LMFDB - Embedded newform 756.2.n.b.19.2

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			19.2
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37782 + 0.318759i) q^{2} +(1.79679 - 0.878385i) q^{4} -0.594537i q^{5} +(2.59555 + 0.512964i) q^{7} +(-2.19566 + 1.78300i) q^{8} +O(q^{10})$	\(q+(-1.37782 + 0.318759i) q^{2} +(1.79679 - 0.878385i) q^{4} -0.594537i q^{5} +(2.59555 + 0.512964i) q^{7} +(-2.19566 + 1.78300i) q^{8} +(0.189514 + 0.819166i) q^{10} +3.04340i q^{11} +(-6.21148 + 3.58620i) q^{13} +(-3.73971 + 0.120581i) q^{14} +(2.45688 - 3.15654i) q^{16} +(-2.28182 + 1.31741i) q^{17} +(-1.15636 + 2.00287i) q^{19} +(-0.522233 - 1.06826i) q^{20} +(-0.970111 - 4.19326i) q^{22} +1.55285i q^{23} +4.64653 q^{25} +(7.41518 - 6.92111i) q^{26} +(5.11422 - 1.35821i) q^{28} +(3.50068 - 6.06335i) q^{29} +(-2.95896 + 5.12507i) q^{31} +(-2.37897 + 5.13230i) q^{32} +(2.72401 - 2.54251i) q^{34} +(0.304976 - 1.54315i) q^{35} +(-2.74961 + 4.76246i) q^{37} +(0.954823 - 3.12820i) q^{38} +(1.06006 + 1.30540i) q^{40} +(-3.27676 + 1.89184i) q^{41} +(2.52490 + 1.45775i) q^{43} +(2.67328 + 5.46834i) q^{44} +(-0.494984 - 2.13955i) q^{46} +(4.83923 + 8.38180i) q^{47} +(6.47374 + 2.66284i) q^{49} +(-6.40208 + 1.48112i) q^{50} +(-8.01063 + 11.8997i) q^{52} +(-4.10505 - 7.11016i) q^{53} +1.80941 q^{55} +(-6.61355 + 3.50157i) q^{56} +(-2.89056 + 9.47008i) q^{58} +(1.88501 - 3.26493i) q^{59} +(2.31834 - 1.33850i) q^{61} +(2.44326 - 8.00462i) q^{62} +(1.64182 - 7.82971i) q^{64} +(2.13213 + 3.69296i) q^{65} +(-7.72990 - 4.46286i) q^{67} +(-2.94275 + 4.37143i) q^{68} +(0.0716899 + 2.22340i) q^{70} +8.75743i q^{71} +(-1.30083 + 0.751036i) q^{73} +(2.27039 - 7.43829i) q^{74} +(-0.318435 + 4.61446i) q^{76} +(-1.56115 + 7.89929i) q^{77} +(-5.83074 + 3.36638i) q^{79} +(-1.87668 - 1.46071i) q^{80} +(3.91175 - 3.65111i) q^{82} +(-4.99378 + 8.64947i) q^{83} +(0.783250 + 1.35663i) q^{85} +(-3.94354 - 1.20369i) q^{86} +(-5.42638 - 6.68227i) q^{88} +(13.7577 + 7.94299i) q^{89} +(-17.9618 + 6.12189i) q^{91} +(1.36400 + 2.79014i) q^{92} +(-9.33938 - 10.0061i) q^{94} +(1.19078 + 0.687498i) q^{95} +(-1.20110 - 0.693454i) q^{97} +(-9.76846 - 1.60536i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.37782	+	0.318759i	−0.974267	+	0.225396i
$2$	−1.37782	+	0.318759i	−0.974267	+	0.225396i
$3$		0			0
$3$		0			0
$4$	1.79679	−	0.878385i	0.898393	−	0.439193i
$5$		−	0.594537i		−	0.265885i	−0.991124	−	0.132943i	$-0.957557\pi$
$5$		−	0.594537i		−	0.265885i	0.991124	−	0.132943i	$-0.0424426\pi$
$6$		0			0
$7$	2.59555	+	0.512964i	0.981025	+	0.193882i
$7$	2.59555	+	0.512964i	0.981025	+	0.193882i
$8$	−2.19566	+	1.78300i	−0.776282	+	0.630386i
$9$		0			0
$10$	0.189514	+	0.819166i	0.0599296	+	0.259043i
$11$			3.04340i			0.917620i	0.888534	+	0.458810i	$0.151724\pi$
$11$			3.04340i			0.917620i	−0.888534	+	0.458810i	$0.848276\pi$
$12$		0			0
$13$	−6.21148	+	3.58620i	−1.72275	+	0.994633i	−0.809644	+	0.586921i	$0.800340\pi$
$13$	−6.21148	+	3.58620i	−1.72275	+	0.994633i	−0.913110	+	0.407712i	$0.866327\pi$
$14$	−3.73971	+	0.120581i	−0.999481	+	0.0322266i
$15$		0			0
$16$	2.45688	−	3.15654i	0.614220	−	0.789135i
$17$	−2.28182	+	1.31741i	−0.553423	+	0.319519i	−0.750502	−	0.660869i	$-0.770188\pi$
$17$	−2.28182	+	1.31741i	−0.553423	+	0.319519i	0.197078	+	0.980388i	$0.436855\pi$
$18$		0			0
$19$	−1.15636	+	2.00287i	−0.265287	+	0.459490i	−0.967639	−	0.252340i	$-0.918800\pi$
$19$	−1.15636	+	2.00287i	−0.265287	+	0.459490i	0.702352	+	0.711830i	$0.252133\pi$
$20$	−0.522233	−	1.06826i	−0.116775	−	0.238869i
$21$		0			0
$22$	−0.970111	−	4.19326i	−0.206828	−	0.894007i
$23$			1.55285i			0.323792i	0.986808	+	0.161896i	$0.0517608\pi$
$23$			1.55285i			0.323792i	−0.986808	+	0.161896i	$0.948239\pi$
$24$		0			0
$25$	4.64653			0.929305
$26$	7.41518	−	6.92111i	1.45424	−	1.35734i
$27$		0			0
$28$	5.11422	−	1.35821i	0.966497	−	0.256677i
$29$	3.50068	−	6.06335i	0.650059	−	1.12594i	−0.333049	−	0.942910i	$-0.608077\pi$
$29$	3.50068	−	6.06335i	0.650059	−	1.12594i	0.983108	−	0.183026i	$-0.0585892\pi$
$30$		0			0
$31$	−2.95896	+	5.12507i	−0.531445	+	0.920489i	0.467882	+	0.883791i	$0.345017\pi$
$31$	−2.95896	+	5.12507i	−0.531445	+	0.920489i	−0.999326	+	0.0366980i	$0.988316\pi$
$32$	−2.37897	+	5.13230i	−0.420546	+	0.907271i
$33$		0			0
$34$	2.72401	−	2.54251i	0.467164	−	0.436037i
$35$	0.304976	−	1.54315i	0.0515503	−	0.260840i
$36$		0			0
$37$	−2.74961	+	4.76246i	−0.452033	+	0.782944i	−0.998512	−	0.0545287i	$-0.982634\pi$
$37$	−2.74961	+	4.76246i	−0.452033	+	0.782944i	0.546479	+	0.837473i	$0.315968\pi$
$38$	0.954823	−	3.12820i	0.154893	−	0.507461i
$39$		0			0
$40$	1.06006	+	1.30540i	0.167610	+	0.206402i
$41$	−3.27676	+	1.89184i	−0.511744	+	0.295456i	−0.733550	−	0.679635i	$-0.762138\pi$
$41$	−3.27676	+	1.89184i	−0.511744	+	0.295456i	0.221806	+	0.975091i	$0.428805\pi$
$42$		0			0
$43$	2.52490	+	1.45775i	0.385044	+	0.222305i	0.680011	−	0.733202i	$-0.261975\pi$
$43$	2.52490	+	1.45775i	0.385044	+	0.222305i	−0.294967	+	0.955508i	$0.595309\pi$
$44$	2.67328	+	5.46834i	0.403012	+	0.824383i
$45$		0			0
$46$	−0.494984	−	2.13955i	−0.0729815	−	0.315459i
$47$	4.83923	+	8.38180i	0.705875	+	1.22261i	0.966375	+	0.257137i	$0.0827793\pi$
$47$	4.83923	+	8.38180i	0.705875	+	1.22261i	−0.260500	+	0.965474i	$0.583887\pi$
$48$		0			0
$49$	6.47374	+	2.66284i	0.924820	+	0.380406i
$50$	−6.40208	+	1.48112i	−0.905391	+	0.209462i
$51$		0			0
$52$	−8.01063	+	11.8997i	−1.11088	+	1.65019i
$53$	−4.10505	−	7.11016i	−0.563872	−	0.976655i	−0.997154	−	0.0753965i	$-0.975978\pi$
$53$	−4.10505	−	7.11016i	−0.563872	−	0.976655i	0.433282	−	0.901259i	$-0.357356\pi$
$54$		0			0
$55$	1.80941			0.243981
$56$	−6.61355	+	3.50157i	−0.883773	+	0.467917i
$57$		0			0
$58$	−2.89056	+	9.47008i	−0.379549	+	1.24348i
$59$	1.88501	−	3.26493i	0.245407	−	0.425057i	−0.716839	−	0.697239i	$-0.754412\pi$
$59$	1.88501	−	3.26493i	0.245407	−	0.425057i	0.962246	+	0.272181i	$0.0877451\pi$
$60$		0			0
$61$	2.31834	−	1.33850i	0.296833	−	0.171377i	−0.344186	−	0.938901i	$-0.611845\pi$
$61$	2.31834	−	1.33850i	0.296833	−	0.171377i	0.641019	+	0.767525i	$0.278512\pi$
$62$	2.44326	−	8.00462i	0.310294	−	1.01659i
$63$		0			0
$64$	1.64182	−	7.82971i	0.205228	−	0.978714i
$65$	2.13213	+	3.69296i	0.264458	+	0.458055i
$66$		0			0
$67$	−7.72990	−	4.46286i	−0.944358	−	0.545225i	−0.0530340	−	0.998593i	$-0.516889\pi$
$67$	−7.72990	−	4.46286i	−0.944358	−	0.545225i	−0.891324	+	0.453368i	$0.850223\pi$
$68$	−2.94275	+	4.37143i	−0.356861	+	0.530113i
$69$		0			0
$70$	0.0716899	+	2.22340i	0.00856858	+	0.265747i
$71$			8.75743i			1.03932i	0.854374	+	0.519658i	$0.173941\pi$
$71$			8.75743i			1.03932i	−0.854374	+	0.519658i	$0.826059\pi$
$72$		0			0
$73$	−1.30083	+	0.751036i	−0.152251	+	0.0879022i	−0.574190	−	0.818722i	$-0.694683\pi$
$73$	−1.30083	+	0.751036i	−0.152251	+	0.0879022i	0.421939	+	0.906624i	$0.361350\pi$
$74$	2.27039	−	7.43829i	0.263928	−	0.864683i
$75$		0			0
$76$	−0.318435	+	4.61446i	−0.0365270	+	0.529315i
$77$	−1.56115	+	7.89929i	−0.177910	+	0.900208i
$78$		0			0
$79$	−5.83074	+	3.36638i	−0.656010	+	0.378747i	−0.790755	−	0.612133i	$-0.790312\pi$
$79$	−5.83074	+	3.36638i	−0.656010	+	0.378747i	0.134745	+	0.990880i	$0.456978\pi$
$80$	−1.87668	−	1.46071i	−0.209819	−	0.163312i
$81$		0			0
$82$	3.91175	−	3.65111i	0.431981	−	0.403198i
$83$	−4.99378	+	8.64947i	−0.548138	+	0.949403i	0.450264	+	0.892895i	$0.351330\pi$
$83$	−4.99378	+	8.64947i	−0.548138	+	0.949403i	−0.998402	+	0.0565077i	$0.982003\pi$
$84$		0			0
$85$	0.783250	+	1.35663i	0.0849554	+	0.147147i
$86$	−3.94354	−	1.20369i	−0.425242	−	0.129797i
$87$		0			0
$88$	−5.42638	−	6.68227i	−0.578454	−	0.712332i
$89$	13.7577	+	7.94299i	1.45831	+	0.841955i	0.998928	−	0.0462839i	$-0.0147379\pi$
$89$	13.7577	+	7.94299i	1.45831	+	0.841955i	0.459381	+	0.888239i	$0.348071\pi$
$90$		0			0
$91$	−17.9618	+	6.12189i	−1.88291	+	0.641748i
$92$	1.36400	+	2.79014i	0.142207	+	0.290892i
$93$		0			0
$94$	−9.33938	−	10.0061i	−0.963283	−	1.03205i
$95$	1.19078	+	0.687498i	0.122172	+	0.0705358i
$96$		0			0
$97$	−1.20110	−	0.693454i	−0.121953	−	0.0704096i	0.437783	−	0.899081i	$-0.355764\pi$
$97$	−1.20110	−	0.693454i	−0.121953	−	0.0704096i	−0.559736	+	0.828671i	$0.689097\pi$
$98$	−9.76846	−	1.60536i	−0.986763	−	0.162166i
$99$		0			0
$100$	8.34881	−	4.08144i	0.834881	−	0.408144i
$101$			7.93291i			0.789354i	0.918820	+	0.394677i	$0.129144\pi$
$101$			7.93291i			0.789354i	−0.918820	+	0.394677i	$0.870856\pi$
$102$		0			0
$103$	9.51396			0.937439			0.468719	−	0.883347i	$-0.344716\pi$
$103$	9.51396			0.937439			0.468719	+	0.883347i	$0.344716\pi$
$104$	7.24409	−	18.9491i	0.710342	−	1.85812i
$105$		0			0
$106$	7.92245	+	8.48801i	0.769497	+	0.824428i
$107$	11.8104	+	6.81874i	1.14176	+	0.659193i	0.946865	−	0.321632i	$-0.104231\pi$
$107$	11.8104	+	6.81874i	1.14176	+	0.659193i	0.194891	+	0.980825i	$0.437565\pi$
$108$		0			0
$109$	−4.57329	−	7.92116i	−0.438041	−	0.758710i	0.559497	−	0.828832i	$-0.310994\pi$
$109$	−4.57329	−	7.92116i	−0.438041	−	0.758710i	−0.997538	+	0.0701225i	$0.977661\pi$
$110$	−2.49305	+	0.576767i	−0.237703	+	0.0549925i
$111$		0			0
$112$	7.99614	−	6.93266i	0.755564	−	0.655075i
$113$	−3.57459	−	6.19136i	−0.336269	−	0.582435i	0.647459	−	0.762100i	$-0.275832\pi$
$113$	−3.57459	−	6.19136i	−0.336269	−	0.582435i	−0.983728	+	0.179666i	$0.942498\pi$
$114$		0			0
$115$	0.923227			0.0860913
$116$	0.964007	−	13.9695i	0.0895058	−	1.29703i
$117$		0			0
$118$	−1.55648	+	5.09935i	−0.143285	+	0.469433i
$119$	−6.59837	+	2.24891i	−0.604871	+	0.206157i
$120$		0			0
$121$	1.73771			0.157974
$122$	−2.76761	+	2.58320i	−0.250567	+	0.233872i
$123$		0			0
$124$	−0.814831	+	11.8078i	−0.0731740	+	1.06037i
$125$		−	5.73522i		−	0.512973i
$126$		0			0
$127$			11.0990i			0.984879i	0.870347	+	0.492439i	$0.163895\pi$
$127$			11.0990i			0.984879i	−0.870347	+	0.492439i	$0.836105\pi$
$128$	0.233649	+	11.3113i	0.0206518	+	0.999787i
$129$		0			0
$130$	−4.11486	−	4.40860i	−0.360897	−	0.386660i
$131$	−4.99144			−0.436104			−0.218052	−	0.975937i	$-0.569970\pi$
$131$	−4.99144			−0.436104			−0.218052	+	0.975937i	$0.569970\pi$
$132$		0			0
$133$	−4.02879	+	4.60538i	−0.349340	+	0.399337i
$134$	12.0730	+	3.68505i	1.04295	+	0.318340i
$135$		0			0
$136$	2.66116	−	6.96107i	0.228192	−	0.596907i
$137$	6.30936			0.539045			0.269523	−	0.962994i	$-0.413134\pi$
$137$	6.30936			0.539045			0.269523	+	0.962994i	$0.413134\pi$
$138$		0			0
$139$	−3.37429	−	5.84444i	−0.286203	−	0.495719i	0.686697	−	0.726944i	$-0.259060\pi$
$139$	−3.37429	−	5.84444i	−0.286203	−	0.495719i	−0.972900	+	0.231225i	$0.925727\pi$
$140$	−0.807504	−	3.04060i	−0.0682465	−	0.256977i
$141$		0			0
$142$	−2.79151	−	12.0662i	−0.234258	−	1.01257i
$143$	−10.9142	−	18.9040i	−0.912695	−	1.58083i
$144$		0			0
$145$	−3.60489	−	2.08128i	−0.299369	−	0.172841i
$146$	1.55292	−	1.44945i	0.128520	−	0.119957i
$147$		0			0
$148$	−0.757180	+	10.9723i	−0.0622399	+	0.901921i
$149$	5.46213			0.447475			0.223737	−	0.974649i	$-0.428174\pi$
$149$	5.46213			0.447475			0.223737	+	0.974649i	$0.428174\pi$
$150$		0			0
$151$		−	13.7754i		−	1.12103i	−0.828146	−	0.560513i	$-0.810604\pi$
$151$		−	13.7754i		−	1.12103i	0.828146	−	0.560513i	$-0.189396\pi$
$152$	−1.03215	−	6.45941i	−0.0837186	−	0.523927i
$153$		0			0
$154$	−0.366976	−	11.3814i	−0.0295718	−	0.917143i
$155$	3.04704	+	1.75921i	0.244744	+	0.141303i
$156$		0			0
$157$	10.2143	+	5.89725i	0.815193	+	0.470652i	0.848756	−	0.528785i	$-0.177352\pi$
$157$	10.2143	+	5.89725i	0.815193	+	0.470652i	−0.0335632	+	0.999437i	$0.510686\pi$
$158$	6.96066	−	6.49687i	0.553760	−	0.516863i
$159$		0			0
$160$	3.05134	+	1.41438i	0.241230	+	0.111817i
$161$	−0.796555	+	4.03050i	−0.0627774	+	0.317648i
$162$		0			0
$163$	2.95281	+	1.70481i	0.231282	+	0.133531i	0.611163	−	0.791505i	$-0.290702\pi$
$163$	2.95281	+	1.70481i	0.231282	+	0.133531i	−0.379881	+	0.925035i	$0.624035\pi$
$164$	−4.22587	+	6.27749i	−0.329985	+	0.490189i
$165$		0			0
$166$	4.12344	−	13.5092i	0.320041	−	1.04852i
$167$	−6.47738	−	11.2191i	−0.501235	−	0.868164i	−0.999999	−	0.00142608i	$-0.999546\pi$
$167$	−6.47738	−	11.2191i	−0.501235	−	0.868164i	0.498764	−	0.866738i	$-0.333787\pi$
$168$		0			0
$169$	19.2217	−	33.2929i	1.47859	−	2.56099i
$170$	−1.51162	−	1.61952i	−0.115936	−	0.124212i
$171$		0			0
$172$	5.81718	+	0.401432i	0.443556	+	0.0306089i
$173$	−1.08031	+	0.623718i	−0.0821345	+	0.0474204i	−0.540505	−	0.841341i	$-0.681767\pi$
$173$	−1.08031	+	0.623718i	−0.0821345	+	0.0474204i	0.458370	+	0.888761i	$0.348433\pi$
$174$		0			0
$175$	12.0603	+	2.38350i	0.911671	+	0.180176i
$176$	9.60662	+	7.47726i	0.724126	+	0.563620i
$177$		0			0
$178$	−21.4875	−	6.55865i	−1.61056	−	0.491592i
$179$	−0.0914691	+	0.0528097i	−0.00683672	+	0.00394718i	−0.503414	−	0.864045i	$-0.667923\pi$
$179$	−0.0914691	+	0.0528097i	−0.00683672	+	0.00394718i	0.496578	+	0.867992i	$0.334590\pi$
$180$		0			0
$181$		−	22.3860i		−	1.66394i	−0.554821	−	0.831970i	$-0.687213\pi$
$181$		−	22.3860i		−	1.66394i	0.554821	−	0.831970i	$-0.312787\pi$
$182$	22.7967	−	14.1603i	1.68981	−	1.04963i
$183$		0			0
$184$	−2.76873	−	3.40953i	−0.204113	−	0.251354i
$185$	2.83146	+	1.63474i	0.208173	+	0.120189i
$186$		0			0
$187$	−4.00941	−	6.94450i	−0.293197	−	0.507832i
$188$	16.0575	+	10.8096i	1.17111	+	0.788370i
$189$		0			0
$190$	−1.85983	−	0.567678i	−0.134926	−	0.0411837i
$191$	18.7377	−	10.8182i	1.35581	−	0.782777i	0.366754	−	0.930318i	$-0.380469\pi$
$191$	18.7377	−	10.8182i	1.35581	−	0.782777i	0.989056	+	0.147541i	$0.0471357\pi$
$192$		0			0
$193$	−0.956641	+	1.65695i	−0.0688605	+	0.119270i	−0.898400	−	0.439178i	$-0.855270\pi$
$193$	−0.956641	+	1.65695i	−0.0688605	+	0.119270i	0.829539	+	0.558448i	$0.188603\pi$
$194$	1.87594	+	0.572596i	0.134685	+	0.0411100i
$195$		0			0
$196$	13.9709	−	0.901877i	0.997923	−	0.0644198i
$197$	−17.4136			−1.24067			−0.620334	−	0.784337i	$-0.713003\pi$
$197$	−17.4136			−1.24067			−0.620334	+	0.784337i	$0.713003\pi$
$198$		0			0
$199$	−1.77704	−	3.07792i	−0.125971	−	0.218188i	0.796141	−	0.605111i	$-0.206871\pi$
$199$	−1.77704	−	3.07792i	−0.125971	−	0.218188i	−0.922112	+	0.386923i	$0.873538\pi$
$200$	−10.2022	+	8.28475i	−0.721403	+	0.585821i
$201$		0			0
$202$	−2.52868	−	10.9301i	−0.177918	−	0.769042i
$203$	12.1964	−	13.9420i	0.856023	−	0.978536i
$204$		0			0
$205$	1.12477	+	1.94816i	0.0785572	+	0.136065i
$206$	−13.1085	+	3.03266i	−0.913316	+	0.211295i
$207$		0			0
$208$	−3.94086	+	28.4177i	−0.273250	+	1.97041i
$209$	−6.09554	−	3.51926i	−0.421638	−	0.243433i
$210$		0			0
$211$	2.88477	−	1.66552i	0.198596	−	0.114659i	−0.397405	−	0.917643i	$-0.630089\pi$
$211$	2.88477	−	1.66552i	0.198596	−	0.114659i	0.596000	+	0.802984i	$0.296756\pi$
$212$	−13.6214	−	9.16961i	−0.935519	−	0.629772i
$213$		0			0
$214$	−18.4462	−	5.63034i	−1.26095	−	0.384882i
$215$	0.866688	−	1.50115i	0.0591076	−	0.102377i
$216$		0			0
$217$	−10.3091	+	11.7845i	−0.699827	+	0.799985i
$218$	8.82611	+	9.45618i	0.597780	+	0.640453i
$219$		0			0
$220$	3.25113	−	1.58936i	0.219191	−	0.107155i
$221$	9.44900	−	16.3662i	0.635609	−	1.10091i
$222$		0			0
$223$	−6.52029	+	11.2935i	−0.436631	+	0.756267i	−0.997427	−	0.0716868i	$-0.977162\pi$
$223$	−6.52029	+	11.2935i	−0.436631	+	0.756267i	0.560796	+	0.827954i	$0.310495\pi$
$224$	−8.80740	+	12.1008i	−0.588469	+	0.808520i
$225$		0			0
$226$	6.89869	+	7.39117i	0.458894	+	0.491653i
$227$	−9.45279			−0.627404			−0.313702	−	0.949522i	$-0.601569\pi$
$227$	−9.45279			−0.627404			−0.313702	+	0.949522i	$0.601569\pi$
$228$		0			0
$229$			14.1912i			0.937780i	0.883256	+	0.468890i	$0.155346\pi$
$229$			14.1912i			0.937780i	−0.883256	+	0.468890i	$0.844654\pi$
$230$	−1.27204	+	0.294287i	−0.0838759	+	0.0194047i
$231$		0			0
$232$	3.12466	+	19.5547i	0.205144	+	1.28383i
$233$	12.9100	−	22.3607i	0.845761	−	1.46490i	−0.0391981	−	0.999231i	$-0.512480\pi$
$233$	12.9100	−	22.3607i	0.845761	−	1.46490i	0.884959	−	0.465669i	$-0.154186\pi$
$234$		0			0
$235$	4.98329	−	2.87710i	0.325074	−	0.187682i
$236$	0.519088	−	7.52214i	0.0337898	−	0.489649i
$237$		0			0
$238$	8.37451	−	5.20189i	0.542839	−	0.337188i
$239$	−18.8003	+	10.8544i	−1.21609	+	0.702110i	−0.964079	−	0.265614i	$-0.914425\pi$
$239$	−18.8003	+	10.8544i	−1.21609	+	0.702110i	−0.252011	+	0.967724i	$0.581092\pi$
$240$		0			0
$241$			3.76974i			0.242830i	0.992602	+	0.121415i	$0.0387432\pi$
$241$			3.76974i			0.242830i	−0.992602	+	0.121415i	$0.961257\pi$
$242$	−2.39426	+	0.553911i	−0.153909	+	0.0356067i
$243$		0			0
$244$	2.98985	−	4.44139i	0.191406	−	0.284331i
$245$	1.58316	−	3.84888i	0.101144	−	0.245896i
$246$		0			0
$247$		−	16.5877i		−	1.05545i
$248$	−2.64113	−	16.5287i	−0.167712	−	1.04957i
$249$		0			0
$250$	1.82815	+	7.90211i	0.115622	+	0.499773i
$251$	13.8993			0.877316			0.438658	−	0.898654i	$-0.355454\pi$
$251$	13.8993			0.877316			0.438658	+	0.898654i	$0.355454\pi$
$252$		0			0
$253$	−4.72594			−0.297118
$254$	−3.53791	−	15.2925i	−0.221988	−	0.959535i
$255$		0			0
$256$	−3.92750	−	15.5105i	−0.245469	−	0.969404i
$257$		−	4.29243i		−	0.267754i	−0.990998	−	0.133877i	$-0.957257\pi$
$257$		−	4.29243i		−	0.267754i	0.990998	−	0.133877i	$-0.0427428\pi$
$258$		0			0
$259$	−9.57971	+	10.9507i	−0.595254	+	0.680446i
$260$	7.07482	+	4.76262i	0.438762	+	0.295365i
$261$		0			0
$262$	6.87731	−	1.59106i	0.424882	−	0.0982962i
$263$		−	17.5231i		−	1.08052i	−0.841498	−	0.540260i	$-0.818326\pi$
$263$		−	17.5231i		−	1.08052i	0.841498	−	0.540260i	$-0.181674\pi$
$264$		0			0
$265$	−4.22725	+	2.44061i	−0.259678	+	0.149925i
$266$	4.08294	−	7.62960i	0.250341	−	0.467801i
$267$		0			0
$268$	−17.8091	−	1.22897i	−1.08786	−	0.0750714i
$269$	−3.89531	+	2.24896i	−0.237501	+	0.137122i	−0.614028	−	0.789284i	$-0.710452\pi$
$269$	−3.89531	+	2.24896i	−0.237501	+	0.137122i	0.376526	+	0.926406i	$0.377118\pi$
$270$		0			0
$271$	10.3784	−	17.9759i	0.630442	−	1.09196i	−0.357019	−	0.934097i	$-0.616207\pi$
$271$	10.3784	−	17.9759i	0.630442	−	1.09196i	0.987461	−	0.157861i	$-0.0504598\pi$
$272$	−1.44770	+	10.4394i	−0.0877796	+	0.632981i
$273$		0			0
$274$	−8.69318	+	2.01116i	−0.525174	+	0.121499i
$275$			14.1412i			0.852749i
$276$		0			0
$277$	−13.7047			−0.823437			−0.411718	−	0.911311i	$-0.635071\pi$
$277$	−13.7047			−0.823437			−0.411718	+	0.911311i	$0.635071\pi$
$278$	6.51213	+	6.97701i	0.390572	+	0.418453i
$279$		0			0
$280$	2.08181	+	3.93200i	0.124412	+	0.234982i
$281$	1.27529	−	2.20886i	0.0760773	−	0.131770i	−0.825477	−	0.564436i	$-0.809094\pi$
$281$	1.27529	−	2.20886i	0.0760773	−	0.131770i	0.901554	+	0.432666i	$0.142427\pi$
$282$		0			0
$283$	−4.29897	+	7.44604i	−0.255547	+	0.442621i	−0.965044	−	0.262088i	$-0.915589\pi$
$283$	−4.29897	+	7.44604i	−0.255547	+	0.442621i	0.709497	+	0.704709i	$0.248922\pi$
$284$	7.69240	+	15.7352i	0.456460	+	0.933714i
$285$		0			0
$286$	21.0637	+	22.5674i	1.24552	+	1.33444i
$287$	−9.47543	+	3.22950i	−0.559317	+	0.190631i
$288$		0			0
$289$	−5.02886	+	8.71023i	−0.295815	+	0.512367i
$290$	5.63032	+	1.71855i	0.330624	+	0.100917i
$291$		0			0
$292$	−1.67762	+	2.49208i	−0.0981752	+	0.145838i
$293$	−17.2244	+	9.94449i	−1.00626	+	0.580963i	−0.910094	−	0.414402i	$-0.863991\pi$
$293$	−17.2244	+	9.94449i	−1.00626	+	0.580963i	−0.0961641	+	0.995365i	$0.530657\pi$
$294$		0			0
$295$	−1.94112	−	1.12071i	−0.113016	−	0.0652500i
$296$	−2.45427	−	15.3593i	−0.142652	−	0.892740i
$297$		0			0
$298$	−7.52584	+	1.74110i	−0.435960	+	0.100859i
$299$	−5.56883	−	9.64550i	−0.322054	−	0.557813i
$300$		0			0
$301$	5.80573	+	5.07885i	0.334637	+	0.292740i
$302$	4.39103	+	18.9800i	0.252675	+	1.09218i
$303$		0			0
$304$	3.48112	+	8.57091i	0.199656	+	0.491575i
$305$	−0.795786	−	1.37834i	−0.0455665	−	0.0789236i
$306$		0			0
$307$	26.7987			1.52948			0.764742	−	0.644337i	$-0.222867\pi$
$307$	26.7987			1.52948			0.764742	+	0.644337i	$0.222867\pi$
$308$	4.13356	+	15.5646i	0.235532	+	0.886877i
$309$		0			0
$310$	−4.75904	−	1.45261i	−0.270296	−	0.0825026i
$311$	2.39677	−	4.15132i	0.135908	−	0.235400i	−0.790036	−	0.613061i	$-0.789938\pi$
$311$	2.39677	−	4.15132i	0.135908	−	0.235400i	0.925944	+	0.377661i	$0.123271\pi$
$312$		0			0
$313$	7.63187	−	4.40626i	0.431379	−	0.249057i	−0.268555	−	0.963264i	$-0.586546\pi$
$313$	7.63187	−	4.40626i	0.431379	−	0.249057i	0.699934	+	0.714208i	$0.253213\pi$
$314$	−15.9533	−	4.86945i	−0.900299	−	0.274799i
$315$		0			0
$316$	−7.51961	+	11.1703i	−0.423011	+	0.628378i
$317$	9.05618	+	15.6858i	0.508646	+	0.881000i	0.999950	+	0.0100123i	$0.00318708\pi$
$317$	9.05618	+	15.6858i	0.508646	+	0.881000i	−0.491304	+	0.870988i	$0.663480\pi$
$318$		0			0
$319$	18.4532	+	10.6540i	1.03318	+	0.596507i
$320$	−4.65506	−	0.976125i	−0.260225	−	0.0545671i
$321$		0			0
$322$	−0.187244	−	5.80721i	−0.0104347	−	0.323623i
$323$		−	6.09360i		−	0.339057i
$324$		0			0
$325$	−28.8618	+	16.6634i	−1.60096	+	0.924318i
$326$	−4.61187	−	1.40768i	−0.255428	−	0.0779644i
$327$		0			0
$328$	3.82150	−	9.99629i	0.211007	−	0.551953i
$329$	8.26091	+	24.2377i	0.455438	+	1.33627i
$330$		0			0
$331$	6.72887	−	3.88491i	0.369852	−	0.213534i	−0.303542	−	0.952818i	$-0.598169\pi$
$331$	6.72887	−	3.88491i	0.369852	−	0.213534i	0.673394	+	0.739284i	$0.264836\pi$
$332$	−1.37517	+	19.9277i	−0.0754725	+	1.09368i
$333$		0			0
$334$	12.5009	+	13.3933i	0.684017	+	0.732847i
$335$	−2.65334	+	4.59571i	−0.144967	+	0.251091i
$336$		0			0
$337$	3.96613	+	6.86954i	0.216049	+	0.374208i	0.953597	−	0.301087i	$-0.0973496\pi$
$337$	3.96613	+	6.86954i	0.216049	+	0.374208i	−0.737548	+	0.675295i	$0.764016\pi$
$338$	−15.8716	+	51.9988i	−0.863303	+	2.82836i
$339$		0			0
$340$	2.59897	+	1.74958i	0.140949	+	0.0948841i
$341$	−15.5976	−	9.00530i	−0.844659	−	0.487664i
$342$		0			0
$343$	15.4370	+	10.2323i	0.833517	+	0.552494i
$344$	−8.14299	+	1.30117i	−0.439041	+	0.0701546i
$345$		0			0
$346$	1.28966	−	1.20373i	0.0693326	−	0.0647130i
$347$	0.723464	+	0.417692i	0.0388376	+	0.0224229i	0.519293	−	0.854596i	$-0.326195\pi$
$347$	0.723464	+	0.417692i	0.0388376	+	0.0224229i	−0.480455	+	0.877019i	$0.659529\pi$
$348$		0			0
$349$	−13.8892	−	8.01895i	−0.743473	−	0.429244i	0.0798577	−	0.996806i	$-0.474553\pi$
$349$	−13.8892	−	8.01895i	−0.743473	−	0.429244i	−0.823331	+	0.567562i	$0.807887\pi$
$350$	−17.3767	+	0.560283i	−0.928822	+	0.0299484i
$351$		0			0
$352$	−15.6197	−	7.24014i	−0.832530	−	0.385901i
$353$		−	13.0342i		−	0.693741i	−0.937913	−	0.346871i	$-0.887244\pi$
$353$		−	13.0342i		−	0.693741i	0.937913	−	0.346871i	$-0.112756\pi$
$354$		0			0
$355$	5.20662			0.276339
$356$	31.6966	+	2.18732i	1.67992	+	0.115928i
$357$		0			0
$358$	0.109195	−	0.101919i	0.00577111	−	0.00538658i
$359$	−6.68926	−	3.86205i	−0.353046	−	0.203831i	0.312980	−	0.949760i	$-0.398673\pi$
$359$	−6.68926	−	3.86205i	−0.353046	−	0.203831i	−0.666026	+	0.745929i	$0.732006\pi$
$360$		0			0
$361$	6.82567	+	11.8224i	0.359246	+	0.622232i
$362$	7.13574	+	30.8439i	0.375046	+	1.62112i
$363$		0			0
$364$	−26.8961	+	26.7771i	−1.40974	+	1.40350i
$365$	0.446519	+	0.773394i	0.0233719	+	0.0404813i
$366$		0			0
$367$	−0.852542			−0.0445023			−0.0222512	−	0.999752i	$-0.507083\pi$
$367$	−0.852542			−0.0445023			−0.0222512	+	0.999752i	$0.507083\pi$
$368$	4.90163	+	3.81516i	0.255515	+	0.198879i
$369$		0			0
$370$	−4.42234	−	1.34983i	−0.229906	−	0.0701745i
$371$	−7.00760	−	20.5605i	−0.363817	−	1.06745i
$372$		0			0
$373$	−2.32991			−0.120638			−0.0603190	−	0.998179i	$-0.519212\pi$
$373$	−2.32991			−0.120638			−0.0603190	+	0.998179i	$0.519212\pi$
$374$	7.73787	+	8.29025i	0.400116	+	0.428679i
$375$		0			0
$376$	−25.5701	−	9.77521i	−1.31867	−	0.504118i
$377$			50.2165i			2.58628i
$378$		0			0
$379$		−	28.9056i		−	1.48478i	−0.669968	−	0.742390i	$-0.733692\pi$
$379$		−	28.9056i		−	1.48478i	0.669968	−	0.742390i	$-0.266308\pi$
$380$	2.74347	+	0.189322i	0.140737	+	0.00971199i
$381$		0			0
$382$	−22.3688	+	20.8783i	−1.14449	+	1.06823i
$383$	−17.7999			−0.909531			−0.454766	−	0.890611i	$-0.650277\pi$
$383$	−17.7999			−0.909531			−0.454766	+	0.890611i	$0.650277\pi$
$384$		0			0
$385$	4.69642	+	0.928164i	0.239352	+	0.0473036i
$386$	0.789913	−	2.58792i	0.0402055	−	0.131722i
$387$		0			0
$388$	−2.76724	−	0.190962i	−0.140485	−	0.00969462i
$389$	−25.6304			−1.29951			−0.649757	−	0.760142i	$-0.725129\pi$
$389$	−25.6304			−1.29951			−0.649757	+	0.760142i	$0.725129\pi$
$390$		0			0
$391$	−2.04574	−	3.54333i	−0.103458	−	0.179194i
$392$	−18.9620	+	5.69598i	−0.957723	+	0.287690i
$393$		0			0
$394$	23.9929	−	5.55074i	1.20874	−	0.279642i
$395$	2.00144	+	3.46659i	0.100703	+	0.174423i
$396$		0			0
$397$	5.33703	+	3.08134i	0.267858	+	0.154648i	0.627914	−	0.778283i	$-0.283909\pi$
$397$	5.33703	+	3.08134i	0.267858	+	0.154648i	−0.360056	+	0.932931i	$0.617242\pi$
$398$	3.42956	+	3.67438i	0.171908	+	0.184180i
$399$		0			0
$400$	11.4159	−	14.6669i	0.570797	−	0.733347i
$401$	−0.271966			−0.0135813			−0.00679066	−	0.999977i	$-0.502162\pi$
$401$	−0.271966			−0.0135813			−0.00679066	+	0.999977i	$0.502162\pi$
$402$		0			0
$403$		−	42.4457i		−	2.11437i
$404$	6.96815	+	14.2537i	0.346679	+	0.709150i
$405$		0			0
$406$	−12.3604	+	23.0973i	−0.613436	+	1.14630i
$407$	−14.4941	−	8.36816i	−0.718445	−	0.414794i
$408$		0			0
$409$	5.65970	+	3.26763i	0.279854	+	0.161574i	0.633357	−	0.773859i	$-0.281676\pi$
$409$	5.65970	+	3.26763i	0.279854	+	0.161574i	−0.353503	+	0.935433i	$0.615010\pi$
$410$	−2.17072	−	2.32568i	−0.107204	−	0.114857i
$411$		0			0
$412$	17.0946	−	8.35693i	0.842188	−	0.411716i
$413$	6.56741	−	7.50733i	0.323161	−	0.369412i
$414$		0			0
$415$	5.14243	+	2.96899i	0.252432	+	0.145742i
$416$	−3.62857	−	40.4106i	−0.177905	−	1.98129i
$417$		0			0
$418$	9.52037	+	2.90591i	0.465656	+	0.142133i
$419$	18.6788	+	32.3526i	0.912519	+	1.58053i	0.810493	+	0.585748i	$0.199199\pi$
$419$	18.6788	+	32.3526i	0.912519	+	1.58053i	0.102026	+	0.994782i	$0.467468\pi$
$420$		0			0
$421$	8.81289	−	15.2644i	0.429514	−	0.743940i	−0.567316	−	0.823500i	$-0.692018\pi$
$421$	8.81289	−	15.2644i	0.429514	−	0.743940i	0.996830	+	0.0795601i	$0.0253516\pi$
$422$	−3.44379	+	3.21434i	−0.167641	+	0.156471i
$423$		0			0
$424$	21.6907	+	8.29216i	1.05339	+	0.402703i
$425$	−10.6026	+	6.12139i	−0.514299	+	0.296931i
$426$		0			0
$427$	6.70397	−	2.28490i	0.324428	−	0.110574i
$428$	27.2103	+	1.87773i	1.31526	+	0.0907634i
$429$		0			0
$430$	−0.715638	+	2.34458i	−0.0345111	+	0.113066i
$431$	26.8406	−	15.4964i	1.29286	−	0.746436i	0.313703	−	0.949521i	$-0.398430\pi$
$431$	26.8406	−	15.4964i	1.29286	−	0.746436i	0.979161	+	0.203085i	$0.0650969\pi$
$432$		0			0
$433$		−	20.1669i		−	0.969161i	−0.874747	−	0.484581i	$-0.838972\pi$
$433$		−	20.1669i		−	0.969161i	0.874747	−	0.484581i	$-0.161028\pi$
$434$	10.4477	−	19.5231i	0.501504	−	0.937138i
$435$		0			0
$436$	−15.1751	−	10.2155i	−0.726753	−	0.489235i
$437$	−3.11016	−	1.79565i	−0.148779	−	0.0858977i
$438$		0			0
$439$	0.655078	+	1.13463i	0.0312652	+	0.0541529i	0.881235	−	0.472679i	$-0.156713\pi$
$439$	0.655078	+	1.13463i	0.0312652	+	0.0541529i	−0.849969	+	0.526832i	$0.823380\pi$
$440$	−3.97285	+	3.22619i	−0.189398	+	0.153802i
$441$		0			0
$442$	−7.80219	+	25.5616i	−0.371112	+	1.21584i
$443$	−2.20451	+	1.27277i	−0.104739	+	0.0604713i	−0.551455	−	0.834205i	$-0.685927\pi$
$443$	−2.20451	+	1.27277i	−0.104739	+	0.0604713i	0.446715	+	0.894676i	$0.352594\pi$
$444$		0			0
$445$	4.72240	−	8.17944i	0.223863	−	0.387743i
$446$	5.38391	−	17.6388i	0.254935	−	0.835221i
$447$		0			0
$448$	8.27779	−	19.4802i	0.391089	−	0.920353i
$449$	30.0500			1.41815			0.709073	−	0.705135i	$-0.249114\pi$
$449$	30.0500			1.41815			0.709073	+	0.705135i	$0.249114\pi$
$450$		0			0
$451$	−5.75762	−	9.97249i	−0.271116	−	0.469586i
$452$	−11.8612	−	7.98469i	−0.557902	−	0.375568i
$453$		0			0
$454$	13.0243	−	3.01316i	0.611259	−	0.141415i
$455$	3.63969	+	10.6789i	0.170631	+	0.500637i
$456$		0			0
$457$	19.1923	+	33.2421i	0.897779	+	1.55500i	0.830327	+	0.557276i	$0.188153\pi$
$457$	19.1923	+	33.2421i	0.897779	+	1.55500i	0.0674513	+	0.997723i	$0.478513\pi$
$458$	−4.52357	−	19.5529i	−0.211372	−	0.913649i
$459$		0			0
$460$	1.65884	−	0.810949i	0.0773438	−	0.0378107i
$461$	−29.8694	−	17.2451i	−1.39116	−	0.803186i	−0.397715	−	0.917509i	$-0.630197\pi$
$461$	−29.8694	−	17.2451i	−1.39116	−	0.803186i	−0.993444	+	0.114323i	$0.963530\pi$
$462$		0			0
$463$	−23.3117	+	13.4590i	−1.08339	+	0.625493i	−0.931808	−	0.362952i	$-0.881769\pi$
$463$	−23.3117	+	13.4590i	−1.08339	+	0.625493i	−0.151578	+	0.988445i	$0.548435\pi$
$464$	−10.5385	−	25.9469i	−0.489236	−	1.20456i
$465$		0			0
$466$	−10.6600	+	34.9243i	−0.493814	+	1.61784i
$467$	−10.1757	+	17.6248i	−0.470874	+	0.815577i	−0.999445	−	0.0333119i	$-0.989395\pi$
$467$	−10.1757	+	17.6248i	−0.470874	+	0.815577i	0.528571	+	0.848889i	$0.322728\pi$
$468$		0			0
$469$	−17.7740	−	15.5487i	−0.820729	−	0.717973i
$470$	−5.94899	+	5.55260i	−0.274406	+	0.256123i
$471$		0			0
$472$	1.68253	+	10.5296i	0.0774450	+	0.484665i
$473$	−4.43653	+	7.68429i	−0.203992	+	0.353324i
$474$		0			0
$475$	−5.37305	+	9.30640i	−0.246533	+	0.427007i
$476$	−9.88044	+	9.83672i	−0.452869	+	0.450865i
$477$		0			0
$478$	22.4436	−	20.9481i	1.02654	−	0.958146i
$479$	−2.19922			−0.100485			−0.0502424	−	0.998737i	$-0.515999\pi$
$479$	−2.19922			−0.100485			−0.0502424	+	0.998737i	$0.515999\pi$
$480$		0			0
$481$		−	39.4426i		−	1.79843i
$482$	−1.20164	−	5.19403i	−0.0547331	−	0.236582i
$483$		0			0
$484$	3.12230	−	1.52638i	0.141923	−	0.0693809i
$485$	−0.412284	+	0.714098i	−0.0187209	+	0.0324255i
$486$		0			0
$487$	−16.7601	+	9.67646i	−0.759473	+	0.438482i	−0.829107	−	0.559090i	$-0.811150\pi$
$487$	−16.7601	+	9.67646i	−0.759473	+	0.438482i	0.0696332	+	0.997573i	$0.477817\pi$
$488$	−2.70375	+	7.07248i	−0.122393	+	0.320156i
$489$		0			0
$490$	−0.954448	+	5.80771i	−0.0431176	+	0.262366i
$491$	20.0539	−	11.5781i	0.905020	−	0.522514i	0.0261947	−	0.999657i	$-0.491661\pi$
$491$	20.0539	−	11.5781i	0.905020	−	0.522514i	0.878826	+	0.477143i	$0.158328\pi$
$492$		0			0
$493$			18.4473i			0.830825i
$494$	5.28749	+	22.8549i	0.237895	+	1.02829i
$495$		0			0
$496$	8.90768	+	21.9317i	0.399967	+	0.984764i
$497$	−4.49224	+	22.7303i	−0.201505	+	1.01959i
$498$		0			0
$499$			5.31695i			0.238019i	0.992893	+	0.119010i	$0.0379719\pi$
$499$			5.31695i			0.238019i	−0.992893	+	0.119010i	$0.962028\pi$
$500$	−5.03773	−	10.3050i	−0.225294	−	0.460852i
$501$		0			0
$502$	−19.1508	+	4.43052i	−0.854740	+	0.197744i
$503$	−1.45521			−0.0648844			−0.0324422	−	0.999474i	$-0.510328\pi$
$503$	−1.45521			−0.0648844			−0.0324422	+	0.999474i	$0.510328\pi$
$504$		0			0
$505$	4.71641			0.209877
$506$	6.51151	−	1.50644i	0.289472	−	0.0669692i
$507$		0			0
$508$	9.74922	+	19.9426i	0.432552	+	0.884808i
$509$		−	43.3106i		−	1.91971i	−0.280502	−	0.959853i	$-0.590501\pi$
$509$		−	43.3106i		−	1.91971i	0.280502	−	0.959853i	$-0.409499\pi$
$510$		0			0
$511$	−3.76163	+	1.28207i	−0.166405	+	0.0567155i
$512$	10.3555	+	20.1187i	0.457652	+	0.889131i
$513$		0			0
$514$	1.36825	+	5.91420i	0.0603509	+	0.260864i
$515$		−	5.65640i		−	0.249251i
$516$		0			0
$517$	−25.5092	+	14.7277i	−1.12189	+	0.647725i
$518$	9.70849	−	18.1418i	0.426566	−	0.797105i
$519$		0			0
$520$	−11.2660	−	4.30688i	−0.494045	−	0.188869i
$521$	−28.2426	+	16.3059i	−1.23733	+	0.714373i	−0.968548	−	0.248827i	$-0.919955\pi$
$521$	−28.2426	+	16.3059i	−1.23733	+	0.714373i	−0.268783	+	0.963201i	$0.586622\pi$
$522$		0			0
$523$	−13.1872	+	22.8409i	−0.576637	+	0.998765i	0.419224	+	0.907883i	$0.362302\pi$
$523$	−13.1872	+	22.8409i	−0.576637	+	0.998765i	−0.995862	+	0.0908822i	$0.971031\pi$
$524$	−8.96854	+	4.38440i	−0.391793	+	0.191534i
$525$		0			0
$526$	5.58564	+	24.1437i	0.243545	+	1.05272i
$527$		−	15.5927i		−	0.679227i
$528$		0			0
$529$	20.5887			0.895159
$530$	5.04644	−	4.71019i	0.219203	−	0.204598i
$531$		0			0
$532$	−3.19357	+	11.8137i	−0.138459	+	0.512189i
$533$	13.5690	−	23.5022i	0.587740	−	1.01799i
$534$		0			0
$535$	4.05400	−	7.02173i	0.175269	−	0.303576i
$536$	24.9295	−	3.98350i	1.07679	−	0.172061i
$537$		0			0
$538$	4.65017	−	4.34033i	0.200483	−	0.187125i
$539$	−8.10410	+	19.7022i	−0.349068	+	0.848633i
$540$		0			0
$541$	12.4508	−	21.5653i	0.535300	−	0.927166i	−0.463849	−	0.885914i	$-0.653532\pi$
$541$	12.4508	−	21.5653i	0.535300	−	0.927166i	0.999149	−	0.0412520i	$-0.0131346\pi$
$542$	−8.56960	+	28.0758i	−0.368096	+	1.20596i
$543$		0			0
$544$	−1.33297	−	14.8451i	−0.0571508	−	0.636478i
$545$	−4.70943	+	2.71899i	−0.201730	+	0.116469i
$546$		0			0
$547$	31.0502	+	17.9268i	1.32761	+	0.766496i	0.984929	−	0.172957i	$-0.0553321\pi$
$547$	31.0502	+	17.9268i	1.32761	+	0.766496i	0.342680	+	0.939452i	$0.388665\pi$
$548$	11.3366	−	5.54205i	0.484275	−	0.236745i
$549$		0			0
$550$	−4.50764	−	19.4841i	−0.192207	−	0.830805i
$551$	8.09607	+	14.0228i	0.344904	+	0.597392i
$552$		0			0
$553$	−16.8608	+	5.74664i	−0.716994	+	0.244372i
$554$	18.8827	−	4.36850i	0.802247	−	0.185600i
$555$		0			0
$556$	−11.1965	−	7.53728i	−0.474839	−	0.319652i
$557$	−3.14023	−	5.43904i	−0.133056	−	0.230459i	0.791797	−	0.610784i	$-0.209146\pi$
$557$	−3.14023	−	5.43904i	−0.133056	−	0.230459i	−0.924853	+	0.380325i	$0.875812\pi$
$558$		0			0
$559$	−20.9112			−0.884448
$560$	−4.12173	−	4.75400i	−0.174175	−	0.200893i
$561$		0			0
$562$	−1.05302	+	3.44993i	−0.0444192	+	0.145526i
$563$	7.78737	−	13.4881i	0.328198	−	0.568456i	−0.653956	−	0.756533i	$-0.726892\pi$
$563$	7.78737	−	13.4881i	0.328198	−	0.568456i	0.982154	+	0.188076i	$0.0602252\pi$
$564$		0			0
$565$	−3.68100	+	2.12522i	−0.154861	+	0.0894088i
$566$	3.54973	−	11.6297i	0.149206	−	0.488831i
$567$		0			0
$568$	−15.6145	−	19.2283i	−0.655170	−	0.806802i
$569$	−1.56749	−	2.71498i	−0.0657128	−	0.113818i	0.831297	−	0.555828i	$-0.187599\pi$
$569$	−1.56749	−	2.71498i	−0.0657128	−	0.113818i	−0.897010	+	0.442010i	$0.854265\pi$
$570$		0			0
$571$	38.5163	+	22.2374i	1.61186	+	0.930606i	0.988940	+	0.148319i	$0.0473863\pi$
$571$	38.5163	+	22.2374i	1.61186	+	0.930606i	0.622918	+	0.782287i	$0.285947\pi$
$572$	−36.2156	−	24.3796i	−1.51425	−	1.01936i
$573$		0			0
$574$	12.0260	−	7.47005i	0.501957	−	0.311794i
$575$			7.21536i			0.300901i
$576$		0			0
$577$	30.5353	−	17.6296i	1.27120	−	0.733929i	0.295988	−	0.955192i	$-0.404351\pi$
$577$	30.5353	−	17.6296i	1.27120	−	0.733929i	0.975214	+	0.221263i	$0.0710179\pi$
$578$	4.15240	−	13.6041i	0.172717	−	0.565858i
$579$		0			0
$580$	−8.30537	−	0.573138i	−0.344862	−	0.0237983i
$581$	−17.3985	+	19.8885i	−0.721809	+	0.825114i
$582$		0			0
$583$	21.6391	−	12.4933i	0.896198	−	0.517420i
$584$	1.51709	−	3.96840i	0.0627775	−	0.164214i
$585$		0			0
$586$	20.5622	−	19.1922i	0.849417	−	0.792820i
$587$	19.6358	−	34.0102i	0.810455	−	1.40375i	−0.102091	−	0.994775i	$-0.532553\pi$
$587$	19.6358	−	34.0102i	0.810455	−	1.40375i	0.912546	−	0.408974i	$-0.134113\pi$
$588$		0			0
$589$	−6.84324	−	11.8528i	−0.281971	−	0.488387i
$590$	3.03175	+	0.925384i	0.124815	+	0.0380975i
$591$		0			0
$592$	8.27745	+	20.3800i	0.340201	+	0.837614i
$593$	28.1689	+	16.2633i	1.15676	+	0.667855i	0.950525	−	0.310648i	$-0.100546\pi$
$593$	28.1689	+	16.2633i	1.15676	+	0.667855i	0.206234	+	0.978503i	$0.433879\pi$
$594$		0			0
$595$	1.33706	+	3.92297i	0.0548142	+	0.160826i
$596$	9.81427	−	4.79785i	0.402008	−	0.196528i
$597$		0			0
$598$	10.7474	+	11.5147i	0.439496	+	0.470869i
$599$	3.80529	+	2.19698i	0.155480	+	0.0897663i	0.575721	−	0.817646i	$-0.304721\pi$
$599$	3.80529	+	2.19698i	0.155480	+	0.0897663i	−0.420242	+	0.907412i	$0.638055\pi$
$600$		0			0
$601$	−14.6174	−	8.43937i	−0.596257	−	0.344249i	0.171311	−	0.985217i	$-0.445200\pi$
$601$	−14.6174	−	8.43937i	−0.596257	−	0.344249i	−0.767568	+	0.640968i	$0.778533\pi$
$602$	−9.61819	−	5.14712i	−0.392008	−	0.209781i
$603$		0			0
$604$	−12.1001	−	24.7514i	−0.492346	−	1.00712i
$605$		−	1.03313i		−	0.0420029i
$606$		0			0
$607$	−33.4611			−1.35814			−0.679072	−	0.734071i	$-0.737618\pi$
$607$	−33.4611			−1.35814			−0.679072	+	0.734071i	$0.737618\pi$
$608$	−7.52841	−	10.6995i	−0.305317	−	0.433924i
$609$		0			0
$610$	1.53581	+	1.64544i	0.0621831	+	0.0666221i
$611$	−60.1176	−	34.7089i	−2.43210	−	1.40417i
$612$		0			0
$613$	18.0048	+	31.1852i	0.727207	+	1.25956i	0.958059	+	0.286570i	$0.0925152\pi$
$613$	18.0048	+	31.1852i	0.727207	+	1.25956i	−0.230852	+	0.972989i	$0.574151\pi$
$614$	−36.9239	+	8.54232i	−1.49013	+	0.344740i
$615$		0			0
$616$	−10.6567	−	20.1277i	−0.429370	−	0.810967i
$617$	−17.8922	−	30.9902i	−0.720314	−	1.24762i	−0.960874	−	0.276986i	$-0.910665\pi$
$617$	−17.8922	−	30.9902i	−0.720314	−	1.24762i	0.240560	−	0.970634i	$-0.422669\pi$
$618$		0			0
$619$	−17.4481			−0.701297			−0.350649	−	0.936507i	$-0.614039\pi$
$619$	−17.4481			−0.701297			−0.350649	+	0.936507i	$0.614039\pi$
$620$	7.02015	+	0.484447i	0.281936	+	0.0194559i
$621$		0			0
$622$	−1.97905	+	6.48377i	−0.0793526	+	0.259976i
$623$	31.6342	+	27.6736i	1.26740	+	1.10872i
$624$		0			0
$625$	19.8228			0.792913
$626$	−9.11082	+	8.50377i	−0.364142	+	0.339879i
$627$		0			0
$628$	23.5330	+	1.62397i	0.939070	+	0.0648035i
$629$		−	14.4895i		−	0.577733i
$630$		0			0
$631$		−	17.8634i		−	0.711133i	−0.934651	−	0.355566i	$-0.884288\pi$
$631$		−	17.8634i		−	0.711133i	0.934651	−	0.355566i	$-0.115712\pi$
$632$	6.80006	−	17.7876i	0.270492	−	0.707554i
$633$		0			0
$634$	−17.4778	−	18.7255i	−0.694131	−	0.743683i
$635$	6.59878			0.261865
$636$		0			0
$637$	−49.7610	+	6.67591i	−1.97160	+	0.264509i
$638$	−28.8213	−	8.79714i	−1.14104	−	0.348282i
$639$		0			0
$640$	6.72498	−	0.138913i	0.265828	−	0.00549101i
$641$	47.0806			1.85957			0.929786	−	0.368101i	$-0.119992\pi$
$641$	47.0806			1.85957			0.929786	+	0.368101i	$0.119992\pi$
$642$		0			0
$643$	−11.4838	−	19.8904i	−0.452875	−	0.784403i	0.545688	−	0.837988i	$-0.316268\pi$
$643$	−11.4838	−	19.8904i	−0.452875	−	0.784403i	−0.998563	+	0.0535856i	$0.982935\pi$
$644$	2.10909	+	7.94162i	0.0831097	+	0.312944i
$645$		0			0
$646$	1.94239	+	8.39590i	0.0764223	+	0.330332i
$647$	17.5968	+	30.4785i	0.691800	+	1.19823i	0.971248	+	0.238072i	$0.0765153\pi$
$647$	17.5968	+	30.4785i	0.691800	+	1.19823i	−0.279448	+	0.960161i	$0.590151\pi$
$648$		0			0
$649$	9.93648	+	5.73683i	0.390041	+	0.225190i
$650$	34.4548	−	32.1591i	1.35143	−	1.26138i
$651$		0			0
$652$	6.80304	+	0.469465i	0.266428	+	0.0183857i
$653$	36.8505			1.44207			0.721036	−	0.692897i	$-0.243666\pi$
$653$	36.8505			1.44207			0.721036	+	0.692897i	$0.243666\pi$
$654$		0			0
$655$			2.96759i			0.115953i
$656$	−2.07894	+	14.9912i	−0.0811688	+	0.585310i
$657$		0			0
$658$	−19.1080	−	30.7620i	−0.744909	−	1.19923i
$659$	6.21863	+	3.59033i	0.242244	+	0.139859i	0.616207	−	0.787584i	$-0.288668\pi$
$659$	6.21863	+	3.59033i	0.242244	+	0.139859i	−0.373964	+	0.927443i	$0.622002\pi$
$660$		0			0
$661$	−1.94004	−	1.12008i	−0.0754589	−	0.0435662i	0.461796	−	0.886986i	$-0.347205\pi$
$661$	−1.94004	−	1.12008i	−0.0754589	−	0.0435662i	−0.537255	+	0.843420i	$0.680539\pi$
$662$	−8.03283	+	7.49760i	−0.312205	+	0.291403i
$663$		0			0
$664$	−4.45739	−	27.8952i	−0.172980	−	1.08254i
$665$	2.73807	+	2.39526i	0.106178	+	0.0928843i
$666$		0			0
$667$	9.41547	+	5.43602i	0.364568	+	0.210484i
$668$	−21.4932	−	14.4688i	−0.831597	−	0.559813i
$669$		0			0
$670$	2.19090	−	7.17785i	0.0846419	−	0.277304i
$671$	4.07358	+	7.05565i	0.157259	+	0.272380i
$672$		0			0
$673$	7.99088	−	13.8406i	0.308026	−	0.533516i	−0.669905	−	0.742447i	$-0.733665\pi$
$673$	7.99088	−	13.8406i	0.308026	−	0.533516i	0.977930	+	0.208931i	$0.0669984\pi$
$674$	−7.65435	−	8.20077i	−0.294835	−	0.315882i
$675$		0			0
$676$	5.29321	−	76.7042i	0.203585	−	2.95016i
$677$	−14.3875	+	8.30660i	−0.552955	+	0.319249i	−0.750313	−	0.661083i	$-0.770097\pi$
$677$	−14.3875	+	8.30660i	−0.552955	+	0.319249i	0.197358	+	0.980331i	$0.436764\pi$
$678$		0			0
$679$	−2.76179	−	2.41601i	−0.105988	−	0.0927181i
$680$	−4.13862	−	1.58216i	−0.158709	−	0.0606730i
$681$		0			0
$682$	24.3613	+	7.43581i	0.932841	+	0.284732i
$683$	−24.9863	+	14.4258i	−0.956073	+	0.551989i	−0.894962	−	0.446142i	$-0.852798\pi$
$683$	−24.9863	+	14.4258i	−0.956073	+	0.551989i	−0.0611106	+	0.998131i	$0.519464\pi$
$684$		0			0
$685$		−	3.75115i		−	0.143324i
$686$	−24.5310	−	9.17766i	−0.936598	−	0.350405i
$687$		0			0
$688$	10.8048	−	4.38843i	0.411930	−	0.167308i
$689$	50.9969	+	29.4431i	1.94283	+	1.12169i
$690$		0			0
$691$	15.7586	+	27.2947i	0.599485	+	1.03834i	0.992897	+	0.118976i	$0.0379611\pi$
$691$	15.7586	+	27.2947i	0.599485	+	1.03834i	−0.393412	+	0.919362i	$0.628706\pi$
$692$	−1.39322	+	2.06962i	−0.0529624	+	0.0786750i
$693$		0			0
$694$	−1.12995	−	0.344895i	−0.0428922	−	0.0130920i
$695$	−3.47474	+	2.00614i	−0.131804	+	0.0760972i
$696$		0			0
$697$	4.98466	−	8.63368i	0.188807	−	0.327024i
$698$	21.6930	+	6.62137i	0.821091	+	0.250622i
$699$		0			0
$700$	23.7634	−	6.31094i	0.898171	−	0.238531i
$701$	−38.3817			−1.44966			−0.724829	−	0.688929i	$-0.758081\pi$
$701$	−38.3817			−1.44966			−0.724829	+	0.688929i	$0.758081\pi$
$702$		0			0
$703$	−6.35907	−	11.0142i	−0.239837	−	0.415410i
$704$	23.8290	+	4.99673i	0.898088	+	0.188321i
$705$		0			0
$706$	4.15477	+	17.9588i	0.156367	+	0.675890i
$707$	−4.06929	+	20.5902i	−0.153042	+	0.774376i
$708$		0			0
$709$	5.28017	+	9.14553i	0.198301	+	0.343467i	0.947978	−	0.318337i	$-0.103124\pi$
$709$	5.28017	+	9.14553i	0.198301	+	0.343467i	−0.749677	+	0.661804i	$0.769791\pi$
$710$	−7.17379	+	1.65965i	−0.269228	+	0.0622857i
$711$		0			0
$712$	−44.3695	+	7.08982i	−1.66282	+	0.265702i
$713$	−7.95846	−	4.59482i	−0.298047	−	0.172077i
$714$		0			0
$715$	−11.2391	+	6.48892i	−0.420320	+	0.242672i
$716$	−0.117963	+	0.175233i	−0.00440849	+	0.00654876i
$717$		0			0
$718$	10.4477	+	3.18895i	0.389904	+	0.119011i
$719$	17.7183	−	30.6890i	0.660782	−	1.14451i	−0.319629	−	0.947543i	$-0.603558\pi$
$719$	17.7183	−	30.6890i	0.660782	−	1.14451i	0.980411	−	0.196965i	$-0.0631084\pi$
$720$		0			0
$721$	24.6939	+	4.88032i	0.919651	+	0.181752i
$722$	−13.1730	−	14.1134i	−0.490250	−	0.525247i
$723$		0			0
$724$	−19.6635	−	40.2229i	−0.730790	−	1.49487i
$725$	16.2660	−	28.1735i	0.604103	−	1.04634i
$726$		0			0
$727$	−16.3858	+	28.3811i	−0.607717	+	1.05260i	0.383898	+	0.923375i	$0.374581\pi$
$727$	−16.3858	+	28.3811i	−0.607717	+	1.05260i	−0.991616	+	0.129222i	$0.958752\pi$
$728$	28.5226	−	45.4674i	1.05712	−	1.68514i
$729$		0			0
$730$	−0.861750	−	0.923267i	−0.0318948	−	0.0341716i
$731$	−7.68184			−0.284123
$732$		0			0
$733$			5.62038i			0.207594i	0.994599	+	0.103797i	$0.0330992\pi$
$733$			5.62038i			0.207594i	−0.994599	+	0.103797i	$0.966901\pi$
$734$	1.17465	−	0.271755i	0.0433572	−	0.0100307i
$735$		0			0
$736$	−7.96969	−	3.69417i	−0.293767	−	0.136169i
$737$	13.5823	−	23.5252i	0.500309	−	0.866561i
$738$		0			0
$739$	−37.9429	+	21.9063i	−1.39575	+	0.805838i	−0.993944	−	0.109886i	$-0.964951\pi$
$739$	−37.9429	+	21.9063i	−1.39575	+	0.805838i	−0.401808	+	0.915724i	$0.631618\pi$
$740$	6.52346	+	0.450172i	0.239807	+	0.0165486i
$741$		0			0
$742$	16.2091	+	26.0950i	0.595054	+	0.957976i
$743$	−9.43980	+	5.45007i	−0.346313	+	0.199944i	−0.663060	−	0.748566i	$-0.730743\pi$
$743$	−9.43980	+	5.45007i	−0.346313	+	0.199944i	0.316747	+	0.948510i	$0.397409\pi$
$744$		0			0
$745$		−	3.24744i		−	0.118977i
$746$	3.21019	−	0.742678i	0.117534	−	0.0271914i
$747$		0			0
$748$	−13.3040	−	8.95598i	−0.486442	−	0.327463i
$749$	27.1567	+	23.7567i	0.992285	+	0.868050i
$750$		0			0
$751$		−	9.57757i		−	0.349490i	−0.984614	−	0.174745i	$-0.944090\pi$
$751$		−	9.57757i		−	0.349490i	0.984614	−	0.174745i	$-0.0559102\pi$
$752$	38.3469	+	5.31782i	1.39837	+	0.193921i
$753$		0			0
$754$	−16.0069	−	69.1894i	−0.582939	−	2.51973i
$755$	−8.18999			−0.298064
$756$		0			0
$757$	−1.91601			−0.0696384			−0.0348192	−	0.999394i	$-0.511086\pi$
$757$	−1.91601			−0.0696384			−0.0348192	+	0.999394i	$0.511086\pi$
$758$	9.21391	+	39.8268i	0.334664	+	1.44657i
$759$		0			0
$760$	−3.84036	+	0.613653i	−0.139304	+	0.0222595i
$761$			0.638114i			0.0231316i	0.999933	+	0.0115658i	$0.00368159\pi$
$761$			0.638114i			0.0231316i	−0.999933	+	0.0115658i	$0.996318\pi$
$762$		0			0
$763$	−7.80691	−	22.9057i	−0.282629	−	0.829242i
$764$	24.1650	−	35.8969i	0.874260	−	1.29870i
$765$		0			0
$766$	24.5251	−	5.67387i	0.886126	−	0.205005i
$767$			27.0400i			0.976359i
$768$		0			0
$769$	−4.56501	+	2.63561i	−0.164618	+	0.0950425i	−0.580046	−	0.814584i	$-0.696965\pi$
$769$	−4.56501	+	2.63561i	−0.164618	+	0.0950425i	0.415427	+	0.909626i	$0.363632\pi$
$770$	−6.76669	+	0.218181i	−0.243855	+	0.00786270i
$771$		0			0
$772$	−0.263437	+	3.81749i	−0.00948132	+	0.137394i
$773$	34.2460	−	19.7719i	1.23174	−	0.711147i	0.264350	−	0.964427i	$-0.414843\pi$
$773$	34.2460	−	19.7719i	1.23174	−	0.711147i	0.967393	+	0.253280i	$0.0815094\pi$
$774$		0			0
$775$	−13.7489	+	23.8138i	−0.493874	+	0.855415i
$776$	3.87363	−	0.618970i	0.139055	−	0.0222197i
$777$		0			0
$778$	35.3142	−	8.16992i	1.26607	−	0.292906i
$779$		−	8.75058i		−	0.313522i
$780$		0			0
$781$	−26.6524			−0.953697
$782$	3.94813	+	4.22998i	0.141185	+	0.151264i
$783$		0			0
$784$	24.3106	−	13.8923i	0.868234	−	0.496155i
$785$	3.50613	−	6.07280i	0.125139	−	0.216748i
$786$		0			0
$787$	1.00854	−	1.74685i	0.0359506	−	0.0622683i	−0.847490	−	0.530811i	$-0.821887\pi$
$787$	1.00854	−	1.74685i	0.0359506	−	0.0622683i	0.883441	+	0.468543i	$0.155221\pi$
$788$	−31.2885	+	15.2959i	−1.11461	+	0.544893i
$789$		0			0
$790$	−3.86263	−	4.13837i	−0.137426	−	0.147237i
$791$	−6.10206	−	17.9036i	−0.216964	−	0.636579i
$792$		0			0
$793$	−9.60023	+	16.6281i	−0.340914	+	0.590481i
$794$	−8.33568	−	2.54431i	−0.295822	−	0.0902941i
$795$		0			0
$796$	−5.89656	−	3.96944i	−0.208998	−	0.140693i
$797$	16.7785	−	9.68708i	0.594326	−	0.343134i	−0.172480	−	0.985013i	$-0.555178\pi$
$797$	16.7785	−	9.68708i	0.594326	−	0.343134i	0.766806	+	0.641879i	$0.221845\pi$
$798$		0			0
$799$	−22.0846	−	12.7505i	−0.781295	−	0.451081i
$800$	−11.0539	+	23.8474i	−0.390815	+	0.843132i
$801$		0			0
$802$	0.374720	−	0.0866915i	0.0132318	−	0.00306118i
$803$	−2.28570	−	3.95896i	−0.0806608	−	0.139709i
$804$		0			0
$805$	2.39628	+	0.473582i	0.0844577	+	0.0166916i
$806$	13.5299	+	58.4826i	0.476571	+	2.05996i
$807$		0			0
$808$	−14.1444	−	17.4180i	−0.497597	−	0.612762i
$809$	9.30812	+	16.1221i	0.327256	+	0.566824i	0.981966	−	0.189056i	$-0.0605427\pi$
$809$	9.30812	+	16.1221i	0.327256	+	0.566824i	−0.654710	+	0.755880i	$0.727209\pi$
$810$		0			0
$811$	1.07212			0.0376471			0.0188236	−	0.999823i	$-0.494008\pi$
$811$	1.07212			0.0376471			0.0188236	+	0.999823i	$0.494008\pi$
$812$	9.66796	−	35.7639i	0.339279	−	1.25507i
$813$		0			0
$814$	22.6377	+	6.90972i	0.793450	+	0.242186i
$815$	1.01357	−	1.75556i	0.0355038	−	0.0614944i
$816$		0			0
$817$	−5.83939	+	3.37137i	−0.204294	+	0.117949i
$818$	−8.83965	−	2.69813i	−0.309071	−	0.0943380i
$819$		0			0
$820$	3.73220	+	2.51244i	0.130334	+	0.0877381i
$821$	19.8186	+	34.3268i	0.691674	+	1.19802i	0.971289	+	0.237903i	$0.0764600\pi$
$821$	19.8186	+	34.3268i	0.691674	+	1.19802i	−0.279615	+	0.960112i	$0.590207\pi$
$822$		0			0
$823$	−18.9735	−	10.9544i	−0.661375	−	0.381845i	0.131426	−	0.991326i	$-0.458044\pi$
$823$	−18.9735	−	10.9544i	−0.661375	−	0.381845i	−0.792801	+	0.609481i	$0.791378\pi$
$824$	−20.8894	+	16.9634i	−0.727717	+	0.590948i
$825$		0			0
$826$	−6.65570	+	12.4372i	−0.231581	+	0.432745i
$827$			40.4761i			1.40749i	0.710451	+	0.703746i	$0.248491\pi$
$827$			40.4761i			1.40749i	−0.710451	+	0.703746i	$0.751509\pi$
$828$		0			0
$829$	4.10818	−	2.37186i	0.142683	−	0.0823780i	−0.426959	−	0.904271i	$-0.640415\pi$
$829$	4.10818	−	2.37186i	0.142683	−	0.0823780i	0.569642	+	0.821893i	$0.307082\pi$
$830$	−8.03175	−	2.45154i	−0.278786	−	0.0850941i
$831$		0			0
$832$	17.8808	+	54.5220i	0.619904	+	1.89021i
$833$	−18.2800	+	2.45244i	−0.633364	+	0.0849719i
$834$		0			0
$835$	−6.67020	+	3.85104i	−0.230832	+	0.133271i
$836$	−14.0437	−	0.969126i	−0.485710	−	0.0335179i
$837$		0			0
$838$	−36.0487	−	38.6221i	−1.24528	−	1.33418i
$839$	−28.2350	+	48.9045i	−0.974782	+	1.68837i	−0.294128	+	0.955766i	$0.595029\pi$
$839$	−28.2350	+	48.9045i	−0.974782	+	1.68837i	−0.680653	+	0.732606i	$0.738304\pi$
$840$		0			0
$841$	−10.0095	−	17.3369i	−0.345154	−	0.597824i
$842$	−7.27694	+	23.8408i	−0.250780	+	0.821607i
$843$		0			0
$844$	3.72034	−	5.52652i	0.128059	−	0.190231i
$845$	−19.7939	−	11.4280i	−0.680930	−	0.393135i
$846$		0			0
$847$	4.51031	+	0.891383i	0.154976	+	0.0306283i
$848$	−32.5291	−	4.51103i	−1.11705	−	0.154909i
$849$		0			0
$850$	12.6572	−	11.8138i	0.434138	−	0.405211i
$851$	−7.39539	−	4.26973i	−0.253511	−	0.146364i
$852$		0			0
$853$	8.07503	+	4.66212i	0.276484	+	0.159628i	0.631830	−	0.775107i	$-0.282304\pi$
$853$	8.07503	+	4.66212i	0.276484	+	0.159628i	−0.355347	+	0.934735i	$0.615637\pi$
$854$	−8.50854	+	5.28514i	−0.291156	+	0.180854i
$855$		0			0
$856$	−38.0894	+	6.08633i	−1.30187	+	0.208027i
$857$		−	16.4868i		−	0.563178i	−0.959535	−	0.281589i	$-0.909139\pi$
$857$		−	16.4868i		−	0.563178i	0.959535	−	0.281589i	$-0.0908615\pi$
$858$		0			0
$859$	−28.4857			−0.971919			−0.485959	−	0.873981i	$-0.661530\pi$
$859$	−28.4857			−0.971919			−0.485959	+	0.873981i	$0.661530\pi$
$860$	0.238666	−	3.45853i	0.00813846	−	0.117935i
$861$		0			0
$862$	−32.0419	+	29.9070i	−1.09135	+	1.01863i
$863$	4.17974	+	2.41317i	0.142280	+	0.0821454i	0.569450	−	0.822026i	$-0.307156\pi$
$863$	4.17974	+	2.41317i	0.142280	+	0.0821454i	−0.427170	+	0.904171i	$0.640489\pi$
$864$		0			0
$865$	0.370823	+	0.642285i	0.0126084	+	0.0218383i
$866$	6.42839	+	27.7864i	0.218445	+	0.944222i
$867$		0			0
$868$	−8.17188	+	30.2296i	−0.277372	+	1.02606i
$869$	−10.2452	−	17.7453i	−0.347546	−	0.601967i
$870$		0			0
$871$	64.0188			2.16920
$872$	24.1648	+	9.23800i	0.818323	+	0.312838i
$873$		0			0
$874$	4.85762	+	1.48270i	0.164312	+	0.0501530i
$875$	2.94196	−	14.8860i	0.0994563	−	0.503240i
$876$		0			0
$877$	23.7771			0.802894			0.401447	−	0.915882i	$-0.368507\pi$
$877$	23.7771			0.802894			0.401447	+	0.915882i	$0.368507\pi$
$878$	−1.26425	−	1.35450i	−0.0426665	−	0.0457123i
$879$		0			0
$880$	4.44551	−	5.71149i	0.149858	−	0.192534i
$881$		−	15.9241i		−	0.536495i	−0.963350	−	0.268248i	$-0.913555\pi$
$881$		−	15.9241i		−	0.536495i	0.963350	−	0.268248i	$-0.0864445\pi$
$882$		0			0
$883$		−	0.631703i		−	0.0212585i	−0.999944	−	0.0106292i	$-0.996617\pi$
$883$		−	0.631703i		−	0.0212585i	0.999944	−	0.0106292i	$-0.00338346\pi$
$884$	2.60204	−	37.7063i	0.0875162	−	1.26820i
$885$		0			0
$886$	2.63171	−	2.45636i	0.0884142	−	0.0825231i
$887$	15.0668			0.505894			0.252947	−	0.967480i	$-0.418600\pi$
$887$	15.0668			0.505894			0.252947	+	0.967480i	$0.418600\pi$
$888$		0			0
$889$	−5.69339	+	28.8080i	−0.190950	+	0.966191i
$890$	−3.89936	+	12.7751i	−0.130707	+	0.428223i
$891$		0			0
$892$	−1.79554	+	26.0193i	−0.0601192	+	0.871190i
$893$	−22.3836			−0.749038
$894$		0			0
$895$	0.0313973	+	0.0543818i	0.00104950	+	0.00181778i
$896$	−5.19584	+	29.4789i	−0.173581	+	0.984820i
$897$		0			0
$898$	−41.4035	+	9.57870i	−1.38165	+	0.319645i
$899$	20.7167	+	35.8824i	0.690941	+	1.19674i
$900$		0			0
$901$	18.7340	+	10.8161i	0.624120	+	0.360336i
$902$	11.1118	+	11.9050i	0.369982	+	0.396394i
$903$		0			0
$904$	18.8878	+	7.22063i	0.628198	+	0.240155i
$905$	−13.3093			−0.442417
$906$		0			0
$907$			29.4808i			0.978895i	0.872033	+	0.489448i	$0.162802\pi$
$907$			29.4808i			0.978895i	−0.872033	+	0.489448i	$0.837198\pi$
$908$	−16.9846	+	8.30319i	−0.563655	+	0.275551i
$909$		0			0
$910$	−8.41885	−	13.5535i	−0.279082	−	0.449294i
$911$	14.4832	+	8.36189i	0.479850	+	0.277042i	0.720354	−	0.693606i	$-0.243979\pi$
$911$	14.4832	+	8.36189i	0.479850	+	0.277042i	−0.240504	+	0.970648i	$0.577313\pi$
$912$		0			0
$913$	−26.3238	−	15.1981i	−0.871191	−	0.502982i
$914$	−37.0398	−	39.6839i	−1.22517	−	1.31263i
$915$		0			0
$916$	12.4653	+	25.4985i	0.411866	+	0.842495i
$917$	−12.9555	−	2.56043i	−0.427829	−	0.0845527i
$918$		0			0
$919$	−0.945149	−	0.545682i	−0.0311776	−	0.0180004i	0.484330	−	0.874885i	$-0.339063\pi$
$919$	−0.945149	−	0.545682i	−0.0311776	−	0.0180004i	−0.515508	+	0.856885i	$0.672397\pi$
$920$	−2.02709	+	1.64611i	−0.0668312	+	0.0542707i
$921$		0			0
$922$	46.6518	+	14.2396i	1.53640	+	0.468955i
$923$	−31.4059	−	54.3966i	−1.03374	−	1.79049i
$924$		0			0
$925$	−12.7761	+	22.1289i	−0.420076	+	0.727594i
$926$	27.8292	−	25.9749i	0.914523	−	0.853588i
$927$		0			0
$928$	22.7909	+	32.3910i	0.748149	+	1.06329i
$929$	14.8355	−	8.56529i	0.486737	−	0.281018i	−0.236483	−	0.971636i	$-0.575995\pi$
$929$	14.8355	−	8.56529i	0.486737	−	0.281018i	0.723220	+	0.690618i	$0.242661\pi$
$930$		0			0
$931$	−12.8193	+	9.88687i	−0.420136	+	0.324029i
$932$	3.55512	−	51.5174i	0.116452	−	1.68751i
$933$		0			0
$934$	8.40220	−	27.5274i	0.274928	−	0.900723i
$935$	−4.12876	+	2.38374i	−0.135025	+	0.0779567i
$936$		0			0
$937$			17.6461i			0.576474i	0.957559	+	0.288237i	$0.0930692\pi$
$937$			17.6461i			0.576474i	−0.957559	+	0.288237i	$0.906931\pi$
$938$	29.4458	+	15.7577i	0.961438	+	0.514509i
$939$		0			0
$940$	6.42670	−	9.54679i	0.209616	−	0.311382i
$941$	12.4442	+	7.18464i	0.405668	+	0.234212i	0.688927	−	0.724831i	$-0.258082\pi$
$941$	12.4442	+	7.18464i	0.405668	+	0.234212i	−0.283259	+	0.959044i	$0.591416\pi$
$942$		0			0
$943$	−2.93774	−	5.08832i	−0.0956660	−	0.165698i
$944$	−5.67464	−	13.9716i	−0.184694	−	0.454738i
$945$		0			0
$946$	3.66331	−	12.0018i	0.119104	−	0.390211i
$947$	−8.53552	+	4.92799i	−0.277367	+	0.160138i	−0.632231	−	0.774780i	$-0.717861\pi$
$947$	−8.53552	+	4.92799i	−0.277367	+	0.160138i	0.354864	+	0.934918i	$0.384527\pi$
$948$		0			0
$949$	5.38673	−	9.33010i	0.174861	−	0.302868i
$950$	4.43661	−	14.5353i	0.143943	−	0.471586i
$951$		0			0
$952$	10.4779	−	16.7027i	0.339592	−	0.541338i
$953$	−9.71521			−0.314707			−0.157353	−	0.987542i	$-0.550296\pi$
$953$	−9.71521			−0.314707			−0.157353	+	0.987542i	$0.550296\pi$
$954$		0			0
$955$	−6.43182	−	11.1402i	−0.208129	−	0.360490i
$956$	−24.2458	+	36.0169i	−0.784166	+	1.16487i
$957$		0			0
$958$	3.03013	−	0.701020i	0.0978991	−	0.0226489i
$959$	16.3763	+	3.23647i	0.528817	+	0.104511i
$960$		0			0
$961$	−2.01087	−	3.48293i	−0.0648668	−	0.112353i
$962$	12.5727	+	54.3449i	0.405359	+	1.75215i
$963$		0			0
$964$	3.31128	+	6.77342i	0.106649	+	0.218157i
$965$	0.985119	+	0.568759i	0.0317121	+	0.0183090i
$966$		0			0
$967$	19.5928	−	11.3119i	0.630061	−	0.363766i	−0.150715	−	0.988577i	$-0.548158\pi$
$967$	19.5928	−	11.3119i	0.630061	−	0.363766i	0.780776	+	0.624812i	$0.214824\pi$
$968$	−3.81542	+	3.09834i	−0.122632	+	0.0995844i
$969$		0			0
$970$	0.340430	−	1.11532i	0.0109305	−	0.0358107i
$971$	8.13371	−	14.0880i	0.261023	−	0.452105i	−0.705491	−	0.708719i	$-0.749273\pi$
$971$	8.13371	−	14.0880i	0.261023	−	0.452105i	0.966514	+	0.256614i	$0.0826068\pi$
$972$		0			0
$973$	−5.76014	−	16.9004i	−0.184662	−	0.541802i
$974$	20.0080	−	18.6749i	0.641098	−	0.598381i
$975$		0			0
$976$	1.47087	−	10.6065i	0.0470814	−	0.339505i
$977$	−17.7665	+	30.7725i	−0.568400	+	0.984498i	0.428324	+	0.903625i	$0.359104\pi$
$977$	−17.7665	+	30.7725i	−0.568400	+	0.984498i	−0.996724	+	0.0808729i	$0.974229\pi$
$978$		0			0
$979$	−24.1737	+	41.8701i	−0.772595	+	1.33817i
$980$	−0.536199	−	8.30623i	−0.0171283	−	0.265333i
$981$		0			0
$982$	−23.9401	+	22.3450i	−0.763959	+	0.713056i
$983$	25.6794			0.819046			0.409523	−	0.912300i	$-0.365695\pi$
$983$	25.6794			0.819046			0.409523	+	0.912300i	$0.365695\pi$
$984$		0			0
$985$			10.3530i			0.329875i
$986$	−5.88024	−	25.4171i	−0.187265	−	0.809446i
$987$		0			0
$988$	−14.5704	−	29.8046i	−0.463547	−	0.948211i
$989$	−2.26367	+	3.92079i	−0.0719805	+	0.124674i
$990$		0			0
$991$	−20.2815	+	11.7096i	−0.644264	+	0.371966i	−0.786255	−	0.617902i	$-0.787983\pi$
$991$	−20.2815	+	11.7096i	−0.644264	+	0.371966i	0.141991	+	0.989868i	$0.454650\pi$
$992$	−19.2641	−	27.3786i	−0.611637	−	0.869272i
$993$		0			0
$994$	−1.05598	−	32.7503i	−0.0334936	−	1.03878i
$995$	−1.82994	+	1.05652i	−0.0580130	+	0.0334938i
$996$		0			0
$997$			1.57741i			0.0499572i	0.999688	+	0.0249786i	$0.00795177\pi$
$997$			1.57741i			0.0499572i	−0.999688	+	0.0249786i	$0.992048\pi$
$998$	−1.69482	−	7.32580i	−0.0536487	−	0.231894i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.2		84
3.2	odd	2		252.2.n.b.187.41	yes	84
4.3	odd	2	inner	756.2.n.b.19.30		84
7.3	odd	6		756.2.bj.b.451.27		84
9.4	even	3		756.2.bj.b.523.27		84
9.5	odd	6		252.2.bj.b.103.16	yes	84
12.11	even	2		252.2.n.b.187.13	yes	84
21.17	even	6		252.2.bj.b.115.16	yes	84
28.3	even	6		756.2.bj.b.451.28		84
36.23	even	6		252.2.bj.b.103.15	yes	84
36.31	odd	6		756.2.bj.b.523.28		84
63.31	odd	6	inner	756.2.n.b.199.30		84
63.59	even	6		252.2.n.b.31.13	✓	84
84.59	odd	6		252.2.bj.b.115.15	yes	84
252.31	even	6	inner	756.2.n.b.199.2		84
252.59	odd	6		252.2.n.b.31.41	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.13	✓	84	63.59	even	6
252.2.n.b.31.41	yes	84	252.59	odd	6
252.2.n.b.187.13	yes	84	12.11	even	2
252.2.n.b.187.41	yes	84	3.2	odd	2
252.2.bj.b.103.15	yes	84	36.23	even	6
252.2.bj.b.103.16	yes	84	9.5	odd	6
252.2.bj.b.115.15	yes	84	84.59	odd	6
252.2.bj.b.115.16	yes	84	21.17	even	6
756.2.n.b.19.2		84	1.1	even	1	trivial
756.2.n.b.19.30		84	4.3	odd	2	inner
756.2.n.b.199.2		84	252.31	even	6	inner
756.2.n.b.199.30		84	63.31	odd	6	inner
756.2.bj.b.451.27		84	7.3	odd	6
756.2.bj.b.451.28		84	28.3	even	6
756.2.bj.b.523.27		84	9.4	even	3
756.2.bj.b.523.28		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)

\(f(q)\)	\(=\)	\(q+(-1.37782 + 0.318759i) q^{2} +(1.79679 - 0.878385i) q^{4} -0.594537i q^{5} +(2.59555 + 0.512964i) q^{7} +(-2.19566 + 1.78300i) q^{8} +O(q^{10})\)	\(q+(-1.37782 + 0.318759i) q^{2} +(1.79679 - 0.878385i) q^{4} -0.594537i q^{5} +(2.59555 + 0.512964i) q^{7} +(-2.19566 + 1.78300i) q^{8} +(0.189514 + 0.819166i) q^{10} +3.04340i q^{11} +(-6.21148 + 3.58620i) q^{13} +(-3.73971 + 0.120581i) q^{14} +(2.45688 - 3.15654i) q^{16} +(-2.28182 + 1.31741i) q^{17} +(-1.15636 + 2.00287i) q^{19} +(-0.522233 - 1.06826i) q^{20} +(-0.970111 - 4.19326i) q^{22} +1.55285i q^{23} +4.64653 q^{25} +(7.41518 - 6.92111i) q^{26} +(5.11422 - 1.35821i) q^{28} +(3.50068 - 6.06335i) q^{29} +(-2.95896 + 5.12507i) q^{31} +(-2.37897 + 5.13230i) q^{32} +(2.72401 - 2.54251i) q^{34} +(0.304976 - 1.54315i) q^{35} +(-2.74961 + 4.76246i) q^{37} +(0.954823 - 3.12820i) q^{38} +(1.06006 + 1.30540i) q^{40} +(-3.27676 + 1.89184i) q^{41} +(2.52490 + 1.45775i) q^{43} +(2.67328 + 5.46834i) q^{44} +(-0.494984 - 2.13955i) q^{46} +(4.83923 + 8.38180i) q^{47} +(6.47374 + 2.66284i) q^{49} +(-6.40208 + 1.48112i) q^{50} +(-8.01063 + 11.8997i) q^{52} +(-4.10505 - 7.11016i) q^{53} +1.80941 q^{55} +(-6.61355 + 3.50157i) q^{56} +(-2.89056 + 9.47008i) q^{58} +(1.88501 - 3.26493i) q^{59} +(2.31834 - 1.33850i) q^{61} +(2.44326 - 8.00462i) q^{62} +(1.64182 - 7.82971i) q^{64} +(2.13213 + 3.69296i) q^{65} +(-7.72990 - 4.46286i) q^{67} +(-2.94275 + 4.37143i) q^{68} +(0.0716899 + 2.22340i) q^{70} +8.75743i q^{71} +(-1.30083 + 0.751036i) q^{73} +(2.27039 - 7.43829i) q^{74} +(-0.318435 + 4.61446i) q^{76} +(-1.56115 + 7.89929i) q^{77} +(-5.83074 + 3.36638i) q^{79} +(-1.87668 - 1.46071i) q^{80} +(3.91175 - 3.65111i) q^{82} +(-4.99378 + 8.64947i) q^{83} +(0.783250 + 1.35663i) q^{85} +(-3.94354 - 1.20369i) q^{86} +(-5.42638 - 6.68227i) q^{88} +(13.7577 + 7.94299i) q^{89} +(-17.9618 + 6.12189i) q^{91} +(1.36400 + 2.79014i) q^{92} +(-9.33938 - 10.0061i) q^{94} +(1.19078 + 0.687498i) q^{95} +(-1.20110 - 0.693454i) q^{97} +(-9.76846 - 1.60536i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 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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