LMFDB - Embedded newform 41.2.g.a.39.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [41,2,Mod(2,41)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(41, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("41.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	41.g (of order $20$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.327386648287$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			39.2
Character	$\chi$	$=$	41.39
Dual form			41.2.g.a.20.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.290902 - 0.0945196i) q^{2} +(0.964912 + 0.964912i) q^{3} +(-1.54234 + 1.12058i) q^{4} +(-2.03721 - 2.80398i) q^{5} +(0.371897 + 0.189491i) q^{6} +(1.29765 - 0.661185i) q^{7} +(-0.702328 + 0.966671i) q^{8} -1.13789i q^{9} +O(q^{10})$	\(q+(0.290902 - 0.0945196i) q^{2} +(0.964912 + 0.964912i) q^{3} +(-1.54234 + 1.12058i) q^{4} +(-2.03721 - 2.80398i) q^{5} +(0.371897 + 0.189491i) q^{6} +(1.29765 - 0.661185i) q^{7} +(-0.702328 + 0.966671i) q^{8} -1.13789i q^{9} +(-0.857659 - 0.623126i) q^{10} +(0.285814 + 1.80456i) q^{11} +(-2.56949 - 0.406967i) q^{12} +(-2.91004 + 5.71127i) q^{13} +(0.314993 - 0.314993i) q^{14} +(0.739865 - 4.67132i) q^{15} +(1.06531 - 3.27868i) q^{16} +(3.14295 - 0.497794i) q^{17} +(-0.107553 - 0.331014i) q^{18} +(1.51872 + 2.98065i) q^{19} +(6.28416 + 2.04185i) q^{20} +(1.89010 + 0.614131i) q^{21} +(0.253710 + 0.497934i) q^{22} +(-1.67386 - 5.15161i) q^{23} +(-1.61044 + 0.255068i) q^{24} +(-2.16699 + 6.66932i) q^{25} +(-0.306707 + 1.93647i) q^{26} +(3.99270 - 3.99270i) q^{27} +(-1.26051 + 2.47389i) q^{28} +(-0.335113 - 0.0530767i) q^{29} +(-0.226304 - 1.42883i) q^{30} +(-3.04183 - 2.21002i) q^{31} -3.44421i q^{32} +(-1.46545 + 2.01702i) q^{33} +(0.867237 - 0.441879i) q^{34} +(-4.49754 - 2.29161i) q^{35} +(1.27510 + 1.75502i) q^{36} +(0.993200 - 0.721602i) q^{37} +(0.723527 + 0.723527i) q^{38} +(-8.31880 + 2.70294i) q^{39} +4.14132 q^{40} +(-6.22198 + 1.51227i) q^{41} +0.607881 q^{42} +(7.02832 - 2.28364i) q^{43} +(-2.46297 - 2.46297i) q^{44} +(-3.19062 + 2.31812i) q^{45} +(-0.973857 - 1.34040i) q^{46} +(-1.40824 - 0.717533i) q^{47} +(4.19156 - 2.13571i) q^{48} +(-2.86777 + 3.94715i) q^{49} +2.14494i q^{50} +(3.51299 + 2.55234i) q^{51} +(-1.91165 - 12.0697i) q^{52} +(1.12895 + 0.178807i) q^{53} +(0.784094 - 1.53887i) q^{54} +(4.47768 - 4.47768i) q^{55} +(-0.272226 + 1.71877i) q^{56} +(-1.41064 + 4.34149i) q^{57} +(-0.102502 + 0.0162347i) q^{58} +(4.16549 + 12.8200i) q^{59} +(4.09346 + 8.03387i) q^{60} +(-4.39785 - 1.42895i) q^{61} +(-1.09376 - 0.355385i) q^{62} +(-0.752356 - 1.47658i) q^{63} +(1.80507 + 5.55543i) q^{64} +(21.9426 - 3.47537i) q^{65} +(-0.235654 + 0.725270i) q^{66} +(1.04355 - 6.58873i) q^{67} +(-4.28969 + 4.28969i) q^{68} +(3.35573 - 6.58598i) q^{69} +(-1.52494 - 0.241527i) q^{70} +(-1.29298 - 8.16358i) q^{71} +(1.09997 + 0.799172i) q^{72} -8.99466i q^{73} +(0.220718 - 0.303792i) q^{74} +(-8.52627 + 4.34435i) q^{75} +(-5.68244 - 2.89535i) q^{76} +(1.56403 + 2.15271i) q^{77} +(-2.16447 + 1.57258i) q^{78} +(7.20521 + 7.20521i) q^{79} +(-11.3636 + 3.69226i) q^{80} +4.29154 q^{81} +(-1.66705 + 1.02802i) q^{82} -7.11449 q^{83} +(-3.60337 + 1.17081i) q^{84} +(-7.79865 - 7.79865i) q^{85} +(1.82870 - 1.32863i) q^{86} +(-0.272140 - 0.374569i) q^{87} +(-1.94515 - 0.991103i) q^{88} +(-12.9260 + 6.58613i) q^{89} +(-0.709049 + 0.975922i) q^{90} +9.33529i q^{91} +(8.35446 + 6.06987i) q^{92} +(-0.802625 - 5.06757i) q^{93} +(-0.477479 - 0.0756253i) q^{94} +(5.26374 - 10.3307i) q^{95} +(3.32336 - 3.32336i) q^{96} +(0.514313 - 3.24724i) q^{97} +(-0.461156 + 1.41929i) q^{98} +(2.05339 - 0.325225i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) $ 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/41\mathbb{Z}\right)^\times$.

$n$	$6$
$\chi(n)$	$e\left(\frac{3}{20}\right)$

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 $

$2$	0.290902	−	0.0945196i	0.205698	−	0.0668355i	−0.204356	−	0.978897i	$-0.565510\pi$
$2$	0.290902	−	0.0945196i	0.205698	−	0.0668355i	0.410054	+	0.912061i	$0.365510\pi$
$3$	0.964912	+	0.964912i	0.557092	+	0.557092i	0.928478	−	0.371386i	$-0.121117\pi$
$3$	0.964912	+	0.964912i	0.557092	+	0.557092i	−0.371386	+	0.928478i	$0.621117\pi$
$4$	−1.54234	+	1.12058i	−0.771172	+	0.560289i
$5$	−2.03721	−	2.80398i	−0.911069	−	1.25398i	−0.966800	−	0.255533i	$-0.917749\pi$
$5$	−2.03721	−	2.80398i	−0.911069	−	1.25398i	0.0557316	−	0.998446i	$-0.482251\pi$
$6$	0.371897	+	0.189491i	0.151826	+	0.0773595i
$7$	1.29765	−	0.661185i	0.490465	−	0.249905i	−0.191224	−	0.981546i	$-0.561246\pi$
$7$	1.29765	−	0.661185i	0.490465	−	0.249905i	0.681689	+	0.731642i	$0.261246\pi$
$8$	−0.702328	+	0.966671i	−0.248310	+	0.341770i
$9$		−	1.13789i		−	0.379297i
$10$	−0.857659	−	0.623126i	−0.271216	−	0.197050i
$11$	0.285814	+	1.80456i	0.0861761	+	0.544095i	0.992571	+	0.121664i	$0.0388230\pi$
$11$	0.285814	+	1.80456i	0.0861761	+	0.544095i	−0.906395	+	0.422431i	$0.861177\pi$
$12$	−2.56949	−	0.406967i	−0.741747	−	0.117481i
$13$	−2.91004	+	5.71127i	−0.807099	+	1.58402i	0.00463289	+	0.999989i	$0.498525\pi$
$13$	−2.91004	+	5.71127i	−0.807099	+	1.58402i	−0.811731	+	0.584031i	$0.801475\pi$
$14$	0.314993	−	0.314993i	0.0841854	−	0.0841854i
$15$	0.739865	−	4.67132i	0.191032	−	1.20613i
$16$	1.06531	−	3.27868i	0.266327	−	0.819670i
$17$	3.14295	−	0.497794i	0.762277	−	0.120733i	0.236821	−	0.971553i	$-0.423895\pi$
$17$	3.14295	−	0.497794i	0.762277	−	0.120733i	0.525456	+	0.850821i	$0.323895\pi$
$18$	−0.107553	−	0.331014i	−0.0253505	−	0.0780207i
$19$	1.51872	+	2.98065i	0.348417	+	0.683808i	0.997005	−	0.0773320i	$-0.0246401\pi$
$19$	1.51872	+	2.98065i	0.348417	+	0.683808i	−0.648588	+	0.761140i	$0.724640\pi$
$20$	6.28416	+	2.04185i	1.40518	+	0.456571i
$21$	1.89010	+	0.614131i	0.412454	+	0.134014i
$22$	0.253710	+	0.497934i	0.0540911	+	0.106160i
$23$	−1.67386	−	5.15161i	−0.349024	−	1.07419i	−0.959394	−	0.282069i	$-0.908979\pi$
$23$	−1.67386	−	5.15161i	−0.349024	−	1.07419i	0.610370	−	0.792117i	$-0.291021\pi$
$24$	−1.61044	+	0.255068i	−0.328729	+	0.0520656i
$25$	−2.16699	+	6.66932i	−0.433399	+	1.33386i
$26$	−0.306707	+	1.93647i	−0.0601502	+	0.379773i
$27$	3.99270	−	3.99270i	0.768395	−	0.768395i
$28$	−1.26051	+	2.47389i	−0.238214	+	0.467522i
$29$	−0.335113	−	0.0530767i	−0.0622289	−	0.00985609i	0.125242	−	0.992126i	$-0.460029\pi$
$29$	−0.335113	−	0.0530767i	−0.0622289	−	0.00985609i	−0.187471	+	0.982270i	$0.560029\pi$
$30$	−0.226304	−	1.42883i	−0.0413173	−	0.260867i
$31$	−3.04183	−	2.21002i	−0.546329	−	0.396931i	0.280101	−	0.959971i	$-0.409632\pi$
$31$	−3.04183	−	2.21002i	−0.546329	−	0.396931i	−0.826430	+	0.563039i	$0.809632\pi$
$32$		−	3.44421i		−	0.608856i
$33$	−1.46545	+	2.01702i	−0.255103	+	0.351119i
$34$	0.867237	−	0.441879i	0.148730	−	0.0757817i
$35$	−4.49754	−	2.29161i	−0.760222	−	0.387353i
$36$	1.27510	+	1.75502i	0.212516	+	0.292503i
$37$	0.993200	−	0.721602i	0.163281	−	0.118631i	−0.503144	−	0.864202i	$-0.667824\pi$
$37$	0.993200	−	0.721602i	0.163281	−	0.118631i	0.666425	+	0.745572i	$0.267824\pi$
$38$	0.723527	+	0.723527i	0.117372	+	0.117372i
$39$	−8.31880	+	2.70294i	−1.33207	+	0.432817i
$40$	4.14132			0.654800
$41$	−6.22198	+	1.51227i	−0.971710	+	0.236176i
$41$	−6.22198	+	1.51227i	−0.971710	+	0.236176i
$42$	0.607881			0.0937981
$43$	7.02832	−	2.28364i	1.07181	−	0.348252i	0.280617	−	0.959820i	$-0.409461\pi$
$43$	7.02832	−	2.28364i	1.07181	−	0.348252i	0.791192	+	0.611568i	$0.209461\pi$
$44$	−2.46297	−	2.46297i	−0.371307	−	0.371307i
$45$	−3.19062	+	2.31812i	−0.475630	+	0.345565i
$46$	−0.973857	−	1.34040i	−0.143587	−	0.197631i
$47$	−1.40824	−	0.717533i	−0.205413	−	0.104663i	0.348258	−	0.937399i	$-0.386773\pi$
$47$	−1.40824	−	0.717533i	−0.205413	−	0.104663i	−0.553671	+	0.832736i	$0.686773\pi$
$48$	4.19156	−	2.13571i	0.605000	−	0.308263i
$49$	−2.86777	+	3.94715i	−0.409681	+	0.563878i
$50$			2.14494i			0.303340i
$51$	3.51299	+	2.55234i	0.491918	+	0.357399i
$52$	−1.91165	−	12.0697i	−0.265098	−	1.67376i
$53$	1.12895	+	0.178807i	0.155073	+	0.0245611i	0.233488	−	0.972360i	$-0.424986\pi$
$53$	1.12895	+	0.178807i	0.155073	+	0.0245611i	−0.0784154	+	0.996921i	$0.524986\pi$
$54$	0.784094	−	1.53887i	0.106702	−	0.209414i
$55$	4.47768	−	4.47768i	0.603771	−	0.603771i
$56$	−0.272226	+	1.71877i	−0.0363778	+	0.229680i
$57$	−1.41064	+	4.34149i	−0.186843	+	0.575045i
$58$	−0.102502	+	0.0162347i	−0.0134591	+	0.00213172i
$59$	4.16549	+	12.8200i	0.542300	+	1.66903i	0.727324	+	0.686294i	$0.240764\pi$
$59$	4.16549	+	12.8200i	0.542300	+	1.66903i	−0.185024	+	0.982734i	$0.559236\pi$
$60$	4.09346	+	8.03387i	0.528463	+	1.03717i
$61$	−4.39785	−	1.42895i	−0.563087	−	0.182958i	0.0136225	−	0.999907i	$-0.495664\pi$
$61$	−4.39785	−	1.42895i	−0.563087	−	0.182958i	−0.576710	+	0.816949i	$0.695664\pi$
$62$	−1.09376	−	0.355385i	−0.138908	−	0.0451340i
$63$	−0.752356	−	1.47658i	−0.0947880	−	0.186032i
$64$	1.80507	+	5.55543i	0.225634	+	0.694429i
$65$	21.9426	−	3.47537i	2.72165	−	0.431067i
$66$	−0.235654	+	0.725270i	−0.0290071	+	0.0892745i
$67$	1.04355	−	6.58873i	0.127490	−	0.804941i	−0.838223	−	0.545328i	$-0.816405\pi$
$67$	1.04355	−	6.58873i	0.127490	−	0.804941i	0.965713	−	0.259613i	$-0.0835950\pi$
$68$	−4.28969	+	4.28969i	−0.520201	+	0.520201i
$69$	3.35573	−	6.58598i	0.403982	−	0.792859i
$70$	−1.52494	−	0.241527i	−0.182265	−	0.0288680i
$71$	−1.29298	−	8.16358i	−0.153449	−	0.968839i	−0.937460	−	0.348092i	$-0.886830\pi$
$71$	−1.29298	−	8.16358i	−0.153449	−	0.968839i	0.784011	−	0.620746i	$-0.213170\pi$
$72$	1.09997	+	0.799172i	0.129632	+	0.0941833i
$73$		−	8.99466i		−	1.05274i	−0.850254	−	0.526372i	$-0.823552\pi$
$73$		−	8.99466i		−	1.05274i	0.850254	−	0.526372i	$-0.176448\pi$
$74$	0.220718	−	0.303792i	0.0256579	−	0.0353151i
$75$	−8.52627	+	4.34435i	−0.984529	+	0.501642i
$76$	−5.68244	−	2.89535i	−0.651820	−	0.332119i
$77$	1.56403	+	2.15271i	0.178238	+	0.245324i
$78$	−2.16447	+	1.57258i	−0.245078	+	0.178060i
$79$	7.20521	+	7.20521i	0.810649	+	0.810649i	0.984731	−	0.174082i	$-0.0556958\pi$
$79$	7.20521	+	7.20521i	0.810649	+	0.810649i	−0.174082	+	0.984731i	$0.555696\pi$
$80$	−11.3636	+	3.69226i	−1.27049	+	0.412807i
$81$	4.29154			0.476837
$82$	−1.66705	+	1.02802i	−0.184094	+	0.113526i
$83$	−7.11449			−0.780916			−0.390458	−	0.920621i	$-0.627683\pi$
$83$	−7.11449			−0.780916			−0.390458	+	0.920621i	$0.627683\pi$
$84$	−3.60337	+	1.17081i	−0.393160	+	0.127745i
$85$	−7.79865	−	7.79865i	−0.845883	−	0.845883i
$86$	1.82870	−	1.32863i	0.197194	−	0.143270i
$87$	−0.272140	−	0.374569i	−0.0291765	−	0.0401580i
$88$	−1.94515	−	0.991103i	−0.207354	−	0.105652i
$89$	−12.9260	+	6.58613i	−1.37015	+	0.698128i	−0.975355	−	0.220639i	$-0.929186\pi$
$89$	−12.9260	+	6.58613i	−1.37015	+	0.698128i	−0.394798	+	0.918768i	$0.629186\pi$
$90$	−0.709049	+	0.975922i	−0.0747403	+	0.102871i
$91$			9.33529i			0.978604i
$92$	8.35446	+	6.06987i	0.871013	+	0.632828i
$93$	−0.802625	−	5.06757i	−0.0832283	−	0.525483i
$94$	−0.477479	−	0.0756253i	−0.0492482	−	0.00780016i
$95$	5.26374	−	10.3307i	0.540048	−	1.05990i
$96$	3.32336	−	3.32336i	0.339189	−	0.339189i
$97$	0.514313	−	3.24724i	0.0522205	−	0.329707i	−0.947723	−	0.319094i	$-0.896621\pi$
$97$	0.514313	−	3.24724i	0.0522205	−	0.329707i	0.999944	−	0.0106137i	$-0.00337850\pi$
$98$	−0.461156	+	1.41929i	−0.0465838	+	0.143370i
$99$	2.05339	−	0.325225i	0.206373	−	0.0326863i
$100$	−4.13125	−	12.7147i	−0.413125	−	1.27147i
$101$	2.96889	+	5.82677i	0.295415	+	0.579785i	0.990237	−	0.139397i	$-0.0445165\pi$
$101$	2.96889	+	5.82677i	0.295415	+	0.579785i	−0.694821	+	0.719183i	$0.744516\pi$
$102$	1.26318	+	0.410433i	0.125074	+	0.0406389i
$103$	15.6950	+	5.09961i	1.54647	+	0.502479i	0.953153	−	0.302488i	$-0.0978173\pi$
$103$	15.6950	+	5.09961i	1.54647	+	0.502479i	0.593319	+	0.804967i	$0.297817\pi$
$104$	−3.47712	−	6.82423i	−0.340959	−	0.669171i
$105$	−2.12853	−	6.55093i	−0.207723	−	0.639305i
$106$	0.345313	−	0.0546922i	0.0335397	−	0.00531217i
$107$	−2.13141	+	6.55981i	−0.206051	+	0.634160i	0.793617	+	0.608417i	$0.208195\pi$
$107$	−2.13141	+	6.55981i	−0.206051	+	0.634160i	−0.999669	+	0.0257432i	$0.991805\pi$
$108$	−1.68398	+	10.6323i	−0.162041	+	1.02309i
$109$	0.909585	−	0.909585i	0.0871225	−	0.0871225i	−0.662202	−	0.749325i	$-0.730378\pi$
$109$	0.909585	−	0.909585i	0.0871225	−	0.0871225i	0.749325	+	0.662202i	$0.230378\pi$
$110$	0.879336	−	1.72579i	0.0838414	−	0.164548i
$111$	1.65463	+	0.262068i	0.157051	+	0.0248744i
$112$	−0.785419	−	4.95894i	−0.0742151	−	0.468576i
$113$	−5.72258	−	4.15770i	−0.538335	−	0.391123i	0.285131	−	0.958489i	$-0.407963\pi$
$113$	−5.72258	−	4.15770i	−0.538335	−	0.391123i	−0.823466	+	0.567365i	$0.807963\pi$
$114$			1.39628i			0.130774i
$115$	−11.0350	+	15.1884i	−1.02902	+	1.41633i
$116$	0.576336	−	0.293658i	0.0535115	−	0.0272655i
$117$	6.49879	+	3.31130i	0.600814	+	0.306130i
$118$	2.42349	+	3.33565i	0.223101	+	0.307072i
$119$	3.74931	−	2.72403i	0.343699	−	0.249712i
$120$	3.99601	+	3.99601i	0.364784	+	0.364784i
$121$	7.28688	−	2.36765i	0.662444	−	0.215241i
$122$	−1.41441			−0.128054
$123$	−7.46287	−	4.54446i	−0.672904	−	0.409760i
$124$	7.16805			0.643710
$125$	6.63390	−	2.15548i	0.593354	−	0.192792i
$126$	−0.358428	−	0.358428i	−0.0319313	−	0.0319313i
$127$	4.45174	−	3.23438i	0.395028	−	0.287005i	−0.372485	−	0.928038i	$-0.621494\pi$
$127$	4.45174	−	3.23438i	0.395028	−	0.287005i	0.767513	+	0.641034i	$0.221494\pi$
$128$	5.09910	+	7.01831i	0.450701	+	0.620337i
$129$	8.98522	+	4.57820i	0.791105	+	0.403088i
$130$	6.05466	−	3.08500i	0.531029	−	0.270573i
$131$	−4.78432	+	6.58506i	−0.418008	+	0.575339i	−0.965149	−	0.261702i	$-0.915716\pi$
$131$	−4.78432	+	6.58506i	−0.418008	+	0.575339i	0.547140	+	0.837041i	$0.315716\pi$
$132$		−	4.75310i		−	0.413704i
$133$	3.94152	+	2.86368i	0.341773	+	0.248313i
$134$	−0.319193	−	2.01531i	−0.0275741	−	0.174096i
$135$	−19.3294	−	3.06148i	−1.66361	−	0.263490i
$136$	−1.72618	+	3.38781i	−0.148018	+	0.290502i
$137$	0.0757881	−	0.0757881i	0.00647501	−	0.00647501i	−0.703862	−	0.710337i	$-0.748543\pi$
$137$	0.0757881	−	0.0757881i	0.00647501	−	0.00647501i	0.710337	+	0.703862i	$0.248543\pi$
$138$	0.353681	−	2.23305i	0.0301073	−	0.190090i
$139$	4.01271	−	12.3499i	0.340354	−	1.04750i	−0.623670	−	0.781688i	$-0.714359\pi$
$139$	4.01271	−	12.3499i	0.340354	−	1.04750i	0.964024	−	0.265814i	$-0.0856408\pi$
$140$	9.50468	−	1.50539i	0.803292	−	0.127229i
$141$	−0.666469	−	2.05118i	−0.0561268	−	0.172741i
$142$	−1.14775	−	2.25259i	−0.0963170	−	0.189033i
$143$	−11.1380	−	3.61897i	−0.931409	−	0.302633i
$144$	−3.73078	−	1.21220i	−0.310898	−	0.101017i
$145$	0.533870	+	1.04778i	0.0443355	+	0.0870133i
$146$	−0.850172	−	2.61656i	−0.0703607	−	0.216548i
$147$	−6.57579	+	1.04150i	−0.542362	+	0.0859017i
$148$	−0.723245	+	2.22592i	−0.0594504	+	0.182969i
$149$	0.0276020	−	0.174272i	0.00226125	−	0.0142769i	−0.986532	−	0.163569i	$-0.947699\pi$
$149$	0.0276020	−	0.174272i	0.00226125	−	0.0142769i	0.988793	+	0.149292i	$0.0476994\pi$
$150$	−2.06968	+	2.06968i	−0.168989	+	0.168989i
$151$	−8.96384	+	17.5925i	−0.729467	+	1.43166i	0.165814	+	0.986157i	$0.446975\pi$
$151$	−8.96384	+	17.5925i	−0.729467	+	1.43166i	−0.895281	+	0.445502i	$0.853025\pi$
$152$	−3.94794	−	0.625293i	−0.320221	−	0.0507180i
$153$	−0.566435	−	3.57633i	−0.0457935	−	0.289129i
$154$	0.658453	+	0.478394i	0.0530596	+	0.0385501i
$155$			13.0315i			1.04672i
$156$	9.80159	−	13.4907i	0.784755	−	1.08012i
$157$	−3.16869	+	1.61453i	−0.252889	+	0.128853i	−0.575840	−	0.817562i	$-0.695325\pi$
$157$	−3.16869	+	1.61453i	−0.252889	+	0.128853i	0.322951	+	0.946416i	$0.395325\pi$
$158$	2.77704	+	1.41497i	0.220929	+	0.112569i
$159$	0.916800	+	1.26187i	0.0727069	+	0.100073i
$160$	−9.65749	+	7.01658i	−0.763492	+	0.554709i
$161$	−5.57826	−	5.57826i	−0.439628	−	0.439628i
$162$	1.24841	−	0.405634i	0.0980847	−	0.0318696i
$163$	−4.06263			−0.318210			−0.159105	−	0.987262i	$-0.550861\pi$
$163$	−4.06263			−0.318210			−0.159105	+	0.987262i	$0.550861\pi$
$164$	7.90183	−	9.30465i	0.617029	−	0.726571i
$165$	8.64114			0.672712
$166$	−2.06961	+	0.672459i	−0.160633	+	0.0521929i
$167$	4.42614	+	4.42614i	0.342505	+	0.342505i	0.857308	−	0.514803i	$-0.172135\pi$
$167$	4.42614	+	4.42614i	0.342505	+	0.342505i	−0.514803	+	0.857308i	$0.672135\pi$
$168$	−1.92113	+	1.39579i	−0.148219	+	0.107687i
$169$	−16.5090	−	22.7227i	−1.26993	−	1.74790i
$170$	−3.00577	−	1.53151i	−0.230532	−	0.117462i
$171$	3.39165	−	1.72813i	0.259366	−	0.132154i
$172$	−8.28109	+	11.3979i	−0.631428	+	0.869085i
$173$		−	5.09639i		−	0.387472i	−0.981054	−	0.193736i	$-0.937940\pi$
$173$		−	5.09639i		−	0.387472i	0.981054	−	0.193736i	$-0.0620605\pi$
$174$	−0.114570	−	0.0832400i	−0.00868554	−	0.00631041i
$175$	1.59766	+	10.0872i	0.120772	+	0.762523i
$176$	6.22105	+	0.985317i	0.468929	+	0.0742710i
$177$	−8.35089	+	16.3895i	−0.627691	+	1.23191i
$178$	−3.13768	+	3.13768i	−0.235179	+	0.235179i
$179$	1.40815	−	8.89068i	0.105250	−	0.664521i	−0.877500	−	0.479578i	$-0.840790\pi$
$179$	1.40815	−	8.89068i	0.105250	−	0.664521i	0.982749	−	0.184943i	$-0.0592101\pi$
$180$	2.32340	−	7.15069i	0.173176	−	0.532981i
$181$	−11.7410	+	1.85960i	−0.872704	+	0.138223i	−0.576692	−	0.816961i	$-0.695657\pi$
$181$	−11.7410	+	1.85960i	−0.872704	+	0.138223i	−0.296012	+	0.955184i	$0.595657\pi$
$182$	0.882368	+	2.71565i	0.0654055	+	0.201297i
$183$	−2.86473	−	5.62235i	−0.211767	−	0.415616i
$184$	6.15552	+	2.00005i	0.453791	+	0.147446i
$185$	−4.04672	−	1.31486i	−0.297521	−	0.0966703i
$186$	−0.712470	−	1.39830i	−0.0522408	−	0.102528i
$187$	1.79660	+	5.52935i	0.131380	+	0.404346i
$188$	2.97604	−	0.471358i	0.217050	−	0.0343773i
$189$	2.54121	−	7.82104i	0.184846	−	0.568897i
$190$	0.554778	−	3.50273i	0.0402479	−	0.254115i
$191$	12.4651	−	12.4651i	0.901943	−	0.901943i	−0.0936612	−	0.995604i	$-0.529857\pi$
$191$	12.4651	−	12.4651i	0.901943	−	0.901943i	0.995604	+	0.0936612i	$0.0298571\pi$
$192$	−3.61877	+	7.10224i	−0.261162	+	0.512560i
$193$	13.5277	+	2.14258i	0.973749	+	0.154227i	0.622982	−	0.782236i	$-0.285921\pi$
$193$	13.5277	+	2.14258i	0.973749	+	0.154227i	0.350767	+	0.936463i	$0.385921\pi$
$194$	−0.157314	−	0.993240i	−0.0112945	−	0.0713105i
$195$	24.5261	+	17.8193i	1.75635	+	1.27607i
$196$		−	9.30142i		−	0.664387i
$197$	2.51439	−	3.46077i	0.179143	−	0.246569i	−0.709997	−	0.704205i	$-0.751304\pi$
$197$	2.51439	−	3.46077i	0.179143	−	0.246569i	0.889140	+	0.457636i	$0.151304\pi$
$198$	0.566594	−	0.288694i	0.0402661	−	0.0205166i
$199$	3.37859	+	1.72148i	0.239502	+	0.122032i	0.569623	−	0.821906i	$-0.307089\pi$
$199$	3.37859	+	1.72148i	0.239502	+	0.122032i	−0.330120	+	0.943939i	$0.607089\pi$
$200$	−4.92510	−	6.77882i	−0.348257	−	0.479335i
$201$	7.36448	−	5.35061i	0.519450	−	0.377403i
$202$	1.41440	+	1.41440i	0.0995167	+	0.0995167i
$203$	−0.469952	+	0.152697i	−0.0329842	+	0.0107172i
$204$	−8.27835			−0.579600
$205$	16.9159	+	14.3655i	1.18145	+	1.00333i
$206$	5.04771			0.351690
$207$	−5.86197	+	1.90467i	−0.407435	+	0.132384i
$208$	15.6253	+	15.6253i	1.08342	+	1.08342i
$209$	−4.94468	+	3.59252i	−0.342031	+	0.248500i
$210$	−1.23838	−	1.70449i	−0.0854565	−	0.117621i
$211$	1.22845	+	0.625927i	0.0845701	+	0.0430906i	0.495764	−	0.868457i	$-0.334888\pi$
$211$	1.22845	+	0.625927i	0.0845701	+	0.0430906i	−0.411194	+	0.911548i	$0.634888\pi$
$212$	−1.94159	+	0.989290i	−0.133349	+	0.0679447i
$213$	6.62952	−	9.12475i	0.454247	−	0.625218i
$214$			2.10972i			0.144217i
$215$	−20.7215	−	15.0550i	−1.41319	−	1.02674i
$216$	1.05544	+	6.66381i	0.0718139	+	0.453415i
$217$	−5.40846	−	0.856616i	−0.367150	−	0.0581509i
$218$	0.178626	−	0.350573i	0.0120981	−	0.0237438i
$219$	8.67905	−	8.67905i	0.586476	−	0.586476i
$220$	−1.88853	+	11.9237i	−0.127325	+	0.803897i
$221$	−6.30305	+	19.3988i	−0.423989	+	1.30490i
$222$	0.506106	−	0.0801593i	0.0339676	−	0.00537994i
$223$	−0.544037	−	1.67437i	−0.0364314	−	0.112124i	0.931187	−	0.364542i	$-0.118774\pi$
$223$	−0.544037	−	1.67437i	−0.0364314	−	0.112124i	−0.967618	+	0.252417i	$0.918774\pi$
$224$	−2.27726	−	4.46937i	−0.152156	−	0.298623i
$225$	7.58896	+	2.46580i	0.505931	+	0.164387i
$226$	−2.05769	−	0.668585i	−0.136876	−	0.0444736i
$227$	0.0104794	+	0.0205670i	0.000695544	+	0.00136508i	0.891354	−	0.453308i	$-0.149756\pi$
$227$	0.0104794	+	0.0205670i	0.000695544	+	0.00136508i	−0.890658	+	0.454673i	$0.849756\pi$
$228$	−2.68930	−	8.27680i	−0.178103	−	0.548145i
$229$	−23.8647	+	3.77980i	−1.57703	+	0.249776i	−0.882719	−	0.469902i	$-0.844289\pi$
$229$	−23.8647	+	3.77980i	−1.57703	+	0.249776i	−0.694308	+	0.719678i	$0.744289\pi$
$230$	−1.77450	+	5.46136i	−0.117007	+	0.360111i
$231$	−0.568018	+	3.58633i	−0.0373729	+	0.235963i
$232$	0.286667	−	0.286667i	0.0188206	−	0.0188206i
$233$	8.63167	−	16.9406i	0.565480	−	1.10982i	−0.414375	−	0.910106i	$-0.636000\pi$
$233$	8.63167	−	16.9406i	0.565480	−	1.10982i	0.979855	−	0.199710i	$-0.0640001\pi$
$234$	2.20349	+	0.348999i	0.144047	+	0.0228148i
$235$	0.856929	+	5.41044i	0.0558999	+	0.352938i
$236$	−20.7905	−	15.1052i	−1.35335	−	0.983263i
$237$			13.9048i			0.903213i
$238$	0.833205	−	1.14681i	0.0540087	−	0.0743366i
$239$	15.9440	−	8.12387i	1.03133	−	0.525490i	0.145433	−	0.989368i	$-0.453543\pi$
$239$	15.9440	−	8.12387i	1.03133	−	0.525490i	0.885899	+	0.463878i	$0.153543\pi$
$240$	−14.5276	−	7.40218i	−0.937752	−	0.477808i
$241$	−3.38611	−	4.66058i	−0.218118	−	0.300214i	0.685910	−	0.727686i	$-0.259404\pi$
$241$	−3.38611	−	4.66058i	−0.218118	−	0.300214i	−0.904029	+	0.427472i	$0.859404\pi$
$242$	1.89598	−	1.37751i	0.121878	−	0.0885495i
$243$	−7.83714	−	7.83714i	−0.502753	−	0.502753i
$244$	8.38425	−	2.72421i	0.536747	−	0.174400i
$245$	16.9100			1.08034
$246$	−2.60050	−	0.616603i	−0.165802	−	0.0393132i
$247$	−21.4428			−1.36437
$248$	4.27273	−	1.38829i	0.271318	−	0.0881567i
$249$	−6.86485	−	6.86485i	−0.435042	−	0.435042i
$250$	1.72608	−	1.25407i	0.109167	−	0.0793142i
$251$	14.5918	+	20.0839i	0.921025	+	1.26768i	0.963259	+	0.268575i	$0.0865527\pi$
$251$	14.5918	+	20.0839i	0.921025	+	1.26768i	−0.0422335	+	0.999108i	$0.513447\pi$
$252$	2.81502	+	1.43432i	0.177330	+	0.0903539i
$253$	8.81797	−	4.49298i	0.554381	−	0.282471i
$254$	0.989306	−	1.36166i	0.0620746	−	0.0854383i
$255$		−	15.0500i		−	0.942469i
$256$	−7.30476	−	5.30722i	−0.456548	−	0.331701i
$257$	1.77211	+	11.1887i	0.110541	+	0.697931i	0.979257	+	0.202620i	$0.0649457\pi$
$257$	1.77211	+	11.1887i	0.110541	+	0.697931i	−0.868716	+	0.495311i	$0.835054\pi$
$258$	3.04655	+	0.482525i	0.189670	+	0.0300407i
$259$	0.811713	−	1.59308i	0.0504374	−	0.0989889i
$260$	−29.9487	+	29.9487i	−1.85734	+	1.85734i
$261$	−0.0603954	+	0.381322i	−0.00373838	+	0.0236032i
$262$	−0.769350	+	2.36782i	−0.0475306	+	0.146284i
$263$	−5.50072	+	0.871229i	−0.339189	+	0.0537223i	−0.323706	−	0.946158i	$-0.604929\pi$
$263$	−5.50072	+	0.871229i	−0.339189	+	0.0537223i	−0.0154834	+	0.999880i	$0.504929\pi$
$264$	−0.920570	−	2.83322i	−0.0566572	−	0.174373i
$265$	−1.79853	−	3.52981i	−0.110483	−	0.216835i
$266$	1.41727	+	0.460499i	0.0868983	+	0.0282350i
$267$	−18.8275	−	6.11742i	−1.15222	−	0.374380i
$268$	5.77367	+	11.3315i	0.352683	+	0.692180i
$269$	2.20004	+	6.77102i	0.134139	+	0.412836i	0.995455	−	0.0952327i	$-0.0303595\pi$
$269$	2.20004	+	6.77102i	0.134139	+	0.412836i	−0.861316	+	0.508069i	$0.830360\pi$
$270$	−5.91233	+	0.936421i	−0.359813	+	0.0569888i
$271$	4.59561	−	14.1438i	0.279164	−	0.859177i	−0.708924	−	0.705285i	$-0.750819\pi$
$271$	4.59561	−	14.1438i	0.279164	−	0.859177i	0.988088	−	0.153892i	$-0.0491809\pi$
$272$	1.71610	−	10.8350i	0.104054	−	0.656970i
$273$	−9.00773	+	9.00773i	−0.545173	+	0.545173i
$274$	0.0148834	−	0.0292103i	0.000899140	−	0.00176466i
$275$	−12.6545	−	2.00428i	−0.763097	−	0.120863i
$276$	2.20443	+	13.9182i	0.132691	+	0.837778i
$277$	−6.93372	−	5.03764i	−0.416607	−	0.302683i	0.359664	−	0.933082i	$-0.382891\pi$
$277$	−6.93372	−	5.03764i	−0.416607	−	0.302683i	−0.776271	+	0.630399i	$0.782891\pi$
$278$		−	3.97188i		−	0.238217i
$279$	−2.51476	+	3.46127i	−0.150555	+	0.207221i
$280$	5.37398	−	2.73818i	0.321157	−	0.163637i
$281$	10.9370	+	5.57269i	0.652448	+	0.332439i	0.748691	−	0.662919i	$-0.230683\pi$
$281$	10.9370	+	5.57269i	0.652448	+	0.332439i	−0.0962434	+	0.995358i	$0.530683\pi$
$282$	−0.387754	−	0.533697i	−0.0230904	−	0.0317812i
$283$	17.0898	−	12.4165i	1.01588	−	0.738083i	0.0504491	−	0.998727i	$-0.483935\pi$
$283$	17.0898	−	12.4165i	1.01588	−	0.738083i	0.965435	+	0.260644i	$0.0839347\pi$
$284$	11.1422	+	11.1422i	0.661166	+	0.661166i
$285$	15.0472	−	4.88914i	0.891321	−	0.289608i
$286$	−3.58214			−0.211816
$287$	−7.07406	+	6.07627i	−0.417569	+	0.358671i
$288$	−3.91913			−0.230937
$289$	−6.53764	+	2.12421i	−0.384567	+	0.124953i
$290$	0.254339	+	0.254339i	0.0149353	+	0.0149353i
$291$	3.62957	−	2.63704i	0.212769	−	0.154586i
$292$	10.0792	+	13.8729i	0.589842	+	0.811848i
$293$	−23.6770	−	12.0640i	−1.38323	−	0.704789i	−0.405387	−	0.914145i	$-0.632863\pi$
$293$	−23.6770	−	12.0640i	−1.38323	−	0.704789i	−0.977839	+	0.209356i	$0.932863\pi$
$294$	−1.81447	+	0.924516i	−0.105822	+	0.0539189i
$295$	27.4612	−	37.7971i	1.59885	−	2.20063i
$296$			1.46690i			0.0852618i
$297$	8.34623	+	6.06389i	0.484297	+	0.351862i
$298$	−0.00844269	−	0.0533050i	−0.000489072	−	0.00308788i
$299$	34.2932	+	5.43151i	1.98323	+	0.314113i
$300$	8.28226	−	16.2548i	0.478176	−	0.938474i
$301$	7.61039	−	7.61039i	0.438655	−	0.438655i
$302$	−0.944756	+	5.96495i	−0.0543646	+	0.343244i
$303$	−2.75760	+	8.48703i	−0.158420	+	0.487567i
$304$	11.3905	−	1.80408i	0.653289	−	0.103471i
$305$	4.95261	+	15.2426i	0.283586	+	0.872787i
$306$	−0.502810	−	0.986820i	−0.0287437	−	0.0564128i
$307$	6.65182	+	2.16131i	0.379639	+	0.123352i	0.492619	−	0.870245i	$-0.336040\pi$
$307$	6.65182	+	2.16131i	0.379639	+	0.123352i	−0.112980	+	0.993597i	$0.536040\pi$
$308$	−4.82455	−	1.56759i	−0.274905	−	0.0893219i
$309$	10.2236	+	20.0649i	0.581600	+	1.14145i
$310$	1.23173	+	3.79089i	0.0699578	+	0.215308i
$311$	−3.25192	+	0.515053i	−0.184399	+	0.0292060i	−0.247951	−	0.968773i	$-0.579757\pi$
$311$	−3.25192	+	0.515053i	−0.184399	+	0.0292060i	0.0635517	+	0.997979i	$0.479757\pi$
$312$	3.22967	−	9.93989i	0.182844	−	0.562735i
$313$	−1.77802	+	11.2260i	−0.100499	+	0.634528i	0.885096	+	0.465408i	$0.154093\pi$
$313$	−1.77802	+	11.2260i	−0.100499	+	0.634528i	−0.985595	+	0.169120i	$0.945907\pi$
$314$	−0.769173	+	0.769173i	−0.0434069	+	0.0434069i
$315$	−2.60760	+	5.11770i	−0.146922	+	0.288350i
$316$	−19.1869	−	3.03891i	−1.07935	−	0.170952i
$317$	4.29092	+	27.0918i	0.241002	+	1.52163i	0.750336	+	0.661057i	$0.229892\pi$
$317$	4.29092	+	27.0918i	0.241002	+	1.52163i	−0.509334	+	0.860569i	$0.670108\pi$
$318$	0.385970	+	0.280423i	0.0216441	+	0.0157254i
$319$		−	0.619901i		−	0.0347078i
$320$	11.9000	−	16.3790i	0.665231	−	0.915612i
$321$	−8.38626	+	4.27301i	−0.468075	+	0.238496i
$322$	−2.14998	−	1.09547i	−0.119814	−	0.0610481i
$323$	6.25700	+	8.61202i	0.348149	+	0.479185i
$324$	−6.61902	+	4.80900i	−0.367724	+	0.267167i
$325$	−31.7843	−	31.7843i	−1.76307	−	1.76307i
$326$	−1.18183	+	0.383998i	−0.0654552	+	0.0212677i
$327$	1.75534			0.0970705
$328$	2.90801	−	7.07672i	0.160568	−	0.390746i
$329$	−2.30182			−0.126903
$330$	2.51372	−	0.816757i	0.138376	−	0.0449610i
$331$	−10.6130	−	10.6130i	−0.583344	−	0.583344i	0.352477	−	0.935821i	$-0.385340\pi$
$331$	−10.6130	−	10.6130i	−0.583344	−	0.583344i	−0.935821	+	0.352477i	$0.885340\pi$
$332$	10.9730	−	7.97234i	0.602221	−	0.437539i
$333$	−0.821104	−	1.13015i	−0.0449962	−	0.0619320i
$334$	1.70593	+	0.869213i	0.0933442	+	0.0475612i
$335$	−20.6006	+	10.4965i	−1.12553	+	0.573487i
$336$	4.02708	−	5.54280i	0.219695	−	0.302385i
$337$			11.4038i			0.621207i	0.950540	+	0.310603i	$0.100531\pi$
$337$			11.4038i			0.621207i	−0.950540	+	0.310603i	$0.899469\pi$
$338$	−6.95025	−	5.04965i	−0.378044	−	0.274665i
$339$	−1.50997	−	9.53360i	−0.0820105	−	0.517794i
$340$	20.7672	+	3.28920i	1.12626	+	0.178382i
$341$	3.11871	−	6.12082i	0.168888	−	0.331461i
$342$	0.823294	−	0.823294i	0.0445186	−	0.0445186i
$343$	−2.70637	+	17.0873i	−0.146130	+	0.922629i
$344$	−2.72866	+	8.39794i	−0.147119	+	0.452787i
$345$	−25.3033	+	4.00765i	−1.36228	+	0.215765i
$346$	−0.481709	−	1.48255i	−0.0258968	−	0.0797023i
$347$	−15.1544	−	29.7422i	−0.813531	−	1.59665i	−0.802460	−	0.596706i	$-0.796476\pi$
$347$	−15.1544	−	29.7422i	−0.813531	−	1.59665i	−0.0110717	−	0.999939i	$-0.503524\pi$
$348$	0.839467	+	0.272760i	0.0450002	+	0.0146214i
$349$	−4.88104	−	1.58595i	−0.261276	−	0.0848938i	0.175450	−	0.984488i	$-0.443862\pi$
$349$	−4.88104	−	1.58595i	−0.261276	−	0.0848938i	−0.436726	+	0.899595i	$0.643862\pi$
$350$	1.41820	+	2.78338i	0.0758061	+	0.148778i
$351$	11.1845	+	34.4223i	0.596983	+	1.83732i
$352$	6.21527	−	0.984402i	0.331275	−	0.0524688i
$353$	7.91928	−	24.3730i	0.421501	−	1.29725i	−0.484804	−	0.874623i	$-0.661109\pi$
$353$	7.91928	−	24.3730i	0.421501	−	1.29725i	0.906305	−	0.422624i	$-0.138891\pi$
$354$	−0.880153	+	5.55707i	−0.0467796	+	0.295355i
$355$	−20.2564	+	20.2564i	−1.07510	+	1.07510i
$356$	12.5561	−	24.6427i	0.665471	−	1.30606i
$357$	6.24620	+	0.989301i	0.330584	+	0.0523594i
$358$	−0.430712	−	2.71941i	−0.0227638	−	0.143725i
$359$	−1.10482	−	0.802698i	−0.0583101	−	0.0423648i	0.558248	−	0.829674i	$-0.311474\pi$
$359$	−1.10482	−	0.802698i	−0.0583101	−	0.0423648i	−0.616559	+	0.787309i	$0.711474\pi$
$360$		−	4.71237i		−	0.248363i
$361$	4.59015	−	6.31780i	0.241587	−	0.332516i
$362$	−3.23972	+	1.65072i	−0.170276	+	0.0867598i
$363$	9.31577	+	4.74662i	0.488951	+	0.249133i
$364$	−10.4609	−	14.3982i	−0.548302	−	0.754672i
$365$	−25.2208	+	18.3240i	−1.32012	+	0.959123i
$366$	−1.36478	−	1.36478i	−0.0713380	−	0.0713380i
$367$	8.38455	−	2.72431i	0.437670	−	0.142208i	−0.0818904	−	0.996641i	$-0.526096\pi$
$367$	8.38455	−	2.72431i	0.437670	−	0.142208i	0.519560	+	0.854434i	$0.326096\pi$
$368$	−18.6737			−0.973432
$369$	1.72079	+	7.07993i	0.0895808	+	0.368567i
$370$	−1.30148			−0.0676606
$371$	1.58320	−	0.514413i	0.0821956	−	0.0267070i
$372$	6.91654	+	6.91654i	0.358606	+	0.358606i
$373$	−13.1261	+	9.53664i	−0.679641	+	0.493788i	−0.873239	−	0.487293i	$-0.837984\pi$
$373$	−13.1261	+	9.53664i	−0.679641	+	0.493788i	0.193597	+	0.981081i	$0.437984\pi$
$374$	1.04527	+	1.43868i	0.0540494	+	0.0743926i
$375$	8.48098	+	4.32128i	0.437956	+	0.223150i
$376$	1.68266	−	0.857359i	0.0867767	−	0.0442149i
$377$	1.27833	−	1.75946i	0.0658371	−	0.0906170i
$378$		−	2.51535i		−	0.129375i
$379$	−9.20110	−	6.68499i	−0.472629	−	0.343385i	0.325836	−	0.945426i	$-0.394354\pi$
$379$	−9.20110	−	6.68499i	−0.472629	−	0.343385i	−0.798465	+	0.602041i	$0.794354\pi$
$380$	3.45783	+	21.8319i	0.177383	+	1.11995i
$381$	7.41643	+	1.17465i	0.379955	+	0.0601790i
$382$	2.44792	−	4.80431i	0.125246	−	0.245810i
$383$	3.21049	−	3.21049i	0.164048	−	0.164048i	−0.620309	−	0.784357i	$-0.712993\pi$
$383$	3.21049	−	3.21049i	0.164048	−	0.164048i	0.784357	+	0.620309i	$0.212993\pi$
$384$	−1.85187	+	11.6922i	−0.0945028	+	0.596667i
$385$	2.84988	−	8.77104i	0.145243	−	0.447014i
$386$	4.13776	−	0.655357i	0.210606	−	0.0333568i
$387$	−2.59853	−	7.99746i	−0.132091	−	0.406534i
$388$	2.84554	+	5.58469i	0.144461	+	0.283520i
$389$	−24.2065	−	7.86516i	−1.22732	−	0.398780i	−0.377576	−	0.925979i	$-0.623242\pi$
$389$	−24.2065	−	7.86516i	−1.22732	−	0.398780i	−0.849742	+	0.527199i	$0.823242\pi$
$390$	8.81896	+	2.86546i	0.446566	+	0.145098i
$391$	−7.82530	−	15.3580i	−0.395742	−	0.776688i
$392$	−1.80148	−	5.54438i	−0.0909884	−	0.280033i
$393$	−10.9705	+	1.73755i	−0.553386	+	0.0876478i
$394$	0.404331	−	1.24440i	0.0203699	−	0.0626920i
$395$	5.52473	−	34.8818i	0.277980	−	1.75509i
$396$	−2.80259	+	2.80259i	−0.140836	+	0.140836i
$397$	10.4510	−	20.5112i	0.524519	−	1.02943i	−0.465039	−	0.885290i	$-0.653960\pi$
$397$	10.4510	−	20.5112i	0.524519	−	1.02943i	0.989558	−	0.144136i	$-0.0460402\pi$
$398$	1.14555	+	0.181438i	0.0574213	+	0.00909464i
$399$	1.04002	+	6.56642i	0.0520661	+	0.328732i
$400$	19.5581	+	14.2098i	0.977903	+	0.710488i
$401$			21.8245i			1.08986i	0.838481	+	0.544931i	$0.183444\pi$
$401$			21.8245i			1.08986i	−0.838481	+	0.544931i	$0.816556\pi$
$402$	1.63660	−	2.25259i	0.0816262	−	0.112349i
$403$	21.4739	−	10.9415i	1.06969	−	0.545034i
$404$	−11.1084	−	5.66001i	−0.552664	−	0.281596i
$405$	−8.74277	−	12.0334i	−0.434432	−	0.597944i
$406$	−0.122277	+	0.0888395i	−0.00606851	+	0.00440903i
$407$	1.58604	+	1.58604i	0.0786173	+	0.0786173i
$408$	−4.93455	+	1.60333i	−0.244296	+	0.0793767i
$409$	−3.45570			−0.170874			−0.0854368	−	0.996344i	$-0.527229\pi$
$409$	−3.45570			−0.170874			−0.0854368	+	0.996344i	$0.527229\pi$
$410$	6.27867	+	2.58007i	0.310082	+	0.127421i
$411$	0.146258			0.00721436
$412$	−29.9216	+	9.72211i	−1.47413	+	0.478974i
$413$	13.8818	+	13.8818i	0.683077	+	0.683077i
$414$	−1.52523	+	1.10814i	−0.0749609	+	0.0544622i
$415$	14.4937	+	19.9489i	0.711468	+	0.979252i
$416$	19.6708	+	10.0228i	0.964440	+	0.491407i
$417$	15.7884	−	8.04462i	0.773164	−	0.393947i
$418$	−1.09885	+	1.51244i	−0.0537466	+	0.0739759i
$419$			18.7536i			0.916172i	0.888908	+	0.458086i	$0.151465\pi$
$419$			18.7536i			0.916172i	−0.888908	+	0.458086i	$0.848535\pi$
$420$	10.6237	+	7.71861i	0.518386	+	0.376629i
$421$	−0.976054	−	6.16256i	−0.0475699	−	0.300345i	0.952420	−	0.304788i	$-0.0985856\pi$
$421$	−0.976054	−	6.16256i	−0.0475699	−	0.300345i	−0.999990	+	0.00444331i	$0.998586\pi$
$422$	0.416521	+	0.0659704i	0.0202759	+	0.00321139i
$423$	−0.816474	+	1.60242i	−0.0396983	+	0.0779123i
$424$	−0.965738	+	0.965738i	−0.0469004	+	0.0469004i
$425$	−3.49080	+	22.0401i	−0.169329	+	1.06910i
$426$	1.06607	−	3.28102i	0.0516512	−	0.158966i
$427$	−6.65167	+	1.05352i	−0.321897	+	0.0509834i
$428$	−4.06341	−	12.5059i	−0.196412	−	0.604495i
$429$	−7.25524	−	14.2392i	−0.350286	−	0.687476i
$430$	−7.45090	−	2.42094i	−0.359314	−	0.116748i
$431$	6.05658	+	1.96790i	0.291735	+	0.0947906i	0.451228	−	0.892408i	$-0.350986\pi$
$431$	6.05658	+	1.96790i	0.291735	+	0.0947906i	−0.159493	+	0.987199i	$0.550986\pi$
$432$	−8.83733	−	17.3442i	−0.425186	−	0.834475i
$433$	−0.625179	−	1.92410i	−0.0300442	−	0.0924664i	0.934910	−	0.354885i	$-0.115480\pi$
$433$	−0.625179	−	1.92410i	−0.0300442	−	0.0924664i	−0.964954	+	0.262418i	$0.915480\pi$
$434$	−1.65430	+	0.262015i	−0.0794088	+	0.0125771i
$435$	−0.495877	+	1.52615i	−0.0237755	+	0.0731734i
$436$	−0.383632	+	2.42216i	−0.0183726	+	0.116000i
$437$	12.8130	−	12.8130i	0.612931	−	0.612931i
$438$	1.70441	−	3.34509i	0.0814398	−	0.159835i
$439$	21.7512	+	3.44505i	1.03813	+	0.164423i	0.652154	−	0.758086i	$-0.273865\pi$
$439$	21.7512	+	3.44505i	1.03813	+	0.164423i	0.385974	+	0.922510i	$0.373865\pi$
$440$	1.18365	+	7.47325i	0.0564281	+	0.356273i
$441$	4.49142	+	3.26321i	0.213877	+	0.155391i
$442$			6.23891i			0.296754i
$443$	−9.35155	+	12.8713i	−0.444305	+	0.611534i	−0.971162	−	0.238420i	$-0.923370\pi$
$443$	−9.35155	+	12.8713i	−0.444305	+	0.611534i	0.526857	+	0.849954i	$0.323370\pi$
$444$	−2.84568	+	1.44995i	−0.135050	+	0.0688115i
$445$	44.8004	+	22.8269i	2.12374	+	1.08210i
$446$	−0.316523	−	0.435656i	−0.0149878	−	0.0206289i
$447$	0.194791	−	0.141524i	0.00921330	−	0.00669385i
$448$	6.01552	+	6.01552i	0.284206	+	0.284206i
$449$	21.4180	−	6.95914i	1.01078	−	0.328422i	0.243615	−	0.969872i	$-0.421667\pi$
$449$	21.4180	−	6.95914i	1.01078	−	0.328422i	0.767165	+	0.641450i	$0.221667\pi$
$450$	2.44071			0.115056
$451$	−4.50730	−	10.7957i	−0.212240	−	0.508350i
$452$	13.4852			0.634291
$453$	−25.6246	+	8.32592i	−1.20395	+	0.391186i
$454$	0.00499247	+	0.00499247i	0.000234308	+	0.000234308i
$455$	26.1760	−	19.0180i	1.22715	−	0.891576i
$456$	−3.20607	−	4.41277i	−0.150138	−	0.206647i
$457$	3.27733	+	1.66988i	0.153307	+	0.0781138i	0.528961	−	0.848646i	$-0.322582\pi$
$457$	3.27733	+	1.66988i	0.153307	+	0.0781138i	−0.375654	+	0.926760i	$0.622582\pi$
$458$	−6.58502	+	3.35524i	−0.307698	+	0.156780i
$459$	10.5613	−	14.5364i	0.492959	−	0.678500i
$460$		−	35.7914i		−	1.66878i
$461$	−3.11530	−	2.26340i	−0.145094	−	0.105417i	0.512870	−	0.858466i	$-0.328582\pi$
$461$	−3.11530	−	2.26340i	−0.145094	−	0.105417i	−0.657964	+	0.753049i	$0.728582\pi$
$462$	0.173741	+	1.09696i	0.00808316	+	0.0510350i
$463$	−31.3684	−	4.96826i	−1.45781	−	0.230895i	−0.623342	−	0.781949i	$-0.714226\pi$
$463$	−31.3684	−	4.96826i	−1.45781	−	0.230895i	−0.834469	+	0.551054i	$0.814226\pi$
$464$	−0.531020	+	1.04218i	−0.0246520	+	0.0483822i
$465$	−12.5743	+	12.5743i	−0.583118	+	0.583118i
$466$	0.909746	−	5.74391i	0.0421432	−	0.266082i
$467$	9.68505	−	29.8075i	0.448171	−	1.37933i	−0.430798	−	0.902448i	$-0.641768\pi$
$467$	9.68505	−	29.8075i	0.448171	−	1.37933i	0.878969	−	0.476879i	$-0.158232\pi$
$468$	−13.7339	+	2.17524i	−0.634852	+	0.100551i
$469$	−3.00221	−	9.23984i	−0.138629	−	0.426656i
$470$	0.760675	+	1.49291i	0.0350873	+	0.0688627i
$471$	−4.61539	−	1.49963i	−0.212666	−	0.0690993i
$472$	−15.3183	−	4.97722i	−0.705082	−	0.229095i
$473$	6.12975	+	12.0303i	0.281846	+	0.553155i
$474$	1.31427	+	4.04492i	0.0603666	+	0.185789i
$475$	−23.1700	+	3.66976i	−1.06311	+	0.168380i
$476$	−2.73023	+	8.40279i	−0.125140	+	0.385141i
$477$	0.203463	−	1.28462i	0.00931594	−	0.0588185i
$478$	3.87027	−	3.87027i	0.177022	−	0.177022i
$479$	−18.7953	+	36.8879i	−0.858780	+	1.68545i	−0.140069	+	0.990142i	$0.544732\pi$
$479$	−18.7953	+	36.8879i	−0.858780	+	1.68545i	−0.718711	+	0.695309i	$0.755268\pi$
$480$	−16.0890	−	2.54825i	−0.734360	−	0.116311i
$481$	1.23101	+	7.77232i	0.0561294	+	0.354387i
$482$	−1.42554	−	1.03572i	−0.0649316	−	0.0471756i
$483$		−	10.7650i		−	0.489827i
$484$	−8.58574	+	11.8173i	−0.390261	+	0.537148i
$485$	−10.1530	+	5.17320i	−0.461023	+	0.234903i
$486$	−3.02060	−	1.53907i	−0.137017	−	0.0698138i
$487$	19.1905	+	26.4134i	0.869602	+	1.19691i	0.979194	+	0.202928i	$0.0650458\pi$
$487$	19.1905	+	26.4134i	0.869602	+	1.19691i	−0.109591	+	0.993977i	$0.534954\pi$
$488$	4.47006	−	3.24769i	0.202350	−	0.147016i
$489$	−3.92008	−	3.92008i	−0.177272	−	0.177272i
$490$	4.91914	−	1.59833i	0.222224	−	0.0722050i
$491$	−40.3633			−1.82157			−0.910786	−	0.412880i	$-0.864523\pi$
$491$	−40.3633			−1.82157			−0.910786	+	0.412880i	$0.864523\pi$
$492$	16.6027	−	1.35361i	0.748509	−	0.0610252i
$493$	−1.07966			−0.0486256
$494$	−6.23774	+	2.02677i	−0.280649	+	0.0911885i
$495$	−5.09511	−	5.09511i	−0.229008	−	0.229008i
$496$	−10.4864	+	7.61884i	−0.470855	+	0.342096i
$497$	−7.07548	−	9.73856i	−0.317379	−	0.436834i
$498$	−2.64586	−	1.34813i	−0.118564	−	0.0604113i
$499$	−9.86612	+	5.02704i	−0.441668	+	0.225041i	−0.660660	−	0.750686i	$-0.729723\pi$
$499$	−9.86612	+	5.02704i	−0.441668	+	0.225041i	0.218992	+	0.975727i	$0.429723\pi$
$500$	−7.81637	+	10.7583i	−0.349559	+	0.481126i
$501$			8.54167i			0.381613i
$502$	6.14309	+	4.46322i	0.274180	+	0.199203i
$503$	5.39469	+	34.0608i	0.240538	+	1.51869i	0.751870	+	0.659311i	$0.229152\pi$
$503$	5.39469	+	34.0608i	0.240538	+	1.51869i	−0.511333	+	0.859383i	$0.670848\pi$
$504$	1.95577	+	0.309764i	0.0871169	+	0.0137980i
$505$	10.2899	−	20.1951i	0.457895	−	0.898669i
$506$	2.14049	−	2.14049i	0.0951562	−	0.0951562i
$507$	5.99568	−	37.8552i	0.266277	−	1.68121i
$508$	−3.24174	+	9.97706i	−0.143829	+	0.442660i
$509$	20.1967	−	3.19884i	0.895202	−	0.141786i	0.308152	−	0.951337i	$-0.400289\pi$
$509$	20.1967	−	3.19884i	0.895202	−	0.141786i	0.587050	+	0.809551i	$0.300289\pi$
$510$	−1.42252	−	4.37808i	−0.0629904	−	0.193864i
$511$	−5.94713	−	11.6719i	−0.263086	−	0.516335i
$512$	−19.1276	−	6.21495i	−0.845331	−	0.274665i
$513$	17.9646	+	5.83706i	0.793157	+	0.257712i
$514$	1.57306	+	3.08731i	0.0693847	+	0.136175i
$515$	−17.6748	−	54.3974i	−0.778844	−	2.39704i
$516$	−18.9885	+	3.00749i	−0.835924	+	0.132397i
$517$	0.892336	−	2.74633i	0.0392449	−	0.120783i
$518$	0.0855515	−	0.540151i	0.00375892	−	0.0237329i
$519$	4.91757	−	4.91757i	0.215857	−	0.215857i
$520$	−12.0514	+	23.6522i	−0.528488	+	1.03722i
$521$	27.5874	+	4.36942i	1.20863	+	0.191428i	0.728050	−	0.685525i	$-0.240427\pi$
$521$	27.5874	+	4.36942i	1.20863	+	0.191428i	0.480577	+	0.876952i	$0.340427\pi$
$522$	0.0184733	+	0.116636i	0.000808553	+	0.00510500i
$523$	29.2671	+	21.2638i	1.27976	+	0.929800i	0.999546	−	0.0301373i	$-0.00959445\pi$
$523$	29.2671	+	21.2638i	1.27976	+	0.929800i	0.280214	+	0.959937i	$0.409594\pi$
$524$		−	15.5176i		−	0.677891i
$525$	−8.19168	+	11.2749i	−0.357514	+	0.492076i
$526$	−1.51782	+	0.773368i	−0.0661801	+	0.0337204i
$527$	−10.6605	−	5.43177i	−0.464377	−	0.236612i
$528$	5.05202	+	6.95350i	0.219861	+	0.302612i
$529$	−5.12993	+	3.72711i	−0.223040	+	0.162048i
$530$	−0.856831	−	0.856831i	−0.0372184	−	0.0372184i
$531$	14.5878	−	4.73987i	0.633057	−	0.205693i
$532$	−9.28817			−0.402693
$533$	9.46924	−	39.9361i	0.410158	−	1.72983i
$534$	−6.05516			−0.262033
$535$	22.7357	−	7.38728i	0.982950	−	0.319380i
$536$	5.63622	+	5.63622i	0.243448	+	0.243448i
$537$	9.93746	−	7.21999i	0.428833	−	0.311565i
$538$	1.27999	+	1.76175i	0.0551842	+	0.0759546i
$539$	−7.94250	−	4.04691i	−0.342108	−	0.174313i
$540$	33.2433	−	16.9383i	1.43056	−	0.728908i
$541$	−20.5933	+	28.3442i	−0.885374	+	1.21861i	0.0895294	+	0.995984i	$0.471464\pi$
$541$	−20.5933	+	28.3442i	−0.885374	+	1.21861i	−0.974903	+	0.222628i	$0.928536\pi$
$542$		−	4.54884i		−	0.195389i
$543$	−13.1234	−	9.53472i	−0.563180	−	0.409174i
$544$	−1.71451	−	10.8250i	−0.0735088	−	0.464116i
$545$	−4.40348	−	0.697442i	−0.188624	−	0.0298751i
$546$	−1.76896	+	3.47177i	−0.0757043	+	0.148578i
$547$	−9.29596	+	9.29596i	−0.397467	+	0.397467i	−0.877339	−	0.479872i	$-0.840683\pi$
$547$	−9.29596	+	9.29596i	−0.397467	+	0.397467i	0.479872	+	0.877339i	$0.340683\pi$
$548$	−0.0319648	+	0.201818i	−0.00136547	+	0.00862123i
$549$	−1.62599	+	5.00427i	−0.0693954	+	0.213577i
$550$	−3.87067	+	0.613054i	−0.165046	+	0.0261407i
$551$	−0.350739	−	1.07946i	−0.0149420	−	0.0459866i
$552$	4.00966	+	7.86940i	0.170662	+	0.334944i
$553$	14.1138	+	4.58585i	0.600180	+	0.195010i
$554$	−2.49319	−	0.810085i	−0.105925	−	0.0344172i
$555$	−2.63600	−	5.17345i	−0.111892	−	0.219601i
$556$	7.65001	+	23.5443i	0.324433	+	0.998501i
$557$	28.1382	−	4.45665i	1.19225	−	0.188834i	0.471399	−	0.881920i	$-0.343749\pi$
$557$	28.1382	−	4.45665i	1.19225	−	0.188834i	0.720855	+	0.693086i	$0.243749\pi$
$558$	−0.404390	+	1.24458i	−0.0171192	+	0.0526874i
$559$	−7.41019	+	46.7861i	−0.313418	+	1.97884i
$560$	−12.3047	+	12.3047i	−0.519969	+	0.519969i
$561$	−3.60178	+	7.06890i	−0.152067	+	0.298449i
$562$	3.70832	+	0.587341i	0.156426	+	0.0247755i
$563$	2.11661	+	13.3638i	0.0892046	+	0.563216i	0.991294	+	0.131667i	$0.0420328\pi$
$563$	2.11661	+	13.3638i	0.0892046	+	0.563216i	−0.902089	+	0.431549i	$0.857967\pi$
$564$	3.32643	+	2.41680i	0.140068	+	0.101765i
$565$			24.5161i			1.03140i
$566$	3.79785	−	5.22730i	0.159636	−	0.219720i
$567$	5.56891	−	2.83750i	0.233872	−	0.119164i
$568$	8.79959	+	4.48362i	0.369223	+	0.188128i
$569$	−26.6643	−	36.7002i	−1.11782	−	1.53855i	−0.809357	−	0.587317i	$-0.800184\pi$
$569$	−26.6643	−	36.7002i	−1.11782	−	1.53855i	−0.308467	−	0.951235i	$-0.599816\pi$
$570$	3.91514	−	2.84452i	0.163987	−	0.119144i
$571$	−1.62367	−	1.62367i	−0.0679486	−	0.0679486i	0.672316	−	0.740264i	$-0.265300\pi$
$571$	−1.62367	−	1.62367i	−0.0679486	−	0.0679486i	−0.740264	+	0.672316i	$0.765300\pi$
$572$	21.2340	−	6.89935i	0.887839	−	0.288476i
$573$	24.0554			1.00493
$574$	−1.48353	+	2.43623i	−0.0619213	+	0.101686i
$575$	37.9850			1.58409
$576$	6.32147	−	2.05397i	0.263395	−	0.0855821i
$577$	−4.24210	−	4.24210i	−0.176601	−	0.176601i	0.613271	−	0.789872i	$-0.289853\pi$
$577$	−4.24210	−	4.24210i	−0.176601	−	0.176601i	−0.789872	+	0.613271i	$0.789853\pi$
$578$	−1.70103	+	1.23587i	−0.0707535	+	0.0514054i
$579$	10.9857	+	15.1205i	0.456549	+	0.628386i
$580$	−1.99753	−	1.01779i	−0.0829429	−	0.0422615i
$581$	−9.23210	+	4.70399i	−0.383012	+	0.195154i
$582$	0.806595	−	1.11018i	0.0334345	−	0.0460186i
$583$			2.08835i			0.0864908i
$584$	8.69487	+	6.31720i	0.359796	+	0.261407i
$585$	−3.95459	−	24.9683i	−0.163502	−	1.03231i
$586$	−8.02797	−	1.27151i	−0.331632	−	0.0525254i
$587$	−16.5667	+	32.5140i	−0.683780	+	1.34199i	0.244331	+	0.969692i	$0.421432\pi$
$587$	−16.5667	+	32.5140i	−0.683780	+	1.34199i	−0.928111	+	0.372303i	$0.878568\pi$
$588$	8.97505	−	8.97505i	0.370125	−	0.370125i
$589$	1.96761	−	12.4230i	0.0810741	−	0.511882i
$590$	4.41594	−	13.5909i	0.181801	−	0.559527i
$591$	5.76550	−	0.913166i	0.237161	−	0.0375626i
$592$	−1.30784	−	4.02511i	−0.0537518	−	0.165431i
$593$	−0.226552	−	0.444634i	−0.00930339	−	0.0182589i	0.886308	−	0.463096i	$-0.153262\pi$
$593$	−0.226552	−	0.444634i	−0.00930339	−	0.0182589i	−0.895611	+	0.444837i	$0.853262\pi$
$594$	3.00109	+	0.975112i	0.123136	+	0.0400093i
$595$	−15.2763	−	4.96356i	−0.626266	−	0.203486i
$596$	0.152714	+	0.299718i	0.00625541	+	0.0122769i
$597$	1.59897	+	4.92112i	0.0654414	+	0.201408i
$598$	10.4893	−	1.66135i	0.428941	−	0.0679376i
$599$	−7.58173	+	23.3342i	−0.309781	+	0.953409i	0.668068	+	0.744100i	$0.267121\pi$
$599$	−7.58173	+	23.3342i	−0.309781	+	0.953409i	−0.977850	+	0.209309i	$0.932879\pi$
$600$	1.78868	−	11.2933i	0.0730224	−	0.461045i
$601$	5.35213	−	5.35213i	0.218318	−	0.218318i	−0.589471	−	0.807789i	$-0.700664\pi$
$601$	5.35213	−	5.35213i	0.218318	−	0.218318i	0.807789	+	0.589471i	$0.200664\pi$
$602$	1.49454	−	2.93320i	0.0609130	−	0.119548i
$603$	−7.49725	−	1.18745i	−0.305312	−	0.0483566i
$604$	−5.88848	−	37.1784i	−0.239599	−	1.51277i
$605$	−21.4838	−	15.6089i	−0.873440	−	0.634591i
$606$			2.72954i			0.110880i
$607$	21.2236	−	29.2118i	0.861440	−	1.18567i	−0.119785	−	0.992800i	$-0.538220\pi$
$607$	21.2236	−	29.2118i	0.861440	−	1.18567i	0.981224	−	0.192870i	$-0.0617796\pi$
$608$	10.2660	−	5.23077i	0.416340	−	0.212136i
$609$	−0.600802	−	0.306124i	−0.0243457	−	0.0124048i
$610$	2.88144	+	3.96597i	0.116666	+	0.160577i
$611$	8.19604	−	5.95477i	0.331576	−	0.240904i
$612$	4.88120	+	4.88120i	0.197311	+	0.197311i
$613$	−30.2951	+	9.84349i	−1.22361	+	0.397575i	−0.848395	−	0.529364i	$-0.822431\pi$
$613$	−30.2951	+	9.84349i	−1.22361	+	0.397575i	−0.375214	+	0.926938i	$0.622431\pi$
$614$	2.13931			0.0863355
$615$	2.46085	+	30.1838i	0.0992312	+	1.21713i
$616$	−3.17942			−0.128103
$617$	18.2794	−	5.93935i	0.735903	−	0.239109i	0.0829983	−	0.996550i	$-0.473550\pi$
$617$	18.2794	−	5.93935i	0.735903	−	0.239109i	0.652904	+	0.757440i	$0.273550\pi$
$618$	4.87059	+	4.87059i	0.195924	+	0.195924i
$619$	−31.0258	+	22.5415i	−1.24703	+	0.906021i	−0.998046	−	0.0624862i	$-0.980097\pi$
$619$	−31.0258	+	22.5415i	−1.24703	+	0.906021i	−0.248985	+	0.968507i	$0.580097\pi$
$620$	−14.6028	−	20.0991i	−0.586464	−	0.807199i
$621$	−27.2521	−	13.8856i	−1.09359	−	0.557211i
$622$	−0.897305	+	0.457200i	−0.0359787	+	0.0183320i
$623$	−12.4188	+	17.0930i	−0.497547	+	0.684815i
$624$			30.1541i			1.20713i
$625$	8.80773	+	6.39919i	0.352309	+	0.255968i
$626$	0.543845	+	3.43370i	0.0217364	+	0.137238i
$627$	−8.23765	−	1.30472i	−0.328980	−	0.0521053i
$628$	3.07801	−	6.04093i	0.122826	−	0.241059i
$629$	2.76237	−	2.76237i	0.110143	−	0.110143i
$630$	−0.274831	+	1.73522i	−0.0109495	+	0.0691327i
$631$	−11.7225	+	36.0782i	−0.466666	+	1.43625i	0.390208	+	0.920727i	$0.372403\pi$
$631$	−11.7225	+	36.0782i	−0.466666	+	1.43625i	−0.856875	+	0.515525i	$0.827597\pi$
$632$	−12.0255	+	1.90465i	−0.478348	+	0.0757629i
$633$	0.581383	+	1.78931i	0.0231079	+	0.0711188i
$634$	3.80894	+	7.47546i	0.151272	+	0.296889i
$635$	−18.1383	−	5.89349i	−0.719796	−	0.233876i
$636$	−2.82804	−	0.918886i	−0.112139	−	0.0364362i
$637$	−14.1979	−	27.8649i	−0.562541	−	1.10405i
$638$	−0.0585928	−	0.180330i	−0.00231971	−	0.00713934i
$639$	−9.28926	+	1.47127i	−0.367477	+	0.0582027i
$640$	9.29127	−	28.5956i	0.367270	−	1.13034i
$641$	4.45397	−	28.1213i	0.175921	−	1.11072i	−0.728802	−	0.684725i	$-0.759923\pi$
$641$	4.45397	−	28.1213i	0.175921	−	1.11072i	0.904723	−	0.426000i	$-0.140077\pi$
$642$	−2.03569	+	2.03569i	−0.0803423	+	0.0803423i
$643$	14.8198	−	29.0856i	0.584437	−	1.14702i	−0.389674	−	0.920953i	$-0.627412\pi$
$643$	14.8198	−	29.0856i	0.584437	−	1.14702i	0.974111	−	0.226070i	$-0.0725878\pi$
$644$	14.8545	+	2.35272i	0.585348	+	0.0927100i
$645$	−5.46762	−	34.5212i	−0.215287	−	1.35927i
$646$	2.63417	+	1.91384i	0.103640	+	0.0752990i
$647$			35.7053i			1.40372i	0.712315	+	0.701860i	$0.247647\pi$
$647$			35.7053i			1.40372i	−0.712315	+	0.701860i	$0.752353\pi$
$648$	−3.01406	+	4.14850i	−0.118404	+	0.162969i
$649$	−21.9440	+	11.1810i	−0.861376	+	0.438893i
$650$	−12.2503	−	6.24185i	−0.480497	−	0.244826i
$651$	−4.39213	−	6.04525i	−0.172141	−	0.236932i
$652$	6.26597	−	4.55250i	0.245394	−	0.178290i
$653$	13.7761	+	13.7761i	0.539102	+	0.539102i	0.923265	−	0.384163i	$-0.125510\pi$
$653$	13.7761	+	13.7761i	0.539102	+	0.539102i	−0.384163	+	0.923265i	$0.625510\pi$
$654$	0.510631	−	0.165914i	0.0199672	−	0.00648775i
$655$	28.2111			1.10230
$656$	−1.67009	+	22.0109i	−0.0652061	+	0.859382i
$657$	−10.2349			−0.399303
$658$	−0.669603	+	0.217567i	−0.0261038	+	0.00848165i
$659$	10.7415	+	10.7415i	0.418431	+	0.418431i	0.884663	−	0.466231i	$-0.154389\pi$
$659$	10.7415	+	10.7415i	0.418431	+	0.418431i	−0.466231	+	0.884663i	$0.654389\pi$
$660$	−13.3276	+	9.68308i	−0.518777	+	0.376913i
$661$	−6.05918	−	8.33975i	−0.235675	−	0.324379i	0.674755	−	0.738042i	$-0.264249\pi$
$661$	−6.05918	−	8.33975i	−0.235675	−	0.324379i	−0.910430	+	0.413663i	$0.864249\pi$
$662$	−4.09048	−	2.08420i	−0.158981	−	0.0810048i
$663$	−24.8000	+	12.6362i	−0.963153	+	0.490751i
$664$	4.99670	−	6.87737i	0.193910	−	0.266894i
$665$		−	16.8859i		−	0.654806i
$666$	−0.345682	−	0.251153i	−0.0133949	−	0.00973197i
$667$	0.287502	+	1.81522i	0.0111321	+	0.0702854i
$668$	−11.7865	−	1.86679i	−0.456032	−	0.0722284i
$669$	1.09068	−	2.14057i	0.0421680	−	0.0827593i
$670$	−5.00062	+	5.00062i	−0.193191	+	0.193191i
$671$	1.32165	−	8.34459i	0.0510219	−	0.322139i
$672$	2.11520	−	6.50990i	0.0815955	−	0.251125i
$673$	−22.8825	+	3.62423i	−0.882055	+	0.139704i	−0.581001	−	0.813903i	$-0.697339\pi$
$673$	−22.8825	+	3.62423i	−0.882055	+	0.139704i	−0.301054	+	0.953607i	$0.597339\pi$
$674$	1.07789	+	3.31739i	0.0415186	+	0.127781i
$675$	17.9764	+	35.2808i	0.691914	+	1.35796i
$676$	50.9253	+	16.5466i	1.95866	+	0.636408i
$677$	10.7253	+	3.48486i	0.412206	+	0.133934i	0.507777	−	0.861489i	$-0.330468\pi$
$677$	10.7253	+	3.48486i	0.412206	+	0.133934i	−0.0955705	+	0.995423i	$0.530468\pi$
$678$	−1.34037	−	2.63062i	−0.0514764	−	0.101028i
$679$	−1.47963	−	4.55384i	−0.0567830	−	0.174760i
$680$	13.0159	−	2.06152i	0.499139	−	0.0790558i
$681$	−0.00973365	+	0.0299571i	−0.000372994	+	0.00114796i
$682$	0.328701	−	2.07533i	0.0125866	−	0.0794687i
$683$	−6.92268	+	6.92268i	−0.264889	+	0.264889i	−0.827037	−	0.562148i	$-0.809975\pi$
$683$	−6.92268	+	6.92268i	−0.264889	+	0.264889i	0.562148	+	0.827037i	$0.309975\pi$
$684$	−3.29459	+	6.46599i	−0.125972	+	0.247233i
$685$	−0.366905	−	0.0581120i	−0.0140187	−	0.00222035i
$686$	0.827801	+	5.22653i	0.0316056	+	0.199550i
$687$	−26.6745	−	19.3802i	−1.01770	−	0.739401i
$688$		−	25.4764i		−	0.971278i
$689$	−4.30649	+	5.92737i	−0.164064	+	0.225815i
$690$	−6.98197	+	3.55749i	−0.265799	+	0.135431i
$691$	−32.0987	−	16.3551i	−1.22109	−	0.622178i	−0.279895	−	0.960031i	$-0.590300\pi$
$691$	−32.0987	−	16.3551i	−1.22109	−	0.622178i	−0.941199	+	0.337852i	$0.890300\pi$
$692$	5.71091	+	7.86039i	0.217096	+	0.298807i
$693$	2.44954	−	1.77970i	0.0930505	−	0.0676051i
$694$	−7.21966	−	7.21966i	−0.274055	−	0.274055i
$695$	−42.8035	+	13.9077i	−1.62363	+	0.527550i
$696$	0.553216			0.0209696
$697$	−18.8026	+	7.85023i	−0.712198	+	0.297349i
$698$	−1.56981			−0.0594180
$699$	24.6750	−	8.01739i	0.933294	−	0.303246i
$700$	−13.7677	−	13.7677i	−0.520369	−	0.520369i
$701$	41.7632	−	30.3427i	1.57737	−	1.14603i	0.657744	−	0.753242i	$-0.271511\pi$
$701$	41.7632	−	30.3427i	1.57737	−	1.14603i	0.919630	−	0.392787i	$-0.128489\pi$
$702$	6.50716	+	8.95634i	0.245597	+	0.338035i
$703$	3.65923	+	1.86447i	0.138011	+	0.0703199i
$704$	−9.50919	+	4.84517i	−0.358391	+	0.182609i
$705$	−4.39374	+	6.04746i	−0.165478	+	0.227760i
$706$		−	7.83868i		−	0.295013i
$707$	7.70515	+	5.59812i	0.289782	+	0.210539i
$708$	−5.48583	−	34.6361i	−0.206170	−	1.30171i
$709$	48.3157	+	7.65246i	1.81453	+	0.287394i	0.969097	−	0.246680i	$-0.0793395\pi$
$709$	48.3157	+	7.65246i	1.81453	+	0.287394i	0.845438	+	0.534074i	$0.179340\pi$
$710$	−3.97800	+	7.80726i	−0.149292	+	0.293001i
$711$	8.19874	−	8.19874i	0.307477	−	0.307477i
$712$	2.71167	−	17.1208i	0.101624	−	0.641630i
$713$	−6.29357	+	19.3696i	−0.235696	+	0.725398i
$714$	1.91054	−	0.302600i	0.0715001	−	0.0113245i
$715$	12.5430	+	38.6035i	0.469082	+	1.44369i
$716$	7.79086	+	15.2904i	0.291158	+	0.571430i
$717$	23.2234	+	7.54573i	0.867293	+	0.281801i
$718$	−0.397264	−	0.129079i	−0.0148258	−	0.00481718i
$719$	9.42790	+	18.5033i	0.351601	+	0.690056i	0.997292	−	0.0735426i	$-0.0234305\pi$
$719$	9.42790	+	18.5033i	0.351601	+	0.690056i	−0.645691	+	0.763599i	$0.723430\pi$
$720$	4.20139	+	12.9305i	0.156576	+	0.481893i
$721$	23.7384	−	3.75979i	0.884063	−	0.140022i
$722$	0.738126	−	2.27172i	0.0274702	−	0.0845446i
$723$	1.22975	−	7.76435i	0.0457350	−	0.288759i
$724$	16.0249	−	16.0249i	0.595561	−	0.595561i
$725$	1.08017	−	2.11996i	0.0401166	−	0.0787333i
$726$	3.15862	+	0.500277i	0.117227	+	0.0185670i
$727$	−2.24680	−	14.1858i	−0.0833293	−	0.526121i	−0.993677	−	0.112276i	$-0.964186\pi$
$727$	−2.24680	−	14.1858i	−0.0833293	−	0.526121i	0.910348	−	0.413844i	$-0.135814\pi$
$728$	−9.02416	−	6.55643i	−0.334457	−	0.242998i
$729$		−	27.9989i		−	1.03700i
$730$	−5.60480	+	7.71435i	−0.207443	+	0.285521i
$731$	20.9529	−	10.6760i	0.774970	−	0.394867i
$732$	10.7187	+	5.46144i	0.396174	+	0.201861i
$733$	14.2196	+	19.5717i	0.525214	+	0.722895i	0.986392	−	0.164413i	$-0.0525728\pi$
$733$	14.2196	+	19.5717i	0.525214	+	0.722895i	−0.461177	+	0.887308i	$0.652573\pi$
$734$	2.18158	−	1.58501i	0.0805235	−	0.0585038i
$735$	16.3166	+	16.3166i	0.601848	+	0.601848i
$736$	−17.7432	+	5.76512i	−0.654024	+	0.212505i
$737$	12.1880			0.448951
$738$	1.16977	+	1.89691i	0.0430600	+	0.0698264i
$739$	0.683852			0.0251559			0.0125780	−	0.999921i	$-0.495996\pi$
$739$	0.683852			0.0251559			0.0125780	+	0.999921i	$0.495996\pi$
$740$	7.71484	−	2.50670i	0.283603	−	0.0921482i
$741$	−20.6904	−	20.6904i	−0.760081	−	0.760081i
$742$	0.411933	−	0.299287i	0.0151225	−	0.0109872i
$743$	−17.7873	−	24.4821i	−0.652553	−	0.898162i	0.346654	−	0.937993i	$-0.387318\pi$
$743$	−17.7873	−	24.4821i	−0.652553	−	0.898162i	−0.999206	+	0.0398315i	$0.987318\pi$
$744$	5.46238	+	2.78322i	0.200261	+	0.102038i
$745$	−0.544888	+	0.277634i	−0.0199631	+	0.0101717i
$746$	−2.91699	+	4.01489i	−0.106799	+	0.146996i
$747$			8.09550i			0.296199i
$748$	−8.96705	−	6.51494i	−0.327868	−	0.238210i
$749$	1.57142	+	9.92158i	0.0574186	+	0.362527i
$750$	2.87558	+	0.455447i	0.105001	+	0.0166306i
$751$	8.69372	−	17.0624i	0.317238	−	0.622615i	−0.676234	−	0.736687i	$-0.736389\pi$
$751$	8.69372	−	17.0624i	0.317238	−	0.622615i	0.993473	+	0.114072i	$0.0363893\pi$
$752$	−3.85277	+	3.85277i	−0.140496	+	0.140496i
$753$	−5.29938	+	33.4590i	−0.193120	+	1.21931i
$754$	0.205563	−	0.632658i	0.00748616	−	0.0230400i
$755$	67.5904	−	10.7053i	2.45986	−	0.389604i
$756$	4.84467	+	14.9104i	0.176199	+	0.542284i
$757$	16.5655	+	32.5117i	0.602085	+	1.18166i	0.967986	+	0.251005i	$0.0807609\pi$
$757$	16.5655	+	32.5117i	0.602085	+	1.18166i	−0.365901	+	0.930654i	$0.619239\pi$
$758$	−3.30848	−	1.07499i	−0.120169	−	0.0390454i
$759$	12.8439	+	4.17324i	0.466204	+	0.151479i
$760$	6.28949	+	12.3438i	0.228144	+	0.447757i
$761$	−5.94946	−	18.3106i	−0.215668	−	0.663758i	−0.999106	−	0.0422871i	$-0.986536\pi$
$761$	−5.94946	−	18.3106i	−0.215668	−	0.663758i	0.783438	−	0.621470i	$-0.213464\pi$
$762$	2.26848	−	0.359292i	0.0821783	−	0.0130158i
$763$	0.578918	−	1.78173i	0.0209582	−	0.0645028i
$764$	−5.25735	+	33.1936i	−0.190204	+	1.20090i
$765$	−8.87401	+	8.87401i	−0.320841	+	0.320841i
$766$	0.630481	−	1.23739i	0.0227802	−	0.0447087i
$767$	−85.3404	−	13.5166i	−3.08146	−	0.488056i
$768$	−1.92745	−	12.1694i	−0.0695509	−	0.439127i
$769$	−14.1385	−	10.2722i	−0.509848	−	0.370427i	0.302918	−	0.953017i	$-0.402039\pi$
$769$	−14.1385	−	10.2722i	−0.509848	−	0.370427i	−0.812766	+	0.582590i	$0.802039\pi$
$770$		−	2.82088i		−	0.101657i
$771$	−9.08616	+	12.5060i	−0.327230	+	0.450394i
$772$	−23.2654	+	11.8543i	−0.837339	+	0.426646i
$773$	−37.4355	−	19.0743i	−1.34646	−	0.686056i	−0.375843	−	0.926683i	$-0.622647\pi$
$773$	−37.4355	−	19.0743i	−1.34646	−	0.686056i	−0.970618	+	0.240627i	$0.922647\pi$
$774$	−1.51183	−	2.08086i	−0.0543417	−	0.0747950i
$775$	21.3310	−	15.4979i	0.766231	−	0.556700i
$776$	2.77780	+	2.77780i	0.0997172	+	0.0997172i
$777$	2.32041	−	0.753947i	0.0832442	−	0.0270477i
$778$	−7.78512			−0.279110
$779$	−13.9570	−	16.2488i	−0.500060	−	0.582175i
$780$	−57.7957			−2.06942
$781$	14.3621	−	4.66653i	0.513916	−	0.166982i
$782$	−3.72803	−	3.72803i	−0.133314	−	0.133314i
$783$	−1.54992	+	1.12609i	−0.0553898	+	0.0402430i
$784$	9.88637	+	13.6074i	0.353085	+	0.485979i
$785$	10.9824	+	5.59582i	0.391979	+	0.199723i
$786$	−3.02709	+	1.54238i	−0.107973	+	0.0550148i
$787$	12.6296	−	17.3831i	0.450195	−	0.619640i	−0.522244	−	0.852796i	$-0.674905\pi$
$787$	12.6296	−	17.3831i	0.450195	−	0.619640i	0.972439	+	0.233156i	$0.0749051\pi$
$788$			8.15527i			0.290519i
$789$	−6.14837	−	4.46705i	−0.218888	−	0.159031i
$790$	−1.68986	−	10.6694i	−0.0601226	−	0.379599i
$791$	−10.1749	−	1.61155i	−0.361778	−	0.0573000i
$792$	−1.12777	+	2.21337i	−0.0400734	+	0.0786485i
$793$	20.9590	−	20.9590i	0.744276	−	0.744276i
$794$	1.10149	−	6.95455i	0.0390905	−	0.246808i
$795$	1.67054	−	5.14138i	0.0592478	−	0.182346i
$796$	−7.14001	+	1.13087i	−0.253071	+	0.0400825i
$797$	7.95385	+	24.4794i	0.281740	+	0.867106i	0.987357	+	0.158513i	$0.0506699\pi$
$797$	7.95385	+	24.4794i	0.281740	+	0.867106i	−0.705617	+	0.708593i	$0.749330\pi$
$798$	0.923199	+	1.81188i	0.0326809	+	0.0641399i
$799$	−4.78320	−	1.55416i	−0.169217	−	0.0549821i
$800$	22.9705	+	7.46358i	0.812131	+	0.263877i
$801$	7.49429	+	14.7084i	0.264798	+	0.519695i
$802$	2.06284	+	6.34877i	0.0728414	+	0.224183i
$803$	16.2314	−	2.57080i	0.572793	−	0.0907215i
$804$	−5.36279	+	16.5050i	−0.189131	+	0.582085i
$805$	−4.27724	+	27.0054i	−0.150753	+	0.951816i
$806$	5.21259	−	5.21259i	0.183606	−	0.183606i
$807$	−4.41059	+	8.65628i	−0.155260	+	0.304715i
$808$	−7.71770	−	1.22236i	−0.271508	−	0.0430026i
$809$	−2.48312	−	15.6778i	−0.0873018	−	0.551202i	−0.992109	−	0.125380i	$-0.959985\pi$
$809$	−2.48312	−	15.6778i	−0.0873018	−	0.551202i	0.904807	−	0.425822i	$-0.140015\pi$
$810$	−3.68068	−	2.67417i	−0.129326	−	0.0939606i
$811$		−	46.8407i		−	1.64480i	−0.568910	−	0.822400i	$-0.692635\pi$
$811$		−	46.8407i		−	1.64480i	0.568910	−	0.822400i	$-0.307365\pi$
$812$	0.553720	−	0.762130i	0.0194318	−	0.0267455i
$813$	18.0819	−	9.21320i	0.634161	−	0.323121i
$814$	0.611295	+	0.311470i	0.0214259	+	0.0109170i
$815$	8.27644	+	11.3915i	0.289911	+	0.399028i
$816$	12.1107	−	8.79896i	0.423960	−	0.308025i
$817$	17.4808	+	17.4808i	0.611574	+	0.611574i
$818$	−1.00527	+	0.326632i	−0.0351484	+	0.0114204i
$819$	10.6225			0.371181
$820$	−42.1878	−	3.20102i	−1.47326	−	0.111785i
$821$	−4.49527			−0.156886			−0.0784431	−	0.996919i	$-0.524995\pi$
$821$	−4.49527			−0.156886			−0.0784431	+	0.996919i	$0.524995\pi$
$822$	0.0425466	−	0.0138242i	0.00148398	−	0.000482175i
$823$	−10.4358	−	10.4358i	−0.363769	−	0.363769i	0.501429	−	0.865199i	$-0.332808\pi$
$823$	−10.4358	−	10.4358i	−0.363769	−	0.363769i	−0.865199	+	0.501429i	$0.832808\pi$
$824$	−15.9527	+	11.5903i	−0.555737	+	0.403767i
$825$	−10.2766	−	14.1445i	−0.357784	−	0.492447i
$826$	5.35033	+	2.72613i	0.186162	+	0.0948541i
$827$	32.6277	−	16.6247i	1.13458	−	0.578096i	0.217205	−	0.976126i	$-0.430306\pi$
$827$	32.6277	−	16.6247i	1.13458	−	0.578096i	0.917372	+	0.398030i	$0.130306\pi$
$828$	6.90685	−	9.50646i	0.240029	−	0.330372i
$829$		−	24.1722i		−	0.839534i	−0.907632	−	0.419767i	$-0.862112\pi$
$829$		−	24.1722i		−	0.839534i	0.907632	−	0.419767i	$-0.137888\pi$
$830$	6.10180	+	4.43322i	0.211797	+	0.153879i
$831$	−1.82955	−	11.5513i	−0.0634663	−	0.400711i
$832$	−36.9814	−	5.85727i	−1.28210	−	0.203064i
$833$	−7.04838	+	13.8332i	−0.244212	+	0.479293i
$834$	3.83251	−	3.83251i	0.132709	−	0.132709i
$835$	3.39383	−	21.4278i	0.117448	−	0.741539i
$836$	3.60070	−	11.0818i	0.124533	−	0.383273i
$837$	−20.9691	+	3.32117i	−0.724797	+	0.114797i
$838$	1.77258	+	5.45544i	0.0612328	+	0.188455i
$839$	−13.7897	−	27.0638i	−0.476074	−	0.934347i	−0.996747	−	0.0805911i	$-0.974319\pi$
$839$	−13.7897	−	27.0638i	−0.476074	−	0.934347i	0.520674	−	0.853756i	$-0.325681\pi$
$840$	7.82751	+	2.54331i	0.270075	+	0.0877527i
$841$	−27.4712	−	8.92592i	−0.947281	−	0.307790i
$842$	−0.866418	−	1.70044i	−0.0298588	−	0.0586011i
$843$	5.17610	+	15.9304i	0.178274	+	0.548672i
$844$	−2.59610	+	0.411181i	−0.0893613	+	0.0141534i
$845$	−30.0817	+	92.5821i	−1.03484	+	3.18492i
$846$	−0.0860533	+	0.543319i	−0.00295857	+	0.0186797i
$847$	7.89036	−	7.89036i	0.271116	−	0.271116i
$848$	1.78893	−	3.51097i	0.0614320	−	0.120567i
$849$	28.4710	+	4.50936i	0.977121	+	0.154761i
$850$	1.06774	+	6.74143i	0.0366231	+	0.231229i
$851$	−5.37990	−	3.90872i	−0.184420	−	0.133989i
$852$			21.5024i			0.736660i
$853$	−0.247241	+	0.340298i	−0.00846537	+	0.0116516i	−0.813229	−	0.581944i	$-0.802292\pi$
$853$	−0.247241	+	0.340298i	−0.00846537	+	0.0116516i	0.804763	+	0.593596i	$0.202292\pi$
$854$	−1.83540	+	0.935184i	−0.0628062	+	0.0320013i
$855$	−11.7552	−	5.98955i	−0.402018	−	0.204838i
$856$	−4.84423	−	6.66751i	−0.165572	−	0.227891i
$857$	−43.6766	+	31.7329i	−1.49196	+	1.08397i	−0.518514	+	0.855069i	$0.673515\pi$
$857$	−43.6766	+	31.7329i	−1.49196	+	1.08397i	−0.973449	+	0.228906i	$0.926485\pi$
$858$	−3.45645	−	3.45645i	−0.118001	−	0.118001i
$859$	−39.5195	+	12.8407i	−1.34839	+	0.438117i	−0.892149	−	0.451741i	$-0.850803\pi$
$859$	−39.5195	+	12.8407i	−1.34839	+	0.438117i	−0.456237	+	0.889858i	$0.650803\pi$
$860$	48.8300			1.66509
$861$	−12.6889	−	0.962779i	−0.432437	−	0.0328114i
$862$	1.94787			0.0663449
$863$	5.06646	−	1.64619i	0.172464	−	0.0560371i	−0.221512	−	0.975158i	$-0.571099\pi$
$863$	5.06646	−	1.64619i	0.172464	−	0.0560371i	0.393976	+	0.919121i	$0.371099\pi$
$864$	−13.7517	−	13.7517i	−0.467842	−	0.467842i
$865$	−14.2902	+	10.3824i	−0.485881	+	0.353013i
$866$	−0.363731	−	0.500633i	−0.0123601	−	0.0170122i
$867$	−8.35792	−	4.25857i	−0.283850	−	0.144629i
$868$	9.30162	−	4.73941i	0.315718	−	0.160866i
$869$	−10.9429	+	15.0616i	−0.371211	+	0.510929i
$870$			0.490830i			0.0166407i
$871$	34.5932	+	25.1334i	1.17215	+	0.851614i
$872$	0.240443	+	1.51810i	0.00814242	+	0.0514092i
$873$	−3.69501	−	0.585231i	−0.125057	−	0.0198071i
$874$	2.51625	−	4.93841i	0.0851134	−	0.167044i
$875$	7.18330	−	7.18330i	0.242840	−	0.242840i
$876$	−3.66052	+	23.1116i	−0.123678	+	0.780870i
$877$	9.32212	−	28.6905i	0.314786	−	0.968811i	−0.661057	−	0.750336i	$-0.729892\pi$
$877$	9.32212	−	28.6905i	0.314786	−	0.968811i	0.975843	−	0.218475i	$-0.0701082\pi$
$878$	6.65309	−	1.05375i	0.224531	−	0.0355622i
$879$	−11.2055	−	34.4870i	−0.377952	−	1.16322i
$880$	−9.91078	−	19.4510i	−0.334092	−	0.655693i
$881$	−11.5811	−	3.76294i	−0.390179	−	0.126777i	0.107356	−	0.994221i	$-0.465761\pi$
$881$	−11.5811	−	3.76294i	−0.390179	−	0.126777i	−0.497535	+	0.867444i	$0.665761\pi$
$882$	1.61500	+	0.524745i	0.0543798	+	0.0176691i
$883$	5.32064	+	10.4423i	0.179054	+	0.351413i	0.963037	−	0.269369i	$-0.0868152\pi$
$883$	5.32064	+	10.4423i	0.179054	+	0.351413i	−0.783983	+	0.620782i	$0.786815\pi$
$884$	−12.0164	−	36.9827i	−0.404156	−	1.24386i
$885$	62.9685	−	9.97323i	2.11666	−	0.335246i
$886$	−1.50379	+	4.62818i	−0.0505208	+	0.155487i
$887$	5.47072	−	34.5408i	0.183689	−	1.15976i	−0.707696	−	0.706517i	$-0.750265\pi$
$887$	5.47072	−	34.5408i	0.183689	−	1.15976i	0.891385	−	0.453248i	$-0.149735\pi$
$888$	−1.41543	+	1.41543i	−0.0474987	+	0.0474987i
$889$	3.63827	−	7.14052i	0.122024	−	0.239485i
$890$	15.1901	+	2.40588i	0.509173	+	0.0806451i
$891$	1.22658	+	7.74432i	0.0410920	+	0.259445i
$892$	2.71536	+	1.97283i	0.0909170	+	0.0660551i
$893$		−	5.28719i		−	0.176929i
$894$	0.0432882	−	0.0595811i	0.00144777	−	0.00199269i
$895$	−27.7980	+	14.1638i	−0.929184	+	0.473443i
$896$	11.2573	+	5.73586i	0.376078	+	0.191622i
$897$	27.8490	+	38.3309i	0.929852	+	1.27983i
$898$	5.57276	−	4.04885i	0.185966	−	0.135112i
$899$	0.902057	+	0.902057i	0.0300853	+	0.0300853i
$900$	−14.4679	+	4.70091i	−0.482264	+	0.156697i
$901$	3.63723			0.121174
$902$	−2.33159	−	2.71446i	−0.0776333	−	0.0903815i
$903$	14.6867			0.488743
$904$	8.03825	−	2.61179i	0.267348	−	0.0868668i
$905$	29.1333	+	29.1333i	0.968422	+	0.968422i
$906$	−6.66726	+	4.84405i	−0.221505	+	0.160933i
$907$	−5.59498	−	7.70083i	−0.185778	−	0.255702i	0.705962	−	0.708250i	$-0.250515\pi$
$907$	−5.59498	−	7.70083i	−0.185778	−	0.255702i	−0.891740	+	0.452548i	$0.850515\pi$
$908$	−0.0392099	−	0.0199784i	−0.00130122	−	0.000663007i
$909$	6.63022	−	3.37827i	0.219911	−	0.112050i
$910$	5.81706	−	8.00650i	0.192834	−	0.265413i
$911$			36.1439i			1.19750i	0.800936	+	0.598750i	$0.204336\pi$
$911$			36.1439i			1.19750i	−0.800936	+	0.598750i	$0.795664\pi$
$912$	12.7316	+	9.25005i	0.421585	+	0.306300i
$913$	−2.03342	−	12.8385i	−0.0672963	−	0.424892i
$914$	1.11122	+	0.175999i	0.0367558	+	0.00582154i
$915$	−9.92890	+	19.4866i	−0.328239	+	0.644206i
$916$	32.5721	−	32.5721i	1.07621	−	1.07621i
$917$	−1.85443	+	11.7084i	−0.0612387	+	0.386646i
$918$	1.69833	−	5.22691i	0.0560531	−	0.172514i
$919$	55.4813	−	8.78737i	1.83016	−	0.289869i	0.856208	−	0.516631i	$-0.172814\pi$
$919$	55.4813	−	8.78737i	1.83016	−	0.289869i	0.973950	+	0.226763i	$0.0728143\pi$
$920$	−6.93199	−	21.3345i	−0.228541	−	0.703377i
$921$	4.33295	+	8.50389i	0.142775	+	0.280213i
$922$	−1.12018	−	0.363969i	−0.0368912	−	0.0119867i
$923$	50.3870	+	16.3717i	1.65851	+	0.538882i
$924$	−3.14268	−	6.16786i	−0.103387	−	0.202908i
$925$	2.66034	+	8.18769i	0.0874714	+	0.269209i
$926$	−9.59470	+	1.51965i	−0.315302	+	0.0499389i
$927$	5.80279	−	17.8592i	0.190589	−	0.586572i
$928$	−0.182807	+	1.15420i	−0.00600094	+	0.0378884i
$929$	37.3268	−	37.3268i	1.22465	−	1.22465i	0.258694	−	0.965959i	$-0.416708\pi$
$929$	37.3268	−	37.3268i	1.22465	−	1.22465i	0.965959	−	0.258694i	$-0.0832921\pi$
$930$	−2.46936	+	4.84639i	−0.0809735	+	0.158919i
$931$	−16.1204	−	2.55322i	−0.528324	−	0.0836784i
$932$	5.67028	+	35.8007i	0.185736	+	1.17269i
$933$	−3.63480	−	2.64083i	−0.118998	−	0.0864570i
$934$		−	9.58648i		−	0.313679i
$935$	11.8442	−	16.3021i	0.387345	−	0.533135i
$936$	−7.76522	+	3.95658i	−0.253814	+	0.129325i
$937$	8.13713	+	4.14608i	0.265829	+	0.135446i	0.581825	−	0.813314i	$-0.302339\pi$
$937$	8.13713	+	4.14608i	0.265829	+	0.135446i	−0.315997	+	0.948760i	$0.602339\pi$
$938$	−1.74669	−	2.40412i	−0.0570315	−	0.0784972i
$939$	−12.5477	+	9.11642i	−0.409478	+	0.297503i
$940$	−7.38450	−	7.38450i	−0.240856	−	0.240856i
$941$	−33.6652	+	10.9385i	−1.09745	+	0.356584i	−0.801122	−	0.598501i	$-0.795763\pi$
$941$	−33.6652	+	10.9385i	−1.09745	+	0.356584i	−0.296331	+	0.955085i	$0.595763\pi$
$942$	−1.48437			−0.0483633
$943$	18.2053	+	29.5219i	0.592847	+	0.961366i
$944$	46.4703			1.51248
$945$	−27.1070	+	8.80760i	−0.881791	+	0.286511i
$946$	2.92026	+	2.92026i	0.0949457	+	0.0949457i
$947$	−21.7998	+	15.8385i	−0.708399	+	0.514682i	−0.882657	−	0.470018i	$-0.844247\pi$
$947$	−21.7998	+	15.8385i	−0.708399	+	0.514682i	0.174258	+	0.984700i	$0.444247\pi$
$948$	−15.5814	−	21.4460i	−0.506060	−	0.696532i
$949$	51.3709	+	26.1748i	1.66757	+	0.849669i
$950$	−6.39331	+	3.25756i	−0.207427	+	0.105689i
$951$	−22.0008	+	30.2815i	−0.713425	+	0.981946i
$952$			5.53751i			0.179472i
$953$	−37.0784	−	26.9390i	−1.20109	−	0.872640i	−0.206695	−	0.978405i	$-0.566271\pi$
$953$	−37.0784	−	26.9390i	−1.20109	−	0.872640i	−0.994391	+	0.105765i	$0.966271\pi$
$954$	−0.0622337	−	0.392928i	−0.00201489	−	0.0127215i
$955$	−60.3459	−	9.55786i	−1.95275	−	0.309285i
$956$	−15.4877	+	30.3963i	−0.500908	+	0.983087i
$957$	0.598150	−	0.598150i	0.0193354	−	0.0193354i
$958$	−1.98096	+	12.5073i	−0.0640018	+	0.404092i
$959$	0.0482364	−	0.148456i	0.00155763	−	0.00479390i
$960$	27.2867	−	4.32179i	0.880676	−	0.139485i
$961$	−5.21097	−	16.0377i	−0.168096	−	0.517346i
$962$	1.09274	+	2.14462i	0.0352314	+	0.0691455i
$963$	7.46434	+	2.42531i	0.240535	+	0.0781545i
$964$	10.4451	+	3.39382i	0.336414	+	0.109307i
$965$	−21.5511	−	42.2965i	−0.693755	−	1.36157i
$966$	−1.01751	−	3.13157i	−0.0327378	−	0.100757i
$967$	12.8592	−	2.03670i	0.413524	−	0.0654957i	0.0537936	−	0.998552i	$-0.482869\pi$
$967$	12.8592	−	2.03670i	0.413524	−	0.0654957i	0.359730	+	0.933056i	$0.382869\pi$
$968$	−2.82904	+	8.70689i	−0.0909287	+	0.279850i
$969$	−2.27239	+	14.3473i	−0.0729996	+	0.460901i
$970$	−2.46455	+	2.46455i	−0.0791318	+	0.0791318i
$971$	14.6907	−	28.8321i	0.471447	−	0.925268i	−0.525763	−	0.850631i	$-0.676220\pi$
$971$	14.6907	−	28.8321i	0.471447	−	0.925268i	0.997211	−	0.0746367i	$-0.0237797\pi$
$972$	20.8697	+	3.30544i	0.669396	+	0.106022i
$973$	−2.95845	−	18.6789i	−0.0948437	−	0.598819i
$974$	8.07912	+	5.86982i	0.258872	+	0.188081i
$975$		−	61.3380i		−	1.96439i
$976$	−9.37013	+	12.8969i	−0.299931	+	0.412819i
$977$	−33.8782	+	17.2618i	−1.08386	+	0.552254i	−0.902292	−	0.431125i	$-0.858117\pi$
$977$	−33.8782	+	17.2618i	−1.08386	+	0.552254i	−0.181567	+	0.983379i	$0.558117\pi$
$978$	−1.51088	−	0.769833i	−0.0483127	−	0.0246165i
$979$	−15.5795	−	21.4433i	−0.497922	−	0.685331i
$980$	−26.0810	+	18.9490i	−0.833127	+	0.605302i
$981$	−1.03501	−	1.03501i	−0.0330453	−	0.0330453i
$982$	−11.7418	+	3.81513i	−0.374694	+	0.121746i
$983$	−2.64592			−0.0843918			−0.0421959	−	0.999109i	$-0.513435\pi$
$983$	−2.64592			−0.0843918			−0.0421959	+	0.999109i	$0.513435\pi$
$984$	9.63438	−	4.02244i	0.307133	−	0.128231i
$985$	−14.8263			−0.472404
$986$	−0.314076	+	0.102049i	−0.0100022	+	0.00324992i
$987$	−2.22105	−	2.22105i	−0.0706969	−	0.0706969i
$988$	33.0722	−	24.0283i	1.05217	−	0.764443i
$989$	−23.5289	−	32.3847i	−0.748175	−	1.02977i
$990$	−1.96376	−	1.00059i	−0.0624125	−	0.0318008i
$991$	8.06220	−	4.10790i	0.256104	−	0.130492i	−0.321225	−	0.947003i	$-0.604095\pi$
$991$	8.06220	−	4.10790i	0.256104	−	0.130492i	0.577330	+	0.816511i	$0.304095\pi$
$992$	−7.61177	+	10.4767i	−0.241674	+	0.332636i
$993$		−	20.4812i		−	0.649952i
$994$	−2.97875	−	2.16419i	−0.0944803	−	0.0686439i
$995$	−2.05591	−	12.9805i	−0.0651768	−	0.411510i
$996$	18.2806	+	2.89536i	0.579242	+	0.0917429i
$997$	−17.3045	+	33.9621i	−0.548040	+	1.07559i	0.436381	+	0.899762i	$0.356260\pi$
$997$	−17.3045	+	33.9621i	−0.548040	+	1.07559i	−0.984421	+	0.175828i	$0.943740\pi$
$998$	−2.39491	+	2.39491i	−0.0758097	+	0.0758097i
$999$	1.08441	−	6.84669i	0.0343092	−	0.216620i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	41.2.g.a.39.2	yes	24
3.2	odd	2		369.2.u.a.244.2		24
4.3	odd	2		656.2.bs.d.449.1		24
41.15	odd	40		1681.2.a.m.1.12		24
41.20	even	20	inner	41.2.g.a.20.2	✓	24
41.26	odd	40		1681.2.a.m.1.11		24
123.20	odd	20		369.2.u.a.307.2		24
164.143	odd	20		656.2.bs.d.225.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
41.2.g.a.20.2	✓	24	41.20	even	20	inner
41.2.g.a.39.2	yes	24	1.1	even	1	trivial
369.2.u.a.244.2		24	3.2	odd	2
369.2.u.a.307.2		24	123.20	odd	20
656.2.bs.d.225.1		24	164.143	odd	20
656.2.bs.d.449.1		24	4.3	odd	2
1681.2.a.m.1.11		24	41.26	odd	40
1681.2.a.m.1.12		24	41.15	odd	40

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:	\( N \)	\(=\)	\( 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	41.g (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.290902 - 0.0945196i) q^{2} +(0.964912 + 0.964912i) q^{3} +(-1.54234 + 1.12058i) q^{4} +(-2.03721 - 2.80398i) q^{5} +(0.371897 + 0.189491i) q^{6} +(1.29765 - 0.661185i) q^{7} +(-0.702328 + 0.966671i) q^{8} -1.13789i q^{9} +O(q^{10})\)	\(q+(0.290902 - 0.0945196i) q^{2} +(0.964912 + 0.964912i) q^{3} +(-1.54234 + 1.12058i) q^{4} +(-2.03721 - 2.80398i) q^{5} +(0.371897 + 0.189491i) q^{6} +(1.29765 - 0.661185i) q^{7} +(-0.702328 + 0.966671i) q^{8} -1.13789i q^{9} +(-0.857659 - 0.623126i) q^{10} +(0.285814 + 1.80456i) q^{11} +(-2.56949 - 0.406967i) q^{12} +(-2.91004 + 5.71127i) q^{13} +(0.314993 - 0.314993i) q^{14} +(0.739865 - 4.67132i) q^{15} +(1.06531 - 3.27868i) q^{16} +(3.14295 - 0.497794i) q^{17} +(-0.107553 - 0.331014i) q^{18} +(1.51872 + 2.98065i) q^{19} +(6.28416 + 2.04185i) q^{20} +(1.89010 + 0.614131i) q^{21} +(0.253710 + 0.497934i) q^{22} +(-1.67386 - 5.15161i) q^{23} +(-1.61044 + 0.255068i) q^{24} +(-2.16699 + 6.66932i) q^{25} +(-0.306707 + 1.93647i) q^{26} +(3.99270 - 3.99270i) q^{27} +(-1.26051 + 2.47389i) q^{28} +(-0.335113 - 0.0530767i) q^{29} +(-0.226304 - 1.42883i) q^{30} +(-3.04183 - 2.21002i) q^{31} -3.44421i q^{32} +(-1.46545 + 2.01702i) q^{33} +(0.867237 - 0.441879i) q^{34} +(-4.49754 - 2.29161i) q^{35} +(1.27510 + 1.75502i) q^{36} +(0.993200 - 0.721602i) q^{37} +(0.723527 + 0.723527i) q^{38} +(-8.31880 + 2.70294i) q^{39} +4.14132 q^{40} +(-6.22198 + 1.51227i) q^{41} +0.607881 q^{42} +(7.02832 - 2.28364i) q^{43} +(-2.46297 - 2.46297i) q^{44} +(-3.19062 + 2.31812i) q^{45} +(-0.973857 - 1.34040i) q^{46} +(-1.40824 - 0.717533i) q^{47} +(4.19156 - 2.13571i) q^{48} +(-2.86777 + 3.94715i) q^{49} +2.14494i q^{50} +(3.51299 + 2.55234i) q^{51} +(-1.91165 - 12.0697i) q^{52} +(1.12895 + 0.178807i) q^{53} +(0.784094 - 1.53887i) q^{54} +(4.47768 - 4.47768i) q^{55} +(-0.272226 + 1.71877i) q^{56} +(-1.41064 + 4.34149i) q^{57} +(-0.102502 + 0.0162347i) q^{58} +(4.16549 + 12.8200i) q^{59} +(4.09346 + 8.03387i) q^{60} +(-4.39785 - 1.42895i) q^{61} +(-1.09376 - 0.355385i) q^{62} +(-0.752356 - 1.47658i) q^{63} +(1.80507 + 5.55543i) q^{64} +(21.9426 - 3.47537i) q^{65} +(-0.235654 + 0.725270i) q^{66} +(1.04355 - 6.58873i) q^{67} +(-4.28969 + 4.28969i) q^{68} +(3.35573 - 6.58598i) q^{69} +(-1.52494 - 0.241527i) q^{70} +(-1.29298 - 8.16358i) q^{71} +(1.09997 + 0.799172i) q^{72} -8.99466i q^{73} +(0.220718 - 0.303792i) q^{74} +(-8.52627 + 4.34435i) q^{75} +(-5.68244 - 2.89535i) q^{76} +(1.56403 + 2.15271i) q^{77} +(-2.16447 + 1.57258i) q^{78} +(7.20521 + 7.20521i) q^{79} +(-11.3636 + 3.69226i) q^{80} +4.29154 q^{81} +(-1.66705 + 1.02802i) q^{82} -7.11449 q^{83} +(-3.60337 + 1.17081i) q^{84} +(-7.79865 - 7.79865i) q^{85} +(1.82870 - 1.32863i) q^{86} +(-0.272140 - 0.374569i) q^{87} +(-1.94515 - 0.991103i) q^{88} +(-12.9260 + 6.58613i) q^{89} +(-0.709049 + 0.975922i) q^{90} +9.33529i q^{91} +(8.35446 + 6.06987i) q^{92} +(-0.802625 - 5.06757i) q^{93} +(-0.477479 - 0.0756253i) q^{94} +(5.26374 - 10.3307i) q^{95} +(3.32336 - 3.32336i) q^{96} +(0.514313 - 3.24724i) q^{97} +(-0.461156 + 1.41929i) q^{98} +(2.05339 - 0.325225i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8}+O(q^{10}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8	\( 24 q - 10 q^{2} - 6 q^{3} - 10 q^{5} - 2 q^{6} - 8 q^{7} - 10 q^{8} + 6 q^{10} - 16 q^{11} + 2 q^{12} + 14 q^{14} + 8 q^{15} - 20 q^{16} + 8 q^{17} + 16 q^{19} + 20 q^{20} - 10 q^{21} + 6 q^{22} + 12 q^{23} + 68 q^{24} - 8 q^{25} - 28 q^{26} - 6 q^{27} + 18 q^{28} + 40 q^{29} - 36 q^{30} - 12 q^{31} + 10 q^{33} - 16 q^{34} - 36 q^{35} - 40 q^{36} + 46 q^{38} - 50 q^{39} - 44 q^{40} - 4 q^{41} - 40 q^{42} - 48 q^{44} + 16 q^{45} + 70 q^{46} - 12 q^{47} - 50 q^{48} - 30 q^{49} - 24 q^{51} + 20 q^{52} - 26 q^{53} + 68 q^{54} + 20 q^{55} + 106 q^{56} + 10 q^{57} - 20 q^{58} + 6 q^{59} + 76 q^{60} + 30 q^{61} - 10 q^{62} + 92 q^{63} + 70 q^{64} + 68 q^{65} + 34 q^{66} - 22 q^{67} - 20 q^{68} - 38 q^{69} - 20 q^{70} + 4 q^{71} - 74 q^{72} + 10 q^{74} + 4 q^{75} - 128 q^{76} - 20 q^{77} - 10 q^{78} - 2 q^{79} - 70 q^{80} + 28 q^{81} - 90 q^{82} + 80 q^{83} - 30 q^{84} - 56 q^{85} - 46 q^{86} - 10 q^{87} + 10 q^{88} - 72 q^{89} - 70 q^{90} - 6 q^{93} - 18 q^{94} - 40 q^{95} + 66 q^{96} - 22 q^{97} + 6 q^{98} + 14 q^{99}+O(q^{100}) \) 24 * q - 10 * q^2 - 6 * q^3 - 10 * q^5 - 2 * q^6 - 8 * q^7 - 10 * q^8 + 6 * q^10 - 16 * q^11 + 2 * q^12 + 14 * q^14 + 8 * q^15 - 20 * q^16 + 8 * q^17 + 16 * q^19 + 20 * q^20 - 10 * q^21 + 6 * q^22 + 12 * q^23 + 68 * q^24 - 8 * q^25 - 28 * q^26 - 6 * q^27 + 18 * q^28 + 40 * q^29 - 36 * q^30 - 12 * q^31 + 10 * q^33 - 16 * q^34 - 36 * q^35 - 40 * q^36 + 46 * q^38 - 50 * q^39 - 44 * q^40 - 4 * q^41 - 40 * q^42 - 48 * q^44 + 16 * q^45 + 70 * q^46 - 12 * q^47 - 50 * q^48 - 30 * q^49 - 24 * q^51 + 20 * q^52 - 26 * q^53 + 68 * q^54 + 20 * q^55 + 106 * q^56 + 10 * q^57 - 20 * q^58 + 6 * q^59 + 76 * q^60 + 30 * q^61 - 10 * q^62 + 92 * q^63 + 70 * q^64 + 68 * q^65 + 34 * q^66 - 22 * q^67 - 20 * q^68 - 38 * q^69 - 20 * q^70 + 4 * q^71 - 74 * q^72 + 10 * q^74 + 4 * q^75 - 128 * q^76 - 20 * q^77 - 10 * q^78 - 2 * q^79 - 70 * q^80 + 28 * q^81 - 90 * q^82 + 80 * q^83 - 30 * q^84 - 56 * q^85 - 46 * q^86 - 10 * q^87 + 10 * q^88 - 72 * q^89 - 70 * q^90 - 6 * q^93 - 18 * q^94 - 40 * q^95 + 66 * q^96 - 22 * q^97 + 6 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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