LMFDB - Embedded newform 483.2.q.f.85.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, 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:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			85.5
Character	$\chi$	$=$	483.85
Dual form			483.2.q.f.358.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.150977 - 0.174237i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.277065 + 1.92703i) q^{4} +(-0.602841 - 1.32004i) q^{5} +(0.0328104 - 0.228201i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.765488 + 0.491950i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})$	\(q+(0.150977 - 0.174237i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.277065 + 1.92703i) q^{4} +(-0.602841 - 1.32004i) q^{5} +(0.0328104 - 0.228201i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.765488 + 0.491950i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.321014 - 0.0942582i) q^{10} +(2.83234 + 3.26869i) q^{11} +(1.27491 + 1.47133i) q^{12} +(1.43715 + 0.421987i) q^{13} +(0.0957731 - 0.209714i) q^{14} +(-1.22081 - 0.784566i) q^{15} +(-3.53469 + 1.03788i) q^{16} +(1.02244 - 7.11120i) q^{17} +(-0.0957731 - 0.209714i) q^{18} +(0.681552 + 4.74030i) q^{19} +(2.37673 - 1.52743i) q^{20} +(0.654861 - 0.755750i) q^{21} +0.997143 q^{22} +(3.74324 + 2.99803i) q^{23} +0.909938 q^{24} +(1.89522 - 2.18720i) q^{25} +(0.290503 - 0.186695i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.808750 + 1.77091i) q^{28} +(0.541382 - 3.76539i) q^{29} +(-0.321014 + 0.0942582i) q^{30} +(0.594299 + 0.381933i) q^{31} +(-1.10882 + 2.42798i) q^{32} +(4.14990 + 1.21852i) q^{33} +(-1.08467 - 1.25177i) q^{34} +(-0.950320 - 1.09673i) q^{35} +(1.86799 + 0.548490i) q^{36} +(-3.76686 + 8.24827i) q^{37} +(0.928832 + 0.596924i) q^{38} +(1.43715 - 0.421987i) q^{39} +(0.187924 - 1.30704i) q^{40} +(-3.36614 - 7.37082i) q^{41} +(-0.0328104 - 0.228201i) q^{42} +(-5.68841 + 3.65572i) q^{43} +(-5.51413 + 6.36364i) q^{44} -1.45118 q^{45} +(1.08751 - 0.199576i) q^{46} +3.95151 q^{47} +(-2.41245 + 2.78411i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.0949560 - 0.660433i) q^{50} +(-2.98448 - 6.53509i) q^{51} +(-0.414996 + 2.88636i) q^{52} +(0.577246 - 0.169495i) q^{53} +(-0.193949 - 0.124644i) q^{54} +(2.60735 - 5.70929i) q^{55} +(0.873079 + 0.256359i) q^{56} +(3.13616 + 3.61932i) q^{57} +(-0.574333 - 0.662816i) q^{58} +(-4.42384 - 1.29896i) q^{59} +(1.17364 - 2.56991i) q^{60} +(-5.84505 - 3.75639i) q^{61} +(0.156272 - 0.0458856i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-2.80507 - 6.14224i) q^{64} +(-0.309338 - 2.15149i) q^{65} +(0.838850 - 0.539096i) q^{66} +(4.12746 - 4.76334i) q^{67} +13.9868 q^{68} +(4.76987 + 0.498355i) q^{69} -0.334566 q^{70} +(-1.13316 + 1.30774i) q^{71} +(0.765488 - 0.491950i) q^{72} +(-0.446232 - 3.10361i) q^{73} +(0.868442 + 1.90162i) q^{74} +(0.411871 - 2.86462i) q^{75} +(-8.94587 + 2.62675i) q^{76} +(3.63850 + 2.33832i) q^{77} +(0.143452 - 0.314115i) q^{78} +(-16.0839 - 4.72266i) q^{79} +(3.50089 + 4.04025i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.79248 - 0.526318i) q^{82} +(-4.26833 + 9.34634i) q^{83} +(1.63779 + 1.05255i) q^{84} +(-10.0034 + 2.93727i) q^{85} +(-0.221858 + 1.54306i) q^{86} +(-1.58029 - 3.46035i) q^{87} +(0.560090 + 3.89551i) q^{88} +(-6.34187 + 4.07567i) q^{89} +(-0.219094 + 0.252848i) q^{90} +1.49783 q^{91} +(-4.74017 + 8.04399i) q^{92} +0.706444 q^{93} +(0.596587 - 0.688498i) q^{94} +(5.84651 - 3.75732i) q^{95} +(0.379866 + 2.64203i) q^{96} +(2.23514 + 4.89426i) q^{97} +(0.0328104 - 0.228201i) q^{98} +(4.14990 - 1.21852i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) $ 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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 $

$2$	0.150977	−	0.174237i	0.106757	−	0.123204i	−0.699856	−	0.714284i	$-0.746753\pi$
$2$	0.150977	−	0.174237i	0.106757	−	0.123204i	0.806613	+	0.591080i	$0.201298\pi$
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$3$	0.841254	−	0.540641i	0.485698	−	0.312139i
$4$	0.277065	+	1.92703i	0.138533	+	0.963516i
$5$	−0.602841	−	1.32004i	−0.269599	−	0.590339i	0.725611	−	0.688106i	$-0.241557\pi$
$5$	−0.602841	−	1.32004i	−0.269599	−	0.590339i	−0.995209	+	0.0977666i	$0.968830\pi$
$6$	0.0328104	−	0.228201i	0.0133948	−	0.0931628i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$7$	0.959493	−	0.281733i	0.362654	−	0.106485i
$8$	0.765488	+	0.491950i	0.270641	+	0.173930i
$9$	0.415415	−	0.909632i	0.138472	−	0.303211i
$10$	−0.321014	−	0.0942582i	−0.101514	−	0.0298071i
$11$	2.83234	+	3.26869i	0.853982	+	0.985548i	0.999993	−	0.00373542i	$-0.00118902\pi$
$11$	2.83234	+	3.26869i	0.853982	+	0.985548i	−0.146011	+	0.989283i	$0.546644\pi$
$12$	1.27491	+	1.47133i	0.368036	+	0.424736i
$13$	1.43715	+	0.421987i	0.398595	+	0.117038i	0.474886	−	0.880048i	$-0.342489\pi$
$13$	1.43715	+	0.421987i	0.398595	+	0.117038i	−0.0762905	+	0.997086i	$0.524308\pi$
$14$	0.0957731	−	0.209714i	0.0255964	−	0.0560484i
$15$	−1.22081	−	0.784566i	−0.315211	−	0.202574i
$16$	−3.53469	+	1.03788i	−0.883672	+	0.259469i
$17$	1.02244	−	7.11120i	0.247977	−	1.72472i	−0.361895	−	0.932219i	$-0.617870\pi$
$17$	1.02244	−	7.11120i	0.247977	−	1.72472i	0.609872	−	0.792500i	$-0.291221\pi$
$18$	−0.0957731	−	0.209714i	−0.0225739	−	0.0494300i
$19$	0.681552	+	4.74030i	0.156359	+	1.08750i	0.905272	+	0.424832i	$0.139667\pi$
$19$	0.681552	+	4.74030i	0.156359	+	1.08750i	−0.748914	+	0.662668i	$0.769424\pi$
$20$	2.37673	−	1.52743i	0.531453	−	0.341544i
$21$	0.654861	−	0.755750i	0.142902	−	0.164918i
$22$	0.997143			0.212592
$23$	3.74324	+	2.99803i	0.780519	+	0.625132i
$23$	3.74324	+	2.99803i	0.780519	+	0.625132i
$24$	0.909938			0.185740
$25$	1.89522	−	2.18720i	0.379044	−	0.437440i
$26$	0.290503	−	0.186695i	0.0569723	−	0.0366138i
$27$	−0.142315	−	0.989821i	−0.0273885	−	0.190491i
$28$	0.808750	+	1.77091i	0.152839	+	0.334671i
$29$	0.541382	−	3.76539i	0.100532	−	0.699216i	−0.875758	−	0.482750i	$-0.839638\pi$
$29$	0.541382	−	3.76539i	0.100532	−	0.699216i	0.976290	−	0.216466i	$-0.0694530\pi$
$30$	−0.321014	+	0.0942582i	−0.0586089	+	0.0172091i
$31$	0.594299	+	0.381933i	0.106739	+	0.0685971i	0.592921	−	0.805260i	$-0.297974\pi$
$31$	0.594299	+	0.381933i	0.106739	+	0.0685971i	−0.486182	+	0.873857i	$0.661611\pi$
$32$	−1.10882	+	2.42798i	−0.196014	+	0.429211i
$33$	4.14990	+	1.21852i	0.722405	+	0.212117i
$34$	−1.08467	−	1.25177i	−0.186019	−	0.214677i
$35$	−0.950320	−	1.09673i	−0.160633	−	0.185381i
$36$	1.86799	+	0.548490i	0.311331	+	0.0914151i
$37$	−3.76686	+	8.24827i	−0.619268	+	1.35601i	0.296783	+	0.954945i	$0.404086\pi$
$37$	−3.76686	+	8.24827i	−0.619268	+	1.35601i	−0.916051	+	0.401062i	$0.868641\pi$
$38$	0.928832	+	0.596924i	0.150676	+	0.0968339i
$39$	1.43715	−	0.421987i	0.230129	−	0.0675720i
$40$	0.187924	−	1.30704i	0.0297134	−	0.206661i
$41$	−3.36614	−	7.37082i	−0.525703	−	1.15113i	−0.967235	−	0.253883i	$-0.918292\pi$
$41$	−3.36614	−	7.37082i	−0.525703	−	1.15113i	0.441532	−	0.897246i	$-0.354435\pi$
$42$	−0.0328104	−	0.228201i	−0.00506276	−	0.0352122i
$43$	−5.68841	+	3.65572i	−0.867474	+	0.557492i	−0.896979	−	0.442073i	$-0.854243\pi$
$43$	−5.68841	+	3.65572i	−0.867474	+	0.557492i	0.0295049	+	0.999565i	$0.490607\pi$
$44$	−5.51413	+	6.36364i	−0.831286	+	0.959355i
$45$	−1.45118			−0.216329
$46$	1.08751	−	0.199576i	0.160344	−	0.0294259i
$47$	3.95151			0.576387			0.288194	−	0.957572i	$-0.406945\pi$
$47$	3.95151			0.576387			0.288194	+	0.957572i	$0.406945\pi$
$48$	−2.41245	+	2.78411i	−0.348207	+	0.401852i
$49$	0.841254	−	0.540641i	0.120179	−	0.0772344i
$50$	−0.0949560	−	0.660433i	−0.0134288	−	0.0933994i
$51$	−2.98448	−	6.53509i	−0.417910	−	0.915096i
$52$	−0.414996	+	2.88636i	−0.0575496	+	0.400266i
$53$	0.577246	−	0.169495i	0.0792909	−	0.0232819i	−0.241847	−	0.970315i	$-0.577753\pi$
$53$	0.577246	−	0.169495i	0.0792909	−	0.0232819i	0.321137	+	0.947033i	$0.395935\pi$
$54$	−0.193949	−	0.124644i	−0.0263932	−	0.0169619i
$55$	2.60735	−	5.70929i	0.351575	−	0.769841i
$56$	0.873079	+	0.256359i	0.116670	+	0.0342574i
$57$	3.13616	+	3.61932i	0.415394	+	0.479391i
$58$	−0.574333	−	0.662816i	−0.0754137	−	0.0870320i
$59$	−4.42384	−	1.29896i	−0.575935	−	0.169110i	−0.0192226	−	0.999815i	$-0.506119\pi$
$59$	−4.42384	−	1.29896i	−0.575935	−	0.169110i	−0.556712	+	0.830706i	$0.687937\pi$
$60$	1.17364	−	2.56991i	0.151516	−	0.331774i
$61$	−5.84505	−	3.75639i	−0.748382	−	0.480956i	0.110023	−	0.993929i	$-0.464908\pi$
$61$	−5.84505	−	3.75639i	−0.748382	−	0.480956i	−0.858405	+	0.512973i	$0.828544\pi$
$62$	0.156272	−	0.0458856i	0.0198466	−	0.00582748i
$63$	0.142315	−	0.989821i	0.0179300	−	0.124706i
$64$	−2.80507	−	6.14224i	−0.350633	−	0.767780i
$65$	−0.309338	−	2.15149i	−0.0383686	−	0.266860i
$66$	0.838850	−	0.539096i	0.103255	−	0.0663581i
$67$	4.12746	−	4.76334i	0.504249	−	0.581934i	−0.445368	−	0.895348i	$-0.646927\pi$
$67$	4.12746	−	4.76334i	0.504249	−	0.581934i	0.949617	+	0.313413i	$0.101473\pi$
$68$	13.9868			1.69615
$69$	4.76987	+	0.498355i	0.574225	+	0.0599948i
$70$	−0.334566			−0.0399883
$71$	−1.13316	+	1.30774i	−0.134482	+	0.155200i	−0.818996	−	0.573799i	$-0.805469\pi$
$71$	−1.13316	+	1.30774i	−0.134482	+	0.155200i	0.684514	+	0.728999i	$0.260014\pi$
$72$	0.765488	−	0.491950i	0.0902137	−	0.0579768i
$73$	−0.446232	−	3.10361i	−0.0522275	−	0.363250i	−0.999129	−	0.0417265i	$-0.986714\pi$
$73$	−0.446232	−	3.10361i	−0.0522275	−	0.363250i	0.946902	−	0.321524i	$-0.104195\pi$
$74$	0.868442	+	1.90162i	0.100954	+	0.221059i
$75$	0.411871	−	2.86462i	0.0475587	−	0.330778i
$76$	−8.94587	+	2.62675i	−1.02616	+	0.301308i
$77$	3.63850	+	2.33832i	0.414646	+	0.266477i
$78$	0.143452	−	0.314115i	0.0162427	−	0.0355665i
$79$	−16.0839	−	4.72266i	−1.80958	−	0.531341i	−0.811022	−	0.585016i	$-0.801088\pi$
$79$	−16.0839	−	4.72266i	−1.80958	−	0.531341i	−0.998558	+	0.0536753i	$0.982906\pi$
$80$	3.50089	+	4.04025i	0.391412	+	0.451713i
$81$	−0.654861	−	0.755750i	−0.0727623	−	0.0839722i
$82$	−1.79248	−	0.526318i	−0.197946	−	0.0581222i
$83$	−4.26833	+	9.34634i	−0.468510	+	1.02589i	0.516955	+	0.856013i	$0.327066\pi$
$83$	−4.26833	+	9.34634i	−0.468510	+	1.02589i	−0.985465	+	0.169881i	$0.945662\pi$
$84$	1.63779	+	1.05255i	0.178698	+	0.114842i
$85$	−10.0034	+	2.93727i	−1.08502	+	0.318592i
$86$	−0.221858	+	1.54306i	−0.0239236	+	0.166392i
$87$	−1.58029	−	3.46035i	−0.169425	−	0.370988i
$88$	0.560090	+	3.89551i	0.0597058	+	0.415263i
$89$	−6.34187	+	4.07567i	−0.672237	+	0.432021i	−0.831731	−	0.555178i	$-0.812650\pi$
$89$	−6.34187	+	4.07567i	−0.672237	+	0.432021i	0.159494	+	0.987199i	$0.449014\pi$
$90$	−0.219094	+	0.252848i	−0.0230946	+	0.0266526i
$91$	1.49783			0.157015
$92$	−4.74017	+	8.04399i	−0.494197	+	0.838644i
$93$	0.706444			0.0732549
$94$	0.596587	−	0.688498i	0.0615332	−	0.0710131i
$95$	5.84651	−	3.75732i	0.599839	−	0.385493i
$96$	0.379866	+	2.64203i	0.0387699	+	0.269651i
$97$	2.23514	+	4.89426i	0.226944	+	0.496937i	0.988511	−	0.151148i	$-0.0482972\pi$
$97$	2.23514	+	4.89426i	0.226944	+	0.496937i	−0.761567	+	0.648086i	$0.775570\pi$
$98$	0.0328104	−	0.228201i	0.00331435	−	0.0230518i
$99$	4.14990	−	1.21852i	0.417081	−	0.122466i
$100$	4.73991	+	3.04615i	0.473991	+	0.304615i
$101$	0.0666257	−	0.145890i	0.00662951	−	0.0145166i	−0.906288	−	0.422660i	$-0.861096\pi$
$101$	0.0666257	−	0.145890i	0.00662951	−	0.0145166i	0.912918	+	0.408143i	$0.133824\pi$
$102$	−1.58924	−	0.466643i	−0.157358	−	0.0462045i
$103$	−7.83150	−	9.03803i	−0.771661	−	0.890544i	0.224817	−	0.974401i	$-0.427822\pi$
$103$	−7.83150	−	9.03803i	−0.771661	−	0.890544i	−0.996478	+	0.0838571i	$0.973276\pi$
$104$	0.892529	+	1.03003i	0.0875197	+	0.101003i
$105$	−1.39240	−	0.408844i	−0.135884	−	0.0398991i
$106$	0.0576186	−	0.126167i	0.00559641	−	0.0122544i
$107$	−13.9250	−	8.94904i	−1.34618	−	0.865136i	−0.348779	−	0.937205i	$-0.613404\pi$
$107$	−13.9250	−	8.94904i	−1.34618	−	0.865136i	−0.997400	+	0.0720688i	$0.977040\pi$
$108$	1.86799	−	0.548490i	0.179747	−	0.0527785i
$109$	−1.65040	+	11.4788i	−0.158080	+	1.09947i	0.744087	+	0.668083i	$0.232885\pi$
$109$	−1.65040	+	11.4788i	−0.158080	+	1.09947i	−0.902167	+	0.431387i	$0.858024\pi$
$110$	−0.601119	−	1.31627i	−0.0573144	−	0.125501i
$111$	1.29047	+	8.97540i	0.122486	+	0.851907i
$112$	−3.09910	+	1.99167i	−0.292838	+	0.188195i
$113$	7.60756	−	8.77959i	0.715659	−	0.825914i	−0.275119	−	0.961410i	$-0.588717\pi$
$113$	7.60756	−	8.77959i	0.715659	−	0.825914i	0.990778	+	0.135496i	$0.0432628\pi$
$114$	1.10411			0.103409
$115$	1.70093	−	6.74855i	0.158613	−	0.629306i
$116$	7.40603			0.687633
$117$	0.980868	−	1.13198i	0.0906813	−	0.104652i
$118$	−0.894223	+	0.574682i	−0.0823199	+	0.0529038i
$119$	−1.02244	−	7.11120i	−0.0937265	−	0.651882i
$120$	−0.548548	−	1.20115i	−0.0500754	−	0.109650i
$121$	−1.09675	+	7.62804i	−0.0997042	+	0.693458i
$122$	−1.53697	+	0.451294i	−0.139150	+	0.0408583i
$123$	−6.81675	−	4.38086i	−0.614645	−	0.395009i
$124$	−0.571337	+	1.25105i	−0.0513076	+	0.112348i
$125$	−10.9917	−	3.22745i	−0.983126	−	0.288672i
$126$	−0.150977	−	0.174237i	−0.0134501	−	0.0155222i
$127$	11.7831	+	13.5985i	1.04558	+	1.20667i	0.977924	+	0.208959i	$0.0670075\pi$
$127$	11.7831	+	13.5985i	1.04558	+	1.20667i	0.0676589	+	0.997709i	$0.478447\pi$
$128$	−6.61585	−	1.94259i	−0.584764	−	0.171702i
$129$	−2.80896	+	6.15077i	−0.247315	+	0.541545i
$130$	−0.421571	−	0.270927i	−0.0369742	−	0.0237619i
$131$	9.35044	−	2.74554i	0.816952	−	0.239879i	0.153549	−	0.988141i	$-0.450930\pi$
$131$	9.35044	−	2.74554i	0.816952	−	0.239879i	0.663403	+	0.748262i	$0.269112\pi$
$132$	−1.19833	+	8.33460i	−0.104302	+	0.725434i
$133$	1.98944	+	4.35627i	0.172506	+	0.377736i
$134$	−0.206797	−	1.43831i	−0.0178646	−	0.124251i
$135$	−1.22081	+	0.784566i	−0.105070	+	0.0675247i
$136$	4.28101	−	4.94055i	0.367094	−	0.423649i
$137$	−13.6347			−1.16489			−0.582445	−	0.812870i	$-0.697904\pi$
$137$	−13.6347			−1.16489			−0.582445	+	0.812870i	$0.697904\pi$
$138$	0.806971	−	0.755845i	0.0686940	−	0.0643418i
$139$	−16.8367			−1.42807			−0.714033	−	0.700112i	$-0.753133\pi$
$139$	−16.8367			−1.42807			−0.714033	+	0.700112i	$0.753133\pi$
$140$	1.85013	−	2.13516i	0.156364	−	0.180454i
$141$	3.32422	−	2.13635i	0.279950	−	0.179913i
$142$	0.0567747	+	0.394877i	0.00476443	+	0.0331373i
$143$	2.69116	+	5.89282i	0.225046	+	0.492783i
$144$	−0.524275	+	3.64641i	−0.0436896	+	0.303868i
$145$	−5.29683	+	1.55529i	−0.439878	+	0.129160i
$146$	−0.608133	−	0.390823i	−0.0503294	−	0.0323448i
$147$	0.415415	−	0.909632i	0.0342629	−	0.0750252i
$148$	−16.9383	−	4.97354i	−1.39232	−	0.408823i
$149$	−10.5674	−	12.1954i	−0.865712	−	0.999085i	−0.999967	−	0.00813811i	$-0.997410\pi$
$149$	−10.5674	−	12.1954i	−0.865712	−	0.999085i	0.134255	−	0.990947i	$-0.457136\pi$
$150$	−0.436939	−	0.504255i	−0.0356759	−	0.0411722i
$151$	12.5848	+	3.69523i	1.02414	+	0.300713i	0.750324	−	0.661070i	$-0.229897\pi$
$151$	12.5848	+	3.69523i	1.02414	+	0.300713i	0.273811	+	0.961783i	$0.411716\pi$
$152$	−1.81027	+	3.96393i	−0.146832	+	0.321518i
$153$	−6.04384	−	3.88414i	−0.488615	−	0.314014i
$154$	0.956752	−	0.280928i	0.0770972	−	0.0226378i
$155$	0.145898	−	1.01474i	0.0117188	−	0.0815060i
$156$	1.21137	+	2.65252i	0.0969870	+	0.212372i
$157$	1.22330	+	8.50827i	0.0976304	+	0.679034i	0.978586	+	0.205836i	$0.0659914\pi$
$157$	1.22330	+	8.50827i	0.0976304	+	0.679034i	−0.880956	+	0.473198i	$0.843100\pi$
$158$	−3.25116	+	2.08939i	−0.258648	+	0.166223i
$159$	0.393975	−	0.454671i	0.0312442	−	0.0360577i
$160$	3.87348			0.306225
$161$	4.43625	+	1.82199i	0.349626	+	0.143593i
$162$	−0.230548			−0.0181136
$163$	−6.40558	+	7.39244i	−0.501724	+	0.579020i	−0.948960	−	0.315395i	$-0.897863\pi$
$163$	−6.40558	+	7.39244i	−0.501724	+	0.579020i	0.447236	+	0.894416i	$0.352408\pi$
$164$	13.2712	−	8.52886i	1.03630	−	0.665992i
$165$	−0.893237	−	6.21260i	−0.0695384	−	0.483650i
$166$	0.984055	+	2.15478i	0.0763775	+	0.167243i
$167$	−0.632274	+	4.39756i	−0.0489268	+	0.340294i	0.950625	+	0.310343i	$0.100444\pi$
$167$	−0.632274	+	4.39756i	−0.0489268	+	0.340294i	−0.999551	+	0.0299503i	$0.990465\pi$
$168$	0.873079	−	0.256359i	0.0673595	−	0.0197785i
$169$	−9.04895	−	5.81541i	−0.696073	−	0.447339i
$170$	−0.998505	+	2.18642i	−0.0765818	+	0.167691i
$171$	4.59506	+	1.34923i	0.351393	+	0.103178i
$172$	−8.62075	−	9.94887i	−0.657326	−	0.758594i
$173$	10.9498	+	12.6368i	0.832501	+	0.960757i	0.999683	−	0.0251687i	$-0.00801229\pi$
$173$	10.9498	+	12.6368i	0.832501	+	0.960757i	−0.167182	+	0.985926i	$0.553467\pi$
$174$	−0.841505	−	0.247088i	−0.0637944	−	0.0187317i
$175$	1.20225	−	2.63255i	0.0908812	−	0.199002i
$176$	−13.4039	−	8.61418i	−1.01036	−	0.649318i
$177$	−4.42384	+	1.29896i	−0.332516	+	0.0976355i
$178$	−0.247344	+	1.72032i	−0.0185393	+	0.128943i
$179$	−3.61584	−	7.91758i	−0.270260	−	0.591787i	0.725031	−	0.688716i	$-0.241825\pi$
$179$	−3.61584	−	7.91758i	−0.270260	−	0.591787i	−0.995291	+	0.0969288i	$0.969098\pi$
$180$	−0.402071	−	2.79647i	−0.0299686	−	0.208436i
$181$	16.6867	−	10.7239i	1.24031	−	0.797100i	0.254847	−	0.966981i	$-0.417975\pi$
$181$	16.6867	−	10.7239i	1.24031	−	0.797100i	0.985464	+	0.169882i	$0.0543386\pi$
$182$	0.226137	−	0.260976i	0.0167624	−	0.0193449i
$183$	−6.94802			−0.513613
$184$	1.39053	+	4.13644i	0.102511	+	0.304942i
$185$	13.1588			0.967458
$186$	0.106657	−	0.123088i	0.00782045	−	0.00902528i
$187$	26.1402	−	16.7993i	1.91156	−	1.22849i
$188$	1.09483	+	7.61469i	0.0798484	+	0.555358i
$189$	−0.415415	−	0.909632i	−0.0302170	−	0.0661660i
$190$	0.228024	−	1.58594i	0.0165426	−	0.115057i
$191$	14.3188	−	4.20438i	1.03607	−	0.304218i	0.280895	−	0.959738i	$-0.409369\pi$
$191$	14.3188	−	4.20438i	1.03607	−	0.304218i	0.755178	+	0.655520i	$0.227550\pi$
$192$	−5.68052	−	3.65065i	−0.409956	−	0.263463i
$193$	7.16229	−	15.6832i	0.515553	−	1.12890i	−0.455543	−	0.890214i	$-0.650555\pi$
$193$	7.16229	−	15.6832i	0.515553	−	1.12890i	0.971096	−	0.238690i	$-0.0767180\pi$
$194$	1.19021	+	0.349478i	0.0854523	+	0.0250911i
$195$	−1.42341	−	1.64271i	−0.101933	−	0.117637i
$196$	1.27491	+	1.47133i	0.0910653	+	0.105095i
$197$	−0.536281	−	0.157466i	−0.0382084	−	0.0112190i	0.262572	−	0.964912i	$-0.415429\pi$
$197$	−0.536281	−	0.157466i	−0.0382084	−	0.0112190i	−0.300781	+	0.953693i	$0.597247\pi$
$198$	0.414228	−	0.907033i	0.0294379	−	0.0644600i
$199$	13.4793	+	8.66263i	0.955523	+	0.614077i	0.922756	−	0.385386i	$-0.125932\pi$
$199$	13.4793	+	8.66263i	0.955523	+	0.614077i	0.0327674	+	0.999463i	$0.489568\pi$
$200$	2.52676	−	0.741924i	0.178669	−	0.0524620i
$201$	0.896982	−	6.23864i	0.0632682	−	0.440040i
$202$	−0.0153604	−	0.0336346i	−0.00108076	−	0.00236653i
$203$	−0.541382	−	3.76539i	−0.0379976	−	0.264279i
$204$	11.7664	−	7.56183i	0.823815	−	0.529434i
$205$	−7.70052	+	8.88687i	−0.537827	+	0.620686i
$206$	−2.75713			−0.192098
$207$	4.28210	−	2.15954i	0.297626	−	0.150099i
$208$	−5.51786			−0.382595
$209$	−13.5642	+	15.6539i	−0.938255	+	1.08280i
$210$	−0.281455	+	0.180880i	−0.0194222	+	0.0124819i
$211$	0.940186	+	6.53914i	0.0647251	+	0.450173i	0.996252	+	0.0865000i	$0.0275683\pi$
$211$	0.940186	+	6.53914i	0.0647251	+	0.450173i	−0.931527	+	0.363673i	$0.881523\pi$
$212$	0.486557	+	1.06541i	0.0334168	+	0.0731727i
$213$	−0.246260	+	1.71277i	−0.0168734	+	0.117357i
$214$	−3.66160	+	1.07514i	−0.250302	+	0.0734952i
$215$	8.25490	+	5.30510i	0.562979	+	0.361805i
$216$	0.378002	−	0.827709i	0.0257198	−	0.0563184i
$217$	0.677828	+	0.199028i	0.0460140	+	0.0135109i
$218$	1.75085	+	2.02059i	0.118583	+	0.136852i
$219$	−2.05333	−	2.36967i	−0.138751	−	0.160128i
$220$	11.7244	+	3.44259i	0.790459	+	0.232100i
$221$	4.47023	−	9.78844i	0.300700	−	0.658442i
$222$	1.75867	+	1.13023i	0.118034	+	0.0758561i
$223$	27.2928	−	8.01388i	1.82766	−	0.536649i	0.827950	−	0.560801i	$-0.189507\pi$
$223$	27.2928	−	8.01388i	1.82766	−	0.536649i	0.999708	+	0.0241524i	$0.00768870\pi$
$224$	−0.379866	+	2.64203i	−0.0253809	+	0.176528i
$225$	−1.20225	−	2.63255i	−0.0801497	−	0.175503i
$226$	−0.381160	−	2.65103i	−0.0253544	−	0.176344i
$227$	6.30037	−	4.04900i	0.418170	−	0.268742i	−0.314591	−	0.949227i	$-0.601867\pi$
$227$	6.30037	−	4.04900i	0.418170	−	0.268742i	0.732761	+	0.680486i	$0.238231\pi$
$228$	−6.10562	+	7.04626i	−0.404355	+	0.466650i
$229$	8.55209			0.565138			0.282569	−	0.959247i	$-0.408813\pi$
$229$	8.55209			0.565138			0.282569	+	0.959247i	$0.408813\pi$
$230$	−0.919043	−	1.31524i	−0.0605999	−	0.0867243i
$231$	4.32510			0.284571
$232$	2.26681	−	2.61603i	0.148823	−	0.171751i
$233$	−8.46856	+	5.44242i	−0.554794	+	0.356544i	−0.787800	−	0.615931i	$-0.788780\pi$
$233$	−8.46856	+	5.44242i	−0.554794	+	0.356544i	0.233006	+	0.972475i	$0.425144\pi$
$234$	−0.0491443	−	0.341806i	−0.00321266	−	0.0223446i
$235$	−2.38213	−	5.21615i	−0.155393	−	0.340264i
$236$	1.27744	−	8.88477i	0.0831541	−	0.578349i
$237$	−16.0839	+	4.72266i	−1.04476	+	0.306770i
$238$	−1.39339	−	0.895480i	−0.0903204	−	0.0580454i
$239$	−6.32751	+	13.8553i	−0.409293	+	0.896226i	0.586950	+	0.809623i	$0.300328\pi$
$239$	−6.32751	+	13.8553i	−0.409293	+	0.896226i	−0.996243	+	0.0866030i	$0.972399\pi$
$240$	5.12946	+	1.50615i	0.331105	+	0.0972213i
$241$	7.51625	+	8.67422i	0.484164	+	0.558755i	0.944297	−	0.329095i	$-0.106744\pi$
$241$	7.51625	+	8.67422i	0.484164	+	0.558755i	−0.460133	+	0.887850i	$0.652198\pi$
$242$	1.16350	+	1.34275i	0.0747926	+	0.0863152i
$243$	−0.959493	−	0.281733i	−0.0615515	−	0.0180732i
$244$	5.61921	−	12.3044i	0.359733	−	0.787706i
$245$	−1.22081	−	0.784566i	−0.0779946	−	0.0501241i
$246$	−1.79248	+	0.526318i	−0.114284	+	0.0335568i
$247$	−1.02085	+	7.10015i	−0.0649550	+	0.451772i
$248$	0.267037	+	0.584730i	0.0169569	+	0.0371304i
$249$	1.46226	+	10.1703i	0.0926672	+	0.644515i
$250$	−2.22183	+	1.42788i	−0.140521	+	0.0903072i
$251$	−9.98078	+	11.5184i	−0.629982	+	0.727037i	−0.977570	−	0.210610i	$-0.932455\pi$
$251$	−9.98078	+	11.5184i	−0.629982	+	0.727037i	0.347589	+	0.937647i	$0.387001\pi$
$252$	1.94685			0.122640
$253$	0.802483	+	20.7269i	0.0504517	+	1.30309i
$254$	4.14833			0.260289
$255$	−6.82740	+	7.87924i	−0.427549	+	0.493417i
$256$	10.0237	−	6.44186i	0.626483	−	0.402616i
$257$	−3.14444	−	21.8701i	−0.196145	−	1.36422i	−0.815341	−	0.578981i	$-0.803450\pi$
$257$	−3.14444	−	21.8701i	−0.196145	−	1.36422i	0.619196	−	0.785237i	$-0.287459\pi$
$258$	0.647601	+	1.41805i	0.0403179	+	0.0882838i
$259$	−1.29047	+	8.97540i	−0.0801858	+	0.557704i
$260$	4.06028	−	1.19221i	0.251808	−	0.0739375i
$261$	−3.20023	−	2.05666i	−0.198089	−	0.127304i
$262$	0.933327	−	2.04370i	0.0576612	−	0.126260i
$263$	−0.975554	−	0.286449i	−0.0601553	−	0.0176632i	0.251516	−	0.967853i	$-0.419071\pi$
$263$	−0.975554	−	0.286449i	−0.0601553	−	0.0176632i	−0.311672	+	0.950190i	$0.600889\pi$
$264$	2.57725	+	2.97431i	0.158619	+	0.183056i
$265$	−0.571727	−	0.659808i	−0.0351209	−	0.0405317i
$266$	1.05938	+	0.311062i	0.0649548	+	0.0190725i
$267$	−3.13165	+	6.85735i	−0.191654	+	0.419663i
$268$	10.3227	+	6.63398i	0.630558	+	0.405235i
$269$	−3.32594	+	0.976584i	−0.202786	+	0.0595434i	−0.381548	−	0.924349i	$-0.624609\pi$
$269$	−3.32594	+	0.976584i	−0.202786	+	0.0595434i	0.178762	+	0.983892i	$0.442791\pi$
$270$	−0.0476137	+	0.331161i	−0.00289768	+	0.0201538i
$271$	−4.51985	−	9.89709i	−0.274561	−	0.601205i	0.721246	−	0.692679i	$-0.243570\pi$
$271$	−4.51985	−	9.89709i	−0.274561	−	0.601205i	−0.995808	+	0.0914736i	$0.970842\pi$
$272$	3.76656	+	26.1970i	0.228381	+	1.58843i
$273$	1.26005	−	0.809787i	0.0762619	−	0.0490105i
$274$	−2.05852	+	2.37566i	−0.124360	+	0.143519i
$275$	12.5172			0.754815
$276$	0.361220	+	9.32976i	0.0217429	+	0.561586i
$277$	27.9572			1.67978			0.839891	−	0.542755i	$-0.182619\pi$
$277$	27.9572			1.67978			0.839891	+	0.542755i	$0.182619\pi$
$278$	−2.54194	+	2.93356i	−0.152456	+	0.175943i
$279$	0.594299	−	0.381933i	0.0355797	−	0.0228657i
$280$	−0.187924	−	1.30704i	−0.0112306	−	0.0781107i
$281$	4.33341	+	9.48885i	0.258510	+	0.566057i	0.993735	−	0.111766i	$-0.0356507\pi$
$281$	4.33341	+	9.48885i	0.258510	+	0.566057i	−0.735225	+	0.677823i	$0.762923\pi$
$282$	0.129651	−	0.901740i	0.00772059	−	0.0536979i
$283$	26.7219	−	7.84627i	1.58845	−	0.466412i	0.636151	−	0.771564i	$-0.280525\pi$
$283$	26.7219	−	7.84627i	1.58845	−	0.466412i	0.952304	+	0.305152i	$0.0987073\pi$
$284$	−2.83401	−	1.82131i	−0.168168	−	0.108075i
$285$	2.88703	−	6.32172i	0.171013	−	0.374467i
$286$	1.43305	+	0.420781i	0.0847379	+	0.0248813i
$287$	−5.30639	−	6.12390i	−0.313226	−	0.361482i
$288$	1.74795	+	2.01724i	0.102999	+	0.118867i
$289$	−33.2124	−	9.75203i	−1.95367	−	0.573649i
$290$	−0.528711	+	1.15771i	−0.0310470	+	0.0679833i
$291$	4.52635	+	2.90891i	0.265340	+	0.170523i
$292$	5.85712	−	1.71981i	0.342762	−	0.100644i
$293$	1.70005	−	11.8241i	0.0993183	−	0.690774i	−0.877948	−	0.478757i	$-0.841088\pi$
$293$	1.70005	−	11.8241i	0.0993183	−	0.690774i	0.977266	−	0.212017i	$-0.0680033\pi$
$294$	−0.0957731	−	0.209714i	−0.00558560	−	0.0122308i
$295$	0.952200	+	6.62270i	0.0554392	+	0.385588i
$296$	−6.94122	+	4.46085i	−0.403450	+	0.259282i
$297$	2.83234	−	3.26869i	0.164349	−	0.189669i
$298$	−3.72031			−0.215512
$299$	4.11448	+	5.88823i	0.237947	+	0.340525i
$300$	5.63434			0.325299
$301$	−4.42805	+	5.11025i	−0.255229	+	0.294550i
$302$	2.54386	−	1.63484i	0.146382	−	0.0940743i
$303$	−0.0228250	−	0.158751i	−0.00131126	−	0.00912001i
$304$	−7.32893	−	16.0481i	−0.420343	−	0.920422i
$305$	−1.43494	+	9.98019i	−0.0821642	+	0.571464i
$306$	−1.58924	+	0.466643i	−0.0908507	+	0.0266762i
$307$	−10.4900	−	6.74151i	−0.598696	−	0.384758i	0.205907	−	0.978572i	$-0.433985\pi$
$307$	−10.4900	−	6.74151i	−0.598696	−	0.384758i	−0.804603	+	0.593813i	$0.797622\pi$
$308$	−3.49792	+	7.65938i	−0.199313	+	0.436434i
$309$	−11.4746	−	3.36925i	−0.652768	−	0.191670i
$310$	−0.154778	−	0.178623i	−0.00879080	−	0.0101451i
$311$	−0.893251	−	1.03087i	−0.0506516	−	0.0584551i	0.729858	−	0.683598i	$-0.239586\pi$
$311$	−0.893251	−	1.03087i	−0.0506516	−	0.0584551i	−0.780510	+	0.625143i	$0.785041\pi$
$312$	1.30772	+	0.383982i	0.0740352	+	0.0217387i
$313$	−9.60001	+	21.0211i	−0.542625	+	1.18818i	0.417517	+	0.908669i	$0.362900\pi$
$313$	−9.60001	+	21.0211i	−0.542625	+	1.18818i	−0.960142	+	0.279513i	$0.909827\pi$
$314$	1.66714	+	1.07141i	0.0940823	+	0.0604630i
$315$	−1.39240	+	0.408844i	−0.0784526	+	0.0230358i
$316$	4.64442	−	32.3027i	0.261269	−	1.81717i
$317$	6.71807	+	14.7105i	0.377324	+	0.826225i	0.999075	+	0.0430094i	$0.0136945\pi$
$317$	6.71807	+	14.7105i	0.377324	+	0.826225i	−0.621750	+	0.783215i	$0.713578\pi$
$318$	−0.0197393	−	0.137290i	−0.00110692	−	0.00769882i
$319$	13.8413	−	8.89526i	0.774963	−	0.498039i
$320$	−6.41698	+	7.40559i	−0.358720	+	0.413985i
$321$	−16.5527			−0.923879
$322$	0.987229	−	0.497878i	0.0550161	−	0.0277457i
$323$	34.4061			1.91440
$324$	1.27491	−	1.47133i	0.0708286	−	0.0817405i
$325$	3.64670	−	2.34359i	0.202282	−	0.129999i
$326$	0.320938	+	2.23217i	0.0177751	+	0.123629i
$327$	4.81750	+	10.5489i	0.266409	+	0.583353i
$328$	1.04933	−	7.29825i	0.0579396	−	0.402978i
$329$	3.79145	−	1.11327i	0.209029	−	0.0613765i
$330$	−1.21732	−	0.782325i	−0.0670113	−	0.0430655i
$331$	9.24582	−	20.2455i	0.508196	−	1.11280i	−0.465521	−	0.885037i	$-0.654133\pi$
$331$	9.24582	−	20.2455i	0.508196	−	1.11280i	0.973718	−	0.227758i	$-0.0731396\pi$
$332$	−19.1933	−	5.63566i	−1.05337	−	0.309297i
$333$	5.93808	+	6.85291i	0.325405	+	0.375537i
$334$	0.670758	+	0.774095i	0.0367022	+	0.0423566i
$335$	−8.77599	−	2.57686i	−0.479483	−	0.140789i
$336$	−1.53035	+	3.35100i	−0.0834875	+	0.182812i
$337$	−2.43098	−	1.56229i	−0.132424	−	0.0851035i	0.472752	−	0.881196i	$-0.343261\pi$
$337$	−2.43098	−	1.56229i	−0.132424	−	0.0851035i	−0.605176	+	0.796092i	$0.706897\pi$
$338$	−2.37944	+	0.698667i	−0.129424	+	0.0380024i
$339$	1.65328	−	11.4988i	0.0897938	−	0.624530i
$340$	−8.43181	−	18.4631i	−0.457279	−	1.00130i
$341$	0.434835	+	3.02434i	0.0235476	+	0.163777i
$342$	0.928832	−	0.596924i	0.0502255	−	0.0322780i
$343$	0.654861	−	0.755750i	0.0353592	−	0.0408066i
$344$	−6.15284			−0.331739
$345$	−2.21763	−	6.59684i	−0.119393	−	0.355162i
$346$	3.85496			0.207244
$347$	3.49304	−	4.03118i	0.187516	−	0.216405i	−0.654206	−	0.756317i	$-0.726997\pi$
$347$	3.49304	−	4.03118i	0.187516	−	0.216405i	0.841722	+	0.539912i	$0.181542\pi$
$348$	6.23035	−	4.00400i	0.333982	−	0.214637i
$349$	−2.17238	−	15.1092i	−0.116285	−	0.808778i	−0.961589	−	0.274493i	$-0.911490\pi$
$349$	−2.17238	−	15.1092i	−0.116285	−	0.808778i	0.845304	−	0.534285i	$-0.179419\pi$
$350$	−0.277175	−	0.606929i	−0.0148156	−	0.0324417i
$351$	0.213163	−	1.48258i	0.0113778	−	0.0791344i
$352$	−11.0769	+	3.25247i	−0.590400	+	0.173357i
$353$	9.57871	+	6.15586i	0.509823	+	0.327643i	0.770135	−	0.637881i	$-0.220189\pi$
$353$	9.57871	+	6.15586i	0.509823	+	0.327643i	−0.260312	+	0.965525i	$0.583825\pi$
$354$	−0.441571	+	0.966907i	−0.0234693	+	0.0513905i
$355$	2.40938	+	0.707458i	0.127877	+	0.0375480i
$356$	−9.61106	−	11.0918i	−0.509385	−	0.587862i
$357$	−4.70473	−	5.42955i	−0.249001	−	0.287362i
$358$	−1.92544	−	0.565360i	−0.101763	−	0.0298802i
$359$	13.4566	−	29.4658i	0.710211	−	1.55514i	−0.116924	−	0.993141i	$-0.537304\pi$
$359$	13.4566	−	29.4658i	0.710211	−	1.55514i	0.827135	−	0.562003i	$-0.189969\pi$
$360$	−1.11086	−	0.713906i	−0.0585475	−	0.0376262i
$361$	−3.77557	+	1.10861i	−0.198714	+	0.0583477i
$362$	0.650811	−	4.52649i	0.0342058	−	0.237907i
$363$	3.20139	+	7.01006i	0.168029	+	0.367933i
$364$	0.414996	+	2.88636i	0.0217517	+	0.151286i
$365$	−3.82788	+	2.46003i	−0.200360	+	0.128764i
$366$	−1.04899	+	1.21060i	−0.0548316	+	0.0632791i
$367$	−28.6119			−1.49353			−0.746763	−	0.665090i	$-0.768393\pi$
$367$	−28.6119			−1.49353			−0.746763	+	0.665090i	$0.768393\pi$
$368$	−16.3428	−	6.71207i	−0.851925	−	0.349891i
$369$	−8.10308			−0.421830
$370$	1.98668	−	2.29275i	0.103283	−	0.119194i
$371$	0.506111	−	0.325258i	0.0262760	−	0.0168866i
$372$	0.195731	+	1.36134i	0.0101482	+	0.0705822i
$373$	9.49308	+	20.7869i	0.491533	+	1.07631i	0.979129	+	0.203238i	$0.0651465\pi$
$373$	9.49308	+	20.7869i	0.491533	+	1.07631i	−0.487596	+	0.873069i	$0.662126\pi$
$374$	1.01951	−	7.09088i	0.0527178	−	0.366661i
$375$	−10.9917	+	3.22745i	−0.567608	+	0.166665i
$376$	3.02484	+	1.94394i	0.155994	+	0.100251i
$377$	2.36700	−	5.18300i	0.121907	−	0.266938i
$378$	−0.221209	−	0.0649529i	−0.0113778	−	0.00334082i
$379$	17.3156	+	19.9833i	0.889444	+	1.02647i	0.999470	+	0.0325442i	$0.0103610\pi$
$379$	17.3156	+	19.9833i	0.889444	+	1.02647i	−0.110026	+	0.993929i	$0.535094\pi$
$380$	8.86035	+	10.2254i	0.454526	+	0.524551i
$381$	17.2645	+	5.06931i	0.884486	+	0.259708i
$382$	1.42925	−	3.12963i	0.0731269	−	0.160126i
$383$	−25.2259	−	16.2117i	−1.28898	−	0.828380i	−0.297017	−	0.954872i	$-0.595992\pi$
$383$	−25.2259	−	16.2117i	−1.28898	−	0.828380i	−0.991968	+	0.126492i	$0.959628\pi$
$384$	−6.61585	+	1.94259i	−0.337614	+	0.0991323i
$385$	0.893237	−	6.21260i	0.0455236	−	0.316624i
$386$	−1.65125	−	3.61574i	−0.0840465	−	0.184036i
$387$	0.962308	+	6.69300i	0.0489169	+	0.340224i
$388$	−8.81212	+	5.66321i	−0.447368	+	0.287506i
$389$	−22.4604	+	25.9206i	−1.13879	+	1.31423i	−0.196085	+	0.980587i	$0.562823\pi$
$389$	−22.4604	+	25.9206i	−1.13879	+	1.31423i	−0.942700	+	0.333641i	$0.891723\pi$
$390$	−0.501123			−0.0253753
$391$	25.1468	−	23.5536i	1.27173	−	1.19116i
$392$	0.909938			0.0459588
$393$	6.38174	−	7.36492i	0.321916	−	0.371511i
$394$	−0.108402	+	0.0696660i	−0.00546123	+	0.00350972i
$395$	3.46195	+	24.0784i	0.174189	+	1.21151i
$396$	3.49792	+	7.65938i	0.175777	+	0.384898i
$397$	−3.41507	+	23.7523i	−0.171397	+	1.19209i	0.704538	+	0.709666i	$0.251154\pi$
$397$	−3.41507	+	23.7523i	−0.171397	+	1.19209i	−0.875936	+	0.482428i	$0.839755\pi$
$398$	3.54441	−	1.04073i	0.177665	−	0.0521672i
$399$	4.02880	+	2.58915i	0.201692	+	0.129620i
$400$	−4.42896	+	9.69808i	−0.221448	+	0.484904i
$401$	−7.61019	−	2.23455i	−0.380035	−	0.111588i	0.0861352	−	0.996283i	$-0.472548\pi$
$401$	−7.61019	−	2.23455i	−0.380035	−	0.111588i	−0.466170	+	0.884695i	$0.654366\pi$
$402$	−0.951577	−	1.09818i	−0.0474603	−	0.0547721i
$403$	0.692929	+	0.799683i	0.0345173	+	0.0398350i
$404$	0.299594	+	0.0879688i	0.0149054	+	0.00437661i
$405$	−0.602841	+	1.32004i	−0.0299554	+	0.0655932i
$406$	−0.737806	−	0.474159i	−0.0366167	−	0.0235321i
$407$	−37.6301	+	11.0492i	−1.86525	+	0.547688i
$408$	0.930353	−	6.47075i	0.0460593	−	0.320350i
$409$	−7.54763	−	16.5270i	−0.373206	−	0.817207i	−0.999298	−	0.0374582i	$-0.988074\pi$
$409$	−7.54763	−	16.5270i	−0.373206	−	0.817207i	0.626092	−	0.779749i	$-0.284653\pi$
$410$	0.385818	+	2.68342i	0.0190542	+	0.132525i
$411$	−11.4702	+	7.37147i	−0.565785	+	0.363608i
$412$	15.2467	−	17.5957i	0.751153	−	0.866877i
$413$	−4.61060			−0.226873
$414$	0.270226	−	1.07214i	0.0132809	−	0.0526928i
$415$	14.9106			0.731935
$416$	−2.61813	+	3.02148i	−0.128364	+	0.148140i
$417$	−14.1639	+	9.10258i	−0.693609	+	0.445755i
$418$	0.679605	+	4.72676i	0.0332406	+	0.231193i
$419$	−7.33336	−	16.0578i	−0.358258	−	0.784476i	−0.999848	−	0.0174282i	$-0.994452\pi$
$419$	−7.33336	−	16.0578i	−0.358258	−	0.784476i	0.641590	−	0.767048i	$-0.278275\pi$
$420$	0.402071	−	2.79647i	0.0196191	−	0.136454i
$421$	−0.908554	+	0.266776i	−0.0442802	+	0.0130019i	−0.303798	−	0.952737i	$-0.598255\pi$
$421$	−0.908554	+	0.266776i	−0.0442802	+	0.0130019i	0.259517	+	0.965738i	$0.416437\pi$
$422$	1.28130	+	0.823444i	0.0623729	+	0.0400846i
$423$	1.64152	−	3.59442i	0.0798133	−	0.174767i
$424$	0.525258	+	0.154230i	0.0255088	+	0.00749006i
$425$	−13.6159	−	15.7136i	−0.660467	−	0.762220i
$426$	0.261248	+	0.301497i	0.0126575	+	0.0146076i
$427$	−6.66658	−	1.95748i	−0.322618	−	0.0947293i
$428$	13.3870	−	29.3133i	0.647083	−	1.41691i
$429$	5.44985	+	3.50241i	0.263121	+	0.169098i
$430$	2.17064	−	0.637357i	0.104678	−	0.0307361i
$431$	0.582725	−	4.05294i	0.0280689	−	0.195223i	−0.970962	−	0.239233i	$-0.923104\pi$
$431$	0.582725	−	4.05294i	0.0280689	−	0.195223i	0.999031	+	0.0440095i	$0.0140132\pi$
$432$	1.53035	+	3.35100i	0.0736291	+	0.161225i
$433$	−0.406611	−	2.82804i	−0.0195405	−	0.135907i	0.977716	−	0.209933i	$-0.0673245\pi$
$433$	−0.406611	−	2.82804i	−0.0195405	−	0.135907i	−0.997256	+	0.0740255i	$0.976415\pi$
$434$	0.137014	−	0.0880538i	0.00657690	−	0.00422672i
$435$	−3.61513	+	4.17208i	−0.173332	+	0.200036i
$436$	−22.5773			−1.08126
$437$	−11.6603	+	19.7874i	−0.557790	+	0.946559i
$438$	−0.722889			−0.0345410
$439$	−15.6320	+	18.0403i	−0.746073	+	0.861014i	−0.994181	−	0.107718i	$-0.965646\pi$
$439$	−15.6320	+	18.0403i	−0.746073	+	0.861014i	0.248108	+	0.968732i	$0.420191\pi$
$440$	4.80458	−	3.08772i	0.229049	−	0.147201i
$441$	−0.142315	−	0.989821i	−0.00677690	−	0.0471344i
$442$	−1.03060	−	2.25670i	−0.0490208	−	0.107341i
$443$	−2.09033	+	14.5385i	−0.0993145	+	0.690747i	0.877954	+	0.478744i	$0.158908\pi$
$443$	−2.09033	+	14.5385i	−0.0993145	+	0.690747i	−0.977269	+	0.212003i	$0.932001\pi$
$444$	−16.9383	+	4.97354i	−0.803858	+	0.236034i
$445$	9.20319	+	5.91453i	0.436273	+	0.280376i
$446$	2.72426	−	5.96531i	0.128998	−	0.282465i
$447$	−15.4832	−	4.54626i	−0.732328	−	0.215031i
$448$	−4.42191	−	5.10316i	−0.208916	−	0.241102i
$449$	0.404298	+	0.466585i	0.0190800	+	0.0220195i	0.765209	−	0.643781i	$-0.222635\pi$
$449$	0.404298	+	0.466585i	0.0190800	+	0.0220195i	−0.746129	+	0.665801i	$0.768090\pi$
$450$	−0.640198	−	0.187979i	−0.0301792	−	0.00886141i
$451$	14.5589	−	31.8795i	0.685552	−	1.50115i
$452$	19.0263	+	12.2275i	0.894923	+	0.575132i
$453$	12.5848	−	3.69523i	0.591285	−	0.173617i
$454$	0.245726	−	1.70906i	0.0115325	−	0.0802102i
$455$	−0.902952	−	1.97719i	−0.0423310	−	0.0926921i
$456$	0.620170	+	4.31338i	0.0290421	+	0.201992i
$457$	−18.2756	+	11.7450i	−0.854894	+	0.549407i	−0.893098	−	0.449863i	$-0.851473\pi$
$457$	−18.2756	+	11.7450i	−0.854894	+	0.549407i	0.0382033	+	0.999270i	$0.487837\pi$
$458$	1.29117	−	1.49009i	0.0603323	−	0.0696272i
$459$	−7.18432			−0.335336
$460$	13.4759	+	1.40796i	0.628319	+	0.0656466i
$461$	−4.66424			−0.217235			−0.108618	−	0.994084i	$-0.534642\pi$
$461$	−4.66424			−0.217235			−0.108618	+	0.994084i	$0.534642\pi$
$462$	0.652990	−	0.753590i	0.0303798	−	0.0350602i
$463$	1.99983	−	1.28521i	0.0929398	−	0.0597288i	−0.493345	−	0.869833i	$-0.664226\pi$
$463$	1.99983	−	1.28521i	0.0929398	−	0.0597288i	0.586285	+	0.810105i	$0.300590\pi$
$464$	1.99440	+	13.8714i	0.0925878	+	0.643963i
$465$	−0.425874	−	0.932534i	−0.0197494	−	0.0432452i
$466$	−0.330289	+	2.29721i	−0.0153004	+	0.106416i
$467$	9.89914	−	2.90665i	0.458078	−	0.134504i	−0.0445493	−	0.999007i	$-0.514185\pi$
$467$	9.89914	−	2.90665i	0.458078	−	0.134504i	0.502627	+	0.864503i	$0.332367\pi$
$468$	2.45313	+	1.57653i	0.113396	+	0.0728752i
$469$	2.61828	−	5.73323i	0.120901	−	0.264736i
$470$	−1.26849	−	0.372462i	−0.0585111	−	0.0171804i
$471$	5.62903	+	6.49625i	0.259372	+	0.299331i
$472$	−2.74738	−	3.17064i	−0.126458	−	0.145941i
$473$	−28.0609	−	8.23943i	−1.29024	−	0.378849i
$474$	−1.60544	+	3.51542i	−0.0737401	+	0.161468i
$475$	11.6597	+	7.49322i	0.534983	+	0.343813i
$476$	13.4202	−	3.94053i	0.615115	−	0.180614i
$477$	0.0856189	−	0.595492i	0.00392022	−	0.0272657i
$478$	1.45880	+	3.19432i	0.0667237	+	0.146105i
$479$	5.11922	+	35.6050i	0.233903	+	1.62683i	0.680955	+	0.732325i	$0.261565\pi$
$479$	5.11922	+	35.6050i	0.233903	+	1.62683i	−0.447052	+	0.894508i	$0.647526\pi$
$480$	3.25858	−	2.09416i	0.148733	−	0.0955849i
$481$	−8.89422	+	10.2645i	−0.405541	+	0.468020i
$482$	2.64615			0.120529
$483$	4.71706	−	0.865659i	0.214634	−	0.0393889i
$484$	−15.0033			−0.681970
$485$	5.11318	−	5.90093i	0.232178	−	0.267947i
$486$	−0.193949	+	0.124644i	−0.00879772	+	0.00565395i
$487$	3.98117	+	27.6896i	0.180404	+	1.25474i	0.855810	+	0.517290i	$0.173059\pi$
$487$	3.98117	+	27.6896i	0.180404	+	1.25474i	−0.675406	+	0.737446i	$0.736032\pi$
$488$	−2.62637	−	5.75094i	−0.118890	−	0.260333i
$489$	−1.39207	+	9.68203i	−0.0629514	+	0.437837i
$490$	−0.321014	+	0.0942582i	−0.0145019	+	0.00425815i
$491$	−17.4541	−	11.2171i	−0.787692	−	0.506219i	0.0838860	−	0.996475i	$-0.473267\pi$
$491$	−17.4541	−	11.2171i	−0.787692	−	0.506219i	−0.871578	+	0.490256i	$0.836903\pi$
$492$	6.55336	−	14.3499i	0.295449	−	0.646942i
$493$	−26.2229	−	7.69975i	−1.18102	−	0.346779i
$494$	1.08298	+	1.24983i	0.0487256	+	0.0562324i
$495$	−4.11023	−	4.74345i	−0.184741	−	0.213202i
$496$	−2.49706	−	0.733203i	−0.112121	−	0.0329218i
$497$	−0.718829	+	1.57402i	−0.0322439	+	0.0706042i
$498$	1.99280	+	1.28070i	0.0892996	+	0.0573893i
$499$	28.1508	−	8.26583i	1.26020	−	0.370029i	0.417634	−	0.908615i	$-0.362860\pi$
$499$	28.1508	−	8.26583i	1.26020	−	0.370029i	0.842570	+	0.538586i	$0.181041\pi$
$500$	3.17398	−	22.0755i	0.141945	−	0.987248i
$501$	1.84560	+	4.04130i	0.0824553	+	0.180552i
$502$	0.500066	+	3.47804i	0.0223190	+	0.155232i
$503$	−24.0798	+	15.4752i	−1.07367	+	0.690004i	−0.953086	−	0.302699i	$-0.902112\pi$
$503$	−24.0798	+	15.4752i	−1.07367	+	0.690004i	−0.120581	+	0.992703i	$0.538476\pi$
$504$	0.595883	−	0.687685i	0.0265427	−	0.0306319i
$505$	−0.232745			−0.0103570
$506$	3.73254	+	2.98946i	0.165932	+	0.132898i
$507$	−10.7565			−0.477714
$508$	−22.9399	+	26.4741i	−1.01780	+	1.17460i
$509$	−11.9284	+	7.66594i	−0.528719	+	0.339787i	−0.777612	−	0.628744i	$-0.783569\pi$
$509$	−11.9284	+	7.66594i	−0.528719	+	0.339787i	0.248894	+	0.968531i	$0.419933\pi$
$510$	0.342073	+	2.37917i	0.0151472	+	0.105351i
$511$	−1.30254	−	2.85217i	−0.0576212	−	0.126173i
$512$	2.35351	−	16.3690i	0.104011	−	0.723415i
$513$	4.59506	−	1.34923i	0.202877	−	0.0595700i
$514$	−4.28531	−	2.75400i	−0.189017	−	0.121474i
$515$	−7.20940	+	15.7864i	−0.317684	+	0.695631i
$516$	−12.6310	−	3.70880i	−0.556049	−	0.163271i
$517$	11.1920	+	12.9163i	0.492224	+	0.568057i
$518$	1.36901	+	1.57992i	0.0601509	+	0.0694179i
$519$	16.0436	+	4.71081i	0.704234	+	0.206782i
$520$	0.821630	−	1.79912i	0.0360309	−	0.0788966i
$521$	−5.76463	−	3.70470i	−0.252553	−	0.162306i	0.408239	−	0.912875i	$-0.366143\pi$
$521$	−5.76463	−	3.70470i	−0.252553	−	0.162306i	−0.660792	+	0.750569i	$0.729779\pi$
$522$	−0.841505	+	0.247088i	−0.0368317	+	0.0108148i
$523$	−4.66134	+	32.4204i	−0.203826	+	1.41764i	0.588969	+	0.808156i	$0.299534\pi$
$523$	−4.66134	+	32.4204i	−0.203826	+	1.41764i	−0.792795	+	0.609488i	$0.791375\pi$
$524$	7.88142	+	17.2579i	0.344301	+	0.753915i
$525$	−0.411871	−	2.86462i	−0.0179755	−	0.125022i
$526$	−0.197196	+	0.126730i	−0.00859815	+	0.00552570i
$527$	3.32363	−	3.83567i	0.144780	−	0.167085i
$528$	−15.9333			−0.693407
$529$	5.02366	+	22.4447i	0.218420	+	0.975855i
$530$	−0.201280			−0.00874306
$531$	−3.01930	+	3.48446i	−0.131026	+	0.151213i
$532$	−7.84346	+	5.04069i	−0.340057	+	0.218542i
$533$	−1.72728	−	12.0135i	−0.0748167	−	0.520362i
$534$	0.721995	+	1.58095i	0.0312438	+	0.0684143i
$535$	−3.41852	+	23.7764i	−0.147796	+	1.02794i
$536$	5.50284	−	1.61578i	0.237687	−	0.0697911i
$537$	−7.32240	−	4.70582i	−0.315985	−	0.203071i
$538$	−0.331983	+	0.726942i	−0.0143128	+	0.0313407i
$539$	4.14990	+	1.21852i	0.178749	+	0.0524854i
$540$	−1.85013	−	2.13516i	−0.0796168	−	0.0918827i
$541$	−14.2962	−	16.4987i	−0.614642	−	0.709335i	0.360038	−	0.932937i	$-0.382764\pi$
$541$	−14.2962	−	16.4987i	−0.614642	−	0.709335i	−0.974680	+	0.223603i	$0.928218\pi$
$542$	−2.40683	−	0.706708i	−0.103382	−	0.0303557i
$543$	8.23996	−	18.0430i	0.353611	−	0.774299i
$544$	16.1322	+	10.3675i	0.691661	+	0.444504i
$545$	16.1474	−	4.74130i	0.691678	−	0.203095i
$546$	0.0491443	−	0.341806i	0.00210318	−	0.0146280i
$547$	12.8691	+	28.1794i	0.550244	+	1.20487i	0.956668	+	0.291182i	$0.0940484\pi$
$547$	12.8691	+	28.1794i	0.550244	+	1.20487i	−0.406424	+	0.913685i	$0.633224\pi$
$548$	−3.77770	−	26.2745i	−0.161375	−	1.12239i
$549$	−5.84505	+	3.75639i	−0.249461	+	0.160319i
$550$	1.88981	−	2.18095i	0.0805816	−	0.0929961i
$551$	18.2181			0.776116
$552$	3.40611	+	2.72802i	0.144974	+	0.116112i
$553$	−16.7629			−0.712832
$554$	4.22088	−	4.87116i	0.179328	−	0.206956i
$555$	11.0699	−	7.11421i	0.469892	−	0.301981i
$556$	−4.66485	−	32.4448i	−0.197834	−	1.37596i
$557$	6.85355	+	15.0072i	0.290394	+	0.635874i	0.997457	−	0.0712767i	$-0.0227073\pi$
$557$	6.85355	+	15.0072i	0.290394	+	0.635874i	−0.707062	+	0.707151i	$0.749980\pi$
$558$	0.0231787	−	0.161212i	0.000981234	−	0.00682463i
$559$	−9.71779	+	2.85340i	−0.411019	+	0.120686i
$560$	4.49735	+	2.89027i	0.190048	+	0.122136i
$561$	12.9082	−	28.2649i	0.544983	−	1.19335i
$562$	2.30755	+	0.677558i	0.0973381	+	0.0285810i
$563$	−26.9863	−	31.1439i	−1.13734	−	1.31256i	−0.943443	−	0.331536i	$-0.892433\pi$
$563$	−26.9863	−	31.1439i	−1.13734	−	1.31256i	−0.193896	−	0.981022i	$-0.562112\pi$
$564$	5.03784	+	5.81397i	0.212131	+	0.244812i
$565$	−16.1755	−	4.74957i	−0.680510	−	0.199816i
$566$	2.66729	−	5.84055i	0.112114	−	0.245496i
$567$	−0.841254	−	0.540641i	−0.0353293	−	0.0227048i
$568$	−1.51076	+	0.443600i	−0.0633903	+	0.0186131i
$569$	3.14156	−	21.8500i	0.131701	−	0.916000i	−0.811636	−	0.584163i	$-0.801423\pi$
$569$	3.14156	−	21.8500i	0.131701	−	0.916000i	0.943337	−	0.331836i	$-0.107668\pi$
$570$	−0.665600	−	1.45746i	−0.0278789	−	0.0610463i
$571$	−5.34773	−	37.1943i	−0.223796	−	1.55653i	−0.723493	−	0.690332i	$-0.757465\pi$
$571$	−5.34773	−	37.1943i	−0.223796	−	1.55653i	0.499697	−	0.866200i	$-0.333445\pi$
$572$	−10.6100	+	6.81865i	−0.443628	+	0.285102i
$573$	9.77269	−	11.2783i	0.408260	−	0.471157i
$574$	−1.86815			−0.0779750
$575$	13.6516	−	2.50529i	0.569309	−	0.104478i
$576$	−6.75244			−0.281352
$577$	5.23266	−	6.03881i	0.217839	−	0.251399i	−0.636304	−	0.771439i	$-0.719537\pi$
$577$	5.23266	−	6.03881i	0.217839	−	0.251399i	0.854142	+	0.520040i	$0.174083\pi$
$578$	−6.71346	+	4.31448i	−0.279243	+	0.179459i
$579$	−2.45369	−	17.0658i	−0.101972	−	0.709231i
$580$	−4.46466	−	9.77625i	−0.185385	−	0.405937i
$581$	−1.46226	+	10.1703i	−0.0606650	+	0.421934i
$582$	1.19021	−	0.349478i	0.0493359	−	0.0144863i
$583$	2.18898	+	1.40677i	0.0906584	+	0.0582626i
$584$	1.18523	−	2.59530i	0.0490453	−	0.107394i
$585$	−2.08557	−	0.612378i	−0.0862276	−	0.0253187i
$586$	−1.80353	−	2.08138i	−0.0745031	−	0.0859811i
$587$	1.46469	+	1.69034i	0.0604540	+	0.0697677i	0.785171	−	0.619279i	$-0.212575\pi$
$587$	1.46469	+	1.69034i	0.0604540	+	0.0697677i	−0.724717	+	0.689047i	$0.758030\pi$
$588$	1.86799	+	0.548490i	0.0770345	+	0.0226194i
$589$	−1.40543	+	3.07746i	−0.0579097	+	0.126805i
$590$	1.29768	+	0.833966i	0.0534245	+	0.0343338i
$591$	−0.536281	+	0.157466i	−0.0220596	+	0.00647730i
$592$	4.75397	−	33.0646i	0.195387	−	1.35895i
$593$	−16.9606	−	37.1385i	−0.696488	−	1.52510i	−0.844179	−	0.536062i	$-0.819911\pi$
$593$	−16.9606	−	37.1385i	−0.696488	−	1.52510i	0.147691	−	0.989034i	$-0.452816\pi$
$594$	−0.141908	−	0.986993i	−0.00582256	−	0.0404968i
$595$	−8.77069	+	5.63658i	−0.359563	+	0.231077i
$596$	20.5730	−	23.7426i	0.842705	−	0.972533i
$597$	16.0229			0.655773
$598$	1.64714	+	0.172092i	0.0673564	+	0.00703738i
$599$	29.7412			1.21519			0.607597	−	0.794245i	$-0.292134\pi$
$599$	29.7412			1.21519			0.607597	+	0.794245i	$0.292134\pi$
$600$	1.72453	−	1.99022i	0.0704038	−	0.0812503i
$601$	17.8613	−	11.4787i	0.728576	−	0.468228i	−0.123034	−	0.992402i	$-0.539263\pi$
$601$	17.8613	−	11.4787i	0.728576	−	0.468228i	0.851611	+	0.524175i	$0.175626\pi$
$602$	0.221858	+	1.54306i	0.00904227	+	0.0628903i
$603$	−2.61828	−	5.73323i	−0.106624	−	0.233475i
$604$	−3.63401	+	25.2751i	−0.147866	+	1.02843i
$605$	10.7305	−	3.15075i	0.436255	−	0.128096i
$606$	−0.0311063	−	0.0199908i	−0.00126361	−	0.000812070i
$607$	2.03074	−	4.44671i	0.0824254	−	0.180486i	−0.863932	−	0.503609i	$-0.832005\pi$
$607$	2.03074	−	4.44671i	0.0824254	−	0.180486i	0.946357	+	0.323122i	$0.104733\pi$
$608$	−12.2651	−	3.60136i	−0.497415	−	0.146054i
$609$	−2.49117	−	2.87496i	−0.100947	−	0.116499i
$610$	1.52227	+	1.75680i	0.0616350	+	0.0711306i
$611$	5.67893	+	1.66749i	0.229745	+	0.0674592i
$612$	5.81032	−	12.7228i	0.234868	−	0.514290i
$613$	−11.3496	−	7.29397i	−0.458408	−	0.294601i	0.290984	−	0.956728i	$-0.406017\pi$
$613$	−11.3496	−	7.29397i	−0.458408	−	0.294601i	−0.749391	+	0.662127i	$0.769654\pi$
$614$	−2.75836	+	0.809929i	−0.111319	+	0.0326861i
$615$	−1.67348	+	11.6393i	−0.0674813	+	0.469343i
$616$	1.63490	+	3.57992i	0.0658718	+	0.144239i
$617$	6.48054	+	45.0732i	0.260897	+	1.81458i	0.526142	+	0.850397i	$0.323638\pi$
$617$	6.48054	+	45.0732i	0.260897	+	1.81458i	−0.265245	+	0.964181i	$0.585453\pi$
$618$	−2.31945	+	1.49062i	−0.0933018	+	0.0599614i
$619$	−16.0582	+	18.5321i	−0.645432	+	0.744869i	−0.980326	−	0.197387i	$-0.936754\pi$
$619$	−16.0582	+	18.5321i	−0.645432	+	0.744869i	0.334893	+	0.942256i	$0.391300\pi$
$620$	1.99586			0.0801558
$621$	2.43479	−	4.13180i	0.0977049	−	0.165803i
$622$	−0.314475			−0.0126093
$623$	−4.93673	+	5.69729i	−0.197786	+	0.228257i
$624$	−4.64192	+	2.98318i	−0.185826	+	0.119423i
$625$	0.306529	+	2.13196i	0.0122612	+	0.0852783i
$626$	2.21326	+	4.84637i	0.0884598	+	0.193700i
$627$	−2.94778	+	20.5023i	−0.117723	+	0.818782i
$628$	−16.0568	+	4.71469i	−0.640735	+	0.188137i
$629$	54.8037	+	35.2202i	2.18517	+	1.40432i
$630$	−0.138984	+	0.304332i	−0.00553725	+	0.0121249i
$631$	16.4420	+	4.82779i	0.654544	+	0.192191i	0.592109	−	0.805858i	$-0.298295\pi$
$631$	16.4420	+	4.82779i	0.654544	+	0.192191i	0.0624347	+	0.998049i	$0.480113\pi$
$632$	−9.98873	−	11.5276i	−0.397330	−	0.458544i
$633$	4.32626	+	4.99277i	0.171953	+	0.198445i
$634$	3.57738	+	1.05041i	0.142076	+	0.0417173i
$635$	10.8471	−	23.7519i	0.430455	−	0.942565i
$636$	0.985322	+	0.633228i	0.0390706	+	0.0251091i
$637$	1.43715	−	0.421987i	0.0569422	−	0.0167197i
$638$	0.539835	−	3.75464i	0.0213723	−	0.148647i
$639$	0.718829	+	1.57402i	0.0284364	+	0.0622671i
$640$	1.42402	+	9.90424i	0.0562892	+	0.391500i
$641$	−16.0669	+	10.3256i	−0.634606	+	0.407837i	−0.818012	−	0.575201i	$-0.804924\pi$
$641$	−16.0669	+	10.3256i	−0.634606	+	0.407837i	0.183406	+	0.983037i	$0.441288\pi$
$642$	−2.49907	+	2.88408i	−0.0986303	+	0.113825i
$643$	15.2271			0.600499			0.300250	−	0.953861i	$-0.402930\pi$
$643$	15.2271			0.600499			0.300250	+	0.953861i	$0.402930\pi$
$644$	−2.28191	+	9.05361i	−0.0899198	+	0.356762i
$645$	9.81261			0.386371
$646$	5.19452	−	5.99479i	0.204376	−	0.235862i
$647$	−31.0124	+	19.9305i	−1.21922	+	0.783547i	−0.982178	−	0.187951i	$-0.939815\pi$
$647$	−31.0124	+	19.9305i	−1.21922	+	0.783547i	−0.237045	+	0.971499i	$0.576179\pi$
$648$	−0.129498	−	0.900676i	−0.00508715	−	0.0353819i
$649$	−8.28391	−	18.1392i	−0.325172	−	0.712027i
$650$	0.142228	−	0.989215i	0.00557863	−	0.0388002i
$651$	0.677828	−	0.199028i	0.0265662	−	0.00780054i
$652$	−16.0202	−	10.2956i	−0.627400	−	0.403206i
$653$	5.94546	−	13.0187i	0.232664	−	0.509462i	−0.756905	−	0.653525i	$-0.773289\pi$
$653$	5.94546	−	13.0187i	0.232664	−	0.509462i	0.989569	+	0.144063i	$0.0460167\pi$
$654$	2.56533	+	0.753248i	0.100312	+	0.0294543i
$655$	−9.26105	−	10.6878i	−0.361859	−	0.417608i
$656$	19.5483	+	22.5599i	0.763232	+	0.880816i
$657$	−3.00851	−	0.883379i	−0.117373	−	0.0344639i
$658$	0.378449	−	0.828687i	0.0147535	−	0.0323056i
$659$	17.1715	+	11.0354i	0.668905	+	0.429879i	0.830531	−	0.556973i	$-0.188037\pi$
$659$	17.1715	+	11.0354i	0.668905	+	0.429879i	−0.161626	+	0.986852i	$0.551674\pi$
$660$	11.7244	−	3.44259i	0.456372	−	0.134003i
$661$	0.124619	−	0.866745i	0.00484712	−	0.0337125i	−0.987254	−	0.159150i	$-0.949125\pi$
$661$	0.124619	−	0.866745i	0.00484712	−	0.0337125i	0.992101	+	0.125438i	$0.0400336\pi$
$662$	−2.13161	−	4.66757i	−0.0828472	−	0.181410i
$663$	−1.53143	−	10.6513i	−0.0594759	−	0.413664i
$664$	−7.86528	+	5.05471i	−0.305232	+	0.196161i
$665$	4.55112	−	5.25228i	0.176485	−	0.203675i
$666$	2.09054			0.0810068
$667$	13.3153	−	12.4717i	0.515570	−	0.482906i
$668$	−8.64942			−0.334656
$669$	18.6275	−	21.4973i	0.720181	−	0.831133i
$670$	−1.77395	+	1.14005i	−0.0685338	+	0.0440440i
$671$	−4.27669	−	29.7450i	−0.165100	−	1.14829i
$672$	1.10882	+	2.42798i	0.0427738	+	0.0936615i
$673$	−3.60770	+	25.0921i	−0.139067	+	0.967230i	0.794100	+	0.607787i	$0.207942\pi$
$673$	−3.60770	+	25.0921i	−0.139067	+	0.967230i	−0.933167	+	0.359443i	$0.882967\pi$
$674$	−0.639230	+	0.187695i	−0.0246222	+	0.00722973i
$675$	−2.43466	−	1.56466i	−0.0937100	−	0.0602237i
$676$	8.69933	−	19.0489i	0.334589	−	0.732649i
$677$	−29.5725	−	8.68325i	−1.13656	−	0.333725i	−0.341278	−	0.939962i	$-0.610860\pi$
$677$	−29.5725	−	8.68325i	−1.13656	−	0.333725i	−0.795283	+	0.606238i	$0.792678\pi$
$678$	−1.75391	−	2.02412i	−0.0673584	−	0.0777357i
$679$	3.52347	+	4.06630i	0.135218	+	0.156050i
$680$	−9.10249	−	2.67273i	−0.349065	−	0.102495i
$681$	3.11115	−	6.81247i	0.119220	−	0.261055i
$682$	0.592601	+	0.380841i	0.0226919	+	0.0145832i
$683$	38.4499	−	11.2899i	1.47125	−	0.431997i	0.554742	−	0.832023i	$-0.312817\pi$
$683$	38.4499	−	11.2899i	1.47125	−	0.431997i	0.916504	+	0.400026i	$0.130999\pi$
$684$	−1.32688	+	9.22864i	−0.0507345	+	0.352866i
$685$	8.21956	+	17.9983i	0.314053	+	0.687680i
$686$	−0.0328104	−	0.228201i	−0.00125271	−	0.00871277i
$687$	7.19448	−	4.62361i	0.274486	−	0.176402i
$688$	16.3126	−	18.8257i	0.621910	−	0.717723i
$689$	0.901117			0.0343298
$690$	−1.48422	−	0.609578i	−0.0565033	−	0.0232062i
$691$	38.0223			1.44644			0.723219	−	0.690619i	$-0.242662\pi$
$691$	38.0223			1.44644			0.723219	+	0.690619i	$0.242662\pi$
$692$	−21.3177	+	24.6019i	−0.810376	+	0.935224i
$693$	3.63850	−	2.33832i	0.138215	−	0.0888256i
$694$	−0.175011	−	1.21723i	−0.00664333	−	0.0462054i
$695$	10.1498	+	22.2250i	0.385005	+	0.843043i
$696$	0.492624	−	3.42628i	0.0186729	−	0.129873i
$697$	−55.8570	+	16.4011i	−2.11574	+	0.621236i
$698$	−2.96056	−	1.90263i	−0.112059	−	0.0720158i
$699$	−4.18182	+	9.15690i	−0.158171	+	0.346346i
$700$	5.40611	+	1.58738i	0.204332	+	0.0599972i
$701$	16.3786	+	18.9020i	0.618613	+	0.713917i	0.975443	−	0.220252i	$-0.0706880\pi$
$701$	16.3786	+	18.9020i	0.618613	+	0.713917i	−0.356830	+	0.934169i	$0.616143\pi$
$702$	−0.226137	−	0.260976i	−0.00853500	−	0.00984992i
$703$	−41.6666	−	12.2344i	−1.57148	−	0.461430i
$704$	12.1322	−	26.5658i	0.457249	−	1.00124i
$705$	−4.82404	−	3.10022i	−0.181684	−	0.116761i
$706$	2.51874	−	0.739569i	0.0947940	−	0.0278340i
$707$	0.0228250	−	0.158751i	0.000858421	−	0.00597045i
$708$	−3.72882	−	8.16498i	−0.140138	−	0.306859i
$709$	3.05937	+	21.2784i	0.114897	+	0.799127i	0.963040	+	0.269359i	$0.0868118\pi$
$709$	3.05937	+	21.2784i	0.114897	+	0.799127i	−0.848143	+	0.529768i	$0.822279\pi$
$710$	0.487026	−	0.312993i	0.0182778	−	0.0117464i
$711$	−10.9774	+	12.6686i	−0.411684	+	0.475108i
$712$	−6.85966			−0.257076
$713$	1.07956	+	3.21139i	0.0404297	+	0.120267i
$714$	−1.65633			−0.0619866
$715$	6.15641	−	7.10487i	0.230237	−	0.265707i
$716$	14.2556	−	9.16151i	0.532757	−	0.342382i
$717$	2.16771	+	15.0767i	0.0809546	+	0.563051i
$718$	−3.10239	−	6.79328i	−0.115780	−	0.253523i
$719$	−6.74253	+	46.8953i	−0.251454	+	1.74890i	0.338045	+	0.941130i	$0.390235\pi$
$719$	−6.74253	+	46.8953i	−0.251454	+	1.74890i	−0.589498	+	0.807770i	$0.700675\pi$
$720$	5.12946	−	1.50615i	0.191164	−	0.0561307i
$721$	−10.0606	−	6.46554i	−0.374675	−	0.240789i
$722$	−0.376863	+	0.825216i	−0.0140254	+	0.0307114i
$723$	11.0127	+	3.23362i	0.409567	+	0.120260i
$724$	25.2886	+	29.1845i	0.939842	+	1.08464i
$725$	−7.20964	−	8.32037i	−0.267759	−	0.309011i
$726$	1.70474	+	0.500558i	0.0632690	+	0.0185774i
$727$	10.4608	−	22.9059i	0.387968	−	0.849531i	−0.610382	−	0.792107i	$-0.708984\pi$
$727$	10.4608	−	22.9059i	0.387968	−	0.849531i	0.998350	−	0.0574239i	$-0.0182887\pi$
$728$	1.14657	+	0.736856i	0.0424947	+	0.0273097i
$729$	−0.959493	+	0.281733i	−0.0355368	+	0.0104345i
$730$	−0.149294	+	1.03836i	−0.00552562	+	0.0384315i
$731$	20.1805	+	44.1891i	0.746403	+	1.63439i
$732$	−1.92506	−	13.3891i	−0.0711521	−	0.494874i
$733$	−2.72637	+	1.75213i	−0.100701	+	0.0647164i	−0.590022	−	0.807387i	$-0.700881\pi$
$733$	−2.72637	+	1.75213i	−0.100701	+	0.0647164i	0.489321	+	0.872104i	$0.337245\pi$
$734$	−4.31973	+	4.98523i	−0.159444	+	0.184008i
$735$	−1.45118			−0.0535275
$736$	−11.4298	+	5.76424i	−0.421306	+	0.212473i
$737$	27.2602			1.00414
$738$	−1.22338	+	1.41185i	−0.0450332	+	0.0519710i
$739$	18.5088	−	11.8949i	0.680857	−	0.437560i	−0.153968	−	0.988076i	$-0.549205\pi$
$739$	18.5088	−	11.8949i	0.680857	−	0.437560i	0.834825	+	0.550515i	$0.185569\pi$
$740$	3.64586	+	25.3575i	0.134024	+	0.932161i
$741$	2.97984	+	6.52494i	0.109467	+	0.239700i
$742$	0.0197393	−	0.137290i	0.000724651	−	0.00504006i
$743$	40.0347	−	11.7552i	1.46873	−	0.431258i	0.553044	−	0.833152i	$-0.313466\pi$
$743$	40.0347	−	11.7552i	1.46873	−	0.431258i	0.915686	+	0.401894i	$0.131648\pi$
$744$	0.540775	+	0.347535i	0.0198258	+	0.0127413i
$745$	−9.72793	+	21.3012i	−0.356404	+	0.780416i
$746$	5.05508	+	1.48431i	0.185080	+	0.0543443i
$747$	6.72860	+	7.76522i	0.246187	+	0.284114i
$748$	39.6153	+	45.7185i	1.44848	+	1.67163i
$749$	−15.8822	−	4.66342i	−0.580321	−	0.170398i
$750$	−1.09715	+	2.40242i	−0.0400622	+	0.0877241i
$751$	−22.3912	−	14.3900i	−0.817067	−	0.525097i	0.0640771	−	0.997945i	$-0.479590\pi$
$751$	−22.3912	−	14.3900i	−0.817067	−	0.525097i	−0.881144	+	0.472848i	$0.843226\pi$
$752$	−13.9674	+	4.10119i	−0.509337	+	0.149555i
$753$	−2.16903	+	15.0859i	−0.0790439	+	0.549762i
$754$	−0.545706	−	1.19493i	−0.0198735	−	0.0435168i
$755$	−2.70879	−	18.8400i	−0.0985829	−	0.685659i
$756$	1.63779	−	1.05255i	0.0595659	−	0.0382807i
$757$	−28.1230	+	32.4556i	−1.02215	+	1.17962i	−0.0385462	+	0.999257i	$0.512273\pi$
$757$	−28.1230	+	32.4556i	−1.02215	+	1.17962i	−0.983600	+	0.180363i	$0.942273\pi$
$758$	6.09608			0.221420
$759$	11.8809	+	17.0027i	0.431250	+	0.617160i
$760$	6.32385			0.229390
$761$	20.5197	−	23.6810i	0.743838	−	0.858435i	−0.250118	−	0.968215i	$-0.580469\pi$
$761$	20.5197	−	23.6810i	0.743838	−	0.858435i	0.993956	+	0.109780i	$0.0350148\pi$
$762$	3.48979	−	2.24275i	0.126422	−	0.0812464i
$763$	1.65040	+	11.4788i	0.0597486	+	0.415561i
$764$	12.0692	+	26.4279i	0.436649	+	0.956129i
$765$	−1.48374	+	10.3196i	−0.0536446	+	0.373106i
$766$	−6.63321	+	1.94768i	−0.239667	+	0.0703727i
$767$	−5.80960	−	3.73360i	−0.209772	−	0.134813i
$768$	4.94976	−	10.8385i	0.178609	−	0.391100i
$769$	−12.3419	−	3.62392i	−0.445062	−	0.130682i	0.0515198	−	0.998672i	$-0.483593\pi$
$769$	−12.3419	−	3.62392i	−0.445062	−	0.130682i	−0.496582	+	0.867990i	$0.665412\pi$
$770$	−0.947604	−	1.09359i	−0.0341493	−	0.0394104i
$771$	−14.4691	−	16.6983i	−0.521093	−	0.601373i
$772$	32.2065	+	9.45669i	1.15914	+	0.340354i
$773$	5.06638	−	11.0938i	0.182225	−	0.399017i	−0.796371	−	0.604809i	$-0.793250\pi$
$773$	5.06638	−	11.0938i	0.182225	−	0.399017i	0.978596	+	0.205791i	$0.0659768\pi$
$774$	1.31145	+	0.842819i	0.0471391	+	0.0302945i
$775$	1.96169	−	0.576004i	0.0704660	−	0.0206907i
$776$	−0.696760	+	4.84608i	−0.0250122	+	0.173964i
$777$	3.76686	+	8.24827i	0.135135	+	0.295905i
$778$	1.12533	+	7.82683i	0.0403450	+	0.280605i
$779$	32.6457	−	20.9801i	1.16965	−	0.751691i
$780$	2.77117	−	3.19810i	0.0992239	−	0.114510i
$781$	−7.48409			−0.267802
$782$	−0.307317	−	7.93754i	−0.0109896	−	0.283846i
$783$	−3.80412			−0.135948
$784$	−2.41245	+	2.78411i	−0.0861589	+	0.0994326i
$785$	10.4938	−	6.74395i	0.374539	−	0.240702i
$786$	−0.319744	−	2.22387i	−0.0114049	−	0.0793227i
$787$	0.0269682	+	0.0590521i	0.000961312	+	0.00210498i	0.910112	−	0.414362i	$-0.135995\pi$
$787$	0.0269682	+	0.0590521i	0.000961312	+	0.00210498i	−0.909151	+	0.416467i	$0.863268\pi$
$788$	0.154858	−	1.07706i	0.00551658	−	0.0383686i
$789$	−0.975554	+	0.286449i	−0.0347307	+	0.0101978i
$790$	4.71801	+	3.03208i	0.167859	+	0.107877i
$791$	4.82590	−	10.5672i	0.171589	−	0.375728i
$792$	3.77615	+	1.10878i	0.134180	+	0.0393987i
$793$	−6.81510	−	7.86504i	−0.242011	−	0.279296i
$794$	3.62292	+	4.18108i	0.128573	+	0.148381i
$795$	−0.837687	−	0.245967i	−0.0297097	−	0.00872355i
$796$	−12.9585	+	28.3752i	−0.459302	+	1.00573i
$797$	22.1551	+	14.2382i	0.784773	+	0.504343i	0.870615	−	0.491966i	$-0.163721\pi$
$797$	22.1551	+	14.2382i	0.784773	+	0.504343i	−0.0858412	+	0.996309i	$0.527358\pi$
$798$	1.05938	−	0.311062i	0.0375017	−	0.0110115i
$799$	4.04017	−	28.1000i	0.142931	−	0.994106i
$800$	3.20903	+	7.02679i	0.113456	+	0.248434i
$801$	1.07285	+	7.46187i	0.0379074	+	0.263652i
$802$	−1.53830	+	0.988608i	−0.0543194	+	0.0349090i
$803$	8.88086	−	10.2491i	0.313399	−	0.361682i
$804$	12.2706			0.432750
$805$	−0.269253	−	6.95440i	−0.00948992	−	0.245110i
$806$	0.243950			0.00859278
$807$	−2.26998	+	2.61969i	−0.0799070	+	0.0922176i
$808$	0.122772	−	0.0789006i	0.00431909	−	0.00277571i
$809$	−3.74575	−	26.0523i	−0.131694	−	0.915949i	−0.943347	−	0.331809i	$-0.892341\pi$
$809$	−3.74575	−	26.0523i	−0.131694	−	0.915949i	0.811653	−	0.584140i	$-0.198568\pi$
$810$	0.138984	+	0.304332i	0.00488339	+	0.0106931i
$811$	1.56752	−	10.9023i	0.0550430	−	0.382832i	−0.943615	−	0.331045i	$-0.892599\pi$
$811$	1.56752	−	10.9023i	0.0550430	−	0.382832i	0.998658	−	0.0517878i	$-0.0164919\pi$
$812$	7.10604	−	2.08652i	0.249373	−	0.0732225i
$813$	−9.15311	−	5.88234i	−0.321013	−	0.206303i
$814$	−3.75610	+	8.22470i	−0.131651	+	0.288276i
$815$	13.6198	+	3.99915i	0.477082	+	0.140084i
$816$	17.3318	+	20.0020i	0.606735	+	0.700209i
$817$	−21.2062	−	24.4732i	−0.741909	−	0.856209i
$818$	−4.01912	−	1.18012i	−0.140525	−	0.0412620i
$819$	0.622220	−	1.36247i	0.0217421	−	0.0476086i
$820$	−19.2588	−	12.3769i	−0.672547	−	0.432220i
$821$	34.2096	−	10.0448i	1.19392	−	0.350567i	0.376396	−	0.926459i	$-0.377163\pi$
$821$	34.2096	−	10.0448i	1.19392	−	0.350567i	0.817526	+	0.575892i	$0.195345\pi$
$822$	−0.447360	+	3.11146i	−0.0156035	+	0.108524i
$823$	8.89850	+	19.4850i	0.310182	+	0.679204i	0.998952	−	0.0457760i	$-0.0145761\pi$
$823$	8.89850	+	19.4850i	0.310182	+	0.679204i	−0.688769	+	0.724980i	$0.741849\pi$
$824$	−1.54867	−	10.7712i	−0.0539504	−	0.375233i
$825$	10.5301	−	6.76730i	0.366612	−	0.235607i
$826$	−0.696094	+	0.803335i	−0.0242202	+	0.0279516i
$827$	−21.8668			−0.760385			−0.380192	−	0.924907i	$-0.624142\pi$
$827$	−21.8668			−0.760385			−0.380192	+	0.924907i	$0.624142\pi$
$828$	5.34793	+	7.65341i	0.185853	+	0.265974i
$829$	−5.38350			−0.186977			−0.0934883	−	0.995620i	$-0.529802\pi$
$829$	−5.38350			−0.186977			−0.0934883	+	0.995620i	$0.529802\pi$
$830$	2.25116	−	2.59798i	0.0781390	−	0.0901772i
$831$	23.5191	−	15.1148i	0.815867	−	0.524326i
$832$	−1.43937	−	10.0111i	−0.0499012	−	0.347071i
$833$	−2.98448	−	6.53509i	−0.103406	−	0.226427i
$834$	−0.552417	+	3.84215i	−0.0191287	+	0.133043i
$835$	6.18611	−	1.81641i	0.214079	−	0.0628593i
$836$	−33.9238	−	21.8015i	−1.17328	−	0.754020i
$837$	0.293468	−	0.642604i	0.0101437	−	0.0222117i
$838$	−3.90503	−	1.14662i	−0.134897	−	0.0396093i
$839$	−14.1564	−	16.3373i	−0.488733	−	0.564028i	0.456794	−	0.889573i	$-0.348998\pi$
$839$	−14.1564	−	16.3373i	−0.488733	−	0.564028i	−0.945527	+	0.325545i	$0.894452\pi$
$840$	−0.864732	−	0.997954i	−0.0298361	−	0.0344327i
$841$	13.9402	+	4.09321i	0.480696	+	0.141145i
$842$	−0.0906886	+	0.198580i	−0.00312534	+	0.00684353i
$843$	8.77556	+	5.63971i	0.302246	+	0.194242i
$844$	−12.3406	+	3.62354i	−0.424782	+	0.124727i
$845$	−2.22148	+	15.4507i	−0.0764212	+	0.531521i
$846$	−0.378449	−	0.828687i	−0.0130113	−	0.0284908i
$847$	1.09675	+	7.62804i	0.0376846	+	0.262102i
$848$	−1.86447	+	1.19822i	−0.0640261	+	0.0411471i
$849$	18.2379	−	21.0477i	0.625924	−	0.722354i
$850$	−4.79356			−0.164418
$851$	−38.8288	+	19.5821i	−1.33103	+	0.671265i
$852$	−3.36880			−0.115413
$853$	6.90980	−	7.97434i	0.236587	−	0.273036i	−0.625023	−	0.780606i	$-0.714911\pi$
$853$	6.90980	−	7.97434i	0.236587	−	0.273036i	0.861611	+	0.507570i	$0.169456\pi$
$854$	−1.34756	+	0.866027i	−0.0461127	+	0.0296348i
$855$	−0.989054	−	6.87902i	−0.0338249	−	0.235258i
$856$	−6.25693	−	13.7008i	−0.213858	−	0.468283i
$857$	7.05940	−	49.0992i	0.241145	−	1.67720i	−0.405260	−	0.914202i	$-0.632819\pi$
$857$	7.05940	−	49.0992i	0.241145	−	1.67720i	0.646404	−	0.762995i	$-0.276272\pi$
$858$	1.43305	−	0.420781i	0.0489235	−	0.0143652i
$859$	−46.3348	−	29.7775i	−1.58092	−	1.01600i	−0.975475	−	0.220111i	$-0.929358\pi$
$859$	−46.3348	−	29.7775i	−1.58092	−	1.01600i	−0.605447	−	0.795886i	$-0.707006\pi$
$860$	−7.93595	+	17.3773i	−0.270614	+	0.592561i
$861$	−7.77485	−	2.28290i	−0.264966	−	0.0778011i
$862$	−0.618192	−	0.713432i	−0.0210557	−	0.0242996i
$863$	26.7617	+	30.8846i	0.910978	+	1.05133i	0.998477	+	0.0551606i	$0.0175671\pi$
$863$	26.7617	+	30.8846i	0.910978	+	1.05133i	−0.0874990	+	0.996165i	$0.527887\pi$
$864$	2.56107	+	0.751999i	0.0871295	+	0.0255835i
$865$	10.0800	−	22.0722i	0.342731	−	0.750477i
$866$	−0.554137	−	0.356122i	−0.0188304	−	0.0121015i
$867$	−33.2124	+	9.75203i	−1.12795	+	0.331196i
$868$	−0.195731	+	1.36134i	−0.00664355	+	0.0462069i
$869$	−30.1181	−	65.9495i	−1.02169	−	2.23718i
$870$	0.181128	+	1.25977i	0.00614082	+	0.0427103i
$871$	7.94186	−	5.10392i	0.269100	−	0.172940i
$872$	−6.91036	+	7.97498i	−0.234014	+	0.270067i
$873$	5.38049			0.182102
$874$	1.68724	+	5.01909i	0.0570719	+	0.169773i
$875$	−11.4557			−0.387274
$876$	3.99752	−	4.61339i	0.135064	−	0.155872i
$877$	−0.265815	+	0.170829i	−0.00897594	+	0.00576849i	−0.545121	−	0.838357i	$-0.683516\pi$
$877$	−0.265815	+	0.170829i	−0.00897594	+	0.00576849i	0.536145	+	0.844126i	$0.319880\pi$
$878$	0.783206	+	5.44732i	0.0264319	+	0.183838i
$879$	−4.96244	−	10.8662i	−0.167379	−	0.366508i
$880$	−3.29061	+	22.8867i	−0.110926	+	0.771510i
$881$	56.2163	−	16.5066i	1.89397	−	0.556121i	0.901649	−	0.432468i	$-0.142357\pi$
$881$	56.2163	−	16.5066i	1.89397	−	0.556121i	0.992326	−	0.123653i	$-0.0394609\pi$
$882$	−0.193949	−	0.124644i	−0.00653061	−	0.00419697i
$883$	11.0777	−	24.2569i	0.372796	−	0.816309i	−0.626523	−	0.779403i	$-0.715523\pi$
$883$	11.0777	−	24.2569i	0.372796	−	0.816309i	0.999319	−	0.0369058i	$-0.0117501\pi$
$884$	20.1012	+	5.90224i	0.676076	+	0.198514i
$885$	4.38154	+	5.05657i	0.147284	+	0.169975i
$886$	2.21756	+	2.55920i	0.0745002	+	0.0859779i
$887$	−32.9103	−	9.66332i	−1.10502	−	0.324463i	−0.322174	−	0.946680i	$-0.604414\pi$
$887$	−32.9103	−	9.66332i	−1.10502	−	0.324463i	−0.782844	+	0.622218i	$0.786232\pi$
$888$	−3.42761	+	7.50541i	−0.115023	+	0.251865i
$889$	15.1370	+	9.72793i	0.507677	+	0.326264i
$890$	2.42000	−	0.710575i	0.0811184	−	0.0238185i
$891$	0.615526	−	4.28108i	0.0206209	−	0.143421i
$892$	23.0049	+	50.3736i	0.770260	+	1.68663i
$893$	2.69316	+	18.7314i	0.0901232	+	0.626821i
$894$	−3.12972	+	2.01135i	−0.104674	+	0.0672696i
$895$	−8.27173	+	9.54608i	−0.276493	+	0.319090i
$896$	−6.89515			−0.230351
$897$	6.64474	+	2.72903i	0.221861	+	0.0911198i
$898$	0.142336			0.00474981
$899$	1.75987	−	2.03100i	0.0586950	−	0.0677376i
$900$	4.73991	−	3.04615i	0.157997	−	0.101538i
$901$	−0.615114	−	4.27821i	−0.0204924	−	0.142528i
$902$	−3.35652	−	7.34976i	−0.111760	−	0.244720i
$903$	−0.962308	+	6.69300i	−0.0320236	+	0.222729i
$904$	10.1426	−	2.97814i	0.337338	−	0.0990514i
$905$	−24.2153	−	15.5623i	−0.804945	−	0.517307i
$906$	1.25617	−	2.75062i	0.0417334	−	0.0913834i
$907$	−3.72368	−	1.09337i	−0.123643	−	0.0363048i	0.219326	−	0.975652i	$-0.429614\pi$
$907$	−3.72368	−	1.09337i	−0.123643	−	0.0363048i	−0.342969	+	0.939347i	$0.611432\pi$
$908$	9.54817	+	11.0192i	0.316867	+	0.365684i
$909$	−0.105029	−	0.121210i	−0.00348359	−	0.00402027i
$910$	−0.480824	−	0.141183i	−0.0159391	−	0.00468016i
$911$	−7.59275	+	16.6258i	−0.251559	+	0.550837i	−0.992714	−	0.120497i	$-0.961551\pi$
$911$	−7.59275	+	16.6258i	−0.251559	+	0.550837i	0.741155	+	0.671334i	$0.234278\pi$
$912$	−14.8417	−	9.53821i	−0.491459	−	0.315842i
$913$	−42.6396	+	12.5201i	−1.41117	+	0.414356i
$914$	−0.712780	+	4.95749i	−0.0235767	+	0.163979i
$915$	4.18856	+	9.17166i	0.138469	+	0.303206i
$916$	2.36949	+	16.4801i	0.0782901	+	0.544519i
$917$	8.19818	−	5.26865i	0.270728	−	0.173986i
$918$	−1.08467	+	1.25177i	−0.0357993	+	0.0413146i
$919$	−13.9478			−0.460096			−0.230048	−	0.973179i	$-0.573888\pi$
$919$	−13.9478			−0.460096			−0.230048	+	0.973179i	$0.573888\pi$
$920$	4.62199	−	4.32916i	0.152383	−	0.142728i
$921$	−12.4695			−0.410883
$922$	−0.704192	+	0.812681i	−0.0231913	+	0.0267642i
$923$	−2.18038	+	1.40124i	−0.0717680	+	0.0461225i
$924$	1.19833	+	8.33460i	0.0394223	+	0.274188i
$925$	10.9016	+	23.8712i	0.358442	+	0.784879i
$926$	0.0779968	−	0.542480i	0.00256313	−	0.0178270i
$927$	−11.4746	+	3.36925i	−0.376876	+	0.110661i
$928$	8.54202	+	5.48962i	0.280406	+	0.180206i
$929$	−16.7335	+	36.6414i	−0.549010	+	1.20216i	0.408233	+	0.912878i	$0.366145\pi$
$929$	−16.7335	+	36.6414i	−0.549010	+	1.20216i	−0.957243	+	0.289286i	$0.906582\pi$
$930$	−0.226779	−	0.0665882i	−0.00743636	−	0.00218351i
$931$	3.13616	+	3.61932i	0.102783	+	0.118618i
$932$	−12.8341	−	14.8113i	−0.420393	−	0.485160i
$933$	−1.30878	−	0.384292i	−0.0428475	−	0.0125812i
$934$	0.988096	−	2.16363i	0.0323315	−	0.0707961i
$935$	−37.9341	−	24.3788i	−1.24058	−	0.797270i
$936$	1.30772	−	0.383982i	0.0427442	−	0.0125508i
$937$	7.14985	−	49.7283i	0.233575	−	1.62455i	−0.448856	−	0.893604i	$-0.648169\pi$
$937$	7.14985	−	49.7283i	0.233575	−	1.62455i	0.682432	−	0.730949i	$-0.260922\pi$
$938$	−0.603639	−	1.32178i	−0.0197095	−	0.0431578i
$939$	3.28882	+	22.8742i	0.107326	+	0.746472i
$940$	9.39167	−	6.03566i	0.306323	−	0.196862i
$941$	−2.82726	+	3.26283i	−0.0921661	+	0.106365i	−0.799959	−	0.600055i	$-0.795146\pi$
$941$	−2.82726	+	3.26283i	−0.0921661	+	0.106365i	0.707793	+	0.706420i	$0.249691\pi$
$942$	1.98174			0.0645685
$943$	9.49766	−	37.6825i	0.309286	−	1.22711i
$944$	16.9850			0.552816
$945$	−0.950320	+	1.09673i	−0.0309139	+	0.0356765i
$946$	−5.67216	+	3.64527i	−0.184418	+	0.118518i
$947$	−1.83159	−	12.7390i	−0.0595188	−	0.413962i	−0.997698	−	0.0678126i	$-0.978398\pi$
$947$	−1.83159	−	12.7390i	−0.0595188	−	0.413962i	0.938179	−	0.346150i	$-0.112511\pi$
$948$	−13.5570	−	29.6857i	−0.440311	−	0.964147i
$949$	0.668378	−	4.64867i	0.0216965	−	0.150902i
$950$	3.06594	−	0.900240i	0.0994721	−	0.0292076i
$951$	13.6047	+	8.74321i	0.441163	+	0.283518i
$952$	2.71569	−	5.94653i	0.0880159	−	0.192728i
$953$	17.9595	+	5.27339i	0.581766	+	0.170822i	0.559357	−	0.828927i	$-0.311048\pi$
$953$	17.9595	+	5.27339i	0.581766	+	0.170822i	0.0224092	+	0.999749i	$0.492866\pi$
$954$	−0.0908301	−	0.104823i	−0.00294073	−	0.00339379i
$955$	−14.1819	−	16.3668i	−0.458916	−	0.529617i
$956$	−28.4528	−	8.35449i	−0.920228	−	0.270203i
$957$	6.83490	−	14.9663i	0.220941	−	0.483793i
$958$	6.97658	+	4.48357i	0.225403	+	0.144858i
$959$	−13.0824	+	3.84134i	−0.422453	+	0.124043i
$960$	−1.39454	+	9.69926i	−0.0450087	+	0.313042i
$961$	−12.6705	−	27.7446i	−0.408727	−	0.894988i
$962$	0.445626	+	3.09940i	0.0143676	+	0.0999285i
$963$	−13.9250	+	8.94904i	−0.448726	+	0.288379i
$964$	−14.6330	+	16.8874i	−0.471297	+	0.543906i
$965$	−25.0202			−0.805429
$966$	0.561337	−	0.952578i	0.0180607	−	0.0306487i
$967$	2.01664			0.0648508			0.0324254	−	0.999474i	$-0.489677\pi$
$967$	2.01664			0.0648508			0.0324254	+	0.999474i	$0.489677\pi$
$968$	−4.59216	+	5.29963i	−0.147597	+	0.170337i
$969$	28.9442	−	18.6013i	0.929822	−	0.597560i
$970$	−0.256185	−	1.78181i	−0.00822561	−	0.0572104i
$971$	18.9981	+	41.6001i	0.609678	+	1.33501i	0.922794	+	0.385294i	$0.125900\pi$
$971$	18.9981	+	41.6001i	0.609678	+	1.33501i	−0.313116	+	0.949715i	$0.601373\pi$
$972$	0.277065	−	1.92703i	0.00888687	−	0.0618096i
$973$	−16.1547	+	4.74343i	−0.517894	+	0.152068i
$974$	5.42561	+	3.48683i	0.173848	+	0.111725i
$975$	1.80076	−	3.94310i	0.0576703	−	0.126280i
$976$	24.5591	+	7.21120i	0.786117	+	0.230825i
$977$	18.5167	+	21.3694i	0.592401	+	0.683668i	0.970224	−	0.242210i	$-0.0778724\pi$
$977$	18.5167	+	21.3694i	0.592401	+	0.683668i	−0.377822	+	0.925878i	$0.623327\pi$
$978$	1.47679	+	1.70431i	0.0472227	+	0.0544979i
$979$	−31.2844	−	9.18594i	−0.999855	−	0.293584i
$980$	1.17364	−	2.56991i	0.0374906	−	0.0820929i
$981$	9.75589	+	6.26973i	0.311481	+	0.200177i
$982$	−4.58959	+	1.34762i	−0.146460	+	0.0430044i
$983$	3.61084	−	25.1139i	0.115168	−	0.801010i	−0.847591	−	0.530650i	$-0.821948\pi$
$983$	3.61084	−	25.1139i	0.115168	−	0.801010i	0.962759	−	0.270361i	$-0.0871429\pi$
$984$	−3.06298	−	6.70699i	−0.0976442	−	0.213811i
$985$	0.115431	+	0.802838i	0.00367793	+	0.0255806i
$986$	−5.30063	+	3.40651i	−0.168807	+	0.108485i
$987$	2.58769	−	2.98635i	0.0823671	−	0.0950567i
$988$	−13.9651			−0.444288
$989$	−32.2530	−	3.36979i	−1.02559	−	0.107153i
$990$	−1.44703			−0.0459897
$991$	10.7430	−	12.3981i	0.341262	−	0.393837i	−0.559013	−	0.829159i	$-0.688820\pi$
$991$	10.7430	−	12.3981i	0.341262	−	0.393837i	0.900275	+	0.435322i	$0.143365\pi$
$992$	−1.58630	+	1.01945i	−0.0503650	+	0.0323676i
$993$	−3.16748	−	22.0303i	−0.100517	−	0.699110i
$994$	0.165725	+	0.362886i	0.00525646	+	0.0115100i
$995$	3.30911	−	23.0154i	0.104906	−	0.729637i
$996$	−19.1933	+	5.63566i	−0.608163	+	0.178573i
$997$	14.9509	+	9.60838i	0.473501	+	0.304300i	0.755540	−	0.655102i	$-0.227375\pi$
$997$	14.9509	+	9.60838i	0.473501	+	0.304300i	−0.282039	+	0.959403i	$0.591011\pi$
$998$	2.80991	−	6.15285i	0.0889463	−	0.194765i
$999$	8.70039	+	2.55467i	0.275268	+	0.0808260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.85.5	✓	80
23.13	even	11	inner	483.2.q.f.358.5	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.85.5	✓	80	1.1	even	1	trivial
483.2.q.f.358.5	yes	80	23.13	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.150977 - 0.174237i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.277065 + 1.92703i) q^{4} +(-0.602841 - 1.32004i) q^{5} +(0.0328104 - 0.228201i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.765488 + 0.491950i) q^{8} +(0.415415 - 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.150977 - 0.174237i) q^{2} +(0.841254 - 0.540641i) q^{3} +(0.277065 + 1.92703i) q^{4} +(-0.602841 - 1.32004i) q^{5} +(0.0328104 - 0.228201i) q^{6} +(0.959493 - 0.281733i) q^{7} +(0.765488 + 0.491950i) q^{8} +(0.415415 - 0.909632i) q^{9} +(-0.321014 - 0.0942582i) q^{10} +(2.83234 + 3.26869i) q^{11} +(1.27491 + 1.47133i) q^{12} +(1.43715 + 0.421987i) q^{13} +(0.0957731 - 0.209714i) q^{14} +(-1.22081 - 0.784566i) q^{15} +(-3.53469 + 1.03788i) q^{16} +(1.02244 - 7.11120i) q^{17} +(-0.0957731 - 0.209714i) q^{18} +(0.681552 + 4.74030i) q^{19} +(2.37673 - 1.52743i) q^{20} +(0.654861 - 0.755750i) q^{21} +0.997143 q^{22} +(3.74324 + 2.99803i) q^{23} +0.909938 q^{24} +(1.89522 - 2.18720i) q^{25} +(0.290503 - 0.186695i) q^{26} +(-0.142315 - 0.989821i) q^{27} +(0.808750 + 1.77091i) q^{28} +(0.541382 - 3.76539i) q^{29} +(-0.321014 + 0.0942582i) q^{30} +(0.594299 + 0.381933i) q^{31} +(-1.10882 + 2.42798i) q^{32} +(4.14990 + 1.21852i) q^{33} +(-1.08467 - 1.25177i) q^{34} +(-0.950320 - 1.09673i) q^{35} +(1.86799 + 0.548490i) q^{36} +(-3.76686 + 8.24827i) q^{37} +(0.928832 + 0.596924i) q^{38} +(1.43715 - 0.421987i) q^{39} +(0.187924 - 1.30704i) q^{40} +(-3.36614 - 7.37082i) q^{41} +(-0.0328104 - 0.228201i) q^{42} +(-5.68841 + 3.65572i) q^{43} +(-5.51413 + 6.36364i) q^{44} -1.45118 q^{45} +(1.08751 - 0.199576i) q^{46} +3.95151 q^{47} +(-2.41245 + 2.78411i) q^{48} +(0.841254 - 0.540641i) q^{49} +(-0.0949560 - 0.660433i) q^{50} +(-2.98448 - 6.53509i) q^{51} +(-0.414996 + 2.88636i) q^{52} +(0.577246 - 0.169495i) q^{53} +(-0.193949 - 0.124644i) q^{54} +(2.60735 - 5.70929i) q^{55} +(0.873079 + 0.256359i) q^{56} +(3.13616 + 3.61932i) q^{57} +(-0.574333 - 0.662816i) q^{58} +(-4.42384 - 1.29896i) q^{59} +(1.17364 - 2.56991i) q^{60} +(-5.84505 - 3.75639i) q^{61} +(0.156272 - 0.0458856i) q^{62} +(0.142315 - 0.989821i) q^{63} +(-2.80507 - 6.14224i) q^{64} +(-0.309338 - 2.15149i) q^{65} +(0.838850 - 0.539096i) q^{66} +(4.12746 - 4.76334i) q^{67} +13.9868 q^{68} +(4.76987 + 0.498355i) q^{69} -0.334566 q^{70} +(-1.13316 + 1.30774i) q^{71} +(0.765488 - 0.491950i) q^{72} +(-0.446232 - 3.10361i) q^{73} +(0.868442 + 1.90162i) q^{74} +(0.411871 - 2.86462i) q^{75} +(-8.94587 + 2.62675i) q^{76} +(3.63850 + 2.33832i) q^{77} +(0.143452 - 0.314115i) q^{78} +(-16.0839 - 4.72266i) q^{79} +(3.50089 + 4.04025i) q^{80} +(-0.654861 - 0.755750i) q^{81} +(-1.79248 - 0.526318i) q^{82} +(-4.26833 + 9.34634i) q^{83} +(1.63779 + 1.05255i) q^{84} +(-10.0034 + 2.93727i) q^{85} +(-0.221858 + 1.54306i) q^{86} +(-1.58029 - 3.46035i) q^{87} +(0.560090 + 3.89551i) q^{88} +(-6.34187 + 4.07567i) q^{89} +(-0.219094 + 0.252848i) q^{90} +1.49783 q^{91} +(-4.74017 + 8.04399i) q^{92} +0.706444 q^{93} +(0.596587 - 0.688498i) q^{94} +(5.84651 - 3.75732i) q^{95} +(0.379866 + 2.64203i) q^{96} +(2.23514 + 4.89426i) q^{97} +(0.0328104 - 0.228201i) q^{98} +(4.14990 - 1.21852i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9}+O(q^{10}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9	\( 80 q + q^{2} - 8 q^{3} - 9 q^{4} + 13 q^{5} + q^{6} + 8 q^{7} - 25 q^{8} - 8 q^{9} + 4 q^{10} + q^{11} - 9 q^{12} - 26 q^{13} - q^{14} + 2 q^{15} - 3 q^{16} - 23 q^{17} + q^{18} + 10 q^{19} + 63 q^{20} + 8 q^{21} - 9 q^{23} + 30 q^{24} - 29 q^{25} - 12 q^{26} - 8 q^{27} + 20 q^{28} + 13 q^{29} + 4 q^{30} - 27 q^{31} + 71 q^{32} + q^{33} - 45 q^{34} - 2 q^{35} - 9 q^{36} + 60 q^{37} - 2 q^{38} - 26 q^{39} + 7 q^{40} - 26 q^{41} - q^{42} + 5 q^{43} - 33 q^{44} - 20 q^{45} - 41 q^{46} + 34 q^{47} - 58 q^{48} - 8 q^{49} - 75 q^{50} - q^{51} + 108 q^{52} - 39 q^{53} - 10 q^{54} + 51 q^{55} + 3 q^{56} + 10 q^{57} + 47 q^{58} - 66 q^{59} + 19 q^{60} + 3 q^{61} + 103 q^{62} + 8 q^{63} - 25 q^{64} + 39 q^{65} - 33 q^{66} + 33 q^{67} - 88 q^{68} + 13 q^{69} + 18 q^{70} - 12 q^{71} - 25 q^{72} - 98 q^{73} + 123 q^{74} + 4 q^{75} - 41 q^{76} - 12 q^{77} + 10 q^{78} - 34 q^{79} + 163 q^{80} - 8 q^{81} + 48 q^{82} + 26 q^{83} + 9 q^{84} + 35 q^{85} + 4 q^{86} + 2 q^{87} + 178 q^{88} - 63 q^{89} + 4 q^{90} - 62 q^{91} - 39 q^{92} + 138 q^{93} - 28 q^{94} - 80 q^{95} - 17 q^{96} - 44 q^{97} + q^{98} + q^{99}+O(q^{100}) \) 80 * q + q^2 - 8 * q^3 - 9 * q^4 + 13 * q^5 + q^6 + 8 * q^7 - 25 * q^8 - 8 * q^9 + 4 * q^10 + q^11 - 9 * q^12 - 26 * q^13 - q^14 + 2 * q^15 - 3 * q^16 - 23 * q^17 + q^18 + 10 * q^19 + 63 * q^20 + 8 * q^21 - 9 * q^23 + 30 * q^24 - 29 * q^25 - 12 * q^26 - 8 * q^27 + 20 * q^28 + 13 * q^29 + 4 * q^30 - 27 * q^31 + 71 * q^32 + q^33 - 45 * q^34 - 2 * q^35 - 9 * q^36 + 60 * q^37 - 2 * q^38 - 26 * q^39 + 7 * q^40 - 26 * q^41 - q^42 + 5 * q^43 - 33 * q^44 - 20 * q^45 - 41 * q^46 + 34 * q^47 - 58 * q^48 - 8 * q^49 - 75 * q^50 - q^51 + 108 * q^52 - 39 * q^53 - 10 * q^54 + 51 * q^55 + 3 * q^56 + 10 * q^57 + 47 * q^58 - 66 * q^59 + 19 * q^60 + 3 * q^61 + 103 * q^62 + 8 * q^63 - 25 * q^64 + 39 * q^65 - 33 * q^66 + 33 * q^67 - 88 * q^68 + 13 * q^69 + 18 * q^70 - 12 * q^71 - 25 * q^72 - 98 * q^73 + 123 * q^74 + 4 * q^75 - 41 * q^76 - 12 * q^77 + 10 * q^78 - 34 * q^79 + 163 * q^80 - 8 * q^81 + 48 * q^82 + 26 * q^83 + 9 * q^84 + 35 * q^85 + 4 * q^86 + 2 * q^87 + 178 * q^88 - 63 * q^89 + 4 * q^90 - 62 * q^91 - 39 * q^92 + 138 * q^93 - 28 * q^94 - 80 * q^95 - 17 * q^96 - 44 * q^97 + q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more