LMFDB - Embedded newform 354.2.e.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, 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:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$2$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	354.7
Dual form			354.2.e.b.253.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.561187 + 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(2.80275 - 1.29669i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(-0.846851 + 3.05008i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})$	\(q+(0.561187 + 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(2.80275 - 1.29669i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(-0.846851 + 3.05008i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(2.64613 + 1.59212i) q^{10} +(-0.0868341 + 0.0822536i) q^{11} +(-0.907575 - 0.419889i) q^{12} +(3.36600 - 0.366075i) q^{13} +(-2.99976 + 1.01074i) q^{14} +(1.14305 + 2.86885i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(0.194991 + 0.702295i) q^{17} +(-0.468408 - 0.883512i) q^{18} +(-1.84943 + 1.40590i) q^{19} +(0.167191 + 3.08365i) q^{20} +(-2.99976 - 1.01074i) q^{21} +(-0.116811 - 0.0257120i) q^{22} +(-0.467812 + 0.882387i) q^{23} +(-0.161782 - 0.986827i) q^{24} +(2.93709 - 3.45781i) q^{25} +(2.19195 + 2.58057i) q^{26} +(0.161782 - 0.986827i) q^{27} +(-2.52000 - 1.91566i) q^{28} +(2.24514 - 3.31133i) q^{29} +(-1.73305 + 2.55605i) q^{30} +(-2.92940 - 2.22687i) q^{31} +(0.161782 - 0.986827i) q^{32} +(-0.0774319 - 0.0911599i) q^{33} +(-0.471855 + 0.555511i) q^{34} +(1.58150 + 9.64674i) q^{35} +(0.468408 - 0.883512i) q^{36} +(-3.49596 - 0.769519i) q^{37} +(-2.20153 - 0.741781i) q^{38} +(0.183306 + 3.38089i) q^{39} +(-2.45848 + 1.86889i) q^{40} +(0.792827 + 1.49543i) q^{41} +(-0.846851 - 3.05008i) q^{42} +(-8.88807 - 8.41923i) q^{43} +(-0.0442711 - 0.111112i) q^{44} +(-2.92652 + 0.986060i) q^{45} +(-0.992873 + 0.107981i) q^{46} +(9.30161 + 4.30338i) q^{47} +(0.725995 - 0.687699i) q^{48} +(-2.58785 - 1.55706i) q^{49} +(4.51025 + 0.490519i) q^{50} +(-0.711821 + 0.156684i) q^{51} +(-0.905811 + 3.26244i) q^{52} +(9.53747 - 5.73850i) q^{53} +(0.907575 - 0.419889i) q^{54} +(-0.136717 + 0.343134i) q^{55} +(0.171375 - 3.16082i) q^{56} +(-1.30371 - 1.92284i) q^{57} +4.00069 q^{58} +(-6.73471 - 3.69373i) q^{59} -3.08818 q^{60} +(-6.40784 - 9.45086i) q^{61} +(0.199216 - 3.67433i) q^{62} +(1.17166 - 2.94064i) q^{63} +(0.907575 - 0.419889i) q^{64} +(8.95939 - 5.39069i) q^{65} +(0.0319982 - 0.115247i) q^{66} +(12.5032 - 2.75216i) q^{67} +(-0.724589 - 0.0788038i) q^{68} +(-0.855766 - 0.514898i) q^{69} +(-7.09698 + 6.72262i) q^{70} +(9.16754 + 4.24136i) q^{71} +(0.994138 - 0.108119i) q^{72} +(9.07193 - 3.05669i) q^{73} +(-1.32496 - 3.32541i) q^{74} +(3.29373 + 3.11998i) q^{75} +(-0.621505 - 2.23846i) q^{76} +(-0.177345 - 0.334508i) q^{77} +(-2.69545 + 2.04903i) q^{78} +(-0.520186 - 9.59426i) q^{79} +(-2.92652 - 0.986060i) q^{80} +(0.976621 + 0.214970i) q^{81} +(-0.792827 + 1.49543i) q^{82} +(-1.94870 - 11.8866i) q^{83} +(2.04928 - 2.41260i) q^{84} +(1.45717 + 1.71552i) q^{85} +(1.98063 - 12.0813i) q^{86} +(3.18493 + 2.42112i) q^{87} +(0.0671219 - 0.0989973i) q^{88} +(-5.81504 + 8.57655i) q^{89} +(-2.45848 - 1.86889i) q^{90} +(-1.73395 + 10.5766i) q^{91} +(-0.646562 - 0.761192i) q^{92} +(2.38220 - 2.80455i) q^{93} +(1.65808 + 10.1138i) q^{94} +(-3.36048 + 6.33855i) q^{95} +(0.976621 + 0.214970i) q^{96} +(-11.8292 - 3.98574i) q^{97} +(-0.163508 - 3.01573i) q^{98} +(0.0952182 - 0.0723830i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) $ 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

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 $

$2$	0.561187	+	0.827689i	0.396819	+	0.585265i
$2$	0.561187	+	0.827689i	0.396819	+	0.585265i
$3$	−0.0541389	+	0.998533i	−0.0312571	+	0.576504i
$3$	−0.0541389	+	0.998533i	−0.0312571	+	0.576504i
$4$	−0.370138	+	0.928977i	−0.185069	+	0.464488i
$5$	2.80275	−	1.29669i	1.25343	−	0.579898i	0.323011	−	0.946395i	$-0.395305\pi$
$5$	2.80275	−	1.29669i	1.25343	−	0.579898i	0.930419	+	0.366497i	$0.119443\pi$
$6$	−0.856857	+	0.515554i	−0.349810	+	0.210474i
$7$	−0.846851	+	3.05008i	−0.320080	+	1.15282i	0.612086	+	0.790791i	$0.290331\pi$
$7$	−0.846851	+	3.05008i	−0.320080	+	1.15282i	−0.932166	+	0.362032i	$0.882083\pi$
$8$	−0.976621	+	0.214970i	−0.345288	+	0.0760035i
$9$	−0.994138	−	0.108119i	−0.331379	−	0.0360397i
$10$	2.64613	+	1.59212i	0.836779	+	0.503473i
$11$	−0.0868341	+	0.0822536i	−0.0261815	+	0.0248004i	−0.700678	−	0.713477i	$-0.747119\pi$
$11$	−0.0868341	+	0.0822536i	−0.0261815	+	0.0248004i	0.674497	+	0.738278i	$0.264361\pi$
$12$	−0.907575	−	0.419889i	−0.261994	−	0.121212i
$13$	3.36600	−	0.366075i	0.933561	−	0.101531i	0.371321	−	0.928505i	$-0.378905\pi$
$13$	3.36600	−	0.366075i	0.933561	−	0.101531i	0.562241	+	0.826974i	$0.309939\pi$
$14$	−2.99976	+	1.01074i	−0.801720	+	0.270131i
$15$	1.14305	+	2.86885i	0.295135	+	0.740733i
$16$	−0.725995	−	0.687699i	−0.181499	−	0.171925i
$17$	0.194991	+	0.702295i	0.0472923	+	0.170332i	0.983425	−	0.181316i	$-0.0580355\pi$
$17$	0.194991	+	0.702295i	0.0472923	+	0.170332i	−0.936133	+	0.351647i	$0.885622\pi$
$18$	−0.468408	−	0.883512i	−0.110405	−	0.208246i
$19$	−1.84943	+	1.40590i	−0.424289	+	0.322536i	−0.795436	−	0.606038i	$-0.792758\pi$
$19$	−1.84943	+	1.40590i	−0.424289	+	0.322536i	0.371146	+	0.928574i	$0.378965\pi$
$20$	0.167191	+	3.08365i	0.0373850	+	0.689525i
$21$	−2.99976	−	1.01074i	−0.654602	−	0.220561i
$22$	−0.116811	−	0.0257120i	−0.0249041	−	0.00548181i
$23$	−0.467812	+	0.882387i	−0.0975456	+	0.183990i	−0.927482	−	0.373867i	$-0.878032\pi$
$23$	−0.467812	+	0.882387i	−0.0975456	+	0.183990i	0.829937	+	0.557858i	$0.188376\pi$
$24$	−0.161782	−	0.986827i	−0.0330236	−	0.201435i
$25$	2.93709	−	3.45781i	0.587418	−	0.691562i
$26$	2.19195	+	2.58057i	0.429878	+	0.506091i
$27$	0.161782	−	0.986827i	0.0311350	−	0.189915i
$28$	−2.52000	−	1.91566i	−0.476236	−	0.362025i
$29$	2.24514	−	3.31133i	0.416912	−	0.614899i	−0.560013	−	0.828484i	$-0.689204\pi$
$29$	2.24514	−	3.31133i	0.416912	−	0.614899i	0.976924	+	0.213585i	$0.0685141\pi$
$30$	−1.73305	+	2.55605i	−0.316409	+	0.466669i
$31$	−2.92940	−	2.22687i	−0.526136	−	0.399959i	0.308110	−	0.951351i	$-0.400304\pi$
$31$	−2.92940	−	2.22687i	−0.526136	−	0.399959i	−0.834246	+	0.551392i	$0.814097\pi$
$32$	0.161782	−	0.986827i	0.0285993	−	0.174448i
$33$	−0.0774319	−	0.0911599i	−0.0134792	−	0.0158689i
$34$	−0.471855	+	0.555511i	−0.0809225	+	0.0952693i
$35$	1.58150	+	9.64674i	0.267323	+	1.63060i
$36$	0.468408	−	0.883512i	0.0780681	−	0.147252i
$37$	−3.49596	−	0.769519i	−0.574732	−	0.126508i	−0.0819123	−	0.996640i	$-0.526103\pi$
$37$	−3.49596	−	0.769519i	−0.574732	−	0.126508i	−0.492820	+	0.870131i	$0.664034\pi$
$38$	−2.20153	−	0.741781i	−0.357135	−	0.120333i
$39$	0.183306	+	3.38089i	0.0293525	+	0.541375i
$40$	−2.45848	+	1.86889i	−0.388719	+	0.295497i
$41$	0.792827	+	1.49543i	0.123819	+	0.233547i	0.937670	−	0.347526i	$-0.112978\pi$
$41$	0.792827	+	1.49543i	0.123819	+	0.233547i	−0.813852	+	0.581073i	$0.802633\pi$
$42$	−0.846851	−	3.05008i	−0.130672	−	0.470638i
$43$	−8.88807	−	8.41923i	−1.35542	−	1.28392i	−0.924322	−	0.381614i	$-0.875368\pi$
$43$	−8.88807	−	8.41923i	−1.35542	−	1.28392i	−0.431096	−	0.902306i	$-0.641873\pi$
$44$	−0.0442711	−	0.111112i	−0.00667412	−	0.0167508i
$45$	−2.92652	+	0.986060i	−0.436260	+	0.146993i
$46$	−0.992873	+	0.107981i	−0.146391	+	0.0159210i
$47$	9.30161	+	4.30338i	1.35678	+	0.627713i	0.957318	−	0.289037i	$-0.0933352\pi$
$47$	9.30161	+	4.30338i	1.35678	+	0.627713i	0.399461	+	0.916750i	$0.369197\pi$
$48$	0.725995	−	0.687699i	0.104788	−	0.0992609i
$49$	−2.58785	−	1.55706i	−0.369693	−	0.222437i
$50$	4.51025	+	0.490519i	0.637845	+	0.0693699i
$51$	−0.711821	+	0.156684i	−0.0996749	+	0.0219401i
$52$	−0.905811	+	3.26244i	−0.125613	+	0.452419i
$53$	9.53747	−	5.73850i	1.31007	−	0.788244i	0.322675	−	0.946510i	$-0.395418\pi$
$53$	9.53747	−	5.73850i	1.31007	−	0.788244i	0.987397	+	0.158266i	$0.0505903\pi$
$54$	0.907575	−	0.419889i	0.123505	−	0.0571397i
$55$	−0.136717	+	0.343134i	−0.0184349	+	0.0462682i
$56$	0.171375	−	3.16082i	0.0229009	−	0.422383i
$57$	−1.30371	−	1.92284i	−0.172681	−	0.254686i
$58$	4.00069			0.525317
$59$	−6.73471	−	3.69373i	−0.876785	−	0.480883i
$59$	−6.73471	−	3.69373i	−0.876785	−	0.480883i
$60$	−3.08818			−0.398682
$61$	−6.40784	−	9.45086i	−0.820440	−	1.21006i	−0.975028	−	0.222080i	$-0.928715\pi$
$61$	−6.40784	−	9.45086i	−0.820440	−	1.21006i	0.154588	−	0.987979i	$-0.450595\pi$
$62$	0.199216	−	3.67433i	0.0253005	−	0.466640i
$63$	1.17166	−	2.94064i	0.147615	−	0.370486i
$64$	0.907575	−	0.419889i	0.113447	−	0.0524861i
$65$	8.95939	−	5.39069i	1.11128	−	0.668633i
$66$	0.0319982	−	0.115247i	0.00393871	−	0.0141860i
$67$	12.5032	−	2.75216i	1.52751	−	0.336230i	0.629778	−	0.776775i	$-0.283146\pi$
$67$	12.5032	−	2.75216i	1.52751	−	0.336230i	0.897731	+	0.440545i	$0.145215\pi$
$68$	−0.724589	−	0.0788038i	−0.0878693	−	0.00955637i
$69$	−0.855766	−	0.514898i	−0.103022	−	0.0619864i
$70$	−7.09698	+	6.72262i	−0.848251	+	0.803506i
$71$	9.16754	+	4.24136i	1.08799	+	0.503356i	0.880096	−	0.474796i	$-0.157478\pi$
$71$	9.16754	+	4.24136i	1.08799	+	0.503356i	0.207891	+	0.978152i	$0.433340\pi$
$72$	0.994138	−	0.108119i	0.117160	−	0.0127419i
$73$	9.07193	−	3.05669i	1.06179	−	0.357759i	0.266403	−	0.963862i	$-0.414165\pi$
$73$	9.07193	−	3.05669i	1.06179	−	0.357759i	0.795386	+	0.606103i	$0.207268\pi$
$74$	−1.32496	−	3.32541i	−0.154024	−	0.386571i
$75$	3.29373	+	3.11998i	0.380327	+	0.360265i
$76$	−0.621505	−	2.23846i	−0.0712915	−	0.256769i
$77$	−0.177345	−	0.334508i	−0.0202103	−	0.0381207i
$78$	−2.69545	+	2.04903i	−0.305200	+	0.232007i
$79$	−0.520186	−	9.59426i	−0.0585255	−	1.07944i	−0.869365	−	0.494170i	$-0.835472\pi$
$79$	−0.520186	−	9.59426i	−0.0585255	−	1.07944i	0.810840	−	0.585268i	$-0.199011\pi$
$80$	−2.92652	−	0.986060i	−0.327195	−	0.110245i
$81$	0.976621	+	0.214970i	0.108513	+	0.0238856i
$82$	−0.792827	+	1.49543i	−0.0875531	+	0.165143i
$83$	−1.94870	−	11.8866i	−0.213898	−	1.30472i	−0.847391	−	0.530970i	$-0.821828\pi$
$83$	−1.94870	−	11.8866i	−0.213898	−	1.30472i	0.633493	−	0.773749i	$-0.281621\pi$
$84$	2.04928	−	2.41260i	0.223595	−	0.263236i
$85$	1.45717	+	1.71552i	0.158053	+	0.186074i
$86$	1.98063	−	12.0813i	0.213577	−	1.30276i
$87$	3.18493	+	2.42112i	0.341460	+	0.259571i
$88$	0.0671219	−	0.0989973i	0.00715521	−	0.0105532i
$89$	−5.81504	+	8.57655i	−0.616393	+	0.909112i	−0.999896	−	0.0144276i	$-0.995407\pi$
$89$	−5.81504	+	8.57655i	−0.616393	+	0.909112i	0.383503	+	0.923540i	$0.374718\pi$
$90$	−2.45848	−	1.86889i	−0.259146	−	0.196998i
$91$	−1.73395	+	10.5766i	−0.181767	+	1.10873i
$92$	−0.646562	−	0.761192i	−0.0674088	−	0.0793597i
$93$	2.38220	−	2.80455i	0.247023	−	0.290818i
$94$	1.65808	+	10.1138i	0.171018	+	1.04316i
$95$	−3.36048	+	6.33855i	−0.344778	+	0.650321i
$96$	0.976621	+	0.214970i	0.0996759	+	0.0219403i
$97$	−11.8292	−	3.98574i	−1.20108	−	0.404690i	−0.353537	−	0.935421i	$-0.615021\pi$
$97$	−11.8292	−	3.98574i	−1.20108	−	0.404690i	−0.847541	+	0.530730i	$0.821918\pi$
$98$	−0.163508	−	3.01573i	−0.0165168	−	0.304635i
$99$	0.0952182	−	0.0723830i	0.00956979	−	0.00727477i
$100$	2.12510	+	4.00836i	0.212510	+	0.400836i
$101$	0.951898	+	3.42843i	0.0947174	+	0.341141i	0.995691	−	0.0927325i	$-0.0295601\pi$
$101$	0.951898	+	3.42843i	0.0947174	+	0.341141i	−0.900974	+	0.433874i	$0.857146\pi$
$102$	−0.529150	−	0.501238i	−0.0523937	−	0.0496299i
$103$	3.11965	+	7.82974i	0.307388	+	0.771487i	0.998798	+	0.0490235i	$0.0156109\pi$
$103$	3.11965	+	7.82974i	0.307388	+	0.771487i	−0.691409	+	0.722463i	$0.743010\pi$
$104$	−3.20861	+	1.08111i	−0.314630	+	0.106011i
$105$	−9.71821	+	1.05692i	−0.948400	+	0.103145i
$106$	10.1020	+	4.67368i	0.981193	+	0.453948i
$107$	−0.0417949	+	0.0395902i	−0.00404047	+	0.00382733i	−0.689717	−	0.724079i	$-0.742265\pi$
$107$	−0.0417949	+	0.0395902i	−0.00404047	+	0.00382733i	0.685677	+	0.727906i	$0.259506\pi$
$108$	0.856857	+	0.515554i	0.0824511	+	0.0496092i
$109$	−2.48575	−	0.270342i	−0.238092	−	0.0258940i	−0.0117048	−	0.999931i	$-0.503726\pi$
$109$	−2.48575	−	0.270342i	−0.238092	−	0.0258940i	−0.226387	+	0.974037i	$0.572691\pi$
$110$	−0.360732	+	0.0794031i	−0.0343944	+	0.00757079i
$111$	0.957657	−	3.44917i	0.0908968	−	0.327381i
$112$	2.71235	−	1.63197i	0.256293	−	0.154206i
$113$	−15.0748	+	6.97434i	−1.41812	+	0.656090i	−0.971152	−	0.238462i	$-0.923357\pi$
$113$	−15.0748	+	6.97434i	−1.41812	+	0.656090i	−0.446964	+	0.894552i	$0.647495\pi$
$114$	0.859882	−	2.15814i	0.0805353	−	0.202128i
$115$	−0.166978	+	3.07972i	−0.0155708	+	0.287186i
$116$	2.24514	+	3.31133i	0.208456	+	0.307449i
$117$	−3.38585			−0.313022
$118$	−0.722169	−	7.64712i	−0.0664811	−	0.703975i
$119$	−2.30719			−0.211499
$120$	−1.73305	−	2.55605i	−0.158205	−	0.233334i
$121$	−0.594753	+	10.9696i	−0.0540685	+	0.997235i
$122$	4.22638	−	10.6074i	0.382638	−	0.960349i
$123$	−1.53616	+	0.710704i	−0.138511	+	0.0640820i
$124$	3.15300	−	1.89710i	0.283148	−	0.170364i
$125$	−0.382649	+	1.37818i	−0.0342251	+	0.123268i
$126$	3.09146	−	0.680481i	0.275409	−	0.0606221i
$127$	−19.7057	−	2.14313i	−1.74860	−	0.190172i	−0.822838	−	0.568276i	$-0.807611\pi$
$127$	−19.7057	−	2.14313i	−1.74860	−	0.190172i	−0.925763	+	0.378104i	$0.876576\pi$
$128$	0.856857	+	0.515554i	0.0757362	+	0.0455690i
$129$	8.88807	−	8.41923i	0.782551	−	0.741272i
$130$	9.48971	+	4.39041i	0.832303	+	0.385064i
$131$	7.16705	−	0.779464i	0.626188	−	0.0681021i	0.210477	−	0.977599i	$-0.432498\pi$
$131$	7.16705	−	0.779464i	0.626188	−	0.0681021i	0.415711	+	0.909497i	$0.363533\pi$
$132$	0.113346	−	0.0381907i	0.00986549	−	0.00332407i
$133$	−2.72192	−	6.83152i	−0.236021	−	0.592368i
$134$	9.29457	+	8.80428i	0.802929	+	0.760574i
$135$	−0.826175	−	2.97561i	−0.0711058	−	0.256100i
$136$	−0.341405	−	0.643958i	−0.0292752	−	0.0552190i
$137$	6.83109	−	5.19286i	0.583619	−	0.443656i	−0.271243	−	0.962511i	$-0.587435\pi$
$137$	6.83109	−	5.19286i	0.583619	−	0.443656i	0.854862	+	0.518855i	$0.173642\pi$
$138$	−0.0540700	−	0.997262i	−0.00460274	−	0.0848926i
$139$	−3.30722	−	1.11433i	−0.280514	−	0.0945163i	0.175528	−	0.984474i	$-0.443837\pi$
$139$	−3.30722	−	1.11433i	−0.280514	−	0.0945163i	−0.456042	+	0.889958i	$0.650733\pi$
$140$	−9.54697	−	2.10145i	−0.806866	−	0.177605i
$141$	−4.80065	+	9.05499i	−0.404288	+	0.762567i
$142$	1.63418	+	9.96807i	0.137137	+	0.836501i
$143$	−0.262173	+	0.308654i	−0.0219240	+	0.0258109i
$144$	0.647386	+	0.762162i	0.0539489	+	0.0635135i
$145$	1.99879	−	12.1921i	0.165991	−	1.01250i
$146$	7.62104	+	5.79337i	0.630722	+	0.479462i
$147$	1.69488	−	2.49975i	0.139791	−	0.206176i
$148$	2.00885	−	2.96284i	0.165127	−	0.243544i
$149$	−10.0025	−	7.60367i	−0.819433	−	0.622917i	0.109157	−	0.994025i	$-0.465185\pi$
$149$	−10.0025	−	7.60367i	−0.819433	−	0.622917i	−0.928590	+	0.371108i	$0.878978\pi$
$150$	−0.733980	+	4.47708i	−0.0599292	+	0.365552i
$151$	8.09423	+	9.52926i	0.658699	+	0.775481i	0.985511	−	0.169609i	$-0.0542504\pi$
$151$	8.09423	+	9.52926i	0.658699	+	0.775481i	−0.326812	+	0.945089i	$0.605975\pi$
$152$	1.50397	−	1.77061i	0.121988	−	0.143615i
$153$	−0.117917	−	0.719260i	−0.00953300	−	0.0581487i
$154$	0.177345	−	0.334508i	0.0142909	−	0.0269554i
$155$	−11.0980	−	2.44285i	−0.891411	−	0.196214i
$156$	−3.20861	−	1.08111i	−0.256895	−	0.0865579i
$157$	0.181092	+	3.34004i	0.0144527	+	0.266564i	0.996825	+	0.0796276i	$0.0253731\pi$
$157$	0.181092	+	3.34004i	0.0144527	+	0.266564i	−0.982372	+	0.186937i	$0.940144\pi$
$158$	7.64914	−	5.81473i	0.608533	−	0.462595i
$159$	5.21374	+	9.83415i	0.413476	+	0.779899i
$160$	−0.826175	−	2.97561i	−0.0653149	−	0.235243i
$161$	−2.29519	−	2.17412i	−0.180886	−	0.171344i
$162$	0.370138	+	0.928977i	0.0290808	+	0.0729873i
$163$	−1.88127	+	0.633873i	−0.147352	+	0.0496488i	−0.392011	−	0.919960i	$-0.628221\pi$
$163$	−1.88127	+	0.633873i	−0.147352	+	0.0496488i	0.244659	+	0.969609i	$0.421324\pi$
$164$	−1.68268	+	0.183002i	−0.131395	+	0.0142901i
$165$	−0.335229	−	0.155093i	−0.0260975	−	0.0120740i
$166$	8.74478	−	8.28350i	0.678727	−	0.642924i
$167$	−1.18680	−	0.714076i	−0.0918377	−	0.0552569i	0.468894	−	0.883254i	$-0.344653\pi$
$167$	−1.18680	−	0.714076i	−0.0918377	−	0.0552569i	−0.560732	+	0.827997i	$0.689480\pi$
$168$	3.14691	+	0.342247i	0.242789	+	0.0264049i
$169$	−1.50010	+	0.330197i	−0.115392	+	0.0253997i
$170$	−0.602167	+	2.16881i	−0.0461841	+	0.166340i
$171$	1.99060	−	1.19770i	0.152225	−	0.0915906i
$172$	11.1111	−	5.14053i	0.847212	−	0.391962i
$173$	−3.01913	+	7.57745i	−0.229540	+	0.576103i	−0.997960	−	0.0638436i	$-0.979664\pi$
$173$	−3.01913	+	7.57745i	−0.229540	+	0.576103i	0.768420	+	0.639946i	$0.221043\pi$
$174$	−0.216593	+	3.99483i	−0.0164199	+	0.302847i
$175$	8.05933	+	11.8866i	0.609228	+	0.898544i
$176$	0.119607			0.00901571
$177$	4.05293	−	6.52486i	0.304637	−	0.490438i
$178$	−10.3620			−0.776668
$179$	4.67880	+	6.90071i	0.349710	+	0.515783i	0.961341	−	0.275359i	$-0.0887969\pi$
$179$	4.67880	+	6.90071i	0.349710	+	0.515783i	−0.611632	+	0.791143i	$0.709487\pi$
$180$	0.167191	−	3.08365i	0.0124617	−	0.229842i
$181$	−7.25966	+	18.2204i	−0.539606	+	1.35431i	0.366167	+	0.930549i	$0.380670\pi$
$181$	−7.25966	+	18.2204i	−0.539606	+	1.35431i	−0.905774	+	0.423761i	$0.860710\pi$
$182$	−9.72720	+	4.50028i	−0.721028	+	0.333583i
$183$	9.78392	−	5.88679i	0.723248	−	0.435164i
$184$	0.267188	−	0.962323i	0.0196973	−	0.0709434i
$185$	−10.7961	+	2.37641i	−0.793748	+	0.174717i
$186$	3.65815	+	0.397848i	0.268229	+	0.0291717i
$187$	−0.0746982	−	0.0449444i	−0.00546247	−	0.00328666i
$188$	−7.44062	+	7.04813i	−0.542663	+	0.514038i
$189$	2.87290	+	1.32914i	0.208973	+	0.0966810i
$190$	−7.13221	+	0.775674i	−0.517425	+	0.0562733i
$191$	−4.37678	+	1.47471i	−0.316693	+	0.106706i	−0.473159	−	0.880977i	$-0.656886\pi$
$191$	−4.37678	+	1.47471i	−0.316693	+	0.106706i	0.156466	+	0.987683i	$0.449990\pi$
$192$	0.370138	+	0.928977i	0.0267124	+	0.0670431i
$193$	1.55891	+	1.47668i	0.112213	+	0.106294i	0.741749	−	0.670677i	$-0.233996\pi$
$193$	1.55891	+	1.47668i	0.112213	+	0.106294i	−0.629536	+	0.776971i	$0.716755\pi$
$194$	−3.33947	−	12.0277i	−0.239760	−	0.863537i
$195$	4.89773	+	9.23810i	0.350734	+	0.661554i
$196$	2.40433	−	1.82772i	0.171738	−	0.130552i
$197$	0.236250	+	4.35737i	0.0168321	+	0.310450i	0.994811	+	0.101744i	$0.0324423\pi$
$197$	0.236250	+	4.35737i	0.0168321	+	0.310450i	−0.977978	+	0.208706i	$0.933075\pi$
$198$	0.113346	+	0.0381907i	0.00805514	+	0.00271409i
$199$	−21.4051	−	4.71162i	−1.51737	−	0.333998i	−0.623319	−	0.781968i	$-0.714216\pi$
$199$	−21.4051	−	4.71162i	−1.51737	−	0.333998i	−0.894049	+	0.447970i	$0.852147\pi$
$200$	−2.12510	+	4.00836i	−0.150267	+	0.283434i
$201$	2.07122	+	12.6339i	0.146092	+	0.891124i
$202$	−2.30348	+	2.71187i	−0.162072	+	0.190806i
$203$	8.19854	+	9.65206i	0.575424	+	0.677442i
$204$	0.117917	−	0.719260i	0.00825582	−	0.0503583i
$205$	4.16121	+	3.16327i	0.290632	+	0.220933i
$206$	−4.72988	+	6.97605i	−0.329546	+	0.486044i
$207$	0.560473	−	0.826635i	0.0389555	−	0.0574551i
$208$	−2.69545	−	2.04903i	−0.186896	−	0.142075i
$209$	0.0449533	−	0.274203i	0.00310948	−	0.0189670i
$210$	−6.32854	−	7.45053i	−0.436710	−	0.514135i
$211$	−7.22436	+	8.50518i	−0.497346	+	0.585521i	−0.952365	−	0.304961i	$-0.901357\pi$
$211$	−7.22436	+	8.50518i	−0.497346	+	0.585521i	0.455019	+	0.890482i	$0.349632\pi$
$212$	1.80076	+	10.9841i	0.123676	+	0.754393i
$213$	−4.73146	+	8.92447i	−0.324194	+	0.611495i
$214$	−0.0562232	−	0.0123757i	−0.00384334	−	0.000845982i
$215$	−35.8282	−	12.0719i	−2.44346	−	0.823299i
$216$	0.0541389	+	0.998533i	0.00368369	+	0.0679416i
$217$	9.27292	−	7.04909i	0.629487	−	0.478524i
$218$	−1.17121	−	2.20914i	−0.0793245	−	0.149622i
$219$	2.56106	+	9.22412i	0.173061	+	0.623308i
$220$	−0.268159	−	0.254014i	−0.0180793	−	0.0171256i
$221$	0.913434	+	2.29255i	0.0614442	+	0.154213i
$222$	3.39227	−	1.14299i	0.227674	−	0.0767123i
$223$	−8.65617	+	0.941416i	−0.579660	+	0.0630419i	−0.393252	−	0.919431i	$-0.628650\pi$
$223$	−8.65617	+	0.941416i	−0.579660	+	0.0630419i	−0.186408	+	0.982472i	$0.559685\pi$
$224$	2.87290	+	1.32914i	0.191954	+	0.0888072i
$225$	−3.29373	+	3.11998i	−0.219582	+	0.207999i
$226$	−14.2324	−	8.56332i	−0.946722	−	0.569624i
$227$	20.2049	+	2.19742i	1.34105	+	0.145848i	0.750348	−	0.661043i	$-0.229886\pi$
$227$	20.2049	+	2.19742i	1.34105	+	0.145848i	0.590701	+	0.806890i	$0.298851\pi$
$228$	2.26882	−	0.499406i	0.150257	−	0.0330740i
$229$	1.28396	−	4.62440i	0.0848464	−	0.305589i	−0.908935	−	0.416938i	$-0.863103\pi$
$229$	1.28396	−	4.62440i	0.0848464	−	0.305589i	0.993781	+	0.111349i	$0.0355171\pi$
$230$	−2.64276	+	1.59010i	−0.174258	+	0.104848i
$231$	0.343618	−	0.158975i	0.0226084	−	0.0104598i
$232$	−1.48081	+	3.71655i	−0.0972199	+	0.244004i
$233$	0.639427	−	11.7935i	0.0418903	−	0.772621i	−0.899834	−	0.436233i	$-0.856312\pi$
$233$	0.639427	−	11.7935i	0.0418903	−	0.772621i	0.941724	−	0.336387i	$-0.109205\pi$
$234$	−1.90010	−	2.80243i	−0.124213	−	0.183201i
$235$	31.6503			2.06464
$236$	5.92417	−	4.88920i	0.385630	−	0.318260i
$237$	9.60835			0.624130
$238$	−1.29476	−	1.90963i	−0.0839270	−	0.123783i
$239$	−1.49506	+	27.5747i	−0.0967071	+	1.78366i	0.400769	+	0.916179i	$0.368743\pi$
$239$	−1.49506	+	27.5747i	−0.0967071	+	1.78366i	−0.497476	+	0.867478i	$0.665740\pi$
$240$	1.14305	−	2.86885i	0.0737837	−	0.185183i
$241$	11.5332	−	5.33584i	0.742920	−	0.343711i	−0.0116489	−	0.999932i	$-0.503708\pi$
$241$	11.5332	−	5.33584i	0.742920	−	0.343711i	0.754569	+	0.656221i	$0.227846\pi$
$242$	−9.41317	+	5.66372i	−0.605102	+	0.364078i
$243$	−0.267528	+	0.963550i	−0.0171620	+	0.0618118i
$244$	11.1514	−	2.45461i	0.713896	−	0.157140i
$245$	−9.27212	−	1.00840i	−0.592374	−	0.0644246i
$246$	−1.45032	−	0.872626i	−0.0924687	−	0.0556366i
$247$	−5.71053	+	5.40931i	−0.363353	+	0.344186i
$248$	3.33963	+	1.54508i	0.212067	+	0.0981125i
$249$	11.9746	−	1.30232i	0.758861	−	0.0825311i
$250$	−1.35544	+	0.456700i	−0.0857254	+	0.0288843i
$251$	7.58146	+	19.0280i	0.478538	+	1.20104i	0.948052	+	0.318114i	$0.103050\pi$
$251$	7.58146	+	19.0280i	0.478538	+	1.20104i	−0.469515	+	0.882925i	$0.655571\pi$
$252$	2.29811	+	2.17689i	0.144767	+	0.137131i
$253$	−0.0319575	−	0.115101i	−0.00200915	−	0.00723631i
$254$	−9.28476	−	17.5129i	−0.582578	−	1.09886i
$255$	−1.79189	+	1.36216i	−0.112213	+	0.0853017i
$256$	0.0541389	+	0.998533i	0.00338368	+	0.0624083i
$257$	13.5302	+	4.55886i	0.843992	+	0.284374i	0.707892	−	0.706321i	$-0.249646\pi$
$257$	13.5302	+	4.55886i	0.843992	+	0.284374i	0.136100	+	0.990695i	$0.456543\pi$
$258$	11.9564	+	2.63180i	0.744371	+	0.163848i
$259$	5.30765	−	10.0113i	0.329801	−	0.622072i
$260$	1.69161	+	10.3184i	0.104909	+	0.639918i
$261$	−2.59000	+	3.04918i	−0.160317	+	0.188739i
$262$	4.66721	+	5.49467i	0.288341	+	0.339462i
$263$	5.00044	−	30.5013i	0.308340	−	1.88079i	−0.144965	−	0.989437i	$-0.546307\pi$
$263$	5.00044	−	30.5013i	0.308340	−	1.88079i	0.453305	−	0.891355i	$-0.350245\pi$
$264$	0.0952182	+	0.0723830i	0.00586028	+	0.00445487i
$265$	19.2901	−	28.4508i	1.18498	−	1.74772i
$266$	4.12686	−	6.08667i	0.253034	−	0.373197i
$267$	−8.24915	−	6.27084i	−0.504840	−	0.383769i
$268$	−2.07122	+	12.6339i	−0.126520	+	0.771736i
$269$	−19.5874	−	23.0600i	−1.19426	−	1.40599i	−0.891556	−	0.452911i	$-0.850386\pi$
$269$	−19.5874	−	23.0600i	−1.19426	−	1.40599i	−0.302707	−	0.953084i	$-0.597890\pi$
$270$	1.99924	−	2.35369i	0.121670	−	0.143241i
$271$	−0.136034	−	0.829768i	−0.00826345	−	0.0504048i	0.982373	−	0.186932i	$-0.0598543\pi$
$271$	−0.136034	−	0.829768i	−0.00826345	−	0.0504048i	−0.990636	+	0.136527i	$0.956406\pi$
$272$	0.341405	−	0.643958i	0.0207007	−	0.0390457i
$273$	−10.4672	−	2.30401i	−0.633505	−	0.139445i
$274$	8.13159	+	2.73985i	0.491247	+	0.165520i
$275$	0.0293778	+	0.541842i	0.00177155	+	0.0326743i
$276$	0.795080	−	0.604404i	0.0478582	−	0.0363808i
$277$	13.2277	+	24.9501i	0.794777	+	1.49911i	0.865109	+	0.501585i	$0.167249\pi$
$277$	13.2277	+	24.9501i	0.794777	+	1.49911i	−0.0703316	+	0.997524i	$0.522406\pi$
$278$	−0.933648	−	3.36270i	−0.0559965	−	0.201681i
$279$	2.67146	+	2.53055i	0.159936	+	0.151500i
$280$	−3.61829	−	9.08123i	−0.216234	−	0.542707i
$281$	−8.99342	+	3.03023i	−0.536502	+	0.180769i	−0.574493	−	0.818509i	$-0.694801\pi$
$281$	−8.99342	+	3.03023i	−0.536502	+	0.180769i	0.0379909	+	0.999278i	$0.487904\pi$
$282$	−10.1888	+	1.10810i	−0.606733	+	0.0659862i
$283$	16.7725	+	7.75977i	0.997020	+	0.461270i	0.849386	−	0.527772i	$-0.176972\pi$
$283$	16.7725	+	7.75977i	0.997020	+	0.461270i	0.147633	+	0.989042i	$0.452834\pi$
$284$	−7.33338	+	6.94654i	−0.435156	+	0.412202i
$285$	−6.14732	−	3.69872i	−0.364136	−	0.219093i
$286$	−0.402597	−	0.0437851i	−0.0238061	−	0.00258907i
$287$	−5.23260	+	1.15178i	−0.308870	+	0.0679875i
$288$	−0.267528	+	0.963550i	−0.0157643	+	0.0567777i
$289$	14.1114	−	8.49053i	0.830081	−	0.499443i
$290$	11.2130	−	5.18767i	0.658448	−	0.304630i
$291$	4.62031	−	11.5961i	0.270848	−	0.679776i
$292$	−0.518275	+	9.55901i	−0.0303297	+	0.559399i
$293$	−4.44406	−	6.55449i	−0.259625	−	0.382918i	0.675428	−	0.737426i	$-0.263959\pi$
$293$	−4.44406	−	6.55449i	−0.259625	−	0.382918i	−0.935053	+	0.354508i	$0.884648\pi$
$294$	3.02016			0.176139
$295$	−23.6654	−	1.61978i	−1.37785	−	0.0943074i
$296$	3.57965			0.208063
$297$	0.0671219	+	0.0989973i	0.00389481	+	0.00574441i
$298$	0.680224	−	12.5460i	0.0394043	−	0.726770i
$299$	−1.25164	+	3.14137i	−0.0723841	+	0.181670i
$300$	−4.11753	+	1.90497i	−0.237726	+	0.109984i
$301$	33.2062	−	19.9795i	1.91397	−	1.15160i
$302$	−3.34489	+	12.0472i	−0.192477	+	0.693239i
$303$	−3.47493	+	0.764891i	−0.199630	+	0.0439418i
$304$	2.30952	+	0.251175i	0.132460	+	0.0144059i
$305$	−30.2145	−	18.1794i	−1.73008	−	1.04095i
$306$	0.529150	−	0.501238i	0.0302495	−	0.0286539i
$307$	−4.92286	−	2.27756i	−0.280962	−	0.129987i	0.274347	−	0.961631i	$-0.411538\pi$
$307$	−4.92286	−	2.27756i	−0.280962	−	0.129987i	−0.555310	+	0.831644i	$0.687400\pi$
$308$	0.376392	−	0.0409351i	0.0214469	−	0.00233249i
$309$	−7.98715	+	2.69118i	−0.454373	+	0.153096i
$310$	−4.20612	−	10.5566i	−0.238892	−	0.599573i
$311$	4.52236	+	4.28381i	0.256440	+	0.242913i	0.805109	−	0.593127i	$-0.202107\pi$
$311$	4.52236	+	4.28381i	0.256440	+	0.242913i	−0.548669	+	0.836039i	$0.684865\pi$
$312$	−0.905811	−	3.26244i	−0.0512815	−	0.184699i
$313$	−14.3338	−	27.0365i	−0.810197	−	1.52819i	−0.848664	−	0.528933i	$-0.822592\pi$
$313$	−14.3338	−	27.0365i	−0.810197	−	1.52819i	0.0384671	−	0.999260i	$-0.487753\pi$
$314$	−2.66289	+	2.02427i	−0.150275	+	0.114236i
$315$	−0.529236	−	9.76118i	−0.0298191	−	0.549980i
$316$	9.10539	+	3.06796i	0.512218	+	0.172586i
$317$	0.160212	+	0.0352654i	0.00899841	+	0.00198070i	0.219467	−	0.975620i	$-0.429568\pi$
$317$	0.160212	+	0.0352654i	0.00899841	+	0.00198070i	−0.210469	+	0.977601i	$0.567499\pi$
$318$	−5.21374	+	9.83415i	−0.292372	+	0.551472i
$319$	0.0774144	+	0.472207i	0.00433438	+	0.0264385i
$320$	1.99924	−	2.35369i	0.111761	−	0.131575i
$321$	−0.0372694	−	0.0438770i	−0.00208018	−	0.00244897i
$322$	0.511463	−	3.11979i	0.0285027	−	0.173859i
$323$	−1.34798	−	1.02471i	−0.0750037	−	0.0570163i
$324$	−0.561187	+	0.827689i	−0.0311771	+	0.0459827i
$325$	8.62044	−	12.7142i	0.478176	−	0.705257i
$326$	−1.58039	−	1.20138i	−0.0875299	−	0.0665385i
$327$	0.404521	−	2.46747i	0.0223701	−	0.136451i
$328$	−1.09576	−	1.29003i	−0.0605035	−	0.0712302i
$329$	−21.0028	+	24.7264i	−1.15792	+	1.36321i
$330$	−0.0597570	−	0.364502i	−0.00328952	−	0.0200652i
$331$	−11.5131	+	21.7161i	−0.632820	+	1.19362i	0.335057	+	0.942198i	$0.391245\pi$
$331$	−11.5131	+	21.7161i	−0.632820	+	1.19362i	−0.967876	+	0.251427i	$0.919100\pi$
$332$	11.7636	+	2.58937i	0.645613	+	0.142110i
$333$	3.39227	+	1.14299i	0.185895	+	0.0626353i
$334$	−0.0749860	−	1.38303i	−0.00410305	−	0.0756763i
$335$	31.4747	−	23.9264i	1.71965	−	1.30724i
$336$	1.48273	+	2.79673i	0.0808896	+	0.152574i
$337$	1.55025	+	5.58351i	0.0844477	+	0.304153i	0.993697	−	0.112099i	$-0.0357573\pi$
$337$	1.55025	+	5.58351i	0.0844477	+	0.304153i	−0.909249	+	0.416252i	$0.863343\pi$
$338$	−1.11514	−	1.05631i	−0.0606554	−	0.0574558i
$339$	−6.14798	−	15.4303i	−0.333912	−	0.838056i
$340$	−2.13303	+	0.718701i	−0.115680	+	0.0389771i
$341$	0.437541	−	0.0475854i	0.0236942	−	0.00257689i
$342$	2.10842	+	0.975460i	0.114010	+	0.0527468i
$343$	−9.14612	+	8.66366i	−0.493844	+	0.467794i
$344$	10.4902	+	6.31172i	0.565591	+	0.340305i
$345$	−3.06617	−	0.333466i	−0.165077	−	0.0179532i
$346$	−7.96607	+	1.75346i	−0.428258	+	0.0942668i
$347$	6.15271	−	22.1600i	0.330295	−	1.18961i	−0.592899	−	0.805277i	$-0.702017\pi$
$347$	6.15271	−	22.1600i	0.330295	−	1.18961i	0.923193	−	0.384336i	$-0.125570\pi$
$348$	−3.42802	+	2.06257i	−0.183761	+	0.110566i
$349$	14.8615	−	6.87565i	0.795517	−	0.368045i	0.0203429	−	0.999793i	$-0.493524\pi$
$349$	14.8615	−	6.87565i	0.795517	−	0.368045i	0.775174	+	0.631748i	$0.217662\pi$
$350$	−5.31563	+	13.3412i	−0.284133	+	0.713119i
$351$	0.183306	−	3.38089i	0.00978417	−	0.180458i
$352$	0.0671219	+	0.0989973i	0.00357761	+	0.00527658i
$353$	−26.9989			−1.43701			−0.718503	−	0.695524i	$-0.755172\pi$
$353$	−26.9989			−1.43701			−0.718503	+	0.695524i	$0.755172\pi$
$354$	7.67500	−	0.307103i	0.407922	−	0.0163224i
$355$	31.1941			1.65561
$356$	−5.81504	−	8.57655i	−0.308197	−	0.454556i
$357$	0.124909	−	2.30380i	0.00661086	−	0.121930i
$358$	−3.08596	+	7.74518i	−0.163098	+	0.409345i
$359$	−6.60833	+	3.05734i	−0.348774	+	0.161360i	−0.586452	−	0.809984i	$-0.699476\pi$
$359$	−6.60833	+	3.05734i	−0.348774	+	0.161360i	0.237678	+	0.971344i	$0.423614\pi$
$360$	2.64613	−	1.59212i	0.139463	−	0.0839122i
$361$	−3.63920	+	13.1072i	−0.191537	+	0.689853i
$362$	−19.1548	+	4.21630i	−1.00676	+	0.221604i
$363$	−10.9213	−	1.18776i	−0.573219	−	0.0623414i
$364$	−9.18362	−	5.52560i	−0.481352	−	0.289620i
$365$	21.4628	−	20.3307i	1.12342	−	1.06416i
$366$	10.3630	+	4.79445i	0.541685	+	0.250610i
$367$	−13.0412	+	1.41832i	−0.680747	+	0.0740356i	−0.441958	−	0.897036i	$-0.645716\pi$
$367$	−13.0412	+	1.41832i	−0.680747	+	0.0740356i	−0.238789	+	0.971072i	$0.576750\pi$
$368$	0.946447	−	0.318895i	0.0493370	−	0.0166236i
$369$	−0.626495	−	1.57238i	−0.0326140	−	0.0818551i
$370$	−8.02558	−	7.60224i	−0.417230	−	0.395221i
$371$	9.42609	+	33.9497i	0.489378	+	1.76258i
$372$	1.72361	+	3.25108i	0.0893652	+	0.168561i
$373$	−16.3042	+	12.3941i	−0.844197	+	0.641742i	−0.935204	−	0.354108i	$-0.884784\pi$
$373$	−16.3042	+	12.3941i	−0.844197	+	0.641742i	0.0910074	+	0.995850i	$0.470991\pi$
$374$	−0.00471966	−	0.0870491i	−0.000244048	−	0.00450120i
$375$	−1.35544	−	0.456700i	−0.0699945	−	0.0235839i
$376$	−10.0092	−	2.20320i	−0.516187	−	0.113621i
$377$	6.34495	−	11.9678i	0.326781	−	0.616375i
$378$	0.512115	+	3.12376i	0.0263404	+	0.160669i
$379$	4.16145	−	4.89924i	0.213760	−	0.251657i	−0.644824	−	0.764331i	$-0.723069\pi$
$379$	4.16145	−	4.89924i	0.213760	−	0.251657i	0.858583	+	0.512674i	$0.171345\pi$
$380$	−4.64452	−	5.46795i	−0.238259	−	0.280500i
$381$	3.20683	−	19.5608i	0.164291	−	1.00213i
$382$	−3.67679	−	2.79502i	−0.188121	−	0.143006i
$383$	8.58967	−	12.6688i	0.438912	−	0.647347i	−0.542321	−	0.840171i	$-0.682454\pi$
$383$	8.58967	−	12.6688i	0.438912	−	0.647347i	0.981233	+	0.192825i	$0.0617648\pi$
$384$	−0.561187	+	0.827689i	−0.0286380	+	0.0422378i
$385$	−0.930808	−	0.707581i	−0.0474383	−	0.0360617i
$386$	−0.347391	+	2.11899i	−0.0176817	+	0.107854i
$387$	7.92569	+	9.33084i	0.402885	+	0.474313i
$388$	8.08111	−	9.51382i	0.410256	−	0.482991i
$389$	4.56526	+	27.8468i	0.231468	+	1.41189i	0.805275	+	0.592901i	$0.202017\pi$
$389$	4.56526	+	27.8468i	0.231468	+	1.41189i	−0.573807	+	0.818990i	$0.694534\pi$
$390$	−4.89773	+	9.23810i	−0.248006	+	0.467789i
$391$	−0.710915	−	0.156484i	−0.0359525	−	0.00791375i
$392$	2.86207	+	0.964342i	0.144556	+	0.0487066i
$393$	0.390304	+	7.19874i	0.0196883	+	0.363129i
$394$	−3.47397	+	2.64084i	−0.175016	+	0.133044i
$395$	−13.8988	−	26.2158i	−0.699322	−	1.31906i
$396$	0.0319982	+	0.115247i	0.00160797	+	0.00579139i
$397$	24.2152	+	22.9378i	1.21532	+	1.15122i	0.983968	+	0.178347i	$0.0570748\pi$
$397$	24.2152	+	22.9378i	1.21532	+	1.15122i	0.231356	+	0.972869i	$0.425684\pi$
$398$	−8.11251	−	20.3609i	−0.406643	−	1.02060i
$399$	6.96886	−	2.34808i	0.348879	−	0.117551i
$400$	−4.51025	+	0.490519i	−0.225512	+	0.0245260i
$401$	29.0763	+	13.4521i	1.45200	+	0.671767i	0.977971	−	0.208743i	$-0.0669371\pi$
$401$	29.0763	+	13.4521i	1.45200	+	0.671767i	0.474029	+	0.880509i	$0.342799\pi$
$402$	−9.29457	+	8.80428i	−0.463571	+	0.439118i
$403$	−10.6756	−	6.42329i	−0.531789	−	0.319967i
$404$	−3.53726	−	0.384701i	−0.175985	−	0.0191396i
$405$	3.01598	−	0.663867i	0.149865	−	0.0329878i
$406$	−3.38799	+	12.2025i	−0.168143	+	0.605597i
$407$	0.366864	−	0.220735i	0.0181848	−	0.0109414i
$408$	0.661497	−	0.306041i	0.0327490	−	0.0151513i
$409$	12.3143	−	30.9065i	0.608901	−	1.52823i	−0.223875	−	0.974618i	$-0.571871\pi$
$409$	12.3143	−	30.9065i	0.608901	−	1.52823i	0.832776	−	0.553610i	$-0.186750\pi$
$410$	−0.282987	+	5.21938i	−0.0139757	+	0.257767i
$411$	4.81541	+	7.10220i	0.237527	+	0.350326i
$412$	−8.42835			−0.415235
$413$	16.9695	−	17.4134i	0.835014	−	0.856856i
$414$	0.998727			0.0490848
$415$	−20.8749	−	30.7882i	−1.02471	−	1.51133i
$416$	0.183306	−	3.38089i	0.00898733	−	0.165762i
$417$	1.29175	−	3.24204i	0.0632571	−	0.158763i
$418$	0.252182	−	0.116672i	0.0123346	−	0.00570660i
$419$	12.4354	−	7.48216i	0.607511	−	0.365527i	−0.178316	−	0.983973i	$-0.557065\pi$
$419$	12.4354	−	7.48216i	0.607511	−	0.365527i	0.785827	+	0.618446i	$0.212237\pi$
$420$	2.61523	−	9.41920i	0.127610	−	0.459610i
$421$	−29.7879	+	6.55681i	−1.45177	+	0.319559i	−0.869701	−	0.493579i	$-0.835689\pi$
$421$	−29.7879	+	6.55681i	−1.45177	+	0.319559i	−0.582071	+	0.813138i	$0.697758\pi$
$422$	−11.0939	−	1.20653i	−0.540041	−	0.0587330i
$423$	−8.78180	−	5.28384i	−0.426986	−	0.256909i
$424$	−8.08088	+	7.65461i	−0.392442	+	0.371741i
$425$	3.00111	+	1.38846i	0.145575	+	0.0673502i
$426$	−10.0419	+	1.09212i	−0.486533	+	0.0529136i
$427$	34.2524	−	11.5410i	1.65759	−	0.558507i
$428$	−0.0213085	−	0.0534803i	−0.00102999	−	0.00258507i
$429$	−0.294007	−	0.278499i	−0.0141948	−	0.0134460i
$430$	−10.1145	−	36.4292i	−0.487766	−	1.75677i
$431$	−12.5218	−	23.6185i	−0.603152	−	1.13767i	−0.977611	−	0.210422i	$-0.932516\pi$
$431$	−12.5218	−	23.6185i	−0.603152	−	1.13767i	0.374459	−	0.927244i	$-0.377829\pi$
$432$	−0.796093	+	0.605174i	−0.0383020	+	0.0291165i
$433$	0.381478	+	7.03594i	0.0183327	+	0.338126i	0.993284	+	0.115706i	$0.0369129\pi$
$433$	0.381478	+	7.03594i	0.0183327	+	0.338126i	−0.974951	+	0.222420i	$0.928604\pi$
$434$	11.0383	+	3.71924i	0.529855	+	0.178529i
$435$	12.0660	+	2.65593i	0.578521	+	0.127342i
$436$	1.17121	−	2.20914i	0.0560909	−	0.105799i
$437$	−0.375363	−	2.28962i	−0.0179561	−	0.109527i
$438$	−6.19746	+	7.29622i	−0.296126	+	0.348627i
$439$	−21.9061	−	25.7898i	−1.04552	−	1.23088i	−0.972342	−	0.233562i	$-0.924962\pi$
$439$	−21.9061	−	25.7898i	−1.04552	−	1.23088i	−0.0731776	−	0.997319i	$-0.523314\pi$
$440$	0.0597570	−	0.364502i	0.00284880	−	0.0173769i
$441$	2.40433	+	1.82772i	0.114492	+	0.0870345i
$442$	−1.38491	+	2.04259i	−0.0658733	+	0.0971559i
$443$	7.00198	−	10.3271i	0.332674	−	0.490657i	−0.624158	−	0.781298i	$-0.714558\pi$
$443$	7.00198	−	10.3271i	0.332674	−	0.490657i	0.956832	+	0.290640i	$0.0938683\pi$
$444$	2.84973	+	2.16631i	0.135242	+	0.102809i
$445$	−5.17700	+	31.5783i	−0.245413	+	1.49695i
$446$	−5.63693	−	6.63631i	−0.266916	−	0.314238i
$447$	8.13404	−	9.57613i	0.384727	−	0.452935i
$448$	0.512115	+	3.12376i	0.0241952	+	0.147584i
$449$	−8.00625	+	15.1014i	−0.377838	+	0.712679i	−0.997384	−	0.0722816i	$-0.976972\pi$
$449$	−8.00625	+	15.1014i	−0.377838	+	0.712679i	0.619546	+	0.784960i	$0.287317\pi$
$450$	−4.43077	−	0.975287i	−0.208869	−	0.0459755i
$451$	−0.191849	−	0.0646415i	−0.00903382	−	0.00304385i
$452$	−0.899244	−	16.5856i	−0.0422969	−	0.780120i
$453$	−9.95350	+	7.56646i	−0.467656	+	0.355503i
$454$	9.51997	+	17.9566i	0.446795	+	0.842744i
$455$	8.85477	+	31.8920i	0.415118	+	1.49512i
$456$	1.68659	+	1.59762i	0.0789817	+	0.0748154i
$457$	6.73452	+	16.9024i	0.315027	+	0.790659i	0.998176	+	0.0603792i	$0.0192310\pi$
$457$	6.73452	+	16.9024i	0.315027	+	0.790659i	−0.683148	+	0.730280i	$0.739390\pi$
$458$	4.54811	−	1.53244i	0.212519	−	0.0716060i
$459$	0.724589	−	0.0788038i	0.0338209	−	0.00367825i
$460$	−2.79919	−	1.29504i	−0.130513	−	0.0603816i
$461$	11.4618	−	10.8572i	0.533831	−	0.505671i	−0.372619	−	0.927984i	$-0.621540\pi$
$461$	11.4618	−	10.8572i	0.533831	−	0.505671i	0.906450	+	0.422313i	$0.138782\pi$
$462$	0.324416	+	0.195195i	0.0150932	+	0.00908127i
$463$	−21.9309	−	2.38513i	−1.01922	−	0.110846i	−0.416775	−	0.909010i	$-0.636840\pi$
$463$	−21.9309	−	2.38513i	−1.01922	−	0.110846i	−0.602441	+	0.798163i	$0.705805\pi$
$464$	−3.90716	+	0.860031i	−0.181385	+	0.0399259i
$465$	3.04010	−	10.9494i	0.140981	−	0.507768i
$466$	10.1202	−	6.08914i	0.468810	−	0.282074i
$467$	20.2018	−	9.34633i	0.934826	−	0.432497i	0.107491	−	0.994206i	$-0.465718\pi$
$467$	20.2018	−	9.34633i	0.934826	−	0.432497i	0.827335	+	0.561709i	$0.189856\pi$
$468$	1.25323	−	3.14538i	0.0579307	−	0.145395i
$469$	−2.19403	+	40.4665i	−0.101311	+	1.86857i
$470$	17.7617	+	26.1966i	0.819288	+	1.20836i
$471$	−3.34495			−0.154127
$472$	7.37130	+	2.15961i	0.339292	+	0.0994042i
$473$	1.46430			0.0673286
$474$	5.39208	+	7.95273i	0.247667	+	0.365281i
$475$	−0.570608	+	10.5243i	−0.0261813	+	0.482886i
$476$	0.853977	−	2.14332i	0.0391420	−	0.0982390i
$477$	−10.1020	+	4.67368i	−0.462539	+	0.213993i
$478$	−23.6623	+	14.2371i	−1.08229	+	0.651190i
$479$	0.366107	−	1.31860i	0.0167279	−	0.0602483i	−0.954715	−	0.297522i	$-0.903840\pi$
$479$	0.366107	−	1.31860i	0.0167279	−	0.0602483i	0.971443	+	0.237273i	$0.0762537\pi$
$480$	3.01598	−	0.663867i	0.137660	−	0.0303012i
$481$	−12.0491	−	1.31042i	−0.549392	−	0.0597500i
$482$	10.8887	+	6.55152i	0.495967	+	0.298413i
$483$	2.29519	−	2.17412i	0.104435	−	0.0989257i
$484$	−9.97035	−	4.61277i	−0.453198	−	0.209672i
$485$	−38.3227	+	4.16785i	−1.74015	+	0.189252i
$486$	−0.947653	+	0.319302i	−0.0429864	+	0.0144838i
$487$	−2.10928	−	5.29389i	−0.0955805	−	0.239889i	0.873411	−	0.486984i	$-0.161903\pi$
$487$	−2.10928	−	5.29389i	−0.0955805	−	0.239889i	−0.968991	+	0.247096i	$0.920524\pi$
$488$	8.28969	+	7.85241i	0.375257	+	0.355462i
$489$	−0.531094	−	1.91283i	−0.0240169	−	0.0865010i
$490$	−4.36875	−	8.24034i	−0.197360	−	0.372261i
$491$	11.3299	−	8.61277i	0.511311	−	0.388689i	−0.317464	−	0.948270i	$-0.602831\pi$
$491$	11.3299	−	8.61277i	0.511311	−	0.388689i	0.828775	+	0.559582i	$0.189038\pi$
$492$	−0.0916354	−	1.69012i	−0.00413124	−	0.0761963i
$493$	2.76331	+	0.931068i	0.124453	+	0.0419332i
$494$	−7.68190	−	1.69091i	−0.345625	−	0.0760778i
$495$	0.173015	−	0.326341i	0.00777644	−	0.0146679i
$496$	0.595313	+	3.63125i	0.0267304	+	0.163048i
$497$	−20.7000	+	24.3700i	−0.928523	+	1.09314i
$498$	7.79792	+	9.18042i	0.349433	+	0.411384i
$499$	−6.38476	+	38.9453i	−0.285821	+	1.74343i	0.319623	+	0.947545i	$0.396444\pi$
$499$	−6.38476	+	38.9453i	−0.285821	+	1.74343i	−0.605444	+	0.795888i	$0.707004\pi$
$500$	−1.13866	−	0.865587i	−0.0509224	−	0.0387102i
$501$	0.777281	−	1.14640i	0.0347264	−	0.0512176i
$502$	−11.4947	+	16.9534i	−0.513033	+	0.756666i
$503$	4.96122	+	3.77142i	0.221210	+	0.168160i	0.709910	−	0.704292i	$-0.248736\pi$
$503$	4.96122	+	3.77142i	0.221210	+	0.168160i	−0.488700	+	0.872452i	$0.662529\pi$
$504$	−0.512115	+	3.12376i	−0.0228114	+	0.139143i
$505$	7.11355	+	8.37472i	0.316549	+	0.372670i
$506$	0.0773333	−	0.0910438i	0.00343789	−	0.00404739i
$507$	−0.248499	−	1.51577i	−0.0110362	−	0.0673179i
$508$	9.28476	−	17.5129i	0.411945	−	0.777010i
$509$	25.3126	+	5.57172i	1.12196	+	0.246962i	0.736948	−	0.675949i	$-0.236266\pi$
$509$	25.3126	+	5.57172i	1.12196	+	0.246962i	0.385013	+	0.922911i	$0.374197\pi$
$510$	−2.13303	−	0.718701i	−0.0944522	−	0.0318246i
$511$	1.64058	+	30.2587i	0.0725750	+	1.33857i
$512$	−0.796093	+	0.605174i	−0.0351827	+	0.0267452i
$513$	1.08818	+	2.05252i	0.0480442	+	0.0906210i
$514$	3.81967	+	13.7572i	0.168478	+	0.606804i
$515$	18.8964	+	17.8996i	0.832674	+	0.788751i
$516$	4.53145	+	11.3731i	0.199486	+	0.500672i
$517$	−1.16167	+	0.391411i	−0.0510900	+	0.0172142i
$518$	11.2648	−	1.22512i	0.494948	−	0.0538288i
$519$	−7.40288	−	3.42494i	−0.324950	−	0.150338i
$520$	−7.59109	+	7.19066i	−0.332891	+	0.315331i
$521$	33.2019	+	19.9769i	1.45460	+	0.875206i	0.999881	−	0.0154279i	$-0.00491104\pi$
$521$	33.2019	+	19.9769i	1.45460	+	0.875206i	0.454722	+	0.890633i	$0.349739\pi$
$522$	−3.97724	−	0.432551i	−0.174079	−	0.0189323i
$523$	−41.1608	+	9.06017i	−1.79983	+	0.396174i	−0.983427	−	0.181303i	$-0.941969\pi$
$523$	−41.1608	+	9.06017i	−1.79983	+	0.396174i	−0.816407	+	0.577477i	$0.804037\pi$
$524$	−1.92870	+	6.94654i	−0.0842555	+	0.303461i
$525$	−12.3055	+	7.40398i	−0.537056	+	0.323136i
$526$	28.0518	−	12.9781i	1.22312	−	0.565874i
$527$	0.992715	−	2.49153i	0.0432433	−	0.108533i
$528$	−0.00647539	+	0.119432i	−0.000281805	+	0.00519759i
$529$	12.3475	+	18.2113i	0.536850	+	0.791794i
$530$	34.3737			1.49310
$531$	6.29587	+	4.40023i	0.273217	+	0.190954i
$532$	7.35381			0.318828
$533$	3.21610	+	4.74339i	0.139305	+	0.205459i
$534$	0.560990	−	10.3468i	0.0242764	−	0.447752i
$535$	−0.0658045	+	0.165157i	−0.00284498	+	0.00714035i
$536$	−11.6193	+	5.37564i	−0.501875	+	0.232192i
$537$	−7.14389	+	4.29834i	−0.308282	+	0.185487i
$538$	8.09436	−	29.1532i	0.348972	−	1.25689i
$539$	0.352787	−	0.0776543i	0.0151956	−	0.00334481i
$540$	3.07007	+	0.333891i	0.132115	+	0.0143684i
$541$	6.07061	+	3.65256i	0.260996	+	0.157036i	0.640038	−	0.768344i	$-0.278919\pi$
$541$	6.07061	+	3.65256i	0.260996	+	0.157036i	−0.379042	+	0.925380i	$0.623746\pi$
$542$	0.610449	−	0.578248i	0.0262211	−	0.0248379i
$543$	−17.8006	−	8.23545i	−0.763898	−	0.353417i
$544$	0.724589	−	0.0788038i	0.0310665	−	0.00337869i
$545$	−7.31750	+	2.46555i	−0.313447	+	0.105613i
$546$	−3.96706	−	9.95658i	−0.169775	−	0.426102i
$547$	−20.4718	−	19.3919i	−0.875310	−	0.829137i	0.111038	−	0.993816i	$-0.464583\pi$
$547$	−20.4718	−	19.3919i	−0.875310	−	0.829137i	−0.986347	+	0.164679i	$0.947341\pi$
$548$	2.29560	+	8.26800i	0.0980631	+	0.353191i
$549$	5.34846	+	10.0883i	0.228267	+	0.430557i
$550$	−0.431990	+	0.328390i	−0.0184201	+	0.0140026i
$551$	0.503176	+	9.28053i	0.0214360	+	0.395364i
$552$	0.946447	+	0.318895i	0.0402835	+	0.0135731i
$553$	29.7038	+	6.53830i	1.26313	+	0.278037i
$554$	−13.2277	+	24.9501i	−0.561992	+	1.06003i
$555$	−1.78843	−	10.9090i	−0.0759148	−	0.463060i
$556$	2.25931	−	2.65987i	0.0958163	−	0.112804i
$557$	−13.4727	−	15.8613i	−0.570858	−	0.672067i	0.398656	−	0.917101i	$-0.369477\pi$
$557$	−13.4727	−	15.8613i	−0.570858	−	0.672067i	−0.969514	+	0.245034i	$0.921201\pi$
$558$	−0.595313	+	3.63125i	−0.0252016	+	0.153723i
$559$	−32.9993	−	25.0855i	−1.39572	−	1.06100i
$560$	5.48589	−	8.09109i	0.231821	−	0.341911i
$561$	0.0489226	−	0.0721554i	0.00206551	−	0.00304640i
$562$	−7.55508	−	5.74322i	−0.318692	−	0.242263i
$563$	−1.84713	+	11.2670i	−0.0778474	+	0.474848i	0.918916	+	0.394454i	$0.129066\pi$
$563$	−1.84713	+	11.2670i	−0.0778474	+	0.474848i	−0.996763	+	0.0803944i	$0.974382\pi$
$564$	−6.63497	−	7.81129i	−0.279383	−	0.328915i
$565$	−33.2073	+	39.0947i	−1.39704	+	1.64473i
$566$	2.98982	+	18.2371i	0.125671	+	0.766561i
$567$	−1.48273	+	2.79673i	−0.0622688	+	0.117451i
$568$	−9.86497	−	2.17144i	−0.413925	−	0.0911118i
$569$	−3.37342	−	1.13664i	−0.141421	−	0.0476503i	0.247701	−	0.968837i	$-0.420325\pi$
$569$	−3.37342	−	1.13664i	−0.141421	−	0.0476503i	−0.389122	+	0.921186i	$0.627222\pi$
$570$	−0.388407	−	7.16374i	−0.0162686	−	0.300056i
$571$	−5.24497	+	3.98712i	−0.219495	+	0.166856i	−0.709144	−	0.705064i	$-0.750918\pi$
$571$	−5.24497	+	3.98712i	−0.219495	+	0.166856i	0.489648	+	0.871920i	$0.337125\pi$
$572$	−0.189692	−	0.357797i	−0.00793142	−	0.0149602i
$573$	−1.23559	−	4.45020i	−0.0516176	−	0.185910i
$574$	−3.88978	−	3.68460i	−0.162356	−	0.153792i
$575$	1.67712	+	4.20926i	0.0699408	+	0.175538i
$576$	−0.947653	+	0.319302i	−0.0394855	+	0.0133042i
$577$	34.8672	−	3.79204i	1.45154	−	0.157865i	0.651883	−	0.758319i	$-0.273979\pi$
$577$	34.8672	−	3.79204i	1.45154	−	0.157865i	0.799659	+	0.600455i	$0.205014\pi$
$578$	14.9466	+	6.91505i	0.621698	+	0.287628i
$579$	−1.55891	+	1.47668i	−0.0647862	+	0.0613688i
$580$	10.5863	+	6.36959i	0.439574	+	0.264483i
$581$	37.9052	+	4.12244i	1.57257	+	0.171028i
$582$	12.1908	−	2.68341i	0.505326	−	0.111231i
$583$	−0.356165	+	1.28279i	−0.0147508	+	0.0531277i
$584$	−8.20274	+	4.93542i	−0.339432	+	0.204229i
$585$	−9.48971	+	4.39041i	−0.392351	+	0.181521i
$586$	2.93113	−	7.35659i	0.121084	−	0.303898i
$587$	1.73389	−	31.9796i	0.0715651	−	1.31994i	−0.713556	−	0.700598i	$-0.752917\pi$
$587$	1.73389	−	31.9796i	0.0715651	−	1.31994i	0.785121	−	0.619342i	$-0.212601\pi$
$588$	1.69488	+	2.49975i	0.0698955	+	0.103088i
$589$	8.54851			0.352235
$590$	−11.9400	−	20.4966i	−0.491563	−	0.843831i
$591$	−4.36377			−0.179502
$592$	2.00885	+	2.96284i	0.0825633	+	0.121772i
$593$	−0.0547276	+	1.00939i	−0.00224740	+	0.0414508i	−0.999442	−	0.0334019i	$-0.989366\pi$
$593$	−0.0547276	+	1.00939i	−0.00224740	+	0.0414508i	0.997195	+	0.0748526i	$0.0238486\pi$
$594$	−0.0442711	+	0.111112i	−0.00181646	+	0.00455898i
$595$	−6.46648	+	2.99171i	−0.265100	+	0.122648i
$596$	10.7659	−	6.47764i	0.440989	−	0.265334i
$597$	5.86356	−	21.1186i	0.239979	−	0.864328i
$598$	−3.30248	+	0.726932i	−0.135049	+	0.0297264i
$599$	0.820520	+	0.0892370i	0.0335256	+	0.00364612i	0.124866	−	0.992174i	$-0.460150\pi$
$599$	0.820520	+	0.0892370i	0.0335256	+	0.00364612i	−0.0913409	+	0.995820i	$0.529115\pi$
$600$	−3.88743	−	2.33899i	−0.158704	−	0.0954887i
$601$	13.8959	−	13.1629i	0.566827	−	0.536927i	−0.349720	−	0.936854i	$-0.613723\pi$
$601$	13.8959	−	13.1629i	0.566827	−	0.536927i	0.916547	+	0.399927i	$0.130965\pi$
$602$	35.1717	+	16.2722i	1.43349	+	0.663204i
$603$	−12.7275	+	1.38420i	−0.518303	+	0.0563688i
$604$	−11.8484	+	3.99221i	−0.482107	+	0.162441i
$605$	12.5572	+	31.5163i	0.510524	+	1.28132i
$606$	−2.58318	−	2.44692i	−0.104935	−	0.0993993i
$607$	−0.638250	−	2.29877i	−0.0259058	−	0.0933041i	0.949467	−	0.313867i	$-0.101624\pi$
$607$	−0.638250	−	2.29877i	−0.0259058	−	0.0933041i	−0.975373	+	0.220563i	$0.929211\pi$
$608$	1.08818	+	2.05252i	0.0441314	+	0.0832407i
$609$	−10.0818	+	7.66396i	−0.408534	+	0.310559i
$610$	−1.90904	−	35.2103i	−0.0772950	−	1.42562i
$611$	32.8846	+	11.0801i	1.33037	+	0.448253i
$612$	0.711821	+	0.156684i	0.0287737	+	0.00633357i
$613$	−12.1027	+	22.8281i	−0.488823	+	0.922018i	0.509289	+	0.860596i	$0.329908\pi$
$613$	−12.1027	+	22.8281i	−0.488823	+	0.922018i	−0.998112	+	0.0614221i	$0.980436\pi$
$614$	−0.877535	−	5.35273i	−0.0354145	−	0.216019i
$615$	−3.38392	+	3.98386i	−0.136453	+	0.160645i
$616$	0.245108	+	0.288563i	0.00987568	+	0.0116265i
$617$	−5.18027	+	31.5983i	−0.208550	+	1.27210i	0.650223	+	0.759743i	$0.274675\pi$
$617$	−5.18027	+	31.5983i	−0.208550	+	1.27210i	−0.858773	+	0.512356i	$0.828773\pi$
$618$	−6.70975	−	5.10062i	−0.269906	−	0.205177i
$619$	7.90926	−	11.6653i	0.317900	−	0.468868i	−0.634845	−	0.772640i	$-0.718936\pi$
$619$	7.90926	−	11.6653i	0.317900	−	0.468868i	0.952745	+	0.303772i	$0.0982462\pi$
$620$	6.37713	−	9.40557i	0.256112	−	0.377737i
$621$	0.795080	+	0.604404i	0.0319055	+	0.0242539i
$622$	−1.00777	+	6.14713i	−0.0404079	+	0.246477i
$623$	−21.2347	−	24.9994i	−0.850750	−	1.00158i
$624$	2.19195	−	2.58057i	0.0877484	−	0.103305i
$625$	4.38450	+	26.7443i	0.175380	+	1.06977i
$626$	14.3338	−	27.0365i	0.572895	−	1.08060i
$627$	0.271367	+	0.0597324i	0.0108374	+	0.00238548i
$628$	−3.16985	−	1.06805i	−0.126491	−	0.0426197i
$629$	−0.141252	−	2.60524i	−0.00563209	−	0.103878i
$630$	7.78222	−	5.91589i	0.310051	−	0.235695i
$631$	10.0147	+	18.8898i	0.398680	+	0.751990i	0.998853	−	0.0478802i	$-0.0152466\pi$
$631$	10.0147	+	18.8898i	0.398680	+	0.751990i	−0.600173	+	0.799870i	$0.704902\pi$
$632$	2.57051	+	9.25813i	0.102249	+	0.368269i
$633$	−8.10159	−	7.67423i	−0.322009	−	0.305023i
$634$	0.0607202	+	0.152396i	0.00241151	+	0.00605243i
$635$	−58.0093	+	19.5456i	−2.30203	+	0.775644i
$636$	−11.0655	+	1.20345i	−0.438776	+	0.0477197i
$637$	−9.28070	−	4.29371i	−0.367715	−	0.170123i
$638$	−0.347397	+	0.329072i	−0.0137536	+	0.0130281i
$639$	−8.65523	−	5.20768i	−0.342396	−	0.206013i
$640$	3.07007	+	0.333891i	0.121355	+	0.0131982i
$641$	−1.80711	+	0.397776i	−0.0713766	+	0.0157112i	−0.250515	−	0.968113i	$-0.580600\pi$
$641$	−1.80711	+	0.397776i	−0.0713766	+	0.0157112i	0.179139	+	0.983824i	$0.442669\pi$
$642$	0.0154014	−	0.0554707i	0.000607843	−	0.00218925i
$643$	25.3996	−	15.2824i	1.00166	−	0.602679i	0.0825121	−	0.996590i	$-0.473706\pi$
$643$	25.3996	−	15.2824i	1.00166	−	0.602679i	0.919149	+	0.393911i	$0.128878\pi$
$644$	2.86924	−	1.32745i	0.113064	−	0.0523089i
$645$	13.9939	−	35.1221i	0.551011	−	1.38293i
$646$	0.0916705	−	1.69076i	0.00360673	−	0.0665222i
$647$	−15.6302	−	23.0529i	−0.614488	−	0.906303i	0.385376	−	0.922760i	$-0.374072\pi$
$647$	−15.6302	−	23.0529i	−0.614488	−	0.906303i	−0.999865	+	0.0164570i	$0.994761\pi$
$648$	−1.00000			−0.0392837
$649$	0.888626	−	0.233212i	0.0348816	−	0.00915438i
$650$	15.3611			0.602511
$651$	6.53673	+	9.64095i	0.256195	+	0.377859i
$652$	0.107476	−	1.98228i	0.00420908	−	0.0776319i
$653$	3.97203	−	9.96903i	0.155437	−	0.390118i	−0.830549	−	0.556946i	$-0.811973\pi$
$653$	3.97203	−	9.96903i	0.155437	−	0.390118i	0.985986	+	0.166828i	$0.0533523\pi$
$654$	2.26931	−	1.04989i	0.0887370	−	0.0410541i
$655$	19.0768	−	11.4781i	0.745391	−	0.448487i
$656$	0.452818	−	1.63090i	0.0176796	−	0.0636761i
$657$	−9.34924	+	2.05792i	−0.364749	+	0.0802872i
$658$	−32.2522	−	3.50764i	−1.25732	−	0.136742i
$659$	10.3210	+	6.20992i	0.402048	+	0.241904i	0.702189	−	0.711991i	$-0.252206\pi$
$659$	10.3210	+	6.20992i	0.402048	+	0.241904i	−0.300141	+	0.953895i	$0.597034\pi$
$660$	0.268159	−	0.254014i	0.0104381	−	0.00988747i
$661$	−2.99015	−	1.38339i	−0.116303	−	0.0538076i	0.360875	−	0.932614i	$-0.382478\pi$
$661$	−2.99015	−	1.38339i	−0.116303	−	0.0538076i	−0.477178	+	0.878807i	$0.658340\pi$
$662$	−24.4352	+	2.65749i	−0.949701	+	0.103286i
$663$	−2.33864	+	0.787978i	−0.0908251	+	0.0306025i
$664$	4.45840	+	11.1897i	0.173019	+	0.434246i
$665$	−16.4873	−	15.6176i	−0.639349	−	0.605623i
$666$	0.957657	+	3.44917i	0.0371085	+	0.133653i
$667$	1.87157	+	3.53016i	0.0724676	+	0.136688i
$668$	1.10264	−	0.838206i	0.0426625	−	0.0324312i
$669$	−0.471399	−	8.69445i	−0.0182253	−	0.336147i
$670$	37.4668	+	12.6240i	1.44747	+	0.487710i
$671$	1.33379	+	0.293589i	0.0514903	+	0.0113339i
$672$	−1.48273	+	2.79673i	−0.0571976	+	0.107886i
$673$	−2.99669	−	18.2790i	−0.115514	−	0.704604i	−0.979554	−	0.201181i	$-0.935522\pi$
$673$	−2.99669	−	18.2790i	−0.115514	−	0.704604i	0.864040	−	0.503423i	$-0.167926\pi$
$674$	−3.75143	+	4.41652i	−0.144500	+	0.170118i
$675$	−2.93709	−	3.45781i	−0.113049	−	0.133091i
$676$	0.248499	−	1.51577i	0.00955764	−	0.0582990i
$677$	−34.9129	−	26.5401i	−1.34181	−	1.02002i	−0.996676	−	0.0814668i	$-0.974040\pi$
$677$	−34.9129	−	26.5401i	−1.34181	−	1.02002i	−0.345136	−	0.938553i	$-0.612167\pi$
$678$	9.32129	−	13.7479i	0.357982	−	0.527984i
$679$	22.1744	−	32.7048i	0.850977	−	1.25510i
$680$	−1.79189	−	1.36216i	−0.0687158	−	0.0522364i
$681$	−3.28807	+	20.0564i	−0.125999	+	0.768561i
$682$	0.284928	+	0.335443i	0.0109105	+	0.0128448i
$683$	7.96059	−	9.37193i	0.304603	−	0.358607i	−0.588469	−	0.808520i	$-0.700269\pi$
$683$	7.96059	−	9.37193i	0.304603	−	0.358607i	0.893072	+	0.449913i	$0.148545\pi$
$684$	0.375842	+	2.29253i	0.0143707	+	0.0876572i
$685$	12.4123	−	23.4121i	0.474250	−	0.894531i
$686$	−12.3035	−	2.70820i	−0.469750	−	0.103400i
$687$	4.54811	+	1.53244i	0.173521	+	0.0584661i
$688$	0.662801	+	12.2246i	0.0252690	+	0.466060i
$689$	30.0024	−	22.8072i	1.14300	−	0.868887i
$690$	−1.44469	−	2.72497i	−0.0549983	−	0.103738i
$691$	−7.23351	−	26.0527i	−0.275176	−	0.991093i	−0.963943	−	0.266110i	$-0.914261\pi$
$691$	−7.23351	−	26.0527i	−0.275176	−	0.991093i	0.688767	−	0.724983i	$-0.258152\pi$
$692$	−5.92178	−	5.60941i	−0.225112	−	0.213238i
$693$	0.140139	+	0.351721i	0.00532342	+	0.0133608i
$694$	21.7944	−	7.34340i	0.827306	−	0.278752i
$695$	−10.7143	+	1.16525i	−0.406415	+	0.0442003i
$696$	−3.63093	−	1.67985i	−0.137630	−	0.0636745i
$697$	−0.895639	+	0.848394i	−0.0339248	+	0.0321352i
$698$	14.0310	+	8.44216i	0.531080	+	0.319540i
$699$	11.7416	+	1.27698i	0.444109	+	0.0482998i
$700$	−14.0255	+	3.08724i	−0.530112	+	0.116687i
$701$	5.75043	−	20.7112i	0.217191	−	0.782250i	−0.772001	−	0.635621i	$-0.780744\pi$
$701$	5.75043	−	20.7112i	0.217191	−	0.782250i	0.989192	−	0.146629i	$-0.0468422\pi$
$702$	2.90119	−	1.74559i	0.109498	−	0.0658830i
$703$	7.54741	−	3.49180i	0.284656	−	0.131696i
$704$	−0.0442711	+	0.111112i	−0.00166853	+	0.00418769i
$705$	−1.71351	+	31.6039i	−0.0645346	+	1.19027i
$706$	−15.1514	−	22.3467i	−0.570231	−	0.841029i
$707$	−11.2631			−0.423593
$708$	4.56130	+	6.18017i	0.171424	+	0.232265i
$709$	−5.65387			−0.212336			−0.106168	−	0.994348i	$-0.533858\pi$
$709$	−5.65387			−0.212336			−0.106168	+	0.994348i	$0.533858\pi$
$710$	17.5057	+	25.8190i	0.656978	+	0.968970i
$711$	−0.520186	+	9.59426i	−0.0195085	+	0.359813i
$712$	3.83539	−	9.62610i	0.143737	−	0.360753i
$713$	3.33538	−	1.54311i	0.124911	−	0.0577899i
$714$	1.97693	−	1.18948i	0.0739847	−	0.0445151i
$715$	−0.334577	+	1.20504i	−0.0125125	+	0.0450659i
$716$	−8.14240	+	1.79228i	−0.304296	+	0.0669806i
$717$	−27.4533	−	2.98572i	−1.02526	−	0.111504i
$718$	−6.23904	−	3.75390i	−0.232839	−	0.140094i
$719$	−34.1735	+	32.3709i	−1.27446	+	1.20723i	−0.307715	+	0.951479i	$0.599564\pi$
$719$	−34.1735	+	32.3709i	−1.27446	+	1.20723i	−0.966743	+	0.255752i	$0.917677\pi$
$720$	2.80275	+	1.29669i	0.104452	+	0.0483249i
$721$	−26.5232	+	2.88457i	−0.987777	+	0.107427i
$722$	−12.8910	+	4.34347i	−0.479752	+	0.161647i
$723$	4.70361	+	11.8052i	0.174929	+	0.439039i
$724$	−14.2392	−	13.4881i	−0.529197	−	0.501282i
$725$	−4.85578	−	17.4889i	−0.180339	−	0.649523i
$726$	−5.14579	−	9.70599i	−0.190978	−	0.360223i
$727$	−27.3769	+	20.8114i	−1.01535	+	0.771852i	−0.973828	−	0.227286i	$-0.927015\pi$
$727$	−27.3769	+	20.8114i	−1.01535	+	0.771852i	−0.0415256	+	0.999137i	$0.513222\pi$
$728$	−0.580250	−	10.7021i	−0.0215055	−	0.396645i
$729$	−0.947653	−	0.319302i	−0.0350983	−	0.0118260i
$730$	28.8721	+	6.35523i	1.06861	+	0.235218i
$731$	4.17968	−	7.88372i	0.154591	−	0.291590i
$732$	1.84729	+	11.2680i	0.0682777	+	0.416476i
$733$	−5.48245	+	6.45444i	−0.202499	+	0.238400i	−0.854032	−	0.520220i	$-0.825850\pi$
$733$	−5.48245	+	6.45444i	−0.202499	+	0.238400i	0.651534	+	0.758620i	$0.274126\pi$
$734$	−8.49249	−	9.99814i	−0.313464	−	0.369038i
$735$	1.50891	−	9.20393i	0.0556569	−	0.339492i
$736$	0.795080	+	0.604404i	0.0293070	+	0.0222786i
$737$	−0.859329	+	1.26742i	−0.0316538	+	0.0466858i
$738$	0.949864	−	1.40095i	0.0349650	−	0.0515695i
$739$	5.69252	+	4.32734i	0.209403	+	0.159184i	0.704619	−	0.709586i	$-0.251118\pi$
$739$	5.69252	+	4.32734i	0.209403	+	0.159184i	−0.495216	+	0.868770i	$0.664911\pi$
$740$	1.78843	−	10.9090i	0.0657441	−	0.401021i
$741$	−5.09221	−	5.99501i	−0.187067	−	0.220232i
$742$	−22.8100	+	26.8540i	−0.837382	+	0.985842i
$743$	−5.66920	−	34.5806i	−0.207983	−	1.26864i	−0.859945	−	0.510387i	$-0.829502\pi$
$743$	−5.66920	−	34.5806i	−0.207983	−	1.26864i	0.651962	−	0.758252i	$-0.273946\pi$
$744$	−1.72361	+	3.25108i	−0.0631908	+	0.119190i
$745$	−37.8940	−	8.34111i	−1.38833	−	0.305595i
$746$	−19.4081	−	6.53936i	−0.710582	−	0.239423i
$747$	0.652116	+	12.0276i	0.0238597	+	0.440066i
$748$	0.0694009	−	0.0527572i	0.00253755	−	0.00192900i
$749$	−0.0853594	−	0.161005i	−0.00311897	−	0.00588299i
$750$	−0.382649	−	1.37818i	−0.0139724	−	0.0503239i
$751$	10.2055	+	9.66720i	0.372405	+	0.352761i	0.850898	−	0.525330i	$-0.176058\pi$
$751$	10.2055	+	9.66720i	0.372405	+	0.352761i	−0.478493	+	0.878091i	$0.658817\pi$
$752$	−3.79349	−	9.52095i	−0.138334	−	0.347193i
$753$	−19.4106	+	6.54019i	−0.707361	+	0.238338i
$754$	13.4664	−	1.46455i	0.490416	−	0.0533359i
$755$	35.0427	+	16.2125i	1.27533	+	0.590032i
$756$	−2.29811	+	2.17689i	−0.0835815	+	0.0791726i
$757$	29.0034	+	17.4508i	1.05415	+	0.634258i	0.933551	−	0.358443i	$-0.116692\pi$
$757$	29.0034	+	17.4508i	1.05415	+	0.634258i	0.120594	+	0.992702i	$0.461520\pi$
$758$	6.39040	+	0.694998i	0.232110	+	0.0252435i
$759$	0.116662	−	0.0256792i	0.00423456	−	0.000932097i
$760$	1.91932	−	6.91276i	0.0696210	−	0.250752i
$761$	−41.4650	+	24.9487i	−1.50311	+	0.904388i	−0.503932	+	0.863744i	$0.668114\pi$
$761$	−41.4650	+	24.9487i	−1.50311	+	0.904388i	−0.999174	+	0.0406449i	$0.987059\pi$
$762$	17.9899	−	8.32301i	0.651705	−	0.301511i
$763$	2.92963	−	7.35280i	0.106060	−	0.266189i
$764$	0.250043	−	4.61177i	0.00904624	−	0.166848i
$765$	−1.26315	−	1.86301i	−0.0456693	−	0.0673572i
$766$	15.3063			0.553038
$767$	−24.0212	−	9.96771i	−0.867357	−	0.359913i
$768$	−1.00000			−0.0360844
$769$	−12.3060	−	18.1499i	−0.443764	−	0.654503i	0.538365	−	0.842712i	$-0.319042\pi$
$769$	−12.3060	−	18.1499i	−0.443764	−	0.654503i	−0.982129	+	0.188209i	$0.939732\pi$
$770$	0.0633003	−	1.16750i	0.00228118	−	0.0420740i
$771$	−5.28469	+	13.2636i	−0.190323	+	0.477676i
$772$	−1.94882	+	0.901618i	−0.0701394	+	0.0324499i
$773$	14.5060	−	8.72796i	0.521744	−	0.313923i	−0.230207	−	0.973142i	$-0.573940\pi$
$773$	14.5060	−	8.72796i	0.521744	−	0.313923i	0.751951	+	0.659219i	$0.229113\pi$
$774$	−3.27524	+	11.7964i	−0.117726	+	0.424011i
$775$	−16.3040	+	3.58879i	−0.585658	+	0.128913i
$776$	12.4095	+	1.34961i	0.445475	+	0.0484483i
$777$	9.70926	+	5.84187i	0.348318	+	0.209576i
$778$	−20.4866	+	19.4059i	−0.734479	+	0.695735i
$779$	−3.56871	−	1.65106i	−0.127862	−	0.0591554i
$780$	−10.3948	+	1.13050i	−0.372194	+	0.0404786i
$781$	−1.14492	+	0.385769i	−0.0409685	+	0.0138039i
$782$	−0.269436	−	0.676234i	−0.00963502	−	0.0241821i
$783$	−2.90449	−	2.75128i	−0.103798	−	0.0983226i
$784$	0.807979	+	2.91008i	0.0288564	+	0.103931i
$785$	4.83856	+	9.12649i	0.172696	+	0.325738i
$786$	−5.73929	+	4.36289i	−0.204714	+	0.155619i
$787$	−0.335838	−	6.19417i	−0.0119713	−	0.220798i	−0.998397	−	0.0565921i	$-0.981977\pi$
$787$	−0.335838	−	6.19417i	−0.0119713	−	0.220798i	0.986426	−	0.164206i	$-0.0525062\pi$
$788$	−4.13534	−	1.39336i	−0.147315	−	0.0496364i
$789$	30.1859	+	6.64441i	1.07465	+	0.236547i
$790$	13.8988	−	26.2158i	0.494496	−	0.932718i
$791$	−8.50620	−	51.8856i	−0.302446	−	1.84484i
$792$	−0.0774319	+	0.0911599i	−0.00275142	+	0.00323922i
$793$	−25.0285	−	29.4659i	−0.888790	−	1.04636i
$794$	−5.39614	+	32.9150i	−0.191502	+	1.16811i
$795$	27.3647	+	20.8021i	0.970526	+	0.737775i
$796$	12.2998	−	18.1409i	0.435956	−	0.642987i
$797$	24.1895	−	35.6768i	0.856835	−	1.26374i	−0.106195	−	0.994345i	$-0.533867\pi$
$797$	24.1895	−	35.6768i	0.856835	−	1.26374i	0.963031	−	0.269392i	$-0.0868227\pi$
$798$	5.85432	+	4.45034i	0.207241	+	0.157540i
$799$	−1.20851	+	7.37159i	−0.0427541	+	0.260788i
$800$	−2.93709	−	3.45781i	−0.103842	−	0.122252i
$801$	6.70824	−	7.89755i	0.237024	−	0.279046i
$802$	5.18306	+	31.6153i	0.183020	+	1.11637i
$803$	−0.536329	+	1.01162i	−0.0189267	+	0.0356995i
$804$	−12.5032	−	2.75216i	−0.440954	−	0.0970613i
$805$	−9.25201	−	3.11736i	−0.326090	−	0.109873i
$806$	−0.674517	−	12.4407i	−0.0237588	−	0.438206i
$807$	24.0866	−	18.3102i	0.847890	−	0.644549i
$808$	−1.66665	−	3.14364i	−0.0586327	−	0.110593i
$809$	14.2801	+	51.4322i	0.502060	+	1.80826i	0.584165	+	0.811635i	$0.301422\pi$
$809$	14.2801	+	51.4322i	0.502060	+	1.80826i	−0.0821047	+	0.996624i	$0.526164\pi$
$810$	2.24200	+	2.12374i	0.0787760	+	0.0746206i
$811$	−10.6756	−	26.7938i	−0.374873	−	0.940859i	−0.988494	−	0.151259i	$-0.951667\pi$
$811$	−10.6756	−	26.7938i	−0.374873	−	0.940859i	0.613622	−	0.789600i	$-0.289712\pi$
$812$	−12.0011	+	4.04365i	−0.421157	+	0.141904i
$813$	0.835916	−	0.0909113i	0.0293168	−	0.00318840i
$814$	0.388579	+	0.179776i	0.0136197	+	0.00630114i
$815$	−4.45079	+	4.21602i	−0.155905	+	0.147681i
$816$	0.624530	+	0.375768i	0.0218629	+	0.0131545i
$817$	28.2745	+	3.07504i	0.989200	+	0.107582i
$818$	32.4916	−	7.15194i	1.13604	−	0.250062i
$819$	2.86731	−	10.3271i	0.100192	−	0.360859i
$820$	−4.47883	+	2.69482i	−0.156408	+	0.0941073i
$821$	−20.2714	+	9.37853i	−0.707475	+	0.327313i	−0.740420	−	0.672144i	$-0.765373\pi$
$821$	−20.2714	+	9.37853i	−0.707475	+	0.327313i	0.0329450	+	0.999457i	$0.489511\pi$
$822$	−3.17607	+	7.97133i	−0.110778	+	0.278032i
$823$	1.26838	−	23.3939i	0.0442131	−	0.815462i	−0.889389	−	0.457151i	$-0.848870\pi$
$823$	1.26838	−	23.3939i	0.0442131	−	0.815462i	0.933602	−	0.358311i	$-0.116647\pi$
$824$	−4.72988	−	6.97605i	−0.164773	−	0.243022i
$825$	−0.542638			−0.0188922
$826$	23.9359	+	4.27330i	0.832837	+	0.148687i
$827$	43.2250			1.50308			0.751540	−	0.659688i	$-0.229311\pi$
$827$	43.2250			1.50308			0.751540	+	0.659688i	$0.229311\pi$
$828$	0.560473	+	0.826635i	0.0194778	+	0.0287276i
$829$	2.55881	−	47.1944i	0.0888711	−	1.63913i	−0.525987	−	0.850493i	$-0.676304\pi$
$829$	2.55881	−	47.1944i	0.0888711	−	1.63913i	0.614858	−	0.788638i	$-0.289213\pi$
$830$	13.7683	−	34.5559i	0.477906	−	1.19945i
$831$	−25.6297	+	11.8576i	−0.889084	+	0.411334i
$832$	2.90119	−	1.74559i	0.100581	−	0.0605174i
$833$	0.588905	−	2.12104i	0.0204043	−	0.0734898i
$834$	3.40831	−	0.750226i	0.118020	−	0.0259782i
$835$	−4.25226	−	0.462461i	−0.147155	−	0.0160041i
$836$	0.238089	+	0.143254i	0.00823449	+	0.00495453i
$837$	−2.67146	+	2.53055i	−0.0923393	+	0.0874684i
$838$	13.1715	+	6.09379i	0.455002	+	0.210506i
$839$	−34.6637	+	3.76991i	−1.19672	+	0.130152i	−0.684704	−	0.728822i	$-0.740068\pi$
$839$	−34.6637	+	3.76991i	−1.19672	+	0.130152i	−0.512021	+	0.858973i	$0.671103\pi$
$840$	9.26380	−	3.12134i	0.319631	−	0.107696i
$841$	4.80974	+	12.0715i	0.165853	+	0.416260i
$842$	−22.1436	−	20.9755i	−0.763118	−	0.722864i
$843$	−2.53890	−	9.14428i	−0.0874442	−	0.314946i
$844$	−5.22710	−	9.85936i	−0.179924	−	0.339373i
$845$	−3.77624	+	2.87063i	−0.129907	+	0.0987525i
$846$	−0.554862	−	10.2338i	−0.0190765	−	0.351846i
$847$	−32.9545	−	11.1037i	−1.13233	−	0.381526i
$848$	−10.8705	−	2.39278i	−0.373295	−	0.0821685i
$849$	−8.65643	+	16.3278i	−0.297088	+	0.560367i
$850$	0.534970	+	3.26317i	0.0183493	+	0.111926i
$851$	2.31447	−	2.72480i	0.0793389	−	0.0934049i
$852$	−6.53933	−	7.69870i	−0.224034	−	0.263753i
$853$	−0.188025	+	1.14690i	−0.00643784	+	0.0392691i	−0.989850	−	0.142115i	$-0.954610\pi$
$853$	−0.188025	+	1.14690i	−0.00643784	+	0.0392691i	0.983412	+	0.181385i	$0.0580579\pi$
$854$	28.7743	+	21.8737i	0.984638	+	0.748502i
$855$	4.02610	−	5.93806i	0.137690	−	0.203077i
$856$	0.0323070	−	0.0476493i	0.00110423	−	0.00162862i
$857$	18.4643	+	14.0362i	0.630730	+	0.479468i	0.871030	−	0.491230i	$-0.163453\pi$
$857$	18.4643	+	14.0362i	0.630730	+	0.479468i	−0.240300	+	0.970699i	$0.577246\pi$
$858$	0.0655171	−	0.399636i	0.00223672	−	0.0136434i
$859$	−12.6770	−	14.9245i	−0.432532	−	0.509216i	0.502111	−	0.864803i	$-0.332557\pi$
$859$	−12.6770	−	14.9245i	−0.432532	−	0.509216i	−0.934643	+	0.355587i	$0.884281\pi$
$860$	24.4759	−	28.8153i	0.834623	−	0.982594i
$861$	−0.866805	−	5.28728i	−0.0295406	−	0.180190i
$862$	12.5218	−	23.6185i	0.426493	−	0.804451i
$863$	5.10436	+	1.12355i	0.173754	+	0.0382462i	0.300995	−	0.953626i	$-0.402681\pi$
$863$	5.10436	+	1.12355i	0.173754	+	0.0382462i	−0.127241	+	0.991872i	$0.540612\pi$
$864$	−0.947653	−	0.319302i	−0.0322398	−	0.0108629i
$865$	1.36373	+	25.1526i	0.0463684	+	0.855214i
$866$	−5.60949	+	4.26423i	−0.190618	+	0.144904i
$867$	7.71411	+	14.5503i	0.261985	+	0.494156i
$868$	3.11618	+	11.2235i	0.105770	+	0.380949i
$869$	0.834333	+	0.790322i	0.0283028	+	0.0268098i
$870$	4.57300	+	11.4774i	0.155039	+	0.389119i
$871$	41.0783	−	13.8409i	1.39189	−	0.468981i
$872$	2.48575	−	0.270342i	0.0841781	−	0.00915492i
$873$	11.3290	+	5.24134i	0.383427	+	0.177392i
$874$	1.68444	−	1.59559i	0.0569770	−	0.0539715i
$875$	−3.87950	−	2.33422i	−0.131151	−	0.0789110i
$876$	−9.51694	−	1.03503i	−0.321547	−	0.0349704i
$877$	−10.0907	+	2.22114i	−0.340740	+	0.0750025i	−0.382044	−	0.924144i	$-0.624780\pi$
$877$	−10.0907	+	2.22114i	−0.340740	+	0.0750025i	0.0413043	+	0.999147i	$0.486849\pi$
$878$	9.05255	−	32.6043i	0.305509	−	1.10034i
$879$	6.78548	−	4.08269i	0.228868	−	0.137706i
$880$	0.335229	−	0.155093i	0.0113006	−	0.00522820i
$881$	12.1500	−	30.4942i	0.409344	−	1.02738i	−0.569358	−	0.822090i	$-0.692808\pi$
$881$	12.1500	−	30.4942i	0.409344	−	1.02738i	0.978702	−	0.205286i	$-0.0658124\pi$
$882$	−0.163508	+	3.01573i	−0.00550561	+	0.101545i
$883$	17.9321	+	26.4478i	0.603462	+	0.890040i	0.999604	−	0.0281492i	$-0.00896136\pi$
$883$	17.9321	+	26.4478i	0.603462	+	0.890040i	−0.396141	+	0.918189i	$0.629651\pi$
$884$	−2.46782			−0.0830017
$885$	2.89862	−	23.5430i	0.0974362	−	0.791388i
$886$	12.4771			0.419176
$887$	1.64482	+	2.42592i	0.0552275	+	0.0814544i	0.854300	−	0.519780i	$-0.173986\pi$
$887$	1.64482	+	2.42592i	0.0552275	+	0.0814544i	−0.799073	+	0.601234i	$0.794676\pi$
$888$	−0.193798	+	3.57440i	−0.00650344	+	0.119949i
$889$	23.2245	−	58.2892i	0.778926	−	1.95496i
$890$	−29.0423	+	13.4364i	−0.973499	+	0.450388i
$891$	−0.102486	+	0.0616638i	−0.00343341	+	0.00206582i
$892$	2.32943	−	8.38984i	0.0779950	−	0.280913i
$893$	−23.2528	+	5.11834i	−0.778127	+	0.171279i
$894$	12.4908	+	1.35845i	0.417754	+	0.0454335i
$895$	22.0616	+	13.2740i	0.737438	+	0.443702i
$896$	−2.29811	+	2.17689i	−0.0767746	+	0.0727247i
$897$	−3.06900	−	1.41987i	−0.102471	−	0.0474082i
$898$	−16.9923	+	1.84802i	−0.567039	+	0.0616692i
$899$	−13.9508	+	4.70058i	−0.465286	+	0.156773i
$900$	−1.67926	−	4.21462i	−0.0559753	−	0.140487i
$901$	5.88984	+	5.57915i	0.196219	+	0.185869i
$902$	−0.0541602	−	0.195067i	−0.00180334	−	0.00649503i
$903$	18.1525	+	34.2392i	0.604076	+	1.13941i
$904$	13.2231	−	10.0519i	0.439793	−	0.334322i
$905$	3.27917	+	60.4808i	0.109003	+	2.01045i
$906$	−11.8484	−	3.99221i	−0.393638	−	0.132632i
$907$	51.4275	+	11.3200i	1.70762	+	0.375876i	0.958173	−	0.286188i	$-0.0923883\pi$
$907$	51.4275	+	11.3200i	1.70762	+	0.375876i	0.749447	+	0.662064i	$0.230319\pi$
$908$	−9.51997	+	17.9566i	−0.315931	+	0.595910i
$909$	−0.575640	−	3.51125i	−0.0190928	−	0.116461i
$910$	−21.4275	+	25.2264i	−0.710314	+	0.836246i
$911$	20.8947	+	24.5991i	0.692271	+	0.815005i	0.990211	−	0.139580i	$-0.0445753\pi$
$911$	20.8947	+	24.5991i	0.692271	+	0.815005i	−0.297940	+	0.954585i	$0.596299\pi$
$912$	−0.375842	+	2.29253i	−0.0124454	+	0.0759134i
$913$	1.14693	+	0.871870i	0.0379577	+	0.0288547i
$914$	−10.2106	+	15.0595i	−0.337736	+	0.498123i
$915$	19.7886	−	29.1859i	0.654190	−	0.964858i
$916$	3.82072	+	2.90443i	0.126240	+	0.0959652i
$917$	−3.69200	+	22.5202i	−0.121921	+	0.743683i
$918$	0.471855	+	0.555511i	0.0155735	+	0.0183346i
$919$	1.86154	−	2.19158i	0.0614067	−	0.0722935i	−0.730601	−	0.682805i	$-0.760760\pi$
$919$	1.86154	−	2.19158i	0.0614067	−	0.0722935i	0.792008	+	0.610511i	$0.209036\pi$
$920$	−0.498976	−	3.04362i	−0.0164507	−	0.100345i
$921$	2.54073	−	4.79233i	0.0837200	−	0.157913i
$922$	15.4186	+	3.39390i	0.507786	+	0.111772i
$923$	32.4106	+	10.9204i	1.06681	+	0.359450i
$924$	0.0204976	+	0.378056i	0.000674322	+	0.0124371i
$925$	−12.9288	+	9.82821i	−0.425096	+	0.323150i
$926$	−10.3332	−	19.4905i	−0.339570	−	0.640497i
$927$	−2.25482	−	8.12113i	−0.0740580	−	0.266733i
$928$	−2.90449	−	2.75128i	−0.0953444	−	0.0903151i
$929$	6.46649	+	16.2297i	0.212159	+	0.532478i	0.996087	−	0.0883728i	$-0.0281667\pi$
$929$	6.46649	+	16.2297i	0.212159	+	0.532478i	−0.783929	+	0.620851i	$0.786787\pi$
$930$	10.7688	−	3.62843i	0.353123	−	0.118981i
$931$	6.97512	−	0.758590i	0.228600	−	0.0248618i
$932$	10.7192	+	4.95925i	0.351121	+	0.162446i
$933$	−4.52236	+	4.28381i	−0.148056	+	0.140246i
$934$	19.0728	+	11.4757i	0.624082	+	0.375498i
$935$	−0.267640	−	0.0291076i	−0.00875275	−	0.000951919i
$936$	3.30669	−	0.727858i	0.108083	−	0.0237908i
$937$	−3.22378	+	11.6110i	−0.105316	+	0.379315i	−0.997358	−	0.0726371i	$-0.976859\pi$
$937$	−3.22378	+	11.6110i	−0.105316	+	0.379315i	0.892042	+	0.451952i	$0.149272\pi$
$938$	−34.7249	+	20.8933i	−1.13381	+	0.682190i
$939$	27.7729	−	12.8491i	0.906333	−	0.419314i
$940$	−11.7150	+	29.4024i	−0.382100	+	0.959000i
$941$	−2.28733	+	42.1873i	−0.0745647	+	1.37527i	0.686755	+	0.726889i	$0.259035\pi$
$941$	−2.28733	+	42.1873i	−0.0745647	+	1.37527i	−0.761320	+	0.648377i	$0.775448\pi$
$942$	−1.87714	−	2.76857i	−0.0611605	−	0.0902050i
$943$	−1.69044			−0.0550484
$944$	2.34919	+	7.31309i	0.0764596	+	0.238021i
$945$	9.77552			0.317998
$946$	0.821746	+	1.21198i	0.0267173	+	0.0394050i
$947$	−0.568997	+	10.4945i	−0.0184899	+	0.341026i	0.974622	+	0.223857i	$0.0718648\pi$
$947$	−0.568997	+	10.4945i	−0.0184899	+	0.341026i	−0.993112	+	0.117169i	$0.962618\pi$
$948$	−3.55642	+	8.92594i	−0.115507	+	0.289901i
$949$	29.4172	−	13.6098i	0.954922	−	0.441794i
$950$	−9.03103	+	5.43379i	−0.293005	+	0.176295i
$951$	−0.0438873	+	0.158068i	−0.00142314	+	0.00512570i
$952$	2.25325	−	0.495977i	0.0730281	−	0.0160747i
$953$	−26.9839	−	2.93467i	−0.874093	−	0.0950634i	−0.339936	−	0.940449i	$-0.610405\pi$
$953$	−26.9839	−	2.93467i	−0.874093	−	0.0950634i	−0.534157	+	0.845385i	$0.679371\pi$
$954$	−9.53747	−	5.73850i	−0.308787	−	0.185791i
$955$	−10.3548	+	9.80858i	−0.335073	+	0.317398i
$956$	−25.0628	−	11.5953i	−0.810590	−	0.375019i
$957$	−0.475706	+	0.0517361i	−0.0153774	+	0.00167239i
$958$	1.29684	−	0.436958i	0.0418991	−	0.0141175i
$959$	10.0537	+	25.2330i	0.324652	+	0.814815i
$960$	2.24200	+	2.12374i	0.0723603	+	0.0685434i
$961$	−4.67094	−	16.8232i	−0.150676	−	0.542684i
$962$	−5.67718	−	10.7083i	−0.183040	−	0.345250i
$963$	0.0458304	−	0.0348393i	0.00147686	−	0.00112268i
$964$	0.687982	+	12.6891i	0.0221584	+	0.408688i
$965$	6.28405	+	2.11734i	0.202291	+	0.0681597i
$966$	3.08752	+	0.679615i	0.0993394	+	0.0218663i
$967$	−13.2371	+	24.9679i	−0.425677	+	0.802912i	−0.999875	−	0.0158043i	$-0.994969\pi$
$967$	−13.2371	+	24.9679i	−0.425677	+	0.802912i	0.574198	+	0.818716i	$0.305314\pi$
$968$	−1.77729	−	10.8410i	−0.0571242	−	0.348442i
$969$	1.09618	−	1.29053i	0.0352145	−	0.0414577i
$970$	−24.9559	−	29.3804i	−0.801286	−	0.943347i
$971$	1.50740	−	9.19473i	0.0483748	−	0.295073i	−0.951548	−	0.307500i	$-0.900508\pi$
$971$	1.50740	−	9.19473i	0.0483748	−	0.295073i	0.999923	+	0.0124272i	$0.00395581\pi$
$972$	−0.796093	−	0.605174i	−0.0255347	−	0.0194110i
$973$	6.19952	−	9.14361i	0.198748	−	0.293131i
$974$	3.19799	−	4.71669i	0.102470	−	0.151132i
$975$	12.2288	+	9.29613i	0.391637	+	0.297714i
$976$	−1.84729	+	11.2680i	−0.0591302	+	0.360678i
$977$	−26.6355	−	31.3577i	−0.852145	−	1.00322i	−0.999899	−	0.0141988i	$-0.995480\pi$
$977$	−26.6355	−	31.3577i	−0.852145	−	1.00322i	0.147754	−	0.989024i	$-0.452796\pi$
$978$	1.28518	−	1.51303i	0.0410956	−	0.0483815i
$979$	−0.200508	−	1.22305i	−0.00640827	−	0.0390887i
$980$	4.36875	−	8.24034i	0.139555	−	0.263228i
$981$	2.44195	+	0.537514i	0.0779654	+	0.0171615i
$982$	13.4869	+	4.54426i	0.430384	+	0.145013i
$983$	1.78969	+	33.0090i	0.0570824	+	1.05282i	0.877046	+	0.480407i	$0.159511\pi$
$983$	1.78969	+	33.0090i	0.0570824	+	1.05282i	−0.819964	+	0.572416i	$0.806006\pi$
$984$	1.34747	−	1.02432i	0.0429556	−	0.0326540i
$985$	6.31232	+	11.9063i	0.201127	+	0.379366i
$986$	0.780100	+	2.80967i	0.0248435	+	0.0894780i
$987$	−23.5530	−	22.3106i	−0.749701	−	0.710154i
$988$	−2.91143	−	7.30714i	−0.0926250	−	0.232471i
$989$	11.5870	−	3.90410i	0.368444	−	0.124143i
$990$	0.367202	−	0.0399357i	0.0116705	−	0.00126924i
$991$	13.4851	+	6.23888i	0.428369	+	0.198184i	0.622213	−	0.782848i	$-0.286234\pi$
$991$	13.4851	+	6.23888i	0.428369	+	0.198184i	−0.193845	+	0.981032i	$0.562096\pi$
$992$	−2.67146	+	2.53055i	−0.0848191	+	0.0803449i
$993$	−21.0609	−	12.6719i	−0.668349	−	0.402132i
$994$	−31.7873	−	3.45708i	−1.00823	−	0.109652i
$995$	−66.1028	+	14.5503i	−2.09560	+	0.461276i
$996$	−3.22244	+	11.6062i	−0.102107	+	0.367756i
$997$	−48.0791	+	28.9282i	−1.52268	+	0.916166i	−0.524791	+	0.851231i	$0.675856\pi$
$997$	−48.0791	+	28.9282i	−1.52268	+	0.916166i	−0.997890	+	0.0649348i	$0.979316\pi$
$998$	−35.8177	+	16.5710i	−1.13379	+	0.524547i
$999$	−1.32496	+	3.32541i	−0.0419200	+	0.105211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.b.7.2	✓	56
59.17	even	29	inner	354.2.e.b.253.2	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.b.7.2	✓	56	1.1	even	1	trivial
354.2.e.b.253.2	yes	56	59.17	even	29	inner

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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(0.561187 + 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(2.80275 - 1.29669i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(-0.846851 + 3.05008i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})\)	\(q+(0.561187 + 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(2.80275 - 1.29669i) q^{5} +(-0.856857 + 0.515554i) q^{6} +(-0.846851 + 3.05008i) q^{7} +(-0.976621 + 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(2.64613 + 1.59212i) q^{10} +(-0.0868341 + 0.0822536i) q^{11} +(-0.907575 - 0.419889i) q^{12} +(3.36600 - 0.366075i) q^{13} +(-2.99976 + 1.01074i) q^{14} +(1.14305 + 2.86885i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(0.194991 + 0.702295i) q^{17} +(-0.468408 - 0.883512i) q^{18} +(-1.84943 + 1.40590i) q^{19} +(0.167191 + 3.08365i) q^{20} +(-2.99976 - 1.01074i) q^{21} +(-0.116811 - 0.0257120i) q^{22} +(-0.467812 + 0.882387i) q^{23} +(-0.161782 - 0.986827i) q^{24} +(2.93709 - 3.45781i) q^{25} +(2.19195 + 2.58057i) q^{26} +(0.161782 - 0.986827i) q^{27} +(-2.52000 - 1.91566i) q^{28} +(2.24514 - 3.31133i) q^{29} +(-1.73305 + 2.55605i) q^{30} +(-2.92940 - 2.22687i) q^{31} +(0.161782 - 0.986827i) q^{32} +(-0.0774319 - 0.0911599i) q^{33} +(-0.471855 + 0.555511i) q^{34} +(1.58150 + 9.64674i) q^{35} +(0.468408 - 0.883512i) q^{36} +(-3.49596 - 0.769519i) q^{37} +(-2.20153 - 0.741781i) q^{38} +(0.183306 + 3.38089i) q^{39} +(-2.45848 + 1.86889i) q^{40} +(0.792827 + 1.49543i) q^{41} +(-0.846851 - 3.05008i) q^{42} +(-8.88807 - 8.41923i) q^{43} +(-0.0442711 - 0.111112i) q^{44} +(-2.92652 + 0.986060i) q^{45} +(-0.992873 + 0.107981i) q^{46} +(9.30161 + 4.30338i) q^{47} +(0.725995 - 0.687699i) q^{48} +(-2.58785 - 1.55706i) q^{49} +(4.51025 + 0.490519i) q^{50} +(-0.711821 + 0.156684i) q^{51} +(-0.905811 + 3.26244i) q^{52} +(9.53747 - 5.73850i) q^{53} +(0.907575 - 0.419889i) q^{54} +(-0.136717 + 0.343134i) q^{55} +(0.171375 - 3.16082i) q^{56} +(-1.30371 - 1.92284i) q^{57} +4.00069 q^{58} +(-6.73471 - 3.69373i) q^{59} -3.08818 q^{60} +(-6.40784 - 9.45086i) q^{61} +(0.199216 - 3.67433i) q^{62} +(1.17166 - 2.94064i) q^{63} +(0.907575 - 0.419889i) q^{64} +(8.95939 - 5.39069i) q^{65} +(0.0319982 - 0.115247i) q^{66} +(12.5032 - 2.75216i) q^{67} +(-0.724589 - 0.0788038i) q^{68} +(-0.855766 - 0.514898i) q^{69} +(-7.09698 + 6.72262i) q^{70} +(9.16754 + 4.24136i) q^{71} +(0.994138 - 0.108119i) q^{72} +(9.07193 - 3.05669i) q^{73} +(-1.32496 - 3.32541i) q^{74} +(3.29373 + 3.11998i) q^{75} +(-0.621505 - 2.23846i) q^{76} +(-0.177345 - 0.334508i) q^{77} +(-2.69545 + 2.04903i) q^{78} +(-0.520186 - 9.59426i) q^{79} +(-2.92652 - 0.986060i) q^{80} +(0.976621 + 0.214970i) q^{81} +(-0.792827 + 1.49543i) q^{82} +(-1.94870 - 11.8866i) q^{83} +(2.04928 - 2.41260i) q^{84} +(1.45717 + 1.71552i) q^{85} +(1.98063 - 12.0813i) q^{86} +(3.18493 + 2.42112i) q^{87} +(0.0671219 - 0.0989973i) q^{88} +(-5.81504 + 8.57655i) q^{89} +(-2.45848 - 1.86889i) q^{90} +(-1.73395 + 10.5766i) q^{91} +(-0.646562 - 0.761192i) q^{92} +(2.38220 - 2.80455i) q^{93} +(1.65808 + 10.1138i) q^{94} +(-3.36048 + 6.33855i) q^{95} +(0.976621 + 0.214970i) q^{96} +(-11.8292 - 3.98574i) q^{97} +(-0.163508 - 3.01573i) q^{98} +(0.0952182 - 0.0723830i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9}+O(q^{10}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9	\( 56 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 2 q^{5} - 2 q^{6} + q^{7} + 2 q^{8} - 2 q^{9} + 2 q^{10} + 30 q^{11} + 2 q^{12} + 5 q^{13} + 28 q^{14} + 2 q^{15} - 2 q^{16} - 3 q^{17} + 2 q^{18} - 4 q^{19} - 2 q^{20} + 28 q^{21} - q^{22} - 2 q^{23} - 2 q^{24} + 64 q^{25} - 34 q^{26} + 2 q^{27} + q^{28} + 8 q^{29} - 2 q^{30} + 2 q^{32} - q^{33} + 32 q^{34} - 87 q^{35} - 2 q^{36} + 47 q^{37} + 4 q^{38} - 5 q^{39} + 2 q^{40} + 3 q^{41} + q^{42} - 61 q^{43} + q^{44} - 2 q^{45} - 27 q^{46} + 50 q^{47} + 2 q^{48} - 45 q^{49} - 6 q^{50} + 3 q^{51} - 24 q^{52} - 27 q^{53} - 2 q^{54} - 95 q^{55} - q^{56} + 4 q^{57} + 50 q^{58} - 58 q^{59} + 2 q^{60} - 74 q^{61} - 29 q^{62} + q^{63} - 2 q^{64} - 17 q^{65} + q^{66} + 4 q^{67} - 32 q^{68} + 31 q^{69} - 58 q^{70} - 47 q^{71} + 2 q^{72} + 43 q^{73} - 18 q^{74} - 6 q^{75} - 33 q^{76} - 5 q^{77} + 5 q^{78} + 19 q^{79} - 2 q^{80} - 2 q^{81} - 3 q^{82} + 47 q^{83} - q^{84} - 149 q^{85} - 55 q^{86} + 21 q^{87} + 28 q^{88} + 36 q^{89} + 2 q^{90} + 175 q^{91} - 2 q^{92} - 29 q^{93} - 21 q^{94} + 50 q^{95} - 2 q^{96} + 10 q^{97} - 13 q^{98} + q^{99}+O(q^{100}) \) 56 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 2 * q^5 - 2 * q^6 + q^7 + 2 * q^8 - 2 * q^9 + 2 * q^10 + 30 * q^11 + 2 * q^12 + 5 * q^13 + 28 * q^14 + 2 * q^15 - 2 * q^16 - 3 * q^17 + 2 * q^18 - 4 * q^19 - 2 * q^20 + 28 * q^21 - q^22 - 2 * q^23 - 2 * q^24 + 64 * q^25 - 34 * q^26 + 2 * q^27 + q^28 + 8 * q^29 - 2 * q^30 + 2 * q^32 - q^33 + 32 * q^34 - 87 * q^35 - 2 * q^36 + 47 * q^37 + 4 * q^38 - 5 * q^39 + 2 * q^40 + 3 * q^41 + q^42 - 61 * q^43 + q^44 - 2 * q^45 - 27 * q^46 + 50 * q^47 + 2 * q^48 - 45 * q^49 - 6 * q^50 + 3 * q^51 - 24 * q^52 - 27 * q^53 - 2 * q^54 - 95 * q^55 - q^56 + 4 * q^57 + 50 * q^58 - 58 * q^59 + 2 * q^60 - 74 * q^61 - 29 * q^62 + q^63 - 2 * q^64 - 17 * q^65 + q^66 + 4 * q^67 - 32 * q^68 + 31 * q^69 - 58 * q^70 - 47 * q^71 + 2 * q^72 + 43 * q^73 - 18 * q^74 - 6 * q^75 - 33 * q^76 - 5 * q^77 + 5 * q^78 + 19 * q^79 - 2 * q^80 - 2 * q^81 - 3 * q^82 + 47 * q^83 - q^84 - 149 * q^85 - 55 * q^86 + 21 * q^87 + 28 * q^88 + 36 * q^89 + 2 * q^90 + 175 * q^91 - 2 * q^92 - 29 * q^93 - 21 * q^94 + 50 * q^95 - 2 * q^96 + 10 * q^97 - 13 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more