LMFDB - Embedded newform 418.2.s.a.107.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(107,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([9, 25]))

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

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

chi := DirichletCharacter("418.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.s (of order $30$, degree $8$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			107.8
Character	$\chi$	$=$	418.107
Dual form			418.2.s.a.293.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.913545 - 0.406737i) q^{2} +(1.34081 + 1.20727i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.264977 - 2.52108i) q^{5} +(-0.733850 - 1.64825i) q^{6} +(-0.512875 - 0.166643i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0266838 + 0.253879i) q^{9} +O(q^{10})$	\(q+(-0.913545 - 0.406737i) q^{2} +(1.34081 + 1.20727i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.264977 - 2.52108i) q^{5} +(-0.733850 - 1.64825i) q^{6} +(-0.512875 - 0.166643i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0266838 + 0.253879i) q^{9} +(-1.26749 + 2.19535i) q^{10} +(0.517100 - 3.27607i) q^{11} +1.80424i q^{12} +(-0.493939 - 4.69951i) q^{13} +(0.400755 + 0.360841i) q^{14} +(3.39892 - 3.06040i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(3.23708 + 0.340231i) q^{17} +(0.0788851 - 0.242783i) q^{18} +(-4.17914 + 1.23887i) q^{19} +(2.05083 - 1.49002i) q^{20} +(-0.486485 - 0.842616i) q^{21} +(-1.80489 + 2.78251i) q^{22} +(-1.23284 + 2.13533i) q^{23} +(0.733850 - 1.64825i) q^{24} +(-1.39491 - 0.296498i) q^{25} +(-1.46023 + 4.49412i) q^{26} +(2.91079 - 4.00636i) q^{27} +(-0.219340 - 0.492646i) q^{28} +(0.0492506 + 0.0546984i) q^{29} +(-4.34984 + 1.41335i) q^{30} +(5.75747 + 7.92448i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.64843 - 3.76830i) q^{33} +(-2.81884 - 1.62746i) q^{34} +(-0.556021 + 1.24884i) q^{35} +(-0.170814 + 0.189708i) q^{36} +(3.73695 + 1.21421i) q^{37} +(4.32173 + 0.568043i) q^{38} +(5.01131 - 6.89747i) q^{39} +(-2.47958 + 0.527050i) q^{40} +(4.98963 - 5.54154i) q^{41} +(0.101703 + 0.967639i) q^{42} +(-9.41201 + 5.43403i) q^{43} +(2.78060 - 1.80784i) q^{44} +0.647121 q^{45} +(1.99477 - 1.44929i) q^{46} +(7.42749 + 1.57876i) q^{47} +(-1.34081 + 1.20727i) q^{48} +(-5.42785 - 3.94356i) q^{49} +(1.15372 + 0.838227i) q^{50} +(3.92957 + 4.36423i) q^{51} +(3.16191 - 3.51165i) q^{52} +(2.58363 - 0.271550i) q^{53} +(-4.28867 + 2.47607i) q^{54} +(-8.12222 - 2.17173i) q^{55} +0.539269i q^{56} +(-7.09909 - 3.38426i) q^{57} +(-0.0227449 - 0.0700015i) q^{58} +(0.475455 + 2.23684i) q^{59} +(4.54864 + 0.478081i) q^{60} +(-0.611583 - 1.37364i) q^{61} +(-2.03653 - 9.58114i) q^{62} +(0.0286218 - 0.134655i) q^{63} +(-0.809017 + 0.587785i) q^{64} -11.9787 q^{65} +(-5.77926 + 1.55183i) q^{66} +(-10.9136 - 6.30094i) q^{67} +(1.91319 + 2.63328i) q^{68} +(-4.23093 + 1.37471i) q^{69} +(1.01590 - 0.914722i) q^{70} +(12.7019 + 1.33502i) q^{71} +(0.233208 - 0.103831i) q^{72} +(0.134766 + 0.634025i) q^{73} +(-2.92001 - 2.62919i) q^{74} +(-1.51236 - 2.08159i) q^{75} +(-3.71705 - 2.27674i) q^{76} +(-0.811141 + 1.59404i) q^{77} +(-7.38351 + 4.26287i) q^{78} +(0.0365000 + 0.0162509i) q^{79} +(2.47958 + 0.527050i) q^{80} +(9.48868 - 2.01688i) q^{81} +(-6.81220 + 3.03299i) q^{82} +(-7.63805 + 10.5129i) q^{83} +(0.300664 - 0.925349i) q^{84} +(1.71550 - 8.07081i) q^{85} +(10.8085 - 1.13602i) q^{86} +0.132799i q^{87} +(-3.27552 + 0.520569i) q^{88} +(7.16280 + 4.13544i) q^{89} +(-0.591174 - 0.263208i) q^{90} +(-0.529813 + 2.49257i) q^{91} +(-2.41179 + 0.512642i) q^{92} +(-1.84732 + 17.5760i) q^{93} +(-6.14321 - 4.46331i) q^{94} +(2.01593 + 10.8642i) q^{95} +(1.71593 - 0.557540i) q^{96} +(-4.60742 + 10.3484i) q^{97} +(3.35459 + 5.81033i) q^{98} +(0.845523 + 0.0438630i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) $ 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{3}{10}\right)$

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 $

$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$2$	−0.913545	−	0.406737i	−0.645974	−	0.287606i
$3$	1.34081	+	1.20727i	0.774117	+	0.697018i	0.958265	−	0.285880i	$-0.0922859\pi$
$3$	1.34081	+	1.20727i	0.774117	+	0.697018i	−0.184148	+	0.982899i	$0.558953\pi$
$4$	0.669131	+	0.743145i	0.334565	+	0.371572i
$5$	0.264977	−	2.52108i	0.118501	−	1.12746i	−0.760067	−	0.649845i	$-0.774834\pi$
$5$	0.264977	−	2.52108i	0.118501	−	1.12746i	0.878568	−	0.477618i	$-0.158500\pi$
$6$	−0.733850	−	1.64825i	−0.299593	−	0.672897i
$7$	−0.512875	−	0.166643i	−0.193848	−	0.0629852i	0.210484	−	0.977597i	$-0.432496\pi$
$7$	−0.512875	−	0.166643i	−0.193848	−	0.0629852i	−0.404332	+	0.914612i	$0.632496\pi$
$8$	−0.309017	−	0.951057i	−0.109254	−	0.336249i
$9$	0.0266838	+	0.253879i	0.00889459	+	0.0846264i
$10$	−1.26749	+	2.19535i	−0.400814	+	0.694230i
$11$	0.517100	−	3.27607i	0.155911	−	0.987771i
$11$	0.517100	−	3.27607i	0.155911	−	0.987771i
$12$			1.80424i			0.520839i
$13$	−0.493939	−	4.69951i	−0.136994	−	1.30341i	−0.819732	−	0.572747i	$-0.805878\pi$
$13$	−0.493939	−	4.69951i	−0.136994	−	1.30341i	0.682738	−	0.730663i	$-0.260789\pi$
$14$	0.400755	+	0.360841i	0.107106	+	0.0964388i
$15$	3.39892	−	3.06040i	0.877596	−	0.790191i
$16$	−0.104528	+	0.994522i	−0.0261321	+	0.248630i
$17$	3.23708	+	0.340231i	0.785108	+	0.0825182i	0.488595	−	0.872511i	$-0.337509\pi$
$17$	3.23708	+	0.340231i	0.785108	+	0.0825182i	0.296513	+	0.955029i	$0.404176\pi$
$18$	0.0788851	−	0.242783i	0.0185934	−	0.0572246i
$19$	−4.17914	+	1.23887i	−0.958760	+	0.284217i
$19$	−4.17914	+	1.23887i	−0.958760	+	0.284217i
$20$	2.05083	−	1.49002i	0.458581	−	0.333178i
$21$	−0.486485	−	0.842616i	−0.106160	−	0.183874i
$22$	−1.80489	+	2.78251i	−0.384804	+	0.593234i
$23$	−1.23284	+	2.13533i	−0.257064	+	0.445248i	−0.965454	−	0.260573i	$-0.916088\pi$
$23$	−1.23284	+	2.13533i	−0.257064	+	0.445248i	0.708390	+	0.705821i	$0.249422\pi$
$24$	0.733850	−	1.64825i	0.149797	−	0.336448i
$25$	−1.39491	−	0.296498i	−0.278983	−	0.0592996i
$26$	−1.46023	+	4.49412i	−0.286374	+	0.881369i
$27$	2.91079	−	4.00636i	0.560182	−	0.771025i
$28$	−0.219340	−	0.492646i	−0.0414514	−	0.0931014i
$29$	0.0492506	+	0.0546984i	0.00914561	+	0.0101572i	0.747700	−	0.664036i	$-0.231158\pi$
$29$	0.0492506	+	0.0546984i	0.00914561	+	0.0101572i	−0.738555	+	0.674194i	$0.764491\pi$
$30$	−4.34984	+	1.41335i	−0.794169	+	0.258041i
$31$	5.75747	+	7.92448i	1.03407	+	1.42328i	0.901846	+	0.432058i	$0.142213\pi$
$31$	5.75747	+	7.92448i	1.03407	+	1.42328i	0.132226	+	0.991220i	$0.457787\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	4.64843	−	3.76830i	0.809188	−	0.655978i
$34$	−2.81884	−	1.62746i	−0.483427	−	0.279107i
$35$	−0.556021	+	1.24884i	−0.0939847	+	0.211093i
$36$	−0.170814	+	0.189708i	−0.0284690	+	0.0316180i
$37$	3.73695	+	1.21421i	0.614351	+	0.199615i	0.599630	−	0.800277i	$-0.295314\pi$
$37$	3.73695	+	1.21421i	0.614351	+	0.199615i	0.0147201	+	0.999892i	$0.495314\pi$
$38$	4.32173	+	0.568043i	0.701077	+	0.0921487i
$39$	5.01131	−	6.89747i	0.802451	−	1.10448i
$40$	−2.47958	+	0.527050i	−0.392055	+	0.0833339i
$41$	4.98963	−	5.54154i	0.779249	−	0.865444i	−0.214541	−	0.976715i	$-0.568826\pi$
$41$	4.98963	−	5.54154i	0.779249	−	0.865444i	0.993790	+	0.111271i	$0.0354922\pi$
$42$	0.101703	+	0.967639i	0.0156931	+	0.149310i
$43$	−9.41201	+	5.43403i	−1.43532	+	0.828681i	−0.997519	−	0.0703918i	$-0.977575\pi$
$43$	−9.41201	+	5.43403i	−1.43532	+	0.828681i	−0.437799	+	0.899073i	$0.644242\pi$
$44$	2.78060	−	1.80784i	0.419191	−	0.272542i
$45$	0.647121			0.0964671
$46$	1.99477	−	1.44929i	0.294113	−	0.213685i
$47$	7.42749	+	1.57876i	1.08341	+	0.230286i	0.714822	−	0.699306i	$-0.246508\pi$
$47$	7.42749	+	1.57876i	1.08341	+	0.230286i	0.368589	+	0.929592i	$0.379841\pi$
$48$	−1.34081	+	1.20727i	−0.193529	+	0.174255i
$49$	−5.42785	−	3.94356i	−0.775407	−	0.563366i
$50$	1.15372	+	0.838227i	0.163161	+	0.118543i
$51$	3.92957	+	4.36423i	0.550249	+	0.611114i
$52$	3.16191	−	3.51165i	0.438478	−	0.486979i
$53$	2.58363	−	0.271550i	0.354889	−	0.0373003i	0.0745931	−	0.997214i	$-0.476234\pi$
$53$	2.58363	−	0.271550i	0.354889	−	0.0373003i	0.280296	+	0.959914i	$0.409568\pi$
$54$	−4.28867	+	2.47607i	−0.583615	+	0.336950i
$55$	−8.12222	−	2.17173i	−1.09520	−	0.292836i
$56$			0.539269i			0.0720628i
$57$	−7.09909	−	3.38426i	−0.940297	−	0.448256i
$58$	−0.0227449	−	0.0700015i	−0.00298655	−	0.00919165i
$59$	0.475455	+	2.23684i	0.0618989	+	0.291212i	0.998199	−	0.0599895i	$-0.0191067\pi$
$59$	0.475455	+	2.23684i	0.0618989	+	0.291212i	−0.936300	+	0.351201i	$0.885773\pi$
$60$	4.54864	+	0.478081i	0.587227	+	0.0617200i
$61$	−0.611583	−	1.37364i	−0.0783052	−	0.175876i	0.870151	−	0.492786i	$-0.164021\pi$
$61$	−0.611583	−	1.37364i	−0.0783052	−	0.175876i	−0.948456	+	0.316910i	$0.897355\pi$
$62$	−2.03653	−	9.58114i	−0.258640	−	1.21681i
$63$	0.0286218	−	0.134655i	0.00360600	−	0.0169649i
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−11.9787			−1.48578
$66$	−5.77926	+	1.55183i	−0.711378	+	0.191017i
$67$	−10.9136	−	6.30094i	−1.33330	−	0.769783i	−0.347499	−	0.937681i	$-0.612969\pi$
$67$	−10.9136	−	6.30094i	−1.33330	−	0.769783i	−0.985804	+	0.167898i	$0.946302\pi$
$68$	1.91319	+	2.63328i	0.232009	+	0.319332i
$69$	−4.23093	+	1.37471i	−0.509344	+	0.165496i
$70$	1.01590	−	0.914722i	0.121423	−	0.109330i
$71$	12.7019	+	1.33502i	1.50744	+	0.158438i	0.821915	−	0.569611i	$-0.192906\pi$
$71$	12.7019	+	1.33502i	1.50744	+	0.158438i	0.685525	+	0.728049i	$0.259573\pi$
$72$	0.233208	−	0.103831i	0.0274838	−	0.0122366i
$73$	0.134766	+	0.634025i	0.0157732	+	0.0742071i	0.985330	−	0.170659i	$-0.0545895\pi$
$73$	0.134766	+	0.634025i	0.0157732	+	0.0742071i	−0.969557	+	0.244866i	$0.921256\pi$
$74$	−2.92001	−	2.62919i	−0.339444	−	0.305637i
$75$	−1.51236	−	2.08159i	−0.174633	−	0.240361i
$76$	−3.71705	−	2.27674i	−0.426375	−	0.261160i
$77$	−0.811141	+	1.59404i	−0.0924381	+	0.181658i
$78$	−7.38351	+	4.26287i	−0.836018	+	0.482675i
$79$	0.0365000	+	0.0162509i	0.00410657	+	0.00182836i	0.408789	−	0.912629i	$-0.365951\pi$
$79$	0.0365000	+	0.0162509i	0.00410657	+	0.00182836i	−0.404682	+	0.914457i	$0.632618\pi$
$80$	2.47958	+	0.527050i	0.277225	+	0.0589260i
$81$	9.48868	−	2.01688i	1.05430	−	0.224098i
$82$	−6.81220	+	3.03299i	−0.752282	+	0.334937i
$83$	−7.63805	+	10.5129i	−0.838385	+	1.15394i	0.147919	+	0.988999i	$0.452742\pi$
$83$	−7.63805	+	10.5129i	−0.838385	+	1.15394i	−0.986304	+	0.164938i	$0.947258\pi$
$84$	0.300664	−	0.925349i	0.0328051	−	0.100964i
$85$	1.71550	−	8.07081i	0.186072	−	0.875402i
$86$	10.8085	−	1.13602i	1.16551	−	0.122500i
$87$			0.132799i			0.0142376i
$88$	−3.27552	+	0.520569i	−0.349171	+	0.0554929i
$89$	7.16280	+	4.13544i	0.759255	+	0.438356i	0.829028	−	0.559207i	$-0.188894\pi$
$89$	7.16280	+	4.13544i	0.759255	+	0.438356i	−0.0697730	+	0.997563i	$0.522227\pi$
$90$	−0.591174	−	0.263208i	−0.0623153	−	0.0277445i
$91$	−0.529813	+	2.49257i	−0.0555395	+	0.261293i
$92$	−2.41179	+	0.512642i	−0.251447	+	0.0534466i
$93$	−1.84732	+	17.5760i	−0.191558	+	1.82255i
$94$	−6.14321	−	4.46331i	−0.633624	−	0.460355i
$95$	2.01593	+	10.8642i	0.206830	+	1.11465i
$96$	1.71593	−	0.557540i	0.175132	−	0.0569037i
$97$	−4.60742	+	10.3484i	−0.467813	+	1.05072i	0.513462	+	0.858112i	$0.328363\pi$
$97$	−4.60742	+	10.3484i	−0.467813	+	1.05072i	−0.981275	+	0.192613i	$0.938304\pi$
$98$	3.35459	+	5.81033i	0.338865	+	0.586932i
$99$	0.845523	+	0.0438630i	0.0849782	+	0.00440840i
$100$	−0.713039	−	1.23502i	−0.0713039	−	0.123502i
$101$	−7.53950	+	0.792433i	−0.750208	+	0.0788501i	−0.471913	−	0.881645i	$-0.656436\pi$
$101$	−7.53950	+	0.792433i	−0.750208	+	0.0788501i	−0.278296	+	0.960495i	$0.589770\pi$
$102$	−1.81475	−	5.58522i	−0.179687	−	0.553019i
$103$	10.0436	+	3.26336i	0.989625	+	0.321549i	0.758712	−	0.651426i	$-0.225829\pi$
$103$	10.0436	+	3.26336i	0.989625	+	0.321549i	0.230913	+	0.972974i	$0.425829\pi$
$104$	−4.31687	+	1.92199i	−0.423303	+	0.188467i
$105$	−2.25321	+	1.00320i	−0.219891	+	0.0979018i
$106$	−2.47071	−	0.802783i	−0.239977	−	0.0779732i
$107$	1.57439	+	4.84548i	0.152202	+	0.468431i	0.997867	−	0.0652844i	$-0.0207955\pi$
$107$	1.57439	+	4.84548i	0.152202	+	0.468431i	−0.845664	+	0.533715i	$0.820795\pi$
$108$	4.92501	−	0.517639i	0.473909	−	0.0498098i
$109$	6.43671	+	11.1487i	0.616525	+	1.06785i	0.990115	+	0.140258i	$0.0447932\pi$
$109$	6.43671	+	11.1487i	0.616525	+	1.06785i	−0.373590	+	0.927594i	$0.621873\pi$
$110$	6.53669	+	5.28758i	0.623249	+	0.504151i
$111$	3.54466	+	6.13953i	0.336444	+	0.582739i
$112$	0.219340	−	0.492646i	0.0207257	−	0.0465507i
$113$	−16.0858	+	5.22660i	−1.51323	+	0.491677i	−0.943843	−	0.330394i	$-0.892818\pi$
$113$	−16.0858	+	5.22660i	−1.51323	+	0.491677i	−0.569384	+	0.822072i	$0.692818\pi$
$114$	5.10884	+	5.97914i	0.478486	+	0.559997i
$115$	5.05668	+	3.67390i	0.471538	+	0.342593i
$116$	−0.00769371	+	0.0732007i	−0.000714343	+	0.00679652i
$117$	1.17993	−	0.250801i	0.109084	−	0.0231866i
$118$	0.475455	−	2.23684i	0.0437691	−	0.205918i
$119$	−1.60352	−	0.713934i	−0.146995	−	0.0654462i
$120$	−3.96093	−	2.28685i	−0.361582	−	0.208760i
$121$	−10.4652	−	3.38810i	−0.951383	−	0.308010i
$122$			1.50364i			0.136133i
$123$	13.3803	−	1.40633i	1.20646	−	0.126804i
$124$	−2.03653	+	9.58114i	−0.182886	+	0.860412i
$125$	2.79963	−	8.61637i	0.250406	−	0.770672i
$126$	−0.0809164	+	0.111372i	−0.00720860	+	0.00992179i
$127$	10.7219	−	4.77369i	0.951413	−	0.423597i	0.128466	−	0.991714i	$-0.458995\pi$
$127$	10.7219	−	4.77369i	0.951413	−	0.423597i	0.822947	+	0.568117i	$0.192328\pi$
$128$	0.978148	−	0.207912i	0.0864569	−	0.0183770i
$129$	−19.1801	−	4.07685i	−1.68871	−	0.358947i
$130$	10.9431	+	4.87219i	0.959776	+	0.427320i
$131$	−10.7368	+	6.19890i	−0.938080	+	0.541601i	−0.889358	−	0.457212i	$-0.848848\pi$
$131$	−10.7368	+	6.19890i	−0.938080	+	0.541601i	−0.0487221	+	0.998812i	$0.515515\pi$
$132$	5.91081	+	0.932971i	0.514470	+	0.0812047i
$133$	2.34982	+	0.0610385i	0.203756	+	0.00529271i
$134$	7.40720	+	10.1951i	0.639885	+	0.880726i
$135$	−9.32908	−	8.39994i	−0.802919	−	0.722952i
$136$	−0.676735	−	3.18379i	−0.0580295	−	0.273008i
$137$	−0.755294	+	0.336279i	−0.0645292	+	0.0287302i	−0.438747	−	0.898610i	$-0.644578\pi$
$137$	−0.755294	+	0.336279i	−0.0645292	+	0.0287302i	0.374218	+	0.927341i	$0.377911\pi$
$138$	4.42429	+	0.465012i	0.376620	+	0.0395844i
$139$	0.464071	−	0.417851i	0.0393620	−	0.0354417i	−0.649215	−	0.760605i	$-0.724902\pi$
$139$	0.464071	−	0.417851i	0.0393620	−	0.0354417i	0.688577	+	0.725163i	$0.258236\pi$
$140$	−1.30012	+	0.422436i	−0.109880	+	0.0357023i
$141$	8.05287	+	11.0838i	0.678174	+	0.933426i
$142$	−11.0608	−	6.38594i	−0.928199	−	0.535896i
$143$	−15.6513	−	0.811940i	−1.30883	−	0.0678978i
$144$	−0.255277			−0.0212731
$145$	0.150949	−	0.109671i	0.0125357	−	0.00910770i
$146$	0.134766	−	0.634025i	0.0111533	−	0.0524723i
$147$	−2.51677	−	11.8405i	−0.207579	−	0.976584i
$148$	1.59817	+	3.58956i	0.131369	+	0.295060i
$149$	16.3048	+	1.71370i	1.33574	+	0.140392i	0.745321	−	0.666706i	$-0.232296\pi$
$149$	16.3048	+	1.71370i	1.33574	+	0.140392i	0.590417	+	0.807098i	$0.298963\pi$
$150$	0.534953	+	2.51676i	0.0436788	+	0.205492i
$151$	−4.45281	−	13.7043i	−0.362364	−	1.11524i	−0.951615	−	0.307293i	$-0.900577\pi$
$151$	−4.45281	−	13.7043i	−0.362364	−	1.11524i	0.589251	−	0.807950i	$-0.299423\pi$
$152$	2.46966	+	3.59176i	0.200316	+	0.291331i
$153$			0.830907i			0.0671748i
$154$	1.38937	−	1.12631i	0.111959	−	0.0907605i
$155$	21.5039	−	12.4153i	1.72723	−	0.997218i
$156$	8.47904	−	0.891183i	0.678867	−	0.0713518i
$157$	−4.36585	+	4.84877i	−0.348433	+	0.386974i	−0.891731	−	0.452566i	$-0.850509\pi$
$157$	−4.36585	+	4.84877i	−0.348433	+	0.386974i	0.543298	+	0.839540i	$0.317175\pi$
$158$	−0.0267346	−	0.0296918i	−0.00212689	−	0.00236215i
$159$	3.79199	+	2.75504i	0.300725	+	0.218489i
$160$	−2.05083	−	1.49002i	−0.162133	−	0.117796i
$161$	0.988129	−	0.889715i	0.0778755	−	0.0701194i
$162$	−9.48868	−	2.01688i	−0.745501	−	0.158461i
$163$	−10.6975	+	7.77217i	−0.837891	+	0.608764i	−0.921781	−	0.387711i	$-0.873266\pi$
$163$	−10.6975	+	7.77217i	−0.837891	+	0.608764i	0.0838895	+	0.996475i	$0.473266\pi$
$164$	7.45688			0.582285
$165$	−8.26849	−	12.7176i	−0.643701	−	0.990064i
$166$	11.2537	−	6.49731i	0.873454	−	0.504289i
$167$	−0.821799	−	7.81890i	−0.0635927	−	0.605045i	−0.979190	−	0.202947i	$-0.934948\pi$
$167$	−0.821799	−	7.81890i	−0.0635927	−	0.605045i	0.915597	−	0.402097i	$-0.131719\pi$
$168$	−0.651043	+	0.723057i	−0.0502291	+	0.0557851i
$169$	−9.12551	+	1.93969i	−0.701963	+	0.149207i
$170$	−4.84988	+	6.67529i	−0.371969	+	0.511972i
$171$	−0.426039	−	1.02794i	−0.0325800	−	0.0786084i
$172$	−10.3361	−	3.35841i	−0.788123	−	0.256077i
$173$	−7.49857	+	8.32800i	−0.570105	+	0.633166i	−0.957391	−	0.288793i	$-0.906746\pi$
$173$	−7.49857	+	8.32800i	−0.570105	+	0.633166i	0.387286	+	0.921960i	$0.373413\pi$
$174$	0.0540142	−	0.121318i	0.00409481	−	0.00919709i
$175$	0.666007	+	0.384519i	0.0503454	+	0.0290669i
$176$	3.20407	+	0.856709i	0.241516	+	0.0645769i
$177$	−2.06298	+	3.57318i	−0.155063	+	0.268577i
$178$	−4.86151	−	6.69129i	−0.364385	−	0.501533i
$179$	11.7604	−	3.82117i	0.879010	−	0.285608i	0.165464	−	0.986216i	$-0.447088\pi$
$179$	11.7604	−	3.82117i	0.879010	−	0.285608i	0.713546	+	0.700608i	$0.247088\pi$
$180$	0.433008	+	0.480905i	0.0322745	+	0.0358445i
$181$	−6.66136	−	14.9617i	−0.495135	−	1.11209i	−0.972397	−	0.233331i	$-0.925038\pi$
$181$	−6.66136	−	14.9617i	−0.495135	−	1.11209i	0.477262	−	0.878761i	$-0.341629\pi$
$182$	1.49783	−	2.06158i	0.111026	−	0.152815i
$183$	0.838337	−	2.58014i	0.0619717	−	0.190729i
$184$	2.41179	+	0.512642i	0.177800	+	0.0377925i
$185$	4.05132	−	9.09942i	0.297859	−	0.669003i
$186$	8.83643	−	15.3051i	0.647919	−	1.12223i
$187$	2.78852	−	10.4290i	0.203916	−	0.762642i
$188$	3.79671	+	6.57610i	0.276904	+	0.479612i
$189$	−2.16050	+	1.56970i	−0.157154	+	0.114179i
$190$	2.57724	−	10.7449i	0.186973	−	0.779518i
$191$	3.02932	−	9.32330i	0.219194	−	0.674610i	−0.779635	−	0.626234i	$-0.784595\pi$
$191$	3.02932	−	9.32330i	0.219194	−	0.674610i	0.998829	−	0.0483761i	$-0.0154046\pi$
$192$	−1.79435	−	0.188594i	−0.129496	−	0.0136106i
$193$	0.628610	−	5.98082i	0.0452483	−	0.430509i	−0.948323	−	0.317305i	$-0.897222\pi$
$193$	0.628610	−	5.98082i	0.0452483	−	0.430509i	0.993572	−	0.113204i	$-0.0361113\pi$
$194$	8.41818	−	7.57976i	0.604390	−	0.544195i
$195$	−16.0612	−	14.4616i	−1.15017	−	1.03562i
$196$	−0.701301	−	6.67244i	−0.0500929	−	0.476603i
$197$			10.7596i			0.766590i	0.923626	+	0.383295i	$0.125211\pi$
$197$			10.7596i			0.766590i	−0.923626	+	0.383295i	$0.874789\pi$
$198$	−0.754583	−	0.383976i	−0.0536259	−	0.0272880i
$199$	−3.51062	+	6.08057i	−0.248861	+	0.431040i	−0.963210	−	0.268750i	$-0.913390\pi$
$199$	−3.51062	+	6.08057i	−0.248861	+	0.431040i	0.714349	+	0.699790i	$0.246723\pi$
$200$	0.149066	+	1.41827i	0.0105405	+	0.100286i
$201$	−7.02606	−	21.6240i	−0.495580	−	1.52524i
$202$	7.20999	+	2.34267i	0.507293	+	0.164829i
$203$	−0.0161443	−	0.0362607i	−0.00113311	−	0.00254500i
$204$	−0.613858	+	5.84047i	−0.0429787	+	0.408915i
$205$	−12.6486	−	14.0477i	−0.883414	−	0.981131i
$206$	−7.84796	−	7.06633i	−0.546793	−	0.492335i
$207$	−0.575013	−	0.256012i	−0.0399662	−	0.0177941i
$208$	4.72540			0.327647
$209$	1.89760	+	14.3318i	0.131259	+	0.991348i
$210$	2.46645			0.170201
$211$	7.28655	+	3.24418i	0.501627	+	0.223339i	0.641920	−	0.766771i	$-0.278138\pi$
$211$	7.28655	+	3.24418i	0.501627	+	0.223339i	−0.140294	+	0.990110i	$0.544805\pi$
$212$	1.93059	+	1.73831i	0.132593	+	0.119387i
$213$	15.4191	+	17.1247i	1.05650	+	1.17336i
$214$	0.532556	−	5.06693i	0.0364048	−	0.346368i
$215$	11.2057	+	25.1684i	0.764221	+	1.71647i
$216$	−4.70976	−	1.53029i	−0.320459	−	0.104123i
$217$	−1.63230	−	5.02371i	−0.110808	−	0.341031i
$218$	−1.34564	−	12.8029i	−0.0911381	−	0.867121i
$219$	−0.584745	+	1.01281i	−0.0395134	+	0.0684392i
$220$	−3.82091	−	7.48916i	−0.257606	−	0.504919i
$221$		−	15.3808i		−	1.03462i
$222$	−0.741036	−	7.05049i	−0.0497351	−	0.473198i
$223$	16.1646	+	14.5546i	1.08246	+	0.974651i	0.999760	−	0.0219235i	$-0.00697904\pi$
$223$	16.1646	+	14.5546i	1.08246	+	0.974651i	0.0826999	+	0.996574i	$0.473646\pi$
$224$	−0.400755	+	0.360841i	−0.0267765	+	0.0241097i
$225$	0.0380531	−	0.362051i	0.00253687	−	0.0241367i
$226$	16.8210	+	1.76796i	1.11892	+	0.117603i
$227$	8.17945	−	25.1737i	0.542889	−	1.67084i	−0.183068	−	0.983100i	$-0.558603\pi$
$227$	8.17945	−	25.1737i	0.542889	−	1.67084i	0.725957	−	0.687740i	$-0.241397\pi$
$228$	−2.23522	−	7.54016i	−0.148031	−	0.499360i
$229$	−2.19401	+	1.59404i	−0.144984	+	0.105337i	−0.657913	−	0.753094i	$-0.728561\pi$
$229$	−2.19401	+	1.59404i	−0.144984	+	0.105337i	0.512929	+	0.858431i	$0.328561\pi$
$230$	−3.12520	−	5.41301i	−0.206070	−	0.356923i
$231$	−3.01203	+	1.15804i	−0.198177	+	0.0761934i
$232$	0.0368020	−	0.0637429i	0.00241617	−	0.00418492i
$233$	−9.02611	+	20.2730i	−0.591320	+	1.32813i	0.331704	+	0.943383i	$0.392376\pi$
$233$	−9.02611	+	20.2730i	−0.591320	+	1.32813i	−0.923024	+	0.384743i	$0.874290\pi$
$234$	−1.17993	−	0.250801i	−0.0771343	−	0.0163954i
$235$	5.94831	−	18.3070i	0.388025	−	1.19422i
$236$	−1.34415	+	1.85007i	−0.0874969	+	0.120429i
$237$	0.0293204	+	0.0658548i	0.00190457	+	0.00427773i
$238$	1.17451	+	1.30442i	0.0761320	+	0.0845531i
$239$	18.6132	−	6.04781i	1.20399	−	0.391200i	0.362763	−	0.931881i	$-0.381833\pi$
$239$	18.6132	−	6.04781i	1.20399	−	0.391200i	0.841228	+	0.540681i	$0.181833\pi$
$240$	2.68835	+	3.70020i	0.173532	+	0.238847i
$241$	−1.03460	+	1.79198i	−0.0666445	+	0.115432i	−0.897422	−	0.441173i	$-0.854563\pi$
$241$	−1.03460	+	1.79198i	−0.0666445	+	0.115432i	0.830778	+	0.556604i	$0.187896\pi$
$242$	8.18238	+	7.35177i	0.525984	+	0.472590i
$243$	2.29143	+	1.32296i	0.146995	+	0.0848677i
$244$	0.611583	−	1.37364i	0.0391526	−	0.0879382i
$245$	−11.3803	+	12.6391i	−0.727061	+	0.807483i
$246$	−12.7955	−	4.15751i	−0.815812	−	0.265073i
$247$	7.88633	+	19.0280i	0.501795	+	1.21072i
$248$	5.75747	−	7.92448i	0.365600	−	0.503205i
$249$	−22.9331	+	4.87457i	−1.45332	+	0.308914i
$250$	−6.06218	+	6.73274i	−0.383406	+	0.425816i
$251$	−1.61257	−	15.3426i	−0.101785	−	0.968415i	−0.919579	−	0.392905i	$-0.871470\pi$
$251$	−1.61257	−	15.3426i	−0.101785	−	0.968415i	0.817795	−	0.575510i	$-0.195196\pi$
$252$	0.119220	−	0.0688316i	0.00751014	−	0.00433598i
$253$	6.35800	+	5.14303i	0.399724	+	0.323340i
$254$	−11.7366			−0.736417
$255$	12.0438	−	8.75035i	0.754213	−	0.547968i
$256$	−0.978148	−	0.207912i	−0.0611342	−	0.0129945i
$257$	14.1085	−	12.7034i	0.880066	−	0.792415i	−0.0991844	−	0.995069i	$-0.531623\pi$
$257$	14.1085	−	12.7034i	0.880066	−	0.792415i	0.979250	+	0.202654i	$0.0649567\pi$
$258$	15.8637	+	11.5256i	0.987628	+	0.717554i
$259$	−1.71425	−	1.24547i	−0.106518	−	0.0773900i
$260$	−8.01535	−	8.90194i	−0.497091	−	0.552075i
$261$	−0.0125726	+	0.0139633i	−0.000778223	+	0.000864304i
$262$	12.3299	−	1.29592i	0.761743	−	0.0800624i
$263$	5.17172	−	2.98589i	0.318902	−	0.184118i	−0.332001	−	0.943279i	$-0.607724\pi$
$263$	5.17172	−	2.98589i	0.318902	−	0.184118i	0.650903	+	0.759161i	$0.274390\pi$
$264$	−5.02032	−	3.25645i	−0.308979	−	0.200421i
$265$		−	6.58550i		−	0.404544i
$266$	−2.12184	−	1.01152i	−0.130099	−	0.0620203i
$267$	4.61136	+	14.1923i	0.282210	+	0.868554i
$268$	−2.62008	−	12.3265i	−0.160047	−	0.752961i
$269$	−13.3149	−	1.39945i	−0.811825	−	0.0853262i	−0.310487	−	0.950578i	$-0.600492\pi$
$269$	−13.3149	−	1.39945i	−0.811825	−	0.0853262i	−0.501338	+	0.865251i	$0.667159\pi$
$270$	5.10598	+	11.4682i	0.310740	+	0.697933i
$271$	4.13058	+	19.4329i	0.250915	+	1.18046i	0.905458	+	0.424437i	$0.139528\pi$
$271$	4.13058	+	19.4329i	0.250915	+	1.18046i	−0.654543	+	0.756025i	$0.727139\pi$
$272$	−0.676735	+	3.18379i	−0.0410331	+	0.193045i
$273$	−3.71959	+	2.70244i	−0.225120	+	0.163559i
$274$	0.826773			0.0499472
$275$	−1.69266	+	4.41651i	−0.102071	+	0.266326i
$276$	−3.85265	−	2.22433i	−0.231902	−	0.133889i
$277$	−5.69006	−	7.83170i	−0.341883	−	0.470561i	0.603107	−	0.797660i	$-0.293929\pi$
$277$	−5.69006	−	7.83170i	−0.341883	−	0.470561i	−0.944990	+	0.327099i	$0.893929\pi$
$278$	−0.593905	+	0.192971i	−0.0356201	+	0.0115737i
$279$	−1.85823	+	1.67316i	−0.111249	+	0.100169i
$280$	1.35954	+	0.142894i	0.0812481	+	0.00853952i
$281$	25.1137	−	11.1814i	1.49816	−	0.667023i	0.516261	−	0.856431i	$-0.327324\pi$
$281$	25.1137	−	11.1814i	1.49816	−	0.667023i	0.981898	+	0.189408i	$0.0606569\pi$
$282$	−2.84846	−	13.4010i	−0.169624	−	0.798016i
$283$	22.1201	+	19.9171i	1.31491	+	1.18395i	0.969388	+	0.245534i	$0.0789634\pi$
$283$	22.1201	+	19.9171i	1.31491	+	1.18395i	0.345518	+	0.938412i	$0.387703\pi$
$284$	7.50712	+	10.3327i	0.445466	+	0.613131i
$285$	−10.4131	+	17.0006i	−0.616819	+	1.00703i
$286$	13.9680	+	7.10771i	0.825942	+	0.420288i
$287$	−3.48252	+	2.01063i	−0.205566	+	0.118684i
$288$	0.233208	+	0.103831i	0.0137419	+	0.00611828i
$289$	−6.26555	−	1.33178i	−0.368562	−	0.0783402i
$290$	−0.182506	+	0.0387930i	−0.0107172	+	0.00227800i
$291$	−18.6711	+	8.31289i	−1.09452	+	0.487310i
$292$	−0.380997	+	0.524397i	−0.0222961	+	0.0306880i
$293$	2.76495	−	8.50963i	0.161530	−	0.497138i	−0.837234	−	0.546845i	$-0.815829\pi$
$293$	2.76495	−	8.50963i	0.161530	−	0.497138i	0.998764	+	0.0497070i	$0.0158288\pi$
$294$	−2.51677	+	11.8405i	−0.146781	+	0.690549i
$295$	5.76524	−	0.605951i	0.335665	−	0.0352798i
$296$		−	3.92926i		−	0.228384i
$297$	−11.6199	−	11.6076i	−0.674257	−	0.673543i
$298$	−14.1981	−	8.19729i	−0.822475	−	0.474856i
$299$	10.6440	+	4.73900i	0.615557	+	0.274064i
$300$	0.534953	−	2.51676i	0.0308856	−	0.145305i
$301$	5.73273	−	1.21853i	0.330429	−	0.0702348i
$302$	−1.50621	+	14.3307i	−0.0866728	+	0.824637i
$303$	−11.0657	−	8.03972i	−0.635709	−	0.461870i
$304$	−0.795246	−	4.28574i	−0.0456105	−	0.245804i
$305$	−3.62511	+	1.17787i	−0.207573	+	0.0674447i
$306$	0.337960	−	0.759071i	0.0193199	−	0.0433932i
$307$	7.81847	+	13.5420i	0.446224	+	0.772882i	0.998137	−	0.0610198i	$-0.0194353\pi$
$307$	7.81847	+	13.5420i	0.446224	+	0.772882i	−0.551913	+	0.833902i	$0.686102\pi$
$308$	−1.72736	+	0.463826i	−0.0984256	+	0.0264289i
$309$	9.52680	+	16.5009i	0.541961	+	0.938704i
$310$	−24.6945	+	2.59550i	−1.40255	+	0.147414i
$311$	−4.88255	−	15.0269i	−0.276864	−	0.852099i	−0.988720	−	0.149774i	$-0.952145\pi$
$311$	−4.88255	−	15.0269i	−0.276864	−	0.852099i	0.711856	−	0.702325i	$-0.247855\pi$
$312$	−8.10847	−	2.63460i	−0.459051	−	0.149155i
$313$	−5.48980	+	2.44422i	−0.310302	+	0.138155i	−0.555979	−	0.831196i	$-0.687656\pi$
$313$	−5.48980	+	2.44422i	−0.310302	+	0.138155i	0.245677	+	0.969352i	$0.420990\pi$
$314$	5.96058	−	2.65382i	0.336375	−	0.149764i
$315$	−0.331892	−	0.107838i	−0.0187000	−	0.00607600i
$316$	0.0123465	+	0.0379987i	0.000694547	+	0.00213760i
$317$	−26.1388	+	2.74730i	−1.46810	+	0.154304i	−0.804577	−	0.593849i	$-0.797608\pi$
$317$	−26.1388	+	2.74730i	−1.46810	+	0.154304i	−0.663527	+	0.748152i	$0.730941\pi$
$318$	−2.34358	−	4.05920i	−0.131421	−	0.227629i
$319$	0.204663	−	0.133064i	0.0114589	−	0.00745014i
$320$	1.26749	+	2.19535i	0.0708546	+	0.122724i
$321$	−3.73885	+	8.39760i	−0.208682	+	0.468708i
$322$	−1.26458	+	0.410887i	−0.0704723	+	0.0228978i
$323$	−13.9497	+	2.58846i	−0.776184	+	0.144026i
$324$	7.84800	+	5.70191i	0.436000	+	0.316773i
$325$	−0.704395	+	6.70187i	−0.0390728	+	0.371753i
$326$	12.9339	−	2.74918i	0.716340	−	0.152263i
$327$	−4.82910	+	22.7191i	−0.267050	+	1.25637i
$328$	−6.81220	−	3.03299i	−0.376141	−	0.167469i
$329$	−3.54629	−	2.04745i	−0.195513	−	0.112880i
$330$	2.38092	+	14.9812i	0.131066	+	0.824688i
$331$			23.8569i			1.31129i	0.755068	+	0.655646i	$0.227604\pi$
$331$			23.8569i			1.31129i	−0.755068	+	0.655646i	$0.772396\pi$
$332$	−12.9234	+	1.35831i	−0.709266	+	0.0745468i
$333$	−0.208546	+	0.981133i	−0.0114283	+	0.0537657i
$334$	−2.42948	+	7.47718i	−0.132935	+	0.409133i
$335$	−18.7770	+	25.8444i	−1.02590	+	1.41203i
$336$	0.888852	−	0.395742i	0.0484908	−	0.0215895i
$337$	−16.5117	+	3.50967i	−0.899450	+	0.191184i	−0.634358	−	0.773039i	$-0.718736\pi$
$337$	−16.5117	+	3.50967i	−0.899450	+	0.191184i	−0.265092	+	0.964223i	$0.585402\pi$
$338$	9.12551	+	1.93969i	0.496363	+	0.105505i
$339$	−27.8780	−	12.4121i	−1.51412	−	0.674131i
$340$	7.14568	−	4.12556i	0.387529	−	0.223740i
$341$	28.9383	−	14.7641i	1.56710	−	0.799521i
$342$	−0.0288942	+	1.11235i	−0.00156242	+	0.0601492i
$343$	4.34546	+	5.98101i	0.234633	+	0.322944i
$344$	8.07654	+	7.27215i	0.435458	+	0.392088i
$345$	2.34467	+	11.0308i	0.126233	+	0.593878i
$346$	10.2376	−	4.55807i	0.550376	−	0.245043i
$347$	5.21986	+	0.548629i	0.280217	+	0.0294520i	0.243594	−	0.969877i	$-0.421673\pi$
$347$	5.21986	+	0.548629i	0.280217	+	0.0294520i	0.0366224	+	0.999329i	$0.488340\pi$
$348$	−0.0986889	+	0.0888599i	−0.00529028	+	0.00476339i
$349$	34.4843	−	11.2046i	1.84590	−	0.599770i	0.848382	−	0.529384i	$-0.177577\pi$
$349$	34.4843	−	11.2046i	1.84590	−	0.599770i	0.997520	−	0.0703859i	$-0.0224231\pi$
$350$	−0.452030	−	0.622165i	−0.0241620	−	0.0332561i
$351$	−20.2657	−	11.7004i	−1.08170	−	0.624521i
$352$	−2.57861	−	2.08585i	−0.137440	−	0.111176i
$353$	4.61967			0.245880			0.122940	−	0.992414i	$-0.460768\pi$
$353$	4.61967			0.245880			0.122940	+	0.992414i	$0.460768\pi$
$354$	3.33797	−	2.42517i	0.177411	−	0.128897i
$355$	6.73142	−	31.6688i	0.357267	−	1.68081i
$356$	1.71961	+	8.09015i	0.0911394	+	0.428777i
$357$	−1.28811	−	2.89314i	−0.0681739	−	0.153121i
$358$	−12.2978	−	1.29255i	−0.649960	−	0.0683136i
$359$	−0.763811	−	3.59345i	−0.0403124	−	0.189655i	0.953384	−	0.301760i	$-0.0975741\pi$
$359$	−0.763811	−	3.59345i	−0.0403124	−	0.189655i	−0.993696	+	0.112105i	$0.964241\pi$
$360$	−0.199971	−	0.615449i	−0.0105394	−	0.0324370i
$361$	15.9304	−	10.3548i	0.838442	−	0.544991i
$362$			16.3776i			0.860786i
$363$	−9.94151	−	17.1772i	−0.521794	−	0.901567i
$364$	−2.20686	+	1.27413i	−0.115671	+	0.0667825i
$365$	1.63414	−	0.171755i	0.0855349	−	0.00899008i
$366$	−1.81530	+	2.01609i	−0.0948870	+	0.105383i
$367$	0.294668	+	0.327262i	0.0153815	+	0.0170829i	0.750787	−	0.660545i	$-0.229675\pi$
$367$	0.294668	+	0.327262i	0.0153815	+	0.0170829i	−0.735405	+	0.677628i	$0.763008\pi$
$368$	−1.99477	−	1.44929i	−0.103985	−	0.0755492i
$369$	1.54002	+	1.11889i	0.0801704	+	0.0582472i
$370$	−7.40214	+	6.66492i	−0.384819	+	0.346492i
$371$	−1.37033	−	0.291273i	−0.0711440	−	0.0151221i
$372$	−14.2976	+	10.3878i	−0.741298	+	0.538585i
$373$	−5.54881			−0.287307			−0.143653	−	0.989628i	$-0.545885\pi$
$373$	−5.54881			−0.287307			−0.143653	+	0.989628i	$0.545885\pi$
$374$	−6.78928	+	8.39315i	−0.351065	+	0.433999i
$375$	14.1561	−	8.17301i	0.731016	−	0.422053i
$376$	−0.793730	−	7.55183i	−0.0409335	−	0.389456i
$377$	0.232729	−	0.258472i	0.0119861	−	0.0133120i
$378$	2.61217	−	0.555235i	0.134356	−	0.0285582i
$379$	−18.3050	+	25.1947i	−0.940267	+	1.29417i	0.0154511	+	0.999881i	$0.495082\pi$
$379$	−18.3050	+	25.1947i	−0.940267	+	1.29417i	−0.955718	+	0.294285i	$0.904918\pi$
$380$	−6.72478	+	8.76771i	−0.344974	+	0.449774i
$381$	20.1392	+	6.54361i	1.03176	+	0.335239i
$382$	−6.55955	+	7.28512i	−0.335616	+	0.372739i
$383$	−1.53610	+	3.45014i	−0.0784912	+	0.176294i	−0.948529	−	0.316692i	$-0.897428\pi$
$383$	−1.53610	+	3.45014i	−0.0784912	+	0.176294i	0.870037	+	0.492986i	$0.164095\pi$
$384$	1.56252	+	0.902119i	0.0797368	+	0.0460361i
$385$	3.80378	+	2.46734i	0.193858	+	0.125747i
$386$	−3.00688	+	5.20808i	−0.153046	+	0.265084i
$387$	−1.63073	−	2.24451i	−0.0828948	−	0.114095i
$388$	−10.7734	+	3.50048i	−0.546934	+	0.177710i
$389$	0.0603649	+	0.0670420i	0.00306062	+	0.00339916i	0.744673	−	0.667429i	$-0.232605\pi$
$389$	0.0603649	+	0.0670420i	0.00306062	+	0.00339916i	−0.741613	+	0.670828i	$0.765939\pi$
$390$	8.79060	+	19.7440i	0.445129	+	0.999777i
$391$	−4.71730	+	6.49281i	−0.238564	+	0.328355i
$392$	−2.07325	+	6.38082i	−0.104715	+	0.322280i
$393$	−21.8798	−	4.65069i	−1.10369	−	0.234597i
$394$	4.37632	−	9.82939i	0.220476	−	0.495197i
$395$	0.0506414	−	0.0877135i	0.00254805	−	0.00441335i
$396$	0.533169	+	0.657696i	0.0267927	+	0.0330505i
$397$	3.87866	+	6.71804i	0.194665	+	0.337169i	0.946790	−	0.321851i	$-0.104305\pi$
$397$	3.87866	+	6.71804i	0.194665	+	0.337169i	−0.752126	+	0.659019i	$0.770972\pi$
$398$	5.68030	−	4.12698i	0.284728	−	0.206867i
$399$	3.07698	+	2.91872i	0.154042	+	0.146119i
$400$	0.440682	−	1.35628i	0.0220341	−	0.0678140i
$401$	29.5463	+	3.10544i	1.47547	+	0.155078i	0.807834	−	0.589410i	$-0.200640\pi$
$401$	29.5463	+	3.10544i	1.47547	+	0.155078i	0.667636	+	0.744488i	$0.267306\pi$
$402$	−2.37664	+	22.6123i	−0.118536	+	1.12780i
$403$	34.3973	−	30.9715i	1.71345	−	1.54280i
$404$	−5.63380	−	5.07270i	−0.280292	−	0.252376i
$405$	−2.57045	−	24.4562i	−0.127727	−	1.21524i
$406$			0.0396923i			0.00196989i
$407$	5.91020	−	11.6146i	0.292958	−	0.575715i
$408$	2.93632	−	5.08586i	0.145370	−	0.251788i
$409$	−0.460153	−	4.37807i	−0.0227531	−	0.216481i	−0.999991	−	0.00433321i	$-0.998621\pi$
$409$	−0.460153	−	4.37807i	−0.0227531	−	0.216481i	0.977237	−	0.212148i	$-0.0680460\pi$
$410$	5.84134	+	17.9778i	0.288483	+	0.887860i
$411$	−1.41869	−	0.460959i	−0.0699786	−	0.0227374i
$412$	4.29533	+	9.64747i	0.211616	+	0.475297i
$413$	0.128905	−	1.22645i	0.00634300	−	0.0603496i
$414$	0.421171	+	0.467758i	0.0206994	+	0.0229890i
$415$	24.4799	+	22.0418i	1.20167	+	1.08199i
$416$	−4.31687	−	1.92199i	−0.211652	−	0.0942334i
$417$	1.12669			0.0551743
$418$	4.09571	−	13.8645i	0.200328	−	0.678136i
$419$	−18.4007			−0.898932			−0.449466	−	0.893297i	$-0.648386\pi$
$419$	−18.4007			−0.898932			−0.449466	+	0.893297i	$0.648386\pi$
$420$	−2.25321	−	1.00320i	−0.109946	−	0.0489509i
$421$	8.09089	+	7.28507i	0.394326	+	0.355053i	0.842314	−	0.538987i	$-0.181193\pi$
$421$	8.09089	+	7.28507i	0.394326	+	0.355053i	−0.447988	+	0.894039i	$0.647859\pi$
$422$	−5.33707	−	5.92741i	−0.259804	−	0.288542i
$423$	−0.202621	+	1.92781i	−0.00985178	+	0.0937335i
$424$	−1.05664	−	2.37326i	−0.0513152	−	0.115256i
$425$	−4.41458	−	1.43438i	−0.214138	−	0.0695778i
$426$	−7.12084	−	21.9157i	−0.345006	−	1.06182i
$427$	0.0847583	+	0.806421i	0.00410174	+	0.0390255i
$428$	−2.54742	+	4.41226i	−0.123134	+	0.213275i
$429$	−20.0052	−	19.9841i	−0.965862	−	0.964839i
$430$		−	27.5502i		−	1.32859i
$431$	−0.608494	−	5.78943i	−0.0293101	−	0.278867i	−0.999354	−	0.0359375i	$-0.988558\pi$
$431$	−0.608494	−	5.78943i	−0.0293101	−	0.278867i	0.970044	−	0.242930i	$-0.0781084\pi$
$432$	3.68015	+	3.31362i	0.177061	+	0.159427i
$433$	−28.1012	+	25.3024i	−1.35046	+	1.21596i	−0.395767	+	0.918351i	$0.629521\pi$
$433$	−28.1012	+	25.3024i	−1.35046	+	1.21596i	−0.954689	+	0.297605i	$0.903812\pi$
$434$	−0.552144	+	5.25330i	−0.0265038	+	0.252167i
$435$	0.334798	+	0.0351886i	0.0160523	+	0.00168717i
$436$	−3.97810	+	12.2433i	−0.190517	+	0.586350i
$437$	2.50679	−	10.4512i	0.119916	−	0.499948i
$438$	0.946137	−	0.687409i	0.0452082	−	0.0328457i
$439$	3.52303	+	6.10207i	0.168145	+	0.291236i	0.937768	−	0.347263i	$-0.112889\pi$
$439$	3.52303	+	6.10207i	0.168145	+	0.291236i	−0.769623	+	0.638499i	$0.779556\pi$
$440$	0.444463	+	8.39579i	0.0211890	+	0.400254i
$441$	0.856353	−	1.48325i	0.0407787	−	0.0706308i
$442$	−6.25592	+	14.0510i	−0.297564	+	0.668339i
$443$	−27.1198	−	5.76449i	−1.28850	−	0.273879i	−0.487805	−	0.872953i	$-0.662202\pi$
$443$	−27.1198	−	5.76449i	−1.28850	−	0.273879i	−0.800694	+	0.599074i	$0.795536\pi$
$444$	−2.19072	+	6.74235i	−0.103967	+	0.319978i
$445$	12.3238	−	16.9622i	0.584203	−	0.804087i
$446$	−8.84716	−	19.8710i	−0.418925	−	0.940921i
$447$	19.7927	+	21.9820i	0.936162	+	1.03971i
$448$	0.512875	−	0.166643i	0.0242311	−	0.00787315i
$449$	−13.0279	−	17.9313i	−0.614822	−	0.846230i	0.382141	−	0.924104i	$-0.375187\pi$
$449$	−13.0279	−	17.9313i	−0.614822	−	0.846230i	−0.996963	+	0.0778737i	$0.975187\pi$
$450$	−0.182023	+	0.315273i	−0.00858063	+	0.0148621i
$451$	−15.5743	−	19.2119i	−0.733366	−	0.904652i
$452$	−14.6476	−	8.45682i	−0.688967	−	0.397775i
$453$	10.5745	−	23.7507i	0.496832	−	1.11590i
$454$	−17.7114	+	19.6705i	−0.831236	+	0.923181i
$455$	6.14360	+	1.99618i	0.288016	+	0.0935822i
$456$	−1.02489	+	7.79743i	−0.0479946	+	0.365148i
$457$	−0.966233	+	1.32991i	−0.0451985	+	0.0622103i	−0.831018	−	0.556245i	$-0.812241\pi$
$457$	−0.966233	+	1.32991i	−0.0451985	+	0.0622103i	0.785820	+	0.618456i	$0.212241\pi$
$458$	2.65268	−	0.563845i	0.123952	−	0.0263467i
$459$	10.7856	−	11.9786i	0.503427	−	0.559113i
$460$	0.653345	+	6.21616i	0.0304624	+	0.289830i
$461$	−5.03177	+	2.90510i	−0.234353	+	0.135304i	−0.612579	−	0.790410i	$-0.709868\pi$
$461$	−5.03177	+	2.90510i	−0.234353	+	0.135304i	0.378226	+	0.925713i	$0.376534\pi$
$462$	3.22264	+	0.167180i	0.149931	+	0.00777792i
$463$	−40.3885			−1.87701			−0.938506	−	0.345264i	$-0.887790\pi$
$463$	−40.3885			−1.87701			−0.938506	+	0.345264i	$0.887790\pi$
$464$	−0.0595468	+	0.0432633i	−0.00276439	+	0.00200845i
$465$	43.8212	+	9.31448i	2.03216	+	0.431949i
$466$	16.4915	−	14.8490i	0.763955	−	0.687868i
$467$	−4.62849	−	3.36279i	−0.214181	−	0.155612i	0.475522	−	0.879704i	$-0.342259\pi$
$467$	−4.62849	−	3.36279i	−0.214181	−	0.155612i	−0.689703	+	0.724092i	$0.742259\pi$
$468$	0.975907	+	0.709038i	0.0451113	+	0.0327753i
$469$	4.54728	+	5.05027i	0.209974	+	0.233200i
$470$	−12.8802	+	14.3049i	−0.594118	+	0.659835i
$471$	−11.7076	+	1.23051i	−0.539456	+	0.0566991i
$472$	1.98044	−	1.14341i	0.0911570	−	0.0526295i
$473$	12.9353	+	33.6443i	0.594765	+	1.54697i
$474$		−	0.0720870i		−	0.00331107i
$475$	6.19686	−	0.489013i	0.284332	−	0.0224375i
$476$	−0.542409	−	1.66936i	−0.0248613	−	0.0765152i
$477$	0.137882	+	0.648683i	0.00631318	+	0.0297012i
$478$	−19.4639	−	2.04574i	−0.890259	−	0.0935700i
$479$	−0.298592	−	0.670649i	−0.0136430	−	0.0306427i	0.906595	−	0.422001i	$-0.138672\pi$
$479$	−0.298592	−	0.670649i	−0.0136430	−	0.0306427i	−0.920238	+	0.391358i	$0.872005\pi$
$480$	−0.950924	−	4.47375i	−0.0434036	−	0.204198i
$481$	3.86036	−	18.1616i	0.176017	−	0.828097i
$482$	1.67402	−	1.21625i	0.0762495	−	0.0553985i
$483$	2.39902			0.109159
$484$	−4.48474	−	10.0443i	−0.203852	−	0.456557i
$485$	24.8684	+	14.3578i	1.12922	+	0.651954i
$486$	−1.55523	−	2.14059i	−0.0705466	−	0.0970991i
$487$	10.4022	−	3.37987i	0.471367	−	0.153156i	−0.0636947	−	0.997969i	$-0.520288\pi$
$487$	10.4022	−	3.37987i	0.471367	−	0.153156i	0.535062	+	0.844813i	$0.320288\pi$
$488$	−1.11742	+	1.00613i	−0.0505832	+	0.0455453i
$489$	−23.7264	−	2.49375i	−1.07295	−	0.112771i
$490$	15.5372	−	6.91761i	0.701900	−	0.312506i
$491$	−6.77210	−	31.8602i	−0.305621	−	1.43783i	−0.816084	−	0.577933i	$-0.803860\pi$
$491$	−6.77210	−	31.8602i	−0.305621	−	1.43783i	0.510464	−	0.859899i	$-0.329474\pi$
$492$	9.99827	+	9.00248i	0.450757	+	0.405863i
$493$	0.140818	+	0.193820i	0.00634214	+	0.00872921i
$494$	0.534856	−	20.5906i	0.0240643	−	0.926414i
$495$	0.334626	−	2.12001i	0.0150403	−	0.0952874i
$496$	−8.48288	+	4.89760i	−0.380893	+	0.219909i
$497$	−6.29202	−	2.80139i	−0.282236	−	0.125659i
$498$	22.9331	+	4.87457i	1.02766	+	0.218435i
$499$	3.96683	−	0.843175i	0.177580	−	0.0377457i	−0.118264	−	0.992982i	$-0.537733\pi$
$499$	3.96683	−	0.843175i	0.177580	−	0.0377457i	0.295843	+	0.955237i	$0.404399\pi$
$500$	8.27653	−	3.68495i	0.370138	−	0.164796i
$501$	8.33766	−	11.4758i	0.372499	−	0.512701i
$502$	−4.76723	+	14.6720i	−0.212772	+	0.654845i
$503$	−7.61199	+	35.8116i	−0.339402	+	1.59676i	0.395420	+	0.918500i	$0.370599\pi$
$503$	−7.61199	+	35.8116i	−0.339402	+	1.59676i	−0.734822	+	0.678260i	$0.762734\pi$
$504$	−0.136909	+	0.0143897i	−0.00609841	+	0.000640969i
$505$			19.2177i			0.855176i
$506$	−3.71646	−	7.28442i	−0.165217	−	0.323832i
$507$	−14.5773	−	8.41622i	−0.647401	−	0.373777i
$508$	10.7219	+	4.77369i	0.475707	+	0.211798i
$509$	5.86400	−	27.5879i	0.259917	−	1.22281i	−0.633556	−	0.773697i	$-0.718405\pi$
$509$	5.86400	−	27.5879i	0.259917	−	1.22281i	0.893473	−	0.449117i	$-0.148261\pi$
$510$	−14.5617	+	3.09518i	−0.644801	+	0.137057i
$511$	0.0365378	−	0.347634i	0.00161634	−	0.0153784i
$512$	0.809017	+	0.587785i	0.0357538	+	0.0259767i
$513$	−7.20123	+	20.3492i	−0.317942	+	0.898441i
$514$	−18.0557	+	5.86666i	−0.796403	+	0.258767i
$515$	10.8885	−	24.4560i	0.479806	−	1.07766i
$516$	−9.80428	−	16.9815i	−0.431609	−	0.747569i
$517$	9.01289	−	23.5166i	0.396386	−	1.03426i
$518$	1.05946	+	1.83504i	0.0465501	+	0.0806272i
$519$	−20.1083	+	2.11347i	−0.882657	+	0.0927710i
$520$	3.70164	+	11.3925i	0.162327	+	0.499593i
$521$	6.49035	+	2.10884i	0.284348	+	0.0923901i	0.447718	−	0.894175i	$-0.352237\pi$
$521$	6.49035	+	2.10884i	0.284348	+	0.0923901i	−0.163371	+	0.986565i	$0.552237\pi$
$522$	0.0171650	−	0.00764235i	0.000751291	−	0.000334496i
$523$	−9.25125	+	4.11892i	−0.404529	+	0.180108i	−0.598907	−	0.800819i	$-0.704398\pi$
$523$	−9.25125	+	4.11892i	−0.404529	+	0.180108i	0.194378	+	0.980927i	$0.437731\pi$
$524$	−11.7910	−	3.83113i	−0.515093	−	0.167364i
$525$	0.428770	+	1.31962i	0.0187131	+	0.0575929i
$526$	−5.93907	+	0.624221i	−0.258956	+	0.0272173i
$527$	15.9413	+	27.6111i	0.694412	+	1.20276i
$528$	3.26177	+	5.01686i	0.141950	+	0.218331i
$529$	8.46023	+	14.6536i	0.367836	+	0.637111i
$530$	−2.67856	+	6.01615i	−0.116349	+	0.261325i
$531$	−0.555199	+	0.180395i	−0.0240936	+	0.00782849i
$532$	1.52698	+	1.78710i	0.0662029	+	0.0774807i
$533$	−28.5071	−	20.7116i	−1.23478	−	0.897120i
$534$	1.55984	−	14.8409i	0.0675010	−	0.642229i
$535$	12.6331	−	2.68524i	0.546174	−	0.116093i
$536$	−2.62008	+	12.3265i	−0.113170	+	0.532424i
$537$	20.3816	+	9.07447i	0.879531	+	0.391592i
$538$	11.5946	+	6.69413i	0.499878	+	0.288604i
$539$	−15.7261	+	15.7428i	−0.677371	+	0.678089i
$540$		−	12.5535i		−	0.540217i
$541$	−3.46944	+	0.364653i	−0.149163	+	0.0156777i	−0.178816	−	0.983883i	$-0.557227\pi$
$541$	−3.46944	+	0.364653i	−0.149163	+	0.0156777i	0.0296526	+	0.999560i	$0.490560\pi$
$542$	4.13058	−	19.4329i	0.177424	−	0.834712i
$543$	9.13116	−	28.1028i	0.391856	−	1.20601i
$544$	1.91319	−	2.63328i	0.0820274	−	0.112901i
$545$	29.8124	−	13.2733i	1.27702	−	0.568567i
$546$	4.49720	−	0.955909i	0.192462	−	0.0409091i
$547$	8.09279	+	1.72018i	0.346023	+	0.0735494i	0.377645	−	0.925950i	$-0.376734\pi$
$547$	8.09279	+	1.72018i	0.346023	+	0.0735494i	−0.0316221	+	0.999500i	$0.510067\pi$
$548$	−0.755294	−	0.336279i	−0.0322646	−	0.0143651i
$549$	0.332419	−	0.191922i	0.0141873	−	0.00819104i
$550$	3.34268	−	3.34622i	0.142532	−	0.142683i
$551$	−0.273590	−	0.167577i	−0.0116553	−	0.00713901i
$552$	2.61486	+	3.59904i	0.111296	+	0.153185i
$553$	−0.0160118	−	0.0144171i	−0.000680893	−	0.000613079i
$554$	2.01269	+	9.46897i	0.0855111	+	0.402298i
$555$	16.4175	−	7.30956i	0.696885	−	0.310273i
$556$	0.621048	+	0.0652748i	0.0263383	+	0.00276827i
$557$	−20.0176	+	18.0239i	−0.848171	+	0.763697i	−0.973565	−	0.228410i	$-0.926647\pi$
$557$	−20.0176	+	18.0239i	−0.848171	+	0.763697i	0.125394	+	0.992107i	$0.459981\pi$
$558$	2.37811	−	0.772694i	0.100673	−	0.0327108i
$559$	30.1862	+	41.5478i	1.27674	+	1.75728i
$560$	−1.18388	−	0.683515i	−0.0500282	−	0.0288838i
$561$	16.3295	−	10.6168i	0.689431	−	0.448241i
$562$	−27.4904			−1.15961
$563$	−8.60518	+	6.25203i	−0.362665	+	0.263492i	−0.754163	−	0.656687i	$-0.771957\pi$
$563$	−8.60518	+	6.25203i	−0.362665	+	0.263492i	0.391498	+	0.920179i	$0.371957\pi$
$564$	−2.84846	+	13.4010i	−0.119942	+	0.564283i
$565$	8.91433	+	41.9386i	0.375029	+	1.76437i
$566$	−12.1068	−	27.1922i	−0.508885	−	1.14297i
$567$	−5.20261	−	0.546816i	−0.218489	−	0.0229641i
$568$	−2.65542	−	12.4928i	−0.111419	−	0.524186i
$569$	8.51587	+	26.2091i	0.357004	+	1.09874i	0.954839	+	0.297125i	$0.0960279\pi$
$569$	8.51587	+	26.2091i	0.357004	+	1.09874i	−0.597835	+	0.801619i	$0.703972\pi$
$570$	16.4276	−	11.2955i	0.688078	−	0.473115i
$571$			26.4798i			1.10815i	0.832468	+	0.554073i	$0.186927\pi$
$571$			26.4798i			1.10815i	−0.832468	+	0.554073i	$0.813073\pi$
$572$	−9.86939	−	12.1745i	−0.412660	−	0.509041i
$573$	15.3175	−	8.84356i	0.639898	−	0.369445i
$574$	3.99923	−	0.420336i	0.166925	−	0.0175445i
$575$	2.35282	−	2.61307i	0.0981195	−	0.108973i
$576$	−0.170814	−	0.189708i	−0.00711725	−	0.00790451i
$577$	33.2131	+	24.1307i	1.38268	+	1.00457i	0.996624	+	0.0820989i	$0.0261623\pi$
$577$	33.2131	+	24.1307i	1.38268	+	1.00457i	0.386054	+	0.922476i	$0.373838\pi$
$578$	5.18218	+	3.76507i	0.215550	+	0.156606i
$579$	8.06333	−	7.26025i	0.335100	−	0.301726i
$580$	0.182506	+	0.0387930i	0.00757817	+	0.00161079i
$581$	5.66926	−	4.11896i	0.235201	−	0.170883i
$582$	20.4380			0.847183
$583$	0.446377	−	8.60456i	0.0184870	−	0.356364i
$584$	0.561349	−	0.324095i	0.0232288	−	0.0134111i
$585$	−0.319638	−	3.04115i	−0.0132154	−	0.125736i
$586$	−5.98708	+	6.64933i	−0.247324	+	0.274681i
$587$	−23.7841	+	5.05547i	−0.981675	+	0.208662i	−0.670678	−	0.741749i	$-0.733997\pi$
$587$	−23.7841	+	5.05547i	−0.981675	+	0.208662i	−0.310998	+	0.950411i	$0.600663\pi$
$588$	7.11513	−	9.79313i	0.293423	−	0.403862i
$589$	−33.8787	−	25.9847i	−1.39595	−	1.07068i
$590$	−5.51327	−	1.79137i	−0.226978	−	0.0737496i
$591$	−12.9898	+	14.4266i	−0.534327	+	0.593431i
$592$	−1.59817	+	3.58956i	−0.0656845	+	0.147530i
$593$	−4.27000	−	2.46528i	−0.175348	−	0.101237i	0.409757	−	0.912195i	$-0.365613\pi$
$593$	−4.27000	−	2.46528i	−0.175348	−	0.101237i	−0.585105	+	0.810958i	$0.698947\pi$
$594$	5.89409	+	15.3304i	0.241837	+	0.629012i
$595$	−2.22478	+	3.85344i	−0.0912072	+	0.157976i
$596$	9.63649	+	13.2635i	0.394726	+	0.543294i
$597$	−12.0480	+	3.91462i	−0.493090	+	0.160215i
$598$	−7.79623	−	8.65859i	−0.318811	−	0.354076i
$599$	−15.1285	−	33.9791i	−0.618133	−	1.38835i	−0.902941	−	0.429764i	$-0.858597\pi$
$599$	−15.1285	−	33.9791i	−0.618133	−	1.38835i	0.284809	−	0.958584i	$-0.408070\pi$
$600$	−1.51236	+	2.08159i	−0.0617419	+	0.0849805i
$601$	10.8220	−	33.3067i	0.441439	−	1.35861i	−0.444903	−	0.895579i	$-0.646762\pi$
$601$	10.8220	−	33.3067i	0.441439	−	1.35861i	0.886342	−	0.463031i	$-0.153238\pi$
$602$	−5.73273	−	1.21853i	−0.233648	−	0.0496635i
$603$	1.30846	−	2.93886i	0.0532847	−	0.119679i
$604$	7.20480	−	12.4791i	0.293159	−	0.507766i
$605$	−11.3147	+	25.4859i	−0.460009	+	1.03615i
$606$	6.83899	+	11.8455i	0.277815	+	0.481190i
$607$	−18.8281	+	13.6794i	−0.764211	+	0.555232i	−0.900199	−	0.435479i	$-0.856579\pi$
$607$	−18.8281	+	13.6794i	−0.764211	+	0.555232i	0.135988	+	0.990710i	$0.456579\pi$
$608$	−1.01667	+	4.23868i	−0.0412316	+	0.171901i
$609$	0.0221301	−	0.0681093i	0.000896755	−	0.00275993i
$610$	3.79079	+	0.398428i	0.153485	+	0.0161319i
$611$	3.75069	−	35.6854i	0.151737	−	1.44368i
$612$	−0.617484	+	0.555985i	−0.0249603	+	0.0224744i
$613$	20.7974	+	18.7260i	0.839998	+	0.756338i	0.972017	−	0.234909i	$-0.0754794\pi$
$613$	20.7974	+	18.7260i	0.839998	+	0.756338i	−0.132019	+	0.991247i	$0.542146\pi$
$614$	−1.63450	−	15.5513i	−0.0659633	−	0.627598i
$615$		−	34.1055i		−	1.37527i
$616$	1.76668	+	0.278856i	0.0711815	+	0.0112354i
$617$	5.25293	−	9.09834i	0.211475	−	0.366285i	−0.740701	−	0.671834i	$-0.765507\pi$
$617$	5.25293	−	9.09834i	0.211475	−	0.366285i	0.952176	+	0.305549i	$0.0988400\pi$
$618$	−1.99164	−	18.9492i	−0.0801157	−	0.762250i
$619$	−8.03749	−	24.7368i	−0.323054	−	0.994258i	−0.972311	−	0.233689i	$-0.924920\pi$
$619$	−8.03749	−	24.7368i	−0.323054	−	0.994258i	0.649257	−	0.760569i	$-0.275080\pi$
$620$	23.6152	+	7.67305i	0.948411	+	0.308157i
$621$	4.96639	+	11.1547i	0.199294	+	0.447623i
$622$	−1.65158	+	15.7137i	−0.0662222	+	0.630062i
$623$	−2.98448	−	3.31460i	−0.119571	−	0.132797i
$624$	6.33586	+	5.70484i	0.253638	+	0.228376i
$625$	−27.4947	−	12.2414i	−1.09979	−	0.489657i
$626$	6.00933			0.240181
$627$	−14.7580	+	21.5071i	−0.589378	+	0.858910i
$628$	−6.52467			−0.260363
$629$	11.6837	+	5.20192i	0.465860	+	0.207414i
$630$	0.259337	+	0.233508i	0.0103322	+	0.00930318i
$631$	−15.2663	−	16.9549i	−0.607741	−	0.674965i	0.358224	−	0.933636i	$-0.383382\pi$
$631$	−15.2663	−	16.9549i	−0.607741	−	0.674965i	−0.965966	+	0.258670i	$0.916716\pi$
$632$	0.00417636	−	0.0397354i	0.000166127	−	0.00158059i
$633$	5.85328	+	13.1467i	0.232647	+	0.522533i
$634$	24.9964	+	8.12184i	0.992736	+	0.322559i
$635$	−9.19383	−	28.2957i	−0.364846	−	1.12288i
$636$	0.489942	+	4.66148i	0.0194274	+	0.184840i
$637$	−15.8518	+	27.4561i	−0.628071	+	1.08785i
$638$	−0.241091	+	0.0383159i	−0.00954488	+	0.00151694i
$639$			3.26037i			0.128978i
$640$	−0.264977	−	2.52108i	−0.0104741	−	0.0996546i
$641$	11.5051	+	10.3592i	0.454424	+	0.409165i	0.864300	−	0.502976i	$-0.167762\pi$
$641$	11.5051	+	10.3592i	0.454424	+	0.409165i	−0.409877	+	0.912141i	$0.634428\pi$
$642$	6.83122	−	6.15086i	0.269607	−	0.242755i
$643$	0.936596	−	8.91112i	0.0369358	−	0.351420i	−0.960409	−	0.278594i	$-0.910132\pi$
$643$	0.936596	−	8.91112i	0.0369358	−	0.351420i	0.997345	−	0.0728260i	$-0.0232018\pi$
$644$	1.32237	+	0.138987i	0.0521089	+	0.00547686i
$645$	−15.3603	+	47.2743i	−0.604813	+	1.86142i
$646$	13.7965	+	3.30919i	0.542817	+	0.130198i
$647$	−21.6321	+	15.7166i	−0.850445	+	0.617885i	−0.925269	−	0.379312i	$-0.876161\pi$
$647$	−21.6321	+	15.7166i	−0.850445	+	0.617885i	0.0748235	+	0.997197i	$0.476161\pi$
$648$	−4.85033	−	8.40102i	−0.190539	−	0.330023i
$649$	7.57389	−	0.400953i	0.297301	−	0.0157388i
$650$	3.36939	−	5.83596i	0.132158	−	0.228905i
$651$	3.87637	−	8.70647i	0.151927	−	0.341234i
$652$	−12.9339	−	2.74918i	−0.506529	−	0.107666i
$653$	7.22197	−	22.2269i	0.282617	−	0.869807i	−0.704485	−	0.709719i	$-0.748822\pi$
$653$	7.22197	−	22.2269i	0.282617	−	0.869807i	0.987103	−	0.160089i	$-0.0511780\pi$
$654$	13.6523	−	18.7908i	0.533848	−	0.734778i
$655$	12.7830	+	28.7110i	0.499471	+	1.12183i
$656$	4.98963	+	5.54154i	0.194812	+	0.216361i
$657$	−0.157370	+	0.0511325i	−0.00613958	+	0.00199487i
$658$	2.40692	+	3.31284i	0.0938315	+	0.129148i
$659$	10.8005	−	18.7070i	0.420728	−	0.728722i	−0.575283	−	0.817955i	$-0.695108\pi$
$659$	10.8005	−	18.7070i	0.420728	−	0.728722i	0.996011	+	0.0892322i	$0.0284413\pi$
$660$	3.91832	−	14.6544i	0.152521	−	0.570423i
$661$	−5.33343	−	3.07926i	−0.207446	−	0.119769i	0.392678	−	0.919676i	$-0.371549\pi$
$661$	−5.33343	−	3.07926i	−0.207446	−	0.119769i	−0.600124	+	0.799907i	$0.704882\pi$
$662$	9.70347	−	21.7943i	0.377136	−	0.847061i
$663$	18.5688	−	20.6227i	0.721151	−	0.800919i
$664$	12.3586	+	4.01556i	0.479608	+	0.155834i
$665$	0.776532	−	5.90793i	0.0301126	−	0.229100i
$666$	0.589579	−	0.811486i	0.0228457	−	0.0314444i
$667$	−0.177517	+	0.0377325i	−0.00687349	+	0.00146101i
$668$	5.26068	−	5.84258i	0.203542	−	0.226056i
$669$	4.10222	+	39.0300i	0.158601	+	1.50899i
$670$	27.6655	−	15.9727i	1.06881	−	0.617080i
$671$	−4.81638	+	1.29328i	−0.185934	+	0.0499265i
$672$	−0.972969			−0.0375331
$673$	32.7796	−	23.8158i	1.26356	−	0.918031i	0.264635	−	0.964349i	$-0.414749\pi$
$673$	32.7796	−	23.8158i	1.26356	−	0.918031i	0.998927	+	0.0463174i	$0.0147486\pi$
$674$	16.5117	+	3.50967i	0.636007	+	0.135188i
$675$	−5.24818	+	4.72549i	−0.202003	+	0.181884i
$676$	−7.54763	−	5.48367i	−0.290293	−	0.210911i
$677$	−31.1917	−	22.6621i	−1.19879	−	0.870975i	−0.204628	−	0.978840i	$-0.565599\pi$
$677$	−31.1917	−	22.6621i	−1.19879	−	0.870975i	−0.994166	+	0.107865i	$0.965599\pi$
$678$	20.4194	+	22.6780i	0.784200	+	0.870943i
$679$	4.08753	−	4.53966i	0.156865	−	0.174216i
$680$	−8.20591	+	0.862476i	−0.314682	+	0.0330745i
$681$	41.3586	−	23.8784i	1.58487	−	0.915023i
$682$	−32.4415	+	1.71742i	−1.24225	+	0.0657633i
$683$		−	7.93761i		−	0.303724i	−0.988402	−	0.151862i	$-0.951473\pi$
$683$		−	7.93761i		−	0.303724i	0.988402	−	0.151862i	$-0.0485270\pi$
$684$	0.478831	−	1.00443i	0.0183086	−	0.0384055i
$685$	0.647652	+	1.99327i	0.0247455	+	0.0761588i
$686$	−1.53708	−	7.23138i	−0.0586859	−	0.276095i
$687$	−4.86619	−	0.511457i	−0.185657	−	0.0195133i
$688$	−4.42044	−	9.92846i	−0.168528	−	0.378519i
$689$	−2.55231	−	12.0077i	−0.0972352	−	0.457456i
$690$	2.34467	−	11.0308i	0.0892599	−	0.419935i
$691$	26.9615	−	19.5887i	1.02566	−	0.745189i	0.0582278	−	0.998303i	$-0.481455\pi$
$691$	26.9615	−	19.5887i	1.02566	−	0.745189i	0.967436	+	0.253115i	$0.0814550\pi$
$692$	−11.2064			−0.426005
$693$	−0.426338	−	0.163397i	−0.0161952	−	0.00620693i
$694$	−4.54543	−	2.62431i	−0.172542	−	0.0996173i
$695$	−0.930470	−	1.28068i	−0.0352947	−	0.0485791i
$696$	0.126299	−	0.0410372i	0.00478737	−	0.00155551i
$697$	18.0373	−	16.2408i	0.683210	−	0.615165i
$698$	−36.0603	−	3.79009i	−1.36490	−	0.143457i
$699$	−36.5773	+	16.2852i	−1.38348	+	0.615965i
$700$	0.159892	+	0.752233i	0.00604335	+	0.0284317i
$701$	26.2756	+	23.6587i	0.992416	+	0.893576i	0.994321	−	0.106422i	$-0.0339396\pi$
$701$	26.2756	+	23.6587i	0.992416	+	0.893576i	−0.00190461	+	0.999998i	$0.500606\pi$
$702$	13.7546	+	18.9316i	0.519136	+	0.714529i
$703$	−17.1215	−	0.444743i	−0.645749	−	0.0167738i
$704$	1.50728	+	2.95434i	0.0568078	+	0.111346i
$705$	30.0771	−	17.3650i	1.13277	−	0.654004i
$706$	−4.22028	−	1.87899i	−0.158832	−	0.0707167i
$707$	3.99887	+	0.849987i	0.150393	+	0.0319670i
$708$	−4.03579	+	0.857834i	−0.151674	+	0.0322394i
$709$	23.6764	−	10.5414i	0.889187	−	0.395892i	0.0892737	−	0.996007i	$-0.471545\pi$
$709$	23.6764	−	10.5414i	0.889187	−	0.395892i	0.799913	+	0.600116i	$0.204879\pi$
$710$	−19.0303	+	26.1930i	−0.714196	+	0.983006i
$711$	−0.00315179	+	0.00970022i	−0.000118202	+	0.000363787i
$712$	1.71961	−	8.09015i	0.0644453	−	0.303191i
$713$	−24.0194	+	2.52454i	−0.899534	+	0.0945448i
$714$			3.16693i			0.118519i
$715$	−6.19420	+	39.2432i	−0.231650	+	1.46761i
$716$	10.7089	+	6.18278i	0.400210	+	0.231061i
$717$	32.2582	+	14.3623i	1.20470	+	0.536369i
$718$	−0.763811	+	3.59345i	−0.0285052	+	0.134106i
$719$	−32.7771	+	6.96698i	−1.22238	+	0.259825i	−0.773516	−	0.633776i	$-0.781504\pi$
$719$	−32.7771	+	6.96698i	−1.22238	+	0.259825i	−0.448862	+	0.893601i	$0.648171\pi$
$720$	−0.0676426	+	0.643576i	−0.00252089	+	0.0239847i
$721$	−4.60729	−	3.34739i	−0.171585	−	0.124663i
$722$	−18.7648	+	2.98014i	−0.698355	+	0.110909i
$723$	−3.55061	+	1.15366i	−0.132049	+	0.0429052i
$724$	6.66136	−	14.9617i	0.247567	−	0.556046i
$725$	−0.0524824	−	0.0909023i	−0.00194915	−	0.00337603i
$726$	2.09544	+	19.7357i	0.0777691	+	0.732460i
$727$	−18.3064	−	31.7076i	−0.678946	−	1.17597i	−0.975299	−	0.220890i	$-0.929104\pi$
$727$	−18.3064	−	31.7076i	−0.678946	−	1.17597i	0.296353	−	0.955079i	$-0.404230\pi$
$728$	2.53430	−	0.266366i	0.0939274	−	0.00987216i
$729$	−7.51781	−	23.1374i	−0.278437	−	0.856942i
$730$	−1.56272	−	0.507759i	−0.0578389	−	0.0187930i
$731$	−32.3163	+	14.3881i	−1.19526	+	0.532165i
$732$	2.47837	−	1.10344i	0.0916033	−	0.0407844i
$733$	−46.7186	−	15.1798i	−1.72559	−	0.560678i	−0.732790	−	0.680455i	$-0.761782\pi$
$733$	−46.7186	−	15.1798i	−1.72559	−	0.560678i	−0.992801	+	0.119777i	$0.961782\pi$
$734$	−0.136083	−	0.418821i	−0.00502292	−	0.0154590i
$735$	−30.5177	+	3.20754i	−1.12566	+	0.118312i
$736$	1.23284	+	2.13533i	0.0454429	+	0.0787094i
$737$	−26.2857	+	32.4953i	−0.968246	+	1.19698i
$738$	−0.951787	−	1.64854i	−0.0350358	−	0.0606837i
$739$	19.2868	−	43.3189i	0.709477	−	1.59351i	−0.0921899	−	0.995741i	$-0.529387\pi$
$739$	19.2868	−	43.3189i	0.709477	−	1.59351i	0.801667	−	0.597771i	$-0.203947\pi$
$740$	9.47306	−	3.07798i	0.348236	−	0.113149i
$741$	−12.3979	+	35.0339i	−0.455447	+	1.28700i
$742$	1.13339	+	0.823454i	0.0416080	+	0.0302300i
$743$	−1.84006	+	17.5070i	−0.0675053	+	0.642270i	0.907495	+	0.420064i	$0.137992\pi$
$743$	−1.84006	+	17.5070i	−0.0675053	+	0.642270i	−0.975000	+	0.222206i	$0.928674\pi$
$744$	17.2867	−	3.67439i	0.633760	−	0.134710i
$745$	8.64076	−	40.6516i	0.316573	−	1.48936i
$746$	5.06909	+	2.25690i	0.185593	+	0.0826311i
$747$	−2.87281	−	1.65862i	−0.105111	−	0.0606856i
$748$	9.61611	−	4.90607i	0.351600	−	0.179384i
$749$		−	2.74749i		−	0.100391i
$750$	−16.2565	+	1.70862i	−0.593603	+	0.0623902i
$751$	−9.05981	+	42.6231i	−0.330597	+	1.55534i	0.428001	+	0.903778i	$0.359218\pi$
$751$	−9.05981	+	42.6231i	−0.330597	+	1.55534i	−0.758598	+	0.651559i	$0.774115\pi$
$752$	−2.34650	+	7.22178i	−0.0855680	+	0.263351i
$753$	16.3605	−	22.5183i	0.596210	−	0.820612i
$754$	−0.317738	+	0.141466i	−0.0115713	+	0.00515189i
$755$	−35.7297	+	7.59458i	−1.30034	+	0.276395i
$756$	−2.61217	−	0.555235i	−0.0950038	−	0.0201937i
$757$	1.27620	+	0.568201i	0.0463843	+	0.0206516i	0.429798	−	0.902925i	$-0.358585\pi$
$757$	1.27620	+	0.568201i	0.0463843	+	0.0206516i	−0.383413	+	0.923577i	$0.625252\pi$
$758$	26.9701	−	15.5712i	0.979598	−	0.565571i
$759$	2.31583	+	14.5717i	0.0840595	+	0.528918i
$760$	9.70954	−	5.27449i	0.352202	−	0.191326i
$761$	−17.7175	−	24.3861i	−0.642260	−	0.883995i	0.356473	−	0.934305i	$-0.383979\pi$
$761$	−17.7175	−	24.3861i	−0.642260	−	0.883995i	−0.998734	+	0.0503100i	$0.983979\pi$
$762$	−15.7365	−	14.1692i	−0.570074	−	0.513297i
$763$	−1.44337	−	6.79052i	−0.0522535	−	0.245833i
$764$	8.95558	−	3.98728i	0.324001	−	0.144255i
$765$	2.09479	+	0.220171i	0.0757371	+	0.00796029i
$766$	2.80660	−	2.52707i	0.101407	−	0.0913069i
$767$	10.2772	−	3.33927i	0.371088	−	0.120574i
$768$	−1.06050	−	1.45966i	−0.0382677	−	0.0526709i
$769$	−7.49726	−	4.32854i	−0.270358	−	0.156091i	0.358692	−	0.933456i	$-0.383223\pi$
$769$	−7.49726	−	4.32854i	−0.270358	−	0.156091i	−0.629050	+	0.777365i	$0.716556\pi$
$770$	−2.47137	−	3.80116i	−0.0890619	−	0.136984i
$771$	34.2533			1.23360
$772$	4.86524	−	3.53480i	0.175104	−	0.127220i
$773$	3.40670	−	16.0272i	0.122530	−	0.576460i	−0.873452	−	0.486910i	$-0.838124\pi$
$773$	3.40670	−	16.0272i	0.122530	−	0.576460i	0.995982	−	0.0895497i	$-0.0285428\pi$
$774$	0.576824	+	2.71374i	0.0207335	+	0.0975435i
$775$	−5.68158	−	12.7610i	−0.204088	−	0.458390i
$776$	11.2657	+	1.18408i	0.404416	+	0.0425058i
$777$	−0.794857	−	3.73951i	−0.0285153	−	0.134154i
$778$	−0.0278776	−	0.0857985i	−0.000999462	−	0.00307603i
$779$	−13.9871	+	29.3404i	−0.501139	+	1.05123i
$780$		−	21.6125i		−	0.773852i
$781$	10.9418	−	40.9220i	0.391528	−	1.46430i
$782$	6.95033	−	4.01277i	0.248543	−	0.143497i
$783$	0.362500	−	0.0381003i	0.0129547	−	0.00136159i
$784$	4.48932	−	4.98590i	0.160333	−	0.178068i
$785$	11.0673	+	12.2915i	0.395009	+	0.438702i
$786$	18.0966	+	13.1479i	0.645484	+	0.468971i
$787$	−15.5902	−	11.3269i	−0.555731	−	0.403762i	0.274163	−	0.961683i	$-0.411599\pi$
$787$	−15.5902	−	11.3269i	−0.555731	−	0.403762i	−0.829894	+	0.557921i	$0.811599\pi$
$788$	−7.99594	+	7.19958i	−0.284844	+	0.256474i
$789$	10.5391	+	2.24015i	0.375201	+	0.0797514i
$790$	−0.0819395	+	0.0595326i	−0.00291528	+	0.00211807i
$791$	9.12099			0.324305
$792$	−0.219565	−	0.817694i	−0.00780189	−	0.0290555i
$793$	−6.15335	+	3.55264i	−0.218512	+	0.126158i
$794$	−0.810861	−	7.71483i	−0.0287764	−	0.273789i
$795$	7.95049	−	8.82991i	0.281975	−	0.313165i
$796$	−6.86780	+	1.45980i	−0.243423	+	0.0517411i
$797$	−2.13086	+	2.93288i	−0.0754791	+	0.103888i	−0.845087	−	0.534628i	$-0.820452\pi$
$797$	−2.13086	+	2.93288i	−0.0754791	+	0.103888i	0.769608	+	0.638516i	$0.220452\pi$
$798$	−1.62381	−	3.91790i	−0.0574823	−	0.138692i
$799$	23.5063	+	7.63765i	0.831593	+	0.270201i
$800$	−0.954232	+	1.05978i	−0.0337372	+	0.0374690i
$801$	−0.858772	+	1.92883i	−0.0303432	+	0.0681520i
$802$	−25.7288	−	14.8545i	−0.908514	−	0.524531i
$803$	2.14680	−	0.113649i	0.0757588	−	0.00401058i
$804$	11.3684	−	19.6907i	0.400933	−	0.694436i
$805$	−1.98122	−	2.72691i	−0.0698287	−	0.0961110i
$806$	−44.0208	+	14.3032i	−1.55057	+	0.503809i
$807$	−16.1633	−	17.9511i	−0.568974	−	0.631910i
$808$	3.08348	+	6.92562i	0.108477	+	0.243642i
$809$	−24.2851	+	33.4256i	−0.853819	+	1.17518i	0.129189	+	0.991620i	$0.458762\pi$
$809$	−24.2851	+	33.4256i	−0.853819	+	1.17518i	−0.983008	+	0.183561i	$0.941238\pi$
$810$	−7.59901	+	23.3873i	−0.267002	+	0.821747i
$811$	−14.8388	−	3.15408i	−0.521059	−	0.110755i	−0.0601285	−	0.998191i	$-0.519151\pi$
$811$	−14.8388	−	3.15408i	−0.521059	−	0.110755i	−0.460931	+	0.887436i	$0.652484\pi$
$812$	0.0161443	−	0.0362607i	0.000566554	−	0.00127250i
$813$	−17.9224	+	31.0425i	−0.628566	+	1.08871i
$814$	−10.1233	+	8.20659i	−0.354823	+	0.287641i
$815$	16.7597	+	29.0287i	0.587068	+	1.01683i
$816$	−4.75107	+	3.45185i	−0.166321	+	0.120839i
$817$	32.6020	−	34.3698i	1.14060	−	1.20245i
$818$	−1.36035	+	4.18672i	−0.0475635	+	0.146385i
$819$	−0.646949	−	0.0679971i	−0.0226062	−	0.00237601i
$820$	1.97590	−	18.7994i	0.0690014	−	0.656504i
$821$	2.74838	−	2.47465i	0.0959190	−	0.0863658i	−0.619776	−	0.784779i	$-0.712777\pi$
$821$	2.74838	−	2.47465i	0.0959190	−	0.0863658i	0.715695	+	0.698413i	$0.246110\pi$
$822$	1.10855	+	0.998139i	0.0386650	+	0.0348141i
$823$	2.49019	+	23.6926i	0.0868025	+	0.825871i	0.948143	+	0.317843i	$0.102959\pi$
$823$	2.49019	+	23.6926i	0.0868025	+	0.825871i	−0.861341	+	0.508028i	$0.830375\pi$
$824$		−	10.5605i		−	0.367891i
$825$	−7.60146	+	3.87821i	−0.264649	+	0.135022i
$826$	−0.616603	+	1.06799i	−0.0214543	+	0.0371600i
$827$	1.43506	+	13.6537i	0.0499018	+	0.474784i	0.990725	+	0.135885i	$0.0433879\pi$
$827$	1.43506	+	13.6537i	0.0499018	+	0.474784i	−0.940823	+	0.338899i	$0.889945\pi$
$828$	−0.194505	−	0.598624i	−0.00675950	−	0.0208036i
$829$	−22.1411	−	7.19407i	−0.768991	−	0.249860i	−0.101858	−	0.994799i	$-0.532479\pi$
$829$	−22.1411	−	7.19407i	−0.768991	−	0.249860i	−0.667133	+	0.744939i	$0.732479\pi$
$830$	−13.3983	−	30.0931i	−0.465062	−	1.04455i
$831$	1.82569	−	17.3703i	0.0633325	−	0.602568i
$832$	3.16191	+	3.51165i	0.109619	+	0.121745i
$833$	−16.2287	−	14.6124i	−0.562290	−	0.506289i
$834$	−1.02928	−	0.458267i	−0.0356412	−	0.0158685i
$835$	−19.9299			−0.689701
$836$	−9.38083	+	11.0000i	−0.324443	+	0.380443i
$837$	48.5071			1.67665
$838$	16.8099	+	7.48423i	0.580687	+	0.258539i
$839$	−2.48013	−	2.23312i	−0.0856237	−	0.0770959i	0.625208	−	0.780459i	$-0.285014\pi$
$839$	−2.48013	−	2.23312i	−0.0856237	−	0.0770959i	−0.710831	+	0.703363i	$0.751681\pi$
$840$	1.65038	+	1.83293i	0.0569434	+	0.0632420i
$841$	3.03076	−	28.8357i	0.104509	−	0.994336i
$842$	−4.42829	−	9.94611i	−0.152609	−	0.342765i
$843$	47.1717	+	15.3270i	1.62468	+	0.527890i
$844$	2.46476	+	7.58574i	0.0848404	+	0.261112i
$845$	2.47207	+	23.5202i	0.0850417	+	0.809118i
$846$	0.969216	−	1.67873i	0.0333223	−	0.0577160i
$847$	4.80274	+	3.48163i	0.165024	+	0.119630i
$848$			2.59786i			0.0892109i
$849$	5.61362	+	53.4100i	0.192659	+	1.83303i
$850$	3.44950	+	3.10594i	0.118317	+	0.106533i
$851$	−7.19978	+	6.48271i	−0.246805	+	0.222225i
$852$	−2.40870	+	22.9173i	−0.0825208	+	0.785133i
$853$	−33.7371	−	3.54592i	−1.15514	−	0.121410i	−0.492474	−	0.870327i	$-0.663907\pi$
$853$	−33.7371	−	3.54592i	−1.15514	−	0.121410i	−0.662663	+	0.748917i	$0.730574\pi$
$854$	0.250570	−	0.771177i	0.00857435	−	0.0263891i
$855$	−2.70441	+	0.801700i	−0.0924888	+	0.0274176i
$856$	4.12182	−	2.99467i	0.140881	−	0.102356i
$857$	16.6328	+	28.8088i	0.568165	+	0.984091i	0.996747	+	0.0805881i	$0.0256798\pi$
$857$	16.6328	+	28.8088i	0.568165	+	0.984091i	−0.428582	+	0.903503i	$0.640987\pi$
$858$	10.1474	+	26.3932i	0.346428	+	0.901049i
$859$	−26.8437	+	46.4947i	−0.915895	+	1.58638i	−0.110311	+	0.993897i	$0.535185\pi$
$859$	−26.8437	+	46.4947i	−0.915895	+	1.58638i	−0.805585	+	0.592480i	$0.798149\pi$
$860$	−11.2057	+	25.1684i	−0.382110	+	0.858234i
$861$	−7.09677	−	1.50847i	−0.241857	−	0.0514084i
$862$	−1.79889	+	5.53640i	−0.0612703	+	0.188571i
$863$	23.2273	−	31.9697i	0.790668	−	1.08826i	−0.203357	−	0.979105i	$-0.565185\pi$
$863$	23.2273	−	31.9697i	0.790668	−	1.08826i	0.994025	−	0.109156i	$-0.0348150\pi$
$864$	−2.01421	−	4.52400i	−0.0685250	−	0.153910i
$865$	19.0086	+	21.1112i	0.646313	+	0.717804i
$866$	35.9631	−	11.6851i	1.22208	−	0.397077i
$867$	−6.79309	−	9.34989i	−0.230706	−	0.317539i
$868$	2.64112	−	4.57455i	0.0896454	−	0.155270i
$869$	0.0721130	−	0.111173i	0.00244627	−	0.00377129i
$870$	−0.291540	−	0.168321i	−0.00988414	−	0.00570661i
$871$	−24.2207	+	54.4007i	−0.820688	+	1.84330i
$872$	8.61399	−	9.56681i	0.291707	−	0.323973i
$873$	−2.75020	−	0.893593i	−0.0930800	−	0.0302435i
$874$	−6.54094	+	8.52803i	−0.221251	+	0.288465i
$875$	−2.87172	+	3.95258i	−0.0970818	+	0.133622i
$876$	−1.14393	+	0.243151i	−0.0386499	+	0.00821530i
$877$	−22.3844	+	24.8603i	−0.755866	+	0.839474i	−0.991191	−	0.132443i	$-0.957718\pi$
$877$	−22.3844	+	24.8603i	−0.755866	+	0.839474i	0.235325	+	0.971917i	$0.424385\pi$
$878$	−0.736514	−	7.00746i	−0.0248562	−	0.236490i
$879$	13.9807	−	8.07176i	0.471557	−	0.272254i
$880$	3.00884	−	7.85072i	0.101428	−	0.264648i
$881$	12.0976			0.407578			0.203789	−	0.979015i	$-0.434674\pi$
$881$	12.0976			0.407578			0.203789	+	0.979015i	$0.434674\pi$
$882$	−1.38561	+	1.00670i	−0.0466558	+	0.0338974i
$883$	32.7982	+	6.97147i	1.10375	+	0.234609i	0.723533	−	0.690290i	$-0.242517\pi$
$883$	32.7982	+	6.97147i	1.10375	+	0.234609i	0.380214	+	0.924899i	$0.375850\pi$
$884$	11.4301	−	10.2917i	0.384437	−	0.346149i
$885$	8.46165	+	6.14775i	0.284435	+	0.206654i
$886$	22.4305	+	16.2967i	0.753568	+	0.547499i
$887$	10.7479	+	11.9367i	0.360878	+	0.400796i	0.896054	−	0.443945i	$-0.146421\pi$
$887$	10.7479	+	11.9367i	0.360878	+	0.400796i	−0.535176	+	0.844741i	$0.679755\pi$
$888$	4.74368	−	5.26839i	0.159188	−	0.176796i
$889$	−6.29449	+	0.661577i	−0.211110	+	0.0221886i
$890$	−18.1575	+	10.4832i	−0.608640	+	0.351399i
$891$	−1.70084	−	32.1285i	−0.0569804	−	1.07634i
$892$			21.7516i			0.728297i
$893$	−32.9964	+	2.60385i	−1.10418	+	0.0871344i
$894$	−9.14064	−	28.1320i	−0.305709	−	0.940874i
$895$	−6.51727	−	30.6614i	−0.217848	−	1.02490i
$896$	−0.536314	−	0.0563689i	−0.0179170	−	0.00188315i
$897$	8.55029	+	19.2043i	0.285486	+	0.641212i
$898$	4.60822	+	21.6800i	0.153778	+	0.723470i
$899$	−0.149897	+	0.705210i	−0.00499934	+	0.0235201i
$900$	0.294519	−	0.213981i	0.00981730	−	0.00713268i
$901$	8.45581			0.281704
$902$	6.41368	+	23.8856i	0.213552	+	0.795303i
$903$	9.15760	+	5.28714i	0.304746	+	0.175945i
$904$	9.94159	+	13.6834i	0.330652	+	0.455104i
$905$	−39.4847	+	12.8294i	−1.31252	+	0.426462i
$906$	−19.3205	+	17.3963i	−0.641882	+	0.577953i
$907$	29.1514	+	3.06393i	0.967956	+	0.101736i	0.575294	−	0.817947i	$-0.304888\pi$
$907$	29.1514	+	3.06393i	0.967956	+	0.101736i	0.392662	+	0.919683i	$0.371554\pi$
$908$	24.1809	−	10.7660i	0.802470	−	0.357283i
$909$	−0.402365	−	1.89298i	−0.0133456	−	0.0627861i
$910$	−4.80054	−	4.32242i	−0.159136	−	0.143287i
$911$	23.1642	+	31.8828i	0.767465	+	1.05632i	0.996556	+	0.0829195i	$0.0264244\pi$
$911$	23.1642	+	31.8828i	0.767465	+	1.05632i	−0.229092	+	0.973405i	$0.573576\pi$
$912$	4.10778	−	6.70645i	0.136022	−	0.222073i
$913$	30.4912	+	30.4589i	1.00911	+	1.00804i
$914$	1.42362	−	0.821927i	0.0470891	−	0.0271869i
$915$	−6.28260	−	2.79719i	−0.207696	−	0.0924724i
$916$	−2.65268	−	0.563845i	−0.0876471	−	0.0186300i
$917$	6.53965	−	1.39005i	0.215958	−	0.0459033i
$918$	−14.7252	+	6.55610i	−0.486005	+	0.216383i
$919$	−29.8344	+	41.0635i	−0.984146	+	1.35456i	−0.0495806	+	0.998770i	$0.515788\pi$
$919$	−29.8344	+	41.0635i	−0.984146	+	1.35456i	−0.934566	+	0.355791i	$0.884212\pi$
$920$	1.93148	−	5.94449i	0.0636790	−	0.195984i
$921$	−5.86576	+	27.5963i	−0.193283	+	0.909327i
$922$	5.77836	−	0.607331i	0.190300	−	0.0200014i
$923$		−	60.3522i		−	1.98652i
$924$	−2.87603	−	1.46349i	−0.0946144	−	0.0481454i
$925$	−4.85271	−	2.80171i	−0.159556	−	0.0921198i
$926$	36.8967	+	16.4275i	1.21250	+	0.539840i
$927$	−0.560499	+	2.63694i	−0.0184092	+	0.0866084i
$928$	0.0719955	−	0.0153031i	0.00236337	−	0.000502349i
$929$	4.11567	−	39.1580i	0.135031	−	1.28473i	−0.691721	−	0.722165i	$-0.743147\pi$
$929$	4.11567	−	39.1580i	0.135031	−	1.28473i	0.826751	−	0.562567i	$-0.190186\pi$
$930$	−36.2441	−	26.3329i	−1.18849	−	0.863490i
$931$	27.5693	+	9.75628i	0.903547	+	0.319749i
$932$	−21.1054	+	6.85756i	−0.691330	+	0.224627i
$933$	11.5950	−	26.0428i	0.379604	−	0.852604i
$934$	2.86056	+	4.95464i	0.0936005	+	0.162121i
$935$	−25.5534	−	9.79351i	−0.835686	−	0.320282i
$936$	−0.603144	−	1.04468i	−0.0197144	−	0.0341463i
$937$	19.8305	−	2.08427i	0.647835	−	0.0680902i	0.225089	−	0.974338i	$-0.427733\pi$
$937$	19.8305	−	2.08427i	0.647835	−	0.0680902i	0.422746	+	0.906248i	$0.361066\pi$
$938$	−2.10002	−	6.46319i	−0.0685680	−	0.211031i
$939$	−10.3116	−	3.35045i	−0.336507	−	0.109338i
$940$	17.5849	−	7.82932i	0.573558	−	0.255364i
$941$	−39.0236	+	17.3744i	−1.27213	+	0.566390i	−0.928017	−	0.372537i	$-0.878488\pi$
$941$	−39.0236	+	17.3744i	−1.27213	+	0.566390i	−0.344115	+	0.938927i	$0.611821\pi$
$942$	11.1959	+	3.63777i	0.364782	+	0.118525i
$943$	5.68165	+	17.4863i	0.185020	+	0.569433i
$944$	−2.27428	+	0.239037i	−0.0740216	+	0.00777998i
$945$	3.38486	+	5.86275i	0.110109	+	0.190715i
$946$	1.86740	−	35.9968i	0.0607144	−	1.17036i
$947$	−4.59726	−	7.96269i	−0.149391	−	0.258753i	0.781612	−	0.623765i	$-0.214398\pi$
$947$	−4.59726	−	7.96269i	−0.149391	−	0.258753i	−0.931003	+	0.365013i	$0.881065\pi$
$948$	−0.0293204	+	0.0658548i	−0.000952283	+	0.00213886i
$949$	2.91304	−	0.946505i	0.0945614	−	0.0307249i
$950$	−5.86001	−	2.07376i	−0.190124	−	0.0672815i
$951$	−38.3640	−	27.8731i	−1.24404	−	0.903846i
$952$	−0.183476	+	1.74566i	−0.00594649	+	0.0565771i
$953$	−27.7566	+	5.89984i	−0.899123	+	0.191114i	−0.634213	−	0.773159i	$-0.718676\pi$
$953$	−27.7566	+	5.89984i	−0.899123	+	0.191114i	−0.264910	+	0.964273i	$0.585342\pi$
$954$	0.137882	−	0.648683i	0.00446409	−	0.0210019i
$955$	−22.7021	−	10.1076i	−0.734623	−	0.327075i
$956$	16.9491	+	9.78556i	0.548173	+	0.316488i
$957$	0.435058	+	0.0686703i	0.0140634	+	0.00221980i
$958$			0.734116i			0.0237182i
$959$	0.443410	−	0.0466043i	0.0143185	−	0.00150493i
$960$	−0.950924	+	4.47375i	−0.0306909	+	0.144390i
$961$	−20.0693	+	61.7671i	−0.647398	+	1.99249i
$962$	−10.9136	+	15.0213i	−0.351868	+	0.484305i
$963$	−1.18816	+	0.529001i	−0.0382878	+	0.0170468i
$964$	−2.02398	+	0.430211i	−0.0651882	+	0.0138562i
$965$	−14.9116	−	3.16956i	−0.480021	−	0.102032i
$966$	−2.19162	−	0.975770i	−0.0705141	−	0.0313949i
$967$	−24.8564	+	14.3509i	−0.799328	+	0.461492i	−0.843236	−	0.537543i	$-0.819352\pi$
$967$	−24.8564	+	14.3509i	−0.799328	+	0.461492i	0.0439080	+	0.999036i	$0.486019\pi$
$968$	0.0116507	+	11.0000i	0.000374467	+	0.353553i
$969$	−21.8289	−	13.3705i	−0.701246	−	0.429521i
$970$	−16.8786	−	23.2314i	−0.541939	−	0.745915i
$971$	−13.9807	−	12.5883i	−0.448663	−	0.403978i	0.413584	−	0.910466i	$-0.364277\pi$
$971$	−13.9807	−	12.5883i	−0.448663	−	0.403978i	−0.862247	+	0.506488i	$0.830943\pi$
$972$	0.550116	+	2.58809i	0.0176450	+	0.0830131i
$973$	−0.307642	+	0.136971i	−0.00986256	+	0.00439109i
$974$	−10.8776	−	1.14328i	−0.348540	−	0.0366330i
$975$	−9.03543	+	8.13554i	−0.289365	+	0.260546i
$976$	1.43004	−	0.464649i	0.0457745	−	0.0148730i
$977$	30.9169	+	42.5535i	0.989120	+	1.36141i	0.931769	+	0.363053i	$0.118265\pi$
$977$	30.9169	+	42.5535i	0.989120	+	1.36141i	0.0573511	+	0.998354i	$0.481735\pi$
$978$	20.6609	+	11.9286i	0.660662	+	0.381433i
$979$	17.2519	−	21.3274i	0.551372	−	0.681626i
$980$	−17.0076			−0.543288
$981$	−2.65867	+	1.93163i	−0.0848847	+	0.0616723i
$982$	−6.77210	+	31.8602i	−0.216106	+	1.01670i
$983$	−8.40333	−	39.5345i	−0.268024	−	1.26096i	−0.881856	−	0.471519i	$-0.843706\pi$
$983$	−8.40333	−	39.5345i	−0.268024	−	1.26096i	0.613831	−	0.789437i	$-0.289627\pi$
$984$	−5.47223	−	12.2908i	−0.174448	−	0.391818i
$985$	27.1259	+	2.85104i	0.864302	+	0.0908418i
$986$	−0.0498103	−	0.234339i	−0.00158628	−	0.00746288i
$987$	−2.28307	−	7.02657i	−0.0726710	−	0.223658i
$988$	−8.86356	+	18.5929i	−0.281987	+	0.591519i
$989$		−	26.7970i		−	0.852096i
$990$	−1.16798	+	1.80062i	−0.0371209	+	0.0572275i
$991$	−9.00337	+	5.19810i	−0.286001	+	0.165123i	−0.636137	−	0.771576i	$-0.719469\pi$
$991$	−9.00337	+	5.19810i	−0.286001	+	0.165123i	0.350136	+	0.936699i	$0.386135\pi$
$992$	9.74153	−	1.02388i	0.309294	−	0.0325081i
$993$	−28.8017	+	31.9876i	−0.913995	+	1.01509i
$994$	4.60862	+	5.11839i	0.146177	+	0.162345i
$995$	14.3994	+	10.4618i	0.456491	+	0.331660i
$996$	−18.9677	−	13.7809i	−0.601015	−	0.436663i
$997$	−8.95121	+	8.05970i	−0.283488	+	0.255253i	−0.798590	−	0.601875i	$-0.794420\pi$
$997$	−8.95121	+	8.05970i	−0.283488	+	0.255253i	0.515103	+	0.857129i	$0.327754\pi$
$998$	−3.96683	−	0.843175i	−0.125568	−	0.0266903i
$999$	15.7420	−	11.4373i	0.498056	−	0.361859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.s.a.107.8	✓	80
11.7	odd	10		418.2.s.b.183.3	yes	80
19.8	odd	6		418.2.s.b.217.3	yes	80
209.84	even	30	inner	418.2.s.a.293.8	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.s.a.107.8	✓	80	1.1	even	1	trivial
418.2.s.a.293.8	yes	80	209.84	even	30	inner
418.2.s.b.183.3	yes	80	11.7	odd	10
418.2.s.b.217.3	yes	80	19.8	odd	6

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.s (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.913545 - 0.406737i) q^{2} +(1.34081 + 1.20727i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.264977 - 2.52108i) q^{5} +(-0.733850 - 1.64825i) q^{6} +(-0.512875 - 0.166643i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0266838 + 0.253879i) q^{9} +O(q^{10})\)	\(q+(-0.913545 - 0.406737i) q^{2} +(1.34081 + 1.20727i) q^{3} +(0.669131 + 0.743145i) q^{4} +(0.264977 - 2.52108i) q^{5} +(-0.733850 - 1.64825i) q^{6} +(-0.512875 - 0.166643i) q^{7} +(-0.309017 - 0.951057i) q^{8} +(0.0266838 + 0.253879i) q^{9} +(-1.26749 + 2.19535i) q^{10} +(0.517100 - 3.27607i) q^{11} +1.80424i q^{12} +(-0.493939 - 4.69951i) q^{13} +(0.400755 + 0.360841i) q^{14} +(3.39892 - 3.06040i) q^{15} +(-0.104528 + 0.994522i) q^{16} +(3.23708 + 0.340231i) q^{17} +(0.0788851 - 0.242783i) q^{18} +(-4.17914 + 1.23887i) q^{19} +(2.05083 - 1.49002i) q^{20} +(-0.486485 - 0.842616i) q^{21} +(-1.80489 + 2.78251i) q^{22} +(-1.23284 + 2.13533i) q^{23} +(0.733850 - 1.64825i) q^{24} +(-1.39491 - 0.296498i) q^{25} +(-1.46023 + 4.49412i) q^{26} +(2.91079 - 4.00636i) q^{27} +(-0.219340 - 0.492646i) q^{28} +(0.0492506 + 0.0546984i) q^{29} +(-4.34984 + 1.41335i) q^{30} +(5.75747 + 7.92448i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.64843 - 3.76830i) q^{33} +(-2.81884 - 1.62746i) q^{34} +(-0.556021 + 1.24884i) q^{35} +(-0.170814 + 0.189708i) q^{36} +(3.73695 + 1.21421i) q^{37} +(4.32173 + 0.568043i) q^{38} +(5.01131 - 6.89747i) q^{39} +(-2.47958 + 0.527050i) q^{40} +(4.98963 - 5.54154i) q^{41} +(0.101703 + 0.967639i) q^{42} +(-9.41201 + 5.43403i) q^{43} +(2.78060 - 1.80784i) q^{44} +0.647121 q^{45} +(1.99477 - 1.44929i) q^{46} +(7.42749 + 1.57876i) q^{47} +(-1.34081 + 1.20727i) q^{48} +(-5.42785 - 3.94356i) q^{49} +(1.15372 + 0.838227i) q^{50} +(3.92957 + 4.36423i) q^{51} +(3.16191 - 3.51165i) q^{52} +(2.58363 - 0.271550i) q^{53} +(-4.28867 + 2.47607i) q^{54} +(-8.12222 - 2.17173i) q^{55} +0.539269i q^{56} +(-7.09909 - 3.38426i) q^{57} +(-0.0227449 - 0.0700015i) q^{58} +(0.475455 + 2.23684i) q^{59} +(4.54864 + 0.478081i) q^{60} +(-0.611583 - 1.37364i) q^{61} +(-2.03653 - 9.58114i) q^{62} +(0.0286218 - 0.134655i) q^{63} +(-0.809017 + 0.587785i) q^{64} -11.9787 q^{65} +(-5.77926 + 1.55183i) q^{66} +(-10.9136 - 6.30094i) q^{67} +(1.91319 + 2.63328i) q^{68} +(-4.23093 + 1.37471i) q^{69} +(1.01590 - 0.914722i) q^{70} +(12.7019 + 1.33502i) q^{71} +(0.233208 - 0.103831i) q^{72} +(0.134766 + 0.634025i) q^{73} +(-2.92001 - 2.62919i) q^{74} +(-1.51236 - 2.08159i) q^{75} +(-3.71705 - 2.27674i) q^{76} +(-0.811141 + 1.59404i) q^{77} +(-7.38351 + 4.26287i) q^{78} +(0.0365000 + 0.0162509i) q^{79} +(2.47958 + 0.527050i) q^{80} +(9.48868 - 2.01688i) q^{81} +(-6.81220 + 3.03299i) q^{82} +(-7.63805 + 10.5129i) q^{83} +(0.300664 - 0.925349i) q^{84} +(1.71550 - 8.07081i) q^{85} +(10.8085 - 1.13602i) q^{86} +0.132799i q^{87} +(-3.27552 + 0.520569i) q^{88} +(7.16280 + 4.13544i) q^{89} +(-0.591174 - 0.263208i) q^{90} +(-0.529813 + 2.49257i) q^{91} +(-2.41179 + 0.512642i) q^{92} +(-1.84732 + 17.5760i) q^{93} +(-6.14321 - 4.46331i) q^{94} +(2.01593 + 10.8642i) q^{95} +(1.71593 - 0.557540i) q^{96} +(-4.60742 + 10.3484i) q^{97} +(3.35459 + 5.81033i) q^{98} +(0.845523 + 0.0438630i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9}+O(q^{10}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9	\( 80 q - 10 q^{2} - 3 q^{3} + 10 q^{4} - 2 q^{5} + 7 q^{6} - 10 q^{7} + 20 q^{8} - 11 q^{9} + 2 q^{10} - q^{11} + 5 q^{13} - 4 q^{14} - 27 q^{15} + 10 q^{16} - 6 q^{17} - 17 q^{18} - 2 q^{19} + 4 q^{20} + 24 q^{21} - 2 q^{22} - 6 q^{23} - 7 q^{24} - 10 q^{26} - 45 q^{27} + 6 q^{28} - 65 q^{29} + 30 q^{30} + 40 q^{32} + 3 q^{33} + 24 q^{34} - 13 q^{35} - q^{36} + 22 q^{38} - 30 q^{39} - 3 q^{40} - 14 q^{41} - 14 q^{42} + 12 q^{43} + 24 q^{44} - 12 q^{45} - 2 q^{46} - q^{47} + 3 q^{48} + 32 q^{49} + 30 q^{50} - 28 q^{51} - 5 q^{52} - q^{53} - 27 q^{54} - 23 q^{55} + 28 q^{57} - 10 q^{58} + 56 q^{59} - 28 q^{60} + 28 q^{61} + 15 q^{62} + 88 q^{63} - 20 q^{64} + 8 q^{65} - 57 q^{66} - 27 q^{67} - 60 q^{69} + 17 q^{70} + 2 q^{71} + 11 q^{72} - q^{73} + 12 q^{74} - 35 q^{75} - 11 q^{76} - 8 q^{77} - 6 q^{79} + 3 q^{80} + 43 q^{81} - 16 q^{82} - 25 q^{83} + 52 q^{84} - 33 q^{85} - 43 q^{86} - 9 q^{88} - 36 q^{89} + 74 q^{90} + 38 q^{91} - 11 q^{92} + 15 q^{93} - 2 q^{94} - 61 q^{95} - 24 q^{97} - 44 q^{98} + 37 q^{99}+O(q^{100}) \) 80 * q - 10 * q^2 - 3 * q^3 + 10 * q^4 - 2 * q^5 + 7 * q^6 - 10 * q^7 + 20 * q^8 - 11 * q^9 + 2 * q^10 - q^11 + 5 * q^13 - 4 * q^14 - 27 * q^15 + 10 * q^16 - 6 * q^17 - 17 * q^18 - 2 * q^19 + 4 * q^20 + 24 * q^21 - 2 * q^22 - 6 * q^23 - 7 * q^24 - 10 * q^26 - 45 * q^27 + 6 * q^28 - 65 * q^29 + 30 * q^30 + 40 * q^32 + 3 * q^33 + 24 * q^34 - 13 * q^35 - q^36 + 22 * q^38 - 30 * q^39 - 3 * q^40 - 14 * q^41 - 14 * q^42 + 12 * q^43 + 24 * q^44 - 12 * q^45 - 2 * q^46 - q^47 + 3 * q^48 + 32 * q^49 + 30 * q^50 - 28 * q^51 - 5 * q^52 - q^53 - 27 * q^54 - 23 * q^55 + 28 * q^57 - 10 * q^58 + 56 * q^59 - 28 * q^60 + 28 * q^61 + 15 * q^62 + 88 * q^63 - 20 * q^64 + 8 * q^65 - 57 * q^66 - 27 * q^67 - 60 * q^69 + 17 * q^70 + 2 * q^71 + 11 * q^72 - q^73 + 12 * q^74 - 35 * q^75 - 11 * q^76 - 8 * q^77 - 6 * q^79 + 3 * q^80 + 43 * q^81 - 16 * q^82 - 25 * q^83 + 52 * q^84 - 33 * q^85 - 43 * q^86 - 9 * q^88 - 36 * q^89 + 74 * q^90 + 38 * q^91 - 11 * q^92 + 15 * q^93 - 2 * q^94 - 61 * q^95 - 24 * q^97 - 44 * q^98 + 37 * q^99

Introduction

L-functions

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