LMFDB - Embedded newform 507.2.m.b.40.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(40,507)]

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, 2]))

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

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

chi := DirichletCharacter("507.40");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.m (of order $13$, 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:	$204$
Relative dimension:	$17$ over $\Q(\zeta_{13})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{13}]$

Embedding invariants

Embedding label			40.9
Character	$\chi$	$=$	507.40
Dual form			507.2.m.b.469.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.203567 + 0.0501748i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.73199 - 0.909018i) q^{4} +(-0.892774 + 1.29341i) q^{5} +(0.0743463 - 0.196035i) q^{6} +(2.37726 + 2.10607i) q^{7} +(-0.620832 - 0.550009i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})$	\(q+(0.203567 + 0.0501748i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.73199 - 0.909018i) q^{4} +(-0.892774 + 1.29341i) q^{5} +(0.0743463 - 0.196035i) q^{6} +(2.37726 + 2.10607i) q^{7} +(-0.620832 - 0.550009i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-0.246636 + 0.218500i) q^{10} +(-5.34006 + 1.31621i) q^{11} +(-1.11116 + 1.60979i) q^{12} +(-1.48920 + 3.28364i) q^{13} +(0.378260 + 0.548005i) q^{14} +(1.17636 + 1.04217i) q^{15} +(2.12353 + 3.07647i) q^{16} +(0.441981 + 0.391561i) q^{17} +(-0.185644 - 0.0974337i) q^{18} +0.461611 q^{19} +(2.72201 - 1.42862i) q^{20} +(2.37726 - 2.10607i) q^{21} -1.15310 q^{22} +3.41893 q^{23} +(-0.620832 + 0.550009i) q^{24} +(0.897170 + 2.36564i) q^{25} +(-0.467908 + 0.593722i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-2.20293 - 5.80865i) q^{28} +(-0.485030 - 0.119549i) q^{29} +(0.187179 + 0.271175i) q^{30} +(-1.34248 + 3.53982i) q^{31} +(0.866155 + 2.28386i) q^{32} +(0.662937 + 5.45978i) q^{33} +(0.0703263 + 0.101885i) q^{34} +(-4.84635 + 1.19452i) q^{35} +(1.46412 + 1.29710i) q^{36} +(-3.91997 + 10.3361i) q^{37} +(0.0939688 + 0.0231612i) q^{38} +(3.08020 + 1.87414i) q^{39} +(1.26565 - 0.311954i) q^{40} +(0.507023 - 4.17571i) q^{41} +(0.589603 - 0.309448i) q^{42} +(-0.397732 - 1.04873i) q^{43} +(10.4454 + 2.57456i) q^{44} +(1.17636 - 1.04217i) q^{45} +(0.695983 + 0.171544i) q^{46} +(-8.42956 + 4.42418i) q^{47} +(3.31000 - 1.73722i) q^{48} +(0.372080 + 3.06435i) q^{49} +(0.0639387 + 0.526583i) q^{50} +(0.441981 - 0.391561i) q^{51} +(5.56416 - 4.33352i) q^{52} +(-3.86763 - 3.42642i) q^{53} +(-0.119100 + 0.172547i) q^{54} +(3.06508 - 8.08195i) q^{55} +(-0.317521 - 2.61502i) q^{56} +(0.0556410 - 0.458245i) q^{57} +(-0.0927380 - 0.0486726i) q^{58} +(-4.09495 + 5.93256i) q^{59} +(-1.09010 - 2.87436i) q^{60} +(9.11311 - 8.07351i) q^{61} +(-0.450894 + 0.653232i) q^{62} +(-1.80416 - 2.61378i) q^{63} +(-0.839449 - 6.91349i) q^{64} +(-2.91756 - 4.85769i) q^{65} +(-0.138991 + 1.14470i) q^{66} +(-5.72735 + 3.00595i) q^{67} +(-0.409570 - 1.07995i) q^{68} +(0.412107 - 3.39400i) q^{69} -1.04649 q^{70} +(1.76864 - 14.5661i) q^{71} +(0.471166 + 0.682601i) q^{72} +(0.681494 - 0.167973i) q^{73} +(-1.31659 + 1.90741i) q^{74} +(2.45654 - 0.605482i) q^{75} +(-0.799505 - 0.419612i) q^{76} +(-15.4667 - 8.11756i) q^{77} +(0.532993 + 0.536062i) q^{78} +(10.3319 - 5.42261i) q^{79} -5.87496 q^{80} +(0.885456 + 0.464723i) q^{81} +(0.312729 - 0.824598i) q^{82} +(0.192845 + 1.58822i) q^{83} +(-6.03184 + 1.48671i) q^{84} +(-0.901036 + 0.222085i) q^{85} +(-0.0283452 - 0.233444i) q^{86} +(-0.177142 + 0.467084i) q^{87} +(4.03921 + 2.11994i) q^{88} -14.1094 q^{89} +(0.291760 - 0.153127i) q^{90} +(-10.4558 + 4.66971i) q^{91} +(-5.92156 - 3.10787i) q^{92} +(3.35219 + 1.75936i) q^{93} +(-1.93797 + 0.477666i) q^{94} +(-0.412114 + 0.597050i) q^{95} +(2.37162 - 0.584551i) q^{96} +(9.45586 + 13.6992i) q^{97} +(-0.0780102 + 0.642472i) q^{98} +5.49988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) $ 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{13}\right)$

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 $

$2$	0.203567	+	0.0501748i	0.143944	+	0.0354790i	0.310629	−	0.950531i	$-0.399460\pi$
$2$	0.203567	+	0.0501748i	0.143944	+	0.0354790i	−0.166685	+	0.986010i	$0.553306\pi$
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$3$	0.120537	−	0.992709i	0.0695919	−	0.573141i
$4$	−1.73199	−	0.909018i	−0.865995	−	0.454509i
$5$	−0.892774	+	1.29341i	−0.399261	+	0.578429i	−0.970122	−	0.242618i	$-0.921994\pi$
$5$	−0.892774	+	1.29341i	−0.399261	+	0.578429i	0.570861	+	0.821046i	$0.306609\pi$
$6$	0.0743463	−	0.196035i	0.0303518	−	0.0800310i
$7$	2.37726	+	2.10607i	0.898519	+	0.796018i	0.979656	−	0.200685i	$-0.0643168\pi$
$7$	2.37726	+	2.10607i	0.898519	+	0.796018i	−0.0811373	+	0.996703i	$0.525855\pi$
$8$	−0.620832	−	0.550009i	−0.219497	−	0.194458i
$9$	−0.970942	−	0.239316i	−0.323647	−	0.0797719i
$10$	−0.246636	+	0.218500i	−0.0779932	+	0.0690959i
$11$	−5.34006	+	1.31621i	−1.61009	+	0.396852i	−0.938833	−	0.344373i	$-0.888092\pi$
$11$	−5.34006	+	1.31621i	−1.61009	+	0.396852i	−0.671257	+	0.741225i	$0.734245\pi$
$12$	−1.11116	+	1.60979i	−0.320764	+	0.464707i
$13$	−1.48920	+	3.28364i	−0.413029	+	0.910718i
$13$	−1.48920	+	3.28364i	−0.413029	+	0.910718i
$14$	0.378260	+	0.548005i	0.101094	+	0.146460i
$15$	1.17636	+	1.04217i	0.303736	+	0.269087i
$16$	2.12353	+	3.07647i	0.530883	+	0.769117i
$17$	0.441981	+	0.391561i	0.107196	+	0.0949674i	0.715018	−	0.699106i	$-0.246418\pi$
$17$	0.441981	+	0.391561i	0.107196	+	0.0949674i	−0.607822	+	0.794073i	$0.707957\pi$
$18$	−0.185644	−	0.0974337i	−0.0437568	−	0.0229653i
$19$	0.461611			0.105901			0.0529504	−	0.998597i	$-0.483137\pi$
$19$	0.461611			0.105901			0.0529504	+	0.998597i	$0.483137\pi$
$20$	2.72201	−	1.42862i	0.608659	−	0.319449i
$21$	2.37726	−	2.10607i	0.518760	−	0.459581i
$22$	−1.15310			−0.245842
$23$	3.41893			0.712897			0.356448	−	0.934315i	$-0.383988\pi$
$23$	3.41893			0.712897			0.356448	+	0.934315i	$0.383988\pi$
$24$	−0.620832	+	0.550009i	−0.126727	+	0.112270i
$25$	0.897170	+	2.36564i	0.179434	+	0.473128i
$26$	−0.467908	+	0.593722i	−0.0917643	+	0.116438i
$27$	−0.354605	+	0.935016i	−0.0682437	+	0.179944i
$28$	−2.20293	−	5.80865i	−0.416315	−	1.09773i
$29$	−0.485030	−	0.119549i	−0.0900679	−	0.0221997i	0.194024	−	0.980997i	$-0.437846\pi$
$29$	−0.485030	−	0.119549i	−0.0900679	−	0.0221997i	−0.284092	+	0.958797i	$0.591692\pi$
$30$	0.187179	+	0.271175i	0.0341740	+	0.0495096i
$31$	−1.34248	+	3.53982i	−0.241116	+	0.635770i	−0.999878	−	0.0155975i	$-0.995035\pi$
$31$	−1.34248	+	3.53982i	−0.241116	+	0.635770i	0.758763	+	0.651367i	$0.225804\pi$
$32$	0.866155	+	2.28386i	0.153116	+	0.403734i
$33$	0.662937	+	5.45978i	0.115403	+	0.950426i
$34$	0.0703263	+	0.101885i	0.0120609	+	0.0174732i
$35$	−4.84635	+	1.19452i	−0.819183	+	0.201910i
$36$	1.46412	+	1.29710i	0.244020	+	0.216183i
$37$	−3.91997	+	10.3361i	−0.644440	+	1.69925i	0.0681576	+	0.997675i	$0.478288\pi$
$37$	−3.91997	+	10.3361i	−0.644440	+	1.69925i	−0.712597	+	0.701573i	$0.752481\pi$
$38$	0.0939688	+	0.0231612i	0.0152438	+	0.00375725i
$39$	3.08020	+	1.87414i	0.493226	+	0.300102i
$40$	1.26565	−	0.311954i	0.200116	−	0.0493243i
$41$	0.507023	−	4.17571i	0.0791837	−	0.652136i	−0.898038	−	0.439917i	$-0.855008\pi$
$41$	0.507023	−	4.17571i	0.0791837	−	0.652136i	0.977222	−	0.212219i	$-0.0680691\pi$
$42$	0.589603	−	0.309448i	0.0909778	−	0.0477488i
$43$	−0.397732	−	1.04873i	−0.0606536	−	0.159930i	0.901264	−	0.433271i	$-0.142641\pi$
$43$	−0.397732	−	1.04873i	−0.0606536	−	0.159930i	−0.961917	+	0.273340i	$0.911871\pi$
$44$	10.4454	+	2.57456i	1.57470	+	0.388129i
$45$	1.17636	−	1.04217i	0.175362	−	0.155357i
$46$	0.695983	+	0.171544i	0.102617	+	0.0252928i
$47$	−8.42956	+	4.42418i	−1.22958	+	0.645332i	−0.949235	−	0.314567i	$-0.898141\pi$
$47$	−8.42956	+	4.42418i	−1.22958	+	0.645332i	−0.280343	+	0.959900i	$0.590448\pi$
$48$	3.31000	−	1.73722i	0.477758	−	0.250747i
$49$	0.372080	+	3.06435i	0.0531543	+	0.437765i
$50$	0.0639387	+	0.526583i	0.00904230	+	0.0744700i
$51$	0.441981	−	0.391561i	0.0618897	−	0.0548295i
$52$	5.56416	−	4.33352i	0.771611	−	0.600952i
$53$	−3.86763	−	3.42642i	−0.531260	−	0.470656i	0.354332	−	0.935120i	$-0.384708\pi$
$53$	−3.86763	−	3.42642i	−0.531260	−	0.470656i	−0.885592	+	0.464464i	$0.846247\pi$
$54$	−0.119100	+	0.172547i	−0.0162075	+	0.0234806i
$55$	3.06508	−	8.08195i	0.413295	−	1.08977i
$56$	−0.317521	−	2.61502i	−0.0424306	−	0.349447i
$57$	0.0556410	−	0.458245i	0.00736983	−	0.0606960i
$58$	−0.0927380	−	0.0486726i	−0.0121771	−	0.00639103i
$59$	−4.09495	+	5.93256i	−0.533117	+	0.772353i	−0.993312	−	0.115465i	$-0.963164\pi$
$59$	−4.09495	+	5.93256i	−0.533117	+	0.772353i	0.460195	+	0.887818i	$0.347780\pi$
$60$	−1.09010	−	2.87436i	−0.140731	−	0.371078i
$61$	9.11311	−	8.07351i	1.16681	−	1.03371i	0.167962	−	0.985793i	$-0.446281\pi$
$61$	9.11311	−	8.07351i	1.16681	−	1.03371i	0.998851	−	0.0479135i	$-0.0152572\pi$
$62$	−0.450894	+	0.653232i	−0.0572636	+	0.0829606i
$63$	−1.80416	−	2.61378i	−0.227303	−	0.329306i
$64$	−0.839449	−	6.91349i	−0.104931	−	0.864186i
$65$	−2.91756	−	4.85769i	−0.361879	−	0.602522i
$66$	−0.138991	+	1.14470i	−0.0171086	+	0.140902i
$67$	−5.72735	+	3.00595i	−0.699707	+	0.367235i	−0.776764	−	0.629792i	$-0.783140\pi$
$67$	−5.72735	+	3.00595i	−0.699707	+	0.367235i	0.0770565	+	0.997027i	$0.475448\pi$
$68$	−0.409570	−	1.07995i	−0.0496677	−	0.130963i
$69$	0.412107	−	3.39400i	0.0496118	−	0.408590i
$70$	−1.04649			−0.125080
$71$	1.76864	−	14.5661i	0.209899	−	1.72867i	−0.383305	−	0.923622i	$-0.625214\pi$
$71$	1.76864	−	14.5661i	0.209899	−	1.72867i	0.593204	−	0.805052i	$-0.297863\pi$
$72$	0.471166	+	0.682601i	0.0555274	+	0.0804453i
$73$	0.681494	−	0.167973i	0.0797628	−	0.0196598i	−0.199232	−	0.979952i	$-0.563845\pi$
$73$	0.681494	−	0.167973i	0.0797628	−	0.0196598i	0.278995	+	0.960293i	$0.409999\pi$
$74$	−1.31659	+	1.90741i	−0.153051	+	0.221732i
$75$	2.45654	−	0.605482i	0.283656	−	0.0699150i
$76$	−0.799505	−	0.419612i	−0.0917095	−	0.0481328i
$77$	−15.4667	−	8.11756i	−1.76260	−	0.925082i
$78$	0.532993	+	0.536062i	0.0603495	+	0.0606970i
$79$	10.3319	−	5.42261i	1.16243	−	0.610091i	0.230623	−	0.973043i	$-0.425923\pi$
$79$	10.3319	−	5.42261i	1.16243	−	0.610091i	0.931808	+	0.362952i	$0.118231\pi$
$80$	−5.87496			−0.656841
$81$	0.885456	+	0.464723i	0.0983840	+	0.0516359i
$82$	0.312729	−	0.824598i	0.0345351	−	0.0910617i
$83$	0.192845	+	1.58822i	0.0211675	+	0.174330i	0.999458	−	0.0329061i	$-0.0104762\pi$
$83$	0.192845	+	1.58822i	0.0211675	+	0.174330i	−0.978291	+	0.207236i	$0.933553\pi$
$84$	−6.03184	+	1.48671i	−0.658127	+	0.162214i
$85$	−0.901036	+	0.222085i	−0.0977311	+	0.0240886i
$86$	−0.0283452	−	0.233444i	−0.00305655	−	0.0251729i
$87$	−0.177142	+	0.467084i	−0.0189916	+	0.0500766i
$88$	4.03921	+	2.11994i	0.430581	+	0.225986i
$89$	−14.1094			−1.49560			−0.747798	−	0.663926i	$-0.768889\pi$
$89$	−14.1094			−1.49560			−0.747798	+	0.663926i	$0.768889\pi$
$90$	0.291760	−	0.153127i	0.0307542	−	0.0161410i
$91$	−10.4558	+	4.66971i	−1.09606	+	0.489518i
$92$	−5.92156	−	3.10787i	−0.617365	−	0.324018i
$93$	3.35219	+	1.75936i	0.347606	+	0.182438i
$94$	−1.93797	+	0.477666i	−0.199886	+	0.0492675i
$95$	−0.412114	+	0.597050i	−0.0422820	+	0.0612560i
$96$	2.37162	−	0.584551i	0.242052	−	0.0596605i
$97$	9.45586	+	13.6992i	0.960098	+	1.39094i	0.920075	+	0.391743i	$0.128128\pi$
$97$	9.45586	+	13.6992i	0.960098	+	1.39094i	0.0400227	+	0.999199i	$0.487257\pi$
$98$	−0.0780102	+	0.642472i	−0.00788022	+	0.0648994i
$99$	5.49988			0.552759
$100$	0.596523	−	4.91281i	0.0596523	−	0.491281i
$101$	4.05480	+	10.6916i	0.403467	+	1.06386i	0.970699	+	0.240298i	$0.0772451\pi$
$101$	4.05480	+	10.6916i	0.403467	+	1.06386i	−0.567232	+	0.823558i	$0.691986\pi$
$102$	0.109619	−	0.0575327i	0.0108539	−	0.00569658i
$103$	1.79628	−	14.7937i	0.176993	−	1.45767i	−0.585501	−	0.810671i	$-0.699102\pi$
$103$	1.79628	−	14.7937i	0.176993	−	1.45767i	0.762494	−	0.646995i	$-0.223975\pi$
$104$	2.73057	−	1.21952i	0.267755	−	0.119583i
$105$	0.601646	+	4.95500i	0.0587146	+	0.483558i
$106$	−0.615404	−	0.891566i	−0.0597733	−	0.0865965i
$107$	2.45131	−	3.55133i	0.236977	−	0.343320i	−0.686394	−	0.727230i	$-0.740807\pi$
$107$	2.45131	−	3.55133i	0.236977	−	0.343320i	0.923371	+	0.383910i	$0.125423\pi$
$108$	1.46412	−	1.29710i	0.140885	−	0.124813i
$109$	−3.80019	−	10.0203i	−0.363992	−	0.959768i	−0.984471	−	0.175545i	$-0.943831\pi$
$109$	−3.80019	−	10.0203i	−0.363992	−	0.959768i	0.620479	−	0.784223i	$-0.286938\pi$
$110$	1.02946	−	1.49143i	0.0981552	−	0.142202i
$111$	9.78826	+	5.13727i	0.929060	+	0.487609i
$112$	−1.43106	+	11.7859i	−0.135223	+	1.11366i
$113$	2.04075	+	16.8071i	0.191978	+	1.58108i	0.696419	+	0.717635i	$0.254775\pi$
$113$	2.04075	+	16.8071i	0.191978	+	1.58108i	−0.504441	+	0.863446i	$0.668302\pi$
$114$	0.0343190	−	0.0904919i	0.00321427	−	0.00847534i
$115$	−3.05233	+	4.42207i	−0.284632	+	0.412360i
$116$	0.731395	+	0.647960i	0.0679083	+	0.0601615i
$117$	2.23175	−	2.83184i	0.206325	−	0.261803i
$118$	−1.13126	+	1.00221i	−0.104141	+	0.0922611i
$119$	0.226049	+	1.86168i	0.0207219	+	0.170660i
$120$	−0.157123	−	1.29402i	−0.0143433	−	0.118127i
$121$	17.0439	−	8.94532i	1.54944	−	0.813210i
$122$	2.26022	−	1.18625i	0.204631	−	0.107398i
$123$	−4.08415	−	1.00665i	−0.368255	−	0.0907668i
$124$	5.54291	−	4.91059i	0.497768	−	0.440984i
$125$	−11.4904	−	2.83213i	−1.02773	−	0.253313i
$126$	−0.236123	−	0.622604i	−0.0210355	−	0.0554660i
$127$	−8.61142	+	4.51962i	−0.764140	+	0.401052i	−0.801304	−	0.598257i	$-0.795860\pi$
$127$	−8.61142	+	4.51962i	−0.764140	+	0.401052i	0.0371636	+	0.999309i	$0.488168\pi$
$128$	0.764843	−	6.29905i	0.0676032	−	0.556762i
$129$	−1.08903	+	0.268421i	−0.0958836	+	0.0236332i
$130$	−0.350187	−	1.13525i	−0.0307135	−	0.0995684i
$131$	−12.1440	−	2.99324i	−1.06103	−	0.261520i	−0.330081	−	0.943953i	$-0.607076\pi$
$131$	−12.1440	−	2.99324i	−1.06103	−	0.261520i	−0.730949	+	0.682432i	$0.760922\pi$
$132$	3.81484	−	10.0589i	0.332039	−	0.875516i
$133$	1.09737	+	0.972182i	0.0951538	+	0.0842989i
$134$	−1.31672	+	0.324543i	−0.113748	+	0.0280363i
$135$	−0.892774	−	1.29341i	−0.0768378	−	0.111319i
$136$	−0.0590338	−	0.486187i	−0.00506210	−	0.0416902i
$137$	−0.568703	−	1.49955i	−0.0485876	−	0.128115i	0.908526	−	0.417829i	$-0.137209\pi$
$137$	−0.568703	−	1.49955i	−0.0485876	−	0.128115i	−0.957113	+	0.289714i	$0.906440\pi$
$138$	0.254185	−	0.670231i	0.0216377	−	0.0570539i
$139$	1.40132	+	2.03017i	0.118859	+	0.172196i	0.877897	−	0.478849i	$-0.158946\pi$
$139$	1.40132	+	2.03017i	0.118859	+	0.172196i	−0.759038	+	0.651046i	$0.774331\pi$
$140$	9.47967	+	2.33653i	0.801178	+	0.197473i
$141$	3.37585	+	8.90138i	0.284298	+	0.749631i
$142$	1.09089	−	2.87643i	0.0915452	−	0.241385i
$143$	3.63046	−	19.4949i	0.303594	−	1.63025i
$144$	−1.32558	−	3.49527i	−0.110465	−	0.291272i
$145$	0.587648	−	0.520611i	0.0488015	−	0.0432344i
$146$	0.147158			0.0121789
$147$	3.08686			0.254600
$148$	16.1851	−	14.3387i	1.33041	−	1.17864i
$149$	9.04125	−	4.74521i	0.740688	−	0.388743i	−0.0517786	−	0.998659i	$-0.516489\pi$
$149$	9.04125	−	4.74521i	0.740688	−	0.388743i	0.792466	+	0.609916i	$0.208797\pi$
$150$	0.530450			0.0433111
$151$	6.75330	+	3.54441i	0.549576	+	0.288440i	0.716566	−	0.697519i	$-0.245713\pi$
$151$	6.75330	+	3.54441i	0.549576	+	0.288440i	−0.166991	+	0.985958i	$0.553405\pi$
$152$	−0.286582	−	0.253890i	−0.0232449	−	0.0205932i
$153$	−0.335431	−	0.485956i	−0.0271180	−	0.0392872i
$154$	−2.74122	−	2.42851i	−0.220894	−	0.195695i
$155$	−3.37989	−	4.89662i	−0.271480	−	0.393306i
$156$	−3.63124	−	6.04594i	−0.290732	−	0.484063i
$157$	−8.97786	+	13.0067i	−0.716511	+	1.03805i	0.280428	+	0.959875i	$0.409523\pi$
$157$	−8.97786	+	13.0067i	−0.716511	+	1.03805i	−0.996940	+	0.0781712i	$0.975092\pi$
$158$	2.37532	−	0.585463i	0.188970	−	0.0465770i
$159$	−3.86763	+	3.42642i	−0.306723	+	0.271733i
$160$	−3.72724	−	0.918683i	−0.294665	−	0.0726283i
$161$	8.12768	+	7.20050i	0.640551	+	0.567479i
$162$	0.156932	+	0.139030i	0.0123298	+	0.0109232i
$163$	−2.24398	+	5.91689i	−0.175762	+	0.463447i	−0.993729	−	0.111819i	$-0.964332\pi$
$163$	−2.24398	+	5.91689i	−0.175762	+	0.463447i	0.817966	+	0.575266i	$0.195101\pi$
$164$	−4.67396	+	6.77140i	−0.364975	+	0.528757i
$165$	−7.65357	−	4.01690i	−0.595830	−	0.312715i
$166$	−0.0404319	+	0.332986i	−0.00313812	+	0.0258448i
$167$	18.3250	+	4.51671i	1.41803	+	0.349514i	0.872516	−	0.488586i	$-0.162487\pi$
$167$	18.3250	+	4.51671i	1.41803	+	0.349514i	0.545517	+	0.838100i	$0.316333\pi$
$168$	−2.63423			−0.203235
$169$	−8.56458	−	9.77997i	−0.658814	−	0.752306i
$170$	−0.194565			−0.0149224
$171$	−0.448197	−	0.110471i	−0.0342745	−	0.00844790i
$172$	−0.264450	+	2.17794i	−0.0201641	+	0.166067i
$173$	9.50472	+	4.98846i	0.722631	+	0.379266i	0.785588	−	0.618750i	$-0.212361\pi$
$173$	9.50472	+	4.98846i	0.722631	+	0.379266i	−0.0629569	+	0.998016i	$0.520053\pi$
$174$	−0.0594961	+	0.0861950i	−0.00451039	+	0.00653442i
$175$	−2.84939	+	7.51324i	−0.215394	+	0.567947i
$176$	−15.3891	−	13.6335i	−1.16000	−	1.02767i
$177$	5.39571	+	4.78018i	0.405567	+	0.359301i
$178$	−2.87222	−	0.707938i	−0.215282	−	0.0530622i
$179$	−4.41993	+	3.91572i	−0.330361	+	0.292674i	−0.811955	−	0.583720i	$-0.801597\pi$
$179$	−4.41993	+	3.91572i	−0.330361	+	0.292674i	0.481594	+	0.876395i	$0.340058\pi$
$180$	−2.98480	+	0.735687i	−0.222474	+	0.0548349i
$181$	−5.79022	+	8.38857i	−0.430383	+	0.623518i	−0.976840	−	0.213969i	$-0.931361\pi$
$181$	−5.79022	+	8.38857i	−0.430383	+	0.623518i	0.546457	+	0.837487i	$0.315976\pi$
$182$	−2.36275	+	0.425984i	−0.175139	+	0.0315760i
$183$	−6.91618	−	10.0198i	−0.511259	−	0.740686i
$184$	−2.12258	−	1.88044i	−0.156479	−	0.138628i
$185$	−9.86915	−	14.2979i	−0.725595	−	1.05121i
$186$	0.594120	+	0.526345i	0.0435630	+	0.0385935i
$187$	−2.87558	−	1.50922i	−0.210283	−	0.110365i
$188$	18.6216			1.35812
$189$	−2.81219	+	1.47595i	−0.204557	+	0.107360i
$190$	−0.113850	+	0.100862i	−0.00825953	+	0.00731731i
$191$	21.6082			1.56351			0.781757	−	0.623584i	$-0.214324\pi$
$191$	21.6082			1.56351			0.781757	+	0.623584i	$0.214324\pi$
$192$	−6.96427			−0.502603
$193$	−1.95317	+	1.73035i	−0.140592	+	0.124554i	−0.730488	−	0.682926i	$-0.760707\pi$
$193$	−1.95317	+	1.73035i	−0.140592	+	0.124554i	0.589896	+	0.807479i	$0.299169\pi$
$194$	1.23755	+	3.26315i	0.0888509	+	0.234281i
$195$	−5.17394	+	2.31076i	−0.370514	+	0.165477i
$196$	2.14112	−	5.64566i	0.152937	−	0.403261i
$197$	−0.217482	−	0.573453i	−0.0154950	−	0.0408569i	0.927046	−	0.374949i	$-0.122340\pi$
$197$	−0.217482	−	0.573453i	−0.0154950	−	0.0408569i	−0.942541	+	0.334092i	$0.891570\pi$
$198$	1.11960	+	0.275956i	0.0795662	+	0.0196113i
$199$	6.00650	+	8.70191i	0.425789	+	0.616862i	0.975897	−	0.218232i	$-0.0700288\pi$
$199$	6.00650	+	8.70191i	0.425789	+	0.616862i	−0.550108	+	0.835094i	$0.685413\pi$
$200$	0.744133	−	1.96212i	0.0526181	−	0.138743i
$201$	2.29367	+	6.04792i	0.161783	+	0.426587i
$202$	0.288974	+	2.37991i	0.0203321	+	0.167450i
$203$	−0.901263	−	1.30571i	−0.0632563	−	0.0916425i
$204$	−1.12144	+	0.276411i	−0.0785167	+	0.0193526i
$205$	4.94823	+	4.38375i	0.345600	+	0.306175i
$206$	1.10794	−	2.92139i	0.0771935	−	0.203543i
$207$	−3.31958	−	0.818204i	−0.230727	−	0.0568691i
$208$	−13.2644	+	2.39145i	−0.919719	+	0.165817i
$209$	−2.46503	+	0.607575i	−0.170510	+	0.0420269i
$210$	−0.126141	+	1.03886i	−0.00870455	+	0.0716884i
$211$	21.3755	−	11.2187i	1.47155	−	0.772329i	0.477232	−	0.878778i	$-0.341640\pi$
$211$	21.3755	−	11.2187i	1.47155	−	0.772329i	0.994318	+	0.106449i	$0.0339480\pi$
$212$	3.58402	+	9.45028i	0.246151	+	0.649048i
$213$	−14.2467	−	3.51149i	−0.976166	−	0.240603i
$214$	0.677193	−	0.599941i	0.0462920	−	0.0410111i
$215$	1.71152	+	0.421853i	0.116725	+	0.0287701i
$216$	0.734417	−	0.385452i	0.0499708	−	0.0262267i
$217$	−10.6465	+	5.58771i	−0.722731	+	0.379318i
$218$	−0.270829	−	2.23047i	−0.0183428	−	0.151067i
$219$	−0.0846034	−	0.696772i	−0.00571697	−	0.0470835i
$220$	−12.6553	+	11.2116i	−0.853222	+	0.755889i
$221$	−1.94394	+	0.868195i	−0.130764	+	0.0584011i
$222$	1.73481	+	1.53691i	0.116433	+	0.103150i
$223$	6.77206	−	9.81102i	0.453491	−	0.656995i	−0.527835	−	0.849347i	$-0.676996\pi$
$223$	6.77206	−	9.81102i	0.453491	−	0.656995i	0.981326	+	0.192352i	$0.0616116\pi$
$224$	−2.75089	+	7.25351i	−0.183802	+	0.484646i
$225$	−0.304964	−	2.51161i	−0.0203310	−	0.167441i
$226$	−0.427864	+	3.52378i	−0.0284611	+	0.234398i
$227$	18.6925	+	9.81057i	1.24066	+	0.651151i	0.951947	−	0.306264i	$-0.0990790\pi$
$227$	18.6925	+	9.81057i	1.24066	+	0.651151i	0.288717	+	0.957414i	$0.406771\pi$
$228$	−0.512923	+	0.743097i	−0.0339691	+	0.0492128i
$229$	4.04134	+	10.6561i	0.267059	+	0.704178i	0.999722	+	0.0235857i	$0.00750824\pi$
$229$	4.04134	+	10.6561i	0.267059	+	0.704178i	−0.732662	+	0.680592i	$0.761723\pi$
$230$	−0.843232	+	0.747038i	−0.0556011	+	0.0492583i
$231$	−9.92268	+	14.3755i	−0.652865	+	0.945838i
$232$	0.235369	+	0.340991i	0.0154527	+	0.0223872i
$233$	2.84379	+	23.4207i	0.186303	+	1.53434i	0.723166	+	0.690674i	$0.242686\pi$
$233$	2.84379	+	23.4207i	0.186303	+	1.53434i	−0.536863	+	0.843669i	$0.680391\pi$
$234$	0.596398	−	0.464491i	0.0389878	−	0.0303648i
$235$	1.80344	−	14.8526i	0.117643	−	0.968880i
$236$	12.4852	−	6.55275i	0.812718	−	0.426548i
$237$	−4.13770	−	10.9102i	−0.268772	−	0.708694i
$238$	−0.0473934	+	0.390319i	−0.00307205	+	0.0253006i
$239$	−3.01662			−0.195129			−0.0975644	−	0.995229i	$-0.531105\pi$
$239$	−3.01662			−0.195129			−0.0975644	+	0.995229i	$0.531105\pi$
$240$	−0.708148	+	5.83213i	−0.0457108	+	0.376462i
$241$	8.69916	+	12.6029i	0.560362	+	0.811825i	0.996098	−	0.0882496i	$-0.0281273\pi$
$241$	8.69916	+	12.6029i	0.560362	+	0.811825i	−0.435736	+	0.900074i	$0.643512\pi$
$242$	3.91841	−	0.965800i	0.251885	−	0.0620840i
$243$	0.568065	−	0.822984i	0.0364414	−	0.0527944i
$244$	−23.1228	+	5.69925i	−1.48028	+	0.364857i
$245$	−4.29564	−	2.25453i	−0.274438	−	0.144036i
$246$	−0.780891	−	0.409843i	−0.0497878	−	0.0261306i
$247$	−0.687429	+	1.51576i	−0.0437401	+	0.0964457i
$248$	2.78038	−	1.45926i	0.176554	−	0.0926629i
$249$	1.59989			0.101389
$250$	−2.19697	−	1.15306i	−0.138948	−	0.0729258i
$251$	5.01562	−	13.2251i	0.316583	−	0.834762i	−0.678397	−	0.734695i	$-0.737325\pi$
$251$	5.01562	−	13.2251i	0.316583	−	0.834762i	0.994981	−	0.100067i	$-0.0319056\pi$
$252$	0.748817	+	6.16706i	0.0471710	+	0.388488i
$253$	−18.2573	+	4.50003i	−1.14783	+	0.282914i
$254$	−1.97978	+	0.487971i	−0.124222	+	0.0306180i
$255$	0.111858	+	0.921236i	0.00700484	+	0.0576900i
$256$	−4.46737	+	11.7795i	−0.279211	+	0.736219i
$257$	−15.4128	−	8.08925i	−0.961422	−	0.504593i	−0.0904369	−	0.995902i	$-0.528826\pi$
$257$	−15.4128	−	8.08925i	−0.961422	−	0.504593i	−0.870985	+	0.491309i	$0.836519\pi$
$258$	−0.235159			−0.0146403
$259$	−31.0873	+	16.3159i	−1.93167	+	1.01382i
$260$	0.637467	+	11.0656i	0.0395340	+	0.686258i
$261$	0.442326	+	0.232151i	0.0273793	+	0.0143698i
$262$	−2.32195	−	1.21865i	−0.143450	−	0.0752885i
$263$	5.36977	−	1.32353i	0.331114	−	0.0816124i	−0.0702539	−	0.997529i	$-0.522381\pi$
$263$	5.36977	−	1.32353i	0.331114	−	0.0816124i	0.401368	+	0.915917i	$0.368535\pi$
$264$	2.59136	−	3.75423i	0.159487	−	0.231057i
$265$	7.88468	−	1.94340i	0.484352	−	0.119382i
$266$	0.174609	+	0.252965i	0.0107060	+	0.0155103i
$267$	−1.70070	+	14.0066i	−0.104081	+	0.857187i
$268$	12.6522			0.772855
$269$	−1.54654	+	12.7369i	−0.0942944	+	0.776584i	0.866472	+	0.499225i	$0.166382\pi$
$269$	−1.54654	+	12.7369i	−0.0942944	+	0.776584i	−0.960767	+	0.277358i	$0.910541\pi$
$270$	−0.116843	−	0.308090i	−0.00711085	−	0.0187498i
$271$	7.99176	−	4.19440i	0.485465	−	0.254792i	−0.204188	−	0.978932i	$-0.565455\pi$
$271$	7.99176	−	4.19440i	0.485465	−	0.254792i	0.689653	+	0.724140i	$0.257763\pi$
$272$	−0.266064	+	2.19123i	−0.0161325	+	0.132863i
$273$	3.37536	+	10.9424i	0.204286	+	0.662264i
$274$	−0.0405299	−	0.333793i	−0.00244850	−	0.0201652i
$275$	−7.90462	−	11.4518i	−0.476667	−	0.690571i
$276$	−3.79898	+	5.50377i	−0.228672	+	0.331288i
$277$	3.04085	−	2.69396i	0.182707	−	0.161864i	−0.566812	−	0.823847i	$-0.691823\pi$
$277$	3.04085	−	2.69396i	0.182707	−	0.161864i	0.749519	+	0.661983i	$0.230285\pi$
$278$	0.183400	+	0.483587i	0.0109996	+	0.0290036i
$279$	2.15060	−	3.11568i	0.128753	−	0.186531i
$280$	3.66576	+	1.92394i	0.219071	+	0.114977i
$281$	−3.42068	+	28.1719i	−0.204061	+	1.68059i	0.426527	+	0.904475i	$0.359737\pi$
$281$	−3.42068	+	28.1719i	−0.204061	+	1.68059i	−0.630588	+	0.776118i	$0.717186\pi$
$282$	0.240587	+	1.98141i	0.0143267	+	0.117991i
$283$	−0.0245991	+	0.0648625i	−0.00146226	+	0.00385568i	−0.935745	−	0.352676i	$-0.885272\pi$
$283$	−0.0245991	+	0.0648625i	−0.00146226	+	0.00385568i	0.934283	+	0.356532i	$0.116041\pi$
$284$	−16.3041	+	23.6205i	−0.967470	+	1.40162i
$285$	0.543022	+	0.481075i	0.0321658	+	0.0284965i
$286$	1.71720	−	3.78638i	0.101540	−	0.223893i
$287$	9.99965	−	8.85891i	0.590260	−	0.522925i
$288$	−0.294422	−	2.42478i	−0.0173490	−	0.142882i
$289$	−2.00710	−	16.5299i	−0.118064	−	0.972349i
$290$	0.145748	−	0.0764942i	0.00855859	−	0.00449189i
$291$	14.7391	−	7.73567i	0.864020	−	0.453473i
$292$	−1.33303	−	0.328563i	−0.0780097	−	0.0192277i
$293$	19.8783	−	17.6106i	1.16130	−	1.02882i	0.162186	−	0.986760i	$-0.448145\pi$
$293$	19.8783	−	17.6106i	1.16130	−	1.02882i	0.999115	−	0.0420630i	$-0.0133930\pi$
$294$	0.628384	+	0.154883i	0.0366481	+	0.00903295i
$295$	−4.01735	−	10.5929i	−0.233899	−	0.616741i
$296$	8.11860	−	4.26097i	0.471884	−	0.247664i
$297$	0.662937	−	5.45978i	0.0384675	−	0.316809i
$298$	2.07859	−	0.512327i	0.120410	−	0.0296783i
$299$	−5.09146	+	11.2265i	−0.294447	+	0.649248i
$300$	−4.80509	−	1.18435i	−0.277422	−	0.0683784i
$301$	1.26319	−	3.33076i	0.0728091	−	0.191982i
$302$	1.19691	+	1.06037i	0.0688745	+	0.0610175i
$303$	11.1024	−	2.73650i	0.637817	−	0.157208i
$304$	0.980245	+	1.42013i	0.0562209	+	0.0814501i
$305$	2.30638	+	18.9948i	0.132063	+	1.08764i
$306$	−0.0439000	−	0.115755i	−0.00250960	−	0.00661727i
$307$	7.94301	−	20.9440i	0.453332	−	1.19534i	−0.492394	−	0.870372i	$-0.663878\pi$
$307$	7.94301	−	20.9440i	0.453332	−	1.19534i	0.945726	−	0.324965i	$-0.105353\pi$
$308$	19.4092	+	28.1191i	1.10594	+	1.60223i
$309$	−14.4693	−	3.56637i	−0.823131	−	0.202884i
$310$	−0.442349	−	1.16638i	−0.0251237	−	0.0662458i
$311$	−1.74360	+	4.59751i	−0.0988707	+	0.260701i	−0.975321	−	0.220792i	$-0.929136\pi$
$311$	−1.74360	+	4.59751i	−0.0988707	+	0.260701i	0.876450	+	0.481492i	$0.159905\pi$
$312$	−0.881491	−	2.85766i	−0.0499046	−	0.161783i
$313$	−2.06701	−	5.45025i	−0.116834	−	0.308067i	0.863824	−	0.503793i	$-0.168063\pi$
$313$	−2.06701	−	5.45025i	−0.116834	−	0.308067i	−0.980658	+	0.195727i	$0.937293\pi$
$314$	−2.48021	+	2.19727i	−0.139966	+	0.123999i
$315$	4.99139			0.281233
$316$	−22.8240			−1.28395
$317$	−4.40663	+	3.90393i	−0.247501	+	0.219267i	−0.777748	−	0.628577i	$-0.783638\pi$
$317$	−4.40663	+	3.90393i	−0.247501	+	0.219267i	0.530247	+	0.847843i	$0.322099\pi$
$318$	−0.959244	+	0.503450i	−0.0537917	+	0.0282321i
$319$	2.74745			0.153827
$320$	9.69139	+	5.08643i	0.541765	+	0.284340i
$321$	−3.22997	−	2.86150i	−0.180279	−	0.159713i
$322$	1.29325	+	1.87359i	0.0720698	+	0.104411i
$323$	0.204023	+	0.180749i	0.0113521	+	0.0100571i
$324$	−1.11116	−	1.60979i	−0.0617311	−	0.0894329i
$325$	−9.10398	−	0.576925i	−0.504998	−	0.0320020i
$326$	−0.753680	+	1.09189i	−0.0417425	+	0.0604744i
$327$	−10.4053	+	2.56467i	−0.575413	+	0.141827i
$328$	−2.61145	+	2.31355i	−0.144193	+	0.127744i
$329$	−29.3568	−	7.23581i	−1.61850	−	0.398923i
$330$	−1.35647	−	1.20173i	−0.0746712	−	0.0661529i
$331$	16.5705	+	14.6802i	0.910799	+	0.806897i	0.981670	−	0.190588i	$-0.0610395\pi$
$331$	16.5705	+	14.6802i	0.910799	+	0.806897i	−0.0708713	+	0.997485i	$0.522578\pi$
$332$	1.10972	−	2.92609i	0.0609037	−	0.160590i
$333$	6.27966	−	9.09766i	0.344123	−	0.498549i
$334$	3.50375	+	1.83891i	0.191717	+	0.100621i
$335$	1.22532	−	10.0914i	0.0669464	−	0.551353i
$336$	11.5274	+	2.84126i	0.628873	+	0.155003i
$337$	16.3352			0.889833			0.444917	−	0.895572i	$-0.353233\pi$
$337$	16.3352			0.889833			0.444917	+	0.895572i	$0.353233\pi$
$338$	−1.25276	−	2.42061i	−0.0681412	−	0.131664i
$339$	16.9306			0.919542
$340$	1.76247	+	0.434409i	0.0955831	+	0.0235591i
$341$	2.50977	−	20.6698i	0.135912	−	1.11933i
$342$	−0.0856954	−	0.0449764i	−0.00463388	−	0.00243205i
$343$	7.05994	−	10.2281i	0.381201	−	0.552265i
$344$	−0.329888	+	0.869843i	−0.0177864	+	0.0468988i
$345$	4.02191	+	3.56310i	0.216532	+	0.191831i
$346$	1.68456	+	1.49239i	0.0905623	+	0.0802312i
$347$	−4.35751	−	1.07403i	−0.233924	−	0.0576570i	0.120611	−	0.992700i	$-0.461515\pi$
$347$	−4.35751	−	1.07403i	−0.233924	−	0.0576570i	−0.354535	+	0.935043i	$0.615361\pi$
$348$	0.731395	−	0.647960i	0.0392069	−	0.0347343i
$349$	−30.2493	+	7.45578i	−1.61921	+	0.399099i	−0.941710	−	0.336426i	$-0.890782\pi$
$349$	−30.2493	+	7.45578i	−1.61921	+	0.399099i	−0.677498	+	0.735525i	$0.736936\pi$
$350$	−0.957019	+	1.38648i	−0.0511548	+	0.0741106i
$351$	−2.54218	−	2.55682i	−0.135692	−	0.136473i
$352$	−7.63136	−	11.0559i	−0.406753	−	0.589284i
$353$	20.0576	+	17.7695i	1.06756	+	0.945773i	0.998655	−	0.0518508i	$-0.0165120\pi$
$353$	20.0576	+	17.7695i	1.06756	+	0.945773i	0.0689017	+	0.997623i	$0.478051\pi$
$354$	0.858546	+	1.24382i	0.0456312	+	0.0661082i
$355$	17.2608	+	15.2918i	0.916110	+	0.811603i
$356$	24.4374	+	12.8257i	1.29518	+	0.679762i
$357$	1.87535			0.0992543
$358$	−1.09622	+	0.575343i	−0.0579372	+	0.0304078i
$359$	−5.51605	+	4.88680i	−0.291126	+	0.257915i	−0.796026	−	0.605263i	$-0.793068\pi$
$359$	−5.51605	+	4.88680i	−0.291126	+	0.257915i	0.504900	+	0.863178i	$0.331530\pi$
$360$	−1.30353			−0.0687018
$361$	−18.7869			−0.988785
$362$	−1.59959	+	1.41712i	−0.0840728	+	0.0744820i
$363$	−6.82568	−	17.9978i	−0.358255	−	0.944642i
$364$	22.3541	+	1.41659i	1.17167	+	0.0742497i
$365$	−0.391162	+	1.03141i	−0.0204744	+	0.0539865i
$366$	−0.905166	−	2.38673i	−0.0473138	−	0.124756i
$367$	−10.0173	−	2.46905i	−0.522900	−	0.128883i	−0.0309741	−	0.999520i	$-0.509861\pi$
$367$	−10.0173	−	2.46905i	−0.522900	−	0.128883i	−0.491926	+	0.870637i	$0.663707\pi$
$368$	7.26022	+	10.5182i	0.378465	+	0.548301i
$369$	−1.49160	+	3.93303i	−0.0776497	+	0.204746i
$370$	−1.29164	−	3.40578i	−0.0671492	−	0.177058i
$371$	−1.97808	−	16.2910i	−0.102697	−	0.845786i
$372$	−4.20666	−	6.09440i	−0.218105	−	0.315980i
$373$	−21.0070	+	5.17777i	−1.08770	+	0.268095i	−0.742102	−	0.670287i	$-0.766171\pi$
$373$	−21.0070	+	5.17777i	−1.08770	+	0.268095i	−0.345601	+	0.938382i	$0.612325\pi$
$374$	−0.509649	−	0.451510i	−0.0263533	−	0.0233470i
$375$	−4.19649	+	11.0652i	−0.216706	+	0.571407i
$376$	7.66668	+	1.88967i	0.395379	+	0.0974521i
$377$	1.11486	−	1.41463i	0.0574183	−	0.0728573i
$378$	−0.646526	+	0.159354i	−0.0332537	+	0.00819630i
$379$	−0.393544	+	3.24112i	−0.0202150	+	0.166485i	−0.999320	−	0.0368695i	$-0.988261\pi$
$379$	−0.393544	+	3.24112i	−0.0202150	+	0.166485i	0.979105	+	0.203355i	$0.0651845\pi$
$380$	1.25651	−	0.659465i	0.0644574	−	0.0338299i
$381$	3.44868	+	9.09342i	0.176681	+	0.465870i
$382$	4.39872	+	1.08419i	0.225058	+	0.0554718i
$383$	16.7580	−	14.8463i	0.856294	−	0.758611i	−0.115782	−	0.993275i	$-0.536937\pi$
$383$	16.7580	−	14.8463i	0.856294	−	0.758611i	0.972077	+	0.234664i	$0.0753990\pi$
$384$	−6.16093	−	1.51853i	−0.314398	−	0.0774923i
$385$	24.3076	−	12.7576i	1.23883	−	0.650188i
$386$	−0.484421	+	0.254244i	−0.0246564	+	0.0129407i
$387$	0.135196	+	1.11344i	0.00687242	+	0.0565995i
$388$	−3.92465	−	32.3224i	−0.199244	−	1.64092i
$389$	−14.0187	+	12.4195i	−0.710779	+	0.629695i	−0.939001	−	0.343914i	$-0.888247\pi$
$389$	−14.0187	+	12.4195i	−0.710779	+	0.629695i	0.228222	+	0.973609i	$0.426709\pi$
$390$	−1.16919	+	0.210794i	−0.0592041	+	0.0106740i
$391$	1.51110	+	1.33872i	0.0764197	+	0.0677020i
$392$	1.45442	−	2.10710i	0.0734595	−	0.106424i
$393$	−4.43522	+	11.6947i	−0.223727	+	0.589920i
$394$	−0.0154993	−	0.127648i	−0.000780845	−	0.00643084i
$395$	−2.21043	+	18.2045i	−0.111219	+	0.915969i
$396$	−9.52574	−	4.99949i	−0.478686	−	0.251234i
$397$	−4.68693	+	6.79019i	−0.235230	+	0.340790i	−0.922766	−	0.385361i	$-0.874077\pi$
$397$	−4.68693	+	6.79019i	−0.235230	+	0.340790i	0.687536	+	0.726150i	$0.258692\pi$
$398$	0.786109	+	2.07280i	0.0394041	+	0.103900i
$399$	1.09737	−	0.972182i	0.0549370	−	0.0486700i
$400$	−5.37266	+	7.78364i	−0.268633	+	0.389182i
$401$	−6.60571	−	9.57003i	−0.329874	−	0.477904i	0.622594	−	0.782545i	$-0.286079\pi$
$401$	−6.60571	−	9.57003i	−0.329874	−	0.477904i	−0.952467	+	0.304641i	$0.901464\pi$
$402$	0.163464	+	1.34624i	0.00815282	+	0.0671445i
$403$	−9.62427	−	9.67969i	−0.479419	−	0.482180i
$404$	2.69601	−	22.2037i	0.134132	−	1.10467i
$405$	−1.39159	+	0.730362i	−0.0691486	+	0.0362920i
$406$	−0.117954	−	0.311020i	−0.00585397	−	0.0154356i
$407$	7.32843	−	60.3551i	0.363257	−	2.99169i
$408$	−0.489758			−0.0242466
$409$	0.760070	−	6.25974i	0.0375830	−	0.309524i	−0.961780	−	0.273825i	$-0.911711\pi$
$409$	0.760070	−	6.25974i	0.0375830	−	0.309524i	0.999363	−	0.0356992i	$-0.0113658\pi$
$410$	0.787345	+	1.14067i	0.0388842	+	0.0563335i
$411$	−1.55716	+	0.383806i	−0.0768092	+	0.0189318i
$412$	−16.5589	+	23.9897i	−0.815798	+	1.18189i
$413$	−22.2291	+	5.47898i	−1.09382	+	0.269603i
$414$	−0.634706	−	0.333119i	−0.0311941	−	0.0163719i
$415$	−2.22639	−	1.16850i	−0.109289	−	0.0573593i
$416$	−8.78926	−	0.556981i	−0.430929	−	0.0273082i
$417$	2.18427	−	1.14640i	0.106964	−	0.0561392i
$418$	−0.532285			−0.0260349
$419$	16.8830	+	8.86090i	0.824790	+	0.432883i	0.823638	−	0.567116i	$-0.191941\pi$
$419$	16.8830	+	8.86090i	0.824790	+	0.432883i	0.00115215	+	0.999999i	$0.499633\pi$
$420$	3.46214	−	9.12892i	0.168935	−	0.445446i
$421$	−1.40562	−	11.5763i	−0.0685057	−	0.564195i	−0.986036	−	0.166530i	$-0.946744\pi$
$421$	−1.40562	−	11.5763i	−0.0685057	−	0.564195i	0.917531	−	0.397665i	$-0.130179\pi$
$422$	4.91425	−	1.21125i	0.239222	−	0.0589629i
$423$	9.24339	−	2.27829i	0.449429	−	0.110774i
$424$	0.516586	+	4.25447i	0.0250876	+	0.206615i
$425$	−0.529761	+	1.39686i	−0.0256972	+	0.0677579i
$426$	−2.72397	−	1.42965i	−0.131977	−	0.0692667i
$427$	38.6675			1.87125
$428$	−7.47386	+	3.92259i	−0.361263	+	0.189605i
$429$	−18.9152	−	5.95384i	−0.913234	−	0.287454i
$430$	0.327244	+	0.171751i	0.0157811	+	0.00828256i
$431$	−21.6392	−	11.3571i	−1.04232	−	0.547054i	−0.145462	−	0.989364i	$-0.546467\pi$
$431$	−21.6392	−	11.3571i	−1.04232	−	0.547054i	−0.896862	+	0.442310i	$0.854159\pi$
$432$	−3.62956	+	0.894607i	−0.174627	+	0.0430418i
$433$	0.902478	−	1.30747i	0.0433703	−	0.0628328i	−0.800699	−	0.599067i	$-0.795538\pi$
$433$	0.902478	−	1.30747i	0.0433703	−	0.0628328i	0.844069	+	0.536234i	$0.180154\pi$
$434$	−2.44764	+	0.603289i	−0.117490	+	0.0289588i
$435$	−0.445982	−	0.646116i	−0.0213832	−	0.0309789i
$436$	−2.52673	+	20.8095i	−0.121008	+	0.996592i
$437$	1.57822			0.0754963
$438$	0.0177379	−	0.146085i	0.000847551	−	0.00698021i
$439$	11.0117	+	29.0355i	0.525560	+	1.38579i	0.890597	+	0.454794i	$0.150287\pi$
$439$	11.0117	+	29.0355i	0.525560	+	1.38579i	−0.365037	+	0.930993i	$0.618944\pi$
$440$	−6.34804	+	3.33171i	−0.302631	+	0.158833i
$441$	0.372080	−	3.06435i	0.0177181	−	0.145922i
$442$	−0.439284	+	0.0791991i	−0.0208946	+	0.00376712i
$443$	2.17007	+	17.8721i	0.103103	+	0.849131i	0.948889	+	0.315609i	$0.102209\pi$
$443$	2.17007	+	17.8721i	0.103103	+	0.849131i	−0.845786	+	0.533522i	$0.820868\pi$
$444$	−12.2833	−	17.7954i	−0.582939	−	0.844533i
$445$	12.5965	−	18.2492i	0.597133	−	0.865096i
$446$	1.87084	−	1.65742i	0.0885867	−	0.0784809i
$447$	−3.62081	−	9.54730i	−0.171259	−	0.451572i
$448$	12.5647	−	18.2031i	0.593625	−	0.860014i
$449$	20.8370	+	10.9361i	0.983358	+	0.516106i	0.878171	−	0.478346i	$-0.158764\pi$
$449$	20.8370	+	10.9361i	0.983358	+	0.516106i	0.105187	+	0.994452i	$0.466456\pi$
$450$	0.0639387	−	0.526583i	0.00301410	−	0.0248233i
$451$	2.78857	+	22.9659i	0.131308	+	1.08142i
$452$	11.7434	−	30.9648i	0.552364	−	1.45646i
$453$	4.33258	−	6.27683i	0.203563	−	0.294911i
$454$	3.31293	+	2.93500i	0.155484	+	0.137747i
$455$	3.29480	−	17.6925i	0.154463	−	0.829439i
$456$	−0.286582	+	0.253890i	−0.0134205	+	0.0118895i
$457$	−2.10061	−	17.3001i	−0.0982626	−	0.809265i	−0.955632	−	0.294563i	$-0.904826\pi$
$457$	−2.10061	−	17.3001i	−0.0982626	−	0.809265i	0.857369	−	0.514702i	$-0.172097\pi$
$458$	0.288015	+	2.37202i	0.0134581	+	0.110837i
$459$	−0.522844	+	0.274410i	−0.0244043	+	0.0128084i
$460$	9.30635	−	4.88435i	0.433911	−	0.227734i
$461$	−18.5568	−	4.57383i	−0.864275	−	0.213025i	−0.217831	−	0.975986i	$-0.569898\pi$
$461$	−18.5568	−	4.57383i	−0.864275	−	0.213025i	−0.646444	+	0.762962i	$0.723744\pi$
$462$	−2.74122	+	2.42851i	−0.127533	+	0.112985i
$463$	−6.67083	−	1.64421i	−0.310020	−	0.0764131i	0.0812362	−	0.996695i	$-0.474113\pi$
$463$	−6.67083	−	1.64421i	−0.310020	−	0.0764131i	−0.391256	+	0.920282i	$0.627959\pi$
$464$	−0.662189	−	1.74605i	−0.0307413	−	0.0810582i
$465$	−5.26832	+	2.76503i	−0.244313	+	0.128225i
$466$	−0.596229	+	4.91038i	−0.0276198	+	0.227469i
$467$	34.8608	−	8.59242i	1.61317	−	0.397610i	0.673360	−	0.739315i	$-0.264851\pi$
$467$	34.8608	−	8.59242i	1.61317	−	0.397610i	0.939807	+	0.341705i	$0.111004\pi$
$468$	−6.43956	+	2.87601i	−0.297669	+	0.132944i
$469$	−19.9461	−	4.91627i	−0.921025	−	0.227012i
$470$	1.11235	−	2.93303i	0.0513089	−	0.135290i
$471$	11.8297	+	10.4802i	0.545083	+	0.482901i
$472$	5.80523	−	1.43086i	0.267208	−	0.0658608i
$473$	3.50427	+	5.07681i	0.161126	+	0.233432i
$474$	−0.294882	−	2.42857i	−0.0135444	−	0.111548i
$475$	0.414143	+	1.09201i	0.0190022	+	0.0501046i
$476$	1.30079	−	3.42990i	0.0596215	−	0.157209i
$477$	2.93525	+	4.25244i	0.134396	+	0.194706i
$478$	−0.614085	−	0.151358i	−0.0280876	−	0.00692296i
$479$	−13.9372	−	36.7494i	−0.636808	−	1.67912i	−0.729975	−	0.683474i	$-0.760468\pi$
$479$	−13.9372	−	36.7494i	−0.636808	−	1.67912i	0.0931671	−	0.995650i	$-0.470301\pi$
$480$	−1.36125	+	3.58933i	−0.0621325	+	0.163830i
$481$	−28.1025	−	28.2643i	−1.28136	−	1.28874i
$482$	1.13852	+	3.00202i	0.0518580	+	0.136738i
$483$	8.12768	−	7.20050i	0.369822	−	0.327634i
$484$	−37.6513			−1.71142
$485$	−26.1606			−1.18789
$486$	0.156932	−	0.139030i	0.00711860	−	0.00630653i
$487$	−18.9281	+	9.93426i	−0.857716	+	0.450164i	−0.835436	−	0.549588i	$-0.814785\pi$
$487$	−18.9281	+	9.93426i	−0.857716	+	0.450164i	−0.0222801	+	0.999752i	$0.507093\pi$
$488$	−10.0982			−0.457124
$489$	5.60327	+	2.94082i	0.253388	+	0.132989i
$490$	−0.761331	−	0.674481i	−0.0343934	−	0.0304699i
$491$	−0.490237	−	0.710230i	−0.0221241	−	0.0320522i	0.811766	−	0.583983i	$-0.198507\pi$
$491$	−0.490237	−	0.710230i	−0.0221241	−	0.0320522i	−0.833890	+	0.551931i	$0.813891\pi$
$492$	6.15864	+	5.45608i	0.277653	+	0.245979i
$493$	−0.167563	−	0.242757i	−0.00754667	−	0.0109332i
$494$	−0.215991	+	0.274068i	−0.00971790	+	0.0123309i
$495$	−4.91015	+	7.11358i	−0.220695	+	0.319732i
$496$	−13.7409	+	3.38683i	−0.616986	+	0.152073i
$497$	34.8816	−	30.9024i	1.56465	−	1.38616i
$498$	0.325685	+	0.0802741i	0.0145943	+	0.00359717i
$499$	0.255173	+	0.226064i	0.0114231	+	0.0101200i	0.668815	−	0.743429i	$-0.266802\pi$
$499$	0.255173	+	0.226064i	0.0114231	+	0.0101200i	−0.657392	+	0.753549i	$0.728340\pi$
$500$	17.3268	+	15.3502i	0.774878	+	0.686482i
$501$	6.69262	−	17.6470i	0.299004	−	0.788409i
$502$	1.68459	−	2.44054i	0.0751867	−	0.108927i
$503$	14.7651	+	7.74932i	0.658343	+	0.345525i	0.760589	−	0.649234i	$-0.224911\pi$
$503$	14.7651	+	7.74932i	0.658343	+	0.345525i	−0.102246	+	0.994759i	$0.532603\pi$
$504$	−0.317521	+	2.61502i	−0.0141435	+	0.116482i
$505$	−17.4486	−	4.30070i	−0.776454	−	0.191379i
$506$	−3.94238			−0.175260
$507$	−10.7410	+	7.32329i	−0.477025	+	0.325239i
$508$	19.0233			0.844023
$509$	20.3742	+	5.02179i	0.903071	+	0.222587i	0.663398	−	0.748267i	$-0.269114\pi$
$509$	20.3742	+	5.02179i	0.903071	+	0.222587i	0.239673	+	0.970854i	$0.422960\pi$
$510$	−0.0234522	+	0.193146i	−0.00103848	+	0.00855265i
$511$	1.97385	+	1.03596i	0.0873179	+	0.0458280i
$512$	−8.70954	+	12.6179i	−0.384911	+	0.557640i
$513$	−0.163689	+	0.431613i	−0.00722706	+	0.0190562i
$514$	−2.73166	−	2.42004i	−0.120488	−	0.106743i
$515$	17.5306	+	15.5307i	0.772490	+	0.684367i
$516$	2.13019	+	0.525044i	0.0937762	+	0.0231138i
$517$	39.1913	−	34.7204i	1.72363	−	1.52700i
$518$	−7.14701	+	1.76158i	−0.314022	+	0.0773994i
$519$	6.09776	−	8.83413i	0.267662	−	0.387775i
$520$	−0.860453	+	4.62049i	−0.0377334	+	0.202622i
$521$	−16.4771	−	23.8712i	−0.721874	−	1.04582i	−0.996445	−	0.0842487i	$-0.973151\pi$
$521$	−16.4771	−	23.8712i	−0.721874	−	1.04582i	0.274570	−	0.961567i	$-0.411464\pi$
$522$	0.0783950	+	0.0694519i	0.00343126	+	0.00303983i
$523$	14.6273	+	21.1913i	0.639607	+	0.926631i	0.999981	−	0.00617686i	$-0.00196617\pi$
$523$	14.6273	+	21.1913i	0.639607	+	0.926631i	−0.360374	+	0.932808i	$0.617351\pi$
$524$	18.3125	+	16.2234i	0.799983	+	0.708723i
$525$	7.11500	+	3.73424i	0.310524	+	0.162976i
$526$	1.15952			0.0505574
$527$	−1.97940	+	1.03887i	−0.0862241	+	0.0452539i
$528$	−15.3891	+	13.6335i	−0.669724	+	0.593323i
$529$	−11.3109			−0.491778
$530$	1.70257			0.0739551
$531$	5.39571	−	4.78018i	0.234154	−	0.207442i
$532$	−1.01690	−	2.68134i	−0.0440881	−	0.116251i
$533$	12.9565	+	7.88334i	0.561207	+	0.341465i
$534$	−1.04898	+	2.76594i	−0.0453940	+	0.119694i
$535$	2.40485	+	6.34107i	0.103971	+	0.274148i
$536$	5.20902	+	1.28391i	0.224995	+	0.0554564i
$537$	3.35440	+	4.85969i	0.144753	+	0.209711i
$538$	−0.953898	+	2.51522i	−0.0411255	+	0.108439i
$539$	−6.02026	−	15.8741i	−0.259311	−	0.683747i
$540$	0.370545	+	3.05171i	0.0159457	+	0.131325i
$541$	−8.71458	−	12.6252i	−0.374669	−	0.542802i	0.589611	−	0.807688i	$-0.299281\pi$
$541$	−8.71458	−	12.6252i	−0.374669	−	0.542802i	−0.964280	+	0.264886i	$0.914666\pi$
$542$	1.83732	−	0.452858i	0.0789194	−	0.0194519i
$543$	7.62948	+	6.75913i	0.327412	+	0.290062i
$544$	−0.511448	+	1.34858i	−0.0219281	+	0.0578197i
$545$	16.3530	+	4.03065i	0.700485	+	0.172654i
$546$	0.138079	+	2.39687i	0.00590925	+	0.102577i
$547$	−23.4844	+	5.78839i	−1.00412	+	0.247494i	−0.706899	−	0.707315i	$-0.749906\pi$
$547$	−23.4844	+	5.78839i	−1.00412	+	0.247494i	−0.297222	+	0.954808i	$0.596060\pi$
$548$	−0.378128	+	3.11416i	−0.0161528	+	0.133030i
$549$	−10.7804	+	5.65800i	−0.460097	+	0.241477i
$550$	−1.03453	−	2.72783i	−0.0441125	−	0.116315i
$551$	−0.223895	−	0.0551852i	−0.00953825	−	0.00235097i
$552$	−2.12258	+	1.88044i	−0.0903431	+	0.0800370i
$553$	35.9820	+	8.86876i	1.53011	+	0.377138i
$554$	0.754187	−	0.395828i	0.0320423	−	0.0168171i
$555$	−15.3833	+	8.07377i	−0.652984	+	0.342713i
$556$	−0.581618	−	4.79005i	−0.0246661	−	0.203144i
$557$	2.99026	+	24.6270i	0.126701	+	1.04348i	0.907897	+	0.419194i	$0.137687\pi$
$557$	2.99026	+	24.6270i	0.126701	+	1.04348i	−0.781195	+	0.624286i	$0.785390\pi$
$558$	0.594120	−	0.526345i	0.0251511	−	0.0222819i
$559$	4.03597	+	0.255762i	0.170703	+	0.0108176i
$560$	−13.9663	−	12.3731i	−0.590183	−	0.522857i
$561$	−1.84483	+	2.67270i	−0.0778888	+	0.112841i
$562$	−2.10986	+	5.56324i	−0.0889990	+	0.234671i
$563$	−2.98256	−	24.5636i	−0.125700	−	1.03523i	−0.909930	−	0.414762i	$-0.863865\pi$
$563$	−2.98256	−	24.5636i	−0.125700	−	1.03523i	0.784230	−	0.620470i	$-0.213058\pi$
$564$	2.24458	−	18.4858i	0.0945140	−	0.778393i
$565$	−23.5604	−	12.3654i	−0.991192	−	0.520218i
$566$	−0.00826204	+	0.0119696i	−0.000347279	+	0.000503121i
$567$	1.12622	+	2.96959i	0.0472967	+	0.124711i
$568$	−9.10949	+	8.07031i	−0.382226	+	0.338623i
$569$	11.0139	−	15.9564i	0.461728	−	0.668928i	−0.521091	−	0.853501i	$-0.674475\pi$
$569$	11.0139	−	15.9564i	0.461728	−	0.668928i	0.982819	+	0.184573i	$0.0590903\pi$
$570$	0.0864036	+	0.125177i	0.00361905	+	0.00524310i
$571$	−1.44286	−	11.8830i	−0.0603817	−	0.497288i	−0.991256	−	0.131949i	$-0.957876\pi$
$571$	−1.44286	−	11.8830i	−0.0603817	−	0.497288i	0.930875	−	0.365338i	$-0.119047\pi$
$572$	−24.0092	+	30.4649i	−1.00387	+	1.27380i
$573$	2.60458	−	21.4506i	0.108808	−	0.896113i
$574$	2.48010	−	1.30165i	0.103517	−	0.0543300i
$575$	3.06736	+	8.08797i	0.127918	+	0.337292i
$576$	−0.839449	+	6.91349i	−0.0349771	+	0.288062i
$577$	17.1254			0.712940			0.356470	−	0.934307i	$-0.383980\pi$
$577$	17.1254			0.712940			0.356470	+	0.934307i	$0.383980\pi$
$578$	0.420807	−	3.46566i	0.0175033	−	0.144152i
$579$	1.48231	+	2.14750i	0.0616027	+	0.0892469i
$580$	−1.49105	+	0.367510i	−0.0619123	+	0.0152600i
$581$	−2.88646	+	4.18176i	−0.119751	+	0.173489i
$582$	3.38853	−	0.835198i	0.140459	−	0.0346201i
$583$	25.1633	+	13.2067i	1.04216	+	0.546966i
$584$	−0.515480	−	0.270545i	−0.0213307	−	0.0111952i
$585$	1.67027	+	5.41475i	0.0690570	+	0.223872i
$586$	4.93018	−	2.58756i	0.203664	−	0.106891i
$587$	9.00430			0.371647			0.185824	−	0.982583i	$-0.440505\pi$
$587$	9.00430			0.371647			0.185824	+	0.982583i	$0.440505\pi$
$588$	−5.34641	−	2.80601i	−0.220482	−	0.115718i
$589$	−0.619701	+	1.63402i	−0.0255343	+	0.0673285i
$590$	−0.286305	−	2.35793i	−0.0117870	−	0.0970745i
$591$	−0.595487	+	0.146774i	−0.0244951	+	0.00603749i
$592$	−40.1230	+	9.88942i	−1.64904	+	0.406453i
$593$	0.584206	+	4.81137i	0.0239905	+	0.197579i	0.999776	−	0.0211486i	$-0.00673233\pi$
$593$	0.584206	+	4.81137i	0.0239905	+	0.197579i	−0.975786	+	0.218728i	$0.929809\pi$
$594$	0.408896	−	1.07817i	0.0167772	−	0.0442379i
$595$	−2.60972	−	1.36969i	−0.106988	−	0.0561517i
$596$	−19.9728			−0.818119
$597$	9.36247	−	4.91380i	0.383180	−	0.201109i
$598$	−1.59975	+	2.02989i	−0.0654185	+	0.0830085i
$599$	5.73740	+	3.01122i	0.234424	+	0.123035i	0.577845	−	0.816146i	$-0.303894\pi$
$599$	5.73740	+	3.01122i	0.234424	+	0.123035i	−0.343422	+	0.939181i	$0.611586\pi$
$600$	−1.85812	−	0.975214i	−0.0758572	−	0.0398130i
$601$	3.25342	−	0.801896i	0.132710	−	0.0327100i	−0.172401	−	0.985027i	$-0.555153\pi$
$601$	3.25342	−	0.801896i	0.132710	−	0.0327100i	0.305111	+	0.952317i	$0.401306\pi$
$602$	0.424265	−	0.614653i	0.0172917	−	0.0250514i
$603$	6.28029	−	1.54795i	0.255753	−	0.0630375i
$604$	−8.47472	−	12.2777i	−0.344831	−	0.499575i
$605$	−3.64640	+	30.0308i	−0.148247	+	1.22093i
$606$	2.39739			0.0973874
$607$	1.56865	−	12.9190i	0.0636697	−	0.524367i	−0.925626	−	0.378440i	$-0.876461\pi$
$607$	1.56865	−	12.9190i	0.0636697	−	0.524367i	0.989295	−	0.145927i	$-0.0466164\pi$
$608$	0.399826	+	1.05426i	0.0162151	+	0.0427557i
$609$	−1.40482	+	0.737307i	−0.0569262	+	0.0298772i
$610$	−0.483555	+	3.98244i	−0.0195786	+	0.161244i
$611$	−1.97412	−	34.2681i	−0.0798644	−	1.38634i
$612$	0.139220	+	1.14658i	0.00562765	+	0.0463479i
$613$	−26.8335	−	38.8750i	−1.08379	−	1.57015i	−0.788803	−	0.614646i	$-0.789299\pi$
$613$	−26.8335	−	38.8750i	−1.08379	−	1.57015i	−0.294990	−	0.955500i	$-0.595316\pi$
$614$	2.66780	−	3.86497i	0.107664	−	0.155978i
$615$	4.94823	−	4.38375i	0.199532	−	0.176770i
$616$	5.13750	+	13.5465i	0.206996	+	0.545803i
$617$	−1.94785	+	2.82195i	−0.0784176	+	0.113608i	−0.860230	−	0.509906i	$-0.829680\pi$
$617$	−1.94785	+	2.82195i	−0.0784176	+	0.113608i	0.781812	+	0.623514i	$0.214295\pi$
$618$	−2.76654	−	1.45199i	−0.111286	−	0.0584077i
$619$	−3.18512	+	26.2318i	−0.128021	+	1.05435i	0.777155	+	0.629309i	$0.216662\pi$
$619$	−3.18512	+	26.2318i	−0.128021	+	1.05435i	−0.905176	+	0.425037i	$0.860261\pi$
$620$	1.40282	+	11.5533i	0.0563387	+	0.463991i
$621$	−1.21237	+	3.19676i	−0.0486507	+	0.128281i
$622$	−0.585620	+	0.848417i	−0.0234812	+	0.0340184i
$623$	−33.5417	−	29.7154i	−1.34382	−	1.19052i
$624$	0.775170	+	13.4559i	0.0310317	+	0.538668i
$625$	4.45256	−	3.94462i	0.178102	−	0.157785i
$626$	−0.147310	−	1.21321i	−0.00588768	−	0.0484894i
$627$	0.306019	+	2.52029i	0.0122212	+	0.100651i
$628$	27.3729	−	14.3664i	1.09230	−	0.573282i
$629$	−5.77977	+	3.03346i	−0.230455	+	0.120952i
$630$	1.01608	+	0.250442i	0.0404818	+	0.00997786i
$631$	26.6133	−	23.5774i	1.05946	−	0.938600i	0.0612333	−	0.998123i	$-0.480497\pi$
$631$	26.6133	−	23.5774i	1.05946	−	0.938600i	0.998227	+	0.0595236i	$0.0189582\pi$
$632$	−9.39686	−	2.31612i	−0.373787	−	0.0921302i
$633$	−8.56040	−	22.5719i	−0.340245	−	0.897153i
$634$	−1.09293	+	0.573611i	−0.0434056	+	0.0227810i
$635$	1.84234	−	15.1731i	0.0731112	−	0.602125i
$636$	9.81339	−	2.41878i	0.389126	−	0.0959110i
$637$	−10.6163	−	3.34165i	−0.420635	−	0.132401i
$638$	0.559290	+	0.137853i	0.0221425	+	0.00545764i
$639$	−5.20313	+	13.7195i	−0.205833	+	0.542736i
$640$	7.46439	+	6.61288i	0.295056	+	0.261397i
$641$	−39.1922	+	9.66000i	−1.54800	+	0.381547i	−0.918489	−	0.395446i	$-0.870590\pi$
$641$	−39.1922	+	9.66000i	−1.54800	+	0.381547i	−0.629509	+	0.776993i	$0.716744\pi$
$642$	−0.513940	−	0.744571i	−0.0202836	−	0.0293859i
$643$	−1.01036	−	8.32102i	−0.0398445	−	0.328149i	−0.998978	−	0.0451956i	$-0.985609\pi$
$643$	−1.01036	−	8.32102i	−0.0398445	−	0.328149i	0.959134	−	0.282953i	$-0.0913142\pi$
$644$	−7.53168	−	19.8594i	−0.296790	−	0.782570i
$645$	0.625078	−	1.64820i	0.0246124	−	0.0648977i
$646$	0.0324634	+	0.0470313i	0.00127725	+	0.00185042i
$647$	−18.5959	−	4.58349i	−0.731082	−	0.180196i	−0.143833	−	0.989602i	$-0.545943\pi$
$647$	−18.5959	−	4.58349i	−0.731082	−	0.180196i	−0.587249	+	0.809406i	$0.699789\pi$
$648$	−0.294117	−	0.775524i	−0.0115540	−	0.0304654i
$649$	14.0588	−	37.0701i	0.551857	−	1.45513i
$650$	−1.82433	−	0.574234i	−0.0715559	−	0.0225233i
$651$	4.26368	+	11.2424i	0.167107	+	0.440624i
$652$	9.26511	−	8.20817i	0.362850	−	0.321457i
$653$	20.7037			0.810197			0.405099	−	0.914273i	$-0.367237\pi$
$653$	20.7037			0.810197			0.405099	+	0.914273i	$0.367237\pi$
$654$	−2.24686			−0.0878590
$655$	14.7134	−	13.0349i	0.574899	−	0.509316i
$656$	13.9231	−	7.30742i	0.543607	−	0.285307i
$657$	−0.701889			−0.0273833
$658$	−5.61304	−	2.94595i	−0.218819	−	0.114845i
$659$	−2.08008	−	1.84279i	−0.0810283	−	0.0717848i	0.621636	−	0.783306i	$-0.286468\pi$
$659$	−2.08008	−	1.84279i	−0.0810283	−	0.0717848i	−0.702665	+	0.711521i	$0.748007\pi$
$660$	9.60447	+	13.9145i	0.373853	+	0.541620i
$661$	7.39598	+	6.55227i	0.287670	+	0.254854i	0.794599	−	0.607134i	$-0.207681\pi$
$661$	7.39598	+	6.55227i	0.287670	+	0.254854i	−0.506929	+	0.861988i	$0.669219\pi$
$662$	2.63664	+	3.81983i	0.102476	+	0.148462i
$663$	0.627548	+	2.03442i	0.0243720	+	0.0790102i
$664$	0.753812	−	1.09209i	0.0292536	−	0.0423812i
$665$	−2.23713	+	0.551402i	−0.0867521	+	0.0213825i
$666$	1.73481	−	1.53691i	0.0672224	−	0.0595539i
$667$	−1.65829	−	0.408731i	−0.0642091	−	0.0158261i
$668$	−27.6330	−	24.4807i	−1.06915	−	0.947186i
$669$	−8.92321	−	7.90527i	−0.344991	−	0.305635i
$670$	0.755771	−	1.99280i	0.0291980	−	0.0769887i
$671$	−38.0382	+	55.1078i	−1.46845	+	2.12741i
$672$	6.86904	+	3.60515i	0.264979	+	0.139072i
$673$	−6.14666	+	50.6223i	−0.236936	+	1.95135i	0.0646496	+	0.997908i	$0.479407\pi$
$673$	−6.14666	+	50.6223i	−0.236936	+	1.95135i	−0.301586	+	0.953439i	$0.597516\pi$
$674$	3.32531	+	0.819615i	0.128086	+	0.0315704i
$675$	−2.53005			−0.0973818
$676$	5.94360	+	24.7242i	0.228600	+	0.950930i
$677$	−45.3353			−1.74238			−0.871189	−	0.490947i	$-0.836651\pi$
$677$	−45.3353			−1.74238			−0.871189	+	0.490947i	$0.836651\pi$
$678$	3.44651	+	0.849488i	0.132362	+	0.0326244i
$679$	−6.37236	+	52.4811i	−0.244549	+	2.01404i
$680$	0.681541	+	0.357700i	0.0261359	+	0.0137172i
$681$	11.9922	−	17.3737i	0.459541	−	0.665760i
$682$	1.54801	−	4.08177i	0.0592765	−	0.156299i
$683$	4.61771	+	4.09094i	0.176692	+	0.156535i	0.746833	−	0.665011i	$-0.231573\pi$
$683$	4.61771	+	4.09094i	0.176692	+	0.156535i	−0.570142	+	0.821546i	$0.693112\pi$
$684$	0.675853	+	0.598753i	0.0258419	+	0.0228939i
$685$	2.44725	+	0.603192i	0.0935045	+	0.0230468i
$686$	1.95037	−	1.72787i	0.0744653	−	0.0659705i
$687$	11.0656	−	2.72742i	0.422178	−	0.104058i
$688$	2.38180	−	3.45063i	0.0908053	−	0.131554i
$689$	17.0108	−	7.59730i	0.648060	−	0.289434i
$690$	0.639951	+	0.927129i	0.0243625	+	0.0352952i
$691$	4.01203	+	3.55435i	0.152625	+	0.135214i	0.735980	−	0.677004i	$-0.236722\pi$
$691$	4.01203	+	3.55435i	0.152625	+	0.135214i	−0.583355	+	0.812217i	$0.698260\pi$
$692$	−11.9275	−	17.2799i	−0.453415	−	0.656885i
$693$	13.0746	+	11.5831i	0.496664	+	0.440006i
$694$	−0.833158	−	0.437275i	−0.0316262	−	0.0165987i
$695$	−3.87689			−0.147059
$696$	0.366875	−	0.192551i	0.0139064	−	0.00729863i
$697$	1.85914	−	1.64705i	0.0704199	−	0.0623866i
$698$	−6.53186			−0.247235
$699$	23.5928			0.892360
$700$	11.7648	−	10.4227i	0.444667	−	0.393941i
$701$	14.3360	+	37.8009i	0.541463	+	1.42772i	0.874601	+	0.484843i	$0.161123\pi$
$701$	14.3360	+	37.8009i	0.541463	+	1.42772i	−0.333138	+	0.942878i	$0.608107\pi$
$702$	−0.389217	−	0.648038i	−0.0146900	−	0.0244586i
$703$	−1.80950	+	4.77126i	−0.0682466	+	0.179952i
$704$	13.5823	+	35.8136i	0.511902	+	1.34978i
$705$	−14.5270	−	3.58058i	−0.547117	−	0.134852i
$706$	3.19149	+	4.62367i	0.120113	+	0.174014i
$707$	−12.8780	+	33.9564i	−0.484326	+	1.27706i
$708$	−5.00004	−	13.1840i	−0.187913	−	0.495486i
$709$	−0.808819	−	6.66123i	−0.0303759	−	0.250168i	−0.999985	−	0.00550783i	$-0.998247\pi$
$709$	−0.808819	−	6.66123i	−0.0303759	−	0.250168i	0.969609	−	0.244660i	$-0.0786763\pi$
$710$	2.74648	+	3.97897i	0.103074	+	0.149328i
$711$	−11.3294	+	2.79245i	−0.424886	+	0.104725i
$712$	8.75958	+	7.76031i	0.328279	+	0.290830i
$713$	−4.58983	+	12.1024i	−0.171891	+	0.453238i
$714$	0.381761	+	0.0940956i	0.0142870	+	0.00352144i
$715$	21.9737	+	22.1002i	0.821770	+	0.826502i
$716$	11.2147	−	2.76418i	0.419114	−	0.103302i
$717$	−0.363613	+	2.99462i	−0.0135794	+	0.111836i
$718$	−1.36808	+	0.718025i	−0.0510564	+	0.0267965i
$719$	3.92037	+	10.3372i	0.146205	+	0.385511i	0.988035	−	0.154232i	$-0.0492904\pi$
$719$	3.92037	+	10.3372i	0.146205	+	0.385511i	−0.841829	+	0.539744i	$0.818521\pi$
$720$	5.70425	+	1.40597i	0.212585	+	0.0523974i
$721$	35.4267	−	31.3853i	1.31936	−	1.16885i
$722$	−3.82440	−	0.942630i	−0.142330	−	0.0350811i
$723$	13.5596	−	7.11662i	0.504287	−	0.264670i
$724$	17.6540	−	9.26551i	0.656104	−	0.344350i
$725$	−0.152344	−	1.25466i	−0.00565791	−	0.0465971i
$726$	−0.486447	−	4.00625i	−0.0180537	−	0.148686i
$727$	6.78406	−	6.01015i	0.251607	−	0.222904i	−0.527886	−	0.849315i	$-0.677015\pi$
$727$	6.78406	−	6.01015i	0.251607	−	0.222904i	0.779493	+	0.626411i	$0.215477\pi$
$728$	9.05965	+	2.85166i	0.335773	+	0.105690i
$729$	−0.748511	−	0.663123i	−0.0277226	−	0.0245601i
$730$	−0.131379	+	0.190335i	−0.00486254	+	0.00704461i
$731$	0.234853	−	0.619257i	0.00868635	−	0.0229040i
$732$	2.87056	+	23.6412i	0.106099	+	0.873802i
$733$	−5.81979	+	47.9303i	−0.214959	+	1.77035i	0.341898	+	0.939737i	$0.388930\pi$
$733$	−5.81979	+	47.9303i	−0.214959	+	1.77035i	−0.556856	+	0.830609i	$0.687993\pi$
$734$	−1.91532	−	1.00524i	−0.0706956	−	0.0371039i
$735$	−2.75587	+	3.99257i	−0.101652	+	0.147268i
$736$	2.96133	+	7.80838i	0.109156	+	0.287821i
$737$	26.6280	−	23.5903i	0.980854	−	0.868961i
$738$	−0.500981	+	0.725796i	−0.0184414	+	0.0267169i
$739$	19.1195	+	27.6993i	0.703321	+	1.01894i	0.997992	+	0.0633372i	$0.0201743\pi$
$739$	19.1195	+	27.6993i	0.703321	+	1.01894i	−0.294672	+	0.955599i	$0.595210\pi$
$740$	4.09619	+	33.7351i	0.150579	+	1.24013i
$741$	1.42185	+	0.865122i	0.0522330	+	0.0317810i
$742$	0.414724	−	3.41556i	0.0152250	−	0.125389i
$743$	−28.8498	+	15.1416i	−1.05840	+	0.555490i	−0.901791	−	0.432172i	$-0.857747\pi$
$743$	−28.8498	+	15.1416i	−1.05840	+	0.555490i	−0.156606	+	0.987661i	$0.550055\pi$
$744$	−1.11348	−	2.93600i	−0.0408221	−	0.107639i
$745$	−1.93430	+	15.9304i	−0.0708673	+	0.583645i
$746$	−4.53614			−0.166080
$747$	0.192845	−	1.58822i	0.00705584	−	0.0581100i
$748$	3.60857	+	5.22791i	0.131942	+	0.191151i
$749$	13.3067	−	3.27981i	0.486217	−	0.119842i
$750$	−1.40947	+	2.04196i	−0.0514664	+	0.0745620i
$751$	−41.2977	+	10.1790i	−1.50698	+	0.371436i	−0.904421	−	0.426641i	$-0.859697\pi$
$751$	−41.2977	+	10.1790i	−1.50698	+	0.371436i	−0.602555	+	0.798078i	$0.705850\pi$
$752$	−31.5113	−	16.5384i	−1.14910	−	0.603094i
$753$	−12.5241	−	6.57317i	−0.456404	−	0.239540i
$754$	0.297929	−	0.232035i	0.0108499	−	0.00845021i
$755$	−10.6135	+	5.57041i	−0.386266	+	0.202728i
$756$	6.21236			0.225941
$757$	−7.63075	−	4.00493i	−0.277344	−	0.145562i	0.320316	−	0.947311i	$-0.396211\pi$
$757$	−7.63075	−	4.00493i	−0.277344	−	0.145562i	−0.597661	+	0.801749i	$0.703903\pi$
$758$	−0.242735	+	0.640041i	−0.00881655	+	0.0232473i
$759$	2.26654	+	18.6666i	0.0822701	+	0.677555i
$760$	0.584236	−	0.144001i	0.0211925	−	0.00522348i
$761$	33.8321	−	8.33887i	1.22641	−	0.302284i	0.427659	−	0.903940i	$-0.359339\pi$
$761$	33.8321	−	8.33887i	1.22641	−	0.302284i	0.798755	+	0.601656i	$0.205492\pi$
$762$	0.245777	+	2.02416i	0.00890358	+	0.0733276i
$763$	12.0693	−	31.8242i	0.436939	−	1.15211i
$764$	−37.4252	−	19.6422i	−1.35399	−	0.710631i
$765$	0.928002			0.0335520
$766$	4.15629	−	2.18139i	0.150173	−	0.0788169i
$767$	−13.3822	−	22.2811i	−0.483203	−	0.804524i
$768$	11.1551	+	5.85466i	0.402526	+	0.211262i
$769$	13.6336	+	7.15547i	0.491640	+	0.258033i	0.692276	−	0.721633i	$-0.256608\pi$
$769$	13.6336	+	7.15547i	0.491640	+	0.258033i	−0.200635	+	0.979666i	$0.564301\pi$
$770$	5.58834	−	1.37740i	0.201390	−	0.0496382i
$771$	−9.88807	+	14.3253i	−0.356110	+	0.515915i
$772$	4.95579	−	1.22149i	0.178363	−	0.0439625i
$773$	30.8971	+	44.7622i	1.11129	+	1.60999i	0.726787	+	0.686863i	$0.241013\pi$
$773$	30.8971	+	44.7622i	1.11129	+	1.60999i	0.384506	+	0.923123i	$0.374372\pi$
$774$	−0.0283452	+	0.233444i	−0.00101885	+	0.00839097i
$775$	−9.57836			−0.344065
$776$	1.66417	−	13.7057i	0.0597403	−	0.492006i
$777$	12.4498	+	32.8273i	0.446633	+	1.17767i
$778$	−3.47691	+	1.82482i	−0.124653	+	0.0654230i
$779$	0.234047	−	1.92755i	0.00838561	−	0.0690617i
$780$	11.0617	+	0.700989i	0.396074	+	0.0250994i
$781$	9.72731	+	80.1116i	0.348071	+	2.86662i
$782$	0.240441	+	0.348339i	0.00859815	+	0.0124566i
$783$	0.283775	−	0.411119i	0.0101413	−	0.0146922i
$784$	−8.63727	+	7.65195i	−0.308474	+	0.273284i
$785$	−8.80772	−	23.2241i	−0.314361	−	0.828902i
$786$	−1.48965	+	2.15812i	−0.0531339	+	0.0769777i
$787$	11.6582	+	6.11871i	0.415571	+	0.218108i	0.659532	−	0.751677i	$-0.270755\pi$
$787$	11.6582	+	6.11871i	0.415571	+	0.218108i	−0.243961	+	0.969785i	$0.578447\pi$
$788$	−0.144603	+	1.19091i	−0.00515126	+	0.0424244i
$789$	−0.666625	−	5.49015i	−0.0237325	−	0.195455i
$790$	−1.36338	+	3.59494i	−0.0485069	+	0.127902i
$791$	−30.5455	+	44.2528i	−1.08607	+	1.57345i
$792$	−3.41450	−	3.02498i	−0.121329	−	0.107488i
$793$	12.9393	+	41.9472i	0.459487	+	1.48959i
$794$	−1.29480	+	1.14709i	−0.0459508	+	0.0407089i
$795$	−0.978837	−	8.06144i	−0.0347158	−	0.285910i
$796$	−2.49299	−	20.5316i	−0.0883618	−	0.727725i
$797$	15.8143	−	8.29999i	0.560172	−	0.294001i	−0.160775	−	0.986991i	$-0.551399\pi$
$797$	15.8143	−	8.29999i	0.560172	−	0.294001i	0.720947	+	0.692990i	$0.243707\pi$
$798$	0.272167	−	0.142844i	0.00963461	−	0.00505663i
$799$	−5.45804	−	1.34529i	−0.193092	−	0.0475928i
$800$	−4.62572	+	4.09803i	−0.163544	+	0.144887i
$801$	13.6994	+	3.37661i	0.484046	+	0.119307i
$802$	−0.864533	−	2.27958i	−0.0305277	−	0.0804949i
$803$	−3.41813	+	1.79397i	−0.120623	+	0.0633080i
$804$	1.52505	−	12.5599i	0.0537844	−	0.442954i
$805$	−16.5693	+	4.08398i	−0.583993	+	0.143941i
$806$	−1.47351	−	2.45336i	−0.0519022	−	0.0864161i
$807$	12.4576	+	3.07053i	0.438530	+	0.108088i
$808$	3.36314	−	8.86787i	0.118315	−	0.311971i
$809$	−11.4367	−	10.1320i	−0.402093	−	0.356223i	0.437709	−	0.899117i	$-0.355790\pi$
$809$	−11.4367	−	10.1320i	−0.402093	−	0.356223i	−0.839801	+	0.542894i	$0.817329\pi$
$810$	−0.319928	+	0.0788551i	−0.0112411	+	0.00277068i
$811$	−28.4806	−	41.2613i	−1.00009	−	1.44888i	−0.890543	−	0.454899i	$-0.849676\pi$
$811$	−28.4806	−	41.2613i	−1.00009	−	1.44888i	−0.109547	−	0.993982i	$-0.534940\pi$
$812$	0.374069	+	3.08073i	0.0131272	+	0.108113i
$813$	−3.20052	−	8.43907i	−0.112247	−	0.295971i
$814$	4.52013	−	11.9186i	0.158431	−	0.417747i
$815$	−5.64958	−	8.18482i	−0.197896	−	0.286702i
$816$	2.14319	+	0.528248i	0.0750265	+	0.0184924i
$817$	−0.183597	−	0.484107i	−0.00642326	−	0.0169367i
$818$	0.468807	−	1.23614i	0.0163914	−	0.0432207i
$819$	11.2695	−	2.03179i	0.393787	−	0.0709964i
$820$	−4.58538	−	12.0907i	−0.160128	−	0.422224i
$821$	4.35691	−	3.85989i	0.152057	−	0.134711i	−0.583664	−	0.811995i	$-0.698382\pi$
$821$	4.35691	−	3.85989i	0.152057	−	0.134711i	0.735722	+	0.677284i	$0.236843\pi$
$822$	−0.336245			−0.0117279
$823$	7.15550			0.249425			0.124713	−	0.992193i	$-0.460199\pi$
$823$	7.15550			0.249425			0.124713	+	0.992193i	$0.460199\pi$
$824$	−9.25185	+	8.19643i	−0.322304	+	0.285536i
$825$	−12.3211	+	6.46662i	−0.428966	+	0.225139i
$826$	−4.80003			−0.167014
$827$	−33.9596	−	17.8234i	−1.18089	−	0.619779i	−0.244127	−	0.969743i	$-0.578501\pi$
$827$	−33.9596	−	17.8234i	−1.18089	−	0.619779i	−0.936763	+	0.349964i	$0.886194\pi$
$828$	5.00572	+	4.43468i	0.173961	+	0.154116i
$829$	−23.4978	−	34.0424i	−0.816112	−	1.18234i	−0.980611	−	0.195965i	$-0.937216\pi$
$829$	−23.4978	−	34.0424i	−0.816112	−	1.18234i	0.164499	−	0.986377i	$-0.447399\pi$
$830$	−0.394590	−	0.349576i	−0.0136964	−	0.0121340i
$831$	−2.30778	−	3.34340i	−0.0800561	−	0.115981i
$832$	23.9515	+	7.53910i	0.830369	+	0.261371i
$833$	−1.03543	+	1.50008i	−0.0358755	+	0.0519746i
$834$	0.502167	−	0.123773i	0.0173886	−	0.00428591i
$835$	−22.2020	+	19.6693i	−0.768333	+	0.680684i
$836$	4.82170	+	1.18844i	0.166762	+	0.0411032i
$837$	−2.83374	−	2.51047i	−0.0979483	−	0.0867746i
$838$	2.99224	+	2.65089i	0.103365	+	0.0915736i
$839$	−1.28220	+	3.38088i	−0.0442664	+	0.116721i	−0.955326	−	0.295553i	$-0.904496\pi$
$839$	−1.28220	+	3.38088i	−0.0442664	+	0.116721i	0.911060	+	0.412274i	$0.135265\pi$
$840$	2.35177	−	3.40713i	0.0811439	−	0.117557i
$841$	−25.4573	−	13.3610i	−0.877837	−	0.460724i
$842$	0.294702	−	2.42709i	0.0101561	−	0.0836430i
$843$	27.5541	+	6.79148i	0.949015	+	0.233911i
$844$	−47.2202			−1.62539
$845$	20.2957	−	2.34618i	0.698194	−	0.0807111i
$846$	1.99597			0.0686227
$847$	59.3571	+	14.6302i	2.03953	+	0.502700i
$848$	2.32824	−	19.1748i	0.0799521	−	0.658465i
$849$	0.0614245	+	0.0322381i	0.00210808	+	0.00110641i
$850$	−0.177929	+	0.257775i	−0.00610293	+	0.00884162i
$851$	−13.4021	+	35.3385i	−0.459419	+	1.21139i
$852$	21.4831	+	19.0324i	0.735998	+	0.652038i
$853$	2.37512	+	2.10418i	0.0813227	+	0.0720456i	0.702805	−	0.711383i	$-0.251931\pi$
$853$	2.37512	+	2.10418i	0.0813227	+	0.0720456i	−0.621482	+	0.783428i	$0.713469\pi$
$854$	7.87145	+	1.94014i	0.269355	+	0.0663901i
$855$	0.543022	−	0.481075i	0.0185710	−	0.0164524i
$856$	−3.47511	+	0.856538i	−0.118777	+	0.0292759i
$857$	1.04007	−	1.50680i	0.0355280	−	0.0514712i	−0.804817	−	0.593523i	$-0.797737\pi$
$857$	1.04007	−	1.50680i	0.0355280	−	0.0514712i	0.840345	+	0.542051i	$0.182352\pi$
$858$	−3.55178	−	2.16107i	−0.121256	−	0.0737779i
$859$	−0.872804	−	1.26447i	−0.0297797	−	0.0431433i	0.807811	−	0.589441i	$-0.200652\pi$
$859$	−0.872804	−	1.26447i	−0.0297797	−	0.0431433i	−0.837591	+	0.546298i	$0.816037\pi$
$860$	−2.58087	−	2.28645i	−0.0880070	−	0.0779674i
$861$	−7.58900	−	10.9946i	−0.258632	−	0.374694i
$862$	−3.83520	−	3.39769i	−0.130627	−	0.115726i
$863$	−24.0065	−	12.5996i	−0.817190	−	0.428894i	0.00369129	−	0.999993i	$-0.498825\pi$
$863$	−24.0065	−	12.5996i	−0.817190	−	0.428894i	−0.820881	+	0.571099i	$0.806517\pi$
$864$	−2.44259			−0.0830987
$865$	−14.9377	+	7.83990i	−0.507896	+	0.266565i
$866$	0.249317	−	0.220876i	0.00847213	−	0.00750566i
$867$	−16.6513			−0.565509
$868$	23.5189			0.798285
$869$	−48.0358	+	42.5560i	−1.62950	+	1.44361i
$870$	−0.0583686	−	0.153905i	−0.00197888	−	0.00521788i
$871$	−1.34129	−	23.2830i	−0.0454479	−	0.788915i
$872$	−3.15196	+	8.31104i	−0.106739	+	0.281447i
$873$	−5.90266	−	15.5640i	−0.199775	−	0.526763i
$874$	0.321273	+	0.0791867i	0.0108672	+	0.00267853i
$875$	−21.3510	−	30.9322i	−0.721795	−	1.04570i
$876$	−0.486846	+	1.28371i	−0.0164490	+	0.0433725i
$877$	20.9663	+	55.2836i	0.707981	+	1.86679i	0.409001	+	0.912534i	$0.365877\pi$
$877$	20.9663	+	55.2836i	0.707981	+	1.86679i	0.298980	+	0.954259i	$0.403354\pi$
$878$	0.784772	+	6.46318i	0.0264848	+	0.218122i
$879$	−15.0862	−	21.8561i	−0.508843	−	0.737187i
$880$	31.3727	−	7.73267i	1.05757	−	0.260668i
$881$	31.9548	+	28.3094i	1.07658	+	0.953769i	0.999066	−	0.0432218i	$-0.0137622\pi$
$881$	31.9548	+	28.3094i	1.07658	+	0.953769i	0.0775174	+	0.996991i	$0.475301\pi$
$882$	0.229497	−	0.605133i	0.00772756	−	0.0203759i
$883$	−10.4785	−	2.58271i	−0.352628	−	0.0869150i	0.0590229	−	0.998257i	$-0.481202\pi$
$883$	−10.4785	−	2.58271i	−0.352628	−	0.0869150i	−0.411651	+	0.911342i	$0.635048\pi$
$884$	4.15609	+	0.263374i	0.139784	+	0.00885823i
$885$	−10.9999	+	2.71123i	−0.369757	+	0.0911368i
$886$	−0.454976	+	3.74706i	−0.0152852	+	0.125885i
$887$	9.73272	−	5.10812i	0.326793	−	0.171514i	−0.293346	−	0.956006i	$-0.594769\pi$
$887$	9.73272	−	5.10812i	0.326793	−	0.171514i	0.620138	+	0.784492i	$0.287076\pi$
$888$	−3.25131	−	8.57301i	−0.109107	−	0.287691i
$889$	−29.9902	−	7.39192i	−1.00584	−	0.247917i
$890$	3.47989	−	3.08292i	0.116646	−	0.103340i
$891$	−5.34006	−	1.31621i	−0.178899	−	0.0440946i
$892$	−20.6475	+	10.8367i	−0.691331	+	0.362838i
$893$	−3.89118	+	2.04225i	−0.130213	+	0.0683412i
$894$	−0.258045	−	2.12519i	−0.00863031	−	0.0710770i
$895$	−1.11861	−	9.21261i	−0.0373911	−	0.307944i
$896$	15.0844	−	13.3636i	0.503935	−	0.446448i
$897$	10.5310	+	6.40755i	0.351619	+	0.213942i
$898$	3.69301	+	3.27172i	0.123237	+	0.109179i
$899$	1.07432	−	1.55643i	0.0358307	−	0.0519097i
$900$	−1.75490	+	4.62730i	−0.0584967	+	0.154243i
$901$	−0.367766	−	3.02883i	−0.0122521	−	0.100905i
$902$	−0.584650	+	4.81503i	−0.0194667	+	0.160323i
$903$	−3.15421	−	1.65546i	−0.104966	−	0.0550902i
$904$	7.97710	−	11.5568i	0.265314	−	0.384374i
$905$	−5.68048	−	14.9782i	−0.188826	−	0.497892i
$906$	1.19691	−	1.06037i	0.0397647	−	0.0352285i
$907$	17.8593	−	25.8736i	0.593008	−	0.859120i	−0.405479	−	0.914104i	$-0.632895\pi$
$907$	17.8593	−	25.8736i	0.593008	−	0.859120i	0.998487	+	0.0549839i	$0.0175108\pi$
$908$	−23.4572	−	33.9836i	−0.778455	−	1.12779i
$909$	−1.37830	−	11.3513i	−0.0457153	−	0.376500i
$910$	1.55844	−	3.43631i	0.0516616	−	0.113913i
$911$	−5.37582	+	44.2739i	−0.178109	+	1.46686i	0.579938	+	0.814660i	$0.303077\pi$
$911$	−5.37582	+	44.2739i	−0.178109	+	1.46686i	−0.758047	+	0.652199i	$0.773846\pi$
$912$	1.52793	−	0.801920i	0.0505949	−	0.0265542i
$913$	−3.12024	−	8.22739i	−0.103265	−	0.272287i
$914$	0.440414	−	3.62714i	0.0145676	−	0.119975i
$915$	19.1343			0.632560
$916$	2.68707	−	22.1300i	0.0887832	−	0.731196i
$917$	−22.5656	−	32.6918i	−0.745180	−	1.07958i
$918$	−0.120202	+	0.0296272i	−0.00396727	+	0.000977845i
$919$	−9.57077	+	13.8657i	−0.315711	+	0.457386i	−0.948426	−	0.316999i	$-0.897325\pi$
$919$	−9.57077	+	13.8657i	−0.315711	+	0.457386i	0.632715	+	0.774384i	$0.281940\pi$
$920$	4.32716	−	1.06655i	0.142662	−	0.0351631i
$921$	−19.8339	−	10.4096i	−0.653548	−	0.343009i
$922$	−3.54806	−	1.86217i	−0.116849	−	0.0613272i
$923$	45.1959	+	27.4993i	1.48764	+	0.905151i
$924$	30.2536	−	15.8783i	0.995270	−	0.522358i
$925$	−27.9684			−0.919597
$926$	−1.27547	−	0.669416i	−0.0419144	−	0.0219984i
$927$	−5.28445	+	13.9339i	−0.173564	+	0.457651i
$928$	−0.147077	−	1.21129i	−0.00482805	−	0.0397626i
$929$	−32.2984	+	7.96083i	−1.05968	+	0.261186i	−0.730380	−	0.683041i	$-0.760657\pi$
$929$	−32.2984	+	7.96083i	−1.05968	+	0.261186i	−0.329295	+	0.944227i	$0.606811\pi$
$930$	−1.21119	+	0.298532i	−0.0397166	+	0.00978926i
$931$	0.171756	+	1.41454i	0.00562908	+	0.0463596i
$932$	16.3645	−	43.1495i	0.536036	−	1.41341i
$933$	4.35382	+	2.28506i	0.142538	+	0.0748095i
$934$	7.52765			0.246312
$935$	4.51928	−	2.37190i	0.147796	−	0.0775695i
$936$	−2.94308	+	0.530611i	−0.0961974	+	0.0173436i
$937$	6.24968	+	3.28009i	0.204168	+	0.107156i	0.563708	−	0.825974i	$-0.309374\pi$
$937$	6.24968	+	3.28009i	0.204168	+	0.107156i	−0.359540	+	0.933130i	$0.617066\pi$
$938$	−3.81370	−	2.00158i	−0.124522	−	0.0653541i
$939$	−5.65967	+	1.39498i	−0.184696	+	0.0455235i
$940$	−16.6249	+	24.0853i	−0.542243	+	0.785575i
$941$	−11.0160	+	2.71521i	−0.359112	+	0.0885132i	−0.414744	−	0.909938i	$-0.636129\pi$
$941$	−11.0160	+	2.71521i	−0.359112	+	0.0885132i	0.0556317	+	0.998451i	$0.482283\pi$
$942$	1.88230	+	2.72698i	0.0613285	+	0.0888497i
$943$	1.73348	−	14.2765i	0.0564498	−	0.464906i
$944$	−26.9471			−0.877053
$945$	0.601646	−	4.95500i	0.0195715	−	0.161186i
$946$	0.458626	+	1.20930i	0.0149112	+	0.0393177i
$947$	13.6224	−	7.14960i	0.442669	−	0.232331i	−0.228636	−	0.973512i	$-0.573426\pi$
$947$	13.6224	−	7.14960i	0.442669	−	0.232331i	0.671305	+	0.741181i	$0.265734\pi$
$948$	−2.75113	+	22.6576i	−0.0893526	+	0.735885i
$949$	−0.463315	+	2.48792i	−0.0150398	+	0.0807615i
$950$	0.0295148	+	0.243076i	0.000957586	+	0.00788643i
$951$	3.34431	+	4.84507i	0.108447	+	0.157112i
$952$	0.883603	−	1.28012i	0.0286377	−	0.0414889i
$953$	−19.2297	+	17.0360i	−0.622910	+	0.551850i	−0.914445	−	0.404710i	$-0.867372\pi$
$953$	−19.2297	+	17.0360i	−0.622910	+	0.551850i	0.291535	+	0.956560i	$0.405834\pi$
$954$	0.384155	+	1.01293i	0.0124375	+	0.0327950i
$955$	−19.2912	+	27.9482i	−0.624249	+	0.904381i
$956$	5.22475	+	2.74216i	0.168980	+	0.0886878i
$957$	0.331168	−	2.72741i	0.0107051	−	0.0881648i
$958$	−0.993266	−	8.18028i	−0.0320910	−	0.264293i
$959$	1.80619	−	4.76254i	0.0583250	−	0.153790i
$960$	6.21751	−	9.00763i	0.200669	−	0.290720i
$961$	12.4758	+	11.0526i	0.402444	+	0.356535i
$962$	−4.30259	−	7.16373i	−0.138721	−	0.230968i
$963$	−3.22997	+	2.86150i	−0.104084	+	0.0922105i
$964$	−3.61058	−	29.7358i	−0.116289	−	0.957726i
$965$	−0.494315	−	4.07105i	−0.0159126	−	0.131052i
$966$	2.01581	−	1.05798i	0.0648577	−	0.0340400i
$967$	−29.1549	+	15.3017i	−0.937558	+	0.492068i	−0.863031	−	0.505151i	$-0.831437\pi$
$967$	−29.1549	+	15.3017i	−0.937558	+	0.492068i	−0.0745265	+	0.997219i	$0.523745\pi$
$968$	−15.5014	−	3.82075i	−0.498233	−	0.122803i
$969$	0.204023	−	0.180749i	0.00655416	−	0.00580648i
$970$	−5.32544	−	1.31260i	−0.170989	−	0.0421451i
$971$	−16.2613	−	42.8775i	−0.521849	−	1.37600i	−0.894099	−	0.447870i	$-0.852183\pi$
$971$	−16.2613	−	42.8775i	−0.521849	−	1.37600i	0.372250	−	0.928133i	$-0.378587\pi$
$972$	−1.73199	+	0.909018i	−0.0555536	+	0.0291568i
$973$	−0.944360	+	7.77750i	−0.0302748	+	0.249335i
$974$	−4.35160	+	1.07257i	−0.139434	+	0.0343675i
$975$	−1.67008	+	8.96806i	−0.0534854	+	0.287208i
$976$	44.1899	+	10.8918i	1.41448	+	0.348639i
$977$	−7.67590	+	20.2397i	−0.245574	+	0.647525i	−0.999960	−	0.00890535i	$-0.997165\pi$
$977$	−7.67590	+	20.2397i	−0.245574	+	0.647525i	0.754386	+	0.656431i	$0.227935\pi$
$978$	0.993087	+	0.879798i	0.0317554	+	0.0281328i
$979$	75.3453	−	18.5709i	2.40805	−	0.593530i
$980$	5.39060	+	7.80963i	0.172196	+	0.249470i
$981$	1.29175	+	10.6385i	0.0412425	+	0.339663i
$982$	−0.0641605	−	0.169177i	−0.00204744	−	0.00539866i
$983$	21.8162	−	57.5246i	0.695828	−	1.83475i	0.167139	−	0.985933i	$-0.446547\pi$
$983$	21.8162	−	57.5246i	0.695828	−	1.83475i	0.528689	−	0.848816i	$-0.322684\pi$
$984$	1.98190	+	2.87128i	0.0631807	+	0.0915331i
$985$	0.935871	+	0.230671i	0.0298193	+	0.00734980i
$986$	−0.0219301	−	0.0578249i	−0.000698397	−	0.00184152i
$987$	−10.7216	+	28.2706i	−0.341273	+	0.899864i
$988$	2.56848	−	2.00040i	0.0817141	−	0.0636412i
$989$	−1.35982	−	3.58555i	−0.0432398	−	0.114014i
$990$	−1.35647	+	1.20173i	−0.0431114	+	0.0381934i
$991$	−13.9616			−0.443504			−0.221752	−	0.975103i	$-0.571178\pi$
$991$	−13.9616			−0.443504			−0.221752	+	0.975103i	$0.571178\pi$
$992$	−9.24725			−0.293600
$993$	16.5705	−	14.6802i	0.525850	−	0.465862i
$994$	8.65128	−	4.54054i	0.274402	−	0.144017i
$995$	−16.6175			−0.526812
$996$	−2.77099	−	1.45433i	−0.0878022	−	0.0460821i
$997$	−20.5455	−	18.2017i	−0.650683	−	0.576455i	0.271866	−	0.962335i	$-0.412359\pi$
$997$	−20.5455	−	18.2017i	−0.650683	−	0.576455i	−0.922549	+	0.385880i	$0.873898\pi$
$998$	0.0406022	+	0.0588224i	0.00128524	+	0.00186199i
$999$	−8.27440	−	7.33048i	−0.261790	−	0.231926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.m.b.40.9	✓	204
169.131	even	13	inner	507.2.m.b.469.9	yes	204

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.m.b.40.9	✓	204	1.1	even	1	trivial
507.2.m.b.469.9	yes	204	169.131	even	13	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.203567 + 0.0501748i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.73199 - 0.909018i) q^{4} +(-0.892774 + 1.29341i) q^{5} +(0.0743463 - 0.196035i) q^{6} +(2.37726 + 2.10607i) q^{7} +(-0.620832 - 0.550009i) q^{8} +(-0.970942 - 0.239316i) q^{9} +O(q^{10})\)	\(q+(0.203567 + 0.0501748i) q^{2} +(0.120537 - 0.992709i) q^{3} +(-1.73199 - 0.909018i) q^{4} +(-0.892774 + 1.29341i) q^{5} +(0.0743463 - 0.196035i) q^{6} +(2.37726 + 2.10607i) q^{7} +(-0.620832 - 0.550009i) q^{8} +(-0.970942 - 0.239316i) q^{9} +(-0.246636 + 0.218500i) q^{10} +(-5.34006 + 1.31621i) q^{11} +(-1.11116 + 1.60979i) q^{12} +(-1.48920 + 3.28364i) q^{13} +(0.378260 + 0.548005i) q^{14} +(1.17636 + 1.04217i) q^{15} +(2.12353 + 3.07647i) q^{16} +(0.441981 + 0.391561i) q^{17} +(-0.185644 - 0.0974337i) q^{18} +0.461611 q^{19} +(2.72201 - 1.42862i) q^{20} +(2.37726 - 2.10607i) q^{21} -1.15310 q^{22} +3.41893 q^{23} +(-0.620832 + 0.550009i) q^{24} +(0.897170 + 2.36564i) q^{25} +(-0.467908 + 0.593722i) q^{26} +(-0.354605 + 0.935016i) q^{27} +(-2.20293 - 5.80865i) q^{28} +(-0.485030 - 0.119549i) q^{29} +(0.187179 + 0.271175i) q^{30} +(-1.34248 + 3.53982i) q^{31} +(0.866155 + 2.28386i) q^{32} +(0.662937 + 5.45978i) q^{33} +(0.0703263 + 0.101885i) q^{34} +(-4.84635 + 1.19452i) q^{35} +(1.46412 + 1.29710i) q^{36} +(-3.91997 + 10.3361i) q^{37} +(0.0939688 + 0.0231612i) q^{38} +(3.08020 + 1.87414i) q^{39} +(1.26565 - 0.311954i) q^{40} +(0.507023 - 4.17571i) q^{41} +(0.589603 - 0.309448i) q^{42} +(-0.397732 - 1.04873i) q^{43} +(10.4454 + 2.57456i) q^{44} +(1.17636 - 1.04217i) q^{45} +(0.695983 + 0.171544i) q^{46} +(-8.42956 + 4.42418i) q^{47} +(3.31000 - 1.73722i) q^{48} +(0.372080 + 3.06435i) q^{49} +(0.0639387 + 0.526583i) q^{50} +(0.441981 - 0.391561i) q^{51} +(5.56416 - 4.33352i) q^{52} +(-3.86763 - 3.42642i) q^{53} +(-0.119100 + 0.172547i) q^{54} +(3.06508 - 8.08195i) q^{55} +(-0.317521 - 2.61502i) q^{56} +(0.0556410 - 0.458245i) q^{57} +(-0.0927380 - 0.0486726i) q^{58} +(-4.09495 + 5.93256i) q^{59} +(-1.09010 - 2.87436i) q^{60} +(9.11311 - 8.07351i) q^{61} +(-0.450894 + 0.653232i) q^{62} +(-1.80416 - 2.61378i) q^{63} +(-0.839449 - 6.91349i) q^{64} +(-2.91756 - 4.85769i) q^{65} +(-0.138991 + 1.14470i) q^{66} +(-5.72735 + 3.00595i) q^{67} +(-0.409570 - 1.07995i) q^{68} +(0.412107 - 3.39400i) q^{69} -1.04649 q^{70} +(1.76864 - 14.5661i) q^{71} +(0.471166 + 0.682601i) q^{72} +(0.681494 - 0.167973i) q^{73} +(-1.31659 + 1.90741i) q^{74} +(2.45654 - 0.605482i) q^{75} +(-0.799505 - 0.419612i) q^{76} +(-15.4667 - 8.11756i) q^{77} +(0.532993 + 0.536062i) q^{78} +(10.3319 - 5.42261i) q^{79} -5.87496 q^{80} +(0.885456 + 0.464723i) q^{81} +(0.312729 - 0.824598i) q^{82} +(0.192845 + 1.58822i) q^{83} +(-6.03184 + 1.48671i) q^{84} +(-0.901036 + 0.222085i) q^{85} +(-0.0283452 - 0.233444i) q^{86} +(-0.177142 + 0.467084i) q^{87} +(4.03921 + 2.11994i) q^{88} -14.1094 q^{89} +(0.291760 - 0.153127i) q^{90} +(-10.4558 + 4.66971i) q^{91} +(-5.92156 - 3.10787i) q^{92} +(3.35219 + 1.75936i) q^{93} +(-1.93797 + 0.477666i) q^{94} +(-0.412114 + 0.597050i) q^{95} +(2.37162 - 0.584551i) q^{96} +(9.45586 + 13.6992i) q^{97} +(-0.0780102 + 0.642472i) q^{98} +5.49988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9}+O(q^{10}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9	\( 204 q - q^{2} - 17 q^{3} - 21 q^{4} - 6 q^{5} - q^{6} - 8 q^{7} - 9 q^{8} - 17 q^{9} - 6 q^{10} - 8 q^{11} - 21 q^{12} + 54 q^{13} - 30 q^{14} - 6 q^{15} - 45 q^{16} - 18 q^{17} - q^{18} - 20 q^{19} - 58 q^{20} - 8 q^{21} + 44 q^{22} + 40 q^{23} - 9 q^{24} + 7 q^{25} - 2 q^{26} - 17 q^{27} - 40 q^{28} + 11 q^{29} - 6 q^{30} + 2 q^{31} + 61 q^{32} + 5 q^{33} - q^{34} + 11 q^{35} - 21 q^{36} - 34 q^{37} + 17 q^{38} - 11 q^{39} - 31 q^{40} - 58 q^{41} + 35 q^{42} + 32 q^{43} - 41 q^{44} - 6 q^{45} + 76 q^{46} - 36 q^{47} - 45 q^{48} + 9 q^{49} - 35 q^{50} - 18 q^{51} - 24 q^{52} + 66 q^{53} - q^{54} + 7 q^{55} - 114 q^{56} - 7 q^{57} - 60 q^{58} + 40 q^{59} + 59 q^{60} - 54 q^{61} - 31 q^{62} - 8 q^{63} + 75 q^{64} - 26 q^{65} + 18 q^{66} + 2 q^{67} + 26 q^{68} - 12 q^{69} - 56 q^{70} - 37 q^{71} - 9 q^{72} + 70 q^{73} + 174 q^{74} - 45 q^{75} - 26 q^{76} + 24 q^{78} - 66 q^{79} + 126 q^{80} - 17 q^{81} - 17 q^{82} - 2 q^{83} - 40 q^{84} + 54 q^{85} + 61 q^{86} + 24 q^{87} + 94 q^{88} - 114 q^{89} - 6 q^{90} + 104 q^{91} - 78 q^{92} + 67 q^{93} - 63 q^{94} - 70 q^{95} - 4 q^{96} + 36 q^{97} - 65 q^{98} + 18 q^{99}+O(q^{100}) \) 204 * q - q^2 - 17 * q^3 - 21 * q^4 - 6 * q^5 - q^6 - 8 * q^7 - 9 * q^8 - 17 * q^9 - 6 * q^10 - 8 * q^11 - 21 * q^12 + 54 * q^13 - 30 * q^14 - 6 * q^15 - 45 * q^16 - 18 * q^17 - q^18 - 20 * q^19 - 58 * q^20 - 8 * q^21 + 44 * q^22 + 40 * q^23 - 9 * q^24 + 7 * q^25 - 2 * q^26 - 17 * q^27 - 40 * q^28 + 11 * q^29 - 6 * q^30 + 2 * q^31 + 61 * q^32 + 5 * q^33 - q^34 + 11 * q^35 - 21 * q^36 - 34 * q^37 + 17 * q^38 - 11 * q^39 - 31 * q^40 - 58 * q^41 + 35 * q^42 + 32 * q^43 - 41 * q^44 - 6 * q^45 + 76 * q^46 - 36 * q^47 - 45 * q^48 + 9 * q^49 - 35 * q^50 - 18 * q^51 - 24 * q^52 + 66 * q^53 - q^54 + 7 * q^55 - 114 * q^56 - 7 * q^57 - 60 * q^58 + 40 * q^59 + 59 * q^60 - 54 * q^61 - 31 * q^62 - 8 * q^63 + 75 * q^64 - 26 * q^65 + 18 * q^66 + 2 * q^67 + 26 * q^68 - 12 * q^69 - 56 * q^70 - 37 * q^71 - 9 * q^72 + 70 * q^73 + 174 * q^74 - 45 * q^75 - 26 * q^76 + 24 * q^78 - 66 * q^79 + 126 * q^80 - 17 * q^81 - 17 * q^82 - 2 * q^83 - 40 * q^84 + 54 * q^85 + 61 * q^86 + 24 * q^87 + 94 * q^88 - 114 * q^89 - 6 * q^90 + 104 * q^91 - 78 * q^92 + 67 * q^93 - 63 * q^94 - 70 * q^95 - 4 * q^96 + 36 * q^97 - 65 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

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Database

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