LMFDB - Embedded newform 483.2.q.f.64.3

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			64.3
Character	$\chi$	$=$	483.64
Dual form			483.2.q.f.400.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.60503 - 0.471280i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.671521 + 0.431561i) q^{4} +(0.344040 - 2.39285i) q^{5} +(1.40724 - 0.904381i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(1.31647 + 1.51928i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-1.60503 - 0.471280i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.671521 + 0.431561i) q^{4} +(0.344040 - 2.39285i) q^{5} +(1.40724 - 0.904381i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(1.31647 + 1.51928i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.67990 + 3.67846i) q^{10} +(5.54984 - 1.62958i) q^{11} +(-0.765905 + 0.224890i) q^{12} +(-1.30521 + 2.85800i) q^{13} +(0.238063 + 1.65577i) q^{14} +(1.58310 + 1.82699i) q^{15} +(-2.06016 - 4.51113i) q^{16} +(-3.77099 + 2.42347i) q^{17} +(-0.238063 + 1.65577i) q^{18} +(-2.90254 - 1.86535i) q^{19} +(1.26369 - 1.45837i) q^{20} +(0.959493 + 0.281733i) q^{21} -9.67567 q^{22} +(3.72382 - 3.02212i) q^{23} -2.01030 q^{24} +(-0.809896 - 0.237807i) q^{25} +(3.44182 - 3.97208i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.113601 - 0.790114i) q^{28} +(3.49040 - 2.24314i) q^{29} +(-1.67990 - 3.67846i) q^{30} +(-5.36093 - 6.18684i) q^{31} +(0.608435 + 4.23176i) q^{32} +(-2.40282 + 5.26143i) q^{33} +(7.19469 - 2.11255i) q^{34} +(-2.31953 + 0.681076i) q^{35} +(0.331600 - 0.726104i) q^{36} +(-0.906769 - 6.30671i) q^{37} +(3.77957 + 4.36186i) q^{38} +(-1.30521 - 2.85800i) q^{39} +(4.08833 - 2.62741i) q^{40} +(1.41083 - 9.81254i) q^{41} +(-1.40724 - 0.904381i) q^{42} +(-2.42834 + 2.80246i) q^{43} +(4.43010 + 1.30079i) q^{44} -2.41745 q^{45} +(-7.40112 + 3.09564i) q^{46} +3.23827 q^{47} +(4.75841 + 1.39719i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(1.18784 + 0.763376i) q^{50} +(0.637938 - 4.43695i) q^{51} +(-2.10988 + 1.35594i) q^{52} +(-4.33245 - 9.48674i) q^{53} +(-1.09545 - 1.26421i) q^{54} +(-1.98997 - 13.8406i) q^{55} +(0.835108 - 1.82863i) q^{56} +(3.31050 - 0.972049i) q^{57} +(-6.65935 + 1.95536i) q^{58} +(-3.11246 + 6.81534i) q^{59} +(0.274626 + 1.91006i) q^{60} +(-5.36141 - 6.18740i) q^{61} +(5.68874 + 12.4566i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-0.393775 + 2.73877i) q^{64} +(6.38973 + 4.10643i) q^{65} +(6.33621 - 7.31238i) q^{66} +(-7.49964 - 2.20209i) q^{67} -3.57817 q^{68} +(-0.154618 + 4.79334i) q^{69} +4.04390 q^{70} +(-12.9318 - 3.79712i) q^{71} +(1.31647 - 1.51928i) q^{72} +(11.2740 + 7.24539i) q^{73} +(-1.51684 + 10.5498i) q^{74} +(0.710091 - 0.456348i) q^{75} +(-1.14411 - 2.50524i) q^{76} +(-3.78780 - 4.37136i) q^{77} +(0.747980 + 5.20231i) q^{78} +(-3.03049 + 6.63585i) q^{79} +(-11.5032 + 3.37765i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-6.88889 + 15.0846i) q^{82} +(-0.467720 - 3.25306i) q^{83} +(0.522735 + 0.603269i) q^{84} +(4.50162 + 9.85717i) q^{85} +(5.21832 - 3.35361i) q^{86} +(-0.590470 + 4.10681i) q^{87} +(9.78196 + 6.28648i) q^{88} +(8.41852 - 9.71549i) q^{89} +(3.88010 + 1.13930i) q^{90} +3.14194 q^{91} +(3.80485 - 0.422363i) q^{92} +8.18637 q^{93} +(-5.19753 - 1.52613i) q^{94} +(-5.46208 + 6.30358i) q^{95} +(-3.59659 - 2.31139i) q^{96} +(0.0647665 - 0.450461i) q^{97} +(1.40724 - 0.904381i) q^{98} +(-2.40282 - 5.26143i) 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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{6}{11}\right)$

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 $

$2$	−1.60503	−	0.471280i	−1.13493	−	0.333246i	−0.340287	−	0.940322i	$-0.610524\pi$
$2$	−1.60503	−	0.471280i	−1.13493	−	0.333246i	−0.794644	+	0.607076i	$0.792342\pi$
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$	0.671521	+	0.431561i	0.335761	+	0.215780i
$5$	0.344040	−	2.39285i	0.153859	−	1.07011i	−0.755813	−	0.654788i	$-0.772758\pi$
$5$	0.344040	−	2.39285i	0.153859	−	1.07011i	0.909672	−	0.415327i	$-0.136333\pi$
$6$	1.40724	−	0.904381i	0.574505	−	0.369212i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$7$	−0.415415	−	0.909632i	−0.157012	−	0.343809i
$8$	1.31647	+	1.51928i	0.465441	+	0.537147i
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$	−1.67990	+	3.67846i	−0.531230	+	1.16323i
$11$	5.54984	−	1.62958i	1.67334	−	0.491337i	0.698755	−	0.715361i	$-0.253738\pi$
$11$	5.54984	−	1.62958i	1.67334	−	0.491337i	0.974584	+	0.224024i	$0.0719194\pi$
$12$	−0.765905	+	0.224890i	−0.221098	+	0.0649201i
$13$	−1.30521	+	2.85800i	−0.361999	+	0.792668i	0.637749	+	0.770244i	$0.279866\pi$
$13$	−1.30521	+	2.85800i	−0.361999	+	0.792668i	−0.999749	+	0.0224239i	$0.992862\pi$
$14$	0.238063	+	1.65577i	0.0636251	+	0.442522i
$15$	1.58310	+	1.82699i	0.408754	+	0.471727i
$16$	−2.06016	−	4.51113i	−0.515041	−	1.12778i
$17$	−3.77099	+	2.42347i	−0.914598	+	0.587777i	−0.911086	−	0.412217i	$-0.864755\pi$
$17$	−3.77099	+	2.42347i	−0.914598	+	0.587777i	−0.00351278	+	0.999994i	$0.501118\pi$
$18$	−0.238063	+	1.65577i	−0.0561121	+	0.390268i
$19$	−2.90254	−	1.86535i	−0.665888	−	0.427940i	0.163553	−	0.986535i	$-0.447705\pi$
$19$	−2.90254	−	1.86535i	−0.665888	−	0.427940i	−0.829441	+	0.558594i	$0.811341\pi$
$20$	1.26369	−	1.45837i	0.282569	−	0.326103i
$21$	0.959493	+	0.281733i	0.209379	+	0.0614791i
$22$	−9.67567			−2.06286
$23$	3.72382	−	3.02212i	0.776469	−	0.630155i
$23$	3.72382	−	3.02212i	0.776469	−	0.630155i
$24$	−2.01030			−0.410350
$25$	−0.809896	−	0.237807i	−0.161979	−	0.0475614i
$26$	3.44182	−	3.97208i	0.674997	−	0.778988i
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$	0.113601	−	0.790114i	0.0214686	−	0.149318i
$29$	3.49040	−	2.24314i	0.648151	−	0.416541i	−0.174839	−	0.984597i	$-0.555941\pi$
$29$	3.49040	−	2.24314i	0.648151	−	0.416541i	0.822990	+	0.568056i	$0.192304\pi$
$30$	−1.67990	−	3.67846i	−0.306706	−	0.671593i
$31$	−5.36093	−	6.18684i	−0.962851	−	1.11119i	−0.993746	−	0.111667i	$-0.964381\pi$
$31$	−5.36093	−	6.18684i	−0.962851	−	1.11119i	0.0308943	−	0.999523i	$-0.490164\pi$
$32$	0.608435	+	4.23176i	0.107557	+	0.748077i
$33$	−2.40282	+	5.26143i	−0.418277	+	0.915898i
$34$	7.19469	−	2.11255i	1.23388	−	0.362300i
$35$	−2.31953	+	0.681076i	−0.392072	+	0.115123i
$36$	0.331600	−	0.726104i	0.0552667	−	0.121017i
$37$	−0.906769	−	6.30671i	−0.149072	−	1.03682i	−0.917743	−	0.397174i	$-0.869991\pi$
$37$	−0.906769	−	6.30671i	−0.149072	−	1.03682i	0.768672	−	0.639644i	$-0.220918\pi$
$38$	3.77957	+	4.36186i	0.613127	+	0.707587i
$39$	−1.30521	−	2.85800i	−0.209000	−	0.457647i
$40$	4.08833	−	2.62741i	0.646422	−	0.415430i
$41$	1.41083	−	9.81254i	0.220335	−	1.53246i	−0.516440	−	0.856323i	$-0.672743\pi$
$41$	1.41083	−	9.81254i	0.220335	−	1.53246i	0.736775	−	0.676138i	$-0.236348\pi$
$42$	−1.40724	−	0.904381i	−0.217142	−	0.139549i
$43$	−2.42834	+	2.80246i	−0.370319	+	0.427371i	−0.910070	−	0.414454i	$-0.863973\pi$
$43$	−2.42834	+	2.80246i	−0.370319	+	0.427371i	0.539752	+	0.841824i	$0.318518\pi$
$44$	4.43010	+	1.30079i	0.667862	+	0.196102i
$45$	−2.41745			−0.360373
$46$	−7.40112	+	3.09564i	−1.09124	+	0.456427i
$47$	3.23827			0.472350			0.236175	−	0.971711i	$-0.424106\pi$
$47$	3.23827			0.472350			0.236175	+	0.971711i	$0.424106\pi$
$48$	4.75841	+	1.39719i	0.686817	+	0.201668i
$49$	−0.654861	+	0.755750i	−0.0935515	+	0.107964i
$50$	1.18784	+	0.763376i	0.167985	+	0.107958i
$51$	0.637938	−	4.43695i	0.0893291	−	0.621298i
$52$	−2.10988	+	1.35594i	−0.292587	+	0.188034i
$53$	−4.33245	−	9.48674i	−0.595108	−	1.30310i	−0.932306	−	0.361671i	$-0.882207\pi$
$53$	−4.33245	−	9.48674i	−0.595108	−	1.30310i	0.337198	−	0.941434i	$-0.390521\pi$
$54$	−1.09545	−	1.26421i	−0.149071	−	0.172038i
$55$	−1.98997	−	13.8406i	−0.268328	−	1.86626i
$56$	0.835108	−	1.82863i	0.111596	−	0.244361i
$57$	3.31050	−	0.972049i	0.438486	−	0.128751i
$58$	−6.65935	+	1.95536i	−0.874416	+	0.256752i
$59$	−3.11246	+	6.81534i	−0.405208	+	0.887282i	0.591508	+	0.806299i	$0.298533\pi$
$59$	−3.11246	+	6.81534i	−0.405208	+	0.887282i	−0.996716	+	0.0809823i	$0.974194\pi$
$60$	0.274626	+	1.91006i	0.0354540	+	0.246588i
$61$	−5.36141	−	6.18740i	−0.686459	−	0.792215i	0.300398	−	0.953814i	$-0.402881\pi$
$61$	−5.36141	−	6.18740i	−0.686459	−	0.792215i	−0.986857	+	0.161598i	$0.948335\pi$
$62$	5.68874	+	12.4566i	0.722470	+	1.58199i
$63$	−0.841254	+	0.540641i	−0.105988	+	0.0681143i
$64$	−0.393775	+	2.73877i	−0.0492219	+	0.342346i
$65$	6.38973	+	4.10643i	0.792548	+	0.509340i
$66$	6.33621	−	7.31238i	0.779934	−	0.900092i
$67$	−7.49964	−	2.20209i	−0.916227	−	0.269028i	−0.210567	−	0.977579i	$-0.567531\pi$
$67$	−7.49964	−	2.20209i	−0.916227	−	0.269028i	−0.705660	+	0.708551i	$0.749349\pi$
$68$	−3.57817			−0.433917
$69$	−0.154618	+	4.79334i	−0.0186138	+	0.577050i
$70$	4.04390			0.483339
$71$	−12.9318	−	3.79712i	−1.53472	−	0.450635i	−0.598230	−	0.801325i	$-0.704129\pi$
$71$	−12.9318	−	3.79712i	−1.53472	−	0.450635i	−0.936492	+	0.350690i	$0.885947\pi$
$72$	1.31647	−	1.51928i	0.155147	−	0.179049i
$73$	11.2740	+	7.24539i	1.31953	+	0.848008i	0.995193	−	0.0979345i	$-0.0312236\pi$
$73$	11.2740	+	7.24539i	1.31953	+	0.848008i	0.324334	+	0.945943i	$0.394860\pi$
$74$	−1.51684	+	10.5498i	−0.176329	+	1.22639i
$75$	0.710091	−	0.456348i	0.0819943	−	0.0526945i
$76$	−1.14411	−	2.50524i	−0.131238	−	0.287371i
$77$	−3.78780	−	4.37136i	−0.431660	−	0.498162i
$78$	0.747980	+	5.20231i	0.0846920	+	0.589046i
$79$	−3.03049	+	6.63585i	−0.340957	+	0.746591i	−0.999985	−	0.00552709i	$-0.998241\pi$
$79$	−3.03049	+	6.63585i	−0.340957	+	0.746591i	0.659028	+	0.752119i	$0.270968\pi$
$80$	−11.5032	+	3.37765i	−1.28610	+	0.377633i
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$	−6.88889	+	15.0846i	−0.760751	+	1.66581i
$83$	−0.467720	−	3.25306i	−0.0513389	−	0.357070i	−0.999257	−	0.0385543i	$-0.987725\pi$
$83$	−0.467720	−	3.25306i	−0.0513389	−	0.357070i	0.947918	−	0.318516i	$-0.103184\pi$
$84$	0.522735	+	0.603269i	0.0570351	+	0.0658220i
$85$	4.50162	+	9.85717i	0.488269	+	1.06916i
$86$	5.21832	−	3.35361i	0.562705	−	0.361629i
$87$	−0.590470	+	4.10681i	−0.0633051	+	0.440296i
$88$	9.78196	+	6.28648i	1.04276	+	0.670141i
$89$	8.41852	−	9.71549i	0.892361	−	1.02984i	−0.107006	−	0.994258i	$-0.534126\pi$
$89$	8.41852	−	9.71549i	0.892361	−	1.02984i	0.999367	−	0.0355810i	$-0.0113282\pi$
$90$	3.88010	+	1.13930i	0.408998	+	0.120093i
$91$	3.14194			0.329364
$92$	3.80485	−	0.422363i	0.396683	−	0.0440344i
$93$	8.18637			0.848887
$94$	−5.19753	−	1.52613i	−0.536084	−	0.157409i
$95$	−5.46208	+	6.30358i	−0.560398	+	0.646734i
$96$	−3.59659	−	2.31139i	−0.367076	−	0.235905i
$97$	0.0647665	−	0.450461i	0.00657605	−	0.0457374i	−0.986269	−	0.165146i	$-0.947191\pi$
$97$	0.0647665	−	0.450461i	0.00657605	−	0.0457374i	0.992845	+	0.119408i	$0.0380997\pi$
$98$	1.40724	−	0.904381i	0.142153	−	0.0913562i
$99$	−2.40282	−	5.26143i	−0.241492	−	0.528794i
$100$	−0.441234	−	0.509211i	−0.0441234	−	0.0509211i
$101$	1.86381	+	12.9631i	0.185456	+	1.28988i	0.843595	+	0.536980i	$0.180435\pi$
$101$	1.86381	+	12.9631i	0.185456	+	1.28988i	−0.658139	+	0.752897i	$0.728656\pi$
$102$	−3.11496	+	6.82081i	−0.308427	+	0.675361i
$103$	−1.36869	+	0.401883i	−0.134861	+	0.0395987i	−0.348466	−	0.937321i	$-0.613297\pi$
$103$	−1.36869	+	0.401883i	−0.134861	+	0.0395987i	0.213606	+	0.976920i	$0.431479\pi$
$104$	−6.06038	+	1.77949i	−0.594269	+	0.174493i
$105$	1.00425	−	2.19899i	0.0980045	−	0.214600i
$106$	2.48281	+	17.2683i	0.241152	+	1.67725i
$107$	−0.917130	−	1.05842i	−0.0886623	−	0.102322i	0.709685	−	0.704519i	$-0.248837\pi$
$107$	−0.917130	−	1.05842i	−0.0886623	−	0.102322i	−0.798347	+	0.602198i	$0.794292\pi$
$108$	0.331600	+	0.726104i	0.0319083	+	0.0698694i
$109$	9.71111	−	6.24095i	0.930156	−	0.597775i	0.0145685	−	0.999894i	$-0.495363\pi$
$109$	9.71111	−	6.24095i	0.930156	−	0.597775i	0.915587	+	0.402119i	$0.131726\pi$
$110$	−3.32881	+	23.1524i	−0.317390	+	2.20749i
$111$	5.36010	+	3.44473i	0.508758	+	0.326959i
$112$	−3.24765	+	3.74798i	−0.306874	+	0.354151i
$113$	3.40523	+	0.999864i	0.320337	+	0.0940593i	0.437948	−	0.899000i	$-0.355705\pi$
$113$	3.40523	+	0.999864i	0.320337	+	0.0940593i	−0.117611	+	0.993060i	$0.537524\pi$
$114$	−5.77156			−0.540557
$115$	−5.95033	−	9.95026i	−0.554871	−	0.927866i
$116$	3.31193			0.307505
$117$	3.01466	+	0.885185i	0.278706	+	0.0818354i
$118$	8.20754	−	9.47201i	0.755566	−	0.871969i
$119$	3.77099	+	2.42347i	0.345686	+	0.222159i
$120$	−0.691622	+	4.81034i	−0.0631362	+	0.439122i
$121$	18.8914	−	12.1408i	1.71740	−	1.10370i
$122$	5.68925	+	12.4577i	0.515080	+	1.12787i
$123$	6.49193	+	7.49208i	0.585357	+	0.675538i
$124$	−0.929981	−	6.46816i	−0.0835148	−	0.580858i
$125$	4.17356	−	9.13883i	0.373295	−	0.817402i
$126$	1.60503	−	0.471280i	0.142988	−	0.0419850i
$127$	6.92444	−	2.03320i	0.614445	−	0.180417i	0.0403225	−	0.999187i	$-0.487161\pi$
$127$	6.92444	−	2.03320i	0.614445	−	0.180417i	0.574123	+	0.818769i	$0.305343\pi$
$128$	5.47478	−	11.9881i	0.483907	−	1.05961i
$129$	−0.527729	−	3.67044i	−0.0464640	−	0.323164i
$130$	−8.32045	−	9.60231i	−0.729752	−	0.842179i
$131$	4.65215	+	10.1868i	0.406460	+	0.890023i	0.996574	+	0.0827034i	$0.0263554\pi$
$131$	4.65215	+	10.1868i	0.406460	+	0.890023i	−0.590114	+	0.807320i	$0.700917\pi$
$132$	−3.88417	+	2.49620i	−0.338074	+	0.217267i
$133$	−0.491022	+	3.41514i	−0.0425770	+	0.296130i
$134$	10.9994	+	7.06887i	0.950201	+	0.610657i
$135$	1.58310	−	1.82699i	0.136251	−	0.157242i
$136$	−8.64630	−	2.53878i	−0.741414	−	0.217699i
$137$	5.97871			0.510796			0.255398	−	0.966836i	$-0.417794\pi$
$137$	5.97871			0.510796			0.255398	+	0.966836i	$0.417794\pi$
$138$	2.50717	−	7.62060i	0.213425	−	0.648709i
$139$	−15.5845			−1.32186			−0.660930	−	0.750447i	$-0.729838\pi$
$139$	−15.5845			−1.32186			−0.660930	+	0.750447i	$0.729838\pi$
$140$	−1.85154	−	0.543661i	−0.156484	−	0.0459477i
$141$	−2.12062	+	2.44732i	−0.178588	+	0.206102i
$142$	18.9665	+	12.1890i	1.59163	+	1.02288i
$143$	−2.58634	+	17.9884i	−0.216281	+	1.50427i
$144$	−4.17202	+	2.68120i	−0.347669	+	0.223433i
$145$	−4.16666	−	9.12372i	−0.346023	−	0.757684i
$146$	−14.6806	−	16.9423i	−1.21498	−	1.40216i
$147$	−0.142315	−	0.989821i	−0.0117379	−	0.0816391i
$148$	2.11281	−	4.62642i	0.173672	−	0.380289i
$149$	18.3453	−	5.38665i	1.50290	−	0.441292i	0.576269	−	0.817260i	$-0.304508\pi$
$149$	18.3453	−	5.38665i	1.50290	−	0.441292i	0.926633	+	0.375968i	$0.122690\pi$
$150$	−1.35479	+	0.397802i	−0.110618	+	0.0324804i
$151$	−6.92745	+	15.1690i	−0.563748	+	1.23444i	0.386312	+	0.922368i	$0.373749\pi$
$151$	−6.92745	+	15.1690i	−0.563748	+	1.23444i	−0.950060	+	0.312068i	$0.898978\pi$
$152$	−0.987102	−	6.86544i	−0.0800645	−	0.556861i
$153$	2.93547	+	3.38771i	0.237318	+	0.273880i
$154$	4.01942	+	8.80129i	0.323894	+	0.709229i
$155$	−16.6485	+	10.6994i	−1.33724	+	0.859394i
$156$	0.356928	−	2.48249i	0.0285771	−	0.198758i
$157$	3.43361	+	2.20665i	0.274032	+	0.176110i	0.670438	−	0.741966i	$-0.266106\pi$
$157$	3.43361	+	2.20665i	0.274032	+	0.176110i	−0.396406	+	0.918075i	$0.629743\pi$
$158$	7.99139	−	9.22255i	0.635761	−	0.733707i
$159$	10.0068	+	2.93825i	0.793587	+	0.233018i
$160$	10.3353			0.817076
$161$	−4.29594	−	2.13187i	−0.338568	−	0.168015i
$162$	1.67279			0.131427
$163$	8.33581	+	2.44761i	0.652911	+	0.191712i	0.591380	−	0.806393i	$-0.298583\pi$
$163$	8.33581	+	2.44761i	0.652911	+	0.191712i	0.0615310	+	0.998105i	$0.480402\pi$
$164$	5.18211	−	5.98047i	0.404655	−	0.466996i
$165$	11.7632	+	7.55972i	0.915760	+	0.588523i
$166$	−0.782399	+	5.44170i	−0.0607259	+	0.422358i
$167$	−6.65928	+	4.27966i	−0.515311	+	0.331170i	−0.772315	−	0.635240i	$-0.780901\pi$
$167$	−6.65928	+	4.27966i	−0.515311	+	0.331170i	0.257004	+	0.966410i	$0.417265\pi$
$168$	0.835108	+	1.82863i	0.0644300	+	0.141082i
$169$	2.04856	+	2.36417i	0.157582	+	0.181859i
$170$	−2.57976	−	17.9426i	−0.197858	−	1.37614i
$171$	−1.43329	+	3.13846i	−0.109606	+	0.240004i
$172$	−2.84011	+	0.833933i	−0.216557	+	0.0635868i
$173$	−18.7693	+	5.51116i	−1.42700	+	0.419006i	−0.901867	−	0.432013i	$-0.857803\pi$
$173$	−18.7693	+	5.51116i	−1.42700	+	0.419006i	−0.525135	+	0.851019i	$0.675985\pi$
$174$	2.88319	−	6.31329i	0.218574	−	0.478610i
$175$	0.120126	+	0.835496i	0.00908068	+	0.0631575i
$176$	−18.7848	−	21.6788i	−1.41596	−	1.63410i
$177$	−3.11246	−	6.81534i	−0.233947	−	0.512272i
$178$	−18.0907	+	11.6262i	−1.35596	+	0.871421i
$179$	2.47845	−	17.2380i	0.185248	−	1.28843i	−0.658863	−	0.752263i	$-0.728962\pi$
$179$	2.47845	−	17.2380i	0.185248	−	1.28843i	0.844111	−	0.536168i	$-0.180129\pi$
$180$	−1.62337	−	1.04328i	−0.120999	−	0.0777614i
$181$	3.69040	−	4.25894i	0.274305	−	0.316565i	−0.601836	−	0.798620i	$-0.705564\pi$
$181$	3.69040	−	4.25894i	0.274305	−	0.316565i	0.876141	+	0.482055i	$0.160109\pi$
$182$	−5.04291	−	1.48073i	−0.373806	−	0.109759i
$183$	8.18710			0.605208
$184$	9.49372	+	1.67902i	0.699887	+	0.123779i
$185$	−15.4030			−1.13245
$186$	−13.1394	−	3.85807i	−0.963427	−	0.282888i
$187$	−16.9791	+	19.5950i	−1.24164	+	1.43293i
$188$	2.17457	+	1.39751i	0.158597	+	0.101924i
$189$	0.142315	−	0.989821i	0.0103519	−	0.0719989i
$190$	11.7376	−	7.54329i	0.851534	−	0.547248i
$191$	0.933553	+	2.04420i	0.0675495	+	0.147913i	0.940395	−	0.340083i	$-0.110455\pi$
$191$	0.933553	+	2.04420i	0.0675495	+	0.147913i	−0.872846	+	0.487996i	$0.837728\pi$
$192$	−1.81195	−	2.09111i	−0.130766	−	0.150913i
$193$	1.74862	+	12.1619i	0.125868	+	0.875433i	0.950713	+	0.310073i	$0.100354\pi$
$193$	1.74862	+	12.1619i	0.125868	+	0.875433i	−0.824844	+	0.565360i	$0.808737\pi$
$194$	−0.316246	+	0.692482i	−0.0227051	+	0.0497173i
$195$	−7.28782	+	2.13990i	−0.521891	+	0.153241i
$196$	−0.765905	+	0.224890i	−0.0547075	+	0.0160636i
$197$	3.33802	−	7.30924i	0.237824	−	0.520762i	−0.752657	−	0.658413i	$-0.771228\pi$
$197$	3.33802	−	7.30924i	0.237824	−	0.520762i	0.990481	+	0.137651i	$0.0439553\pi$
$198$	1.37699	+	9.57718i	0.0978585	+	0.680621i
$199$	−5.37881	−	6.20748i	−0.381294	−	0.440037i	0.532367	−	0.846514i	$-0.321303\pi$
$199$	−5.37881	−	6.20748i	−0.381294	−	0.440037i	−0.913661	+	0.406477i	$0.866757\pi$
$200$	−0.704904	−	1.54352i	−0.0498442	−	0.109144i
$201$	6.57545	−	4.22579i	0.463797	−	0.298064i
$202$	3.11777	−	21.6846i	0.219366	−	1.52572i
$203$	−3.49040	−	2.24314i	−0.244978	−	0.157438i
$204$	2.34320	−	2.70420i	0.164057	−	0.189332i
$205$	−22.9945	−	6.75181i	−1.60601	−	0.471567i
$206$	2.38619			0.166254
$207$	−3.52131	−	3.25582i	−0.244748	−	0.226295i
$208$	15.5818			1.08040
$209$	−19.1484	−	5.62246i	−1.32452	−	0.388914i
$210$	−2.64819	+	3.05618i	−0.182743	+	0.210896i
$211$	−2.16604	−	1.39203i	−0.149117	−	0.0958314i	0.463955	−	0.885859i	$-0.346430\pi$
$211$	−2.16604	−	1.39203i	−0.149117	−	0.0958314i	−0.613072	+	0.790027i	$0.710066\pi$
$212$	1.18477	−	8.24026i	0.0813704	−	0.565944i
$213$	11.3382	−	7.28661i	0.776880	−	0.499270i
$214$	0.973210	+	2.13103i	0.0665272	+	0.145674i
$215$	5.87041	+	6.77481i	0.400359	+	0.462038i
$216$	0.286095	+	1.98984i	0.0194663	+	0.135391i
$217$	−3.40074	+	7.44658i	−0.230857	+	0.505507i
$218$	−18.5279	+	5.44028i	−1.25487	+	0.368463i
$219$	−12.8586	+	3.77563i	−0.868905	+	0.255134i
$220$	4.63673	−	10.1530i	0.312608	−	0.684517i
$221$	−2.00436	−	13.9406i	−0.134828	−	0.937748i
$222$	−6.97971	−	8.05502i	−0.468448	−	0.540617i
$223$	3.18498	+	6.97413i	0.213282	+	0.467022i	0.985790	−	0.167983i	$-0.0537253\pi$
$223$	3.18498	+	6.97413i	0.213282	+	0.467022i	−0.772508	+	0.635005i	$0.780998\pi$
$224$	3.59659	−	2.31139i	0.240307	−	0.154436i
$225$	−0.120126	+	0.835496i	−0.00800841	+	0.0556997i
$226$	−4.99429	−	3.20963i	−0.332215	−	0.213502i
$227$	16.7955	−	19.3831i	1.11476	−	1.28650i	0.160658	−	0.987010i	$-0.448638\pi$
$227$	16.7955	−	19.3831i	1.11476	−	1.28650i	0.954100	−	0.299489i	$-0.0968162\pi$
$228$	2.64257	+	0.775927i	0.175008	+	0.0513870i
$229$	6.23672			0.412134			0.206067	−	0.978538i	$-0.433933\pi$
$229$	6.23672			0.412134			0.206067	+	0.978538i	$0.433933\pi$
$230$	4.86111	+	18.7748i	0.320532	+	1.23797i
$231$	5.78414			0.380568
$232$	8.00295	+	2.34988i	0.525420	+	0.154277i
$233$	−18.2031	+	21.0075i	−1.19252	+	1.37624i	−0.283779	+	0.958890i	$0.591588\pi$
$233$	−18.2031	+	21.0075i	−1.19252	+	1.37624i	−0.908744	+	0.417355i	$0.862957\pi$
$234$	−4.42147	−	2.84151i	−0.289040	−	0.185755i
$235$	1.11409	−	7.74869i	0.0726754	−	0.505469i
$236$	−5.03132	+	3.23343i	−0.327511	+	0.210478i
$237$	−3.03049	−	6.63585i	−0.196852	−	0.431045i
$238$	−4.91043	−	5.66694i	−0.318296	−	0.367333i
$239$	−3.11554	−	21.6691i	−0.201528	−	1.40165i	−0.799754	−	0.600328i	$-0.795037\pi$
$239$	−3.11554	−	21.6691i	−0.201528	−	1.40165i	0.598227	−	0.801327i	$-0.295872\pi$
$240$	4.98035	−	10.9055i	0.321480	−	0.703944i
$241$	12.3720	−	3.63276i	0.796953	−	0.234006i	0.142188	−	0.989840i	$-0.454586\pi$
$241$	12.3720	−	3.63276i	0.796953	−	0.234006i	0.654764	+	0.755833i	$0.272768\pi$
$242$	−36.0430	+	10.5832i	−2.31693	+	0.680313i
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$	−0.930065	−	6.46875i	−0.0595413	−	0.414119i
$245$	1.58310	+	1.82699i	0.101140	+	0.116722i
$246$	−6.88889	−	15.0846i	−0.439220	−	0.961757i
$247$	9.11959	−	5.86080i	0.580266	−	0.372914i
$248$	2.34208	−	16.2895i	0.148722	−	1.03439i
$249$	2.76479	+	1.77682i	0.175212	+	0.112602i
$250$	−11.0057	+	12.7012i	−0.696059	+	0.803295i
$251$	17.6223	+	5.17438i	1.11231	+	0.326604i	0.785733	−	0.618566i	$-0.212286\pi$
$251$	17.6223	+	5.17438i	1.11231	+	0.326604i	0.326579	+	0.945170i	$0.394104\pi$
$252$	−0.798239			−0.0502843
$253$	15.7418	−	22.8405i	0.989678	−	1.43597i
$254$	−12.0722			−0.757476
$255$	−10.3975	−	3.05298i	−0.651116	−	0.191185i
$256$	−10.8130	+	12.4789i	−0.675816	+	0.779933i
$257$	−3.92305	−	2.52119i	−0.244713	−	0.157268i	0.412535	−	0.910942i	$-0.364643\pi$
$257$	−3.92305	−	2.52119i	−0.244713	−	0.157268i	−0.657248	+	0.753674i	$0.728280\pi$
$258$	−0.882782	+	6.13989i	−0.0549596	+	0.382253i
$259$	−5.36010	+	3.44473i	−0.333061	+	0.214045i
$260$	2.51867	+	5.51511i	0.156201	+	0.342033i
$261$	−2.71705	−	3.13564i	−0.168181	−	0.194091i
$262$	−2.66602	−	18.5426i	−0.164707	−	1.14557i
$263$	−3.44620	+	7.54613i	−0.212502	+	0.465315i	−0.985626	−	0.168940i	$-0.945966\pi$
$263$	−3.44620	+	7.54613i	−0.212502	+	0.465315i	0.773124	+	0.634255i	$0.218693\pi$
$264$	−11.1568	+	3.27594i	−0.686655	+	0.201620i
$265$	−24.1909	+	7.10308i	−1.48603	+	0.436339i
$266$	2.39759	−	5.25000i	0.147006	−	0.321898i
$267$	1.82952	+	12.7246i	0.111965	+	0.778732i
$268$	−4.08583	−	4.71530i	−0.249582	−	0.288033i
$269$	10.8068	+	23.6635i	0.658899	+	1.44279i	0.883544	+	0.468348i	$0.155151\pi$
$269$	10.8068	+	23.6635i	0.658899	+	1.44279i	−0.224645	+	0.974441i	$0.572122\pi$
$270$	−3.40195	+	2.18630i	−0.207036	+	0.133054i
$271$	4.23923	−	29.4845i	0.257515	−	1.79105i	−0.292879	−	0.956150i	$-0.594613\pi$
$271$	4.23923	−	29.4845i	0.257515	−	1.79105i	0.550394	−	0.834905i	$-0.314478\pi$
$272$	18.7014	+	12.0187i	1.13394	+	0.728739i
$273$	−2.05753	+	2.37452i	−0.124527	+	0.143712i
$274$	−9.59603	−	2.81765i	−0.579718	−	0.170220i
$275$	−4.88231			−0.294415
$276$	−2.17245	+	3.15210i	−0.130766	+	0.189734i
$277$	25.5033			1.53235			0.766173	−	0.642634i	$-0.222158\pi$
$277$	25.5033			1.53235			0.766173	+	0.642634i	$0.222158\pi$
$278$	25.0137	+	7.34467i	1.50022	+	0.440504i
$279$	−5.36093	+	6.18684i	−0.320950	+	0.370397i
$280$	−4.08833	−	2.62741i	−0.244324	−	0.157018i
$281$	0.824744	−	5.73622i	0.0492001	−	0.342194i	−0.950322	−	0.311270i	$-0.899246\pi$
$281$	0.824744	−	5.73622i	0.0492001	−	0.342194i	0.999522	−	0.0309245i	$-0.00984514\pi$
$282$	4.55703	−	2.92863i	0.271367	−	0.174397i
$283$	5.17324	+	11.3278i	0.307517	+	0.673368i	0.998788	−	0.0492277i	$-0.0156760\pi$
$283$	5.17324	+	11.3278i	0.307517	+	0.673368i	−0.691271	+	0.722596i	$0.742949\pi$
$284$	−7.04529	−	8.13069i	−0.418061	−	0.482468i
$285$	−1.18702	−	8.25594i	−0.0703133	−	0.489039i
$286$	12.6287	−	27.6531i	0.746753	−	1.63516i
$287$	−9.51188	+	2.79294i	−0.561469	+	0.164862i
$288$	4.10210	−	1.20448i	0.241718	−	0.0709749i
$289$	1.28509	−	2.81396i	0.0755938	−	0.165527i
$290$	2.38781	+	16.6075i	0.140217	+	0.975229i
$291$	0.298023	+	0.343937i	0.0174704	+	0.0201619i
$292$	4.44394	+	9.73086i	0.260062	+	0.569456i
$293$	7.43401	−	4.77755i	0.434299	−	0.279107i	−0.305169	−	0.952298i	$-0.598713\pi$
$293$	7.43401	−	4.77755i	0.434299	−	0.279107i	0.739469	+	0.673191i	$0.235077\pi$
$294$	−0.238063	+	1.65577i	−0.0138841	+	0.0965663i
$295$	15.2373	+	9.79240i	0.887148	+	0.570135i
$296$	8.38795	−	9.68021i	0.487540	−	0.562651i
$297$	5.54984	+	1.62958i	0.322034	+	0.0945578i
$298$	−31.9834			−1.85275
$299$	3.77687	+	14.5872i	0.218422	+	0.843598i
$300$	0.673783			0.0389009
$301$	3.55797	+	1.04472i	0.205078	+	0.0602164i
$302$	18.2676	−	21.0820i	1.05119	−	1.21313i
$303$	−11.0174	−	7.08045i	−0.632933	−	0.406761i
$304$	−2.43512	+	16.9367i	−0.139664	+	0.971384i
$305$	−16.6501	+	10.7003i	−0.953379	+	0.612700i
$306$	−3.11496	−	6.82081i	−0.178070	−	0.389920i
$307$	−1.65818	−	1.91364i	−0.0946372	−	0.109217i	0.706455	−	0.707758i	$-0.250293\pi$
$307$	−1.65818	−	1.91364i	−0.0946372	−	0.109217i	−0.801093	+	0.598540i	$0.795748\pi$
$308$	−0.657085	−	4.57013i	−0.0374409	−	0.260407i
$309$	0.592577	−	1.29756i	0.0337105	−	0.0738158i
$310$	31.7639	−	9.32672i	1.80407	−	0.529722i
$311$	−5.83811	+	1.71422i	−0.331049	+	0.0972047i	−0.443033	−	0.896505i	$-0.646098\pi$
$311$	−5.83811	+	1.71422i	−0.331049	+	0.0972047i	0.111984	+	0.993710i	$0.464279\pi$
$312$	2.62386	−	5.74544i	0.148547	−	0.325272i
$313$	1.68481	+	11.7181i	0.0952312	+	0.662347i	0.980391	+	0.197061i	$0.0631396\pi$
$313$	1.68481	+	11.7181i	0.0952312	+	0.662347i	−0.885160	+	0.465287i	$0.845951\pi$
$314$	−4.47112	−	5.15994i	−0.252320	−	0.291192i
$315$	1.00425	+	2.19899i	0.0565829	+	0.123899i
$316$	−4.89881	+	3.14827i	−0.275580	+	0.177104i
$317$	−1.22547	+	8.52336i	−0.0688295	+	0.478720i	0.926030	+	0.377451i	$0.123199\pi$
$317$	−1.22547	+	8.52336i	−0.0688295	+	0.478720i	−0.994859	+	0.101269i	$0.967710\pi$
$318$	−14.6764	−	9.43197i	−0.823014	−	0.528919i
$319$	15.7158	−	18.1370i	0.879914	−	1.01547i
$320$	6.41798	+	1.88449i	0.358776	+	0.105346i
$321$	1.40050			0.0781681
$322$	5.89043	+	5.44632i	0.328261	+	0.303511i
$323$	15.4660			0.860554
$324$	−0.765905	−	0.224890i	−0.0425503	−	0.0124939i
$325$	1.73673	−	2.00430i	0.0963367	−	0.111178i
$326$	−12.2257	−	7.85700i	−0.677121	−	0.435159i
$327$	−1.64283	+	11.4261i	−0.0908486	+	0.631866i
$328$	16.7653	−	10.7744i	0.925710	−	0.594918i
$329$	−1.34523	−	2.94563i	−0.0741647	−	0.162398i
$330$	−15.3175	−	17.6773i	−0.843201	−	0.973106i
$331$	−0.749539	−	5.21316i	−0.0411984	−	0.286541i	−0.999997	−	0.00245444i	$-0.999219\pi$
$331$	−0.749539	−	5.21316i	−0.0411984	−	0.286541i	0.958799	−	0.284087i	$-0.0916904\pi$
$332$	1.08981	−	2.38635i	0.0598111	−	0.130968i
$333$	−6.11347	+	1.79508i	−0.335016	+	0.0983697i
$334$	12.7053	−	3.73061i	0.695203	−	0.204130i
$335$	−7.84945	+	17.1879i	−0.428861	+	0.939075i
$336$	−0.705781	−	4.90881i	−0.0385035	−	0.267798i
$337$	−12.7026	−	14.6595i	−0.691953	−	0.798556i	0.295689	−	0.955284i	$-0.404451\pi$
$337$	−12.7026	−	14.6595i	−0.691953	−	0.798556i	−0.987642	+	0.156728i	$0.949905\pi$
$338$	−2.17383	−	4.76002i	−0.118241	−	0.258911i
$339$	−2.98560	+	1.91873i	−0.162155	+	0.104211i
$340$	−1.23103	+	8.56202i	−0.0667621	+	0.464341i
$341$	−39.8342	−	25.5999i	−2.15714	−	1.38631i
$342$	3.77957	−	4.36186i	0.204376	−	0.235862i
$343$	0.959493	+	0.281733i	0.0518078	+	0.0152121i
$344$	−7.45455			−0.401923
$345$	11.4165	+	2.01908i	0.614646	+	0.108703i
$346$	32.7226			1.75918
$347$	31.5650	+	9.26831i	1.69450	+	0.497549i	0.979477	−	0.201555i	$-0.0645995\pi$
$347$	31.5650	+	9.26831i	1.69450	+	0.497549i	0.715020	+	0.699104i	$0.246418\pi$
$348$	−2.16885	+	2.50299i	−0.116263	+	0.134174i
$349$	−10.4043	−	6.68643i	−0.556928	−	0.357916i	0.231699	−	0.972788i	$-0.425572\pi$
$349$	−10.4043	−	6.68643i	−0.556928	−	0.357916i	−0.788627	+	0.614871i	$0.789208\pi$
$350$	0.200946	−	1.39761i	0.0107410	−	0.0747055i
$351$	−2.64316	+	1.69866i	−0.141082	+	0.0906677i
$352$	10.2727	+	22.4941i	0.547537	+	1.19894i
$353$	17.8512	+	20.6014i	0.950123	+	1.09650i	0.995234	+	0.0975185i	$0.0310905\pi$
$353$	17.8512	+	20.6014i	0.950123	+	1.09650i	−0.0451106	+	0.998982i	$0.514364\pi$
$354$	1.78367	+	12.4057i	0.0948010	+	0.659355i
$355$	−13.5350	+	29.6375i	−0.718362	+	1.57299i
$356$	9.84603	−	2.89106i	0.521839	−	0.153226i
$357$	−4.30100	+	1.26289i	−0.227633	+	0.0668392i
$358$	−12.1020	+	26.4996i	−0.639608	+	1.40055i
$359$	1.76828	+	12.2987i	0.0933263	+	0.649099i	0.981764	+	0.190102i	$0.0608819\pi$
$359$	1.76828	+	12.2987i	0.0933263	+	0.649099i	−0.888438	+	0.458997i	$0.848209\pi$
$360$	−3.18250	−	3.67280i	−0.167732	−	0.193573i
$361$	−2.94768	−	6.45451i	−0.155141	−	0.339711i
$362$	−7.93037	+	5.09654i	−0.416811	+	0.267868i
$363$	−3.19585	+	22.2277i	−0.167739	+	1.16665i
$364$	2.10988	+	1.35594i	0.110588	+	0.0710703i
$365$	21.2158	−	24.4844i	1.11049	−	1.28157i
$366$	−13.1406	−	3.85842i	−0.686869	−	0.201683i
$367$	−1.08220			−0.0564906			−0.0282453	−	0.999601i	$-0.508992\pi$
$367$	−1.08220			−0.0564906			−0.0282453	+	0.999601i	$0.508992\pi$
$368$	−21.3048	−	10.5726i	−1.11059	−	0.551133i
$369$	−9.91345			−0.516073
$370$	24.7223	+	7.25912i	1.28525	+	0.377384i
$371$	−6.82968	+	7.88187i	−0.354579	+	0.409206i
$372$	5.49732	+	3.53291i	0.285023	+	0.183173i
$373$	−3.40980	+	23.7157i	−0.176553	+	1.22795i	0.688113	+	0.725603i	$0.258439\pi$
$373$	−3.40980	+	23.7157i	−0.176553	+	1.22795i	−0.864666	+	0.502347i	$0.832470\pi$
$374$	36.4868	−	23.4486i	1.88669	−	1.21250i
$375$	4.17356	+	9.13883i	0.215522	+	0.471927i
$376$	4.26307	+	4.91984i	0.219851	+	0.253722i
$377$	1.85522	+	12.9033i	0.0955487	+	0.664556i
$378$	−0.694904	+	1.52163i	−0.0357420	+	0.0782640i
$379$	−22.4451	+	6.59049i	−1.15293	+	0.338531i	−0.801681	−	0.597752i	$-0.796061\pi$
$379$	−22.4451	+	6.59049i	−1.15293	+	0.338531i	−0.351248	+	0.936282i	$0.614243\pi$
$380$	−6.38828	+	1.87577i	−0.327712	+	0.0962249i
$381$	−2.99796	+	6.56461i	−0.153590	+	0.336315i
$382$	−0.534994	−	3.72097i	−0.0273727	−	0.190381i
$383$	−15.5423	−	17.9368i	−0.794175	−	0.916527i	0.203871	−	0.978998i	$-0.434648\pi$
$383$	−15.5423	−	17.9368i	−0.794175	−	0.916527i	−0.998047	+	0.0624703i	$0.980102\pi$
$384$	5.47478	+	11.9881i	0.279384	+	0.611765i
$385$	−11.7632	+	7.55972i	−0.599506	+	0.385279i
$386$	2.92508	−	20.3444i	0.148882	−	1.03550i
$387$	3.11952	+	2.00479i	0.158574	+	0.101909i
$388$	0.237893	−	0.274544i	0.0120772	−	0.0139378i
$389$	20.4259	+	5.99758i	1.03563	+	0.304089i	0.754999	−	0.655726i	$-0.227637\pi$
$389$	20.4259	+	5.99758i	1.03563	+	0.304089i	0.280633	+	0.959815i	$0.409455\pi$
$390$	12.7057			0.643377
$391$	−6.71847	+	20.4209i	−0.339767	+	1.03273i
$392$	−2.01030			−0.101535
$393$	−10.7452	−	3.15506i	−0.542022	−	0.159152i
$394$	−8.80234	+	10.1584i	−0.443455	+	0.511775i
$395$	14.8360	+	9.53450i	0.746479	+	0.479733i
$396$	0.657085	−	4.57013i	0.0330198	−	0.229657i
$397$	−2.59860	+	1.67002i	−0.130420	+	0.0838159i	−0.604224	−	0.796814i	$-0.706517\pi$
$397$	−2.59860	+	1.67002i	−0.130420	+	0.0838159i	0.473804	+	0.880630i	$0.342880\pi$
$398$	5.70771	+	12.4981i	0.286102	+	0.626475i
$399$	−2.25944	−	2.60753i	−0.113113	−	0.130540i
$400$	0.595741	+	4.14347i	0.0297870	+	0.207173i
$401$	−12.3499	+	27.0425i	−0.616725	+	1.35044i	0.301152	+	0.953576i	$0.402629\pi$
$401$	−12.3499	+	27.0425i	−0.616725	+	1.35044i	−0.917877	+	0.396864i	$0.870098\pi$
$402$	−12.5454	+	3.68365i	−0.625705	+	0.183724i
$403$	24.6791	−	7.24645i	1.22936	−	0.360971i
$404$	−4.34277	+	9.50934i	−0.216061	+	0.473108i
$405$	0.344040	+	2.39285i	0.0170955	+	0.118902i
$406$	4.54506	+	5.24528i	0.225567	+	0.260319i
$407$	−15.3097	−	33.5236i	−0.758874	−	1.66170i
$408$	7.58081	−	4.87189i	0.375306	−	0.241194i
$409$	1.87884	−	13.0676i	0.0929026	−	0.646152i	−0.889160	−	0.457596i	$-0.848710\pi$
$409$	1.87884	−	13.0676i	0.0929026	−	0.646152i	0.982063	−	0.188555i	$-0.0603805\pi$
$410$	33.7250	+	21.6738i	1.66556	+	1.07039i
$411$	−3.91522	+	4.51841i	−0.193124	+	0.222877i
$412$	−1.09254	−	0.320799i	−0.0538256	−	0.0158046i
$413$	7.49241			0.368678
$414$	4.11742	+	6.88523i	0.202360	+	0.338391i
$415$	−7.94500			−0.390005
$416$	−12.8885	−	3.78441i	−0.631912	−	0.185546i
$417$	10.2057	−	11.7780i	0.499774	−	0.576770i
$418$	28.0840	+	18.0485i	1.37363	+	0.882780i
$419$	−3.87484	+	26.9501i	−0.189298	+	1.31660i	0.644532	+	0.764577i	$0.277052\pi$
$419$	−3.87484	+	26.9501i	−0.189298	+	1.31660i	−0.833831	+	0.552020i	$0.813857\pi$
$420$	1.62337	−	1.04328i	0.0792125	−	0.0509068i
$421$	6.53534	+	14.3104i	0.318513	+	0.697446i	0.999389	−	0.0349528i	$-0.0111281\pi$
$421$	6.53534	+	14.3104i	0.318513	+	0.697446i	−0.680876	+	0.732399i	$0.738401\pi$
$422$	2.82054	+	3.25507i	0.137302	+	0.158454i
$423$	−0.460854	−	3.20531i	−0.0224075	−	0.155847i
$424$	8.70952	−	19.0712i	0.422972	−	0.926178i
$425$	3.63042	−	1.06599i	0.176101	−	0.0517080i
$426$	−21.6322	+	6.35179i	−1.04808	+	0.307745i
$427$	−3.40105	+	7.44725i	−0.164588	+	0.360398i
$428$	−0.159098	−	1.10655i	−0.00769030	−	0.0534872i
$429$	−11.9010	−	13.7345i	−0.574587	−	0.663109i
$430$	−6.22937	−	13.6404i	−0.300407	−	0.657799i
$431$	11.3105	−	7.26884i	0.544809	−	0.350128i	−0.239108	−	0.970993i	$-0.576855\pi$
$431$	11.3105	−	7.26884i	0.544809	−	0.350128i	0.783917	+	0.620865i	$0.213219\pi$
$432$	0.705781	−	4.90881i	0.0339569	−	0.236175i
$433$	−15.4804	−	9.94867i	−0.743942	−	0.478102i	0.112949	−	0.993601i	$-0.463970\pi$
$433$	−15.4804	−	9.94867i	−0.743942	−	0.478102i	−0.856891	+	0.515498i	$0.827607\pi$
$434$	8.96773	−	10.3493i	0.430465	−	0.496783i
$435$	9.62383	+	2.82581i	0.461428	+	0.135487i
$436$	9.21457			0.441298
$437$	−16.4458	+	1.82559i	−0.786710	+	0.0873300i
$438$	22.4179			1.07117
$439$	27.3323	+	8.02548i	1.30450	+	0.383035i	0.858875	−	0.512186i	$-0.171164\pi$
$439$	27.3323	+	8.02548i	1.30450	+	0.383035i	0.445623	+	0.895221i	$0.352982\pi$
$440$	18.4080	−	21.2439i	0.877566	−	1.01277i
$441$	0.841254	+	0.540641i	0.0400597	+	0.0257448i
$442$	−3.35288	+	23.3198i	−0.159480	+	1.10921i
$443$	21.7049	−	13.9489i	1.03123	−	0.662732i	0.0884284	−	0.996083i	$-0.471816\pi$
$443$	21.7049	−	13.9489i	1.03123	−	0.662732i	0.942803	+	0.333350i	$0.108179\pi$
$444$	2.11281	+	4.62642i	0.100270	+	0.219560i
$445$	−20.3514	−	23.4867i	−0.964748	−	1.11338i
$446$	−1.82523	−	12.6947i	−0.0864270	−	0.601113i
$447$	−7.94263	+	17.3919i	−0.375673	+	0.822610i
$448$	2.65485	−	0.779534i	0.125430	−	0.0368295i
$449$	9.61013	−	2.82179i	0.453530	−	0.133168i	−0.0469862	−	0.998896i	$-0.514962\pi$
$449$	9.61013	−	2.82179i	0.453530	−	0.133168i	0.500516	+	0.865727i	$0.333143\pi$
$450$	0.586559	−	1.28439i	0.0276507	−	0.0605465i
$451$	−8.16043	−	56.7571i	−0.384260	−	2.67259i
$452$	1.85518	+	2.14099i	0.0872603	+	0.100704i
$453$	−6.92745	−	15.1690i	−0.325480	−	0.712702i
$454$	−36.0922	+	23.1951i	−1.69389	+	1.08860i
$455$	1.08095	−	7.51818i	0.0506757	−	0.352457i
$456$	5.83497	+	3.74991i	0.273247	+	0.175605i
$457$	−21.8115	+	25.1718i	−1.02030	+	1.17749i	−0.0362954	+	0.999341i	$0.511556\pi$
$457$	−21.8115	+	25.1718i	−1.02030	+	1.17749i	−0.984004	+	0.178147i	$0.942990\pi$
$458$	−10.0101	−	2.93924i	−0.467744	−	0.137342i
$459$	−4.48258			−0.209229
$460$	0.298368	−	9.24974i	0.0139115	−	0.431271i
$461$	28.3296			1.31944			0.659721	−	0.751511i	$-0.270675\pi$
$461$	28.3296			1.31944			0.659721	+	0.751511i	$0.270675\pi$
$462$	−9.28373	−	2.72595i	−0.431918	−	0.126823i
$463$	−5.78530	+	6.67660i	−0.268866	+	0.310288i	−0.874087	−	0.485770i	$-0.838539\pi$
$463$	−5.78530	+	6.67660i	−0.268866	+	0.310288i	0.605221	+	0.796058i	$0.293085\pi$
$464$	−17.3099	−	11.1244i	−0.803592	−	0.516437i
$465$	2.81643	−	19.5887i	0.130609	−	0.908406i
$466$	39.1169	−	25.1389i	1.81206	−	1.16454i
$467$	−0.0360304	−	0.0788956i	−0.00166729	−	0.00365085i	0.908797	−	0.417240i	$-0.137002\pi$
$467$	−0.0360304	−	0.0788956i	−0.00166729	−	0.00365085i	−0.910464	+	0.413589i	$0.864275\pi$
$468$	1.64240	+	1.89543i	0.0759200	+	0.0876163i
$469$	1.11237	+	7.73669i	0.0513644	+	0.357247i
$470$	−5.43996	+	11.9119i	−0.250927	+	0.549453i
$471$	−3.91621	+	1.14990i	−0.180450	+	0.0529848i
$472$	−14.4519	+	4.24345i	−0.665201	+	0.195321i
$473$	−8.91008	+	19.5104i	−0.409686	+	0.897087i
$474$	1.73669	+	12.0790i	0.0797690	+	0.554806i
$475$	1.90716	+	2.20098i	0.0875066	+	0.100988i
$476$	1.48643	+	3.25482i	0.0681302	+	0.149184i
$477$	−8.77361	+	5.63846i	−0.401716	+	0.258167i
$478$	−5.21166	+	36.2479i	−0.238376	+	1.65794i
$479$	13.5365	+	8.69936i	0.618497	+	0.397484i	0.812035	−	0.583609i	$-0.198360\pi$
$479$	13.5365	+	8.69936i	0.618497	+	0.397484i	−0.193538	+	0.981093i	$0.561996\pi$
$480$	−6.76817	+	7.81089i	−0.308923	+	0.356517i
$481$	19.2081	+	5.64002i	0.875816	+	0.257163i
$482$	−21.5696			−0.982467
$483$	4.42440	−	1.85058i	0.201317	−	0.0842043i
$484$	17.9254			0.814792
$485$	−1.05560	−	0.309953i	−0.0479325	−	0.0140742i
$486$	−1.09545	+	1.26421i	−0.0496905	+	0.0573459i
$487$	−7.11434	−	4.57211i	−0.322381	−	0.207182i	0.369433	−	0.929257i	$-0.379552\pi$
$487$	−7.11434	−	4.57211i	−0.322381	−	0.207182i	−0.691814	+	0.722075i	$0.743188\pi$
$488$	2.34229	−	16.2910i	0.106031	−	0.737459i
$489$	−7.30857	+	4.69694i	−0.330505	+	0.212403i
$490$	−1.67990	−	3.67846i	−0.0758901	−	0.166176i
$491$	1.26127	+	1.45558i	0.0569203	+	0.0656895i	0.783496	−	0.621397i	$-0.213435\pi$
$491$	1.26127	+	1.45558i	0.0569203	+	0.0656895i	−0.726575	+	0.687087i	$0.758889\pi$
$492$	1.12618	+	7.83275i	0.0507721	+	0.353128i
$493$	−7.72606	+	16.9177i	−0.347964	+	0.761936i
$494$	−17.3993	+	5.10890i	−0.782833	+	0.229861i
$495$	−13.4165	+	3.93943i	−0.603026	+	0.177064i
$496$	−16.8653	+	36.9298i	−0.757273	+	1.65820i
$497$	1.91808	+	13.3405i	0.0860377	+	0.598405i
$498$	−3.60020	−	4.15485i	−0.161329	−	0.186183i
$499$	4.85229	+	10.6250i	0.217218	+	0.475642i	0.986602	−	0.163145i	$-0.0521638\pi$
$499$	4.85229	+	10.6250i	0.217218	+	0.475642i	−0.769384	+	0.638787i	$0.779437\pi$
$500$	6.74659	−	4.33577i	0.301717	−	0.193902i
$501$	1.12655	−	7.83533i	0.0503306	−	0.350057i
$502$	−25.8458	−	16.6101i	−1.15356	−	0.741346i
$503$	−25.0799	+	28.9438i	−1.11826	+	1.29054i	−0.165703	+	0.986176i	$0.552989\pi$
$503$	−25.0799	+	28.9438i	−1.11826	+	1.29054i	−0.952556	+	0.304364i	$0.901556\pi$
$504$	−1.92887	−	0.566367i	−0.0859186	−	0.0252280i
$505$	31.6600			1.40885
$506$	−36.0304	+	29.2410i	−1.60175	+	1.29992i
$507$	−3.12824			−0.138930
$508$	5.52736	+	1.62298i	0.245237	+	0.0720081i
$509$	9.73849	−	11.2388i	0.431651	−	0.498152i	−0.497700	−	0.867349i	$-0.665822\pi$
$509$	9.73849	−	11.2388i	0.431651	−	0.498152i	0.929351	+	0.369198i	$0.120367\pi$
$510$	15.2495	+	9.80026i	0.675259	+	0.433963i
$511$	1.90723	−	13.2651i	0.0843708	−	0.586812i
$512$	1.06253	−	0.682845i	0.0469576	−	0.0301778i
$513$	−1.43329	−	3.13846i	−0.0632812	−	0.138566i
$514$	5.10844	+	5.89546i	0.225324	+	0.260037i
$515$	0.490762	+	3.41333i	0.0216256	+	0.150409i
$516$	1.22963	−	2.69252i	0.0541316	−	0.118532i
$517$	17.9719	−	5.27702i	0.790402	−	0.232083i
$518$	10.2266	−	3.00280i	0.449330	−	0.131935i
$519$	8.12621	−	17.7939i	0.356701	−	0.781066i
$520$	2.17303	+	15.1138i	0.0952938	+	0.662783i
$521$	−8.37597	−	9.66638i	−0.366958	−	0.423492i	0.542001	−	0.840378i	$-0.317667\pi$
$521$	−8.37597	−	9.66638i	−0.366958	−	0.423492i	−0.908959	+	0.416886i	$0.863121\pi$
$522$	2.88319	+	6.31329i	0.126194	+	0.276325i
$523$	−23.8416	+	15.3220i	−1.04252	+	0.669986i	−0.945608	−	0.325307i	$-0.894532\pi$
$523$	−23.8416	+	15.3220i	−1.04252	+	0.669986i	−0.0969104	+	0.995293i	$0.530896\pi$
$524$	−1.27220	+	8.84832i	−0.0555762	+	0.386541i
$525$	−0.710091	−	0.456348i	−0.0309909	−	0.0199167i
$526$	9.08762	−	10.4877i	0.396239	−	0.457284i
$527$	35.2096	+	10.3385i	1.53375	+	0.450351i
$528$	28.6852			1.24836
$529$	4.73362	−	22.5076i	0.205810	−	0.978592i
$530$	42.1747			1.83195
$531$	7.18892	+	2.11086i	0.311973	+	0.0916034i
$532$	−1.80357	+	2.08143i	−0.0781947	+	0.0902415i
$533$	26.2029	+	16.8396i	1.13497	+	0.729402i
$534$	3.06041	−	21.2856i	0.132437	−	0.921118i
$535$	−2.84818	+	1.83041i	−0.123137	+	0.0791356i
$536$	−6.52742	−	14.2930i	−0.281941	−	0.617366i
$537$	11.4046	+	13.1616i	0.492145	+	0.567965i
$538$	−6.19306	−	43.0737i	−0.267002	−	1.85704i
$539$	−2.40282	+	5.26143i	−0.103497	+	0.226626i
$540$	1.85154	−	0.543661i	0.0796776	−	0.0233954i
$541$	−21.2225	+	6.23150i	−0.912428	+	0.267913i	−0.704062	−	0.710138i	$-0.748632\pi$
$541$	−21.2225	+	6.23150i	−0.912428	+	0.267913i	−0.208365	+	0.978051i	$0.566814\pi$
$542$	−20.6996	+	45.3257i	−0.889123	+	1.94691i
$543$	0.802000	+	5.57803i	0.0344171	+	0.239376i
$544$	−12.5499	−	14.4834i	−0.538074	−	0.620970i
$545$	−11.5926	−	25.3844i	−0.496574	−	1.08735i
$546$	4.42147	−	2.84151i	0.189221	−	0.121605i
$547$	−3.12624	+	21.7435i	−0.133668	+	0.929684i	0.807047	+	0.590487i	$0.201064\pi$
$547$	−3.12624	+	21.7435i	−0.133668	+	0.929684i	−0.940715	+	0.339197i	$0.889845\pi$
$548$	4.01483	+	2.58018i	0.171505	+	0.110220i
$549$	−5.36141	+	6.18740i	−0.228820	+	0.264072i
$550$	7.83628	+	2.30094i	0.334140	+	0.0981124i
$551$	−14.3153			−0.609850
$552$	−7.48598	+	6.07536i	−0.318625	+	0.258584i
$553$	7.29509			0.310219
$554$	−40.9337	−	12.0192i	−1.73911	−	0.510648i
$555$	10.0868	−	11.6408i	0.428161	−	0.494124i
$556$	−10.4653	−	6.72566i	−0.443829	−	0.285231i
$557$	4.14259	−	28.8124i	0.175527	−	1.22082i	−0.691433	−	0.722441i	$-0.743020\pi$
$557$	4.14259	−	28.8124i	0.175527	−	1.22082i	0.866960	−	0.498378i	$-0.166071\pi$
$558$	11.5202	−	7.40359i	0.487689	−	0.313419i
$559$	−4.83995	−	10.5980i	−0.204708	−	0.448248i
$560$	7.85104	+	9.06058i	0.331767	+	0.382879i
$561$	−3.68992	−	25.6639i	−0.155788	−	1.08353i
$562$	−4.02711	+	8.81814i	−0.169873	+	0.371971i
$563$	−14.2024	+	4.17019i	−0.598558	+	0.175752i	−0.566956	−	0.823748i	$-0.691879\pi$
$563$	−14.2024	+	4.17019i	−0.598558	+	0.175752i	−0.0316019	+	0.999501i	$0.510061\pi$
$564$	−2.48021	+	0.728254i	−0.104435	+	0.0306650i
$565$	3.56406	−	7.80420i	0.149941	−	0.328325i
$566$	−2.96465	−	20.6196i	−0.124613	−	0.866705i
$567$	0.654861	+	0.755750i	0.0275016	+	0.0317385i
$568$	−11.2554	−	24.6458i	−0.472265	−	1.03412i
$569$	32.3271	−	20.7754i	1.35522	−	0.870950i	0.357215	−	0.934022i	$-0.383726\pi$
$569$	32.3271	−	20.7754i	1.35522	−	0.870950i	0.998009	+	0.0630725i	$0.0200899\pi$
$570$	−1.98565	+	13.8105i	−0.0831696	+	0.578457i
$571$	1.18306	+	0.760306i	0.0495095	+	0.0318178i	0.565161	−	0.824980i	$-0.308814\pi$
$571$	1.18306	+	0.760306i	0.0495095	+	0.0318178i	−0.515652	+	0.856798i	$0.672450\pi$
$572$	−9.49987	+	10.9634i	−0.397209	+	0.458404i
$573$	−2.15625	−	0.633131i	−0.0900785	−	0.0264494i
$574$	16.5832			0.692167
$575$	−3.73458	+	1.56205i	−0.155743	+	0.0651420i
$576$	2.76693			0.115289
$577$	−14.2128	−	4.17325i	−0.591686	−	0.173735i	−0.0278367	−	0.999612i	$-0.508862\pi$
$577$	−14.2128	−	4.17325i	−0.591686	−	0.173735i	−0.563849	+	0.825878i	$0.690680\pi$
$578$	−3.38879	+	3.91087i	−0.140955	+	0.162671i
$579$	−10.3365	−	6.64284i	−0.429568	−	0.276067i
$580$	1.13943	−	7.92494i	0.0473124	−	0.329065i
$581$	−2.76479	+	1.77682i	−0.114703	+	0.0737151i
$582$	−0.316246	−	0.692482i	−0.0131088	−	0.0287043i
$583$	−39.5038	−	45.5898i	−1.63608	−	1.88814i
$584$	3.83410	+	26.6667i	0.158656	+	1.10348i
$585$	3.15528	−	6.90910i	0.130455	−	0.285656i
$586$	−14.1834	+	4.16462i	−0.585911	+	0.172039i
$587$	11.3322	−	3.32743i	0.467730	−	0.137338i	−0.0393710	−	0.999225i	$-0.512535\pi$
$587$	11.3322	−	3.32743i	0.467730	−	0.137338i	0.507101	+	0.861887i	$0.330717\pi$
$588$	0.331600	−	0.726104i	0.0136750	−	0.0299440i
$589$	4.01969	+	27.9576i	0.165628	+	1.15197i
$590$	−19.8414	−	22.8982i	−0.816856	−	0.942702i
$591$	3.33802	+	7.30924i	0.137308	+	0.300662i
$592$	−26.5823	+	17.0834i	−1.09253	+	0.702124i
$593$	−1.28213	+	8.91743i	−0.0526509	+	0.366195i	0.946414	+	0.322956i	$0.104677\pi$
$593$	−1.28213	+	8.91743i	−0.0526509	+	0.366195i	−0.999065	+	0.0432387i	$0.986232\pi$
$594$	−8.13969	−	5.23106i	−0.333975	−	0.214633i
$595$	7.09635	−	8.18963i	0.290922	−	0.335742i
$596$	14.6439	+	4.29984i	0.599837	+	0.176128i
$597$	8.21367			0.336163
$598$	0.812644	−	25.1929i	0.0332315	−	1.03021i
$599$	−13.1075			−0.535560			−0.267780	−	0.963480i	$-0.586290\pi$
$599$	−13.1075			−0.535560			−0.267780	+	0.963480i	$0.586290\pi$
$600$	1.62813	+	0.478063i	0.0664682	+	0.0195168i
$601$	11.3515	−	13.1004i	0.463038	−	0.534375i	−0.475424	−	0.879757i	$-0.657705\pi$
$601$	11.3515	−	13.1004i	0.463038	−	0.534375i	0.938462	+	0.345382i	$0.112251\pi$
$602$	−5.21832	−	3.35361i	−0.212683	−	0.136683i
$603$	−1.11237	+	7.73669i	−0.0452992	+	0.315063i
$604$	−11.1983	+	7.19669i	−0.455651	+	0.292829i
$605$	−22.5516	−	49.3811i	−0.916853	−	2.00763i
$606$	14.3464	+	16.5566i	0.582783	+	0.672568i
$607$	−1.63100	−	11.3439i	−0.0662003	−	0.460433i	−0.995777	−	0.0918047i	$-0.970736\pi$
$607$	−1.63100	−	11.3439i	−0.0662003	−	0.460433i	0.929577	−	0.368629i	$-0.120173\pi$
$608$	6.12770	−	13.4178i	0.248511	−	0.544163i
$609$	3.98098	−	1.16892i	0.161317	−	0.0473671i
$610$	31.7668	−	9.32756i	1.28620	−	0.377662i
$611$	−4.22661	+	9.25499i	−0.170990	+	0.374417i
$612$	0.509227	+	3.54175i	0.0205843	+	0.143167i
$613$	−9.18122	−	10.5957i	−0.370826	−	0.427956i	0.539412	−	0.842042i	$-0.318647\pi$
$613$	−9.18122	−	10.5957i	−0.370826	−	0.427956i	−0.910238	+	0.414086i	$0.864101\pi$
$614$	1.75957	+	3.85292i	0.0710105	+	0.155491i
$615$	20.1609	−	12.9566i	0.812966	−	0.522461i
$616$	1.65481	−	11.5095i	0.0666744	−	0.463730i
$617$	28.7407	+	18.4705i	1.15706	+	0.743596i	0.971032	−	0.238949i	$-0.0768028\pi$
$617$	28.7407	+	18.4705i	1.15706	+	0.743596i	0.186026	+	0.982545i	$0.440439\pi$
$618$	−1.56262	+	1.80336i	−0.0628579	+	0.0725419i
$619$	−13.1261	−	3.85417i	−0.527583	−	0.154912i	0.00708447	−	0.999975i	$-0.497745\pi$
$619$	−13.1261	−	3.85417i	−0.527583	−	0.154912i	−0.534667	+	0.845063i	$0.679563\pi$
$620$	−15.7973			−0.634434
$621$	4.76655	−	0.529119i	0.191275	−	0.0212328i
$622$	10.1782			0.408110
$623$	−12.3347	−	3.62179i	−0.494179	−	0.145104i
$624$	−10.2039	+	11.7759i	−0.408483	+	0.471414i
$625$	−23.9824	−	15.4126i	−0.959297	−	0.616503i
$626$	2.81834	−	19.6020i	0.112644	−	0.783453i
$627$	16.7887	−	10.7894i	0.670475	−	0.430888i
$628$	1.35344	+	2.96363i	0.0540082	+	0.118262i
$629$	18.7035	+	21.5850i	0.745758	+	0.860651i
$630$	−0.575507	−	4.00274i	−0.0229288	−	0.159473i
$631$	−6.26801	+	13.7250i	−0.249525	+	0.546384i	−0.992401	−	0.123045i	$-0.960734\pi$
$631$	−6.26801	+	13.7250i	−0.249525	+	0.546384i	0.742876	+	0.669429i	$0.233461\pi$
$632$	−14.0713	+	4.13170i	−0.559725	+	0.164350i
$633$	2.47048	−	0.725400i	0.0981929	−	0.0288320i
$634$	5.98382	−	13.1027i	0.237648	−	0.520376i
$635$	−2.48286	−	17.2686i	−0.0985292	−	0.685285i
$636$	5.45172	+	6.29161i	0.216175	+	0.249479i
$637$	−1.30521	−	2.85800i	−0.0517142	−	0.113238i
$638$	−33.7719	+	21.7039i	−1.33704	+	0.859265i
$639$	−1.91808	+	13.3405i	−0.0758781	+	0.527744i
$640$	−26.8021	−	17.2247i	−1.05945	−	0.680866i
$641$	−19.2445	+	22.2093i	−0.760112	+	0.877216i	−0.995507	−	0.0946836i	$-0.969816\pi$
$641$	−19.2445	+	22.2093i	−0.760112	+	0.877216i	0.235395	+	0.971900i	$0.424362\pi$
$642$	−2.24784	−	0.660026i	−0.0887153	−	0.0260492i
$643$	−11.4676			−0.452237			−0.226118	−	0.974100i	$-0.572604\pi$
$643$	−11.4676			−0.452237			−0.226118	+	0.974100i	$0.572604\pi$
$644$	−1.96479	−	3.28556i	−0.0774234	−	0.129469i
$645$	−8.96436			−0.352971
$646$	−24.8235	−	7.28884i	−0.976668	−	0.286776i
$647$	−1.36849	+	1.57933i	−0.0538011	+	0.0620898i	−0.782012	−	0.623263i	$-0.785807\pi$
$647$	−1.36849	+	1.57933i	−0.0538011	+	0.0620898i	0.728211	+	0.685353i	$0.240352\pi$
$648$	−1.69117	−	1.08685i	−0.0664355	−	0.0426955i
$649$	−6.16752	+	42.8960i	−0.242096	+	1.68382i
$650$	−3.73211	+	2.39848i	−0.146385	+	0.0940761i
$651$	−3.40074	−	7.44658i	−0.133285	−	0.291854i
$652$	4.54138	+	5.24103i	0.177854	+	0.205255i
$653$	−5.97342	−	41.5461i	−0.233758	−	1.62582i	−0.681610	−	0.731716i	$-0.738720\pi$
$653$	−5.97342	−	41.5461i	−0.233758	−	1.62582i	0.447852	−	0.894108i	$-0.352189\pi$
$654$	8.02171	−	17.5651i	0.313673	−	0.686849i
$655$	25.9759	−	7.62723i	1.01496	−	0.298020i
$656$	−47.1722	+	13.8510i	−1.84177	+	0.540791i
$657$	5.56717	−	12.1904i	0.217196	−	0.475593i
$658$	0.770913	+	5.36182i	0.0300533	+	0.209025i
$659$	9.54179	+	11.0118i	0.371695	+	0.428959i	0.910524	−	0.413456i	$-0.135678\pi$
$659$	9.54179	+	11.0118i	0.371695	+	0.428959i	−0.538829	+	0.842415i	$0.681133\pi$
$660$	4.63673	+	10.1530i	0.180484	+	0.395206i
$661$	39.0720	−	25.1100i	1.51972	−	0.976667i	0.527864	−	0.849329i	$-0.322993\pi$
$661$	39.0720	−	25.1100i	1.51972	−	0.976667i	0.991859	−	0.127338i	$-0.0406431\pi$
$662$	−1.25382	+	8.72054i	−0.0487313	+	0.338933i
$663$	11.8482	+	7.61437i	0.460146	+	0.295718i
$664$	4.32658	−	4.99314i	0.167904	−	0.193772i
$665$	8.00297	+	2.34988i	0.310342	+	0.0911246i
$666$	10.6583			0.413001
$667$	6.21856	−	18.9014i	0.240784	−	0.731867i
$668$	−6.31878			−0.244481
$669$	−7.35641	−	2.16004i	−0.284415	−	0.0835119i
$670$	20.6989	−	23.8879i	0.799670	−	0.922869i
$671$	−39.8378	−	25.6022i	−1.53792	−	0.988363i
$672$	−0.608435	+	4.23176i	−0.0234709	+	0.163244i
$673$	−22.5081	+	14.4651i	−0.867622	+	0.557587i	−0.897025	−	0.441981i	$-0.854276\pi$
$673$	−22.5081	+	14.4651i	−0.867622	+	0.557587i	0.0294022	+	0.999568i	$0.490640\pi$
$674$	13.4793	+	29.5155i	0.519203	+	1.13690i
$675$	−0.552760	−	0.637919i	−0.0212757	−	0.0245535i
$676$	0.355372	+	2.47167i	0.0136682	+	0.0950641i
$677$	19.3441	−	42.3577i	0.743455	−	1.62794i	−0.0343316	−	0.999410i	$-0.510930\pi$
$677$	19.3441	−	42.3577i	0.743455	−	1.62794i	0.777787	−	0.628529i	$-0.216342\pi$
$678$	5.69624	−	1.67257i	0.218763	−	0.0642345i
$679$	−0.436659	+	0.128215i	−0.0167574	+	0.00492043i
$680$	−9.04959	+	19.8158i	−0.347036	+	0.759903i
$681$	3.65002	+	25.3864i	0.139869	+	0.972810i
$682$	51.8706	+	59.8618i	1.98623	+	2.29223i
$683$	16.9060	+	37.0190i	0.646890	+	1.41649i	0.894250	+	0.447567i	$0.147710\pi$
$683$	16.9060	+	37.0190i	0.646890	+	1.41649i	−0.247360	+	0.968924i	$0.579563\pi$
$684$	−2.31692	+	1.48899i	−0.0885896	+	0.0569331i
$685$	2.05691	−	14.3061i	0.0785906	−	0.546610i
$686$	−1.40724	−	0.904381i	−0.0537288	−	0.0345294i
$687$	−4.08418	+	4.71340i	−0.155821	+	0.179827i
$688$	17.6450	+	5.18105i	0.672711	+	0.197526i
$689$	32.7679			1.24836
$690$	−17.3724	−	8.62108i	−0.661355	−	0.328199i
$691$	15.5759			0.592536			0.296268	−	0.955105i	$-0.404258\pi$
$691$	15.5759			0.592536			0.296268	+	0.955105i	$0.404258\pi$
$692$	−14.9824	−	4.39922i	−0.569544	−	0.167233i
$693$	−3.78780	+	4.37136i	−0.143887	+	0.166054i
$694$	−46.2949	−	29.7519i	−1.75733	−	1.12937i
$695$	−5.36169	+	37.2914i	−0.203380	+	1.41454i
$696$	−7.01674	+	4.50939i	−0.265969	+	0.170928i
$697$	18.4601	+	40.4221i	0.699227	+	1.53109i
$698$	13.5480	+	15.6353i	0.512801	+	0.591804i
$699$	−3.95591	−	27.5139i	−0.149626	−	1.04067i
$700$	−0.279900	+	0.612895i	−0.0105792	+	0.0231652i
$701$	41.1693	−	12.0884i	1.55494	−	0.456573i	0.612371	−	0.790571i	$-0.290216\pi$
$701$	41.1693	−	12.0884i	1.55494	−	0.456573i	0.942574	+	0.333998i	$0.108398\pi$
$702$	5.04291	−	1.48073i	0.190332	−	0.0558867i
$703$	−9.13229	+	19.9969i	−0.344431	+	0.754198i
$704$	2.27765	+	15.8414i	0.0858421	+	0.597045i
$705$	5.12649	+	5.91629i	0.193075	+	0.222820i
$706$	−18.9427	−	41.4788i	−0.712920	−	1.56108i
$707$	11.0174	−	7.08045i	0.414352	−	0.266288i
$708$	0.851148	−	5.91986i	0.0319881	−	0.222482i
$709$	42.4976	+	27.3116i	1.59603	+	1.02571i	0.969111	+	0.246623i	$0.0793209\pi$
$709$	42.4976	+	27.3116i	1.59603	+	1.02571i	0.626920	+	0.779084i	$0.284315\pi$
$710$	35.6916	−	41.1904i	1.33948	−	1.54585i
$711$	6.99959	+	2.05527i	0.262505	+	0.0770785i
$712$	25.8432			0.968517
$713$	−38.6605	−	6.83731i	−1.44785	−	0.256059i
$714$	7.49843			0.280622
$715$	42.1537	+	12.3774i	1.57646	+	0.462890i
$716$	9.10359	−	10.5061i	0.340217	−	0.392631i
$717$	18.4166	+	11.8356i	0.687781	+	0.442010i
$718$	2.95797	−	20.5731i	0.110390	−	0.767782i
$719$	−8.60561	+	5.53049i	−0.320935	+	0.206252i	−0.691182	−	0.722681i	$-0.742910\pi$
$719$	−8.60561	+	5.53049i	−0.320935	+	0.206252i	0.370247	+	0.928933i	$0.379273\pi$
$720$	4.98035	+	10.9055i	0.185607	+	0.406422i
$721$	0.934140	+	1.07805i	0.0347892	+	0.0401488i
$722$	1.68924	+	11.7489i	0.0628669	+	0.437249i
$723$	−5.35650	+	11.7291i	−0.199211	+	0.436210i
$724$	4.31617	−	1.26734i	0.160409	−	0.0471004i
$725$	−3.36029	+	0.986671i	−0.124798	+	0.0366440i
$726$	15.6049	−	34.1700i	0.579153	−	1.26817i
$727$	1.27600	+	8.87479i	0.0473243	+	0.329148i	0.999706	+	0.0242400i	$0.00771659\pi$
$727$	1.27600	+	8.87479i	0.0473243	+	0.329148i	−0.952382	+	0.304908i	$0.901374\pi$
$728$	4.13625	+	4.77349i	0.153300	+	0.176917i
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$	−45.5911	+	29.2996i	−1.68740	+	1.08443i
$731$	2.36559	−	16.4530i	0.0874944	−	0.608537i
$732$	5.49781	+	3.53323i	0.203205	+	0.130592i
$733$	9.54378	−	11.0141i	0.352507	−	0.406815i	−0.551608	−	0.834103i	$-0.685986\pi$
$733$	9.54378	−	11.0141i	0.352507	−	0.406815i	0.904116	+	0.427288i	$0.140531\pi$
$734$	1.73698	+	0.510022i	0.0641129	+	0.0188253i
$735$	−2.41745			−0.0891692
$736$	15.0546	+	13.9195i	0.554919	+	0.513081i
$737$	−45.2103			−1.66534
$738$	15.9114	+	4.67201i	0.585707	+	0.171979i
$739$	−17.4020	+	20.0830i	−0.640142	+	0.738764i	−0.979400	−	0.201930i	$-0.935279\pi$
$739$	−17.4020	+	20.0830i	−0.640142	+	0.738764i	0.339258	+	0.940693i	$0.389824\pi$
$740$	−10.3434	−	6.64732i	−0.380232	−	0.244360i
$741$	−1.54276	+	10.7301i	−0.0566747	+	0.394181i
$742$	14.6764	−	9.43197i	0.538789	−	0.346259i
$743$	−4.80275	−	10.5166i	−0.176196	−	0.385815i	0.800844	−	0.598874i	$-0.204385\pi$
$743$	−4.80275	−	10.5166i	−0.176196	−	0.385815i	−0.977039	+	0.213058i	$0.931658\pi$
$744$	10.7771	+	12.4374i	0.395106	+	0.455977i
$745$	−6.57795	−	45.7506i	−0.240997	−	1.67617i
$746$	16.6496	−	36.4575i	0.609584	−	1.33480i
$747$	−3.15339	+	0.925918i	−0.115376	+	0.0338776i
$748$	−19.8583	+	5.83091i	−0.726090	+	0.213199i
$749$	−0.581787	+	1.27394i	−0.0212580	+	0.0465486i
$750$	−2.39176	−	16.6350i	−0.0873347	−	0.607426i
$751$	−15.5486	−	17.9441i	−0.567378	−	0.654789i	0.397465	−	0.917618i	$-0.369890\pi$
$751$	−15.5486	−	17.9441i	−0.567378	−	0.654789i	−0.964843	+	0.262828i	$0.915345\pi$
$752$	−6.67137	−	14.6083i	−0.243280	−	0.532708i
$753$	−15.4507	+	9.92957i	−0.563055	+	0.361854i
$754$	3.10340	−	21.5846i	0.113019	−	0.786066i
$755$	33.9138	+	21.7951i	1.23425	+	0.793204i
$756$	0.522735	−	0.603269i	0.0190117	−	0.0219407i
$757$	−31.3440	−	9.20344i	−1.13922	−	0.334505i	−0.342894	−	0.939374i	$-0.611407\pi$
$757$	−31.3440	−	9.20344i	−1.13922	−	0.334505i	−0.796325	+	0.604869i	$0.793225\pi$
$758$	39.1312			1.42131
$759$	6.95302	+	26.8542i	0.252379	+	0.974746i
$760$	−16.7676			−0.608224
$761$	−17.5423	−	5.15088i	−0.635907	−	0.186719i	−0.0521395	−	0.998640i	$-0.516604\pi$
$761$	−17.5423	−	5.15088i	−0.635907	−	0.186719i	−0.583768	+	0.811921i	$0.698422\pi$
$762$	7.90559	−	9.12354i	0.286389	−	0.330511i
$763$	−9.71111	−	6.24095i	−0.351566	−	0.225938i
$764$	−0.255293	+	1.77561i	−0.00923619	+	0.0642391i
$765$	9.11619	−	5.85862i	0.329596	−	0.211819i
$766$	16.4927	+	36.1140i	0.595905	+	1.30485i
$767$	−15.4159	−	17.7909i	−0.556635	−	0.642391i
$768$	−2.34990	−	16.3439i	−0.0847947	−	0.589760i
$769$	−16.6928	+	36.5521i	−0.601957	+	1.31810i	0.325984	+	0.945375i	$0.394304\pi$
$769$	−16.6928	+	36.5521i	−0.601957	+	1.31810i	−0.927941	+	0.372727i	$0.878423\pi$
$770$	22.4430	−	6.58986i	0.808790	−	0.237482i
$771$	4.47444	−	1.31382i	0.161143	−	0.0473159i
$772$	−4.07436	+	8.92161i	−0.146640	+	0.321096i
$773$	0.980635	+	6.82047i	0.0352710	+	0.245315i	0.999828	−	0.0185603i	$-0.00590827\pi$
$773$	0.980635	+	6.82047i	0.0352710	+	0.245315i	−0.964557	+	0.263876i	$0.914999\pi$
$774$	−4.06212	−	4.68793i	−0.146010	−	0.168504i
$775$	2.87052	+	6.28556i	0.103112	+	0.225784i
$776$	0.769641	−	0.494618i	0.0276285	−	0.0177558i
$777$	0.906769	−	6.30671i	0.0325301	−	0.226252i
$778$	−29.9577	−	19.2526i	−1.07403	−	0.690240i
$779$	−22.3988	+	25.8496i	−0.802520	+	0.926158i
$780$	−5.81742	−	1.70815i	−0.208297	−	0.0611615i
$781$	−77.9570			−2.78952
$782$	20.4073	−	29.6100i	0.729765	−	1.05885i
$783$	4.14904			0.148275
$784$	4.75841	+	1.39719i	0.169943	+	0.0498998i
$785$	6.46148	−	7.45694i	0.230620	−	0.266150i
$786$	15.7594	+	10.1280i	0.562120	+	0.361253i
$787$	−0.00390466	+	0.0271575i	−0.000139186	+	0.000968061i	−0.989891	−	0.141831i	$-0.954701\pi$
$787$	−0.00390466	+	0.0271575i	−0.000139186	+	0.000968061i	0.989752	+	0.142799i	$0.0456102\pi$
$788$	5.39593	−	3.46776i	0.192222	−	0.123534i
$789$	−3.44620	−	7.54613i	−0.122688	−	0.268649i
$790$	−19.3188	−	22.2951i	−0.687333	−	0.793224i
$791$	−0.505073	−	3.51286i	−0.0179583	−	0.124903i
$792$	4.83038	−	10.5771i	0.171640	−	0.375839i
$793$	24.6814	−	7.24711i	0.876461	−	0.257352i
$794$	4.95789	−	1.45577i	0.175949	−	0.0516633i
$795$	10.4735	−	22.9338i	0.371457	−	0.813377i
$796$	−0.933084	−	6.48974i	−0.0330723	−	0.230023i
$797$	10.9973	+	12.6915i	0.389544	+	0.449557i	0.916320	−	0.400447i	$-0.131145\pi$
$797$	10.9973	+	12.6915i	0.389544	+	0.449557i	−0.526777	+	0.850004i	$0.676600\pi$
$798$	2.39759	+	5.25000i	0.0848739	+	0.185848i
$799$	−12.2115	+	7.84783i	−0.432011	+	0.277636i
$800$	0.513572	−	3.57197i	0.0181575	−	0.126288i
$801$	−10.8147	−	6.95017i	−0.382118	−	0.245572i
$802$	32.5667	−	37.5839i	1.14997	−	1.32713i
$803$	74.3760	+	21.8388i	2.62467	+	0.770673i
$804$	6.23924			0.220041
$805$	−6.57922	+	9.54609i	−0.231887	+	0.336456i
$806$	−43.0260			−1.51553
$807$	−24.9606	−	7.32909i	−0.878654	−	0.257996i
$808$	−17.2410	+	19.8971i	−0.606535	+	0.699978i
$809$	7.55062	+	4.85249i	0.265466	+	0.170604i	0.666602	−	0.745414i	$-0.267748\pi$
$809$	7.55062	+	4.85249i	0.265466	+	0.170604i	−0.401136	+	0.916018i	$0.631385\pi$
$810$	0.575507	−	4.00274i	0.0202213	−	0.140642i
$811$	5.77362	−	3.71048i	0.202739	−	0.130293i	−0.435332	−	0.900270i	$-0.643369\pi$
$811$	5.77362	−	3.71048i	0.202739	−	0.130293i	0.638071	+	0.769977i	$0.279733\pi$
$812$	−1.37582	−	3.01264i	−0.0482820	−	0.105723i
$813$	19.5068	+	22.5120i	0.684133	+	0.789531i
$814$	8.77359	+	61.0217i	0.307514	+	2.13881i
$815$	8.72462	−	19.1042i	0.305610	−	0.669192i
$816$	−21.3299	+	6.26303i	−0.746697	+	0.219250i
$817$	12.2759	−	3.60453i	0.429480	−	0.126107i
$818$	−9.17411	+	20.0885i	−0.320765	+	0.702378i
$819$	−0.447144	−	3.10996i	−0.0156245	−	0.108671i
$820$	−12.5275	−	14.4575i	−0.437480	−	0.504878i
$821$	−3.32530	−	7.28139i	−0.116054	−	0.254122i	0.842687	−	0.538403i	$-0.180972\pi$
$821$	−3.32530	−	7.28139i	−0.116054	−	0.254122i	−0.958741	+	0.284281i	$0.908245\pi$
$822$	8.41350	−	5.40703i	0.293455	−	0.188592i
$823$	4.09938	−	28.5118i	0.142896	−	0.993860i	−0.784594	−	0.620010i	$-0.787128\pi$
$823$	4.09938	−	28.5118i	0.142896	−	0.993860i	0.927489	−	0.373850i	$-0.121962\pi$
$824$	−2.41241	−	1.55036i	−0.0840401	−	0.0540093i
$825$	3.19724	−	3.68981i	0.111313	−	0.128463i
$826$	−12.0256	−	3.53103i	−0.418423	−	0.122860i
$827$	−9.88421			−0.343708			−0.171854	−	0.985122i	$-0.554976\pi$
$827$	−9.88421			−0.343708			−0.171854	+	0.985122i	$0.554976\pi$
$828$	−0.959551	−	3.70601i	−0.0333467	−	0.128793i
$829$	−1.00608			−0.0349425			−0.0174713	−	0.999847i	$-0.505562\pi$
$829$	−1.00608			−0.0349425			−0.0174713	+	0.999847i	$0.505562\pi$
$830$	12.7520	+	3.74432i	0.442628	+	0.129967i
$831$	−16.7011	+	19.2741i	−0.579356	+	0.668612i
$832$	−7.31345	−	4.70007i	−0.253548	−	0.162946i
$833$	0.637938	−	4.43695i	0.0221032	−	0.153731i
$834$	−21.9312	+	14.0943i	−0.759415	+	0.488047i
$835$	7.94952	+	17.4070i	0.275105	+	0.602395i
$836$	−10.4321	−	12.0393i	−0.360801	−	0.416387i
$837$	−1.16504	−	8.10304i	−0.0402697	−	0.280082i
$838$	18.9203	−	41.4297i	0.653591	−	1.43116i
$839$	−27.2054	+	7.98823i	−0.939235	+	0.275784i	−0.715298	−	0.698819i	$-0.753709\pi$
$839$	−27.2054	+	7.98823i	−0.939235	+	0.275784i	−0.223937	+	0.974604i	$0.571891\pi$
$840$	4.66295	−	1.36917i	0.160887	−	0.0472407i
$841$	−4.89585	+	10.7204i	−0.168822	+	0.369669i
$842$	−3.74523	−	26.0486i	−0.129069	−	0.897695i
$843$	3.79505	+	4.37972i	0.130709	+	0.150846i
$844$	−0.853798	−	1.86956i	−0.0293890	−	0.0643528i
$845$	6.36188	−	4.08853i	0.218855	−	0.140650i
$846$	−0.770913	+	5.36182i	−0.0265045	+	0.184343i
$847$	−18.8914	−	12.1408i	−0.649115	−	0.417161i
$848$	−33.8704	+	39.0885i	−1.16311	+	1.34230i
$849$	−11.9487	−	3.50847i	−0.410080	−	0.120410i
$850$	−6.32933			−0.217094
$851$	−22.4363	−	20.7447i	−0.769105	−	0.711119i
$852$	10.7585			0.368578
$853$	11.2663	+	3.30808i	0.385751	+	0.113267i	0.468857	−	0.883274i	$-0.344666\pi$
$853$	11.2663	+	3.30808i	0.385751	+	0.113267i	−0.0831063	+	0.996541i	$0.526484\pi$
$854$	8.96854	−	10.3502i	0.306897	−	0.354178i
$855$	7.01676	+	4.50940i	0.239968	+	0.154218i
$856$	0.400675	−	2.78676i	0.0136948	−	0.0952494i
$857$	−17.0437	+	10.9533i	−0.582200	+	0.374158i	−0.798342	−	0.602205i	$-0.794289\pi$
$857$	−17.0437	+	10.9533i	−0.582200	+	0.374158i	0.216141	+	0.976362i	$0.430653\pi$
$858$	12.6287	+	27.6531i	0.431138	+	0.944061i
$859$	−12.3166	−	14.2141i	−0.420237	−	0.484979i	0.505672	−	0.862726i	$-0.331245\pi$
$859$	−12.3166	−	14.2141i	−0.420237	−	0.484979i	−0.925909	+	0.377746i	$0.876699\pi$
$860$	1.01836	+	7.08287i	0.0347259	+	0.241524i
$861$	4.11819	−	9.01759i	0.140348	−	0.307319i
$862$	−21.5794	+	6.33630i	−0.734999	+	0.215815i
$863$	−32.6546	+	9.58826i	−1.11158	+	0.326388i	−0.785442	−	0.618935i	$-0.787564\pi$
$863$	−32.6546	+	9.58826i	−1.11158	+	0.326388i	−0.326134	+	0.945323i	$0.605746\pi$
$864$	−1.77601	+	3.88893i	−0.0604212	+	0.132304i
$865$	6.72999	+	46.8081i	0.228827	+	1.59152i
$866$	20.1580	+	23.2636i	0.684997	+	0.790528i
$867$	1.28509	+	2.81396i	0.0436441	+	0.0955672i
$868$	−5.49732	+	3.53291i	−0.186591	+	0.119915i
$869$	−6.00509	+	41.7663i	−0.203709	+	1.41683i
$870$	−14.1148	−	9.07105i	−0.478537	−	0.307537i
$871$	16.0822	−	18.5598i	0.544924	−	0.628876i
$872$	22.2661	+	6.53792i	0.754026	+	0.221402i
$873$	−0.455093			−0.0154026
$874$	27.2565	+	4.82045i	0.921964	+	0.163054i
$875$	−10.0467			−0.339641
$876$	−10.2643	−	3.01386i	−0.346797	−	0.101829i
$877$	16.8096	−	19.3993i	0.567619	−	0.655067i	−0.397277	−	0.917699i	$-0.630045\pi$
$877$	16.8096	−	19.3993i	0.567619	−	0.655067i	0.964896	+	0.262631i	$0.0845903\pi$
$878$	−40.0870	−	25.7623i	−1.35287	−	0.869436i
$879$	−1.25761	+	8.74688i	−0.0424182	+	0.295025i
$880$	−58.3369	+	37.4909i	−1.96654	+	1.26382i
$881$	−10.5155	−	23.0256i	−0.354275	−	0.775753i	−0.999927	−	0.0121213i	$-0.996142\pi$
$881$	−10.5155	−	23.0256i	−0.354275	−	0.775753i	0.645652	−	0.763632i	$-0.276586\pi$
$882$	−1.09545	−	1.26421i	−0.0368856	−	0.0425683i
$883$	−4.13008	−	28.7253i	−0.138988	−	0.966684i	−0.933281	−	0.359148i	$-0.883067\pi$
$883$	−4.13008	−	28.7253i	−0.138988	−	0.966684i	0.794292	−	0.607536i	$-0.207842\pi$
$884$	4.67025	−	10.2264i	0.157078	−	0.343952i
$885$	−17.3789	+	5.10290i	−0.584185	+	0.171532i
$886$	−41.4110	+	12.1594i	−1.39123	+	0.408502i
$887$	0.0430357	−	0.0942350i	0.00144500	−	0.00316410i	−0.908908	−	0.416996i	$-0.863083\pi$
$887$	0.0430357	−	0.0942350i	0.00144500	−	0.00316410i	0.910353	+	0.413832i	$0.135810\pi$
$888$	1.82288	+	12.6784i	0.0611717	+	0.425458i
$889$	−4.72598	−	5.45407i	−0.158504	−	0.182924i
$890$	21.5958	+	47.2882i	0.723893	+	1.58511i
$891$	−4.86592	+	3.12714i	−0.163015	+	0.104763i
$892$	−0.870978	+	6.05779i	−0.0291625	+	0.202830i
$893$	−9.39920	−	6.04050i	−0.314532	−	0.202138i
$894$	20.9447	−	24.1714i	0.700494	−	0.808414i
$895$	−40.3953	−	11.8611i	−1.35027	−	0.396474i
$896$	−13.1791			−0.440281
$897$	−13.4976	−	6.69820i	−0.450671	−	0.223646i
$898$	−16.7544			−0.559103
$899$	−32.5897	−	9.56921i	−1.08693	−	0.319151i
$900$	−0.441234	+	0.509211i	−0.0147078	+	0.0169737i
$901$	39.3284	+	25.2748i	1.31022	+	0.842027i
$902$	−13.6507	+	94.9429i	−0.454519	+	3.16125i
$903$	−3.11952	+	2.00479i	−0.103811	+	0.0667154i
$904$	2.96379	+	6.48979i	0.0985741	+	0.215847i
$905$	−8.92137	−	10.2958i	−0.296556	−	0.342244i
$906$	3.96994	+	27.6115i	0.131892	+	0.917332i
$907$	12.2275	−	26.7745i	0.406007	−	0.889032i	−0.590618	−	0.806951i	$-0.701116\pi$
$907$	12.2275	−	26.7745i	0.406007	−	0.889032i	0.996626	−	0.0820809i	$-0.0261566\pi$
$908$	19.6435	−	5.76786i	0.651893	−	0.191413i
$909$	12.5659	−	3.68968i	0.416785	−	0.122379i
$910$	−5.27813	+	11.5575i	−0.174968	+	0.383127i
$911$	−3.55023	−	24.6924i	−0.117624	−	0.818096i	−0.960159	−	0.279454i	$-0.909847\pi$
$911$	−3.55023	−	24.6924i	−0.117624	−	0.818096i	0.842535	−	0.538642i	$-0.181062\pi$
$912$	−11.2052	−	12.9315i	−0.371041	−	0.428205i
$913$	−7.89689	−	17.2918i	−0.261349	−	0.572274i
$914$	46.8712	−	30.1223i	1.55036	−	0.996357i
$915$	2.81669	−	19.5905i	0.0931169	−	0.647642i
$916$	4.18809	+	2.69152i	0.138378	+	0.0889304i
$917$	7.33365	−	8.46348i	0.242178	−	0.279489i
$918$	7.19469	+	2.11255i	0.237460	+	0.0697246i
$919$	34.1463			1.12638			0.563192	−	0.826326i	$-0.309573\pi$
$919$	34.1463			1.12638			0.563192	+	0.826326i	$0.309573\pi$
$920$	7.28385	−	22.1394i	0.240141	−	0.729914i
$921$	2.53211			0.0834358
$922$	−45.4700	−	13.3512i	−1.49747	−	0.439698i
$923$	27.7308	−	32.0031i	0.912772	−	1.05339i
$924$	3.88417	+	2.49620i	0.127780	+	0.0821191i
$925$	−0.765392	+	5.32342i	−0.0251659	+	0.175033i
$926$	12.4322	−	7.98966i	0.408546	−	0.262557i
$927$	0.592577	+	1.29756i	0.0194628	+	0.0426176i
$928$	11.6161	+	13.4057i	0.381318	+	0.440064i
$929$	−5.50364	−	38.2787i	−0.180569	−	1.25588i	−0.855423	−	0.517931i	$-0.826702\pi$
$929$	−5.50364	−	38.2787i	−0.180569	−	1.25588i	0.674854	−	0.737951i	$-0.264207\pi$
$930$	−13.7523	+	30.1132i	−0.450954	+	0.987452i
$931$	3.31050	−	0.972049i	0.108497	−	0.0318576i
$932$	−21.2897	+	6.25123i	−0.697369	+	0.204766i
$933$	2.52762	−	5.53473i	0.0827507	−	0.181199i
$934$	0.0206481	+	0.143611i	0.000675626	+	0.00469908i
$935$	41.0463	+	47.3699i	1.34236	+	1.54916i
$936$	2.62386	+	5.74544i	0.0857634	+	0.187796i
$937$	38.0192	−	24.4335i	1.24203	−	0.798206i	0.256312	−	0.966594i	$-0.417492\pi$
$937$	38.0192	−	24.4335i	1.24203	−	0.798206i	0.985721	+	0.168388i	$0.0538561\pi$
$938$	1.86076	−	12.9419i	0.0607561	−	0.422568i
$939$	−9.95928	−	6.40044i	−0.325009	−	0.208870i
$940$	4.09216	−	4.72261i	0.133472	−	0.154035i
$941$	25.7688	+	7.56640i	0.840039	+	0.246658i	0.673324	−	0.739348i	$-0.264866\pi$
$941$	25.7688	+	7.56640i	0.840039	+	0.246658i	0.166715	+	0.986005i	$0.446684\pi$
$942$	6.82758			0.222455
$943$	−24.4010	−	40.8038i	−0.794605	−	1.32875i
$944$	37.1571			1.20936
$945$	−2.31953	−	0.681076i	−0.0754543	−	0.0221554i
$946$	23.4958	−	27.1156i	0.763915	−	0.881605i
$947$	−39.4919	−	25.3799i	−1.28331	−	0.824736i	−0.292022	−	0.956412i	$-0.594328\pi$
$947$	−39.4919	−	25.3799i	−1.28331	−	0.824736i	−0.991293	+	0.131675i	$0.957964\pi$
$948$	0.828732	−	5.76395i	0.0269160	−	0.187205i
$949$	−35.4223	+	22.7645i	−1.14986	+	0.738968i
$950$	−2.02378	−	4.43146i	−0.0656601	−	0.143775i
$951$	−5.63901	−	6.50776i	−0.182857	−	0.211029i
$952$	1.28244	+	8.91960i	0.0415643	+	0.289086i
$953$	0.302813	−	0.663068i	0.00980908	−	0.0214789i	−0.904664	−	0.426125i	$-0.859878\pi$
$953$	0.302813	−	0.663068i	0.00980908	−	0.0214789i	0.914473	+	0.404647i	$0.132605\pi$
$954$	16.7392	−	4.91508i	0.541953	−	0.159132i
$955$	5.21263	−	1.53057i	0.168677	−	0.0495280i
$956$	7.25936	−	15.8958i	0.234784	−	0.514106i
$957$	3.41536	+	23.7544i	0.110403	+	0.767869i
$958$	−17.6267	−	20.3423i	−0.569492	−	0.657228i
$959$	−2.48365	−	5.43843i	−0.0802011	−	0.175616i
$960$	−5.62708	+	3.61631i	−0.181613	+	0.116716i
$961$	−5.12569	+	35.6500i	−0.165345	+	1.15000i
$962$	−28.1717	−	18.1048i	−0.908292	−	0.583724i
$963$	−0.917130	+	1.05842i	−0.0295541	+	0.0341072i
$964$	9.87584	+	2.89981i	0.318079	+	0.0933965i
$965$	29.7032			0.956179
$966$	−7.97346	+	0.885107i	−0.256542	+	0.0284778i
$967$	18.2681			0.587463			0.293731	−	0.955888i	$-0.405103\pi$
$967$	18.2681			0.587463			0.293731	+	0.955888i	$0.405103\pi$
$968$	43.3151	+	12.7185i	1.39220	+	0.408787i
$969$	−10.1281	+	11.6885i	−0.325362	+	0.375487i
$970$	1.54820	+	0.994970i	0.0497098	+	0.0319466i
$971$	5.23316	−	36.3974i	0.167940	−	1.16805i	−0.715193	−	0.698927i	$-0.753661\pi$
$971$	5.23316	−	36.3974i	0.167940	−	1.16805i	0.883133	−	0.469123i	$-0.155430\pi$
$972$	0.671521	−	0.431561i	0.0215391	−	0.0138423i
$973$	6.47404	+	14.1762i	0.207548	+	0.454467i
$974$	9.26401	+	10.6912i	0.296838	+	0.342569i
$975$	0.377429	+	2.62507i	0.0120874	+	0.0840696i
$976$	−16.8668	+	36.9331i	−0.539893	+	1.18220i
$977$	22.8272	−	6.70267i	0.730307	−	0.214438i	0.104621	−	0.994512i	$-0.466637\pi$
$977$	22.8272	−	6.70267i	0.730307	−	0.214438i	0.625686	+	0.780075i	$0.284819\pi$
$978$	13.9441	−	4.09435i	0.445883	−	0.130923i
$979$	30.8892	−	67.6380i	0.987224	−	2.16172i
$980$	0.274626	+	1.91006i	0.00877260	+	0.0610148i
$981$	−7.55947	−	8.72409i	−0.241355	−	0.278539i
$982$	−1.33839	−	2.93067i	−0.0427098	−	0.0935215i
$983$	−31.8122	+	20.4445i	−1.01465	+	0.652077i	−0.938593	−	0.345026i	$-0.887870\pi$
$983$	−31.8122	+	20.4445i	−1.01465	+	0.652077i	−0.0760591	+	0.997103i	$0.524234\pi$
$984$	−2.83619	+	19.7261i	−0.0904144	+	0.628846i
$985$	−16.3415	−	10.5020i	−0.520684	−	0.334623i
$986$	20.3736	−	23.5124i	0.648827	−	0.748786i
$987$	3.10710	+	0.912326i	0.0989000	+	0.0290397i
$988$	8.65329			0.275298
$989$	−0.573352	+	17.7746i	−0.0182315	+	0.565198i
$990$	23.3905			0.743398
$991$	44.2070	+	12.9804i	1.40428	+	0.412335i	0.894153	−	0.447762i	$-0.147779\pi$
$991$	44.2070	+	12.9804i	1.40428	+	0.412335i	0.510130	+	0.860097i	$0.329597\pi$
$992$	22.9195	−	26.4505i	0.727693	−	0.839803i
$993$	4.43069	+	2.84743i	0.140604	+	0.0903604i
$994$	3.20855	−	22.3160i	0.101769	−	0.707820i
$995$	−16.7041	+	10.7351i	−0.529555	+	0.340324i
$996$	1.08981	+	2.38635i	0.0345319	+	0.0756144i
$997$	11.7170	+	13.5222i	0.371082	+	0.428251i	0.910322	−	0.413901i	$-0.135834\pi$
$997$	11.7170	+	13.5222i	0.371082	+	0.428251i	−0.539240	+	0.842152i	$0.681289\pi$
$998$	−2.78072	−	19.3403i	−0.0880221	−	0.612207i
$999$	2.64684	−	5.79578i	0.0837425	−	0.183370i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.f.64.3	✓	80
23.9	even	11	inner	483.2.q.f.400.3	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.f.64.3	✓	80	1.1	even	1	trivial
483.2.q.f.400.3	yes	80	23.9	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)

\(f(q)\)	\(=\)	\(q+(-1.60503 - 0.471280i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.671521 + 0.431561i) q^{4} +(0.344040 - 2.39285i) q^{5} +(1.40724 - 0.904381i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(1.31647 + 1.51928i) q^{8} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-1.60503 - 0.471280i) q^{2} +(-0.654861 + 0.755750i) q^{3} +(0.671521 + 0.431561i) q^{4} +(0.344040 - 2.39285i) q^{5} +(1.40724 - 0.904381i) q^{6} +(-0.415415 - 0.909632i) q^{7} +(1.31647 + 1.51928i) q^{8} +(-0.142315 - 0.989821i) q^{9} +(-1.67990 + 3.67846i) q^{10} +(5.54984 - 1.62958i) q^{11} +(-0.765905 + 0.224890i) q^{12} +(-1.30521 + 2.85800i) q^{13} +(0.238063 + 1.65577i) q^{14} +(1.58310 + 1.82699i) q^{15} +(-2.06016 - 4.51113i) q^{16} +(-3.77099 + 2.42347i) q^{17} +(-0.238063 + 1.65577i) q^{18} +(-2.90254 - 1.86535i) q^{19} +(1.26369 - 1.45837i) q^{20} +(0.959493 + 0.281733i) q^{21} -9.67567 q^{22} +(3.72382 - 3.02212i) q^{23} -2.01030 q^{24} +(-0.809896 - 0.237807i) q^{25} +(3.44182 - 3.97208i) q^{26} +(0.841254 + 0.540641i) q^{27} +(0.113601 - 0.790114i) q^{28} +(3.49040 - 2.24314i) q^{29} +(-1.67990 - 3.67846i) q^{30} +(-5.36093 - 6.18684i) q^{31} +(0.608435 + 4.23176i) q^{32} +(-2.40282 + 5.26143i) q^{33} +(7.19469 - 2.11255i) q^{34} +(-2.31953 + 0.681076i) q^{35} +(0.331600 - 0.726104i) q^{36} +(-0.906769 - 6.30671i) q^{37} +(3.77957 + 4.36186i) q^{38} +(-1.30521 - 2.85800i) q^{39} +(4.08833 - 2.62741i) q^{40} +(1.41083 - 9.81254i) q^{41} +(-1.40724 - 0.904381i) q^{42} +(-2.42834 + 2.80246i) q^{43} +(4.43010 + 1.30079i) q^{44} -2.41745 q^{45} +(-7.40112 + 3.09564i) q^{46} +3.23827 q^{47} +(4.75841 + 1.39719i) q^{48} +(-0.654861 + 0.755750i) q^{49} +(1.18784 + 0.763376i) q^{50} +(0.637938 - 4.43695i) q^{51} +(-2.10988 + 1.35594i) q^{52} +(-4.33245 - 9.48674i) q^{53} +(-1.09545 - 1.26421i) q^{54} +(-1.98997 - 13.8406i) q^{55} +(0.835108 - 1.82863i) q^{56} +(3.31050 - 0.972049i) q^{57} +(-6.65935 + 1.95536i) q^{58} +(-3.11246 + 6.81534i) q^{59} +(0.274626 + 1.91006i) q^{60} +(-5.36141 - 6.18740i) q^{61} +(5.68874 + 12.4566i) q^{62} +(-0.841254 + 0.540641i) q^{63} +(-0.393775 + 2.73877i) q^{64} +(6.38973 + 4.10643i) q^{65} +(6.33621 - 7.31238i) q^{66} +(-7.49964 - 2.20209i) q^{67} -3.57817 q^{68} +(-0.154618 + 4.79334i) q^{69} +4.04390 q^{70} +(-12.9318 - 3.79712i) q^{71} +(1.31647 - 1.51928i) q^{72} +(11.2740 + 7.24539i) q^{73} +(-1.51684 + 10.5498i) q^{74} +(0.710091 - 0.456348i) q^{75} +(-1.14411 - 2.50524i) q^{76} +(-3.78780 - 4.37136i) q^{77} +(0.747980 + 5.20231i) q^{78} +(-3.03049 + 6.63585i) q^{79} +(-11.5032 + 3.37765i) q^{80} +(-0.959493 + 0.281733i) q^{81} +(-6.88889 + 15.0846i) q^{82} +(-0.467720 - 3.25306i) q^{83} +(0.522735 + 0.603269i) q^{84} +(4.50162 + 9.85717i) q^{85} +(5.21832 - 3.35361i) q^{86} +(-0.590470 + 4.10681i) q^{87} +(9.78196 + 6.28648i) q^{88} +(8.41852 - 9.71549i) q^{89} +(3.88010 + 1.13930i) q^{90} +3.14194 q^{91} +(3.80485 - 0.422363i) q^{92} +8.18637 q^{93} +(-5.19753 - 1.52613i) q^{94} +(-5.46208 + 6.30358i) q^{95} +(-3.59659 - 2.31139i) q^{96} +(0.0647665 - 0.450461i) q^{97} +(1.40724 - 0.904381i) q^{98} +(-2.40282 - 5.26143i) 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