LMFDB - Embedded newform 637.2.bl.a.53.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$324$
Relative dimension:	$27$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.13
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.a.625.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.434073 - 0.295946i) q^{2} +(0.0114514 + 0.0106254i) q^{3} +(-0.629847 - 1.60482i) q^{4} +(3.15579 - 0.973431i) q^{5} +(-0.00182622 - 0.00800119i) q^{6} +(0.290350 + 2.62977i) q^{7} +(-0.435349 + 1.90739i) q^{8} +(-0.224172 - 2.99137i) q^{9} +O(q^{10})$	\(q+(-0.434073 - 0.295946i) q^{2} +(0.0114514 + 0.0106254i) q^{3} +(-0.629847 - 1.60482i) q^{4} +(3.15579 - 0.973431i) q^{5} +(-0.00182622 - 0.00800119i) q^{6} +(0.290350 + 2.62977i) q^{7} +(-0.435349 + 1.90739i) q^{8} +(-0.224172 - 2.99137i) q^{9} +(-1.65792 - 0.511402i) q^{10} +(0.374533 - 4.99780i) q^{11} +(0.00983921 - 0.0250699i) q^{12} +(0.900969 - 0.433884i) q^{13} +(0.652237 - 1.22744i) q^{14} +(0.0464814 + 0.0223842i) q^{15} +(-1.77410 + 1.64613i) q^{16} +(2.27014 - 0.342169i) q^{17} +(-0.787976 + 1.36481i) q^{18} +(3.22092 + 5.57880i) q^{19} +(-3.54985 - 4.45137i) q^{20} +(-0.0246174 + 0.0331997i) q^{21} +(-1.64165 + 2.05857i) q^{22} +(-2.99486 - 0.451403i) q^{23} +(-0.0252521 + 0.0172166i) q^{24} +(4.88022 - 3.32728i) q^{25} +(-0.519492 - 0.0783008i) q^{26} +(0.0584370 - 0.0732777i) q^{27} +(4.03744 - 2.12231i) q^{28} +(-3.36162 - 4.21533i) q^{29} +(-0.0135518 - 0.0234724i) q^{30} +(-0.250312 + 0.433553i) q^{31} +(5.12643 - 0.772685i) q^{32} +(0.0573924 - 0.0532524i) q^{33} +(-1.08667 - 0.523313i) q^{34} +(3.47618 + 8.01636i) q^{35} +(-4.65942 + 2.24386i) q^{36} +(3.24368 - 8.26475i) q^{37} +(0.252908 - 3.37482i) q^{38} +(0.0149276 + 0.00460455i) q^{39} +(0.482843 + 6.44309i) q^{40} +(-1.00158 + 4.38821i) q^{41} +(0.0205111 - 0.00712569i) q^{42} +(-0.292136 - 1.27993i) q^{43} +(-8.25648 + 2.54679i) q^{44} +(-3.61933 - 9.22190i) q^{45} +(1.16640 + 1.08226i) q^{46} +(-3.48199 - 2.37398i) q^{47} -0.0378067 q^{48} +(-6.83139 + 1.52711i) q^{49} -3.10307 q^{50} +(0.0296321 + 0.0202028i) q^{51} +(-1.26378 - 1.17262i) q^{52} +(-4.37696 - 11.1523i) q^{53} +(-0.0470522 + 0.0145137i) q^{54} +(-3.68306 - 16.1366i) q^{55} +(-5.14239 - 0.591057i) q^{56} +(-0.0223927 + 0.0981088i) q^{57} +(0.211676 + 2.82462i) q^{58} +(12.3991 + 3.82460i) q^{59} +(0.00664662 - 0.0886930i) q^{60} +(-1.78320 + 4.54352i) q^{61} +(0.236962 - 0.114115i) q^{62} +(7.80153 - 1.45807i) q^{63} +(1.90706 + 0.918392i) q^{64} +(2.42091 - 2.24628i) q^{65} +(-0.0406723 + 0.00613036i) q^{66} +(0.633089 - 1.09654i) q^{67} +(-1.97896 - 3.42766i) q^{68} +(-0.0294991 - 0.0369907i) q^{69} +(0.863491 - 4.50845i) q^{70} +(-1.72860 + 2.16760i) q^{71} +(5.80329 + 0.874705i) q^{72} +(2.41834 - 1.64880i) q^{73} +(-3.85391 + 2.62755i) q^{74} +(0.0912392 + 0.0137521i) q^{75} +(6.92430 - 8.68280i) q^{76} +(13.2518 - 0.466174i) q^{77} +(-0.00511696 - 0.00641646i) q^{78} +(0.610481 + 1.05738i) q^{79} +(-3.99630 + 6.92179i) q^{80} +(-8.89731 + 1.34105i) q^{81} +(1.73343 - 1.60839i) q^{82} +(7.91177 + 3.81011i) q^{83} +(0.0687849 + 0.0185958i) q^{84} +(6.83100 - 3.28964i) q^{85} +(-0.251982 + 0.642040i) q^{86} +(0.00629419 - 0.0839901i) q^{87} +(9.36968 + 2.89016i) q^{88} +(0.387876 + 5.17585i) q^{89} +(-1.15813 + 5.07410i) q^{90} +(1.40261 + 2.24336i) q^{91} +(1.16188 + 5.09054i) q^{92} +(-0.00747309 + 0.00230514i) q^{93} +(0.808868 + 2.06096i) q^{94} +(15.5951 + 14.4701i) q^{95} +(0.0669150 + 0.0456219i) q^{96} -5.70005 q^{97} +(3.41726 + 1.35885i) q^{98} -15.0342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) $ 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	−0.434073	−	0.295946i	−0.306936	−	0.209265i	0.400049	−	0.916494i	$-0.368993\pi$
$2$	−0.434073	−	0.295946i	−0.306936	−	0.209265i	−0.706985	+	0.707228i	$0.749945\pi$
$3$	0.0114514	+	0.0106254i	0.00661149	+	0.00613457i	0.683472	−	0.729977i	$-0.260469\pi$
$3$	0.0114514	+	0.0106254i	0.00661149	+	0.00613457i	−0.676860	+	0.736112i	$0.736660\pi$
$4$	−0.629847	−	1.60482i	−0.314923	−	0.802412i
$5$	3.15579	−	0.973431i	1.41131	−	0.435332i	0.506904	−	0.862003i	$-0.330790\pi$
$5$	3.15579	−	0.973431i	1.41131	−	0.435332i	0.904407	+	0.426671i	$0.140314\pi$
$6$	−0.00182622	−	0.00800119i	−0.000745551	−	0.00326647i
$7$	0.290350	+	2.62977i	0.109742	+	0.993960i
$7$	0.290350	+	2.62977i	0.109742	+	0.993960i
$8$	−0.435349	+	1.90739i	−0.153919	+	0.674363i
$9$	−0.224172	−	2.99137i	−0.0747240	−	0.997123i
$10$	−1.65792	−	0.511402i	−0.524281	−	0.161719i
$11$	0.374533	−	4.99780i	0.112926	−	1.50689i	−0.596786	−	0.802400i	$-0.703556\pi$
$11$	0.374533	−	4.99780i	0.112926	−	1.50689i	0.709712	−	0.704492i	$-0.248825\pi$
$12$	0.00983921	−	0.0250699i	0.00284034	−	0.00723706i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$13$	0.900969	−	0.433884i	0.249884	−	0.120338i
$14$	0.652237	−	1.22744i	0.174318	−	0.328047i
$15$	0.0464814	+	0.0223842i	0.0120014	+	0.00577959i
$16$	−1.77410	+	1.64613i	−0.443526	+	0.411532i
$17$	2.27014	−	0.342169i	0.550590	−	0.0829881i	0.132145	−	0.991230i	$-0.457813\pi$
$17$	2.27014	−	0.342169i	0.550590	−	0.0829881i	0.418445	+	0.908242i	$0.362575\pi$
$18$	−0.787976	+	1.36481i	−0.185728	+	0.321690i
$19$	3.22092	+	5.57880i	0.738930	+	1.27986i	0.952978	+	0.303041i	$0.0980019\pi$
$19$	3.22092	+	5.57880i	0.738930	+	1.27986i	−0.214048	+	0.976823i	$0.568665\pi$
$20$	−3.54985	−	4.45137i	−0.793770	−	0.995356i
$21$	−0.0246174	+	0.0331997i	−0.00537196	+	0.00724478i
$22$	−1.64165	+	2.05857i	−0.350001	+	0.438888i
$23$	−2.99486	−	0.451403i	−0.624471	−	0.0941239i	−0.170819	−	0.985302i	$-0.554641\pi$
$23$	−2.99486	−	0.451403i	−0.624471	−	0.0941239i	−0.453653	+	0.891179i	$0.649879\pi$
$24$	−0.0252521	+	0.0172166i	−0.00515456	+	0.00351432i
$25$	4.88022	−	3.32728i	0.976044	−	0.665456i
$26$	−0.519492	−	0.0783008i	−0.101881	−	0.0153561i
$27$	0.0584370	−	0.0732777i	0.0112462	−	0.0141023i
$28$	4.03744	−	2.12231i	0.763005	−	0.401080i
$29$	−3.36162	−	4.21533i	−0.624236	−	0.782768i	0.364697	−	0.931126i	$-0.381172\pi$
$29$	−3.36162	−	4.21533i	−0.624236	−	0.782768i	−0.988934	+	0.148359i	$0.952601\pi$
$30$	−0.0135518	−	0.0234724i	−0.00247420	−	0.00428545i
$31$	−0.250312	+	0.433553i	−0.0449573	+	0.0778683i	−0.887628	−	0.460560i	$-0.847649\pi$
$31$	−0.250312	+	0.433553i	−0.0449573	+	0.0778683i	0.842671	+	0.538429i	$0.180982\pi$
$32$	5.12643	−	0.772685i	0.906233	−	0.136593i
$33$	0.0573924	−	0.0532524i	0.00999074	−	0.00927005i
$34$	−1.08667	−	0.523313i	−0.186362	−	0.0897474i
$35$	3.47618	+	8.01636i	0.587582	+	1.35501i
$36$	−4.65942	+	2.24386i	−0.776571	+	0.373977i
$37$	3.24368	−	8.26475i	0.533257	−	1.35872i	−0.369766	−	0.929125i	$-0.620562\pi$
$37$	3.24368	−	8.26475i	0.533257	−	1.35872i	0.903023	−	0.429592i	$-0.141343\pi$
$38$	0.252908	−	3.37482i	0.0410271	−	0.547469i
$39$	0.0149276	+	0.00460455i	0.00239032	+	0.000737317i
$40$	0.482843	+	6.44309i	0.0763441	+	1.01874i
$41$	−1.00158	+	4.38821i	−0.156420	+	0.685323i	0.834515	+	0.550985i	$0.185748\pi$
$41$	−1.00158	+	4.38821i	−0.156420	+	0.685323i	−0.990936	+	0.134338i	$0.957109\pi$
$42$	0.0205111	−	0.00712569i	0.00316493	−	0.00109952i
$43$	−0.292136	−	1.27993i	−0.0445504	−	0.195188i	0.947756	−	0.318997i	$-0.103346\pi$
$43$	−0.292136	−	1.27993i	−0.0445504	−	0.195188i	−0.992306	+	0.123809i	$0.960489\pi$
$44$	−8.25648	+	2.54679i	−1.24471	+	0.383942i
$45$	−3.61933	−	9.22190i	−0.539538	−	1.37472i
$46$	1.16640	+	1.08226i	0.171976	+	0.159570i
$47$	−3.48199	−	2.37398i	−0.507901	−	0.346281i	0.282102	−	0.959385i	$-0.408968\pi$
$47$	−3.48199	−	2.37398i	−0.507901	−	0.346281i	−0.790003	+	0.613104i	$0.789921\pi$
$48$	−0.0378067			−0.00545693
$49$	−6.83139	+	1.52711i	−0.975913	+	0.218158i
$50$	−3.10307			−0.438840
$51$	0.0296321	+	0.0202028i	0.00414932	+	0.00282896i
$52$	−1.26378	−	1.17262i	−0.175255	−	0.162613i
$53$	−4.37696	−	11.1523i	−0.601221	−	1.53189i	−0.829626	−	0.558320i	$-0.811446\pi$
$53$	−4.37696	−	11.1523i	−0.601221	−	1.53189i	0.228405	−	0.973566i	$-0.426649\pi$
$54$	−0.0470522	+	0.0145137i	−0.00640299	+	0.00197506i
$55$	−3.68306	−	16.1366i	−0.496624	−	2.17585i
$56$	−5.14239	−	0.591057i	−0.687181	−	0.0789834i
$57$	−0.0223927	+	0.0981088i	−0.00296598	+	0.0129948i
$58$	0.211676	+	2.82462i	0.0277944	+	0.370890i
$59$	12.3991	+	3.82460i	1.61422	+	0.497921i	0.964905	−	0.262599i	$-0.0845796\pi$
$59$	12.3991	+	3.82460i	1.61422	+	0.497921i	0.649315	+	0.760520i	$0.275056\pi$
$60$	0.00664662	−	0.0886930i	0.000858075	−	0.0114502i
$61$	−1.78320	+	4.54352i	−0.228316	+	0.581739i	−0.998421	−	0.0561783i	$-0.982108\pi$
$61$	−1.78320	+	4.54352i	−0.228316	+	0.581739i	0.770105	+	0.637917i	$0.220204\pi$
$62$	0.236962	−	0.114115i	0.0300942	−	0.0144926i
$63$	7.80153	−	1.45807i	0.982900	−	0.183699i
$64$	1.90706	+	0.918392i	0.238383	+	0.114799i
$65$	2.42091	−	2.24628i	0.300277	−	0.278616i
$66$	−0.0406723	+	0.00613036i	−0.00500642	+	0.000754596i
$67$	0.633089	−	1.09654i	0.0773441	−	0.133964i	−0.824759	−	0.565484i	$-0.808689\pi$
$67$	0.633089	−	1.09654i	0.0773441	−	0.133964i	0.902103	+	0.431520i	$0.142023\pi$
$68$	−1.97896	−	3.42766i	−0.239984	−	0.415665i
$69$	−0.0294991	−	0.0369907i	−0.00355128	−	0.00445316i
$70$	0.863491	−	4.50845i	0.103207	−	0.538862i
$71$	−1.72860	+	2.16760i	−0.205147	+	0.257246i	−0.873752	−	0.486371i	$-0.838320\pi$
$71$	−1.72860	+	2.16760i	−0.205147	+	0.257246i	0.668605	+	0.743618i	$0.266892\pi$
$72$	5.80329	+	0.874705i	0.683924	+	0.103085i
$73$	2.41834	−	1.64880i	0.283045	−	0.192977i	−0.413472	−	0.910517i	$-0.635684\pi$
$73$	2.41834	−	1.64880i	0.283045	−	0.192977i	0.696518	+	0.717540i	$0.254732\pi$
$74$	−3.85391	+	2.62755i	−0.448008	+	0.305447i
$75$	0.0912392	+	0.0137521i	0.0105354	+	0.00158795i
$76$	6.92430	−	8.68280i	0.794272	−	0.995985i
$77$	13.2518	−	0.466174i	1.51018	−	0.0531255i
$78$	−0.00511696	−	0.00641646i	−0.000579381	−	0.000726521i
$79$	0.610481	+	1.05738i	0.0686845	+	0.118965i	0.898322	−	0.439337i	$-0.144786\pi$
$79$	0.610481	+	1.05738i	0.0686845	+	0.118965i	−0.829638	+	0.558302i	$0.811453\pi$
$80$	−3.99630	+	6.92179i	−0.446799	+	0.773879i
$81$	−8.89731	+	1.34105i	−0.988590	+	0.149006i
$82$	1.73343	−	1.60839i	0.191425	−	0.177617i
$83$	7.91177	+	3.81011i	0.868429	+	0.418213i	0.814385	−	0.580325i	$-0.197075\pi$
$83$	7.91177	+	3.81011i	0.868429	+	0.418213i	0.0540443	+	0.998539i	$0.482789\pi$
$84$	0.0687849	+	0.0185958i	0.00750505	+	0.00202897i
$85$	6.83100	−	3.28964i	0.740926	−	0.356811i
$86$	−0.251982	+	0.642040i	−0.0271719	+	0.0692330i
$87$	0.00629419	−	0.0839901i	0.000674807	−	0.00900468i
$88$	9.36968	+	2.89016i	0.998811	+	0.308092i
$89$	0.387876	+	5.17585i	0.0411148	+	0.548639i	0.979288	+	0.202472i	$0.0648976\pi$
$89$	0.387876	+	5.17585i	0.0411148	+	0.548639i	−0.938173	+	0.346166i	$0.887483\pi$
$90$	−1.15813	+	5.07410i	−0.122078	+	0.534857i
$91$	1.40261	+	2.24336i	0.147034	+	0.235168i
$92$	1.16188	+	5.09054i	0.121135	+	0.530725i
$93$	−0.00747309	+	0.00230514i	−0.000774923	+	0.000239032i
$94$	0.808868	+	2.06096i	0.0834284	+	0.212572i
$95$	15.5951	+	14.4701i	1.60002	+	1.48461i
$96$	0.0669150	+	0.0456219i	0.00682949	+	0.00465627i
$97$	−5.70005			−0.578752			−0.289376	−	0.957215i	$-0.593448\pi$
$97$	−5.70005			−0.578752			−0.289376	+	0.957215i	$0.593448\pi$
$98$	3.41726	+	1.35885i	0.345196	+	0.137264i
$99$	−15.0342			−1.51099
$100$	−8.41349	−	5.73622i	−0.841349	−	0.573622i
$101$	1.74096	+	1.61538i	0.173232	+	0.160736i	0.762024	−	0.647549i	$-0.224206\pi$
$101$	1.74096	+	1.61538i	0.173232	+	0.160736i	−0.588792	+	0.808285i	$0.700396\pi$
$102$	−0.00688354	−	0.0175390i	−0.000681572	−	0.00173662i
$103$	−5.41215	+	1.66943i	−0.533275	+	0.164493i	−0.549685	−	0.835372i	$-0.685252\pi$
$103$	−5.41215	+	1.66943i	−0.533275	+	0.164493i	0.0164106	+	0.999865i	$0.494776\pi$
$104$	0.435349	+	1.90739i	0.0426894	+	0.187035i
$105$	−0.0453696	+	0.128735i	−0.00442762	+	0.0125632i
$106$	−1.40056	+	6.13625i	−0.136034	+	0.596006i
$107$	−0.937744	−	12.5133i	−0.0906551	−	1.20971i	−0.838150	−	0.545440i	$-0.816362\pi$
$107$	−0.937744	−	12.5133i	−0.0906551	−	1.20971i	0.747494	−	0.664268i	$-0.231257\pi$
$108$	−0.154404	−	0.0476274i	−0.0148576	−	0.00458295i
$109$	−0.907198	+	12.1057i	−0.0868938	+	1.15952i	0.767907	+	0.640561i	$0.221298\pi$
$109$	−0.907198	+	12.1057i	−0.0868938	+	1.15952i	−0.854801	+	0.518956i	$0.826321\pi$
$110$	−3.17683	+	8.09443i	−0.302899	+	0.771773i
$111$	0.124961	−	0.0601780i	0.0118608	−	0.00571184i
$112$	−4.84405	−	4.18753i	−0.457719	−	0.395684i
$113$	16.8669	+	8.12266i	1.58670	+	0.764116i	0.998989	−	0.0449532i	$-0.0143139\pi$
$113$	16.8669	+	8.12266i	1.58670	+	0.764116i	0.587714	+	0.809069i	$0.300028\pi$
$114$	0.0387549	−	0.0359593i	0.00362973	−	0.00336790i
$115$	−9.89055	+	1.49076i	−0.922298	+	0.139014i
$116$	−4.64756	+	8.04981i	−0.431515	+	0.747406i
$117$	−1.49988	−	2.59786i	−0.138664	−	0.240173i
$118$	−4.25022	−	5.32961i	−0.391264	−	0.490630i
$119$	1.55896	+	5.87060i	0.142910	+	0.538157i
$120$	−0.0629310	+	0.0789130i	−0.00574479	+	0.00720374i
$121$	−13.9605	−	2.10421i	−1.26914	−	0.191292i
$122$	2.11868	−	1.44449i	0.191816	−	0.130778i
$123$	−0.0580959	+	0.0396091i	−0.00523833	+	0.00357143i
$124$	0.853433	+	0.128634i	0.0766406	+	0.0115517i
$125$	1.86666	−	2.34072i	0.166959	−	0.209360i
$126$	−3.81794	−	1.67592i	−0.340129	−	0.149303i
$127$	12.9577	+	16.2484i	1.14981	+	1.44181i	0.877483	+	0.479608i	$0.159221\pi$
$127$	12.9577	+	16.2484i	1.14981	+	1.44181i	0.272325	+	0.962205i	$0.412207\pi$
$128$	−5.74034	−	9.94256i	−0.507379	−	0.878807i
$129$	0.0102544	−	0.0177611i	0.000902849	−	0.00156378i
$130$	−1.71563	+	0.258589i	−0.150470	+	0.0226798i
$131$	−9.71602	+	9.01515i	−0.848892	+	0.787657i	−0.979004	−	0.203842i	$-0.934657\pi$
$131$	−9.71602	+	9.01515i	−0.848892	+	0.787657i	0.130111	+	0.991499i	$0.458467\pi$
$132$	−0.121609	−	0.0585639i	−0.0105847	−	0.00509733i
$133$	−13.7358	+	10.0901i	−1.19104	+	0.874922i
$134$	−0.599324	+	0.288619i	−0.0517737	+	0.0249329i
$135$	0.113084	−	0.288133i	0.00973272	−	0.0247986i
$136$	−0.335655	+	4.47900i	−0.0287822	+	0.384071i
$137$	−8.04501	−	2.48156i	−0.687331	−	0.212014i	−0.0686326	−	0.997642i	$-0.521864\pi$
$137$	−8.04501	−	2.48156i	−0.687331	−	0.212014i	−0.618699	+	0.785628i	$0.712340\pi$
$138$	0.00185752	+	0.0247868i	0.000158122	+	0.00210999i
$139$	−4.27315	+	18.7219i	−0.362444	+	1.58797i	0.384528	+	0.923113i	$0.374364\pi$
$139$	−4.27315	+	18.7219i	−0.362444	+	1.58797i	−0.746972	+	0.664856i	$0.768493\pi$
$140$	10.6754	−	10.6277i	0.902234	−	0.898208i
$141$	−0.0146494	−	0.0641830i	−0.00123370	−	0.00540519i
$142$	1.39183	−	0.429323i	0.116800	−	0.0360280i
$143$	−1.83102	−	4.66536i	−0.153118	−	0.390137i
$144$	5.32187	+	4.93798i	0.443489	+	0.411498i
$145$	−14.7119	−	10.0304i	−1.22175	−	0.832978i
$146$	−1.53769			−0.127260
$147$	−0.0944554	−	0.0550986i	−0.00779055	−	0.00454445i
$148$	−15.3065			−1.25819
$149$	8.59098	+	5.85723i	0.703800	+	0.479843i	0.861574	−	0.507632i	$-0.169479\pi$
$149$	8.59098	+	5.85723i	0.703800	+	0.479843i	−0.157773	+	0.987475i	$0.550432\pi$
$150$	−0.0355346	−	0.0329713i	−0.00290139	−	0.00269209i
$151$	3.80083	+	9.68436i	0.309307	+	0.788102i	0.998010	+	0.0630579i	$0.0200853\pi$
$151$	3.80083	+	9.68436i	0.309307	+	0.788102i	−0.688703	+	0.725044i	$0.741819\pi$
$152$	−12.0432	+	3.71482i	−0.976829	+	0.301312i
$153$	−1.53245	−	6.71412i	−0.123892	−	0.542805i
$154$	−5.89021	−	3.71946i	−0.474647	−	0.299723i
$155$	−0.367897	+	1.61186i	−0.0295502	+	0.129468i
$156$	−0.00201260	−	0.0268563i	−0.000161137	−	0.00215022i
$157$	18.9485	+	5.84482i	1.51225	+	0.466468i	0.936355	−	0.351055i	$-0.114177\pi$
$157$	18.9485	+	5.84482i	1.51225	+	0.466468i	0.575896	+	0.817523i	$0.304653\pi$
$158$	0.0479352	−	0.639651i	0.00381352	−	0.0508879i
$159$	0.0683750	−	0.174217i	0.00542249	−	0.0138163i
$160$	15.4258	−	7.42865i	1.21951	−	0.587286i
$161$	0.317528	−	8.00686i	0.0250247	−	0.631029i
$162$	4.25896	+	2.05101i	0.334615	+	0.161142i
$163$	−14.1082	+	13.0905i	−1.10504	+	1.02533i	−0.105517	+	0.994417i	$0.533650\pi$
$163$	−14.1082	+	13.0905i	−1.10504	+	1.02533i	−0.999522	+	0.0309092i	$0.990160\pi$
$164$	7.67314	−	1.15654i	0.599171	−	0.0903106i
$165$	0.129281	−	0.223921i	0.0100645	−	0.0174322i
$166$	−2.30670	−	3.99532i	−0.179034	−	0.310097i
$167$	2.52050	+	3.16061i	0.195042	+	0.244575i	0.869730	−	0.493528i	$-0.164293\pi$
$167$	2.52050	+	3.16061i	0.195042	+	0.244575i	−0.674687	+	0.738104i	$0.735722\pi$
$168$	−0.0526076	−	0.0614084i	−0.00405876	−	0.00473776i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−3.93871	−	0.593665i	−0.302085	−	0.0455320i
$171$	15.9662	−	10.8856i	1.22097	−	0.832440i
$172$	−1.87006	+	1.27499i	−0.142591	+	0.0972170i
$173$	14.1011	+	2.12540i	1.07209	+	0.161591i	0.661287	−	0.750133i	$-0.270011\pi$
$173$	14.1011	+	2.12540i	1.07209	+	0.161591i	0.410802	+	0.911725i	$0.365249\pi$
$174$	−0.0275886	+	0.0345951i	−0.00209149	+	0.00262264i
$175$	10.1670	+	11.8678i	0.768550	+	0.897121i
$176$	7.56254	+	9.48313i	0.570048	+	0.714818i
$177$	0.101349	+	0.175542i	0.00761787	+	0.0131945i
$178$	1.36340	−	2.36148i	0.102191	−	0.177001i
$179$	12.3450	−	1.86071i	0.922707	−	0.139076i	0.329527	−	0.944146i	$-0.393111\pi$
$179$	12.3450	−	1.86071i	0.922707	−	0.139076i	0.593179	+	0.805070i	$0.297873\pi$
$180$	−12.5199	+	11.6168i	−0.933178	+	0.865863i
$181$	−16.2500	−	7.82558i	−1.20785	−	0.581671i	−0.281948	−	0.959430i	$-0.590980\pi$
$181$	−16.2500	−	7.82558i	−1.20785	−	0.581671i	−0.925904	+	0.377759i	$0.876695\pi$
$182$	0.0550787	−	1.38888i	0.00408271	−	0.102951i
$183$	−0.0686969	+	0.0330827i	−0.00507822	+	0.00244554i
$184$	2.16481	−	5.51584i	0.159592	−	0.406633i
$185$	2.19118	−	29.2393i	0.161099	−	2.14971i
$186$	0.00392606	+	0.00121103i	0.000287873	+	8.87970e-5i
$187$	−0.859847	−	11.4739i	−0.0628782	−	0.839051i
$188$	−1.61670	+	7.08323i	−0.117910	+	0.516598i
$189$	0.209671	+	0.132400i	0.0152513	+	0.00963067i
$190$	−2.48703	−	10.8964i	−0.180428	−	0.790508i
$191$	−10.1253	+	3.12325i	−0.732643	+	0.225990i	−0.638558	−	0.769574i	$-0.720469\pi$
$191$	−10.1253	+	3.12325i	−0.732643	+	0.225990i	−0.0940849	+	0.995564i	$0.529993\pi$
$192$	0.0120803	+	0.0307801i	0.000871822	+	0.00222137i
$193$	−2.91694	−	2.70652i	−0.209966	−	0.194820i	0.568179	−	0.822905i	$-0.307648\pi$
$193$	−2.91694	−	2.70652i	−0.209966	−	0.194820i	−0.778144	+	0.628086i	$0.783839\pi$
$194$	2.47424	+	1.68691i	0.177640	+	0.121113i
$195$	0.0515904			0.00369447
$196$	6.75347	+	10.0013i	0.482391	+	0.714381i
$197$	8.87070			0.632011			0.316006	−	0.948757i	$-0.397658\pi$
$197$	8.87070			0.632011			0.316006	+	0.948757i	$0.397658\pi$
$198$	6.52594	+	4.44931i	0.463778	+	0.316199i
$199$	7.54148	+	6.99747i	0.534602	+	0.496038i	0.900642	−	0.434561i	$-0.143096\pi$
$199$	7.54148	+	6.99747i	0.534602	+	0.496038i	−0.366041	+	0.930599i	$0.619287\pi$
$200$	4.22181	+	10.7570i	0.298527	+	0.760635i
$201$	0.0189010	−	0.00583017i	0.00133317	−	0.000411229i
$202$	−0.277641	−	1.21642i	−0.0195347	−	0.0855872i
$203$	10.1093	−	10.0642i	0.709535	−	0.706368i
$204$	0.0137583	−	0.0602789i	0.000963271	−	0.00422037i
$205$	1.11085	+	14.8232i	0.0775848	+	1.03530i
$206$	2.84332	+	0.877049i	0.198104	+	0.0611069i
$207$	−0.678947	+	9.05992i	−0.0471901	+	0.629708i
$208$	−0.884183	+	2.25286i	−0.0613071	+	0.156208i
$209$	29.0880	−	14.0081i	2.01206	−	0.968958i
$210$	0.0577922	−	0.0424533i	0.00398804	−	0.00292955i
$211$	0.498228	+	0.239934i	0.0342994	+	0.0165177i	0.450955	−	0.892547i	$-0.351084\pi$
$211$	0.498228	+	0.239934i	0.0342994	+	0.0165177i	−0.416655	+	0.909064i	$0.636798\pi$
$212$	−15.1407	+	14.0485i	−1.03986	+	0.964854i
$213$	−0.0428265	+	0.00645506i	−0.00293442	+	0.000442293i
$214$	−3.29622	+	5.70921i	−0.225325	+	0.390274i
$215$	−2.16785	−	3.75482i	−0.147846	−	0.256076i
$216$	0.114329	+	0.143363i	0.00777907	+	0.00975464i
$217$	−1.21282	−	0.532381i	−0.0823317	−	0.0361403i
$218$	3.97643	−	4.98628i	0.269318	−	0.337714i
$219$	0.0452125	+	0.00681469i	0.00305518	+	0.000460494i
$220$	−23.5766	+	16.0742i	−1.58953	+	1.08372i
$221$	1.89687	−	1.29326i	0.127597	−	0.0869941i
$222$	−0.0720515	−	0.0108600i	−0.00483578	−	0.000728877i
$223$	2.27819	−	2.85676i	0.152559	−	0.191303i	−0.699679	−	0.714457i	$-0.746674\pi$
$223$	2.27819	−	2.85676i	0.152559	−	0.191303i	0.852238	+	0.523155i	$0.175245\pi$
$224$	3.52044	+	13.2570i	0.235219	+	0.885769i
$225$	−11.0471	−	13.8527i	−0.736475	−	0.923511i
$226$	−4.91759	−	8.51751i	−0.327113	−	0.566576i
$227$	7.38938	−	12.7988i	0.490450	−	0.849485i	−0.509489	−	0.860477i	$-0.670166\pi$
$227$	7.38938	−	12.7988i	0.490450	−	0.849485i	0.999940	+	0.0109922i	$0.00349901\pi$
$228$	0.171551	−	0.0258572i	0.0113613	−	0.00171243i
$229$	13.4443	−	12.4745i	0.888424	−	0.824337i	−0.0968540	−	0.995299i	$-0.530878\pi$
$229$	13.4443	−	12.4745i	0.888424	−	0.824337i	0.985278	+	0.170962i	$0.0546875\pi$
$230$	4.73440	+	2.27997i	0.312177	+	0.150337i
$231$	0.156705	+	0.135467i	0.0103105	+	0.00891308i
$232$	9.50374	−	4.57676i	0.623951	−	0.300479i
$233$	−7.40406	+	18.8652i	−0.485056	+	1.23590i	0.453649	+	0.891180i	$0.350122\pi$
$233$	−7.40406	+	18.8652i	−0.485056	+	1.23590i	−0.938705	+	0.344722i	$0.887973\pi$
$234$	−0.117771	+	1.57155i	−0.00769893	+	0.102735i
$235$	−13.2993	−	4.10230i	−0.867553	−	0.267605i
$236$	−1.67169	−	22.3072i	−0.108818	−	1.45208i
$237$	−0.00424422	+	0.0185952i	−0.000275692	+	0.00120789i
$238$	1.06068	−	3.00964i	0.0687535	−	0.195086i
$239$	4.97901	+	21.8145i	0.322065	+	1.41106i	0.833871	+	0.551960i	$0.186120\pi$
$239$	4.97901	+	21.8145i	0.322065	+	1.41106i	−0.511805	+	0.859101i	$0.671023\pi$
$240$	−0.119310	+	0.0368022i	−0.00770142	+	0.00237557i
$241$	−10.2506	−	26.1180i	−0.660297	−	1.68241i	−0.728772	−	0.684756i	$-0.759909\pi$
$241$	−10.2506	−	26.1180i	−0.660297	−	1.68241i	0.0684757	−	0.997653i	$-0.478186\pi$
$242$	5.43716	+	5.04495i	0.349514	+	0.324301i
$243$	−0.348456	−	0.237573i	−0.0223534	−	0.0152403i
$244$	8.41470			0.538696
$245$	−20.0719	+	11.4691i	−1.28235	+	0.732735i
$246$	0.0369400			0.00235521
$247$	5.32250	+	3.62882i	0.338663	+	0.230896i
$248$	−0.717980	−	0.666188i	−0.0455918	−	0.0423030i
$249$	0.0501173	+	0.127697i	0.00317605	+	0.00809245i
$250$	−1.50299	+	0.463612i	−0.0950577	+	0.0293214i
$251$	−2.19866	−	9.63297i	−0.138778	−	0.608028i	−0.995704	−	0.0925885i	$-0.970486\pi$
$251$	−2.19866	−	9.63297i	−0.138778	−	0.608028i	0.856926	−	0.515439i	$-0.172371\pi$
$252$	−7.25370	−	11.6017i	−0.456940	−	0.730839i
$253$	−3.37769	+	14.7986i	−0.212354	+	0.930382i
$254$	−0.815925	−	10.8878i	−0.0511957	−	0.683159i
$255$	0.113178	+	0.0349109i	0.00708751	+	0.00218621i
$256$	−0.134375	+	1.79311i	−0.00839844	+	0.112069i
$257$	−9.66200	+	24.6184i	−0.602699	+	1.53565i	0.224929	+	0.974375i	$0.427785\pi$
$257$	−9.66200	+	24.6184i	−0.602699	+	1.53565i	−0.827628	+	0.561277i	$0.810310\pi$
$258$	−0.00970748	+	0.00467488i	−0.000604361	+	0.000291045i
$259$	22.6762	+	6.13045i	1.40903	+	0.380928i
$260$	−5.12968	−	2.47032i	−0.318129	−	0.153203i
$261$	−11.8560	+	11.0008i	−0.733870	+	0.680932i
$262$	6.88545	−	1.03782i	0.425385	−	0.0641164i
$263$	11.8665	−	20.5534i	0.731721	−	1.26738i	−0.224426	−	0.974491i	$-0.572051\pi$
$263$	11.8665	−	20.5534i	0.731721	−	1.26738i	0.956147	−	0.292887i	$-0.0946159\pi$
$264$	0.0765872	+	0.132653i	0.00471362	+	0.00816422i
$265$	−24.6687	−	30.9336i	−1.51539	−	1.90024i
$266$	8.94844	−	0.314790i	0.548664	−	0.0193010i
$267$	−0.0505536	+	0.0633922i	−0.00309383	+	0.00387954i
$268$	−2.15851	−	0.325342i	−0.131852	−	0.0198734i
$269$	9.93508	−	6.77362i	0.605752	−	0.412995i	−0.221231	−	0.975221i	$-0.571007\pi$
$269$	9.93508	−	6.77362i	0.605752	−	0.412995i	0.826983	+	0.562226i	$0.190055\pi$
$270$	−0.134359	+	0.0916041i	−0.00817680	+	0.00557485i
$271$	−25.7535	−	3.88171i	−1.56441	−	0.235797i	−0.691028	−	0.722828i	$-0.742842\pi$
$271$	−25.7535	−	3.88171i	−1.56441	−	0.235797i	−0.873385	+	0.487030i	$0.838080\pi$
$272$	−3.46421	+	4.34398i	−0.210049	+	0.263393i
$273$	−0.00777468	+	0.0405930i	−0.000470545	+	0.00245680i
$274$	2.75771	+	3.45806i	0.166599	+	0.208909i
$275$	−14.8013	−	25.6365i	−0.892549	−	1.54594i
$276$	−0.0407837	+	0.0706394i	−0.00245489	+	0.00425199i
$277$	19.9477	−	3.00663i	1.19854	−	0.180651i	0.480717	−	0.876876i	$-0.340376\pi$
$277$	19.9477	−	3.00663i	1.19854	−	0.180651i	0.717824	+	0.696225i	$0.245138\pi$
$278$	7.39552	−	6.86204i	0.443554	−	0.411558i
$279$	1.35303	+	0.651584i	0.0810037	+	0.0390093i
$280$	−16.8037	+	3.14052i	−1.00421	+	0.187682i
$281$	−22.6753	+	10.9199i	−1.35270	+	0.651424i	−0.962996	−	0.269517i	$-0.913136\pi$
$281$	−22.6753	+	10.9199i	−1.35270	+	0.651424i	−0.389701	+	0.920941i	$0.627422\pi$
$282$	−0.0126358	+	0.0321955i	−0.000752451	+	0.00191722i
$283$	−1.02849	+	13.7243i	−0.0611374	+	0.815822i	0.879389	+	0.476103i	$0.157951\pi$
$283$	−1.02849	+	13.7243i	−0.0611374	+	0.815822i	−0.940527	+	0.339719i	$0.889668\pi$
$284$	4.56736	+	1.40885i	0.271023	+	0.0835996i
$285$	0.0248356	+	0.331408i	0.00147113	+	0.0196309i
$286$	−0.585899	+	2.56699i	−0.0346449	+	0.151789i
$287$	−11.8308	−	1.35981i	−0.698349	−	0.0802670i
$288$	−3.46059	−	15.1618i	−0.203917	−	0.893419i
$289$	−11.2083	+	3.45729i	−0.659310	+	0.203370i
$290$	3.41757	+	8.70784i	0.200687	+	0.511342i
$291$	−0.0652737	−	0.0605652i	−0.00382641	−	0.00355039i
$292$	−4.16921	−	2.84252i	−0.243984	−	0.166346i
$293$	−5.45660			−0.318778			−0.159389	−	0.987216i	$-0.550952\pi$
$293$	−5.45660			−0.318778			−0.159389	+	0.987216i	$0.550952\pi$
$294$	0.0246943	+	0.0518705i	0.00144020	+	0.00302515i
$295$	42.8518			2.49493
$296$	14.3519	+	9.78499i	0.834190	+	0.568741i
$297$	−0.344341	−	0.319501i	−0.0199807	−	0.0185393i
$298$	−1.99569	−	5.08493i	−0.115607	−	0.294562i
$299$	−2.89413	+	0.892721i	−0.167372	+	0.0516274i
$300$	−0.0353970	−	0.155084i	−0.00204365	−	0.00895381i
$301$	3.28111	−	1.13988i	0.189120	−	0.0657016i
$302$	1.21621	−	5.32856i	0.0699849	−	0.306624i
$303$	0.00277253	+	0.0369968i	0.000159278	+	0.00212541i
$304$	−14.8976	−	4.59532i	−0.854439	−	0.263559i
$305$	−1.20460	+	16.0742i	−0.0689750	+	0.920407i
$306$	−1.32182	+	3.36794i	−0.0755634	+	0.192532i
$307$	−14.9628	+	7.20572i	−0.853974	+	0.411252i	−0.809051	−	0.587738i	$-0.800018\pi$
$307$	−14.9628	+	7.20572i	−0.853974	+	0.411252i	−0.0449227	+	0.998990i	$0.514304\pi$
$308$	−9.09473	−	20.9732i	−0.518221	−	1.19506i
$309$	−0.0797151	−	0.0383888i	−0.00453484	−	0.00218386i
$310$	0.636717	−	0.590787i	0.0361631	−	0.0335545i
$311$	31.2133	−	4.70465i	1.76994	−	0.266776i	0.818480	−	0.574535i	$-0.194817\pi$
$311$	31.2133	−	4.70465i	1.76994	−	0.266776i	0.951464	+	0.307759i	$0.0995792\pi$
$312$	−0.0152813	+	0.0264681i	−0.000865136	+	0.00149846i
$313$	7.81520	+	13.5363i	0.441741	+	0.765118i	0.997819	−	0.0660120i	$-0.0210276\pi$
$313$	7.81520	+	13.5363i	0.441741	+	0.765118i	−0.556077	+	0.831130i	$0.687694\pi$
$314$	−6.49526	−	8.14479i	−0.366549	−	0.459637i
$315$	23.2006	−	12.1956i	1.30721	−	0.687144i
$316$	1.31241	−	1.64570i	0.0738286	−	0.0925781i
$317$	30.0952	+	4.53611i	1.69031	+	0.254774i	0.922527	−	0.385933i	$-0.126121\pi$
$317$	30.0952	+	4.53611i	1.69031	+	0.254774i	0.767786	+	0.640707i	$0.221359\pi$
$318$	−0.0812384	+	0.0553874i	−0.00455563	+	0.00310597i
$319$	−22.3264	+	15.2219i	−1.25004	+	0.852262i
$320$	6.91226	+	1.04186i	0.386407	+	0.0582415i
$321$	0.122220	−	0.153259i	0.00682167	−	0.00855411i
$322$	−2.50743	+	3.38159i	−0.139733	+	0.188449i
$323$	9.22084	+	11.5626i	0.513061	+	0.643358i
$324$	7.75609	+	13.4339i	0.430894	+	0.746330i
$325$	2.95328	−	5.11522i	0.163818	−	0.283742i
$326$	9.99806	−	1.50697i	0.553741	−	0.0834631i
$327$	−0.139017	+	0.128989i	−0.00768763	+	0.00713308i
$328$	−7.93397	−	3.82080i	−0.438080	−	0.210968i
$329$	5.23203	−	9.84613i	0.288451	−	0.542835i
$330$	−0.122386	+	0.0589378i	−0.00673711	+	0.00324442i
$331$	5.67972	−	14.4717i	0.312186	−	0.795436i	−0.685540	−	0.728035i	$-0.740434\pi$
$331$	5.67972	−	14.4717i	0.312186	−	0.795436i	0.997726	−	0.0674014i	$-0.0214708\pi$
$332$	1.13135	−	15.0968i	0.0620907	−	0.828543i
$333$	−25.4501	−	7.85030i	−1.39465	−	0.430194i
$334$	−0.158712	−	2.11787i	−0.00868434	−	0.115885i
$335$	0.930485	−	4.07672i	0.0508378	−	0.222735i
$336$	−0.0109772	−	0.0994231i	−0.000598855	−	0.00542397i
$337$	−1.27689	−	5.59443i	−0.0695567	−	0.304748i	0.928168	−	0.372160i	$-0.121383\pi$
$337$	−1.27689	−	5.59443i	−0.0695567	−	0.304748i	−0.997725	+	0.0674124i	$0.978526\pi$
$338$	−0.502020	+	0.154853i	−0.0273063	+	0.00842287i
$339$	0.106844	+	0.272233i	0.00580295	+	0.0147857i
$340$	−9.58177	−	8.89059i	−0.519645	−	0.482160i
$341$	2.07306	+	1.41339i	0.112262	+	0.0765392i
$342$	−10.1520			−0.548959
$343$	−5.99944	−	17.5216i	−0.323939	−	0.946078i
$344$	2.56851			0.138485
$345$	−0.129101	−	0.0880195i	−0.00695056	−	0.00473881i
$346$	−5.49191	−	5.09575i	−0.295247	−	0.273949i
$347$	−8.45691	−	21.5478i	−0.453991	−	1.15675i	−0.956385	−	0.292110i	$-0.905643\pi$
$347$	−8.45691	−	21.5478i	−0.453991	−	1.15675i	0.502394	−	0.864639i	$-0.332453\pi$
$348$	−0.138754	+	0.0427998i	−0.00743797	+	0.00229431i
$349$	−7.04450	−	30.8640i	−0.377083	−	1.65211i	−0.706342	−	0.707871i	$-0.749656\pi$
$349$	−7.04450	−	30.8640i	−0.377083	−	1.65211i	0.329258	−	0.944240i	$-0.393201\pi$
$350$	−0.900975	−	8.16035i	−0.0481592	−	0.436189i
$351$	0.0208559	−	0.0913758i	0.00111321	−	0.00487728i
$352$	−1.94170	−	25.9102i	−0.103493	−	1.38102i
$353$	−13.1142	−	4.04519i	−0.697997	−	0.215303i	−0.0746050	−	0.997213i	$-0.523770\pi$
$353$	−13.1142	−	4.04519i	−0.697997	−	0.215303i	−0.623392	+	0.781910i	$0.714246\pi$
$354$	0.00795798	−	0.106192i	0.000422962	−	0.00564403i
$355$	−3.34509	+	8.52314i	−0.177539	+	0.452362i
$356$	8.06202	−	3.88246i	0.427286	−	0.205770i
$357$	−0.0445251	+	0.0837914i	−0.00235652	+	0.00443471i
$358$	−5.90928	−	2.84576i	−0.312315	−	0.150403i
$359$	−3.64723	+	3.38413i	−0.192493	+	0.178608i	−0.770531	−	0.637402i	$-0.780009\pi$
$359$	−3.64723	+	3.38413i	−0.192493	+	0.178608i	0.578038	+	0.816010i	$0.303819\pi$
$360$	19.1654	−	2.88872i	1.01011	−	0.152249i
$361$	−11.2487	+	19.4833i	−0.592035	+	1.02543i
$362$	4.73773	+	8.20599i	0.249009	+	0.431297i
$363$	−0.137510	−	0.172432i	−0.00721741	−	0.00905035i
$364$	2.71677	−	3.66392i	0.142398	−	0.192042i
$365$	6.02677	−	7.55733i	0.315456	−	0.395569i
$366$	0.0396101	+	0.00597027i	0.00207046	+	0.000312071i
$367$	−27.8976	+	19.0203i	−1.45624	+	0.992850i	−0.461866	+	0.886950i	$0.652820\pi$
$367$	−27.8976	+	19.0203i	−1.45624	+	0.992850i	−0.994377	+	0.105900i	$0.966228\pi$
$368$	6.05625	−	4.12908i	0.315704	−	0.215243i
$369$	13.3513	+	2.01238i	0.695039	+	0.104760i
$370$	−9.60437	+	12.0435i	−0.499308	+	0.626112i
$371$	28.0572	−	14.7485i	1.45665	−	0.765702i
$372$	0.00840625	+	0.0105411i	0.000435844	+	0.000546531i
$373$	−13.2879	−	23.0153i	−0.688021	−	1.19169i	−0.972477	−	0.232998i	$-0.925146\pi$
$373$	−13.2879	−	23.0153i	−0.688021	−	1.19169i	0.284456	−	0.958689i	$-0.408187\pi$
$374$	−3.02240	+	5.23496i	−0.156285	+	0.270693i
$375$	0.0462470	−	0.00697062i	0.00238819	−	0.000359961i
$376$	6.04398	−	5.60800i	0.311695	−	0.289210i
$377$	−4.85768	−	2.33933i	−0.250183	−	0.120482i
$378$	−0.0518292	−	0.119522i	−0.00266581	−	0.00614757i
$379$	10.3202	−	4.96994i	0.530112	−	0.255289i	−0.149627	−	0.988743i	$-0.547807\pi$
$379$	10.3202	−	4.96994i	0.530112	−	0.255289i	0.679739	+	0.733454i	$0.262093\pi$
$380$	13.3995	−	34.1414i	0.687380	−	1.75142i
$381$	−0.0242616	+	0.323748i	−0.00124296	+	0.0165861i
$382$	5.31944	+	1.64083i	0.272166	+	0.0839522i
$383$	−0.211801	−	2.82629i	−0.0108225	−	0.144417i	0.989175	−	0.146742i	$-0.0468788\pi$
$383$	−0.211801	−	2.82629i	−0.0108225	−	0.144417i	−0.999997	+	0.00232559i	$0.999260\pi$
$384$	0.0399084	−	0.174850i	0.00203656	−	0.00892277i
$385$	41.3661	−	14.3709i	2.10821	−	0.732407i
$386$	0.465179	+	2.03808i	0.0236770	+	0.103736i
$387$	−3.76326	+	1.16081i	−0.191297	+	0.0590074i
$388$	3.59016	+	9.14757i	0.182263	+	0.464398i
$389$	21.0660	+	19.5463i	1.06809	+	0.991039i	0.999978	−	0.00663867i	$-0.00211317\pi$
$389$	21.0660	+	19.5463i	1.06809	+	0.991039i	0.0681083	+	0.997678i	$0.478304\pi$
$390$	−0.0223940	−	0.0152680i	−0.00113396	−	0.000773124i
$391$	−6.95321			−0.351639
$392$	0.0612512	−	13.6949i	0.00309365	−	0.691699i
$393$	−0.207052			−0.0104444
$394$	−3.85053	−	2.62525i	−0.193987	−	0.132258i
$395$	2.95584	+	2.74262i	0.148724	+	0.137996i
$396$	9.46925	+	24.1272i	0.475847	+	1.21244i
$397$	−18.3967	+	5.67463i	−0.923303	+	0.284801i	−0.719727	−	0.694258i	$-0.755733\pi$
$397$	−18.3967	+	5.67463i	−0.923303	+	0.284801i	−0.203577	+	0.979059i	$0.565257\pi$
$398$	−1.20268	−	5.26928i	−0.0602849	−	0.264125i
$399$	−0.264505	−	0.0304018i	−0.0132418	−	0.00152199i
$400$	−3.18089	+	13.9364i	−0.159045	+	0.696820i
$401$	−0.685936	−	9.15318i	−0.0342540	−	0.457088i	−0.987788	−	0.155803i	$-0.950204\pi$
$401$	−0.685936	−	9.15318i	−0.0342540	−	0.457088i	0.953534	−	0.301285i	$-0.0974155\pi$
$402$	−0.00992981	−	0.00306294i	−0.000495254	−	0.000152766i
$403$	−0.0374116	+	0.499224i	−0.00186361	+	0.0248681i
$404$	1.49586	−	3.81138i	0.0744217	−	0.189623i
$405$	−26.7726	+	12.8930i	−1.33034	+	0.640658i
$406$	−7.36664	+	1.37679i	−0.365600	+	0.0683288i
$407$	−40.0907	−	19.3066i	−1.98722	−	0.956995i
$408$	−0.0514348	+	0.0477245i	−0.00254640	+	0.00236272i
$409$	−22.5828	+	3.40382i	−1.11665	+	0.168308i	−0.681336	−	0.731971i	$-0.738601\pi$
$409$	−22.5828	+	3.40382i	−1.11665	+	0.168308i	−0.435314	+	0.900279i	$0.643363\pi$
$410$	3.90468	−	6.76310i	0.192838	−	0.334006i
$411$	−0.0657594	−	0.113899i	−0.00324367	−	0.00561821i
$412$	6.08796	+	7.63406i	0.299932	+	0.376103i
$413$	−6.45776	+	33.7172i	−0.317766	+	1.65911i
$414$	2.97596	−	3.73173i	0.146260	−	0.183405i
$415$	28.6767	+	4.32232i	1.40768	+	0.212174i
$416$	4.28350	−	2.92044i	0.210016	−	0.143186i
$417$	−0.247861	+	0.168989i	−0.0121378	+	0.00827541i
$418$	−16.7720	−	2.52796i	−0.820343	−	0.123647i
$419$	1.10657	−	1.38760i	0.0540596	−	0.0677886i	−0.754067	−	0.656798i	$-0.771910\pi$
$419$	1.10657	−	1.38760i	0.0540596	−	0.0677886i	0.808126	+	0.589009i	$0.200482\pi$
$420$	0.235172	−	0.00827292i	0.0114752	−	0.000403677i
$421$	−16.9250	−	21.2233i	−0.824874	−	1.03436i	−0.998769	−	0.0495955i	$-0.984207\pi$
$421$	−16.9250	−	21.2233i	−0.824874	−	1.03436i	0.173895	−	0.984764i	$-0.444365\pi$
$422$	−0.145260	−	0.251597i	−0.00707113	−	0.0122476i
$423$	−6.32089	+	10.9481i	−0.307332	+	0.532315i
$424$	23.1773	−	3.49341i	1.12559	−	0.169655i
$425$	9.94030	−	9.22325i	0.482176	−	0.447394i
$426$	0.0205002	+	0.00987236i	0.000993236	+	0.000478317i
$427$	−12.4662	−	3.37020i	−0.603281	−	0.163095i
$428$	−19.4910	+	9.38639i	−0.942135	+	0.453708i
$429$	0.0286034	−	0.0728804i	0.00138099	−	0.00351870i
$430$	−0.170220	+	2.27143i	−0.00820874	+	0.109538i
$431$	−12.9633	−	3.99865i	−0.624420	−	0.192608i	−0.0336313	−	0.999434i	$-0.510707\pi$
$431$	−12.9633	−	3.99865i	−0.624420	−	0.192608i	−0.590789	+	0.806826i	$0.701183\pi$
$432$	0.0169511	+	0.226197i	0.000815561	+	0.0108829i
$433$	1.04805	−	4.59181i	0.0503661	−	0.220668i	−0.943481	−	0.331426i	$-0.892470\pi$
$433$	1.04805	−	4.59181i	0.0503661	−	0.220668i	0.993848	+	0.110757i	$0.0353276\pi$
$434$	0.368897	+	0.590022i	0.0177076	+	0.0283219i
$435$	−0.0618954	−	0.271182i	−0.00296766	−	0.0130022i
$436$	19.9989	−	6.16885i	0.957775	−	0.295435i
$437$	−7.12792	−	18.1617i	−0.340975	−	0.868790i
$438$	−0.0176088	−	0.0163385i	−0.000841379	−	0.000780685i
$439$	0.651735	+	0.444346i	0.0311056	+	0.0212075i	0.578773	−	0.815489i	$-0.303532\pi$
$439$	0.651735	+	0.444346i	0.0311056	+	0.0212075i	−0.547667	+	0.836696i	$0.684484\pi$
$440$	32.3821			1.54375
$441$	6.09955	+	20.0929i	0.290455	+	0.956804i
$442$	−1.20611			−0.0573689
$443$	12.2305	+	8.33864i	0.581090	+	0.396181i	0.817887	−	0.575378i	$-0.195145\pi$
$443$	12.2305	+	8.33864i	0.581090	+	0.396181i	−0.236797	+	0.971559i	$0.576098\pi$
$444$	−0.175281	−	0.162637i	−0.00831848	−	0.00771842i
$445$	6.26238	+	15.9563i	0.296865	+	0.756401i
$446$	−1.83434	+	0.565820i	−0.0868587	+	0.0267924i
$447$	0.0361438	+	0.158356i	0.00170954	+	0.00748999i
$448$	−1.86145	+	5.28179i	−0.0879450	+	0.249541i
$449$	−4.20648	+	18.4298i	−0.198516	+	0.869757i	0.773304	+	0.634035i	$0.218603\pi$
$449$	−4.20648	+	18.4298i	−0.198516	+	0.869757i	−0.971821	+	0.235722i	$0.924255\pi$
$450$	0.695621	+	9.28241i	0.0327919	+	0.437577i
$451$	21.5562	+	6.64922i	1.01504	+	0.313099i
$452$	2.41189	−	32.1844i	0.113446	−	1.51383i
$453$	−0.0593750	+	0.151285i	−0.00278968	+	0.00710799i
$454$	−6.99527	+	3.36875i	−0.328304	+	0.158103i
$455$	6.61010	+	5.71423i	0.309886	+	0.267887i
$456$	−0.177383	−	0.0854230i	−0.00830671	−	0.00400030i
$457$	0.361508	−	0.335430i	0.0169106	−	0.0156908i	−0.671672	−	0.740848i	$-0.734424\pi$
$457$	0.361508	−	0.335430i	0.0169106	−	0.0156908i	0.688583	+	0.725158i	$0.258233\pi$
$458$	−9.52757	+	1.43605i	−0.445194	+	0.0671022i
$459$	0.107587	−	0.186346i	0.00502173	−	0.00869789i
$460$	8.62193	+	14.9336i	0.402000	+	0.696284i
$461$	8.28587	+	10.3902i	0.385911	+	0.483918i	0.936405	−	0.350922i	$-0.114132\pi$
$461$	8.28587	+	10.3902i	0.385911	+	0.483918i	−0.550493	+	0.834840i	$0.685560\pi$
$462$	−0.0279307	−	0.105179i	−0.00129945	−	0.00489337i
$463$	15.5605	−	19.5122i	0.723156	−	0.906809i	−0.275356	−	0.961342i	$-0.588796\pi$
$463$	15.5605	−	19.5122i	0.723156	−	0.906809i	0.998512	+	0.0545333i	$0.0173671\pi$
$464$	12.9028	+	1.94479i	0.598998	+	0.0902845i
$465$	−0.0213396	+	0.0145491i	−0.000989599	+	0.000674697i
$466$	8.79698	−	5.99768i	0.407512	−	0.277837i
$467$	−9.51236	−	1.43376i	−0.440179	−	0.0663464i	−0.0747860	−	0.997200i	$-0.523827\pi$
$467$	−9.51236	−	1.43376i	−0.440179	−	0.0663464i	−0.365393	+	0.930853i	$0.619065\pi$
$468$	−3.22442	+	4.04330i	−0.149049	+	0.186901i
$469$	3.06747	+	1.34650i	0.141643	+	0.0621755i
$470$	4.55882	+	5.71658i	0.210283	+	0.263686i
$471$	0.154884	+	0.268266i	0.00713666	+	0.0123611i
$472$	−12.6929	+	21.9848i	−0.584239	+	1.01193i
$473$	−6.50626	+	0.980660i	−0.299158	+	0.0450908i
$474$	0.00734546	−	0.00681559i	0.000337388	−	0.000313051i
$475$	34.2810	+	16.5089i	1.57292	+	0.757479i
$476$	8.43938	−	6.19944i	0.386818	−	0.284151i
$477$	−32.3794	+	15.5931i	−1.48255	+	0.713960i
$478$	4.29465	−	10.9426i	0.196433	−	0.500502i
$479$	−1.90388	+	25.4056i	−0.0869906	+	1.16081i	0.767397	+	0.641173i	$0.221552\pi$
$479$	−1.90388	+	25.4056i	−0.0869906	+	1.16081i	−0.854387	+	0.519637i	$0.826067\pi$
$480$	0.255579	+	0.0788358i	0.0116655	+	0.00359834i
$481$	−0.663490	−	8.85366i	−0.0302525	−	0.403692i
$482$	−3.28002	+	14.3707i	−0.149401	+	0.654569i
$483$	0.0887121	−	0.0883162i	0.00403654	−	0.00401853i
$484$	5.41611	+	23.7295i	0.246187	+	1.07862i
$485$	−17.9881	+	5.54860i	−0.816799	+	0.251949i
$486$	0.0809464	+	0.206248i	0.00367180	+	0.00935560i
$487$	4.28691	+	3.97768i	0.194259	+	0.180246i	0.771305	−	0.636466i	$-0.219604\pi$
$487$	4.28691	+	3.97768i	0.194259	+	0.180246i	−0.577046	+	0.816711i	$0.695795\pi$
$488$	−7.88994	−	5.37927i	−0.357161	−	0.243508i
$489$	−0.300651			−0.0135959
$490$	12.1069	+	0.961757i	0.546934	+	0.0434478i
$491$	−23.5091			−1.06095			−0.530477	−	0.847700i	$-0.677987\pi$
$491$	−23.5091			−1.06095			−0.530477	+	0.847700i	$0.677987\pi$
$492$	0.100157	+	0.0682860i	0.00451543	+	0.00307857i
$493$	−9.07370	−	8.41916i	−0.408659	−	0.379180i
$494$	−1.23642	−	3.15034i	−0.0556291	−	0.141741i
$495$	−47.4447	+	14.6348i	−2.13248	+	0.657784i
$496$	−0.269604	−	1.18121i	−0.0121056	−	0.0530380i
$497$	−6.20218	−	3.91646i	−0.278206	−	0.175677i
$498$	0.0160368	−	0.0702617i	0.000718625	−	0.00314850i
$499$	2.14194	+	28.5821i	0.0958862	+	1.27951i	0.812879	+	0.582432i	$0.197899\pi$
$499$	2.14194	+	28.5821i	0.0958862	+	1.27951i	−0.716993	+	0.697080i	$0.754482\pi$
$500$	−4.93215	−	1.52137i	−0.220573	−	0.0680377i
$501$	−0.00471931	+	0.0629748i	−0.000210843	+	0.00281351i
$502$	−1.89646	+	4.83210i	−0.0846431	+	0.215667i
$503$	24.7544	−	11.9211i	1.10374	−	0.531535i	0.208910	−	0.977935i	$-0.433009\pi$
$503$	24.7544	−	11.9211i	1.10374	−	0.531535i	0.894833	+	0.446400i	$0.147294\pi$
$504$	−0.615289	+	15.5153i	−0.0274072	+	0.691106i
$505$	7.06657	+	3.40308i	0.314458	+	0.151435i
$506$	5.84576	−	5.42407i	0.259876	−	0.241129i
$507$	0.0154471	−	0.00232828i	0.000686030	−	0.000103402i
$508$	17.9145	−	31.0288i	0.794827	−	1.37668i
$509$	2.74820	+	4.76002i	0.121812	+	0.210984i	0.920482	−	0.390785i	$-0.127796\pi$
$509$	2.74820	+	4.76002i	0.121812	+	0.210984i	−0.798670	+	0.601769i	$0.794463\pi$
$510$	−0.0387959	−	0.0486486i	−0.00171791	−	0.00215419i
$511$	5.03812	+	5.88095i	0.222873	+	0.260158i
$512$	−13.7272	+	17.2133i	−0.606662	+	0.760730i
$513$	0.597023	+	0.0899867i	0.0263592	+	0.00397301i
$514$	11.4797	−	7.82674i	0.506349	−	0.345223i
$515$	−15.4545	+	10.5367i	−0.681007	+	0.464302i
$516$	−0.0349622	−	0.00526970i	−0.00153912	−	0.000231986i
$517$	−13.1688	+	16.5132i	−0.579163	+	0.726248i
$518$	−8.02884	−	9.37199i	−0.352767	−	0.411782i
$519$	0.138895	+	0.174169i	0.00609681	+	0.00764516i
$520$	3.23058	+	5.59552i	0.141670	+	0.245380i
$521$	−11.4580	+	19.8459i	−0.501986	+	0.869465i	0.498012	+	0.867170i	$0.334064\pi$
$521$	−11.4580	+	19.8459i	−0.501986	+	0.869465i	−0.999997	+	0.00229430i	$0.999270\pi$
$522$	8.40202	−	1.26640i	0.367746	−	0.0554288i
$523$	3.85657	−	3.57838i	0.168636	−	0.156471i	−0.591340	−	0.806422i	$-0.701401\pi$
$523$	3.85657	−	3.57838i	0.168636	−	0.156471i	0.759976	+	0.649951i	$0.225210\pi$
$524$	20.5873	+	9.91433i	0.899361	+	0.433110i
$525$	−0.00967356	+	0.243931i	−0.000422189	+	0.0106460i
$526$	−11.2336	+	5.40983i	−0.489810	+	0.235880i
$527$	−0.419895	+	1.06987i	−0.0182909	+	0.0466045i
$528$	−0.0141599	+	0.188950i	−0.000616229	+	0.00822301i
$529$	−13.2128	−	4.07559i	−0.574468	−	0.177200i
$530$	1.55335	+	20.7280i	0.0674733	+	0.900369i
$531$	8.66127	−	37.9475i	0.375867	−	1.64678i
$532$	24.8442	+	15.6883i	1.07713	+	0.680173i
$533$	1.00158	+	4.38821i	0.0433832	+	0.190074i
$534$	0.0407046	−	0.0125557i	0.00176146	−	0.000543339i
$535$	−15.1402	−	38.5765i	−0.654567	−	1.66781i
$536$	1.81592	+	1.68492i	0.0784356	+	0.0727776i
$537$	0.161138	+	0.109862i	0.00695363	+	0.00474091i
$538$	−6.31717			−0.272353
$539$	5.07359	+	34.7139i	0.218535	+	1.49523i
$540$	−0.533629			−0.0229637
$541$	4.90237	+	3.34238i	0.210769	+	0.143700i	0.664104	−	0.747640i	$-0.268813\pi$
$541$	4.90237	+	3.34238i	0.210769	+	0.143700i	−0.453334	+	0.891341i	$0.649766\pi$
$542$	10.0301	+	9.30658i	0.430830	+	0.399752i
$543$	−0.102936	−	0.262276i	−0.00441740	−	0.0112554i
$544$	11.3733	−	3.50821i	0.487627	−	0.150413i
$545$	8.92116	+	39.0861i	0.382140	+	1.67427i
$546$	0.0153881	−	0.0153194i	0.000658550	−	0.000655612i
$547$	−3.26263	+	14.2945i	−0.139500	+	0.611189i	0.856045	+	0.516901i	$0.172915\pi$
$547$	−3.26263	+	14.2945i	−0.139500	+	0.611189i	−0.995545	+	0.0942879i	$0.969943\pi$
$548$	1.08466	+	14.4738i	0.0463345	+	0.618291i
$549$	13.9911	+	4.31568i	0.597125	+	0.184189i
$550$	−1.16220	+	15.5085i	−0.0495564	+	0.661284i
$551$	12.6890	−	32.3310i	0.540569	−	1.37735i
$552$	0.0833981	−	0.0401624i	0.00354966	−	0.00170942i
$553$	−2.60343	+	1.91244i	−0.110709	+	0.0813251i
$554$	−9.54855	−	4.59834i	−0.405679	−	0.195365i
$555$	0.335771	−	0.311550i	0.0142527	−	0.0132245i
$556$	32.7367	−	4.93427i	1.38835	−	0.209260i
$557$	6.63617	−	11.4942i	0.281184	−	0.487025i	−0.690493	−	0.723339i	$-0.742606\pi$
$557$	6.63617	−	11.4942i	0.281184	−	0.487025i	0.971677	+	0.236315i	$0.0759396\pi$
$558$	−0.394479	−	0.683258i	−0.0166996	−	0.0289246i
$559$	−0.818548	−	1.02643i	−0.0346209	−	0.0434132i
$560$	−19.3630	−	8.49960i	−0.818238	−	0.359174i
$561$	0.112068	−	0.140528i	0.00473150	−	0.00593311i
$562$	13.0744	+	1.97065i	0.551512	+	0.0831270i
$563$	−17.4749	+	11.9142i	−0.736479	+	0.502123i	−0.872519	−	0.488581i	$-0.837515\pi$
$563$	−17.4749	+	11.9142i	−0.736479	+	0.502123i	0.136040	+	0.990703i	$0.456562\pi$
$564$	−0.0937756	+	0.0639351i	−0.00394866	+	0.00269215i
$565$	61.1351	+	9.21464i	2.57197	+	0.387663i
$566$	4.50808	−	5.65295i	0.189489	−	0.237611i
$567$	−6.11000	−	23.0085i	−0.256596	−	0.966266i
$568$	−3.38190	−	4.24077i	−0.141901	−	0.177939i
$569$	−15.1275	−	26.2016i	−0.634179	−	1.09843i	−0.986688	−	0.162622i	$-0.948005\pi$
$569$	−15.1275	−	26.2016i	−0.634179	−	1.09843i	0.352510	−	0.935808i	$-0.385328\pi$
$570$	0.0872984	−	0.151205i	0.00365653	−	0.00633329i
$571$	7.47791	−	1.12711i	0.312941	−	0.0471682i	0.00930580	−	0.999957i	$-0.497038\pi$
$571$	7.47791	−	1.12711i	0.312941	−	0.0471682i	0.303635	+	0.952788i	$0.401800\pi$
$572$	−6.33382	+	5.87693i	−0.264830	+	0.245727i
$573$	−0.149135	−	0.0718197i	−0.00623021	−	0.00300031i
$574$	4.73299	+	4.09153i	0.197551	+	0.170777i
$575$	−16.1175	+	7.76179i	−0.672147	+	0.323689i
$576$	2.31974	−	5.91060i	0.0966558	−	0.246275i
$577$	2.54405	−	33.9480i	0.105910	−	1.41327i	−0.650664	−	0.759366i	$-0.725509\pi$
$577$	2.54405	−	33.9480i	0.105910	−	1.41327i	0.756574	−	0.653908i	$-0.226872\pi$
$578$	5.88838	+	1.81632i	0.244924	+	0.0755491i
$579$	−0.00464529	−	0.0619872i	−0.000193052	−	0.00257610i
$580$	−6.83077	+	29.9276i	−0.283632	+	1.24267i
$581$	−7.72253	+	21.9124i	−0.320384	+	0.909080i
$582$	0.0104095	+	0.0456072i	0.000431489	+	0.00189048i
$583$	−57.3762	+	17.6982i	−2.37628	+	0.732986i
$584$	2.09207	+	5.33051i	0.0865705	+	0.220578i
$585$	−7.26214	−	6.73828i	−0.300252	−	0.278593i
$586$	2.36856	+	1.61486i	0.0978444	+	0.0667092i
$587$	−26.7346			−1.10346			−0.551728	−	0.834024i	$-0.686031\pi$
$587$	−26.7346			−1.10346			−0.551728	+	0.834024i	$0.686031\pi$
$588$	−0.0289311	+	0.186288i	−0.00119310	+	0.00768238i
$589$	−3.22494			−0.132881
$590$	−18.6008	−	12.6818i	−0.765782	−	0.522101i
$591$	0.101582	+	0.0942546i	0.00417854	+	0.00387712i
$592$	7.85021	+	20.0020i	0.322642	+	0.822078i
$593$	28.4618	−	8.77932i	1.16879	−	0.360523i	0.351185	−	0.936306i	$-0.385779\pi$
$593$	28.4618	−	8.77932i	1.16879	−	0.360523i	0.817603	+	0.575783i	$0.195303\pi$
$594$	0.0549138	+	0.240593i	0.00225314	+	0.00987165i
$595$	10.6344	+	17.0088i	0.435967	+	0.697294i
$596$	3.98882	−	17.4762i	0.163388	−	0.715851i
$597$	0.0120100	+	0.160262i	0.000491536	+	0.00655910i
$598$	1.52046	+	0.469000i	0.0621763	+	0.0191788i
$599$	2.83880	−	37.8811i	0.115990	−	1.54778i	−0.570899	−	0.821020i	$-0.693405\pi$
$599$	2.83880	−	37.8811i	0.115990	−	1.54778i	0.686890	−	0.726762i	$-0.258976\pi$
$600$	−0.0659514	+	0.168041i	−0.00269245	+	0.00686026i
$601$	−29.4024	+	14.1595i	−1.19935	+	0.577576i	−0.923490	−	0.383622i	$-0.874677\pi$
$601$	−29.4024	+	14.1595i	−1.19935	+	0.577576i	−0.275859	+	0.961198i	$0.588962\pi$
$602$	−1.76158	−	0.476239i	−0.0717967	−	0.0194101i
$603$	−3.42208	−	1.64799i	−0.139358	−	0.0671112i
$604$	13.1477	−	12.1993i	0.534974	−	0.496383i
$605$	−46.1048	+	6.94918i	−1.87443	+	0.282524i
$606$	0.00974557	−	0.0168798i	0.000395887	−	0.000685696i
$607$	9.35472	+	16.2029i	0.379696	+	0.657653i	0.991018	−	0.133729i	$-0.0426951\pi$
$607$	9.35472	+	16.2029i	0.379696	+	0.657653i	−0.611322	+	0.791382i	$0.709362\pi$
$608$	20.8225	+	26.1106i	0.844463	+	1.05892i
$609$	0.222702	−	0.00783425i	0.00902435	−	0.000317460i
$610$	5.27998	−	6.62088i	0.213780	−	0.268072i
$611$	−4.16720	−	0.628104i	−0.168587	−	0.0254104i
$612$	−9.80977	+	6.68819i	−0.396537	+	0.270354i
$613$	8.78561	−	5.98993i	0.354848	−	0.241931i	−0.372755	−	0.927930i	$-0.621587\pi$
$613$	8.78561	−	5.98993i	0.354848	−	0.241931i	0.727603	+	0.685999i	$0.240634\pi$
$614$	8.62746	+	1.30038i	0.348176	+	0.0524791i
$615$	−0.144781	+	0.181550i	−0.00583815	+	0.00732081i
$616$	−4.87998	+	25.4793i	−0.196620	+	1.02659i
$617$	−9.19113	−	11.5253i	−0.370021	−	0.463992i	0.561607	−	0.827404i	$-0.310183\pi$
$617$	−9.19113	−	11.5253i	−0.370021	−	0.463992i	−0.931629	+	0.363412i	$0.881612\pi$
$618$	0.0232412	+	0.0402549i	0.000934897	+	0.00161929i
$619$	−2.30929	+	3.99981i	−0.0928183	+	0.160766i	−0.908696	−	0.417459i	$-0.862921\pi$
$619$	−2.30929	+	3.99981i	−0.0928183	+	0.160766i	0.815878	+	0.578225i	$0.196254\pi$
$620$	2.81847	−	0.424816i	0.113192	−	0.0170610i
$621$	−0.208089	+	0.193078i	−0.00835030	+	0.00774795i
$622$	−14.9412	−	7.19529i	−0.599086	−	0.288505i
$623$	−13.4987	+	2.52283i	−0.540813	+	0.101075i
$624$	−0.0340627	+	0.0164037i	−0.00136360	+	0.000656675i
$625$	−7.17727	+	18.2874i	−0.287091	+	0.731496i
$626$	0.613653	−	8.18863i	0.0245265	−	0.327283i
$627$	0.481941	+	0.148659i	0.0192469	+	0.00593687i
$628$	−2.55471	−	34.0903i	−0.101944	−	1.36035i
$629$	4.53566	−	19.8720i	0.180849	−	0.792350i
$630$	−13.6800	−	1.57235i	−0.545024	−	0.0626440i
$631$	−9.82205	−	43.0332i	−0.391010	−	1.71313i	−0.661106	−	0.750292i	$-0.729913\pi$
$631$	−9.82205	−	43.0332i	−0.391010	−	1.71313i	0.270097	−	0.962833i	$-0.412944\pi$
$632$	−2.28261	+	0.704093i	−0.0907975	+	0.0280073i
$633$	0.00315604	+	0.00804145i	0.000125441	+	0.000319619i
$634$	−11.7210	−	10.8755i	−0.465502	−	0.431923i
$635$	56.7084	+	38.6631i	2.25040	+	1.53430i
$636$	−0.322653			−0.0127940
$637$	−5.49229	+	4.33991i	−0.217612	+	0.171953i
$638$	14.1961			0.562030
$639$	6.87158	+	4.68497i	0.271836	+	0.185334i
$640$	−27.7937	−	25.7888i	−1.09864	−	1.01939i
$641$	−8.15467	−	20.7778i	−0.322090	−	0.820672i	−0.996599	−	0.0824054i	$-0.973740\pi$
$641$	−8.15467	−	20.7778i	−0.322090	−	0.820672i	0.674509	−	0.738267i	$-0.264355\pi$
$642$	−0.0984090	+	0.0303552i	−0.00388389	+	0.00119802i
$643$	−2.96168	−	12.9760i	−0.116797	−	0.511722i	−0.999153	−	0.0411401i	$-0.986901\pi$
$643$	−2.96168	−	12.9760i	−0.116797	−	0.511722i	0.882356	−	0.470582i	$-0.155956\pi$
$644$	−13.0496	+	4.53352i	−0.514226	+	0.178646i
$645$	0.0150714	−	0.0660322i	0.000593437	−	0.00260002i
$646$	−0.580622	−	7.74786i	−0.0228443	−	0.304836i
$647$	14.2616	+	4.39911i	0.560680	+	0.172947i	0.562125	−	0.827052i	$-0.309984\pi$
$647$	14.2616	+	4.39911i	0.560680	+	0.172947i	−0.00144523	+	0.999999i	$0.500460\pi$
$648$	1.31552	−	17.5544i	0.0516786	−	0.689603i
$649$	23.7584	−	60.5355i	0.932600	−	2.37623i
$650$	−2.79577	+	1.34637i	−0.109659	+	0.0528090i
$651$	−0.00823181	−	0.0189832i	−0.000322630	−	0.000744011i
$652$	29.8939	+	14.3962i	1.17074	+	0.563797i
$653$	17.1636	−	15.9255i	0.671666	−	0.623215i	−0.268763	−	0.963206i	$-0.586615\pi$
$653$	17.1636	−	15.9255i	0.671666	−	0.623215i	0.940428	+	0.339992i	$0.110424\pi$
$654$	0.0985169	−	0.0148490i	0.00385232	−	0.000580643i
$655$	−21.8860	+	37.9077i	−0.855159	+	1.48118i
$656$	−5.44664	−	9.43385i	−0.212655	−	0.368330i
$657$	−5.47428	−	6.86453i	−0.213572	−	0.267811i
$658$	−5.18501	+	2.72554i	−0.202133	+	0.106253i
$659$	−19.9960	+	25.0742i	−0.778935	+	0.976754i	0.221064	+	0.975259i	$0.429047\pi$
$659$	−19.9960	+	25.0742i	−0.778935	+	0.976754i	−0.999999	+	0.00149465i	$0.999524\pi$
$660$	−0.440780	−	0.0664369i	−0.0171573	−	0.00258605i
$661$	−20.9799	+	14.3039i	−0.816023	+	0.556355i	−0.897855	−	0.440291i	$-0.854875\pi$
$661$	−20.9799	+	14.3039i	−0.816023	+	0.556355i	0.0818318	+	0.996646i	$0.473923\pi$
$662$	−6.74825	+	4.60088i	−0.262278	+	0.178818i
$663$	0.0354632	+	0.00534522i	0.00137728	+	0.000207591i
$664$	−10.7117	+	13.4321i	−0.415695	+	0.521266i
$665$	−33.5251	+	45.2130i	−1.30005	+	1.75328i
$666$	8.72391	+	10.9394i	0.338045	+	0.423895i
$667$	8.16476	+	14.1418i	0.316141	+	0.547572i
$668$	3.48469	−	6.03566i	0.134827	−	0.233527i
$669$	0.0564426	−	0.00850736i	0.00218220	−	0.000328913i
$670$	−1.61039	+	1.49422i	−0.0622147	+	0.0577268i
$671$	22.0397	+	10.6138i	0.850835	+	0.409740i
$672$	−0.100546	+	0.189218i	−0.00387866	+	0.00729923i
$673$	23.5326	−	11.3327i	0.907115	−	0.436843i	0.0786612	−	0.996901i	$-0.474935\pi$
$673$	23.5326	−	11.3327i	0.907115	−	0.436843i	0.828453	+	0.560058i	$0.189221\pi$
$674$	−1.10138	+	2.80628i	−0.0424237	+	0.108094i
$675$	0.0413703	−	0.552048i	0.00159234	−	0.0212483i
$676$	−1.64740	−	0.508157i	−0.0633617	−	0.0195445i
$677$	−0.640092	−	8.54143i	−0.0246007	−	0.328274i	−0.995903	−	0.0904261i	$-0.971177\pi$
$677$	−0.640092	−	8.54143i	−0.0246007	−	0.328274i	0.971302	−	0.237848i	$-0.0764419\pi$
$678$	0.0341884	−	0.149789i	0.00131300	−	0.00575261i
$679$	−1.65501	−	14.9898i	−0.0635134	−	0.575257i
$680$	3.30074	+	14.4615i	0.126578	+	0.554573i
$681$	0.220611	−	0.0680494i	0.00845383	−	0.00260766i
$682$	−0.481572	−	1.22703i	−0.0184403	−	0.0469852i
$683$	−1.62001	−	1.50315i	−0.0619880	−	0.0575164i	0.648571	−	0.761155i	$-0.275367\pi$
$683$	−1.62001	−	1.50315i	−0.0619880	−	0.0575164i	−0.710558	+	0.703638i	$0.751558\pi$
$684$	−27.5257	−	18.7667i	−1.05247	−	0.717562i
$685$	−27.8039			−1.06233
$686$	−2.58125	+	9.38116i	−0.0985527	+	0.358174i
$687$	0.286502			0.0109308
$688$	2.62521	+	1.78984i	0.100085	+	0.0682369i
$689$	−8.78230	−	8.14879i	−0.334579	−	0.310444i
$690$	0.0299902	+	0.0764137i	0.00114171	+	0.00290902i
$691$	19.8227	−	6.11449i	0.754091	−	0.232606i	0.106206	−	0.994344i	$-0.466130\pi$
$691$	19.8227	−	6.11449i	0.754091	−	0.232606i	0.647885	+	0.761738i	$0.275654\pi$
$692$	−5.47065	−	23.9685i	−0.207963	−	0.911146i
$693$	−4.36518	−	39.5365i	−0.165820	−	1.50187i
$694$	−2.70608	+	11.8561i	−0.102721	+	0.450052i
$695$	4.73932	+	63.2419i	0.179773	+	2.39890i
$696$	0.157461	+	0.0485704i	0.00596856	+	0.00184106i
$697$	−0.772220	+	10.3046i	−0.0292499	+	0.390313i
$698$	−6.07624	+	15.4820i	−0.229989	+	0.586002i
$699$	−0.285237	+	0.137363i	−0.0107887	+	0.00519555i
$700$	12.6421	−	23.7911i	0.477826	−	0.899218i
$701$	−25.8768	−	12.4616i	−0.977353	−	0.470669i	−0.124159	−	0.992262i	$-0.539623\pi$
$701$	−25.8768	−	12.4616i	−0.977353	−	0.470669i	−0.853194	+	0.521594i	$0.825338\pi$
$702$	−0.0360953	+	0.0334915i	−0.00136233	+	0.00126406i
$703$	56.5550	−	8.52430i	2.13301	−	0.321500i
$704$	5.30419	−	9.18713i	0.199909	−	0.346253i
$705$	−0.108708	−	0.188288i	−0.00409418	−	0.00709133i
$706$	4.49535	+	5.63699i	0.169185	+	0.212151i
$707$	−3.74259	+	5.04736i	−0.140754	+	0.189826i
$708$	0.217879	−	0.273212i	0.00818841	−	0.0102679i
$709$	27.5421	+	4.15131i	1.03437	+	0.155906i	0.644215	−	0.764845i	$-0.277184\pi$
$709$	27.5421	+	4.15131i	1.03437	+	0.155906i	0.390152	+	0.920750i	$0.372422\pi$
$710$	3.97440	−	2.70970i	0.149157	−	0.101693i
$711$	3.02617	−	2.06321i	0.113490	−	0.0773764i
$712$	−10.0412	−	1.51347i	−0.376310	−	0.0567196i
$713$	0.945355	−	1.18544i	0.0354038	−	0.0443950i
$714$	0.0441248	−	0.0231946i	0.00165133	−	0.000868035i
$715$	−10.3197	−	12.9405i	−0.385935	−	0.483948i
$716$	−10.7615	−	18.6395i	−0.402178	−	0.696592i
$717$	−0.174770	+	0.302711i	−0.00652691	+	0.0113049i
$718$	2.58468	−	0.389578i	0.0964595	−	0.0145389i
$719$	−27.0657	+	25.1133i	−1.00938	+	0.936567i	−0.997990	−	0.0633683i	$-0.979816\pi$
$719$	−27.0657	+	25.1133i	−1.00938	+	0.936567i	−0.0113888	+	0.999935i	$0.503625\pi$
$720$	21.6015	+	10.4027i	0.805039	+	0.387687i
$721$	−5.96162	−	13.7480i	−0.222022	−	0.512002i
$722$	10.6487	−	5.12816i	0.396305	−	0.190850i
$723$	0.160130	−	0.408005i	0.00595530	−	0.0151739i
$724$	−2.32367	+	31.0073i	−0.0863586	+	1.15238i
$725$	−30.4310	−	9.38673i	−1.13018	−	0.348614i
$726$	0.00865881	+	0.115544i	0.000321359	+	0.00428823i
$727$	−4.31810	+	18.9189i	−0.160150	+	0.701661i	0.829542	+	0.558445i	$0.188602\pi$
$727$	−4.31810	+	18.9189i	−0.160150	+	0.701661i	−0.989691	+	0.143217i	$0.954255\pi$
$728$	−4.88959	+	1.69868i	−0.181220	+	0.0629572i
$729$	6.00513	+	26.3102i	0.222412	+	0.974452i
$730$	−4.85262	+	1.49683i	−0.179603	+	0.0554003i
$731$	−1.10114	−	2.80567i	−0.0407273	−	0.103771i
$732$	0.0963604	+	0.0894094i	0.00356158	+	0.00330467i
$733$	31.2435	+	21.3014i	1.15400	+	0.786787i	0.980203	−	0.197994i	$-0.0634426\pi$
$733$	31.2435	+	21.3014i	1.15400	+	0.786787i	0.173801	+	0.984781i	$0.444395\pi$
$734$	17.7386			0.654742
$735$	−0.351716	−	0.0819335i	−0.0129732	−	0.00302216i
$736$	−15.7017			−0.578773
$737$	−5.24318	−	3.57474i	−0.193135	−	0.131677i
$738$	−5.19987	−	4.82477i	−0.191410	−	0.177602i
$739$	0.890707	+	2.26949i	0.0327652	+	0.0834844i	0.946320	−	0.323231i	$-0.104769\pi$
$739$	0.890707	+	2.26949i	0.0327652	+	0.0834844i	−0.913555	+	0.406716i	$0.866674\pi$
$740$	−48.3040	+	14.8998i	−1.77569	+	0.547728i
$741$	0.0223927	+	0.0981088i	0.000822616	+	0.00360412i
$742$	−16.5436	−	1.90149i	−0.607334	−	0.0698059i
$743$	2.63949	−	11.5643i	0.0968334	−	0.424255i	−0.903154	−	0.429317i	$-0.858754\pi$
$743$	2.63949	−	11.5643i	0.0968334	−	0.424255i	0.999987	+	0.00506241i	$0.00161142\pi$
$744$	−0.00114340	−	0.0152576i	−4.19191e−5	−	0.000559371i
$745$	32.8129	+	10.1214i	1.20217	+	0.370821i
$746$	−1.04337	+	13.9228i	−0.0382005	+	0.509750i
$747$	9.62383	−	24.5211i	0.352118	−	0.897181i
$748$	−17.8719	+	8.60667i	−0.653463	+	0.314691i
$749$	32.6349	−	6.09930i	1.19245	−	0.222863i
$750$	−0.0221375	−	0.0106609i	−0.000808347	−	0.000389279i
$751$	19.7418	−	18.3177i	0.720387	−	0.668422i	−0.232206	−	0.972667i	$-0.574595\pi$
$751$	19.7418	−	18.3177i	0.720387	−	0.668422i	0.952594	+	0.304245i	$0.0984040\pi$
$752$	10.0853	−	1.52011i	0.367773	−	0.0554328i
$753$	0.0771762	−	0.133673i	0.00281246	−	0.00487132i
$754$	1.41627	+	2.45305i	0.0515775	+	0.0893348i
$755$	21.4217	+	26.8619i	0.779614	+	0.977605i
$756$	0.0804179	−	0.419876i	0.00292477	−	0.0152708i
$757$	21.3002	−	26.7096i	0.774168	−	0.970776i	−0.225826	−	0.974168i	$-0.572508\pi$
$757$	21.3002	−	26.7096i	0.774168	−	0.970776i	0.999994	+	0.00339143i	$0.00107953\pi$
$758$	−5.95054	−	0.896900i	−0.216133	−	0.0325769i
$759$	−0.195921	+	0.133576i	−0.00711146	+	0.00484851i
$760$	−34.3895	+	23.4464i	−1.24744	+	0.850489i
$761$	14.1847	+	2.13801i	0.514197	+	0.0775027i	0.401015	−	0.916072i	$-0.368658\pi$
$761$	14.1847	+	2.13801i	0.514197	+	0.0775027i	0.113182	+	0.993574i	$0.463896\pi$
$762$	0.106343	−	0.133350i	0.00385241	−	0.00483076i
$763$	−32.0987	+	1.12917i	−1.16205	+	0.0408788i
$764$	11.3897	+	14.2822i	0.412064	+	0.516712i
$765$	−11.3718	−	19.6966i	−0.411150	−	0.712132i
$766$	−0.744491	+	1.28950i	−0.0268996	+	0.0465914i
$767$	12.8306	−	1.93390i	0.463286	−	0.0698291i
$768$	−0.0205913	+	0.0191059i	−0.000743023	+	0.000689425i
$769$	44.3051	+	21.3362i	1.59768	+	0.769403i	0.999489	−	0.0319495i	$-0.0101716\pi$
$769$	44.3051	+	21.3362i	1.59768	+	0.769403i	0.598192	+	0.801353i	$0.295886\pi$
$770$	−22.2089	−	6.00411i	−0.800353	−	0.216373i
$771$	−0.372224	+	0.179253i	−0.0134053	+	0.00645565i
$772$	−2.50627	+	6.38586i	−0.0902025	+	0.229832i
$773$	−0.569679	+	7.60184i	−0.0204899	+	0.273419i	0.977543	+	0.210734i	$0.0675854\pi$
$773$	−0.569679	+	7.60184i	−0.0204899	+	0.273419i	−0.998033	+	0.0626850i	$0.980034\pi$
$774$	1.97707	+	0.609844i	0.0710642	+	0.0219204i
$775$	0.220974	+	2.94869i	0.00793761	+	0.105920i
$776$	2.48151	−	10.8722i	0.0890810	−	0.390289i
$777$	0.194537	+	0.311146i	0.00697897	+	0.0111623i
$778$	−3.35950	−	14.7189i	−0.120444	−	0.527699i
$779$	−27.7069	+	8.54646i	−0.992704	+	0.306209i
$780$	−0.0324941	−	0.0827935i	−0.00116347	−	0.00296448i
$781$	10.1858	+	9.45103i	0.364476	+	0.338184i
$782$	3.01820	+	2.05777i	0.107931	+	0.0735858i
$783$	−0.505333			−0.0180591
$784$	9.60578	−	13.9546i	0.343063	−	0.498378i
$785$	65.4868			2.33732
$786$	0.0898755	+	0.0612761i	0.00320575	+	0.00218565i
$787$	10.4756	+	9.71997i	0.373416	+	0.346479i	0.844449	−	0.535636i	$-0.179928\pi$
$787$	10.4756	+	9.71997i	0.373416	+	0.346479i	−0.471033	+	0.882116i	$0.656119\pi$
$788$	−5.58718	−	14.2359i	−0.199035	−	0.507133i
$789$	0.354277	−	0.109280i	0.0126126	−	0.00389047i
$790$	−0.471383	−	2.06526i	−0.0167710	−	0.0734788i
$791$	−16.4634	+	46.7145i	−0.585373	+	1.66097i
$792$	6.54512	−	28.6760i	0.232571	−	1.01896i
$793$	0.364752	+	4.86728i	0.0129527	+	0.172842i
$794$	9.66488	+	2.98122i	0.342994	+	0.105800i
$795$	0.0461890	−	0.616349i	0.00163815	−	0.0218596i
$796$	6.47973	−	16.5101i	0.229668	−	0.585184i
$797$	−1.56374	+	0.753056i	−0.0553904	+	0.0266746i	−0.461374	−	0.887206i	$-0.652643\pi$
$797$	−1.56374	+	0.753056i	−0.0553904	+	0.0266746i	0.405983	+	0.913880i	$0.366929\pi$
$798$	0.105817	+	0.0914758i	0.00374589	+	0.00323821i
$799$	−8.71692	−	4.19785i	−0.308382	−	0.148509i
$800$	22.4472	−	20.8279i	0.793627	−	0.736379i
$801$	15.3959	−	2.32056i	0.543988	−	0.0819930i
$802$	−2.41110	+	4.17614i	−0.0851388	+	0.147465i
$803$	−7.33460	−	12.7039i	−0.258832	−	0.448311i
$804$	−0.0212611	−	0.0266606i	−0.000749821	−	0.000940246i
$805$	−6.79208	−	25.5770i	−0.239389	−	0.901472i
$806$	0.163983	−	0.205628i	0.00577604	−	0.00724292i
$807$	0.185743	+	0.0279963i	0.00653847	+	0.000985516i
$808$	−3.83908	+	2.61744i	−0.135058	+	0.0920812i
$809$	−17.1080	+	11.6641i	−0.601487	+	0.410087i	−0.825421	−	0.564517i	$-0.809062\pi$
$809$	−17.1080	+	11.6641i	−0.601487	+	0.410087i	0.223934	+	0.974604i	$0.428110\pi$
$810$	15.4369	+	2.32673i	0.542396	+	0.0817531i
$811$	−23.7407	+	29.7699i	−0.833650	+	1.04536i	0.164608	+	0.986359i	$0.447364\pi$
$811$	−23.7407	+	29.7699i	−0.833650	+	1.04536i	−0.998258	+	0.0590048i	$0.981207\pi$
$812$	−22.5186	−	9.88476i	−0.790247	−	0.346887i
$813$	−0.253670	−	0.318092i	−0.00889659	−	0.0111560i
$814$	11.6885	+	20.2452i	0.409683	+	0.709592i
$815$	−31.7798	+	55.0442i	−1.11320	+	1.92811i
$816$	−0.0858266	+	0.0129363i	−0.00300453	+	0.000452861i
$817$	6.19954	−	5.75233i	0.216894	−	0.201249i
$818$	10.8099	+	5.20579i	0.377961	+	0.182016i
$819$	6.39630	−	4.69863i	0.223505	−	0.164183i
$820$	23.0890	−	11.1191i	0.806302	−	0.388294i
$821$	−6.75288	+	17.2061i	−0.235677	+	0.600496i	−0.998961	−	0.0455673i	$-0.985490\pi$
$821$	−6.75288	+	17.2061i	−0.235677	+	0.600496i	0.763284	+	0.646063i	$0.223586\pi$
$822$	−0.00516346	+	0.0689015i	−0.000180096	+	0.00240322i
$823$	−2.84786	−	0.878447i	−0.0992700	−	0.0306207i	0.244722	−	0.969593i	$-0.421303\pi$
$823$	−2.84786	−	0.878447i	−0.0992700	−	0.0306207i	−0.343992	+	0.938972i	$0.611779\pi$
$824$	−0.828071	−	11.0498i	−0.0288472	−	0.384939i
$825$	0.102902	−	0.450844i	0.00358260	−	0.0156964i
$826$	12.7816	−	12.7246i	0.444728	−	0.442744i
$827$	−5.26382	−	23.0623i	−0.183041	−	0.801955i	−0.980172	−	0.198149i	$-0.936507\pi$
$827$	−5.26382	−	23.0623i	−0.183041	−	0.801955i	0.797131	−	0.603806i	$-0.206350\pi$
$828$	14.9672	−	4.61677i	0.520146	−	0.160444i
$829$	−0.0852396	−	0.217187i	−0.00296049	−	0.00754321i	0.929386	−	0.369110i	$-0.120337\pi$
$829$	−0.0852396	−	0.217187i	−0.00296049	−	0.00754321i	−0.932346	+	0.361566i	$0.882242\pi$
$830$	−11.1686	−	10.3630i	−0.387668	−	0.359703i
$831$	0.260376	+	0.177522i	0.00903236	+	0.00615816i
$832$	2.11668			0.0733826
$833$	−14.9857	+	5.80424i	−0.519224	+	0.201105i
$834$	0.157601			0.00545728
$835$	11.0308	+	7.52067i	0.381737	+	0.260264i
$836$	−40.8015	−	37.8582i	−1.41115	−	1.30935i
$837$	0.0171423	+	0.0436778i	0.000592524	+	0.00150973i
$838$	−0.890987	+	0.274833i	−0.0307786	+	0.00949395i
$839$	1.06994	+	4.68770i	0.0369384	+	0.161838i	0.990033	−	0.140834i	$-0.0449785\pi$
$839$	1.06994	+	4.68770i	0.0369384	+	0.161838i	−0.953095	+	0.302672i	$0.902121\pi$
$840$	−0.225795	−	0.142582i	−0.00779067	−	0.00491954i
$841$	−0.0154623	+	0.0677448i	−0.000533183	+	0.00233603i
$842$	1.06574	+	14.2213i	0.0367279	+	0.490100i
$843$	−0.375693	−	0.115886i	−0.0129395	−	0.00399132i
$844$	0.0712443	−	0.950689i	0.00245233	−	0.0327241i
$845$	1.20654	−	3.07422i	0.0415063	−	0.105756i
$846$	5.98377	−	2.88163i	0.205726	−	0.0990726i
$847$	1.48016	−	37.3240i	0.0508587	−	1.28247i
$848$	26.1233	+	12.5803i	0.897076	+	0.432009i
$849$	−0.157603	+	0.146234i	−0.00540893	+	0.00501875i
$850$	−7.04440	+	1.06177i	−0.241621	+	0.0364185i
$851$	−13.4451	+	23.2876i	−0.460892	+	0.798288i
$852$	0.0373334	+	0.0646633i	0.00127902	+	0.00221533i
$853$	−8.77414	−	11.0024i	−0.300421	−	0.376716i	0.608592	−	0.793483i	$-0.291734\pi$
$853$	−8.77414	−	11.0024i	−0.300421	−	0.376716i	−0.909013	+	0.416767i	$0.863163\pi$
$854$	4.41383	+	5.15223i	0.151038	+	0.176306i
$855$	39.7896	−	49.8945i	1.36077	−	1.70636i
$856$	24.2760	+	3.65902i	0.829736	+	0.125063i
$857$	16.6908	−	11.3796i	0.570147	−	0.388719i	−0.243655	−	0.969862i	$-0.578347\pi$
$857$	16.6908	−	11.3796i	0.570147	−	0.388719i	0.813802	+	0.581143i	$0.197394\pi$
$858$	−0.0339846	+	0.0231703i	−0.00116022	+	0.000791022i
$859$	−43.7754	−	6.59808i	−1.49360	−	0.225123i	−0.649108	−	0.760696i	$-0.724858\pi$
$859$	−43.7754	−	6.59808i	−1.49360	−	0.225123i	−0.844489	+	0.535573i	$0.820096\pi$
$860$	−4.66041	+	5.84397i	−0.158919	+	0.199278i
$861$	−0.121031	−	0.141278i	−0.00412473	−	0.00481476i
$862$	4.44363	+	5.57214i	0.151351	+	0.189788i
$863$	2.21917	+	3.84372i	0.0755415	+	0.130842i	0.901322	−	0.433150i	$-0.142598\pi$
$863$	2.21917	+	3.84372i	0.0755415	+	0.130842i	−0.825780	+	0.563992i	$0.809265\pi$
$864$	0.242953	−	0.420806i	0.00826542	−	0.0143161i
$865$	46.5691	−	7.01916i	1.58340	−	0.238659i
$866$	−1.81386	+	1.68301i	−0.0616374	+	0.0571912i
$867$	−0.165086	−	0.0795012i	−0.00560661	−	0.00270000i
$868$	−0.0904846	+	2.28168i	−0.00307125	+	0.0774454i
$869$	5.51323	−	2.65503i	0.187024	−	0.0900659i
$870$	−0.0533879	+	0.136030i	−0.00181002	+	0.00461186i
$871$	0.0946216	−	1.26264i	0.00320613	−	0.0427828i
$872$	−22.6953	−	7.00058i	−0.768561	−	0.237070i
$873$	1.27779	+	17.0509i	0.0432467	+	0.577087i
$874$	−2.28083	+	9.99296i	−0.0771501	+	0.338017i
$875$	6.69754	+	4.22927i	0.226418	+	0.142975i
$876$	−0.0175406	−	0.0768504i	−0.000592642	−	0.00259653i
$877$	15.4500	−	4.76570i	0.521710	−	0.160926i	−0.0227049	−	0.999742i	$-0.507228\pi$
$877$	15.4500	−	4.76570i	0.521710	−	0.160926i	0.544415	+	0.838816i	$0.316752\pi$
$878$	−0.151398	−	0.385757i	−0.00510945	−	0.0130187i
$879$	−0.0624859	−	0.0579785i	−0.00210760	−	0.00195557i
$880$	33.0969	+	22.5651i	1.11570	+	0.760670i
$881$	10.9700			0.369590			0.184795	−	0.982777i	$-0.440838\pi$
$881$	10.9700			0.369590			0.184795	+	0.982777i	$0.440838\pi$
$882$	3.29875	−	10.5269i	0.111075	−	0.354459i
$883$	−21.5548			−0.725378			−0.362689	−	0.931910i	$-0.618141\pi$
$883$	−21.5548			−0.725378			−0.362689	+	0.931910i	$0.618141\pi$
$884$	−3.27019	−	2.22958i	−0.109988	−	0.0749888i
$885$	0.490714	+	0.455316i	0.0164952	+	0.0153053i
$886$	−2.84116	−	7.23915i	−0.0954506	−	0.243204i
$887$	25.6026	−	7.89735i	0.859651	−	0.265167i	0.166572	−	0.986029i	$-0.446730\pi$
$887$	25.6026	−	7.89735i	0.859651	−	0.265167i	0.693078	+	0.720862i	$0.256254\pi$
$888$	0.0603812	+	0.264547i	0.00202626	+	0.00887762i
$889$	−38.9673	+	38.7935i	−1.30692	+	1.30109i
$890$	2.00387	−	8.77952i	0.0671698	−	0.294290i
$891$	3.36997	+	44.9692i	0.112898	+	1.50652i
$892$	−6.01950	−	1.85677i	−0.201548	−	0.0621692i
$893$	2.02875	−	27.0717i	0.0678894	−	0.905922i
$894$	0.0311758	−	0.0794347i	0.00104268	−	0.00265669i
$895$	37.1468	−	17.8890i	1.24168	−	0.597962i
$896$	24.4800	−	17.9826i	0.817818	−	0.600757i
$897$	−0.0426275	−	0.0205283i	−0.00142329	−	0.000685420i
$898$	7.28015	−	6.75499i	0.242942	−	0.225417i
$899$	2.66902	−	0.402290i	0.0890168	−	0.0134171i
$900$	−15.2731	+	26.4537i	−0.509102	+	0.881791i
$901$	−13.7523	−	23.8196i	−0.458155	−	0.793547i
$902$	−7.38917	−	9.26572i	−0.246032	−	0.308515i
$903$	0.0496851	+	0.0218098i	0.00165342	+	0.000725783i
$904$	−22.8360	+	28.6355i	−0.759515	+	0.952402i
$905$	−58.8991	−	8.87761i	−1.95787	−	0.295102i
$906$	0.0705453	−	0.0480969i	0.00234371	−	0.00159791i
$907$	−5.46179	+	3.72378i	−0.181356	+	0.123646i	−0.650595	−	0.759425i	$-0.725480\pi$
$907$	−5.46179	+	3.72378i	−0.181356	+	0.123646i	0.469239	+	0.883071i	$0.344528\pi$
$908$	−25.1940	−	3.79738i	−0.836091	−	0.126020i
$909$	4.44192	−	5.56999i	0.147329	−	0.184745i
$910$	−1.17816	−	4.43662i	−0.0390557	−	0.147073i
$911$	−28.7960	−	36.1091i	−0.954056	−	1.19635i	−0.980464	−	0.196697i	$-0.936979\pi$
$911$	−28.7960	−	36.1091i	−0.954056	−	1.19635i	0.0264088	−	0.999651i	$-0.491593\pi$
$912$	−0.121773	−	0.210916i	−0.00403229	−	0.00698413i
$913$	22.0053	−	38.1144i	0.728271	−	1.26140i
$914$	−0.256190	+	0.0386144i	−0.00847400	+	0.00127725i
$915$	−0.184589	+	0.171274i	−0.00610232	+	0.00566213i
$916$	−28.4872	−	13.7187i	−0.941243	−	0.453279i
$917$	−26.5288	−	22.9334i	−0.876059	−	0.757326i
$918$	−0.101849	+	0.0490479i	−0.00336152	+	0.00161882i
$919$	−11.3499	+	28.9190i	−0.374398	+	0.953950i	0.612189	+	0.790712i	$0.290289\pi$
$919$	−11.3499	+	28.9190i	−0.374398	+	0.953950i	−0.986587	+	0.163239i	$0.947806\pi$
$920$	1.46238	−	19.5141i	0.0482132	−	0.643361i
$921$	−0.247909	−	0.0764699i	−0.00816889	−	0.00251977i
$922$	−0.521749	−	6.96225i	−0.0171829	−	0.229290i
$923$	−0.616930	+	2.70295i	−0.0203065	+	0.0889686i
$924$	0.118700	−	0.336808i	0.00390495	−	0.0110802i
$925$	−11.6693	−	51.1264i	−0.383683	−	1.68103i
$926$	−12.5289	+	3.86466i	−0.411726	+	0.127001i
$927$	6.20712	+	15.8155i	0.203869	+	0.519449i
$928$	−20.4902	−	19.0121i	−0.672624	−	0.624104i
$929$	−12.8360	−	8.75146i	−0.421136	−	0.287126i	0.334151	−	0.942520i	$-0.391550\pi$
$929$	−12.8360	−	8.75146i	−0.421136	−	0.287126i	−0.755288	+	0.655394i	$0.772503\pi$
$930$	0.0135687			0.000444934
$931$	−30.5228	−	33.1923i	−1.00034	−	1.08783i
$932$	34.9388			1.14446
$933$	0.407426	+	0.277778i	0.0133385	+	0.00909405i
$934$	3.70474	+	3.43750i	0.121223	+	0.112478i
$935$	−13.8825	−	35.3720i	−0.454006	−	1.15679i
$936$	5.60810	−	1.72987i	0.183307	−	0.0565426i
$937$	2.95946	+	12.9663i	0.0966815	+	0.423589i	0.999985	−	0.00541201i	$-0.00172271\pi$
$937$	2.95946	+	12.9663i	0.0966815	+	0.423589i	−0.903304	+	0.429001i	$0.858866\pi$
$938$	−0.933016	−	1.49228i	−0.0304640	−	0.0487248i
$939$	−0.0543333	+	0.238050i	−0.00177310	+	0.00776847i
$940$	1.79307	+	23.9269i	0.0584836	+	0.780409i
$941$	−35.7624	−	11.0312i	−1.16582	−	0.359608i	−0.349348	−	0.936993i	$-0.613597\pi$
$941$	−35.7624	−	11.0312i	−1.16582	−	0.359608i	−0.816472	+	0.577385i	$0.804073\pi$
$942$	0.0121615	−	0.162284i	0.000396244	−	0.00528750i
$943$	4.98044	−	12.6899i	0.162185	−	0.413242i
$944$	−28.2930	+	13.6252i	−0.920858	+	0.443462i
$945$	0.790559	+	0.213725i	0.0257169	+	0.00695249i
$946$	3.11441	+	1.49982i	0.101258	+	0.0487634i
$947$	−17.0803	+	15.8482i	−0.555034	+	0.514996i	−0.907064	−	0.420993i	$-0.861682\pi$
$947$	−17.0803	+	15.8482i	−0.555034	+	0.514996i	0.352030	+	0.935989i	$0.385491\pi$
$948$	0.0325152	−	0.00490087i	0.00105604	−	0.000159173i
$949$	1.46346	−	2.53479i	0.0475060	−	0.0822828i
$950$	−9.99473	−	17.3114i	−0.324272	−	0.561655i
$951$	0.296435	+	0.371718i	0.00961256	+	0.0120538i
$952$	−11.8762	+	0.417783i	−0.384910	+	0.0135404i
$953$	33.1075	−	41.5155i	1.07246	−	1.34482i	0.137322	−	0.990526i	$-0.456150\pi$
$953$	33.1075	−	41.5155i	1.07246	−	1.34482i	0.935135	−	0.354292i	$-0.115278\pi$
$954$	18.6698	+	2.81401i	0.604456	+	0.0911070i
$955$	−28.9131	+	19.7126i	−0.935606	+	0.637885i
$956$	31.8724	−	21.7302i	1.03083	−	0.702805i
$957$	−0.417408	−	0.0629141i	−0.0134929	−	0.00203372i
$958$	8.34509	−	10.4644i	0.269618	−	0.338090i
$959$	4.19006	−	21.8770i	0.135304	−	0.706447i
$960$	0.0680852	+	0.0853762i	0.00219744	+	0.00275550i
$961$	15.3747	+	26.6297i	0.495958	+	0.859024i
$962$	−2.33220	+	4.03949i	−0.0751932	+	0.130238i
$963$	−37.2217	+	5.61027i	−1.19945	+	0.180789i
$964$	−35.4585	+	32.9007i	−1.14204	+	1.05966i
$965$	−11.8398	−	5.70177i	−0.381138	−	0.183546i
$966$	−0.0646443	+	0.0120817i	−0.00207990	+	0.000388722i
$967$	42.7104	−	20.5683i	1.37347	−	0.661430i	0.405877	−	0.913928i	$-0.366966\pi$
$967$	42.7104	−	20.5683i	1.37347	−	0.661430i	0.967598	+	0.252497i	$0.0812519\pi$
$968$	10.0913	−	25.7121i	0.324345	−	0.826418i
$969$	−0.0172648	+	0.230383i	−0.000554626	+	0.00740096i
$970$	9.45024	+	2.91501i	0.303429	+	0.0935955i
$971$	−1.07506	−	14.3457i	−0.0345003	−	0.460374i	−0.987523	−	0.157475i	$-0.949665\pi$
$971$	−1.07506	−	14.3457i	−0.0345003	−	0.460374i	0.953023	−	0.302899i	$-0.0979545\pi$
$972$	−0.161789	+	0.708844i	−0.00518939	+	0.0227362i
$973$	−50.4750	−	5.80150i	−1.61815	−	0.185988i
$974$	−0.683657	−	2.99529i	−0.0219058	−	0.0959754i
$975$	0.0881705	−	0.0271970i	0.00282371	−	0.000871001i
$976$	−4.31563	−	10.9961i	−0.138140	−	0.351975i
$977$	13.3001	+	12.3407i	0.425508	+	0.394814i	0.863650	−	0.504092i	$-0.168173\pi$
$977$	13.3001	+	12.3407i	0.425508	+	0.394814i	−0.438142	+	0.898906i	$0.644363\pi$
$978$	0.130504	+	0.0889763i	0.00417307	+	0.00284515i
$979$	26.0131			0.831382
$980$	31.0481	+	24.9880i	0.991796	+	0.798214i
$981$	36.4160			1.16267
$982$	10.2047	+	6.95743i	0.325644	+	0.222021i
$983$	20.9636	+	19.4514i	0.668634	+	0.620402i	0.939636	−	0.342177i	$-0.111164\pi$
$983$	20.9636	+	19.4514i	0.668634	+	0.620402i	−0.271001	+	0.962579i	$0.587355\pi$
$984$	−0.0502579	−	0.128055i	−0.00160216	−	0.00408225i
$985$	27.9940	−	8.63502i	0.891964	−	0.275135i
$986$	1.44703	+	6.33985i	0.0460828	+	0.201902i
$987$	0.164533	−	0.0571600i	0.00523715	−	0.00181942i
$988$	2.47125	−	10.8273i	0.0786211	−	0.344461i
$989$	0.297142	+	3.96509i	0.00944858	+	0.126083i
$990$	24.9256	+	7.68852i	0.792186	+	0.244357i
$991$	1.45571	−	19.4251i	0.0462421	−	0.617058i	−0.925154	−	0.379592i	$-0.876064\pi$
$991$	1.45571	−	19.4251i	0.0462421	−	0.617058i	0.971396	−	0.237465i	$-0.0763166\pi$
$992$	−0.948206	+	2.41599i	−0.0301056	+	0.0767077i
$993$	0.218808	−	0.105372i	0.00694367	−	0.00334389i
$994$	1.53314	+	3.53554i	0.0486282	+	0.112141i
$995$	30.6109	+	14.7414i	0.970430	+	0.467334i
$996$	0.173364	−	0.160859i	0.00549326	−	0.00509700i
$997$	−43.2379	+	6.51707i	−1.36936	+	0.206398i	−0.792213	−	0.610244i	$-0.791071\pi$
$997$	−43.2379	+	6.51707i	−1.36936	+	0.206398i	−0.577145	+	0.816642i	$0.695833\pi$
$998$	7.52901	−	13.0406i	0.238327	−	0.412794i
$999$	−0.416071	−	0.720657i	−0.0131639	−	0.0228006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.a.53.13	✓	324
49.37	even	21	inner	637.2.bl.a.625.13	yes	324

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.a.53.13	✓	324	1.1	even	1	trivial
637.2.bl.a.625.13	yes	324	49.37	even	21	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:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.434073 - 0.295946i) q^{2} +(0.0114514 + 0.0106254i) q^{3} +(-0.629847 - 1.60482i) q^{4} +(3.15579 - 0.973431i) q^{5} +(-0.00182622 - 0.00800119i) q^{6} +(0.290350 + 2.62977i) q^{7} +(-0.435349 + 1.90739i) q^{8} +(-0.224172 - 2.99137i) q^{9} +O(q^{10})\)	\(q+(-0.434073 - 0.295946i) q^{2} +(0.0114514 + 0.0106254i) q^{3} +(-0.629847 - 1.60482i) q^{4} +(3.15579 - 0.973431i) q^{5} +(-0.00182622 - 0.00800119i) q^{6} +(0.290350 + 2.62977i) q^{7} +(-0.435349 + 1.90739i) q^{8} +(-0.224172 - 2.99137i) q^{9} +(-1.65792 - 0.511402i) q^{10} +(0.374533 - 4.99780i) q^{11} +(0.00983921 - 0.0250699i) q^{12} +(0.900969 - 0.433884i) q^{13} +(0.652237 - 1.22744i) q^{14} +(0.0464814 + 0.0223842i) q^{15} +(-1.77410 + 1.64613i) q^{16} +(2.27014 - 0.342169i) q^{17} +(-0.787976 + 1.36481i) q^{18} +(3.22092 + 5.57880i) q^{19} +(-3.54985 - 4.45137i) q^{20} +(-0.0246174 + 0.0331997i) q^{21} +(-1.64165 + 2.05857i) q^{22} +(-2.99486 - 0.451403i) q^{23} +(-0.0252521 + 0.0172166i) q^{24} +(4.88022 - 3.32728i) q^{25} +(-0.519492 - 0.0783008i) q^{26} +(0.0584370 - 0.0732777i) q^{27} +(4.03744 - 2.12231i) q^{28} +(-3.36162 - 4.21533i) q^{29} +(-0.0135518 - 0.0234724i) q^{30} +(-0.250312 + 0.433553i) q^{31} +(5.12643 - 0.772685i) q^{32} +(0.0573924 - 0.0532524i) q^{33} +(-1.08667 - 0.523313i) q^{34} +(3.47618 + 8.01636i) q^{35} +(-4.65942 + 2.24386i) q^{36} +(3.24368 - 8.26475i) q^{37} +(0.252908 - 3.37482i) q^{38} +(0.0149276 + 0.00460455i) q^{39} +(0.482843 + 6.44309i) q^{40} +(-1.00158 + 4.38821i) q^{41} +(0.0205111 - 0.00712569i) q^{42} +(-0.292136 - 1.27993i) q^{43} +(-8.25648 + 2.54679i) q^{44} +(-3.61933 - 9.22190i) q^{45} +(1.16640 + 1.08226i) q^{46} +(-3.48199 - 2.37398i) q^{47} -0.0378067 q^{48} +(-6.83139 + 1.52711i) q^{49} -3.10307 q^{50} +(0.0296321 + 0.0202028i) q^{51} +(-1.26378 - 1.17262i) q^{52} +(-4.37696 - 11.1523i) q^{53} +(-0.0470522 + 0.0145137i) q^{54} +(-3.68306 - 16.1366i) q^{55} +(-5.14239 - 0.591057i) q^{56} +(-0.0223927 + 0.0981088i) q^{57} +(0.211676 + 2.82462i) q^{58} +(12.3991 + 3.82460i) q^{59} +(0.00664662 - 0.0886930i) q^{60} +(-1.78320 + 4.54352i) q^{61} +(0.236962 - 0.114115i) q^{62} +(7.80153 - 1.45807i) q^{63} +(1.90706 + 0.918392i) q^{64} +(2.42091 - 2.24628i) q^{65} +(-0.0406723 + 0.00613036i) q^{66} +(0.633089 - 1.09654i) q^{67} +(-1.97896 - 3.42766i) q^{68} +(-0.0294991 - 0.0369907i) q^{69} +(0.863491 - 4.50845i) q^{70} +(-1.72860 + 2.16760i) q^{71} +(5.80329 + 0.874705i) q^{72} +(2.41834 - 1.64880i) q^{73} +(-3.85391 + 2.62755i) q^{74} +(0.0912392 + 0.0137521i) q^{75} +(6.92430 - 8.68280i) q^{76} +(13.2518 - 0.466174i) q^{77} +(-0.00511696 - 0.00641646i) q^{78} +(0.610481 + 1.05738i) q^{79} +(-3.99630 + 6.92179i) q^{80} +(-8.89731 + 1.34105i) q^{81} +(1.73343 - 1.60839i) q^{82} +(7.91177 + 3.81011i) q^{83} +(0.0687849 + 0.0185958i) q^{84} +(6.83100 - 3.28964i) q^{85} +(-0.251982 + 0.642040i) q^{86} +(0.00629419 - 0.0839901i) q^{87} +(9.36968 + 2.89016i) q^{88} +(0.387876 + 5.17585i) q^{89} +(-1.15813 + 5.07410i) q^{90} +(1.40261 + 2.24336i) q^{91} +(1.16188 + 5.09054i) q^{92} +(-0.00747309 + 0.00230514i) q^{93} +(0.808868 + 2.06096i) q^{94} +(15.5951 + 14.4701i) q^{95} +(0.0669150 + 0.0456219i) q^{96} -5.70005 q^{97} +(3.41726 + 1.35885i) q^{98} -15.0342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9}+O(q^{10}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9	\( 324 q - 3 q^{2} + 25 q^{4} + q^{5} - 24 q^{6} - 21 q^{7} + 24 q^{8} + 11 q^{9} - 5 q^{10} - 18 q^{11} - 40 q^{12} + 54 q^{13} - 15 q^{14} + 6 q^{15} + 29 q^{16} - 6 q^{17} + 49 q^{18} - 24 q^{19} + 11 q^{20} - 6 q^{22} - 42 q^{23} + 20 q^{24} + 14 q^{25} + 3 q^{26} - 33 q^{27} + 7 q^{28} - 22 q^{29} + 57 q^{30} - 31 q^{31} - 139 q^{32} + 6 q^{33} + 50 q^{34} + 42 q^{35} - 78 q^{36} - 4 q^{37} - 90 q^{38} + 40 q^{40} + 8 q^{41} + 20 q^{42} + 34 q^{43} - 256 q^{44} + 19 q^{45} + 85 q^{46} + 34 q^{47} - 10 q^{48} + 51 q^{49} - 54 q^{50} + 74 q^{51} - 25 q^{52} + 10 q^{53} + 111 q^{54} - 10 q^{55} - 196 q^{56} - 5 q^{57} - 21 q^{58} + 65 q^{59} + 87 q^{60} + 3 q^{61} - 54 q^{62} - 35 q^{63} - 28 q^{64} - q^{65} - 110 q^{66} + 135 q^{67} - 158 q^{68} + 42 q^{69} + 44 q^{70} + 9 q^{71} - 133 q^{72} + 31 q^{73} - 97 q^{74} - 315 q^{75} - 177 q^{76} + 6 q^{77} - 25 q^{78} + 43 q^{79} - 20 q^{80} - 259 q^{81} + 96 q^{82} + 59 q^{83} + 285 q^{84} + 6 q^{85} + 95 q^{86} - 206 q^{87} + 228 q^{88} + 43 q^{89} - 61 q^{90} - 7 q^{91} + 53 q^{92} - 10 q^{93} - 36 q^{94} - 17 q^{95} + 277 q^{96} + 66 q^{97} + 260 q^{98} - 206 q^{99}+O(q^{100}) \) 324 * q - 3 * q^2 + 25 * q^4 + q^5 - 24 * q^6 - 21 * q^7 + 24 * q^8 + 11 * q^9 - 5 * q^10 - 18 * q^11 - 40 * q^12 + 54 * q^13 - 15 * q^14 + 6 * q^15 + 29 * q^16 - 6 * q^17 + 49 * q^18 - 24 * q^19 + 11 * q^20 - 6 * q^22 - 42 * q^23 + 20 * q^24 + 14 * q^25 + 3 * q^26 - 33 * q^27 + 7 * q^28 - 22 * q^29 + 57 * q^30 - 31 * q^31 - 139 * q^32 + 6 * q^33 + 50 * q^34 + 42 * q^35 - 78 * q^36 - 4 * q^37 - 90 * q^38 + 40 * q^40 + 8 * q^41 + 20 * q^42 + 34 * q^43 - 256 * q^44 + 19 * q^45 + 85 * q^46 + 34 * q^47 - 10 * q^48 + 51 * q^49 - 54 * q^50 + 74 * q^51 - 25 * q^52 + 10 * q^53 + 111 * q^54 - 10 * q^55 - 196 * q^56 - 5 * q^57 - 21 * q^58 + 65 * q^59 + 87 * q^60 + 3 * q^61 - 54 * q^62 - 35 * q^63 - 28 * q^64 - q^65 - 110 * q^66 + 135 * q^67 - 158 * q^68 + 42 * q^69 + 44 * q^70 + 9 * q^71 - 133 * q^72 + 31 * q^73 - 97 * q^74 - 315 * q^75 - 177 * q^76 + 6 * q^77 - 25 * q^78 + 43 * q^79 - 20 * q^80 - 259 * q^81 + 96 * q^82 + 59 * q^83 + 285 * q^84 + 6 * q^85 + 95 * q^86 - 206 * q^87 + 228 * q^88 + 43 * q^89 - 61 * q^90 - 7 * q^91 + 53 * q^92 - 10 * q^93 - 36 * q^94 - 17 * q^95 + 277 * q^96 + 66 * q^97 + 260 * q^98 - 206 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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