LMFDB - Embedded newform 357.2.d.b.188.14

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			188.14
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.886197i q^{2} +(0.730545 + 1.57045i) q^{3} +1.21466 q^{4} +2.83371 q^{5} +(-1.39173 + 0.647406i) q^{6} +(-2.45773 - 0.979562i) q^{7} +2.84882i q^{8} +(-1.93261 + 2.29456i) q^{9} +O(q^{10})$	\(q+0.886197i q^{2} +(0.730545 + 1.57045i) q^{3} +1.21466 q^{4} +2.83371 q^{5} +(-1.39173 + 0.647406i) q^{6} +(-2.45773 - 0.979562i) q^{7} +2.84882i q^{8} +(-1.93261 + 2.29456i) q^{9} +2.51122i q^{10} +0.938759i q^{11} +(0.887360 + 1.90755i) q^{12} -3.81201i q^{13} +(0.868084 - 2.17804i) q^{14} +(2.07015 + 4.45018i) q^{15} -0.0953011 q^{16} +1.00000 q^{17} +(-2.03343 - 1.71267i) q^{18} -3.64941i q^{19} +3.44198 q^{20} +(-0.257135 - 4.57536i) q^{21} -0.831925 q^{22} +1.96572i q^{23} +(-4.47392 + 2.08119i) q^{24} +3.02988 q^{25} +3.37819 q^{26} +(-5.01535 - 1.35878i) q^{27} +(-2.98530 - 1.18983i) q^{28} -5.06446i q^{29} +(-3.94374 + 1.83456i) q^{30} +1.71588i q^{31} +5.61318i q^{32} +(-1.47427 + 0.685806i) q^{33} +0.886197i q^{34} +(-6.96449 - 2.77579i) q^{35} +(-2.34745 + 2.78710i) q^{36} -5.82642 q^{37} +3.23409 q^{38} +(5.98655 - 2.78484i) q^{39} +8.07271i q^{40} +4.40202 q^{41} +(4.05467 - 0.227872i) q^{42} -10.1872 q^{43} +1.14027i q^{44} +(-5.47644 + 6.50212i) q^{45} -1.74201 q^{46} +3.33648 q^{47} +(-0.0696217 - 0.149665i) q^{48} +(5.08092 + 4.81501i) q^{49} +2.68507i q^{50} +(0.730545 + 1.57045i) q^{51} -4.63027i q^{52} -8.71740i q^{53} +(1.20414 - 4.44459i) q^{54} +2.66017i q^{55} +(2.79059 - 7.00164i) q^{56} +(5.73120 - 2.66605i) q^{57} +4.48811 q^{58} -0.484102 q^{59} +(2.51452 + 5.40544i) q^{60} +0.444459i q^{61} -1.52061 q^{62} +(6.99751 - 3.74632i) q^{63} -5.16498 q^{64} -10.8021i q^{65} +(-0.607759 - 1.30649i) q^{66} +11.2460 q^{67} +1.21466 q^{68} +(-3.08706 + 1.43605i) q^{69} +(2.45990 - 6.17191i) q^{70} +10.1759i q^{71} +(-6.53679 - 5.50565i) q^{72} -15.8667i q^{73} -5.16336i q^{74} +(2.21347 + 4.75827i) q^{75} -4.43277i q^{76} +(0.919573 - 2.30722i) q^{77} +(2.46792 + 5.30526i) q^{78} +7.20074 q^{79} -0.270055 q^{80} +(-1.53005 - 8.86899i) q^{81} +3.90105i q^{82} -7.26097 q^{83} +(-0.312330 - 5.55748i) q^{84} +2.83371 q^{85} -9.02790i q^{86} +(7.95347 - 3.69982i) q^{87} -2.67435 q^{88} -15.8649 q^{89} +(-5.76215 - 4.85321i) q^{90} +(-3.73410 + 9.36890i) q^{91} +2.38767i q^{92} +(-2.69470 + 1.25353i) q^{93} +2.95677i q^{94} -10.3413i q^{95} +(-8.81520 + 4.10068i) q^{96} +9.09720i q^{97} +(-4.26704 + 4.50269i) q^{98} +(-2.15404 - 1.81425i) 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 $

$2$			0.886197i			0.626636i	0.949648	+	0.313318i	$0.101441\pi$
$2$			0.886197i			0.626636i	−0.949648	+	0.313318i	$0.898559\pi$
$3$	0.730545	+	1.57045i	0.421780	+	0.906698i
$3$	0.730545	+	1.57045i	0.421780	+	0.906698i
$4$	1.21466			0.607328
$5$	2.83371			1.26727			0.633636	−	0.773632i	$-0.281562\pi$
$5$	2.83371			1.26727			0.633636	+	0.773632i	$0.281562\pi$
$6$	−1.39173	+	0.647406i	−0.568169	+	0.264303i
$7$	−2.45773	−	0.979562i	−0.928936	−	0.370240i
$7$	−2.45773	−	0.979562i	−0.928936	−	0.370240i
$8$			2.84882i			1.00721i
$9$	−1.93261	+	2.29456i	−0.644203	+	0.764855i
$10$			2.51122i			0.794117i
$11$			0.938759i			0.283047i	0.989935	+	0.141523i	$0.0452000\pi$
$11$			0.938759i			0.283047i	−0.989935	+	0.141523i	$0.954800\pi$
$12$	0.887360	+	1.90755i	0.256159	+	0.550663i
$13$		−	3.81201i		−	1.05726i	−0.848852	−	0.528630i	$-0.822706\pi$
$13$		−	3.81201i		−	1.05726i	0.848852	−	0.528630i	$-0.177294\pi$
$14$	0.868084	−	2.17804i	0.232005	−	0.582105i
$15$	2.07015	+	4.45018i	0.534510	+	1.14903i
$16$	−0.0953011			−0.0238253
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	−2.03343	−	1.71267i	−0.479285	−	0.403681i
$19$		−	3.64941i		−	0.837231i	−0.908164	−	0.418616i	$-0.862515\pi$
$19$		−	3.64941i		−	0.837231i	0.908164	−	0.418616i	$-0.137485\pi$
$20$	3.44198			0.769649
$21$	−0.257135	−	4.57536i	−0.0561114	−	0.998425i
$22$	−0.831925			−0.177367
$23$			1.96572i			0.409881i	0.978774	+	0.204940i	$0.0657001\pi$
$23$			1.96572i			0.409881i	−0.978774	+	0.204940i	$0.934300\pi$
$24$	−4.47392	+	2.08119i	−0.913234	+	0.424821i
$25$	3.02988			0.605977
$26$	3.37819			0.662517
$27$	−5.01535	−	1.35878i	−0.965204	−	0.261497i
$28$	−2.98530	−	1.18983i	−0.564169	−	0.224857i
$29$		−	5.06446i		−	0.940447i	−0.882547	−	0.470224i	$-0.844173\pi$
$29$		−	5.06446i		−	0.940447i	0.882547	−	0.470224i	$-0.155827\pi$
$30$	−3.94374	+	1.83456i	−0.720025	+	0.334943i
$31$			1.71588i			0.308181i	0.988057	+	0.154091i	$0.0492448\pi$
$31$			1.71588i			0.308181i	−0.988057	+	0.154091i	$0.950755\pi$
$32$			5.61318i			0.992279i
$33$	−1.47427	+	0.685806i	−0.256638	+	0.119383i
$34$			0.886197i			0.151981i
$35$	−6.96449	−	2.77579i	−1.17721	−	0.469194i
$36$	−2.34745	+	2.78710i	−0.391242	+	0.464517i
$37$	−5.82642			−0.957858			−0.478929	−	0.877854i	$-0.658975\pi$
$37$	−5.82642			−0.957858			−0.478929	+	0.877854i	$0.658975\pi$
$38$	3.23409			0.524639
$39$	5.98655	−	2.78484i	0.958616	−	0.445931i
$40$			8.07271i			1.27641i
$41$	4.40202			0.687479			0.343740	−	0.939065i	$-0.388306\pi$
$41$	4.40202			0.687479			0.343740	+	0.939065i	$0.388306\pi$
$42$	4.05467	−	0.227872i	0.625648	−	0.0351614i
$43$	−10.1872			−1.55354			−0.776770	−	0.629785i	$-0.783143\pi$
$43$	−10.1872			−1.55354			−0.776770	+	0.629785i	$0.783143\pi$
$44$			1.14027i			0.171902i
$45$	−5.47644	+	6.50212i	−0.816380	+	0.969278i
$46$	−1.74201			−0.256846
$47$	3.33648			0.486675			0.243338	−	0.969942i	$-0.421758\pi$
$47$	3.33648			0.486675			0.243338	+	0.969942i	$0.421758\pi$
$48$	−0.0696217	−	0.149665i	−0.0100490	−	0.0216023i
$49$	5.08092	+	4.81501i	0.725845	+	0.687858i
$50$			2.68507i			0.379727i
$51$	0.730545	+	1.57045i	0.102297	+	0.219907i
$52$		−	4.63027i		−	0.642103i
$53$		−	8.71740i		−	1.19743i	−0.800963	−	0.598714i	$-0.795679\pi$
$53$		−	8.71740i		−	1.19743i	0.800963	−	0.598714i	$-0.204321\pi$
$54$	1.20414	−	4.44459i	0.163863	−	0.604831i
$55$			2.66017i			0.358697i
$56$	2.79059	−	7.00164i	0.372909	−	0.935633i
$57$	5.73120	−	2.66605i	0.759116	−	0.353128i
$58$	4.48811			0.589318
$59$	−0.484102			−0.0630247			−0.0315124	−	0.999503i	$-0.510032\pi$
$59$	−0.484102			−0.0630247			−0.0315124	+	0.999503i	$0.510032\pi$
$60$	2.51452	+	5.40544i	0.324623	+	0.697839i
$61$			0.444459i			0.0569072i	0.999595	+	0.0284536i	$0.00905828\pi$
$61$			0.444459i			0.0569072i	−0.999595	+	0.0284536i	$0.990942\pi$
$62$	−1.52061			−0.193117
$63$	6.99751	−	3.74632i	0.881603	−	0.471992i
$64$	−5.16498			−0.645623
$65$		−	10.8021i		−	1.33984i
$66$	−0.607759	−	1.30649i	−0.0748099	−	0.160818i
$67$	11.2460			1.37392			0.686958	−	0.726697i	$-0.258945\pi$
$67$	11.2460			1.37392			0.686958	+	0.726697i	$0.258945\pi$
$68$	1.21466			0.147299
$69$	−3.08706	+	1.43605i	−0.371638	+	0.172880i
$70$	2.45990	−	6.17191i	0.294014	−	0.737685i
$71$			10.1759i			1.20766i	0.797114	+	0.603829i	$0.206359\pi$
$71$			10.1759i			1.20766i	−0.797114	+	0.603829i	$0.793641\pi$
$72$	−6.53679	−	5.50565i	−0.770368	−	0.648847i
$73$		−	15.8667i		−	1.85706i	−0.371263	−	0.928528i	$-0.621075\pi$
$73$		−	15.8667i		−	1.85706i	0.371263	−	0.928528i	$-0.378925\pi$
$74$		−	5.16336i		−	0.600228i
$75$	2.21347	+	4.75827i	0.255589	+	0.549438i
$76$		−	4.43277i		−	0.508474i
$77$	0.919573	−	2.30722i	0.104795	−	0.262932i
$78$	2.46792	+	5.30526i	0.279437	+	0.600703i
$79$	7.20074			0.810146			0.405073	−	0.914284i	$-0.367246\pi$
$79$	7.20074			0.810146			0.405073	+	0.914284i	$0.367246\pi$
$80$	−0.270055			−0.0301931
$81$	−1.53005	−	8.86899i	−0.170005	−	0.985443i
$82$			3.90105i			0.430799i
$83$	−7.26097			−0.796995			−0.398497	−	0.917169i	$-0.630468\pi$
$83$	−7.26097			−0.796995			−0.398497	+	0.917169i	$0.630468\pi$
$84$	−0.312330	−	5.55748i	−0.0340780	−	0.606371i
$85$	2.83371			0.307358
$86$		−	9.02790i		−	0.973503i
$87$	7.95347	−	3.69982i	0.852702	−	0.396662i
$88$	−2.67435			−0.285087
$89$	−15.8649			−1.68168			−0.840840	−	0.541284i	$-0.817938\pi$
$89$	−15.8649			−1.68168			−0.840840	+	0.541284i	$0.817938\pi$
$90$	−5.76215	−	4.85321i	−0.607384	−	0.511573i
$91$	−3.73410	+	9.36890i	−0.391440	+	0.982127i
$92$			2.38767i			0.248932i
$93$	−2.69470	+	1.25353i	−0.279427	+	0.129985i
$94$			2.95677i			0.304968i
$95$		−	10.3413i		−	1.06100i
$96$	−8.81520	+	4.10068i	−0.899698	+	0.418524i
$97$			9.09720i			0.923681i	0.886963	+	0.461840i	$0.152811\pi$
$97$			9.09720i			0.923681i	−0.886963	+	0.461840i	$0.847189\pi$
$98$	−4.26704	+	4.50269i	−0.431036	+	0.454841i
$99$	−2.15404	−	1.81425i	−0.216489	−	0.182339i
$100$	3.68027			0.368027
$101$	19.6672			1.95696			0.978480	−	0.206340i	$-0.0661552\pi$
$101$	19.6672			1.95696			0.978480	+	0.206340i	$0.0661552\pi$
$102$	−1.39173	+	0.647406i	−0.137801	+	0.0641028i
$103$		−	9.03899i		−	0.890638i	−0.895372	−	0.445319i	$-0.853090\pi$
$103$		−	9.03899i		−	0.890638i	0.895372	−	0.445319i	$-0.146910\pi$
$104$	10.8597			1.06488
$105$	−0.728644	−	12.9652i	−0.0711084	−	1.26527i
$106$	7.72533			0.750351
$107$			15.1571i			1.46529i	0.680610	+	0.732646i	$0.261715\pi$
$107$			15.1571i			1.46529i	−0.680610	+	0.732646i	$0.738285\pi$
$108$	−6.09192	−	1.65045i	−0.586195	−	0.158814i
$109$	14.4534			1.38439			0.692195	−	0.721711i	$-0.256644\pi$
$109$	14.4534			1.38439			0.692195	+	0.721711i	$0.256644\pi$
$110$	−2.35743			−0.224772
$111$	−4.25646	−	9.15009i	−0.404006	−	0.868488i
$112$	0.234225	+	0.0933533i	0.0221322	+	0.00882106i
$113$			9.88669i			0.930062i	0.885294	+	0.465031i	$0.153957\pi$
$113$			9.88669i			0.930062i	−0.885294	+	0.465031i	$0.846043\pi$
$114$	2.36265	+	5.07897i	0.221282	+	0.475689i
$115$			5.57027i			0.519430i
$116$		−	6.15158i		−	0.571160i
$117$	8.74689	+	7.36712i	0.808650	+	0.681090i
$118$		−	0.429010i		−	0.0394935i
$119$	−2.45773	−	0.979562i	−0.225300	−	0.0897963i
$120$	−12.6778	+	5.89747i	−1.15732	+	0.538363i
$121$	10.1187			0.919885
$122$	−0.393878			−0.0356601
$123$	3.21587	+	6.91313i	0.289965	+	0.623336i
$124$			2.08420i			0.187167i
$125$	−5.58273			−0.499334
$126$	3.31998	+	6.20117i	0.295767	+	0.552444i
$127$	−13.8128			−1.22569			−0.612843	−	0.790205i	$-0.709974\pi$
$127$	−13.8128			−1.22569			−0.612843	+	0.790205i	$0.709974\pi$
$128$			6.64917i			0.587709i
$129$	−7.44224	−	15.9985i	−0.655252	−	1.40859i
$130$	9.57278			0.839589
$131$	−11.1263			−0.972108			−0.486054	−	0.873929i	$-0.661564\pi$
$131$	−11.1263			−0.972108			−0.486054	+	0.873929i	$0.661564\pi$
$132$	−1.79073	+	0.833017i	−0.155863	+	0.0725049i
$133$	−3.57482	+	8.96927i	−0.309976	+	0.777734i
$134$			9.96616i			0.860945i
$135$	−14.2120	−	3.85038i	−1.22318	−	0.331388i
$136$			2.84882i			0.244284i
$137$		−	7.07672i		−	0.604605i	−0.953212	−	0.302303i	$-0.902245\pi$
$137$		−	7.07672i		−	0.604605i	0.953212	−	0.302303i	$-0.0977553\pi$
$138$	−1.27262	−	2.73574i	−0.108333	−	0.232882i
$139$		−	7.16718i		−	0.607912i	−0.952686	−	0.303956i	$-0.901692\pi$
$139$		−	7.16718i		−	0.607912i	0.952686	−	0.303956i	$-0.0983077\pi$
$140$	−8.45946	−	3.37163i	−0.714955	−	0.284955i
$141$	2.43744	+	5.23976i	0.205270	+	0.441267i
$142$	−9.01785			−0.756761
$143$	3.57855			0.299254
$144$	0.184180	−	0.218674i	0.0153483	−	0.0182229i
$145$		−	14.3512i		−	1.19180i
$146$	14.0610			1.16370
$147$	−3.84988	+	11.4969i	−0.317532	+	0.948247i
$148$	−7.07710			−0.581734
$149$		−	9.38088i		−	0.768512i	−0.923227	−	0.384256i	$-0.874458\pi$
$149$		−	9.38088i		−	0.768512i	0.923227	−	0.384256i	$-0.125542\pi$
$150$	−4.21677	+	1.96157i	−0.344297	+	0.160161i
$151$	−6.68765			−0.544233			−0.272117	−	0.962264i	$-0.587724\pi$
$151$	−6.68765			−0.544233			−0.272117	+	0.962264i	$0.587724\pi$
$152$	10.3965			0.843267
$153$	−1.93261	+	2.29456i	−0.156242	+	0.185504i
$154$	2.04465	+	0.814922i	0.164763	+	0.0656683i
$155$			4.86230i			0.390549i
$156$	7.27160	−	3.38262i	0.582194	−	0.270827i
$157$			7.60243i			0.606740i	0.952873	+	0.303370i	$0.0981118\pi$
$157$			7.60243i			0.606740i	−0.952873	+	0.303370i	$0.901888\pi$
$158$			6.38127i			0.507666i
$159$	13.6902	−	6.36845i	1.08571	−	0.505051i
$160$			15.9061i			1.25749i
$161$	1.92554	−	4.83122i	0.151754	−	0.380753i
$162$	7.85967	−	1.35592i	0.617514	−	0.106531i
$163$	−11.4479			−0.896671			−0.448336	−	0.893865i	$-0.647983\pi$
$163$	−11.4479			−0.896671			−0.448336	+	0.893865i	$0.647983\pi$
$164$	5.34693			0.417525
$165$	−4.17765	+	1.94337i	−0.325230	+	0.151291i
$166$		−	6.43465i		−	0.499425i
$167$	7.66452			0.593098			0.296549	−	0.955018i	$-0.404164\pi$
$167$	7.66452			0.593098			0.296549	+	0.955018i	$0.404164\pi$
$168$	13.0344	−	0.732530i	1.00562	−	0.0565159i
$169$	−1.53139			−0.117799
$170$			2.51122i			0.192602i
$171$	8.37379	+	7.05287i	0.640360	+	0.539347i
$172$	−12.3740			−0.943508
$173$	2.25410			0.171376			0.0856880	−	0.996322i	$-0.472691\pi$
$173$	2.25410			0.171376			0.0856880	+	0.996322i	$0.472691\pi$
$174$	3.27877	+	7.04834i	0.248563	+	0.534333i
$175$	−7.44665	−	2.96796i	−0.562914	−	0.224357i
$176$		−	0.0894647i		−	0.00674366i
$177$	−0.353658	−	0.760257i	−0.0265826	−	0.0571444i
$178$		−	14.0594i		−	1.05380i
$179$		−	14.1527i		−	1.05783i	−0.848676	−	0.528913i	$-0.822600\pi$
$179$		−	14.1527i		−	1.05783i	0.848676	−	0.528913i	$-0.177400\pi$
$180$	−6.65199	+	7.89783i	−0.495810	+	0.588670i
$181$			15.2747i			1.13536i	0.823248	+	0.567681i	$0.192159\pi$
$181$			15.2747i			1.13536i	−0.823248	+	0.567681i	$0.807841\pi$
$182$	−8.30269	−	3.30914i	−0.615436	−	0.245290i
$183$	−0.698000	+	0.324697i	−0.0515976	+	0.0240023i
$184$	−5.59997			−0.412836
$185$	−16.5104			−1.21387
$186$	−1.11087	−	2.38804i	−0.0814531	−	0.175099i
$187$			0.938759i			0.0686489i
$188$	4.05267			0.295571
$189$	10.9954	+	8.25236i	0.799797	+	0.600271i
$190$	9.16446			0.664860
$191$			26.0604i			1.88567i	0.333266	+	0.942833i	$0.391849\pi$
$191$			26.0604i			1.88567i	−0.333266	+	0.942833i	$0.608151\pi$
$192$	−3.77325	−	8.11133i	−0.272311	−	0.585385i
$193$	−3.82564			−0.275376			−0.137688	−	0.990476i	$-0.543967\pi$
$193$	−3.82564			−0.275376			−0.137688	+	0.990476i	$0.543967\pi$
$194$	−8.06191			−0.578811
$195$	16.9641	−	7.89142i	1.21483	−	0.565116i
$196$	6.17156	+	5.84857i	0.440826	+	0.417755i
$197$			4.46441i			0.318076i	0.987272	+	0.159038i	$0.0508392\pi$
$197$			4.46441i			0.318076i	−0.987272	+	0.159038i	$0.949161\pi$
$198$	1.60779	−	1.90891i	0.114260	−	0.135660i
$199$			3.37817i			0.239472i	0.992806	+	0.119736i	$0.0382048\pi$
$199$			3.37817i			0.239472i	−0.992806	+	0.119736i	$0.961795\pi$
$200$			8.63159i			0.610345i
$201$	8.21570	+	17.6612i	0.579491	+	1.24573i
$202$			17.4290i			1.22630i
$203$	−4.96095	+	12.4471i	−0.348191	+	0.873615i
$204$	0.887360	+	1.90755i	0.0621276	+	0.133555i
$205$	12.4740			0.871223
$206$	8.01032			0.558106
$207$	−4.51047	−	3.79897i	−0.313499	−	0.264046i
$208$			0.363288i			0.0251895i
$209$	3.42591			0.236975
$210$	11.4897	−	0.645722i	0.792866	−	0.0445591i
$211$	−14.8307			−1.02098			−0.510492	−	0.859882i	$-0.670537\pi$
$211$	−14.8307			−1.02098			−0.510492	+	0.859882i	$0.670537\pi$
$212$		−	10.5886i		−	0.727231i
$213$	−15.9807	+	7.43395i	−1.09498	+	0.509366i
$214$	−13.4322			−0.918204
$215$	−28.8676			−1.96876
$216$	3.87091	−	14.2878i	0.263382	−	0.972162i
$217$	1.68081	−	4.21718i	0.114101	−	0.286281i
$218$			12.8086i			0.867508i
$219$	24.9178	−	11.5913i	1.68379	−	0.783269i
$220$			3.23119i			0.217846i
$221$		−	3.81201i		−	0.256423i
$222$	8.10878	−	3.77206i	0.544226	−	0.253164i
$223$		−	5.41722i		−	0.362764i	−0.983413	−	0.181382i	$-0.941943\pi$
$223$		−	5.41722i		−	0.362764i	0.983413	−	0.181382i	$-0.0580571\pi$
$224$	5.49846	−	13.7957i	0.367381	−	0.921764i
$225$	−5.85558	+	6.95226i	−0.390372	+	0.463484i
$226$	−8.76155			−0.582810
$227$	−14.2894			−0.948423			−0.474212	−	0.880411i	$-0.657267\pi$
$227$	−14.2894			−0.948423			−0.474212	+	0.880411i	$0.657267\pi$
$228$	6.96143	−	3.23834i	0.461032	−	0.214464i
$229$		−	19.3407i		−	1.27807i	−0.769179	−	0.639034i	$-0.779334\pi$
$229$		−	19.3407i		−	1.27807i	0.769179	−	0.639034i	$-0.220666\pi$
$230$	−4.93635			−0.325493
$231$	4.29516	−	0.241388i	0.282601	−	0.0158821i
$232$	14.4277			0.947227
$233$			27.2963i			1.78824i	0.447827	+	0.894120i	$0.352198\pi$
$233$			27.2963i			1.78824i	−0.447827	+	0.894120i	$0.647802\pi$
$234$	−6.52871	+	7.75147i	−0.426795	+	0.506729i
$235$	9.45459			0.616749
$236$	−0.588017			−0.0382767
$237$	5.26046	+	11.3084i	0.341704	+	0.734558i
$238$	0.868084	−	2.17804i	0.0562696	−	0.141181i
$239$			29.3026i			1.89543i	0.319122	+	0.947714i	$0.396612\pi$
$239$			29.3026i			1.89543i	−0.319122	+	0.947714i	$0.603388\pi$
$240$	−0.197287	−	0.424107i	−0.0127348	−	0.0273760i
$241$			9.26214i			0.596627i	0.954468	+	0.298313i	$0.0964241\pi$
$241$			9.26214i			0.596627i	−0.954468	+	0.298313i	$0.903576\pi$
$242$			8.96719i			0.576433i
$243$	12.8105	−	8.88205i	0.821795	−	0.569784i
$244$			0.539865i			0.0345613i
$245$	14.3978	+	13.6443i	0.919843	+	0.871703i
$246$	−6.12639	+	2.84989i	−0.390605	+	0.181703i
$247$	−13.9116			−0.885171
$248$	−4.88823			−0.310403
$249$	−5.30446	−	11.4030i	−0.336157	−	0.722634i
$250$		−	4.94739i		−	0.312901i
$251$	−14.8365			−0.936473			−0.468237	−	0.883603i	$-0.655110\pi$
$251$	−14.8365			−0.936473			−0.468237	+	0.883603i	$0.655110\pi$
$252$	8.49956	−	4.55049i	0.535422	−	0.286654i
$253$	−1.84534			−0.116015
$254$		−	12.2408i		−	0.768059i
$255$	2.07015	+	4.45018i	0.129638	+	0.278681i
$256$	−16.2224			−1.01390
$257$	−24.1051			−1.50363			−0.751816	−	0.659373i	$-0.770822\pi$
$257$	−24.1051			−1.50363			−0.751816	+	0.659373i	$0.770822\pi$
$258$	14.1778	−	6.59528i	0.882674	−	0.410604i
$259$	14.3198	+	5.70734i	0.889789	+	0.354637i
$260$		−	13.1208i		−	0.813719i
$261$	11.6207	+	9.78762i	0.719305	+	0.605839i
$262$		−	9.86007i		−	0.609157i
$263$			7.68372i			0.473798i	0.971534	+	0.236899i	$0.0761311\pi$
$263$			7.68372i			0.473798i	−0.971534	+	0.236899i	$0.923869\pi$
$264$	−1.95373	−	4.19993i	−0.120244	−	0.258488i
$265$		−	24.7025i		−	1.51747i
$266$	−7.94854	−	3.16799i	−0.487356	−	0.194242i
$267$	−11.5900	−	24.9150i	−0.709299	−	1.52478i
$268$	13.6600			0.834418
$269$	5.74644			0.350366			0.175183	−	0.984536i	$-0.443948\pi$
$269$	5.74644			0.350366			0.175183	+	0.984536i	$0.443948\pi$
$270$	3.41219	−	12.5946i	0.207659	−	0.766486i
$271$		−	23.5267i		−	1.42914i	−0.699563	−	0.714571i	$-0.746622\pi$
$271$		−	23.5267i		−	1.42914i	0.699563	−	0.714571i	$-0.253378\pi$
$272$	−0.0953011			−0.00577848
$273$	−17.4413	+	0.980199i	−1.05559	+	0.0593244i
$274$	6.27137			0.378867
$275$			2.84433i			0.171520i
$276$	−3.74971	+	1.74430i	−0.225706	+	0.104995i
$277$	−16.0638			−0.965179			−0.482590	−	0.875847i	$-0.660304\pi$
$277$	−16.0638			−0.965179			−0.482590	+	0.875847i	$0.660304\pi$
$278$	6.35153			0.380940
$279$	−3.93720	−	3.31613i	−0.235714	−	0.198531i
$280$	7.90772	−	19.8406i	0.472576	−	1.18570i
$281$		−	28.0545i		−	1.67359i	−0.547513	−	0.836797i	$-0.684425\pi$
$281$		−	28.0545i		−	1.67359i	0.547513	−	0.836797i	$-0.315575\pi$
$282$	−4.64346	+	2.16006i	−0.276514	+	0.128629i
$283$			32.4605i			1.92958i	0.263028	+	0.964788i	$0.415279\pi$
$283$			32.4605i			1.92958i	−0.263028	+	0.964788i	$0.584721\pi$
$284$			12.3602i			0.733444i
$285$	16.2405	−	7.55481i	0.962006	−	0.447508i
$286$			3.17130i			0.187523i
$287$	−10.8190	−	4.31205i	−0.638624	−	0.254532i
$288$	−12.8798	−	10.8481i	−0.758949	−	0.639229i
$289$	1.00000			0.0588235
$290$	12.7180			0.746826
$291$	−14.2867	+	6.64591i	−0.837500	+	0.389590i
$292$		−	19.2726i		−	1.12784i
$293$	−22.2438			−1.29949			−0.649747	−	0.760150i	$-0.725125\pi$
$293$	−22.2438			−1.29949			−0.649747	+	0.760150i	$0.725125\pi$
$294$	−10.1885	−	3.41175i	−0.594206	−	0.198977i
$295$	−1.37180			−0.0798694
$296$		−	16.5984i		−	0.964763i
$297$	1.27557	−	4.70820i	0.0740158	−	0.273198i
$298$	8.31331			0.481577
$299$	7.49333			0.433351
$300$	2.68860	+	5.77966i	0.155226	+	0.333689i
$301$	25.0375	+	9.97903i	1.44314	+	0.575182i
$302$		−	5.92657i		−	0.341036i
$303$	14.3678	+	30.8863i	0.825407	+	1.77437i
$304$			0.347792i			0.0199473i
$305$			1.25947i			0.0721169i
$306$	−2.03343	−	1.71267i	−0.116244	−	0.0979069i
$307$		−	20.5608i		−	1.17347i	−0.809779	−	0.586734i	$-0.800413\pi$
$307$		−	20.5608i		−	1.17347i	0.809779	−	0.586734i	$-0.199587\pi$
$308$	1.11696	−	2.80248i	0.0636449	−	0.159686i
$309$	14.1953	−	6.60339i	0.807540	−	0.375654i
$310$	−4.30896			−0.244732
$311$	29.3915			1.66664			0.833318	−	0.552794i	$-0.186438\pi$
$311$	29.3915			1.66664			0.833318	+	0.552794i	$0.186438\pi$
$312$	7.93350	+	17.0546i	0.449146	+	0.965526i
$313$			8.43615i			0.476839i	0.971162	+	0.238420i	$0.0766294\pi$
$313$			8.43615i			0.476839i	−0.971162	+	0.238420i	$0.923371\pi$
$314$	−6.73725			−0.380205
$315$	19.8289	−	10.6160i	1.11723	−	0.598142i
$316$	8.74641			0.492024
$317$		−	4.73125i		−	0.265734i	−0.991134	−	0.132867i	$-0.957582\pi$
$317$		−	4.73125i		−	0.265734i	0.991134	−	0.132867i	$-0.0424182\pi$
$318$	5.64370	+	12.1322i	0.316483	+	0.680342i
$319$	4.75431			0.266190
$320$	−14.6360			−0.818179
$321$	−23.8034	+	11.0729i	−1.32858	+	0.618031i
$322$	4.28141	+	1.70641i	0.238594	+	0.0950945i
$323$		−	3.64941i		−	0.203058i
$324$	−1.85848	−	10.7728i	−0.103249	−	0.598487i
$325$		−	11.5499i		−	0.640675i
$326$		−	10.1451i		−	0.561886i
$327$	10.5589	+	22.6984i	0.583908	+	1.25522i
$328$			12.5405i			0.692435i
$329$	−8.20017	−	3.26828i	−0.452090	−	0.180186i
$330$	−1.72221	−	3.70222i	−0.0948045	−	0.203801i
$331$	5.22527			0.287207			0.143603	−	0.989635i	$-0.454131\pi$
$331$	5.22527			0.287207			0.143603	+	0.989635i	$0.454131\pi$
$332$	−8.81958			−0.484037
$333$	11.2602	−	13.3691i	0.617055	−	0.732622i
$334$			6.79227i			0.371656i
$335$	31.8678			1.74113
$336$	0.0245052	+	0.436036i	0.00133687	+	0.0237877i
$337$	8.24358			0.449057			0.224528	−	0.974468i	$-0.427916\pi$
$337$	8.24358			0.449057			0.224528	+	0.974468i	$0.427916\pi$
$338$		−	1.35711i		−	0.0738170i
$339$	−15.5265	+	7.22267i	−0.843285	+	0.392282i
$340$	3.44198			0.186667
$341$	−1.61080			−0.0872297
$342$	−6.25023	+	7.42083i	−0.337974	+	0.401272i
$343$	−7.77095	−	16.8111i	−0.419592	−	0.907713i
$344$		−	29.0216i		−	1.56474i
$345$	−8.74781	+	4.06933i	−0.470966	+	0.219085i
$346$			1.99758i			0.107390i
$347$			2.00961i			0.107881i	0.998544	+	0.0539406i	$0.0171782\pi$
$347$			2.00961i			0.107881i	−0.998544	+	0.0539406i	$0.982822\pi$
$348$	9.66073	−	4.49400i	0.517869	−	0.240904i
$349$			13.9457i			0.746497i	0.927731	+	0.373249i	$0.121756\pi$
$349$			13.9457i			0.746497i	−0.927731	+	0.373249i	$0.878244\pi$
$350$	2.63020	−	6.59920i	0.140590	−	0.352742i
$351$	−5.17967	+	19.1185i	−0.276470	+	1.02047i
$352$	−5.26942			−0.280861
$353$	12.1151			0.644821			0.322411	−	0.946600i	$-0.395507\pi$
$353$	12.1151			0.644821			0.322411	+	0.946600i	$0.395507\pi$
$354$	0.673737	−	0.313411i	0.0358087	−	0.0166576i
$355$			28.8355i			1.53043i
$356$	−19.2704			−1.02133
$357$	−0.257135	−	4.57536i	−0.0136090	−	0.242154i
$358$	12.5421			0.662871
$359$		−	19.1698i		−	1.01174i	−0.862609	−	0.505871i	$-0.831171\pi$
$359$		−	19.1698i		−	1.01174i	0.862609	−	0.505871i	$-0.168829\pi$
$360$	−18.5233	−	15.6014i	−0.976266	−	0.822265i
$361$	5.68184			0.299044
$362$	−13.5364			−0.711459
$363$	7.39219	+	15.8909i	0.387989	+	0.834058i
$364$	−4.53564	+	11.3800i	−0.237732	+	0.596473i
$365$		−	44.9615i		−	2.35339i
$366$	−0.287746	−	0.618565i	−0.0150407	−	0.0323329i
$367$			1.33993i			0.0699437i	0.999388	+	0.0349718i	$0.0111341\pi$
$367$			1.33993i			0.0699437i	−0.999388	+	0.0349718i	$0.988866\pi$
$368$		−	0.187335i		−	0.00976552i
$369$	−8.50737	+	10.1007i	−0.442876	+	0.525822i
$370$		−	14.6314i		−	0.760652i
$371$	−8.53923	+	21.4251i	−0.443335	+	1.11233i
$372$	−3.27313	+	1.52260i	−0.169704	+	0.0789434i
$373$	6.83092			0.353692			0.176846	−	0.984239i	$-0.443411\pi$
$373$	6.83092			0.353692			0.176846	+	0.984239i	$0.443411\pi$
$374$	−0.831925			−0.0430178
$375$	−4.07843	−	8.76738i	−0.210609	−	0.452745i
$376$			9.50501i			0.490183i
$377$	−19.3058			−0.994297
$378$	−7.31321	+	9.74408i	−0.376151	+	0.501181i
$379$	7.66408			0.393678			0.196839	−	0.980436i	$-0.436932\pi$
$379$	7.66408			0.393678			0.196839	+	0.980436i	$0.436932\pi$
$380$		−	12.5612i		−	0.644374i
$381$	−10.0909	−	21.6922i	−0.516970	−	1.11133i
$382$	−23.0947			−1.18163
$383$	15.2462			0.779043			0.389522	−	0.921017i	$-0.372640\pi$
$383$	15.2462			0.779043			0.389522	+	0.921017i	$0.372640\pi$
$384$	−10.4422	+	4.85751i	−0.532875	+	0.247884i
$385$	2.60580	−	6.53798i	0.132804	−	0.333206i
$386$		−	3.39027i		−	0.172560i
$387$	19.6880	−	23.3753i	1.00079	−	1.18823i
$388$			11.0500i			0.560977i
$389$		−	8.00884i		−	0.406065i	−0.979172	−	0.203032i	$-0.934920\pi$
$389$		−	8.00884i		−	0.406065i	0.979172	−	0.203032i	$-0.0650796\pi$
$390$	6.99335	+	15.0336i	0.354122	+	0.761254i
$391$			1.96572i			0.0994107i
$392$	−13.7171	+	14.4746i	−0.692817	+	0.731078i
$393$	−8.12825	−	17.4732i	−0.410016	−	0.881408i
$394$	−3.95634			−0.199318
$395$	20.4048			1.02667
$396$	−2.61642	−	2.20369i	−0.131480	−	0.110740i
$397$			28.2434i			1.41749i	0.705463	+	0.708747i	$0.250739\pi$
$397$			28.2434i			1.41749i	−0.705463	+	0.708747i	$0.749261\pi$
$398$	−2.99372			−0.150062
$399$	−16.6973	+	0.938389i	−0.835912	+	0.0469782i
$400$	−0.288751			−0.0144376
$401$			33.3981i			1.66782i	0.551898	+	0.833911i	$0.313904\pi$
$401$			33.3981i			1.66782i	−0.551898	+	0.833911i	$0.686096\pi$
$402$	−15.6513	+	7.28073i	−0.780617	+	0.363130i
$403$	6.54095			0.325828
$404$	23.8889			1.18852
$405$	−4.33570	−	25.1321i	−0.215443	−	1.24882i
$406$	−11.0306	−	4.39638i	−0.547439	−	0.218189i
$407$		−	5.46961i		−	0.271118i
$408$	−4.47392	+	2.08119i	−0.221492	+	0.103034i
$409$		−	36.8650i		−	1.82286i	−0.411459	−	0.911428i	$-0.634981\pi$
$409$		−	36.8650i		−	1.82286i	0.411459	−	0.911428i	$-0.365019\pi$
$410$			11.0544i			0.545939i
$411$	11.1136	−	5.16986i	0.548194	−	0.255010i
$412$		−	10.9793i		−	0.540909i
$413$	1.18979	+	0.474208i	0.0585460	+	0.0233342i
$414$	3.36663	−	3.99716i	0.165461	−	0.196450i
$415$	−20.5754			−1.01001
$416$	21.3975			1.04910
$417$	11.2557	−	5.23595i	0.551193	−	0.256405i
$418$			3.03603i			0.148497i
$419$	10.6581			0.520683			0.260342	−	0.965517i	$-0.416165\pi$
$419$	10.6581			0.520683			0.260342	+	0.965517i	$0.416165\pi$
$420$	−0.885052	−	15.7483i	−0.0431861	−	0.768437i
$421$	−24.7086			−1.20422			−0.602111	−	0.798413i	$-0.705673\pi$
$421$	−24.7086			−1.20422			−0.602111	+	0.798413i	$0.705673\pi$
$422$		−	13.1429i		−	0.639785i
$423$	−6.44810	+	7.65576i	−0.313517	+	0.372236i
$424$	24.8343			1.20606
$425$	3.02988			0.146971
$426$	−6.58795	−	14.1621i	−0.319187	−	0.686154i
$427$	0.435375	−	1.09236i	0.0210693	−	0.0528632i
$428$			18.4107i			0.889913i
$429$	2.61429	+	5.61993i	0.126219	+	0.271333i
$430$		−	25.5824i		−	1.23369i
$431$			29.0080i			1.39727i	0.715479	+	0.698634i	$0.246208\pi$
$431$			29.0080i			1.39727i	−0.715479	+	0.698634i	$0.753792\pi$
$432$	0.477968	+	0.129493i	0.0229963	+	0.00623024i
$433$			7.12124i			0.342225i	0.985252	+	0.171112i	$0.0547361\pi$
$433$			7.12124i			0.342225i	−0.985252	+	0.171112i	$0.945264\pi$
$434$	3.73725	+	1.48953i	0.179394	+	0.0714997i
$435$	22.5378	−	10.4842i	1.08060	−	0.502678i
$436$	17.5560			0.840778
$437$	7.17371			0.343165
$438$	10.2722	+	22.0821i	0.490824	+	1.05512i
$439$			1.21737i			0.0581021i	0.999578	+	0.0290510i	$0.00924853\pi$
$439$			1.21737i			0.0581021i	−0.999578	+	0.0290510i	$0.990751\pi$
$440$	−7.57833			−0.361283
$441$	−20.8678	+	2.35297i	−0.993703	+	0.112046i
$442$	3.37819			0.160684
$443$		−	10.9210i		−	0.518872i	−0.965760	−	0.259436i	$-0.916463\pi$
$443$		−	10.9210i		−	0.518872i	0.965760	−	0.259436i	$-0.0835367\pi$
$444$	−5.17014	−	11.1142i	−0.245364	−	0.527457i
$445$	−44.9565			−2.13114
$446$	4.80073			0.227321
$447$	14.7322	−	6.85315i	0.696808	−	0.324143i
$448$	12.6942	+	5.05942i	0.599742	+	0.239035i
$449$		−	8.82069i		−	0.416274i	−0.978100	−	0.208137i	$-0.933260\pi$
$449$		−	8.82069i		−	0.416274i	0.978100	−	0.208137i	$-0.0667400\pi$
$450$	−6.16107	−	5.18920i	−0.290436	−	0.244621i
$451$			4.13243i			0.194589i
$452$			12.0089i			0.564852i
$453$	−4.88563	−	10.5026i	−0.229547	−	0.493455i
$454$		−	12.6633i		−	0.594316i
$455$	−10.5813	+	26.5487i	−0.496060	+	1.24462i
$456$	7.59510	+	16.3271i	0.355673	+	0.764588i
$457$	−23.0707			−1.07920			−0.539600	−	0.841922i	$-0.681425\pi$
$457$	−23.0707			−1.07920			−0.539600	+	0.841922i	$0.681425\pi$
$458$	17.1396			0.800882
$459$	−5.01535	−	1.35878i	−0.234096	−	0.0634223i
$460$			6.76596i			0.315464i
$461$	21.2624			0.990291			0.495145	−	0.868810i	$-0.335115\pi$
$461$	21.2624			0.990291			0.495145	+	0.868810i	$0.335115\pi$
$462$	0.213917	+	3.80635i	0.00995232	+	0.177088i
$463$	3.15498			0.146624			0.0733121	−	0.997309i	$-0.476643\pi$
$463$	3.15498			0.146624			0.0733121	+	0.997309i	$0.476643\pi$
$464$			0.482649i			0.0224064i
$465$	−7.63599	+	3.55213i	−0.354110	+	0.164726i
$466$	−24.1899			−1.12058
$467$	−3.86095			−0.178664			−0.0893318	−	0.996002i	$-0.528473\pi$
$467$	−3.86095			−0.178664			−0.0893318	+	0.996002i	$0.528473\pi$
$468$	10.6245	+	8.94851i	0.491116	+	0.413645i
$469$	−27.6397	−	11.0161i	−1.27628	−	0.508678i
$470$			8.37862i			0.386477i
$471$	−11.9392	+	5.55391i	−0.550130	+	0.255911i
$472$		−	1.37912i		−	0.0634791i
$473$		−	9.56336i		−	0.439724i
$474$	−10.0214	+	4.66180i	−0.460300	+	0.214124i
$475$		−	11.0573i		−	0.507343i
$476$	−2.98530	−	1.18983i	−0.136831	−	0.0545358i
$477$	20.0026	+	16.8473i	0.915858	+	0.771386i
$478$	−25.9679			−1.18774
$479$	8.16016			0.372847			0.186424	−	0.982469i	$-0.440310\pi$
$479$	8.16016			0.372847			0.186424	+	0.982469i	$0.440310\pi$
$480$	−24.9797	+	11.6201i	−1.14016	+	0.530383i
$481$			22.2104i			1.01271i
$482$	−8.20808			−0.373868
$483$	8.99387	−	0.505455i	0.409235	−	0.0229990i
$484$	12.2908			0.558671
$485$			25.7788i			1.17055i
$486$	7.87124	+	11.3526i	0.357047	+	0.514966i
$487$	31.4904			1.42697			0.713483	−	0.700673i	$-0.247117\pi$
$487$	31.4904			1.42697			0.713483	+	0.700673i	$0.247117\pi$
$488$	−1.26618			−0.0573174
$489$	−8.36323	−	17.9784i	−0.378198	−	0.813010i
$490$	−12.0915	+	12.7593i	−0.546240	+	0.576406i
$491$			16.1285i			0.727870i	0.931424	+	0.363935i	$0.118567\pi$
$491$			16.1285i			0.727870i	−0.931424	+	0.363935i	$0.881433\pi$
$492$	3.90617	+	8.39707i	0.176104	+	0.378569i
$493$		−	5.06446i		−	0.228092i
$494$		−	12.3284i		−	0.554680i
$495$	−6.10392	−	5.14106i	−0.274351	−	0.231073i
$496$		−	0.163525i		−	0.00734250i
$497$	9.96793	−	25.0097i	0.447123	−	1.12184i
$498$	10.1053	−	4.70080i	0.452828	−	0.210648i
$499$	−3.50615			−0.156957			−0.0784783	−	0.996916i	$-0.525006\pi$
$499$	−3.50615			−0.156957			−0.0784783	+	0.996916i	$0.525006\pi$
$500$	−6.78109			−0.303260
$501$	5.59927	+	12.0367i	0.250157	+	0.537761i
$502$		−	13.1481i		−	0.586827i
$503$	6.56810			0.292857			0.146429	−	0.989221i	$-0.453222\pi$
$503$	6.56810			0.292857			0.146429	+	0.989221i	$0.453222\pi$
$504$	10.6726	+	19.9346i	0.475394	+	0.887958i
$505$	55.7311			2.48000
$506$		−	1.63533i		−	0.0726993i
$507$	−1.11875	−	2.40496i	−0.0496853	−	0.106808i
$508$	−16.7778			−0.744393
$509$	−25.2820			−1.12061			−0.560303	−	0.828288i	$-0.689315\pi$
$509$	−25.2820			−1.12061			−0.560303	+	0.828288i	$0.689315\pi$
$510$	−3.94374	+	1.83456i	−0.174632	+	0.0812356i
$511$	−15.5424	+	38.9961i	−0.687555	+	1.72509i
$512$		−	1.07793i		−	0.0476383i
$513$	−4.95873	+	18.3030i	−0.218933	+	0.808099i
$514$		−	21.3618i		−	0.942230i
$515$		−	25.6138i		−	1.12868i
$516$	−9.03975	−	19.4327i	−0.397953	−	0.855477i
$517$			3.13215i			0.137752i
$518$	−5.05783	+	12.6902i	−0.222228	+	0.557574i
$519$	1.64672	+	3.53994i	0.0722830	+	0.155386i
$520$	30.7732			1.34949
$521$	−5.98457			−0.262189			−0.131094	−	0.991370i	$-0.541849\pi$
$521$	−5.98457			−0.262189			−0.131094	+	0.991370i	$0.541849\pi$
$522$	−8.67376	+	10.2983i	−0.379640	+	0.450742i
$523$			36.5687i			1.59904i	0.600640	+	0.799519i	$0.294912\pi$
$523$			36.5687i			1.59904i	−0.600640	+	0.799519i	$0.705088\pi$
$524$	−13.5146			−0.590388
$525$	−0.779089	−	13.8628i	−0.0340022	−	0.605022i
$526$	−6.80928			−0.296899
$527$			1.71588i			0.0747450i
$528$	0.140500	−	0.0653580i	0.00611446	−	0.00284434i
$529$	19.1359			0.831998
$530$	21.8913			0.950898
$531$	0.935580	−	1.11080i	0.0406007	−	0.0482048i
$532$	−4.34217	+	10.8946i	−0.188257	+	0.472340i
$533$		−	16.7805i		−	0.726844i
$534$	22.0796	−	10.2711i	0.955479	−	0.444472i
$535$			42.9508i			1.85692i
$536$			32.0378i			1.38382i
$537$	22.2261	−	10.3392i	0.959128	−	0.446170i
$538$			5.09247i			0.219552i
$539$	−4.52013	+	4.76976i	−0.194696	+	0.205448i
$540$	−17.2627	−	4.67688i	−0.742869	−	0.201261i
$541$	16.1944			0.696251			0.348126	−	0.937448i	$-0.386818\pi$
$541$	16.1944			0.696251			0.348126	+	0.937448i	$0.386818\pi$
$542$	20.8492			0.895552
$543$	−23.9882	+	11.1589i	−1.02943	+	0.478874i
$544$			5.61318i			0.240663i
$545$	40.9568			1.75440
$546$	−0.868649	−	15.4564i	−0.0371748	−	0.661473i
$547$	19.6208			0.838925			0.419462	−	0.907773i	$-0.362219\pi$
$547$	19.6208			0.838925			0.419462	+	0.907773i	$0.362219\pi$
$548$		−	8.59578i		−	0.367193i
$549$	−1.01984	−	0.858966i	−0.0435257	−	0.0366598i
$550$	−2.52064			−0.107480
$551$	−18.4823			−0.787372
$552$	−4.09103	−	8.79446i	−0.174126	−	0.374317i
$553$	−17.6975	−	7.05357i	−0.752574	−	0.299948i
$554$		−	14.2357i		−	0.604816i
$555$	−12.0616	−	25.9287i	−0.511985	−	1.10061i
$556$		−	8.70566i		−	0.369202i
$557$			34.1730i			1.44795i	0.689824	+	0.723977i	$0.257688\pi$
$557$			34.1730i			1.44795i	−0.689824	+	0.723977i	$0.742312\pi$
$558$	2.93874	−	3.48913i	0.124407	−	0.147707i
$559$			38.8338i			1.64250i
$560$	0.663724	+	0.264536i	0.0280475	+	0.0111787i
$561$	−1.47427	+	0.685806i	−0.0622438	+	0.0289547i
$562$	24.8618			1.04873
$563$	−23.3405			−0.983686			−0.491843	−	0.870684i	$-0.663677\pi$
$563$	−23.3405			−0.983686			−0.491843	+	0.870684i	$0.663677\pi$
$564$	2.96066	+	6.36450i	0.124666	+	0.267994i
$565$			28.0160i			1.17864i
$566$	−28.7664			−1.20914
$567$	−4.92727	+	23.2964i	−0.206926	+	0.978357i
$568$	−28.9893			−1.21636
$569$		−	19.7136i		−	0.826438i	−0.910632	−	0.413219i	$-0.864404\pi$
$569$		−	19.7136i		−	0.826438i	0.910632	−	0.413219i	$-0.135596\pi$
$570$	6.69505	+	14.3923i	0.280425	+	0.602827i
$571$	14.6030			0.611118			0.305559	−	0.952173i	$-0.401157\pi$
$571$	14.6030			0.611118			0.305559	+	0.952173i	$0.401157\pi$
$572$	4.34671			0.181745
$573$	−40.9265	+	19.0383i	−1.70973	+	0.795337i
$574$	3.82132	−	9.58775i	0.159499	−	0.400185i
$575$			5.95590i			0.248378i
$576$	9.98189	−	11.8514i	0.415912	−	0.493808i
$577$		−	20.6290i		−	0.858795i	−0.903116	−	0.429398i	$-0.858726\pi$
$577$		−	20.6290i		−	0.858795i	0.903116	−	0.429398i	$-0.141274\pi$
$578$			0.886197i			0.0368609i
$579$	−2.79480	−	6.00797i	−0.116148	−	0.249683i
$580$		−	17.4318i		−	0.723814i
$581$	17.8455	+	7.11257i	0.740357	+	0.295079i
$582$	−5.88959	−	12.6608i	−0.244131	−	0.524807i
$583$	8.18354			0.338928
$584$	45.2013			1.87044
$585$	24.7861	+	20.8762i	1.02478	+	0.863126i
$586$		−	19.7123i		−	0.814309i
$587$	28.3209			1.16893			0.584465	−	0.811419i	$-0.301305\pi$
$587$	28.3209			1.16893			0.584465	+	0.811419i	$0.301305\pi$
$588$	−4.67627	+	13.9648i	−0.192846	+	0.575897i
$589$	6.26195			0.258019
$590$		−	1.21569i		−	0.0500490i
$591$	−7.01112	+	3.26145i	−0.288399	+	0.134158i
$592$	0.555264			0.0228212
$593$	24.8830			1.02182			0.510911	−	0.859634i	$-0.329308\pi$
$593$	24.8830			1.02182			0.510911	+	0.859634i	$0.329308\pi$
$594$	4.17239	+	1.13040i	0.171195	+	0.0463809i
$595$	−6.96449	−	2.77579i	−0.285516	−	0.113796i
$596$		−	11.3945i		−	0.466739i
$597$	−5.30523	+	2.46790i	−0.217129	+	0.101005i
$598$			6.64057i			0.271553i
$599$		−	14.6110i		−	0.596989i	−0.954411	−	0.298495i	$-0.903515\pi$
$599$		−	14.6110i		−	0.596989i	0.954411	−	0.298495i	$-0.0964845\pi$
$600$	−13.5554	+	6.30576i	−0.553399	+	0.257432i
$601$		−	34.8611i		−	1.42201i	−0.703185	−	0.711007i	$-0.748240\pi$
$601$		−	34.8611i		−	1.42201i	0.703185	−	0.711007i	$-0.251760\pi$
$602$	−8.84339	+	22.1882i	−0.360429	+	0.904323i
$603$	−21.7341	+	25.8046i	−0.885081	+	1.05085i
$604$	−8.12319			−0.330528
$605$	28.6735			1.16574
$606$	−27.3714	+	12.7327i	−1.11189	+	0.517230i
$607$		−	27.2280i		−	1.10515i	−0.833463	−	0.552575i	$-0.813645\pi$
$607$		−	27.2280i		−	1.10515i	0.833463	−	0.552575i	$-0.186355\pi$
$608$	20.4848			0.830767
$609$	−23.1717	+	1.30225i	−0.938965	+	0.0527698i
$610$	−1.11614			−0.0451910
$611$		−	12.7187i		−	0.514542i
$612$	−2.34745	+	2.78710i	−0.0948902	+	0.112662i
$613$	24.1251			0.974403			0.487201	−	0.873290i	$-0.338018\pi$
$613$	24.1251			0.974403			0.487201	+	0.873290i	$0.338018\pi$
$614$	18.2209			0.735338
$615$	9.11282	+	19.5898i	0.367465	+	0.789936i
$616$	6.57285	+	2.61969i	0.264828	+	0.105550i
$617$		−	18.8576i		−	0.759180i	−0.925155	−	0.379590i	$-0.876065\pi$
$617$		−	18.8576i		−	0.759180i	0.925155	−	0.379590i	$-0.123935\pi$
$618$	5.85190	+	12.5798i	0.235398	+	0.506033i
$619$		−	11.8460i		−	0.476131i	−0.971249	−	0.238066i	$-0.923487\pi$
$619$		−	11.8460i		−	0.476131i	0.971249	−	0.238066i	$-0.0765133\pi$
$620$			5.90602i			0.237192i
$621$	2.67098	−	9.85877i	0.107183	−	0.395619i
$622$			26.0466i			1.04437i
$623$	38.9918	+	15.5407i	1.56217	+	0.622624i
$624$	−0.570525	+	0.265398i	−0.0228393	+	0.0106244i
$625$	−30.9692			−1.23877
$626$	−7.47609			−0.298805
$627$	2.50278	+	5.38021i	0.0999515	+	0.214865i
$628$			9.23433i			0.368490i
$629$	−5.82642			−0.232315
$630$	9.40783	+	17.5723i	0.374817	+	0.700096i
$631$	−10.1870			−0.405538			−0.202769	−	0.979227i	$-0.564994\pi$
$631$	−10.1870			−0.405538			−0.202769	+	0.979227i	$0.564994\pi$
$632$			20.5136i			0.815986i
$633$	−10.8345	−	23.2908i	−0.430631	−	0.925725i
$634$	4.19282			0.166518
$635$	−39.1414			−1.55328
$636$	16.6289	−	7.73548i	0.659379	−	0.306732i
$637$	18.3548	−	19.3685i	0.727245	−	0.767407i
$638$			4.21325i			0.166804i
$639$	−23.3493	−	19.6660i	−0.923683	−	0.777977i
$640$			18.8418i			0.744787i
$641$			39.5130i			1.56067i	0.625363	+	0.780334i	$0.284951\pi$
$641$			39.5130i			1.56067i	−0.625363	+	0.780334i	$0.715049\pi$
$642$	−9.81280	−	21.0945i	−0.387280	−	0.832534i
$643$		−	19.3543i		−	0.763261i	−0.924315	−	0.381630i	$-0.875363\pi$
$643$		−	19.3543i		−	0.763261i	0.924315	−	0.381630i	$-0.124637\pi$
$644$	2.33887	−	5.86826i	0.0921645	−	0.231242i
$645$	−21.0891	−	45.3351i	−0.830383	−	1.78507i
$646$	3.23409			0.127244
$647$	−1.80458			−0.0709454			−0.0354727	−	0.999371i	$-0.511294\pi$
$647$	−1.80458			−0.0709454			−0.0354727	+	0.999371i	$0.511294\pi$
$648$	25.2661	−	4.35882i	0.992547	−	0.171231i
$649$		−	0.454455i		−	0.0178389i
$650$	10.2355			0.401470
$651$	7.85077	−	0.441213i	0.307696	−	0.0172925i
$652$	−13.9053			−0.544573
$653$		−	25.1971i		−	0.986039i	−0.870018	−	0.493019i	$-0.835893\pi$
$653$		−	25.1971i		−	0.986039i	0.870018	−	0.493019i	$-0.164107\pi$
$654$	−20.1152	+	9.35725i	−0.786567	+	0.365898i
$655$	−31.5286			−1.23192
$656$	−0.419517			−0.0163794
$657$	36.4071	+	30.6641i	1.42038	+	1.19632i
$658$	2.89634	−	7.26696i	0.112911	−	0.283296i
$659$		−	24.3687i		−	0.949271i	−0.880182	−	0.474636i	$-0.842580\pi$
$659$		−	24.3687i		−	0.949271i	0.880182	−	0.474636i	$-0.157420\pi$
$660$	−5.07441	+	2.36053i	−0.197521	+	0.0918833i
$661$			28.6533i			1.11448i	0.830350	+	0.557242i	$0.188140\pi$
$661$			28.6533i			1.11448i	−0.830350	+	0.557242i	$0.811860\pi$
$662$			4.63062i			0.179974i
$663$	5.98655	−	2.78484i	0.232498	−	0.108154i
$664$		−	20.6852i		−	0.802740i
$665$	−10.1300	+	25.4163i	−0.392824	+	0.985600i
$666$	11.8477	+	9.97875i	0.459087	+	0.386669i
$667$	9.95531			0.385471
$668$	9.30975			0.360205
$669$	8.50746	−	3.95752i	0.328918	−	0.153007i
$670$			28.2412i			1.09105i
$671$	−0.417240			−0.0161074
$672$	25.6823	−	1.44334i	0.990716	−	0.0556782i
$673$	−29.7973			−1.14860			−0.574300	−	0.818645i	$-0.694726\pi$
$673$	−29.7973			−1.14860			−0.574300	+	0.818645i	$0.694726\pi$
$674$			7.30544i			0.281395i
$675$	−15.1959	−	4.11694i	−0.584891	−	0.158461i
$676$	−1.86011			−0.0715426
$677$	13.2183			0.508021			0.254011	−	0.967201i	$-0.418250\pi$
$677$	13.2183			0.508021			0.254011	+	0.967201i	$0.418250\pi$
$678$	−6.40071	−	13.7596i	−0.245818	−	0.528433i
$679$	8.91127	−	22.3585i	0.341983	−	0.858041i
$680$			8.07271i			0.309574i
$681$	−10.4391	−	22.4408i	−0.400026	−	0.859934i
$682$		−	1.42748i		−	0.0546612i
$683$		−	23.2310i		−	0.888911i	−0.895801	−	0.444455i	$-0.853397\pi$
$683$		−	23.2310i		−	0.888911i	0.895801	−	0.444455i	$-0.146603\pi$
$684$	10.1713	+	8.56681i	0.388908	+	0.327560i
$685$		−	20.0533i		−	0.766199i
$686$	14.8979	−	6.88659i	0.568805	−	0.262931i
$687$	30.3735	−	14.1292i	1.15882	−	0.539063i
$688$	0.970855			0.0370135
$689$	−33.2308			−1.26599
$690$	−3.60623	−	7.75228i	−0.137287	−	0.295124i
$691$		−	36.6530i		−	1.39434i	−0.716903	−	0.697172i	$-0.754441\pi$
$691$		−	36.6530i		−	1.39434i	0.716903	−	0.697172i	$-0.245559\pi$
$692$	2.73795			0.104081
$693$	3.51689	+	6.56897i	0.133596	+	0.249535i
$694$	−1.78091			−0.0676023
$695$		−	20.3097i		−	0.770390i
$696$	10.5401	+	22.6580i	0.399521	+	0.858849i
$697$	4.40202			0.166738
$698$	−12.3586			−0.467782
$699$	−42.8674	+	19.9412i	−1.62139	+	0.754244i
$700$	−9.04511	−	3.60505i	−0.341873	−	0.136258i
$701$		−	25.2305i		−	0.952943i	−0.879190	−	0.476472i	$-0.841916\pi$
$701$		−	25.2305i		−	0.952943i	0.879190	−	0.476472i	$-0.158084\pi$
$702$	−16.9428	−	4.59021i	−0.639464	−	0.173246i
$703$			21.2630i			0.801948i
$704$		−	4.84867i		−	0.182741i
$705$	6.90700	+	14.8479i	0.260133	+	0.559205i
$706$			10.7364i			0.404068i
$707$	−48.3368	−	19.2653i	−1.81789	−	0.724544i
$708$	−0.429573	−	0.923450i	−0.0161443	−	0.0347054i
$709$	−24.3248			−0.913536			−0.456768	−	0.889586i	$-0.650993\pi$
$709$	−24.3248			−0.913536			−0.456768	+	0.889586i	$0.650993\pi$
$710$	−25.5539			−0.959022
$711$	−13.9162	+	16.5225i	−0.521898	+	0.619644i
$712$		−	45.1963i		−	1.69380i
$713$	−3.37294			−0.126318
$714$	4.05467	−	0.227872i	0.151742	−	0.00852790i
$715$	10.1406			0.379236
$716$		−	17.1907i		−	0.642447i
$717$	−46.0182	+	21.4069i	−1.71858	+	0.799454i
$718$	16.9882			0.633994
$719$	−36.3025			−1.35385			−0.676927	−	0.736050i	$-0.736689\pi$
$719$	−36.3025			−1.35385			−0.676927	+	0.736050i	$0.736689\pi$
$720$	0.521911	−	0.619659i	0.0194505	−	0.0230933i
$721$	−8.85425	+	22.2154i	−0.329749	+	0.827346i
$722$			5.03523i			0.187392i
$723$	−14.5457	+	6.76641i	−0.540961	+	0.251645i
$724$			18.5536i			0.689537i
$725$		−	15.3447i		−	0.569889i
$726$	−14.0825	+	6.55093i	−0.522650	+	0.243128i
$727$			22.4657i			0.833208i	0.909088	+	0.416604i	$0.136780\pi$
$727$			22.4657i			0.833208i	−0.909088	+	0.416604i	$0.863220\pi$
$728$	−26.6903	−	10.6378i	−0.989207	−	0.394261i
$729$	23.3074	+	13.6295i	0.863239	+	0.504796i
$730$	39.8447			1.47472
$731$	−10.1872			−0.376789
$732$	−0.847830	+	0.394396i	−0.0313367	+	0.0145773i
$733$		−	22.7049i		−	0.838625i	−0.907842	−	0.419313i	$-0.862271\pi$
$733$		−	22.7049i		−	0.838625i	0.907842	−	0.419313i	$-0.137729\pi$
$734$	−1.18744			−0.0438292
$735$	−10.9094	+	32.5788i	−0.402400	+	1.20169i
$736$	−11.0339			−0.406716
$737$			10.5573i			0.388882i
$738$	−8.95121	−	7.53921i	−0.329499	−	0.277522i
$739$	19.0672			0.701399			0.350699	−	0.936488i	$-0.385944\pi$
$739$	19.0672			0.701399			0.350699	+	0.936488i	$0.385944\pi$
$740$	−20.0544			−0.737215
$741$	−10.1630	−	21.8474i	−0.373348	−	0.802583i
$742$	−18.9868	−	7.56744i	−0.697028	−	0.277810i
$743$		−	24.4663i		−	0.897582i	−0.893637	−	0.448791i	$-0.851855\pi$
$743$		−	24.4663i		−	0.897582i	0.893637	−	0.448791i	$-0.148145\pi$
$744$	−3.57107	−	7.67671i	−0.130922	−	0.281442i
$745$		−	26.5827i		−	0.973913i
$746$			6.05354i			0.221636i
$747$	14.0326	−	16.6608i	0.513426	−	0.609585i
$748$			1.14027i			0.0416924i
$749$	14.8473	−	37.2521i	0.542509	−	1.36116i
$750$	7.76962	−	3.61429i	0.283706	−	0.131975i
$751$	26.2144			0.956577			0.478289	−	0.878203i	$-0.341257\pi$
$751$	26.2144			0.956577			0.478289	+	0.878203i	$0.341257\pi$
$752$	−0.317970			−0.0115952
$753$	−10.8387	−	23.3000i	−0.394986	−	0.849098i
$754$		−	17.1087i		−	0.623062i
$755$	−18.9508			−0.689691
$756$	13.3556	+	10.0238i	0.485739	+	0.364561i
$757$	3.17355			0.115344			0.0576722	−	0.998336i	$-0.481632\pi$
$757$	3.17355			0.115344			0.0576722	+	0.998336i	$0.481632\pi$
$758$			6.79188i			0.246692i
$759$	−1.34810	−	2.89800i	−0.0489330	−	0.105191i
$760$	29.4606			1.06865
$761$	50.1209			1.81688			0.908440	−	0.418015i	$-0.137274\pi$
$761$	50.1209			1.81688			0.908440	+	0.418015i	$0.137274\pi$
$762$	19.2236	−	8.94248i	0.696397	−	0.323952i
$763$	−35.5227	−	14.1580i	−1.28601	−	0.512556i
$764$			31.6544i			1.14522i
$765$	−5.47644	+	6.50212i	−0.198001	+	0.235085i
$766$			13.5111i			0.488176i
$767$			1.84540i			0.0666335i
$768$	−11.8512	−	25.4765i	−0.427644	−	0.919303i
$769$			9.26598i			0.334140i	0.985945	+	0.167070i	$0.0534306\pi$
$769$			9.26598i			0.334140i	−0.985945	+	0.167070i	$0.946569\pi$
$770$	5.79394	+	2.30925i	0.208799	+	0.0832196i
$771$	−17.6098	−	37.8557i	−0.634202	−	1.36334i
$772$	−4.64684			−0.167243
$773$	−6.03411			−0.217032			−0.108516	−	0.994095i	$-0.534610\pi$
$773$	−6.03411			−0.217032			−0.108516	+	0.994095i	$0.534610\pi$
$774$	20.7151	+	17.4474i	0.744589	+	0.627134i
$775$			5.19892i			0.186751i
$776$	−25.9163			−0.930340
$777$	1.49818	+	26.6580i	0.0537468	+	0.956349i
$778$	7.09741			0.254454
$779$		−	16.0647i		−	0.575579i
$780$	20.6056	−	9.58535i	0.737798	−	0.343211i
$781$	−9.55272			−0.341823
$782$	−1.74201			−0.0622943
$783$	−6.88148	+	25.4000i	−0.245924	+	0.907724i
$784$	−0.484217	−	0.458875i	−0.0172935	−	0.0163884i
$785$			21.5430i			0.768904i
$786$	15.4847	−	7.20322i	0.552322	−	0.256931i
$787$		−	46.2559i		−	1.64885i	−0.565974	−	0.824423i	$-0.691500\pi$
$787$		−	46.2559i		−	1.64885i	0.565974	−	0.824423i	$-0.308500\pi$
$788$			5.42272i			0.193176i
$789$	−12.0669	+	5.61330i	−0.429592	+	0.199839i
$790$			18.0826i			0.643351i
$791$	9.68463	−	24.2989i	0.344346	−	0.863968i
$792$	5.16848	−	6.13647i	0.183654	−	0.218050i
$793$	1.69428			0.0601657
$794$	−25.0292			−0.888252
$795$	38.7940	−	18.0463i	1.37588	−	0.640037i
$796$			4.10331i			0.145438i
$797$	28.4341			1.00719			0.503593	−	0.863941i	$-0.332011\pi$
$797$	28.4341			1.00719			0.503593	+	0.863941i	$0.332011\pi$
$798$	−0.831597	−	14.7971i	−0.0294382	−	0.523812i
$799$	3.33648			0.118036
$800$			17.0073i			0.601298i
$801$	30.6607	−	36.4031i	1.08334	−	1.28624i
$802$	−29.5973			−1.04512
$803$	14.8950			0.525633
$804$	9.97925	+	21.4523i	0.351941	+	0.756565i
$805$	5.45642	−	13.6902i	0.192314	−	0.482518i
$806$			5.79657i			0.204175i
$807$	4.19803	+	9.02447i	0.147778	+	0.317676i
$808$			56.0283i			1.97107i
$809$		−	7.64578i		−	0.268811i	−0.990926	−	0.134406i	$-0.957087\pi$
$809$		−	7.64578i		−	0.268811i	0.990926	−	0.134406i	$-0.0429125\pi$
$810$	22.2720	−	3.84229i	0.782558	−	0.135004i
$811$		−	12.5627i		−	0.441135i	−0.975372	−	0.220567i	$-0.929209\pi$
$811$		−	12.5627i		−	0.441135i	0.975372	−	0.220567i	$-0.0707909\pi$
$812$	−6.02585	+	15.1189i	−0.211466	+	0.530571i
$813$	36.9474	−	17.1873i	1.29580	−	0.602784i
$814$	4.84715			0.169892
$815$	−32.4401			−1.13633
$816$	−0.0696217	−	0.149665i	−0.00243725	−	0.00523933i
$817$			37.1774i			1.30067i
$818$	32.6696			1.14227
$819$	−14.2810	−	26.6745i	−0.499018	−	0.932084i
$820$	15.1516			0.529118
$821$		−	3.03566i		−	0.105945i	−0.998596	−	0.0529726i	$-0.983130\pi$
$821$		−	3.03566i		−	0.105945i	0.998596	−	0.0529726i	$-0.0168696\pi$
$822$	4.58151	+	9.84885i	0.159799	+	0.343518i
$823$	13.0264			0.454072			0.227036	−	0.973886i	$-0.427096\pi$
$823$	13.0264			0.454072			0.227036	+	0.973886i	$0.427096\pi$
$824$	25.7504			0.897059
$825$	−4.46687	+	2.07791i	−0.155517	+	0.0723436i
$826$	−0.420242	+	1.05439i	−0.0146221	+	0.0366870i
$827$		−	27.7899i		−	0.966348i	−0.875524	−	0.483174i	$-0.839484\pi$
$827$		−	27.7899i		−	0.966348i	0.875524	−	0.483174i	$-0.160516\pi$
$828$	−5.47867	−	4.61444i	−0.190397	−	0.160363i
$829$			29.5041i			1.02472i	0.858770	+	0.512361i	$0.171229\pi$
$829$			29.5041i			1.02472i	−0.858770	+	0.512361i	$0.828771\pi$
$830$		−	18.2339i		−	0.632908i
$831$	−11.7353	−	25.2273i	−0.407093	−	0.875126i
$832$			19.6889i			0.682591i
$833$	5.08092	+	4.81501i	0.176043	+	0.166830i
$834$	4.64008	+	9.97475i	0.160673	+	0.345397i
$835$	21.7190			0.751616
$836$	4.16130			0.143922
$837$	2.33150	−	8.60574i	0.0805885	−	0.297458i
$838$			9.44519i			0.326279i
$839$	28.4593			0.982524			0.491262	−	0.871012i	$-0.336536\pi$
$839$	28.4593			0.982524			0.491262	+	0.871012i	$0.336536\pi$
$840$	36.9355	−	2.07577i	1.27440	−	0.0716210i
$841$	3.35122			0.115559
$842$		−	21.8966i		−	0.754608i
$843$	44.0582	−	20.4951i	1.51744	−	0.705889i
$844$	−18.0141			−0.620072
$845$	−4.33950			−0.149283
$846$	−6.78451	−	5.71429i	−0.233256	−	0.196461i
$847$	−24.8692	−	9.91192i	−0.854514	−	0.340578i
$848$			0.830778i			0.0285290i
$849$	−50.9775	+	23.7138i	−1.74954	+	0.813857i
$850$			2.68507i			0.0920973i
$851$		−	11.4531i		−	0.392608i
$852$	−19.4111	+	9.02969i	−0.665012	+	0.309352i
$853$			9.60402i			0.328836i	0.986391	+	0.164418i	$0.0525745\pi$
$853$			9.60402i			0.328836i	−0.986391	+	0.164418i	$0.947425\pi$
$854$	0.968049	+	0.385828i	0.0331259	+	0.0132028i
$855$	23.7289	+	19.9858i	0.811510	+	0.683499i
$856$	−43.1798			−1.47586
$857$	19.5036			0.666230			0.333115	−	0.942886i	$-0.391900\pi$
$857$	19.5036			0.666230			0.333115	+	0.942886i	$0.391900\pi$
$858$	−4.98036	+	2.31678i	−0.170027	+	0.0790935i
$859$		−	52.3783i		−	1.78712i	−0.448939	−	0.893562i	$-0.648198\pi$
$859$		−	52.3783i		−	1.78712i	0.448939	−	0.893562i	$-0.351802\pi$
$860$	−35.0642			−1.19568
$861$	−1.13191	−	20.1408i	−0.0385754	−	0.686396i
$862$	−25.7068			−0.875578
$863$		−	5.29540i		−	0.180257i	−0.995930	−	0.0901287i	$-0.971272\pi$
$863$		−	5.29540i		−	0.180257i	0.995930	−	0.0901287i	$-0.0287278\pi$
$864$	7.62706	−	28.1520i	0.259478	−	0.957752i
$865$	6.38745			0.217180
$866$	−6.31082			−0.214450
$867$	0.730545	+	1.57045i	0.0248106	+	0.0533352i
$868$	2.04161	−	5.12242i	0.0692967	−	0.173866i
$869$			6.75976i			0.229309i
$870$	9.29105	+	19.9729i	0.314996	+	0.677145i
$871$		−	42.8698i		−	1.45259i
$872$			41.1752i			1.39437i
$873$	−20.8741	−	17.5813i	−0.706482	−	0.595038i
$874$			6.35732i			0.215039i
$875$	13.7209	+	5.46863i	0.463850	+	0.184873i
$876$	30.2665	−	14.0795i	1.02261	−	0.475701i
$877$	1.28656			0.0434439			0.0217220	−	0.999764i	$-0.493085\pi$
$877$	1.28656			0.0434439			0.0217220	+	0.999764i	$0.493085\pi$
$878$	−1.07883			−0.0364088
$879$	−16.2501	−	34.9327i	−0.548101	−	1.17825i
$880$		−	0.253517i		−	0.00854605i
$881$	−33.4687			−1.12759			−0.563795	−	0.825915i	$-0.690659\pi$
$881$	−33.4687			−1.12759			−0.563795	+	0.825915i	$0.690659\pi$
$882$	−2.08519	−	18.4929i	−0.0702120	−	0.622690i
$883$	32.4370			1.09159			0.545797	−	0.837918i	$-0.316227\pi$
$883$	32.4370			1.09159			0.545797	+	0.837918i	$0.316227\pi$
$884$		−	4.63027i		−	0.155733i
$885$	−1.00216	−	2.15434i	−0.0336873	−	0.0724175i
$886$	9.67815			0.325144
$887$	−51.0707			−1.71479			−0.857394	−	0.514661i	$-0.827918\pi$
$887$	−51.0707			−1.71479			−0.857394	+	0.514661i	$0.827918\pi$
$888$	26.0669	−	12.1259i	0.874749	−	0.406918i
$889$	33.9482	+	13.5305i	1.13858	+	0.453798i
$890$		−	39.8403i		−	1.33545i
$891$	8.32584	−	1.43635i	0.278926	−	0.0481194i
$892$		−	6.58006i		−	0.220317i
$893$		−	12.1762i		−	0.407459i
$894$	6.07324	+	13.0556i	0.203120	+	0.436645i
$895$		−	40.1047i		−	1.34055i
$896$	6.51327	−	16.3419i	0.217593	−	0.545944i
$897$	5.47422	+	11.7679i	0.182779	+	0.392918i
$898$	7.81687			0.260852
$899$	8.69002			0.289828
$900$	−7.11251	+	8.44460i	−0.237084	+	0.281487i
$901$		−	8.71740i		−	0.290419i
$902$	−3.66215			−0.121936
$903$	2.61949	+	46.6103i	0.0871713	+	1.55109i
$904$	−28.1654			−0.936766
$905$			43.2841i			1.43881i
$906$	9.30737	−	4.32963i	0.309217	−	0.143842i
$907$	34.8042			1.15565			0.577827	−	0.816160i	$-0.303901\pi$
$907$	34.8042			1.15565			0.577827	+	0.816160i	$0.303901\pi$
$908$	−17.3567			−0.576004
$909$	−38.0090	+	45.1277i	−1.26068	+	1.49679i
$910$	−23.5274	−	9.37713i	−0.779924	−	0.310849i
$911$			46.1039i			1.52749i	0.645518	+	0.763745i	$0.276641\pi$
$911$			46.1039i			1.52749i	−0.645518	+	0.763745i	$0.723359\pi$
$912$	−0.546189	+	0.254078i	−0.0180861	+	0.00841336i
$913$		−	6.81630i		−	0.225587i
$914$		−	20.4451i		−	0.676265i
$915$	−1.97793	+	0.920097i	−0.0653882	+	0.0304175i
$916$		−	23.4922i		−	0.776206i
$917$	27.3454	+	10.8989i	0.903026	+	0.359913i
$918$	1.20414	−	4.44459i	0.0397427	−	0.146693i
$919$	−6.73335			−0.222113			−0.111056	−	0.993814i	$-0.535423\pi$
$919$	−6.73335			−0.222113			−0.111056	+	0.993814i	$0.535423\pi$
$920$	−15.8687			−0.523175
$921$	32.2897	−	15.0206i	1.06398	−	0.494946i
$922$			18.8427i			0.620552i
$923$	38.7906			1.27681
$924$	5.21714	−	0.293203i	0.171631	−	0.00964567i
$925$	−17.6534			−0.580440
$926$			2.79593i			0.0918800i
$927$	20.7405	+	17.4688i	0.681209	+	0.573752i
$928$	28.4277			0.933186
$929$	4.89576			0.160625			0.0803124	−	0.996770i	$-0.474408\pi$
$929$	4.89576			0.160625			0.0803124	+	0.996770i	$0.474408\pi$
$930$	−3.14788	−	6.76699i	−0.103223	−	0.221898i
$931$	17.5719	−	18.5423i	0.575896	−	0.607700i
$932$			33.1556i			1.08605i
$933$	21.4718	+	46.1577i	0.702954	+	1.51114i
$934$		−	3.42156i		−	0.111957i
$935$			2.66017i			0.0869967i
$936$	−20.9876	+	24.9183i	−0.686000	+	0.814480i
$937$			41.6138i			1.35946i	0.733460	+	0.679732i	$0.237904\pi$
$937$			41.6138i			1.35946i	−0.733460	+	0.679732i	$0.762096\pi$
$938$	9.76247	−	24.4942i	0.318756	−	0.799763i
$939$	−13.2485	+	6.16299i	−0.432349	+	0.201121i
$940$	11.4841			0.374569
$941$	−26.3105			−0.857697			−0.428849	−	0.903376i	$-0.641081\pi$
$941$	−26.3105			−0.857697			−0.428849	+	0.903376i	$0.641081\pi$
$942$	−4.92186	−	10.5805i	−0.160363	−	0.344731i
$943$			8.65313i			0.281785i
$944$	0.0461355			0.00150158
$945$	31.1577	+	23.3848i	1.01356	+	0.760706i
$946$	8.47502			0.275547
$947$		−	29.5200i		−	0.959271i	−0.877468	−	0.479636i	$-0.840769\pi$
$947$		−	29.5200i		−	0.959271i	0.877468	−	0.479636i	$-0.159231\pi$
$948$	6.38965	+	13.7358i	0.207526	+	0.446117i
$949$	−60.4839			−1.96339
$950$	9.79892			0.317919
$951$	7.43018	−	3.45639i	0.240940	−	0.112081i
$952$	2.79059	−	7.00164i	0.0904436	−	0.226924i
$953$			25.0199i			0.810475i	0.914212	+	0.405237i	$0.132811\pi$
$953$			25.0199i			0.810475i	−0.914212	+	0.405237i	$0.867189\pi$
$954$	−14.9300	+	17.7263i	−0.483378	+	0.573909i
$955$			73.8475i			2.38965i
$956$			35.5926i			1.15115i
$957$	3.47324	+	7.46639i	0.112274	+	0.241354i
$958$			7.23151i			0.233639i
$959$	−6.93209	+	17.3927i	−0.223849	+	0.561640i
$960$	−10.6923	−	22.9851i	−0.345092	−	0.741842i
$961$	28.0558			0.905024
$962$	−19.6827			−0.634597
$963$	−34.7789	−	29.2927i	−1.12074	−	0.943946i
$964$			11.2503i			0.362348i
$965$	−10.8407			−0.348976
$966$	0.447932	+	7.97033i	0.0144120	+	0.256441i
$967$	50.0314			1.60890			0.804450	−	0.594020i	$-0.202460\pi$
$967$	50.0314			1.60890			0.804450	+	0.594020i	$0.202460\pi$
$968$			28.8264i			0.926516i
$969$	5.73120	−	2.66605i	0.184113	−	0.0856460i
$970$	−22.8451			−0.733511
$971$	−12.7524			−0.409245			−0.204623	−	0.978841i	$-0.565597\pi$
$971$	−12.7524			−0.409245			−0.204623	+	0.978841i	$0.565597\pi$
$972$	15.5604	−	10.7886i	0.499099	−	0.346046i
$973$	−7.02070	+	17.6150i	−0.225073	+	0.564712i
$974$			27.9067i			0.894188i
$975$	18.1386	−	8.43774i	0.580899	−	0.270224i
$976$		−	0.0423575i		−	0.00135583i
$977$		−	10.2712i		−	0.328603i	−0.986410	−	0.164302i	$-0.947463\pi$
$977$		−	10.2712i		−	0.328603i	0.986410	−	0.164302i	$-0.0525371\pi$
$978$	15.9324	−	7.41146i	0.509461	−	0.236992i
$979$		−	14.8933i		−	0.475993i
$980$	17.4884	+	16.5731i	0.558646	+	0.529409i
$981$	−27.9329	+	33.1644i	−0.891827	+	1.05886i
$982$	−14.2930			−0.456109
$983$	24.7523			0.789475			0.394738	−	0.918794i	$-0.370836\pi$
$983$	24.7523			0.789475			0.394738	+	0.918794i	$0.370836\pi$
$984$	−19.6942	+	9.16142i	−0.627830	+	0.292055i
$985$			12.6508i			0.403089i
$986$	4.48811			0.142931
$987$	−0.857924	−	15.2656i	−0.0273080	−	0.485908i
$988$	−16.8977			−0.537589
$989$		−	20.0253i		−	0.636766i
$990$	4.55599	−	5.40927i	0.144799	−	0.171918i
$991$	−17.9852			−0.571318			−0.285659	−	0.958331i	$-0.592212\pi$
$991$	−17.9852			−0.571318			−0.285659	+	0.958331i	$0.592212\pi$
$992$	−9.63155			−0.305802
$993$	3.81729	+	8.20601i	0.121138	+	0.260410i
$994$	22.1635	+	8.83355i	0.702983	+	0.280183i
$995$			9.57273i			0.303476i
$996$	−6.44309	−	13.8507i	−0.204157	−	0.438876i
$997$		−	42.3405i		−	1.34094i	−0.741937	−	0.670469i	$-0.766093\pi$
$997$		−	42.3405i		−	1.34094i	0.741937	−	0.670469i	$-0.233907\pi$
$998$		−	3.10714i		−	0.0983546i
$999$	29.2215	+	7.91682i	0.924529	+	0.250477i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.14	yes	22
3.2	odd	2		357.2.d.a.188.9	✓	22
7.6	odd	2		357.2.d.a.188.14	yes	22
21.20	even	2	inner	357.2.d.b.188.9	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.9	✓	22	3.2	odd	2
357.2.d.a.188.14	yes	22	7.6	odd	2
357.2.d.b.188.9	yes	22	21.20	even	2	inner
357.2.d.b.188.14	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)

\(f(q)\)	\(=\)	\(q+0.886197i q^{2} +(0.730545 + 1.57045i) q^{3} +1.21466 q^{4} +2.83371 q^{5} +(-1.39173 + 0.647406i) q^{6} +(-2.45773 - 0.979562i) q^{7} +2.84882i q^{8} +(-1.93261 + 2.29456i) q^{9} +O(q^{10})\)	\(q+0.886197i q^{2} +(0.730545 + 1.57045i) q^{3} +1.21466 q^{4} +2.83371 q^{5} +(-1.39173 + 0.647406i) q^{6} +(-2.45773 - 0.979562i) q^{7} +2.84882i q^{8} +(-1.93261 + 2.29456i) q^{9} +2.51122i q^{10} +0.938759i q^{11} +(0.887360 + 1.90755i) q^{12} -3.81201i q^{13} +(0.868084 - 2.17804i) q^{14} +(2.07015 + 4.45018i) q^{15} -0.0953011 q^{16} +1.00000 q^{17} +(-2.03343 - 1.71267i) q^{18} -3.64941i q^{19} +3.44198 q^{20} +(-0.257135 - 4.57536i) q^{21} -0.831925 q^{22} +1.96572i q^{23} +(-4.47392 + 2.08119i) q^{24} +3.02988 q^{25} +3.37819 q^{26} +(-5.01535 - 1.35878i) q^{27} +(-2.98530 - 1.18983i) q^{28} -5.06446i q^{29} +(-3.94374 + 1.83456i) q^{30} +1.71588i q^{31} +5.61318i q^{32} +(-1.47427 + 0.685806i) q^{33} +0.886197i q^{34} +(-6.96449 - 2.77579i) q^{35} +(-2.34745 + 2.78710i) q^{36} -5.82642 q^{37} +3.23409 q^{38} +(5.98655 - 2.78484i) q^{39} +8.07271i q^{40} +4.40202 q^{41} +(4.05467 - 0.227872i) q^{42} -10.1872 q^{43} +1.14027i q^{44} +(-5.47644 + 6.50212i) q^{45} -1.74201 q^{46} +3.33648 q^{47} +(-0.0696217 - 0.149665i) q^{48} +(5.08092 + 4.81501i) q^{49} +2.68507i q^{50} +(0.730545 + 1.57045i) q^{51} -4.63027i q^{52} -8.71740i q^{53} +(1.20414 - 4.44459i) q^{54} +2.66017i q^{55} +(2.79059 - 7.00164i) q^{56} +(5.73120 - 2.66605i) q^{57} +4.48811 q^{58} -0.484102 q^{59} +(2.51452 + 5.40544i) q^{60} +0.444459i q^{61} -1.52061 q^{62} +(6.99751 - 3.74632i) q^{63} -5.16498 q^{64} -10.8021i q^{65} +(-0.607759 - 1.30649i) q^{66} +11.2460 q^{67} +1.21466 q^{68} +(-3.08706 + 1.43605i) q^{69} +(2.45990 - 6.17191i) q^{70} +10.1759i q^{71} +(-6.53679 - 5.50565i) q^{72} -15.8667i q^{73} -5.16336i q^{74} +(2.21347 + 4.75827i) q^{75} -4.43277i q^{76} +(0.919573 - 2.30722i) q^{77} +(2.46792 + 5.30526i) q^{78} +7.20074 q^{79} -0.270055 q^{80} +(-1.53005 - 8.86899i) q^{81} +3.90105i q^{82} -7.26097 q^{83} +(-0.312330 - 5.55748i) q^{84} +2.83371 q^{85} -9.02790i q^{86} +(7.95347 - 3.69982i) q^{87} -2.67435 q^{88} -15.8649 q^{89} +(-5.76215 - 4.85321i) q^{90} +(-3.73410 + 9.36890i) q^{91} +2.38767i q^{92} +(-2.69470 + 1.25353i) q^{93} +2.95677i q^{94} -10.3413i q^{95} +(-8.81520 + 4.10068i) q^{96} +9.09720i q^{97} +(-4.26704 + 4.50269i) q^{98} +(-2.15404 - 1.81425i) 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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