LMFDB - Embedded newform 357.2.d.b.188.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(188,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("357.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.d (of order $2$, degree $1$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			188.15
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.889073i q^{2} +(0.351208 - 1.69607i) q^{3} +1.20955 q^{4} +1.21532 q^{5} +(1.50793 + 0.312249i) q^{6} +(1.43665 + 2.22172i) q^{7} +2.85352i q^{8} +(-2.75331 - 1.19135i) q^{9} +O(q^{10})$	\(q+0.889073i q^{2} +(0.351208 - 1.69607i) q^{3} +1.20955 q^{4} +1.21532 q^{5} +(1.50793 + 0.312249i) q^{6} +(1.43665 + 2.22172i) q^{7} +2.85352i q^{8} +(-2.75331 - 1.19135i) q^{9} +1.08051i q^{10} +5.85090i q^{11} +(0.424803 - 2.05148i) q^{12} -5.22274i q^{13} +(-1.97527 + 1.27729i) q^{14} +(0.426830 - 2.06127i) q^{15} -0.117889 q^{16} +1.00000 q^{17} +(1.05919 - 2.44789i) q^{18} -0.437929i q^{19} +1.46999 q^{20} +(4.27275 - 1.65638i) q^{21} -5.20188 q^{22} -7.36125i q^{23} +(4.83977 + 1.00218i) q^{24} -3.52299 q^{25} +4.64339 q^{26} +(-2.98759 + 4.25139i) q^{27} +(1.73770 + 2.68728i) q^{28} -3.77181i q^{29} +(1.83262 + 0.379483i) q^{30} -1.75453i q^{31} +5.60223i q^{32} +(9.92354 + 2.05488i) q^{33} +0.889073i q^{34} +(1.74600 + 2.70010i) q^{35} +(-3.33026 - 1.44099i) q^{36} +5.74758 q^{37} +0.389351 q^{38} +(-8.85813 - 1.83427i) q^{39} +3.46795i q^{40} -11.2806 q^{41} +(1.47264 + 3.79879i) q^{42} +2.95528 q^{43} +7.07696i q^{44} +(-3.34615 - 1.44787i) q^{45} +6.54469 q^{46} -4.88465 q^{47} +(-0.0414037 + 0.199949i) q^{48} +(-2.87206 + 6.38367i) q^{49} -3.13220i q^{50} +(0.351208 - 1.69607i) q^{51} -6.31716i q^{52} +0.530724i q^{53} +(-3.77979 - 2.65618i) q^{54} +7.11073i q^{55} +(-6.33972 + 4.09952i) q^{56} +(-0.742758 - 0.153804i) q^{57} +3.35341 q^{58} +0.268780 q^{59} +(0.516273 - 2.49321i) q^{60} -7.68884i q^{61} +1.55990 q^{62} +(-1.30871 - 7.82862i) q^{63} -5.21657 q^{64} -6.34731i q^{65} +(-1.82694 + 8.82275i) q^{66} -8.07271 q^{67} +1.20955 q^{68} +(-12.4852 - 2.58533i) q^{69} +(-2.40059 + 1.55232i) q^{70} -4.66476i q^{71} +(3.39953 - 7.85662i) q^{72} +6.01687i q^{73} +5.11002i q^{74} +(-1.23730 + 5.97524i) q^{75} -0.529697i q^{76} +(-12.9991 + 8.40572i) q^{77} +(1.63080 - 7.87552i) q^{78} +10.4190 q^{79} -0.143274 q^{80} +(6.16139 + 6.56028i) q^{81} -10.0293i q^{82} +10.0944 q^{83} +(5.16811 - 2.00347i) q^{84} +1.21532 q^{85} +2.62746i q^{86} +(-6.39725 - 1.32469i) q^{87} -16.6957 q^{88} -9.27913 q^{89} +(1.28726 - 2.97497i) q^{90} +(11.6034 - 7.50326i) q^{91} -8.90380i q^{92} +(-2.97580 - 0.616203i) q^{93} -4.34281i q^{94} -0.532224i q^{95} +(9.50178 + 1.96755i) q^{96} +11.7517i q^{97} +(-5.67555 - 2.55347i) q^{98} +(6.97045 - 16.1093i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	$ 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) $ 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$			0.889073i			0.628669i	0.949312	+	0.314335i	$0.101781\pi$
$2$			0.889073i			0.628669i	−0.949312	+	0.314335i	$0.898219\pi$
$3$	0.351208	−	1.69607i	0.202770	−	0.979226i
$3$	0.351208	−	1.69607i	0.202770	−	0.979226i
$4$	1.20955			0.604775
$5$	1.21532			0.543508			0.271754	−	0.962367i	$-0.412396\pi$
$5$	1.21532			0.543508			0.271754	+	0.962367i	$0.412396\pi$
$6$	1.50793	+	0.312249i	0.615610	+	0.127475i
$7$	1.43665	+	2.22172i	0.543004	+	0.839730i
$7$	1.43665	+	2.22172i	0.543004	+	0.839730i
$8$			2.85352i			1.00887i
$9$	−2.75331	−	1.19135i	−0.917769	−	0.397115i
$10$			1.08051i			0.341687i
$11$			5.85090i			1.76411i	0.471143	+	0.882057i	$0.343842\pi$
$11$			5.85090i			1.76411i	−0.471143	+	0.882057i	$0.656158\pi$
$12$	0.424803	−	2.05148i	0.122630	−	0.592212i
$13$		−	5.22274i		−	1.44853i	−0.689523	−	0.724263i	$-0.742180\pi$
$13$		−	5.22274i		−	1.44853i	0.689523	−	0.724263i	$-0.257820\pi$
$14$	−1.97527	+	1.27729i	−0.527913	+	0.341370i
$15$	0.426830	−	2.06127i	0.110207	−	0.532218i
$16$	−0.117889			−0.0294723
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	1.05919	−	2.44789i	0.249654	−	0.576973i
$19$		−	0.437929i		−	0.100468i	−0.998737	−	0.0502339i	$-0.984003\pi$
$19$		−	0.437929i		−	0.100468i	0.998737	−	0.0502339i	$-0.0159967\pi$
$20$	1.46999			0.328700
$21$	4.27275	−	1.65638i	0.932391	−	0.361452i
$22$	−5.20188			−1.10904
$23$		−	7.36125i		−	1.53493i	−0.641093	−	0.767463i	$-0.721519\pi$
$23$		−	7.36125i		−	1.53493i	0.641093	−	0.767463i	$-0.278481\pi$
$24$	4.83977	+	1.00218i	0.987915	+	0.204569i
$25$	−3.52299			−0.704599
$26$	4.64339			0.910644
$27$	−2.98759	+	4.25139i	−0.574962	+	0.818180i
$28$	1.73770	+	2.68728i	0.328395	+	0.507848i
$29$		−	3.77181i		−	0.700407i	−0.936674	−	0.350204i	$-0.886112\pi$
$29$		−	3.77181i		−	0.700407i	0.936674	−	0.350204i	$-0.113888\pi$
$30$	1.83262	+	0.379483i	0.334589	+	0.0692838i
$31$		−	1.75453i		−	0.315122i	−0.987509	−	0.157561i	$-0.949637\pi$
$31$		−	1.75453i		−	0.315122i	0.987509	−	0.157561i	$-0.0503631\pi$
$32$			5.60223i			0.990344i
$33$	9.92354	+	2.05488i	1.72747	+	0.357709i
$34$			0.889073i			0.152475i
$35$	1.74600	+	2.70010i	0.295127	+	0.456400i
$36$	−3.33026	−	1.44099i	−0.555044	−	0.240165i
$37$	5.74758			0.944897			0.472449	−	0.881358i	$-0.343370\pi$
$37$	5.74758			0.944897			0.472449	+	0.881358i	$0.343370\pi$
$38$	0.389351			0.0631610
$39$	−8.85813	−	1.83427i	−1.41844	−	0.293718i
$40$			3.46795i			0.548331i
$41$	−11.2806			−1.76174			−0.880869	−	0.473360i	$-0.843041\pi$
$41$	−11.2806			−1.76174			−0.880869	+	0.473360i	$0.843041\pi$
$42$	1.47264	+	3.79879i	0.227234	+	0.586166i
$43$	2.95528			0.450676			0.225338	−	0.974281i	$-0.427651\pi$
$43$	2.95528			0.450676			0.225338	+	0.974281i	$0.427651\pi$
$44$			7.07696i			1.06689i
$45$	−3.34615	−	1.44787i	−0.498815	−	0.215835i
$46$	6.54469			0.964961
$47$	−4.88465			−0.712500			−0.356250	−	0.934391i	$-0.615945\pi$
$47$	−4.88465			−0.712500			−0.356250	+	0.934391i	$0.615945\pi$
$48$	−0.0414037	+	0.199949i	−0.00597610	+	0.0288601i
$49$	−2.87206	+	6.38367i	−0.410294	+	0.911953i
$50$		−	3.13220i		−	0.442960i
$51$	0.351208	−	1.69607i	0.0491789	−	0.237497i
$52$		−	6.31716i		−	0.876033i
$53$			0.530724i			0.0729005i	0.999335	+	0.0364502i	$0.0116050\pi$
$53$			0.530724i			0.0729005i	−0.999335	+	0.0364502i	$0.988395\pi$
$54$	−3.77979	−	2.65618i	−0.514365	−	0.361461i
$55$			7.11073i			0.958811i
$56$	−6.33972	+	4.09952i	−0.847181	+	0.547822i
$57$	−0.742758	−	0.153804i	−0.0983807	−	0.0203718i
$58$	3.35341			0.440325
$59$	0.268780			0.0349922			0.0174961	−	0.999847i	$-0.494431\pi$
$59$	0.268780			0.0349922			0.0174961	+	0.999847i	$0.494431\pi$
$60$	0.516273	−	2.49321i	0.0666505	−	0.321872i
$61$		−	7.68884i		−	0.984455i	−0.870467	−	0.492227i	$-0.836183\pi$
$61$		−	7.68884i		−	0.984455i	0.870467	−	0.492227i	$-0.163817\pi$
$62$	1.55990			0.198108
$63$	−1.30871	−	7.82862i	−0.164882	−	0.986313i
$64$	−5.21657			−0.652071
$65$		−	6.34731i		−	0.787287i
$66$	−1.82694	+	8.82275i	−0.224881	+	1.08601i
$67$	−8.07271			−0.986239			−0.493119	−	0.869962i	$-0.664143\pi$
$67$	−8.07271			−0.986239			−0.493119	+	0.869962i	$0.664143\pi$
$68$	1.20955			0.146679
$69$	−12.4852	−	2.58533i	−1.50304	−	0.311237i
$70$	−2.40059	+	1.55232i	−0.286925	+	0.185537i
$71$		−	4.66476i		−	0.553605i	−0.960927	−	0.276803i	$-0.910725\pi$
$71$		−	4.66476i		−	0.553605i	0.960927	−	0.276803i	$-0.0892748\pi$
$72$	3.39953	−	7.85662i	0.400639	−	0.925912i
$73$			6.01687i			0.704222i	0.935958	+	0.352111i	$0.114536\pi$
$73$			6.01687i			0.704222i	−0.935958	+	0.352111i	$0.885464\pi$
$74$			5.11002i			0.594028i
$75$	−1.23730	+	5.97524i	−0.142871	+	0.689962i
$76$		−	0.529697i		−	0.0607604i
$77$	−12.9991	+	8.40572i	−1.48138	+	0.957920i
$78$	1.63080	−	7.87552i	0.184651	−	0.891727i
$79$	10.4190			1.17223			0.586114	−	0.810229i	$-0.300657\pi$
$79$	10.4190			1.17223			0.586114	+	0.810229i	$0.300657\pi$
$80$	−0.143274			−0.0160185
$81$	6.16139	+	6.56028i	0.684599	+	0.728920i
$82$		−	10.0293i		−	1.10755i
$83$	10.0944			1.10801			0.554003	−	0.832515i	$-0.313100\pi$
$83$	10.0944			1.10801			0.554003	+	0.832515i	$0.313100\pi$
$84$	5.16811	−	2.00347i	0.563887	−	0.218597i
$85$	1.21532			0.131820
$86$			2.62746i			0.283326i
$87$	−6.39725	−	1.32469i	−0.685857	−	0.142022i
$88$	−16.6957			−1.77977
$89$	−9.27913			−0.983586			−0.491793	−	0.870712i	$-0.663658\pi$
$89$	−9.27913			−0.983586			−0.491793	+	0.870712i	$0.663658\pi$
$90$	1.28726	−	2.97497i	0.135689	−	0.313590i
$91$	11.6034	−	7.50326i	1.21637	−	0.786556i
$92$		−	8.90380i		−	0.928285i
$93$	−2.97580	−	0.616203i	−0.308576	−	0.0638973i
$94$		−	4.34281i		−	0.447927i
$95$		−	0.532224i		−	0.0546051i
$96$	9.50178	+	1.96755i	0.969771	+	0.200812i
$97$			11.7517i			1.19320i	0.802537	+	0.596602i	$0.203483\pi$
$97$			11.7517i			1.19320i	−0.802537	+	0.596602i	$0.796517\pi$
$98$	−5.67555	−	2.55347i	−0.573317	−	0.257939i
$99$	6.97045	−	16.1093i	0.700557	−	1.61905i
$100$	−4.26124			−0.426124
$101$	−10.4662			−1.04142			−0.520711	−	0.853733i	$-0.674333\pi$
$101$	−10.4662			−1.04142			−0.520711	+	0.853733i	$0.674333\pi$
$102$	1.50793	+	0.312249i	0.149307	+	0.0309173i
$103$			4.39332i			0.432886i	0.976295	+	0.216443i	$0.0694456\pi$
$103$			4.39332i			0.432886i	−0.976295	+	0.216443i	$0.930554\pi$
$104$	14.9032			1.46138
$105$	5.19277	−	2.01303i	0.506762	−	0.196452i
$106$	−0.471852			−0.0458303
$107$		−	2.33222i		−	0.225464i	−0.993625	−	0.112732i	$-0.964040\pi$
$107$		−	2.33222i		−	0.225464i	0.993625	−	0.112732i	$-0.0359602\pi$
$108$	−3.61364	+	5.14227i	−0.347722	+	0.494815i
$109$	3.90775			0.374294			0.187147	−	0.982332i	$-0.440076\pi$
$109$	3.90775			0.374294			0.187147	+	0.982332i	$0.440076\pi$
$110$	−6.32196			−0.602775
$111$	2.01860	−	9.74830i	0.191597	−	0.925268i
$112$	−0.169366	−	0.261917i	−0.0160036	−	0.0247488i
$113$		−	12.2923i		−	1.15636i	−0.815909	−	0.578181i	$-0.803763\pi$
$113$		−	12.2923i		−	1.15636i	0.815909	−	0.578181i	$-0.196237\pi$
$114$	0.136743	−	0.660366i	0.0128071	−	0.0618489i
$115$		−	8.94629i		−	0.834246i
$116$		−	4.56219i		−	0.423589i
$117$	−6.22209	+	14.3798i	−0.575232	+	1.32941i
$118$			0.238965i			0.0219985i
$119$	1.43665	+	2.22172i	0.131698	+	0.203665i
$120$	5.88188	+	1.21797i	0.536940	+	0.111185i
$121$	−23.2331			−2.11210
$122$	6.83594			0.618896
$123$	−3.96184	+	19.1327i	−0.357227	+	1.72514i
$124$		−	2.12219i		−	0.190578i
$125$	−10.3582			−0.926464
$126$	6.96021	−	1.16354i	0.620065	−	0.103656i
$127$	−10.8527			−0.963025			−0.481512	−	0.876439i	$-0.659912\pi$
$127$	−10.8527			−0.963025			−0.481512	+	0.876439i	$0.659912\pi$
$128$			6.56656i			0.580407i
$129$	1.03792	−	5.01236i	0.0913835	−	0.441314i
$130$	5.64322			0.494943
$131$	−4.49522			−0.392749			−0.196374	−	0.980529i	$-0.562917\pi$
$131$	−4.49522			−0.392749			−0.196374	+	0.980529i	$0.562917\pi$
$132$	12.0030	+	2.48548i	1.04473	+	0.216334i
$133$	0.972954	−	0.629152i	0.0843658	−	0.0545544i
$134$		−	7.17723i		−	0.620018i
$135$	−3.63088	+	5.16681i	−0.312496	+	0.444688i
$136$			2.85352i			0.244688i
$137$			11.5470i			0.986523i	0.869881	+	0.493262i	$0.164195\pi$
$137$			11.5470i			0.986523i	−0.869881	+	0.493262i	$0.835805\pi$
$138$	2.29854	−	11.1002i	0.195665	−	0.944916i
$139$		−	7.83126i		−	0.664239i	−0.943237	−	0.332119i	$-0.892236\pi$
$139$		−	7.83126i		−	0.664239i	0.943237	−	0.332119i	$-0.107764\pi$
$140$	2.11187	+	3.26591i	0.178485	+	0.276020i
$141$	−1.71553	+	8.28471i	−0.144474	+	0.697699i
$142$	4.14731			0.348035
$143$	30.5577			2.55537
$144$	0.324586	+	0.140447i	0.0270488	+	0.0117039i
$145$		−	4.58396i		−	0.380677i
$146$	−5.34944			−0.442723
$147$	9.81847	+	7.11321i	0.809814	+	0.586687i
$148$	6.95199			0.571450
$149$			0.274428i			0.0224820i	0.999937	+	0.0112410i	$0.00357820\pi$
$149$			0.274428i			0.0224820i	−0.999937	+	0.0112410i	$0.996422\pi$
$150$	−5.31242	−	1.10005i	−0.433758	−	0.0898188i
$151$	17.6947			1.43998			0.719988	−	0.693987i	$-0.244147\pi$
$151$	17.6947			1.43998			0.719988	+	0.693987i	$0.244147\pi$
$152$	1.24964			0.101359
$153$	−2.75331	−	1.19135i	−0.222592	−	0.0963146i
$154$	−7.47329	−	11.5571i	−0.602215	−	0.931298i
$155$		−	2.13231i		−	0.171272i
$156$	−10.7143	−	2.21864i	−0.857834	−	0.177633i
$157$			18.6998i			1.49240i	0.665720	+	0.746202i	$0.268125\pi$
$157$			18.6998i			1.49240i	−0.665720	+	0.746202i	$0.731875\pi$
$158$			9.26323i			0.736943i
$159$	0.900144	+	0.186394i	0.0713861	+	0.0147820i
$160$			6.80852i			0.538260i
$161$	16.3546	−	10.5756i	1.28892	−	0.833471i
$162$	−5.83256	+	5.47792i	−0.458250	+	0.430386i
$163$	−4.91267			−0.384790			−0.192395	−	0.981318i	$-0.561625\pi$
$163$	−4.91267			−0.384790			−0.192395	+	0.981318i	$0.561625\pi$
$164$	−13.6445			−1.06545
$165$	12.0603	+	2.49734i	0.938893	+	0.194418i
$166$			8.97466i			0.696569i
$167$	25.3485			1.96153			0.980764	−	0.195196i	$-0.0625343\pi$
$167$	25.3485			1.96153			0.980764	+	0.195196i	$0.0625343\pi$
$168$	4.72652	+	12.1924i	0.364659	+	0.940664i
$169$	−14.2770			−1.09823
$170$			1.08051i			0.0828713i
$171$	−0.521725	+	1.20575i	−0.0398973	+	0.0922062i
$172$	3.57456			0.272558
$173$	−4.85505			−0.369122			−0.184561	−	0.982821i	$-0.559086\pi$
$173$	−4.85505			−0.369122			−0.184561	+	0.982821i	$0.559086\pi$
$174$	1.17774	−	5.68762i	0.0892846	−	0.431178i
$175$	−5.06132	−	7.82710i	−0.382600	−	0.591673i
$176$		−	0.689759i		−	0.0519926i
$177$	0.0943978	−	0.455870i	0.00709537	−	0.0342653i
$178$		−	8.24982i		−	0.618350i
$179$			0.299032i			0.0223507i	0.999938	+	0.0111753i	$0.00355730\pi$
$179$			0.299032i			0.0223507i	−0.999938	+	0.0111753i	$0.996443\pi$
$180$	−4.04734	−	1.75127i	−0.301671	−	0.130532i
$181$			15.9531i			1.18578i	0.805282	+	0.592892i	$0.202014\pi$
$181$			15.9531i			1.18578i	−0.805282	+	0.592892i	$0.797986\pi$
$182$	6.67094	+	10.3163i	0.494483	+	0.764696i
$183$	−13.0408	−	2.70038i	−0.964004	−	0.199618i
$184$	21.0055			1.54855
$185$	6.98516			0.513559
$186$	0.547849	−	2.64570i	0.0401702	−	0.193992i
$187$			5.85090i			0.427860i
$188$	−5.90823			−0.430902
$189$	−13.7375	−	0.529805i	−0.999257	−	0.0385376i
$190$	0.473186			0.0343285
$191$			14.0537i			1.01689i	0.861094	+	0.508446i	$0.169780\pi$
$191$			14.0537i			1.01689i	−0.861094	+	0.508446i	$0.830220\pi$
$192$	−1.83210	+	8.84767i	−0.132220	+	0.638526i
$193$	18.6017			1.33898			0.669491	−	0.742820i	$-0.266512\pi$
$193$	18.6017			1.33898			0.669491	+	0.742820i	$0.266512\pi$
$194$	−10.4481			−0.750131
$195$	−10.7655	−	2.22922i	−0.770932	−	0.159638i
$196$	−3.47390	+	7.72137i	−0.248135	+	0.551527i
$197$			9.66111i			0.688325i	0.938910	+	0.344163i	$0.111837\pi$
$197$			9.66111i			0.688325i	−0.938910	+	0.344163i	$0.888163\pi$
$198$	14.3224	+	6.19724i	1.01785	+	0.440418i
$199$			3.14488i			0.222935i	0.993768	+	0.111467i	$0.0355551\pi$
$199$			3.14488i			0.222935i	−0.993768	+	0.111467i	$0.964445\pi$
$200$		−	10.0529i		−	0.710850i
$201$	−2.83520	+	13.6919i	−0.199979	+	0.965751i
$202$		−	9.30517i		−	0.654709i
$203$	8.37990	−	5.41878i	0.588153	−	0.380324i
$204$	0.424803	−	2.05148i	0.0297422	−	0.143632i
$205$	−13.7096			−0.957519
$206$	−3.90598			−0.272142
$207$	−8.76979	+	20.2678i	−0.609543	+	1.40871i
$208$			0.615705i			0.0426915i
$209$	2.56228			0.177237
$210$	1.78973	+	4.61675i	0.123503	+	0.318586i
$211$	−12.9698			−0.892881			−0.446441	−	0.894813i	$-0.647309\pi$
$211$	−12.9698			−0.892881			−0.446441	+	0.894813i	$0.647309\pi$
$212$			0.641937i			0.0440884i
$213$	−7.91176	−	1.63830i	−0.542105	−	0.112254i
$214$	2.07351			0.141743
$215$	3.59162			0.244946
$216$	−12.1314	−	8.52515i	−0.825440	−	0.580063i
$217$	3.89806	−	2.52064i	0.264618	−	0.171112i
$218$			3.47427i			0.235307i
$219$	10.2050	+	2.11317i	0.689593	+	0.142795i
$220$			8.60078i			0.579865i
$221$		−	5.22274i		−	0.351319i
$222$	8.66695	+	1.79468i	0.581688	+	0.120451i
$223$		−	9.87623i		−	0.661361i	−0.943743	−	0.330681i	$-0.892722\pi$
$223$		−	9.87623i		−	0.661361i	0.943743	−	0.330681i	$-0.107278\pi$
$224$	−12.4466	+	8.04846i	−0.831622	+	0.537761i
$225$	9.69988	+	4.19710i	0.646659	+	0.279807i
$226$	10.9287			0.726969
$227$	29.8138			1.97881			0.989405	−	0.145181i	$-0.0463765\pi$
$227$	29.8138			1.97881			0.989405	+	0.145181i	$0.0463765\pi$
$228$	−0.898403	−	0.186034i	−0.0594982	−	0.0123204i
$229$		−	16.8779i		−	1.11532i	−0.830069	−	0.557660i	$-0.811699\pi$
$229$		−	16.8779i		−	1.11532i	0.830069	−	0.557660i	$-0.188301\pi$
$230$	7.95390			0.524465
$231$	9.69132	+	24.9995i	0.637642	+	1.64484i
$232$	10.7629			0.706622
$233$		−	29.4032i		−	1.92627i	−0.269018	−	0.963135i	$-0.586699\pi$
$233$		−	29.4032i		−	1.92627i	0.269018	−	0.963135i	$-0.413301\pi$
$234$	−12.7847	−	5.53189i	−0.835761	−	0.361631i
$235$	−5.93643			−0.387250
$236$	0.325103			0.0211624
$237$	3.65923	−	17.6713i	0.237692	−	1.14788i
$238$	−1.97527	+	1.27729i	−0.128038	+	0.0827943i
$239$		−	19.9887i		−	1.29296i	−0.762929	−	0.646482i	$-0.776240\pi$
$239$		−	19.9887i		−	1.29296i	0.762929	−	0.646482i	$-0.223760\pi$
$240$	−0.0503188	+	0.243002i	−0.00324806	+	0.0156857i
$241$		−	22.5053i		−	1.44970i	−0.688909	−	0.724848i	$-0.741910\pi$
$241$		−	22.5053i		−	1.44970i	0.688909	−	0.724848i	$-0.258090\pi$
$242$		−	20.6559i		−	1.32781i
$243$	13.2906	−	8.14613i	0.852594	−	0.522574i
$244$		−	9.30003i		−	0.595374i
$245$	−3.49047	+	7.75822i	−0.222998	+	0.495654i
$246$	−17.0104	−	3.52237i	−1.08454	−	0.224578i
$247$	−2.28719			−0.145530
$248$	5.00658			0.317918
$249$	3.54524	−	17.1208i	0.224670	−	1.08499i
$250$		−	9.20917i		−	0.582439i
$251$	9.93294			0.626962			0.313481	−	0.949595i	$-0.398505\pi$
$251$	9.93294			0.626962			0.313481	+	0.949595i	$0.398505\pi$
$252$	−1.58295	−	9.46910i	−0.0997166	−	0.596498i
$253$	43.0700			2.70779
$254$		−	9.64887i		−	0.605424i
$255$	0.426830	−	2.06127i	0.0267292	−	0.129082i
$256$	−16.2713			−1.01696
$257$	7.86922			0.490869			0.245434	−	0.969413i	$-0.421069\pi$
$257$	7.86922			0.490869			0.245434	+	0.969413i	$0.421069\pi$
$258$	4.45635	+	0.922784i	0.277440	+	0.0574500i
$259$	8.25728	+	12.7695i	0.513083	+	0.793459i
$260$		−	7.67738i		−	0.476131i
$261$	−4.49353	+	10.3849i	−0.278142	+	0.642812i
$262$		−	3.99657i		−	0.246909i
$263$			27.6675i			1.70605i	0.521867	+	0.853027i	$0.325236\pi$
$263$			27.6675i			1.70605i	−0.521867	+	0.853027i	$0.674764\pi$
$264$	−5.86365	+	28.3171i	−0.360883	+	1.74279i
$265$			0.645000i			0.0396220i
$266$	0.559362	+	0.865027i	0.0342967	+	0.0530382i
$267$	−3.25890	+	15.7381i	−0.199442	+	0.963153i
$268$	−9.76435			−0.596452
$269$	1.34352			0.0819160			0.0409580	−	0.999161i	$-0.486959\pi$
$269$	1.34352			0.0819160			0.0409580	+	0.999161i	$0.486959\pi$
$270$	−4.59367	−	3.22812i	−0.279562	−	0.196457i
$271$			3.16147i			0.192046i	0.995379	+	0.0960228i	$0.0306122\pi$
$271$			3.16147i			0.192046i	−0.995379	+	0.0960228i	$0.969388\pi$
$272$	−0.117889			−0.00714809
$273$	−8.65084	−	22.3155i	−0.523572	−	1.35059i
$274$	−10.2661			−0.620197
$275$		−	20.6127i		−	1.24299i
$276$	−15.1015	−	3.12708i	−0.909001	−	0.188228i
$277$	−16.1564			−0.970741			−0.485371	−	0.874308i	$-0.661315\pi$
$277$	−16.1564			−0.970741			−0.485371	+	0.874308i	$0.661315\pi$
$278$	6.96256			0.417586
$279$	−2.09025	+	4.83075i	−0.125140	+	0.289209i
$280$	−7.70480	+	4.98224i	−0.460450	+	0.297746i
$281$		−	9.21004i		−	0.549425i	−0.961526	−	0.274712i	$-0.911417\pi$
$281$		−	9.21004i		−	0.549425i	0.961526	−	0.274712i	$-0.0885827\pi$
$282$	−7.36571	−	1.52523i	−0.438622	−	0.0908261i
$283$			10.4459i			0.620946i	0.950582	+	0.310473i	$0.100487\pi$
$283$			10.4459i			0.620946i	−0.950582	+	0.310473i	$0.899513\pi$
$284$		−	5.64226i		−	0.334807i
$285$	−0.902690	−	0.186921i	−0.0534707	−	0.0110723i
$286$			27.1681i			1.60648i
$287$	−16.2063	−	25.0624i	−0.956630	−	1.47938i
$288$	6.67420	−	15.4247i	0.393281	−	0.908907i
$289$	1.00000			0.0588235
$290$	4.07548			0.239320
$291$	19.9317	+	4.12729i	1.16842	+	0.241946i
$292$			7.27771i			0.425896i
$293$	15.5934			0.910975			0.455488	−	0.890242i	$-0.349465\pi$
$293$	15.5934			0.910975			0.455488	+	0.890242i	$0.349465\pi$
$294$	−6.32416	+	8.72933i	−0.368832	+	0.509105i
$295$	0.326655			0.0190186
$296$			16.4009i			0.953281i
$297$	−24.8745	−	17.4801i	−1.44336	−	1.01430i
$298$	−0.243986			−0.0141337
$299$	−38.4459			−2.22338
$300$	−1.49658	+	7.22735i	−0.0864050	+	0.417271i
$301$	4.24571	+	6.56580i	0.244719	+	0.378446i
$302$			15.7319i			0.905268i
$303$	−3.67579	+	17.7513i	−0.211169	+	1.01979i
$304$			0.0516272i			0.00296102i
$305$		−	9.34441i		−	0.535059i
$306$	1.05919	−	2.44789i	0.0605500	−	0.139937i
$307$			7.98350i			0.455643i	0.973703	+	0.227821i	$0.0731602\pi$
$307$			7.98350i			0.455643i	−0.973703	+	0.227821i	$0.926840\pi$
$308$	−15.7230	+	10.1671i	−0.895901	+	0.579326i
$309$	7.45137	+	1.54297i	0.423894	+	0.0877763i
$310$	1.89578			0.107673
$311$	0.795966			0.0451351			0.0225676	−	0.999745i	$-0.492816\pi$
$311$	0.795966			0.0451351			0.0225676	+	0.999745i	$0.492816\pi$
$312$	5.23412	−	25.2769i	0.296324	−	1.43102i
$313$		−	25.8326i		−	1.46014i	−0.683370	−	0.730072i	$-0.739486\pi$
$313$		−	25.8326i		−	1.46014i	0.683370	−	0.730072i	$-0.260514\pi$
$314$	−16.6255			−0.938229
$315$	−1.59051	−	9.51429i	−0.0896149	−	0.536070i
$316$	12.6023			0.708934
$317$			2.26857i			0.127415i	0.997969	+	0.0637077i	$0.0202925\pi$
$317$			2.26857i			0.127415i	−0.997969	+	0.0637077i	$0.979707\pi$
$318$	−0.165718	+	0.800294i	−0.00929300	+	0.0448782i
$319$	22.0685			1.23560
$320$	−6.33981			−0.354406
$321$	−3.95561	−	0.819094i	−0.220781	−	0.0457174i
$322$	9.40244	+	14.5404i	0.523978	+	0.810307i
$323$		−	0.437929i		−	0.0243670i
$324$	7.45251	+	7.93498i	0.414028	+	0.440832i
$325$			18.3997i			1.02063i
$326$		−	4.36772i		−	0.241906i
$327$	1.37243	−	6.62781i	0.0758956	−	0.366519i
$328$		−	32.1895i		−	1.77737i
$329$	−7.01755	−	10.8523i	−0.386890	−	0.598308i
$330$	−2.22032	+	10.7225i	−0.122225	+	0.590253i
$331$	−20.3150			−1.11661			−0.558307	−	0.829635i	$-0.688549\pi$
$331$	−20.3150			−1.11661			−0.558307	+	0.829635i	$0.688549\pi$
$332$	12.2097			0.670094
$333$	−15.8249	−	6.84736i	−0.867197	−	0.375233i
$334$			22.5367i			1.23315i
$335$	−9.81094			−0.536029
$336$	−0.503712	+	0.195270i	−0.0274797	+	0.0106528i
$337$	18.1157			0.986826			0.493413	−	0.869795i	$-0.335749\pi$
$337$	18.1157			0.986826			0.493413	+	0.869795i	$0.335749\pi$
$338$		−	12.6933i		−	0.690424i
$339$	−20.8486	−	4.31715i	−1.13234	−	0.234475i
$340$	1.46999			0.0797215
$341$	10.2656			0.555911
$342$	−1.07200	−	0.463851i	−0.0579672	−	0.0250822i
$343$	−18.3089	+	2.79022i	−0.988586	+	0.150658i
$344$			8.43296i			0.454675i
$345$	−15.1735	−	3.14201i	−0.816915	−	0.169160i
$346$		−	4.31649i		−	0.232056i
$347$		−	22.3981i		−	1.20239i	−0.799102	−	0.601195i	$-0.794691\pi$
$347$		−	22.3981i		−	1.20239i	0.799102	−	0.601195i	$-0.205309\pi$
$348$	−7.73780	−	1.60228i	−0.414789	−	0.0858911i
$349$		−	2.47654i		−	0.132566i	−0.997801	−	0.0662830i	$-0.978886\pi$
$349$		−	2.47654i		−	0.132566i	0.997801	−	0.0662830i	$-0.0211140\pi$
$350$	6.95886	−	4.49988i	0.371967	−	0.240529i
$351$	22.2039	+	15.6034i	1.18516	+	0.832847i
$352$	−32.7781			−1.74708
$353$	−3.21220			−0.170968			−0.0854840	−	0.996340i	$-0.527244\pi$
$353$	−3.21220			−0.170968			−0.0854840	+	0.996340i	$0.527244\pi$
$354$	0.405302	+	0.0839265i	0.0215416	+	0.00446064i
$355$		−	5.66918i		−	0.300889i
$356$	−11.2236			−0.594848
$357$	4.27275	−	1.65638i	0.226138	−	0.0876649i
$358$	−0.265861			−0.0140512
$359$			4.04812i			0.213652i	0.994278	+	0.106826i	$0.0340687\pi$
$359$			4.04812i			0.213652i	−0.994278	+	0.106826i	$0.965931\pi$
$360$	4.13153	−	9.54832i	0.217751	−	0.503241i
$361$	18.8082			0.989906
$362$	−14.1835			−0.745466
$363$	−8.15964	+	39.4049i	−0.428270	+	2.06822i
$364$	14.0350	−	9.07557i	0.735631	−	0.475689i
$365$			7.31244i			0.382750i
$366$	2.40083	−	11.5942i	0.125494	−	0.606040i
$367$		−	10.5010i		−	0.548149i	−0.961708	−	0.274075i	$-0.911628\pi$
$367$		−	10.5010i		−	0.548149i	0.961708	−	0.274075i	$-0.0883715\pi$
$368$			0.867813i			0.0452379i
$369$	31.0590	+	13.4391i	1.61687	+	0.699613i
$370$			6.21032i			0.322859i
$371$	−1.17912	+	0.762466i	−0.0612168	+	0.0395852i
$372$	−3.59938	−	0.745328i	−0.186619	−	0.0386435i
$373$	2.95861			0.153191			0.0765956	−	0.997062i	$-0.475595\pi$
$373$	2.95861			0.153191			0.0765956	+	0.997062i	$0.475595\pi$
$374$	−5.20188			−0.268983
$375$	−3.63787	+	17.5682i	−0.187859	+	0.907218i
$376$		−	13.9385i		−	0.718822i
$377$	−19.6992			−1.01456
$378$	0.471035	−	12.2136i	0.0242274	−	0.628202i
$379$	−8.35791			−0.429317			−0.214659	−	0.976689i	$-0.568864\pi$
$379$	−8.35791			−0.429317			−0.214659	+	0.976689i	$0.568864\pi$
$380$		−	0.643752i		−	0.0330238i
$381$	−3.81157	+	18.4070i	−0.195272	+	0.943019i
$382$	−12.4948			−0.639288
$383$	5.98798			0.305972			0.152986	−	0.988228i	$-0.451111\pi$
$383$	5.98798			0.305972			0.152986	+	0.988228i	$0.451111\pi$
$384$	11.1373	+	2.30623i	0.568350	+	0.117689i
$385$	−15.7980	+	10.2157i	−0.805142	+	0.520638i
$386$			16.5383i			0.841777i
$387$	−8.13679	−	3.52076i	−0.413616	−	0.178970i
$388$			14.2143i			0.721620i
$389$			19.9971i			1.01389i	0.861977	+	0.506947i	$0.169226\pi$
$389$			19.9971i			1.01389i	−0.861977	+	0.506947i	$0.830774\pi$
$390$	1.98194	−	9.57129i	0.100360	−	0.484661i
$391$		−	7.36125i		−	0.372274i
$392$	−18.2160	−	8.19548i	−0.920045	−	0.413934i
$393$	−1.57875	+	7.62420i	−0.0796376	+	0.384590i
$394$	−8.58942			−0.432729
$395$	12.6624			0.637115
$396$	8.43111	−	19.4850i	0.423679	−	0.979160i
$397$			29.3138i			1.47121i	0.677408	+	0.735607i	$0.263103\pi$
$397$			29.3138i			1.47121i	−0.677408	+	0.735607i	$0.736897\pi$
$398$	−2.79603			−0.140152
$399$	−0.725376	−	1.87116i	−0.0363142	−	0.0936752i
$400$	0.415323			0.0207662
$401$		−	4.45376i		−	0.222410i	−0.993797	−	0.111205i	$-0.964529\pi$
$401$		−	4.45376i		−	0.222410i	0.993797	−	0.111205i	$-0.0354711\pi$
$402$	−12.1731	−	2.52070i	−0.607138	−	0.125721i
$403$	−9.16343			−0.456463
$404$	−12.6593			−0.629825
$405$	7.48807	+	7.97285i	0.372085	+	0.396174i
$406$	4.81769	+	7.45034i	0.239098	+	0.369754i
$407$			33.6286i			1.66691i
$408$	4.83977	+	1.00218i	0.239605	+	0.0496153i
$409$			33.6627i			1.66451i	0.554390	+	0.832257i	$0.312952\pi$
$409$			33.6627i			1.66451i	−0.554390	+	0.832257i	$0.687048\pi$
$410$		−	12.1888i		−	0.601963i
$411$	19.5844	+	4.05538i	0.966030	+	0.200037i
$412$			5.31394i			0.261799i
$413$	0.386144	+	0.597154i	0.0190009	+	0.0293840i
$414$	−18.0195	−	7.79698i	−0.885611	−	0.383201i
$415$	12.2680			0.602210
$416$	29.2590			1.43454
$417$	−13.2824	−	2.75040i	−0.650440	−	0.134688i
$418$			2.27805i			0.111423i
$419$	−11.9192			−0.582291			−0.291145	−	0.956679i	$-0.594036\pi$
$419$	−11.9192			−0.582291			−0.291145	+	0.956679i	$0.594036\pi$
$420$	6.28091	−	2.43486i	0.306477	−	0.118809i
$421$	−22.6151			−1.10219			−0.551096	−	0.834442i	$-0.685790\pi$
$421$	−22.6151			−1.10219			−0.551096	+	0.834442i	$0.685790\pi$
$422$		−	11.5311i		−	0.561327i
$423$	13.4489	+	5.81931i	0.653910	+	0.282945i
$424$	−1.51443			−0.0735473
$425$	−3.52299			−0.170890
$426$	1.45657	−	7.03413i	0.0705709	−	0.340805i
$427$	17.0824	−	11.0462i	0.826676	−	0.534563i
$428$		−	2.82094i		−	0.136355i
$429$	10.7321	−	51.8281i	0.518151	−	2.50228i
$430$			3.19321i			0.153990i
$431$			7.51454i			0.361963i	0.983487	+	0.180981i	$0.0579274\pi$
$431$			7.51454i			0.361963i	−0.983487	+	0.180981i	$0.942073\pi$
$432$	0.352205	−	0.501194i	0.0169455	−	0.0241137i
$433$		−	5.49766i		−	0.264201i	−0.991236	−	0.132100i	$-0.957828\pi$
$433$		−	5.49766i		−	0.264201i	0.991236	−	0.132100i	$-0.0421721\pi$
$434$	2.24104	+	3.46566i	0.107573	+	0.166357i
$435$	−7.77472	−	1.60992i	−0.372769	−	0.0771899i
$436$	4.72661			0.226364
$437$	−3.22370			−0.154211
$438$	−1.87876	+	9.07302i	−0.0897708	+	0.433526i
$439$		−	8.05106i		−	0.384256i	−0.981370	−	0.192128i	$-0.938461\pi$
$439$		−	8.05106i		−	0.384256i	0.981370	−	0.192128i	$-0.0615389\pi$
$440$	−20.2906			−0.967318
$441$	15.5128	−	14.1546i	0.738705	−	0.674028i
$442$	4.64339			0.220864
$443$			30.7322i			1.46013i	0.683376	+	0.730066i	$0.260511\pi$
$443$			30.7322i			1.46013i	−0.683376	+	0.730066i	$0.739489\pi$
$444$	2.44159	−	11.7911i	0.115873	−	0.559579i
$445$	−11.2771			−0.534587
$446$	8.78068			0.415777
$447$	0.465449	+	0.0963811i	0.0220150	+	0.00455867i
$448$	−7.49440	−	11.5897i	−0.354077	−	0.547564i
$449$			11.3122i			0.533853i	0.963717	+	0.266927i	$0.0860082\pi$
$449$			11.3122i			0.533853i	−0.963717	+	0.266927i	$0.913992\pi$
$450$	−3.73153	+	8.62390i	−0.175906	+	0.406534i
$451$		−	66.0019i		−	3.10791i
$452$		−	14.8681i		−	0.699339i
$453$	6.21452	−	30.0115i	0.291984	−	1.41006i
$454$			26.5066i			1.24402i
$455$	14.1019	−	9.11888i	0.661108	−	0.427500i
$456$	0.438883	−	2.11948i	0.0205526	−	0.0992536i
$457$	22.8590			1.06930			0.534650	−	0.845073i	$-0.320443\pi$
$457$	22.8590			1.06930			0.534650	+	0.845073i	$0.320443\pi$
$458$	15.0056			0.701168
$459$	−2.98759	+	4.25139i	−0.139449	+	0.198438i
$460$		−	10.8210i		−	0.504531i
$461$	−14.8796			−0.693012			−0.346506	−	0.938048i	$-0.612632\pi$
$461$	−14.8796			−0.693012			−0.346506	+	0.938048i	$0.612632\pi$
$462$	−22.2263	+	8.61628i	−1.03406	+	0.400866i
$463$	6.75980			0.314155			0.157077	−	0.987586i	$-0.449793\pi$
$463$	6.75980			0.314155			0.157077	+	0.987586i	$0.449793\pi$
$464$			0.444656i			0.0206427i
$465$	−3.61655	−	0.748885i	−0.167714	−	0.0347287i
$466$	26.1416			1.21099
$467$	18.5605			0.858877			0.429439	−	0.903096i	$-0.358711\pi$
$467$	18.5605			0.858877			0.429439	+	0.903096i	$0.358711\pi$
$468$	−7.52592	+	17.3931i	−0.347886	+	0.803996i
$469$	−11.5977	−	17.9353i	−0.535531	−	0.828174i
$470$		−	5.27791i		−	0.243452i
$471$	31.7161	+	6.56750i	1.46140	+	0.302615i
$472$			0.766971i			0.0353027i
$473$			17.2911i			0.795044i
$474$	15.7111	+	3.25332i	0.721634	+	0.149430i
$475$			1.54282i			0.0707895i
$476$	1.73770	+	2.68728i	0.0796475	+	0.123171i
$477$	0.632275	−	1.46124i	0.0289499	−	0.0669058i
$478$	17.7714			0.812847
$479$	−4.73122			−0.216175			−0.108087	−	0.994141i	$-0.534473\pi$
$479$	−4.73122			−0.216175			−0.108087	+	0.994141i	$0.534473\pi$
$480$	11.5477	+	2.39120i	0.527079	+	0.109143i
$481$		−	30.0181i		−	1.36871i
$482$	20.0089			0.911379
$483$	−12.1930	−	31.4528i	−0.554802	−	1.43115i
$484$	−28.1016			−1.27734
$485$			14.2821i			0.648517i
$486$	7.24250	+	11.8163i	0.328526	+	0.535999i
$487$	19.8587			0.899882			0.449941	−	0.893058i	$-0.351445\pi$
$487$	19.8587			0.899882			0.449941	+	0.893058i	$0.351445\pi$
$488$	21.9403			0.993190
$489$	−1.72537	+	8.33223i	−0.0780238	+	0.376797i
$490$	−6.89762	−	3.10328i	−0.311603	−	0.140192i
$491$			8.61247i			0.388676i	0.980935	+	0.194338i	$0.0622558\pi$
$491$			8.61247i			0.388676i	−0.980935	+	0.194338i	$0.937744\pi$
$492$	−4.79205	+	23.1420i	−0.216042	+	1.04332i
$493$		−	3.77181i		−	0.169874i
$494$		−	2.03348i		−	0.0914904i
$495$	8.47134	−	19.5780i	0.380758	−	0.879967i
$496$			0.206840i			0.00928739i
$497$	10.3638	−	6.70164i	0.464879	−	0.300610i
$498$	15.2217	+	3.15197i	0.682099	+	0.141243i
$499$	−6.28847			−0.281510			−0.140755	−	0.990044i	$-0.544953\pi$
$499$	−6.28847			−0.281510			−0.140755	+	0.990044i	$0.544953\pi$
$500$	−12.5287			−0.560302
$501$	8.90260	−	42.9929i	0.397739	−	1.92078i
$502$			8.83111i			0.394152i
$503$	43.2556			1.92867			0.964336	−	0.264680i	$-0.0852663\pi$
$503$	43.2556			1.92867			0.964336	+	0.264680i	$0.0852663\pi$
$504$	22.3391	−	3.73444i	0.995065	−	0.166345i
$505$	−12.7197			−0.566021
$506$			38.2923i			1.70230i
$507$	−5.01419	+	24.2148i	−0.222688	+	1.07542i
$508$	−13.1269			−0.582413
$509$	−14.0422			−0.622408			−0.311204	−	0.950343i	$-0.600732\pi$
$509$	−14.0422			−0.622408			−0.311204	+	0.950343i	$0.600732\pi$
$510$	1.83262	+	0.379483i	0.0811497	+	0.0168038i
$511$	−13.3678	+	8.64416i	−0.591356	+	0.382395i
$512$		−	1.33324i		−	0.0589216i
$513$	1.86181	+	1.30835i	0.0822008	+	0.0577651i
$514$			6.99631i			0.308594i
$515$			5.33929i			0.235277i
$516$	1.25541	−	6.06270i	0.0552665	−	0.266896i
$517$		−	28.5796i		−	1.25693i
$518$	−11.3530	+	7.34132i	−0.498823	+	0.322559i
$519$	−1.70513	+	8.23450i	−0.0748469	+	0.361454i
$520$	18.1122			0.794272
$521$	33.8795			1.48429			0.742144	−	0.670241i	$-0.233809\pi$
$521$	33.8795			1.48429			0.742144	+	0.670241i	$0.233809\pi$
$522$	−9.23297	−	3.99507i	−0.404116	−	0.174860i
$523$			27.5076i			1.20283i	0.798939	+	0.601413i	$0.205395\pi$
$523$			27.5076i			1.20283i	−0.798939	+	0.601413i	$0.794605\pi$
$524$	−5.43719			−0.237525
$525$	−15.0529	+	5.83541i	−0.656961	+	0.254678i
$526$	−24.5985			−1.07254
$527$		−	1.75453i		−	0.0764283i
$528$	−1.16988	−	0.242249i	−0.0509125	−	0.0105425i
$529$	−31.1880			−1.35600
$530$	−0.573452			−0.0249092
$531$	−0.740035	−	0.320210i	−0.0321148	−	0.0138959i
$532$	1.17684	−	0.760990i	0.0510223	−	0.0329931i
$533$			58.9158i			2.55192i
$534$	−13.9923	−	2.89740i	−0.605505	−	0.125383i
$535$		−	2.83440i		−	0.122542i
$536$		−	23.0357i		−	0.994989i
$537$	0.507179	+	0.105022i	0.0218864	+	0.00453205i
$538$			1.19449i			0.0514980i
$539$	−37.3503	−	16.8041i	−1.60879	−	0.723805i
$540$	−4.39173	+	6.24951i	−0.188990	+	0.268936i
$541$	−16.9806			−0.730055			−0.365027	−	0.930997i	$-0.618940\pi$
$541$	−16.9806			−0.730055			−0.365027	+	0.930997i	$0.618940\pi$
$542$	−2.81078			−0.120733
$543$	27.0576	+	5.60285i	1.16115	+	0.240441i
$544$			5.60223i			0.240194i
$545$	4.74917			0.203432
$546$	19.8401	−	7.69122i	0.849077	−	0.329154i
$547$	41.8477			1.78928			0.894640	−	0.446788i	$-0.147432\pi$
$547$	41.8477			1.78928			0.894640	+	0.446788i	$0.147432\pi$
$548$			13.9666i			0.596625i
$549$	−9.16006	+	21.1697i	−0.390942	+	0.903502i
$550$	18.3262			0.781431
$551$	−1.65178			−0.0703684
$552$	7.37729	−	35.6268i	0.313998	−	1.51638i
$553$	14.9685	+	23.1480i	0.636524	+	0.984355i
$554$		−	14.3642i		−	0.610275i
$555$	2.45324	−	11.8473i	0.104134	−	0.502891i
$556$		−	9.47230i		−	0.401715i
$557$		−	27.3604i		−	1.15930i	−0.814866	−	0.579649i	$-0.803190\pi$
$557$		−	27.3604i		−	1.15930i	0.814866	−	0.579649i	$-0.196810\pi$
$558$	−4.29488	−	1.85838i	−0.181817	−	0.0786715i
$559$		−	15.4347i		−	0.652816i
$560$	−0.205834	−	0.318313i	−0.00869809	−	0.0134512i
$561$	9.92354	+	2.05488i	0.418972	+	0.0867572i
$562$	8.18839			0.345407
$563$	1.84028			0.0775586			0.0387793	−	0.999248i	$-0.487653\pi$
$563$	1.84028			0.0775586			0.0387793	+	0.999248i	$0.487653\pi$
$564$	−2.07502	+	10.0208i	−0.0873740	+	0.421951i
$565$		−	14.9391i		−	0.628492i
$566$	−9.28719			−0.390370
$567$	−5.72331	+	23.1137i	−0.240356	+	0.970685i
$568$	13.3110			0.558517
$569$		−	8.16011i		−	0.342090i	−0.985263	−	0.171045i	$-0.945286\pi$
$569$		−	8.16011i		−	0.342090i	0.985263	−	0.171045i	$-0.0547143\pi$
$570$	0.166187	−	0.802557i	0.00696079	−	0.0336154i
$571$	−39.6265			−1.65832			−0.829158	−	0.559015i	$-0.811180\pi$
$571$	−39.6265			−1.65832			−0.829158	+	0.559015i	$0.811180\pi$
$572$	36.9611			1.54542
$573$	23.8361	+	4.93577i	0.995767	+	0.206195i
$574$	22.2823	−	14.4086i	0.930044	−	0.601404i
$575$			25.9336i			1.08151i
$576$	14.3628	+	6.21474i	0.598451	+	0.258947i
$577$		−	0.447275i		−	0.0186203i	−0.999957	−	0.00931014i	$-0.997036\pi$
$577$		−	0.447275i		−	0.0186203i	0.999957	−	0.00931014i	$-0.00296355\pi$
$578$			0.889073i			0.0369805i
$579$	6.53307	−	31.5498i	0.271505	−	1.31117i
$580$		−	5.54453i		−	0.230224i
$581$	14.5022	+	22.4269i	0.601651	+	0.930426i
$582$	−3.66946	+	17.7207i	−0.152104	+	0.734548i
$583$	−3.10521			−0.128605
$584$	−17.1693			−0.710470
$585$	−7.56184	+	17.4761i	−0.312643	+	0.722547i
$586$			13.8636i			0.572702i
$587$	−24.6386			−1.01694			−0.508472	−	0.861078i	$-0.669790\pi$
$587$	−24.6386			−1.01694			−0.508472	+	0.861078i	$0.669790\pi$
$588$	11.8759	+	8.60378i	0.489755	+	0.354814i
$589$	−0.768357			−0.0316596
$590$			0.290420i			0.0119564i
$591$	16.3859	+	3.39305i	0.674026	+	0.139572i
$592$	−0.677579			−0.0278483
$593$	−35.6016			−1.46198			−0.730991	−	0.682387i	$-0.760942\pi$
$593$	−35.6016			−1.46198			−0.730991	+	0.682387i	$0.760942\pi$
$594$	15.5411	−	22.1152i	0.637658	−	0.907398i
$595$	1.74600	+	2.70010i	0.0715788	+	0.110693i
$596$			0.331934i			0.0135965i
$597$	5.33394	+	1.10451i	0.218304	+	0.0452045i
$598$		−	34.1812i		−	1.39777i
$599$		−	16.8325i		−	0.687755i	−0.939014	−	0.343878i	$-0.888259\pi$
$599$		−	16.8325i		−	0.687755i	0.939014	−	0.343878i	$-0.111741\pi$
$600$	−17.0505	−	3.53067i	−0.696083	−	0.144139i
$601$		−	11.7633i		−	0.479833i	−0.970793	−	0.239917i	$-0.922880\pi$
$601$		−	11.7633i		−	0.479833i	0.970793	−	0.239917i	$-0.0771201\pi$
$602$	−5.83747	+	3.77475i	−0.237918	+	0.153847i
$603$	22.2266	+	9.61739i	0.905139	+	0.391650i
$604$	21.4026			0.870861
$605$	−28.2357			−1.14794
$606$	−15.7822	−	3.26805i	−0.641109	−	0.132755i
$607$			10.2686i			0.416788i	0.978045	+	0.208394i	$0.0668237\pi$
$607$			10.2686i			0.416788i	−0.978045	+	0.208394i	$0.933176\pi$
$608$	2.45338			0.0994977
$609$	−6.24755	−	16.1160i	−0.253163	−	0.653054i
$610$	8.30786			0.336375
$611$			25.5113i			1.03208i
$612$	−3.33026	−	1.44099i	−0.134618	−	0.0582486i
$613$	−29.7171			−1.20026			−0.600131	−	0.799902i	$-0.704885\pi$
$613$	−29.7171			−1.20026			−0.600131	+	0.799902i	$0.704885\pi$
$614$	−7.09791			−0.286449
$615$	−4.81491	+	23.2524i	−0.194156	+	0.937628i
$616$	−23.9859	−	37.0931i	−0.966420	−	1.49452i
$617$		−	11.3997i		−	0.458933i	−0.973317	−	0.229467i	$-0.926302\pi$
$617$		−	11.3997i		−	0.458933i	0.973317	−	0.229467i	$-0.0736981\pi$
$618$	−1.37181	+	6.62481i	−0.0551823	+	0.266489i
$619$			29.6798i			1.19293i	0.802638	+	0.596466i	$0.203429\pi$
$619$			29.6798i			1.19293i	−0.802638	+	0.596466i	$0.796571\pi$
$620$		−	2.57914i		−	0.103581i
$621$	31.2955	+	21.9924i	1.25585	+	0.882524i
$622$			0.707672i			0.0283751i
$623$	−13.3309	−	20.6156i	−0.534091	−	0.825947i
$624$	1.04428	+	0.216240i	0.0418046	+	0.00865655i
$625$	5.02645			0.201058
$626$	22.9671			0.917948
$627$	0.899892	−	4.34581i	0.0359382	−	0.173555i
$628$			22.6183i			0.902569i
$629$	5.74758			0.229171
$630$	8.45890	−	1.41408i	0.337010	−	0.0563381i
$631$	−1.18458			−0.0471574			−0.0235787	−	0.999722i	$-0.507506\pi$
$631$	−1.18458			−0.0471574			−0.0235787	+	0.999722i	$0.507506\pi$
$632$			29.7308i			1.18263i
$633$	−4.55511	+	21.9978i	−0.181049	+	0.874333i
$634$	−2.01692			−0.0801021
$635$	−13.1896			−0.523412
$636$	1.08877	+	0.225453i	0.0431725	+	0.00893980i
$637$	33.3403	+	15.0000i	1.32099	+	0.594322i
$638$			19.6205i			0.776783i
$639$	−5.55734	+	12.8435i	−0.219845	+	0.508082i
$640$			7.98048i			0.315456i
$641$			24.6738i			0.974556i	0.873247	+	0.487278i	$0.162010\pi$
$641$			24.6738i			0.974556i	−0.873247	+	0.487278i	$0.837990\pi$
$642$	0.728234	−	3.51683i	0.0287411	−	0.138798i
$643$			14.3397i			0.565502i	0.959193	+	0.282751i	$0.0912471\pi$
$643$			14.3397i			0.565502i	−0.959193	+	0.282751i	$0.908753\pi$
$644$	19.7817	−	12.7917i	0.779509	−	0.504062i
$645$	1.26140	−	6.09163i	0.0496677	−	0.239858i
$646$	0.389351			0.0153188
$647$	−7.37116			−0.289790			−0.144895	−	0.989447i	$-0.546284\pi$
$647$	−7.37116			−0.289790			−0.144895	+	0.989447i	$0.546284\pi$
$648$	−18.7199	+	17.5817i	−0.735387	+	0.690673i
$649$			1.57261i			0.0617303i
$650$	−16.3586			−0.641639
$651$	−2.90616	−	7.49665i	−0.113901	−	0.293817i
$652$	−5.94212			−0.232711
$653$			7.88816i			0.308688i	0.988017	+	0.154344i	$0.0493264\pi$
$653$			7.88816i			0.308688i	−0.988017	+	0.154344i	$0.950674\pi$
$654$	5.89261	+	1.22019i	0.230419	+	0.0477132i
$655$	−5.46313			−0.213462
$656$	1.32987			0.0519225
$657$	7.16818	−	16.5663i	0.279657	−	0.646313i
$658$	9.64850	−	6.23911i	0.376138	−	0.243226i
$659$		−	24.0967i		−	0.938674i	−0.883019	−	0.469337i	$-0.844493\pi$
$659$		−	24.0967i		−	0.938674i	0.883019	−	0.469337i	$-0.155507\pi$
$660$	14.5875	+	3.02066i	0.567819	+	0.117579i
$661$		−	13.2687i		−	0.516092i	−0.966133	−	0.258046i	$-0.916921\pi$
$661$		−	13.2687i		−	0.516092i	0.966133	−	0.258046i	$-0.0830787\pi$
$662$		−	18.0615i		−	0.701981i
$663$	−8.85813	−	1.83427i	−0.344021	−	0.0712370i
$664$			28.8046i			1.11784i
$665$	1.18245	−	0.764622i	0.0458535	−	0.0296508i
$666$	6.08780	−	14.0694i	0.235897	−	0.545180i
$667$	−27.7652			−1.07507
$668$	30.6603			1.18628
$669$	−16.7508	−	3.46861i	−0.647622	−	0.134104i
$670$		−	8.72264i		−	0.336985i
$671$	44.9867			1.73669
$672$	9.27942	+	23.9370i	0.357962	+	0.923388i
$673$	−16.9749			−0.654336			−0.327168	−	0.944966i	$-0.606094\pi$
$673$	−16.9749			−0.654336			−0.327168	+	0.944966i	$0.606094\pi$
$674$			16.1062i			0.620387i
$675$	10.5253	−	14.9776i	0.405117	−	0.576489i
$676$	−17.2687			−0.664182
$677$	−35.3627			−1.35910			−0.679550	−	0.733629i	$-0.737825\pi$
$677$	−35.3627			−1.35910			−0.679550	+	0.733629i	$0.737825\pi$
$678$	3.83826	−	18.5359i	0.147407	−	0.711868i
$679$	−26.1090	+	16.8831i	−1.00197	+	0.647914i
$680$			3.46795i			0.132990i
$681$	10.4708	−	50.5663i	0.401243	−	1.93770i
$682$			9.12683i			0.349484i
$683$			3.97816i			0.152220i	0.997099	+	0.0761101i	$0.0242500\pi$
$683$			3.97816i			0.152220i	−0.997099	+	0.0761101i	$0.975750\pi$
$684$	−0.631052	+	1.45842i	−0.0241289	+	0.0557640i
$685$			14.0333i			0.536184i
$686$	−2.48071	−	16.2779i	−0.0947140	−	0.621494i
$687$	−28.6260	−	5.92763i	−1.09215	−	0.226153i
$688$	−0.348396			−0.0132825
$689$	2.77183			0.105598
$690$	2.79347	−	13.4904i	0.106346	−	0.513570i
$691$			49.1621i			1.87022i	0.354364	+	0.935108i	$0.384697\pi$
$691$			49.1621i			1.87022i	−0.354364	+	0.935108i	$0.615303\pi$
$692$	−5.87242			−0.223236
$693$	45.8045	−	7.65715i	1.73997	−	0.290871i
$694$	19.9135			0.755906
$695$		−	9.51750i		−	0.361019i
$696$	3.78003	−	18.2547i	0.143282	−	0.691943i
$697$	−11.2806			−0.427284
$698$	2.20182			0.0833401
$699$	−49.8699	−	10.3266i	−1.88625	−	0.390590i
$700$	−6.12192	−	9.46726i	−0.231387	−	0.357829i
$701$		−	7.07609i		−	0.267260i	−0.991031	−	0.133630i	$-0.957337\pi$
$701$		−	7.07609i		−	0.267260i	0.991031	−	0.133630i	$-0.0426634\pi$
$702$	−13.8725	+	19.7409i	−0.523586	+	0.745071i
$703$		−	2.51703i		−	0.0949317i
$704$		−	30.5217i		−	1.15033i
$705$	−2.08492	+	10.0686i	−0.0785226	+	0.379205i
$706$		−	2.85587i		−	0.107482i
$707$	−15.0362	−	23.2528i	−0.565496	−	0.874513i
$708$	0.114179	−	0.551398i	0.00429110	−	0.0207228i
$709$	27.8655			1.04651			0.523255	−	0.852176i	$-0.324718\pi$
$709$	27.8655			1.04651			0.523255	+	0.852176i	$0.324718\pi$
$710$	5.04032			0.189160
$711$	−28.6867	−	12.4126i	−1.07583	−	0.465509i
$712$		−	26.4782i		−	0.992313i
$713$	−12.9155			−0.483689
$714$	1.47264	+	3.79879i	0.0551122	+	0.142166i
$715$	37.1375			1.38886
$716$			0.361694i			0.0135171i
$717$	−33.9023	−	7.02020i	−1.26610	−	0.262174i
$718$	−3.59907			−0.134316
$719$	0.362178			0.0135070			0.00675349	−	0.999977i	$-0.497850\pi$
$719$	0.362178			0.0135070			0.00675349	+	0.999977i	$0.497850\pi$
$720$	0.394476	+	0.170688i	0.0147012	+	0.00636118i
$721$	−9.76071	+	6.31167i	−0.363508	+	0.235059i
$722$			16.7219i			0.622324i
$723$	−38.1706	−	7.90404i	−1.41958	−	0.293954i
$724$			19.2961i			0.717132i
$725$			13.2881i			0.493506i
$726$	−35.0338	−	7.25451i	−1.30023	−	0.269240i
$727$		−	18.7030i		−	0.693655i	−0.937929	−	0.346828i	$-0.887259\pi$
$727$		−	18.7030i		−	0.693655i	0.937929	−	0.346828i	$-0.112741\pi$
$728$	21.4107	+	33.1107i	0.793534	+	1.22716i
$729$	−9.14864	−	25.4028i	−0.338838	−	0.940845i
$730$	−6.50129			−0.240623
$731$	2.95528			0.109305
$732$	−15.7735	−	3.26624i	−0.583006	−	0.120724i
$733$			25.6927i			0.948981i	0.880261	+	0.474490i	$0.157368\pi$
$733$			25.6927i			0.948981i	−0.880261	+	0.474490i	$0.842632\pi$
$734$	9.33618			0.344605
$735$	11.9326	+	8.64483i	0.440140	+	0.318869i
$736$	41.2394			1.52011
$737$		−	47.2327i		−	1.73984i
$738$	−11.9484	+	27.6137i	−0.439825	+	1.01648i
$739$	20.1429			0.740968			0.370484	−	0.928839i	$-0.379192\pi$
$739$	20.1429			0.740968			0.370484	+	0.928839i	$0.379192\pi$
$740$	8.44890			0.310588
$741$	−0.803278	+	3.87923i	−0.0295092	+	0.142507i
$742$	−0.677887	−	1.04832i	−0.0248860	−	0.0384851i
$743$			4.62365i			0.169625i	0.996397	+	0.0848126i	$0.0270292\pi$
$743$			4.62365i			0.169625i	−0.996397	+	0.0848126i	$0.972971\pi$
$744$	1.75835	−	8.49151i	0.0644642	−	0.311314i
$745$			0.333518i			0.0122192i
$746$			2.63042i			0.0963066i
$747$	−27.7930	−	12.0259i	−1.01689	−	0.440006i
$748$			7.07696i			0.258759i
$749$	5.18154	−	3.35059i	0.189329	−	0.122428i
$750$	−15.6194	−	3.23433i	−0.570340	−	0.118101i
$751$	17.9179			0.653835			0.326917	−	0.945053i	$-0.393990\pi$
$751$	17.9179			0.653835			0.326917	+	0.945053i	$0.393990\pi$
$752$	0.575849			0.0209990
$753$	3.48853	−	16.8470i	0.127129	−	0.613937i
$754$		−	17.5140i		−	0.637822i
$755$	21.5048			0.782639
$756$	−16.6162	−	0.640825i	−0.604326	−	0.0233066i
$757$	−42.9624			−1.56150			−0.780748	−	0.624846i	$-0.785162\pi$
$757$	−42.9624			−1.56150			−0.780748	+	0.624846i	$0.785162\pi$
$758$		−	7.43079i		−	0.269898i
$759$	15.1265	−	73.0497i	0.549057	−	2.65154i
$760$	1.51871			0.0550896
$761$	−48.2921			−1.75059			−0.875293	−	0.483592i	$-0.839332\pi$
$761$	−48.2921			−1.75059			−0.875293	+	0.483592i	$0.839332\pi$
$762$	−16.3652	−	3.38876i	−0.592847	−	0.122762i
$763$	5.61408	+	8.68191i	0.203243	+	0.314306i
$764$			16.9987i			0.614990i
$765$	−3.34615	−	1.44787i	−0.120980	−	0.0523478i
$766$			5.32375i			0.192355i
$767$		−	1.40377i		−	0.0506872i
$768$	−5.71460	+	27.5972i	−0.206208	+	0.995830i
$769$		−	6.79930i		−	0.245189i	−0.992457	−	0.122594i	$-0.960879\pi$
$769$		−	6.79930i		−	0.245189i	0.992457	−	0.122594i	$-0.0391215\pi$
$770$	−9.08246	−	14.0456i	−0.327309	−	0.506168i
$771$	2.76373	−	13.3468i	0.0995334	−	0.480672i
$772$	22.4997			0.809783
$773$	−50.1087			−1.80229			−0.901143	−	0.433523i	$-0.857270\pi$
$773$	−50.1087			−1.80229			−0.901143	+	0.433523i	$0.857270\pi$
$774$	3.13021	−	7.23420i	0.112513	−	0.260028i
$775$			6.18118i			0.222035i
$776$	−33.5337			−1.20379
$777$	24.5580	−	9.52018i	0.881013	−	0.341535i
$778$	−17.7789			−0.637404
$779$			4.94011i			0.176998i
$780$	−13.0214	−	2.69636i	−0.466240	−	0.0965451i
$781$	27.2931			0.976623
$782$	6.54469			0.234037
$783$	16.0354	+	11.2686i	0.573060	+	0.402707i
$784$	0.338585	−	0.752567i	0.0120923	−	0.0268774i
$785$			22.7262i			0.811134i
$786$	−6.77847	−	1.40363i	−0.241780	−	0.0500657i
$787$			39.7194i			1.41584i	0.706291	+	0.707922i	$0.250367\pi$
$787$			39.7194i			1.41584i	−0.706291	+	0.707922i	$0.749633\pi$
$788$			11.6856i			0.416282i
$789$	46.9261	+	9.71705i	1.67061	+	0.345936i
$790$			11.2578i			0.400535i
$791$	27.3100	−	17.6598i	0.971032	−	0.627909i
$792$	45.9683	+	19.8903i	1.63341	+	0.706772i
$793$	−40.1568			−1.42601
$794$	−26.0621			−0.924908
$795$	1.09397	+	0.226529i	0.0387989	+	0.00803415i
$796$			3.80389i			0.134825i
$797$	40.1065			1.42065			0.710323	−	0.703876i	$-0.248549\pi$
$797$	40.1065			1.42065			0.710323	+	0.703876i	$0.248549\pi$
$798$	1.66360	−	0.644912i	0.0588907	−	0.0228296i
$799$	−4.88465			−0.172807
$800$		−	19.7366i		−	0.697795i
$801$	25.5483	+	11.0546i	0.902704	+	0.390597i
$802$	3.95972			0.139822
$803$	−35.2042			−1.24233
$804$	−3.42931	+	16.5610i	−0.120943	+	0.584062i
$805$	19.8761	−	12.8527i	0.700541	−	0.452998i
$806$		−	8.14695i		−	0.286964i
$807$	0.471855	−	2.27871i	0.0166101	−	0.0802143i
$808$		−	29.8654i		−	1.05066i
$809$			41.6670i			1.46493i	0.680803	+	0.732467i	$0.261631\pi$
$809$			41.6670i			1.46493i	−0.680803	+	0.732467i	$0.738369\pi$
$810$	−7.08844	+	6.65744i	−0.249062	+	0.233919i
$811$		−	8.82398i		−	0.309852i	−0.987926	−	0.154926i	$-0.950486\pi$
$811$		−	8.82398i		−	0.309852i	0.987926	−	0.154926i	$-0.0495139\pi$
$812$	10.1359	−	6.55429i	0.355700	−	0.230010i
$813$	5.36207	+	1.11033i	0.188056	+	0.0389411i
$814$	−29.8982			−1.04793
$815$	−5.97047			−0.209137
$816$	−0.0414037	+	0.199949i	−0.00144942	+	0.00699960i
$817$		−	1.29420i		−	0.0452784i
$818$	−29.9286			−1.04643
$819$	−40.8868	+	6.83506i	−1.42870	+	0.238836i
$820$	−16.5824			−0.579084
$821$		−	27.1192i		−	0.946468i	−0.880937	−	0.473234i	$-0.843087\pi$
$821$		−	27.1192i		−	0.946468i	0.880937	−	0.473234i	$-0.156913\pi$
$822$	−3.60553	+	17.4120i	−0.125757	+	0.607313i
$823$	27.1234			0.945464			0.472732	−	0.881206i	$-0.343268\pi$
$823$	27.1234			0.945464			0.472732	+	0.881206i	$0.343268\pi$
$824$	−12.5364			−0.436727
$825$	−34.9606	−	7.23934i	−1.21717	−	0.252041i
$826$	−0.530913	+	0.343310i	−0.0184728	+	0.0119453i
$827$		−	46.8067i		−	1.62763i	−0.581125	−	0.813814i	$-0.697387\pi$
$827$		−	46.8067i		−	1.62763i	0.581125	−	0.813814i	$-0.302613\pi$
$828$	−10.6075	+	24.5149i	−0.368636	+	0.851951i
$829$		−	51.2961i		−	1.78159i	−0.454408	−	0.890794i	$-0.650149\pi$
$829$		−	51.2961i		−	1.78159i	0.454408	−	0.890794i	$-0.349851\pi$
$830$			10.9071i			0.378591i
$831$	−5.67424	+	27.4023i	−0.196837	+	0.950576i
$832$			27.2448i			0.944543i
$833$	−2.87206	+	6.38367i	−0.0995109	+	0.221181i
$834$	2.44530	−	11.8090i	0.0846739	−	0.408912i
$835$	30.8066			1.06611
$836$	3.09921			0.107188
$837$	7.45917	+	5.24180i	0.257827	+	0.181183i
$838$		−	10.5970i		−	0.366068i
$839$	21.7861			0.752140			0.376070	−	0.926591i	$-0.377275\pi$
$839$	21.7861			0.752140			0.376070	+	0.926591i	$0.377275\pi$
$840$	5.74424	+	14.8177i	0.198195	+	0.511259i
$841$	14.7735			0.509429
$842$		−	20.1065i		−	0.692915i
$843$	−15.6209	−	3.23464i	−0.538011	−	0.111407i
$844$	−15.6877			−0.539992
$845$	−17.3511			−0.596897
$846$	−5.17379	+	11.9571i	−0.177879	+	0.411093i
$847$	−33.3779	−	51.6173i	−1.14688	−	1.77359i
$848$		−	0.0625667i		−	0.00214855i
$849$	17.7170	+	3.66869i	0.608047	+	0.125909i
$850$		−	3.13220i		−	0.107433i
$851$		−	42.3094i		−	1.45035i
$852$	−9.56967	−	1.98161i	−0.327851	−	0.0678887i
$853$		−	37.6474i		−	1.28902i	−0.764595	−	0.644511i	$-0.777061\pi$
$853$		−	37.6474i		−	1.28902i	0.764595	−	0.644511i	$-0.222939\pi$
$854$	9.82087	+	15.1875i	0.336063	+	0.519706i
$855$	−0.634063	+	1.46538i	−0.0216845	+	0.0501148i
$856$	6.65505			0.227465
$857$	−40.5213			−1.38418			−0.692091	−	0.721810i	$-0.743310\pi$
$857$	−40.5213			−1.38418			−0.692091	+	0.721810i	$0.743310\pi$
$858$	46.0789	+	9.54163i	1.57311	+	0.325746i
$859$		−	4.33811i		−	0.148014i	−0.997258	−	0.0740072i	$-0.976421\pi$
$859$		−	4.33811i		−	0.148014i	0.997258	−	0.0740072i	$-0.0235788\pi$
$860$	4.34424			0.148137
$861$	−48.1993	+	18.6850i	−1.64263	+	0.636783i
$862$	−6.68098			−0.227555
$863$		−	17.2118i		−	0.585897i	−0.956128	−	0.292949i	$-0.905364\pi$
$863$		−	17.2118i		−	0.585897i	0.956128	−	0.292949i	$-0.0946365\pi$
$864$	−23.8173	−	16.7372i	−0.810280	−	0.569410i
$865$	−5.90044			−0.200621
$866$	4.88782			0.166095
$867$	0.351208	−	1.69607i	0.0119276	−	0.0576016i
$868$	4.71490	−	3.04884i	0.160034	−	0.103485i
$869$			60.9605i			2.06794i
$870$	1.43134	−	6.91229i	0.0485269	−	0.234349i
$871$			42.1617i			1.42859i
$872$			11.1508i			0.377615i
$873$	14.0003	−	32.3560i	0.473840	−	1.09509i
$874$		−	2.86611i		−	0.0969475i
$875$	−14.8811	−	23.0129i	−0.503073	−	0.777980i
$876$	12.3435	+	2.55599i	0.417048	+	0.0863588i
$877$	58.4647			1.97421			0.987106	−	0.160070i	$-0.0511720\pi$
$877$	58.4647			1.97421			0.987106	+	0.160070i	$0.0511720\pi$
$878$	7.15797			0.241570
$879$	5.47652	−	26.4475i	0.184718	−	0.892051i
$880$		−	0.838280i		−	0.0282584i
$881$	−19.9854			−0.673327			−0.336663	−	0.941625i	$-0.609298\pi$
$881$	−19.9854			−0.673327			−0.336663	+	0.941625i	$0.609298\pi$
$882$	12.5845	+	13.7920i	0.423741	+	0.464401i
$883$	−42.4803			−1.42958			−0.714788	−	0.699342i	$-0.753477\pi$
$883$	−42.4803			−1.42958			−0.714788	+	0.699342i	$0.753477\pi$
$884$		−	6.31716i		−	0.212469i
$885$	0.114724	−	0.554029i	0.00385639	−	0.0186235i
$886$	−27.3232			−0.917940
$887$	14.6483			0.491840			0.245920	−	0.969290i	$-0.420910\pi$
$887$	14.6483			0.491840			0.245920	+	0.969290i	$0.420910\pi$
$888$	27.8170	+	5.76011i	0.933478	+	0.193297i
$889$	−15.5916	−	24.1117i	−0.522926	−	0.808681i
$890$		−	10.0262i		−	0.336078i
$891$	−38.3836	+	36.0497i	−1.28590	+	1.20771i
$892$		−	11.9458i		−	0.399975i
$893$			2.13913i			0.0715833i
$894$	−0.0856898	+	0.413818i	−0.00286590	+	0.0138401i
$895$			0.363420i			0.0121478i
$896$	−14.5890	+	9.43386i	−0.487385	+	0.315163i
$897$	−13.5025	+	65.2069i	−0.450835	+	2.17720i
$898$	−10.0573			−0.335617
$899$	−6.61774			−0.220714
$900$	11.7325	+	5.07660i	0.391083	+	0.169220i
$901$			0.530724i			0.0176810i
$902$	58.6804			1.95384
$903$	12.6272	−	4.89506i	0.420206	−	0.162898i
$904$	35.0764			1.16662
$905$			19.3881i			0.644484i
$906$	26.6824	+	5.52516i	0.886463	+	0.183561i
$907$	7.78936			0.258642			0.129321	−	0.991603i	$-0.458720\pi$
$907$	7.78936			0.258642			0.129321	+	0.991603i	$0.458720\pi$
$908$	36.0613			1.19673
$909$	28.8165	+	12.4688i	0.955784	+	0.413564i
$910$	8.10734	+	12.5376i	0.268756	+	0.415619i
$911$		−	25.3972i		−	0.841448i	−0.907189	−	0.420724i	$-0.861776\pi$
$911$		−	25.3972i		−	0.841448i	0.907189	−	0.420724i	$-0.138224\pi$
$912$	0.0875633	+	0.0181319i	0.00289951	+	0.000600406i
$913$			59.0614i			1.95465i
$914$			20.3233i			0.672237i
$915$	−15.8488	−	3.28183i	−0.523944	−	0.108494i
$916$		−	20.4146i		−	0.674518i
$917$	−6.45806	−	9.98710i	−0.213264	−	0.329803i
$918$	−3.77979	−	2.65618i	−0.124752	−	0.0876671i
$919$	23.2479			0.766878			0.383439	−	0.923566i	$-0.374740\pi$
$919$	23.2479			0.766878			0.383439	+	0.923566i	$0.374740\pi$
$920$	25.5284			0.841648
$921$	13.5406	+	2.80387i	0.446177	+	0.0923906i
$922$		−	13.2291i		−	0.435676i
$923$	−24.3628			−0.801912
$924$	11.7221	+	30.2381i	0.385630	+	0.994760i
$925$	−20.2487			−0.665773
$926$			6.00996i			0.197499i
$927$	5.23396	−	12.0961i	0.171906	−	0.397290i
$928$	21.1306			0.693645
$929$	9.94197			0.326185			0.163093	−	0.986611i	$-0.447853\pi$
$929$	9.94197			0.326185			0.163093	+	0.986611i	$0.447853\pi$
$930$	0.665813	−	3.21538i	0.0218329	−	0.105436i
$931$	2.79560	+	1.25776i	0.0916219	+	0.0412213i
$932$		−	35.5647i		−	1.16496i
$933$	0.279549	−	1.35001i	0.00915204	−	0.0441975i
$934$			16.5016i			0.539950i
$935$			7.11073i			0.232546i
$936$	−41.0331	−	17.7549i	−1.34121	−	0.580336i
$937$			12.3654i			0.403959i	0.979390	+	0.201980i	$0.0647375\pi$
$937$			12.3654i			0.403959i	−0.979390	+	0.201980i	$0.935263\pi$
$938$	15.9458	−	10.3112i	0.520648	−	0.336672i
$939$	−43.8139	−	9.07261i	−1.42981	−	0.296073i
$940$	−7.18040			−0.234199
$941$	−28.0370			−0.913979			−0.456990	−	0.889472i	$-0.651072\pi$
$941$	−28.0370			−0.913979			−0.456990	+	0.889472i	$0.651072\pi$
$942$	−5.83899	+	28.1979i	−0.190244	+	0.918738i
$943$			83.0395i			2.70414i
$944$	−0.0316864			−0.00103130
$945$	−16.6955	−	0.643883i	−0.543105	−	0.0209455i
$946$	−15.3730			−0.499820
$947$		−	0.512890i		−	0.0166667i	−0.999965	−	0.00833334i	$-0.997347\pi$
$947$		−	0.512890i		−	0.0166667i	0.999965	−	0.00833334i	$-0.00265262\pi$
$948$	4.42602	−	21.3743i	0.143750	−	0.694207i
$949$	31.4246			1.02008
$950$	−1.37168			−0.0445032
$951$	3.84765	+	0.796738i	0.124768	+	0.0258360i
$952$	−6.33972	+	4.09952i	−0.205472	+	0.132866i
$953$		−	0.409399i		−	0.0132617i	−0.999978	−	0.00663087i	$-0.997889\pi$
$953$		−	0.409399i		−	0.0132617i	0.999978	−	0.00663087i	$-0.00211069\pi$
$954$	1.29915	+	0.562139i	0.0420616	+	0.0181999i
$955$			17.0798i			0.552689i
$956$		−	24.1774i		−	0.781952i
$957$	7.75063	−	37.4297i	0.250542	−	1.20993i
$958$		−	4.20639i		−	0.135902i
$959$	−25.6541	+	16.5890i	−0.828413	+	0.535686i
$960$	−2.22659	+	10.7528i	−0.0718629	+	0.347044i
$961$	27.9216			0.900698
$962$	26.6883			0.860465
$963$	−2.77848	+	6.42132i	−0.0895353	+	0.206924i
$964$		−	27.2213i		−	0.876739i
$965$	22.6071			0.727748
$966$	27.9638	−	10.8405i	0.899721	−	0.348787i
$967$	−15.4103			−0.495562			−0.247781	−	0.968816i	$-0.579701\pi$
$967$	−15.4103			−0.495562			−0.247781	+	0.968816i	$0.579701\pi$
$968$		−	66.2961i		−	2.13084i
$969$	−0.742758	−	0.153804i	−0.0238608	−	0.00494090i
$970$	−12.6978			−0.407702
$971$	47.3568			1.51975			0.759876	−	0.650068i	$-0.225260\pi$
$971$	47.3568			1.51975			0.759876	+	0.650068i	$0.225260\pi$
$972$	16.0757	−	9.85315i	0.515627	−	0.316040i
$973$	17.3988	−	11.2508i	0.557781	−	0.360684i
$974$			17.6558i			0.565728i
$975$	31.2071	+	6.46211i	0.999428	+	0.206953i
$976$			0.906432i			0.0290142i
$977$			10.9253i			0.349531i	0.984610	+	0.174766i	$0.0559168\pi$
$977$			10.9253i			0.349531i	−0.984610	+	0.174766i	$0.944083\pi$
$978$	−7.40796	−	1.53398i	−0.236880	−	0.0490512i
$979$		−	54.2913i		−	1.73516i
$980$	−4.22190	+	9.38395i	−0.134864	+	0.299759i
$981$	−10.7592	−	4.65548i	−0.343516	−	0.148638i
$982$	−7.65712			−0.244348
$983$	0.194994			0.00621933			0.00310966	−	0.999995i	$-0.499010\pi$
$983$	0.194994			0.00621933			0.00310966	+	0.999995i	$0.499010\pi$
$984$	−54.5957	−	11.3052i	−1.74045	−	0.360397i
$985$			11.7414i			0.374111i
$986$	3.35341			0.106794
$987$	−20.8709	+	8.09084i	−0.664329	+	0.257534i
$988$	−2.76647			−0.0880131
$989$		−	21.7546i		−	0.691755i
$990$	17.4063	+	7.53164i	0.553208	+	0.239371i
$991$	−9.71383			−0.308570			−0.154285	−	0.988026i	$-0.549307\pi$
$991$	−9.71383			−0.308570			−0.154285	+	0.988026i	$0.549307\pi$
$992$	9.82926			0.312079
$993$	−7.13478	+	34.4557i	−0.226416	+	1.09342i
$994$	5.95825	+	9.21415i	0.188984	+	0.292255i
$995$			3.82204i			0.121167i
$996$	4.28814	−	20.7085i	0.135875	−	0.656174i
$997$		−	56.8100i		−	1.79919i	−0.436725	−	0.899595i	$-0.643862\pi$
$997$		−	56.8100i		−	1.79919i	0.436725	−	0.899595i	$-0.356138\pi$
$998$		−	5.59090i		−	0.176977i
$999$	−17.1714	+	24.4352i	−0.543279	+	0.773096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.15	yes	22
3.2	odd	2		357.2.d.a.188.8	✓	22
7.6	odd	2		357.2.d.a.188.15	yes	22
21.20	even	2	inner	357.2.d.b.188.8	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.8	✓	22	3.2	odd	2
357.2.d.a.188.15	yes	22	7.6	odd	2
357.2.d.b.188.8	yes	22	21.20	even	2	inner
357.2.d.b.188.15	yes	22	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.889073i q^{2} +(0.351208 - 1.69607i) q^{3} +1.20955 q^{4} +1.21532 q^{5} +(1.50793 + 0.312249i) q^{6} +(1.43665 + 2.22172i) q^{7} +2.85352i q^{8} +(-2.75331 - 1.19135i) q^{9} +O(q^{10})\)	\(q+0.889073i q^{2} +(0.351208 - 1.69607i) q^{3} +1.20955 q^{4} +1.21532 q^{5} +(1.50793 + 0.312249i) q^{6} +(1.43665 + 2.22172i) q^{7} +2.85352i q^{8} +(-2.75331 - 1.19135i) q^{9} +1.08051i q^{10} +5.85090i q^{11} +(0.424803 - 2.05148i) q^{12} -5.22274i q^{13} +(-1.97527 + 1.27729i) q^{14} +(0.426830 - 2.06127i) q^{15} -0.117889 q^{16} +1.00000 q^{17} +(1.05919 - 2.44789i) q^{18} -0.437929i q^{19} +1.46999 q^{20} +(4.27275 - 1.65638i) q^{21} -5.20188 q^{22} -7.36125i q^{23} +(4.83977 + 1.00218i) q^{24} -3.52299 q^{25} +4.64339 q^{26} +(-2.98759 + 4.25139i) q^{27} +(1.73770 + 2.68728i) q^{28} -3.77181i q^{29} +(1.83262 + 0.379483i) q^{30} -1.75453i q^{31} +5.60223i q^{32} +(9.92354 + 2.05488i) q^{33} +0.889073i q^{34} +(1.74600 + 2.70010i) q^{35} +(-3.33026 - 1.44099i) q^{36} +5.74758 q^{37} +0.389351 q^{38} +(-8.85813 - 1.83427i) q^{39} +3.46795i q^{40} -11.2806 q^{41} +(1.47264 + 3.79879i) q^{42} +2.95528 q^{43} +7.07696i q^{44} +(-3.34615 - 1.44787i) q^{45} +6.54469 q^{46} -4.88465 q^{47} +(-0.0414037 + 0.199949i) q^{48} +(-2.87206 + 6.38367i) q^{49} -3.13220i q^{50} +(0.351208 - 1.69607i) q^{51} -6.31716i q^{52} +0.530724i q^{53} +(-3.77979 - 2.65618i) q^{54} +7.11073i q^{55} +(-6.33972 + 4.09952i) q^{56} +(-0.742758 - 0.153804i) q^{57} +3.35341 q^{58} +0.268780 q^{59} +(0.516273 - 2.49321i) q^{60} -7.68884i q^{61} +1.55990 q^{62} +(-1.30871 - 7.82862i) q^{63} -5.21657 q^{64} -6.34731i q^{65} +(-1.82694 + 8.82275i) q^{66} -8.07271 q^{67} +1.20955 q^{68} +(-12.4852 - 2.58533i) q^{69} +(-2.40059 + 1.55232i) q^{70} -4.66476i q^{71} +(3.39953 - 7.85662i) q^{72} +6.01687i q^{73} +5.11002i q^{74} +(-1.23730 + 5.97524i) q^{75} -0.529697i q^{76} +(-12.9991 + 8.40572i) q^{77} +(1.63080 - 7.87552i) q^{78} +10.4190 q^{79} -0.143274 q^{80} +(6.16139 + 6.56028i) q^{81} -10.0293i q^{82} +10.0944 q^{83} +(5.16811 - 2.00347i) q^{84} +1.21532 q^{85} +2.62746i q^{86} +(-6.39725 - 1.32469i) q^{87} -16.6957 q^{88} -9.27913 q^{89} +(1.28726 - 2.97497i) q^{90} +(11.6034 - 7.50326i) q^{91} -8.90380i q^{92} +(-2.97580 - 0.616203i) q^{93} -4.34281i q^{94} -0.532224i q^{95} +(9.50178 + 1.96755i) q^{96} +11.7517i q^{97} +(-5.67555 - 2.55347i) q^{98} +(6.97045 - 16.1093i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9	\( 22 q - 24 q^{4} + 5 q^{6} - 2 q^{7} - 4 q^{9} - 8 q^{14} - 4 q^{15} + 20 q^{16} + 22 q^{17} + 8 q^{18} - 30 q^{20} - 4 q^{21} - 12 q^{22} - 44 q^{24} + 14 q^{25} - 24 q^{26} + 6 q^{27} + 8 q^{28} + 5 q^{30} + 28 q^{33} + 10 q^{35} - 3 q^{36} - 16 q^{37} + 88 q^{38} - 14 q^{39} - 16 q^{41} + 19 q^{42} - 24 q^{43} - 46 q^{45} + 4 q^{46} - 16 q^{47} + 25 q^{48} + 6 q^{49} + 36 q^{54} - 40 q^{56} - 6 q^{57} + 24 q^{58} + 24 q^{59} - 21 q^{60} - 20 q^{62} - 6 q^{63} - 20 q^{64} - 116 q^{66} + 8 q^{67} - 24 q^{68} + 6 q^{69} + 4 q^{70} - 7 q^{72} + 54 q^{75} + 6 q^{77} + 2 q^{78} + 16 q^{79} + 128 q^{80} - 4 q^{81} + 8 q^{83} + 42 q^{84} - 48 q^{87} + 32 q^{88} - 100 q^{89} + 47 q^{90} + 18 q^{91} + 20 q^{93} + 88 q^{96} - 8 q^{98} + 18 q^{99}+O(q^{100}) \) 22 * q - 24 * q^4 + 5 * q^6 - 2 * q^7 - 4 * q^9 - 8 * q^14 - 4 * q^15 + 20 * q^16 + 22 * q^17 + 8 * q^18 - 30 * q^20 - 4 * q^21 - 12 * q^22 - 44 * q^24 + 14 * q^25 - 24 * q^26 + 6 * q^27 + 8 * q^28 + 5 * q^30 + 28 * q^33 + 10 * q^35 - 3 * q^36 - 16 * q^37 + 88 * q^38 - 14 * q^39 - 16 * q^41 + 19 * q^42 - 24 * q^43 - 46 * q^45 + 4 * q^46 - 16 * q^47 + 25 * q^48 + 6 * q^49 + 36 * q^54 - 40 * q^56 - 6 * q^57 + 24 * q^58 + 24 * q^59 - 21 * q^60 - 20 * q^62 - 6 * q^63 - 20 * q^64 - 116 * q^66 + 8 * q^67 - 24 * q^68 + 6 * q^69 + 4 * q^70 - 7 * q^72 + 54 * q^75 + 6 * q^77 + 2 * q^78 + 16 * q^79 + 128 * q^80 - 4 * q^81 + 8 * q^83 + 42 * q^84 - 48 * q^87 + 32 * q^88 - 100 * q^89 + 47 * q^90 + 18 * q^91 + 20 * q^93 + 88 * q^96 - 8 * q^98 + 18 * q^99

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