LMFDB - Embedded newform 121.2.g.a.5.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,2,Mod(4,121)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(121, base_ring=CyclotomicField(110))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("121.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	121.g (of order $55$, degree $40$, 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:	$0.966189864457$
Analytic rank:	$0$
Dimension:	$400$
Relative dimension:	$10$ over $\Q(\zeta_{55})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{55}]$

Embedding invariants

Embedding label			5.4
Character	$\chi$	$=$	121.5
Dual form			121.2.g.a.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.631909 + 1.04790i) q^{2} +(1.62812 + 1.18290i) q^{3} +(0.234543 + 0.444508i) q^{4} +(0.863348 - 0.705956i) q^{5} +(-2.26838 + 0.958627i) q^{6} +(1.34281 - 1.74139i) q^{7} +(-3.05739 - 0.174828i) q^{8} +(0.324472 + 0.998622i) q^{9} +O(q^{10})$	\(q+(-0.631909 + 1.04790i) q^{2} +(1.62812 + 1.18290i) q^{3} +(0.234543 + 0.444508i) q^{4} +(0.863348 - 0.705956i) q^{5} +(-2.26838 + 0.958627i) q^{6} +(1.34281 - 1.74139i) q^{7} +(-3.05739 - 0.174828i) q^{8} +(0.324472 + 0.998622i) q^{9} +(0.194216 + 1.35080i) q^{10} +(-3.16707 - 0.984725i) q^{11} +(-0.143944 + 1.00115i) q^{12} +(-0.721138 + 0.124798i) q^{13} +(0.976273 + 2.50754i) q^{14} +(2.24071 - 0.128128i) q^{15} +(1.54783 - 2.26363i) q^{16} +(-0.852598 + 0.0978266i) q^{17} +(-1.25150 - 0.291023i) q^{18} +(-2.04776 + 1.15643i) q^{19} +(0.516295 + 0.218188i) q^{20} +(4.24614 - 1.24678i) q^{21} +(3.03319 - 2.69652i) q^{22} +(0.872436 + 0.256170i) q^{23} +(-4.77099 - 3.90122i) q^{24} +(-0.745957 + 3.68144i) q^{25} +(0.324917 - 0.834544i) q^{26} +(1.21267 - 3.73221i) q^{27} +(1.08901 + 0.188460i) q^{28} +(-1.09215 - 5.38995i) q^{29} +(-1.28166 + 2.42901i) q^{30} +(5.59334 - 2.75006i) q^{31} +(-1.15035 - 2.51891i) q^{32} +(-3.99153 - 5.34956i) q^{33} +(0.436252 - 0.955258i) q^{34} +(-0.0700306 - 2.45139i) q^{35} +(-0.367793 + 0.378450i) q^{36} +(1.17903 + 1.21320i) q^{37} +(0.0821782 - 2.87661i) q^{38} +(-1.32172 - 0.649847i) q^{39} +(-2.76301 + 2.00745i) q^{40} +(0.817187 + 9.51434i) q^{41} +(-1.37667 + 5.23740i) q^{42} +(6.59326 - 4.23723i) q^{43} +(-0.305095 - 1.63875i) q^{44} +(0.985115 + 0.633095i) q^{45} +(-0.819741 + 0.752352i) q^{46} +(-10.0970 + 2.34795i) q^{47} +(5.19768 - 1.85453i) q^{48} +(0.550234 + 2.09331i) q^{49} +(-3.38642 - 3.10803i) q^{50} +(-1.50385 - 0.849263i) q^{51} +(-0.224611 - 0.291281i) q^{52} +(4.02437 + 5.88545i) q^{53} +(3.14470 + 3.62918i) q^{54} +(-3.42945 + 1.38565i) q^{55} +(-4.40995 + 5.08935i) q^{56} +(-4.70193 - 0.539497i) q^{57} +(6.33829 + 2.26150i) q^{58} +(-0.718368 + 8.36381i) q^{59} +(0.582495 + 0.965959i) q^{60} +(3.01289 + 4.99632i) q^{61} +(-0.652684 + 7.59906i) q^{62} +(2.17470 + 0.775930i) q^{63} +(8.81518 + 1.01145i) q^{64} +(-0.534491 + 0.616836i) q^{65} +(8.12811 - 0.802303i) q^{66} +(-8.85724 - 10.2218i) q^{67} +(-0.243455 - 0.356042i) q^{68} +(1.11741 + 1.44908i) q^{69} +(2.61307 + 1.47567i) q^{70} +(-1.24009 - 1.13814i) q^{71} +(-0.817451 - 3.10991i) q^{72} +(-0.106099 + 0.0378560i) q^{73} +(-2.01635 + 0.468883i) q^{74} +(-5.56927 + 5.11143i) q^{75} +(-0.994328 - 0.639016i) q^{76} +(-5.96757 + 4.19280i) q^{77} +(1.51618 - 0.974392i) q^{78} +(-3.47683 + 13.2272i) q^{79} +(-0.261707 - 3.04700i) q^{80} +(8.93762 - 6.49356i) q^{81} +(-10.4865 - 5.15586i) q^{82} +(0.273573 - 9.57631i) q^{83} +(1.55010 + 1.59502i) q^{84} +(-0.667028 + 0.686355i) q^{85} +(0.273868 + 9.58665i) q^{86} +(4.59762 - 10.0674i) q^{87} +(9.51081 + 3.56438i) q^{88} +(-6.49736 - 14.2272i) q^{89} +(-1.28593 + 0.632247i) q^{90} +(-0.751031 + 1.42336i) q^{91} +(0.0907537 + 0.447887i) q^{92} +(12.3597 + 2.13892i) q^{93} +(3.91994 - 12.0643i) q^{94} +(-0.951547 + 2.44403i) q^{95} +(1.10671 - 5.46183i) q^{96} +(-9.04427 - 7.39546i) q^{97} +(-2.54128 - 0.746188i) q^{98} +(-0.0442570 - 3.48222i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9}+O(q^{10}) $ 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9	\( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9} - 22 q^{10} - 33 q^{11} + 6 q^{12} - 11 q^{13} - 18 q^{14} + 16 q^{15} - 30 q^{16} - 44 q^{17} + 11 q^{18} - 44 q^{19} - 36 q^{20} - 11 q^{21} - 34 q^{23} + 77 q^{24} - 31 q^{25} - 38 q^{26} + 40 q^{27} - 44 q^{28} - 44 q^{29} - 11 q^{30} - 17 q^{31} - 44 q^{32} - 11 q^{33} - 76 q^{34} - 44 q^{35} + 57 q^{36} - 4 q^{37} + 34 q^{38} - 11 q^{39} + 33 q^{40} - 44 q^{41} + 3 q^{42} - 44 q^{43} - 33 q^{44} - 12 q^{45} - 44 q^{46} - 36 q^{47} + 9 q^{48} + 16 q^{49} + 88 q^{50} + 154 q^{51} + 110 q^{52} + 78 q^{53} + 231 q^{54} + 44 q^{55} - 55 q^{56} + 66 q^{57} + 73 q^{58} - 33 q^{59} + 15 q^{60} - 44 q^{61} + 11 q^{62} + 121 q^{63} + 96 q^{64} - 11 q^{65} - 41 q^{67} - 44 q^{68} + 8 q^{69} + 24 q^{70} + 15 q^{71} + 77 q^{72} - 22 q^{73} - 44 q^{74} + 7 q^{75} + 176 q^{76} + 88 q^{77} - 21 q^{78} + 44 q^{79} + 171 q^{80} + 37 q^{81} + 22 q^{82} - 44 q^{83} - 11 q^{84} + 66 q^{85} - 20 q^{86} - 11 q^{87} + 77 q^{88} + 3 q^{89} + 264 q^{90} + 79 q^{91} + 228 q^{92} + 49 q^{93} + 143 q^{94} + 44 q^{95} + 121 q^{96} + 10 q^{97} + 132 q^{98} + 143 q^{99}+O(q^{100}) \) 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9 - 22 * q^10 - 33 * q^11 + 6 * q^12 - 11 * q^13 - 18 * q^14 + 16 * q^15 - 30 * q^16 - 44 * q^17 + 11 * q^18 - 44 * q^19 - 36 * q^20 - 11 * q^21 - 34 * q^23 + 77 * q^24 - 31 * q^25 - 38 * q^26 + 40 * q^27 - 44 * q^28 - 44 * q^29 - 11 * q^30 - 17 * q^31 - 44 * q^32 - 11 * q^33 - 76 * q^34 - 44 * q^35 + 57 * q^36 - 4 * q^37 + 34 * q^38 - 11 * q^39 + 33 * q^40 - 44 * q^41 + 3 * q^42 - 44 * q^43 - 33 * q^44 - 12 * q^45 - 44 * q^46 - 36 * q^47 + 9 * q^48 + 16 * q^49 + 88 * q^50 + 154 * q^51 + 110 * q^52 + 78 * q^53 + 231 * q^54 + 44 * q^55 - 55 * q^56 + 66 * q^57 + 73 * q^58 - 33 * q^59 + 15 * q^60 - 44 * q^61 + 11 * q^62 + 121 * q^63 + 96 * q^64 - 11 * q^65 - 41 * q^67 - 44 * q^68 + 8 * q^69 + 24 * q^70 + 15 * q^71 + 77 * q^72 - 22 * q^73 - 44 * q^74 + 7 * q^75 + 176 * q^76 + 88 * q^77 - 21 * q^78 + 44 * q^79 + 171 * q^80 + 37 * q^81 + 22 * q^82 - 44 * q^83 - 11 * q^84 + 66 * q^85 - 20 * q^86 - 11 * q^87 + 77 * q^88 + 3 * q^89 + 264 * q^90 + 79 * q^91 + 228 * q^92 + 49 * q^93 + 143 * q^94 + 44 * q^95 + 121 * q^96 + 10 * q^97 + 132 * q^98 + 143 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{37}{55}\right)$

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 $

$2$	−0.631909	+	1.04790i	−0.446827	+	0.740979i	−0.995470	−	0.0950775i	$-0.969690\pi$
$2$	−0.631909	+	1.04790i	−0.446827	+	0.740979i	0.548643	+	0.836057i	$0.315145\pi$
$3$	1.62812	+	1.18290i	0.939994	+	0.682946i	0.948419	−	0.317019i	$-0.102682\pi$
$3$	1.62812	+	1.18290i	0.939994	+	0.682946i	−0.00842495	+	0.999965i	$0.502682\pi$
$4$	0.234543	+	0.444508i	0.117271	+	0.222254i
$5$	0.863348	−	0.705956i	0.386101	−	0.315713i	−0.419963	−	0.907541i	$-0.637957\pi$
$5$	0.863348	−	0.705956i	0.386101	−	0.315713i	0.806064	+	0.591828i	$0.201593\pi$
$6$	−2.26838	+	0.958627i	−0.926064	+	0.391358i
$7$	1.34281	−	1.74139i	0.507535	−	0.658184i	−0.466515	−	0.884513i	$-0.654491\pi$
$7$	1.34281	−	1.74139i	0.507535	−	0.658184i	0.974051	+	0.226330i	$0.0726726\pi$
$8$	−3.05739	−	0.174828i	−1.08095	−	0.0618110i
$9$	0.324472	+	0.998622i	0.108157	+	0.332874i
$10$	0.194216	+	1.35080i	0.0614166	+	0.427162i
$11$	−3.16707	−	0.984725i	−0.954907	−	0.296906i
$11$	−3.16707	−	0.984725i	−0.954907	−	0.296906i
$12$	−0.143944	+	1.00115i	−0.0415530	+	0.289007i
$13$	−0.721138	+	0.124798i	−0.200008	+	0.0346127i	−0.269646	−	0.962960i	$-0.586907\pi$
$13$	−0.721138	+	0.124798i	−0.200008	+	0.0346127i	0.0696378	+	0.997572i	$0.477816\pi$
$14$	0.976273	+	2.50754i	0.260920	+	0.670167i
$15$	2.24071	−	0.128128i	0.578548	−	0.0330826i
$16$	1.54783	−	2.26363i	0.386957	−	0.565907i
$17$	−0.852598	+	0.0978266i	−0.206786	+	0.0237264i	−0.216765	−	0.976224i	$-0.569551\pi$
$17$	−0.852598	+	0.0978266i	−0.206786	+	0.0237264i	0.00997967	+	0.999950i	$0.496823\pi$
$18$	−1.25150	−	0.291023i	−0.294980	−	0.0685947i
$19$	−2.04776	+	1.15643i	−0.469789	+	0.265302i	−0.708397	−	0.705814i	$-0.750582\pi$
$19$	−2.04776	+	1.15643i	−0.469789	+	0.265302i	0.238608	+	0.971116i	$0.423309\pi$
$20$	0.516295	+	0.218188i	0.115447	+	0.0487883i
$21$	4.24614	−	1.24678i	0.926584	−	0.272070i
$22$	3.03319	−	2.69652i	0.646679	−	0.574901i
$23$	0.872436	+	0.256170i	0.181915	+	0.0534152i	0.371421	−	0.928464i	$-0.378870\pi$
$23$	0.872436	+	0.256170i	0.181915	+	0.0534152i	−0.189506	+	0.981880i	$0.560689\pi$
$24$	−4.77099	−	3.90122i	−0.973875	−	0.796333i
$25$	−0.745957	+	3.68144i	−0.149191	+	0.736288i
$26$	0.324917	−	0.834544i	0.0637216	−	0.163667i
$27$	1.21267	−	3.73221i	0.233378	−	0.718264i
$28$	1.08901	+	0.188460i	0.205803	+	0.0356156i
$29$	−1.09215	−	5.38995i	−0.202806	−	1.00089i	−0.944088	−	0.329695i	$-0.893054\pi$
$29$	−1.09215	−	5.38995i	−0.202806	−	1.00089i	0.741281	−	0.671195i	$-0.234219\pi$
$30$	−1.28166	+	2.42901i	−0.233997	+	0.443474i
$31$	5.59334	−	2.75006i	1.00459	−	0.493925i	0.136666	−	0.990617i	$-0.456361\pi$
$31$	5.59334	−	2.75006i	1.00459	−	0.493925i	0.867927	+	0.496692i	$0.165452\pi$
$32$	−1.15035	−	2.51891i	−0.203355	−	0.445285i
$33$	−3.99153	−	5.34956i	−0.694837	−	0.931239i
$34$	0.436252	−	0.955258i	0.0748165	−	0.163825i
$35$	−0.0700306	−	2.45139i	−0.0118373	−	0.414361i
$36$	−0.367793	+	0.378450i	−0.0612988	+	0.0630750i
$37$	1.17903	+	1.21320i	0.193832	+	0.199448i	0.807080	−	0.590442i	$-0.201047\pi$
$37$	1.17903	+	1.21320i	0.193832	+	0.199448i	−0.613248	+	0.789890i	$0.710137\pi$
$38$	0.0821782	−	2.87661i	0.0133311	−	0.466648i
$39$	−1.32172	−	0.649847i	−0.211645	−	0.104059i
$40$	−2.76301	+	2.00745i	−0.436871	+	0.317405i
$41$	0.817187	+	9.51434i	0.127623	+	1.48589i	0.727671	+	0.685926i	$0.240603\pi$
$41$	0.817187	+	9.51434i	0.127623	+	1.48589i	−0.600048	+	0.799964i	$0.704852\pi$
$42$	−1.37667	+	5.23740i	−0.212425	+	0.808148i
$43$	6.59326	−	4.23723i	1.00546	−	0.646172i	0.0692482	−	0.997599i	$-0.477940\pi$
$43$	6.59326	−	4.23723i	1.00546	−	0.646172i	0.936215	+	0.351427i	$0.114304\pi$
$44$	−0.305095	−	1.63875i	−0.0459948	−	0.247050i
$45$	0.985115	+	0.633095i	0.146852	+	0.0943763i
$46$	−0.819741	+	0.752352i	−0.120864	+	0.110928i
$47$	−10.0970	+	2.34795i	−1.47280	+	0.342484i	−0.884644	−	0.466267i	$-0.845599\pi$
$47$	−10.0970	+	2.34795i	−1.47280	+	0.342484i	−0.588152	+	0.808751i	$0.700144\pi$
$48$	5.19768	−	1.85453i	0.750221	−	0.267678i
$49$	0.550234	+	2.09331i	0.0786049	+	0.299044i
$50$	−3.38642	−	3.10803i	−0.478912	−	0.439541i
$51$	−1.50385	−	0.849263i	−0.210581	−	0.118921i
$52$	−0.224611	−	0.291281i	−0.0311480	−	0.0403934i
$53$	4.02437	+	5.88545i	0.552789	+	0.808429i	0.996127	−	0.0879261i	$-0.0280239\pi$
$53$	4.02437	+	5.88545i	0.552789	+	0.808429i	−0.443338	+	0.896355i	$0.646206\pi$
$54$	3.14470	+	3.62918i	0.427939	+	0.493868i
$55$	−3.42945	+	1.38565i	−0.462427	+	0.186841i
$56$	−4.40995	+	5.08935i	−0.589304	+	0.680093i
$57$	−4.70193	−	0.539497i	−0.622786	−	0.0714581i
$58$	6.33829	+	2.26150i	0.832258	+	0.296949i
$59$	−0.718368	+	8.36381i	−0.0935236	+	1.08888i	0.787663	+	0.616107i	$0.211291\pi$
$59$	−0.718368	+	8.36381i	−0.0935236	+	1.08888i	−0.881186	+	0.472769i	$0.843255\pi$
$60$	0.582495	+	0.965959i	0.0751998	+	0.124705i
$61$	3.01289	+	4.99632i	0.385761	+	0.639713i	0.987252	−	0.159167i	$-0.0508807\pi$
$61$	3.01289	+	4.99632i	0.385761	+	0.639713i	−0.601490	+	0.798880i	$0.705426\pi$
$62$	−0.652684	+	7.59906i	−0.0828910	+	0.965082i
$63$	2.17470	+	0.775930i	0.273986	+	0.0977580i
$64$	8.81518	+	1.01145i	1.10190	+	0.126431i
$65$	−0.534491	+	0.616836i	−0.0662955	+	0.0765091i
$66$	8.12811	−	0.802303i	1.00050	−	0.0987567i
$67$	−8.85724	−	10.2218i	−1.08208	−	1.24879i	−0.966820	−	0.255457i	$-0.917774\pi$
$67$	−8.85724	−	10.2218i	−1.08208	−	1.24879i	−0.115264	−	0.993335i	$-0.536771\pi$
$68$	−0.243455	−	0.356042i	−0.0295233	−	0.0431764i
$69$	1.11741	+	1.44908i	0.134520	+	0.174448i
$70$	2.61307	+	1.47567i	0.312322	+	0.176376i
$71$	−1.24009	−	1.13814i	−0.147171	−	0.135072i	0.599208	−	0.800593i	$-0.295482\pi$
$71$	−1.24009	−	1.13814i	−0.147171	−	0.135072i	−0.746379	+	0.665521i	$0.768209\pi$
$72$	−0.817451	−	3.10991i	−0.0963375	−	0.366506i
$73$	−0.106099	+	0.0378560i	−0.0124179	+	0.00443071i	−0.342251	−	0.939609i	$-0.611189\pi$
$73$	−0.106099	+	0.0378560i	−0.0124179	+	0.00443071i	0.329833	+	0.944039i	$0.393008\pi$
$74$	−2.01635	+	0.468883i	−0.234396	+	0.0545066i
$75$	−5.56927	+	5.11143i	−0.643084	+	0.590217i
$76$	−0.994328	−	0.639016i	−0.114057	−	0.0733001i
$77$	−5.96757	+	4.19280i	−0.680067	+	0.477814i
$78$	1.51618	−	0.974392i	0.171674	−	0.110328i
$79$	−3.47683	+	13.2272i	−0.391173	+	1.48818i	0.422236	+	0.906486i	$0.361245\pi$
$79$	−3.47683	+	13.2272i	−0.391173	+	1.48818i	−0.813409	+	0.581692i	$0.802391\pi$
$80$	−0.261707	−	3.04700i	−0.0292597	−	0.340665i
$81$	8.93762	−	6.49356i	0.993069	−	0.721507i
$82$	−10.4865	−	5.15586i	−1.15804	−	0.569370i
$83$	0.273573	−	9.57631i	0.0300286	−	1.05114i	−0.835258	−	0.549859i	$-0.814682\pi$
$83$	0.273573	−	9.57631i	0.0300286	−	1.05114i	0.865286	−	0.501278i	$-0.167137\pi$
$84$	1.55010	+	1.59502i	0.169130	+	0.174031i
$85$	−0.667028	+	0.686355i	−0.0723493	+	0.0744457i
$86$	0.273868	+	9.58665i	0.0295320	+	1.03375i
$87$	4.59762	−	10.0674i	0.492916	−	1.07934i
$88$	9.51081	+	3.56438i	1.01386	+	0.379964i
$89$	−6.49736	−	14.2272i	−0.688719	−	1.50808i	−0.853133	−	0.521693i	$-0.825301\pi$
$89$	−6.49736	−	14.2272i	−0.688719	−	1.50808i	0.164414	−	0.986391i	$-0.447427\pi$
$90$	−1.28593	+	0.632247i	−0.135548	+	0.0666447i
$91$	−0.751031	+	1.42336i	−0.0787295	+	0.149209i
$92$	0.0907537	+	0.447887i	0.00946173	+	0.0466955i
$93$	12.3597	+	2.13892i	1.28164	+	0.221796i
$94$	3.91994	−	12.0643i	0.404311	−	1.24434i
$95$	−0.951547	+	2.44403i	−0.0976267	+	0.250752i
$96$	1.10671	−	5.46183i	0.112953	−	0.557445i
$97$	−9.04427	−	7.39546i	−0.918306	−	0.750895i	0.0504975	−	0.998724i	$-0.483919\pi$
$97$	−9.04427	−	7.39546i	−0.918306	−	0.750895i	−0.968804	+	0.247829i	$0.920283\pi$
$98$	−2.54128	−	0.746188i	−0.256708	−	0.0753763i
$99$	−0.0442570	−	3.48222i	−0.00444799	−	0.349976i
$100$	−1.81139	+	0.531871i	−0.181139	+	0.0531871i
$101$	13.9485	+	5.89468i	1.38793	+	0.586543i	0.949938	−	0.312438i	$-0.101146\pi$
$101$	13.9485	+	5.89468i	1.38793	+	0.586543i	0.437989	+	0.898981i	$0.355691\pi$
$102$	1.84024	−	1.03923i	0.182211	−	0.102899i
$103$	−4.32534	−	1.00582i	−0.426189	−	0.0991059i	0.00791532	−	0.999969i	$-0.497480\pi$
$103$	−4.32534	−	1.00582i	−0.426189	−	0.0991059i	−0.434104	+	0.900863i	$0.642935\pi$
$104$	2.22662	−	0.255481i	0.218338	−	0.0250520i
$105$	2.78573	−	4.07399i	0.271859	−	0.397581i
$106$	−8.71041	+	0.498079i	−0.846030	+	0.0483777i
$107$	−3.38261	−	8.68815i	−0.327009	−	0.839915i	−0.995373	−	0.0960815i	$-0.969369\pi$
$107$	−3.38261	−	8.68815i	−0.327009	−	0.839915i	0.668365	−	0.743834i	$-0.266995\pi$
$108$	1.94342	−	0.336322i	0.187006	−	0.0323626i
$109$	−0.378846	+	2.63493i	−0.0362869	+	0.252381i	−0.999888	−	0.0149632i	$-0.995237\pi$
$109$	−0.378846	+	2.63493i	−0.0362869	+	0.252381i	0.963601	+	0.267344i	$0.0861460\pi$
$110$	0.715074	−	4.46934i	0.0681796	−	0.426135i
$111$	0.484519	+	3.36990i	0.0459885	+	0.319857i
$112$	−1.86341	−	5.73500i	−0.176076	−	0.541906i
$113$	1.55681	+	0.0890217i	0.146452	+	0.00837446i	0.130161	−	0.991493i	$-0.458450\pi$
$113$	1.55681	+	0.0890217i	0.146452	+	0.00837446i	0.0162912	+	0.999867i	$0.494814\pi$
$114$	3.53653	−	4.58626i	0.331227	−	0.429542i
$115$	0.934060	−	0.394737i	0.0871016	−	0.0368094i
$116$	2.13972	−	1.74964i	0.198668	−	0.162450i
$117$	−0.358615	−	0.679651i	−0.0331540	−	0.0628338i
$118$	−8.31052	−	6.03795i	−0.765045	−	0.555838i
$119$	−0.974525	+	1.61607i	−0.0893346	+	0.148145i
$120$	−6.87312			−0.627427
$121$	9.06063	+	6.23738i	0.823694	+	0.567034i
$122$	−7.13953			−0.646383
$123$	−9.92401	+	16.4571i	−0.894817	+	1.48389i
$124$	2.53430	+	1.84128i	0.227587	+	0.165351i
$125$	4.55713	+	8.63672i	0.407602	+	0.772492i
$126$	−2.18731	+	1.78855i	−0.194861	+	0.159337i
$127$	−15.6750	+	6.62431i	−1.39093	+	0.587812i	−0.950711	−	0.310078i	$-0.899645\pi$
$127$	−15.6750	+	6.62431i	−1.39093	+	0.587812i	−0.440220	+	0.897890i	$0.645100\pi$
$128$	−3.24834	+	4.21252i	−0.287115	+	0.372337i
$129$	15.7468	+	0.900436i	1.38643	+	0.0792790i
$130$	−0.308634	−	0.949879i	−0.0270690	−	0.0833099i
$131$	0.964664	+	6.70939i	0.0842831	+	0.586202i	0.987572	+	0.157169i	$0.0502366\pi$
$131$	0.964664	+	6.70939i	0.0842831	+	0.586202i	−0.903289	+	0.429033i	$0.858854\pi$
$132$	1.44174	−	3.02897i	0.125487	−	0.263638i
$133$	−0.735975	+	5.11882i	−0.0638171	+	0.443858i
$134$	16.3084	−	2.82228i	1.40883	−	0.243808i
$135$	−1.58782	−	4.07829i	−0.136658	−	0.351003i
$136$	2.62383	−	0.150036i	0.224992	−	0.0128655i
$137$	0.797407	−	1.16617i	0.0681271	−	0.0996326i	−0.789904	−	0.613231i	$-0.789870\pi$
$137$	0.797407	−	1.16617i	0.0681271	−	0.0996326i	0.858031	+	0.513598i	$0.171688\pi$
$138$	−2.22459	+	0.255248i	−0.189370	+	0.0217281i
$139$	−15.9894	−	3.71817i	−1.35620	−	0.315371i	−0.515509	−	0.856884i	$-0.672397\pi$
$139$	−15.9894	−	3.71817i	−1.35620	−	0.315371i	−0.840693	+	0.541513i	$0.817852\pi$
$140$	1.07324	−	0.606085i	0.0907051	−	0.0512235i
$141$	−19.2165	−	8.12094i	−1.61832	−	0.683907i
$142$	1.97628	−	0.580289i	0.165846	−	0.0486968i
$143$	2.40679	+	0.314879i	0.201265	+	0.0263315i
$144$	2.76273	+	0.811212i	0.230228	+	0.0676010i
$145$	−4.74797	−	3.88240i	−0.394298	−	0.322416i
$146$	0.0273754	−	0.135103i	0.00226560	−	0.0111812i
$147$	−1.58032	+	4.05902i	−0.130343	+	0.334783i
$148$	−0.262742	+	0.808636i	−0.0215972	+	0.0664695i
$149$	20.1294	+	3.48354i	1.64907	+	0.285382i	0.917899	−	0.396815i	$-0.129884\pi$
$149$	20.1294	+	3.48354i	1.64907	+	0.285382i	0.731169	+	0.682197i	$0.238975\pi$
$150$	−1.83701	−	9.06601i	−0.149991	−	0.740237i
$151$	0.787543	−	1.49256i	0.0640893	−	0.121463i	−0.850301	−	0.526297i	$-0.823580\pi$
$151$	0.787543	−	1.49256i	0.0640893	−	0.121463i	0.914390	+	0.404834i	$0.132671\pi$
$152$	6.46299	−	3.17764i	0.524218	−	0.257741i
$153$	−0.374336	−	0.819682i	−0.0302633	−	0.0662673i
$154$	−0.622689	−	8.90290i	−0.0501777	−	0.717416i
$155$	2.88758	−	6.32291i	0.231936	−	0.507868i
$156$	−0.0211382	−	0.739932i	−0.00169241	−	0.0592420i
$157$	3.32220	−	3.41846i	0.265141	−	0.272823i	−0.571468	−	0.820624i	$-0.693626\pi$
$157$	3.32220	−	3.41846i	0.265141	−	0.272823i	0.836609	+	0.547801i	$0.184535\pi$
$158$	−11.6638	−	12.0018i	−0.927922	−	0.954810i
$159$	−0.409736	+	14.3426i	−0.0324941	+	1.13744i
$160$	−2.77139	−	1.36260i	−0.219098	−	0.107723i
$161$	1.61761	−	1.17526i	0.127485	−	0.0926236i
$162$	1.15686	+	13.4691i	0.0908917	+	1.05823i
$163$	6.25823	−	23.8088i	0.490182	−	1.86485i	−0.0117365	−	0.999931i	$-0.503736\pi$
$163$	6.25823	−	23.8088i	0.490182	−	1.86485i	0.501919	−	0.864915i	$-0.332628\pi$
$164$	−4.03753	+	2.59476i	−0.315278	+	0.202617i
$165$	−7.22264	−	1.80069i	−0.562281	−	0.140183i
$166$	9.86217	+	6.33803i	0.765453	+	0.491927i
$167$	−1.28648	+	1.18072i	−0.0995504	+	0.0913666i	−0.724405	−	0.689374i	$-0.757885\pi$
$167$	−1.28648	+	1.18072i	−0.0995504	+	0.0913666i	0.624855	+	0.780741i	$0.285158\pi$
$168$	−13.2001	+	3.06955i	−1.01841	+	0.236821i
$169$	−11.7395	+	4.18865i	−0.903039	+	0.322204i
$170$	−0.297733	−	1.13269i	−0.0228351	−	0.0868737i
$171$	−1.81927	−	1.66971i	−0.139123	−	0.127686i
$172$	3.42988	+	1.93694i	0.261526	+	0.147691i
$173$	12.8604	+	16.6776i	0.977755	+	1.26798i	0.963397	+	0.268079i	$0.0863888\pi$
$173$	12.8604	+	16.6776i	0.977755	+	1.26798i	0.0143585	+	0.999897i	$0.495429\pi$
$174$	7.64436	+	11.1795i	0.579517	+	0.847517i
$175$	5.40915	+	6.24249i	0.408893	+	0.471888i
$176$	−7.13113	+	5.64487i	−0.537529	+	0.425498i
$177$	−11.0631	+	12.7675i	−0.831555	+	0.959665i
$178$	19.0145	+	2.18171i	1.42520	+	0.163526i
$179$	15.1181	+	5.39414i	1.12998	+	0.403177i	0.833862	−	0.551974i	$-0.186125\pi$
$179$	15.1181	+	5.39414i	1.12998	+	0.403177i	0.296121	+	0.955151i	$0.404307\pi$
$180$	−0.0503642	+	0.586379i	−0.00375392	+	0.0437061i
$181$	−1.18047	−	1.95759i	−0.0877435	−	0.145506i	0.809381	−	0.587284i	$-0.199803\pi$
$181$	−1.18047	−	1.95759i	−0.0877435	−	0.145506i	−0.897125	+	0.441777i	$0.854348\pi$
$182$	−1.01696	−	1.68644i	−0.0753823	−	0.125008i
$183$	−1.00479	+	11.6985i	−0.0742761	+	0.864781i
$184$	−2.62259	−	0.935739i	−0.193340	−	0.0689836i
$185$	1.87438	+	0.215065i	0.137807	+	0.0158119i
$186$	−10.0516	+	11.6001i	−0.737016	+	0.850561i
$187$	2.79657	+	0.529751i	0.204505	+	0.0387393i
$188$	−3.41185	−	3.93749i	−0.248835	−	0.287171i
$189$	−4.87085	−	7.12339i	−0.354302	−	0.518150i
$190$	−1.95981	−	2.54153i	−0.142180	−	0.184382i
$191$	−1.69137	−	0.955159i	−0.122383	−	0.0691129i	0.429326	−	0.903150i	$-0.358751\pi$
$191$	−1.69137	−	0.955159i	−0.122383	−	0.0691129i	−0.551709	+	0.834037i	$0.686024\pi$
$192$	13.1557	+	12.0742i	0.949432	+	0.871381i
$193$	4.52649	+	17.2205i	0.325824	+	1.23956i	0.905370	+	0.424623i	$0.139593\pi$
$193$	4.52649	+	17.2205i	0.325824	+	1.23956i	−0.579547	+	0.814939i	$0.696770\pi$
$194$	13.4649	−	4.80426i	0.966722	−	0.344926i
$195$	−1.59987	+	0.372033i	−0.114569	+	0.0266419i
$196$	−0.801438	+	0.735553i	−0.0572456	+	0.0525395i
$197$	−1.87583	−	1.20552i	−0.133647	−	0.0858899i	0.472109	−	0.881540i	$-0.343493\pi$
$197$	−1.87583	−	1.20552i	−0.133647	−	0.0858899i	−0.605756	+	0.795650i	$0.707129\pi$
$198$	3.67699	+	2.15407i	0.261313	+	0.153083i
$199$	16.4173	−	10.5507i	1.16379	−	0.747922i	0.191452	−	0.981502i	$-0.438680\pi$
$199$	16.4173	−	10.5507i	1.16379	−	0.747922i	0.972338	+	0.233580i	$0.0750439\pi$
$200$	2.92430	−	11.1252i	0.206779	−	0.786670i
$201$	−2.32930	−	27.1195i	−0.164296	−	1.91286i
$202$	−14.9912	+	10.8918i	−1.05478	+	0.766342i
$203$	−10.8526	−	5.33584i	−0.761700	−	0.374503i
$204$	0.0247871	−	0.867661i	0.00173544	−	0.0607484i
$205$	7.42222	+	7.63729i	0.518390	+	0.533411i
$206$	3.78722	−	3.89696i	0.263868	−	0.271514i
$207$	0.0272637	+	0.954353i	0.00189496	+	0.0663322i
$208$	−0.833702	+	1.82555i	−0.0578069	+	0.126579i
$209$	7.62417	−	1.64599i	0.527375	−	0.113856i
$210$	2.50883	+	5.49356i	0.173125	+	0.379092i
$211$	−8.02672	+	3.94647i	−0.552582	+	0.271686i	−0.696080	−	0.717964i	$-0.745074\pi$
$211$	−8.02672	+	3.94647i	−0.552582	+	0.271686i	0.143498	+	0.989651i	$0.454165\pi$
$212$	−1.67224	+	3.16925i	−0.114850	+	0.217665i
$213$	−0.672703	−	3.31992i	−0.0460929	−	0.227477i
$214$	11.2418	+	1.94548i	0.768476	+	0.132990i
$215$	2.70098	−	8.31276i	0.184205	−	0.566926i
$216$	−4.36010	+	11.1988i	−0.296667	+	0.761984i
$217$	2.72188	−	13.4330i	0.184773	−	0.911891i
$218$	−2.52176	−	2.06203i	−0.170795	−	0.139658i
$219$	−0.217521	−	0.0638699i	−0.0146987	−	0.00431593i
$220$	−1.42029	−	1.19942i	−0.0957556	−	0.0808652i
$221$	0.602633	−	0.176949i	0.0405375	−	0.0119029i
$222$	−3.83750	−	1.62174i	−0.257556	−	0.108844i
$223$	−2.74671	+	1.55114i	−0.183933	+	0.103872i	−0.580949	−	0.813940i	$-0.697318\pi$
$223$	−2.74671	+	1.55114i	−0.183933	+	0.103872i	0.397016	+	0.917812i	$0.370046\pi$
$224$	−5.93111	−	1.37922i	−0.396289	−	0.0921530i
$225$	−3.91841	+	0.449596i	−0.261227	+	0.0299731i
$226$	−1.07705	+	1.57513i	−0.0716442	+	0.104776i
$227$	23.2064	−	1.32699i	1.54027	−	0.0880756i	0.733804	−	0.679362i	$-0.237743\pi$
$227$	23.2064	−	1.32699i	1.54027	−	0.0880756i	0.806462	+	0.591286i	$0.201380\pi$
$228$	−0.862993	−	2.21658i	−0.0571531	−	0.146797i
$229$	0.102980	−	0.0178215i	0.00680513	−	0.00117767i	−0.167119	−	0.985937i	$-0.553446\pi$
$229$	0.102980	−	0.0178215i	0.00680513	−	0.00117767i	0.173924	+	0.984759i	$0.444355\pi$
$230$	−0.176595	+	1.22824i	−0.0116443	+	0.0809879i
$231$	−14.6756	−	0.232645i	−0.965580	−	0.0153069i
$232$	2.39680	+	16.6701i	0.157358	+	1.09445i
$233$	−4.53445	−	13.9556i	−0.297062	−	0.914261i	−0.982521	−	0.186151i	$-0.940399\pi$
$233$	−4.53445	−	13.9556i	−0.297062	−	0.914261i	0.685460	−	0.728111i	$-0.259601\pi$
$234$	0.938820	+	0.0536837i	0.0613726	+	0.00350941i
$235$	−7.05965	+	9.15512i	−0.460521	+	0.597214i
$236$	−3.88627	+	1.64235i	−0.252974	+	0.106908i
$237$	−21.3071	+	17.4227i	−1.38405	+	1.13173i
$238$	−1.07767	−	2.04242i	−0.0698551	−	0.132390i
$239$	−2.78032	−	2.02002i	−0.179844	−	0.130664i	0.494221	−	0.869336i	$-0.335453\pi$
$239$	−2.78032	−	2.02002i	−0.179844	−	0.130664i	−0.674065	+	0.738672i	$0.735453\pi$
$240$	3.17819	−	5.27044i	0.205151	−	0.340206i
$241$	2.38508			0.153636			0.0768182	−	0.997045i	$-0.475524\pi$
$241$	2.38508			0.153636			0.0768182	+	0.997045i	$0.475524\pi$
$242$	−12.2617	+	5.55321i	−0.788210	+	0.356974i
$243$	10.4599			0.671002
$244$	−1.51425	+	2.51110i	−0.0969400	+	0.160757i
$245$	1.95283	+	1.41881i	0.124762	+	0.0906446i
$246$	−10.9744	−	20.7988i	−0.699702	−	1.32608i
$247$	1.33240	−	1.08950i	0.0847787	−	0.0693232i
$248$	−17.5818	+	7.43014i	−1.11645	+	0.471814i
$249$	11.7732	−	15.2678i	0.746096	−	0.967554i
$250$	−11.9301	−	0.682190i	−0.754528	−	0.0431455i
$251$	−6.16844	−	18.9845i	−0.389349	−	1.19829i	−0.933276	−	0.359160i	$-0.883063\pi$
$251$	−6.16844	−	18.9845i	−0.389349	−	1.19829i	0.543928	−	0.839132i	$-0.316937\pi$
$252$	0.165152	+	1.14866i	0.0104036	+	0.0723586i
$253$	−2.51081	−	1.67042i	−0.157853	−	0.105018i
$254$	2.96353	−	20.6118i	0.185949	−	1.29330i
$255$	−1.89789	+	0.328442i	−0.118850	+	0.0205679i
$256$	4.07674	+	10.4710i	0.254796	+	0.654439i
$257$	−8.47702	+	0.484733i	−0.528782	+	0.0302368i	−0.319441	−	0.947606i	$-0.603495\pi$
$257$	−8.47702	+	0.484733i	−0.528782	+	0.0302368i	−0.209340	+	0.977843i	$0.567132\pi$
$258$	−10.8941	+	15.9321i	−0.678239	+	0.991892i
$259$	3.69587	−	0.424062i	0.229650	−	0.0263499i
$260$	−0.399549	−	0.0929112i	−0.0247790	−	0.00576211i
$261$	5.02816	−	2.83953i	0.311235	−	0.175763i
$262$	−7.64037	−	3.22885i	−0.472023	−	0.199479i
$263$	−12.4755	+	3.66312i	−0.769270	+	0.225878i	−0.642739	−	0.766085i	$-0.722202\pi$
$263$	−12.4755	+	3.66312i	−0.769270	+	0.225878i	−0.126530	+	0.991963i	$0.540384\pi$
$264$	11.2684	+	17.0535i	0.693524	+	1.04957i
$265$	7.62930	+	2.24016i	0.468664	+	0.137612i
$266$	−4.89896	−	4.00586i	−0.300374	−	0.245615i
$267$	6.25089	−	30.8493i	0.382548	−	1.88795i
$268$	2.46627	−	6.33456i	0.150651	−	0.386945i
$269$	5.45120	−	16.7771i	0.332366	−	1.02292i	−0.635640	−	0.771986i	$-0.719264\pi$
$269$	5.45120	−	16.7771i	0.332366	−	1.02292i	0.968005	−	0.250930i	$-0.0807364\pi$
$270$	5.27701	+	0.913222i	0.321148	+	0.0555769i
$271$	−4.72165	−	23.3023i	−0.286820	−	1.41551i	−0.821380	−	0.570382i	$-0.806795\pi$
$271$	−4.72165	−	23.3023i	−0.286820	−	1.41551i	0.534559	−	0.845131i	$-0.320478\pi$
$272$	−1.09823	+	2.08138i	−0.0665902	+	0.126202i
$273$	−2.90646	+	1.42901i	−0.175907	+	0.0864876i
$274$	0.718145	+	1.57252i	0.0433847	+	0.0949993i
$275$	5.98770	−	10.9248i	0.361072	−	0.658791i
$276$	−0.382047	+	0.836565i	−0.0229965	+	0.0503553i
$277$	−0.0805151	−	2.81840i	−0.00483769	−	0.169341i	−0.998419	−	0.0562171i	$-0.982096\pi$
$277$	−0.0805151	−	2.81840i	−0.00483769	−	0.169341i	0.993581	−	0.113124i	$-0.0360857\pi$
$278$	14.0001	−	14.4058i	0.839671	−	0.864001i
$279$	4.56115	+	4.69331i	0.273069	+	0.280981i
$280$	−0.214461	+	7.50711i	−0.0128165	+	0.448636i
$281$	17.7822	+	8.74290i	1.06079	+	0.521558i	0.886305	−	0.463101i	$-0.153263\pi$
$281$	17.7822	+	8.74290i	1.06079	+	0.521558i	0.174490	+	0.984659i	$0.444172\pi$
$282$	20.6530	−	15.0053i	1.22987	−	0.893552i
$283$	−0.686276	−	7.99017i	−0.0407949	−	0.474966i	−0.988012	−	0.154375i	$-0.950664\pi$
$283$	−0.686276	−	7.99017i	−0.0407949	−	0.474966i	0.947218	−	0.320592i	$-0.103882\pi$
$284$	0.215059	−	0.818170i	0.0127614	−	0.0485495i
$285$	−4.44026	+	2.85358i	−0.263019	+	0.169032i
$286$	−1.85083	+	2.32310i	−0.109442	+	0.137368i
$287$	17.6655	+	11.3529i	1.04276	+	0.670142i
$288$	2.14218	−	1.96608i	0.126229	−	0.115852i
$289$	−15.8408	+	3.68363i	−0.931815	+	0.216684i
$290$	7.06866	−	2.52209i	0.415086	−	0.148102i
$291$	−5.97707	−	22.7391i	−0.350382	−	1.33299i
$292$	−0.0417120	−	0.0382829i	−0.00244101	−	0.00224034i
$293$	8.51069	+	4.80621i	0.497200	+	0.280782i	0.719866	−	0.694113i	$-0.244203\pi$
$293$	8.51069	+	4.80621i	0.497200	+	0.280782i	−0.222666	+	0.974895i	$0.571476\pi$
$294$	−3.25484	−	4.22096i	−0.189826	−	0.246171i
$295$	5.28428	+	7.72802i	0.307663	+	0.449942i
$296$	−3.39267	−	3.91535i	−0.197195	−	0.227575i
$297$	−7.51580	+	10.6260i	−0.436111	+	0.616584i
$298$	−16.3704	+	18.8924i	−0.948310	+	1.09441i
$299$	−0.661116	−	0.0758560i	−0.0382333	−	0.00438687i
$300$	−3.57830	−	1.27674i	−0.206593	−	0.0737124i
$301$	1.47484	−	17.1713i	0.0850084	−	0.989735i
$302$	1.06640	+	1.76843i	0.0613646	+	0.101762i
$303$	15.7370	+	26.0969i	0.904066	+	1.49923i
$304$	−0.551871	+	6.42532i	−0.0316520	+	0.368517i
$305$	6.12836	+	2.18659i	0.350909	+	0.125204i
$306$	1.09549	+	0.125696i	0.0626252	+	0.00718557i
$307$	13.6079	−	15.7043i	0.776643	−	0.896294i	−0.220219	−	0.975450i	$-0.570677\pi$
$307$	13.6079	−	15.7043i	0.776643	−	0.896294i	0.996862	+	0.0791567i	$0.0252227\pi$
$308$	−3.26338	−	1.66924i	−0.185948	−	0.0951137i
$309$	−5.85239	−	6.75402i	−0.332931	−	0.384223i
$310$	4.80111	+	7.02140i	0.272685	+	0.398789i
$311$	16.5284	+	21.4344i	0.937239	+	1.21543i	0.976350	+	0.216198i	$0.0693656\pi$
$311$	16.5284	+	21.4344i	0.937239	+	1.21543i	−0.0391109	+	0.999235i	$0.512453\pi$
$312$	3.92741	+	2.21791i	0.222346	+	0.125564i
$313$	0.0330162	+	0.0303020i	0.00186619	+	0.00171277i	0.677107	−	0.735884i	$-0.263233\pi$
$313$	0.0330162	+	0.0303020i	0.00186619	+	0.00171277i	−0.675241	+	0.737597i	$0.735960\pi$
$314$	1.48289	+	5.64150i	0.0836844	+	0.318368i
$315$	2.42529	−	0.865342i	0.136650	−	0.0487565i
$316$	−6.69506	+	1.55687i	−0.376627	+	0.0875808i
$317$	−24.7906	+	22.7526i	−1.39238	+	1.27791i	−0.474951	+	0.880012i	$0.657534\pi$
$317$	−24.7906	+	22.7526i	−1.39238	+	1.27791i	−0.917428	+	0.397902i	$0.869738\pi$
$318$	−14.7708	−	9.49259i	−0.828303	−	0.532318i
$319$	−1.84872	+	18.1458i	−0.103508	+	1.01597i
$320$	8.32461	−	5.34990i	0.465360	−	0.299069i
$321$	4.76991	−	18.1466i	0.266230	−	1.01284i
$322$	0.209379	+	2.43776i	0.0116682	+	0.135851i
$323$	1.63279	−	1.18629i	0.0908509	−	0.0660071i
$324$	4.98269	+	2.44983i	0.276816	+	0.136101i
$325$	0.0785018	−	2.74792i	0.00435450	−	0.152427i
$326$	20.9946	+	21.6030i	1.16279	+	1.19648i
$327$	−3.73366	+	3.84184i	−0.206472	+	0.212454i
$328$	−0.835089	−	29.2319i	−0.0461101	−	1.61406i
$329$	−9.46965	+	20.7356i	−0.522079	+	1.14319i
$330$	6.45099	−	6.43075i	0.355115	−	0.354001i
$331$	14.7561	+	32.3113i	0.811067	+	1.77599i	0.602755	+	0.797926i	$0.294069\pi$
$331$	14.7561	+	32.3113i	0.811067	+	1.77599i	0.208311	+	0.978063i	$0.433203\pi$
$332$	4.32091	−	2.12445i	0.237141	−	0.116594i
$333$	−0.828962	+	1.57106i	−0.0454268	+	0.0860934i
$334$	−0.424341	−	2.09421i	−0.0232189	−	0.114590i
$335$	−14.8630	−	2.57215i	−0.812054	−	0.140531i
$336$	3.75005	−	11.5415i	0.204582	−	0.629639i
$337$	−3.68303	+	9.45979i	−0.200628	+	0.515308i	−0.995850	−	0.0910101i	$-0.970990\pi$
$337$	−3.68303	+	9.45979i	−0.200628	+	0.515308i	0.795222	+	0.606318i	$0.207354\pi$
$338$	3.02900	−	14.9487i	0.164756	−	0.813103i
$339$	2.42937	+	1.98649i	0.131945	+	0.107891i
$340$	−0.461537	−	0.135519i	−0.0250303	−	0.00734957i
$341$	−20.4225	+	3.20173i	−1.10594	+	0.173383i
$342$	2.89931	−	0.851315i	0.156777	−	0.0460339i
$343$	18.5630	+	7.84477i	1.00231	+	0.423578i
$344$	−20.8990	+	11.8022i	−1.12680	+	0.636332i
$345$	1.98769	+	0.462218i	0.107014	+	0.0248850i
$346$	−25.6031	+	2.93768i	−1.37643	+	0.157931i
$347$	11.0383	−	16.1429i	0.592565	−	0.866599i	−0.406324	−	0.913729i	$-0.633190\pi$
$347$	11.0383	−	16.1429i	0.592565	−	0.866599i	0.998889	+	0.0471306i	$0.0150077\pi$
$348$	5.55336	−	0.317553i	0.297692	−	0.0170226i
$349$	−9.10940	−	23.3973i	−0.487615	−	1.25243i	−0.933899	−	0.357537i	$-0.883617\pi$
$349$	−9.10940	−	23.3973i	−0.487615	−	1.25243i	0.446284	−	0.894891i	$-0.352747\pi$
$350$	−9.95961	+	1.72358i	−0.532363	+	0.0921291i
$351$	−0.408730	+	2.84278i	−0.0218164	+	0.151736i
$352$	1.16280	+	9.11034i	0.0619773	+	0.485583i
$353$	0.00910489	+	0.0633259i	0.000484605	+	0.00337050i	0.990062	−	0.140629i	$-0.0449126\pi$
$353$	0.00910489	+	0.0633259i	0.000484605	+	0.00337050i	−0.989578	+	0.144000i	$0.954004\pi$
$354$	−6.38824	−	19.6610i	−0.339531	−	1.04497i
$355$	−1.87410	−	0.107165i	−0.0994670	−	0.00568773i
$356$	4.80021	−	6.22502i	0.254411	−	0.329926i
$357$	−3.49829	+	1.47839i	−0.185149	+	0.0782446i
$358$	−15.2058	+	12.4337i	−0.803652	+	0.657143i
$359$	−8.70137	−	16.4909i	−0.459241	−	0.870358i	−0.999582	−	0.0289122i	$-0.990796\pi$
$359$	−8.70137	−	16.4909i	−0.459241	−	0.870358i	0.540341	−	0.841446i	$-0.318295\pi$
$360$	−2.90120	−	2.10785i	−0.152907	−	0.111093i
$361$	−6.95554	+	11.5345i	−0.366081	+	0.607077i
$362$	2.79731			0.147023
$363$	7.37361	+	20.8730i	0.387014	+	1.09555i
$364$	−0.808845			−0.0423950
$365$	−0.0648755	+	0.107584i	−0.00339574	+	0.00563120i
$366$	−11.6240	−	8.44533i	−0.607596	−	0.441445i
$367$	16.3782	+	31.0402i	0.854938	+	1.62029i	0.782277	+	0.622930i	$0.214058\pi$
$367$	16.3782	+	31.0402i	0.854938	+	1.62029i	0.0726603	+	0.997357i	$0.476851\pi$
$368$	1.93025	−	1.57836i	0.100621	−	0.0822778i
$369$	−9.23607	+	3.90320i	−0.480811	+	0.203192i
$370$	−1.40980	+	1.82827i	−0.0732922	+	0.0950471i
$371$	15.6528	+	0.895061i	0.812654	+	0.0464693i
$372$	1.94810	+	5.99563i	0.101004	+	0.310859i
$373$	−4.45205	−	30.9647i	−0.230519	−	1.60329i	−0.695871	−	0.718167i	$-0.744981\pi$
$373$	−4.45205	−	30.9647i	−0.230519	−	1.60329i	0.465352	−	0.885126i	$-0.345928\pi$
$374$	−2.32230	+	2.59578i	−0.120084	+	0.134225i
$375$	−2.79681	+	19.4522i	−0.144426	+	1.00451i
$376$	31.2809	−	5.41338i	1.61319	−	0.279174i
$377$	1.46024	+	3.75060i	0.0752064	+	0.193166i
$378$	10.5426	−	0.602845i	0.542250	−	0.0310070i
$379$	−17.2131	+	25.1734i	−0.884178	+	1.29307i	0.0711336	+	0.997467i	$0.477338\pi$
$379$	−17.2131	+	25.1734i	−0.884178	+	1.29307i	−0.955311	+	0.295602i	$0.904480\pi$
$380$	−1.30957	+	0.150259i	−0.0671794	+	0.00770812i
$381$	−33.3566	−	7.75675i	−1.70891	−	0.397390i
$382$	2.06970	−	1.16882i	0.105895	−	0.0598018i
$383$	13.5451	+	5.72420i	0.692122	+	0.292493i	0.706815	−	0.707399i	$-0.250132\pi$
$383$	13.5451	+	5.72420i	0.692122	+	0.292493i	−0.0146927	+	0.999892i	$0.504677\pi$
$384$	−10.2716	+	3.01603i	−0.524173	+	0.153911i
$385$	−2.19215	+	7.83268i	−0.111723	+	0.399191i
$386$	−20.9058	−	6.13849i	−1.06408	−	0.312441i
$387$	6.37072	+	5.20932i	0.323842	+	0.264804i
$388$	1.16607	−	5.75480i	0.0591984	−	0.292156i
$389$	−2.56938	+	6.59939i	−0.130273	+	0.334602i	−0.981859	−	0.189612i	$-0.939277\pi$
$389$	−2.56938	+	6.59939i	−0.130273	+	0.334602i	0.851587	+	0.524214i	$0.175641\pi$
$390$	0.621116	−	1.91160i	0.0314514	−	0.0967975i
$391$	−0.768897	−	0.133063i	−0.0388848	−	0.00672928i
$392$	−1.31631	−	6.49626i	−0.0664839	−	0.328111i
$393$	−6.36592	+	12.0648i	−0.321118	+	0.608587i
$394$	2.44862	−	1.20391i	0.123360	−	0.0606519i
$395$	6.33612	+	13.8742i	0.318805	+	0.698086i
$396$	1.53749	−	0.836401i	0.0772619	−	0.0420307i
$397$	9.65365	−	21.1386i	0.484503	−	1.06091i	−0.496698	−	0.867924i	$-0.665454\pi$
$397$	9.65365	−	21.1386i	0.484503	−	1.06091i	0.981201	−	0.192990i	$-0.0618185\pi$
$398$	0.681934	+	23.8708i	0.0341823	+	1.19654i
$399$	−7.25329	+	7.46346i	−0.363119	+	0.373640i
$400$	7.17880	+	7.38681i	0.358940	+	0.369340i
$401$	−0.444041	+	15.5435i	−0.0221744	+	0.776204i	0.910087	+	0.414418i	$0.136015\pi$
$401$	−0.444041	+	15.5435i	−0.0221744	+	0.776204i	−0.932261	+	0.361786i	$0.882167\pi$
$402$	29.8905	+	14.6962i	1.49080	+	0.732979i
$403$	−3.69037	+	2.68121i	−0.183830	+	0.133561i
$404$	0.651284	+	7.58277i	0.0324026	+	0.377257i
$405$	3.13211	−	11.9158i	0.155636	−	0.592100i
$406$	12.4493	−	8.00066i	0.617847	−	0.397066i
$407$	−2.53941	−	5.00330i	−0.125874	−	0.248004i
$408$	4.44938	+	2.85945i	0.220277	+	0.141564i
$409$	6.07744	−	5.57783i	0.300510	−	0.275806i	−0.511708	−	0.859159i	$-0.670987\pi$
$409$	6.07744	−	5.57783i	0.300510	−	0.275806i	0.812218	+	0.583354i	$0.198260\pi$
$410$	−12.6933	+	2.95170i	−0.626878	+	0.145774i
$411$	2.67773	−	0.955413i	0.132083	−	0.0471270i
$412$	−0.567385	−	2.15855i	−0.0279530	−	0.106344i
$413$	13.6000	+	12.4820i	0.669213	+	0.614199i
$414$	−1.01730	−	0.574495i	−0.0499975	−	0.0282349i
$415$	−6.52426	−	8.46082i	−0.320264	−	0.415325i
$416$	1.14391	+	1.67292i	0.0560850	+	0.0820217i
$417$	−21.6344	−	24.9674i	−1.05944	−	1.22266i
$418$	−3.09294	+	9.02951i	−0.151280	+	0.441648i
$419$	13.5764	−	15.6680i	0.663249	−	0.765430i	−0.320055	−	0.947399i	$-0.603701\pi$
$419$	13.5764	−	15.6680i	0.663249	−	0.765430i	0.983304	+	0.181969i	$0.0582469\pi$
$420$	2.46429	+	0.282751i	0.120245	+	0.0137968i
$421$	8.29664	+	2.96024i	0.404354	+	0.144273i	0.530392	−	0.847752i	$-0.322045\pi$
$421$	8.29664	+	2.96024i	0.404354	+	0.144273i	−0.126039	+	0.992025i	$0.540226\pi$
$422$	0.936634	−	10.9050i	0.0455946	−	0.530849i
$423$	−5.62090	−	9.32122i	−0.273298	−	0.453213i
$424$	−11.2751	−	18.6977i	−0.547569	−	0.908041i
$425$	0.275859	−	3.21177i	0.0133811	−	0.155794i
$426$	3.90404	+	1.39296i	0.189151	+	0.0674891i
$427$	12.7463	+	1.46250i	0.616836	+	0.0707754i
$428$	3.06858	−	3.54134i	0.148326	−	0.171177i
$429$	3.54606	+	3.35964i	0.171205	+	0.162205i
$430$	7.00419	+	8.08327i	0.337772	+	0.389810i
$431$	−6.16218	−	9.01190i	−0.296822	−	0.434088i	0.648016	−	0.761627i	$-0.275599\pi$
$431$	−6.16218	−	9.01190i	−0.296822	−	0.434088i	−0.944838	+	0.327539i	$0.893781\pi$
$432$	−6.57133	−	8.52185i	−0.316163	−	0.410008i
$433$	−14.2786	−	8.06352i	−0.686188	−	0.387508i	0.108858	−	0.994057i	$-0.465281\pi$
$433$	−14.2786	−	8.06352i	−0.686188	−	0.387508i	−0.795046	+	0.606549i	$0.792553\pi$
$434$	12.3565	+	11.3407i	0.593131	+	0.544371i
$435$	−3.13778	−	11.9374i	−0.150445	−	0.572353i
$436$	−1.26010	+	0.449604i	−0.0603480	+	0.0215321i
$437$	−2.08278	+	0.484331i	−0.0996331	+	0.0231687i
$438$	0.204383	−	0.187581i	0.00976580	−	0.00896297i
$439$	19.1745	+	12.3227i	0.915149	+	0.588131i	0.911246	−	0.411862i	$-0.135121\pi$
$439$	19.1745	+	12.3227i	0.915149	+	0.588131i	0.00390299	+	0.999992i	$0.498758\pi$
$440$	10.7274	−	3.63691i	0.511410	−	0.173383i
$441$	−1.91189	+	1.22870i	−0.0910423	+	0.0585093i
$442$	−0.195384	+	0.743316i	−0.00929345	+	0.0353560i
$443$	−2.85742	−	33.2683i	−0.135760	−	1.58063i	−0.674578	−	0.738203i	$-0.735675\pi$
$443$	−2.85742	−	33.2683i	−0.135760	−	1.58063i	0.538818	−	0.842422i	$-0.318871\pi$
$444$	−1.38431	+	1.00576i	−0.0656963	+	0.0477312i
$445$	−15.6533	−	7.69621i	−0.742037	−	0.364835i
$446$	0.110227	−	3.85846i	0.00521942	−	0.182703i
$447$	28.6524	+	29.4827i	1.35521	+	1.39448i
$448$	13.5985	−	13.9925i	0.642467	−	0.661083i
$449$	0.581380	+	20.3509i	0.0274370	+	0.960420i	0.890407	+	0.455165i	$0.150420\pi$
$449$	0.581380	+	20.3509i	0.0274370	+	0.960420i	−0.862970	+	0.505255i	$0.831398\pi$
$450$	2.00495	−	4.39022i	0.0945140	−	0.206957i
$451$	6.78092	−	30.9373i	0.319301	−	1.45678i
$452$	0.325568	+	0.712894i	0.0153134	+	0.0335317i
$453$	3.04776	−	1.49848i	0.143196	−	0.0704048i
$454$	−13.2738	+	25.1566i	−0.622970	+	1.18066i
$455$	0.356430	+	1.75905i	0.0167097	+	0.0824657i
$456$	14.2813	+	2.47148i	0.668785	+	0.115738i
$457$	5.23445	−	16.1100i	0.244857	−	0.753592i	−0.750803	−	0.660526i	$-0.770333\pi$
$457$	5.23445	−	16.1100i	0.244857	−	0.753592i	0.995660	−	0.0930661i	$-0.0296668\pi$
$458$	−0.0463990	+	0.119175i	−0.00216808	+	0.00556868i
$459$	−0.668810	+	3.30071i	−0.0312174	+	0.154064i
$460$	0.394541	+	0.322614i	0.0183956	+	0.0150420i
$461$	−14.0031	−	4.11169i	−0.652192	−	0.191501i	−0.0611333	−	0.998130i	$-0.519471\pi$
$461$	−14.0031	−	4.11169i	−0.652192	−	0.191501i	−0.591058	+	0.806629i	$0.701290\pi$
$462$	9.51740	−	15.2315i	0.442789	−	0.708636i
$463$	13.5557	−	3.98031i	0.629986	−	0.184981i	0.0488751	−	0.998805i	$-0.484436\pi$
$463$	13.5557	−	3.98031i	0.629986	−	0.184981i	0.581111	+	0.813824i	$0.302618\pi$
$464$	−13.8913	−	5.87051i	−0.644887	−	0.272532i
$465$	12.1807	−	6.87874i	0.564865	−	0.318994i
$466$	17.4895	+	4.06700i	0.810184	+	0.188400i
$467$	−23.6684	+	2.71570i	−1.09524	+	0.125667i	−0.642732	−	0.766091i	$-0.722199\pi$
$467$	−23.6684	+	2.71570i	−1.09524	+	0.125667i	−0.452511	+	0.891759i	$0.649472\pi$
$468$	0.218000	−	0.318814i	0.0100770	−	0.0147372i
$469$	−29.6938	+	1.69795i	−1.37113	+	0.0784041i
$470$	−5.13262	−	13.1830i	−0.236750	−	0.608088i
$471$	9.45263	−	1.63584i	0.435554	−	0.0753756i
$472$	3.65856	−	25.4459i	0.168399	−	1.17124i
$473$	−25.0538	+	6.92706i	−1.15198	+	0.318506i
$474$	−4.79319	−	33.3374i	−0.220159	−	1.53124i
$475$	−2.72977	−	8.40137i	−0.125250	−	0.385481i
$476$	−0.946923	−	0.0541470i	−0.0434021	−	0.00248182i
$477$	−4.57154	+	5.92848i	−0.209317	+	0.271447i
$478$	3.87369	−	1.63704i	0.177178	−	0.0748762i
$479$	−12.8417	+	10.5006i	−0.586750	+	0.479783i	−0.879171	−	0.476507i	$-0.841903\pi$
$479$	−12.8417	+	10.5006i	−0.586750	+	0.479783i	0.292421	+	0.956290i	$0.405539\pi$
$480$	−2.90033	−	5.49675i	−0.132382	−	0.250891i
$481$	−1.00165	−	0.727742i	−0.0456713	−	0.0331822i
$482$	−1.50715	+	2.49933i	−0.0686489	+	0.113841i
$483$	4.02387			0.183093
$484$	−0.647458	+	5.49045i	−0.0294299	+	0.249566i
$485$	−13.0292			−0.591626
$486$	−6.60970	+	10.9609i	−0.299822	+	0.497199i
$487$	−27.0986	−	19.6883i	−1.22795	−	0.892160i	−0.231218	−	0.972902i	$-0.574271\pi$
$487$	−27.0986	−	19.6883i	−1.22795	−	0.892160i	−0.996735	+	0.0807415i	$0.974271\pi$
$488$	−8.33810	−	15.8025i	−0.377448	−	0.715343i
$489$	38.3524	−	31.3606i	1.73436	−	1.41818i
$490$	−2.72079	+	1.14981i	−0.122913	+	0.0519433i
$491$	−3.33910	+	4.33023i	−0.150692	+	0.195420i	−0.861197	−	0.508271i	$-0.830285\pi$
$491$	−3.33910	+	4.33023i	−0.150692	+	0.195420i	0.710505	+	0.703692i	$0.248466\pi$
$492$	−9.64292	−	0.551402i	−0.434736	−	0.0248591i
$493$	1.45844	+	4.48863i	0.0656850	+	0.202158i
$494$	0.299733	+	2.08469i	0.0134856	+	0.0937947i
$495$	−2.49650	−	2.97512i	−0.112209	−	0.133722i
$496$	2.43242	−	16.9178i	0.109219	−	0.759634i
$497$	−3.64715	+	0.631164i	−0.163597	+	0.0283116i
$498$	8.55954	+	21.9850i	0.383562	+	0.985171i
$499$	−25.1735	+	1.43947i	−1.12692	+	0.0644396i	−0.610588	−	0.791948i	$-0.709067\pi$
$499$	−25.1735	+	1.43947i	−1.12692	+	0.0644396i	−0.516333	+	0.856388i	$0.672703\pi$
$500$	−2.77025	+	4.05136i	−0.123889	+	0.181182i
$501$	−3.49120	+	0.400578i	−0.155975	+	0.0178965i
$502$	23.7918	+	5.53255i	1.06188	+	0.246930i
$503$	7.86171	−	4.43971i	0.350536	−	0.197957i	−0.306400	−	0.951903i	$-0.599125\pi$
$503$	7.86171	−	4.43971i	0.350536	−	0.197957i	0.656937	+	0.753946i	$0.271852\pi$
$504$	−6.51324	−	2.75252i	−0.290123	−	0.122607i
$505$	16.2038	−	4.75786i	0.721059	−	0.211722i
$506$	3.33704	−	1.57553i	0.148349	−	0.0700408i
$507$	−24.0680	−	7.06702i	−1.06890	−	0.313857i
$508$	−6.62101	−	5.41397i	−0.293760	−	0.240206i
$509$	4.13459	−	20.4050i	0.183263	−	0.904437i	−0.777886	−	0.628405i	$-0.783708\pi$
$509$	4.13459	−	20.4050i	0.183263	−	0.904437i	0.961149	−	0.276031i	$-0.0890193\pi$
$510$	0.855116	−	2.19635i	0.0378652	−	0.0972559i
$511$	−0.0765487	+	0.235593i	−0.00338632	+	0.0104220i
$512$	−24.0319	−	4.15889i	−1.06207	−	0.183799i
$513$	1.83276	+	9.04505i	0.0809185	+	0.399349i
$514$	4.84875	−	9.18940i	0.213869	−	0.405327i
$515$	−4.44434	+	2.18513i	−0.195841	+	0.0962885i
$516$	3.29305	+	7.21077i	0.144968	+	0.317437i
$517$	34.2899	+	2.50662i	1.50807	+	0.110241i
$518$	−1.89108	+	4.14088i	−0.0830891	+	0.181940i
$519$	1.21029	+	42.3656i	0.0531258	+	1.85964i
$520$	1.74199	−	1.79247i	0.0763913	−	0.0786048i
$521$	−0.641203	−	0.659783i	−0.0280916	−	0.0289056i	0.702940	−	0.711249i	$-0.251870\pi$
$521$	−0.641203	−	0.659783i	−0.0280916	−	0.0289056i	−0.731032	+	0.682343i	$0.760961\pi$
$522$	−0.201784	+	7.06334i	−0.00883182	+	0.309154i
$523$	−11.1935	−	5.50347i	−0.489457	−	0.240650i	0.179769	−	0.983709i	$-0.442465\pi$
$523$	−11.1935	−	5.50347i	−0.489457	−	0.240650i	−0.669226	+	0.743059i	$0.733374\pi$
$524$	−2.75612	+	2.00244i	−0.120402	+	0.0874769i
$525$	1.42251	+	16.5620i	0.0620834	+	0.722823i
$526$	4.04475	−	15.3878i	0.176360	−	0.670941i
$527$	−4.49984	+	2.89187i	−0.196016	+	0.125972i
$528$	−18.2876	+	0.755134i	−0.795866	+	0.0328630i
$529$	−18.6533	−	11.9878i	−0.811014	−	0.521207i
$530$	−7.16849	+	6.57918i	−0.311379	+	0.285781i
$531$	−8.58538	+	1.99644i	−0.372574	+	0.0866383i
$532$	−2.44797	+	0.873434i	−0.106133	+	0.0378682i
$533$	−1.77667	−	6.75917i	−0.0769563	−	0.292772i
$534$	28.3771	+	26.0443i	1.22800	+	1.12705i
$535$	−9.05382	−	5.11293i	−0.391431	−	0.221051i
$536$	25.2930	+	32.8006i	1.09249	+	1.41677i
$537$	18.2334	+	26.6655i	0.786829	+	1.15070i
$538$	14.1361	+	16.3139i	0.609450	+	0.703342i
$539$	0.318703	−	7.17148i	0.0137275	−	0.308897i
$540$	1.44042	−	1.66233i	0.0619857	−	0.0715353i
$541$	−11.5155	−	1.32129i	−0.495092	−	0.0568065i	−0.137150	−	0.990550i	$-0.543794\pi$
$541$	−11.5155	−	1.32129i	−0.495092	−	0.0568065i	−0.357942	+	0.933744i	$0.616521\pi$
$542$	27.4022	+	9.77708i	1.17702	+	0.419962i
$543$	0.393682	−	4.58355i	0.0168945	−	0.196699i
$544$	1.22720	+	2.03509i	0.0526158	+	0.0872536i
$545$	1.53307	+	2.54231i	0.0656695	+	0.108901i
$546$	0.339153	−	3.94869i	0.0145144	−	0.168988i
$547$	−13.0657	−	4.66185i	−0.558651	−	0.199326i	0.0416053	−	0.999134i	$-0.486753\pi$
$547$	−13.0657	−	4.66185i	−0.558651	−	0.199326i	−0.600256	+	0.799808i	$0.704935\pi$
$548$	0.705397	+	0.0809368i	0.0301331	+	0.00345745i
$549$	−4.01184	+	4.62991i	−0.171221	+	0.197600i
$550$	7.66446	+	13.1780i	0.326814	+	0.561912i
$551$	8.46954	+	9.77437i	0.360814	+	0.416402i
$552$	−3.16301	−	4.62575i	−0.134627	−	0.196885i
$553$	18.3650	+	23.8162i	0.780960	+	1.01277i
$554$	3.00429	+	1.69660i	0.127640	+	0.0720815i
$555$	2.79731	+	2.56735i	0.118739	+	0.108978i
$556$	−2.09744	−	7.97947i	−0.0889511	−	0.338405i
$557$	−3.08230	+	1.09976i	−0.130601	+	0.0465984i	−0.400541	−	0.916279i	$-0.631178\pi$
$557$	−3.08230	+	1.09976i	−0.130601	+	0.0465984i	0.269940	+	0.962877i	$0.412996\pi$
$558$	−7.80037	+	1.81390i	−0.330216	+	0.0767884i
$559$	−4.22586	+	3.87846i	−0.178735	+	0.164041i
$560$	−5.65743	−	3.63581i	−0.239070	−	0.153641i
$561$	3.92650	+	4.17055i	0.165777	+	0.176081i
$562$	−20.3984	+	13.1093i	−0.860455	+	0.552981i
$563$	2.96283	−	11.2718i	0.124868	−	0.475049i	−0.875092	−	0.483957i	$-0.839199\pi$
$563$	2.96283	−	11.2718i	0.124868	−	0.475049i	0.999960	+	0.00890804i	$0.00283556\pi$
$564$	−0.897257	−	10.4466i	−0.0377813	−	0.439880i
$565$	1.40692	−	1.02218i	0.0591894	−	0.0430036i
$566$	8.80658	+	4.32991i	0.370168	+	0.181999i
$567$	0.693725	−	24.2835i	0.0291337	−	1.01981i
$568$	3.59245	+	3.69654i	0.150736	+	0.155104i
$569$	−21.0516	+	21.6616i	−0.882529	+	0.908101i	−0.996347	−	0.0854010i	$-0.972783\pi$
$569$	−21.0516	+	21.6616i	−0.882529	+	0.908101i	0.113818	+	0.993502i	$0.463692\pi$
$570$	−0.184438	−	6.45617i	−0.00772526	−	0.270419i
$571$	−8.92280	+	19.5382i	−0.373407	+	0.817648i	0.625881	+	0.779919i	$0.284740\pi$
$571$	−8.92280	+	19.5382i	−0.373407	+	0.817648i	−0.999288	+	0.0377293i	$0.987988\pi$
$572$	0.424527	+	1.14369i	0.0177504	+	0.0478200i
$573$	−1.62389	−	3.55582i	−0.0678390	−	0.148547i
$574$	−23.0598	+	11.3377i	−0.962496	+	0.473227i
$575$	−1.59387	+	3.02073i	−0.0664692	+	0.125973i
$576$	1.85023	+	9.13122i	0.0770927	+	0.380468i
$577$	19.5377	+	3.38114i	0.813366	+	0.140759i	0.562004	−	0.827135i	$-0.310031\pi$
$577$	19.5377	+	3.38114i	0.813366	+	0.140759i	0.251362	+	0.967893i	$0.419121\pi$
$578$	6.14988	−	18.9274i	0.255801	−	0.787276i
$579$	−13.0005	+	33.3914i	−0.540281	+	1.38770i
$580$	0.612154	−	3.02110i	0.0254183	−	0.125444i
$581$	−16.3087	−	13.3356i	−0.676600	−	0.553253i
$582$	27.6054	+	8.10566i	1.14428	+	0.335991i
$583$	−6.94990	−	22.6025i	−0.287835	−	0.936100i
$584$	0.331004	−	0.0971915i	0.0136970	−	0.00402181i
$585$	−0.789413	−	0.333609i	−0.0326382	−	0.0137930i
$586$	−10.4144	+	5.88129i	−0.430216	+	0.242954i
$587$	20.6476	+	4.80138i	0.852216	+	0.198174i	0.629780	−	0.776773i	$-0.283145\pi$
$587$	20.6476	+	4.80138i	0.852216	+	0.198174i	0.222435	+	0.974947i	$0.428599\pi$
$588$	−2.17492	+	0.249549i	−0.0896922	+	0.0102912i
$589$	−8.27360	+	12.0997i	−0.340908	+	0.498561i
$590$	−11.4374	+	0.654014i	−0.470870	+	0.0269253i
$591$	−1.62806	−	4.18164i	−0.0669695	−	0.172010i
$592$	4.57117	−	0.791071i	0.187874	−	0.0325128i
$593$	−2.64865	+	18.4217i	−0.108767	+	0.756490i	0.860317	+	0.509759i	$0.170265\pi$
$593$	−2.64865	+	18.4217i	−0.108767	+	0.756490i	−0.969084	+	0.246731i	$0.920644\pi$
$594$	−6.38574	−	14.5905i	−0.262010	−	0.598656i
$595$	0.299519	+	2.08320i	0.0122791	+	0.0854030i
$596$	3.17275	+	9.76472i	0.129961	+	0.399979i
$597$	39.2097	+	2.24209i	1.60475	+	0.0917627i
$598$	0.497255	−	0.644852i	0.0203343	−	0.0263699i
$599$	27.0070	−	11.4132i	1.10348	−	0.466333i	0.240025	−	0.970767i	$-0.422844\pi$
$599$	27.0070	−	11.4132i	1.10348	−	0.466333i	0.863450	+	0.504434i	$0.168299\pi$
$600$	17.9211	−	14.6540i	0.731625	−	0.598247i
$601$	−11.0947	−	21.0269i	−0.452564	−	0.857704i	−0.999785	−	0.0207164i	$-0.993405\pi$
$601$	−11.0947	−	21.0269i	−0.452564	−	0.857704i	0.547221	−	0.836988i	$-0.315686\pi$
$602$	17.0618	+	12.3962i	0.695389	+	0.505230i
$603$	7.33379	−	12.1617i	0.298655	−	0.495264i
$604$	0.848166			0.0345114
$605$	12.2258	−	1.01138i	0.497049	−	0.0411185i
$606$	−37.2913			−1.51486
$607$	−10.2833	+	17.0529i	−0.417385	+	0.692155i	−0.991996	−	0.126271i	$-0.959699\pi$
$607$	−10.2833	+	17.0529i	−0.417385	+	0.692155i	0.574611	+	0.818427i	$0.305153\pi$
$608$	5.26857	+	3.82784i	0.213669	+	0.155240i
$609$	−11.3575	−	21.5248i	−0.460229	−	0.872231i
$610$	−6.16390	+	5.04020i	−0.249569	+	0.204072i
$611$	6.98830	−	2.95328i	0.282716	−	0.119477i
$612$	0.276557	−	0.358646i	0.0111792	−	0.0144974i
$613$	33.4769	+	1.91428i	1.35212	+	0.0773170i	0.718068	−	0.695973i	$-0.245027\pi$
$613$	33.4769	+	1.91428i	1.35212	+	0.0773170i	0.634052	+	0.773290i	$0.281391\pi$
$614$	7.85768	+	24.1834i	0.317110	+	0.975965i
$615$	3.05013	+	21.2141i	0.122993	+	0.855436i
$616$	18.9782	−	11.7757i	0.764654	−	0.474458i
$617$	−3.02097	+	21.0113i	−0.121620	+	0.845883i	0.834102	+	0.551610i	$0.185986\pi$
$617$	−3.02097	+	21.0113i	−0.121620	+	0.845883i	−0.955722	+	0.294272i	$0.904923\pi$
$618$	10.7757	−	1.86481i	0.433464	−	0.0750139i
$619$	9.24673	+	23.7500i	0.371658	+	0.954595i	0.986177	+	0.165693i	$0.0529861\pi$
$619$	9.24673	+	23.7500i	0.371658	+	0.954595i	−0.614520	+	0.788901i	$0.710650\pi$
$620$	3.48784	−	0.199442i	0.140075	−	0.00800978i
$621$	2.01406	−	2.94546i	0.0808213	−	0.118197i
$622$	−32.9056	+	3.77557i	−1.31939	+	0.151386i
$623$	−33.4999	−	7.79007i	−1.34215	−	0.312103i
$624$	−3.51681	+	1.98603i	−0.140785	+	0.0795049i
$625$	−7.26835	−	3.07163i	−0.290734	−	0.122865i
$626$	−0.0526168	+	0.0154497i	−0.00210299	+	0.000617493i
$627$	14.3601	+	6.33873i	0.573487	+	0.253145i
$628$	2.29873	+	0.674968i	0.0917294	+	0.0269342i
$629$	−1.12393	−	0.919029i	−0.0448138	−	0.0366441i
$630$	−0.625768	+	3.08829i	−0.0249312	+	0.123040i
$631$	5.00986	−	12.8677i	0.199440	−	0.512256i	−0.796254	−	0.604963i	$-0.793188\pi$
$631$	5.00986	−	12.8677i	0.199440	−	0.512256i	0.995694	+	0.0927062i	$0.0295517\pi$
$632$	12.9425	−	39.8329i	0.514825	−	1.58447i
$633$	−17.7367	−	3.06946i	−0.704971	−	0.122000i
$634$	−8.17713	−	40.3557i	−0.324755	−	1.60273i
$635$	−8.85650	+	16.7849i	−0.351460	+	0.666090i
$636$	−6.47150	+	3.18182i	−0.256612	+	0.126168i
$637$	−0.658035	−	1.44090i	−0.0260723	−	0.0570904i
$638$	−17.8468	−	13.4038i	−0.706563	−	0.530661i
$639$	0.734199	−	1.60767i	0.0290445	−	0.0635985i
$640$	0.169408	+	5.93005i	0.00669643	+	0.234406i
$641$	−12.6607	+	13.0276i	−0.500068	+	0.514558i	−0.919426	−	0.393263i	$-0.871346\pi$
$641$	−12.6607	+	13.0276i	−0.500068	+	0.514558i	0.419358	+	0.907821i	$0.362255\pi$
$642$	16.0017	+	16.4654i	0.631538	+	0.649838i
$643$	−0.255925	+	8.95853i	−0.0100927	+	0.353290i	0.978814	+	0.204752i	$0.0656387\pi$
$643$	−0.255925	+	8.95853i	−0.0100927	+	0.353290i	−0.988907	+	0.148538i	$0.952543\pi$
$644$	0.901811	+	0.443391i	0.0355363	+	0.0174720i
$645$	14.2307	−	10.3392i	0.560331	−	0.407105i
$646$	0.211344	+	2.46064i	0.00831522	+	0.0968124i
$647$	0.827651	−	3.14871i	0.0325383	−	0.123789i	−0.948895	−	0.315591i	$-0.897797\pi$
$647$	0.827651	−	3.14871i	0.0325383	−	0.123789i	0.981433	+	0.191803i	$0.0614334\pi$
$648$	−28.4611	+	18.2908i	−1.11806	+	0.718532i
$649$	10.5112	−	25.7814i	0.412600	−	1.01201i
$650$	2.82995	+	1.81870i	0.111000	+	0.0713352i
$651$	20.3214	−	18.6508i	0.796458	−	0.730982i
$652$	12.0510	−	2.80234i	0.471953	−	0.109748i
$653$	−6.20516	+	2.21400i	−0.242827	+	0.0866404i	−0.454659	−	0.890666i	$-0.650239\pi$
$653$	−6.20516	+	2.21400i	−0.242827	+	0.0866404i	0.211832	+	0.977306i	$0.432057\pi$
$654$	−1.66655	−	6.34021i	−0.0651672	−	0.247922i
$655$	5.56937	+	5.11152i	0.217613	+	0.199724i
$656$	22.8018	+	12.8768i	0.890260	+	0.502753i
$657$	−0.0722299	−	0.0936694i	−0.00281796	−	0.00365439i
$658$	−15.7450	−	23.0263i	−0.613803	−	0.897659i
$659$	−1.34080	−	1.54737i	−0.0522303	−	0.0602769i	0.729033	−	0.684478i	$-0.239970\pi$
$659$	−1.34080	−	1.54737i	−0.0522303	−	0.0602769i	−0.781264	+	0.624201i	$0.785424\pi$
$660$	−0.893597	−	3.63286i	−0.0347832	−	0.141409i
$661$	12.8100	−	14.7835i	0.498250	−	0.575011i	−0.449801	−	0.893129i	$-0.648505\pi$
$661$	12.8100	−	14.7835i	0.498250	−	0.575011i	0.948051	+	0.318117i	$0.103051\pi$
$662$	−43.1836	−	4.95485i	−1.67838	−	0.192576i
$663$	1.19047	+	0.424759i	0.0462340	+	0.0164963i
$664$	−2.51063	+	29.2307i	−0.0974312	+	1.13437i
$665$	2.97826	+	4.93889i	0.115492	+	0.191522i
$666$	−1.12249	−	1.86144i	−0.0434955	−	0.0721292i
$667$	0.427918	−	4.98216i	0.0165691	−	0.192910i
$668$	−0.826571	−	0.294920i	−0.0319810	−	0.0114108i
$669$	−6.30680	−	0.723638i	−0.243835	−	0.0279775i
$670$	12.0874	−	13.9496i	0.466978	−	0.538922i
$671$	−4.62203	−	18.7906i	−0.178432	−	0.725401i
$672$	−8.02507	−	9.26142i	−0.309574	−	0.357267i
$673$	26.2069	+	38.3264i	1.01020	+	1.47737i	0.873538	+	0.486757i	$0.161820\pi$
$673$	26.2069	+	38.3264i	1.01020	+	1.47737i	0.136665	+	0.990617i	$0.456362\pi$
$674$	−7.58560	−	9.83719i	−0.292187	−	0.378914i
$675$	12.8353	+	7.24844i	0.494032	+	0.278992i
$676$	−4.61530	−	4.23589i	−0.177512	−	0.162919i
$677$	−9.31831	−	35.4505i	−0.358132	−	1.36247i	−0.865571	−	0.500787i	$-0.833044\pi$
$677$	−9.31831	−	35.4505i	−0.358132	−	1.36247i	0.507439	−	0.861688i	$-0.330592\pi$
$678$	−3.61678	+	1.29047i	−0.138902	+	0.0495600i
$679$	−25.0231	+	5.81888i	−0.960300	+	0.223308i
$680$	2.15936	−	1.98184i	0.0828077	−	0.0760002i
$681$	39.3525	+	25.2903i	1.50799	+	0.969127i
$682$	9.55008	−	23.4240i	0.365691	−	0.896952i
$683$	−12.8597	+	8.26440i	−0.492061	+	0.316228i	−0.763034	−	0.646359i	$-0.776291\pi$
$683$	−12.8597	+	8.26440i	−0.492061	+	0.316228i	0.270973	+	0.962587i	$0.412655\pi$
$684$	0.315504	−	1.20030i	0.0120636	−	0.0458946i
$685$	−0.134825	−	1.56974i	−0.00515142	−	0.0599769i
$686$	−19.9507	+	14.4950i	−0.761720	+	0.553422i
$687$	0.188745	+	0.0927997i	0.00720108	+	0.00354053i
$688$	0.613726	−	21.4832i	0.0233981	−	0.819039i
$689$	−3.63662	−	3.74199i	−0.138544	−	0.142558i
$690$	−1.74040	+	1.79083i	−0.0662559	+	0.0681757i
$691$	−0.590514	−	20.6707i	−0.0224642	−	0.786350i	−0.930252	−	0.366921i	$-0.880412\pi$
$691$	−0.590514	−	20.6707i	−0.0224642	−	0.786350i	0.907788	−	0.419429i	$-0.137770\pi$
$692$	−4.39703	+	9.62814i	−0.167150	+	0.366007i
$693$	−6.12333	−	4.59890i	−0.232606	−	0.174698i
$694$	9.94106	+	21.7679i	0.377358	+	0.826298i
$695$	−16.4293	+	8.07773i	−0.623198	+	0.306406i
$696$	−15.8168	+	29.9761i	−0.599534	+	1.13624i
$697$	−1.62749	−	8.03197i	−0.0616455	−	0.304232i
$698$	30.2744	+	5.23919i	1.14590	+	0.198306i
$699$	9.12541	−	28.0851i	0.345155	−	1.06228i
$700$	−1.50616	+	3.86854i	−0.0569274	+	0.146217i
$701$	−6.69755	+	33.0537i	−0.252963	+	1.24842i	0.629113	+	0.777314i	$0.283418\pi$
$701$	−6.69755	+	33.0537i	−0.252963	+	1.24842i	−0.882076	+	0.471107i	$0.843854\pi$
$702$	−2.72068	−	2.22469i	−0.102685	−	0.0839654i
$703$	−3.81735	−	1.12088i	−0.143974	−	0.0422746i
$704$	−26.9223	−	11.8839i	−1.01467	−	0.447890i
$705$	−22.3235	+	6.55478i	−0.840752	+	0.246867i
$706$	−0.0721129	−	0.0304752i	−0.00271400	−	0.00114695i
$707$	28.9951	−	16.3743i	1.09047	−	0.615819i
$708$	−8.27003	−	1.92311i	−0.310807	−	0.0722750i
$709$	39.9258	−	4.58106i	1.49944	−	0.172045i	0.674928	−	0.737884i	$-0.264175\pi$
$709$	39.9258	−	4.58106i	1.49944	−	0.172045i	0.824516	+	0.565838i	$0.191447\pi$
$710$	1.29656	−	1.89616i	0.0486590	−	0.0711616i
$711$	−14.3371	+	0.819826i	−0.537684	+	0.0307459i
$712$	17.3777	+	44.6342i	0.651256	+	1.67274i
$713$	5.58431	−	0.966403i	0.209134	−	0.0361921i
$714$	0.661390	−	4.60007i	0.0247519	−	0.172153i
$715$	2.30018	−	1.42723i	0.0860220	−	0.0533755i
$716$	1.14811	+	7.98528i	0.0429069	+	0.298424i
$717$	−2.13721	−	6.57766i	−0.0798156	−	0.245647i
$718$	22.7794	+	1.30257i	0.850119	+	0.0486116i
$719$	12.4948	−	16.2035i	0.465977	−	0.604290i	−0.499007	−	0.866598i	$-0.666302\pi$
$719$	12.4948	−	16.2035i	0.465977	−	0.604290i	0.964984	+	0.262308i	$0.0844836\pi$
$720$	2.95788	−	1.25001i	0.110234	−	0.0465852i
$721$	−7.55964	+	6.18149i	−0.281536	+	0.230211i
$722$	−7.69173	−	14.5775i	−0.286257	−	0.542517i
$723$	3.88319	+	2.82130i	0.144417	+	0.104925i
$724$	0.593292	−	0.983865i	0.0220495	−	0.0365650i
$725$	20.6575			0.767200
$726$	−26.5323	−	5.46300i	−0.984706	−	0.202751i
$727$	43.8875			1.62770			0.813848	−	0.581078i	$-0.197369\pi$
$727$	43.8875			1.62770			0.813848	+	0.581078i	$0.197369\pi$
$728$	2.54504	−	4.22048i	0.0943255	−	0.156421i
$729$	−9.78294	−	7.10772i	−0.362331	−	0.263249i
$730$	−0.0717421	−	0.135966i	−0.00265530	−	0.00503235i
$731$	−5.20689	+	4.25766i	−0.192584	+	0.157475i
$732$	−5.43576	+	2.29717i	−0.200911	+	0.0849059i
$733$	0.591602	−	0.767203i	0.0218513	−	0.0283373i	−0.780850	−	0.624719i	$-0.785214\pi$
$733$	0.591602	−	0.767203i	0.0218513	−	0.0283373i	0.802701	+	0.596381i	$0.203395\pi$
$734$	−42.8767	−	2.45178i	−1.58261	−	0.0904968i
$735$	1.50112	+	4.61999i	0.0553698	+	0.170411i
$736$	−0.358335	−	2.49227i	−0.0132084	−	0.0918664i
$737$	17.9858	+	41.0951i	0.662516	+	1.51376i
$738$	1.74618	−	12.1450i	0.0642779	−	0.447063i
$739$	−27.4781	+	4.75527i	−1.01080	+	0.174925i	−0.651782	−	0.758406i	$-0.725978\pi$
$739$	−27.4781	+	4.75527i	−1.01080	+	0.174925i	−0.359015	+	0.933332i	$0.616887\pi$
$740$	0.344024	+	0.883618i	0.0126466	+	0.0324824i
$741$	3.45807	−	0.197740i	0.127035	−	0.00726415i
$742$	−10.8291	+	15.8371i	−0.397549	+	0.581396i
$743$	−19.6765	+	2.25767i	−0.721861	+	0.0828258i	−0.467133	−	0.884187i	$-0.654713\pi$
$743$	−19.6765	+	2.25767i	−0.721861	+	0.0828258i	−0.254728	+	0.967013i	$0.581986\pi$
$744$	−37.4144	−	8.70034i	−1.37168	−	0.318970i
$745$	19.8379	−	11.2030i	0.726805	−	0.410446i
$746$	35.2613	+	14.9016i	1.29101	+	0.545585i
$747$	9.65188	−	2.83405i	0.353144	−	0.103692i
$748$	0.420436	+	1.36735i	0.0153727	+	0.0499951i
$749$	−19.6717	−	5.77612i	−0.718787	−	0.211055i
$750$	−18.6167	−	15.2228i	−0.679786	−	0.555858i
$751$	−0.802569	+	3.96083i	−0.0292861	+	0.144533i	−0.992058	−	0.125783i	$-0.959856\pi$
$751$	−0.802569	+	3.96083i	−0.0292861	+	0.144533i	0.962772	+	0.270316i	$0.0871283\pi$
$752$	−10.3135	+	26.4900i	−0.376095	+	0.965992i
$753$	12.4138	−	38.2057i	0.452383	−	1.39229i
$754$	−4.85301	−	0.839846i	−0.176736	−	0.0305854i
$755$	−0.373758	−	1.84457i	−0.0136024	−	0.0671307i
$756$	2.02398	−	3.83587i	0.0736114	−	0.139509i
$757$	19.1463	−	9.41362i	0.695886	−	0.342144i	−0.0587641	−	0.998272i	$-0.518716\pi$
$757$	19.1463	−	9.41362i	0.695886	−	0.342144i	0.754650	+	0.656128i	$0.227807\pi$
$758$	−15.5021	−	33.9449i	−0.563063	−	1.23294i
$759$	−2.11196	−	5.68966i	−0.0766591	−	0.206522i
$760$	3.33654	−	7.30600i	0.121029	−	0.265016i
$761$	−0.961739	−	33.6653i	−0.0348630	−	1.22036i	−0.809178	−	0.587564i	$-0.800087\pi$
$761$	−0.961739	−	33.6653i	−0.0348630	−	1.22036i	0.774315	−	0.632801i	$-0.218095\pi$
$762$	29.2067	−	30.0529i	1.05805	−	1.08870i
$763$	4.07972	+	4.19794i	0.147696	+	0.151976i
$764$	0.0278778	−	0.975851i	0.00100858	−	0.0353051i
$765$	−0.901841	−	0.443406i	−0.0326061	−	0.0160314i
$766$	−14.5577	+	10.5768i	−0.525990	+	0.382154i
$767$	−0.525743	−	6.12112i	−0.0189835	−	0.221021i
$768$	−5.74873	+	21.8704i	−0.207439	+	0.789182i
$769$	−2.84002	+	1.82517i	−0.102414	+	0.0658173i	−0.590845	−	0.806785i	$-0.701206\pi$
$769$	−2.84002	+	1.82517i	−0.102414	+	0.0658173i	0.488431	+	0.872602i	$0.337569\pi$
$770$	−6.82265	−	7.24671i	−0.245871	−	0.261153i
$771$	−14.3750	−	9.23823i	−0.517702	−	0.332707i
$772$	−6.59301	+	6.05101i	−0.237288	+	0.217781i
$773$	−18.6011	+	4.32550i	−0.669035	+	0.155577i	−0.547237	−	0.836978i	$-0.684320\pi$
$773$	−18.6011	+	4.32550i	−0.669035	+	0.155577i	−0.121798	+	0.992555i	$0.538866\pi$
$774$	−9.48457	+	3.38409i	−0.340916	+	0.121639i
$775$	5.95179	+	22.6430i	0.213795	+	0.813360i
$776$	26.3589	+	24.1920i	0.946231	+	0.868443i
$777$	6.51893	+	3.68141i	0.233865	+	0.132070i
$778$	−5.29191	−	6.86267i	−0.189724	−	0.246039i
$779$	−12.6760	−	18.5381i	−0.454166	−	0.664196i
$780$	−0.540609	−	0.623896i	−0.0193569	−	0.0223391i
$781$	2.80668	+	4.82571i	0.100431	+	0.172678i
$782$	0.625310	−	0.721646i	0.0223610	−	0.0258060i
$783$	−21.4409	−	2.46011i	−0.766234	−	0.0879171i
$784$	5.59014	+	1.99456i	0.199648	+	0.0712342i
$785$	0.454930	−	5.29665i	0.0162371	−	0.189046i
$786$	−8.62002	−	14.2947i	−0.307466	−	0.509875i
$787$	−11.4045	−	18.9123i	−0.406528	−	0.674151i	0.583955	−	0.811786i	$-0.301504\pi$
$787$	−11.4045	−	18.9123i	−0.406528	−	0.674151i	−0.990483	+	0.137635i	$0.956050\pi$
$788$	0.0959020	−	1.11657i	0.00341637	−	0.0397760i
$789$	−24.6446	−	8.79318i	−0.877371	−	0.313046i
$790$	−18.5426	−	2.12757i	−0.659718	−	0.0756955i
$791$	2.24553	−	2.59148i	0.0798417	−	0.0921423i
$792$	−0.473479	+	10.6542i	−0.0168243	+	0.378582i
$793$	−2.79624	−	3.22704i	−0.0992975	−	0.114595i
$794$	16.0509	+	23.4737i	0.569626	+	0.833052i
$795$	9.77151	+	12.6719i	0.346560	+	0.449427i
$796$	8.54044	+	4.82301i	0.302708	+	0.170947i
$797$	8.90773	+	8.17544i	0.315528	+	0.289589i	0.818254	−	0.574857i	$-0.194942\pi$
$797$	8.90773	+	8.17544i	0.315528	+	0.289589i	−0.502726	+	0.864446i	$0.667670\pi$
$798$	−3.23756	−	12.3170i	−0.114608	−	0.436016i
$799$	8.37898	−	2.98961i	0.296427	−	0.105765i
$800$	10.1313	−	2.35594i	0.358197	−	0.0832951i
$801$	12.0994	−	11.1048i	0.427512	−	0.392367i
$802$	−16.0075	−	10.2874i	−0.565243	−	0.363260i
$803$	0.373300	−	0.0154143i	0.0131735	−	0.000543960i
$804$	11.5085	−	7.39607i	0.405874	−	0.260839i
$805$	0.566876	−	2.15662i	0.0199798	−	0.0760109i
$806$	−0.477671	−	5.56143i	−0.0168253	−	0.195893i
$807$	28.7207	−	20.8668i	1.01102	−	0.734548i
$808$	−41.6155	−	20.4609i	−1.46403	−	0.719813i
$809$	0.402308	−	14.0826i	0.0141444	−	0.495118i	−0.961380	−	0.275226i	$-0.911247\pi$
$809$	0.402308	−	14.0826i	0.0141444	−	0.495118i	0.975524	−	0.219893i	$-0.0705707\pi$
$810$	10.5074	+	10.8118i	0.369191	+	0.379889i
$811$	−6.07618	+	6.25224i	−0.213363	+	0.219546i	−0.815362	−	0.578951i	$-0.803462\pi$
$811$	−6.07618	+	6.25224i	−0.213363	+	0.219546i	0.601999	+	0.798497i	$0.294371\pi$
$812$	−0.173564	−	6.07553i	−0.00609090	−	0.213209i
$813$	19.8768	−	43.5241i	0.697109	−	1.52646i
$814$	6.84765	+	0.500569i	0.240010	+	0.0175449i
$815$	−11.4049	−	24.9733i	−0.399497	−	0.874776i
$816$	−4.25012	+	2.08964i	−0.148784	+	0.0731521i
$817$	−8.60140	+	16.3015i	−0.300925	+	0.570316i
$818$	2.00463	+	9.89325i	0.0700903	+	0.345909i
$819$	−1.66509	−	0.288155i	−0.0581830	−	0.0100690i
$820$	−1.65400	+	5.09050i	−0.0577604	+	0.177768i
$821$	−5.89557	+	15.1427i	−0.205757	+	0.528482i	−0.996493	−	0.0836747i	$-0.973334\pi$
$821$	−5.89557	+	15.1427i	−0.205757	+	0.528482i	0.790736	+	0.612157i	$0.209698\pi$
$822$	−0.690902	+	3.40974i	−0.0240980	+	0.118928i
$823$	35.3390	+	28.8966i	1.23184	+	1.00727i	0.999399	+	0.0346607i	$0.0110351\pi$
$823$	35.3390	+	28.8966i	1.23184	+	1.00727i	0.232442	+	0.972610i	$0.425329\pi$
$824$	13.0484	+	3.83136i	0.454564	+	0.133472i
$825$	22.6716	−	10.7040i	0.789324	−	0.372667i
$826$	−21.6739	+	6.36403i	−0.754131	+	0.221433i
$827$	18.8500	+	7.96607i	0.655479	+	0.277008i	0.691536	−	0.722342i	$-0.256934\pi$
$827$	18.8500	+	7.96607i	0.655479	+	0.277008i	−0.0360573	+	0.999350i	$0.511480\pi$
$828$	−0.417823	+	0.235955i	−0.0145204	+	0.00820002i
$829$	−16.5916	−	3.85820i	−0.576249	−	0.134001i	−0.0717642	−	0.997422i	$-0.522863\pi$
$829$	−16.5916	−	3.85820i	−0.576249	−	0.134001i	−0.504485	+	0.863421i	$0.668317\pi$
$830$	12.9889	−	1.49033i	0.450850	−	0.0517302i
$831$	3.20279	−	4.68392i	0.111103	−	0.162484i
$832$	−6.48319	+	0.370722i	−0.224764	+	0.0128525i
$833$	−0.673910	−	1.73092i	−0.0233496	−	0.0599730i
$834$	39.8344	−	6.89361i	1.37935	−	0.238706i
$835$	−0.277142	+	1.92756i	−0.00959089	+	0.0667061i
$836$	2.51985	+	3.00294i	0.0871508	+	0.103859i
$837$	−3.48093	−	24.2104i	−0.120319	−	0.836835i
$838$	7.83948	+	24.1274i	0.270810	+	0.833469i
$839$	−49.9450	−	2.85596i	−1.72429	−	0.0985987i	−0.833359	−	0.552732i	$-0.813585\pi$
$839$	−49.9450	−	2.85596i	−1.72429	−	0.0985987i	−0.890934	+	0.454133i	$0.849949\pi$
$840$	−9.22931	+	11.9688i	−0.318441	+	0.412962i
$841$	−1.14624	+	0.484403i	−0.0395254	+	0.0167036i
$842$	−8.34476	+	6.82348i	−0.287579	+	0.235153i
$843$	18.6095	+	35.2689i	0.640946	+	1.21473i
$844$	−3.63685	−	2.64232i	−0.125185	−	0.0909525i
$845$	−7.17828	+	11.9038i	−0.246940	+	0.409505i
$846$	13.3196			0.457938
$847$	23.0284	−	7.40247i	0.791267	−	0.254352i
$848$	19.5515			0.671401
$849$	8.33420	−	13.8207i	0.286029	−	0.474326i
$850$	3.19130	+	2.31862i	0.109461	+	0.0795279i
$851$	0.717846	+	1.36047i	0.0246074	+	0.0466363i
$852$	1.31795	−	1.07768i	0.0451523	−	0.0369209i
$853$	−43.4655	+	18.3687i	−1.48823	+	0.628932i	−0.973555	−	0.228453i	$-0.926633\pi$
$853$	−43.4655	+	18.3687i	−1.48823	+	0.628932i	−0.514676	+	0.857385i	$0.672088\pi$
$854$	−9.58705	+	12.4327i	−0.328062	+	0.425439i
$855$	−2.74941	−	0.157217i	−0.0940279	−	0.00537671i
$856$	8.82302	+	27.1545i	0.301565	+	0.928121i
$857$	−4.63471	−	32.2351i	−0.158319	−	1.10113i	−0.901731	−	0.432298i	$-0.857703\pi$
$857$	−4.63471	−	32.2351i	−0.158319	−	1.10113i	0.743412	−	0.668834i	$-0.233206\pi$
$858$	−5.76136	+	1.59294i	−0.196690	+	0.0543821i
$859$	0.531182	−	3.69445i	0.0181237	−	0.126053i	−0.978751	−	0.205053i	$-0.934263\pi$
$859$	0.531182	−	3.69445i	0.0181237	−	0.126053i	0.996875	+	0.0789995i	$0.0251725\pi$
$860$	4.32858	−	0.749090i	0.147603	−	0.0255438i
$861$	15.3322	+	39.3804i	0.522519	+	1.34208i
$862$	13.3375	−	0.762668i	0.454278	−	0.0259766i
$863$	−15.8326	+	23.1544i	−0.538948	+	0.788186i	−0.994798	−	0.101871i	$-0.967517\pi$
$863$	−15.8326	+	23.1544i	−0.538948	+	0.788186i	0.455850	+	0.890057i	$0.349335\pi$
$864$	−10.7961	+	1.23874i	−0.367291	+	0.0421427i
$865$	22.8766	+	5.31973i	0.777829	+	0.180876i
$866$	17.4726	−	9.86723i	0.593743	−	0.335302i
$867$	−30.1481	−	12.7407i	−1.02388	−	0.432697i
$868$	6.60947	−	1.94071i	0.224340	−	0.0658721i
$869$	24.0365	−	38.4678i	0.815383	−	1.30493i
$870$	14.4920	+	4.25523i	0.491325	+	0.144266i
$871$	7.66296	+	6.26597i	0.259649	+	0.212314i
$872$	1.61894	−	7.98979i	0.0548242	−	0.270568i
$873$	4.45066	−	11.4314i	0.150632	−	0.386895i
$874$	0.808598	−	2.48861i	0.0273512	−	0.0841784i
$875$	21.1593	+	3.66175i	0.715314	+	0.123790i
$876$	−0.0226273	−	0.111670i	−0.000764505	−	0.00377298i
$877$	−7.34709	+	13.9243i	−0.248094	+	0.470190i	−0.976662	−	0.214784i	$-0.931095\pi$
$877$	−7.34709	+	13.9243i	−0.248094	+	0.470190i	0.728568	+	0.684974i	$0.240186\pi$
$878$	−25.0295	+	12.3062i	−0.844706	+	0.415314i
$879$	8.17116	+	17.8923i	0.275606	+	0.603494i
$880$	−2.17161	+	9.90775i	−0.0732049	+	0.333990i
$881$	−13.8315	+	30.2868i	−0.465995	+	1.02039i	0.520084	+	0.854115i	$0.325900\pi$
$881$	−13.8315	+	30.2868i	−0.465995	+	1.02039i	−0.986080	+	0.166273i	$0.946827\pi$
$882$	−0.0794153	−	2.77990i	−0.00267405	−	0.0936040i
$883$	−10.4702	+	10.7735i	−0.352349	+	0.362559i	−0.870016	−	0.493024i	$-0.835892\pi$
$883$	−10.4702	+	10.7735i	−0.352349	+	0.362559i	0.517667	+	0.855582i	$0.326801\pi$
$884$	0.219998	+	0.226373i	0.00739934	+	0.00761374i
$885$	−0.538012	+	18.8329i	−0.0180851	+	0.633060i
$886$	36.6676	+	18.0282i	1.23187	+	0.605671i
$887$	28.6948	−	20.8480i	0.963478	−	0.700007i	0.00952183	−	0.999955i	$-0.496969\pi$
$887$	28.6948	−	20.8480i	0.963478	−	0.700007i	0.953956	+	0.299947i	$0.0969691\pi$
$888$	−0.892211	−	10.3878i	−0.0299406	−	0.348593i
$889$	−9.51307	+	36.1915i	−0.319058	+	1.21382i
$890$	17.9563	−	11.5398i	0.601898	−	0.386816i
$891$	−34.7004	+	11.7645i	−1.16251	+	0.394124i
$892$	−1.33371	−	0.857125i	−0.0446560	−	0.0286987i
$893$	17.9610	−	16.4845i	0.601042	−	0.551631i
$894$	−49.0007	+	11.3946i	−1.63883	+	0.381093i
$895$	16.8602	−	6.01572i	0.563575	−	0.201083i
$896$	2.97373	+	11.3132i	0.0993453	+	0.377949i
$897$	−0.986645	−	0.905535i	−0.0329431	−	0.0302349i
$898$	−21.6932	−	12.2507i	−0.723911	−	0.408811i
$899$	−20.9314	−	27.1444i	−0.698102	−	0.905315i
$900$	−1.11888	−	1.63631i	−0.0372961	−	0.0545438i
$901$	−4.00692	−	4.62423i	−0.133490	−	0.154056i
$902$	28.1343	+	26.6553i	0.936771	+	0.887523i
$903$	22.7130	−	26.2122i	0.755843	−	0.872289i
$904$	−4.74422	−	0.544349i	−0.157790	−	0.0181048i
$905$	−2.40112	−	0.856720i	−0.0798161	−	0.0284783i
$906$	−0.355641	+	4.14066i	−0.0118154	+	0.137564i
$907$	−3.65836	−	6.06670i	−0.121474	−	0.201442i	0.789668	−	0.613534i	$-0.210253\pi$
$907$	−3.65836	−	6.06670i	−0.121474	−	0.201442i	−0.911142	+	0.412092i	$0.864798\pi$
$908$	6.03276	+	10.0042i	0.200204	+	0.332001i
$909$	−1.36066	+	15.8419i	−0.0451304	+	0.525444i
$910$	−2.06855	−	0.738056i	−0.0685717	−	0.0244663i
$911$	0.0506105	+	0.00580701i	0.00167680	+	0.000192395i	0.114830	−	0.993385i	$-0.463368\pi$
$911$	0.0506105	+	0.00580701i	0.00167680	+	0.000192395i	−0.113153	+	0.993578i	$0.536095\pi$
$912$	−8.49900	+	9.80837i	−0.281430	+	0.324788i
$913$	−10.2965	+	30.0594i	−0.340763	+	0.994822i
$914$	13.5740	+	15.6652i	0.448988	+	0.518159i
$915$	7.39117	+	10.8092i	0.244345	+	0.357343i
$916$	0.0320751	+	0.0415957i	0.00105979	+	0.00137436i
$917$	12.9790	+	7.32959i	0.428605	+	0.242044i
$918$	−3.03620	−	2.78659i	−0.100209	−	0.0919713i
$919$	2.77370	+	10.5522i	0.0914958	+	0.348086i	0.997106	−	0.0760251i	$-0.0242229\pi$
$919$	2.77370	+	10.5522i	0.0914958	+	0.348086i	−0.905610	+	0.424111i	$0.860587\pi$
$920$	−2.92480	+	1.04357i	−0.0964278	+	0.0344054i
$921$	40.7319	−	9.47179i	1.34216	−	0.312106i
$922$	13.1574	−	12.0757i	0.433315	−	0.397693i
$923$	1.03631	+	0.665997i	0.0341106	+	0.0219215i
$924$	−3.33863	−	6.57796i	−0.109833	−	0.216399i
$925$	−5.34582	+	3.43555i	−0.175770	+	0.112960i
$926$	−4.39498	+	16.7202i	−0.144428	+	0.549461i
$927$	−0.399023	−	4.64574i	−0.0131056	−	0.152586i
$928$	−12.3205	+	8.95134i	−0.404439	+	0.293842i
$929$	−18.7577	−	9.22252i	−0.615419	−	0.302581i	0.106763	−	0.994285i	$-0.465951\pi$
$929$	−18.7577	−	9.22252i	−0.615419	−	0.302581i	−0.722182	+	0.691703i	$0.756861\pi$
$930$	−0.488819	+	17.1109i	−0.0160290	+	0.561088i
$931$	−3.54750	−	3.65030i	−0.116265	−	0.119634i
$932$	5.13985	−	5.28878i	0.168361	−	0.173240i
$933$	1.55549	+	54.4491i	0.0509243	+	1.78258i
$934$	12.1105	−	26.5183i	0.396267	−	0.867704i
$935$	2.78839	−	1.51690i	0.0911902	−	0.0496078i
$936$	0.977605	+	2.14066i	0.0319540	+	0.0699695i
$937$	−14.2490	+	7.00574i	−0.465493	+	0.228868i	−0.658870	−	0.752257i	$-0.728965\pi$
$937$	−14.2490	+	7.00574i	−0.465493	+	0.228868i	0.193377	+	0.981125i	$0.438056\pi$
$938$	16.9845	−	32.1891i	0.554562	−	1.05101i
$939$	0.0179101	+	0.0883900i	0.000584475	+	0.00288450i
$940$	−5.72531	−	0.990804i	−0.186739	−	0.0323165i
$941$	−13.6849	+	42.1177i	−0.446114	+	1.37300i	0.435143	+	0.900361i	$0.356698\pi$
$941$	−13.6849	+	42.1177i	−0.446114	+	1.37300i	−0.881257	+	0.472637i	$0.843302\pi$
$942$	−4.25899	+	10.9391i	−0.138766	+	0.356416i
$943$	−1.72435	+	8.50999i	−0.0561525	+	0.277123i
$944$	17.8206	+	14.5719i	0.580012	+	0.474274i
$945$	−9.23403	−	2.71136i	−0.300383	−	0.0882005i
$946$	8.57285	−	30.6312i	0.278727	−	0.995908i
$947$	−35.7080	+	10.4848i	−1.16035	+	0.340711i	−0.804570	−	0.593858i	$-0.797604\pi$
$947$	−35.7080	+	10.4848i	−1.16035	+	0.340711i	−0.355784	+	0.934568i	$0.615786\pi$
$948$	−12.7420	−	5.38480i	−0.413840	−	0.174890i
$949$	0.0717875	−	0.0405403i	0.00233032	−	0.00131599i
$950$	10.5288	+	2.44836i	0.341599	+	0.0794354i
$951$	−67.2760	+	7.71921i	−2.18157	+	0.250312i
$952$	3.26204	−	4.77058i	0.105723	−	0.154615i
$953$	−5.57280	+	0.318664i	−0.180521	+	0.0103225i	−0.147115	−	0.989119i	$-0.546999\pi$
$953$	−5.57280	+	0.318664i	−0.180521	+	0.0103225i	−0.0334053	+	0.999442i	$0.510635\pi$
$954$	−3.32368	−	8.53680i	−0.107608	−	0.276389i
$955$	−2.13454	+	0.369396i	−0.0690720	+	0.0119534i
$956$	0.245811	−	1.70965i	0.00795009	−	0.0552941i
$957$	−24.4746	+	27.3567i	−0.791150	+	0.884316i
$958$	−2.88882	−	20.0922i	−0.0933336	−	0.649150i
$959$	−0.959989	−	2.95454i	−0.0309997	−	0.0954072i
$960$	19.8818	+	1.13688i	0.641683	+	0.0366928i
$961$	4.79252	−	6.21505i	0.154597	−	0.200485i
$962$	1.39555	−	0.589766i	0.0449945	−	0.0190148i
$963$	7.57862	−	6.19701i	0.244218	−	0.199696i
$964$	0.559403	+	1.06019i	0.0180172	+	0.0341463i
$965$	16.0649	+	11.6718i	0.517147	+	0.375729i
$966$	−2.54272	+	4.21663i	−0.0818107	+	0.135668i
$967$	−38.5732			−1.24043			−0.620215	−	0.784432i	$-0.712955\pi$
$967$	−38.5732			−1.24043			−0.620215	+	0.784432i	$0.712955\pi$
$968$	−26.6114	−	20.6542i	−0.855324	−	0.663850i
$969$	4.06164			0.130479
$970$	8.23328	−	13.6534i	0.264355	−	0.438383i
$971$	−31.1366	−	22.6220i	−0.999220	−	0.725976i	−0.0372992	−	0.999304i	$-0.511875\pi$
$971$	−31.1366	−	22.6220i	−0.999220	−	0.725976i	−0.961921	+	0.273328i	$0.911875\pi$
$972$	2.45329	+	4.64950i	0.0786893	+	0.149133i
$973$	−27.9455	+	22.8509i	−0.895892	+	0.732568i
$974$	37.7552	−	15.9555i	1.20976	−	0.511247i
$975$	3.37832	−	4.38108i	0.108193	−	0.140307i
$976$	15.9732	+	0.913383i	0.511291	+	0.0292367i
$977$	2.93818	+	9.04279i	0.0940007	+	0.289305i	0.986992	−	0.160770i	$-0.0513976\pi$
$977$	2.93818	+	9.04279i	0.0940007	+	0.289305i	−0.892991	+	0.450074i	$0.851398\pi$
$978$	8.62766	+	60.0067i	0.275882	+	1.91880i
$979$	6.56768	+	51.4568i	0.209904	+	1.64456i
$980$	−0.172652	+	1.20082i	−0.00551515	+	0.0383587i
$981$	−2.75423	+	0.476637i	−0.0879356	+	0.0152179i
$982$	−2.42765	−	6.23537i	−0.0774694	−	0.198979i
$983$	22.8089	−	1.30426i	0.727489	−	0.0415993i	0.310580	−	0.950547i	$-0.399477\pi$
$983$	22.8089	−	1.30426i	0.727489	−	0.0415993i	0.416910	+	0.908948i	$0.363113\pi$
$984$	33.2187	−	48.5809i	1.05897	−	1.54870i
$985$	−2.47054	+	0.283468i	−0.0787179	+	0.00903203i
$986$	−5.62525	−	1.30810i	−0.179144	−	0.0416582i
$987$	−39.9458	+	22.5584i	−1.27149	+	0.718043i
$988$	0.796796	+	0.336729i	0.0253494	+	0.0107128i
$989$	6.83765	−	2.00772i	0.217425	−	0.0638416i
$990$	4.69520	−	0.736087i	0.149223	−	0.0233944i
$991$	18.9468	+	5.56329i	0.601866	+	0.176724i	0.568450	−	0.822718i	$-0.307543\pi$
$991$	18.9468	+	5.56329i	0.601866	+	0.176724i	0.0334157	+	0.999442i	$0.489361\pi$
$992$	−13.3614	−	10.9256i	−0.424226	−	0.346888i
$993$	−14.1963	+	70.0615i	−0.450506	+	2.22333i
$994$	1.64327	−	4.22070i	0.0521213	−	0.133872i
$995$	6.72546	−	20.6988i	0.213211	−	0.656197i
$996$	9.54795	+	1.65234i	0.302538	+	0.0523563i
$997$	−9.50159	−	46.8922i	−0.300918	−	1.48509i	−0.790137	−	0.612930i	$-0.789991\pi$
$997$	−9.50159	−	46.8922i	−0.300918	−	1.48509i	0.489219	−	0.872161i	$-0.337282\pi$
$998$	14.3989	−	27.2890i	0.455790	−	0.863818i
$999$	5.95768	−	2.92920i	0.188493	−	0.0926757i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.2.g.a.5.4	✓	400
121.97	even	55	inner	121.2.g.a.97.4	yes	400

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.2.g.a.5.4	✓	400	1.1	even	1	trivial
121.2.g.a.97.4	yes	400	121.97	even	55	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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	121.g (of order \(55\), degree \(40\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.631909 + 1.04790i) q^{2} +(1.62812 + 1.18290i) q^{3} +(0.234543 + 0.444508i) q^{4} +(0.863348 - 0.705956i) q^{5} +(-2.26838 + 0.958627i) q^{6} +(1.34281 - 1.74139i) q^{7} +(-3.05739 - 0.174828i) q^{8} +(0.324472 + 0.998622i) q^{9} +O(q^{10})\)	\(q+(-0.631909 + 1.04790i) q^{2} +(1.62812 + 1.18290i) q^{3} +(0.234543 + 0.444508i) q^{4} +(0.863348 - 0.705956i) q^{5} +(-2.26838 + 0.958627i) q^{6} +(1.34281 - 1.74139i) q^{7} +(-3.05739 - 0.174828i) q^{8} +(0.324472 + 0.998622i) q^{9} +(0.194216 + 1.35080i) q^{10} +(-3.16707 - 0.984725i) q^{11} +(-0.143944 + 1.00115i) q^{12} +(-0.721138 + 0.124798i) q^{13} +(0.976273 + 2.50754i) q^{14} +(2.24071 - 0.128128i) q^{15} +(1.54783 - 2.26363i) q^{16} +(-0.852598 + 0.0978266i) q^{17} +(-1.25150 - 0.291023i) q^{18} +(-2.04776 + 1.15643i) q^{19} +(0.516295 + 0.218188i) q^{20} +(4.24614 - 1.24678i) q^{21} +(3.03319 - 2.69652i) q^{22} +(0.872436 + 0.256170i) q^{23} +(-4.77099 - 3.90122i) q^{24} +(-0.745957 + 3.68144i) q^{25} +(0.324917 - 0.834544i) q^{26} +(1.21267 - 3.73221i) q^{27} +(1.08901 + 0.188460i) q^{28} +(-1.09215 - 5.38995i) q^{29} +(-1.28166 + 2.42901i) q^{30} +(5.59334 - 2.75006i) q^{31} +(-1.15035 - 2.51891i) q^{32} +(-3.99153 - 5.34956i) q^{33} +(0.436252 - 0.955258i) q^{34} +(-0.0700306 - 2.45139i) q^{35} +(-0.367793 + 0.378450i) q^{36} +(1.17903 + 1.21320i) q^{37} +(0.0821782 - 2.87661i) q^{38} +(-1.32172 - 0.649847i) q^{39} +(-2.76301 + 2.00745i) q^{40} +(0.817187 + 9.51434i) q^{41} +(-1.37667 + 5.23740i) q^{42} +(6.59326 - 4.23723i) q^{43} +(-0.305095 - 1.63875i) q^{44} +(0.985115 + 0.633095i) q^{45} +(-0.819741 + 0.752352i) q^{46} +(-10.0970 + 2.34795i) q^{47} +(5.19768 - 1.85453i) q^{48} +(0.550234 + 2.09331i) q^{49} +(-3.38642 - 3.10803i) q^{50} +(-1.50385 - 0.849263i) q^{51} +(-0.224611 - 0.291281i) q^{52} +(4.02437 + 5.88545i) q^{53} +(3.14470 + 3.62918i) q^{54} +(-3.42945 + 1.38565i) q^{55} +(-4.40995 + 5.08935i) q^{56} +(-4.70193 - 0.539497i) q^{57} +(6.33829 + 2.26150i) q^{58} +(-0.718368 + 8.36381i) q^{59} +(0.582495 + 0.965959i) q^{60} +(3.01289 + 4.99632i) q^{61} +(-0.652684 + 7.59906i) q^{62} +(2.17470 + 0.775930i) q^{63} +(8.81518 + 1.01145i) q^{64} +(-0.534491 + 0.616836i) q^{65} +(8.12811 - 0.802303i) q^{66} +(-8.85724 - 10.2218i) q^{67} +(-0.243455 - 0.356042i) q^{68} +(1.11741 + 1.44908i) q^{69} +(2.61307 + 1.47567i) q^{70} +(-1.24009 - 1.13814i) q^{71} +(-0.817451 - 3.10991i) q^{72} +(-0.106099 + 0.0378560i) q^{73} +(-2.01635 + 0.468883i) q^{74} +(-5.56927 + 5.11143i) q^{75} +(-0.994328 - 0.639016i) q^{76} +(-5.96757 + 4.19280i) q^{77} +(1.51618 - 0.974392i) q^{78} +(-3.47683 + 13.2272i) q^{79} +(-0.261707 - 3.04700i) q^{80} +(8.93762 - 6.49356i) q^{81} +(-10.4865 - 5.15586i) q^{82} +(0.273573 - 9.57631i) q^{83} +(1.55010 + 1.59502i) q^{84} +(-0.667028 + 0.686355i) q^{85} +(0.273868 + 9.58665i) q^{86} +(4.59762 - 10.0674i) q^{87} +(9.51081 + 3.56438i) q^{88} +(-6.49736 - 14.2272i) q^{89} +(-1.28593 + 0.632247i) q^{90} +(-0.751031 + 1.42336i) q^{91} +(0.0907537 + 0.447887i) q^{92} +(12.3597 + 2.13892i) q^{93} +(3.91994 - 12.0643i) q^{94} +(-0.951547 + 2.44403i) q^{95} +(1.10671 - 5.46183i) q^{96} +(-9.04427 - 7.39546i) q^{97} +(-2.54128 - 0.746188i) q^{98} +(-0.0442570 - 3.48222i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9}+O(q^{10}) \) 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9	\( 400 q - 44 q^{2} - 32 q^{3} - 34 q^{4} - 43 q^{5} - 22 q^{6} - 44 q^{7} - 44 q^{8} - 110 q^{9} - 22 q^{10} - 33 q^{11} + 6 q^{12} - 11 q^{13} - 18 q^{14} + 16 q^{15} - 30 q^{16} - 44 q^{17} + 11 q^{18} - 44 q^{19} - 36 q^{20} - 11 q^{21} - 34 q^{23} + 77 q^{24} - 31 q^{25} - 38 q^{26} + 40 q^{27} - 44 q^{28} - 44 q^{29} - 11 q^{30} - 17 q^{31} - 44 q^{32} - 11 q^{33} - 76 q^{34} - 44 q^{35} + 57 q^{36} - 4 q^{37} + 34 q^{38} - 11 q^{39} + 33 q^{40} - 44 q^{41} + 3 q^{42} - 44 q^{43} - 33 q^{44} - 12 q^{45} - 44 q^{46} - 36 q^{47} + 9 q^{48} + 16 q^{49} + 88 q^{50} + 154 q^{51} + 110 q^{52} + 78 q^{53} + 231 q^{54} + 44 q^{55} - 55 q^{56} + 66 q^{57} + 73 q^{58} - 33 q^{59} + 15 q^{60} - 44 q^{61} + 11 q^{62} + 121 q^{63} + 96 q^{64} - 11 q^{65} - 41 q^{67} - 44 q^{68} + 8 q^{69} + 24 q^{70} + 15 q^{71} + 77 q^{72} - 22 q^{73} - 44 q^{74} + 7 q^{75} + 176 q^{76} + 88 q^{77} - 21 q^{78} + 44 q^{79} + 171 q^{80} + 37 q^{81} + 22 q^{82} - 44 q^{83} - 11 q^{84} + 66 q^{85} - 20 q^{86} - 11 q^{87} + 77 q^{88} + 3 q^{89} + 264 q^{90} + 79 q^{91} + 228 q^{92} + 49 q^{93} + 143 q^{94} + 44 q^{95} + 121 q^{96} + 10 q^{97} + 132 q^{98} + 143 q^{99}+O(q^{100}) \) 400 * q - 44 * q^2 - 32 * q^3 - 34 * q^4 - 43 * q^5 - 22 * q^6 - 44 * q^7 - 44 * q^8 - 110 * q^9 - 22 * q^10 - 33 * q^11 + 6 * q^12 - 11 * q^13 - 18 * q^14 + 16 * q^15 - 30 * q^16 - 44 * q^17 + 11 * q^18 - 44 * q^19 - 36 * q^20 - 11 * q^21 - 34 * q^23 + 77 * q^24 - 31 * q^25 - 38 * q^26 + 40 * q^27 - 44 * q^28 - 44 * q^29 - 11 * q^30 - 17 * q^31 - 44 * q^32 - 11 * q^33 - 76 * q^34 - 44 * q^35 + 57 * q^36 - 4 * q^37 + 34 * q^38 - 11 * q^39 + 33 * q^40 - 44 * q^41 + 3 * q^42 - 44 * q^43 - 33 * q^44 - 12 * q^45 - 44 * q^46 - 36 * q^47 + 9 * q^48 + 16 * q^49 + 88 * q^50 + 154 * q^51 + 110 * q^52 + 78 * q^53 + 231 * q^54 + 44 * q^55 - 55 * q^56 + 66 * q^57 + 73 * q^58 - 33 * q^59 + 15 * q^60 - 44 * q^61 + 11 * q^62 + 121 * q^63 + 96 * q^64 - 11 * q^65 - 41 * q^67 - 44 * q^68 + 8 * q^69 + 24 * q^70 + 15 * q^71 + 77 * q^72 - 22 * q^73 - 44 * q^74 + 7 * q^75 + 176 * q^76 + 88 * q^77 - 21 * q^78 + 44 * q^79 + 171 * q^80 + 37 * q^81 + 22 * q^82 - 44 * q^83 - 11 * q^84 + 66 * q^85 - 20 * q^86 - 11 * q^87 + 77 * q^88 + 3 * q^89 + 264 * q^90 + 79 * q^91 + 228 * q^92 + 49 * q^93 + 143 * q^94 + 44 * q^95 + 121 * q^96 + 10 * q^97 + 132 * q^98 + 143 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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