LMFDB - Embedded newform 87.2.g.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [87,2,Mod(7,87)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(87, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("87.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.g (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:	$0.694698497585$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{7}]$

Embedding invariants

Embedding label			7.1
Root			$-1.38228 + 0.665671i$ of defining polynomial
Character	$\chi$	$=$	87.7
Dual form			87.2.g.a.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.563916 - 2.47068i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-3.98431 + 1.91874i) q^{4} +(-0.242440 - 1.06220i) q^{5} +(-0.563916 + 2.47068i) q^{6} +(-1.55919 - 0.750867i) q^{7} +(3.82730 + 4.79928i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})$	\(q+(-0.563916 - 2.47068i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-3.98431 + 1.91874i) q^{4} +(-0.242440 - 1.06220i) q^{5} +(-0.563916 + 2.47068i) q^{6} +(-1.55919 - 0.750867i) q^{7} +(3.82730 + 4.79928i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-2.48764 + 1.19798i) q^{10} +(3.92495 - 4.92173i) q^{11} +4.42225 q^{12} +(-0.797744 + 1.00034i) q^{13} +(-0.975897 + 4.27568i) q^{14} +(-0.242440 + 1.06220i) q^{15} +(4.18475 - 5.24750i) q^{16} -5.08291 q^{17} +(1.58006 - 1.98133i) q^{18} +(5.88048 - 2.83189i) q^{19} +(3.00404 + 3.76695i) q^{20} +(1.07899 + 1.35302i) q^{21} +(-14.3734 - 6.92184i) q^{22} +(1.00672 - 4.41072i) q^{23} +(-1.36595 - 5.98461i) q^{24} +(3.43536 - 1.65438i) q^{25} +(2.92138 + 1.40686i) q^{26} +(-0.222521 - 0.974928i) q^{27} +7.65302 q^{28} +(-1.89363 + 5.04125i) q^{29} +2.76107 q^{30} +(1.52535 + 6.68301i) q^{31} +(-4.26353 - 2.05321i) q^{32} +(-5.67172 + 2.73136i) q^{33} +(2.86633 + 12.5582i) q^{34} +(-0.419560 + 1.83821i) q^{35} +(-3.98431 - 1.91874i) q^{36} +(3.84958 + 4.82721i) q^{37} +(-10.3128 - 12.9318i) q^{38} +(1.15277 - 0.555147i) q^{39} +(4.16990 - 5.22889i) q^{40} +4.04550 q^{41} +(2.73440 - 3.42883i) q^{42} +(-0.407490 + 1.78533i) q^{43} +(-6.19468 + 27.1407i) q^{44} +(0.679302 - 0.851817i) q^{45} -11.4652 q^{46} +(0.945516 - 1.18564i) q^{47} +(-6.04713 + 2.91215i) q^{48} +(-2.49715 - 3.13133i) q^{49} +(-6.02469 - 7.55473i) q^{50} +(4.57954 + 2.20539i) q^{51} +(1.25907 - 5.51633i) q^{52} +(0.839814 + 3.67947i) q^{53} +(-2.28325 + 1.09956i) q^{54} +(-6.17942 - 2.97585i) q^{55} +(-2.36387 - 10.3568i) q^{56} -6.52684 q^{57} +(13.5231 + 1.83571i) q^{58} -8.72197 q^{59} +(-1.07213 - 4.69731i) q^{60} +(2.78187 + 1.33968i) q^{61} +(15.6514 - 7.53731i) q^{62} +(-0.385088 - 1.68718i) q^{63} +(0.318497 - 1.39543i) q^{64} +(1.25596 + 0.604841i) q^{65} +(9.94667 + 12.4727i) q^{66} +(-1.49443 - 1.87396i) q^{67} +(20.2519 - 9.75280i) q^{68} +(-2.82076 + 3.53712i) q^{69} +4.77822 q^{70} +(5.82579 - 7.30531i) q^{71} +(-1.36595 + 5.98461i) q^{72} +(0.400049 - 1.75273i) q^{73} +(9.75566 - 12.2332i) q^{74} -3.81296 q^{75} +(-17.9960 + 22.5663i) q^{76} +(-9.81531 + 4.72681i) q^{77} +(-2.02166 - 2.53508i) q^{78} +(-1.78668 - 2.24043i) q^{79} +(-6.58844 - 3.17283i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-2.28132 - 9.99513i) q^{82} +(-5.94056 + 2.86082i) q^{83} +(-6.89514 - 3.32052i) q^{84} +(1.23230 + 5.39906i) q^{85} +4.64077 q^{86} +(3.89342 - 3.72039i) q^{87} +38.6427 q^{88} +(-0.744447 - 3.26164i) q^{89} +(-2.48764 - 1.19798i) q^{90} +(1.99496 - 0.960721i) q^{91} +(4.45196 + 19.5053i) q^{92} +(1.52535 - 6.68301i) q^{93} +(-3.46252 - 1.66746i) q^{94} +(-4.43370 - 5.55968i) q^{95} +(2.95045 + 3.69975i) q^{96} +(-2.04297 + 0.983843i) q^{97} +(-6.32833 + 7.93547i) q^{98} +6.29513 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) $ 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{7}\right)$	$1$

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	−0.632333	−	0.774697i	$-0.717903\pi$
$2$	−0.563916	−	2.47068i	−0.398749	−	1.74703i	0.233584	−	0.972337i	$-0.424955\pi$
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$3$	−0.900969	−	0.433884i	−0.520175	−	0.250503i
$4$	−3.98431	+	1.91874i	−1.99216	+	0.959372i
$5$	−0.242440	−	1.06220i	−0.108422	−	0.475030i	−0.999765	−	0.0216985i	$-0.993093\pi$
$5$	−0.242440	−	1.06220i	−0.108422	−	0.475030i	0.891342	−	0.453331i	$-0.149765\pi$
$6$	−0.563916	+	2.47068i	−0.230218	+	1.00865i
$7$	−1.55919	−	0.750867i	−0.589319	−	0.283801i	0.115364	−	0.993323i	$-0.463196\pi$
$7$	−1.55919	−	0.750867i	−0.589319	−	0.283801i	−0.704683	+	0.709522i	$0.748911\pi$
$8$	3.82730	+	4.79928i	1.35315	+	1.69680i
$9$	0.623490	+	0.781831i	0.207830	+	0.260610i
$10$	−2.48764	+	1.19798i	−0.786659	+	0.378835i
$11$	3.92495	−	4.92173i	1.18342	−	1.48396i	0.345279	−	0.938500i	$-0.387784\pi$
$11$	3.92495	−	4.92173i	1.18342	−	1.48396i	0.838138	−	0.545458i	$-0.183644\pi$
$12$	4.42225			1.27659
$13$	−0.797744	+	1.00034i	−0.221255	+	0.277444i	−0.880053	−	0.474875i	$-0.842493\pi$
$13$	−0.797744	+	1.00034i	−0.221255	+	0.277444i	0.658799	+	0.752319i	$0.271065\pi$
$14$	−0.975897	+	4.27568i	−0.260819	+	1.14272i
$15$	−0.242440	+	1.06220i	−0.0625977	+	0.274259i
$16$	4.18475	−	5.24750i	1.04619	−	1.31188i
$17$	−5.08291			−1.23279			−0.616393	−	0.787439i	$-0.711407\pi$
$17$	−5.08291			−1.23279			−0.616393	+	0.787439i	$0.711407\pi$
$18$	1.58006	−	1.98133i	0.372423	−	0.467004i
$19$	5.88048	−	2.83189i	1.34908	−	0.649680i	0.386903	−	0.922121i	$-0.373545\pi$
$19$	5.88048	−	2.83189i	1.34908	−	0.649680i	0.962173	+	0.272440i	$0.0878307\pi$
$20$	3.00404	+	3.76695i	0.671724	+	0.842316i
$21$	1.07899	+	1.35302i	0.235456	+	0.295252i
$22$	−14.3734	−	6.92184i	−3.06441	−	1.47574i
$23$	1.00672	−	4.41072i	0.209915	−	0.919699i	−0.754707	−	0.656062i	$-0.772221\pi$
$23$	1.00672	−	4.41072i	0.209915	−	0.919699i	0.964622	−	0.263637i	$-0.0849220\pi$
$24$	−1.36595	−	5.98461i	−0.278823	−	1.22160i
$25$	3.43536	−	1.65438i	0.687071	−	0.330876i
$26$	2.92138	+	1.40686i	0.572930	+	0.275908i
$27$	−0.222521	−	0.974928i	−0.0428242	−	0.187625i
$28$	7.65302			1.44629
$29$	−1.89363	+	5.04125i	−0.351638	+	0.936136i
$29$	−1.89363	+	5.04125i	−0.351638	+	0.936136i
$30$	2.76107			0.504100
$31$	1.52535	+	6.68301i	0.273961	+	1.20030i	0.905292	+	0.424790i	$0.139652\pi$
$31$	1.52535	+	6.68301i	0.273961	+	1.20030i	−0.631331	+	0.775514i	$0.717491\pi$
$32$	−4.26353	−	2.05321i	−0.753692	−	0.362959i
$33$	−5.67172	+	2.73136i	−0.987319	+	0.475468i
$34$	2.86633	+	12.5582i	0.491572	+	2.15372i
$35$	−0.419560	+	1.83821i	−0.0709185	+	0.310714i
$36$	−3.98431	−	1.91874i	−0.664052	−	0.319791i
$37$	3.84958	+	4.82721i	0.632866	+	0.793589i	0.990091	−	0.140429i	$-0.0448483\pi$
$37$	3.84958	+	4.82721i	0.632866	+	0.793589i	−0.357224	+	0.934019i	$0.616277\pi$
$38$	−10.3128	−	12.9318i	−1.67296	−	2.09782i
$39$	1.15277	−	0.555147i	0.184592	−	0.0888946i
$40$	4.16990	−	5.22889i	0.659319	−	0.826760i
$41$	4.04550			0.631801			0.315901	−	0.948792i	$-0.397693\pi$
$41$	4.04550			0.631801			0.315901	+	0.948792i	$0.397693\pi$
$42$	2.73440	−	3.42883i	0.421928	−	0.529080i
$43$	−0.407490	+	1.78533i	−0.0621417	+	0.272260i	−0.996448	−	0.0842108i	$-0.973163\pi$
$43$	−0.407490	+	1.78533i	−0.0621417	+	0.272260i	0.934306	+	0.356471i	$0.116020\pi$
$44$	−6.19468	+	27.1407i	−0.933884	+	4.09161i
$45$	0.679302	−	0.851817i	0.101264	−	0.126981i
$46$	−11.4652			−1.69045
$47$	0.945516	−	1.18564i	0.137918	−	0.172943i	−0.708076	−	0.706136i	$-0.750437\pi$
$47$	0.945516	−	1.18564i	0.137918	−	0.172943i	0.845994	+	0.533193i	$0.179008\pi$
$48$	−6.04713	+	2.91215i	−0.872828	+	0.420332i
$49$	−2.49715	−	3.13133i	−0.356736	−	0.447333i
$50$	−6.02469	−	7.55473i	−0.852020	−	1.06840i
$51$	4.57954	+	2.20539i	0.641264	+	0.308817i
$52$	1.25907	−	5.51633i	0.174601	−	0.764978i
$53$	0.839814	+	3.67947i	0.115357	+	0.505414i	0.999286	+	0.0377912i	$0.0120322\pi$
$53$	0.839814	+	3.67947i	0.115357	+	0.505414i	−0.883928	+	0.467622i	$0.845111\pi$
$54$	−2.28325	+	1.09956i	−0.310711	+	0.149631i
$55$	−6.17942	−	2.97585i	−0.833233	−	0.401264i
$56$	−2.36387	−	10.3568i	−0.315885	−	1.38398i
$57$	−6.52684			−0.864502
$58$	13.5231	+	1.83571i	1.77568	+	0.241041i
$59$	−8.72197			−1.13550			−0.567752	−	0.823200i	$-0.692187\pi$
$59$	−8.72197			−1.13550			−0.567752	+	0.823200i	$0.692187\pi$
$60$	−1.07213	−	4.69731i	−0.138411	−	0.606420i
$61$	2.78187	+	1.33968i	0.356182	+	0.171528i	0.603414	−	0.797428i	$-0.293807\pi$
$61$	2.78187	+	1.33968i	0.356182	+	0.171528i	−0.247232	+	0.968956i	$0.579521\pi$
$62$	15.6514	−	7.53731i	1.98773	−	0.957240i
$63$	−0.385088	−	1.68718i	−0.0485166	−	0.212565i
$64$	0.318497	−	1.39543i	0.0398121	−	0.174428i
$65$	1.25596	+	0.604841i	0.155783	+	0.0750213i
$66$	9.94667	+	12.4727i	1.22435	+	1.53529i
$67$	−1.49443	−	1.87396i	−0.182574	−	0.228941i	0.682119	−	0.731241i	$-0.261059\pi$
$67$	−1.49443	−	1.87396i	−0.182574	−	0.228941i	−0.864693	+	0.502300i	$0.832487\pi$
$68$	20.2519	−	9.75280i	2.45590	−	1.18270i
$69$	−2.82076	+	3.53712i	−0.339580	+	0.425820i
$70$	4.77822			0.571107
$71$	5.82579	−	7.30531i	0.691394	−	0.866980i	−0.304954	−	0.952367i	$-0.598641\pi$
$71$	5.82579	−	7.30531i	0.691394	−	0.866980i	0.996348	+	0.0853867i	$0.0272126\pi$
$72$	−1.36595	+	5.98461i	−0.160978	+	0.705293i
$73$	0.400049	−	1.75273i	0.0468222	−	0.205142i	−0.946106	−	0.323857i	$-0.895020\pi$
$73$	0.400049	−	1.75273i	0.0468222	−	0.205142i	0.992928	+	0.118715i	$0.0378775\pi$
$74$	9.75566	−	12.2332i	1.13407	−	1.42208i
$75$	−3.81296			−0.440282
$76$	−17.9960	+	22.5663i	−2.06428	+	2.58853i
$77$	−9.81531	+	4.72681i	−1.11856	+	0.538669i
$78$	−2.02166	−	2.53508i	−0.228908	−	0.287041i
$79$	−1.78668	−	2.24043i	−0.201018	−	0.252068i	0.671097	−	0.741369i	$-0.265823\pi$
$79$	−1.78668	−	2.24043i	−0.201018	−	0.252068i	−0.872115	+	0.489301i	$0.837252\pi$
$80$	−6.58844	−	3.17283i	−0.736610	−	0.354733i
$81$	−0.222521	+	0.974928i	−0.0247245	+	0.108325i
$82$	−2.28132	−	9.99513i	−0.251930	−	1.10378i
$83$	−5.94056	+	2.86082i	−0.652061	+	0.314016i	−0.730510	−	0.682902i	$-0.760717\pi$
$83$	−5.94056	+	2.86082i	−0.652061	+	0.314016i	0.0784490	+	0.996918i	$0.475003\pi$
$84$	−6.89514	−	3.32052i	−0.752321	−	0.362299i
$85$	1.23230	+	5.39906i	0.133662	+	0.585610i
$86$	4.64077			0.500427
$87$	3.89342	−	3.72039i	0.417418	−	0.398868i
$88$	38.6427			4.11933
$89$	−0.744447	−	3.26164i	−0.0789113	−	0.345733i	0.920024	−	0.391861i	$-0.128169\pi$
$89$	−0.744447	−	3.26164i	−0.0789113	−	0.345733i	−0.998936	+	0.0461286i	$0.985312\pi$
$90$	−2.48764	−	1.19798i	−0.262220	−	0.126278i
$91$	1.99496	−	0.960721i	0.209128	−	0.100711i
$92$	4.45196	+	19.5053i	0.464149	+	2.03357i
$93$	1.52535	−	6.68301i	0.158172	−	0.692996i
$94$	−3.46252	−	1.66746i	−0.357132	−	0.171986i
$95$	−4.43370	−	5.55968i	−0.454888	−	0.570411i
$96$	2.95045	+	3.69975i	0.301129	+	0.377604i
$97$	−2.04297	+	0.983843i	−0.207432	+	0.0998941i	−0.534715	−	0.845032i	$-0.679581\pi$
$97$	−2.04297	+	0.983843i	−0.207432	+	0.0998941i	0.327283	+	0.944926i	$0.393867\pi$
$98$	−6.32833	+	7.93547i	−0.639257	+	0.801604i
$99$	6.29513			0.632685
$100$	−10.5132	+	13.1831i	−1.05132	+	1.31831i
$101$	−2.79423	+	12.2423i	−0.278036	+	1.21816i	0.622237	+	0.782829i	$0.286224\pi$
$101$	−2.79423	+	12.2423i	−0.278036	+	1.21816i	−0.900273	+	0.435326i	$0.856633\pi$
$102$	2.86633	−	12.5582i	0.283809	−	1.24345i
$103$	1.73041	−	2.16986i	0.170502	−	0.213803i	−0.689237	−	0.724536i	$-0.742054\pi$
$103$	1.73041	−	2.16986i	0.170502	−	0.213803i	0.859740	+	0.510732i	$0.170626\pi$
$104$	−7.85412			−0.770160
$105$	1.17558	−	1.47413i	0.114725	−	0.143860i
$106$	8.61719	−	4.14982i	0.836976	−	0.403066i
$107$	6.20858	+	7.78532i	0.600206	+	0.752635i	0.985410	−	0.170197i	$-0.0544403\pi$
$107$	6.20858	+	7.78532i	0.600206	+	0.752635i	−0.385204	+	0.922832i	$0.625869\pi$
$108$	2.75723	+	3.45746i	0.265314	+	0.332694i
$109$	4.25748	+	2.05029i	0.407793	+	0.196383i	0.626523	−	0.779403i	$-0.284477\pi$
$109$	4.25748	+	2.05029i	0.407793	+	0.196383i	−0.218731	+	0.975785i	$0.570192\pi$
$110$	−3.86770	+	16.9455i	−0.368771	+	1.61569i
$111$	−1.37390	−	6.01944i	−0.130405	−	0.571340i
$112$	−10.4650	+	5.03967i	−0.988849	+	0.476205i
$113$	0.494143	+	0.237967i	0.0464851	+	0.0223860i	0.456982	−	0.889476i	$-0.348930\pi$
$113$	0.494143	+	0.237967i	0.0464851	+	0.0223860i	−0.410497	+	0.911862i	$0.634645\pi$
$114$	3.68059	+	16.1257i	0.344719	+	1.51031i
$115$	−4.92913			−0.459644
$116$	−2.12804	−	23.7193i	−0.197584	−	2.20228i
$117$	−1.27948			−0.118288
$118$	4.91846	+	21.5492i	0.452781	+	1.98376i
$119$	7.92522	+	3.81659i	0.726504	+	0.349866i
$120$	−6.02568	+	2.90181i	−0.550067	+	0.264898i
$121$	−6.37048	−	27.9109i	−0.579135	−	2.53735i
$122$	1.74117	−	7.62857i	0.157638	−	0.690659i
$123$	−3.64487	−	1.75528i	−0.328647	−	0.158268i
$124$	−18.9005	−	23.7004i	−1.69731	−	2.12836i
$125$	−5.98666	−	7.50703i	−0.535463	−	0.671449i
$126$	−3.95133	+	1.90286i	−0.352012	+	0.169520i
$127$	8.88268	−	11.1385i	0.788211	−	0.988385i	−0.211728	−	0.977329i	$-0.567909\pi$
$127$	8.88268	−	11.1385i	0.788211	−	0.988385i	0.999939	−	0.0110562i	$-0.00351937\pi$
$128$	−13.0916			−1.15714
$129$	1.14176	−	1.43172i	0.100527	−	0.126056i
$130$	0.786108	−	3.44416i	0.0689462	−	0.302073i
$131$	−1.52161	+	6.66661i	−0.132944	+	0.582464i	0.863941	+	0.503593i	$0.167989\pi$
$131$	−1.52161	+	6.66661i	−0.132944	+	0.582464i	−0.996885	+	0.0788714i	$0.974868\pi$
$132$	17.3571	−	21.7651i	1.51074	−	1.89441i
$133$	−11.2952			−0.979415
$134$	−3.78722	+	4.74902i	−0.327166	+	0.410253i
$135$	−0.981619	+	0.472723i	−0.0844843	+	0.0406855i
$136$	−19.4538	−	24.3943i	−1.66815	−	2.09179i
$137$	8.40101	+	10.5345i	0.717746	+	0.900026i	0.998208	−	0.0598397i	$-0.0190590\pi$
$137$	8.40101	+	10.5345i	0.717746	+	0.900026i	−0.280462	+	0.959865i	$0.590488\pi$
$138$	10.3298	+	4.97455i	0.879328	+	0.423462i
$139$	−2.62174	+	11.4866i	−0.222373	+	0.974278i	0.733313	+	0.679891i	$0.237973\pi$
$139$	−2.62174	+	11.4866i	−0.222373	+	0.974278i	−0.955686	+	0.294388i	$0.904884\pi$
$140$	−1.85540	−	8.12903i	−0.156810	−	0.687028i
$141$	−1.36631	+	0.657980i	−0.115064	+	0.0554119i
$142$	−21.3343	−	10.2741i	−1.79034	−	0.862180i
$143$	1.79230	+	7.85257i	0.149879	+	0.656665i
$144$	6.71181			0.559317
$145$	5.81390	+	0.789213i	0.482818	+	0.0655405i
$146$	−4.55603			−0.377060
$147$	0.891224	+	3.90471i	0.0735069	+	0.322055i
$148$	−24.6001	−	11.8468i	−2.02212	−	0.973799i
$149$	−0.686505	+	0.330603i	−0.0562406	+	0.0270841i	−0.461793	−	0.886988i	$-0.652794\pi$
$149$	−0.686505	+	0.330603i	−0.0562406	+	0.0270841i	0.405552	+	0.914072i	$0.367079\pi$
$150$	2.15019	+	9.42059i	0.175562	+	0.769188i
$151$	−4.10254	+	17.9744i	−0.333860	+	1.46274i	0.477730	+	0.878507i	$0.341460\pi$
$151$	−4.10254	+	17.9744i	−0.333860	+	1.46274i	−0.811589	+	0.584228i	$0.801397\pi$
$152$	36.0974	+	17.3836i	2.92789	+	1.41000i
$153$	−3.16914	−	3.97398i	−0.256210	−	0.321277i
$154$	17.2134	+	21.5850i	1.38710	+	1.73937i
$155$	6.72887	−	3.24046i	0.540476	−	0.260280i
$156$	−3.52783	+	4.42376i	−0.282452	+	0.354184i
$157$	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
$159$	0.839814	−	3.67947i	0.0666016	−	0.291801i
$160$	−1.14726	+	5.02649i	−0.0906991	+	0.397379i
$161$	−4.88153	+	6.12125i	−0.384719	+	0.482422i
$162$	2.53422			0.199107
$163$	14.8705	−	18.6470i	1.16475	−	1.46055i	0.303155	−	0.952941i	$-0.401960\pi$
$163$	14.8705	−	18.6470i	1.16475	−	1.46055i	0.861590	−	0.507604i	$-0.169469\pi$
$164$	−16.1185	+	7.76228i	−1.25865	+	0.606132i
$165$	4.27629	+	5.36230i	0.332909	+	0.417455i
$166$	10.4181	+	13.0639i	0.808605	+	1.01396i
$167$	12.9629	+	6.24261i	1.00310	+	0.483068i	0.861990	−	0.506926i	$-0.169218\pi$
$167$	12.9629	+	6.24261i	1.00310	+	0.483068i	0.141111	+	0.989994i	$0.454932\pi$
$168$	−2.36387	+	10.3568i	−0.182376	+	0.799043i
$169$	2.52849	+	11.0780i	0.194499	+	0.852156i
$170$	12.6444	−	6.08923i	0.969783	−	0.467023i
$171$	5.88048	+	2.83189i	0.449692	+	0.216560i
$172$	−1.80202	−	7.89518i	−0.137403	−	0.602002i
$173$	−3.94904			−0.300240			−0.150120	−	0.988668i	$-0.547966\pi$
$173$	−3.94904			−0.300240			−0.150120	+	0.988668i	$0.547966\pi$
$174$	−11.3874	−	7.52139i	−0.863280	−	0.570195i
$175$	−6.59859			−0.498807
$176$	−9.40189	−	41.1924i	−0.708694	−	3.10499i
$177$	7.85822	+	3.78432i	0.590660	+	0.284447i
$178$	−7.63865	+	3.67858i	−0.572541	+	0.275721i
$179$	−3.65240	−	16.0022i	−0.272993	−	1.19606i	−0.906460	−	0.422291i	$-0.861226\pi$
$179$	−3.65240	−	16.0022i	−0.272993	−	1.19606i	0.633467	−	0.773770i	$-0.281631\pi$
$180$	−1.07213	+	4.69731i	−0.0799119	+	0.350117i
$181$	15.0941	+	7.26893i	1.12193	+	0.540295i	0.900489	−	0.434878i	$-0.143208\pi$
$181$	15.0941	+	7.26893i	1.12193	+	0.540295i	0.221445	+	0.975173i	$0.428923\pi$
$182$	−3.49862	−	4.38713i	−0.259335	−	0.325196i
$183$	−1.92511	−	2.41402i	−0.142309	−	0.178449i
$184$	25.0213	−	12.0496i	1.84460	−	0.888310i
$185$	4.19417	−	5.25932i	0.308362	−	0.386673i
$186$	−17.3717			−1.27376
$187$	−19.9502	+	25.0167i	−1.45890	+	1.82940i
$188$	−1.49229	+	6.53816i	−0.108837	+	0.476844i
$189$	−0.385088	+	1.68718i	−0.0280111	+	0.122724i
$190$	−11.2359	+	14.0894i	−0.815141	+	1.02215i
$191$	−2.95004			−0.213457			−0.106729	−	0.994288i	$-0.534038\pi$
$191$	−2.95004			−0.213457			−0.106729	+	0.994288i	$0.534038\pi$
$192$	−0.892409	+	1.11905i	−0.0644041	+	0.0807601i
$193$	4.39974	−	2.11880i	0.316700	−	0.152515i	−0.268780	−	0.963202i	$-0.586620\pi$
$193$	4.39974	−	2.11880i	0.316700	−	0.152515i	0.585480	+	0.810687i	$0.300906\pi$
$194$	3.58282	+	4.49272i	0.257232	+	0.322559i
$195$	−0.869155	−	1.08989i	−0.0622415	−	0.0780483i
$196$	15.9577	+	7.68480i	1.13983	+	0.548914i
$197$	0.560429	−	2.45540i	0.0399289	−	0.174940i	−0.951032	−	0.309094i	$-0.899974\pi$
$197$	0.560429	−	2.45540i	0.0399289	−	0.174940i	0.990961	+	0.134153i	$0.0428315\pi$
$198$	−3.54993	−	15.5532i	−0.252282	−	1.10532i
$199$	−23.0213	+	11.0865i	−1.63193	+	0.785898i	−0.631994	+	0.774974i	$0.717763\pi$
$199$	−23.0213	+	11.0865i	−1.63193	+	0.785898i	−0.999940	+	0.0109244i	$0.996523\pi$
$200$	21.0880	+	10.1554i	1.49114	+	0.718097i
$201$	0.533357	+	2.33679i	0.0376201	+	0.164825i
$202$	31.8225			2.23903
$203$	6.73784	−	6.43840i	0.472903	−	0.451887i
$204$	−22.4779			−1.57377
$205$	−0.980791	−	4.29713i	−0.0685014	−	0.300124i
$206$	−6.33684	−	3.05166i	−0.441509	−	0.212619i
$207$	4.07612	−	1.96296i	0.283310	−	0.136435i
$208$	1.91093	+	8.37234i	0.132499	+	0.580517i
$209$	9.14279	−	40.0572i	0.632420	−	2.77081i
$210$	−4.30503	−	2.07319i	−0.297075	−	0.143064i
$211$	−1.15041	−	1.44257i	−0.0791974	−	0.0993104i	0.740654	−	0.671886i	$-0.234516\pi$
$211$	−1.15041	−	1.44257i	−0.0791974	−	0.0993104i	−0.819852	+	0.572576i	$0.805944\pi$
$212$	−10.4060	−	13.0488i	−0.714689	−	0.896192i
$213$	−8.41851	+	4.05414i	−0.576827	+	0.277785i
$214$	15.7339	−	19.7297i	1.07555	−	1.34869i
$215$	1.99517			0.136069
$216$	3.82730	−	4.79928i	0.260415	−	0.326550i
$217$	2.63973	−	11.5654i	0.179197	−	0.785112i
$218$	2.66476	−	11.6751i	0.180480	−	0.790735i
$219$	−1.12091	+	1.40558i	−0.0757443	+	0.0949803i
$220$	30.3306			2.04489
$221$	4.05486	−	5.08464i	0.272760	−	0.342030i
$222$	−14.0973	+	6.78892i	−0.946151	+	0.455642i
$223$	−14.9944	−	18.8024i	−1.00410	−	1.25910i	−0.965652	−	0.259840i	$-0.916330\pi$
$223$	−14.9944	−	18.8024i	−1.00410	−	1.25910i	−0.0384478	−	0.999261i	$-0.512241\pi$
$224$	5.10597	+	6.40268i	0.341157	+	0.427797i
$225$	3.43536	+	1.65438i	0.229024	+	0.110292i
$226$	0.309284	−	1.35506i	0.0205733	−	0.0901374i
$227$	5.03786	+	22.0723i	0.334374	+	1.46499i	0.810565	+	0.585648i	$0.199160\pi$
$227$	5.03786	+	22.0723i	0.334374	+	1.46499i	−0.476191	+	0.879342i	$0.657983\pi$
$228$	26.0050	−	12.5233i	1.72222	−	0.829378i
$229$	12.4353	+	5.98852i	0.821747	+	0.395733i	0.797013	−	0.603962i	$-0.206412\pi$
$229$	12.4353	+	5.98852i	0.821747	+	0.395733i	0.0247336	+	0.999694i	$0.492126\pi$
$230$	2.77962	+	12.1783i	0.183283	+	0.803013i
$231$	10.8942			0.716784
$232$	−31.4418	+	10.2063i	−2.06426	+	0.670076i
$233$	−6.69816			−0.438811			−0.219405	−	0.975634i	$-0.570412\pi$
$233$	−6.69816			−0.438811			−0.219405	+	0.975634i	$0.570412\pi$
$234$	0.721521	+	3.16119i	0.0471673	+	0.206653i
$235$	−1.48861	−	0.716879i	−0.0971065	−	0.0467640i
$236$	34.7511	−	16.7352i	2.26210	−	1.08937i
$237$	0.637660	+	2.79377i	0.0414205	+	0.181475i
$238$	4.96040	−	21.7329i	0.321535	−	1.40874i
$239$	−10.9580	−	5.27711i	−0.708816	−	0.341348i	0.0444976	−	0.999009i	$-0.485831\pi$
$239$	−10.9580	−	5.27711i	−0.708816	−	0.341348i	−0.753313	+	0.657662i	$0.771546\pi$
$240$	4.55934	+	5.71723i	0.294304	+	0.369046i
$241$	1.65610	+	2.07668i	0.106679	+	0.133771i	0.832305	−	0.554319i	$-0.187021\pi$
$241$	1.65610	+	2.07668i	0.106679	+	0.133771i	−0.725626	+	0.688089i	$0.758450\pi$
$242$	−65.3664	+	31.4788i	−4.20191	+	2.02353i
$243$	0.623490	−	0.781831i	0.0399969	−	0.0501545i
$244$	−13.6543			−0.874129
$245$	−2.72069	+	3.41163i	−0.173818	+	0.217961i
$246$	−2.28132	+	9.99513i	−0.145452	+	0.637266i
$247$	−1.85827	+	8.14161i	−0.118239	+	0.518038i
$248$	−26.2356	+	32.8985i	−1.66597	+	2.08905i
$249$	6.59352			0.417847
$250$	−15.1715	+	19.0244i	−0.959529	+	1.20321i
$251$	20.5109	−	9.87755i	1.29464	−	0.623465i	0.345529	−	0.938408i	$-0.387700\pi$
$251$	20.5109	−	9.87755i	1.29464	−	0.623465i	0.949111	+	0.314943i	$0.101985\pi$
$252$	4.77158	+	5.98337i	0.300581	+	0.376917i
$253$	−17.7571	−	22.2667i	−1.11638	−	1.39989i
$254$	−32.5288	−	15.6651i	−2.04104	−	0.982913i
$255$	1.23230	−	5.39906i	0.0771696	−	0.338102i
$256$	6.74555	+	29.5542i	0.421597	+	1.84714i
$257$	−6.94501	+	3.34454i	−0.433218	+	0.208627i	−0.637767	−	0.770230i	$-0.720142\pi$
$257$	−6.94501	+	3.34454i	−0.433218	+	0.208627i	0.204549	+	0.978856i	$0.434427\pi$
$258$	−4.18119	−	2.01355i	−0.260309	−	0.125358i
$259$	−2.37763	−	10.4171i	−0.147739	−	0.647285i
$260$	−6.16469			−0.382318
$261$	−5.12206	+	1.66267i	−0.317048	+	0.102916i
$262$	17.3291			1.07060
$263$	0.171243	+	0.750263i	0.0105593	+	0.0462632i	0.979933	−	0.199327i	$-0.0638755\pi$
$263$	0.171243	+	0.750263i	0.0105593	+	0.0462632i	−0.969374	+	0.245590i	$0.921018\pi$
$264$	−34.8159	−	16.7665i	−2.14277	−	1.03190i
$265$	3.70472	−	1.78410i	0.227579	−	0.109596i
$266$	6.36953	+	27.9067i	0.390541	+	1.71107i
$267$	−0.744447	+	3.26164i	−0.0455594	+	0.199609i
$268$	9.54994	+	4.59901i	0.583356	+	0.280929i
$269$	9.56842	+	11.9984i	0.583397	+	0.731556i	0.982688	−	0.185268i	$-0.0593152\pi$
$269$	9.56842	+	11.9984i	0.583397	+	0.731556i	−0.399291	+	0.916824i	$0.630744\pi$
$270$	1.72150	+	2.15869i	0.104767	+	0.131374i
$271$	−14.1724	+	6.82505i	−0.860910	+	0.414592i	−0.811616	−	0.584192i	$-0.801412\pi$
$271$	−14.1724	+	6.82505i	−0.860910	+	0.414592i	−0.0492945	+	0.998784i	$0.515697\pi$
$272$	−21.2707	+	26.6726i	−1.28972	+	1.61726i
$273$	−2.21424			−0.134012
$274$	21.2900	−	26.6968i	1.28617	−	1.61281i
$275$	5.34118	−	23.4013i	0.322086	−	1.41115i
$276$	4.45196	−	19.5053i	0.267977	−	1.17408i
$277$	−14.1068	+	17.6894i	−0.847595	+	1.06285i	0.149655	+	0.988738i	$0.452184\pi$
$277$	−14.1068	+	17.6894i	−0.847595	+	1.06285i	−0.997250	+	0.0741120i	$0.976388\pi$
$278$	29.8581			1.79077
$279$	−4.27394	+	5.35936i	−0.255874	+	0.320856i
$280$	−10.4279	+	5.02180i	−0.623184	+	0.300110i
$281$	−13.7451	−	17.2358i	−0.819965	−	1.02820i	−0.999015	−	0.0443636i	$-0.985874\pi$
$281$	−13.7451	−	17.2358i	−0.819965	−	1.02820i	0.179051	−	0.983840i	$-0.442697\pi$
$282$	2.39614	+	3.00467i	0.142688	+	0.178925i
$283$	−4.66832	−	2.24815i	−0.277503	−	0.133638i	0.289956	−	0.957040i	$-0.406359\pi$
$283$	−4.66832	−	2.24815i	−0.277503	−	0.133638i	−0.567459	+	0.823402i	$0.692074\pi$
$284$	−9.19474	+	40.2848i	−0.545608	+	2.39046i
$285$	1.58237	+	6.93280i	0.0937314	+	0.410664i
$286$	18.3905	−	8.85638i	1.08745	−	0.523689i
$287$	−6.30771	−	3.03763i	−0.372332	−	0.179306i
$288$	−1.05300	−	4.61351i	−0.0620488	−	0.271854i
$289$	8.83596			0.519762
$290$	−1.32866	−	14.8093i	−0.0780216	−	0.869633i
$291$	2.26753			0.132925
$292$	1.76912	+	7.75102i	0.103530	+	0.453594i
$293$	−3.38919	−	1.63215i	−0.197999	−	0.0953511i	0.332257	−	0.943189i	$-0.392190\pi$
$293$	−3.38919	−	1.63215i	−0.197999	−	0.0953511i	−0.530256	+	0.847838i	$0.677904\pi$
$294$	9.14470	−	4.40385i	0.533330	−	0.256838i
$295$	2.11455	+	9.26447i	0.123114	+	0.539398i
$296$	−8.43369	+	36.9504i	−0.490198	+	2.14770i
$297$	−5.67172	−	2.73136i	−0.329106	−	0.158489i
$298$	1.20395	+	1.50970i	0.0697427	+	0.0874545i
$299$	3.60912	+	4.52569i	0.208721	+	0.261727i
$300$	15.1920	−	7.31609i	0.877111	−	0.422394i
$301$	1.97590	−	2.47770i	0.113889	−	0.142812i
$302$	46.7224			2.68857
$303$	7.82925	−	9.81757i	0.449779	−	0.564005i
$304$	9.74796	−	42.7086i	0.559084	−	2.44951i
$305$	0.748568	−	3.27969i	0.0428629	−	0.187795i
$306$	−8.03129	+	10.0709i	−0.459118	+	0.575716i
$307$	−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
$309$	−2.50051	+	1.20418i	−0.142249	+	0.0685036i
$310$	−11.8006	−	14.7975i	−0.670232	−	0.840444i
$311$	−5.11268	−	6.41109i	−0.289913	−	0.363540i	0.615451	−	0.788175i	$-0.288974\pi$
$311$	−5.11268	−	6.41109i	−0.289913	−	0.363540i	−0.905365	+	0.424635i	$0.860402\pi$
$312$	7.07632	+	3.40777i	0.400618	+	0.192927i
$313$	1.29402	−	5.66946i	0.0731421	−	0.320457i	−0.925100	−	0.379723i	$-0.876019\pi$
$313$	1.29402	−	5.66946i	0.0731421	−	0.320457i	0.998242	+	0.0592668i	$0.0188763\pi$
$314$	−6.18511	−	27.0987i	−0.349046	−	1.52927i
$315$	−1.69876	+	0.818081i	−0.0957144	+	0.0460936i
$316$	11.4175	+	5.49839i	0.642285	+	0.309308i
$317$	2.46889	+	10.8169i	0.138666	+	0.607537i	0.995729	+	0.0923249i	$0.0294299\pi$
$317$	2.46889	+	10.8169i	0.138666	+	0.607537i	−0.857062	+	0.515212i	$0.827713\pi$
$318$	−9.56436			−0.536343
$319$	17.3793	+	29.1066i	0.973052	+	1.62966i
$320$	−1.55944			−0.0871752
$321$	−2.21582	−	9.70813i	−0.123675	−	0.541855i
$322$	17.8764	+	8.60882i	0.996213	+	0.479751i
$323$	−29.8900	+	14.3942i	−1.66312	+	0.800917i
$324$	−0.984044	−	4.31138i	−0.0546691	−	0.239521i
$325$	−1.08559	+	4.75630i	−0.0602179	+	0.263832i
$326$	−54.4564	−	26.2248i	−3.01606	−	1.45246i
$327$	−2.94627	−	3.69450i	−0.162929	−	0.204307i
$328$	15.4833	+	19.4155i	0.854925	+	1.07204i
$329$	−2.36450	+	1.13868i	−0.130359	+	0.0627775i
$330$	10.8371	−	13.5892i	0.596560	−	0.748063i
$331$	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
$333$	−1.37390	+	6.01944i	−0.0752891	+	0.329863i
$334$	8.11349	−	35.5475i	0.443950	−	1.94507i
$335$	−1.62821	+	2.04171i	−0.0889585	+	0.111550i
$336$	11.6153			0.633665
$337$	13.1418	−	16.4793i	0.715880	−	0.897685i	−0.282217	−	0.959351i	$-0.591070\pi$
$337$	13.1418	−	16.4793i	0.715880	−	0.897685i	0.998097	+	0.0616653i	$0.0196411\pi$
$338$	25.9444	−	12.4942i	1.41119	−	0.679593i
$339$	−0.341958	−	0.428801i	−0.0185726	−	0.0232893i
$340$	−15.2693	−	19.1471i	−0.828093	−	1.03840i
$341$	38.8789	+	18.7231i	2.10541	+	1.01391i
$342$	3.68059	−	16.1257i	0.199024	−	0.871980i
$343$	4.23794	+	18.5676i	0.228828	+	1.00256i
$344$	−10.1279	+	4.87734i	−0.546059	+	0.262968i
$345$	4.44099	+	2.13867i	0.239095	+	0.115142i
$346$	2.22693	+	9.75680i	0.119720	+	0.524529i
$347$	−31.0309			−1.66583			−0.832914	−	0.553402i	$-0.813329\pi$
$347$	−31.0309			−1.66583			−0.832914	+	0.553402i	$0.813329\pi$
$348$	−8.37411	+	22.2937i	−0.448900	+	1.19507i
$349$	−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
$351$	1.15277	+	0.555147i	0.0615305	+	0.0296315i
$352$	−26.8395	+	12.9252i	−1.43055	+	0.688915i
$353$	1.34141	+	5.87712i	0.0713962	+	0.312807i	0.997999	−	0.0632352i	$-0.0201418\pi$
$353$	1.34141	+	5.87712i	0.0713962	+	0.312807i	−0.926602	+	0.376042i	$0.877285\pi$
$354$	4.91846	−	21.5492i	0.261413	−	1.14533i
$355$	−9.17209	−	4.41705i	−0.486804	−	0.234432i
$356$	9.22436	+	11.5670i	0.488890	+	0.613048i
$357$	−5.48443	−	6.87725i	−0.290267	−	0.363983i
$358$	−37.4766	+	18.0478i	−1.98070	+	0.953856i
$359$	−3.56260	+	4.46736i	−0.188027	+	0.235778i	−0.866906	−	0.498472i	$-0.833895\pi$
$359$	−3.56260	+	4.46736i	−0.188027	+	0.235778i	0.678879	+	0.734250i	$0.262466\pi$
$360$	6.68800			0.352489
$361$	14.7142	−	18.4510i	0.774430	−	0.971104i
$362$	9.44738	−	41.3917i	0.496543	−	2.17550i
$363$	−6.37048	+	27.9109i	−0.334364	+	1.46494i
$364$	−6.10516	+	7.65562i	−0.319997	+	0.401264i
$365$	−1.95874			−0.102525
$366$	−4.87866	+	6.11764i	−0.255011	+	0.319774i
$367$	−24.6356	+	11.8639i	−1.28597	+	0.619290i	−0.946917	−	0.321478i	$-0.895820\pi$
$367$	−24.6356	+	11.8639i	−1.28597	+	0.619290i	−0.339051	+	0.940768i	$0.610106\pi$
$368$	−18.9324	−	23.7405i	−0.986921	−	1.23756i
$369$	2.52233	+	3.16290i	0.131307	+	0.164654i
$370$	−15.3593	−	7.39663i	−0.798490	−	0.384532i
$371$	1.45336	−	6.36758i	0.0754546	−	0.330588i
$372$	6.74549	+	29.5539i	0.349738	+	1.53230i
$373$	11.3717	−	5.47631i	0.588803	−	0.283552i	−0.115665	−	0.993288i	$-0.536900\pi$
$373$	11.3717	−	5.47631i	0.588803	−	0.283552i	0.704468	+	0.709736i	$0.251186\pi$
$374$	73.0585	+	35.1831i	3.77776	+	1.81927i
$375$	2.13661	+	9.36111i	0.110334	+	0.483406i
$376$	9.30899			0.480074
$377$	−3.53233	−	5.91590i	−0.181924	−	0.304684i
$378$	4.38564			0.225573
$379$	0.734451	+	3.21784i	0.0377262	+	0.165289i	0.990282	−	0.139075i	$-0.0444130\pi$
$379$	0.734451	+	3.21784i	0.0377262	+	0.165289i	−0.952556	+	0.304365i	$0.901556\pi$
$380$	28.3328	+	13.6444i	1.45344	+	0.699941i
$381$	−12.8358	+	6.18142i	−0.657600	+	0.316684i
$382$	1.66357	+	7.28859i	0.0851158	+	0.372917i
$383$	−2.14467	+	9.39639i	−0.109587	+	0.480133i	0.890115	+	0.455736i	$0.150624\pi$
$383$	−2.14467	+	9.39639i	−0.109587	+	0.480133i	−0.999702	+	0.0243974i	$0.992233\pi$
$384$	11.7951	+	5.68022i	0.601916	+	0.289867i
$385$	7.40043	+	9.27984i	0.377161	+	0.472945i
$386$	−7.71596	−	9.67551i	−0.392732	−	0.492470i
$387$	−1.64989	+	0.794547i	−0.0838688	+	0.0403891i
$388$	6.25209	−	7.83988i	0.317402	−	0.398009i
$389$	10.7987			0.547518			0.273759	−	0.961798i	$-0.411733\pi$
$389$	10.7987			0.547518			0.273759	+	0.961798i	$0.411733\pi$
$390$	−2.20263	+	2.76201i	−0.111534	+	0.139860i
$391$	−5.11706	+	22.4193i	−0.258781	+	1.13379i
$392$	5.47079	−	23.9691i	0.276316	−	1.21062i
$393$	4.26346	−	5.34620i	0.215063	−	0.269680i
$394$	−6.38254			−0.321548
$395$	−1.94662	+	2.44098i	−0.0979450	+	0.122819i
$396$	−25.0818	+	12.0787i	−1.26041	+	0.606980i
$397$	18.5378	+	23.2457i	0.930385	+	1.16667i	0.985753	+	0.168200i	$0.0537955\pi$
$397$	18.5378	+	23.2457i	0.930385	+	1.16667i	−0.0553677	+	0.998466i	$0.517633\pi$
$398$	40.3731	+	50.6263i	2.02372	+	2.53767i
$399$	10.1766	+	4.90079i	0.509467	+	0.245346i
$400$	5.69472	−	24.9502i	0.284736	−	1.24751i
$401$	−2.54450	−	11.1482i	−0.127066	−	0.556713i	−0.997879	−	0.0650982i	$-0.979264\pi$
$401$	−2.54450	−	11.1482i	−0.127066	−	0.556713i	0.870813	−	0.491615i	$-0.163593\pi$
$402$	5.47269	−	2.63551i	0.272953	−	0.131447i
$403$	−7.90212	−	3.80546i	−0.393633	−	0.189564i
$404$	−12.3568	−	54.1386i	−0.614773	−	2.69350i
$405$	1.08952			0.0541384
$406$	−19.7068	−	13.0163i	−0.978032	−	0.645988i
$407$	38.8677			1.92660
$408$	6.94298	+	30.4192i	0.343729	+	1.50597i
$409$	−26.9918	−	12.9985i	−1.33466	−	0.642737i	−0.375820	−	0.926693i	$-0.622639\pi$
$409$	−26.9918	−	12.9985i	−1.33466	−	0.642737i	−0.958837	+	0.283956i	$0.908353\pi$
$410$	−10.0637	+	4.84644i	−0.497012	+	0.239349i
$411$	−2.99828	−	13.1363i	−0.147894	−	0.647968i
$412$	−2.73108	+	11.9656i	−0.134550	+	0.589504i
$413$	13.5992	+	6.54904i	0.669174	+	0.322257i
$414$	−7.14842	−	8.96384i	−0.351326	−	0.440549i
$415$	4.47899	+	5.61647i	0.219865	+	0.275702i
$416$	5.45511	−	2.62704i	0.267459	−	0.128801i
$417$	7.34594	−	9.21152i	0.359732	−	0.451090i
$418$	−104.124			−5.09288
$419$	−12.7136	+	15.9424i	−0.621101	+	0.778836i	−0.988499	−	0.151228i	$-0.951677\pi$
$419$	−12.7136	+	15.9424i	−0.621101	+	0.778836i	0.367398	+	0.930064i	$0.380249\pi$
$420$	−1.85540	+	8.12903i	−0.0905342	+	0.396656i
$421$	5.11531	−	22.4116i	0.249305	−	1.09228i	−0.682948	−	0.730467i	$-0.739302\pi$
$421$	5.11531	−	22.4116i	0.249305	−	1.09228i	0.932253	−	0.361808i	$-0.117840\pi$
$422$	−2.91539	+	3.65578i	−0.141919	+	0.177960i
$423$	1.51649			0.0737342
$424$	−14.4446	+	18.1129i	−0.701491	+	0.879641i
$425$	−17.4616	+	8.40906i	−0.847012	+	0.407899i
$426$	14.7638	+	18.5132i	0.715309	+	0.896969i
$427$	−3.33155	−	4.17763i	−0.161225	−	0.202170i
$428$	−39.6750	−	19.1065i	−1.91776	−	0.923545i
$429$	1.79230	−	7.85257i	0.0865329	−	0.379126i
$430$	−1.12511	−	4.92942i	−0.0542575	−	0.237718i
$431$	3.64629	−	1.75596i	0.175636	−	0.0845817i	−0.344000	−	0.938970i	$-0.611782\pi$
$431$	3.64629	−	1.75596i	0.175636	−	0.0845817i	0.519636	+	0.854388i	$0.326068\pi$
$432$	−6.04713	−	2.91215i	−0.290943	−	0.140111i
$433$	−0.585130	−	2.56362i	−0.0281196	−	0.123200i	0.958920	−	0.283676i	$-0.0915541\pi$
$433$	−0.585130	−	2.56362i	−0.0281196	−	0.123200i	−0.987040	+	0.160476i	$0.948697\pi$
$434$	−30.0630			−1.44307
$435$	−4.89571	−	3.23361i	−0.234731	−	0.155040i
$436$	−20.8971			−1.00079
$437$	−6.57069	−	28.7881i	−0.314319	−	1.37712i
$438$	4.10484	+	1.97679i	0.196137	+	0.0944545i
$439$	23.4338	−	11.2851i	1.11843	−	0.538609i	0.219025	−	0.975719i	$-0.429712\pi$
$439$	23.4338	−	11.2851i	1.11843	−	0.538609i	0.899408	+	0.437110i	$0.143998\pi$
$440$	−9.36854	−	41.0463i	−0.446628	−	1.95680i
$441$	0.891224	−	3.90471i	0.0424392	−	0.185938i
$442$	−14.8491	−	7.15095i	−0.706300	−	0.340136i
$443$	11.7311	+	14.7103i	0.557360	+	0.698907i	0.978067	−	0.208290i	$-0.0667896\pi$
$443$	11.7311	+	14.7103i	0.557360	+	0.698907i	−0.420708	+	0.907196i	$0.638218\pi$
$444$	17.0238	+	21.3472i	0.807913	+	1.01309i
$445$	−3.28402	+	1.58150i	−0.155678	+	0.0749704i
$446$	−37.9991	+	47.6493i	−1.79931	+	2.25626i
$447$	0.761963			0.0360396
$448$	−1.54438	+	1.93659i	−0.0729650	+	0.0914952i
$449$	−2.75254	+	12.0597i	−0.129900	+	0.569130i	0.867523	+	0.497396i	$0.165710\pi$
$449$	−2.75254	+	12.0597i	−0.129900	+	0.569130i	−0.997424	+	0.0717342i	$0.977147\pi$
$450$	2.15019	−	9.42059i	0.101361	−	0.444091i
$451$	15.8784	−	19.9109i	0.747684	−	0.937567i
$452$	−2.42542			−0.114082
$453$	11.4951	−	14.4143i	0.540085	−	0.677245i
$454$	51.6926	−	24.8939i	2.42606	−	1.16833i
$455$	−1.50413	−	1.88612i	−0.0705149	−	0.0884229i
$456$	−24.9802	−	31.3242i	−1.16980	−	1.46689i
$457$	18.1340	+	8.73289i	0.848275	+	0.408508i	0.806937	−	0.590638i	$-0.201124\pi$
$457$	18.1340	+	8.73289i	0.848275	+	0.408508i	0.0413378	+	0.999145i	$0.486838\pi$
$458$	7.78324	−	34.1006i	0.363687	−	1.59342i
$459$	1.13105	+	4.95547i	0.0527931	+	0.231301i
$460$	19.6392	−	9.45774i	0.915682	−	0.440969i
$461$	−17.8198	−	8.58155i	−0.829950	−	0.399683i	−0.0298534	−	0.999554i	$-0.509504\pi$
$461$	−17.8198	−	8.58155i	−0.829950	−	0.399683i	−0.800096	+	0.599872i	$0.795218\pi$
$462$	−6.14340	−	26.9160i	−0.285817	−	1.25225i
$463$	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
$465$	−7.46849			−0.346343
$466$	3.77720	+	16.5490i	0.174975	+	0.766617i
$467$	−4.17491	−	2.01053i	−0.193192	−	0.0930362i	0.334787	−	0.942294i	$-0.391336\pi$
$467$	−4.17491	−	2.01053i	−0.193192	−	0.0930362i	−0.527979	+	0.849258i	$0.677050\pi$
$468$	5.09786	−	2.45500i	0.235649	−	0.113482i
$469$	0.923013	+	4.04398i	0.0426208	+	0.186734i
$470$	−0.931724	+	4.08215i	−0.0429772	+	0.188295i
$471$	−9.88195	−	4.75890i	−0.455336	−	0.219278i
$472$	−33.3816	−	41.8592i	−1.53651	−	1.92673i
$473$	7.18754	+	9.01289i	0.330484	+	0.414413i
$474$	6.54292	−	3.15091i	0.300526	−	0.144726i
$475$	15.5165	−	19.4571i	0.711947	−	0.892753i
$476$	−38.8996			−1.78296
$477$	−2.35311	+	2.95070i	−0.107741	+	0.135103i
$478$	−6.85863	+	30.0496i	−0.313706	+	1.37444i
$479$	2.11528	−	9.26766i	0.0966498	−	0.423450i	−0.903335	−	0.428935i	$-0.858889\pi$
$479$	2.11528	−	9.26766i	0.0966498	−	0.423450i	0.999985	+	0.00548500i	$0.00174594\pi$
$480$	3.21456	−	4.03093i	0.146724	−	0.183986i
$481$	−7.89983			−0.360201
$482$	4.19691	−	5.26276i	0.191164	−	0.239712i
$483$	7.05402	−	3.39704i	0.320969	−	0.154570i
$484$	78.9358	+	98.9824i	3.58799	+	4.49920i
$485$	1.54033	+	1.93152i	0.0699430	+	0.0877057i
$486$	−2.28325	−	1.09956i	−0.103570	−	0.0498768i
$487$	−1.69061	+	7.40706i	−0.0766090	+	0.335646i	−0.998679	−	0.0513764i	$-0.983639\pi$
$487$	−1.69061	+	7.40706i	−0.0766090	+	0.335646i	0.922070	+	0.387022i	$0.126496\pi$
$488$	4.21756	+	18.4783i	0.190920	+	0.836475i
$489$	−21.4885	+	10.3483i	−0.971742	+	0.467966i
$490$	9.96328	+	4.79807i	0.450095	+	0.216754i
$491$	5.01175	+	21.9579i	0.226177	+	0.990947i	0.952726	+	0.303832i	$0.0982662\pi$
$491$	5.01175	+	21.9579i	0.226177	+	0.990947i	−0.726548	+	0.687115i	$0.758877\pi$
$492$	17.8902			0.806554
$493$	9.62515	−	25.6242i	0.433495	−	1.15406i
$494$	21.1632			0.952177
$495$	−1.52619	−	6.68668i	−0.0685972	−	0.300544i
$496$	41.4523	+	19.9624i	1.86126	+	0.896338i
$497$	−14.5688	+	7.01598i	−0.653501	+	0.314710i
$498$	−3.71819	−	16.2905i	−0.166616	−	0.729993i
$499$	6.40406	−	28.0580i	0.286685	−	1.25605i	−0.602358	−	0.798226i	$-0.705772\pi$
$499$	6.40406	−	28.0580i	0.286685	−	1.25605i	0.889043	−	0.457823i	$-0.151371\pi$
$500$	38.2568	+	18.4235i	1.71089	+	0.823923i
$501$	−8.97062	−	11.2488i	−0.400778	−	0.502559i
$502$	−35.9707	−	45.1058i	−1.60545	−	2.01317i
$503$	4.50964	−	2.17173i	0.201075	−	0.0968325i	−0.330637	−	0.943758i	$-0.607263\pi$
$503$	4.50964	−	2.17173i	0.201075	−	0.0968325i	0.531711	+	0.846926i	$0.321549\pi$
$504$	6.62341	−	8.30550i	0.295030	−	0.369956i
$505$	13.6812			0.608805
$506$	−45.0003	+	56.4285i	−2.00051	+	2.50855i
$507$	2.52849	−	11.0780i	0.112294	−	0.491993i
$508$	−14.0194	+	61.4230i	−0.622010	+	2.72520i
$509$	3.10581	−	3.89456i	0.137663	−	0.172623i	−0.708221	−	0.705990i	$-0.750502\pi$
$509$	3.10581	−	3.89456i	0.137663	−	0.172623i	0.845884	+	0.533367i	$0.179074\pi$
$510$	−14.0342			−0.621447
$511$	−1.93982	+	2.43246i	−0.0858126	+	0.107606i
$512$	45.6248	−	21.9717i	2.01635	−	0.971023i
$513$	−4.06942	−	5.10289i	−0.179669	−	0.225298i
$514$	12.1797	+	15.2728i	0.537223	+	0.673657i
$515$	−2.72435	−	1.31198i	−0.120049	−	0.0578126i
$516$	−1.80202	+	7.89518i	−0.0793297	+	0.347566i
$517$	−2.12430	−	9.30715i	−0.0934264	−	0.409328i
$518$	−24.3964	+	11.7487i	−1.07192	+	0.516209i
$519$	3.55796	+	1.71342i	0.156177	+	0.0752109i
$520$	1.90415	+	8.34263i	0.0835026	+	0.365849i
$521$	4.54404			0.199078			0.0995389	−	0.995034i	$-0.468263\pi$
$521$	4.54404			0.199078			0.0995389	+	0.995034i	$0.468263\pi$
$522$	6.99633	+	11.7174i	0.306221	+	0.512855i
$523$	−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
$525$	5.94513	+	2.86302i	0.259467	+	0.124953i
$526$	1.75709	−	0.846171i	0.0766129	−	0.0368948i
$527$	−7.75323	−	33.9691i	−0.337736	−	1.47972i
$528$	−9.40189	+	41.1924i	−0.409165	+	1.79267i
$529$	2.28130	+	1.09862i	0.0991869	+	0.0477659i
$530$	−6.49709	−	8.14709i	−0.282215	−	0.353887i
$531$	−5.43806	−	6.81911i	−0.235992	−	0.295924i
$532$	45.0035	−	21.6725i	1.95115	−	0.939623i
$533$	−3.22728	+	4.04688i	−0.139789	+	0.175290i
$534$	8.47826			0.366890
$535$	6.76434	−	8.48222i	0.292448	−	0.366718i
$536$	3.27402	−	14.3444i	0.141416	−	0.619585i
$537$	−3.65240	+	16.0022i	−0.157613	+	0.690546i
$538$	24.2484	−	30.4066i	1.04542	−	1.31092i
$539$	−25.2128			−1.08599
$540$	3.00404	−	3.76695i	0.129273	−	0.162104i
$541$	−19.3355	+	9.31147i	−0.831297	+	0.400331i	−0.800601	−	0.599197i	$-0.795486\pi$
$541$	−19.3355	+	9.31147i	−0.831297	+	0.400331i	−0.0306954	+	0.999529i	$0.509772\pi$
$542$	24.8545	+	31.1666i	1.06759	+	1.33872i
$543$	−10.4454	−	13.0982i	−0.448256	−	0.562095i
$544$	21.6711	+	10.4363i	0.929141	+	0.447451i
$545$	1.14564	−	5.01936i	0.0490737	−	0.215006i
$546$	1.24864	+	5.47067i	0.0534370	+	0.234123i
$547$	13.0776	−	6.29785i	0.559158	−	0.269276i	−0.132886	−	0.991131i	$-0.542424\pi$
$547$	13.0776	−	6.29785i	0.559158	−	0.269276i	0.692045	+	0.721855i	$0.256710\pi$
$548$	−53.6853	−	25.8535i	−2.29332	−	1.10441i
$549$	0.687065	+	3.01023i	0.0293232	+	0.128473i
$550$	−60.8290			−2.59376
$551$	3.14080	+	35.0075i	0.133803	+	1.49137i
$552$	−27.7716			−1.18204
$553$	1.10352	+	4.83482i	0.0469263	+	0.205597i
$554$	51.6597	+	24.8780i	2.19481	+	1.05697i
$555$	−6.06075	+	2.91870i	−0.257265	+	0.123892i
$556$	−11.5940	−	50.7965i	−0.491694	−	2.15425i
$557$	−5.37517	+	23.5502i	−0.227753	+	0.997852i	0.723714	+	0.690100i	$0.242434\pi$
$557$	−5.37517	+	23.5502i	−0.227753	+	0.997852i	−0.951467	+	0.307752i	$0.900423\pi$
$558$	15.6514	+	7.53731i	0.662576	+	0.319080i
$559$	−1.46086	−	1.83187i	−0.0617880	−	0.0774797i
$560$	7.89027	+	9.89408i	0.333425	+	0.418101i
$561$	28.8288	−	13.8832i	1.21715	−	0.586150i
$562$	−34.8331	+	43.6793i	−1.46935	+	1.84250i
$563$	−7.54185			−0.317851			−0.158926	−	0.987291i	$-0.550803\pi$
$563$	−7.54185			−0.317851			−0.158926	+	0.987291i	$0.550803\pi$
$564$	4.18131	−	5.24319i	0.176065	−	0.220778i
$565$	0.132968	−	0.582571i	0.00559400	−	0.0245089i
$566$	−2.92190	+	12.8017i	−0.122817	+	0.538095i
$567$	1.07899	−	1.35302i	0.0453135	−	0.0568213i
$568$	57.3572			2.40666
$569$	−12.5014	+	15.6763i	−0.524086	+	0.657183i	−0.971471	−	0.237159i	$-0.923784\pi$
$569$	−12.5014	+	15.6763i	−0.524086	+	0.657183i	0.447385	+	0.894341i	$0.352355\pi$
$570$	16.2364	−	7.81904i	0.680068	−	0.327504i
$571$	−2.84040	−	3.56175i	−0.118867	−	0.149054i	0.718838	−	0.695178i	$-0.244674\pi$
$571$	−2.84040	−	3.56175i	−0.118867	−	0.149054i	−0.837705	+	0.546123i	$0.816103\pi$
$572$	−22.2081	−	27.8481i	−0.928569	−	1.16439i
$573$	2.65789	+	1.27997i	0.111035	+	0.0534716i
$574$	−3.94799	+	17.2973i	−0.164786	+	0.721975i
$575$	−3.83857	−	16.8179i	−0.160080	−	0.701355i
$576$	1.28957	−	0.621023i	0.0537320	−	0.0258760i
$577$	−17.6920	−	8.52003i	−0.736528	−	0.354693i	0.0277198	−	0.999616i	$-0.491175\pi$
$577$	−17.6920	−	8.52003i	−0.736528	−	0.354693i	−0.764248	+	0.644922i	$0.776890\pi$
$578$	−4.98274	−	21.8308i	−0.207255	−	0.908042i
$579$	−4.88334			−0.202945
$580$	−24.6787	+	8.01091i	−1.02473	+	0.332635i
$581$	11.4106			0.473390
$582$	−1.27870	−	5.60233i	−0.0530036	−	0.232224i
$583$	21.4056	+	10.3084i	0.886529	+	0.426930i
$584$	9.94295	−	4.78827i	0.411442	−	0.198140i
$585$	0.310198	+	1.35906i	0.0128251	+	0.0561904i
$586$	−2.12129	+	9.29399i	−0.0876298	+	0.383931i
$587$	36.2181	+	17.4417i	1.49488	+	0.719897i	0.989705	−	0.143120i	$-0.0457135\pi$
$587$	36.2181	+	17.4417i	1.49488	+	0.719897i	0.505176	+	0.863017i	$0.331428\pi$
$588$	−11.0430	−	13.8475i	−0.455407	−	0.571063i
$589$	27.8954	+	34.9797i	1.14941	+	1.44131i
$590$	21.6971	−	10.4488i	0.893255	−	0.430169i
$591$	−1.57029	+	1.96908i	−0.0645930	+	0.0809971i
$592$	41.4403			1.70319
$593$	28.6572	−	35.9350i	1.17681	−	1.47567i	0.329834	−	0.944039i	$-0.393007\pi$
$593$	28.6572	−	35.9350i	1.17681	−	1.47567i	0.846975	−	0.531633i	$-0.178421\pi$
$594$	−3.54993	+	15.5532i	−0.145655	+	0.638157i
$595$	2.13258	−	9.34346i	0.0874274	−	0.383044i
$596$	2.10091	−	2.63445i	0.0860564	−	0.107911i
$597$	25.5517			1.04576
$598$	9.14628	−	11.4691i	0.374019	−	0.469005i
$599$	9.05961	−	4.36288i	0.370166	−	0.178262i	−0.239547	−	0.970885i	$-0.576999\pi$
$599$	9.05961	−	4.36288i	0.370166	−	0.178262i	0.609713	+	0.792622i	$0.291285\pi$
$600$	−14.5933	−	18.2995i	−0.595770	−	0.747072i
$601$	−0.763319	−	0.957172i	−0.0311364	−	0.0390439i	0.766019	−	0.642817i	$-0.222235\pi$
$601$	−0.763319	−	0.957172i	−0.0311364	−	0.0390439i	−0.797156	+	0.603773i	$0.793663\pi$
$602$	−7.23584	−	3.48460i	−0.294911	−	0.142022i
$603$	0.533357	−	2.33679i	0.0217200	−	0.0951615i
$604$	−18.1425	−	79.4873i	−0.738206	−	3.23429i
$605$	−28.1025	+	13.5334i	−1.14253	+	0.550212i
$606$	−28.6711	−	13.8073i	−1.16468	−	0.560882i
$607$	−6.84845	−	30.0050i	−0.277970	−	1.21787i	−0.900355	−	0.435155i	$-0.856693\pi$
$607$	−6.84845	−	30.0050i	−0.277970	−	1.21787i	0.622385	−	0.782711i	$-0.286164\pi$
$608$	−30.8860			−1.25259
$609$	−8.86410	+	2.87736i	−0.359191	+	0.116597i
$610$	−8.52519			−0.345175
$611$	0.431762	+	1.89167i	0.0174672	+	0.0765289i
$612$	20.2519	+	9.75280i	0.818634	+	0.394233i
$613$	7.12528	−	3.43135i	0.287787	−	0.138591i	−0.284421	−	0.958700i	$-0.591801\pi$
$613$	7.12528	−	3.43135i	0.287787	−	0.138591i	0.572208	+	0.820109i	$0.306087\pi$
$614$	2.34029	+	10.2535i	0.0944464	+	0.413797i
$615$	−0.980791	+	4.29713i	−0.0395493	+	0.173277i
$616$	−60.2514	−	29.0155i	−2.42760	−	1.16907i
$617$	−7.98066	−	10.0074i	−0.321289	−	0.402884i	0.594790	−	0.803881i	$-0.297235\pi$
$617$	−7.98066	−	10.0074i	−0.321289	−	0.402884i	−0.916079	+	0.400997i	$0.868664\pi$
$618$	4.38523	+	5.49891i	0.176400	+	0.221198i
$619$	38.2518	−	18.4211i	1.53747	−	0.740406i	0.542449	−	0.840089i	$-0.317497\pi$
$619$	38.2518	−	18.4211i	1.53747	−	0.740406i	0.995019	+	0.0996833i	$0.0317830\pi$
$620$	−20.5923	+	25.8220i	−0.827008	+	1.03704i
$621$	−4.52415			−0.181548
$622$	−12.9566	+	16.2471i	−0.519513	+	0.651449i
$623$	−1.28832	+	5.64450i	−0.0516154	+	0.226142i
$624$	1.91093	−	8.37234i	0.0764985	−	0.335162i
$625$	5.36415	−	6.72643i	0.214566	−	0.269057i
$626$	−14.7371			−0.589014
$627$	−25.6175	+	32.1234i	−1.02307	+	1.28288i
$628$	−43.7005	+	21.0450i	−1.74384	+	0.839789i
$629$	−19.5670	−	24.5363i	−0.780189	−	0.978326i
$630$	2.97917	+	3.73577i	0.118693	+	0.148836i
$631$	−39.7014	−	19.1192i	−1.58049	−	0.761123i	−0.581850	−	0.813296i	$-0.697671\pi$
$631$	−39.7014	−	19.1192i	−1.58049	−	0.761123i	−0.998638	+	0.0521737i	$0.983385\pi$
$632$	3.91428	−	17.1496i	0.155702	−	0.682174i
$633$	0.410576	+	1.79885i	0.0163189	+	0.0714979i
$634$	25.3328	−	12.1996i	1.00610	−	0.484510i
$635$	−13.9848	−	6.73475i	−0.554972	−	0.267260i
$636$	3.71387	+	16.2715i	0.147265	+	0.645208i
$637$	5.12449			0.203040
$638$	62.1126	−	59.3522i	2.45906	−	2.34978i
$639$	9.34384			0.369636
$640$	3.17392	+	13.9058i	0.125460	+	0.549677i
$641$	36.3896	+	17.5243i	1.43730	+	0.692168i	0.980339	−	0.197318i	$-0.0632233\pi$
$641$	36.3896	+	17.5243i	1.43730	+	0.692168i	0.456962	+	0.889486i	$0.348938\pi$
$642$	−22.7361	+	10.9491i	−0.897324	+	0.432128i
$643$	−1.71136	−	7.49794i	−0.0674893	−	0.295690i	0.929908	−	0.367792i	$-0.119886\pi$
$643$	−1.71136	−	7.49794i	−0.0674893	−	0.295690i	−0.997397	+	0.0721025i	$0.977029\pi$
$644$	7.70444	−	33.7554i	0.303597	−	1.33015i
$645$	−1.79758	−	0.865671i	−0.0707798	−	0.0340858i
$646$	52.4190	+	65.7313i	2.06240	+	2.58616i
$647$	−15.3144	−	19.2037i	−0.602072	−	0.754975i	0.383627	−	0.923488i	$-0.374675\pi$
$647$	−15.3144	−	19.2037i	−0.602072	−	0.754975i	−0.985699	+	0.168513i	$0.946103\pi$
$648$	−5.53061	+	2.66340i	−0.217263	+	0.104628i
$649$	−34.2333	+	42.9272i	−1.34377	+	1.68504i
$650$	12.3635			0.484935
$651$	−7.39636	+	9.27475i	−0.289886	+	0.363506i
$652$	−23.4698	+	102.828i	−0.919150	+	4.02706i
$653$	−5.93369	+	25.9972i	−0.232203	+	1.01735i	0.715604	+	0.698506i	$0.246152\pi$
$653$	−5.93369	+	25.9972i	−0.232203	+	1.01735i	−0.947807	+	0.318843i	$0.896706\pi$
$654$	−7.46648	+	9.36267i	−0.291963	+	0.366109i
$655$	7.45016			0.291102
$656$	16.9294	−	21.2288i	0.660982	−	0.828845i
$657$	1.61977	−	0.780038i	0.0631931	−	0.0304322i
$658$	4.14669	+	5.19979i	0.161655	+	0.202709i
$659$	−7.62974	−	9.56739i	−0.297212	−	0.372693i	0.610693	−	0.791867i	$-0.290891\pi$
$659$	−7.62974	−	9.56739i	−0.297212	−	0.372693i	−0.907906	+	0.419175i	$0.862319\pi$
$660$	−27.3270	−	13.1600i	−1.06370	−	0.512251i
$661$	−8.99484	+	39.4090i	−0.349859	+	1.53283i	0.427641	+	0.903949i	$0.359345\pi$
$661$	−8.99484	+	39.4090i	−0.349859	+	1.53283i	−0.777500	+	0.628883i	$0.783512\pi$
$662$	−9.46959	−	41.4890i	−0.368046	−	1.61252i
$663$	−5.85945	+	2.82176i	−0.227562	+	0.109588i
$664$	−36.4662	−	17.5612i	−1.41516	−	0.681506i
$665$	2.73840	+	11.9977i	0.106191	+	0.465251i
$666$	15.6469			0.606303
$667$	20.3292	+	13.4274i	0.787149	+	0.519911i
$668$	−63.6263			−2.46178
$669$	5.35144	+	23.4462i	0.206899	+	0.906482i
$670$	5.96258	+	2.87143i	0.230355	+	0.110933i
$671$	17.5122	−	8.43345i	0.676053	−	0.325570i
$672$	−1.82230	−	7.98401i	−0.0702967	−	0.307990i
$673$	−10.7198	+	46.9663i	−0.413216	+	1.81042i	0.155443	+	0.987845i	$0.450320\pi$
$673$	−10.7198	+	46.9663i	−0.413216	+	1.81042i	−0.568659	+	0.822573i	$0.692538\pi$
$674$	−48.1260	−	23.1762i	−1.85374	−	0.892715i
$675$	−2.37734	−	2.98109i	−0.0915038	−	0.114742i
$676$	−31.3302	−	39.2868i	−1.20501	−	1.51103i
$677$	−2.03915	+	0.982003i	−0.0783709	+	0.0377415i	−0.472659	−	0.881246i	$-0.656706\pi$
$677$	−2.03915	+	0.982003i	−0.0783709	+	0.0377415i	0.394288	+	0.918987i	$0.370991\pi$
$678$	−0.866594	+	1.08668i	−0.0332814	+	0.0417335i
$679$	3.92412			0.150594
$680$	−21.1952	+	26.5780i	−0.812800	+	1.01922i
$681$	5.03786	−	22.0723i	0.193051	−	0.845812i
$682$	24.3343	−	106.616i	0.931808	−	4.08252i
$683$	−17.4383	+	21.8669i	−0.667258	+	0.836715i	−0.994112	−	0.108360i	$-0.965440\pi$
$683$	−17.4383	+	21.8669i	−0.667258	+	0.836715i	0.326854	+	0.945075i	$0.394011\pi$
$684$	−28.8633			−1.10362
$685$	9.15302	−	11.4775i	0.349719	−	0.438534i
$686$	43.4848	−	20.9412i	1.66026	−	0.799539i
$687$	−8.60549	−	10.7909i	−0.328320	−	0.411700i
$688$	7.66329	+	9.60946i	0.292160	+	0.366357i
$689$	−4.35068	−	2.09517i	−0.165748	−	0.0798198i
$690$	2.77962	−	12.1783i	0.105818	−	0.463620i
$691$	2.65566	+	11.6352i	0.101026	+	0.442623i	0.999989	+	0.00459992i	$0.00146421\pi$
$691$	2.65566	+	11.6352i	0.101026	+	0.442623i	−0.898964	+	0.438024i	$0.855679\pi$
$692$	15.7342	−	7.57719i	0.598124	−	0.288041i
$693$	−9.81531	−	4.72681i	−0.372853	−	0.179556i
$694$	17.4988	+	76.6675i	0.664247	+	2.91026i
$695$	12.8366			0.486921
$696$	32.7565	+	4.44656i	1.24163	+	0.168546i
$697$	−20.5629			−0.778876
$698$	20.1622	+	88.3364i	0.763151	+	3.34358i
$699$	6.03483	+	2.90622i	0.228258	+	0.109923i
$700$	26.2909	−	12.6610i	0.993701	−	0.478541i
$701$	0.764903	+	3.35126i	0.0288900	+	0.126575i	0.987317	−	0.158764i	$-0.0507509\pi$
$701$	0.764903	+	3.35126i	0.0288900	+	0.126575i	−0.958427	+	0.285339i	$0.907894\pi$
$702$	0.721521	−	3.16119i	0.0272321	−	0.119311i
$703$	36.3075	+	17.4848i	1.36936	+	0.659451i
$704$	−5.61783	−	7.04454i	−0.211730	−	0.265501i
$705$	1.03015	+	1.29177i	0.0387978	+	0.0486509i
$706$	13.7640	−	6.62840i	0.518016	−	0.249463i
$707$	13.5491	−	16.9900i	0.509566	−	0.638975i
$708$	−38.5708			−1.44958
$709$	−16.5529	+	20.7566i	−0.621656	+	0.779532i	−0.988576	−	0.150721i	$-0.951841\pi$
$709$	−16.5529	+	20.7566i	−0.621656	+	0.779532i	0.366921	+	0.930252i	$0.380412\pi$
$710$	−5.74081	+	25.1521i	−0.215449	+	0.943942i
$711$	0.637660	−	2.79377i	0.0239141	−	0.104775i
$712$	12.8043	−	16.0561i	0.479861	−	0.601727i
$713$	31.0125			1.16143
$714$	−13.8987	+	17.4284i	−0.520147	+	0.652243i
$715$	7.90646	−	3.80755i	0.295685	−	0.142394i
$716$	45.2564	+	56.7497i	1.69131	+	2.12084i
$717$	7.58319	+	9.50902i	0.283199	+	0.355121i
$718$	13.0464	+	6.28282i	0.486888	+	0.234473i
$719$	6.93957	−	30.4043i	0.258802	−	1.13389i	−0.663731	−	0.747971i	$-0.731028\pi$
$719$	6.93957	−	30.4043i	0.258802	−	1.13389i	0.922534	−	0.385916i	$-0.126115\pi$
$720$	−1.62721	−	7.12928i	−0.0606426	−	0.265692i
$721$	−4.32732	+	2.08393i	−0.161158	+	0.0776095i
$722$	−53.8840	−	25.9492i	−2.00535	−	0.965728i
$723$	−0.591055	−	2.58958i	−0.0219816	−	0.0963075i
$724$	−74.0867			−2.75341
$725$	1.83484	+	20.4513i	0.0681443	+	0.759541i
$726$	72.5513			2.69263
$727$	−3.81660	−	16.7216i	−0.141550	−	0.620170i	−0.995076	−	0.0991196i	$-0.968397\pi$
$727$	−3.81660	−	16.7216i	−0.141550	−	0.620170i	0.853526	−	0.521051i	$-0.174460\pi$
$728$	12.2461	+	5.89740i	0.453870	+	0.218572i
$729$	−0.900969	+	0.433884i	−0.0333692	+	0.0160698i
$730$	1.10456	+	4.83941i	0.0408817	+	0.179114i
$731$	2.07124	−	9.07467i	0.0766074	−	0.335639i
$732$	12.3021	+	5.92440i	0.454700	+	0.218972i
$733$	13.3386	+	16.7261i	0.492673	+	0.617792i	0.964559	−	0.263867i	$-0.0849982\pi$
$733$	13.3386	+	16.7261i	0.492673	+	0.617792i	−0.471886	+	0.881659i	$0.656427\pi$
$734$	43.2042	+	54.1764i	1.59470	+	1.99969i
$735$	3.93151	−	1.89331i	0.145016	−	0.0698359i
$736$	−13.3483	+	16.7382i	−0.492024	+	0.616979i
$737$	−15.0887			−0.555800
$738$	6.39213	−	8.01548i	0.235297	−	0.295054i
$739$	3.85619	−	16.8951i	0.141852	−	0.621495i	−0.853152	−	0.521662i	$-0.825312\pi$
$739$	3.85619	−	16.8951i	0.141852	−	0.621495i	0.995004	−	0.0998329i	$-0.0318308\pi$
$740$	−6.61959	+	29.0023i	−0.243341	+	1.06615i
$741$	5.20675	−	6.52906i	0.191275	−	0.239851i
$742$	−16.5518			−0.607636
$743$	−32.5068	+	40.7623i	−1.19256	+	1.49542i	−0.367831	+	0.929893i	$0.619900\pi$
$743$	−32.5068	+	40.7623i	−1.19256	+	1.49542i	−0.824728	+	0.565529i	$0.808672\pi$
$744$	37.9116	−	18.2573i	1.38991	−	0.669344i
$745$	0.517602	+	0.649053i	0.0189635	+	0.0237795i
$746$	−19.9429	−	25.0076i	−0.730160	−	0.915592i
$747$	−5.94056	−	2.86082i	−0.217354	−	0.104672i
$748$	31.4870	−	137.954i	1.15128	−	5.04408i
$749$	−3.83463	−	16.8006i	−0.140114	−	0.613881i
$750$	21.9234	−	10.5578i	0.800530	−	0.385515i
$751$	−21.6113	−	10.4075i	−0.788607	−	0.379773i	−0.00417787	−	0.999991i	$-0.501330\pi$
$751$	−21.6113	−	10.4075i	−0.788607	−	0.379773i	−0.784430	+	0.620218i	$0.787044\pi$
$752$	−2.26490	−	9.92319i	−0.0825926	−	0.361862i
$753$	−22.7654			−0.829618
$754$	−12.6244	+	12.0633i	−0.459752	+	0.439320i
$755$	20.0870			0.731041
$756$	−1.70296	−	7.46115i	−0.0619360	−	0.271359i
$757$	−42.7511	−	20.5878i	−1.55381	−	0.748277i	−0.557190	−	0.830385i	$-0.688120\pi$
$757$	−42.7511	−	20.5878i	−1.55381	−	0.748277i	−0.996623	+	0.0821079i	$0.973835\pi$
$758$	7.53608	−	3.62918i	0.273723	−	0.131818i
$759$	6.33743	+	27.7661i	0.230034	+	1.00784i
$760$	9.71338	−	42.5571i	0.352341	−	1.54371i
$761$	−34.8798	−	16.7972i	−1.26439	−	0.608899i	−0.323059	−	0.946379i	$-0.604711\pi$
$761$	−34.8798	−	16.7972i	−1.26439	−	0.608899i	−0.941333	+	0.337480i	$0.890425\pi$
$762$	22.5106	+	28.2274i	0.815474	+	1.02257i
$763$	−5.09873	−	6.39360i	−0.184586	−	0.231464i
$764$	11.7539	−	5.66036i	0.425240	−	0.204785i
$765$	−3.45283	+	4.32971i	−0.124837	+	0.156541i

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:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.g (of order \(7\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.563916 - 2.47068i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-3.98431 + 1.91874i) q^{4} +(-0.242440 - 1.06220i) q^{5} +(-0.563916 + 2.47068i) q^{6} +(-1.55919 - 0.750867i) q^{7} +(3.82730 + 4.79928i) q^{8} +(0.623490 + 0.781831i) q^{9} +O(q^{10})\)	\(q+(-0.563916 - 2.47068i) q^{2} +(-0.900969 - 0.433884i) q^{3} +(-3.98431 + 1.91874i) q^{4} +(-0.242440 - 1.06220i) q^{5} +(-0.563916 + 2.47068i) q^{6} +(-1.55919 - 0.750867i) q^{7} +(3.82730 + 4.79928i) q^{8} +(0.623490 + 0.781831i) q^{9} +(-2.48764 + 1.19798i) q^{10} +(3.92495 - 4.92173i) q^{11} +4.42225 q^{12} +(-0.797744 + 1.00034i) q^{13} +(-0.975897 + 4.27568i) q^{14} +(-0.242440 + 1.06220i) q^{15} +(4.18475 - 5.24750i) q^{16} -5.08291 q^{17} +(1.58006 - 1.98133i) q^{18} +(5.88048 - 2.83189i) q^{19} +(3.00404 + 3.76695i) q^{20} +(1.07899 + 1.35302i) q^{21} +(-14.3734 - 6.92184i) q^{22} +(1.00672 - 4.41072i) q^{23} +(-1.36595 - 5.98461i) q^{24} +(3.43536 - 1.65438i) q^{25} +(2.92138 + 1.40686i) q^{26} +(-0.222521 - 0.974928i) q^{27} +7.65302 q^{28} +(-1.89363 + 5.04125i) q^{29} +2.76107 q^{30} +(1.52535 + 6.68301i) q^{31} +(-4.26353 - 2.05321i) q^{32} +(-5.67172 + 2.73136i) q^{33} +(2.86633 + 12.5582i) q^{34} +(-0.419560 + 1.83821i) q^{35} +(-3.98431 - 1.91874i) q^{36} +(3.84958 + 4.82721i) q^{37} +(-10.3128 - 12.9318i) q^{38} +(1.15277 - 0.555147i) q^{39} +(4.16990 - 5.22889i) q^{40} +4.04550 q^{41} +(2.73440 - 3.42883i) q^{42} +(-0.407490 + 1.78533i) q^{43} +(-6.19468 + 27.1407i) q^{44} +(0.679302 - 0.851817i) q^{45} -11.4652 q^{46} +(0.945516 - 1.18564i) q^{47} +(-6.04713 + 2.91215i) q^{48} +(-2.49715 - 3.13133i) q^{49} +(-6.02469 - 7.55473i) q^{50} +(4.57954 + 2.20539i) q^{51} +(1.25907 - 5.51633i) q^{52} +(0.839814 + 3.67947i) q^{53} +(-2.28325 + 1.09956i) q^{54} +(-6.17942 - 2.97585i) q^{55} +(-2.36387 - 10.3568i) q^{56} -6.52684 q^{57} +(13.5231 + 1.83571i) q^{58} -8.72197 q^{59} +(-1.07213 - 4.69731i) q^{60} +(2.78187 + 1.33968i) q^{61} +(15.6514 - 7.53731i) q^{62} +(-0.385088 - 1.68718i) q^{63} +(0.318497 - 1.39543i) q^{64} +(1.25596 + 0.604841i) q^{65} +(9.94667 + 12.4727i) q^{66} +(-1.49443 - 1.87396i) q^{67} +(20.2519 - 9.75280i) q^{68} +(-2.82076 + 3.53712i) q^{69} +4.77822 q^{70} +(5.82579 - 7.30531i) q^{71} +(-1.36595 + 5.98461i) q^{72} +(0.400049 - 1.75273i) q^{73} +(9.75566 - 12.2332i) q^{74} -3.81296 q^{75} +(-17.9960 + 22.5663i) q^{76} +(-9.81531 + 4.72681i) q^{77} +(-2.02166 - 2.53508i) q^{78} +(-1.78668 - 2.24043i) q^{79} +(-6.58844 - 3.17283i) q^{80} +(-0.222521 + 0.974928i) q^{81} +(-2.28132 - 9.99513i) q^{82} +(-5.94056 + 2.86082i) q^{83} +(-6.89514 - 3.32052i) q^{84} +(1.23230 + 5.39906i) q^{85} +4.64077 q^{86} +(3.89342 - 3.72039i) q^{87} +38.6427 q^{88} +(-0.744447 - 3.26164i) q^{89} +(-2.48764 - 1.19798i) q^{90} +(1.99496 - 0.960721i) q^{91} +(4.45196 + 19.5053i) q^{92} +(1.52535 - 6.68301i) q^{93} +(-3.46252 - 1.66746i) q^{94} +(-4.43370 - 5.55968i) q^{95} +(2.95045 + 3.69975i) q^{96} +(-2.04297 + 0.983843i) q^{97} +(-6.32833 + 7.93547i) q^{98} +6.29513 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9}+O(q^{10}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9	\( 18 q - 4 q^{2} - 3 q^{3} - 6 q^{4} - q^{5} - 4 q^{6} - 4 q^{7} - 15 q^{8} - 3 q^{9} - 14 q^{10} + 26 q^{11} + 22 q^{12} + 9 q^{13} - 10 q^{14} - q^{15} - 14 q^{16} + 4 q^{17} - 4 q^{18} - 10 q^{19} - q^{20} - 4 q^{21} - 8 q^{22} - 8 q^{23} - 8 q^{24} + 16 q^{25} + 5 q^{26} - 3 q^{27} + 80 q^{28} + 8 q^{29} - 12 q^{31} + 9 q^{32} - 16 q^{33} - 22 q^{34} + 9 q^{35} - 6 q^{36} - 16 q^{37} - 32 q^{38} + 2 q^{39} + 33 q^{40} + 24 q^{41} - 3 q^{42} - 31 q^{43} - 52 q^{44} + 6 q^{45} - 44 q^{46} + 5 q^{47} - 47 q^{49} - 7 q^{50} + 11 q^{51} + 80 q^{52} + 5 q^{53} + 3 q^{54} - 17 q^{55} + 45 q^{56} + 18 q^{57} + 54 q^{58} - 32 q^{59} + 27 q^{60} - 28 q^{61} + 69 q^{62} + 3 q^{63} - 75 q^{64} + 22 q^{65} + 34 q^{66} + 6 q^{67} + 38 q^{68} + 20 q^{69} - 12 q^{70} + 46 q^{71} - 8 q^{72} - q^{73} - 35 q^{74} + 2 q^{75} - 45 q^{76} - 36 q^{77} - 51 q^{78} - 15 q^{79} - 86 q^{80} - 3 q^{81} + 47 q^{82} - 16 q^{83} - 25 q^{84} + 19 q^{85} + 116 q^{86} + 43 q^{87} + 54 q^{88} - 72 q^{89} - 14 q^{90} - 47 q^{91} - 121 q^{92} - 12 q^{93} - 22 q^{94} - 72 q^{95} - 12 q^{96} + 43 q^{97} + 31 q^{98} - 2 q^{99}+O(q^{100}) \) 18 * q - 4 * q^2 - 3 * q^3 - 6 * q^4 - q^5 - 4 * q^6 - 4 * q^7 - 15 * q^8 - 3 * q^9 - 14 * q^10 + 26 * q^11 + 22 * q^12 + 9 * q^13 - 10 * q^14 - q^15 - 14 * q^16 + 4 * q^17 - 4 * q^18 - 10 * q^19 - q^20 - 4 * q^21 - 8 * q^22 - 8 * q^23 - 8 * q^24 + 16 * q^25 + 5 * q^26 - 3 * q^27 + 80 * q^28 + 8 * q^29 - 12 * q^31 + 9 * q^32 - 16 * q^33 - 22 * q^34 + 9 * q^35 - 6 * q^36 - 16 * q^37 - 32 * q^38 + 2 * q^39 + 33 * q^40 + 24 * q^41 - 3 * q^42 - 31 * q^43 - 52 * q^44 + 6 * q^45 - 44 * q^46 + 5 * q^47 - 47 * q^49 - 7 * q^50 + 11 * q^51 + 80 * q^52 + 5 * q^53 + 3 * q^54 - 17 * q^55 + 45 * q^56 + 18 * q^57 + 54 * q^58 - 32 * q^59 + 27 * q^60 - 28 * q^61 + 69 * q^62 + 3 * q^63 - 75 * q^64 + 22 * q^65 + 34 * q^66 + 6 * q^67 + 38 * q^68 + 20 * q^69 - 12 * q^70 + 46 * q^71 - 8 * q^72 - q^73 - 35 * q^74 + 2 * q^75 - 45 * q^76 - 36 * q^77 - 51 * q^78 - 15 * q^79 - 86 * q^80 - 3 * q^81 + 47 * q^82 - 16 * q^83 - 25 * q^84 + 19 * q^85 + 116 * q^86 + 43 * q^87 + 54 * q^88 - 72 * q^89 - 14 * q^90 - 47 * q^91 - 121 * q^92 - 12 * q^93 - 22 * q^94 - 72 * q^95 - 12 * q^96 + 43 * q^97 + 31 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more