LMFDB - Embedded newform 37.2.h.a.4.1

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			4.1
Root			$0.660907i$ of defining polynomial
Character	$\chi$	$=$	37.4
Dual form			37.2.h.a.28.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.59056 - 0.456785i) q^{2} +(0.354362 + 2.00969i) q^{3} +(4.62296 + 1.68262i) q^{4} +(0.640888 + 0.763781i) q^{5} -5.36808i q^{6} +(-1.58572 + 1.33057i) q^{7} +(-6.65125 - 3.84010i) q^{8} +(-1.09419 + 0.398252i) q^{9} +O(q^{10})$	\(q+(-2.59056 - 0.456785i) q^{2} +(0.354362 + 2.00969i) q^{3} +(4.62296 + 1.68262i) q^{4} +(0.640888 + 0.763781i) q^{5} -5.36808i q^{6} +(-1.58572 + 1.33057i) q^{7} +(-6.65125 - 3.84010i) q^{8} +(-1.09419 + 0.398252i) q^{9} +(-1.31137 - 2.27137i) q^{10} +(0.884822 - 1.53256i) q^{11} +(-1.74334 + 9.88695i) q^{12} +(1.83841 - 5.05098i) q^{13} +(4.71567 - 2.72260i) q^{14} +(-1.30785 + 1.55864i) q^{15} +(7.93902 + 6.66163i) q^{16} +(0.448257 + 1.23158i) q^{17} +(3.01648 - 0.531886i) q^{18} +(-4.12204 + 0.726826i) q^{19} +(1.67765 + 4.60930i) q^{20} +(-3.23595 - 2.71529i) q^{21} +(-2.99223 + 3.56601i) q^{22} +(3.05179 - 1.76195i) q^{23} +(5.36045 - 14.7277i) q^{24} +(0.695618 - 3.94504i) q^{25} +(-7.06972 + 12.2451i) q^{26} +(1.87293 + 3.24402i) q^{27} +(-9.56954 + 3.48303i) q^{28} +(-0.525410 - 0.303345i) q^{29} +(4.10003 - 3.44034i) q^{30} -1.55107i q^{31} +(-7.65009 - 9.11702i) q^{32} +(3.39351 + 1.23514i) q^{33} +(-0.598670 - 3.39523i) q^{34} +(-2.03253 - 0.358390i) q^{35} -5.72849 q^{36} +(-6.03673 - 0.746918i) q^{37} +11.0104 q^{38} +(10.8023 + 1.90475i) q^{39} +(-1.32971 - 7.54117i) q^{40} +(2.15024 + 0.782625i) q^{41} +(7.14262 + 8.51224i) q^{42} +8.37985i q^{43} +(6.66921 - 5.59613i) q^{44} +(-1.00543 - 0.580485i) q^{45} +(-8.71067 + 3.17042i) q^{46} +(-1.79110 - 3.10228i) q^{47} +(-10.5745 + 18.3156i) q^{48} +(-0.471469 + 2.67384i) q^{49} +(-3.60408 + 9.90212i) q^{50} +(-2.31624 + 1.33728i) q^{51} +(16.9978 - 20.2571i) q^{52} +(-8.47562 - 7.11189i) q^{53} +(-3.37012 - 9.25934i) q^{54} +(1.73761 - 0.306387i) q^{55} +(15.6565 - 2.76067i) q^{56} +(-2.92139 - 8.02644i) q^{57} +(1.22254 + 1.02583i) q^{58} +(-6.76937 + 8.06742i) q^{59} +(-8.66875 + 5.00490i) q^{60} +(-1.41913 + 3.89904i) q^{61} +(-0.708506 + 4.01814i) q^{62} +(1.20517 - 2.08741i) q^{63} +(5.28982 + 9.16224i) q^{64} +(5.03605 - 1.83297i) q^{65} +(-8.22689 - 4.74979i) q^{66} +(3.77420 - 3.16693i) q^{67} +6.44777i q^{68} +(4.62240 + 5.50876i) q^{69} +(5.10169 + 1.85686i) q^{70} +(-1.05928 - 6.00749i) q^{71} +(8.80705 + 1.55292i) q^{72} +13.5583 q^{73} +(15.2973 + 4.69242i) q^{74} +8.17480 q^{75} +(-20.2790 - 3.57573i) q^{76} +(0.636103 + 3.60752i) q^{77} +(-27.1141 - 9.86871i) q^{78} +(-8.59215 - 10.2397i) q^{79} +10.3330i q^{80} +(-8.53173 + 7.15897i) q^{81} +(-5.21284 - 3.00964i) q^{82} +(1.39469 - 0.507624i) q^{83} +(-10.3909 - 17.9975i) q^{84} +(-0.653371 + 1.13167i) q^{85} +(3.82779 - 21.7085i) q^{86} +(0.423444 - 1.16340i) q^{87} +(-11.7704 + 6.79562i) q^{88} +(-4.42899 + 5.27827i) q^{89} +(2.33947 + 1.96305i) q^{90} +(3.80551 + 10.4556i) q^{91} +(17.0730 - 3.01043i) q^{92} +(3.11716 - 0.549640i) q^{93} +(3.22288 + 8.85480i) q^{94} +(-3.19690 - 2.68252i) q^{95} +(15.6114 - 18.6050i) q^{96} +(-6.55603 + 3.78513i) q^{97} +(2.44274 - 6.71137i) q^{98} +(-0.357818 + 2.02929i) 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 $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−2.59056	−	0.456785i	−1.83180	−	0.322996i	−0.852088	−	0.523398i	$-0.824664\pi$
$2$	−2.59056	−	0.456785i	−1.83180	−	0.322996i	−0.979714	+	0.200402i	$0.935775\pi$
$3$	0.354362	+	2.00969i	0.204591	+	1.16029i	0.898082	+	0.439828i	$0.144961\pi$
$3$	0.354362	+	2.00969i	0.204591	+	1.16029i	−0.693491	+	0.720465i	$0.743928\pi$
$4$	4.62296	+	1.68262i	2.31148	+	0.841310i
$5$	0.640888	+	0.763781i	0.286614	+	0.341573i	0.890071	−	0.455823i	$-0.150655\pi$
$5$	0.640888	+	0.763781i	0.286614	+	0.341573i	−0.603457	+	0.797396i	$0.706210\pi$
$6$		−	5.36808i		−	2.19151i
$7$	−1.58572	+	1.33057i	−0.599344	+	0.502909i	−0.891235	−	0.453542i	$-0.850160\pi$
$7$	−1.58572	+	1.33057i	−0.599344	+	0.502909i	0.291891	+	0.956452i	$0.405716\pi$
$8$	−6.65125	−	3.84010i	−2.35157	−	1.35768i
$9$	−1.09419	+	0.398252i	−0.364729	+	0.132751i
$10$	−1.31137	−	2.27137i	−0.414693	−	0.718269i
$11$	0.884822	−	1.53256i	0.266784	−	0.462083i	−0.701246	−	0.712920i	$-0.747372\pi$
$11$	0.884822	−	1.53256i	0.266784	−	0.462083i	0.968029	+	0.250837i	$0.0807057\pi$
$12$	−1.74334	+	9.88695i	−0.503258	+	2.85412i
$13$	1.83841	−	5.05098i	0.509882	−	1.40089i	−0.371476	−	0.928442i	$-0.621148\pi$
$13$	1.83841	−	5.05098i	0.509882	−	1.40089i	0.881359	−	0.472448i	$-0.156629\pi$
$14$	4.71567	−	2.72260i	1.26032	−	0.727644i
$15$	−1.30785	+	1.55864i	−0.337686	+	0.402439i
$16$	7.93902	+	6.66163i	1.98476	+	1.66541i
$17$	0.448257	+	1.23158i	0.108718	+	0.298701i	0.982107	−	0.188322i	$-0.0603049\pi$
$17$	0.448257	+	1.23158i	0.108718	+	0.298701i	−0.873389	+	0.487023i	$0.838083\pi$
$18$	3.01648	−	0.531886i	0.710990	−	0.125367i
$19$	−4.12204	+	0.726826i	−0.945660	+	0.166745i	−0.625154	−	0.780501i	$-0.714964\pi$
$19$	−4.12204	+	0.726826i	−0.945660	+	0.166745i	−0.320506	+	0.947247i	$0.603853\pi$
$20$	1.67765	+	4.60930i	0.375133	+	1.03067i
$21$	−3.23595	−	2.71529i	−0.706142	−	0.592524i
$22$	−2.99223	+	3.56601i	−0.637946	+	0.760275i
$23$	3.05179	−	1.76195i	0.636341	−	0.367392i	−0.146862	−	0.989157i	$-0.546917\pi$
$23$	3.05179	−	1.76195i	0.636341	−	0.367392i	0.783204	+	0.621765i	$0.213584\pi$
$24$	5.36045	−	14.7277i	1.09420	−	3.00628i
$25$	0.695618	−	3.94504i	0.139124	−	0.789009i
$26$	−7.06972	+	12.2451i	−1.38649	+	2.40146i
$27$	1.87293	+	3.24402i	0.360446	+	0.624311i
$28$	−9.56954	+	3.48303i	−1.80847	+	0.658231i
$29$	−0.525410	−	0.303345i	−0.0975661	−	0.0563298i	0.450423	−	0.892815i	$-0.351273\pi$
$29$	−0.525410	−	0.303345i	−0.0975661	−	0.0563298i	−0.547989	+	0.836485i	$0.684607\pi$
$30$	4.10003	−	3.44034i	0.748560	−	0.628117i
$31$		−	1.55107i		−	0.278580i	−0.990252	−	0.139290i	$-0.955518\pi$
$31$		−	1.55107i		−	0.278580i	0.990252	−	0.139290i	$-0.0444821\pi$
$32$	−7.65009	−	9.11702i	−1.35236	−	1.61168i
$33$	3.39351	+	1.23514i	0.590734	+	0.215009i
$34$	−0.598670	−	3.39523i	−0.102671	−	0.582277i
$35$	−2.03253	−	0.358390i	−0.343560	−	0.0605790i
$36$	−5.72849			−0.954749
$37$	−6.03673	−	0.746918i	−0.992432	−	0.122792i
$37$	−6.03673	−	0.746918i	−0.992432	−	0.122792i
$38$	11.0104			1.78612
$39$	10.8023	+	1.90475i	1.72976	+	0.305003i
$40$	−1.32971	−	7.54117i	−0.210246	−	1.19236i
$41$	2.15024	+	0.782625i	0.335812	+	0.122225i	0.504422	−	0.863457i	$-0.331706\pi$
$41$	2.15024	+	0.782625i	0.335812	+	0.122225i	−0.168610	+	0.985683i	$0.553928\pi$
$42$	7.14262	+	8.51224i	1.10213	+	1.31347i
$43$			8.37985i			1.27791i	0.769242	+	0.638957i	$0.220634\pi$
$43$			8.37985i			1.27791i	−0.769242	+	0.638957i	$0.779366\pi$
$44$	6.66921	−	5.59613i	1.00542	−	0.843648i
$45$	−1.00543	−	0.580485i	−0.149881	−	0.0865336i
$46$	−8.71067	+	3.17042i	−1.28432	+	0.467453i
$47$	−1.79110	−	3.10228i	−0.261259	−	0.452514i	0.705318	−	0.708892i	$-0.250804\pi$
$47$	−1.79110	−	3.10228i	−0.261259	−	0.452514i	−0.966577	+	0.256377i	$0.917471\pi$
$48$	−10.5745	+	18.3156i	−1.52630	+	2.64362i
$49$	−0.471469	+	2.67384i	−0.0673528	+	0.381977i
$50$	−3.60408	+	9.90212i	−0.509693	+	1.40037i
$51$	−2.31624	+	1.33728i	−0.324338	+	0.187257i
$52$	16.9978	−	20.2571i	2.35716	−	2.80916i
$53$	−8.47562	−	7.11189i	−1.16422	−	0.976893i	−0.164261	−	0.986417i	$-0.552524\pi$
$53$	−8.47562	−	7.11189i	−1.16422	−	0.976893i	−0.999955	+	0.00952421i	$0.996968\pi$
$54$	−3.37012	−	9.25934i	−0.458616	−	1.26004i
$55$	1.73761	−	0.306387i	0.234299	−	0.0413133i
$56$	15.6565	−	2.76067i	2.09219	−	0.368910i
$57$	−2.92139	−	8.02644i	−0.386947	−	1.06313i
$58$	1.22254	+	1.02583i	0.160527	+	0.134699i
$59$	−6.76937	+	8.06742i	−0.881296	+	1.05029i	0.117068	+	0.993124i	$0.462650\pi$
$59$	−6.76937	+	8.06742i	−0.881296	+	1.05029i	−0.998365	+	0.0571643i	$0.981794\pi$
$60$	−8.66875	+	5.00490i	−1.11913	+	0.646130i
$61$	−1.41913	+	3.89904i	−0.181701	+	0.499220i	−0.996785	−	0.0801229i	$-0.974469\pi$
$61$	−1.41913	+	3.89904i	−0.181701	+	0.499220i	0.815084	+	0.579343i	$0.196691\pi$
$62$	−0.708506	+	4.01814i	−0.0899804	+	0.510304i
$63$	1.20517	−	2.08741i	0.151837	−	0.262989i
$64$	5.28982	+	9.16224i	0.661228	+	1.14528i
$65$	5.03605	−	1.83297i	0.624646	−	0.227352i
$66$	−8.22689	−	4.74979i	−1.01266	−	0.584659i
$67$	3.77420	−	3.16693i	0.461091	−	0.386902i	−0.382441	−	0.923980i	$-0.624916\pi$
$67$	3.77420	−	3.16693i	0.461091	−	0.386902i	0.843532	+	0.537078i	$0.180472\pi$
$68$			6.44777i			0.781907i
$69$	4.62240	+	5.50876i	0.556472	+	0.663177i
$70$	5.10169	+	1.85686i	0.609768	+	0.221937i
$71$	−1.05928	−	6.00749i	−0.125714	−	0.712958i	−0.980881	−	0.194606i	$-0.937657\pi$
$71$	−1.05928	−	6.00749i	−0.125714	−	0.712958i	0.855168	−	0.518351i	$-0.173454\pi$
$72$	8.80705	+	1.55292i	1.03792	+	0.183014i
$73$	13.5583			1.58688			0.793439	−	0.608649i	$-0.208288\pi$
$73$	13.5583			1.58688			0.793439	+	0.608649i	$0.208288\pi$
$74$	15.2973	+	4.69242i	1.77828	+	0.545483i
$75$	8.17480			0.943945
$76$	−20.2790	−	3.57573i	−2.32616	−	0.410165i
$77$	0.636103	+	3.60752i	0.0724907	+	0.411115i
$78$	−27.1141	−	9.86871i	−3.07006	−	1.11741i
$79$	−8.59215	−	10.2397i	−0.966692	−	1.15206i	−0.988335	−	0.152293i	$-0.951334\pi$
$79$	−8.59215	−	10.2397i	−0.966692	−	1.15206i	0.0216434	−	0.999766i	$-0.493110\pi$
$80$			10.3330i			1.15527i
$81$	−8.53173	+	7.15897i	−0.947970	+	0.795441i
$82$	−5.21284	−	3.00964i	−0.575662	−	0.332359i
$83$	1.39469	−	0.507624i	0.153087	−	0.0557190i	−0.264340	−	0.964429i	$-0.585154\pi$
$83$	1.39469	−	0.507624i	0.153087	−	0.0557190i	0.417427	+	0.908710i	$0.362932\pi$
$84$	−10.3909	−	17.9975i	−1.13374	−	1.96369i
$85$	−0.653371	+	1.13167i	−0.0708681	+	0.122747i
$86$	3.82779	−	21.7085i	0.412761	−	2.34089i
$87$	0.423444	−	1.16340i	0.0453980	−	0.124730i
$88$	−11.7704	+	6.79562i	−1.25472	+	0.724415i
$89$	−4.42899	+	5.27827i	−0.469473	+	0.559496i	−0.947874	−	0.318646i	$-0.896772\pi$
$89$	−4.42899	+	5.27827i	−0.469473	+	0.559496i	0.478401	+	0.878141i	$0.341216\pi$
$90$	2.33947	+	1.96305i	0.246601	+	0.206923i
$91$	3.80551	+	10.4556i	0.398926	+	1.09604i
$92$	17.0730	−	3.01043i	1.77998	−	0.313859i
$93$	3.11716	−	0.549640i	0.323235	−	0.0569950i
$94$	3.22288	+	8.85480i	0.332415	+	0.913302i
$95$	−3.19690	−	2.68252i	−0.327995	−	0.275220i
$96$	15.6114	−	18.6050i	1.59334	−	1.89886i
$97$	−6.55603	+	3.78513i	−0.665664	+	0.384321i	−0.794432	−	0.607353i	$-0.792231\pi$
$97$	−6.55603	+	3.78513i	−0.665664	+	0.384321i	0.128768	+	0.991675i	$0.458898\pi$
$98$	2.44274	−	6.71137i	0.246754	−	0.677951i
$99$	−0.357818	+	2.02929i	−0.0359621	+	0.203951i
$100$	9.85382	−	17.0673i	0.985382	−	1.70673i
$101$	5.67466	+	9.82879i	0.564649	+	0.978002i	0.997082	+	0.0763353i	$0.0243220\pi$
$101$	5.67466	+	9.82879i	0.564649	+	0.978002i	−0.432433	+	0.901666i	$0.642345\pi$
$102$	6.61120	−	2.40628i	0.654606	−	0.238257i
$103$	1.72830	+	0.997837i	0.170295	+	0.0983198i	0.582725	−	0.812670i	$-0.301987\pi$
$103$	1.72830	+	0.997837i	0.170295	+	0.0983198i	−0.412430	+	0.910989i	$0.635320\pi$
$104$	−31.6240	+	26.5357i	−3.10099	+	2.60204i
$105$		−	4.21175i		−	0.411025i
$106$	18.7080	+	22.2953i	1.81708	+	2.16551i
$107$	−17.6836	−	6.43630i	−1.70954	−	0.622220i	−0.712683	−	0.701486i	$-0.752520\pi$
$107$	−17.6836	−	6.43630i	−1.70954	−	0.622220i	−0.996854	+	0.0792658i	$0.974742\pi$
$108$	3.20005	+	18.1484i	0.307925	+	1.74633i
$109$	7.67973	+	1.35414i	0.735585	+	0.129703i	0.528876	−	0.848699i	$-0.322614\pi$
$109$	7.67973	+	1.35414i	0.735585	+	0.129703i	0.206709	+	0.978403i	$0.433725\pi$
$110$	−4.64133			−0.442534
$111$	−0.638117	−	12.3966i	−0.0605674	−	1.17663i
$112$	−21.4528			−2.02710
$113$	9.87190	+	1.74068i	0.928670	+	0.163750i	0.617470	−	0.786595i	$-0.288158\pi$
$113$	9.87190	+	1.74068i	0.928670	+	0.163750i	0.311200	+	0.950344i	$0.399269\pi$
$114$	3.90166	+	22.1274i	0.365424	+	2.07242i
$115$	3.30160	+	1.20168i	0.307875	+	0.112057i
$116$	−1.91853	−	2.28642i	−0.178131	−	0.212289i
$117$			6.25888i			0.578633i
$118$	21.2215	−	17.8070i	1.95360	−	1.63926i
$119$	−2.34951	−	1.35649i	−0.215379	−	0.124349i
$120$	14.6842	−	5.34461i	1.34048	−	0.487894i
$121$	3.93418	+	6.81420i	0.357653	+	0.619473i
$122$	5.45737	−	9.45245i	0.494087	−	0.855784i
$123$	−0.810866	+	4.59865i	−0.0731133	+	0.414646i
$124$	2.60986	−	7.17053i	0.234372	−	0.643933i
$125$	7.77629	−	4.48964i	0.695533	−	0.401566i
$126$	−4.07556	+	4.85706i	−0.363080	+	0.432701i
$127$	1.01023	+	0.847688i	0.0896438	+	0.0752201i	0.686508	−	0.727122i	$-0.259143\pi$
$127$	1.01023	+	0.847688i	0.0896438	+	0.0752201i	−0.596864	+	0.802342i	$0.703587\pi$
$128$	−1.37737	−	3.78429i	−0.121743	−	0.334487i
$129$	−16.8409	+	2.96950i	−1.48276	+	0.261450i
$130$	−13.8835	+	2.44803i	−1.21766	+	0.214706i
$131$	−3.32807	−	9.14381i	−0.290775	−	0.798898i	−0.995954	−	0.0898684i	$-0.971355\pi$
$131$	−3.32807	−	9.14381i	−0.290775	−	0.798898i	0.705178	−	0.709030i	$-0.250867\pi$
$132$	13.6098	+	11.4200i	1.18458	+	0.993980i
$133$	5.56928	−	6.63721i	0.482918	−	0.575519i
$134$	−11.2239	+	6.48011i	−0.969596	+	0.559797i
$135$	−1.27738	+	3.50956i	−0.109939	+	0.302055i
$136$	1.74791	−	9.91288i	0.149882	−	0.850022i
$137$	3.74079	−	6.47924i	0.319598	−	0.553559i	−0.660807	−	0.750556i	$-0.729786\pi$
$137$	3.74079	−	6.47924i	0.319598	−	0.553559i	0.980404	+	0.196997i	$0.0631189\pi$
$138$	−9.45828	−	16.3822i	−0.805143	−	1.39455i
$139$	5.21741	−	1.89898i	0.442535	−	0.161069i	−0.111136	−	0.993805i	$-0.535449\pi$
$139$	5.21741	−	1.89898i	0.442535	−	0.161069i	0.553671	+	0.832736i	$0.313227\pi$
$140$	−8.79327	−	5.07680i	−0.743167	−	0.429068i
$141$	5.59992	−	4.69889i	0.471598	−	0.395718i
$142$			16.0466i			1.34660i
$143$	−6.11425	−	7.28668i	−0.511300	−	0.609343i
$144$	−11.3398	−	4.12735i	−0.944983	−	0.343946i
$145$	−0.105039	−	0.595708i	−0.00872305	−	0.0494709i
$146$	−35.1236	−	6.19323i	−2.90685	−	0.512556i
$147$	−5.54064			−0.456984
$148$	−26.6508	−	13.6105i	−2.19068	−	1.11878i
$149$	−7.32465			−0.600059			−0.300029	−	0.953930i	$-0.596997\pi$
$149$	−7.32465			−0.600059			−0.300029	+	0.953930i	$0.596997\pi$
$150$	−21.1773	−	3.73413i	−1.72912	−	0.304890i
$151$	−0.793519	−	4.50027i	−0.0645757	−	0.366227i	−0.999922	−	0.0124935i	$-0.996023\pi$
$151$	−0.793519	−	4.50027i	−0.0645757	−	0.366227i	0.935346	−	0.353733i	$-0.115088\pi$
$152$	30.2078	+	10.9947i	2.45018	+	0.891791i
$153$	−0.980956	−	1.16906i	−0.0793056	−	0.0945127i
$154$		−	9.63605i		−	0.776495i
$155$	1.18468	−	0.994062i	0.0951556	−	0.0798450i
$156$	46.7339	+	26.9818i	3.74170	+	2.16027i
$157$	−11.9534	+	4.35068i	−0.953986	+	0.347222i	−0.771674	−	0.636018i	$-0.780580\pi$
$157$	−11.9534	+	4.35068i	−0.953986	+	0.347222i	−0.182312	+	0.983241i	$0.558358\pi$
$158$	17.5811	+	30.4514i	1.39868	+	2.42258i
$159$	11.2892	−	19.5535i	0.895294	−	1.55069i
$160$	2.06055	−	11.6860i	0.162901	−	0.923857i
$161$	−2.49486	+	6.85457i	−0.196623	+	0.540216i
$162$	25.3721	−	14.6486i	1.99342	−	1.15090i
$163$	−8.22159	+	9.79811i	−0.643965	+	0.767447i	−0.984991	−	0.172607i	$-0.944781\pi$
$163$	−8.22159	+	9.79811i	−0.643965	+	0.767447i	0.341026	+	0.940054i	$0.389226\pi$
$164$	8.62363	+	7.23608i	0.673392	+	0.565043i
$165$	1.23148	+	3.38348i	0.0958710	+	0.263403i
$166$	−3.84489	+	0.677958i	−0.298422	+	0.0526198i
$167$	23.1506	−	4.08207i	1.79144	−	0.315880i	0.823551	−	0.567243i	$-0.191990\pi$
$167$	23.1506	−	4.08207i	1.79144	−	0.315880i	0.967893	+	0.251363i	$0.0808788\pi$
$168$	11.0962	+	30.4864i	0.856087	+	2.35208i
$169$	−12.1741	−	10.2153i	−0.936469	−	0.785791i
$170$	2.20953	−	2.63321i	0.169463	−	0.201958i
$171$	4.22083	−	2.43689i	0.322775	−	0.186354i
$172$	−14.1001	+	38.7397i	−1.07512	+	2.95387i
$173$	−0.813008	+	4.61080i	−0.0618118	+	0.350552i	0.938178	+	0.346152i	$0.112512\pi$
$173$	−0.813008	+	4.61080i	−0.0618118	+	0.350552i	−0.999990	+	0.00440047i	$0.998599\pi$
$174$	−1.62838	+	2.82044i	−0.123447	+	0.213817i
$175$	4.14612	+	7.18128i	0.313417	+	0.542854i
$176$	17.2339	−	6.27264i	1.29906	−	0.472818i
$177$	−18.6118	−	10.7455i	−1.39895	−	0.807682i
$178$	13.8846	−	11.6506i	1.04070	−	0.873247i
$179$		−	9.73125i		−	0.727348i	−0.931526	−	0.363674i	$-0.881522\pi$
$179$		−	9.73125i		−	0.727348i	0.931526	−	0.363674i	$-0.118478\pi$
$180$	−3.67132	−	4.37531i	−0.273644	−	0.326117i
$181$	8.32509	+	3.03008i	0.618799	+	0.225224i	0.632349	−	0.774684i	$-0.282091\pi$
$181$	8.32509	+	3.03008i	0.618799	+	0.225224i	−0.0135499	+	0.999908i	$0.504313\pi$
$182$	−5.08245	−	28.8240i	−0.376737	−	2.13658i
$183$	−8.33873	−	1.47034i	−0.616416	−	0.108691i
$184$	−27.0643			−1.99520
$185$	−3.29839	−	5.08943i	−0.242502	−	0.374182i
$186$	−8.32627			−0.610511
$187$	2.28409	+	0.402746i	0.167029	+	0.0294517i
$188$	−3.06024	−	17.3555i	−0.223191	−	1.26578i
$189$	−7.28634	−	2.65201i	−0.530003	−	0.192905i
$190$	7.05642	+	8.40952i	0.511927	+	0.610091i
$191$			6.57730i			0.475917i	0.971275	+	0.237958i	$0.0764782\pi$
$191$			6.57730i			0.475917i	−0.971275	+	0.237958i	$0.923522\pi$
$192$	−16.5387	+	13.8776i	−1.19358	+	1.00153i
$193$	−2.10282	−	1.21406i	−0.151364	−	0.0873902i	0.422405	−	0.906407i	$-0.361186\pi$
$193$	−2.10282	−	1.21406i	−0.151364	−	0.0873902i	−0.573769	+	0.819017i	$0.694519\pi$
$194$	18.7128	−	6.81089i	1.34350	−	0.488994i
$195$	5.46829	+	9.47135i	0.391592	+	0.678258i
$196$	−6.67863	+	11.5677i	−0.477045	+	0.826266i
$197$	−4.74016	+	26.8828i	−0.337722	+	1.91532i	0.0607805	+	0.998151i	$0.480641\pi$
$197$	−4.74016	+	26.8828i	−0.337722	+	1.91532i	−0.398503	+	0.917167i	$0.630470\pi$
$198$	1.85390	−	5.09355i	0.131751	−	0.361982i
$199$	11.5142	−	6.64774i	0.816222	−	0.471246i	−0.0328902	−	0.999459i	$-0.510471\pi$
$199$	11.5142	−	6.64774i	0.816222	−	0.471246i	0.849112	+	0.528213i	$0.177138\pi$
$200$	−19.7761	+	23.5682i	−1.39838	+	1.66653i
$201$	7.70196	+	6.46271i	0.543254	+	0.455845i
$202$	−10.2109	−	28.0542i	−0.718435	−	1.97388i
$203$	1.23677	−	0.218076i	0.0868045	−	0.0153060i
$204$	−12.9580	+	2.28484i	−0.907241	+	0.159971i
$205$	0.780312	+	2.14389i	0.0544993	+	0.149736i
$206$	−4.02148	−	3.37442i	−0.280190	−	0.235107i
$207$	−2.63753	+	3.14328i	−0.183321	+	0.218473i
$208$	48.2429	−	27.8531i	3.34504	−	1.93126i
$209$	−2.53337	+	6.96037i	−0.175237	+	0.481459i
$210$	−1.92387	+	10.9108i	−0.132759	+	0.752916i
$211$	−3.16578	+	5.48329i	−0.217941	+	0.377485i	−0.954178	−	0.299238i	$-0.903267\pi$
$211$	−3.16578	+	5.48329i	−0.217941	+	0.377485i	0.736237	+	0.676724i	$0.236601\pi$
$212$	−27.2158	−	47.1392i	−1.86919	−	3.23753i
$213$	11.6978	−	4.25765i	0.801520	−	0.291729i
$214$	42.8704	+	24.7512i	2.93056	+	1.69196i
$215$	−6.40036	+	5.37054i	−0.436501	+	0.366268i
$216$		−	28.7690i		−	1.95748i
$217$	2.06381	+	2.45956i	0.140101	+	0.166965i
$218$	−19.2762	−	7.01598i	−1.30555	−	0.475182i
$219$	4.80454	+	27.2479i	0.324661	+	1.84124i
$220$	8.54843	+	1.50732i	0.576335	+	0.101623i
$221$	7.04475			0.473881
$222$	−4.00951	+	32.4056i	−0.269101	+	2.17492i
$223$	2.43018			0.162737			0.0813683	−	0.996684i	$-0.474071\pi$
$223$	2.43018			0.162737			0.0813683	+	0.996684i	$0.474071\pi$
$224$	24.2617	+	4.27799i	1.62105	+	0.285836i
$225$	0.809985	+	4.59365i	0.0539990	+	0.306243i
$226$	−24.7786	−	9.01868i	−1.64825	−	0.599914i
$227$	−3.25909	−	3.88403i	−0.216313	−	0.257792i	0.646966	−	0.762519i	$-0.276038\pi$
$227$	−3.25909	−	3.88403i	−0.216313	−	0.257792i	−0.863279	+	0.504727i	$0.831593\pi$
$228$		−	42.0215i		−	2.78294i
$229$	7.51681	−	6.30735i	0.496724	−	0.416801i	−0.359704	−	0.933066i	$-0.617122\pi$
$229$	7.51681	−	6.30735i	0.496724	−	0.416801i	0.856429	+	0.516265i	$0.172678\pi$
$230$	−8.00407	−	4.62115i	−0.527773	−	0.304710i
$231$	−7.02457	+	2.55673i	−0.462183	+	0.168221i
$232$	2.32975	+	4.03525i	0.152956	+	0.264927i
$233$	1.38405	−	2.39725i	0.0906722	−	0.157049i	−0.817122	−	0.576465i	$-0.804432\pi$
$233$	1.38405	−	2.39725i	0.0906722	−	0.157049i	0.907794	+	0.419416i	$0.137765\pi$
$234$	2.85896	−	16.2140i	0.186896	−	1.05994i
$235$	1.22157	−	3.35623i	0.0796862	−	0.218936i
$236$	−44.8689	+	25.9051i	−2.92072	+	1.68628i
$237$	17.5339	−	20.8961i	1.13895	−	1.35735i
$238$	5.46692	+	4.58729i	0.354368	+	0.297350i
$239$	6.50378	+	17.8690i	0.420694	+	1.15585i	0.951310	+	0.308236i	$0.0997385\pi$
$239$	6.50378	+	17.8690i	0.420694	+	1.15585i	−0.530616	+	0.847613i	$0.678039\pi$
$240$	−20.7661	+	3.66163i	−1.34045	+	0.236357i
$241$	−1.49887	+	0.264292i	−0.0965509	+	0.0170245i	−0.221715	−	0.975112i	$-0.571165\pi$
$241$	−1.49887	+	0.264292i	−0.0965509	+	0.0170245i	0.125164	+	0.992136i	$0.460054\pi$
$242$	−7.07910	−	19.4497i	−0.455062	−	1.25027i
$243$	−8.80210	−	7.38584i	−0.564655	−	0.473802i
$244$	−13.1212	+	15.6372i	−0.839998	+	1.00107i
$245$	−2.34438	+	1.35353i	−0.149777	+	0.0864739i
$246$	4.20119	−	11.5427i	0.267858	−	0.735934i
$247$	−3.90680	+	22.1565i	−0.248583	+	1.40979i
$248$	−5.95627	+	10.3166i	−0.378223	+	0.655102i
$249$	1.51439	+	2.62300i	0.0959705	+	0.166226i
$250$	−22.1957	+	8.07859i	−1.40378	+	0.510935i
$251$	13.8969	+	8.02336i	0.877163	+	0.506430i	0.869722	−	0.493542i	$-0.164298\pi$
$251$	13.8969	+	8.02336i	0.877163	+	0.506430i	0.00744072	+	0.999972i	$0.497632\pi$
$252$	9.08376	−	7.62218i	0.572223	−	0.480152i
$253$		−	6.23605i		−	0.392057i
$254$	−2.22986	−	2.65745i	−0.139914	−	0.166743i
$255$	−2.50584	−	0.912050i	−0.156922	−	0.0571148i
$256$	−1.83473	−	10.4052i	−0.114670	−	0.650328i
$257$	15.4121	+	2.71756i	0.961378	+	0.169517i	0.632246	−	0.774767i	$-0.282133\pi$
$257$	15.4121	+	2.71756i	0.961378	+	0.169517i	0.329131	+	0.944284i	$0.393244\pi$
$258$	44.9837			2.80056
$259$	10.5664	−	6.84791i	0.656562	−	0.425509i
$260$	26.3657			1.63513
$261$	0.695705	+	0.122672i	0.0430631	+	0.00759318i
$262$	4.44481	+	25.2078i	0.274602	+	1.55734i
$263$	−4.31802	−	1.57163i	−0.266260	−	0.0969108i	0.205440	−	0.978670i	$-0.434137\pi$
$263$	−4.31802	−	1.57163i	−0.266260	−	0.0969108i	−0.471700	+	0.881759i	$0.656360\pi$
$264$	−17.8280	−	21.2466i	−1.09724	−	1.30764i
$265$		−	11.0314i		−	0.677656i
$266$	−17.4593	+	14.6501i	−1.07050	+	0.898257i
$267$	−12.1771	−	7.03047i	−0.745229	−	0.430258i
$268$	22.7767	−	8.29004i	1.39131	−	0.506395i
$269$	−8.68426	−	15.0416i	−0.529489	−	0.917102i	−0.999408	−	0.0343925i	$-0.989050\pi$
$269$	−8.68426	−	15.0416i	−0.529489	−	0.917102i	0.469919	−	0.882709i	$-0.344283\pi$
$270$	4.91223	−	8.50824i	0.298949	−	0.517795i
$271$	2.93250	−	16.6310i	0.178137	−	1.01026i	−0.756324	−	0.654197i	$-0.773007\pi$
$271$	2.93250	−	16.6310i	0.178137	−	1.01026i	0.934461	−	0.356066i	$-0.115882\pi$
$272$	−4.64558	+	12.7636i	−0.281680	+	0.773909i
$273$	−19.6639	+	11.3529i	−1.19011	+	0.687111i
$274$	−12.6504	+	15.0761i	−0.764237	+	0.910782i
$275$	−5.43051	−	4.55674i	−0.327472	−	0.274781i
$276$	12.1000	+	33.2445i	0.728336	+	2.00109i
$277$	−23.5704	+	4.15610i	−1.41621	+	0.249716i	−0.828787	−	0.559565i	$-0.810968\pi$
$277$	−23.5704	+	4.15610i	−1.41621	+	0.249716i	−0.587422	+	0.809281i	$0.699857\pi$
$278$	−14.3834	+	2.53619i	−0.862661	+	0.152110i
$279$	0.617717	+	1.69716i	0.0369817	+	0.101607i
$280$	12.1426	+	10.1889i	0.725661	+	0.608902i
$281$	9.92422	−	11.8272i	0.592029	−	0.705553i	−0.383966	−	0.923347i	$-0.625442\pi$
$281$	9.92422	−	11.8272i	0.592029	−	0.705553i	0.975995	+	0.217795i	$0.0698863\pi$
$282$	−16.6533	+	9.61478i	−0.991689	+	0.572552i
$283$	1.03854	−	2.85336i	0.0617347	−	0.169615i	−0.904990	−	0.425432i	$-0.860122\pi$
$283$	1.03854	−	2.85336i	0.0617347	−	0.169615i	0.966725	+	0.255817i	$0.0823445\pi$
$284$	5.21130	−	29.5547i	0.309234	−	1.75375i
$285$	4.25816	−	7.37535i	0.252232	−	0.436878i
$286$	12.5109	+	21.6695i	0.739784	+	1.28134i
$287$	−4.45101	+	1.62004i	−0.262735	+	0.0956277i
$288$	12.0015	+	6.92907i	0.707196	+	0.408300i
$289$	11.7069	−	9.82326i	0.688642	−	0.577839i
$290$			1.59120i			0.0934383i
$291$	−9.93012	−	11.8343i	−0.582114	−	0.693737i
$292$	62.6794	+	22.8135i	3.66804	+	1.33506i
$293$	2.32678	+	13.1958i	0.135932	+	0.770908i	0.974206	+	0.225660i	$0.0724537\pi$
$293$	2.32678	+	13.1958i	0.135932	+	0.770908i	−0.838274	+	0.545249i	$0.816435\pi$
$294$	14.3534	+	2.53088i	0.837105	+	0.147604i
$295$	−10.5001			−0.611342
$296$	37.2836	+	28.1496i	2.16706	+	1.63616i
$297$	6.62885			0.384645
$298$	18.9749	+	3.34579i	1.09919	+	0.193817i
$299$	−3.28915	−	18.6537i	−0.190216	−	1.07877i
$300$	37.7918	+	13.7551i	2.18191	+	0.794150i
$301$	−11.1500	−	13.2880i	−0.642675	−	0.765910i
$302$			12.0207i			0.691713i
$303$	−17.7419	+	14.8872i	−1.01925	+	0.855249i
$304$	−37.5668	−	21.6892i	−2.15460	−	1.24396i
$305$	−3.88751	+	1.41494i	−0.222598	+	0.0810192i
$306$	2.00721	+	3.47660i	0.114745	+	0.198744i
$307$	−17.1776	+	29.7525i	−0.980378	+	1.69807i	−0.319474	+	0.947595i	$0.603506\pi$
$307$	−17.1776	+	29.7525i	−0.980378	+	1.69807i	−0.660904	+	0.750470i	$0.729827\pi$
$308$	−3.12940	+	17.7477i	−0.178314	+	1.01127i
$309$	−1.39289	+	3.82694i	−0.0792389	+	0.217707i
$310$	−3.52305	+	2.03403i	−0.200096	+	0.115525i
$311$	2.41229	−	2.87486i	0.136788	−	0.163018i	−0.693301	−	0.720648i	$-0.743845\pi$
$311$	2.41229	−	2.87486i	0.136788	−	0.163018i	0.830090	+	0.557630i	$0.188289\pi$
$312$	−64.5347	−	54.1511i	−3.65356	−	3.06570i
$313$	−5.68575	−	15.6215i	−0.321377	−	0.882977i	−0.990213	−	0.139566i	$-0.955429\pi$
$313$	−5.68575	−	15.6215i	−0.321377	−	0.882977i	0.668835	−	0.743411i	$-0.266793\pi$
$314$	32.9533	−	5.81056i	1.85966	−	0.327909i
$315$	2.36670	−	0.417313i	0.133349	−	0.0235129i
$316$	−22.4916	−	61.7951i	−1.26525	−	3.47625i
$317$	17.8110	+	14.9452i	1.00036	+	0.839404i	0.987035	−	0.160507i	$-0.0513129\pi$
$317$	17.8110	+	14.9452i	1.00036	+	0.839404i	0.0133284	+	0.999911i	$0.495757\pi$
$318$	−38.1772	+	45.4978i	−2.14087	+	2.55139i
$319$	−0.929788	+	0.536813i	−0.0520581	+	0.0300558i
$320$	−3.60776	+	9.91223i	−0.201680	+	0.554111i
$321$	6.66855	−	37.8192i	0.372202	−	2.11086i
$322$	9.59415	−	16.6176i	0.534661	−	0.926061i
$323$	−2.74287	−	4.75080i	−0.152618	−	0.264341i
$324$	−51.4876	+	18.7400i	−2.86042	+	1.04111i
$325$	−18.6475	−	10.7661i	−1.03438	−	0.597198i
$326$	25.7742	−	21.6271i	1.42750	−	1.19781i
$327$			15.9137i			0.880030i
$328$	−11.2965	−	13.4626i	−0.623743	−	0.743347i
$329$	6.96799	+	2.53614i	0.384158	+	0.139822i
$330$	−1.64471	−	9.32762i	−0.0905384	−	0.513469i
$331$	13.5378	+	2.38708i	0.744106	+	0.131206i	0.532832	−	0.846221i	$-0.321128\pi$
$331$	13.5378	+	2.38708i	0.744106	+	0.131206i	0.211274	+	0.977427i	$0.432239\pi$
$332$	7.30172			0.400734
$333$	6.90278	−	1.58687i	0.378270	−	0.0869600i
$334$	−61.8375			−3.38360
$335$	4.83767	+	0.853012i	0.264310	+	0.0466050i
$336$	−7.60206	−	43.1134i	−0.414726	−	2.35203i
$337$	11.1617	+	4.06251i	0.608015	+	0.221299i	0.627634	−	0.778508i	$-0.284023\pi$
$337$	11.1617	+	4.06251i	0.608015	+	0.221299i	−0.0196197	+	0.999808i	$0.506246\pi$
$338$	26.8715	+	32.0242i	1.46162	+	1.74189i
$339$			20.4563i			1.11103i
$340$	−4.92468	+	4.13230i	−0.267078	+	0.224105i
$341$	−2.37710	−	1.37242i	−0.128727	−	0.0743208i
$342$	−12.0474	+	4.38491i	−0.651451	+	0.237109i
$343$	−10.0551	−	17.4160i	−0.542926	−	0.940375i
$344$	32.1795	−	55.7365i	1.73500	−	3.00511i
$345$	−1.24505	+	7.06100i	−0.0670310	+	0.380152i
$346$	4.21229	−	11.5732i	0.226454	−	0.622178i
$347$	25.1199	−	14.5030i	1.34851	−	0.778560i	0.360468	−	0.932772i	$-0.382617\pi$
$347$	25.1199	−	14.5030i	1.34851	−	0.778560i	0.988038	+	0.154212i	$0.0492837\pi$
$348$	3.91513	−	4.66587i	0.209873	−	0.250117i
$349$	−11.1805	−	9.38157i	−0.598480	−	0.502184i	0.292477	−	0.956273i	$-0.405521\pi$
$349$	−11.1805	−	9.38157i	−0.598480	−	0.502184i	−0.890957	+	0.454088i	$0.849965\pi$
$350$	−7.46045	−	20.4974i	−0.398778	−	1.09563i
$351$	19.8287	−	3.49633i	1.05838	−	0.186620i
$352$	−20.7413	+	3.65725i	−1.10552	+	0.194932i
$353$	9.35264	+	25.6962i	0.497791	+	1.36767i	0.893405	+	0.449252i	$0.148309\pi$
$353$	9.35264	+	25.6962i	0.497791	+	1.36767i	−0.395615	+	0.918417i	$0.629468\pi$
$354$	43.3065	+	36.3385i	2.30172	+	1.93137i
$355$	3.90952	−	4.65919i	0.207496	−	0.247284i
$356$	−29.3564	+	16.9489i	−1.55589	+	0.898291i
$357$	1.89354	−	5.20247i	0.100217	−	0.275344i
$358$	−4.44510	+	25.2094i	−0.234931	+	1.33236i
$359$	−5.37405	+	9.30813i	−0.283632	+	0.491264i	−0.972276	−	0.233835i	$-0.924873\pi$
$359$	−5.37405	+	9.30813i	−0.283632	+	0.491264i	0.688645	+	0.725099i	$0.258206\pi$
$360$	4.45824	+	7.72190i	0.234970	+	0.406980i
$361$	−1.39124	+	0.506372i	−0.0732234	+	0.0266511i
$362$	−20.1825	−	11.6524i	−1.06077	−	0.612436i
$363$	−12.3003	+	10.3212i	−0.645597	+	0.541720i
$364$			54.7388i			2.86909i
$365$	8.68935	+	10.3556i	0.454821	+	0.542035i
$366$	20.9303	+	7.61802i	1.09405	+	0.398200i
$367$	−1.47729	−	8.37816i	−0.0771142	−	0.437336i	−0.998781	−	0.0493547i	$-0.984284\pi$
$367$	−1.47729	−	8.37816i	−0.0771142	−	0.437336i	0.921667	−	0.387982i	$-0.126828\pi$
$368$	35.9656	+	6.34171i	1.87484	+	0.330585i
$369$	−2.66445			−0.138706
$370$	6.21989	+	14.6911i	0.323357	+	0.763755i
$371$	22.9028			1.18905
$372$	15.3354	+	2.70404i	0.795101	+	0.140198i
$373$	−2.57728	−	14.6165i	−0.133447	−	0.756813i	−0.975929	−	0.218089i	$-0.930018\pi$
$373$	−2.57728	−	14.6165i	−0.133447	−	0.756813i	0.842482	−	0.538724i	$-0.181093\pi$
$374$	−5.73310	−	2.08668i	−0.296451	−	0.107899i
$375$	11.7784	+	14.0369i	0.608234	+	0.724865i
$376$			27.5121i			1.41883i
$377$	−2.49811	+	2.09616i	−0.128659	+	0.107958i
$378$	17.6643	+	10.1985i	0.908553	+	0.524553i
$379$	−4.61165	+	1.67850i	−0.236885	+	0.0862190i	−0.457735	−	0.889089i	$-0.651339\pi$
$379$	−4.61165	+	1.67850i	−0.236885	+	0.0862190i	0.220850	+	0.975308i	$0.429117\pi$
$380$	−10.2655	−	17.7803i	−0.526608	−	0.912112i
$381$	−1.34560	+	2.33064i	−0.0689371	+	0.119402i
$382$	3.00442	−	17.0389i	0.153719	−	0.871786i
$383$	−10.4996	+	28.8475i	−0.536506	+	1.47404i	0.314692	+	0.949194i	$0.398099\pi$
$383$	−10.4996	+	28.8475i	−0.536506	+	1.47404i	−0.851198	+	0.524844i	$0.824124\pi$
$384$	7.11715	−	4.10909i	0.363196	−	0.209691i
$385$	−2.34768	+	2.79786i	−0.119649	+	0.142592i
$386$	4.89291	+	4.10564i	0.249043	+	0.208972i
$387$	−3.33729	−	9.16913i	−0.169644	−	0.466093i
$388$	−36.6772	+	6.46718i	−1.86200	+	0.328321i
$389$	−38.5245	+	6.79290i	−1.95327	+	0.344414i	−0.954307	+	0.298827i	$0.903405\pi$
$389$	−38.5245	+	6.79290i	−1.95327	+	0.344414i	−0.998960	+	0.0455870i	$0.985484\pi$
$390$	−9.83955	−	27.0339i	−0.498245	−	1.36892i
$391$	3.53796	+	2.96870i	0.178922	+	0.150134i
$392$	13.4037	−	15.9739i	0.676987	−	0.806802i
$393$	17.1968	−	9.92860i	0.867466	−	0.500832i
$394$	24.5593	−	67.4762i	1.23728	−	3.39940i
$395$	2.31430	−	13.1250i	0.116445	−	0.660392i
$396$	−5.06870	+	8.77924i	−0.254712	+	0.441174i
$397$	4.59778	+	7.96360i	0.230756	+	0.399681i	0.958031	−	0.286665i	$-0.0925467\pi$
$397$	4.59778	+	7.96360i	0.230756	+	0.399681i	−0.727275	+	0.686347i	$0.759213\pi$
$398$	−32.8649	+	11.9618i	−1.64737	+	0.599592i
$399$	15.3123	+	8.84053i	0.766571	+	0.442580i
$400$	31.8029	−	26.6858i	1.59015	−	1.33429i
$401$			2.45751i			0.122722i	0.998116	+	0.0613612i	$0.0195441\pi$
$401$			2.45751i			0.122722i	−0.998116	+	0.0613612i	$0.980456\pi$
$402$	−17.0003	−	20.2602i	−0.847898	−	1.01049i
$403$	−7.83443	−	2.85150i	−0.390261	−	0.142043i
$404$	9.69558	+	54.9864i	0.482373	+	2.73568i
$405$	−10.9358	−	1.92827i	−0.543402	−	0.0958165i
$406$	−3.30355			−0.163952
$407$	−6.48613	+	8.59074i	−0.321505	+	0.425827i
$408$	20.5412			1.01694
$409$	3.26072	+	0.574953i	0.161232	+	0.0284296i	0.253681	−	0.967288i	$-0.418358\pi$
$409$	3.26072	+	0.574953i	0.161232	+	0.0284296i	−0.0924493	+	0.995717i	$0.529470\pi$
$410$	−1.04215	−	5.91031i	−0.0514680	−	0.291889i
$411$	14.3468	+	5.22182i	0.707678	+	0.257574i
$412$	6.31090	+	7.52103i	0.310916	+	0.370535i
$413$		−	21.7998i		−	1.07270i
$414$	8.26848	−	6.93808i	0.406374	−	0.340988i
$415$	1.28155	+	0.739904i	0.0629089	+	0.0363205i
$416$	−60.1139	+	21.8797i	−2.94732	+	1.07274i
$417$	5.66521	+	9.81243i	0.277426	+	0.480517i
$418$	9.74223	−	16.8740i	0.476508	−	0.825336i
$419$	2.49037	−	14.1236i	0.121663	−	0.689984i	−0.861571	−	0.507636i	$-0.830519\pi$
$419$	2.49037	−	14.1236i	0.121663	−	0.689984i	0.983234	−	0.182347i	$-0.0583696\pi$
$420$	7.08677	−	19.4707i	0.345799	−	0.950075i
$421$	−8.86400	+	5.11763i	−0.432005	+	0.249418i	−0.700200	−	0.713946i	$-0.746906\pi$
$421$	−8.86400	+	5.11763i	−0.432005	+	0.249418i	0.268196	+	0.963364i	$0.413573\pi$
$422$	10.7058	−	12.7587i	0.521151	−	0.621084i
$423$	3.19530	+	2.68117i	0.155361	+	0.130363i
$424$	29.0631	+	79.8502i	1.41143	+	3.87787i
$425$	5.17044	−	0.911688i	0.250803	−	0.0442233i
$426$	−32.2487	+	5.68631i	−1.56245	+	0.275503i
$427$	−2.93761	−	8.07102i	−0.142161	−	0.390584i
$428$	−70.9206	−	59.5095i	−3.42808	−	2.87650i
$429$	12.4773	−	14.8699i	0.602409	−	0.717923i
$430$	19.0337	−	10.9891i	0.917887	−	0.529942i
$431$	−3.97821	+	10.9300i	−0.191623	+	0.526481i	−0.997880	−	0.0650853i	$-0.979268\pi$
$431$	−3.97821	+	10.9300i	−0.191623	+	0.526481i	0.806256	+	0.591566i	$0.201490\pi$
$432$	−6.74117	+	38.2311i	−0.324335	+	1.83939i
$433$	−18.0948	+	31.3411i	−0.869579	+	1.50616i	−0.00715178	+	0.999974i	$0.502277\pi$
$433$	−18.0948	+	31.3411i	−0.869579	+	1.50616i	−0.862427	+	0.506181i	$0.831057\pi$
$434$	−4.22294	−	7.31434i	−0.202708	−	0.351100i
$435$	1.15996	−	0.422192i	0.0556160	−	0.0202426i
$436$	33.2246	+	19.1822i	1.59117	+	0.918661i
$437$	−11.2989	+	9.48094i	−0.540502	+	0.453535i
$438$		−	72.7820i		−	3.47766i
$439$	7.71832	+	9.19834i	0.368376	+	0.439013i	0.918109	−	0.396327i	$-0.129715\pi$
$439$	7.71832	+	9.19834i	0.368376	+	0.439013i	−0.549734	+	0.835340i	$0.685271\pi$
$440$	−12.7338	−	4.63474i	−0.607062	−	0.220952i
$441$	−0.548984	−	3.11344i	−0.0261421	−	0.148259i
$442$	−18.2498	−	3.21794i	−0.868056	−	0.153062i
$443$	−23.5359			−1.11822			−0.559112	−	0.829092i	$-0.688858\pi$
$443$	−23.5359			−1.11822			−0.559112	+	0.829092i	$0.688858\pi$
$444$	17.9088	−	58.3827i	0.849914	−	2.77072i
$445$	−6.86993			−0.325666
$446$	−6.29552	−	1.11007i	−0.298101	−	0.0525633i
$447$	−2.59558	−	14.7203i	−0.122767	−	0.696244i
$448$	−20.5792	−	7.49021i	−0.972275	−	0.353879i
$449$	−3.20730	−	3.82231i	−0.151362	−	0.180386i	0.685035	−	0.728510i	$-0.259787\pi$
$449$	−3.20730	−	3.82231i	−0.151362	−	0.180386i	−0.836397	+	0.548124i	$0.815342\pi$
$450$		−	12.2701i		−	0.578419i
$451$	3.10200	−	2.60289i	0.146068	−	0.122565i
$452$	42.7085	+	24.6578i	2.00884	+	1.15980i
$453$	8.76294	−	3.18945i	0.411719	−	0.149853i
$454$	6.66870	+	11.5505i	0.312977	+	0.542093i
$455$	−5.54684	+	9.60741i	−0.260040	+	0.450402i
$456$	−11.3915	+	64.6043i	−0.533455	+	3.02537i
$457$	7.86915	−	21.6203i	0.368103	−	1.01136i	−0.607979	−	0.793953i	$-0.708020\pi$
$457$	7.86915	−	21.6203i	0.368103	−	1.01136i	0.976082	−	0.217402i	$-0.0697583\pi$
$458$	−22.3538	+	12.9060i	−1.04453	+	0.603057i
$459$	−3.15570	+	3.76081i	−0.147295	+	0.175540i
$460$	13.2412	+	11.1107i	0.617373	+	0.518037i
$461$	−4.42243	−	12.1505i	−0.205973	−	0.565906i	0.793094	−	0.609100i	$-0.208469\pi$
$461$	−4.42243	−	12.1505i	−0.205973	−	0.565906i	−0.999067	+	0.0431934i	$0.986247\pi$
$462$	19.3654	−	3.41465i	0.900962	−	0.158864i
$463$	10.6682	−	1.88110i	0.495795	−	0.0874220i	0.0798407	−	0.996808i	$-0.474559\pi$
$463$	10.6682	−	1.88110i	0.495795	−	0.0874220i	0.415954	+	0.909386i	$0.363448\pi$
$464$	−2.15046	−	5.90835i	−0.0998328	−	0.274288i
$465$	2.41756	+	2.02857i	0.112112	+	0.0940728i
$466$	−4.68050	+	5.57800i	−0.216820	+	0.258396i
$467$	30.6966	−	17.7227i	1.42047	−	0.820109i	0.424131	−	0.905601i	$-0.360580\pi$
$467$	30.6966	−	17.7227i	1.42047	−	0.820109i	0.996339	+	0.0854922i	$0.0272463\pi$
$468$	−10.5313	+	28.9345i	−0.486810	+	1.33750i
$469$	−1.77097	+	10.0437i	−0.0817759	+	0.463774i
$470$	−4.69761	+	8.13651i	−0.216685	+	0.375309i
$471$	−12.9793	−	22.4809i	−0.598057	−	1.03586i
$472$	76.0045	−	27.6634i	3.49839	−	1.27331i
$473$	12.8426	+	7.41467i	0.590503	+	0.340927i
$474$	−54.9676	+	46.1233i	−2.52475	+	2.11851i
$475$			16.7672i			0.769332i
$476$	−8.57923	−	10.2243i	−0.393228	−	0.468631i
$477$	12.1062	+	4.40631i	0.554307	+	0.201751i
$478$	−8.68613	−	49.2615i	−0.397294	−	2.25317i
$479$	−8.88677	−	1.56698i	−0.406047	−	0.0715970i	−0.0331054	−	0.999452i	$-0.510540\pi$
$479$	−8.88677	−	1.56698i	−0.406047	−	0.0715970i	−0.372942	+	0.927855i	$0.621651\pi$
$480$	24.2153			1.10527
$481$	−14.8706	+	29.1183i	−0.678043	+	1.32768i
$482$	4.00365			0.182361
$483$	−14.6596	−	2.58489i	−0.667036	−	0.117616i
$484$	6.72185	+	38.1215i	0.305538	+	1.73279i
$485$	−7.09269	−	2.58153i	−0.322062	−	0.117221i
$486$	19.4286	+	23.1541i	0.881300	+	1.05029i
$487$		−	9.71169i		−	0.440079i	−0.975491	−	0.220039i	$-0.929381\pi$
$487$		−	9.71169i		−	0.440079i	0.975491	−	0.220039i	$-0.0706186\pi$
$488$	24.4117	−	20.4839i	1.10507	−	0.927261i
$489$	−22.6045	−	13.0507i	−1.02221	−	0.590175i
$490$	6.69153	−	2.43552i	0.302293	−	0.110026i
$491$	−15.2008	−	26.3286i	−0.686003	−	1.18819i	−0.973121	−	0.230296i	$-0.926030\pi$
$491$	−15.2008	−	26.3286i	−0.686003	−	1.18819i	0.287118	−	0.957895i	$-0.407303\pi$
$492$	−11.4864	+	19.8950i	−0.517846	+	0.896935i
$493$	0.138074	−	0.783059i	0.00621856	−	0.0352672i
$494$	20.2416	−	55.6133i	0.910711	−	2.50216i
$495$	−1.77925	+	1.02725i	−0.0799714	+	0.0461715i
$496$	10.3327	−	12.3140i	0.463950	−	0.552914i
$497$	9.67312	+	8.11671i	0.433899	+	0.364084i
$498$	−2.72497	−	7.48679i	−0.122109	−	0.335491i
$499$	26.9165	−	4.74611i	1.20495	−	0.212465i	0.465112	−	0.885252i	$-0.346014\pi$
$499$	26.9165	−	4.74611i	1.20495	−	0.212465i	0.739836	+	0.672787i	$0.234903\pi$
$500$	43.5038	−	7.67090i	1.94555	−	0.343053i
$501$	16.4073	+	45.0788i	0.733026	+	2.01397i
$502$	−32.3357	−	27.1329i	−1.44321	−	1.21100i
$503$	0.270169	−	0.321975i	0.0120462	−	0.0143562i	−0.759988	−	0.649937i	$-0.774795\pi$
$503$	0.270169	−	0.321975i	0.0120462	−	0.0143562i	0.772034	+	0.635581i	$0.219240\pi$
$504$	−16.0318	+	9.25594i	−0.714111	+	0.412292i
$505$	−3.87022	+	10.6333i	−0.172223	+	0.473178i
$506$	−2.84854	+	16.1548i	−0.126633	+	0.718171i
$507$	16.2155	−	28.0860i	0.720154	−	1.24734i
$508$	3.24394	+	5.61867i	0.143926	+	0.249288i
$509$	17.6912	−	6.43907i	0.784149	−	0.285407i	0.0812473	−	0.996694i	$-0.474110\pi$
$509$	17.6912	−	6.43907i	0.784149	−	0.285407i	0.702902	+	0.711287i	$0.251887\pi$
$510$	6.07491	+	3.50735i	0.269001	+	0.155308i
$511$	−21.4996	+	18.0403i	−0.951086	+	0.798056i
$512$			35.8478i			1.58426i
$513$	−10.0781	−	12.0107i	−0.444961	−	0.530283i
$514$	−38.6845	−	14.0800i	−1.70630	−	0.621042i
$515$	0.345521	+	1.95955i	0.0152255	+	0.0863479i
$516$	−82.8512	−	14.6089i	−3.64732	−	0.643121i
$517$	−6.33923			−0.278799
$518$	−30.5008	+	12.9134i	−1.34013	+	0.567380i
$519$	−9.55435			−0.419390
$520$	−40.5349	−	7.14739i	−1.77757	−	0.313434i
$521$	4.62461	+	26.2275i	0.202608	+	1.14905i	0.901160	+	0.433487i	$0.142717\pi$
$521$	4.62461	+	26.2275i	0.202608	+	1.14905i	−0.698552	+	0.715559i	$0.746172\pi$
$522$	−1.74623	−	0.635576i	−0.0764304	−	0.0278184i
$523$	−1.75455	−	2.09099i	−0.0767210	−	0.0914325i	0.726319	−	0.687358i	$-0.241230\pi$
$523$	−1.75455	−	2.09099i	−0.0767210	−	0.0914325i	−0.803040	+	0.595926i	$0.796785\pi$
$524$		−	47.8713i		−	2.09127i
$525$	−12.9629	+	10.8772i	−0.565747	+	0.474718i
$526$	10.4682	+	6.04381i	0.456434	+	0.263522i
$527$	1.91026	−	0.695278i	0.0832123	−	0.0302868i
$528$	18.7131	+	32.4120i	0.814383	+	1.41055i
$529$	−5.29107	+	9.16440i	−0.230046	+	0.398452i
$530$	−5.03900	+	28.5776i	−0.218880	+	1.24133i
$531$	4.19410	−	11.5232i	0.182008	−	0.500064i
$532$	36.9145	−	21.3126i	1.60044	−	0.924017i
$533$	7.90605	−	9.42206i	0.342449	−	0.408115i
$534$	28.3342	+	23.7752i	1.22614	+	1.02885i
$535$	−6.41728	−	17.6313i	−0.277443	−	0.762269i
$536$	−37.2645	+	6.57073i	−1.60958	+	0.283812i
$537$	19.5568	−	3.44839i	0.843937	−	0.148809i
$538$	15.6263	+	42.9330i	0.673699	+	1.85097i
$539$	3.68064	+	3.08842i	0.158536	+	0.133028i
$540$	−11.8105	+	14.0752i	−0.508243	+	0.605701i
$541$	35.3132	−	20.3881i	1.51823	−	0.876552i	0.518463	−	0.855100i	$-0.326504\pi$
$541$	35.3132	−	20.3881i	1.51823	−	0.876552i	0.999770	−	0.0214527i	$-0.00682912\pi$
$542$	−15.1936	+	41.7441i	−0.652622	+	1.79306i
$543$	−3.13942	+	17.8046i	−0.134726	+	0.764067i
$544$	7.79910	−	13.5084i	0.334383	−	0.579169i
$545$	3.88758	+	6.73348i	0.166526	+	0.288431i
$546$	56.1262	−	20.4283i	2.40198	−	0.874249i
$547$	−7.52538	−	4.34478i	−0.321762	−	0.185770i	0.330416	−	0.943836i	$-0.392811\pi$
$547$	−7.52538	−	4.34478i	−0.321762	−	0.185770i	−0.652178	+	0.758066i	$0.726144\pi$
$548$	28.1956	−	23.6589i	1.20446	−	1.01066i
$549$		−	4.83145i		−	0.206201i
$550$	11.9866	+	14.2851i	0.511110	+	0.609117i
$551$	2.38624	+	0.868519i	0.101657	+	0.0370002i
$552$	−9.59055	−	54.3907i	−0.408201	−	2.31502i
$553$	27.2494	+	4.80480i	1.15876	+	0.204321i
$554$	62.9590			2.67487
$555$	9.05933	−	8.43222i	0.384547	−	0.357928i
$556$	27.3151			1.15842
$557$	−39.5716	−	6.97753i	−1.67670	−	0.295648i	−0.747236	−	0.664558i	$-0.768620\pi$
$557$	−39.5716	−	6.97753i	−1.67670	−	0.295648i	−0.929465	+	0.368911i	$0.879731\pi$
$558$	−0.824993	−	4.67877i	−0.0349247	−	0.198068i
$559$	42.3265	+	15.4056i	1.79022	+	0.651586i
$560$	−13.7488	−	16.3852i	−0.580995	−	0.692403i
$561$			4.73302i			0.199828i
$562$	−31.1118	+	26.1059i	−1.31237	+	1.10121i
$563$	36.2097	+	20.9057i	1.52606	+	0.881070i	0.999522	+	0.0309168i	$0.00984269\pi$
$563$	36.2097	+	20.9057i	1.52606	+	0.881070i	0.526536	+	0.850153i	$0.323491\pi$
$564$	33.7946	−	12.3002i	1.42301	−	0.517933i
$565$	4.99728	+	8.65555i	0.210237	+	0.364142i
$566$	−3.99377	+	6.91741i	−0.167871	+	0.290761i
$567$	4.00336	−	22.7042i	0.168125	−	0.953486i
$568$	−16.0238	+	44.0251i	−0.672344	+	1.84725i
$569$	−19.8909	+	11.4840i	−0.833870	+	0.481435i	−0.855176	−	0.518338i	$-0.826551\pi$
$569$	−19.8909	+	11.4840i	−0.833870	+	0.481435i	0.0213056	+	0.999773i	$0.493218\pi$
$570$	−14.4000	+	17.1612i	−0.603148	+	0.718804i
$571$	−5.14388	−	4.31623i	−0.215265	−	0.180629i	0.528779	−	0.848760i	$-0.322650\pi$
$571$	−5.14388	−	4.31623i	−0.215265	−	0.180629i	−0.744044	+	0.668131i	$0.767095\pi$
$572$	−16.0052	−	43.9740i	−0.669212	−	1.83865i
$573$	−13.2183	+	2.33075i	−0.552203	+	0.0973683i
$574$	12.2706	−	2.16364i	0.512166	−	0.0903087i
$575$	−4.82809	−	13.2651i	−0.201345	−	0.553192i
$576$	−9.43694	−	7.91854i	−0.393206	−	0.329939i
$577$	16.7269	−	19.9344i	0.696351	−	0.829879i	−0.295757	−	0.955263i	$-0.595572\pi$
$577$	16.7269	−	19.9344i	0.696351	−	0.829879i	0.992108	+	0.125385i	$0.0400164\pi$
$578$	−34.8146	+	20.1002i	−1.44810	+	0.836058i
$579$	1.69473	−	4.65622i	0.0704304	−	0.193506i
$580$	0.516757	−	2.93068i	0.0214572	−	0.121690i
$581$	−1.53614	+	2.66068i	−0.0637300	+	0.110384i
$582$	20.3189	+	35.1933i	0.842244	+	1.45881i
$583$	−18.3988	+	6.69661i	−0.762000	+	0.277345i
$584$	−90.1797	−	52.0653i	−3.73166	−	2.15448i
$585$	−4.78041	+	4.01124i	−0.197645	+	0.165844i
$586$		−	35.2474i		−	1.45606i
$587$	−23.1752	−	27.6192i	−0.956544	−	1.13996i	−0.990077	−	0.140527i	$-0.955120\pi$
$587$	−23.1752	−	27.6192i	−0.956544	−	1.13996i	0.0335329	−	0.999438i	$-0.489324\pi$
$588$	−25.6142	−	9.32279i	−1.05631	−	0.384465i
$589$	1.12736	+	6.39357i	0.0464520	+	0.263442i
$590$	27.2012	+	4.79631i	1.11986	+	0.197461i
$591$	−55.7057			−2.29143
$592$	−42.9500	−	46.1443i	−1.76524	−	1.89652i
$593$	−33.1977			−1.36326			−0.681632	−	0.731695i	$-0.738730\pi$
$593$	−33.1977			−1.36326			−0.681632	+	0.731695i	$0.738730\pi$
$594$	−17.1724	−	3.02796i	−0.704593	−	0.124239i
$595$	−0.469712	−	2.66387i	−0.0192563	−	0.109208i
$596$	−33.8616	−	12.3246i	−1.38702	−	0.504835i
$597$	17.4401	+	20.7843i	0.713775	+	0.850643i
$598$			49.8259i			2.03753i
$599$	−3.49652	+	2.93393i	−0.142864	+	0.119877i	−0.711419	−	0.702768i	$-0.751947\pi$
$599$	−3.49652	+	2.93393i	−0.142864	+	0.119877i	0.568555	+	0.822645i	$0.307503\pi$
$600$	−54.3727	−	31.3921i	−2.21975	−	1.28158i
$601$	5.93036	−	2.15848i	0.241905	−	0.0880460i	−0.218223	−	0.975899i	$-0.570026\pi$
$601$	5.93036	−	2.15848i	0.241905	−	0.0880460i	0.460127	+	0.887853i	$0.347804\pi$
$602$	22.8149	+	39.5166i	0.929868	+	1.61058i
$603$	−2.86845	+	4.96830i	−0.116812	+	0.202325i
$604$	3.90384	−	22.1398i	0.158845	−	0.900854i
$605$	−2.68318	+	7.37199i	−0.109087	+	0.299714i
$606$	52.7617	−	30.4620i	2.14330	−	1.23743i
$607$	−9.16078	+	10.9174i	−0.371824	+	0.443123i	−0.919216	−	0.393753i	$-0.871176\pi$
$607$	−9.16078	+	10.9174i	−0.371824	+	0.443123i	0.547392	+	0.836877i	$0.315621\pi$
$608$	38.1604	+	32.0204i	1.54761	+	1.29860i
$609$	0.876531	+	2.40825i	0.0355188	+	0.0975871i
$610$	10.7172	−	1.88972i	0.433925	−	0.0765127i
$611$	−18.9623	+	3.34357i	−0.767134	+	0.135267i
$612$	−2.56784	−	7.05508i	−0.103799	−	0.285185i
$613$	17.1875	+	14.4220i	0.694196	+	0.582500i	0.920116	−	0.391646i	$-0.128094\pi$
$613$	17.1875	+	14.4220i	0.694196	+	0.582500i	−0.225920	+	0.974146i	$0.572539\pi$
$614$	58.0901	−	69.2291i	2.34433	−	2.79386i
$615$	−4.03203	+	2.32789i	−0.162587	+	0.0938698i
$616$	9.62236	−	26.4372i	0.387696	−	1.06519i
$617$	7.41495	−	42.0523i	0.298515	−	1.69296i	−0.354048	−	0.935227i	$-0.615195\pi$
$617$	7.41495	−	42.0523i	0.298515	−	1.69296i	0.652563	−	0.757734i	$-0.273694\pi$
$618$	5.35647	−	9.27767i	0.215469	−	0.373203i
$619$	−16.4533	−	28.4980i	−0.661315	−	1.14543i	−0.980270	−	0.197661i	$-0.936665\pi$
$619$	−16.4533	−	28.4980i	−0.661315	−	1.14543i	0.318956	−	0.947770i	$-0.396668\pi$
$620$	7.14934	−	2.60215i	0.287124	−	0.104505i
$621$	11.4316	+	6.60003i	0.458734	+	0.264850i
$622$	−7.56237	+	6.34559i	−0.303224	+	0.254435i
$623$		−	14.2629i		−	0.571432i
$624$	73.0714	+	87.0831i	2.92520	+	3.48611i
$625$	−10.4088	−	3.78848i	−0.416350	−	0.151539i
$626$	7.59361	+	43.0655i	0.303502	+	1.72124i
$627$	−14.8859	−	2.62478i	−0.594485	−	0.104824i
$628$	−62.5807			−2.49724
$629$	−1.78612	−	7.76951i	−0.0712173	−	0.309790i
$630$	−6.32170			−0.251863
$631$	8.99243	+	1.58561i	0.357983	+	0.0631221i	0.349747	−	0.936844i	$-0.386267\pi$
$631$	8.99243	+	1.58561i	0.357983	+	0.0631221i	0.00823558	+	0.999966i	$0.497379\pi$
$632$	17.8270	+	101.102i	0.709118	+	4.02161i
$633$	−12.1415	−	4.41915i	−0.482582	−	0.175646i
$634$	−39.3136	−	46.8521i	−1.56134	−	1.86074i
$635$			1.31487i			0.0521790i
$636$	85.0907	−	71.3996i	3.37407	−	2.83118i
$637$	12.6387	+	7.29698i	0.500765	+	0.289117i
$638$	2.65388	−	0.965933i	0.105068	−	0.0382417i
$639$	3.55155	+	6.15146i	0.140497	+	0.243348i
$640$	2.00763	−	3.47731i	0.0793585	−	0.137453i
$641$	3.28290	−	18.6183i	0.129667	−	0.735378i	−0.848759	−	0.528780i	$-0.822650\pi$
$641$	3.28290	−	18.6183i	0.129667	−	0.735378i	0.978426	−	0.206598i	$-0.0662392\pi$
$642$	−34.5506	+	94.9269i	−1.36360	+	3.74646i
$643$	4.95729	−	2.86209i	0.195496	−	0.112870i	−0.399057	−	0.916926i	$-0.630662\pi$
$643$	4.95729	−	2.86209i	0.195496	−	0.112870i	0.594553	+	0.804056i	$0.297329\pi$
$644$	−23.0673	+	27.4905i	−0.908978	+	1.08328i
$645$	−13.0612	−	10.9596i	−0.514282	−	0.431534i
$646$	4.93548	+	13.5601i	0.194184	+	0.533516i
$647$	−8.39393	+	1.48008i	−0.330000	+	0.0581878i	−0.336193	−	0.941793i	$-0.609140\pi$
$647$	−8.39393	+	1.48008i	−0.330000	+	0.0581878i	0.00619377	+	0.999981i	$0.498028\pi$
$648$	84.2379	−	14.8534i	3.30918	−	0.583497i
$649$	6.37409	+	17.5127i	0.250205	+	0.687432i
$650$	43.3897	+	36.4083i	1.70188	+	1.42805i
$651$	−4.21160	+	5.01919i	−0.165066	+	0.196717i
$652$	−54.4946	+	31.4625i	−2.13417	+	1.23216i
$653$	8.56441	−	23.5305i	0.335151	−	0.920820i	−0.651598	−	0.758565i	$-0.725901\pi$
$653$	8.56441	−	23.5305i	0.335151	−	0.920820i	0.986749	−	0.162255i	$-0.0518768\pi$
$654$	7.26915	−	41.2254i	0.284246	−	1.61204i
$655$	4.85094	−	8.40207i	0.189542	−	0.328296i
$656$	11.8573	+	20.5374i	0.462949	+	0.801851i
$657$	−14.8353	+	5.39962i	−0.578781	+	0.210659i
$658$	−16.8925	−	9.75290i	−0.658539	−	0.380208i
$659$	12.2404	−	10.2709i	0.476820	−	0.400099i	−0.372455	−	0.928050i	$-0.621484\pi$
$659$	12.2404	−	10.2709i	0.476820	−	0.400099i	0.849275	+	0.527951i	$0.177040\pi$
$660$			17.7138i			0.689508i
$661$	15.1978	+	18.1120i	0.591125	+	0.704476i	0.975822	−	0.218567i	$-0.0701383\pi$
$661$	15.1978	+	18.1120i	0.591125	+	0.704476i	−0.384696	+	0.923043i	$0.625694\pi$
$662$	−33.9801	−	12.3678i	−1.32068	−	0.480686i
$663$	2.49639	+	14.1577i	0.0969518	+	0.549841i
$664$	−11.2257	−	1.97940i	−0.435643	−	0.0768157i
$665$	8.63866			0.334993
$666$	−18.6069	+	0.957794i	−0.721004	+	0.0371138i
$667$	−2.13792			−0.0827805
$668$	113.893	+	20.0823i	4.40664	+	0.777009i
$669$	0.861162	+	4.88389i	0.0332944	+	0.188822i
$670$	−12.1426	−	4.41956i	−0.469111	−	0.170742i
$671$	4.71981	+	5.62486i	0.182206	+	0.217145i
$672$			50.2744i			1.93938i
$673$	29.9818	−	25.1577i	1.15571	−	0.969758i	0.155875	−	0.987777i	$-0.450180\pi$
$673$	29.9818	−	25.1577i	1.15571	−	0.969758i	0.999838	+	0.0180192i	$0.00573598\pi$
$674$	−27.0593	−	15.6227i	−1.04228	−	0.601763i
$675$	14.1006	−	5.13221i	0.542733	−	0.197539i
$676$	−39.0919	−	67.7092i	−1.50354	−	2.60420i
$677$	6.70016	−	11.6050i	0.257508	−	0.446017i	−0.708066	−	0.706147i	$-0.750432\pi$
$677$	6.70016	−	11.6050i	0.257508	−	0.446017i	0.965574	+	0.260129i	$0.0837652\pi$
$678$	9.34412	−	52.9931i	0.358859	−	2.03519i
$679$	5.35961	−	14.7254i	0.205683	−	0.565109i
$680$	8.69148	−	5.01803i	0.333303	−	0.192433i
$681$	6.65079	−	7.92610i	0.254859	−	0.303729i
$682$	5.53112	+	4.64116i	0.211798	+	0.177719i
$683$	−10.3475	−	28.4296i	−0.395938	−	1.08783i	−0.964245	−	0.265013i	$-0.914624\pi$
$683$	−10.3475	−	28.4296i	−0.395938	−	1.08783i	0.568307	−	0.822817i	$-0.307599\pi$
$684$	23.6131	−	4.16362i	0.902868	−	0.159200i
$685$	7.34615	−	1.29532i	0.280682	−	0.0494918i
$686$	18.0930	+	49.7102i	0.690795	+	1.89794i
$687$	15.3395	+	12.8713i	0.585237	+	0.491072i
$688$	−55.8234	+	66.5278i	−2.12825	+	2.53635i
$689$	−51.5036	+	29.7356i	−1.96213	+	1.13284i
$690$	6.45073	−	17.7232i	0.245575	−	0.674712i
$691$	−4.08085	+	23.1436i	−0.155243	+	0.880426i	0.803321	+	0.595547i	$0.203065\pi$
$691$	−4.08085	+	23.1436i	−0.155243	+	0.880426i	−0.958563	+	0.284879i	$0.908047\pi$
$692$	−11.5167	+	19.9475i	−0.437800	+	0.758292i
$693$	−2.13272	−	3.69398i	−0.0810153	−	0.140323i
$694$	−71.6993	+	26.0964i	−2.72167	+	0.990606i
$695$	4.79418	+	2.76792i	0.181854	+	0.104993i
$696$	−7.28402	+	6.11202i	−0.276100	+	0.231675i
$697$			2.99901i			0.113595i
$698$	24.6784	+	29.4106i	0.934093	+	1.11321i
$699$	5.30817	+	1.93202i	0.200773	+	0.0730756i
$700$	7.08396	+	40.1751i	0.267748	+	1.51848i
$701$	19.5898	+	3.45422i	0.739898	+	0.130464i	0.530879	−	0.847448i	$-0.321862\pi$
$701$	19.5898	+	3.45422i	0.739898	+	0.130464i	0.209019	+	0.977912i	$0.432973\pi$
$702$	−52.9644			−1.99901
$703$	25.4265	−	1.30883i	0.958979	−	0.0493636i
$704$	18.7222			0.705620
$705$	7.17784	+	1.26565i	0.270333	+	0.0476670i
$706$	−12.4909	−	70.8396i	−0.470102	−	2.66608i
$707$	−22.0763	−	8.03512i	−0.830265	−	0.302192i
$708$	−67.9609	−	80.9926i	−2.55413	−	3.04389i
$709$			2.65540i			0.0997258i	0.998756	+	0.0498629i	$0.0158784\pi$
$709$			2.65540i			0.0997258i	−0.998756	+	0.0498629i	$0.984122\pi$
$710$	−12.2561	+	10.2841i	−0.459963	+	0.385955i
$711$	13.4794	+	7.78235i	0.505518	+	0.291861i
$712$	49.7275	−	18.0993i	1.86362	−	0.678301i
$713$	−2.73291	−	4.73353i	−0.102348	−	0.177272i
$714$	−7.28175	+	12.6124i	−0.272512	+	0.472005i
$715$	1.64688	−	9.33989i	0.0615897	−	0.349292i
$716$	16.3740	−	44.9872i	0.611925	−	1.68125i
$717$	−33.6064	+	19.4026i	−1.25505	+	0.724605i
$718$	18.1736	−	21.6585i	0.678233	−	0.808287i
$719$	33.7594	+	28.3275i	1.25901	+	1.05644i	0.995786	+	0.0917029i	$0.0292310\pi$
$719$	33.7594	+	28.3275i	1.25901	+	1.05644i	0.263226	+	0.964734i	$0.415213\pi$
$720$	−4.11515	−	11.3063i	−0.153363	−	0.421360i
$721$	−4.06829	+	0.717350i	−0.151511	+	0.0267155i
$722$	3.83540	−	0.676285i	0.142739	−	0.0251687i
$723$	−1.06229	−	2.91861i	−0.0395069	−	0.108544i
$724$	33.3881	+	28.0159i	1.24086	+	1.04120i
$725$	−1.56219	+	1.86175i	−0.0580185	+	0.0691437i
$726$	36.5792	−	21.1190i	1.35758	−	0.783799i
$727$	−3.72743	+	10.2410i	−0.138243	+	0.379819i	−0.989424	−	0.145053i	$-0.953665\pi$
$727$	−3.72743	+	10.2410i	−0.138243	+	0.379819i	0.851181	+	0.524872i	$0.175887\pi$
$728$	14.8390	−	84.1561i	0.549969	−	3.11903i
$729$	−4.98198	+	8.62904i	−0.184518	+	0.319594i
$730$	−17.7800	−	30.7959i	−0.658067	−	1.13981i
$731$	−10.3204	+	3.75633i	−0.381715	+	0.138933i
$732$	−36.0756	−	20.8282i	−1.33339	−	0.769834i
$733$	−24.0430	+	20.1744i	−0.888047	+	0.745160i	−0.967817	−	0.251653i	$-0.919026\pi$
$733$	−24.0430	+	20.1744i	−0.888047	+	0.745160i	0.0797705	+	0.996813i	$0.474581\pi$
$734$			22.3789i			0.826021i
$735$	−3.55093	−	4.23183i	−0.130978	−	0.156094i
$736$	−39.4101	−	14.3441i	−1.45268	−	0.528731i
$737$	−1.51400	−	8.58634i	−0.0557690	−	0.316282i
$738$	6.90243	+	1.21708i	0.254082	+	0.0448015i
$739$	32.4797			1.19479			0.597393	−	0.801949i	$-0.296203\pi$
$739$	32.4797			1.19479			0.597393	+	0.801949i	$0.296203\pi$
$740$	−6.68474	−	29.0781i	−0.245736	−	1.06893i
$741$	−45.9121			−1.68662
$742$	−59.3310	−	10.4617i	−2.17811	−	0.384060i
$743$	−3.91602	−	22.2089i	−0.143665	−	0.814764i	−0.968429	−	0.249288i	$-0.919803\pi$
$743$	−3.91602	−	22.2089i	−0.143665	−	0.814764i	0.824764	−	0.565476i	$-0.191308\pi$
$744$	−22.8437	−	8.31444i	−0.837492	−	0.304822i
$745$	−4.69428	−	5.59443i	−0.171985	−	0.204964i
$746$			39.0421i			1.42943i
$747$	−1.32389	+	1.11087i	−0.0484385	+	0.0406447i
$748$	9.88158	+	5.70513i	0.361306	+	0.208600i
$749$	36.6051	−	13.3232i	1.33752	−	0.486818i
$750$	−24.1008	−	41.7437i	−0.880035	−	1.52427i
$751$	−12.7936	+	22.1592i	−0.466845	+	0.808599i	−0.999283	−	0.0378699i	$-0.987943\pi$
$751$	−12.7936	+	22.1592i	−0.466845	+	0.808599i	0.532438	+	0.846469i	$0.321276\pi$
$752$	6.44665	−	36.5608i	0.235085	−	1.33323i
$753$	−11.1999	+	30.7715i	−0.408148	+	1.12138i
$754$	7.42899	−	4.28913i	0.270548	−	0.156201i
$755$	2.92866	−	3.49024i	0.106585	−	0.127023i
$756$	−29.2221	−	24.5203i	−1.06280	−	0.891793i
$757$	13.8986	+	38.1860i	0.505152	+	1.38789i	0.886185	+	0.463332i	$0.153346\pi$
$757$	13.8986	+	38.1860i	0.505152	+	1.38789i	−0.381033	+	0.924562i	$0.624431\pi$
$758$	12.7135	−	2.24173i	0.461774	−	0.0814233i
$759$	12.5325	−	2.20982i	0.454901	−	0.0802113i
$760$	10.9622	+	30.1185i	0.397642	+	1.09251i
$761$	−13.3742	−	11.2223i	−0.484814	−	0.406807i	0.367349	−	0.930083i	$-0.380265\pi$
$761$	−13.3742	−	11.2223i	−0.484814	−	0.406807i	−0.852163	+	0.523276i	$0.824710\pi$
$762$	4.55045	−	5.42302i	0.164846	−	0.196455i
$763$	−13.9796	+	8.07115i	−0.506097	+	0.292195i
$764$	−11.0671	+	30.4066i	−0.400394	+	1.10007i
$765$	0.264221	−	1.49847i	0.00955292	−	0.0541773i
$766$	40.3770	−	69.9351i	1.45888	−	2.52686i
$767$	28.3035	+	49.0231i	1.02198	+	1.77012i
$768$	20.2611	−	7.37444i	0.731110	−	0.266102i
$769$	−17.3511	−	10.0177i	−0.625698	−	0.361247i	0.153386	−	0.988166i	$-0.450982\pi$
$769$	−17.3511	−	10.0177i	−0.625698	−	0.361247i	−0.779084	+	0.626920i	$0.784315\pi$
$770$	7.35983	−	6.17563i	0.265230	−	0.222554i
$771$			31.9364i			1.15016i
$772$	−7.67844	−	9.15081i	−0.276353	−	0.329345i
$773$	38.3674	+	13.9646i	1.37998	+	0.502271i	0.922172	−	0.386781i	$-0.126413\pi$
$773$	38.3674	+	13.9646i	1.37998	+	0.502271i	0.457807	+	0.889052i	$0.348635\pi$
$774$	4.45712	+	25.2776i	0.160208	+	0.908585i
$775$	−6.11904	−	1.07895i	−0.219802	−	0.0387571i
$776$	58.1411			2.08714
$777$	17.5065	+	18.8084i	0.628041	+	0.674749i
$778$	102.903			3.68924
$779$	−9.43222	−	1.66315i	−0.337944	−	0.0595887i
$780$	9.34299	+	52.9867i	0.334533	+	1.89723i
$781$	−10.1441	−	3.69215i	−0.362984	−	0.132115i
$782$	−7.80924	−	9.30668i	−0.279258	−	0.332806i
$783$		−	2.27258i		−	0.0812155i
$784$	−21.5551	+	18.0869i	−0.769825	+	0.645960i
$785$	−10.9838	−	6.34148i	−0.392027	−	0.226337i
$786$	−49.0847	+	17.8654i	−1.75079	+	0.637236i
$787$	26.5477	+	45.9819i	0.946322	+	1.63908i	0.753082	+	0.657927i	$0.228566\pi$
$787$	26.5477	+	45.9819i	0.946322	+	1.63908i	0.193240	+	0.981151i	$0.438100\pi$
$788$	−67.1470	+	116.302i	−2.39201	+	4.14309i
$789$	1.62834	−	9.23478i	0.0579705	−	0.328767i
$790$	−11.9906	+	32.9440i	−0.426608	+	1.17210i
$791$	−17.9701	+	10.3751i	−0.638944	+	0.368895i
$792$	10.1726	−	12.1233i	0.361468	−	0.430781i
$793$	17.0850	+	14.3360i	0.606707	+	0.509087i
$794$	−8.27318	−	22.7304i	−0.293604	−	0.806671i
$795$	22.1697	−	3.90912i	0.786279	−	0.138642i
$796$	64.4154	−	11.3582i	2.28314	−	0.402580i
$797$	−13.8787	−	38.1313i	−0.491608	−	1.35068i	−0.899208	−	0.437521i	$-0.855857\pi$
$797$	−13.8787	−	38.1313i	−0.491608	−	1.35068i	0.407601	−	0.913160i	$-0.366366\pi$
$798$	−35.6291	−	29.8963i	−1.26126	−	1.05832i
$799$	3.01782	−	3.59650i	0.106763	−	0.127235i
$800$	−41.2886	+	23.8380i	−1.45977	+	0.842799i
$801$	2.74407	−	7.53928i	0.0969571	−	0.266387i
$802$	1.12256	−	6.36633i	0.0396388	−	0.224803i
$803$	11.9967	−	20.7789i	0.423354	−	0.733270i
$804$	24.7316	+	42.8363i	0.872215	+	1.51072i
$805$	−6.83432	+	2.48749i	−0.240878	+	0.0876724i
$806$	18.9930	+	10.9656i	0.669001	+	0.386248i
$807$	27.1515	−	22.7828i	0.955778	−	0.801993i
$808$		−	87.1651i		−	3.06646i
$809$	−10.2354	−	12.1980i	−0.359856	−	0.428860i	0.555493	−	0.831521i	$-0.312530\pi$
$809$	−10.2354	−	12.1980i	−0.359856	−	0.428860i	−0.915349	+	0.402661i	$0.868085\pi$
$810$	27.4489	+	9.99060i	0.964457	+	0.351034i
$811$	−1.84097	−	10.4407i	−0.0646452	−	0.366621i	−0.999919	−	0.0126972i	$-0.995958\pi$
$811$	−1.84097	−	10.4407i	−0.0646452	−	0.366621i	0.935274	−	0.353924i	$-0.115153\pi$
$812$	6.08449	+	1.07286i	0.213524	+	0.0376500i
$813$	34.4623			1.20865
$814$	20.7268	−	19.2921i	0.726475	−	0.676186i
$815$	−12.7527			−0.446708
$816$	−27.2971	−	4.81322i	−0.955590	−	0.168496i
$817$	−6.09069	−	34.5420i	−0.213086	−	1.20847i
$818$	−8.18446	−	2.97890i	−0.286163	−	0.104155i
$819$	−8.32789	−	9.92479i	−0.291000	−	0.346800i
$820$			11.2241i			0.391962i
$821$	−1.11689	+	0.937186i	−0.0389799	+	0.0327080i	−0.662069	−	0.749442i	$-0.730322\pi$
$821$	−1.11689	+	0.937186i	−0.0389799	+	0.0327080i	0.623090	+	0.782150i	$0.285877\pi$
$822$	−34.7811	−	20.0809i	−1.21313	−	0.700401i
$823$	−28.6794	+	10.4384i	−0.999700	+	0.363861i	−0.789469	−	0.613790i	$-0.789644\pi$
$823$	−28.6794	+	10.4384i	−0.999700	+	0.363861i	−0.210231	+	0.977652i	$0.567422\pi$
$824$	−7.66359	−	13.2737i	−0.266974	−	0.462412i
$825$	7.23324	−	12.5283i	0.251829	−	0.436181i
$826$	−9.95781	+	56.4736i	−0.346477	+	1.96497i
$827$	−7.35407	+	20.2051i	−0.255726	+	0.702602i	0.743693	+	0.668521i	$0.233072\pi$
$827$	−7.35407	+	20.2051i	−0.255726	+	0.702602i	−0.999419	+	0.0340804i	$0.989150\pi$
$828$	−17.4821	+	10.0933i	−0.607546	+	0.350767i
$829$	−2.16679	+	2.58228i	−0.0752559	+	0.0896865i	−0.802359	−	0.596842i	$-0.796422\pi$
$829$	−2.16679	+	2.58228i	−0.0752559	+	0.0896865i	0.727103	+	0.686529i	$0.240866\pi$
$830$	−2.98196	−	2.50216i	−0.103505	−	0.0868512i
$831$	−16.7049	−	45.8964i	−0.579487	−	1.59213i
$832$	56.0032	−	9.87487i	1.94156	−	0.342349i
$833$	−3.50437	+	0.617915i	−0.121419	+	0.0214095i
$834$	−10.1939	−	28.0075i	−0.352985	−	0.969819i
$835$	17.9547	+	15.0658i	0.621348	+	0.521373i
$836$	−23.4233	+	27.9148i	−0.810112	+	0.965454i
$837$	5.03170	−	2.90505i	0.173921	−	0.100413i
$838$	−12.9029	+	35.4505i	−0.445724	+	1.22462i
$839$	−7.89313	+	44.7641i	−0.272501	+	1.54543i	0.474289	+	0.880369i	$0.342705\pi$
$839$	−7.89313	+	44.7641i	−0.272501	+	1.54543i	−0.746790	+	0.665060i	$0.768406\pi$
$840$	−16.1736	+	28.0134i	−0.558041	+	0.966555i
$841$	−14.3160	−	24.7960i	−0.493654	−	0.855034i
$842$	25.3004	−	9.20858i	0.871908	−	0.317349i
$843$	27.2858	+	15.7534i	0.939772	+	0.542577i
$844$	−23.8616	+	20.0222i	−0.821349	+	0.689193i
$845$		−	15.8452i		−	0.545091i
$846$	−7.05288	−	8.40530i	−0.242483	−	0.288980i
$847$	−15.3053	−	5.57066i	−0.525896	−	0.191410i
$848$	−19.9113	−	112.923i	−0.683758	−	3.87779i
$849$	6.10238	+	1.07601i	0.209433	+	0.0369287i
$850$	−13.8108			−0.473705
$851$	−19.7388	+	8.35698i	−0.676639	+	0.286474i
$852$	61.2424			2.09813
$853$	−18.9115	−	3.33461i	−0.647518	−	0.114175i	−0.159763	−	0.987155i	$-0.551073\pi$
$853$	−18.9115	−	3.33461i	−0.647518	−	0.114175i	−0.487755	+	0.872981i	$0.662184\pi$
$854$	3.92333	+	22.2503i	0.134254	+	0.761390i
$855$	4.56633	+	1.66201i	0.156165	+	0.0568395i
$856$	92.9019	+	110.716i	3.17532	+	3.78420i
$857$		−	53.4371i		−	1.82538i	−0.408655	−	0.912689i	$-0.634002\pi$
$857$		−	53.4371i		−	1.82538i	0.408655	−	0.912689i	$-0.365998\pi$
$858$	−39.1155	+	32.8218i	−1.33538	+	1.12052i
$859$	−10.1449	−	5.85715i	−0.346139	−	0.199843i	0.316845	−	0.948477i	$-0.397377\pi$
$859$	−10.1449	−	5.85715i	−0.346139	−	0.199843i	−0.662983	+	0.748634i	$0.730710\pi$
$860$	−38.6252	+	14.0584i	−1.31711	+	0.479388i
$861$	−4.83303	−	8.37106i	−0.164709	−	0.285285i
$862$	15.2985	−	26.4977i	0.521068	−	0.902516i
$863$	−2.09213	+	11.8651i	−0.0712170	+	0.403891i	0.928271	+	0.371904i	$0.121295\pi$
$863$	−2.09213	+	11.8651i	−0.0712170	+	0.403891i	−0.999488	+	0.0319877i	$0.989816\pi$
$864$	15.2476	−	41.8926i	0.518735	−	1.42521i
$865$	−4.04268	+	2.33404i	−0.137455	+	0.0793599i
$866$	61.1917	−	72.9254i	2.07938	−	2.47811i
$867$	23.8902	+	20.0462i	0.811352	+	0.680805i
$868$	5.40242	+	14.8430i	0.183370	+	0.503805i
$869$	−23.2955	+	4.10762i	−0.790245	+	0.139342i
$870$	−3.19781	+	0.563860i	−0.108416	+	0.0191166i
$871$	−9.05758	−	24.8855i	−0.306904	−	0.843213i
$872$	−45.8798	−	38.4977i	−1.55369	−	1.30370i
$873$	5.66610	−	6.75259i	0.191768	−	0.228541i
$874$	33.6013	−	19.3997i	1.13658	−	0.656206i
$875$	−6.35718	+	17.4662i	−0.214912	+	0.590466i
$876$	−23.6367	+	134.050i	−0.798609	+	4.52914i
$877$	11.8245	−	20.4807i	0.399286	−	0.691583i	−0.594352	−	0.804205i	$-0.702591\pi$
$877$	11.8245	−	20.4807i	0.399286	−	0.691583i	0.993638	+	0.112622i	$0.0359248\pi$
$878$	−15.7931	−	27.3545i	−0.532992	−	0.923169i
$879$	−25.6949	+	9.35220i	−0.866669	+	0.315442i
$880$	15.8360	+	9.14289i	0.533830	+	0.308207i
$881$	−5.89364	+	4.94535i	−0.198562	+	0.166613i	−0.736647	−	0.676277i	$-0.763592\pi$
$881$	−5.89364	+	4.94535i	−0.198562	+	0.166613i	0.538086	+	0.842890i	$0.319148\pi$
$882$			8.31633i			0.280025i
$883$	−21.1313	−	25.1833i	−0.711126	−	0.847486i	0.282611	−	0.959235i	$-0.408799\pi$
$883$	−21.1313	−	25.1833i	−0.711126	−	0.847486i	−0.993737	+	0.111748i	$0.964355\pi$
$884$	32.5676	+	11.8536i	1.09537	+	0.398681i
$885$	−3.72085	−	21.1020i	−0.125075	−	0.709336i
$886$	60.9712	+	10.7509i	2.04837	+	0.361182i
$887$	16.4422			0.552075			0.276037	−	0.961147i	$-0.410979\pi$
$887$	16.4422			0.552075			0.276037	+	0.961147i	$0.410979\pi$
$888$	−43.3600	+	84.9034i	−1.45507	+	2.84917i
$889$	−2.72985			−0.0915564
$890$	17.7970	+	3.13808i	0.596555	+	0.105189i
$891$	3.42247	+	19.4098i	0.114657	+	0.650252i
$892$	11.2346	+	4.08906i	0.376162	+	0.136912i
$893$	9.63782	+	11.4859i	0.322517	+	0.384361i
$894$			39.3193i			1.31503i
$895$	7.43254	−	6.23664i	0.248442	−	0.208468i
$896$	7.21939	+	4.16812i	0.241183	+	0.139247i
$897$	36.3225	−	13.2203i	1.21277	−	0.441414i
$898$	6.56272	+	11.3670i	0.219001	+	0.379321i
$899$	−0.470510	+	0.814947i	−0.0156924	+	0.0271800i
$900$	−3.98484	+	22.5992i	−0.132828	+	0.753305i
$901$	4.95958	−	13.6263i	0.165227	−	0.453959i
$902$	−9.22488	+	5.32599i	−0.307155	+	0.177336i
$903$	22.7537	−	27.1168i	0.757195	−	0.902390i
$904$	−58.9761	−	49.4868i	−1.96152	−	1.64591i
$905$	3.02113	+	8.30048i	0.100426	+	0.275917i
$906$	−24.1578	+	4.25967i	−0.802590	+	0.141518i
$907$	−9.14252	+	1.61207i	−0.303572	+	0.0535280i	−0.323359	−	0.946276i	$-0.604812\pi$
$907$	−9.14252	+	1.61207i	−0.303572	+	0.0535280i	0.0197871	+	0.999804i	$0.493701\pi$
$908$	−8.53129	−	23.4395i	−0.283121	−	0.777868i
$909$	−10.1235	−	8.49461i	−0.335775	−	0.281748i
$910$	18.7579	−	22.3548i	0.621820	−	0.741056i
$911$	−12.4920	+	7.21223i	−0.413877	+	0.238952i	−0.692454	−	0.721462i	$-0.743471\pi$
$911$	−12.4920	+	7.21223i	−0.413877	+	0.238952i	0.278577	+	0.960414i	$0.410137\pi$
$912$	30.2762	−	83.1833i	1.00255	−	2.75447i
$913$	0.456086	−	2.58659i	0.0150943	−	0.0856037i
$914$	−30.2613	+	52.4142i	−1.00096	+	1.73371i
$915$	−4.22117	−	7.31128i	−0.139548	−	0.241704i
$916$	45.3627	−	16.5107i	1.49883	−	0.545529i
$917$	17.4439	+	10.0712i	0.576048	+	0.332581i
$918$	9.89290	−	8.30113i	0.326514	−	0.273978i
$919$		−	35.5649i		−	1.17318i	−0.809885	−	0.586588i	$-0.800471\pi$
$919$		−	35.5649i		−	1.17318i	0.809885	−	0.586588i	$-0.199529\pi$
$920$	−17.3452	−	20.6712i	−0.571853	−	0.681508i
$921$	−65.8803	−	23.9785i	−2.17083	−	0.790117i
$922$	5.90638	+	33.4967i	0.194516	+	1.10316i
$923$	−32.2911	−	5.69379i	−1.06287	−	0.187413i
$924$	−36.7763			−1.20985
$925$	−7.14588	+	23.2956i	−0.234955	+	0.765954i
$926$	−28.4959			−0.936435
$927$	−2.28848	−	0.403521i	−0.0751636	−	0.0132534i
$928$	1.25382	+	7.11079i	0.0411588	+	0.233423i
$929$	10.3365	+	3.76219i	0.339131	+	0.123434i	0.505971	−	0.862550i	$-0.331134\pi$
$929$	10.3365	+	3.76219i	0.339131	+	0.123434i	−0.166840	+	0.985984i	$0.553356\pi$
$930$	−5.33620	−	6.35944i	−0.174981	−	0.208534i
$931$		−	11.3643i		−	0.372451i
$932$	10.4321	−	8.75355i	0.341714	−	0.286732i
$933$	6.63238	+	3.82921i	0.217134	+	0.125363i
$934$	−87.6169	+	31.8899i	−2.86691	+	1.04347i
$935$	1.15623	+	2.00266i	0.0378129	+	0.0654939i
$936$	24.0347	−	41.6294i	0.785599	−	1.36070i
$937$	−8.45256	+	47.9368i	−0.276133	+	1.56603i	0.459206	+	0.888330i	$0.348134\pi$
$937$	−8.45256	+	47.9368i	−0.276133	+	1.56603i	−0.735340	+	0.677699i	$0.762977\pi$
$938$	9.17562	−	25.2098i	0.299595	−	0.823129i
$939$	29.3794	−	16.9622i	0.958761	−	0.553541i
$940$	11.2945	−	13.4603i	0.368386	−	0.439025i
$941$	−15.0774	−	12.6514i	−0.491508	−	0.412424i	0.363058	−	0.931766i	$-0.381733\pi$
$941$	−15.0774	−	12.6514i	−0.491508	−	0.412424i	−0.854566	+	0.519342i	$0.826177\pi$
$942$	23.3548	+	64.1668i	0.760941	+	2.09067i
$943$	7.94103	−	1.40022i	0.258596	−	0.0455974i
$944$	−107.484	+	18.9524i	−3.49832	+	0.616847i
$945$	−2.64417	−	7.26480i	−0.0860149	−	0.236324i
$946$	−29.8826	−	25.0745i	−0.971567	−	0.815241i
$947$	−12.2906	+	14.6473i	−0.399390	+	0.475974i	−0.927834	−	0.372994i	$-0.878331\pi$
$947$	−12.2906	+	14.6473i	−0.399390	+	0.475974i	0.528444	+	0.848968i	$0.322776\pi$
$948$	116.219	−	67.0989i	3.77461	−	2.17927i
$949$	24.9257	−	68.4827i	0.809121	−	2.22304i
$950$	7.65902	−	43.4364i	0.248491	−	1.40926i
$951$	−23.7236	+	41.0904i	−0.769290	+	1.33245i
$952$	10.4181	+	18.0447i	0.337653	+	0.584833i
$953$	43.9106	−	15.9822i	1.42240	−	0.517713i	0.487660	−	0.873034i	$-0.337851\pi$
$953$	43.9106	−	15.9822i	1.42240	−	0.517713i	0.934744	+	0.355321i	$0.115629\pi$
$954$	−29.3492	−	16.9448i	−0.950216	−	0.548607i
$955$	−5.02362	+	4.21531i	−0.162560	+	0.136404i
$956$			93.5509i			3.02565i
$957$	−1.40831	−	1.67836i	−0.0455241	−	0.0542536i
$958$	22.3059	+	8.11870i	0.720672	+	0.262303i
$959$	2.68927	+	15.2516i	0.0868412	+	0.492501i
$960$	−21.1989	−	3.73794i	−0.684193	−	0.120642i
$961$	28.5942			0.922393
$962$	51.8241	−	68.6399i	1.67087	−	2.21304i
$963$	21.9124			0.706119
$964$	−7.37393	−	1.30022i	−0.237498	−	0.0418774i
$965$	−0.420394	−	2.38417i	−0.0135329	−	0.0767491i
$966$	36.7959	+	13.3926i	1.18389	+	0.430900i
$967$	−5.95207	−	7.09340i	−0.191406	−	0.228108i	0.661803	−	0.749677i	$-0.269791\pi$
$967$	−5.95207	−	7.09340i	−0.191406	−	0.228108i	−0.853209	+	0.521569i	$0.825347\pi$
$968$		−	60.4306i		−	1.94231i
$969$	8.57564	−	7.19582i	0.275489	−	0.231163i
$970$	17.1948	+	9.92743i	0.552092	+	0.318751i
$971$	−4.93742	+	1.79707i	−0.158449	+	0.0576708i	−0.420027	−	0.907512i	$-0.637979\pi$
$971$	−4.93742	+	1.79707i	−0.158449	+	0.0576708i	0.261578	+	0.965182i	$0.415757\pi$
$972$	−28.2642	−	48.9550i	−0.906575	−	1.57023i
$973$	−5.74659	+	9.95338i	−0.184227	+	0.319091i
$974$	−4.43616	+	25.1587i	−0.142144	+	0.806137i
$975$	15.0286	−	41.2908i	0.481301	−	1.32236i
$976$	−37.2405	+	21.5008i	−1.19204	+	0.688224i
$977$	−12.7485	+	15.1930i	−0.407860	+	0.486069i	−0.930400	−	0.366546i	$-0.880540\pi$
$977$	−12.7485	+	15.1930i	−0.407860	+	0.486069i	0.522540	+	0.852615i	$0.324985\pi$
$978$	52.5970	+	44.1341i	1.68187	+	1.41125i
$979$	4.17038	+	11.4580i	0.133286	+	0.366200i
$980$	−13.1155	+	2.31261i	−0.418958	+	0.0738736i
$981$	−8.94236	+	1.57678i	−0.285508	+	0.0503427i
$982$	27.3521	+	75.1492i	0.872840	+	2.39811i
$983$	−9.79880	−	8.22217i	−0.312533	−	0.262246i	0.473005	−	0.881060i	$-0.343169\pi$
$983$	−9.79880	−	8.22217i	−0.312533	−	0.262246i	−0.785538	+	0.618813i	$0.787614\pi$
$984$	23.0526	−	27.4730i	0.734889	−	0.875806i
$985$	−23.5704	+	13.6084i	−0.751017	+	0.433600i
$986$	−0.715380	+	1.96549i	−0.0227823	+	0.0625939i
$987$	−2.62766	+	14.9022i	−0.0836393	+	0.474342i
$988$	−55.3420	+	95.8551i	−1.76066	+	3.04956i
$989$	14.7649	+	25.5735i	0.469495	+	0.813190i
$990$	5.07849	−	1.84842i	0.161405	−	0.0587466i
$991$	−31.1868	−	18.0057i	−0.990683	−	0.571971i	−0.0852045	−	0.996363i	$-0.527154\pi$
$991$	−31.1868	−	18.0057i	−0.990683	−	0.571971i	−0.905478	+	0.424392i	$0.860488\pi$
$992$	−14.1411	+	11.8658i	−0.448981	+	0.376740i
$993$			28.0527i			0.890224i
$994$	−21.3512	−	25.4454i	−0.677219	−	0.807078i
$995$	12.4567	+	4.53388i	0.394905	+	0.143734i
$996$	2.58745	+	14.6742i	0.0819865	+	0.464968i
$997$	−32.5484	−	5.73917i	−1.03082	−	0.181761i	−0.367442	−	0.930046i	$-0.619766\pi$
$997$	−32.5484	−	5.73917i	−1.03082	−	0.181761i	−0.663377	+	0.748285i	$0.730878\pi$
$998$	−71.8968			−2.27585
$999$	−8.88338	−	20.9822i	−0.281058	−	0.663847i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.h.a.4.1	✓	18
3.2	odd	2		333.2.bl.d.226.3		18
4.3	odd	2		592.2.bq.d.337.1		18
5.2	odd	4		925.2.ba.a.374.6		36
5.3	odd	4		925.2.ba.a.374.1		36
5.4	even	2		925.2.bb.a.226.3		18
37.3	even	18		1369.2.b.g.1368.18		18
37.18	odd	36		1369.2.a.m.1.18		18
37.19	odd	36		1369.2.a.m.1.1		18
37.28	even	18	inner	37.2.h.a.28.1	yes	18
37.34	even	9		1369.2.b.g.1368.1		18
111.65	odd	18		333.2.bl.d.28.3		18
148.139	odd	18		592.2.bq.d.65.1		18
185.28	odd	36		925.2.ba.a.324.6		36
185.102	odd	36		925.2.ba.a.324.1		36
185.139	even	18		925.2.bb.a.176.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.h.a.4.1	✓	18	1.1	even	1	trivial
37.2.h.a.28.1	yes	18	37.28	even	18	inner
333.2.bl.d.28.3		18	111.65	odd	18
333.2.bl.d.226.3		18	3.2	odd	2
592.2.bq.d.65.1		18	148.139	odd	18
592.2.bq.d.337.1		18	4.3	odd	2
925.2.ba.a.324.1		36	185.102	odd	36
925.2.ba.a.324.6		36	185.28	odd	36
925.2.ba.a.374.1		36	5.3	odd	4
925.2.ba.a.374.6		36	5.2	odd	4
925.2.bb.a.176.3		18	185.139	even	18
925.2.bb.a.226.3		18	5.4	even	2
1369.2.a.m.1.1		18	37.19	odd	36
1369.2.a.m.1.18		18	37.18	odd	36
1369.2.b.g.1368.1		18	37.34	even	9
1369.2.b.g.1368.18		18	37.3	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)

\(f(q)\)	\(=\)	\(q+(-2.59056 - 0.456785i) q^{2} +(0.354362 + 2.00969i) q^{3} +(4.62296 + 1.68262i) q^{4} +(0.640888 + 0.763781i) q^{5} -5.36808i q^{6} +(-1.58572 + 1.33057i) q^{7} +(-6.65125 - 3.84010i) q^{8} +(-1.09419 + 0.398252i) q^{9} +O(q^{10})\)	\(q+(-2.59056 - 0.456785i) q^{2} +(0.354362 + 2.00969i) q^{3} +(4.62296 + 1.68262i) q^{4} +(0.640888 + 0.763781i) q^{5} -5.36808i q^{6} +(-1.58572 + 1.33057i) q^{7} +(-6.65125 - 3.84010i) q^{8} +(-1.09419 + 0.398252i) q^{9} +(-1.31137 - 2.27137i) q^{10} +(0.884822 - 1.53256i) q^{11} +(-1.74334 + 9.88695i) q^{12} +(1.83841 - 5.05098i) q^{13} +(4.71567 - 2.72260i) q^{14} +(-1.30785 + 1.55864i) q^{15} +(7.93902 + 6.66163i) q^{16} +(0.448257 + 1.23158i) q^{17} +(3.01648 - 0.531886i) q^{18} +(-4.12204 + 0.726826i) q^{19} +(1.67765 + 4.60930i) q^{20} +(-3.23595 - 2.71529i) q^{21} +(-2.99223 + 3.56601i) q^{22} +(3.05179 - 1.76195i) q^{23} +(5.36045 - 14.7277i) q^{24} +(0.695618 - 3.94504i) q^{25} +(-7.06972 + 12.2451i) q^{26} +(1.87293 + 3.24402i) q^{27} +(-9.56954 + 3.48303i) q^{28} +(-0.525410 - 0.303345i) q^{29} +(4.10003 - 3.44034i) q^{30} -1.55107i q^{31} +(-7.65009 - 9.11702i) q^{32} +(3.39351 + 1.23514i) q^{33} +(-0.598670 - 3.39523i) q^{34} +(-2.03253 - 0.358390i) q^{35} -5.72849 q^{36} +(-6.03673 - 0.746918i) q^{37} +11.0104 q^{38} +(10.8023 + 1.90475i) q^{39} +(-1.32971 - 7.54117i) q^{40} +(2.15024 + 0.782625i) q^{41} +(7.14262 + 8.51224i) q^{42} +8.37985i q^{43} +(6.66921 - 5.59613i) q^{44} +(-1.00543 - 0.580485i) q^{45} +(-8.71067 + 3.17042i) q^{46} +(-1.79110 - 3.10228i) q^{47} +(-10.5745 + 18.3156i) q^{48} +(-0.471469 + 2.67384i) q^{49} +(-3.60408 + 9.90212i) q^{50} +(-2.31624 + 1.33728i) q^{51} +(16.9978 - 20.2571i) q^{52} +(-8.47562 - 7.11189i) q^{53} +(-3.37012 - 9.25934i) q^{54} +(1.73761 - 0.306387i) q^{55} +(15.6565 - 2.76067i) q^{56} +(-2.92139 - 8.02644i) q^{57} +(1.22254 + 1.02583i) q^{58} +(-6.76937 + 8.06742i) q^{59} +(-8.66875 + 5.00490i) q^{60} +(-1.41913 + 3.89904i) q^{61} +(-0.708506 + 4.01814i) q^{62} +(1.20517 - 2.08741i) q^{63} +(5.28982 + 9.16224i) q^{64} +(5.03605 - 1.83297i) q^{65} +(-8.22689 - 4.74979i) q^{66} +(3.77420 - 3.16693i) q^{67} +6.44777i q^{68} +(4.62240 + 5.50876i) q^{69} +(5.10169 + 1.85686i) q^{70} +(-1.05928 - 6.00749i) q^{71} +(8.80705 + 1.55292i) q^{72} +13.5583 q^{73} +(15.2973 + 4.69242i) q^{74} +8.17480 q^{75} +(-20.2790 - 3.57573i) q^{76} +(0.636103 + 3.60752i) q^{77} +(-27.1141 - 9.86871i) q^{78} +(-8.59215 - 10.2397i) q^{79} +10.3330i q^{80} +(-8.53173 + 7.15897i) q^{81} +(-5.21284 - 3.00964i) q^{82} +(1.39469 - 0.507624i) q^{83} +(-10.3909 - 17.9975i) q^{84} +(-0.653371 + 1.13167i) q^{85} +(3.82779 - 21.7085i) q^{86} +(0.423444 - 1.16340i) q^{87} +(-11.7704 + 6.79562i) q^{88} +(-4.42899 + 5.27827i) q^{89} +(2.33947 + 1.96305i) q^{90} +(3.80551 + 10.4556i) q^{91} +(17.0730 - 3.01043i) q^{92} +(3.11716 - 0.549640i) q^{93} +(3.22288 + 8.85480i) q^{94} +(-3.19690 - 2.68252i) q^{95} +(15.6114 - 18.6050i) q^{96} +(-6.55603 + 3.78513i) q^{97} +(2.44274 - 6.71137i) q^{98} +(-0.357818 + 2.02929i) 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

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