	0.0992023i
$940$	19.2478	+	11.6024i	0.627794	+	0.378427i
$941$	26.8917	+	46.5777i	0.876643	+	1.51839i	0.855002	+	0.518624i	$0.173556\pi$
$941$	26.8917	+	46.5777i	0.876643	+	1.51839i	0.0216408	+	0.999766i	$0.493111\pi$
$942$	20.4682	−	11.8173i	0.666890	−	0.385029i
$943$	38.2104	+	22.0608i	1.24430	+	0.718397i
$944$	5.59523	−	1.49924i	0.182109	−	0.0487960i
$945$	−7.19772	−	29.0435i	−0.234142	−	0.944786i
$946$	39.6670	−	22.9018i	1.28969	−	0.744601i
$947$	−19.2168	+	11.0948i	−0.624461	+	0.360533i	−0.778604	−	0.627516i	$-0.784072\pi$
$947$	−19.2168	+	11.0948i	−0.624461	+	0.360533i	0.154143	+	0.988049i	$0.450738\pi$
$948$	−37.7713			−1.22675
$949$	1.12550	+	4.20042i	0.0365353	+	0.136351i
$950$	19.8994	−	18.4515i	0.645623	−	0.598646i
$951$	−36.4260			−1.18119
$952$	4.60982	+	4.60982i	0.149405	+	0.149405i
$953$	−28.6102	−	7.66607i	−0.926774	−	0.248328i	−0.236296	−	0.971681i	$-0.575933\pi$
$953$	−28.6102	−	7.66607i	−0.926774	−	0.248328i	−0.690479	+	0.723353i	$0.742600\pi$
$954$	−35.6319	+	35.6319i	−1.15363	+	1.15363i
$955$	0.192695	−	10.2113i	0.00623547	−	0.330431i
$956$	6.75018	+	6.75018i	0.218316	+	0.218316i
$957$	−14.6888	+	25.4417i	−0.474821	+	0.822414i
$958$	−5.92489	+	1.58757i	−0.191424	+	0.0512920i
$959$	31.5047	+	18.1892i	1.01734	+	0.587361i
$960$	5.61465	+	3.38445i	0.181212	+	0.109233i
$961$		−	2.80400i		−	0.0904516i
$962$	0.997305	+	2.19221i	0.0321544	+	0.0706796i
$963$	12.2503	+	12.2503i	0.394761	+	0.394761i
$964$	−3.86989	−	1.03693i	−0.124641	−	0.0333974i
$965$	28.2784	−	27.2309i	0.910314	−	0.876594i
$966$	32.5042	+	18.7663i	1.04581	+	0.603797i
$967$	46.1225	+	26.6289i	1.48320	+	0.856327i	0.999818	−	0.0190824i	$-0.00607447\pi$
$967$	46.1225	+	26.6289i	1.48320	+	0.856327i	0.483383	+	0.875409i	$0.339408\pi$
$968$	−17.0203			−0.547053
$969$	51.0940	+	29.4991i	1.64137	+	0.947648i
$970$	6.66715	−	23.1275i	0.214069	−	0.742580i
$971$	−19.1752	−	33.2124i	−0.615361	−	1.06584i	−0.990321	−	0.138796i	$-0.955677\pi$
$971$	−19.1752	−	33.2124i	−0.615361	−	1.06584i	0.374960	−	0.927041i	$-0.377657\pi$
$972$	−4.68955	+	4.68955i	−0.150417	+	0.150417i
$973$	−27.6218	+	27.6218i	−0.885513	+	0.885513i
$974$	36.3688	−	20.9976i	1.16533	−	0.672805i
$975$	1.71268	−	5.54572i	0.0548495	−	0.177605i
$976$	0.580992	+	0.580992i	0.0185971	+	0.0185971i
$977$	−11.3284	−	19.6214i	−0.362428	−	0.627744i	0.625932	−	0.779878i	$-0.284719\pi$
$977$	−11.3284	−	19.6214i	−0.362428	−	0.627744i	−0.988360	+	0.152134i	$0.951386\pi$
$978$	0.456001	−	1.70182i	0.0145813	−	0.0544182i
$979$	−0.626346	+	2.33756i	−0.0200181	+	0.0747086i
$980$	−6.06180	−	6.29498i	−0.193637	−	0.201086i
$981$	2.87122	+	10.7155i	0.0916711	+	0.342121i
$982$	0.617167	+	1.06896i	0.0196946	+	0.0341120i
$983$	−32.3781	−	8.67568i	−1.03270	−	0.276711i	−0.297615	−	0.954686i	$-0.596191\pi$
$983$	−32.3781	−	8.67568i	−1.03270	−	0.276711i	−0.735085	+	0.677975i	$0.762858\pi$
$984$	−4.59857	+	17.1621i	−0.146597	+	0.547108i
$985$	0.867267	−	0.479131i	0.0276334	−	0.0152664i
$986$	6.77920	−	1.81648i	0.215894	−	0.0578485i
$987$	−13.4104	+	50.0482i	−0.426857	+	1.59305i
$988$	1.51954	+	1.51954i	0.0483431	+	0.0483431i
$989$	−62.9983			−2.00323
$990$	−15.9325	−	64.2890i	−0.506367	−	2.04324i
$991$	22.5979	+	22.5979i	0.717847	+	0.717847i	0.968164	−	0.250317i	$-0.0805347\pi$
$991$	22.5979	+	22.5979i	0.717847	+	0.717847i	−0.250317	+	0.968164i	$0.580535\pi$
$992$	−5.12906	+	1.37433i	−0.162848	+	0.0436349i
$993$			6.46609i			0.205195i
$994$	1.11489	+	4.16083i	0.0353622	+	0.131973i
$995$	−1.13962	+	60.3910i	−0.0361285	+	1.91452i
$996$	−2.94403	+	5.09921i	−0.0932852	+	0.161575i
$997$	−26.1333	+	15.0881i	−0.827651	+	0.477845i	−0.853048	−	0.521833i	$-0.825249\pi$
$997$	−26.1333	+	15.0881i	−0.827651	+	0.477845i	0.0253965	+	0.999677i	$0.491915\pi$
$998$	27.2645	−	27.2645i	0.863041	−	0.863041i
$999$	−16.2403	+	43.3498i	−0.513821	+	1.37153i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.q.e.103.1	yes	16
5.2	odd	4		370.2.r.e.177.2	yes	16
37.23	odd	12		370.2.r.e.23.2	yes	16
185.97	even	12	inner	370.2.q.e.97.1	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.e.97.1	✓	16	185.97	even	12	inner
370.2.q.e.103.1	yes	16	1.1	even	1	trivial
370.2.r.e.23.2	yes	16	37.23	odd	12
370.2.r.e.177.2	yes	16	5.2	odd	4

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.758819 - 2.83195i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61069 + 1.55103i) q^{5} +(-2.07313 + 2.07313i) q^{6} +(0.455091 + 1.69842i) q^{7} +1.00000 q^{8} +(-4.84607 + 2.79788i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.758819 - 2.83195i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-1.61069 + 1.55103i) q^{5} +(-2.07313 + 2.07313i) q^{6} +(0.455091 + 1.69842i) q^{7} +1.00000 q^{8} +(-4.84607 + 2.79788i) q^{9} +(2.14857 + 0.619385i) q^{10} +5.29342i q^{11} +(2.83195 + 0.758819i) q^{12} +(-0.197969 + 0.342893i) q^{13} +(1.24333 - 1.24333i) q^{14} +(5.61465 + 3.38445i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.21090 - 1.85382i) q^{17} +(4.84607 + 2.79788i) q^{18} +(-5.24257 + 1.40474i) q^{19} +(-0.537883 - 2.17041i) q^{20} +(4.46452 - 2.57759i) q^{21} +(4.58424 - 2.64671i) q^{22} -7.28057 q^{23} +(-0.758819 - 2.83195i) q^{24} +(0.188640 - 4.99644i) q^{25} +0.395938 q^{26} +(5.38134 + 5.38134i) q^{27} +(-1.69842 - 0.455091i) q^{28} +(-1.33851 + 1.33851i) q^{29} +(0.123691 - 6.55465i) q^{30} +(3.75473 + 3.75473i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(14.9907 - 4.01675i) q^{33} +(-3.21090 - 1.85382i) q^{34} +(-3.36731 - 2.02977i) q^{35} -5.59575i q^{36} +(2.51884 + 5.53674i) q^{37} +(3.83783 + 3.83783i) q^{38} +(1.12128 + 0.300446i) q^{39} +(-1.61069 + 1.55103i) q^{40} +(-5.24826 - 3.03009i) q^{41} +(-4.46452 - 2.57759i) q^{42} +8.65292 q^{43} +(-4.58424 - 2.64671i) q^{44} +(3.46593 - 12.0229i) q^{45} +(3.64029 + 6.30516i) q^{46} +(-7.10699 + 7.10699i) q^{47} +(-2.07313 + 2.07313i) q^{48} +(3.38465 - 1.95413i) q^{49} +(-4.42136 + 2.33485i) q^{50} +(-7.68641 - 7.68641i) q^{51} +(-0.197969 - 0.342893i) q^{52} +(-2.33073 + 8.69839i) q^{53} +(1.96971 - 7.35105i) q^{54} +(-8.21023 - 8.52606i) q^{55} +(0.455091 + 1.69842i) q^{56} +(7.95632 + 13.7808i) q^{57} +(1.82844 + 0.489930i) q^{58} +(-1.49924 + 5.59523i) q^{59} +(-5.73834 + 3.17021i) q^{60} +(-0.793650 + 0.212658i) q^{61} +(1.37433 - 5.12906i) q^{62} +(-6.95738 - 6.95738i) q^{63} +1.00000 q^{64} +(-0.212968 - 0.859349i) q^{65} +(-10.9740 - 10.9740i) q^{66} +(-3.42259 + 0.917081i) q^{67} +3.70763i q^{68} +(5.52464 + 20.6182i) q^{69} +(-0.0741820 + 3.93106i) q^{70} +(-1.22491 + 2.12161i) q^{71} +(-4.84607 + 2.79788i) q^{72} +(7.76616 - 7.76616i) q^{73} +(3.53553 - 4.94975i) q^{74} +(-14.2928 + 3.25717i) q^{75} +(1.40474 - 5.24257i) q^{76} +(-8.99046 + 2.40899i) q^{77} +(-0.300446 - 1.12128i) q^{78} +(-12.4441 + 3.33439i) q^{79} +(2.14857 + 0.619385i) q^{80} +(2.76260 - 4.78497i) q^{81} +6.06017i q^{82} +(-0.519789 + 1.93988i) q^{83} +5.15518i q^{84} +(-2.29645 + 7.96612i) q^{85} +(-4.32646 - 7.49365i) q^{86} +(4.80629 + 2.77491i) q^{87} +5.29342i q^{88} +(0.441597 + 0.118325i) q^{89} +(-12.1451 + 3.00986i) q^{90} +(-0.672471 - 0.180188i) q^{91} +(3.64029 - 6.30516i) q^{92} +(7.78405 - 13.4824i) q^{93} +(9.70832 + 2.60134i) q^{94} +(6.26536 - 10.3940i) q^{95} +(2.83195 + 0.758819i) q^{96} -10.7641i q^{97} +(-3.38465 - 1.95413i) q^{98} +(-14.8103 - 25.6523i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9}+O(q^{10}) \) 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9	\( 16 q - 8 q^{2} - 8 q^{3} - 8 q^{4} - 4 q^{5} - 8 q^{6} + 16 q^{8} - 24 q^{9} - 4 q^{10} + 16 q^{12} - 4 q^{13} + 8 q^{15} - 8 q^{16} + 24 q^{18} - 24 q^{19} + 8 q^{20} - 12 q^{21} - 8 q^{23} - 8 q^{24} + 32 q^{25} + 8 q^{26} + 16 q^{27} + 16 q^{29} - 4 q^{30} + 24 q^{31} - 8 q^{32} + 12 q^{33} - 20 q^{35} - 4 q^{40} - 36 q^{41} + 12 q^{42} - 16 q^{43} + 4 q^{45} + 4 q^{46} + 32 q^{47} - 8 q^{48} + 24 q^{49} - 16 q^{50} - 16 q^{51} - 4 q^{52} - 48 q^{53} - 8 q^{54} - 24 q^{55} + 20 q^{57} - 8 q^{58} - 8 q^{59} - 4 q^{60} + 8 q^{61} - 12 q^{62} + 16 q^{63} + 16 q^{64} + 24 q^{65} - 24 q^{66} - 8 q^{67} - 8 q^{69} + 28 q^{70} + 4 q^{71} - 24 q^{72} + 48 q^{73} - 36 q^{75} + 24 q^{76} - 60 q^{77} + 20 q^{79} - 4 q^{80} + 16 q^{81} + 24 q^{83} + 8 q^{85} + 8 q^{86} + 12 q^{87} - 8 q^{89} - 8 q^{90} - 8 q^{91} + 4 q^{92} + 36 q^{93} - 28 q^{94} + 28 q^{95} + 16 q^{96} - 24 q^{98} + 8 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 4 * q^5 - 8 * q^6 + 16 * q^8 - 24 * q^9 - 4 * q^10 + 16 * q^12 - 4 * q^13 + 8 * q^15 - 8 * q^16 + 24 * q^18 - 24 * q^19 + 8 * q^20 - 12 * q^21 - 8 * q^23 - 8 * q^24 + 32 * q^25 + 8 * q^26 + 16 * q^27 + 16 * q^29 - 4 * q^30 + 24 * q^31 - 8 * q^32 + 12 * q^33 - 20 * q^35 - 4 * q^40 - 36 * q^41 + 12 * q^42 - 16 * q^43 + 4 * q^45 + 4 * q^46 + 32 * q^47 - 8 * q^48 + 24 * q^49 - 16 * q^50 - 16 * q^51 - 4 * q^52 - 48 * q^53 - 8 * q^54 - 24 * q^55 + 20 * q^57 - 8 * q^58 - 8 * q^59 - 4 * q^60 + 8 * q^61 - 12 * q^62 + 16 * q^63 + 16 * q^64 + 24 * q^65 - 24 * q^66 - 8 * q^67 - 8 * q^69 + 28 * q^70 + 4 * q^71 - 24 * q^72 + 48 * q^73 - 36 * q^75 + 24 * q^76 - 60 * q^77 + 20 * q^79 - 4 * q^80 + 16 * q^81 + 24 * q^83 + 8 * q^85 + 8 * q^86 + 12 * q^87 - 8 * q^89 - 8 * q^90 - 8 * q^91 + 4 * q^92 + 36 * q^93 - 28 * q^94 + 28 * q^95 + 16 * q^96 - 24 * q^98 + 8 * q^99

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