LMFDB - Embedded newform 357.2.d.b.188.12

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			188.12
Character	$\chi$	$=$	357.188
Dual form			357.2.d.b.188.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.126768i q^{2} +(-1.54802 + 0.776930i) q^{3} +1.98393 q^{4} +0.342053 q^{5} +(-0.0984896 - 0.196239i) q^{6} +(-1.39775 + 2.24640i) q^{7} +0.505033i q^{8} +(1.79276 - 2.40541i) q^{9} +O(q^{10})$	\(q+0.126768i q^{2} +(-1.54802 + 0.776930i) q^{3} +1.98393 q^{4} +0.342053 q^{5} +(-0.0984896 - 0.196239i) q^{6} +(-1.39775 + 2.24640i) q^{7} +0.505033i q^{8} +(1.79276 - 2.40541i) q^{9} +0.0433612i q^{10} +2.26817i q^{11} +(-3.07117 + 1.54137i) q^{12} +2.72251i q^{13} +(-0.284770 - 0.177189i) q^{14} +(-0.529506 + 0.265751i) q^{15} +3.90384 q^{16} +1.00000 q^{17} +(0.304929 + 0.227264i) q^{18} -2.19819i q^{19} +0.678609 q^{20} +(0.418455 - 4.56343i) q^{21} -0.287531 q^{22} +6.18352i q^{23} +(-0.392375 - 0.781804i) q^{24} -4.88300 q^{25} -0.345126 q^{26} +(-0.906399 + 5.11649i) q^{27} +(-2.77303 + 4.45669i) q^{28} +5.37149i q^{29} +(-0.0336886 - 0.0671242i) q^{30} +0.179858i q^{31} +1.50495i q^{32} +(-1.76221 - 3.51119i) q^{33} +0.126768i q^{34} +(-0.478103 + 0.768386i) q^{35} +(3.55671 - 4.77217i) q^{36} +5.04917 q^{37} +0.278659 q^{38} +(-2.11520 - 4.21451i) q^{39} +0.172748i q^{40} +9.29342 q^{41} +(0.578495 + 0.0530465i) q^{42} +2.96400 q^{43} +4.49990i q^{44} +(0.613218 - 0.822778i) q^{45} -0.783871 q^{46} -7.28406 q^{47} +(-6.04324 + 3.03301i) q^{48} +(-3.09260 - 6.27979i) q^{49} -0.619006i q^{50} +(-1.54802 + 0.776930i) q^{51} +5.40127i q^{52} -12.2081i q^{53} +(-0.648605 - 0.114902i) q^{54} +0.775835i q^{55} +(-1.13451 - 0.705909i) q^{56} +(1.70784 + 3.40285i) q^{57} -0.680931 q^{58} +1.11852 q^{59} +(-1.05050 + 0.527231i) q^{60} -11.8658i q^{61} -0.0228002 q^{62} +(2.89769 + 7.38941i) q^{63} +7.61690 q^{64} +0.931242i q^{65} +(0.445105 - 0.223391i) q^{66} -4.48809 q^{67} +1.98393 q^{68} +(-4.80416 - 9.57225i) q^{69} +(-0.0974065 - 0.0606080i) q^{70} -6.05224i q^{71} +(1.21481 + 0.905404i) q^{72} -12.2644i q^{73} +0.640071i q^{74} +(7.55900 - 3.79375i) q^{75} -4.36106i q^{76} +(-5.09522 - 3.17034i) q^{77} +(0.534264 - 0.268139i) q^{78} -4.07544 q^{79} +1.33532 q^{80} +(-2.57202 - 8.62466i) q^{81} +1.17810i q^{82} +16.7872 q^{83} +(0.830185 - 9.05353i) q^{84} +0.342053 q^{85} +0.375739i q^{86} +(-4.17327 - 8.31520i) q^{87} -1.14550 q^{88} +5.48367 q^{89} +(0.104302 + 0.0777362i) q^{90} +(-6.11584 - 3.80538i) q^{91} +12.2677i q^{92} +(-0.139737 - 0.278424i) q^{93} -0.923384i q^{94} -0.751897i q^{95} +(-1.16924 - 2.32969i) q^{96} -2.79541i q^{97} +(0.796075 - 0.392042i) q^{98} +(5.45589 + 4.06629i) 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 $

$2$			0.126768i			0.0896383i	0.998995	+	0.0448191i	$0.0142712\pi$
$2$			0.126768i			0.0896383i	−0.998995	+	0.0448191i	$0.985729\pi$
$3$	−1.54802	+	0.776930i	−0.893752	+	0.448561i
$3$	−1.54802	+	0.776930i	−0.893752	+	0.448561i
$4$	1.98393			0.991965
$5$	0.342053			0.152971			0.0764853	−	0.997071i	$-0.475630\pi$
$5$	0.342053			0.152971			0.0764853	+	0.997071i	$0.475630\pi$
$6$	−0.0984896	−	0.196239i	−0.0402082	−	0.0801144i
$7$	−1.39775	+	2.24640i	−0.528299	+	0.849058i
$7$	−1.39775	+	2.24640i	−0.528299	+	0.849058i
$8$			0.505033i			0.178556i
$9$	1.79276	−	2.40541i	0.597587	−	0.801804i
$10$			0.0433612i			0.0137120i
$11$			2.26817i			0.683880i	0.939722	+	0.341940i	$0.111084\pi$
$11$			2.26817i			0.683880i	−0.939722	+	0.341940i	$0.888916\pi$
$12$	−3.07117	+	1.54137i	−0.886571	+	0.444956i
$13$			2.72251i			0.755088i	0.925992	+	0.377544i	$0.123231\pi$
$13$			2.72251i			0.755088i	−0.925992	+	0.377544i	$0.876769\pi$
$14$	−0.284770	−	0.177189i	−0.0761081	−	0.0473558i
$15$	−0.529506	+	0.265751i	−0.136718	+	0.0686166i
$16$	3.90384			0.975960
$17$	1.00000			0.242536
$17$	1.00000			0.242536
$18$	0.304929	+	0.227264i	0.0718723	+	0.0535666i
$19$		−	2.19819i		−	0.504300i	−0.967688	−	0.252150i	$-0.918862\pi$
$19$		−	2.19819i		−	0.504300i	0.967688	−	0.252150i	$-0.0811376\pi$
$20$	0.678609			0.151741
$21$	0.418455	−	4.56343i	0.0913144	−	0.995822i
$22$	−0.287531			−0.0613018
$23$			6.18352i			1.28935i	0.764455	+	0.644677i	$0.223008\pi$
$23$			6.18352i			1.28935i	−0.764455	+	0.644677i	$0.776992\pi$
$24$	−0.392375	−	0.781804i	−0.0800933	−	0.159585i
$25$	−4.88300			−0.976600
$26$	−0.345126			−0.0676848
$27$	−0.906399	+	5.11649i	−0.174437	+	0.984668i
$28$	−2.77303	+	4.45669i	−0.524054	+	0.842236i
$29$			5.37149i			0.997461i	0.866757	+	0.498731i	$0.166200\pi$
$29$			5.37149i			0.997461i	−0.866757	+	0.498731i	$0.833800\pi$
$30$	−0.0336886	−	0.0671242i	−0.00615067	−	0.0122551i
$31$			0.179858i			0.0323034i	0.999870	+	0.0161517i	$0.00514147\pi$
$31$			0.179858i			0.0323034i	−0.999870	+	0.0161517i	$0.994859\pi$
$32$			1.50495i			0.266040i
$33$	−1.76221	−	3.51119i	−0.306762	−	0.611219i
$34$			0.126768i			0.0217405i
$35$	−0.478103	+	0.768386i	−0.0808142	+	0.129881i
$36$	3.55671	−	4.77217i	0.592785	−	0.795362i
$37$	5.04917			0.830078			0.415039	−	0.909804i	$-0.363768\pi$
$37$	5.04917			0.830078			0.415039	+	0.909804i	$0.363768\pi$
$38$	0.278659			0.0452045
$39$	−2.11520	−	4.21451i	−0.338703	−	0.674862i
$40$			0.172748i			0.0273139i
$41$	9.29342			1.45139			0.725694	−	0.688018i	$-0.241519\pi$
$41$	9.29342			1.45139			0.725694	+	0.688018i	$0.241519\pi$
$42$	0.578495	+	0.0530465i	0.0892638	+	0.00818526i
$43$	2.96400			0.452006			0.226003	−	0.974127i	$-0.427434\pi$
$43$	2.96400			0.452006			0.226003	+	0.974127i	$0.427434\pi$
$44$			4.49990i			0.678385i
$45$	0.613218	−	0.822778i	0.0914132	−	0.122652i
$46$	−0.783871			−0.115575
$47$	−7.28406			−1.06249			−0.531245	−	0.847218i	$-0.678276\pi$
$47$	−7.28406			−1.06249			−0.531245	+	0.847218i	$0.678276\pi$
$48$	−6.04324	+	3.03301i	−0.872266	+	0.437777i
$49$	−3.09260	−	6.27979i	−0.441800	−	0.897113i
$50$		−	0.619006i		−	0.0875407i
$51$	−1.54802	+	0.776930i	−0.216767	+	0.108792i
$52$			5.40127i			0.749021i
$53$		−	12.2081i		−	1.67691i	−0.544973	−	0.838454i	$-0.683460\pi$
$53$		−	12.2081i		−	1.67691i	0.544973	−	0.838454i	$-0.316540\pi$
$54$	−0.648605	−	0.114902i	−0.0882640	−	0.0156362i
$55$			0.775835i			0.104614i
$56$	−1.13451	−	0.705909i	−0.151605	−	0.0943311i
$57$	1.70784	+	3.40285i	0.226209	+	0.450719i
$58$	−0.680931			−0.0894107
$59$	1.11852			0.145619			0.0728093	−	0.997346i	$-0.476804\pi$
$59$	1.11852			0.145619			0.0728093	+	0.997346i	$0.476804\pi$
$60$	−1.05050	+	0.527231i	−0.135619	+	0.0680653i
$61$		−	11.8658i		−	1.51927i	−0.650352	−	0.759633i	$-0.725379\pi$
$61$		−	11.8658i		−	1.51927i	0.650352	−	0.759633i	$-0.274621\pi$
$62$	−0.0228002			−0.00289562
$63$	2.89769	+	7.38941i	0.365074	+	0.930978i
$64$	7.61690			0.952112
$65$			0.931242i			0.115506i
$66$	0.445105	−	0.223391i	0.0547886	−	0.0274976i
$67$	−4.48809			−0.548307			−0.274154	−	0.961686i	$-0.588398\pi$
$67$	−4.48809			−0.548307			−0.274154	+	0.961686i	$0.588398\pi$
$68$	1.98393			0.240587
$69$	−4.80416	−	9.57225i	−0.578353	−	1.15236i
$70$	−0.0974065	−	0.0606080i	−0.0116423	−	0.00724405i
$71$		−	6.05224i		−	0.718269i	−0.933286	−	0.359134i	$-0.883072\pi$
$71$		−	6.05224i		−	0.718269i	0.933286	−	0.359134i	$-0.116928\pi$
$72$	1.21481	+	0.905404i	0.143167	+	0.106703i
$73$		−	12.2644i		−	1.43543i	−0.696335	−	0.717717i	$-0.745187\pi$
$73$		−	12.2644i		−	1.43543i	0.696335	−	0.717717i	$-0.254813\pi$
$74$			0.640071i			0.0744068i
$75$	7.55900	−	3.79375i	0.872839	−	0.438064i
$76$		−	4.36106i		−	0.500248i
$77$	−5.09522	−	3.17034i	−0.580654	−	0.361293i
$78$	0.534264	−	0.268139i	0.0604935	−	0.0303607i
$79$	−4.07544			−0.458523			−0.229262	−	0.973365i	$-0.573631\pi$
$79$	−4.07544			−0.458523			−0.229262	+	0.973365i	$0.573631\pi$
$80$	1.33532			0.149293
$81$	−2.57202	−	8.62466i	−0.285780	−	0.958295i
$82$			1.17810i			0.130100i
$83$	16.7872			1.84263			0.921317	−	0.388813i	$-0.127115\pi$
$83$	16.7872			1.84263			0.921317	+	0.388813i	$0.127115\pi$
$84$	0.830185	−	9.05353i	0.0905806	−	0.987821i
$85$	0.342053			0.0371008
$86$			0.375739i			0.0405170i
$87$	−4.17327	−	8.31520i	−0.447422	−	0.891483i
$88$	−1.14550			−0.122111
$89$	5.48367			0.581268			0.290634	−	0.956834i	$-0.406134\pi$
$89$	5.48367			0.581268			0.290634	+	0.956834i	$0.406134\pi$
$90$	0.104302	+	0.0777362i	0.0109944	+	0.00819412i
$91$	−6.11584	−	3.80538i	−0.641114	−	0.398912i
$92$			12.2677i			1.27899i
$93$	−0.139737	−	0.278424i	−0.0144900	−	0.0288713i
$94$		−	0.923384i		−	0.0952397i
$95$		−	0.751897i		−	0.0771430i
$96$	−1.16924	−	2.32969i	−0.119335	−	0.237773i
$97$		−	2.79541i		−	0.283831i	−0.989879	−	0.141915i	$-0.954674\pi$
$97$		−	2.79541i		−	0.283831i	0.989879	−	0.141915i	$-0.0453261\pi$
$98$	0.796075	−	0.392042i	0.0804157	−	0.0396022i
$99$	5.45589	+	4.06629i	0.548338	+	0.408678i
$100$	−9.68753			−0.968753
$101$	2.33282			0.232124			0.116062	−	0.993242i	$-0.462973\pi$
$101$	2.33282			0.232124			0.116062	+	0.993242i	$0.462973\pi$
$102$	−0.0984896	−	0.196239i	−0.00975192	−	0.0194306i
$103$			13.8110i			1.36084i	0.732822	+	0.680421i	$0.238203\pi$
$103$			13.8110i			1.36084i	−0.732822	+	0.680421i	$0.761797\pi$
$104$	−1.37496			−0.134826
$105$	0.143134	−	1.56093i	0.0139684	−	0.152332i
$106$	1.54759			0.150315
$107$		−	19.1401i		−	1.85034i	−0.379550	−	0.925171i	$-0.623921\pi$
$107$		−	19.1401i		−	1.85034i	0.379550	−	0.925171i	$-0.376079\pi$
$108$	−1.79823	+	10.1508i	−0.173035	+	0.976757i
$109$	−11.2782			−1.08025			−0.540126	−	0.841584i	$-0.681623\pi$
$109$	−11.2782			−1.08025			−0.540126	+	0.841584i	$0.681623\pi$
$110$	−0.0983508			−0.00937738
$111$	−7.81624	+	3.92285i	−0.741885	+	0.372341i
$112$	−5.45658	+	8.76957i	−0.515598	+	0.828647i
$113$			15.6077i			1.46825i	0.679013	+	0.734127i	$0.262408\pi$
$113$			15.6077i			1.46825i	−0.679013	+	0.734127i	$0.737592\pi$
$114$	−0.431372	+	0.216499i	−0.0404017	+	0.0202770i
$115$			2.11509i			0.197233i
$116$			10.6567i			0.989446i
$117$	6.54876	+	4.88081i	0.605433	+	0.451231i
$118$			0.141792i			0.0130530i
$119$	−1.39775	+	2.24640i	−0.128131	+	0.205927i
$120$	−0.134213	−	0.267418i	−0.0122519	−	0.0244118i
$121$	5.85539			0.532308
$122$	1.50421			0.136184
$123$	−14.3864	+	7.22033i	−1.29718	+	0.651036i
$124$			0.356825i			0.0320439i
$125$	−3.38051			−0.302362
$126$	−0.936738	+	0.367333i	−0.0834513	+	0.0327246i
$127$	14.6838			1.30297			0.651487	−	0.758659i	$-0.274145\pi$
$127$	14.6838			1.30297			0.651487	+	0.758659i	$0.274145\pi$
$128$			3.97547i			0.351385i
$129$	−4.58835	+	2.30282i	−0.403981	+	0.202752i
$130$	−0.118051			−0.0103538
$131$	−4.23296			−0.369835			−0.184918	−	0.982754i	$-0.559202\pi$
$131$	−4.23296			−0.369835			−0.184918	+	0.982754i	$0.559202\pi$
$132$	−3.49610	−	6.96595i	−0.304297	−	0.606308i
$133$	4.93801	+	3.07252i	0.428180	+	0.266421i
$134$		−	0.568944i		−	0.0491493i
$135$	−0.310036	+	1.75011i	−0.0266837	+	0.150625i
$136$			0.505033i			0.0433063i
$137$		−	1.56028i		−	0.133304i	−0.997776	−	0.0666519i	$-0.978768\pi$
$137$		−	1.56028i		−	0.133304i	0.997776	−	0.0666519i	$-0.0212317\pi$
$138$	1.21345	−	0.609013i	0.103296	−	0.0518426i
$139$		−	2.40246i		−	0.203774i	−0.994796	−	0.101887i	$-0.967512\pi$
$139$		−	2.40246i		−	0.203774i	0.994796	−	0.101887i	$-0.0324880\pi$
$140$	−0.948524	+	1.52442i	−0.0801649	+	0.128837i
$141$	11.2759	−	5.65921i	0.949603	−	0.476591i
$142$	0.767228			0.0643844
$143$	−6.17513			−0.516390
$144$	6.99864	−	9.39034i	0.583220	−	0.782529i
$145$			1.83733i			0.152582i
$146$	1.55472			0.128670
$147$	9.66638	+	7.31854i	0.797270	+	0.603623i
$148$	10.0172			0.823409
$149$		−	0.142404i		−	0.0116662i	−0.999983	−	0.00583311i	$-0.998143\pi$
$149$		−	0.142404i		−	0.0116662i	0.999983	−	0.00583311i	$-0.00185675\pi$
$150$	0.480925	+	0.958237i	0.0392673	+	0.0782397i
$151$	−3.86097			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$151$	−3.86097			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$152$	1.11016			0.0900458
$153$	1.79276	−	2.40541i	0.144936	−	0.194466i
$154$	0.401896	−	0.645909i	0.0323857	−	0.0520488i
$155$			0.0615209i			0.00494147i
$156$	−4.19641	−	8.36130i	−0.335981	−	0.669440i
$157$			2.82103i			0.225143i	0.993644	+	0.112571i	$0.0359087\pi$
$157$			2.82103i			0.225143i	−0.993644	+	0.112571i	$0.964091\pi$
$158$		−	0.516635i		−	0.0411012i
$159$	9.48481	+	18.8984i	0.752195	+	1.49874i
$160$			0.514771i			0.0406962i
$161$	−13.8907	−	8.64301i	−1.09474	−	0.681164i
$162$	1.09333	−	0.326049i	0.0858999	−	0.0256168i
$163$	4.96653			0.389008			0.194504	−	0.980902i	$-0.437690\pi$
$163$	4.96653			0.389008			0.194504	+	0.980902i	$0.437690\pi$
$164$	18.4375			1.43973
$165$	−0.602769	−	1.20101i	−0.0469255	−	0.0934986i
$166$			2.12807i			0.165170i
$167$	−9.36648			−0.724800			−0.362400	−	0.932023i	$-0.618043\pi$
$167$	−9.36648			−0.724800			−0.362400	+	0.932023i	$0.618043\pi$
$168$	2.30468	+	0.211334i	0.177810	+	0.0163047i
$169$	5.58794			0.429842
$170$			0.0433612i			0.00332565i
$171$	−5.28756	−	3.94083i	−0.404350	−	0.301363i
$172$	5.88037			0.448374
$173$	−18.1717			−1.38157			−0.690783	−	0.723062i	$-0.742734\pi$
$173$	−18.1717			−1.38157			−0.690783	+	0.723062i	$0.742734\pi$
$174$	1.05410	−	0.529036i	0.0799110	−	0.0401061i
$175$	6.82520	−	10.9692i	0.515937	−	0.829190i
$176$			8.85458i			0.667439i
$177$	−1.73149	+	0.869009i	−0.130147	+	0.0653188i
$178$			0.695152i			0.0521039i
$179$		−	9.44378i		−	0.705861i	−0.935650	−	0.352931i	$-0.885185\pi$
$179$		−	9.44378i		−	0.705861i	0.935650	−	0.352931i	$-0.114815\pi$
$180$	1.21658	−	1.63233i	0.0906787	−	0.121667i
$181$			17.2187i			1.27986i	0.768435	+	0.639928i	$0.221036\pi$
$181$			17.2187i			1.27986i	−0.768435	+	0.639928i	$0.778964\pi$
$182$	0.482399	−	0.775290i	0.0357578	−	0.0574684i
$183$	9.21893	+	18.3686i	0.681483	+	1.35785i
$184$	−3.12289			−0.230222
$185$	1.72708			0.126978
$186$	0.0352952	−	0.0177141i	0.00258797	−	0.00129886i
$187$			2.26817i			0.165865i
$188$	−14.4511			−1.05395
$189$	−10.2267	−	9.18769i	−0.743886	−	0.668306i
$190$	0.0953162			0.00691496
$191$			15.2346i			1.10233i	0.834395	+	0.551167i	$0.185817\pi$
$191$			15.2346i			1.10233i	−0.834395	+	0.551167i	$0.814183\pi$
$192$	−11.7911	+	5.91779i	−0.850953	+	0.427080i
$193$	−12.5109			−0.900551			−0.450276	−	0.892890i	$-0.648674\pi$
$193$	−12.5109			−0.900551			−0.450276	+	0.892890i	$0.648674\pi$
$194$	0.354367			0.0254421
$195$	−0.723510	−	1.44159i	−0.0518116	−	0.103234i
$196$	−6.13551	−	12.4587i	−0.438250	−	0.889905i
$197$		−	17.6916i		−	1.26047i	−0.776403	−	0.630237i	$-0.782958\pi$
$197$		−	17.6916i		−	1.26047i	0.776403	−	0.630237i	$-0.217042\pi$
$198$	−0.515474	+	0.691631i	−0.0366332	+	0.0491521i
$199$			5.83741i			0.413803i	0.978362	+	0.206902i	$0.0663380\pi$
$199$			5.83741i			0.413803i	−0.978362	+	0.206902i	$0.933662\pi$
$200$		−	2.46608i		−	0.174378i
$201$	6.94767	−	3.48693i	0.490051	−	0.245949i
$202$			0.295726i			0.0208072i
$203$	−12.0665	−	7.50799i	−0.846903	−	0.526958i
$204$	−3.07117	+	1.54137i	−0.215025	+	0.107918i
$205$	3.17884			0.222020
$206$	−1.75079			−0.121983
$207$	14.8739	+	11.0856i	1.03381	+	0.770501i
$208$			10.6282i			0.736936i
$209$	4.98588			0.344880
$210$	0.197876	+	0.0181447i	0.0136547	+	0.00125210i
$211$	11.5366			0.794215			0.397107	−	0.917772i	$-0.370014\pi$
$211$	11.5366			0.794215			0.397107	+	0.917772i	$0.370014\pi$
$212$		−	24.2200i		−	1.66343i
$213$	4.70217	+	9.36902i	0.322187	+	0.641954i
$214$	2.42634			0.165861
$215$	1.01384			0.0691436
$216$	−2.58400	−	0.457762i	−0.175819	−	0.0311468i
$217$	−0.404032	−	0.251396i	−0.0274275	−	0.0170659i
$218$		−	1.42970i		−	0.0968318i
$219$	9.52854	+	18.9855i	0.643879	+	1.28292i
$220$			1.53920i			0.103773i
$221$			2.72251i			0.183136i
$222$	−0.497291	−	0.990846i	−0.0333760	−	0.0665012i
$223$			17.1130i			1.14597i	0.819566	+	0.572985i	$0.194215\pi$
$223$			17.1130i			1.14597i	−0.819566	+	0.572985i	$0.805785\pi$
$224$	−3.38071	−	2.10354i	−0.225883	−	0.140548i
$225$	−8.75405	+	11.7456i	−0.583603	+	0.783042i
$226$	−1.97856			−0.131612
$227$	13.7251			0.910970			0.455485	−	0.890243i	$-0.349466\pi$
$227$	13.7251			0.910970			0.455485	+	0.890243i	$0.349466\pi$
$228$	3.38824	+	6.75102i	0.224391	+	0.447097i
$229$		−	10.8787i		−	0.718887i	−0.933167	−	0.359443i	$-0.882967\pi$
$229$		−	10.8787i		−	0.718887i	0.933167	−	0.359443i	$-0.117033\pi$
$230$	−0.268125			−0.0176796
$231$	10.3507	+	0.949129i	0.681023	+	0.0624481i
$232$	−2.71278			−0.178103
$233$			8.91360i			0.583949i	0.956426	+	0.291975i	$0.0943123\pi$
$233$			8.91360i			0.583949i	−0.956426	+	0.291975i	$0.905688\pi$
$234$	−0.618728	+	0.830171i	−0.0404475	+	0.0542700i
$235$	−2.49153			−0.162530
$236$	2.21906			0.144449
$237$	6.30889	−	3.16633i	0.409806	−	0.205676i
$238$	−0.284770	−	0.177189i	−0.0184589	−	0.0114855i
$239$		−	23.8423i		−	1.54223i	−0.636694	−	0.771117i	$-0.719698\pi$
$239$		−	23.8423i		−	1.54223i	0.636694	−	0.771117i	$-0.280302\pi$
$240$	−2.06711	+	1.03745i	−0.133431	+	0.0669670i
$241$			4.56161i			0.293839i	0.989148	+	0.146919i	$0.0469358\pi$
$241$			4.56161i			0.293839i	−0.989148	+	0.146919i	$0.953064\pi$
$242$			0.742274i			0.0477152i
$243$	10.6823	+	11.3529i	0.685270	+	0.728289i
$244$		−	23.5410i		−	1.50706i
$245$	−1.05783	−	2.14802i	−0.0675825	−	0.137232i
$246$	−0.915305	−	1.82373i	−0.0583577	−	0.116277i
$247$	5.98460			0.380791
$248$	−0.0908342			−0.00576798
$249$	−25.9870	+	13.0425i	−1.64686	+	0.826533i
$250$		−	0.428539i		−	0.0271032i
$251$	−13.9707			−0.881820			−0.440910	−	0.897551i	$-0.645344\pi$
$251$	−13.9707			−0.881820			−0.440910	+	0.897551i	$0.645344\pi$
$252$	5.74881	+	14.6601i	0.362141	+	0.923498i
$253$	−14.0253			−0.881764
$254$			1.86143i			0.116796i
$255$	−0.529506	+	0.265751i	−0.0331589	+	0.0166420i
$256$	14.7298			0.920615
$257$	−4.11045			−0.256403			−0.128201	−	0.991748i	$-0.540920\pi$
$257$	−4.11045			−0.256403			−0.128201	+	0.991748i	$0.540920\pi$
$258$	−0.291923	−	0.581654i	−0.0181743	−	0.0362122i
$259$	−7.05747	+	11.3424i	−0.438530	+	0.704785i
$260$			1.84752i			0.114578i
$261$	12.9207	+	9.62980i	0.799769	+	0.596069i
$262$		−	0.536602i		−	0.0331514i
$263$		−	15.9389i		−	0.982835i	−0.870924	−	0.491417i	$-0.836479\pi$
$263$		−	15.9389i		−	0.982835i	0.870924	−	0.491417i	$-0.163521\pi$
$264$	1.77327	−	0.889976i	0.109137	−	0.0547742i
$265$		−	4.17580i		−	0.256518i
$266$	−0.389496	+	0.625980i	−0.0238815	+	0.0383813i
$267$	−8.48886	+	4.26043i	−0.519510	+	0.260734i
$268$	−8.90405			−0.543902
$269$	16.4231			1.00133			0.500666	−	0.865641i	$-0.333089\pi$
$269$	16.4231			1.00133			0.500666	+	0.865641i	$0.333089\pi$
$270$	−0.221857	−	0.0393026i	−0.0135018	−	0.00239188i
$271$			21.5259i			1.30761i	0.756665	+	0.653803i	$0.226828\pi$
$271$			21.5259i			1.30761i	−0.756665	+	0.653803i	$0.773172\pi$
$272$	3.90384			0.236705
$273$	12.4240	+	1.13925i	0.751934	+	0.0689504i
$274$	0.197793			0.0119491
$275$		−	11.0755i		−	0.667877i
$276$	−9.53113	−	18.9907i	−0.573706	−	1.14310i
$277$	4.37169			0.262669			0.131335	−	0.991338i	$-0.458074\pi$
$277$	4.37169			0.262669			0.131335	+	0.991338i	$0.458074\pi$
$278$	0.304554			0.0182659
$279$	0.432632	+	0.322442i	0.0259010	+	0.0193041i
$280$	−0.388061	−	0.241458i	−0.0231911	−	0.0144299i
$281$			4.34091i			0.258957i	0.991582	+	0.129479i	$0.0413304\pi$
$281$			4.34091i			0.258957i	−0.991582	+	0.129479i	$0.958670\pi$
$282$	0.717404	+	1.42942i	0.0427208	+	0.0851208i
$283$			14.2518i			0.847180i	0.905854	+	0.423590i	$0.139230\pi$
$283$			14.2518i			0.847180i	−0.905854	+	0.423590i	$0.860770\pi$
$284$		−	12.0072i		−	0.712498i
$285$	0.584171	+	1.16396i	0.0346033	+	0.0689468i
$286$		−	0.782806i		−	0.0462883i
$287$	−12.9899	+	20.8767i	−0.766767	+	1.23231i
$288$	3.62002	+	2.69801i	0.213312	+	0.158982i
$289$	1.00000			0.0588235
$290$	−0.232914			−0.0136772
$291$	2.17184	+	4.32736i	0.127315	+	0.253674i
$292$		−	24.3316i		−	1.42390i
$293$	7.79366			0.455310			0.227655	−	0.973742i	$-0.426894\pi$
$293$	7.79366			0.455310			0.227655	+	0.973742i	$0.426894\pi$
$294$	−0.927754	+	1.22538i	−0.0541077	+	0.0714659i
$295$	0.382592			0.0222754
$296$			2.55000i			0.148216i
$297$	−11.6051	−	2.05587i	−0.673395	−	0.119294i
$298$	0.0180523			0.00104574
$299$	−16.8347			−0.973576
$300$	14.9965	−	7.52653i	0.865825	−	0.434544i
$301$	−4.14293	+	6.65832i	−0.238794	+	0.383779i
$302$		−	0.489447i		−	0.0281645i
$303$	−3.61126	+	1.81244i	−0.207462	+	0.104122i
$304$		−	8.58138i		−	0.492176i
$305$		−	4.05875i		−	0.232403i
$306$	0.304929	+	0.227264i	0.0174316	+	0.0129918i
$307$		−	22.0955i		−	1.26105i	−0.776167	−	0.630527i	$-0.782839\pi$
$307$		−	22.0955i		−	1.26105i	0.776167	−	0.630527i	$-0.217161\pi$
$308$	−10.1086	−	6.28972i	−0.575989	−	0.358390i
$309$	−10.7302	−	21.3798i	−0.610420	−	1.21626i
$310$	−0.00779885			−0.000442945
$311$	−28.8935			−1.63840			−0.819201	−	0.573506i	$-0.805583\pi$
$311$	−28.8935			−1.63840			−0.819201	+	0.573506i	$0.805583\pi$
$312$	2.12847	−	1.06825i	0.120501	−	0.0604775i
$313$		−	1.96312i		−	0.110962i	−0.998460	−	0.0554812i	$-0.982331\pi$
$313$		−	1.96312i		−	0.110962i	0.998460	−	0.0554812i	$-0.0176693\pi$
$314$	−0.357615			−0.0201814
$315$	0.991161	+	2.52757i	0.0558456	+	0.142412i
$316$	−8.08540			−0.454839
$317$			16.7112i			0.938592i	0.883041	+	0.469296i	$0.155492\pi$
$317$			16.7112i			0.938592i	−0.883041	+	0.469296i	$0.844508\pi$
$318$	−2.39570	+	1.20237i	−0.134344	+	0.0674254i
$319$	−12.1835			−0.682144
$320$	2.60538			0.145645
$321$	14.8705	+	29.6293i	0.829991	+	1.65375i
$322$	1.09565	−	1.76089i	0.0610584	−	0.0981303i
$323$		−	2.19819i		−	0.122311i
$324$	−5.10271	−	17.1107i	−0.283484	−	0.950595i
$325$		−	13.2940i		−	0.737419i
$326$			0.629595i			0.0348700i
$327$	17.4589	−	8.76233i	0.965477	−	0.484558i
$328$			4.69349i			0.259154i
$329$	10.1813	−	16.3629i	0.561312	−	0.902116i
$330$	0.152249	−	0.0764116i	0.00838105	−	0.00420632i
$331$	12.9242			0.710381			0.355190	−	0.934794i	$-0.384416\pi$
$331$	12.9242			0.710381			0.355190	+	0.934794i	$0.384416\pi$
$332$	33.3046			1.82783
$333$	9.05195	−	12.1453i	0.496044	−	0.665560i
$334$		−	1.18737i		−	0.0649698i
$335$	−1.53516			−0.0838749
$336$	1.63358	−	17.8149i	0.0891191	−	0.971882i
$337$	−30.2770			−1.64929			−0.824646	−	0.565649i	$-0.808626\pi$
$337$	−30.2770			−1.64929			−0.824646	+	0.565649i	$0.808626\pi$
$338$			0.708370i			0.0385302i
$339$	−12.1261	−	24.1612i	−0.658601	−	1.31225i
$340$	0.678609			0.0368027
$341$	−0.407949			−0.0220917
$342$	0.499570	−	0.670291i	0.0270136	−	0.0362452i
$343$	18.4296	+	1.83036i	0.995104	+	0.0988300i
$344$			1.49692i			0.0807085i
$345$	−1.64328	−	3.27421i	−0.0884711	−	0.176278i
$346$		−	2.30358i		−	0.123841i
$347$		−	23.4384i		−	1.25824i	−0.777308	−	0.629120i	$-0.783415\pi$
$347$		−	23.4384i		−	1.25824i	0.777308	−	0.629120i	$-0.216585\pi$
$348$	−8.27948	−	16.4968i	−0.443827	−	0.884320i
$349$		−	24.7185i		−	1.32315i	−0.749879	−	0.661575i	$-0.769888\pi$
$349$		−	24.7185i		−	1.32315i	0.749879	−	0.661575i	$-0.230112\pi$
$350$	1.39053	+	0.865215i	0.0743272	+	0.0462477i
$351$	−13.9297	−	2.46768i	−0.743512	−	0.131715i
$352$	−3.41348			−0.181939
$353$	32.3729			1.72304			0.861519	−	0.507725i	$-0.169514\pi$
$353$	32.3729			1.72304			0.861519	+	0.507725i	$0.169514\pi$
$354$	−0.110162	−	0.219497i	−0.00585506	−	0.0116661i
$355$		−	2.07019i		−	0.109874i
$356$	10.8792			0.576598
$357$	0.418455	−	4.56343i	0.0221470	−	0.241522i
$358$	1.19717			0.0632722
$359$		−	0.234643i		−	0.0123840i	−0.999981	−	0.00619199i	$-0.998029\pi$
$359$		−	0.234643i		−	0.0123840i	0.999981	−	0.00619199i	$-0.00197098\pi$
$360$	0.415530	+	0.309696i	0.0219004	+	0.0163224i
$361$	14.1680			0.745682
$362$	−2.18277			−0.114724
$363$	−9.06428	+	4.54923i	−0.475752	+	0.238772i
$364$	−12.1334	−	7.54961i	−0.635963	−	0.395707i
$365$		−	4.19506i		−	0.219579i
$366$	−2.32855	+	1.16866i	−0.121715	+	0.0610870i
$367$		−	16.9219i		−	0.883315i	−0.897184	−	0.441658i	$-0.854391\pi$
$367$		−	16.9219i		−	0.883315i	0.897184	−	0.441658i	$-0.145609\pi$
$368$			24.1395i			1.25836i
$369$	16.6609	−	22.3545i	0.867330	−	1.16373i
$370$			0.218938i			0.0113821i
$371$	27.4242	+	17.0638i	1.42379	+	0.885909i
$372$	−0.277228	−	0.552374i	−0.0143736	−	0.0286393i
$373$	23.4538			1.21439			0.607195	−	0.794553i	$-0.292295\pi$
$373$	23.4538			1.21439			0.607195	+	0.794553i	$0.292295\pi$
$374$	−0.287531			−0.0148679
$375$	5.23311	−	2.62642i	0.270237	−	0.135628i
$376$		−	3.67870i		−	0.189714i
$377$	−14.6239			−0.753171
$378$	1.16470	−	1.29642i	0.0599058	−	0.0666807i
$379$	−20.0429			−1.02954			−0.514768	−	0.857329i	$-0.672122\pi$
$379$	−20.0429			−1.02954			−0.514768	+	0.857329i	$0.672122\pi$
$380$		−	1.49171i		−	0.0765232i
$381$	−22.7309	+	11.4083i	−1.16454	+	0.584463i
$382$	−1.93125			−0.0988113
$383$	−32.3999			−1.65556			−0.827779	−	0.561054i	$-0.810396\pi$
$383$	−32.3999			−1.65556			−0.827779	+	0.561054i	$0.810396\pi$
$384$	−3.08866	−	6.15413i	−0.157618	−	0.314051i
$385$	−1.74283	−	1.08442i	−0.0888230	−	0.0552672i
$386$		−	1.58597i		−	0.0807238i
$387$	5.31374	−	7.12964i	0.270113	−	0.362420i
$388$		−	5.54590i		−	0.281550i
$389$			33.3116i			1.68897i	0.535583	+	0.844483i	$0.320092\pi$
$389$			33.3116i			1.68897i	−0.535583	+	0.844483i	$0.679908\pi$
$390$	0.182746	−	0.0917176i	0.00925372	−	0.00464430i
$391$			6.18352i			0.312714i
$392$	3.17151	−	1.56187i	0.160185	−	0.0788862i
$393$	6.55273	−	3.28871i	0.330541	−	0.165894i
$394$	2.24272			0.112987
$395$	−1.39402			−0.0701406
$396$	10.8241	+	8.06724i	0.543932	+	0.405394i
$397$		−	20.8701i		−	1.04744i	−0.851890	−	0.523721i	$-0.824543\pi$
$397$		−	20.8701i		−	1.04744i	0.851890	−	0.523721i	$-0.175457\pi$
$398$	−0.739995			−0.0370926
$399$	−10.0313	−	0.919844i	−0.502193	−	0.0460498i
$400$	−19.0624			−0.953122
$401$		−	21.6618i		−	1.08174i	−0.841107	−	0.540869i	$-0.818095\pi$
$401$		−	21.6618i		−	1.08174i	0.841107	−	0.540869i	$-0.181905\pi$
$402$	0.442030	+	0.880740i	0.0220464	+	0.0439273i
$403$	−0.489665			−0.0243919
$404$	4.62815			0.230259
$405$	−0.879767	−	2.95009i	−0.0437160	−	0.146591i
$406$	0.951770	−	1.52964i	0.0472356	−	0.0759149i
$407$			11.4524i			0.567674i
$408$	−0.392375	−	0.781804i	−0.0194255	−	0.0387051i
$409$		−	0.630883i		−	0.0311952i	−0.999878	−	0.0155976i	$-0.995035\pi$
$409$		−	0.630883i		−	0.0311952i	0.999878	−	0.0155976i	$-0.00496507\pi$
$410$			0.402974i			0.0199015i
$411$	1.21223	+	2.41535i	0.0597948	+	0.119141i
$412$			27.4001i			1.34991i
$413$	−1.56341	+	2.51263i	−0.0769301	+	0.123639i
$414$	−1.40529	+	1.88553i	−0.0690663	+	0.0926689i
$415$	5.74210			0.281869
$416$	−4.09723			−0.200883
$417$	1.86654	+	3.71907i	0.0914050	+	0.182123i
$418$			0.632048i			0.0309145i
$419$	13.4058			0.654917			0.327459	−	0.944866i	$-0.393808\pi$
$419$	13.4058			0.654917			0.327459	+	0.944866i	$0.393808\pi$
$420$	0.283967	−	3.09678i	0.0138562	−	0.151108i
$421$	3.03897			0.148110			0.0740551	−	0.997254i	$-0.476406\pi$
$421$	3.03897			0.148110			0.0740551	+	0.997254i	$0.476406\pi$
$422$			1.46247i			0.0711920i
$423$	−13.0586	+	17.5212i	−0.634930	+	0.851909i
$424$	6.16548			0.299422
$425$	−4.88300			−0.236860
$426$	−1.18769	+	0.596083i	−0.0575437	+	0.0288803i
$427$	26.6554	+	16.5855i	1.28995	+	0.802627i
$428$		−	37.9726i		−	1.83548i
$429$	9.55925	−	4.79764i	0.461525	−	0.231632i
$430$			0.128523i			0.00619791i
$431$			14.7261i			0.709334i	0.934993	+	0.354667i	$0.115406\pi$
$431$			14.7261i			0.709334i	−0.934993	+	0.354667i	$0.884594\pi$
$432$	−3.53844	+	19.9739i	−0.170243	+	0.960996i
$433$			27.5550i			1.32421i	0.749412	+	0.662104i	$0.230336\pi$
$433$			27.5550i			1.32421i	−0.749412	+	0.662104i	$0.769664\pi$
$434$	0.0318689	−	0.0512182i	0.00152975	−	0.00245855i
$435$	−1.42748	−	2.84424i	−0.0684424	−	0.136371i
$436$	−22.3751			−1.07157
$437$	13.5926			0.650221
$438$	−2.40675	+	1.20791i	−0.114999	+	0.0577162i
$439$		−	6.48029i		−	0.309288i	−0.987970	−	0.154644i	$-0.950577\pi$
$439$		−	6.48029i		−	0.309288i	0.987970	−	0.154644i	$-0.0494230\pi$
$440$	−0.391823			−0.0186794
$441$	−20.6498	−	3.81918i	−0.983323	−	0.181866i
$442$	−0.345126			−0.0164160
$443$		−	8.52860i		−	0.405206i	−0.979261	−	0.202603i	$-0.935060\pi$
$443$		−	8.52860i		−	0.405206i	0.979261	−	0.202603i	$-0.0649401\pi$
$444$	−15.5069	+	7.78266i	−0.735924	+	0.369349i
$445$	1.87570			0.0889169
$446$	−2.16937			−0.102723
$447$	0.110638	+	0.220446i	0.00523301	+	0.0104267i
$448$	−10.6465	+	17.1106i	−0.503000	+	0.808399i
$449$			11.1583i			0.526593i	0.964715	+	0.263296i	$0.0848097\pi$
$449$			11.1583i			0.526593i	−0.964715	+	0.263296i	$0.915190\pi$
$450$	−1.48897	−	1.10973i	−0.0701905	−	0.0523132i
$451$			21.0791i			0.992575i
$452$			30.9647i			1.45646i
$453$	5.97688	−	2.99971i	0.280818	−	0.140938i
$454$			1.73990i			0.0816578i
$455$	−2.09194	−	1.30164i	−0.0980716	−	0.0610219i
$456$	−1.71855	+	0.862516i	−0.0804787	+	0.0403910i
$457$	−30.8351			−1.44240			−0.721202	−	0.692725i	$-0.756410\pi$
$457$	−30.8351			−1.44240			−0.721202	+	0.692725i	$0.756410\pi$
$458$	1.37907			0.0644398
$459$	−0.906399	+	5.11649i	−0.0423071	+	0.238817i
$460$			4.19619i			0.195648i
$461$	21.2546			0.989925			0.494962	−	0.868914i	$-0.335182\pi$
$461$	21.2546			0.989925			0.494962	+	0.868914i	$0.335182\pi$
$462$	−0.120319	+	1.31213i	−0.00559774	+	0.0610457i
$463$	4.43684			0.206197			0.103099	−	0.994671i	$-0.467124\pi$
$463$	4.43684			0.206197			0.103099	+	0.994671i	$0.467124\pi$
$464$			20.9694i			0.973482i
$465$	−0.0477974	−	0.0952358i	−0.00221655	−	0.00441645i
$466$	−1.12996			−0.0523442
$467$	−31.1344			−1.44073			−0.720364	−	0.693596i	$-0.756025\pi$
$467$	−31.1344			−1.44073			−0.720364	+	0.693596i	$0.756025\pi$
$468$	12.9923	+	9.68318i	0.600568	+	0.447605i
$469$	6.27322	−	10.0820i	0.289670	−	0.465545i
$470$		−	0.315846i		−	0.0145689i
$471$	−2.19174	−	4.36702i	−0.100990	−	0.201222i
$472$			0.564889i			0.0260011i
$473$			6.72287i			0.309118i
$474$	0.401389	+	0.799763i	0.0184364	+	0.0367343i
$475$			10.7338i			0.492499i
$476$	−2.77303	+	4.45669i	−0.127102	+	0.204272i
$477$	−29.3655	−	21.8861i	−1.34455	−	1.00210i
$478$	3.02244			0.138243
$479$	37.8264			1.72833			0.864166	−	0.503207i	$-0.167847\pi$
$479$	37.8264			1.72833			0.864166	+	0.503207i	$0.167847\pi$
$480$	−0.399941	−	0.796878i	−0.0182547	−	0.0363724i
$481$			13.7464i			0.626783i
$482$	−0.578264			−0.0263392
$483$	28.2181	+	2.58753i	1.28397	+	0.117737i
$484$	11.6167			0.528031
$485$		−	0.956177i		−	0.0434178i
$486$	−1.43918	+	1.35417i	−0.0652825	+	0.0614264i
$487$	36.5379			1.65569			0.827846	−	0.560956i	$-0.189566\pi$
$487$	36.5379			1.65569			0.827846	+	0.560956i	$0.189566\pi$
$488$	5.99265			0.271274
$489$	−7.68830	+	3.85864i	−0.347677	+	0.174494i
$490$	0.272299	−	0.134099i	0.0123012	−	0.00605797i
$491$			9.13241i			0.412140i	0.978537	+	0.206070i	$0.0660674\pi$
$491$			9.13241i			0.412140i	−0.978537	+	0.206070i	$0.933933\pi$
$492$	−28.5417	+	14.3246i	−1.28676	+	0.645804i
$493$			5.37149i			0.241920i
$494$			0.758653i			0.0341334i
$495$	1.86620	+	1.39089i	0.0838796	+	0.0625157i
$496$			0.702136i			0.0315268i
$497$	13.5957	+	8.45951i	0.609852	+	0.379461i
$498$	−1.65336	−	3.29431i	−0.0740890	−	0.147621i
$499$	−30.1101			−1.34791			−0.673956	−	0.738771i	$-0.735406\pi$
$499$	−30.1101			−1.34791			−0.673956	+	0.738771i	$0.735406\pi$
$500$	−6.70669			−0.299932
$501$	14.4995	−	7.27710i	0.647792	−	0.325117i
$502$		−	1.77103i		−	0.0790448i
$503$	−13.2998			−0.593008			−0.296504	−	0.955032i	$-0.595821\pi$
$503$	−13.2998			−0.593008			−0.296504	+	0.955032i	$0.595821\pi$
$504$	−3.73190	+	1.46343i	−0.166232	+	0.0651863i
$505$	0.797947			0.0355082
$506$		−	1.77796i		−	0.0790397i
$507$	−8.65027	+	4.34144i	−0.384172	+	0.192810i
$508$	29.1316			1.29251
$509$	−16.0178			−0.709978			−0.354989	−	0.934870i	$-0.615515\pi$
$509$	−16.0178			−0.709978			−0.354989	+	0.934870i	$0.615515\pi$
$510$	−0.0336886	−	0.0671242i	−0.00149176	−	0.00297231i
$511$	27.5506	+	17.1425i	1.21877	+	0.758339i
$512$			9.81821i			0.433908i
$513$	11.2470	+	1.99244i	0.496568	+	0.0879683i
$514$		−	0.521072i		−	0.0229835i
$515$			4.72410i			0.208169i
$516$	−9.10296	+	4.56863i	−0.400735	+	0.201123i
$517$		−	16.5215i		−	0.726616i
$518$	−1.43785	−	0.894658i	−0.0631757	−	0.0393090i
$519$	28.1302	−	14.1181i	1.23478	−	0.619716i
$520$	−0.470308			−0.0206244
$521$	18.5938			0.814609			0.407305	−	0.913292i	$-0.366469\pi$
$521$	18.5938			0.814609			0.407305	+	0.913292i	$0.366469\pi$
$522$	−1.22075	+	1.63792i	−0.0534306	+	0.0716899i
$523$		−	34.7173i		−	1.51808i	−0.651043	−	0.759041i	$-0.725668\pi$
$523$		−	34.7173i		−	1.51808i	0.651043	−	0.759041i	$-0.274332\pi$
$524$	−8.39790			−0.366864
$525$	−2.04332	+	22.2832i	−0.0891776	+	0.972520i
$526$	2.02054			0.0880996
$527$			0.179858i			0.00783473i
$528$	−6.87939	−	13.7071i	−0.299387	−	0.596525i
$529$	−15.2360			−0.662434
$530$	0.529357			0.0229938
$531$	2.00523	−	2.69050i	0.0870197	−	0.116758i
$532$	9.79667	+	6.09566i	0.424739	+	0.264280i
$533$			25.3014i			1.09593i
$534$	−0.540084	−	1.07611i	−0.0233717	−	0.0465679i
$535$		−	6.54692i		−	0.283048i
$536$		−	2.26663i		−	0.0979037i
$537$	7.33715	+	14.6192i	0.316621	+	0.630865i
$538$			2.08191i			0.0897576i
$539$	14.2437	−	7.01456i	0.613518	−	0.302138i
$540$	−0.615090	+	3.47209i	−0.0264693	+	0.149415i
$541$	−9.77731			−0.420359			−0.210180	−	0.977663i	$-0.567405\pi$
$541$	−9.77731			−0.420359			−0.210180	+	0.977663i	$0.567405\pi$
$542$	−2.72879			−0.117212
$543$	−13.3777	−	26.6550i	−0.574093	−	1.14387i
$544$			1.50495i			0.0645241i
$545$	−3.85772			−0.165247
$546$	−0.144420	+	1.57496i	−0.00618059	+	0.0674020i
$547$	−35.8789			−1.53407			−0.767037	−	0.641603i	$-0.778270\pi$
$547$	−35.8789			−1.53407			−0.767037	+	0.641603i	$0.778270\pi$
$548$		−	3.09549i		−	0.132233i
$549$	−28.5423	−	21.2726i	−1.21815	−	0.907893i
$550$	1.40401			0.0598674
$551$	11.8076			0.503019
$552$	4.83430	−	2.42626i	0.205762	−	0.103269i
$553$	5.69644	−	9.15507i	0.242237	−	0.389313i
$554$			0.554188i			0.0235452i
$555$	−2.67357	+	1.34182i	−0.113487	+	0.0569572i
$556$		−	4.76631i		−	0.202137i
$557$		−	29.9333i		−	1.26832i	−0.773204	−	0.634158i	$-0.781347\pi$
$557$		−	29.9333i		−	1.26832i	0.773204	−	0.634158i	$-0.218653\pi$
$558$	−0.0408752	+	0.0548438i	−0.00173039	+	0.00232172i
$559$			8.06952i			0.341304i
$560$	−1.86644	+	2.99966i	−0.0788714	+	0.126759i
$561$	−1.76221	−	3.51119i	−0.0744006	−	0.148243i
$562$	−0.550287			−0.0232125
$563$	−33.0068			−1.39107			−0.695535	−	0.718493i	$-0.744832\pi$
$563$	−33.0068			−1.39107			−0.695535	+	0.718493i	$0.744832\pi$
$564$	22.3706	−	11.2275i	0.941973	−	0.472762i
$565$			5.33867i			0.224600i
$566$	−1.80666			−0.0759398
$567$	22.9694	+	6.27731i	0.964626	+	0.263622i
$568$	3.05658			0.128251
$569$			29.9549i			1.25578i	0.778304	+	0.627888i	$0.216080\pi$
$569$			29.9549i			1.25578i	−0.778304	+	0.627888i	$0.783920\pi$
$570$	−0.147552	+	0.0740540i	−0.00618027	+	0.00310178i
$571$	−1.66141			−0.0695278			−0.0347639	−	0.999396i	$-0.511068\pi$
$571$	−1.66141			−0.0695278			−0.0347639	+	0.999396i	$0.511068\pi$
$572$	−12.2510			−0.512241
$573$	−11.8362	−	23.5835i	−0.494463	−	0.985213i
$574$	−2.64649	−	1.64669i	−0.110462	−	0.0687316i
$575$		−	30.1941i		−	1.25918i
$576$	13.6553	−	18.3218i	0.568970	−	0.763408i
$577$			39.7782i			1.65599i	0.560737	+	0.827994i	$0.310518\pi$
$577$			39.7782i			1.65599i	−0.560737	+	0.827994i	$0.689482\pi$
$578$			0.126768i			0.00527284i
$579$	19.3671	−	9.72006i	0.804870	−	0.403952i
$580$			3.64514i			0.151356i
$581$	−23.4643	+	37.7107i	−0.973461	+	1.56450i
$582$	−0.548569	+	0.275319i	−0.0227389	+	0.0114123i
$583$	27.6900			1.14680
$584$	6.19391			0.256306
$585$	2.24002	+	1.66949i	0.0926135	+	0.0690250i
$586$			0.987984i			0.0408132i
$587$	−1.32316			−0.0546127			−0.0273064	−	0.999627i	$-0.508693\pi$
$587$	−1.32316			−0.0546127			−0.0273064	+	0.999627i	$0.508693\pi$
$588$	19.1774	+	14.5195i	0.790864	+	0.598773i
$589$	0.395362			0.0162906
$590$			0.0485003i			0.00199672i
$591$	13.7451	+	27.3870i	0.565399	+	1.12655i
$592$	19.7111			0.810123
$593$	3.82275			0.156982			0.0784908	−	0.996915i	$-0.474990\pi$
$593$	3.82275			0.156982			0.0784908	+	0.996915i	$0.474990\pi$
$594$	0.260618	−	1.47115i	0.0106933	−	0.0603620i
$595$	−0.478103	+	0.768386i	−0.0196003	+	0.0315008i
$596$		−	0.282521i		−	0.0115725i
$597$	−4.53526	−	9.03646i	−0.185616	−	0.369838i
$598$		−	2.13410i		−	0.0872697i
$599$		−	2.08086i		−	0.0850215i	−0.999096	−	0.0425108i	$-0.986464\pi$
$599$		−	2.08086i		−	0.0850215i	0.999096	−	0.0425108i	$-0.0135357\pi$
$600$	1.91597	+	3.81755i	0.0782191	+	0.155851i
$601$			20.5433i			0.837977i	0.907992	+	0.418988i	$0.137615\pi$
$601$			20.5433i			0.837977i	−0.907992	+	0.418988i	$0.862385\pi$
$602$	−0.844060	−	0.525189i	−0.0344013	−	0.0214051i
$603$	−8.04607	+	10.7957i	−0.327661	+	0.439635i
$604$	−7.65990			−0.311677
$605$	2.00285			0.0814275
$606$	−0.229758	−	0.457791i	−0.00933329	−	0.0185965i
$607$			42.4857i			1.72444i	0.506533	+	0.862220i	$0.330927\pi$
$607$			42.4857i			1.72444i	−0.506533	+	0.862220i	$0.669073\pi$
$608$	3.30816			0.134164
$609$	24.5124	+	2.24773i	0.993294	+	0.0910825i
$610$	0.514518			0.0208322
$611$		−	19.8309i		−	0.802274i
$612$	3.55671	−	4.77217i	0.143771	−	0.192904i
$613$	−14.7409			−0.595381			−0.297691	−	0.954662i	$-0.596216\pi$
$613$	−14.7409			−0.595381			−0.297691	+	0.954662i	$0.596216\pi$
$614$	2.80099			0.113039
$615$	−4.92092	+	2.46973i	−0.198431	+	0.0995893i
$616$	1.60113	−	2.57326i	0.0645112	−	0.103679i
$617$		−	41.0238i		−	1.65156i	−0.563995	−	0.825778i	$-0.690736\pi$
$617$		−	41.0238i		−	1.65156i	0.563995	−	0.825778i	$-0.309264\pi$
$618$	2.71027	−	1.36024i	0.109023	−	0.0547170i
$619$		−	35.6579i		−	1.43321i	−0.697478	−	0.716606i	$-0.745695\pi$
$619$		−	35.6579i		−	1.43321i	0.697478	−	0.716606i	$-0.254305\pi$
$620$			0.122053i			0.00490177i
$621$	−31.6379	−	5.60474i	−1.26959	−	0.224911i
$622$		−	3.66277i		−	0.146864i
$623$	−7.66479	+	12.3185i	−0.307083	+	0.493531i
$624$	−8.25740	−	16.4528i	−0.330560	−	0.658638i
$625$	23.2587			0.930348
$626$	0.248861			0.00994647
$627$	−7.71826	+	3.87368i	−0.308238	+	0.154700i
$628$			5.59672i			0.223334i
$629$	5.04917			0.201324
$630$	−0.320414	+	0.125647i	−0.0127656	+	0.00500590i
$631$	−4.64852			−0.185055			−0.0925273	−	0.995710i	$-0.529495\pi$
$631$	−4.64852			−0.185055			−0.0925273	+	0.995710i	$0.529495\pi$
$632$		−	2.05824i		−	0.0818722i
$633$	−17.8590	+	8.96315i	−0.709831	+	0.356253i
$634$	−2.11843			−0.0841338
$635$	5.02263			0.199317
$636$	18.8172	+	37.4931i	0.746151	+	1.48670i
$637$	17.0968	−	8.41964i	0.677400	−	0.333598i
$638$		−	1.54447i		−	0.0611462i
$639$	−14.5581	−	10.8502i	−0.575911	−	0.429228i
$640$			1.35982i			0.0537516i
$641$			24.4456i			0.965542i	0.875747	+	0.482771i	$0.160370\pi$
$641$			24.4456i			0.965542i	−0.875747	+	0.482771i	$0.839630\pi$
$642$	−3.75604	+	1.88510i	−0.148239	+	0.0743989i
$643$		−	34.7178i		−	1.36914i	−0.728949	−	0.684568i	$-0.759991\pi$
$643$		−	34.7178i		−	1.36914i	0.728949	−	0.684568i	$-0.240009\pi$
$644$	−27.5581	−	17.1471i	−1.08594	−	0.675691i
$645$	−1.56946	+	0.787686i	−0.0617973	+	0.0310151i
$646$	0.278659			0.0109637
$647$	−2.53288			−0.0995779			−0.0497890	−	0.998760i	$-0.515855\pi$
$647$	−2.53288			−0.0995779			−0.0497890	+	0.998760i	$0.515855\pi$
$648$	4.35574	−	1.29896i	0.171110	−	0.0510279i
$649$			2.53699i			0.0995856i
$650$	1.68525			0.0661010
$651$	0.820769	+	0.0752624i	0.0321685	+	0.00294977i
$652$	9.85324			0.385883
$653$			24.0525i			0.941247i	0.882334	+	0.470624i	$0.155971\pi$
$653$			24.0525i			0.941247i	−0.882334	+	0.470624i	$0.844029\pi$
$654$	1.11078	+	2.21322i	0.0434349	+	0.0865437i
$655$	−1.44790			−0.0565739
$656$	36.2800			1.41650
$657$	−29.5008	−	21.9870i	−1.15094	−	0.857796i
$658$	2.07429	+	1.29066i	0.0808641	+	0.0503151i
$659$			27.5464i			1.07305i	0.843883	+	0.536527i	$0.180264\pi$
$659$			27.5464i			1.07305i	−0.843883	+	0.536527i	$0.819736\pi$
$660$	−1.19585	−	2.38272i	−0.0465485	−	0.0927474i
$661$		−	8.38514i		−	0.326144i	−0.986614	−	0.163072i	$-0.947860\pi$
$661$		−	8.38514i		−	0.326144i	0.986614	−	0.163072i	$-0.0521403\pi$
$662$			1.63838i			0.0636773i
$663$	−2.11520	−	4.21451i	−0.0821475	−	0.163678i
$664$			8.47809i			0.329014i
$665$	1.68906	+	1.05096i	0.0654989	+	0.0407546i
$666$	1.53964	+	1.14749i	0.0596597	+	0.0444645i
$667$	−33.2148			−1.28608
$668$	−18.5824			−0.718976
$669$	−13.2956	−	26.4913i	−0.514037	−	1.02421i
$670$		−	0.194609i		−	0.00751840i
$671$	26.9138			1.03900
$672$	6.86772	+	0.629753i	0.264928	+	0.0242932i
$673$	−22.2619			−0.858135			−0.429067	−	0.903272i	$-0.641158\pi$
$673$	−22.2619			−0.858135			−0.429067	+	0.903272i	$0.641158\pi$
$674$		−	3.83814i		−	0.147840i
$675$	4.42595	−	24.9838i	0.170355	−	0.961627i
$676$	11.0861			0.426388
$677$	4.68755			0.180157			0.0900786	−	0.995935i	$-0.471288\pi$
$677$	4.68755			0.180157			0.0900786	+	0.995935i	$0.471288\pi$
$678$	3.06285	−	1.53720i	0.117628	−	0.0590358i
$679$	6.27960	+	3.90728i	0.240989	+	0.149948i
$680$			0.172748i			0.00662458i
$681$	−21.2469	+	10.6635i	−0.814182	+	0.408625i
$682$		−	0.0517147i		−	0.00198026i
$683$			13.5066i			0.516816i	0.966036	+	0.258408i	$0.0831979\pi$
$683$			13.5066i			0.516816i	−0.966036	+	0.258408i	$0.916802\pi$
$684$	−10.4901	−	7.81833i	−0.401101	−	0.298941i
$685$		−	0.533698i		−	0.0203916i
$686$	−0.232030	+	2.33628i	−0.00885895	+	0.0891994i
$687$	8.45201	+	16.8405i	0.322464	+	0.642507i
$688$	11.5710			0.441139
$689$	33.2366			1.26621
$690$	0.415064	−	0.208314i	0.0158012	−	0.00793039i
$691$			17.7351i			0.674676i	0.941384	+	0.337338i	$0.109526\pi$
$691$			17.7351i			0.674676i	−0.941384	+	0.337338i	$0.890474\pi$
$692$	−36.0513			−1.37047
$693$	−16.7605	+	6.57246i	−0.636678	+	0.249667i
$694$	2.97123			0.112787
$695$		−	0.821768i		−	0.0311714i
$696$	4.19945	−	2.10764i	0.159180	−	0.0798900i
$697$	9.29342			0.352013
$698$	3.13350			0.118605
$699$	−6.92524	−	13.7985i	−0.261937	−	0.521906i
$700$	13.5407	−	21.7620i	0.511791	−	0.822528i
$701$			5.15378i			0.194655i	0.995252	+	0.0973277i	$0.0310295\pi$
$701$			5.15378i			0.194655i	−0.995252	+	0.0973277i	$0.968971\pi$
$702$	0.312822	−	1.76583i	0.0118067	−	0.0666471i
$703$		−	11.0990i		−	0.418608i
$704$			17.2764i			0.651131i
$705$	3.85696	−	1.93575i	0.145261	−	0.0729044i
$706$			4.10384i			0.154450i
$707$	−3.26069	+	5.24044i	−0.122631	+	0.197087i
$708$	−3.43516	+	1.72405i	−0.129101	+	0.0647939i
$709$	8.05612			0.302554			0.151277	−	0.988491i	$-0.451661\pi$
$709$	8.05612			0.302554			0.151277	+	0.988491i	$0.451661\pi$
$710$	0.262432			0.00984892
$711$	−7.30629	+	9.80313i	−0.274007	+	0.367646i
$712$			2.76944i			0.103789i
$713$	−1.11216			−0.0416505
$714$	0.578495	+	0.0530465i	0.0216496	+	0.00198522i
$715$	−2.11222			−0.0789925
$716$		−	18.7358i		−	0.700189i
$717$	18.5238	+	36.9085i	0.691785	+	1.37837i
$718$	0.0297451			0.00111008
$719$	38.9758			1.45355			0.726776	−	0.686875i	$-0.241018\pi$
$719$	38.9758			1.45355			0.726776	+	0.686875i	$0.241018\pi$
$720$	2.39391	−	3.21199i	0.0892156	−	0.119704i
$721$	−31.0251	−	19.3043i	−1.15543	−	0.718931i
$722$			1.79604i			0.0668416i
$723$	−3.54405	−	7.06148i	−0.131805	−	0.262619i
$724$			34.1607i			1.26957i
$725$		−	26.2290i		−	0.974120i
$726$	−0.576695	−	1.14906i	−0.0214031	−	0.0426455i
$727$		−	35.1536i		−	1.30378i	−0.758315	−	0.651888i	$-0.773977\pi$
$727$		−	35.1536i		−	1.30378i	0.758315	−	0.651888i	$-0.226023\pi$
$728$	1.92185	−	3.08870i	0.0712283	−	0.114475i
$729$	−25.3569	−	9.27516i	−0.939144	−	0.343525i
$730$	0.531797			0.0196827
$731$	2.96400			0.109628
$732$	18.2897	+	36.4421i	0.676007	+	1.34694i
$733$			13.6736i			0.505047i	0.967591	+	0.252524i	$0.0812605\pi$
$733$			13.6736i			0.505047i	−0.967591	+	0.252524i	$0.918739\pi$
$734$	2.14515			0.0791788
$735$	3.30641	+	2.50333i	0.121959	+	0.0923366i
$736$	−9.30588			−0.343019
$737$		−	10.1798i		−	0.374976i
$738$	2.83383	+	2.11206i	0.104315	+	0.0777460i
$739$	−30.0352			−1.10486			−0.552431	−	0.833558i	$-0.686300\pi$
$739$	−30.0352			−1.10486			−0.552431	+	0.833558i	$0.686300\pi$
$740$	3.42641			0.125957
$741$	−9.26430	+	4.64961i	−0.340333	+	0.170808i
$742$	−2.16314	+	3.47650i	−0.0794113	+	0.127626i
$743$			19.0114i			0.697462i	0.937223	+	0.348731i	$0.113387\pi$
$743$			19.0114i			0.697462i	−0.937223	+	0.348731i	$0.886613\pi$
$744$	0.140614	−	0.0705718i	0.00515514	−	0.00258729i
$745$		−	0.0487098i		−	0.00178459i
$746$			2.97318i			0.108856i
$747$	30.0954	−	40.3801i	1.10113	−	1.47743i
$748$			4.49990i			0.164533i
$749$	42.9963	+	26.7530i	1.57105	+	0.977534i
$750$	0.332945	+	0.663389i	0.0121574	+	0.0242235i
$751$	−49.2225			−1.79616			−0.898078	−	0.439837i	$-0.855036\pi$
$751$	−49.2225			−1.79616			−0.898078	+	0.439837i	$0.855036\pi$
$752$	−28.4358			−1.03695
$753$	21.6269	−	10.8542i	0.788129	−	0.395550i
$754$		−	1.85384i		−	0.0675130i
$755$	−1.32066			−0.0480636
$756$	−20.2891	−	18.2277i	−0.737909	−	0.662936i
$757$	−24.8810			−0.904314			−0.452157	−	0.891938i	$-0.649345\pi$
$757$	−24.8810			−0.904314			−0.452157	+	0.891938i	$0.649345\pi$
$758$		−	2.54080i		−	0.0922859i
$759$	21.7115	−	10.8967i	0.788078	−	0.395524i
$760$	0.379733			0.0137744
$761$	−25.8683			−0.937726			−0.468863	−	0.883271i	$-0.655336\pi$
$761$	−25.8683			−0.937726			−0.468863	+	0.883271i	$0.655336\pi$
$762$	−1.44620	−	2.88154i	−0.0523903	−	0.104387i
$763$	15.7640	−	25.3352i	0.570696	−	0.917196i
$764$			30.2243i			1.09348i
$765$	0.613218	−	0.822778i	0.0221710	−	0.0297476i
$766$		−	4.10726i		−	0.148401i
$767$			3.04517i			0.109955i
$768$	−22.8021	+	11.4440i	−0.822802	+	0.412952i
$769$		−	40.4873i		−	1.46001i	−0.683442	−	0.730005i	$-0.739518\pi$
$769$		−	40.4873i		−	1.46001i	0.683442	−	0.730005i	$-0.260482\pi$
$770$	0.137470	−	0.220935i	0.00495406	−	0.00796194i
$771$	6.36308	−	3.19353i	0.229161	−	0.115012i
$772$	−24.8207			−0.893315
$773$	49.4031			1.77691			0.888453	−	0.458967i	$-0.151780\pi$
$773$	49.4031			1.77691			0.888453	+	0.458967i	$0.151780\pi$
$774$	0.903808	+	0.673610i	0.0324867	+	0.0242124i
$775$		−	0.878246i		−	0.0315475i
$776$	1.41177			0.0506798
$777$	2.11285	−	23.0415i	0.0757981	−	0.826610i
$778$	−4.22283			−0.151396
$779$		−	20.4287i		−	0.731934i
$780$	−1.43539	−	2.86000i	−0.0513953	−	0.102405i
$781$	13.7275			0.491210
$782$	−0.783871			−0.0280312
$783$	−27.4832	−	4.86872i	−0.982168	−	0.173994i
$784$	−12.0730	−	24.5153i	−0.431179	−	0.875546i
$785$			0.964940i			0.0344402i
$786$	0.416902	+	0.830674i	0.0148704	+	0.0296291i
$787$		−	40.8196i		−	1.45506i	−0.686075	−	0.727531i	$-0.740668\pi$
$787$		−	40.8196i		−	1.45506i	0.686075	−	0.727531i	$-0.259332\pi$
$788$		−	35.0989i		−	1.25035i
$789$	12.3834	+	24.6738i	0.440861	+	0.878411i
$790$		−	0.176716i		−	0.00628728i
$791$	−35.0612	−	21.8157i	−1.24663	−	0.775677i
$792$	−2.05361	+	2.75541i	−0.0729720	+	0.0979092i
$793$	32.3049			1.14718
$794$	2.64566			0.0938909
$795$	3.24431	+	6.46425i	0.115064	+	0.229263i
$796$			11.5810i			0.410478i
$797$	42.2771			1.49753			0.748765	−	0.662835i	$-0.230647\pi$
$797$	42.2771			1.49753			0.748765	+	0.662835i	$0.230647\pi$
$798$	0.116606	−	1.27164i	0.00412782	−	0.0450157i
$799$	−7.28406			−0.257692
$800$		−	7.34866i		−	0.259814i
$801$	9.83091	−	13.1905i	0.347358	−	0.466063i
$802$	2.74601			0.0969651
$803$	27.8177			0.981665
$804$	13.7837	−	6.91783i	0.486113	−	0.243973i
$805$	−4.75134	−	2.95636i	−0.167463	−	0.104198i
$806$		−	0.0620736i		−	0.00218645i
$807$	−25.4233	+	12.7596i	−0.894943	+	0.449158i
$808$			1.17815i			0.0414472i
$809$		−	10.7872i		−	0.379257i	−0.981856	−	0.189629i	$-0.939272\pi$
$809$		−	10.7872i		−	0.379257i	0.981856	−	0.189629i	$-0.0607284\pi$
$810$	0.373976	−	0.111526i	0.0131402	−	0.00391862i
$811$			18.3567i			0.644592i	0.946639	+	0.322296i	$0.104455\pi$
$811$			18.3567i			0.644592i	−0.946639	+	0.322296i	$0.895545\pi$
$812$	−23.9391	−	14.8953i	−0.840098	−	0.522724i
$813$	−16.7241	−	33.3226i	−0.586541	−	1.16868i
$814$	−1.45179			−0.0508853
$815$	1.69881			0.0595068
$816$	−6.04324	+	3.03301i	−0.211556	+	0.106177i
$817$		−	6.51544i		−	0.227946i
$818$	0.0799756			0.00279628
$819$	−20.1177	+	7.88898i	−0.702971	+	0.275663i
$820$	6.30659			0.220236
$821$			8.00926i			0.279525i	0.990185	+	0.139763i	$0.0446339\pi$
$821$			8.00926i			0.279525i	−0.990185	+	0.139763i	$0.955366\pi$
$822$	−0.306188	+	0.153671i	−0.0106795	+	0.00535990i
$823$	−20.8202			−0.725746			−0.362873	−	0.931839i	$-0.618204\pi$
$823$	−20.8202			−0.725746			−0.362873	+	0.931839i	$0.618204\pi$
$824$	−6.97503			−0.242987
$825$	8.60488	+	17.1451i	0.299583	+	0.596917i
$826$	−0.318521	−	0.198189i	−0.0110828	−	0.00689588i
$827$		−	53.5695i		−	1.86279i	−0.364004	−	0.931397i	$-0.618591\pi$
$827$		−	53.5695i		−	1.86279i	0.364004	−	0.931397i	$-0.381409\pi$
$828$	29.5088	+	21.9930i	1.02550	+	0.764310i
$829$			1.75398i			0.0609183i	0.999536	+	0.0304591i	$0.00969695\pi$
$829$			1.75398i			0.0609183i	−0.999536	+	0.0304591i	$0.990303\pi$
$830$			0.727913i			0.0252662i
$831$	−6.76748	+	3.39649i	−0.234761	+	0.117823i
$832$			20.7371i			0.718929i
$833$	−3.09260	−	6.27979i	−0.107152	−	0.217582i
$834$	−0.471457	+	0.236617i	−0.0163252	+	0.00819338i
$835$	−3.20383			−0.110873
$836$	9.89163			0.342109
$837$	−0.920240	−	0.163023i	−0.0318082	−	0.00563490i
$838$			1.69942i			0.0587056i
$839$	−4.70753			−0.162522			−0.0812609	−	0.996693i	$-0.525895\pi$
$839$	−4.70753			−0.162522			−0.0812609	+	0.996693i	$0.525895\pi$
$840$	0.788324	+	0.0722873i	0.0271997	+	0.00249415i
$841$	0.147073			0.00507148
$842$			0.385243i			0.0132763i
$843$	−3.37259	−	6.71984i	−0.116158	−	0.231444i
$844$	22.8879			0.787833
$845$	1.91137			0.0657531
$846$	−2.22112	−	1.65541i	−0.0763636	−	0.0569140i
$847$	−8.18436	+	13.1535i	−0.281218	+	0.451961i
$848$		−	47.6583i		−	1.63659i
$849$	−11.0726	−	22.0621i	−0.380012	−	0.757169i
$850$		−	0.619006i		−	0.0212317i
$851$			31.2217i			1.07026i
$852$	9.32877	+	18.5875i	0.319598	+	0.636796i
$853$		−	17.7282i		−	0.607002i	−0.952831	−	0.303501i	$-0.901844\pi$
$853$		−	17.7282i		−	0.607002i	0.952831	−	0.303501i	$-0.0981556\pi$
$854$	−2.10250	+	3.37904i	−0.0719461	+	0.115628i
$855$	−1.80862	−	1.34797i	−0.0618536	−	0.0460996i
$856$	9.66639			0.330390
$857$	−25.5092			−0.871377			−0.435688	−	0.900098i	$-0.643495\pi$
$857$	−25.5092			−0.871377			−0.435688	+	0.900098i	$0.643495\pi$
$858$	0.608185	+	1.21180i	0.0207631	+	0.0413703i
$859$		−	56.7276i		−	1.93552i	−0.251876	−	0.967760i	$-0.581047\pi$
$859$		−	56.7276i		−	1.93552i	0.251876	−	0.967760i	$-0.418953\pi$
$860$	2.01140			0.0685880
$861$	3.88888	−	42.4099i	0.132533	−	1.44532i
$862$	−1.86680			−0.0635834
$863$			41.9117i			1.42669i	0.700813	+	0.713345i	$0.252821\pi$
$863$			41.9117i			1.42669i	−0.700813	+	0.713345i	$0.747179\pi$
$864$	−7.70004	−	1.36408i	−0.261961	−	0.0464071i
$865$	−6.21567			−0.211339
$866$	−3.49308			−0.118700
$867$	−1.54802	+	0.776930i	−0.0525737	+	0.0263859i
$868$	−0.801571	−	0.498752i	−0.0272071	−	0.0169287i
$869$		−	9.24382i		−	0.313575i
$870$	0.360557	−	0.180958i	0.0122240	−	0.00613506i
$871$		−	12.2189i		−	0.414021i
$872$		−	5.69584i		−	0.192886i
$873$	−6.72411	−	5.01150i	−0.227577	−	0.169613i
$874$			1.72310i			0.0582846i
$875$	4.72510	−	7.59396i	0.159737	−	0.256723i
$876$	18.9040	+	37.6660i	0.638706	+	1.27261i
$877$	39.4701			1.33281			0.666405	−	0.745590i	$-0.267832\pi$
$877$	39.4701			1.33281			0.666405	+	0.745590i	$0.267832\pi$
$878$	0.821492			0.0277240
$879$	−12.0648	+	6.05513i	−0.406935	+	0.204234i
$880$			3.02873i			0.102099i
$881$	−29.3959			−0.990375			−0.495187	−	0.868786i	$-0.664901\pi$
$881$	−29.3959			−0.990375			−0.495187	+	0.868786i	$0.664901\pi$
$882$	0.484148	−	2.61773i	0.0163021	−	0.0881434i
$883$	34.8614			1.17318			0.586590	−	0.809884i	$-0.300470\pi$
$883$	34.8614			1.17318			0.586590	+	0.809884i	$0.300470\pi$
$884$			5.40127i			0.181664i
$885$	−0.592262	+	0.297247i	−0.0199087	+	0.00999185i
$886$	1.08115			0.0363219
$887$	−4.26278			−0.143130			−0.0715652	−	0.997436i	$-0.522799\pi$
$887$	−4.26278			−0.143130			−0.0715652	+	0.997436i	$0.522799\pi$
$888$	−1.98117	−	3.94746i	−0.0664837	−	0.132468i
$889$	−20.5242	+	32.9856i	−0.688360	+	1.10630i
$890$			0.237779i			0.00797036i
$891$	19.5622	−	5.83379i	0.655359	−	0.195439i
$892$			33.9510i			1.13676i
$893$			16.0118i			0.535813i
$894$	−0.0279454	+	0.0140254i	−0.000934633	+	0.000469078i
$895$		−	3.23027i		−	0.107976i
$896$	−8.93049	−	5.55671i	−0.298347	−	0.185636i
$897$	26.0605	−	13.0794i	0.870136	−	0.436708i
$898$	−1.41451			−0.0472029
$899$	−0.966105			−0.0322214
$900$	−17.3674	+	23.3025i	−0.578914	+	0.776750i
$901$		−	12.2081i		−	0.406710i
$902$	−2.67215			−0.0889727
$903$	1.24030	−	13.5260i	0.0412746	−	0.450117i
$904$	−7.88243			−0.262166
$905$			5.88971i			0.195780i
$906$	0.380266	+	0.757675i	0.0126335	+	0.0251721i
$907$	16.2612			0.539945			0.269973	−	0.962868i	$-0.412985\pi$
$907$	16.2612			0.539945			0.269973	+	0.962868i	$0.412985\pi$
$908$	27.2297			0.903650
$909$	4.18218	−	5.61139i	0.138714	−	0.186118i
$910$	0.165006	−	0.265190i	0.00546990	−	0.00879097i
$911$			1.74435i			0.0577929i	0.999582	+	0.0288965i	$0.00919931\pi$
$911$			1.74435i			0.0577929i	−0.999582	+	0.0288965i	$0.990801\pi$
$912$	6.66713	+	13.2842i	0.220771	+	0.439883i
$913$			38.0763i			1.26014i
$914$		−	3.90889i		−	0.129295i
$915$	3.15336	+	6.28304i	0.104247	+	0.207711i
$916$		−	21.5826i		−	0.713111i
$917$	5.91661	−	9.50891i	0.195384	−	0.314012i
$918$	−0.648605	−	0.114902i	−0.0214072	−	0.00379233i
$919$	18.0362			0.594960			0.297480	−	0.954728i	$-0.403854\pi$
$919$	18.0362			0.594960			0.297480	+	0.954728i	$0.403854\pi$
$920$	−1.06819			−0.0352172
$921$	17.1666	+	34.2043i	0.565659	+	1.12707i
$922$			2.69439i			0.0887351i
$923$	16.4773			0.542356
$924$	20.5350	+	1.88300i	0.675551	+	0.0619463i
$925$	−24.6551			−0.810655
$926$			0.562448i			0.0184832i
$927$	33.2212	+	24.7599i	1.09113	+	0.813221i
$928$	−8.08381			−0.265364
$929$	−44.7511			−1.46824			−0.734119	−	0.679021i	$-0.762404\pi$
$929$	−44.7511			−1.46824			−0.734119	+	0.679021i	$0.762404\pi$
$930$	0.0120728	−	0.00605916i	0.000395883	−	0.000198688i
$931$	−13.8042	+	6.79813i	−0.452414	+	0.222800i
$932$			17.6840i			0.579257i
$933$	44.7279	−	22.4483i	1.46433	−	0.734923i
$934$		−	3.94683i		−	0.129144i
$935$			0.775835i			0.0253725i
$936$	−2.46497	+	3.30734i	−0.0805701	+	0.108104i
$937$		−	40.2695i		−	1.31555i	−0.753215	−	0.657774i	$-0.771498\pi$
$937$		−	40.2695i		−	1.31555i	0.753215	−	0.657774i	$-0.228502\pi$
$938$	1.27808	+	0.795241i	0.0417306	+	0.0259655i
$939$	1.52521	+	3.03896i	0.0497733	+	0.0991728i
$940$	−4.94303			−0.161224
$941$	−41.1920			−1.34282			−0.671410	−	0.741086i	$-0.734311\pi$
$941$	−41.1920			−1.34282			−0.671410	+	0.741086i	$0.734311\pi$
$942$	0.553597	−	0.277842i	0.0180372	−	0.00905258i
$943$			57.4661i			1.87135i
$944$	4.36651			0.142118
$945$	−3.49809	−	3.14267i	−0.113793	−	0.102231i
$946$	−0.852242			−0.0277088
$947$		−	22.7979i		−	0.740831i	−0.928866	−	0.370416i	$-0.879215\pi$
$947$		−	22.7979i		−	0.740831i	0.928866	−	0.370416i	$-0.120785\pi$
$948$	12.5164	−	6.28179i	0.406514	−	0.204023i
$949$	33.3898			1.08388
$950$	−1.36069			−0.0441467
$951$	−12.9834	−	25.8693i	−0.421016	−	0.838869i
$952$	−1.13451	−	0.705909i	−0.0367695	−	0.0228787i
$953$			0.295255i			0.00956426i	0.999989	+	0.00478213i	$0.00152221\pi$
$953$			0.295255i			0.00956426i	−0.999989	+	0.00478213i	$0.998478\pi$
$954$	2.77445	−	3.72259i	0.0898263	−	0.120523i
$955$			5.21102i			0.168625i
$956$		−	47.3016i		−	1.52984i
$957$	18.8603	−	9.46571i	0.609668	−	0.305983i
$958$			4.79516i			0.154925i
$959$	3.50501	+	2.18088i	0.113183	+	0.0704242i
$960$	−4.03319	+	2.02420i	−0.130171	+	0.0653307i
$961$	30.9677			0.998956
$962$	−1.74260			−0.0561837
$963$	−46.0398	−	34.3136i	−1.48361	−	1.10574i
$964$			9.04991i			0.291478i
$965$	−4.27937			−0.137758
$966$	−0.328015	+	3.57714i	−0.0105537	+	0.115093i
$967$	10.0207			0.322244			0.161122	−	0.986935i	$-0.448489\pi$
$967$	10.0207			0.322244			0.161122	+	0.986935i	$0.448489\pi$
$968$			2.95717i			0.0950469i
$969$	1.70784	+	3.40285i	0.0548637	+	0.109315i
$970$	0.121212			0.00389189
$971$	7.97452			0.255915			0.127957	−	0.991780i	$-0.459158\pi$
$971$	7.97452			0.255915			0.127957	+	0.991780i	$0.459158\pi$
$972$	21.1930	+	22.5234i	0.679764	+	0.722437i
$973$	5.39688	+	3.35803i	0.173016	+	0.107654i
$974$			4.63183i			0.148413i
$975$	10.3285	+	20.5795i	0.330777	+	0.659070i
$976$		−	46.3224i		−	1.48274i
$977$			32.4948i			1.03960i	0.854288	+	0.519800i	$0.173994\pi$
$977$			32.4948i			1.03960i	−0.854288	+	0.519800i	$0.826006\pi$
$978$	−0.489151	−	0.974628i	−0.0156413	−	0.0311652i
$979$			12.4379i			0.397518i
$980$	−2.09867	−	4.26152i	−0.0670394	−	0.136129i
$981$	−20.2190	+	27.1286i	−0.645544	+	0.866150i
$982$	−1.15769			−0.0369435
$983$	−62.1602			−1.98260			−0.991301	−	0.131611i	$-0.957985\pi$
$983$	−62.1602			−1.98260			−0.991301	+	0.131611i	$0.957985\pi$
$984$	−3.64651	−	7.26563i	−0.116246	−	0.231620i
$985$		−	6.05146i		−	0.192815i
$986$	−0.680931			−0.0216853
$987$	−3.04805	+	33.2403i	−0.0970206	+	1.05805i
$988$	11.8730			0.377731
$989$			18.3280i			0.582795i
$990$	−0.176319	+	0.236574i	−0.00560380	+	0.00751882i
$991$	−7.67487			−0.243800			−0.121900	−	0.992542i	$-0.538899\pi$
$991$	−7.67487			−0.243800			−0.121900	+	0.992542i	$0.538899\pi$
$992$	−0.270676			−0.00859399
$993$	−20.0071	+	10.0412i	−0.634905	+	0.318649i
$994$	−1.07239	+	1.72350i	−0.0340142	+	0.0546661i
$995$			1.99670i			0.0632998i
$996$	−51.5564	+	25.8753i	−1.63363	+	0.819892i
$997$			58.0102i			1.83720i	0.395188	+	0.918600i	$0.370679\pi$
$997$			58.0102i			1.83720i	−0.395188	+	0.918600i	$0.629321\pi$
$998$		−	3.81698i		−	0.120824i
$999$	−4.57657	+	25.8340i	−0.144796	+	0.817352i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.d.b.188.12	yes	22
3.2	odd	2		357.2.d.a.188.11	✓	22
7.6	odd	2		357.2.d.a.188.12	yes	22
21.20	even	2	inner	357.2.d.b.188.11	yes	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.d.a.188.11	✓	22	3.2	odd	2
357.2.d.a.188.12	yes	22	7.6	odd	2
357.2.d.b.188.11	yes	22	21.20	even	2	inner
357.2.d.b.188.12	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)

\(f(q)\)	\(=\)	\(q+0.126768i q^{2} +(-1.54802 + 0.776930i) q^{3} +1.98393 q^{4} +0.342053 q^{5} +(-0.0984896 - 0.196239i) q^{6} +(-1.39775 + 2.24640i) q^{7} +0.505033i q^{8} +(1.79276 - 2.40541i) q^{9} +O(q^{10})\)	\(q+0.126768i q^{2} +(-1.54802 + 0.776930i) q^{3} +1.98393 q^{4} +0.342053 q^{5} +(-0.0984896 - 0.196239i) q^{6} +(-1.39775 + 2.24640i) q^{7} +0.505033i q^{8} +(1.79276 - 2.40541i) q^{9} +0.0433612i q^{10} +2.26817i q^{11} +(-3.07117 + 1.54137i) q^{12} +2.72251i q^{13} +(-0.284770 - 0.177189i) q^{14} +(-0.529506 + 0.265751i) q^{15} +3.90384 q^{16} +1.00000 q^{17} +(0.304929 + 0.227264i) q^{18} -2.19819i q^{19} +0.678609 q^{20} +(0.418455 - 4.56343i) q^{21} -0.287531 q^{22} +6.18352i q^{23} +(-0.392375 - 0.781804i) q^{24} -4.88300 q^{25} -0.345126 q^{26} +(-0.906399 + 5.11649i) q^{27} +(-2.77303 + 4.45669i) q^{28} +5.37149i q^{29} +(-0.0336886 - 0.0671242i) q^{30} +0.179858i q^{31} +1.50495i q^{32} +(-1.76221 - 3.51119i) q^{33} +0.126768i q^{34} +(-0.478103 + 0.768386i) q^{35} +(3.55671 - 4.77217i) q^{36} +5.04917 q^{37} +0.278659 q^{38} +(-2.11520 - 4.21451i) q^{39} +0.172748i q^{40} +9.29342 q^{41} +(0.578495 + 0.0530465i) q^{42} +2.96400 q^{43} +4.49990i q^{44} +(0.613218 - 0.822778i) q^{45} -0.783871 q^{46} -7.28406 q^{47} +(-6.04324 + 3.03301i) q^{48} +(-3.09260 - 6.27979i) q^{49} -0.619006i q^{50} +(-1.54802 + 0.776930i) q^{51} +5.40127i q^{52} -12.2081i q^{53} +(-0.648605 - 0.114902i) q^{54} +0.775835i q^{55} +(-1.13451 - 0.705909i) q^{56} +(1.70784 + 3.40285i) q^{57} -0.680931 q^{58} +1.11852 q^{59} +(-1.05050 + 0.527231i) q^{60} -11.8658i q^{61} -0.0228002 q^{62} +(2.89769 + 7.38941i) q^{63} +7.61690 q^{64} +0.931242i q^{65} +(0.445105 - 0.223391i) q^{66} -4.48809 q^{67} +1.98393 q^{68} +(-4.80416 - 9.57225i) q^{69} +(-0.0974065 - 0.0606080i) q^{70} -6.05224i q^{71} +(1.21481 + 0.905404i) q^{72} -12.2644i q^{73} +0.640071i q^{74} +(7.55900 - 3.79375i) q^{75} -4.36106i q^{76} +(-5.09522 - 3.17034i) q^{77} +(0.534264 - 0.268139i) q^{78} -4.07544 q^{79} +1.33532 q^{80} +(-2.57202 - 8.62466i) q^{81} +1.17810i q^{82} +16.7872 q^{83} +(0.830185 - 9.05353i) q^{84} +0.342053 q^{85} +0.375739i q^{86} +(-4.17327 - 8.31520i) q^{87} -1.14550 q^{88} +5.48367 q^{89} +(0.104302 + 0.0777362i) q^{90} +(-6.11584 - 3.80538i) q^{91} +12.2677i q^{92} +(-0.139737 - 0.278424i) q^{93} -0.923384i q^{94} -0.751897i q^{95} +(-1.16924 - 2.32969i) q^{96} -2.79541i q^{97} +(0.796075 - 0.392042i) q^{98} +(5.45589 + 4.06629i) 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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