LMFDB - Embedded newform 25.2.d.a.16.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,2,Mod(6,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("25.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	25.d (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:	$0.199626005053$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{10})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + x^{2} - x + 1 $ x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			16.1
Root			$0.809017 - 0.587785i$ of defining polynomial
Character	$\chi$	$=$	25.16
Dual form			25.2.d.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.363271i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 - 0.587785i) q^{6} -1.61803 q^{7} +(-0.690983 + 2.12663i) q^{8} +(1.61803 - 1.17557i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.363271i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 - 0.587785i) q^{6} -1.61803 q^{7} +(-0.690983 + 2.12663i) q^{8} +(1.61803 - 1.17557i) q^{9} +1.38197 q^{10} +(0.618034 + 0.449028i) q^{11} +(1.30902 - 0.951057i) q^{12} +(3.92705 - 2.85317i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-1.80902 - 1.31433i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(-0.236068 + 0.726543i) q^{17} -1.23607 q^{18} +(-1.80902 + 5.56758i) q^{19} +(2.92705 + 2.12663i) q^{20} +(-0.500000 - 1.53884i) q^{21} +(-0.145898 - 0.449028i) q^{22} +(-6.66312 - 4.84104i) q^{23} -2.23607 q^{24} +(1.54508 - 4.75528i) q^{25} -3.00000 q^{26} +(4.04508 + 2.93893i) q^{27} +(0.809017 + 2.48990i) q^{28} +(-0.427051 - 1.31433i) q^{29} +(0.427051 + 1.31433i) q^{30} +(-0.927051 + 2.85317i) q^{31} +5.61803 q^{32} +(-0.236068 + 0.726543i) q^{33} +(0.381966 - 0.277515i) q^{34} +(2.92705 - 2.12663i) q^{35} +(-2.61803 - 1.90211i) q^{36} +(-3.42705 + 2.48990i) q^{37} +(2.92705 - 2.12663i) q^{38} +(3.92705 + 2.85317i) q^{39} +(-1.54508 - 4.75528i) q^{40} +(4.23607 - 3.07768i) q^{41} +(-0.309017 + 0.951057i) q^{42} +1.85410 q^{43} +(0.381966 - 1.17557i) q^{44} +(-1.38197 + 4.25325i) q^{45} +(1.57295 + 4.84104i) q^{46} +(-0.500000 - 1.53884i) q^{47} +(-1.50000 - 1.08981i) q^{48} -4.38197 q^{49} +(-2.50000 + 1.81636i) q^{50} -0.763932 q^{51} +(-6.35410 - 4.61653i) q^{52} +(1.69098 + 5.20431i) q^{53} +(-0.954915 - 2.93893i) q^{54} -1.70820 q^{55} +(1.11803 - 3.44095i) q^{56} -5.85410 q^{57} +(-0.263932 + 0.812299i) q^{58} +(3.35410 - 2.43690i) q^{59} +(-1.11803 + 3.44095i) q^{60} +(3.80902 + 2.76741i) q^{61} +(1.50000 - 1.08981i) q^{62} +(-2.61803 + 1.90211i) q^{63} +(0.190983 + 0.138757i) q^{64} +(-3.35410 + 10.3229i) q^{65} +(0.381966 - 0.277515i) q^{66} +(2.85410 - 8.78402i) q^{67} +1.23607 q^{68} +(2.54508 - 7.83297i) q^{69} -2.23607 q^{70} +(-1.35410 - 4.16750i) q^{71} +(1.38197 + 4.25325i) q^{72} +(7.28115 + 5.29007i) q^{73} +2.61803 q^{74} +5.00000 q^{75} +9.47214 q^{76} +(-1.00000 - 0.726543i) q^{77} +(-0.927051 - 2.85317i) q^{78} +(0.954915 + 2.93893i) q^{79} +(1.28115 - 3.94298i) q^{80} +(0.309017 - 0.951057i) q^{81} -3.23607 q^{82} +(-0.545085 + 1.67760i) q^{83} +(-2.11803 + 1.53884i) q^{84} +(-0.527864 - 1.62460i) q^{85} +(-0.927051 - 0.673542i) q^{86} +(1.11803 - 0.812299i) q^{87} +(-1.38197 + 1.00406i) q^{88} +(-7.23607 - 5.25731i) q^{89} +(2.23607 - 1.62460i) q^{90} +(-6.35410 + 4.61653i) q^{91} +(-4.11803 + 12.6740i) q^{92} -3.00000 q^{93} +(-0.309017 + 0.951057i) q^{94} +(-4.04508 - 12.4495i) q^{95} +(1.73607 + 5.34307i) q^{96} +(0.881966 + 2.71441i) q^{97} +(2.19098 + 1.59184i) q^{98} +1.52786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} + 9 q^{13} + q^{14} - 5 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} - 5 q^{19} + 5 q^{20} - 2 q^{21} - 14 q^{22} - 11 q^{23} - 5 q^{25} - 12 q^{26} + 5 q^{27} + q^{28} + 5 q^{29} - 5 q^{30} + 3 q^{31} + 18 q^{32} + 8 q^{33} + 6 q^{34} + 5 q^{35} - 6 q^{36} - 7 q^{37} + 5 q^{38} + 9 q^{39} + 5 q^{40} + 8 q^{41} + q^{42} - 6 q^{43} + 6 q^{44} - 10 q^{45} + 13 q^{46} - 2 q^{47} - 6 q^{48} - 22 q^{49} - 10 q^{50} - 12 q^{51} - 12 q^{52} + 9 q^{53} - 15 q^{54} + 20 q^{55} - 10 q^{57} - 10 q^{58} + 13 q^{61} + 6 q^{62} - 6 q^{63} + 3 q^{64} + 6 q^{66} - 2 q^{67} - 4 q^{68} - q^{69} + 8 q^{71} + 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{75} + 20 q^{76} - 4 q^{77} + 3 q^{78} + 15 q^{79} - 15 q^{80} - q^{81} - 4 q^{82} + 9 q^{83} - 4 q^{84} - 20 q^{85} + 3 q^{86} - 10 q^{88} - 20 q^{89} - 12 q^{91} - 12 q^{92} - 12 q^{93} + q^{94} - 5 q^{95} - 2 q^{96} + 8 q^{97} + 11 q^{98} + 24 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 - q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 10 * q^10 - 2 * q^11 + 3 * q^12 + 9 * q^13 + q^14 - 5 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 - 5 * q^19 + 5 * q^20 - 2 * q^21 - 14 * q^22 - 11 * q^23 - 5 * q^25 - 12 * q^26 + 5 * q^27 + q^28 + 5 * q^29 - 5 * q^30 + 3 * q^31 + 18 * q^32 + 8 * q^33 + 6 * q^34 + 5 * q^35 - 6 * q^36 - 7 * q^37 + 5 * q^38 + 9 * q^39 + 5 * q^40 + 8 * q^41 + q^42 - 6 * q^43 + 6 * q^44 - 10 * q^45 + 13 * q^46 - 2 * q^47 - 6 * q^48 - 22 * q^49 - 10 * q^50 - 12 * q^51 - 12 * q^52 + 9 * q^53 - 15 * q^54 + 20 * q^55 - 10 * q^57 - 10 * q^58 + 13 * q^61 + 6 * q^62 - 6 * q^63 + 3 * q^64 + 6 * q^66 - 2 * q^67 - 4 * q^68 - q^69 + 8 * q^71 + 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^75 + 20 * q^76 - 4 * q^77 + 3 * q^78 + 15 * q^79 - 15 * q^80 - q^81 - 4 * q^82 + 9 * q^83 - 4 * q^84 - 20 * q^85 + 3 * q^86 - 10 * q^88 - 20 * q^89 - 12 * q^91 - 12 * q^92 - 12 * q^93 + q^94 - 5 * q^95 - 2 * q^96 + 8 * q^97 + 11 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.500000	−	0.363271i	−0.353553	−	0.256872i	0.396805	−	0.917903i	$-0.370119\pi$
$2$	−0.500000	−	0.363271i	−0.353553	−	0.256872i	−0.750358	+	0.661031i	$0.770119\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	0.999773	−	0.0213149i	$-0.00678525\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i	−0.821362	+	0.570408i	$0.806785\pi$
$4$	−0.500000	−	1.53884i	−0.250000	−	0.769421i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$5$	−1.80902	+	1.31433i	−0.809017	+	0.587785i
$6$	0.190983	−	0.587785i	0.0779685	−	0.239962i
$7$	−1.61803			−0.611559			−0.305780	−	0.952102i	$-0.598917\pi$
$7$	−1.61803			−0.611559			−0.305780	+	0.952102i	$0.598917\pi$
$8$	−0.690983	+	2.12663i	−0.244299	+	0.751876i
$9$	1.61803	−	1.17557i	0.539345	−	0.391857i
$10$	1.38197			0.437016
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	0.677046	−	0.735940i	$-0.263260\pi$
$11$	0.618034	+	0.449028i	0.186344	+	0.135387i	−0.490702	+	0.871327i	$0.663260\pi$
$12$	1.30902	−	0.951057i	0.377881	−	0.274546i
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.109909	−	0.993942i	$-0.464944\pi$
$13$	3.92705	−	2.85317i	1.08917	−	0.791327i	0.979259	+	0.202615i	$0.0649439\pi$
$14$	0.809017	+	0.587785i	0.216219	+	0.157092i
$15$	−1.80902	−	1.31433i	−0.467086	−	0.339358i
$16$	−1.50000	+	1.08981i	−0.375000	+	0.272453i
$17$	−0.236068	+	0.726543i	−0.0572549	+	0.176212i	−0.975594	−	0.219582i	$-0.929531\pi$
$17$	−0.236068	+	0.726543i	−0.0572549	+	0.176212i	0.918339	+	0.395794i	$0.129531\pi$
$18$	−1.23607			−0.291344
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	0.497219	+	0.867625i	$0.334355\pi$
$19$	−1.80902	+	5.56758i	−0.415017	+	1.27729i	−0.912236	+	0.409666i	$0.865645\pi$
$20$	2.92705	+	2.12663i	0.654508	+	0.475528i
$21$	−0.500000	−	1.53884i	−0.109109	−	0.335803i
$22$	−0.145898	−	0.449028i	−0.0311056	−	0.0957331i
$23$	−6.66312	−	4.84104i	−1.38936	−	1.00943i	−0.995936	−	0.0900679i	$-0.971292\pi$
$23$	−6.66312	−	4.84104i	−1.38936	−	1.00943i	−0.393421	−	0.919359i	$-0.628708\pi$
$24$	−2.23607			−0.456435
$25$	1.54508	−	4.75528i	0.309017	−	0.951057i
$26$	−3.00000			−0.588348
$27$	4.04508	+	2.93893i	0.778477	+	0.565597i
$28$	0.809017	+	2.48990i	0.152890	+	0.470547i
$29$	−0.427051	−	1.31433i	−0.0793014	−	0.244065i	0.903544	−	0.428495i	$-0.140956\pi$
$29$	−0.427051	−	1.31433i	−0.0793014	−	0.244065i	−0.982846	+	0.184430i	$0.940956\pi$
$30$	0.427051	+	1.31433i	0.0779685	+	0.239962i
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	−0.999144	−	0.0413693i	$-0.986828\pi$
$31$	−0.927051	+	2.85317i	−0.166503	+	0.512444i	0.832641	+	0.553814i	$0.186828\pi$
$32$	5.61803			0.993137
$33$	−0.236068	+	0.726543i	−0.0410942	+	0.126475i
$34$	0.381966	−	0.277515i	0.0655066	−	0.0475934i
$35$	2.92705	−	2.12663i	0.494762	−	0.359466i
$36$	−2.61803	−	1.90211i	−0.436339	−	0.317019i
$37$	−3.42705	+	2.48990i	−0.563404	+	0.409337i	−0.832703	−	0.553720i	$-0.813208\pi$
$37$	−3.42705	+	2.48990i	−0.563404	+	0.409337i	0.269299	+	0.963057i	$0.413208\pi$
$38$	2.92705	−	2.12663i	0.474830	−	0.344984i
$39$	3.92705	+	2.85317i	0.628831	+	0.456873i
$40$	−1.54508	−	4.75528i	−0.244299	−	0.751876i
$41$	4.23607	−	3.07768i	0.661563	−	0.480653i	−0.205628	−	0.978630i	$-0.565924\pi$
$41$	4.23607	−	3.07768i	0.661563	−	0.480653i	0.867190	+	0.497977i	$0.165924\pi$
$42$	−0.309017	+	0.951057i	−0.0476824	+	0.146751i
$43$	1.85410			0.282748			0.141374	−	0.989956i	$-0.454848\pi$
$43$	1.85410			0.282748			0.141374	+	0.989956i	$0.454848\pi$
$44$	0.381966	−	1.17557i	0.0575835	−	0.177224i
$45$	−1.38197	+	4.25325i	−0.206011	+	0.634038i
$46$	1.57295	+	4.84104i	0.231919	+	0.713772i
$47$	−0.500000	−	1.53884i	−0.0729325	−	0.224463i	0.907945	−	0.419089i	$-0.137651\pi$
$47$	−0.500000	−	1.53884i	−0.0729325	−	0.224463i	−0.980877	+	0.194626i	$0.937651\pi$
$48$	−1.50000	−	1.08981i	−0.216506	−	0.157301i
$49$	−4.38197			−0.625995
$50$	−2.50000	+	1.81636i	−0.353553	+	0.256872i
$51$	−0.763932			−0.106972
$52$	−6.35410	−	4.61653i	−0.881155	−	0.640197i
$53$	1.69098	+	5.20431i	0.232274	+	0.714867i	0.997471	+	0.0710707i	$0.0226416\pi$
$53$	1.69098	+	5.20431i	0.232274	+	0.714867i	−0.765197	+	0.643796i	$0.777358\pi$
$54$	−0.954915	−	2.93893i	−0.129947	−	0.399937i
$55$	−1.70820			−0.230334
$56$	1.11803	−	3.44095i	0.149404	−	0.459817i
$57$	−5.85410			−0.775395
$58$	−0.263932	+	0.812299i	−0.0346560	+	0.106660i
$59$	3.35410	−	2.43690i	0.436667	−	0.317257i	−0.347642	−	0.937627i	$-0.613018\pi$
$59$	3.35410	−	2.43690i	0.436667	−	0.317257i	0.784309	+	0.620370i	$0.213018\pi$
$60$	−1.11803	+	3.44095i	−0.144338	+	0.444225i
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	0.804297	−	0.594227i	$-0.202542\pi$
$61$	3.80902	+	2.76741i	0.487695	+	0.354331i	−0.316602	+	0.948558i	$0.602542\pi$
$62$	1.50000	−	1.08981i	0.190500	−	0.138406i
$63$	−2.61803	+	1.90211i	−0.329841	+	0.239644i
$64$	0.190983	+	0.138757i	0.0238729	+	0.0173447i
$65$	−3.35410	+	10.3229i	−0.416025	+	1.28039i
$66$	0.381966	−	0.277515i	0.0470168	−	0.0341597i
$67$	2.85410	−	8.78402i	0.348684	−	1.07314i	−0.610898	−	0.791709i	$-0.709191\pi$
$67$	2.85410	−	8.78402i	0.348684	−	1.07314i	0.959582	−	0.281430i	$-0.0908086\pi$
$68$	1.23607			0.149895
$69$	2.54508	−	7.83297i	0.306392	−	0.942978i
$70$	−2.23607			−0.267261
$71$	−1.35410	−	4.16750i	−0.160702	−	0.494591i	0.837992	−	0.545683i	$-0.183730\pi$
$71$	−1.35410	−	4.16750i	−0.160702	−	0.494591i	−0.998694	+	0.0510922i	$0.983730\pi$
$72$	1.38197	+	4.25325i	0.162866	+	0.501251i
$73$	7.28115	+	5.29007i	0.852194	+	0.619156i	0.925750	−	0.378136i	$-0.123435\pi$
$73$	7.28115	+	5.29007i	0.852194	+	0.619156i	−0.0735557	+	0.997291i	$0.523435\pi$
$74$	2.61803			0.304340
$75$	5.00000			0.577350
$76$	9.47214			1.08653
$77$	−1.00000	−	0.726543i	−0.113961	−	0.0827972i
$78$	−0.927051	−	2.85317i	−0.104968	−	0.323058i
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	0.990295	−	0.138985i	$-0.0443839\pi$
$79$	0.954915	+	2.93893i	0.107436	+	0.330655i	−0.882858	+	0.469640i	$0.844384\pi$
$80$	1.28115	−	3.94298i	0.143237	−	0.440839i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−3.23607			−0.357364
$83$	−0.545085	+	1.67760i	−0.0598308	+	0.184140i	−0.976505	−	0.215495i	$-0.930863\pi$
$83$	−0.545085	+	1.67760i	−0.0598308	+	0.184140i	0.916674	+	0.399636i	$0.130863\pi$
$84$	−2.11803	+	1.53884i	−0.231096	+	0.167901i
$85$	−0.527864	−	1.62460i	−0.0572549	−	0.176212i
$86$	−0.927051	−	0.673542i	−0.0999665	−	0.0726299i
$87$	1.11803	−	0.812299i	0.119866	−	0.0870876i
$88$	−1.38197	+	1.00406i	−0.147318	+	0.107033i
$89$	−7.23607	−	5.25731i	−0.767022	−	0.557274i	0.134034	−	0.990977i	$-0.457207\pi$
$89$	−7.23607	−	5.25731i	−0.767022	−	0.557274i	−0.901056	+	0.433703i	$0.857207\pi$
$90$	2.23607	−	1.62460i	0.235702	−	0.171248i
$91$	−6.35410	+	4.61653i	−0.666091	+	0.483943i
$92$	−4.11803	+	12.6740i	−0.429335	+	1.32136i
$93$	−3.00000			−0.311086
$94$	−0.309017	+	0.951057i	−0.0318727	+	0.0980940i
$95$	−4.04508	−	12.4495i	−0.415017	−	1.27729i
$96$	1.73607	+	5.34307i	0.177187	+	0.545325i
$97$	0.881966	+	2.71441i	0.0895501	+	0.275607i	0.985795	−	0.167953i	$-0.0537155\pi$
$97$	0.881966	+	2.71441i	0.0895501	+	0.275607i	−0.896245	+	0.443559i	$0.853716\pi$
$98$	2.19098	+	1.59184i	0.221323	+	0.160800i
$99$	1.52786			0.153556
$100$	−8.09017			−0.809017
$101$	−7.47214			−0.743505			−0.371753	−	0.928332i	$-0.621243\pi$
$101$	−7.47214			−0.743505			−0.371753	+	0.928332i	$0.621243\pi$
$102$	0.381966	+	0.277515i	0.0378203	+	0.0274780i
$103$	−3.57295	−	10.9964i	−0.352053	−	1.08351i	−0.957699	−	0.287773i	$-0.907085\pi$
$103$	−3.57295	−	10.9964i	−0.352053	−	1.08351i	0.605645	−	0.795735i	$-0.292915\pi$
$104$	3.35410	+	10.3229i	0.328897	+	1.01224i
$105$	2.92705	+	2.12663i	0.285651	+	0.207538i
$106$	1.04508	−	3.21644i	0.101508	−	0.312408i
$107$	10.4164			1.00699			0.503496	−	0.863998i	$-0.332047\pi$
$107$	10.4164			1.00699			0.503496	+	0.863998i	$0.332047\pi$
$108$	2.50000	−	7.69421i	0.240563	−	0.740376i
$109$	−8.09017	+	5.87785i	−0.774898	+	0.562996i	−0.903443	−	0.428707i	$-0.858969\pi$
$109$	−8.09017	+	5.87785i	−0.774898	+	0.562996i	0.128546	+	0.991704i	$0.458969\pi$
$110$	0.854102	+	0.620541i	0.0814354	+	0.0591663i
$111$	−3.42705	−	2.48990i	−0.325281	−	0.236331i
$112$	2.42705	−	1.76336i	0.229335	−	0.166621i
$113$	−8.20820	+	5.96361i	−0.772163	+	0.561009i	−0.902617	−	0.430445i	$-0.858357\pi$
$113$	−8.20820	+	5.96361i	−0.772163	+	0.561009i	0.130454	+	0.991454i	$0.458357\pi$
$114$	2.92705	+	2.12663i	0.274143	+	0.199177i
$115$	18.4164			1.71734
$116$	−1.80902	+	1.31433i	−0.167963	+	0.122032i
$117$	3.00000	−	9.23305i	0.277350	−	0.853596i
$118$	−2.56231			−0.235879
$119$	0.381966	−	1.17557i	0.0350148	−	0.107764i
$120$	4.04508	−	2.93893i	0.369264	−	0.268286i
$121$	−3.21885	−	9.90659i	−0.292622	−	0.900599i
$122$	−0.899187	−	2.76741i	−0.0814086	−	0.250550i
$123$	4.23607	+	3.07768i	0.381953	+	0.277505i
$124$	4.85410			0.435911
$125$	3.45492	+	10.6331i	0.309017	+	0.951057i
$126$	2.00000			0.178174
$127$	12.8541	+	9.33905i	1.14062	+	0.828707i	0.987205	−	0.159455i	$-0.0509738\pi$
$127$	12.8541	+	9.33905i	1.14062	+	0.828707i	0.153412	+	0.988162i	$0.450974\pi$
$128$	−3.51722	−	10.8249i	−0.310881	−	0.956794i
$129$	0.572949	+	1.76336i	0.0504453	+	0.155255i
$130$	5.42705	−	3.94298i	0.475984	−	0.345823i
$131$	−5.50000	+	16.9273i	−0.480537	+	1.47894i	0.357805	+	0.933797i	$0.383525\pi$
$131$	−5.50000	+	16.9273i	−0.480537	+	1.47894i	−0.838342	+	0.545145i	$0.816475\pi$
$132$	1.23607			0.107586
$133$	2.92705	−	9.00854i	0.253808	−	0.781139i
$134$	−4.61803	+	3.35520i	−0.398937	+	0.289845i
$135$	−11.1803			−0.962250
$136$	−1.38197	−	1.00406i	−0.118503	−	0.0860972i
$137$	−4.80902	+	3.49396i	−0.410862	+	0.298509i	−0.773951	−	0.633246i	$-0.781722\pi$
$137$	−4.80902	+	3.49396i	−0.410862	+	0.298509i	0.363089	+	0.931755i	$0.381722\pi$
$138$	−4.11803	+	2.99193i	−0.350550	+	0.254690i
$139$	−4.04508	−	2.93893i	−0.343100	−	0.249276i	0.402869	−	0.915258i	$-0.368013\pi$
$139$	−4.04508	−	2.93893i	−0.343100	−	0.249276i	−0.745968	+	0.665981i	$0.768013\pi$
$140$	−4.73607	−	3.44095i	−0.400271	−	0.290814i
$141$	1.30902	−	0.951057i	0.110239	−	0.0800934i
$142$	−0.836881	+	2.57565i	−0.0702295	+	0.216144i
$143$	3.70820			0.310096
$144$	−1.14590	+	3.52671i	−0.0954915	+	0.293893i
$145$	2.50000	+	1.81636i	0.207614	+	0.150840i
$146$	−1.71885	−	5.29007i	−0.142253	−	0.437809i
$147$	−1.35410	−	4.16750i	−0.111684	−	0.343729i
$148$	5.54508	+	4.02874i	0.455803	+	0.331160i
$149$	13.9443			1.14236			0.571180	−	0.820825i	$-0.306486\pi$
$149$	13.9443			1.14236			0.571180	+	0.820825i	$0.306486\pi$
$150$	−2.50000	−	1.81636i	−0.204124	−	0.148305i
$151$	−5.56231			−0.452654			−0.226327	−	0.974051i	$-0.572672\pi$
$151$	−5.56231			−0.452654			−0.226327	+	0.974051i	$0.572672\pi$
$152$	−10.5902	−	7.69421i	−0.858976	−	0.624083i
$153$	0.472136	+	1.45309i	0.0381699	+	0.117475i
$154$	0.236068	+	0.726543i	0.0190229	+	0.0585465i
$155$	−2.07295	−	6.37988i	−0.166503	−	0.512444i
$156$	2.42705	−	7.46969i	0.194320	−	0.598054i
$157$	−9.18034			−0.732671			−0.366335	−	0.930483i	$-0.619388\pi$
$157$	−9.18034			−0.732671			−0.366335	+	0.930483i	$0.619388\pi$
$158$	0.590170	−	1.81636i	0.0469514	−	0.144502i
$159$	−4.42705	+	3.21644i	−0.351088	+	0.255080i
$160$	−10.1631	+	7.38394i	−0.803465	+	0.583752i
$161$	10.7812	+	7.83297i	0.849674	+	0.617324i
$162$	−0.500000	+	0.363271i	−0.0392837	+	0.0285413i
$163$	−8.89919	+	6.46564i	−0.697038	+	0.506428i	−0.878966	−	0.476884i	$-0.841766\pi$
$163$	−8.89919	+	6.46564i	−0.697038	+	0.506428i	0.181928	+	0.983312i	$0.441766\pi$
$164$	−6.85410	−	4.97980i	−0.535215	−	0.388857i
$165$	−0.527864	−	1.62460i	−0.0410942	−	0.126475i
$166$	0.881966	−	0.640786i	0.0684538	−	0.0497346i
$167$	−1.71885	+	5.29007i	−0.133008	+	0.409358i	−0.995275	−	0.0970971i	$-0.969044\pi$
$167$	−1.71885	+	5.29007i	−0.133008	+	0.409358i	0.862267	+	0.506455i	$0.169044\pi$
$168$	3.61803			0.279137
$169$	3.26393	−	10.0453i	0.251072	−	0.772719i
$170$	−0.326238	+	1.00406i	−0.0250213	+	0.0770077i
$171$	3.61803	+	11.1352i	0.276678	+	0.851527i
$172$	−0.927051	−	2.85317i	−0.0706870	−	0.217552i
$173$	13.6631	+	9.92684i	1.03879	+	0.754723i	0.970049	−	0.242911i	$-0.0781024\pi$
$173$	13.6631	+	9.92684i	1.03879	+	0.754723i	0.0687392	+	0.997635i	$0.478102\pi$
$174$	−0.854102			−0.0647493
$175$	−2.50000	+	7.69421i	−0.188982	+	0.581628i
$176$	−1.41641			−0.106766
$177$	3.35410	+	2.43690i	0.252110	+	0.183168i
$178$	1.70820	+	5.25731i	0.128035	+	0.394052i
$179$	−2.92705	−	9.00854i	−0.218778	−	0.673330i	−0.998864	−	0.0476570i	$-0.984825\pi$
$179$	−2.92705	−	9.00854i	−0.218778	−	0.673330i	0.780086	−	0.625673i	$-0.215175\pi$
$180$	7.23607			0.539345
$181$	4.23607	−	13.0373i	0.314864	−	0.969053i	−0.660946	−	0.750434i	$-0.729845\pi$
$181$	4.23607	−	13.0373i	0.314864	−	0.969053i	0.975810	−	0.218619i	$-0.0701553\pi$
$182$	4.85410			0.359810
$183$	−1.45492	+	4.47777i	−0.107550	+	0.331006i
$184$	14.8992	−	10.8249i	1.09838	−	0.798022i
$185$	2.92705	−	9.00854i	0.215201	−	0.662321i
$186$	1.50000	+	1.08981i	0.109985	+	0.0799090i
$187$	−0.472136	+	0.343027i	−0.0345260	+	0.0250846i
$188$	−2.11803	+	1.53884i	−0.154474	+	0.112232i
$189$	−6.54508	−	4.75528i	−0.476085	−	0.345896i
$190$	−2.50000	+	7.69421i	−0.181369	+	0.558197i
$191$	19.5623	−	14.2128i	1.41548	−	1.02841i	0.422982	−	0.906138i	$-0.360984\pi$
$191$	19.5623	−	14.2128i	1.41548	−	1.02841i	0.992497	−	0.122267i	$-0.0390165\pi$
$192$	−0.0729490	+	0.224514i	−0.00526464	+	0.0162029i
$193$	−5.70820			−0.410886			−0.205443	−	0.978669i	$-0.565863\pi$
$193$	−5.70820			−0.410886			−0.205443	+	0.978669i	$0.565863\pi$
$194$	0.545085	−	1.67760i	0.0391348	−	0.120445i
$195$	−10.8541			−0.777278
$196$	2.19098	+	6.74315i	0.156499	+	0.481654i
$197$	−3.00000	−	9.23305i	−0.213741	−	0.657828i	−0.999241	−	0.0389652i	$-0.987594\pi$
$197$	−3.00000	−	9.23305i	−0.213741	−	0.657828i	0.785499	−	0.618862i	$-0.212406\pi$
$198$	−0.763932	−	0.555029i	−0.0542903	−	0.0394442i
$199$	2.56231			0.181637			0.0908185	−	0.995867i	$-0.471052\pi$
$199$	2.56231			0.181637			0.0908185	+	0.995867i	$0.471052\pi$
$200$	9.04508	+	6.57164i	0.639584	+	0.464685i
$201$	9.23607			0.651462
$202$	3.73607	+	2.71441i	0.262869	+	0.190985i
$203$	0.690983	+	2.12663i	0.0484975	+	0.149260i
$204$	0.381966	+	1.17557i	0.0267430	+	0.0823064i
$205$	−3.61803	+	11.1352i	−0.252694	+	0.777714i
$206$	−2.20820	+	6.79615i	−0.153853	+	0.473510i
$207$	−16.4721			−1.14489
$208$	−2.78115	+	8.55951i	−0.192838	+	0.593495i
$209$	−3.61803	+	2.62866i	−0.250265	+	0.181828i
$210$	−0.690983	−	2.12663i	−0.0476824	−	0.146751i
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	0.156772	−	0.987635i	$-0.449891\pi$
$211$	−10.6631	−	7.74721i	−0.734079	−	0.533340i	−0.890851	+	0.454295i	$0.849891\pi$
$212$	7.16312	−	5.20431i	0.491965	−	0.357434i
$213$	3.54508	−	2.57565i	0.242905	−	0.176481i
$214$	−5.20820	−	3.78398i	−0.356025	−	0.258668i
$215$	−3.35410	+	2.43690i	−0.228748	+	0.166195i
$216$	−9.04508	+	6.57164i	−0.615440	+	0.447143i
$217$	1.50000	−	4.61653i	0.101827	−	0.313390i
$218$	6.18034			0.418585
$219$	−2.78115	+	8.55951i	−0.187933	+	0.578398i
$220$	0.854102	+	2.62866i	0.0575835	+	0.177224i
$221$	1.14590	+	3.52671i	0.0770814	+	0.237232i
$222$	0.809017	+	2.48990i	0.0542977	+	0.167111i
$223$	−17.9443	−	13.0373i	−1.20164	−	0.873041i	−0.207193	−	0.978300i	$-0.566433\pi$
$223$	−17.9443	−	13.0373i	−1.20164	−	0.873041i	−0.994445	+	0.105260i	$0.966433\pi$
$224$	−9.09017			−0.607363
$225$	−3.09017	−	9.51057i	−0.206011	−	0.634038i
$226$	6.27051			0.417108
$227$	−15.5623	−	11.3067i	−1.03291	−	0.750451i	−0.0640182	−	0.997949i	$-0.520392\pi$
$227$	−15.5623	−	11.3067i	−1.03291	−	0.750451i	−0.968888	+	0.247498i	$0.920392\pi$
$228$	2.92705	+	9.00854i	0.193849	+	0.596605i
$229$	2.56231	+	7.88597i	0.169322	+	0.521119i	0.999329	−	0.0366339i	$-0.0116635\pi$
$229$	2.56231	+	7.88597i	0.169322	+	0.521119i	−0.830007	+	0.557753i	$0.811664\pi$
$230$	−9.20820	−	6.69015i	−0.607171	−	0.441136i
$231$	0.381966	−	1.17557i	0.0251315	−	0.0773469i
$232$	3.09017			0.202880
$233$	4.61803	−	14.2128i	0.302537	−	0.931115i	−0.678047	−	0.735018i	$-0.737174\pi$
$233$	4.61803	−	14.2128i	0.302537	−	0.931115i	0.980585	−	0.196096i	$-0.0628265\pi$
$234$	−4.85410	+	3.52671i	−0.317323	+	0.230548i
$235$	2.92705	+	2.12663i	0.190940	+	0.138726i
$236$	−5.42705	−	3.94298i	−0.353271	−	0.256666i
$237$	−2.50000	+	1.81636i	−0.162392	+	0.117985i
$238$	−0.618034	+	0.449028i	−0.0400612	+	0.0291062i
$239$	23.8435	+	17.3233i	1.54231	+	1.12055i	0.948869	+	0.315669i	$0.102229\pi$
$239$	23.8435	+	17.3233i	1.54231	+	1.12055i	0.593436	+	0.804881i	$0.297771\pi$
$240$	4.14590			0.267617
$241$	−9.28115	+	6.74315i	−0.597852	+	0.434365i	−0.845116	−	0.534584i	$-0.820468\pi$
$241$	−9.28115	+	6.74315i	−0.597852	+	0.434365i	0.247264	+	0.968948i	$0.420468\pi$
$242$	−1.98936	+	6.12261i	−0.127881	+	0.393576i
$243$	16.0000			1.02640
$244$	2.35410	−	7.24518i	0.150706	−	0.463825i
$245$	7.92705	−	5.75934i	0.506441	−	0.367951i
$246$	−1.00000	−	3.07768i	−0.0637577	−	0.196226i
$247$	8.78115	+	27.0256i	0.558731	+	1.71960i
$248$	−5.42705	−	3.94298i	−0.344618	−	0.250380i
$249$	−1.76393			−0.111785
$250$	2.13525	−	6.57164i	0.135045	−	0.415627i
$251$	−6.81966			−0.430453			−0.215227	−	0.976564i	$-0.569049\pi$
$251$	−6.81966			−0.430453			−0.215227	+	0.976564i	$0.569049\pi$
$252$	4.23607	+	3.07768i	0.266847	+	0.193876i
$253$	−1.94427	−	5.98385i	−0.122235	−	0.376202i
$254$	−3.03444	−	9.33905i	−0.190398	−	0.585984i
$255$	1.38197	−	1.00406i	0.0865421	−	0.0628765i
$256$	−2.02786	+	6.24112i	−0.126742	+	0.390070i
$257$	16.1459			1.00715			0.503577	−	0.863951i	$-0.332017\pi$
$257$	16.1459			1.00715			0.503577	+	0.863951i	$0.332017\pi$
$258$	0.354102	−	1.08981i	0.0220454	−	0.0678488i
$259$	5.54508	−	4.02874i	0.344555	−	0.250334i
$260$	17.5623			1.08917
$261$	−2.23607	−	1.62460i	−0.138409	−	0.100560i
$262$	8.89919	−	6.46564i	0.549794	−	0.399448i
$263$	17.8713	−	12.9843i	1.10199	−	0.800645i	0.120609	−	0.992700i	$-0.461515\pi$
$263$	17.8713	−	12.9843i	1.10199	−	0.800645i	0.981384	+	0.192055i	$0.0615153\pi$
$264$	−1.38197	−	1.00406i	−0.0850541	−	0.0617954i
$265$	−9.89919	−	7.19218i	−0.608102	−	0.441812i
$266$	−4.73607	+	3.44095i	−0.290387	+	0.210978i
$267$	2.76393	−	8.50651i	0.169150	−	0.520590i
$268$	−14.9443			−0.912867
$269$	−5.32624	+	16.3925i	−0.324746	+	0.999467i	0.646808	+	0.762652i	$0.276103\pi$
$269$	−5.32624	+	16.3925i	−0.324746	+	0.999467i	−0.971555	+	0.236814i	$0.923897\pi$
$270$	5.59017	+	4.06150i	0.340207	+	0.247175i
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	0.847468	−	0.530846i	$-0.178126\pi$
$271$	−2.47214	−	7.60845i	−0.150172	−	0.462181i	−0.997640	+	0.0686657i	$0.978126\pi$
$272$	−0.437694	−	1.34708i	−0.0265391	−	0.0816790i
$273$	−6.35410	−	4.61653i	−0.384568	−	0.279405i
$274$	3.67376			0.221940
$275$	3.09017	−	2.24514i	0.186344	−	0.135387i
$276$	−13.3262			−0.802145
$277$	9.13525	+	6.63715i	0.548884	+	0.398788i	0.827374	−	0.561651i	$-0.189834\pi$
$277$	9.13525	+	6.63715i	0.548884	+	0.398788i	−0.278490	+	0.960439i	$0.589834\pi$
$278$	0.954915	+	2.93893i	0.0572720	+	0.176265i
$279$	1.85410	+	5.70634i	0.111002	+	0.341630i
$280$	2.50000	+	7.69421i	0.149404	+	0.459817i
$281$	−0.336881	+	1.03681i	−0.0200966	+	0.0618511i	−0.960602	−	0.277928i	$-0.910352\pi$
$281$	−0.336881	+	1.03681i	−0.0200966	+	0.0618511i	0.940505	+	0.339779i	$0.110352\pi$
$282$	−1.00000			−0.0595491
$283$	−7.15248	+	22.0131i	−0.425171	+	1.30854i	0.477660	+	0.878545i	$0.341485\pi$
$283$	−7.15248	+	22.0131i	−0.425171	+	1.30854i	−0.902831	+	0.429996i	$0.858515\pi$
$284$	−5.73607	+	4.16750i	−0.340373	+	0.247295i
$285$	10.5902	−	7.69421i	0.627308	−	0.455766i
$286$	−1.85410	−	1.34708i	−0.109635	−	0.0796547i
$287$	−6.85410	+	4.97980i	−0.404585	+	0.293948i
$288$	9.09017	−	6.60440i	0.535643	−	0.389168i
$289$	13.2812	+	9.64932i	0.781244	+	0.567607i
$290$	−0.590170	−	1.81636i	−0.0346560	−	0.106660i
$291$	−2.30902	+	1.67760i	−0.135357	+	0.0983426i
$292$	4.50000	−	13.8496i	0.263343	−	0.810485i
$293$	−28.4721			−1.66336			−0.831680	−	0.555255i	$-0.812621\pi$
$293$	−28.4721			−1.66336			−0.831680	+	0.555255i	$0.812621\pi$
$294$	−0.836881	+	2.57565i	−0.0488079	+	0.150215i
$295$	−2.86475	+	8.81678i	−0.166792	+	0.513333i
$296$	−2.92705	−	9.00854i	−0.170131	−	0.523611i
$297$	1.18034	+	3.63271i	0.0684903	+	0.210791i
$298$	−6.97214	−	5.06555i	−0.403885	−	0.293440i
$299$	−39.9787			−2.31203
$300$	−2.50000	−	7.69421i	−0.144338	−	0.444225i
$301$	−3.00000			−0.172917
$302$	2.78115	+	2.02063i	0.160037	+	0.116274i
$303$	−2.30902	−	7.10642i	−0.132650	−	0.408253i
$304$	−3.35410	−	10.3229i	−0.192371	−	0.592057i
$305$	−10.5279			−0.602824
$306$	0.291796	−	0.898056i	0.0166809	−	0.0513384i
$307$	4.76393			0.271892			0.135946	−	0.990716i	$-0.456593\pi$
$307$	4.76393			0.271892			0.135946	+	0.990716i	$0.456593\pi$
$308$	−0.618034	+	1.90211i	−0.0352158	+	0.108383i
$309$	9.35410	−	6.79615i	0.532136	−	0.386620i
$310$	−1.28115	+	3.94298i	−0.0727646	+	0.223946i
$311$	23.8713	+	17.3435i	1.35362	+	0.983461i	0.998822	+	0.0485178i	$0.0154498\pi$
$311$	23.8713	+	17.3435i	1.35362	+	0.983461i	0.354796	+	0.934944i	$0.384550\pi$
$312$	−8.78115	+	6.37988i	−0.497135	+	0.361190i
$313$	17.1803	−	12.4822i	0.971090	−	0.705538i	0.0153904	−	0.999882i	$-0.495101\pi$
$313$	17.1803	−	12.4822i	0.971090	−	0.705538i	0.955700	+	0.294343i	$0.0951009\pi$
$314$	4.59017	+	3.33495i	0.259038	+	0.188202i
$315$	2.23607	−	6.88191i	0.125988	−	0.387752i
$316$	4.04508	−	2.93893i	0.227554	−	0.165328i
$317$	−7.30902	+	22.4948i	−0.410515	+	1.26344i	0.505686	+	0.862718i	$0.331239\pi$
$317$	−7.30902	+	22.4948i	−0.410515	+	1.26344i	−0.916201	+	0.400719i	$0.868761\pi$
$318$	3.38197			0.189651
$319$	0.326238	−	1.00406i	0.0182658	−	0.0562164i
$320$	−0.527864			−0.0295085
$321$	3.21885	+	9.90659i	0.179659	+	0.552932i
$322$	−2.54508	−	7.83297i	−0.141832	−	0.436514i
$323$	−3.61803	−	2.62866i	−0.201313	−	0.146262i
$324$	−1.61803			−0.0898908
$325$	−7.50000	−	23.0826i	−0.416025	−	1.28039i
$326$	6.79837			0.376527
$327$	−8.09017	−	5.87785i	−0.447387	−	0.325046i
$328$	3.61803	+	11.1352i	0.199773	+	0.614837i
$329$	0.809017	+	2.48990i	0.0446026	+	0.137273i
$330$	−0.326238	+	1.00406i	−0.0179588	+	0.0552715i
$331$	5.29180	−	16.2865i	0.290863	−	0.895186i	−0.693716	−	0.720248i	$-0.744028\pi$
$331$	5.29180	−	16.2865i	0.290863	−	0.895186i	0.984580	−	0.174937i	$-0.0559722\pi$
$332$	2.85410			0.156639
$333$	−2.61803	+	8.05748i	−0.143467	+	0.441547i
$334$	2.78115	−	2.02063i	0.152178	−	0.110564i
$335$	6.38197	+	19.6417i	0.348684	+	1.07314i
$336$	2.42705	+	1.76336i	0.132406	+	0.0961989i
$337$	−0.927051	+	0.673542i	−0.0504997	+	0.0366902i	−0.612749	−	0.790278i	$-0.709936\pi$
$337$	−0.927051	+	0.673542i	−0.0504997	+	0.0366902i	0.562249	+	0.826968i	$0.309936\pi$
$338$	−5.28115	+	3.83698i	−0.287257	+	0.208704i
$339$	−8.20820	−	5.96361i	−0.445808	−	0.323899i
$340$	−2.23607	+	1.62460i	−0.121268	+	0.0881062i
$341$	−1.85410	+	1.34708i	−0.100405	+	0.0729487i
$342$	2.23607	−	6.88191i	0.120913	−	0.372131i
$343$	18.4164			0.994393
$344$	−1.28115	+	3.94298i	−0.0690751	+	0.212591i
$345$	5.69098	+	17.5150i	0.306392	+	0.942978i
$346$	−3.22542	−	9.92684i	−0.173400	−	0.533670i
$347$	−9.60739	−	29.5685i	−0.515752	−	1.58732i	−0.781910	−	0.623391i	$-0.785754\pi$
$347$	−9.60739	−	29.5685i	−0.515752	−	1.58732i	0.266158	−	0.963929i	$-0.414246\pi$
$348$	−1.80902	−	1.31433i	−0.0969735	−	0.0704554i
$349$	8.29180			0.443850			0.221925	−	0.975064i	$-0.428766\pi$
$349$	8.29180			0.443850			0.221925	+	0.975064i	$0.428766\pi$
$350$	4.04508	−	2.93893i	0.216219	−	0.157092i
$351$	24.2705			1.29546
$352$	3.47214	+	2.52265i	0.185065	+	0.134458i
$353$	7.44427	+	22.9111i	0.396219	+	1.21944i	0.928008	+	0.372559i	$0.121520\pi$
$353$	7.44427	+	22.9111i	0.396219	+	1.21944i	−0.531790	+	0.846876i	$0.678480\pi$
$354$	−0.791796	−	2.43690i	−0.0420835	−	0.129520i
$355$	7.92705	+	5.75934i	0.420724	+	0.305674i
$356$	−4.47214	+	13.7638i	−0.237023	+	0.729481i
$357$	1.23607			0.0654197
$358$	−1.80902	+	5.56758i	−0.0956095	+	0.294256i
$359$	23.2533	−	16.8945i	1.22726	−	0.891658i	0.230580	−	0.973053i	$-0.425938\pi$
$359$	23.2533	−	16.8945i	1.22726	−	0.891658i	0.996682	+	0.0813956i	$0.0259377\pi$
$360$	−8.09017	−	5.87785i	−0.426389	−	0.309790i
$361$	−12.3541	−	8.97578i	−0.650216	−	0.472409i
$362$	−6.85410	+	4.97980i	−0.360244	+	0.261732i
$363$	8.42705	−	6.12261i	0.442305	−	0.321354i
$364$	10.2812	+	7.46969i	0.538879	+	0.391518i
$365$	−20.1246			−1.05337
$366$	2.35410	−	1.71036i	0.123051	−	0.0894017i
$367$	−1.68034	+	5.17155i	−0.0877130	+	0.269953i	−0.985286	−	0.170913i	$-0.945328\pi$
$367$	−1.68034	+	5.17155i	−0.0877130	+	0.269953i	0.897573	+	0.440866i	$0.145328\pi$
$368$	15.2705			0.796030
$369$	3.23607	−	9.95959i	0.168463	−	0.518476i
$370$	−4.73607	+	3.44095i	−0.246216	+	0.178887i
$371$	−2.73607	−	8.42075i	−0.142050	−	0.437184i
$372$	1.50000	+	4.61653i	0.0777714	+	0.239356i
$373$	−4.26393	−	3.09793i	−0.220778	−	0.160405i	0.471899	−	0.881653i	$-0.343569\pi$
$373$	−4.26393	−	3.09793i	−0.220778	−	0.160405i	−0.692677	+	0.721248i	$0.743569\pi$
$374$	0.360680			0.0186503
$375$	−9.04508	+	6.57164i	−0.467086	+	0.339358i
$376$	3.61803			0.186586
$377$	−5.42705	−	3.94298i	−0.279507	−	0.203074i
$378$	1.54508	+	4.75528i	0.0794706	+	0.244585i
$379$	−10.6910	−	32.9035i	−0.549159	−	1.69014i	−0.710891	−	0.703303i	$-0.751708\pi$
$379$	−10.6910	−	32.9035i	−0.549159	−	1.69014i	0.161732	−	0.986835i	$-0.448292\pi$
$380$	−17.1353	+	12.4495i	−0.879020	+	0.638645i
$381$	−4.90983	+	15.1109i	−0.251538	+	0.774155i
$382$	−14.9443			−0.764615
$383$	−3.51064	+	10.8046i	−0.179385	+	0.552092i	−0.999807	−	0.0196680i	$-0.993739\pi$
$383$	−3.51064	+	10.8046i	−0.179385	+	0.552092i	0.820421	+	0.571760i	$0.193739\pi$
$384$	9.20820	−	6.69015i	0.469904	−	0.341405i
$385$	2.76393			0.140863
$386$	2.85410	+	2.07363i	0.145270	+	0.105545i
$387$	3.00000	−	2.17963i	0.152499	−	0.110797i
$388$	3.73607	−	2.71441i	0.189670	−	0.137803i
$389$	−12.1353	−	8.81678i	−0.615282	−	0.447028i	0.235988	−	0.971756i	$-0.424167\pi$
$389$	−12.1353	−	8.81678i	−0.615282	−	0.447028i	−0.851270	+	0.524727i	$0.824167\pi$
$390$	5.42705	+	3.94298i	0.274809	+	0.199661i
$391$	5.09017	−	3.69822i	0.257421	−	0.187027i
$392$	3.02786	−	9.31881i	0.152930	−	0.470671i
$393$	−17.7984			−0.897809
$394$	−1.85410	+	5.70634i	−0.0934083	+	0.287481i
$395$	−5.59017	−	4.06150i	−0.281272	−	0.204356i
$396$	−0.763932	−	2.35114i	−0.0383890	−	0.118149i
$397$	−0.0106431	−	0.0327561i	−0.000534163	−	0.00164398i	0.950789	−	0.309839i	$-0.100275\pi$
$397$	−0.0106431	−	0.0327561i	−0.000534163	−	0.00164398i	−0.951323	+	0.308195i	$0.900275\pi$
$398$	−1.28115	−	0.930812i	−0.0642184	−	0.0466574i
$399$	9.47214			0.474200
$400$	2.86475	+	8.81678i	0.143237	+	0.440839i
$401$	−22.5967			−1.12843			−0.564214	−	0.825629i	$-0.690821\pi$
$401$	−22.5967			−1.12843			−0.564214	+	0.825629i	$0.690821\pi$
$402$	−4.61803	−	3.35520i	−0.230327	−	0.167342i
$403$	4.50000	+	13.8496i	0.224161	+	0.689897i
$404$	3.73607	+	11.4984i	0.185876	+	0.572069i
$405$	0.690983	+	2.12663i	0.0343352	+	0.105673i
$406$	0.427051	−	1.31433i	0.0211942	−	0.0652290i
$407$	−3.23607			−0.160406
$408$	0.527864	−	1.62460i	0.0261332	−	0.0804296i
$409$	−22.9894	+	16.7027i	−1.13675	+	0.825898i	−0.986663	−	0.162775i	$-0.947955\pi$
$409$	−22.9894	+	16.7027i	−1.13675	+	0.825898i	−0.150087	+	0.988673i	$0.547955\pi$
$410$	5.85410	−	4.25325i	0.289113	−	0.210053i
$411$	−4.80902	−	3.49396i	−0.237211	−	0.172344i
$412$	−15.1353	+	10.9964i	−0.745660	+	0.541754i
$413$	−5.42705	+	3.94298i	−0.267048	+	0.194022i
$414$	8.23607	+	5.98385i	0.404781	+	0.294090i
$415$	−1.21885	−	3.75123i	−0.0598308	−	0.184140i
$416$	22.0623	−	16.0292i	1.08169	−	0.785896i
$417$	1.54508	−	4.75528i	0.0756631	−	0.232867i
$418$	2.76393			0.135188
$419$	−0.163119	+	0.502029i	−0.00796888	+	0.0245257i	−0.954962	−	0.296728i	$-0.904104\pi$
$419$	−0.163119	+	0.502029i	−0.00796888	+	0.0245257i	0.946993	+	0.321254i	$0.104104\pi$
$420$	1.80902	−	5.56758i	0.0882710	−	0.271670i
$421$	9.88854	+	30.4338i	0.481938	+	1.48325i	0.836367	+	0.548170i	$0.184675\pi$
$421$	9.88854	+	30.4338i	0.481938	+	1.48325i	−0.354429	+	0.935083i	$0.615325\pi$
$422$	2.51722	+	7.74721i	0.122536	+	0.377128i
$423$	−2.61803	−	1.90211i	−0.127293	−	0.0924839i
$424$	−12.2361			−0.594236
$425$	3.09017	+	2.24514i	0.149895	+	0.108905i
$426$	−2.70820			−0.131213
$427$	−6.16312	−	4.47777i	−0.298254	−	0.216694i
$428$	−5.20820	−	16.0292i	−0.251748	−	0.774801i
$429$	1.14590	+	3.52671i	0.0553245	+	0.170271i
$430$	2.56231			0.123565
$431$	7.36475	−	22.6664i	0.354747	−	1.09180i	−0.601409	−	0.798942i	$-0.705394\pi$
$431$	7.36475	−	22.6664i	0.354747	−	1.09180i	0.956156	−	0.292858i	$-0.0946064\pi$
$432$	−9.27051			−0.446028
$433$	6.22542	−	19.1599i	0.299175	−	0.920765i	−0.682612	−	0.730781i	$-0.739156\pi$
$433$	6.22542	−	19.1599i	0.299175	−	0.920765i	0.981787	−	0.189985i	$-0.0608438\pi$
$434$	−2.42705	+	1.76336i	−0.116502	+	0.0846438i
$435$	−0.954915	+	2.93893i	−0.0457847	+	0.140911i
$436$	13.0902	+	9.51057i	0.626905	+	0.455473i
$437$	39.0066	−	28.3399i	1.86594	−	1.35568i
$438$	4.50000	−	3.26944i	0.215018	−	0.156220i
$439$	−4.83688	−	3.51420i	−0.230852	−	0.167724i	0.466346	−	0.884602i	$-0.345570\pi$
$439$	−4.83688	−	3.51420i	−0.230852	−	0.167724i	−0.697198	+	0.716879i	$0.745570\pi$
$440$	1.18034	−	3.63271i	0.0562705	−	0.173183i
$441$	−7.09017	+	5.15131i	−0.337627	+	0.245300i
$442$	0.708204	−	2.17963i	0.0336858	−	0.103674i
$443$	12.0557			0.572785			0.286392	−	0.958112i	$-0.407544\pi$
$443$	12.0557			0.572785			0.286392	+	0.958112i	$0.407544\pi$
$444$	−2.11803	+	6.51864i	−0.100517	+	0.309361i
$445$	20.0000			0.948091
$446$	4.23607	+	13.0373i	0.200584	+	0.617333i
$447$	4.30902	+	13.2618i	0.203810	+	0.627261i
$448$	−0.309017	−	0.224514i	−0.0145997	−	0.0106073i
$449$	20.3262			0.959254			0.479627	−	0.877472i	$-0.340772\pi$
$449$	20.3262			0.959254			0.479627	+	0.877472i	$0.340772\pi$
$450$	−1.90983	+	5.87785i	−0.0900303	+	0.277085i
$451$	4.00000			0.188353
$452$	13.2812	+	9.64932i	0.624693	+	0.453866i
$453$	−1.71885	−	5.29007i	−0.0807585	−	0.248549i
$454$	3.67376	+	11.3067i	0.172418	+	0.530649i
$455$	5.42705	−	16.7027i	0.254424	−	0.783037i
$456$	4.04508	−	12.4495i	0.189428	−	0.583001i
$457$	5.41641			0.253369			0.126684	−	0.991943i	$-0.459566\pi$
$457$	5.41641			0.253369			0.126684	+	0.991943i	$0.459566\pi$
$458$	1.58359	−	4.87380i	0.0739964	−	0.227738i
$459$	−3.09017	+	2.24514i	−0.144237	+	0.104794i
$460$	−9.20820	−	28.3399i	−0.429335	−	1.32136i
$461$	−18.7533	−	13.6251i	−0.873428	−	0.634582i	0.0580768	−	0.998312i	$-0.481503\pi$
$461$	−18.7533	−	13.6251i	−0.873428	−	0.634582i	−0.931505	+	0.363730i	$0.881503\pi$
$462$	−0.618034	+	0.449028i	−0.0287535	+	0.0208907i
$463$	−13.0451	+	9.47781i	−0.606257	+	0.440471i	−0.848094	−	0.529846i	$-0.822250\pi$
$463$	−13.0451	+	9.47781i	−0.606257	+	0.440471i	0.241838	+	0.970317i	$0.422250\pi$
$464$	2.07295	+	1.50609i	0.0962342	+	0.0699183i
$465$	5.42705	−	3.94298i	0.251673	−	0.182851i
$466$	−7.47214	+	5.42882i	−0.346140	+	0.251485i
$467$	−8.79180	+	27.0584i	−0.406836	+	1.25211i	0.512517	+	0.858677i	$0.328713\pi$
$467$	−8.79180	+	27.0584i	−0.406836	+	1.25211i	−0.919353	+	0.393435i	$0.871287\pi$
$468$	−15.7082			−0.726112
$469$	−4.61803	+	14.2128i	−0.213241	+	0.656288i
$470$	−0.690983	−	2.12663i	−0.0318727	−	0.0980940i
$471$	−2.83688	−	8.73102i	−0.130717	−	0.402304i
$472$	2.86475	+	8.81678i	0.131861	+	0.405825i
$473$	1.14590	+	0.832544i	0.0526884	+	0.0382804i
$474$	1.90983			0.0877214
$475$	23.6803	+	17.2048i	1.08653	+	0.789409i
$476$	−2.00000			−0.0916698
$477$	8.85410	+	6.43288i	0.405401	+	0.294541i
$478$	−5.62868	−	17.3233i	−0.257450	−	0.792349i
$479$	−1.28115	−	3.94298i	−0.0585374	−	0.180160i	0.917512	−	0.397708i	$-0.130194\pi$
$479$	−1.28115	−	3.94298i	−0.0585374	−	0.180160i	−0.976050	+	0.217548i	$0.930194\pi$
$480$	−10.1631	−	7.38394i	−0.463881	−	0.337029i
$481$	−6.35410	+	19.5559i	−0.289722	+	0.891673i
$482$	7.09017			0.322948
$483$	−4.11803	+	12.6740i	−0.187377	+	0.576687i
$484$	−13.6353	+	9.90659i	−0.619784	+	0.450300i
$485$	−5.16312	−	3.75123i	−0.234445	−	0.170334i
$486$	−8.00000	−	5.81234i	−0.362887	−	0.263653i
$487$	7.75329	−	5.63309i	0.351335	−	0.255260i	−0.398094	−	0.917345i	$-0.630328\pi$
$487$	7.75329	−	5.63309i	0.351335	−	0.255260i	0.749429	+	0.662085i	$0.230328\pi$
$488$	−8.51722	+	6.18812i	−0.385556	+	0.280123i
$489$	−8.89919	−	6.46564i	−0.402435	−	0.292386i
$490$	−6.05573			−0.273570
$491$	−30.1353	+	21.8945i	−1.35999	+	0.988087i	−0.361539	+	0.932357i	$0.617749\pi$
$491$	−30.1353	+	21.8945i	−1.35999	+	0.988087i	−0.998446	+	0.0557300i	$0.982251\pi$
$492$	2.61803	−	8.05748i	0.118030	−	0.363259i
$493$	1.05573			0.0475476
$494$	5.42705	−	16.7027i	0.244175	−	0.751492i
$495$	−2.76393	+	2.00811i	−0.124230	+	0.0902580i
$496$	−1.71885	−	5.29007i	−0.0771785	−	0.237531i
$497$	2.19098	+	6.74315i	0.0982790	+	0.302472i
$498$	0.881966	+	0.640786i	0.0395218	+	0.0287143i
$499$	−12.5623			−0.562366			−0.281183	−	0.959654i	$-0.590727\pi$
$499$	−12.5623			−0.562366			−0.281183	+	0.959654i	$0.590727\pi$
$500$	14.6353	−	10.6331i	0.654508	−	0.475528i
$501$	−5.56231			−0.248506
$502$	3.40983	+	2.47739i	0.152188	+	0.110571i
$503$	−3.27051	−	10.0656i	−0.145825	−	0.448803i	0.851291	−	0.524693i	$-0.175820\pi$
$503$	−3.27051	−	10.0656i	−0.145825	−	0.448803i	−0.997116	+	0.0758907i	$0.975820\pi$
$504$	−2.23607	−	6.88191i	−0.0996024	−	0.306545i
$505$	13.5172	−	9.82084i	0.601508	−	0.437021i
$506$	−1.20163	+	3.69822i	−0.0534188	+	0.164406i
$507$	10.5623			0.469088
$508$	7.94427	−	24.4500i	0.352470	−	1.08479i
$509$	3.78115	−	2.74717i	0.167597	−	0.121766i	−0.500825	−	0.865548i	$-0.666970\pi$
$509$	3.78115	−	2.74717i	0.167597	−	0.121766i	0.668422	+	0.743782i	$0.266970\pi$
$510$	−1.05573			−0.0467484
$511$	−11.7812	−	8.55951i	−0.521168	−	0.378650i
$512$	−15.1353	+	10.9964i	−0.668890	+	0.485977i
$513$	−23.6803	+	17.2048i	−1.04551	+	0.759609i
$514$	−8.07295	−	5.86534i	−0.356083	−	0.258709i
$515$	20.9164	+	15.1967i	0.921687	+	0.669645i
$516$	2.42705	−	1.76336i	0.106845	−	0.0776274i
$517$	0.381966	−	1.17557i	0.0167988	−	0.0517015i
$518$	−4.23607			−0.186122
$519$	−5.21885	+	16.0620i	−0.229082	+	0.705042i
$520$	−19.6353	−	14.2658i	−0.861063	−	0.625599i
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	−0.999579	−	0.0290150i	$-0.990763\pi$
$521$	−4.74671	−	14.6089i	−0.207957	−	0.640026i	0.791622	−	0.611011i	$-0.209237\pi$
$522$	0.527864	+	1.62460i	0.0231040	+	0.0711067i
$523$	16.0623	+	11.6699i	0.702356	+	0.510291i	0.880699	−	0.473677i	$-0.157074\pi$
$523$	16.0623	+	11.6699i	0.702356	+	0.510291i	−0.178343	+	0.983968i	$0.557074\pi$
$524$	28.7984			1.25806
$525$	−8.09017			−0.353084
$526$	−13.6525			−0.595276
$527$	−1.85410	−	1.34708i	−0.0807660	−	0.0586799i
$528$	−0.437694	−	1.34708i	−0.0190482	−	0.0586243i
$529$	13.8541	+	42.6385i	0.602352	+	1.85385i
$530$	2.33688	+	7.19218i	0.101508	+	0.312408i
$531$	2.56231	−	7.88597i	0.111195	−	0.342222i
$532$	−15.3262			−0.664477
$533$	7.85410	−	24.1724i	0.340199	−	1.04702i
$534$	−4.47214	+	3.24920i	−0.193528	+	0.140607i
$535$	−18.8435	+	13.6906i	−0.814674	+	0.591895i
$536$	16.7082	+	12.1392i	0.721684	+	0.524334i
$537$	7.66312	−	5.56758i	0.330688	−	0.240259i
$538$	8.61803	−	6.26137i	0.371550	−	0.269947i
$539$	−2.70820	−	1.96763i	−0.116651	−	0.0847516i
$540$	5.59017	+	17.2048i	0.240563	+	0.740376i
$541$	10.6180	−	7.71445i	0.456505	−	0.331670i	−0.335654	−	0.941985i	$-0.608957\pi$
$541$	10.6180	−	7.71445i	0.456505	−	0.331670i	0.792159	+	0.610315i	$0.208957\pi$
$542$	−1.52786	+	4.70228i	−0.0656274	+	0.201980i
$543$	13.7082			0.588275
$544$	−1.32624	+	4.08174i	−0.0568620	+	0.175003i
$545$	6.90983	−	21.2663i	0.295985	−	0.910947i
$546$	1.50000	+	4.61653i	0.0641941	+	0.197569i
$547$	−10.7254	−	33.0095i	−0.458586	−	1.41138i	−0.866873	−	0.498529i	$-0.833874\pi$
$547$	−10.7254	−	33.0095i	−0.458586	−	1.41138i	0.408287	−	0.912854i	$-0.366126\pi$
$548$	7.78115	+	5.65334i	0.332394	+	0.241499i
$549$	9.41641			0.401882
$550$	−2.36068			−0.100660
$551$	8.09017			0.344653
$552$	14.8992	+	10.8249i	0.634152	+	0.460738i
$553$	−1.54508	−	4.75528i	−0.0657037	−	0.202215i
$554$	−2.15654	−	6.63715i	−0.0916227	−	0.281986i
$555$	9.47214			0.402070
$556$	−2.50000	+	7.69421i	−0.106024	+	0.326307i
$557$	9.23607			0.391345			0.195672	−	0.980669i	$-0.437311\pi$
$557$	9.23607			0.391345			0.195672	+	0.980669i	$0.437311\pi$
$558$	1.14590	−	3.52671i	0.0485097	−	0.149298i
$559$	7.28115	−	5.29007i	0.307960	−	0.223746i
$560$	−2.07295	+	6.37988i	−0.0875981	+	0.269599i
$561$	−0.472136	−	0.343027i	−0.0199336	−	0.0144826i
$562$	0.545085	−	0.396027i	0.0229930	−	0.0167054i
$563$	−7.78115	+	5.65334i	−0.327936	+	0.238260i	−0.739555	−	0.673097i	$-0.764964\pi$
$563$	−7.78115	+	5.65334i	−0.327936	+	0.238260i	0.411618	+	0.911356i	$0.364964\pi$
$564$	−2.11803	−	1.53884i	−0.0891853	−	0.0647969i
$565$	7.01064	−	21.5765i	0.294940	−	0.907732i
$566$	11.5729	−	8.40824i	0.486447	−	0.353425i
$567$	−0.500000	+	1.53884i	−0.0209980	+	0.0646253i
$568$	9.79837			0.411131
$569$	9.10739	−	28.0297i	0.381802	−	1.17506i	−0.556972	−	0.830531i	$-0.688037\pi$
$569$	9.10739	−	28.0297i	0.381802	−	1.17506i	0.938774	−	0.344534i	$-0.111963\pi$
$570$	−8.09017			−0.338860
$571$	9.92705	+	30.5523i	0.415434	+	1.27857i	0.911862	+	0.410497i	$0.134645\pi$
$571$	9.92705	+	30.5523i	0.415434	+	1.27857i	−0.496428	+	0.868078i	$0.665355\pi$
$572$	−1.85410	−	5.70634i	−0.0775239	−	0.238594i
$573$	19.5623	+	14.2128i	0.817227	+	0.593750i
$574$	5.23607			0.218549
$575$	−33.3156	+	24.2052i	−1.38936	+	1.00943i
$576$	0.472136			0.0196723
$577$	−30.5623	−	22.2048i	−1.27233	−	0.924399i	−0.273033	−	0.962005i	$-0.588027\pi$
$577$	−30.5623	−	22.2048i	−1.27233	−	0.924399i	−0.999293	+	0.0376062i	$0.988027\pi$
$578$	−3.13525	−	9.64932i	−0.130409	−	0.401359i
$579$	−1.76393	−	5.42882i	−0.0733065	−	0.225614i
$580$	1.54508	−	4.75528i	0.0641562	−	0.197452i
$581$	0.881966	−	2.71441i	0.0365901	−	0.112613i
$582$	1.76393			0.0731173
$583$	−1.29180	+	3.97574i	−0.0535007	+	0.164658i
$584$	−16.2812	+	11.8290i	−0.673719	+	0.489485i
$585$	6.70820	+	20.6457i	0.277350	+	0.853596i
$586$	14.2361	+	10.3431i	0.588087	+	0.427270i
$587$	−15.1353	+	10.9964i	−0.624699	+	0.453870i	−0.854560	−	0.519353i	$-0.826173\pi$
$587$	−15.1353	+	10.9964i	−0.624699	+	0.453870i	0.229861	+	0.973224i	$0.426173\pi$
$588$	−5.73607	+	4.16750i	−0.236551	+	0.171865i
$589$	−14.2082	−	10.3229i	−0.585439	−	0.425346i
$590$	4.63525	−	3.36771i	0.190830	−	0.138646i
$591$	7.85410	−	5.70634i	0.323075	−	0.234727i
$592$	2.42705	−	7.46969i	0.0997512	−	0.307003i
$593$	−22.0902			−0.907135			−0.453567	−	0.891222i	$-0.649849\pi$
$593$	−22.0902			−0.907135			−0.453567	+	0.891222i	$0.649849\pi$
$594$	0.729490	−	2.24514i	0.0299313	−	0.0921192i
$595$	0.854102	+	2.62866i	0.0350148	+	0.107764i
$596$	−6.97214	−	21.4580i	−0.285590	−	0.878955i
$597$	0.791796	+	2.43690i	0.0324061	+	0.0997356i
$598$	19.9894	+	14.5231i	0.817426	+	0.593894i
$599$	−0.527864			−0.0215679			−0.0107840	−	0.999942i	$-0.503433\pi$
$599$	−0.527864			−0.0215679			−0.0107840	+	0.999942i	$0.503433\pi$
$600$	−3.45492	+	10.6331i	−0.141046	+	0.434096i
$601$	36.2705			1.47950			0.739752	−	0.672879i	$-0.234943\pi$
$601$	36.2705			1.47950			0.739752	+	0.672879i	$0.234943\pi$
$602$	1.50000	+	1.08981i	0.0611354	+	0.0444175i
$603$	−5.70820	−	17.5680i	−0.232456	−	0.715426i
$604$	2.78115	+	8.55951i	0.113164	+	0.348281i
$605$	18.8435	+	13.6906i	0.766096	+	0.556601i
$606$	−1.42705	+	4.39201i	−0.0579700	+	0.178413i
$607$	−15.4377			−0.626597			−0.313298	−	0.949655i	$-0.601434\pi$
$607$	−15.4377			−0.626597			−0.313298	+	0.949655i	$0.601434\pi$
$608$	−10.1631	+	31.2789i	−0.412169	+	1.26853i
$609$	−1.80902	+	1.31433i	−0.0733051	+	0.0532592i
$610$	5.26393	+	3.82447i	0.213130	+	0.154848i
$611$	−6.35410	−	4.61653i	−0.257059	−	0.186765i
$612$	2.00000	−	1.45309i	0.0808452	−	0.0587375i
$613$	−25.8713	+	18.7966i	−1.04493	+	0.759188i	−0.971242	−	0.238093i	$-0.923478\pi$
$613$	−25.8713	+	18.7966i	−1.04493	+	0.759188i	−0.0736905	+	0.997281i	$0.523478\pi$
$614$	−2.38197	−	1.73060i	−0.0961283	−	0.0698413i
$615$	−11.7082			−0.472120
$616$	2.23607	−	1.62460i	0.0900937	−	0.0654569i
$617$	3.01722	−	9.28605i	0.121469	−	0.373842i	−0.871772	−	0.489911i	$-0.837029\pi$
$617$	3.01722	−	9.28605i	0.121469	−	0.373842i	0.993241	+	0.116069i	$0.0370293\pi$
$618$	−7.14590			−0.287450
$619$	12.1976	−	37.5402i	0.490261	−	1.50887i	−0.333952	−	0.942590i	$-0.608382\pi$
$619$	12.1976	−	37.5402i	0.490261	−	1.50887i	0.824213	−	0.566279i	$-0.191618\pi$
$620$	−8.78115	+	6.37988i	−0.352660	+	0.256222i
$621$	−12.7254	−	39.1648i	−0.510654	−	1.57163i
$622$	−5.63525	−	17.3435i	−0.225953	−	0.695412i
$623$	11.7082	+	8.50651i	0.469079	+	0.340806i
$624$	−9.00000			−0.360288
$625$	−20.2254	−	14.6946i	−0.809017	−	0.587785i
$626$	−13.1246			−0.524565
$627$	−3.61803	−	2.62866i	−0.144490	−	0.104978i
$628$	4.59017	+	14.1271i	0.183168	+	0.563732i
$629$	−1.00000	−	3.07768i	−0.0398726	−	0.122715i
$630$	−3.61803	+	2.62866i	−0.144146	+	0.104728i
$631$	−1.78115	+	5.48183i	−0.0709066	+	0.218228i	−0.980230	−	0.197862i	$-0.936600\pi$
$631$	−1.78115	+	5.48183i	−0.0709066	+	0.218228i	0.909323	+	0.416090i	$0.136600\pi$
$632$	−6.90983			−0.274858
$633$	4.07295	−	12.5352i	0.161885	−	0.498231i
$634$	11.8262	−	8.59226i	0.469680	−	0.341242i
$635$	−35.5279			−1.40988
$636$	7.16312	+	5.20431i	0.284036	+	0.206364i
$637$	−17.2082	+	12.5025i	−0.681814	+	0.495367i
$638$	−0.527864	+	0.383516i	−0.0208983	+	0.0151835i
$639$	−7.09017	−	5.15131i	−0.280483	−	0.203783i
$640$	20.5902	+	14.9596i	0.813898	+	0.591331i
$641$	−8.16312	+	5.93085i	−0.322424	+	0.234255i	−0.737209	−	0.675665i	$-0.763857\pi$
$641$	−8.16312	+	5.93085i	−0.322424	+	0.234255i	0.414785	+	0.909919i	$0.363857\pi$
$642$	1.98936	−	6.12261i	0.0785137	−	0.241640i
$643$	22.8328			0.900438			0.450219	−	0.892918i	$-0.351346\pi$
$643$	22.8328			0.900438			0.450219	+	0.892918i	$0.351346\pi$
$644$	6.66312	−	20.5070i	0.262564	−	0.808088i
$645$	−3.35410	−	2.43690i	−0.132068	−	0.0959528i
$646$	0.854102	+	2.62866i	0.0336042	+	0.103423i
$647$	9.43769	+	29.0462i	0.371034	+	1.14193i	0.946116	+	0.323829i	$0.104970\pi$
$647$	9.43769	+	29.0462i	0.371034	+	1.14193i	−0.575082	+	0.818096i	$0.695030\pi$
$648$	1.80902	+	1.31433i	0.0710649	+	0.0516317i
$649$	3.16718			0.124323
$650$	−4.63525	+	14.2658i	−0.181810	+	0.559553i
$651$	4.85410			0.190247
$652$	14.3992	+	10.4616i	0.563916	+	0.409709i
$653$	2.44427	+	7.52270i	0.0956518	+	0.294386i	0.987423	−	0.158101i	$-0.0505371\pi$
$653$	2.44427	+	7.52270i	0.0956518	+	0.294386i	−0.891771	+	0.452487i	$0.850537\pi$
$654$	1.90983	+	5.87785i	0.0746803	+	0.229842i
$655$	−12.2984	−	37.8505i	−0.480537	−	1.47894i
$656$	−3.00000	+	9.23305i	−0.117130	+	0.360490i
$657$	18.0000			0.702247
$658$	0.500000	−	1.53884i	0.0194920	−	0.0599903i
$659$	−19.7984	+	14.3844i	−0.771235	+	0.560335i	−0.902336	−	0.431034i	$-0.858149\pi$
$659$	−19.7984	+	14.3844i	−0.771235	+	0.560335i	0.131101	+	0.991369i	$0.458149\pi$
$660$	−2.23607	+	1.62460i	−0.0870388	+	0.0632374i
$661$	32.9164	+	23.9152i	1.28030	+	0.930192i	0.999562	−	0.0295922i	$-0.00942086\pi$
$661$	32.9164	+	23.9152i	1.28030	+	0.930192i	0.280738	+	0.959784i	$0.409421\pi$
$662$	−8.56231	+	6.22088i	−0.332783	+	0.241781i
$663$	−3.00000	+	2.17963i	−0.116510	+	0.0846497i
$664$	−3.19098	−	2.31838i	−0.123834	−	0.0899708i
$665$	6.54508	+	20.1437i	0.253808	+	0.781139i
$666$	4.23607	−	3.07768i	0.164144	−	0.119258i
$667$	−3.51722	+	10.8249i	−0.136187	+	0.419142i
$668$	9.00000			0.348220
$669$	6.85410	−	21.0948i	0.264995	−	0.815570i
$670$	3.94427	−	12.1392i	0.152381	−	0.468979i
$671$	1.11146	+	3.42071i	0.0429073	+	0.132055i
$672$	−2.80902	−	8.64527i	−0.108360	−	0.333498i
$673$	8.23607	+	5.98385i	0.317477	+	0.230661i	0.735098	−	0.677961i	$-0.237136\pi$
$673$	8.23607	+	5.98385i	0.317477	+	0.230661i	−0.417621	+	0.908621i	$0.637136\pi$
$674$	0.708204			0.0272790
$675$	20.2254	−	14.6946i	0.778477	−	0.565597i
$676$	−17.0902			−0.657314
$677$	−6.78115	−	4.92680i	−0.260621	−	0.189352i	0.449800	−	0.893129i	$-0.351495\pi$
$677$	−6.78115	−	4.92680i	−0.260621	−	0.189352i	−0.710421	+	0.703777i	$0.751495\pi$
$678$	1.93769	+	5.96361i	0.0744167	+	0.229031i
$679$	−1.42705	−	4.39201i	−0.0547652	−	0.168550i
$680$	3.81966			0.146477
$681$	5.94427	−	18.2946i	0.227785	−	0.701050i
$682$	1.41641			0.0542371
$683$	−1.39919	+	4.30625i	−0.0535384	+	0.164774i	−0.974251	−	0.225468i	$-0.927609\pi$
$683$	−1.39919	+	4.30625i	−0.0535384	+	0.164774i	0.920712	+	0.390242i	$0.127609\pi$
$684$	15.3262	−	11.1352i	0.586013	−	0.425764i
$685$	4.10739	−	12.6412i	0.156935	−	0.482997i
$686$	−9.20820	−	6.69015i	−0.351571	−	0.255431i
$687$	−6.70820	+	4.87380i	−0.255934	+	0.185947i
$688$	−2.78115	+	2.02063i	−0.106030	+	0.0770356i
$689$	21.4894	+	15.6129i	0.818679	+	0.594805i
$690$	3.51722	−	10.8249i	0.133898	−	0.412097i
$691$	−2.20820	+	1.60435i	−0.0840040	+	0.0610325i	−0.628995	−	0.777410i	$-0.716533\pi$
$691$	−2.20820	+	1.60435i	−0.0840040	+	0.0610325i	0.544991	+	0.838442i	$0.316533\pi$
$692$	8.44427	−	25.9888i	0.321003	−	0.987946i
$693$	−2.47214			−0.0939087
$694$	−5.93769	+	18.2743i	−0.225392	+	0.693685i
$695$	11.1803			0.424094
$696$	0.954915	+	2.93893i	0.0361960	+	0.111400i
$697$	1.23607	+	3.80423i	0.0468194	+	0.144095i
$698$	−4.14590	−	3.01217i	−0.156925	−	0.114012i
$699$	14.9443			0.565244
$700$	13.0902			0.494762
$701$	35.0132			1.32243			0.661214	−	0.750197i	$-0.270041\pi$
$701$	35.0132			1.32243			0.661214	+	0.750197i	$0.270041\pi$
$702$	−12.1353	−	8.81678i	−0.458016	−	0.332768i
$703$	−7.66312	−	23.5847i	−0.289020	−	0.889512i
$704$	0.0557281	+	0.171513i	0.00210033	+	0.00646416i
$705$	−1.11803	+	3.44095i	−0.0421076	+	0.129594i
$706$	4.60081	−	14.1598i	0.173154	−	0.532913i
$707$	12.0902			0.454698
$708$	2.07295	−	6.37988i	0.0779062	−	0.239771i
$709$	−27.1353	+	19.7149i	−1.01909	+	0.740409i	−0.966095	−	0.258186i	$-0.916875\pi$
$709$	−27.1353	+	19.7149i	−1.01909	+	0.740409i	−0.0529906	+	0.998595i	$0.516875\pi$
$710$	−1.87132	−	5.75934i	−0.0702295	−	0.216144i
$711$	5.00000	+	3.63271i	0.187515	+	0.136237i
$712$	16.1803	−	11.7557i	0.606384	−	0.440564i
$713$	19.9894	−	14.5231i	0.748607	−	0.543895i
$714$	−0.618034	−	0.449028i	−0.0231293	−	0.0168044i
$715$	−6.70820	+	4.87380i	−0.250873	+	0.182270i
$716$	−12.3992	+	9.00854i	−0.463379	+	0.336665i
$717$	−9.10739	+	28.0297i	−0.340122	+	1.04679i
$718$	−17.7639			−0.662944
$719$	−11.3435	+	34.9116i	−0.423040	+	1.30198i	0.481819	+	0.876271i	$0.339976\pi$
$719$	−11.3435	+	34.9116i	−0.423040	+	1.30198i	−0.904859	+	0.425712i	$0.860024\pi$
$720$	−2.56231	−	7.88597i	−0.0954915	−	0.293893i
$721$	5.78115	+	17.7926i	0.215301	+	0.662630i
$722$	2.91641	+	8.97578i	0.108537	+	0.334044i
$723$	−9.28115	−	6.74315i	−0.345170	−	0.250781i
$724$	−22.1803			−0.824326
$725$	−6.90983			−0.256625
$726$	−6.43769			−0.238925
$727$	−3.59017	−	2.60841i	−0.133152	−	0.0967406i	0.519216	−	0.854643i	$-0.326224\pi$
$727$	−3.59017	−	2.60841i	−0.133152	−	0.0967406i	−0.652368	+	0.757903i	$0.726224\pi$
$728$	−5.42705	−	16.7027i	−0.201140	−	0.619045i
$729$	4.01722	+	12.3637i	0.148786	+	0.457916i
$730$	10.0623	+	7.31069i	0.372423	+	0.270581i
$731$	−0.437694	+	1.34708i	−0.0161887	+	0.0498237i
$732$	7.61803			0.281571
$733$	8.33688	−	25.6583i	0.307930	−	0.947710i	−0.670638	−	0.741785i	$-0.733980\pi$
$733$	8.33688	−	25.6583i	0.307930	−	0.947710i	0.978568	−	0.205925i	$-0.0660204\pi$
$734$	2.71885	−	1.97536i	0.100354	−	0.0729118i
$735$	7.92705	+	5.75934i	0.292394	+	0.212436i
$736$	−37.4336	−	27.1971i	−1.37982	−	1.00250i
$737$	5.70820	−	4.14725i	0.210264	−	0.152766i
$738$	−5.23607	+	3.80423i	−0.192742	+	0.140035i
$739$	25.0623	+	18.2088i	0.921932	+	0.669823i	0.944004	−	0.329934i	$-0.107026\pi$
$739$	25.0623	+	18.2088i	0.921932	+	0.669823i	−0.0220723	+	0.999756i	$0.507026\pi$
$740$	−15.3262			−0.563404
$741$	−22.9894	+	16.7027i	−0.844535	+	0.613591i
$742$	−1.69098	+	5.20431i	−0.0620779	+	0.191056i
$743$	−16.3607			−0.600215			−0.300108	−	0.953905i	$-0.597023\pi$
$743$	−16.3607			−0.600215			−0.300108	+	0.953905i	$0.597023\pi$
$744$	2.07295	−	6.37988i	0.0759980	−	0.233898i
$745$	−25.2254	+	18.3273i	−0.924188	+	0.671462i
$746$	1.00658	+	3.09793i	0.0368534	+	0.113423i
$747$	1.09017	+	3.35520i	0.0398872	+	0.122760i
$748$	0.763932	+	0.555029i	0.0279321	+	0.0202939i
$749$	−16.8541			−0.615835
$750$	6.90983			0.252311
$751$	−40.8885			−1.49204			−0.746022	−	0.665921i	$-0.768039\pi$
$751$	−40.8885			−1.49204			−0.746022	+	0.665921i	$0.768039\pi$
$752$	2.42705	+	1.76336i	0.0885054	+	0.0643030i
$753$	−2.10739	−	6.48588i	−0.0767976	−	0.236359i
$754$	1.28115	+	3.94298i	0.0466568	+	0.143595i
$755$	10.0623	−	7.31069i	0.366205	−	0.266063i
$756$	−4.04508	+	12.4495i	−0.147118	+	0.452784i
$757$	3.58359			0.130248			0.0651239	−	0.997877i	$-0.479256\pi$
$757$	3.58359			0.130248			0.0651239	+	0.997877i	$0.479256\pi$
$758$	−6.60739	+	20.3355i	−0.239991	+	0.738617i
$759$	5.09017	−	3.69822i	0.184761	−	0.134237i
$760$	29.2705			1.06175
$761$	−30.2984	−	22.0131i	−1.09832	−	0.797973i	−0.117531	−	0.993069i	$-0.537498\pi$
$761$	−30.2984	−	22.0131i	−1.09832	−	0.797973i	−0.980784	+	0.195096i	$0.937498\pi$
$762$	7.94427	−	5.77185i	0.287791	−	0.209092i
$763$	13.0902	−	9.51057i	0.473896	−	0.344306i
$764$	−31.6525	−	22.9969i	−1.14515	−	0.831998i
$765$	−2.76393	−	2.00811i	−0.0999302	−	0.0726035i
$766$	5.68034	−	4.12701i	0.205239	−	0.149115i
$767$	6.21885	−	19.1396i	0.224550	−	0.691092i
$768$	−6.56231			−0.236797
$769$	−4.14590	+	12.7598i	−0.149505	+	0.460129i	−0.997563	−	0.0697749i	$-0.977772\pi$
$769$	−4.14590	+	12.7598i	−0.149505	+	0.460129i	0.848058	+	0.529904i	$0.177772\pi$
$770$	−1.38197	−	1.00406i	−0.0498026	−	0.0361837i
$771$	4.98936	+	15.3557i	0.179687	+	0.553021i
$772$	2.85410	+	8.78402i	0.102721	+	0.316144i
$773$	−26.8262	−	19.4904i	−0.964873	−	0.701021i	−0.0105954	−	0.999944i	$-0.503373\pi$
$773$	−26.8262	−	19.4904i	−0.964873	−	0.701021i	−0.954277	+	0.298923i	$0.903373\pi$
$774$	−2.29180			−0.0823769
$775$	12.1353	+	8.81678i	0.435911	+	0.316708i
$776$	−6.38197			−0.229099
$777$	5.54508	+	4.02874i	0.198929	+	0.144530i
$778$	2.86475	+	8.81678i	0.102706	+	0.316097i
$779$	9.47214	+	29.1522i	0.339374	+	1.04449i
$780$	5.42705	+	16.7027i	0.194320	+	0.598054i
$781$	1.03444	−	3.18368i	0.0370152	−	0.113921i
$782$	−3.88854			−0.139054
$783$	2.13525	−	6.57164i	0.0763078	−	0.234851i
$784$	6.57295	−	4.77553i	0.234748	−	0.170555i
$785$	16.6074	−	12.0660i	0.592743	−	0.430653i
$786$	8.89919	+	6.46564i	0.317423	+	0.230622i
$787$	27.6525	−	20.0907i	0.985704	−	0.716156i	0.0267281	−	0.999643i	$-0.491491\pi$
$787$	27.6525	−	20.0907i	0.985704	−	0.716156i	0.958976	+	0.283487i	$0.0914912\pi$
$788$	−12.7082	+	9.23305i	−0.452711	+	0.328914i
$789$	17.8713	+	12.9843i	0.636236	+	0.462252i
$790$	1.31966	+	4.06150i	0.0469514	+	0.144502i
$791$	13.2812	−	9.64932i	0.472223	−	0.343090i
$792$	−1.05573	+	3.24920i	−0.0375137	+	0.115455i
$793$	22.8541			0.811573
$794$	−0.00657781	+	0.0202444i	−0.000233438	+	0.000718447i
$795$	3.78115	−	11.6372i	0.134104	−	0.412729i
$796$	−1.28115	−	3.94298i	−0.0454093	−	0.139755i
$797$	4.39919	+	13.5393i	0.155827	+	0.479587i	0.998244	−	0.0592400i	$-0.0188677\pi$
$797$	4.39919	+	13.5393i	0.155827	+	0.479587i	−0.842417	+	0.538827i	$0.818868\pi$
$798$	−4.73607	−	3.44095i	−0.167655	−	0.121808i
$799$	1.23607			0.0437289
$800$	8.68034	−	26.7153i	0.306896	−	0.944530i
$801$	−17.8885			−0.632061
$802$	11.2984	+	8.20875i	0.398959	+	0.289861i
$803$	2.12461	+	6.53888i	0.0749759	+	0.230752i
$804$	−4.61803	−	14.2128i	−0.162866	−	0.501248i
$805$	−29.7984			−1.05025
$806$	2.78115	−	8.55951i	0.0979619	−	0.301496i
$807$	−17.2361			−0.606738
$808$	5.16312	−	15.8904i	0.181638	−	0.559024i
$809$	12.9271	−	9.39205i	0.454491	−	0.330207i	−0.336875	−	0.941549i	$-0.609370\pi$
$809$	12.9271	−	9.39205i	0.454491	−	0.330207i	0.791366	+	0.611342i	$0.209370\pi$
$810$	0.427051	−	1.31433i	0.0150050	−	0.0461808i
$811$	1.04508	+	0.759299i	0.0366979	+	0.0266626i	0.605983	−	0.795478i	$-0.292780\pi$
$811$	1.04508	+	0.759299i	0.0366979	+	0.0266626i	−0.569285	+	0.822140i	$0.692780\pi$
$812$	2.92705	−	2.12663i	0.102719	−	0.0746300i
$813$	6.47214	−	4.70228i	0.226988	−	0.164916i
$814$	1.61803	+	1.17557i	0.0567121	+	0.0412037i
$815$	7.60081	−	23.3929i	0.266245	−	0.819417i
$816$	1.14590	−	0.832544i	0.0401145	−	0.0291449i
$817$	−3.35410	+	10.3229i	−0.117345	+	0.361151i
$818$	17.5623			0.614052
$819$	−4.85410	+	14.9394i	−0.169616	+	0.522025i
$820$	18.9443			0.661563
$821$	6.08359	+	18.7234i	0.212319	+	0.653450i	0.999333	+	0.0365154i	$0.0116258\pi$
$821$	6.08359	+	18.7234i	0.212319	+	0.653450i	−0.787014	+	0.616935i	$0.788374\pi$
$822$	1.13525	+	3.49396i	0.0395966	+	0.121866i
$823$	−27.7426	−	20.1562i	−0.967048	−	0.702601i	−0.0122710	−	0.999925i	$-0.503906\pi$
$823$	−27.7426	−	20.1562i	−0.967048	−	0.702601i	−0.954777	+	0.297323i	$0.903906\pi$
$824$	25.8541			0.900670
$825$	3.09017	+	2.24514i	0.107586	+	0.0781657i
$826$	4.14590			0.144254
$827$	24.2984	+	17.6538i	0.844937	+	0.613883i	0.923745	−	0.383007i	$-0.125111\pi$
$827$	24.2984	+	17.6538i	0.844937	+	0.613883i	−0.0788082	+	0.996890i	$0.525111\pi$
$828$	8.23607	+	25.3480i	0.286223	+	0.880904i
$829$	−9.00658	−	27.7194i	−0.312811	−	0.962734i	−0.976646	−	0.214855i	$-0.931072\pi$
$829$	−9.00658	−	27.7194i	−0.312811	−	0.962734i	0.663835	−	0.747879i	$-0.268928\pi$
$830$	−0.753289	+	2.31838i	−0.0261470	+	0.0804723i
$831$	−3.48936	+	10.7391i	−0.121044	+	0.372537i
$832$	1.14590			0.0397269
$833$	1.03444	−	3.18368i	0.0358413	−	0.110308i
$834$	−2.50000	+	1.81636i	−0.0865679	+	0.0628953i
$835$	−3.84346	−	11.8290i	−0.133008	−	0.409358i
$836$	5.85410	+	4.25325i	0.202468	+	0.147102i
$837$	−12.1353	+	8.81678i	−0.419456	+	0.304752i
$838$	0.263932	−	0.191758i	0.00911738	−	0.00662416i
$839$	−3.35410	−	2.43690i	−0.115796	−	0.0841311i	0.528380	−	0.849008i	$-0.322800\pi$
$839$	−3.35410	−	2.43690i	−0.115796	−	0.0841311i	−0.644176	+	0.764877i	$0.722800\pi$
$840$	−6.54508	+	4.75528i	−0.225827	+	0.164073i
$841$	21.9164	−	15.9232i	0.755738	−	0.549076i
$842$	6.11146	−	18.8091i	0.210615	−	0.648205i
$843$	−1.09017			−0.0375474
$844$	−6.59017	+	20.2825i	−0.226843	+	0.698151i
$845$	7.29837	+	22.4621i	0.251072	+	0.772719i
$846$	0.618034	+	1.90211i	0.0212484	+	0.0653960i
$847$	5.20820	+	16.0292i	0.178956	+	0.550770i
$848$	−8.20820	−	5.96361i	−0.281871	−	0.204791i
$849$	−23.1459			−0.794365
$850$	−0.729490	−	2.24514i	−0.0250213	−	0.0770077i
$851$	34.8885			1.19596
$852$	−5.73607	−	4.16750i	−0.196514	−	0.142776i
$853$	14.6180	+	44.9897i	0.500512	+	1.54042i	0.808187	+	0.588926i	$0.200449\pi$
$853$	14.6180	+	44.9897i	0.500512	+	1.54042i	−0.307675	+	0.951491i	$0.599551\pi$
$854$	1.45492	+	4.47777i	0.0497862	+	0.153226i
$855$	−21.1803	−	15.3884i	−0.724352	−	0.526273i
$856$	−7.19756	+	22.1518i	−0.246008	+	0.757133i
$857$	−40.6869			−1.38984			−0.694919	−	0.719088i	$-0.744560\pi$
$857$	−40.6869			−1.38984			−0.694919	+	0.719088i	$0.744560\pi$
$858$	0.708204	−	2.17963i	0.0241777	−	0.0744113i
$859$	22.9894	−	16.7027i	0.784387	−	0.569890i	−0.121906	−	0.992542i	$-0.538901\pi$
$859$	22.9894	−	16.7027i	0.784387	−	0.569890i	0.906292	+	0.422651i	$0.138901\pi$
$860$	5.42705	+	3.94298i	0.185061	+	0.134455i
$861$	−6.85410	−	4.97980i	−0.233587	−	0.169711i
$862$	−11.9164	+	8.65778i	−0.405874	+	0.294885i
$863$	33.6246	−	24.4297i	1.14460	−	0.831597i	0.156842	−	0.987624i	$-0.449869\pi$
$863$	33.6246	−	24.4297i	1.14460	−	0.831597i	0.987753	+	0.156027i	$0.0498686\pi$
$864$	22.7254	+	16.5110i	0.773135	+	0.561715i
$865$	−37.7639			−1.28401
$866$	−10.0729	+	7.31843i	−0.342293	+	0.248690i
$867$	−5.07295	+	15.6129i	−0.172286	+	0.530243i
$868$	−7.85410			−0.266586
$869$	−0.729490	+	2.24514i	−0.0247463	+	0.0761612i
$870$	1.54508	−	1.12257i	0.0523833	−	0.0380587i
$871$	−13.8541	−	42.6385i	−0.469428	−	1.44475i
$872$	−6.90983	−	21.2663i	−0.233996	−	0.720167i
$873$	4.61803	+	3.35520i	0.156297	+	0.113556i
$874$	−29.7984			−1.00795
$875$	−5.59017	−	17.2048i	−0.188982	−	0.581628i
$876$	14.5623			0.492015
$877$	−24.7082	−	17.9516i	−0.834337	−	0.606181i	0.0864462	−	0.996257i	$-0.472449\pi$
$877$	−24.7082	−	17.9516i	−0.834337	−	0.606181i	−0.920783	+	0.390075i	$0.872449\pi$
$878$	1.14183	+	3.51420i	0.0385350	+	0.118598i
$879$	−8.79837	−	27.0786i	−0.296762	−	0.913339i
$880$	2.56231	−	1.86162i	0.0863753	−	0.0627553i
$881$	1.34752	−	4.14725i	0.0453992	−	0.139725i	−0.925787	−	0.378044i	$-0.876597\pi$
$881$	1.34752	−	4.14725i	0.0453992	−	0.139725i	0.971187	+	0.238320i	$0.0765967\pi$
$882$	5.41641			0.182380
$883$	−14.6525	+	45.0957i	−0.493095	+	1.51759i	0.326809	+	0.945090i	$0.394026\pi$
$883$	−14.6525	+	45.0957i	−0.493095	+	1.51759i	−0.819904	+	0.572500i	$0.805974\pi$
$884$	4.85410	−	3.52671i	0.163261	−	0.118616i
$885$	−9.27051			−0.311625
$886$	−6.02786	−	4.37950i	−0.202510	−	0.147132i
$887$	4.76393	−	3.46120i	0.159957	−	0.116216i	−0.504927	−	0.863162i	$-0.668481\pi$
$887$	4.76393	−	3.46120i	0.159957	−	0.116216i	0.664885	+	0.746946i	$0.268481\pi$
$888$	7.66312	−	5.56758i	0.257157	−	0.186836i
$889$	−20.7984	−	15.1109i	−0.697555	−	0.506803i
$890$	−10.0000	−	7.26543i	−0.335201	−	0.243538i
$891$	0.618034	−	0.449028i	0.0207049	−	0.0150430i
$892$	−11.0902	+	34.1320i	−0.371326	+	1.14283i
$893$	9.47214			0.316973
$894$	2.66312	−	8.19624i	0.0890680	−	0.274123i
$895$	17.1353	+	12.4495i	0.572768	+	0.416141i
$896$	5.69098	+	17.5150i	0.190122	+	0.585137i
$897$	−12.3541	−	38.0220i	−0.412491	−	1.26952i
$898$	−10.1631	−	7.38394i	−0.339148	−	0.246405i
$899$	4.14590			0.138273
$900$	−13.0902	+	9.51057i	−0.436339	+	0.317019i
$901$	−4.18034			−0.139267
$902$	−2.00000	−	1.45309i	−0.0665927	−	0.0483824i
$903$	−0.927051	−	2.85317i	−0.0308503	−	0.0949475i
$904$	−7.01064	−	21.5765i	−0.233171	−	0.717625i
$905$	9.47214	+	29.1522i	0.314864	+	0.969053i
$906$	−1.06231	+	3.26944i	−0.0352927	+	0.108620i
$907$	47.2492			1.56888			0.784442	−	0.620202i	$-0.212949\pi$
$907$	47.2492			1.56888			0.784442	+	0.620202i	$0.212949\pi$
$908$	−9.61803	+	29.6013i	−0.319186	+	0.982352i
$909$	−12.0902	+	8.78402i	−0.401006	+	0.291348i
$910$	−8.78115	+	6.37988i	−0.291092	+	0.211491i
$911$	28.9336	+	21.0215i	0.958614	+	0.696474i	0.952828	−	0.303510i	$-0.0981584\pi$
$911$	28.9336	+	21.0215i	0.958614	+	0.696474i	0.00578548	+	0.999983i	$0.498158\pi$
$912$	8.78115	−	6.37988i	0.290773	−	0.211259i
$913$	−1.09017	+	0.792055i	−0.0360794	+	0.0262132i
$914$	−2.70820	−	1.96763i	−0.0895794	−	0.0650833i
$915$	−3.25329	−	10.0126i	−0.107550	−	0.331006i
$916$	10.8541	−	7.88597i	0.358630	−	0.260560i
$917$	8.89919	−	27.3889i	0.293877	−	0.904461i
$918$	2.36068			0.0779140
$919$	−0.551663	+	1.69784i	−0.0181977	+	0.0560067i	−0.959743	−	0.280880i	$-0.909374\pi$
$919$	−0.551663	+	1.69784i	−0.0181977	+	0.0560067i	0.941545	+	0.336886i	$0.109374\pi$
$920$	−12.7254	+	39.1648i	−0.419545	+	1.29123i
$921$	1.47214	+	4.53077i	0.0485085	+	0.149294i
$922$	4.42705	+	13.6251i	0.145797	+	0.448718i
$923$	−17.2082	−	12.5025i	−0.566415	−	0.411525i
$924$	−2.00000			−0.0657952
$925$	6.54508	+	20.1437i	0.215201	+	0.662321i
$926$	9.96556			0.327489
$927$	−18.7082	−	13.5923i	−0.614458	−	0.446430i
$928$	−2.39919	−	7.38394i	−0.0787572	−	0.242390i
$929$	−11.3197	−	34.8383i	−0.371386	−	1.14301i	−0.945885	−	0.324503i	$-0.894803\pi$
$929$	−11.3197	−	34.8383i	−0.371386	−	1.14301i	0.574499	−	0.818506i	$-0.305197\pi$
$930$	−4.14590			−0.135949
$931$	7.92705	−	24.3970i	0.259799	−	0.799578i
$932$	−24.1803			−0.792053
$933$	−9.11803	+	28.0624i	−0.298511	+	0.918722i
$934$	14.2254	−	10.3354i	0.465470	−	0.338184i
$935$	0.403252	−	1.24108i	0.0131878	−	0.0405877i
$936$	17.5623	+	12.7598i	0.574042	+	0.417066i
$937$	−41.4787	+	30.1360i	−1.35505	+	0.984502i	−0.356308	+	0.934369i	$0.615965\pi$
$937$	−41.4787	+	30.1360i	−1.35505	+	0.984502i	−0.998743	+	0.0501333i	$0.984035\pi$
$938$	7.47214	−	5.42882i	0.243974	−	0.177257i
$939$	17.1803	+	12.4822i	0.560659	+	0.407343i
$940$	1.80902	−	5.56758i	0.0590036	−	0.181594i
$941$	15.8435	−	11.5109i	0.516482	−	0.375246i	−0.298795	−	0.954317i	$-0.596585\pi$
$941$	15.8435	−	11.5109i	0.516482	−	0.375246i	0.815277	+	0.579071i	$0.196585\pi$
$942$	−1.75329	+	5.39607i	−0.0571252	+	0.175813i
$943$	−43.1246			−1.40433
$944$	−2.37539	+	7.31069i	−0.0773123	+	0.237943i
$945$	18.0902			0.588473
$946$	−0.270510	−	0.832544i	−0.00879503	−	0.0270683i
$947$	−8.85410	−	27.2501i	−0.287720	−	0.885510i	−0.985570	−	0.169267i	$-0.945860\pi$
$947$	−8.85410	−	27.2501i	−0.287720	−	0.885510i	0.697851	−	0.716243i	$-0.254140\pi$
$948$	4.04508	+	2.93893i	0.131378	+	0.0954519i
$949$	43.6869			1.41814
$950$	−5.59017	−	17.2048i	−0.181369	−	0.558197i
$951$	−23.6525			−0.766984
$952$	2.23607	+	1.62460i	0.0724714	+	0.0526535i
$953$	10.7361	+	33.0422i	0.347775	+	1.07034i	0.960081	+	0.279721i	$0.0902421\pi$
$953$	10.7361	+	33.0422i	0.347775	+	1.07034i	−0.612306	+	0.790621i	$0.709758\pi$
$954$	−2.09017	−	6.43288i	−0.0676718	−	0.208272i
$955$	−16.7082	+	51.4226i	−0.540665	+	1.66400i
$956$	14.7361	−	45.3530i	0.476598	−	1.46682i
$957$	1.05573			0.0341268
$958$	−0.791796	+	2.43690i	−0.0255818	+	0.0787326i
$959$	7.78115	−	5.65334i	0.251267	−	0.182556i
$960$	−0.163119	−	0.502029i	−0.00526464	−	0.0162029i
$961$	17.7984	+	12.9313i	0.574141	+	0.417138i
$962$	10.2812	−	7.46969i	0.331478	−	0.240833i
$963$	16.8541	−	12.2452i	0.543116	−	0.394597i
$964$	15.0172	+	10.9106i	0.483672	+	0.351408i
$965$	10.3262	−	7.50245i	0.332413	−	0.241512i
$966$	6.66312	−	4.84104i	0.214382	−	0.155758i
$967$	12.3262	−	37.9363i	0.396385	−	1.21995i	−0.531493	−	0.847063i	$-0.678369\pi$
$967$	12.3262	−	37.9363i	0.396385	−	1.21995i	0.927878	−	0.372885i	$-0.121631\pi$
$968$	23.2918			0.748627
$969$	1.38197	−	4.25325i	0.0443951	−	0.136634i
$970$	1.21885	+	3.75123i	0.0391348	+	0.120445i
$971$	1.04508	+	3.21644i	0.0335384	+	0.103220i	0.966424	−	0.256951i	$-0.0827180\pi$
$971$	1.04508	+	3.21644i	0.0335384	+	0.103220i	−0.932886	+	0.360172i	$0.882718\pi$
$972$	−8.00000	−	24.6215i	−0.256600	−	0.789734i
$973$	6.54508	+	4.75528i	0.209826	+	0.152447i
$974$	−5.92299			−0.189785
$975$	19.6353	−	14.2658i	0.628831	−	0.456873i
$976$	−8.72949			−0.279424
$977$	27.2254	+	19.7804i	0.871019	+	0.632832i	0.930860	−	0.365376i	$-0.119060\pi$
$977$	27.2254	+	19.7804i	0.871019	+	0.632832i	−0.0598416	+	0.998208i	$0.519060\pi$
$978$	2.10081	+	6.46564i	0.0671766	+	0.206748i
$979$	−2.11146	−	6.49839i	−0.0674824	−	0.207690i
$980$	−12.8262	−	9.31881i	−0.409719	−	0.297678i
$981$	−6.18034	+	19.0211i	−0.197323	+	0.607298i
$982$	23.0213			0.734639
$983$	2.28115	−	7.02067i	0.0727575	−	0.223924i	−0.908064	−	0.418830i	$-0.862440\pi$
$983$	2.28115	−	7.02067i	0.0727575	−	0.223924i	0.980822	+	0.194906i	$0.0624402\pi$
$984$	−9.47214	+	6.88191i	−0.301961	+	0.219387i
$985$	17.5623	+	12.7598i	0.559582	+	0.406560i
$986$	−0.527864	−	0.383516i	−0.0168106	−	0.0122136i
$987$	−2.11803	+	1.53884i	−0.0674178	+	0.0489819i
$988$	37.1976	−	27.0256i	1.18341	−	0.859799i
$989$	−12.3541	−	8.97578i	−0.392838	−	0.285413i
$990$	2.11146			0.0671065
$991$	−23.7533	+	17.2578i	−0.754548	+	0.548211i	−0.897233	−	0.441557i	$-0.854426\pi$
$991$	−23.7533	+	17.2578i	−0.754548	+	0.548211i	0.142685	+	0.989768i	$0.454426\pi$
$992$	−5.20820	+	16.0292i	−0.165361	+	0.508928i
$993$	17.1246			0.543433
$994$	1.35410	−	4.16750i	0.0429495	−	0.132185i
$995$	−4.63525	+	3.36771i	−0.146947	+	0.106764i
$996$	0.881966	+	2.71441i	0.0279462	+	0.0860094i
$997$	−3.36475	−	10.3556i	−0.106563	−	0.327966i	0.883531	−	0.468372i	$-0.155159\pi$
$997$	−3.36475	−	10.3556i	−0.106563	−	0.327966i	−0.990094	+	0.140406i	$0.955159\pi$
$998$	6.28115	+	4.56352i	0.198826	+	0.144456i
$999$	−21.1803			−0.670116

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.2.d.a.16.1	yes	4
3.2	odd	2		225.2.h.b.91.1		4
4.3	odd	2		400.2.u.b.241.1		4
5.2	odd	4		125.2.e.a.49.2		8
5.3	odd	4		125.2.e.a.49.1		8
5.4	even	2		125.2.d.a.76.1		4
25.2	odd	20		125.2.e.a.74.1		8
25.3	odd	20		625.2.e.c.499.2		8
25.4	even	10		625.2.d.b.126.1		4
25.6	even	5		625.2.a.b.1.2		2
25.8	odd	20		625.2.b.a.624.2		4
25.9	even	10		625.2.d.b.501.1		4
25.11	even	5	inner	25.2.d.a.11.1	✓	4
25.12	odd	20		625.2.e.c.124.2		8
25.13	odd	20		625.2.e.c.124.1		8
25.14	even	10		125.2.d.a.51.1		4
25.16	even	5		625.2.d.h.501.1		4
25.17	odd	20		625.2.b.a.624.3		4
25.19	even	10		625.2.a.c.1.1		2
25.21	even	5		625.2.d.h.126.1		4
25.22	odd	20		625.2.e.c.499.1		8
25.23	odd	20		125.2.e.a.74.2		8
75.11	odd	10		225.2.h.b.136.1		4
75.44	odd	10		5625.2.a.d.1.2		2
75.56	odd	10		5625.2.a.f.1.1		2
100.11	odd	10		400.2.u.b.161.1		4
100.19	odd	10		10000.2.a.l.1.1		2
100.31	odd	10		10000.2.a.c.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.d.a.11.1	✓	4	25.11	even	5	inner
25.2.d.a.16.1	yes	4	1.1	even	1	trivial
125.2.d.a.51.1		4	25.14	even	10
125.2.d.a.76.1		4	5.4	even	2
125.2.e.a.49.1		8	5.3	odd	4
125.2.e.a.49.2		8	5.2	odd	4
125.2.e.a.74.1		8	25.2	odd	20
125.2.e.a.74.2		8	25.23	odd	20
225.2.h.b.91.1		4	3.2	odd	2
225.2.h.b.136.1		4	75.11	odd	10
400.2.u.b.161.1		4	100.11	odd	10
400.2.u.b.241.1		4	4.3	odd	2
625.2.a.b.1.2		2	25.6	even	5
625.2.a.c.1.1		2	25.19	even	10
625.2.b.a.624.2		4	25.8	odd	20
625.2.b.a.624.3		4	25.17	odd	20
625.2.d.b.126.1		4	25.4	even	10
625.2.d.b.501.1		4	25.9	even	10
625.2.d.h.126.1		4	25.21	even	5
625.2.d.h.501.1		4	25.16	even	5
625.2.e.c.124.1		8	25.13	odd	20
625.2.e.c.124.2		8	25.12	odd	20
625.2.e.c.499.1		8	25.22	odd	20
625.2.e.c.499.2		8	25.3	odd	20
5625.2.a.d.1.2		2	75.44	odd	10
5625.2.a.f.1.1		2	75.56	odd	10
10000.2.a.c.1.2		2	100.31	odd	10
10000.2.a.l.1.1		2	100.19	odd	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	25.d (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.363271i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 - 0.587785i) q^{6} -1.61803 q^{7} +(-0.690983 + 2.12663i) q^{8} +(1.61803 - 1.17557i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.363271i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.500000 - 1.53884i) q^{4} +(-1.80902 + 1.31433i) q^{5} +(0.190983 - 0.587785i) q^{6} -1.61803 q^{7} +(-0.690983 + 2.12663i) q^{8} +(1.61803 - 1.17557i) q^{9} +1.38197 q^{10} +(0.618034 + 0.449028i) q^{11} +(1.30902 - 0.951057i) q^{12} +(3.92705 - 2.85317i) q^{13} +(0.809017 + 0.587785i) q^{14} +(-1.80902 - 1.31433i) q^{15} +(-1.50000 + 1.08981i) q^{16} +(-0.236068 + 0.726543i) q^{17} -1.23607 q^{18} +(-1.80902 + 5.56758i) q^{19} +(2.92705 + 2.12663i) q^{20} +(-0.500000 - 1.53884i) q^{21} +(-0.145898 - 0.449028i) q^{22} +(-6.66312 - 4.84104i) q^{23} -2.23607 q^{24} +(1.54508 - 4.75528i) q^{25} -3.00000 q^{26} +(4.04508 + 2.93893i) q^{27} +(0.809017 + 2.48990i) q^{28} +(-0.427051 - 1.31433i) q^{29} +(0.427051 + 1.31433i) q^{30} +(-0.927051 + 2.85317i) q^{31} +5.61803 q^{32} +(-0.236068 + 0.726543i) q^{33} +(0.381966 - 0.277515i) q^{34} +(2.92705 - 2.12663i) q^{35} +(-2.61803 - 1.90211i) q^{36} +(-3.42705 + 2.48990i) q^{37} +(2.92705 - 2.12663i) q^{38} +(3.92705 + 2.85317i) q^{39} +(-1.54508 - 4.75528i) q^{40} +(4.23607 - 3.07768i) q^{41} +(-0.309017 + 0.951057i) q^{42} +1.85410 q^{43} +(0.381966 - 1.17557i) q^{44} +(-1.38197 + 4.25325i) q^{45} +(1.57295 + 4.84104i) q^{46} +(-0.500000 - 1.53884i) q^{47} +(-1.50000 - 1.08981i) q^{48} -4.38197 q^{49} +(-2.50000 + 1.81636i) q^{50} -0.763932 q^{51} +(-6.35410 - 4.61653i) q^{52} +(1.69098 + 5.20431i) q^{53} +(-0.954915 - 2.93893i) q^{54} -1.70820 q^{55} +(1.11803 - 3.44095i) q^{56} -5.85410 q^{57} +(-0.263932 + 0.812299i) q^{58} +(3.35410 - 2.43690i) q^{59} +(-1.11803 + 3.44095i) q^{60} +(3.80902 + 2.76741i) q^{61} +(1.50000 - 1.08981i) q^{62} +(-2.61803 + 1.90211i) q^{63} +(0.190983 + 0.138757i) q^{64} +(-3.35410 + 10.3229i) q^{65} +(0.381966 - 0.277515i) q^{66} +(2.85410 - 8.78402i) q^{67} +1.23607 q^{68} +(2.54508 - 7.83297i) q^{69} -2.23607 q^{70} +(-1.35410 - 4.16750i) q^{71} +(1.38197 + 4.25325i) q^{72} +(7.28115 + 5.29007i) q^{73} +2.61803 q^{74} +5.00000 q^{75} +9.47214 q^{76} +(-1.00000 - 0.726543i) q^{77} +(-0.927051 - 2.85317i) q^{78} +(0.954915 + 2.93893i) q^{79} +(1.28115 - 3.94298i) q^{80} +(0.309017 - 0.951057i) q^{81} -3.23607 q^{82} +(-0.545085 + 1.67760i) q^{83} +(-2.11803 + 1.53884i) q^{84} +(-0.527864 - 1.62460i) q^{85} +(-0.927051 - 0.673542i) q^{86} +(1.11803 - 0.812299i) q^{87} +(-1.38197 + 1.00406i) q^{88} +(-7.23607 - 5.25731i) q^{89} +(2.23607 - 1.62460i) q^{90} +(-6.35410 + 4.61653i) q^{91} +(-4.11803 + 12.6740i) q^{92} -3.00000 q^{93} +(-0.309017 + 0.951057i) q^{94} +(-4.04508 - 12.4495i) q^{95} +(1.73607 + 5.34307i) q^{96} +(0.881966 + 2.71441i) q^{97} +(2.19098 + 1.59184i) q^{98} +1.52786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} - q^{3} - 2 q^{4} - 5 q^{5} + 3 q^{6} - 2 q^{7} - 5 q^{8} + 2 q^{9} + 10 q^{10} - 2 q^{11} + 3 q^{12} + 9 q^{13} + q^{14} - 5 q^{15} - 6 q^{16} + 8 q^{17} + 4 q^{18} - 5 q^{19} + 5 q^{20} - 2 q^{21} - 14 q^{22} - 11 q^{23} - 5 q^{25} - 12 q^{26} + 5 q^{27} + q^{28} + 5 q^{29} - 5 q^{30} + 3 q^{31} + 18 q^{32} + 8 q^{33} + 6 q^{34} + 5 q^{35} - 6 q^{36} - 7 q^{37} + 5 q^{38} + 9 q^{39} + 5 q^{40} + 8 q^{41} + q^{42} - 6 q^{43} + 6 q^{44} - 10 q^{45} + 13 q^{46} - 2 q^{47} - 6 q^{48} - 22 q^{49} - 10 q^{50} - 12 q^{51} - 12 q^{52} + 9 q^{53} - 15 q^{54} + 20 q^{55} - 10 q^{57} - 10 q^{58} + 13 q^{61} + 6 q^{62} - 6 q^{63} + 3 q^{64} + 6 q^{66} - 2 q^{67} - 4 q^{68} - q^{69} + 8 q^{71} + 10 q^{72} + 9 q^{73} + 6 q^{74} + 20 q^{75} + 20 q^{76} - 4 q^{77} + 3 q^{78} + 15 q^{79} - 15 q^{80} - q^{81} - 4 q^{82} + 9 q^{83} - 4 q^{84} - 20 q^{85} + 3 q^{86} - 10 q^{88} - 20 q^{89} - 12 q^{91} - 12 q^{92} - 12 q^{93} + q^{94} - 5 q^{95} - 2 q^{96} + 8 q^{97} + 11 q^{98} + 24 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 - q^3 - 2 * q^4 - 5 * q^5 + 3 * q^6 - 2 * q^7 - 5 * q^8 + 2 * q^9 + 10 * q^10 - 2 * q^11 + 3 * q^12 + 9 * q^13 + q^14 - 5 * q^15 - 6 * q^16 + 8 * q^17 + 4 * q^18 - 5 * q^19 + 5 * q^20 - 2 * q^21 - 14 * q^22 - 11 * q^23 - 5 * q^25 - 12 * q^26 + 5 * q^27 + q^28 + 5 * q^29 - 5 * q^30 + 3 * q^31 + 18 * q^32 + 8 * q^33 + 6 * q^34 + 5 * q^35 - 6 * q^36 - 7 * q^37 + 5 * q^38 + 9 * q^39 + 5 * q^40 + 8 * q^41 + q^42 - 6 * q^43 + 6 * q^44 - 10 * q^45 + 13 * q^46 - 2 * q^47 - 6 * q^48 - 22 * q^49 - 10 * q^50 - 12 * q^51 - 12 * q^52 + 9 * q^53 - 15 * q^54 + 20 * q^55 - 10 * q^57 - 10 * q^58 + 13 * q^61 + 6 * q^62 - 6 * q^63 + 3 * q^64 + 6 * q^66 - 2 * q^67 - 4 * q^68 - q^69 + 8 * q^71 + 10 * q^72 + 9 * q^73 + 6 * q^74 + 20 * q^75 + 20 * q^76 - 4 * q^77 + 3 * q^78 + 15 * q^79 - 15 * q^80 - q^81 - 4 * q^82 + 9 * q^83 - 4 * q^84 - 20 * q^85 + 3 * q^86 - 10 * q^88 - 20 * q^89 - 12 * q^91 - 12 * q^92 - 12 * q^93 + q^94 - 5 * q^95 - 2 * q^96 + 8 * q^97 + 11 * q^98 + 24 * q^99

Introduction

L-functions

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