LMFDB - Embedded newform 819.2.s.d.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 2]))

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.4
Root			$0.756174 - 1.30973i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.d.802.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.851125 q^{2} -1.27559 q^{4} +(1.72074 - 2.98041i) q^{5} +(-2.57273 - 0.617304i) q^{7} -2.78793 q^{8} +O(q^{10})$	\(q+0.851125 q^{2} -1.27559 q^{4} +(1.72074 - 2.98041i) q^{5} +(-2.57273 - 0.617304i) q^{7} -2.78793 q^{8} +(1.46456 - 2.53670i) q^{10} +(-0.448993 + 0.777679i) q^{11} +(-3.07517 + 1.88237i) q^{13} +(-2.18972 - 0.525403i) q^{14} +0.178289 q^{16} -1.93681 q^{17} +(-0.519020 - 0.898968i) q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} -5.65013 q^{23} +(-3.42189 - 5.92688i) q^{25} +(-2.61736 + 1.60213i) q^{26} +(3.28174 + 0.787424i) q^{28} +(-0.917969 - 1.58997i) q^{29} +(4.56692 + 7.91014i) q^{31} +5.72761 q^{32} -1.64847 q^{34} +(-6.26681 + 6.60556i) q^{35} -10.6000 q^{37} +(-0.441751 - 0.765135i) q^{38} +(-4.79731 + 8.30918i) q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +(0.572729 - 0.991996i) q^{44} -4.80897 q^{46} +(3.59565 - 6.22784i) q^{47} +(6.23787 + 3.17631i) q^{49} +(-2.91246 - 5.04452i) q^{50} +(3.92265 - 2.40112i) q^{52} +(-4.69324 - 8.12893i) q^{53} +(1.54520 + 2.67637i) q^{55} +(7.17260 + 1.72100i) q^{56} +(-0.781307 - 1.35326i) q^{58} +0.510517 q^{59} +(-0.718095 - 1.24378i) q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(0.318655 + 12.4043i) q^{65} +(4.22466 - 7.31732i) q^{67} +2.47057 q^{68} +(-5.33385 + 5.62216i) q^{70} +(-1.72419 + 2.98638i) q^{71} +(-5.45026 - 9.44013i) q^{73} -9.02195 q^{74} +(0.662054 + 1.14671i) q^{76} +(1.63520 - 1.72359i) q^{77} +(6.04589 - 10.4718i) q^{79} +(0.306789 - 0.531375i) q^{80} +(-2.26886 - 3.92977i) q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +(1.66593 - 2.88547i) q^{86} +(1.25176 - 2.16812i) q^{88} -13.6078 q^{89} +(9.07358 - 2.94451i) q^{91} +7.20722 q^{92} +(3.06035 - 5.30067i) q^{94} -3.57239 q^{95} +(-0.253120 + 0.438417i) q^{97} +(5.30921 + 2.70344i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} + 16 q^{32} + 32 q^{34} - 20 q^{35} + 26 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} - 32 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} + 41 q^{52} + 2 q^{53} + 9 q^{55} - 9 q^{56} - 8 q^{58} + 26 q^{59} - 5 q^{61} - 5 q^{62} - 30 q^{64} + 5 q^{65} - 11 q^{67} + 58 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} - 6 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} + 7 q^{80} + q^{82} + 54 q^{83} - q^{85} + 7 q^{86} + 8 q^{89} - 23 q^{91} - 54 q^{92} + 45 q^{94} - 12 q^{95} - 35 q^{97} - 20 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.851125			0.601837			0.300918	−	0.953650i	$-0.402707\pi$
$2$	0.851125			0.601837			0.300918	+	0.953650i	$0.402707\pi$
$3$		0			0
$3$		0			0
$4$	−1.27559			−0.637793
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	−0.168276	−	0.985740i	$-0.553820\pi$
$5$	1.72074	−	2.98041i	0.769538	−	1.33288i	0.937814	−	0.347139i	$-0.112847\pi$
$6$		0			0
$7$	−2.57273	−	0.617304i	−0.972400	−	0.233319i
$7$	−2.57273	−	0.617304i	−0.972400	−	0.233319i
$8$	−2.78793			−0.985684
$9$		0			0
$10$	1.46456	−	2.53670i	0.463136	−	0.802175i
$11$	−0.448993	+	0.777679i	−0.135377	+	0.234479i	−0.925741	−	0.378158i	$-0.876558\pi$
$11$	−0.448993	+	0.777679i	−0.135377	+	0.234479i	0.790365	+	0.612637i	$0.209891\pi$
$12$		0			0
$13$	−3.07517	+	1.88237i	−0.852900	+	0.522075i
$13$	−3.07517	+	1.88237i	−0.852900	+	0.522075i
$14$	−2.18972	−	0.525403i	−0.585226	−	0.140420i
$15$		0			0
$16$	0.178289			0.0445723
$17$	−1.93681			−0.469745			−0.234873	−	0.972026i	$-0.575467\pi$
$17$	−1.93681			−0.469745			−0.234873	+	0.972026i	$0.575467\pi$
$18$		0			0
$19$	−0.519020	−	0.898968i	−0.119071	−	0.206237i	0.800329	−	0.599562i	$-0.204658\pi$
$19$	−0.519020	−	0.898968i	−0.119071	−	0.206237i	−0.919400	+	0.393324i	$0.871325\pi$
$20$	−2.19495	+	3.80177i	−0.490806	+	0.850101i
$21$		0			0
$22$	−0.382150	+	0.661902i	−0.0814745	+	0.141118i
$23$	−5.65013			−1.17813			−0.589067	−	0.808084i	$-0.700504\pi$
$23$	−5.65013			−1.17813			−0.589067	+	0.808084i	$0.700504\pi$
$24$		0			0
$25$	−3.42189	−	5.92688i	−0.684378	−	1.18538i
$26$	−2.61736	+	1.60213i	−0.513306	+	0.314204i
$27$		0			0
$28$	3.28174	+	0.787424i	0.620190	+	0.148809i
$29$	−0.917969	−	1.58997i	−0.170463	−	0.295250i	0.768119	−	0.640307i	$-0.221193\pi$
$29$	−0.917969	−	1.58997i	−0.170463	−	0.295250i	−0.938582	+	0.345057i	$0.887860\pi$
$30$		0			0
$31$	4.56692	+	7.91014i	0.820244	+	1.42070i	0.905501	+	0.424345i	$0.139495\pi$
$31$	4.56692	+	7.91014i	0.820244	+	1.42070i	−0.0852573	+	0.996359i	$0.527171\pi$
$32$	5.72761			1.01251
$33$		0			0
$34$	−1.64847			−0.282710
$35$	−6.26681	+	6.60556i	−1.05929	+	1.11654i
$36$		0			0
$37$	−10.6000			−1.74263			−0.871316	−	0.490722i	$-0.836733\pi$
$37$	−10.6000			−1.74263			−0.871316	+	0.490722i	$0.836733\pi$
$38$	−0.441751	−	0.765135i	−0.0716614	−	0.124121i
$39$		0			0
$40$	−4.79731	+	8.30918i	−0.758521	+	1.31380i
$41$	−2.66571	−	4.61715i	−0.416314	−	0.721078i	0.579251	−	0.815149i	$-0.303345\pi$
$41$	−2.66571	−	4.61715i	−0.416314	−	0.721078i	−0.995565	+	0.0940715i	$0.970012\pi$
$42$		0			0
$43$	1.95732	−	3.39018i	0.298489	−	0.516998i	−0.677302	−	0.735706i	$-0.736851\pi$
$43$	1.95732	−	3.39018i	0.298489	−	0.516998i	0.975790	+	0.218708i	$0.0701841\pi$
$44$	0.572729	−	0.991996i	0.0863422	−	0.149549i
$45$		0			0
$46$	−4.80897			−0.709044
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	−0.475115	−	0.879924i	$-0.657593\pi$
$47$	3.59565	−	6.22784i	0.524479	−	0.908424i	0.999594	−	0.0285004i	$-0.00907317\pi$
$48$		0			0
$49$	6.23787	+	3.17631i	0.891124	+	0.453759i
$50$	−2.91246	−	5.04452i	−0.411883	−	0.713403i
$51$		0			0
$52$	3.92265	−	2.40112i	0.543973	−	0.332976i
$53$	−4.69324	−	8.12893i	−0.644666	−	1.11659i	−0.984378	−	0.176065i	$-0.943663\pi$
$53$	−4.69324	−	8.12893i	−0.644666	−	1.11659i	0.339712	−	0.940529i	$-0.389670\pi$
$54$		0			0
$55$	1.54520	+	2.67637i	0.208355	+	0.360881i
$56$	7.17260	+	1.72100i	0.958479	+	0.229979i
$57$		0			0
$58$	−0.781307	−	1.35326i	−0.102591	−	0.177692i
$59$	0.510517			0.0664637			0.0332318	−	0.999448i	$-0.489420\pi$
$59$	0.510517			0.0664637			0.0332318	+	0.999448i	$0.489420\pi$
$60$		0			0
$61$	−0.718095	−	1.24378i	−0.0919426	−	0.159249i	0.816386	−	0.577507i	$-0.195974\pi$
$61$	−0.718095	−	1.24378i	−0.0919426	−	0.159249i	−0.908328	+	0.418258i	$0.862641\pi$
$62$	3.88702	+	6.73252i	0.493653	+	0.855031i
$63$		0			0
$64$	4.51834			0.564792
$65$	0.318655	+	12.4043i	0.0395242	+	1.53857i
$66$		0			0
$67$	4.22466	−	7.31732i	0.516124	−	0.893953i	−0.483701	−	0.875233i	$-0.660708\pi$
$67$	4.22466	−	7.31732i	0.516124	−	0.893953i	0.999825	−	0.0187197i	$-0.00595900\pi$
$68$	2.47057			0.299600
$69$		0			0
$70$	−5.33385	+	5.62216i	−0.637516	+	0.671977i
$71$	−1.72419	+	2.98638i	−0.204623	+	0.354418i	−0.950013	−	0.312211i	$-0.898930\pi$
$71$	−1.72419	+	2.98638i	−0.204623	+	0.354418i	0.745389	+	0.666629i	$0.232264\pi$
$72$		0			0
$73$	−5.45026	−	9.44013i	−0.637905	−	1.10488i	−0.985892	−	0.167384i	$-0.946468\pi$
$73$	−5.45026	−	9.44013i	−0.637905	−	1.10488i	0.347987	−	0.937499i	$-0.386865\pi$
$74$	−9.02195			−1.04878
$75$		0			0
$76$	0.662054	+	1.14671i	0.0759428	+	0.131537i
$77$	1.63520	−	1.72359i	0.186349	−	0.196422i
$78$		0			0
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	−0.294699	−	0.955590i	$-0.595219\pi$
$79$	6.04589	−	10.4718i	0.680216	−	1.17817i	0.974915	−	0.222578i	$-0.0714472\pi$
$80$	0.306789	−	0.531375i	0.0343001	−	0.0594095i
$81$		0			0
$82$	−2.26886	−	3.92977i	−0.250553	−	0.433971i
$83$	−1.51669			−0.166479			−0.0832393	−	0.996530i	$-0.526527\pi$
$83$	−1.51669			−0.166479			−0.0832393	+	0.996530i	$0.526527\pi$
$84$		0			0
$85$	−3.33274	+	5.77248i	−0.361487	+	0.626113i
$86$	1.66593	−	2.88547i	0.179642	−	0.311148i
$87$		0			0
$88$	1.25176	−	2.16812i	0.133438	−	0.231122i
$89$	−13.6078			−1.44243			−0.721213	−	0.692714i	$-0.756415\pi$
$89$	−13.6078			−1.44243			−0.721213	+	0.692714i	$0.756415\pi$
$90$		0			0
$91$	9.07358	−	2.94451i	0.951170	−	0.308668i
$92$	7.20722			0.751405
$93$		0			0
$94$	3.06035	−	5.30067i	0.315651	−	0.546723i
$95$	−3.57239			−0.366519
$96$		0			0
$97$	−0.253120	+	0.438417i	−0.0257005	+	0.0445145i	−0.878590	−	0.477578i	$-0.841515\pi$
$97$	−0.253120	+	0.438417i	−0.0257005	+	0.0445145i	0.852889	+	0.522092i	$0.174848\pi$
$98$	5.30921	+	2.70344i	0.536311	+	0.273089i
$99$		0			0
$100$	4.36491	+	7.56025i	0.436491	+	0.756025i
$101$	−2.99327	+	5.18450i	−0.297842	+	0.515877i	−0.975642	−	0.219369i	$-0.929600\pi$
$101$	−2.99327	+	5.18450i	−0.297842	+	0.515877i	0.677800	+	0.735246i	$0.262933\pi$
$102$		0			0
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	−0.746073	−	0.665865i	$-0.768063\pi$
$103$	2.06651	−	3.57930i	0.203619	−	0.352679i	0.949692	+	0.313186i	$0.101396\pi$
$104$	8.57338	−	5.24792i	0.840689	−	0.514601i
$105$		0			0
$106$	−3.99454	−	6.91874i	−0.387984	−	0.672008i
$107$	14.1234			1.36536			0.682679	−	0.730718i	$-0.260815\pi$
$107$	14.1234			1.36536			0.682679	+	0.730718i	$0.260815\pi$
$108$		0			0
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	0.948934	−	0.315475i	$-0.102164\pi$
$109$	2.10119	+	3.63936i	0.201257	+	0.348588i	−0.747677	+	0.664063i	$0.768831\pi$
$110$	1.31516	+	2.27792i	0.125396	+	0.217191i
$111$		0			0
$112$	−0.458690	−	0.110059i	−0.0433421	−	0.0103996i
$113$	6.88472	−	11.9247i	0.647660	−	1.12178i	−0.336020	−	0.941855i	$-0.609081\pi$
$113$	6.88472	−	11.9247i	0.647660	−	1.12178i	0.983680	−	0.179926i	$-0.0575857\pi$
$114$		0			0
$115$	−9.72240	+	16.8397i	−0.906618	+	1.57031i
$116$	1.17095	+	2.02814i	0.108720	+	0.188308i
$117$		0			0
$118$	0.434514			0.0400003
$119$	4.98288	+	1.19560i	0.456780	+	0.109601i
$120$		0			0
$121$	5.09681	+	8.82793i	0.463346	+	0.802539i
$122$	−0.611189	−	1.05861i	−0.0553344	−	0.0958420i
$123$		0			0
$124$	−5.82550	−	10.0901i	−0.523145	−	0.906114i
$125$	−6.34531			−0.567542
$126$		0			0
$127$	−0.972482	−	1.68439i	−0.0862938	−	0.149465i	0.819648	−	0.572868i	$-0.194169\pi$
$127$	−0.972482	−	1.68439i	−0.0862938	−	0.149465i	−0.905942	+	0.423402i	$0.860836\pi$
$128$	−7.60956			−0.672596
$129$		0			0
$130$	0.271215	+	10.5576i	0.0237871	+	0.925967i
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	0.473780	+	0.880643i	$0.342889\pi$
$131$	−6.01770	+	10.4230i	−0.525769	+	0.910659i	−0.999549	+	0.0300158i	$0.990444\pi$
$132$		0			0
$133$	0.780360	+	2.63319i	0.0676658	+	0.228327i
$134$	3.59571	−	6.22796i	0.310622	−	0.538014i
$135$		0			0
$136$	5.39970			0.463020
$137$	−8.71715			−0.744756			−0.372378	−	0.928081i	$-0.621457\pi$
$137$	−8.71715			−0.744756			−0.372378	+	0.928081i	$0.621457\pi$
$138$		0			0
$139$	−2.10625	+	3.64813i	−0.178650	+	0.309430i	−0.941418	−	0.337241i	$-0.890506\pi$
$139$	−2.10625	+	3.64813i	−0.178650	+	0.309430i	0.762769	+	0.646672i	$0.223840\pi$
$140$	7.99386	−	8.42596i	0.675604	−	0.712124i
$141$		0			0
$142$	−1.46750	+	2.54178i	−0.123150	+	0.213302i
$143$	−0.0831467	−	3.23667i	−0.00695307	−	0.270664i
$144$		0			0
$145$	−6.31834			−0.524710
$146$	−4.63885	−	8.03473i	−0.383914	−	0.664959i
$147$		0			0
$148$	13.5212			1.11144
$149$	2.93242	+	5.07910i	0.240233	+	0.416096i	0.960781	−	0.277310i	$-0.0894428\pi$
$149$	2.93242	+	5.07910i	0.240233	+	0.416096i	−0.720548	+	0.693406i	$0.756109\pi$
$150$		0			0
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	0.973155	+	0.230150i	$0.0739216\pi$
$151$	8.42840	+	14.5984i	0.685893	+	1.18800i	−0.287262	+	0.957852i	$0.592745\pi$
$152$	1.44699	+	2.50626i	0.117367	+	0.203285i
$153$		0			0
$154$	1.39176	−	1.46699i	0.112151	−	0.118214i
$155$	31.4339			2.52483
$156$		0			0
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	0.902116	−	0.431493i	$-0.142013\pi$
$157$	0.969500	+	1.67922i	0.0773746	+	0.134017i	−0.824742	+	0.565509i	$0.808680\pi$
$158$	5.14581	−	8.91280i	0.409379	−	0.709065i
$159$		0			0
$160$	9.85573	−	17.0706i	0.779164	−	1.34955i
$161$	14.5362	+	3.48785i	1.14562	+	0.274881i
$162$		0			0
$163$	5.94797	+	10.3022i	0.465881	+	0.806929i	0.999241	−	0.0389590i	$-0.0124042\pi$
$163$	5.94797	+	10.3022i	0.465881	+	0.806929i	−0.533360	+	0.845888i	$0.679071\pi$
$164$	3.40035	+	5.88957i	0.265522	+	0.459898i
$165$		0			0
$166$	−1.29090			−0.100193
$167$	8.28801	+	14.3553i	0.641346	+	1.11084i	0.985133	+	0.171796i	$0.0549569\pi$
$167$	8.28801	+	14.3553i	0.641346	+	1.11084i	−0.343787	+	0.939048i	$0.611710\pi$
$168$		0			0
$169$	5.91338	−	11.5772i	0.454875	−	0.890555i
$170$	−2.83658	+	4.91310i	−0.217556	+	0.376818i
$171$		0			0
$172$	−2.49673	+	4.32447i	−0.190374	+	0.329738i
$173$	−4.99328	−	8.64862i	−0.379632	−	0.657542i	0.611377	−	0.791340i	$-0.290616\pi$
$173$	−4.99328	−	8.64862i	−0.379632	−	0.657542i	−0.991009	+	0.133798i	$0.957283\pi$
$174$		0			0
$175$	5.14490	+	17.3606i	0.388918	+	1.31234i
$176$	−0.0800507	+	0.138652i	−0.00603405	+	0.0104513i
$177$		0			0
$178$	−11.5820			−0.868105
$179$	4.58829	−	7.94715i	0.342945	−	0.593998i	−0.642033	−	0.766677i	$-0.721909\pi$
$179$	4.58829	−	7.94715i	0.342945	−	0.593998i	0.984978	+	0.172679i	$0.0552423\pi$
$180$		0			0
$181$	6.00489			0.446340			0.223170	−	0.974780i	$-0.428360\pi$
$181$	6.00489			0.446340			0.223170	+	0.974780i	$0.428360\pi$
$182$	7.72276	−	2.50614i	0.572449	−	0.185768i
$183$		0			0
$184$	15.7522			1.16127
$185$	−18.2399	+	31.5924i	−1.34102	+	2.32272i
$186$		0			0
$187$	0.869614	−	1.50622i	0.0635925	−	0.110145i
$188$	−4.58655	+	7.94415i	−0.334509	+	0.579386i
$189$		0			0
$190$	−3.04055			−0.220585
$191$	0.658061	+	1.13980i	0.0476156	+	0.0824727i	0.888851	−	0.458197i	$-0.151504\pi$
$191$	0.658061	+	1.13980i	0.0476156	+	0.0824727i	−0.841235	+	0.540669i	$0.818171\pi$
$192$		0			0
$193$	8.21270	−	14.2248i	0.591163	−	1.02392i	−0.402913	−	0.915238i	$-0.632002\pi$
$193$	8.21270	−	14.2248i	0.591163	−	1.02392i	0.994076	−	0.108686i	$-0.0346643\pi$
$194$	−0.215437	+	0.373148i	−0.0154675	+	0.0267905i
$195$		0			0
$196$	−7.95694	−	4.05166i	−0.568353	−	0.289404i
$197$	−12.7938	−	22.1594i	−0.911517	−	1.57879i	−0.811922	−	0.583766i	$-0.801579\pi$
$197$	−12.7938	−	22.1594i	−0.911517	−	1.57879i	−0.0995951	−	0.995028i	$-0.531755\pi$
$198$		0			0
$199$	−25.3788			−1.79906			−0.899528	−	0.436864i	$-0.856089\pi$
$199$	−25.3788			−1.79906			−0.899528	+	0.436864i	$0.856089\pi$
$200$	9.54000	+	16.5238i	0.674580	+	1.16841i
$201$		0			0
$202$	−2.54765	+	4.41266i	−0.179252	+	0.310473i
$203$	1.38019	+	4.65723i	0.0968704	+	0.326873i
$204$		0			0
$205$	−18.3480			−1.28148
$206$	1.75886	−	3.04643i	0.122546	−	0.212255i
$207$		0			0
$208$	−0.548271	+	0.335606i	−0.0380157	+	0.0232701i
$209$	0.932145			0.0644778
$210$		0			0
$211$	2.84824	+	4.93330i	0.196081	+	0.339622i	0.947254	−	0.320483i	$-0.103845\pi$
$211$	2.84824	+	4.93330i	0.196081	+	0.339622i	−0.751173	+	0.660105i	$0.770512\pi$
$212$	5.98663	+	10.3691i	0.411164	+	0.712156i
$213$		0			0
$214$	12.0208			0.821723
$215$	−6.73608	−	11.6672i	−0.459397	−	0.795699i
$216$		0			0
$217$	−6.86649	−	23.1698i	−0.466128	−	1.57287i
$218$	1.78837	+	3.09755i	0.121124	+	0.209793i
$219$		0			0
$220$	−1.97104	−	3.41393i	−0.132887	−	0.230167i
$221$	5.95602	−	3.64579i	0.400645	−	0.245242i
$222$		0			0
$223$	−1.17906	−	2.04219i	−0.0789558	−	0.136755i	0.823844	−	0.566817i	$-0.191825\pi$
$223$	−1.17906	−	2.04219i	−0.0789558	−	0.136755i	−0.902800	+	0.430061i	$0.858492\pi$
$224$	−14.7356	−	3.53568i	−0.984564	−	0.236238i
$225$		0			0
$226$	5.85976	−	10.1494i	0.389786	−	0.675129i
$227$	−26.2926			−1.74510			−0.872551	−	0.488523i	$-0.837536\pi$
$227$	−26.2926			−1.74510			−0.872551	+	0.488523i	$0.837536\pi$
$228$		0			0
$229$	−0.0342777	+	0.0593708i	−0.00226514	+	0.00392333i	−0.867156	−	0.498037i	$-0.834054\pi$
$229$	−0.0342777	+	0.0593708i	−0.00226514	+	0.00392333i	0.864891	+	0.501960i	$0.167388\pi$
$230$	−8.27498	+	14.3327i	−0.545636	+	0.945069i
$231$		0			0
$232$	2.55924	+	4.43273i	0.168022	+	0.291023i
$233$	7.33514	−	12.7048i	0.480541	−	0.832322i	−0.519210	−	0.854647i	$-0.673774\pi$
$233$	7.33514	−	12.7048i	0.480541	−	0.832322i	0.999751	+	0.0223253i	$0.00710694\pi$
$234$		0			0
$235$	−12.3743	−	21.4330i	−0.807213	−	1.39813i
$236$	−0.651208			−0.0423901
$237$		0			0
$238$	4.24106	+	1.01761i	0.274907	+	0.0659616i
$239$	−3.35434			−0.216974			−0.108487	−	0.994098i	$-0.534601\pi$
$239$	−3.35434			−0.216974			−0.108487	+	0.994098i	$0.534601\pi$
$240$		0			0
$241$	−8.57978			−0.552672			−0.276336	−	0.961061i	$-0.589120\pi$
$241$	−8.57978			−0.552672			−0.276336	+	0.961061i	$0.589120\pi$
$242$	4.33802	+	7.51368i	0.278859	+	0.482998i
$243$		0			0
$244$	0.915991	+	1.58654i	0.0586403	+	0.101568i
$245$	20.2005	−	13.1258i	1.29056	−	0.838576i
$246$		0			0
$247$	3.28826	+	1.78750i	0.209227	+	0.113736i
$248$	−12.7323	−	22.0530i	−0.808501	−	1.40036i
$249$		0			0
$250$	−5.40066			−0.341568
$251$	10.7575	−	18.6326i	0.679010	−	1.17608i	−0.296270	−	0.955104i	$-0.595743\pi$
$251$	10.7575	−	18.6326i	0.679010	−	1.17608i	0.975280	−	0.220975i	$-0.0709238\pi$
$252$		0			0
$253$	2.53687	−	4.39399i	0.159492	−	0.276248i
$254$	−0.827704	−	1.43363i	−0.0519348	−	0.0899537i
$255$		0			0
$256$	−15.5134			−0.969585
$257$	−4.93792			−0.308019			−0.154010	−	0.988069i	$-0.549219\pi$
$257$	−4.93792			−0.308019			−0.154010	+	0.988069i	$0.549219\pi$
$258$		0			0
$259$	27.2710	+	6.54344i	1.69454	+	0.406590i
$260$	−0.406471	−	15.8228i	−0.0252083	−	0.981288i
$261$		0			0
$262$	−5.12182	+	8.87125i	−0.316427	+	0.548068i
$263$	−4.47719	+	7.75473i	−0.276076	+	0.478177i	−0.970406	−	0.241480i	$-0.922367\pi$
$263$	−4.47719	+	7.75473i	−0.276076	+	0.478177i	0.694330	+	0.719656i	$0.255701\pi$
$264$		0			0
$265$	−32.3034			−1.98438
$266$	0.664184	+	2.24118i	0.0407237	+	0.137415i
$267$		0			0
$268$	−5.38891	+	9.33387i	−0.329180	+	0.570157i
$269$	4.82345			0.294091			0.147045	−	0.989130i	$-0.453024\pi$
$269$	4.82345			0.294091			0.147045	+	0.989130i	$0.453024\pi$
$270$		0			0
$271$	−7.42144			−0.450820			−0.225410	−	0.974264i	$-0.572372\pi$
$271$	−7.42144			−0.450820			−0.225410	+	0.974264i	$0.572372\pi$
$272$	−0.345312			−0.0209376
$273$		0			0
$274$	−7.41938			−0.448221
$275$	6.14562			0.370595
$276$		0			0
$277$	3.81631			0.229300			0.114650	−	0.993406i	$-0.463425\pi$
$277$	3.81631			0.229300			0.114650	+	0.993406i	$0.463425\pi$
$278$	−1.79268	+	3.10502i	−0.107518	+	0.186226i
$279$		0			0
$280$	17.4715	−	18.4159i	1.04412	−	1.10056i
$281$	−8.54978			−0.510037			−0.255019	−	0.966936i	$-0.582082\pi$
$281$	−8.54978			−0.510037			−0.255019	+	0.966936i	$0.582082\pi$
$282$		0			0
$283$	−7.63217	+	13.2193i	−0.453686	+	0.785807i	−0.998612	−	0.0526775i	$-0.983224\pi$
$283$	−7.63217	+	13.2193i	−0.453686	+	0.785807i	0.544926	+	0.838484i	$0.316558\pi$
$284$	2.19935	−	3.80938i	0.130507	−	0.226045i
$285$		0			0
$286$	−0.0707683	−	2.75481i	−0.00418461	−	0.162895i
$287$	4.00797	+	13.5242i	0.236583	+	0.798310i
$288$		0			0
$289$	−13.2488			−0.779340
$290$	−5.37770			−0.315790
$291$		0			0
$292$	6.95227	+	12.0417i	0.406851	+	0.704687i
$293$	−2.96982	+	5.14388i	−0.173499	+	0.300509i	−0.939641	−	0.342163i	$-0.888841\pi$
$293$	−2.96982	+	5.14388i	−0.173499	+	0.300509i	0.766142	+	0.642671i	$0.222174\pi$
$294$		0			0
$295$	0.878467	−	1.52155i	0.0511463	−	0.0885881i
$296$	29.5522			1.71768
$297$		0			0
$298$	2.49586	+	4.32295i	0.144581	+	0.250422i
$299$	17.3751	−	10.6356i	1.00483	−	0.615074i
$300$		0			0
$301$	−7.12843	+	7.51376i	−0.410876	+	0.433086i
$302$	7.17362	+	12.4251i	0.412796	+	0.714983i
$303$		0			0
$304$	−0.0925356	−	0.160276i	−0.00530728	−	0.00919248i
$305$	−4.94262			−0.283013
$306$		0			0
$307$	22.2133			1.26778			0.633891	−	0.773422i	$-0.281457\pi$
$307$	22.2133			1.26778			0.633891	+	0.773422i	$0.281457\pi$
$308$	−2.08584	+	2.19859i	−0.118852	+	0.125276i
$309$		0			0
$310$	26.7542			1.51954
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	0.971152	−	0.238463i	$-0.0766435\pi$
$311$	4.92130	+	8.52394i	0.279061	+	0.483348i	−0.692091	+	0.721811i	$0.743310\pi$
$312$		0			0
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	−0.403072	−	0.915168i	$-0.632058\pi$
$313$	10.4563	−	18.1108i	0.591023	−	1.02368i	0.994095	−	0.108513i	$-0.0346090\pi$
$314$	0.825166	+	1.42923i	0.0465668	+	0.0806561i
$315$		0			0
$316$	−7.71205	+	13.3577i	−0.433837	+	0.751427i
$317$	−12.6801	+	21.9626i	−0.712188	+	1.23355i	0.251847	+	0.967767i	$0.418962\pi$
$317$	−12.6801	+	21.9626i	−0.712188	+	1.23355i	−0.964034	+	0.265778i	$0.914371\pi$
$318$		0			0
$319$	1.64865			0.0923065
$320$	7.77489	−	13.4665i	0.434629	−	0.752800i
$321$		0			0
$322$	12.3722	+	2.96860i	0.689474	+	0.165433i
$323$	1.00524	+	1.74113i	0.0559331	+	0.0968790i
$324$		0			0
$325$	21.6795	+	11.7849i	1.20256	+	0.653711i
$326$	5.06247	+	8.76845i	0.280384	+	0.485640i
$327$		0			0
$328$	7.43183	+	12.8723i	0.410354	+	0.710755i
$329$	−13.0951	+	13.8029i	−0.721956	+	0.760981i
$330$		0			0
$331$	−0.891417	−	1.54398i	−0.0489967	−	0.0848648i	0.840487	−	0.541832i	$-0.182269\pi$
$331$	−0.891417	−	1.54398i	−0.0489967	−	0.0848648i	−0.889484	+	0.456967i	$0.848936\pi$
$332$	1.93467			0.106179
$333$		0			0
$334$	7.05414	+	12.2181i	0.385985	+	0.668546i
$335$	−14.5391	−	25.1824i	−0.794354	−	1.37586i
$336$		0			0
$337$	9.56149			0.520848			0.260424	−	0.965494i	$-0.416138\pi$
$337$	9.56149			0.520848			0.260424	+	0.965494i	$0.416138\pi$
$338$	5.03303	−	9.85366i	0.273761	−	0.535969i
$339$		0			0
$340$	4.25120	−	7.36329i	0.230554	−	0.399331i
$341$	−8.20207			−0.444167
$342$		0			0
$343$	−14.0876	−	12.0225i	−0.760659	−	0.649152i
$344$	−5.45689	+	9.45160i	−0.294216	+	0.509596i
$345$		0			0
$346$	−4.24991	−	7.36106i	−0.228477	−	0.395733i
$347$	−0.633389			−0.0340021			−0.0170010	−	0.999855i	$-0.505412\pi$
$347$	−0.633389			−0.0340021			−0.0170010	+	0.999855i	$0.505412\pi$
$348$		0			0
$349$	−15.2994	−	26.4994i	−0.818960	−	1.41848i	−0.906449	−	0.422315i	$-0.861217\pi$
$349$	−15.2994	−	26.4994i	−0.818960	−	1.41848i	0.0874885	−	0.996166i	$-0.472116\pi$
$350$	4.37895	+	14.7761i	0.234065	+	0.789813i
$351$		0			0
$352$	−2.57166	+	4.45425i	−0.137070	+	0.237412i
$353$	−0.550173	+	0.952928i	−0.0292828	+	0.0507192i	−0.880295	−	0.474426i	$-0.842656\pi$
$353$	−0.550173	+	0.952928i	−0.0292828	+	0.0507192i	0.851013	+	0.525145i	$0.175989\pi$
$354$		0			0
$355$	5.93375	+	10.2776i	0.314931	+	0.545476i
$356$	17.3579			0.919969
$357$		0			0
$358$	3.90521	−	6.76402i	0.206397	−	0.357489i
$359$	−4.88693	+	8.46441i	−0.257922	+	0.446734i	−0.965685	−	0.259716i	$-0.916371\pi$
$359$	−4.88693	+	8.46441i	−0.257922	+	0.446734i	0.707763	+	0.706450i	$0.249705\pi$
$360$		0			0
$361$	8.96124	−	15.5213i	0.471644	−	0.816912i
$362$	5.11091			0.268624
$363$		0			0
$364$	−11.5741	+	3.75597i	−0.606649	+	0.196866i
$365$	−37.5139			−1.96357
$366$		0			0
$367$	5.57363	−	9.65381i	0.290941	−	0.503925i	−0.683092	−	0.730333i	$-0.739365\pi$
$367$	5.57363	−	9.65381i	0.290941	−	0.503925i	0.974033	+	0.226408i	$0.0726983\pi$
$368$	−1.00736			−0.0525121
$369$		0			0
$370$	−15.5244	+	26.8891i	−0.807076	+	1.39790i
$371$	7.05641	+	23.8107i	0.366351	+	1.23619i
$372$		0			0
$373$	15.3651	+	26.6131i	0.795573	+	1.37797i	0.922475	+	0.386057i	$0.126163\pi$
$373$	15.3651	+	26.6131i	0.795573	+	1.37797i	−0.126902	+	0.991915i	$0.540504\pi$
$374$	0.740150	−	1.28198i	0.0382723	−	0.0662895i
$375$		0			0
$376$	−10.0244	+	17.3628i	−0.516970	+	0.895419i
$377$	5.81582	+	3.16147i	0.299530	+	0.162824i
$378$		0			0
$379$	−11.3286	−	19.6217i	−0.581912	−	1.00790i	−0.995253	−	0.0973246i	$-0.968972\pi$
$379$	−11.3286	−	19.6217i	−0.581912	−	1.00790i	0.413341	−	0.910576i	$-0.364362\pi$
$380$	4.55689			0.233763
$381$		0			0
$382$	0.560093	+	0.970109i	0.0286568	+	0.0496351i
$383$	−0.294631	−	0.510317i	−0.0150550	−	0.0260760i	0.858400	−	0.512981i	$-0.171459\pi$
$383$	−0.294631	−	0.510317i	−0.0150550	−	0.0260760i	−0.873455	+	0.486905i	$0.838126\pi$
$384$		0			0
$385$	−2.32325	−	7.83942i	−0.118404	−	0.399534i
$386$	6.99004	−	12.1071i	0.355783	−	0.616235i
$387$		0			0
$388$	0.322877	−	0.559239i	0.0163916	−	0.0283910i
$389$	2.84973	+	4.93587i	0.144487	+	0.250259i	0.929181	−	0.369624i	$-0.120514\pi$
$389$	2.84973	+	4.93587i	0.144487	+	0.250259i	−0.784695	+	0.619883i	$0.787180\pi$
$390$		0			0
$391$	10.9432			0.553422
$392$	−17.3908	−	8.85535i	−0.878367	−	0.447263i
$393$		0			0
$394$	−10.8891	−	18.8605i	−0.548584	−	0.950176i
$395$	−20.8068	−	36.0384i	−1.04690	−	1.81329i
$396$		0			0
$397$	12.7641	+	22.1082i	0.640614	+	1.10958i	0.985296	+	0.170857i	$0.0546535\pi$
$397$	12.7641	+	22.1082i	0.640614	+	1.10958i	−0.344682	+	0.938720i	$0.612013\pi$
$398$	−21.6005			−1.08274
$399$		0			0
$400$	−0.610086	−	1.05670i	−0.0305043	−	0.0528350i
$401$	−25.5011			−1.27347			−0.636733	−	0.771085i	$-0.719714\pi$
$401$	−25.5011			−1.27347			−0.636733	+	0.771085i	$0.719714\pi$
$402$		0			0
$403$	−28.9339	−	15.7284i	−1.44130	−	0.783489i
$404$	3.81817	−	6.61327i	0.189961	−	0.329022i
$405$		0			0
$406$	1.17472	+	3.96388i	0.0583002	+	0.196724i
$407$	4.75934	−	8.24341i	0.235912	−	0.408611i
$408$		0			0
$409$	0.146988			0.00726807			0.00363403	−	0.999993i	$-0.498843\pi$
$409$	0.146988			0.00726807			0.00363403	+	0.999993i	$0.498843\pi$
$410$	−15.6164			−0.771241
$411$		0			0
$412$	−2.63601	+	4.56570i	−0.129867	+	0.224936i
$413$	−1.31342	−	0.315145i	−0.0646293	−	0.0155072i
$414$		0			0
$415$	−2.60983	+	4.52036i	−0.128112	+	0.221896i
$416$	−17.6134	+	10.7815i	−0.863568	+	0.528606i
$417$		0			0
$418$	0.793372			0.0388051
$419$	6.84795	+	11.8610i	0.334544	+	0.579447i	0.983397	−	0.181466i	$-0.0580844\pi$
$419$	6.84795	+	11.8610i	0.334544	+	0.579447i	−0.648853	+	0.760914i	$0.724751\pi$
$420$		0			0
$421$	3.44169			0.167738			0.0838688	−	0.996477i	$-0.473272\pi$
$421$	3.44169			0.167738			0.0838688	+	0.996477i	$0.473272\pi$
$422$	2.42421	+	4.19885i	0.118009	+	0.204397i
$423$		0			0
$424$	13.0844	+	22.6629i	0.635437	+	1.10061i
$425$	6.62754	+	11.4792i	0.321483	+	0.556825i
$426$		0			0
$427$	1.07967	+	3.64318i	0.0522491	+	0.176306i
$428$	−18.0156			−0.870816
$429$		0			0
$430$	−5.73325	−	9.93028i	−0.276482	−	0.478881i
$431$	11.1455	−	19.3046i	0.536861	−	0.929870i	−0.462210	−	0.886771i	$-0.652943\pi$
$431$	11.1455	−	19.3046i	0.536861	−	0.929870i	0.999071	−	0.0430997i	$-0.0137233\pi$
$432$		0			0
$433$	12.9481	−	22.4268i	0.622247	−	1.07776i	−0.366819	−	0.930292i	$-0.619553\pi$
$433$	12.9481	−	22.4268i	0.622247	−	1.07776i	0.989066	−	0.147472i	$-0.0471136\pi$
$434$	−5.84424	−	19.7204i	−0.280533	−	0.946611i
$435$		0			0
$436$	−2.68024	−	4.64232i	−0.128360	−	0.222327i
$437$	2.93253	+	5.07929i	0.140282	+	0.242975i
$438$		0			0
$439$	−27.9838			−1.33560			−0.667798	−	0.744343i	$-0.732763\pi$
$439$	−27.9838			−1.33560			−0.667798	+	0.744343i	$0.732763\pi$
$440$	−4.30792	−	7.46153i	−0.205372	−	0.355715i
$441$		0			0
$442$	5.06932	−	3.10302i	0.241123	−	0.147596i
$443$	16.6044	−	28.7597i	0.788900	−	1.36642i	−0.137741	−	0.990468i	$-0.543984\pi$
$443$	16.6044	−	28.7597i	0.788900	−	1.36642i	0.926641	−	0.375947i	$-0.122683\pi$
$444$		0			0
$445$	−23.4155	+	40.5568i	−1.11000	+	1.92258i
$446$	−1.00353	−	1.73816i	−0.0475185	−	0.0823044i
$447$		0			0
$448$	−11.6245	−	2.78919i	−0.549204	−	0.131777i
$449$	9.84320	−	17.0489i	0.464529	−	0.804589i	−0.534651	−	0.845073i	$-0.679557\pi$
$449$	9.84320	−	17.0489i	0.464529	−	0.804589i	0.999180	+	0.0404845i	$0.0128901\pi$
$450$		0			0
$451$	4.78755			0.225437
$452$	−8.78205	+	15.2110i	−0.413073	+	0.715464i
$453$		0			0
$454$	−22.3783			−1.05027
$455$	6.83744	−	32.1097i	0.320544	−	1.50533i
$456$		0			0
$457$	−0.746942			−0.0349405			−0.0174702	−	0.999847i	$-0.505561\pi$
$457$	−0.746942			−0.0349405			−0.0174702	+	0.999847i	$0.505561\pi$
$458$	−0.0291746	+	0.0505320i	−0.00136324	+	0.00236120i
$459$		0			0
$460$	12.4017	−	21.4805i	0.578235	−	1.00153i
$461$	−16.5855	+	28.7269i	−0.772464	+	1.33795i	0.163744	+	0.986503i	$0.447643\pi$
$461$	−16.5855	+	28.7269i	−0.772464	+	1.33795i	−0.936209	+	0.351445i	$0.885691\pi$
$462$		0			0
$463$	−30.7521			−1.42917			−0.714586	−	0.699548i	$-0.753385\pi$
$463$	−30.7521			−1.42917			−0.714586	+	0.699548i	$0.753385\pi$
$464$	−0.163664	−	0.283475i	−0.00759792	−	0.0131600i
$465$		0			0
$466$	6.24313	−	10.8134i	0.289207	−	0.500922i
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	0.288420	+	0.957504i	$0.406870\pi$
$467$	−14.8033	+	25.6400i	−0.685013	+	1.18648i	−0.973433	+	0.228973i	$0.926463\pi$
$468$		0			0
$469$	−15.3859	+	16.2176i	−0.710456	+	0.748859i
$470$	−10.5321	−	18.2422i	−0.485810	−	0.841448i
$471$		0			0
$472$	−1.42329			−0.0655122
$473$	1.75765	+	3.04434i	0.0808168	+	0.139979i
$474$		0			0
$475$	−3.55205	+	6.15234i	−0.162979	+	0.282289i
$476$	−6.35609	−	1.52509i	−0.291331	−	0.0699024i
$477$		0			0
$478$	−2.85496			−0.130583
$479$	7.04527	−	12.2028i	0.321907	−	0.557559i	−0.658975	−	0.752165i	$-0.729010\pi$
$479$	7.04527	−	12.2028i	0.321907	−	0.557559i	0.980881	+	0.194606i	$0.0623429\pi$
$480$		0			0
$481$	32.5969	−	19.9531i	1.48629	−	0.909785i
$482$	−7.30247			−0.332618
$483$		0			0
$484$	−6.50142	−	11.2608i	−0.295519	−	0.511854i
$485$	0.871108	+	1.50880i	0.0395550	+	0.0685112i
$486$		0			0
$487$	−16.7955			−0.761075			−0.380537	−	0.924766i	$-0.624261\pi$
$487$	−16.7955			−0.761075			−0.380537	+	0.924766i	$0.624261\pi$
$488$	2.00200	+	3.46757i	0.0906263	+	0.156969i
$489$		0			0
$490$	17.1931	−	11.1717i	0.776706	−	0.504686i
$491$	10.8345	+	18.7659i	0.488954	+	0.846893i	0.999919	−	0.0127081i	$-0.00404524\pi$
$491$	10.8345	+	18.7659i	0.488954	+	0.846893i	−0.510965	+	0.859601i	$0.670712\pi$
$492$		0			0
$493$	1.77793	+	3.07947i	0.0800740	+	0.138692i
$494$	2.79873	+	1.52138i	0.125921	+	0.0684503i
$495$		0			0
$496$	0.814234	+	1.41029i	0.0365602	+	0.0633241i
$497$	6.27937	−	6.61880i	0.281668	−	0.296894i
$498$		0			0
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	−0.478051	−	0.878332i	$-0.658656\pi$
$499$	11.6524	−	20.1825i	0.521633	−	0.903495i	0.999683	−	0.0251622i	$-0.00801023\pi$
$500$	8.09399			0.361974
$501$		0			0
$502$	9.15601	−	15.8587i	0.408653	−	0.707807i
$503$	−21.9415	+	38.0037i	−0.978322	+	1.69450i	−0.309816	+	0.950796i	$0.600268\pi$
$503$	−21.9415	+	38.0037i	−0.978322	+	1.69450i	−0.668506	+	0.743707i	$0.733066\pi$
$504$		0			0
$505$	10.3013	+	17.8423i	0.458401	+	0.793974i
$506$	2.15919	−	3.73983i	0.0959879	−	0.166256i
$507$		0			0
$508$	1.24048	+	2.14858i	0.0550376	+	0.0953279i
$509$	−19.9242			−0.883125			−0.441563	−	0.897230i	$-0.645576\pi$
$509$	−19.9242			−0.883125			−0.441563	+	0.897230i	$0.645576\pi$
$510$		0			0
$511$	8.19461	+	27.6514i	0.362508	+	1.22322i
$512$	2.01529			0.0890641
$513$		0			0
$514$	−4.20279			−0.185377
$515$	−7.11185	−	12.3181i	−0.313386	−	0.542800i
$516$		0			0
$517$	3.22884	+	5.59252i	0.142004	+	0.245959i
$518$	23.2110	+	5.56929i	1.01983	+	0.244700i
$519$		0			0
$520$	−0.888388	−	34.5825i	−0.0389584	−	1.51654i
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	0.626318	−	0.779568i	$-0.284561\pi$
$521$	−8.26204	−	14.3103i	−0.361967	−	0.626944i	−0.988284	+	0.152623i	$0.951228\pi$
$522$		0			0
$523$	−11.9962			−0.524556			−0.262278	−	0.964992i	$-0.584474\pi$
$523$	−11.9962			−0.524556			−0.262278	+	0.964992i	$0.584474\pi$
$524$	7.67609	−	13.2954i	0.335332	−	0.580812i
$525$		0			0
$526$	−3.81065	+	6.60024i	−0.166152	+	0.287784i
$527$	−8.84526	−	15.3204i	−0.385305	−	0.667369i
$528$		0			0
$529$	8.92395			0.387998
$530$	−27.4942			−1.19427
$531$		0			0
$532$	−0.995416	−	3.35886i	−0.0431567	−	0.145625i
$533$	16.8887	+	9.18068i	0.731531	+	0.397660i
$534$		0			0
$535$	24.3026	−	42.0934i	1.05070	−	1.81986i
$536$	−11.7781	+	20.4002i	−0.508735	+	0.881155i
$537$		0			0
$538$	4.10536			0.176995
$539$	−5.27091	+	3.42492i	−0.227034	+	0.147522i
$540$		0			0
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	0.153739	+	0.988112i	$0.450869\pi$
$541$	−18.1158	+	31.3775i	−0.778860	+	1.34903i	−0.932599	+	0.360914i	$0.882465\pi$
$542$	−6.31658			−0.271320
$543$		0			0
$544$	−11.0933			−0.475621
$545$	14.4624			0.619500
$546$		0			0
$547$	−7.34857			−0.314202			−0.157101	−	0.987583i	$-0.550215\pi$
$547$	−7.34857			−0.314202			−0.157101	+	0.987583i	$0.550215\pi$
$548$	11.1195			0.475000
$549$		0			0
$550$	5.23069			0.223037
$551$	−0.952888	+	1.65045i	−0.0405944	+	0.0703115i
$552$		0			0
$553$	−22.0187	+	23.2089i	−0.936331	+	0.986944i
$554$	3.24816			0.138001
$555$		0			0
$556$	2.68670	−	4.65350i	0.113941	−	0.197352i
$557$	5.41399	−	9.37731i	0.229398	−	0.397329i	−0.728232	−	0.685331i	$-0.759658\pi$
$557$	5.41399	−	9.37731i	0.229398	−	0.397329i	0.957630	+	0.288002i	$0.0929909\pi$
$558$		0			0
$559$	0.362466	+	14.1098i	0.0153307	+	0.596781i
$560$	−1.11731	+	1.17770i	−0.0472148	+	0.0497670i
$561$		0			0
$562$	−7.27694			−0.306959
$563$	13.8599			0.584127			0.292064	−	0.956399i	$-0.405658\pi$
$563$	13.8599			0.584127			0.292064	+	0.956399i	$0.405658\pi$
$564$		0			0
$565$	−23.6936	−	41.0386i	−0.996798	−	1.72651i
$566$	−6.49594	+	11.2513i	−0.273045	+	0.472927i
$567$		0			0
$568$	4.80692	−	8.32583i	0.201694	−	0.349344i
$569$	−27.4120			−1.14917			−0.574586	−	0.818444i	$-0.694837\pi$
$569$	−27.4120			−1.14917			−0.574586	+	0.818444i	$0.694837\pi$
$570$		0			0
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	0.868191	−	0.496230i	$-0.165283\pi$
$571$	0.103879	+	0.179923i	0.00434719	+	0.00752956i	−0.863844	+	0.503760i	$0.831950\pi$
$572$	0.106061	+	4.12865i	0.00443462	+	0.172627i
$573$		0			0
$574$	3.41129	+	11.5108i	0.142384	+	0.480452i
$575$	19.3341	+	33.4876i	0.806288	+	1.39653i
$576$		0			0
$577$	1.66328	+	2.88089i	0.0692434	+	0.119933i	0.898568	−	0.438833i	$-0.144608\pi$
$577$	1.66328	+	2.88089i	0.0692434	+	0.119933i	−0.829325	+	0.558766i	$0.811275\pi$
$578$	−11.2764			−0.469035
$579$		0			0
$580$	8.05959			0.334656
$581$	3.90204	+	0.936261i	0.161884	+	0.0388426i
$582$		0			0
$583$	8.42893			0.349091
$584$	15.1950	+	26.3185i	0.628772	+	1.08907i
$585$		0			0
$586$	−2.52769	+	4.37809i	−0.104418	+	0.180857i
$587$	−7.54051	−	13.0606i	−0.311230	−	0.539067i	0.667399	−	0.744701i	$-0.267408\pi$
$587$	−7.54051	−	13.0606i	−0.311230	−	0.539067i	−0.978629	+	0.205634i	$0.934074\pi$
$588$		0			0
$589$	4.74064	−	8.21104i	0.195335	−	0.338330i
$590$	0.747686	−	1.29503i	0.0307817	−	0.0533155i
$591$		0			0
$592$	−1.88987			−0.0776732
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	−0.468609	−	0.883405i	$-0.655245\pi$
$593$	12.9245	−	22.3859i	0.530747	−	0.919281i	0.999356	−	0.0358751i	$-0.0114218\pi$
$594$		0			0
$595$	12.1376	−	12.7937i	0.497594	−	0.524491i
$596$	−3.74055	−	6.47882i	−0.153219	−	0.265383i
$597$		0			0
$598$	14.7884	−	9.05225i	0.604743	−	0.370174i
$599$	−17.7734	−	30.7845i	−0.726203	−	1.25782i	−0.958477	−	0.285170i	$-0.907950\pi$
$599$	−17.7734	−	30.7845i	−0.726203	−	1.25782i	0.232274	−	0.972650i	$-0.425383\pi$
$600$		0			0
$601$	13.6474	+	23.6379i	0.556688	+	0.964212i	0.997770	+	0.0667449i	$0.0212614\pi$
$601$	13.6474	+	23.6379i	0.556688	+	0.964212i	−0.441082	+	0.897467i	$0.645405\pi$
$602$	−6.06719	+	6.39515i	−0.247280	+	0.260647i
$603$		0			0
$604$	−10.7511	−	18.6215i	−0.437458	−	0.757699i
$605$	35.0811			1.42625
$606$		0			0
$607$	19.4629	+	33.7108i	0.789976	+	1.36828i	0.925981	+	0.377570i	$0.123240\pi$
$607$	19.4629	+	33.7108i	0.789976	+	1.36828i	−0.136006	+	0.990708i	$0.543426\pi$
$608$	−2.97274	−	5.14894i	−0.120561	−	0.208817i
$609$		0			0
$610$	−4.20679			−0.170328
$611$	0.665859	+	25.9200i	0.0269378	+	1.04861i
$612$		0			0
$613$	−0.443322	+	0.767857i	−0.0179056	+	0.0310135i	−0.874839	−	0.484413i	$-0.839033\pi$
$613$	−0.443322	+	0.767857i	−0.0179056	+	0.0310135i	0.856934	+	0.515427i	$0.172367\pi$
$614$	18.9063			0.762997
$615$		0			0
$616$	−4.55884	+	4.80526i	−0.183681	+	0.193609i
$617$	17.3944	−	30.1280i	0.700272	−	1.21291i	−0.268099	−	0.963391i	$-0.586395\pi$
$617$	17.3944	−	30.1280i	0.700272	−	1.21291i	0.968371	−	0.249515i	$-0.0802712\pi$
$618$		0			0
$619$	−1.02781	−	1.78021i	−0.0413111	−	0.0715529i	0.844631	−	0.535350i	$-0.179820\pi$
$619$	−1.02781	−	1.78021i	−0.0413111	−	0.0715529i	−0.885942	+	0.463797i	$0.846487\pi$
$620$	−40.0967			−1.61032
$621$		0			0
$622$	4.18864	+	7.25494i	0.167949	+	0.290897i
$623$	35.0092	+	8.40016i	1.40262	+	0.336545i
$624$		0			0
$625$	6.19081	−	10.7228i	0.247632	−	0.428912i
$626$	8.89959	−	15.4145i	0.355699	−	0.616089i
$627$		0			0
$628$	−1.23668	−	2.14199i	−0.0493489	−	0.0854749i
$629$	20.5302			0.818593
$630$		0			0
$631$	22.6169	−	39.1736i	0.900363	−	1.55947i	0.0733401	−	0.997307i	$-0.476634\pi$
$631$	22.6169	−	39.1736i	0.900363	−	1.55947i	0.827023	−	0.562168i	$-0.190033\pi$
$632$	−16.8555	+	29.1946i	−0.670477	+	1.16130i
$633$		0			0
$634$	−10.7924	+	18.6930i	−0.428621	+	0.742393i
$635$	−6.69355			−0.265625
$636$		0			0
$637$	−25.1615	+	1.97426i	−0.996936	+	0.0782229i
$638$	1.40321			0.0555534
$639$		0			0
$640$	−13.0941	+	22.6796i	−0.517588	+	0.896489i
$641$	19.0619			0.752902			0.376451	−	0.926437i	$-0.377144\pi$
$641$	19.0619			0.752902			0.376451	+	0.926437i	$0.377144\pi$
$642$		0			0
$643$	5.26755	−	9.12367i	0.207732	−	0.359802i	−0.743268	−	0.668994i	$-0.766725\pi$
$643$	5.26755	−	9.12367i	0.207732	−	0.359802i	0.951000	+	0.309192i	$0.100058\pi$
$644$	−18.5422	−	4.44905i	−0.730666	−	0.175317i
$645$		0			0
$646$	0.855587	+	1.48192i	0.0336626	+	0.0583053i
$647$	−12.0804	+	20.9239i	−0.474930	+	0.822603i	−0.999588	−	0.0287105i	$-0.990860\pi$
$647$	−12.0804	+	20.9239i	−0.474930	+	0.822603i	0.524658	+	0.851313i	$0.324193\pi$
$648$		0			0
$649$	−0.229219	+	0.397019i	−0.00899762	+	0.0155843i
$650$	18.4520	+	10.0305i	0.723745	+	0.393427i
$651$		0			0
$652$	−7.58714	−	13.1413i	−0.297135	−	0.514654i
$653$	33.6890			1.31835			0.659176	−	0.751988i	$-0.270905\pi$
$653$	33.6890			1.31835			0.659176	+	0.751988i	$0.270905\pi$
$654$		0			0
$655$	20.7098	+	35.8704i	0.809199	+	1.40157i
$656$	−0.475268	−	0.823189i	−0.0185561	−	0.0321401i
$657$		0			0
$658$	−11.1456	+	11.7480i	−0.434500	+	0.457986i
$659$	−2.10030	+	3.63782i	−0.0818159	+	0.141709i	−0.904030	−	0.427469i	$-0.859405\pi$
$659$	−2.10030	+	3.63782i	−0.0818159	+	0.141709i	0.822214	+	0.569178i	$0.192739\pi$
$660$		0			0
$661$	−8.83631	+	15.3049i	−0.343693	+	0.595293i	−0.985115	−	0.171894i	$-0.945011\pi$
$661$	−8.83631	+	15.3049i	−0.343693	+	0.595293i	0.641423	+	0.767188i	$0.278345\pi$
$662$	−0.758708	−	1.31412i	−0.0294880	−	0.0510748i
$663$		0			0
$664$	4.22844			0.164095
$665$	9.19079	+	2.20525i	0.356404	+	0.0855160i
$666$		0			0
$667$	5.18664	+	8.98353i	0.200828	+	0.347844i
$668$	−10.5721	−	18.3114i	−0.409046	−	0.708488i
$669$		0			0
$670$	−12.3746	−	21.4334i	−0.478071	−	0.828044i
$671$	1.28968			0.0497875
$672$		0			0
$673$	10.3052	+	17.8491i	0.397235	+	0.688031i	0.993384	−	0.114843i	$-0.0366366\pi$
$673$	10.3052	+	17.8491i	0.397235	+	0.688031i	−0.596149	+	0.802874i	$0.703303\pi$
$674$	8.13803			0.313465
$675$		0			0
$676$	−7.54302	+	14.7677i	−0.290116	+	0.567990i
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	−0.994829	−	0.101567i	$-0.967614\pi$
$677$	−10.6537	+	18.4527i	−0.409455	+	0.709196i	0.585374	+	0.810763i	$0.300948\pi$
$678$		0			0
$679$	0.921847	−	0.971677i	0.0353772	−	0.0372895i
$680$	9.29147	−	16.0933i	0.356312	−	0.617150i
$681$		0			0
$682$	−6.98099			−0.267316
$683$	6.69757			0.256275			0.128138	−	0.991756i	$-0.459100\pi$
$683$	6.69757			0.256275			0.128138	+	0.991756i	$0.459100\pi$
$684$		0			0
$685$	−14.9999	+	25.9806i	−0.573118	+	0.992670i
$686$	−11.9903	−	10.2326i	−0.457792	−	0.390683i
$687$		0			0
$688$	0.348970	−	0.604433i	0.0133043	−	0.0230438i
$689$	29.7342	+	16.1635i	1.13278	+	0.615779i
$690$		0			0
$691$	−24.9263			−0.948242			−0.474121	−	0.880460i	$-0.657234\pi$
$691$	−24.9263			−0.948242			−0.474121	+	0.880460i	$0.657234\pi$
$692$	6.36936	+	11.0321i	0.242127	+	0.419376i
$693$		0			0
$694$	−0.539093			−0.0204637
$695$	7.24861	+	12.5550i	0.274955	+	0.476237i
$696$		0			0
$697$	5.16298	+	8.94254i	0.195562	+	0.338723i
$698$	−13.0217	−	22.5543i	−0.492880	−	0.853694i
$699$		0			0
$700$	−6.56276	−	22.1449i	−0.248049	−	0.837000i
$701$	4.94583			0.186801			0.0934007	−	0.995629i	$-0.470226\pi$
$701$	4.94583			0.186801			0.0934007	+	0.995629i	$0.470226\pi$
$702$		0			0
$703$	5.50162	+	9.52908i	0.207497	+	0.359396i
$704$	−2.02870	+	3.51382i	−0.0764597	+	0.132432i
$705$		0			0
$706$	−0.468266	+	0.811061i	−0.0176234	+	0.0305247i
$707$	10.9013	−	11.4905i	0.409985	−	0.432147i
$708$		0			0
$709$	2.32249	+	4.02267i	0.0872228	+	0.151074i	0.906336	−	0.422557i	$-0.138867\pi$
$709$	2.32249	+	4.02267i	0.0872228	+	0.151074i	−0.819113	+	0.573632i	$0.805534\pi$
$710$	5.05037	+	8.74749i	0.189537	+	0.328288i
$711$		0			0
$712$	37.9377			1.42178
$713$	−25.8037	−	44.6933i	−0.966356	−	1.67378i
$714$		0			0
$715$	−9.78966	−	5.32165i	−0.366113	−	0.199018i
$716$	−5.85275	+	10.1373i	−0.218728	+	0.378847i
$717$		0			0
$718$	−4.15939	+	7.20427i	−0.155227	+	0.268861i
$719$	15.8706	+	27.4887i	0.591875	+	1.02516i	0.993980	+	0.109564i	$0.0349453\pi$
$719$	15.8706	+	27.4887i	0.591875	+	1.02516i	−0.402105	+	0.915594i	$0.631721\pi$
$720$		0			0
$721$	−7.52609	+	7.93291i	−0.280286	+	0.295437i
$722$	7.62714	−	13.2106i	0.283853	−	0.491647i
$723$		0			0
$724$	−7.65975			−0.284672
$725$	−6.28237	+	10.8814i	−0.233322	+	0.404125i
$726$		0			0
$727$	47.8755			1.77560			0.887801	−	0.460227i	$-0.152232\pi$
$727$	47.8755			1.77560			0.887801	+	0.460227i	$0.152232\pi$
$728$	−25.2965	+	8.20909i	−0.937552	+	0.304249i
$729$		0			0
$730$	−31.9290			−1.18175
$731$	−3.79096	+	6.56613i	−0.140214	+	0.242857i
$732$		0			0
$733$	3.80104	−	6.58359i	0.140395	−	0.243171i	−0.787251	−	0.616633i	$-0.788496\pi$
$733$	3.80104	−	6.58359i	0.140395	−	0.243171i	0.927645	+	0.373463i	$0.121830\pi$
$734$	4.74386	−	8.21660i	0.175099	−	0.303280i
$735$		0			0
$736$	−32.3618			−1.19287
$737$	3.79368	+	6.57086i	0.139742	+	0.242041i
$738$		0			0
$739$	16.7118	−	28.9457i	0.614754	−	1.06479i	−0.375673	−	0.926752i	$-0.622589\pi$
$739$	16.7118	−	28.9457i	0.614754	−	1.06479i	0.990428	−	0.138033i	$-0.0440781\pi$
$740$	23.2665	−	40.2988i	0.855294	−	1.48141i
$741$		0			0
$742$	6.00589	+	20.2659i	0.220483	+	0.743984i
$743$	−1.46912	−	2.54458i	−0.0538966	−	0.0933517i	0.837818	−	0.545949i	$-0.183831\pi$
$743$	−1.46912	−	2.54458i	−0.0538966	−	0.0933517i	−0.891715	+	0.452597i	$0.850497\pi$
$744$		0			0
$745$	20.1837			0.739474
$746$	13.0776	+	22.6511i	0.478805	+	0.829314i
$747$		0			0
$748$	−1.10927	+	1.92131i	−0.0405588	+	0.0702499i
$749$	−36.3356	−	8.71842i	−1.32767	−	0.318564i
$750$		0			0
$751$	1.19678			0.0436711			0.0218355	−	0.999762i	$-0.493049\pi$
$751$	1.19678			0.0436711			0.0218355	+	0.999762i	$0.493049\pi$
$752$	0.641065	−	1.11036i	0.0233773	−	0.0404906i
$753$		0			0
$754$	4.94999	+	2.69081i	0.180268	+	0.0979936i
$755$	58.0123			2.11128
$756$		0			0
$757$	−5.77321	−	9.99950i	−0.209831	−	0.363438i	0.741830	−	0.670588i	$-0.233958\pi$
$757$	−5.77321	−	9.99950i	−0.209831	−	0.363438i	−0.951661	+	0.307150i	$0.900625\pi$
$758$	−9.64207	−	16.7006i	−0.350216	−	0.606592i
$759$		0			0
$760$	9.95959			0.361272
$761$	17.3249	+	30.0075i	0.628026	+	1.08777i	0.987947	+	0.154790i	$0.0494702\pi$
$761$	17.3249	+	30.0075i	0.628026	+	1.08777i	−0.359921	+	0.932983i	$0.617197\pi$
$762$		0			0
$763$	−3.15919	−	10.6602i	−0.114370	−	0.385924i
$764$	−0.839413	−	1.45391i	−0.0303689	−	0.0526005i
$765$		0			0
$766$	−0.250768	−	0.434344i	−0.00906063	−	0.0156935i
$767$	−1.56993	+	0.960982i	−0.0566869	+	0.0346990i
$768$		0			0
$769$	3.27437	+	5.67138i	0.118077	+	0.204515i	0.919006	−	0.394245i	$-0.128994\pi$
$769$	3.27437	+	5.67138i	0.118077	+	0.204515i	−0.800929	+	0.598760i	$0.795660\pi$
$770$	−1.97738	−	6.67233i	−0.0712597	−	0.240454i
$771$		0			0
$772$	−10.4760	+	18.1450i	−0.377039	+	0.653051i
$773$	−33.9275			−1.22029			−0.610143	−	0.792291i	$-0.708888\pi$
$773$	−33.9275			−1.22029			−0.610143	+	0.792291i	$0.708888\pi$
$774$		0			0
$775$	31.2550	−	54.1352i	1.12271	−	1.94459i
$776$	0.705683	−	1.22228i	0.0253325	−	0.0438772i
$777$		0			0
$778$	2.42547	+	4.20104i	0.0869575	+	0.150615i
$779$	−2.76711	+	4.79278i	−0.0991422	+	0.171719i
$780$		0			0
$781$	−1.54830	−	2.68173i	−0.0554024	−	0.0959598i
$782$	9.31405			0.333070
$783$		0			0
$784$	1.11215	+	0.566303i	0.0397195	+	0.0202251i
$785$	6.67303			0.238171
$786$		0			0
$787$	12.9743			0.462485			0.231243	−	0.972896i	$-0.425721\pi$
$787$	12.9743			0.462485			0.231243	+	0.972896i	$0.425721\pi$
$788$	16.3195	+	28.2662i	0.581359	+	1.00694i
$789$		0			0
$790$	−17.7092	−	30.6732i	−0.630065	−	1.09130i
$791$	−25.0737	+	26.4290i	−0.891518	+	0.939708i
$792$		0			0
$793$	4.54951	+	2.47311i	0.161558	+	0.0878227i
$794$	10.8639	+	18.8168i	0.385545	+	0.667784i
$795$		0			0
$796$	32.3728			1.14742
$797$	2.20956	−	3.82707i	0.0782667	−	0.135562i	−0.824235	−	0.566247i	$-0.808395\pi$
$797$	2.20956	−	3.82707i	0.0782667	−	0.135562i	0.902502	+	0.430685i	$0.141728\pi$
$798$		0			0
$799$	−6.96408	+	12.0621i	−0.246371	+	0.426728i
$800$	−19.5993	−	33.9469i	−0.692938	−	1.20020i
$801$		0			0
$802$	−21.7047			−0.766418
$803$	9.78852			0.345429
$804$		0			0
$805$	35.4083	−	37.3223i	1.24798	−	1.31544i
$806$	−24.6264	−	13.3869i	−0.867427	−	0.471532i
$807$		0			0
$808$	8.34504	−	14.4540i	0.293578	−	0.508491i
$809$	5.73580	−	9.93470i	0.201660	−	0.349285i	−0.747403	−	0.664371i	$-0.768700\pi$
$809$	5.73580	−	9.93470i	0.201660	−	0.349285i	0.949063	+	0.315085i	$0.102033\pi$
$810$		0			0
$811$	23.8664			0.838063			0.419032	−	0.907972i	$-0.362370\pi$
$811$	23.8664			0.838063			0.419032	+	0.907972i	$0.362370\pi$
$812$	−1.76055	−	5.94069i	−0.0617833	−	0.208477i
$813$		0			0
$814$	4.05079	−	7.01618i	0.141980	−	0.245917i
$815$	40.9396			1.43405
$816$		0			0
$817$	−4.06355			−0.142166
$818$	0.125105			0.00437419
$819$		0			0
$820$	23.4044			0.817318
$821$	−30.9694			−1.08084			−0.540420	−	0.841395i	$-0.681735\pi$
$821$	−30.9694			−1.08084			−0.540420	+	0.841395i	$0.681735\pi$
$822$		0			0
$823$	−8.61357			−0.300250			−0.150125	−	0.988667i	$-0.547968\pi$
$823$	−8.61357			−0.300250			−0.150125	+	0.988667i	$0.547968\pi$
$824$	−5.76129	+	9.97885i	−0.200704	+	0.347630i
$825$		0			0
$826$	−1.11789	−	0.268228i	−0.0388963	−	0.00933283i
$827$	−22.9128			−0.796756			−0.398378	−	0.917221i	$-0.630427\pi$
$827$	−22.9128			−0.796756			−0.398378	+	0.917221i	$0.630427\pi$
$828$		0			0
$829$	21.2806	−	36.8590i	0.739104	−	1.28017i	−0.213795	−	0.976879i	$-0.568582\pi$
$829$	21.2806	−	36.8590i	0.739104	−	1.28017i	0.952899	−	0.303287i	$-0.0980842\pi$
$830$	−2.22129	+	3.84739i	−0.0771022	+	0.133545i
$831$		0			0
$832$	−13.8947	+	8.50518i	−0.481711	+	0.294864i
$833$	−12.0816	−	6.15191i	−0.418601	−	0.213151i
$834$		0			0
$835$	57.0460			1.97416
$836$	−1.18903			−0.0411235
$837$		0			0
$838$	5.82846	+	10.0952i	0.201341	+	0.348733i
$839$	0.920524	−	1.59439i	0.0317800	−	0.0550446i	−0.849698	−	0.527270i	$-0.823216\pi$
$839$	0.920524	−	1.59439i	0.0317800	−	0.0550446i	0.881478	+	0.472225i	$0.156549\pi$
$840$		0			0
$841$	12.8147	−	22.1957i	0.441885	−	0.765367i
$842$	2.92931			0.100951
$843$		0			0
$844$	−3.63317	−	6.29284i	−0.125059	−	0.216609i
$845$	−24.3294	−	37.5457i	−0.836958	−	1.29161i
$846$		0			0
$847$	−7.66319	−	25.8582i	−0.263310	−	0.888497i
$848$	−0.836755	−	1.44930i	−0.0287343	−	0.0497692i
$849$		0			0
$850$	5.64087	+	9.77027i	0.193480	+	0.335118i
$851$	59.8915			2.05305
$852$		0			0
$853$	−27.0293			−0.925466			−0.462733	−	0.886498i	$-0.653131\pi$
$853$	−27.0293			−0.925466			−0.462733	+	0.886498i	$0.653131\pi$
$854$	0.918939	+	3.10081i	0.0314454	+	0.106107i
$855$		0			0
$856$	−39.3750			−1.34581
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	0.973017	−	0.230732i	$-0.0741122\pi$
$857$	8.39268	+	14.5365i	0.286688	+	0.496559i	−0.686329	+	0.727291i	$0.740779\pi$
$858$		0			0
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.0296769	+	0.999560i	$0.509448\pi$
$859$	−25.8058	+	44.6969i	−0.880482	+	1.52504i	−0.850806	+	0.525481i	$0.823886\pi$
$860$	8.59245	+	14.8826i	0.293000	+	0.507491i
$861$		0			0
$862$	9.48624	−	16.4306i	0.323102	−	0.559630i
$863$	10.9807	−	19.0191i	0.373787	−	0.647417i	−0.616358	−	0.787466i	$-0.711393\pi$
$863$	10.9807	−	19.0191i	0.373787	−	0.647417i	0.990145	+	0.140049i	$0.0447259\pi$
$864$		0			0
$865$	−34.3685			−1.16857
$866$	11.0205	−	19.0880i	0.374491	−	0.648638i
$867$		0			0
$868$	8.75880	+	29.5551i	0.297293	+	1.00317i
$869$	5.42913	+	9.40352i	0.184170	+	0.318993i
$870$		0			0
$871$	0.782342	+	30.4544i	0.0265086	+	1.03191i
$872$	−5.85797	−	10.1463i	−0.198376	−	0.343597i
$873$		0			0
$874$	2.49595	+	4.32311i	0.0844267	+	0.146231i
$875$	16.3248	+	3.91699i	0.551878	+	0.132418i
$876$		0			0
$877$	4.80873	+	8.32896i	0.162379	+	0.281249i	0.935721	−	0.352740i	$-0.114750\pi$
$877$	4.80873	+	8.32896i	0.162379	+	0.281249i	−0.773342	+	0.633989i	$0.781417\pi$
$878$	−23.8178			−0.803811
$879$		0			0
$880$	0.275493	+	0.477167i	0.00928686	+	0.0160853i
$881$	14.4863	+	25.0910i	0.488055	+	0.845336i	0.999906	−	0.0137383i	$-0.00437318\pi$
$881$	14.4863	+	25.0910i	0.488055	+	0.845336i	−0.511851	+	0.859075i	$0.671040\pi$
$882$		0			0
$883$	6.60727			0.222352			0.111176	−	0.993801i	$-0.464538\pi$
$883$	6.60727			0.222352			0.111176	+	0.993801i	$0.464538\pi$
$884$	−7.59742	+	4.65051i	−0.255529	+	0.156414i
$885$		0			0
$886$	14.1325	−	24.4781i	0.474789	−	0.822359i
$887$	31.4144			1.05479			0.527397	−	0.849619i	$-0.323168\pi$
$887$	31.4144			1.05479			0.527397	+	0.849619i	$0.323168\pi$
$888$		0			0
$889$	1.46215	+	4.93379i	0.0490390	+	0.165474i
$890$	−19.9295	+	34.5190i	−0.668039	+	1.15708i
$891$		0			0
$892$	1.50399	+	2.60499i	0.0503574	+	0.0872216i
$893$	−7.46484			−0.249801
$894$		0			0
$895$	−15.7905	−	27.3499i	−0.527818	−	0.914208i
$896$	19.5773	+	4.69741i	0.654033	+	0.156930i
$897$		0			0
$898$	8.37780	−	14.5108i	0.279571	−	0.484231i
$899$	8.38459	−	14.5225i	0.279642	−	0.484354i
$900$		0			0
$901$	9.08991	+	15.7442i	0.302829	+	0.524515i
$902$	4.07480			0.135676
$903$		0			0
$904$	−19.1942	+	33.2453i	−0.638388	+	1.10572i
$905$	10.3328	−	17.8970i	0.343475	−	0.594917i
$906$		0			0
$907$	−4.86821	+	8.43198i	−0.161646	+	0.279979i	−0.935459	−	0.353435i	$-0.885014\pi$
$907$	−4.86821	+	8.43198i	−0.161646	+	0.279979i	0.773813	+	0.633414i	$0.218347\pi$
$908$	33.5385			1.11301
$909$		0			0
$910$	5.81952	−	27.3294i	0.192915	−	0.905960i
$911$	38.4372			1.27348			0.636740	−	0.771078i	$-0.280282\pi$
$911$	38.4372			1.27348			0.636740	+	0.771078i	$0.280282\pi$
$912$		0			0
$913$	0.680984	−	1.17950i	0.0225373	−	0.0390357i
$914$	−0.635741			−0.0210285
$915$		0			0
$916$	0.0437242	−	0.0757325i	0.00144469	−	0.00250227i
$917$	21.9161	−	23.1007i	0.723732	−	0.762853i
$918$		0			0
$919$	−27.1402	−	47.0082i	−0.895273	−	1.55066i	−0.833467	−	0.552569i	$-0.813647\pi$
$919$	−27.1402	−	47.0082i	−0.895273	−	1.55066i	−0.0618056	−	0.998088i	$-0.519686\pi$
$920$	27.1054	−	46.9479i	0.893639	−	1.54783i
$921$		0			0
$922$	−14.1164	+	24.4502i	−0.464897	+	0.805226i
$923$	−0.319293	−	12.4292i	−0.0105097	−	0.409112i
$924$		0			0
$925$	36.2721	+	62.8251i	1.19262	+	2.06568i
$926$	−26.1739			−0.860128
$927$		0			0
$928$	−5.25777	−	9.10673i	−0.172595	−	0.298943i
$929$	−19.0960	−	33.0752i	−0.626519	−	1.08516i	−0.988245	−	0.152878i	$-0.951146\pi$
$929$	−19.0960	−	33.0752i	−0.626519	−	1.08516i	0.361726	−	0.932284i	$-0.382188\pi$
$930$		0			0
$931$	−0.382172	−	7.25622i	−0.0125252	−	0.237813i
$932$	−9.35660	+	16.2061i	−0.306486	+	0.530849i
$933$		0			0
$934$	−12.5994	+	21.8228i	−0.412266	+	0.714065i
$935$	−2.99276	−	5.18361i	−0.0978736	−	0.169522i
$936$		0			0
$937$	−19.0376			−0.621931			−0.310966	−	0.950421i	$-0.600652\pi$
$937$	−19.0376			−0.621931			−0.310966	+	0.950421i	$0.600652\pi$
$938$	−13.0953	+	13.8032i	−0.427578	+	0.450691i
$939$		0			0
$940$	15.7845	+	27.3396i	0.514835	+	0.891720i
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	0.946646	+	0.322275i	$0.104448\pi$
$941$	23.0811	+	39.9776i	0.752422	+	1.30323i	−0.194224	+	0.980957i	$0.562219\pi$
$942$		0			0
$943$	15.0616	+	26.0875i	0.490474	+	0.849526i
$944$	0.0910198			0.00296244
$945$		0			0
$946$	1.49598	+	2.59111i	0.0486385	+	0.0842443i
$947$	9.19374			0.298756			0.149378	−	0.988780i	$-0.452273\pi$
$947$	9.19374			0.298756			0.149378	+	0.988780i	$0.452273\pi$
$948$		0			0
$949$	34.5303	+	18.7706i	1.12090	+	0.609320i
$950$	−3.02324	+	5.23641i	−0.0980869	+	0.169892i
$951$		0			0
$952$	−13.8920	−	3.33325i	−0.450241	−	0.108031i
$953$	−22.3232	+	38.6648i	−0.723118	+	1.25248i	0.236626	+	0.971601i	$0.423958\pi$
$953$	−22.3232	+	38.6648i	−0.723118	+	1.25248i	−0.959744	+	0.280876i	$0.909375\pi$
$954$		0			0
$955$	4.52941			0.146568
$956$	4.27874			0.138385
$957$		0			0
$958$	5.99641	−	10.3861i	0.193735	−	0.335559i
$959$	22.4269	+	5.38113i	0.724201	+	0.173766i
$960$		0			0
$961$	−26.2136	+	45.4032i	−0.845599	+	1.46462i
$962$	27.7441	−	16.9826i	0.894504	−	0.547542i
$963$		0			0
$964$	10.9442			0.352490
$965$	−28.2638	−	48.9544i	−0.909845	−	1.57590i
$966$		0			0
$967$	13.8268			0.444639			0.222320	−	0.974974i	$-0.428637\pi$
$967$	13.8268			0.444639			0.222320	+	0.974974i	$0.428637\pi$
$968$	−14.2096	−	24.6117i	−0.456713	−	0.791050i
$969$		0			0
$970$	0.741422	+	1.28418i	0.0238056	+	0.0412326i
$971$	3.63437	+	6.29491i	0.116632	+	0.202013i	0.918431	−	0.395581i	$-0.129457\pi$
$971$	3.63437	+	6.29491i	0.116632	+	0.202013i	−0.801799	+	0.597594i	$0.796123\pi$
$972$		0			0
$973$	7.67081	−	8.08545i	0.245915	−	0.259208i
$974$	−14.2950			−0.458043
$975$		0			0
$976$	−0.128029	−	0.221752i	−0.00409810	−	0.00709811i
$977$	21.4050	−	37.0746i	0.684808	−	1.18612i	−0.288689	−	0.957423i	$-0.593219\pi$
$977$	21.4050	−	37.0746i	0.684808	−	1.18612i	0.973497	−	0.228699i	$-0.0734473\pi$
$978$		0			0
$979$	6.10982	−	10.5825i	0.195271	−	0.338219i
$980$	−25.7674	+	16.7431i	−0.823110	+	0.534838i
$981$		0			0
$982$	9.22152	+	15.9721i	0.294270	+	0.509691i
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	−0.953166	−	0.302448i	$-0.902196\pi$
$983$	−23.1544	−	40.1046i	−0.738511	−	1.27914i	0.214655	−	0.976690i	$-0.431137\pi$
$984$		0			0
$985$	−88.0588			−2.80579
$986$	1.51324	+	2.62101i	0.0481914	+	0.0834700i
$987$		0			0
$988$	−4.19446	−	2.28010i	−0.133444	−	0.0725398i
$989$	−11.0591	+	19.1550i	−0.351660	+	0.609092i
$990$		0			0
$991$	29.1162	−	50.4307i	0.924907	−	1.60199i	0.133195	−	0.991090i	$-0.457476\pi$
$991$	29.1162	−	50.4307i	0.924907	−	1.60199i	0.791711	−	0.610896i	$-0.209190\pi$
$992$	26.1576	+	45.3062i	0.830504	+	1.43847i
$993$		0			0
$994$	5.34453	−	5.63343i	0.169518	−	0.178681i
$995$	−43.6703	+	75.6392i	−1.38444	+	2.39792i
$996$		0			0
$997$	−4.49479			−0.142351			−0.0711757	−	0.997464i	$-0.522675\pi$
$997$	−4.49479			−0.142351			−0.0711757	+	0.997464i	$0.522675\pi$
$998$	9.91765	−	17.1779i	0.313938	−	0.543756i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.d.289.4		12
3.2	odd	2		91.2.h.b.16.3	yes	12
7.4	even	3		819.2.n.d.172.3		12
13.9	even	3		819.2.n.d.100.3		12
21.2	odd	6		637.2.f.k.393.4		12
21.5	even	6		637.2.f.j.393.4		12
21.11	odd	6		91.2.g.b.81.4	yes	12
21.17	even	6		637.2.g.l.263.4		12
21.20	even	2		637.2.h.l.471.3		12
39.23	odd	6		1183.2.e.g.170.3		12
39.29	odd	6		1183.2.e.h.170.4		12
39.35	odd	6		91.2.g.b.9.4	✓	12
91.74	even	3	inner	819.2.s.d.802.4		12
273.23	odd	6		8281.2.a.ce.1.4		6
273.68	even	6		8281.2.a.ca.1.3		6
273.74	odd	6		91.2.h.b.74.3	yes	12
273.107	odd	6		8281.2.a.bz.1.3		6
273.152	even	6		637.2.f.j.295.4		12
273.179	odd	6		1183.2.e.g.508.3		12
273.191	odd	6		637.2.f.k.295.4		12
273.230	even	6		637.2.g.l.373.4		12
273.257	even	6		8281.2.a.cf.1.4		6
273.263	odd	6		1183.2.e.h.508.4		12
273.269	even	6		637.2.h.l.165.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.4	✓	12	39.35	odd	6
91.2.g.b.81.4	yes	12	21.11	odd	6
91.2.h.b.16.3	yes	12	3.2	odd	2
91.2.h.b.74.3	yes	12	273.74	odd	6
637.2.f.j.295.4		12	273.152	even	6
637.2.f.j.393.4		12	21.5	even	6
637.2.f.k.295.4		12	273.191	odd	6
637.2.f.k.393.4		12	21.2	odd	6
637.2.g.l.263.4		12	21.17	even	6
637.2.g.l.373.4		12	273.230	even	6
637.2.h.l.165.3		12	273.269	even	6
637.2.h.l.471.3		12	21.20	even	2
819.2.n.d.100.3		12	13.9	even	3
819.2.n.d.172.3		12	7.4	even	3
819.2.s.d.289.4		12	1.1	even	1	trivial
819.2.s.d.802.4		12	91.74	even	3	inner
1183.2.e.g.170.3		12	39.23	odd	6
1183.2.e.g.508.3		12	273.179	odd	6
1183.2.e.h.170.4		12	39.29	odd	6
1183.2.e.h.508.4		12	273.263	odd	6
8281.2.a.bz.1.3		6	273.107	odd	6
8281.2.a.ca.1.3		6	273.68	even	6
8281.2.a.ce.1.4		6	273.23	odd	6
8281.2.a.cf.1.4		6	273.257	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.851125 q^{2} -1.27559 q^{4} +(1.72074 - 2.98041i) q^{5} +(-2.57273 - 0.617304i) q^{7} -2.78793 q^{8} +O(q^{10})\)	\(q+0.851125 q^{2} -1.27559 q^{4} +(1.72074 - 2.98041i) q^{5} +(-2.57273 - 0.617304i) q^{7} -2.78793 q^{8} +(1.46456 - 2.53670i) q^{10} +(-0.448993 + 0.777679i) q^{11} +(-3.07517 + 1.88237i) q^{13} +(-2.18972 - 0.525403i) q^{14} +0.178289 q^{16} -1.93681 q^{17} +(-0.519020 - 0.898968i) q^{19} +(-2.19495 + 3.80177i) q^{20} +(-0.382150 + 0.661902i) q^{22} -5.65013 q^{23} +(-3.42189 - 5.92688i) q^{25} +(-2.61736 + 1.60213i) q^{26} +(3.28174 + 0.787424i) q^{28} +(-0.917969 - 1.58997i) q^{29} +(4.56692 + 7.91014i) q^{31} +5.72761 q^{32} -1.64847 q^{34} +(-6.26681 + 6.60556i) q^{35} -10.6000 q^{37} +(-0.441751 - 0.765135i) q^{38} +(-4.79731 + 8.30918i) q^{40} +(-2.66571 - 4.61715i) q^{41} +(1.95732 - 3.39018i) q^{43} +(0.572729 - 0.991996i) q^{44} -4.80897 q^{46} +(3.59565 - 6.22784i) q^{47} +(6.23787 + 3.17631i) q^{49} +(-2.91246 - 5.04452i) q^{50} +(3.92265 - 2.40112i) q^{52} +(-4.69324 - 8.12893i) q^{53} +(1.54520 + 2.67637i) q^{55} +(7.17260 + 1.72100i) q^{56} +(-0.781307 - 1.35326i) q^{58} +0.510517 q^{59} +(-0.718095 - 1.24378i) q^{61} +(3.88702 + 6.73252i) q^{62} +4.51834 q^{64} +(0.318655 + 12.4043i) q^{65} +(4.22466 - 7.31732i) q^{67} +2.47057 q^{68} +(-5.33385 + 5.62216i) q^{70} +(-1.72419 + 2.98638i) q^{71} +(-5.45026 - 9.44013i) q^{73} -9.02195 q^{74} +(0.662054 + 1.14671i) q^{76} +(1.63520 - 1.72359i) q^{77} +(6.04589 - 10.4718i) q^{79} +(0.306789 - 0.531375i) q^{80} +(-2.26886 - 3.92977i) q^{82} -1.51669 q^{83} +(-3.33274 + 5.77248i) q^{85} +(1.66593 - 2.88547i) q^{86} +(1.25176 - 2.16812i) q^{88} -13.6078 q^{89} +(9.07358 - 2.94451i) q^{91} +7.20722 q^{92} +(3.06035 - 5.30067i) q^{94} -3.57239 q^{95} +(-0.253120 + 0.438417i) q^{97} +(5.30921 + 2.70344i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} + 16 q^{32} + 32 q^{34} - 20 q^{35} + 26 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} - 32 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} + 41 q^{52} + 2 q^{53} + 9 q^{55} - 9 q^{56} - 8 q^{58} + 26 q^{59} - 5 q^{61} - 5 q^{62} - 30 q^{64} + 5 q^{65} - 11 q^{67} + 58 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} - 6 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} + 7 q^{80} + q^{82} + 54 q^{83} - q^{85} + 7 q^{86} + 8 q^{89} - 23 q^{91} - 54 q^{92} + 45 q^{94} - 12 q^{95} - 35 q^{97} - 20 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

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