LMFDB - Embedded newform 783.2.m.a.737.21

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			737.21
Character	$\chi$	$=$	783.737
Dual form			783.2.m.a.17.21

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.390005 + 1.45552i) q^{2} +(-0.234384 + 0.135322i) q^{4} +(1.15386 + 1.99855i) q^{5} +(-1.71329 + 2.96750i) q^{7} +(1.84266 + 1.84266i) q^{8} +O(q^{10})$	\(q+(0.390005 + 1.45552i) q^{2} +(-0.234384 + 0.135322i) q^{4} +(1.15386 + 1.99855i) q^{5} +(-1.71329 + 2.96750i) q^{7} +(1.84266 + 1.84266i) q^{8} +(-2.45892 + 2.45892i) q^{10} +(-0.253547 - 0.946251i) q^{11} +(3.15830 - 1.82344i) q^{13} +(-4.98745 - 1.33638i) q^{14} +(-2.23402 + 3.86943i) q^{16} +(-4.51260 + 4.51260i) q^{17} +(-2.21952 - 2.21952i) q^{19} +(-0.540893 - 0.312285i) q^{20} +(1.27840 - 0.738086i) q^{22} +(1.53305 - 0.885107i) q^{23} +(-0.162800 + 0.281977i) q^{25} +(3.88581 + 3.88581i) q^{26} -0.927379i q^{28} +(4.95814 - 2.10164i) q^{29} +(1.19335 - 4.45364i) q^{31} +(-1.46909 - 0.393642i) q^{32} +(-8.32812 - 4.80824i) q^{34} -7.90760 q^{35} +(-3.10705 + 3.10705i) q^{37} +(2.36493 - 4.09618i) q^{38} +(-1.55647 + 5.80881i) q^{40} +(-2.26013 + 8.43493i) q^{41} +(2.44664 - 0.655574i) q^{43} +(0.187475 + 0.187475i) q^{44} +(1.88619 + 1.88619i) q^{46} +(-7.43340 + 1.99177i) q^{47} +(-2.37071 - 4.10619i) q^{49} +(-0.473916 - 0.126985i) q^{50} +(-0.493502 + 0.854771i) q^{52} +5.72088i q^{53} +(1.59857 - 1.59857i) q^{55} +(-8.62508 + 2.31108i) q^{56} +(4.99268 + 6.39702i) q^{58} +(7.90468 - 4.56377i) q^{59} +(-7.38070 + 1.97765i) q^{61} +6.94778 q^{62} +6.64426i q^{64} +(7.28848 + 4.20801i) q^{65} +(10.0431 - 5.79839i) q^{67} +(0.447028 - 1.66833i) q^{68} +(-3.08401 - 11.5097i) q^{70} -3.89929 q^{71} +(9.73964 - 9.73964i) q^{73} +(-5.73414 - 3.31061i) q^{74} +(0.820568 + 0.219871i) q^{76} +(3.24240 + 0.868799i) q^{77} +(5.28760 - 1.41681i) q^{79} -10.3110 q^{80} -13.1587 q^{82} +(1.28536 + 0.742103i) q^{83} +(-14.2256 - 3.81173i) q^{85} +(1.90840 + 3.30545i) q^{86} +(1.27641 - 2.21081i) q^{88} +(-4.22391 + 4.22391i) q^{89} +12.4963i q^{91} +(-0.239548 + 0.414909i) q^{92} +(-5.79813 - 10.0427i) q^{94} +(1.87480 - 6.99684i) q^{95} +(3.81516 + 14.2384i) q^{97} +(5.05205 - 5.05205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/783\mathbb{Z}\right)^\times$.

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

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 $

$2$	0.390005	+	1.45552i	0.275775	+	1.02921i	0.955320	+	0.295574i	$0.0955108\pi$
$2$	0.390005	+	1.45552i	0.275775	+	1.02921i	−0.679544	+	0.733634i	$0.737823\pi$
$3$		0			0
$3$		0			0
$4$	−0.234384	+	0.135322i	−0.117192	+	0.0676608i
$5$	1.15386	+	1.99855i	0.516023	+	0.893778i	0.999827	+	0.0186019i	$0.00592151\pi$
$5$	1.15386	+	1.99855i	0.516023	+	0.893778i	−0.483804	+	0.875177i	$0.660745\pi$
$6$		0			0
$7$	−1.71329	+	2.96750i	−0.647562	+	1.12161i	0.336142	+	0.941811i	$0.390878\pi$
$7$	−1.71329	+	2.96750i	−0.647562	+	1.12161i	−0.983703	+	0.179798i	$0.942455\pi$
$8$	1.84266	+	1.84266i	0.651477	+	0.651477i
$9$		0			0
$10$	−2.45892	+	2.45892i	−0.777577	+	0.777577i
$11$	−0.253547	−	0.946251i	−0.0764474	−	0.285305i	0.917110	−	0.398634i	$-0.130516\pi$
$11$	−0.253547	−	0.946251i	−0.0764474	−	0.285305i	−0.993558	+	0.113328i	$0.963849\pi$
$12$		0			0
$13$	3.15830	−	1.82344i	0.875954	−	0.505732i	0.00663158	−	0.999978i	$-0.497889\pi$
$13$	3.15830	−	1.82344i	0.875954	−	0.505732i	0.869322	+	0.494246i	$0.164556\pi$
$14$	−4.98745	−	1.33638i	−1.33295	−	0.357163i
$15$		0			0
$16$	−2.23402	+	3.86943i	−0.558505	+	0.967359i
$17$	−4.51260	+	4.51260i	−1.09447	+	1.09447i	−0.0994203	+	0.995046i	$0.531699\pi$
$17$	−4.51260	+	4.51260i	−1.09447	+	1.09447i	−0.995046	+	0.0994203i	$0.968301\pi$
$18$		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	−0.331579	−	0.943427i	$-0.607581\pi$
$23$	1.53305	−	0.885107i	0.319663	−	0.184557i	0.651242	+	0.758870i	$0.274248\pi$
$24$		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
$29$	4.95814	−	2.10164i	0.920703	−	0.390264i
$29$	4.95814	−	2.10164i	0.920703	−	0.390264i
$30$		0			0
$31$	1.19335	−	4.45364i	0.214332	−	0.799898i	−0.772069	−	0.635539i	$-0.780778\pi$
$31$	1.19335	−	4.45364i	0.214332	−	0.799898i	0.986401	−	0.164359i	$-0.0525555\pi$
$32$	−1.46909	−	0.393642i	−0.259701	−	0.0695867i
$33$		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
$40$	−1.55647	+	5.80881i	−0.246099	+	0.918453i
$41$	−2.26013	+	8.43493i	−0.352973	+	1.31731i	0.530042	+	0.847971i	$0.322176\pi$
$41$	−2.26013	+	8.43493i	−0.352973	+	1.31731i	−0.883016	+	0.469343i	$0.844491\pi$
$42$		0			0
$43$	2.44664	−	0.655574i	0.373109	−	0.0999741i	−0.0673918	−	0.997727i	$-0.521468\pi$
$43$	2.44664	−	0.655574i	0.373109	−	0.0999741i	0.440500	+	0.897752i	$0.354801\pi$
$44$	0.187475	+	0.187475i	0.0282630	+	0.0282630i
$45$		0			0
$46$	1.88619	+	1.88619i	0.278103	+	0.278103i
$47$	−7.43340	+	1.99177i	−1.08427	+	0.290530i	−0.756345	−	0.654173i	$-0.773017\pi$
$47$	−7.43340	+	1.99177i	−1.08427	+	0.290530i	−0.327927	+	0.944703i	$0.606350\pi$
$48$		0			0
$49$	−2.37071	−	4.10619i	−0.338672	−	0.586598i
$50$	−0.473916	−	0.126985i	−0.0670218	−	0.0179584i
$51$		0			0
$52$	−0.493502	+	0.854771i	−0.0684364	+	0.118535i
$53$			5.72088i			0.785823i	0.919576	+	0.392911i	$0.128532\pi$
$53$			5.72088i			0.785823i	−0.919576	+	0.392911i	$0.871468\pi$
$54$		0			0
$55$	1.59857	−	1.59857i	0.215551	−	0.215551i
$56$	−8.62508	+	2.31108i	−1.15257	+	0.308831i
$57$		0			0
$58$	4.99268	+	6.39702i	0.655571	+	0.839969i
$59$	7.90468	−	4.56377i	1.02910	−	0.594152i	0.112375	−	0.993666i	$-0.464154\pi$
$59$	7.90468	−	4.56377i	1.02910	−	0.594152i	0.916727	+	0.399513i	$0.130821\pi$
$60$		0			0
$61$	−7.38070	+	1.97765i	−0.945002	+	0.253213i	−0.698240	−	0.715864i	$-0.746033\pi$
$61$	−7.38070	+	1.97765i	−0.945002	+	0.253213i	−0.246762	+	0.969076i	$0.579367\pi$
$62$	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	$-0.416090\pi$
$67$	10.0431	−	5.79839i	1.22696	−	0.708386i	0.966393	+	0.257070i	$0.0827571\pi$
$68$	0.447028	−	1.66833i	0.0542101	−	0.202315i
$69$		0			0
$70$	−3.08401	−	11.5097i	−0.368609	−	1.37567i
$71$	−3.89929			−0.462761			−0.231380	−	0.972863i	$-0.574324\pi$
$71$	−3.89929			−0.462761			−0.231380	+	0.972863i	$0.574324\pi$
$72$		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
$76$	0.820568	+	0.219871i	0.0941257	+	0.0252209i
$77$	3.24240	+	0.868799i	0.369506	+	0.0990088i
$78$		0			0
$79$	5.28760	−	1.41681i	0.594902	−	0.159403i	0.0512093	−	0.998688i	$-0.483692\pi$
$79$	5.28760	−	1.41681i	0.594902	−	0.159403i	0.543692	+	0.839285i	$0.317026\pi$
$80$	−10.3110			−1.15281
$81$		0			0
$82$	−13.1587			−1.45313
$83$	1.28536	+	0.742103i	0.141087	+	0.0814563i	0.568882	−	0.822419i	$-0.307376\pi$
$83$	1.28536	+	0.742103i	0.141087	+	0.0814563i	−0.427795	+	0.903876i	$0.640710\pi$
$84$		0			0
$85$	−14.2256	−	3.81173i	−1.54298	−	0.413440i
$86$	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	−0.894600	−	0.446867i	$-0.852540\pi$
$89$	−4.22391	+	4.22391i	−0.447734	+	0.447734i	0.446867	+	0.894600i	$0.352540\pi$
$90$		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
$95$	1.87480	−	6.99684i	0.192350	−	0.717861i
$96$		0			0
$97$	3.81516	+	14.2384i	0.387371	+	1.44569i	0.834395	+	0.551167i	$0.185817\pi$
$97$	3.81516	+	14.2384i	0.387371	+	1.44569i	−0.447024	+	0.894522i	$0.647516\pi$
$98$	5.05205	−	5.05205i	0.510334	−	0.510334i
$99$		0			0
$100$		−	0.0881211i		−	0.00881211i
$101$	−3.50530	−	13.0819i	−0.348790	−	1.30170i	−0.888121	−	0.459609i	$-0.847990\pi$
$101$	−3.50530	−	13.0819i	−0.348790	−	1.30170i	0.539331	−	0.842094i	$-0.318677\pi$
$102$		0			0
$103$	−1.08059	−	1.87164i	−0.106474	−	0.184418i	0.807866	−	0.589367i	$-0.200623\pi$
$103$	−1.08059	−	1.87164i	−0.106474	−	0.184418i	−0.914339	+	0.404949i	$0.867289\pi$
$104$	9.17963	+	2.45967i	0.900137	+	0.241191i
$105$		0			0
$106$	−8.32685	+	2.23117i	−0.808775	+	0.216711i
$107$		−	11.7414i		−	1.13509i	−0.823343	−	0.567544i	$-0.807894\pi$
$107$		−	11.7414i		−	1.13509i	0.823343	−	0.567544i	$-0.192106\pi$
$108$		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
$113$	0.596633	−	2.22666i	0.0561265	−	0.209467i	−0.932168	−	0.362027i	$-0.882085\pi$
$113$	0.596633	−	2.22666i	0.0561265	−	0.209467i	0.988294	+	0.152560i	$0.0487516\pi$
$114$		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
$119$	−5.65976	−	21.1225i	−0.518829	−	1.93630i
$120$		0			0
$121$	8.69517	−	5.02016i	0.790470	−	0.456378i
$122$	−5.75703	−	9.97147i	−0.521217	−	0.902774i
$123$		0			0
$124$	0.322972	+	1.20535i	0.0290037	+	0.108243i
$125$	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	$0.350016\pi$
$128$	−12.6090	+	3.37858i	−1.11449	+	0.298627i
$129$		0			0
$130$	−3.28229	+	12.2497i	−0.287876	+	1.07437i
$131$	5.80303	−	21.6572i	0.507013	−	1.89220i	0.0588036	−	0.998270i	$-0.481271\pi$
$131$	5.80303	−	21.6572i	0.507013	−	1.89220i	0.448209	−	0.893929i	$-0.352062\pi$
$132$		0			0
$133$	10.3891	−	2.78375i	0.900850	−	0.241382i
$134$	12.3565	+	12.3565i	1.06744	+	1.06744i
$135$		0			0
$136$	−16.6303			−1.42604
$137$	6.02993	+	22.5040i	0.515172	+	1.92265i	0.351762	+	0.936089i	$0.385582\pi$
$137$	6.02993	+	22.5040i	0.515172	+	1.92265i	0.163409	+	0.986558i	$0.447751\pi$
$138$		0			0
$139$	3.60927	+	6.25144i	0.306134	+	0.530240i	0.977513	−	0.210874i	$-0.0676310\pi$
$139$	3.60927	+	6.25144i	0.306134	+	0.530240i	−0.671379	+	0.741114i	$0.734298\pi$
$140$	1.85341	−	1.07007i	0.156642	−	0.0904372i
$141$		0			0
$142$	−1.52075	−	5.67550i	−0.127618	−	0.476277i
$143$	−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
$148$	0.307792	−	1.14869i	0.0253003	−	0.0944220i
$149$	0.868063	+	1.50353i	0.0711145	+	0.123174i	0.899390	−	0.437147i	$-0.144011\pi$
$149$	0.868063	+	1.50353i	0.0711145	+	0.123174i	−0.828276	+	0.560321i	$0.810678\pi$
$150$		0			0
$151$	−15.1953	−	8.77300i	−1.23657	−	0.713937i	−0.268182	−	0.963368i	$-0.586423\pi$
$151$	−15.1953	−	8.77300i	−1.23657	−	0.713937i	−0.968392	+	0.249432i	$0.919756\pi$
$152$		−	8.17962i		−	0.663455i
$153$		0			0
$154$			5.05821i			0.407603i
$155$	10.2778	−	2.75392i	0.825532	−	0.221201i
$156$		0			0
$157$	13.2975	+	3.56305i	1.06126	+	0.284363i	0.746896	−	0.664941i	$-0.231543\pi$
$157$	13.2975	+	3.56305i	1.06126	+	0.284363i	0.314360	+	0.949304i	$0.398210\pi$
$158$	4.12439	+	7.14365i	0.328119	+	0.568318i
$159$		0			0
$160$	−0.908418	−	3.39026i	−0.0718167	−	0.268024i
$161$			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	$0.0275717\pi$
$164$	−0.611689	−	2.28285i	−0.0477649	−	0.178261i
$165$		0			0
$166$	−0.578848	+	2.16029i	−0.0449273	+	0.167671i
$167$	0.894361	+	1.54908i	0.0692077	+	0.119871i	0.898553	−	0.438865i	$-0.144620\pi$
$167$	0.894361	+	1.54908i	0.0692077	+	0.119871i	−0.829345	+	0.558737i	$0.811286\pi$
$168$		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	$-0.802518\pi$
$173$	1.27135	−	2.20203i	0.0966586	−	0.167418i	0.910300	+	0.413950i	$0.135851\pi$
$174$		0			0
$175$	−0.557845	−	0.966215i	−0.0421691	−	0.0730390i
$176$	4.22789	+	1.13286i	0.318689	+	0.0853924i
$177$		0			0
$178$	−7.79533	−	4.50064i	−0.584285	−	0.337337i
$179$	2.12556			0.158872			0.0794360	−	0.996840i	$-0.474688\pi$
$179$	2.12556			0.158872			0.0794360	+	0.996840i	$0.474688\pi$
$180$		0			0
$181$	−6.51616			−0.484342			−0.242171	−	0.970234i	$-0.577860\pi$
$181$	−6.51616			−0.484342			−0.242171	+	0.970234i	$0.577860\pi$
$182$	−18.1887	+	4.87364i	−1.34823	+	0.361258i
$183$		0			0
$184$	4.45583	+	1.19394i	0.328488	+	0.0880181i
$185$	−9.79471	−	2.62448i	−0.720121	−	0.192956i
$186$		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
$191$	0.651235	+	2.43044i	0.0471217	+	0.175861i	0.985476	−	0.169814i	$-0.0543167\pi$
$191$	0.651235	+	2.43044i	0.0471217	+	0.175861i	−0.938354	+	0.345675i	$0.887650\pi$
$192$		0			0
$193$	−1.85013	+	6.90478i	−0.133175	+	0.497017i	−0.999999	−	0.00159839i	$-0.999491\pi$
$193$	−1.85013	+	6.90478i	−0.133175	+	0.497017i	0.866823	+	0.498615i	$0.166158\pi$
$194$	−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	$-0.687239\pi$
$197$		−	23.3533i		−	1.66385i	0.554887	−	0.831925i	$-0.312761\pi$
$198$		0			0
$199$	11.8223			0.838057			0.419029	−	0.907973i	$-0.362371\pi$
$199$	11.8223			0.838057			0.419029	+	0.907973i	$0.362371\pi$
$200$	−0.819570	+	0.219603i	−0.0579523	+	0.0155283i
$201$		0			0
$202$	17.6740	−	10.2041i	1.24354	−	0.717955i
$203$	−2.25810	+	18.3140i	−0.158487	+	1.28539i
$204$		0			0
$205$	−19.4655	+	5.21577i	−1.35953	+	0.364285i
$206$	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
$211$	−6.11147	−	1.63756i	−0.420731	−	0.112735i	0.0422410	−	0.999107i	$-0.486550\pi$
$211$	−6.11147	−	1.63756i	−0.420731	−	0.112735i	−0.462972	+	0.886373i	$0.653217\pi$
$212$	−0.774158	−	1.34088i	−0.0531694	−	0.0920920i
$213$		0			0
$214$	17.0899	−	4.57923i	1.16824	−	0.313030i
$215$	4.13328	+	4.13328i	0.281887	+	0.281887i
$216$		0			0
$217$	11.1716	+	11.1716i	0.758380	+	0.758380i
$218$	18.0749	−	4.84315i	1.22419	−	0.328019i
$219$		0			0
$220$	−0.158358	+	0.591000i	−0.0106765	+	0.0398452i
$221$	−6.02366	+	22.4806i	−0.405195	+	1.51221i
$222$		0			0
$223$	0.919993	−	1.59347i	0.0616073	−	0.106707i	−0.833577	−	0.552404i	$-0.813711\pi$
$223$	0.919993	−	1.59347i	0.0616073	−	0.106707i	0.895184	+	0.445697i	$0.147044\pi$
$224$	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	0.226315	−	0.974054i	$-0.427332\pi$
$227$	−7.59478	−	4.38485i	−0.504083	−	0.291032i	−0.730398	+	0.683022i	$0.760665\pi$
$228$		0			0
$229$	24.5820	+	6.58672i	1.62442	+	0.435262i	0.952296	−	0.305175i	$-0.0987150\pi$
$229$	24.5820	+	6.58672i	1.62442	+	0.435262i	0.672125	+	0.740437i	$0.265382\pi$
$230$	−1.59324	+	5.94604i	−0.105055	+	0.392070i
$231$		0			0
$232$	13.0087	+	5.26354i	0.854065	+	0.345568i
$233$			4.40613i			0.288655i	0.989530	+	0.144327i	$0.0461019\pi$
$233$			4.40613i			0.288655i	−0.989530	+	0.144327i	$0.953898\pi$
$234$		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	−0.797491	−	0.603331i	$-0.793840\pi$
$239$	−10.4157	+	6.01352i	−0.673737	+	0.388982i	0.123754	+	0.992313i	$0.460507\pi$
$240$		0			0
$241$	−11.8938	−	6.86687i	−0.766144	−	0.442334i	0.0653530	−	0.997862i	$-0.479183\pi$
$241$	−11.8938	−	6.86687i	−0.766144	−	0.442334i	−0.831498	+	0.555528i	$0.812516\pi$
$242$	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
$247$	−11.0571	−	2.96273i	−0.703545	−	0.188514i
$248$	10.4055	−	6.00760i	0.660747	−	0.381483i
$249$		0			0
$250$	4.20708	+	15.7010i	0.266079	+	0.993021i
$251$	0.591952	−	0.591952i	0.0373637	−	0.0373637i	−0.688178	−	0.725542i	$-0.741589\pi$
$251$	0.591952	−	0.591952i	0.0373637	−	0.0373637i	0.725542	+	0.688178i	$0.241589\pi$
$252$		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	−0.715204	−	0.698916i	$-0.753666\pi$
$257$	−7.49503	+	4.32726i	−0.467527	+	0.269927i	0.247677	+	0.968843i	$0.420333\pi$
$258$		0			0
$259$	−3.89691	−	14.5435i	−0.242142	−	0.903686i
$260$	−2.27774			−0.141259
$261$		0			0
$262$	33.7857			2.08729
$263$	−2.90897	−	10.8564i	−0.179375	−	0.669435i	−0.995765	−	0.0919347i	$-0.970695\pi$
$263$	−2.90897	−	10.8564i	−0.179375	−	0.669435i	0.816390	−	0.577500i	$-0.195972\pi$
$264$		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	0.561594	−	0.827413i	$-0.310188\pi$
$269$	−4.35975	−	4.35975i	−0.265818	−	0.265818i	−0.827413	+	0.561594i	$0.810188\pi$
$270$		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	$0.938938\pi$
$272$	−7.37997	−	27.5424i	−0.447477	−	1.67001i
$273$		0			0
$274$	−30.4033	+	17.5534i	−1.83673	+	1.06044i
$275$	0.308098	+	0.0825547i	0.0185790	+	0.00497824i
$276$		0			0
$277$	−4.16756	+	7.21842i	−0.250404	+	0.433713i	−0.963637	−	0.267214i	$-0.913897\pi$
$277$	−4.16756	+	7.21842i	−0.250404	+	0.433713i	0.713233	+	0.700927i	$0.247230\pi$
$278$	−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	0.983064	−	0.183264i	$-0.0586663\pi$
$281$	22.0582	+	12.7353i	1.31588	+	0.759726i	0.332821	+	0.942990i	$0.392000\pi$
$282$		0			0
$283$	1.90239	−	1.09835i	0.113086	−	0.0652899i	−0.442390	−	0.896823i	$-0.645869\pi$
$283$	1.90239	−	1.09835i	0.113086	−	0.0652899i	0.555476	+	0.831533i	$0.312536\pi$
$284$	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
$290$	−7.02389	+	17.3594i	−0.412457	+	1.01938i
$291$		0			0
$292$	−0.964830	+	3.60079i	−0.0564624	+	0.210721i
$293$	−14.9866	−	4.01564i	−0.875526	−	0.234596i	−0.207050	−	0.978330i	$-0.566386\pi$
$293$	−14.9866	−	4.01564i	−0.875526	−	0.234596i	−0.668476	+	0.743734i	$0.733053\pi$
$294$		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
$301$	−2.24637	+	8.38358i	−0.129479	+	0.483222i
$302$	6.84303	−	25.5386i	0.393772	−	1.46958i
$303$		0			0
$304$	13.5467	−	3.62984i	0.776959	−	0.208186i
$305$	−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	$-0.562976\pi$
$308$	−0.877533	+	0.235134i	−0.0500021	+	0.0133980i
$309$		0			0
$310$	8.01679	+	13.8855i	0.455323	+	0.788642i
$311$	−14.8754	−	3.98585i	−0.843507	−	0.226017i	−0.188909	−	0.981995i	$-0.560495\pi$
$311$	−14.8754	−	3.98585i	−0.843507	−	0.226017i	−0.654598	+	0.755978i	$0.727162\pi$
$312$		0			0
$313$	14.0279	−	24.2970i	0.792904	−	1.37335i	−0.131258	−	0.991348i	$-0.541902\pi$
$313$	14.0279	−	24.2970i	0.792904	−	1.37335i	0.924162	−	0.382001i	$-0.124765\pi$
$314$			20.7444i			1.17067i
$315$		0			0
$316$	−1.04760	+	1.04760i	−0.0589323	+	0.0589323i
$317$	11.8329	−	3.17060i	0.664599	−	0.178079i	0.0892785	−	0.996007i	$-0.471544\pi$
$317$	11.8329	−	3.17060i	0.664599	−	0.178079i	0.575321	+	0.817928i	$0.304877\pi$
$318$		0			0
$319$	−3.24580	−	4.15878i	−0.181730	−	0.232847i
$320$	−13.2789	+	7.66657i	−0.742312	+	0.428574i
$321$		0			0
$322$	−8.82885	+	2.36568i	−0.492012	+	0.131834i
$323$	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
$329$	6.82496	−	25.4711i	0.376272	−	1.40427i
$330$		0			0
$331$	6.61124	+	24.6735i	0.363387	+	1.35618i	0.869595	+	0.493766i	$0.164380\pi$
$331$	6.61124	+	24.6735i	0.363387	+	1.35618i	−0.506208	+	0.862411i	$0.668953\pi$
$332$	−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
$337$	−30.9347	−	8.28893i	−1.68512	−	0.451527i	−0.715998	−	0.698102i	$-0.754028\pi$
$337$	−30.9347	−	8.28893i	−1.68512	−	0.451527i	−0.969124	+	0.246575i	$0.920695\pi$
$338$	0.436334	+	0.116915i	0.0237335	+	0.00635936i
$339$		0			0
$340$	3.85005	−	1.03162i	0.208798	−	0.0559473i
$341$	−4.51684			−0.244600
$342$		0			0
$343$	−7.73921			−0.417878
$344$	5.71630	+	3.30031i	0.308203	+	0.177941i
$345$		0			0
$346$	3.70094	+	0.991663i	0.198964	+	0.0533121i
$347$	−7.85064	−	13.5977i	−0.421445	−	0.729963i	0.574636	−	0.818409i	$-0.305143\pi$
$347$	−7.85064	−	13.5977i	−0.421445	−	0.729963i	−0.996081	+	0.0884454i	$0.971810\pi$
$348$		0			0
$349$	−7.20890	+	12.4862i	−0.385883	+	0.668370i	−0.991891	−	0.127089i	$-0.959437\pi$
$349$	−7.20890	+	12.4862i	−0.385883	+	0.668370i	0.606008	+	0.795459i	$0.292770\pi$
$350$	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	$-0.781836\pi$
$353$	3.02639	−	5.24187i	0.161079	−	0.278996i	0.935256	+	0.353973i	$0.115169\pi$
$354$		0			0
$355$	−4.49925	−	7.79293i	−0.238795	−	0.413606i
$356$	0.418430	−	1.56160i	0.0221767	−	0.0827647i
$357$		0			0
$358$	0.828981	+	3.09380i	0.0438130	+	0.163512i
$359$	10.6622	−	10.6622i	0.562731	−	0.562731i	−0.367351	−	0.930082i	$-0.619735\pi$
$359$	10.6622	−	10.6622i	0.562731	−	0.562731i	0.930082	+	0.367351i	$0.119735\pi$
$360$		0			0
$361$		−	9.14746i		−	0.481445i
$362$	−2.54134	−	9.48440i	−0.133570	−	0.498489i
$363$		0			0
$364$	−1.69102	−	2.92894i	−0.0886336	−	0.153518i
$365$	30.7033	+	8.22694i	1.60709	+	0.430618i
$366$		0			0
$367$	−20.5533	+	5.50723i	−1.07287	+	0.287475i	−0.751673	−	0.659536i	$-0.770753\pi$
$367$	−20.5533	+	5.50723i	−1.07287	+	0.287475i	−0.321200	+	0.947012i	$0.604086\pi$
$368$			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	0.894729	−	0.446609i	$-0.147368\pi$
$373$	1.17019	+	2.02682i	0.0605899	+	0.104945i	−0.834139	+	0.551554i	$0.814035\pi$
$374$	−2.43823	+	9.09960i	−0.126078	+	0.470529i
$375$		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	$0.957484\pi$
$380$	0.507401	+	1.89365i	0.0260291	+	0.0971420i
$381$		0			0
$382$	−3.28357	+	1.89577i	−0.168002	+	0.0969961i
$383$	4.48217	+	7.76335i	0.229028	+	0.396689i	0.957520	−	0.288365i	$-0.0931118\pi$
$383$	4.48217	+	7.76335i	0.229028	+	0.396689i	−0.728492	+	0.685054i	$0.759778\pi$
$384$		0			0
$385$	2.00495	+	7.48257i	0.102182	+	0.381347i
$386$	−10.7716			−0.548260
$387$		0			0
$388$	−2.82097	−	2.82097i	−0.143213	−	0.143213i
$389$	6.22009	−	1.66667i	0.315371	−	0.0845034i	−0.0976615	−	0.995220i	$-0.531136\pi$
$389$	6.22009	−	1.66667i	0.315371	−	0.0845034i	0.413033	+	0.910716i	$0.364470\pi$
$390$		0			0
$391$	−2.92391	+	10.9122i	−0.147868	+	0.551852i
$392$	3.19789	−	11.9347i	0.161518	−	0.602792i
$393$		0			0
$394$	33.9911	−	9.10790i	1.71245	−	0.458849i
$395$	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	$0.812116\pi$
$398$	4.61074	+	17.2075i	0.231116	+	0.862535i
$399$		0			0
$400$	−0.727395	−	1.25988i	−0.0363697	−	0.0629942i
$401$	2.97078	−	1.71518i	0.148354	−	0.0856521i	−0.423986	−	0.905669i	$-0.639369\pi$
$401$	2.97078	−	1.71518i	0.148354	−	0.0856521i	0.572339	+	0.820017i	$0.306036\pi$
$402$		0			0
$403$	−4.35201	−	16.2419i	−0.216789	−	0.809068i
$404$	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
$409$	2.21789	−	8.27727i	0.109667	−	0.409285i	−0.889165	−	0.457586i	$-0.848714\pi$
$409$	2.21789	−	8.27727i	0.109667	−	0.409285i	0.998833	+	0.0483015i	$0.0153808\pi$
$410$	−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
$416$	−5.35761	+	1.43557i	−0.262679	+	0.0703845i
$417$		0			0
$418$	−4.47564	−	1.19924i	−0.218911	−	0.0586569i
$419$	0.276281	+	0.478533i	0.0134972	+	0.0233779i	0.872695	−	0.488266i	$-0.162370\pi$
$419$	0.276281	+	0.478533i	0.0134972	+	0.0233779i	−0.859198	+	0.511643i	$0.829037\pi$
$420$		0			0
$421$	−5.30967	−	19.8159i	−0.258777	−	0.965770i	−0.965950	−	0.258729i	$-0.916696\pi$
$421$	−5.30967	−	19.8159i	−0.258777	−	0.965770i	0.707173	−	0.707041i	$-0.249970\pi$
$422$		−	9.53403i		−	0.464109i
$423$		0			0
$424$	−10.5416	+	10.5416i	−0.511945	+	0.511945i
$425$	−0.537800	−	2.00710i	−0.0260871	−	0.0973586i
$426$		0			0
$427$	6.77658	−	25.2905i	0.327942	−	1.22389i
$428$	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	$-0.942310\pi$
$431$		−	7.48413i		−	0.360498i	0.983621	−	0.180249i	$-0.0576903\pi$
$432$		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
$437$	−5.36715	−	1.43812i	−0.256745	−	0.0687947i
$438$		0			0
$439$	−1.02365	−	0.591004i	−0.0488561	−	0.0282071i	0.475373	−	0.879784i	$-0.342313\pi$
$439$	−1.02365	−	0.591004i	−0.0488561	−	0.0282071i	−0.524229	+	0.851577i	$0.675646\pi$
$440$	5.89123			0.280853
$441$		0			0
$442$	−35.0702			−1.66812
$443$	−13.1603	+	3.52628i	−0.625263	+	0.167539i	−0.557519	−	0.830164i	$-0.688247\pi$
$443$	−13.1603	+	3.52628i	−0.625263	+	0.167539i	−0.0677439	+	0.997703i	$0.521580\pi$
$444$		0			0
$445$	−13.3155	−	3.56788i	−0.631216	−	0.169134i
$446$	2.67814	+	0.717604i	0.126813	+	0.0339796i
$447$		0			0
$448$	−19.7169	−	11.3835i	−0.931534	−	0.537821i
$449$	−15.2510	+	15.2510i	−0.719737	+	0.719737i	−0.968551	−	0.248814i	$-0.919959\pi$
$449$	−15.2510	+	15.2510i	−0.719737	+	0.719737i	0.248814	+	0.968551i	$0.419959\pi$
$450$		0			0
$451$	8.55461			0.402821
$452$	0.161475	+	0.602631i	0.00759512	+	0.0283454i
$453$		0			0
$454$	3.42023	−	12.7645i	0.160519	−	0.599066i
$455$	−24.9745	+	14.4191i	−1.17082	+	0.675976i
$456$		0			0
$457$	24.0428	+	13.8811i	1.12468	+	0.649332i	0.942591	−	0.333951i	$-0.108382\pi$
$457$	24.0428	+	13.8811i	1.12468	+	0.649332i	0.182086	+	0.983283i	$0.441715\pi$
$458$			38.3484i			1.79190i
$459$		0			0
$460$	−1.10562			−0.0515499
$461$	−25.5486	+	6.84572i	−1.18992	+	0.318837i	−0.798852	−	0.601527i	$-0.794559\pi$
$461$	−25.5486	+	6.84572i	−1.18992	+	0.318837i	−0.391063	+	0.920364i	$0.627893\pi$
$462$		0			0
$463$	−19.8255	+	11.4462i	−0.921367	+	0.531952i	−0.884071	−	0.467353i	$-0.845208\pi$
$463$	−19.8255	+	11.4462i	−0.921367	+	0.531952i	−0.0372963	+	0.999304i	$0.511875\pi$
$464$	−2.94442	+	23.8803i	−0.136691	+	1.10861i
$465$		0			0
$466$	−6.41321	+	1.71841i	−0.297086	+	0.0796040i
$467$	−8.43163	+	8.43163i	−0.390169	+	0.390169i	−0.874748	−	0.484578i	$-0.838973\pi$
$467$	−8.43163	+	8.43163i	−0.390169	+	0.390169i	0.484578	+	0.874748i	$0.338973\pi$
$468$		0			0
$469$			39.7372i			1.83489i
$470$	13.3805	−	23.1757i	0.617196	−	1.06902i
$471$		0			0
$472$	22.9751	+	6.15615i	1.05751	+	0.283360i
$473$	−1.24068	−	2.14891i	−0.0570463	−	0.0988072i
$474$		0			0
$475$	0.987191	−	0.264517i	0.0452954	−	0.0121369i
$476$	4.18489	+	4.18489i	0.191814	+	0.191814i
$477$		0			0
$478$	−12.8150	−	12.8150i	−0.586144	−	0.586144i
$479$	−25.2404	+	6.76315i	−1.15326	+	0.309016i	−0.784273	−	0.620416i	$-0.786964\pi$
$479$	−25.2404	+	6.76315i	−1.15326	+	0.309016i	−0.368992	+	0.929433i	$0.620297\pi$
$480$		0			0
$481$	−4.14746	+	15.4785i	−0.189108	+	0.705760i
$482$	5.35623	−	19.9897i	0.243970	−	0.910507i
$483$		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
$490$	15.9261	+	4.26739i	0.719469	+	0.192781i
$491$	8.34392	−	31.1399i	0.376556	−	1.40532i	−0.474503	−	0.880254i	$-0.657372\pi$
$491$	8.34392	−	31.1399i	0.376556	−	1.40532i	0.851059	−	0.525071i	$-0.175961\pi$
$492$		0			0
$493$	−12.8902	+	31.8579i	−0.580547	+	1.43481i
$494$		−	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	$-0.709873\pi$
$499$	−5.23568	+	3.02282i	−0.234381	+	0.135320i	0.378210	+	0.925720i	$0.376540\pi$
$500$	−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	$0.116555\pi$
$503$	28.9708	+	28.9708i	1.29175	+	1.29175i	0.358039	+	0.933707i	$0.383445\pi$
$504$		0			0
$505$	22.1003	−	22.1003i	0.983450	−	0.983450i
$506$	1.30657	−	2.26305i	0.0580841	−	0.100605i
$507$		0			0
$508$	−5.60366	−	1.50150i	−0.248622	−	0.0666181i
$509$	−7.53944	+	4.35290i	−0.334180	+	0.192939i	−0.657695	−	0.753284i	$-0.728469\pi$
$509$	−7.53944	+	4.35290i	−0.334180	+	0.192939i	0.323515	+	0.946223i	$0.395135\pi$
$510$		0			0
$511$	12.2156	+	45.5892i	0.540385	+	2.01675i
$512$	−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
$520$	5.67625	+	21.1841i	0.248920	+	0.928983i
$521$	−13.1697			−0.576977			−0.288489	−	0.957483i	$-0.593153\pi$
$521$	−13.1697			−0.576977			−0.288489	+	0.957483i	$0.593153\pi$
$522$		0			0
$523$	8.93957			0.390900			0.195450	−	0.980714i	$-0.437383\pi$
$523$	8.93957			0.390900			0.195450	+	0.980714i	$0.437383\pi$
$524$	1.57055	+	5.86137i	0.0686098	+	0.256055i
$525$		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
$533$	8.24245	+	30.7612i	0.357020	+	1.33242i
$534$		0			0
$535$	23.4659	−	13.5480i	1.01452	−	0.585732i
$536$	29.1904	+	7.82154i	1.26083	+	0.337839i
$537$		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	−0.415112	−	0.909770i	$-0.636258\pi$
$547$	13.5727	−	23.5087i	0.580328	−	1.00516i	0.995440	−	0.0953875i	$-0.0304090\pi$
$548$	−4.45860	−	4.45860i	−0.190462	−	0.190462i
$549$		0			0
$550$			0.480640i			0.0204946i
$551$	−15.6693	−	6.34006i	−0.667535	−	0.270095i
$552$		0			0
$553$	−4.85480	+	18.1184i	−0.206447	+	0.770471i
$554$	−12.1319	−	3.25074i	−0.515436	−	0.138111i
$555$		0			0
$556$	−1.69191	−	0.976824i	−0.0717529	−	0.0414266i
$557$	21.8377			0.925292			0.462646	−	0.886543i	$-0.346900\pi$
$557$	21.8377			0.925292			0.462646	+	0.886543i	$0.346900\pi$
$558$		0			0
$559$	6.53180	−	6.53180i	0.276266	−	0.276266i
$560$	17.6657	−	30.5979i	0.746513	−	1.29300i
$561$		0			0
$562$	−9.93370	+	37.0731i	−0.419028	+	1.56383i
$563$	−0.340125	+	1.26936i	−0.0143345	+	0.0534973i	−0.972723	−	0.231971i	$-0.925483\pi$
$563$	−0.340125	+	1.26936i	−0.0143345	+	0.0534973i	0.958388	+	0.285468i	$0.0921492\pi$
$564$		0			0
$565$	5.13853	−	1.37686i	0.216180	−	0.0579251i
$566$	2.34061	+	2.34061i	0.0983832	+	0.0983832i
$567$		0			0
$568$	−7.18505	−	7.18505i	−0.301478	−	0.301478i
$569$	−13.2755	+	3.55717i	−0.556540	+	0.149124i	−0.526116	−	0.850413i	$-0.676352\pi$
$569$	−13.2755	+	3.55717i	−0.556540	+	0.149124i	−0.0304237	+	0.999537i	$0.509686\pi$
$570$		0			0
$571$	1.96191	+	3.39812i	0.0821032	+	0.142207i	0.904153	−	0.427208i	$-0.140503\pi$
$571$	1.96191	+	3.39812i	0.0821032	+	0.142207i	−0.822050	+	0.569415i	$0.807170\pi$
$572$	0.933954	+	0.250252i	0.0390506	+	0.0104636i
$573$		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	$0.359803\pi$
$578$	34.5352	−	9.25369i	1.43648	−	0.384903i
$579$		0			0
$580$	−3.33813	−	0.411589i	−0.138608	−	0.0170903i
$581$	−4.40438	+	2.54287i	−0.182724	+	0.105496i
$582$		0			0
$583$	5.41339	−	1.45051i	0.224200	−	0.0600741i
$584$	35.8936			1.48529
$585$		0			0
$586$		−	23.3794i		−	0.965794i
$587$	−27.9575	−	16.1413i	−1.15393	−	0.666222i	−0.204089	−	0.978952i	$-0.565423\pi$
$587$	−27.9575	−	16.1413i	−1.15393	−	0.666222i	−0.949842	+	0.312730i	$0.898756\pi$
$588$		0			0
$589$	−12.5336	+	7.23629i	−0.516439	+	0.298166i
$590$	−8.21502	+	30.6589i	−0.338207	+	1.26221i
$591$		0			0
$592$	−5.08132	−	18.9638i	−0.208841	−	0.779405i
$593$	8.81748			0.362090			0.181045	−	0.983475i	$-0.442052\pi$
$593$	8.81748			0.362090			0.181045	+	0.983475i	$0.442052\pi$
$594$		0			0
$595$	35.6838	−	35.6838i	1.46289	−	1.46289i
$596$	−0.406920	−	0.234935i	−0.0166681	−	0.00962332i
$597$		0			0
$598$	9.39650	+	2.51778i	0.384251	+	0.102960i
$599$	−27.0487	−	7.24767i	−1.10518	−	0.296132i	−0.340307	−	0.940315i	$-0.610531\pi$
$599$	−27.0487	−	7.24767i	−1.10518	−	0.296132i	−0.764871	+	0.644183i	$0.777198\pi$
$600$		0			0
$601$	−7.43028	+	1.99094i	−0.303087	+	0.0812120i	−0.407158	−	0.913358i	$-0.633480\pi$
$601$	−7.43028	+	1.99094i	−0.303087	+	0.0812120i	0.104070	+	0.994570i	$0.466813\pi$
$602$	−13.0786			−0.533043
$603$		0			0
$604$	4.74870			0.193222
$605$	20.0661	+	11.5852i	0.815802	+	0.471004i
$606$		0			0
$607$	−23.9519	−	6.41790i	−0.972178	−	0.260494i	−0.262431	−	0.964951i	$-0.584524\pi$
$607$	−23.9519	−	6.41790i	−0.972178	−	0.260494i	−0.709747	+	0.704456i	$0.751191\pi$
$608$	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
$617$	−9.10157	+	33.9675i	−0.366416	+	1.36748i	0.499076	+	0.866558i	$0.333673\pi$
$617$	−9.10157	+	33.9675i	−0.366416	+	1.36748i	−0.865492	+	0.500923i	$0.832994\pi$
$618$		0			0
$619$	0.247073	+	0.922089i	0.00993070	+	0.0370619i	0.970713	−	0.240240i	$-0.0772263\pi$
$619$	0.247073	+	0.922089i	0.00993070	+	0.0370619i	−0.960783	+	0.277302i	$0.910560\pi$
$620$	−2.03628	+	2.03628i	−0.0817790	+	0.0817790i
$621$		0			0
$622$		−	23.2060i		−	0.930474i
$623$	−5.29769	−	19.7712i	−0.212247	−	0.792118i
$624$		0			0
$625$	13.2610	+	22.9687i	0.530440	+	0.918748i
$626$	40.8358	+	10.9419i	1.63213	+	0.437327i
$627$		0			0
$628$	−3.59887	+	0.964315i	−0.143611	+	0.0384804i
$629$		−	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
$635$	−12.8030	+	47.7814i	−0.508071	+	1.89615i
$636$		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
$641$	−1.58096	−	5.90023i	−0.0624442	−	0.233045i	0.927650	−	0.373451i	$-0.121826\pi$
$641$	−1.58096	−	5.90023i	−0.0624442	−	0.233045i	−0.990094	+	0.140406i	$0.955159\pi$
$642$		0			0
$643$	30.1525	−	17.4086i	1.18910	−	0.686526i	0.230997	−	0.972955i	$-0.425801\pi$
$643$	30.1525	−	17.4086i	1.18910	−	0.686526i	0.958102	+	0.286428i	$0.0924680\pi$
$644$	−0.820829	−	1.42172i	−0.0323452	−	0.0560235i
$645$		0			0
$646$	7.81244	+	29.1564i	0.307376	+	1.14714i
$647$	22.6415			0.890129			0.445065	−	0.895498i	$-0.353181\pi$
$647$	22.6415			0.890129			0.445065	+	0.895498i	$0.353181\pi$
$648$		0			0
$649$	−6.32269	−	6.32269i	−0.248187	−	0.248187i
$650$	−1.72832	+	0.463101i	−0.0677902	+	0.0181643i
$651$		0			0
$652$	−1.15059	+	4.29405i	−0.0450604	+	0.168168i
$653$	7.17016	−	26.7594i	0.280590	−	1.04718i	−0.671412	−	0.741084i	$-0.734312\pi$
$653$	7.17016	−	26.7594i	0.280590	−	1.04718i	0.952002	−	0.306092i	$-0.0990214\pi$
$654$		0			0
$655$	49.9789	−	13.3918i	1.95284	−	0.523261i
$656$	−27.5892	−	27.5892i	−1.07718	−	1.07718i
$657$		0			0
$658$	39.7354			1.54905
$659$	12.1882	+	45.4870i	0.474785	+	1.77192i	0.622212	+	0.782849i	$0.286234\pi$
$659$	12.1882	+	45.4870i	0.474785	+	1.77192i	−0.147427	+	0.989073i	$0.547099\pi$
$660$		0			0
$661$	10.4366	+	18.0767i	0.405937	+	0.703103i	0.994430	−	0.105399i	$-0.0336119\pi$
$661$	10.4366	+	18.0767i	0.405937	+	0.703103i	−0.588493	+	0.808502i	$0.700279\pi$
$662$	−33.3343	+	19.2456i	−1.29558	+	0.748001i
$663$		0			0
$664$	1.00104	+	3.73591i	0.0388477	+	0.144982i
$665$	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
$670$	−10.4374	+	38.9529i	−0.403232	+	1.50488i
$671$	3.74271	+	6.48257i	0.144486	+	0.250257i
$672$		0			0
$673$	−31.4119	−	18.1357i	−1.21084	−	0.699079i	−0.247898	−	0.968786i	$-0.579740\pi$
$673$	−31.4119	−	18.1357i	−1.21084	−	0.699079i	−0.962942	+	0.269707i	$0.913073\pi$
$674$		−	48.2588i		−	1.85886i
$675$		0			0
$676$			0.0811331i			0.00312050i
$677$	−45.5535	+	12.2060i	−1.75076	+	0.469115i	−0.984789	−	0.173756i	$-0.944409\pi$
$677$	−45.5535	+	12.2060i	−1.75076	+	0.469115i	−0.765974	+	0.642872i	$0.777743\pi$
$678$		0			0
$679$	−48.7889	−	13.0729i	−1.87235	−	0.501693i
$680$	−19.1891	−	33.2365i	−0.735869	−	1.27456i
$681$		0			0
$682$	−1.76159	−	6.57434i	−0.0674548	−	0.251745i
$683$			30.2941i			1.15917i	0.814911	+	0.579585i	$0.196786\pi$
$683$			30.2941i			1.15917i	−0.814911	+	0.579585i	$0.803214\pi$
$684$		0			0
$685$	−38.0177	+	38.0177i	−1.45258	+	1.45258i
$686$	−3.01834	−	11.2646i	−0.115241	−	0.430084i
$687$		0			0
$688$	−2.92913	+	10.9317i	−0.111672	+	0.416766i
$689$	10.4317	+	18.0682i	0.397416	+	0.688344i
$690$		0			0
$691$	−8.52230	+	14.7611i	−0.324204	+	0.561537i	−0.981351	−	0.192225i	$-0.938430\pi$
$691$	−8.52230	+	14.7611i	−0.324204	+	0.561537i	0.657147	+	0.753762i	$0.271763\pi$
$692$			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
$698$	−20.9854	−	5.62302i	−0.794309	−	0.212834i
$699$		0			0
$700$	0.261499	+	0.150977i	0.00988375	+	0.00570639i
$701$	9.26597			0.349971			0.174986	−	0.984571i	$-0.444012\pi$
$701$	9.26597			0.349971			0.174986	+	0.984571i	$0.444012\pi$
$702$		0			0
$703$	13.7923			0.520188
$704$	6.28714	−	1.68463i	0.236955	−	0.0634920i
$705$		0			0
$706$	8.80995	+	2.36062i	0.331567	+	0.0888431i
$707$	44.8263	+	12.0112i	1.68587	+	0.451726i
$708$		0			0
$709$	2.72384	+	1.57261i	0.102296	+	0.0590606i	0.550275	−	0.834983i	$-0.314523\pi$
$709$	2.72384	+	1.57261i	0.102296	+	0.0590606i	−0.447979	+	0.894044i	$0.647856\pi$
$710$	9.58803	−	9.58803i	0.359832	−	0.359832i
$711$		0			0
$712$	−15.5664			−0.583376
$713$	−2.11248	−	7.88390i	−0.0791131	−	0.295254i
$714$		0			0
$715$	2.13386	−	7.96366i	0.0798017	−	0.297824i
$716$	−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	$-0.648488\pi$
$719$		−	47.8983i		−	1.78631i	0.449753	−	0.893153i	$-0.351512\pi$
$720$		0			0
$721$	7.40544			0.275793
$722$	13.3143	−	3.56756i	0.495507	−	0.132771i
$723$		0			0
$724$	1.52728	−	0.881777i	0.0567610	−	0.0327710i
$725$	−0.214568	+	1.74023i	−0.00796887	+	0.0646304i
$726$		0			0
$727$	30.8883	−	8.27648i	1.14558	−	0.306958i	0.364389	−	0.931247i	$-0.381278\pi$
$727$	30.8883	−	8.27648i	1.14558	−	0.306958i	0.781193	+	0.624289i	$0.214611\pi$
$728$	−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
$733$	1.74858	+	0.468531i	0.0645854	+	0.0173056i	0.290967	−	0.956733i	$-0.406023\pi$
$733$	1.74858	+	0.468531i	0.0645854	+	0.0173056i	−0.226382	+	0.974039i	$0.572690\pi$
$734$	−16.0318	−	27.7679i	−0.591744	−	1.02493i
$735$		0			0
$736$	−2.60061	+	0.696830i	−0.0958596	+	0.0256855i
$737$	−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	$0.915403\pi$
$740$	2.65087	−	0.710298i	0.0974479	−	0.0261111i
$741$		0			0
$742$	7.64528	−	28.5326i	0.280667	−	1.04746i
$743$	7.34361	−	27.4067i	0.269411	−	1.00545i	−0.690084	−	0.723729i	$-0.742427\pi$
$743$	7.34361	−	27.4067i	0.269411	−	1.00545i	0.959495	−	0.281726i	$-0.0909068\pi$
$744$		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
$751$	−13.8771	−	3.71835i	−0.506382	−	0.135685i	−0.00342162	−	0.999994i	$-0.501089\pi$
$751$	−13.8771	−	3.71835i	−0.506382	−	0.135685i	−0.502960	+	0.864310i	$0.667756\pi$
$752$	8.89932	−	33.2127i	0.324525	−	1.21114i
$753$		0			0
$754$	27.4329	+	11.0998i	0.999049	+	0.404231i
$755$		−	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	0.0904223	−	0.995904i	$-0.471178\pi$
$761$	27.5341	−	15.8968i	0.998111	−	0.576260i	0.907689	+	0.419644i	$0.137845\pi$
$762$		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
$769$	−11.8524	−	3.17584i	−0.427409	−	0.114524i	0.0387008	−	0.999251i	$-0.487678\pi$
$769$	−11.8524	−	3.17584i	−0.427409	−	0.114524i	−0.466110	+	0.884727i	$0.654345\pi$
$770$	−10.1091	+	5.83649i	−0.364306	+	0.210332i
$771$		0			0
$772$	−0.500725	−	1.86873i	−0.0180215	−	0.0672571i
$773$	−21.0505	+	21.0505i	−0.757134	+	0.757134i	−0.975800	−	0.218665i	$-0.929830\pi$
$773$	−21.0505	+	21.0505i	−0.757134	+	0.757134i	0.218665	+	0.975800i	$0.429830\pi$
$774$		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
$781$	0.988655	+	3.68971i	0.0353769	+	0.132028i
$782$	−17.0232			−0.608749
$783$		0			0
$784$	21.1848			0.756601
$785$	8.22255	+	30.6870i	0.293475	+	1.09526i
$786$		0			0
$787$	−42.0497	+	24.2774i	−1.49891	+	0.865396i	−0.999999	−	0.00125841i	$-0.999599\pi$
$787$	−42.0497	+	24.2774i	−1.49891	+	0.865396i	−0.498910	+	0.866654i	$0.666266\pi$
$788$	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
$794$	−12.9119	−	48.1880i	−0.458228	−	1.71013i
$795$		0			0
$796$	−2.77094	+	1.59981i	−0.0982135	+	0.0567036i
$797$	12.5182	+	3.35424i	0.443418	+	0.118813i	0.473618	−	0.880730i	$-0.342948\pi$
$797$	12.5182	+	3.35424i	0.443418	+	0.118813i	−0.0302002	+	0.999544i	$0.509614\pi$
$798$		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	$-0.966477\pi$
$809$	−31.2753	−	31.2753i	−1.09958	−	1.09958i	−0.105121	−	0.994459i	$-0.533523\pi$
$810$		0			0
$811$			52.5371i			1.84483i	0.386202	+	0.922414i	$0.373787\pi$
$811$			52.5371i			1.84483i	−0.386202	+	0.922414i	$0.626213\pi$
$812$	−1.94901	−	4.59807i	−0.0683970	−	0.161361i
$813$		0			0
$814$	−1.67879	+	6.26534i	−0.0588416	+	0.219600i
$815$	36.6146	+	9.81085i	1.28255	+	0.343659i
$816$		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	$-0.717105\pi$
$821$	10.2315	−	17.7215i	0.357082	−	0.618485i	0.987472	+	0.157794i	$0.0504382\pi$
$822$		0			0
$823$	3.57813	−	13.3538i	0.124726	−	0.465483i	−0.875104	−	0.483935i	$-0.839207\pi$
$823$	3.57813	−	13.3538i	0.124726	−	0.465483i	0.999830	+	0.0184521i	$0.00587381\pi$
$824$	1.45763	−	5.43993i	0.0507788	−	0.189509i
$825$		0			0
$826$	−45.5232	+	12.1979i	−1.58395	+	0.424419i
$827$	2.40919	+	2.40919i	0.0837756	+	0.0837756i	0.747753	−	0.663977i	$-0.231133\pi$
$827$	2.40919	+	2.40919i	0.0837756	+	0.0837756i	−0.663977	+	0.747753i	$0.731133\pi$
$828$		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	$0.554713\pi$
$830$	−4.98536	+	1.33582i	−0.173044	+	0.0463671i
$831$		0			0
$832$	12.1154	+	20.9845i	0.420027	+	0.727508i
$833$	29.2276	+	7.83152i	1.01268	+	0.271346i
$834$		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
$839$	16.0505	−	4.30071i	0.554124	−	0.148477i	0.0291187	−	0.999576i	$-0.490730\pi$
$839$	16.0505	−	4.30071i	0.554124	−	0.148477i	0.525006	+	0.851099i	$0.324063\pi$
$840$		0			0
$841$	20.1662	−	20.8404i	0.695387	−	0.718635i
$842$	26.7717	−	15.4567i	0.922614	−	0.532672i
$843$		0			0
$844$	1.65403	−	0.443195i	0.0569340	−	0.0152554i
$845$	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
$851$	−2.01319	+	7.51334i	−0.0690114	+	0.257554i
$852$		0			0
$853$	5.42787	+	20.2571i	0.185847	+	0.693589i	0.994448	+	0.105232i	$0.0335584\pi$
$853$	5.42787	+	20.2571i	0.185847	+	0.693589i	−0.808601	+	0.588357i	$0.799775\pi$
$854$	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	−0.306463	−	0.951882i	$-0.599146\pi$
$857$	−37.5900	−	21.7026i	−1.28405	−	0.741346i	−0.977586	+	0.210536i	$0.932479\pi$
$858$		0			0
$859$	−7.88230	−	2.11206i	−0.268941	−	0.0720624i	0.121828	−	0.992551i	$-0.461124\pi$
$859$	−7.88230	−	2.11206i	−0.268941	−	0.0720624i	−0.390769	+	0.920489i	$0.627791\pi$
$860$	−1.52810	−	0.409452i	−0.0521076	−	0.0139622i
$861$		0			0
$862$	10.8933	−	2.91885i	0.371027	−	0.0994164i
$863$	8.84629			0.301131			0.150566	−	0.988600i	$-0.451890\pi$
$863$	8.84629			0.301131			0.150566	+	0.988600i	$0.451890\pi$
$864$		0			0
$865$	5.86783			0.199512
$866$	29.7588	+	17.1813i	1.01125	+	0.583843i
$867$		0			0
$868$	−4.13021	−	1.10669i	−0.140189	−	0.0375634i
$869$	−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	0.995498	+	0.0947835i	$0.0302159\pi$
$877$	17.1713	+	29.7416i	0.579834	+	1.00430i	−0.415664	+	0.909518i	$0.636451\pi$
$878$	0.460989	−	1.72044i	0.0155576	−	0.0580619i
$879$		0			0
$880$	2.61433	+	9.75680i	0.0881290	+	0.328902i
$881$	−10.6186	+	10.6186i	−0.357750	+	0.357750i	−0.862983	−	0.505233i	$-0.831406\pi$
$881$	−10.6186	+	10.6186i	−0.357750	+	0.357750i	0.505233	+	0.862983i	$0.331406\pi$
$882$		0			0
$883$		−	32.4616i		−	1.09242i	−0.837648	−	0.546211i	$-0.816070\pi$
$883$		−	32.4616i		−	1.09242i	0.837648	−	0.546211i	$-0.183930\pi$
$884$	−1.63026	−	6.08421i	−0.0548316	−	0.204634i
$885$		0			0
$886$	−10.2652	−	17.7798i	−0.344864	−	0.597323i
$887$	−25.1123	−	6.72883i	−0.843190	−	0.225932i	−0.188730	−	0.982029i	$-0.560437\pi$
$887$	−25.1123	−	6.72883i	−0.843190	−	0.225932i	−0.654460	+	0.756097i	$0.727104\pi$
$888$		0			0
$889$	−70.9472	+	19.0102i	−2.37949	+	0.637583i
$890$		−	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
$896$	11.5770	−	43.2058i	0.386759	−	1.44341i
$897$		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
$902$	3.33635	+	12.4514i	0.111088	+	0.414587i
$903$		0			0
$904$	5.20236	−	3.00359i	0.173028	−	0.0998978i
$905$	−7.51875	−	13.0229i	−0.249932	−	0.432895i
$906$		0			0
$907$	−8.93732	−	33.3545i	−0.296759	−	1.10752i	−0.939810	−	0.341696i	$-0.888999\pi$
$907$	−8.93732	−	33.3545i	−0.296759	−	1.10752i	0.643052	−	0.765823i	$-0.277668\pi$
$908$	2.37346			0.0787659
$909$		0			0
$910$	−30.7274	−	30.7274i	−1.01860	−	1.01860i
$911$	3.15410	−	0.845139i	0.104500	−	0.0280007i	−0.206190	−	0.978512i	$-0.566107\pi$
$911$	3.15410	−	0.845139i	0.104500	−	0.0280007i	0.310690	+	0.950511i	$0.399440\pi$
$912$		0			0
$913$	0.376316	−	1.40443i	0.0124542	−	0.0464799i
$914$	−10.8274	+	40.4085i	−0.358140	+	1.33660i
$915$		0			0
$916$	−6.65294	+	1.78265i	−0.219819	+	0.0589004i
$917$	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	$0.483265\pi$
$920$	2.75528	+	10.2828i	0.0908388	+	0.339015i
$921$		0			0
$922$	−19.9282	−	34.5166i	−0.656299	−	1.13674i
$923$	−12.3151	+	7.11014i	−0.405357	+	0.234033i
$924$		0			0
$925$	−0.370291	−	1.38194i	−0.0121751	−	0.0454380i
$926$	−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	0.726117	−	0.687572i	$-0.241323\pi$
$929$	15.0484	+	8.68817i	0.493721	+	0.285050i	−0.232396	+	0.972621i	$0.574657\pi$
$930$		0			0
$931$	−3.85193	+	14.3756i	−0.126242	+	0.471141i
$932$	−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	$0.924999\pi$
$938$	−57.8383	+	15.4977i	−1.88849	+	0.506019i
$939$		0			0
$940$	4.64268	+	1.24400i	0.151427	+	0.0405748i
$941$	−11.6261	−	20.1370i	−0.378999	−	0.656446i	0.611918	−	0.790922i	$-0.290398\pi$
$941$	−11.6261	−	20.1370i	−0.378999	−	0.656446i	−0.990917	+	0.134475i	$0.957065\pi$
$942$		0			0
$943$	4.00092	+	14.9316i	0.130288	+	0.486241i
$944$			40.7822i			1.32735i
$945$		0			0
$946$	2.64392	−	2.64392i	0.0859611	−	0.0859611i
$947$	−10.8166	−	40.3682i	−0.351493	−	1.31179i	−0.884841	−	0.465894i	$-0.845733\pi$
$947$	−10.8166	−	40.3682i	−0.351493	−	1.31179i	0.533348	−	0.845896i	$-0.320934\pi$
$948$		0			0
$949$	13.0010	−	48.5203i	0.422030	−	1.57504i
$950$	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	$-0.885964\pi$
$953$		−	21.6490i		−	0.701279i	0.936511	−	0.350640i	$-0.114036\pi$
$954$		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
$959$	−77.1117	−	20.6620i	−2.49007	−	0.667211i
$960$		0			0
$961$	8.43594	+	4.87049i	0.272127	+	0.157113i
$962$	−24.1468			−0.778525
$963$		0			0
$964$	3.71694			0.119715
$965$	−15.9343	+	4.26959i	−0.512944	+	0.137443i
$966$		0			0
$967$	−10.2861	−	2.75616i	−0.330780	−	0.0886323i	0.0896068	−	0.995977i	$-0.471439\pi$
$967$	−10.2861	−	2.75616i	−0.330780	−	0.0886323i	−0.420387	+	0.907345i	$0.638106\pi$
$968$	25.2726	+	6.77178i	0.812293	+	0.217653i
$969$		0			0
$970$	−44.3921	−	25.6298i	−1.42535	−	0.822924i
$971$	3.39160	−	3.39160i	0.108842	−	0.108842i	−0.650589	−	0.759430i	$-0.725478\pi$
$971$	3.39160	−	3.39160i	0.108842	−	0.108842i	0.759430	+	0.650589i	$0.225478\pi$
$972$		0			0
$973$	−24.7349			−0.792964
$974$	9.62901	+	35.9359i	0.308533	+	1.15146i
$975$		0			0
$976$	8.83623	−	32.9773i	0.282841	−	1.05558i
$977$	17.6662	−	10.1996i	0.565193	−	0.326314i	−0.190034	−	0.981777i	$-0.560860\pi$
$977$	17.6662	−	10.1996i	0.565193	−	0.326314i	0.755227	+	0.655463i	$0.227527\pi$
$978$		0			0
$979$	5.06784	+	2.92592i	0.161969	+	0.0935128i
$980$			2.96134i			0.0945967i
$981$		0			0
$982$	48.5789			1.55022
$983$	−3.39666	+	0.910132i	−0.108337	+	0.0290287i	−0.312580	−	0.949891i	$-0.601193\pi$
$983$	−3.39666	+	0.910132i	−0.108337	+	0.0290287i	0.204243	+	0.978920i	$0.434527\pi$
$984$		0			0
$985$	46.6726	−	26.9465i	1.48711	−	0.858586i
$986$	−51.3971	−	6.33722i	−1.63682	−	0.201818i
$987$		0			0
$988$	2.99252	−	0.801843i	0.0952047	−	0.0255100i
$989$	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
$994$	19.4475	+	5.21095i	0.616838	+	0.165281i
$995$	13.6413	+	23.6274i	0.432457	+	0.749038i
$996$		0			0
$997$	7.85304	−	2.10421i	0.248708	−	0.0666412i	−0.132311	−	0.991208i	$-0.542240\pi$
$997$	7.85304	−	2.10421i	0.248708	−	0.0666412i	0.381019	+	0.924567i	$0.375573\pi$
$998$	−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.737.21		112
3.2	odd	2		261.2.l.a.128.8	yes	112
9.4	even	3		261.2.l.a.41.8	✓	112
9.5	odd	6	inner	783.2.m.a.476.21		112
29.17	odd	4	inner	783.2.m.a.278.21		112
87.17	even	4		261.2.l.a.191.8	yes	112
261.104	even	12	inner	783.2.m.a.17.21		112
261.220	odd	12		261.2.l.a.104.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.l.a.41.8	✓	112	9.4	even	3
261.2.l.a.104.8	yes	112	261.220	odd	12
261.2.l.a.128.8	yes	112	3.2	odd	2
261.2.l.a.191.8	yes	112	87.17	even	4
783.2.m.a.17.21		112	261.104	even	12	inner
783.2.m.a.278.21		112	29.17	odd	4	inner
783.2.m.a.476.21		112	9.5	odd	6	inner
783.2.m.a.737.21		112	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(0.390005 + 1.45552i) q^{2} +(-0.234384 + 0.135322i) q^{4} +(1.15386 + 1.99855i) q^{5} +(-1.71329 + 2.96750i) q^{7} +(1.84266 + 1.84266i) q^{8} +O(q^{10})\)	\(q+(0.390005 + 1.45552i) q^{2} +(-0.234384 + 0.135322i) q^{4} +(1.15386 + 1.99855i) q^{5} +(-1.71329 + 2.96750i) q^{7} +(1.84266 + 1.84266i) q^{8} +(-2.45892 + 2.45892i) q^{10} +(-0.253547 - 0.946251i) q^{11} +(3.15830 - 1.82344i) q^{13} +(-4.98745 - 1.33638i) q^{14} +(-2.23402 + 3.86943i) q^{16} +(-4.51260 + 4.51260i) q^{17} +(-2.21952 - 2.21952i) q^{19} +(-0.540893 - 0.312285i) q^{20} +(1.27840 - 0.738086i) q^{22} +(1.53305 - 0.885107i) q^{23} +(-0.162800 + 0.281977i) q^{25} +(3.88581 + 3.88581i) q^{26} -0.927379i q^{28} +(4.95814 - 2.10164i) q^{29} +(1.19335 - 4.45364i) q^{31} +(-1.46909 - 0.393642i) q^{32} +(-8.32812 - 4.80824i) q^{34} -7.90760 q^{35} +(-3.10705 + 3.10705i) q^{37} +(2.36493 - 4.09618i) q^{38} +(-1.55647 + 5.80881i) q^{40} +(-2.26013 + 8.43493i) q^{41} +(2.44664 - 0.655574i) q^{43} +(0.187475 + 0.187475i) q^{44} +(1.88619 + 1.88619i) q^{46} +(-7.43340 + 1.99177i) q^{47} +(-2.37071 - 4.10619i) q^{49} +(-0.473916 - 0.126985i) q^{50} +(-0.493502 + 0.854771i) q^{52} +5.72088i q^{53} +(1.59857 - 1.59857i) q^{55} +(-8.62508 + 2.31108i) q^{56} +(4.99268 + 6.39702i) q^{58} +(7.90468 - 4.56377i) q^{59} +(-7.38070 + 1.97765i) q^{61} +6.94778 q^{62} +6.64426i q^{64} +(7.28848 + 4.20801i) q^{65} +(10.0431 - 5.79839i) q^{67} +(0.447028 - 1.66833i) q^{68} +(-3.08401 - 11.5097i) q^{70} -3.89929 q^{71} +(9.73964 - 9.73964i) q^{73} +(-5.73414 - 3.31061i) q^{74} +(0.820568 + 0.219871i) q^{76} +(3.24240 + 0.868799i) q^{77} +(5.28760 - 1.41681i) q^{79} -10.3110 q^{80} -13.1587 q^{82} +(1.28536 + 0.742103i) q^{83} +(-14.2256 - 3.81173i) q^{85} +(1.90840 + 3.30545i) q^{86} +(1.27641 - 2.21081i) q^{88} +(-4.22391 + 4.22391i) q^{89} +12.4963i q^{91} +(-0.239548 + 0.414909i) q^{92} +(-5.79813 - 10.0427i) q^{94} +(1.87480 - 6.99684i) q^{95} +(3.81516 + 14.2384i) q^{97} +(5.05205 - 5.05205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 6 q^{2} - 4 q^{7}+O(q^{10}) \) 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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