LMFDB - Embedded newform 350.2.h.d.281.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [350,2,Mod(71,350)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(350, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("350.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 350 = 2 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	350.h (of order $5$, degree $4$, 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:	$2.79476407074$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 15 x^{18} - 30 x^{17} + 145 x^{16} - 194 x^{15} + 1187 x^{14} - 1490 x^{13} + \cdots + 400 $ x^20 - 3x^19 + 15x^18 - 30x^17 + 145x^16 - 194x^15 + 1187x^14 - 1490x^13 + 10170x^12 - 13920x^11 + 42087x^10 - 591x^9 + 65635x^8 + 120715x^7 + 257180x^6 + 306283x^5 + 246171x^4 + 99850x^3 + 26260x^2 + 4200*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			281.4
Root			$1.88692 - 1.37093i$ of defining polynomial
Character	$\chi$	$=$	350.281
Dual form			350.2.h.d.71.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 - 0.951057i) q^{2} +(1.88692 - 1.37093i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.06221 + 1.96767i) q^{5} +(-1.88692 - 1.37093i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.753978 - 2.32051i) q^{9} +O(q^{10})$	\(q+(-0.309017 - 0.951057i) q^{2} +(1.88692 - 1.37093i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.06221 + 1.96767i) q^{5} +(-1.88692 - 1.37093i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.753978 - 2.32051i) q^{9} +(1.54312 - 1.61826i) q^{10} +(-0.266278 - 0.819519i) q^{11} +(-0.720740 + 2.21821i) q^{12} +(1.36720 - 4.20782i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(4.70184 + 2.25662i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.22852 + 2.34566i) q^{17} -2.43992 q^{18} +(-1.11960 - 0.813435i) q^{19} +(-2.01591 - 0.967523i) q^{20} +(1.88692 - 1.37093i) q^{21} +(-0.697124 + 0.506490i) q^{22} +(-0.705847 - 2.17238i) q^{23} +2.33236 q^{24} +(-2.74342 + 4.18015i) q^{25} -4.42436 q^{26} +(0.403669 + 1.24237i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-0.564037 + 0.409797i) q^{29} +(0.693221 - 5.16905i) q^{30} +(-6.02141 - 4.37481i) q^{31} -1.00000 q^{32} +(-1.62595 - 1.18132i) q^{33} +(1.23318 - 3.79535i) q^{34} +(1.06221 + 1.96767i) q^{35} +(0.753978 + 2.32051i) q^{36} +(-2.65369 + 8.16721i) q^{37} +(-0.427648 + 1.31617i) q^{38} +(-3.18881 - 9.81416i) q^{39} +(-0.297218 + 2.21623i) q^{40} +(-0.109311 + 0.336424i) q^{41} +(-1.88692 - 1.37093i) q^{42} -6.63436 q^{43} +(0.697124 + 0.506490i) q^{44} +(5.36686 - 0.981290i) q^{45} +(-1.84793 + 1.34260i) q^{46} +(-4.27541 + 3.10627i) q^{47} +(-0.720740 - 2.21821i) q^{48} +1.00000 q^{49} +(4.82332 + 1.31741i) q^{50} +9.30770 q^{51} +(1.36720 + 4.20782i) q^{52} +(-0.878059 + 0.637947i) q^{53} +(1.05682 - 0.767824i) q^{54} +(1.32970 - 1.39445i) q^{55} +(0.809017 + 0.587785i) q^{56} -3.22776 q^{57} +(0.564037 + 0.409797i) q^{58} +(3.30840 - 10.1822i) q^{59} +(-5.13027 + 0.938032i) q^{60} +(3.54391 + 10.9070i) q^{61} +(-2.29998 + 7.07860i) q^{62} +(0.753978 - 2.32051i) q^{63} +(0.309017 + 0.951057i) q^{64} +(9.73183 - 1.77939i) q^{65} +(-0.621057 + 1.91142i) q^{66} +(-0.460717 - 0.334731i) q^{67} -3.99067 q^{68} +(-4.31005 - 3.13144i) q^{69} +(1.54312 - 1.61826i) q^{70} +(5.14835 - 3.74049i) q^{71} +(1.97394 - 1.43415i) q^{72} +(-3.28881 - 10.1219i) q^{73} +8.58751 q^{74} +(0.554080 + 11.6487i) q^{75} +1.38390 q^{76} +(-0.266278 - 0.819519i) q^{77} +(-8.34842 + 6.06548i) q^{78} +(-10.2363 + 7.43709i) q^{79} +(2.19960 - 0.402181i) q^{80} +(8.38671 + 6.09330i) q^{81} +0.353737 q^{82} +(11.0446 + 8.02434i) q^{83} +(-0.720740 + 2.21821i) q^{84} +(-1.18610 + 8.84423i) q^{85} +(2.05013 + 6.30965i) q^{86} +(-0.502492 + 1.54651i) q^{87} +(0.266278 - 0.819519i) q^{88} +(3.71234 + 11.4254i) q^{89} +(-2.59171 - 4.80095i) q^{90} +(1.36720 - 4.20782i) q^{91} +(1.84793 + 1.34260i) q^{92} -17.3595 q^{93} +(4.27541 + 3.10627i) q^{94} +(0.411320 - 3.06703i) q^{95} +(-1.88692 + 1.37093i) q^{96} +(-11.2145 + 8.14780i) q^{97} +(-0.309017 - 0.951057i) q^{98} -2.10247 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) $ 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9} - 9 q^{11} - 2 q^{12} + 5 q^{13} + 5 q^{14} - 5 q^{16} - 12 q^{17} - 34 q^{18} + 2 q^{19} + 5 q^{20} + 3 q^{21} - 6 q^{22} - 5 q^{23} + 2 q^{24} - 35 q^{25} + 20 q^{26} - 6 q^{27} - 5 q^{28} - 22 q^{29} - 25 q^{30} - 7 q^{31} - 20 q^{32} + 25 q^{33} - 18 q^{34} - 5 q^{35} - 6 q^{36} - 3 q^{37} + 8 q^{38} - 22 q^{39} + 19 q^{41} - 3 q^{42} + 2 q^{43} + 6 q^{44} + 45 q^{45} - 10 q^{46} - 14 q^{47} - 2 q^{48} + 20 q^{49} + 10 q^{50} + 38 q^{51} + 5 q^{52} - q^{53} - 19 q^{54} - 20 q^{55} + 5 q^{56} + 116 q^{57} + 22 q^{58} + 17 q^{59} - 5 q^{60} - 38 q^{61} + 7 q^{62} - 6 q^{63} - 5 q^{64} + 15 q^{65} - 16 q^{67} - 12 q^{68} + 35 q^{69} + q^{71} + 11 q^{72} + 19 q^{73} + 18 q^{74} + 35 q^{75} + 12 q^{76} - 9 q^{77} - 18 q^{78} - 64 q^{79} - 40 q^{81} + 26 q^{82} + 57 q^{83} - 2 q^{84} - 40 q^{85} - 2 q^{86} - 78 q^{87} + 9 q^{88} - 6 q^{89} + 10 q^{90} + 5 q^{91} + 10 q^{92} - 22 q^{93} + 14 q^{94} + 60 q^{95} - 3 q^{96} - 18 q^{97} + 5 q^{98} + 112 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9 - 9 * q^11 - 2 * q^12 + 5 * q^13 + 5 * q^14 - 5 * q^16 - 12 * q^17 - 34 * q^18 + 2 * q^19 + 5 * q^20 + 3 * q^21 - 6 * q^22 - 5 * q^23 + 2 * q^24 - 35 * q^25 + 20 * q^26 - 6 * q^27 - 5 * q^28 - 22 * q^29 - 25 * q^30 - 7 * q^31 - 20 * q^32 + 25 * q^33 - 18 * q^34 - 5 * q^35 - 6 * q^36 - 3 * q^37 + 8 * q^38 - 22 * q^39 + 19 * q^41 - 3 * q^42 + 2 * q^43 + 6 * q^44 + 45 * q^45 - 10 * q^46 - 14 * q^47 - 2 * q^48 + 20 * q^49 + 10 * q^50 + 38 * q^51 + 5 * q^52 - q^53 - 19 * q^54 - 20 * q^55 + 5 * q^56 + 116 * q^57 + 22 * q^58 + 17 * q^59 - 5 * q^60 - 38 * q^61 + 7 * q^62 - 6 * q^63 - 5 * q^64 + 15 * q^65 - 16 * q^67 - 12 * q^68 + 35 * q^69 + q^71 + 11 * q^72 + 19 * q^73 + 18 * q^74 + 35 * q^75 + 12 * q^76 - 9 * q^77 - 18 * q^78 - 64 * q^79 - 40 * q^81 + 26 * q^82 + 57 * q^83 - 2 * q^84 - 40 * q^85 - 2 * q^86 - 78 * q^87 + 9 * q^88 - 6 * q^89 + 10 * q^90 + 5 * q^91 + 10 * q^92 - 22 * q^93 + 14 * q^94 + 60 * q^95 - 3 * q^96 - 18 * q^97 + 5 * q^98 + 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

Coefficient data

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

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

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

$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$2$	−0.309017	−	0.951057i	−0.218508	−	0.672499i
$3$	1.88692	−	1.37093i	1.08942	−	0.791506i	0.110115	−	0.993919i	$-0.464878\pi$
$3$	1.88692	−	1.37093i	1.08942	−	0.791506i	0.979300	+	0.202412i	$0.0648781\pi$
$4$	−0.809017	+	0.587785i	−0.404508	+	0.293893i
$5$	1.06221	+	1.96767i	0.475035	+	0.879967i
$5$	1.06221	+	1.96767i	0.475035	+	0.879967i
$6$	−1.88692	−	1.37093i	−0.770333	−	0.559680i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	0.809017	+	0.587785i	0.286031	+	0.207813i
$9$	0.753978	−	2.32051i	0.251326	−	0.773502i
$10$	1.54312	−	1.61826i	0.487977	−	0.511740i
$11$	−0.266278	−	0.819519i	−0.0802858	−	0.247094i	0.902855	−	0.429946i	$-0.141467\pi$
$11$	−0.266278	−	0.819519i	−0.0802858	−	0.247094i	−0.983141	+	0.182851i	$0.941467\pi$
$12$	−0.720740	+	2.21821i	−0.208060	+	0.640342i
$13$	1.36720	−	4.20782i	0.379194	−	1.16704i	−0.561412	−	0.827537i	$-0.689742\pi$
$13$	1.36720	−	4.20782i	0.379194	−	1.16704i	0.940606	−	0.339501i	$-0.110258\pi$
$14$	−0.309017	−	0.951057i	−0.0825883	−	0.254181i
$15$	4.70184	+	2.25662i	1.21401	+	0.582656i
$16$	0.309017	−	0.951057i	0.0772542	−	0.237764i
$17$	3.22852	+	2.34566i	0.783031	+	0.568905i	0.905887	−	0.423519i	$-0.139205\pi$
$17$	3.22852	+	2.34566i	0.783031	+	0.568905i	−0.122856	+	0.992424i	$0.539205\pi$
$18$	−2.43992			−0.575096
$19$	−1.11960	−	0.813435i	−0.256853	−	0.186615i	0.451905	−	0.892066i	$-0.350744\pi$
$19$	−1.11960	−	0.813435i	−0.256853	−	0.186615i	−0.708759	+	0.705451i	$0.750744\pi$
$20$	−2.01591	−	0.967523i	−0.450772	−	0.216345i
$21$	1.88692	−	1.37093i	0.411760	−	0.299161i
$22$	−0.697124	+	0.506490i	−0.148627	+	0.107984i
$23$	−0.705847	−	2.17238i	−0.147179	−	0.452972i	0.850105	−	0.526612i	$-0.176538\pi$
$23$	−0.705847	−	2.17238i	−0.147179	−	0.452972i	−0.997285	+	0.0736410i	$0.976538\pi$
$24$	2.33236			0.476092
$25$	−2.74342	+	4.18015i	−0.548683	+	0.836030i
$26$	−4.42436			−0.867688
$27$	0.403669	+	1.24237i	0.0776862	+	0.239093i
$28$	−0.809017	+	0.587785i	−0.152890	+	0.111081i
$29$	−0.564037	+	0.409797i	−0.104739	+	0.0760974i	−0.638922	−	0.769272i	$-0.720619\pi$
$29$	−0.564037	+	0.409797i	−0.104739	+	0.0760974i	0.534183	+	0.845369i	$0.320619\pi$
$30$	0.693221	−	5.16905i	0.126564	−	0.943735i
$31$	−6.02141	−	4.37481i	−1.08148	−	0.785740i	−0.103538	−	0.994626i	$-0.533016\pi$
$31$	−6.02141	−	4.37481i	−1.08148	−	0.785740i	−0.977940	+	0.208886i	$0.933016\pi$
$32$	−1.00000			−0.176777
$33$	−1.62595	−	1.18132i	−0.283041	−	0.205641i
$34$	1.23318	−	3.79535i	0.211489	−	0.650898i
$35$	1.06221	+	1.96767i	0.179546	+	0.332596i
$36$	0.753978	+	2.32051i	0.125663	+	0.386751i
$37$	−2.65369	+	8.16721i	−0.436263	+	1.34268i	0.455523	+	0.890224i	$0.349452\pi$
$37$	−2.65369	+	8.16721i	−0.436263	+	1.34268i	−0.891787	+	0.452456i	$0.850548\pi$
$38$	−0.427648	+	1.31617i	−0.0693737	+	0.213510i
$39$	−3.18881	−	9.81416i	−0.510619	−	1.57152i
$40$	−0.297218	+	2.21623i	−0.0469943	+	0.350416i
$41$	−0.109311	+	0.336424i	−0.0170715	+	0.0525405i	−0.959229	−	0.282629i	$-0.908794\pi$
$41$	−0.109311	+	0.336424i	−0.0170715	+	0.0525405i	0.942158	+	0.335169i	$0.108794\pi$
$42$	−1.88692	−	1.37093i	−0.291158	−	0.211539i
$43$	−6.63436			−1.01173			−0.505865	−	0.862612i	$-0.668827\pi$
$43$	−6.63436			−1.01173			−0.505865	+	0.862612i	$0.668827\pi$
$44$	0.697124	+	0.506490i	0.105095	+	0.0763563i
$45$	5.36686	−	0.981290i	0.800045	−	0.146282i
$46$	−1.84793	+	1.34260i	−0.272463	+	0.197956i
$47$	−4.27541	+	3.10627i	−0.623632	+	0.453096i	−0.854188	−	0.519964i	$-0.825946\pi$
$47$	−4.27541	+	3.10627i	−0.623632	+	0.453096i	0.230556	+	0.973059i	$0.425946\pi$
$48$	−0.720740	−	2.21821i	−0.104030	−	0.320171i
$49$	1.00000			0.142857
$50$	4.82332	+	1.31741i	0.682121	+	0.186309i
$51$	9.30770			1.30334
$52$	1.36720	+	4.20782i	0.189597	+	0.583519i
$53$	−0.878059	+	0.637947i	−0.120611	+	0.0876288i	−0.646455	−	0.762952i	$-0.723749\pi$
$53$	−0.878059	+	0.637947i	−0.120611	+	0.0876288i	0.525845	+	0.850581i	$0.323749\pi$
$54$	1.05682	−	0.767824i	0.143815	−	0.104488i
$55$	1.32970	−	1.39445i	0.179296	−	0.188027i
$56$	0.809017	+	0.587785i	0.108109	+	0.0785461i
$57$	−3.22776			−0.427527
$58$	0.564037	+	0.409797i	0.0740617	+	0.0538090i
$59$	3.30840	−	10.1822i	0.430717	−	1.32561i	−0.466695	−	0.884418i	$-0.654555\pi$
$59$	3.30840	−	10.1822i	0.430717	−	1.32561i	0.897412	−	0.441193i	$-0.145445\pi$
$60$	−5.13027	+	0.938032i	−0.662316	+	0.121099i
$61$	3.54391	+	10.9070i	0.453751	+	1.39650i	0.872595	+	0.488444i	$0.162435\pi$
$61$	3.54391	+	10.9070i	0.453751	+	1.39650i	−0.418844	+	0.908058i	$0.637565\pi$
$62$	−2.29998	+	7.07860i	−0.292097	+	0.898983i
$63$	0.753978	−	2.32051i	0.0949923	−	0.292356i
$64$	0.309017	+	0.951057i	0.0386271	+	0.118882i
$65$	9.73183	−	1.77939i	1.20709	−	0.220706i
$66$	−0.621057	+	1.91142i	−0.0764468	+	0.235279i
$67$	−0.460717	−	0.334731i	−0.0562856	−	0.0408939i	0.559287	−	0.828974i	$-0.311075\pi$
$67$	−0.460717	−	0.334731i	−0.0562856	−	0.0408939i	−0.615572	+	0.788080i	$0.711075\pi$
$68$	−3.99067			−0.483940
$69$	−4.31005	−	3.13144i	−0.518869	−	0.376981i
$70$	1.54312	−	1.61826i	0.184438	−	0.193420i
$71$	5.14835	−	3.74049i	0.610996	−	0.443915i	−0.238769	−	0.971076i	$-0.576744\pi$
$71$	5.14835	−	3.74049i	0.610996	−	0.443915i	0.849765	+	0.527162i	$0.176744\pi$
$72$	1.97394	−	1.43415i	0.232631	−	0.169016i
$73$	−3.28881	−	10.1219i	−0.384926	−	1.18468i	−0.936534	−	0.350577i	$-0.885985\pi$
$73$	−3.28881	−	10.1219i	−0.384926	−	1.18468i	0.551608	−	0.834104i	$-0.314015\pi$
$74$	8.58751			0.998277
$75$	0.554080	+	11.6487i	0.0639796	+	1.34507i
$76$	1.38390			0.158744
$77$	−0.266278	−	0.819519i	−0.0303452	−	0.0933928i
$78$	−8.34842	+	6.06548i	−0.945273	+	0.686781i
$79$	−10.2363	+	7.43709i	−1.15167	+	0.836738i	−0.988702	−	0.149893i	$-0.952107\pi$
$79$	−10.2363	+	7.43709i	−1.15167	+	0.836738i	−0.162969	+	0.986631i	$0.552107\pi$
$80$	2.19960	−	0.402181i	0.245923	−	0.0449651i
$81$	8.38671	+	6.09330i	0.931857	+	0.677033i
$82$	0.353737			0.0390637
$83$	11.0446	+	8.02434i	1.21230	+	0.880786i	0.995437	−	0.0954169i	$-0.0304184\pi$
$83$	11.0446	+	8.02434i	1.21230	+	0.880786i	0.216860	+	0.976203i	$0.430418\pi$
$84$	−0.720740	+	2.21821i	−0.0786392	+	0.242027i
$85$	−1.18610	+	8.84423i	−0.128651	+	0.959291i
$86$	2.05013	+	6.30965i	0.221071	+	0.680388i
$87$	−0.502492	+	1.54651i	−0.0538728	+	0.165803i
$88$	0.266278	−	0.819519i	0.0283853	−	0.0873610i
$89$	3.71234	+	11.4254i	0.393507	+	1.21109i	0.930118	+	0.367260i	$0.119704\pi$
$89$	3.71234	+	11.4254i	0.393507	+	1.21109i	−0.536611	+	0.843830i	$0.680296\pi$
$90$	−2.59171	−	4.80095i	−0.273191	−	0.506065i
$91$	1.36720	−	4.20782i	0.143322	−	0.441099i
$92$	1.84793	+	1.34260i	0.192660	+	0.139976i
$93$	−17.3595			−1.80010
$94$	4.27541	+	3.10627i	0.440975	+	0.320387i
$95$	0.411320	−	3.06703i	0.0422005	−	0.314671i
$96$	−1.88692	+	1.37093i	−0.192583	+	0.139920i
$97$	−11.2145	+	8.14780i	−1.13866	+	0.827284i	−0.986932	−	0.161139i	$-0.948483\pi$
$97$	−11.2145	+	8.14780i	−1.13866	+	0.827284i	−0.151726	+	0.988423i	$0.548483\pi$
$98$	−0.309017	−	0.951057i	−0.0312154	−	0.0960712i
$99$	−2.10247			−0.211306
$100$	−0.237562	−	4.99435i	−0.0237562	−	0.499435i
$101$	−19.4355			−1.93390			−0.966952	−	0.254958i	$-0.917939\pi$
$101$	−19.4355			−1.93390			−0.966952	+	0.254958i	$0.917939\pi$
$102$	−2.87624	−	8.85215i	−0.284790	−	0.876493i
$103$	−7.08993	+	5.15114i	−0.698592	+	0.507557i	−0.879473	−	0.475948i	$-0.842105\pi$
$103$	−7.08993	+	5.15114i	−0.698592	+	0.507557i	0.180881	+	0.983505i	$0.442105\pi$
$104$	3.57938	−	2.60057i	0.350987	−	0.255007i
$105$	4.70184	+	2.25662i	0.458853	+	0.220223i
$106$	0.878059	+	0.637947i	0.0852846	+	0.0619629i
$107$	5.68246			0.549344			0.274672	−	0.961538i	$-0.411431\pi$
$107$	5.68246			0.549344			0.274672	+	0.961538i	$0.411431\pi$
$108$	−1.05682	−	0.767824i	−0.101693	−	0.0738839i
$109$	5.33867	−	16.4307i	0.511352	−	1.57378i	−0.278471	−	0.960445i	$-0.589828\pi$
$109$	5.33867	−	16.4307i	0.511352	−	1.57378i	0.789823	−	0.613335i	$-0.210172\pi$
$110$	−1.73710	−	0.833708i	−0.165626	−	0.0794909i
$111$	6.18936	+	19.0489i	0.587468	+	1.80804i
$112$	0.309017	−	0.951057i	0.0291994	−	0.0898664i
$113$	−0.443906	+	1.36620i	−0.0417592	+	0.128521i	−0.969763	−	0.244050i	$-0.921524\pi$
$113$	−0.443906	+	1.36620i	−0.0417592	+	0.128521i	0.928003	+	0.372572i	$0.121524\pi$
$114$	0.997432	+	3.06978i	0.0934180	+	0.287511i
$115$	3.52475	−	3.69639i	0.328685	−	0.344690i
$116$	0.215443	−	0.663066i	0.0200034	−	0.0615641i
$117$	−8.73342	−	6.34520i	−0.807405	−	0.586614i
$118$	−10.7062			−0.985587
$119$	3.22852	+	2.34566i	0.295958	+	0.215026i
$120$	2.47746	+	4.58931i	0.226160	+	0.418945i
$121$	8.29848	−	6.02920i	0.754407	−	0.548109i
$122$	9.27808	−	6.74092i	0.839998	−	0.610294i
$123$	0.254952	+	0.784663i	0.0229883	+	0.0707506i
$124$	7.44288			0.668390
$125$	−11.1392	−	0.957922i	−0.996323	−	0.0856792i
$126$	−2.43992			−0.217366
$127$	−2.37638	−	7.31373i	−0.210869	−	0.648989i	−0.999421	−	0.0340205i	$-0.989169\pi$
$127$	−2.37638	−	7.31373i	−0.210869	−	0.648989i	0.788552	−	0.614968i	$-0.210831\pi$
$128$	0.809017	−	0.587785i	0.0715077	−	0.0519534i
$129$	−12.5185	+	9.09524i	−1.10220	+	0.800792i
$130$	−4.69960	−	8.70566i	−0.412182	−	0.763537i
$131$	7.63850	+	5.54969i	0.667379	+	0.484879i	0.869147	−	0.494554i	$-0.164669\pi$
$131$	7.63850	+	5.54969i	0.667379	+	0.484879i	−0.201768	+	0.979433i	$0.564669\pi$
$132$	2.00978			0.174929
$133$	−1.11960	−	0.813435i	−0.0970814	−	0.0705338i
$134$	−0.175978	+	0.541606i	−0.0152022	+	0.0467876i
$135$	−2.01578	+	2.11394i	−0.173491	+	0.181939i
$136$	1.23318	+	3.79535i	0.105745	+	0.325449i
$137$	2.82009	−	8.67934i	0.240937	−	0.741526i	−0.755342	−	0.655331i	$-0.772529\pi$
$137$	2.82009	−	8.67934i	0.240937	−	0.741526i	0.996278	−	0.0861953i	$-0.0274709\pi$
$138$	−1.64629	+	5.06677i	−0.140142	+	0.431312i
$139$	−3.32056	−	10.2196i	−0.281647	−	0.866819i	−0.987384	−	0.158345i	$-0.949384\pi$
$139$	−3.32056	−	10.2196i	−0.281647	−	0.866819i	0.705737	−	0.708474i	$-0.250616\pi$
$140$	−2.01591	−	0.967523i	−0.170376	−	0.0817706i
$141$	−3.80889	+	11.7226i	−0.320767	+	0.987218i
$142$	−5.14835	−	3.74049i	−0.432040	−	0.313895i
$143$	−3.81244			−0.318812
$144$	−1.97394	−	1.43415i	−0.164495	−	0.119513i
$145$	−1.40547	−	0.674546i	−0.116718	−	0.0560180i
$146$	−8.61022	+	6.25569i	−0.712587	+	0.517724i
$147$	1.88692	−	1.37093i	0.155631	−	0.113072i
$148$	−2.65369	−	8.16721i	−0.218132	−	0.671340i
$149$	13.6171			1.11555			0.557776	−	0.829991i	$-0.311655\pi$
$149$	13.6171			1.11555			0.557776	+	0.829991i	$0.311655\pi$
$150$	10.9073	−	4.12659i	0.890578	−	0.336935i
$151$	−3.21189			−0.261380			−0.130690	−	0.991423i	$-0.541719\pi$
$151$	−3.21189			−0.261380			−0.130690	+	0.991423i	$0.541719\pi$
$152$	−0.427648	−	1.31617i	−0.0346869	−	0.106755i
$153$	7.87734	−	5.72322i	0.636845	−	0.462695i
$154$	−0.697124	+	0.506490i	−0.0561759	+	0.0408142i
$155$	2.21216	−	16.4951i	0.177685	−	1.32492i
$156$	8.34842	+	6.06548i	0.668409	+	0.485627i
$157$	−10.2808			−0.820498			−0.410249	−	0.911974i	$-0.634558\pi$
$157$	−10.2808			−0.820498			−0.410249	+	0.911974i	$0.634558\pi$
$158$	10.2363	+	7.43709i	0.814355	+	0.591663i
$159$	−0.782249	+	2.40751i	−0.0620363	+	0.190928i
$160$	−1.06221	−	1.96767i	−0.0839751	−	0.155558i
$161$	−0.705847	−	2.17238i	−0.0556286	−	0.171207i
$162$	3.20344	−	9.85917i	0.251686	−	0.774609i
$163$	1.05979	−	3.26171i	0.0830095	−	0.255477i	−0.900934	−	0.433956i	$-0.857117\pi$
$163$	1.05979	−	3.26171i	0.0830095	−	0.255477i	0.983944	+	0.178479i	$0.0571175\pi$
$164$	−0.109311	−	0.336424i	−0.00853573	−	0.0262703i
$165$	0.597344	−	4.45413i	0.0465031	−	0.346754i
$166$	4.21865	−	12.9837i	0.327430	−	1.00773i
$167$	16.8272	+	12.2257i	1.30213	+	0.946052i	0.999974	−	0.00720650i	$-0.00229392\pi$
$167$	16.8272	+	12.2257i	1.30213	+	0.946052i	0.302155	+	0.953259i	$0.402294\pi$
$168$	2.33236			0.179946
$169$	−5.31925	−	3.86466i	−0.409173	−	0.297282i
$170$	8.77789	−	1.60497i	0.673233	−	0.123096i
$171$	−2.73173	+	1.98472i	−0.208901	+	0.151775i
$172$	5.36731	−	3.89958i	0.409254	−	0.297340i
$173$	0.415359	+	1.27834i	0.0315792	+	0.0971907i	0.965604	−	0.260018i	$-0.0837285\pi$
$173$	0.415359	+	1.27834i	0.0315792	+	0.0971907i	−0.934025	+	0.357209i	$0.883728\pi$
$174$	1.62610			0.123274
$175$	−2.74342	+	4.18015i	−0.207383	+	0.315990i
$176$	−0.861693			−0.0649525
$177$	−7.71640	−	23.7486i	−0.580000	−	1.78506i
$178$	9.71902	−	7.06128i	0.728472	−	0.529266i
$179$	18.9058	−	13.7359i	1.41309	−	1.02667i	0.420221	−	0.907422i	$-0.361953\pi$
$179$	18.9058	−	13.7359i	1.41309	−	1.02667i	0.992865	−	0.119245i	$-0.0380473\pi$
$180$	−3.76510	+	3.94844i	−0.280634	+	0.294300i
$181$	−15.1066	−	10.9756i	−1.12287	−	0.815810i	−0.138225	−	0.990401i	$-0.544140\pi$
$181$	−15.1066	−	10.9756i	−1.12287	−	0.815810i	−0.984641	+	0.174591i	$0.944140\pi$
$182$	−4.42436			−0.327955
$183$	21.6399	+	15.7223i	1.59966	+	1.16222i
$184$	0.705847	−	2.17238i	0.0520358	−	0.160150i
$185$	−18.8891	+	3.45373i	−1.38875	+	0.253923i
$186$	5.36438	+	16.5099i	0.393335	+	1.21056i
$187$	1.06263	−	3.27043i	0.0777069	−	0.239157i
$188$	1.63306	−	5.02604i	0.119103	−	0.366562i
$189$	0.403669	+	1.24237i	0.0293626	+	0.0903688i
$190$	−3.04403	+	0.556577i	−0.220837	+	0.0403784i
$191$	7.81630	−	24.0561i	0.565568	−	1.74064i	−0.100691	−	0.994918i	$-0.532105\pi$
$191$	7.81630	−	24.0561i	0.565568	−	1.74064i	0.666259	−	0.745721i	$-0.267895\pi$
$192$	1.88692	+	1.37093i	0.136177	+	0.0989383i
$193$	21.0222			1.51321			0.756606	−	0.653871i	$-0.226856\pi$
$193$	21.0222			1.51321			0.756606	+	0.653871i	$0.226856\pi$
$194$	11.2145	+	8.14780i	0.805153	+	0.584978i
$195$	15.9238	−	16.6992i	1.14033	−	1.19586i
$196$	−0.809017	+	0.587785i	−0.0577869	+	0.0419847i
$197$	−15.7201	+	11.4213i	−1.12001	+	0.813735i	−0.984211	−	0.177001i	$-0.943360\pi$
$197$	−15.7201	+	11.4213i	−1.12001	+	0.813735i	−0.135800	+	0.990736i	$0.543360\pi$
$198$	0.649697	+	1.99956i	0.0461720	+	0.142103i
$199$	−9.01284			−0.638904			−0.319452	−	0.947603i	$-0.603499\pi$
$199$	−9.01284			−0.638904			−0.319452	+	0.947603i	$0.603499\pi$
$200$	−4.67650	+	1.76927i	−0.330679	+	0.125107i
$201$	−1.32823			−0.0936861
$202$	6.00590	+	18.4843i	0.422574	+	1.30055i
$203$	−0.564037	+	0.409797i	−0.0395877	+	0.0287621i
$204$	−7.53008	+	5.47093i	−0.527211	+	0.383041i
$205$	−0.778080	+	0.142266i	−0.0543435	+	0.00993629i
$206$	7.08993	+	5.15114i	0.493979	+	0.358897i
$207$	−5.57320			−0.387364
$208$	−3.57938	−	2.60057i	−0.248185	−	0.180317i
$209$	−0.368501	+	1.13413i	−0.0254898	+	0.0784495i
$210$	0.693221	−	5.16905i	0.0478368	−	0.356698i
$211$	−5.95165	−	18.3173i	−0.409728	−	1.26101i	−0.916882	−	0.399158i	$-0.869302\pi$
$211$	−5.95165	−	18.3173i	−0.409728	−	1.26101i	0.507154	−	0.861856i	$-0.330698\pi$
$212$	0.335389	−	1.03222i	0.0230346	−	0.0708932i
$213$	4.58658	−	14.1160i	0.314267	−	0.967215i
$214$	−1.75598	−	5.40434i	−0.120036	−	0.369433i
$215$	−7.04709	−	13.0542i	−0.480608	−	0.890290i
$216$	−0.403669	+	1.24237i	−0.0274662	+	0.0845323i
$217$	−6.02141	−	4.37481i	−0.408760	−	0.296982i
$218$	−17.2763			−1.17010
$219$	−20.0822	−	14.5905i	−1.35703	−	0.985938i
$220$	−0.256111	+	1.90971i	−0.0172670	+	0.128752i
$221$	14.2841	−	10.3780i	0.960855	−	0.698102i
$222$	16.2040	−	11.7729i	1.08754	−	0.790143i
$223$	−1.88817	−	5.81117i	−0.126441	−	0.389145i	0.867720	−	0.497053i	$-0.165585\pi$
$223$	−1.88817	−	5.81117i	−0.126441	−	0.389145i	−0.994161	+	0.107908i	$0.965585\pi$
$224$	−1.00000			−0.0668153
$225$	7.63159	+	9.51785i	0.508773	+	0.634524i
$226$	1.43651			0.0955552
$227$	2.02463	+	6.23117i	0.134379	+	0.413577i	0.995493	−	0.0948355i	$-0.0302325\pi$
$227$	2.02463	+	6.23117i	0.134379	+	0.413577i	−0.861114	+	0.508413i	$0.830233\pi$
$228$	2.61131	−	1.89723i	0.172938	−	0.125647i
$229$	−18.4372	+	13.3954i	−1.21837	+	0.885195i	−0.995963	−	0.0897600i	$-0.971390\pi$
$229$	−18.4372	+	13.3954i	−1.21837	+	0.885195i	−0.222403	+	0.974955i	$0.571390\pi$
$230$	−4.60469	−	2.20999i	−0.303624	−	0.145722i
$231$	−1.62595	−	1.18132i	−0.106979	−	0.0777252i
$232$	−0.697188			−0.0457727
$233$	−6.66411	−	4.84176i	−0.436580	−	0.317194i	0.347694	−	0.937608i	$-0.386965\pi$
$233$	−6.66411	−	4.84176i	−0.436580	−	0.317194i	−0.784275	+	0.620414i	$0.786965\pi$
$234$	−3.33587	+	10.2668i	−0.218073	+	0.671158i
$235$	−10.6535	−	5.11306i	−0.694956	−	0.333540i
$236$	3.30840	+	10.1822i	0.215359	+	0.662806i
$237$	−9.11934	+	28.0664i	−0.592365	+	1.82311i
$238$	1.23318	−	3.79535i	0.0799355	−	0.246016i
$239$	−0.326868	−	1.00600i	−0.0211433	−	0.0650724i	0.939928	−	0.341372i	$-0.110892\pi$
$239$	−0.326868	−	1.00600i	−0.0211433	−	0.0650724i	−0.961071	+	0.276300i	$0.910892\pi$
$240$	3.59912	−	3.77438i	0.232322	−	0.243635i
$241$	−3.14926	+	9.69241i	−0.202861	+	0.624343i	0.796933	+	0.604068i	$0.206454\pi$
$241$	−3.14926	+	9.69241i	−0.202861	+	0.624343i	−0.999794	+	0.0202756i	$0.993546\pi$
$242$	−8.29848	−	6.02920i	−0.533447	−	0.387572i
$243$	20.2597			1.29966
$244$	−9.27808	−	6.74092i	−0.593968	−	0.431543i
$245$	1.06221	+	1.96767i	0.0678622	+	0.125710i
$246$	0.667474	−	0.484948i	0.0425566	−	0.0309192i
$247$	−4.95350	+	3.59893i	−0.315184	+	0.228994i
$248$	−2.29998	−	7.07860i	−0.146049	−	0.449491i
$249$	31.8410			2.01784
$250$	2.53117	+	10.8900i	0.160085	+	0.688747i
$251$	−15.4513			−0.975277			−0.487638	−	0.873046i	$-0.662142\pi$
$251$	−15.4513			−0.975277			−0.487638	+	0.873046i	$0.662142\pi$
$252$	0.753978	+	2.32051i	0.0474962	+	0.146178i
$253$	−1.59235	+	1.15691i	−0.100110	+	0.0727343i
$254$	−6.22143	+	4.52013i	−0.390367	+	0.283618i
$255$	9.88674	+	18.3144i	0.619132	+	1.14689i
$256$	−0.809017	−	0.587785i	−0.0505636	−	0.0367366i
$257$	−30.1014			−1.87767			−0.938836	−	0.344365i	$-0.888094\pi$
$257$	−30.1014			−1.87767			−0.938836	+	0.344365i	$0.888094\pi$
$258$	12.5185	+	9.09524i	0.779370	+	0.566245i
$259$	−2.65369	+	8.16721i	−0.164892	+	0.507485i
$260$	−6.82732	+	7.15978i	−0.423412	+	0.444031i
$261$	0.525665	+	1.61783i	0.0325378	+	0.100141i
$262$	2.91765	−	8.97959i	0.180253	−	0.554761i
$263$	−6.93879	+	21.3554i	−0.427864	+	1.31683i	0.472360	+	0.881406i	$0.343402\pi$
$263$	−6.93879	+	21.3554i	−0.427864	+	1.31683i	−0.900225	+	0.435426i	$0.856598\pi$
$264$	−0.621057	−	1.91142i	−0.0382234	−	0.117640i
$265$	−2.18795	−	1.05009i	−0.134405	−	0.0645066i
$266$	−0.427648	+	1.31617i	−0.0262208	+	0.0806993i
$267$	22.6683	+	16.4695i	1.38728	+	1.00792i
$268$	0.569478			0.0347864
$269$	13.6544	+	9.92050i	0.832523	+	0.604864i	0.920272	−	0.391279i	$-0.127967\pi$
$269$	13.6544	+	9.92050i	0.832523	+	0.604864i	−0.0877488	+	0.996143i	$0.527967\pi$
$270$	2.63339	+	1.26388i	0.160263	+	0.0769171i
$271$	13.0658	−	9.49283i	0.793688	−	0.576648i	−0.115368	−	0.993323i	$-0.536805\pi$
$271$	13.0658	−	9.49283i	0.793688	−	0.576648i	0.909056	+	0.416675i	$0.136805\pi$
$272$	3.22852	−	2.34566i	0.195758	−	0.142226i
$273$	−3.18881	−	9.81416i	−0.192996	−	0.593980i
$274$	−9.12600			−0.551322
$275$	4.15622	+	1.13520i	0.250630	+	0.0684551i
$276$	5.32752			0.320679
$277$	4.39717	+	13.5331i	0.264200	+	0.813124i	0.991877	+	0.127204i	$0.0406002\pi$
$277$	4.39717	+	13.5331i	0.264200	+	0.813124i	−0.727677	+	0.685920i	$0.759400\pi$
$278$	−8.69335	+	6.31609i	−0.521392	+	0.378814i
$279$	−14.6918	+	10.6742i	−0.879575	+	0.639048i
$280$	−0.297218	+	2.21623i	−0.0177622	+	0.132445i
$281$	−7.64997	−	5.55803i	−0.456359	−	0.331564i	0.335743	−	0.941954i	$-0.391013\pi$
$281$	−7.64997	−	5.55803i	−0.456359	−	0.331564i	−0.792101	+	0.610390i	$0.791013\pi$
$282$	12.3258			0.733993
$283$	18.8982	+	13.7304i	1.12338	+	0.816185i	0.984718	−	0.174154i	$-0.0557191\pi$
$283$	18.8982	+	13.7304i	1.12338	+	0.816185i	0.138664	+	0.990339i	$0.455719\pi$
$284$	−1.96649	+	6.05224i	−0.116690	+	0.359135i
$285$	−3.42856	−	6.35115i	−0.203090	−	0.376209i
$286$	1.17811	+	3.62584i	0.0696630	+	0.214401i
$287$	−0.109311	+	0.336424i	−0.00645240	+	0.0198585i
$288$	−0.753978	+	2.32051i	−0.0444286	+	0.136737i
$289$	−0.332055	−	1.02196i	−0.0195327	−	0.0601154i
$290$	−0.207217	+	1.54513i	−0.0121682	+	0.0907330i
$291$	−9.99080	+	30.7485i	−0.585671	+	1.80251i
$292$	8.61022	+	6.25569i	0.503875	+	0.366086i
$293$	24.0320			1.40396			0.701981	−	0.712195i	$-0.252299\pi$
$293$	24.0320			1.40396			0.701981	+	0.712195i	$0.252299\pi$
$294$	−1.88692	−	1.37093i	−0.110048	−	0.0799542i
$295$	23.5494	−	4.30583i	1.37110	−	0.250695i
$296$	−6.94744	+	5.04761i	−0.403812	+	0.293386i
$297$	0.910654	−	0.661629i	0.0528415	−	0.0383916i
$298$	−4.20790	−	12.9506i	−0.243757	−	0.750208i
$299$	−10.1060			−0.584444
$300$	−7.29517	−	9.09828i	−0.421187	−	0.525289i
$301$	−6.63436			−0.382398
$302$	0.992530	+	3.05469i	0.0571137	+	0.175778i
$303$	−36.6733	+	26.6447i	−2.10682	+	1.53070i
$304$	−1.11960	+	0.813435i	−0.0642133	+	0.0466537i
$305$	−17.6970	+	18.5588i	−1.01333	+	1.06267i
$306$	−7.87734	−	5.72322i	−0.450318	−	0.327175i
$307$	26.7287			1.52549			0.762744	−	0.646700i	$-0.223852\pi$
$307$	26.7287			1.52549			0.762744	+	0.646700i	$0.223852\pi$
$308$	0.697124	+	0.506490i	0.0397223	+	0.0288600i
$309$	−6.31631	+	19.4396i	−0.359322	+	1.10588i
$310$	−16.3714	+	2.99338i	−0.929831	+	0.170013i
$311$	−10.4684	−	32.2183i	−0.593607	−	1.82693i	−0.561542	−	0.827448i	$-0.689792\pi$
$311$	−10.4684	−	32.2183i	−0.593607	−	1.82693i	−0.0320649	−	0.999486i	$-0.510208\pi$
$312$	3.18881	−	9.81416i	0.180531	−	0.555617i
$313$	4.59529	−	14.1428i	0.259741	−	0.799401i	−0.733117	−	0.680102i	$-0.761935\pi$
$313$	4.59529	−	14.1428i	0.259741	−	0.799401i	0.992858	−	0.119299i	$-0.0380646\pi$
$314$	3.17694	+	9.77763i	0.179285	+	0.551784i
$315$	5.36686	−	0.981290i	0.302388	−	0.0552894i
$316$	3.90991	−	12.0335i	0.219950	−	0.676935i
$317$	9.06777	+	6.58812i	0.509297	+	0.370026i	0.812557	−	0.582882i	$-0.198075\pi$
$317$	9.06777	+	6.58812i	0.509297	+	0.370026i	−0.303260	+	0.952908i	$0.598075\pi$
$318$	2.53141			0.141954
$319$	0.486027	+	0.353119i	0.0272123	+	0.0197709i
$320$	−1.54312	+	1.61826i	−0.0862630	+	0.0904637i
$321$	10.7224	−	7.79025i	0.598463	−	0.434809i
$322$	−1.84793	+	1.34260i	−0.102981	+	0.0748203i
$323$	−1.70660	−	5.25238i	−0.0949579	−	0.292251i
$324$	−10.3665			−0.575919
$325$	13.8385	+	17.2589i	0.767622	+	0.957352i
$326$	−3.42957			−0.189946
$327$	−12.4517	−	38.3225i	−0.688582	−	2.11924i
$328$	−0.286179	+	0.207921i	−0.0158016	+	0.0114805i
$329$	−4.27541	+	3.10627i	−0.235711	+	0.171254i
$330$	−4.42072	+	0.808295i	−0.243353	+	0.0444952i
$331$	1.08435	+	0.787823i	0.0596010	+	0.0433027i	0.617187	−	0.786817i	$-0.288272\pi$
$331$	1.08435	+	0.787823i	0.0596010	+	0.0433027i	−0.557586	+	0.830119i	$0.688272\pi$
$332$	−13.6518			−0.749241
$333$	16.9512	+	12.3158i	0.928921	+	0.674901i
$334$	6.42743	−	19.7816i	0.351693	−	1.08240i
$335$	0.169259	−	1.26209i	0.00924762	−	0.0689555i
$336$	−0.720740	−	2.21821i	−0.0393196	−	0.121013i
$337$	0.402868	−	1.23990i	0.0219456	−	0.0675417i	−0.939484	−	0.342593i	$-0.888695\pi$
$337$	0.402868	−	1.23990i	0.0219456	−	0.0675417i	0.961430	+	0.275051i	$0.0886948\pi$
$338$	−2.03177	+	6.25315i	−0.110514	+	0.340127i
$339$	1.03535	+	3.18648i	0.0562325	+	0.173066i
$340$	−4.23893	−	7.85230i	−0.229888	−	0.425851i
$341$	−1.98187	+	6.09958i	−0.107324	+	0.330311i
$342$	2.73173	+	1.98472i	0.147715	+	0.107321i
$343$	1.00000			0.0539949
$344$	−5.36731	−	3.89958i	−0.289386	−	0.210251i
$345$	1.58343	−	11.8070i	0.0852493	−	0.635667i
$346$	1.08742	−	0.790060i	0.0584603	−	0.0424739i
$347$	2.73310	−	1.98571i	0.146720	−	0.106599i	−0.512004	−	0.858983i	$-0.671097\pi$
$347$	2.73310	−	1.98571i	0.146720	−	0.106599i	0.658724	+	0.752385i	$0.271097\pi$
$348$	−0.502492	−	1.54651i	−0.0269364	−	0.0829017i
$349$	−6.96709			−0.372940			−0.186470	−	0.982461i	$-0.559705\pi$
$349$	−6.96709			−0.372940			−0.186470	+	0.982461i	$0.559705\pi$
$350$	4.82332	+	1.31741i	0.257817	+	0.0704183i
$351$	5.77954			0.308489
$352$	0.266278	+	0.819519i	0.0141927	+	0.0436805i
$353$	12.6164	−	9.16636i	0.671504	−	0.487876i	−0.199024	−	0.979995i	$-0.563777\pi$
$353$	12.6164	−	9.16636i	0.671504	−	0.487876i	0.870528	+	0.492118i	$0.163777\pi$
$354$	−20.2018	+	14.6775i	−1.07371	+	0.780098i
$355$	12.8287	+	6.15703i	0.680875	+	0.326781i
$356$	−9.71902	−	7.06128i	−0.515107	−	0.374247i
$357$	9.30770			0.492616
$358$	−18.9058	−	13.7359i	−0.999202	−	0.725963i
$359$	3.74651	−	11.5306i	0.197733	−	0.608560i	−0.802201	−	0.597054i	$-0.796338\pi$
$359$	3.74651	−	11.5306i	0.197733	−	0.608560i	0.999934	−	0.0115055i	$-0.00366238\pi$
$360$	4.91867	+	2.36068i	0.259237	+	0.124419i
$361$	−5.27950	−	16.2486i	−0.277868	−	0.855191i
$362$	−5.77022	+	17.7589i	−0.303276	+	0.933387i
$363$	7.39298	−	22.7533i	0.388031	−	1.19424i
$364$	1.36720	+	4.20782i	0.0716609	+	0.220549i
$365$	16.4231	−	17.2229i	0.859626	−	0.901487i
$366$	8.26569	−	25.4392i	0.432055	−	1.32973i
$367$	12.5454	+	9.11477i	0.654865	+	0.475787i	0.864925	−	0.501901i	$-0.167366\pi$
$367$	12.5454	+	9.11477i	0.654865	+	0.475787i	−0.210060	+	0.977688i	$0.567366\pi$
$368$	−2.28417			−0.119071
$369$	0.698255	+	0.507312i	0.0363497	+	0.0264096i
$370$	9.12174	+	16.8973i	0.474217	+	0.878451i
$371$	−0.878059	+	0.637947i	−0.0455865	+	0.0331206i
$372$	14.0441	−	10.2037i	0.728154	−	0.529035i
$373$	8.88591	+	27.3480i	0.460095	+	1.41603i	0.865048	+	0.501689i	$0.167288\pi$
$373$	8.88591	+	27.3480i	0.460095	+	1.41603i	−0.404953	+	0.914338i	$0.632712\pi$
$374$	−3.43873			−0.177813
$375$	−22.3321	+	13.4636i	−1.15322	+	0.695256i
$376$	−5.28470			−0.272537
$377$	0.953197	+	2.93364i	0.0490922	+	0.151090i
$378$	1.05682	−	0.767824i	0.0543569	−	0.0394926i
$379$	−11.2974	+	8.20807i	−0.580310	+	0.421620i	−0.838836	−	0.544384i	$-0.816763\pi$
$379$	−11.2974	+	8.20807i	−0.580310	+	0.421620i	0.258526	+	0.966004i	$0.416763\pi$
$380$	1.46999	+	2.72305i	0.0754090	+	0.139690i
$381$	−14.5106	−	10.5426i	−0.743403	−	0.540114i
$382$	−25.2941			−1.29416
$383$	7.14294	+	5.18965i	0.364987	+	0.265179i	0.755129	−	0.655576i	$-0.227574\pi$
$383$	7.14294	+	5.18965i	0.364987	+	0.265179i	−0.390142	+	0.920755i	$0.627574\pi$
$384$	0.720740	−	2.21821i	0.0367801	−	0.113198i
$385$	1.32970	−	1.39445i	0.0677676	−	0.0710676i
$386$	−6.49622	−	19.9933i	−0.330649	−	1.01763i
$387$	−5.00216	+	15.3951i	−0.254274	+	0.782576i
$388$	4.28355	−	13.1834i	0.217464	−	0.669286i
$389$	6.08115	+	18.7159i	0.308327	+	0.948932i	0.978415	+	0.206651i	$0.0662563\pi$
$389$	6.08115	+	18.7159i	0.308327	+	0.948932i	−0.670088	+	0.742282i	$0.733744\pi$
$390$	−20.8026	−	9.98408i	−1.05338	−	0.505564i
$391$	2.81680	−	8.66923i	0.142452	−	0.438422i
$392$	0.809017	+	0.587785i	0.0408615	+	0.0296876i
$393$	22.0215			1.11084
$394$	15.7201	+	11.4213i	0.791967	+	0.575398i
$395$	−25.5068	−	12.2418i	−1.28339	−	0.615952i
$396$	1.70093	−	1.23580i	0.0854749	−	0.0621012i
$397$	21.6755	−	15.7482i	1.08786	−	0.790380i	0.108827	−	0.994061i	$-0.465291\pi$
$397$	21.6755	−	15.7482i	1.08786	−	0.790380i	0.979037	+	0.203681i	$0.0652905\pi$
$398$	2.78512	+	8.57172i	0.139606	+	0.429662i
$399$	−3.22776			−0.161590
$400$	3.12780	+	3.90088i	0.156390	+	0.195044i
$401$	14.4476			0.721481			0.360740	−	0.932666i	$-0.382524\pi$
$401$	14.4476			0.721481			0.360740	+	0.932666i	$0.382524\pi$
$402$	0.410446	+	1.26322i	0.0204712	+	0.0630038i
$403$	−26.6409	+	19.3557i	−1.32708	+	0.964178i
$404$	15.7236	−	11.4239i	0.782281	−	0.568360i
$405$	−3.08112	+	22.9746i	−0.153102	+	1.14162i
$406$	0.564037	+	0.409797i	0.0279927	+	0.0203379i
$407$	7.39979			0.366794
$408$	7.53008	+	5.47093i	0.372795	+	0.270851i
$409$	4.26071	−	13.1131i	0.210678	−	0.648401i	−0.788754	−	0.614709i	$-0.789273\pi$
$409$	4.26071	−	13.1131i	0.210678	−	0.648401i	0.999432	−	0.0336921i	$-0.0107266\pi$
$410$	0.375743	+	0.696036i	0.0185566	+	0.0343748i
$411$	−6.57748	−	20.2434i	−0.324443	−	0.998533i
$412$	2.70811	−	8.33472i	0.133419	−	0.410622i
$413$	3.30840	−	10.1822i	0.162796	−	0.501034i
$414$	1.72221	+	5.30043i	0.0846422	+	0.260502i
$415$	−4.05757	+	30.2555i	−0.199178	+	1.48519i
$416$	−1.36720	+	4.20782i	−0.0670326	+	0.206305i
$417$	−20.2761	−	14.7314i	−0.992923	−	0.721401i
$418$	1.19250			0.0583269
$419$	9.29073	+	6.75011i	0.453882	+	0.329764i	0.791126	−	0.611653i	$-0.209495\pi$
$419$	9.29073	+	6.75011i	0.453882	+	0.329764i	−0.337245	+	0.941417i	$0.609495\pi$
$420$	−5.13027	+	0.938032i	−0.250332	+	0.0457713i
$421$	−6.39505	+	4.64627i	−0.311676	+	0.226446i	−0.732615	−	0.680643i	$-0.761700\pi$
$421$	−6.39505	+	4.64627i	−0.311676	+	0.226446i	0.420940	+	0.907089i	$0.361700\pi$
$422$	−15.5816	+	11.3207i	−0.758501	+	0.551083i
$423$	3.98454	+	12.2632i	0.193735	+	0.596256i
$424$	−1.08534			−0.0527088
$425$	−18.6624	+	7.06059i	−0.905258	+	0.342489i
$426$	−14.8425			−0.719121
$427$	3.54391	+	10.9070i	0.171502	+	0.527828i
$428$	−4.59720	+	3.34006i	−0.222214	+	0.161448i
$429$	−7.19378	+	5.22658i	−0.347319	+	0.252342i
$430$	−10.2376	+	10.7362i	−0.493702	+	0.517743i
$431$	−14.7685	−	10.7300i	−0.711374	−	0.516844i	0.172242	−	0.985055i	$-0.444899\pi$
$431$	−14.7685	−	10.7300i	−0.711374	−	0.516844i	−0.883617	+	0.468211i	$0.844899\pi$
$432$	1.30630			0.0628494
$433$	−9.56606	−	6.95015i	−0.459715	−	0.334003i	0.333704	−	0.942678i	$-0.391701\pi$
$433$	−9.56606	−	6.95015i	−0.459715	−	0.334003i	−0.793420	+	0.608675i	$0.791701\pi$
$434$	−2.29998	+	7.07860i	−0.110402	+	0.339783i
$435$	−3.57677	+	0.653985i	−0.171493	+	0.0313562i
$436$	5.33867	+	16.4307i	0.255676	+	0.786890i
$437$	−0.976822	+	3.00635i	−0.0467277	+	0.143813i
$438$	−7.67070	+	23.6080i	−0.366520	+	1.12803i
$439$	5.82411	+	17.9248i	0.277970	+	0.855503i	0.988418	+	0.151754i	$0.0484921\pi$
$439$	5.82411	+	17.9248i	0.277970	+	0.855503i	−0.710449	+	0.703749i	$0.751508\pi$
$440$	1.89538	−	0.346556i	0.0903588	−	0.0165214i
$441$	0.753978	−	2.32051i	0.0359037	−	0.110500i
$442$	−14.2841	−	10.3780i	−0.679427	−	0.493632i
$443$	−3.54679			−0.168513			−0.0842565	−	0.996444i	$-0.526852\pi$
$443$	−3.54679			−0.168513			−0.0842565	+	0.996444i	$0.526852\pi$
$444$	−16.2040	−	11.7729i	−0.769006	−	0.558716i
$445$	−18.5381	+	19.4408i	−0.878789	+	0.921583i
$446$	−4.94328	+	3.59150i	−0.234071	+	0.170063i
$447$	25.6943	−	18.6680i	1.21530	−	0.882967i
$448$	0.309017	+	0.951057i	0.0145997	+	0.0449332i
$449$	20.0062			0.944153			0.472076	−	0.881558i	$-0.343505\pi$
$449$	20.0062			0.944153			0.472076	+	0.881558i	$0.343505\pi$
$450$	6.69373	−	10.1993i	0.315545	−	0.480797i
$451$	0.304812			0.0143531
$452$	−0.443906	−	1.36620i	−0.0208796	−	0.0642607i
$453$	−6.06059	+	4.40328i	−0.284752	+	0.206884i
$454$	5.30055	−	3.85107i	0.248767	−	0.180740i
$455$	9.73183	−	1.77939i	0.456235	−	0.0834191i
$456$	−2.61131	−	1.89723i	−0.122286	−	0.0888458i
$457$	37.5506			1.75654			0.878272	−	0.478162i	$-0.158697\pi$
$457$	37.5506			1.75654			0.878272	+	0.478162i	$0.158697\pi$
$458$	18.4372	+	13.3954i	0.861515	+	0.625927i
$459$	−1.61091	+	4.95787i	−0.0751909	+	0.231414i
$460$	−0.678897	+	5.06224i	−0.0316537	+	0.236028i
$461$	−1.90890	−	5.87500i	−0.0889064	−	0.273626i	0.896711	−	0.442616i	$-0.145949\pi$
$461$	−1.90890	−	5.87500i	−0.0889064	−	0.273626i	−0.985618	+	0.168990i	$0.945949\pi$
$462$	−0.621057	+	1.91142i	−0.0288942	+	0.0889271i
$463$	10.5727	−	32.5394i	0.491355	−	1.51224i	−0.331206	−	0.943558i	$-0.607456\pi$
$463$	10.5727	−	32.5394i	0.491355	−	1.51224i	0.822561	−	0.568677i	$-0.192544\pi$
$464$	0.215443	+	0.663066i	0.0100017	+	0.0307820i
$465$	−18.4395	−	34.1577i	−0.855109	−	1.58403i
$466$	−2.54546	+	7.83413i	−0.117916	+	0.362909i
$467$	−16.0604	−	11.6685i	−0.743184	−	0.539955i	0.150522	−	0.988607i	$-0.451904\pi$
$467$	−16.0604	−	11.6685i	−0.743184	−	0.539955i	−0.893707	+	0.448652i	$0.851904\pi$
$468$	10.7951			0.499004
$469$	−0.460717	−	0.334731i	−0.0212740	−	0.0154564i
$470$	−1.57071	+	11.7121i	−0.0724513	+	0.540238i
$471$	−19.3991	+	14.0943i	−0.893863	+	0.649429i
$472$	8.66151	−	6.29295i	0.398678	−	0.289657i
$473$	1.76658	+	5.43698i	0.0812276	+	0.249993i
$474$	29.5108			1.35548
$475$	6.47181	−	2.44850i	0.296947	−	0.112345i
$476$	−3.99067			−0.182912
$477$	0.818323	+	2.51854i	0.0374684	+	0.115316i
$478$	−0.855751	+	0.621739i	−0.0391411	+	0.0284377i
$479$	−2.99876	+	2.17873i	−0.137017	+	0.0995486i	−0.654182	−	0.756337i	$-0.726987\pi$
$479$	−2.99876	+	2.17873i	−0.137017	+	0.0995486i	0.517166	+	0.855885i	$0.326987\pi$
$480$	−4.70184	−	2.25662i	−0.214609	−	0.103000i
$481$	30.7380	+	22.3324i	1.40153	+	1.01827i
$482$	10.1912			0.464197
$483$	−4.31005	−	3.13144i	−0.196114	−	0.142485i
$484$	−3.16974	+	9.75545i	−0.144079	+	0.443429i
$485$	−27.9443	−	13.4117i	−1.26888	−	0.608993i
$486$	−6.26058	−	19.2681i	−0.283986	−	0.874018i
$487$	12.0923	−	37.2161i	0.547952	−	1.68642i	−0.165912	−	0.986141i	$-0.553057\pi$
$487$	12.0923	−	37.2161i	0.547952	−	1.68642i	0.713865	−	0.700284i	$-0.246943\pi$
$488$	−3.54391	+	10.9070i	−0.160425	+	0.493738i
$489$	−2.47183	−	7.60750i	−0.111780	−	0.344023i
$490$	1.54312	−	1.61826i	0.0697111	−	0.0731057i
$491$	−3.45850	+	10.6442i	−0.156080	+	0.480365i	−0.998269	−	0.0588178i	$-0.981267\pi$
$491$	−3.45850	+	10.6442i	−0.156080	+	0.480365i	0.842189	+	0.539183i	$0.181267\pi$
$492$	−0.667474	−	0.484948i	−0.0300920	−	0.0218632i
$493$	−2.78225			−0.125306
$494$	4.95350	+	3.59893i	0.222869	+	0.161924i
$495$	−2.23326	−	4.13695i	−0.100378	−	0.185942i
$496$	−6.02141	+	4.37481i	−0.270369	+	0.196435i
$497$	5.14835	−	3.74049i	0.230935	−	0.167784i
$498$	−9.83942	−	30.2826i	−0.440915	−	1.35700i
$499$	−3.49294			−0.156365			−0.0781827	−	0.996939i	$-0.524912\pi$
$499$	−3.49294			−0.156365			−0.0781827	+	0.996939i	$0.524912\pi$
$500$	9.57488	−	5.77250i	0.428202	−	0.258154i
$501$	48.5122			2.16737
$502$	4.77471	+	14.6951i	0.213106	+	0.655872i
$503$	−29.7302	+	21.6003i	−1.32561	+	0.963109i	−0.325761	+	0.945452i	$0.605621\pi$
$503$	−29.7302	+	21.6003i	−1.32561	+	0.963109i	−0.999844	+	0.0176565i	$0.994379\pi$
$504$	1.97394	−	1.43415i	0.0879263	−	0.0638822i
$505$	−20.6446	−	38.2426i	−0.918673	−	1.70177i
$506$	1.59235	+	1.15691i	0.0707886	+	0.0514309i
$507$	−15.3352			−0.681059
$508$	6.22143	+	4.52013i	0.276031	+	0.200549i
$509$	7.63948	−	23.5119i	0.338614	−	1.04215i	−0.626300	−	0.779582i	$-0.715432\pi$
$509$	7.63948	−	23.5119i	0.338614	−	1.04215i	0.964914	−	0.262565i	$-0.0845684\pi$
$510$	14.3629	−	15.0623i	0.636000	−	0.666971i
$511$	−3.28881	−	10.1219i	−0.145488	−	0.447767i
$512$	−0.309017	+	0.951057i	−0.0136568	+	0.0420312i
$513$	0.558637	−	1.71931i	0.0246644	−	0.0759094i
$514$	9.30184	+	28.6281i	0.410286	+	1.26273i
$515$	−17.6667	−	8.47902i	−0.778489	−	0.373630i
$516$	4.78165	−	14.7164i	0.210501	−	0.647854i
$517$	3.68409	+	2.67665i	0.162026	+	0.117719i
$518$	8.58751			0.377313
$519$	2.53627	+	1.84271i	0.111330	+	0.0808859i
$520$	8.91912	+	4.28067i	0.391129	+	0.187720i
$521$	11.3138	−	8.21994i	0.495666	−	0.360122i	−0.311693	−	0.950183i	$-0.600896\pi$
$521$	11.3138	−	8.21994i	0.495666	−	0.360122i	0.807359	+	0.590061i	$0.200896\pi$
$522$	1.37621	−	0.999874i	0.0602350	−	0.0437633i
$523$	7.85703	+	24.1815i	0.343564	+	1.05738i	0.962348	+	0.271820i	$0.0876255\pi$
$523$	7.85703	+	24.1815i	0.343564	+	1.05738i	−0.618784	+	0.785561i	$0.712374\pi$
$524$	−9.44170			−0.412463
$525$	0.554080	+	11.6487i	0.0241820	+	0.508389i
$526$	22.4544			0.979059
$527$	−9.17844	−	28.2483i	−0.399819	−	1.23052i
$528$	−1.62595	+	1.18132i	−0.0707603	+	0.0514104i
$529$	14.3864	−	10.4523i	0.625496	−	0.454449i
$530$	−0.322583	+	2.40536i	−0.0140121	+	0.104482i
$531$	−21.1334	−	15.3543i	−0.917112	−	0.666321i
$532$	1.38390			0.0599996
$533$	1.26616	+	0.919918i	0.0548434	+	0.0398461i
$534$	8.65852	−	26.6482i	0.374691	−	1.15318i
$535$	6.03597	+	11.1812i	0.260958	+	0.483404i
$536$	−0.175978	−	0.541606i	−0.00760111	−	0.0233938i
$537$	16.8429	−	51.8370i	0.726823	−	2.23693i
$538$	5.21552	−	16.0517i	0.224857	−	0.692038i
$539$	−0.266278	−	0.819519i	−0.0114694	−	0.0352992i
$540$	0.388256	−	2.89506i	0.0167079	−	0.124584i
$541$	1.44665	−	4.45233i	0.0621964	−	0.191421i	−0.915130	−	0.403159i	$-0.867912\pi$
$541$	1.44665	−	4.45233i	0.0621964	−	0.191421i	0.977326	+	0.211738i	$0.0679123\pi$
$542$	−13.0658	−	9.49283i	−0.561222	−	0.407752i
$543$	−43.5518			−1.86899
$544$	−3.22852	−	2.34566i	−0.138422	−	0.100569i
$545$	38.0010	−	6.94819i	1.62778	−	0.297628i
$546$	−8.34842	+	6.06548i	−0.357280	+	0.259579i
$547$	6.83925	−	4.96901i	0.292425	−	0.212459i	−0.431893	−	0.901925i	$-0.642154\pi$
$547$	6.83925	−	4.96901i	0.292425	−	0.212459i	0.724319	+	0.689465i	$0.242154\pi$
$548$	2.82009	+	8.67934i	0.120468	+	0.370763i
$549$	27.9819			1.19424
$550$	−0.204705	−	4.30360i	−0.00872865	−	0.183506i
$551$	0.964838			0.0411035
$552$	−1.64629	−	5.06677i	−0.0700709	−	0.215656i
$553$	−10.2363	+	7.43709i	−0.435291	+	0.316257i
$554$	11.5119	−	8.36391i	0.489095	−	0.355348i
$555$	−30.9075	+	32.4125i	−1.31195	+	1.37584i
$556$	8.69335	+	6.31609i	0.368680	+	0.267862i
$557$	25.6015			1.08477			0.542386	−	0.840130i	$-0.317521\pi$
$557$	25.6015			1.08477			0.542386	+	0.840130i	$0.317521\pi$
$558$	14.6918	+	10.6742i	0.621953	+	0.451875i
$559$	−9.07052	+	27.9162i	−0.383642	+	1.18073i
$560$	2.19960	−	0.402181i	0.0929502	−	0.0169952i
$561$	−2.47843	−	7.62783i	−0.104639	−	0.322047i
$562$	−2.92203	+	8.99307i	−0.123258	+	0.379350i
$563$	−3.04586	+	9.37420i	−0.128368	+	0.395076i	−0.994500	−	0.104740i	$-0.966599\pi$
$563$	−3.04586	+	9.37420i	−0.128368	+	0.395076i	0.866132	+	0.499816i	$0.166599\pi$
$564$	−3.80889	−	11.7226i	−0.160383	−	0.493609i
$565$	−3.15975	+	0.577736i	−0.132932	+	0.0243055i
$566$	7.21848	−	22.2162i	0.303415	−	0.933816i
$567$	8.38671	+	6.09330i	0.352209	+	0.255895i
$568$	6.36371			0.267015
$569$	10.1276	+	7.35812i	0.424570	+	0.308468i	0.779474	−	0.626434i	$-0.215486\pi$
$569$	10.1276	+	7.35812i	0.424570	+	0.308468i	−0.354904	+	0.934903i	$0.615486\pi$
$570$	−4.98082	+	5.22337i	−0.208623	+	0.218783i
$571$	−18.7122	+	13.5952i	−0.783081	+	0.568942i	−0.905902	−	0.423487i	$-0.860806\pi$
$571$	−18.7122	+	13.5952i	−0.783081	+	0.568942i	0.122821	+	0.992429i	$0.460806\pi$
$572$	3.08433	−	2.24090i	0.128962	−	0.0936965i
$573$	−18.2305	−	56.1076i	−0.761589	−	2.34393i
$574$	0.353737			0.0147647
$575$	11.0173	+	3.00918i	0.459453	+	0.125491i
$576$	2.43992			0.101664
$577$	11.8204	+	36.3794i	0.492089	+	1.51449i	0.821445	+	0.570288i	$0.193168\pi$
$577$	11.8204	+	36.3794i	0.492089	+	1.51449i	−0.329356	+	0.944206i	$0.606832\pi$
$578$	−0.869332	+	0.631607i	−0.0361595	+	0.0262714i
$579$	39.6673	−	28.8200i	1.64852	−	1.19772i
$580$	1.53354	−	0.280396i	0.0636767	−	0.0116428i
$581$	11.0446	+	8.02434i	0.458205	+	0.332906i
$582$	32.3309			1.34016
$583$	0.756617	+	0.549714i	0.0313359	+	0.0227668i
$584$	3.28881	−	10.1219i	0.136092	−	0.418848i
$585$	3.20850	−	23.9244i	0.132655	−	0.989152i
$586$	−7.42629	−	22.8558i	−0.306777	−	0.944163i
$587$	4.80508	−	14.7885i	0.198327	−	0.610388i	−0.801595	−	0.597868i	$-0.796015\pi$
$587$	4.80508	−	14.7885i	0.198327	−	0.610388i	0.999922	−	0.0125199i	$-0.00398530\pi$
$588$	−0.720740	+	2.21821i	−0.0297228	+	0.0914775i
$589$	3.18293	+	9.79606i	0.131150	+	0.403640i
$590$	−11.3723	−	21.0662i	−0.468188	−	0.867284i
$591$	−14.0048	+	43.1023i	−0.576080	+	1.77299i
$592$	6.94744	+	5.04761i	0.285538	+	0.207456i
$593$	−11.4111			−0.468599			−0.234300	−	0.972164i	$-0.575280\pi$
$593$	−11.4111			−0.468599			−0.234300	+	0.972164i	$0.575280\pi$
$594$	−0.910654	−	0.661629i	−0.0373646	−	0.0271470i
$595$	−1.18610	+	8.84423i	−0.0486253	+	0.362578i
$596$	−11.0164	+	8.00391i	−0.451251	+	0.327853i
$597$	−17.0065	+	12.3560i	−0.696031	+	0.505696i
$598$	3.12292	+	9.61137i	0.127706	+	0.393038i
$599$	13.6745			0.558725			0.279362	−	0.960186i	$-0.409877\pi$
$599$	13.6745			0.558725			0.279362	+	0.960186i	$0.409877\pi$
$600$	−6.39865	+	9.74964i	−0.261224	+	0.398027i
$601$	39.1796			1.59817			0.799084	−	0.601220i	$-0.205318\pi$
$601$	39.1796			1.59817			0.799084	+	0.601220i	$0.205318\pi$
$602$	2.05013	+	6.30965i	0.0835571	+	0.257162i
$603$	−1.12412	+	0.816718i	−0.0457775	+	0.0332593i
$604$	2.59848	−	1.88790i	0.105731	−	0.0768177i
$605$	20.6782	+	9.92435i	0.840688	+	0.403482i
$606$	36.6733	+	26.6447i	1.48975	+	1.08237i
$607$	−8.38016			−0.340140			−0.170070	−	0.985432i	$-0.554399\pi$
$607$	−8.38016			−0.340140			−0.170070	+	0.985432i	$0.554399\pi$
$608$	1.11960	+	0.813435i	0.0454057	+	0.0329892i
$609$	−0.502492	+	1.54651i	−0.0203620	+	0.0626678i
$610$	23.1191	+	11.0959i	0.936067	+	0.449259i
$611$	7.22525	+	22.2370i	0.292302	+	0.899614i
$612$	−3.00888	+	9.26037i	−0.121627	+	0.374328i
$613$	0.541091	−	1.66531i	0.0218545	−	0.0672611i	−0.939534	−	0.342454i	$-0.888742\pi$
$613$	0.541091	−	1.66531i	0.0218545	−	0.0672611i	0.961389	+	0.275193i	$0.0887418\pi$
$614$	−8.25963	−	25.4205i	−0.333331	−	1.02589i
$615$	−1.27314	+	1.33514i	−0.0513380	+	0.0538380i
$616$	0.266278	−	0.819519i	0.0107286	−	0.0330193i
$617$	7.21917	+	5.24503i	0.290633	+	0.211157i	0.723542	−	0.690281i	$-0.242513\pi$
$617$	7.21917	+	5.24503i	0.290633	+	0.211157i	−0.432909	+	0.901438i	$0.642513\pi$
$618$	20.4400			0.822217
$619$	−12.5338	−	9.10631i	−0.503774	−	0.366013i	0.306683	−	0.951812i	$-0.400781\pi$
$619$	−12.5338	−	9.10631i	−0.503774	−	0.366013i	−0.810457	+	0.585799i	$0.800781\pi$
$620$	7.90590	+	14.6451i	0.317509	+	0.588161i
$621$	2.41396	−	1.75384i	0.0968687	−	0.0703793i
$622$	−27.4066	+	19.9120i	−1.09890	+	0.798399i
$623$	3.71234	+	11.4254i	0.148732	+	0.457749i
$624$	−10.3192			−0.413099
$625$	−9.94734	−	22.9358i	−0.397894	−	0.917432i
$626$	−14.8707			−0.594351
$627$	0.859480	+	2.64521i	0.0343243	+	0.105639i
$628$	8.31735	−	6.04291i	0.331898	−	0.241138i
$629$	−27.7249	+	20.1433i	−1.10547	+	0.803168i
$630$	−2.59171	−	4.80095i	−0.103256	−	0.191275i
$631$	4.70064	+	3.41521i	0.187129	+	0.135957i	0.677406	−	0.735610i	$-0.263104\pi$
$631$	4.70064	+	3.41521i	0.187129	+	0.135957i	−0.490276	+	0.871567i	$0.663104\pi$
$632$	−12.6527			−0.503299
$633$	−36.3420	−	26.4040i	−1.44447	−	1.04947i
$634$	3.46358	−	10.6598i	0.137556	−	0.423355i
$635$	11.8668	−	12.4446i	0.470918	−	0.493850i
$636$	−0.782249	−	2.40751i	−0.0310182	−	0.0954641i
$637$	1.36720	−	4.20782i	0.0541705	−	0.166720i
$638$	0.185646	−	0.571359i	0.00734978	−	0.0226203i
$639$	−4.79810	−	14.7670i	−0.189810	−	0.584174i
$640$	2.01591	+	0.967523i	0.0796859	+	0.0382447i
$641$	−2.54773	+	7.84110i	−0.100629	+	0.309705i	−0.988680	−	0.150041i	$-0.952059\pi$
$641$	−2.54773	+	7.84110i	−0.100629	+	0.309705i	0.888051	+	0.459746i	$0.152059\pi$
$642$	−10.7224	−	7.79025i	−0.423178	−	0.307456i
$643$	−37.4693			−1.47765			−0.738823	−	0.673899i	$-0.764618\pi$
$643$	−37.4693			−1.47765			−0.738823	+	0.673899i	$0.764618\pi$
$644$	1.84793	+	1.34260i	0.0728187	+	0.0529059i
$645$	−31.1937	−	14.9712i	−1.22825	−	0.589491i
$646$	−4.46795	+	3.24615i	−0.175789	+	0.127718i
$647$	−0.465786	+	0.338414i	−0.0183119	+	0.0133044i	−0.596904	−	0.802313i	$-0.703603\pi$
$647$	−0.465786	+	0.338414i	−0.0183119	+	0.0133044i	0.578592	+	0.815617i	$0.303603\pi$
$648$	3.20344	+	9.85917i	0.125843	+	0.387305i
$649$	−9.22547			−0.362131
$650$	12.1379	−	18.4945i	0.476086	−	0.725414i
$651$	−17.3595			−0.680372
$652$	1.05979	+	3.26171i	0.0415048	+	0.127739i
$653$	−1.73678	+	1.26185i	−0.0679655	+	0.0493798i	−0.621249	−	0.783613i	$-0.713375\pi$
$653$	−1.73678	+	1.26185i	−0.0679655	+	0.0493798i	0.553284	+	0.832993i	$0.313375\pi$
$654$	−32.5990	+	23.6846i	−1.27472	+	0.926141i
$655$	−2.80624	+	20.9250i	−0.109649	+	0.817606i
$656$	0.286179	+	0.207921i	0.0111734	+	0.00811796i
$657$	−25.9677			−1.01309
$658$	4.27541	+	3.10627i	0.166673	+	0.121095i
$659$	8.30657	−	25.5650i	0.323578	−	0.995871i	−0.648500	−	0.761214i	$-0.724603\pi$
$659$	8.30657	−	25.5650i	0.323578	−	0.995871i	0.972078	−	0.234656i	$-0.0753965\pi$
$660$	2.13481	+	3.95458i	0.0830974	+	0.153932i
$661$	−1.69433	−	5.21460i	−0.0659016	−	0.202824i	0.912683	−	0.408667i	$-0.134006\pi$
$661$	−1.69433	−	5.21460i	−0.0659016	−	0.202824i	−0.978585	+	0.205843i	$0.934006\pi$
$662$	0.414183	−	1.27472i	0.0160977	−	0.0495436i
$663$	12.7255	−	39.1651i	0.494218	−	1.52105i
$664$	4.21865	+	12.9837i	0.163715	+	0.503864i
$665$	0.411320	−	3.06703i	0.0159503	−	0.118934i
$666$	6.47479	−	19.9274i	0.250893	−	0.772170i
$667$	1.28836	+	0.936046i	0.0498854	+	0.0362439i
$668$	−20.7996			−0.804760
$669$	−11.5295	−	8.37670i	−0.445757	−	0.323862i
$670$	−1.25263	+	0.229033i	−0.0483931	+	0.00884831i
$671$	7.99485	−	5.80860i	0.308638	−	0.224239i
$672$	−1.88692	+	1.37093i	−0.0727896	+	0.0528848i
$673$	−1.10973	−	3.41539i	−0.0427769	−	0.131654i	0.927387	−	0.374103i	$-0.122049\pi$
$673$	−1.10973	−	3.41539i	−0.0427769	−	0.131654i	−0.970164	+	0.242449i	$0.922049\pi$
$674$	−1.30371			−0.0502170
$675$	−6.30071	−	1.72093i	−0.242515	−	0.0662386i
$676$	6.57495			0.252883
$677$	8.87333	+	27.3093i	0.341030	+	1.04958i	0.963675	+	0.267077i	$0.0860579\pi$
$677$	8.87333	+	27.3093i	0.341030	+	1.04958i	−0.622645	+	0.782504i	$0.713942\pi$
$678$	2.71058	−	1.96935i	0.104099	−	0.0756326i
$679$	−11.2145	+	8.14780i	−0.430372	+	0.312684i
$680$	−6.15808	+	6.45796i	−0.236152	+	0.247651i
$681$	12.3628	+	8.98211i	0.473744	+	0.344195i
$682$	6.41347			0.245585
$683$	14.7347	+	10.7054i	0.563808	+	0.409630i	0.832850	−	0.553498i	$-0.186707\pi$
$683$	14.7347	+	10.7054i	0.563808	+	0.409630i	−0.269043	+	0.963128i	$0.586707\pi$
$684$	1.04343	−	3.21135i	0.0398965	−	0.122789i
$685$	20.0736	−	3.67030i	0.766972	−	0.140235i
$686$	−0.309017	−	0.951057i	−0.0117983	−	0.0363115i
$687$	−16.4254	+	50.5523i	−0.626669	+	1.92869i
$688$	−2.05013	+	6.30965i	−0.0781605	+	0.240553i
$689$	1.48388	+	4.56691i	0.0565313	+	0.173986i
$690$	−11.7184	+	2.14262i	−0.446113	+	0.0815683i
$691$	−12.1838	+	37.4979i	−0.463494	+	1.42649i	0.397374	+	0.917657i	$0.369922\pi$
$691$	−12.1838	+	37.4979i	−0.463494	+	1.42649i	−0.860867	+	0.508830i	$0.830078\pi$
$692$	−1.08742	−	0.790060i	−0.0413377	−	0.0300336i
$693$	−2.10247			−0.0798660
$694$	−2.73310	−	1.98571i	−0.103747	−	0.0753766i
$695$	16.5817	−	17.3892i	0.628980	−	0.659609i
$696$	−1.31554	+	0.955796i	−0.0498654	+	0.0362294i
$697$	−1.14205	+	0.829745i	−0.0432581	+	0.0314288i
$698$	2.15295	+	6.62610i	0.0814904	+	0.250802i
$699$	−19.2124			−0.726678
$700$	−0.237562	−	4.99435i	−0.00897898	−	0.188769i
$701$	−6.34305			−0.239574			−0.119787	−	0.992800i	$-0.538221\pi$
$701$	−6.34305			−0.239574			−0.119787	+	0.992800i	$0.538221\pi$
$702$	−1.78598	−	5.49667i	−0.0674074	−	0.207459i
$703$	9.61456	−	6.98538i	0.362620	−	0.263459i
$704$	0.697124	−	0.506490i	0.0262739	−	0.0190891i
$705$	−27.1119	+	4.95721i	−1.02109	+	0.186699i
$706$	−12.6164	−	9.16636i	−0.474825	−	0.344981i
$707$	−19.4355			−0.730947
$708$	20.2018	+	14.6775i	0.759230	+	0.551613i
$709$	−5.71112	+	17.5770i	−0.214486	+	0.660119i	0.784704	+	0.619871i	$0.212815\pi$
$709$	−5.71112	+	17.5770i	−0.214486	+	0.660119i	−0.999190	+	0.0402485i	$0.987185\pi$
$710$	1.89141	−	14.1034i	0.0709833	−	0.529292i
$711$	9.53989	+	29.3607i	0.357774	+	1.10111i
$712$	−3.71234	+	11.4254i	−0.139126	+	0.428185i
$713$	−5.25354	+	16.1687i	−0.196746	+	0.605523i
$714$	−2.87624	−	8.85215i	−0.107640	−	0.331283i
$715$	−4.04961	−	7.50160i	−0.151447	−	0.280544i
$716$	−7.22137	+	22.2251i	−0.269875	+	0.830591i
$717$	−1.99592	−	1.45012i	−0.0745391	−	0.0541558i
$718$	−12.1240			−0.452462
$719$	−26.5637	−	19.2997i	−0.990660	−	0.719757i	−0.0305947	−	0.999532i	$-0.509740\pi$
$719$	−26.5637	−	19.2997i	−0.990660	−	0.719757i	−0.960066	+	0.279775i	$0.909740\pi$
$720$	0.725190	−	5.40743i	0.0270262	−	0.201523i
$721$	−7.08993	+	5.15114i	−0.264043	+	0.191838i
$722$	−13.8219	+	10.0422i	−0.514398	+	0.373732i
$723$	7.34521	+	22.6062i	0.273171	+	0.840735i
$724$	18.6728			0.693970
$725$	−0.165625	−	3.48201i	−0.00615116	−	0.129318i
$726$	−23.9242			−0.887910
$727$	−13.1128	−	40.3569i	−0.486326	−	1.49676i	−0.830052	−	0.557686i	$-0.811689\pi$
$727$	−13.1128	−	40.3569i	−0.486326	−	1.49676i	0.343726	−	0.939070i	$-0.388311\pi$
$728$	3.57938	−	2.60057i	0.132661	−	0.0963836i
$729$	13.0683	−	9.49465i	0.484010	−	0.351654i
$730$	−21.4550	−	10.2972i	−0.794084	−	0.381115i
$731$	−21.4192	−	15.5619i	−0.792217	−	0.575579i
$732$	−26.7483			−0.988647
$733$	−12.8110	−	9.30773i	−0.473185	−	0.343789i	0.325497	−	0.945543i	$-0.394469\pi$
$733$	−12.8110	−	9.30773i	−0.473185	−	0.343789i	−0.798681	+	0.601755i	$0.794469\pi$
$734$	4.79192	−	14.7480i	0.176873	−	0.544359i
$735$	4.70184	+	2.25662i	0.173430	+	0.0832365i
$736$	0.705847	+	2.17238i	0.0260179	+	0.0800748i
$737$	−0.151639	+	0.466698i	−0.00558571	+	0.0171910i
$738$	0.266710	−	0.820848i	0.00981772	−	0.0302158i
$739$	0.615651	+	1.89478i	0.0226471	+	0.0697006i	0.961741	−	0.273959i	$-0.0883333\pi$
$739$	0.615651	+	1.89478i	0.0226471	+	0.0697006i	−0.939094	+	0.343660i	$0.888333\pi$
$740$	13.2516	−	13.8969i	0.487137	−	0.510859i
$741$	−4.41300	+	13.5818i	−0.162115	+	0.498940i
$742$	0.878059	+	0.637947i	0.0322346	+	0.0234198i
$743$	19.4460			0.713405			0.356702	−	0.934218i	$-0.383901\pi$
$743$	19.4460			0.713405			0.356702	+	0.934218i	$0.383901\pi$
$744$	−14.0441	−	10.2037i	−0.514883	−	0.374084i
$745$	14.4642	+	26.7938i	0.529927	+	0.981649i
$746$	23.2636	−	16.9020i	0.851741	−	0.618826i
$747$	26.9479	−	19.5788i	0.985971	−	0.716350i
$748$	1.06263	+	3.27043i	0.0388535	+	0.119579i
$749$	5.68246			0.207632
$750$	19.7056	+	17.0786i	0.719547	+	0.623623i
$751$	23.0775			0.842110			0.421055	−	0.907035i	$-0.361660\pi$
$751$	23.0775			0.842110			0.421055	+	0.907035i	$0.361660\pi$
$752$	1.63306	+	5.02604i	0.0595516	+	0.183281i
$753$	−29.1554	+	21.1826i	−1.06248	+	0.771938i
$754$	2.49550	−	1.81309i	0.0908809	−	0.0660288i
$755$	−3.41171	−	6.31993i	−0.124165	−	0.230006i
$756$	−1.05682	−	0.767824i	−0.0384362	−	0.0279255i
$757$	−13.0180			−0.473148			−0.236574	−	0.971614i	$-0.576025\pi$
$757$	−13.0180			−0.473148			−0.236574	+	0.971614i	$0.576025\pi$
$758$	11.2974	+	8.20807i	0.410341	+	0.298130i
$759$	−1.41860	+	4.36600i	−0.0514919	+	0.158476i
$760$	2.13552	−	2.23952i	0.0774635	−	0.0812357i
$761$	2.34010	+	7.20208i	0.0848285	+	0.261075i	0.984470	−	0.175555i	$-0.0561719\pi$
$761$	2.34010	+	7.20208i	0.0848285	+	0.261075i	−0.899641	+	0.436630i	$0.856172\pi$
$762$	−5.54257	+	17.0583i	−0.200786	+	0.617956i
$763$	5.33867	−	16.4307i	0.193273	−	0.594833i
$764$	7.81630	+	24.0561i	0.282784	+	0.870319i
$765$	19.6288	+	9.42071i	0.709681	+	0.340606i
$766$	2.72836	−	8.39703i	0.0985796	−	0.303397i
$767$	−38.3216	−	27.8423i	−1.38371	−	1.00533i
$768$	−2.33236			−0.0841620
$769$	−22.6706	−	16.4712i	−0.817524	−	0.593966i	0.0984783	−	0.995139i	$-0.468603\pi$
$769$	−22.6706	−	16.4712i	−0.817524	−	0.593966i	−0.916002	+	0.401173i	$0.868603\pi$
$770$	−1.73710	−	0.833708i	−0.0626006	−	0.0300447i
$771$	−56.7990	+	41.2669i	−2.04556	+	1.48619i
$772$	−17.0073	+	12.3566i	−0.612107	+	0.444722i
$773$	3.02268	+	9.30284i	0.108718	+	0.334600i	0.990585	−	0.136898i	$-0.0437133\pi$
$773$	3.02268	+	9.30284i	0.108718	+	0.334600i	−0.881867	+	0.471498i	$0.843713\pi$
$774$	16.1873			0.581842
$775$	34.8066	−	13.1685i	1.25029	−	0.473026i
$776$	−13.8619			−0.497612
$777$	6.18936	+	19.0489i	0.222042	+	0.683375i
$778$	15.9207	−	11.5670i	0.570784	−	0.414699i
$779$	0.396043	−	0.287742i	0.0141897	−	0.0103094i
$780$	−3.06706	+	22.8697i	−0.109818	+	0.818868i
$781$	−4.43629	−	3.22316i	−0.158743	−	0.115334i
$782$	−9.11537			−0.325965
$783$	−0.736802	−	0.535318i	−0.0263312	−	0.0191307i
$784$	0.309017	−	0.951057i	0.0110363	−	0.0339663i
$785$	−10.9204	−	20.2292i	−0.389765	−	0.722011i
$786$	−6.80501	−	20.9437i	−0.242727	−	0.747036i
$787$	−0.0936544	+	0.288239i	−0.00333842	+	0.0102746i	−0.952712	−	0.303875i	$-0.901719\pi$
$787$	−0.0936544	+	0.288239i	−0.00333842	+	0.0102746i	0.949373	+	0.314150i	$0.101719\pi$
$788$	6.00454	−	18.4801i	0.213903	−	0.658326i
$789$	16.1838	+	49.8086i	0.576158	+	1.77323i
$790$	−3.76062	+	28.0413i	−0.133797	+	0.997666i
$791$	−0.443906	+	1.36620i	−0.0157835	+	0.0485765i
$792$	−1.70093	−	1.23580i	−0.0604399	−	0.0439122i
$793$	50.7400			1.80183
$794$	−21.6755	−	15.7482i	−0.769236	−	0.558883i
$795$	−5.56809	+	1.01808i	−0.197480	+	0.0361077i
$796$	7.29154	−	5.29762i	0.258442	−	0.187769i
$797$	−40.7120	+	29.5790i	−1.44209	+	1.04774i	−0.454492	+	0.890751i	$0.650179\pi$
$797$	−40.7120	+	29.5790i	−1.44209	+	1.04774i	−0.987600	+	0.156990i	$0.949821\pi$
$798$	0.997432	+	3.06978i	0.0353087	+	0.108669i
$799$	−21.0895			−0.746092
$800$	2.74342	−	4.18015i	0.0969944	−	0.147791i
$801$	29.3117			1.03568
$802$	−4.46457	−	13.7405i	−0.157649	−	0.485195i
$803$	−7.41936	+	5.39048i	−0.261824	+	0.190226i
$804$	1.07456	−	0.780714i	0.0378968	−	0.0275337i
$805$	3.52475	−	3.69639i	0.124231	−	0.130281i
$806$	26.6409	+	19.3557i	0.938385	+	0.681777i
$807$	39.3651			1.38572
$808$	−15.7236	−	11.4239i	−0.553156	−	0.401891i
$809$	1.59316	−	4.90326i	0.0560127	−	0.172389i	−0.919136	−	0.393940i	$-0.871112\pi$
$809$	1.59316	−	4.90326i	0.0560127	−	0.172389i	0.975149	+	0.221551i	$0.0711118\pi$
$810$	22.8023	−	4.16922i	0.801190	−	0.146492i
$811$	2.75069	+	8.46576i	0.0965899	+	0.297273i	0.987665	−	0.156583i	$-0.0500479\pi$
$811$	2.75069	+	8.46576i	0.0965899	+	0.297273i	−0.891075	+	0.453856i	$0.850048\pi$
$812$	0.215443	−	0.663066i	0.00756057	−	0.0232690i
$813$	11.6401	−	35.8245i	0.408235	−	1.25642i
$814$	−2.28666	−	7.03762i	−0.0801475	−	0.246669i
$815$	7.54368	−	1.37931i	0.264244	−	0.0483149i
$816$	2.87624	−	8.85215i	0.100688	−	0.309887i
$817$	7.42782	+	5.39663i	0.259866	+	0.188804i
$818$	−13.7879			−0.482084
$819$	−8.73342	−	6.34520i	−0.305170	−	0.221719i
$820$	0.545858	−	0.572440i	0.0190622	−	0.0199905i
$821$	−38.1758	+	27.7363i	−1.33234	+	0.968004i	−0.332655	+	0.943049i	$0.607944\pi$
$821$	−38.1758	+	27.7363i	−1.33234	+	0.968004i	−0.999689	+	0.0249552i	$0.992056\pi$
$822$	−17.2201	+	12.5111i	−0.600619	+	0.436375i
$823$	−0.335141	−	1.03146i	−0.0116823	−	0.0359544i	0.945045	−	0.326939i	$-0.106017\pi$
$823$	−0.335141	−	1.03146i	−0.0116823	−	0.0359544i	−0.956728	+	0.290985i	$0.906017\pi$
$824$	−8.76364			−0.305296
$825$	9.39875	−	3.55586i	0.327222	−	0.123799i
$826$	−10.7062			−0.372517
$827$	12.0425	+	37.0630i	0.418759	+	1.28881i	0.908845	+	0.417133i	$0.136965\pi$
$827$	12.0425	+	37.0630i	0.418759	+	1.28881i	−0.490087	+	0.871674i	$0.663035\pi$
$828$	4.50882	−	3.27585i	0.156692	−	0.113844i
$829$	−43.6457	+	31.7105i	−1.51588	+	1.10135i	−0.552395	+	0.833583i	$0.686286\pi$
$829$	−43.6457	+	31.7105i	−1.51588	+	1.10135i	−0.963484	+	0.267767i	$0.913714\pi$
$830$	30.0286	−	5.49050i	1.04231	−	0.190578i
$831$	26.8500	+	19.5077i	0.931417	+	0.676714i
$832$	4.42436			0.153387
$833$	3.22852	+	2.34566i	0.111862	+	0.0812722i
$834$	−7.74476	+	23.8359i	−0.268179	+	0.825371i
$835$	−6.18201	+	46.0966i	−0.213937	+	1.59524i
$836$	−0.368501	−	1.13413i	−0.0127449	−	0.0392247i
$837$	3.00446	−	9.24678i	0.103849	−	0.319615i
$838$	3.54874	−	10.9219i	0.122589	−	0.377291i
$839$	9.91498	+	30.5152i	0.342303	+	1.05350i	0.963012	+	0.269459i	$0.0868450\pi$
$839$	9.91498	+	30.5152i	0.342303	+	1.05350i	−0.620709	+	0.784041i	$0.713155\pi$
$840$	2.47746	+	4.58931i	0.0854806	+	0.158346i
$841$	−8.81129	+	27.1184i	−0.303838	+	0.935116i
$842$	6.39505	+	4.64627i	0.220388	+	0.160121i
$843$	−22.0546			−0.759599
$844$	15.5816	+	11.3207i	0.536341	+	0.389675i
$845$	1.95420	−	14.5716i	0.0672264	−	0.501278i
$846$	10.4317	−	7.57905i	0.358648	−	0.260573i
$847$	8.29848	−	6.02920i	0.285139	−	0.207166i
$848$	0.335389	+	1.03222i	0.0115173	+	0.0354466i
$849$	54.4828			1.86985
$850$	12.4820	+	15.5671i	0.428129	+	0.533948i
$851$	19.6153			0.672405
$852$	4.58658	+	14.1160i	0.157134	+	0.483608i
$853$	−4.79948	+	3.48703i	−0.164331	+	0.119393i	−0.666911	−	0.745137i	$-0.732384\pi$
$853$	−4.79948	+	3.48703i	−0.164331	+	0.119393i	0.502580	+	0.864530i	$0.332384\pi$
$854$	9.27808	−	6.74092i	0.317489	−	0.230669i
$855$	−6.80694	−	3.26695i	−0.232793	−	0.111727i
$856$	4.59720	+	3.34006i	0.157129	+	0.114161i
$857$	−11.4247			−0.390261			−0.195130	−	0.980777i	$-0.562513\pi$
$857$	−11.4247			−0.390261			−0.195130	+	0.980777i	$0.562513\pi$
$858$	7.19378	+	5.22658i	0.245591	+	0.178433i
$859$	14.8917	−	45.8321i	0.508100	−	1.56377i	−0.287396	−	0.957812i	$-0.592790\pi$
$859$	14.8917	−	45.8321i	0.508100	−	1.56377i	0.795496	−	0.605959i	$-0.207210\pi$
$860$	13.3743	+	6.41890i	0.456059	+	0.218883i
$861$	0.254952	+	0.784663i	0.00868875	+	0.0267412i
$862$	−5.64107	+	17.3614i	−0.192136	+	0.591333i
$863$	14.2570	−	43.8784i	0.485312	−	1.49364i	−0.346216	−	0.938155i	$-0.612533\pi$
$863$	14.2570	−	43.8784i	0.485312	−	1.49364i	0.831528	−	0.555483i	$-0.187467\pi$
$864$	−0.403669	−	1.24237i	−0.0137331	−	0.0422662i
$865$	−2.07415	+	2.17516i	−0.0705234	+	0.0739576i
$866$	−3.65391	+	11.2456i	−0.124165	+	0.382140i
$867$	−2.02760	−	1.47314i	−0.0688609	−	0.0500304i
$868$	7.44288			0.252628
$869$	8.82053	+	6.40849i	0.299216	+	0.217393i
$870$	1.72726	+	3.19962i	0.0585595	+	0.108477i
$871$	−2.03838	+	1.48097i	−0.0690678	+	0.0501807i
$872$	13.9768	−	10.1548i	0.473315	−	0.343883i
$873$	10.4515	+	32.1665i	0.353731	+	1.08867i
$874$	3.16106			0.106924
$875$	−11.1392	−	0.957922i	−0.376575	−	0.0323837i
$876$	24.8229			0.838689
$877$	−4.91297	−	15.1206i	−0.165899	−	0.510586i	0.833202	−	0.552969i	$-0.186505\pi$
$877$	−4.91297	−	15.1206i	−0.165899	−	0.510586i	−0.999101	+	0.0423829i	$0.986505\pi$
$878$	15.2477	−	11.0781i	0.514586	−	0.373868i
$879$	45.3465	−	32.9461i	1.52950	−	1.11125i
$880$	−0.915300	−	1.69552i	−0.0308547	−	0.0571561i
$881$	−19.6447	−	14.2727i	−0.661848	−	0.480861i	0.205438	−	0.978670i	$-0.434138\pi$
$881$	−19.6447	−	14.2727i	−0.661848	−	0.480861i	−0.867287	+	0.497809i	$0.834138\pi$
$882$	−2.43992			−0.0821565
$883$	26.6599	+	19.3695i	0.897175	+	0.651836i	0.937739	−	0.347341i	$-0.112915\pi$
$883$	26.6599	+	19.3695i	0.897175	+	0.651836i	−0.0405635	+	0.999177i	$0.512915\pi$
$884$	−5.45605	+	16.7920i	−0.183507	+	0.564776i
$885$	38.5329	−	40.4093i	1.29527	−	1.35835i
$886$	1.09602	+	3.37320i	0.0368215	+	0.113325i
$887$	7.65374	−	23.5558i	0.256987	−	0.790926i	−0.736444	−	0.676498i	$-0.763497\pi$
$887$	7.65374	−	23.5558i	0.256987	−	0.790926i	0.993432	−	0.114427i	$-0.0365034\pi$
$888$	−6.18936	+	19.0489i	−0.207701	+	0.639239i
$889$	−2.37638	−	7.31373i	−0.0797011	−	0.245295i
$890$	24.2179	+	11.6232i	0.811786	+	0.389611i
$891$	2.76038	−	8.49557i	0.0924762	−	0.284612i
$892$	4.94328	+	3.59150i	0.165513	+	0.120252i
$893$	7.31349			0.244736
$894$	−25.6943	−	18.6680i	−0.859347	−	0.624352i
$895$	47.1095	+	22.6099i	1.57470	+	0.755766i
$896$	0.809017	−	0.587785i	0.0270274	−	0.0196365i
$897$	−19.0692	+	13.8546i	−0.636703	+	0.462592i
$898$	−6.18227	−	19.0271i	−0.206305	−	0.634941i
$899$	5.18909			0.173066
$900$	−11.7685	−	3.21437i	−0.392285	−	0.107146i
$901$	−4.33124			−0.144294
$902$	−0.0941922	−	0.289894i	−0.00313626	−	0.00965241i
$903$	−12.5185	+	9.09524i	−0.416591	+	0.302671i
$904$	−1.16216	+	0.844359i	−0.0386529	+	0.0280830i
$905$	5.54990	−	41.3832i	0.184485	−	1.37562i
$906$	6.06059	+	4.40328i	0.201350	+	0.146289i
$907$	−29.1813			−0.968949			−0.484475	−	0.874805i	$-0.660989\pi$
$907$	−29.1813			−0.968949			−0.484475	+	0.874805i	$0.660989\pi$
$908$	−5.30055	−	3.85107i	−0.175905	−	0.127802i
$909$	−14.6539	+	45.1002i	−0.486040	+	1.49588i
$910$	−4.69960	−	8.70566i	−0.155790	−	0.288590i
$911$	−9.86191	−	30.3518i	−0.326740	−	1.00560i	−0.970649	−	0.240499i	$-0.922689\pi$
$911$	−9.86191	−	30.3518i	−0.326740	−	1.00560i	0.643910	−	0.765101i	$-0.277311\pi$
$912$	−0.997432	+	3.06978i	−0.0330283	+	0.101651i
$913$	3.63518	−	11.1879i	0.120307	−	0.370266i
$914$	−11.6038	−	35.7127i	−0.383819	−	1.18127i
$915$	−7.95009	+	59.2804i	−0.262822	+	1.95975i
$916$	7.04239	−	21.6743i	0.232687	−	0.716138i
$917$	7.63850	+	5.54969i	0.252245	+	0.183267i
$918$	5.21302			0.172055
$919$	−8.74185	−	6.35133i	−0.288367	−	0.209511i	0.434192	−	0.900821i	$-0.357034\pi$
$919$	−8.74185	−	6.35133i	−0.288367	−	0.209511i	−0.722559	+	0.691310i	$0.757034\pi$
$920$	5.02427	−	0.918649i	0.165645	−	0.0302870i
$921$	50.4350	−	36.6432i	1.66189	−	1.20743i
$922$	−4.99757	+	3.63095i	−0.164586	+	0.119579i
$923$	−8.70047	−	26.7773i	−0.286380	−	0.881386i
$924$	2.00978			0.0661170
$925$	−26.8600	−	33.4988i	−0.883151	−	1.10144i
$926$	−34.2140			−1.12434
$927$	6.60759	+	20.3361i	0.217022	+	0.667924i
$928$	0.564037	−	0.409797i	0.0185154	−	0.0134522i
$929$	−6.18394	+	4.49290i	−0.202889	+	0.147407i	−0.684590	−	0.728928i	$-0.740019\pi$
$929$	−6.18394	+	4.49290i	−0.202889	+	0.147407i	0.481702	+	0.876335i	$0.340019\pi$
$930$	−26.7878	+	28.0923i	−0.878406	+	0.921182i
$931$	−1.11960	−	0.813435i	−0.0366933	−	0.0266593i
$932$	8.23729			0.269821
$933$	−63.9221	−	46.4421i	−2.09271	−	1.52045i
$934$	−6.13451	+	18.8801i	−0.200727	+	0.617775i
$935$	7.56384	−	1.38299i	0.247364	−	0.0452286i
$936$	−3.33587	−	10.2668i	−0.109036	−	0.335579i
$937$	9.62849	−	29.6334i	0.314549	−	0.968082i	−0.661391	−	0.750042i	$-0.730033\pi$
$937$	9.62849	−	29.6334i	0.314549	−	0.968082i	0.975940	−	0.218041i	$-0.0699666\pi$
$938$	−0.175978	+	0.541606i	−0.00574590	+	0.0176841i
$939$	−10.7179	−	32.9863i	−0.349765	−	1.07647i
$940$	11.6242	−	2.12540i	0.379141	−	0.0693230i
$941$	3.13148	−	9.63771i	0.102083	−	0.314180i	−0.886951	−	0.461863i	$-0.847181\pi$
$941$	3.13148	−	9.63771i	0.102083	−	0.314180i	0.989035	+	0.147682i	$0.0471813\pi$
$942$	19.3991	+	14.0943i	0.632057	+	0.459216i
$943$	0.807995			0.0263119
$944$	−8.66151	−	6.29295i	−0.281908	−	0.204818i
$945$	−2.01578	+	2.11394i	−0.0655733	+	0.0687665i
$946$	4.62497	−	3.36024i	0.150371	−	0.109251i
$947$	−47.4822	+	34.4978i	−1.54296	+	1.12103i	−0.594522	+	0.804080i	$0.702659\pi$
$947$	−47.4822	+	34.4978i	−1.54296	+	1.12103i	−0.948442	+	0.316949i	$0.897341\pi$
$948$	−9.11934	−	28.0664i	−0.296182	−	0.911555i
$949$	−47.0876			−1.52853
$950$	−4.32856	−	5.39843i	−0.140437	−	0.175148i
$951$	26.1420			0.847713
$952$	1.23318	+	3.79535i	0.0399677	+	0.123008i
$953$	−27.5410	+	20.0097i	−0.892142	+	0.648179i	−0.936436	−	0.350839i	$-0.885896\pi$
$953$	−27.5410	+	20.0097i	−0.892142	+	0.648179i	0.0442937	+	0.999019i	$0.485896\pi$
$954$	2.14240	−	1.55654i	0.0693627	−	0.0503949i
$955$	55.6369	−	10.1728i	1.80037	−	0.329184i
$956$	0.855751	+	0.621739i	0.0276770	+	0.0201085i
$957$	1.40120			0.0452942
$958$	2.99876	+	2.17873i	0.0968856	+	0.0703915i
$959$	2.82009	−	8.67934i	0.0910655	−	0.280271i
$960$	−0.693221	+	5.16905i	−0.0223736	+	0.166830i
$961$	7.53890	+	23.2024i	0.243190	+	0.748463i
$962$	11.7409	−	36.1346i	0.378540	−	1.16503i
$963$	4.28445	−	13.1862i	0.138064	−	0.424918i
$964$	−3.14926	−	9.69241i	−0.101431	−	0.312172i
$965$	22.3300	+	41.3647i	0.718829	+	1.33158i
$966$	−1.64629	+	5.06677i	−0.0529686	+	0.163021i
$967$	−41.3212	−	30.0216i	−1.32880	−	0.965431i	−0.999777	−	0.0211093i	$-0.993280\pi$
$967$	−41.3212	−	30.0216i	−1.32880	−	0.965431i	−0.329024	−	0.944321i	$-0.606720\pi$
$968$	10.2575			0.329688
$969$	−10.4209	−	7.57121i	−0.334767	−	0.243222i
$970$	−4.12000	+	30.7210i	−0.132285	+	0.986393i
$971$	28.2087	−	20.4948i	0.905261	−	0.657711i	−0.0345506	−	0.999403i	$-0.511000\pi$
$971$	28.2087	−	20.4948i	0.905261	−	0.657711i	0.939812	+	0.341692i	$0.111000\pi$
$972$	−16.3904	+	11.9083i	−0.525722	+	0.381960i
$973$	−3.32056	−	10.2196i	−0.106452	−	0.327627i
$974$	−39.1314			−1.25385
$975$	49.7729	+	13.5946i	1.59401	+	0.435375i
$976$	11.4683			0.367092
$977$	−3.62565	−	11.1586i	−0.115995	−	0.356996i	0.876158	−	0.482024i	$-0.160098\pi$
$977$	−3.62565	−	11.1586i	−0.115995	−	0.356996i	−0.992153	+	0.125028i	$0.960098\pi$
$978$	−6.47133	+	4.70169i	−0.206930	+	0.150344i
$979$	8.37481	−	6.08466i	0.267660	−	0.194466i
$980$	−2.01591	−	0.967523i	−0.0643959	−	0.0309064i
$981$	−34.1024	−	24.7768i	−1.08881	−	0.791063i
$982$	11.1920			0.357150
$983$	−32.2125	−	23.4037i	−1.02742	−	0.746463i	−0.0596282	−	0.998221i	$-0.518992\pi$
$983$	−32.2125	−	23.4037i	−1.02742	−	0.746463i	−0.967790	+	0.251757i	$0.918992\pi$
$984$	−0.254952	+	0.784663i	−0.00812758	+	0.0250141i
$985$	−39.1714	−	18.8000i	−1.24810	−	0.599019i
$986$	0.859762	+	2.64608i	0.0273804	+	0.0842682i
$987$	−3.80889	+	11.7226i	−0.121238	+	0.373133i
$988$	1.89207	−	5.82319i	0.0601948	−	0.185260i
$989$	4.68285	+	14.4123i	0.148906	+	0.458285i
$990$	−3.24436	+	3.40235i	−0.103112	+	0.108134i
$991$	−9.01394	+	27.7421i	−0.286337	+	0.881256i	0.699657	+	0.714479i	$0.253336\pi$
$991$	−9.01394	+	27.7421i	−0.286337	+	0.881256i	−0.985995	+	0.166777i	$0.946664\pi$
$992$	6.02141	+	4.37481i	0.191180	+	0.138900i
$993$	3.12613			0.0992046
$994$	−5.14835	−	3.74049i	−0.163296	−	0.118641i
$995$	−9.57354	−	17.7343i	−0.303502	−	0.562214i
$996$	−25.7599	+	18.7157i	−0.816235	+	0.593029i
$997$	32.8733	−	23.8838i	1.04111	−	0.756408i	0.0706053	−	0.997504i	$-0.477507\pi$
$997$	32.8733	−	23.8838i	1.04111	−	0.756408i	0.970501	+	0.241096i	$0.0775069\pi$
$998$	1.07938	+	3.32198i	0.0341671	+	0.105156i
$999$	−11.2179			−0.354918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.d.281.4	yes	20
25.11	even	5		8750.2.a.w.1.3		10
25.14	even	10		8750.2.a.x.1.8		10
25.21	even	5	inner	350.2.h.d.71.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.d.71.4	✓	20	25.21	even	5	inner
350.2.h.d.281.4	yes	20	1.1	even	1	trivial
8750.2.a.w.1.3		10	25.11	even	5
8750.2.a.x.1.8		10	25.14	even	10

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:	\( N \)	\(=\)	\( 350 = 2 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	350.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 - 0.951057i) q^{2} +(1.88692 - 1.37093i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.06221 + 1.96767i) q^{5} +(-1.88692 - 1.37093i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.753978 - 2.32051i) q^{9} +O(q^{10})\)	\(q+(-0.309017 - 0.951057i) q^{2} +(1.88692 - 1.37093i) q^{3} +(-0.809017 + 0.587785i) q^{4} +(1.06221 + 1.96767i) q^{5} +(-1.88692 - 1.37093i) q^{6} +1.00000 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.753978 - 2.32051i) q^{9} +(1.54312 - 1.61826i) q^{10} +(-0.266278 - 0.819519i) q^{11} +(-0.720740 + 2.21821i) q^{12} +(1.36720 - 4.20782i) q^{13} +(-0.309017 - 0.951057i) q^{14} +(4.70184 + 2.25662i) q^{15} +(0.309017 - 0.951057i) q^{16} +(3.22852 + 2.34566i) q^{17} -2.43992 q^{18} +(-1.11960 - 0.813435i) q^{19} +(-2.01591 - 0.967523i) q^{20} +(1.88692 - 1.37093i) q^{21} +(-0.697124 + 0.506490i) q^{22} +(-0.705847 - 2.17238i) q^{23} +2.33236 q^{24} +(-2.74342 + 4.18015i) q^{25} -4.42436 q^{26} +(0.403669 + 1.24237i) q^{27} +(-0.809017 + 0.587785i) q^{28} +(-0.564037 + 0.409797i) q^{29} +(0.693221 - 5.16905i) q^{30} +(-6.02141 - 4.37481i) q^{31} -1.00000 q^{32} +(-1.62595 - 1.18132i) q^{33} +(1.23318 - 3.79535i) q^{34} +(1.06221 + 1.96767i) q^{35} +(0.753978 + 2.32051i) q^{36} +(-2.65369 + 8.16721i) q^{37} +(-0.427648 + 1.31617i) q^{38} +(-3.18881 - 9.81416i) q^{39} +(-0.297218 + 2.21623i) q^{40} +(-0.109311 + 0.336424i) q^{41} +(-1.88692 - 1.37093i) q^{42} -6.63436 q^{43} +(0.697124 + 0.506490i) q^{44} +(5.36686 - 0.981290i) q^{45} +(-1.84793 + 1.34260i) q^{46} +(-4.27541 + 3.10627i) q^{47} +(-0.720740 - 2.21821i) q^{48} +1.00000 q^{49} +(4.82332 + 1.31741i) q^{50} +9.30770 q^{51} +(1.36720 + 4.20782i) q^{52} +(-0.878059 + 0.637947i) q^{53} +(1.05682 - 0.767824i) q^{54} +(1.32970 - 1.39445i) q^{55} +(0.809017 + 0.587785i) q^{56} -3.22776 q^{57} +(0.564037 + 0.409797i) q^{58} +(3.30840 - 10.1822i) q^{59} +(-5.13027 + 0.938032i) q^{60} +(3.54391 + 10.9070i) q^{61} +(-2.29998 + 7.07860i) q^{62} +(0.753978 - 2.32051i) q^{63} +(0.309017 + 0.951057i) q^{64} +(9.73183 - 1.77939i) q^{65} +(-0.621057 + 1.91142i) q^{66} +(-0.460717 - 0.334731i) q^{67} -3.99067 q^{68} +(-4.31005 - 3.13144i) q^{69} +(1.54312 - 1.61826i) q^{70} +(5.14835 - 3.74049i) q^{71} +(1.97394 - 1.43415i) q^{72} +(-3.28881 - 10.1219i) q^{73} +8.58751 q^{74} +(0.554080 + 11.6487i) q^{75} +1.38390 q^{76} +(-0.266278 - 0.819519i) q^{77} +(-8.34842 + 6.06548i) q^{78} +(-10.2363 + 7.43709i) q^{79} +(2.19960 - 0.402181i) q^{80} +(8.38671 + 6.09330i) q^{81} +0.353737 q^{82} +(11.0446 + 8.02434i) q^{83} +(-0.720740 + 2.21821i) q^{84} +(-1.18610 + 8.84423i) q^{85} +(2.05013 + 6.30965i) q^{86} +(-0.502492 + 1.54651i) q^{87} +(0.266278 - 0.819519i) q^{88} +(3.71234 + 11.4254i) q^{89} +(-2.59171 - 4.80095i) q^{90} +(1.36720 - 4.20782i) q^{91} +(1.84793 + 1.34260i) q^{92} -17.3595 q^{93} +(4.27541 + 3.10627i) q^{94} +(0.411320 - 3.06703i) q^{95} +(-1.88692 + 1.37093i) q^{96} +(-11.2145 + 8.14780i) q^{97} +(-0.309017 - 0.951057i) q^{98} -2.10247 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9}+O(q^{10}) \) 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9	\( 20 q + 5 q^{2} + 3 q^{3} - 5 q^{4} - 5 q^{5} - 3 q^{6} + 20 q^{7} + 5 q^{8} - 6 q^{9} - 9 q^{11} - 2 q^{12} + 5 q^{13} + 5 q^{14} - 5 q^{16} - 12 q^{17} - 34 q^{18} + 2 q^{19} + 5 q^{20} + 3 q^{21} - 6 q^{22} - 5 q^{23} + 2 q^{24} - 35 q^{25} + 20 q^{26} - 6 q^{27} - 5 q^{28} - 22 q^{29} - 25 q^{30} - 7 q^{31} - 20 q^{32} + 25 q^{33} - 18 q^{34} - 5 q^{35} - 6 q^{36} - 3 q^{37} + 8 q^{38} - 22 q^{39} + 19 q^{41} - 3 q^{42} + 2 q^{43} + 6 q^{44} + 45 q^{45} - 10 q^{46} - 14 q^{47} - 2 q^{48} + 20 q^{49} + 10 q^{50} + 38 q^{51} + 5 q^{52} - q^{53} - 19 q^{54} - 20 q^{55} + 5 q^{56} + 116 q^{57} + 22 q^{58} + 17 q^{59} - 5 q^{60} - 38 q^{61} + 7 q^{62} - 6 q^{63} - 5 q^{64} + 15 q^{65} - 16 q^{67} - 12 q^{68} + 35 q^{69} + q^{71} + 11 q^{72} + 19 q^{73} + 18 q^{74} + 35 q^{75} + 12 q^{76} - 9 q^{77} - 18 q^{78} - 64 q^{79} - 40 q^{81} + 26 q^{82} + 57 q^{83} - 2 q^{84} - 40 q^{85} - 2 q^{86} - 78 q^{87} + 9 q^{88} - 6 q^{89} + 10 q^{90} + 5 q^{91} + 10 q^{92} - 22 q^{93} + 14 q^{94} + 60 q^{95} - 3 q^{96} - 18 q^{97} + 5 q^{98} + 112 q^{99}+O(q^{100}) \) 20 * q + 5 * q^2 + 3 * q^3 - 5 * q^4 - 5 * q^5 - 3 * q^6 + 20 * q^7 + 5 * q^8 - 6 * q^9 - 9 * q^11 - 2 * q^12 + 5 * q^13 + 5 * q^14 - 5 * q^16 - 12 * q^17 - 34 * q^18 + 2 * q^19 + 5 * q^20 + 3 * q^21 - 6 * q^22 - 5 * q^23 + 2 * q^24 - 35 * q^25 + 20 * q^26 - 6 * q^27 - 5 * q^28 - 22 * q^29 - 25 * q^30 - 7 * q^31 - 20 * q^32 + 25 * q^33 - 18 * q^34 - 5 * q^35 - 6 * q^36 - 3 * q^37 + 8 * q^38 - 22 * q^39 + 19 * q^41 - 3 * q^42 + 2 * q^43 + 6 * q^44 + 45 * q^45 - 10 * q^46 - 14 * q^47 - 2 * q^48 + 20 * q^49 + 10 * q^50 + 38 * q^51 + 5 * q^52 - q^53 - 19 * q^54 - 20 * q^55 + 5 * q^56 + 116 * q^57 + 22 * q^58 + 17 * q^59 - 5 * q^60 - 38 * q^61 + 7 * q^62 - 6 * q^63 - 5 * q^64 + 15 * q^65 - 16 * q^67 - 12 * q^68 + 35 * q^69 + q^71 + 11 * q^72 + 19 * q^73 + 18 * q^74 + 35 * q^75 + 12 * q^76 - 9 * q^77 - 18 * q^78 - 64 * q^79 - 40 * q^81 + 26 * q^82 + 57 * q^83 - 2 * q^84 - 40 * q^85 - 2 * q^86 - 78 * q^87 + 9 * q^88 - 6 * q^89 + 10 * q^90 + 5 * q^91 + 10 * q^92 - 22 * q^93 + 14 * q^94 + 60 * q^95 - 3 * q^96 - 18 * q^97 + 5 * q^98 + 112 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more