LMFDB - Embedded newform 833.2.g.h.344.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [833,2,Mod(344,833)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(833, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("833.344");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 833 = 7^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	833.g (of order $4$, degree $2$, 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:	$6.65153848837$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 32 x^{18} + 432 x^{16} + 3200 x^{14} + 14160 x^{12} + 38162 x^{10} + 61088 x^{8} + 53872 x^{6} + \cdots + 49 $ x^20 + 32x^18 + 432x^16 + 3200x^14 + 14160x^12 + 38162x^10 + 61088x^8 + 53872x^6 + 22464x^4 + 3504*x^2 + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	no (minimal twist has level 119)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			344.7
Root			$0.710316i$ of defining polynomial
Character	$\chi$	$=$	833.344
Dual form			833.2.g.h.540.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.710316i q^{2} +(-2.11910 + 2.11910i) q^{3} +1.49545 q^{4} +(2.66663 - 2.66663i) q^{5} +(-1.50523 - 1.50523i) q^{6} +2.48287i q^{8} -5.98113i q^{9} +O(q^{10})$	\(q+0.710316i q^{2} +(-2.11910 + 2.11910i) q^{3} +1.49545 q^{4} +(2.66663 - 2.66663i) q^{5} +(-1.50523 - 1.50523i) q^{6} +2.48287i q^{8} -5.98113i q^{9} +(1.89415 + 1.89415i) q^{10} +(-1.85556 - 1.85556i) q^{11} +(-3.16900 + 3.16900i) q^{12} +0.409675 q^{13} +11.3017i q^{15} +1.22728 q^{16} +(4.07663 - 0.617307i) q^{17} +4.24849 q^{18} -1.76835i q^{19} +(3.98781 - 3.98781i) q^{20} +(1.31804 - 1.31804i) q^{22} +(2.19761 + 2.19761i) q^{23} +(-5.26145 - 5.26145i) q^{24} -9.22180i q^{25} +0.290999i q^{26} +(6.31730 + 6.31730i) q^{27} +(3.96073 - 3.96073i) q^{29} -8.02776 q^{30} +(4.51562 - 4.51562i) q^{31} +5.83750i q^{32} +7.86423 q^{33} +(0.438483 + 2.89570i) q^{34} -8.94449i q^{36} +(2.68522 - 2.68522i) q^{37} +1.25609 q^{38} +(-0.868141 + 0.868141i) q^{39} +(6.62090 + 6.62090i) q^{40} +(5.30764 + 5.30764i) q^{41} +5.57516i q^{43} +(-2.77491 - 2.77491i) q^{44} +(-15.9494 - 15.9494i) q^{45} +(-1.56100 + 1.56100i) q^{46} -11.8629 q^{47} +(-2.60072 + 2.60072i) q^{48} +6.55039 q^{50} +(-7.33064 + 9.94690i) q^{51} +0.612649 q^{52} +4.05188i q^{53} +(-4.48728 + 4.48728i) q^{54} -9.89619 q^{55} +(3.74730 + 3.74730i) q^{57} +(2.81337 + 2.81337i) q^{58} +9.32696i q^{59} +16.9011i q^{60} +(0.426653 + 0.426653i) q^{61} +(3.20752 + 3.20752i) q^{62} -1.69192 q^{64} +(1.09245 - 1.09245i) q^{65} +5.58609i q^{66} +7.70207 q^{67} +(6.09641 - 0.923152i) q^{68} -9.31391 q^{69} +(-2.60890 + 2.60890i) q^{71} +14.8504 q^{72} +(-0.547298 + 0.547298i) q^{73} +(1.90735 + 1.90735i) q^{74} +(19.5419 + 19.5419i) q^{75} -2.64448i q^{76} +(-0.616654 - 0.616654i) q^{78} +(-11.1002 - 11.1002i) q^{79} +(3.27269 - 3.27269i) q^{80} -8.83053 q^{81} +(-3.77010 + 3.77010i) q^{82} -2.28876i q^{83} +(9.22473 - 12.5170i) q^{85} -3.96013 q^{86} +16.7863i q^{87} +(4.60713 - 4.60713i) q^{88} -12.7366 q^{89} +(11.3291 - 11.3291i) q^{90} +(3.28643 + 3.28643i) q^{92} +19.1381i q^{93} -8.42638i q^{94} +(-4.71553 - 4.71553i) q^{95} +(-12.3702 - 12.3702i) q^{96} +(-0.408884 + 0.408884i) q^{97} +(-11.0984 + 11.0984i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) $ 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6	$ 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{10} - 4 q^{11} - 12 q^{12} + 16 q^{16} + 12 q^{17} - 8 q^{18} - 20 q^{20} - 20 q^{22} - 4 q^{24} - 8 q^{27} + 16 q^{29} - 36 q^{30} - 4 q^{31} + 16 q^{33} - 36 q^{34} - 28 q^{37} - 48 q^{38} + 20 q^{39} + 24 q^{40} + 24 q^{41} - 28 q^{44} - 36 q^{45} + 8 q^{46} - 40 q^{47} + 8 q^{48} - 28 q^{50} - 40 q^{51} + 28 q^{54} + 40 q^{55} + 36 q^{57} + 56 q^{58} + 16 q^{61} + 40 q^{62} + 32 q^{64} + 8 q^{65} + 32 q^{68} + 88 q^{69} - 8 q^{71} + 108 q^{72} - 8 q^{73} + 36 q^{74} - 8 q^{75} - 44 q^{78} - 4 q^{79} + 116 q^{80} + 4 q^{81} + 16 q^{82} + 16 q^{85} + 44 q^{86} + 72 q^{88} - 48 q^{89} - 56 q^{90} - 32 q^{92} + 44 q^{95} - 68 q^{96} - 24 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^10 - 4 * q^11 - 12 * q^12 + 16 * q^16 + 12 * q^17 - 8 * q^18 - 20 * q^20 - 20 * q^22 - 4 * q^24 - 8 * q^27 + 16 * q^29 - 36 * q^30 - 4 * q^31 + 16 * q^33 - 36 * q^34 - 28 * q^37 - 48 * q^38 + 20 * q^39 + 24 * q^40 + 24 * q^41 - 28 * q^44 - 36 * q^45 + 8 * q^46 - 40 * q^47 + 8 * q^48 - 28 * q^50 - 40 * q^51 + 28 * q^54 + 40 * q^55 + 36 * q^57 + 56 * q^58 + 16 * q^61 + 40 * q^62 + 32 * q^64 + 8 * q^65 + 32 * q^68 + 88 * q^69 - 8 * q^71 + 108 * q^72 - 8 * q^73 + 36 * q^74 - 8 * q^75 - 44 * q^78 - 4 * q^79 + 116 * q^80 + 4 * q^81 + 16 * q^82 + 16 * q^85 + 44 * q^86 + 72 * q^88 - 48 * q^89 - 56 * q^90 - 32 * q^92 + 44 * q^95 - 68 * q^96 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/833\mathbb{Z}\right)^\times$.

$n$	$52$	$785$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			0.710316i			0.502269i	0.967952	+	0.251135i	$0.0808037\pi$
$2$			0.710316i			0.502269i	−0.967952	+	0.251135i	$0.919196\pi$
$3$	−2.11910	+	2.11910i	−1.22346	+	1.22346i	−0.257067	+	0.966394i	$0.582756\pi$
$3$	−2.11910	+	2.11910i	−1.22346	+	1.22346i	−0.966394	+	0.257067i	$0.917244\pi$
$4$	1.49545			0.747726
$5$	2.66663	−	2.66663i	1.19255	−	1.19255i	0.216203	−	0.976348i	$-0.430633\pi$
$5$	2.66663	−	2.66663i	1.19255	−	1.19255i	0.976348	−	0.216203i	$-0.0693674\pi$
$6$	−1.50523	−	1.50523i	−0.614506	−	0.614506i
$7$		0			0
$7$		0			0
$8$			2.48287i			0.877829i
$9$		−	5.98113i		−	1.99371i
$10$	1.89415	+	1.89415i	0.598982	+	0.598982i
$11$	−1.85556	−	1.85556i	−0.559474	−	0.559474i	0.369684	−	0.929158i	$-0.379466\pi$
$11$	−1.85556	−	1.85556i	−0.559474	−	0.559474i	−0.929158	+	0.369684i	$0.879466\pi$
$12$	−3.16900	+	3.16900i	−0.914813	+	0.914813i
$13$	0.409675			0.113623			0.0568117	−	0.998385i	$-0.481907\pi$
$13$	0.409675			0.113623			0.0568117	+	0.998385i	$0.481907\pi$
$14$		0			0
$15$			11.3017i			2.91808i
$16$	1.22728			0.306819
$17$	4.07663	−	0.617307i	0.988729	−	0.149719i
$17$	4.07663	−	0.617307i	0.988729	−	0.149719i
$18$	4.24849			1.00138
$19$		−	1.76835i		−	0.405687i	−0.979211	−	0.202844i	$-0.934982\pi$
$19$		−	1.76835i		−	0.405687i	0.979211	−	0.202844i	$-0.0650183\pi$
$20$	3.98781	−	3.98781i	0.891702	−	0.891702i
$21$		0			0
$22$	1.31804	−	1.31804i	0.281006	−	0.281006i
$23$	2.19761	+	2.19761i	0.458234	+	0.458234i	0.898076	−	0.439841i	$-0.144965\pi$
$23$	2.19761	+	2.19761i	0.458234	+	0.458234i	−0.439841	+	0.898076i	$0.644965\pi$
$24$	−5.26145	−	5.26145i	−1.07399	−	1.07399i
$25$		−	9.22180i		−	1.84436i
$26$			0.290999i			0.0570696i
$27$	6.31730	+	6.31730i	1.21576	+	1.21576i
$28$		0			0
$29$	3.96073	−	3.96073i	0.735489	−	0.735489i	−0.236213	−	0.971701i	$-0.575906\pi$
$29$	3.96073	−	3.96073i	0.735489	−	0.735489i	0.971701	+	0.236213i	$0.0759062\pi$
$30$	−8.02776			−1.46566
$31$	4.51562	−	4.51562i	0.811029	−	0.811029i	−0.173759	−	0.984788i	$-0.555591\pi$
$31$	4.51562	−	4.51562i	0.811029	−	0.811029i	0.984788	+	0.173759i	$0.0555914\pi$
$32$			5.83750i			1.03193i
$33$	7.86423			1.36899
$34$	0.438483	+	2.89570i	0.0751992	+	0.496608i
$35$		0			0
$36$		−	8.94449i		−	1.49075i
$37$	2.68522	−	2.68522i	0.441447	−	0.441447i	−0.451051	−	0.892498i	$-0.648951\pi$
$37$	2.68522	−	2.68522i	0.441447	−	0.441447i	0.892498	+	0.451051i	$0.148951\pi$
$38$	1.25609			0.203764
$39$	−0.868141	+	0.868141i	−0.139014	+	0.139014i
$40$	6.62090	+	6.62090i	1.04686	+	1.04686i
$41$	5.30764	+	5.30764i	0.828913	+	0.828913i	0.987366	−	0.158453i	$-0.0506507\pi$
$41$	5.30764	+	5.30764i	0.828913	+	0.828913i	−0.158453	+	0.987366i	$0.550651\pi$
$42$		0			0
$43$			5.57516i			0.850204i	0.905145	+	0.425102i	$0.139762\pi$
$43$			5.57516i			0.850204i	−0.905145	+	0.425102i	$0.860238\pi$
$44$	−2.77491	−	2.77491i	−0.418333	−	0.418333i
$45$	−15.9494	−	15.9494i	−2.37760	−	2.37760i
$46$	−1.56100	+	1.56100i	−0.230157	+	0.230157i
$47$	−11.8629			−1.73038			−0.865189	−	0.501447i	$-0.832801\pi$
$47$	−11.8629			−1.73038			−0.865189	+	0.501447i	$0.832801\pi$
$48$	−2.60072	+	2.60072i	−0.375381	+	0.375381i
$49$		0			0
$50$	6.55039			0.926365
$51$	−7.33064	+	9.94690i	−1.02650	+	1.39285i
$52$	0.612649			0.0849592
$53$			4.05188i			0.556569i	0.960499	+	0.278285i	$0.0897658\pi$
$53$			4.05188i			0.556569i	−0.960499	+	0.278285i	$0.910234\pi$
$54$	−4.48728	+	4.48728i	−0.610641	+	0.610641i
$55$	−9.89619			−1.33440
$56$		0			0
$57$	3.74730	+	3.74730i	0.496342	+	0.496342i
$58$	2.81337	+	2.81337i	0.369413	+	0.369413i
$59$			9.32696i			1.21427i	0.794600	+	0.607133i	$0.207681\pi$
$59$			9.32696i			1.21427i	−0.794600	+	0.607133i	$0.792319\pi$
$60$			16.9011i			2.18192i
$61$	0.426653	+	0.426653i	0.0546274	+	0.0546274i	0.733893	−	0.679265i	$-0.237701\pi$
$61$	0.426653	+	0.426653i	0.0546274	+	0.0546274i	−0.679265	+	0.733893i	$0.737701\pi$
$62$	3.20752	+	3.20752i	0.407355	+	0.407355i
$63$		0			0
$64$	−1.69192			−0.211490
$65$	1.09245	−	1.09245i	0.135502	−	0.135502i
$66$			5.58609i			0.687600i
$67$	7.70207			0.940957			0.470479	−	0.882411i	$-0.344081\pi$
$67$	7.70207			0.940957			0.470479	+	0.882411i	$0.344081\pi$
$68$	6.09641	−	0.923152i	0.739298	−	0.111949i
$69$	−9.31391			−1.12126
$70$		0			0
$71$	−2.60890	+	2.60890i	−0.309620	+	0.309620i	−0.844762	−	0.535142i	$-0.820258\pi$
$71$	−2.60890	+	2.60890i	−0.309620	+	0.309620i	0.535142	+	0.844762i	$0.320258\pi$
$72$	14.8504			1.75014
$73$	−0.547298	+	0.547298i	−0.0640564	+	0.0640564i	−0.738409	−	0.674353i	$-0.764423\pi$
$73$	−0.547298	+	0.547298i	−0.0640564	+	0.0640564i	0.674353	+	0.738409i	$0.264423\pi$
$74$	1.90735	+	1.90735i	0.221725	+	0.221725i
$75$	19.5419	+	19.5419i	2.25650	+	2.25650i
$76$		−	2.64448i		−	0.303343i
$77$		0			0
$78$	−0.616654	−	0.616654i	−0.0698223	−	0.0698223i
$79$	−11.1002	−	11.1002i	−1.24887	−	1.24887i	−0.956221	−	0.292646i	$-0.905464\pi$
$79$	−11.1002	−	11.1002i	−1.24887	−	1.24887i	−0.292646	−	0.956221i	$-0.594536\pi$
$80$	3.27269	−	3.27269i	0.365898	−	0.365898i
$81$	−8.83053			−0.981170
$82$	−3.77010	+	3.77010i	−0.416338	+	0.416338i
$83$		−	2.28876i		−	0.251224i	−0.992079	−	0.125612i	$-0.959911\pi$
$83$		−	2.28876i		−	0.251224i	0.992079	−	0.125612i	$-0.0400895\pi$
$84$		0			0
$85$	9.22473	−	12.5170i	1.00056	−	1.35766i
$86$	−3.96013			−0.427032
$87$			16.7863i			1.79968i
$88$	4.60713	−	4.60713i	0.491122	−	0.491122i
$89$	−12.7366			−1.35007			−0.675037	−	0.737784i	$-0.735872\pi$
$89$	−12.7366			−1.35007			−0.675037	+	0.737784i	$0.735872\pi$
$90$	11.3291	−	11.3291i	1.19420	−	1.19420i
$91$		0			0
$92$	3.28643	+	3.28643i	0.342634	+	0.342634i
$93$			19.1381i			1.98452i
$94$		−	8.42638i		−	0.869115i
$95$	−4.71553	−	4.71553i	−0.483803	−	0.483803i
$96$	−12.3702	−	12.3702i	−1.26253	−	1.26253i
$97$	−0.408884	+	0.408884i	−0.0415159	+	0.0415159i	−0.727560	−	0.686044i	$-0.759346\pi$
$97$	−0.408884	+	0.408884i	−0.0415159	+	0.0415159i	0.686044	+	0.727560i	$0.259346\pi$
$98$		0			0
$99$	−11.0984	+	11.0984i	−1.11543	+	1.11543i
$100$		−	13.7907i		−	1.37907i
$101$	−1.35729			−0.135055			−0.0675275	−	0.997717i	$-0.521511\pi$
$101$	−1.35729			−0.135055			−0.0675275	+	0.997717i	$0.521511\pi$
$102$	−7.06544	−	5.20707i	−0.699583	−	0.515577i
$103$	5.99049			0.590261			0.295130	−	0.955457i	$-0.404637\pi$
$103$	5.99049			0.590261			0.295130	+	0.955457i	$0.404637\pi$
$104$			1.01717i			0.0997419i
$105$		0			0
$106$	−2.87812			−0.279547
$107$	2.33866	−	2.33866i	0.226087	−	0.226087i	−0.584969	−	0.811056i	$-0.698893\pi$
$107$	2.33866	−	2.33866i	0.226087	−	0.226087i	0.811056	+	0.584969i	$0.198893\pi$
$108$	9.44721	+	9.44721i	0.909058	+	0.909058i
$109$	8.04311	+	8.04311i	0.770391	+	0.770391i	0.978175	−	0.207784i	$-0.0666251\pi$
$109$	8.04311	+	8.04311i	0.770391	+	0.770391i	−0.207784	+	0.978175i	$0.566625\pi$
$110$		−	7.02942i		−	0.670229i
$111$			11.3805i			1.08019i
$112$		0			0
$113$	−0.643322	−	0.643322i	−0.0605187	−	0.0605187i	0.676200	−	0.736718i	$-0.263626\pi$
$113$	−0.643322	−	0.643322i	−0.0605187	−	0.0605187i	−0.736718	+	0.676200i	$0.763626\pi$
$114$	−2.66177	+	2.66177i	−0.249297	+	0.249297i
$115$	11.7204			1.09294
$116$	5.92308	−	5.92308i	0.549944	−	0.549944i
$117$		−	2.45032i		−	0.226532i
$118$	−6.62509			−0.609889
$119$		0			0
$120$	−28.0606			−2.56157
$121$		−	4.11376i		−	0.373979i
$122$	−0.303059	+	0.303059i	−0.0274376	+	0.0274376i
$123$	−22.4948			−2.02829
$124$	6.75289	−	6.75289i	0.606427	−	0.606427i
$125$	−11.2580	−	11.2580i	−1.00694	−	1.00694i
$126$		0			0
$127$			14.7826i			1.31175i	0.754871	+	0.655873i	$0.227700\pi$
$127$			14.7826i			1.31175i	−0.754871	+	0.655873i	$0.772300\pi$
$128$			10.4732i			0.925710i
$129$	−11.8143	−	11.8143i	−1.04019	−	1.04019i
$130$	0.775985	+	0.775985i	0.0680584	+	0.0680584i
$131$	5.50981	−	5.50981i	0.481395	−	0.481395i	−0.424182	−	0.905577i	$-0.639438\pi$
$131$	5.50981	−	5.50981i	0.481395	−	0.481395i	0.905577	+	0.424182i	$0.139438\pi$
$132$	11.7606			1.02363
$133$		0			0
$134$			5.47090i			0.472614i
$135$	33.6918			2.89972
$136$	1.53269	+	10.1218i	0.131427	+	0.867934i
$137$	−15.2981			−1.30700			−0.653501	−	0.756925i	$-0.726701\pi$
$137$	−15.2981			−1.30700			−0.653501	+	0.756925i	$0.726701\pi$
$138$		−	6.61582i		−	0.563176i
$139$	−8.93048	+	8.93048i	−0.757473	+	0.757473i	−0.975862	−	0.218389i	$-0.929920\pi$
$139$	−8.93048	+	8.93048i	−0.757473	+	0.757473i	0.218389	+	0.975862i	$0.429920\pi$
$140$		0			0
$141$	25.1385	−	25.1385i	2.11705	−	2.11705i
$142$	−1.85315	−	1.85315i	−0.155513	−	0.155513i
$143$	−0.760179	−	0.760179i	−0.0635693	−	0.0635693i
$144$		−	7.34051i		−	0.611709i
$145$		−	21.1236i		−	1.75422i
$146$	−0.388754	−	0.388754i	−0.0321735	−	0.0321735i
$147$		0			0
$148$	4.01561	−	4.01561i	0.330081	−	0.330081i
$149$	−16.3884			−1.34259			−0.671295	−	0.741190i	$-0.734262\pi$
$149$	−16.3884			−1.34259			−0.671295	+	0.741190i	$0.734262\pi$
$150$	−13.8809	+	13.8809i	−1.13337	+	1.13337i
$151$		−	0.260597i		−	0.0212071i	−0.999944	−	0.0106036i	$-0.996625\pi$
$151$		−	0.260597i		−	0.0212071i	0.999944	−	0.0106036i	$-0.00337528\pi$
$152$	4.39059			0.356124
$153$	−3.69219	−	24.3829i	−0.298496	−	1.97124i
$154$		0			0
$155$		−	24.0829i		−	1.93439i
$156$	−1.29826	+	1.29826i	−0.103944	+	0.103944i
$157$	16.0287			1.27923			0.639614	−	0.768696i	$-0.279094\pi$
$157$	16.0287			1.27923			0.639614	+	0.768696i	$0.279094\pi$
$158$	7.88463	−	7.88463i	0.627267	−	0.627267i
$159$	−8.58633	−	8.58633i	−0.680940	−	0.680940i
$160$	15.5664	+	15.5664i	1.23064	+	1.23064i
$161$		0			0
$162$		−	6.27246i		−	0.492811i
$163$	2.51732	+	2.51732i	0.197172	+	0.197172i	0.798787	−	0.601615i	$-0.205476\pi$
$163$	2.51732	+	2.51732i	0.197172	+	0.197172i	−0.601615	+	0.798787i	$0.705476\pi$
$164$	7.93731	+	7.93731i	0.619800	+	0.619800i
$165$	20.9710	−	20.9710i	1.63259	−	1.63259i
$166$	1.62574			0.126182
$167$	13.9205	−	13.9205i	1.07720	−	1.07720i	0.0804404	−	0.996759i	$-0.474367\pi$
$167$	13.9205	−	13.9205i	1.07720	−	1.07720i	0.996759	−	0.0804404i	$-0.0256327\pi$
$168$		0			0
$169$	−12.8322			−0.987090
$170$	8.89101	+	6.55247i	0.681910	+	0.502552i
$171$	−10.5767			−0.808823
$172$			8.33739i			0.635720i
$173$	−4.60956	+	4.60956i	−0.350458	+	0.350458i	−0.860280	−	0.509822i	$-0.829711\pi$
$173$	−4.60956	+	4.60956i	−0.350458	+	0.350458i	0.509822	+	0.860280i	$0.329711\pi$
$174$	−11.9236			−0.903925
$175$		0			0
$176$	−2.27729	−	2.27729i	−0.171657	−	0.171657i
$177$	−19.7647	−	19.7647i	−1.48561	−	1.48561i
$178$		−	9.04699i		−	0.678101i
$179$		−	13.6903i		−	1.02326i	−0.859206	−	0.511629i	$-0.829042\pi$
$179$		−	13.6903i		−	1.02326i	0.859206	−	0.511629i	$-0.170958\pi$
$180$	−23.8516	−	23.8516i	−1.77779	−	1.77779i
$181$	−6.75360	−	6.75360i	−0.501991	−	0.501991i	0.410065	−	0.912056i	$-0.365506\pi$
$181$	−6.75360	−	6.75360i	−0.501991	−	0.501991i	−0.912056	+	0.410065i	$0.865506\pi$
$182$		0			0
$183$	−1.80824			−0.133669
$184$	−5.45640	+	5.45640i	−0.402251	+	0.402251i
$185$		−	14.3209i		−	1.05290i
$186$	−13.5941			−0.996765
$187$	−8.70990	−	6.41900i	−0.636931	−	0.469404i
$188$	−17.7403			−1.29385
$189$		0			0
$190$	3.34951	−	3.34951i	0.242999	−	0.242999i
$191$	6.30054			0.455891			0.227946	−	0.973674i	$-0.426799\pi$
$191$	6.30054			0.455891			0.227946	+	0.973674i	$0.426799\pi$
$192$	3.58533	−	3.58533i	0.258749	−	0.258749i
$193$	1.36847	+	1.36847i	0.0985047	+	0.0985047i	0.754642	−	0.656137i	$-0.227811\pi$
$193$	1.36847	+	1.36847i	0.0985047	+	0.0985047i	−0.656137	+	0.754642i	$0.727811\pi$
$194$	−0.290437	−	0.290437i	−0.0208522	−	0.0208522i
$195$			4.63001i			0.331562i
$196$		0			0
$197$	−7.86389	−	7.86389i	−0.560279	−	0.560279i	0.369108	−	0.929387i	$-0.379663\pi$
$197$	−7.86389	−	7.86389i	−0.560279	−	0.560279i	−0.929387	+	0.369108i	$0.879663\pi$
$198$	−7.88335	−	7.88335i	−0.560245	−	0.560245i
$199$	12.7021	−	12.7021i	0.900429	−	0.900429i	−0.0950441	−	0.995473i	$-0.530299\pi$
$199$	12.7021	−	12.7021i	0.900429	−	0.900429i	0.995473	+	0.0950441i	$0.0302992\pi$
$200$	22.8966			1.61903
$201$	−16.3214	+	16.3214i	−1.15122	+	1.15122i
$202$		−	0.964102i		−	0.0678340i
$203$		0			0
$204$	−10.9626	+	14.8751i	−0.767537	+	1.04147i
$205$	28.3070			1.97704
$206$			4.25514i			0.296470i
$207$	13.1442	−	13.1442i	0.913586	−	0.913586i
$208$	0.502785			0.0348619
$209$	−3.28129	+	3.28129i	−0.226971	+	0.226971i
$210$		0			0
$211$	8.77026	+	8.77026i	0.603770	+	0.603770i	0.941311	−	0.337541i	$-0.109595\pi$
$211$	8.77026	+	8.77026i	0.603770	+	0.603770i	−0.337541	+	0.941311i	$0.609595\pi$
$212$			6.05939i			0.416161i
$213$		−	11.0570i		−	0.757616i
$214$	1.66119	+	1.66119i	0.113557	+	0.113557i
$215$	14.8669	+	14.8669i	1.01391	+	1.01391i
$216$	−15.6851	+	15.6851i	−1.06723	+	1.06723i
$217$		0			0
$218$	−5.71315	+	5.71315i	−0.386944	+	0.386944i
$219$		−	2.31955i		−	0.156741i
$220$	−14.7993			−0.997767
$221$	1.67010	−	0.252895i	0.112343	−	0.0170116i
$222$	−8.08372			−0.542544
$223$		−	28.6104i		−	1.91589i	−0.286950	−	0.957945i	$-0.592641\pi$
$223$		−	28.6104i		−	1.91589i	0.286950	−	0.957945i	$-0.407359\pi$
$224$		0			0
$225$	−55.1568			−3.67712
$226$	0.456962	−	0.456962i	0.0303967	−	0.0303967i
$227$	6.59544	+	6.59544i	0.437755	+	0.437755i	0.891256	−	0.453501i	$-0.149825\pi$
$227$	6.59544	+	6.59544i	0.437755	+	0.437755i	−0.453501	+	0.891256i	$0.649825\pi$
$228$	5.60391	+	5.60391i	0.371128	+	0.371128i
$229$			24.6970i			1.63202i	0.578035	+	0.816012i	$0.303820\pi$
$229$			24.6970i			1.63202i	−0.578035	+	0.816012i	$0.696180\pi$
$230$			8.32521i			0.548948i
$231$		0			0
$232$	9.83399	+	9.83399i	0.645633	+	0.645633i
$233$	−6.53842	+	6.53842i	−0.428346	+	0.428346i	−0.888065	−	0.459719i	$-0.847950\pi$
$233$	−6.53842	+	6.53842i	−0.428346	+	0.428346i	0.459719	+	0.888065i	$0.347950\pi$
$234$	1.74050			0.113780
$235$	−31.6338	+	31.6338i	−2.06356	+	2.06356i
$236$			13.9480i			0.907938i
$237$	47.0446			3.05588
$238$		0			0
$239$	−12.3284			−0.797455			−0.398728	−	0.917069i	$-0.630548\pi$
$239$	−12.3284			−0.797455			−0.398728	+	0.917069i	$0.630548\pi$
$240$			13.8703i			0.895323i
$241$	6.60939	−	6.60939i	0.425748	−	0.425748i	−0.461429	−	0.887177i	$-0.652663\pi$
$241$	6.60939	−	6.60939i	0.425748	−	0.425748i	0.887177	+	0.461429i	$0.152663\pi$
$242$	2.92207			0.187838
$243$	−0.239169	+	0.239169i	−0.0153427	+	0.0153427i
$244$	0.638039	+	0.638039i	0.0408463	+	0.0408463i
$245$		0			0
$246$		−	15.9784i		−	1.01875i
$247$		−	0.724449i		−	0.0460956i
$248$	11.2117	+	11.2117i	0.711945	+	0.711945i
$249$	4.85011	+	4.85011i	0.307363	+	0.307363i
$250$	7.99670	−	7.99670i	0.505756	−	0.505756i
$251$	−25.4353			−1.60546			−0.802732	−	0.596340i	$-0.796621\pi$
$251$	−25.4353			−1.60546			−0.802732	+	0.596340i	$0.796621\pi$
$252$		0			0
$253$		−	8.15563i		−	0.512740i
$254$	−10.5003			−0.658850
$255$	6.97660	+	46.0728i	0.436891	+	2.88519i
$256$	−10.8231			−0.676445
$257$			10.2663i			0.640396i	0.947351	+	0.320198i	$0.103749\pi$
$257$			10.2663i			0.640396i	−0.947351	+	0.320198i	$0.896251\pi$
$258$	8.39189	−	8.39189i	0.522456	−	0.522456i
$259$		0			0
$260$	1.63371	−	1.63371i	0.101318	−	0.101318i
$261$	−23.6896	−	23.6896i	−1.46635	−	1.46635i
$262$	3.91371	+	3.91371i	0.241790	+	0.241790i
$263$			11.0929i			0.684018i	0.939697	+	0.342009i	$0.111107\pi$
$263$			11.0929i			0.684018i	−0.939697	+	0.342009i	$0.888893\pi$
$264$			19.5259i			1.20174i
$265$	10.8049	+	10.8049i	0.663737	+	0.663737i
$266$		0			0
$267$	26.9900	−	26.9900i	1.65176	−	1.65176i
$268$	11.5181			0.703578
$269$	−10.2117	+	10.2117i	−0.622620	+	0.622620i	−0.946201	−	0.323580i	$-0.895113\pi$
$269$	−10.2117	+	10.2117i	−0.622620	+	0.622620i	0.323580	+	0.946201i	$0.395113\pi$
$270$			23.9318i			1.45644i
$271$	21.1528			1.28494			0.642472	−	0.766309i	$-0.277909\pi$
$271$	21.1528			1.28494			0.642472	+	0.766309i	$0.277909\pi$
$272$	5.00316	−	0.757606i	0.303361	−	0.0459366i
$273$		0			0
$274$		−	10.8665i		−	0.656467i
$275$	−17.1116	+	17.1116i	−1.03187	+	1.03187i
$276$	−13.9285			−0.838397
$277$	−5.88486	+	5.88486i	−0.353587	+	0.353587i	−0.861442	−	0.507855i	$-0.830438\pi$
$277$	−5.88486	+	5.88486i	−0.353587	+	0.353587i	0.507855	+	0.861442i	$0.330438\pi$
$278$	−6.34346	−	6.34346i	−0.380456	−	0.380456i
$279$	−27.0085	−	27.0085i	−1.61696	−	1.61696i
$280$		0			0
$281$			12.0888i			0.721160i	0.932728	+	0.360580i	$0.117421\pi$
$281$			12.0888i			0.721160i	−0.932728	+	0.360580i	$0.882579\pi$
$282$	17.8563	+	17.8563i	1.06333	+	1.06333i
$283$	−12.0790	−	12.0790i	−0.718023	−	0.718023i	0.250177	−	0.968200i	$-0.419511\pi$
$283$	−12.0790	−	12.0790i	−0.718023	−	0.718023i	−0.968200	+	0.250177i	$0.919511\pi$
$284$	−3.90149	+	3.90149i	−0.231511	+	0.231511i
$285$	19.9853			1.18383
$286$	0.539967	−	0.539967i	0.0319289	−	0.0319289i
$287$		0			0
$288$	34.9149			2.05738
$289$	16.2379	−	5.03306i	0.955169	−	0.296063i
$290$	15.0044			0.881089
$291$		−	1.73293i		−	0.101586i
$292$	−0.818457	+	0.818457i	−0.0478966	+	0.0478966i
$293$	−2.86968			−0.167649			−0.0838243	−	0.996481i	$-0.526713\pi$
$293$	−2.86968			−0.167649			−0.0838243	+	0.996481i	$0.526713\pi$
$294$		0			0
$295$	24.8715	+	24.8715i	1.44808	+	1.44808i
$296$	6.66706	+	6.66706i	0.387515	+	0.387515i
$297$		−	23.4443i		−	1.36038i
$298$		−	11.6409i		−	0.674342i
$299$	0.900308	+	0.900308i	0.0520662	+	0.0520662i
$300$	29.2239	+	29.2239i	1.68724	+	1.68724i
$301$		0			0
$302$	0.185106			0.0106517
$303$	2.87622	−	2.87622i	0.165234	−	0.165234i
$304$		−	2.17026i		−	0.124473i
$305$	2.27545			0.130292
$306$	17.3195	−	2.62262i	0.990092	−	0.149925i
$307$	−10.4120			−0.594247			−0.297123	−	0.954839i	$-0.596027\pi$
$307$	−10.4120			−0.594247			−0.297123	+	0.954839i	$0.596027\pi$
$308$		0			0
$309$	−12.6944	+	12.6944i	−0.722160	+	0.722160i
$310$	17.1065			0.971584
$311$	−9.98201	+	9.98201i	−0.566028	+	0.566028i	−0.931013	−	0.364985i	$-0.881074\pi$
$311$	−9.98201	+	9.98201i	−0.566028	+	0.566028i	0.364985	+	0.931013i	$0.381074\pi$
$312$	−2.15548	−	2.15548i	−0.122030	−	0.122030i
$313$	−15.3949	−	15.3949i	−0.870174	−	0.870174i	0.122317	−	0.992491i	$-0.460968\pi$
$313$	−15.3949	−	15.3949i	−0.870174	−	0.870174i	−0.992491	+	0.122317i	$0.960968\pi$
$314$			11.3854i			0.642517i
$315$		0			0
$316$	−16.5998	−	16.5998i	−0.933810	−	0.933810i
$317$	12.1719	+	12.1719i	0.683644	+	0.683644i	0.960819	−	0.277176i	$-0.0893984\pi$
$317$	12.1719	+	12.1719i	0.683644	+	0.683644i	−0.277176	+	0.960819i	$0.589398\pi$
$318$	6.09901	−	6.09901i	0.342015	−	0.342015i
$319$	−14.6988			−0.822973
$320$	−4.51171	+	4.51171i	−0.252212	+	0.252212i
$321$			9.91170i			0.553217i
$322$		0			0
$323$	−1.09161	−	7.20891i	−0.0607390	−	0.401115i
$324$	−13.2056			−0.733646
$325$		−	3.77794i		−	0.209562i
$326$	−1.78809	+	1.78809i	−0.0990334	+	0.0990334i
$327$	−34.0883			−1.88508
$328$	−13.1782	+	13.1782i	−0.727644	+	0.727644i
$329$		0			0
$330$	14.8960	+	14.8960i	0.819999	+	0.819999i
$331$			0.996395i			0.0547668i	0.999625	+	0.0273834i	$0.00871750\pi$
$331$			0.996395i			0.0547668i	−0.999625	+	0.0273834i	$0.991283\pi$
$332$		−	3.42273i		−	0.187847i
$333$	−16.0606	−	16.0606i	−0.880117	−	0.880117i
$334$	9.88795	+	9.88795i	0.541044	+	0.541044i
$335$	20.5385	−	20.5385i	1.12214	−	1.12214i
$336$		0			0
$337$	10.9224	−	10.9224i	0.594979	−	0.594979i	−0.343993	−	0.938972i	$-0.611780\pi$
$337$	10.9224	−	10.9224i	0.594979	−	0.594979i	0.938972	+	0.343993i	$0.111780\pi$
$338$		−	9.11489i		−	0.495785i
$339$	2.72652			0.148084
$340$	13.7951	−	18.7185i	0.748146	−	1.01516i
$341$	−16.7580			−0.907499
$342$		−	7.51282i		−	0.406247i
$343$		0			0
$344$	−13.8424			−0.746334
$345$	−24.8367	+	24.8367i	−1.33716	+	1.33716i
$346$	−3.27424	−	3.27424i	−0.176024	−	0.176024i
$347$	−9.09219	−	9.09219i	−0.488094	−	0.488094i	0.419610	−	0.907704i	$-0.362167\pi$
$347$	−9.09219	−	9.09219i	−0.488094	−	0.488094i	−0.907704	+	0.419610i	$0.862167\pi$
$348$			25.1031i			1.34567i
$349$			6.23304i			0.333647i	0.985987	+	0.166824i	$0.0533510\pi$
$349$			6.23304i			0.333647i	−0.985987	+	0.166824i	$0.946649\pi$
$350$		0			0
$351$	2.58804	+	2.58804i	0.138139	+	0.138139i
$352$	10.8319	−	10.8319i	0.577340	−	0.577340i
$353$	−12.3569			−0.657689			−0.328845	−	0.944384i	$-0.606659\pi$
$353$	−12.3569			−0.657689			−0.328845	+	0.944384i	$0.606659\pi$
$354$	14.0392	−	14.0392i	0.746175	−	0.746175i
$355$			13.9140i			0.738476i
$356$	−19.0469			−1.00949
$357$		0			0
$358$	9.72441			0.513951
$359$		−	4.04930i		−	0.213714i	−0.994274	−	0.106857i	$-0.965921\pi$
$359$		−	4.04930i		−	0.213714i	0.994274	−	0.106857i	$-0.0340787\pi$
$360$	39.6005	−	39.6005i	2.08713	−	2.08713i
$361$	15.8729			0.835418
$362$	4.79719	−	4.79719i	0.252135	−	0.252135i
$363$	8.71746	+	8.71746i	0.457548	+	0.457548i
$364$		0			0
$365$			2.91888i			0.152781i
$366$		−	1.28442i		−	0.0671377i
$367$	6.03422	+	6.03422i	0.314984	+	0.314984i	0.846837	−	0.531853i	$-0.178504\pi$
$367$	6.03422	+	6.03422i	0.314984	+	0.314984i	−0.531853	+	0.846837i	$0.678504\pi$
$368$	2.69708	+	2.69708i	0.140595	+	0.140595i
$369$	31.7457	−	31.7457i	1.65261	−	1.65261i
$370$	10.1724			0.528838
$371$		0			0
$372$			28.6200i			1.48388i
$373$	−13.2410			−0.685594			−0.342797	−	0.939410i	$-0.611374\pi$
$373$	−13.2410			−0.685594			−0.342797	+	0.939410i	$0.611374\pi$
$374$	4.55952	−	6.18678i	0.235767	−	0.319911i
$375$	47.7134			2.46391
$376$		−	29.4540i		−	1.51897i
$377$	1.62261	−	1.62261i	0.0835688	−	0.0835688i
$378$		0			0
$379$	6.55582	−	6.55582i	0.336750	−	0.336750i	−0.518393	−	0.855143i	$-0.673469\pi$
$379$	6.55582	−	6.55582i	0.336750	−	0.336750i	0.855143	+	0.518393i	$0.173469\pi$
$380$	−7.05184	−	7.05184i	−0.361752	−	0.361752i
$381$	−31.3258	−	31.3258i	−1.60487	−	1.60487i
$382$			4.47538i			0.228980i
$383$			18.1687i			0.928379i	0.885736	+	0.464190i	$0.153654\pi$
$383$			18.1687i			0.928379i	−0.885736	+	0.464190i	$0.846346\pi$
$384$	−22.1937	−	22.1937i	−1.13257	−	1.13257i
$385$		0			0
$386$	−0.972046	+	0.972046i	−0.0494759	+	0.0494759i
$387$	33.3458			1.69506
$388$	−0.611467	+	0.611467i	−0.0310425	+	0.0310425i
$389$		−	8.09990i		−	0.410681i	−0.978691	−	0.205341i	$-0.934170\pi$
$389$		−	8.09990i		−	0.410681i	0.978691	−	0.205341i	$-0.0658302\pi$
$390$	−3.28877			−0.166533
$391$	10.3155	+	7.60227i	0.521676	+	0.384463i
$392$		0			0
$393$			23.3516i			1.17793i
$394$	5.58585	−	5.58585i	0.281411	−	0.281411i
$395$	−59.2000			−2.97868
$396$	−16.5971	+	16.5971i	−0.834034	+	0.834034i
$397$	−4.29561	−	4.29561i	−0.215591	−	0.215591i	0.591047	−	0.806637i	$-0.298715\pi$
$397$	−4.29561	−	4.29561i	−0.215591	−	0.215591i	−0.806637	+	0.591047i	$0.798715\pi$
$398$	9.02251	+	9.02251i	0.452258	+	0.452258i
$399$		0			0
$400$		−	11.3177i		−	0.565885i
$401$	−28.2109	−	28.2109i	−1.40878	−	1.40878i	−0.766299	−	0.642484i	$-0.777904\pi$
$401$	−28.2109	−	28.2109i	−1.40878	−	1.40878i	−0.642484	−	0.766299i	$-0.722096\pi$
$402$	−11.5934	−	11.5934i	−0.578224	−	0.578224i
$403$	1.84994	−	1.84994i	0.0921519	−	0.0921519i
$404$	−2.02975			−0.100984
$405$	−23.5477	+	23.5477i	−1.17010	+	1.17010i
$406$		0			0
$407$	−9.96519			−0.493956
$408$	−24.6969	−	18.2011i	−1.22268	−	0.901087i
$409$	15.8498			0.783721			0.391860	−	0.920025i	$-0.371832\pi$
$409$	15.8498			0.783721			0.391860	+	0.920025i	$0.371832\pi$
$410$			20.1069i			0.993008i
$411$	32.4181	−	32.4181i	1.59907	−	1.59907i
$412$	8.95849			0.441353
$413$		0			0
$414$	9.33655	+	9.33655i	0.458866	+	0.458866i
$415$	−6.10328	−	6.10328i	−0.299598	−	0.299598i
$416$			2.39148i			0.117252i
$417$		−	37.8491i		−	1.85348i
$418$	−2.33075	−	2.33075i	−0.114001	−	0.114001i
$419$	−4.90962	−	4.90962i	−0.239851	−	0.239851i	0.576938	−	0.816788i	$-0.304248\pi$
$419$	−4.90962	−	4.90962i	−0.239851	−	0.239851i	−0.816788	+	0.576938i	$0.804248\pi$
$420$		0			0
$421$	−0.950160			−0.0463079			−0.0231540	−	0.999732i	$-0.507371\pi$
$421$	−0.950160			−0.0463079			−0.0231540	+	0.999732i	$0.507371\pi$
$422$	−6.22966	+	6.22966i	−0.303255	+	0.303255i
$423$			70.9534i			3.44987i
$424$	−10.0603			−0.488572
$425$	−5.69268	−	37.5939i	−0.276135	−	1.82357i
$426$	7.85399			0.380527
$427$		0			0
$428$	3.49736	−	3.49736i	0.169051	−	0.169051i
$429$	3.22178			0.155549
$430$	−10.5602	+	10.5602i	−0.509257	+	0.509257i
$431$	1.92269	+	1.92269i	0.0926129	+	0.0926129i	0.751895	−	0.659282i	$-0.229140\pi$
$431$	1.92269	+	1.92269i	0.0926129	+	0.0926129i	−0.659282	+	0.751895i	$0.729140\pi$
$432$	7.75308	+	7.75308i	0.373020	+	0.373020i
$433$			38.1244i			1.83214i	0.401014	+	0.916072i	$0.368658\pi$
$433$			38.1244i			1.83214i	−0.401014	+	0.916072i	$0.631342\pi$
$434$		0			0
$435$	44.7629	+	44.7629i	2.14621	+	2.14621i
$436$	12.0281	+	12.0281i	0.576041	+	0.576041i
$437$	3.88615	−	3.88615i	0.185900	−	0.185900i
$438$	1.64762			0.0787261
$439$	8.57127	−	8.57127i	0.409084	−	0.409084i	−0.472335	−	0.881419i	$-0.656589\pi$
$439$	8.57127	−	8.57127i	0.409084	−	0.409084i	0.881419	+	0.472335i	$0.156589\pi$
$440$		−	24.5710i		−	1.17138i
$441$		0			0
$442$	0.179635	+	1.18630i	0.00854439	+	0.0564263i
$443$	−9.12438			−0.433513			−0.216756	−	0.976226i	$-0.569548\pi$
$443$	−9.12438			−0.433513			−0.216756	+	0.976226i	$0.569548\pi$
$444$			17.0189i			0.807683i
$445$	−33.9637	+	33.9637i	−1.61003	+	1.61003i
$446$	20.3224			0.962293
$447$	34.7286	−	34.7286i	1.64261	−	1.64261i
$448$		0			0
$449$	12.7040	+	12.7040i	0.599539	+	0.599539i	0.940190	−	0.340651i	$-0.110647\pi$
$449$	12.7040	+	12.7040i	0.599539	+	0.599539i	−0.340651	+	0.940190i	$0.610647\pi$
$450$		−	39.1787i		−	1.84690i
$451$		−	19.6973i		−	0.927510i
$452$	−0.962057	−	0.962057i	−0.0452514	−	0.0452514i
$453$	0.552230	+	0.552230i	0.0259460	+	0.0259460i
$454$	−4.68485	+	4.68485i	−0.219871	+	0.219871i
$455$		0			0
$456$	−9.30408	+	9.30408i	−0.435703	+	0.435703i
$457$		−	34.4513i		−	1.61156i	−0.592212	−	0.805782i	$-0.701745\pi$
$457$		−	34.4513i		−	1.61156i	0.592212	−	0.805782i	$-0.298255\pi$
$458$	−17.5427			−0.819716
$459$	29.6530	+	21.8536i	1.38408	+	1.02004i
$460$	17.5273			0.817217
$461$			39.6206i			1.84531i	0.385621	+	0.922657i	$0.373987\pi$
$461$			39.6206i			1.84531i	−0.385621	+	0.922657i	$0.626013\pi$
$462$		0			0
$463$	−27.3322			−1.27024			−0.635118	−	0.772415i	$-0.719049\pi$
$463$	−27.3322			−1.27024			−0.635118	+	0.772415i	$0.719049\pi$
$464$	4.86091	−	4.86091i	0.225662	−	0.225662i
$465$	51.0341	+	51.0341i	2.36665	+	2.36665i
$466$	−4.64434	−	4.64434i	−0.215145	−	0.215145i
$467$		−	3.18961i		−	0.147597i	−0.997273	−	0.0737987i	$-0.976488\pi$
$467$		−	3.18961i		−	0.147597i	0.997273	−	0.0737987i	$-0.0235122\pi$
$468$		−	3.66434i		−	0.169384i
$469$		0			0
$470$	−22.4700	−	22.4700i	−1.03646	−	1.03646i
$471$	−33.9663	+	33.9663i	−1.56508	+	1.56508i
$472$	−23.1577			−1.06592
$473$	10.3451	−	10.3451i	0.475667	−	0.475667i
$474$			33.4166i			1.53487i
$475$	−16.3074			−0.748233
$476$		0			0
$477$	24.2348			1.10964
$478$		−	8.75703i		−	0.400537i
$479$	−4.70120	+	4.70120i	−0.214803	+	0.214803i	−0.806304	−	0.591501i	$-0.798536\pi$
$479$	−4.70120	+	4.70120i	−0.214803	+	0.214803i	0.591501	+	0.806304i	$0.298536\pi$
$480$	−65.9736			−3.01127
$481$	1.10007	−	1.10007i	0.0501587	−	0.0501587i
$482$	4.69475	+	4.69475i	0.213840	+	0.213840i
$483$		0			0
$484$		−	6.15193i		−	0.279633i
$485$			2.18068i			0.0990198i
$486$	−0.169885	−	0.169885i	−0.00770616	−	0.00770616i
$487$	−16.9019	−	16.9019i	−0.765898	−	0.765898i	0.211484	−	0.977381i	$-0.432170\pi$
$487$	−16.9019	−	16.9019i	−0.765898	−	0.765898i	−0.977381	+	0.211484i	$0.932170\pi$
$488$	−1.05933	+	1.05933i	−0.0479535	+	0.0479535i
$489$	−10.6689			−0.482464
$490$		0			0
$491$			37.9028i			1.71053i	0.518192	+	0.855264i	$0.326605\pi$
$491$			37.9028i			1.71053i	−0.518192	+	0.855264i	$0.673395\pi$
$492$	−33.6398			−1.51660
$493$	13.7014	−	18.5914i	0.617082	−	0.837315i
$494$	0.514588			0.0231524
$495$			59.1904i			2.66041i
$496$	5.54192	−	5.54192i	0.248839	−	0.248839i
$497$		0			0
$498$	−3.44511	+	3.44511i	−0.154379	+	0.154379i
$499$	9.11350	+	9.11350i	0.407976	+	0.407976i	0.881032	−	0.473056i	$-0.156849\pi$
$499$	9.11350	+	9.11350i	0.407976	+	0.407976i	−0.473056	+	0.881032i	$0.656849\pi$
$500$	−16.8357	−	16.8357i	−0.752916	−	0.752916i
$501$			58.9977i			2.63582i
$502$		−	18.0671i		−	0.806375i
$503$	−11.9184	−	11.9184i	−0.531414	−	0.531414i	0.389579	−	0.920993i	$-0.372620\pi$
$503$	−11.9184	−	11.9184i	−0.531414	−	0.531414i	−0.920993	+	0.389579i	$0.872620\pi$
$504$		0			0
$505$	−3.61937	+	3.61937i	−0.161060	+	0.161060i
$506$	5.79307			0.257534
$507$	27.1926	−	27.1926i	1.20767	−	1.20767i
$508$			22.1067i			0.980827i
$509$	−29.9007			−1.32532			−0.662662	−	0.748919i	$-0.730573\pi$
$509$	−29.9007			−1.32532			−0.662662	+	0.748919i	$0.730573\pi$
$510$	−32.7262	+	4.95559i	−1.44914	+	0.219437i
$511$		0			0
$512$			13.2586i			0.585952i
$513$	11.1712	−	11.1712i	0.493220	−	0.493220i
$514$	−7.29234			−0.321651
$515$	15.9744	−	15.9744i	0.703916	−	0.703916i
$516$	−17.6677	−	17.6677i	−0.777778	−	0.777778i
$517$	22.0123	+	22.0123i	0.968100	+	0.968100i
$518$		0			0
$519$		−	19.5362i		−	0.857543i
$520$	2.71242	+	2.71242i	0.118947	+	0.118947i
$521$	−7.61771	−	7.61771i	−0.333738	−	0.333738i	0.520266	−	0.854004i	$-0.325833\pi$
$521$	−7.61771	−	7.61771i	−0.333738	−	0.333738i	−0.854004	+	0.520266i	$0.825833\pi$
$522$	16.8271	−	16.8271i	0.736503	−	0.736503i
$523$	−15.9552			−0.697672			−0.348836	−	0.937184i	$-0.613423\pi$
$523$	−15.9552			−0.697672			−0.348836	+	0.937184i	$0.613423\pi$
$524$	8.23966	−	8.23966i	0.359951	−	0.359951i
$525$		0			0
$526$	−7.87947			−0.343561
$527$	15.6210	−	21.1960i	0.680461	−	0.923314i
$528$	9.65160			0.420032
$529$		−	13.3410i		−	0.580043i
$530$	−7.67486	+	7.67486i	−0.333375	+	0.333375i
$531$	55.7858			2.42090
$532$		0			0
$533$	2.17441	+	2.17441i	0.0941840	+	0.0941840i
$534$	19.1714	+	19.1714i	0.829629	+	0.829629i
$535$		−	12.4727i		−	0.539241i
$536$			19.1233i			0.825999i
$537$	29.0110	+	29.0110i	1.25192	+	1.25192i
$538$	−7.25355	−	7.25355i	−0.312723	−	0.312723i
$539$		0			0
$540$	50.3844			2.16820
$541$	17.2741	−	17.2741i	0.742673	−	0.742673i	−0.230419	−	0.973092i	$-0.574010\pi$
$541$	17.2741	−	17.2741i	0.742673	−	0.742673i	0.973092	+	0.230419i	$0.0740097\pi$
$542$			15.0252i			0.645388i
$543$	28.6231			1.22833
$544$	3.60353	+	23.7974i	0.154500	+	1.02030i
$545$	42.8960			1.83746
$546$		0			0
$547$	−0.0381169	+	0.0381169i	−0.00162976	+	0.00162976i	−0.707921	−	0.706291i	$-0.750367\pi$
$547$	−0.0381169	+	0.0381169i	−0.00162976	+	0.00162976i	0.706291	+	0.707921i	$0.250367\pi$
$548$	−22.8775			−0.977279
$549$	2.55187	−	2.55187i	0.108911	−	0.108911i
$550$	−12.1547	−	12.1547i	−0.518277	−	0.518277i
$551$	−7.00395	−	7.00395i	−0.298378	−	0.298378i
$552$		−	23.1253i		−	0.984277i
$553$		0			0
$554$	−4.18011	−	4.18011i	−0.177596	−	0.177596i
$555$	30.3474	+	30.3474i	1.28818	+	1.28818i
$556$	−13.3551	+	13.3551i	−0.566382	+	0.566382i
$557$	27.2548			1.15482			0.577411	−	0.816454i	$-0.304063\pi$
$557$	27.2548			1.15482			0.577411	+	0.816454i	$0.304063\pi$
$558$	19.1846	−	19.1846i	0.812148	−	0.812148i
$559$			2.28401i			0.0966032i
$560$		0			0
$561$	32.0596	−	4.85464i	1.35356	−	0.204963i
$562$	−8.58690			−0.362216
$563$		−	20.8563i		−	0.878987i	−0.898246	−	0.439494i	$-0.855158\pi$
$563$		−	20.8563i		−	0.878987i	0.898246	−	0.439494i	$-0.144842\pi$
$564$	37.5935	−	37.5935i	1.58297	−	1.58297i
$565$	−3.43100			−0.144343
$566$	8.57992	−	8.57992i	0.360641	−	0.360641i
$567$		0			0
$568$	−6.47758	−	6.47758i	−0.271793	−	0.271793i
$569$			17.2619i			0.723659i	0.932244	+	0.361829i	$0.117848\pi$
$569$			17.2619i			0.723659i	−0.932244	+	0.361829i	$0.882152\pi$
$570$			14.1959i			0.594600i
$571$	24.6198	+	24.6198i	1.03031	+	1.03031i	0.999526	+	0.0307809i	$0.00979940\pi$
$571$	24.6198	+	24.6198i	1.03031	+	1.03031i	0.0307809	+	0.999526i	$0.490201\pi$
$572$	−1.13681	−	1.13681i	−0.0475324	−	0.0475324i
$573$	−13.3514	+	13.3514i	−0.557765	+	0.557765i
$574$		0			0
$575$	20.2660	−	20.2660i	0.845149	−	0.845149i
$576$			10.1196i			0.421649i
$577$	−22.4399			−0.934186			−0.467093	−	0.884208i	$-0.654699\pi$
$577$	−22.4399			−0.934186			−0.467093	+	0.884208i	$0.654699\pi$
$578$	3.57507	+	11.5340i	0.148703	+	0.479752i
$579$	−5.79984			−0.241033
$580$		−	31.5893i		−	1.31167i
$581$		0			0
$582$	1.23093			0.0510236
$583$	7.51853	−	7.51853i	0.311386	−	0.311386i
$584$	−1.35887	−	1.35887i	−0.0562305	−	0.0562305i
$585$	−6.53409	−	6.53409i	−0.270151	−	0.270151i
$586$		−	2.03838i		−	0.0842047i
$587$			4.91137i			0.202714i	0.994850	+	0.101357i	$0.0323184\pi$
$587$			4.91137i			0.202714i	−0.994850	+	0.101357i	$0.967682\pi$
$588$		0			0
$589$	−7.98520	−	7.98520i	−0.329024	−	0.329024i
$590$	−17.6666	+	17.6666i	−0.727324	+	0.727324i
$591$	33.3287			1.37096
$592$	3.29551	−	3.29551i	0.135444	−	0.135444i
$593$		−	13.7217i		−	0.563482i	−0.959490	−	0.281741i	$-0.909088\pi$
$593$		−	13.7217i		−	0.563482i	0.959490	−	0.281741i	$-0.0909120\pi$
$594$	16.6529			0.683275
$595$		0			0
$596$	−24.5081			−1.00389
$597$			53.8340i			2.20328i
$598$	−0.639503	+	0.639503i	−0.0261512	+	0.0261512i
$599$	−19.9906			−0.816795			−0.408397	−	0.912804i	$-0.633912\pi$
$599$	−19.9906			−0.816795			−0.408397	+	0.912804i	$0.633912\pi$
$600$	−48.5200	+	48.5200i	−1.98082	+	1.98082i
$601$	−18.4941	−	18.4941i	−0.754391	−	0.754391i	0.220904	−	0.975295i	$-0.429099\pi$
$601$	−18.4941	−	18.4941i	−0.754391	−	0.754391i	−0.975295	+	0.220904i	$0.929099\pi$
$602$		0			0
$603$		−	46.0671i		−	1.87600i
$604$		−	0.389710i		−	0.0158571i
$605$	−10.9699	−	10.9699i	−0.445989	−	0.445989i
$606$	2.04302	+	2.04302i	0.0829922	+	0.0829922i
$607$	−28.0201	+	28.0201i	−1.13730	+	1.13730i	−0.148367	+	0.988932i	$0.547402\pi$
$607$	−28.0201	+	28.0201i	−1.13730	+	1.13730i	−0.988932	+	0.148367i	$0.952598\pi$
$608$	10.3227			0.418643
$609$		0			0
$610$			1.61629i			0.0654416i
$611$	−4.85992			−0.196611
$612$	−5.52149	−	36.4634i	−0.223193	−	1.47395i
$613$	−21.6660			−0.875082			−0.437541	−	0.899198i	$-0.644151\pi$
$613$	−21.6660			−0.875082			−0.437541	+	0.899198i	$0.644151\pi$
$614$		−	7.39584i		−	0.298472i
$615$	−59.9852	+	59.9852i	−2.41883	+	2.41883i
$616$		0			0
$617$	−24.0750	+	24.0750i	−0.969222	+	0.969222i	−0.999540	−	0.0303184i	$-0.990348\pi$
$617$	−24.0750	+	24.0750i	−0.969222	+	0.969222i	0.0303184	+	0.999540i	$0.490348\pi$
$618$	−9.01705	−	9.01705i	−0.362719	−	0.362719i
$619$	11.7457	+	11.7457i	0.472101	+	0.472101i	0.902594	−	0.430493i	$-0.141660\pi$
$619$	11.7457	+	11.7457i	0.472101	+	0.472101i	−0.430493	+	0.902594i	$0.641660\pi$
$620$		−	36.0149i		−	1.44639i
$621$			27.7660i			1.11421i
$622$	−7.09038	−	7.09038i	−0.284298	−	0.284298i
$623$		0			0
$624$	−1.06545	+	1.06545i	−0.0426521	+	0.0426521i
$625$	−13.9325			−0.557302
$626$	10.9353	−	10.9353i	0.437062	−	0.437062i
$627$		−	13.9067i		−	0.555381i
$628$	23.9701			0.956511
$629$	9.28904	−	12.6042i	0.370378	−	0.502564i
$630$		0			0
$631$			2.07847i			0.0827427i	0.999144	+	0.0413714i	$0.0131727\pi$
$631$			2.07847i			0.0827427i	−0.999144	+	0.0413714i	$0.986827\pi$
$632$	27.5603	−	27.5603i	1.09629	−	1.09629i
$633$	−37.1701			−1.47738
$634$	−8.64591	+	8.64591i	−0.343373	+	0.343373i
$635$	39.4198	+	39.4198i	1.56433	+	1.56433i
$636$	−12.8404	−	12.8404i	−0.509156	−	0.509156i
$637$		0			0
$638$		−	10.4408i		−	0.413354i
$639$	15.6042	+	15.6042i	0.617293	+	0.617293i
$640$	27.9281	+	27.9281i	1.10396	+	1.10396i
$641$	−28.6113	+	28.6113i	−1.13008	+	1.13008i	−0.139916	+	0.990163i	$0.544683\pi$
$641$	−28.6113	+	28.6113i	−1.13008	+	1.13008i	−0.990163	+	0.139916i	$0.955317\pi$
$642$	−7.04044			−0.277864
$643$	−21.4678	+	21.4678i	−0.846607	+	0.846607i	−0.989708	−	0.143101i	$-0.954293\pi$
$643$	−21.4678	+	21.4678i	−0.846607	+	0.846607i	0.143101	+	0.989708i	$0.454293\pi$
$644$		0			0
$645$	−63.0087			−2.48096
$646$	5.12060	−	0.775391i	0.201468	−	0.0305073i
$647$	15.2471			0.599424			0.299712	−	0.954030i	$-0.403109\pi$
$647$	15.2471			0.599424			0.299712	+	0.954030i	$0.403109\pi$
$648$		−	21.9251i		−	0.861299i
$649$	17.3068	−	17.3068i	0.679350	−	0.679350i
$650$	2.68353			0.105257
$651$		0			0
$652$	3.76453	+	3.76453i	0.147430	+	0.147430i
$653$	26.2578	+	26.2578i	1.02755	+	1.02755i	0.999610	+	0.0279383i	$0.00889419\pi$
$653$	26.2578	+	26.2578i	1.02755	+	1.02755i	0.0279383	+	0.999610i	$0.491106\pi$
$654$		−	24.2134i		−	0.946820i
$655$		−	29.3852i		−	1.14818i
$656$	6.51394	+	6.51394i	0.254327	+	0.254327i
$657$	3.27346	+	3.27346i	0.127710	+	0.127710i
$658$		0			0
$659$	−19.0915			−0.743697			−0.371849	−	0.928293i	$-0.621276\pi$
$659$	−19.0915			−0.743697			−0.371849	+	0.928293i	$0.621276\pi$
$660$	31.3611	−	31.3611i	1.22073	−	1.22073i
$661$			43.8023i			1.70371i	0.523775	+	0.851857i	$0.324523\pi$
$661$			43.8023i			1.70371i	−0.523775	+	0.851857i	$0.675477\pi$
$662$	−0.707755			−0.0275077
$663$	−3.00318	+	4.07500i	−0.116634	+	0.158260i
$664$	5.68271			0.220532
$665$		0			0
$666$	11.4081	−	11.4081i	0.442056	−	0.442056i
$667$	17.4083			0.674052
$668$	20.8174	−	20.8174i	0.805450	−	0.805450i
$669$	60.6281	+	60.6281i	2.34402	+	2.34402i
$670$	14.5888	+	14.5888i	0.563616	+	0.563616i
$671$		−	1.58337i		−	0.0611251i
$672$		0			0
$673$	−7.02754	−	7.02754i	−0.270892	−	0.270892i	0.558567	−	0.829459i	$-0.311351\pi$
$673$	−7.02754	−	7.02754i	−0.270892	−	0.270892i	−0.829459	+	0.558567i	$0.811351\pi$
$674$	7.75832	+	7.75832i	0.298839	+	0.298839i
$675$	58.2568	−	58.2568i	2.24231	−	2.24231i
$676$	−19.1899			−0.738072
$677$	−21.5008	+	21.5008i	−0.826344	+	0.826344i	−0.987009	−	0.160665i	$-0.948636\pi$
$677$	−21.5008	+	21.5008i	−0.826344	+	0.826344i	0.160665	+	0.987009i	$0.448636\pi$
$678$			1.93669i			0.0743782i
$679$		0			0
$680$	31.0781	+	22.9039i	1.19179	+	0.878323i
$681$	−27.9527			−1.07115
$682$		−	11.9035i		−	0.455809i
$683$	−3.56647	+	3.56647i	−0.136467	+	0.136467i	−0.772041	−	0.635573i	$-0.780764\pi$
$683$	−3.56647	+	3.56647i	−0.136467	+	0.136467i	0.635573	+	0.772041i	$0.280764\pi$
$684$	−15.8170			−0.604778
$685$	−40.7942	+	40.7942i	−1.55867	+	1.55867i
$686$		0			0
$687$	−52.3353	−	52.3353i	−1.99672	−	1.99672i
$688$			6.84227i			0.260859i
$689$			1.65996i			0.0632393i
$690$	−17.6419	−	17.6419i	−0.671616	−	0.671616i
$691$	−8.27607	−	8.27607i	−0.314837	−	0.314837i	0.531943	−	0.846780i	$-0.321462\pi$
$691$	−8.27607	−	8.27607i	−0.314837	−	0.314837i	−0.846780	+	0.531943i	$0.821462\pi$
$692$	−6.89337	+	6.89337i	−0.262047	+	0.262047i
$693$		0			0
$694$	6.45832	−	6.45832i	0.245155	−	0.245155i
$695$			47.6285i			1.80665i
$696$	−41.6783			−1.57981
$697$	24.9137	+	18.3608i	0.943674	+	0.695466i
$698$	−4.42743			−0.167581
$699$		−	27.7111i		−	1.04813i
$700$		0			0
$701$	31.0131			1.17135			0.585673	−	0.810547i	$-0.300830\pi$
$701$	31.0131			1.17135			0.585673	+	0.810547i	$0.300830\pi$
$702$	−1.83833	+	1.83833i	−0.0693832	+	0.0693832i
$703$	−4.74840	−	4.74840i	−0.179089	−	0.179089i
$704$	3.13946	+	3.13946i	0.118323	+	0.118323i
$705$		−	134.070i		−	5.04938i
$706$		−	8.77727i		−	0.330337i
$707$		0			0
$708$	−29.5572	−	29.5572i	−1.11083	−	1.11083i
$709$	−12.7383	+	12.7383i	−0.478397	+	0.478397i	−0.904619	−	0.426222i	$-0.859844\pi$
$709$	−12.7383	+	12.7383i	−0.478397	+	0.478397i	0.426222	+	0.904619i	$0.359844\pi$
$710$	−9.88330			−0.370914
$711$	−66.3916	+	66.3916i	−2.48988	+	2.48988i
$712$		−	31.6233i		−	1.18513i
$713$	19.8472			0.743283
$714$		0			0
$715$	−4.05422			−0.151619
$716$		−	20.4731i		−	0.765117i
$717$	26.1250	−	26.1250i	0.975655	−	0.975655i
$718$	2.87628			0.107342
$719$	20.2358	−	20.2358i	0.754669	−	0.754669i	−0.220677	−	0.975347i	$-0.570827\pi$
$719$	20.2358	−	20.2358i	0.754669	−	0.754669i	0.975347	+	0.220677i	$0.0708268\pi$
$720$	−19.5744	−	19.5744i	−0.729494	−	0.729494i
$721$		0			0
$722$			11.2748i			0.419605i
$723$			28.0118i			1.04177i
$724$	−10.0997	−	10.0997i	−0.375352	−	0.375352i
$725$	−36.5250	−	36.5250i	−1.35651	−	1.35651i
$726$	−6.19215	+	6.19215i	−0.229812	+	0.229812i
$727$	−18.0516			−0.669498			−0.334749	−	0.942307i	$-0.608652\pi$
$727$	−18.0516			−0.669498			−0.334749	+	0.942307i	$0.608652\pi$
$728$		0			0
$729$		−	27.5052i		−	1.01871i
$730$	−2.07333			−0.0767372
$731$	3.44159	+	22.7279i	0.127292	+	0.840621i
$732$	−2.70413			−0.0999476
$733$			50.3289i			1.85894i	0.368897	+	0.929470i	$0.379736\pi$
$733$			50.3289i			1.85894i	−0.368897	+	0.929470i	$0.620264\pi$
$734$	−4.28620	+	4.28620i	−0.158207	+	0.158207i
$735$		0			0
$736$	−12.8286	+	12.8286i	−0.472868	+	0.472868i
$737$	−14.2917	−	14.2917i	−0.526441	−	0.526441i
$738$	22.5494	+	22.5494i	0.830057	+	0.830057i
$739$		−	51.2182i		−	1.88409i	−0.335485	−	0.942045i	$-0.608900\pi$
$739$		−	51.2182i		−	1.88409i	0.335485	−	0.942045i	$-0.391100\pi$
$740$		−	21.4163i		−	0.787278i
$741$	1.53518	+	1.53518i	0.0563961	+	0.0563961i
$742$		0			0
$743$	6.02128	−	6.02128i	0.220899	−	0.220899i	−0.587978	−	0.808877i	$-0.700076\pi$
$743$	6.02128	−	6.02128i	0.220899	−	0.220899i	0.808877	+	0.587978i	$0.200076\pi$
$744$	−47.5174			−1.74207
$745$	−43.7017	+	43.7017i	−1.60111	+	1.60111i
$746$		−	9.40531i		−	0.344353i
$747$	−13.6894			−0.500869
$748$	−13.0252	−	9.59930i	−0.476250	−	0.350985i
$749$		0			0
$750$			33.8916i			1.23754i
$751$	−8.74476	+	8.74476i	−0.319101	+	0.319101i	−0.848422	−	0.529321i	$-0.822447\pi$
$751$	−8.74476	+	8.74476i	−0.319101	+	0.319101i	0.529321	+	0.848422i	$0.322447\pi$
$752$	−14.5590			−0.530913
$753$	53.8999	−	53.8999i	1.96422	−	1.96422i
$754$	1.15257	+	1.15257i	0.0419740	+	0.0419740i
$755$	−0.694916	−	0.694916i	−0.0252906	−	0.0252906i
$756$		0			0
$757$			1.96401i			0.0713832i	0.999363	+	0.0356916i	$0.0113634\pi$
$757$			1.96401i			0.0713832i	−0.999363	+	0.0356916i	$0.988637\pi$
$758$	4.65670	+	4.65670i	0.169139	+	0.169139i
$759$	17.2826	+	17.2826i	0.627317	+	0.627317i
$760$	11.7081	−	11.7081i	0.424696	−	0.424696i
$761$	−0.582376			−0.0211111			−0.0105556	−	0.999944i	$-0.503360\pi$
$761$	−0.582376			−0.0211111			−0.0105556	+	0.999944i	$0.503360\pi$
$762$	22.2512	−	22.2512i	0.806077	−	0.806077i
$763$		0			0
$764$	9.42215			0.340882
$765$	−74.8657	−	55.1743i	−2.70678	−	1.99483i
$766$	−12.9055			−0.466296
$767$			3.82102i			0.137969i
$768$	22.9352	−	22.9352i	0.827604	−	0.827604i
$769$	47.7776			1.72290			0.861452	−	0.507838i	$-0.169555\pi$
$769$	47.7776			1.72290			0.861452	+	0.507838i	$0.169555\pi$
$770$		0			0
$771$	−21.7553	−	21.7553i	−0.783499	−	0.783499i
$772$	2.04648	+	2.04648i	0.0736545	+	0.0736545i
$773$			29.7638i			1.07053i	0.844684	+	0.535265i	$0.179788\pi$
$773$			29.7638i			1.07053i	−0.844684	+	0.535265i	$0.820212\pi$
$774$			23.6860i			0.851377i
$775$	−41.6421	−	41.6421i	−1.49583	−	1.49583i
$776$	−1.01521	−	1.01521i	−0.0364439	−	0.0364439i
$777$		0			0
$778$	5.75349			0.206273
$779$	9.38576	−	9.38576i	0.336280	−	0.336280i
$780$			6.92396i			0.247918i
$781$	9.68198			0.346448
$782$	−5.40001	+	7.32724i	−0.193104	+	0.262022i
$783$	50.0422			1.78836
$784$		0			0
$785$	42.7425	−	42.7425i	1.52554	−	1.52554i
$786$	−16.5870			−0.591640
$787$	−6.30910	+	6.30910i	−0.224895	+	0.224895i	−0.810556	−	0.585661i	$-0.800835\pi$
$787$	−6.30910	+	6.30910i	−0.224895	+	0.224895i	0.585661	+	0.810556i	$0.300835\pi$
$788$	−11.7601	−	11.7601i	−0.418935	−	0.418935i
$789$	−23.5069	−	23.5069i	−0.836869	−	0.836869i
$790$		−	42.0507i		−	1.49610i
$791$		0			0
$792$	−27.5559	−	27.5559i	−0.979155	−	0.979155i
$793$	0.174789	+	0.174789i	0.00620695	+	0.00620695i
$794$	3.05124	−	3.05124i	0.108285	−	0.108285i
$795$	−45.7931			−1.62411
$796$	18.9954	−	18.9954i	0.673274	−	0.673274i
$797$		−	18.3449i		−	0.649810i	−0.945747	−	0.324905i	$-0.894668\pi$
$797$		−	18.3449i		−	0.649810i	0.945747	−	0.324905i	$-0.105332\pi$
$798$		0			0
$799$	−48.3606	+	7.32303i	−1.71087	+	0.259070i
$800$	53.8323			1.90326
$801$			76.1791i			2.69166i
$802$	20.0386	−	20.0386i	0.707588	−	0.707588i
$803$	2.03109			0.0716757
$804$	−24.4079	+	24.4079i	−0.860799	+	0.860799i
$805$		0			0
$806$	1.31404	+	1.31404i	0.0462851	+	0.0462851i
$807$		−	43.2793i		−	1.52350i
$808$		−	3.36997i		−	0.118555i
$809$	−26.0041	−	26.0041i	−0.914257	−	0.914257i	0.0823466	−	0.996604i	$-0.473759\pi$
$809$	−26.0041	−	26.0041i	−0.914257	−	0.914257i	−0.996604	+	0.0823466i	$0.973759\pi$
$810$	−16.7263	−	16.7263i	−0.587703	−	0.587703i
$811$	12.7177	−	12.7177i	0.446580	−	0.446580i	−0.447636	−	0.894216i	$-0.647734\pi$
$811$	12.7177	−	12.7177i	0.446580	−	0.446580i	0.894216	+	0.447636i	$0.147734\pi$
$812$		0			0
$813$	−44.8249	+	44.8249i	−1.57208	+	1.57208i
$814$		−	7.07843i		−	0.248099i
$815$	13.4255			0.470275
$816$	−8.99673	+	12.2076i	−0.314949	+	0.427352i
$817$	9.85884			0.344917
$818$			11.2583i			0.393639i
$819$		0			0
$820$	42.3317			1.47829
$821$	18.9846	−	18.9846i	0.662568	−	0.662568i	−0.293417	−	0.955985i	$-0.594792\pi$
$821$	18.9846	−	18.9846i	0.662568	−	0.662568i	0.955985	+	0.293417i	$0.0947923\pi$
$822$	23.0271	+	23.0271i	0.803161	+	0.803161i
$823$	18.3108	+	18.3108i	0.638276	+	0.638276i	0.950130	−	0.311854i	$-0.100950\pi$
$823$	18.3108	+	18.3108i	0.638276	+	0.638276i	−0.311854	+	0.950130i	$0.600950\pi$
$824$			14.8736i			0.518148i
$825$		−	72.5224i		−	2.52490i
$826$		0			0
$827$	33.8532	+	33.8532i	1.17719	+	1.17719i	0.980457	+	0.196733i	$0.0630332\pi$
$827$	33.8532	+	33.8532i	1.17719	+	1.17719i	0.196733	+	0.980457i	$0.436967\pi$
$828$	19.6565	−	19.6565i	0.683112	−	0.683112i
$829$	41.4715			1.44036			0.720182	−	0.693785i	$-0.244058\pi$
$829$	41.4715			1.44036			0.720182	+	0.693785i	$0.244058\pi$
$830$	4.33525	−	4.33525i	0.150479	−	0.150479i
$831$		−	24.9412i		−	0.865199i
$832$	−0.693137			−0.0240302
$833$		0			0
$834$	26.8848			0.930944
$835$		−	74.2415i		−	2.56923i
$836$	−4.90700	+	4.90700i	−0.169712	+	0.169712i
$837$	57.0530			1.97204
$838$	3.48738	−	3.48738i	0.120470	−	0.120470i
$839$	2.00167	+	2.00167i	0.0691053	+	0.0691053i	0.740815	−	0.671709i	$-0.234440\pi$
$839$	2.00167	+	2.00167i	0.0691053	+	0.0691053i	−0.671709	+	0.740815i	$0.734440\pi$
$840$		0			0
$841$		−	2.37473i		−	0.0818873i
$842$		−	0.674913i		−	0.0232591i
$843$	−25.6174	−	25.6174i	−0.882311	−	0.882311i
$844$	13.1155	+	13.1155i	0.451454	+	0.451454i
$845$	−34.2186	+	34.2186i	−1.17716	+	1.17716i
$846$	−50.3993			−1.73276
$847$		0			0
$848$			4.97278i			0.170766i
$849$	51.1932			1.75694
$850$	26.7035	−	4.04360i	0.915923	−	0.138694i
$851$	11.8021			0.404572
$852$		−	16.5353i		−	0.566489i
$853$	27.6517	−	27.6517i	0.946776	−	0.946776i	−0.0518773	−	0.998653i	$-0.516520\pi$
$853$	27.6517	−	27.6517i	0.946776	−	0.946776i	0.998653	+	0.0518773i	$0.0165205\pi$
$854$		0			0
$855$	−28.2042	+	28.2042i	−0.964563	+	0.964563i
$856$	5.80661	+	5.80661i	0.198466	+	0.198466i
$857$	34.3344	+	34.3344i	1.17284	+	1.17284i	0.981529	+	0.191311i	$0.0612740\pi$
$857$	34.3344	+	34.3344i	1.17284	+	1.17284i	0.191311	+	0.981529i	$0.438726\pi$
$858$			2.28848i			0.0781275i
$859$		−	15.8799i		−	0.541815i	−0.962605	−	0.270908i	$-0.912676\pi$
$859$		−	15.8799i		−	0.541815i	0.962605	−	0.270908i	$-0.0873238\pi$
$860$	22.2327	+	22.2327i	0.758129	+	0.758129i
$861$		0			0
$862$	−1.36572	+	1.36572i	−0.0465166	+	0.0465166i
$863$	45.9978			1.56578			0.782891	−	0.622159i	$-0.213744\pi$
$863$	45.9978			1.56578			0.782891	+	0.622159i	$0.213744\pi$
$864$	−36.8773	+	36.8773i	−1.25459	+	1.25459i
$865$			24.5839i			0.835879i
$866$	−27.0804			−0.920230
$867$	−23.7440	+	45.0751i	−0.806390	+	1.53083i
$868$		0			0
$869$			41.1942i			1.39742i
$870$	−31.7958	+	31.7958i	−1.07798	+	1.07798i
$871$	3.15535			0.106915
$872$	−19.9700	+	19.9700i	−0.676271	+	0.676271i
$873$	2.44559	+	2.44559i	0.0827707	+	0.0827707i
$874$	2.76040	+	2.76040i	0.0933718	+	0.0933718i
$875$		0			0
$876$		−	3.46878i		−	0.117199i
$877$	28.4913	+	28.4913i	0.962083	+	0.962083i	0.999307	−	0.0372235i	$-0.0118513\pi$
$877$	28.4913	+	28.4913i	0.962083	+	0.962083i	−0.0372235	+	0.999307i	$0.511851\pi$
$878$	6.08831	+	6.08831i	0.205470	+	0.205470i
$879$	6.08113	−	6.08113i	0.205111	−	0.205111i
$880$	−12.1454			−0.409420
$881$	3.34499	−	3.34499i	0.112696	−	0.112696i	−0.648510	−	0.761206i	$-0.724608\pi$
$881$	3.34499	−	3.34499i	0.112696	−	0.112696i	0.761206	+	0.648510i	$0.224608\pi$
$882$		0			0
$883$	−49.7125			−1.67296			−0.836480	−	0.547998i	$-0.815390\pi$
$883$	−49.7125			−1.67296			−0.836480	+	0.547998i	$0.815390\pi$
$884$	2.49755	−	0.378192i	0.0840016	−	0.0127200i
$885$	−105.410			−3.54333
$886$		−	6.48119i		−	0.217740i
$887$	30.0478	−	30.0478i	1.00891	−	1.00891i	0.00894523	−	0.999960i	$-0.497153\pi$
$887$	30.0478	−	30.0478i	1.00891	−	1.00891i	0.999960	−	0.00894523i	$-0.00284739\pi$
$888$	−28.2563			−0.948218
$889$		0			0
$890$	−24.1250	−	24.1250i	−0.808670	−	0.808670i
$891$	16.3856	+	16.3856i	0.548939	+	0.548939i
$892$		−	42.7854i		−	1.43256i
$893$			20.9777i			0.701992i
$894$	24.6683	+	24.6683i	0.825030	+	0.825030i
$895$	−36.5068	−	36.5068i	−1.22029	−	1.22029i
$896$		0			0
$897$	−3.81568			−0.127402
$898$	−9.02386	+	9.02386i	−0.301130	+	0.301130i
$899$		−	35.7703i		−	1.19301i
$900$	−82.4843			−2.74948
$901$	2.50125	+	16.5180i	0.0833289	+	0.550296i
$902$	13.9913			0.465860
$903$		0			0
$904$	1.59729	−	1.59729i	0.0531250	−	0.0531250i
$905$	−36.0187			−1.19730
$906$	−0.392258	+	0.392258i	−0.0130319	+	0.0130319i
$907$	−5.96258	−	5.96258i	−0.197984	−	0.197984i	0.601151	−	0.799135i	$-0.294709\pi$
$907$	−5.96258	−	5.96258i	−0.197984	−	0.197984i	−0.799135	+	0.601151i	$0.794709\pi$
$908$	9.86316	+	9.86316i	0.327320	+	0.327320i
$909$			8.11810i			0.269260i
$910$		0			0
$911$	−4.86385	−	4.86385i	−0.161146	−	0.161146i	0.621928	−	0.783074i	$-0.286350\pi$
$911$	−4.86385	−	4.86385i	−0.161146	−	0.161146i	−0.783074	+	0.621928i	$0.786350\pi$
$912$	4.59898	+	4.59898i	0.152287	+	0.152287i
$913$	−4.24695	+	4.24695i	−0.140553	+	0.140553i
$914$	24.4713			0.809439
$915$	−4.82190	+	4.82190i	−0.159407	+	0.159407i
$916$			36.9332i			1.22031i
$917$		0			0
$918$	−15.5230	+	21.0630i	−0.512334	+	0.695183i
$919$	31.8219			1.04971			0.524853	−	0.851193i	$-0.324120\pi$
$919$	31.8219			1.04971			0.524853	+	0.851193i	$0.324120\pi$
$920$			29.1004i			0.959411i
$921$	22.0641	−	22.0641i	0.727037	−	0.727037i
$922$	−28.1431			−0.926845
$923$	−1.06880	+	1.06880i	−0.0351801	+	0.0351801i
$924$		0			0
$925$	−24.7625	−	24.7625i	−0.814187	−	0.814187i
$926$		−	19.4145i		−	0.638001i
$927$		−	35.8299i		−	1.17681i
$928$	23.1208	+	23.1208i	0.758976	+	0.758976i
$929$	−38.9210	−	38.9210i	−1.27695	−	1.27695i	−0.942363	−	0.334592i	$-0.891402\pi$
$929$	−38.9210	−	38.9210i	−1.27695	−	1.27695i	−0.334592	−	0.942363i	$-0.608598\pi$
$930$	−36.2503	+	36.2503i	−1.18869	+	1.18869i
$931$		0			0
$932$	−9.77789	+	9.77789i	−0.320285	+	0.320285i
$933$		−	42.3057i		−	1.38503i
$934$	2.26563			0.0741336
$935$	−40.3431	+	6.10899i	−1.31936	+	0.199785i
$936$	6.08384			0.198856
$937$			4.92438i			0.160873i	0.996760	+	0.0804363i	$0.0256313\pi$
$937$			4.92438i			0.160873i	−0.996760	+	0.0804363i	$0.974369\pi$
$938$		0			0
$939$	65.2467			2.12925
$940$	−47.3069	+	47.3069i	−1.54298	+	1.54298i
$941$	−0.114228	−	0.114228i	−0.00372371	−	0.00372371i	0.705242	−	0.708966i	$-0.250838\pi$
$941$	−0.114228	−	0.114228i	−0.00372371	−	0.00372371i	−0.708966	+	0.705242i	$0.750838\pi$
$942$	−24.1268	−	24.1268i	−0.786093	−	0.786093i
$943$			23.3283i			0.759673i
$944$			11.4468i			0.372561i
$945$		0			0
$946$	7.34827	+	7.34827i	0.238913	+	0.238913i
$947$	−32.2807	+	32.2807i	−1.04898	+	1.04898i	−0.0502454	+	0.998737i	$0.516000\pi$
$947$	−32.2807	+	32.2807i	−1.04898	+	1.04898i	−0.998737	+	0.0502454i	$0.984000\pi$
$948$	70.3530			2.28496
$949$	−0.224214	+	0.224214i	−0.00727831	+	0.00727831i
$950$		−	11.5834i		−	0.375814i
$951$	−51.5870			−1.67282
$952$		0			0
$953$	48.4329			1.56889			0.784447	−	0.620195i	$-0.212947\pi$
$953$	48.4329			1.56889			0.784447	+	0.620195i	$0.212947\pi$
$954$			17.2144i			0.557337i
$955$	16.8012	−	16.8012i	0.543674	−	0.543674i
$956$	−18.4365			−0.596278
$957$	31.1481	−	31.1481i	1.00687	−	1.00687i
$958$	−3.33934	−	3.33934i	−0.107889	−	0.107889i
$959$		0			0
$960$		−	19.1215i		−	0.617144i
$961$		−	9.78165i		−	0.315537i
$962$	0.781395	+	0.781395i	0.0251932	+	0.0251932i
$963$	−13.9879	−	13.9879i	−0.450752	−	0.450752i
$964$	9.88402	−	9.88402i	0.318343	−	0.318343i
$965$	7.29840			0.234944
$966$		0			0
$967$		−	22.1661i		−	0.712814i	−0.934331	−	0.356407i	$-0.884002\pi$
$967$		−	22.1661i		−	0.712814i	0.934331	−	0.356407i	$-0.115998\pi$
$968$	10.2140			0.328289
$969$	17.5896	+	12.9631i	0.565060	+	0.416436i
$970$	−1.54897			−0.0497346
$971$		−	39.0963i		−	1.25466i	−0.778753	−	0.627330i	$-0.784148\pi$
$971$		−	39.0963i		−	1.25466i	0.778753	−	0.627330i	$-0.215852\pi$
$972$	−0.357665	+	0.357665i	−0.0114721	+	0.0114721i
$973$		0			0
$974$	12.0057	−	12.0057i	0.384687	−	0.384687i
$975$	8.00582	+	8.00582i	0.256391	+	0.256391i
$976$	0.523622	+	0.523622i	0.0167607	+	0.0167607i
$977$			31.1539i			0.996701i	0.866976	+	0.498350i	$0.166061\pi$
$977$			31.1539i			0.996701i	−0.866976	+	0.498350i	$0.833939\pi$
$978$		−	7.57828i		−	0.242327i
$979$	23.6335	+	23.6335i	0.755331	+	0.755331i
$980$		0			0
$981$	48.1069	−	48.1069i	1.53594	−	1.53594i
$982$	−26.9229			−0.859146
$983$	−19.8614	+	19.8614i	−0.633480	+	0.633480i	−0.948939	−	0.315459i	$-0.897841\pi$
$983$	−19.8614	+	19.8614i	−0.633480	+	0.633480i	0.315459	+	0.948939i	$0.397841\pi$
$984$		−	55.8517i		−	1.78049i
$985$	−41.9401			−1.33632
$986$	13.2058	+	9.73236i	0.420558	+	0.309941i
$987$		0			0
$988$		−	1.08338i		−	0.0344669i
$989$	−12.2521	+	12.2521i	−0.389593	+	0.389593i
$990$	−42.0439			−1.33624
$991$	−8.76410	+	8.76410i	−0.278401	+	0.278401i	−0.832470	−	0.554070i	$-0.813074\pi$
$991$	−8.76410	+	8.76410i	−0.278401	+	0.278401i	0.554070	+	0.832470i	$0.313074\pi$
$992$	26.3599	+	26.3599i	0.836929	+	0.836929i
$993$	−2.11146	−	2.11146i	−0.0670050	−	0.0670050i
$994$		0			0
$995$		−	67.7436i		−	2.14762i
$996$	7.25310	+	7.25310i	0.229823	+	0.229823i
$997$	−22.0323	−	22.0323i	−0.697770	−	0.697770i	0.266159	−	0.963929i	$-0.414245\pi$
$997$	−22.0323	−	22.0323i	−0.697770	−	0.697770i	−0.963929	+	0.266159i	$0.914245\pi$
$998$	−6.47346	+	6.47346i	−0.204914	+	0.204914i
$999$	33.9266			1.07339

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	833.2.g.h.344.7		20
7.2	even	3		833.2.o.f.361.7		40
7.3	odd	6		833.2.o.g.667.4		40
7.4	even	3		833.2.o.f.667.4		40
7.5	odd	6		833.2.o.g.361.7		40
7.6	odd	2		119.2.g.a.106.7	yes	20
17.13	even	4	inner	833.2.g.h.540.4		20
21.20	even	2		1071.2.n.c.820.4		20
119.13	odd	4		119.2.g.a.64.4	✓	20
119.30	even	12		833.2.o.f.557.4		40
119.47	odd	12		833.2.o.g.557.4		40
119.76	odd	8		2023.2.a.m.1.7		10
119.81	even	12		833.2.o.f.30.7		40
119.111	odd	8		2023.2.a.n.1.7		10
119.115	odd	12		833.2.o.g.30.7		40
357.251	even	4		1071.2.n.c.64.7		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.g.a.64.4	✓	20	119.13	odd	4
119.2.g.a.106.7	yes	20	7.6	odd	2
833.2.g.h.344.7		20	1.1	even	1	trivial
833.2.g.h.540.4		20	17.13	even	4	inner
833.2.o.f.30.7		40	119.81	even	12
833.2.o.f.361.7		40	7.2	even	3
833.2.o.f.557.4		40	119.30	even	12
833.2.o.f.667.4		40	7.4	even	3
833.2.o.g.30.7		40	119.115	odd	12
833.2.o.g.361.7		40	7.5	odd	6
833.2.o.g.557.4		40	119.47	odd	12
833.2.o.g.667.4		40	7.3	odd	6
1071.2.n.c.64.7		20	357.251	even	4
1071.2.n.c.820.4		20	21.20	even	2
2023.2.a.m.1.7		10	119.76	odd	8
2023.2.a.n.1.7		10	119.111	odd	8

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:	\( N \)	\(=\)	\( 833 = 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	833.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.710316i q^{2} +(-2.11910 + 2.11910i) q^{3} +1.49545 q^{4} +(2.66663 - 2.66663i) q^{5} +(-1.50523 - 1.50523i) q^{6} +2.48287i q^{8} -5.98113i q^{9} +O(q^{10})\)	\(q+0.710316i q^{2} +(-2.11910 + 2.11910i) q^{3} +1.49545 q^{4} +(2.66663 - 2.66663i) q^{5} +(-1.50523 - 1.50523i) q^{6} +2.48287i q^{8} -5.98113i q^{9} +(1.89415 + 1.89415i) q^{10} +(-1.85556 - 1.85556i) q^{11} +(-3.16900 + 3.16900i) q^{12} +0.409675 q^{13} +11.3017i q^{15} +1.22728 q^{16} +(4.07663 - 0.617307i) q^{17} +4.24849 q^{18} -1.76835i q^{19} +(3.98781 - 3.98781i) q^{20} +(1.31804 - 1.31804i) q^{22} +(2.19761 + 2.19761i) q^{23} +(-5.26145 - 5.26145i) q^{24} -9.22180i q^{25} +0.290999i q^{26} +(6.31730 + 6.31730i) q^{27} +(3.96073 - 3.96073i) q^{29} -8.02776 q^{30} +(4.51562 - 4.51562i) q^{31} +5.83750i q^{32} +7.86423 q^{33} +(0.438483 + 2.89570i) q^{34} -8.94449i q^{36} +(2.68522 - 2.68522i) q^{37} +1.25609 q^{38} +(-0.868141 + 0.868141i) q^{39} +(6.62090 + 6.62090i) q^{40} +(5.30764 + 5.30764i) q^{41} +5.57516i q^{43} +(-2.77491 - 2.77491i) q^{44} +(-15.9494 - 15.9494i) q^{45} +(-1.56100 + 1.56100i) q^{46} -11.8629 q^{47} +(-2.60072 + 2.60072i) q^{48} +6.55039 q^{50} +(-7.33064 + 9.94690i) q^{51} +0.612649 q^{52} +4.05188i q^{53} +(-4.48728 + 4.48728i) q^{54} -9.89619 q^{55} +(3.74730 + 3.74730i) q^{57} +(2.81337 + 2.81337i) q^{58} +9.32696i q^{59} +16.9011i q^{60} +(0.426653 + 0.426653i) q^{61} +(3.20752 + 3.20752i) q^{62} -1.69192 q^{64} +(1.09245 - 1.09245i) q^{65} +5.58609i q^{66} +7.70207 q^{67} +(6.09641 - 0.923152i) q^{68} -9.31391 q^{69} +(-2.60890 + 2.60890i) q^{71} +14.8504 q^{72} +(-0.547298 + 0.547298i) q^{73} +(1.90735 + 1.90735i) q^{74} +(19.5419 + 19.5419i) q^{75} -2.64448i q^{76} +(-0.616654 - 0.616654i) q^{78} +(-11.1002 - 11.1002i) q^{79} +(3.27269 - 3.27269i) q^{80} -8.83053 q^{81} +(-3.77010 + 3.77010i) q^{82} -2.28876i q^{83} +(9.22473 - 12.5170i) q^{85} -3.96013 q^{86} +16.7863i q^{87} +(4.60713 - 4.60713i) q^{88} -12.7366 q^{89} +(11.3291 - 11.3291i) q^{90} +(3.28643 + 3.28643i) q^{92} +19.1381i q^{93} -8.42638i q^{94} +(-4.71553 - 4.71553i) q^{95} +(-12.3702 - 12.3702i) q^{96} +(-0.408884 + 0.408884i) q^{97} +(-11.0984 + 11.0984i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6}+O(q^{10}) \) 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6	\( 20 q + 4 q^{3} - 24 q^{4} + 8 q^{5} - 4 q^{6} - 4 q^{10} - 4 q^{11} - 12 q^{12} + 16 q^{16} + 12 q^{17} - 8 q^{18} - 20 q^{20} - 20 q^{22} - 4 q^{24} - 8 q^{27} + 16 q^{29} - 36 q^{30} - 4 q^{31} + 16 q^{33} - 36 q^{34} - 28 q^{37} - 48 q^{38} + 20 q^{39} + 24 q^{40} + 24 q^{41} - 28 q^{44} - 36 q^{45} + 8 q^{46} - 40 q^{47} + 8 q^{48} - 28 q^{50} - 40 q^{51} + 28 q^{54} + 40 q^{55} + 36 q^{57} + 56 q^{58} + 16 q^{61} + 40 q^{62} + 32 q^{64} + 8 q^{65} + 32 q^{68} + 88 q^{69} - 8 q^{71} + 108 q^{72} - 8 q^{73} + 36 q^{74} - 8 q^{75} - 44 q^{78} - 4 q^{79} + 116 q^{80} + 4 q^{81} + 16 q^{82} + 16 q^{85} + 44 q^{86} + 72 q^{88} - 48 q^{89} - 56 q^{90} - 32 q^{92} + 44 q^{95} - 68 q^{96} - 24 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 24 * q^4 + 8 * q^5 - 4 * q^6 - 4 * q^10 - 4 * q^11 - 12 * q^12 + 16 * q^16 + 12 * q^17 - 8 * q^18 - 20 * q^20 - 20 * q^22 - 4 * q^24 - 8 * q^27 + 16 * q^29 - 36 * q^30 - 4 * q^31 + 16 * q^33 - 36 * q^34 - 28 * q^37 - 48 * q^38 + 20 * q^39 + 24 * q^40 + 24 * q^41 - 28 * q^44 - 36 * q^45 + 8 * q^46 - 40 * q^47 + 8 * q^48 - 28 * q^50 - 40 * q^51 + 28 * q^54 + 40 * q^55 + 36 * q^57 + 56 * q^58 + 16 * q^61 + 40 * q^62 + 32 * q^64 + 8 * q^65 + 32 * q^68 + 88 * q^69 - 8 * q^71 + 108 * q^72 - 8 * q^73 + 36 * q^74 - 8 * q^75 - 44 * q^78 - 4 * q^79 + 116 * q^80 + 4 * q^81 + 16 * q^82 + 16 * q^85 + 44 * q^86 + 72 * q^88 - 48 * q^89 - 56 * q^90 - 32 * q^92 + 44 * q^95 - 68 * q^96 - 24 * q^99

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