LMFDB - Embedded newform 783.2.m.a.476.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [783,2,Mod(17,783)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(783, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

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

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

chi := DirichletCharacter("783.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 783 = 3^{3} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	783.m (of order $12$, degree $4$, 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:	$6.25228647827$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 261)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			476.21
Character	$\chi$	$=$	783.476
Dual form			783.2.m.a.278.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45552 + 0.390005i) q^{2} +(0.234384 + 0.135322i) q^{4} +(-1.15386 + 1.99855i) q^{5} +(-1.71329 - 2.96750i) q^{7} +(-1.84266 - 1.84266i) q^{8} +O(q^{10})$	\(q+(1.45552 + 0.390005i) q^{2} +(0.234384 + 0.135322i) q^{4} +(-1.15386 + 1.99855i) q^{5} +(-1.71329 - 2.96750i) q^{7} +(-1.84266 - 1.84266i) q^{8} +(-2.45892 + 2.45892i) q^{10} +(-0.946251 - 0.253547i) q^{11} +(-3.15830 - 1.82344i) q^{13} +(-1.33638 - 4.98745i) q^{14} +(-2.23402 - 3.86943i) q^{16} +(4.51260 - 4.51260i) q^{17} +(-2.21952 - 2.21952i) q^{19} +(-0.540893 + 0.312285i) q^{20} +(-1.27840 - 0.738086i) q^{22} +(1.53305 + 0.885107i) q^{23} +(-0.162800 - 0.281977i) q^{25} +(-3.88581 - 3.88581i) q^{26} -0.927379i q^{28} +(0.658996 - 5.34469i) q^{29} +(-4.45364 + 1.19335i) q^{31} +(-0.393642 - 1.46909i) q^{32} +(8.32812 - 4.80824i) q^{34} +7.90760 q^{35} +(-3.10705 + 3.10705i) q^{37} +(-2.36493 - 4.09618i) q^{38} +(5.80881 - 1.55647i) q^{40} +(-8.43493 + 2.26013i) q^{41} +(-0.655574 + 2.44664i) q^{43} +(-0.187475 - 0.187475i) q^{44} +(1.88619 + 1.88619i) q^{46} +(-1.99177 + 7.43340i) q^{47} +(-2.37071 + 4.10619i) q^{49} +(-0.126985 - 0.473916i) q^{50} +(-0.493502 - 0.854771i) q^{52} -5.72088i q^{53} +(1.59857 - 1.59857i) q^{55} +(-2.31108 + 8.62508i) q^{56} +(3.04364 - 7.52229i) q^{58} +(7.90468 + 4.56377i) q^{59} +(1.97765 - 7.38070i) q^{61} -6.94778 q^{62} +6.64426i q^{64} +(7.28848 - 4.20801i) q^{65} +(-10.0431 - 5.79839i) q^{67} +(1.66833 - 0.447028i) q^{68} +(11.5097 + 3.08401i) q^{70} +3.89929 q^{71} +(9.73964 - 9.73964i) q^{73} +(-5.73414 + 3.31061i) q^{74} +(-0.219871 - 0.820568i) q^{76} +(0.868799 + 3.24240i) q^{77} +(-1.41681 + 5.28760i) q^{79} +10.3110 q^{80} -13.1587 q^{82} +(1.28536 - 0.742103i) q^{83} +(3.81173 + 14.2256i) q^{85} +(-1.90840 + 3.30545i) q^{86} +(1.27641 + 2.21081i) q^{88} +(4.22391 - 4.22391i) q^{89} +12.4963i q^{91} +(0.239548 + 0.414909i) q^{92} +(-5.79813 + 10.0427i) q^{94} +(6.99684 - 1.87480i) q^{95} +(-14.2384 - 3.81516i) q^{97} +(-5.05205 + 5.05205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 6 q^{2} - 4 q^{7}+O(q^{10}) $ 112 * q + 6 * q^2 - 4 * q^7	$ 112 q + 6 q^{2} - 4 q^{7} - 6 q^{11} + 18 q^{14} + 40 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{23} - 44 q^{25} + 42 q^{29} - 2 q^{31} + 66 q^{32} - 8 q^{37} - 12 q^{40} + 18 q^{41} - 2 q^{43} + 8 q^{46} - 36 q^{49} - 24 q^{50} - 36 q^{52} + 36 q^{55} - 84 q^{56} + 28 q^{58} - 48 q^{59} - 14 q^{61} - 24 q^{65} + 102 q^{68} - 8 q^{73} - 144 q^{74} + 14 q^{76} + 72 q^{77} - 2 q^{79} + 80 q^{82} + 120 q^{83} - 48 q^{85} - 36 q^{88} - 40 q^{94} - 204 q^{95} + 22 q^{97}+O(q^{100}) $ 112 * q + 6 * q^2 - 4 * q^7 - 6 * q^11 + 18 * q^14 + 40 * q^16 - 8 * q^19 + 12 * q^20 + 12 * q^23 - 44 * q^25 + 42 * q^29 - 2 * q^31 + 66 * q^32 - 8 * q^37 - 12 * q^40 + 18 * q^41 - 2 * q^43 + 8 * q^46 - 36 * q^49 - 24 * q^50 - 36 * q^52 + 36 * q^55 - 84 * q^56 + 28 * q^58 - 48 * q^59 - 14 * q^61 - 24 * q^65 + 102 * q^68 - 8 * q^73 - 144 * q^74 + 14 * q^76 + 72 * q^77 - 2 * q^79 + 80 * q^82 + 120 * q^83 - 48 * q^85 - 36 * q^88 - 40 * q^94 - 204 * q^95 + 22 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

$n$	$379$	$407$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.45552	+	0.390005i	1.02921	+	0.275775i	0.733634	−	0.679544i	$-0.237823\pi$
$2$	1.45552	+	0.390005i	1.02921	+	0.275775i	0.295574	+	0.955320i	$0.404489\pi$
$3$		0			0
$3$		0			0
$4$	0.234384	+	0.135322i	0.117192	+	0.0676608i
$5$	−1.15386	+	1.99855i	−0.516023	+	0.893778i	0.483804	+	0.875177i	$0.339255\pi$
$5$	−1.15386	+	1.99855i	−0.516023	+	0.893778i	−0.999827	+	0.0186019i	$0.994078\pi$
$6$		0			0
$7$	−1.71329	−	2.96750i	−0.647562	−	1.12161i	−0.983703	−	0.179798i	$-0.942455\pi$
$7$	−1.71329	−	2.96750i	−0.647562	−	1.12161i	0.336142	−	0.941811i	$-0.390878\pi$
$8$	−1.84266	−	1.84266i	−0.651477	−	0.651477i
$9$		0			0
$10$	−2.45892	+	2.45892i	−0.777577	+	0.777577i
$11$	−0.946251	−	0.253547i	−0.285305	−	0.0764474i	0.113328	−	0.993558i	$-0.463849\pi$
$11$	−0.946251	−	0.253547i	−0.285305	−	0.0764474i	−0.398634	+	0.917110i	$0.630516\pi$
$12$		0			0
$13$	−3.15830	−	1.82344i	−0.875954	−	0.505732i	−0.00663158	−	0.999978i	$-0.502111\pi$
$13$	−3.15830	−	1.82344i	−0.875954	−	0.505732i	−0.869322	+	0.494246i	$0.835444\pi$
$14$	−1.33638	−	4.98745i	−0.357163	−	1.33295i
$15$		0			0
$16$	−2.23402	−	3.86943i	−0.558505	−	0.967359i
$17$	4.51260	−	4.51260i	1.09447	−	1.09447i	0.0994203	−	0.995046i	$-0.468301\pi$
$17$	4.51260	−	4.51260i	1.09447	−	1.09447i	0.995046	−	0.0994203i	$-0.0316988\pi$
$18$		0			0
$19$	−2.21952	−	2.21952i	−0.509193	−	0.509193i	0.405086	−	0.914279i	$-0.367242\pi$
$19$	−2.21952	−	2.21952i	−0.509193	−	0.509193i	−0.914279	+	0.405086i	$0.867242\pi$
$20$	−0.540893	+	0.312285i	−0.120947	+	0.0698290i
$21$		0			0
$22$	−1.27840	−	0.738086i	−0.272556	−	0.157361i
$23$	1.53305	+	0.885107i	0.319663	+	0.184557i	0.651242	−	0.758870i	$-0.274248\pi$
$23$	1.53305	+	0.885107i	0.319663	+	0.184557i	−0.331579	+	0.943427i	$0.607581\pi$
$24$		0			0
$25$	−0.162800	−	0.281977i	−0.0325599	−	0.0563954i
$26$	−3.88581	−	3.88581i	−0.762070	−	0.762070i
$27$		0			0
$28$		−	0.927379i		−	0.175258i
$29$	0.658996	−	5.34469i	0.122372	−	0.992484i
$29$	0.658996	−	5.34469i	0.122372	−	0.992484i
$30$		0			0
$31$	−4.45364	+	1.19335i	−0.799898	+	0.214332i	−0.635539	−	0.772069i	$-0.719222\pi$
$31$	−4.45364	+	1.19335i	−0.799898	+	0.214332i	−0.164359	+	0.986401i	$0.552555\pi$
$32$	−0.393642	−	1.46909i	−0.0695867	−	0.259701i
$33$		0			0
$34$	8.32812	−	4.80824i	1.42826	−	0.824606i
$35$	7.90760			1.33663
$36$		0			0
$37$	−3.10705	+	3.10705i	−0.510796	+	0.510796i	−0.914770	−	0.403974i	$-0.867629\pi$
$37$	−3.10705	+	3.10705i	−0.510796	+	0.510796i	0.403974	+	0.914770i	$0.367629\pi$
$38$	−2.36493	−	4.09618i	−0.383643	−	0.664488i
$39$		0			0
$40$	5.80881	−	1.55647i	0.918453	−	0.246099i
$41$	−8.43493	+	2.26013i	−1.31731	+	0.352973i	−0.847971	−	0.530042i	$-0.822176\pi$
$41$	−8.43493	+	2.26013i	−1.31731	+	0.352973i	−0.469343	+	0.883016i	$0.655509\pi$
$42$		0			0
$43$	−0.655574	+	2.44664i	−0.0999741	+	0.373109i	−0.997727	−	0.0673918i	$-0.978532\pi$
$43$	−0.655574	+	2.44664i	−0.0999741	+	0.373109i	0.897752	+	0.440500i	$0.145199\pi$
$44$	−0.187475	−	0.187475i	−0.0282630	−	0.0282630i
$45$		0			0
$46$	1.88619	+	1.88619i	0.278103	+	0.278103i
$47$	−1.99177	+	7.43340i	−0.290530	+	1.08427i	0.654173	+	0.756345i	$0.273017\pi$
$47$	−1.99177	+	7.43340i	−0.290530	+	1.08427i	−0.944703	+	0.327927i	$0.893650\pi$
$48$		0			0
$49$	−2.37071	+	4.10619i	−0.338672	+	0.586598i
$50$	−0.126985	−	0.473916i	−0.0179584	−	0.0670218i
$51$		0			0
$52$	−0.493502	−	0.854771i	−0.0684364	−	0.118535i
$53$		−	5.72088i		−	0.785823i	−0.919576	−	0.392911i	$-0.871468\pi$
$53$		−	5.72088i		−	0.785823i	0.919576	−	0.392911i	$-0.128532\pi$
$54$		0			0
$55$	1.59857	−	1.59857i	0.215551	−	0.215551i
$56$	−2.31108	+	8.62508i	−0.308831	+	1.15257i
$57$		0			0
$58$	3.04364	−	7.52229i	0.399650	−	0.987726i
$59$	7.90468	+	4.56377i	1.02910	+	0.594152i	0.916727	−	0.399513i	$-0.130821\pi$
$59$	7.90468	+	4.56377i	1.02910	+	0.594152i	0.112375	+	0.993666i	$0.464154\pi$
$60$		0			0
$61$	1.97765	−	7.38070i	0.253213	−	0.945002i	−0.715864	−	0.698240i	$-0.753967\pi$
$61$	1.97765	−	7.38070i	0.253213	−	0.945002i	0.969076	−	0.246762i	$-0.0793666\pi$
$62$	−6.94778			−0.882369
$63$		0			0
$64$			6.64426i			0.830533i
$65$	7.28848	−	4.20801i	0.904025	−	0.521939i
$66$		0			0
$67$	−10.0431	−	5.79839i	−1.22696	−	0.708386i	−0.260567	−	0.965456i	$-0.583910\pi$
$67$	−10.0431	−	5.79839i	−1.22696	−	0.708386i	−0.966393	+	0.257070i	$0.917243\pi$
$68$	1.66833	−	0.447028i	0.202315	−	0.0542101i
$69$		0			0
$70$	11.5097	+	3.08401i	1.37567	+	0.368609i
$71$	3.89929			0.462761			0.231380	−	0.972863i	$-0.425676\pi$
$71$	3.89929			0.462761			0.231380	+	0.972863i	$0.425676\pi$
$72$		0			0
$73$	9.73964	−	9.73964i	1.13994	−	1.13994i	0.151477	−	0.988461i	$-0.451597\pi$
$73$	9.73964	−	9.73964i	1.13994	−	1.13994i	0.988461	−	0.151477i	$-0.0484031\pi$
$74$	−5.73414	+	3.31061i	−0.666581	+	0.384851i
$75$		0			0
$76$	−0.219871	−	0.820568i	−0.0252209	−	0.0941257i
$77$	0.868799	+	3.24240i	0.0990088	+	0.369506i
$78$		0			0
$79$	−1.41681	+	5.28760i	−0.159403	+	0.594902i	0.839285	+	0.543692i	$0.182974\pi$
$79$	−1.41681	+	5.28760i	−0.159403	+	0.594902i	−0.998688	+	0.0512093i	$0.983692\pi$
$80$	10.3110			1.15281
$81$		0			0
$82$	−13.1587			−1.45313
$83$	1.28536	−	0.742103i	0.141087	−	0.0814563i	−0.427795	−	0.903876i	$-0.640710\pi$
$83$	1.28536	−	0.742103i	0.141087	−	0.0814563i	0.568882	+	0.822419i	$0.307376\pi$
$84$		0			0
$85$	3.81173	+	14.2256i	0.413440	+	1.54298i
$86$	−1.90840	+	3.30545i	−0.205788	+	0.356436i
$87$		0			0
$88$	1.27641	+	2.21081i	0.136066	+	0.235674i
$89$	4.22391	−	4.22391i	0.447734	−	0.447734i	−0.446867	−	0.894600i	$-0.647460\pi$
$89$	4.22391	−	4.22391i	0.447734	−	0.447734i	0.894600	+	0.446867i	$0.147460\pi$
$90$		0			0
$91$			12.4963i			1.30997i
$92$	0.239548	+	0.414909i	0.0249746	+	0.0432573i
$93$		0			0
$94$	−5.79813	+	10.0427i	−0.598031	+	1.03582i
$95$	6.99684	−	1.87480i	0.717861	−	0.192350i
$96$		0			0
$97$	−14.2384	−	3.81516i	−1.44569	−	0.387371i	−0.551167	−	0.834395i	$-0.685817\pi$
$97$	−14.2384	−	3.81516i	−1.44569	−	0.387371i	−0.894522	+	0.447024i	$0.852484\pi$
$98$	−5.05205	+	5.05205i	−0.510334	+	0.510334i
$99$		0			0
$100$		−	0.0881211i		−	0.00881211i
$101$	−13.0819	−	3.50530i	−1.30170	−	0.348790i	−0.459609	−	0.888121i	$-0.652010\pi$
$101$	−13.0819	−	3.50530i	−1.30170	−	0.348790i	−0.842094	+	0.539331i	$0.818677\pi$
$102$		0			0
$103$	−1.08059	+	1.87164i	−0.106474	+	0.184418i	−0.914339	−	0.404949i	$-0.867289\pi$
$103$	−1.08059	+	1.87164i	−0.106474	+	0.184418i	0.807866	+	0.589367i	$0.200623\pi$
$104$	2.45967	+	9.17963i	0.241191	+	0.900137i
$105$		0			0
$106$	2.23117	−	8.32685i	0.216711	−	0.808775i
$107$			11.7414i			1.13509i	0.823343	+	0.567544i	$0.192106\pi$
$107$			11.7414i			1.13509i	−0.823343	+	0.567544i	$0.807894\pi$
$108$		0			0
$109$		−	12.4182i		−	1.18944i	−0.803932	−	0.594722i	$-0.797262\pi$
$109$		−	12.4182i		−	1.18944i	0.803932	−	0.594722i	$-0.202738\pi$
$110$	2.95020	−	1.70330i	0.281291	−	0.162403i
$111$		0			0
$112$	−7.65503	+	13.2589i	−0.723333	+	1.25285i
$113$	2.22666	−	0.596633i	0.209467	−	0.0561265i	−0.152560	−	0.988294i	$-0.548752\pi$
$113$	2.22666	−	0.596633i	0.209467	−	0.0561265i	0.362027	+	0.932168i	$0.382085\pi$
$114$		0			0
$115$	−3.53786	+	2.04258i	−0.329907	+	0.190472i
$116$	0.877710	−	1.16353i	0.0814933	−	0.108031i
$117$		0			0
$118$	9.72553	+	9.72553i	0.895308	+	0.895308i
$119$	−21.1225	−	5.65976i	−1.93630	−	0.518829i
$120$		0			0
$121$	−8.69517	−	5.02016i	−0.790470	−	0.456378i
$122$	5.75703	−	9.97147i	0.521217	−	0.902774i
$123$		0			0
$124$	−1.20535	−	0.322972i	−0.108243	−	0.0290037i
$125$	−10.7872			−0.964840
$126$		0			0
$127$	15.1571	+	15.1571i	1.34498	+	1.34498i	0.891029	+	0.453946i	$0.149984\pi$
$127$	15.1571	+	15.1571i	1.34498	+	1.34498i	0.453946	+	0.891029i	$0.350016\pi$
$128$	−3.37858	+	12.6090i	−0.298627	+	1.11449i
$129$		0			0
$130$	12.2497	−	3.28229i	1.07437	−	0.287876i
$131$	21.6572	−	5.80303i	1.89220	−	0.507013i	0.893929	−	0.448209i	$-0.147938\pi$
$131$	21.6572	−	5.80303i	1.89220	−	0.507013i	0.998270	−	0.0588036i	$-0.0187286\pi$
$132$		0			0
$133$	−2.78375	+	10.3891i	−0.241382	+	0.900850i
$134$	−12.3565	−	12.3565i	−1.06744	−	1.06744i
$135$		0			0
$136$	−16.6303			−1.42604
$137$	22.5040	+	6.02993i	1.92265	+	0.515172i	0.986558	+	0.163409i	$0.0522491\pi$
$137$	22.5040	+	6.02993i	1.92265	+	0.515172i	0.936089	+	0.351762i	$0.114418\pi$
$138$		0			0
$139$	3.60927	−	6.25144i	0.306134	−	0.530240i	−0.671379	−	0.741114i	$-0.734298\pi$
$139$	3.60927	−	6.25144i	0.306134	−	0.530240i	0.977513	+	0.210874i	$0.0676310\pi$
$140$	1.85341	+	1.07007i	0.156642	+	0.0904372i
$141$		0			0
$142$	5.67550	+	1.52075i	0.476277	+	0.127618i
$143$	2.52621	+	2.52621i	0.211252	+	0.211252i
$144$		0			0
$145$	9.92124	+	7.48408i	0.823914	+	0.621519i
$146$	17.9747	−	10.3777i	1.48760	−	0.858867i
$147$		0			0
$148$	−1.14869	+	0.307792i	−0.0944220	+	0.0253003i
$149$	−0.868063	+	1.50353i	−0.0711145	+	0.123174i	−0.899390	−	0.437147i	$-0.855989\pi$
$149$	−0.868063	+	1.50353i	−0.0711145	+	0.123174i	0.828276	+	0.560321i	$0.189322\pi$
$150$		0			0
$151$	15.1953	−	8.77300i	1.23657	−	0.713937i	0.268182	−	0.963368i	$-0.413577\pi$
$151$	15.1953	−	8.77300i	1.23657	−	0.713937i	0.968392	+	0.249432i	$0.0802438\pi$
$152$			8.17962i			0.663455i
$153$		0			0
$154$			5.05821i			0.407603i
$155$	2.75392	−	10.2778i	0.221201	−	0.825532i
$156$		0			0
$157$	−3.56305	−	13.2975i	−0.284363	−	1.06126i	−0.949304	−	0.314360i	$-0.898210\pi$
$157$	−3.56305	−	13.2975i	−0.284363	−	1.06126i	0.664941	−	0.746896i	$-0.268457\pi$
$158$	−4.12439	+	7.14365i	−0.328119	+	0.568318i
$159$		0			0
$160$	3.39026	+	0.908418i	0.268024	+	0.0718167i
$161$		−	6.06577i		−	0.478049i
$162$		0			0
$163$	11.6148	−	11.6148i	0.909740	−	0.909740i	−0.0865108	−	0.996251i	$-0.527572\pi$
$163$	11.6148	−	11.6148i	0.909740	−	0.909740i	0.996251	+	0.0865108i	$0.0275717\pi$
$164$	−2.28285	−	0.611689i	−0.178261	−	0.0477649i
$165$		0			0
$166$	2.16029	−	0.578848i	0.167671	−	0.0449273i
$167$	−0.894361	+	1.54908i	−0.0692077	+	0.119871i	−0.898553	−	0.438865i	$-0.855380\pi$
$167$	−0.894361	+	1.54908i	−0.0692077	+	0.119871i	0.829345	+	0.558737i	$0.188714\pi$
$168$		0			0
$169$	0.149890	+	0.259616i	0.0115300	+	0.0199705i
$170$			22.1922i			1.70206i
$171$		0			0
$172$	−0.484739	+	0.484739i	−0.0369610	+	0.0369610i
$173$	−1.27135	−	2.20203i	−0.0966586	−	0.167418i	0.813641	−	0.581368i	$-0.197482\pi$
$173$	−1.27135	−	2.20203i	−0.0966586	−	0.167418i	−0.910300	+	0.413950i	$0.864149\pi$
$174$		0			0
$175$	−0.557845	+	0.966215i	−0.0421691	+	0.0730390i
$176$	1.13286	+	4.22789i	0.0853924	+	0.318689i
$177$		0			0
$178$	7.79533	−	4.50064i	0.584285	−	0.337337i
$179$	−2.12556			−0.158872			−0.0794360	−	0.996840i	$-0.525312\pi$
$179$	−2.12556			−0.158872			−0.0794360	+	0.996840i	$0.525312\pi$
$180$		0			0
$181$	−6.51616			−0.484342			−0.242171	−	0.970234i	$-0.577860\pi$
$181$	−6.51616			−0.484342			−0.242171	+	0.970234i	$0.577860\pi$
$182$	−4.87364	+	18.1887i	−0.361258	+	1.34823i
$183$		0			0
$184$	−1.19394	−	4.45583i	−0.0880181	−	0.328488i
$185$	−2.62448	−	9.79471i	−0.192956	−	0.720121i
$186$		0			0
$187$	−5.41421	+	3.12589i	−0.395926	+	0.228588i
$188$	−1.47274	+	1.47274i	−0.107410	+	0.107410i
$189$		0			0
$190$	10.9152			0.791874
$191$	2.43044	+	0.651235i	0.175861	+	0.0471217i	0.345675	−	0.938354i	$-0.387650\pi$
$191$	2.43044	+	0.651235i	0.175861	+	0.0471217i	−0.169814	+	0.985476i	$0.554317\pi$
$192$		0			0
$193$	6.90478	−	1.85013i	0.497017	−	0.133175i	−0.00159839	−	0.999999i	$-0.500509\pi$
$193$	6.90478	−	1.85013i	0.497017	−	0.133175i	0.498615	+	0.866823i	$0.333842\pi$
$194$	−19.2363	−	11.1061i	−1.38109	−	0.797371i
$195$		0			0
$196$	−1.11131	+	0.641615i	−0.0793793	+	0.0458297i
$197$			23.3533i			1.66385i	0.554887	+	0.831925i	$0.312761\pi$
$197$			23.3533i			1.66385i	−0.554887	+	0.831925i	$0.687239\pi$
$198$		0			0
$199$	11.8223			0.838057			0.419029	−	0.907973i	$-0.362371\pi$
$199$	11.8223			0.838057			0.419029	+	0.907973i	$0.362371\pi$
$200$	−0.219603	+	0.819570i	−0.0155283	+	0.0579523i
$201$		0			0
$202$	−17.6740	−	10.2041i	−1.24354	−	0.717955i
$203$	−16.9894	+	7.20142i	−1.19242	+	0.505441i
$204$		0			0
$205$	5.21577	−	19.4655i	0.364285	−	1.35953i
$206$	−2.30277	+	2.30277i	−0.160441	+	0.160441i
$207$		0			0
$208$			16.2944i			1.12982i
$209$	1.53747	+	2.66298i	0.106349	+	0.184202i
$210$		0			0
$211$	1.63756	+	6.11147i	0.112735	+	0.420731i	0.999107	−	0.0422410i	$-0.0134497\pi$
$211$	1.63756	+	6.11147i	0.112735	+	0.420731i	−0.886373	+	0.462972i	$0.846783\pi$
$212$	0.774158	−	1.34088i	0.0531694	−	0.0920920i
$213$		0			0
$214$	−4.57923	+	17.0899i	−0.313030	+	1.16824i
$215$	−4.13328	−	4.13328i	−0.281887	−	0.281887i
$216$		0			0
$217$	11.1716	+	11.1716i	0.758380	+	0.758380i
$218$	4.84315	−	18.0749i	0.328019	−	1.22419i
$219$		0			0
$220$	0.591000	−	0.158358i	0.0398452	−	0.0106765i
$221$	−22.4806	+	6.02366i	−1.51221	+	0.405195i
$222$		0			0
$223$	0.919993	+	1.59347i	0.0616073	+	0.106707i	0.895184	−	0.445697i	$-0.147044\pi$
$223$	0.919993	+	1.59347i	0.0616073	+	0.106707i	−0.833577	+	0.552404i	$0.813711\pi$
$224$	−3.68511	+	3.68511i	−0.246222	+	0.246222i
$225$		0			0
$226$	3.47364			0.231063
$227$	−7.59478	+	4.38485i	−0.504083	+	0.291032i	−0.730398	−	0.683022i	$-0.760665\pi$
$227$	−7.59478	+	4.38485i	−0.504083	+	0.291032i	0.226315	+	0.974054i	$0.427332\pi$
$228$		0			0
$229$	−6.58672	−	24.5820i	−0.435262	−	1.62442i	−0.740437	−	0.672125i	$-0.765382\pi$
$229$	−6.58672	−	24.5820i	−0.435262	−	1.62442i	0.305175	−	0.952296i	$-0.401285\pi$
$230$	−5.94604	+	1.59324i	−0.392070	+	0.105055i
$231$		0			0
$232$	−11.0627	+	8.63412i	−0.726304	+	0.566858i
$233$		−	4.40613i		−	0.288655i	−0.989530	−	0.144327i	$-0.953898\pi$
$233$		−	4.40613i		−	0.288655i	0.989530	−	0.144327i	$-0.0461019\pi$
$234$		0			0
$235$	−12.5578	−	12.5578i	−0.819179	−	0.819179i
$236$	1.23515	+	2.13935i	0.0804016	+	0.139260i
$237$		0			0
$238$	−28.5369	−	16.4758i	−1.84977	−	1.06797i
$239$	−10.4157	−	6.01352i	−0.673737	−	0.388982i	0.123754	−	0.992313i	$-0.460507\pi$
$239$	−10.4157	−	6.01352i	−0.673737	−	0.388982i	−0.797491	+	0.603331i	$0.793840\pi$
$240$		0			0
$241$	11.8938	−	6.86687i	0.766144	−	0.442334i	−0.0653530	−	0.997862i	$-0.520817\pi$
$241$	11.8938	−	6.86687i	0.766144	−	0.442334i	0.831498	+	0.555528i	$0.187484\pi$
$242$	−10.6981	−	10.6981i	−0.687701	−	0.687701i
$243$		0			0
$244$	1.46230	−	1.46230i	0.0936140	−	0.0936140i
$245$	−5.47094	−	9.47595i	−0.349526	−	0.605396i
$246$		0			0
$247$	2.96273	+	11.0571i	0.188514	+	0.703545i
$248$	10.4055	+	6.00760i	0.660747	+	0.381483i
$249$		0			0
$250$	−15.7010	−	4.20708i	−0.993021	−	0.266079i
$251$	−0.591952	+	0.591952i	−0.0373637	+	0.0373637i	−0.725542	−	0.688178i	$-0.758411\pi$
$251$	−0.591952	+	0.591952i	−0.0373637	+	0.0373637i	0.688178	+	0.725542i	$0.258411\pi$
$252$		0			0
$253$	−1.22623	−	1.22623i	−0.0770926	−	0.0770926i
$254$	16.1501	+	27.9728i	1.01335	+	1.75517i
$255$		0			0
$256$	−3.19093	+	5.52685i	−0.199433	+	0.345428i
$257$	−7.49503	−	4.32726i	−0.467527	−	0.269927i	0.247677	−	0.968843i	$-0.420333\pi$
$257$	−7.49503	−	4.32726i	−0.467527	−	0.269927i	−0.715204	+	0.698916i	$0.753666\pi$
$258$		0			0
$259$	14.5435	+	3.89691i	0.903686	+	0.242142i
$260$	2.27774			0.141259
$261$		0			0
$262$	33.7857			2.08729
$263$	−10.8564	−	2.90897i	−0.669435	−	0.179375i	−0.0919347	−	0.995765i	$-0.529305\pi$
$263$	−10.8564	−	2.90897i	−0.669435	−	0.179375i	−0.577500	+	0.816390i	$0.695972\pi$
$264$		0			0
$265$	11.4335	+	6.60111i	0.702351	+	0.405503i
$266$	−8.10362	+	14.0359i	−0.496865	+	0.860595i
$267$		0			0
$268$	−1.56929	−	2.71809i	−0.0958598	−	0.166034i
$269$	4.35975	+	4.35975i	0.265818	+	0.265818i	0.827413	−	0.561594i	$-0.189812\pi$
$269$	4.35975	+	4.35975i	0.265818	+	0.265818i	−0.561594	+	0.827413i	$0.689812\pi$
$270$		0			0
$271$	−19.2987	+	19.2987i	−1.17231	+	1.17231i	−0.190658	+	0.981656i	$0.561062\pi$
$271$	−19.2987	+	19.2987i	−1.17231	+	1.17231i	−0.981656	+	0.190658i	$0.938938\pi$
$272$	−27.5424	−	7.37997i	−1.67001	−	0.447477i
$273$		0			0
$274$	30.4033	+	17.5534i	1.83673	+	1.06044i
$275$	0.0825547	+	0.308098i	0.00497824	+	0.0185790i
$276$		0			0
$277$	−4.16756	−	7.21842i	−0.250404	−	0.433713i	0.713233	−	0.700927i	$-0.247230\pi$
$277$	−4.16756	−	7.21842i	−0.250404	−	0.433713i	−0.963637	+	0.267214i	$0.913897\pi$
$278$	7.69146	−	7.69146i	0.461303	−	0.461303i
$279$		0			0
$280$	−14.5710	−	14.5710i	−0.870782	−	0.870782i
$281$	22.0582	−	12.7353i	1.31588	−	0.759726i	0.332821	−	0.942990i	$-0.392000\pi$
$281$	22.0582	−	12.7353i	1.31588	−	0.759726i	0.983064	+	0.183264i	$0.0586663\pi$
$282$		0			0
$283$	−1.90239	−	1.09835i	−0.113086	−	0.0652899i	0.442390	−	0.896823i	$-0.354131\pi$
$283$	−1.90239	−	1.09835i	−0.113086	−	0.0652899i	−0.555476	+	0.831533i	$0.687464\pi$
$284$	0.913931	+	0.527658i	0.0542318	+	0.0313108i
$285$		0			0
$286$	2.69172	+	4.66219i	0.159165	+	0.275681i
$287$	21.1584	+	21.1584i	1.24894	+	1.24894i
$288$		0			0
$289$		−	23.7271i		−	1.39571i
$290$	11.5217	+	14.7626i	0.676579	+	0.866887i
$291$		0			0
$292$	3.60079	−	0.964830i	0.210721	−	0.0564624i
$293$	−4.01564	−	14.9866i	−0.234596	−	0.875526i	−0.978330	−	0.207050i	$-0.933614\pi$
$293$	−4.01564	−	14.9866i	−0.234596	−	0.875526i	0.743734	−	0.668476i	$-0.233053\pi$
$294$		0			0
$295$	−18.2418	+	10.5319i	−1.06208	+	0.613193i
$296$	11.4505			0.665544
$297$		0			0
$298$	−1.84987	+	1.84987i	−0.107160	+	0.107160i
$299$	−3.22788	−	5.59086i	−0.186673	−	0.323328i
$300$		0			0
$301$	8.38358	−	2.24637i	0.483222	−	0.129479i
$302$	25.5386	−	6.84303i	1.46958	−	0.393772i
$303$		0			0
$304$	−3.62984	+	13.5467i	−0.208186	+	0.776959i
$305$	12.4688	+	12.4688i	0.713959	+	0.713959i
$306$		0			0
$307$	−20.6236	−	20.6236i	−1.17705	−	1.17705i	−0.980492	−	0.196557i	$-0.937024\pi$
$307$	−20.6236	−	20.6236i	−1.17705	−	1.17705i	−0.196557	−	0.980492i	$-0.562976\pi$
$308$	−0.235134	+	0.877533i	−0.0133980	+	0.0500021i
$309$		0			0
$310$	8.01679	−	13.8855i	0.455323	−	0.788642i
$311$	−3.98585	−	14.8754i	−0.226017	−	0.843507i	−0.981995	−	0.188909i	$-0.939505\pi$
$311$	−3.98585	−	14.8754i	−0.226017	−	0.843507i	0.755978	−	0.654598i	$-0.227162\pi$
$312$		0			0
$313$	14.0279	+	24.2970i	0.792904	+	1.37335i	0.924162	+	0.382001i	$0.124765\pi$
$313$	14.0279	+	24.2970i	0.792904	+	1.37335i	−0.131258	+	0.991348i	$0.541902\pi$
$314$		−	20.7444i		−	1.17067i
$315$		0			0
$316$	−1.04760	+	1.04760i	−0.0589323	+	0.0589323i
$317$	3.17060	−	11.8329i	0.178079	−	0.664599i	−0.817928	−	0.575321i	$-0.804877\pi$
$317$	3.17060	−	11.8329i	0.178079	−	0.664599i	0.996007	−	0.0892785i	$-0.0284561\pi$
$318$		0			0
$319$	−1.97871	+	4.89033i	−0.110786	+	0.273806i
$320$	−13.2789	−	7.66657i	−0.742312	−	0.428574i
$321$		0			0
$322$	2.36568	−	8.82885i	0.131834	−	0.492012i
$323$	−20.0316			−1.11459
$324$		0			0
$325$			1.18742i			0.0658664i
$326$	21.4354	−	12.3757i	1.18720	−	0.685428i
$327$		0			0
$328$	19.7073	+	11.3780i	1.08815	+	0.628246i
$329$	25.4711	−	6.82496i	1.40427	−	0.376272i
$330$		0			0
$331$	−24.6735	−	6.61124i	−1.35618	−	0.363387i	−0.493766	−	0.869595i	$-0.664380\pi$
$331$	−24.6735	−	6.61124i	−1.35618	−	0.363387i	−0.862411	+	0.506208i	$0.831047\pi$
$332$	0.401690			0.0220456
$333$		0			0
$334$	−1.90591	+	1.90591i	−0.104287	+	0.104287i
$335$	23.1767	−	13.3811i	1.26628	−	0.731087i
$336$		0			0
$337$	8.28893	+	30.9347i	0.451527	+	1.68512i	0.698102	+	0.715998i	$0.254028\pi$
$337$	8.28893	+	30.9347i	0.451527	+	1.68512i	−0.246575	+	0.969124i	$0.579305\pi$
$338$	0.116915	+	0.436334i	0.00635936	+	0.0237335i
$339$		0			0
$340$	−1.03162	+	3.85005i	−0.0559473	+	0.208798i
$341$	4.51684			0.244600
$342$		0			0
$343$	−7.73921			−0.417878
$344$	5.71630	−	3.30031i	0.308203	−	0.177941i
$345$		0			0
$346$	−0.991663	−	3.70094i	−0.0533121	−	0.198964i
$347$	7.85064	−	13.5977i	0.421445	−	0.729963i	−0.574636	−	0.818409i	$-0.694857\pi$
$347$	7.85064	−	13.5977i	0.421445	−	0.729963i	0.996081	+	0.0884454i	$0.0281899\pi$
$348$		0			0
$349$	−7.20890	−	12.4862i	−0.385883	−	0.668370i	0.606008	−	0.795459i	$-0.292770\pi$
$349$	−7.20890	−	12.4862i	−0.385883	−	0.668370i	−0.991891	+	0.127089i	$0.959437\pi$
$350$	−1.18878	+	1.18878i	−0.0635432	+	0.0635432i
$351$		0			0
$352$			1.48994i			0.0794139i
$353$	−3.02639	−	5.24187i	−0.161079	−	0.278996i	0.774177	−	0.632969i	$-0.218164\pi$
$353$	−3.02639	−	5.24187i	−0.161079	−	0.278996i	−0.935256	+	0.353973i	$0.884831\pi$
$354$		0			0
$355$	−4.49925	+	7.79293i	−0.238795	+	0.413606i
$356$	1.56160	−	0.418430i	0.0827647	−	0.0221767i
$357$		0			0
$358$	−3.09380	−	0.828981i	−0.163512	−	0.0438130i
$359$	−10.6622	+	10.6622i	−0.562731	+	0.562731i	−0.930082	−	0.367351i	$-0.880265\pi$
$359$	−10.6622	+	10.6622i	−0.562731	+	0.562731i	0.367351	+	0.930082i	$0.380265\pi$
$360$		0			0
$361$		−	9.14746i		−	0.481445i
$362$	−9.48440	−	2.54134i	−0.498489	−	0.133570i
$363$		0			0
$364$	−1.69102	+	2.92894i	−0.0886336	+	0.153518i
$365$	8.22694	+	30.7033i	0.430618	+	1.60709i
$366$		0			0
$367$	5.50723	−	20.5533i	0.287475	−	1.07287i	−0.659536	−	0.751673i	$-0.729247\pi$
$367$	5.50723	−	20.5533i	0.287475	−	1.07287i	0.947012	−	0.321200i	$-0.104086\pi$
$368$		−	7.90938i		−	0.412305i
$369$		0			0
$370$		−	15.2800i		−	0.794367i
$371$	−16.9767	+	9.80150i	−0.881387	+	0.508869i
$372$		0			0
$373$	1.17019	−	2.02682i	0.0605899	−	0.104945i	−0.834139	−	0.551554i	$-0.814035\pi$
$373$	1.17019	−	2.02682i	0.0605899	−	0.104945i	0.894729	+	0.446609i	$0.147368\pi$
$374$	−9.09960	+	2.43823i	−0.470529	+	0.126078i
$375$		0			0
$376$	17.3673	−	10.0270i	0.895652	−	0.517105i
$377$	−11.8270	+	15.6785i	−0.609124	+	0.807483i
$378$		0			0
$379$	−16.7020	−	16.7020i	−0.857924	−	0.857924i	0.133170	−	0.991093i	$-0.457484\pi$
$379$	−16.7020	−	16.7020i	−0.857924	−	0.857924i	−0.991093	+	0.133170i	$0.957484\pi$
$380$	1.89365	+	0.507401i	0.0971420	+	0.0260291i
$381$		0			0
$382$	3.28357	+	1.89577i	0.168002	+	0.0969961i
$383$	−4.48217	+	7.76335i	−0.229028	+	0.396689i	−0.957520	−	0.288365i	$-0.906888\pi$
$383$	−4.48217	+	7.76335i	−0.229028	+	0.396689i	0.728492	+	0.685054i	$0.240222\pi$
$384$		0			0
$385$	−7.48257	−	2.00495i	−0.381347	−	0.102182i
$386$	10.7716			0.548260
$387$		0			0
$388$	−2.82097	−	2.82097i	−0.143213	−	0.143213i
$389$	1.66667	−	6.22009i	0.0845034	−	0.315371i	−0.910716	−	0.413033i	$-0.864470\pi$
$389$	1.66667	−	6.22009i	0.0845034	−	0.315371i	0.995220	+	0.0976615i	$0.0311362\pi$
$390$		0			0
$391$	10.9122	−	2.92391i	0.551852	−	0.147868i
$392$	11.9347	−	3.19789i	0.602792	−	0.161518i
$393$		0			0
$394$	−9.10790	+	33.9911i	−0.458849	+	1.71245i
$395$	−8.93273	−	8.93273i	−0.449454	−	0.449454i
$396$		0			0
$397$	−33.1071			−1.66160			−0.830798	−	0.556574i	$-0.812116\pi$
$397$	−33.1071			−1.66160			−0.830798	+	0.556574i	$0.812116\pi$
$398$	17.2075	+	4.61074i	0.862535	+	0.231116i
$399$		0			0
$400$	−0.727395	+	1.25988i	−0.0363697	+	0.0629942i
$401$	2.97078	+	1.71518i	0.148354	+	0.0856521i	0.572339	−	0.820017i	$-0.306036\pi$
$401$	2.97078	+	1.71518i	0.148354	+	0.0856521i	−0.423986	+	0.905669i	$0.639369\pi$
$402$		0			0
$403$	16.2419	+	4.35201i	0.809068	+	0.216789i
$404$	−2.59185	−	2.59185i	−0.128950	−	0.128950i
$405$		0			0
$406$	−27.5370	+	3.85584i	−1.36664	+	0.191362i
$407$	3.72784	−	2.15227i	0.184782	−	0.106684i
$408$		0			0
$409$	−8.27727	+	2.21789i	−0.409285	+	0.109667i	−0.457586	−	0.889165i	$-0.651286\pi$
$409$	−8.27727	+	2.21789i	−0.409285	+	0.109667i	0.0483015	+	0.998833i	$0.484619\pi$
$410$	15.1833	−	26.2983i	0.749850	−	1.29878i
$411$		0			0
$412$	−0.506545	+	0.292454i	−0.0249557	+	0.0144082i
$413$		−	31.2762i		−	1.53900i
$414$		0			0
$415$			3.42514i			0.168133i
$416$	−1.43557	+	5.35761i	−0.0703845	+	0.262679i
$417$		0			0
$418$	1.19924	+	4.47564i	0.0586569	+	0.218911i
$419$	−0.276281	+	0.478533i	−0.0134972	+	0.0233779i	−0.872695	−	0.488266i	$-0.837630\pi$
$419$	−0.276281	+	0.478533i	−0.0134972	+	0.0233779i	0.859198	+	0.511643i	$0.170963\pi$
$420$		0			0
$421$	19.8159	+	5.30967i	0.965770	+	0.258777i	0.707041	−	0.707173i	$-0.250030\pi$
$421$	19.8159	+	5.30967i	0.965770	+	0.258777i	0.258729	+	0.965950i	$0.416696\pi$
$422$			9.53403i			0.464109i
$423$		0			0
$424$	−10.5416	+	10.5416i	−0.511945	+	0.511945i
$425$	−2.00710	−	0.537800i	−0.0973586	−	0.0260871i
$426$		0			0
$427$	−25.2905	+	6.77658i	−1.22389	+	0.327942i
$428$	−1.58887	+	2.75200i	−0.0768009	+	0.133023i
$429$		0			0
$430$	−4.40407	−	7.62808i	−0.212383	−	0.367858i
$431$			7.48413i			0.360498i	0.983621	+	0.180249i	$0.0576903\pi$
$431$			7.48413i			0.360498i	−0.983621	+	0.180249i	$0.942310\pi$
$432$		0			0
$433$	16.1248	−	16.1248i	0.774911	−	0.774911i	−0.204050	−	0.978961i	$-0.565410\pi$
$433$	16.1248	−	16.1248i	0.774911	−	0.774911i	0.978961	+	0.204050i	$0.0654104\pi$
$434$	11.9035	+	20.6175i	0.571388	+	0.989674i
$435$		0			0
$436$	1.68044	−	2.91061i	0.0804787	−	0.139393i
$437$	−1.43812	−	5.36715i	−0.0687947	−	0.256745i
$438$		0			0
$439$	1.02365	−	0.591004i	0.0488561	−	0.0282071i	−0.475373	−	0.879784i	$-0.657687\pi$
$439$	1.02365	−	0.591004i	0.0488561	−	0.0282071i	0.524229	+	0.851577i	$0.324354\pi$
$440$	−5.89123			−0.280853
$441$		0			0
$442$	−35.0702			−1.66812
$443$	−3.52628	+	13.1603i	−0.167539	+	0.625263i	0.830164	+	0.557519i	$0.188247\pi$
$443$	−3.52628	+	13.1603i	−0.167539	+	0.625263i	−0.997703	+	0.0677439i	$0.978420\pi$
$444$		0			0
$445$	3.56788	+	13.3155i	0.169134	+	0.631216i
$446$	0.717604	+	2.67814i	0.0339796	+	0.126813i
$447$		0			0
$448$	19.7169	−	11.3835i	0.931534	−	0.537821i
$449$	15.2510	−	15.2510i	0.719737	−	0.719737i	−0.248814	−	0.968551i	$-0.580041\pi$
$449$	15.2510	−	15.2510i	0.719737	−	0.719737i	0.968551	+	0.248814i	$0.0800408\pi$
$450$		0			0
$451$	8.55461			0.402821
$452$	0.602631	+	0.161475i	0.0283454	+	0.00759512i
$453$		0			0
$454$	−12.7645	+	3.42023i	−0.599066	+	0.160519i
$455$	−24.9745	−	14.4191i	−1.17082	−	0.675976i
$456$		0			0
$457$	−24.0428	+	13.8811i	−1.12468	+	0.649332i	−0.942591	−	0.333951i	$-0.891618\pi$
$457$	−24.0428	+	13.8811i	−1.12468	+	0.649332i	−0.182086	+	0.983283i	$0.558285\pi$
$458$		−	38.3484i		−	1.79190i
$459$		0			0
$460$	−1.10562			−0.0515499
$461$	−6.84572	+	25.5486i	−0.318837	+	1.18992i	0.601527	+	0.798852i	$0.294559\pi$
$461$	−6.84572	+	25.5486i	−0.318837	+	1.18992i	−0.920364	+	0.391063i	$0.872107\pi$
$462$		0			0
$463$	19.8255	+	11.4462i	0.921367	+	0.531952i	0.884071	−	0.467353i	$-0.154792\pi$
$463$	19.8255	+	11.4462i	0.921367	+	0.531952i	0.0372963	+	0.999304i	$0.488125\pi$
$464$	−22.1531	+	9.39020i	−1.02843	+	0.435929i
$465$		0			0
$466$	1.71841	−	6.41321i	0.0796040	−	0.297086i
$467$	8.43163	−	8.43163i	0.390169	−	0.390169i	−0.484578	−	0.874748i	$-0.661027\pi$
$467$	8.43163	−	8.43163i	0.390169	−	0.390169i	0.874748	+	0.484578i	$0.161027\pi$
$468$		0			0
$469$			39.7372i			1.83489i
$470$	−13.3805	−	23.1757i	−0.617196	−	1.06902i
$471$		0			0
$472$	−6.15615	−	22.9751i	−0.283360	−	1.05751i
$473$	1.24068	−	2.14891i	0.0570463	−	0.0988072i
$474$		0			0
$475$	−0.264517	+	0.987191i	−0.0121369	+	0.0452954i
$476$	−4.18489	−	4.18489i	−0.191814	−	0.191814i
$477$		0			0
$478$	−12.8150	−	12.8150i	−0.586144	−	0.586144i
$479$	−6.76315	+	25.2404i	−0.309016	+	1.15326i	0.620416	+	0.784273i	$0.286964\pi$
$479$	−6.76315	+	25.2404i	−0.309016	+	1.15326i	−0.929433	+	0.368992i	$0.879703\pi$
$480$		0			0
$481$	15.4785	−	4.14746i	0.705760	−	0.189108i
$482$	19.9897	−	5.35623i	0.910507	−	0.243970i
$483$		0			0
$484$	−1.35867	−	2.35329i	−0.0617578	−	0.106968i
$485$	24.0539	−	24.0539i	1.09223	−	1.09223i
$486$		0			0
$487$	24.6894			1.11878			0.559392	−	0.828903i	$-0.311035\pi$
$487$	24.6894			1.11878			0.559392	+	0.828903i	$0.311035\pi$
$488$	−17.2442	+	9.95596i	−0.780609	+	0.450685i
$489$		0			0
$490$	−4.26739	−	15.9261i	−0.192781	−	0.719469i
$491$	31.1399	−	8.34392i	1.40532	−	0.376556i	0.525071	−	0.851059i	$-0.324039\pi$
$491$	31.1399	−	8.34392i	1.40532	−	0.376556i	0.880254	+	0.474503i	$0.157372\pi$
$492$		0			0
$493$	−21.1447	−	27.0922i	−0.952308	−	1.22017i
$494$			17.2493i			0.776081i
$495$		0			0
$496$	14.5671	+	14.5671i	0.654083	+	0.654083i
$497$	−6.68061	−	11.5712i	−0.299666	−	0.519037i
$498$		0			0
$499$	5.23568	+	3.02282i	0.234381	+	0.135320i	0.612592	−	0.790400i	$-0.290127\pi$
$499$	5.23568	+	3.02282i	0.234381	+	0.135320i	−0.378210	+	0.925720i	$0.623460\pi$
$500$	−2.52835	−	1.45975i	−0.113071	−	0.0652818i
$501$		0			0
$502$	−1.09246	+	0.630734i	−0.0487590	+	0.0281510i
$503$	−28.9708	−	28.9708i	−1.29175	−	1.29175i	−0.933707	−	0.358039i	$-0.883445\pi$
$503$	−28.9708	−	28.9708i	−1.29175	−	1.29175i	−0.358039	−	0.933707i	$-0.616555\pi$
$504$		0			0
$505$	22.1003	−	22.1003i	0.983450	−	0.983450i
$506$	−1.30657	−	2.26305i	−0.0580841	−	0.100605i
$507$		0			0
$508$	1.50150	+	5.60366i	0.0666181	+	0.248622i
$509$	−7.53944	−	4.35290i	−0.334180	−	0.192939i	0.323515	−	0.946223i	$-0.395135\pi$
$509$	−7.53944	−	4.35290i	−0.334180	−	0.192939i	−0.657695	+	0.753284i	$0.728469\pi$
$510$		0			0
$511$	−45.5892	−	12.2156i	−2.01675	−	0.540385i
$512$	11.6610	−	11.6610i	0.515346	−	0.515346i
$513$		0			0
$514$	−9.22151	−	9.22151i	−0.406743	−	0.406743i
$515$	−2.49370	−	4.31922i	−0.109886	−	0.190328i
$516$		0			0
$517$	3.76943	−	6.52885i	0.165780	−	0.287139i
$518$	19.6485	+	11.3441i	0.863304	+	0.498429i
$519$		0			0
$520$	−21.1841	−	5.67625i	−0.928983	−	0.248920i
$521$	13.1697			0.576977			0.288489	−	0.957483i	$-0.406847\pi$
$521$	13.1697			0.576977			0.288489	+	0.957483i	$0.406847\pi$
$522$		0			0
$523$	8.93957			0.390900			0.195450	−	0.980714i	$-0.437383\pi$
$523$	8.93957			0.390900			0.195450	+	0.980714i	$0.437383\pi$
$524$	5.86137	+	1.57055i	0.256055	+	0.0686098i
$525$		0			0
$526$	−14.6672	−	8.46812i	−0.639521	−	0.369228i
$527$	−14.7124	+	25.4826i	−0.640882	+	1.11004i
$528$		0			0
$529$	−9.93317	−	17.2048i	−0.431877	−	0.748033i
$530$	14.0672	+	14.0672i	0.611038	+	0.611038i
$531$		0			0
$532$	−2.05834	+	2.05834i	−0.0892402	+	0.0892402i
$533$	30.7612	+	8.24245i	1.33242	+	0.357020i
$534$		0			0
$535$	−23.4659	−	13.5480i	−1.01452	−	0.585732i
$536$	7.82154	+	29.1904i	0.337839	+	1.26083i
$537$		0			0
$538$	4.64537	+	8.04602i	0.200276	+	0.346889i
$539$	3.28440	−	3.28440i	0.141469	−	0.141469i
$540$		0			0
$541$	22.5156	+	22.5156i	0.968021	+	0.968021i	0.999504	−	0.0314831i	$-0.0100230\pi$
$541$	22.5156	+	22.5156i	0.968021	+	0.968021i	−0.0314831	+	0.999504i	$0.510023\pi$
$542$	−35.6163	+	20.5631i	−1.52985	+	0.883260i
$543$		0			0
$544$	−8.40577	−	4.85307i	−0.360394	−	0.208074i
$545$	24.8183	+	14.3289i	1.06310	+	0.613781i
$546$		0			0
$547$	13.5727	+	23.5087i	0.580328	+	1.00516i	0.995440	+	0.0953875i	$0.0304090\pi$
$547$	13.5727	+	23.5087i	0.580328	+	1.00516i	−0.415112	+	0.909770i	$0.636258\pi$
$548$	4.45860	+	4.45860i	0.190462	+	0.190462i
$549$		0			0
$550$			0.480640i			0.0204946i
$551$	−13.3253	+	10.4000i	−0.567677	+	0.443055i
$552$		0			0
$553$	18.1184	−	4.85480i	0.770471	−	0.206447i
$554$	−3.25074	−	12.1319i	−0.138111	−	0.515436i
$555$		0			0
$556$	1.69191	−	0.976824i	0.0717529	−	0.0414266i
$557$	−21.8377			−0.925292			−0.462646	−	0.886543i	$-0.653100\pi$
$557$	−21.8377			−0.925292			−0.462646	+	0.886543i	$0.653100\pi$
$558$		0			0
$559$	6.53180	−	6.53180i	0.276266	−	0.276266i
$560$	−17.6657	−	30.5979i	−0.746513	−	1.29300i
$561$		0			0
$562$	37.0731	−	9.93370i	1.56383	−	0.419028i
$563$	−1.26936	+	0.340125i	−0.0534973	+	0.0143345i	−0.285468	−	0.958388i	$-0.592149\pi$
$563$	−1.26936	+	0.340125i	−0.0534973	+	0.0143345i	0.231971	+	0.972723i	$0.425483\pi$
$564$		0			0
$565$	−1.37686	+	5.13853i	−0.0579251	+	0.216180i
$566$	−2.34061	−	2.34061i	−0.0983832	−	0.0983832i
$567$		0			0
$568$	−7.18505	−	7.18505i	−0.301478	−	0.301478i
$569$	−3.55717	+	13.2755i	−0.149124	+	0.556540i	0.850413	+	0.526116i	$0.176352\pi$
$569$	−3.55717	+	13.2755i	−0.149124	+	0.556540i	−0.999537	+	0.0304237i	$0.990314\pi$
$570$		0			0
$571$	1.96191	−	3.39812i	0.0821032	−	0.142207i	−0.822050	−	0.569415i	$-0.807170\pi$
$571$	1.96191	−	3.39812i	0.0821032	−	0.142207i	0.904153	+	0.427208i	$0.140503\pi$
$572$	0.250252	+	0.933954i	0.0104636	+	0.0390506i
$573$		0			0
$574$	22.5446	+	39.0484i	0.940993	+	1.62985i
$575$		−	0.576380i		−	0.0240367i
$576$		0			0
$577$	−11.4873	+	11.4873i	−0.478224	+	0.478224i	−0.904563	−	0.426340i	$-0.859803\pi$
$577$	−11.4873	+	11.4873i	−0.478224	+	0.478224i	0.426340	+	0.904563i	$0.359803\pi$
$578$	9.25369	−	34.5352i	0.384903	−	1.43648i
$579$		0			0
$580$	1.31262	+	3.09670i	0.0545036	+	0.128584i
$581$	−4.40438	−	2.54287i	−0.182724	−	0.105496i
$582$		0			0
$583$	−1.45051	+	5.41339i	−0.0600741	+	0.224200i
$584$	−35.8936			−1.48529
$585$		0			0
$586$		−	23.3794i		−	0.965794i
$587$	−27.9575	+	16.1413i	−1.15393	+	0.666222i	−0.949842	−	0.312730i	$-0.898756\pi$
$587$	−27.9575	+	16.1413i	−1.15393	+	0.666222i	−0.204089	+	0.978952i	$0.565423\pi$
$588$		0			0
$589$	12.5336	+	7.23629i	0.516439	+	0.298166i
$590$	−30.6589	+	8.21502i	−1.26221	+	0.338207i
$591$		0			0
$592$	18.9638	+	5.08132i	0.779405	+	0.208841i
$593$	−8.81748			−0.362090			−0.181045	−	0.983475i	$-0.557948\pi$
$593$	−8.81748			−0.362090			−0.181045	+	0.983475i	$0.557948\pi$
$594$		0			0
$595$	35.6838	−	35.6838i	1.46289	−	1.46289i
$596$	−0.406920	+	0.234935i	−0.0166681	+	0.00962332i
$597$		0			0
$598$	−2.51778	−	9.39650i	−0.102960	−	0.384251i
$599$	−7.24767	−	27.0487i	−0.296132	−	1.10518i	−0.940315	−	0.340307i	$-0.889469\pi$
$599$	−7.24767	−	27.0487i	−0.296132	−	1.10518i	0.644183	−	0.764871i	$-0.277198\pi$
$600$		0			0
$601$	1.99094	−	7.43028i	0.0812120	−	0.303087i	−0.913358	−	0.407158i	$-0.866520\pi$
$601$	1.99094	−	7.43028i	0.0812120	−	0.303087i	0.994570	+	0.104070i	$0.0331867\pi$
$602$	13.0786			0.533043
$603$		0			0
$604$	4.74870			0.193222
$605$	20.0661	−	11.5852i	0.815802	−	0.471004i
$606$		0			0
$607$	6.41790	+	23.9519i	0.260494	+	0.972178i	0.964951	+	0.262431i	$0.0845242\pi$
$607$	6.41790	+	23.9519i	0.260494	+	0.972178i	−0.704456	+	0.709747i	$0.748809\pi$
$608$	−2.38698	+	4.13438i	−0.0968050	+	0.167671i
$609$		0			0
$610$	13.2856	+	23.0114i	0.537920	+	0.931705i
$611$	19.8450	−	19.8450i	0.802842	−	0.802842i
$612$		0			0
$613$		−	4.60604i		−	0.186036i	−0.995664	−	0.0930181i	$-0.970349\pi$
$613$		−	4.60604i		−	0.186036i	0.995664	−	0.0930181i	$-0.0296515\pi$
$614$	−21.9747	−	38.0613i	−0.886828	−	1.53603i
$615$		0			0
$616$	4.37373	−	7.57552i	0.176223	−	0.305226i
$617$	−33.9675	+	9.10157i	−1.36748	+	0.366416i	−0.866558	−	0.499076i	$-0.833673\pi$
$617$	−33.9675	+	9.10157i	−1.36748	+	0.366416i	−0.500923	+	0.865492i	$0.667006\pi$
$618$		0			0
$619$	−0.922089	−	0.247073i	−0.0370619	−	0.00993070i	0.240240	−	0.970713i	$-0.422774\pi$
$619$	−0.922089	−	0.247073i	−0.0370619	−	0.00993070i	−0.277302	+	0.960783i	$0.589440\pi$
$620$	2.03628	−	2.03628i	0.0817790	−	0.0817790i
$621$		0			0
$622$		−	23.2060i		−	0.930474i
$623$	−19.7712	−	5.29769i	−0.792118	−	0.212247i
$624$		0			0
$625$	13.2610	−	22.9687i	0.530440	−	0.918748i
$626$	10.9419	+	40.8358i	0.437327	+	1.63213i
$627$		0			0
$628$	0.964315	−	3.59887i	0.0384804	−	0.143611i
$629$			28.0418i			1.11810i
$630$		0			0
$631$		−	4.87983i		−	0.194263i	−0.995272	−	0.0971315i	$-0.969033\pi$
$631$		−	4.87983i		−	0.194263i	0.995272	−	0.0971315i	$-0.0309667\pi$
$632$	12.3539	−	7.13254i	0.491412	−	0.283717i
$633$		0			0
$634$	9.22976	−	15.9864i	0.366560	−	0.634901i
$635$	−47.7814	+	12.8030i	−1.89615	+	0.508071i
$636$		0			0
$637$	14.9748	−	8.64570i	0.593323	−	0.342555i
$638$	−4.78731	+	6.34627i	−0.189531	+	0.251251i
$639$		0			0
$640$	−21.3014	−	21.3014i	−0.842010	−	0.842010i
$641$	−5.90023	−	1.58096i	−0.233045	−	0.0624442i	0.140406	−	0.990094i	$-0.455159\pi$
$641$	−5.90023	−	1.58096i	−0.233045	−	0.0624442i	−0.373451	+	0.927650i	$0.621826\pi$
$642$		0			0
$643$	−30.1525	−	17.4086i	−1.18910	−	0.686526i	−0.230997	−	0.972955i	$-0.574199\pi$
$643$	−30.1525	−	17.4086i	−1.18910	−	0.686526i	−0.958102	+	0.286428i	$0.907532\pi$
$644$	0.820829	−	1.42172i	0.0323452	−	0.0560235i
$645$		0			0
$646$	−29.1564	−	7.81244i	−1.14714	−	0.307376i
$647$	−22.6415			−0.890129			−0.445065	−	0.895498i	$-0.646819\pi$
$647$	−22.6415			−0.890129			−0.445065	+	0.895498i	$0.646819\pi$
$648$		0			0
$649$	−6.32269	−	6.32269i	−0.248187	−	0.248187i
$650$	−0.463101	+	1.72832i	−0.0181643	+	0.0677902i
$651$		0			0
$652$	4.29405	−	1.15059i	0.168168	−	0.0450604i
$653$	26.7594	−	7.17016i	1.04718	−	0.280590i	0.306092	−	0.952002i	$-0.400979\pi$
$653$	26.7594	−	7.17016i	1.04718	−	0.280590i	0.741084	+	0.671412i	$0.234312\pi$
$654$		0			0
$655$	−13.3918	+	49.9789i	−0.523261	+	1.95284i
$656$	27.5892	+	27.5892i	1.07718	+	1.07718i
$657$		0			0
$658$	39.7354			1.54905
$659$	45.4870	+	12.1882i	1.77192	+	0.474785i	0.989073	−	0.147427i	$-0.0470992\pi$
$659$	45.4870	+	12.1882i	1.77192	+	0.474785i	0.782849	+	0.622212i	$0.213766\pi$
$660$		0			0
$661$	10.4366	−	18.0767i	0.405937	−	0.703103i	−0.588493	−	0.808502i	$-0.700279\pi$
$661$	10.4366	−	18.0767i	0.405937	−	0.703103i	0.994430	+	0.105399i	$0.0336119\pi$
$662$	−33.3343	−	19.2456i	−1.29558	−	0.748001i
$663$		0			0
$664$	−3.73591	−	1.00104i	−0.144982	−	0.0388477i
$665$	−17.5511	−	17.5511i	−0.680601	−	0.680601i
$666$		0			0
$667$	5.74089	−	7.61040i	0.222288	−	0.294676i
$668$	−0.419247	+	0.242053i	−0.0162212	+	0.00936529i
$669$		0			0
$670$	38.9529	−	10.4374i	1.50488	−	0.403232i
$671$	−3.74271	+	6.48257i	−0.144486	+	0.250257i
$672$		0			0
$673$	31.4119	−	18.1357i	1.21084	−	0.699079i	0.247898	−	0.968786i	$-0.420260\pi$
$673$	31.4119	−	18.1357i	1.21084	−	0.699079i	0.962942	+	0.269707i	$0.0869270\pi$
$674$			48.2588i			1.85886i
$675$		0			0
$676$			0.0811331i			0.00312050i
$677$	−12.2060	+	45.5535i	−0.469115	+	1.75076i	0.173756	+	0.984789i	$0.444409\pi$
$677$	−12.2060	+	45.5535i	−0.469115	+	1.75076i	−0.642872	+	0.765974i	$0.722257\pi$
$678$		0			0
$679$	13.0729	+	48.7889i	0.501693	+	1.87235i
$680$	19.1891	−	33.2365i	0.735869	−	1.27456i
$681$		0			0
$682$	6.57434	+	1.76159i	0.251745	+	0.0674548i
$683$		−	30.2941i		−	1.15917i	−0.814911	−	0.579585i	$-0.803214\pi$
$683$		−	30.2941i		−	1.15917i	0.814911	−	0.579585i	$-0.196786\pi$
$684$		0			0
$685$	−38.0177	+	38.0177i	−1.45258	+	1.45258i
$686$	−11.2646	−	3.01834i	−0.430084	−	0.115241i
$687$		0			0
$688$	10.9317	−	2.92913i	0.416766	−	0.111672i
$689$	−10.4317	+	18.0682i	−0.397416	+	0.688344i
$690$		0			0
$691$	−8.52230	−	14.7611i	−0.324204	−	0.561537i	0.657147	−	0.753762i	$-0.271763\pi$
$691$	−8.52230	−	14.7611i	−0.324204	−	0.561537i	−0.981351	+	0.192225i	$0.938430\pi$
$692$		−	0.688161i		−	0.0261600i
$693$		0			0
$694$	16.7299	−	16.7299i	0.635060	−	0.635060i
$695$	8.32921	+	14.4266i	0.315945	+	0.547233i
$696$		0			0
$697$	−27.8644	+	48.2625i	−1.05544	+	1.82807i
$698$	−5.62302	−	20.9854i	−0.212834	−	0.794309i
$699$		0			0
$700$	−0.261499	+	0.150977i	−0.00988375	+	0.00570639i
$701$	−9.26597			−0.349971			−0.174986	−	0.984571i	$-0.555988\pi$
$701$	−9.26597			−0.349971			−0.174986	+	0.984571i	$0.555988\pi$
$702$		0			0
$703$	13.7923			0.520188
$704$	1.68463	−	6.28714i	0.0634920	−	0.236955i
$705$		0			0
$706$	−2.36062	−	8.80995i	−0.0888431	−	0.331567i
$707$	12.0112	+	44.8263i	0.451726	+	1.68587i
$708$		0			0
$709$	−2.72384	+	1.57261i	−0.102296	+	0.0590606i	−0.550275	−	0.834983i	$-0.685477\pi$
$709$	−2.72384	+	1.57261i	−0.102296	+	0.0590606i	0.447979	+	0.894044i	$0.352144\pi$
$710$	−9.58803	+	9.58803i	−0.359832	+	0.359832i
$711$		0			0
$712$	−15.5664			−0.583376
$713$	−7.88390	−	2.11248i	−0.295254	−	0.0791131i
$714$		0			0
$715$	−7.96366	+	2.13386i	−0.297824	+	0.0798017i
$716$	−0.498197	−	0.287634i	−0.0186185	−	0.0107494i
$717$		0			0
$718$	−19.6774	+	11.3608i	−0.734355	+	0.423980i
$719$			47.8983i			1.78631i	0.449753	+	0.893153i	$0.351512\pi$
$719$			47.8983i			1.78631i	−0.449753	+	0.893153i	$0.648488\pi$
$720$		0			0
$721$	7.40544			0.275793
$722$	3.56756	−	13.3143i	0.132771	−	0.495507i
$723$		0			0
$724$	−1.52728	−	0.881777i	−0.0567610	−	0.0327710i
$725$	−1.61436	+	0.684291i	−0.0599560	+	0.0254139i
$726$		0			0
$727$	−8.27648	+	30.8883i	−0.306958	+	1.14558i	0.624289	+	0.781193i	$0.285389\pi$
$727$	−8.27648	+	30.8883i	−0.306958	+	1.14558i	−0.931247	+	0.364389i	$0.881278\pi$
$728$	23.0264	−	23.0264i	0.853416	−	0.853416i
$729$		0			0
$730$			47.8979i			1.77278i
$731$	8.08234	+	13.9990i	0.298936	+	0.517773i
$732$		0			0
$733$	−0.468531	−	1.74858i	−0.0173056	−	0.0645854i	0.956733	−	0.290967i	$-0.0939770\pi$
$733$	−0.468531	−	1.74858i	−0.0173056	−	0.0645854i	−0.974039	+	0.226382i	$0.927310\pi$
$734$	16.0318	−	27.7679i	0.591744	−	1.02493i
$735$		0			0
$736$	0.696830	−	2.60061i	0.0256855	−	0.0958596i
$737$	8.03313	+	8.03313i	0.295904	+	0.295904i
$738$		0			0
$739$	−19.0901	−	19.0901i	−0.702240	−	0.702240i	0.262651	−	0.964891i	$-0.415403\pi$
$739$	−19.0901	−	19.0901i	−0.702240	−	0.702240i	−0.964891	+	0.262651i	$0.915403\pi$
$740$	0.710298	−	2.65087i	0.0261111	−	0.0974479i
$741$		0			0
$742$	−28.5326	+	7.64528i	−1.04746	+	0.280667i
$743$	27.4067	−	7.34361i	1.00545	−	0.269411i	0.281726	−	0.959495i	$-0.409093\pi$
$743$	27.4067	−	7.34361i	1.00545	−	0.269411i	0.723729	+	0.690084i	$0.242427\pi$
$744$		0			0
$745$	−2.00325	−	3.46973i	−0.0733934	−	0.127121i
$746$	2.49370	−	2.49370i	0.0913008	−	0.0913008i
$747$		0			0
$748$	−1.69200			−0.0618658
$749$	34.8427	−	20.1165i	1.27313	−	0.735040i
$750$		0			0
$751$	3.71835	+	13.8771i	0.135685	+	0.506382i	0.999994	+	0.00342162i	$0.00108914\pi$
$751$	3.71835	+	13.8771i	0.135685	+	0.506382i	−0.864310	+	0.502960i	$0.832244\pi$
$752$	33.2127	−	8.89932i	1.21114	−	0.324525i
$753$		0			0
$754$	−23.3292	+	18.2077i	−0.849599	+	0.663086i
$755$			40.4914i			1.47363i
$756$		0			0
$757$	2.14430	+	2.14430i	0.0779359	+	0.0779359i	0.745000	−	0.667064i	$-0.232449\pi$
$757$	2.14430	+	2.14430i	0.0779359	+	0.0779359i	−0.667064	+	0.745000i	$0.732449\pi$
$758$	−17.7962	−	30.8239i	−0.646388	−	1.11958i
$759$		0			0
$760$	−16.3474	−	9.43816i	−0.592982	−	0.342358i
$761$	27.5341	+	15.8968i	0.998111	+	0.576260i	0.907689	−	0.419644i	$-0.137845\pi$
$761$	27.5341	+	15.8968i	0.998111	+	0.576260i	0.0904223	+	0.995904i	$0.471178\pi$
$762$		0			0
$763$	−36.8509	+	21.2759i	−1.33409	+	0.770238i
$764$	0.481530	+	0.481530i	0.0174211	+	0.0174211i
$765$		0			0
$766$	−9.55164	+	9.55164i	−0.345115	+	0.345115i
$767$	−16.6436	−	28.8275i	−0.600964	−	1.04090i
$768$		0			0
$769$	3.17584	+	11.8524i	0.114524	+	0.427409i	0.999251	−	0.0387008i	$-0.0123219\pi$
$769$	3.17584	+	11.8524i	0.114524	+	0.427409i	−0.884727	+	0.466110i	$0.845655\pi$
$770$	−10.1091	−	5.83649i	−0.364306	−	0.210332i
$771$		0			0
$772$	1.86873	+	0.500725i	0.0672571	+	0.0180215i
$773$	21.0505	−	21.0505i	0.757134	−	0.757134i	−0.218665	−	0.975800i	$-0.570170\pi$
$773$	21.0505	−	21.0505i	0.757134	−	0.757134i	0.975800	+	0.218665i	$0.0701703\pi$
$774$		0			0
$775$	1.06155	+	1.06155i	0.0381319	+	0.0381319i
$776$	19.2064	+	33.2665i	0.689470	+	1.19420i
$777$		0			0
$778$	4.85174	−	8.40346i	0.173943	−	0.301278i
$779$	23.7379	+	13.7051i	0.850499	+	0.491036i
$780$		0			0
$781$	−3.68971	−	0.988655i	−0.132028	−	0.0353769i
$782$	17.0232			0.608749
$783$		0			0
$784$	21.1848			0.756601
$785$	30.6870	+	8.22255i	1.09526	+	0.293475i
$786$		0			0
$787$	42.0497	+	24.2774i	1.49891	+	0.865396i	0.999999	−	0.00125841i	$-0.000400565\pi$
$787$	42.0497	+	24.2774i	1.49891	+	0.865396i	0.498910	+	0.866654i	$0.333734\pi$
$788$	−3.16020	+	5.47362i	−0.112577	+	0.194990i
$789$		0			0
$790$	−9.51796	−	16.4856i	−0.338634	−	0.586531i
$791$	−5.58542	−	5.58542i	−0.198595	−	0.198595i
$792$		0			0
$793$	−19.7043	+	19.7043i	−0.699720	+	0.699720i
$794$	−48.1880	−	12.9119i	−1.71013	−	0.458228i
$795$		0			0
$796$	2.77094	+	1.59981i	0.0982135	+	0.0567036i
$797$	3.35424	+	12.5182i	0.118813	+	0.443418i	0.999544	−	0.0302002i	$-0.00961447\pi$
$797$	3.35424	+	12.5182i	0.118813	+	0.443418i	−0.880730	+	0.473618i	$0.842948\pi$
$798$		0			0
$799$	24.5559	+	42.5320i	0.868724	+	1.50467i
$800$	−0.350166	+	0.350166i	−0.0123802	+	0.0123802i
$801$		0			0
$802$	3.65510	+	3.65510i	0.129066	+	0.129066i
$803$	−11.6856	+	6.74668i	−0.412376	+	0.238085i
$804$		0			0
$805$	12.1227	+	6.99906i	0.427270	+	0.246685i
$806$	21.9431	+	12.6689i	0.772914	+	0.446242i
$807$		0			0
$808$	17.6465	+	30.5646i	0.620801	+	1.07526i
$809$	31.2753	+	31.2753i	1.09958	+	1.09958i	0.994459	+	0.105121i	$0.0335231\pi$
$809$	31.2753	+	31.2753i	1.09958	+	1.09958i	0.105121	+	0.994459i	$0.466477\pi$
$810$		0			0
$811$			52.5371i			1.84483i	0.386202	+	0.922414i	$0.373787\pi$
$811$			52.5371i			1.84483i	−0.386202	+	0.922414i	$0.626213\pi$
$812$	−4.95655	−	0.611139i	−0.173941	−	0.0214468i
$813$		0			0
$814$	6.26534	−	1.67879i	0.219600	−	0.0588416i
$815$	9.81085	+	36.6146i	0.343659	+	1.28255i
$816$		0			0
$817$	6.88542	−	3.97530i	0.240890	−	0.139078i
$818$	−12.9127			−0.451483
$819$		0			0
$820$	3.85659	−	3.85659i	0.134678	−	0.134678i
$821$	−10.2315	−	17.7215i	−0.357082	−	0.618485i	0.630390	−	0.776279i	$-0.282895\pi$
$821$	−10.2315	−	17.7215i	−0.357082	−	0.618485i	−0.987472	+	0.157794i	$0.949562\pi$
$822$		0			0
$823$	−13.3538	+	3.57813i	−0.465483	+	0.124726i	−0.483935	−	0.875104i	$-0.660793\pi$
$823$	−13.3538	+	3.57813i	−0.465483	+	0.124726i	0.0184521	+	0.999830i	$0.494126\pi$
$824$	5.43993	−	1.45763i	0.189509	−	0.0507788i
$825$		0			0
$826$	12.1979	−	45.5232i	0.424419	−	1.58395i
$827$	−2.40919	−	2.40919i	−0.0837756	−	0.0837756i	0.663977	−	0.747753i	$-0.268867\pi$
$827$	−2.40919	−	2.40919i	−0.0837756	−	0.0837756i	−0.747753	+	0.663977i	$0.768867\pi$
$828$		0			0
$829$	23.4435	+	23.4435i	0.814225	+	0.814225i	0.985264	−	0.171039i	$-0.0547125\pi$
$829$	23.4435	+	23.4435i	0.814225	+	0.814225i	−0.171039	+	0.985264i	$0.554713\pi$
$830$	−1.33582	+	4.98536i	−0.0463671	+	0.173044i
$831$		0			0
$832$	12.1154	−	20.9845i	0.420027	−	0.727508i
$833$	7.83152	+	29.2276i	0.271346	+	1.01268i
$834$		0			0
$835$	−2.06394	−	3.57485i	−0.0714256	−	0.123713i
$836$			0.832211i			0.0287826i
$837$		0			0
$838$	−0.588763	+	0.588763i	−0.0203385	+	0.0203385i
$839$	4.30071	−	16.0505i	0.148477	−	0.554124i	−0.851099	−	0.525006i	$-0.824063\pi$
$839$	4.30071	−	16.0505i	0.148477	−	0.554124i	0.999576	−	0.0291187i	$-0.00927009\pi$
$840$		0			0
$841$	−28.1314	−	7.04426i	−0.970050	−	0.242906i
$842$	26.7717	+	15.4567i	0.922614	+	0.532672i
$843$		0			0
$844$	−0.443195	+	1.65403i	−0.0152554	+	0.0569340i
$845$	−0.691808			−0.0237989
$846$		0			0
$847$			34.4039i			1.18213i
$848$	−22.1366	+	12.7805i	−0.760173	+	0.438886i
$849$		0			0
$850$	−2.71163	−	1.56556i	−0.0930080	−	0.0536982i
$851$	−7.51334	+	2.01319i	−0.257554	+	0.0690114i
$852$		0			0
$853$	−20.2571	−	5.42787i	−0.693589	−	0.185847i	−0.105232	−	0.994448i	$-0.533558\pi$
$853$	−20.2571	−	5.42787i	−0.693589	−	0.185847i	−0.588357	+	0.808601i	$0.700225\pi$
$854$	−39.4538			−1.35008
$855$		0			0
$856$	21.6354	−	21.6354i	0.739484	−	0.739484i
$857$	−37.5900	+	21.7026i	−1.28405	+	0.741346i	−0.977586	−	0.210536i	$-0.932479\pi$
$857$	−37.5900	+	21.7026i	−1.28405	+	0.741346i	−0.306463	+	0.951882i	$0.599146\pi$
$858$		0			0
$859$	2.11206	+	7.88230i	0.0720624	+	0.268941i	0.992551	−	0.121828i	$-0.0388758\pi$
$859$	2.11206	+	7.88230i	0.0720624	+	0.268941i	−0.920489	+	0.390769i	$0.872209\pi$
$860$	−0.409452	−	1.52810i	−0.0139622	−	0.0521076i
$861$		0			0
$862$	−2.91885	+	10.8933i	−0.0994164	+	0.371027i
$863$	−8.84629			−0.301131			−0.150566	−	0.988600i	$-0.548110\pi$
$863$	−8.84629			−0.301131			−0.150566	+	0.988600i	$0.548110\pi$
$864$		0			0
$865$	5.86783			0.199512
$866$	29.7588	−	17.1813i	1.01125	−	0.583843i
$867$		0			0
$868$	1.10669	+	4.13021i	0.0375634	+	0.140189i
$869$	2.68131	−	4.64417i	0.0909573	−	0.157543i
$870$		0			0
$871$	21.1461	+	36.6260i	0.716507	+	1.24103i
$872$	−22.8824	+	22.8824i	−0.774895	+	0.774895i
$873$		0			0
$874$		−	8.37287i		−	0.283216i
$875$	18.4816	+	32.0111i	0.624793	+	1.08217i
$876$		0			0
$877$	17.1713	−	29.7416i	0.579834	−	1.00430i	−0.415664	−	0.909518i	$-0.636451\pi$
$877$	17.1713	−	29.7416i	0.579834	−	1.00430i	0.995498	−	0.0947835i	$-0.0302159\pi$
$878$	1.72044	−	0.460989i	0.0580619	−	0.0155576i
$879$		0			0
$880$	−9.75680	−	2.61433i	−0.328902	−	0.0881290i
$881$	10.6186	−	10.6186i	0.357750	−	0.357750i	−0.505233	−	0.862983i	$-0.668594\pi$
$881$	10.6186	−	10.6186i	0.357750	−	0.357750i	0.862983	+	0.505233i	$0.168594\pi$
$882$		0			0
$883$		−	32.4616i		−	1.09242i	−0.837648	−	0.546211i	$-0.816070\pi$
$883$		−	32.4616i		−	1.09242i	0.837648	−	0.546211i	$-0.183930\pi$
$884$	−6.08421	−	1.63026i	−0.204634	−	0.0548316i
$885$		0			0
$886$	−10.2652	+	17.7798i	−0.344864	+	0.597323i
$887$	−6.72883	−	25.1123i	−0.225932	−	0.843190i	−0.982029	−	0.188730i	$-0.939563\pi$
$887$	−6.72883	−	25.1123i	−0.225932	−	0.843190i	0.756097	−	0.654460i	$-0.227104\pi$
$888$		0			0
$889$	19.0102	−	70.9472i	0.637583	−	2.37949i
$890$			20.7725i			0.696295i
$891$		0			0
$892$			0.497979i			0.0166736i
$893$	20.9194	−	12.0778i	0.700039	−	0.404168i
$894$		0			0
$895$	2.45261	−	4.24804i	0.0819817	−	0.141996i
$896$	43.2058	−	11.5770i	1.44341	−	0.386759i
$897$		0			0
$898$	28.1460	−	16.2501i	0.939245	−	0.542274i
$899$	3.44315	+	24.5898i	0.114836	+	0.820114i
$900$		0			0
$901$	−25.8160	−	25.8160i	−0.860056	−	0.860056i
$902$	12.4514	+	3.33635i	0.414587	+	0.111088i
$903$		0			0
$904$	−5.20236	−	3.00359i	−0.173028	−	0.0998978i
$905$	7.51875	−	13.0229i	0.249932	−	0.432895i
$906$		0			0
$907$	33.3545	+	8.93732i	1.10752	+	0.296759i	0.765823	−	0.643052i	$-0.222332\pi$
$907$	33.3545	+	8.93732i	1.10752	+	0.296759i	0.341696	+	0.939810i	$0.388999\pi$
$908$	−2.37346			−0.0787659
$909$		0			0
$910$	−30.7274	−	30.7274i	−1.01860	−	1.01860i
$911$	0.845139	−	3.15410i	0.0280007	−	0.104500i	−0.950511	−	0.310690i	$-0.899440\pi$
$911$	0.845139	−	3.15410i	0.0280007	−	0.104500i	0.978512	+	0.206190i	$0.0661065\pi$
$912$		0			0
$913$	−1.40443	+	0.376316i	−0.0464799	+	0.0124542i
$914$	−40.4085	+	10.8274i	−1.33660	+	0.358140i
$915$		0			0
$916$	1.78265	−	6.65294i	0.0589004	−	0.219819i
$917$	−54.3255	−	54.3255i	−1.79399	−	1.79399i
$918$		0			0
$919$	3.18622			0.105104			0.0525519	−	0.998618i	$-0.483265\pi$
$919$	3.18622			0.105104			0.0525519	+	0.998618i	$0.483265\pi$
$920$	10.2828	+	2.75528i	0.339015	+	0.0908388i
$921$		0			0
$922$	−19.9282	+	34.5166i	−0.656299	+	1.13674i
$923$	−12.3151	−	7.11014i	−0.405357	−	0.234033i
$924$		0			0
$925$	1.38194	+	0.370291i	0.0454380	+	0.0121751i
$926$	24.3923	+	24.3923i	0.801580	+	0.801580i
$927$		0			0
$928$	−8.11125	+	1.13577i	−0.266265	+	0.0372835i
$929$	15.0484	−	8.68817i	0.493721	−	0.285050i	−0.232396	−	0.972621i	$-0.574657\pi$
$929$	15.0484	−	8.68817i	0.493721	−	0.285050i	0.726117	+	0.687572i	$0.241323\pi$
$930$		0			0
$931$	14.3756	−	3.85193i	0.471141	−	0.126242i
$932$	0.596244	−	1.03272i	0.0195306	−	0.0338280i
$933$		0			0
$934$	15.5608	−	8.98403i	0.509165	−	0.293966i
$935$		−	14.4274i		−	0.471827i
$936$		0			0
$937$			14.2919i			0.466897i	0.972369	+	0.233448i	$0.0750010\pi$
$937$			14.2919i			0.466897i	−0.972369	+	0.233448i	$0.924999\pi$
$938$	−15.4977	+	57.8383i	−0.506019	+	1.88849i
$939$		0			0
$940$	−1.24400	−	4.64268i	−0.0405748	−	0.151427i
$941$	11.6261	−	20.1370i	0.378999	−	0.656446i	−0.611918	−	0.790922i	$-0.709602\pi$
$941$	11.6261	−	20.1370i	0.378999	−	0.656446i	0.990917	+	0.134475i	$0.0429349\pi$
$942$		0			0
$943$	−14.9316	−	4.00092i	−0.486241	−	0.130288i
$944$		−	40.7822i		−	1.32735i
$945$		0			0
$946$	2.64392	−	2.64392i	0.0859611	−	0.0859611i
$947$	−40.3682	−	10.8166i	−1.31179	−	0.351493i	−0.465894	−	0.884841i	$-0.654267\pi$
$947$	−40.3682	−	10.8166i	−1.31179	−	0.351493i	−0.845896	+	0.533348i	$0.820934\pi$
$948$		0			0
$949$	−48.5203	+	13.0010i	−1.57504	+	0.422030i
$950$	−0.770020	+	1.33371i	−0.0249827	+	0.0432714i
$951$		0			0
$952$	28.4925	+	49.3505i	0.923448	+	1.59946i
$953$			21.6490i			0.701279i	0.936511	+	0.350640i	$0.114036\pi$
$953$			21.6490i			0.701279i	−0.936511	+	0.350640i	$0.885964\pi$
$954$		0			0
$955$	−4.10592	+	4.10592i	−0.132865	+	0.132865i
$956$	−1.62752	−	2.81894i	−0.0526377	−	0.0911711i
$957$		0			0
$958$	−19.6878	+	34.1003i	−0.636084	+	1.10173i
$959$	−20.6620	−	77.1117i	−0.667211	−	2.49007i
$960$		0			0
$961$	−8.43594	+	4.87049i	−0.272127	+	0.157113i
$962$	24.1468			0.778525
$963$		0			0
$964$	3.71694			0.119715
$965$	−4.26959	+	15.9343i	−0.137443	+	0.512944i
$966$		0			0
$967$	2.75616	+	10.2861i	0.0886323	+	0.330780i	0.995977	−	0.0896068i	$-0.0285610\pi$
$967$	2.75616	+	10.2861i	0.0886323	+	0.330780i	−0.907345	+	0.420387i	$0.861894\pi$
$968$	6.77178	+	25.2726i	0.217653	+	0.812293i
$969$		0			0
$970$	44.3921	−	25.6298i	1.42535	−	0.822924i
$971$	−3.39160	+	3.39160i	−0.108842	+	0.108842i	−0.759430	−	0.650589i	$-0.774522\pi$
$971$	−3.39160	+	3.39160i	−0.108842	+	0.108842i	0.650589	+	0.759430i	$0.274522\pi$
$972$		0			0
$973$	−24.7349			−0.792964
$974$	35.9359	+	9.62901i	1.15146	+	0.308533i
$975$		0			0
$976$	−32.9773	+	8.83623i	−1.05558	+	0.282841i
$977$	17.6662	+	10.1996i	0.565193	+	0.326314i	0.755227	−	0.655463i	$-0.227527\pi$
$977$	17.6662	+	10.1996i	0.565193	+	0.326314i	−0.190034	+	0.981777i	$0.560860\pi$
$978$		0			0
$979$	−5.06784	+	2.92592i	−0.161969	+	0.0935128i
$980$		−	2.96134i		−	0.0945967i
$981$		0			0
$982$	48.5789			1.55022
$983$	−0.910132	+	3.39666i	−0.0290287	+	0.108337i	−0.978920	−	0.204243i	$-0.934527\pi$
$983$	−0.910132	+	3.39666i	−0.0290287	+	0.108337i	0.949891	+	0.312580i	$0.101193\pi$
$984$		0			0
$985$	−46.6726	−	26.9465i	−1.48711	−	0.858586i
$986$	−20.2104	−	47.6798i	−0.643629	−	1.51843i
$987$		0			0
$988$	−0.801843	+	2.99252i	−0.0255100	+	0.0952047i
$989$	−3.17056	+	3.17056i	−0.100818	+	0.100818i
$990$		0			0
$991$			7.89205i			0.250699i	0.992113	+	0.125350i	$0.0400052\pi$
$991$			7.89205i			0.250699i	−0.992113	+	0.125350i	$0.959995\pi$
$992$	3.50628	+	6.07306i	0.111325	+	0.192820i
$993$		0			0
$994$	−5.21095	−	19.4475i	−0.165281	−	0.616838i
$995$	−13.6413	+	23.6274i	−0.432457	+	0.749038i
$996$		0			0
$997$	−2.10421	+	7.85304i	−0.0666412	+	0.248708i	−0.991208	−	0.132311i	$-0.957760\pi$
$997$	−2.10421	+	7.85304i	−0.0666412	+	0.248708i	0.924567	+	0.381019i	$0.124427\pi$
$998$	6.44172	+	6.44172i	0.203909	+	0.203909i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	783.2.m.a.476.21		112
3.2	odd	2		261.2.l.a.41.8	✓	112
9.2	odd	6	inner	783.2.m.a.737.21		112
9.7	even	3		261.2.l.a.128.8	yes	112
29.17	odd	4	inner	783.2.m.a.17.21		112
87.17	even	4		261.2.l.a.104.8	yes	112
261.133	odd	12		261.2.l.a.191.8	yes	112
261.191	even	12	inner	783.2.m.a.278.21		112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.l.a.41.8	✓	112	3.2	odd	2
261.2.l.a.104.8	yes	112	87.17	even	4
261.2.l.a.128.8	yes	112	9.7	even	3
261.2.l.a.191.8	yes	112	261.133	odd	12
783.2.m.a.17.21		112	29.17	odd	4	inner
783.2.m.a.278.21		112	261.191	even	12	inner
783.2.m.a.476.21		112	1.1	even	1	trivial
783.2.m.a.737.21		112	9.2	odd	6	inner

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:	\( N \)	\(=\)	\( 783 = 3^{3} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	783.m (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.45552 + 0.390005i) q^{2} +(0.234384 + 0.135322i) q^{4} +(-1.15386 + 1.99855i) q^{5} +(-1.71329 - 2.96750i) q^{7} +(-1.84266 - 1.84266i) q^{8} +O(q^{10})\)	\(q+(1.45552 + 0.390005i) q^{2} +(0.234384 + 0.135322i) q^{4} +(-1.15386 + 1.99855i) q^{5} +(-1.71329 - 2.96750i) q^{7} +(-1.84266 - 1.84266i) q^{8} +(-2.45892 + 2.45892i) q^{10} +(-0.946251 - 0.253547i) q^{11} +(-3.15830 - 1.82344i) q^{13} +(-1.33638 - 4.98745i) q^{14} +(-2.23402 - 3.86943i) q^{16} +(4.51260 - 4.51260i) q^{17} +(-2.21952 - 2.21952i) q^{19} +(-0.540893 + 0.312285i) q^{20} +(-1.27840 - 0.738086i) q^{22} +(1.53305 + 0.885107i) q^{23} +(-0.162800 - 0.281977i) q^{25} +(-3.88581 - 3.88581i) q^{26} -0.927379i q^{28} +(0.658996 - 5.34469i) q^{29} +(-4.45364 + 1.19335i) q^{31} +(-0.393642 - 1.46909i) q^{32} +(8.32812 - 4.80824i) q^{34} +7.90760 q^{35} +(-3.10705 + 3.10705i) q^{37} +(-2.36493 - 4.09618i) q^{38} +(5.80881 - 1.55647i) q^{40} +(-8.43493 + 2.26013i) q^{41} +(-0.655574 + 2.44664i) q^{43} +(-0.187475 - 0.187475i) q^{44} +(1.88619 + 1.88619i) q^{46} +(-1.99177 + 7.43340i) q^{47} +(-2.37071 + 4.10619i) q^{49} +(-0.126985 - 0.473916i) q^{50} +(-0.493502 - 0.854771i) q^{52} -5.72088i q^{53} +(1.59857 - 1.59857i) q^{55} +(-2.31108 + 8.62508i) q^{56} +(3.04364 - 7.52229i) q^{58} +(7.90468 + 4.56377i) q^{59} +(1.97765 - 7.38070i) q^{61} -6.94778 q^{62} +6.64426i q^{64} +(7.28848 - 4.20801i) q^{65} +(-10.0431 - 5.79839i) q^{67} +(1.66833 - 0.447028i) q^{68} +(11.5097 + 3.08401i) q^{70} +3.89929 q^{71} +(9.73964 - 9.73964i) q^{73} +(-5.73414 + 3.31061i) q^{74} +(-0.219871 - 0.820568i) q^{76} +(0.868799 + 3.24240i) q^{77} +(-1.41681 + 5.28760i) q^{79} +10.3110 q^{80} -13.1587 q^{82} +(1.28536 - 0.742103i) q^{83} +(3.81173 + 14.2256i) q^{85} +(-1.90840 + 3.30545i) q^{86} +(1.27641 + 2.21081i) q^{88} +(4.22391 - 4.22391i) q^{89} +12.4963i q^{91} +(0.239548 + 0.414909i) q^{92} +(-5.79813 + 10.0427i) q^{94} +(6.99684 - 1.87480i) q^{95} +(-14.2384 - 3.81516i) q^{97} +(-5.05205 + 5.05205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 6 q^{2} - 4 q^{7}+O(q^{10}) \) 112 * q + 6 * q^2 - 4 * q^7	\( 112 q + 6 q^{2} - 4 q^{7} - 6 q^{11} + 18 q^{14} + 40 q^{16} - 8 q^{19} + 12 q^{20} + 12 q^{23} - 44 q^{25} + 42 q^{29} - 2 q^{31} + 66 q^{32} - 8 q^{37} - 12 q^{40} + 18 q^{41} - 2 q^{43} + 8 q^{46} - 36 q^{49} - 24 q^{50} - 36 q^{52} + 36 q^{55} - 84 q^{56} + 28 q^{58} - 48 q^{59} - 14 q^{61} - 24 q^{65} + 102 q^{68} - 8 q^{73} - 144 q^{74} + 14 q^{76} + 72 q^{77} - 2 q^{79} + 80 q^{82} + 120 q^{83} - 48 q^{85} - 36 q^{88} - 40 q^{94} - 204 q^{95} + 22 q^{97}+O(q^{100}) \) 112 * q + 6 * q^2 - 4 * q^7 - 6 * q^11 + 18 * q^14 + 40 * q^16 - 8 * q^19 + 12 * q^20 + 12 * q^23 - 44 * q^25 + 42 * q^29 - 2 * q^31 + 66 * q^32 - 8 * q^37 - 12 * q^40 + 18 * q^41 - 2 * q^43 + 8 * q^46 - 36 * q^49 - 24 * q^50 - 36 * q^52 + 36 * q^55 - 84 * q^56 + 28 * q^58 - 48 * q^59 - 14 * q^61 - 24 * q^65 + 102 * q^68 - 8 * q^73 - 144 * q^74 + 14 * q^76 + 72 * q^77 - 2 * q^79 + 80 * q^82 + 120 * q^83 - 48 * q^85 - 36 * q^88 - 40 * q^94 - 204 * q^95 + 22 * q^97

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