LMFDB - Embedded newform 370.2.o.b.271.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(71,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("370.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.o (of order $9$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{9})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 3 x^{17} + 18 x^{16} - 25 x^{15} + 132 x^{14} - 135 x^{13} + 666 x^{12} - 297 x^{11} + 1845 x^{10} + \cdots + 9 $ x^18 - 3x^17 + 18x^16 - 25x^15 + 132x^14 - 135x^13 + 666x^12 - 297x^11 + 1845x^10 - 382x^9 + 3810x^8 - 63x^7 + 3325x^6 - 1329x^5 + 1332x^4 - 192x^3 + 117x^2 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			271.3
Root			$-0.647764 - 1.12196i$ of defining polynomial
Character	$\chi$	$=$	370.271
Dual form			370.2.o.b.71.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 + 0.642788i) q^{2} +(0.992431 + 0.832749i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -1.29553 q^{6} +(-3.09818 + 1.12765i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.229495 - 1.30153i) q^{9} +O(q^{10})$	\(q+(-0.766044 + 0.642788i) q^{2} +(0.992431 + 0.832749i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -1.29553 q^{6} +(-3.09818 + 1.12765i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.229495 - 1.30153i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(3.04991 + 5.28259i) q^{11} +(0.992431 - 0.832749i) q^{12} +(-0.733221 + 4.15830i) q^{13} +(1.64851 - 2.85530i) q^{14} +(1.21740 + 0.443096i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.443166 + 2.51332i) q^{17} +(1.01241 + 0.849514i) q^{18} +(4.21718 + 3.53863i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(-4.01378 - 1.46090i) q^{21} +(-5.73195 - 2.08626i) q^{22} +(0.278339 - 0.482098i) q^{23} +(-0.224966 + 1.27585i) q^{24} +(0.766044 - 0.642788i) q^{25} +(-2.11123 - 3.65675i) q^{26} +(2.79938 - 4.84867i) q^{27} +(0.572521 + 3.24693i) q^{28} +(-3.76711 - 6.52482i) q^{29} +(-1.21740 + 0.443096i) q^{30} +10.1985 q^{31} +(0.939693 - 0.342020i) q^{32} +(-1.37225 + 7.78242i) q^{33} +(-1.95502 - 1.64045i) q^{34} +(-2.52566 + 2.11928i) q^{35} -1.32161 q^{36} +(-5.66958 + 2.20359i) q^{37} -5.50513 q^{38} +(-4.19049 + 3.51624i) q^{39} +(0.766044 + 0.642788i) q^{40} +(-1.13335 + 6.42753i) q^{41} +(4.01378 - 1.46090i) q^{42} -8.25269 q^{43} +(5.73195 - 2.08626i) q^{44} +(-0.660805 - 1.14455i) q^{45} +(0.0966663 + 0.548222i) q^{46} +(3.46631 - 6.00383i) q^{47} +(-0.647764 - 1.12196i) q^{48} +(2.96485 - 2.48780i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(-1.65315 + 2.86334i) q^{51} +(3.96781 + 1.44416i) q^{52} +(-1.81282 - 0.659812i) q^{53} +(0.972215 + 5.51370i) q^{54} +(4.67273 + 3.92088i) q^{55} +(-2.52566 - 2.11928i) q^{56} +(1.23847 + 7.02370i) q^{57} +(7.07984 + 2.57685i) q^{58} +(-9.75769 - 3.55151i) q^{59} +(0.647764 - 1.12196i) q^{60} +(2.19419 - 12.4439i) q^{61} +(-7.81253 + 6.55549i) q^{62} +(2.17869 + 3.77359i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.733221 + 4.15830i) q^{65} +(-3.95124 - 6.84374i) q^{66} +(8.69429 - 3.16446i) q^{67} +2.55209 q^{68} +(0.677700 - 0.246662i) q^{69} +(0.572521 - 3.24693i) q^{70} +(-10.3975 - 8.72453i) q^{71} +(1.01241 - 0.849514i) q^{72} +10.6326 q^{73} +(2.92671 - 5.33239i) q^{74} +1.29553 q^{75} +(4.21718 - 3.53863i) q^{76} +(-15.4061 - 12.9272i) q^{77} +(0.949908 - 5.38719i) q^{78} +(12.4177 - 4.51968i) q^{79} -1.00000 q^{80} +(3.09020 - 1.12474i) q^{81} +(-3.26334 - 5.65227i) q^{82} +(1.17240 + 6.64899i) q^{83} +(-2.13569 + 3.69912i) q^{84} +(1.27605 + 2.21018i) q^{85} +(6.32193 - 5.30473i) q^{86} +(1.69494 - 9.61249i) q^{87} +(-3.04991 + 5.28259i) q^{88} +(-0.306111 - 0.111415i) q^{89} +(1.24191 + 0.452017i) q^{90} +(-2.41744 - 13.7100i) q^{91} +(-0.426441 - 0.357826i) q^{92} +(10.1213 + 8.49281i) q^{93} +(1.20384 + 6.82730i) q^{94} +(5.17313 + 1.88287i) q^{95} +(1.21740 + 0.443096i) q^{96} +(3.19592 - 5.53550i) q^{97} +(-0.672077 + 3.81154i) q^{98} +(6.17552 - 5.18188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	$ 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) $ 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$2$	−0.766044	+	0.642788i	−0.541675	+	0.454519i
$3$	0.992431	+	0.832749i	0.572981	+	0.480788i	0.882633	−	0.470062i	$-0.155768\pi$
$3$	0.992431	+	0.832749i	0.572981	+	0.480788i	−0.309653	+	0.950850i	$0.600213\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$5$	0.939693	−	0.342020i	0.420243	−	0.152956i
$6$	−1.29553			−0.528897
$7$	−3.09818	+	1.12765i	−1.17100	+	0.426210i	−0.853016	−	0.521884i	$-0.825229\pi$
$7$	−3.09818	+	1.12765i	−1.17100	+	0.426210i	−0.317987	+	0.948095i	$0.603007\pi$
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	−0.229495	−	1.30153i	−0.0764983	−	0.433844i
$10$	−0.500000	+	0.866025i	−0.158114	+	0.273861i
$11$	3.04991	+	5.28259i	0.919581	+	1.59276i	0.800052	+	0.599931i	$0.204805\pi$
$11$	3.04991	+	5.28259i	0.919581	+	1.59276i	0.119530	+	0.992831i	$0.461861\pi$
$12$	0.992431	−	0.832749i	0.286490	−	0.240394i
$13$	−0.733221	+	4.15830i	−0.203359	+	1.15331i	0.696642	+	0.717418i	$0.254676\pi$
$13$	−0.733221	+	4.15830i	−0.203359	+	1.15331i	−0.900001	+	0.435887i	$0.856435\pi$
$14$	1.64851	−	2.85530i	0.440583	−	0.763112i
$15$	1.21740	+	0.443096i	0.314331	+	0.114407i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	0.443166	+	2.51332i	0.107484	+	0.609570i	0.990199	+	0.139662i	$0.0446016\pi$
$17$	0.443166	+	2.51332i	0.107484	+	0.609570i	−0.882716	+	0.469908i	$0.844287\pi$
$18$	1.01241	+	0.849514i	0.238628	+	0.200232i
$19$	4.21718	+	3.53863i	0.967487	+	0.811818i	0.982155	−	0.188075i	$-0.0602248\pi$
$19$	4.21718	+	3.53863i	0.967487	+	0.811818i	−0.0146682	+	0.999892i	$0.504669\pi$
$20$	−0.173648	−	0.984808i	−0.0388289	−	0.220210i
$21$	−4.01378	−	1.46090i	−0.875879	−	0.318794i
$22$	−5.73195	−	2.08626i	−1.22206	−	0.444792i
$23$	0.278339	−	0.482098i	0.0580378	−	0.100524i	−0.835547	−	0.549419i	$-0.814849\pi$
$23$	0.278339	−	0.482098i	0.0580378	−	0.100524i	0.893585	+	0.448895i	$0.148182\pi$
$24$	−0.224966	+	1.27585i	−0.0459210	+	0.260431i
$25$	0.766044	−	0.642788i	0.153209	−	0.128558i
$26$	−2.11123	−	3.65675i	−0.414045	−	0.717148i
$27$	2.79938	−	4.84867i	0.538741	−	0.933127i
$28$	0.572521	+	3.24693i	0.108196	+	0.613612i
$29$	−3.76711	−	6.52482i	−0.699534	−	1.21163i	−0.968628	−	0.248515i	$-0.920058\pi$
$29$	−3.76711	−	6.52482i	−0.699534	−	1.21163i	0.269094	−	0.963114i	$-0.413276\pi$
$30$	−1.21740	+	0.443096i	−0.222265	+	0.0808980i
$31$	10.1985			1.83171			0.915855	−	0.401510i	$-0.131514\pi$
$31$	10.1985			1.83171			0.915855	+	0.401510i	$0.131514\pi$
$32$	0.939693	−	0.342020i	0.166116	−	0.0604612i
$33$	−1.37225	+	7.78242i	−0.238878	+	1.35474i
$34$	−1.95502	−	1.64045i	−0.335282	−	0.281335i
$35$	−2.52566	+	2.11928i	−0.426915	+	0.358224i
$36$	−1.32161			−0.220268
$37$	−5.66958	+	2.20359i	−0.932074	+	0.362268i
$37$	−5.66958	+	2.20359i	−0.932074	+	0.362268i
$38$	−5.50513			−0.893050
$39$	−4.19049	+	3.51624i	−0.671016	+	0.563049i
$40$	0.766044	+	0.642788i	0.121122	+	0.101634i
$41$	−1.13335	+	6.42753i	−0.176999	+	1.00381i	0.758812	+	0.651310i	$0.225780\pi$
$41$	−1.13335	+	6.42753i	−0.176999	+	1.00381i	−0.935811	+	0.352502i	$0.885331\pi$
$42$	4.01378	−	1.46090i	0.619340	−	0.225421i
$43$	−8.25269			−1.25852			−0.629262	−	0.777194i	$-0.716643\pi$
$43$	−8.25269			−1.25852			−0.629262	+	0.777194i	$0.716643\pi$
$44$	5.73195	−	2.08626i	0.864124	−	0.314515i
$45$	−0.660805	−	1.14455i	−0.0985069	−	0.170619i
$46$	0.0966663	+	0.548222i	0.0142527	+	0.0808309i
$47$	3.46631	−	6.00383i	0.505614	−	0.875749i	−0.494365	−	0.869254i	$-0.664599\pi$
$47$	3.46631	−	6.00383i	0.505614	−	0.875749i	0.999979	−	0.00649441i	$-0.00206725\pi$
$48$	−0.647764	−	1.12196i	−0.0934966	−	0.161941i
$49$	2.96485	−	2.48780i	0.423550	−	0.355400i
$50$	−0.173648	+	0.984808i	−0.0245576	+	0.139273i
$51$	−1.65315	+	2.86334i	−0.231488	+	0.400948i
$52$	3.96781	+	1.44416i	0.550236	+	0.200269i
$53$	−1.81282	−	0.659812i	−0.249010	−	0.0906321i	0.214500	−	0.976724i	$-0.431188\pi$
$53$	−1.81282	−	0.659812i	−0.249010	−	0.0906321i	−0.463510	+	0.886092i	$0.653410\pi$
$54$	0.972215	+	5.51370i	0.132302	+	0.750320i
$55$	4.67273	+	3.92088i	0.630070	+	0.528692i
$56$	−2.52566	−	2.11928i	−0.337506	−	0.283201i
$57$	1.23847	+	7.02370i	0.164039	+	0.930311i
$58$	7.07984	+	2.57685i	0.929629	+	0.338357i
$59$	−9.75769	−	3.55151i	−1.27034	−	0.462367i	−0.383116	−	0.923700i	$-0.625149\pi$
$59$	−9.75769	−	3.55151i	−1.27034	−	0.462367i	−0.887227	+	0.461333i	$0.847371\pi$
$60$	0.647764	−	1.12196i	0.0836259	−	0.144844i
$61$	2.19419	−	12.4439i	0.280937	−	1.59327i	−0.438510	−	0.898726i	$-0.644494\pi$
$61$	2.19419	−	12.4439i	0.280937	−	1.59327i	0.719447	−	0.694547i	$-0.244395\pi$
$62$	−7.81253	+	6.55549i	−0.992192	+	0.832548i
$63$	2.17869	+	3.77359i	0.274489	+	0.475428i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.733221	+	4.15830i	0.0909449	+	0.515774i
$66$	−3.95124	−	6.84374i	−0.486364	−	0.842406i
$67$	8.69429	−	3.16446i	1.06218	−	0.386601i	0.248931	−	0.968521i	$-0.419921\pi$
$67$	8.69429	−	3.16446i	1.06218	−	0.386601i	0.813246	+	0.581920i	$0.197699\pi$
$68$	2.55209			0.309487
$69$	0.677700	−	0.246662i	0.0815854	−	0.0296947i
$70$	0.572521	−	3.24693i	0.0684294	−	0.388082i
$71$	−10.3975	−	8.72453i	−1.23395	−	1.03541i	−0.997972	−	0.0636536i	$-0.979725\pi$
$71$	−10.3975	−	8.72453i	−1.23395	−	1.03541i	−0.235983	−	0.971757i	$-0.575831\pi$
$72$	1.01241	−	0.849514i	0.119314	−	0.100116i
$73$	10.6326			1.24445			0.622227	−	0.782837i	$-0.286228\pi$
$73$	10.6326			1.24445			0.622227	+	0.782837i	$0.286228\pi$
$74$	2.92671	−	5.33239i	0.340223	−	0.619877i
$75$	1.29553			0.149595
$76$	4.21718	−	3.53863i	0.483743	−	0.405909i
$77$	−15.4061	−	12.9272i	−1.75568	−	1.47319i
$78$	0.949908	−	5.38719i	0.107556	−	0.609980i
$79$	12.4177	−	4.51968i	1.39710	−	0.508503i	0.469785	−	0.882781i	$-0.344332\pi$
$79$	12.4177	−	4.51968i	1.39710	−	0.508503i	0.927317	+	0.374278i	$0.122109\pi$
$80$	−1.00000			−0.111803
$81$	3.09020	−	1.12474i	0.343355	−	0.124971i
$82$	−3.26334	−	5.65227i	−0.360376	−	0.624189i
$83$	1.17240	+	6.64899i	0.128687	+	0.729821i	0.979049	+	0.203623i	$0.0652718\pi$
$83$	1.17240	+	6.64899i	0.128687	+	0.729821i	−0.850362	+	0.526198i	$0.823617\pi$
$84$	−2.13569	+	3.69912i	−0.233023	+	0.403607i
$85$	1.27605	+	2.21018i	0.138407	+	0.239727i
$86$	6.32193	−	5.30473i	0.681711	−	0.572023i
$87$	1.69494	−	9.61249i	0.181717	−	1.03057i
$88$	−3.04991	+	5.28259i	−0.325121	+	0.563126i
$89$	−0.306111	−	0.111415i	−0.0324477	−	0.0118100i	0.325745	−	0.945458i	$-0.394385\pi$
$89$	−0.306111	−	0.111415i	−0.0324477	−	0.0118100i	−0.358193	+	0.933648i	$0.616607\pi$
$90$	1.24191	+	0.452017i	0.130908	+	0.0476468i
$91$	−2.41744	−	13.7100i	−0.253417	−	1.43720i
$92$	−0.426441	−	0.357826i	−0.0444595	−	0.0373060i
$93$	10.1213	+	8.49281i	1.04953	+	0.880664i
$94$	1.20384	+	6.82730i	0.124166	+	0.704183i
$95$	5.17313	+	1.88287i	0.530752	+	0.193178i
$96$	1.21740	+	0.443096i	0.124250	+	0.0452233i
$97$	3.19592	−	5.53550i	0.324497	−	0.562045i	−0.656914	−	0.753966i	$-0.728138\pi$
$97$	3.19592	−	5.53550i	0.324497	−	0.562045i	0.981410	+	0.191921i	$0.0614717\pi$
$98$	−0.672077	+	3.81154i	−0.0678900	+	0.385023i
$99$	6.17552	−	5.18188i	0.620663	−	0.520798i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	3.46496	−	6.00148i	0.344776	−	0.597170i	−0.640537	−	0.767927i	$-0.721288\pi$
$101$	3.46496	−	6.00148i	0.344776	−	0.597170i	0.985313	+	0.170758i	$0.0546215\pi$
$102$	−0.574134	−	3.25607i	−0.0568477	−	0.322399i
$103$	3.03011	+	5.24831i	0.298566	+	0.517131i	0.975808	−	0.218629i	$-0.0701585\pi$
$103$	3.03011	+	5.24831i	0.298566	+	0.517131i	−0.677242	+	0.735760i	$0.736825\pi$
$104$	−3.96781	+	1.44416i	−0.389075	+	0.141612i
$105$	−4.27138			−0.416844
$106$	1.81282	−	0.659812i	0.176076	−	0.0640866i
$107$	−0.718873	+	4.07693i	−0.0694961	+	0.394132i	0.930141	+	0.367202i	$0.119684\pi$
$107$	−0.718873	+	4.07693i	−0.0694961	+	0.394132i	−0.999637	+	0.0269299i	$0.991427\pi$
$108$	−4.28890	−	3.59882i	−0.412700	−	0.346296i
$109$	−6.69830	+	5.62054i	−0.641580	+	0.538350i	−0.904503	−	0.426467i	$-0.859758\pi$
$109$	−6.69830	+	5.62054i	−0.641580	+	0.538350i	0.262923	+	0.964817i	$0.415314\pi$
$110$	−6.09981			−0.581594
$111$	−7.46171	−	2.53443i	−0.708234	−	0.240557i
$112$	3.29702			0.311539
$113$	8.33546	−	6.99428i	0.784134	−	0.657967i	−0.160152	−	0.987092i	$-0.551198\pi$
$113$	8.33546	−	6.99428i	0.784134	−	0.657967i	0.944286	+	0.329126i	$0.106754\pi$
$114$	−5.46347	−	4.58439i	−0.511701	−	0.429368i
$115$	0.0966663	−	0.548222i	0.00901418	−	0.0511219i
$116$	−7.07984	+	2.57685i	−0.657347	+	0.239255i
$117$	5.58043			0.515911
$118$	9.75769	−	3.55151i	0.898268	−	0.326943i
$119$	−4.20715	−	7.28699i	−0.385669	−	0.667998i
$120$	0.224966	+	1.27585i	0.0205365	+	0.116468i
$121$	−13.1039	+	22.6965i	−1.19126	+	2.06332i
$122$	6.31791	+	10.9429i	0.571997	+	0.990728i
$123$	−6.47729	+	5.43509i	−0.584037	+	0.490065i
$124$	1.77096	−	10.0436i	0.159037	−	0.901941i
$125$	0.500000	−	0.866025i	0.0447214	−	0.0774597i
$126$	−4.09459	−	1.49031i	−0.364775	−	0.132767i
$127$	−0.586917	−	0.213620i	−0.0520805	−	0.0189557i	0.315849	−	0.948810i	$-0.397711\pi$
$127$	−0.586917	−	0.213620i	−0.0520805	−	0.0189557i	−0.367929	+	0.929854i	$0.619933\pi$
$128$	−0.173648	−	0.984808i	−0.0153485	−	0.0870455i
$129$	−8.19023	−	6.87242i	−0.721109	−	0.605083i
$130$	−3.23459	−	2.71414i	−0.283692	−	0.238046i
$131$	−2.41158	−	13.6767i	−0.210700	−	1.19494i	−0.888214	−	0.459431i	$-0.848053\pi$
$131$	−2.41158	−	13.6767i	−0.210700	−	1.19494i	0.677513	−	0.735511i	$-0.263058\pi$
$132$	7.42590	+	2.70280i	0.646341	+	0.235249i
$133$	−17.0559	−	6.20785i	−1.47894	−	0.538288i
$134$	−4.62614	+	8.01270i	−0.399637	+	0.692192i
$135$	0.972215	−	5.51370i	0.0836749	−	0.474544i
$136$	−1.95502	+	1.64045i	−0.167641	+	0.140668i
$137$	−0.823079	−	1.42561i	−0.0703204	−	0.121799i	0.828721	−	0.559661i	$-0.189069\pi$
$137$	−0.823079	−	1.42561i	−0.0703204	−	0.121799i	−0.899042	+	0.437863i	$0.855735\pi$
$138$	−0.360596	+	0.624571i	−0.0306960	+	0.0531670i
$139$	1.05297	+	5.97168i	0.0893116	+	0.506512i	0.996343	+	0.0854477i	$0.0272321\pi$
$139$	1.05297	+	5.97168i	0.0893116	+	0.506512i	−0.907031	+	0.421064i	$0.861657\pi$
$140$	1.64851	+	2.85530i	0.139324	+	0.241317i
$141$	8.43976	−	3.07182i	0.710756	−	0.258694i
$142$	13.5730			1.13902
$143$	−24.2029	+	8.80913i	−2.02395	+	0.736656i
$144$	−0.229495	+	1.30153i	−0.0191246	+	0.108461i
$145$	−5.77154	−	4.84290i	−0.479300	−	0.402181i
$146$	−8.14506	+	6.83451i	−0.674090	+	0.565628i
$147$	5.01412			0.413558
$148$	1.18560	+	5.96610i	0.0974557	+	0.490410i
$149$	0.756988			0.0620148			0.0310074	−	0.999519i	$-0.490128\pi$
$149$	0.756988			0.0620148			0.0310074	+	0.999519i	$0.490128\pi$
$150$	−0.992431	+	0.832749i	−0.0810317	+	0.0679937i
$151$	17.8005	+	14.9364i	1.44859	+	1.21551i	0.933604	+	0.358306i	$0.116645\pi$
$151$	17.8005	+	14.9364i	1.44859	+	1.21551i	0.514981	+	0.857202i	$0.327799\pi$
$152$	−0.955956	+	5.42150i	−0.0775383	+	0.439741i
$153$	3.16946	−	1.15359i	0.256236	−	0.0932621i
$154$	20.1112			1.62061
$155$	9.58348	−	3.48810i	0.769764	−	0.280171i
$156$	2.73515	+	4.73742i	0.218987	+	0.379297i
$157$	0.589909	+	3.34554i	0.0470799	+	0.267003i	0.999257	−	0.0385435i	$-0.0122718\pi$
$157$	0.589909	+	3.34554i	0.0470799	+	0.267003i	−0.952177	+	0.305547i	$0.901161\pi$
$158$	−6.60732	+	11.4442i	−0.525651	+	0.910453i
$159$	−1.24964	−	2.16444i	−0.0991029	−	0.171651i
$160$	0.766044	−	0.642788i	0.0605611	−	0.0508168i
$161$	−0.318711	+	1.80750i	−0.0251179	+	0.142451i
$162$	−1.64426	+	2.84794i	−0.129185	+	0.223756i
$163$	12.5829	+	4.57981i	0.985571	+	0.358719i	0.784004	−	0.620756i	$-0.213174\pi$
$163$	12.5829	+	4.57981i	0.985571	+	0.358719i	0.201567	+	0.979475i	$0.435397\pi$
$164$	6.13308	+	2.23226i	0.478913	+	0.174310i
$165$	1.37225	+	7.78242i	0.106830	+	0.605860i
$166$	−5.17200	−	4.33982i	−0.401425	−	0.336835i
$167$	−7.44294	−	6.24537i	−0.575952	−	0.483281i	0.307663	−	0.951495i	$-0.400453\pi$
$167$	−7.44294	−	6.24537i	−0.575952	−	0.483281i	−0.883615	+	0.468214i	$0.844897\pi$
$168$	−0.741717	−	4.20649i	−0.0572247	−	0.324537i
$169$	−4.53786	−	1.65165i	−0.349066	−	0.127050i
$170$	−2.39818	−	0.872867i	−0.183932	−	0.0669458i
$171$	3.63782	−	6.30088i	0.278191	−	0.481841i
$172$	−1.43306	+	8.12731i	−0.109270	+	0.619702i
$173$	−3.09248	+	2.59490i	−0.235117	+	0.197286i	−0.752732	−	0.658327i	$-0.771264\pi$
$173$	−3.09248	+	2.59490i	−0.235117	+	0.197286i	0.517615	+	0.855614i	$0.326820\pi$
$174$	4.88039	+	8.45308i	0.369981	+	0.640826i
$175$	−1.64851	+	2.85530i	−0.124616	+	0.215841i
$176$	−1.05922	−	6.00714i	−0.0798418	−	0.452805i
$177$	−6.72632	−	11.6503i	−0.505581	−	0.875693i
$178$	0.306111	−	0.111415i	0.0229440	−	0.00835093i
$179$	−9.38015			−0.701106			−0.350553	−	0.936543i	$-0.614006\pi$
$179$	−9.38015			−0.701106			−0.350553	+	0.936543i	$0.614006\pi$
$180$	−1.24191	+	0.452017i	−0.0925662	+	0.0336914i
$181$	0.0658799	−	0.373624i	0.00489682	−	0.0277712i	−0.982261	−	0.187517i	$-0.939956\pi$
$181$	0.0658799	−	0.373624i	0.00489682	−	0.0277712i	0.987158	+	0.159745i	$0.0510673\pi$
$182$	10.6645	+	8.94857i	0.790505	+	0.663312i
$183$	12.5402	−	10.5225i	0.926998	−	0.777843i
$184$	0.556679			0.0410389
$185$	−4.57399	+	4.00981i	−0.336287	+	0.294807i
$186$	−13.2125			−0.968785
$187$	−11.9252	+	10.0065i	−0.872059	+	0.731745i
$188$	−5.31070	−	4.45621i	−0.387323	−	0.325002i
$189$	−3.20541	+	18.1788i	−0.233159	+	1.32231i
$190$	−5.17313	+	1.88287i	−0.375298	+	0.136597i
$191$	16.1607			1.16935			0.584673	−	0.811269i	$-0.301223\pi$
$191$	16.1607			1.16935			0.584673	+	0.811269i	$0.301223\pi$
$192$	−1.21740	+	0.443096i	−0.0878581	+	0.0319777i
$193$	−9.88183	−	17.1158i	−0.711310	−	1.23202i	−0.964366	−	0.264573i	$-0.914769\pi$
$193$	−9.88183	−	17.1158i	−0.711310	−	1.23202i	0.253056	−	0.967452i	$-0.418564\pi$
$194$	1.10993	+	6.29474i	0.0796885	+	0.451936i
$195$	−2.73515	+	4.73742i	−0.195868	+	0.339254i
$196$	−1.93517	−	3.35181i	−0.138226	−	0.239415i
$197$	−11.1904	+	9.38990i	−0.797286	+	0.669002i	−0.947537	−	0.319645i	$-0.896436\pi$
$197$	−11.1904	+	9.38990i	−0.797286	+	0.669002i	0.150251	+	0.988648i	$0.451992\pi$
$198$	−1.39988	+	7.93909i	−0.0994849	+	0.564207i
$199$	−1.72060	+	2.98016i	−0.121970	+	0.211258i	−0.920544	−	0.390638i	$-0.872254\pi$
$199$	−1.72060	+	2.98016i	−0.121970	+	0.211258i	0.798575	+	0.601896i	$0.205588\pi$
$200$	0.939693	+	0.342020i	0.0664463	+	0.0241845i
$201$	11.2637	+	4.09965i	0.794480	+	0.289167i
$202$	1.20337	+	6.82463i	0.0846686	+	0.480180i
$203$	19.0289	+	15.9671i	1.33557	+	1.12067i
$204$	2.53278	+	2.12525i	0.177330	+	0.148797i
$205$	1.13335	+	6.42753i	0.0791564	+	0.448918i
$206$	−5.69475	−	2.07272i	−0.396772	−	0.144413i
$207$	−0.691343	−	0.251628i	−0.0480517	−	0.0174894i
$208$	2.11123	−	3.65675i	0.146387	−	0.253550i
$209$	−5.83115	+	33.0701i	−0.403349	+	2.28751i
$210$	3.27207	−	2.74559i	0.225794	−	0.189464i
$211$	6.88081	+	11.9179i	0.473694	+	0.820463i	0.999546	−	0.0301132i	$-0.00958678\pi$
$211$	6.88081	+	11.9179i	0.473694	+	0.820463i	−0.525852	+	0.850576i	$0.676253\pi$
$212$	−0.964580	+	1.67070i	−0.0662477	+	0.114744i
$213$	−3.05345	−	17.3170i	−0.209219	−	1.18654i
$214$	−2.06991	−	3.58519i	−0.141496	−	0.245079i
$215$	−7.75499	+	2.82259i	−0.528886	+	0.192499i
$216$	5.59876			0.380948
$217$	−31.5969	+	11.5003i	−2.14494	+	0.780694i
$218$	1.51838	−	8.61116i	0.102838	−	0.583222i
$219$	10.5521	+	8.85430i	0.713048	+	0.598318i
$220$	4.67273	−	3.92088i	0.315035	−	0.264346i
$221$	−10.7761			−0.724878
$222$	7.34510	−	2.85481i	0.492971	−	0.191602i
$223$	4.46590			0.299059			0.149529	−	0.988757i	$-0.452224\pi$
$223$	4.46590			0.299059			0.149529	+	0.988757i	$0.452224\pi$
$224$	−2.52566	+	2.11928i	−0.168753	+	0.141601i
$225$	−1.01241	−	0.849514i	−0.0674941	−	0.0566343i
$226$	−1.88950	+	10.7159i	−0.125687	+	0.712809i
$227$	21.4136	−	7.79391i	1.42127	−	0.517300i	0.486853	−	0.873484i	$-0.338145\pi$
$227$	21.4136	−	7.79391i	1.42127	−	0.517300i	0.934416	+	0.356184i	$0.115922\pi$
$228$	7.13205			0.472331
$229$	−3.40485	+	1.23926i	−0.224999	+	0.0818928i	−0.452060	−	0.891988i	$-0.649311\pi$
$229$	−3.40485	+	1.23926i	−0.224999	+	0.0818928i	0.227061	+	0.973881i	$0.427088\pi$
$230$	0.278339	+	0.482098i	0.0183532	+	0.0317886i
$231$	−4.52433	−	25.6588i	−0.297679	−	1.68822i
$232$	3.76711	−	6.52482i	0.247323	−	0.428375i
$233$	3.05944	+	5.29911i	0.200431	+	0.347156i	0.948667	−	0.316276i	$-0.102432\pi$
$233$	3.05944	+	5.29911i	0.200431	+	0.347156i	−0.748236	+	0.663432i	$0.769099\pi$
$234$	−4.27486	+	3.58703i	−0.279456	+	0.234492i
$235$	1.20384	−	6.82730i	0.0785297	−	0.445364i
$236$	−5.19196	+	8.99274i	−0.337968	+	0.585377i
$237$	16.0875	+	5.85536i	1.04499	+	0.380347i
$238$	7.90685	+	2.87786i	0.512525	+	0.186544i
$239$	−3.37100	−	19.1179i	−0.218052	−	1.23663i	−0.875531	−	0.483162i	$-0.839488\pi$
$239$	−3.37100	−	19.1179i	−0.218052	−	1.23663i	0.657479	−	0.753473i	$-0.271623\pi$
$240$	−0.992431	−	0.832749i	−0.0640612	−	0.0537537i
$241$	1.22979	+	1.03192i	0.0792177	+	0.0664716i	0.681537	−	0.731784i	$-0.261312\pi$
$241$	1.22979	+	1.03192i	0.0792177	+	0.0664716i	−0.602319	+	0.798256i	$0.705756\pi$
$242$	−4.55092	−	25.8096i	−0.292544	−	1.65910i
$243$	−11.7799	−	4.28754i	−0.755682	−	0.275046i
$244$	−11.8738	−	4.32171i	−0.760142	−	0.276669i
$245$	1.93517	−	3.35181i	0.123633	−	0.214139i
$246$	1.46828	−	8.32704i	0.0936142	−	0.530913i
$247$	−17.8068	+	14.9417i	−1.13302	+	0.950717i
$248$	5.09926	+	8.83218i	0.323804	+	0.560844i
$249$	−4.37342	+	7.57498i	−0.277154	+	0.480045i
$250$	0.173648	+	0.984808i	0.0109825	+	0.0622847i
$251$	7.22715	+	12.5178i	0.456174	+	0.790116i	0.998755	−	0.0498874i	$-0.0158863\pi$
$251$	7.22715	+	12.5178i	0.456174	+	0.790116i	−0.542581	+	0.840003i	$0.682553\pi$
$252$	4.09459	−	1.49031i	0.257935	−	0.0938806i
$253$	3.39564			0.213482
$254$	0.586917	−	0.213620i	0.0368265	−	0.0134037i
$255$	−0.574134	+	3.25607i	−0.0359537	+	0.203903i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	−2.10715	+	1.76811i	−0.131441	+	0.110292i	−0.706138	−	0.708074i	$-0.749564\pi$
$257$	−2.10715	+	1.76811i	−0.131441	+	0.110292i	0.574697	+	0.818366i	$0.305120\pi$
$258$	10.6916			0.665629
$259$	15.0805	−	13.2204i	0.937060	−	0.821477i
$260$	4.22245			0.261865
$261$	−7.62772	+	6.40042i	−0.472144	+	0.396176i
$262$	10.6386	+	8.92685i	0.657255	+	0.551503i
$263$	3.57682	−	20.2851i	0.220556	−	1.25084i	−0.650444	−	0.759554i	$-0.725417\pi$
$263$	3.57682	−	20.2851i	0.220556	−	1.25084i	0.871001	−	0.491282i	$-0.163472\pi$
$264$	−7.42590	+	2.70280i	−0.457032	+	0.166346i
$265$	−1.92916			−0.118507
$266$	17.0559	−	6.20785i	1.04577	−	0.380627i
$267$	−0.211013	−	0.365486i	−0.0129138	−	0.0223674i
$268$	−1.60664	−	9.11171i	−0.0981412	−	0.556586i
$269$	1.56772	−	2.71537i	0.0955856	−	0.165559i	−0.814267	−	0.580490i	$-0.802861\pi$
$269$	1.56772	−	2.71537i	0.0955856	−	0.165559i	0.909853	+	0.414931i	$0.136194\pi$
$270$	2.79938	+	4.84867i	0.170365	+	0.295081i
$271$	−21.1745	+	17.7675i	−1.28626	+	1.07930i	−0.293910	+	0.955833i	$0.594956\pi$
$271$	−21.1745	+	17.7675i	−1.28626	+	1.07930i	−0.992349	+	0.123466i	$0.960599\pi$
$272$	0.443166	−	2.51332i	0.0268709	−	0.152392i
$273$	9.01784	−	15.6194i	0.545785	−	0.945327i
$274$	1.54688	+	0.563019i	0.0934506	+	0.0340132i
$275$	5.73195	+	2.08626i	0.345650	+	0.125806i
$276$	−0.125234	−	0.710236i	−0.00753819	−	0.0427512i
$277$	−19.1328	−	16.0543i	−1.14958	−	0.964609i	−0.149867	−	0.988706i	$-0.547884\pi$
$277$	−19.1328	−	16.0543i	−1.14958	−	0.964609i	−0.999710	+	0.0240971i	$0.992329\pi$
$278$	−4.64514	−	3.89774i	−0.278597	−	0.233771i
$279$	−2.34051	−	13.2737i	−0.140123	−	0.794676i
$280$	−3.09818	−	1.12765i	−0.185152	−	0.0673898i
$281$	−10.2449	−	3.72885i	−0.611161	−	0.222444i	0.0178501	−	0.999841i	$-0.494318\pi$
$281$	−10.2449	−	3.72885i	−0.611161	−	0.222444i	−0.629011	+	0.777396i	$0.716540\pi$
$282$	−4.49070	+	7.77813i	−0.267418	+	0.463181i
$283$	1.85823	−	10.5385i	0.110460	−	0.626450i	−0.878438	−	0.477856i	$-0.841414\pi$
$283$	1.85823	−	10.5385i	0.110460	−	0.626450i	0.988898	−	0.148594i	$-0.0474748\pi$
$284$	−10.3975	+	8.72453i	−0.616977	+	0.517705i
$285$	3.56602	+	6.17654i	0.211233	+	0.365866i
$286$	12.8781	−	22.3055i	0.761497	−	1.31895i
$287$	−3.73667	−	21.1917i	−0.220568	−	1.25091i
$288$	−0.660805	−	1.14455i	−0.0389383	−	0.0674431i
$289$	9.85439	−	3.58671i	0.579670	−	0.210983i
$290$	7.53421			0.442424
$291$	7.78141	−	2.83220i	0.456155	−	0.166027i
$292$	1.84633	−	10.4711i	0.108049	−	0.612774i
$293$	−12.1255	−	10.1745i	−0.708377	−	0.594399i	0.215766	−	0.976445i	$-0.430775\pi$
$293$	−12.1255	−	10.1745i	−0.708377	−	0.594399i	−0.924143	+	0.382046i	$0.875220\pi$
$294$	−3.84104	+	3.22302i	−0.224014	+	0.187970i
$295$	−10.3839			−0.604575
$296$	−4.74316	−	3.80821i	−0.275690	−	0.221348i
$297$	34.1514			1.98167
$298$	−0.579886	+	0.486582i	−0.0335919	+	0.0281870i
$299$	1.80063	+	1.51090i	0.104133	+	0.0873778i
$300$	0.224966	−	1.27585i	0.0129884	−	0.0736610i
$301$	25.5684	−	9.30612i	1.47374	−	0.536396i
$302$	−23.2369			−1.33713
$303$	8.43646	−	3.07062i	0.484662	−	0.176403i
$304$	−2.75257	−	4.76758i	−0.157870	−	0.273440i
$305$	−2.19419	−	12.4439i	−0.125639	−	0.712533i
$306$	−1.68643	+	2.92099i	−0.0964070	+	0.166982i
$307$	−5.25100	−	9.09500i	−0.299690	−	0.519079i	0.676375	−	0.736558i	$-0.263550\pi$
$307$	−5.25100	−	9.09500i	−0.299690	−	0.519079i	−0.976065	+	0.217479i	$0.930217\pi$
$308$	−15.4061	+	12.9272i	−0.877842	+	0.736597i
$309$	−1.36334	+	7.73191i	−0.0775579	+	0.439853i
$310$	−5.09926	+	8.83218i	−0.289619	+	0.501634i
$311$	2.30390	+	0.838551i	0.130642	+	0.0475499i	0.406514	−	0.913645i	$-0.366744\pi$
$311$	2.30390	+	0.838551i	0.130642	+	0.0475499i	−0.275872	+	0.961194i	$0.588967\pi$
$312$	−5.14040	−	1.87095i	−0.291018	−	0.105922i
$313$	−3.47438	−	19.7042i	−0.196384	−	1.11375i	−0.910434	−	0.413654i	$-0.864252\pi$
$313$	−3.47438	−	19.7042i	−0.196384	−	1.11375i	0.714051	−	0.700094i	$-0.246859\pi$
$314$	−2.60237	−	2.18365i	−0.146860	−	0.123230i
$315$	3.33794	+	2.80086i	0.188072	+	0.157811i
$316$	−2.29470	−	13.0139i	−0.129087	−	0.732088i
$317$	−0.167221	−	0.0608635i	−0.00939207	−	0.00341843i	0.337320	−	0.941390i	$-0.390480\pi$
$317$	−0.167221	−	0.0608635i	−0.00939207	−	0.00341843i	−0.346712	+	0.937972i	$0.612702\pi$
$318$	2.34856	+	0.854804i	0.131700	+	0.0479350i
$319$	22.9786	−	39.8002i	1.28656	−	2.22838i
$320$	−0.173648	+	0.984808i	−0.00970723	+	0.0550524i
$321$	−4.10849	+	3.44743i	−0.229314	+	0.192417i
$322$	−0.917691	−	1.58949i	−0.0511409	−	0.0885786i
$323$	−7.02480	+	12.1673i	−0.390870	+	0.677007i
$324$	−0.571046	−	3.23856i	−0.0317248	−	0.179920i
$325$	2.11123	+	3.65675i	0.117110	+	0.202840i
$326$	−12.5829	+	4.57981i	−0.696904	+	0.253652i
$327$	−11.3281			−0.626445
$328$	−6.13308	+	2.23226i	−0.338642	+	0.123256i
$329$	−3.96908	+	22.5098i	−0.218822	+	1.24100i
$330$	−6.05365	−	5.07961i	−0.333242	−	0.279623i
$331$	−13.6574	+	11.4599i	−0.750676	+	0.629892i	−0.935682	−	0.352845i	$-0.885214\pi$
$331$	−13.6574	+	11.4599i	−0.750676	+	0.629892i	0.185005	+	0.982738i	$0.440770\pi$
$332$	6.75156			0.370540
$333$	4.16918	+	6.87343i	0.228470	+	0.376661i
$334$	9.71606			0.531639
$335$	7.08765	−	5.94725i	0.387240	−	0.324933i
$336$	3.27207	+	2.74559i	0.178506	+	0.149784i
$337$	−3.45928	+	19.6185i	−0.188439	+	1.06869i	0.733018	+	0.680209i	$0.238111\pi$
$337$	−3.45928	+	19.6185i	−0.188439	+	1.06869i	−0.921457	+	0.388480i	$0.873000\pi$
$338$	4.53786	−	1.65165i	0.246827	−	0.0898377i
$339$	14.0969			0.765636
$340$	2.39818	−	0.872867i	0.130060	−	0.0473379i
$341$	31.1046	+	53.8747i	1.68441	+	2.91748i
$342$	1.26340	+	7.16510i	0.0683169	+	0.387444i
$343$	5.15928	−	8.93614i	0.278575	−	0.482506i
$344$	−4.12634	−	7.14704i	−0.222478	−	0.385342i
$345$	0.552466	−	0.463574i	0.0297438	−	0.0249580i
$346$	0.701008	−	3.97562i	0.0376864	−	0.213730i
$347$	1.98438	−	3.43705i	0.106527	−	0.184510i	−0.807834	−	0.589410i	$-0.799360\pi$
$347$	1.98438	−	3.43705i	0.106527	−	0.184510i	0.914361	+	0.404900i	$0.132694\pi$
$348$	−9.17213	−	3.33838i	−0.491678	−	0.178956i
$349$	−11.3965	−	4.14800i	−0.610043	−	0.222037i	0.0184793	−	0.999829i	$-0.494118\pi$
$349$	−11.3965	−	4.14800i	−0.610043	−	0.222037i	−0.628522	+	0.777792i	$0.716340\pi$
$350$	−0.572521	−	3.24693i	−0.0306026	−	0.173556i
$351$	18.1097	+	15.1958i	0.966623	+	0.811093i
$352$	4.67273	+	3.92088i	0.249057	+	0.208984i
$353$	−4.03124	−	22.8623i	−0.214561	−	1.21684i	−0.881666	−	0.471873i	$-0.843578\pi$
$353$	−4.03124	−	22.8623i	−0.214561	−	1.21684i	0.667105	−	0.744963i	$-0.267533\pi$
$354$	12.6414	+	4.60108i	0.671880	+	0.244544i
$355$	−12.7544	−	4.64222i	−0.676934	−	0.246384i
$356$	−0.162878	+	0.282113i	−0.00863253	+	0.0149520i
$357$	1.89293	−	10.7353i	0.100184	−	0.568174i
$358$	7.18562	−	6.02945i	0.379772	−	0.318666i
$359$	13.7426	+	23.8029i	0.725306	+	1.25627i	0.958848	+	0.283920i	$0.0916351\pi$
$359$	13.7426	+	23.8029i	0.725306	+	1.25627i	−0.233542	+	0.972347i	$0.575032\pi$
$360$	0.660805	−	1.14455i	0.0348275	−	0.0603229i
$361$	1.96335	+	11.1347i	0.103334	+	0.586037i
$362$	0.189694	+	0.328559i	0.00997008	+	0.0172687i
$363$	−31.9052	+	11.6125i	−1.67459	+	0.609500i
$364$	−13.9215			−0.729685
$365$	9.99139	−	3.63657i	0.522973	−	0.190347i
$366$	−2.84263	+	16.1214i	−0.148587	+	0.842677i
$367$	11.8958	+	9.98173i	0.620954	+	0.521042i	0.898103	−	0.439785i	$-0.144945\pi$
$367$	11.8958	+	9.98173i	0.620954	+	0.521042i	−0.277149	+	0.960827i	$0.589390\pi$
$368$	−0.426441	+	0.357826i	−0.0222298	+	0.0186530i
$369$	8.62572			0.449037
$370$	0.926427	−	6.01180i	0.0481626	−	0.312539i
$371$	6.36048			0.330220
$372$	10.1213	−	8.49281i	0.524767	−	0.440332i
$373$	−13.6323	−	11.4389i	−0.705854	−	0.592282i	0.217578	−	0.976043i	$-0.430184\pi$
$373$	−13.6323	−	11.4389i	−0.705854	−	0.592282i	−0.923432	+	0.383761i	$0.874629\pi$
$374$	2.70323	−	15.3308i	0.139781	−	0.792736i
$375$	1.21740	−	0.443096i	0.0628661	−	0.0228814i
$376$	6.93263			0.357523
$377$	29.8943	−	10.8806i	1.53963	−	0.560381i
$378$	−9.22961	−	15.9862i	−0.474720	−	0.822239i
$379$	0.589157	+	3.34127i	0.0302629	+	0.171630i	0.996193	−	0.0871728i	$-0.0277832\pi$
$379$	0.589157	+	3.34127i	0.0302629	+	0.171630i	−0.965930	+	0.258802i	$0.916672\pi$
$380$	2.75257	−	4.76758i	0.141204	−	0.244572i
$381$	−0.404583	−	0.700758i	−0.0207274	−	0.0359009i
$382$	−12.3798	+	10.3879i	−0.633406	+	0.531491i
$383$	−3.26690	+	18.5275i	−0.166931	+	0.946713i	0.780120	+	0.625630i	$0.215158\pi$
$383$	−3.26690	+	18.5275i	−0.166931	+	0.946713i	−0.947051	+	0.321083i	$0.895953\pi$
$384$	0.647764	−	1.12196i	0.0330560	−	0.0572548i
$385$	−18.8983	−	6.87843i	−0.963149	−	0.350558i
$386$	18.5718	+	6.75957i	0.945278	+	0.344053i
$387$	1.89395	+	10.7411i	0.0962749	+	0.546002i
$388$	−4.89644	−	4.10860i	−0.248579	−	0.208582i
$389$	−19.2778	−	16.1760i	−0.977421	−	0.820154i	0.00627731	−	0.999980i	$-0.498002\pi$
$389$	−19.2778	−	16.1760i	−0.977421	−	0.820154i	−0.983698	+	0.179827i	$0.942446\pi$
$390$	−0.949908	−	5.38719i	−0.0481004	−	0.272791i
$391$	1.33502	+	0.485907i	0.0675147	+	0.0245734i
$392$	3.63693	+	1.32373i	0.183692	+	0.0668586i
$393$	8.99596	−	15.5815i	0.453786	−	0.785981i
$394$	2.53667	−	14.3862i	0.127795	−	0.724764i
$395$	10.1230	−	8.49421i	0.509344	−	0.427390i
$396$	−4.03078	−	6.98152i	−0.202555	−	0.350835i
$397$	−9.26899	+	16.0544i	−0.465197	+	0.805745i	−0.999210	−	0.0397309i	$-0.987350\pi$
$397$	−9.26899	+	16.0544i	−0.465197	+	0.805745i	0.534013	+	0.845476i	$0.320683\pi$
$398$	−0.597557	−	3.38892i	−0.0299528	−	0.169871i
$399$	−11.7573	−	20.3642i	−0.588599	−	1.01948i
$400$	−0.939693	+	0.342020i	−0.0469846	+	0.0171010i
$401$	18.7379			0.935726			0.467863	−	0.883801i	$-0.345024\pi$
$401$	18.7379			0.935726			0.467863	+	0.883801i	$0.345024\pi$
$402$	−11.2637	+	4.09965i	−0.561782	+	0.204472i
$403$	−7.47777	+	42.4086i	−0.372494	+	2.11252i
$404$	−5.30862	−	4.45446i	−0.264114	−	0.221618i
$405$	2.51915	−	2.11382i	0.125178	−	0.105037i
$406$	−24.8404			−1.23281
$407$	−28.9324	−	23.2294i	−1.43412	−	1.15144i
$408$	−3.30630			−0.163686
$409$	24.6671	−	20.6982i	1.21971	−	1.02346i	0.220870	−	0.975303i	$-0.429110\pi$
$409$	24.6671	−	20.6982i	1.21971	−	1.02346i	0.998840	−	0.0481551i	$-0.0153342\pi$
$410$	−4.99973	−	4.19527i	−0.246919	−	0.207190i
$411$	0.370330	−	2.10024i	0.0182670	−	0.103597i
$412$	5.69475	−	2.07272i	0.280560	−	0.102115i
$413$	34.2360			1.68464
$414$	0.691343	−	0.251628i	0.0339777	−	0.0123669i
$415$	3.37578	+	5.84702i	0.165711	+	0.287019i
$416$	0.733221	+	4.15830i	0.0359491	+	0.203878i
$417$	−3.92791	+	6.80334i	−0.192351	+	0.333161i
$418$	−16.7901	−	29.0814i	−0.821232	−	1.42242i
$419$	−19.5042	+	16.3660i	−0.952845	+	0.799532i	−0.979774	−	0.200106i	$-0.935871\pi$
$419$	−19.5042	+	16.3660i	−0.952845	+	0.799532i	0.0269295	+	0.999637i	$0.491427\pi$
$420$	−0.741717	+	4.20649i	−0.0361921	+	0.205256i
$421$	9.10071	−	15.7629i	0.443541	−	0.768236i	−0.554408	−	0.832245i	$-0.687055\pi$
$421$	9.10071	−	15.7629i	0.443541	−	0.768236i	0.997949	+	0.0640087i	$0.0203885\pi$
$422$	−12.9317	−	4.70675i	−0.629505	−	0.229121i
$423$	−8.60967	−	3.13366i	−0.418617	−	0.152364i
$424$	−0.334995	−	1.89985i	−0.0162688	−	0.0922650i
$425$	1.95502	+	1.64045i	0.0948322	+	0.0795737i
$426$	13.4702	+	11.3029i	0.652635	+	0.547625i
$427$	7.23428	+	41.0276i	0.350091	+	1.98547i
$428$	3.89016	+	1.41590i	0.188038	+	0.0684403i
$429$	−31.3555	−	11.4125i	−1.51386	−	0.550999i
$430$	4.12634	−	7.14704i	0.198990	−	0.344661i
$431$	−3.14758	+	17.8508i	−0.151614	+	0.859844i	0.810203	+	0.586149i	$0.199357\pi$
$431$	−3.14758	+	17.8508i	−0.151614	+	0.859844i	−0.961817	+	0.273694i	$0.911754\pi$
$432$	−4.28890	+	3.59882i	−0.206350	+	0.173148i
$433$	12.9553	+	22.4392i	0.622591	+	1.07836i	0.989001	+	0.147906i	$0.0472532\pi$
$433$	12.9553	+	22.4392i	0.622591	+	1.07836i	−0.366411	+	0.930453i	$0.619413\pi$
$434$	16.8124	−	29.1199i	0.807020	−	1.39780i
$435$	−1.69494	−	9.61249i	−0.0812662	−	0.460884i
$436$	4.37200	+	7.57253i	0.209381	+	0.362658i
$437$	2.87977	−	1.04815i	0.137758	−	0.0501399i
$438$	−13.7748			−0.658188
$439$	2.93078	−	1.06672i	0.139878	−	0.0509116i	−0.271132	−	0.962542i	$-0.587398\pi$
$439$	2.93078	−	1.06672i	0.139878	−	0.0509116i	0.411011	+	0.911630i	$0.365176\pi$
$440$	−1.05922	+	6.00714i	−0.0504964	+	0.286379i
$441$	−3.91837	−	3.28790i	−0.186589	−	0.156567i
$442$	8.25496	−	6.92673i	0.392648	−	0.329471i
$443$	−10.3028			−0.489500			−0.244750	−	0.969586i	$-0.578706\pi$
$443$	−10.3028			−0.489500			−0.244750	+	0.969586i	$0.578706\pi$
$444$	−3.79164	+	6.90825i	−0.179943	+	0.327851i
$445$	−0.325757			−0.0154423
$446$	−3.42108	+	2.87062i	−0.161993	+	0.135928i
$447$	0.751258	+	0.630380i	0.0355333	+	0.0298160i
$448$	0.572521	−	3.24693i	0.0270491	−	0.153403i
$449$	6.14163	−	2.23537i	0.289841	−	0.105494i	−0.193008	−	0.981197i	$-0.561824\pi$
$449$	6.14163	−	2.23537i	0.289841	−	0.105494i	0.482849	+	0.875704i	$0.339602\pi$
$450$	1.32161			0.0623013
$451$	−37.4106	+	13.6164i	−1.76160	+	0.641169i
$452$	−5.44059	−	9.42337i	−0.255904	−	0.443238i
$453$	5.22752	+	29.6467i	0.245610	+	1.39292i
$454$	−11.3939	+	19.7349i	−0.534744	+	0.926203i
$455$	−6.96075	−	12.0564i	−0.326325	−	0.565212i
$456$	−5.46347	+	4.58439i	−0.255850	+	0.214684i
$457$	3.69210	−	20.9389i	0.172709	−	0.979483i	−0.768046	−	0.640395i	$-0.778771\pi$
$457$	3.69210	−	20.9389i	0.172709	−	0.979483i	0.940755	−	0.339088i	$-0.110118\pi$
$458$	1.81168	−	3.13792i	0.0846543	−	0.146626i
$459$	13.4269	+	4.88697i	0.626712	+	0.228104i
$460$	−0.523107	−	0.190395i	−0.0243900	−	0.00887723i
$461$	0.496095	+	2.81349i	0.0231054	+	0.131037i	0.994179	−	0.107745i	$-0.0343629\pi$
$461$	0.496095	+	2.81349i	0.0231054	+	0.131037i	−0.971073	+	0.238782i	$0.923252\pi$
$462$	19.9590	+	16.7476i	0.928576	+	0.779168i
$463$	−10.6399	−	8.92794i	−0.494478	−	0.414916i	0.361150	−	0.932508i	$-0.382384\pi$
$463$	−10.6399	−	8.92794i	−0.494478	−	0.414916i	−0.855628	+	0.517591i	$0.826829\pi$
$464$	1.30830	+	7.41975i	0.0607364	+	0.344453i
$465$	12.4157	+	4.51893i	0.575762	+	0.209560i
$466$	−5.74988	−	2.09278i	−0.266358	−	0.0969463i
$467$	−11.3503	+	19.6593i	−0.525229	+	0.909723i	0.474339	+	0.880342i	$0.342687\pi$
$467$	−11.3503	+	19.6593i	−0.525229	+	0.909723i	−0.999568	+	0.0293810i	$0.990646\pi$
$468$	0.969032	−	5.49565i	0.0447935	−	0.254037i
$469$	−23.3681	+	19.6082i	−1.07904	+	0.905422i
$470$	3.46631	+	6.00383i	0.159889	+	0.276936i
$471$	−2.20055	+	3.81147i	−0.101396	+	0.175623i
$472$	−1.80315	−	10.2262i	−0.0829966	−	0.470697i
$473$	−25.1699	−	43.5956i	−1.15731	−	2.00453i
$474$	−16.0875	+	5.85536i	−0.738922	+	0.268946i
$475$	5.50513			0.252593
$476$	−7.90685	+	2.87786i	−0.362410	+	0.131906i
$477$	−0.442733	+	2.51086i	−0.0202713	+	0.114965i
$478$	14.8711	+	12.4783i	0.680188	+	0.570745i
$479$	−4.12926	+	3.46486i	−0.188671	+	0.158314i	−0.732230	−	0.681057i	$-0.761521\pi$
$479$	−4.12926	+	3.46486i	−0.188671	+	0.158314i	0.543560	+	0.839371i	$0.317076\pi$
$480$	1.29553			0.0591325
$481$	−5.00614	−	25.1916i	−0.228260	−	1.14864i
$482$	−1.60538			−0.0731229
$483$	−1.82149	+	1.52841i	−0.0828807	+	0.0695451i
$484$	20.0763	+	16.8460i	0.912558	+	0.765727i
$485$	1.10993	−	6.29474i	0.0503994	−	0.285829i
$486$	11.7799	−	4.28754i	0.534348	−	0.194487i
$487$	1.88797			0.0855521			0.0427760	−	0.999085i	$-0.486380\pi$
$487$	1.88797			0.0855521			0.0427760	+	0.999085i	$0.486380\pi$
$488$	11.8738	−	4.32171i	0.537501	−	0.195634i
$489$	8.67386	+	15.0236i	0.392246	+	0.679389i
$490$	0.672077	+	3.81154i	0.0303613	+	0.172188i
$491$	−3.11340	+	5.39256i	−0.140506	+	0.243363i	−0.927687	−	0.373358i	$-0.878206\pi$
$491$	−3.11340	+	5.39256i	−0.140506	+	0.243363i	0.787181	+	0.616721i	$0.211539\pi$
$492$	4.22775	+	7.32267i	0.190602	+	0.330132i
$493$	14.7295	−	12.3595i	0.663384	−	0.556645i
$494$	4.03648	−	22.8920i	0.181610	−	1.02996i
$495$	4.03078	−	6.98152i	0.181170	−	0.313796i
$496$	−9.58348	−	3.48810i	−0.430311	−	0.156620i
$497$	42.0515	+	15.3055i	1.88627	+	0.686546i
$498$	−1.51887	−	8.61395i	−0.0680622	−	0.386000i
$499$	11.8511	+	9.94429i	0.530530	+	0.445168i	0.868284	−	0.496067i	$-0.165223\pi$
$499$	11.8511	+	9.94429i	0.530530	+	0.445168i	−0.337754	+	0.941234i	$0.609667\pi$
$500$	−0.766044	−	0.642788i	−0.0342585	−	0.0287463i
$501$	−2.18578	−	12.3962i	−0.0976536	−	0.553821i
$502$	−13.5826	−	4.94366i	−0.606221	−	0.220646i
$503$	9.54886	+	3.47550i	0.425763	+	0.154965i	0.546009	−	0.837779i	$-0.316146\pi$
$503$	9.54886	+	3.47550i	0.425763	+	0.154965i	−0.120247	+	0.992744i	$0.538369\pi$
$504$	−2.17869	+	3.77359i	−0.0970464	+	0.168089i
$505$	1.20337	−	6.82463i	0.0535491	−	0.303692i
$506$	−2.60121	+	2.18267i	−0.115638	+	0.0970317i
$507$	−3.12811	−	5.41805i	−0.138924	−	0.240624i
$508$	−0.312292	+	0.540906i	−0.0138557	+	0.0239988i
$509$	−3.60501	−	20.4450i	−0.159789	−	0.906210i	−0.954276	−	0.298928i	$-0.903371\pi$
$509$	−3.60501	−	20.4450i	−0.159789	−	0.906210i	0.794486	−	0.607282i	$-0.207740\pi$
$510$	−1.65315	−	2.86334i	−0.0732028	−	0.126791i
$511$	−32.9418	+	11.9898i	−1.45726	+	0.530399i
$512$	−1.00000			−0.0441942
$513$	28.9631	−	10.5417i	1.27875	−	0.465428i
$514$	0.477653	−	2.70890i	0.0210684	−	0.119485i
$515$	4.64240	+	3.89544i	0.204569	+	0.171653i
$516$	−8.19023	+	6.87242i	−0.360555	+	0.302541i
$517$	42.2877			1.85981
$518$	−3.05445	+	19.8210i	−0.134205	+	0.870886i
$519$	−5.22997			−0.229570
$520$	−3.23459	+	2.71414i	−0.141846	+	0.119023i
$521$	−4.52845	−	3.79982i	−0.198395	−	0.166473i	0.538178	−	0.842831i	$-0.319113\pi$
$521$	−4.52845	−	3.79982i	−0.198395	−	0.166473i	−0.736573	+	0.676358i	$0.763557\pi$
$522$	1.72906	−	9.80601i	0.0756791	−	0.429197i
$523$	−6.84693	+	2.49208i	−0.299395	+	0.108971i	−0.487350	−	0.873207i	$-0.662036\pi$
$523$	−6.84693	+	2.49208i	−0.299395	+	0.108971i	0.187955	+	0.982178i	$0.439814\pi$
$524$	−13.8877			−0.606688
$525$	−4.01378	+	1.46090i	−0.175176	+	0.0637588i
$526$	10.2990	+	17.8385i	0.449059	+	0.777794i
$527$	4.51964	+	25.6322i	0.196879	+	1.11655i
$528$	3.95124	−	6.84374i	0.171955	−	0.297836i
$529$	11.3451	+	19.6502i	0.493263	+	0.854357i
$530$	1.47782	−	1.24004i	0.0641925	−	0.0538639i
$531$	−2.38306	+	13.5150i	−0.103416	+	0.586501i
$532$	−9.07526	+	15.7188i	−0.393463	+	0.681497i
$533$	−25.8966	−	9.42560i	−1.12171	−	0.408268i
$534$	0.396575	+	0.144342i	0.0171615	+	0.00624627i
$535$	0.718873	+	4.07693i	0.0310796	+	0.176261i
$536$	7.08765	+	5.94725i	0.306140	+	0.256882i
$537$	−9.30916	−	7.81131i	−0.401720	−	0.337083i
$538$	0.544464	+	3.08781i	0.0234735	+	0.133125i
$539$	22.1846	+	8.07452i	0.955557	+	0.347794i
$540$	−5.26112	−	1.91489i	−0.226402	−	0.0824037i
$541$	−5.64065	+	9.76989i	−0.242510	+	0.420040i	−0.961429	−	0.275054i	$-0.911304\pi$
$541$	−5.64065	+	9.76989i	−0.242510	+	0.420040i	0.718918	+	0.695095i	$0.244638\pi$
$542$	4.79987	−	27.2214i	0.206172	−	1.16926i
$543$	0.376516	−	0.315934i	0.0161578	−	0.0135580i
$544$	1.27605	+	2.21018i	0.0547100	+	0.0947605i
$545$	−4.37200	+	7.57253i	−0.187276	+	0.324372i
$546$	3.13186	+	17.7617i	0.134031	+	0.760130i
$547$	−0.997292	−	1.72736i	−0.0426411	−	0.0738566i	0.843917	−	0.536474i	$-0.180244\pi$
$547$	−0.997292	−	1.72736i	−0.0426411	−	0.0738566i	−0.886558	+	0.462617i	$0.846911\pi$
$548$	−1.54688	+	0.563019i	−0.0660796	+	0.0240510i
$549$	−16.6996			−0.712723
$550$	−5.73195	+	2.08626i	−0.244411	+	0.0889584i
$551$	7.20238	−	40.8467i	0.306832	−	1.74013i
$552$	0.552466	+	0.463574i	0.0235145	+	0.0197310i
$553$	−33.3758	+	28.0056i	−1.41928	+	1.19092i
$554$	24.9760			1.06113
$555$	−7.87854	+	0.170473i	−0.334425	+	0.00723617i
$556$	6.06381			0.257163
$557$	9.24650	−	7.75874i	0.391787	−	0.328748i	−0.425522	−	0.904948i	$-0.639909\pi$
$557$	9.24650	−	7.75874i	0.391787	−	0.328748i	0.817309	+	0.576200i	$0.195465\pi$
$558$	10.3251	+	8.66379i	0.437097	+	0.366768i
$559$	6.05104	−	34.3172i	0.255932	−	1.45146i
$560$	3.09818	−	1.12765i	0.130922	−	0.0476518i
$561$	−20.1678			−0.851487
$562$	10.2449	−	3.72885i	0.432156	−	0.157292i
$563$	−5.66797	−	9.81721i	−0.238876	−	0.413746i	0.721516	−	0.692398i	$-0.243446\pi$
$563$	−5.66797	−	9.81721i	−0.238876	−	0.413746i	−0.960392	+	0.278652i	$0.910112\pi$
$564$	−1.55960	−	8.84496i	−0.0656712	−	0.372440i
$565$	5.44059	−	9.42337i	0.228887	−	0.396444i
$566$	5.35055	+	9.26742i	0.224900	+	0.389539i
$567$	−8.30570	+	6.96931i	−0.348807	+	0.292683i
$568$	2.35692	−	13.3668i	0.0988941	−	0.560856i
$569$	−15.7679	+	27.3108i	−0.661024	+	1.14493i	0.319323	+	0.947646i	$0.396544\pi$
$569$	−15.7679	+	27.3108i	−0.661024	+	1.14493i	−0.980347	+	0.197281i	$0.936789\pi$
$570$	−6.70193	−	2.43930i	−0.280713	−	0.102171i
$571$	−0.754725	−	0.274697i	−0.0315843	−	0.0114957i	0.326180	−	0.945308i	$-0.394239\pi$
$571$	−0.754725	−	0.274697i	−0.0315843	−	0.0114957i	−0.357764	+	0.933812i	$0.616461\pi$
$572$	4.47251	+	25.3649i	0.187005	+	1.06056i
$573$	16.0384	+	13.4578i	0.670013	+	0.562208i
$574$	16.4842	+	13.8319i	0.688037	+	0.577332i
$575$	−0.0966663	−	0.548222i	−0.00403126	−	0.0228624i
$576$	1.24191	+	0.452017i	0.0517461	+	0.0188340i
$577$	−33.1919	−	12.0809i	−1.38180	−	0.502933i	−0.459074	−	0.888398i	$-0.651819\pi$
$577$	−33.1919	−	12.0809i	−1.38180	−	0.502933i	−0.922722	+	0.385466i	$0.874041\pi$
$578$	−5.24341	+	9.08186i	−0.218097	+	0.377756i
$579$	4.44615	−	25.2154i	0.184776	−	1.04792i
$580$	−5.77154	+	4.84290i	−0.239650	+	0.201090i
$581$	−11.1300	−	19.2777i	−0.461751	−	0.799776i
$582$	−4.14040	+	7.17139i	−0.171625	+	0.297264i
$583$	−2.04341	−	11.5887i	−0.0846293	−	0.479957i
$584$	5.31631	+	9.20812i	0.219990	+	0.381035i
$585$	5.24389	−	1.90862i	0.216808	−	0.0789117i
$586$	15.8287			0.653876
$587$	14.6445	−	5.33016i	0.604443	−	0.219999i	−0.0216271	−	0.999766i	$-0.506885\pi$
$587$	14.6445	−	5.33016i	0.604443	−	0.219999i	0.626070	+	0.779767i	$0.284662\pi$
$588$	0.870694	−	4.93795i	0.0359068	−	0.203638i
$589$	43.0090	+	36.0888i	1.77215	+	1.48701i
$590$	7.95454	−	6.67465i	0.327483	−	0.274791i
$591$	−18.9252			−0.778478
$592$	6.08134	−	0.131586i	0.249941	−	0.00540814i
$593$	6.04145			0.248092			0.124046	−	0.992276i	$-0.460413\pi$
$593$	6.04145			0.248092			0.124046	+	0.992276i	$0.460413\pi$
$594$	−26.1615	+	21.9521i	−1.07342	+	0.900705i
$595$	−6.44572	−	5.40861i	−0.264249	−	0.221731i
$596$	0.131450	−	0.745487i	0.00538438	−	0.0305363i
$597$	−4.18930	+	1.52478i	−0.171457	+	0.0624052i
$598$	−2.35055			−0.0961211
$599$	−3.96215	+	1.44211i	−0.161889	+	0.0589229i	−0.421693	−	0.906738i	$-0.638564\pi$
$599$	−3.96215	+	1.44211i	−0.161889	+	0.0589229i	0.259804	+	0.965661i	$0.416342\pi$
$600$	0.647764	+	1.12196i	0.0264448	+	0.0458038i
$601$	−1.02321	−	5.80290i	−0.0417375	−	0.236705i	0.956801	−	0.290742i	$-0.0939022\pi$
$601$	−1.02321	−	5.80290i	−0.0417375	−	0.236705i	−0.998539	+	0.0540370i	$0.982791\pi$
$602$	−13.6046	+	23.5639i	−0.554484	+	0.960394i
$603$	−6.11394	−	10.5897i	−0.248979	−	0.431244i
$604$	17.8005	−	14.9364i	0.724293	−	0.607754i
$605$	−4.55092	+	25.8096i	−0.185021	+	1.04931i
$606$	−4.48895	+	7.77508i	−0.182351	+	0.315841i
$607$	30.3644	+	11.0518i	1.23245	+	0.448577i	0.874438	−	0.485138i	$-0.161231\pi$
$607$	30.3644	+	11.0518i	1.23245	+	0.448577i	0.358017	+	0.933715i	$0.383453\pi$
$608$	5.17313	+	1.88287i	0.209798	+	0.0763603i
$609$	5.58825	+	31.6926i	0.226447	+	1.28425i
$610$	9.67960	+	8.12215i	0.391916	+	0.328856i
$611$	22.4242	+	18.8161i	0.907185	+	0.761219i
$612$	−0.585692	−	3.32163i	−0.0236752	−	0.134269i
$613$	44.6739	+	16.2600i	1.80436	+	0.656734i	0.997852	+	0.0655142i	$0.0208688\pi$
$613$	44.6739	+	16.2600i	1.80436	+	0.656734i	0.806510	+	0.591220i	$0.201353\pi$
$614$	9.86865	+	3.59190i	0.398266	+	0.144957i
$615$	−4.22775	+	7.32267i	−0.170479	+	0.295279i
$616$	3.49227	−	19.8057i	0.140708	−	0.797993i
$617$	2.87911	−	2.41586i	0.115909	−	0.0972590i	−0.582991	−	0.812479i	$-0.698118\pi$
$617$	2.87911	−	2.41586i	0.115909	−	0.0972590i	0.698900	+	0.715220i	$0.253673\pi$
$618$	−3.92559	−	6.79932i	−0.157910	−	0.273509i
$619$	−2.31932	+	4.01718i	−0.0932213	+	0.161464i	−0.908865	−	0.417091i	$-0.863050\pi$
$619$	−2.31932	+	4.01718i	−0.0932213	+	0.161464i	0.815644	+	0.578555i	$0.196383\pi$
$620$	−1.77096	−	10.0436i	−0.0711233	−	0.403360i
$621$	−1.55836	−	2.69915i	−0.0625347	−	0.108313i
$622$	−2.30390	+	0.838551i	−0.0923780	+	0.0336228i
$623$	1.07403			0.0430299
$624$	5.14040	−	1.87095i	0.205781	−	0.0748981i
$625$	0.173648	−	0.984808i	0.00694593	−	0.0393923i
$626$	15.3272	+	12.8610i	0.612596	+	0.514029i
$627$	−33.3261	+	27.9639i	−1.33092	+	1.11677i
$628$	3.39715			0.135561
$629$	−8.05090	−	13.2729i	−0.321010	−	0.529226i
$630$	−4.35737			−0.173602
$631$	−7.39879	+	6.20832i	−0.294541	+	0.247150i	−0.778068	−	0.628180i	$-0.783800\pi$
$631$	−7.39879	+	6.20832i	−0.294541	+	0.247150i	0.483527	+	0.875330i	$0.339356\pi$
$632$	10.1230	+	8.49421i	0.402672	+	0.337882i
$633$	−3.09590	+	17.5577i	−0.123051	+	0.697856i
$634$	0.167221	−	0.0608635i	0.00664119	−	0.00241720i
$635$	−0.624584			−0.0247859
$636$	−2.34856	+	0.854804i	−0.0931263	+	0.0338952i
$637$	8.17115	+	14.1528i	0.323753	+	0.560756i
$638$	7.98040	+	45.2591i	0.315947	+	1.79182i
$639$	−8.96907	+	15.5349i	−0.354811	+	0.614551i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	10.1284	−	8.49877i	0.400049	−	0.335681i	−0.420464	−	0.907309i	$-0.638133\pi$
$641$	10.1284	−	8.49877i	0.400049	−	0.335681i	0.820513	+	0.571628i	$0.193688\pi$
$642$	0.931319	−	5.28177i	0.0367562	−	0.208455i
$643$	−8.26898	+	14.3223i	−0.326097	+	0.564816i	−0.981734	−	0.190260i	$-0.939067\pi$
$643$	−8.26898	+	14.3223i	−0.326097	+	0.564816i	0.655637	+	0.755076i	$0.272400\pi$
$644$	1.72469	+	0.627737i	0.0679625	+	0.0247363i
$645$	−10.0468	−	3.65674i	−0.395592	−	0.143984i
$646$	−2.43969	−	13.8362i	−0.0959882	−	0.544376i
$647$	−5.84064	−	4.90088i	−0.229619	−	0.192673i	0.520718	−	0.853729i	$-0.325664\pi$
$647$	−5.84064	−	4.90088i	−0.229619	−	0.192673i	−0.750337	+	0.661055i	$0.770109\pi$
$648$	2.51915	+	2.11382i	0.0989617	+	0.0830387i
$649$	−10.9989	−	62.3777i	−0.431743	−	2.44854i
$650$	−3.96781	−	1.44416i	−0.155630	−	0.0566447i
$651$	−40.9347	−	14.8990i	−1.60436	−	0.583938i
$652$	6.69524	−	11.5965i	0.262206	−	0.454154i
$653$	2.41595	−	13.7015i	0.0945435	−	0.536183i	−0.900343	−	0.435181i	$-0.856684\pi$
$653$	2.41595	−	13.7015i	0.0945435	−	0.536183i	0.994886	−	0.101001i	$-0.0322046\pi$
$654$	8.67783	−	7.28156i	0.339330	−	0.284732i
$655$	−6.94386	−	12.0271i	−0.271319	−	0.469938i
$656$	3.26334	−	5.65227i	0.127412	−	0.220684i
$657$	−2.44013	−	13.8387i	−0.0951986	−	0.539898i
$658$	−11.4285	−	19.7947i	−0.445529	−	0.771680i
$659$	21.6929	−	7.89559i	0.845037	−	0.307568i	0.117022	−	0.993129i	$-0.462665\pi$
$659$	21.6929	−	7.89559i	0.845037	−	0.307568i	0.728015	+	0.685561i	$0.240443\pi$
$660$	7.90247			0.307603
$661$	−4.35395	+	1.58471i	−0.169349	+	0.0616380i	−0.425303	−	0.905051i	$-0.639833\pi$
$661$	−4.35395	+	1.58471i	−0.169349	+	0.0616380i	0.255954	+	0.966689i	$0.417610\pi$
$662$	3.09587	−	17.5576i	0.120324	−	0.682394i
$663$	−10.6945	−	8.97377i	−0.415341	−	0.348512i
$664$	−5.17200	+	4.33982i	−0.200712	+	0.168418i
$665$	−18.1505			−0.703847
$666$	−7.61193	−	2.58545i	−0.294956	−	0.100184i
$667$	−4.19414			−0.162398
$668$	−7.44294	+	6.24537i	−0.287976	+	0.241640i
$669$	4.43210	+	3.71897i	0.171355	+	0.143784i
$670$	−1.60664	+	9.11171i	−0.0620699	+	0.352016i
$671$	72.4279	−	26.3616i	2.79605	−	1.01768i
$672$	−4.27138			−0.164772
$673$	15.4928	−	5.63891i	0.597203	−	0.217364i	−0.0256917	−	0.999670i	$-0.508179\pi$
$673$	15.4928	−	5.63891i	0.597203	−	0.217364i	0.622894	+	0.782306i	$0.285957\pi$
$674$	−9.96059	−	17.2522i	−0.383667	−	0.664532i
$675$	−0.972215	−	5.51370i	−0.0374206	−	0.212223i
$676$	−2.41455	+	4.18212i	−0.0928672	+	0.160851i
$677$	11.5427	+	19.9925i	0.443621	+	0.768374i	0.997955	−	0.0639204i	$-0.0203604\pi$
$677$	11.5427	+	19.9925i	0.443621	+	0.768374i	−0.554334	+	0.832294i	$0.687027\pi$
$678$	−10.7988	+	9.06128i	−0.414726	+	0.347997i
$679$	−3.65947	+	20.7539i	−0.140437	+	0.796460i
$680$	−1.27605	+	2.21018i	−0.0489341	+	0.0847564i
$681$	27.7419	+	10.0972i	1.06307	+	0.386926i
$682$	−58.4574	−	21.2768i	−2.23845	−	0.814730i
$683$	−1.86489	−	10.5763i	−0.0713582	−	0.404692i	−0.999475	−	0.0324030i	$-0.989684\pi$
$683$	−1.86489	−	10.5763i	−0.0713582	−	0.404692i	0.928117	−	0.372289i	$-0.121427\pi$
$684$	−5.57346	−	4.67669i	−0.213107	−	0.178818i
$685$	−1.26103	−	1.05813i	−0.0481815	−	0.0404291i
$686$	1.79180	+	10.1618i	0.0684112	+	0.387979i
$687$	−4.41107	−	1.60550i	−0.168293	−	0.0612536i
$688$	7.75499	+	2.82259i	0.295656	+	0.107610i
$689$	4.07289	−	7.05446i	0.155165	−	0.268753i
$690$	−0.125234	+	0.710236i	−0.00476757	+	0.0270382i
$691$	−21.8881	+	18.3663i	−0.832661	+	0.698686i	−0.955900	−	0.293691i	$-0.905116\pi$
$691$	−21.8881	+	18.3663i	−0.832661	+	0.698686i	0.123239	+	0.992377i	$0.460672\pi$
$692$	2.01847	+	3.49610i	0.0767308	+	0.132902i
$693$	−13.2896	+	23.0182i	−0.504829	+	0.874390i
$694$	0.689168	+	3.90847i	0.0261605	+	0.148363i
$695$	3.03190	+	5.25141i	0.115007	+	0.199197i
$696$	9.17213	−	3.33838i	0.347669	−	0.126541i
$697$	−16.6567			−0.630917
$698$	11.3965	−	4.14800i	0.431365	−	0.157004i
$699$	−1.37654	+	7.80676i	−0.0520656	+	0.295279i
$700$	2.52566	+	2.11928i	0.0954611	+	0.0801014i
$701$	0.435309	−	0.365267i	0.0164414	−	0.0137960i	−0.634530	−	0.772898i	$-0.718806\pi$
$701$	0.435309	−	0.365267i	0.0164414	−	0.0137960i	0.650971	+	0.759102i	$0.274362\pi$
$702$	−23.6405			−0.892253
$703$	−31.7073	−	10.7696i	−1.19586	−	0.406185i
$704$	−6.09981			−0.229895
$705$	6.88016	−	5.77314i	0.259122	−	0.217429i
$706$	17.7837	+	14.9223i	0.669298	+	0.561608i
$707$	−3.96752	+	22.5009i	−0.149214	+	0.846235i
$708$	−12.6414	+	4.60108i	−0.475091	+	0.172919i
$709$	−34.5935			−1.29919			−0.649593	−	0.760282i	$-0.725061\pi$
$709$	−34.5935			−1.29919			−0.649593	+	0.760282i	$0.725061\pi$
$710$	12.7544	−	4.64222i	0.478664	−	0.174220i
$711$	−8.73230	−	15.1248i	−0.327487	−	0.567224i
$712$	−0.0565670	−	0.320808i	−0.00211994	−	0.0120228i
$713$	2.83865	−	4.91669i	0.106308	−	0.184132i
$714$	5.45047	+	9.44050i	0.203979	+	0.353302i
$715$	−19.7304	+	16.5557i	−0.737874	+	0.619150i
$716$	−1.62885	+	9.23765i	−0.0608729	+	0.345227i
$717$	12.5749	−	21.7804i	0.469619	−	0.813404i
$718$	−25.8276	−	9.40048i	−0.963878	−	0.350823i
$719$	−12.4063	−	4.51554i	−0.462678	−	0.168401i	0.100155	−	0.994972i	$-0.468066\pi$
$719$	−12.4063	−	4.51554i	−0.462678	−	0.168401i	−0.562833	+	0.826571i	$0.690288\pi$
$720$	0.229495	+	1.30153i	0.00855277	+	0.0485052i
$721$	−15.3061	−	12.8433i	−0.570028	−	0.478310i
$722$	−8.66127	−	7.26767i	−0.322339	−	0.270475i
$723$	0.361155	+	2.04821i	0.0134315	+	0.0761738i
$724$	−0.356507	−	0.129758i	−0.0132495	−	0.00482242i
$725$	−7.07984	−	2.57685i	−0.262939	−	0.0957019i
$726$	16.9764	−	29.4040i	0.630053	−	1.09128i
$727$	0.408180	−	2.31491i	0.0151386	−	0.0858551i	−0.976302	−	0.216411i	$-0.930565\pi$
$727$	0.408180	−	2.31491i	0.0151386	−	0.0858551i	0.991441	+	0.130556i	$0.0416761\pi$
$728$	10.6645	−	8.94857i	0.395252	−	0.331656i
$729$	−13.0531	−	22.6086i	−0.483448	−	0.837356i
$730$	−5.31631	+	9.20812i	−0.196765	+	0.340808i
$731$	−3.65731	−	20.7416i	−0.135271	−	0.767158i
$732$	−8.18503	−	14.1769i	−0.302527	−	0.523993i
$733$	38.9863	−	14.1898i	1.43999	−	0.524114i	0.500213	−	0.865902i	$-0.333255\pi$
$733$	38.9863	−	14.1898i	1.43999	−	0.524114i	0.939777	+	0.341789i	$0.111033\pi$
$734$	−15.5288			−0.573179
$735$	4.71174	−	1.71493i	0.173795	−	0.0632562i
$736$	0.0966663	−	0.548222i	0.00356317	−	0.0202077i
$737$	43.2333	+	36.2771i	1.59252	+	1.33628i
$738$	−6.60769	+	5.54451i	−0.243232	+	0.204096i
$739$	32.5303			1.19665			0.598323	−	0.801255i	$-0.295834\pi$
$739$	32.5303			1.19665			0.598323	+	0.801255i	$0.295834\pi$
$740$	3.15463	+	5.20080i	0.115966	+	0.191185i
$741$	−30.1147			−1.10629
$742$	−4.87241	+	4.08844i	−0.178872	+	0.150091i
$743$	−34.7529	−	29.1611i	−1.27496	−	1.06982i	−0.993918	−	0.110123i	$-0.964876\pi$
$743$	−34.7529	−	29.1611i	−1.27496	−	1.06982i	−0.281042	−	0.959696i	$-0.590680\pi$
$744$	−2.29432	+	13.0117i	−0.0841139	+	0.477034i
$745$	0.711336	−	0.258905i	0.0260613	−	0.00948554i
$746$	17.7957			0.651547
$747$	8.38481	−	3.05182i	0.306784	−	0.111660i
$748$	7.78364	+	13.4817i	0.284598	+	0.492938i
$749$	−2.37014	−	13.4417i	−0.0866029	−	0.491150i
$750$	−0.647764	+	1.12196i	−0.0236530	+	0.0409682i
$751$	−6.36217	−	11.0196i	−0.232159	−	0.402111i	0.726284	−	0.687395i	$-0.241246\pi$
$751$	−6.36217	−	11.0196i	−0.232159	−	0.402111i	−0.958443	+	0.285283i	$0.907912\pi$
$752$	−5.31070	+	4.45621i	−0.193661	+	0.162501i
$753$	−3.25173	+	18.4414i	−0.118499	+	0.672044i
$754$	−15.9064	+	27.5507i	−0.579278	+	1.00334i
$755$	21.8356	+	7.94749i	0.794677	+	0.289239i
$756$	17.3460	+	6.31343i	0.630868	+	0.229617i
$757$	−3.08192	−	17.4785i	−0.112014	−	0.635265i	−0.988185	−	0.153265i	$-0.951021\pi$
$757$	−3.08192	−	17.4785i	−0.112014	−	0.635265i	0.876171	−	0.482001i	$-0.160090\pi$
$758$	−2.59905	−	2.18086i	−0.0944017	−	0.0792125i
$759$	3.36994	+	2.82771i	0.122321	+	0.102639i
$760$	0.955956	+	5.42150i	0.0346762	+	0.196658i
$761$	3.64593	+	1.32701i	0.132165	+	0.0481041i	0.407256	−	0.913314i	$-0.366486\pi$
$761$	3.64593	+	1.32701i	0.132165	+	0.0481041i	−0.275091	+	0.961418i	$0.588708\pi$
$762$	0.760367	+	0.276751i	0.0275452	+	0.0100256i
$763$	14.4146	−	24.9668i	0.521843	−	0.903858i
$764$	2.80627	−	15.9152i	0.101527	−	0.575791i
$765$	2.58377	−	2.16804i	0.0934163	−	0.0783856i
$766$	−9.40668	−	16.2928i	−0.339877	−	0.588684i
$767$	21.9228	−	37.9714i	0.791586	−	1.37107i
$768$	0.224966	+	1.27585i	0.00811776	+	0.0460381i
$769$	−10.9823	−	19.0220i	−0.396033	−	0.685949i	0.597199	−	0.802093i	$-0.296280\pi$
$769$	−10.9823	−	19.0220i	−0.396033	−	0.685949i	−0.993232	+	0.116144i	$0.962947\pi$
$770$	18.8983	−	6.87843i	0.681049	−	0.247882i
$771$	−3.56360			−0.128340
$772$	−18.5718	+	6.75957i	−0.668412	+	0.243282i
$773$	2.92910	−	16.6118i	0.105352	−	0.597483i	−0.885727	−	0.464207i	$-0.846339\pi$
$773$	2.92910	−	16.6118i	0.105352	−	0.597483i	0.991079	−	0.133276i	$-0.0425497\pi$
$774$	−8.35512	−	7.01078i	−0.300318	−	0.251997i
$775$	7.81253	−	6.55549i	0.280634	−	0.235480i
$776$	6.39184			0.229454
$777$	25.9757	−	0.562052i	0.931873	−	0.0201635i
$778$	25.1653			0.902221
$779$	−27.5242	+	23.0955i	−0.986156	+	0.827483i
$780$	4.19049	+	3.51624i	0.150044	+	0.125902i
$781$	14.3768	−	81.5347i	0.514441	−	2.91754i
$782$	−1.33502	+	0.485907i	−0.0477401	+	0.0173760i
$783$	−42.1823			−1.50747
$784$	−3.63693	+	1.32373i	−0.129890	+	0.0472762i
$785$	1.69858	+	2.94202i	0.0606248	+	0.105005i
$786$	3.12426	+	17.7186i	0.111439	+	0.632001i
$787$	−9.83114	+	17.0280i	−0.350442	+	0.606984i	−0.986327	−	0.164800i	$-0.947302\pi$
$787$	−9.83114	+	17.0280i	−0.350442	+	0.606984i	0.635885	+	0.771784i	$0.280635\pi$
$788$	7.30404	+	12.6510i	0.260196	+	0.450672i
$789$	20.4422	−	17.1530i	0.727761	−	0.610664i
$790$	−2.29470	+	13.0139i	−0.0816418	+	0.463013i
$791$	−17.9377	+	31.0690i	−0.637792	+	1.10469i
$792$	7.57540	+	2.75722i	0.269180	+	0.0979735i
$793$	50.1365	+	18.2482i	1.78040	+	0.648012i
$794$	−3.21909	−	18.2563i	−0.114241	−	0.647893i
$795$	−1.91456	−	1.60651i	−0.0679024	−	0.0569769i
$796$	2.63611	+	2.21196i	0.0934344	+	0.0784008i
$797$	−2.16585	−	12.2831i	−0.0767182	−	0.435091i	−0.998838	−	0.0481869i	$-0.984656\pi$
$797$	−2.16585	−	12.2831i	−0.0767182	−	0.435091i	0.922120	−	0.386904i	$-0.126455\pi$
$798$	22.0964	+	8.04243i	0.782204	+	0.284699i
$799$	16.6257	+	6.05126i	0.588175	+	0.214078i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−0.0747595	+	0.423982i	−0.00264150	+	0.0149807i
$802$	−14.3541	+	12.0445i	−0.506860	+	0.425306i
$803$	32.4285	+	56.1678i	1.14438	+	1.98212i
$804$	5.99329	−	10.3807i	0.211367	−	0.366098i
$805$	0.318711	+	1.80750i	0.0112331	+	0.0637059i
$806$	−21.5314	−	37.2935i	−0.758411	−	1.31361i
$807$	3.81708	−	1.38930i	0.134368	−	0.0489058i
$808$	6.92991			0.243794
$809$	−1.43536	+	0.522427i	−0.0504644	+	0.0183676i	−0.367129	−	0.930170i	$-0.619659\pi$
$809$	−1.43536	+	0.522427i	−0.0504644	+	0.0183676i	0.316665	+	0.948538i	$0.397437\pi$
$810$	−0.571046	+	3.23856i	−0.0200645	+	0.113791i
$811$	−30.9475	−	25.9681i	−1.08671	−	0.911862i	−0.0902540	−	0.995919i	$-0.528768\pi$
$811$	−30.9475	−	25.9681i	−1.08671	−	0.911862i	−0.996461	+	0.0840567i	$0.973212\pi$
$812$	19.0289	−	15.9671i	0.667783	−	0.560336i
$813$	−35.8101			−1.25591
$814$	37.0950	−	0.802648i	1.30018	−	0.0281328i
$815$	13.3905			0.469048
$816$	2.53278	−	2.12525i	0.0886649	−	0.0743987i
$817$	−34.8030	−	29.2032i	−1.21760	−	1.02169i
$818$	−5.59158	+	31.7114i	−0.195505	+	1.10876i
$819$	−17.2892	+	6.29275i	−0.604134	+	0.219887i
$820$	6.52668			0.227922
$821$	−27.8369	+	10.1318i	−0.971515	+	0.353602i	−0.778536	−	0.627600i	$-0.784037\pi$
$821$	−27.8369	+	10.1318i	−0.971515	+	0.353602i	−0.192979	+	0.981203i	$0.561815\pi$
$822$	1.06632	+	1.84692i	0.0371922	+	0.0644188i
$823$	7.38206	+	41.8657i	0.257322	+	1.45935i	0.790040	+	0.613055i	$0.210060\pi$
$823$	7.38206	+	41.8657i	0.257322	+	1.45935i	−0.532718	+	0.846293i	$0.678829\pi$
$824$	−3.03011	+	5.24831i	−0.105559	+	0.182833i
$825$	3.95124	+	6.84374i	0.137564	+	0.238269i
$826$	−26.2263	+	22.0065i	−0.912529	+	0.765703i
$827$	3.49535	−	19.8231i	0.121545	−	0.689316i	−0.861755	−	0.507325i	$-0.830635\pi$
$827$	3.49535	−	19.8231i	0.121545	−	0.689316i	0.983300	−	0.181992i	$-0.0582544\pi$
$828$	−0.367856	+	0.637145i	−0.0127839	+	0.0221423i
$829$	−37.3352	−	13.5889i	−1.29671	−	0.471962i	−0.400784	−	0.916173i	$-0.631262\pi$
$829$	−37.3352	−	13.5889i	−1.29671	−	0.471962i	−0.895923	+	0.444210i	$0.853484\pi$
$830$	−6.34439	−	2.30917i	−0.220217	−	0.0801525i
$831$	−5.61876	−	31.8656i	−0.194913	−	1.10540i
$832$	−3.23459	−	2.71414i	−0.112139	−	0.0940958i
$833$	7.56657	+	6.34910i	0.262166	+	0.219983i
$834$	−1.36415	−	7.73648i	−0.0472366	−	0.267892i
$835$	−9.13011	−	3.32309i	−0.315961	−	0.115000i
$836$	31.5551	+	11.4851i	1.09136	+	0.397222i
$837$	28.5496	−	49.4493i	0.986817	−	1.70922i
$838$	4.42125	−	25.0742i	0.152730	−	0.866173i
$839$	−6.61289	+	5.54887i	−0.228302	+	0.191568i	−0.749762	−	0.661708i	$-0.769832\pi$
$839$	−6.61289	+	5.54887i	−0.228302	+	0.191568i	0.521460	+	0.853276i	$0.325388\pi$
$840$	−2.13569	−	3.69912i	−0.0736883	−	0.127632i
$841$	−13.8822	+	24.0446i	−0.478696	+	0.829125i
$842$	3.16064	+	17.9249i	0.108923	+	0.617733i
$843$	−7.06219	−	12.2321i	−0.243235	−	0.421295i
$844$	12.9317	−	4.70675i	0.445127	−	0.162013i
$845$	−4.82909			−0.166126
$846$	8.60967	−	3.13366i	0.296007	−	0.107738i
$847$	15.0045	−	85.0946i	0.515560	−	2.92389i
$848$	1.47782	+	1.24004i	0.0507487	+	0.0425832i
$849$	10.6201	−	8.91132i	0.364481	−	0.305836i
$850$	−2.55209			−0.0875360
$851$	−0.515722	+	3.34664i	−0.0176787	+	0.114721i
$852$	−17.5841			−0.602422
$853$	8.99408	−	7.54693i	0.307952	−	0.258402i	−0.475693	−	0.879611i	$-0.657803\pi$
$853$	8.99408	−	7.54693i	0.307952	−	0.258402i	0.783645	+	0.621209i	$0.213358\pi$
$854$	−31.9138	−	26.7789i	−1.09207	−	0.916355i
$855$	1.26340	−	7.16510i	0.0432074	−	0.245041i
$856$	−3.89016	+	1.41590i	−0.132963	+	0.0483946i
$857$	−54.2984			−1.85480			−0.927398	−	0.374076i	$-0.877960\pi$
$857$	−54.2984			−1.85480			−0.927398	+	0.374076i	$0.877960\pi$
$858$	31.3555	−	11.4125i	1.07046	−	0.389615i
$859$	14.9542	+	25.9014i	0.510230	+	0.883744i	0.999930	+	0.0118527i	$0.00377291\pi$
$859$	14.9542	+	25.9014i	0.510230	+	0.883744i	−0.489700	+	0.871891i	$0.662894\pi$
$860$	1.43306	+	8.12731i	0.0488671	+	0.277139i
$861$	13.9390	−	24.1430i	0.475039	−	0.822791i
$862$	−9.06310	−	15.6977i	−0.308690	−	0.534667i
$863$	−0.215220	+	0.180591i	−0.00732619	+	0.00614740i	−0.646443	−	0.762962i	$-0.723744\pi$
$863$	−0.215220	+	0.180591i	−0.00732619	+	0.00614740i	0.639117	+	0.769109i	$0.279300\pi$
$864$	0.972215	−	5.51370i	0.0330754	−	0.187580i
$865$	−2.01847	+	3.49610i	−0.0686301	+	0.118871i
$866$	−24.3480	−	8.86193i	−0.827377	−	0.301141i
$867$	12.7666	+	4.64668i	0.433578	+	0.157809i
$868$	5.83887	+	33.1139i	0.198184	+	1.12396i
$869$	61.7485	+	51.8131i	2.09467	+	1.75764i
$870$	7.47719	+	6.27411i	0.253500	+	0.212712i
$871$	6.78396	+	38.4737i	0.229866	+	1.30363i
$872$	−8.21668	−	2.99063i	−0.278252	−	0.101275i
$873$	−7.93807	−	2.88922i	−0.268663	−	0.0977854i
$874$	−1.53230	+	2.65401i	−0.0518307	+	0.0897734i
$875$	−0.572521	+	3.24693i	−0.0193548	+	0.109766i
$876$	10.5521	−	8.85430i	0.356524	−	0.299159i
$877$	16.3065	+	28.2437i	0.550632	+	0.953723i	0.998229	+	0.0594877i	$0.0189467\pi$
$877$	16.3065	+	28.2437i	0.550632	+	0.953723i	−0.447597	+	0.894236i	$0.647720\pi$
$878$	−1.55944	+	2.70102i	−0.0526284	+	0.0911551i
$879$	−3.56091	−	20.1949i	−0.120107	−	0.681158i
$880$	−3.04991	−	5.28259i	−0.102812	−	0.178076i
$881$	−11.0296	+	4.01446i	−0.371598	+	0.135251i	−0.521067	−	0.853516i	$-0.674466\pi$
$881$	−11.0296	+	4.01446i	−0.371598	+	0.135251i	0.149469	+	0.988766i	$0.452244\pi$
$882$	5.11507			0.172233
$883$	−1.12672	+	0.410093i	−0.0379172	+	0.0138007i	−0.360909	−	0.932601i	$-0.617534\pi$
$883$	−1.12672	+	0.410093i	−0.0379172	+	0.0138007i	0.322992	+	0.946402i	$0.395311\pi$
$884$	−1.87125	+	10.6124i	−0.0629369	+	0.356933i
$885$	−10.3053	−	8.64719i	−0.346410	−	0.290672i
$886$	7.89238	−	6.62250i	0.265150	−	0.222487i
$887$	−13.5867			−0.456198			−0.228099	−	0.973638i	$-0.573251\pi$
$887$	−13.5867			−0.456198			−0.228099	+	0.973638i	$0.573251\pi$
$888$	−1.53598	−	7.72925i	−0.0515440	−	0.259376i
$889$	2.05927			0.0690656
$890$	0.249544	−	0.209392i	0.00836473	−	0.00701884i
$891$	15.3664	+	12.8939i	0.514793	+	0.431962i
$892$	0.775495	−	4.39805i	0.0259655	−	0.147258i
$893$	35.8634	−	13.0532i	1.20012	−	0.436809i
$894$	−0.980698			−0.0327994
$895$	−8.81446	+	3.20820i	−0.294635	+	0.107238i
$896$	1.64851	+	2.85530i	0.0550728	+	0.0953890i
$897$	0.528794	+	2.99894i	0.0176559	+	0.100132i
$898$	−3.26789	+	5.66015i	−0.109051	+	0.188882i
$899$	−38.4189	−	66.5436i	−1.28134	−	2.21935i
$900$	−1.01241	+	0.849514i	−0.0337470	+	0.0283171i
$901$	0.854939	−	4.84860i	0.0284821	−	0.161530i
$902$	19.9058	−	34.4778i	0.662790	−	1.14799i
$903$	33.1245	+	12.0563i	1.10231	+	0.401210i
$904$	10.2250	+	3.72158i	0.340077	+	0.123778i
$905$	−0.0658799	−	0.373624i	−0.00218992	−	0.0124197i
$906$	−23.0610	−	19.3505i	−0.766152	−	0.642878i
$907$	34.7437	+	29.1535i	1.15365	+	0.968025i	0.999799	−	0.0200698i	$-0.00638885\pi$
$907$	34.7437	+	29.1535i	1.15365	+	0.968025i	0.153848	+	0.988094i	$0.450833\pi$
$908$	−3.95707	−	22.4417i	−0.131320	−	0.744753i
$909$	−8.60630	−	3.13244i	−0.285453	−	0.103896i
$910$	13.0819	+	4.76143i	0.433662	+	0.157840i
$911$	−2.92636	+	5.06860i	−0.0969545	+	0.167930i	−0.910423	−	0.413679i	$-0.864243\pi$
$911$	−2.92636	+	5.06860i	−0.0969545	+	0.167930i	0.813468	+	0.581609i	$0.197577\pi$
$912$	1.23847	−	7.02370i	0.0410097	−	0.232578i
$913$	−31.5482	+	26.4721i	−1.04409	+	0.876098i
$914$	10.6310	+	18.4134i	0.351642	+	0.609061i
$915$	8.18503	−	14.1769i	0.270589	−	0.468673i
$916$	0.629190	+	3.56832i	0.0207890	+	0.117900i
$917$	22.8940	+	39.6536i	0.756028	+	1.30948i
$918$	−13.4269	+	4.88697i	−0.443152	+	0.161294i
$919$	25.9845			0.857150			0.428575	−	0.903506i	$-0.359016\pi$
$919$	25.9845			0.857150			0.428575	+	0.903506i	$0.359016\pi$
$920$	0.523107	−	0.190395i	0.0172463	−	0.00627715i
$921$	2.36259	−	13.3989i	0.0778501	−	0.441510i
$922$	−2.18851	−	1.83638i	−0.0720747	−	0.0604778i
$923$	43.9029	−	36.8389i	1.44508	−	1.21257i
$924$	−26.0546			−0.857134
$925$	−2.92671	+	5.33239i	−0.0962297	+	0.175328i
$926$	13.8894			0.456434
$927$	6.13544	−	5.14824i	0.201514	−	0.169091i
$928$	−5.77154	−	4.84290i	−0.189460	−	0.158976i
$929$	−4.94237	+	28.0296i	−0.162154	+	0.919621i	0.789797	+	0.613369i	$0.210186\pi$
$929$	−4.94237	+	28.0296i	−0.162154	+	0.919621i	−0.951951	+	0.306252i	$0.900925\pi$
$930$	−12.4157	+	4.51893i	−0.407126	+	0.148182i
$931$	21.3067			0.698299
$932$	5.74988	−	2.09278i	0.188343	−	0.0685514i
$933$	1.58816	+	2.75077i	0.0519940	+	0.0900563i
$934$	−3.94191	−	22.3557i	−0.128983	−	0.731501i
$935$	−7.78364	+	13.4817i	−0.254552	+	0.440897i
$936$	2.79022	+	4.83279i	0.0912010	+	0.157965i
$937$	−27.0541	+	22.7011i	−0.883819	+	0.741612i	−0.966961	−	0.254925i	$-0.917949\pi$
$937$	−27.0541	+	22.7011i	−0.883819	+	0.741612i	0.0831415	+	0.996538i	$0.473505\pi$
$938$	5.29712	−	30.0415i	0.172957	−	0.980889i
$939$	12.9606	−	22.4484i	0.422952	−	0.732575i
$940$	−6.51454	−	2.37110i	−0.212481	−	0.0773367i
$941$	−9.82655	−	3.57657i	−0.320336	−	0.116593i	0.176847	−	0.984238i	$-0.443410\pi$
$941$	−9.82655	−	3.57657i	−0.320336	−	0.116593i	−0.497183	+	0.867645i	$0.665632\pi$
$942$	−0.764244	−	4.33424i	−0.0249004	−	0.141217i
$943$	2.78324	+	2.33542i	0.0906349	+	0.0760517i
$944$	7.95454	+	6.67465i	0.258898	+	0.217241i
$945$	3.20541	+	18.1788i	0.104272	+	0.591356i
$946$	47.3040	+	17.2172i	1.53799	+	0.559781i
$947$	−16.8175	−	6.12106i	−0.546494	−	0.198908i	0.0539938	−	0.998541i	$-0.482805\pi$
$947$	−16.8175	−	6.12106i	−0.546494	−	0.198908i	−0.600488	+	0.799634i	$0.705027\pi$
$948$	8.55997	−	14.8263i	0.278015	−	0.481536i
$949$	−7.79606	+	44.2136i	−0.253071	+	1.43524i
$950$	−4.21718	+	3.53863i	−0.136823	+	0.114808i
$951$	−0.115271	−	0.199656i	−0.00373793	−	0.00647429i
$952$	4.20715	−	7.28699i	0.136354	−	0.236173i
$953$	1.67293	+	9.48767i	0.0541916	+	0.307336i	0.999841	−	0.0178533i	$-0.00568319\pi$
$953$	1.67293	+	9.48767i	0.0541916	+	0.307336i	−0.945649	+	0.325189i	$0.894572\pi$
$954$	−1.27480	−	2.20802i	−0.0412731	−	0.0714871i
$955$	15.1861	−	5.52728i	0.491410	−	0.178859i
$956$	−19.4128			−0.627856
$957$	55.9483	−	20.3635i	1.80855	−	0.658259i
$958$	0.936028	−	5.30848i	0.0302417	−	0.171509i
$959$	4.15764	+	3.48868i	0.134257	+	0.112655i
$960$	−0.992431	+	0.832749i	−0.0320306	+	0.0268769i
$961$	73.0100			2.35516
$962$	20.0278	+	16.0800i	0.645721	+	0.518439i
$963$	5.47123			0.176308
$964$	1.22979	−	1.03192i	0.0396089	−	0.0332358i
$965$	−15.1398	−	12.7038i	−0.487369	−	0.408951i
$966$	0.412898	−	2.34166i	0.0132848	−	0.0753418i
$967$	−41.3511	+	15.0506i	−1.32976	+	0.483993i	−0.906573	−	0.422049i	$-0.861311\pi$
$967$	−41.3511	+	15.0506i	−1.32976	+	0.483993i	−0.423188	+	0.906042i	$0.639089\pi$
$968$	−26.2077			−0.842348
$969$	−17.1040	+	6.22533i	−0.549458	+	0.199986i
$970$	3.19592	+	5.53550i	0.102615	+	0.177734i
$971$	−9.14214	−	51.8476i	−0.293385	−	1.66387i	−0.673694	−	0.739010i	$-0.735293\pi$
$971$	−9.14214	−	51.8476i	−0.293385	−	1.66387i	0.380309	−	0.924860i	$-0.375818\pi$
$972$	−6.26796	+	10.8564i	−0.201045	+	0.348220i
$973$	−9.99624	−	17.3140i	−0.320465	−	0.555061i
$974$	−1.44627	+	1.21356i	−0.0463414	+	0.0388851i
$975$	−0.949908	+	5.38719i	−0.0304214	+	0.172528i
$976$	−6.31791	+	10.9429i	−0.202231	+	0.350275i
$977$	−28.1439	−	10.2435i	−0.900402	−	0.327720i	−0.149988	−	0.988688i	$-0.547924\pi$
$977$	−28.1439	−	10.2435i	−0.900402	−	0.327720i	−0.750414	+	0.660968i	$0.770146\pi$
$978$	−16.3015	−	5.93327i	−0.521265	−	0.189725i
$979$	−0.345048	−	1.95687i	−0.0110278	−	0.0625417i
$980$	−2.96485	−	2.48780i	−0.0947086	−	0.0794700i
$981$	8.85253	+	7.42816i	0.282640	+	0.237163i
$982$	−1.08127	−	6.13220i	−0.0345048	−	0.195686i
$983$	−27.6044	−	10.0472i	−0.880445	−	0.320456i	−0.138055	−	0.990424i	$-0.544085\pi$
$983$	−27.6044	−	10.0472i	−0.880445	−	0.320456i	−0.742389	+	0.669969i	$0.766307\pi$
$984$	−7.94557	−	2.89195i	−0.253295	−	0.0921920i
$985$	−7.30404	+	12.6510i	−0.232726	+	0.403094i
$986$	−3.33891	+	18.9359i	−0.106332	+	0.603041i
$987$	−22.6840	+	19.0341i	−0.722040	+	0.605863i
$988$	11.6226	+	20.1309i	0.369763	+	0.640449i
$989$	−2.29705	+	3.97861i	−0.0730419	+	0.126512i
$990$	1.39988	+	7.93909i	0.0444910	+	0.252321i
$991$	−15.0402	−	26.0505i	−0.477769	−	0.827520i	0.521906	−	0.853003i	$-0.325221\pi$
$991$	−15.0402	−	26.0505i	−0.477769	−	0.827520i	−0.999675	+	0.0254826i	$0.991888\pi$
$992$	9.58348	−	3.48810i	0.304276	−	0.110747i
$993$	−23.0972			−0.732967
$994$	−42.0515	+	15.3055i	−1.33379	+	0.485461i
$995$	−0.597557	+	3.38892i	−0.0189438	+	0.107436i
$996$	6.70046	+	5.62235i	0.212312	+	0.178151i
$997$	−27.8394	+	23.3600i	−0.881682	+	0.739819i	−0.966524	−	0.256576i	$-0.917406\pi$
$997$	−27.8394	+	23.3600i	−0.881682	+	0.739819i	0.0848426	+	0.996394i	$0.472961\pi$
$998$	−15.4706			−0.489712
$999$	−5.18684	+	33.6586i	−0.164104	+	1.06491i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.o.b.271.3	yes	18
37.34	even	9	inner	370.2.o.b.71.3	✓	18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.o.b.71.3	✓	18	37.34	even	9	inner
370.2.o.b.271.3	yes	18	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.o (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.992431 + 0.832749i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -1.29553 q^{6} +(-3.09818 + 1.12765i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.229495 - 1.30153i) q^{9} +O(q^{10})\)	\(q+(-0.766044 + 0.642788i) q^{2} +(0.992431 + 0.832749i) q^{3} +(0.173648 - 0.984808i) q^{4} +(0.939693 - 0.342020i) q^{5} -1.29553 q^{6} +(-3.09818 + 1.12765i) q^{7} +(0.500000 + 0.866025i) q^{8} +(-0.229495 - 1.30153i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(3.04991 + 5.28259i) q^{11} +(0.992431 - 0.832749i) q^{12} +(-0.733221 + 4.15830i) q^{13} +(1.64851 - 2.85530i) q^{14} +(1.21740 + 0.443096i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(0.443166 + 2.51332i) q^{17} +(1.01241 + 0.849514i) q^{18} +(4.21718 + 3.53863i) q^{19} +(-0.173648 - 0.984808i) q^{20} +(-4.01378 - 1.46090i) q^{21} +(-5.73195 - 2.08626i) q^{22} +(0.278339 - 0.482098i) q^{23} +(-0.224966 + 1.27585i) q^{24} +(0.766044 - 0.642788i) q^{25} +(-2.11123 - 3.65675i) q^{26} +(2.79938 - 4.84867i) q^{27} +(0.572521 + 3.24693i) q^{28} +(-3.76711 - 6.52482i) q^{29} +(-1.21740 + 0.443096i) q^{30} +10.1985 q^{31} +(0.939693 - 0.342020i) q^{32} +(-1.37225 + 7.78242i) q^{33} +(-1.95502 - 1.64045i) q^{34} +(-2.52566 + 2.11928i) q^{35} -1.32161 q^{36} +(-5.66958 + 2.20359i) q^{37} -5.50513 q^{38} +(-4.19049 + 3.51624i) q^{39} +(0.766044 + 0.642788i) q^{40} +(-1.13335 + 6.42753i) q^{41} +(4.01378 - 1.46090i) q^{42} -8.25269 q^{43} +(5.73195 - 2.08626i) q^{44} +(-0.660805 - 1.14455i) q^{45} +(0.0966663 + 0.548222i) q^{46} +(3.46631 - 6.00383i) q^{47} +(-0.647764 - 1.12196i) q^{48} +(2.96485 - 2.48780i) q^{49} +(-0.173648 + 0.984808i) q^{50} +(-1.65315 + 2.86334i) q^{51} +(3.96781 + 1.44416i) q^{52} +(-1.81282 - 0.659812i) q^{53} +(0.972215 + 5.51370i) q^{54} +(4.67273 + 3.92088i) q^{55} +(-2.52566 - 2.11928i) q^{56} +(1.23847 + 7.02370i) q^{57} +(7.07984 + 2.57685i) q^{58} +(-9.75769 - 3.55151i) q^{59} +(0.647764 - 1.12196i) q^{60} +(2.19419 - 12.4439i) q^{61} +(-7.81253 + 6.55549i) q^{62} +(2.17869 + 3.77359i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.733221 + 4.15830i) q^{65} +(-3.95124 - 6.84374i) q^{66} +(8.69429 - 3.16446i) q^{67} +2.55209 q^{68} +(0.677700 - 0.246662i) q^{69} +(0.572521 - 3.24693i) q^{70} +(-10.3975 - 8.72453i) q^{71} +(1.01241 - 0.849514i) q^{72} +10.6326 q^{73} +(2.92671 - 5.33239i) q^{74} +1.29553 q^{75} +(4.21718 - 3.53863i) q^{76} +(-15.4061 - 12.9272i) q^{77} +(0.949908 - 5.38719i) q^{78} +(12.4177 - 4.51968i) q^{79} -1.00000 q^{80} +(3.09020 - 1.12474i) q^{81} +(-3.26334 - 5.65227i) q^{82} +(1.17240 + 6.64899i) q^{83} +(-2.13569 + 3.69912i) q^{84} +(1.27605 + 2.21018i) q^{85} +(6.32193 - 5.30473i) q^{86} +(1.69494 - 9.61249i) q^{87} +(-3.04991 + 5.28259i) q^{88} +(-0.306111 - 0.111415i) q^{89} +(1.24191 + 0.452017i) q^{90} +(-2.41744 - 13.7100i) q^{91} +(-0.426441 - 0.357826i) q^{92} +(10.1213 + 8.49281i) q^{93} +(1.20384 + 6.82730i) q^{94} +(5.17313 + 1.88287i) q^{95} +(1.21740 + 0.443096i) q^{96} +(3.19592 - 5.53550i) q^{97} +(-0.672077 + 3.81154i) q^{98} +(6.17552 - 5.18188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9}+O(q^{10}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9	\( 18 q + 6 q^{6} - 9 q^{7} + 9 q^{8} - 12 q^{9} - 9 q^{10} + 15 q^{11} + 3 q^{13} - 6 q^{14} + 6 q^{17} - 6 q^{18} - 3 q^{19} - 12 q^{21} - 12 q^{22} + 15 q^{23} + 6 q^{26} + 12 q^{27} + 9 q^{28} - 12 q^{29} + 54 q^{31} + 9 q^{33} + 3 q^{34} - 12 q^{37} - 24 q^{38} - 30 q^{39} + 15 q^{41} + 12 q^{42} - 60 q^{43} + 12 q^{44} - 6 q^{46} + 6 q^{47} + 3 q^{48} - 27 q^{49} - 6 q^{51} - 6 q^{52} + 12 q^{53} - 9 q^{54} + 6 q^{55} + 45 q^{57} + 3 q^{58} - 27 q^{59} - 3 q^{60} - 9 q^{62} + 18 q^{63} - 9 q^{64} - 3 q^{65} - 9 q^{66} - 54 q^{67} + 12 q^{68} - 6 q^{69} + 9 q^{70} + 36 q^{71} - 6 q^{72} - 6 q^{73} + 18 q^{74} - 6 q^{75} - 3 q^{76} - 24 q^{77} + 12 q^{78} + 12 q^{79} - 18 q^{80} - 6 q^{81} + 3 q^{82} - 15 q^{83} - 6 q^{84} + 6 q^{85} + 30 q^{87} - 15 q^{88} + 84 q^{89} + 6 q^{90} + 12 q^{91} - 12 q^{92} - 18 q^{93} + 36 q^{94} - 24 q^{95} - 9 q^{97} - 30 q^{99}+O(q^{100}) \) 18 * q + 6 * q^6 - 9 * q^7 + 9 * q^8 - 12 * q^9 - 9 * q^10 + 15 * q^11 + 3 * q^13 - 6 * q^14 + 6 * q^17 - 6 * q^18 - 3 * q^19 - 12 * q^21 - 12 * q^22 + 15 * q^23 + 6 * q^26 + 12 * q^27 + 9 * q^28 - 12 * q^29 + 54 * q^31 + 9 * q^33 + 3 * q^34 - 12 * q^37 - 24 * q^38 - 30 * q^39 + 15 * q^41 + 12 * q^42 - 60 * q^43 + 12 * q^44 - 6 * q^46 + 6 * q^47 + 3 * q^48 - 27 * q^49 - 6 * q^51 - 6 * q^52 + 12 * q^53 - 9 * q^54 + 6 * q^55 + 45 * q^57 + 3 * q^58 - 27 * q^59 - 3 * q^60 - 9 * q^62 + 18 * q^63 - 9 * q^64 - 3 * q^65 - 9 * q^66 - 54 * q^67 + 12 * q^68 - 6 * q^69 + 9 * q^70 + 36 * q^71 - 6 * q^72 - 6 * q^73 + 18 * q^74 - 6 * q^75 - 3 * q^76 - 24 * q^77 + 12 * q^78 + 12 * q^79 - 18 * q^80 - 6 * q^81 + 3 * q^82 - 15 * q^83 - 6 * q^84 + 6 * q^85 + 30 * q^87 - 15 * q^88 + 84 * q^89 + 6 * q^90 + 12 * q^91 - 12 * q^92 - 18 * q^93 + 36 * q^94 - 24 * q^95 - 9 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more