LMFDB - Embedded newform 350.2.h.d.211.4

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			211.4
Root			$0.671167 - 2.06564i$ of defining polynomial
Character	$\chi$	$=$	350.211
Dual form			350.2.h.d.141.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.809017 - 0.587785i) q^{2} +(0.671167 - 2.06564i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.284771 - 2.21786i) q^{5} +(-0.671167 - 2.06564i) q^{6} +1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.38935 - 1.00942i) q^{9} +O(q^{10})$	\(q+(0.809017 - 0.587785i) q^{2} +(0.671167 - 2.06564i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.284771 - 2.21786i) q^{5} +(-0.671167 - 2.06564i) q^{6} +1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.38935 - 1.00942i) q^{9} +(-1.53401 - 1.62690i) q^{10} +(-4.04230 + 2.93690i) q^{11} +(-1.75714 - 1.27664i) q^{12} +(4.05333 + 2.94492i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-4.77243 - 0.900320i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.205835 - 0.633496i) q^{17} -1.71733 q^{18} +(1.26984 + 3.90816i) q^{19} +(-2.19731 - 0.414523i) q^{20} +(0.671167 - 2.06564i) q^{21} +(-1.54402 + 4.75200i) q^{22} +(1.55928 - 1.13288i) q^{23} -2.17194 q^{24} +(-4.83781 + 1.26317i) q^{25} +5.01019 q^{26} +(2.25383 - 1.63750i) q^{27} +(0.309017 - 0.951057i) q^{28} +(2.49503 - 7.67890i) q^{29} +(-4.39017 + 2.07679i) q^{30} +(0.881759 + 2.71378i) q^{31} -1.00000 q^{32} +(3.35352 + 10.3211i) q^{33} +(-0.538884 - 0.391522i) q^{34} +(-0.284771 - 2.21786i) q^{35} +(-1.38935 + 1.00942i) q^{36} +(-7.72186 - 5.61026i) q^{37} +(3.32448 + 2.41537i) q^{38} +(8.80360 - 6.39619i) q^{39} +(-2.02131 + 0.956190i) q^{40} +(-0.985264 - 0.715836i) q^{41} +(-0.671167 - 2.06564i) q^{42} +8.81281 q^{43} +(1.54402 + 4.75200i) q^{44} +(-1.84311 + 3.36884i) q^{45} +(0.595591 - 1.83304i) q^{46} +(-1.69053 + 5.20292i) q^{47} +(-1.75714 + 1.27664i) q^{48} +1.00000 q^{49} +(-3.17140 + 3.86552i) q^{50} -1.44672 q^{51} +(4.05333 - 2.94492i) q^{52} +(-4.01539 + 12.3581i) q^{53} +(0.860885 - 2.64953i) q^{54} +(7.66476 + 8.12890i) q^{55} +(-0.309017 - 0.951057i) q^{56} +8.92511 q^{57} +(-2.49503 - 7.67890i) q^{58} +(-8.07302 - 5.86539i) q^{59} +(-2.33102 + 4.26064i) q^{60} +(8.36560 - 6.07797i) q^{61} +(2.30848 + 1.67721i) q^{62} +(-1.38935 - 1.00942i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(5.37715 - 9.82835i) q^{65} +(8.77963 + 6.37878i) q^{66} +(0.633135 + 1.94859i) q^{67} -0.666097 q^{68} +(-1.29359 - 3.98126i) q^{69} +(-1.53401 - 1.62690i) q^{70} +(0.599857 - 1.84617i) q^{71} +(-0.530684 + 1.63328i) q^{72} +(0.439142 - 0.319055i) q^{73} -9.54474 q^{74} +(-0.637734 + 10.8410i) q^{75} +4.10928 q^{76} +(-4.04230 + 2.93690i) q^{77} +(3.36268 - 10.3493i) q^{78} +(-3.49703 + 10.7627i) q^{79} +(-1.07324 + 1.96167i) q^{80} +(-3.46185 - 10.6545i) q^{81} -1.21785 q^{82} +(3.70932 + 11.4161i) q^{83} +(-1.75714 - 1.27664i) q^{84} +(-1.34639 + 0.636916i) q^{85} +(7.12971 - 5.18004i) q^{86} +(-14.1873 - 10.3076i) q^{87} +(4.04230 + 2.93690i) q^{88} +(-3.67873 + 2.67275i) q^{89} +(0.489046 + 3.80880i) q^{90} +(4.05333 + 2.94492i) q^{91} +(-0.595591 - 1.83304i) q^{92} +6.19749 q^{93} +(1.69053 + 5.20292i) q^{94} +(8.30613 - 3.92925i) q^{95} +(-0.671167 + 2.06564i) q^{96} +(1.07581 - 3.31099i) q^{97} +(0.809017 - 0.587785i) q^{98} +8.58073 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 $\left(\mathbb{Z}/350\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$2$	0.809017	−	0.587785i	0.572061	−	0.415627i
$3$	0.671167	−	2.06564i	0.387498	−	1.19260i	−0.547153	−	0.837032i	$-0.684288\pi$
$3$	0.671167	−	2.06564i	0.387498	−	1.19260i	0.934652	−	0.355565i	$-0.115712\pi$
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−0.284771	−	2.21786i	−0.127354	−	0.991857i
$5$	−0.284771	−	2.21786i	−0.127354	−	0.991857i
$6$	−0.671167	−	2.06564i	−0.274003	−	0.843294i
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	−1.38935	−	1.00942i	−0.463117	−	0.336474i
$10$	−1.53401	−	1.62690i	−0.485097	−	0.514472i
$11$	−4.04230	+	2.93690i	−1.21880	+	0.885509i	−0.996000	−	0.0893559i	$-0.971519\pi$
$11$	−4.04230	+	2.93690i	−1.21880	+	0.885509i	−0.222798	+	0.974865i	$0.571519\pi$
$12$	−1.75714	−	1.27664i	−0.507242	−	0.368533i
$13$	4.05333	+	2.94492i	1.12419	+	0.816773i	0.984839	−	0.173469i	$-0.0554978\pi$
$13$	4.05333	+	2.94492i	1.12419	+	0.816773i	0.139353	+	0.990243i	$0.455498\pi$
$14$	0.809017	−	0.587785i	0.216219	−	0.157092i
$15$	−4.77243	−	0.900320i	−1.23224	−	0.232462i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	−0.205835	−	0.633496i	−0.0499224	−	0.153645i	0.922988	−	0.384830i	$-0.125740\pi$
$17$	−0.205835	−	0.633496i	−0.0499224	−	0.153645i	−0.972910	+	0.231185i	$0.925740\pi$
$18$	−1.71733			−0.404779
$19$	1.26984	+	3.90816i	0.291321	+	0.896592i	0.984433	+	0.175763i	$0.0562391\pi$
$19$	1.26984	+	3.90816i	0.291321	+	0.896592i	−0.693112	+	0.720830i	$0.743761\pi$
$20$	−2.19731	−	0.414523i	−0.491333	−	0.0926902i
$21$	0.671167	−	2.06564i	0.146461	−	0.450759i
$22$	−1.54402	+	4.75200i	−0.329186	+	1.01313i
$23$	1.55928	−	1.13288i	0.325132	−	0.236222i	−0.413230	−	0.910627i	$-0.635600\pi$
$23$	1.55928	−	1.13288i	0.325132	−	0.236222i	0.738362	+	0.674404i	$0.235600\pi$
$24$	−2.17194			−0.443346
$25$	−4.83781	+	1.26317i	−0.967562	+	0.252633i
$26$	5.01019			0.982580
$27$	2.25383	−	1.63750i	0.433749	−	0.315137i
$28$	0.309017	−	0.951057i	0.0583987	−	0.179733i
$29$	2.49503	−	7.67890i	0.463315	−	1.42594i	−0.397775	−	0.917483i	$-0.630218\pi$
$29$	2.49503	−	7.67890i	0.463315	−	1.42594i	0.861090	−	0.508453i	$-0.169782\pi$
$30$	−4.39017	+	2.07679i	−0.801532	+	0.379168i
$31$	0.881759	+	2.71378i	0.158369	+	0.487409i	0.998487	−	0.0549951i	$-0.0175143\pi$
$31$	0.881759	+	2.71378i	0.158369	+	0.487409i	−0.840118	+	0.542404i	$0.817514\pi$
$32$	−1.00000			−0.176777
$33$	3.35352	+	10.3211i	0.583773	+	1.79667i
$34$	−0.538884	−	0.391522i	−0.0924178	−	0.0671455i
$35$	−0.284771	−	2.21786i	−0.0481351	−	0.374887i
$36$	−1.38935	+	1.00942i	−0.231558	+	0.168237i
$37$	−7.72186	−	5.61026i	−1.26947	−	0.922321i	−0.270285	−	0.962780i	$-0.587118\pi$
$37$	−7.72186	−	5.61026i	−1.26947	−	0.922321i	−0.999181	+	0.0404593i	$0.987118\pi$
$38$	3.32448	+	2.41537i	0.539301	+	0.391825i
$39$	8.80360	−	6.39619i	1.40970	−	1.02421i
$40$	−2.02131	+	0.956190i	−0.319597	+	0.151187i
$41$	−0.985264	−	0.715836i	−0.153872	−	0.111795i	0.508185	−	0.861248i	$-0.330317\pi$
$41$	−0.985264	−	0.715836i	−0.153872	−	0.111795i	−0.662058	+	0.749453i	$0.730317\pi$
$42$	−0.671167	−	2.06564i	−0.103563	−	0.318735i
$43$	8.81281			1.34394			0.671970	−	0.740578i	$-0.265448\pi$
$43$	8.81281			1.34394			0.671970	+	0.740578i	$0.265448\pi$
$44$	1.54402	+	4.75200i	0.232770	+	0.716392i
$45$	−1.84311	+	3.36884i	−0.274755	+	0.502197i
$46$	0.595591	−	1.83304i	0.0878151	−	0.270267i
$47$	−1.69053	+	5.20292i	−0.246589	+	0.758924i	0.748782	+	0.662817i	$0.230639\pi$
$47$	−1.69053	+	5.20292i	−0.246589	+	0.758924i	−0.995371	+	0.0961072i	$0.969361\pi$
$48$	−1.75714	+	1.27664i	−0.253621	+	0.184266i
$49$	1.00000			0.142857
$50$	−3.17140	+	3.86552i	−0.448504	+	0.546667i
$51$	−1.44672			−0.202582
$52$	4.05333	−	2.94492i	0.562096	−	0.408387i
$53$	−4.01539	+	12.3581i	−0.551556	+	1.69752i	0.153312	+	0.988178i	$0.451006\pi$
$53$	−4.01539	+	12.3581i	−0.551556	+	1.69752i	−0.704868	+	0.709338i	$0.748994\pi$
$54$	0.860885	−	2.64953i	0.117152	−	0.360556i
$55$	7.66476	+	8.12890i	1.03352	+	1.09610i
$56$	−0.309017	−	0.951057i	−0.0412941	−	0.127090i
$57$	8.92511			1.18216
$58$	−2.49503	−	7.67890i	−0.327613	−	1.00829i
$59$	−8.07302	−	5.86539i	−1.05102	−	0.763609i	−0.0786122	−	0.996905i	$-0.525049\pi$
$59$	−8.07302	−	5.86539i	−1.05102	−	0.763609i	−0.972406	+	0.233296i	$0.925049\pi$
$60$	−2.33102	+	4.26064i	−0.300933	+	0.550046i
$61$	8.36560	−	6.07797i	1.07111	−	0.778204i	0.0949951	−	0.995478i	$-0.469716\pi$
$61$	8.36560	−	6.07797i	1.07111	−	0.778204i	0.976111	+	0.217274i	$0.0697164\pi$
$62$	2.30848	+	1.67721i	0.293177	+	0.213005i
$63$	−1.38935	−	1.00942i	−0.175042	−	0.127175i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	5.37715	−	9.82835i	0.666953	−	1.21906i
$66$	8.77963	+	6.37878i	1.08070	+	0.785173i
$67$	0.633135	+	1.94859i	0.0773497	+	0.238058i	0.982253	−	0.187558i	$-0.0600573\pi$
$67$	0.633135	+	1.94859i	0.0773497	+	0.238058i	−0.904904	+	0.425616i	$0.860057\pi$
$68$	−0.666097			−0.0807762
$69$	−1.29359	−	3.98126i	−0.155730	−	0.479287i
$70$	−1.53401	−	1.62690i	−0.183349	−	0.194452i
$71$	0.599857	−	1.84617i	0.0711899	−	0.219100i	−0.909131	−	0.416510i	$-0.863253\pi$
$71$	0.599857	−	1.84617i	0.0711899	−	0.219100i	0.980321	+	0.197410i	$0.0632531\pi$
$72$	−0.530684	+	1.63328i	−0.0625418	+	0.192484i
$73$	0.439142	−	0.319055i	0.0513977	−	0.0373426i	−0.561790	−	0.827280i	$-0.689887\pi$
$73$	0.439142	−	0.319055i	0.0513977	−	0.0373426i	0.613187	+	0.789937i	$0.289887\pi$
$74$	−9.54474			−1.10955
$75$	−0.637734	+	10.8410i	−0.0736392	+	1.25181i
$76$	4.10928			0.471366
$77$	−4.04230	+	2.93690i	−0.460662	+	0.334691i
$78$	3.36268	−	10.3493i	0.380748	−	1.17182i
$79$	−3.49703	+	10.7627i	−0.393446	+	1.21090i	0.536718	+	0.843761i	$0.319664\pi$
$79$	−3.49703	+	10.7627i	−0.393446	+	1.21090i	−0.930165	+	0.367142i	$0.880336\pi$
$80$	−1.07324	+	1.96167i	−0.119992	+	0.219322i
$81$	−3.46185	−	10.6545i	−0.384649	−	1.18383i
$82$	−1.21785			−0.134489
$83$	3.70932	+	11.4161i	0.407151	+	1.25308i	0.919086	+	0.394058i	$0.128929\pi$
$83$	3.70932	+	11.4161i	0.407151	+	1.25308i	−0.511934	+	0.859025i	$0.671071\pi$
$84$	−1.75714	−	1.27664i	−0.191719	−	0.139292i
$85$	−1.34639	+	0.636916i	−0.146037	+	0.0690832i
$86$	7.12971	−	5.18004i	0.768817	−	0.558578i
$87$	−14.1873	−	10.3076i	−1.52103	−	1.10510i
$88$	4.04230	+	2.93690i	0.430910	+	0.313075i
$89$	−3.67873	+	2.67275i	−0.389945	+	0.283311i	−0.765433	−	0.643516i	$-0.777475\pi$
$89$	−3.67873	+	2.67275i	−0.389945	+	0.283311i	0.375488	+	0.926827i	$0.377475\pi$
$90$	0.489046	+	3.80880i	0.0515500	+	0.401483i
$91$	4.05333	+	2.94492i	0.424905	+	0.308711i
$92$	−0.595591	−	1.83304i	−0.0620947	−	0.191108i
$93$	6.19749			0.642650
$94$	1.69053	+	5.20292i	0.174365	+	0.536640i
$95$	8.30613	−	3.92925i	0.852191	−	0.403133i
$96$	−0.671167	+	2.06564i	−0.0685007	+	0.210823i
$97$	1.07581	−	3.31099i	0.109232	−	0.336181i	−0.881469	−	0.472243i	$-0.843445\pi$
$97$	1.07581	−	3.31099i	0.109232	−	0.336181i	0.990700	+	0.136062i	$0.0434446\pi$
$98$	0.809017	−	0.587785i	0.0817231	−	0.0593753i
$99$	8.58073			0.862396
$100$	−0.293624	+	4.99137i	−0.0293624	+	0.499137i
$101$	5.98229			0.595260			0.297630	−	0.954681i	$-0.403804\pi$
$101$	5.98229			0.595260			0.297630	+	0.954681i	$0.403804\pi$
$102$	−1.17042	+	0.850363i	−0.115889	+	0.0841985i
$103$	−4.79779	+	14.7661i	−0.472741	+	1.45495i	0.376240	+	0.926522i	$0.377217\pi$
$103$	−4.79779	+	14.7661i	−0.472741	+	1.45495i	−0.848981	+	0.528424i	$0.822783\pi$
$104$	1.54824	−	4.76498i	0.151817	−	0.467245i
$105$	−4.77243	−	0.900320i	−0.465741	−	0.0878622i
$106$	4.01539	+	12.3581i	0.390009	+	1.20033i
$107$	3.11928			0.301552			0.150776	−	0.988568i	$-0.451823\pi$
$107$	3.11928			0.301552			0.150776	+	0.988568i	$0.451823\pi$
$108$	−0.860885	−	2.64953i	−0.0828387	−	0.254951i
$109$	1.71623	+	1.24692i	0.164385	+	0.119433i	0.666937	−	0.745115i	$-0.267605\pi$
$109$	1.71623	+	1.24692i	0.164385	+	0.119433i	−0.502551	+	0.864547i	$0.667605\pi$
$110$	10.9790	+	2.07119i	1.04680	+	0.197480i
$111$	−16.7714	+	12.1852i	−1.59187	+	1.15656i
$112$	−0.809017	−	0.587785i	−0.0764449	−	0.0555405i
$113$	4.24990	+	3.08773i	0.399797	+	0.290469i	0.769458	−	0.638697i	$-0.220526\pi$
$113$	4.24990	+	3.08773i	0.399797	+	0.290469i	−0.369661	+	0.929167i	$0.620526\pi$
$114$	7.22057	−	5.24605i	0.676268	−	0.491338i
$115$	−2.95661	−	3.13565i	−0.275705	−	0.292401i
$116$	−6.53206	−	4.74582i	−0.606487	−	0.440638i
$117$	−2.65883	−	8.18304i	−0.245809	−	0.756523i
$118$	−9.97880			−0.918623
$119$	−0.205835	−	0.633496i	−0.0188689	−	0.0580725i
$120$	0.618506	+	4.81706i	0.0564617	+	0.439736i
$121$	4.31559	−	13.2820i	0.392326	−	1.20746i
$122$	3.19538	−	9.83436i	0.289296	−	0.890361i
$123$	−2.13994	+	1.55475i	−0.192951	+	0.140187i
$124$	2.85343			0.256246
$125$	4.17919	+	10.3699i	0.373798	+	0.927510i
$126$	−1.71733			−0.152992
$127$	−18.0002	+	13.0779i	−1.59726	+	1.16048i	−0.704742	+	0.709464i	$0.748937\pi$
$127$	−18.0002	+	13.0779i	−1.59726	+	1.16048i	−0.892517	+	0.451013i	$0.851063\pi$
$128$	−0.309017	+	0.951057i	−0.0273135	+	0.0840623i
$129$	5.91486	−	18.2041i	0.520775	−	1.60278i
$130$	−1.42676	−	11.1119i	−0.125135	−	0.974579i
$131$	0.712332	+	2.19233i	0.0622367	+	0.191545i	0.977340	−	0.211674i	$-0.0678914\pi$
$131$	0.712332	+	2.19233i	0.0622367	+	0.191545i	−0.915104	+	0.403219i	$0.867891\pi$
$132$	10.8522			0.944565
$133$	1.26984	+	3.90816i	0.110109	+	0.338880i
$134$	1.65757	+	1.20429i	0.143192	+	0.104035i
$135$	−4.27357	−	4.53236i	−0.367811	−	0.390083i
$136$	−0.538884	+	0.391522i	−0.0462089	+	0.0335727i
$137$	−17.5371	−	12.7414i	−1.49829	−	1.08857i	−0.971054	−	0.238858i	$-0.923227\pi$
$137$	−17.5371	−	12.7414i	−1.49829	−	1.08857i	−0.527240	−	0.849716i	$-0.676773\pi$
$138$	−3.38666	−	2.46055i	−0.288292	−	0.209456i
$139$	−1.17400	+	0.852958i	−0.0995770	+	0.0723469i	−0.636460	−	0.771310i	$-0.719602\pi$
$139$	−1.17400	+	0.852958i	−0.0995770	+	0.0723469i	0.536883	+	0.843657i	$0.319602\pi$
$140$	−2.19731	−	0.414523i	−0.185707	−	0.0350336i
$141$	9.61273	+	6.98406i	0.809538	+	0.588164i
$142$	−0.599857	−	1.84617i	−0.0503388	−	0.154927i
$143$	−25.0337			−2.09342
$144$	0.530684	+	1.63328i	0.0442237	+	0.136107i
$145$	−17.7412	−	3.34689i	−1.47333	−	0.277944i
$146$	0.167737	−	0.516243i	0.0138820	−	0.0427245i
$147$	0.671167	−	2.06564i	0.0553569	−	0.170371i
$148$	−7.72186	+	5.61026i	−0.634733	+	0.461161i
$149$	−11.2883			−0.924774			−0.462387	−	0.886678i	$-0.653007\pi$
$149$	−11.2883			−0.924774			−0.462387	+	0.886678i	$0.653007\pi$
$150$	5.85622	+	9.14538i	0.478159	+	0.746717i
$151$	0.261168			0.0212536			0.0106268	−	0.999944i	$-0.496617\pi$
$151$	0.261168			0.0212536			0.0106268	+	0.999944i	$0.496617\pi$
$152$	3.32448	−	2.41537i	0.269651	−	0.195913i
$153$	−0.353487	+	1.08792i	−0.0285778	+	0.0879533i
$154$	−1.54402	+	4.75200i	−0.124421	+	0.382927i
$155$	5.76768	−	2.72842i	0.463271	−	0.219152i
$156$	−3.36268	−	10.3493i	−0.269230	−	0.828604i
$157$	17.1146			1.36589			0.682945	−	0.730470i	$-0.260699\pi$
$157$	17.1146			1.36589			0.682945	+	0.730470i	$0.260699\pi$
$158$	3.49703	+	10.7627i	0.278209	+	0.856238i
$159$	22.8324	+	16.5887i	1.81073	+	1.31557i
$160$	0.284771	+	2.21786i	0.0225131	+	0.175337i
$161$	1.55928	−	1.13288i	0.122888	−	0.0892836i
$162$	−9.06323	−	6.58482i	−0.712075	−	0.517352i
$163$	−12.7783	−	9.28396i	−1.00087	−	0.727176i	−0.0385966	−	0.999255i	$-0.512289\pi$
$163$	−12.7783	−	9.28396i	−1.00087	−	0.727176i	−0.962275	+	0.272079i	$0.912289\pi$
$164$	−0.985264	+	0.715836i	−0.0769362	+	0.0558974i
$165$	21.9357	−	10.3768i	1.70769	−	0.807832i
$166$	9.71114	+	7.05555i	0.753730	+	0.547617i
$167$	−1.84719	−	5.68506i	−0.142940	−	0.439923i	0.853801	−	0.520600i	$-0.174292\pi$
$167$	−1.84719	−	5.68506i	−0.142940	−	0.439923i	−0.996740	+	0.0806770i	$0.974292\pi$
$168$	−2.17194			−0.167569
$169$	3.73974	+	11.5097i	0.287672	+	0.885364i
$170$	−0.714883	+	1.30666i	−0.0548290	+	0.100217i
$171$	2.18073	−	6.71160i	0.166765	−	0.513249i
$172$	2.72331	−	8.38148i	0.207650	−	0.639082i
$173$	18.9544	−	13.7712i	1.44108	−	1.04701i	0.453265	−	0.891376i	$-0.350259\pi$
$173$	18.9544	−	13.7712i	1.44108	−	1.04701i	0.987815	−	0.155630i	$-0.0497407\pi$
$174$	−17.5364			−1.32943
$175$	−4.83781	+	1.26317i	−0.365704	+	0.0954863i
$176$	4.99655			0.376629
$177$	−17.5341	+	12.7393i	−1.31795	+	0.957544i
$178$	−1.40515	+	4.32461i	−0.105320	+	0.324143i
$179$	8.04180	−	24.7501i	0.601073	−	1.84991i	0.0792549	−	0.996854i	$-0.474746\pi$
$179$	8.04180	−	24.7501i	0.601073	−	1.84991i	0.521818	−	0.853057i	$-0.325254\pi$
$180$	2.63440	+	2.79393i	0.196357	+	0.208247i
$181$	0.724321	+	2.22923i	0.0538384	+	0.165697i	0.974360	−	0.224994i	$-0.0722361\pi$
$181$	0.724321	+	2.22923i	0.0538384	+	0.165697i	−0.920522	+	0.390691i	$0.872236\pi$
$182$	5.01019			0.371380
$183$	−6.94017	−	21.3597i	−0.513032	−	1.57895i
$184$	−1.55928	−	1.13288i	−0.114951	−	0.0835172i
$185$	−10.2438	+	18.7237i	−0.753140	+	1.37659i
$186$	5.01388	−	3.64279i	0.367635	−	0.267103i
$187$	2.69256	+	1.95626i	0.196900	+	0.143056i
$188$	4.42587	+	3.21558i	0.322790	+	0.234520i
$189$	2.25383	−	1.63750i	0.163942	−	0.119111i
$190$	4.41025	−	8.06105i	0.319953	−	0.584810i
$191$	−1.60053	−	1.16286i	−0.115811	−	0.0841413i	0.528372	−	0.849013i	$-0.322802\pi$
$191$	−1.60053	−	1.16286i	−0.115811	−	0.0841413i	−0.644183	+	0.764871i	$0.722802\pi$
$192$	0.671167	+	2.06564i	0.0484373	+	0.149075i
$193$	−14.7688			−1.06308			−0.531539	−	0.847034i	$-0.678386\pi$
$193$	−14.7688			−1.06308			−0.531539	+	0.847034i	$0.678386\pi$
$194$	−1.07581	−	3.31099i	−0.0772385	−	0.237716i
$195$	−16.6929	−	17.7037i	−1.19540	−	1.26779i
$196$	0.309017	−	0.951057i	0.0220726	−	0.0679326i
$197$	−0.437302	+	1.34588i	−0.0311565	+	0.0958899i	−0.965425	−	0.260679i	$-0.916054\pi$
$197$	−0.437302	+	1.34588i	−0.0311565	+	0.0958899i	0.934269	+	0.356569i	$0.116054\pi$
$198$	6.94196	−	5.04363i	0.493344	−	0.358435i
$199$	1.30278			0.0923514			0.0461757	−	0.998933i	$-0.485297\pi$
$199$	1.30278			0.0923514			0.0461757	+	0.998933i	$0.485297\pi$
$200$	2.69631	+	4.21069i	0.190658	+	0.297741i
$201$	4.45002			0.313880
$202$	4.83978	−	3.51630i	0.340526	−	0.247406i
$203$	2.49503	−	7.67890i	0.175116	−	0.538953i
$204$	−0.447062	+	1.37592i	−0.0313006	+	0.0963334i
$205$	−1.30705	+	2.38903i	−0.0912883	+	0.166857i
$206$	4.79779	+	14.7661i	0.334278	+	1.02880i
$207$	−3.30994			−0.230057
$208$	−1.54824	−	4.76498i	−0.107351	−	0.330392i
$209$	−16.6109	−	12.0685i	−1.14900	−	0.834798i
$210$	−4.39017	+	2.07679i	−0.302951	+	0.143312i
$211$	−7.93668	+	5.76634i	−0.546384	+	0.396971i	−0.826450	−	0.563010i	$-0.809643\pi$
$211$	−7.93668	+	5.76634i	−0.546384	+	0.396971i	0.280067	+	0.959981i	$0.409643\pi$
$212$	10.5124	+	7.63773i	0.721997	+	0.524561i
$213$	−3.41091	−	2.47817i	−0.233712	−	0.169802i
$214$	2.52355	−	1.83347i	0.172507	−	0.125333i
$215$	−2.50963	−	19.5456i	−0.171156	−	1.33300i
$216$	−2.25383	−	1.63750i	−0.153353	−	0.111418i
$217$	0.881759	+	2.71378i	0.0598577	+	0.184223i
$218$	2.12138			0.143678
$219$	−0.364316	−	1.12125i	−0.0246182	−	0.0757670i
$220$	10.0996	−	4.77765i	0.680914	−	0.322109i
$221$	1.03128	−	3.17394i	0.0693711	−	0.213502i
$222$	−6.40612	+	19.7160i	−0.429950	+	1.32325i
$223$	5.30280	−	3.85271i	0.355102	−	0.257997i	−0.395904	−	0.918292i	$-0.629569\pi$
$223$	5.30280	−	3.85271i	0.355102	−	0.257997i	0.751006	+	0.660295i	$0.229569\pi$
$224$	−1.00000			−0.0668153
$225$	7.99648	+	3.12841i	0.533099	+	0.208561i
$226$	5.25316			0.349435
$227$	−1.72960	+	1.25663i	−0.114798	+	0.0834054i	−0.643703	−	0.765276i	$-0.722603\pi$
$227$	−1.72960	+	1.25663i	−0.114798	+	0.0834054i	0.528905	+	0.848681i	$0.322603\pi$
$228$	2.75801	−	8.48829i	0.182654	−	0.562150i
$229$	−1.47533	+	4.54059i	−0.0974923	+	0.300051i	−0.987895	−	0.155123i	$-0.950423\pi$
$229$	−1.47533	+	4.54059i	−0.0974923	+	0.300051i	0.890403	+	0.455173i	$0.150423\pi$
$230$	−4.23504	−	0.798941i	−0.279250	−	0.0526806i
$231$	3.35352	+	10.3211i	0.220645	+	0.679077i
$232$	−8.07407			−0.530089
$233$	−2.59877	−	7.99820i	−0.170251	−	0.523980i	0.829134	−	0.559051i	$-0.188834\pi$
$233$	−2.59877	−	7.99820i	−0.170251	−	0.523980i	−0.999385	+	0.0350710i	$0.988834\pi$
$234$	−6.96091	−	5.05740i	−0.455049	−	0.330613i
$235$	12.0208	+	2.26772i	0.784148	+	0.147930i
$236$	−8.07302	+	5.86539i	−0.525509	+	0.381805i
$237$	19.8849	+	14.4472i	1.29166	+	0.938446i
$238$	−0.538884	−	0.391522i	−0.0349307	−	0.0253786i
$239$	−21.1637	+	15.3763i	−1.36897	+	0.994613i	−0.371151	+	0.928573i	$0.621037\pi$
$239$	−21.1637	+	15.3763i	−1.36897	+	0.994613i	−0.997817	+	0.0660408i	$0.978963\pi$
$240$	3.33178	+	3.53354i	0.215066	+	0.228089i
$241$	−17.5325	−	12.7381i	−1.12937	−	0.820533i	−0.143764	−	0.989612i	$-0.545921\pi$
$241$	−17.5325	−	12.7381i	−1.12937	−	0.820533i	−0.985603	+	0.169079i	$0.945921\pi$
$242$	−4.31559	−	13.2820i	−0.277417	−	0.853800i
$243$	−15.9741			−1.02474
$244$	−3.19538	−	9.83436i	−0.204563	−	0.629580i
$245$	−0.284771	−	2.21786i	−0.0181934	−	0.141694i
$246$	−0.817383	+	2.51564i	−0.0521144	+	0.160392i
$247$	−6.36213	+	19.5806i	−0.404813	+	1.24588i
$248$	2.30848	−	1.67721i	0.146588	−	0.106503i
$249$	26.0712			1.65219
$250$	9.47630	+	5.93294i	0.599334	+	0.375232i
$251$	−6.69160			−0.422370			−0.211185	−	0.977446i	$-0.567732\pi$
$251$	−6.69160			−0.422370			−0.211185	+	0.977446i	$0.567732\pi$
$252$	−1.38935	+	1.00942i	−0.0875208	+	0.0635876i
$253$	−2.97590	+	9.15889i	−0.187093	+	0.575814i
$254$	−6.87546	+	21.1605i	−0.431405	+	1.32773i
$255$	0.411985	+	3.20863i	0.0257995	+	0.200932i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−6.37109			−0.397417			−0.198709	−	0.980059i	$-0.563675\pi$
$257$	−6.37109			−0.397417			−0.198709	+	0.980059i	$0.563675\pi$
$258$	−5.91486	−	18.2041i	−0.368243	−	1.13334i
$259$	−7.72186	−	5.61026i	−0.479813	−	0.348605i
$260$	−7.68569	−	8.15110i	−0.476646	−	0.505510i
$261$	−11.2177	+	8.15014i	−0.694359	+	0.504481i
$262$	1.86491	+	1.35494i	0.115214	+	0.0837082i
$263$	10.7331	+	7.79807i	0.661833	+	0.480850i	0.867281	−	0.497818i	$-0.165865\pi$
$263$	10.7331	+	7.79807i	0.661833	+	0.480850i	−0.205449	+	0.978668i	$0.565865\pi$
$264$	8.77963	−	6.37878i	0.540349	−	0.392587i
$265$	28.5520	+	5.38635i	1.75394	+	0.330881i
$266$	3.32448	+	2.41537i	0.203837	+	0.148096i
$267$	3.05190	+	9.39279i	0.186773	+	0.574830i
$268$	2.04887			0.125155
$269$	−0.589669	−	1.81481i	−0.0359527	−	0.110651i	0.931470	−	0.363819i	$-0.118527\pi$
$269$	−0.589669	−	1.81481i	−0.0359527	−	0.110651i	−0.967422	+	0.253168i	$0.918527\pi$
$270$	−6.12145	−	1.15481i	−0.372539	−	0.0702797i
$271$	3.97393	−	12.2305i	0.241399	−	0.742950i	−0.754809	−	0.655945i	$-0.772270\pi$
$271$	3.97393	−	12.2305i	0.241399	−	0.742950i	0.996208	−	0.0870049i	$-0.0277296\pi$
$272$	−0.205835	+	0.633496i	−0.0124806	+	0.0384113i
$273$	8.80360	−	6.39619i	0.532818	−	0.387115i
$274$	−21.6770			−1.30956
$275$	15.8461	−	19.3143i	0.955554	−	1.16469i
$276$	−4.18614			−0.251976
$277$	−11.8144	+	8.58364i	−0.709857	+	0.515741i	−0.883128	−	0.469133i	$-0.844566\pi$
$277$	−11.8144	+	8.58364i	−0.709857	+	0.515741i	0.173271	+	0.984874i	$0.444566\pi$
$278$	−0.448426	+	1.38011i	−0.0268948	+	0.0827738i
$279$	1.51427	−	4.66045i	0.0906571	−	0.279014i
$280$	−2.02131	+	0.956190i	−0.120796	+	0.0571433i
$281$	−7.36510	−	22.6675i	−0.439365	−	1.35223i	−0.888547	−	0.458786i	$-0.848284\pi$
$281$	−7.36510	−	22.6675i	−0.439365	−	1.35223i	0.449181	−	0.893441i	$-0.351716\pi$
$282$	11.8820			0.707562
$283$	0.916330	+	2.82017i	0.0544702	+	0.167642i	0.974591	−	0.223993i	$-0.0719094\pi$
$283$	0.916330	+	2.82017i	0.0544702	+	0.167642i	−0.920120	+	0.391635i	$0.871909\pi$
$284$	−1.57044	−	1.14099i	−0.0931888	−	0.0677056i
$285$	−2.54161	−	19.7947i	−0.150552	−	1.17253i
$286$	−20.2527	+	14.7144i	−1.19757	+	0.870083i
$287$	−0.985264	−	0.715836i	−0.0581583	−	0.0422545i
$288$	1.38935	+	1.00942i	0.0818682	+	0.0594807i
$289$	13.3943	−	9.73156i	0.787902	−	0.572445i
$290$	−16.3202	+	7.72035i	−0.958356	+	0.453354i
$291$	−6.11727	−	4.44446i	−0.358601	−	0.260539i
$292$	−0.167737	−	0.516243i	−0.00981609	−	0.0302108i
$293$	28.8409			1.68490			0.842451	−	0.538774i	$-0.181112\pi$
$293$	28.8409			1.68490			0.842451	+	0.538774i	$0.181112\pi$
$294$	−0.671167	−	2.06564i	−0.0391432	−	0.120471i
$295$	−10.7097	+	19.5751i	−0.623541	+	1.13971i
$296$	−2.94949	+	9.07759i	−0.171436	+	0.527624i
$297$	−4.30146	+	13.2385i	−0.249596	+	0.768177i
$298$	−9.13243	+	6.63510i	−0.529027	+	0.384361i
$299$	9.65652			0.558451
$300$	10.1133	+	3.95656i	0.583892	+	0.228432i
$301$	8.81281			0.507962
$302$	0.211290	−	0.153511i	0.0121584	−	0.00883356i
$303$	4.01512	−	12.3573i	0.230662	−	0.709906i
$304$	1.26984	−	3.90816i	0.0728301	−	0.224148i
$305$	−15.8624	−	16.8229i	−0.908276	−	0.963277i
$306$	0.353487	+	1.08792i	0.0202075	+	0.0621924i
$307$	25.1865			1.43747			0.718733	−	0.695286i	$-0.244722\pi$
$307$	25.1865			1.43747			0.718733	+	0.695286i	$0.244722\pi$
$308$	1.54402	+	4.75200i	0.0879787	+	0.270771i
$309$	27.2813	+	19.8210i	1.55198	+	1.12758i
$310$	3.06242	−	5.59750i	0.173934	−	0.317917i
$311$	−16.7800	+	12.1914i	−0.951504	+	0.691308i	−0.951162	−	0.308692i	$-0.900109\pi$
$311$	−16.7800	+	12.1914i	−0.951504	+	0.691308i	−0.000341978		1.00000i	$0.500109\pi$
$312$	−8.80360	−	6.39619i	−0.498406	−	0.362113i
$313$	20.9643	+	15.2314i	1.18497	+	0.860931i	0.992724	−	0.120416i	$-0.0384228\pi$
$313$	20.9643	+	15.2314i	1.18497	+	0.860931i	0.192246	+	0.981347i	$0.438423\pi$
$314$	13.8460	−	10.0597i	0.781373	−	0.567701i
$315$	−1.84311	+	3.36884i	−0.103847	+	0.189813i
$316$	9.15534	+	6.65174i	0.515028	+	0.374190i
$317$	8.89649	+	27.3806i	0.499677	+	1.53785i	0.809539	+	0.587066i	$0.199717\pi$
$317$	8.89649	+	27.3806i	0.499677	+	1.53785i	−0.309862	+	0.950781i	$0.600283\pi$
$318$	28.2224			1.58263
$319$	12.4665	+	38.3680i	0.697991	+	2.14820i
$320$	1.53401	+	1.62690i	0.0857538	+	0.0909466i
$321$	2.09356	−	6.44331i	0.116851	−	0.359631i
$322$	0.595591	−	1.83304i	0.0331910	−	0.102151i
$323$	2.21442	−	1.60887i	0.123214	−	0.0895201i
$324$	−11.2028			−0.622376
$325$	−23.3292	−	9.12693i	−1.29407	−	0.506271i
$326$	−15.7948			−0.874794
$327$	3.72756	−	2.70823i	0.206134	−	0.149765i
$328$	−0.376337	+	1.15825i	−0.0207797	+	0.0639535i
$329$	−1.69053	+	5.20292i	−0.0932020	+	0.286846i
$330$	11.6470	−	21.2885i	0.641149	−	1.17189i
$331$	6.42762	+	19.7822i	0.353294	+	1.08733i	0.956992	+	0.290114i	$0.0936932\pi$
$331$	6.42762	+	19.7822i	0.353294	+	1.08733i	−0.603698	+	0.797213i	$0.706307\pi$
$332$	12.0036			0.658784
$333$	5.06525	+	15.5892i	0.277574	+	0.854284i
$334$	−4.83600	−	3.51356i	−0.264614	−	0.192253i
$335$	4.14140	−	1.95911i	0.226269	−	0.107037i
$336$	−1.75714	+	1.27664i	−0.0958597	+	0.0696462i
$337$	14.0959	+	10.2413i	0.767855	+	0.557879i	0.901310	−	0.433176i	$-0.142607\pi$
$337$	14.0959	+	10.2413i	0.767855	+	0.557879i	−0.133455	+	0.991055i	$0.542607\pi$
$338$	9.79076	+	7.11341i	0.532547	+	0.386918i
$339$	9.23053	−	6.70637i	0.501334	−	0.364240i
$340$	0.189685	+	1.47731i	0.0102871	+	0.0801184i
$341$	−11.5344	−	8.38025i	−0.624624	−	0.453816i
$342$	−2.18073	−	6.71160i	−0.117920	−	0.362922i
$343$	1.00000			0.0539949
$344$	−2.72331	−	8.38148i	−0.146831	−	0.451899i
$345$	−8.46150	+	4.00275i	−0.455552	+	0.215501i
$346$	7.23995	−	22.2823i	0.389222	−	1.19790i
$347$	−4.31612	+	13.2836i	−0.231701	+	0.713104i	0.765840	+	0.643031i	$0.222323\pi$
$347$	−4.31612	+	13.2836i	−0.231701	+	0.713104i	−0.997542	+	0.0700730i	$0.977677\pi$
$348$	−14.1873	+	10.3076i	−0.760517	+	0.552548i
$349$	−31.9657			−1.71108			−0.855541	−	0.517734i	$-0.826776\pi$
$349$	−31.9657			−1.71108			−0.855541	+	0.517734i	$0.826776\pi$
$350$	−3.17140	+	3.86552i	−0.169519	+	0.206621i
$351$	13.9578			0.745013
$352$	4.04230	−	2.93690i	0.215455	−	0.156537i
$353$	3.10980	−	9.57098i	0.165518	−	0.509412i	−0.833556	−	0.552435i	$-0.813699\pi$
$353$	3.10980	−	9.57098i	0.165518	−	0.509412i	0.999074	+	0.0430228i	$0.0136988\pi$
$354$	−6.69744	+	20.6126i	−0.355965	+	1.09555i
$355$	−4.26537	−	0.804663i	−0.226382	−	0.0427071i
$356$	1.40515	+	4.32461i	0.0744728	+	0.229204i
$357$	−1.44672			−0.0765688
$358$	−8.04180	−	24.7501i	−0.425023	−	1.30808i
$359$	9.97744	+	7.24903i	0.526589	+	0.382589i	0.819080	−	0.573679i	$-0.194484\pi$
$359$	9.97744	+	7.24903i	0.526589	+	0.382589i	−0.292491	+	0.956268i	$0.594484\pi$
$360$	3.77351	+	0.711873i	0.198881	+	0.0375190i
$361$	1.71013	−	1.24248i	0.0900068	−	0.0653938i
$362$	1.89630	+	1.37774i	0.0996672	+	0.0724124i
$363$	−24.5394	−	17.8289i	−1.28798	−	0.935775i
$364$	4.05333	−	2.94492i	0.212452	−	0.154356i
$365$	−0.832676	−	0.883098i	−0.0435842	−	0.0462235i
$366$	−18.1696	−	13.2010i	−0.949740	−	0.690027i
$367$	−3.52350	−	10.8442i	−0.183925	−	0.566063i	0.816003	−	0.578047i	$-0.196185\pi$
$367$	−3.52350	−	10.8442i	−0.183925	−	0.566063i	−0.999928	+	0.0119844i	$0.996185\pi$
$368$	−1.92737			−0.100471
$369$	0.646296	+	1.98909i	0.0336448	+	0.103548i
$370$	2.71807	+	21.1689i	0.141306	+	1.10052i
$371$	−4.01539	+	12.3581i	−0.208469	+	0.641601i
$372$	1.91513	−	5.89416i	0.0992949	−	0.305598i
$373$	−3.04159	+	2.20985i	−0.157488	+	0.114421i	−0.663738	−	0.747965i	$-0.731031\pi$
$373$	−3.04159	+	2.20985i	−0.157488	+	0.114421i	0.506251	+	0.862386i	$0.331031\pi$
$374$	3.32819			0.172097
$375$	24.2254	−	1.67279i	1.25099	−	0.0863825i
$376$	5.47067			0.282128
$377$	32.7269	−	23.7775i	1.68552	−	1.22460i
$378$	0.860885	−	2.64953i	0.0442791	−	0.136277i
$379$	4.31010	−	13.2651i	0.221395	−	0.681384i	−0.777243	−	0.629201i	$-0.783382\pi$
$379$	4.31010	−	13.2651i	0.221395	−	0.681384i	0.998638	−	0.0521827i	$-0.0166178\pi$
$380$	−1.17020	−	9.11380i	−0.0600302	−	0.467528i
$381$	14.9331	+	45.9594i	0.765046	+	2.35457i
$382$	−1.97837			−0.101222
$383$	3.73989	+	11.5102i	0.191100	+	0.588144i	1.00000		0.000198488i	$6.31807e-5\pi$
$383$	3.73989	+	11.5102i	0.191100	+	0.588144i	−0.808900	+	0.587946i	$0.799937\pi$
$384$	1.75714	+	1.27664i	0.0896686	+	0.0651480i
$385$	7.66476	+	8.12890i	0.390633	+	0.414287i
$386$	−11.9482	+	8.68085i	−0.608146	+	0.441844i
$387$	−12.2441	−	8.89584i	−0.622401	−	0.452201i
$388$	−2.81650	−	2.04631i	−0.142986	−	0.103885i
$389$	−12.7415	+	9.25724i	−0.646020	+	0.469361i	−0.861913	−	0.507056i	$-0.830734\pi$
$389$	−12.7415	+	9.25724i	−0.646020	+	0.469361i	0.215893	+	0.976417i	$0.430734\pi$
$390$	−23.9108	−	4.51078i	−1.21077	−	0.228412i
$391$	−1.03863	−	0.754609i	−0.0525258	−	0.0381622i
$392$	−0.309017	−	0.951057i	−0.0156077	−	0.0480356i
$393$	5.00666			0.252553
$394$	0.437302	+	1.34588i	0.0220310	+	0.0678044i
$395$	24.8661	+	4.69100i	1.25115	+	0.236030i
$396$	2.65159	−	8.16076i	0.133248	−	0.410094i
$397$	0.296903	−	0.913772i	0.0149011	−	0.0458609i	−0.943329	−	0.331858i	$-0.892325\pi$
$397$	0.296903	−	0.913772i	0.0149011	−	0.0458609i	0.958231	+	0.285997i	$0.0923246\pi$
$398$	1.05397	−	0.765753i	0.0528307	−	0.0383837i
$399$	8.92511			0.446814
$400$	4.65634	+	1.82167i	0.232817	+	0.0910836i
$401$	−14.5970			−0.728938			−0.364469	−	0.931216i	$-0.618749\pi$
$401$	−14.5970			−0.728938			−0.364469	+	0.931216i	$0.618749\pi$
$402$	3.60014	−	2.61566i	0.179559	−	0.130457i
$403$	−4.41779	+	13.5965i	−0.220066	+	0.677292i
$404$	1.84863	−	5.68950i	0.0919728	−	0.283063i
$405$	−22.6443	+	10.7120i	−1.12520	+	0.532282i
$406$	−2.49503	−	7.67890i	−0.123826	−	0.381097i
$407$	47.6908			2.36395
$408$	0.447062	+	1.37592i	0.0221329	+	0.0681180i
$409$	−1.38232	−	1.00431i	−0.0683513	−	0.0496601i	0.553085	−	0.833125i	$-0.313451\pi$
$409$	−1.38232	−	1.00431i	−0.0683513	−	0.0496601i	−0.621436	+	0.783465i	$0.713451\pi$
$410$	0.346809	+	2.70103i	0.0171277	+	0.133394i
$411$	−38.0895	+	27.6737i	−1.87882	+	1.36504i
$412$	12.5608	+	9.12595i	0.618826	+	0.449603i
$413$	−8.07302	−	5.86539i	−0.397247	−	0.288617i
$414$	−2.67780	+	1.94553i	−0.131607	+	0.0956177i
$415$	24.2631	−	11.4777i	1.19103	−	0.563420i
$416$	−4.05333	−	2.94492i	−0.198731	−	0.144387i
$417$	0.973956	+	2.99753i	0.0476948	+	0.146790i
$418$	−20.5322			−1.00426
$419$	−4.22139	−	12.9921i	−0.206228	−	0.634705i	−0.999661	−	0.0260471i	$-0.991708\pi$
$419$	−4.22139	−	12.9921i	−0.206228	−	0.634705i	0.793432	−	0.608658i	$-0.208292\pi$
$420$	−2.33102	+	4.26064i	−0.113742	+	0.207898i
$421$	1.76632	−	5.43616i	0.0860849	−	0.264942i	−0.898743	−	0.438476i	$-0.855519\pi$
$421$	1.76632	−	5.43616i	0.0860849	−	0.264942i	0.984828	+	0.173534i	$0.0555185\pi$
$422$	−3.03154	+	9.33013i	−0.147573	+	0.454184i
$423$	7.60068	−	5.52222i	0.369558	−	0.268499i
$424$	12.9941			0.631048
$425$	1.79600	+	2.80473i	0.0871189	+	0.136049i
$426$	−4.21612			−0.204272
$427$	8.36560	−	6.07797i	0.404840	−	0.294133i
$428$	0.963911	−	2.96661i	0.0465924	−	0.143397i
$429$	−16.8018	+	51.7106i	−0.811198	+	2.49661i
$430$	−13.5189	−	14.3376i	−0.651941	−	0.691419i
$431$	−3.49650	−	10.7611i	−0.168421	−	0.518345i	0.830852	−	0.556494i	$-0.187854\pi$
$431$	−3.49650	−	10.7611i	−0.168421	−	0.518345i	−0.999272	+	0.0381491i	$0.987854\pi$
$432$	−2.78588			−0.134036
$433$	−9.08720	−	27.9675i	−0.436703	−	1.34403i	−0.891331	−	0.453353i	$-0.850228\pi$
$433$	−9.08720	−	27.9675i	−0.436703	−	1.34403i	0.454628	−	0.890681i	$-0.349772\pi$
$434$	2.30848	+	1.67721i	0.110810	+	0.0805085i
$435$	−18.8208	+	34.4007i	−0.902388	+	1.64939i
$436$	1.71623	−	1.24692i	0.0821926	−	0.0597164i
$437$	6.40751	+	4.65533i	0.306513	+	0.222694i
$438$	−0.953791	−	0.692970i	−0.0455739	−	0.0331114i
$439$	−31.3930	+	22.8083i	−1.49830	+	1.08858i	−0.527254	+	0.849707i	$0.676779\pi$
$439$	−31.3930	+	22.8083i	−1.49830	+	1.08858i	−0.971050	+	0.238875i	$0.923221\pi$
$440$	5.36251	−	9.80159i	0.255647	−	0.467273i
$441$	−1.38935	−	1.00942i	−0.0661595	−	0.0480677i
$442$	−1.03128	−	3.17394i	−0.0490528	−	0.150969i
$443$	17.2107			0.817707			0.408853	−	0.912600i	$-0.365929\pi$
$443$	17.2107			0.817707			0.408853	+	0.912600i	$0.365929\pi$
$444$	6.40612	+	19.7160i	0.304021	+	0.935680i
$445$	6.97539	+	7.39779i	0.330665	+	0.350689i
$446$	2.02549	−	6.23382i	0.0959098	−	0.295180i
$447$	−7.57633	+	23.3176i	−0.358348	+	1.10288i
$448$	−0.809017	+	0.587785i	−0.0382225	+	0.0277702i
$449$	−6.57448			−0.310269			−0.155134	−	0.987893i	$-0.549581\pi$
$449$	−6.57448			−0.310269			−0.155134	+	0.987893i	$0.549581\pi$
$450$	8.30812	−	2.16927i	0.391649	−	0.102261i
$451$	6.08507			0.286535
$452$	4.24990	−	3.08773i	0.199898	−	0.145235i
$453$	0.175288	−	0.539480i	0.00823573	−	0.0253470i
$454$	−0.660649	+	2.03327i	−0.0310058	+	0.0954261i
$455$	5.37715	−	9.82835i	0.252084	−	0.460760i
$456$	−2.75801	−	8.48829i	−0.129156	−	0.397500i
$457$	3.74235			0.175060			0.0875300	−	0.996162i	$-0.472103\pi$
$457$	3.74235			0.175060			0.0875300	+	0.996162i	$0.472103\pi$
$458$	1.47533	+	4.54059i	0.0689375	+	0.212168i
$459$	−1.50127	−	1.09073i	−0.0700732	−	0.0509111i
$460$	−3.89582	+	1.84294i	−0.181644	+	0.0859273i
$461$	22.9427	−	16.6689i	1.06855	−	0.776346i	0.0928976	−	0.995676i	$-0.470387\pi$
$461$	22.9427	−	16.6689i	1.06855	−	0.776346i	0.975651	+	0.219330i	$0.0703871\pi$
$462$	8.77963	+	6.37878i	0.408465	+	0.296768i
$463$	−28.8213	−	20.9399i	−1.33944	−	0.973160i	−0.999464	−	0.0327256i	$-0.989581\pi$
$463$	−28.8213	−	20.9399i	−1.33944	−	0.973160i	−0.339975	−	0.940434i	$-0.610419\pi$
$464$	−6.53206	+	4.74582i	−0.303243	+	0.220319i
$465$	−1.76487	−	13.7452i	−0.0818437	−	0.637417i
$466$	−6.80368	−	4.94316i	−0.315174	−	0.228987i
$467$	−10.0111	−	30.8110i	−0.463259	−	1.42576i	−0.861159	−	0.508335i	$-0.830261\pi$
$467$	−10.0111	−	30.8110i	−0.463259	−	1.42576i	0.397901	−	0.917428i	$-0.369739\pi$
$468$	−8.60416			−0.397728
$469$	0.633135	+	1.94859i	0.0292355	+	0.0899775i
$470$	11.0579	−	5.23100i	0.510065	−	0.241288i
$471$	11.4867	−	35.3525i	0.529280	−	1.62896i
$472$	−3.08362	+	9.49041i	−0.141935	+	0.436831i
$473$	−35.6240	+	25.8823i	−1.63799	+	1.19007i
$474$	24.5790			1.12895
$475$	−11.0799	−	17.3029i	−0.508380	−	0.793912i
$476$	−0.666097			−0.0305305
$477$	18.0533	−	13.1165i	0.826605	−	0.600564i
$478$	−8.08383	+	24.8795i	−0.369746	+	1.13796i
$479$	3.32814	−	10.2430i	0.152067	−	0.468013i	−0.845785	−	0.533523i	$-0.820868\pi$
$479$	3.32814	−	10.2430i	0.152067	−	0.468013i	0.997852	+	0.0655106i	$0.0208676\pi$
$480$	4.77243	+	0.900320i	0.217831	+	0.0410938i
$481$	−14.7775	−	45.4805i	−0.673796	−	2.07373i
$482$	−21.6713			−0.987103
$483$	−1.29359	−	3.98126i	−0.0588604	−	0.181154i
$484$	−11.2984	−	8.20874i	−0.513562	−	0.373124i
$485$	−7.64968	−	1.44311i	−0.347354	−	0.0655285i
$486$	−12.9233	+	9.38935i	−0.586214	+	0.425909i
$487$	−0.717822	−	0.521528i	−0.0325276	−	0.0236327i	0.571403	−	0.820670i	$-0.306399\pi$
$487$	−0.717822	−	0.521528i	−0.0325276	−	0.0236327i	−0.603930	+	0.797037i	$0.706399\pi$
$488$	−8.36560	−	6.07797i	−0.378693	−	0.275137i
$489$	−27.7537	+	20.1642i	−1.25506	+	0.911857i
$490$	−1.53401	−	1.62690i	−0.0692995	−	0.0734960i
$491$	−17.5795	−	12.7722i	−0.793350	−	0.576403i	0.115605	−	0.993295i	$-0.463119\pi$
$491$	−17.5795	−	12.7722i	−0.793350	−	0.576403i	−0.908956	+	0.416892i	$0.863119\pi$
$492$	0.817383	+	2.51564i	0.0368505	+	0.113414i
$493$	−5.37812			−0.242218
$494$	6.36213	+	19.5806i	0.286246	+	0.880974i
$495$	−2.44355	−	19.0309i	−0.109829	−	0.855374i
$496$	0.881759	−	2.71378i	0.0395922	−	0.121852i
$497$	0.599857	−	1.84617i	0.0269072	−	0.0828120i
$498$	21.0920	−	15.3243i	0.945156	−	0.686696i
$499$	27.6905			1.23960			0.619799	−	0.784761i	$-0.287214\pi$
$499$	27.6905			1.23960			0.619799	+	0.784761i	$0.287214\pi$
$500$	11.1538	−	0.770182i	0.498812	−	0.0344436i
$501$	−12.9831			−0.580040
$502$	−5.41361	+	3.93322i	−0.241621	+	0.175548i
$503$	3.04549	−	9.37306i	0.135792	−	0.417924i	−0.859921	−	0.510428i	$-0.829487\pi$
$503$	3.04549	−	9.37306i	0.135792	−	0.417924i	0.995712	+	0.0925039i	$0.0294871\pi$
$504$	−0.530684	+	1.63328i	−0.0236386	+	0.0727520i
$505$	−1.70358	−	13.2679i	−0.0758085	−	0.590414i
$506$	2.97590	+	9.15889i	0.132295	+	0.407162i
$507$	26.2849			1.16736
$508$	6.87546	+	21.1605i	0.305049	+	0.938845i
$509$	−22.6999	−	16.4924i	−1.00616	−	0.731014i	−0.0427559	−	0.999086i	$-0.513614\pi$
$509$	−22.6999	−	16.4924i	−1.00616	−	0.731014i	−0.963399	+	0.268071i	$0.913614\pi$
$510$	2.21929	+	2.35368i	0.0982718	+	0.104223i
$511$	0.439142	−	0.319055i	0.0194265	−	0.0141142i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	9.26160	+	6.72894i	0.408910	+	0.297090i
$514$	−5.15432	+	3.74483i	−0.227347	+	0.165177i
$515$	34.1154	+	6.43588i	1.50330	+	0.283599i
$516$	−15.4853	−	11.2507i	−0.681703	−	0.495286i
$517$	−8.44683	−	25.9967i	−0.371491	−	1.14333i
$518$	−9.54474			−0.419372
$519$	−15.7248	−	48.3958i	−0.690240	−	2.12434i
$520$	−11.0089	−	2.07684i	−0.482774	−	0.0910755i
$521$	−9.10897	+	28.0345i	−0.399071	+	1.22821i	0.526674	+	0.850067i	$0.323439\pi$
$521$	−9.10897	+	28.0345i	−0.399071	+	1.22821i	−0.925745	+	0.378147i	$0.876561\pi$
$522$	−4.28478	+	13.1872i	−0.187540	+	0.577188i
$523$	25.0128	−	18.1729i	1.09373	−	0.794645i	0.113709	−	0.993514i	$-0.463727\pi$
$523$	25.0128	−	18.1729i	1.09373	−	0.794645i	0.980026	+	0.198869i	$0.0637269\pi$
$524$	2.30515			0.100701
$525$	−0.637734	+	10.8410i	−0.0278330	+	0.473139i
$526$	13.2669			0.578463
$527$	1.53767	−	1.11718i	0.0669819	−	0.0486652i
$528$	3.35352	−	10.3211i	0.145943	−	0.449167i
$529$	−5.95946	+	18.3413i	−0.259107	+	0.797450i
$530$	26.2651	−	12.4248i	1.14088	−	0.539699i
$531$	5.29560	+	16.2982i	0.229809	+	0.707280i
$532$	4.10928			0.178160
$533$	−1.88552	−	5.80304i	−0.0816711	−	0.251358i
$534$	7.98999	+	5.80507i	0.345761	+	0.251210i
$535$	−0.888282	−	6.91813i	−0.0384038	−	0.299097i
$536$	1.65757	−	1.20429i	0.0715961	−	0.0520176i
$537$	−45.7274	−	33.2229i	−1.97328	−	1.43368i
$538$	−1.54377	−	1.12162i	−0.0665567	−	0.0483563i
$539$	−4.04230	+	2.93690i	−0.174114	+	0.126501i
$540$	−5.63114	+	2.66383i	−0.242326	+	0.114633i
$541$	−14.6048	−	10.6110i	−0.627908	−	0.456202i	0.227767	−	0.973716i	$-0.426858\pi$
$541$	−14.6048	−	10.6110i	−0.627908	−	0.456202i	−0.855675	+	0.517514i	$0.826858\pi$
$542$	−3.97393	−	12.2305i	−0.170695	−	0.525345i
$543$	5.09093			0.218473
$544$	0.205835	+	0.633496i	0.00882512	+	0.0271609i
$545$	2.27675	−	4.16145i	0.0975254	−	0.178257i
$546$	3.36268	−	10.3493i	0.143909	−	0.442907i
$547$	7.40007	−	22.7751i	0.316404	−	0.973792i	−0.658768	−	0.752346i	$-0.728922\pi$
$547$	7.40007	−	22.7751i	0.316404	−	0.973792i	0.975173	−	0.221446i	$-0.0710777\pi$
$548$	−17.5371	+	12.7414i	−0.749147	+	0.544287i
$549$	−17.7580			−0.757892
$550$	1.46711	−	24.9396i	0.0625577	−	1.06343i
$551$	33.1786			1.41346
$552$	−3.38666	+	2.46055i	−0.144146	+	0.104728i
$553$	−3.49703	+	10.7627i	−0.148709	+	0.457678i
$554$	−4.51269	+	13.8886i	−0.191726	+	0.590071i
$555$	31.8010	+	33.7267i	1.34988	+	1.43162i
$556$	0.448426	+	1.38011i	0.0190175	+	0.0585299i
$557$	7.45853			0.316028			0.158014	−	0.987437i	$-0.449491\pi$
$557$	7.45853			0.316028			0.158014	+	0.987437i	$0.449491\pi$
$558$	−1.51427	−	4.66045i	−0.0641043	−	0.197293i
$559$	35.7212	+	25.9530i	1.51085	+	1.09769i
$560$	−1.07324	+	1.96167i	−0.0453527	+	0.0828957i
$561$	5.84809	−	4.24889i	0.246906	−	0.179388i
$562$	−19.2821	−	14.0093i	−0.813366	−	0.590945i
$563$	22.5315	+	16.3701i	0.949590	+	0.689918i	0.950710	−	0.310082i	$-0.100356\pi$
$563$	22.5315	+	16.3701i	0.949590	+	0.689918i	−0.00111965	+	0.999999i	$0.500356\pi$
$564$	9.61273	−	6.98406i	0.404769	−	0.294082i
$565$	5.63791	−	10.3050i	0.237189	−	0.433534i
$566$	2.39898	+	1.74296i	0.100837	+	0.0732622i
$567$	−3.46185	−	10.6545i	−0.145384	−	0.447445i
$568$	−1.94118			−0.0814500
$569$	−12.8340	−	39.4991i	−0.538031	−	1.65589i	−0.737007	−	0.675885i	$-0.763761\pi$
$569$	−12.8340	−	39.4991i	−0.538031	−	1.65589i	0.198976	−	0.980004i	$-0.436239\pi$
$570$	−13.6912	−	14.5203i	−0.573462	−	0.608188i
$571$	7.54469	−	23.2202i	0.315736	−	0.971734i	−0.659715	−	0.751516i	$-0.729323\pi$
$571$	7.54469	−	23.2202i	0.315736	−	0.971734i	0.975451	−	0.220218i	$-0.0706770\pi$
$572$	−7.73584	+	23.8085i	−0.323452	+	0.995482i
$573$	−3.47626	+	2.52565i	−0.145223	+	0.105511i
$574$	−1.21785			−0.0508322
$575$	−6.11247	+	7.45029i	−0.254908	+	0.310699i
$576$	1.71733			0.0715555
$577$	27.5768	−	20.0358i	1.14804	−	0.834099i	0.159820	−	0.987146i	$-0.448909\pi$
$577$	27.5768	−	20.0358i	1.14804	−	0.834099i	0.988219	+	0.153047i	$0.0489086\pi$
$578$	5.11618	−	15.7460i	0.212805	−	0.654947i
$579$	−9.91230	+	30.5069i	−0.411941	+	1.26782i
$580$	−8.66542	+	15.8387i	−0.359812	+	0.657665i
$581$	3.70932	+	11.4161i	0.153889	+	0.473621i
$582$	−7.56137			−0.313429
$583$	−20.0631	−	61.7479i	−0.830929	−	2.55734i
$584$	−0.439142	−	0.319055i	−0.0181718	−	0.0132026i
$585$	−17.3917	+	8.22721i	−0.719058	+	0.340153i
$586$	23.3327	−	16.9522i	0.963867	−	0.700290i
$587$	−7.42758	−	5.39646i	−0.306569	−	0.222736i	0.423854	−	0.905731i	$-0.360677\pi$
$587$	−7.42758	−	5.39646i	−0.306569	−	0.222736i	−0.730423	+	0.682995i	$0.760677\pi$
$588$	−1.75714	−	1.27664i	−0.0724631	−	0.0526476i
$589$	−9.48617	+	6.89211i	−0.390871	+	0.283984i
$590$	2.84168	+	22.1316i	0.116990	+	0.911143i
$591$	2.48660	+	1.80662i	0.102285	+	0.0743143i
$592$	2.94949	+	9.07759i	0.121223	+	0.373087i
$593$	−26.1434			−1.07358			−0.536791	−	0.843715i	$-0.680364\pi$
$593$	−26.1434			−1.07358			−0.536791	+	0.843715i	$0.680364\pi$
$594$	4.30146	+	13.2385i	0.176491	+	0.543183i
$595$	−1.34639	+	0.636916i	−0.0551966	+	0.0261110i
$596$	−3.48828	+	10.7358i	−0.142885	+	0.439756i
$597$	0.874380	−	2.69107i	0.0357860	−	0.110138i
$598$	7.81229	−	5.67596i	0.319468	−	0.232107i
$599$	24.2404			0.990438			0.495219	−	0.868768i	$-0.335088\pi$
$599$	24.2404			0.990438			0.495219	+	0.868768i	$0.335088\pi$
$600$	10.5074	−	2.74352i	0.428965	−	0.112004i
$601$	6.92663			0.282543			0.141271	−	0.989971i	$-0.454881\pi$
$601$	6.92663			0.282543			0.141271	+	0.989971i	$0.454881\pi$
$602$	7.12971	−	5.18004i	0.290585	−	0.211123i
$603$	1.08730	−	3.34637i	0.0442784	−	0.136275i
$604$	0.0807055	−	0.248386i	0.00328386	−	0.0101067i
$605$	−30.6866	−	5.78904i	−1.24759	−	0.235358i
$606$	−4.01512	−	12.3573i	−0.163103	−	0.501979i
$607$	−36.9449			−1.49955			−0.749774	−	0.661694i	$-0.769838\pi$
$607$	−36.9449			−1.49955			−0.749774	+	0.661694i	$0.769838\pi$
$608$	−1.26984	−	3.90816i	−0.0514987	−	0.158497i
$609$	−14.1873	−	10.3076i	−0.574897	−	0.417687i
$610$	−22.7212	−	4.28636i	−0.919954	−	0.173550i
$611$	−22.1745	+	16.1107i	−0.897083	+	0.651769i
$612$	0.925442	+	0.672373i	0.0374088	+	0.0271791i
$613$	−12.8016	−	9.30089i	−0.517051	−	0.375660i	0.298441	−	0.954428i	$-0.403533\pi$
$613$	−12.8016	−	9.30089i	−0.517051	−	0.375660i	−0.815492	+	0.578769i	$0.803533\pi$
$614$	20.3763	−	14.8042i	0.822319	−	0.597450i
$615$	4.05762	+	4.30333i	0.163619	+	0.173527i
$616$	4.04230	+	2.93690i	0.162869	+	0.118331i
$617$	−3.68388	−	11.3378i	−0.148308	−	0.456444i	0.849114	−	0.528210i	$-0.177137\pi$
$617$	−3.68388	−	11.3378i	−0.148308	−	0.456444i	−0.997421	+	0.0717660i	$0.977137\pi$
$618$	33.7215			1.35648
$619$	−8.83935	−	27.2047i	−0.355283	−	1.09345i	−0.955845	−	0.293871i	$-0.905056\pi$
$619$	−8.83935	−	27.2047i	−0.355283	−	1.09345i	0.600562	−	0.799579i	$-0.294944\pi$
$620$	−0.812576	−	6.32852i	−0.0326338	−	0.254159i
$621$	1.65925	−	5.10664i	0.0665833	−	0.204922i
$622$	−6.40937	+	19.7260i	−0.256992	+	0.790941i
$623$	−3.67873	+	2.67275i	−0.147385	+	0.107082i
$624$	−10.8819			−0.435623
$625$	21.8088	−	12.2219i	0.872353	−	0.488876i
$626$	25.9132			1.03570
$627$	−36.0779	+	26.2122i	−1.44081	+	1.04681i
$628$	5.28869	−	16.2769i	0.211042	−	0.649519i
$629$	−1.96465	+	6.04656i	−0.0783356	+	0.241092i
$630$	0.489046	+	3.80880i	0.0194841	+	0.151746i
$631$	3.03605	+	9.34399i	0.120863	+	0.371979i	0.993125	−	0.117061i	$-0.0373473\pi$
$631$	3.03605	+	9.34399i	0.120863	+	0.371979i	−0.872262	+	0.489040i	$0.837347\pi$
$632$	11.3166			0.450151
$633$	6.58433	+	20.2645i	0.261704	+	0.805441i
$634$	23.2913	+	16.9221i	0.925017	+	0.672064i
$635$	34.1309	+	36.1977i	1.35444	+	1.43646i
$636$	22.8324	−	16.5887i	0.905363	−	0.657785i
$637$	4.05333	+	2.94492i	0.160599	+	0.116682i
$638$	32.6378	+	23.7127i	1.29214	+	0.938796i
$639$	−2.69697	+	1.95947i	−0.106691	+	0.0775153i
$640$	2.19731	+	0.414523i	0.0868563	+	0.0163855i
$641$	20.9909	+	15.2508i	0.829091	+	0.602370i	0.919302	−	0.393553i	$-0.128754\pi$
$641$	20.9909	+	15.2508i	0.829091	+	0.602370i	−0.0902108	+	0.995923i	$0.528754\pi$
$642$	−2.09356	−	6.44331i	−0.0826262	−	0.254297i
$643$	9.24487			0.364582			0.182291	−	0.983245i	$-0.441649\pi$
$643$	9.24487			0.364582			0.182291	+	0.983245i	$0.441649\pi$
$644$	−0.595591	−	1.83304i	−0.0234696	−	0.0722319i
$645$	−42.0585	−	7.93435i	−1.65605	−	0.312415i
$646$	0.845835	−	2.60321i	0.0332789	−	0.102422i
$647$	−5.24469	+	16.1415i	−0.206190	+	0.634588i	0.793472	+	0.608606i	$0.208271\pi$
$647$	−5.24469	+	16.1415i	−0.206190	+	0.634588i	−0.999662	+	0.0259814i	$0.991729\pi$
$648$	−9.06323	+	6.58482i	−0.356037	+	0.258676i
$649$	49.8596			1.95716
$650$	−24.2384	+	6.32871i	−0.950707	+	0.248232i
$651$	6.19749			0.242899
$652$	−12.7783	+	9.28396i	−0.500436	+	0.363588i
$653$	−15.4016	+	47.4012i	−0.602710	+	1.85495i	−0.0908837	+	0.995862i	$0.528969\pi$
$653$	−15.4016	+	47.4012i	−0.602710	+	1.85495i	−0.511826	+	0.859089i	$0.671031\pi$
$654$	1.42380	−	4.38201i	0.0556750	−	0.171350i
$655$	4.65944	−	2.20417i	0.182059	−	0.0861239i
$656$	0.376337	+	1.15825i	0.0146935	+	0.0452219i
$657$	−0.932184			−0.0363679
$658$	1.69053	+	5.20292i	0.0659038	+	0.202831i
$659$	−21.3984	−	15.5469i	−0.833565	−	0.605620i	0.0870008	−	0.996208i	$-0.472272\pi$
$659$	−21.3984	−	15.5469i	−0.833565	−	0.605620i	−0.920566	+	0.390588i	$0.872272\pi$
$660$	−3.09040	−	24.0687i	−0.120294	−	0.936873i
$661$	38.5288	−	27.9928i	1.49860	−	1.08880i	0.527663	−	0.849454i	$-0.323068\pi$
$661$	38.5288	−	27.9928i	1.49860	−	1.08880i	0.970935	−	0.239341i	$-0.0769315\pi$
$662$	16.8277	+	12.2261i	0.654028	+	0.475179i
$663$	−5.86406	−	4.26049i	−0.227741	−	0.165464i
$664$	9.71114	−	7.05555i	0.376865	−	0.273809i
$665$	8.30613	−	3.92925i	0.322098	−	0.152370i
$666$	13.2610	+	9.63467i	0.513853	+	0.373336i
$667$	−4.80885	−	14.8001i	−0.186199	−	0.573062i
$668$	−5.97763			−0.231281
$669$	−4.39925	−	13.5395i	−0.170085	−	0.523467i
$670$	2.19893	−	4.01920i	0.0849520	−	0.155275i
$671$	−15.9659	+	49.1379i	−0.616355	+	1.89695i
$672$	−0.671167	+	2.06564i	−0.0258908	+	0.0796838i
$673$	−10.8066	+	7.85148i	−0.416565	+	0.302652i	−0.776254	−	0.630420i	$-0.782883\pi$
$673$	−10.8066	+	7.85148i	−0.416565	+	0.302652i	0.359689	+	0.933072i	$0.382883\pi$
$674$	17.4235			0.671130
$675$	−8.83515	+	10.7689i	−0.340065	+	0.414494i
$676$	12.1020			0.465463
$677$	16.3610	−	11.8869i	0.628804	−	0.456853i	−0.227182	−	0.973852i	$-0.572951\pi$
$677$	16.3610	−	11.8869i	0.628804	−	0.456853i	0.855986	+	0.517000i	$0.172951\pi$
$678$	3.52575	−	10.8511i	0.135406	−	0.416735i
$679$	1.07581	−	3.31099i	0.0412857	−	0.127064i
$680$	1.02180	+	1.08368i	0.0391842	+	0.0415571i
$681$	1.43489	+	4.41614i	0.0549852	+	0.169227i
$682$	−14.2573			−0.545941
$683$	5.18428	+	15.9556i	0.198371	+	0.610523i	0.999921	+	0.0125948i	$0.00400917\pi$
$683$	5.18428	+	15.9556i	0.198371	+	0.610523i	−0.801550	+	0.597928i	$0.795991\pi$
$684$	−5.70922	−	4.14799i	−0.218298	−	0.158603i
$685$	−23.2647	+	42.5232i	−0.888898	+	1.62473i
$686$	0.809017	−	0.587785i	0.0308884	−	0.0224417i
$687$	8.38903	+	6.09499i	0.320061	+	0.232538i
$688$	−7.12971	−	5.18004i	−0.271818	−	0.197487i
$689$	−52.6693	+	38.2665i	−2.00654	+	1.45784i
$690$	−4.49274	+	8.21184i	−0.171036	+	0.312619i
$691$	−15.7563	−	11.4476i	−0.599396	−	0.435487i	0.246268	−	0.969202i	$-0.420796\pi$
$691$	−15.7563	−	11.4476i	−0.599396	−	0.435487i	−0.845665	+	0.533715i	$0.820796\pi$
$692$	−7.23995	−	22.2823i	−0.275222	−	0.847046i
$693$	8.58073			0.325955
$694$	4.31612	+	13.2836i	0.163838	+	0.504240i
$695$	2.22606	+	2.36086i	0.0844393	+	0.0895526i
$696$	−5.41905	+	16.6781i	−0.205409	+	0.632182i
$697$	−0.250677	+	0.771505i	−0.00949508	+	0.0292228i
$698$	−25.8608	+	18.7889i	−0.978844	+	0.711172i
$699$	−18.2656			−0.690869
$700$	−0.293624	+	4.99137i	−0.0110979	+	0.188656i
$701$	−30.2516			−1.14259			−0.571294	−	0.820746i	$-0.693558\pi$
$701$	−30.2516			−1.14259			−0.571294	+	0.820746i	$0.693558\pi$
$702$	11.2921	−	8.20420i	0.426193	−	0.309647i
$703$	12.1203	−	37.3023i	0.457125	−	1.40688i
$704$	1.54402	−	4.75200i	0.0581924	−	0.179098i
$705$	12.7522	−	23.3085i	0.480277	−	0.877851i
$706$	−3.10980	−	9.57098i	−0.117039	−	0.360209i
$707$	5.98229			0.224987
$708$	6.69744	+	20.6126i	0.251705	+	0.774669i
$709$	3.20661	+	2.32974i	0.120427	+	0.0874952i	0.646368	−	0.763026i	$-0.276287\pi$
$709$	3.20661	+	2.32974i	0.120427	+	0.0874952i	−0.525942	+	0.850521i	$0.676287\pi$
$710$	−3.92372	+	1.85613i	−0.147255	+	0.0696595i
$711$	15.7227	−	11.4232i	0.589649	−	0.428405i
$712$	3.67873	+	2.67275i	0.137866	+	0.100166i
$713$	4.44930	+	3.23260i	0.166627	+	0.121062i
$714$	−1.17042	+	0.850363i	−0.0438020	+	0.0318240i
$715$	7.12888	+	55.5213i	0.266605	+	2.07638i
$716$	−21.0537	−	15.2964i	−0.786814	−	0.571654i
$717$	17.5576	+	54.0367i	0.655700	+	2.01804i
$718$	12.3328			0.460256
$719$	−13.7392	−	42.2849i	−0.512386	−	1.57696i	−0.787988	−	0.615691i	$-0.788877\pi$
$719$	−13.7392	−	42.2849i	−0.512386	−	1.57696i	0.275602	−	0.961272i	$-0.411123\pi$
$720$	3.47126	−	1.64209i	0.129366	−	0.0611973i
$721$	−4.79779	+	14.7661i	−0.178679	+	0.549918i
$722$	0.653212	−	2.01038i	0.0243100	−	0.0748185i
$723$	−38.0795	+	27.6664i	−1.41619	+	1.02892i
$724$	2.34395			0.0871123
$725$	−2.37074	+	40.3007i	−0.0880471	+	1.49673i
$726$	−30.3323			−1.12574
$727$	−35.2543	+	25.6137i	−1.30751	+	0.949961i	−0.999999	−	0.00158434i	$-0.999496\pi$
$727$	−35.2543	+	25.6137i	−1.30751	+	0.949961i	−0.307510	+	0.951545i	$0.599496\pi$
$728$	1.54824	−	4.76498i	0.0573814	−	0.176602i
$729$	−0.335758	+	1.03336i	−0.0124355	+	0.0382725i
$730$	−1.19272	−	0.225007i	−0.0441446	−	0.00832789i
$731$	−1.81399	−	5.58288i	−0.0670928	−	0.206490i
$732$	−22.4589			−0.830104
$733$	14.1629	+	43.5890i	0.523120	+	1.61000i	0.768005	+	0.640444i	$0.221250\pi$
$733$	14.1629	+	43.5890i	0.523120	+	1.61000i	−0.244885	+	0.969552i	$0.578750\pi$
$734$	−9.22463	−	6.70209i	−0.340487	−	0.247379i
$735$	−4.77243	−	0.900320i	−0.176034	−	0.0332088i
$736$	−1.55928	+	1.13288i	−0.0574757	+	0.0417586i
$737$	−8.28213	−	6.01732i	−0.305076	−	0.221651i
$738$	1.69202	+	1.22933i	0.0622843	+	0.0452522i
$739$	−8.71212	+	6.32973i	−0.320481	+	0.232843i	−0.736381	−	0.676568i	$-0.763467\pi$
$739$	−8.71212	+	6.32973i	−0.320481	+	0.232843i	0.415900	+	0.909410i	$0.363467\pi$
$740$	14.6417	+	15.5284i	0.538241	+	0.570834i
$741$	36.1764	+	26.2837i	1.32897	+	0.965557i
$742$	4.01539	+	12.3581i	0.147410	+	0.453680i
$743$	11.2231			0.411737			0.205868	−	0.978580i	$-0.433998\pi$
$743$	11.2231			0.411737			0.205868	+	0.978580i	$0.433998\pi$
$744$	−1.91513	−	5.89416i	−0.0702121	−	0.216091i
$745$	3.21458	+	25.0359i	0.117773	+	0.917244i
$746$	−1.16178	+	3.57560i	−0.0425360	+	0.130912i
$747$	6.37014	−	19.6053i	0.233071	−	0.717319i
$748$	2.69256	−	1.95626i	0.0984498	−	0.0715280i
$749$	3.11928			0.113976
$750$	18.6155	−	15.5926i	0.679742	−	0.569362i
$751$	21.2318			0.774761			0.387380	−	0.921920i	$-0.373380\pi$
$751$	21.2318			0.774761			0.387380	+	0.921920i	$0.373380\pi$
$752$	4.42587	−	3.21558i	0.161395	−	0.117260i
$753$	−4.49118	+	13.8224i	−0.163668	+	0.503717i
$754$	12.5006	−	38.4728i	0.455244	−	1.40110i
$755$	−0.0743733	−	0.579235i	−0.00270672	−	0.0210805i
$756$	−0.860885	−	2.64953i	−0.0313101	−	0.0963625i
$757$	32.7501			1.19032			0.595161	−	0.803607i	$-0.297088\pi$
$757$	32.7501			1.19032			0.595161	+	0.803607i	$0.297088\pi$
$758$	−4.31010	−	13.2651i	−0.156550	−	0.481811i
$759$	16.9216	+	12.2943i	0.614216	+	0.446254i
$760$	−6.30367	−	6.68539i	−0.228658	−	0.242505i
$761$	9.72256	−	7.06385i	0.352442	−	0.256064i	−0.397451	−	0.917624i	$-0.630105\pi$
$761$	9.72256	−	7.06385i	0.352442	−	0.256064i	0.749893	+	0.661559i	$0.230105\pi$
$762$	39.0954	+	28.4045i	1.41628	+	1.02898i
$763$	1.71623	+	1.24692i	0.0621318	+	0.0451414i
$764$	−1.60053	+	1.16286i	−0.0579053	+	0.0420706i
$765$	2.51352	+	0.474177i	0.0908766	+	0.0171439i
$766$	9.79117	+	7.11370i	0.353769	+	0.257028i
$767$	−15.4495	−	47.5488i	−0.557850	−	1.71689i
$768$	2.17194			0.0783732
$769$	8.87702	+	27.3207i	0.320113	+	0.985208i	0.973598	+	0.228268i	$0.0733063\pi$
$769$	8.87702	+	27.3207i	0.320113	+	0.985208i	−0.653485	+	0.756940i	$0.726694\pi$
$770$	10.9790	+	2.07119i	0.395655	+	0.0746404i
$771$	−4.27606	+	13.1604i	−0.153999	+	0.473959i
$772$	−4.56380	+	14.0459i	−0.164255	+	0.505524i
$773$	13.4872	−	9.79900i	0.485100	−	0.352445i	−0.318197	−	0.948025i	$-0.603077\pi$
$773$	13.4872	−	9.79900i	0.485100	−	0.352445i	0.803297	+	0.595579i	$0.203077\pi$
$774$	−15.1345			−0.543999
$775$	−7.69373	−	12.0149i	−0.276367	−	0.431589i
$776$	−3.48139			−0.124974
$777$	−16.7714	+	12.1852i	−0.601672	+	0.437140i
$778$	−4.86682	+	14.9785i	−0.174484	+	0.537006i
$779$	1.54647	−	4.75956i	0.0554082	−	0.170529i
$780$	−21.9956	+	10.4051i	−0.787569	+	0.372563i
$781$	2.99721	+	9.22448i	0.107249	+	0.330078i
$782$	−1.28382			−0.0459092
$783$	−6.95085	−	21.3925i	−0.248403	−	0.764506i
$784$	−0.809017	−	0.587785i	−0.0288935	−	0.0209923i
$785$	−4.87373	−	37.9577i	−0.173951	−	1.35477i
$786$	4.05047	−	2.94284i	0.144476	−	0.104968i
$787$	−8.52329	−	6.19253i	−0.303823	−	0.220740i	0.425419	−	0.904997i	$-0.360127\pi$
$787$	−8.52329	−	6.19253i	−0.303823	−	0.220740i	−0.729241	+	0.684257i	$0.760127\pi$
$788$	1.14487	+	0.831799i	0.0407844	+	0.0296316i
$789$	23.3117	−	16.9370i	0.829919	−	0.602972i
$790$	22.8744	−	10.8208i	0.813835	−	0.384988i
$791$	4.24990	+	3.08773i	0.151109	+	0.109787i
$792$	−2.65159	−	8.16076i	−0.0942202	−	0.289980i
$793$	51.8077			1.83975
$794$	−0.296903	−	0.913772i	−0.0105367	−	0.0324286i
$795$	30.2894	−	55.3630i	1.07425	−	1.96352i
$796$	0.402580	−	1.23901i	0.0142691	−	0.0439157i
$797$	−12.5275	+	38.5557i	−0.443748	+	1.36571i	0.440104	+	0.897947i	$0.354942\pi$
$797$	−12.5275	+	38.5557i	−0.443748	+	1.36571i	−0.883851	+	0.467768i	$0.845058\pi$
$798$	7.22057	−	5.24605i	0.255605	−	0.185708i
$799$	3.64400			0.128915
$800$	4.83781	−	1.26317i	0.171042	−	0.0446596i
$801$	7.80898			0.275917
$802$	−11.8092	+	8.57988i	−0.416997	+	0.302966i
$803$	−0.838109	+	2.57943i	−0.0295762	+	0.0910262i
$804$	1.37513	−	4.23222i	0.0484972	−	0.149259i
$805$	−2.95661	−	3.13565i	−0.104207	−	0.110517i
$806$	4.41779	+	13.5965i	0.155610	+	0.478918i
$807$	−4.14452			−0.145894
$808$	−1.84863	−	5.68950i	−0.0650346	−	0.200156i
$809$	39.7941	+	28.9121i	1.39908	+	1.01649i	0.994799	+	0.101862i	$0.0324799\pi$
$809$	39.7941	+	28.9121i	1.39908	+	1.01649i	0.404286	+	0.914633i	$0.367520\pi$
$810$	−12.0233	+	21.9761i	−0.422455	+	0.772163i
$811$	1.80882	−	1.31418i	0.0635162	−	0.0461472i	−0.555574	−	0.831467i	$-0.687501\pi$
$811$	1.80882	−	1.31418i	0.0635162	−	0.0461472i	0.619090	+	0.785320i	$0.287501\pi$
$812$	−6.53206	−	4.74582i	−0.229230	−	0.166546i
$813$	−22.5966	−	16.4174i	−0.792498	−	0.575784i
$814$	38.5827	−	28.0320i	1.35232	−	0.982520i
$815$	−16.9516	+	30.9842i	−0.593790	+	1.08533i
$816$	1.17042	+	0.850363i	0.0409731	+	0.0297687i
$817$	11.1908	+	34.4418i	0.391517	+	1.20497i
$818$	−1.70864			−0.0597412
$819$	−2.65883	−	8.18304i	−0.0929071	−	0.285939i
$820$	1.86820	+	1.98133i	0.0652403	+	0.0691910i
$821$	−8.90022	+	27.3921i	−0.310620	+	0.955989i	0.666900	+	0.745147i	$0.267621\pi$
$821$	−8.90022	+	27.3921i	−0.310620	+	0.955989i	−0.977520	+	0.210842i	$0.932379\pi$
$822$	−14.5489	+	44.7769i	−0.507451	+	1.56177i
$823$	42.6616	−	30.9955i	1.48709	−	1.08043i	0.511905	−	0.859042i	$-0.328940\pi$
$823$	42.6616	−	30.9955i	1.48709	−	1.08043i	0.975185	−	0.221393i	$-0.0710602\pi$
$824$	15.5260			0.540873
$825$	−29.2609	−	45.6954i	−1.01873	−	1.59091i
$826$	−9.97880			−0.347207
$827$	−11.7904	+	8.56620i	−0.409991	+	0.297876i	−0.773598	−	0.633677i	$-0.781545\pi$
$827$	−11.7904	+	8.56620i	−0.409991	+	0.297876i	0.363607	+	0.931552i	$0.381545\pi$
$828$	−1.02283	+	3.14794i	−0.0355457	+	0.109398i
$829$	6.50374	−	20.0165i	0.225884	−	0.695201i	−0.772316	−	0.635238i	$-0.780902\pi$
$829$	6.50374	−	20.0165i	0.225884	−	0.695201i	0.998201	−	0.0599624i	$-0.0190981\pi$
$830$	12.8828	−	23.5472i	0.447168	−	0.817334i
$831$	9.80130	+	30.1653i	0.340003	+	1.04642i
$832$	−5.01019			−0.173697
$833$	−0.205835	−	0.633496i	−0.00713177	−	0.0219493i
$834$	2.54985	+	1.85257i	0.0882941	+	0.0641494i
$835$	−12.0826	+	5.71575i	−0.418137	+	0.197802i
$836$	−16.6109	+	12.0685i	−0.574501	+	0.417399i
$837$	6.43114	+	4.67250i	0.222293	+	0.161505i
$838$	−11.0517	−	8.02956i	−0.381776	−	0.277376i
$839$	14.9131	−	10.8350i	0.514858	−	0.374066i	−0.299805	−	0.954000i	$-0.596922\pi$
$839$	14.9131	−	10.8350i	0.514858	−	0.374066i	0.814663	+	0.579934i	$0.196922\pi$
$840$	0.618506	+	4.81706i	0.0213405	+	0.166204i
$841$	−29.2788	−	21.2723i	−1.00961	−	0.733528i
$842$	−1.76632	−	5.43616i	−0.0608712	−	0.187342i
$843$	−51.7660			−1.78292
$844$	3.03154	+	9.33013i	0.104350	+	0.321156i
$845$	24.4620	−	11.5719i	0.841519	−	0.398084i
$846$	2.90320	−	8.93514i	0.0998141	−	0.307196i
$847$	4.31559	−	13.2820i	0.148285	−	0.456376i
$848$	10.5124	−	7.63773i	0.360998	−	0.262281i
$849$	6.44047			0.221037
$850$	3.10158	+	1.21341i	0.106383	+	0.0416196i
$851$	−18.3963			−0.630617
$852$	−3.41091	+	2.47817i	−0.116856	+	0.0849009i
$853$	16.3966	−	50.4635i	0.561408	−	1.72784i	−0.116982	−	0.993134i	$-0.537322\pi$
$853$	16.3966	−	50.4635i	0.561408	−	1.72784i	0.678390	−	0.734702i	$-0.262678\pi$
$854$	3.19538	−	9.83436i	0.109344	−	0.336525i
$855$	−15.5064	−	2.92529i	−0.530307	−	0.100043i
$856$	−0.963911	−	2.96661i	−0.0329458	−	0.101397i
$857$	3.71994			0.127071			0.0635353	−	0.997980i	$-0.479762\pi$
$857$	3.71994			0.127071			0.0635353	+	0.997980i	$0.479762\pi$
$858$	16.8018	+	51.7106i	0.573604	+	1.76537i
$859$	−29.3667	−	21.3362i	−1.00198	−	0.727981i	−0.0394679	−	0.999221i	$-0.512566\pi$
$859$	−29.3667	−	21.3362i	−1.00198	−	0.727981i	−0.962512	+	0.271240i	$0.912566\pi$
$860$	−19.3645	−	3.65311i	−0.660323	−	0.124570i
$861$	−2.13994	+	1.55475i	−0.0729288	+	0.0529859i
$862$	−9.15396	−	6.65074i	−0.311785	−	0.226525i
$863$	26.6287	+	19.3469i	0.906452	+	0.658576i	0.940115	−	0.340857i	$-0.110717\pi$
$863$	26.6287	+	19.3469i	0.906452	+	0.658576i	−0.0336631	+	0.999433i	$0.510717\pi$
$864$	−2.25383	+	1.63750i	−0.0766767	+	0.0557089i
$865$	−35.9403	−	38.1167i	−1.22201	−	1.29601i
$866$	−23.7906	−	17.2849i	−0.808438	−	0.587364i
$867$	−11.1121	−	34.1994i	−0.377385	−	1.16147i
$868$	2.85343			0.0968518
$869$	−17.4731	−	53.7766i	−0.592734	−	1.82425i
$870$	4.99386	+	38.8933i	0.169308	+	1.31861i
$871$	−3.17213	+	9.76281i	−0.107484	+	0.330800i
$872$	0.655543	−	2.01755i	0.0221995	−	0.0683230i
$873$	−4.83686	+	3.51419i	−0.163703	+	0.118937i
$874$	7.92011			0.267902
$875$	4.17919	+	10.3699i	0.141283	+	0.350566i
$876$	−1.17895			−0.0398331
$877$	24.3907	−	17.7209i	0.823615	−	0.598391i	−0.0941309	−	0.995560i	$-0.530007\pi$
$877$	24.3907	−	17.7209i	0.823615	−	0.598391i	0.917746	+	0.397169i	$0.130007\pi$
$878$	−11.9910	+	36.9047i	−0.404678	+	1.24547i
$879$	19.3570	−	59.5748i	0.652897	−	2.00941i
$880$	−1.42287	−	11.0817i	−0.0479651	−	0.373563i
$881$	10.8978	+	33.5400i	0.367157	+	1.12999i	0.948619	+	0.316419i	$0.102481\pi$
$881$	10.8978	+	33.5400i	0.367157	+	1.12999i	−0.581463	+	0.813573i	$0.697519\pi$
$882$	−1.71733			−0.0578255
$883$	9.53699	+	29.3518i	0.320945	+	0.987768i	0.973238	+	0.229801i	$0.0738075\pi$
$883$	9.53699	+	29.3518i	0.320945	+	0.987768i	−0.652292	+	0.757968i	$0.726193\pi$
$884$	−2.69991	−	1.96160i	−0.0908079	−	0.0659758i
$885$	33.2472	+	35.2605i	1.11759	+	1.18527i
$886$	13.9238	−	10.1162i	0.467779	−	0.339861i
$887$	7.06092	+	5.13006i	0.237082	+	0.172250i	0.699982	−	0.714160i	$-0.253191\pi$
$887$	7.06092	+	5.13006i	0.237082	+	0.172250i	−0.462900	+	0.886410i	$0.653191\pi$
$888$	16.7714	+	12.1852i	0.562812	+	0.408907i
$889$	−18.0002	+	13.0779i	−0.603707	+	0.438619i
$890$	9.99152	+	1.88490i	0.334917	+	0.0631821i
$891$	45.2849	+	32.9014i	1.51710	+	1.10224i
$892$	−2.02549	−	6.23382i	−0.0678184	−	0.208724i
$893$	−22.4805			−0.752282
$894$	7.57633	+	23.3176i	0.253391	+	0.779856i
$895$	−57.1824	−	10.7875i	−1.91140	−	0.360586i
$896$	−0.309017	+	0.951057i	−0.0103235	+	0.0317726i
$897$	6.48113	−	19.9469i	0.216399	−	0.666007i
$898$	−5.31886	+	3.86438i	−0.177493	+	0.128956i
$899$	23.0388			0.768388
$900$	5.44635	−	6.63837i	0.181545	−	0.221279i
$901$	8.65532			0.288351
$902$	4.92292	−	3.57671i	0.163915	−	0.119091i
$903$	5.91486	−	18.2041i	0.196834	−	0.605794i
$904$	1.62332	−	4.99605i	0.0539907	−	0.166166i
$905$	4.73786	−	2.24126i	0.157492	−	0.0745021i
$906$	−0.175288	−	0.539480i	−0.00582354	−	0.0179230i
$907$	−34.1478			−1.13386			−0.566929	−	0.823767i	$-0.691869\pi$
$907$	−34.1478			−1.13386			−0.566929	+	0.823767i	$0.691869\pi$
$908$	0.660649	+	2.03327i	0.0219244	+	0.0674764i
$909$	−8.31150	−	6.03866i	−0.275675	−	0.200290i
$910$	−1.42676	−	11.1119i	−0.0472966	−	0.368356i
$911$	24.4100	−	17.7349i	0.808738	−	0.587583i	−0.104726	−	0.994501i	$-0.533397\pi$
$911$	24.4100	−	17.7349i	0.808738	−	0.587583i	0.913465	+	0.406918i	$0.133397\pi$
$912$	−7.22057	−	5.24605i	−0.239097	−	0.173714i
$913$	−48.5222	−	35.2534i	−1.60585	−	1.16672i
$914$	3.02763	−	2.19970i	0.100145	−	0.0727596i
$915$	−45.3964	+	21.4749i	−1.50076	+	0.709940i
$916$	3.86246	+	2.80624i	0.127619	+	0.0927207i
$917$	0.712332	+	2.19233i	0.0235233	+	0.0723972i
$918$	−1.85567			−0.0612462
$919$	−17.5693	−	54.0729i	−0.579559	−	1.78370i	−0.620101	−	0.784522i	$-0.712908\pi$
$919$	−17.5693	−	54.0729i	−0.579559	−	1.78370i	0.0405413	−	0.999178i	$-0.487092\pi$
$920$	−2.06854	+	3.78087i	−0.0681976	+	0.124652i
$921$	16.9043	−	52.0261i	0.557016	−	1.71432i
$922$	8.76333	−	26.9708i	0.288605	−	0.888235i
$923$	7.86823	−	5.71661i	0.258986	−	0.188164i
$924$	10.8522			0.357012
$925$	44.4436	+	17.3874i	1.46130	+	0.571694i
$926$	−35.6251			−1.17071
$927$	21.5710	−	15.6723i	0.708485	−	0.514745i
$928$	−2.49503	+	7.67890i	−0.0819032	+	0.252072i
$929$	−11.8201	+	36.3785i	−0.387805	+	1.19354i	0.546621	+	0.837380i	$0.315914\pi$
$929$	−11.8201	+	36.3785i	−0.387805	+	1.19354i	−0.934425	+	0.356159i	$0.884086\pi$
$930$	−9.50702	−	10.0827i	−0.311747	−	0.330625i
$931$	1.26984	+	3.90816i	0.0416172	+	0.128085i
$932$	−8.40981			−0.275472
$933$	13.9208	+	42.8438i	0.455746	+	1.40264i
$934$	−26.2094	−	19.0423i	−0.857598	−	0.623082i
$935$	3.57195	−	6.52881i	0.116815	−	0.213515i
$936$	−6.96091	+	5.05740i	−0.227525	+	0.165306i
$937$	−22.7949	−	16.5615i	−0.744678	−	0.541041i	0.149494	−	0.988763i	$-0.452235\pi$
$937$	−22.7949	−	16.5615i	−0.744678	−	0.541041i	−0.894173	+	0.447722i	$0.852235\pi$
$938$	1.65757	+	1.20429i	0.0541215	+	0.0393216i
$939$	45.5331	−	33.0818i	1.48592	−	1.07958i
$940$	5.87135	−	10.7317i	0.191502	−	0.350028i
$941$	−10.5764	−	7.68418i	−0.344780	−	0.250497i	0.401896	−	0.915685i	$-0.368351\pi$
$941$	−10.5764	−	7.68418i	−0.344780	−	0.250497i	−0.746676	+	0.665188i	$0.768351\pi$
$942$	−11.4867	−	35.3525i	−0.374258	−	1.15185i
$943$	−2.34726			−0.0764372
$944$	3.08362	+	9.49041i	0.100363	+	0.308886i
$945$	−4.27357	−	4.53236i	−0.139019	−	0.147438i
$946$	−13.6071	+	41.8785i	−0.442407	+	1.36159i
$947$	10.0872	−	31.0452i	0.327790	−	1.00883i	−0.642376	−	0.766390i	$-0.722051\pi$
$947$	10.0872	−	31.0452i	0.327790	−	1.00883i	0.970166	−	0.242443i	$-0.0779487\pi$
$948$	19.8849	−	14.4472i	0.645830	−	0.469223i
$949$	2.71958			0.0882814
$950$	−19.1342	−	7.48575i	−0.620795	−	0.242870i
$951$	62.5295			2.02766
$952$	−0.538884	+	0.391522i	−0.0174653	+	0.0126893i
$953$	−4.25291	+	13.0891i	−0.137765	+	0.423998i	−0.996010	−	0.0892430i	$-0.971555\pi$
$953$	−4.25291	+	13.0891i	−0.137765	+	0.423998i	0.858245	+	0.513241i	$0.171555\pi$
$954$	6.89576	−	21.2230i	0.223258	−	0.687119i
$955$	−2.12327	+	3.88091i	−0.0687073	+	0.125583i
$956$	8.08383	+	24.8795i	0.261450	+	0.804659i
$957$	87.6216			2.83240
$958$	−3.32814	−	10.2430i	−0.107527	−	0.330935i
$959$	−17.5371	−	12.7414i	−0.566302	−	0.411443i
$960$	4.39017	−	2.07679i	0.141692	−	0.0670281i
$961$	18.4924	−	13.4355i	0.596530	−	0.433405i
$962$	−38.6880	−	28.1085i	−1.24735	−	0.906254i
$963$	−4.33378	−	3.14867i	−0.139654	−	0.101465i
$964$	−17.5325	+	12.7381i	−0.564683	+	0.410267i
$965$	4.20572	+	32.7550i	0.135387	+	1.05442i
$966$	−3.38666	−	2.46055i	−0.108964	−	0.0791670i
$967$	7.39636	+	22.7637i	0.237851	+	0.732030i	0.996730	+	0.0807990i	$0.0257472\pi$
$967$	7.39636	+	22.7637i	0.237851	+	0.732030i	−0.758879	+	0.651231i	$0.774253\pi$
$968$	−13.9655			−0.448869
$969$	−1.83710	−	5.65402i	−0.0590163	−	0.181633i
$970$	−7.03696	+	3.32887i	−0.225943	+	0.106883i
$971$	−7.82527	+	24.0837i	−0.251125	+	0.772883i	0.743444	+	0.668798i	$0.233191\pi$
$971$	−7.82527	+	24.0837i	−0.251125	+	0.772883i	−0.994569	+	0.104084i	$0.966809\pi$
$972$	−4.93627	+	15.1923i	−0.158331	+	0.487293i
$973$	−1.17400	+	0.852958i	−0.0376366	+	0.0273446i
$974$	−0.887277			−0.0284302
$975$	−34.5107	+	42.0640i	−1.10523	+	1.34713i
$976$	−10.3405			−0.330990
$977$	−2.18917	+	1.59053i	−0.0700379	+	0.0508855i	−0.622253	−	0.782816i	$-0.713783\pi$
$977$	−2.18917	+	1.59053i	−0.0700379	+	0.0508855i	0.552215	+	0.833701i	$0.313783\pi$
$978$	−10.6010	+	32.6264i	−0.338981	+	1.04328i
$979$	7.02091	−	21.6081i	0.224389	−	0.690599i
$980$	−2.19731	−	0.414523i	−0.0701905	−	0.0132415i
$981$	−1.12578	−	3.46481i	−0.0359435	−	0.110623i
$982$	−21.7294			−0.693414
$983$	5.47804	+	16.8597i	0.174722	+	0.537740i	0.999621	−	0.0275412i	$-0.00876775\pi$
$983$	5.47804	+	16.8597i	0.174722	+	0.537740i	−0.824898	+	0.565281i	$0.808768\pi$
$984$	2.13994	+	1.55475i	0.0682186	+	0.0495637i
$985$	3.10950	+	0.586608i	0.0990770	+	0.0186909i
$986$	−4.35099	+	3.16118i	−0.138564	+	0.100672i
$987$	9.61273	+	6.98406i	0.305976	+	0.222305i
$988$	16.6563	+	12.1015i	0.529907	+	0.385000i
$989$	13.7416	−	9.98387i	0.436958	−	0.317469i
$990$	−13.1629	−	13.9600i	−0.418346	−	0.443679i
$991$	−9.43944	−	6.85815i	−0.299854	−	0.217856i	0.427677	−	0.903932i	$-0.359332\pi$
$991$	−9.43944	−	6.85815i	−0.299854	−	0.217856i	−0.727531	+	0.686075i	$0.759332\pi$
$992$	−0.881759	−	2.71378i	−0.0279959	−	0.0861625i
$993$	45.1768			1.43364
$994$	−0.599857	−	1.84617i	−0.0190263	−	0.0585569i
$995$	−0.370993	−	2.88938i	−0.0117613	−	0.0915994i
$996$	8.05644	−	24.7952i	0.255278	−	0.785665i
$997$	6.24357	−	19.2157i	0.197736	−	0.608568i	−0.802198	−	0.597058i	$-0.796336\pi$
$997$	6.24357	−	19.2157i	0.197736	−	0.608568i	0.999934	−	0.0115099i	$-0.00366380\pi$
$998$	22.4021	−	16.2761i	0.709126	−	0.515210i
$999$	−26.5905			−0.841287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	350.2.h.d.211.4	yes	20
25.4	even	10		8750.2.a.x.1.3		10
25.16	even	5	inner	350.2.h.d.141.4	✓	20
25.21	even	5		8750.2.a.w.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
350.2.h.d.141.4	✓	20	25.16	even	5	inner
350.2.h.d.211.4	yes	20	1.1	even	1	trivial
8750.2.a.w.1.8		10	25.21	even	5
8750.2.a.x.1.3		10	25.4	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)

\(f(q)\)	\(=\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.671167 - 2.06564i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.284771 - 2.21786i) q^{5} +(-0.671167 - 2.06564i) q^{6} +1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.38935 - 1.00942i) q^{9} +O(q^{10})\)	\(q+(0.809017 - 0.587785i) q^{2} +(0.671167 - 2.06564i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.284771 - 2.21786i) q^{5} +(-0.671167 - 2.06564i) q^{6} +1.00000 q^{7} +(-0.309017 - 0.951057i) q^{8} +(-1.38935 - 1.00942i) q^{9} +(-1.53401 - 1.62690i) q^{10} +(-4.04230 + 2.93690i) q^{11} +(-1.75714 - 1.27664i) q^{12} +(4.05333 + 2.94492i) q^{13} +(0.809017 - 0.587785i) q^{14} +(-4.77243 - 0.900320i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(-0.205835 - 0.633496i) q^{17} -1.71733 q^{18} +(1.26984 + 3.90816i) q^{19} +(-2.19731 - 0.414523i) q^{20} +(0.671167 - 2.06564i) q^{21} +(-1.54402 + 4.75200i) q^{22} +(1.55928 - 1.13288i) q^{23} -2.17194 q^{24} +(-4.83781 + 1.26317i) q^{25} +5.01019 q^{26} +(2.25383 - 1.63750i) q^{27} +(0.309017 - 0.951057i) q^{28} +(2.49503 - 7.67890i) q^{29} +(-4.39017 + 2.07679i) q^{30} +(0.881759 + 2.71378i) q^{31} -1.00000 q^{32} +(3.35352 + 10.3211i) q^{33} +(-0.538884 - 0.391522i) q^{34} +(-0.284771 - 2.21786i) q^{35} +(-1.38935 + 1.00942i) q^{36} +(-7.72186 - 5.61026i) q^{37} +(3.32448 + 2.41537i) q^{38} +(8.80360 - 6.39619i) q^{39} +(-2.02131 + 0.956190i) q^{40} +(-0.985264 - 0.715836i) q^{41} +(-0.671167 - 2.06564i) q^{42} +8.81281 q^{43} +(1.54402 + 4.75200i) q^{44} +(-1.84311 + 3.36884i) q^{45} +(0.595591 - 1.83304i) q^{46} +(-1.69053 + 5.20292i) q^{47} +(-1.75714 + 1.27664i) q^{48} +1.00000 q^{49} +(-3.17140 + 3.86552i) q^{50} -1.44672 q^{51} +(4.05333 - 2.94492i) q^{52} +(-4.01539 + 12.3581i) q^{53} +(0.860885 - 2.64953i) q^{54} +(7.66476 + 8.12890i) q^{55} +(-0.309017 - 0.951057i) q^{56} +8.92511 q^{57} +(-2.49503 - 7.67890i) q^{58} +(-8.07302 - 5.86539i) q^{59} +(-2.33102 + 4.26064i) q^{60} +(8.36560 - 6.07797i) q^{61} +(2.30848 + 1.67721i) q^{62} +(-1.38935 - 1.00942i) q^{63} +(-0.809017 + 0.587785i) q^{64} +(5.37715 - 9.82835i) q^{65} +(8.77963 + 6.37878i) q^{66} +(0.633135 + 1.94859i) q^{67} -0.666097 q^{68} +(-1.29359 - 3.98126i) q^{69} +(-1.53401 - 1.62690i) q^{70} +(0.599857 - 1.84617i) q^{71} +(-0.530684 + 1.63328i) q^{72} +(0.439142 - 0.319055i) q^{73} -9.54474 q^{74} +(-0.637734 + 10.8410i) q^{75} +4.10928 q^{76} +(-4.04230 + 2.93690i) q^{77} +(3.36268 - 10.3493i) q^{78} +(-3.49703 + 10.7627i) q^{79} +(-1.07324 + 1.96167i) q^{80} +(-3.46185 - 10.6545i) q^{81} -1.21785 q^{82} +(3.70932 + 11.4161i) q^{83} +(-1.75714 - 1.27664i) q^{84} +(-1.34639 + 0.636916i) q^{85} +(7.12971 - 5.18004i) q^{86} +(-14.1873 - 10.3076i) q^{87} +(4.04230 + 2.93690i) q^{88} +(-3.67873 + 2.67275i) q^{89} +(0.489046 + 3.80880i) q^{90} +(4.05333 + 2.94492i) q^{91} +(-0.595591 - 1.83304i) q^{92} +6.19749 q^{93} +(1.69053 + 5.20292i) q^{94} +(8.30613 - 3.92925i) q^{95} +(-0.671167 + 2.06564i) q^{96} +(1.07581 - 3.31099i) q^{97} +(0.809017 - 0.587785i) q^{98} +8.58073 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

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