LMFDB - Embedded newform 261.2.k.c.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [261,2,Mod(82,261)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(261, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("261.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.k (of order $7$, degree $6$, 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:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{7})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} + 18 x^{16} - 37 x^{15} + 71 x^{14} - 83 x^{13} + 225 x^{12} - 237 x^{11} + 485 x^{10} + \cdots + 64 $ x^18 - 6x^17 + 18x^16 - 37x^15 + 71x^14 - 83x^13 + 225x^12 - 237x^11 + 485x^10 - 319x^9 + 1092x^8 - 1080x^7 + 1833x^6 - 4032x^5 + 6004x^4 - 4480x^3 + 3200x^2 - 576*x + 64
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 87)
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			199.3
Root			$-1.38228 - 0.665671i$ of defining polynomial
Character	$\chi$	$=$	261.199
Dual form			261.2.k.c.181.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.563916 - 2.47068i) q^{2} +(-3.98431 - 1.91874i) q^{4} +(0.242440 - 1.06220i) q^{5} +(-1.55919 + 0.750867i) q^{7} +(-3.82730 + 4.79928i) q^{8} +(-2.48764 - 1.19798i) q^{10} +(-3.92495 - 4.92173i) q^{11} +(-0.797744 - 1.00034i) q^{13} +(0.975897 + 4.27568i) q^{14} +(4.18475 + 5.24750i) q^{16} +5.08291 q^{17} +(5.88048 + 2.83189i) q^{19} +(-3.00404 + 3.76695i) q^{20} +(-14.3734 + 6.92184i) q^{22} +(-1.00672 - 4.41072i) q^{23} +(3.43536 + 1.65438i) q^{25} +(-2.92138 + 1.40686i) q^{26} +7.65302 q^{28} +(1.89363 + 5.04125i) q^{29} +(1.52535 - 6.68301i) q^{31} +(4.26353 - 2.05321i) q^{32} +(2.86633 - 12.5582i) q^{34} +(0.419560 + 1.83821i) q^{35} +(3.84958 - 4.82721i) q^{37} +(10.3128 - 12.9318i) q^{38} +(4.16990 + 5.22889i) q^{40} -4.04550 q^{41} +(-0.407490 - 1.78533i) q^{43} +(6.19468 + 27.1407i) q^{44} -11.4652 q^{46} +(-0.945516 - 1.18564i) q^{47} +(-2.49715 + 3.13133i) q^{49} +(6.02469 - 7.55473i) q^{50} +(1.25907 + 5.51633i) q^{52} +(-0.839814 + 3.67947i) q^{53} +(-6.17942 + 2.97585i) q^{55} +(2.36387 - 10.3568i) q^{56} +(13.5231 - 1.83571i) q^{58} +8.72197 q^{59} +(2.78187 - 1.33968i) q^{61} +(-15.6514 - 7.53731i) q^{62} +(0.318497 + 1.39543i) q^{64} +(-1.25596 + 0.604841i) q^{65} +(-1.49443 + 1.87396i) q^{67} +(-20.2519 - 9.75280i) q^{68} +4.77822 q^{70} +(-5.82579 - 7.30531i) q^{71} +(0.400049 + 1.75273i) q^{73} +(-9.75566 - 12.2332i) q^{74} +(-17.9960 - 22.5663i) q^{76} +(9.81531 + 4.72681i) q^{77} +(-1.78668 + 2.24043i) q^{79} +(6.58844 - 3.17283i) q^{80} +(-2.28132 + 9.99513i) q^{82} +(5.94056 + 2.86082i) q^{83} +(1.23230 - 5.39906i) q^{85} -4.64077 q^{86} +38.6427 q^{88} +(0.744447 - 3.26164i) q^{89} +(1.99496 + 0.960721i) q^{91} +(-4.45196 + 19.5053i) q^{92} +(-3.46252 + 1.66746i) q^{94} +(4.43370 - 5.55968i) q^{95} +(-2.04297 - 0.983843i) q^{97} +(6.32833 + 7.93547i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) $ 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{4}{7}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.563916	−	2.47068i	0.398749	−	1.74703i	−0.233584	−	0.972337i	$-0.575045\pi$
$2$	0.563916	−	2.47068i	0.398749	−	1.74703i	0.632333	−	0.774697i	$-0.282097\pi$
$3$		0			0
$3$		0			0
$4$	−3.98431	−	1.91874i	−1.99216	−	0.959372i
$5$	0.242440	−	1.06220i	0.108422	−	0.475030i	−0.891342	−	0.453331i	$-0.850235\pi$
$5$	0.242440	−	1.06220i	0.108422	−	0.475030i	0.999765	−	0.0216985i	$-0.00690738\pi$
$6$		0			0
$7$	−1.55919	+	0.750867i	−0.589319	+	0.283801i	−0.704683	−	0.709522i	$-0.748911\pi$
$7$	−1.55919	+	0.750867i	−0.589319	+	0.283801i	0.115364	+	0.993323i	$0.463196\pi$
$8$	−3.82730	+	4.79928i	−1.35315	+	1.69680i
$9$		0			0
$10$	−2.48764	−	1.19798i	−0.786659	−	0.378835i
$11$	−3.92495	−	4.92173i	−1.18342	−	1.48396i	−0.838138	−	0.545458i	$-0.816356\pi$
$11$	−3.92495	−	4.92173i	−1.18342	−	1.48396i	−0.345279	−	0.938500i	$-0.612216\pi$
$12$		0			0
$13$	−0.797744	−	1.00034i	−0.221255	−	0.277444i	0.658799	−	0.752319i	$-0.271065\pi$
$13$	−0.797744	−	1.00034i	−0.221255	−	0.277444i	−0.880053	+	0.474875i	$0.842493\pi$
$14$	0.975897	+	4.27568i	0.260819	+	1.14272i
$15$		0			0
$16$	4.18475	+	5.24750i	1.04619	+	1.31188i
$17$	5.08291			1.23279			0.616393	−	0.787439i	$-0.288593\pi$
$17$	5.08291			1.23279			0.616393	+	0.787439i	$0.288593\pi$
$18$		0			0
$19$	5.88048	+	2.83189i	1.34908	+	0.649680i	0.962173	−	0.272440i	$-0.0878307\pi$
$19$	5.88048	+	2.83189i	1.34908	+	0.649680i	0.386903	+	0.922121i	$0.373545\pi$
$20$	−3.00404	+	3.76695i	−0.671724	+	0.842316i
$21$		0			0
$22$	−14.3734	+	6.92184i	−3.06441	+	1.47574i
$23$	−1.00672	−	4.41072i	−0.209915	−	0.919699i	−0.964622	−	0.263637i	$-0.915078\pi$
$23$	−1.00672	−	4.41072i	−0.209915	−	0.919699i	0.754707	−	0.656062i	$-0.227779\pi$
$24$		0			0
$25$	3.43536	+	1.65438i	0.687071	+	0.330876i
$26$	−2.92138	+	1.40686i	−0.572930	+	0.275908i
$27$		0			0
$28$	7.65302			1.44629
$29$	1.89363	+	5.04125i	0.351638	+	0.936136i
$29$	1.89363	+	5.04125i	0.351638	+	0.936136i
$30$		0			0
$31$	1.52535	−	6.68301i	0.273961	−	1.20030i	−0.631331	−	0.775514i	$-0.717491\pi$
$31$	1.52535	−	6.68301i	0.273961	−	1.20030i	0.905292	−	0.424790i	$-0.139652\pi$
$32$	4.26353	−	2.05321i	0.753692	−	0.362959i
$33$		0			0
$34$	2.86633	−	12.5582i	0.491572	−	2.15372i
$35$	0.419560	+	1.83821i	0.0709185	+	0.310714i
$36$		0			0
$37$	3.84958	−	4.82721i	0.632866	−	0.793589i	−0.357224	−	0.934019i	$-0.616277\pi$
$37$	3.84958	−	4.82721i	0.632866	−	0.793589i	0.990091	+	0.140429i	$0.0448483\pi$
$38$	10.3128	−	12.9318i	1.67296	−	2.09782i
$39$		0			0
$40$	4.16990	+	5.22889i	0.659319	+	0.826760i
$41$	−4.04550			−0.631801			−0.315901	−	0.948792i	$-0.602307\pi$
$41$	−4.04550			−0.631801			−0.315901	+	0.948792i	$0.602307\pi$
$42$		0			0
$43$	−0.407490	−	1.78533i	−0.0621417	−	0.272260i	0.934306	−	0.356471i	$-0.116020\pi$
$43$	−0.407490	−	1.78533i	−0.0621417	−	0.272260i	−0.996448	+	0.0842108i	$0.973163\pi$
$44$	6.19468	+	27.1407i	0.933884	+	4.09161i
$45$		0			0
$46$	−11.4652			−1.69045
$47$	−0.945516	−	1.18564i	−0.137918	−	0.172943i	0.708076	−	0.706136i	$-0.249563\pi$
$47$	−0.945516	−	1.18564i	−0.137918	−	0.172943i	−0.845994	+	0.533193i	$0.820992\pi$
$48$		0			0
$49$	−2.49715	+	3.13133i	−0.356736	+	0.447333i
$50$	6.02469	−	7.55473i	0.852020	−	1.06840i
$51$		0			0
$52$	1.25907	+	5.51633i	0.174601	+	0.764978i
$53$	−0.839814	+	3.67947i	−0.115357	+	0.505414i	0.883928	+	0.467622i	$0.154889\pi$
$53$	−0.839814	+	3.67947i	−0.115357	+	0.505414i	−0.999286	+	0.0377912i	$0.987968\pi$
$54$		0			0
$55$	−6.17942	+	2.97585i	−0.833233	+	0.401264i
$56$	2.36387	−	10.3568i	0.315885	−	1.38398i
$57$		0			0
$58$	13.5231	−	1.83571i	1.77568	−	0.241041i
$59$	8.72197			1.13550			0.567752	−	0.823200i	$-0.307813\pi$
$59$	8.72197			1.13550			0.567752	+	0.823200i	$0.307813\pi$
$60$		0			0
$61$	2.78187	−	1.33968i	0.356182	−	0.171528i	−0.247232	−	0.968956i	$-0.579521\pi$
$61$	2.78187	−	1.33968i	0.356182	−	0.171528i	0.603414	+	0.797428i	$0.293807\pi$
$62$	−15.6514	−	7.53731i	−1.98773	−	0.957240i
$63$		0			0
$64$	0.318497	+	1.39543i	0.0398121	+	0.174428i
$65$	−1.25596	+	0.604841i	−0.155783	+	0.0750213i
$66$		0			0
$67$	−1.49443	+	1.87396i	−0.182574	+	0.228941i	−0.864693	−	0.502300i	$-0.832487\pi$
$67$	−1.49443	+	1.87396i	−0.182574	+	0.228941i	0.682119	+	0.731241i	$0.261059\pi$
$68$	−20.2519	−	9.75280i	−2.45590	−	1.18270i
$69$		0			0
$70$	4.77822			0.571107
$71$	−5.82579	−	7.30531i	−0.691394	−	0.866980i	0.304954	−	0.952367i	$-0.401359\pi$
$71$	−5.82579	−	7.30531i	−0.691394	−	0.866980i	−0.996348	+	0.0853867i	$0.972787\pi$
$72$		0			0
$73$	0.400049	+	1.75273i	0.0468222	+	0.205142i	0.992928	−	0.118715i	$-0.0378775\pi$
$73$	0.400049	+	1.75273i	0.0468222	+	0.205142i	−0.946106	+	0.323857i	$0.895020\pi$
$74$	−9.75566	−	12.2332i	−1.13407	−	1.42208i
$75$		0			0
$76$	−17.9960	−	22.5663i	−2.06428	−	2.58853i
$77$	9.81531	+	4.72681i	1.11856	+	0.538669i
$78$		0			0
$79$	−1.78668	+	2.24043i	−0.201018	+	0.252068i	−0.872115	−	0.489301i	$-0.837252\pi$
$79$	−1.78668	+	2.24043i	−0.201018	+	0.252068i	0.671097	+	0.741369i	$0.265823\pi$
$80$	6.58844	−	3.17283i	0.736610	−	0.354733i
$81$		0			0
$82$	−2.28132	+	9.99513i	−0.251930	+	1.10378i
$83$	5.94056	+	2.86082i	0.652061	+	0.314016i	0.730510	−	0.682902i	$-0.239283\pi$
$83$	5.94056	+	2.86082i	0.652061	+	0.314016i	−0.0784490	+	0.996918i	$0.524997\pi$
$84$		0			0
$85$	1.23230	−	5.39906i	0.133662	−	0.585610i
$86$	−4.64077			−0.500427
$87$		0			0
$88$	38.6427			4.11933
$89$	0.744447	−	3.26164i	0.0789113	−	0.345733i	−0.920024	−	0.391861i	$-0.871831\pi$
$89$	0.744447	−	3.26164i	0.0789113	−	0.345733i	0.998936	+	0.0461286i	$0.0146884\pi$
$90$		0			0
$91$	1.99496	+	0.960721i	0.209128	+	0.100711i
$92$	−4.45196	+	19.5053i	−0.464149	+	2.03357i
$93$		0			0
$94$	−3.46252	+	1.66746i	−0.357132	+	0.171986i
$95$	4.43370	−	5.55968i	0.454888	−	0.570411i
$96$		0			0
$97$	−2.04297	−	0.983843i	−0.207432	−	0.0998941i	0.327283	−	0.944926i	$-0.393867\pi$
$97$	−2.04297	−	0.983843i	−0.207432	−	0.0998941i	−0.534715	+	0.845032i	$0.679581\pi$
$98$	6.32833	+	7.93547i	0.639257	+	0.801604i
$99$		0			0
$100$	−10.5132	−	13.1831i	−1.05132	−	1.31831i
$101$	2.79423	+	12.2423i	0.278036	+	1.21816i	0.900273	+	0.435326i	$0.143367\pi$
$101$	2.79423	+	12.2423i	0.278036	+	1.21816i	−0.622237	+	0.782829i	$0.713776\pi$
$102$		0			0
$103$	1.73041	+	2.16986i	0.170502	+	0.213803i	0.859740	−	0.510732i	$-0.170626\pi$
$103$	1.73041	+	2.16986i	0.170502	+	0.213803i	−0.689237	+	0.724536i	$0.742054\pi$
$104$	7.85412			0.770160
$105$		0			0
$106$	8.61719	+	4.14982i	0.836976	+	0.403066i
$107$	−6.20858	+	7.78532i	−0.600206	+	0.752635i	−0.985410	−	0.170197i	$-0.945560\pi$
$107$	−6.20858	+	7.78532i	−0.600206	+	0.752635i	0.385204	+	0.922832i	$0.374131\pi$
$108$		0			0
$109$	4.25748	−	2.05029i	0.407793	−	0.196383i	−0.218731	−	0.975785i	$-0.570192\pi$
$109$	4.25748	−	2.05029i	0.407793	−	0.196383i	0.626523	+	0.779403i	$0.284477\pi$
$110$	3.86770	+	16.9455i	0.368771	+	1.61569i
$111$		0			0
$112$	−10.4650	−	5.03967i	−0.988849	−	0.476205i
$113$	−0.494143	+	0.237967i	−0.0464851	+	0.0223860i	−0.456982	−	0.889476i	$-0.651070\pi$
$113$	−0.494143	+	0.237967i	−0.0464851	+	0.0223860i	0.410497	+	0.911862i	$0.365355\pi$
$114$		0			0
$115$	−4.92913			−0.459644
$116$	2.12804	−	23.7193i	0.197584	−	2.20228i
$117$		0			0
$118$	4.91846	−	21.5492i	0.452781	−	1.98376i
$119$	−7.92522	+	3.81659i	−0.726504	+	0.349866i
$120$		0			0
$121$	−6.37048	+	27.9109i	−0.579135	+	2.53735i
$122$	−1.74117	−	7.62857i	−0.157638	−	0.690659i
$123$		0			0
$124$	−18.9005	+	23.7004i	−1.69731	+	2.12836i
$125$	5.98666	−	7.50703i	0.535463	−	0.671449i
$126$		0			0
$127$	8.88268	+	11.1385i	0.788211	+	0.988385i	0.999939	+	0.0110562i	$0.00351937\pi$
$127$	8.88268	+	11.1385i	0.788211	+	0.988385i	−0.211728	+	0.977329i	$0.567909\pi$
$128$	13.0916			1.15714
$129$		0			0
$130$	0.786108	+	3.44416i	0.0689462	+	0.302073i
$131$	1.52161	+	6.66661i	0.132944	+	0.582464i	0.996885	+	0.0788714i	$0.0251316\pi$
$131$	1.52161	+	6.66661i	0.132944	+	0.582464i	−0.863941	+	0.503593i	$0.832011\pi$
$132$		0			0
$133$	−11.2952			−0.979415
$134$	3.78722	+	4.74902i	0.327166	+	0.410253i
$135$		0			0
$136$	−19.4538	+	24.3943i	−1.66815	+	2.09179i
$137$	−8.40101	+	10.5345i	−0.717746	+	0.900026i	−0.998208	−	0.0598397i	$-0.980941\pi$
$137$	−8.40101	+	10.5345i	−0.717746	+	0.900026i	0.280462	+	0.959865i	$0.409512\pi$
$138$		0			0
$139$	−2.62174	−	11.4866i	−0.222373	−	0.974278i	−0.955686	−	0.294388i	$-0.904884\pi$
$139$	−2.62174	−	11.4866i	−0.222373	−	0.974278i	0.733313	−	0.679891i	$-0.237973\pi$
$140$	1.85540	−	8.12903i	0.156810	−	0.687028i
$141$		0			0
$142$	−21.3343	+	10.2741i	−1.79034	+	0.862180i
$143$	−1.79230	+	7.85257i	−0.149879	+	0.656665i
$144$		0			0
$145$	5.81390	−	0.789213i	0.482818	−	0.0655405i
$146$	4.55603			0.377060
$147$		0			0
$148$	−24.6001	+	11.8468i	−2.02212	+	0.973799i
$149$	0.686505	+	0.330603i	0.0562406	+	0.0270841i	0.461793	−	0.886988i	$-0.347206\pi$
$149$	0.686505	+	0.330603i	0.0562406	+	0.0270841i	−0.405552	+	0.914072i	$0.632921\pi$
$150$		0			0
$151$	−4.10254	−	17.9744i	−0.333860	−	1.46274i	−0.811589	−	0.584228i	$-0.801397\pi$
$151$	−4.10254	−	17.9744i	−0.333860	−	1.46274i	0.477730	−	0.878507i	$-0.341460\pi$
$152$	−36.0974	+	17.3836i	−2.92789	+	1.41000i
$153$		0			0
$154$	17.2134	−	21.5850i	1.38710	−	1.73937i
$155$	−6.72887	−	3.24046i	−0.540476	−	0.260280i
$156$		0			0
$157$	10.9681			0.875353			0.437676	−	0.899133i	$-0.355802\pi$
$157$	10.9681			0.875353			0.437676	+	0.899133i	$0.355802\pi$
$158$	4.52784	+	5.67773i	0.360216	+	0.451696i
$159$		0			0
$160$	−1.14726	−	5.02649i	−0.0906991	−	0.397379i
$161$	4.88153	+	6.12125i	0.384719	+	0.482422i
$162$		0			0
$163$	14.8705	+	18.6470i	1.16475	+	1.46055i	0.861590	+	0.507604i	$0.169469\pi$
$163$	14.8705	+	18.6470i	1.16475	+	1.46055i	0.303155	+	0.952941i	$0.401960\pi$
$164$	16.1185	+	7.76228i	1.25865	+	0.606132i
$165$		0			0
$166$	10.4181	−	13.0639i	0.808605	−	1.01396i
$167$	−12.9629	+	6.24261i	−1.00310	+	0.483068i	−0.861990	−	0.506926i	$-0.830782\pi$
$167$	−12.9629	+	6.24261i	−1.00310	+	0.483068i	−0.141111	+	0.989994i	$0.545068\pi$
$168$		0			0
$169$	2.52849	−	11.0780i	0.194499	−	0.852156i
$170$	−12.6444	−	6.08923i	−0.969783	−	0.467023i
$171$		0			0
$172$	−1.80202	+	7.89518i	−0.137403	+	0.602002i
$173$	3.94904			0.300240			0.150120	−	0.988668i	$-0.452034\pi$
$173$	3.94904			0.300240			0.150120	+	0.988668i	$0.452034\pi$
$174$		0			0
$175$	−6.59859			−0.498807
$176$	9.40189	−	41.1924i	0.708694	−	3.10499i
$177$		0			0
$178$	−7.63865	−	3.67858i	−0.572541	−	0.275721i
$179$	3.65240	−	16.0022i	0.272993	−	1.19606i	−0.633467	−	0.773770i	$-0.718369\pi$
$179$	3.65240	−	16.0022i	0.272993	−	1.19606i	0.906460	−	0.422291i	$-0.138774\pi$
$180$		0			0
$181$	15.0941	−	7.26893i	1.12193	−	0.540295i	0.221445	−	0.975173i	$-0.428923\pi$
$181$	15.0941	−	7.26893i	1.12193	−	0.540295i	0.900489	+	0.434878i	$0.143208\pi$
$182$	3.49862	−	4.38713i	0.259335	−	0.325196i
$183$		0			0
$184$	25.0213	+	12.0496i	1.84460	+	0.888310i
$185$	−4.19417	−	5.25932i	−0.308362	−	0.386673i
$186$		0			0
$187$	−19.9502	−	25.0167i	−1.45890	−	1.82940i
$188$	1.49229	+	6.53816i	0.108837	+	0.476844i
$189$		0			0
$190$	−11.2359	−	14.0894i	−0.815141	−	1.02215i
$191$	2.95004			0.213457			0.106729	−	0.994288i	$-0.465962\pi$
$191$	2.95004			0.213457			0.106729	+	0.994288i	$0.465962\pi$
$192$		0			0
$193$	4.39974	+	2.11880i	0.316700	+	0.152515i	0.585480	−	0.810687i	$-0.300906\pi$
$193$	4.39974	+	2.11880i	0.316700	+	0.152515i	−0.268780	+	0.963202i	$0.586620\pi$
$194$	−3.58282	+	4.49272i	−0.257232	+	0.322559i
$195$		0			0
$196$	15.9577	−	7.68480i	1.13983	−	0.548914i
$197$	−0.560429	−	2.45540i	−0.0399289	−	0.174940i	0.951032	−	0.309094i	$-0.100026\pi$
$197$	−0.560429	−	2.45540i	−0.0399289	−	0.174940i	−0.990961	+	0.134153i	$0.957168\pi$
$198$		0			0
$199$	−23.0213	−	11.0865i	−1.63193	−	0.785898i	−0.999940	−	0.0109244i	$-0.996523\pi$
$199$	−23.0213	−	11.0865i	−1.63193	−	0.785898i	−0.631994	−	0.774974i	$-0.717763\pi$
$200$	−21.0880	+	10.1554i	−1.49114	+	0.718097i
$201$		0			0
$202$	31.8225			2.23903
$203$	−6.73784	−	6.43840i	−0.472903	−	0.451887i
$204$		0			0
$205$	−0.980791	+	4.29713i	−0.0685014	+	0.300124i
$206$	6.33684	−	3.05166i	0.441509	−	0.212619i
$207$		0			0
$208$	1.91093	−	8.37234i	0.132499	−	0.580517i
$209$	−9.14279	−	40.0572i	−0.632420	−	2.77081i
$210$		0			0
$211$	−1.15041	+	1.44257i	−0.0791974	+	0.0993104i	−0.819852	−	0.572576i	$-0.805944\pi$
$211$	−1.15041	+	1.44257i	−0.0791974	+	0.0993104i	0.740654	+	0.671886i	$0.234516\pi$
$212$	10.4060	−	13.0488i	0.714689	−	0.896192i
$213$		0			0
$214$	15.7339	+	19.7297i	1.07555	+	1.34869i
$215$	−1.99517			−0.136069
$216$		0			0
$217$	2.63973	+	11.5654i	0.179197	+	0.785112i
$218$	−2.66476	−	11.6751i	−0.180480	−	0.790735i
$219$		0			0
$220$	30.3306			2.04489
$221$	−4.05486	−	5.08464i	−0.272760	−	0.342030i
$222$		0			0
$223$	−14.9944	+	18.8024i	−1.00410	+	1.25910i	−0.0384478	+	0.999261i	$0.512241\pi$
$223$	−14.9944	+	18.8024i	−1.00410	+	1.25910i	−0.965652	+	0.259840i	$0.916330\pi$
$224$	−5.10597	+	6.40268i	−0.341157	+	0.427797i
$225$		0			0
$226$	0.309284	+	1.35506i	0.0205733	+	0.0901374i
$227$	−5.03786	+	22.0723i	−0.334374	+	1.46499i	0.476191	+	0.879342i	$0.342017\pi$
$227$	−5.03786	+	22.0723i	−0.334374	+	1.46499i	−0.810565	+	0.585648i	$0.800840\pi$
$228$		0			0
$229$	12.4353	−	5.98852i	0.821747	−	0.395733i	0.0247336	−	0.999694i	$-0.492126\pi$
$229$	12.4353	−	5.98852i	0.821747	−	0.395733i	0.797013	+	0.603962i	$0.206412\pi$
$230$	−2.77962	+	12.1783i	−0.183283	+	0.803013i
$231$		0			0
$232$	−31.4418	−	10.2063i	−2.06426	−	0.670076i
$233$	6.69816			0.438811			0.219405	−	0.975634i	$-0.429588\pi$
$233$	6.69816			0.438811			0.219405	+	0.975634i	$0.429588\pi$
$234$		0			0
$235$	−1.48861	+	0.716879i	−0.0971065	+	0.0467640i
$236$	−34.7511	−	16.7352i	−2.26210	−	1.08937i
$237$		0			0
$238$	4.96040	+	21.7329i	0.321535	+	1.40874i
$239$	10.9580	−	5.27711i	0.708816	−	0.341348i	−0.0444976	−	0.999009i	$-0.514169\pi$
$239$	10.9580	−	5.27711i	0.708816	−	0.341348i	0.753313	+	0.657662i	$0.228454\pi$
$240$		0			0
$241$	1.65610	−	2.07668i	0.106679	−	0.133771i	−0.725626	−	0.688089i	$-0.758450\pi$
$241$	1.65610	−	2.07668i	0.106679	−	0.133771i	0.832305	+	0.554319i	$0.187021\pi$
$242$	65.3664	+	31.4788i	4.20191	+	2.02353i
$243$		0			0
$244$	−13.6543			−0.874129
$245$	2.72069	+	3.41163i	0.173818	+	0.217961i
$246$		0			0
$247$	−1.85827	−	8.14161i	−0.118239	−	0.518038i
$248$	26.2356	+	32.8985i	1.66597	+	2.08905i
$249$		0			0
$250$	−15.1715	−	19.0244i	−0.959529	−	1.20321i
$251$	−20.5109	−	9.87755i	−1.29464	−	0.623465i	−0.345529	−	0.938408i	$-0.612300\pi$
$251$	−20.5109	−	9.87755i	−1.29464	−	0.623465i	−0.949111	+	0.314943i	$0.898015\pi$
$252$		0			0
$253$	−17.7571	+	22.2667i	−1.11638	+	1.39989i
$254$	32.5288	−	15.6651i	2.04104	−	0.982913i
$255$		0			0
$256$	6.74555	−	29.5542i	0.421597	−	1.84714i
$257$	6.94501	+	3.34454i	0.433218	+	0.208627i	0.637767	−	0.770230i	$-0.279858\pi$
$257$	6.94501	+	3.34454i	0.433218	+	0.208627i	−0.204549	+	0.978856i	$0.565573\pi$
$258$		0			0
$259$	−2.37763	+	10.4171i	−0.147739	+	0.647285i
$260$	6.16469			0.382318
$261$		0			0
$262$	17.3291			1.07060
$263$	−0.171243	+	0.750263i	−0.0105593	+	0.0462632i	−0.979933	−	0.199327i	$-0.936125\pi$
$263$	−0.171243	+	0.750263i	−0.0105593	+	0.0462632i	0.969374	+	0.245590i	$0.0789817\pi$
$264$		0			0
$265$	3.70472	+	1.78410i	0.227579	+	0.109596i
$266$	−6.36953	+	27.9067i	−0.390541	+	1.71107i
$267$		0			0
$268$	9.54994	−	4.59901i	0.583356	−	0.280929i
$269$	−9.56842	+	11.9984i	−0.583397	+	0.731556i	−0.982688	−	0.185268i	$-0.940685\pi$
$269$	−9.56842	+	11.9984i	−0.583397	+	0.731556i	0.399291	+	0.916824i	$0.369256\pi$
$270$		0			0
$271$	−14.1724	−	6.82505i	−0.860910	−	0.414592i	−0.0492945	−	0.998784i	$-0.515697\pi$
$271$	−14.1724	−	6.82505i	−0.860910	−	0.414592i	−0.811616	+	0.584192i	$0.801412\pi$
$272$	21.2707	+	26.6726i	1.28972	+	1.61726i
$273$		0			0
$274$	21.2900	+	26.6968i	1.28617	+	1.61281i
$275$	−5.34118	−	23.4013i	−0.322086	−	1.41115i
$276$		0			0
$277$	−14.1068	−	17.6894i	−0.847595	−	1.06285i	−0.997250	−	0.0741120i	$-0.976388\pi$
$277$	−14.1068	−	17.6894i	−0.847595	−	1.06285i	0.149655	−	0.988738i	$-0.452184\pi$
$278$	−29.8581			−1.79077
$279$		0			0
$280$	−10.4279	−	5.02180i	−0.623184	−	0.300110i
$281$	13.7451	−	17.2358i	0.819965	−	1.02820i	−0.179051	−	0.983840i	$-0.557303\pi$
$281$	13.7451	−	17.2358i	0.819965	−	1.02820i	0.999015	−	0.0443636i	$-0.0141260\pi$
$282$		0			0
$283$	−4.66832	+	2.24815i	−0.277503	+	0.133638i	−0.567459	−	0.823402i	$-0.692074\pi$
$283$	−4.66832	+	2.24815i	−0.277503	+	0.133638i	0.289956	+	0.957040i	$0.406359\pi$
$284$	9.19474	+	40.2848i	0.545608	+	2.39046i
$285$		0			0
$286$	18.3905	+	8.85638i	1.08745	+	0.523689i
$287$	6.30771	−	3.03763i	0.372332	−	0.179306i
$288$		0			0
$289$	8.83596			0.519762
$290$	1.32866	−	14.8093i	0.0780216	−	0.869633i
$291$		0			0
$292$	1.76912	−	7.75102i	0.103530	−	0.453594i
$293$	3.38919	−	1.63215i	0.197999	−	0.0953511i	−0.332257	−	0.943189i	$-0.607810\pi$
$293$	3.38919	−	1.63215i	0.197999	−	0.0953511i	0.530256	+	0.847838i	$0.322096\pi$
$294$		0			0
$295$	2.11455	−	9.26447i	0.123114	−	0.539398i
$296$	8.43369	+	36.9504i	0.490198	+	2.14770i
$297$		0			0
$298$	1.20395	−	1.50970i	0.0697427	−	0.0874545i
$299$	−3.60912	+	4.52569i	−0.208721	+	0.261727i
$300$		0			0
$301$	1.97590	+	2.47770i	0.113889	+	0.142812i
$302$	−46.7224			−2.68857
$303$		0			0
$304$	9.74796	+	42.7086i	0.559084	+	2.44951i
$305$	−0.748568	−	3.27969i	−0.0428629	−	0.187795i
$306$		0			0
$307$	−4.15007			−0.236857			−0.118428	−	0.992963i	$-0.537786\pi$
$307$	−4.15007			−0.236857			−0.118428	+	0.992963i	$0.537786\pi$
$308$	−30.0377	−	37.6661i	−1.71156	−	2.14623i
$309$		0			0
$310$	−11.8006	+	14.7975i	−0.670232	+	0.840444i
$311$	5.11268	−	6.41109i	0.289913	−	0.363540i	−0.615451	−	0.788175i	$-0.711026\pi$
$311$	5.11268	−	6.41109i	0.289913	−	0.363540i	0.905365	+	0.424635i	$0.139598\pi$
$312$		0			0
$313$	1.29402	+	5.66946i	0.0731421	+	0.320457i	0.998242	−	0.0592668i	$-0.0188763\pi$
$313$	1.29402	+	5.66946i	0.0731421	+	0.320457i	−0.925100	+	0.379723i	$0.876019\pi$
$314$	6.18511	−	27.0987i	0.349046	−	1.52927i
$315$		0			0
$316$	11.4175	−	5.49839i	0.642285	−	0.309308i
$317$	−2.46889	+	10.8169i	−0.138666	+	0.607537i	0.857062	+	0.515212i	$0.172287\pi$
$317$	−2.46889	+	10.8169i	−0.138666	+	0.607537i	−0.995729	+	0.0923249i	$0.970570\pi$
$318$		0			0
$319$	17.3793	−	29.1066i	0.973052	−	1.62966i
$320$	1.55944			0.0871752
$321$		0			0
$322$	17.8764	−	8.60882i	0.996213	−	0.479751i
$323$	29.8900	+	14.3942i	1.66312	+	0.800917i
$324$		0			0
$325$	−1.08559	−	4.75630i	−0.0602179	−	0.263832i
$326$	54.4564	−	26.2248i	3.01606	−	1.45246i
$327$		0			0
$328$	15.4833	−	19.4155i	0.854925	−	1.07204i
$329$	2.36450	+	1.13868i	0.130359	+	0.0627775i
$330$		0			0
$331$	16.7926			0.923002			0.461501	−	0.887140i	$-0.347311\pi$
$331$	16.7926			0.923002			0.461501	+	0.887140i	$0.347311\pi$
$332$	−18.1798	−	22.7968i	−0.997749	−	1.25114i
$333$		0			0
$334$	8.11349	+	35.5475i	0.443950	+	1.94507i
$335$	1.62821	+	2.04171i	0.0889585	+	0.111550i
$336$		0			0
$337$	13.1418	+	16.4793i	0.715880	+	0.897685i	0.998097	−	0.0616653i	$-0.0196411\pi$
$337$	13.1418	+	16.4793i	0.715880	+	0.897685i	−0.282217	+	0.959351i	$0.591070\pi$
$338$	−25.9444	−	12.4942i	−1.41119	−	0.679593i
$339$		0			0
$340$	−15.2693	+	19.1471i	−0.828093	+	1.03840i
$341$	−38.8789	+	18.7231i	−2.10541	+	1.01391i
$342$		0			0
$343$	4.23794	−	18.5676i	0.228828	−	1.00256i
$344$	10.1279	+	4.87734i	0.546059	+	0.262968i
$345$		0			0
$346$	2.22693	−	9.75680i	0.119720	−	0.524529i
$347$	31.0309			1.66583			0.832914	−	0.553402i	$-0.186671\pi$
$347$	31.0309			1.66583			0.832914	+	0.553402i	$0.186671\pi$
$348$		0			0
$349$	−35.7539			−1.91386			−0.956931	−	0.290315i	$-0.906240\pi$
$349$	−35.7539			−1.91386			−0.956931	+	0.290315i	$0.906240\pi$
$350$	−3.72105	+	16.3030i	−0.198899	+	0.871432i
$351$		0			0
$352$	−26.8395	−	12.9252i	−1.43055	−	0.688915i
$353$	−1.34141	+	5.87712i	−0.0713962	+	0.312807i	−0.997999	−	0.0632352i	$-0.979858\pi$
$353$	−1.34141	+	5.87712i	−0.0713962	+	0.312807i	0.926602	+	0.376042i	$0.122715\pi$
$354$		0			0
$355$	−9.17209	+	4.41705i	−0.486804	+	0.234432i
$356$	−9.22436	+	11.5670i	−0.488890	+	0.613048i
$357$		0			0
$358$	−37.4766	−	18.0478i	−1.98070	−	0.953856i
$359$	3.56260	+	4.46736i	0.188027	+	0.235778i	0.866906	−	0.498472i	$-0.166105\pi$
$359$	3.56260	+	4.46736i	0.188027	+	0.235778i	−0.678879	+	0.734250i	$0.737534\pi$
$360$		0			0
$361$	14.7142	+	18.4510i	0.774430	+	0.971104i
$362$	−9.44738	−	41.3917i	−0.496543	−	2.17550i
$363$		0			0
$364$	−6.10516	−	7.65562i	−0.319997	−	0.401264i
$365$	1.95874			0.102525
$366$		0			0
$367$	−24.6356	−	11.8639i	−1.28597	−	0.619290i	−0.339051	−	0.940768i	$-0.610106\pi$
$367$	−24.6356	−	11.8639i	−1.28597	−	0.619290i	−0.946917	+	0.321478i	$0.895820\pi$
$368$	18.9324	−	23.7405i	0.986921	−	1.23756i
$369$		0			0
$370$	−15.3593	+	7.39663i	−0.798490	+	0.384532i
$371$	−1.45336	−	6.36758i	−0.0754546	−	0.330588i
$372$		0			0
$373$	11.3717	+	5.47631i	0.588803	+	0.283552i	0.704468	−	0.709736i	$-0.251186\pi$
$373$	11.3717	+	5.47631i	0.588803	+	0.283552i	−0.115665	+	0.993288i	$0.536900\pi$
$374$	−73.0585	+	35.1831i	−3.77776	+	1.81927i
$375$		0			0
$376$	9.30899			0.480074
$377$	3.53233	−	5.91590i	0.181924	−	0.304684i
$378$		0			0
$379$	0.734451	−	3.21784i	0.0377262	−	0.165289i	−0.952556	−	0.304365i	$-0.901556\pi$
$379$	0.734451	−	3.21784i	0.0377262	−	0.165289i	0.990282	+	0.139075i	$0.0444130\pi$
$380$	−28.3328	+	13.6444i	−1.45344	+	0.699941i
$381$		0			0
$382$	1.66357	−	7.28859i	0.0851158	−	0.372917i
$383$	2.14467	+	9.39639i	0.109587	+	0.480133i	0.999702	+	0.0243974i	$0.00776669\pi$
$383$	2.14467	+	9.39639i	0.109587	+	0.480133i	−0.890115	+	0.455736i	$0.849376\pi$
$384$		0			0
$385$	7.40043	−	9.27984i	0.377161	−	0.472945i
$386$	7.71596	−	9.67551i	0.392732	−	0.492470i
$387$		0			0
$388$	6.25209	+	7.83988i	0.317402	+	0.398009i
$389$	−10.7987			−0.547518			−0.273759	−	0.961798i	$-0.588267\pi$
$389$	−10.7987			−0.547518			−0.273759	+	0.961798i	$0.588267\pi$
$390$		0			0
$391$	−5.11706	−	22.4193i	−0.258781	−	1.13379i
$392$	−5.47079	−	23.9691i	−0.276316	−	1.21062i
$393$		0			0
$394$	−6.38254			−0.321548
$395$	1.94662	+	2.44098i	0.0979450	+	0.122819i
$396$		0			0
$397$	18.5378	−	23.2457i	0.930385	−	1.16667i	−0.0553677	−	0.998466i	$-0.517633\pi$
$397$	18.5378	−	23.2457i	0.930385	−	1.16667i	0.985753	−	0.168200i	$-0.0537955\pi$
$398$	−40.3731	+	50.6263i	−2.02372	+	2.53767i
$399$		0			0
$400$	5.69472	+	24.9502i	0.284736	+	1.24751i
$401$	2.54450	−	11.1482i	0.127066	−	0.556713i	−0.870813	−	0.491615i	$-0.836407\pi$
$401$	2.54450	−	11.1482i	0.127066	−	0.556713i	0.997879	−	0.0650982i	$-0.0207361\pi$
$402$		0			0
$403$	−7.90212	+	3.80546i	−0.393633	+	0.189564i
$404$	12.3568	−	54.1386i	0.614773	−	2.69350i
$405$		0			0
$406$	−19.7068	+	13.0163i	−0.978032	+	0.645988i
$407$	−38.8677			−1.92660
$408$		0			0
$409$	−26.9918	+	12.9985i	−1.33466	+	0.642737i	−0.958837	−	0.283956i	$-0.908353\pi$
$409$	−26.9918	+	12.9985i	−1.33466	+	0.642737i	−0.375820	+	0.926693i	$0.622639\pi$
$410$	10.0637	+	4.84644i	0.497012	+	0.239349i
$411$		0			0
$412$	−2.73108	−	11.9656i	−0.134550	−	0.589504i
$413$	−13.5992	+	6.54904i	−0.669174	+	0.322257i
$414$		0			0
$415$	4.47899	−	5.61647i	0.219865	−	0.275702i
$416$	−5.45511	−	2.62704i	−0.267459	−	0.128801i
$417$		0			0
$418$	−104.124			−5.09288
$419$	12.7136	+	15.9424i	0.621101	+	0.778836i	0.988499	−	0.151228i	$-0.0483228\pi$
$419$	12.7136	+	15.9424i	0.621101	+	0.778836i	−0.367398	+	0.930064i	$0.619751\pi$
$420$		0			0
$421$	5.11531	+	22.4116i	0.249305	+	1.09228i	0.932253	+	0.361808i	$0.117840\pi$
$421$	5.11531	+	22.4116i	0.249305	+	1.09228i	−0.682948	+	0.730467i	$0.739302\pi$
$422$	2.91539	+	3.65578i	0.141919	+	0.177960i
$423$		0			0
$424$	−14.4446	−	18.1129i	−0.701491	−	0.879641i
$425$	17.4616	+	8.40906i	0.847012	+	0.407899i
$426$		0			0
$427$	−3.33155	+	4.17763i	−0.161225	+	0.202170i
$428$	39.6750	−	19.1065i	1.91776	−	0.923545i
$429$		0			0
$430$	−1.12511	+	4.92942i	−0.0542575	+	0.237718i
$431$	−3.64629	−	1.75596i	−0.175636	−	0.0845817i	0.344000	−	0.938970i	$-0.388218\pi$
$431$	−3.64629	−	1.75596i	−0.175636	−	0.0845817i	−0.519636	+	0.854388i	$0.673932\pi$
$432$		0			0
$433$	−0.585130	+	2.56362i	−0.0281196	+	0.123200i	−0.987040	−	0.160476i	$-0.948697\pi$
$433$	−0.585130	+	2.56362i	−0.0281196	+	0.123200i	0.958920	+	0.283676i	$0.0915541\pi$
$434$	30.0630			1.44307
$435$		0			0
$436$	−20.8971			−1.00079
$437$	6.57069	−	28.7881i	0.314319	−	1.37712i
$438$		0			0
$439$	23.4338	+	11.2851i	1.11843	+	0.538609i	0.899408	−	0.437110i	$-0.143998\pi$
$439$	23.4338	+	11.2851i	1.11843	+	0.538609i	0.219025	+	0.975719i	$0.429712\pi$
$440$	9.36854	−	41.0463i	0.446628	−	1.95680i
$441$		0			0
$442$	−14.8491	+	7.15095i	−0.706300	+	0.340136i
$443$	−11.7311	+	14.7103i	−0.557360	+	0.698907i	−0.978067	−	0.208290i	$-0.933210\pi$
$443$	−11.7311	+	14.7103i	−0.557360	+	0.698907i	0.420708	+	0.907196i	$0.361782\pi$
$444$		0			0
$445$	−3.28402	−	1.58150i	−0.155678	−	0.0749704i
$446$	37.9991	+	47.6493i	1.79931	+	2.25626i
$447$		0			0
$448$	−1.54438	−	1.93659i	−0.0729650	−	0.0914952i
$449$	2.75254	+	12.0597i	0.129900	+	0.569130i	0.997424	+	0.0717342i	$0.0228533\pi$
$449$	2.75254	+	12.0597i	0.129900	+	0.569130i	−0.867523	+	0.497396i	$0.834290\pi$
$450$		0			0
$451$	15.8784	+	19.9109i	0.747684	+	0.937567i
$452$	2.42542			0.114082
$453$		0			0
$454$	51.6926	+	24.8939i	2.42606	+	1.16833i
$455$	1.50413	−	1.88612i	0.0705149	−	0.0884229i
$456$		0			0
$457$	18.1340	−	8.73289i	0.848275	−	0.408508i	0.0413378	−	0.999145i	$-0.486838\pi$
$457$	18.1340	−	8.73289i	0.848275	−	0.408508i	0.806937	+	0.590638i	$0.201124\pi$
$458$	−7.78324	−	34.1006i	−0.363687	−	1.59342i
$459$		0			0
$460$	19.6392	+	9.45774i	0.915682	+	0.440969i
$461$	17.8198	−	8.58155i	0.829950	−	0.399683i	0.0298534	−	0.999554i	$-0.490496\pi$
$461$	17.8198	−	8.58155i	0.829950	−	0.399683i	0.800096	+	0.599872i	$0.204782\pi$
$462$		0			0
$463$	2.22268			0.103297			0.0516484	−	0.998665i	$-0.483552\pi$
$463$	2.22268			0.103297			0.0516484	+	0.998665i	$0.483552\pi$
$464$	−18.5296	+	31.0332i	−0.860215	+	1.44068i
$465$		0			0
$466$	3.77720	−	16.5490i	0.174975	−	0.766617i
$467$	4.17491	−	2.01053i	0.193192	−	0.0930362i	−0.334787	−	0.942294i	$-0.608664\pi$
$467$	4.17491	−	2.01053i	0.193192	−	0.0930362i	0.527979	+	0.849258i	$0.322950\pi$
$468$		0			0
$469$	0.923013	−	4.04398i	0.0426208	−	0.186734i
$470$	0.931724	+	4.08215i	0.0429772	+	0.188295i
$471$		0			0
$472$	−33.3816	+	41.8592i	−1.53651	+	1.92673i
$473$	−7.18754	+	9.01289i	−0.330484	+	0.414413i
$474$		0			0
$475$	15.5165	+	19.4571i	0.711947	+	0.892753i
$476$	38.8996			1.78296
$477$		0			0
$478$	−6.85863	−	30.0496i	−0.313706	−	1.37444i
$479$	−2.11528	−	9.26766i	−0.0966498	−	0.423450i	0.903335	−	0.428935i	$-0.141111\pi$
$479$	−2.11528	−	9.26766i	−0.0966498	−	0.423450i	−0.999985	+	0.00548500i	$0.998254\pi$
$480$		0			0
$481$	−7.89983			−0.360201
$482$	−4.19691	−	5.26276i	−0.191164	−	0.239712i
$483$		0			0
$484$	78.9358	−	98.9824i	3.58799	−	4.49920i
$485$	−1.54033	+	1.93152i	−0.0699430	+	0.0877057i
$486$		0			0
$487$	−1.69061	−	7.40706i	−0.0766090	−	0.335646i	0.922070	−	0.387022i	$-0.126496\pi$
$487$	−1.69061	−	7.40706i	−0.0766090	−	0.335646i	−0.998679	+	0.0513764i	$0.983639\pi$
$488$	−4.21756	+	18.4783i	−0.190920	+	0.836475i
$489$		0			0
$490$	9.96328	−	4.79807i	0.450095	−	0.216754i
$491$	−5.01175	+	21.9579i	−0.226177	+	0.990947i	0.726548	+	0.687115i	$0.241123\pi$
$491$	−5.01175	+	21.9579i	−0.226177	+	0.990947i	−0.952726	+	0.303832i	$0.901734\pi$
$492$		0			0
$493$	9.62515	+	25.6242i	0.433495	+	1.15406i
$494$	−21.1632			−0.952177
$495$		0			0
$496$	41.4523	−	19.9624i	1.86126	−	0.896338i
$497$	14.5688	+	7.01598i	0.653501	+	0.314710i
$498$		0			0
$499$	6.40406	+	28.0580i	0.286685	+	1.25605i	0.889043	+	0.457823i	$0.151371\pi$
$499$	6.40406	+	28.0580i	0.286685	+	1.25605i	−0.602358	+	0.798226i	$0.705772\pi$
$500$	−38.2568	+	18.4235i	−1.71089	+	0.823923i
$501$		0			0
$502$	−35.9707	+	45.1058i	−1.60545	+	2.01317i
$503$	−4.50964	−	2.17173i	−0.201075	−	0.0968325i	0.330637	−	0.943758i	$-0.392737\pi$
$503$	−4.50964	−	2.17173i	−0.201075	−	0.0968325i	−0.531711	+	0.846926i	$0.678451\pi$
$504$		0			0
$505$	13.6812			0.608805
$506$	45.0003	+	56.4285i	2.00051	+	2.50855i
$507$		0			0
$508$	−14.0194	−	61.4230i	−0.622010	−	2.72520i
$509$	−3.10581	−	3.89456i	−0.137663	−	0.172623i	0.708221	−	0.705990i	$-0.249498\pi$
$509$	−3.10581	−	3.89456i	−0.137663	−	0.172623i	−0.845884	+	0.533367i	$0.820926\pi$
$510$		0			0
$511$	−1.93982	−	2.43246i	−0.0858126	−	0.107606i
$512$	−45.6248	−	21.9717i	−2.01635	−	0.971023i
$513$		0			0
$514$	12.1797	−	15.2728i	0.537223	−	0.673657i
$515$	2.72435	−	1.31198i	0.120049	−	0.0578126i
$516$		0			0
$517$	−2.12430	+	9.30715i	−0.0934264	+	0.409328i
$518$	24.3964	+	11.7487i	1.07192	+	0.516209i
$519$		0			0
$520$	1.90415	−	8.34263i	0.0835026	−	0.365849i
$521$	−4.54404			−0.199078			−0.0995389	−	0.995034i	$-0.531737\pi$
$521$	−4.54404			−0.199078			−0.0995389	+	0.995034i	$0.531737\pi$
$522$		0			0
$523$	−3.08967			−0.135102			−0.0675510	−	0.997716i	$-0.521519\pi$
$523$	−3.08967			−0.135102			−0.0675510	+	0.997716i	$0.521519\pi$
$524$	6.72894	−	29.4814i	0.293955	−	1.28790i
$525$		0			0
$526$	1.75709	+	0.846171i	0.0766129	+	0.0368948i
$527$	7.75323	−	33.9691i	0.337736	−	1.47972i
$528$		0			0
$529$	2.28130	−	1.09862i	0.0991869	−	0.0477659i
$530$	6.49709	−	8.14709i	0.282215	−	0.353887i
$531$		0			0
$532$	45.0035	+	21.6725i	1.95115	+	0.939623i
$533$	3.22728	+	4.04688i	0.139789	+	0.175290i
$534$		0			0
$535$	6.76434	+	8.48222i	0.292448	+	0.366718i
$536$	−3.27402	−	14.3444i	−0.141416	−	0.619585i
$537$		0			0
$538$	24.2484	+	30.4066i	1.04542	+	1.31092i
$539$	25.2128			1.08599
$540$		0			0
$541$	−19.3355	−	9.31147i	−0.831297	−	0.400331i	−0.0306954	−	0.999529i	$-0.509772\pi$
$541$	−19.3355	−	9.31147i	−0.831297	−	0.400331i	−0.800601	+	0.599197i	$0.795486\pi$
$542$	−24.8545	+	31.1666i	−1.06759	+	1.33872i
$543$		0			0
$544$	21.6711	−	10.4363i	0.929141	−	0.447451i
$545$	−1.14564	−	5.01936i	−0.0490737	−	0.215006i
$546$		0			0
$547$	13.0776	+	6.29785i	0.559158	+	0.269276i	0.692045	−	0.721855i	$-0.256710\pi$
$547$	13.0776	+	6.29785i	0.559158	+	0.269276i	−0.132886	+	0.991131i	$0.542424\pi$
$548$	53.6853	−	25.8535i	2.29332	−	1.10441i
$549$		0			0
$550$	−60.8290			−2.59376
$551$	−3.14080	+	35.0075i	−0.133803	+	1.49137i
$552$		0			0
$553$	1.10352	−	4.83482i	0.0469263	−	0.205597i
$554$	−51.6597	+	24.8780i	−2.19481	+	1.05697i
$555$		0			0
$556$	−11.5940	+	50.7965i	−0.491694	+	2.15425i
$557$	5.37517	+	23.5502i	0.227753	+	0.997852i	0.951467	+	0.307752i	$0.0995765\pi$
$557$	5.37517	+	23.5502i	0.227753	+	0.997852i	−0.723714	+	0.690100i	$0.757566\pi$
$558$		0			0
$559$	−1.46086	+	1.83187i	−0.0617880	+	0.0774797i
$560$	−7.89027	+	9.89408i	−0.333425	+	0.418101i
$561$		0			0
$562$	−34.8331	−	43.6793i	−1.46935	−	1.84250i
$563$	7.54185			0.317851			0.158926	−	0.987291i	$-0.449197\pi$
$563$	7.54185			0.317851			0.158926	+	0.987291i	$0.449197\pi$
$564$		0			0
$565$	0.132968	+	0.582571i	0.00559400	+	0.0245089i
$566$	2.92190	+	12.8017i	0.122817	+	0.538095i
$567$		0			0
$568$	57.3572			2.40666
$569$	12.5014	+	15.6763i	0.524086	+	0.657183i	0.971471	−	0.237159i	$-0.0762161\pi$
$569$	12.5014	+	15.6763i	0.524086	+	0.657183i	−0.447385	+	0.894341i	$0.647645\pi$
$570$		0			0
$571$	−2.84040	+	3.56175i	−0.118867	+	0.149054i	−0.837705	−	0.546123i	$-0.816103\pi$
$571$	−2.84040	+	3.56175i	−0.118867	+	0.149054i	0.718838	+	0.695178i	$0.244674\pi$
$572$	22.2081	−	27.8481i	0.928569	−	1.16439i
$573$		0			0
$574$	−3.94799	−	17.2973i	−0.164786	−	0.721975i
$575$	3.83857	−	16.8179i	0.160080	−	0.701355i
$576$		0			0
$577$	−17.6920	+	8.52003i	−0.736528	+	0.354693i	−0.764248	−	0.644922i	$-0.776890\pi$
$577$	−17.6920	+	8.52003i	−0.736528	+	0.354693i	0.0277198	+	0.999616i	$0.491175\pi$
$578$	4.98274	−	21.8308i	0.207255	−	0.908042i
$579$		0			0
$580$	−24.6787	−	8.01091i	−1.02473	−	0.332635i
$581$	−11.4106			−0.473390
$582$		0			0
$583$	21.4056	−	10.3084i	0.886529	−	0.426930i
$584$	−9.94295	−	4.78827i	−0.411442	−	0.198140i
$585$		0			0
$586$	−2.12129	−	9.29399i	−0.0876298	−	0.383931i
$587$	−36.2181	+	17.4417i	−1.49488	+	0.719897i	−0.989705	−	0.143120i	$-0.954287\pi$
$587$	−36.2181	+	17.4417i	−1.49488	+	0.719897i	−0.505176	+	0.863017i	$0.668572\pi$
$588$		0			0
$589$	27.8954	−	34.9797i	1.14941	−	1.44131i
$590$	−21.6971	−	10.4488i	−0.893255	−	0.430169i
$591$		0			0
$592$	41.4403			1.70319
$593$	−28.6572	−	35.9350i	−1.17681	−	1.47567i	−0.846975	−	0.531633i	$-0.821579\pi$
$593$	−28.6572	−	35.9350i	−1.17681	−	1.47567i	−0.329834	−	0.944039i	$-0.606993\pi$
$594$		0			0
$595$	2.13258	+	9.34346i	0.0874274	+	0.383044i
$596$	−2.10091	−	2.63445i	−0.0860564	−	0.107911i
$597$		0			0
$598$	9.14628	+	11.4691i	0.374019	+	0.469005i
$599$	−9.05961	−	4.36288i	−0.370166	−	0.178262i	0.239547	−	0.970885i	$-0.423001\pi$
$599$	−9.05961	−	4.36288i	−0.370166	−	0.178262i	−0.609713	+	0.792622i	$0.708715\pi$
$600$		0			0
$601$	−0.763319	+	0.957172i	−0.0311364	+	0.0390439i	−0.797156	−	0.603773i	$-0.793663\pi$
$601$	−0.763319	+	0.957172i	−0.0311364	+	0.0390439i	0.766019	+	0.642817i	$0.222235\pi$
$602$	7.23584	−	3.48460i	0.294911	−	0.142022i
$603$		0			0
$604$	−18.1425	+	79.4873i	−0.738206	+	3.23429i
$605$	28.1025	+	13.5334i	1.14253	+	0.550212i
$606$		0			0
$607$	−6.84845	+	30.0050i	−0.277970	+	1.21787i	0.622385	+	0.782711i	$0.286164\pi$
$607$	−6.84845	+	30.0050i	−0.277970	+	1.21787i	−0.900355	+	0.435155i	$0.856693\pi$
$608$	30.8860			1.25259
$609$		0			0
$610$	−8.52519			−0.345175
$611$	−0.431762	+	1.89167i	−0.0174672	+	0.0765289i
$612$		0			0
$613$	7.12528	+	3.43135i	0.287787	+	0.138591i	0.572208	−	0.820109i	$-0.306087\pi$
$613$	7.12528	+	3.43135i	0.287787	+	0.138591i	−0.284421	+	0.958700i	$0.591801\pi$
$614$	−2.34029	+	10.2535i	−0.0944464	+	0.413797i
$615$		0			0
$616$	−60.2514	+	29.0155i	−2.42760	+	1.16907i
$617$	7.98066	−	10.0074i	0.321289	−	0.402884i	−0.594790	−	0.803881i	$-0.702765\pi$
$617$	7.98066	−	10.0074i	0.321289	−	0.402884i	0.916079	+	0.400997i	$0.131336\pi$
$618$		0			0
$619$	38.2518	+	18.4211i	1.53747	+	0.740406i	0.995019	−	0.0996833i	$-0.0317830\pi$
$619$	38.2518	+	18.4211i	1.53747	+	0.740406i	0.542449	+	0.840089i	$0.317497\pi$
$620$	20.5923	+	25.8220i	0.827008	+	1.03704i
$621$		0			0
$622$	−12.9566	−	16.2471i	−0.519513	−	0.651449i
$623$	1.28832	+	5.64450i	0.0516154	+	0.226142i
$624$		0			0
$625$	5.36415	+	6.72643i	0.214566	+	0.269057i
$626$	14.7371			0.589014
$627$		0			0
$628$	−43.7005	−	21.0450i	−1.74384	−	0.839789i
$629$	19.5670	−	24.5363i	0.780189	−	0.978326i
$630$		0			0
$631$	−39.7014	+	19.1192i	−1.58049	+	0.761123i	−0.998638	−	0.0521737i	$-0.983385\pi$
$631$	−39.7014	+	19.1192i	−1.58049	+	0.761123i	−0.581850	+	0.813296i	$0.697671\pi$
$632$	−3.91428	−	17.1496i	−0.155702	−	0.682174i
$633$		0			0
$634$	25.3328	+	12.1996i	1.00610	+	0.484510i
$635$	13.9848	−	6.73475i	0.554972	−	0.267260i
$636$		0			0
$637$	5.12449			0.203040
$638$	−62.1126	−	59.3522i	−2.45906	−	2.34978i
$639$		0			0
$640$	3.17392	−	13.9058i	0.125460	−	0.549677i
$641$	−36.3896	+	17.5243i	−1.43730	+	0.692168i	−0.980339	−	0.197318i	$-0.936777\pi$
$641$	−36.3896	+	17.5243i	−1.43730	+	0.692168i	−0.456962	+	0.889486i	$0.651062\pi$
$642$		0			0
$643$	−1.71136	+	7.49794i	−0.0674893	+	0.295690i	−0.997397	−	0.0721025i	$-0.977029\pi$
$643$	−1.71136	+	7.49794i	−0.0674893	+	0.295690i	0.929908	+	0.367792i	$0.119886\pi$
$644$	−7.70444	−	33.7554i	−0.303597	−	1.33015i
$645$		0			0
$646$	52.4190	−	65.7313i	2.06240	−	2.58616i
$647$	15.3144	−	19.2037i	0.602072	−	0.754975i	−0.383627	−	0.923488i	$-0.625325\pi$
$647$	15.3144	−	19.2037i	0.602072	−	0.754975i	0.985699	+	0.168513i	$0.0538966\pi$
$648$		0			0
$649$	−34.2333	−	42.9272i	−1.34377	−	1.68504i
$650$	−12.3635			−0.484935
$651$		0			0
$652$	−23.4698	−	102.828i	−0.919150	−	4.02706i
$653$	5.93369	+	25.9972i	0.232203	+	1.01735i	0.947807	+	0.318843i	$0.103294\pi$
$653$	5.93369	+	25.9972i	0.232203	+	1.01735i	−0.715604	+	0.698506i	$0.753848\pi$
$654$		0			0
$655$	7.45016			0.291102
$656$	−16.9294	−	21.2288i	−0.660982	−	0.828845i
$657$		0			0
$658$	4.14669	−	5.19979i	0.161655	−	0.202709i
$659$	7.62974	−	9.56739i	0.297212	−	0.372693i	−0.610693	−	0.791867i	$-0.709109\pi$
$659$	7.62974	−	9.56739i	0.297212	−	0.372693i	0.907906	+	0.419175i	$0.137681\pi$
$660$		0			0
$661$	−8.99484	−	39.4090i	−0.349859	−	1.53283i	−0.777500	−	0.628883i	$-0.783512\pi$
$661$	−8.99484	−	39.4090i	−0.349859	−	1.53283i	0.427641	−	0.903949i	$-0.359345\pi$
$662$	9.46959	−	41.4890i	0.368046	−	1.61252i
$663$		0			0
$664$	−36.4662	+	17.5612i	−1.41516	+	0.681506i
$665$	−2.73840	+	11.9977i	−0.106191	+	0.465251i
$666$		0			0
$667$	20.3292	−	13.4274i	0.787149	−	0.519911i
$668$	63.6263			2.46178
$669$		0			0
$670$	5.96258	−	2.87143i	0.230355	−	0.110933i
$671$	−17.5122	−	8.43345i	−0.676053	−	0.325570i
$672$		0			0
$673$	−10.7198	−	46.9663i	−0.413216	−	1.81042i	−0.568659	−	0.822573i	$-0.692538\pi$
$673$	−10.7198	−	46.9663i	−0.413216	−	1.81042i	0.155443	−	0.987845i	$-0.450320\pi$
$674$	48.1260	−	23.1762i	1.85374	−	0.892715i
$675$		0			0
$676$	−31.3302	+	39.2868i	−1.20501	+	1.51103i
$677$	2.03915	+	0.982003i	0.0783709	+	0.0377415i	0.472659	−	0.881246i	$-0.343294\pi$
$677$	2.03915	+	0.982003i	0.0783709	+	0.0377415i	−0.394288	+	0.918987i	$0.629009\pi$
$678$		0			0
$679$	3.92412			0.150594
$680$	21.1952	+	26.5780i	0.812800	+	1.01922i
$681$		0			0
$682$	24.3343	+	106.616i	0.931808	+	4.08252i
$683$	17.4383	+	21.8669i	0.667258	+	0.836715i	0.994112	−	0.108360i	$-0.0345600\pi$
$683$	17.4383	+	21.8669i	0.667258	+	0.836715i	−0.326854	+	0.945075i	$0.605989\pi$
$684$		0			0
$685$	9.15302	+	11.4775i	0.349719	+	0.438534i
$686$	−43.4848	−	20.9412i	−1.66026	−	0.799539i
$687$		0			0
$688$	7.66329	−	9.60946i	0.292160	−	0.366357i
$689$	4.35068	−	2.09517i	0.165748	−	0.0798198i
$690$		0			0
$691$	2.65566	−	11.6352i	0.101026	−	0.442623i	−0.898964	−	0.438024i	$-0.855679\pi$
$691$	2.65566	−	11.6352i	0.101026	−	0.442623i	0.999989	−	0.00459992i	$-0.00146421\pi$
$692$	−15.7342	−	7.57719i	−0.598124	−	0.288041i
$693$		0			0
$694$	17.4988	−	76.6675i	0.664247	−	2.91026i
$695$	−12.8366			−0.486921
$696$		0			0
$697$	−20.5629			−0.778876
$698$	−20.1622	+	88.3364i	−0.763151	+	3.34358i
$699$		0			0
$700$	26.2909	+	12.6610i	0.993701	+	0.478541i
$701$	−0.764903	+	3.35126i	−0.0288900	+	0.126575i	−0.987317	−	0.158764i	$-0.949249\pi$
$701$	−0.764903	+	3.35126i	−0.0288900	+	0.126575i	0.958427	+	0.285339i	$0.0921063\pi$
$702$		0			0
$703$	36.3075	−	17.4848i	1.36936	−	0.659451i
$704$	5.61783	−	7.04454i	0.211730	−	0.265501i
$705$		0			0
$706$	13.7640	+	6.62840i	0.518016	+	0.249463i
$707$	−13.5491	−	16.9900i	−0.509566	−	0.638975i
$708$		0			0
$709$	−16.5529	−	20.7566i	−0.621656	−	0.779532i	0.366921	−	0.930252i	$-0.380412\pi$
$709$	−16.5529	−	20.7566i	−0.621656	−	0.779532i	−0.988576	+	0.150721i	$0.951841\pi$
$710$	5.74081	+	25.1521i	0.215449	+	0.943942i
$711$		0			0
$712$	12.8043	+	16.0561i	0.479861	+	0.601727i
$713$	−31.0125			−1.16143
$714$		0			0
$715$	7.90646	+	3.80755i	0.295685	+	0.142394i
$716$	−45.2564	+	56.7497i	−1.69131	+	2.12084i
$717$		0			0
$718$	13.0464	−	6.28282i	0.486888	−	0.234473i
$719$	−6.93957	−	30.4043i	−0.258802	−	1.13389i	−0.922534	−	0.385916i	$-0.873885\pi$
$719$	−6.93957	−	30.4043i	−0.258802	−	1.13389i	0.663731	−	0.747971i	$-0.268972\pi$
$720$		0			0
$721$	−4.32732	−	2.08393i	−0.161158	−	0.0776095i
$722$	53.8840	−	25.9492i	2.00535	−	0.965728i
$723$		0			0
$724$	−74.0867			−2.75341
$725$	−1.83484	+	20.4513i	−0.0681443	+	0.759541i
$726$		0			0
$727$	−3.81660	+	16.7216i	−0.141550	+	0.620170i	0.853526	+	0.521051i	$0.174460\pi$
$727$	−3.81660	+	16.7216i	−0.141550	+	0.620170i	−0.995076	+	0.0991196i	$0.968397\pi$
$728$	−12.2461	+	5.89740i	−0.453870	+	0.218572i
$729$		0			0
$730$	1.10456	−	4.83941i	0.0408817	−	0.179114i
$731$	−2.07124	−	9.07467i	−0.0766074	−	0.335639i
$732$		0			0
$733$	13.3386	−	16.7261i	0.492673	−	0.617792i	−0.471886	−	0.881659i	$-0.656427\pi$
$733$	13.3386	−	16.7261i	0.492673	−	0.617792i	0.964559	+	0.263867i	$0.0849982\pi$
$734$	−43.2042	+	54.1764i	−1.59470	+	1.99969i
$735$		0			0
$736$	−13.3483	−	16.7382i	−0.492024	−	0.616979i
$737$	15.0887			0.555800
$738$		0			0
$739$	3.85619	+	16.8951i	0.141852	+	0.621495i	0.995004	+	0.0998329i	$0.0318308\pi$
$739$	3.85619	+	16.8951i	0.141852	+	0.621495i	−0.853152	+	0.521662i	$0.825312\pi$
$740$	6.61959	+	29.0023i	0.243341	+	1.06615i
$741$		0			0
$742$	−16.5518			−0.607636
$743$	32.5068	+	40.7623i	1.19256	+	1.49542i	0.824728	+	0.565529i	$0.191328\pi$
$743$	32.5068	+	40.7623i	1.19256	+	1.49542i	0.367831	+	0.929893i	$0.380100\pi$
$744$		0			0
$745$	0.517602	−	0.649053i	0.0189635	−	0.0237795i
$746$	19.9429	−	25.0076i	0.730160	−	0.915592i
$747$		0			0
$748$	31.4870	+	137.954i	1.15128	+	5.04408i
$749$	3.83463	−	16.8006i	0.140114	−	0.613881i
$750$		0			0
$751$	−21.6113	+	10.4075i	−0.788607	+	0.379773i	−0.784430	−	0.620218i	$-0.787044\pi$
$751$	−21.6113	+	10.4075i	−0.788607	+	0.379773i	−0.00417787	+	0.999991i	$0.501330\pi$
$752$	2.26490	−	9.92319i	0.0825926	−	0.361862i
$753$		0			0
$754$	−12.6244	−	12.0633i	−0.459752	−	0.439320i
$755$	−20.0870			−0.731041
$756$		0			0
$757$	−42.7511	+	20.5878i	−1.55381	+	0.748277i	−0.996623	−	0.0821079i	$-0.973835\pi$
$757$	−42.7511	+	20.5878i	−1.55381	+	0.748277i	−0.557190	+	0.830385i	$0.688120\pi$
$758$	−7.53608	−	3.62918i	−0.273723	−	0.131818i
$759$		0			0
$760$	9.71338	+	42.5571i	0.352341	+	1.54371i
$761$	34.8798	−	16.7972i	1.26439	−	0.608899i	0.323059	−	0.946379i	$-0.395289\pi$
$761$	34.8798	−	16.7972i	1.26439	−	0.608899i	0.941333	+	0.337480i	$0.109575\pi$
$762$		0			0
$763$	−5.09873	+	6.39360i	−0.184586	+	0.231464i
$764$	−11.7539	−	5.66036i	−0.425240	−	0.204785i
$765$		0			0
$766$	24.4249			0.882507
$767$	−6.95790	−	8.72494i	−0.251235	−	0.315039i
$768$		0			0
$769$	−9.55795	−	41.8761i	−0.344669	−	1.51009i	−0.789092	−	0.614275i	$-0.789449\pi$
$769$	−9.55795	−	41.8761i	−0.344669	−	1.51009i	0.444423	−	0.895817i	$-0.353409\pi$
$770$	−18.7543	−	23.5171i	−0.675858	−	0.847499i
$771$		0			0
$772$	−13.4645	−	16.8839i	−0.484598	−	0.607666i
$773$	25.4268	+	12.2449i	0.914539	+	0.440419i	0.831118	−	0.556096i	$-0.187701\pi$
$773$	25.4268	+	12.2449i	0.914539	+	0.440419i	0.0834206	+	0.996514i	$0.473415\pi$
$774$		0			0
$775$	16.2964	−	20.4350i	0.585383	−	0.734047i
$776$	12.5408	−	6.03933i	0.450189	−	0.216799i
$777$		0			0
$778$	−6.08959	+	26.6802i	−0.218322	+	0.956533i
$779$	−23.7895	−	11.4564i	−0.852348	−	0.410469i
$780$		0			0
$781$	−13.0888	+	57.3459i	−0.468355	+	2.05200i
$782$	−58.2765			−2.08396
$783$		0			0
$784$	−26.8816			−0.960058
$785$	2.65911	−	11.6503i	0.0949079	−	0.415819i
$786$		0			0
$787$	−12.0574	−	5.80654i	−0.429800	−	0.206981i	0.206461	−	0.978455i	$-0.433805\pi$
$787$	−12.0574	−	5.80654i	−0.429800	−	0.206981i	−0.636261	+	0.771474i	$0.719520\pi$
$788$	−2.47836	+	10.8584i	−0.0882879	+	0.386815i
$789$		0			0
$790$	7.12861	−	3.43296i	0.253625	−	0.122139i
$791$	0.591782	−	0.742071i	0.0210413	−	0.0263850i
$792$		0			0
$793$	−3.55936	−	1.71410i	−0.126396	−	0.0608693i
$794$	−46.9788	−	58.9095i	−1.66721	−	2.09062i
$795$		0			0
$796$	70.4518	+	88.3438i	2.49710	+	3.13126i
$797$	−6.61398	−	28.9777i	−0.234279	−	1.02644i	−0.946047	−	0.324029i	$-0.894962\pi$
$797$	−6.61398	−	28.9777i	−0.234279	−	1.02644i	0.711768	−	0.702415i	$-0.247895\pi$
$798$		0			0
$799$	−4.80597	−	6.02649i	−0.170023	−	0.213202i
$800$	18.0435			0.637934
$801$		0			0
$802$	−26.1087	−	12.5733i	−0.921929	−	0.443978i
$803$	7.05630	−	8.84832i	0.249011	−	0.312250i
$804$		0			0
$805$	7.68546	−	3.70112i	0.270877	−	0.130447i
$806$	4.94594	+	21.6696i	0.174213	+	0.763278i
$807$		0			0
$808$	−69.4486	−	33.4447i	−2.44319	−	1.17658i
$809$	−42.2376	+	20.3406i	−1.48500	+	0.715137i	−0.988262	−	0.152766i	$-0.951182\pi$
$809$	−42.2376	+	20.3406i	−1.48500	+	0.715137i	−0.496734	+	0.867903i	$0.665468\pi$
$810$		0			0
$811$	5.86820			0.206060			0.103030	−	0.994678i	$-0.467146\pi$
$811$	5.86820			0.206060			0.103030	+	0.994678i	$0.467146\pi$
$812$	14.4920	+	38.5808i	0.508569	+	1.35392i
$813$		0			0
$814$	−21.9181	+	96.0295i	−0.768229	+	3.36583i
$815$	23.4120	−	11.2746i	0.820087	−	0.394933i
$816$		0			0
$817$	2.65962	−	11.6526i	0.0930485	−	0.407672i
$818$	16.8941	+	74.0181i	0.590690	+	2.58798i
$819$		0			0
$820$	12.1529	−	15.2392i	0.424396	−	0.532176i
$821$	13.9203	−	17.4555i	0.485822	−	0.609202i	−0.477144	−	0.878825i	$-0.658328\pi$
$821$	13.9203	−	17.4555i	0.485822	−	0.609202i	0.962966	+	0.269624i	$0.0868993\pi$
$822$		0			0
$823$	−11.4860	−	14.4029i	−0.400375	−	0.502055i	0.540249	−	0.841505i	$-0.318330\pi$
$823$	−11.4860	−	14.4029i	−0.400375	−	0.502055i	−0.940624	+	0.339451i	$0.889759\pi$
$824$	−17.0366			−0.593497
$825$		0			0
$826$	8.51175	+	37.2924i	0.296162	+	1.29757i
$827$	6.31476	+	27.6668i	0.219586	+	0.962067i	0.957785	+	0.287485i	$0.0928191\pi$
$827$	6.31476	+	27.6668i	0.219586	+	0.962067i	−0.738200	+	0.674582i	$0.764324\pi$
$828$		0			0
$829$	−9.92857			−0.344833			−0.172417	−	0.985024i	$-0.555158\pi$
$829$	−9.92857			−0.344833			−0.172417	+	0.985024i	$0.555158\pi$
$830$	−11.3507	−	14.2334i	−0.393989	−	0.494047i
$831$		0			0
$832$	1.14182	−	1.43180i	0.0395855	−	0.0496387i
$833$	−12.6928	+	15.9163i	−0.439779	+	0.551466i
$834$		0			0
$835$	3.48817	+	15.2827i	0.120713	+	0.528878i
$836$	−40.4317	+	177.143i	−1.39836	+	6.12662i
$837$		0			0
$838$	46.5579	−	22.4211i	1.60831	−	0.774524i
$839$	11.7856	−	51.6360i	0.406884	−	1.78267i	−0.191531	−	0.981487i	$-0.561345\pi$
$839$	11.7856	−	51.6360i	0.406884	−	1.78267i	0.598415	−	0.801187i	$-0.295798\pi$
$840$		0			0
$841$	−21.8283	+	19.0925i	−0.752701	+	0.658363i
$842$	58.2565			2.00765
$843$		0			0
$844$	7.35150	−	3.54030i	0.253049	−	0.121862i
$845$	−11.1541	−	5.37151i	−0.383711	−	0.184786i
$846$		0			0
$847$	−11.0246	−	48.3018i	−0.378809	−	1.65967i
$848$	−22.8224	+	10.9907i	−0.783725	+	0.377422i
$849$		0			0
$850$	30.6230	−	38.4000i	1.05036	−	1.31711i
$851$	−25.1669	−	12.1198i	−0.862712	−	0.415460i
$852$		0			0
$853$	44.7737			1.53302			0.766512	−	0.642230i	$-0.221991\pi$
$853$	44.7737			1.53302			0.766512	+	0.642230i	$0.221991\pi$
$854$	8.44286	+	10.5870i	0.288909	+	0.362280i
$855$		0			0
$856$	−13.6018	−	59.5935i	−0.464901	−	2.03686i
$857$	−0.131742	−	0.165199i	−0.00450022	−	0.00564309i	0.779576	−	0.626307i	$-0.215434\pi$
$857$	−0.131742	−	0.165199i	−0.00450022	−	0.00564309i	−0.784077	+	0.620664i	$0.786863\pi$
$858$		0			0
$859$	34.9569	+	43.8346i	1.19271	+	1.49562i	0.824488	+	0.565880i	$0.191463\pi$
$859$	34.9569	+	43.8346i	1.19271	+	1.49562i	0.368227	+	0.929736i	$0.379965\pi$
$860$	7.94937	+	3.82822i	0.271071	+	0.130541i
$861$		0			0
$862$	−6.39462	+	8.01860i	−0.217802	+	0.273114i
$863$	23.7321	−	11.4288i	0.807851	−	0.389040i	0.0160891	−	0.999871i	$-0.494878\pi$
$863$	23.7321	−	11.4288i	0.807851	−	0.389040i	0.791762	+	0.610830i	$0.209164\pi$
$864$		0			0
$865$	0.957404	−	4.19466i	0.0325527	−	0.142623i
$866$	6.00392	+	2.89134i	0.204022	+	0.0982516i
$867$		0			0
$868$	11.6736	−	51.1452i	0.396226	−	1.73598i
$869$	18.0394			0.611946
$870$		0			0
$871$	3.06678			0.103914
$872$	−6.45471	+	28.2799i	−0.218584	+	0.957680i
$873$		0			0
$874$	−67.4208	−	32.4681i	−2.28054	−	1.09825i
$875$	−3.69756	+	16.2001i	−0.125000	+	0.547662i
$876$		0			0
$877$	−30.3310	+	14.6066i	−1.02420	+	0.493231i	−0.869084	−	0.494665i	$-0.835291\pi$
$877$	−30.3310	+	14.6066i	−1.02420	+	0.493231i	−0.155120	+	0.987896i	$0.549577\pi$
$878$	41.0966	−	51.5334i	1.38694	−	1.73917i
$879$		0			0
$880$	−41.4751	−	19.9734i	−1.39813	−	0.673302i
$881$	10.2428	+	12.8441i	0.345090	+	0.432729i	0.923842	−	0.382775i	$-0.125031\pi$
$881$	10.2428	+	12.8441i	0.345090	+	0.432729i	−0.578752	+	0.815504i	$0.696460\pi$
$882$		0			0
$883$	2.67490	+	3.35421i	0.0900175	+	0.112878i	0.824800	−	0.565424i	$-0.191287\pi$
$883$	2.67490	+	3.35421i	0.0900175	+	0.112878i	−0.734783	+	0.678302i	$0.762716\pi$
$884$	6.39972	+	28.0390i	0.215246	+	0.943054i
$885$		0			0
$886$	29.7290	+	37.2790i	0.998767	+	1.25241i
$887$	39.5279			1.32722			0.663608	−	0.748081i	$-0.269024\pi$
$887$	39.5279			1.32722			0.663608	+	0.748081i	$0.269024\pi$
$888$		0			0
$889$	−22.2133	−	10.6974i	−0.745012	−	0.358779i
$890$	−5.75930	+	7.22193i	−0.193052	+	0.242080i
$891$		0			0
$892$	95.8193	−	46.1442i	3.20827	−	1.54502i
$893$	−2.20249	−	9.64973i	−0.0737034	−	0.322916i
$894$		0			0
$895$	−16.1120	−	7.75915i	−0.538566	−	0.259360i
$896$	−20.4123	+	9.83002i	−0.681926	+	0.328398i
$897$		0			0
$898$	31.3477			1.04609
$899$	36.5791	−	4.96547i	1.21998	−	0.165608i
$900$		0			0
$901$	−4.26870	+	18.7024i	−0.142211	+	0.623067i
$902$	58.1475	−	28.0023i	1.93610	−	0.932376i
$903$		0			0
$904$	0.749164	−	3.28230i	0.0249168	−	0.109168i
$905$	−4.06164	−	17.7952i	−0.135013	−	0.591532i
$906$		0			0
$907$	16.9123	−	21.2074i	0.561565	−	0.704180i	−0.417281	−	0.908777i	$-0.637017\pi$
$907$	16.9123	−	21.2074i	0.561565	−	0.704180i	0.978846	+	0.204597i	$0.0655884\pi$
$908$	62.4235	−	78.2766i	2.07160	−	2.59770i
$909$		0			0
$910$	−3.81180	−	4.77985i	−0.126360	−	0.158450i
$911$	12.8679			0.426333			0.213166	−	0.977016i	$-0.431622\pi$
$911$	12.8679			0.426333			0.213166	+	0.977016i	$0.431622\pi$
$912$		0			0
$913$	−9.23619	−	40.4664i	−0.305673	−	1.33924i
$914$	−11.3501	−	49.7280i	−0.375428	−	1.64486i
$915$		0			0
$916$	−61.0365			−2.01670
$917$	−7.37821	−	9.25199i	−0.243650	−	0.305528i
$918$		0			0
$919$	−14.5746	+	18.2759i	−0.480771	+	0.602868i	−0.961772	−	0.273853i	$-0.911702\pi$
$919$	−14.5746	+	18.2759i	−0.480771	+	0.602868i	0.481001	+	0.876720i	$0.340273\pi$
$920$	18.8653	−	23.6563i	0.621969	−	0.779925i
$921$		0			0
$922$	−11.1534	−	48.8662i	−0.367317	−	1.60932i
$923$	−2.66030	+	11.6555i	−0.0875648	+	0.383647i
$924$		0			0
$925$	21.2107	−	10.2145i	0.697404	−	0.335852i
$926$	1.25341	−	5.49154i	0.0411895	−	0.180463i
$927$		0			0
$928$	18.4243	+	17.6055i	0.604806	+	0.577928i
$929$	6.68335			0.219274			0.109637	−	0.993972i	$-0.465031\pi$
$929$	6.68335			0.219274			0.109637	+	0.993972i	$0.465031\pi$
$930$		0			0
$931$	−23.5521	+	11.3421i	−0.771888	+	0.371721i
$932$	−26.6875	−	12.8520i	−0.874179	−	0.420983i
$933$		0			0
$934$	−2.61307	−	11.4486i	−0.0855024	−	0.374610i
$935$	−31.4094	+	15.1260i	−1.02720	+	0.494673i
$936$		0			0
$937$	−22.0868	+	27.6960i	−0.721544	+	0.904787i	−0.998424	−	0.0561169i	$-0.982128\pi$
$937$	−22.0868	+	27.6960i	−0.721544	+	0.904787i	0.276880	+	0.960904i	$0.410699\pi$
$938$	−9.47088	−	4.56094i	−0.309235	−	0.148920i
$939$		0			0
$940$	7.30661			0.238315
$941$	−33.6797	−	42.2330i	−1.09793	−	1.37676i	−0.919632	−	0.392781i	$-0.871513\pi$
$941$	−33.6797	−	42.2330i	−1.09793	−	1.37676i	−0.178296	−	0.983977i	$-0.557058\pi$
$942$		0			0
$943$	4.07268	+	17.8436i	0.132625	+	0.581067i
$944$	36.4992	+	45.7686i	1.18795	+	1.48964i
$945$		0			0
$946$	18.2148	+	22.8406i	0.592214	+	0.742613i
$947$	−42.3350	−	20.3874i	−1.37570	−	0.662503i	−0.407623	−	0.913150i	$-0.633642\pi$
$947$	−42.3350	−	20.3874i	−1.37570	−	0.662503i	−0.968078	+	0.250648i	$0.919356\pi$
$948$		0			0
$949$	1.43419	−	1.79842i	0.0465558	−	0.0583791i
$950$	56.8223	−	27.3642i	1.84356	−	0.887811i
$951$		0			0
$952$	12.0153	−	52.6426i	0.389419	−	1.70616i
$953$	−35.5481	−	17.1191i	−1.15152	−	0.554541i	−0.242028	−	0.970269i	$-0.577812\pi$
$953$	−35.5481	−	17.1191i	−1.15152	−	0.554541i	−0.909489	+	0.415728i	$0.863527\pi$
$954$		0			0
$955$	0.715206	−	3.13352i	0.0231435	−	0.101398i
$956$	−53.7856			−1.73955
$957$		0			0
$958$	−24.0903			−0.778321
$959$	5.18875	−	22.7334i	0.167553	−	0.734099i
$960$		0			0
$961$	−14.4058	−	6.93749i	−0.464705	−	0.223790i
$962$	−4.45484	+	19.5179i	−0.143630	+	0.629284i
$963$		0			0
$964$	−10.5830	+	5.09652i	−0.340857	+	0.164148i
$965$	3.31726	−	4.15971i	0.106786	−	0.133906i
$966$		0			0
$967$	17.2328	+	8.29889i	0.554170	+	0.266874i	0.689940	−	0.723866i	$-0.257637\pi$
$967$	17.2328	+	8.29889i	0.554170	+	0.266874i	−0.135771	+	0.990740i	$0.543351\pi$
$968$	−109.571	−	137.397i	−3.52173	−	4.41611i
$969$		0			0
$970$	3.90354	+	4.89489i	0.125335	+	0.157165i
$971$	4.15554	+	18.2066i	0.133358	+	0.584278i	0.996807	+	0.0798432i	$0.0254420\pi$
$971$	4.15554	+	18.2066i	0.133358	+	0.584278i	−0.863450	+	0.504435i	$0.831701\pi$
$972$		0			0
$973$	12.7127	+	15.9412i	0.407550	+	0.511051i
$974$	−19.2538			−0.616932
$975$		0			0
$976$	18.6714	+	8.99167i	0.597657	+	0.287816i
$977$	−33.6793	+	42.2325i	−1.07750	+	1.35114i	−0.145217	+	0.989400i	$0.546388\pi$
$977$	−33.6793	+	42.2325i	−1.07750	+	1.35114i	−0.932280	+	0.361738i	$0.882183\pi$
$978$		0			0
$979$	−18.9748	+	9.13779i	−0.606438	+	0.292045i
$980$	−4.29401	−	18.8133i	−0.137167	−	0.600969i
$981$		0			0
$982$	51.4248	+	24.7649i	1.64103	+	0.790278i
$983$	−48.3831	+	23.3001i	−1.54318	+	0.743157i	−0.995610	−	0.0936012i	$-0.970162\pi$
$983$	−48.3831	+	23.3001i	−1.54318	+	0.743157i	−0.547572	+	0.836758i	$0.684448\pi$
$984$		0			0
$985$	−2.74399			−0.0874309
$986$	68.7369	−	9.33075i	2.18903	−	0.297152i
$987$		0			0
$988$	−8.21773	+	36.0042i	−0.261441	+	1.14545i
$989$	−7.46437	+	3.59465i	−0.237353	+	0.114303i
$990$		0			0
$991$	0.691898	−	3.03140i	0.0219789	−	0.0962957i	−0.962749	−	0.270397i	$-0.912845\pi$
$991$	0.691898	−	3.03140i	0.0219789	−	0.0962957i	0.984728	+	0.174102i	$0.0557021\pi$
$992$	−7.21821	−	31.6250i	−0.229178	−	1.00410i
$993$		0			0
$994$	25.5498	−	32.0385i	0.810391	−	1.01620i
$995$	−17.3573	+	21.7654i	−0.550263	+	0.690008i
$996$		0			0
$997$	−23.5799	−	29.5682i	−0.746782	−	0.936435i	0.252735	−	0.967536i	$-0.418670\pi$
$997$	−23.5799	−	29.5682i	−0.746782	−	0.936435i	−0.999516	+	0.0311010i	$0.990099\pi$
$998$	72.9337			2.30868
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.k.c.199.3		18
3.2	odd	2		87.2.g.a.25.1	yes	18
29.6	even	14		7569.2.a.bm.1.7		9
29.7	even	7	inner	261.2.k.c.181.3		18
29.23	even	7		7569.2.a.bj.1.3		9
87.23	odd	14		2523.2.a.r.1.7		9
87.35	odd	14		2523.2.a.o.1.3		9
87.65	odd	14		87.2.g.a.7.1	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.g.a.7.1	✓	18	87.65	odd	14
87.2.g.a.25.1	yes	18	3.2	odd	2
261.2.k.c.181.3		18	29.7	even	7	inner
261.2.k.c.199.3		18	1.1	even	1	trivial
2523.2.a.o.1.3		9	87.35	odd	14
2523.2.a.r.1.7		9	87.23	odd	14
7569.2.a.bj.1.3		9	29.23	even	7
7569.2.a.bm.1.7		9	29.6	even	14

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:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.k (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.563916 - 2.47068i) q^{2} +(-3.98431 - 1.91874i) q^{4} +(0.242440 - 1.06220i) q^{5} +(-1.55919 + 0.750867i) q^{7} +(-3.82730 + 4.79928i) q^{8} +(-2.48764 - 1.19798i) q^{10} +(-3.92495 - 4.92173i) q^{11} +(-0.797744 - 1.00034i) q^{13} +(0.975897 + 4.27568i) q^{14} +(4.18475 + 5.24750i) q^{16} +5.08291 q^{17} +(5.88048 + 2.83189i) q^{19} +(-3.00404 + 3.76695i) q^{20} +(-14.3734 + 6.92184i) q^{22} +(-1.00672 - 4.41072i) q^{23} +(3.43536 + 1.65438i) q^{25} +(-2.92138 + 1.40686i) q^{26} +7.65302 q^{28} +(1.89363 + 5.04125i) q^{29} +(1.52535 - 6.68301i) q^{31} +(4.26353 - 2.05321i) q^{32} +(2.86633 - 12.5582i) q^{34} +(0.419560 + 1.83821i) q^{35} +(3.84958 - 4.82721i) q^{37} +(10.3128 - 12.9318i) q^{38} +(4.16990 + 5.22889i) q^{40} -4.04550 q^{41} +(-0.407490 - 1.78533i) q^{43} +(6.19468 + 27.1407i) q^{44} -11.4652 q^{46} +(-0.945516 - 1.18564i) q^{47} +(-2.49715 + 3.13133i) q^{49} +(6.02469 - 7.55473i) q^{50} +(1.25907 + 5.51633i) q^{52} +(-0.839814 + 3.67947i) q^{53} +(-6.17942 + 2.97585i) q^{55} +(2.36387 - 10.3568i) q^{56} +(13.5231 - 1.83571i) q^{58} +8.72197 q^{59} +(2.78187 - 1.33968i) q^{61} +(-15.6514 - 7.53731i) q^{62} +(0.318497 + 1.39543i) q^{64} +(-1.25596 + 0.604841i) q^{65} +(-1.49443 + 1.87396i) q^{67} +(-20.2519 - 9.75280i) q^{68} +4.77822 q^{70} +(-5.82579 - 7.30531i) q^{71} +(0.400049 + 1.75273i) q^{73} +(-9.75566 - 12.2332i) q^{74} +(-17.9960 - 22.5663i) q^{76} +(9.81531 + 4.72681i) q^{77} +(-1.78668 + 2.24043i) q^{79} +(6.58844 - 3.17283i) q^{80} +(-2.28132 + 9.99513i) q^{82} +(5.94056 + 2.86082i) q^{83} +(1.23230 - 5.39906i) q^{85} -4.64077 q^{86} +38.6427 q^{88} +(0.744447 - 3.26164i) q^{89} +(1.99496 + 0.960721i) q^{91} +(-4.45196 + 19.5053i) q^{92} +(-3.46252 + 1.66746i) q^{94} +(4.43370 - 5.55968i) q^{95} +(-2.04297 - 0.983843i) q^{97} +(6.32833 + 7.93547i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{2} - 6 q^{4} + q^{5} - 4 q^{7} + 15 q^{8} - 14 q^{10} - 26 q^{11} + 9 q^{13} + 10 q^{14} - 14 q^{16} - 4 q^{17} - 10 q^{19} + q^{20} - 8 q^{22} + 8 q^{23} + 16 q^{25} - 5 q^{26} + 80 q^{28}+ \cdots - 31 q^{98}+O(q^{100}) \) 18 * q + 4 * q^2 - 6 * q^4 + q^5 - 4 * q^7 + 15 * q^8 - 14 * q^10 - 26 * q^11 + 9 * q^13 + 10 * q^14 - 14 * q^16 - 4 * q^17 - 10 * q^19 + q^20 - 8 * q^22 + 8 * q^23 + 16 * q^25 - 5 * q^26 + 80 * q^28 - 8 * q^29 - 12 * q^31 - 9 * q^32 - 22 * q^34 - 9 * q^35 - 16 * q^37 + 32 * q^38 + 33 * q^40 - 24 * q^41 - 31 * q^43 + 52 * q^44 - 44 * q^46 - 5 * q^47 - 47 * q^49 + 7 * q^50 + 80 * q^52 - 5 * q^53 - 17 * q^55 - 45 * q^56 + 54 * q^58 + 32 * q^59 - 28 * q^61 - 69 * q^62 - 75 * q^64 - 22 * q^65 + 6 * q^67 - 38 * q^68 - 12 * q^70 - 46 * q^71 - q^73 + 35 * q^74 - 45 * q^76 + 36 * q^77 - 15 * q^79 + 86 * q^80 + 47 * q^82 + 16 * q^83 + 19 * q^85 - 116 * q^86 + 54 * q^88 + 72 * q^89 - 47 * q^91 + 121 * q^92 - 22 * q^94 + 72 * q^95 + 43 * q^97 - 31 * q^98

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