LMFDB - Embedded newform 37.2.h.a.25.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(3,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("37.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.h (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$3$ over $\Q(\zeta_{18})$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 30x^{16} + 333x^{14} + 1826x^{12} + 5490x^{10} + 9432x^{8} + 9385x^{6} + 5316x^{4} + 1584x^{2} + 192 $ x^18 + 30x^16 + 333x^14 + 1826x^12 + 5490x^10 + 9432x^8 + 9385x^6 + 5316x^4 + 1584x^2 + 192
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			25.1
Root			$1.23399i$ of defining polynomial
Character	$\chi$	$=$	37.25
Dual form			37.2.h.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.61954 - 1.93010i) q^{2} +(-0.968719 - 0.812851i) q^{3} +(-0.755055 + 4.28213i) q^{4} +(-0.681528 - 1.87248i) q^{5} +3.18617i q^{6} +(2.99976 - 1.09182i) q^{7} +(5.12375 - 2.95820i) q^{8} +(-0.243256 - 1.37957i) q^{9} +O(q^{10})$	\(q+(-1.61954 - 1.93010i) q^{2} +(-0.968719 - 0.812851i) q^{3} +(-0.755055 + 4.28213i) q^{4} +(-0.681528 - 1.87248i) q^{5} +3.18617i q^{6} +(2.99976 - 1.09182i) q^{7} +(5.12375 - 2.95820i) q^{8} +(-0.243256 - 1.37957i) q^{9} +(-2.51031 + 4.34798i) q^{10} +(2.73288 + 4.73349i) q^{11} +(4.21217 - 3.53443i) q^{12} +(-1.50836 - 0.265964i) q^{13} +(-6.96557 - 4.02158i) q^{14} +(-0.861842 + 2.36789i) q^{15} +(-5.83582 - 2.12407i) q^{16} +(-0.794131 + 0.140027i) q^{17} +(-2.26875 + 2.70379i) q^{18} +(-1.35888 + 1.61945i) q^{19} +(8.53281 - 1.50456i) q^{20} +(-3.79342 - 1.38069i) q^{21} +(4.71007 - 12.9408i) q^{22} +(3.02834 + 1.74842i) q^{23} +(-7.36805 - 1.29919i) q^{24} +(0.788506 - 0.661636i) q^{25} +(1.92951 + 3.34201i) q^{26} +(-2.78260 + 4.81961i) q^{27} +(2.41035 + 13.6698i) q^{28} +(-0.122232 + 0.0705708i) q^{29} +(5.96605 - 2.17146i) q^{30} -3.37454i q^{31} +(1.30466 + 3.58452i) q^{32} +(1.20023 - 6.80685i) q^{33} +(1.55639 + 1.30597i) q^{34} +(-4.08885 - 4.87290i) q^{35} +6.09119 q^{36} +(0.539604 + 6.05878i) q^{37} +5.32646 q^{38} +(1.24498 + 1.48371i) q^{39} +(-9.03117 - 7.57805i) q^{40} +(0.0732041 - 0.415161i) q^{41} +(3.47874 + 9.55775i) q^{42} -2.00540i q^{43} +(-22.3329 + 8.12851i) q^{44} +(-2.41745 + 1.39571i) q^{45} +(-1.52992 - 8.67663i) q^{46} +(-0.842972 + 1.46007i) q^{47} +(3.92672 + 6.80128i) q^{48} +(2.44419 - 2.05092i) q^{49} +(-2.55404 - 0.450346i) q^{50} +(0.883111 + 0.509864i) q^{51} +(2.27778 - 6.25815i) q^{52} +(-6.86119 - 2.49727i) q^{53} +(13.8088 - 2.43487i) q^{54} +(7.00085 - 8.34329i) q^{55} +(12.1402 - 14.4681i) q^{56} +(2.63275 - 0.464224i) q^{57} +(0.334169 + 0.121628i) q^{58} +(-3.65272 + 10.0358i) q^{59} +(-9.48888 - 5.47841i) q^{60} +(11.3492 + 2.00116i) q^{61} +(-6.51318 + 5.46521i) q^{62} +(-2.23597 - 3.87281i) q^{63} +(-1.40484 + 2.43325i) q^{64} +(0.529974 + 3.00563i) q^{65} +(-15.0817 + 8.70742i) q^{66} +(-7.25752 + 2.64152i) q^{67} -3.50630i q^{68} +(-1.51241 - 4.15532i) q^{69} +(-2.78310 + 15.7837i) q^{70} +(6.78889 + 5.69655i) q^{71} +(-5.32744 - 6.34900i) q^{72} -8.77446 q^{73} +(10.8201 - 10.8539i) q^{74} -1.30165 q^{75} +(-5.90867 - 7.04167i) q^{76} +(13.3662 + 11.2155i) q^{77} +(0.847405 - 4.80587i) q^{78} +(1.54413 + 4.24247i) q^{79} +12.3751i q^{80} +(2.66406 - 0.969637i) q^{81} +(-0.919858 + 0.531080i) q^{82} +(-1.81973 - 10.3202i) q^{83} +(8.77654 - 15.2014i) q^{84} +(0.803421 + 1.39157i) q^{85} +(-3.87061 + 3.24783i) q^{86} +(0.175772 + 0.0309934i) q^{87} +(28.0052 + 16.1688i) q^{88} +(0.914163 - 2.51164i) q^{89} +(6.60902 + 2.40549i) q^{90} +(-4.81510 + 0.849032i) q^{91} +(-9.77350 + 11.6476i) q^{92} +(-2.74300 + 3.26898i) q^{93} +(4.18331 - 0.737630i) q^{94} +(3.95851 + 1.44078i) q^{95} +(1.64984 - 4.53289i) q^{96} +(-13.3681 - 7.71809i) q^{97} +(-7.91695 - 1.39597i) q^{98} +(5.86542 - 4.92167i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) $ 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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 $

$2$	−1.61954	−	1.93010i	−1.14519	−	1.36478i	−0.920683	−	0.390311i	$-0.872367\pi$
$2$	−1.61954	−	1.93010i	−1.14519	−	1.36478i	−0.224506	−	0.974473i	$-0.572077\pi$
$3$	−0.968719	−	0.812851i	−0.559290	−	0.469300i	0.318782	−	0.947828i	$-0.396726\pi$
$3$	−0.968719	−	0.812851i	−0.559290	−	0.469300i	−0.878072	+	0.478528i	$0.841171\pi$
$4$	−0.755055	+	4.28213i	−0.377527	+	2.14106i
$5$	−0.681528	−	1.87248i	−0.304789	−	0.837400i	−0.993651	−	0.112508i	$-0.964112\pi$
$5$	−0.681528	−	1.87248i	−0.304789	−	0.837400i	0.688862	−	0.724892i	$-0.258111\pi$
$6$			3.18617i			1.30075i
$7$	2.99976	−	1.09182i	1.13380	−	0.412671i	0.294132	−	0.955765i	$-0.404969\pi$
$7$	2.99976	−	1.09182i	1.13380	−	0.412671i	0.839672	+	0.543094i	$0.182747\pi$
$8$	5.12375	−	2.95820i	1.81152	−	1.04588i
$9$	−0.243256	−	1.37957i	−0.0810854	−	0.459858i
$10$	−2.51031	+	4.34798i	−0.793829	+	1.37495i
$11$	2.73288	+	4.73349i	0.823995	+	1.42720i	0.902685	+	0.430303i	$0.141593\pi$
$11$	2.73288	+	4.73349i	0.823995	+	1.42720i	−0.0786894	+	0.996899i	$0.525074\pi$
$12$	4.21217	−	3.53443i	1.21595	−	1.02030i
$13$	−1.50836	−	0.265964i	−0.418343	−	0.0737651i	−0.0394852	−	0.999220i	$-0.512572\pi$
$13$	−1.50836	−	0.265964i	−0.418343	−	0.0737651i	−0.378857	+	0.925455i	$0.623683\pi$
$14$	−6.96557	−	4.02158i	−1.86163	−	1.07481i
$15$	−0.861842	+	2.36789i	−0.222527	+	0.611387i
$16$	−5.83582	−	2.12407i	−1.45896	−	0.531017i
$17$	−0.794131	+	0.140027i	−0.192605	+	0.0339615i	−0.269118	−	0.963107i	$-0.586732\pi$
$17$	−0.794131	+	0.140027i	−0.192605	+	0.0339615i	0.0765134	+	0.997069i	$0.475621\pi$
$18$	−2.26875	+	2.70379i	−0.534749	+	0.637289i
$19$	−1.35888	+	1.61945i	−0.311749	+	0.371527i	−0.899054	−	0.437838i	$-0.855744\pi$
$19$	−1.35888	+	1.61945i	−0.311749	+	0.371527i	0.587305	+	0.809365i	$0.300189\pi$
$20$	8.53281	−	1.50456i	1.90799	−	0.336431i
$21$	−3.79342	−	1.38069i	−0.827792	−	0.301292i
$22$	4.71007	−	12.9408i	1.00419	−	2.75899i
$23$	3.02834	+	1.74842i	0.631453	+	0.364570i	0.781315	−	0.624137i	$-0.214549\pi$
$23$	3.02834	+	1.74842i	0.631453	+	0.364570i	−0.149861	+	0.988707i	$0.547883\pi$
$24$	−7.36805	−	1.29919i	−1.50400	−	0.265195i
$25$	0.788506	−	0.661636i	0.157701	−	0.132327i
$26$	1.92951	+	3.34201i	0.378408	+	0.655422i
$27$	−2.78260	+	4.81961i	−0.535512	+	0.927534i
$28$	2.41035	+	13.6698i	0.455513	+	2.58334i
$29$	−0.122232	+	0.0705708i	−0.0226980	+	0.0131047i	−0.511306	−	0.859399i	$-0.670838\pi$
$29$	−0.122232	+	0.0705708i	−0.0226980	+	0.0131047i	0.488608	+	0.872503i	$0.337505\pi$
$30$	5.96605	−	2.17146i	1.08925	−	0.396453i
$31$		−	3.37454i		−	0.606085i	−0.952977	−	0.303042i	$-0.901998\pi$
$31$		−	3.37454i		−	0.606085i	0.952977	−	0.303042i	$-0.0980024\pi$
$32$	1.30466	+	3.58452i	0.230633	+	0.633660i
$33$	1.20023	−	6.80685i	0.208933	−	1.18492i
$34$	1.55639	+	1.30597i	0.266919	+	0.223972i
$35$	−4.08885	−	4.87290i	−0.691142	−	0.823671i
$36$	6.09119			1.01520
$37$	0.539604	+	6.05878i	0.0887103	+	0.996057i
$37$	0.539604	+	6.05878i	0.0887103	+	0.996057i
$38$	5.32646			0.864066
$39$	1.24498	+	1.48371i	0.199357	+	0.237584i
$40$	−9.03117	−	7.57805i	−1.42795	−	1.19819i
$41$	0.0732041	−	0.415161i	0.0114326	−	0.0648373i	−0.978558	−	0.205973i	$-0.933964\pi$
$41$	0.0732041	−	0.415161i	0.0114326	−	0.0648373i	0.989990	+	0.141135i	$0.0450753\pi$
$42$	3.47874	+	9.55775i	0.536781	+	1.47479i
$43$		−	2.00540i		−	0.305820i	−0.988240	−	0.152910i	$-0.951135\pi$
$43$		−	2.00540i		−	0.305820i	0.988240	−	0.152910i	$-0.0488645\pi$
$44$	−22.3329	+	8.12851i	−3.36681	+	1.22542i
$45$	−2.41745	+	1.39571i	−0.360372	+	0.208061i
$46$	−1.52992	−	8.67663i	−0.225575	−	1.27930i
$47$	−0.842972	+	1.46007i	−0.122960	+	0.212973i	−0.920934	−	0.389719i	$-0.872572\pi$
$47$	−0.842972	+	1.46007i	−0.122960	+	0.212973i	0.797974	+	0.602692i	$0.205905\pi$
$48$	3.92672	+	6.80128i	0.566773	+	0.981680i
$49$	2.44419	−	2.05092i	0.349171	−	0.292989i
$50$	−2.55404	−	0.450346i	−0.361196	−	0.0636886i
$51$	0.883111	+	0.509864i	0.123660	+	0.0713953i
$52$	2.27778	−	6.25815i	0.315872	−	0.867850i
$53$	−6.86119	−	2.49727i	−0.942457	−	0.343026i	−0.175321	−	0.984511i	$-0.556096\pi$
$53$	−6.86119	−	2.49727i	−0.942457	−	0.343026i	−0.767136	+	0.641485i	$0.778319\pi$
$54$	13.8088	−	2.43487i	1.87915	−	0.331344i
$55$	7.00085	−	8.34329i	0.943995	−	1.12501i
$56$	12.1402	−	14.4681i	1.62230	−	1.93339i
$57$	2.63275	−	0.464224i	0.348716	−	0.0614880i
$58$	0.334169	+	0.121628i	0.0438785	+	0.0159705i
$59$	−3.65272	+	10.0358i	−0.475544	+	1.30655i	0.437696	+	0.899123i	$0.355795\pi$
$59$	−3.65272	+	10.0358i	−0.475544	+	1.30655i	−0.913240	+	0.407422i	$0.866428\pi$
$60$	−9.48888	−	5.47841i	−1.22501	−	0.707259i
$61$	11.3492	+	2.00116i	1.45311	+	0.256222i	0.843778	−	0.536693i	$-0.180327\pi$
$61$	11.3492	+	2.00116i	1.45311	+	0.256222i	0.609332	+	0.792915i	$0.291438\pi$
$62$	−6.51318	+	5.46521i	−0.827175	+	0.694082i
$63$	−2.23597	−	3.87281i	−0.281705	−	0.487928i
$64$	−1.40484	+	2.43325i	−0.175605	+	0.304156i
$65$	0.529974	+	3.00563i	0.0657352	+	0.372803i
$66$	−15.0817	+	8.70742i	−1.85643	+	1.07181i
$67$	−7.25752	+	2.64152i	−0.886648	+	0.322713i	−0.744889	−	0.667188i	$-0.767498\pi$
$67$	−7.25752	+	2.64152i	−0.886648	+	0.322713i	−0.141758	+	0.989901i	$0.545276\pi$
$68$		−	3.50630i		−	0.425201i
$69$	−1.51241	−	4.15532i	−0.182073	−	0.500241i
$70$	−2.78310	+	15.7837i	−0.332644	+	1.88652i
$71$	6.78889	+	5.69655i	0.805693	+	0.676056i	0.949576	−	0.313538i	$-0.101514\pi$
$71$	6.78889	+	5.69655i	0.805693	+	0.676056i	−0.143883	+	0.989595i	$0.545959\pi$
$72$	−5.32744	−	6.34900i	−0.627845	−	0.748237i
$73$	−8.77446			−1.02697			−0.513486	−	0.858098i	$-0.671646\pi$
$73$	−8.77446			−1.02697			−0.513486	+	0.858098i	$0.671646\pi$
$74$	10.8201	−	10.8539i	1.25781	−	1.26174i
$75$	−1.30165			−0.150302
$76$	−5.90867	−	7.04167i	−0.677770	−	0.807735i
$77$	13.3662	+	11.2155i	1.52321	+	1.27813i
$78$	0.847405	−	4.80587i	0.0959497	−	0.544158i
$79$	1.54413	+	4.24247i	0.173729	+	0.477316i	0.995745	−	0.0921478i	$-0.0293732\pi$
$79$	1.54413	+	4.24247i	0.173729	+	0.477316i	−0.822017	+	0.569463i	$0.807151\pi$
$80$			12.3751i			1.38358i
$81$	2.66406	−	0.969637i	0.296006	−	0.107737i
$82$	−0.919858	+	0.531080i	−0.101581	+	0.0586480i
$83$	−1.81973	−	10.3202i	−0.199741	−	1.13279i	−0.905504	−	0.424338i	$-0.860507\pi$
$83$	−1.81973	−	10.3202i	−0.199741	−	1.13279i	0.705763	−	0.708448i	$-0.250604\pi$
$84$	8.77654	−	15.2014i	0.957599	−	1.65861i
$85$	0.803421	+	1.39157i	0.0871432	+	0.150937i
$86$	−3.87061	+	3.24783i	−0.417379	+	0.350222i
$87$	0.175772	+	0.0309934i	0.0188448	+	0.00332284i
$88$	28.0052	+	16.1688i	2.98537	+	1.72360i
$89$	0.914163	−	2.51164i	0.0969011	−	0.266234i	−0.881766	−	0.471688i	$-0.843645\pi$
$89$	0.914163	−	2.51164i	0.0969011	−	0.266234i	0.978667	+	0.205454i	$0.0658672\pi$
$90$	6.60902	+	2.40549i	0.696651	+	0.253560i
$91$	−4.81510	+	0.849032i	−0.504759	+	0.0890027i
$92$	−9.77350	+	11.6476i	−1.01896	+	1.21435i
$93$	−2.74300	+	3.26898i	−0.284436	+	0.338977i
$94$	4.18331	−	0.737630i	0.431475	−	0.0760807i
$95$	3.95851	+	1.44078i	0.406135	+	0.147821i
$96$	1.64984	−	4.53289i	0.168386	−	0.462636i
$97$	−13.3681	−	7.71809i	−1.35733	−	0.783654i	−0.368065	−	0.929800i	$-0.619980\pi$
$97$	−13.3681	−	7.71809i	−1.35733	−	0.783654i	−0.989263	+	0.146146i	$0.953313\pi$
$98$	−7.91695	−	1.39597i	−0.799733	−	0.141015i
$99$	5.86542	−	4.92167i	0.589497	−	0.494646i
$100$	2.23784	+	3.87606i	0.223784	+	0.387606i
$101$	8.33907	−	14.4437i	0.829769	−	1.43720i	−0.0684504	−	0.997655i	$-0.521805\pi$
$101$	8.33907	−	14.4437i	0.829769	−	1.43720i	0.898219	−	0.439547i	$-0.144861\pi$
$102$	−0.446149	−	2.53023i	−0.0441753	−	0.250531i
$103$	3.81111	−	2.20034i	0.375520	−	0.216806i	−0.300348	−	0.953830i	$-0.597103\pi$
$103$	3.81111	−	2.20034i	0.375520	−	0.216806i	0.675867	+	0.737024i	$0.263769\pi$
$104$	−8.51521	+	3.09928i	−0.834985	+	0.303910i
$105$			8.04410i			0.785024i
$106$	6.29202	+	17.2872i	0.611135	+	1.67908i
$107$	1.47160	−	8.34584i	0.142265	−	0.806823i	−0.827258	−	0.561822i	$-0.810101\pi$
$107$	1.47160	−	8.34584i	0.142265	−	0.806823i	0.969523	−	0.245001i	$-0.0787882\pi$
$108$	−18.5372	−	15.5545i	−1.78374	−	1.49673i
$109$	−6.61006	−	7.87757i	−0.633129	−	0.754534i	0.350139	−	0.936698i	$-0.386134\pi$
$109$	−6.61006	−	7.87757i	−0.633129	−	0.754534i	−0.983268	+	0.182164i	$0.941690\pi$
$110$	−27.4415			−2.61645
$111$	4.40216	−	6.30787i	0.417835	−	0.598717i
$112$	−19.8252			−1.87331
$113$	7.37783	+	8.79256i	0.694048	+	0.827134i	0.991839	−	0.127497i	$-0.0406943\pi$
$113$	7.37783	+	8.79256i	0.694048	+	0.827134i	−0.297791	+	0.954631i	$0.596250\pi$
$114$	−5.15984	−	4.32962i	−0.483263	−	0.405506i
$115$	1.20998	−	6.86212i	0.112831	−	0.639896i
$116$	−0.209901	−	0.576699i	−0.0194888	−	0.0535452i
$117$			2.14559i			0.198360i
$118$	25.2857	−	9.20325i	2.32774	−	0.847228i
$119$	−2.22932	+	1.28710i	−0.204362	+	0.117988i
$120$	2.58883	+	14.6820i	0.236327	+	1.34028i
$121$	−9.43730	+	16.3459i	−0.857937	+	1.48599i
$122$	−14.5180	−	25.1459i	−1.31440	−	2.27660i
$123$	−0.408378	+	0.342670i	−0.0368222	+	0.0308975i
$124$	14.4502	+	2.54796i	1.29767	+	0.228814i
$125$	−10.4047	−	6.00718i	−0.930629	−	0.537299i
$126$	−3.85364	+	10.5878i	−0.343310	+	0.943236i
$127$	1.92172	+	0.699449i	0.170525	+	0.0620660i	0.425872	−	0.904783i	$-0.359967\pi$
$127$	1.92172	+	0.699449i	0.170525	+	0.0620660i	−0.255347	+	0.966850i	$0.582190\pi$
$128$	14.4848	−	2.55407i	1.28029	−	0.225750i
$129$	−1.63009	+	1.94267i	−0.143521	+	0.171042i
$130$	4.94284	−	5.89065i	0.433516	−	0.516644i
$131$	−19.0577	+	3.36038i	−1.66508	+	0.293598i	−0.925295	−	0.379248i	$-0.876183\pi$
$131$	−19.0577	+	3.36038i	−1.66508	+	0.293598i	−0.739782	+	0.672846i	$0.765072\pi$
$132$	28.2416	+	10.2791i	2.45811	+	0.894680i
$133$	−2.30816	+	6.34163i	−0.200143	+	0.549889i
$134$	16.8523	+	9.72965i	1.45581	+	0.840514i
$135$	10.9211	+	1.92568i	0.939935	+	0.165736i
$136$	−3.65471	+	3.06666i	−0.313388	+	0.262964i
$137$	8.52635	+	14.7681i	0.728456	+	1.26172i	0.957536	+	0.288314i	$0.0930948\pi$
$137$	8.52635	+	14.7681i	0.728456	+	1.26172i	−0.229080	+	0.973408i	$0.573572\pi$
$138$	−5.57074	+	9.64881i	−0.474213	+	0.821361i
$139$	−1.47009	−	8.33729i	−0.124691	−	0.707160i	−0.981491	−	0.191510i	$-0.938662\pi$
$139$	−1.47009	−	8.33729i	−0.124691	−	0.707160i	0.856799	−	0.515650i	$-0.172449\pi$
$140$	23.9537	−	13.8297i	2.02446	−	1.16882i
$141$	2.00342	−	0.729186i	0.168719	−	0.0614086i
$142$		−	22.3290i		−	1.87381i
$143$	−2.86322	−	7.86664i	−0.239435	−	0.657841i
$144$	−1.51071	+	8.56765i	−0.125892	+	0.713971i
$145$	0.215448	+	0.180782i	0.0178919	+	0.0150131i
$146$	14.2106	+	16.9355i	1.17608	+	1.40160i
$147$	−4.03483			−0.332787
$148$	−26.3519	−	2.26406i	−2.16611	−	0.186105i
$149$	8.48511			0.695128			0.347564	−	0.937656i	$-0.387009\pi$
$149$	8.48511			0.695128			0.347564	+	0.937656i	$0.387009\pi$
$150$	2.10808	+	2.51231i	0.172124	+	0.205130i
$151$	−9.09996	−	7.63577i	−0.740544	−	0.621391i	0.192439	−	0.981309i	$-0.438360\pi$
$151$	−9.09996	−	7.63577i	−0.740544	−	0.621391i	−0.932984	+	0.359918i	$0.882805\pi$
$152$	−2.17191	+	12.3175i	−0.176165	+	0.999081i
$153$	0.386355	+	1.06150i	0.0312349	+	0.0858173i
$154$		−	43.9620i		−	3.54256i
$155$	−6.31877	+	2.29984i	−0.507536	+	0.184728i
$156$	−7.29348	+	4.21089i	−0.583946	+	0.337141i
$157$	3.91222	+	22.1873i	0.312230	+	1.77074i	0.587351	+	0.809332i	$0.300171\pi$
$157$	3.91222	+	22.1873i	0.312230	+	1.77074i	−0.275122	+	0.961409i	$0.588718\pi$
$158$	5.68759	−	9.85119i	0.452480	−	0.783719i
$159$	4.61665	+	7.99628i	0.366125	+	0.634146i
$160$	5.82280	−	4.88591i	0.460333	−	0.386265i
$161$	10.9933	+	1.93841i	0.866392	+	0.152768i
$162$	−6.18604	−	3.57151i	−0.486021	−	0.280605i
$163$	−6.68120	+	18.3564i	−0.523312	+	1.43779i	0.343501	+	0.939152i	$0.388387\pi$
$163$	−6.68120	+	18.3564i	−0.523312	+	1.43779i	−0.866812	+	0.498635i	$0.833835\pi$
$164$	1.72250	+	0.626939i	0.134505	+	0.0489557i
$165$	−13.5637	+	2.39165i	−1.05593	+	0.186190i
$166$	−16.9718	+	20.2262i	−1.31727	+	1.56986i
$167$	−9.74390	+	11.6123i	−0.754006	+	0.898589i	−0.997453	−	0.0713251i	$-0.977277\pi$
$167$	−9.74390	+	11.6123i	−0.754006	+	0.898589i	0.243447	+	0.969914i	$0.421722\pi$
$168$	−23.5209	+	4.14737i	−1.81468	+	0.319977i
$169$	−10.0116	−	3.64393i	−0.770123	−	0.280302i
$170$	1.38468	−	3.80438i	0.106200	−	0.291783i
$171$	2.56471	+	1.48074i	0.196128	+	0.113235i
$172$	8.58737	+	1.51419i	0.654781	+	0.115456i
$173$	6.01265	−	5.04521i	0.457133	−	0.383580i	−0.384942	−	0.922941i	$-0.625778\pi$
$173$	6.01265	−	5.04521i	0.457133	−	0.383580i	0.842075	+	0.539361i	$0.181334\pi$
$174$	−0.224850	−	0.389452i	−0.0170459	−	0.0295243i
$175$	1.64294	−	2.84566i	0.124195	−	0.215112i
$176$	−5.89437	−	33.4287i	−0.444305	−	2.51978i
$177$	11.6960	−	6.75271i	0.879128	−	0.507565i
$178$	−6.32824	+	2.30329i	−0.474321	+	0.172639i
$179$		−	3.28655i		−	0.245648i	−0.992428	−	0.122824i	$-0.960805\pi$
$179$		−	3.28655i		−	0.245648i	0.992428	−	0.122824i	$-0.0391951\pi$
$180$	−4.15132	−	11.4057i	−0.309421	−	0.850127i
$181$	3.52659	−	20.0003i	0.262129	−	1.48661i	−0.514959	−	0.857215i	$-0.672193\pi$
$181$	3.52659	−	20.0003i	0.262129	−	1.48661i	0.777088	−	0.629392i	$-0.216696\pi$
$182$	9.43697	+	7.91856i	0.699515	+	0.586962i
$183$	−9.36749	−	11.1637i	−0.692465	−	0.825247i
$184$	20.6886			1.52519
$185$	10.9772	−	5.13963i	0.807061	−	0.377873i
$186$	10.7518			0.788363
$187$	−2.83308	−	3.37634i	−0.207176	−	0.246902i
$188$	−5.61572	−	4.71215i	−0.409568	−	0.343669i
$189$	−3.08498	+	17.4958i	−0.224399	+	1.27263i
$190$	−3.63013	−	9.97371i	−0.263358	−	0.723569i
$191$		−	8.10362i		−	0.586357i	−0.956058	−	0.293179i	$-0.905287\pi$
$191$		−	8.10362i		−	0.586357i	0.956058	−	0.293179i	$-0.0947131\pi$
$192$	3.33876	−	1.21521i	0.240954	−	0.0877002i
$193$	5.43147	−	3.13586i	0.390966	−	0.225724i	−0.291613	−	0.956536i	$-0.594192\pi$
$193$	5.43147	−	3.13586i	0.390966	−	0.225724i	0.682579	+	0.730812i	$0.260859\pi$
$194$	6.75360	+	38.3015i	0.484880	+	2.74989i
$195$	1.92974	−	3.34240i	0.138191	−	0.239354i
$196$	6.93681	+	12.0149i	0.495487	+	0.858208i
$197$	3.58285	−	3.00637i	0.255268	−	0.214195i	−0.506169	−	0.862434i	$-0.668939\pi$
$197$	3.58285	−	3.00637i	0.255268	−	0.214195i	0.761437	+	0.648239i	$0.224494\pi$
$198$	−18.9986	−	3.34996i	−1.35017	−	0.238071i
$199$	16.7401	+	9.66490i	1.18667	+	0.685126i	0.957549	−	0.288271i	$-0.0930803\pi$
$199$	16.7401	+	9.66490i	1.18667	+	0.685126i	0.229125	+	0.973397i	$0.426414\pi$
$200$	2.08286	−	5.72262i	0.147281	−	0.404650i
$201$	9.17766	+	3.34040i	0.647342	+	0.235613i
$202$	−41.3832	+	7.29698i	−2.91171	+	0.513413i
$203$	−0.289617	+	0.345152i	−0.0203271	+	0.0242249i
$204$	−2.85010	+	3.39662i	−0.199547	+	0.237811i
$205$	−0.827273	+	0.145871i	−0.0577793	+	0.0101880i
$206$	−10.4191	−	3.79225i	−0.725935	−	0.264219i
$207$	1.67541	−	4.60314i	0.116449	−	0.319940i
$208$	8.23757	+	4.75597i	0.571173	+	0.329767i
$209$	−11.3793	−	2.00648i	−0.787124	−	0.138791i
$210$	15.5259	−	13.0278i	1.07139	−	0.899001i
$211$	−5.13734	−	8.89813i	−0.353669	−	0.612573i	0.633220	−	0.773972i	$-0.281733\pi$
$211$	−5.13734	−	8.89813i	−0.353669	−	0.612573i	−0.986889	+	0.161399i	$0.948399\pi$
$212$	15.8742	−	27.4949i	1.09024	−	1.88836i
$213$	−1.94607	−	11.0367i	−0.133343	−	0.756223i
$214$	−18.4916	+	10.6761i	−1.26406	+	0.729804i
$215$	−3.75508	+	1.36674i	−0.256094	+	0.0932106i
$216$			32.9260i			2.24033i
$217$	−3.68440	−	10.1228i	−0.250114	−	0.687182i
$218$	−4.49918	+	25.5161i	−0.304723	+	1.72817i
$219$	8.49998	+	7.13233i	0.574375	+	0.481958i
$220$	30.4410	+	36.2782i	2.05233	+	2.44587i
$221$	1.23507			0.0830801
$222$	−19.3043	+	1.71927i	−1.29562	+	0.115390i
$223$	14.0167			0.938628			0.469314	−	0.883031i	$-0.344501\pi$
$223$	14.0167			0.938628			0.469314	+	0.883031i	$0.344501\pi$
$224$	7.82734	+	9.32826i	0.522986	+	0.623271i
$225$	−1.10458	−	0.926857i	−0.0736390	−	0.0617904i
$226$	5.02176	−	28.4798i	0.334043	−	1.89445i
$227$	1.16095	+	3.18969i	0.0770552	+	0.211707i	0.972239	−	0.233990i	$-0.0751781\pi$
$227$	1.16095	+	3.18969i	0.0770552	+	0.211707i	−0.895184	+	0.445697i	$0.852956\pi$
$228$			11.6243i			0.769836i
$229$	2.11117	−	0.768402i	0.139510	−	0.0507774i	−0.271322	−	0.962489i	$-0.587461\pi$
$229$	2.11117	−	0.768402i	0.139510	−	0.0507774i	0.410831	+	0.911711i	$0.365238\pi$
$230$	−15.2042	+	8.77812i	−1.00253	+	0.578812i
$231$	−3.83148	−	21.7294i	−0.252093	−	1.42969i
$232$	−0.417525	+	0.723175i	−0.0274119	+	0.0474788i
$233$	−5.01753	−	8.69062i	−0.328709	−	0.569341i	0.653547	−	0.756886i	$-0.273280\pi$
$233$	−5.01753	−	8.69062i	−0.328709	−	0.569341i	−0.982256	+	0.187545i	$0.939947\pi$
$234$	4.14119	−	3.47487i	0.270718	−	0.227159i
$235$	3.30847	+	0.583372i	0.215821	+	0.0380550i
$236$	−40.2164	−	23.2190i	−2.61787	−	1.51143i
$237$	1.95267	−	5.36491i	0.126839	−	0.348489i
$238$	6.09471	+	2.21829i	0.395061	+	0.143791i
$239$	0.0459930	−	0.00810981i	0.00297504	−	0.000524580i	−0.172160	−	0.985069i	$-0.555075\pi$
$239$	0.0459930	−	0.00810981i	0.00297504	−	0.000524580i	0.175136	+	0.984544i	$0.443964\pi$
$240$	10.0591	−	11.9880i	0.649313	−	0.773821i
$241$	0.670857	−	0.799496i	0.0432137	−	0.0515000i	−0.744005	−	0.668174i	$-0.767076\pi$
$241$	0.670857	−	0.799496i	0.0432137	−	0.0515000i	0.787218	+	0.616674i	$0.211520\pi$
$242$	46.8332	−	8.25796i	3.01055	−	0.530842i
$243$	12.3198	+	4.48406i	0.790318	+	0.287652i
$244$	−17.1385	+	47.0875i	−1.09718	+	3.01447i
$245$	−5.50611	−	3.17895i	−0.351772	−	0.203096i
$246$	1.32277	+	0.233240i	0.0843369	+	0.0148709i
$247$	2.48039	−	2.08129i	0.157823	−	0.132430i
$248$	−9.98256	−	17.2903i	−0.633893	−	1.09793i
$249$	−6.62597	+	11.4765i	−0.419904	+	0.727295i
$250$	5.25649	+	29.8110i	0.332450	+	1.88542i
$251$	−3.41584	+	1.97214i	−0.215606	+	0.124480i	−0.603914	−	0.797050i	$-0.706393\pi$
$251$	−3.41584	+	1.97214i	−0.215606	+	0.124480i	0.388308	+	0.921530i	$0.373060\pi$
$252$	18.2721	−	6.65051i	1.15104	−	0.418943i
$253$			19.1129i			1.20162i
$254$	−1.76230	−	4.84189i	−0.110577	−	0.303807i
$255$	0.352848	−	2.00110i	0.0220962	−	0.125314i
$256$	−24.0837	−	20.2086i	−1.50523	−	1.26304i
$257$	−10.7236	−	12.7799i	−0.668918	−	0.797186i	0.319718	−	0.947513i	$-0.396412\pi$
$257$	−10.7236	−	12.7799i	−0.668918	−	0.797186i	−0.988636	+	0.150327i	$0.951967\pi$
$258$	6.38953			0.397795
$259$	8.23381	+	17.5858i	0.511624	+	1.09273i
$260$	−13.2707			−0.823012
$261$	0.127092	+	0.151462i	0.00786677	+	0.00937525i
$262$	37.3506	+	31.3409i	2.30753	+	1.93625i
$263$	−2.41429	+	13.6921i	−0.148872	+	0.844292i	0.815305	+	0.579032i	$0.196569\pi$
$263$	−2.41429	+	13.6921i	−0.148872	+	0.844292i	−0.964177	+	0.265261i	$0.914542\pi$
$264$	−13.9863	−	38.4271i	−0.860799	−	2.36503i
$265$			14.5494i			0.893765i
$266$	15.9781	−	5.81556i	0.979682	−	0.356575i
$267$	−2.92716	+	1.69000i	−0.179139	+	0.103426i
$268$	−5.83151	−	33.0721i	−0.356216	−	2.02020i
$269$	3.35403	−	5.80935i	0.204499	−	0.354202i	−0.745474	−	0.666535i	$-0.767777\pi$
$269$	3.35403	−	5.80935i	0.204499	−	0.354202i	0.949973	+	0.312332i	$0.101110\pi$
$270$	−13.9704	−	24.1974i	−0.850210	−	1.47261i
$271$	3.46200	−	2.90496i	0.210302	−	0.176464i	−0.531552	−	0.847025i	$-0.678391\pi$
$271$	3.46200	−	2.90496i	0.210302	−	0.176464i	0.741854	+	0.670561i	$0.233947\pi$
$272$	4.93184	+	0.869616i	0.299037	+	0.0527282i
$273$	5.35461	+	3.09149i	0.324076	+	0.187105i
$274$	14.6950	−	40.3742i	0.887758	−	2.43909i
$275$	5.28674	+	1.92422i	0.318803	+	0.116035i
$276$	18.9355	−	3.33885i	1.13979	−	0.200975i
$277$	5.61647	−	6.69345i	0.337461	−	0.402170i	−0.570451	−	0.821332i	$-0.693231\pi$
$277$	5.61647	−	6.69345i	0.337461	−	0.402170i	0.907912	+	0.419161i	$0.137676\pi$
$278$	−13.7109	+	16.3400i	−0.822325	+	0.980008i
$279$	−4.65543	+	0.820877i	−0.278713	+	0.0491446i
$280$	−35.3653	−	12.8719i	−2.11348	−	0.769244i
$281$	0.335767	−	0.922512i	0.0200302	−	0.0550324i	−0.929275	−	0.369390i	$-0.879567\pi$
$281$	0.335767	−	0.922512i	0.0200302	−	0.0550324i	0.949305	+	0.314357i	$0.101789\pi$
$282$	−4.65203	−	2.68585i	−0.277024	−	0.159940i
$283$	−6.22077	−	1.09689i	−0.369786	−	0.0652033i	−0.0143328	−	0.999897i	$-0.504562\pi$
$283$	−6.22077	−	1.09689i	−0.369786	−	0.0652033i	−0.355453	+	0.934694i	$0.615674\pi$
$284$	−29.5194	+	24.7697i	−1.75165	+	1.46981i
$285$	−2.66354	−	4.61339i	−0.157775	−	0.273274i
$286$	−10.5463	+	18.2666i	−0.623613	+	1.08013i
$287$	−0.233688	−	1.32531i	−0.0137942	−	0.0782307i
$288$	4.62775	−	2.67183i	0.272693	−	0.157439i
$289$	−15.3637	+	5.59194i	−0.903749	+	0.328938i
$290$		−	0.708618i		−	0.0416115i
$291$	6.67629	+	18.3430i	0.391371	+	1.07528i
$292$	6.62519	−	37.5733i	0.387710	−	2.19881i
$293$	−3.33190	−	2.79580i	−0.194652	−	0.163332i	0.540253	−	0.841503i	$-0.318329\pi$
$293$	−3.33190	−	2.79580i	−0.194652	−	0.163332i	−0.734904	+	0.678171i	$0.762773\pi$
$294$	6.53458	+	7.78761i	0.381105	+	0.454183i
$295$	21.2812			1.23904
$296$	20.6879	+	29.4474i	1.20246	+	1.71160i
$297$	−30.4181			−1.76504
$298$	−13.7420	−	16.3771i	−0.796053	−	0.948699i
$299$	−4.10280	−	3.44266i	−0.237271	−	0.199094i
$300$	0.982819	−	5.57384i	0.0567431	−	0.321806i
$301$	−2.18954	−	6.01572i	−0.126203	−	0.346740i
$302$			29.9303i			1.72229i
$303$	−19.8188	+	7.21345i	−1.13856	+	0.414402i
$304$	11.3700	−	6.56448i	0.652115	−	0.376499i
$305$	−3.98763	−	22.6150i	−0.228331	−	1.29493i
$306$	1.42308	−	2.46485i	0.0813521	−	0.140906i
$307$	8.24984	+	14.2892i	0.470844	+	0.815525i	0.999444	−	0.0333459i	$-0.0106163\pi$
$307$	8.24984	+	14.2892i	0.470844	+	0.815525i	−0.528600	+	0.848871i	$0.677283\pi$
$308$	−58.1185	+	48.7672i	−3.31161	+	2.77877i
$309$	−5.48044	−	0.966350i	−0.311771	−	0.0549737i
$310$	14.6724	+	8.47113i	0.833338	+	0.481128i
$311$	−7.85426	+	21.5794i	−0.445374	+	1.22366i	0.490537	+	0.871420i	$0.336801\pi$
$311$	−7.85426	+	21.5794i	−0.445374	+	1.22366i	−0.935912	+	0.352235i	$0.885422\pi$
$312$	10.7681	+	3.91927i	0.609624	+	0.221885i
$313$	31.3739	−	5.53206i	1.77336	−	0.312691i	0.811115	−	0.584887i	$-0.198861\pi$
$313$	31.3739	−	5.53206i	1.77336	−	0.312691i	0.962242	+	0.272196i	$0.0877499\pi$
$314$	36.4877	−	43.4843i	2.05912	−	2.45396i
$315$	−5.72789	+	6.82624i	−0.322730	+	0.384615i
$316$	−19.3327	+	3.40888i	−1.08755	+	0.191765i
$317$	−8.34465	−	3.03720i	−0.468682	−	0.170586i	0.0968731	−	0.995297i	$-0.469116\pi$
$317$	−8.34465	−	3.03720i	−0.468682	−	0.170586i	−0.565555	+	0.824710i	$0.691338\pi$
$318$	7.95672	−	21.8609i	0.446191	−	1.22590i
$319$	−0.668093	−	0.385724i	−0.0374060	−	0.0215964i
$320$	5.51365	+	0.972206i	0.308223	+	0.0543480i
$321$	−8.20949	+	6.88858i	−0.458209	+	0.384483i
$322$	−14.0628	−	24.3574i	−0.783687	−	1.35739i
$323$	0.852363	−	1.47634i	0.0474267	−	0.0821455i
$324$	2.14060	+	12.1400i	0.118922	+	0.674442i
$325$	−1.36532	+	0.788267i	−0.0757343	+	0.0437252i
$326$	46.2502	−	16.8337i	2.56156	−	0.932331i
$327$			13.0041i			0.719131i
$328$	−0.853050	−	2.34374i	−0.0471018	−	0.129411i
$329$	−0.934576	+	5.30025i	−0.0515249	+	0.292212i
$330$	26.5831	+	22.3059i	1.46335	+	1.22790i
$331$	9.58689	+	11.4252i	0.526943	+	0.627986i	0.962208	−	0.272316i	$-0.0877897\pi$
$331$	9.58689	+	11.4252i	0.526943	+	0.627986i	−0.435265	+	0.900302i	$0.643345\pi$
$332$	45.5663			2.50078
$333$	8.22728	−	2.21826i	0.450852	−	0.121560i
$334$	38.1936			2.08986
$335$	9.89242	+	11.7893i	0.540480	+	0.644120i
$336$	19.2050	+	16.1149i	1.04772	+	0.879143i
$337$	5.18509	−	29.4061i	0.282450	−	1.60185i	−0.431806	−	0.901966i	$-0.642124\pi$
$337$	5.18509	−	29.4061i	0.282450	−	1.60185i	0.714256	−	0.699885i	$-0.246765\pi$
$338$	9.18109	+	25.2248i	0.499386	+	1.37205i
$339$		−	14.5146i		−	0.788325i
$340$	−6.56549	+	2.38964i	−0.356064	+	0.129597i
$341$	15.9733	−	9.22222i	0.865005	−	0.499411i
$342$	−1.29569	−	7.34825i	−0.0700631	−	0.397348i
$343$	−6.08023	+	10.5313i	−0.328302	+	0.568635i
$344$	−5.93237	−	10.2752i	−0.319852	−	0.554000i
$345$	−6.75001	+	5.66393i	−0.363408	+	0.304936i
$346$	−19.4755	−	3.43405i	−1.04701	−	0.184616i
$347$	−5.67160	−	3.27450i	−0.304467	−	0.175784i	0.339981	−	0.940432i	$-0.389579\pi$
$347$	−5.67160	−	3.27450i	−0.304467	−	0.175784i	−0.644448	+	0.764648i	$0.722913\pi$
$348$	−0.265435	+	0.729278i	−0.0142288	+	0.0390934i
$349$	−29.2299	−	10.6388i	−1.56464	−	0.569483i	−0.592848	−	0.805314i	$-0.701997\pi$
$349$	−29.2299	−	10.6388i	−1.56464	−	0.569483i	−0.971794	+	0.235831i	$0.924219\pi$
$350$	−8.15322	+	1.43763i	−0.435808	+	0.0768447i
$351$	5.47899	−	6.52961i	0.292447	−	0.348525i
$352$	−13.4018	+	15.9717i	−0.714320	+	0.851293i
$353$	−18.9726	+	3.34538i	−1.00981	+	0.178056i	−0.653994	−	0.756500i	$-0.726908\pi$
$353$	−18.9726	+	3.34538i	−1.00981	+	0.178056i	−0.355815	+	0.934556i	$0.615797\pi$
$354$	−31.9756	−	11.6382i	−1.69949	−	0.618562i
$355$	6.03988	−	16.5944i	0.320564	−	0.880742i
$356$	10.0649	+	5.81099i	0.533440	+	0.307982i
$357$	3.20581	+	0.565270i	0.169669	+	0.0299173i
$358$	−6.34335	+	5.32271i	−0.335257	+	0.281314i
$359$	−6.15563	−	10.6619i	−0.324882	−	0.562712i	0.656607	−	0.754233i	$-0.271991\pi$
$359$	−6.15563	−	10.6619i	−0.324882	−	0.562712i	−0.981488	+	0.191521i	$0.938658\pi$
$360$	−8.25760	+	14.3026i	−0.435214	+	0.753812i
$361$	2.52325	+	14.3101i	0.132803	+	0.753161i
$362$	−44.3139	+	25.5846i	−2.32909	+	1.34470i
$363$	22.4289	−	8.16344i	1.17721	−	0.428469i
$364$		−	21.2599i		−	1.11432i
$365$	5.98004	+	16.4300i	0.313010	+	0.859987i
$366$	−6.37603	+	36.1603i	−0.333281	+	1.89013i
$367$	−20.8149	−	17.4658i	−1.08653	−	0.911707i	−0.0900839	−	0.995934i	$-0.528714\pi$
$367$	−20.8149	−	17.4658i	−1.08653	−	0.911707i	−0.996447	+	0.0842269i	$0.973158\pi$
$368$	−13.9591	−	16.6358i	−0.727670	−	0.867204i
$369$	−0.590553			−0.0307430
$370$	−27.6980	−	12.8632i	−1.43995	−	0.668727i
$371$	−23.3085			−1.21012
$372$	−11.9271	−	14.2141i	−0.618390	−	0.736968i
$373$	6.53564	+	5.48405i	0.338403	+	0.283954i	0.796113	−	0.605148i	$-0.206886\pi$
$373$	6.53564	+	5.48405i	0.338403	+	0.283954i	−0.457711	+	0.889101i	$0.651330\pi$
$374$	−1.92836	+	10.9362i	−0.0997129	+	0.565500i
$375$	5.19632	+	14.2768i	0.268337	+	0.737250i
$376$			9.97472i			0.514407i
$377$	0.203139	−	0.0739366i	0.0104622	−	0.00380793i
$378$	38.7648	−	22.3809i	1.99385	−	1.15115i
$379$	0.430632	+	2.44224i	0.0221201	+	0.125449i	0.993868	−	0.110571i	$-0.0352679\pi$
$379$	0.430632	+	2.44224i	0.0221201	+	0.125449i	−0.971748	+	0.236020i	$0.924157\pi$
$380$	−9.15850	+	15.8630i	−0.469821	+	0.813754i
$381$	−1.29306	−	2.23964i	−0.0662453	−	0.114740i
$382$	−15.6408	+	13.1242i	−0.800251	+	0.671490i
$383$	−8.54812	−	1.50726i	−0.436789	−	0.0770176i	−0.0490699	−	0.998795i	$-0.515626\pi$
$383$	−8.54812	−	1.50726i	−0.436789	−	0.0770176i	−0.387719	+	0.921778i	$0.626737\pi$
$384$	−16.1078	−	9.29984i	−0.821998	−	0.474581i
$385$	11.8915	−	32.6716i	0.606047	−	1.66510i
$386$	−14.8490	−	5.40460i	−0.755795	−	0.275087i
$387$	−2.76660	+	0.487826i	−0.140634	+	0.0247976i
$388$	43.1435	−	51.4165i	2.19028	−	2.61028i
$389$	19.5961	−	23.3537i	0.993561	−	1.18408i	0.0106603	−	0.999943i	$-0.496607\pi$
$389$	19.5961	−	23.3537i	0.993561	−	1.18408i	0.982901	−	0.184137i	$-0.0589489\pi$
$390$	−9.57645	+	1.68859i	−0.484922	+	0.0855049i
$391$	−2.64973	−	0.964422i	−0.134002	−	0.0487729i
$392$	6.45641	−	17.7388i	0.326098	−	0.895946i
$393$	21.1930	+	12.2358i	1.06905	+	0.617214i
$394$	−11.6052	−	2.04630i	−0.584660	−	0.103091i
$395$	6.89159	−	5.78273i	0.346754	−	0.290961i
$396$	16.6465	+	28.8326i	0.836518	+	1.44889i
$397$	1.48812	−	2.57749i	0.0746865	−	0.129361i	−0.826263	−	0.563284i	$-0.809538\pi$
$397$	1.48812	−	2.57749i	0.0746865	−	0.129361i	0.900950	+	0.433923i	$0.142871\pi$
$398$	−8.45712	−	47.9627i	−0.423917	−	2.40415i
$399$	7.39076	−	4.26706i	0.370001	−	0.213620i
$400$	−6.00694	+	2.18635i	−0.300347	+	0.109317i
$401$		−	14.5237i		−	0.725279i	−0.931930	−	0.362639i	$-0.881876\pi$
$401$		−	14.5237i		−	0.725279i	0.931930	−	0.362639i	$-0.118124\pi$
$402$	−8.41633	−	23.1237i	−0.419768	−	1.15330i
$403$	−0.897505	+	5.09000i	−0.0447079	+	0.253551i
$404$	55.5533	+	46.6148i	2.76388	+	2.31917i
$405$	−3.63126	−	4.32757i	−0.180439	−	0.215039i
$406$	1.13522			0.0563402
$407$	−27.2045	+	19.1122i	−1.34848	+	0.947354i
$408$	6.03312			0.298684
$409$	18.9147	+	22.5417i	0.935272	+	1.11461i	0.993215	+	0.116294i	$0.0371014\pi$
$409$	18.9147	+	22.5417i	0.935272	+	1.11461i	−0.0579428	+	0.998320i	$0.518454\pi$
$410$	1.62135	+	1.36047i	0.0800727	+	0.0671890i
$411$	3.74462	−	21.2368i	0.184708	−	1.04753i
$412$	6.54456	+	17.9810i	0.322427	+	0.885862i
$413$			34.0931i			1.67761i
$414$	−11.5979	+	4.22129i	−0.570005	+	0.207465i
$415$	−18.0842	+	10.4409i	−0.887717	+	0.512524i
$416$	−1.01454	−	5.75373i	−0.0497418	−	0.282100i
$417$	−5.35287	+	9.27145i	−0.262131	+	0.454025i
$418$	14.5566	+	25.2128i	0.711986	+	1.23320i
$419$	26.4711	−	22.2119i	1.29320	−	1.08512i	0.301921	−	0.953333i	$-0.402372\pi$
$419$	26.4711	−	22.2119i	1.29320	−	1.08512i	0.991278	−	0.131789i	$-0.0420723\pi$
$420$	−34.4459	−	6.07373i	−1.68079	−	0.296368i
$421$	−1.37981	−	0.796635i	−0.0672480	−	0.0388256i	0.465999	−	0.884785i	$-0.345695\pi$
$421$	−1.37981	−	0.796635i	−0.0672480	−	0.0388256i	−0.533247	+	0.845960i	$0.679028\pi$
$422$	−8.85411	+	24.3265i	−0.431011	+	1.18419i
$423$	2.21933	+	0.807772i	0.107908	+	0.0392752i
$424$	−42.5425	+	7.50139i	−2.06604	+	0.364299i
$425$	−0.533531	+	0.635837i	−0.0258801	+	0.0308426i
$426$	−18.1502	+	21.6305i	−0.879379	+	1.04800i
$427$	36.2297	−	6.38827i	1.75328	−	0.309150i
$428$	34.6268	+	12.6031i	1.67375	+	0.609195i
$429$	−3.62075	+	9.94793i	−0.174812	+	0.480291i
$430$	8.71944	+	5.03417i	0.420489	+	0.242769i
$431$	−15.9475	−	2.81198i	−0.768165	−	0.135448i	−0.224185	−	0.974547i	$-0.571972\pi$
$431$	−15.9475	−	2.81198i	−0.768165	−	0.135448i	−0.543980	+	0.839098i	$0.683083\pi$
$432$	26.4759	−	22.2159i	1.27382	−	1.06887i
$433$	10.7421	+	18.6058i	0.516231	+	0.894139i	0.999822	+	0.0188448i	$0.00599884\pi$
$433$	10.7421	+	18.6058i	0.516231	+	0.894139i	−0.483591	+	0.875294i	$0.660668\pi$
$434$	−13.5710	+	23.5056i	−0.651427	+	1.12830i
$435$	−0.0617592	−	0.350254i	−0.00296113	−	0.0167934i
$436$	38.7237	−	22.3571i	1.85453	−	1.07071i
$437$	−6.94663	+	2.52837i	−0.332302	+	0.120948i
$438$		−	27.9569i		−	1.33583i
$439$	−0.818338	−	2.24837i	−0.0390572	−	0.107309i	0.918631	−	0.395116i	$-0.129296\pi$
$439$	−0.818338	−	2.24837i	−0.0390572	−	0.107309i	−0.957688	+	0.287808i	$0.907074\pi$
$440$	11.1895	−	63.4589i	0.533439	−	3.02528i
$441$	−3.42397	−	2.87305i	−0.163046	−	0.136812i
$442$	−2.00026	−	2.38381i	−0.0951425	−	0.113386i
$443$	6.54020			0.310734			0.155367	−	0.987857i	$-0.450344\pi$
$443$	6.54020			0.310734			0.155367	+	0.987857i	$0.450344\pi$
$444$	23.6872	+	23.6134i	1.12415	+	1.12064i
$445$	−5.32604			−0.252478
$446$	−22.7006	−	27.0536i	−1.07491	−	1.28102i
$447$	−8.21969	−	6.89714i	−0.388778	−	0.326223i
$448$	−1.55750	+	8.83301i	−0.0735848	+	0.417320i
$449$	−13.2795	−	36.4852i	−0.626699	−	1.72184i	−0.689964	−	0.723844i	$-0.742373\pi$
$449$	−13.2795	−	36.4852i	−0.626699	−	1.72184i	0.0632647	−	0.997997i	$-0.479849\pi$
$450$			3.63304i			0.171263i
$451$	2.16522	−	0.788076i	0.101956	−	0.0371090i
$452$	−43.2215	+	24.9540i	−2.03297	+	1.17374i
$453$	2.60855	+	14.7938i	0.122560	+	0.695075i
$454$	4.27620	−	7.40659i	0.200692	−	0.347609i
$455$	4.87142	+	8.43755i	0.228376	+	0.395559i
$456$	12.1163	−	10.1668i	0.567396	−	0.476102i
$457$	15.0919	+	2.66111i	0.705969	+	0.124481i	0.515095	−	0.857133i	$-0.327757\pi$
$457$	15.0919	+	2.66111i	0.705969	+	0.124481i	0.190874	+	0.981615i	$0.438868\pi$
$458$	−4.90221	−	2.83029i	−0.229065	−	0.132251i
$459$	1.53488	−	4.21704i	0.0716419	−	0.196835i
$460$	28.4709	+	10.3626i	1.32746	+	0.483156i
$461$	−15.9863	+	2.81882i	−0.744557	+	0.131285i	−0.533041	−	0.846089i	$-0.678951\pi$
$461$	−15.9863	+	2.81882i	−0.744557	+	0.131285i	−0.211516	+	0.977375i	$0.567840\pi$
$462$	−35.7346	+	42.5868i	−1.66252	+	1.98132i
$463$	−5.36317	+	6.39158i	−0.249248	+	0.297042i	−0.876133	−	0.482070i	$-0.839885\pi$
$463$	−5.36317	+	6.39158i	−0.249248	+	0.297042i	0.626885	+	0.779112i	$0.284330\pi$
$464$	0.863223	−	0.152210i	0.0400741	−	0.00706615i
$465$	7.99054	+	2.90832i	0.370552	+	0.134870i
$466$	−8.64762	+	23.7591i	−0.400593	+	1.10062i
$467$	−5.78049	−	3.33737i	−0.267489	−	0.154435i	0.360257	−	0.932853i	$-0.382689\pi$
$467$	−5.78049	−	3.33737i	−0.267489	−	0.154435i	−0.627746	+	0.778418i	$0.716022\pi$
$468$	−9.18768	−	1.62004i	−0.424701	−	0.0748862i
$469$	−18.8868	+	15.8479i	−0.872110	+	0.731788i
$470$	−4.23224	−	7.33046i	−0.195219	−	0.338129i
$471$	14.2452	−	24.6733i	0.656382	−	1.13689i
$472$	10.9722	+	62.2262i	0.505035	+	2.86420i
$473$	9.49254	−	5.48052i	0.436467	−	0.251995i
$474$	−13.5172	+	4.91987i	−0.620867	+	0.225977i
$475$			2.17603i			0.0998431i
$476$	−3.82827	−	10.5181i	−0.175468	−	0.482095i
$477$	−1.77614	+	10.0730i	−0.0813240	+	0.461211i
$478$	−0.0901404	−	0.0756368i	−0.00412292	−	0.00345954i
$479$	22.6567	+	27.0012i	1.03521	+	1.23372i	0.971819	+	0.235729i	$0.0757476\pi$
$479$	22.6567	+	27.0012i	1.03521	+	1.23372i	0.0633927	+	0.997989i	$0.479808\pi$
$480$	−9.61217			−0.438733
$481$	0.797502	−	9.28231i	0.0363630	−	0.423237i
$482$	−2.62958			−0.119774
$483$	−9.07375	−	10.8137i	−0.412870	−	0.492039i
$484$	−62.8695	−	52.7538i	−2.85770	−	2.39790i
$485$	−5.34125	+	30.2917i	−0.242533	+	1.37548i
$486$	−11.2979	−	31.0406i	−0.512481	−	1.40803i
$487$			7.27548i			0.329683i	0.986320	+	0.164842i	$0.0527113\pi$
$487$			7.27548i			0.329683i	−0.986320	+	0.164842i	$0.947289\pi$
$488$	64.0701	−	23.3196i	2.90032	−	1.05563i
$489$	21.3933	−	12.3514i	0.967436	−	0.558550i
$490$	2.78169	+	15.7758i	0.125664	+	0.712676i
$491$	11.2013	−	19.4012i	0.505506	−	0.875562i	−0.494474	−	0.869193i	$-0.664639\pi$
$491$	11.2013	−	19.4012i	0.505506	−	0.875562i	0.999980	−	0.00636940i	$-0.00202746\pi$
$492$	−1.15901	−	2.00746i	−0.0522522	−	0.0905035i
$493$	0.0871867	−	0.0731583i	0.00392669	−	0.00329488i
$494$	−8.03419	−	1.41665i	−0.361475	−	0.0637379i
$495$	−13.2132	−	7.62864i	−0.593889	−	0.342882i
$496$	−7.16774	+	19.6932i	−0.321841	+	0.884251i
$497$	26.5847	+	9.67604i	1.19249	+	0.434030i
$498$	32.8818	−	5.79795i	1.47347	−	0.259812i
$499$	−14.4636	+	17.2370i	−0.647478	+	0.771634i	−0.985531	−	0.169493i	$-0.945787\pi$
$499$	−14.4636	+	17.2370i	−0.647478	+	0.771634i	0.338054	+	0.941127i	$0.390231\pi$
$500$	33.5797	−	40.0187i	1.50173	−	1.78969i
$501$	18.8782	−	3.32874i	0.843416	−	0.148717i
$502$	9.33850	+	3.39894i	0.416798	+	0.151702i
$503$	9.70488	−	26.6639i	0.432719	−	1.18889i	−0.511417	−	0.859332i	$-0.670879\pi$
$503$	9.70488	−	26.6639i	0.432719	−	1.18889i	0.944137	−	0.329554i	$-0.106898\pi$
$504$	−22.9131	−	13.2289i	−1.02063	−	0.589261i
$505$	−32.7289	−	5.77099i	−1.45642	−	0.256806i
$506$	36.8896	−	30.9541i	1.63994	−	1.37608i
$507$	6.73646	+	11.6679i	0.299177	+	0.518189i
$508$	−4.44613	+	7.70093i	−0.197265	+	0.341673i
$509$	0.834169	+	4.73081i	0.0369739	+	0.209689i	0.997698	−	0.0678167i	$-0.0216033\pi$
$509$	0.834169	+	4.73081i	0.0369739	+	0.209689i	−0.960724	+	0.277506i	$0.910492\pi$
$510$	−4.43376	+	2.55983i	−0.196330	+	0.113351i
$511$	−26.3213	+	9.58017i	−1.16439	+	0.423802i
$512$			49.7961i			2.20070i
$513$	−4.02389	−	11.0556i	−0.177659	−	0.488115i
$514$	−7.29906	+	41.3950i	−0.321948	+	1.82586i
$515$	−6.71749	−	5.63664i	−0.296008	−	0.248380i
$516$	−7.08794	−	8.44708i	−0.312029	−	0.371862i
$517$	−9.21498			−0.405274
$518$	20.6072	−	44.3729i	0.905428	−	1.94963i
$519$	−9.92557			−0.435684
$520$	11.6067	+	13.8324i	0.508988	+	0.606589i
$521$	−7.02658	−	5.89600i	−0.307840	−	0.258309i	0.475758	−	0.879576i	$-0.342174\pi$
$521$	−7.02658	−	5.89600i	−0.307840	−	0.258309i	−0.783599	+	0.621267i	$0.786618\pi$
$522$	0.0865056	−	0.490598i	0.00378625	−	0.0214729i
$523$	−3.70717	−	10.1854i	−0.162103	−	0.445375i	0.831874	−	0.554965i	$-0.187268\pi$
$523$	−3.70717	−	10.1854i	−0.162103	−	0.445375i	−0.993977	+	0.109590i	$0.965046\pi$
$524$		−	84.1447i		−	3.67588i
$525$	−3.90465	+	1.42118i	−0.170413	+	0.0620252i
$526$	30.3371	−	17.5152i	1.32276	−	0.763697i
$527$	0.472526	+	2.67983i	0.0205835	+	0.116735i
$528$	−21.4625	+	37.1742i	−0.934037	+	1.61780i
$529$	−5.38609	−	9.32898i	−0.234178	−	0.405608i
$530$	28.0818	−	23.5634i	1.21980	−	1.02353i
$531$	14.7336	+	2.59794i	0.639385	+	0.112741i
$532$	−25.4129	−	14.6721i	−1.10179	−	0.636118i
$533$	−0.220836	+	0.606741i	−0.00956545	+	0.0262809i
$534$	8.00251	+	2.91268i	0.346303	+	0.126044i
$535$	−16.6304	+	2.93239i	−0.718994	+	0.126778i
$536$	−29.3716	+	35.0037i	−1.26866	+	1.51193i
$537$	−2.67148	+	3.18374i	−0.115283	+	0.137389i
$538$	−16.6446	+	2.93489i	−0.717599	+	0.126532i
$539$	16.3877	+	5.96464i	0.705869	+	0.256915i
$540$	−16.4920	+	45.3114i	−0.709702	+	1.94989i
$541$	5.20115	+	3.00288i	0.223615	+	0.129104i	0.607623	−	0.794226i	$-0.292123\pi$
$541$	5.20115	+	3.00288i	0.223615	+	0.129104i	−0.384008	+	0.923330i	$0.625457\pi$
$542$	−11.2137	−	1.97728i	−0.481671	−	0.0849315i
$543$	−19.6735	+	16.5080i	−0.844271	+	0.708427i
$544$	−1.53800	−	2.66389i	−0.0659412	−	0.114214i
$545$	−10.2457	+	17.7460i	−0.438876	+	0.760156i
$546$	−2.70516	−	15.3417i	−0.115770	−	0.656564i
$547$	36.1860	−	20.8920i	1.54720	−	0.893276i	0.548846	−	0.835924i	$-0.315067\pi$
$547$	36.1860	−	20.8920i	1.54720	−	0.893276i	0.998354	−	0.0573527i	$-0.0182660\pi$
$548$	−69.6767	+	25.3602i	−2.97644	+	1.08334i
$549$		−	16.1438i		−	0.689000i
$550$	−4.84818	−	13.3203i	−0.206727	−	0.567978i
$551$	0.0518131	−	0.293846i	0.00220731	−	0.0125183i
$552$	−20.0415	−	16.8168i	−0.853022	−	0.715770i
$553$	9.26408	+	11.0405i	0.393949	+	0.469490i
$554$	−22.0151			−0.935332
$555$	−14.8116	−	3.94399i	−0.628717	−	0.167413i
$556$	36.8113			1.56115
$557$	5.05953	+	6.02971i	0.214379	+	0.255487i	0.862508	−	0.506044i	$-0.168893\pi$
$557$	5.05953	+	6.02971i	0.214379	+	0.255487i	−0.648129	+	0.761531i	$0.724448\pi$
$558$	9.12403	+	7.65597i	0.386251	+	0.324103i
$559$	−0.533363	+	3.02485i	−0.0225589	+	0.127938i
$560$	13.5114	+	37.1224i	0.570963	+	1.56871i
$561$			5.57360i			0.235317i
$562$	−2.32432	+	0.845985i	−0.0980457	+	0.0356857i
$563$	−20.1096	+	11.6103i	−0.847517	+	0.489314i	−0.859812	−	0.510610i	$-0.829420\pi$
$563$	−20.1096	+	11.6103i	−0.847517	+	0.489314i	0.0122951	+	0.999924i	$0.496086\pi$
$564$	1.60978	+	9.12949i	0.0677838	+	0.384421i
$565$	11.4357	−	19.8073i	0.481104	−	0.833297i
$566$	7.95770	+	13.7831i	0.334487	+	0.579348i
$567$	6.93287	−	5.81737i	0.291153	−	0.244306i
$568$	51.6361	+	9.10484i	2.16660	+	0.382031i
$569$	35.3242	+	20.3944i	1.48087	+	0.854978i	0.999765	−	0.0216869i	$-0.00690369\pi$
$569$	35.3242	+	20.3944i	1.48087	+	0.854978i	0.481101	+	0.876665i	$0.340237\pi$
$570$	−4.59057	+	12.6125i	−0.192278	+	0.528279i
$571$	−33.6112	−	12.2335i	−1.40658	−	0.511954i	−0.476458	−	0.879197i	$-0.658080\pi$
$571$	−33.6112	−	12.2335i	−1.40658	−	0.511954i	−0.930125	+	0.367243i	$0.880302\pi$
$572$	35.8478	−	6.32094i	1.49887	−	0.264292i
$573$	−6.58704	+	7.85013i	−0.275177	+	0.327944i
$574$	−2.17951	+	2.59744i	−0.0909710	+	0.108415i
$575$	3.54468	−	0.625023i	0.147823	−	0.0260653i
$576$	3.69858	+	1.34617i	0.154108	+	0.0560906i
$577$	3.63320	−	9.98213i	0.151252	−	0.415561i	−0.840807	−	0.541335i	$-0.817919\pi$
$577$	3.63320	−	9.98213i	0.151252	−	0.415561i	0.992059	+	0.125774i	$0.0401413\pi$
$578$	35.6752	+	20.5971i	1.48389	+	0.856726i
$579$	−7.81055	−	1.37721i	−0.324596	−	0.0572350i
$580$	−0.936806	+	0.786074i	−0.0388988	+	0.0326399i
$581$	−16.7266	−	28.9713i	−0.693935	−	1.20193i
$582$	24.5911	−	42.5931i	1.01934	−	1.76554i
$583$	−6.93003	−	39.3021i	−0.287012	−	1.62773i
$584$	−44.9581	+	25.9566i	−1.86038	+	1.07409i
$585$	4.01758	−	1.46228i	0.166106	−	0.0604578i
$586$			10.9588i			0.452704i
$587$	3.49256	+	9.59573i	0.144153	+	0.396058i	0.990666	−	0.136310i	$-0.0435243\pi$
$587$	3.49256	+	9.59573i	0.144153	+	0.396058i	−0.846513	+	0.532368i	$0.821302\pi$
$588$	3.04652	−	17.2777i	0.125636	−	0.712519i
$589$	5.46490	+	4.58559i	0.225177	+	0.188946i
$590$	−34.4659	−	41.0748i	−1.41894	−	1.69102i
$591$	−5.91451			−0.243290
$592$	9.72022	−	36.5041i	0.399499	−	1.50031i
$593$	−9.92034			−0.407380			−0.203690	−	0.979035i	$-0.565293\pi$
$593$	−9.92034			−0.407380			−0.203690	+	0.979035i	$0.565293\pi$
$594$	49.2634	+	58.7098i	2.02130	+	2.40889i
$595$	3.92942	+	3.29718i	0.161091	+	0.135171i
$596$	−6.40673	+	36.3343i	−0.262430	+	1.48831i
$597$	−8.36031	−	22.9698i	−0.342165	−	0.940090i
$598$			13.4943i			0.551825i
$599$	−16.4377	+	5.98284i	−0.671627	+	0.244452i	−0.655248	−	0.755414i	$-0.727436\pi$
$599$	−16.4377	+	5.98284i	−0.671627	+	0.244452i	−0.0163788	+	0.999866i	$0.505214\pi$
$600$	−6.66934	+	3.85055i	−0.272275	+	0.157198i
$601$	8.06439	+	45.7354i	0.328953	+	1.86559i	0.480297	+	0.877106i	$0.340529\pi$
$601$	8.06439	+	45.7354i	0.328953	+	1.86559i	−0.151344	+	0.988481i	$0.548360\pi$
$602$	−8.06486	+	13.9687i	−0.328699	+	0.569324i
$603$	5.40962	+	9.36973i	0.220297	+	0.381565i
$604$	39.5683	−	33.2018i	1.61001	−	1.35096i
$605$	37.0392	+	6.53101i	1.50586	+	0.265523i
$606$	46.0200	+	26.5697i	1.86944	+	1.07932i
$607$	14.1766	−	38.9499i	0.575411	−	1.58093i	−0.220417	−	0.975406i	$-0.570742\pi$
$607$	14.1766	−	38.9499i	0.575411	−	1.58093i	0.795828	−	0.605523i	$-0.207036\pi$
$608$	−7.57783	−	2.75811i	−0.307322	−	0.111856i
$609$	0.561115	−	0.0989397i	0.0227375	−	0.00400924i
$610$	−37.1909	+	44.3224i	−1.50582	+	1.79456i
$611$	1.65983	−	1.97811i	0.0671494	−	0.0800256i
$612$	−4.83720	+	0.852929i	−0.195532	+	0.0344776i
$613$	−24.4090	−	8.88414i	−0.985869	−	0.358827i	−0.201750	−	0.979437i	$-0.564663\pi$
$613$	−24.4090	−	8.88414i	−0.985869	−	0.358827i	−0.784119	+	0.620610i	$0.786885\pi$
$614$	14.2185	−	39.0649i	0.573810	−	1.57653i
$615$	0.919966	+	0.531143i	0.0370966	+	0.0214177i
$616$	101.663	+	17.9259i	4.09610	+	0.722254i
$617$	−13.0464	+	10.9472i	−0.525229	+	0.440720i	−0.866450	−	0.499264i	$-0.833604\pi$
$617$	−13.0464	+	10.9472i	−0.525229	+	0.440720i	0.341221	+	0.939983i	$0.389160\pi$
$618$	7.01066	+	12.1428i	0.282010	+	0.488456i
$619$	2.04260	−	3.53788i	0.0820989	−	0.142199i	−0.822052	−	0.569412i	$-0.807171\pi$
$619$	2.04260	−	3.53788i	0.0820989	−	0.142199i	0.904151	+	0.427212i	$0.140504\pi$
$620$	−5.07721	−	28.7943i	−0.203906	−	1.15641i
$621$	−16.8533	+	9.73028i	−0.676301	+	0.390463i
$622$	54.3706	−	19.7893i	2.18006	−	0.793478i
$623$		−	8.53244i		−	0.341845i
$624$	−4.11400	−	11.3031i	−0.164692	−	0.452487i
$625$	−3.26352	+	18.5084i	−0.130541	+	0.740335i
$626$	−61.4887	−	51.5952i	−2.45758	−	2.06216i
$627$	9.39239	+	11.1934i	0.375096	+	0.447022i
$628$	−97.9629			−3.90915
$629$	−1.27691	−	4.73591i	−0.0509136	−	0.188833i
$630$	22.4519			0.894503
$631$	−23.5841	−	28.1064i	−0.938867	−	1.11890i	−0.992731	−	0.120350i	$-0.961598\pi$
$631$	−23.5841	−	28.1064i	−0.938867	−	1.11890i	0.0538642	−	0.998548i	$-0.482846\pi$
$632$	20.4618	+	17.1695i	0.813929	+	0.682967i
$633$	−2.25622	+	12.7957i	−0.0896768	+	0.508583i
$634$	7.65242	+	21.0249i	0.303916	+	0.835004i
$635$		−	4.07508i		−	0.161715i
$636$	−37.7269	+	13.7315i	−1.49597	+	0.544489i
$637$	−4.23219	+	2.44345i	−0.167685	+	0.0968131i
$638$	0.337521	+	1.91418i	0.0133626	+	0.0757831i
$639$	6.20738	−	10.7515i	0.245560	−	0.425323i
$640$	−14.6543	−	25.3819i	−0.579261	−	1.00331i
$641$	−24.6811	+	20.7099i	−0.974847	+	0.817993i	−0.983304	−	0.181971i	$-0.941752\pi$
$641$	−24.6811	+	20.7099i	−0.974847	+	0.817993i	0.00845730	+	0.999964i	$0.497308\pi$
$642$	26.5912	+	4.68875i	1.04947	+	0.185050i
$643$	19.5344	+	11.2782i	0.770363	+	0.444769i	0.833004	−	0.553267i	$-0.186619\pi$
$643$	19.5344	+	11.2782i	0.770363	+	0.444769i	−0.0626409	+	0.998036i	$0.519952\pi$
$644$	−16.6011	+	45.6110i	−0.654173	+	1.79733i
$645$	4.74857	+	1.72834i	0.186975	+	0.0680532i
$646$	−4.22991	+	0.745847i	−0.166423	+	0.0293450i
$647$	−5.02992	+	5.99443i	−0.197747	+	0.235665i	−0.855801	−	0.517305i	$-0.826935\pi$
$647$	−5.02992	+	5.99443i	−0.197747	+	0.235665i	0.658054	+	0.752970i	$0.271380\pi$
$648$	10.7816	−	12.8490i	0.423541	−	0.504756i
$649$	−57.4867	+	10.1365i	−2.25655	+	0.397891i
$650$	3.73262	+	1.35856i	0.146406	+	0.0532873i
$651$	−4.65920	+	12.8010i	−0.182608	+	0.501712i
$652$	−73.5599	−	42.4699i	−2.88083	−	1.66325i
$653$	33.1336	+	5.84235i	1.29662	+	0.228629i	0.779022	−	0.626996i	$-0.215716\pi$
$653$	33.1336	+	5.84235i	1.29662	+	0.228629i	0.517596	+	0.855625i	$0.326827\pi$
$654$	25.0992	−	21.0608i	0.981458	−	0.823541i
$655$	19.2806	+	33.3950i	0.753356	+	1.30485i
$656$	−1.30904	+	2.26732i	−0.0511093	+	0.0885239i
$657$	2.13444	+	12.1050i	0.0832725	+	0.472262i
$658$	11.7436	−	6.78015i	0.457812	−	0.264318i
$659$	25.7385	−	9.36806i	1.00263	−	0.364928i	0.212032	−	0.977263i	$-0.431992\pi$
$659$	25.7385	−	9.36806i	1.00263	−	0.364928i	0.790598	+	0.612335i	$0.209770\pi$
$660$		−	59.8874i		−	2.33111i
$661$	12.3983	+	34.0640i	0.482237	+	1.32493i	0.907571	+	0.419898i	$0.137934\pi$
$661$	12.3983	+	34.0640i	0.482237	+	1.32493i	−0.425334	+	0.905036i	$0.639844\pi$
$662$	6.52537	−	37.0072i	0.253616	−	1.43833i
$663$	−1.19644	−	1.00393i	−0.0464659	−	0.0389895i
$664$	−39.8530	−	47.4949i	−1.54660	−	1.84316i
$665$	13.4477			0.521479
$666$	−17.6059	−	12.2869i	−0.682214	−	0.476107i
$667$	−0.493548			−0.0191103
$668$	−42.3683	−	50.4926i	−1.63928	−	1.95362i
$669$	−13.5782	−	11.3935i	−0.524965	−	0.440498i
$670$	6.73333	−	38.1866i	0.260131	−	1.47528i
$671$	21.5434	+	59.1901i	0.831675	+	2.28501i
$672$		−	15.3989i		−	0.594026i
$673$	11.4951	−	4.18387i	0.443103	−	0.161276i	−0.110827	−	0.993840i	$-0.535350\pi$
$673$	11.4951	−	4.18387i	0.443103	−	0.161276i	0.553930	+	0.832564i	$0.313128\pi$
$674$	−65.1540	+	37.6167i	−2.50964	+	1.44894i
$675$	0.994724	+	5.64136i	0.0382869	+	0.217136i
$676$	23.1631	−	40.1196i	0.890887	−	1.54306i
$677$	0.924945	+	1.60205i	0.0355485	+	0.0615719i	0.883252	−	0.468898i	$-0.155349\pi$
$677$	0.924945	+	1.60205i	0.0355485	+	0.0615719i	−0.847704	+	0.530470i	$0.822015\pi$
$678$	−28.0146	+	23.5070i	−1.07589	+	0.902781i
$679$	−48.5280	−	8.55680i	−1.86234	−	0.328380i
$680$	8.23306	+	4.75336i	0.315723	+	0.182283i
$681$	1.46811	−	4.03360i	0.0562581	−	0.154568i
$682$	−43.6693	−	15.8943i	−1.67218	−	0.608625i
$683$	9.88984	−	1.74385i	0.378424	−	0.0667264i	0.0187992	−	0.999823i	$-0.494016\pi$
$683$	9.88984	−	1.74385i	0.378424	−	0.0667264i	0.359625	+	0.933097i	$0.382905\pi$
$684$	−8.27720	+	9.86438i	−0.316486	+	0.377174i
$685$	21.8420	−	26.0303i	0.834541	−	0.994568i
$686$	30.1735	−	5.32041i	1.15203	−	0.203134i
$687$	−2.66972	−	0.971699i	−0.101856	−	0.0370726i
$688$	−4.25960	+	11.7032i	−0.162396	+	0.446179i
$689$	9.68493	+	5.59160i	0.368967	+	0.213023i
$690$	21.8639	+	3.85519i	0.832343	+	0.146765i
$691$	5.08725	−	4.26871i	0.193528	−	0.162389i	−0.540875	−	0.841103i	$-0.681907\pi$
$691$	5.08725	−	4.26871i	0.193528	−	0.162389i	0.734403	+	0.678714i	$0.237462\pi$
$692$	17.0644	+	29.5563i	0.648690	+	1.12356i
$693$	12.2213	−	21.1679i	0.464248	−	0.804100i
$694$	2.86530	+	16.2499i	0.108765	+	0.616839i
$695$	−14.6095	+	8.43482i	−0.554171	+	0.319951i
$696$	0.992298	−	0.361167i	0.0376130	−	0.0136900i
$697$			0.339943i			0.0128763i
$698$	26.8052	+	73.6466i	1.01459	+	2.78756i
$699$	−2.20361	+	12.4973i	−0.0833481	+	0.472690i
$700$	10.9450	+	9.18393i	0.413681	+	0.347120i
$701$	10.4394	+	12.4412i	0.394290	+	0.469897i	0.926270	−	0.376860i	$-0.122996\pi$
$701$	10.4394	+	12.4412i	0.394290	+	0.469897i	−0.531980	+	0.846757i	$0.678552\pi$
$702$	−21.4762			−0.810568
$703$	−10.5452	−	7.35930i	−0.397718	−	0.277561i
$704$	−15.3570			−0.578789
$705$	−2.73078	−	3.25442i	−0.102847	−	0.122568i
$706$	37.1838	+	31.2009i	1.39943	+	1.17426i
$707$	9.24527	−	52.4325i	0.347704	−	1.97193i
$708$	20.0848	+	55.1826i	0.754834	+	2.07389i
$709$		−	18.3839i		−	0.690421i	−0.938525	−	0.345210i	$-0.887808\pi$
$709$		−	18.3839i		−	0.690421i	0.938525	−	0.345210i	$-0.112192\pi$
$710$	−41.8107	+	15.2179i	−1.56913	+	0.571116i
$711$	5.47719	−	3.16226i	0.205411	−	0.118594i
$712$	−2.74599	−	15.5733i	−0.102911	−	0.583635i
$713$	5.90009	−	10.2193i	0.220960	−	0.382714i
$714$	−4.10091	−	7.10299i	−0.153473	−	0.265823i
$715$	−12.7788	+	10.7227i	−0.477900	+	0.401005i
$716$	14.0734	+	2.48152i	0.525948	+	0.0927389i
$717$	−0.0511464	−	0.0295294i	−0.00191010	−	0.00110279i
$718$	−10.6091	+	29.1483i	−0.395929	+	1.08780i
$719$	27.7891	+	10.1144i	1.03636	+	0.377203i	0.803498	−	0.595307i	$-0.202970\pi$
$719$	27.7891	+	10.1144i	1.03636	+	0.377203i	0.232859	+	0.972511i	$0.425192\pi$
$720$	17.0724	−	3.01032i	0.636250	−	0.112188i
$721$	9.03003	−	10.7616i	0.336296	−	0.400782i
$722$	23.5333	−	28.0459i	0.875818	−	1.04376i
$723$	−1.29974	+	0.229180i	−0.0483379	+	0.00852328i
$724$	82.9809	+	30.2026i	3.08396	+	1.12247i
$725$	−0.0496888	+	0.136519i	−0.00184539	+	0.00507018i
$726$	−52.0807	−	30.0688i	−1.93290	−	1.11596i
$727$	9.40598	+	1.65853i	0.348848	+	0.0615114i	0.345327	−	0.938482i	$-0.387768\pi$
$727$	9.40598	+	1.65853i	0.348848	+	0.0615114i	0.00352135	+	0.999994i	$0.498879\pi$
$728$	−22.1598	+	18.5942i	−0.821295	+	0.689149i
$729$	−12.5421	−	21.7236i	−0.464524	−	0.804578i
$730$	22.0266	−	38.1512i	0.815241	−	1.41204i
$731$	0.280809	+	1.59255i	0.0103861	+	0.0589026i
$732$	54.8775	−	31.6835i	2.02833	−	1.17106i
$733$	11.7162	−	4.26436i	0.432749	−	0.157508i	−0.116455	−	0.993196i	$-0.537153\pi$
$733$	11.7162	−	4.26436i	0.432749	−	0.157508i	0.549204	+	0.835688i	$0.314931\pi$
$734$			68.4614i			2.52696i
$735$	2.74985	+	7.55516i	0.101430	+	0.278676i
$736$	−2.31628	+	13.1363i	−0.0853790	+	0.484209i
$737$	−32.3376	−	27.1345i	−1.19117	−	0.999511i
$738$	0.956426	+	1.13982i	0.0352065	+	0.0419575i
$739$	42.1916			1.55204			0.776022	−	0.630706i	$-0.217235\pi$
$739$	42.1916			1.55204			0.776022	+	0.630706i	$0.217235\pi$
$740$	13.7202	+	50.8865i	0.504363	+	1.87063i
$741$	−4.09458			−0.150418
$742$	37.7492	+	44.9877i	1.38582	+	1.65155i
$743$	−14.1347	−	11.8604i	−0.518551	−	0.435116i	0.345575	−	0.938391i	$-0.387684\pi$
$743$	−14.1347	−	11.8604i	−0.518551	−	0.435116i	−0.864126	+	0.503275i	$0.832128\pi$
$744$	−4.38415	+	24.8638i	−0.160731	+	0.911550i
$745$	−5.78285	−	15.8882i	−0.211867	−	0.582100i
$746$		−	21.4961i		−	0.787027i
$747$	−13.7948	+	5.02090i	−0.504725	+	0.183705i
$748$	16.5970	−	9.58231i	0.606848	−	0.350364i
$749$	−4.69775	−	26.6423i	−0.171652	−	0.973488i
$750$	19.1399	−	33.1513i	0.698890	−	1.21051i
$751$	−17.8761	−	30.9623i	−0.652307	−	1.12983i	−0.982562	−	0.185937i	$-0.940468\pi$
$751$	−17.8761	−	30.9623i	−0.652307	−	1.12983i	0.330254	−	0.943892i	$-0.392865\pi$
$752$	8.02073	−	6.73019i	0.292486	−	0.245425i
$753$	4.91204	+	0.866125i	0.179005	+	0.0315633i
$754$	−0.471697	−	0.272334i	−0.0171782	−	0.00991783i
$755$	−8.09598	+	22.2435i	−0.294643	+	0.809525i
$756$	−72.5899	−	26.4206i	−2.64007	−	0.960907i
$757$	36.2457	−	6.39109i	1.31737	−	0.232288i	0.529595	−	0.848250i	$-0.322344\pi$
$757$	36.2457	−	6.39109i	1.31737	−	0.232288i	0.787776	+	0.615962i	$0.211233\pi$
$758$	4.01632	−	4.78647i	0.145879	−	0.173852i
$759$	15.5359	−	18.5150i	0.563918	−	0.672051i
$760$	24.5445	−	4.32787i	0.890324	−	0.156988i
$761$	11.1361	+	4.05322i	0.403684	+	0.146929i	0.535879	−	0.844295i	$-0.319980\pi$
$761$	11.1361	+	4.05322i	0.403684	+	0.146929i	−0.132195	+	0.991224i	$0.542202\pi$
$762$	−2.22856	+	6.12292i	−0.0807322	+	0.221810i
$763$	−28.4296	−	16.4138i	−1.02922	−	0.594220i
$764$	34.7007	+	6.11867i	1.25543	+	0.221366i
$765$	1.72433	−	1.44689i	0.0623434	−	0.0523123i
$766$	10.9349	+	18.9398i	0.395093	+	0.684322i
$767$	8.17875	−	14.1660i	0.295318	−	0.511505i
$768$	6.90372	+	39.1530i	0.249117	+	1.41281i
$769$	−35.2131	+	20.3303i	−1.26982	+	0.733129i	−0.974953	−	0.222410i	$-0.928607\pi$
$769$	−35.2131	+	20.3303i	−1.26982	+	0.733129i	−0.294863	+	0.955539i	$0.595274\pi$
$770$	−82.3181	+	29.9613i	−2.96654	+	1.07973i
$771$			21.0968i			0.759781i
$772$	9.32710	+	25.6260i	0.335690	+	0.922300i
$773$	−3.57314	+	20.2643i	−0.128517	+	0.728856i	0.850640	+	0.525749i	$0.176215\pi$
$773$	−3.57314	+	20.2643i	−0.128517	+	0.728856i	−0.979157	+	0.203107i	$0.934896\pi$
$774$	5.42217	+	4.54974i	0.194896	+	0.163537i
$775$	−2.23271	−	2.66084i	−0.0802015	−	0.0955804i
$776$	−91.3266			−3.27844
$777$	6.31837	−	23.7285i	0.226670	−	0.851256i
$778$	−76.8116			−2.75383
$779$	0.572857	+	0.682705i	0.0205247	+	0.0244604i
$780$	12.8555	+	10.7871i	0.460302	+	0.386239i
$781$	−8.41135	+	47.7032i	−0.300982	+	1.70695i
$782$	2.42992	+	6.67615i	0.0868938	+	0.238739i
$783$		−	0.785482i		−	0.0280708i
$784$	−18.6202	+	6.77719i	−0.665007	+	0.242043i
$785$	38.8791	−	22.4469i	1.38766	−	0.801163i
$786$	−10.7067	−	60.7210i	−0.381897	−	2.16584i
$787$	−10.1490	+	17.5786i	−0.361773	+	0.626609i	−0.988253	−	0.152828i	$-0.951162\pi$
$787$	−10.1490	+	17.5786i	−0.361773	+	0.626609i	0.626480	+	0.779438i	$0.284495\pi$
$788$	10.1684	+	17.6122i	0.362235	+	0.627409i
$789$	13.4684	−	11.3014i	0.479489	−	0.402339i
$790$	−22.3225	−	3.93605i	−0.794197	−	0.140038i
$791$	31.7317	+	18.3203i	1.12825	+	0.651395i
$792$	15.4937	−	42.5685i	0.550543	−	1.51261i
$793$	−16.5863	−	6.03693i	−0.588997	−	0.214378i
$794$	−7.38488	+	1.30215i	−0.262080	+	0.0462117i
$795$	11.8265	−	14.0943i	0.419444	−	0.499874i
$796$	−54.0260	+	64.3857i	−1.91490	+	2.28209i
$797$	0.177449	−	0.0312890i	0.00628557	−	0.00110831i	−0.170505	−	0.985357i	$-0.554540\pi$
$797$	0.177449	−	0.0312890i	0.00628557	−	0.00110831i	0.176790	+	0.984249i	$0.443429\pi$
$798$	−20.2055	−	7.35420i	−0.715267	−	0.260336i
$799$	0.464982	−	1.27753i	0.0164499	−	0.0451956i
$800$	3.40038	+	1.96321i	0.120222	+	0.0694100i
$801$	−3.68737	−	0.650184i	−0.130287	−	0.0229731i
$802$	−28.0321	+	23.5217i	−0.989849	+	0.830582i
$803$	−23.9796	−	41.5338i	−0.846220	−	1.46570i
$804$	−21.2336	+	36.7777i	−0.748853	+	1.29705i
$805$	−3.86259	−	21.9058i	−0.136138	−	0.772079i
$806$	11.2777	−	6.51121i	0.397241	−	0.229347i
$807$	−7.97125	+	2.90130i	−0.280601	+	0.102130i
$808$		−	98.6746i		−	3.47136i
$809$	−8.22721	−	22.6041i	−0.289253	−	0.794717i	−0.996171	−	0.0874217i	$-0.972137\pi$
$809$	−8.22721	−	22.6041i	−0.289253	−	0.794717i	0.706918	−	0.707296i	$-0.250085\pi$
$810$	−2.47164	+	14.0174i	−0.0868445	+	0.492520i
$811$	31.4326	+	26.3751i	1.10375	+	0.926154i	0.997671	−	0.0682040i	$-0.0217269\pi$
$811$	31.4326	+	26.3751i	1.10375	+	0.926154i	0.106076	+	0.994358i	$0.466171\pi$
$812$	−1.25931	−	1.50079i	−0.0441931	−	0.0526673i
$813$	−5.71501			−0.200434
$814$	80.9472	+	21.5544i	2.83720	+	0.755481i
$815$	38.9256			1.36350
$816$	−4.07069	−	4.85126i	−0.142503	−	0.169828i
$817$	3.24764	+	2.72510i	0.113621	+	0.0953390i
$818$	12.8744	−	73.0144i	0.450143	−	2.55289i
$819$	2.34261	+	6.43625i	0.0818572	+	0.224901i
$820$		−	3.65263i		−	0.127555i
$821$	9.77043	−	3.55615i	0.340991	−	0.124110i	−0.165848	−	0.986151i	$-0.553036\pi$
$821$	9.77043	−	3.55615i	0.340991	−	0.124110i	0.506839	+	0.862041i	$0.330814\pi$
$822$	−47.0536	+	27.1664i	−1.64118	+	0.947536i
$823$	−1.48559	−	8.42523i	−0.0517846	−	0.293685i	0.947906	−	0.318549i	$-0.103196\pi$
$823$	−1.48559	−	8.42523i	−0.0517846	−	0.293685i	−0.999691	+	0.0248645i	$0.992085\pi$
$824$	13.0181	−	22.5480i	0.453507	−	0.785498i
$825$	−3.55726	−	6.16136i	−0.123848	−	0.214511i
$826$	65.8029	−	55.2152i	2.28957	−	1.92118i
$827$	−28.5159	−	5.02812i	−0.991595	−	0.174845i	−0.345761	−	0.938323i	$-0.612379\pi$
$827$	−28.5159	−	5.02812i	−0.991595	−	0.174845i	−0.645834	+	0.763478i	$0.723490\pi$
$828$	18.4462	+	10.6499i	0.641050	+	0.370110i
$829$	2.47167	−	6.79085i	0.0858446	−	0.235856i	−0.889341	−	0.457244i	$-0.848837\pi$
$829$	2.47167	−	6.79085i	0.0858446	−	0.235856i	0.975186	+	0.221388i	$0.0710588\pi$
$830$	49.4400	+	17.9947i	1.71609	+	0.624605i
$831$	−10.8816	+	1.91871i	−0.377477	+	0.0665594i
$832$	2.76615	−	3.29657i	0.0958990	−	0.114288i
$833$	−1.65383	+	1.97095i	−0.0573017	+	0.0682895i
$834$	26.5640	−	4.68395i	0.919836	−	0.162192i
$835$	28.3846	+	10.3312i	0.982291	+	0.357525i
$836$	17.1840	−	47.2127i	0.594322	−	1.63289i
$837$	16.2639	+	9.38999i	0.562164	+	0.324566i
$838$	−85.7422	−	15.1187i	−2.96191	−	0.522266i
$839$	2.80572	−	2.35428i	0.0968643	−	0.0812788i	−0.593069	−	0.805151i	$-0.702084\pi$
$839$	2.80572	−	2.35428i	0.0968643	−	0.0812788i	0.689934	+	0.723872i	$0.257640\pi$
$840$	23.7960	+	41.2160i	0.821042	+	1.42209i
$841$	−14.4900	+	25.0975i	−0.499657	+	0.865431i
$842$	0.697083	+	3.95336i	0.0240231	+	0.136242i
$843$	−1.07513	+	0.620726i	−0.0370294	+	0.0213789i
$844$	41.9819	−	15.2802i	1.44508	−	0.525965i
$845$			21.2300i			0.730335i
$846$	−2.03523	−	5.59175i	−0.0699727	−	0.192248i
$847$	−10.4628	+	59.3377i	−0.359507	+	2.03887i
$848$	34.7363	+	29.1473i	1.19285	+	1.00092i
$849$	5.13456	+	6.11914i	0.176218	+	0.210008i
$850$	2.09130			0.0717311
$851$	−8.95916	+	19.2915i	−0.307116	+	0.661305i
$852$	48.7300			1.66946
$853$	−20.4726	−	24.3983i	−0.700968	−	0.835381i	0.291667	−	0.956520i	$-0.405790\pi$
$853$	−20.4726	−	24.3983i	−0.700968	−	0.835381i	−0.992636	+	0.121138i	$0.961345\pi$
$854$	−71.0055	−	59.5807i	−2.42976	−	2.03881i
$855$	1.02473	−	5.81154i	0.0350451	−	0.198751i
$856$	−17.1486	−	47.1153i	−0.586126	−	1.61037i
$857$			2.91354i			0.0995246i	0.998761	+	0.0497623i	$0.0158464\pi$
$857$			2.91354i			0.0995246i	−0.998761	+	0.0497623i	$0.984154\pi$
$858$	25.0644	−	9.12270i	0.855685	−	0.311444i
$859$	−27.9477	+	16.1356i	−0.953564	+	0.550541i	−0.894186	−	0.447695i	$-0.852245\pi$
$859$	−27.9477	+	16.1356i	−0.953564	+	0.550541i	−0.0593778	+	0.998236i	$0.518912\pi$
$860$	−3.01725	−	17.1117i	−0.102887	−	0.583503i
$861$	−0.850903	+	1.47381i	−0.0289987	+	0.0502272i
$862$	20.4003	+	35.3344i	0.694837	+	1.20349i
$863$	−13.5923	+	11.4053i	−0.462686	+	0.388240i	−0.844118	−	0.536157i	$-0.819875\pi$
$863$	−13.5923	+	11.4053i	−0.462686	+	0.388240i	0.381432	+	0.924397i	$0.375431\pi$
$864$	−20.9063	−	3.68635i	−0.711248	−	0.125412i
$865$	−13.5449	−	7.82013i	−0.460539	−	0.265893i
$866$	18.5138	−	50.8662i	0.629123	−	1.72850i
$867$	19.4286	+	7.07142i	0.659828	+	0.240158i
$868$	46.1291	−	8.13381i	1.56572	−	0.276080i
$869$	−15.8618	+	18.9033i	−0.538074	+	0.641252i
$870$	−0.576001	+	0.686452i	−0.0195283	+	0.0232729i
$871$	11.6495	−	2.05412i	0.394727	−	0.0696011i
$872$	−57.1718	−	20.8088i	−1.93608	−	0.704675i
$873$	−7.39581	+	20.3198i	−0.250310	+	0.687721i
$874$	16.1303	+	9.31286i	0.545617	+	0.315012i
$875$	−37.7706	−	6.65997i	−1.27688	−	0.225148i
$876$	−36.9595	+	31.0127i	−1.24875	+	1.04782i
$877$	1.59299	+	2.75913i	0.0537913	+	0.0931693i	0.891667	−	0.452691i	$-0.149536\pi$
$877$	1.59299	+	2.75913i	0.0537913	+	0.0931693i	−0.837876	+	0.545861i	$0.816203\pi$
$878$	−3.01423	+	5.22079i	−0.101725	+	0.176193i
$879$	0.955106	+	5.41668i	0.0322149	+	0.182700i
$880$	−58.5775	+	33.8197i	−1.97465	+	1.14006i
$881$	5.23136	−	1.90406i	0.176249	−	0.0641493i	−0.252388	−	0.967626i	$-0.581216\pi$
$881$	5.23136	−	1.90406i	0.176249	−	0.0641493i	0.428637	+	0.903477i	$0.358994\pi$
$882$			11.2616i			0.379198i
$883$	4.46487	+	12.2671i	0.150255	+	0.412822i	0.991870	−	0.127256i	$-0.0406170\pi$
$883$	4.46487	+	12.2671i	0.150255	+	0.412822i	−0.841615	+	0.540078i	$0.818395\pi$
$884$	−0.932549	+	5.28875i	−0.0313650	+	0.177880i
$885$	−20.6155	−	17.2985i	−0.692984	−	0.581482i
$886$	−10.5921	−	12.6232i	−0.355850	−	0.424085i
$887$	4.57250			0.153529			0.0767647	−	0.997049i	$-0.475541\pi$
$887$	4.57250			0.153529			0.0767647	+	0.997049i	$0.475541\pi$
$888$	3.89566	−	45.3425i	0.130730	−	1.52159i
$889$	6.52838			0.218955
$890$	8.62575	+	10.2798i	0.289136	+	0.344578i
$891$	11.8703	+	9.96038i	0.397671	+	0.333685i
$892$	−10.5834	+	60.0213i	−0.354358	+	2.00966i
$893$	−1.21901	−	3.34921i	−0.0407927	−	0.112077i
$894$			27.0350i			0.904185i
$895$	−6.15401	+	2.23988i	−0.205706	+	0.0748708i
$896$	40.6625	−	23.4765i	1.35844	−	0.784295i
$897$	1.17609	+	6.66994i	0.0392685	+	0.222703i
$898$	−48.9131	+	84.7200i	−1.63225	+	2.82714i
$899$	0.238144	+	0.412477i	0.00794255	+	0.0137569i
$900$	4.80294	−	4.03015i	0.160098	−	0.134338i
$901$	5.79837	+	1.02241i	0.193172	+	0.0340614i
$902$	−5.02773	−	2.90276i	−0.167405	−	0.0966513i
$903$	−2.76884	+	7.60732i	−0.0921411	+	0.253156i
$904$	63.8123	+	23.2258i	2.12237	+	0.772478i
$905$	−39.8536	+	7.02727i	−1.32478	+	0.233594i
$906$	24.3289	−	28.9940i	0.808272	−	0.963261i
$907$	8.33097	−	9.92846i	0.276625	−	0.329669i	−0.609787	−	0.792565i	$-0.708745\pi$
$907$	8.33097	−	9.92846i	0.276625	−	0.329669i	0.886413	+	0.462896i	$0.153190\pi$
$908$	−14.5353	+	2.56296i	−0.482369	+	0.0850548i
$909$	−21.9547	−	7.99086i	−0.728191	−	0.265040i
$910$	8.39581	−	23.0673i	0.278318	−	0.764673i
$911$	−5.79091	−	3.34338i	−0.191861	−	0.110771i	0.400992	−	0.916081i	$-0.368665\pi$
$911$	−5.79091	−	3.34338i	−0.191861	−	0.110771i	−0.592854	+	0.805310i	$0.701999\pi$
$912$	−16.3503	−	2.88300i	−0.541412	−	0.0954655i
$913$	43.8774	−	36.8175i	1.45213	−	1.21848i
$914$	−19.3058	−	33.4386i	−0.638578	−	1.10605i
$915$	−14.5197	+	25.1489i	−0.480007	+	0.831396i
$916$	1.69635	+	9.62047i	0.0560489	+	0.317869i
$917$	−53.4996	+	30.8880i	−1.76671	+	1.02001i
$918$	−10.6251	+	3.86721i	−0.350680	+	0.127637i
$919$			1.26433i			0.0417065i	0.999783	+	0.0208533i	$0.00663828\pi$
$919$			1.26433i			0.0417065i	−0.999783	+	0.0208533i	$0.993362\pi$
$920$	−14.0999	−	38.7392i	−0.464860	−	1.27719i
$921$	3.62318	−	20.5481i	0.119388	−	0.677082i
$922$	31.3311	+	26.2899i	1.03184	+	0.865812i
$923$	−8.72498	−	10.3980i	−0.287186	−	0.342255i
$924$	95.9410			3.15623
$925$	4.43419	+	4.42037i	0.145795	+	0.145341i
$926$	21.0222			0.690833
$927$	−3.96261	−	4.72246i	−0.130149	−	0.155106i
$928$	−0.412434	−	0.346073i	−0.0135388	−	0.0113604i
$929$	−3.85014	+	21.8352i	−0.126319	+	0.716391i	0.854197	+	0.519950i	$0.174049\pi$
$929$	−3.85014	+	21.8352i	−0.126319	+	0.716391i	−0.980516	+	0.196441i	$0.937062\pi$
$930$	−7.32769	−	20.1326i	−0.240284	−	0.660176i
$931$			6.74521i			0.221065i
$932$	41.0029	−	14.9238i	1.34309	−	0.488846i
$933$	25.1494	−	14.5200i	0.823355	−	0.475364i
$934$	2.92031	+	16.5619i	0.0955556	+	0.541923i
$935$	−4.39131	+	7.60598i	−0.143611	+	0.248742i
$936$	6.34707	+	10.9935i	0.207461	+	0.359332i
$937$	14.4280	−	12.1065i	0.471342	−	0.395503i	−0.375942	−	0.926643i	$-0.622681\pi$
$937$	14.4280	−	12.1065i	0.471342	−	0.395503i	0.847284	+	0.531140i	$0.178236\pi$
$938$	61.1759	+	10.7870i	1.99746	+	0.352207i
$939$	−34.8892	−	20.1433i	−1.13857	−	0.657352i
$940$	−4.99615	+	13.7268i	−0.162956	+	0.447719i
$941$	−16.9915	−	6.18442i	−0.553908	−	0.201606i	0.0498737	−	0.998756i	$-0.484118\pi$
$941$	−16.9915	−	6.18442i	−0.553908	−	0.201606i	−0.603782	+	0.797149i	$0.706340\pi$
$942$	−70.6925	+	12.4650i	−2.30329	+	0.406132i
$943$	0.947561	−	1.12926i	0.0308568	−	0.0367737i
$944$	42.6333	−	50.8083i	1.38759	−	1.65367i
$945$	34.8631	−	6.14731i	1.13410	−	0.199972i
$946$	−25.9515	−	9.44557i	−0.843756	−	0.307102i
$947$	0.896201	−	2.46229i	0.0291226	−	0.0800138i	−0.924279	−	0.381717i	$-0.875333\pi$
$947$	0.896201	−	2.46229i	0.0291226	−	0.0800138i	0.953402	+	0.301703i	$0.0975551\pi$
$948$	21.4989	+	12.4124i	0.698251	+	0.403135i
$949$	13.2350	+	2.33369i	0.429626	+	0.0757547i
$950$	4.19995	−	3.52417i	0.136264	−	0.114339i
$951$	5.61482	+	9.72516i	0.182073	+	0.315360i
$952$	−7.61500	+	13.1896i	−0.246803	+	0.427476i
$953$	7.73875	+	43.8886i	0.250683	+	1.42169i	0.806916	+	0.590666i	$0.201135\pi$
$953$	7.73875	+	43.8886i	0.250683	+	1.42169i	−0.556234	+	0.831026i	$0.687754\pi$
$954$	22.3184	−	12.8855i	0.722585	−	0.417185i
$955$	−15.1739	+	5.52285i	−0.491016	+	0.178715i
$956$			0.203071i			0.00656780i
$957$	0.333658	+	0.916718i	0.0107856	+	0.0296333i
$958$	15.4214	−	87.4592i	0.498244	−	2.82568i
$959$	41.7012	+	34.9915i	1.34660	+	1.12993i
$960$	−4.55092	−	5.42358i	−0.146880	−	0.175045i
$961$	19.6125			0.632661
$962$	−19.2073	+	13.4938i	−0.619269	+	0.435059i
$963$	−11.8717			−0.382560
$964$	2.91701	+	3.47636i	0.0939506	+	0.111966i
$965$	−9.57355	−	8.03316i	−0.308184	−	0.258597i
$966$	−6.17610	+	35.0264i	−0.198713	+	1.12696i
$967$	6.97181	+	19.1549i	0.224198	+	0.615980i	0.999885	−	0.0151377i	$-0.00481867\pi$
$967$	6.97181	+	19.1549i	0.224198	+	0.615980i	−0.775687	+	0.631118i	$0.782596\pi$
$968$			111.670i			3.58920i
$969$	−2.02574	+	0.737310i	−0.0650762	+	0.0236858i
$970$	67.1163	−	38.7496i	2.15497	−	1.24417i
$971$	7.13666	+	40.4740i	0.229026	+	1.29887i	0.854837	+	0.518897i	$0.173657\pi$
$971$	7.13666	+	40.4740i	0.229026	+	1.29887i	−0.625810	+	0.779975i	$0.715232\pi$
$972$	−28.5035	+	49.3694i	−0.914249	+	1.58353i
$973$	−13.5128	−	23.4048i	−0.433200	−	0.750324i
$974$	14.0424	−	11.7829i	0.449947	−	0.377550i
$975$	1.96335	+	0.346192i	0.0628777	+	0.0110870i
$976$	−61.9811	−	35.7848i	−1.98397	−	1.14544i
$977$	−9.00892	+	24.7518i	−0.288221	+	0.791881i	0.708095	+	0.706118i	$0.249555\pi$
$977$	−9.00892	+	24.7518i	−0.288221	+	0.791881i	−0.996316	+	0.0857630i	$0.972667\pi$
$978$	−58.4867	−	21.2874i	−1.87020	−	0.680696i
$979$	14.3871	−	2.53684i	0.459815	−	0.0810778i
$980$	17.7701	−	21.1776i	0.567645	−	0.676493i
$981$	−9.25975	+	11.0353i	−0.295641	+	0.352331i
$982$	−55.5870	+	9.80149i	−1.77385	+	0.312778i
$983$	35.2068	+	12.8142i	1.12292	+	0.408710i	0.835718	−	0.549159i	$-0.185052\pi$
$983$	35.2068	+	12.8142i	1.12292	+	0.408710i	0.287204	+	0.957869i	$0.407274\pi$
$984$	−1.07874	+	2.96382i	−0.0343891	+	0.0944832i
$985$	−8.07120	−	4.65991i	−0.257170	−	0.148477i
$986$	−0.282405	−	0.0497956i	−0.00899361	−	0.00158582i
$987$	5.21365	−	4.37478i	0.165952	−	0.139251i
$988$	7.03954	+	12.1928i	0.223958	+	0.387906i
$989$	3.50627	−	6.07303i	0.111493	−	0.193111i
$990$	6.67532	+	37.8576i	0.212156	+	1.20319i
$991$	49.3800	−	28.5095i	1.56861	−	0.905635i	0.572275	−	0.820062i	$-0.306061\pi$
$991$	49.3800	−	28.5095i	1.56861	−	0.905635i	0.996332	−	0.0855733i	$-0.0272722\pi$
$992$	12.0961	−	4.40262i	0.384052	−	0.139783i
$993$		−	18.8605i		−	0.598521i
$994$	−24.3794	−	66.9818i	−0.773267	−	2.12453i
$995$	6.68852	−	37.9325i	0.212040	−	1.20254i
$996$	−44.1409	−	37.0386i	−1.39866	−	1.17361i
$997$	−7.64536	−	9.11139i	−0.242131	−	0.288560i	0.631269	−	0.775564i	$-0.282534\pi$
$997$	−7.64536	−	9.11139i	−0.242131	−	0.288560i	−0.873400	+	0.487003i	$0.838090\pi$
$998$	56.6934			1.79460
$999$	−30.7024	−	14.2585i	−0.971382	−	0.451119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.h.a.25.1	yes	18
3.2	odd	2		333.2.bl.d.136.3		18
4.3	odd	2		592.2.bq.d.321.2		18
5.2	odd	4		925.2.ba.a.99.6		36
5.3	odd	4		925.2.ba.a.99.1		36
5.4	even	2		925.2.bb.a.876.3		18
37.3	even	18	inner	37.2.h.a.3.1	✓	18
37.15	odd	36		1369.2.a.m.1.17		18
37.16	even	9		1369.2.b.g.1368.2		18
37.21	even	18		1369.2.b.g.1368.17		18
37.22	odd	36		1369.2.a.m.1.2		18
111.77	odd	18		333.2.bl.d.262.3		18
148.3	odd	18		592.2.bq.d.225.2		18
185.3	odd	36		925.2.ba.a.299.6		36
185.77	odd	36		925.2.ba.a.299.1		36
185.114	even	18		925.2.bb.a.151.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.3.1	✓	18	37.3	even	18	inner
37.2.h.a.25.1	yes	18	1.1	even	1	trivial
333.2.bl.d.136.3		18	3.2	odd	2
333.2.bl.d.262.3		18	111.77	odd	18
592.2.bq.d.225.2		18	148.3	odd	18
592.2.bq.d.321.2		18	4.3	odd	2
925.2.ba.a.99.1		36	5.3	odd	4
925.2.ba.a.99.6		36	5.2	odd	4
925.2.ba.a.299.1		36	185.77	odd	36
925.2.ba.a.299.6		36	185.3	odd	36
925.2.bb.a.151.3		18	185.114	even	18
925.2.bb.a.876.3		18	5.4	even	2
1369.2.a.m.1.2		18	37.22	odd	36
1369.2.a.m.1.17		18	37.15	odd	36
1369.2.b.g.1368.2		18	37.16	even	9
1369.2.b.g.1368.17		18	37.21	even	18

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.h (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61954 - 1.93010i) q^{2} +(-0.968719 - 0.812851i) q^{3} +(-0.755055 + 4.28213i) q^{4} +(-0.681528 - 1.87248i) q^{5} +3.18617i q^{6} +(2.99976 - 1.09182i) q^{7} +(5.12375 - 2.95820i) q^{8} +(-0.243256 - 1.37957i) q^{9} +O(q^{10})\)	\(q+(-1.61954 - 1.93010i) q^{2} +(-0.968719 - 0.812851i) q^{3} +(-0.755055 + 4.28213i) q^{4} +(-0.681528 - 1.87248i) q^{5} +3.18617i q^{6} +(2.99976 - 1.09182i) q^{7} +(5.12375 - 2.95820i) q^{8} +(-0.243256 - 1.37957i) q^{9} +(-2.51031 + 4.34798i) q^{10} +(2.73288 + 4.73349i) q^{11} +(4.21217 - 3.53443i) q^{12} +(-1.50836 - 0.265964i) q^{13} +(-6.96557 - 4.02158i) q^{14} +(-0.861842 + 2.36789i) q^{15} +(-5.83582 - 2.12407i) q^{16} +(-0.794131 + 0.140027i) q^{17} +(-2.26875 + 2.70379i) q^{18} +(-1.35888 + 1.61945i) q^{19} +(8.53281 - 1.50456i) q^{20} +(-3.79342 - 1.38069i) q^{21} +(4.71007 - 12.9408i) q^{22} +(3.02834 + 1.74842i) q^{23} +(-7.36805 - 1.29919i) q^{24} +(0.788506 - 0.661636i) q^{25} +(1.92951 + 3.34201i) q^{26} +(-2.78260 + 4.81961i) q^{27} +(2.41035 + 13.6698i) q^{28} +(-0.122232 + 0.0705708i) q^{29} +(5.96605 - 2.17146i) q^{30} -3.37454i q^{31} +(1.30466 + 3.58452i) q^{32} +(1.20023 - 6.80685i) q^{33} +(1.55639 + 1.30597i) q^{34} +(-4.08885 - 4.87290i) q^{35} +6.09119 q^{36} +(0.539604 + 6.05878i) q^{37} +5.32646 q^{38} +(1.24498 + 1.48371i) q^{39} +(-9.03117 - 7.57805i) q^{40} +(0.0732041 - 0.415161i) q^{41} +(3.47874 + 9.55775i) q^{42} -2.00540i q^{43} +(-22.3329 + 8.12851i) q^{44} +(-2.41745 + 1.39571i) q^{45} +(-1.52992 - 8.67663i) q^{46} +(-0.842972 + 1.46007i) q^{47} +(3.92672 + 6.80128i) q^{48} +(2.44419 - 2.05092i) q^{49} +(-2.55404 - 0.450346i) q^{50} +(0.883111 + 0.509864i) q^{51} +(2.27778 - 6.25815i) q^{52} +(-6.86119 - 2.49727i) q^{53} +(13.8088 - 2.43487i) q^{54} +(7.00085 - 8.34329i) q^{55} +(12.1402 - 14.4681i) q^{56} +(2.63275 - 0.464224i) q^{57} +(0.334169 + 0.121628i) q^{58} +(-3.65272 + 10.0358i) q^{59} +(-9.48888 - 5.47841i) q^{60} +(11.3492 + 2.00116i) q^{61} +(-6.51318 + 5.46521i) q^{62} +(-2.23597 - 3.87281i) q^{63} +(-1.40484 + 2.43325i) q^{64} +(0.529974 + 3.00563i) q^{65} +(-15.0817 + 8.70742i) q^{66} +(-7.25752 + 2.64152i) q^{67} -3.50630i q^{68} +(-1.51241 - 4.15532i) q^{69} +(-2.78310 + 15.7837i) q^{70} +(6.78889 + 5.69655i) q^{71} +(-5.32744 - 6.34900i) q^{72} -8.77446 q^{73} +(10.8201 - 10.8539i) q^{74} -1.30165 q^{75} +(-5.90867 - 7.04167i) q^{76} +(13.3662 + 11.2155i) q^{77} +(0.847405 - 4.80587i) q^{78} +(1.54413 + 4.24247i) q^{79} +12.3751i q^{80} +(2.66406 - 0.969637i) q^{81} +(-0.919858 + 0.531080i) q^{82} +(-1.81973 - 10.3202i) q^{83} +(8.77654 - 15.2014i) q^{84} +(0.803421 + 1.39157i) q^{85} +(-3.87061 + 3.24783i) q^{86} +(0.175772 + 0.0309934i) q^{87} +(28.0052 + 16.1688i) q^{88} +(0.914163 - 2.51164i) q^{89} +(6.60902 + 2.40549i) q^{90} +(-4.81510 + 0.849032i) q^{91} +(-9.77350 + 11.6476i) q^{92} +(-2.74300 + 3.26898i) q^{93} +(4.18331 - 0.737630i) q^{94} +(3.95851 + 1.44078i) q^{95} +(1.64984 - 4.53289i) q^{96} +(-13.3681 - 7.71809i) q^{97} +(-7.91695 - 1.39597i) q^{98} +(5.86542 - 4.92167i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9}+O(q^{10}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9	\( 18 q - 9 q^{2} - 9 q^{3} - 3 q^{4} - 3 q^{5} - 3 q^{7} - 3 q^{9} - 9 q^{10} + 9 q^{11} + 3 q^{12} + 9 q^{13} + 9 q^{14} - 15 q^{15} - 3 q^{16} - 15 q^{17} + 6 q^{18} + 6 q^{19} + 48 q^{20} - 12 q^{21} - 15 q^{22} - 9 q^{23} + 45 q^{24} + 21 q^{25} - 15 q^{26} + 21 q^{27} - 27 q^{28} - 18 q^{29} + 6 q^{30} + 6 q^{33} - 33 q^{34} - 12 q^{35} - 72 q^{36} + 6 q^{37} + 54 q^{38} - 6 q^{39} - 75 q^{40} - 24 q^{41} + 21 q^{42} + 18 q^{46} - 36 q^{47} + 3 q^{48} + 21 q^{49} + 3 q^{50} + 81 q^{51} + 51 q^{52} - 39 q^{53} + 45 q^{54} + 12 q^{55} + 81 q^{56} + 15 q^{57} + 33 q^{58} - 6 q^{59} - 18 q^{60} + 42 q^{61} - 24 q^{62} - 27 q^{63} + 6 q^{64} + 18 q^{65} - 81 q^{66} - 36 q^{69} - 12 q^{70} - 9 q^{71} - 63 q^{72} - 54 q^{73} + 15 q^{74} + 18 q^{75} - 69 q^{76} + 33 q^{77} - 45 q^{78} - 6 q^{79} - 45 q^{81} + 27 q^{82} - 24 q^{83} - 24 q^{84} + 6 q^{85} - 42 q^{86} + 21 q^{87} + 54 q^{88} + 18 q^{89} + 60 q^{90} - 3 q^{91} + 66 q^{92} + 66 q^{93} + 18 q^{94} - 15 q^{95} + 15 q^{96} - 9 q^{97} - 45 q^{98} + 60 q^{99}+O(q^{100}) \) 18 * q - 9 * q^2 - 9 * q^3 - 3 * q^4 - 3 * q^5 - 3 * q^7 - 3 * q^9 - 9 * q^10 + 9 * q^11 + 3 * q^12 + 9 * q^13 + 9 * q^14 - 15 * q^15 - 3 * q^16 - 15 * q^17 + 6 * q^18 + 6 * q^19 + 48 * q^20 - 12 * q^21 - 15 * q^22 - 9 * q^23 + 45 * q^24 + 21 * q^25 - 15 * q^26 + 21 * q^27 - 27 * q^28 - 18 * q^29 + 6 * q^30 + 6 * q^33 - 33 * q^34 - 12 * q^35 - 72 * q^36 + 6 * q^37 + 54 * q^38 - 6 * q^39 - 75 * q^40 - 24 * q^41 + 21 * q^42 + 18 * q^46 - 36 * q^47 + 3 * q^48 + 21 * q^49 + 3 * q^50 + 81 * q^51 + 51 * q^52 - 39 * q^53 + 45 * q^54 + 12 * q^55 + 81 * q^56 + 15 * q^57 + 33 * q^58 - 6 * q^59 - 18 * q^60 + 42 * q^61 - 24 * q^62 - 27 * q^63 + 6 * q^64 + 18 * q^65 - 81 * q^66 - 36 * q^69 - 12 * q^70 - 9 * q^71 - 63 * q^72 - 54 * q^73 + 15 * q^74 + 18 * q^75 - 69 * q^76 + 33 * q^77 - 45 * q^78 - 6 * q^79 - 45 * q^81 + 27 * q^82 - 24 * q^83 - 24 * q^84 + 6 * q^85 - 42 * q^86 + 21 * q^87 + 54 * q^88 + 18 * q^89 + 60 * q^90 - 3 * q^91 + 66 * q^92 + 66 * q^93 + 18 * q^94 - 15 * q^95 + 15 * q^96 - 9 * q^97 - 45 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

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