LMFDB - Embedded newform 507.2.p.a.142.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(25,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(26))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("507.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.p (of order $26$, degree $12$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$14$ over $\Q(\zeta_{26})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{26}]$

Embedding invariants

Embedding label			142.5
Character	$\chi$	$=$	507.142
Dual form			507.2.p.a.25.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.911757 + 0.345784i) q^{2} +(0.568065 - 0.822984i) q^{3} +(-0.785288 + 0.695704i) q^{4} +(2.27932 - 0.276760i) q^{5} +(-0.233362 + 0.946788i) q^{6} +(1.78194 - 3.39521i) q^{7} +(1.38175 - 2.63271i) q^{8} +(-0.354605 - 0.935016i) q^{9} +O(q^{10})$	\(q+(-0.911757 + 0.345784i) q^{2} +(0.568065 - 0.822984i) q^{3} +(-0.785288 + 0.695704i) q^{4} +(2.27932 - 0.276760i) q^{5} +(-0.233362 + 0.946788i) q^{6} +(1.78194 - 3.39521i) q^{7} +(1.38175 - 2.63271i) q^{8} +(-0.354605 - 0.935016i) q^{9} +(-1.98249 + 1.04049i) q^{10} +(-0.0539466 - 0.0204593i) q^{11} +(0.126459 + 1.04148i) q^{12} +(-1.20767 + 3.39728i) q^{13} +(-0.450690 + 3.71177i) q^{14} +(1.06703 - 2.03306i) q^{15} +(-0.0965561 + 0.795211i) q^{16} +(-4.90759 - 2.57570i) q^{17} +(0.646627 + 0.729891i) q^{18} -6.27486i q^{19} +(-1.59738 + 1.80307i) q^{20} +(-1.78194 - 3.39521i) q^{21} +0.0562607 q^{22} +3.51596 q^{23} +(-1.38175 - 2.63271i) q^{24} +(0.263995 - 0.0650689i) q^{25} +(-0.0736285 - 3.51509i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(0.962722 + 3.90592i) q^{28} +(2.75100 + 7.25379i) q^{29} +(-0.269875 + 2.22262i) q^{30} +(1.70007 - 6.89744i) q^{31} +(1.23617 + 5.01534i) q^{32} +(-0.0474828 + 0.0327750i) q^{33} +(5.36517 + 0.651449i) q^{34} +(3.12196 - 8.23193i) q^{35} +(0.928962 + 0.487557i) q^{36} +(1.92301 - 7.80196i) q^{37} +(2.16974 + 5.72114i) q^{38} +(2.10988 + 2.92377i) q^{39} +(2.42083 - 6.38320i) q^{40} +(8.26566 + 5.70537i) q^{41} +(2.79870 + 2.47944i) q^{42} +(-1.62225 + 0.399848i) q^{43} +(0.0565972 - 0.0214645i) q^{44} +(-1.06703 - 2.03306i) q^{45} +(-3.20570 + 1.21576i) q^{46} +(2.41926 - 2.73079i) q^{47} +(0.599595 + 0.531195i) q^{48} +(-4.37566 - 6.33923i) q^{49} +(-0.218199 + 0.150612i) q^{50} +(-4.90759 + 2.57570i) q^{51} +(-1.41514 - 3.50802i) q^{52} +(-3.03124 - 1.59092i) q^{53} +(0.968014 - 0.117538i) q^{54} +(-0.128624 - 0.0317030i) q^{55} +(-6.47639 - 9.38267i) q^{56} +(-5.16410 - 3.56452i) q^{57} +(-5.01648 - 5.66244i) q^{58} +(-3.83224 + 0.465318i) q^{59} +(0.576481 + 2.33888i) q^{60} +(10.9982 - 5.77228i) q^{61} +(0.834976 + 6.87665i) q^{62} +(-3.80646 - 0.462188i) q^{63} +(-3.77141 - 5.46383i) q^{64} +(-1.81243 + 8.07773i) q^{65} +(0.0319597 - 0.0463016i) q^{66} +(-2.39165 + 2.69961i) q^{67} +(5.64580 - 1.39156i) q^{68} +(1.99729 - 2.89358i) q^{69} +8.58504i q^{70} +(7.11787 + 4.91311i) q^{71} +(-2.95160 - 0.358390i) q^{72} +(-9.89374 - 3.75220i) q^{73} +(0.944473 + 7.77843i) q^{74} +(0.0964155 - 0.254227i) q^{75} +(4.36544 + 4.92757i) q^{76} +(-0.165593 + 0.146703i) q^{77} +(-2.93469 - 1.93620i) q^{78} +(10.5509 + 9.34727i) q^{79} +1.83926i q^{80} +(-0.748511 + 0.663123i) q^{81} +(-9.50909 - 2.34378i) q^{82} +(-2.75551 + 1.90199i) q^{83} +(3.76140 + 1.42651i) q^{84} +(-11.8988 - 4.51263i) q^{85} +(1.34083 - 0.925510i) q^{86} +(7.53249 + 1.85659i) q^{87} +(-0.128404 + 0.113756i) q^{88} +15.4794i q^{89} +(1.67587 + 1.48469i) q^{90} +(9.38249 + 10.1540i) q^{91} +(-2.76104 + 2.44607i) q^{92} +(-4.71074 - 5.31732i) q^{93} +(-1.26152 + 3.32635i) q^{94} +(-1.73663 - 14.3024i) q^{95} +(4.82977 + 1.83169i) q^{96} +(3.45109 + 0.419038i) q^{97} +(6.18153 + 4.26681i) q^{98} +0.0576959i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	$ 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) $ 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{23}{26}\right)$

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 $

$2$	−0.911757	+	0.345784i	−0.644709	+	0.244506i	−0.655219	−	0.755439i	$-0.727424\pi$
$2$	−0.911757	+	0.345784i	−0.644709	+	0.244506i	0.0105100	+	0.999945i	$0.496655\pi$
$3$	0.568065	−	0.822984i	0.327972	−	0.475150i
$3$	0.568065	−	0.822984i	0.327972	−	0.475150i
$4$	−0.785288	+	0.695704i	−0.392644	+	0.347852i
$5$	2.27932	−	0.276760i	1.01934	−	0.123771i	0.406234	−	0.913769i	$-0.366842\pi$
$5$	2.27932	−	0.276760i	1.01934	−	0.123771i	0.613109	+	0.789998i	$0.289919\pi$
$6$	−0.233362	+	0.946788i	−0.0952698	+	0.386525i
$7$	1.78194	−	3.39521i	0.673511	−	1.28327i	−0.273440	−	0.961889i	$-0.588162\pi$
$7$	1.78194	−	3.39521i	0.673511	−	1.28327i	0.946951	−	0.321378i	$-0.104146\pi$
$8$	1.38175	−	2.63271i	0.488524	−	0.930804i
$9$	−0.354605	−	0.935016i	−0.118202	−	0.311672i
$10$	−1.98249	+	1.04049i	−0.626917	+	0.329031i
$11$	−0.0539466	−	0.0204593i	−0.0162655	−	0.00616870i	0.346459	−	0.938065i	$-0.387384\pi$
$11$	−0.0539466	−	0.0204593i	−0.0162655	−	0.00616870i	−0.362724	+	0.931897i	$0.618153\pi$
$12$	0.126459	+	1.04148i	0.0365056	+	0.300651i
$13$	−1.20767	+	3.39728i	−0.334946	+	0.942237i
$13$	−1.20767	+	3.39728i	−0.334946	+	0.942237i
$14$	−0.450690	+	3.71177i	−0.120452	+	0.992012i
$15$	1.06703	−	2.03306i	0.275507	−	0.524934i
$16$	−0.0965561	+	0.795211i	−0.0241390	+	0.198803i
$17$	−4.90759	−	2.57570i	−1.19027	−	0.624700i	−0.251033	−	0.967979i	$-0.580770\pi$
$17$	−4.90759	−	2.57570i	−1.19027	−	0.624700i	−0.939234	+	0.343279i	$0.888462\pi$
$18$	0.646627	+	0.729891i	0.152411	+	0.172037i
$19$		−	6.27486i		−	1.43955i	−0.694207	−	0.719775i	$-0.744245\pi$
$19$		−	6.27486i		−	1.43955i	0.694207	−	0.719775i	$-0.255755\pi$
$20$	−1.59738	+	1.80307i	−0.357185	+	0.403178i
$21$	−1.78194	−	3.39521i	−0.388852	−	0.740895i
$22$	0.0562607			0.0119948
$23$	3.51596			0.733128			0.366564	−	0.930393i	$-0.380534\pi$
$23$	3.51596			0.733128			0.366564	+	0.930393i	$0.380534\pi$
$24$	−1.38175	−	2.63271i	−0.282049	−	0.537400i
$25$	0.263995	−	0.0650689i	0.0527990	−	0.0130138i
$26$	−0.0736285	−	3.51509i	−0.0144397	−	0.689365i
$27$	−0.970942	−	0.239316i	−0.186858	−	0.0460563i
$28$	0.962722	+	3.90592i	0.181937	+	0.738149i
$29$	2.75100	+	7.25379i	0.510848	+	1.34699i	0.904004	+	0.427523i	$0.140614\pi$
$29$	2.75100	+	7.25379i	0.510848	+	1.34699i	−0.393157	+	0.919471i	$0.628617\pi$
$30$	−0.269875	+	2.22262i	−0.0492722	+	0.405793i
$31$	1.70007	−	6.89744i	0.305341	−	1.23882i	−0.595033	−	0.803701i	$-0.702861\pi$
$31$	1.70007	−	6.89744i	0.305341	−	1.23882i	0.900374	−	0.435116i	$-0.143293\pi$
$32$	1.23617	+	5.01534i	0.218526	+	0.886596i
$33$	−0.0474828	+	0.0327750i	−0.00826570	+	0.00570540i
$34$	5.36517	+	0.651449i	0.920118	+	0.111723i
$35$	3.12196	−	8.23193i	0.527707	−	1.39145i
$36$	0.928962	+	0.487557i	0.154827	+	0.0812595i
$37$	1.92301	−	7.80196i	0.316141	−	1.28263i	−0.570929	−	0.820999i	$-0.693417\pi$
$37$	1.92301	−	7.80196i	0.316141	−	1.28263i	0.887070	−	0.461635i	$-0.152737\pi$
$38$	2.16974	+	5.72114i	0.351979	+	0.928092i
$39$	2.10988	+	2.92377i	0.337851	+	0.468177i
$40$	2.42083	−	6.38320i	0.382767	−	1.00927i
$41$	8.26566	+	5.70537i	1.29088	+	0.891029i	0.997880	−	0.0650833i	$-0.0207313\pi$
$41$	8.26566	+	5.70537i	1.29088	+	0.891029i	0.292999	+	0.956113i	$0.405347\pi$
$42$	2.79870	+	2.47944i	0.431849	+	0.382585i
$43$	−1.62225	+	0.399848i	−0.247390	+	0.0609762i	−0.361061	−	0.932542i	$-0.617585\pi$
$43$	−1.62225	+	0.399848i	−0.247390	+	0.0609762i	0.113671	+	0.993519i	$0.463739\pi$
$44$	0.0565972	−	0.0214645i	0.00853235	−	0.00323589i
$45$	−1.06703	−	2.03306i	−0.159064	−	0.303071i
$46$	−3.20570	+	1.21576i	−0.472654	+	0.179254i
$47$	2.41926	−	2.73079i	0.352886	−	0.398326i	−0.545085	−	0.838381i	$-0.683503\pi$
$47$	2.41926	−	2.73079i	0.352886	−	0.398326i	0.897971	+	0.440055i	$0.145041\pi$
$48$	0.599595	+	0.531195i	0.0865441	+	0.0766714i
$49$	−4.37566	−	6.33923i	−0.625094	−	0.905604i
$50$	−0.218199	+	0.150612i	−0.0308580	+	0.0212998i
$51$	−4.90759	+	2.57570i	−0.687200	+	0.360671i
$52$	−1.41514	−	3.50802i	−0.196245	−	0.486475i
$53$	−3.03124	−	1.59092i	−0.416373	−	0.218530i	0.243509	−	0.969899i	$-0.421702\pi$
$53$	−3.03124	−	1.59092i	−0.416373	−	0.218530i	−0.659882	+	0.751369i	$0.729394\pi$
$54$	0.968014	−	0.117538i	0.131730	−	0.0159949i
$55$	−0.128624	−	0.0317030i	−0.0173436	−	0.00427483i
$56$	−6.47639	−	9.38267i	−0.865444	−	1.25381i
$57$	−5.16410	−	3.56452i	−0.684002	−	0.472133i
$58$	−5.01648	−	5.66244i	−0.658696	−	0.743514i
$59$	−3.83224	+	0.465318i	−0.498915	+	0.0605793i	−0.366127	−	0.930565i	$-0.619316\pi$
$59$	−3.83224	+	0.465318i	−0.498915	+	0.0605793i	−0.132789	+	0.991144i	$0.542393\pi$
$60$	0.576481	+	2.33888i	0.0744234	+	0.301948i
$61$	10.9982	−	5.77228i	1.40817	−	0.739065i	0.422282	−	0.906465i	$-0.361229\pi$
$61$	10.9982	−	5.77228i	1.40817	−	0.739065i	0.985889	+	0.167399i	$0.0535369\pi$
$62$	0.834976	+	6.87665i	0.106042	+	0.873335i
$63$	−3.80646	−	0.462188i	−0.479569	−	0.0582302i
$64$	−3.77141	−	5.46383i	−0.471426	−	0.682979i
$65$	−1.81243	+	8.07773i	−0.224804	+	1.00192i
$66$	0.0319597	−	0.0463016i	0.00393397	−	0.00569934i
$67$	−2.39165	+	2.69961i	−0.292186	+	0.329810i	−0.876213	−	0.481925i	$-0.839938\pi$
$67$	−2.39165	+	2.69961i	−0.292186	+	0.329810i	0.584027	+	0.811735i	$0.301476\pi$
$68$	5.64580	−	1.39156i	0.684654	−	0.168752i
$69$	1.99729	−	2.89358i	0.240446	−	0.348346i
$70$			8.58504i			1.02611i
$71$	7.11787	+	4.91311i	0.844736	+	0.583079i	0.909915	−	0.414795i	$-0.136147\pi$
$71$	7.11787	+	4.91311i	0.844736	+	0.583079i	−0.0651793	+	0.997874i	$0.520762\pi$
$72$	−2.95160	−	0.358390i	−0.347850	−	0.0422366i
$73$	−9.89374	−	3.75220i	−1.15798	−	0.439162i	−0.300548	−	0.953767i	$-0.597169\pi$
$73$	−9.89374	−	3.75220i	−1.15798	−	0.439162i	−0.857427	+	0.514605i	$0.827939\pi$
$74$	0.944473	+	7.77843i	0.109793	+	0.904224i
$75$	0.0964155	−	0.254227i	0.0111331	−	0.0293556i
$76$	4.36544	+	4.92757i	0.500751	+	0.565231i
$77$	−0.165593	+	0.146703i	−0.0188711	+	0.0167183i
$78$	−2.93469	−	1.93620i	−0.332288	−	0.219232i
$79$	10.5509	+	9.34727i	1.18707	+	1.05165i	0.997563	+	0.0697696i	$0.0222264\pi$
$79$	10.5509	+	9.34727i	1.18707	+	1.05165i	0.189504	+	0.981880i	$0.439312\pi$
$80$			1.83926i			0.205636i
$81$	−0.748511	+	0.663123i	−0.0831679	+	0.0736803i
$82$	−9.50909	−	2.34378i	−1.05010	−	0.258827i
$83$	−2.75551	+	1.90199i	−0.302456	+	0.208771i	−0.709620	−	0.704585i	$-0.751133\pi$
$83$	−2.75551	+	1.90199i	−0.302456	+	0.208771i	0.407164	+	0.913355i	$0.366518\pi$
$84$	3.76140	+	1.42651i	0.410402	+	0.155645i
$85$	−11.8988	−	4.51263i	−1.29061	−	0.489463i
$86$	1.34083	−	0.925510i	0.144586	−	0.0998004i
$87$	7.53249	+	1.85659i	0.807568	+	0.199048i
$88$	−0.128404	+	0.113756i	−0.0136879	+	0.0121265i
$89$			15.4794i			1.64081i	0.571783	+	0.820405i	$0.306252\pi$
$89$			15.4794i			1.64081i	−0.571783	+	0.820405i	$0.693748\pi$
$90$	1.67587	+	1.48469i	0.176653	+	0.156501i
$91$	9.38249	+	10.1540i	0.983552	+	1.06443i
$92$	−2.76104	+	2.44607i	−0.287858	+	0.255020i
$93$	−4.71074	−	5.31732i	−0.488481	−	0.551381i
$94$	−1.26152	+	3.32635i	−0.130116	+	0.343087i
$95$	−1.73663	−	14.3024i	−0.178174	−	1.46740i
$96$	4.82977	+	1.83169i	0.492936	+	0.186946i
$97$	3.45109	+	0.419038i	0.350405	+	0.0425469i	0.293847	−	0.955852i	$-0.405064\pi$
$97$	3.45109	+	0.419038i	0.350405	+	0.0425469i	0.0565579	+	0.998399i	$0.481987\pi$
$98$	6.18153	+	4.26681i	0.624429	+	0.431012i
$99$			0.0576959i			0.00579866i
$100$	−0.162043	+	0.234760i	−0.0162043	+	0.0234760i
$101$	−1.97747	+	0.487402i	−0.196766	+	0.0484984i	−0.336467	−	0.941695i	$-0.609232\pi$
$101$	−1.97747	+	0.487402i	−0.196766	+	0.0484984i	0.139701	+	0.990194i	$0.455386\pi$
$102$	3.58389	−	4.04538i	0.354858	−	0.400552i
$103$	−8.26110	+	11.9683i	−0.813990	+	1.17927i	0.167142	+	0.985933i	$0.446546\pi$
$103$	−8.26110	+	11.9683i	−0.813990	+	1.17927i	−0.981133	+	0.193336i	$0.938069\pi$
$104$	7.27537	+	7.87364i	0.713409	+	0.772074i
$105$	−5.00127	−	7.24559i	−0.488074	−	0.707097i
$106$	3.31387	+	0.402377i	0.321872	+	0.0390823i
$107$	1.26971	+	10.4570i	0.122748	+	1.01092i	0.915764	+	0.401717i	$0.131586\pi$
$107$	1.26971	+	10.4570i	0.122748	+	1.01092i	−0.793017	+	0.609200i	$0.791491\pi$
$108$	0.928962	−	0.487557i	0.0893894	−	0.0469152i
$109$	0.717329	+	2.91032i	0.0687076	+	0.278758i	0.995240	−	0.0974582i	$-0.0310712\pi$
$109$	0.717329	+	2.91032i	0.0687076	+	0.278758i	−0.926532	+	0.376216i	$0.877225\pi$
$110$	0.128236	−	0.0155707i	0.0122268	−	0.00148461i
$111$	−5.32849	−	6.01462i	−0.505758	−	0.570883i
$112$	2.52785	+	1.74485i	0.238859	+	0.164873i
$113$	−5.73111	−	8.30295i	−0.539137	−	0.781075i	0.454850	−	0.890568i	$-0.349693\pi$
$113$	−5.73111	−	8.30295i	−0.539137	−	0.781075i	−0.993988	+	0.109493i	$0.965077\pi$
$114$	5.94096	+	1.46432i	0.556422	+	0.137146i
$115$	8.01399	−	0.973075i	0.747309	−	0.0907397i
$116$	−7.20682	−	3.78243i	−0.669136	−	0.351190i
$117$	3.60476	−	0.0755068i	0.333260	−	0.00698061i
$118$	3.33317	−	1.74938i	0.306843	−	0.161044i
$119$	−17.4901	+	12.0725i	−1.60331	+	1.10669i
$120$	−3.87809	−	5.61838i	−0.354019	−	0.512885i
$121$	−8.23113	−	7.29214i	−0.748284	−	0.662922i
$122$	−8.03169	+	9.06590i	−0.727155	+	0.820788i
$123$	9.39086	−	3.56148i	0.846745	−	0.321128i
$124$	3.46354	+	6.59922i	0.311035	+	0.592628i
$125$	−10.1506	+	3.84960i	−0.907893	+	0.344318i
$126$	3.63038	−	0.894808i	0.323420	−	0.0797159i
$127$	−1.65813	−	1.46897i	−0.147135	−	0.130350i	0.586344	−	0.810062i	$-0.300567\pi$
$127$	−1.65813	−	1.46897i	−0.147135	−	0.130350i	−0.733480	+	0.679712i	$0.762105\pi$
$128$	−3.17424	−	2.19102i	−0.280566	−	0.193661i
$129$	−0.592473	+	1.56222i	−0.0521643	+	0.137546i
$130$	−1.14066	−	7.99163i	−0.100042	−	0.700913i
$131$	−0.248315	−	0.654754i	−0.0216954	−	0.0572061i	0.923731	−	0.383042i	$-0.125124\pi$
$131$	−0.248315	−	0.654754i	−0.0216954	−	0.0572061i	−0.945426	+	0.325836i	$0.894354\pi$
$132$	0.0144860	−	0.0587718i	0.00126084	−	0.00511543i
$133$	−21.3044	−	11.1814i	−1.84733	−	0.969553i
$134$	1.24712	−	3.28838i	0.107735	−	0.284073i
$135$	−2.27932	−	0.276760i	−0.196173	−	0.0238197i
$136$	−13.5622	+	9.36129i	−1.16295	+	0.802724i
$137$	4.88924	+	19.8364i	0.417716	+	1.69474i	0.682874	+	0.730537i	$0.260730\pi$
$137$	4.88924	+	19.8364i	0.417716	+	1.69474i	−0.265157	+	0.964205i	$0.585424\pi$
$138$	−0.820492	+	3.32887i	−0.0698450	+	0.283372i
$139$	1.76448	−	14.5318i	0.149661	−	1.23257i	−0.703413	−	0.710781i	$-0.748342\pi$
$139$	1.76448	−	14.5318i	0.149661	−	1.23257i	0.853074	−	0.521789i	$-0.174735\pi$
$140$	3.27535	+	8.63640i	0.276818	+	0.729909i
$141$	−0.873093	−	3.54228i	−0.0735277	−	0.298314i
$142$	−8.18864	−	2.01832i	−0.687175	−	0.169373i
$143$	0.134655	−	0.158564i	0.0112605	−	0.0132598i
$144$	0.777774	−	0.191704i	0.0648145	−	0.0159753i
$145$	8.27796	+	15.7723i	0.687447	+	1.30982i
$146$	10.3181			0.853935
$147$	−7.70274			−0.635311
$148$	3.91774	+	7.46463i	0.322036	+	0.613589i
$149$	2.41896	−	2.73044i	0.198169	−	0.223687i	−0.641023	−	0.767522i	$-0.721490\pi$
$149$	2.41896	−	2.73044i	0.198169	−	0.223687i	0.839192	+	0.543835i	$0.183028\pi$
$150$			0.265132i			0.0216479i
$151$	11.7390	+	13.2505i	0.955303	+	1.07831i	0.996861	+	0.0791777i	$0.0252295\pi$
$151$	11.7390	+	13.2505i	0.955303	+	1.07831i	−0.0415578	+	0.999136i	$0.513232\pi$
$152$	−16.5199	−	8.67030i	−1.33994	−	0.703254i
$153$	−0.668068	+	5.50204i	−0.0540101	+	0.444813i
$154$	0.100253	−	0.191017i	0.00807864	−	0.0153926i
$155$	1.96606	−	16.1920i	0.157918	−	1.30057i
$156$	−3.69094	−	0.828147i	−0.295512	−	0.0663048i
$157$	0.554368	+	4.56563i	0.0442434	+	0.364377i	0.997969	+	0.0636992i	$0.0202898\pi$
$157$	0.554368	+	4.56563i	0.0442434	+	0.364377i	−0.953726	+	0.300678i	$0.902787\pi$
$158$	−12.8520	−	4.87411i	−1.02245	−	0.387763i
$159$	−3.03124	+	1.59092i	−0.240393	+	0.126168i
$160$	4.20567	+	11.0894i	0.332488	+	0.876698i
$161$	6.26523	−	11.9374i	0.493770	−	0.940799i
$162$	0.453163	−	0.863429i	0.0356038	−	0.0678374i
$163$	−3.67923	+	14.9272i	−0.288179	+	1.16919i	0.631137	+	0.775671i	$0.282588\pi$
$163$	−3.67923	+	14.9272i	−0.288179	+	1.16919i	−0.919317	+	0.393519i	$0.871258\pi$
$164$	−10.4602	+	1.27009i	−0.816802	+	0.0991778i
$165$	−0.0991577	+	0.0878461i	−0.00771942	+	0.00683881i
$166$	1.85468	−	2.68696i	0.143951	−	0.208549i
$167$	18.4683	−	7.00412i	1.42912	−	0.541995i	0.485859	−	0.874037i	$-0.338507\pi$
$167$	18.4683	−	7.00412i	1.42912	−	0.541995i	0.943264	+	0.332042i	$0.107738\pi$
$168$	−11.4008			−0.879591
$169$	−10.0831	−	8.20557i	−0.775622	−	0.631198i
$170$	12.4092			0.951744
$171$	−5.86709	+	2.22509i	−0.448668	+	0.170157i
$172$	0.995755	−	1.44260i	0.0759256	−	0.109997i
$173$	5.55983	−	4.92558i	0.422706	−	0.374485i	−0.424785	−	0.905294i	$-0.639650\pi$
$173$	5.55983	−	4.92558i	0.422706	−	0.374485i	0.847491	+	0.530809i	$0.178112\pi$
$174$	−7.50978	+	0.911853i	−0.569315	+	0.0691274i
$175$	0.249501	−	1.01227i	0.0188605	−	0.0765201i
$176$	0.0214783	−	0.0409235i	0.00161899	−	0.00308472i
$177$	−1.79401	+	3.41820i	−0.134846	+	0.256928i
$178$	−5.35251	−	14.1134i	−0.401188	−	1.05785i
$179$	0.573905	−	0.301209i	0.0428957	−	0.0225134i	−0.443139	−	0.896453i	$-0.646135\pi$
$179$	0.573905	−	0.301209i	0.0428957	−	0.0225134i	0.486035	+	0.873940i	$0.338443\pi$
$180$	2.25234	+	0.854199i	0.167879	+	0.0636682i
$181$	0.441933	+	3.63965i	0.0328486	+	0.270533i	0.999874	+	0.0158540i	$0.00504669\pi$
$181$	0.441933	+	3.63965i	0.0328486	+	0.270533i	−0.967026	+	0.254679i	$0.918030\pi$
$182$	−12.0656	−	6.01370i	−0.894365	−	0.445765i
$183$	1.49718	−	12.3303i	0.110674	−	0.911485i
$184$	4.85819	−	9.25650i	0.358150	−	0.682398i
$185$	2.22389	−	18.3154i	0.163504	−	1.34657i
$186$	6.13369	+	3.21921i	0.449744	+	0.236044i
$187$	0.212051	+	0.239356i	0.0155067	+	0.0175035i
$188$			3.82755i			0.279152i
$189$	−2.54269	+	2.87010i	−0.184953	+	0.208769i
$190$	6.52892	+	12.4398i	0.473657	+	0.902479i
$191$	−1.93249			−0.139830			−0.0699149	−	0.997553i	$-0.522273\pi$
$191$	−1.93249			−0.139830			−0.0699149	+	0.997553i	$0.522273\pi$
$192$	−6.63905			−0.479132
$193$	5.72884	+	10.9154i	0.412371	+	0.785708i	0.999721	−	0.0236257i	$-0.00752099\pi$
$193$	5.72884	+	10.9154i	0.412371	+	0.785708i	−0.587350	+	0.809333i	$0.699829\pi$
$194$	−3.29145	+	0.811269i	−0.236312	+	0.0582457i
$195$	5.61827	+	6.08027i	0.402333	+	0.435417i
$196$	7.84638	+	1.93396i	0.560456	+	0.138140i
$197$	−2.54838	−	10.3392i	−0.181564	−	0.736636i	−0.989153	−	0.146890i	$-0.953074\pi$
$197$	−2.54838	−	10.3392i	−0.181564	−	0.736636i	0.807588	−	0.589747i	$-0.200772\pi$
$198$	−0.0199503	−	0.0526046i	−0.00141781	−	0.00373845i
$199$	−2.98542	+	24.5871i	−0.211630	+	1.74293i	0.369597	+	0.929192i	$0.379496\pi$
$199$	−2.98542	+	24.5871i	−0.211630	+	1.74293i	−0.581227	+	0.813741i	$0.697427\pi$
$200$	0.193468	−	0.784931i	0.0136803	−	0.0555030i
$201$	0.863126	+	3.50184i	0.0608802	+	0.247001i
$202$	1.63444	−	1.12817i	0.114998	−	0.0793777i
$203$	29.5302	+	3.58562i	2.07262	+	0.251661i
$204$	2.06194	−	5.43690i	0.144365	−	0.380659i
$205$	20.4191	+	10.7168i	1.42613	+	0.748492i
$206$	3.39368	−	13.7687i	0.236449	−	0.959311i
$207$	−1.24678	−	3.28748i	−0.0866569	−	0.228496i
$208$	−2.58495	−	1.28838i	−0.179234	−	0.0893329i
$209$	−0.128379	+	0.338507i	−0.00888015	+	0.0234150i
$210$	7.06535	+	4.87686i	0.487555	+	0.336535i
$211$	−0.112192	−	0.0993933i	−0.00772361	−	0.00684252i	0.659252	−	0.751922i	$-0.270873\pi$
$211$	−0.112192	−	0.0993933i	−0.00772361	−	0.00684252i	−0.666976	+	0.745080i	$0.732411\pi$
$212$	3.48721	−	0.859520i	0.239503	−	0.0590321i
$213$	8.08682	−	3.06693i	0.554100	−	0.210142i
$214$	−4.77353	−	9.09520i	−0.326312	−	0.621735i
$215$	−3.58696	+	1.36035i	−0.244629	+	0.0927754i
$216$	−1.97165	+	2.22553i	−0.134154	+	0.151428i
$217$	−20.3888	−	18.0629i	−1.38408	−	1.22619i
$218$	−1.66037	−	2.40546i	−0.112454	−	0.162918i
$219$	−8.70829	+	6.01090i	−0.588452	+	0.406179i
$220$	0.123063	−	0.0645883i	0.00829689	−	0.00435454i
$221$	14.6771	−	13.5619i	0.987290	−	0.912272i
$222$	6.93805	+	3.64137i	0.465651	+	0.244393i
$223$	−12.9252	+	1.56940i	−0.865533	+	0.105095i	−0.541246	−	0.840864i	$-0.682047\pi$
$223$	−12.9252	+	1.56940i	−0.865533	+	0.105095i	−0.324287	+	0.945959i	$0.605124\pi$
$224$	19.2309	+	4.73999i	1.28492	+	0.316704i
$225$	−0.154454	−	0.223766i	−0.0102970	−	0.0149177i
$226$	8.09640	+	5.58854i	0.538564	+	0.371744i
$227$	−14.8498	−	16.7619i	−0.985614	−	1.11253i	−0.993645	−	0.112560i	$-0.964095\pi$
$227$	−14.8498	−	16.7619i	−0.985614	−	1.11253i	0.00803114	−	0.999968i	$-0.497444\pi$
$228$	6.53516	−	0.793513i	0.432802	−	0.0525517i
$229$	0.641171	+	2.60133i	0.0423698	+	0.171901i	0.988315	−	0.152426i	$-0.0487085\pi$
$229$	0.641171	+	2.60133i	0.0423698	+	0.171901i	−0.945945	+	0.324327i	$0.894862\pi$
$230$	−6.97034	+	3.65832i	−0.459611	+	0.241222i
$231$	0.0266663	+	0.219617i	0.00175452	+	0.0144497i
$232$	22.8983	+	2.78036i	1.50335	+	0.182540i
$233$	−2.88709	−	4.18268i	−0.189140	−	0.274016i	0.716929	−	0.697146i	$-0.245547\pi$
$233$	−2.88709	−	4.18268i	−0.189140	−	0.274016i	−0.906069	+	0.423129i	$0.860932\pi$
$234$	−3.26056	+	1.31531i	−0.213149	+	0.0859846i
$235$	4.75851	−	6.89389i	0.310411	−	0.449708i
$236$	2.68569	−	3.03152i	0.174823	−	0.197335i
$237$	13.6862	−	3.37335i	0.889016	−	0.219123i
$238$	11.7722	−	17.0550i	0.763079	−	1.10551i
$239$			14.5658i			0.942186i	0.882084	+	0.471093i	$0.156140\pi$
$239$			14.5658i			0.942186i	−0.882084	+	0.471093i	$0.843860\pi$
$240$	1.51368	+	1.04482i	0.0977078	+	0.0674428i
$241$	−18.8653	−	2.29066i	−1.21522	−	0.147554i	−0.512290	−	0.858813i	$-0.671203\pi$
$241$	−18.8653	−	2.29066i	−1.21522	−	0.147554i	−0.702931	+	0.711258i	$0.748126\pi$
$242$	10.0263	+	3.80247i	0.644514	+	0.244432i
$243$	0.120537	+	0.992709i	0.00773243	+	0.0636823i
$244$	−4.62093	+	12.1844i	−0.295824	+	0.780025i
$245$	−11.7280	−	13.2381i	−0.749272	−	0.845753i
$246$	−7.33067	+	6.49441i	−0.467387	+	0.414068i
$247$	21.3175	+	7.57793i	1.35640	+	0.482172i
$248$	−15.8099	−	14.0064i	−1.00393	−	0.889404i
$249$			3.34819i			0.212183i
$250$	7.92370	−	7.01979i	0.501139	−	0.443970i
$251$	−14.0494	−	3.46286i	−0.886790	−	0.218574i	−0.230490	−	0.973075i	$-0.574033\pi$
$251$	−14.0494	−	3.46286i	−0.886790	−	0.218574i	−0.656299	+	0.754501i	$0.727879\pi$
$252$	3.31071	−	2.28522i	0.208555	−	0.143955i
$253$	−0.189674	−	0.0719339i	−0.0119247	−	0.00452245i
$254$	2.01976	+	0.765993i	0.126731	+	0.0480626i
$255$	−10.4731	+	7.22908i	−0.655852	+	0.452702i
$256$	16.5440	+	4.07773i	1.03400	+	0.254858i
$257$	8.71362	−	7.71959i	0.543541	−	0.481535i	−0.346099	−	0.938198i	$-0.612494\pi$
$257$	8.71362	−	7.71959i	0.543541	−	0.481535i	0.889640	+	0.456663i	$0.150955\pi$
$258$		−	1.62923i		−	0.101432i
$259$	−23.0626	−	20.4317i	−1.43304	−	1.26956i
$260$	−4.19644	−	7.60426i	−0.260252	−	0.471596i
$261$	5.80689	−	5.14446i	0.359438	−	0.318434i
$262$	0.452806	+	0.511113i	0.0279745	+	0.0315766i
$263$	3.26985	−	8.62188i	0.201627	−	0.531648i	−0.795620	−	0.605796i	$-0.792855\pi$
$263$	3.26985	−	8.62188i	0.201627	−	0.531648i	0.997247	+	0.0741485i	$0.0236239\pi$
$264$	0.0206776	+	0.170296i	0.00127262	+	0.0104810i
$265$	−7.34948	−	2.78729i	−0.451475	−	0.171222i
$266$	23.2908	+	2.82802i	1.42805	+	0.173397i
$267$	12.7393	+	8.79329i	0.779631	+	0.538140i
$268$		−	3.78385i		−	0.231135i
$269$	−8.71975	+	12.6327i	−0.531652	+	0.770231i	−0.993142	−	0.116914i	$-0.962700\pi$
$269$	−8.71975	+	12.6327i	−0.531652	+	0.770231i	0.461490	+	0.887146i	$0.347315\pi$
$270$	2.17388	−	0.535814i	0.132298	−	0.0326086i
$271$	5.25772	−	5.93474i	0.319384	−	0.360510i	−0.566790	−	0.823862i	$-0.691815\pi$
$271$	5.25772	−	5.93474i	0.319384	−	0.360510i	0.886174	+	0.463352i	$0.153353\pi$
$272$	2.52208	−	3.65387i	0.152924	−	0.221548i
$273$	13.6865	−	1.95349i	0.828343	−	0.118231i
$274$	−11.3169	−	16.3954i	−0.683680	−	0.990482i
$275$	−0.0155729	−	0.00189089i	−0.000939081	−	0.000114025i
$276$	0.444625	+	3.66182i	0.0267633	+	0.220415i
$277$	6.19389	−	3.25081i	0.372155	−	0.195322i	−0.268268	−	0.963344i	$-0.586451\pi$
$277$	6.19389	−	3.25081i	0.372155	−	0.195322i	0.640423	+	0.768022i	$0.278759\pi$
$278$	3.41608	+	13.8596i	0.204883	+	0.831243i
$279$	−7.05208	+	0.856277i	−0.422197	+	0.0512640i
$280$	−17.3585	−	19.5937i	−1.03737	−	1.17095i
$281$	4.26225	+	2.94202i	0.254264	+	0.175506i	0.688378	−	0.725352i	$-0.258323\pi$
$281$	4.26225	+	2.94202i	0.254264	+	0.175506i	−0.434114	+	0.900858i	$0.642938\pi$
$282$	2.02091	+	2.92779i	0.120343	+	0.174348i
$283$	10.3006	+	2.53886i	0.612305	+	0.150920i	0.533260	−	0.845952i	$-0.320967\pi$
$283$	10.3006	+	2.53886i	0.612305	+	0.150920i	0.0790448	+	0.996871i	$0.474813\pi$
$284$	−9.00765	+	1.09373i	−0.534506	+	0.0649007i
$285$	−12.7572	−	6.69548i	−0.755669	−	0.396606i
$286$	−0.0679441	+	0.191134i	−0.00401762	+	0.0113020i
$287$	34.0998	−	17.8970i	2.01285	−	1.05642i
$288$	4.25107	−	2.93431i	0.250497	−	0.172906i
$289$	7.79312	+	11.2903i	0.458419	+	0.664134i
$290$	−13.0013	−	11.5181i	−0.763463	−	0.676369i
$291$	2.30530	−	2.60215i	0.135139	−	0.152541i
$292$	10.3799	−	3.93656i	0.607435	−	0.230370i
$293$	8.98205	+	17.1139i	0.524737	+	0.999803i	0.993211	+	0.116326i	$0.0371117\pi$
$293$	8.98205	+	17.1139i	0.524737	+	0.999803i	−0.468474	+	0.883477i	$0.655196\pi$
$294$	7.02302	−	2.66348i	0.409591	−	0.155337i
$295$	−8.60612	+	2.12122i	−0.501068	+	0.123502i
$296$	−17.8832	−	15.8431i	−1.03944	−	0.920862i
$297$	0.0474828	+	0.0327750i	0.00275523	+	0.00190180i
$298$	−1.26136	+	3.32594i	−0.0730687	+	0.192666i
$299$	−4.24610	+	11.9447i	−0.245558	+	0.690781i
$300$	0.101153	+	0.266718i	0.00584006	+	0.0153990i
$301$	−1.53318	+	6.22037i	−0.0883712	+	0.358536i
$302$	−15.2849	−	8.02213i	−0.879547	−	0.461622i
$303$	−0.722206	+	1.90430i	−0.0414897	+	0.109399i
$304$	4.98983	+	0.605875i	0.286186	+	0.0347493i
$305$	23.4708	−	16.2007i	1.34393	−	0.927651i
$306$	−1.29340	−	5.24752i	−0.0739387	−	0.299981i
$307$	6.31970	−	25.6401i	0.360685	−	1.46335i	−0.457918	−	0.888994i	$-0.651405\pi$
$307$	6.31970	−	25.6401i	0.360685	−	1.46335i	0.818602	−	0.574360i	$-0.194749\pi$
$308$	0.0279766	−	0.230408i	0.00159411	−	0.0131287i
$309$	5.15685	+	13.5975i	0.293363	+	0.773535i
$310$	3.80635	+	15.4430i	0.216186	+	0.877103i
$311$	19.0370	+	4.69220i	1.07949	+	0.266070i	0.738676	−	0.674060i	$-0.235451\pi$
$311$	19.0370	+	4.69220i	1.07949	+	0.266070i	0.340814	+	0.940131i	$0.389297\pi$
$312$	10.6128	−	1.51478i	0.600830	−	0.0857573i
$313$	−3.93825	+	0.970692i	−0.222603	+	0.0548667i	−0.349040	−	0.937108i	$-0.613492\pi$
$313$	−3.93825	+	0.970692i	−0.222603	+	0.0548667i	0.126437	+	0.991975i	$0.459646\pi$
$314$	−2.08417	−	3.97105i	−0.117616	−	0.224099i
$315$	−8.80405			−0.496052
$316$	−14.7884			−0.831913
$317$	0.544207	+	1.03690i	0.0305657	+	0.0582381i	0.900260	−	0.435353i	$-0.143376\pi$
$317$	0.544207	+	1.03690i	0.0305657	+	0.0582381i	−0.869694	+	0.493591i	$0.835684\pi$
$318$	2.21364	−	2.49869i	0.124135	−	0.140119i
$319$		−	0.447601i		−	0.0250608i
$320$	−10.1084	−	11.4100i	−0.565078	−	0.637841i
$321$	9.32722	+	4.89530i	0.520595	+	0.273229i
$322$	−1.58461	+	13.0504i	−0.0883068	+	0.727272i
$323$	−16.1622	+	30.7944i	−0.899287	+	1.71345i
$324$	0.126459	−	1.04148i	0.00702550	−	0.0578602i
$325$	−0.0977599	+	0.975447i	−0.00542275	+	0.0541081i
$326$	−1.80703	−	14.8822i	−0.100082	−	0.824249i
$327$	2.80263	+	1.06290i	0.154986	+	0.0587784i
$328$	26.4417	−	13.8777i	1.46000	−	0.766266i
$329$	−4.96059	−	13.0800i	−0.273486	−	0.721124i
$330$	0.0600320	−	0.114381i	0.00330465	−	0.00629649i
$331$	13.2263	−	25.2006i	0.726983	−	1.38515i	−0.188207	−	0.982129i	$-0.560268\pi$
$331$	13.2263	−	25.2006i	0.726983	−	1.38515i	0.915191	−	0.403022i	$-0.132040\pi$
$332$	0.840644	−	3.41063i	0.0461364	−	0.187183i
$333$	−7.97687	+	0.968567i	−0.437130	+	0.0530771i
$334$	−14.4167	+	12.7721i	−0.788848	+	0.698858i
$335$	−4.70418	+	6.81519i	−0.257017	+	0.372353i
$336$	2.87196	−	1.08919i	0.156678	−	0.0594203i
$337$	13.2768			0.723235			0.361617	−	0.932327i	$-0.382225\pi$
$337$	13.2768			0.723235			0.361617	+	0.932327i	$0.382225\pi$
$338$	12.0307	+	3.99491i	0.654382	+	0.217295i
$339$	−10.0888			−0.547950
$340$	12.4835	−	4.73435i	0.677011	−	0.256756i
$341$	−0.232830	+	0.337312i	−0.0126084	+	0.0182665i
$342$	4.57996	−	4.05749i	0.247656	−	0.219404i
$343$	−2.67495	+	0.324798i	−0.144434	+	0.0175374i
$344$	−1.18886	+	4.82340i	−0.0640991	+	0.260060i
$345$	3.75164	−	7.14816i	0.201982	−	0.384844i
$346$	−3.36603	+	6.41343i	−0.180959	+	0.344788i
$347$	10.0302	+	26.4475i	0.538449	+	1.41977i	0.877760	+	0.479100i	$0.159037\pi$
$347$	10.0302	+	26.4475i	0.538449	+	1.41977i	−0.339311	+	0.940674i	$0.610194\pi$
$348$	−7.20682	+	3.78243i	−0.386326	+	0.202759i
$349$	−4.81456	−	1.82592i	−0.257717	−	0.0977393i	0.222363	−	0.974964i	$-0.428623\pi$
$349$	−4.81456	−	1.82592i	−0.257717	−	0.0977393i	−0.480080	+	0.877225i	$0.659392\pi$
$350$	0.122541	+	1.00921i	0.00655008	+	0.0539447i
$351$	1.98560	−	3.00955i	0.105983	−	0.160638i
$352$	0.0359229	−	0.295852i	0.00191470	−	0.0157690i
$353$	−10.8093	+	20.5953i	−0.575320	+	1.09618i	0.407775	+	0.913082i	$0.366305\pi$
$353$	−10.8093	+	20.5953i	−0.575320	+	1.09618i	−0.983095	+	0.183097i	$0.941388\pi$
$354$	0.453743	−	3.73691i	0.0241162	−	0.198614i
$355$	17.5837	+	9.22861i	0.933243	+	0.489804i
$356$	−10.7691	−	12.1558i	−0.570759	−	0.644254i
$357$			21.2520i			1.12478i
$358$	−0.419109	+	0.473076i	−0.0221506	+	0.0250029i
$359$	9.43463	+	17.9762i	0.497941	+	0.948747i	0.996635	+	0.0819691i	$0.0261209\pi$
$359$	9.43463	+	17.9762i	0.497941	+	0.948747i	−0.498694	+	0.866778i	$0.666187\pi$
$360$	−6.82684			−0.359806
$361$	−20.3738			−1.07231
$362$	−1.66147	−	3.16566i	−0.0873247	−	0.166383i
$363$	−10.6771	+	2.63168i	−0.560404	+	0.138127i
$364$	−14.4322	−	1.44640i	−0.756451	−	0.0758120i
$365$	−23.5895	−	5.81428i	−1.23473	−	0.304333i
$366$	2.89857	+	11.7600i	0.151511	+	0.614704i
$367$	7.29173	+	19.2267i	0.380625	+	1.00363i	0.979261	+	0.202605i	$0.0649406\pi$
$367$	7.29173	+	19.2267i	0.380625	+	1.00363i	−0.598635	+	0.801022i	$0.704290\pi$
$368$	−0.339487	+	2.79593i	−0.0176970	+	0.145748i
$369$	2.40357	−	9.75168i	0.125125	−	0.507652i
$370$	4.30551	+	17.4681i	0.223833	+	0.908126i
$371$	−10.8030	+	7.45677i	−0.560864	+	0.387136i
$372$	7.39857	+	0.898349i	0.383598	+	0.0465772i
$373$	12.2779	−	32.3742i	0.635726	−	1.67627i	−0.0966051	−	0.995323i	$-0.530798\pi$
$373$	12.2779	−	32.3742i	0.635726	−	1.67627i	0.732331	−	0.680949i	$-0.238432\pi$
$374$	−0.276104	−	0.144911i	−0.0142770	−	0.00749316i
$375$	−2.59801	+	10.5406i	−0.134161	+	0.544312i
$376$	−3.84654	−	10.1425i	−0.198370	−	0.523059i
$377$	−27.9655	+	0.585777i	−1.44029	+	0.0301690i
$378$	1.32588	−	3.49605i	0.0681958	−	0.179818i
$379$	2.52465	+	1.74264i	0.129682	+	0.0895133i	0.631140	−	0.775669i	$-0.282587\pi$
$379$	2.52465	+	1.74264i	0.129682	+	0.0895133i	−0.501458	+	0.865182i	$0.667203\pi$
$380$	11.3140	+	10.0233i	0.580396	+	0.514186i
$381$	−2.15087	+	0.530141i	−0.110192	+	0.0271599i
$382$	1.76196	−	0.668222i	0.0901495	−	0.0341892i
$383$	−16.9993	−	32.3895i	−0.868626	−	1.65503i	−0.749357	−	0.662166i	$-0.769637\pi$
$383$	−16.9993	−	32.3895i	−0.868626	−	1.65503i	−0.119268	−	0.992862i	$-0.538055\pi$
$384$	−3.60635	+	1.36771i	−0.184036	+	0.0697955i
$385$	−0.336838	+	0.380212i	−0.0171669	+	0.0193774i
$386$	−8.99768	−	7.97125i	−0.457970	−	0.405726i
$387$	0.949121	+	1.37504i	0.0482465	+	0.0698972i
$388$	−3.00162	+	2.07187i	−0.152384	+	0.105183i
$389$	−26.2912	+	13.7987i	−1.33302	+	0.699622i	−0.972450	−	0.233111i	$-0.925109\pi$
$389$	−26.2912	+	13.7987i	−1.33302	+	0.699622i	−0.360568	+	0.932733i	$0.617417\pi$
$390$	−7.22495	−	3.60102i	−0.365850	−	0.182345i
$391$	−17.2549	−	9.05607i	−0.872617	−	0.457985i
$392$	−22.7354	+	2.76058i	−1.14831	+	0.139430i
$393$	−0.679911	−	0.167583i	−0.0342970	−	0.00845344i
$394$	5.89862	+	8.54563i	0.297168	+	0.430522i
$395$	26.6358	+	18.3854i	1.34019	+	0.925067i
$396$	−0.0401393	−	0.0453079i	−0.00201708	−	0.00227681i
$397$	−30.1560	+	3.66160i	−1.51349	+	0.183771i	−0.834758	−	0.550617i	$-0.814392\pi$
$397$	−30.1560	+	3.66160i	−1.51349	+	0.183771i	−0.678730	+	0.734388i	$0.737469\pi$
$398$	−5.77985	−	23.4498i	−0.289718	−	1.17543i
$399$	−21.3044	+	11.1814i	−1.06656	+	0.559771i
$400$	0.0262532	+	0.216214i	0.00131266	+	0.0108107i
$401$	−6.69329	−	0.812713i	−0.334247	−	0.0405849i	−0.0483072	−	0.998833i	$-0.515383\pi$
$401$	−6.69329	−	0.812713i	−0.334247	−	0.0405849i	−0.285940	+	0.958248i	$0.592306\pi$
$402$	−1.99784	−	2.89437i	−0.0996432	−	0.144358i
$403$	21.3795	+	14.1054i	1.06499	+	0.702641i
$404$	1.21379	−	1.75849i	0.0603885	−	0.0874879i
$405$	−1.52257	+	1.71863i	−0.0756571	+	0.0853992i
$406$	−28.1642	+	6.94186i	−1.39777	+	0.344519i
$407$	−0.263362	+	0.381546i	−0.0130544	+	0.0189125i
$408$			16.4793i			0.815845i
$409$	31.3002	+	21.6049i	1.54769	+	1.06830i	0.967195	+	0.254034i	$0.0817576\pi$
$409$	31.3002	+	21.6049i	1.54769	+	1.06830i	0.580498	+	0.814261i	$0.302858\pi$
$410$	−22.3229	−	2.71049i	−1.10245	−	0.133862i
$411$	19.1025	+	7.24462i	0.942256	+	0.357351i
$412$	−1.83904	−	15.1458i	−0.0906028	−	0.746181i
$413$	−5.24898	+	13.8404i	−0.258285	+	0.681042i
$414$	2.27351	+	2.56627i	0.111737	+	0.126125i
$415$	−5.75429	+	5.09786i	−0.282467	+	0.250244i
$416$	−18.5314	−	1.85723i	−0.908578	−	0.0910583i
$417$	−10.9571	−	9.70714i	−0.536571	−	0.475361i
$418$		−	0.353028i		−	0.0172671i
$419$	−15.1161	+	13.3917i	−0.738470	+	0.654228i	−0.946061	−	0.323988i	$-0.894976\pi$
$419$	−15.1161	+	13.3917i	−0.738470	+	0.654228i	0.207591	+	0.978216i	$0.433438\pi$
$420$	8.96823	+	2.21047i	0.437605	+	0.107860i
$421$	−33.5670	+	23.1696i	−1.63596	+	1.12922i	−0.755420	+	0.655241i	$0.772567\pi$
$421$	−33.5670	+	23.1696i	−1.63596	+	1.12922i	−0.880536	+	0.473978i	$0.842817\pi$
$422$	0.136660	+	0.0518284i	0.00665252	+	0.00252297i
$423$	−3.41121	−	1.29370i	−0.165859	−	0.0629019i
$424$	−8.37686	+	5.78213i	−0.406817	+	0.280805i
$425$	−1.46318	−	0.360641i	−0.0709745	−	0.0174936i
$426$	−6.31272	+	5.59258i	−0.305852	+	0.270961i
$427$		−	47.6269i		−	2.30483i
$428$	−8.27207	−	7.32841i	−0.399846	−	0.354232i
$429$	−0.0540027	−	0.200894i	−0.00260728	−	0.00969925i
$430$	2.80004	−	2.48062i	0.135030	−	0.119626i
$431$	0.146023	+	0.164826i	0.00703368	+	0.00793939i	0.752017	−	0.659144i	$-0.229081\pi$
$431$	0.146023	+	0.164826i	0.00703368	+	0.00793939i	−0.744983	+	0.667083i	$0.767543\pi$
$432$	0.284057	−	0.748996i	0.0136667	−	0.0360361i
$433$	−1.93451	−	15.9322i	−0.0929668	−	0.765651i	−0.962407	−	0.271612i	$-0.912443\pi$
$433$	−1.93451	−	15.9322i	−0.0929668	−	0.765651i	0.869440	−	0.494039i	$-0.164480\pi$
$434$	24.8355	+	9.41887i	1.19214	+	0.452120i
$435$	17.6828	+	2.14708i	0.847825	+	0.102945i
$436$	−2.58803	−	1.78639i	−0.123944	−	0.0855525i
$437$		−	22.0621i		−	1.05537i
$438$	5.86137	−	8.49166i	0.280067	−	0.405747i
$439$	−28.6495	+	7.06148i	−1.36737	+	0.337026i	−0.853612	−	0.520910i	$-0.825593\pi$
$439$	−28.6495	+	7.06148i	−1.36737	+	0.337026i	−0.513757	+	0.857936i	$0.671747\pi$
$440$	−0.261191	+	0.294824i	−0.0124518	+	0.0140552i
$441$	−4.37566	+	6.33923i	−0.208365	+	0.301868i
$442$	−8.69248	+	17.4403i	−0.413459	+	0.829549i
$443$	21.0862	+	30.5487i	1.00184	+	1.45141i	0.889059	+	0.457792i	$0.151360\pi$
$443$	21.0862	+	30.5487i	1.00184	+	1.45141i	0.112778	+	0.993620i	$0.464025\pi$
$444$	8.36880	+	1.01616i	0.397166	+	0.0482246i
$445$	4.28406	+	35.2824i	0.203084	+	1.67255i
$446$	11.2419	−	5.90022i	0.532321	−	0.279383i
$447$	−0.872984	−	3.54183i	−0.0412907	−	0.167523i
$448$	−25.2713	+	3.06849i	−1.19395	+	0.144972i
$449$	4.98481	+	5.62668i	0.235248	+	0.265540i	0.854265	−	0.519838i	$-0.174008\pi$
$449$	4.98481	+	5.62668i	0.235248	+	0.265540i	−0.619018	+	0.785377i	$0.712469\pi$
$450$	0.218199	+	0.150612i	0.0102860	+	0.00709992i
$451$	−0.329177	−	0.476895i	−0.0155003	−	0.0224561i
$452$	10.2770	+	2.53304i	0.483388	+	0.119144i
$453$	17.5735	−	2.13381i	0.825674	−	0.100255i
$454$	19.3354	+	10.1480i	0.907454	+	0.476269i
$455$	24.1959	+	20.5476i	1.13432	+	0.963287i
$456$	−16.5199	+	8.67030i	−0.773614	+	0.406024i
$457$	4.67382	−	3.22610i	0.218632	−	0.150911i	−0.453715	−	0.891147i	$-0.649902\pi$
$457$	4.67382	−	3.22610i	0.218632	−	0.150911i	0.672347	+	0.740236i	$0.265286\pi$
$458$	−1.48409	−	2.15008i	−0.0693470	−	0.100467i
$459$	4.14858	+	3.67532i	0.193639	+	0.171549i
$460$	−5.61632	+	6.33951i	−0.261862	+	0.295581i
$461$	29.2596	−	11.0967i	1.36276	−	0.516825i	0.438546	−	0.898709i	$-0.355494\pi$
$461$	29.2596	−	11.0967i	1.36276	−	0.516825i	0.924210	+	0.381884i	$0.124724\pi$
$462$	−0.100253	−	0.191017i	−0.00466420	−	0.00888690i
$463$	−0.482895	+	0.183138i	−0.0224420	+	0.00851114i	−0.365800	−	0.930693i	$-0.619205\pi$
$463$	−0.482895	+	0.183138i	−0.0224420	+	0.00851114i	0.343358	+	0.939204i	$0.388435\pi$
$464$	−6.03391	+	1.48723i	−0.280117	+	0.0690427i
$465$	−12.2089	−	10.8161i	−0.566174	−	0.501586i
$466$	4.07863	+	2.81527i	0.188939	+	0.130415i
$467$	12.0141	−	31.6785i	0.555945	−	1.46591i	−0.302574	−	0.953126i	$-0.597846\pi$
$467$	12.0141	−	31.6785i	0.555945	−	1.46591i	0.858519	−	0.512782i	$-0.171385\pi$
$468$	−2.77824	+	2.56714i	−0.128424	+	0.118666i
$469$	4.90396	+	12.9307i	0.226444	+	0.597083i
$470$	−1.95481	+	7.93096i	−0.0901685	+	0.365828i
$471$	4.07236	+	2.13734i	0.187644	+	0.0984833i
$472$	−4.07016	+	10.7321i	−0.187344	+	0.493987i
$473$	0.0956954	+	0.0116195i	0.00440008	+	0.000534266i
$474$	−11.3121	+	7.80815i	−0.519580	+	0.358640i
$475$	−0.408298	−	1.65653i	−0.0187340	−	0.0760068i
$476$	5.33584	−	21.6483i	0.244568	−	0.992250i
$477$	−0.412642	+	3.39841i	−0.0188936	+	0.155603i
$478$	−5.03663	−	13.2805i	−0.230370	−	0.607436i
$479$	−4.48690	−	18.2041i	−0.205012	−	0.831764i	−0.979871	−	0.199631i	$-0.936026\pi$
$479$	−4.48690	−	18.2041i	−0.205012	−	0.831764i	0.774860	−	0.632133i	$-0.217821\pi$
$480$	11.5155	+	2.83832i	0.525610	+	0.129551i
$481$	24.1831	+	15.9552i	1.10266	+	0.727493i
$482$	17.9926	−	4.43478i	0.819542	−	0.201999i
$483$	−6.26523	−	11.9374i	−0.285078	−	0.543171i
$484$	11.5370			0.524408
$485$	7.98211			0.362449
$486$	−0.453163	−	0.863429i	−0.0205559	−	0.0391659i
$487$	6.31437	−	7.12745i	0.286131	−	0.322975i	−0.587817	−	0.808994i	$-0.700013\pi$
$487$	6.31437	−	7.12745i	0.286131	−	0.322975i	0.873949	+	0.486018i	$0.161551\pi$
$488$		−	36.9309i		−	1.67178i
$489$	10.1948	+	11.5076i	0.461026	+	0.520390i
$490$	15.2706	+	8.01462i	0.689854	+	0.362063i
$491$	0.558368	−	4.59858i	0.0251988	−	0.207531i	−0.974671	−	0.223642i	$-0.928205\pi$
$491$	0.558368	−	4.59858i	0.0251988	−	0.207531i	0.999870	+	0.0161109i	$0.00512850\pi$
$492$	−4.89679	+	9.33005i	−0.220764	+	0.420631i
$493$	5.18282	−	42.6844i	0.233423	−	1.92241i
$494$	−22.0567	+	0.462008i	−0.992376	+	0.0207867i
$495$	0.0159679	+	0.131507i	0.000717704	+	0.00591082i
$496$	5.32077	+	2.01790i	0.238910	+	0.0906065i
$497$	29.3647	−	15.4118i	1.31718	−	0.691312i
$498$	−1.15775	−	3.05274i	−0.0518800	−	0.136796i
$499$	3.26649	−	6.22378i	0.146228	−	0.278615i	−0.801315	−	0.598243i	$-0.795866\pi$
$499$	3.26649	−	6.22378i	0.146228	−	0.278615i	0.947543	+	0.319628i	$0.103558\pi$
$500$	5.29292	−	10.0848i	0.236707	−	0.451007i
$501$	4.72694	−	19.1779i	0.211184	−	0.856807i
$502$	14.0070	−	1.70076i	0.625164	−	0.0759087i
$503$	4.65419	−	4.12325i	0.207520	−	0.183847i	−0.552960	−	0.833208i	$-0.686502\pi$
$503$	4.65419	−	4.12325i	0.207520	−	0.183847i	0.760481	+	0.649361i	$0.224963\pi$
$504$	−6.47639	+	9.38267i	−0.288481	+	0.417938i
$505$	−4.37239	+	1.65823i	−0.194569	+	0.0737903i
$506$	0.197810			0.00879374
$507$	−12.4809	+	3.63692i	−0.554296	+	0.161521i
$508$	2.32408			0.103114
$509$	−1.36299	+	0.516913i	−0.0604134	+	0.0229118i	−0.384627	−	0.923072i	$-0.625670\pi$
$509$	−1.36299	+	0.516913i	−0.0604134	+	0.0229118i	0.324213	+	0.945984i	$0.394901\pi$
$510$	7.04924	−	10.2126i	0.312146	−	0.452221i
$511$	−30.3696	+	26.9051i	−1.34347	+	1.19021i
$512$	−8.83639	+	1.07293i	−0.390517	+	0.0474173i
$513$	−1.50167	+	6.09252i	−0.0663004	+	0.268991i
$514$	−5.27539	+	10.0514i	−0.232687	+	0.443349i
$515$	−15.5174	+	29.5658i	−0.683776	+	1.30283i
$516$	−0.621583	−	1.63898i	−0.0273637	−	0.0721521i
$517$	−0.186381	+	0.0978203i	−0.00819703	+	0.00430213i
$518$	28.0924	+	10.6540i	1.23431	+	0.468111i
$519$	−0.895329	−	7.37370i	−0.0393006	−	0.323669i
$520$	18.7620	+	15.9330i	0.822769	+	0.698709i
$521$	1.26690	−	10.4338i	0.0555038	−	0.457115i	−0.938288	−	0.345856i	$-0.887589\pi$
$521$	1.26690	−	10.4338i	0.0555038	−	0.457115i	0.993791	−	0.111259i	$-0.0354883\pi$
$522$	−3.51560	+	6.69842i	−0.153874	+	0.293182i
$523$	−2.18713	+	18.0126i	−0.0956366	+	0.787638i	0.863432	+	0.504465i	$0.168310\pi$
$523$	−2.18713	+	18.0126i	−0.0956366	+	0.787638i	−0.959069	+	0.283173i	$0.908613\pi$
$524$	0.650514	+	0.341416i	0.0284178	+	0.0149148i
$525$	−0.691346	−	0.780368i	−0.0301728	−	0.0340580i
$526$			8.99171i			0.392057i
$527$	−26.1090	+	29.4710i	−1.13733	+	1.28378i
$528$	−0.0214783	−	0.0409235i	−0.000934723	−	0.00178097i
$529$	−10.6380			−0.462523
$530$	7.66473			0.332935
$531$	1.79401	+	3.41820i	0.0778535	+	0.148337i
$532$	24.5091	−	6.04094i	1.06260	−	0.261908i
$533$	−29.3649	+	21.1906i	−1.27194	+	0.917867i
$534$	−14.6557	−	3.61230i	−0.634214	−	0.156320i
$535$	5.78815	+	23.4835i	0.250244	+	1.01528i
$536$	3.80263	+	10.0267i	0.164249	+	0.433088i
$537$	0.0781255	−	0.643421i	0.00337136	−	0.0277657i
$538$	3.58209	−	14.5331i	0.154435	−	0.626568i
$539$	0.106356	+	0.431503i	0.00458107	+	0.0185861i
$540$	1.98247	−	1.36840i	0.0853117	−	0.0588864i
$541$	10.3015	+	1.25083i	0.442896	+	0.0537773i	0.338947	−	0.940805i	$-0.389929\pi$
$541$	10.3015	+	1.25083i	0.442896	+	0.0537773i	0.103949	+	0.994583i	$0.466852\pi$
$542$	−2.74163	+	7.22908i	−0.117763	+	0.310515i
$543$	3.24642	+	1.70385i	0.139317	+	0.0731193i
$544$	6.85141	−	27.7973i	0.293752	−	1.19180i
$545$	2.44048	+	6.43502i	0.104539	+	0.275646i
$546$	−11.8032	+	6.51366i	−0.505132	+	0.278759i
$547$	−0.899526	+	2.37186i	−0.0384610	+	0.101413i	−0.952871	−	0.303376i	$-0.901886\pi$
$547$	−0.899526	+	2.37186i	−0.0384610	+	0.101413i	0.914410	+	0.404790i	$0.132655\pi$
$548$	−17.6398	−	12.1758i	−0.753533	−	0.520127i
$549$	−9.29718	−	8.23659i	−0.396794	−	0.351529i
$550$	0.0148525	−	0.00366082i	0.000633314	−	0.000156098i
$551$	45.5165	−	17.2621i	1.93907	−	0.735391i
$552$	−4.85819	−	9.25650i	−0.206778	−	0.393983i
$553$	50.5370	−	19.1661i	2.14905	−	0.815027i
$554$	−4.52325	+	5.10569i	−0.192174	+	0.216920i
$555$	−13.8099	−	12.2345i	−0.586199	−	0.519327i
$556$	8.72421	+	12.6392i	0.369989	+	0.536021i
$557$	−9.25443	+	6.38787i	−0.392123	+	0.270663i	−0.747770	−	0.663957i	$-0.768876\pi$
$557$	−9.25443	+	6.38787i	−0.392123	+	0.270663i	0.355648	+	0.934620i	$0.384260\pi$
$558$	6.13369	−	3.21921i	0.259660	−	0.136280i
$559$	0.600734	−	5.99412i	0.0254084	−	0.253524i
$560$	6.24467	+	3.27746i	0.263886	+	0.138498i
$561$	0.317445	−	0.0385448i	0.0134025	−	0.00162736i
$562$	−4.90343	−	1.20859i	−0.206839	−	0.0509812i
$563$	−2.81913	−	4.08421i	−0.118812	−	0.172129i	0.759065	−	0.651014i	$-0.225656\pi$
$563$	−2.81913	−	4.08421i	−0.118812	−	0.172129i	−0.877877	+	0.478886i	$0.841041\pi$
$564$	3.15001	+	2.17429i	0.132639	+	0.0915543i
$565$	−15.3610	−	17.3389i	−0.646240	−	0.729454i
$566$	−10.2695	+	1.24694i	−0.431659	+	0.0524129i
$567$	0.917636	+	3.72299i	0.0385371	+	0.156351i
$568$	22.7699	−	11.9506i	0.955406	−	0.501436i
$569$	−0.0482430	−	0.397317i	−0.00202245	−	0.0166564i	0.991663	−	0.128861i	$-0.0411320\pi$
$569$	−0.0482430	−	0.397317i	−0.00202245	−	0.0166564i	−0.993685	+	0.112204i	$0.964209\pi$
$570$	13.9466	+	1.69343i	0.584159	+	0.0709298i
$571$	20.2074	+	29.2755i	0.845655	+	1.22514i	0.972426	+	0.233211i	$0.0749231\pi$
$571$	20.2074	+	29.2755i	0.845655	+	1.22514i	−0.126771	+	0.991932i	$0.540461\pi$
$572$	0.00457049	+	0.218199i	0.000191102	+	0.00912335i
$573$	−1.09778	+	1.59040i	−0.0458603	+	0.0664401i
$574$	−24.9023	+	28.1088i	−1.03940	+	1.17324i
$575$	0.928195	−	0.228779i	0.0387084	−	0.00954076i
$576$	−3.77141	+	5.46383i	−0.157142	+	0.227660i
$577$		−	19.4376i		−	0.809199i	−0.914494	−	0.404600i	$-0.867411\pi$
$577$		−	19.4376i		−	0.809199i	0.914494	−	0.404600i	$-0.132589\pi$
$578$	−11.0094	−	7.59925i	−0.457931	−	0.316087i
$579$	12.2376	+	1.48591i	0.508575	+	0.0617522i
$580$	−17.4735	−	6.62681i	−0.725546	−	0.275163i
$581$	1.54749	+	12.7448i	0.0642008	+	0.528741i
$582$	−1.20209	+	3.16966i	−0.0498284	+	0.131387i
$583$	0.130976	+	0.147842i	0.00542449	+	0.00612298i
$584$	−23.5492	+	20.8627i	−0.974472	+	0.863307i
$585$	8.19551	−	1.16976i	0.338842	−	0.0483635i
$586$	−14.1071	−	12.4978i	−0.582761	−	0.516281i
$587$		−	34.8719i		−	1.43932i	−0.694329	−	0.719658i	$-0.744299\pi$
$587$		−	34.8719i		−	1.43932i	0.694329	−	0.719658i	$-0.255701\pi$
$588$	6.04887	−	5.35883i	0.249451	−	0.220994i
$589$	−43.2805	−	10.6677i	−1.78334	−	0.439554i
$590$	7.11321	−	4.90989i	0.292846	−	0.202137i
$591$	−9.95662	−	3.77605i	−0.409561	−	0.155326i
$592$	6.01852	+	2.28252i	0.247360	+	0.0938112i
$593$	−8.27060	+	5.70878i	−0.339633	+	0.234432i	−0.725656	−	0.688057i	$-0.758464\pi$
$593$	−8.27060	+	5.70878i	−0.339633	+	0.234432i	0.386024	+	0.922489i	$0.373848\pi$
$594$	−0.0546258	−	0.0134641i	−0.00224133	−	0.000552437i
$595$	−36.5243	+	32.3577i	−1.49735	+	1.32654i
$596$			3.82707i			0.156763i
$597$	18.5389	+	16.4240i	0.758746	+	0.672190i
$598$	−0.258875	−	12.3589i	−0.0105862	−	0.505393i
$599$	24.9646	−	22.1167i	1.02003	−	0.903664i	0.0246478	−	0.999696i	$-0.492154\pi$
$599$	24.9646	−	22.1167i	1.02003	−	0.903664i	0.995378	+	0.0960319i	$0.0306151\pi$
$600$	−0.536083	−	0.605113i	−0.0218855	−	0.0247036i
$601$	10.1338	−	26.7205i	0.413365	−	1.08995i	−0.553091	−	0.833121i	$-0.686552\pi$
$601$	10.1338	−	26.7205i	0.413365	−	1.08995i	0.966456	−	0.256832i	$-0.0826788\pi$
$602$	−0.753012	−	6.20161i	−0.0306905	−	0.252759i
$603$	3.37227	+	1.27893i	0.137329	+	0.0520822i
$604$	−18.4369	−	2.23865i	−0.750188	−	0.0910893i
$605$	−20.7795	−	14.3431i	−0.844808	−	0.583129i
$606$		−	1.98599i		−	0.0806752i
$607$	−17.4739	+	25.3152i	−0.709242	+	1.02751i	0.288307	+	0.957538i	$0.406908\pi$
$607$	−17.4739	+	25.3152i	−0.709242	+	1.02751i	−0.997549	+	0.0699760i	$0.977708\pi$
$608$	31.4706	−	7.75679i	1.27630	−	0.314580i
$609$	19.7260	−	22.2660i	0.799337	−	0.902265i
$610$	−15.7977	+	22.8869i	−0.639631	+	0.926665i
$611$	6.35559	+	11.5168i	0.257120	+	0.465920i
$612$	−3.30316	−	4.78546i	−0.133523	−	0.193441i
$613$	10.2825	+	1.24852i	0.415304	+	0.0504271i	0.325522	−	0.945534i	$-0.394460\pi$
$613$	10.2825	+	1.24852i	0.415304	+	0.0504271i	0.0897821	+	0.995961i	$0.471383\pi$
$614$	3.10388	+	25.5627i	0.125262	+	1.03163i
$615$	20.4191	−	10.7168i	0.823377	−	0.432142i
$616$	0.157417	+	0.638666i	0.00634251	+	0.0257326i
$617$	−0.247133	+	0.0300073i	−0.00994919	+	0.00120805i	−0.125510	−	0.992092i	$-0.540057\pi$
$617$	−0.247133	+	0.0300073i	−0.00994919	+	0.00120805i	0.115561	+	0.993300i	$0.463134\pi$
$618$	−9.40359	−	10.6145i	−0.378268	−	0.426976i
$619$	−13.2799	−	9.16642i	−0.533762	−	0.368429i	0.270485	−	0.962724i	$-0.412816\pi$
$619$	−13.2799	−	9.16642i	−0.533762	−	0.368429i	−0.804247	+	0.594295i	$0.797431\pi$
$620$	9.72091	+	14.0832i	0.390401	+	0.565594i
$621$	−3.41379	−	0.841424i	−0.136991	−	0.0337652i
$622$	−18.9796	+	2.30454i	−0.761013	+	0.0924037i
$623$	52.5557	+	27.5833i	2.10560	+	1.10510i
$624$	−2.52873	+	1.39549i	−0.101230	+	0.0558643i
$625$	−23.2747	+	12.2155i	−0.930988	+	0.488620i
$626$	3.25508	−	2.24682i	0.130099	−	0.0898009i
$627$	0.205659	+	0.297948i	0.00821321	+	0.0118989i
$628$	−3.61167	−	3.19966i	−0.144121	−	0.127680i
$629$	−29.5329	+	33.3357i	−1.17755	+	1.32918i
$630$	8.02715	−	3.04430i	0.319809	−	0.121288i
$631$	−20.4654	−	38.9936i	−0.814716	−	1.55231i	−0.833520	−	0.552489i	$-0.813678\pi$
$631$	−20.4654	−	38.9936i	−0.814716	−	1.55231i	0.0188035	−	0.999823i	$-0.494014\pi$
$632$	39.1874	−	14.8618i	1.55879	−	0.591171i
$633$	−0.145531	+	0.0358703i	−0.00578435	+	0.00142571i
$634$	−0.854727	−	0.757222i	−0.0339455	−	0.0300731i
$635$	−4.18596	−	2.88936i	−0.166115	−	0.114661i
$636$	1.27359	−	3.35818i	0.0505011	−	0.133160i
$637$	26.8205	−	7.20968i	1.06267	−	0.285658i
$638$	0.154773	+	0.408103i	0.00612752	+	0.0161569i
$639$	2.06981	−	8.39754i	0.0818803	−	0.332201i
$640$	−7.84150	−	4.11553i	−0.309962	−	0.162681i
$641$	−8.72359	+	23.0022i	−0.344561	+	0.908533i	0.644969	+	0.764209i	$0.276870\pi$
$641$	−8.72359	+	23.0022i	−0.344561	+	0.908533i	−0.989530	+	0.144325i	$0.953899\pi$
$642$	−10.1969	−	1.23812i	−0.402438	−	0.0488649i
$643$	6.36208	−	4.39143i	0.250896	−	0.173181i	−0.435979	−	0.899957i	$-0.643598\pi$
$643$	6.36208	−	4.39143i	0.250896	−	0.173181i	0.686874	+	0.726776i	$0.258982\pi$
$644$	3.38489	+	13.7330i	0.133383	+	0.541158i
$645$	−0.918075	+	3.72478i	−0.0361492	+	0.146663i
$646$	4.08775	−	33.6656i	0.160830	−	1.32456i
$647$	−3.22928	−	8.51491i	−0.126956	−	0.334756i	0.856435	−	0.516255i	$-0.172674\pi$
$647$	−3.22928	−	8.51491i	−0.126956	−	0.334756i	−0.983391	+	0.181499i	$0.941905\pi$
$648$	0.711553	+	2.88688i	0.0279524	+	0.113408i
$649$	0.216257	+	0.0533025i	0.00848881	+	0.00209230i
$650$	−0.248160	−	0.923174i	−0.00973365	−	0.0362099i
$651$	−26.4477	+	6.51876i	−1.03657	+	0.255491i
$652$	−7.49567	−	14.2818i	−0.293553	−	0.559319i
$653$	−24.1099			−0.943492			−0.471746	−	0.881735i	$-0.656376\pi$
$653$	−24.1099			−0.943492			−0.471746	+	0.881735i	$0.656376\pi$
$654$	−2.92285			−0.114293
$655$	−0.747199	−	1.42367i	−0.0291955	−	0.0556274i
$656$	−5.33507	+	6.02205i	−0.208300	+	0.235122i
$657$			10.5814i			0.412818i
$658$	9.04570	+	10.2105i	0.352638	+	0.398046i
$659$	−15.6868	−	8.23309i	−0.611072	−	0.320715i	0.130644	−	0.991429i	$-0.458296\pi$
$659$	−15.6868	−	8.23309i	−0.611072	−	0.320715i	−0.741716	+	0.670714i	$0.765988\pi$
$660$	0.0167525	−	0.137969i	0.000652089	−	0.00537043i
$661$	4.75390	−	9.05780i	0.184905	−	0.352308i	−0.775304	−	0.631588i	$-0.782404\pi$
$661$	4.75390	−	9.05780i	0.184905	−	0.352308i	0.960210	+	0.279280i	$0.0900958\pi$
$662$	−3.34521	+	27.5503i	−0.130015	+	1.07077i
$663$	−2.82367	−	19.7831i	−0.109662	−	0.768311i
$664$	1.19996	+	9.88254i	0.0465674	+	0.383517i
$665$	−51.6542	−	19.5898i	−2.00306	−	0.759662i
$666$	6.93805	−	3.64137i	0.268844	−	0.141100i
$667$	9.67240	+	25.5040i	0.374517	+	0.987519i
$668$	−9.63017	+	18.3488i	−0.372602	+	0.709935i
$669$	−6.05074	+	11.5287i	−0.233935	+	0.445726i
$670$	1.93249	−	7.84042i	0.0746586	−	0.302902i
$671$	−0.711411	+	0.0863809i	−0.0274637	+	0.00333470i
$672$	14.8253	−	13.1341i	0.571900	−	0.506659i
$673$	16.9004	−	24.4844i	0.651462	−	0.943806i	−0.348517	−	0.937302i	$-0.613315\pi$
$673$	16.9004	−	24.4844i	0.651462	−	0.943806i	0.999979	−	0.00650303i	$-0.00206999\pi$
$674$	−12.1052	+	4.59091i	−0.466276	+	0.176835i
$675$	−0.271896			−0.0104653
$676$	13.6268	−	0.571115i	0.524107	−	0.0219660i
$677$	−30.9113			−1.18802			−0.594009	−	0.804459i	$-0.702455\pi$
$677$	−30.9113			−1.18802			−0.594009	+	0.804459i	$0.702455\pi$
$678$	9.19856	−	3.48855i	0.353269	−	0.133977i
$679$	7.57236	−	10.9705i	0.290600	−	0.421007i
$680$	−28.3217	+	25.0908i	−1.08609	+	0.962189i
$681$	−22.2304	+	2.69926i	−0.851872	+	0.103436i
$682$	0.0956469	−	0.388055i	0.00366251	−	0.0148594i
$683$	−11.9913	+	22.8474i	−0.458833	+	0.874233i	0.540623	+	0.841265i	$0.318188\pi$
$683$	−11.9913	+	22.8474i	−0.458833	+	0.874233i	−0.999456	+	0.0329685i	$0.989504\pi$
$684$	3.05935	−	5.82910i	0.116977	−	0.222881i
$685$	16.6341	+	43.8605i	0.635555	+	1.67582i
$686$	2.32659	−	1.22109i	0.0888298	−	0.0466215i
$687$	2.50508	+	0.950053i	0.0955749	+	0.0362468i
$688$	−0.161326	−	1.32864i	−0.00615048	−	0.0506538i
$689$	9.06554	−	8.37670i	0.345369	−	0.319127i
$690$	−0.948869	+	7.81464i	−0.0361228	+	0.297498i
$691$	−9.52643	+	18.1511i	−0.362402	+	0.690500i	−0.996575	−	0.0826912i	$-0.973648\pi$
$691$	−9.52643	+	18.1511i	−0.362402	+	0.690500i	0.634173	+	0.773191i	$0.281341\pi$
$692$	−0.939320	+	7.73599i	−0.0357076	+	0.294078i
$693$	0.195890	+	0.102811i	0.00744123	+	0.00390546i
$694$	−18.2902	−	20.6454i	−0.694287	−	0.783688i
$695$		−	33.6109i		−	1.27494i
$696$	15.2959	−	17.2655i	0.579790	−	0.654448i
$697$	−25.8691	−	49.2895i	−0.979863	−	1.86697i
$698$	5.02108			0.190051
$699$	−5.08233			−0.192231
$700$	0.508307	+	0.968499i	0.0192122	+	0.0366058i
$701$	13.9685	−	3.44293i	0.527584	−	0.130038i	0.0334781	−	0.999439i	$-0.489342\pi$
$701$	13.9685	−	3.44293i	0.527584	−	0.130038i	0.494106	+	0.869402i	$0.335495\pi$
$702$	−0.769727	+	3.43057i	−0.0290515	+	0.129478i
$703$	−48.9562	−	12.0666i	−1.84642	−	0.455101i
$704$	0.0916689	+	0.371915i	0.00345490	+	0.0140171i
$705$	−2.97042	−	7.83235i	−0.111872	−	0.294983i
$706$	2.73389	−	22.5156i	0.102891	−	0.847386i
$707$	−1.86890	+	7.58244i	−0.0702874	+	0.285167i
$708$	−0.969243	−	3.93237i	−0.0364264	−	0.147788i
$709$	28.4162	−	19.6143i	1.06719	−	0.736631i	0.101115	−	0.994875i	$-0.467759\pi$
$709$	28.4162	−	19.6143i	1.06719	−	0.736631i	0.966080	+	0.258244i	$0.0831437\pi$
$710$	−19.2231	−	2.33411i	−0.721431	−	0.0875975i
$711$	4.99845	−	13.1798i	0.187457	−	0.494282i
$712$	40.7527	+	21.3887i	1.52727	+	0.801574i
$713$	5.97737	−	24.2511i	0.223854	−	0.908212i
$714$	−7.34861	−	19.3767i	−0.275015	−	0.725154i
$715$	0.263039	−	0.398686i	0.00983709	−	0.0149100i
$716$	−0.241129	+	0.635804i	−0.00901140	+	0.0237611i
$717$	11.9875	+	8.27434i	0.447680	+	0.309011i
$718$	−14.8180	−	13.1276i	−0.553002	−	0.489917i
$719$	40.8372	−	10.0655i	1.52297	−	0.375379i	0.613011	−	0.790074i	$-0.289958\pi$
$719$	40.8372	−	10.0655i	1.52297	−	0.375379i	0.909960	+	0.414695i	$0.136112\pi$
$720$	1.71974	−	0.652211i	0.0640909	−	0.0243065i
$721$	25.9139	+	49.3749i	0.965086	+	1.83882i
$722$	18.5760	−	7.04493i	0.691326	−	0.262185i
$723$	−12.6019	+	14.2246i	−0.468669	+	0.529018i
$724$	−2.87916	−	2.55072i	−0.107003	−	0.0947966i
$725$	1.19825	+	1.73596i	0.0445017	+	0.0644719i
$726$	8.82495	−	6.09142i	0.327525	−	0.226074i
$727$	−6.45083	+	3.38566i	−0.239248	+	0.125567i	−0.580087	−	0.814555i	$-0.696981\pi$
$727$	−6.45083	+	3.38566i	−0.239248	+	0.125567i	0.340839	+	0.940122i	$0.389289\pi$
$728$	39.6969	−	10.6710i	1.47127	−	0.395494i
$729$	0.885456	+	0.464723i	0.0327947	+	0.0172120i
$730$	23.5183	−	2.85564i	0.870453	−	0.105692i
$731$	8.99122	+	2.21614i	0.332552	+	0.0819667i
$732$	7.40256	+	10.7245i	0.273607	+	0.396388i
$733$	−20.1047	−	13.8772i	−0.742583	−	0.512568i	0.135676	−	0.990753i	$-0.456679\pi$
$733$	−20.1047	−	13.8772i	−0.742583	−	0.512568i	−0.878259	+	0.478185i	$0.841295\pi$
$734$	−13.2966	−	15.0087i	−0.490785	−	0.553982i
$735$	−17.5570	+	2.13181i	−0.647600	+	0.0786329i
$736$	4.34633	+	17.6337i	0.160208	+	0.649988i
$737$	0.184253	−	0.0967036i	0.00678706	−	0.00356212i
$738$	1.18050	+	9.72227i	0.0434547	+	0.357882i
$739$	33.9840	+	4.12641i	1.25012	+	0.151792i	0.718703	−	0.695317i	$-0.244736\pi$
$739$	33.9840	+	4.12641i	1.25012	+	0.151792i	0.531419	+	0.847109i	$0.321659\pi$
$740$	10.9957	+	15.9300i	0.404210	+	0.585599i
$741$	18.3462	−	13.2392i	0.673965	−	0.486353i
$742$	7.27128	−	10.5343i	0.266937	−	0.386725i
$743$	9.97400	−	11.2583i	0.365911	−	0.413028i	−0.536503	−	0.843898i	$-0.680255\pi$
$743$	9.97400	−	11.2583i	0.365911	−	0.413028i	0.902414	+	0.430871i	$0.141794\pi$
$744$	−20.5081	+	5.05478i	−0.751862	+	0.185317i
$745$	4.75791	−	6.89302i	0.174316	−	0.252541i
$746$			33.7629i			1.23615i
$747$	2.75551	+	1.90199i	0.100819	+	0.0695902i
$748$	−0.333042	−	0.0404387i	−0.0121772	−	0.00147858i
$749$	37.7662	+	14.3228i	1.37995	+	0.523345i
$750$	−1.27600	−	10.5088i	−0.0465928	−	0.383726i
$751$	15.5664	−	41.0452i	0.568025	−	1.49776i	−0.275840	−	0.961204i	$-0.588956\pi$
$751$	15.5664	−	41.0452i	0.568025	−	1.49776i	0.843865	−	0.536556i	$-0.180275\pi$
$752$	1.93795	+	2.18750i	0.0706699	+	0.0797699i
$753$	−10.8308	+	9.59529i	−0.394698	+	0.349672i
$754$	25.2951	−	10.2041i	0.921195	−	0.371611i
$755$	30.4241	+	26.9534i	1.10724	+	0.980933i
$756$		−	4.02281i		−	0.146308i
$757$	1.29055	−	1.14332i	0.0469057	−	0.0415548i	−0.639344	−	0.768921i	$-0.720794\pi$
$757$	1.29055	−	1.14332i	0.0469057	−	0.0415548i	0.686250	+	0.727366i	$0.259256\pi$
$758$	−2.90444	−	0.715880i	−0.105494	−	0.0260019i
$759$	−0.166948	+	0.115236i	−0.00605981	+	0.00418279i
$760$	−40.0537	−	15.1904i	−1.45290	−	0.551012i
$761$	25.7556	+	9.76781i	0.933640	+	0.354083i	0.774067	−	0.633103i	$-0.218219\pi$
$761$	25.7556	+	9.76781i	0.933640	+	0.354083i	0.159572	+	0.987186i	$0.448988\pi$
$762$	1.77775	−	1.22709i	0.0644012	−	0.0444529i
$763$	11.1594	+	2.75054i	0.403996	+	0.0995761i
$764$	1.51756	−	1.34444i	0.0549033	−	0.0486401i
$765$			12.7258i			0.460102i
$766$	26.6990	+	23.6533i	0.964675	+	0.854628i
$767$	3.04725	−	13.5812i	0.110030	−	0.490387i
$768$	12.7540	−	11.2990i	0.460219	−	0.407719i
$769$	−0.508884	−	0.574411i	−0.0183508	−	0.0207138i	0.739264	−	0.673416i	$-0.235174\pi$
$769$	−0.508884	−	0.574411i	−0.0183508	−	0.0207138i	−0.757615	+	0.652702i	$0.773635\pi$
$770$	0.175644	−	0.463134i	0.00632975	−	0.0166902i
$771$	−1.40320	−	11.5564i	−0.0505350	−	0.416193i
$772$	−12.0927	−	4.58615i	−0.435225	−	0.165059i
$773$	−2.01501	−	0.244666i	−0.0724748	−	0.00880003i	0.0842190	−	0.996447i	$-0.473160\pi$
$773$	−2.01501	−	0.244666i	−0.0724748	−	0.00880003i	−0.156694	+	0.987647i	$0.550084\pi$
$774$	−1.34083	−	0.925510i	−0.0481953	−	0.0332668i
$775$		−	1.93151i		−	0.0693819i
$776$	5.87176	−	8.50671i	0.210784	−	0.305373i
$777$	−29.9159	+	7.37362i	−1.07323	+	0.264527i
$778$	19.1998	−	21.6721i	0.688347	−	0.776984i
$779$	35.8004	−	51.8658i	1.28268	−	1.85829i
$780$	−8.64203	−	0.866110i	−0.309434	−	0.0310117i
$781$	−0.283467	−	0.410672i	−0.0101432	−	0.0146950i
$782$	18.8637	+	2.29047i	0.674565	+	0.0819070i
$783$	−0.935115	−	7.70136i	−0.0334183	−	0.275224i
$784$	5.46352	−	2.86748i	0.195126	−	0.102410i
$785$	2.52716	+	10.2531i	0.0901984	+	0.365949i
$786$	0.677861	−	0.0823072i	0.0241785	−	0.00293580i
$787$	20.5250	+	23.1679i	0.731637	+	0.825847i	0.990128	−	0.140167i	$-0.0447638\pi$
$787$	20.5250	+	23.1679i	0.731637	+	0.825847i	−0.258491	+	0.966014i	$0.583225\pi$
$788$	9.19422	+	6.34631i	0.327531	+	0.226078i
$789$	−5.23818	−	7.58882i	−0.186484	−	0.270169i
$790$	−30.6427	−	7.55275i	−1.09022	−	0.268715i
$791$	−38.4027	+	4.66293i	−1.36544	+	0.165795i
$792$	0.151897	+	0.0797215i	0.00539741	+	0.00283278i
$793$	6.32798	+	44.3349i	0.224713	+	1.57438i
$794$	26.2288	−	13.7660i	0.930826	−	0.488535i
$795$	−6.46887	+	4.46514i	−0.229427	+	0.158362i
$796$	−14.7609	−	21.3849i	−0.523188	−	0.757968i
$797$	−29.8665	−	26.4594i	−1.05793	−	0.937241i	−0.0597869	−	0.998211i	$-0.519042\pi$
$797$	−29.8665	−	26.4594i	−1.05793	−	0.937241i	−0.998140	+	0.0609701i	$0.980581\pi$
$798$	15.5581	−	17.5615i	0.550751	−	0.621669i
$799$	−18.9065	+	7.17027i	−0.668862	+	0.253666i
$800$	0.652685	+	1.24359i	0.0230759	+	0.0439675i
$801$	14.4735	−	5.48906i	0.511395	−	0.193946i
$802$	6.38368	−	1.57343i	0.225415	−	0.0555599i
$803$	0.456967	+	0.404837i	0.0161260	+	0.0142864i
$804$	−3.11405	−	2.14947i	−0.109824	−	0.0758060i
$805$	10.9767	−	28.9431i	0.386877	−	1.02011i
$806$	−24.3703	−	5.46804i	−0.858407	−	0.192603i
$807$	5.44316	+	14.3524i	0.191608	+	0.505229i
$808$	−1.44919	+	5.87958i	−0.0509822	+	0.206843i
$809$	−1.07254	−	0.562910i	−0.0377083	−	0.0197909i	0.445764	−	0.895151i	$-0.352932\pi$
$809$	−1.07254	−	0.562910i	−0.0377083	−	0.0197909i	−0.483472	+	0.875360i	$0.660624\pi$
$810$	0.793940	−	2.09345i	0.0278962	−	0.0735563i
$811$	−2.62674	−	0.318944i	−0.0922374	−	0.0111996i	0.0742878	−	0.997237i	$-0.476332\pi$
$811$	−2.62674	−	0.318944i	−0.0922374	−	0.0111996i	−0.166525	+	0.986037i	$0.553255\pi$
$812$	−25.6843	+	17.7286i	−0.901341	+	0.622150i
$813$	−1.89747	−	7.69834i	−0.0665472	−	0.269993i
$814$	0.108190	−	0.438943i	0.00379205	−	0.0153850i
$815$	−4.25489	+	35.0422i	−0.149042	+	1.22747i
$816$	−1.57437	−	4.15127i	−0.0551139	−	0.145324i
$817$	2.50899	+	10.1794i	0.0877784	+	0.356131i
$818$	−36.0088	−	8.87536i	−1.25902	−	0.310320i
$819$	6.16711	−	12.3735i	0.215496	−	0.432363i
$820$	−23.4906	+	5.78991i	−0.820326	+	0.202192i
$821$	−18.5411	−	35.3272i	−0.647090	−	1.23293i	−0.959159	−	0.282868i	$-0.908714\pi$
$821$	−18.5411	−	35.3272i	−0.647090	−	1.23293i	0.312069	−	0.950060i	$-0.398978\pi$
$822$	−19.9219			−0.694855
$823$	13.6249			0.474935			0.237467	−	0.971395i	$-0.423683\pi$
$823$	13.6249			0.474935			0.237467	+	0.971395i	$0.423683\pi$
$824$	20.0942	+	38.2863i	0.700014	+	1.33377i
$825$	−0.0104026	+	0.0117421i	−0.000362172	+	0.000408807i
$826$		−	14.4341i		−	0.502227i
$827$	6.21417	+	7.01435i	0.216088	+	0.243913i	0.846553	−	0.532305i	$-0.178674\pi$
$827$	6.21417	+	7.01435i	0.216088	+	0.243913i	−0.630465	+	0.776218i	$0.717136\pi$
$828$	3.26619	+	1.71423i	0.113508	+	0.0595736i
$829$	−0.300422	+	2.47420i	−0.0104341	+	0.0859324i	−0.996996	−	0.0774575i	$-0.975320\pi$
$829$	−0.300422	+	2.47420i	−0.0104341	+	0.0859324i	0.986562	+	0.163390i	$0.0522429\pi$
$830$	3.48376	−	6.63774i	0.120923	−	0.230399i
$831$	0.843172	−	6.94414i	0.0292493	−	0.240890i
$832$	23.1168	−	6.21407i	0.801430	−	0.215434i
$833$	5.14596	+	42.3808i	0.178297	+	1.46841i
$834$	13.3468	+	5.06176i	0.462161	+	0.175275i
$835$	40.1568	−	21.0759i	1.38968	−	0.729362i
$836$	−0.134687	−	0.355139i	−0.00465823	−	0.0122828i
$837$	−3.30133	+	6.29016i	−0.114111	+	0.217420i
$838$	9.15158	−	17.4369i	0.316136	−	0.602347i
$839$	−0.301381	+	1.22275i	−0.0104048	+	0.0422140i	−0.975915	−	0.218152i	$-0.929997\pi$
$839$	−0.301381	+	1.22275i	−0.0104048	+	0.0422140i	0.965510	+	0.260366i	$0.0838433\pi$
$840$	−25.9861	+	3.15528i	−0.896605	+	0.108868i
$841$	−23.3426	+	20.6798i	−0.804918	+	0.713095i
$842$	22.5933	−	32.7320i	0.778615	−	1.12802i
$843$	4.84246	−	1.83650i	0.166783	−	0.0632526i
$844$	0.157251			0.00541281
$845$	−25.2536	−	15.9125i	−0.868749	−	0.547407i
$846$	3.55754			0.122311
$847$	−39.4257	+	14.9522i	−1.35468	+	0.513764i
$848$	1.55780	−	2.25686i	0.0534951	−	0.0775011i
$849$	7.94082	−	7.03496i	0.272528	−	0.241439i
$850$	1.45877	−	0.177126i	0.0500352	−	0.00607538i
$851$	6.76122	−	27.4314i	0.231772	−	0.940335i
$852$	−4.21681	+	8.03446i	−0.144465	+	0.275256i
$853$	−16.4107	+	31.2679i	−0.561890	+	1.07059i	0.424385	+	0.905482i	$0.360490\pi$
$853$	−16.4107	+	31.2679i	−0.561890	+	1.07059i	−0.986275	+	0.165111i	$0.947202\pi$
$854$	16.4686	+	43.4242i	0.563544	+	1.48594i
$855$	−12.7572	+	6.69548i	−0.436286	+	0.228980i
$856$	29.2847	+	11.1062i	1.00093	+	0.379603i
$857$	−1.84975	−	15.2340i	−0.0631862	−	0.520385i	−0.989597	−	0.143870i	$-0.954045\pi$
$857$	−1.84975	−	15.2340i	−0.0631862	−	0.520385i	0.926410	−	0.376515i	$-0.122878\pi$
$858$	0.118703	+	0.164493i	0.00405246	+	0.00561570i
$859$	−5.25129	+	43.2483i	−0.179172	+	1.47561i	0.574577	+	0.818450i	$0.305167\pi$
$859$	−5.25129	+	43.2483i	−0.179172	+	1.47561i	−0.753749	+	0.657162i	$0.771757\pi$
$860$	1.87039	−	3.56373i	0.0637798	−	0.121522i
$861$	4.64199	−	38.2303i	0.158199	−	1.30288i
$862$	−0.190132	−	0.0997888i	−0.00647591	−	0.00339882i
$863$	−3.82858	−	4.32157i	−0.130326	−	0.147108i	0.679725	−	0.733467i	$-0.262099\pi$
$863$	−3.82858	−	4.32157i	−0.130326	−	0.147108i	−0.810051	+	0.586359i	$0.800561\pi$
$864$		−	5.16544i		−	0.175732i
$865$	11.3094	−	12.7657i	0.384532	−	0.434047i
$866$	7.27288	+	13.8573i	0.247143	+	0.470891i
$867$	13.7187			0.465912
$868$	28.5775			0.969985
$869$	−0.377946	−	0.720117i	−0.0128210	−	0.0244283i
$870$	−16.8648	+	4.15681i	−0.571771	+	0.140929i
$871$	−6.28304	−	11.3853i	−0.212893	−	0.385777i
$872$	8.65319	+	2.13282i	0.293034	+	0.0722264i
$873$	−0.831965	−	3.37542i	−0.0281578	−	0.114241i
$874$	7.62872	+	20.1153i	0.258045	+	0.680410i
$875$	−5.01752	+	41.3230i	−0.169623	+	1.39697i
$876$	2.65671	−	10.7787i	0.0897618	−	0.364178i
$877$	8.25185	+	33.4791i	0.278645	+	1.13051i	0.928763	+	0.370675i	$0.120874\pi$
$877$	8.25185	+	33.4791i	0.278645	+	1.13051i	−0.650117	+	0.759834i	$0.725280\pi$
$878$	23.6797	−	16.3449i	0.799150	−	0.551613i
$879$	19.1868	+	2.32970i	0.647156	+	0.0785789i
$880$	0.0376299	−	0.0992220i	0.00126851	−	0.00334477i
$881$	−11.2543	−	5.90671i	−0.379167	−	0.199002i	0.264363	−	0.964423i	$-0.414838\pi$
$881$	−11.2543	−	5.90671i	−0.379167	−	0.199002i	−0.643530	+	0.765421i	$0.722531\pi$
$882$	1.79753	−	7.29287i	0.0605260	−	0.245564i
$883$	−20.3580	−	53.6797i	−0.685102	−	1.80647i	−0.584264	−	0.811564i	$-0.698617\pi$
$883$	−20.3580	−	53.6797i	−0.685102	−	1.80647i	−0.100839	−	0.994903i	$-0.532153\pi$
$884$	−2.09070	+	20.8609i	−0.0703177	+	0.701629i
$885$	−3.14311	+	8.28769i	−0.105654	+	0.278588i
$886$	−29.7888	−	20.5617i	−1.00077	−	0.690784i
$887$	−9.87765	−	8.75084i	−0.331659	−	0.293824i	0.480814	−	0.876822i	$-0.340341\pi$
$887$	−9.87765	−	8.75084i	−0.331659	−	0.293824i	−0.812474	+	0.582998i	$0.801880\pi$
$888$	−23.1974	+	5.71765i	−0.778455	+	0.191872i
$889$	−7.94216	+	3.01206i	−0.266371	+	0.101021i
$890$	−16.1061	−	30.6876i	−0.539878	−	1.02865i
$891$	0.0539466	−	0.0204593i	0.00180728	−	0.000685411i
$892$	9.05813	−	10.2245i	0.303289	−	0.342342i
$893$	−17.1353	−	15.1805i	−0.573410	−	0.507997i
$894$	2.02066	+	2.92743i	0.0675809	+	0.0979078i
$895$	1.22475	−	0.845385i	0.0409389	−	0.0282581i
$896$	−13.0953	+	6.87293i	−0.437482	+	0.229609i
$897$	7.41824	+	10.2798i	0.247688	+	0.343234i
$898$	−6.49054	−	3.40650i	−0.216592	−	0.113676i
$899$	54.7095	−	6.64293i	1.82466	−	0.221554i
$900$	0.276966	+	0.0682660i	0.00923220	+	0.00227553i
$901$	10.7784	+	15.6152i	0.359080	+	0.520217i
$902$	0.465032	+	0.320988i	0.0154839	+	0.0106877i
$903$	4.24832	+	4.79536i	0.141375	+	0.159579i
$904$	−29.7782	+	3.61573i	−0.990409	+	0.120257i
$905$	2.01461	+	8.17361i	0.0669681	+	0.271700i
$906$	−15.2849	+	8.02213i	−0.507806	+	0.266517i
$907$	−2.65394	−	21.8572i	−0.0881228	−	0.725756i	−0.968069	−	0.250683i	$-0.919345\pi$
$907$	−2.65394	−	21.8572i	−0.0881228	−	0.725756i	0.879946	−	0.475073i	$-0.157578\pi$
$908$	23.3227	+	2.83189i	0.773990	+	0.0939795i
$909$	1.15695	+	1.67613i	0.0383736	+	0.0555938i
$910$	−29.1658	−	10.3679i	−0.966838	−	0.343691i
$911$	−18.3870	+	26.6382i	−0.609188	+	0.882562i	−0.999269	−	0.0382188i	$-0.987832\pi$
$911$	−18.3870	+	26.6382i	−0.609188	+	0.882562i	0.390081	+	0.920781i	$0.372447\pi$
$912$	3.33317	−	3.76237i	0.110372	−	0.124585i
$913$	0.187564	−	0.0462303i	0.00620745	−	0.00153000i
$914$	−3.14585	+	4.55755i	−0.104055	+	0.150750i
$915$		−	28.5192i		−	0.942814i
$916$	−2.31326	−	1.59673i	−0.0764324	−	0.0527575i
$917$	−2.66551	−	0.323651i	−0.0880228	−	0.0106879i
$918$	−5.05336	−	1.91649i	−0.166786	−	0.0632535i
$919$	−2.85191	−	23.4876i	−0.0940757	−	0.774783i	−0.961039	−	0.276412i	$-0.910855\pi$
$919$	−2.85191	−	23.4876i	−0.0940757	−	0.774783i	0.866964	−	0.498371i	$-0.166068\pi$
$920$	8.51154	−	22.4431i	0.280617	−	0.739926i
$921$	−17.5113	−	19.7662i	−0.577018	−	0.651319i
$922$	−22.8406	+	20.2350i	−0.752215	+	0.666404i
$923$	−25.2872	+	18.2480i	−0.832340	+	0.600641i
$924$	−0.173729	−	0.153911i	−0.00571528	−	0.00506329i
$925$		−	2.18480i		−	0.0718359i
$926$	0.376957	−	0.333955i	0.0123876	−	0.0109744i
$927$	14.1200	+	3.48026i	0.463760	+	0.114307i
$928$	−32.9795	+	22.7641i	−1.08261	+	0.747269i
$929$	6.94239	+	2.63290i	0.227772	+	0.0863827i	0.465851	−	0.884863i	$-0.345748\pi$
$929$	6.94239	+	2.63290i	0.227772	+	0.0863827i	−0.238078	+	0.971246i	$0.576518\pi$
$930$	14.8716	+	5.64005i	0.487659	+	0.184944i
$931$	−39.7778	+	27.4566i	−1.30366	+	0.899854i
$932$	5.17711	+	1.27604i	0.169582	+	0.0417981i
$933$	14.6759	−	13.0017i	0.480466	−	0.425656i
$934$			33.0374i			1.08102i
$935$	0.549576	+	0.486882i	0.0179731	+	0.0159228i
$936$	4.78210	−	9.59462i	0.156308	−	0.313610i
$937$	23.2291	−	20.5792i	0.758861	−	0.672292i	−0.192179	−	0.981360i	$-0.561556\pi$
$937$	23.2291	−	20.5792i	0.758861	−	0.672292i	0.951040	+	0.309068i	$0.100017\pi$
$938$	−8.94244	−	10.0939i	−0.291981	−	0.329578i
$939$	−1.43832	+	3.79253i	−0.0469377	+	0.123765i
$940$	1.05931	+	8.72420i	0.0345509	+	0.284552i
$941$	−43.6385	−	16.5499i	−1.42257	−	0.539511i	−0.481121	−	0.876654i	$-0.659770\pi$
$941$	−43.6385	−	16.5499i	−1.42257	−	0.539511i	−0.941454	+	0.337143i	$0.890540\pi$
$942$	−4.45206	−	0.540577i	−0.145056	−	0.0176130i
$943$	29.0617	+	20.0599i	0.946380	+	0.653239i
$944$		−	3.09237i		−	0.100648i
$945$	−5.00127	+	7.24559i	−0.162691	+	0.235699i
$946$	−0.0912687	+	0.0224957i	−0.00296740	+	0.000731399i
$947$	−9.34488	+	10.5482i	−0.303668	+	0.342770i	−0.880460	−	0.474121i	$-0.842766\pi$
$947$	−9.34488	+	10.5482i	−0.303668	+	0.342770i	0.576792	+	0.816891i	$0.304304\pi$
$948$	−8.40078	+	12.1706i	−0.272845	+	0.395284i
$949$	24.6956	−	29.0805i	0.801654	−	0.943992i
$950$	0.945069	+	1.36917i	0.0306621	+	0.0444217i
$951$	1.16250	+	0.141153i	0.0376965	+	0.00457718i
$952$	7.61651	+	62.7276i	0.246853	+	2.03301i
$953$	33.0606	−	17.3515i	1.07094	−	0.562071i	0.165351	−	0.986235i	$-0.447124\pi$
$953$	33.0606	−	17.3515i	1.07094	−	0.562071i	0.905585	+	0.424164i	$0.139432\pi$
$954$	−0.798886	−	3.24121i	−0.0258649	−	0.104938i
$955$	−4.40475	+	0.534834i	−0.142534	+	0.0173068i
$956$	−10.1335	−	11.4384i	−0.327741	−	0.369944i
$957$	−0.368368	−	0.254266i	−0.0119077	−	0.00821926i
$958$	10.3856	+	15.0462i	0.335544	+	0.486120i
$959$	76.0612	+	18.7474i	2.45614	+	0.605385i
$960$	−15.1325	+	1.83742i	−0.488400	+	0.0593025i
$961$	−17.2354	−	9.04582i	−0.555980	−	0.291801i
$962$	−27.5662	−	6.18510i	−0.888769	−	0.199416i
$963$	9.32722	−	4.89530i	0.300566	−	0.157749i
$964$	16.4083	−	11.3258i	0.528476	−	0.364781i
$965$	16.0788	+	23.2942i	0.517595	+	0.749866i
$966$	9.84013	+	8.71759i	0.316601	+	0.280484i
$967$	8.87326	−	10.0158i	0.285345	−	0.322088i	−0.588309	−	0.808637i	$-0.700206\pi$
$967$	8.87326	−	10.0158i	0.285345	−	0.322088i	0.873653	+	0.486549i	$0.161744\pi$
$968$	−30.5715	+	11.5942i	−0.982605	+	0.372653i
$969$	16.1622	+	30.7944i	0.519204	+	0.989260i
$970$	−7.27774	+	2.76008i	−0.233674	+	0.0886209i
$971$	30.0183	−	7.39886i	0.963334	−	0.237441i	0.273875	−	0.961765i	$-0.411694\pi$
$971$	30.0183	−	7.39886i	0.963334	−	0.237441i	0.689459	+	0.724325i	$0.257848\pi$
$972$	−0.785288	−	0.695704i	−0.0251881	−	0.0223147i
$973$	−46.1942	−	31.8856i	−1.48092	−	1.02220i
$974$	−3.29261	+	8.68190i	−0.105502	+	0.278186i
$975$	0.747243	+	0.634572i	0.0239309	+	0.0203226i
$976$	3.52824	+	9.30321i	0.112936	+	0.297788i
$977$	−2.07477	+	8.41766i	−0.0663777	+	0.269305i	−0.994748	−	0.102351i	$-0.967364\pi$
$977$	−2.07477	+	8.41766i	−0.0663777	+	0.269305i	0.928371	+	0.371656i	$0.121210\pi$
$978$	−13.2743	−	6.96690i	−0.424466	−	0.222777i
$979$	0.316696	−	0.835060i	0.0101217	−	0.0266886i
$980$	18.4197	+	2.23655i	0.588394	+	0.0714440i
$981$	2.46683	−	1.70273i	0.0787597	−	0.0543639i
$982$	1.08102	+	4.38586i	0.0344966	+	0.139958i
$983$	10.6212	−	43.0920i	0.338764	−	1.37442i	−0.516526	−	0.856272i	$-0.672775\pi$
$983$	10.6212	−	43.0920i	0.338764	−	1.37442i	0.855290	−	0.518150i	$-0.173379\pi$
$984$	3.59949	−	29.6445i	0.114748	−	0.945032i
$985$	−8.67004	−	22.8610i	−0.276250	−	0.728412i
$986$	10.0341	+	40.7099i	0.319551	+	1.29647i
$987$	−13.5826	−	3.34780i	−0.432338	−	0.106562i
$988$	−22.0123	+	8.87980i	−0.700306	+	0.282504i
$989$	−5.70375	+	1.40585i	−0.181369	+	0.0447034i
$990$	−0.0600320	−	0.114381i	−0.00190794	−	0.00363528i
$991$	−17.0170			−0.540563			−0.270282	−	0.962781i	$-0.587117\pi$
$991$	−17.0170			−0.540563			−0.270282	+	0.962781i	$0.587117\pi$
$992$	36.6946			1.16506
$993$	−13.2263	−	25.2006i	−0.419724	−	0.799717i
$994$	−21.4443	+	24.2056i	−0.680171	+	0.767755i
$995$			56.8681i			1.80284i
$996$	−2.32935	−	2.62929i	−0.0738083	−	0.0833124i
$997$	−36.9184	−	19.3763i	−1.16922	−	0.613653i	−0.235574	−	0.971856i	$-0.575697\pi$
$997$	−36.9184	−	19.3763i	−1.16922	−	0.613653i	−0.933644	+	0.358203i	$0.883389\pi$
$998$	−0.826164	+	6.80408i	−0.0261518	+	0.215379i
$999$	−3.73426	+	7.11504i	−0.118147	+	0.225110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.p.a.142.5	yes	168
169.25	even	26	inner	507.2.p.a.25.5	✓	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.p.a.25.5	✓	168	169.25	even	26	inner
507.2.p.a.142.5	yes	168	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.p (of order \(26\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.911757 + 0.345784i) q^{2} +(0.568065 - 0.822984i) q^{3} +(-0.785288 + 0.695704i) q^{4} +(2.27932 - 0.276760i) q^{5} +(-0.233362 + 0.946788i) q^{6} +(1.78194 - 3.39521i) q^{7} +(1.38175 - 2.63271i) q^{8} +(-0.354605 - 0.935016i) q^{9} +O(q^{10})\)	\(q+(-0.911757 + 0.345784i) q^{2} +(0.568065 - 0.822984i) q^{3} +(-0.785288 + 0.695704i) q^{4} +(2.27932 - 0.276760i) q^{5} +(-0.233362 + 0.946788i) q^{6} +(1.78194 - 3.39521i) q^{7} +(1.38175 - 2.63271i) q^{8} +(-0.354605 - 0.935016i) q^{9} +(-1.98249 + 1.04049i) q^{10} +(-0.0539466 - 0.0204593i) q^{11} +(0.126459 + 1.04148i) q^{12} +(-1.20767 + 3.39728i) q^{13} +(-0.450690 + 3.71177i) q^{14} +(1.06703 - 2.03306i) q^{15} +(-0.0965561 + 0.795211i) q^{16} +(-4.90759 - 2.57570i) q^{17} +(0.646627 + 0.729891i) q^{18} -6.27486i q^{19} +(-1.59738 + 1.80307i) q^{20} +(-1.78194 - 3.39521i) q^{21} +0.0562607 q^{22} +3.51596 q^{23} +(-1.38175 - 2.63271i) q^{24} +(0.263995 - 0.0650689i) q^{25} +(-0.0736285 - 3.51509i) q^{26} +(-0.970942 - 0.239316i) q^{27} +(0.962722 + 3.90592i) q^{28} +(2.75100 + 7.25379i) q^{29} +(-0.269875 + 2.22262i) q^{30} +(1.70007 - 6.89744i) q^{31} +(1.23617 + 5.01534i) q^{32} +(-0.0474828 + 0.0327750i) q^{33} +(5.36517 + 0.651449i) q^{34} +(3.12196 - 8.23193i) q^{35} +(0.928962 + 0.487557i) q^{36} +(1.92301 - 7.80196i) q^{37} +(2.16974 + 5.72114i) q^{38} +(2.10988 + 2.92377i) q^{39} +(2.42083 - 6.38320i) q^{40} +(8.26566 + 5.70537i) q^{41} +(2.79870 + 2.47944i) q^{42} +(-1.62225 + 0.399848i) q^{43} +(0.0565972 - 0.0214645i) q^{44} +(-1.06703 - 2.03306i) q^{45} +(-3.20570 + 1.21576i) q^{46} +(2.41926 - 2.73079i) q^{47} +(0.599595 + 0.531195i) q^{48} +(-4.37566 - 6.33923i) q^{49} +(-0.218199 + 0.150612i) q^{50} +(-4.90759 + 2.57570i) q^{51} +(-1.41514 - 3.50802i) q^{52} +(-3.03124 - 1.59092i) q^{53} +(0.968014 - 0.117538i) q^{54} +(-0.128624 - 0.0317030i) q^{55} +(-6.47639 - 9.38267i) q^{56} +(-5.16410 - 3.56452i) q^{57} +(-5.01648 - 5.66244i) q^{58} +(-3.83224 + 0.465318i) q^{59} +(0.576481 + 2.33888i) q^{60} +(10.9982 - 5.77228i) q^{61} +(0.834976 + 6.87665i) q^{62} +(-3.80646 - 0.462188i) q^{63} +(-3.77141 - 5.46383i) q^{64} +(-1.81243 + 8.07773i) q^{65} +(0.0319597 - 0.0463016i) q^{66} +(-2.39165 + 2.69961i) q^{67} +(5.64580 - 1.39156i) q^{68} +(1.99729 - 2.89358i) q^{69} +8.58504i q^{70} +(7.11787 + 4.91311i) q^{71} +(-2.95160 - 0.358390i) q^{72} +(-9.89374 - 3.75220i) q^{73} +(0.944473 + 7.77843i) q^{74} +(0.0964155 - 0.254227i) q^{75} +(4.36544 + 4.92757i) q^{76} +(-0.165593 + 0.146703i) q^{77} +(-2.93469 - 1.93620i) q^{78} +(10.5509 + 9.34727i) q^{79} +1.83926i q^{80} +(-0.748511 + 0.663123i) q^{81} +(-9.50909 - 2.34378i) q^{82} +(-2.75551 + 1.90199i) q^{83} +(3.76140 + 1.42651i) q^{84} +(-11.8988 - 4.51263i) q^{85} +(1.34083 - 0.925510i) q^{86} +(7.53249 + 1.85659i) q^{87} +(-0.128404 + 0.113756i) q^{88} +15.4794i q^{89} +(1.67587 + 1.48469i) q^{90} +(9.38249 + 10.1540i) q^{91} +(-2.76104 + 2.44607i) q^{92} +(-4.71074 - 5.31732i) q^{93} +(-1.26152 + 3.32635i) q^{94} +(-1.73663 - 14.3024i) q^{95} +(4.82977 + 1.83169i) q^{96} +(3.45109 + 0.419038i) q^{97} +(6.18153 + 4.26681i) q^{98} +0.0576959i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9}+O(q^{10}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9	\( 168 q - 14 q^{3} + 12 q^{4} - 14 q^{9} - 4 q^{10} + 12 q^{12} + 13 q^{13} + 2 q^{14} - 8 q^{16} - 4 q^{17} - 72 q^{22} + 48 q^{23} - 44 q^{25} - 39 q^{26} - 14 q^{27} + 45 q^{29} - 4 q^{30} - 26 q^{31} + 130 q^{32} + 13 q^{33} - 65 q^{34} - 35 q^{35} + 12 q^{36} + 61 q^{38} + 12 q^{40} - 63 q^{42} + 72 q^{43} - 39 q^{44} - 8 q^{48} - 68 q^{49} - 52 q^{50} - 4 q^{51} + 65 q^{52} - q^{53} + 53 q^{55} - 14 q^{56} - 13 q^{57} - 26 q^{58} - 104 q^{59} + 117 q^{60} + 12 q^{61} + 49 q^{62} - 32 q^{64} - 52 q^{65} - 46 q^{66} + 26 q^{67} - 84 q^{68} - 4 q^{69} - 39 q^{71} - 52 q^{73} + 29 q^{74} + 8 q^{75} - 130 q^{76} + 60 q^{77} + 65 q^{78} + 14 q^{79} - 14 q^{81} + 45 q^{82} + 78 q^{83} - 13 q^{85} - 13 q^{86} - 46 q^{87} - 26 q^{88} - 4 q^{90} - 208 q^{91} + 82 q^{92} - 39 q^{93} + 25 q^{94} - 66 q^{95} + 65 q^{96} + 26 q^{97} - 104 q^{98}+O(q^{100}) \) 168 * q - 14 * q^3 + 12 * q^4 - 14 * q^9 - 4 * q^10 + 12 * q^12 + 13 * q^13 + 2 * q^14 - 8 * q^16 - 4 * q^17 - 72 * q^22 + 48 * q^23 - 44 * q^25 - 39 * q^26 - 14 * q^27 + 45 * q^29 - 4 * q^30 - 26 * q^31 + 130 * q^32 + 13 * q^33 - 65 * q^34 - 35 * q^35 + 12 * q^36 + 61 * q^38 + 12 * q^40 - 63 * q^42 + 72 * q^43 - 39 * q^44 - 8 * q^48 - 68 * q^49 - 52 * q^50 - 4 * q^51 + 65 * q^52 - q^53 + 53 * q^55 - 14 * q^56 - 13 * q^57 - 26 * q^58 - 104 * q^59 + 117 * q^60 + 12 * q^61 + 49 * q^62 - 32 * q^64 - 52 * q^65 - 46 * q^66 + 26 * q^67 - 84 * q^68 - 4 * q^69 - 39 * q^71 - 52 * q^73 + 29 * q^74 + 8 * q^75 - 130 * q^76 + 60 * q^77 + 65 * q^78 + 14 * q^79 - 14 * q^81 + 45 * q^82 + 78 * q^83 - 13 * q^85 - 13 * q^86 - 46 * q^87 - 26 * q^88 - 4 * q^90 - 208 * q^91 + 82 * q^92 - 39 * q^93 + 25 * q^94 - 66 * q^95 + 65 * q^96 + 26 * q^97 - 104 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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