LMFDB - Embedded newform 756.2.n.b.19.19

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			19.19
Character	$\chi$	$=$	756.19
Dual form			756.2.n.b.199.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.270834 + 1.38804i) q^{2} +(-1.85330 - 0.751856i) q^{4} -2.69249i q^{5} +(-1.51663 + 2.16791i) q^{7} +(1.54554 - 2.36882i) q^{8} +O(q^{10})$	\(q+(-0.270834 + 1.38804i) q^{2} +(-1.85330 - 0.751856i) q^{4} -2.69249i q^{5} +(-1.51663 + 2.16791i) q^{7} +(1.54554 - 2.36882i) q^{8} +(3.73728 + 0.729218i) q^{10} +1.41334i q^{11} +(-2.46297 + 1.42199i) q^{13} +(-2.59838 - 2.69229i) q^{14} +(2.86942 + 2.78683i) q^{16} +(1.23338 - 0.712090i) q^{17} +(-1.48153 + 2.56609i) q^{19} +(-2.02437 + 4.98999i) q^{20} +(-1.96178 - 0.382782i) q^{22} +1.93542i q^{23} -2.24950 q^{25} +(-1.30673 - 3.80381i) q^{26} +(4.44073 - 2.87749i) q^{28} +(-0.423772 + 0.733994i) q^{29} +(-4.93678 + 8.55076i) q^{31} +(-4.64536 + 3.22810i) q^{32} +(0.654368 + 1.90483i) q^{34} +(5.83707 + 4.08352i) q^{35} +(-5.49245 + 9.51321i) q^{37} +(-3.16057 - 2.75140i) q^{38} +(-6.37802 - 4.16135i) q^{40} +(-5.99620 + 3.46191i) q^{41} +(-5.96812 - 3.44570i) q^{43} +(1.06263 - 2.61935i) q^{44} +(-2.68643 - 0.524177i) q^{46} +(-5.34240 - 9.25331i) q^{47} +(-2.39965 - 6.57584i) q^{49} +(0.609243 - 3.12240i) q^{50} +(5.63374 - 0.783582i) q^{52} +(6.58617 + 11.4076i) q^{53} +3.80542 q^{55} +(2.79136 + 6.94322i) q^{56} +(-0.904040 - 0.787002i) q^{58} +(-0.710958 + 1.23142i) q^{59} +(-1.76037 + 1.01635i) q^{61} +(-10.5317 - 9.16828i) q^{62} +(-3.22261 - 7.32221i) q^{64} +(3.82871 + 6.63151i) q^{65} +(7.57214 + 4.37178i) q^{67} +(-2.82120 + 0.392394i) q^{68} +(-7.24896 + 6.99612i) q^{70} -1.95293i q^{71} +(7.16234 - 4.13518i) q^{73} +(-11.7171 - 10.2002i) q^{74} +(4.67504 - 3.64182i) q^{76} +(-3.06400 - 2.14352i) q^{77} +(10.2495 - 5.91755i) q^{79} +(7.50350 - 7.72590i) q^{80} +(-3.18128 - 9.26055i) q^{82} +(2.85384 - 4.94299i) q^{83} +(-1.91730 - 3.32085i) q^{85} +(6.39913 - 7.35077i) q^{86} +(3.34796 + 2.18438i) q^{88} +(-5.75795 - 3.32435i) q^{89} +(0.652664 - 7.49613i) q^{91} +(1.45516 - 3.58690i) q^{92} +(14.2908 - 4.90934i) q^{94} +(6.90916 + 3.98901i) q^{95} +(-13.1164 - 7.57275i) q^{97} +(9.77742 - 1.54984i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.270834	+	1.38804i	−0.191509	+	0.981491i
$2$	−0.270834	+	1.38804i	−0.191509	+	0.981491i
$3$		0			0
$3$		0			0
$4$	−1.85330	−	0.751856i	−0.926649	−	0.375928i
$5$		−	2.69249i		−	1.20412i	−0.798451	−	0.602059i	$-0.794347\pi$
$5$		−	2.69249i		−	1.20412i	0.798451	−	0.602059i	$-0.205653\pi$
$6$		0			0
$7$	−1.51663	+	2.16791i	−0.573233	+	0.819392i
$7$	−1.51663	+	2.16791i	−0.573233	+	0.819392i
$8$	1.54554	−	2.36882i	0.546431	−	0.837504i
$9$		0			0
$10$	3.73728	+	0.729218i	1.18183	+	0.230599i
$11$			1.41334i			0.426139i	0.977037	+	0.213070i	$0.0683461\pi$
$11$			1.41334i			0.426139i	−0.977037	+	0.213070i	$0.931654\pi$
$12$		0			0
$13$	−2.46297	+	1.42199i	−0.683104	+	0.394390i	−0.801024	−	0.598633i	$-0.795711\pi$
$13$	−2.46297	+	1.42199i	−0.683104	+	0.394390i	0.117920	+	0.993023i	$0.462378\pi$
$14$	−2.59838	−	2.69229i	−0.694447	−	0.719544i
$15$		0			0
$16$	2.86942	+	2.78683i	0.717356	+	0.696707i
$17$	1.23338	−	0.712090i	0.299138	−	0.172707i	−0.342918	−	0.939365i	$-0.611415\pi$
$17$	1.23338	−	0.712090i	0.299138	−	0.172707i	0.642055	+	0.766658i	$0.278082\pi$
$18$		0			0
$19$	−1.48153	+	2.56609i	−0.339886	+	0.588700i	−0.984411	−	0.175883i	$-0.943722\pi$
$19$	−1.48153	+	2.56609i	−0.339886	+	0.588700i	0.644525	+	0.764583i	$0.277055\pi$
$20$	−2.02437	+	4.98999i	−0.452662	+	1.11579i
$21$		0			0
$22$	−1.96178	−	0.382782i	−0.418252	−	0.0816094i
$23$			1.93542i			0.403562i	0.979431	+	0.201781i	$0.0646730\pi$
$23$			1.93542i			0.403562i	−0.979431	+	0.201781i	$0.935327\pi$
$24$		0			0
$25$	−2.24950			−0.449901
$26$	−1.30673	−	3.80381i	−0.256270	−	0.745989i
$27$		0			0
$28$	4.44073	−	2.87749i	0.839219	−	0.543794i
$29$	−0.423772	+	0.733994i	−0.0786924	+	0.136299i	−0.902686	−	0.430300i	$-0.858408\pi$
$29$	−0.423772	+	0.733994i	−0.0786924	+	0.136299i	0.823994	+	0.566599i	$0.191741\pi$
$30$		0			0
$31$	−4.93678	+	8.55076i	−0.886672	+	1.53576i	−0.0428874	+	0.999080i	$0.513656\pi$
$31$	−4.93678	+	8.55076i	−0.886672	+	1.53576i	−0.843785	+	0.536682i	$0.819678\pi$
$32$	−4.64536	+	3.22810i	−0.821191	+	0.570653i
$33$		0			0
$34$	0.654368	+	1.90483i	0.112223	+	0.326676i
$35$	5.83707	+	4.08352i	0.986645	+	0.690241i
$36$		0			0
$37$	−5.49245	+	9.51321i	−0.902953	+	1.56396i	−0.0793124	+	0.996850i	$0.525272\pi$
$37$	−5.49245	+	9.51321i	−0.902953	+	1.56396i	−0.823641	+	0.567111i	$0.808061\pi$
$38$	−3.16057	−	2.75140i	−0.512713	−	0.446337i
$39$		0			0
$40$	−6.37802	−	4.16135i	−1.00845	−	0.657968i
$41$	−5.99620	+	3.46191i	−0.936449	+	0.540659i	−0.888845	−	0.458207i	$-0.848492\pi$
$41$	−5.99620	+	3.46191i	−0.936449	+	0.540659i	−0.0476034	+	0.998866i	$0.515158\pi$
$42$		0			0
$43$	−5.96812	−	3.44570i	−0.910131	−	0.525464i	−0.0296574	−	0.999560i	$-0.509442\pi$
$43$	−5.96812	−	3.44570i	−0.910131	−	0.525464i	−0.880473	+	0.474096i	$0.842775\pi$
$44$	1.06263	−	2.61935i	0.160198	−	0.394882i
$45$		0			0
$46$	−2.68643	−	0.524177i	−0.396093	−	0.0772857i
$47$	−5.34240	−	9.25331i	−0.779269	−	1.34973i	−0.932364	−	0.361522i	$-0.882257\pi$
$47$	−5.34240	−	9.25331i	−0.779269	−	1.34973i	0.153095	−	0.988212i	$-0.451076\pi$
$48$		0			0
$49$	−2.39965	−	6.57584i	−0.342807	−	0.939406i
$50$	0.609243	−	3.12240i	0.0861599	−	0.441574i
$51$		0			0
$52$	5.63374	−	0.783582i	0.781260	−	0.108663i
$53$	6.58617	+	11.4076i	0.904681	+	1.56695i	0.821345	+	0.570431i	$0.193224\pi$
$53$	6.58617	+	11.4076i	0.904681	+	1.56695i	0.0833354	+	0.996522i	$0.473443\pi$
$54$		0			0
$55$	3.80542			0.513122
$56$	2.79136	+	6.94322i	0.373011	+	0.927827i
$57$		0			0
$58$	−0.904040	−	0.787002i	−0.118706	−	0.103338i
$59$	−0.710958	+	1.23142i	−0.0925589	+	0.160317i	−0.908587	−	0.417695i	$-0.862838\pi$
$59$	−0.710958	+	1.23142i	−0.0925589	+	0.160317i	0.816028	+	0.578012i	$0.196171\pi$
$60$		0			0
$61$	−1.76037	+	1.01635i	−0.225392	+	0.130130i	−0.608444	−	0.793597i	$-0.708206\pi$
$61$	−1.76037	+	1.01635i	−0.225392	+	0.130130i	0.383053	+	0.923727i	$0.374873\pi$
$62$	−10.5317	−	9.16828i	−1.33753	−	1.16437i
$63$		0			0
$64$	−3.22261	−	7.32221i	−0.402826	−	0.915277i
$65$	3.82871	+	6.63151i	0.474893	+	0.822538i
$66$		0			0
$67$	7.57214	+	4.37178i	0.925085	+	0.534098i	0.885254	−	0.465109i	$-0.153985\pi$
$67$	7.57214	+	4.37178i	0.925085	+	0.534098i	0.0398309	+	0.999206i	$0.487318\pi$
$68$	−2.82120	+	0.392394i	−0.342121	+	0.0475847i
$69$		0			0
$70$	−7.24896	+	6.99612i	−0.866416	+	0.836196i
$71$		−	1.95293i		−	0.231770i	−0.993263	−	0.115885i	$-0.963030\pi$
$71$		−	1.95293i		−	0.231770i	0.993263	−	0.115885i	$-0.0369704\pi$
$72$		0			0
$73$	7.16234	−	4.13518i	0.838289	−	0.483986i	−0.0183933	−	0.999831i	$-0.505855\pi$
$73$	7.16234	−	4.13518i	0.838289	−	0.483986i	0.856682	+	0.515844i	$0.172522\pi$
$74$	−11.7171	−	10.2002i	−1.36209	−	1.18575i
$75$		0			0
$76$	4.67504	−	3.64182i	0.536264	−	0.417746i
$77$	−3.06400	−	2.14352i	−0.349175	−	0.244277i
$78$		0			0
$79$	10.2495	−	5.91755i	1.15316	−	0.665776i	0.203503	−	0.979074i	$-0.434767\pi$
$79$	10.2495	−	5.91755i	1.15316	−	0.665776i	0.949655	+	0.313298i	$0.101434\pi$
$80$	7.50350	−	7.72590i	0.838917	−	0.863782i
$81$		0			0
$82$	−3.18128	−	9.26055i	−0.351314	−	1.02266i
$83$	2.85384	−	4.94299i	0.313249	−	0.542563i	−0.665815	−	0.746117i	$-0.731916\pi$
$83$	2.85384	−	4.94299i	0.313249	−	0.542563i	0.979064	+	0.203554i	$0.0652492\pi$
$84$		0			0
$85$	−1.91730	−	3.32085i	−0.207960	−	0.360197i
$86$	6.39913	−	7.35077i	0.690036	−	0.792654i
$87$		0			0
$88$	3.34796	+	2.18438i	0.356893	+	0.232856i
$89$	−5.75795	−	3.32435i	−0.610341	−	0.352381i	0.162758	−	0.986666i	$-0.447961\pi$
$89$	−5.75795	−	3.32435i	−0.610341	−	0.352381i	−0.773099	+	0.634285i	$0.781294\pi$
$90$		0			0
$91$	0.652664	−	7.49613i	0.0684177	−	0.785808i
$92$	1.45516	−	3.58690i	0.151710	−	0.373961i
$93$		0			0
$94$	14.2908	−	4.90934i	1.47399	−	0.506360i
$95$	6.90916	+	3.98901i	0.708865	+	0.409263i
$96$		0			0
$97$	−13.1164	−	7.57275i	−1.33177	−	0.768896i	−0.346197	−	0.938162i	$-0.612527\pi$
$97$	−13.1164	−	7.57275i	−1.33177	−	0.768896i	−0.985570	+	0.169266i	$0.945860\pi$
$98$	9.77742	−	1.54984i	0.987669	−	0.156558i
$99$		0			0
$100$	4.16900	+	1.69130i	0.416900	+	0.169130i
$101$			16.7653i			1.66821i	0.551606	+	0.834105i	$0.314015\pi$
$101$			16.7653i			1.66821i	−0.551606	+	0.834105i	$0.685985\pi$
$102$		0			0
$103$	2.63629			0.259762			0.129881	−	0.991530i	$-0.458541\pi$
$103$	2.63629			0.259762			0.129881	+	0.991530i	$0.458541\pi$
$104$	−0.438169	+	8.03207i	−0.0429660	+	0.787609i
$105$		0			0
$106$	−17.6179	+	6.05229i	−1.71120	+	0.587851i
$107$	0.702055	+	0.405332i	0.0678702	+	0.0391849i	0.533551	−	0.845768i	$-0.320857\pi$
$107$	0.702055	+	0.405332i	0.0678702	+	0.0391849i	−0.465681	+	0.884953i	$0.654191\pi$
$108$		0			0
$109$	5.19986	+	9.00642i	0.498056	+	0.862659i	0.999997	−	0.00224278i	$-0.000713901\pi$
$109$	5.19986	+	9.00642i	0.498056	+	0.862659i	−0.501941	+	0.864902i	$0.667381\pi$
$110$	−1.03064	+	5.28206i	−0.0982674	+	0.503625i
$111$		0			0
$112$	−10.3934	+	1.99405i	−0.982088	+	0.188420i
$113$	−4.37629	−	7.57996i	−0.411687	−	0.713063i	0.583387	−	0.812194i	$-0.301727\pi$
$113$	−4.37629	−	7.57996i	−0.411687	−	0.713063i	−0.995074	+	0.0991313i	$0.968394\pi$
$114$		0			0
$115$	5.21109			0.485937
$116$	1.33723	−	1.04169i	0.124159	−	0.0967189i
$117$		0			0
$118$	−1.51670	−	1.32035i	−0.139624	−	0.121548i
$119$	−0.326834	+	3.75383i	−0.0299608	+	0.344113i
$120$		0			0
$121$	9.00246			0.818405
$122$	−0.933962	−	2.71872i	−0.0845569	−	0.246141i
$123$		0			0
$124$	15.5783	−	12.1353i	1.39897	−	1.08979i
$125$		−	7.40568i		−	0.662384i
$126$		0			0
$127$			15.2544i			1.35361i	0.736164	+	0.676803i	$0.236635\pi$
$127$			15.2544i			1.35361i	−0.736164	+	0.676803i	$0.763365\pi$
$128$	11.0363	−	2.48999i	0.975480	−	0.220086i
$129$		0			0
$130$	−10.2417	+	3.51835i	−0.898260	+	0.308580i
$131$	0.0679194			0.00593415			0.00296707	−	0.999996i	$-0.499056\pi$
$131$	0.0679194			0.00593415			0.00296707	+	0.999996i	$0.499056\pi$
$132$		0			0
$133$	−3.31610	−	7.10363i	−0.287542	−	0.615963i
$134$	−8.11899	+	9.32639i	−0.701374	+	0.805678i
$135$		0			0
$136$	0.219421	−	4.02221i	0.0188152	−	0.344902i
$137$	−5.18966			−0.443383			−0.221691	−	0.975117i	$-0.571158\pi$
$137$	−5.18966			−0.443383			−0.221691	+	0.975117i	$0.571158\pi$
$138$		0			0
$139$	5.27411	+	9.13502i	0.447344	+	0.774823i	0.998212	−	0.0597697i	$-0.0190366\pi$
$139$	5.27411	+	9.13502i	0.447344	+	0.774823i	−0.550868	+	0.834592i	$0.685703\pi$
$140$	−7.74761	−	11.9566i	−0.654793	−	1.01052i
$141$		0			0
$142$	2.71074	+	0.528920i	0.227480	+	0.0443859i
$143$	−2.00977	−	3.48102i	−0.168065	−	0.291097i
$144$		0			0
$145$	1.97627	+	1.14100i	0.164120	+	0.0947550i
$146$	3.79998	+	11.0616i	0.314489	+	0.915461i
$147$		0			0
$148$	17.3317	−	13.5013i	1.42466	−	1.10980i
$149$	−18.3667			−1.50466			−0.752330	−	0.658787i	$-0.771070\pi$
$149$	−18.3667			−1.50466			−0.752330	+	0.658787i	$0.771070\pi$
$150$		0			0
$151$			5.08081i			0.413471i	0.978397	+	0.206735i	$0.0662839\pi$
$151$			5.08081i			0.413471i	−0.978397	+	0.206735i	$0.933716\pi$
$152$	3.78883	+	7.47547i	0.307314	+	0.606340i
$153$		0			0
$154$	3.80513	−	3.67241i	0.306626	−	0.295931i
$155$	23.0228	+	13.2922i	1.84924	+	1.06766i
$156$		0			0
$157$	−2.09319	−	1.20850i	−0.167055	−	0.0964492i	0.414142	−	0.910213i	$-0.364082\pi$
$157$	−2.09319	−	1.20850i	−0.167055	−	0.0964492i	−0.581196	+	0.813763i	$0.697415\pi$
$158$	5.43787	+	15.8294i	0.432613	+	1.25932i
$159$		0			0
$160$	8.69163	+	12.5076i	0.687134	+	0.988811i
$161$	−4.19581	−	2.93532i	−0.330676	−	0.231335i
$162$		0			0
$163$	−13.8321	−	7.98598i	−1.08342	−	0.625510i	−0.151600	−	0.988442i	$-0.548442\pi$
$163$	−13.8321	−	7.98598i	−1.08342	−	0.625510i	−0.931816	+	0.362932i	$0.881776\pi$
$164$	13.7156	−	1.90766i	1.07101	−	0.148964i
$165$		0			0
$166$	6.08814	+	5.29996i	0.472531	+	0.411357i
$167$	−6.99445	−	12.1147i	−0.541247	−	0.937467i	−0.998833	−	0.0483016i	$-0.984619\pi$
$167$	−6.99445	−	12.1147i	−0.541247	−	0.937467i	0.457586	−	0.889165i	$-0.348714\pi$
$168$		0			0
$169$	−2.45586	+	4.25368i	−0.188913	+	0.327206i
$170$	5.12874	−	1.76188i	0.393357	−	0.135130i
$171$		0			0
$172$	8.47004	+	10.8731i	0.645835	+	0.829064i
$173$	21.6132	−	12.4784i	1.64322	−	0.948716i	0.663547	−	0.748135i	$-0.269050\pi$
$173$	21.6132	−	12.4784i	1.64322	−	0.948716i	0.979677	−	0.200581i	$-0.0642829\pi$
$174$		0			0
$175$	3.41167	−	4.87672i	0.257898	−	0.368645i
$176$	−3.93875	+	4.05549i	−0.296894	+	0.305694i
$177$		0			0
$178$	6.17377	−	7.09190i	0.462744	−	0.531560i
$179$	0.618502	−	0.357092i	0.0462290	−	0.0266903i	−0.476707	−	0.879062i	$-0.658170\pi$
$179$	0.618502	−	0.357092i	0.0462290	−	0.0266903i	0.522936	+	0.852372i	$0.324837\pi$
$180$		0			0
$181$			13.5134i			1.00445i	0.864738	+	0.502223i	$0.167484\pi$
$181$			13.5134i			1.00445i	−0.864738	+	0.502223i	$0.832516\pi$
$182$	10.2281	+	2.93613i	0.758161	+	0.217640i
$183$		0			0
$184$	4.58465	+	2.99127i	0.337985	+	0.220519i
$185$	25.6142	+	14.7884i	1.88319	+	1.08726i
$186$		0			0
$187$	1.00643	+	1.74319i	0.0735974	+	0.127474i
$188$	2.94390	+	21.1658i	0.214706	+	1.54368i
$189$		0			0
$190$	−7.40813	+	8.50982i	−0.537442	+	0.617367i
$191$	−13.2173	+	7.63101i	−0.956371	+	0.552161i	−0.895054	−	0.445958i	$-0.852863\pi$
$191$	−13.2173	+	7.63101i	−0.956371	+	0.552161i	−0.0613164	+	0.998118i	$0.519530\pi$
$192$		0			0
$193$	−4.46524	+	7.73402i	−0.321415	+	0.556707i	−0.980780	−	0.195116i	$-0.937492\pi$
$193$	−4.46524	+	7.73402i	−0.321415	+	0.556707i	0.659365	+	0.751823i	$0.270825\pi$
$194$	14.0636	−	16.1551i	1.00971	−	1.15987i
$195$		0			0
$196$	−0.496823	+	13.9912i	−0.0354874	+	0.999370i
$197$	3.57570			0.254758			0.127379	−	0.991854i	$-0.459344\pi$
$197$	3.57570			0.254758			0.127379	+	0.991854i	$0.459344\pi$
$198$		0			0
$199$	−7.27270	−	12.5967i	−0.515548	−	0.892955i	−0.999837	−	0.0180470i	$-0.994255\pi$
$199$	−7.27270	−	12.5967i	−0.515548	−	0.892955i	0.484289	−	0.874908i	$-0.339078\pi$
$200$	−3.47670	+	5.32867i	−0.245840	+	0.376794i
$201$		0			0
$202$	−23.2709	−	4.54061i	−1.63733	−	0.319477i
$203$	−0.948525	−	2.03190i	−0.0665734	−	0.142611i
$204$		0			0
$205$	9.32115	+	16.1447i	0.651017	+	1.12760i
$206$	−0.713998	+	3.65927i	−0.0497466	+	0.254954i
$207$		0			0
$208$	−11.0301	−	2.78355i	−0.764803	−	0.193005i
$209$	−3.62676	−	2.09391i	−0.250868	−	0.144839i
$210$		0			0
$211$	11.3933	−	6.57792i	0.784347	−	0.452843i	−0.0536217	−	0.998561i	$-0.517077\pi$
$211$	11.3933	−	6.57792i	0.784347	−	0.452843i	0.837969	+	0.545718i	$0.183743\pi$
$212$	−3.62928	−	26.0935i	−0.249260	−	1.79211i
$213$		0			0
$214$	−0.752756	+	0.864701i	−0.0514574	+	0.0591098i
$215$	−9.27751	+	16.0691i	−0.632721	+	1.09590i
$216$		0			0
$217$	−11.0500	−	23.6709i	−0.750121	−	1.60688i
$218$	−13.9096	+	4.77836i	−0.942074	+	0.323631i
$219$		0			0
$220$	−7.05257	−	2.86113i	−0.475484	−	0.192897i
$221$	−2.02518	+	3.50771i	−0.136228	+	0.235954i
$222$		0			0
$223$	7.88047	−	13.6494i	0.527715	−	0.914030i	−0.471763	−	0.881726i	$-0.656382\pi$
$223$	7.88047	−	13.6494i	0.527715	−	0.914030i	0.999478	−	0.0323043i	$-0.0102846\pi$
$224$	0.0470774	−	14.9666i	0.00314549	−	0.999995i
$225$		0			0
$226$	11.7065	−	4.02155i	0.778706	−	0.267509i
$227$	1.89582			0.125830			0.0629152	−	0.998019i	$-0.479960\pi$
$227$	1.89582			0.125830			0.0629152	+	0.998019i	$0.479960\pi$
$228$		0			0
$229$			8.53695i			0.564138i	0.959394	+	0.282069i	$0.0910207\pi$
$229$			8.53695i			0.564138i	−0.959394	+	0.282069i	$0.908979\pi$
$230$	−1.41134	+	7.23319i	−0.0930611	+	0.476943i
$231$		0			0
$232$	1.08374	+	2.13826i	0.0711512	+	0.140383i
$233$	8.18028	−	14.1687i	0.535908	−	0.928220i	−0.463211	−	0.886248i	$-0.653303\pi$
$233$	8.18028	−	14.1687i	0.535908	−	0.928220i	0.999119	−	0.0419719i	$-0.0133640\pi$
$234$		0			0
$235$	−24.9144	+	14.3844i	−1.62524	+	0.938332i
$236$	2.24347	−	1.74764i	0.146037	−	0.113762i
$237$		0			0
$238$	−5.12194	−	1.47032i	−0.332006	−	0.0953068i
$239$	5.95333	−	3.43716i	0.385089	−	0.222331i	−0.294941	−	0.955515i	$-0.595300\pi$
$239$	5.95333	−	3.43716i	0.385089	−	0.222331i	0.680030	+	0.733184i	$0.261967\pi$
$240$		0			0
$241$		−	9.97557i		−	0.642583i	−0.946980	−	0.321292i	$-0.895883\pi$
$241$		−	9.97557i		−	0.642583i	0.946980	−	0.321292i	$-0.104117\pi$
$242$	−2.43817	+	12.4958i	−0.156732	+	0.803257i
$243$		0			0
$244$	4.02663	−	0.560053i	0.257779	−	0.0358537i
$245$	−17.7054	+	6.46103i	−1.13116	+	0.412780i
$246$		0			0
$247$		−	8.42691i		−	0.536191i
$248$	12.6252	+	24.9099i	0.801701	+	1.58178i
$249$		0			0
$250$	10.2794	+	2.00571i	0.650124	+	0.126852i
$251$	16.6175			1.04889			0.524444	−	0.851445i	$-0.324273\pi$
$251$	16.6175			1.04889			0.524444	+	0.851445i	$0.324273\pi$
$252$		0			0
$253$	−2.73541			−0.171974
$254$	−21.1736	−	4.13140i	−1.32855	−	0.259227i
$255$		0			0
$256$	0.467195	+	15.9932i	0.0291997	+	0.999574i
$257$		−	7.66440i		−	0.478092i	−0.971008	−	0.239046i	$-0.923165\pi$
$257$		−	7.66440i		−	0.478092i	0.971008	−	0.239046i	$-0.0768347\pi$
$258$		0			0
$259$	−12.2937	−	26.3352i	−0.763894	−	1.63639i
$260$	−2.10979	−	15.1688i	−0.130843	−	0.940729i
$261$		0			0
$262$	−0.0183949	+	0.0942747i	−0.00113644	+	0.00582431i
$263$			11.4173i			0.704020i	0.935996	+	0.352010i	$0.114502\pi$
$263$			11.4173i			0.704020i	−0.935996	+	0.352010i	$0.885498\pi$
$264$		0			0
$265$	30.7148	−	17.7332i	1.88680	−	1.08934i
$266$	10.7582	−	2.67896i	0.659629	−	0.164258i
$267$		0			0
$268$	−10.7465	−	13.7954i	−0.656446	−	0.842686i
$269$	4.88573	−	2.82078i	0.297888	−	0.171986i	−0.343606	−	0.939114i	$-0.611648\pi$
$269$	4.88573	−	2.82078i	0.297888	−	0.171986i	0.641494	+	0.767128i	$0.278315\pi$
$270$		0			0
$271$	3.13192	−	5.42464i	0.190251	−	0.329524i	−0.755083	−	0.655630i	$-0.772403\pi$
$271$	3.13192	−	5.42464i	0.190251	−	0.329524i	0.945333	+	0.326106i	$0.105737\pi$
$272$	5.52355	+	1.39392i	0.334915	+	0.0845187i
$273$		0			0
$274$	1.40554	−	7.20345i	0.0849117	−	0.435176i
$275$		−	3.17932i		−	0.191720i
$276$		0			0
$277$	20.0358			1.20383			0.601917	−	0.798559i	$-0.294404\pi$
$277$	20.0358			1.20383			0.601917	+	0.798559i	$0.294404\pi$
$278$	−14.1082	+	4.84658i	−0.846152	+	0.290679i
$279$		0			0
$280$	18.6946	−	7.51572i	1.11721	−	0.449150i
$281$	9.81283	−	16.9963i	0.585384	−	1.01392i	−0.409443	−	0.912336i	$-0.634277\pi$
$281$	9.81283	−	16.9963i	0.585384	−	1.01392i	0.994827	−	0.101580i	$-0.0323897\pi$
$282$		0			0
$283$	−0.839099	+	1.45336i	−0.0498792	+	0.0863934i	−0.889887	−	0.456181i	$-0.849217\pi$
$283$	−0.839099	+	1.45336i	−0.0498792	+	0.0863934i	0.840008	+	0.542574i	$0.182550\pi$
$284$	−1.46832	+	3.61936i	−0.0871288	+	0.214769i
$285$		0			0
$286$	5.37610	−	1.84685i	0.317895	−	0.109207i
$287$	1.58894	−	18.2496i	0.0937920	−	1.07724i
$288$		0			0
$289$	−7.48585	+	12.9659i	−0.440344	+	0.762699i
$290$	−2.11899	+	2.43412i	−0.124432	+	0.142936i
$291$		0			0
$292$	−16.3830	+	2.27867i	−0.958744	+	0.133349i
$293$	−9.06774	+	5.23526i	−0.529743	+	0.305847i	−0.740912	−	0.671602i	$-0.765606\pi$
$293$	−9.06774	+	5.23526i	−0.529743	+	0.305847i	0.211169	+	0.977450i	$0.432273\pi$
$294$		0			0
$295$	3.31558	+	1.91425i	0.193040	+	0.111452i
$296$	14.0462	+	27.7137i	0.816422	+	1.61082i
$297$		0			0
$298$	4.97433	−	25.4937i	0.288155	−	1.47681i
$299$	−2.75215	−	4.76687i	−0.159161	−	0.275675i
$300$		0			0
$301$	16.5214	−	7.71248i	0.952278	−	0.444540i
$302$	−7.05236	−	1.37606i	−0.405818	−	0.0791832i
$303$		0			0
$304$	−11.4024	+	3.23442i	−0.653971	+	0.185507i
$305$	2.73651	+	4.73977i	0.156692	+	0.271398i
$306$		0			0
$307$	−0.644576			−0.0367879			−0.0183939	−	0.999831i	$-0.505855\pi$
$307$	−0.644576			−0.0367879			−0.0183939	+	0.999831i	$0.505855\pi$
$308$	4.06688	+	6.27628i	0.231732	+	0.357624i
$309$		0			0
$310$	−24.6855	+	28.3566i	−1.40204	+	1.61054i
$311$	−9.04564	+	15.6675i	−0.512931	+	0.888423i	0.486957	+	0.873426i	$0.338107\pi$
$311$	−9.04564	+	15.6675i	−0.512931	+	0.888423i	−0.999888	+	0.0149963i	$0.995226\pi$
$312$		0			0
$313$	−0.0540039	+	0.0311792i	−0.00305248	+	0.00176235i	−0.501525	−	0.865143i	$-0.667228\pi$
$313$	−0.0540039	+	0.0311792i	−0.00305248	+	0.00176235i	0.498473	+	0.866905i	$0.333894\pi$
$314$	2.24436	−	2.57812i	0.126656	−	0.145492i
$315$		0			0
$316$	−23.4445	+	3.26083i	−1.31886	+	0.183436i
$317$	−4.22265	−	7.31385i	−0.237168	−	0.410787i	0.722733	−	0.691128i	$-0.242886\pi$
$317$	−4.22265	−	7.31385i	−0.237168	−	0.410787i	−0.959900	+	0.280341i	$0.909552\pi$
$318$		0			0
$319$	−1.03739	−	0.598935i	−0.0580825	−	0.0335339i
$320$	−19.7150	+	8.67683i	−1.10210	+	0.485050i
$321$		0			0
$322$	5.21070	−	5.02895i	0.290381	−	0.280253i
$323$			4.21993i			0.234803i
$324$		0			0
$325$	5.54045	−	3.19878i	0.307329	−	0.177437i
$326$	14.8311	−	17.0366i	0.821416	−	0.943572i
$327$		0			0
$328$	−1.06674	+	19.5544i	−0.0589009	+	1.07971i
$329$	28.1628	+	2.45204i	1.55266	+	0.135185i
$330$		0			0
$331$	−13.3974	+	7.73498i	−0.736387	+	0.425153i	−0.820754	−	0.571282i	$-0.806446\pi$
$331$	−13.3974	+	7.73498i	−0.736387	+	0.425153i	0.0843675	+	0.996435i	$0.473113\pi$
$332$	−9.00542	+	7.01515i	−0.494237	+	0.385007i
$333$		0			0
$334$	18.7101	−	6.42747i	1.02377	−	0.351696i
$335$	11.7710	−	20.3879i	0.643117	−	1.11391i
$336$		0			0
$337$	1.49961	+	2.59739i	0.0816887	+	0.141489i	0.903975	−	0.427584i	$-0.140635\pi$
$337$	1.49961	+	2.59739i	0.0816887	+	0.141489i	−0.822287	+	0.569073i	$0.807302\pi$
$338$	−5.23914	−	4.56088i	−0.284972	−	0.248079i
$339$		0			0
$340$	1.05652	+	7.59606i	0.0572976	+	0.411954i
$341$	−12.0852	−	6.97737i	−0.654448	−	0.377846i
$342$		0			0
$343$	17.8952	+	4.77092i	0.966250	+	0.257605i
$344$	−17.3862	+	8.81194i	−0.937402	+	0.475108i
$345$		0			0
$346$	11.4669	+	33.3796i	0.616464	+	1.79450i
$347$	−26.0052	−	15.0141i	−1.39603	−	0.806001i	−0.402060	−	0.915613i	$-0.631706\pi$
$347$	−26.0052	−	15.0141i	−1.39603	−	0.806001i	−0.993974	+	0.109613i	$0.965039\pi$
$348$		0			0
$349$	−16.0196	−	9.24890i	−0.857507	−	0.495082i	0.00566949	−	0.999984i	$-0.498195\pi$
$349$	−16.0196	−	9.24890i	−0.857507	−	0.495082i	−0.863177	+	0.504902i	$0.831529\pi$
$350$	5.84507	+	6.05631i	0.312432	+	0.323724i
$351$		0			0
$352$	−4.56242	−	6.56549i	−0.243178	−	0.349942i
$353$		−	7.86508i		−	0.418616i	−0.977850	−	0.209308i	$-0.932879\pi$
$353$		−	7.86508i		−	0.418616i	0.977850	−	0.209308i	$-0.0671211\pi$
$354$		0			0
$355$	−5.25824			−0.279078
$356$	8.17175	+	10.4902i	0.433102	+	0.555977i
$357$		0			0
$358$	0.328146	+	0.955216i	0.0173430	+	0.0504847i
$359$	−15.0238	−	8.67397i	−0.792924	−	0.457795i	0.0480670	−	0.998844i	$-0.484694\pi$
$359$	−15.0238	−	8.67397i	−0.792924	−	0.457795i	−0.840991	+	0.541049i	$0.818027\pi$
$360$		0			0
$361$	5.11014	+	8.85102i	0.268955	+	0.465843i
$362$	−18.7572	−	3.65990i	−0.985855	−	0.192360i
$363$		0			0
$364$	−6.84559	+	13.4018i	−0.358806	+	0.702448i
$365$	−11.1339	−	19.2845i	−0.582777	−	1.00940i
$366$		0			0
$367$	1.02014			0.0532509			0.0266254	−	0.999645i	$-0.491524\pi$
$367$	1.02014			0.0532509			0.0266254	+	0.999645i	$0.491524\pi$
$368$	−5.39367	+	5.55353i	−0.281165	+	0.289498i
$369$		0			0
$370$	−27.4640	+	31.5483i	−1.42779	+	1.64012i
$371$	−34.7194	−	3.02291i	−1.80254	−	0.156941i
$372$		0			0
$373$	−0.0753662			−0.00390232			−0.00195116	−	0.999998i	$-0.500621\pi$
$373$	−0.0753662			−0.00390232			−0.00195116	+	0.999998i	$0.500621\pi$
$374$	−2.69218	+	0.924847i	−0.139209	+	0.0478227i
$375$		0			0
$376$	−30.1763	−	1.64619i	−1.55622	−	0.0848958i
$377$		−	2.41040i		−	0.124142i
$378$		0			0
$379$			29.5406i			1.51740i	0.651442	+	0.758699i	$0.274165\pi$
$379$			29.5406i			1.51740i	−0.651442	+	0.758699i	$0.725835\pi$
$380$	−9.80557	−	12.5875i	−0.503015	−	0.645726i
$381$		0			0
$382$	−7.01244	−	20.4129i	−0.358788	−	1.04441i
$383$	28.4714			1.45482			0.727410	−	0.686203i	$-0.240724\pi$
$383$	28.4714			1.45482			0.727410	+	0.686203i	$0.240724\pi$
$384$		0			0
$385$	−5.77142	+	8.24979i	−0.294139	+	0.420448i
$386$	−9.52577	−	8.29256i	−0.484849	−	0.422080i
$387$		0			0
$388$	18.6149	+	23.8962i	0.945031	+	1.21315i
$389$	−21.7756			−1.10406			−0.552032	−	0.833823i	$-0.686148\pi$
$389$	−21.7756			−1.10406			−0.552032	+	0.833823i	$0.686148\pi$
$390$		0			0
$391$	1.37819	+	2.38710i	0.0696982	+	0.120721i
$392$	−19.2857	−	4.47890i	−0.974077	−	0.226219i
$393$		0			0
$394$	−0.968421	+	4.96320i	−0.0487883	+	0.250042i
$395$	−15.9329	−	27.5967i	−0.801673	−	1.38854i
$396$		0			0
$397$	−1.28100	−	0.739586i	−0.0642915	−	0.0371187i	0.467510	−	0.883988i	$-0.345151\pi$
$397$	−1.28100	−	0.739586i	−0.0642915	−	0.0371187i	−0.531801	+	0.846869i	$0.678485\pi$
$398$	19.4544	−	6.68317i	0.975159	−	0.334997i
$399$		0			0
$400$	−6.45478	−	6.26898i	−0.322739	−	0.313449i
$401$	24.8006			1.23848			0.619242	−	0.785200i	$-0.287440\pi$
$401$	24.8006			1.23848			0.619242	+	0.785200i	$0.287440\pi$
$402$		0			0
$403$		−	28.0803i		−	1.39878i
$404$	12.6051	−	31.0711i	0.627127	−	1.54584i
$405$		0			0
$406$	3.07724	−	0.766282i	0.152721	−	0.0380299i
$407$	−13.4454	−	7.76273i	−0.666465	−	0.384784i
$408$		0			0
$409$	8.10807	+	4.68120i	0.400918	+	0.231470i	0.686880	−	0.726771i	$-0.258980\pi$
$409$	8.10807	+	4.68120i	0.400918	+	0.231470i	−0.285962	+	0.958241i	$0.592313\pi$
$410$	−24.9339	+	8.56557i	−1.23140	+	0.423023i
$411$		0			0
$412$	−4.88584	−	1.98211i	−0.240708	−	0.0976517i
$413$	−1.59133	−	3.40890i	−0.0783044	−	0.167741i
$414$		0			0
$415$	−13.3089	−	7.68392i	−0.653311	−	0.377189i
$416$	6.85102	−	14.5564i	0.335899	−	0.713685i
$417$		0			0
$418$	3.88868	−	4.46698i	0.190202	−	0.218487i
$419$	5.21230	+	9.02797i	0.254637	+	0.441045i	0.964797	−	0.262996i	$-0.0847105\pi$
$419$	5.21230	+	9.02797i	0.254637	+	0.441045i	−0.710160	+	0.704041i	$0.751377\pi$
$420$		0			0
$421$	−3.45213	+	5.97927i	−0.168247	+	0.291412i	−0.937803	−	0.347167i	$-0.887144\pi$
$421$	−3.45213	+	5.97927i	−0.168247	+	0.291412i	0.769557	+	0.638578i	$0.220477\pi$
$422$	6.04471	+	17.5959i	0.294252	+	0.856553i
$423$		0			0
$424$	37.2017	+	2.02944i	1.80668	+	0.0985585i
$425$	−2.77449	+	1.60185i	−0.134582	+	0.0777012i
$426$		0			0
$427$	0.466481	−	5.35774i	0.0225746	−	0.259279i
$428$	−0.996366	−	1.27905i	−0.0481612	−	0.0618250i
$429$		0			0
$430$	−19.7919	−	17.2296i	−0.954449	−	0.830885i
$431$	−12.4348	+	7.17921i	−0.598961	+	0.345810i	−0.768633	−	0.639690i	$-0.779063\pi$
$431$	−12.4348	+	7.17921i	−0.598961	+	0.345810i	0.169672	+	0.985501i	$0.445729\pi$
$432$		0			0
$433$		−	25.8458i		−	1.24207i	−0.783783	−	0.621035i	$-0.786712\pi$
$433$		−	25.8458i		−	1.24207i	0.783783	−	0.621035i	$-0.213288\pi$
$434$	35.8487	−	8.92690i	1.72079	−	0.428505i
$435$		0			0
$436$	−2.86536	−	20.6011i	−0.137226	−	0.986615i
$437$	−4.96645	−	2.86738i	−0.237577	−	0.137165i
$438$		0			0
$439$	7.29345	+	12.6326i	0.348097	+	0.602922i	0.985911	−	0.167268i	$-0.0534945\pi$
$439$	7.29345	+	12.6326i	0.348097	+	0.602922i	−0.637814	+	0.770190i	$0.720161\pi$
$440$	5.88143	−	9.01434i	0.280386	−	0.429742i
$441$		0			0
$442$	−4.32035	−	3.76103i	−0.205498	−	0.178894i
$443$	−30.6417	+	17.6910i	−1.45583	+	0.840524i	−0.998802	−	0.0489286i	$-0.984419\pi$
$443$	−30.6417	+	17.6910i	−1.45583	+	0.840524i	−0.457028	+	0.889452i	$0.651086\pi$
$444$		0			0
$445$	−8.95078	+	15.5032i	−0.424308	+	0.734923i
$446$	16.8115	+	14.6351i	0.796050	+	0.692992i
$447$		0			0
$448$	20.7614	+	4.11880i	0.980884	+	0.194595i
$449$	0.329740			0.0155614			0.00778070	−	0.999970i	$-0.497523\pi$
$449$	0.329740			0.0155614			0.00778070	+	0.999970i	$0.497523\pi$
$450$		0			0
$451$	−4.89287	−	8.47469i	−0.230396	−	0.399058i
$452$	2.41153	+	17.3383i	0.113429	+	0.815523i
$453$		0			0
$454$	−0.513454	+	2.63148i	−0.0240976	+	0.123501i
$455$	−20.1833	−	1.75729i	−0.946205	−	0.0823830i
$456$		0			0
$457$	−12.9421	−	22.4164i	−0.605407	−	1.04860i	−0.991987	−	0.126340i	$-0.959677\pi$
$457$	−12.9421	−	22.4164i	−0.605407	−	1.04860i	0.386580	−	0.922256i	$-0.373656\pi$
$458$	−11.8496	−	2.31210i	−0.553696	−	0.108037i
$459$		0			0
$460$	−9.65770	−	3.91799i	−0.450293	−	0.182677i
$461$	−24.3535	−	14.0605i	−1.13426	−	0.654863i	−0.189254	−	0.981928i	$-0.560607\pi$
$461$	−24.3535	−	14.0605i	−1.13426	−	0.654863i	−0.945002	+	0.327065i	$0.893940\pi$
$462$		0			0
$463$	−17.0012	+	9.81564i	−0.790112	+	0.456171i	−0.840002	−	0.542583i	$-0.817446\pi$
$463$	−17.0012	+	9.81564i	−0.790112	+	0.456171i	0.0498901	+	0.998755i	$0.484113\pi$
$464$	−3.26149	+	0.925162i	−0.151411	+	0.0429496i
$465$		0			0
$466$	17.4511	+	15.1919i	0.808409	+	0.703751i
$467$	−10.9101	+	18.8969i	−0.504861	+	0.874446i	0.495123	+	0.868823i	$0.335123\pi$
$467$	−10.9101	+	18.8969i	−0.504861	+	0.874446i	−0.999984	+	0.00562261i	$0.998210\pi$
$468$		0			0
$469$	−20.9618	+	9.78532i	−0.967925	+	0.451844i
$470$	−13.2184	−	38.4780i	−0.609717	−	1.77486i
$471$		0			0
$472$	1.81819	+	3.58734i	0.0836888	+	0.165121i
$473$	4.86996	−	8.43502i	0.223921	−	0.387842i
$474$		0			0
$475$	3.33271	−	5.77242i	0.152915	−	0.264857i
$476$	3.42806	−	6.71123i	0.157125	−	0.307609i
$477$		0			0
$478$	3.15854	+	9.19435i	0.144468	+	0.420540i
$479$	29.4061			1.34360			0.671799	−	0.740733i	$-0.265522\pi$
$479$	29.4061			1.34360			0.671799	+	0.740733i	$0.265522\pi$
$480$		0			0
$481$		−	31.2409i		−	1.42446i
$482$	13.8465	+	2.70173i	0.630689	+	0.123060i
$483$		0			0
$484$	−16.6842	−	6.76855i	−0.758374	−	0.307662i
$485$	−20.3896	+	35.3157i	−0.925842	+	1.60361i
$486$		0			0
$487$	−3.83992	+	2.21698i	−0.174003	+	0.100461i	−0.584472	−	0.811414i	$-0.698698\pi$
$487$	−3.83992	+	2.21698i	−0.174003	+	0.100461i	0.410469	+	0.911875i	$0.365365\pi$
$488$	−0.313174	+	5.74079i	−0.0141767	+	0.259874i
$489$		0			0
$490$	−4.17293	−	26.3256i	−0.188514	−	1.18927i
$491$	0.492024	−	0.284070i	0.0222047	−	0.0128199i	−0.488857	−	0.872364i	$-0.662586\pi$
$491$	0.492024	−	0.284070i	0.0222047	−	0.0128199i	0.511061	+	0.859544i	$0.329253\pi$
$492$		0			0
$493$			1.20705i			0.0543630i
$494$	11.6969	+	2.28230i	0.526267	+	0.102685i
$495$		0			0
$496$	−37.9952	+	10.7778i	−1.70604	+	0.483937i
$497$	4.23377	+	2.96187i	0.189910	+	0.132858i
$498$		0			0
$499$			8.20964i			0.367514i	0.982972	+	0.183757i	$0.0588259\pi$
$499$			8.20964i			0.367514i	−0.982972	+	0.183757i	$0.941174\pi$
$500$	−5.56801	+	13.7249i	−0.249009	+	0.613798i
$501$		0			0
$502$	−4.50059	+	23.0657i	−0.200871	+	1.02947i
$503$	−23.6082			−1.05264			−0.526319	−	0.850287i	$-0.676428\pi$
$503$	−23.6082			−1.05264			−0.526319	+	0.850287i	$0.676428\pi$
$504$		0			0
$505$	45.1404			2.00872
$506$	0.740843	−	3.79685i	0.0329345	−	0.168791i
$507$		0			0
$508$	11.4691	−	28.2709i	0.508858	−	1.25432i
$509$			31.7425i			1.40696i	0.710713	+	0.703482i	$0.248372\pi$
$509$			31.7425i			1.40696i	−0.710713	+	0.703482i	$0.751628\pi$
$510$		0			0
$511$	−1.89796	+	21.7989i	−0.0839606	+	0.964325i
$512$	−22.3257	−	3.68301i	−0.986664	−	0.162768i
$513$		0			0
$514$	10.6385	+	2.07578i	0.469243	+	0.0915587i
$515$		−	7.09819i		−	0.312784i
$516$		0			0
$517$	13.0781	−	7.55065i	0.575175	−	0.332077i
$518$	39.8838	−	9.93168i	1.75239	−	0.436373i
$519$		0			0
$520$	21.6263	+	1.17977i	0.948375	+	0.0517362i
$521$	2.09032	−	1.20685i	0.0915786	−	0.0528730i	−0.453511	−	0.891251i	$-0.649829\pi$
$521$	2.09032	−	1.20685i	0.0915786	−	0.0528730i	0.545090	+	0.838378i	$0.316495\pi$
$522$		0			0
$523$	4.85017	−	8.40075i	0.212083	−	0.367339i	−0.740283	−	0.672295i	$-0.765309\pi$
$523$	4.85017	−	8.40075i	0.212083	−	0.367339i	0.952366	+	0.304956i	$0.0986419\pi$
$524$	−0.125875	−	0.0510656i	−0.00549887	−	0.00223081i
$525$		0			0
$526$	−15.8476	−	3.09219i	−0.690989	−	0.134826i
$527$			14.0617i			0.612539i
$528$		0			0
$529$	19.2542			0.837137
$530$	16.2957	+	47.4361i	0.707842	+	2.06049i
$531$		0			0
$532$	0.804810	+	15.6584i	0.0348930	+	0.678876i
$533$	9.84562	−	17.0531i	0.426461	−	0.738653i
$534$		0			0
$535$	1.09135	−	1.89028i	0.0471833	−	0.0817238i
$536$	22.0590	−	11.1803i	0.952804	−	0.482914i
$537$		0			0
$538$	2.59212	+	7.54555i	0.111754	+	0.325312i
$539$	9.29393	−	3.39153i	0.400318	−	0.146084i
$540$		0			0
$541$	−2.43786	+	4.22250i	−0.104812	+	0.181539i	−0.913661	−	0.406476i	$-0.866757\pi$
$541$	−2.43786	+	4.22250i	−0.104812	+	0.181539i	0.808850	+	0.588016i	$0.200091\pi$
$542$	6.68138	+	5.81640i	0.286990	+	0.249836i
$543$		0			0
$544$	−3.43078	+	7.28938i	−0.147093	+	0.312530i
$545$	24.2497	−	14.0006i	1.03874	−	0.599719i
$546$		0			0
$547$	22.7649	+	13.1433i	0.973356	+	0.561967i	0.900258	−	0.435357i	$-0.143378\pi$
$547$	22.7649	+	13.1433i	0.973356	+	0.561967i	0.0730983	+	0.997325i	$0.476711\pi$
$548$	9.61799	+	3.90188i	0.410860	+	0.166680i
$549$		0			0
$550$	4.41302	+	0.861070i	0.188172	+	0.0367161i
$551$	−1.25566	−	2.17487i	−0.0534930	−	0.0926525i
$552$		0			0
$553$	−2.71602	+	31.1947i	−0.115497	+	1.32653i
$554$	−5.42638	+	27.8104i	−0.230545	+	1.18155i
$555$		0			0
$556$	−2.90627	−	20.8953i	−0.123253	−	0.886158i
$557$	0.740402	+	1.28241i	0.0313719	+	0.0543377i	0.881285	−	0.472585i	$-0.156679\pi$
$557$	0.740402	+	1.28241i	0.0313719	+	0.0543377i	−0.849913	+	0.526923i	$0.823346\pi$
$558$		0			0
$559$	19.5991			0.828952
$560$	5.36897	+	27.9843i	0.226881	+	1.18255i
$561$		0			0
$562$	20.9339	+	18.2238i	0.883042	+	0.768723i
$563$	0.100448	−	0.173981i	0.00423339	−	0.00733244i	−0.863901	−	0.503662i	$-0.831986\pi$
$563$	0.100448	−	0.173981i	0.00423339	−	0.00733244i	0.868134	+	0.496329i	$0.165319\pi$
$564$		0			0
$565$	−20.4090	+	11.7831i	−0.858612	+	0.495720i
$566$	−1.79006	−	1.55832i	−0.0752420	−	0.0655011i
$567$		0			0
$568$	−4.62613	−	3.01833i	−0.194108	−	0.126646i
$569$	21.9082	+	37.9462i	0.918441	+	1.59079i	0.801784	+	0.597613i	$0.203884\pi$
$569$	21.9082	+	37.9462i	0.918441	+	1.59079i	0.116656	+	0.993172i	$0.462782\pi$
$570$		0			0
$571$	−11.5167	−	6.64914i	−0.481957	−	0.278258i	0.239275	−	0.970952i	$-0.423090\pi$
$571$	−11.5167	−	6.64914i	−0.481957	−	0.278258i	−0.721232	+	0.692694i	$0.756424\pi$
$572$	1.10747	+	7.96242i	0.0463057	+	0.332926i
$573$		0			0
$574$	24.9009	+	7.14813i	1.03934	+	0.298357i
$575$		−	4.35373i		−	0.181563i
$576$		0			0
$577$	7.21473	−	4.16543i	0.300353	−	0.173409i	−0.342248	−	0.939610i	$-0.611188\pi$
$577$	7.21473	−	4.16543i	0.300353	−	0.173409i	0.642602	+	0.766201i	$0.277855\pi$
$578$	−15.9697	−	13.9023i	−0.664252	−	0.578257i
$579$		0			0
$580$	−2.80475	−	3.60049i	−0.116461	−	0.149502i
$581$	6.38772	+	13.6836i	0.265007	+	0.567689i
$582$		0			0
$583$	−16.1229	+	9.30853i	−0.667740	+	0.385520i
$584$	1.27420	−	23.3574i	0.0527269	−	0.966536i
$585$		0			0
$586$	−4.81089	−	14.0043i	−0.198736	−	0.578511i
$587$	4.37925	−	7.58509i	0.180751	−	0.313070i	−0.761385	−	0.648299i	$-0.775480\pi$
$587$	4.37925	−	7.58509i	0.180751	−	0.313070i	0.942137	+	0.335229i	$0.108814\pi$
$588$		0			0
$589$	−14.6280	−	25.3364i	−0.602736	−	1.04397i
$590$	−3.55502	+	4.08370i	−0.146358	+	0.168123i
$591$		0			0
$592$	−42.2718	+	11.9909i	−1.73736	+	0.492824i
$593$	10.4931	+	6.05820i	0.430900	+	0.248780i	0.699730	−	0.714407i	$-0.253304\pi$
$593$	10.4931	+	6.05820i	0.430900	+	0.248780i	−0.268830	+	0.963188i	$0.586637\pi$
$594$		0			0
$595$	10.1071	+	0.879996i	0.414352	+	0.0360763i
$596$	34.0390	+	13.8091i	1.39429	+	0.565644i
$597$		0			0
$598$	7.36197	−	2.52906i	0.301053	−	0.103421i
$599$	34.1856	+	19.7371i	1.39679	+	0.806434i	0.994054	−	0.108884i	$-0.0347277\pi$
$599$	34.1856	+	19.7371i	1.39679	+	0.806434i	0.402731	+	0.915318i	$0.368061\pi$
$600$		0			0
$601$	3.43670	+	1.98418i	0.140186	+	0.0809363i	0.568453	−	0.822716i	$-0.307542\pi$
$601$	3.43670	+	1.98418i	0.140186	+	0.0809363i	−0.428267	+	0.903652i	$0.640876\pi$
$602$	6.23066	+	25.0211i	0.253943	+	1.01979i
$603$		0			0
$604$	3.82004	−	9.41626i	0.155435	−	0.383142i
$605$		−	24.2390i		−	0.985457i
$606$		0			0
$607$	−28.6846			−1.16427			−0.582136	−	0.813091i	$-0.697783\pi$
$607$	−28.6846			−1.16427			−0.582136	+	0.813091i	$0.697783\pi$
$608$	−1.40135	−	16.7029i	−0.0568321	−	0.677393i
$609$		0			0
$610$	−7.32012	+	2.51468i	−0.296383	+	0.101817i
$611$	26.3163	+	15.1937i	1.06464	+	0.614672i
$612$		0			0
$613$	−1.55941	−	2.70099i	−0.0629842	−	0.109092i	0.832814	−	0.553553i	$-0.186728\pi$
$613$	−1.55941	−	2.70099i	−0.0629842	−	0.109092i	−0.895798	+	0.444461i	$0.853395\pi$
$614$	0.174573	−	0.894695i	0.00704520	−	0.0361070i
$615$		0			0
$616$	−9.81316	+	3.94516i	−0.395384	+	0.158955i
$617$	−1.30847	−	2.26634i	−0.0526770	−	0.0912393i	0.838485	−	0.544925i	$-0.183442\pi$
$617$	−1.30847	−	2.26634i	−0.0526770	−	0.0912393i	−0.891162	+	0.453686i	$0.850109\pi$
$618$		0			0
$619$	24.6368			0.990238			0.495119	−	0.868825i	$-0.335125\pi$
$619$	24.6368			0.990238			0.495119	+	0.868825i	$0.335125\pi$
$620$	−32.6743	−	41.9443i	−1.31223	−	1.68453i
$621$		0			0
$622$	−19.2972	−	16.7990i	−0.773748	−	0.673578i
$623$	15.9396	−	7.44087i	0.638606	−	0.298112i
$624$		0			0
$625$	−31.1873			−1.24749
$626$	−0.0286518	−	0.0834038i	−0.00114515	−	0.00333349i
$627$		0			0
$628$	2.97069	+	3.81350i	0.118543	+	0.152175i
$629$			15.6445i			0.623787i
$630$		0			0
$631$		−	8.86244i		−	0.352808i	−0.984318	−	0.176404i	$-0.943553\pi$
$631$		−	8.86244i		−	0.352808i	0.984318	−	0.176404i	$-0.0564466\pi$
$632$	1.82342	−	33.4250i	0.0725316	−	1.32958i
$633$		0			0
$634$	11.2955	−	3.88036i	0.448603	−	0.154109i
$635$	41.0722			1.62990
$636$		0			0
$637$	15.2611	+	12.7838i	0.604665	+	0.506512i
$638$	1.11230	−	1.27772i	0.0440366	−	0.0505854i
$639$		0			0
$640$	−6.70428	−	29.7151i	−0.265010	−	1.17459i
$641$	36.6795			1.44875			0.724376	−	0.689405i	$-0.242128\pi$
$641$	36.6795			1.44875			0.724376	+	0.689405i	$0.242128\pi$
$642$		0			0
$643$	10.9509	+	18.9675i	0.431860	+	0.748004i	0.997034	−	0.0769685i	$-0.0245241\pi$
$643$	10.9509	+	18.9675i	0.431860	+	0.748004i	−0.565173	+	0.824972i	$0.691191\pi$
$644$	5.56914	+	8.59466i	0.219455	+	0.338677i
$645$		0			0
$646$	−5.85743	−	1.14290i	−0.230457	−	0.0449669i
$647$	15.1436	+	26.2296i	0.595358	+	1.03119i	0.993496	+	0.113865i	$0.0363232\pi$
$647$	15.1436	+	26.2296i	0.595358	+	1.03119i	−0.398138	+	0.917326i	$0.630343\pi$
$648$		0			0
$649$	−1.74042	−	1.00483i	−0.0683173	−	0.0394430i
$650$	2.93949	+	8.55670i	0.115296	+	0.335621i
$651$		0			0
$652$	19.6307	+	25.2002i	0.768799	+	0.986914i
$653$	−8.73012			−0.341636			−0.170818	−	0.985303i	$-0.554641\pi$
$653$	−8.73012			−0.341636			−0.170818	+	0.985303i	$0.554641\pi$
$654$		0			0
$655$		−	0.182872i		−	0.00714541i
$656$	−26.8534	−	6.77668i	−1.04845	−	0.264585i
$657$		0			0
$658$	−11.0310	+	38.4269i	−0.430032	+	1.49804i
$659$	38.1510	+	22.0265i	1.48615	+	0.858030i	0.999876	−	0.0157758i	$-0.00502180\pi$
$659$	38.1510	+	22.0265i	1.48615	+	0.858030i	0.486276	+	0.873806i	$0.338355\pi$
$660$		0			0
$661$	−33.7531	−	19.4874i	−1.31284	−	0.757971i	−0.330277	−	0.943884i	$-0.607142\pi$
$661$	−33.7531	−	19.4874i	−1.31284	−	0.757971i	−0.982566	+	0.185913i	$0.940476\pi$
$662$	−7.10798	−	20.6910i	−0.276259	−	0.804177i
$663$		0			0
$664$	−7.29832	−	14.3998i	−0.283230	−	0.558821i
$665$	−19.1265	+	8.92856i	−0.741692	+	0.346235i
$666$		0			0
$667$	−1.42058	−	0.820175i	−0.0550053	−	0.0317573i
$668$	3.85425	+	27.7110i	0.149126	+	1.07217i
$669$		0			0
$670$	25.1112	+	21.8603i	0.970131	+	0.844537i
$671$	−1.43645	−	2.48800i	−0.0554535	−	0.0960483i
$672$		0			0
$673$	6.18407	−	10.7111i	0.238379	−	0.412884i	−0.721871	−	0.692028i	$-0.756717\pi$
$673$	6.18407	−	10.7111i	0.238379	−	0.412884i	0.960249	+	0.279144i	$0.0900508\pi$
$674$	−4.01142	+	1.37805i	−0.154514	+	0.0530804i
$675$		0			0
$676$	7.74961	−	6.03688i	0.298062	−	0.232188i
$677$	−11.6502	+	6.72625i	−0.447754	+	0.258511i	−0.706881	−	0.707332i	$-0.749898\pi$
$677$	−11.6502	+	6.72625i	−0.447754	+	0.258511i	0.259127	+	0.965843i	$0.416565\pi$
$678$		0			0
$679$	36.3098	−	16.9500i	1.39344	−	0.650483i
$680$	−10.8298	−	0.590790i	−0.415303	−	0.0226558i
$681$		0			0
$682$	12.9579	−	14.8850i	0.496185	−	0.569974i
$683$	13.0760	−	7.54945i	0.500340	−	0.288872i	−0.228514	−	0.973541i	$-0.573387\pi$
$683$	13.0760	−	7.54945i	0.500340	−	0.288872i	0.728854	+	0.684669i	$0.240053\pi$
$684$		0			0
$685$			13.9731i			0.533886i
$686$	−11.4689	+	23.5471i	−0.437883	+	0.899032i
$687$		0			0
$688$	−7.52252	−	26.5193i	−0.286793	−	1.01104i
$689$	−32.4431	−	18.7310i	−1.23598	−	0.713594i
$690$		0			0
$691$	13.2006	+	22.8641i	0.502175	+	0.869793i	0.999997	+	0.00251366i	$0.000800122\pi$
$691$	13.2006	+	22.8641i	0.502175	+	0.869793i	−0.497822	+	0.867279i	$0.665867\pi$
$692$	−49.4377	+	6.87616i	−1.87934	+	0.261392i
$693$		0			0
$694$	27.8833	−	32.0299i	1.05843	−	1.21584i
$695$	24.5960	−	14.2005i	0.932978	−	0.538655i
$696$		0			0
$697$	−4.93038	+	8.53967i	−0.186751	+	0.323463i
$698$	17.1765	−	19.7308i	0.650139	−	0.746823i
$699$		0			0
$700$	−9.98944	+	6.47292i	−0.377565	+	0.244654i
$701$	9.14551			0.345421			0.172711	−	0.984973i	$-0.444747\pi$
$701$	9.14551			0.345421			0.172711	+	0.984973i	$0.444747\pi$
$702$		0			0
$703$	−16.2745	−	28.1882i	−0.613803	−	1.06314i
$704$	10.3488	−	4.55465i	0.390035	−	0.171660i
$705$		0			0
$706$	10.9170	+	2.13013i	0.410868	+	0.0801686i
$707$	−36.3456	−	25.4268i	−1.36692	−	0.956273i
$708$		0			0
$709$	9.59758	+	16.6235i	0.360445	+	0.624309i	0.988034	−	0.154236i	$-0.0492916\pi$
$709$	9.59758	+	16.6235i	0.360445	+	0.624309i	−0.627589	+	0.778545i	$0.715958\pi$
$710$	1.42411	−	7.29863i	0.0534459	−	0.273913i
$711$		0			0
$712$	−16.7739	+	8.50161i	−0.628630	+	0.318611i
$713$	−16.5493	−	9.55473i	−0.619776	−	0.357828i
$714$		0			0
$715$	−9.37261	+	5.41128i	−0.350516	+	0.202370i
$716$	−1.41475	+	0.196774i	−0.0528717	+	0.00735378i
$717$		0			0
$718$	16.1088	−	18.5043i	0.601173	−	0.690576i
$719$	2.31150	−	4.00364i	0.0862046	−	0.149311i	−0.819699	−	0.572794i	$-0.805859\pi$
$719$	2.31150	−	4.00364i	0.0862046	−	0.149311i	0.905904	+	0.423483i	$0.139193\pi$
$720$		0			0
$721$	−3.99829	+	5.71524i	−0.148904	+	0.212847i
$722$	−13.6695	+	4.69591i	−0.508728	+	0.174764i
$723$		0			0
$724$	10.1602	−	25.0444i	0.377600	−	0.930769i
$725$	0.953276	−	1.65112i	0.0354038	−	0.0613212i
$726$		0			0
$727$	−4.10913	+	7.11723i	−0.152399	+	0.263963i	−0.932109	−	0.362178i	$-0.882033\pi$
$727$	−4.10913	+	7.11723i	−0.152399	+	0.263963i	0.779710	+	0.626141i	$0.215367\pi$
$728$	−16.7482	−	13.1316i	−0.620731	−	0.486690i
$729$		0			0
$730$	29.7831	−	10.2314i	1.10232	−	0.378681i
$731$	−9.81460			−0.363006
$732$		0			0
$733$			21.8501i			0.807052i	0.914968	+	0.403526i	$0.132215\pi$
$733$			21.8501i			0.807052i	−0.914968	+	0.403526i	$0.867785\pi$
$734$	−0.276289	+	1.41599i	−0.0101980	+	0.0522652i
$735$		0			0
$736$	−6.24772	−	8.99071i	−0.230294	−	0.331402i
$737$	−6.17883	+	10.7020i	−0.227600	+	0.394215i
$738$		0			0
$739$	16.9483	−	9.78511i	0.623454	−	0.359951i	−0.154759	−	0.987952i	$-0.549460\pi$
$739$	16.9483	−	9.78511i	0.623454	−	0.359951i	0.778212	+	0.628001i	$0.216127\pi$
$740$	−36.3520	−	46.6655i	−1.33633	−	1.71546i
$741$		0			0
$742$	13.5991	−	47.3731i	0.499239	−	1.73912i
$743$	7.26557	−	4.19478i	0.266548	−	0.153892i	−0.360770	−	0.932655i	$-0.617486\pi$
$743$	7.26557	−	4.19478i	0.266548	−	0.153892i	0.627318	+	0.778763i	$0.284153\pi$
$744$		0			0
$745$			49.4522i			1.81179i
$746$	0.0204118	−	0.104611i	0.000747328	−	0.00383009i
$747$		0			0
$748$	−0.554587	−	3.98733i	−0.0202777	−	0.145791i
$749$	−1.94348	+	0.907251i	−0.0710133	+	0.0331502i
$750$		0			0
$751$		−	13.6543i		−	0.498254i	−0.968471	−	0.249127i	$-0.919856\pi$
$751$		−	13.6543i		−	0.498254i	0.968471	−	0.249127i	$-0.0801436\pi$
$752$	10.4578	−	41.4400i	0.381355	−	1.51116i
$753$		0			0
$754$	3.34573	+	0.652820i	0.121844	+	0.0237743i
$755$	13.6800			0.497868
$756$		0			0
$757$	22.0851			0.802697			0.401348	−	0.915925i	$-0.368542\pi$
$757$	22.0851			0.802697			0.401348	+	0.915925i	$0.368542\pi$
$758$	−41.0034	−	8.00060i	−1.48931	−	0.290595i
$759$		0			0
$760$	20.1276	−	10.2014i	0.730106	−	0.370043i
$761$			26.1139i			0.946628i	0.880894	+	0.473314i	$0.156942\pi$
$761$			26.1139i			0.946628i	−0.880894	+	0.473314i	$0.843058\pi$
$762$		0			0
$763$	−27.4114	−	2.38662i	−0.992359	−	0.0864014i
$764$	30.2330	−	4.20503i	1.09379	−	0.152133i
$765$		0			0
$766$	−7.71103	+	39.5194i	−0.278611	+	1.42789i
$767$		−	4.04392i		−	0.146017i
$768$		0			0
$769$	−14.6518	+	8.45923i	−0.528358	+	0.305048i	−0.740348	−	0.672224i	$-0.765339\pi$
$769$	−14.6518	+	8.45923i	−0.528358	+	0.305048i	0.211989	+	0.977272i	$0.432006\pi$
$770$	−9.88792	−	10.2453i	−0.356336	−	0.369214i
$771$		0			0
$772$	14.0903	−	10.9762i	0.507121	−	0.395043i
$773$	−18.8030	+	10.8559i	−0.676298	+	0.390461i	−0.798459	−	0.602049i	$-0.794351\pi$
$773$	−18.8030	+	10.8559i	−0.676298	+	0.390461i	0.122161	+	0.992510i	$0.461018\pi$
$774$		0			0
$775$	11.1053	−	19.2350i	0.398915	−	0.690940i
$776$	−38.2104	+	19.3663i	−1.37167	+	0.695211i
$777$		0			0
$778$	5.89757	−	30.2253i	0.211438	−	1.08363i
$779$		−	20.5157i		−	0.735050i
$780$		0			0
$781$	2.76016			0.0987663
$782$	−3.68664	+	1.26647i	−0.131834	+	0.0452890i
$783$		0			0
$784$	11.4401	−	25.5563i	0.408576	−	0.912724i
$785$	−3.25389	+	5.63590i	−0.116136	+	0.201154i
$786$		0			0
$787$	9.75938	−	16.9037i	0.347884	−	0.602553i	−0.637989	−	0.770045i	$-0.720234\pi$
$787$	9.75938	−	16.9037i	0.347884	−	0.602553i	0.985873	+	0.167492i	$0.0535668\pi$
$788$	−6.62683	−	2.68841i	−0.236071	−	0.0957706i
$789$		0			0
$790$	42.6204	−	14.6414i	1.51637	−	0.520918i
$791$	23.0699	+	2.00862i	0.820271	+	0.0714183i
$792$		0			0
$793$	2.89048	−	5.00646i	0.102644	−	0.177785i
$794$	1.37351	−	1.57777i	0.0487441	−	0.0559930i
$795$		0			0
$796$	4.00758	+	28.8134i	0.142045	+	1.02126i
$797$	−23.1795	+	13.3827i	−0.821059	+	0.474039i	−0.850782	−	0.525519i	$-0.823871\pi$
$797$	−23.1795	+	13.3827i	−0.821059	+	0.474039i	0.0297223	+	0.999558i	$0.490538\pi$
$798$		0			0
$799$	−13.1784	−	7.60854i	−0.466218	−	0.269171i
$800$	10.4498	−	7.26163i	0.369455	−	0.256737i
$801$		0			0
$802$	−6.71686	+	34.4242i	−0.237181	+	1.21556i
$803$	5.84444	+	10.1229i	0.206246	+	0.357228i
$804$		0			0
$805$	−7.90331	+	11.2972i	−0.278555	+	0.398173i
$806$	38.9765	+	7.60511i	1.37289	+	0.267878i
$807$		0			0
$808$	39.7139	+	25.9115i	1.39713	+	0.911562i
$809$	−13.9813	−	24.2164i	−0.491557	−	0.851402i	0.508395	−	0.861124i	$-0.330239\pi$
$809$	−13.9813	−	24.2164i	−0.491557	−	0.851402i	−0.999953	+	0.00972146i	$0.996906\pi$
$810$		0			0
$811$	44.1723			1.55110			0.775550	−	0.631286i	$-0.217473\pi$
$811$	44.1723			1.55110			0.775550	+	0.631286i	$0.217473\pi$
$812$	0.230205	+	4.47887i	0.00807862	+	0.157177i
$813$		0			0
$814$	14.4164	−	16.5604i	0.505296	−	0.580440i
$815$	−21.5022	+	37.2429i	−0.753188	+	1.30456i
$816$		0			0
$817$	17.6839	−	10.2098i	0.618682	−	0.357196i
$818$	−8.69362	+	9.98648i	−0.303965	+	0.349169i
$819$		0			0
$820$	−5.13637	−	36.9291i	−0.179370	−	1.28962i
$821$	−5.29454	−	9.17041i	−0.184781	−	0.320050i	0.758722	−	0.651415i	$-0.225824\pi$
$821$	−5.29454	−	9.17041i	−0.184781	−	0.320050i	−0.943503	+	0.331365i	$0.892491\pi$
$822$		0			0
$823$	1.35573	+	0.782731i	0.0472577	+	0.0272843i	0.523443	−	0.852061i	$-0.324647\pi$
$823$	1.35573	+	0.782731i	0.0472577	+	0.0272843i	−0.476185	+	0.879345i	$0.657981\pi$
$824$	4.07450	−	6.24490i	0.141942	−	0.217551i
$825$		0			0
$826$	5.16267	−	1.28558i	0.179632	−	0.0447312i
$827$			1.44507i			0.0502499i	0.999684	+	0.0251249i	$0.00799836\pi$
$827$			1.44507i			0.0502499i	−0.999684	+	0.0251249i	$0.992002\pi$
$828$		0			0
$829$	−33.2429	+	19.1928i	−1.15457	+	0.666594i	−0.949998	−	0.312257i	$-0.898915\pi$
$829$	−33.2429	+	19.1928i	−1.15457	+	0.666594i	−0.204577	+	0.978851i	$0.565582\pi$
$830$	14.2701	−	16.3923i	0.495322	−	0.568983i
$831$		0			0
$832$	18.3493	+	13.4518i	0.636148	+	0.466359i
$833$	−7.64226	−	6.40172i	−0.264789	−	0.221807i
$834$		0			0
$835$	−32.6188	+	18.8325i	−1.12882	+	0.651725i
$836$	5.14715	+	6.60745i	0.178018	+	0.228523i
$837$		0			0
$838$	−13.9428	+	4.78979i	−0.481647	+	0.165460i
$839$	8.96149	−	15.5217i	0.309385	−	0.535870i	−0.668843	−	0.743404i	$-0.733210\pi$
$839$	8.96149	−	15.5217i	0.309385	−	0.535870i	0.978228	+	0.207533i	$0.0665435\pi$
$840$		0			0
$841$	14.1408	+	24.4926i	0.487615	+	0.844574i
$842$	−7.36449	−	6.41108i	−0.253797	−	0.220940i
$843$		0			0
$844$	−26.0608	+	3.62473i	−0.897051	+	0.124768i
$845$	11.4530	+	6.61239i	0.393995	+	0.227473i
$846$		0			0
$847$	−13.6534	+	19.5165i	−0.469137	+	0.670595i
$848$	−12.8924	+	51.0877i	−0.442728	+	1.75436i
$849$		0			0
$850$	−1.47200	−	4.28493i	−0.0504893	−	0.146972i
$851$	−18.4120	−	10.6302i	−0.631156	−	0.364398i
$852$		0			0
$853$	−13.3860	−	7.72843i	−0.458329	−	0.264616i	0.253013	−	0.967463i	$-0.418579\pi$
$853$	−13.3860	−	7.72843i	−0.458329	−	0.264616i	−0.711341	+	0.702847i	$0.751912\pi$
$854$	7.31040	+	2.09855i	0.250157	+	0.0718110i
$855$		0			0
$856$	2.04521	−	1.03658i	0.0699039	−	0.0354297i
$857$			22.7616i			0.777520i	0.921339	+	0.388760i	$0.127097\pi$
$857$			22.7616i			0.777520i	−0.921339	+	0.388760i	$0.872903\pi$
$858$		0			0
$859$	−0.888166			−0.0303038			−0.0151519	−	0.999885i	$-0.504823\pi$
$859$	−0.888166			−0.0303038			−0.0151519	+	0.999885i	$0.504823\pi$
$860$	29.2757	−	22.8055i	0.998292	−	0.777661i
$861$		0			0
$862$	−6.59726	−	19.2043i	−0.224703	−	0.654101i
$863$	39.6368	+	22.8843i	1.34925	+	0.778992i	0.988144	−	0.153531i	$-0.0490646\pi$
$863$	39.6368	+	22.8843i	1.34925	+	0.778992i	0.361110	+	0.932523i	$0.382398\pi$
$864$		0			0
$865$	−33.5980	−	58.1934i	−1.14237	−	1.97864i
$866$	35.8750	+	6.99993i	1.21908	+	0.237867i
$867$		0			0
$868$	2.68180	+	52.1771i	0.0910264	+	1.77101i
$869$	8.36353	+	14.4861i	0.283713	+	0.491406i
$870$		0			0
$871$	−24.8666			−0.842572
$872$	29.3712	+	1.60227i	0.994634	+	0.0542597i
$873$		0			0
$874$	5.32511	−	6.11703i	0.180125	−	0.206912i
$875$	16.0548	+	11.2317i	0.542753	+	0.379701i
$876$		0			0
$877$	−31.4867			−1.06323			−0.531616	−	0.846986i	$-0.678415\pi$
$877$	−31.4867			−1.06323			−0.531616	+	0.846986i	$0.678415\pi$
$878$	−19.5099	+	6.70224i	−0.658426	+	0.226190i
$879$		0			0
$880$	10.9194	+	10.6050i	0.368091	+	0.357496i
$881$		−	12.0700i		−	0.406649i	−0.979111	−	0.203324i	$-0.934825\pi$
$881$		−	12.0700i		−	0.406649i	0.979111	−	0.203324i	$-0.0651746\pi$
$882$		0			0
$883$		−	26.0164i		−	0.875522i	−0.899091	−	0.437761i	$-0.855772\pi$
$883$		−	26.0164i		−	0.875522i	0.899091	−	0.437761i	$-0.144228\pi$
$884$	6.39055	−	4.97819i	0.214937	−	0.167435i
$885$		0			0
$886$	−16.2569	−	47.3231i	−0.546162	−	1.58985i
$887$	−25.4380			−0.854125			−0.427063	−	0.904222i	$-0.640452\pi$
$887$	−25.4380			−0.854125			−0.427063	+	0.904222i	$0.640452\pi$
$888$		0			0
$889$	−33.0700	−	23.1353i	−1.10913	−	0.775932i
$890$	−19.0949	−	16.6228i	−0.640061	−	0.557198i
$891$		0			0
$892$	−24.8672	+	19.3714i	−0.832616	+	0.648602i
$893$	31.6597			1.05945
$894$		0			0
$895$	−0.961467	−	1.66531i	−0.0321383	−	0.0556652i
$896$	−11.3399	+	27.7021i	−0.378841	+	0.925462i
$897$		0			0
$898$	−0.0893049	+	0.457692i	−0.00298014	+	0.0152734i
$899$	−4.18414	−	7.24714i	−0.139549	−	0.241706i
$900$		0			0
$901$	16.2465	+	9.37990i	0.541248	+	0.312490i
$902$	13.0883	−	4.49625i	0.435794	−	0.149709i
$903$		0			0
$904$	−24.7193	−	1.34850i	−0.822152	−	0.0448504i
$905$	36.3848			1.20947
$906$		0			0
$907$			29.3255i			0.973737i	0.873475	+	0.486868i	$0.161861\pi$
$907$			29.3255i			0.973737i	−0.873475	+	0.486868i	$0.838139\pi$
$908$	−3.51353	−	1.42539i	−0.116601	−	0.0473031i
$909$		0			0
$910$	7.90550	−	27.5392i	0.262065	−	0.912915i
$911$	12.1668	+	7.02448i	0.403103	+	0.232731i	0.687822	−	0.725880i	$-0.258567\pi$
$911$	12.1668	+	7.02448i	0.403103	+	0.232731i	−0.284719	+	0.958611i	$0.591900\pi$
$912$		0			0
$913$	6.98614	+	4.03345i	0.231208	+	0.133488i
$914$	34.6200	−	11.8930i	1.14513	−	0.393386i
$915$		0			0
$916$	6.41856	−	15.8215i	0.212075	−	0.522758i
$917$	−0.103009	+	0.147243i	−0.00340165	+	0.00486239i
$918$		0			0
$919$	43.1553	+	24.9157i	1.42356	+	0.821894i	0.996601	−	0.0823755i	$-0.0262507\pi$
$919$	43.1553	+	24.9157i	1.42356	+	0.821894i	0.426961	+	0.904270i	$0.359584\pi$
$920$	8.05396	−	12.3441i	0.265531	−	0.406974i
$921$		0			0
$922$	26.1123	−	29.9955i	0.859962	−	0.987850i
$923$	2.77705	+	4.80999i	0.0914078	+	0.158323i
$924$		0			0
$925$	12.3553	−	21.4000i	0.406240	−	0.703628i
$926$	−9.01997	−	26.2567i	−0.296415	−	0.862848i
$927$		0			0
$928$	−0.400836	−	4.77764i	−0.0131581	−	0.156834i
$929$	−23.9255	+	13.8134i	−0.784971	+	0.453203i	−0.838189	−	0.545380i	$-0.816385\pi$
$929$	−23.9255	+	13.8134i	−0.784971	+	0.453203i	0.0532181	+	0.998583i	$0.483052\pi$
$930$		0			0
$931$	20.4293	+	3.58460i	0.669544	+	0.117481i
$932$	−25.8133	+	20.1084i	−0.845543	+	0.658671i
$933$		0			0
$934$	−23.2748	−	20.2616i	−0.761575	−	0.662981i
$935$	4.69351	−	2.70980i	0.153494	−	0.0886199i
$936$		0			0
$937$		−	5.47306i		−	0.178797i	−0.995996	−	0.0893986i	$-0.971505\pi$
$937$		−	5.47306i		−	0.178797i	0.995996	−	0.0893986i	$-0.0284945\pi$
$938$	−7.90523	−	31.7459i	−0.258115	−	1.03654i
$939$		0			0
$940$	56.9888	−	7.92642i	1.85877	−	0.258531i
$941$	−12.5229	−	7.23008i	−0.408234	−	0.235694i	0.281797	−	0.959474i	$-0.409070\pi$
$941$	−12.5229	−	7.23008i	−0.408234	−	0.235694i	−0.690031	+	0.723780i	$0.742403\pi$
$942$		0			0
$943$	−6.70023	−	11.6051i	−0.218190	−	0.377915i
$944$	−5.47178	+	1.55214i	−0.178091	+	0.0505178i
$945$		0			0
$946$	10.3892	+	9.04418i	0.337781	+	0.294052i
$947$	−36.7178	+	21.1991i	−1.19317	+	0.688877i	−0.959024	−	0.283325i	$-0.908563\pi$
$947$	−36.7178	+	21.1991i	−1.19317	+	0.688877i	−0.234145	+	0.972202i	$0.575229\pi$
$948$		0			0
$949$	−11.7604	+	20.3696i	−0.381759	+	0.661226i
$950$	7.10973	+	6.18929i	0.230670	+	0.200807i
$951$		0			0
$952$	8.38700	+	6.57590i	0.271824	+	0.213126i
$953$	11.7969			0.382138			0.191069	−	0.981577i	$-0.438804\pi$
$953$	11.7969			0.382138			0.191069	+	0.981577i	$0.438804\pi$
$954$		0			0
$955$	20.5464	+	35.5875i	0.664867	+	1.15158i
$956$	−13.6176	+	1.89403i	−0.440423	+	0.0612572i
$957$		0			0
$958$	−7.96418	+	40.8168i	−0.257311	+	1.31873i
$959$	7.87082	−	11.2507i	0.254162	−	0.363305i
$960$		0			0
$961$	−33.2436	−	57.5797i	−1.07238	−	1.85741i
$962$	43.3636	+	8.46111i	1.39810	+	0.272797i
$963$		0			0
$964$	−7.50020	+	18.4877i	−0.241565	+	0.595449i
$965$	20.8238	+	12.0226i	0.670341	+	0.387022i
$966$		0			0
$967$	−9.83637	+	5.67903i	−0.316316	+	0.182625i	−0.649749	−	0.760148i	$-0.725126\pi$
$967$	−9.83637	+	5.67903i	−0.316316	+	0.182625i	0.333433	+	0.942774i	$0.391793\pi$
$968$	13.9137	−	21.3252i	0.447202	−	0.685418i
$969$		0			0
$970$	−43.4974	−	37.8662i	−1.39662	−	1.21581i
$971$	9.77591	−	16.9324i	0.313724	−	0.543386i	−0.665442	−	0.746450i	$-0.731757\pi$
$971$	9.77591	−	16.9324i	0.313724	−	0.543386i	0.979165	+	0.203064i	$0.0650901\pi$
$972$		0			0
$973$	−27.8028	−	2.42070i	−0.891316	−	0.0776040i
$974$	−2.03727	−	5.93038i	−0.0652782	−	0.190022i
$975$		0			0
$976$	−7.88362	−	1.98950i	−0.252349	−	0.0636824i
$977$	−2.13163	+	3.69208i	−0.0681967	+	0.118120i	−0.898108	−	0.439776i	$-0.855058\pi$
$977$	−2.13163	+	3.69208i	−0.0681967	+	0.118120i	0.829911	+	0.557896i	$0.188391\pi$
$978$		0			0
$979$	4.69845	−	8.13796i	0.150163	−	0.260090i
$980$	37.6711	+	1.33769i	1.20336	+	0.0427310i
$981$		0			0
$982$	0.261043	+	0.759884i	0.00833022	+	0.0242489i
$983$	−35.6565			−1.13727			−0.568633	−	0.822591i	$-0.692528\pi$
$983$	−35.6565			−1.13727			−0.568633	+	0.822591i	$0.692528\pi$
$984$		0			0
$985$		−	9.62753i		−	0.306758i
$986$	−1.67544	−	0.326912i	−0.0533568	−	0.0104110i
$987$		0			0
$988$	−6.33582	+	15.6176i	−0.201569	+	0.496861i
$989$	6.66886	−	11.5508i	0.212058	−	0.367294i
$990$		0			0
$991$	−21.9593	+	12.6782i	−0.697561	+	0.402737i	−0.806438	−	0.591318i	$-0.798608\pi$
$991$	−21.9593	+	12.6782i	−0.697561	+	0.402737i	0.108877	+	0.994055i	$0.465274\pi$
$992$	−4.66959	−	55.6578i	−0.148260	−	1.76714i
$993$		0			0
$994$	−5.25784	+	5.07445i	−0.166769	+	0.160952i
$995$	−33.9164	+	19.5817i	−1.07522	+	0.620780i
$996$		0			0
$997$			27.0390i			0.856333i	0.903700	+	0.428166i	$0.140840\pi$
$997$			27.0390i			0.856333i	−0.903700	+	0.428166i	$0.859160\pi$
$998$	−11.3953	−	2.22345i	−0.360711	−	0.0703821i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.n.b.19.19		84
3.2	odd	2		252.2.n.b.187.24	yes	84
4.3	odd	2	inner	756.2.n.b.19.38		84
7.3	odd	6		756.2.bj.b.451.9		84
9.4	even	3		756.2.bj.b.523.9		84
9.5	odd	6		252.2.bj.b.103.34	yes	84
12.11	even	2		252.2.n.b.187.5	yes	84
21.17	even	6		252.2.bj.b.115.34	yes	84
28.3	even	6		756.2.bj.b.451.10		84
36.23	even	6		252.2.bj.b.103.33	yes	84
36.31	odd	6		756.2.bj.b.523.10		84
63.31	odd	6	inner	756.2.n.b.199.38		84
63.59	even	6		252.2.n.b.31.5	✓	84
84.59	odd	6		252.2.bj.b.115.33	yes	84
252.31	even	6	inner	756.2.n.b.199.19		84
252.59	odd	6		252.2.n.b.31.24	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.n.b.31.5	✓	84	63.59	even	6
252.2.n.b.31.24	yes	84	252.59	odd	6
252.2.n.b.187.5	yes	84	12.11	even	2
252.2.n.b.187.24	yes	84	3.2	odd	2
252.2.bj.b.103.33	yes	84	36.23	even	6
252.2.bj.b.103.34	yes	84	9.5	odd	6
252.2.bj.b.115.33	yes	84	84.59	odd	6
252.2.bj.b.115.34	yes	84	21.17	even	6
756.2.n.b.19.19		84	1.1	even	1	trivial
756.2.n.b.19.38		84	4.3	odd	2	inner
756.2.n.b.199.19		84	252.31	even	6	inner
756.2.n.b.199.38		84	63.31	odd	6	inner
756.2.bj.b.451.9		84	7.3	odd	6
756.2.bj.b.451.10		84	28.3	even	6
756.2.bj.b.523.9		84	9.4	even	3
756.2.bj.b.523.10		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)

\(f(q)\)	\(=\)	\(q+(-0.270834 + 1.38804i) q^{2} +(-1.85330 - 0.751856i) q^{4} -2.69249i q^{5} +(-1.51663 + 2.16791i) q^{7} +(1.54554 - 2.36882i) q^{8} +O(q^{10})\)	\(q+(-0.270834 + 1.38804i) q^{2} +(-1.85330 - 0.751856i) q^{4} -2.69249i q^{5} +(-1.51663 + 2.16791i) q^{7} +(1.54554 - 2.36882i) q^{8} +(3.73728 + 0.729218i) q^{10} +1.41334i q^{11} +(-2.46297 + 1.42199i) q^{13} +(-2.59838 - 2.69229i) q^{14} +(2.86942 + 2.78683i) q^{16} +(1.23338 - 0.712090i) q^{17} +(-1.48153 + 2.56609i) q^{19} +(-2.02437 + 4.98999i) q^{20} +(-1.96178 - 0.382782i) q^{22} +1.93542i q^{23} -2.24950 q^{25} +(-1.30673 - 3.80381i) q^{26} +(4.44073 - 2.87749i) q^{28} +(-0.423772 + 0.733994i) q^{29} +(-4.93678 + 8.55076i) q^{31} +(-4.64536 + 3.22810i) q^{32} +(0.654368 + 1.90483i) q^{34} +(5.83707 + 4.08352i) q^{35} +(-5.49245 + 9.51321i) q^{37} +(-3.16057 - 2.75140i) q^{38} +(-6.37802 - 4.16135i) q^{40} +(-5.99620 + 3.46191i) q^{41} +(-5.96812 - 3.44570i) q^{43} +(1.06263 - 2.61935i) q^{44} +(-2.68643 - 0.524177i) q^{46} +(-5.34240 - 9.25331i) q^{47} +(-2.39965 - 6.57584i) q^{49} +(0.609243 - 3.12240i) q^{50} +(5.63374 - 0.783582i) q^{52} +(6.58617 + 11.4076i) q^{53} +3.80542 q^{55} +(2.79136 + 6.94322i) q^{56} +(-0.904040 - 0.787002i) q^{58} +(-0.710958 + 1.23142i) q^{59} +(-1.76037 + 1.01635i) q^{61} +(-10.5317 - 9.16828i) q^{62} +(-3.22261 - 7.32221i) q^{64} +(3.82871 + 6.63151i) q^{65} +(7.57214 + 4.37178i) q^{67} +(-2.82120 + 0.392394i) q^{68} +(-7.24896 + 6.99612i) q^{70} -1.95293i q^{71} +(7.16234 - 4.13518i) q^{73} +(-11.7171 - 10.2002i) q^{74} +(4.67504 - 3.64182i) q^{76} +(-3.06400 - 2.14352i) q^{77} +(10.2495 - 5.91755i) q^{79} +(7.50350 - 7.72590i) q^{80} +(-3.18128 - 9.26055i) q^{82} +(2.85384 - 4.94299i) q^{83} +(-1.91730 - 3.32085i) q^{85} +(6.39913 - 7.35077i) q^{86} +(3.34796 + 2.18438i) q^{88} +(-5.75795 - 3.32435i) q^{89} +(0.652664 - 7.49613i) q^{91} +(1.45516 - 3.58690i) q^{92} +(14.2908 - 4.90934i) q^{94} +(6.90916 + 3.98901i) q^{95} +(-13.1164 - 7.57275i) q^{97} +(9.77742 - 1.54984i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q + q^{2} + q^{4} + 16 q^{8}+O(q^{10}) \) 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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