LMFDB - Embedded newform 315.2.bx.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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([2, 3, 4]))

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

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

chi := DirichletCharacter("315.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bx (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			2.4
Character	$\chi$	$=$	315.2
Dual form			315.2.bx.a.158.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.41637 - 0.647465i) q^{2} +(-1.67924 - 0.424464i) q^{3} +(3.68760 + 2.12903i) q^{4} +(-2.17829 - 0.505032i) q^{5} +(3.78283 + 2.11291i) q^{6} +(0.757887 - 2.53488i) q^{7} +(-3.99432 - 3.99432i) q^{8} +(2.63966 + 1.42555i) q^{9} +O(q^{10})$	\(q+(-2.41637 - 0.647465i) q^{2} +(-1.67924 - 0.424464i) q^{3} +(3.68760 + 2.12903i) q^{4} +(-2.17829 - 0.505032i) q^{5} +(3.78283 + 2.11291i) q^{6} +(0.757887 - 2.53488i) q^{7} +(-3.99432 - 3.99432i) q^{8} +(2.63966 + 1.42555i) q^{9} +(4.93657 + 2.63071i) q^{10} -4.55123i q^{11} +(-5.28864 - 5.14040i) q^{12} +(-2.57794 - 0.690757i) q^{13} +(-3.47258 + 5.63450i) q^{14} +(3.44349 + 1.77267i) q^{15} +(2.80751 + 4.86274i) q^{16} +(1.30202 + 0.348875i) q^{17} +(-5.45541 - 5.15375i) q^{18} +(-3.44985 - 1.99177i) q^{19} +(-6.95742 - 6.50001i) q^{20} +(-2.34864 + 3.93496i) q^{21} +(-2.94676 + 10.9975i) q^{22} +(2.11644 + 2.11644i) q^{23} +(5.01195 + 8.40284i) q^{24} +(4.48988 + 2.20021i) q^{25} +(5.78203 + 3.33825i) q^{26} +(-3.82752 - 3.51427i) q^{27} +(8.19162 - 7.73404i) q^{28} +(-4.20021 + 7.27498i) q^{29} +(-7.17301 - 6.51298i) q^{30} +(-0.300325 + 0.520178i) q^{31} +(-0.711483 - 2.65529i) q^{32} +(-1.93183 + 7.64258i) q^{33} +(-2.92028 - 1.68602i) q^{34} +(-2.93109 + 5.13894i) q^{35} +(6.69896 + 10.8768i) q^{36} +(-7.62381 + 2.04279i) q^{37} +(7.04653 + 7.04653i) q^{38} +(4.03577 + 2.25419i) q^{39} +(6.68351 + 10.7180i) q^{40} +(-2.13612 + 1.23329i) q^{41} +(8.22293 - 7.98767i) q^{42} +(3.08519 + 11.5141i) q^{43} +(9.68972 - 16.7831i) q^{44} +(-5.02999 - 4.43837i) q^{45} +(-3.74379 - 6.48443i) q^{46} +(-1.34918 - 0.361511i) q^{47} +(-2.65040 - 9.35737i) q^{48} +(-5.85121 - 3.84230i) q^{49} +(-9.42467 - 8.22358i) q^{50} +(-2.03831 - 1.13850i) q^{51} +(-8.03576 - 8.03576i) q^{52} +(2.42524 - 9.05112i) q^{53} +(6.97334 + 10.9700i) q^{54} +(-2.29852 + 9.91389i) q^{55} +(-13.1523 + 7.09786i) q^{56} +(4.94768 + 4.80900i) q^{57} +(14.8596 - 14.8596i) q^{58} +(-4.14298 + 7.17586i) q^{59} +(8.92412 + 13.8682i) q^{60} +(-2.15596 - 3.73423i) q^{61} +(1.06249 - 1.06249i) q^{62} +(5.61416 - 5.61081i) q^{63} -4.35319i q^{64} +(5.26665 + 2.80661i) q^{65} +(9.61633 - 17.2165i) q^{66} +(-4.57100 + 1.22480i) q^{67} +(4.05855 + 4.05855i) q^{68} +(-2.65565 - 4.45235i) q^{69} +(10.4099 - 10.5198i) q^{70} -13.5042i q^{71} +(-4.84954 - 16.2377i) q^{72} +(-2.89604 - 0.775991i) q^{73} +19.7446 q^{74} +(-6.60566 - 5.60047i) q^{75} +(-8.48111 - 14.6897i) q^{76} +(-11.5368 - 3.44932i) q^{77} +(-8.29241 - 8.05998i) q^{78} +(2.24217 - 1.29451i) q^{79} +(-3.65972 - 12.0103i) q^{80} +(4.93562 + 7.52593i) q^{81} +(5.96017 - 1.59702i) q^{82} +(5.57938 - 1.49499i) q^{83} +(-17.0385 + 9.51022i) q^{84} +(-2.65998 - 1.41751i) q^{85} -29.8199i q^{86} +(10.1411 - 10.4336i) q^{87} +(-18.1790 + 18.1790i) q^{88} +(-3.29726 + 5.71101i) q^{89} +(9.28065 + 13.9815i) q^{90} +(-3.70477 + 6.01125i) q^{91} +(3.29860 + 12.3106i) q^{92} +(0.725113 - 0.746024i) q^{93} +(3.02605 + 1.74709i) q^{94} +(6.50887 + 6.08095i) q^{95} +(0.0676719 + 4.76085i) q^{96} +(-5.79094 + 1.55168i) q^{97} +(11.6510 + 13.0729i) q^{98} +(6.48800 - 12.0137i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 176 q - 6 q^{2} - 2 q^{3} - 24 q^{6} - 2 q^{7}+O(q^{10}) $ 176 * q - 6 * q^2 - 2 * q^3 - 24 * q^6 - 2 * q^7	$ 176 q - 6 q^{2} - 2 q^{3} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 22 q^{12} - 4 q^{13} - 14 q^{15} + 68 q^{16} - 18 q^{17} - 10 q^{18} - 12 q^{20} + 20 q^{21} + 4 q^{22} - 4 q^{25} - 32 q^{27} - 4 q^{28} - 20 q^{30} + 4 q^{31} - 90 q^{32} + 32 q^{33} + 8 q^{36} - 4 q^{37} - 36 q^{40} - 36 q^{41} + 14 q^{42} - 4 q^{43} - 68 q^{45} + 4 q^{46} - 6 q^{47} + 38 q^{48} + 36 q^{50} + 20 q^{51} - 52 q^{52} + 4 q^{55} - 96 q^{56} + 32 q^{57} - 12 q^{58} - 74 q^{60} - 8 q^{61} + 14 q^{63} - 78 q^{65} - 92 q^{66} + 2 q^{67} - 42 q^{70} - 46 q^{72} - 4 q^{73} + 54 q^{75} - 24 q^{76} + 42 q^{77} + 54 q^{78} + 36 q^{80} + 20 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 28 q^{87} + 12 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} + 4 q^{93} - 66 q^{95} - 4 q^{97} + 12 q^{98}+O(q^{100}) $ 176 * q - 6 * q^2 - 2 * q^3 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 22 * q^12 - 4 * q^13 - 14 * q^15 + 68 * q^16 - 18 * q^17 - 10 * q^18 - 12 * q^20 + 20 * q^21 + 4 * q^22 - 4 * q^25 - 32 * q^27 - 4 * q^28 - 20 * q^30 + 4 * q^31 - 90 * q^32 + 32 * q^33 + 8 * q^36 - 4 * q^37 - 36 * q^40 - 36 * q^41 + 14 * q^42 - 4 * q^43 - 68 * q^45 + 4 * q^46 - 6 * q^47 + 38 * q^48 + 36 * q^50 + 20 * q^51 - 52 * q^52 + 4 * q^55 - 96 * q^56 + 32 * q^57 - 12 * q^58 - 74 * q^60 - 8 * q^61 + 14 * q^63 - 78 * q^65 - 92 * q^66 + 2 * q^67 - 42 * q^70 - 46 * q^72 - 4 * q^73 + 54 * q^75 - 24 * q^76 + 42 * q^77 + 54 * q^78 + 36 * q^80 + 20 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 28 * q^87 + 12 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 + 4 * q^93 - 66 * q^95 - 4 * q^97 + 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−2.41637	−	0.647465i	−1.70863	−	0.457827i	−0.733545	−	0.679641i	$-0.762135\pi$
$2$	−2.41637	−	0.647465i	−1.70863	−	0.457827i	−0.975089	+	0.221814i	$0.928802\pi$
$3$	−1.67924	−	0.424464i	−0.969507	−	0.245064i
$3$	−1.67924	−	0.424464i	−0.969507	−	0.245064i
$4$	3.68760	+	2.12903i	1.84380	+	1.06452i
$5$	−2.17829	−	0.505032i	−0.974160	−	0.225857i
$5$	−2.17829	−	0.505032i	−0.974160	−	0.225857i
$6$	3.78283	+	2.11291i	1.54433	+	0.862592i
$7$	0.757887	−	2.53488i	0.286454	−	0.958094i
$7$	0.757887	−	2.53488i	0.286454	−	0.958094i
$8$	−3.99432	−	3.99432i	−1.41220	−	1.41220i
$9$	2.63966	+	1.42555i	0.879887	+	0.475183i
$10$	4.93657	+	2.63071i	1.56108	+	0.831904i
$11$		−	4.55123i		−	1.37225i	−0.727485	−	0.686123i	$-0.759311\pi$
$11$		−	4.55123i		−	1.37225i	0.727485	−	0.686123i	$-0.240689\pi$
$12$	−5.28864	−	5.14040i	−1.52670	−	1.48391i
$13$	−2.57794	−	0.690757i	−0.714992	−	0.191582i	−0.117056	−	0.993125i	$-0.537346\pi$
$13$	−2.57794	−	0.690757i	−0.714992	−	0.191582i	−0.597936	+	0.801544i	$0.704012\pi$
$14$	−3.47258	+	5.63450i	−0.928087	+	1.50588i
$15$	3.44349	+	1.77267i	0.889106	+	0.457702i
$16$	2.80751	+	4.86274i	0.701876	+	1.21569i
$17$	1.30202	+	0.348875i	0.315786	+	0.0846145i	0.413231	−	0.910626i	$-0.364400\pi$
$17$	1.30202	+	0.348875i	0.315786	+	0.0846145i	−0.0974449	+	0.995241i	$0.531067\pi$
$18$	−5.45541	−	5.15375i	−1.28585	−	1.21475i
$19$	−3.44985	−	1.99177i	−0.791451	−	0.456944i	0.0490222	−	0.998798i	$-0.484390\pi$
$19$	−3.44985	−	1.99177i	−0.791451	−	0.456944i	−0.840473	+	0.541853i	$0.817723\pi$
$20$	−6.95742	−	6.50001i	−1.55573	−	1.45345i
$21$	−2.34864	+	3.93496i	−0.512514	+	0.858679i
$22$	−2.94676	+	10.9975i	−0.628252	+	2.34467i
$23$	2.11644	+	2.11644i	0.441308	+	0.441308i	0.892452	−	0.451143i	$-0.148984\pi$
$23$	2.11644	+	2.11644i	0.441308	+	0.441308i	−0.451143	+	0.892452i	$0.648984\pi$
$24$	5.01195	+	8.40284i	1.02306	+	1.71522i
$25$	4.48988	+	2.20021i	0.897977	+	0.440043i
$26$	5.78203	+	3.33825i	1.13395	+	0.654686i
$27$	−3.82752	−	3.51427i	−0.736606	−	0.676322i
$28$	8.19162	−	7.73404i	1.54807	−	1.46160i
$29$	−4.20021	+	7.27498i	−0.779959	+	1.35093i	0.152005	+	0.988380i	$0.451427\pi$
$29$	−4.20021	+	7.27498i	−0.779959	+	1.35093i	−0.931964	+	0.362550i	$0.881906\pi$
$30$	−7.17301	−	6.51298i	−1.30961	−	1.18910i
$31$	−0.300325	+	0.520178i	−0.0539400	+	0.0934268i	−0.891735	−	0.452559i	$-0.850511\pi$
$31$	−0.300325	+	0.520178i	−0.0539400	+	0.0934268i	0.837795	+	0.545985i	$0.183845\pi$
$32$	−0.711483	−	2.65529i	−0.125774	−	0.469393i
$33$	−1.93183	+	7.64258i	−0.336289	+	1.33040i
$34$	−2.92028	−	1.68602i	−0.500823	−	0.289150i
$35$	−2.93109	+	5.13894i	−0.495445	+	0.868639i
$36$	6.69896	+	10.8768i	1.11649	+	1.81280i
$37$	−7.62381	+	2.04279i	−1.25335	+	0.335833i	−0.823629	−	0.567130i	$-0.808054\pi$
$37$	−7.62381	+	2.04279i	−1.25335	+	0.335833i	−0.429718	+	0.902963i	$0.641387\pi$
$38$	7.04653	+	7.04653i	1.14310	+	1.14310i
$39$	4.03577	+	2.25419i	0.646240	+	0.360959i
$40$	6.68351	+	10.7180i	1.05676	+	1.69467i
$41$	−2.13612	+	1.23329i	−0.333605	+	0.192607i	−0.657441	−	0.753506i	$-0.728361\pi$
$41$	−2.13612	+	1.23329i	−0.333605	+	0.192607i	0.323835	+	0.946113i	$0.395028\pi$
$42$	8.22293	−	7.98767i	1.26883	−	1.23252i
$43$	3.08519	+	11.5141i	0.470488	+	1.75588i	0.638023	+	0.770017i	$0.279752\pi$
$43$	3.08519	+	11.5141i	0.470488	+	1.75588i	−0.167535	+	0.985866i	$0.553581\pi$
$44$	9.68972	−	16.7831i	1.46078	−	2.53015i
$45$	−5.02999	−	4.43837i	−0.749827	−	0.661634i
$46$	−3.74379	−	6.48443i	−0.551991	−	0.956077i
$47$	−1.34918	−	0.361511i	−0.196798	−	0.0527318i	0.159074	−	0.987267i	$-0.449149\pi$
$47$	−1.34918	−	0.361511i	−0.196798	−	0.0527318i	−0.355872	+	0.934535i	$0.615816\pi$
$48$	−2.65040	−	9.35737i	−0.382553	−	1.35062i
$49$	−5.85121	−	3.84230i	−0.835888	−	0.548901i
$50$	−9.42467	−	8.22358i	−1.33285	−	1.16299i
$51$	−2.03831	−	1.13850i	−0.285420	−	0.159422i
$52$	−8.03576	−	8.03576i	−1.11436	−	1.11436i
$53$	2.42524	−	9.05112i	0.333132	−	1.24327i	−0.572748	−	0.819732i	$-0.694123\pi$
$53$	2.42524	−	9.05112i	0.333132	−	1.24327i	0.905880	−	0.423535i	$-0.139211\pi$
$54$	6.97334	+	10.9700i	0.948951	+	1.49283i
$55$	−2.29852	+	9.91389i	−0.309932	+	1.33679i
$56$	−13.1523	+	7.09786i	−1.75756	+	0.948492i
$57$	4.94768	+	4.80900i	0.655336	+	0.636967i
$58$	14.8596	−	14.8596i	1.95116	−	1.95116i
$59$	−4.14298	+	7.17586i	−0.539370	+	0.934217i	0.459568	+	0.888143i	$0.348004\pi$
$59$	−4.14298	+	7.17586i	−0.539370	+	0.934217i	−0.998938	+	0.0460741i	$0.985329\pi$
$60$	8.92412	+	13.8682i	1.15210	+	1.79038i
$61$	−2.15596	−	3.73423i	−0.276042	−	0.478119i	0.694355	−	0.719632i	$-0.255690\pi$
$61$	−2.15596	−	3.73423i	−0.276042	−	0.478119i	−0.970398	+	0.241513i	$0.922356\pi$
$62$	1.06249	−	1.06249i	0.134937	−	0.134937i
$63$	5.61416	−	5.61081i	0.707318	−	0.706896i
$64$		−	4.35319i		−	0.544149i
$65$	5.26665	+	2.80661i	0.653247	+	0.348117i
$66$	9.61633	−	17.2165i	1.18369	−	2.11921i
$67$	−4.57100	+	1.22480i	−0.558437	+	0.149633i	−0.526988	−	0.849873i	$-0.676679\pi$
$67$	−4.57100	+	1.22480i	−0.558437	+	0.149633i	−0.0314486	+	0.999505i	$0.510012\pi$
$68$	4.05855	+	4.05855i	0.492171	+	0.492171i
$69$	−2.65565	−	4.45235i	−0.319703	−	0.536000i
$70$	10.4099	−	10.5198i	1.24422	−	1.25736i
$71$		−	13.5042i		−	1.60266i	−0.598225	−	0.801328i	$-0.704127\pi$
$71$		−	13.5042i		−	1.60266i	0.598225	−	0.801328i	$-0.295873\pi$
$72$	−4.84954	−	16.2377i	−0.571524	−	1.91363i
$73$	−2.89604	−	0.775991i	−0.338955	−	0.0908228i	0.0853263	−	0.996353i	$-0.472807\pi$
$73$	−2.89604	−	0.775991i	−0.338955	−	0.0908228i	−0.424282	+	0.905530i	$0.639473\pi$
$74$	19.7446			2.29526
$75$	−6.60566	−	5.60047i	−0.762756	−	0.646686i
$76$	−8.48111	−	14.6897i	−0.972850	−	1.68503i
$77$	−11.5368	−	3.44932i	−1.31474	−	0.393086i
$78$	−8.29241	−	8.05998i	−0.938931	−	0.912612i
$79$	2.24217	−	1.29451i	0.252263	−	0.145644i	−0.368537	−	0.929613i	$-0.620141\pi$
$79$	2.24217	−	1.29451i	0.252263	−	0.145644i	0.620800	+	0.783969i	$0.286808\pi$
$80$	−3.65972	−	12.0103i	−0.409169	−	1.34280i
$81$	4.93562	+	7.52593i	0.548402	+	0.836215i
$82$	5.96017	−	1.59702i	0.658190	−	0.176362i
$83$	5.57938	−	1.49499i	0.612417	−	0.164097i	0.0607388	−	0.998154i	$-0.480654\pi$
$83$	5.57938	−	1.49499i	0.612417	−	0.164097i	0.551678	+	0.834057i	$0.313988\pi$
$84$	−17.0385	+	9.51022i	−1.85905	+	1.03765i
$85$	−2.65998	−	1.41751i	−0.288515	−	0.153751i
$86$		−	29.8199i		−	3.21556i
$87$	10.1411	−	10.4336i	1.08724	−	1.11860i
$88$	−18.1790	+	18.1790i	−1.93789	+	1.93789i
$89$	−3.29726	+	5.71101i	−0.349508	+	0.605366i	−0.986162	−	0.165783i	$-0.946985\pi$
$89$	−3.29726	+	5.71101i	−0.349508	+	0.605366i	0.636654	+	0.771150i	$0.280318\pi$
$90$	9.28065	+	13.9815i	0.978266	+	1.47378i
$91$	−3.70477	+	6.01125i	−0.388366	+	0.630150i
$92$	3.29860	+	12.3106i	0.343903	+	1.28346i
$93$	0.725113	−	0.746024i	0.0751908	−	0.0773591i
$94$	3.02605	+	1.74709i	0.312113	+	0.180199i
$95$	6.50887	+	6.08095i	0.667796	+	0.623892i
$96$	0.0676719	+	4.76085i	0.00690674	+	0.485903i
$97$	−5.79094	+	1.55168i	−0.587981	+	0.157549i	−0.540530	−	0.841325i	$-0.681776\pi$
$97$	−5.79094	+	1.55168i	−0.587981	+	0.157549i	−0.0474505	+	0.998874i	$0.515110\pi$
$98$	11.6510	+	13.0729i	1.17692	+	1.32056i
$99$	6.48800	−	12.0137i	0.652069	−	1.20742i
$100$	11.8725	+	17.6726i	1.18725	+	1.76726i
$101$			14.8525i			1.47788i	0.673772	+	0.738939i	$0.264673\pi$
$101$			14.8525i			1.47788i	−0.673772	+	0.738939i	$0.735327\pi$
$102$	4.18817	+	4.07078i	0.414691	+	0.403067i
$103$	−3.79764	+	3.79764i	−0.374193	+	0.374193i	−0.869002	−	0.494809i	$-0.835238\pi$
$103$	−3.79764	+	3.79764i	−0.374193	+	0.374193i	0.494809	+	0.869002i	$0.335238\pi$
$104$	7.53801	+	13.0562i	0.739162	+	1.28027i
$105$	7.10329	−	7.38534i	0.693210	−	0.720736i
$106$	−11.7206	+	20.3006i	−1.13840	+	1.97177i
$107$	1.88329	+	7.02853i	0.182064	+	0.679474i	0.995240	+	0.0974551i	$0.0310702\pi$
$107$	1.88329	+	7.02853i	0.182064	+	0.679474i	−0.813176	+	0.582019i	$0.802263\pi$
$108$	−6.63232	−	21.1081i	−0.638196	−	2.03113i
$109$	1.55606	−	0.898392i	0.149044	−	0.0860504i	−0.423624	−	0.905838i	$-0.639242\pi$
$109$	1.55606	−	0.898392i	0.149044	−	0.0860504i	0.572667	+	0.819788i	$0.305909\pi$
$110$	11.9730	−	22.4674i	1.14158	−	2.14219i
$111$	13.6693	−	0.194298i	1.29743	−	0.0184420i
$112$	14.4542	−	3.43127i	1.36580	−	0.324225i
$113$	−1.39248	+	5.19681i	−0.130994	+	0.488875i	−0.999982	−	0.00595726i	$-0.998104\pi$
$113$	−1.39248	+	5.19681i	−0.130994	+	0.488875i	0.868989	+	0.494832i	$0.164770\pi$
$114$	−8.84178	−	14.8238i	−0.828109	−	1.38837i
$115$	−3.54135	−	5.67909i	−0.330232	−	0.529578i
$116$	−30.9774	+	17.8848i	−2.87618	+	1.66056i
$117$	−5.82018	−	5.49835i	−0.538076	−	0.508322i
$118$	14.6571	−	14.6571i	1.34930	−	1.34930i
$119$	1.87114	−	3.03605i	0.171527	−	0.278314i
$120$	−6.67377	−	20.8350i	−0.609229	−	1.90197i
$121$	−9.71367			−0.883061
$122$	2.79182	+	10.4192i	0.252759	+	0.943311i
$123$	4.11053	−	1.16428i	0.370634	−	0.104979i
$124$	−2.21496	+	1.27880i	−0.198909	+	0.114840i
$125$	−8.66909	−	7.06024i	−0.775387	−	0.631487i
$126$	−17.1987	+	9.92284i	−1.53218	+	0.883997i
$127$	1.14460	+	1.14460i	0.101567	+	0.101567i	0.756064	−	0.654497i	$-0.227120\pi$
$127$	1.14460	+	1.14460i	0.101567	+	0.101567i	−0.654497	+	0.756064i	$0.727120\pi$
$128$	−4.24151	+	15.8295i	−0.374900	+	1.39914i
$129$	−0.293445	−	20.6444i	−0.0258364	−	1.81764i
$130$	−10.9090	−	10.1918i	−0.956782	−	0.893879i
$131$			3.58612i			0.313321i	0.987653	+	0.156660i	$0.0500728\pi$
$131$			3.58612i			0.313321i	−0.987653	+	0.156660i	$0.949927\pi$
$132$	−23.3951	+	24.0698i	−2.03628	+	2.09501i
$133$	−7.66351	+	7.23542i	−0.664510	+	0.627390i
$134$	11.8383			1.02267
$135$	6.56261	+	9.58812i	0.564820	+	0.825214i
$136$	−3.80715	−	6.59418i	−0.326461	−	0.565447i
$137$	0.921779	−	0.921779i	0.0787529	−	0.0787529i	−0.666633	−	0.745386i	$-0.732265\pi$
$137$	0.921779	−	0.921779i	0.0787529	−	0.0787529i	0.745386	+	0.666633i	$0.232265\pi$
$138$	3.53429	+	12.4780i	0.300859	+	1.06220i
$139$	19.8981	−	11.4881i	1.68773	−	0.974412i	0.731481	−	0.681862i	$-0.238830\pi$
$139$	19.8981	−	11.4881i	1.68773	−	0.974412i	0.956250	−	0.292550i	$-0.0945038\pi$
$140$	−21.7497	+	12.7099i	−1.83818	+	1.07419i
$141$	2.11214	+	1.17974i	0.177874	+	0.0993520i
$142$	−8.74351	+	32.6312i	−0.733739	+	2.73835i
$143$	−3.14379	+	11.7328i	−0.262897	+	0.981146i
$144$	0.478782	+	16.8382i	0.0398985	+	1.40319i
$145$	12.8234	−	13.7258i	1.06492	−	1.13986i
$146$	6.49548	+	3.75017i	0.537570	+	0.310366i
$147$	8.19464	+	8.93576i	0.675883	+	0.737009i
$148$	−32.4627	−	8.69836i	−2.66842	−	0.715001i
$149$	−17.5202			−1.43531			−0.717654	−	0.696400i	$-0.754784\pi$
$149$	−17.5202			−1.43531			−0.717654	+	0.696400i	$0.754784\pi$
$150$	12.3356	+	17.8098i	1.00720	+	1.45416i
$151$	12.4917			1.01656			0.508279	−	0.861193i	$-0.330282\pi$
$151$	12.4917			1.01656			0.508279	+	0.861193i	$0.330282\pi$
$152$	5.82403	+	21.7356i	0.472391	+	1.76299i
$153$	2.93955	+	2.77700i	0.237648	+	0.224507i
$154$	25.6439	+	15.8045i	2.06645	+	1.27356i
$155$	0.916902	−	0.981425i	0.0736473	−	0.0788299i
$156$	10.0830	+	16.9048i	0.807289	+	1.35347i
$157$	1.56179	−	0.418481i	0.124645	−	0.0333984i	−0.195957	−	0.980612i	$-0.562781\pi$
$157$	1.56179	−	0.418481i	0.124645	−	0.0333984i	0.320602	+	0.947214i	$0.396115\pi$
$158$	−6.25606	+	1.67631i	−0.497706	+	0.133360i
$159$	−7.91442	+	14.1695i	−0.627654	+	1.12372i
$160$	0.208807	+	6.14331i	0.0165077	+	0.485671i
$161$	6.96894	−	3.76090i	0.549230	−	0.296400i
$162$	−7.05351	−	21.3811i	−0.554176	−	1.67986i
$163$	−0.145389	−	0.542600i	−0.0113878	−	0.0424997i	0.959998	−	0.280006i	$-0.0903365\pi$
$163$	−0.145389	−	0.542600i	−0.0113878	−	0.0424997i	−0.971386	+	0.237507i	$0.923670\pi$
$164$	−10.5028			−0.820135
$165$	8.06784	−	15.6721i	0.628080	−	1.22007i
$166$	−14.4498			−1.12152
$167$	−10.2091	−	2.73552i	−0.790004	−	0.211681i	−0.158813	−	0.987309i	$-0.550767\pi$
$167$	−10.2091	−	2.73552i	−0.790004	−	0.211681i	−0.631191	+	0.775628i	$0.717433\pi$
$168$	25.0987	−	6.33628i	1.93640	−	0.488855i
$169$	−5.08969	−	2.93854i	−0.391515	−	0.226041i
$170$	5.50971	+	5.14748i	0.422575	+	0.394794i
$171$	−6.26707	−	10.1755i	−0.479255	−	0.778144i
$172$	−13.1370	+	49.0278i	−1.00168	+	3.73834i
$173$	2.92433	−	10.9138i	0.222333	−	0.829757i	−0.761123	−	0.648608i	$-0.775352\pi$
$173$	2.92433	−	10.9138i	0.222333	−	0.829757i	0.983456	−	0.181149i	$-0.0579818\pi$
$174$	−31.2601	+	18.6454i	−2.36982	+	1.41350i
$175$	8.98010	−	9.71380i	0.678832	−	0.734294i
$176$	22.1314	−	12.7776i	1.66822	−	0.963148i
$177$	10.0029	−	10.2914i	0.751866	−	0.773549i
$178$	11.6651	−	11.6651i	0.874335	−	0.874335i
$179$	−6.17534	−	10.6960i	−0.461566	−	0.799457i	0.537473	−	0.843281i	$-0.319379\pi$
$179$	−6.17534	−	10.6960i	−0.461566	−	0.799457i	−0.999039	+	0.0438245i	$0.986046\pi$
$180$	−9.09914	−	27.0760i	−0.678210	−	2.01812i
$181$	0.935584			0.0695414			0.0347707	−	0.999395i	$-0.488930\pi$
$181$	0.935584			0.0695414			0.0347707	+	0.999395i	$0.488930\pi$
$182$	12.8442	−	12.1267i	0.952075	−	0.898892i
$183$	2.03532	+	7.18578i	0.150455	+	0.531188i
$184$		−	16.9075i		−	1.24643i
$185$	17.6385	−	0.599523i	1.29681	−	0.0440778i
$186$	−2.23517	+	1.33319i	−0.163891	+	0.0977541i
$187$	1.58781	−	5.92578i	0.116112	−	0.433336i
$188$	−4.20556	−	4.20556i	−0.306722	−	0.306722i
$189$	−11.8091	+	7.03886i	−0.858984	+	0.512002i
$190$	−11.7907	−	18.9081i	−0.855384	−	1.37174i
$191$	11.5264	−	6.65478i	0.834022	−	0.481523i	−0.0212056	−	0.999775i	$-0.506750\pi$
$191$	11.5264	−	6.65478i	0.834022	−	0.481523i	0.855228	+	0.518252i	$0.173417\pi$
$192$	−1.84777	+	7.31003i	−0.133352	+	0.527556i
$193$	−1.97410	−	7.36744i	−0.142099	−	0.530320i	−0.999867	−	0.0162841i	$-0.994816\pi$
$193$	−1.97410	−	7.36744i	−0.142099	−	0.530320i	0.857769	−	0.514036i	$-0.171850\pi$
$194$	14.9977			1.07677
$195$	−7.65263	−	6.94846i	−0.548016	−	0.497590i
$196$	−13.3965	−	26.6263i	−0.956894	−	1.90188i
$197$	−2.37455	+	2.37455i	−0.169180	+	0.169180i	−0.786619	−	0.617439i	$-0.788170\pi$
$197$	−2.37455	+	2.37455i	−0.169180	+	0.169180i	0.617439	+	0.786619i	$0.288170\pi$
$198$	−23.4559	+	24.8288i	−1.66694	+	1.76451i
$199$	−22.0750	+	12.7450i	−1.56485	+	0.903469i	−0.568100	+	0.822959i	$0.692321\pi$
$199$	−22.0750	+	12.7450i	−1.56485	+	0.903469i	−0.996754	+	0.0805093i	$0.974345\pi$
$200$	−9.14567	−	26.7224i	−0.646696	−	1.88956i
$201$	8.19567	−	0.116495i	0.578078	−	0.00821693i
$202$	9.61647	−	35.8892i	0.676613	−	2.52515i
$203$	15.2579	+	16.1606i	1.07089	+	1.13425i
$204$	−5.09255	−	8.53797i	−0.356550	−	0.597777i
$205$	5.27593	−	1.60765i	0.368487	−	0.112283i
$206$	11.6354	−	6.71768i	0.810674	−	0.468043i
$207$	2.56959	+	8.60378i	0.178599	+	0.598004i
$208$	−3.87861	−	14.4752i	−0.268933	−	1.00367i
$209$	−9.06502	+	15.7011i	−0.627040	+	1.08607i
$210$	−21.9459	+	13.2466i	−1.51441	+	0.914103i
$211$	10.7573	+	18.6323i	0.740566	+	1.28270i	0.952238	+	0.305357i	$0.0987758\pi$
$211$	10.7573	+	18.6323i	0.740566	+	1.28270i	−0.211672	+	0.977341i	$0.567891\pi$
$212$	28.2134	−	28.2134i	1.93771	−	1.93771i
$213$	−5.73206	+	22.6768i	−0.392754	+	1.55379i
$214$		−	18.2029i		−	1.24433i
$215$	−0.905449	−	26.6392i	−0.0617511	−	1.81678i
$216$	1.25119	+	29.3254i	0.0851327	+	1.99534i
$217$	1.09098	+	1.15552i	0.0740603	+	0.0784421i
$218$	−4.34170	+	1.16336i	−0.294057	+	0.0787924i
$219$	4.53375	+	2.53233i	0.306362	+	0.171119i
$220$	−29.5830	+	31.6648i	−1.99449	+	2.13484i
$221$	−3.11554	−	1.79876i	−0.209574	−	0.120997i
$222$	−33.1558	−	8.38088i	−2.22527	−	0.562488i
$223$	−3.79377	−	14.1586i	−0.254050	−	0.948127i	−0.968617	−	0.248560i	$-0.920043\pi$
$223$	−3.79377	−	14.1586i	−0.254050	−	0.948127i	0.714567	−	0.699567i	$-0.246624\pi$
$224$	−7.27006	−	0.208888i	−0.485751	−	0.0139569i
$225$	8.71526	+	12.2084i	0.581017	+	0.813891i
$226$	6.72951	−	11.6558i	0.447640	−	0.775335i
$227$	12.6424	−	12.6424i	0.839106	−	0.839106i	−0.149635	−	0.988741i	$-0.547810\pi$
$227$	12.6424	−	12.6424i	0.839106	−	0.839106i	0.988741	+	0.149635i	$0.0478100\pi$
$228$	8.00653	+	28.2674i	0.530245	+	1.87206i
$229$			8.27868i			0.547070i	0.961862	+	0.273535i	$0.0881930\pi$
$229$			8.27868i			0.547070i	−0.961862	+	0.273535i	$0.911807\pi$
$230$	4.88020	+	16.0157i	0.321791	+	1.05604i
$231$	17.9089	+	10.6892i	1.17832	+	0.703296i
$232$	45.8355	−	12.2816i	3.00925	−	0.806326i
$233$	−6.79838	+	1.82162i	−0.445376	+	0.119338i	−0.474535	−	0.880237i	$-0.657384\pi$
$233$	−6.79838	+	1.82162i	−0.445376	+	0.119338i	0.0291587	+	0.999575i	$0.490717\pi$
$234$	10.5037	+	17.0544i	0.686651	+	1.11488i
$235$	2.75633	+	1.46885i	0.179803	+	0.0958175i
$236$	−30.5553	+	17.6411i	−1.98898	+	1.14834i
$237$	−4.31460	+	1.22208i	−0.280263	+	0.0793824i
$238$	−6.48710	+	6.12473i	−0.420496	+	0.397007i
$239$	−1.14624	−	1.98534i	−0.0741440	−	0.128421i	0.826570	−	0.562834i	$-0.190289\pi$
$239$	−1.14624	−	1.98534i	−0.0741440	−	0.128421i	−0.900714	+	0.434413i	$0.856956\pi$
$240$	1.04757	+	21.7216i	0.0676201	+	1.40212i
$241$	−24.0642			−1.55011			−0.775054	−	0.631895i	$-0.782277\pi$
$241$	−24.0642			−1.55011			−0.775054	+	0.631895i	$0.782277\pi$
$242$	23.4718	+	6.28926i	1.50883	+	0.404289i
$243$	−5.09357	−	14.7328i	−0.326753	−	0.945110i
$244$		−	18.3605i		−	1.17541i
$245$	10.8051	+	11.3247i	0.690315	+	0.723509i
$246$	−10.6864	+	0.151899i	−0.681340	+	0.00968472i
$247$	7.51769	+	7.51769i	0.478339	+	0.478339i
$248$	3.27735	−	0.878163i	0.208112	−	0.0557634i
$249$	−10.0037	+	0.142194i	−0.633957	+	0.00901121i
$250$	16.3765	+	22.6731i	1.03574	+	1.43397i
$251$		−	13.9827i		−	0.882579i	−0.897365	−	0.441290i	$-0.854521\pi$
$251$		−	13.9827i		−	0.882579i	0.897365	−	0.441290i	$-0.145479\pi$
$252$	32.6484	−	8.73767i	2.05665	−	0.550421i
$253$	9.63240	−	9.63240i	0.605584	−	0.605584i
$254$	−2.02470	−	3.50688i	−0.127041	−	0.220041i
$255$	3.86505	+	3.50940i	0.242039	+	0.219767i
$256$	16.1449	−	27.9638i	1.00906	−	1.74774i
$257$	1.74198	−	1.74198i	0.108662	−	0.108662i	−0.650686	−	0.759347i	$-0.725518\pi$
$257$	1.74198	−	1.74198i	0.108662	−	0.108662i	0.759347	+	0.650686i	$0.225518\pi$
$258$	−12.6575	+	50.0746i	−0.788020	+	3.11751i
$259$	−0.599756	+	20.8736i	−0.0372670	+	1.29703i
$260$	13.4459	+	21.5625i	0.833878	+	1.33725i
$261$	−21.4580	+	13.2159i	−1.32822	+	0.818041i
$262$	2.32189	−	8.66540i	0.143447	−	0.535350i
$263$	−13.9060	−	13.9060i	−0.857484	−	0.857484i	0.133557	−	0.991041i	$-0.457360\pi$
$263$	−13.9060	−	13.9060i	−0.857484	−	0.857484i	−0.991041	+	0.133557i	$0.957360\pi$
$264$	38.2432	−	22.8105i	2.35371	−	1.40389i
$265$	−9.85398	+	18.4911i	−0.605325	+	1.13590i
$266$	23.2026	−	12.5216i	1.42264	−	0.767750i
$267$	7.96099	−	8.19057i	0.487204	−	0.501255i
$268$	−19.4636	−	5.21526i	−1.18893	−	0.318573i
$269$	−12.3548	−	21.3991i	−0.753284	−	1.30473i	−0.946223	−	0.323515i	$-0.895135\pi$
$269$	−12.3548	−	21.3991i	−0.753284	−	1.30473i	0.192939	−	0.981211i	$-0.438198\pi$
$270$	−9.64975	−	27.4175i	−0.587265	−	1.66858i
$271$	−15.5893	+	27.0015i	−0.946984	+	1.64022i	−0.195253	+	0.980753i	$0.562553\pi$
$271$	−15.5893	+	27.0015i	−0.946984	+	1.64022i	−0.751730	+	0.659471i	$0.770780\pi$
$272$	1.95894	+	7.31085i	0.118778	+	0.443285i
$273$	8.77275	−	8.52176i	0.530951	−	0.515760i
$274$	−2.82418	+	1.63054i	−0.170615	+	0.0985046i
$275$	10.0137	−	20.4345i	0.603847	−	1.23225i
$276$	−0.313743	−	22.0724i	−0.0188851	−	1.32861i
$277$	−8.26260	−	8.26260i	−0.496451	−	0.496451i	0.413880	−	0.910331i	$-0.364173\pi$
$277$	−8.26260	−	8.26260i	−0.496451	−	0.496451i	−0.910331	+	0.413880i	$0.864173\pi$
$278$	−55.5193	+	14.8764i	−3.32983	+	0.892224i
$279$	−1.53430	+	0.944966i	−0.0918559	+	0.0565736i
$280$	32.2343	−	8.81883i	1.92636	−	0.527026i
$281$	6.29183	+	3.63259i	0.375339	+	0.216702i	0.675788	−	0.737096i	$-0.263803\pi$
$281$	6.29183	+	3.63259i	0.375339	+	0.216702i	−0.300449	+	0.953798i	$0.597137\pi$
$282$	−4.33988	−	4.21823i	−0.258436	−	0.251192i
$283$	−5.30092	−	19.7833i	−0.315107	−	1.17600i	−0.923890	−	0.382659i	$-0.875008\pi$
$283$	−5.30092	−	19.7833i	−0.315107	−	1.17600i	0.608782	−	0.793337i	$-0.291658\pi$
$284$	28.7510	−	49.7981i	1.70606	−	2.95497i
$285$	−8.34878	−	12.9741i	−0.494539	−	0.768521i
$286$	15.1932	−	26.3153i	0.898390	−	1.55606i
$287$	1.50730	+	6.34949i	0.0889730	+	0.374799i
$288$	1.90717	−	8.02332i	0.112381	−	0.472779i
$289$	−13.1489	−	7.59152i	−0.773464	−	0.446560i
$290$	−39.8730	+	24.8639i	−2.34142	+	1.46006i
$291$	10.3830	−	0.147586i	0.608661	−	0.00865165i
$292$	−9.02730	−	9.02730i	−0.528283	−	0.528283i
$293$	−3.44348	+	12.8512i	−0.201170	+	0.750777i	0.789413	+	0.613863i	$0.210385\pi$
$293$	−3.44348	+	12.8512i	−0.201170	+	0.750777i	−0.990583	+	0.136914i	$0.956282\pi$
$294$	−14.0157	−	26.8979i	−0.817413	−	1.56872i
$295$	12.6487	−	13.5387i	0.736433	−	0.788256i
$296$	38.6115	+	22.2923i	2.24425	+	1.29572i
$297$	−15.9943	+	17.4199i	−0.928081	+	1.01080i
$298$	42.3352	+	11.3437i	2.45241	+	0.657123i
$299$	−3.99411	−	6.91801i	−0.230986	−	0.400079i
$300$	−12.4354	−	34.7159i	−0.717959	−	2.00433i
$301$	31.5251	+	0.905800i	1.81707	+	0.0522095i
$302$	−30.1845	−	8.08792i	−1.73692	−	0.465408i
$303$	6.30435	−	24.9408i	0.362175	−	1.43281i
$304$		−	22.3677i		−	1.28287i
$305$	2.81040	+	9.22307i	0.160923	+	0.528111i
$306$	−5.30503	−	8.61353i	−0.303268	−	0.492402i
$307$	7.65627	+	7.65627i	0.436967	+	0.436967i	0.890990	−	0.454023i	$-0.150012\pi$
$307$	7.65627	+	7.65627i	0.436967	+	0.436967i	−0.454023	+	0.890990i	$0.650012\pi$
$308$	−35.1994	−	37.2819i	−2.00567	−	2.12434i
$309$	7.98910	−	4.76517i	0.454484	−	0.271081i
$310$	−2.85101	+	1.77783i	−0.161927	+	0.100974i
$311$	−9.82660	−	5.67339i	−0.557215	−	0.321708i	0.194812	−	0.980841i	$-0.437590\pi$
$311$	−9.82660	−	5.67339i	−0.557215	−	0.321708i	−0.752027	+	0.659132i	$0.770924\pi$
$312$	−7.11619	−	25.1241i	−0.402875	−	1.42237i
$313$	18.7396	+	5.02125i	1.05922	+	0.283818i	0.746058	−	0.665881i	$-0.231944\pi$
$313$	18.7396	+	5.02125i	1.05922	+	0.283818i	0.313165	+	0.949699i	$0.398611\pi$
$314$	−4.04483			−0.228263
$315$	−15.0629	+	9.38664i	−0.848698	+	0.528877i
$316$	11.0243			0.620164
$317$	−3.87875	−	1.03931i	−0.217852	−	0.0583733i	0.148242	−	0.988951i	$-0.452639\pi$
$317$	−3.87875	−	1.03931i	−0.217852	−	0.0583733i	−0.366094	+	0.930578i	$0.619305\pi$
$318$	28.2985	−	29.1145i	1.58690	−	1.63266i
$319$	33.1101	+	19.1161i	1.85381	+	1.07030i
$320$	−2.19850	+	9.48251i	−0.122900	+	0.530088i
$321$	−0.179127	−	12.6019i	−0.00999789	−	0.703372i
$322$	−19.2746	+	4.57558i	−1.07413	+	0.254987i
$323$	−3.79689	−	3.79689i	−0.211265	−	0.211265i
$324$	2.17759	+	38.2607i	0.120977	+	2.12559i
$325$	−10.0548	−	8.77344i	−0.557742	−	0.486663i
$326$			1.40526i			0.0778300i
$327$	−2.99433	+	0.848120i	−0.165587	+	0.0469011i
$328$	13.4585	+	3.60618i	0.743119	+	0.199118i
$329$	−1.93891	+	3.14602i	−0.106896	+	0.173446i
$330$	−29.6421	+	32.6460i	−1.63174	+	1.79710i
$331$	−3.89648	−	6.74889i	−0.214170	−	0.370953i	0.738846	−	0.673875i	$-0.235371\pi$
$331$	−3.89648	−	6.74889i	−0.214170	−	0.370953i	−0.953015	+	0.302922i	$0.902038\pi$
$332$	23.7574	+	6.36578i	1.30386	+	0.349367i
$333$	−23.0364	−	5.47584i	−1.26239	−	0.300074i
$334$	22.8978	+	13.2201i	1.25291	+	0.723370i
$335$	10.5755	−	0.359456i	0.577802	−	0.0196392i
$336$	−25.7285	−	0.373386i	−1.40361	−	0.0203699i
$337$	3.27681	−	12.2292i	0.178499	−	0.666169i	−0.817430	−	0.576029i	$-0.804602\pi$
$337$	3.27681	−	12.2292i	0.178499	−	0.666169i	0.995929	−	0.0901406i	$-0.0287316\pi$
$338$	10.3960	+	10.3960i	0.565468	+	0.565468i
$339$	4.54416	−	8.13561i	0.246805	−	0.441866i
$340$	−6.79099	−	10.8904i	−0.368293	−	0.590614i
$341$	2.36745	+	1.36685i	0.128205	+	0.0740190i
$342$	8.55527	+	28.6456i	0.462616	+	1.54898i
$343$	−14.1743	+	11.9201i	−0.765342	+	0.643624i
$344$	33.6677	−	58.3142i	1.81524	−	3.14409i
$345$	3.53619	+	11.0397i	0.190382	+	0.594358i
$346$	−14.1325	+	24.4783i	−0.759770	+	1.31596i
$347$	−4.46374	−	16.6589i	−0.239626	−	0.894296i	−0.976009	−	0.217731i	$-0.930134\pi$
$347$	−4.46374	−	16.6589i	−0.239626	−	0.894296i	0.736383	−	0.676565i	$-0.236532\pi$
$348$	59.6097	−	16.8840i	3.19542	−	0.905077i
$349$	15.2254	+	8.79039i	0.814997	+	0.470539i	0.848688	−	0.528893i	$-0.177393\pi$
$349$	15.2254	+	8.79039i	0.814997	+	0.470539i	−0.0336910	+	0.999432i	$0.510726\pi$
$350$	−27.9886	+	17.6579i	−1.49605	+	0.943852i
$351$	7.43960	+	11.7035i	0.397097	+	0.624685i
$352$	−12.0848	+	3.23812i	−0.644123	+	0.172592i
$353$	9.96267	+	9.96267i	0.530260	+	0.530260i	0.920650	−	0.390390i	$-0.127660\pi$
$353$	9.96267	+	9.96267i	0.530260	+	0.530260i	−0.390390	+	0.920650i	$0.627660\pi$
$354$	−30.8341	+	18.3913i	−1.63882	+	0.977487i
$355$	−6.82007	+	29.4161i	−0.361972	+	1.56124i
$356$	−24.3179	+	14.0399i	−1.28885	+	0.744115i
$357$	−4.43077	+	4.30401i	−0.234501	+	0.227792i
$358$	7.99663	+	29.8438i	0.422635	+	1.57730i
$359$	0.764675	−	1.32446i	0.0403580	−	0.0699021i	−0.845141	−	0.534544i	$-0.820483\pi$
$359$	0.764675	−	1.32446i	0.0403580	−	0.0699021i	0.885499	+	0.464642i	$0.153817\pi$
$360$	2.36312	+	37.8196i	0.124548	+	1.99327i
$361$	−1.56567	−	2.71182i	−0.0824036	−	0.142727i
$362$	−2.26072	−	0.605758i	−0.118821	−	0.0318379i
$363$	16.3115	+	4.12310i	0.856133	+	0.216407i
$364$	−26.4599	+	14.2795i	−1.38687	+	0.748448i
$365$	5.91650	+	3.15292i	0.309684	+	0.165032i
$366$	−0.265541	−	18.6813i	−0.0138800	−	0.976488i
$367$	0.478637	+	0.478637i	0.0249847	+	0.0249847i	0.719489	−	0.694504i	$-0.244376\pi$
$367$	0.478637	+	0.478637i	0.0249847	+	0.0249847i	−0.694504	+	0.719489i	$0.744376\pi$
$368$	−4.34979	+	16.2336i	−0.226748	+	0.846236i
$369$	−7.39674	+	0.210320i	−0.385059	+	0.0109488i
$370$	−43.0095	−	9.97167i	−2.23596	−	0.518402i
$371$	−21.1054	−	13.0074i	−1.09574	−	0.675311i
$372$	4.26224	−	1.20725i	0.220987	−	0.0625928i
$373$	−9.67306	+	9.67306i	−0.500852	+	0.500852i	−0.911703	−	0.410851i	$-0.865232\pi$
$373$	−9.67306	+	9.67306i	−0.500852	+	0.500852i	0.410851	+	0.911703i	$0.365232\pi$
$374$	−7.67347	+	13.2908i	−0.396786	+	0.687253i
$375$	11.5606	+	15.5355i	0.596988	+	0.802250i
$376$	3.94505	+	6.83303i	0.203451	+	0.352387i
$377$	15.8531	−	15.8531i	0.816478	−	0.816478i
$378$	33.0926	−	9.36255i	1.70210	−	0.481558i
$379$		−	6.57984i		−	0.337983i	−0.985617	−	0.168992i	$-0.945949\pi$
$379$		−	6.57984i		−	0.337983i	0.985617	−	0.168992i	$-0.0540511\pi$
$380$	11.0555	+	36.2817i	0.567137	+	1.86121i
$381$	−1.43621	−	2.40790i	−0.0735795	−	0.123360i
$382$	−32.1609	+	8.61748i	−1.64549	+	0.440908i
$383$	−27.0221	−	27.0221i	−1.38077	−	1.38077i	−0.843259	−	0.537507i	$-0.819366\pi$
$383$	−27.0221	−	27.0221i	−1.38077	−	1.38077i	−0.537507	−	0.843259i	$-0.680634\pi$
$384$	13.8415	−	24.7811i	0.706348	−	1.26461i
$385$	23.3885	+	13.3401i	1.19199	+	0.679873i
$386$			19.0807i			0.971180i
$387$	−8.27005	+	34.7914i	−0.420390	+	1.76855i
$388$	−24.6582	−	6.60715i	−1.25183	−	0.335427i
$389$	−35.1534			−1.78235			−0.891174	−	0.453661i	$-0.850118\pi$
$389$	−35.1534			−1.78235			−0.891174	+	0.453661i	$0.850118\pi$
$390$	13.9927	+	21.7449i	0.708549	+	1.10110i
$391$	2.01727	+	3.49402i	0.102018	+	0.176700i
$392$	8.02422	+	38.7190i	0.405284	+	1.95560i
$393$	1.52218	−	6.02194i	0.0767837	−	0.303767i
$394$	7.27524	−	4.20036i	0.366521	−	0.211611i
$395$	−5.53786	+	1.68746i	−0.278640	+	0.0849054i
$396$	49.5027	−	30.4885i	2.48760	−	1.53210i
$397$	10.1750	−	2.72638i	0.510668	−	0.136833i	0.00572144	−	0.999984i	$-0.498179\pi$
$397$	10.1750	−	2.72638i	0.510668	−	0.136833i	0.504947	+	0.863151i	$0.331512\pi$
$398$	61.5933	−	16.5039i	3.08739	−	0.827265i
$399$	15.9400	−	8.89709i	0.797998	−	0.445412i
$400$	1.90631	+	28.0103i	0.0953153	+	1.40051i
$401$			30.3140i			1.51381i	0.653525	+	0.756905i	$0.273289\pi$
$401$			30.3140i			1.51381i	−0.653525	+	0.756905i	$0.726711\pi$
$402$	−19.8792	−	5.02491i	−0.991485	−	0.250620i
$403$	1.13354	−	1.13354i	0.0564655	−	0.0564655i
$404$	−31.6215	+	54.7700i	−1.57323	+	2.72491i
$405$	−6.95036	−	18.8863i	−0.345366	−	0.938468i
$406$	−26.4053	−	48.9291i	−1.31047	−	2.42831i
$407$	9.29722	+	34.6977i	0.460846	+	1.71990i
$408$	3.59411	+	12.6892i	0.177935	+	0.628208i
$409$	25.0800	+	14.4800i	1.24013	+	0.715988i	0.969120	−	0.246589i	$-0.0793098\pi$
$409$	25.0800	+	14.4800i	1.24013	+	0.715988i	0.271008	+	0.962577i	$0.412643\pi$
$410$	−13.7895	+	0.468697i	−0.681015	+	0.0231473i
$411$	−1.93915	+	1.15662i	−0.0956510	+	0.0570519i
$412$	−22.0895	+	5.91886i	−1.08827	+	0.291601i
$413$	15.0500	+	15.9404i	0.740562	+	0.784378i
$414$	−0.638452	−	22.4537i	−0.0313782	−	1.10354i
$415$	−12.9085	+	0.438753i	−0.633655	+	0.0215375i
$416$			7.33664i			0.359709i
$417$	−38.2898	+	10.8453i	−1.87506	+	0.531096i
$418$	32.0704	−	32.0704i	1.56861	−	1.56861i
$419$	2.15746	+	3.73684i	0.105399	+	0.182556i	0.913901	−	0.405937i	$-0.133055\pi$
$419$	2.15746	+	3.73684i	0.105399	+	0.182556i	−0.808502	+	0.588493i	$0.799721\pi$
$420$	41.9177	−	12.1110i	2.04537	−	0.590957i
$421$	4.35376	−	7.54093i	0.212189	−	0.367523i	−0.740210	−	0.672376i	$-0.765274\pi$
$421$	4.35376	−	7.54093i	0.212189	−	0.367523i	0.952399	+	0.304853i	$0.0986073\pi$
$422$	−13.9300	−	51.9875i	−0.678102	−	2.53071i
$423$	−3.04602	−	2.87759i	−0.148103	−	0.139913i
$424$	−45.8402	+	26.4658i	−2.22620	+	1.28529i
$425$	5.07831	+	4.43112i	0.246334	+	0.214941i
$426$	28.5332	−	51.0842i	1.38244	−	2.47504i
$427$	−11.0998	+	2.63497i	−0.537157	+	0.127515i
$428$	−8.01917	+	29.9280i	−0.387621	+	1.44662i
$429$	10.2593	−	18.3677i	0.495324	−	0.886801i
$430$	−15.0600	+	64.9564i	−0.726259	+	3.13247i
$431$	−33.1618	+	19.1460i	−1.59735	+	0.922230i	−0.605353	+	0.795957i	$0.706968\pi$
$431$	−33.1618	+	19.1460i	−1.59735	+	0.922230i	−0.991996	+	0.126273i	$0.959698\pi$
$432$	6.34323	−	28.4786i	0.305189	−	1.37018i
$433$	−6.30915	+	6.30915i	−0.303198	+	0.303198i	−0.842264	−	0.539065i	$-0.818778\pi$
$433$	−6.30915	+	6.30915i	−0.303198	+	0.303198i	0.539065	+	0.842264i	$0.318778\pi$
$434$	−1.88804	−	3.49855i	−0.0906290	−	0.167936i
$435$	−27.3595	+	17.6057i	−1.31179	+	0.844130i
$436$	7.65083			0.366408
$437$	−3.08594	−	11.5169i	−0.147621	−	0.550927i
$438$	−9.31562	−	9.05451i	−0.445118	−	0.432641i
$439$	10.9206	−	6.30502i	0.521213	−	0.300922i	−0.216218	−	0.976345i	$-0.569372\pi$
$439$	10.9206	−	6.30502i	0.521213	−	0.300922i	0.737431	+	0.675423i	$0.236039\pi$
$440$	48.7802	−	30.4182i	2.32550	−	1.45013i
$441$	−9.96782	−	18.4836i	−0.474658	−	0.880170i
$442$	6.36367	+	6.36367i	0.302689	+	0.302689i
$443$	−0.972362	+	3.62890i	−0.0461983	+	0.172414i	−0.985170	−	0.171579i	$-0.945113\pi$
$443$	−0.972362	+	3.62890i	−0.0461983	+	0.172414i	0.938972	+	0.343993i	$0.111780\pi$
$444$	50.8204	+	28.3858i	2.41183	+	1.34713i
$445$	10.0666	−	10.7750i	0.477204	−	0.510785i
$446$			36.6687i			1.73631i
$447$	29.4205	+	7.43668i	1.39154	+	0.351743i
$448$	−11.0348	−	3.29923i	−0.521346	−	0.155874i
$449$	0.568700			0.0268386			0.0134193	−	0.999910i	$-0.495728\pi$
$449$	0.568700			0.0268386			0.0134193	+	0.999910i	$0.495728\pi$
$450$	−13.1548	−	35.1428i	−0.620124	−	1.65665i
$451$	5.61297	+	9.72195i	0.264305	+	0.457789i
$452$	−16.1991	+	16.1991i	−0.761941	+	0.761941i
$453$	−20.9764	−	5.30226i	−0.985560	−	0.249122i
$454$	−38.7343	+	22.3632i	−1.81789	+	1.04956i
$455$	11.1059	−	11.2232i	0.520655	−	0.526152i
$456$	−0.553946	−	38.9712i	−0.0259409	−	1.82500i
$457$	−3.59882	+	13.4310i	−0.168346	+	0.628275i	0.829244	+	0.558887i	$0.188771\pi$
$457$	−3.59882	+	13.4310i	−0.168346	+	0.628275i	−0.997590	+	0.0693881i	$0.977895\pi$
$458$	5.36016	−	20.0044i	0.250464	−	0.934743i
$459$	−3.75745	−	5.91097i	−0.175383	−	0.275900i
$460$	−0.968081	−	28.4818i	−0.0451370	−	1.32797i
$461$	−19.2093	−	11.0905i	−0.894667	−	0.516536i	−0.0192005	−	0.999816i	$-0.506112\pi$
$461$	−19.2093	−	11.0905i	−0.894667	−	0.516536i	−0.875466	+	0.483280i	$0.839445\pi$
$462$	−36.3537	−	37.4244i	−1.69133	−	1.74114i
$463$	−34.0248	−	9.11691i	−1.58127	−	0.423699i	−0.641948	−	0.766748i	$-0.721874\pi$
$463$	−34.0248	−	9.11691i	−1.58127	−	0.423699i	−0.939317	+	0.343049i	$0.888540\pi$
$464$	−47.1685			−2.18974
$465$	−1.95627	+	1.25885i	−0.0907200	+	0.0583778i
$466$	17.6068			0.815621
$467$	−7.53504	−	28.1212i	−0.348680	−	1.30129i	−0.888254	−	0.459353i	$-0.848081\pi$
$467$	−7.53504	−	28.1212i	−0.348680	−	1.30129i	0.539573	−	0.841939i	$-0.318586\pi$
$468$	−9.75630	−	32.6670i	−0.450985	−	1.51003i
$469$	−0.359595	+	12.5152i	−0.0166046	+	0.577898i
$470$	−5.70928	−	5.33393i	−0.263349	−	0.246036i
$471$	−2.80025	+	0.0398034i	−0.129029	+	0.00183404i
$472$	45.2110	−	12.1143i	2.08101	−	0.557604i
$473$	52.4033	−	14.0414i	2.40951	−	0.645625i
$474$	11.2169	−	0.159440i	0.515211	−	0.00732333i
$475$	−11.1071	−	16.5333i	−0.509630	−	0.758598i
$476$	13.3639	−	7.21200i	0.612531	−	0.330562i
$477$	19.3046	−	20.4346i	0.883898	−	0.935635i
$478$	1.48430	+	5.53948i	0.0678902	+	0.253370i
$479$	30.3167			1.38521			0.692603	−	0.721319i	$-0.256464\pi$
$479$	30.3167			1.38521			0.692603	+	0.721319i	$0.256464\pi$
$480$	2.25698	−	10.4047i	0.103016	−	0.474907i
$481$	21.0648			0.960473
$482$	58.1480	+	15.5807i	2.64857	+	0.709681i
$483$	−13.2989	+	3.35736i	−0.605119	+	0.152765i
$484$	−35.8201	−	20.6807i	−1.62819	−	0.940033i
$485$	13.3980	−	0.455389i	0.608371	−	0.0206782i
$486$	2.76899	+	38.8979i	0.125604	+	1.76444i
$487$	4.73227	−	17.6611i	0.214440	−	0.800300i	−0.771923	−	0.635716i	$-0.780705\pi$
$487$	4.73227	−	17.6611i	0.214440	−	0.800300i	0.986363	−	0.164585i	$-0.0526283\pi$
$488$	−6.30412	+	23.5273i	−0.285374	+	1.06503i
$489$	0.0138285	+	0.972865i	0.000625348	+	0.0439945i
$490$	−18.7769	−	34.3607i	−0.848254	−	1.55226i
$491$	8.80385	−	5.08290i	0.397312	−	0.229388i	−0.288011	−	0.957627i	$-0.592994\pi$
$491$	8.80385	−	5.08290i	0.397312	−	0.229388i	0.685324	+	0.728239i	$0.259661\pi$
$492$	17.6368	+	4.45808i	0.795126	+	0.200986i
$493$	−8.00680	+	8.00680i	−0.360608	+	0.360608i
$494$	−13.2981	−	23.0330i	−0.598310	−	1.03630i
$495$	−20.2000	+	22.8926i	−0.907924	+	1.02895i
$496$	−3.37266			−0.151437
$497$	−34.2316	−	10.2347i	−1.53550	−	0.459088i
$498$	24.2647	+	6.13343i	1.08733	+	0.274846i
$499$		−	6.56170i		−	0.293742i	−0.989156	−	0.146871i	$-0.953080\pi$
$499$		−	6.56170i		−	0.293742i	0.989156	−	0.146871i	$-0.0469203\pi$
$500$	−16.9366	−	44.4921i	−0.757428	−	1.98975i
$501$	15.9823	+	8.92697i	0.714038	+	0.398828i
$502$	−9.05330	+	33.7874i	−0.404069	+	1.50800i
$503$	−0.0377817	−	0.0377817i	−0.00168460	−	0.00168460i	0.706264	−	0.707949i	$-0.250379\pi$
$503$	−0.0377817	−	0.0377817i	−0.00168460	−	0.00168460i	−0.707949	+	0.706264i	$0.750379\pi$
$504$	−44.8361	−	0.0133719i	−1.99716	−	0.000595634i
$505$	7.50099	−	32.3530i	0.333790	−	1.43969i
$506$	−29.5121	+	17.0388i	−1.31197	+	0.757468i
$507$	7.29949	+	7.09489i	0.324182	+	0.315095i
$508$	1.78393	+	6.65773i	0.0791493	+	0.295389i
$509$	8.50128			0.376813			0.188406	−	0.982091i	$-0.439668\pi$
$509$	8.50128			0.376813			0.188406	+	0.982091i	$0.439668\pi$
$510$	−7.06718	−	10.9825i	−0.312940	−	0.486313i
$511$	−4.16191	+	6.75299i	−0.184112	+	0.298735i
$512$	−33.9418	+	33.9418i	−1.50003	+	1.50003i
$513$	6.20473	+	19.7473i	0.273946	+	0.871864i
$514$	−5.33714	+	3.08140i	−0.235411	+	0.135915i
$515$	10.1903	−	6.35443i	0.449038	−	0.280010i
$516$	42.8706	−	76.7531i	1.88727	−	3.37887i
$517$	−1.64532	+	6.14042i	−0.0723611	+	0.270055i
$518$	14.9642	−	50.0502i	0.657489	−	2.19908i
$519$	−9.54313	+	17.0855i	−0.418897	+	0.749969i
$520$	−9.82615	−	32.2471i	−0.430905	−	1.41413i
$521$	−3.23579	+	1.86818i	−0.141763	+	0.0818466i	−0.569204	−	0.822197i	$-0.692748\pi$
$521$	−3.23579	+	1.86818i	−0.141763	+	0.0818466i	0.427441	+	0.904043i	$0.359415\pi$
$522$	60.4073	−	18.0412i	2.64395	−	0.789640i
$523$	3.43874	+	12.8336i	0.150366	+	0.561172i	0.999458	+	0.0329274i	$0.0104830\pi$
$523$	3.43874	+	12.8336i	0.150366	+	0.561172i	−0.849092	+	0.528245i	$0.822850\pi$
$524$	−7.63497	+	13.2242i	−0.333535	+	0.577700i
$525$	−19.2029	+	12.5000i	−0.838081	+	0.545546i
$526$	24.5985	+	42.6059i	1.07255	+	1.85770i
$527$	−0.572506	+	0.572506i	−0.0249387	+	0.0249387i
$528$	−42.5875	+	12.0626i	−1.85338	+	0.524957i
$529$		−	14.0414i		−	0.610494i
$530$	35.7832	−	38.3013i	1.55432	−	1.66370i
$531$	−21.1656	+	13.0358i	−0.918509	+	0.565705i
$532$	−43.6644	+	10.3654i	−1.89309	+	0.449399i
$533$	6.35869	−	1.70380i	0.275425	−	0.0738000i
$534$	−24.5398	+	14.6370i	−1.06194	+	0.633405i
$535$	−0.552712	−	16.2613i	−0.0238958	−	0.703037i
$536$	23.1502	+	13.3658i	0.999938	+	0.577314i
$537$	5.82978	+	20.5823i	0.251574	+	0.888192i
$538$	15.9986	+	59.7075i	0.689747	+	2.57417i
$539$	−17.4872	+	26.6302i	−0.753227	+	1.14704i
$540$	3.78682	+	49.3292i	0.162959	+	2.12279i
$541$	12.4842	−	21.6233i	0.536739	−	0.929659i	−0.462338	−	0.886704i	$-0.652989\pi$
$541$	12.4842	−	21.6233i	0.536739	−	0.929659i	0.999077	−	0.0429550i	$-0.0136772\pi$
$542$	55.1521	−	55.1521i	2.36899	−	2.36899i
$543$	−1.57107	−	0.397122i	−0.0674209	−	0.0170421i
$544$		−	3.70545i		−	0.158870i
$545$	−3.84327	+	1.17110i	−0.164627	+	0.0501643i
$546$	−26.7158	+	14.9117i	−1.14333	+	0.638162i
$547$	−0.352043	+	0.0943295i	−0.0150523	+	0.00403324i	−0.266337	−	0.963880i	$-0.585814\pi$
$547$	−0.352043	+	0.0943295i	−0.0150523	+	0.00403324i	0.251285	+	0.967913i	$0.419147\pi$
$548$	5.36165	−	1.43665i	0.229038	−	0.0613706i
$549$	−0.367670	−	12.9305i	−0.0156918	−	0.551862i
$550$	−37.4274	+	42.8938i	−1.59591	+	1.82900i
$551$	28.9802	−	16.7317i	1.23460	−	0.712796i
$552$	−7.17661	+	28.3916i	−0.305457	+	1.20843i
$553$	−1.58213	−	6.66471i	−0.0672790	−	0.283412i
$554$	14.6158	+	25.3153i	0.620965	+	1.07554i
$555$	−29.8737	−	6.48018i	−1.26807	−	0.275069i
$556$	97.8346			4.14911
$557$	9.45122	+	2.53245i	0.400461	+	0.107303i	0.453428	−	0.891293i	$-0.350201\pi$
$557$	9.45122	+	2.53245i	0.400461	+	0.107303i	−0.0529667	+	0.998596i	$0.516868\pi$
$558$	4.31926	−	1.28999i	0.182849	−	0.0546095i
$559$		−	31.8138i		−	1.34558i
$560$	−33.2184	+	0.174449i	−1.40373	+	0.00737181i
$561$	−5.18158	+	9.27681i	−0.218767	+	0.391667i
$562$	−12.8514	−	12.8514i	−0.542105	−	0.542105i
$563$	−15.0385	+	4.02956i	−0.633798	+	0.169826i	−0.561393	−	0.827550i	$-0.689734\pi$
$563$	−15.0385	+	4.02956i	−0.633798	+	0.169826i	−0.0724055	+	0.997375i	$0.523068\pi$
$564$	5.27701	+	8.84722i	0.222202	+	0.372535i
$565$	5.65778	−	10.6169i	0.238025	−	0.446657i
$566$			51.2360i			2.15361i
$567$	22.8180	−	6.80738i	0.958265	−	0.285883i
$568$	−53.9401	+	53.9401i	−2.26328	+	2.26328i
$569$	0.343539	+	0.595026i	0.0144019	+	0.0249448i	0.873137	−	0.487476i	$-0.162082\pi$
$569$	0.343539	+	0.595026i	0.0144019	+	0.0249448i	−0.858735	+	0.512421i	$0.828749\pi$
$570$	11.7735	+	36.7559i	0.493136	+	1.53953i
$571$	−15.4051	+	26.6824i	−0.644683	+	1.11662i	0.339691	+	0.940537i	$0.389677\pi$
$571$	−15.4051	+	26.6824i	−0.644683	+	1.11662i	−0.984375	+	0.176087i	$0.943656\pi$
$572$	−36.5726	+	36.5726i	−1.52918	+	1.52918i
$573$	−22.1803	+	6.28239i	−0.926594	+	0.262451i
$574$	0.468879	−	16.3187i	0.0195706	−	0.681128i
$575$	4.84595	+	14.1592i	0.202090	+	0.590479i
$576$	6.20569	−	11.4910i	0.258571	−	0.478790i
$577$	3.69299	−	13.7824i	0.153741	−	0.573769i	−0.845469	−	0.534025i	$-0.820679\pi$
$577$	3.69299	−	13.7824i	0.153741	−	0.573769i	0.999210	−	0.0397445i	$-0.0126544\pi$
$578$	26.8574	+	26.8574i	1.11712	+	1.11712i
$579$	0.187764	+	13.2096i	0.00780322	+	0.548972i
$580$	76.5100	−	23.3137i	3.17691	−	0.968047i
$581$	0.438923	−	15.2761i	0.0182096	−	0.633759i
$582$	−25.1847	−	6.36599i	−1.04394	−	0.263879i
$583$	−41.1937	−	11.0378i	−1.70607	−	0.457140i
$584$	8.46813	+	14.6672i	0.350414	+	0.606934i
$585$	9.90119	+	14.9164i	0.409364	+	0.616716i
$586$	16.6414	−	28.8238i	0.687452	−	1.19070i
$587$	3.81103	+	14.2230i	0.157298	+	0.587044i	0.998898	+	0.0469423i	$0.0149477\pi$
$587$	3.81103	+	14.2230i	0.157298	+	0.587044i	−0.841600	+	0.540102i	$0.818386\pi$
$588$	11.1940	+	50.3981i	0.461632	+	2.07838i
$589$	2.07216	−	1.19636i	0.0853817	−	0.0492951i
$590$	−39.3297	+	24.5251i	−1.61918	+	1.00968i
$591$	4.99534	−	2.97952i	0.205481	−	0.122561i
$592$	−31.3375	−	31.3375i	−1.28796	−	1.28796i
$593$	36.3628	−	9.74339i	1.49324	−	0.400113i	0.582412	−	0.812894i	$-0.302109\pi$
$593$	36.3628	−	9.74339i	1.49324	−	0.400113i	0.910830	+	0.412781i	$0.135442\pi$
$594$	49.9269	−	31.7372i	2.04852	−	1.30219i
$595$	−5.60918	+	5.66841i	−0.229954	+	0.232382i
$596$	−64.6073	−	37.3010i	−2.64642	−	1.52791i
$597$	42.4789	−	12.0318i	1.73854	−	0.492429i
$598$	5.17210	+	19.3025i	0.211503	+	0.789339i
$599$	−3.77067	+	6.53100i	−0.154066	+	0.266849i	−0.932718	−	0.360606i	$-0.882570\pi$
$599$	−3.77067	+	6.53100i	−0.154066	+	0.266849i	0.778653	+	0.627455i	$0.215903\pi$
$600$	4.01505	+	48.7551i	0.163914	+	1.99042i
$601$	−7.10144	+	12.3001i	−0.289674	+	0.501730i	−0.973732	−	0.227698i	$-0.926880\pi$
$601$	−7.10144	+	12.3001i	−0.289674	+	0.501730i	0.684058	+	0.729428i	$0.260214\pi$
$602$	−75.5898	−	22.6001i	−3.08081	−	0.921112i
$603$	−13.8119	−	3.28314i	−0.562464	−	0.133700i
$604$	46.0642	+	26.5952i	1.87433	+	1.08214i
$605$	21.1592	+	4.90572i	0.860243	+	0.199446i
$606$	−31.3820	+	56.1845i	−1.27481	+	2.28234i
$607$	−14.5439	−	14.5439i	−0.590320	−	0.590320i	0.347398	−	0.937718i	$-0.387065\pi$
$607$	−14.5439	−	14.5439i	−0.590320	−	0.590320i	−0.937718	+	0.347398i	$0.887065\pi$
$608$	−2.83423	+	10.5775i	−0.114943	+	0.428973i
$609$	−18.7620	−	33.6139i	−0.760274	−	1.36211i
$610$	−0.819349	−	24.1060i	−0.0331745	−	0.976023i
$611$	3.22839	+	1.86391i	0.130607	+	0.0754057i
$612$	4.92753	+	16.4989i	0.199184	+	0.666927i
$613$	8.25325	+	2.21145i	0.333346	+	0.0893197i	0.421610	−	0.906777i	$-0.361465\pi$
$613$	8.25325	+	2.21145i	0.333346	+	0.0893197i	−0.0882639	+	0.996097i	$0.528132\pi$
$614$	−13.5432	−	23.4576i	−0.546561	−	0.946671i
$615$	−9.54192	+	0.460177i	−0.384767	+	0.0185561i
$616$	32.3040	+	59.8593i	1.30156	+	2.41180i
$617$	−26.9708	−	7.22679i	−1.08580	−	0.290940i	−0.328831	−	0.944389i	$-0.606655\pi$
$617$	−26.9708	−	7.22679i	−1.08580	−	0.290940i	−0.756970	+	0.653449i	$0.773321\pi$
$618$	−22.3899	+	6.34177i	−0.900654	+	0.255103i
$619$		−	16.7961i		−	0.675091i	−0.941309	−	0.337545i	$-0.890403\pi$
$619$		−	16.7961i		−	0.675091i	0.941309	−	0.337545i	$-0.109597\pi$
$620$	5.47065	−	1.66698i	0.219707	−	0.0669476i
$621$	−0.662959	−	15.5385i	−0.0266036	−	0.623537i
$622$	20.0714	+	20.0714i	0.804790	+	0.804790i
$623$	11.9778	+	12.6864i	0.479879	+	0.508272i
$624$	0.368910	+	25.9535i	0.0147682	+	1.03897i
$625$	15.3181	+	19.7574i	0.612725	+	0.790296i
$626$	−42.0307	−	24.2664i	−1.67988	−	0.969881i
$627$	21.8868	−	22.5180i	0.874076	−	0.899283i
$628$	6.65022	+	1.78192i	0.265373	+	0.0711064i
$629$	−10.6390			−0.424205
$630$	42.4751	−	12.9289i	1.69225	−	0.515100i
$631$	17.3083			0.689031			0.344515	−	0.938781i	$-0.388043\pi$
$631$	17.3083			0.689031			0.344515	+	0.938781i	$0.388043\pi$
$632$	−14.1266	−	3.78522i	−0.561927	−	0.150568i
$633$	−10.1554	−	35.8541i	−0.403640	−	1.42507i
$634$	8.69958	+	5.02271i	0.345505	+	0.199477i
$635$	−1.91521	−	3.07134i	−0.0760030	−	0.121882i
$636$	−59.3526	+	35.4014i	−2.35348	+	1.40376i
$637$	12.4300	+	13.9470i	0.492494	+	0.552600i
$638$	−67.6293	−	67.6293i	−2.67747	−	2.67747i
$639$	19.2509	−	35.6466i	0.761555	−	1.41016i
$640$	17.2336	−	32.3392i	0.681220	−	1.27832i
$641$		−	9.14816i		−	0.361330i	−0.983545	−	0.180665i	$-0.942175\pi$
$641$		−	9.14816i		−	0.361330i	0.983545	−	0.180665i	$-0.0578251\pi$
$642$	−7.72648	+	30.5670i	−0.304940	+	1.20638i
$643$	35.8594	+	9.60851i	1.41416	+	0.378923i	0.883408	−	0.468605i	$-0.155243\pi$
$643$	35.8594	+	9.60851i	1.41416	+	0.378923i	0.530751	+	0.847528i	$0.321910\pi$
$644$	33.7057	+	0.968456i	1.32819	+	0.0381625i
$645$	−9.78690	+	45.1177i	−0.385359	+	1.77651i
$646$	6.71635	+	11.6331i	0.264251	+	0.457697i
$647$	16.7661	+	4.49246i	0.659143	+	0.176617i	0.572859	−	0.819654i	$-0.305834\pi$
$647$	16.7661	+	4.49246i	0.659143	+	0.176617i	0.0862836	+	0.996271i	$0.472501\pi$
$648$	10.3465	−	49.7754i	0.406451	−	1.95536i
$649$	32.6589	+	18.8557i	1.28198	+	0.740149i
$650$	18.6158	+	27.7101i	0.730170	+	1.08688i
$651$	−1.34153	−	2.40348i	−0.0525786	−	0.0941997i
$652$	0.619077	−	2.31043i	0.0242449	−	0.0904833i
$653$	−10.8819	−	10.8819i	−0.425841	−	0.425841i	0.461368	−	0.887209i	$-0.347359\pi$
$653$	−10.8819	−	10.8819i	−0.425841	−	0.425841i	−0.887209	+	0.461368i	$0.847359\pi$
$654$	7.78454	−	0.110651i	0.304400	−	0.00432681i
$655$	1.81111	−	7.81160i	0.0707658	−	0.305225i
$656$	−11.9943	−	6.92493i	−0.468300	−	0.270373i
$657$	−6.53834	−	6.17680i	−0.255085	−	0.240980i
$658$	6.72207	−	6.34657i	0.262054	−	0.247415i
$659$	−11.1630	+	19.3349i	−0.434848	+	0.753180i	−0.997283	−	0.0736620i	$-0.976531\pi$
$659$	−11.1630	+	19.3349i	−0.434848	+	0.753180i	0.562435	+	0.826842i	$0.309865\pi$
$660$	63.1174	−	40.6157i	2.45684	−	1.58096i
$661$	13.7428	−	23.8032i	0.534532	−	0.925837i	−0.464653	−	0.885493i	$-0.653821\pi$
$661$	13.7428	−	23.8032i	0.534532	−	0.925837i	0.999186	−	0.0403446i	$-0.0128456\pi$
$662$	5.04566	+	18.8307i	0.196105	+	0.731875i
$663$	4.46821	+	4.34297i	0.173531	+	0.168667i
$664$	−28.2573	−	16.3144i	−1.09660	−	0.633120i
$665$	20.3475	−	11.8905i	0.789040	−	0.461094i
$666$	52.1191	+	28.1469i	2.01957	+	1.09067i
$667$	−24.2866	+	6.50756i	−0.940379	+	0.251974i
$668$	−31.8230	−	31.8230i	−1.23127	−	1.23127i
$669$	0.360841	+	25.3859i	0.0139509	+	0.981474i
$670$	−25.7871	−	5.97870i	−0.996244	−	0.230977i
$671$	−16.9953	+	9.81226i	−0.656098	+	0.378798i
$672$	12.1195	+	3.43665i	0.467519	+	0.132572i
$673$	−11.0836	−	41.3645i	−0.427240	−	1.59448i	−0.758981	−	0.651112i	$-0.774303\pi$
$673$	−11.0836	−	41.3645i	−0.427240	−	1.59448i	0.331741	−	0.943370i	$-0.392364\pi$
$674$	−15.8360	+	27.4288i	−0.609980	+	1.05652i
$675$	−9.45295	−	24.2000i	−0.363844	−	0.931460i
$676$	−12.5125	−	21.6723i	−0.481250	−	0.833549i
$677$	3.23704	+	0.867362i	0.124409	+	0.0333354i	0.320487	−	0.947253i	$-0.396154\pi$
$677$	3.23704	+	0.867362i	0.124409	+	0.0333354i	−0.196077	+	0.980588i	$0.562820\pi$
$678$	−16.2479	+	16.7165i	−0.623997	+	0.641992i
$679$	−0.455566	+	15.8553i	−0.0174830	+	0.608471i
$680$	4.96280	+	16.2868i	0.190315	+	0.624569i
$681$	−26.5958	+	15.8633i	−1.01915	+	0.607884i
$682$	−4.83565	−	4.83565i	−0.185167	−	0.185167i
$683$	3.96434	−	14.7951i	0.151691	−	0.566120i	−0.847675	−	0.530517i	$-0.821998\pi$
$683$	3.96434	−	14.7951i	0.151691	−	0.566120i	0.999366	−	0.0356035i	$-0.0113353\pi$
$684$	−1.44634	−	50.8661i	−0.0553021	−	1.94491i
$685$	−2.47343	+	1.54237i	−0.0945048	+	0.0589310i
$686$	41.9683	−	19.6260i	1.60236	−	0.749323i
$687$	3.51400	−	13.9018i	0.134067	−	0.530388i
$688$	−47.3284	+	47.3284i	−1.80438	+	1.80438i
$689$	−12.5042	+	21.6580i	−0.476374	+	0.825104i
$690$	−1.39692	−	28.9656i	−0.0531799	−	1.10270i
$691$	2.35288	+	4.07531i	0.0895079	+	0.155032i	0.907303	−	0.420477i	$-0.138137\pi$
$691$	2.35288	+	4.07531i	0.0895079	+	0.155032i	−0.817795	+	0.575509i	$0.804804\pi$
$692$	34.0195	−	34.0195i	1.29323	−	1.29323i
$693$	−25.5361	−	25.5513i	−0.970035	−	0.970614i
$694$			43.1442i			1.63773i
$695$	−49.1456	+	14.9753i	−1.86420	+	0.568047i
$696$	−82.1817	+	1.16815i	−3.11509	+	0.0442786i
$697$	−3.21153	+	0.860526i	−0.121645	+	0.0325947i
$698$	−31.0988	−	31.0988i	−1.17711	−	1.17711i
$699$	12.1893	−	0.173261i	0.461041	−	0.00655335i
$700$	53.7960	−	16.7016i	2.03330	−	0.631262i
$701$		−	42.8919i		−	1.62000i	−0.586427	−	0.810002i	$-0.699466\pi$
$701$		−	42.8919i		−	1.62000i	0.586427	−	0.810002i	$-0.300534\pi$
$702$	−10.3993	−	33.0968i	−0.392495	−	1.24916i
$703$	30.3698	+	8.13757i	1.14542	+	0.306914i
$704$	−19.8124			−0.746707
$705$	−4.00504	−	3.63651i	−0.150839	−	0.136959i
$706$	−17.6231	−	30.5240i	−0.663252	−	1.14879i
$707$	37.6493	+	11.2565i	1.41595	+	0.423345i
$708$	58.7975	−	16.6539i	2.20975	−	0.625893i
$709$	30.3886	−	17.5449i	1.14127	−	0.658912i	0.194524	−	0.980898i	$-0.437684\pi$
$709$	30.3886	−	17.5449i	1.14127	−	0.658912i	0.946744	+	0.321986i	$0.104350\pi$
$710$	35.5257	−	66.6645i	1.33326	−	2.50187i
$711$	7.76395	−	0.220762i	0.291171	−	0.00827922i
$712$	35.9819	−	9.64131i	1.34848	−	0.361323i
$713$	−1.73655	+	0.465306i	−0.0650342	+	0.0174259i
$714$	13.4931	−	7.53132i	0.504966	−	0.281853i
$715$	12.7735	−	23.9697i	0.477703	−	0.896416i
$716$		−	52.5900i		−	1.96538i
$717$	1.08210	+	3.82039i	0.0404116	+	0.142675i
$718$	−2.70528	+	2.70528i	−0.100960	+	0.100960i
$719$	16.1678	−	28.0034i	0.602956	−	1.04435i	−0.389415	−	0.921062i	$-0.627323\pi$
$719$	16.1678	−	28.0034i	0.602956	−	1.04435i	0.992371	−	0.123287i	$-0.0393437\pi$
$720$	7.46093	−	36.9203i	0.278052	−	1.37594i
$721$	6.74837	+	12.5047i	0.251323	+	0.465701i
$722$	2.02743	+	7.56648i	0.0754532	+	0.281595i
$723$	40.4094	+	10.2144i	1.50284	+	0.379876i
$724$	3.45006	+	1.99189i	0.128220	+	0.0740281i
$725$	−34.8650	+	23.4225i	−1.29485	+	0.869888i
$726$	−36.7452	−	20.5241i	−1.36374	−	0.761721i
$727$	−40.9609	+	10.9755i	−1.51916	+	0.407057i	−0.919464	−	0.393173i	$-0.871377\pi$
$727$	−40.9609	+	10.9755i	−1.51916	+	0.407057i	−0.599693	+	0.800230i	$0.704711\pi$
$728$	38.8089	−	9.21279i	1.43835	−	0.341449i
$729$	2.29976	+	26.9019i	0.0851763	+	0.996366i
$730$	−12.2551	−	11.4494i	−0.453580	−	0.423760i
$731$			16.0679i			0.594293i
$732$	−7.79335	+	30.8315i	−0.288051	+	1.13957i
$733$	−33.6967	+	33.6967i	−1.24461	+	1.24461i	−0.286549	+	0.958066i	$0.592508\pi$
$733$	−33.6967	+	33.6967i	−1.24461	+	1.24461i	−0.958066	+	0.286549i	$0.907492\pi$
$734$	−0.846665	−	1.46647i	−0.0312510	−	0.0541283i
$735$	−13.3375	−	23.6032i	−0.491959	−	0.870618i
$736$	4.11395	−	7.12557i	0.151642	−	0.262652i
$737$	5.57432	+	20.8037i	0.205333	+	0.766313i
$738$	18.0094	+	4.28092i	0.662937	+	0.157583i
$739$	−3.74243	+	2.16069i	−0.137667	+	0.0794823i	−0.567252	−	0.823544i	$-0.691993\pi$
$739$	−3.74243	+	2.16069i	−0.137667	+	0.0794823i	0.429584	+	0.903027i	$0.358660\pi$
$740$	66.3202	+	35.3423i	2.43798	+	1.29921i
$741$	−9.43298	−	15.8150i	−0.346529	−	0.580977i
$742$	42.5767	+	45.0958i	1.56304	+	1.65552i
$743$	1.48953	−	5.55901i	0.0546457	−	0.203940i	−0.933206	−	0.359343i	$-0.883001\pi$
$743$	1.48953	−	5.55901i	0.0546457	−	0.203940i	0.987851	+	0.155403i	$0.0496675\pi$
$744$	−5.87619	+	0.0835255i	−0.215432	+	0.00306219i
$745$	38.1640	+	8.84825i	1.39822	+	0.324175i
$746$	29.6367	−	17.1107i	1.08508	−	0.626469i
$747$	16.8589	+	4.00742i	0.616834	+	0.146624i
$748$	18.4714	−	18.4714i	0.675381	−	0.675381i
$749$	19.2438	+	0.552926i	0.703153	+	0.0202035i
$750$	−17.8761	−	45.0247i	−0.652741	−	1.64407i
$751$	−26.5928			−0.970384			−0.485192	−	0.874408i	$-0.661250\pi$
$751$	−26.5928			−0.970384			−0.485192	+	0.874408i	$0.661250\pi$
$752$	−2.02989	−	7.57565i	−0.0740225	−	0.276256i
$753$	−5.93514	+	23.4802i	−0.216289	+	0.855666i
$754$	−48.5715	+	28.0427i	−1.76887	+	1.02126i
$755$	−27.2105	−	6.30870i	−0.990290	−	0.229597i
$756$	−58.5331	+	0.814543i	−2.12883	+	0.0296246i
$757$	5.17117	+	5.17117i	0.187949	+	0.187949i	0.794809	−	0.606860i	$-0.207571\pi$
$757$	5.17117	+	5.17117i	0.187949	+	0.187949i	−0.606860	+	0.794809i	$0.707571\pi$
$758$	−4.26021	+	15.8993i	−0.154738	+	0.577490i
$759$	−20.2637	+	12.0865i	−0.735525	+	0.438711i
$760$	−1.70925	−	50.2877i	−0.0620010	−	1.82413i
$761$			41.8891i			1.51848i	0.650811	+	0.759240i	$0.274429\pi$
$761$			41.8891i			1.51848i	−0.650811	+	0.759240i	$0.725571\pi$
$762$	1.91140	+	6.74828i	0.0692427	+	0.244465i
$763$	−1.09800	−	4.62530i	−0.0397501	−	0.167447i
$764$	56.6730			2.05036
$765$	−5.00071	−	7.53368i	−0.180801	−	0.272381i
$766$	47.7997	+	82.7914i	1.72707	+	2.99138i
$767$	15.6371	−	15.6371i	0.564624	−	0.564624i
$768$	−38.9808	+	40.1049i	−1.40660	+	1.44716i
$769$	6.74062	−	3.89170i	0.243073	−	0.140338i	−0.373515	−	0.927624i	$-0.621848\pi$
$769$	6.74062	−	3.89170i	0.243073	−	0.140338i	0.616588	+	0.787286i	$0.288514\pi$
$770$	−47.8781	−	47.3778i	−1.72541	−	1.70738i
$771$	−3.66460	+	2.18579i	−0.131977	+	0.0787191i
$772$	8.40586	−	31.3711i	0.302533	−	1.12907i
$773$	−13.4330	+	50.1327i	−0.483152	+	1.80315i	0.105091	+	0.994463i	$0.466487\pi$
$773$	−13.4330	+	50.1327i	−0.483152	+	1.80315i	−0.588243	+	0.808684i	$0.700180\pi$
$774$	42.5098	−	78.7144i	1.52798	−	2.82933i
$775$	−2.49293	+	1.67476i	−0.0895486	+	0.0601592i
$776$	29.3287	+	16.9329i	1.05284	+	0.607857i
$777$	9.86724	−	34.7972i	0.353985	−	1.24834i
$778$	84.9437	+	22.7606i	3.04538	+	0.816007i
$779$	9.82572			0.352043
$780$	−13.4263	−	41.9158i	−0.480738	−	1.50083i
$781$	−61.4608			−2.19924
$782$	−2.61223	−	9.74896i	−0.0934130	−	0.348622i
$783$	41.6426	−	13.0844i	1.48819	−	0.467599i
$784$	2.25682	−	39.2402i	0.0806007	−	1.40144i
$785$	−3.61338	+	0.122817i	−0.128967	+	0.00438352i
$786$	−7.57714	+	13.5657i	−0.270268	+	0.483872i
$787$	−28.5968	+	7.66248i	−1.01936	+	0.273138i	−0.729537	−	0.683941i	$-0.760264\pi$
$787$	−28.5968	+	7.66248i	−1.01936	+	0.273138i	−0.289827	+	0.957079i	$0.593598\pi$
$788$	−13.8119	+	3.70088i	−0.492028	+	0.131838i
$789$	17.4489	+	29.2541i	0.621197	+	1.04147i
$790$	14.4741	−	0.491966i	0.514965	−	0.0175034i
$791$	12.1179	+	7.46837i	0.430864	+	0.265545i
$792$	−73.9016	+	22.0714i	−2.62598	+	0.784272i
$793$	2.97849	+	11.1159i	0.105769	+	0.394736i
$794$	−26.3518			−0.935191
$795$	24.3960	−	26.8683i	0.865235	−	0.952920i
$796$	−108.538			−3.84703
$797$	−17.3406	−	4.64641i	−0.614237	−	0.164584i	−0.0617302	−	0.998093i	$-0.519662\pi$
$797$	−17.3406	−	4.64641i	−0.614237	−	0.164584i	−0.552506	+	0.833509i	$0.686329\pi$
$798$	−44.2775	+	11.1781i	−1.56741	+	0.395700i
$799$	−1.63053	−	0.941388i	−0.0576841	−	0.0333039i
$800$	2.64773	−	13.4874i	0.0936113	−	0.476850i
$801$	−16.8450	+	10.3747i	−0.595188	+	0.366573i
$802$	19.6273	−	73.2499i	0.693063	−	2.58655i
$803$	−3.53171	+	13.1805i	−0.124631	+	0.465130i
$804$	30.4703	+	17.0193i	1.07461	+	0.600223i
$805$	−17.0797	+	4.67277i	−0.601982	+	0.164694i
$806$	−3.47297	+	2.00512i	−0.122330	+	0.0706274i
$807$	11.6634	+	41.1783i	0.410572	+	1.44954i
$808$	59.3255	−	59.3255i	2.08707	−	2.08707i
$809$	13.2006	+	22.8642i	0.464110	+	0.803862i	0.999161	−	0.0409576i	$-0.0130409\pi$
$809$	13.2006	+	22.8642i	0.464110	+	0.803862i	−0.535051	+	0.844820i	$0.679708\pi$
$810$	4.56643	+	50.1365i	0.160448	+	1.76162i
$811$	−13.2437			−0.465051			−0.232525	−	0.972590i	$-0.574699\pi$
$811$	−13.2437			−0.465051			−0.232525	+	0.972590i	$0.574699\pi$
$812$	21.8584	+	92.0785i	0.767080	+	3.23132i
$813$	37.6393	−	38.7247i	1.32007	−	1.35814i
$814$		−	89.8622i		−	3.14967i
$815$	0.0426691	+	1.25537i	0.00149463	+	0.0439735i
$816$	−0.186322	−	13.1081i	−0.00652257	−	0.458876i
$817$	12.2900	−	45.8670i	0.429973	−	1.60468i
$818$	−51.2274	−	51.2274i	−1.79113	−	1.79113i
$819$	−18.3487	+	10.5863i	−0.641155	+	0.369916i
$820$	22.8782	+	5.30428i	0.798943	+	0.185233i
$821$	−22.8620	+	13.1994i	−0.797890	+	0.460662i	−0.842733	−	0.538332i	$-0.819055\pi$
$821$	−22.8620	+	13.1994i	−0.797890	+	0.460662i	0.0448429	+	0.998994i	$0.485721\pi$
$822$	5.43457	−	1.53930i	0.189552	−	0.0536892i
$823$	−10.5916	−	39.5285i	−0.369201	−	1.37788i	−0.861635	−	0.507528i	$-0.830559\pi$
$823$	−10.5916	−	39.5285i	−0.369201	−	1.37788i	0.492434	−	0.870350i	$-0.336107\pi$
$824$	30.3380			1.05687
$825$	−25.4890	+	30.0639i	−0.887413	+	1.04669i
$826$	−26.0455	−	48.2624i	−0.906240	−	1.67926i
$827$	−3.72951	+	3.72951i	−0.129688	+	0.129688i	−0.768971	−	0.639283i	$-0.779231\pi$
$827$	−3.72951	+	3.72951i	−0.129688	+	0.129688i	0.639283	+	0.768971i	$0.279231\pi$
$828$	−8.84211	+	37.1980i	−0.307285	+	1.29272i
$829$	−30.6933	+	17.7208i	−1.06602	+	0.615468i	−0.927092	−	0.374834i	$-0.877700\pi$
$829$	−30.6933	+	17.7208i	−1.06602	+	0.615468i	−0.138930	+	0.990302i	$0.544366\pi$
$830$	31.4759	+	7.29763i	1.09254	+	0.253304i
$831$	10.3677	+	17.3820i	0.359650	+	0.602975i
$832$	−3.00700	+	11.2223i	−0.104249	+	0.389062i
$833$	−6.27790	−	7.04409i	−0.217516	−	0.244063i
$834$	99.5444	−	1.41495i	3.44694	−	0.0489956i
$835$	20.8568	+	11.1147i	0.721781	+	0.384639i
$836$	−66.8562	+	38.5995i	−2.31227	+	1.33499i
$837$	2.97755	−	0.935566i	0.102919	−	0.0323379i
$838$	−2.79377	−	10.4265i	−0.0965090	−	0.360177i
$839$	11.5706	−	20.0409i	0.399462	−	0.691888i	−0.594198	−	0.804319i	$-0.702530\pi$
$839$	11.5706	−	20.0409i	0.399462	−	0.691888i	0.993660	+	0.112431i	$0.0358637\pi$
$840$	−57.8722	+	1.12661i	−1.99678	+	0.0388718i
$841$	−20.7835	−	35.9981i	−0.716674	−	1.24132i
$842$	−15.4028	+	15.4028i	−0.530816	+	0.530816i
$843$	−9.02356	−	8.77063i	−0.310788	−	0.302076i
$844$			91.6110i			3.15338i
$845$	9.60277	+	8.97144i	0.330345	+	0.308627i
$846$	5.49719	+	8.92552i	0.188997	+	0.306866i
$847$	−7.36187	+	24.6230i	−0.252957	+	0.846055i
$848$	50.8221	−	13.6177i	1.74524	−	0.467635i
$849$	0.504192	+	35.4709i	0.0173038	+	1.21736i
$850$	−9.40210	−	13.9953i	−0.322489	−	0.480034i
$851$	−20.4588	−	11.8119i	−0.701319	−	0.404906i
$852$	−69.4171	+	71.4190i	−2.37819	+	2.44677i
$853$	2.86327	+	10.6859i	0.0980365	+	0.365877i	0.997462	−	0.0711962i	$-0.0226817\pi$
$853$	2.86327	+	10.6859i	0.0980365	+	0.365877i	−0.899426	+	0.437073i	$0.856015\pi$
$854$	28.5273	+	0.819666i	0.976184	+	0.0280484i
$855$	8.51251	+	25.3304i	0.291122	+	0.866280i
$856$	20.5517	−	35.5966i	0.702443	−	1.21667i
$857$	11.3063	−	11.3063i	0.386215	−	0.386215i	−0.487120	−	0.873335i	$-0.661953\pi$
$857$	11.3063	−	11.3063i	0.386215	−	0.386215i	0.873335	+	0.487120i	$0.161953\pi$
$858$	−36.6828	+	37.7406i	−1.25233	+	1.28844i
$859$		−	52.2492i		−	1.78272i	−0.453297	−	0.891359i	$-0.649752\pi$
$859$		−	52.2492i		−	1.78272i	0.453297	−	0.891359i	$-0.350248\pi$
$860$	53.3767	−	100.162i	1.82013	−	3.41550i
$861$	0.164022	−	11.3021i	0.00558985	−	0.385174i
$862$	92.5277	−	24.7927i	3.15151	−	0.844443i
$863$	15.6807	−	4.20163i	0.533777	−	0.143025i	0.0181450	−	0.999835i	$-0.494224\pi$
$863$	15.6807	−	4.20163i	0.533777	−	0.143025i	0.515632	+	0.856810i	$0.327557\pi$
$864$	−6.60820	+	12.6635i	−0.224816	+	0.430821i
$865$	−11.8818	+	22.2964i	−0.403995	+	0.758101i
$866$	19.3302	−	11.1603i	0.656867	−	0.379243i
$867$	18.8578	+	18.3292i	0.640443	+	0.622491i
$868$	1.56293	+	6.58383i	0.0530492	+	0.223470i
$869$	−5.89163	−	10.2046i	−0.199860	−	0.346168i
$870$	77.5100	−	24.8276i	2.62783	−	0.841735i
$871$	12.6298			0.427945
$872$	−9.80386	−	2.62694i	−0.332001	−	0.0889593i
$873$	−17.4981	−	4.15937i	−0.592221	−	0.140773i
$874$			29.8271i			1.00892i
$875$	−24.4670	+	16.6242i	−0.827137	+	0.562001i
$876$	11.3272	+	18.9907i	0.382710	+	0.641637i
$877$	−16.1806	−	16.1806i	−0.546380	−	0.546380i	0.379012	−	0.925392i	$-0.376264\pi$
$877$	−16.1806	−	16.1806i	−0.546380	−	0.546380i	−0.925392	+	0.379012i	$0.876264\pi$
$878$	−30.4706	+	8.16457i	−1.02833	+	0.275541i
$879$	11.2373	−	20.1186i	0.379024	−	0.678584i
$880$	−54.6618	+	16.6562i	−1.84265	+	0.561480i
$881$		−	2.25878i		−	0.0761003i	−0.999276	−	0.0380502i	$-0.987885\pi$
$881$		−	2.25878i		−	0.0761003i	0.999276	−	0.0380502i	$-0.0121147\pi$
$882$	12.1185	+	51.1170i	0.408051	+	1.72120i
$883$	−11.8372	+	11.8372i	−0.398354	+	0.398354i	−0.877652	−	0.479298i	$-0.840891\pi$
$883$	−11.8372	+	11.8372i	−0.398354	+	0.398354i	0.479298	+	0.877652i	$0.340891\pi$
$884$	−7.65923	−	13.2662i	−0.257608	−	0.446190i
$885$	−26.9868	+	17.3658i	−0.907150	+	0.583746i
$886$	4.69918	−	8.13922i	0.157872	−	0.273442i
$887$	9.24024	−	9.24024i	0.310257	−	0.310257i	−0.534752	−	0.845009i	$-0.679595\pi$
$887$	9.24024	−	9.24024i	0.310257	−	0.310257i	0.845009	+	0.534752i	$0.179595\pi$
$888$	−55.3754	−	53.8233i	−1.85828	−	1.80619i
$889$	3.76891	−	2.03395i	0.126405	−	0.0682165i
$890$	−31.3012	+	19.5187i	−1.04922	+	0.654267i
$891$	34.2522	−	22.4631i	1.14749	−	0.752543i
$892$	16.1541	−	60.2881i	0.540881	−	2.01860i
$893$	3.93442	+	3.93442i	0.131660	+	0.131660i
$894$	−66.2758	−	37.0185i	−2.21660	−	1.23808i
$895$	8.04984	+	26.4177i	0.269077	+	0.883047i
$896$	36.9113	+	22.7487i	1.23312	+	0.759980i
$897$	3.77061	+	13.3123i	0.125897	+	0.444485i
$898$	−1.37419	−	0.368213i	−0.0458573	−	0.0122874i
$899$	−2.52286	−	4.36972i	−0.0841420	−	0.145738i
$900$	6.14631	+	63.5746i	0.204877	+	2.11915i
$901$	6.31541	−	10.9386i	0.210397	−	0.364418i
$902$	−7.26841	−	27.1261i	−0.242012	−	0.903199i
$903$	−52.5535	−	14.9023i	−1.74887	−	0.495918i
$904$	26.3197	−	15.1957i	0.875380	−	0.505401i
$905$	−2.03797	−	0.472500i	−0.0677445	−	0.0157064i
$906$	47.2539	+	26.3938i	1.56991	+	0.876874i
$907$	−12.1725	−	12.1725i	−0.404180	−	0.404180i	0.475523	−	0.879703i	$-0.342259\pi$
$907$	−12.1725	−	12.1725i	−0.404180	−	0.404180i	−0.879703	+	0.475523i	$0.842259\pi$
$908$	73.5362	−	19.7040i	2.44038	−	0.653899i
$909$	−21.1730	+	39.2055i	−0.702263	+	1.30037i
$910$	−34.1027	+	19.9287i	−1.13049	+	0.660631i
$911$	−17.7586	−	10.2529i	−0.588369	−	0.339695i	0.176084	−	0.984375i	$-0.443657\pi$
$911$	−17.7586	−	10.2529i	−0.588369	−	0.339695i	−0.764452	+	0.644680i	$0.776990\pi$
$912$	−9.49427	+	37.5606i	−0.314387	+	1.24376i
$913$	−6.80405	−	25.3930i	−0.225181	−	0.840387i
$914$	17.3922	−	30.1241i	0.575282	−	0.996418i
$915$	−0.804455	−	16.6806i	−0.0265944	−	0.551444i
$916$	−17.6256	+	30.5284i	−0.582366	+	1.00869i
$917$	9.09037	+	2.71787i	0.300191	+	0.0897521i
$918$	5.25226	+	16.7159i	0.173350	+	0.551708i
$919$	−16.2656	−	9.39094i	−0.536552	−	0.309779i	0.207128	−	0.978314i	$-0.433588\pi$
$919$	−16.2656	−	9.39094i	−0.536552	−	0.309779i	−0.743681	+	0.668535i	$0.766922\pi$
$920$	−8.53882	+	36.8293i	−0.281516	+	1.21423i
$921$	−9.60687	−	16.1065i	−0.316557	−	0.530727i
$922$	39.2361	+	39.2361i	1.29217	+	1.29217i
$923$	−9.32814	+	34.8131i	−0.307039	+	1.14589i
$924$	43.2832	+	77.5460i	1.42391	+	2.55108i
$925$	−38.7246	−	7.60210i	−1.27326	−	0.249956i
$926$	76.3137	+	44.0597i	2.50782	+	1.44789i
$927$	−15.4382	+	4.61076i	−0.507057	+	0.151437i
$928$	22.3056	+	5.97675i	0.732216	+	0.196197i
$929$	−11.2868	−	19.5493i	−0.370309	−	0.641393i	0.619304	−	0.785151i	$-0.287415\pi$
$929$	−11.2868	−	19.5493i	−0.370309	−	0.641393i	−0.989613	+	0.143758i	$0.954081\pi$
$930$	5.54215	−	1.77523i	0.181734	−	0.0582122i
$931$	12.5328	+	24.9097i	0.410747	+	0.816382i
$932$	−28.9480	−	7.75658i	−0.948222	−	0.254075i
$933$	14.0930	+	13.6980i	0.461385	+	0.448452i
$934$			72.8299i			2.38307i
$935$	−6.45141	+	12.1062i	−0.210984	+	0.395914i
$936$	1.28550	+	45.2098i	0.0420180	+	1.47773i
$937$	−16.2021	−	16.2021i	−0.529301	−	0.529301i	0.391063	−	0.920364i	$-0.372107\pi$
$937$	−16.2021	−	16.2021i	−0.529301	−	0.529301i	−0.920364	+	0.391063i	$0.872107\pi$
$938$	8.97206	−	30.0085i	0.292948	−	0.979813i
$939$	−29.3368	−	16.3861i	−0.957370	−	0.534741i
$940$	7.03697	+	11.2849i	0.229521	+	0.368071i
$941$	26.6214	+	15.3699i	0.867834	+	0.501044i	0.866628	−	0.498955i	$-0.166283\pi$
$941$	26.6214	+	15.3699i	0.867834	+	0.501044i	0.00120626	+	0.999999i	$0.499616\pi$
$942$	6.79221	+	1.71688i	0.221302	+	0.0559391i
$943$	−7.13115	−	1.91078i	−0.232222	−	0.0622237i
$944$	−46.5258			−1.51429
$945$	29.2784	−	9.36871i	0.952428	−	0.304764i
$946$	−135.717			−4.41255
$947$	24.7030	+	6.61916i	0.802741	+	0.215094i	0.636787	−	0.771040i	$-0.280263\pi$
$947$	24.7030	+	6.61916i	0.802741	+	0.215094i	0.165954	+	0.986134i	$0.446930\pi$
$948$	−18.5123	−	4.67940i	−0.601253	−	0.151980i
$949$	6.92979	+	4.00092i	0.224951	+	0.129875i
$950$	16.1342	+	47.1420i	0.523464	+	1.52949i
$951$	6.07218	+	3.39163i	0.196904	+	0.109981i
$952$	−19.6008	+	4.65302i	−0.635267	+	0.150805i
$953$	1.48614	+	1.48614i	0.0481408	+	0.0481408i	0.730767	−	0.682627i	$-0.239162\pi$
$953$	1.48614	+	1.48614i	0.0481408	+	0.0481408i	−0.682627	+	0.730767i	$0.739162\pi$
$954$	−59.8778	+	36.8785i	−1.93862	+	1.19398i
$955$	−28.4687	+	8.67482i	−0.921227	+	0.280711i
$956$		−	9.76152i		−	0.315710i
$957$	−47.4855	−	46.1545i	−1.53499	−	1.49196i
$958$	−73.2565	−	19.6290i	−2.36681	−	0.634185i
$959$	−1.63799	−	3.03520i	−0.0528935	−	0.0980118i
$960$	7.71679	−	14.9902i	0.249058	−	0.483806i
$961$	15.3196	+	26.5343i	0.494181	+	0.855947i
$962$	−50.9004	−	13.6387i	−1.64110	−	0.439730i
$963$	−5.04827	+	21.2377i	−0.162678	+	0.684374i
$964$	−88.7389	−	51.2334i	−2.85809	−	1.65012i
$965$	0.579363	+	17.0454i	0.0186504	+	0.548711i
$966$	34.3088	+	0.497907i	1.10387	+	0.0160199i
$967$	−4.98059	+	18.5878i	−0.160165	+	0.597743i	0.838443	+	0.544990i	$0.183466\pi$
$967$	−4.98059	+	18.5878i	−0.160165	+	0.597743i	−0.998608	+	0.0527536i	$0.983200\pi$
$968$	38.7995	+	38.7995i	1.24706	+	1.24706i
$969$	4.76423	+	7.98752i	0.153049	+	0.256596i
$970$	−32.6694	−	7.57433i	−1.04895	−	0.243197i
$971$	29.4238	+	16.9879i	0.944255	+	0.545166i	0.891292	−	0.453430i	$-0.149800\pi$
$971$	29.4238	+	16.9879i	0.944255	+	0.545166i	0.0529636	+	0.998596i	$0.483133\pi$
$972$	12.5836	−	65.1730i	0.403619	−	2.09043i
$973$	−14.0406	−	59.1459i	−0.450120	−	1.89613i
$974$	−22.8699	+	39.6118i	−0.732798	+	1.26924i
$975$	13.1604	+	19.0006i	0.421471	+	0.608506i
$976$	12.1057	−	20.9678i	0.387495	−	0.671162i
$977$	15.0975	+	56.3448i	0.483013	+	1.80263i	0.588845	+	0.808246i	$0.299583\pi$
$977$	15.0975	+	56.3448i	0.483013	+	1.80263i	−0.105831	+	0.994384i	$0.533750\pi$
$978$	0.596481	−	2.35976i	0.0190734	−	0.0754567i
$979$	25.9921	+	15.0066i	0.830712	+	0.479612i
$980$	15.7343	+	64.7654i	0.502615	+	2.06886i
$981$	5.38817	−	0.153209i	0.172031	−	0.00489157i
$982$	−24.5644	+	6.58201i	−0.783881	+	0.210040i
$983$	−1.37133	−	1.37133i	−0.0437385	−	0.0437385i	0.684899	−	0.728638i	$-0.259846\pi$
$983$	−1.37133	−	1.37133i	−0.0437385	−	0.0437385i	−0.728638	+	0.684899i	$0.759846\pi$
$984$	−21.0692	−	11.7683i	−0.671662	−	0.375159i
$985$	6.37168	−	3.97323i	0.203019	−	0.126598i
$986$	24.5316	−	14.1633i	0.781244	−	0.451051i
$987$	4.59126	−	4.45991i	0.146141	−	0.141960i
$988$	11.7168	+	43.7276i	0.372760	+	1.39116i
$989$	−17.8393	+	30.8985i	−0.567256	+	0.982516i
$990$	63.6330	−	42.2383i	2.02239	−	1.34242i
$991$	19.8799	+	34.4330i	0.631506	+	1.09380i	0.987244	+	0.159215i	$0.0508963\pi$
$991$	19.8799	+	34.4330i	0.631506	+	1.09380i	−0.355738	+	0.934586i	$0.615770\pi$
$992$	1.59490	+	0.427352i	0.0506381	+	0.0135684i
$993$	3.67844	+	12.9869i	0.116732	+	0.412127i
$994$	76.0896	+	46.8945i	2.41342	+	1.48740i
$995$	54.5223	−	16.6137i	1.72847	−	0.526690i
$996$	−37.1922	−	20.7738i	−1.17848	−	0.658243i
$997$	31.1635	+	31.1635i	0.986959	+	0.986959i	0.999916	−	0.0129569i	$-0.00412443\pi$
$997$	31.1635	+	31.1635i	0.986959	+	0.986959i	−0.0129569	+	0.999916i	$0.504124\pi$
$998$	−4.24847	+	15.8555i	−0.134483	+	0.501898i
$999$	36.3592	+	18.9733i	1.15035	+	0.600290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bx.a.2.4	yes	176
3.2	odd	2		945.2.ca.a.737.41		176
5.3	odd	4	inner	315.2.bx.a.128.4	yes	176
7.4	even	3		315.2.bv.a.137.41	yes	176
9.4	even	3		945.2.by.a.422.41		176
9.5	odd	6		315.2.bv.a.212.4	yes	176
15.8	even	4		945.2.ca.a.548.41		176
21.11	odd	6		945.2.by.a.872.4		176
35.18	odd	12		315.2.bv.a.263.4	yes	176
45.13	odd	12		945.2.by.a.233.4		176
45.23	even	12		315.2.bv.a.23.41	✓	176
63.4	even	3		945.2.ca.a.557.41		176
63.32	odd	6	inner	315.2.bx.a.32.4	yes	176
105.53	even	12		945.2.by.a.683.41		176
315.158	even	12	inner	315.2.bx.a.158.4	yes	176
315.193	odd	12		945.2.ca.a.368.41		176

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bv.a.23.41	✓	176	45.23	even	12
315.2.bv.a.137.41	yes	176	7.4	even	3
315.2.bv.a.212.4	yes	176	9.5	odd	6
315.2.bv.a.263.4	yes	176	35.18	odd	12
315.2.bx.a.2.4	yes	176	1.1	even	1	trivial
315.2.bx.a.32.4	yes	176	63.32	odd	6	inner
315.2.bx.a.128.4	yes	176	5.3	odd	4	inner
315.2.bx.a.158.4	yes	176	315.158	even	12	inner
945.2.by.a.233.4		176	45.13	odd	12
945.2.by.a.422.41		176	9.4	even	3
945.2.by.a.683.41		176	105.53	even	12
945.2.by.a.872.4		176	21.11	odd	6
945.2.ca.a.368.41		176	315.193	odd	12
945.2.ca.a.548.41		176	15.8	even	4
945.2.ca.a.557.41		176	63.4	even	3
945.2.ca.a.737.41		176	3.2	odd	2

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.bx (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.41637 - 0.647465i) q^{2} +(-1.67924 - 0.424464i) q^{3} +(3.68760 + 2.12903i) q^{4} +(-2.17829 - 0.505032i) q^{5} +(3.78283 + 2.11291i) q^{6} +(0.757887 - 2.53488i) q^{7} +(-3.99432 - 3.99432i) q^{8} +(2.63966 + 1.42555i) q^{9} +O(q^{10})\)	\(q+(-2.41637 - 0.647465i) q^{2} +(-1.67924 - 0.424464i) q^{3} +(3.68760 + 2.12903i) q^{4} +(-2.17829 - 0.505032i) q^{5} +(3.78283 + 2.11291i) q^{6} +(0.757887 - 2.53488i) q^{7} +(-3.99432 - 3.99432i) q^{8} +(2.63966 + 1.42555i) q^{9} +(4.93657 + 2.63071i) q^{10} -4.55123i q^{11} +(-5.28864 - 5.14040i) q^{12} +(-2.57794 - 0.690757i) q^{13} +(-3.47258 + 5.63450i) q^{14} +(3.44349 + 1.77267i) q^{15} +(2.80751 + 4.86274i) q^{16} +(1.30202 + 0.348875i) q^{17} +(-5.45541 - 5.15375i) q^{18} +(-3.44985 - 1.99177i) q^{19} +(-6.95742 - 6.50001i) q^{20} +(-2.34864 + 3.93496i) q^{21} +(-2.94676 + 10.9975i) q^{22} +(2.11644 + 2.11644i) q^{23} +(5.01195 + 8.40284i) q^{24} +(4.48988 + 2.20021i) q^{25} +(5.78203 + 3.33825i) q^{26} +(-3.82752 - 3.51427i) q^{27} +(8.19162 - 7.73404i) q^{28} +(-4.20021 + 7.27498i) q^{29} +(-7.17301 - 6.51298i) q^{30} +(-0.300325 + 0.520178i) q^{31} +(-0.711483 - 2.65529i) q^{32} +(-1.93183 + 7.64258i) q^{33} +(-2.92028 - 1.68602i) q^{34} +(-2.93109 + 5.13894i) q^{35} +(6.69896 + 10.8768i) q^{36} +(-7.62381 + 2.04279i) q^{37} +(7.04653 + 7.04653i) q^{38} +(4.03577 + 2.25419i) q^{39} +(6.68351 + 10.7180i) q^{40} +(-2.13612 + 1.23329i) q^{41} +(8.22293 - 7.98767i) q^{42} +(3.08519 + 11.5141i) q^{43} +(9.68972 - 16.7831i) q^{44} +(-5.02999 - 4.43837i) q^{45} +(-3.74379 - 6.48443i) q^{46} +(-1.34918 - 0.361511i) q^{47} +(-2.65040 - 9.35737i) q^{48} +(-5.85121 - 3.84230i) q^{49} +(-9.42467 - 8.22358i) q^{50} +(-2.03831 - 1.13850i) q^{51} +(-8.03576 - 8.03576i) q^{52} +(2.42524 - 9.05112i) q^{53} +(6.97334 + 10.9700i) q^{54} +(-2.29852 + 9.91389i) q^{55} +(-13.1523 + 7.09786i) q^{56} +(4.94768 + 4.80900i) q^{57} +(14.8596 - 14.8596i) q^{58} +(-4.14298 + 7.17586i) q^{59} +(8.92412 + 13.8682i) q^{60} +(-2.15596 - 3.73423i) q^{61} +(1.06249 - 1.06249i) q^{62} +(5.61416 - 5.61081i) q^{63} -4.35319i q^{64} +(5.26665 + 2.80661i) q^{65} +(9.61633 - 17.2165i) q^{66} +(-4.57100 + 1.22480i) q^{67} +(4.05855 + 4.05855i) q^{68} +(-2.65565 - 4.45235i) q^{69} +(10.4099 - 10.5198i) q^{70} -13.5042i q^{71} +(-4.84954 - 16.2377i) q^{72} +(-2.89604 - 0.775991i) q^{73} +19.7446 q^{74} +(-6.60566 - 5.60047i) q^{75} +(-8.48111 - 14.6897i) q^{76} +(-11.5368 - 3.44932i) q^{77} +(-8.29241 - 8.05998i) q^{78} +(2.24217 - 1.29451i) q^{79} +(-3.65972 - 12.0103i) q^{80} +(4.93562 + 7.52593i) q^{81} +(5.96017 - 1.59702i) q^{82} +(5.57938 - 1.49499i) q^{83} +(-17.0385 + 9.51022i) q^{84} +(-2.65998 - 1.41751i) q^{85} -29.8199i q^{86} +(10.1411 - 10.4336i) q^{87} +(-18.1790 + 18.1790i) q^{88} +(-3.29726 + 5.71101i) q^{89} +(9.28065 + 13.9815i) q^{90} +(-3.70477 + 6.01125i) q^{91} +(3.29860 + 12.3106i) q^{92} +(0.725113 - 0.746024i) q^{93} +(3.02605 + 1.74709i) q^{94} +(6.50887 + 6.08095i) q^{95} +(0.0676719 + 4.76085i) q^{96} +(-5.79094 + 1.55168i) q^{97} +(11.6510 + 13.0729i) q^{98} +(6.48800 - 12.0137i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 176 q - 6 q^{2} - 2 q^{3} - 24 q^{6} - 2 q^{7}+O(q^{10}) \) 176 * q - 6 * q^2 - 2 * q^3 - 24 * q^6 - 2 * q^7	\( 176 q - 6 q^{2} - 2 q^{3} - 24 q^{6} - 2 q^{7} - 4 q^{10} - 22 q^{12} - 4 q^{13} - 14 q^{15} + 68 q^{16} - 18 q^{17} - 10 q^{18} - 12 q^{20} + 20 q^{21} + 4 q^{22} - 4 q^{25} - 32 q^{27} - 4 q^{28} - 20 q^{30} + 4 q^{31} - 90 q^{32} + 32 q^{33} + 8 q^{36} - 4 q^{37} - 36 q^{40} - 36 q^{41} + 14 q^{42} - 4 q^{43} - 68 q^{45} + 4 q^{46} - 6 q^{47} + 38 q^{48} + 36 q^{50} + 20 q^{51} - 52 q^{52} + 4 q^{55} - 96 q^{56} + 32 q^{57} - 12 q^{58} - 74 q^{60} - 8 q^{61} + 14 q^{63} - 78 q^{65} - 92 q^{66} + 2 q^{67} - 42 q^{70} - 46 q^{72} - 4 q^{73} + 54 q^{75} - 24 q^{76} + 42 q^{77} + 54 q^{78} + 36 q^{80} + 20 q^{81} - 8 q^{82} - 12 q^{83} - 4 q^{85} - 28 q^{87} + 12 q^{88} - 24 q^{90} - 16 q^{91} + 72 q^{92} + 4 q^{93} - 66 q^{95} - 4 q^{97} + 12 q^{98}+O(q^{100}) \) 176 * q - 6 * q^2 - 2 * q^3 - 24 * q^6 - 2 * q^7 - 4 * q^10 - 22 * q^12 - 4 * q^13 - 14 * q^15 + 68 * q^16 - 18 * q^17 - 10 * q^18 - 12 * q^20 + 20 * q^21 + 4 * q^22 - 4 * q^25 - 32 * q^27 - 4 * q^28 - 20 * q^30 + 4 * q^31 - 90 * q^32 + 32 * q^33 + 8 * q^36 - 4 * q^37 - 36 * q^40 - 36 * q^41 + 14 * q^42 - 4 * q^43 - 68 * q^45 + 4 * q^46 - 6 * q^47 + 38 * q^48 + 36 * q^50 + 20 * q^51 - 52 * q^52 + 4 * q^55 - 96 * q^56 + 32 * q^57 - 12 * q^58 - 74 * q^60 - 8 * q^61 + 14 * q^63 - 78 * q^65 - 92 * q^66 + 2 * q^67 - 42 * q^70 - 46 * q^72 - 4 * q^73 + 54 * q^75 - 24 * q^76 + 42 * q^77 + 54 * q^78 + 36 * q^80 + 20 * q^81 - 8 * q^82 - 12 * q^83 - 4 * q^85 - 28 * q^87 + 12 * q^88 - 24 * q^90 - 16 * q^91 + 72 * q^92 + 4 * q^93 - 66 * q^95 - 4 * q^97 + 12 * q^98

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