LMFDB - Embedded newform 756.2.n.b.19.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [756,2,Mod(19,756)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(756, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 5]))

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

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

chi := DirichletCharacter("756.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.n (of order $6$, degree $2$, not 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:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$42$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.18
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.447581 + 1.34152i) q^{2} +(-1.59934 - 1.20088i) q^{4} +3.94623i q^{5} +(-2.37341 + 1.16916i) q^{7} +(2.32683 - 1.60806i) q^{8} +O(q^{10})$	\(q+(-0.447581 + 1.34152i) q^{2} +(-1.59934 - 1.20088i) q^{4} +3.94623i q^{5} +(-2.37341 + 1.16916i) q^{7} +(2.32683 - 1.60806i) q^{8} +(-5.29393 - 1.76626i) q^{10} +4.89244i q^{11} +(1.13829 - 0.657191i) q^{13} +(-0.506153 - 3.70726i) q^{14} +(1.11579 + 3.84122i) q^{16} +(-1.67931 + 0.969547i) q^{17} +(1.49477 - 2.58902i) q^{19} +(4.73893 - 6.31137i) q^{20} +(-6.56330 - 2.18976i) q^{22} -3.37433i q^{23} -10.5727 q^{25} +(0.372157 + 1.82118i) q^{26} +(5.19991 + 0.980288i) q^{28} +(1.32976 - 2.30322i) q^{29} +(-0.443302 + 0.767822i) q^{31} +(-5.65248 - 0.222403i) q^{32} +(-0.549040 - 2.68677i) q^{34} +(-4.61376 - 9.36601i) q^{35} +(0.237205 - 0.410852i) q^{37} +(2.80419 + 3.16406i) q^{38} +(6.34576 + 9.18221i) q^{40} +(-8.79016 + 5.07500i) q^{41} +(2.31047 + 1.33395i) q^{43} +(5.87522 - 7.82469i) q^{44} +(4.52673 + 1.51029i) q^{46} +(1.23083 + 2.13186i) q^{47} +(4.26614 - 5.54978i) q^{49} +(4.73214 - 14.1835i) q^{50} +(-2.60972 - 0.315870i) q^{52} +(-6.34427 - 10.9886i) q^{53} -19.3067 q^{55} +(-3.64245 + 6.53701i) q^{56} +(2.49463 + 2.81478i) q^{58} +(-3.49742 + 6.05771i) q^{59} +(2.05369 - 1.18570i) q^{61} +(-0.831634 - 0.938361i) q^{62} +(2.82830 - 7.48336i) q^{64} +(2.59342 + 4.49194i) q^{65} +(-1.20793 - 0.697399i) q^{67} +(3.85009 + 0.465999i) q^{68} +(14.6297 - 1.99739i) q^{70} +2.15535i q^{71} +(3.96915 - 2.29159i) q^{73} +(0.444996 + 0.502105i) q^{74} +(-5.49974 + 2.34569i) q^{76} +(-5.72003 - 11.6118i) q^{77} +(-8.70741 + 5.02722i) q^{79} +(-15.1583 + 4.40317i) q^{80} +(-2.87390 - 14.0636i) q^{82} +(-1.29635 + 2.24535i) q^{83} +(-3.82605 - 6.62692i) q^{85} +(-2.82365 + 2.50249i) q^{86} +(7.86733 + 11.3839i) q^{88} +(11.6706 + 6.73801i) q^{89} +(-1.93326 + 2.89062i) q^{91} +(-4.05215 + 5.39671i) q^{92} +(-3.41082 + 0.697000i) q^{94} +(10.2169 + 5.89870i) q^{95} +(1.88401 + 1.08773i) q^{97} +(5.53568 + 8.20708i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) $ 84 * q + q^2 + q^4 + 16 * q^8	$ 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) $ 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{6}\right)$	$-1$

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 $

$2$	−0.447581	+	1.34152i	−0.316488	+	0.948597i
$2$	−0.447581	+	1.34152i	−0.316488	+	0.948597i
$3$		0			0
$3$		0			0
$4$	−1.59934	−	1.20088i	−0.799671	−	0.600438i
$5$			3.94623i			1.76481i	0.470494	+	0.882403i	$0.344076\pi$
$5$			3.94623i			1.76481i	−0.470494	+	0.882403i	$0.655924\pi$
$6$		0			0
$7$	−2.37341	+	1.16916i	−0.897064	+	0.441900i
$7$	−2.37341	+	1.16916i	−0.897064	+	0.441900i
$8$	2.32683	−	1.60806i	0.822660	−	0.568534i
$9$		0			0
$10$	−5.29393	−	1.76626i	−1.67409	−	0.558539i
$11$			4.89244i			1.47513i	0.675278	+	0.737563i	$0.264024\pi$
$11$			4.89244i			1.47513i	−0.675278	+	0.737563i	$0.735976\pi$
$12$		0			0
$13$	1.13829	−	0.657191i	0.315704	−	0.182272i	−0.333772	−	0.942654i	$-0.608322\pi$
$13$	1.13829	−	0.657191i	0.315704	−	0.182272i	0.649476	+	0.760382i	$0.274988\pi$
$14$	−0.506153	−	3.70726i	−0.135275	−	0.990808i
$15$		0			0
$16$	1.11579	+	3.84122i	0.278948	+	0.960306i
$17$	−1.67931	+	0.969547i	−0.407291	+	0.235150i	−0.689625	−	0.724166i	$-0.742225\pi$
$17$	−1.67931	+	0.969547i	−0.407291	+	0.235150i	0.282334	+	0.959316i	$0.408891\pi$
$18$		0			0
$19$	1.49477	−	2.58902i	0.342924	−	0.593962i	−0.642050	−	0.766662i	$-0.721916\pi$
$19$	1.49477	−	2.58902i	0.342924	−	0.593962i	0.984974	+	0.172701i	$0.0552493\pi$
$20$	4.73893	−	6.31137i	1.05966	−	1.41126i
$21$		0			0
$22$	−6.56330	−	2.18976i	−1.39930	−	0.466859i
$23$		−	3.37433i		−	0.703597i	−0.936076	−	0.351798i	$-0.885570\pi$
$23$		−	3.37433i		−	0.703597i	0.936076	−	0.351798i	$-0.114430\pi$
$24$		0			0
$25$	−10.5727			−2.11454
$26$	0.372157	+	1.82118i	0.0729861	+	0.357163i
$27$		0			0
$28$	5.19991	+	0.980288i	0.982690	+	0.185257i
$29$	1.32976	−	2.30322i	0.246931	−	0.427697i	−0.715742	−	0.698365i	$-0.753911\pi$
$29$	1.32976	−	2.30322i	0.246931	−	0.427697i	0.962673	+	0.270668i	$0.0872445\pi$
$30$		0			0
$31$	−0.443302	+	0.767822i	−0.0796195	+	0.137905i	−0.903086	−	0.429460i	$-0.858704\pi$
$31$	−0.443302	+	0.767822i	−0.0796195	+	0.137905i	0.823466	+	0.567365i	$0.192037\pi$
$32$	−5.65248	−	0.222403i	−0.999227	−	0.0393156i
$33$		0			0
$34$	−0.549040	−	2.68677i	−0.0941596	−	0.460777i
$35$	−4.61376	−	9.36601i	−0.779868	−	1.58314i
$36$		0			0
$37$	0.237205	−	0.410852i	0.0389963	−	0.0675436i	−0.845869	−	0.533391i	$-0.820917\pi$
$37$	0.237205	−	0.410852i	0.0389963	−	0.0675436i	0.884865	+	0.465848i	$0.154251\pi$
$38$	2.80419	+	3.16406i	0.454899	+	0.513278i
$39$		0			0
$40$	6.34576	+	9.18221i	1.00335	+	1.45183i
$41$	−8.79016	+	5.07500i	−1.37279	+	0.792582i	−0.991279	−	0.131781i	$-0.957930\pi$
$41$	−8.79016	+	5.07500i	−1.37279	+	0.792582i	−0.381514	+	0.924363i	$0.624597\pi$
$42$		0			0
$43$	2.31047	+	1.33395i	0.352344	+	0.203426i	0.665717	−	0.746204i	$-0.268126\pi$
$43$	2.31047	+	1.33395i	0.352344	+	0.203426i	−0.313373	+	0.949630i	$0.601459\pi$
$44$	5.87522	−	7.82469i	0.885722	−	1.17962i
$45$		0			0
$46$	4.52673	+	1.51029i	0.667430	+	0.222680i
$47$	1.23083	+	2.13186i	0.179535	+	0.310963i	0.941721	−	0.336394i	$-0.109207\pi$
$47$	1.23083	+	2.13186i	0.179535	+	0.310963i	−0.762186	+	0.647358i	$0.775874\pi$
$48$		0			0
$49$	4.26614	−	5.54978i	0.609449	−	0.792825i
$50$	4.73214	−	14.1835i	0.669226	−	2.00585i
$51$		0			0
$52$	−2.60972	−	0.315870i	−0.361903	−	0.0438032i
$53$	−6.34427	−	10.9886i	−0.871453	−	1.50940i	−0.860494	−	0.509460i	$-0.829845\pi$
$53$	−6.34427	−	10.9886i	−0.871453	−	1.50940i	−0.0109585	−	0.999940i	$-0.503488\pi$
$54$		0			0
$55$	−19.3067			−2.60331
$56$	−3.64245	+	6.53701i	−0.486743	+	0.873545i
$57$		0			0
$58$	2.49463	+	2.81478i	0.327562	+	0.369599i
$59$	−3.49742	+	6.05771i	−0.455325	+	0.788646i	−0.998707	−	0.0508394i	$-0.983810\pi$
$59$	−3.49742	+	6.05771i	−0.455325	+	0.788646i	0.543382	+	0.839486i	$0.317144\pi$
$60$		0			0
$61$	2.05369	−	1.18570i	0.262948	−	0.151813i	−0.362731	−	0.931894i	$-0.618156\pi$
$61$	2.05369	−	1.18570i	0.262948	−	0.151813i	0.625679	+	0.780081i	$0.284822\pi$
$62$	−0.831634	−	0.938361i	−0.105618	−	0.119172i
$63$		0			0
$64$	2.82830	−	7.48336i	0.353538	−	0.935420i
$65$	2.59342	+	4.49194i	0.321675	+	0.557157i
$66$		0			0
$67$	−1.20793	−	0.697399i	−0.147572	−	0.0852008i	0.424396	−	0.905477i	$-0.360487\pi$
$67$	−1.20793	−	0.697399i	−0.147572	−	0.0852008i	−0.571968	+	0.820276i	$0.693820\pi$
$68$	3.85009	+	0.465999i	0.466892	+	0.0565107i
$69$		0			0
$70$	14.6297	−	1.99739i	1.74858	−	0.238734i
$71$			2.15535i			0.255793i	0.991788	+	0.127896i	$0.0408225\pi$
$71$			2.15535i			0.255793i	−0.991788	+	0.127896i	$0.959177\pi$
$72$		0			0
$73$	3.96915	−	2.29159i	0.464554	−	0.268210i	−0.249403	−	0.968400i	$-0.580234\pi$
$73$	3.96915	−	2.29159i	0.464554	−	0.268210i	0.713957	+	0.700189i	$0.246901\pi$
$74$	0.444996	+	0.502105i	0.0517298	+	0.0583685i
$75$		0			0
$76$	−5.49974	+	2.34569i	−0.630864	+	0.269070i
$77$	−5.72003	−	11.6118i	−0.651858	−	1.32328i
$78$		0			0
$79$	−8.70741	+	5.02722i	−0.979660	+	0.565607i	−0.902167	−	0.431386i	$-0.858025\pi$
$79$	−8.70741	+	5.02722i	−0.979660	+	0.565607i	−0.0774925	+	0.996993i	$0.524691\pi$
$80$	−15.1583	+	4.40317i	−1.69475	+	0.492289i
$81$		0			0
$82$	−2.87390	−	14.0636i	−0.317369	−	1.55307i
$83$	−1.29635	+	2.24535i	−0.142293	+	0.246459i	−0.928360	−	0.371683i	$-0.878781\pi$
$83$	−1.29635	+	2.24535i	−0.142293	+	0.246459i	0.786067	+	0.618142i	$0.212114\pi$
$84$		0			0
$85$	−3.82605	−	6.62692i	−0.414994	−	0.718790i
$86$	−2.82365	+	2.50249i	−0.304481	+	0.269850i
$87$		0			0
$88$	7.86733	+	11.3839i	0.838660	+	1.21353i
$89$	11.6706	+	6.73801i	1.23708	+	0.714227i	0.968496	−	0.249029i	$-0.0801115\pi$
$89$	11.6706	+	6.73801i	1.23708	+	0.714227i	0.268582	+	0.963257i	$0.413445\pi$
$90$		0			0
$91$	−1.93326	+	2.89062i	−0.202661	+	0.303019i
$92$	−4.05215	+	5.39671i	−0.422466	+	0.562646i
$93$		0			0
$94$	−3.41082	+	0.697000i	−0.351799	+	0.0718901i
$95$	10.2169	+	5.89870i	1.04823	+	0.605194i
$96$		0			0
$97$	1.88401	+	1.08773i	0.191292	+	0.110442i	0.592587	−	0.805506i	$-0.298107\pi$
$97$	1.88401	+	1.08773i	0.191292	+	0.110442i	−0.401295	+	0.915949i	$0.631440\pi$
$98$	5.53568	+	8.20708i	0.559188	+	0.829041i
$99$		0			0
$100$	16.9094	+	12.6965i	1.69094	+	1.26965i
$101$		−	0.713750i		−	0.0710208i	−0.999369	−	0.0355104i	$-0.988694\pi$
$101$		−	0.713750i		−	0.0710208i	0.999369	−	0.0355104i	$-0.0113057\pi$
$102$		0			0
$103$	1.16468			0.114760			0.0573798	−	0.998352i	$-0.481725\pi$
$103$	1.16468			0.114760			0.0573798	+	0.998352i	$0.481725\pi$
$104$	1.59180	−	3.35961i	0.156089	−	0.329436i
$105$		0			0
$106$	17.5810	−	3.59267i	1.70762	−	0.348951i
$107$	10.5529	+	6.09270i	1.02018	+	0.589004i	0.914157	−	0.405360i	$-0.132854\pi$
$107$	10.5529	+	6.09270i	1.02018	+	0.589004i	0.106027	+	0.994363i	$0.466187\pi$
$108$		0			0
$109$	−4.74875	−	8.22508i	−0.454848	−	0.787820i	0.543832	−	0.839194i	$-0.316973\pi$
$109$	−4.74875	−	8.22508i	−0.454848	−	0.787820i	−0.998679	+	0.0513747i	$0.983640\pi$
$110$	8.64130	−	25.9003i	0.823916	−	2.46949i
$111$		0			0
$112$	−7.13923	−	7.81226i	−0.674594	−	0.738189i
$113$	6.24802	+	10.8219i	0.587764	+	1.01804i	0.994525	+	0.104502i	$0.0333250\pi$
$113$	6.24802	+	10.8219i	0.587764	+	1.01804i	−0.406761	+	0.913535i	$0.633342\pi$
$114$		0			0
$115$	13.3159			1.24171
$116$	−4.89263	+	2.08675i	−0.454269	+	0.193750i
$117$		0			0
$118$	−6.56115	−	7.40317i	−0.604003	−	0.681517i
$119$	2.85213	−	4.26450i	0.261454	−	0.390927i
$120$		0			0
$121$	−12.9360			−1.17600
$122$	0.671443	+	3.28576i	0.0607896	+	0.297478i
$123$		0			0
$124$	1.63105	−	0.695659i	0.146473	−	0.0624721i
$125$		−	21.9911i		−	1.96695i
$126$		0			0
$127$			6.01418i			0.533672i	0.963742	+	0.266836i	$0.0859782\pi$
$127$			6.01418i			0.533672i	−0.963742	+	0.266836i	$0.914022\pi$
$128$	8.77317	+	7.14363i	0.775446	+	0.631413i
$129$		0			0
$130$	−7.18679	+	1.46862i	−0.630323	+	0.128806i
$131$	1.99858			0.174617			0.0873085	−	0.996181i	$-0.472173\pi$
$131$	1.99858			0.174617			0.0873085	+	0.996181i	$0.472173\pi$
$132$		0			0
$133$	−0.520732	+	7.89243i	−0.0451532	+	0.684360i
$134$	1.47622	−	1.30832i	0.127526	−	0.113021i
$135$		0			0
$136$	−2.34837	+	4.95639i	−0.201371	+	0.425007i
$137$	−10.0616			−0.859622			−0.429811	−	0.902919i	$-0.641420\pi$
$137$	−10.0616			−0.859622			−0.429811	+	0.902919i	$0.641420\pi$
$138$		0			0
$139$	8.02010	+	13.8912i	0.680256	+	1.17824i	0.974903	+	0.222631i	$0.0714646\pi$
$139$	8.02010	+	13.8912i	0.680256	+	1.17824i	−0.294647	+	0.955606i	$0.595202\pi$
$140$	−3.86844	+	20.5200i	−0.326943	+	1.73426i
$141$		0			0
$142$	−2.89144	−	0.964693i	−0.242644	−	0.0809553i
$143$	3.21527	+	5.56901i	0.268874	+	0.465704i
$144$		0			0
$145$	9.08903	+	5.24755i	0.754803	+	0.435785i
$146$	1.29769	+	6.35036i	0.107398	+	0.525560i
$147$		0			0
$148$	−0.872754	+	0.372238i	−0.0717400	+	0.0305978i
$149$	−9.69055			−0.793881			−0.396940	−	0.917844i	$-0.629928\pi$
$149$	−9.69055			−0.793881			−0.396940	+	0.917844i	$0.629928\pi$
$150$		0			0
$151$		−	16.5476i		−	1.34663i	−0.739357	−	0.673314i	$-0.764870\pi$
$151$		−	16.5476i		−	1.34663i	0.739357	−	0.673314i	$-0.235130\pi$
$152$	−0.685211	−	8.42789i	−0.0555779	−	0.683592i
$153$		0			0
$154$	18.1376	−	2.47632i	1.46157	−	0.199548i
$155$	−3.03000	−	1.74937i	−0.243375	−	0.140513i
$156$		0			0
$157$	11.3438	+	6.54936i	0.905335	+	0.522696i	0.878927	−	0.476956i	$-0.158260\pi$
$157$	11.3438	+	6.54936i	0.905335	+	0.522696i	0.0264079	+	0.999651i	$0.491593\pi$
$158$	−2.84684	−	13.9312i	−0.226483	−	1.10831i
$159$		0			0
$160$	0.877652	−	22.3060i	0.0693845	−	1.76344i
$161$	3.94512	+	8.00867i	0.310919	+	0.631172i
$162$		0			0
$163$	6.95666	+	4.01643i	0.544888	+	0.314591i	0.747057	−	0.664759i	$-0.231466\pi$
$163$	6.95666	+	4.01643i	0.544888	+	0.314591i	−0.202170	+	0.979350i	$0.564799\pi$
$164$	20.1529	+	2.43923i	1.57368	+	0.190472i
$165$		0			0
$166$	−2.43195	−	2.74405i	−0.188756	−	0.212980i
$167$	4.83680	+	8.37758i	0.374283	+	0.648277i	0.990219	−	0.139519i	$-0.0445556\pi$
$167$	4.83680	+	8.37758i	0.374283	+	0.648277i	−0.615937	+	0.787796i	$0.711222\pi$
$168$		0			0
$169$	−5.63620	+	9.76219i	−0.433554	+	0.750937i
$170$	10.6026	−	2.16664i	0.813182	−	0.166173i
$171$		0			0
$172$	−2.09333	−	4.90804i	−0.159615	−	0.374234i
$173$	−14.1923	+	8.19394i	−1.07902	+	0.622974i	−0.930633	−	0.365955i	$-0.880742\pi$
$173$	−14.1923	+	8.19394i	−1.07902	+	0.622974i	−0.148390	+	0.988929i	$0.547409\pi$
$174$		0			0
$175$	25.0933	−	12.3611i	1.89688	−	0.934415i
$176$	−18.7930	+	5.45895i	−1.41657	+	0.411484i
$177$		0			0
$178$	−14.2627	+	12.6405i	−1.06903	+	0.947444i
$179$	−16.0572	+	9.27065i	−1.20017	+	0.692921i	−0.960594	−	0.277955i	$-0.910343\pi$
$179$	−16.0572	+	9.27065i	−1.20017	+	0.692921i	−0.239581	+	0.970876i	$0.577010\pi$
$180$		0			0
$181$			23.0045i			1.70991i	0.518700	+	0.854956i	$0.326416\pi$
$181$			23.0045i			1.70991i	−0.518700	+	0.854956i	$0.673584\pi$
$182$	−3.01253	−	3.88729i	−0.223303	−	0.288145i
$183$		0			0
$184$	−5.42612	−	7.85151i	−0.400019	−	0.578821i
$185$	1.62131	+	0.936066i	0.119201	+	0.0688209i
$186$		0			0
$187$	−4.74345	−	8.21590i	−0.346876	−	0.600806i
$188$	0.591581	−	4.88764i	0.0431455	−	0.356468i
$189$		0			0
$190$	−12.4861	+	11.0660i	−0.905836	+	0.802808i
$191$	−3.41570	+	1.97206i	−0.247152	+	0.142693i	−0.618459	−	0.785817i	$-0.712243\pi$
$191$	−3.41570	+	1.97206i	−0.247152	+	0.142693i	0.371308	+	0.928510i	$0.378910\pi$
$192$		0			0
$193$	−2.87501	+	4.97966i	−0.206947	+	0.358443i	−0.950751	−	0.309954i	$-0.899686\pi$
$193$	−2.87501	+	4.97966i	−0.206947	+	0.358443i	0.743804	+	0.668398i	$0.233020\pi$
$194$	−2.30246	+	2.04058i	−0.165307	+	0.146505i
$195$		0			0
$196$	−13.4876	+	3.75289i	−0.963401	+	0.268063i
$197$	16.6012			1.18279			0.591393	−	0.806384i	$-0.298578\pi$
$197$	16.6012			1.18279			0.591393	+	0.806384i	$0.298578\pi$
$198$		0			0
$199$	6.23391	+	10.7974i	0.441910	+	0.765411i	0.997831	−	0.0658244i	$-0.0209677\pi$
$199$	6.23391	+	10.7974i	0.441910	+	0.765411i	−0.555921	+	0.831235i	$0.687634\pi$
$200$	−24.6009	+	17.0015i	−1.73955	+	1.20219i
$201$		0			0
$202$	0.957509	+	0.319461i	0.0673701	+	0.0224772i
$203$	−0.463249	+	7.02119i	−0.0325137	+	0.492791i
$204$		0			0
$205$	−20.0271	−	34.6880i	−1.39875	−	2.42271i
$206$	−0.521290	+	1.56244i	−0.0363200	+	0.108861i
$207$		0			0
$208$	3.79451	+	3.63913i	0.263102	+	0.252328i
$209$	12.6666	+	7.31308i	0.876169	+	0.505856i
$210$		0			0
$211$	−19.4166	+	11.2102i	−1.33669	+	0.771739i	−0.986315	−	0.164870i	$-0.947279\pi$
$211$	−19.4166	+	11.2102i	−1.33669	+	0.771739i	−0.350376	+	0.936609i	$0.613946\pi$
$212$	−3.04929	+	25.1932i	−0.209426	+	1.73028i
$213$		0			0
$214$	−12.8967	+	11.4299i	−0.881603	+	0.781331i
$215$	−5.26408	+	9.11765i	−0.359007	+	0.621819i
$216$		0			0
$217$	0.154433	−	2.34065i	0.0104836	−	0.158893i
$218$	13.1595	−	2.68915i	0.891277	−	0.182132i
$219$		0			0
$220$	30.8780	+	23.1849i	2.08179	+	1.56313i
$221$	−1.27436	+	2.20725i	−0.0857224	+	0.148476i
$222$		0			0
$223$	4.48502	−	7.76829i	0.300339	−	0.520203i	−0.675873	−	0.737018i	$-0.736233\pi$
$223$	4.48502	−	7.76829i	0.300339	−	0.520203i	0.976213	+	0.216815i	$0.0695668\pi$
$224$	13.6757	−	6.08079i	0.913744	−	0.406290i
$225$		0			0
$226$	−17.3142	+	3.53816i	−1.15173	+	0.235355i
$227$	−7.79377			−0.517291			−0.258645	−	0.965972i	$-0.583276\pi$
$227$	−7.79377			−0.517291			−0.258645	+	0.965972i	$0.583276\pi$
$228$		0			0
$229$		−	6.80092i		−	0.449417i	−0.974426	−	0.224709i	$-0.927857\pi$
$229$		−	6.80092i		−	0.449417i	0.974426	−	0.224709i	$-0.0721430\pi$
$230$	−5.95993	+	17.8635i	−0.392986	+	1.17788i
$231$		0			0
$232$	−0.609571	−	7.49755i	−0.0400203	−	0.492238i
$233$	−8.45700	+	14.6480i	−0.554037	+	0.959619i	0.443941	+	0.896056i	$0.353580\pi$
$233$	−8.45700	+	14.6480i	−0.554037	+	0.959619i	−0.997978	+	0.0635635i	$0.979753\pi$
$234$		0			0
$235$	−8.41279	+	4.85713i	−0.548790	+	0.316844i
$236$	12.8681	−	5.48838i	0.837644	−	0.357263i
$237$		0			0
$238$	4.44435	+	5.73489i	0.288085	+	0.371738i
$239$	−16.8495	+	9.72804i	−1.08990	+	0.629254i	−0.933550	−	0.358447i	$-0.883306\pi$
$239$	−16.8495	+	9.72804i	−1.08990	+	0.629254i	−0.156351	+	0.987702i	$0.549973\pi$
$240$		0			0
$241$			23.5574i			1.51747i	0.651401	+	0.758734i	$0.274182\pi$
$241$			23.5574i			1.51747i	−0.651401	+	0.758734i	$0.725818\pi$
$242$	5.78990	−	17.3539i	0.372189	−	1.11555i
$243$		0			0
$244$	−4.70843	−	0.569889i	−0.301426	−	0.0364834i
$245$	21.9007	+	16.8352i	1.39918	+	1.07556i
$246$		0			0
$247$		−	3.92940i		−	0.250022i
$248$	0.203212	+	2.49945i	0.0129040	+	0.158715i
$249$		0			0
$250$	29.5015	+	9.84281i	1.86584	+	0.622514i
$251$	4.53190			0.286051			0.143026	−	0.989719i	$-0.454317\pi$
$251$	4.53190			0.286051			0.143026	+	0.989719i	$0.454317\pi$
$252$		0			0
$253$	16.5087			1.03789
$254$	−8.06813	−	2.69183i	−0.506240	−	0.168901i
$255$		0			0
$256$	−13.5100	+	8.57202i	−0.844376	+	0.535751i
$257$		−	23.8841i		−	1.48985i	−0.667149	−	0.744924i	$-0.732486\pi$
$257$		−	23.8841i		−	1.48985i	0.667149	−	0.744924i	$-0.267514\pi$
$258$		0			0
$259$	−0.0826350	+	1.25245i	−0.00513469	+	0.0778234i
$260$	1.24649	−	10.2985i	0.0773042	−	0.638688i
$261$		0			0
$262$	−0.894528	+	2.68113i	−0.0552641	+	0.165641i
$263$		−	27.2015i		−	1.67732i	−0.544656	−	0.838660i	$-0.683340\pi$
$263$		−	27.2015i		−	1.67732i	0.544656	−	0.838660i	$-0.316660\pi$
$264$		0			0
$265$	43.3635	−	25.0359i	2.66380	−	1.53794i
$266$	−10.3548	−	4.23107i	−0.634891	−	0.259424i
$267$		0			0
$268$	1.09440	+	2.56595i	0.0668514	+	0.156741i
$269$	−15.8637	+	9.15891i	−0.967227	+	0.558429i	−0.898390	−	0.439199i	$-0.855262\pi$
$269$	−15.8637	+	9.15891i	−0.967227	+	0.558429i	−0.0688372	+	0.997628i	$0.521929\pi$
$270$		0			0
$271$	0.772505	−	1.33802i	0.0469264	−	0.0812788i	−0.841608	−	0.540089i	$-0.818391\pi$
$271$	0.772505	−	1.33802i	0.0469264	−	0.0812788i	0.888535	+	0.458810i	$0.151724\pi$
$272$	−5.59801	−	5.36878i	−0.339429	−	0.325530i
$273$		0			0
$274$	4.50339	−	13.4978i	0.272060	−	0.815435i
$275$		−	51.7263i		−	3.11921i
$276$		0			0
$277$	0.486092			0.0292065			0.0146032	−	0.999893i	$-0.495351\pi$
$277$	0.486092			0.0292065			0.0146032	+	0.999893i	$0.495351\pi$
$278$	−22.2250	+	4.54166i	−1.33296	+	0.272391i
$279$		0			0
$280$	−25.7965	−	14.3739i	−1.54164	−	0.859007i
$281$	13.1672	−	22.8062i	0.785489	−	1.36051i	−0.143218	−	0.989691i	$-0.545745\pi$
$281$	13.1672	−	22.8062i	0.785489	−	1.36051i	0.928707	−	0.370815i	$-0.120922\pi$
$282$		0			0
$283$	8.58849	−	14.8757i	0.510533	−	0.884268i	−0.489393	−	0.872063i	$-0.662782\pi$
$283$	8.58849	−	14.8757i	0.510533	−	0.884268i	0.999926	−	0.0122050i	$-0.00388506\pi$
$284$	2.58831	−	3.44714i	0.153588	−	0.204550i
$285$		0			0
$286$	−8.91002	+	1.82076i	−0.526860	+	0.107664i
$287$	14.9292	−	22.3221i	0.881241	−	1.31763i
$288$		0			0
$289$	−6.61996	+	11.4661i	−0.389409	+	0.674476i
$290$	−11.1078	+	9.84439i	−0.652270	+	0.578082i
$291$		0			0
$292$	−9.09995	−	1.10142i	−0.532534	−	0.0644558i
$293$	21.5170	−	12.4229i	1.25704	−	0.725751i	0.284540	−	0.958664i	$-0.408159\pi$
$293$	21.5170	−	12.4229i	1.25704	−	0.725751i	0.972498	+	0.232913i	$0.0748258\pi$
$294$		0			0
$295$	−23.9051	−	13.8016i	−1.39181	−	0.803561i
$296$	−0.108736	−	1.33742i	−0.00632016	−	0.0777361i
$297$		0			0
$298$	4.33730	−	13.0000i	0.251253	−	0.753072i
$299$	−2.21758	−	3.84096i	−0.128246	−	0.222128i
$300$		0			0
$301$	−7.04330	−	0.464708i	−0.405969	−	0.0267853i
$302$	22.1990	+	7.40641i	1.27741	+	0.426191i
$303$		0			0
$304$	11.6129	+	2.85294i	0.666043	+	0.163627i
$305$	4.67903	+	8.10432i	0.267921	+	0.464052i
$306$		0			0
$307$	32.0881			1.83136			0.915682	−	0.401904i	$-0.131652\pi$
$307$	32.0881			1.83136			0.915682	+	0.401904i	$0.131652\pi$
$308$	−4.79600	+	25.4402i	−0.273277	+	1.44959i
$309$		0			0
$310$	3.70298	−	3.28181i	0.210315	−	0.186395i
$311$	6.52427	−	11.3004i	0.369957	−	0.640785i	−0.619601	−	0.784917i	$-0.712706\pi$
$311$	6.52427	−	11.3004i	0.369957	−	0.640785i	0.989559	+	0.144132i	$0.0460389\pi$
$312$		0			0
$313$	11.5365	−	6.66061i	0.652083	−	0.376480i	−0.137171	−	0.990547i	$-0.543801\pi$
$313$	11.5365	−	6.66061i	0.652083	−	0.376480i	0.789254	+	0.614067i	$0.210468\pi$
$314$	−13.8634	+	12.2866i	−0.782355	+	0.693371i
$315$		0			0
$316$	19.9632	+	2.41627i	1.12302	+	0.135926i
$317$	−9.82677	−	17.0205i	−0.551927	−	0.955965i	−0.998136	−	0.0610362i	$-0.980559\pi$
$317$	−9.82677	−	17.0205i	−0.551927	−	0.955965i	0.446209	−	0.894929i	$-0.352774\pi$
$318$		0			0
$319$	11.2684	+	6.50579i	0.630907	+	0.364255i
$320$	29.5310	+	11.1611i	1.65084	+	0.623925i
$321$		0			0
$322$	−12.5095	+	1.70793i	−0.697129	+	0.0951791i
$323$			5.79701i			0.322554i
$324$		0			0
$325$	−12.0348	+	6.94828i	−0.667569	+	0.385421i
$326$	−8.50178	+	7.53481i	−0.470870	+	0.417314i
$327$		0			0
$328$	−12.2923	+	25.9438i	−0.678731	+	1.43250i
$329$	−5.41374	−	3.62074i	−0.298469	−	0.199618i
$330$		0			0
$331$	12.4763	−	7.20320i	0.685760	−	0.395924i	−0.116262	−	0.993219i	$-0.537091\pi$
$331$	12.4763	−	7.20320i	0.685760	−	0.395924i	0.802022	+	0.597295i	$0.203758\pi$
$332$	4.76969	−	2.03432i	0.261771	−	0.111648i
$333$		0			0
$334$	−13.4035	+	2.73901i	−0.733409	+	0.149872i
$335$	2.75209	−	4.76677i	0.150363	−	0.260436i
$336$		0			0
$337$	−0.489878	−	0.848494i	−0.0266854	−	0.0462204i	0.852374	−	0.522932i	$-0.175162\pi$
$337$	−0.489878	−	0.848494i	−0.0266854	−	0.0462204i	−0.879060	+	0.476712i	$0.841829\pi$
$338$	−10.5735	−	11.9304i	−0.575122	−	0.648930i
$339$		0			0
$340$	−1.83894	+	15.1933i	−0.0997305	+	0.823974i
$341$	−3.75652	−	2.16883i	−0.203427	−	0.117449i
$342$		0			0
$343$	−3.63674	+	18.1597i	−0.196365	+	0.980531i
$344$	7.52116	−	0.611491i	0.405514	−	0.0329694i
$345$		0			0
$346$	−4.64011	−	22.7067i	−0.249454	−	1.22072i
$347$	−23.7580	−	13.7167i	−1.27540	−	0.736351i	−0.299399	−	0.954128i	$-0.596786\pi$
$347$	−23.7580	−	13.7167i	−1.27540	−	0.736351i	−0.975998	+	0.217777i	$0.930119\pi$
$348$		0			0
$349$	−13.0352	−	7.52589i	−0.697760	−	0.402852i	0.108753	−	0.994069i	$-0.465314\pi$
$349$	−13.0352	−	7.52589i	−0.697760	−	0.402852i	−0.806512	+	0.591217i	$0.798648\pi$
$350$	5.35140	+	39.1958i	0.286045	+	2.09510i
$351$		0			0
$352$	1.08809	−	27.6544i	0.0579955	−	1.47399i
$353$			18.5070i			0.985026i	0.870305	+	0.492513i	$0.163922\pi$
$353$			18.5070i			0.985026i	−0.870305	+	0.492513i	$0.836078\pi$
$354$		0			0
$355$	−8.50550			−0.451425
$356$	−10.5737	−	24.7913i	−0.560407	−	1.31394i
$357$		0			0
$358$	−5.24983	−	25.6904i	−0.277462	−	1.35778i
$359$	5.04854	+	2.91478i	0.266452	+	0.153836i	0.627274	−	0.778799i	$-0.284171\pi$
$359$	5.04854	+	2.91478i	0.266452	+	0.153836i	−0.360822	+	0.932635i	$0.617504\pi$
$360$		0			0
$361$	5.03132	+	8.71450i	0.264806	+	0.458658i
$362$	−30.8610	−	10.2964i	−1.62202	−	0.541166i
$363$		0			0
$364$	6.56323	−	2.30148i	0.344007	−	0.120630i
$365$	9.04313	+	15.6632i	0.473339	+	0.819848i
$366$		0			0
$367$	−1.80797			−0.0943752			−0.0471876	−	0.998886i	$-0.515026\pi$
$367$	−1.80797			−0.0943752			−0.0471876	+	0.998886i	$0.515026\pi$
$368$	12.9616	−	3.76505i	0.675668	−	0.196267i
$369$		0			0
$370$	−1.98142	+	1.75606i	−0.103009	+	0.0912930i
$371$	27.9050	+	18.6630i	1.44875	+	0.968934i
$372$		0			0
$373$	−5.95914			−0.308553			−0.154276	−	0.988028i	$-0.549305\pi$
$373$	−5.95914			−0.308553			−0.154276	+	0.988028i	$0.549305\pi$
$374$	13.1449	−	2.68615i	0.679705	−	0.138897i
$375$		0			0
$376$	6.29208	+	2.98123i	0.324489	+	0.153745i
$377$		−	3.49564i		−	0.180034i
$378$		0			0
$379$		−	16.5311i		−	0.849146i	−0.905394	−	0.424573i	$-0.860424\pi$
$379$		−	16.5311i		−	0.849146i	0.905394	−	0.424573i	$-0.139576\pi$
$380$	−9.25664	−	21.7032i	−0.474855	−	1.11335i
$381$		0			0
$382$	−1.11675	−	5.46489i	−0.0571378	−	0.279608i
$383$	3.29801			0.168520			0.0842601	−	0.996444i	$-0.473147\pi$
$383$	3.29801			0.168520			0.0842601	+	0.996444i	$0.473147\pi$
$384$		0			0
$385$	45.8226	−	22.5725i	2.33534	−	1.15040i
$386$	−5.39350	−	6.08567i	−0.274522	−	0.309753i
$387$		0			0
$388$	−1.70694	−	4.00211i	−0.0866567	−	0.203176i
$389$	−9.64882			−0.489215			−0.244607	−	0.969622i	$-0.578659\pi$
$389$	−9.64882			−0.489215			−0.244607	+	0.969622i	$0.578659\pi$
$390$		0			0
$391$	3.27157	+	5.66653i	0.165451	+	0.286569i
$392$	1.00224	−	19.7736i	0.0506206	−	0.998718i
$393$		0			0
$394$	−7.43037	+	22.2708i	−0.374337	+	1.12199i
$395$	−19.8386	−	34.3614i	−0.998186	−	1.72891i
$396$		0			0
$397$	−3.22184	−	1.86013i	−0.161700	−	0.0933573i	0.416967	−	0.908922i	$-0.363093\pi$
$397$	−3.22184	−	1.86013i	−0.161700	−	0.0933573i	−0.578666	+	0.815565i	$0.696427\pi$
$398$	−17.2751	+	3.53017i	−0.865925	+	0.176951i
$399$		0			0
$400$	−11.7969	−	40.6121i	−0.589847	−	2.03061i
$401$	23.9720			1.19711			0.598553	−	0.801083i	$-0.295743\pi$
$401$	23.9720			1.19711			0.598553	+	0.801083i	$0.295743\pi$
$402$		0			0
$403$			1.16534i			0.0580496i
$404$	−0.857125	+	1.14153i	−0.0426436	+	0.0567933i
$405$		0			0
$406$	−9.21171	−	3.76401i	−0.457169	−	0.186805i
$407$	2.01007	+	1.16051i	0.0996353	+	0.0575245i
$408$		0			0
$409$	−19.1868	−	11.0775i	−0.948726	−	0.547747i	−0.0560410	−	0.998428i	$-0.517848\pi$
$409$	−19.1868	−	11.0775i	−0.948726	−	0.547747i	−0.892685	+	0.450681i	$0.851181\pi$
$410$	55.4983	−	11.3411i	2.74087	−	0.560095i
$411$		0			0
$412$	−1.86273	−	1.39864i	−0.0917700	−	0.0689061i
$413$	1.21839	−	18.4665i	0.0599532	−	0.908675i
$414$		0			0
$415$	−8.86064	−	5.11570i	−0.434952	−	0.251120i
$416$	−6.58031	+	3.46160i	−0.322626	+	0.169719i
$417$		0			0
$418$	−15.4800	+	13.7193i	−0.757150	+	0.671034i
$419$	17.6835	+	30.6287i	0.863895	+	1.49631i	0.868140	+	0.496319i	$0.165315\pi$
$419$	17.6835	+	30.6287i	0.863895	+	1.49631i	−0.00424524	+	0.999991i	$0.501351\pi$
$420$		0			0
$421$	−15.4856	+	26.8219i	−0.754723	+	1.30722i	0.190788	+	0.981631i	$0.438896\pi$
$421$	−15.4856	+	26.8219i	−0.754723	+	1.30722i	−0.945512	+	0.325588i	$0.894438\pi$
$422$	−6.34815	−	31.0651i	−0.309023	−	1.51223i
$423$		0			0
$424$	−32.4324	−	15.3667i	−1.57505	−	0.746272i
$425$	17.7548	−	10.2507i	0.861234	−	0.497234i
$426$		0			0
$427$	−3.48798	+	5.21523i	−0.168795	+	0.252383i
$428$	−9.56107	−	22.4170i	−0.462152	−	1.08357i
$429$		0			0
$430$	−9.87539	−	11.1427i	−0.476234	−	0.537351i
$431$	−4.22345	+	2.43841i	−0.203437	+	0.117454i	−0.598257	−	0.801304i	$-0.704140\pi$
$431$	−4.22345	+	2.43841i	−0.203437	+	0.117454i	0.394821	+	0.918758i	$0.370807\pi$
$432$		0			0
$433$			13.0744i			0.628314i	0.949371	+	0.314157i	$0.101722\pi$
$433$			13.0744i			0.628314i	−0.949371	+	0.314157i	$0.898278\pi$
$434$	3.07090	+	1.25480i	0.147408	+	0.0602325i
$435$		0			0
$436$	−2.28242	+	18.8574i	−0.109308	+	0.903105i
$437$	−8.73621	−	5.04385i	−0.417910	−	0.241280i
$438$		0			0
$439$	−0.958667	−	1.66046i	−0.0457547	−	0.0792494i	0.842241	−	0.539101i	$-0.181236\pi$
$439$	−0.958667	−	1.66046i	−0.0457547	−	0.0792494i	−0.887996	+	0.459852i	$0.847903\pi$
$440$	−44.9234	+	31.0463i	−2.14164	+	1.48007i
$441$		0			0
$442$	−2.39069	−	2.69749i	−0.113713	−	0.128307i
$443$	−18.4381	+	10.6452i	−0.876020	+	0.505770i	−0.869344	−	0.494207i	$-0.835458\pi$
$443$	−18.4381	+	10.6452i	−0.876020	+	0.505770i	−0.00667575	+	0.999978i	$0.502125\pi$
$444$		0			0
$445$	−26.5897	+	46.0547i	−1.26047	+	2.18320i
$446$	8.41389	+	9.49368i	0.398409	+	0.449539i
$447$		0			0
$448$	2.03651	+	21.0678i	0.0962162	+	0.995360i
$449$	−5.99969			−0.283143			−0.141572	−	0.989928i	$-0.545216\pi$
$449$	−5.99969			−0.283143			−0.141572	+	0.989928i	$0.545216\pi$
$450$		0			0
$451$	−24.8291	−	43.0053i	−1.16916	−	2.02504i
$452$	3.00302	−	24.8110i	0.141250	−	1.16701i
$453$		0			0
$454$	3.48834	−	10.4555i	0.163716	−	0.490700i
$455$	−11.4070	−	7.62909i	−0.534770	−	0.357657i
$456$		0			0
$457$	12.6676	+	21.9408i	0.592563	+	1.02635i	0.993886	+	0.110413i	$0.0352173\pi$
$457$	12.6676	+	21.9408i	0.592563	+	1.02635i	−0.401323	+	0.915937i	$0.631449\pi$
$458$	9.12356	+	3.04396i	0.426316	+	0.142235i
$459$		0			0
$460$	−21.2966	−	15.9907i	−0.992961	−	0.745571i
$461$	−17.3693	−	10.0282i	−0.808970	−	0.467059i	0.0376278	−	0.999292i	$-0.488020\pi$
$461$	−17.3693	−	10.0282i	−0.808970	−	0.467059i	−0.846598	+	0.532233i	$0.821353\pi$
$462$		0			0
$463$	33.2880	−	19.2188i	1.54702	−	0.893175i	0.548658	−	0.836047i	$-0.315139\pi$
$463$	33.2880	−	19.2188i	1.54702	−	0.893175i	0.998367	−	0.0571279i	$-0.0181943\pi$
$464$	10.3309	+	2.53801i	0.479601	+	0.117824i
$465$		0			0
$466$	−15.8653	−	17.9014i	−0.734946	−	0.829265i
$467$	16.3595	−	28.3355i	0.757028	−	1.31121i	−0.187332	−	0.982297i	$-0.559984\pi$
$467$	16.3595	−	28.3355i	0.757028	−	1.31121i	0.944360	−	0.328914i	$-0.106683\pi$
$468$		0			0
$469$	3.68228	+	0.242952i	0.170032	+	0.0112185i
$470$	−2.75052	−	13.4599i	−0.126872	−	0.620858i
$471$		0			0
$472$	1.60323	+	19.7193i	0.0737949	+	0.907656i
$473$	−6.52628	+	11.3039i	−0.300079	+	0.519752i
$474$		0			0
$475$	−15.8038	+	27.3729i	−0.725126	+	1.25596i
$476$	−9.68267	+	3.39535i	−0.443804	+	0.155626i
$477$		0			0
$478$	−5.50884	−	26.9579i	−0.251969	−	1.23303i
$479$	36.7966			1.68128			0.840639	−	0.541595i	$-0.182180\pi$
$479$	36.7966			1.68128			0.840639	+	0.541595i	$0.182180\pi$
$480$		0			0
$481$		−	0.623556i		−	0.0284317i
$482$	−31.6027	−	10.5439i	−1.43946	−	0.480259i
$483$		0			0
$484$	20.6891	+	15.5345i	0.940412	+	0.706114i
$485$	−4.29243	+	7.43471i	−0.194909	+	0.337593i
$486$		0			0
$487$	−3.93075	+	2.26942i	−0.178119	+	0.102837i	−0.586409	−	0.810015i	$-0.699459\pi$
$487$	−3.93075	+	2.26942i	−0.178119	+	0.102837i	0.408289	+	0.912853i	$0.366125\pi$
$488$	2.87192	−	6.06137i	0.130006	−	0.274385i
$489$		0			0
$490$	−32.3870	+	21.8451i	−1.46310	+	0.986859i
$491$	−10.6660	+	6.15804i	−0.481351	+	0.277908i	−0.720980	−	0.692956i	$-0.756308\pi$
$491$	−10.6660	+	6.15804i	−0.481351	+	0.277908i	0.239628	+	0.970865i	$0.422975\pi$
$492$		0			0
$493$			5.15708i			0.232263i
$494$	5.27136	+	1.75872i	0.237170	+	0.0791288i
$495$		0			0
$496$	−3.44401	−	0.846093i	−0.154641	−	0.0379907i
$497$	−2.51994	−	5.11553i	−0.113035	−	0.229463i
$498$		0			0
$499$		−	12.9516i		−	0.579793i	−0.957058	−	0.289896i	$-0.906379\pi$
$499$		−	12.9516i		−	0.579793i	0.957058	−	0.289896i	$-0.0936209\pi$
$500$	−26.4086	+	35.1713i	−1.18103	+	1.57291i
$501$		0			0
$502$	−2.02839	+	6.07963i	−0.0905316	+	0.271347i
$503$	−20.4872			−0.913480			−0.456740	−	0.889600i	$-0.650983\pi$
$503$	−20.4872			−0.913480			−0.456740	+	0.889600i	$0.650983\pi$
$504$		0			0
$505$	2.81662			0.125338
$506$	−7.38899	+	22.1467i	−0.328481	+	0.984543i
$507$		0			0
$508$	7.22229	−	9.61873i	0.320437	−	0.426762i
$509$			28.4509i			1.26107i	0.776163	+	0.630533i	$0.217163\pi$
$509$			28.4509i			1.26107i	−0.776163	+	0.630533i	$0.782837\pi$
$510$		0			0
$511$	−6.74119	+	10.0794i	−0.298213	+	0.445888i
$512$	−5.45270	−	21.9606i	−0.240977	−	0.970531i
$513$		0			0
$514$	32.0409	+	10.6901i	1.41327	+	0.471519i
$515$			4.59610i			0.202528i
$516$		0			0
$517$	−10.4300	+	6.02176i	−0.458710	+	0.264837i
$518$	−1.64320	−	0.671429i	−0.0721980	−	0.0295009i
$519$		0			0
$520$	13.2578	+	6.28162i	0.581391	+	0.275467i
$521$	−32.0751	+	18.5186i	−1.40524	+	0.811314i	−0.994924	−	0.100630i	$-0.967914\pi$
$521$	−32.0751	+	18.5186i	−1.40524	+	0.811314i	−0.410314	+	0.911944i	$0.634581\pi$
$522$		0			0
$523$	2.33168	−	4.03859i	0.101957	−	0.176595i	−0.810534	−	0.585692i	$-0.800823\pi$
$523$	2.33168	−	4.03859i	0.101957	−	0.176595i	0.912491	+	0.409097i	$0.134156\pi$
$524$	−3.19642	−	2.40005i	−0.139636	−	0.104847i
$525$		0			0
$526$	36.4914	+	12.1749i	1.59110	+	0.530851i
$527$		−	1.71921i		−	0.0748900i
$528$		0			0
$529$	11.6139			0.504952
$530$	14.1775	+	69.3785i	0.615830	+	3.01361i
$531$		0			0
$532$	10.3107	−	11.9974i	0.447024	−	0.520151i
$533$	−6.67049	+	11.5536i	−0.288931	+	0.500443i
$534$		0			0
$535$	−24.0432	+	41.6440i	−1.03948	+	1.80043i
$536$	−3.93211	+	0.319691i	−0.169841	+	0.0138086i
$537$		0			0
$538$	−5.18656	−	25.3808i	−0.223608	−	1.09424i
$539$	27.1520	+	20.8718i	1.16952	+	0.899014i
$540$		0			0
$541$	11.6836	−	20.2366i	0.502318	−	0.870040i	−0.497678	−	0.867362i	$-0.665814\pi$
$541$	11.6836	−	20.2366i	0.502318	−	0.870040i	0.999996	−	0.00267870i	$-0.000852658\pi$
$542$	1.44922	+	1.63520i	0.0622492	+	0.0702379i
$543$		0			0
$544$	9.70787	−	5.10687i	0.416222	−	0.218955i
$545$	32.4580	−	18.7396i	1.39035	−	0.802718i
$546$		0			0
$547$	−21.8092	−	12.5915i	−0.932493	−	0.538375i	−0.0448939	−	0.998992i	$-0.514295\pi$
$547$	−21.8092	−	12.5915i	−0.932493	−	0.538375i	−0.887599	+	0.460617i	$0.847628\pi$
$548$	16.0920	+	12.0828i	0.687415	+	0.516150i
$549$		0			0
$550$	69.3918	+	23.1517i	2.95888	+	0.987192i
$551$	−3.97539	−	6.88557i	−0.169357	−	0.293335i
$552$		0			0
$553$	14.7886	−	22.1120i	0.628876	−	0.940297i
$554$	−0.217566	+	0.652102i	−0.00924348	+	0.0277051i
$555$		0			0
$556$	3.85475	−	31.8480i	0.163478	−	1.35065i
$557$	3.17042	+	5.49134i	0.134335	+	0.232675i	0.925343	−	0.379130i	$-0.123777\pi$
$557$	3.17042	+	5.49134i	0.134335	+	0.232675i	−0.791008	+	0.611806i	$0.790443\pi$
$558$		0			0
$559$	3.50664			0.148315
$560$	30.8289	−	28.1730i	1.30276	−	1.19053i
$561$		0			0
$562$	24.7016	+	27.8717i	1.04197	+	1.17570i
$563$	0.642577	−	1.11298i	0.0270814	−	0.0469064i	−0.852167	−	0.523270i	$-0.824712\pi$
$563$	0.642577	−	1.11298i	0.0270814	−	0.0469064i	0.879248	+	0.476363i	$0.158045\pi$
$564$		0			0
$565$	−42.7056	+	24.6561i	−1.79664	+	1.03729i
$566$	16.1120	+	18.1797i	0.677237	+	0.764149i
$567$		0			0
$568$	3.46593	+	5.01514i	0.145427	+	0.210430i
$569$	−9.93849	−	17.2140i	−0.416643	−	0.721647i	0.578956	−	0.815359i	$-0.303460\pi$
$569$	−9.93849	−	17.2140i	−0.416643	−	0.721647i	−0.995599	+	0.0937117i	$0.970127\pi$
$570$		0			0
$571$	−12.4246	−	7.17336i	−0.519954	−	0.300196i	0.216962	−	0.976180i	$-0.430385\pi$
$571$	−12.4246	−	7.17336i	−0.519954	−	0.300196i	−0.736916	+	0.675985i	$0.763719\pi$
$572$	1.54537	−	12.7679i	0.0646153	−	0.533852i
$573$		0			0
$574$	23.2635	+	30.0187i	0.971001	+	1.25296i
$575$			35.6758i			1.48778i
$576$		0			0
$577$	10.9881	−	6.34398i	0.457440	−	0.264103i	−0.253527	−	0.967328i	$-0.581591\pi$
$577$	10.9881	−	6.34398i	0.457440	−	0.264103i	0.710967	+	0.703225i	$0.248257\pi$
$578$	−12.4190	−	14.0128i	−0.516563	−	0.582856i
$579$		0			0
$580$	−8.23481	−	19.3074i	−0.341932	−	0.801697i
$581$	0.451609	−	6.84476i	0.0187359	−	0.283969i
$582$		0			0
$583$	53.7611	−	31.0390i	2.22656	−	1.28550i
$584$	5.55054	−	11.7148i	0.229683	−	0.484761i
$585$		0			0
$586$	7.03488	+	34.4257i	0.290608	+	1.42211i
$587$	12.4489	−	21.5622i	0.513823	−	0.889967i	−0.486049	−	0.873932i	$-0.661562\pi$
$587$	12.4489	−	21.5622i	0.513823	−	0.889967i	0.999871	−	0.0160352i	$-0.00510440\pi$
$588$		0			0
$589$	1.32527	+	2.29544i	0.0546068	+	0.0945818i
$590$	29.2146	−	25.8918i	1.20274	−	1.06595i
$591$		0			0
$592$	1.84285	+	0.452734i	0.0757405	+	0.0186072i
$593$	22.9565	+	13.2540i	0.942712	+	0.544275i	0.890809	−	0.454377i	$-0.150138\pi$
$593$	22.9565	+	13.2540i	0.942712	+	0.544275i	0.0519027	+	0.998652i	$0.483471\pi$
$594$		0			0
$595$	16.8287	+	11.2551i	0.689909	+	0.461415i
$596$	15.4985	+	11.6371i	0.634843	+	0.476676i
$597$		0			0
$598$	6.14527	−	1.25578i	0.251299	−	0.0513528i
$599$	21.3471	+	12.3248i	0.872219	+	0.503576i	0.868085	−	0.496415i	$-0.165351\pi$
$599$	21.3471	+	12.3248i	0.872219	+	0.503576i	0.00413416	+	0.999991i	$0.498684\pi$
$600$		0			0
$601$	−0.673377	−	0.388774i	−0.0274676	−	0.0158584i	0.486203	−	0.873846i	$-0.338381\pi$
$601$	−0.673377	−	0.388774i	−0.0274676	−	0.0158584i	−0.513671	+	0.857987i	$0.671715\pi$
$602$	3.77586	−	9.24072i	0.153893	−	0.376624i
$603$		0			0
$604$	−19.8717	+	26.4653i	−0.808566	+	1.07686i
$605$		−	51.0483i		−	2.07541i
$606$		0			0
$607$	−42.1687			−1.71157			−0.855787	−	0.517328i	$-0.826927\pi$
$607$	−42.1687			−1.71157			−0.855787	+	0.517328i	$0.826927\pi$
$608$	−9.02497	+	14.3019i	−0.366011	+	0.580020i
$609$		0			0
$610$	−12.9663	+	2.64967i	−0.524992	+	0.107282i
$611$	2.80208	+	1.61778i	0.113360	+	0.0654483i
$612$		0			0
$613$	4.18716	+	7.25237i	0.169118	+	0.292921i	0.938110	−	0.346338i	$-0.112575\pi$
$613$	4.18716	+	7.25237i	0.169118	+	0.292921i	−0.768992	+	0.639258i	$0.779241\pi$
$614$	−14.3620	+	43.0467i	−0.579604	+	1.73723i
$615$		0			0
$616$	−31.9819	−	17.8205i	−1.28859	−	0.718008i
$617$	8.84616	+	15.3220i	0.356133	+	0.616840i	0.987311	−	0.158797i	$-0.0507617\pi$
$617$	8.84616	+	15.3220i	0.356133	+	0.616840i	−0.631178	+	0.775638i	$0.717428\pi$
$618$		0			0
$619$	28.2667			1.13614			0.568068	−	0.822982i	$-0.307691\pi$
$619$	28.2667			1.13614			0.568068	+	0.822982i	$0.307691\pi$
$620$	2.74523	+	6.43650i	0.110251	+	0.258496i
$621$		0			0
$622$	12.2395	+	13.8103i	0.490760	+	0.553741i
$623$	−35.5768	−	2.34732i	−1.42536	−	0.0940432i
$624$		0			0
$625$	33.9185			1.35674
$626$	3.77181	+	18.4576i	0.150752	+	0.737715i
$627$		0			0
$628$	−10.2777	−	24.0972i	−0.410124	−	0.961582i
$629$			0.919927i			0.0366799i
$630$		0			0
$631$			21.2515i			0.846007i	0.906128	+	0.423004i	$0.139024\pi$
$631$			21.2515i			0.846007i	−0.906128	+	0.423004i	$0.860976\pi$
$632$	−12.1766	+	25.6995i	−0.484360	+	1.02227i
$633$		0			0
$634$	27.2316	−	5.56476i	1.08150	−	0.221005i
$635$	−23.7333			−0.941828
$636$		0			0
$637$	1.20884	−	9.12091i	0.0478958	−	0.361384i
$638$	−13.7711	+	12.2049i	−0.545205	+	0.483195i
$639$		0			0
$640$	−28.1904	+	34.6209i	−1.11432	+	1.36851i
$641$	34.5020			1.36275			0.681373	−	0.731936i	$-0.261383\pi$
$641$	34.5020			1.36275			0.681373	+	0.731936i	$0.261383\pi$
$642$		0			0
$643$	3.50574	+	6.07213i	0.138253	+	0.239461i	0.926835	−	0.375468i	$-0.122518\pi$
$643$	3.50574	+	6.07213i	0.138253	+	0.239461i	−0.788582	+	0.614929i	$0.789185\pi$
$644$	3.30782	−	17.5462i	0.130346	−	0.691418i
$645$		0			0
$646$	−7.77679	−	2.59463i	−0.305974	−	0.102084i
$647$	0.330066	+	0.571691i	0.0129762	+	0.0224755i	0.872441	−	0.488720i	$-0.162536\pi$
$647$	0.330066	+	0.571691i	0.0129762	+	0.0224755i	−0.859464	+	0.511196i	$0.829203\pi$
$648$		0			0
$649$	−29.6370	−	17.1109i	−1.16335	−	0.671662i
$650$	−3.93471	−	19.2548i	−0.154332	−	0.755235i
$651$		0			0
$652$	−6.30285	−	14.7777i	−0.246839	−	0.578741i
$653$	−2.38048			−0.0931552			−0.0465776	−	0.998915i	$-0.514831\pi$
$653$	−2.38048			−0.0931552			−0.0465776	+	0.998915i	$0.514831\pi$
$654$		0			0
$655$			7.88686i			0.308165i
$656$	−29.3022	−	28.1023i	−1.14406	−	1.09721i
$657$		0			0
$658$	7.28037	−	5.64205i	0.283819	−	0.219950i
$659$	−4.53599	−	2.61885i	−0.176697	−	0.102016i	0.409043	−	0.912515i	$-0.365863\pi$
$659$	−4.53599	−	2.61885i	−0.176697	−	0.102016i	−0.585740	+	0.810499i	$0.699196\pi$
$660$		0			0
$661$	−6.35756	−	3.67054i	−0.247280	−	0.142767i	0.371238	−	0.928538i	$-0.378933\pi$
$661$	−6.35756	−	3.67054i	−0.247280	−	0.142767i	−0.618518	+	0.785770i	$0.712267\pi$
$662$	4.07906	+	19.9612i	0.158537	+	0.775814i
$663$		0			0
$664$	0.594254	+	7.30915i	0.0230615	+	0.283650i
$665$	−31.1453	−	2.05493i	−1.20776	−	0.0796867i
$666$		0			0
$667$	−7.77183	−	4.48707i	−0.300926	−	0.173740i
$668$	2.32474	−	19.2070i	0.0899469	−	0.743142i
$669$		0			0
$670$	5.16292	+	5.82550i	0.199461	+	0.225059i
$671$	5.80096	+	10.0476i	0.223943	+	0.387881i
$672$		0			0
$673$	6.21172	−	10.7590i	0.239444	−	0.414730i	−0.721111	−	0.692820i	$-0.756368\pi$
$673$	6.21172	−	10.7590i	0.239444	−	0.414730i	0.960555	+	0.278090i	$0.0897014\pi$
$674$	1.35753	−	0.277411i	0.0522901	−	0.0106855i
$675$		0			0
$676$	20.7374	−	8.84470i	0.797592	−	0.340181i
$677$	−25.8330	+	14.9147i	−0.992843	+	0.573218i	−0.906123	−	0.423014i	$-0.860972\pi$
$677$	−25.8330	+	14.9147i	−0.992843	+	0.573218i	−0.0867203	+	0.996233i	$0.527639\pi$
$678$		0			0
$679$	−5.74324	−	0.378932i	−0.220405	−	0.0145421i
$680$	−19.5591	−	9.26722i	−0.750055	−	0.355382i
$681$		0			0
$682$	4.59087	−	4.06872i	0.175794	−	0.155799i
$683$	−9.32990	+	5.38662i	−0.356999	+	0.206113i	−0.667763	−	0.744374i	$-0.732748\pi$
$683$	−9.32990	+	5.38662i	−0.356999	+	0.206113i	0.310765	+	0.950487i	$0.399415\pi$
$684$		0			0
$685$		−	39.7054i		−	1.51707i
$686$	−22.7338	−	13.0067i	−0.867981	−	0.496597i
$687$		0			0
$688$	−2.54600	+	10.3635i	−0.0970654	+	0.395103i
$689$	−14.4432	−	8.33879i	−0.550243	−	0.317683i
$690$		0			0
$691$	23.6969	+	41.0442i	0.901471	+	1.56139i	0.825586	+	0.564277i	$0.190845\pi$
$691$	23.6969	+	41.0442i	0.901471	+	1.56139i	0.0758850	+	0.997117i	$0.475822\pi$
$692$	32.5383	+	3.93831i	1.23692	+	0.149712i
$693$		0			0
$694$	29.0348	−	25.7325i	1.10215	−	0.976791i
$695$	−54.8179	+	31.6491i	−2.07936	+	1.20052i
$696$		0			0
$697$	9.84091	−	17.0450i	0.372751	−	0.645624i
$698$	15.9304	−	14.1185i	0.602976	−	0.534395i
$699$		0			0
$700$	−54.9771	−	10.3643i	−2.07794	−	0.391733i
$701$	39.5982			1.49560			0.747801	−	0.663923i	$-0.231110\pi$
$701$	39.5982			1.49560			0.747801	+	0.663923i	$0.231110\pi$
$702$		0			0
$703$	−0.709135	−	1.22826i	−0.0267455	−	0.0463246i
$704$	36.6119	+	13.8373i	1.37986	+	0.521513i
$705$		0			0
$706$	−24.8274	−	8.28336i	−0.934392	−	0.311749i
$707$	0.834486	+	1.69402i	0.0313841	+	0.0637102i
$708$		0			0
$709$	−13.7496	−	23.8150i	−0.516378	−	0.894393i	−0.999819	−	0.0190160i	$-0.993947\pi$
$709$	−13.7496	−	23.8150i	−0.516378	−	0.894393i	0.483441	−	0.875377i	$-0.339387\pi$
$710$	3.80690	−	11.4103i	0.142870	−	0.428220i
$711$		0			0
$712$	37.9906	−	3.08874i	1.42376	−	0.115755i
$713$	2.59089	+	1.49585i	0.0970295	+	0.0560200i
$714$		0			0
$715$	−21.9766	+	12.6882i	−0.821877	+	0.474511i
$716$	36.8139	+	4.45581i	1.37580	+	0.166521i
$717$		0			0
$718$	−6.16986	+	5.46811i	−0.230257	+	0.204068i
$719$	−26.4956	+	45.8917i	−0.988118	+	1.71147i	−0.360954	+	0.932584i	$0.617549\pi$
$719$	−26.4956	+	45.8917i	−0.988118	+	1.71147i	−0.627164	+	0.778887i	$0.715784\pi$
$720$		0			0
$721$	−2.76427	+	1.36170i	−0.102947	+	0.0507123i
$722$	−13.9426	+	2.84916i	−0.518889	+	0.106035i
$723$		0			0
$724$	27.6256	−	36.7921i	1.02670	−	1.36737i
$725$	−14.0592	+	24.3513i	−0.522146	+	0.904383i
$726$		0			0
$727$	−15.2977	+	26.4963i	−0.567359	+	0.982694i	0.429467	+	0.903082i	$0.358701\pi$
$727$	−15.2977	+	26.4963i	−0.567359	+	0.982694i	−0.996826	+	0.0796118i	$0.974632\pi$
$728$	0.149904	+	9.83479i	0.00555580	+	0.364502i
$729$		0			0
$730$	−25.0600	+	5.12099i	−0.927511	+	0.189536i
$731$	−5.17332			−0.191342
$732$		0			0
$733$		−	0.705255i		−	0.0260492i	−0.999915	−	0.0130246i	$-0.995854\pi$
$733$		−	0.705255i		−	0.0260492i	0.999915	−	0.0130246i	$-0.00414597\pi$
$734$	0.809212	−	2.42542i	0.0298686	−	0.0895240i
$735$		0			0
$736$	−0.750461	+	19.0733i	−0.0276624	+	0.703053i
$737$	3.41198	−	5.90973i	0.125682	−	0.217688i
$738$		0			0
$739$	−29.5374	+	17.0534i	−1.08655	+	0.627321i	−0.932656	−	0.360766i	$-0.882515\pi$
$739$	−29.5374	+	17.0534i	−1.08655	+	0.627321i	−0.153896	+	0.988087i	$0.549182\pi$
$740$	−1.46894	−	3.44409i	−0.0539992	−	0.126607i
$741$		0			0
$742$	−37.5265	+	29.0818i	−1.37764	+	1.06763i
$743$	32.7970	−	18.9353i	1.20320	−	0.694670i	0.241938	−	0.970292i	$-0.422217\pi$
$743$	32.7970	−	18.9353i	1.20320	−	0.694670i	0.961266	+	0.275621i	$0.0888836\pi$
$744$		0			0
$745$		−	38.2411i		−	1.40105i
$746$	2.66720	−	7.99429i	0.0976530	−	0.292692i
$747$		0			0
$748$	−2.27987	+	18.8363i	−0.0833605	+	0.688725i
$749$	−32.1696	−	2.12251i	−1.17545	−	0.0775548i
$750$		0			0
$751$		−	18.1205i		−	0.661227i	−0.943766	−	0.330613i	$-0.892744\pi$
$751$		−	18.1205i		−	0.661227i	0.943766	−	0.330613i	$-0.107256\pi$
$752$	−6.81560	+	7.10660i	−0.248539	+	0.259151i
$753$		0			0
$754$	4.68946	+	1.56458i	0.170780	+	0.0569787i
$755$	65.3007			2.37654
$756$		0			0
$757$	−30.0755			−1.09311			−0.546555	−	0.837423i	$-0.684061\pi$
$757$	−30.0755			−1.09311			−0.546555	+	0.837423i	$0.684061\pi$
$758$	22.1768	+	7.39901i	0.805497	+	0.268744i
$759$		0			0
$760$	33.2584	−	2.70400i	1.20641	−	0.0980842i
$761$		−	22.2505i		−	0.806579i	−0.915072	−	0.403290i	$-0.867867\pi$
$761$		−	22.2505i		−	0.806579i	0.915072	−	0.403290i	$-0.132133\pi$
$762$		0			0
$763$	20.8871	+	13.9694i	0.756165	+	0.505728i
$764$	7.83108	+	0.947842i	0.283318	+	0.0342917i
$765$		0			0
$766$	−1.47613	+	4.42434i	−0.0533346	+	0.159858i
$767$			9.19389i			0.331972i
$768$		0			0
$769$	−9.46235	+	5.46309i	−0.341221	+	0.197004i	−0.660812	−	0.750552i	$-0.729788\pi$
$769$	−9.46235	+	5.46309i	−0.341221	+	0.197004i	0.319591	+	0.947556i	$0.396455\pi$
$770$	9.77213	+	71.5750i	0.352163	+	2.57938i
$771$		0			0
$772$	10.5781	−	4.51165i	0.380713	−	0.162378i
$773$	10.6286	−	6.13643i	0.382284	−	0.220712i	−0.296527	−	0.955024i	$-0.595829\pi$
$773$	10.6286	−	6.13643i	0.382284	−	0.220712i	0.678812	+	0.734312i	$0.262495\pi$
$774$		0			0
$775$	4.68690	−	8.11795i	0.168359	−	0.291605i
$776$	6.13290	−	0.498621i	0.220158	−	0.0178995i
$777$		0			0
$778$	4.31863	−	12.9441i	0.154830	−	0.464067i
$779$			30.3439i			1.08718i
$780$		0			0
$781$	−10.5449			−0.377327
$782$	−9.06605	+	1.85264i	−0.324201	+	0.0662504i
$783$		0			0
$784$	26.0781	+	10.1948i	0.931360	+	0.364100i
$785$	−25.8452	+	44.7653i	−0.922456	+	1.59774i
$786$		0			0
$787$	−1.13525	+	1.96631i	−0.0404672	+	0.0700913i	−0.885550	−	0.464545i	$-0.846218\pi$
$787$	−1.13525	+	1.96631i	−0.0404672	+	0.0700913i	0.845082	+	0.534636i	$0.179551\pi$
$788$	−26.5510	−	19.9360i	−0.945839	−	0.710189i
$789$		0			0
$790$	54.9758	−	11.2343i	1.95595	−	0.399698i
$791$	−27.4816	−	18.3798i	−0.977133	−	0.653512i
$792$		0			0
$793$	1.55846	−	2.69933i	0.0553425	−	0.0958560i
$794$	3.93743	−	3.48960i	0.139734	−	0.123841i
$795$		0			0
$796$	2.99624	−	24.7550i	0.106199	−	0.877416i
$797$	4.92030	−	2.84074i	0.174286	−	0.100624i	−0.410319	−	0.911942i	$-0.634583\pi$
$797$	4.92030	−	2.84074i	0.174286	−	0.100624i	0.584605	+	0.811318i	$0.301249\pi$
$798$		0			0
$799$	−4.13388	−	2.38669i	−0.146246	−	0.0844352i
$800$	59.7620	+	2.35140i	2.11290	+	0.0831345i
$801$		0			0
$802$	−10.7294	+	32.1589i	−0.378869	+	1.13557i
$803$	11.2115	+	19.4188i	0.395644	+	0.685276i
$804$		0			0
$805$	−31.6040	+	15.5684i	−1.11390	+	0.548712i
$806$	−1.56332	−	0.521583i	−0.0550656	−	0.0183720i
$807$		0			0
$808$	−1.14775	−	1.66078i	−0.0403777	−	0.0584259i
$809$	8.28527	+	14.3505i	0.291295	+	0.504537i	0.974116	−	0.226048i	$-0.0725806\pi$
$809$	8.28527	+	14.3505i	0.291295	+	0.504537i	−0.682821	+	0.730585i	$0.739247\pi$
$810$		0			0
$811$	10.2931			0.361438			0.180719	−	0.983535i	$-0.442158\pi$
$811$	10.2931			0.361438			0.180719	+	0.983535i	$0.442158\pi$
$812$	9.17247	−	10.6730i	0.321891	−	0.374548i
$813$		0			0
$814$	−2.45652	+	2.17712i	−0.0861009	+	0.0763080i
$815$	−15.8497	+	27.4526i	−0.555192	+	0.961621i
$816$		0			0
$817$	6.90726	−	3.98791i	0.241654	−	0.139519i
$818$	23.4483	−	20.7814i	0.819851	−	0.726603i
$819$		0			0
$820$	−9.62575	+	79.5280i	−0.336146	+	2.77724i
$821$	−0.0507961	−	0.0879815i	−0.00177280	−	0.00307058i	0.865138	−	0.501535i	$-0.167231\pi$
$821$	−0.0507961	−	0.0879815i	−0.00177280	−	0.00307058i	−0.866910	+	0.498464i	$0.833898\pi$
$822$		0			0
$823$	47.7924	+	27.5929i	1.66594	+	0.961829i	0.969794	+	0.243927i	$0.0784358\pi$
$823$	47.7924	+	27.5929i	1.66594	+	0.961829i	0.696144	+	0.717902i	$0.254898\pi$
$824$	2.71002	−	1.87288i	0.0944081	−	0.0652448i
$825$		0			0
$826$	24.2278	+	9.89973i	0.842991	+	0.344456i
$827$		−	37.1634i		−	1.29230i	−0.763211	−	0.646149i	$-0.776378\pi$
$827$		−	37.1634i		−	1.29230i	0.763211	−	0.646149i	$-0.223622\pi$
$828$		0			0
$829$	33.4823	−	19.3310i	1.16289	−	0.671393i	0.210893	−	0.977509i	$-0.432363\pi$
$829$	33.4823	−	19.3310i	1.16289	−	0.671393i	0.951994	+	0.306116i	$0.0990295\pi$
$830$	10.8287	−	9.59703i	0.375868	−	0.333118i
$831$		0			0
$832$	−1.69858	−	10.3770i	−0.0588876	−	0.359756i
$833$	−1.78338	+	13.4560i	−0.0617906	+	0.466223i
$834$		0			0
$835$	−33.0598	+	19.0871i	−1.14408	+	0.660537i
$836$	−11.4762	−	26.9072i	−0.396912	−	0.930604i
$837$		0			0
$838$	−49.0038	+	10.0139i	−1.69281	+	0.345924i
$839$	2.58403	−	4.47567i	0.0892106	−	0.154517i	−0.817967	−	0.575265i	$-0.804899\pi$
$839$	2.58403	−	4.47567i	0.0892106	−	0.154517i	0.907178	+	0.420748i	$0.138232\pi$
$840$		0			0
$841$	10.9635	+	18.9893i	0.378050	+	0.654802i
$842$	−29.0510	−	32.7792i	−1.00116	−	1.12965i
$843$		0			0
$844$	44.5157	+	5.38801i	1.53229	+	0.185463i
$845$	−38.5238	−	22.2417i	−1.32526	−	0.765138i
$846$		0			0
$847$	30.7024	−	15.1242i	1.05495	−	0.519673i
$848$	35.1308	−	36.6308i	1.20640	−	1.25791i
$849$		0			0
$850$	5.80484	+	28.4064i	0.199104	+	0.974332i
$851$	−1.38635	−	0.800409i	−0.0475234	−	0.0274377i
$852$		0			0
$853$	30.1332	+	17.3974i	1.03174	+	0.595675i	0.917483	−	0.397776i	$-0.130218\pi$
$853$	30.1332	+	17.3974i	1.03174	+	0.595675i	0.114257	+	0.993451i	$0.463551\pi$
$854$	−5.43518	−	7.01342i	−0.185988	−	0.239994i
$855$		0			0
$856$	34.3522	−	2.79293i	1.17413	−	0.0954602i
$857$			42.8423i			1.46347i	0.681592	+	0.731733i	$0.261288\pi$
$857$			42.8423i			1.46347i	−0.681592	+	0.731733i	$0.738712\pi$
$858$		0			0
$859$	31.9433			1.08989			0.544945	−	0.838472i	$-0.316550\pi$
$859$	31.9433			1.08989			0.544945	+	0.838472i	$0.316550\pi$
$860$	19.3682	−	8.26074i	0.660451	−	0.281689i
$861$		0			0
$862$	−1.38084	−	6.75722i	−0.0470315	−	0.230152i
$863$	−30.0490	−	17.3488i	−1.02288	−	0.590560i	−0.107943	−	0.994157i	$-0.534426\pi$
$863$	−30.0490	−	17.3488i	−1.02288	−	0.590560i	−0.914937	+	0.403597i	$0.867760\pi$
$864$		0			0
$865$	−32.3352	−	56.0061i	−1.09943	−	1.90427i
$866$	−17.5395	−	5.85184i	−0.596017	−	0.198854i
$867$		0			0
$868$	−3.05782	+	3.55804i	−0.103789	+	0.120768i
$869$	−24.5954	−	42.6005i	−0.834342	−	1.44512i
$870$		0			0
$871$	−1.83330			−0.0621189
$872$	−24.2760	−	11.5021i	−0.822088	−	0.389511i
$873$		0			0
$874$	10.6766	−	9.46225i	0.361141	−	0.320065i
$875$	25.7111	+	52.1939i	0.869193	+	1.76448i
$876$		0			0
$877$	−22.2426			−0.751081			−0.375540	−	0.926806i	$-0.622543\pi$
$877$	−22.2426			−0.751081			−0.375540	+	0.926806i	$0.622543\pi$
$878$	2.65662	−	0.542879i	0.0896565	−	0.0183213i
$879$		0			0
$880$	−21.5422	−	74.1613i	−0.726189	−	2.49998i
$881$			20.4228i			0.688061i	0.938958	+	0.344031i	$0.111792\pi$
$881$			20.4228i			0.688061i	−0.938958	+	0.344031i	$0.888208\pi$
$882$		0			0
$883$			11.6027i			0.390461i	0.980757	+	0.195231i	$0.0625456\pi$
$883$			11.6027i			0.390461i	−0.980757	+	0.195231i	$0.937454\pi$
$884$	4.68876	−	1.99980i	0.157700	−	0.0672606i
$885$		0			0
$886$	−6.02824	−	29.4996i	−0.202523	−	0.991059i
$887$	53.0798			1.78225			0.891123	−	0.453763i	$-0.149919\pi$
$887$	53.0798			1.78225			0.891123	+	0.453763i	$0.149919\pi$
$888$		0			0
$889$	−7.03152	−	14.2741i	−0.235830	−	0.478738i
$890$	−49.8822	−	56.2838i	−1.67206	−	1.88664i
$891$		0			0
$892$	−16.5018	+	7.03819i	−0.552522	+	0.235656i
$893$	7.35923			0.246267
$894$		0			0
$895$	−36.5841	−	63.3655i	−1.22287	−	2.11808i
$896$	−29.1744	−	6.69753i	−0.974647	−	0.223749i
$897$		0			0
$898$	2.68535	−	8.04870i	0.0896113	−	0.268589i
$899$	1.17898	+	2.04205i	0.0393210	+	0.0681060i
$900$		0			0
$901$	21.3079	+	12.3021i	0.709870	+	0.409844i
$902$	68.8055	−	14.0604i	2.29097	−	0.468159i
$903$		0			0
$904$	31.9403	+	15.1335i	1.06232	+	0.503334i
$905$	−90.7810			−3.01766
$906$		0			0
$907$		−	54.6847i		−	1.81578i	−0.419213	−	0.907888i	$-0.637694\pi$
$907$		−	54.6847i		−	1.81578i	0.419213	−	0.907888i	$-0.362306\pi$
$908$	12.4649	+	9.35935i	0.413662	+	0.310601i
$909$		0			0
$910$	15.3401	−	11.8881i	0.508521	−	0.394087i
$911$	−1.27865	−	0.738229i	−0.0423636	−	0.0244586i	0.478669	−	0.877996i	$-0.341120\pi$
$911$	−1.27865	−	0.738229i	−0.0423636	−	0.0244586i	−0.521032	+	0.853537i	$0.674453\pi$
$912$		0			0
$913$	−10.9852	−	6.34232i	−0.363558	−	0.209900i
$914$	−35.1038	+	7.17345i	−1.16113	+	0.237277i
$915$		0			0
$916$	−8.16706	+	10.8770i	−0.269847	+	0.359386i
$917$	−4.74345	+	2.33666i	−0.156643	+	0.0771632i
$918$		0			0
$919$	16.9505	+	9.78639i	0.559146	+	0.322823i	0.752803	−	0.658246i	$-0.228701\pi$
$919$	16.9505	+	9.78639i	0.559146	+	0.322823i	−0.193657	+	0.981069i	$0.562035\pi$
$920$	30.9838	−	21.4127i	1.02151	−	0.705956i
$921$		0			0
$922$	21.2272	−	18.8128i	0.699080	−	0.619568i
$923$	1.41648	+	2.45341i	0.0466239	+	0.0807549i
$924$		0			0
$925$	−2.50790	+	4.34381i	−0.0824592	+	0.142824i
$926$	10.8833	+	53.2584i	0.357649	+	1.75018i
$927$		0			0
$928$	−8.02871	+	12.7232i	−0.263555	+	0.417658i
$929$	12.5102	−	7.22275i	0.410445	−	0.236971i	−0.280536	−	0.959844i	$-0.590512\pi$
$929$	12.5102	−	7.22275i	0.410445	−	0.236971i	0.690981	+	0.722873i	$0.257179\pi$
$930$		0			0
$931$	−7.99158	−	19.3408i	−0.261913	−	0.633868i
$932$	31.1160	−	13.2713i	1.01924	−	0.434715i
$933$		0			0
$934$	30.6904	+	34.6290i	1.00422	+	1.13310i
$935$	32.4218	−	18.7187i	1.06031	−	0.612168i
$936$		0			0
$937$			31.4809i			1.02844i	0.857659	+	0.514218i	$0.171918\pi$
$937$			31.4809i			1.02844i	−0.857659	+	0.514218i	$0.828082\pi$
$938$	−1.97404	+	4.83111i	−0.0644548	+	0.157741i
$939$		0			0
$940$	19.2878	+	2.33451i	0.629097	+	0.0761434i
$941$	34.9308	+	20.1673i	1.13871	+	0.657435i	0.946111	−	0.323842i	$-0.104975\pi$
$941$	34.9308	+	20.1673i	1.13871	+	0.657435i	0.192600	+	0.981277i	$0.438308\pi$
$942$		0			0
$943$	17.1247	+	29.6609i	0.557658	+	0.965892i
$944$	−27.1714	−	6.67523i	−0.884354	−	0.217260i
$945$		0			0
$946$	−12.2433	−	13.8145i	−0.398064	−	0.449149i
$947$	12.8689	−	7.42986i	0.418183	−	0.241438i	−0.276117	−	0.961124i	$-0.589048\pi$
$947$	12.8689	−	7.42986i	0.418183	−	0.241438i	0.694300	+	0.719686i	$0.255714\pi$
$948$		0			0
$949$	3.01202	−	5.21698i	0.0977745	−	0.169350i
$950$	−29.6478	−	33.4526i	−0.961902	−	1.08535i
$951$		0			0
$952$	−0.221152	−	14.5092i	−0.00716757	−	0.470245i
$953$	11.8041			0.382371			0.191185	−	0.981554i	$-0.438767\pi$
$953$	11.8041			0.382371			0.191185	+	0.981554i	$0.438767\pi$
$954$		0			0
$955$	−7.78219	−	13.4791i	−0.251826	−	0.436175i
$956$	38.6302	+	4.67565i	1.24939	+	0.151221i
$957$		0			0
$958$	−16.4694	+	49.3633i	−0.532104	+	1.59486i
$959$	23.8803	−	11.7636i	0.771137	−	0.379867i
$960$		0			0
$961$	15.1070	+	26.1660i	0.487321	+	0.844066i
$962$	0.836512	+	0.279092i	0.0269702	+	0.00899829i
$963$		0			0
$964$	28.2895	−	37.6764i	0.911145	−	1.21347i
$965$	−19.6508	−	11.3454i	−0.632583	−	0.365222i
$966$		0			0
$967$	−2.41663	+	1.39524i	−0.0777137	+	0.0448680i	−0.538353	−	0.842719i	$-0.680953\pi$
$967$	−2.41663	+	1.39524i	−0.0777137	+	0.0448680i	0.460640	+	0.887587i	$0.347620\pi$
$968$	−30.0999	+	20.8018i	−0.967446	+	0.668595i
$969$		0			0
$970$	−8.05259	−	9.08601i	−0.258553	−	0.291734i
$971$	−26.2483	+	45.4633i	−0.842347	+	1.45899i	0.0455582	+	0.998962i	$0.485493\pi$
$971$	−26.2483	+	45.4633i	−0.842347	+	1.45899i	−0.887905	+	0.460026i	$0.847840\pi$
$972$		0			0
$973$	−35.2760	−	23.5928i	−1.13090	−	0.756350i
$974$	−1.28514	−	6.28893i	−0.0411786	−	0.201510i
$975$		0			0
$976$	6.84602	+	6.56569i	0.219136	+	0.210163i
$977$	−5.14397	+	8.90962i	−0.164570	+	0.285044i	−0.936503	−	0.350661i	$-0.885957\pi$
$977$	−5.14397	+	8.90962i	−0.164570	+	0.285044i	0.771932	+	0.635705i	$0.219290\pi$
$978$		0			0
$979$	−32.9653	+	57.0976i	−1.05358	+	1.82485i
$980$	−14.8097	−	53.2252i	−0.473080	−	1.70022i
$981$		0			0
$982$	−3.48721	−	17.0649i	−0.111281	−	0.544563i
$983$	32.9047			1.04950			0.524749	−	0.851257i	$-0.324159\pi$
$983$	32.9047			1.04950			0.524749	+	0.851257i	$0.324159\pi$
$984$		0			0
$985$			65.5120i			2.08739i
$986$	−6.91832	−	2.30821i	−0.220324	−	0.0735084i
$987$		0			0
$988$	−4.71872	+	6.28445i	−0.150123	+	0.199935i
$989$	4.50120	−	7.79630i	0.143130	−	0.247908i
$990$		0			0
$991$	48.3716	−	27.9273i	1.53657	−	0.887141i	0.537537	−	0.843240i	$-0.319355\pi$
$991$	48.3716	−	27.9273i	1.53657	−	0.887141i	0.999036	−	0.0439007i	$-0.0139785\pi$
$992$	2.67652	−	4.24151i	0.0849797	−	0.134668i
$993$		0			0
$994$	7.99045	−	1.09094i	0.253442	−	0.0346024i
$995$	−42.6092	+	24.6004i	−1.35080	+	0.779885i
$996$		0			0
$997$		−	0.253367i		−	0.00802422i	−0.999992	−	0.00401211i	$-0.998723\pi$
$997$		−	0.253367i		−	0.00802422i	0.999992	−	0.00401211i	$-0.00127710\pi$
$998$	17.3748	+	5.79689i	0.549990	+	0.183497i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.18		84
3.2	odd	2		252.2.n.b.187.25	yes	84
4.3	odd	2	inner	756.2.n.b.19.39		84
7.3	odd	6		756.2.bj.b.451.11		84
9.4	even	3		756.2.bj.b.523.11		84
9.5	odd	6		252.2.bj.b.103.32	yes	84
12.11	even	2		252.2.n.b.187.4	yes	84
21.17	even	6		252.2.bj.b.115.32	yes	84
28.3	even	6		756.2.bj.b.451.12		84
36.23	even	6		252.2.bj.b.103.31	yes	84
36.31	odd	6		756.2.bj.b.523.12		84
63.31	odd	6	inner	756.2.n.b.199.39		84
63.59	even	6		252.2.n.b.31.4	✓	84
84.59	odd	6		252.2.bj.b.115.31	yes	84
252.31	even	6	inner	756.2.n.b.199.18		84
252.59	odd	6		252.2.n.b.31.25	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.4	✓	84	63.59	even	6
252.2.n.b.31.25	yes	84	252.59	odd	6
252.2.n.b.187.4	yes	84	12.11	even	2
252.2.n.b.187.25	yes	84	3.2	odd	2
252.2.bj.b.103.31	yes	84	36.23	even	6
252.2.bj.b.103.32	yes	84	9.5	odd	6
252.2.bj.b.115.31	yes	84	84.59	odd	6
252.2.bj.b.115.32	yes	84	21.17	even	6
756.2.n.b.19.18		84	1.1	even	1	trivial
756.2.n.b.19.39		84	4.3	odd	2	inner
756.2.n.b.199.18		84	252.31	even	6	inner
756.2.n.b.199.39		84	63.31	odd	6	inner
756.2.bj.b.451.11		84	7.3	odd	6
756.2.bj.b.451.12		84	28.3	even	6
756.2.bj.b.523.11		84	9.4	even	3
756.2.bj.b.523.12		84	36.31	odd	6

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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.n (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.447581 + 1.34152i) q^{2} +(-1.59934 - 1.20088i) q^{4} +3.94623i q^{5} +(-2.37341 + 1.16916i) q^{7} +(2.32683 - 1.60806i) q^{8} +O(q^{10})\)	\(q+(-0.447581 + 1.34152i) q^{2} +(-1.59934 - 1.20088i) q^{4} +3.94623i q^{5} +(-2.37341 + 1.16916i) q^{7} +(2.32683 - 1.60806i) q^{8} +(-5.29393 - 1.76626i) q^{10} +4.89244i q^{11} +(1.13829 - 0.657191i) q^{13} +(-0.506153 - 3.70726i) q^{14} +(1.11579 + 3.84122i) q^{16} +(-1.67931 + 0.969547i) q^{17} +(1.49477 - 2.58902i) q^{19} +(4.73893 - 6.31137i) q^{20} +(-6.56330 - 2.18976i) q^{22} -3.37433i q^{23} -10.5727 q^{25} +(0.372157 + 1.82118i) q^{26} +(5.19991 + 0.980288i) q^{28} +(1.32976 - 2.30322i) q^{29} +(-0.443302 + 0.767822i) q^{31} +(-5.65248 - 0.222403i) q^{32} +(-0.549040 - 2.68677i) q^{34} +(-4.61376 - 9.36601i) q^{35} +(0.237205 - 0.410852i) q^{37} +(2.80419 + 3.16406i) q^{38} +(6.34576 + 9.18221i) q^{40} +(-8.79016 + 5.07500i) q^{41} +(2.31047 + 1.33395i) q^{43} +(5.87522 - 7.82469i) q^{44} +(4.52673 + 1.51029i) q^{46} +(1.23083 + 2.13186i) q^{47} +(4.26614 - 5.54978i) q^{49} +(4.73214 - 14.1835i) q^{50} +(-2.60972 - 0.315870i) q^{52} +(-6.34427 - 10.9886i) q^{53} -19.3067 q^{55} +(-3.64245 + 6.53701i) q^{56} +(2.49463 + 2.81478i) q^{58} +(-3.49742 + 6.05771i) q^{59} +(2.05369 - 1.18570i) q^{61} +(-0.831634 - 0.938361i) q^{62} +(2.82830 - 7.48336i) q^{64} +(2.59342 + 4.49194i) q^{65} +(-1.20793 - 0.697399i) q^{67} +(3.85009 + 0.465999i) q^{68} +(14.6297 - 1.99739i) q^{70} +2.15535i q^{71} +(3.96915 - 2.29159i) q^{73} +(0.444996 + 0.502105i) q^{74} +(-5.49974 + 2.34569i) q^{76} +(-5.72003 - 11.6118i) q^{77} +(-8.70741 + 5.02722i) q^{79} +(-15.1583 + 4.40317i) q^{80} +(-2.87390 - 14.0636i) q^{82} +(-1.29635 + 2.24535i) q^{83} +(-3.82605 - 6.62692i) q^{85} +(-2.82365 + 2.50249i) q^{86} +(7.86733 + 11.3839i) q^{88} +(11.6706 + 6.73801i) q^{89} +(-1.93326 + 2.89062i) q^{91} +(-4.05215 + 5.39671i) q^{92} +(-3.41082 + 0.697000i) q^{94} +(10.2169 + 5.89870i) q^{95} +(1.88401 + 1.08773i) q^{97} +(5.53568 + 8.20708i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 84 * q + q^2 + q^4 + 16 * q^8	\( 84 q + q^{2} + q^{4} + 16 q^{8} - 18 q^{10} - 18 q^{13} + 25 q^{14} - 7 q^{16} - 6 q^{17} - 24 q^{20} + 6 q^{22} - 32 q^{25} + 30 q^{26} - 4 q^{28} - 10 q^{29} - 9 q^{32} + 24 q^{34} + 2 q^{37} + 6 q^{41} + 13 q^{44} + 10 q^{46} + 2 q^{49} + 17 q^{50} + 2 q^{53} + 32 q^{56} + 26 q^{58} - 24 q^{61} - 8 q^{64} - 50 q^{65} - 4 q^{70} + 30 q^{73} - 46 q^{74} - 46 q^{77} - 3 q^{80} - 18 q^{82} - 50 q^{85} - 18 q^{86} - 2 q^{88} + 102 q^{89} - 28 q^{92} + 3 q^{94} - 6 q^{97} - 21 q^{98}+O(q^{100}) \) 84 * q + q^2 + q^4 + 16 * q^8 - 18 * q^10 - 18 * q^13 + 25 * q^14 - 7 * q^16 - 6 * q^17 - 24 * q^20 + 6 * q^22 - 32 * q^25 + 30 * q^26 - 4 * q^28 - 10 * q^29 - 9 * q^32 + 24 * q^34 + 2 * q^37 + 6 * q^41 + 13 * q^44 + 10 * q^46 + 2 * q^49 + 17 * q^50 + 2 * q^53 + 32 * q^56 + 26 * q^58 - 24 * q^61 - 8 * q^64 - 50 * q^65 - 4 * q^70 + 30 * q^73 - 46 * q^74 - 46 * q^77 - 3 * q^80 - 18 * q^82 - 50 * q^85 - 18 * q^86 - 2 * q^88 + 102 * q^89 - 28 * q^92 + 3 * q^94 - 6 * q^97 - 21 * q^98

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