LMFDB - Embedded newform 276.3.f.b.139.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,3,Mod(139,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("276.139");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	276.f (of order $2$, degree $1$, 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:	$7.52045529634$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			139.13
Character	$\chi$	$=$	276.139
Dual form			276.3.f.b.139.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.678740 - 1.88131i) q^{2} -1.73205i q^{3} +(-3.07862 + 2.55384i) q^{4} +4.99031 q^{5} +(-3.25852 + 1.17561i) q^{6} +2.08864i q^{7} +(6.89413 + 4.05844i) q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(-0.678740 - 1.88131i) q^{2} -1.73205i q^{3} +(-3.07862 + 2.55384i) q^{4} +4.99031 q^{5} +(-3.25852 + 1.17561i) q^{6} +2.08864i q^{7} +(6.89413 + 4.05844i) q^{8} -3.00000 q^{9} +(-3.38713 - 9.38830i) q^{10} -19.2563i q^{11} +(4.42337 + 5.33233i) q^{12} -0.674821 q^{13} +(3.92937 - 1.41764i) q^{14} -8.64347i q^{15} +(2.95584 - 15.7246i) q^{16} +14.9945 q^{17} +(2.03622 + 5.64392i) q^{18} -26.4472i q^{19} +(-15.3633 + 12.7444i) q^{20} +3.61763 q^{21} +(-36.2270 + 13.0700i) q^{22} -4.79583i q^{23} +(7.02943 - 11.9410i) q^{24} -0.0967887 q^{25} +(0.458028 + 1.26954i) q^{26} +5.19615i q^{27} +(-5.33404 - 6.43013i) q^{28} -17.9282 q^{29} +(-16.2610 + 5.86667i) q^{30} +5.50459i q^{31} +(-31.5890 + 5.11207i) q^{32} -33.3529 q^{33} +(-10.1774 - 28.2093i) q^{34} +10.4230i q^{35} +(9.23587 - 7.66151i) q^{36} -8.99597 q^{37} +(-49.7552 + 17.9508i) q^{38} +1.16882i q^{39} +(34.4039 + 20.2529i) q^{40} +9.20603 q^{41} +(-2.45543 - 6.80586i) q^{42} -67.6848i q^{43} +(49.1774 + 59.2829i) q^{44} -14.9709 q^{45} +(-9.02243 + 3.25512i) q^{46} +77.8580i q^{47} +(-27.2358 - 5.11967i) q^{48} +44.6376 q^{49} +(0.0656944 + 0.182089i) q^{50} -25.9713i q^{51} +(2.07752 - 1.72338i) q^{52} -10.3701 q^{53} +(9.77555 - 3.52684i) q^{54} -96.0949i q^{55} +(-8.47661 + 14.3993i) q^{56} -45.8078 q^{57} +(12.1686 + 33.7284i) q^{58} -13.2518i q^{59} +(22.0740 + 26.6100i) q^{60} -17.0970 q^{61} +(10.3558 - 3.73619i) q^{62} -6.26591i q^{63} +(31.0581 + 55.9589i) q^{64} -3.36757 q^{65} +(22.6379 + 62.7470i) q^{66} -39.0544i q^{67} +(-46.1626 + 38.2936i) q^{68} -8.30662 q^{69} +(19.6088 - 7.07448i) q^{70} +42.7770i q^{71} +(-20.6824 - 12.1753i) q^{72} +98.4117 q^{73} +(6.10593 + 16.9242i) q^{74} +0.167643i q^{75} +(67.5417 + 81.4209i) q^{76} +40.2194 q^{77} +(2.19892 - 0.793328i) q^{78} -34.1723i q^{79} +(14.7506 - 78.4706i) q^{80} +9.00000 q^{81} +(-6.24850 - 17.3194i) q^{82} -91.0011i q^{83} +(-11.1373 + 9.23882i) q^{84} +74.8275 q^{85} +(-127.336 + 45.9404i) q^{86} +31.0526i q^{87} +(78.1505 - 132.755i) q^{88} +111.186 q^{89} +(10.1614 + 28.1649i) q^{90} -1.40946i q^{91} +(12.2478 + 14.7646i) q^{92} +9.53423 q^{93} +(146.475 - 52.8454i) q^{94} -131.980i q^{95} +(8.85437 + 54.7138i) q^{96} +16.5643 q^{97} +(-30.2973 - 83.9770i) q^{98} +57.7689i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	$ 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) $ 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.678740	−	1.88131i	−0.339370	−	0.940653i
$2$	−0.678740	−	1.88131i	−0.339370	−	0.940653i
$3$		−	1.73205i		−	0.577350i
$3$		−	1.73205i		−	0.577350i
$4$	−3.07862	+	2.55384i	−0.769656	+	0.638459i
$5$	4.99031			0.998062			0.499031	−	0.866584i	$-0.333689\pi$
$5$	4.99031			0.998062			0.499031	+	0.866584i	$0.333689\pi$
$6$	−3.25852	+	1.17561i	−0.543086	+	0.195935i
$7$			2.08864i			0.298377i	0.988809	+	0.149188i	$0.0476661\pi$
$7$			2.08864i			0.298377i	−0.988809	+	0.149188i	$0.952334\pi$
$8$	6.89413	+	4.05844i	0.861767	+	0.507305i
$9$	−3.00000			−0.333333
$10$	−3.38713	−	9.38830i	−0.338713	−	0.938830i
$11$		−	19.2563i		−	1.75057i	−0.483606	−	0.875286i	$-0.660673\pi$
$11$		−	19.2563i		−	1.75057i	0.483606	−	0.875286i	$-0.339327\pi$
$12$	4.42337	+	5.33233i	0.368614	+	0.444361i
$13$	−0.674821			−0.0519093			−0.0259547	−	0.999663i	$-0.508263\pi$
$13$	−0.674821			−0.0519093			−0.0259547	+	0.999663i	$0.508263\pi$
$14$	3.92937	−	1.41764i	0.280669	−	0.101260i
$15$		−	8.64347i		−	0.576232i
$16$	2.95584	−	15.7246i	0.184740	−	0.982787i
$17$	14.9945			0.882032			0.441016	−	0.897499i	$-0.354618\pi$
$17$	14.9945			0.882032			0.441016	+	0.897499i	$0.354618\pi$
$18$	2.03622	+	5.64392i	0.113123	+	0.313551i
$19$		−	26.4472i		−	1.39196i	−0.718063	−	0.695978i	$-0.754971\pi$
$19$		−	26.4472i		−	1.39196i	0.718063	−	0.695978i	$-0.245029\pi$
$20$	−15.3633	+	12.7444i	−0.768165	+	0.637222i
$21$	3.61763			0.172268
$22$	−36.2270	+	13.0700i	−1.64668	+	0.594092i
$23$		−	4.79583i		−	0.208514i
$23$		−	4.79583i		−	0.208514i
$24$	7.02943	−	11.9410i	0.292893	−	0.497541i
$25$	−0.0967887			−0.00387155
$26$	0.458028	+	1.26954i	0.0176165	+	0.0488286i
$27$			5.19615i			0.192450i
$28$	−5.33404	−	6.43013i	−0.190501	−	0.229647i
$29$	−17.9282			−0.618214			−0.309107	−	0.951027i	$-0.600030\pi$
$29$	−17.9282			−0.618214			−0.309107	+	0.951027i	$0.600030\pi$
$30$	−16.2610	+	5.86667i	−0.542034	+	0.195556i
$31$			5.50459i			0.177567i	0.996051	+	0.0887837i	$0.0282980\pi$
$31$			5.50459i			0.177567i	−0.996051	+	0.0887837i	$0.971702\pi$
$32$	−31.5890	+	5.11207i	−0.987157	+	0.159752i
$33$	−33.3529			−1.01069
$34$	−10.1774	−	28.2093i	−0.299335	−	0.829686i
$35$			10.4230i			0.297799i
$36$	9.23587	−	7.66151i	0.256552	−	0.212820i
$37$	−8.99597			−0.243134			−0.121567	−	0.992583i	$-0.538792\pi$
$37$	−8.99597			−0.243134			−0.121567	+	0.992583i	$0.538792\pi$
$38$	−49.7552	+	17.9508i	−1.30935	+	0.472388i
$39$			1.16882i			0.0299699i
$40$	34.4039	+	20.2529i	0.860097	+	0.506322i
$41$	9.20603			0.224537			0.112269	−	0.993678i	$-0.464188\pi$
$41$	9.20603			0.224537			0.112269	+	0.993678i	$0.464188\pi$
$42$	−2.45543	−	6.80586i	−0.0584626	−	0.162044i
$43$		−	67.6848i		−	1.57407i	−0.616911	−	0.787033i	$-0.711616\pi$
$43$		−	67.6848i		−	1.57407i	0.616911	−	0.787033i	$-0.288384\pi$
$44$	49.1774	+	59.2829i	1.11767	+	1.34734i
$45$	−14.9709			−0.332687
$46$	−9.02243	+	3.25512i	−0.196140	+	0.0707636i
$47$			77.8580i			1.65655i	0.560319	+	0.828277i	$0.310678\pi$
$47$			77.8580i			1.65655i	−0.560319	+	0.828277i	$0.689322\pi$
$48$	−27.2358	−	5.11967i	−0.567413	−	0.106660i
$49$	44.6376			0.910971
$50$	0.0656944	+	0.182089i	0.00131389	+	0.00364178i
$51$		−	25.9713i		−	0.509242i
$52$	2.07752	−	1.72338i	0.0399523	−	0.0331420i
$53$	−10.3701			−0.195663			−0.0978314	−	0.995203i	$-0.531191\pi$
$53$	−10.3701			−0.195663			−0.0978314	+	0.995203i	$0.531191\pi$
$54$	9.77555	−	3.52684i	0.181029	−	0.0653118i
$55$		−	96.0949i		−	1.74718i
$56$	−8.47661	+	14.3993i	−0.151368	+	0.257131i
$57$	−45.8078			−0.803646
$58$	12.1686	+	33.7284i	0.209803	+	0.581525i
$59$		−	13.2518i		−	0.224606i	−0.993674	−	0.112303i	$-0.964177\pi$
$59$		−	13.2518i		−	0.224606i	0.993674	−	0.112303i	$-0.0358228\pi$
$60$	22.0740	+	26.6100i	0.367900	+	0.443500i
$61$	−17.0970			−0.280278			−0.140139	−	0.990132i	$-0.544755\pi$
$61$	−17.0970			−0.280278			−0.140139	+	0.990132i	$0.544755\pi$
$62$	10.3558	−	3.73619i	0.167029	−	0.0602611i
$63$		−	6.26591i		−	0.0994589i
$64$	31.0581	+	55.9589i	0.485283	+	0.874357i
$65$	−3.36757			−0.0518087
$66$	22.6379	+	62.7470i	0.342999	+	0.950712i
$67$		−	39.0544i		−	0.582901i	−0.956586	−	0.291451i	$-0.905862\pi$
$67$		−	39.0544i		−	0.582901i	0.956586	−	0.291451i	$-0.0941379\pi$
$68$	−46.1626	+	38.2936i	−0.678861	+	0.563141i
$69$	−8.30662			−0.120386
$70$	19.6088	−	7.07448i	0.280125	−	0.101064i
$71$			42.7770i			0.602493i	0.953546	+	0.301247i	$0.0974027\pi$
$71$			42.7770i			0.602493i	−0.953546	+	0.301247i	$0.902597\pi$
$72$	−20.6824	−	12.1753i	−0.287256	−	0.169102i
$73$	98.4117			1.34811			0.674053	−	0.738683i	$-0.264552\pi$
$73$	98.4117			1.34811			0.674053	+	0.738683i	$0.264552\pi$
$74$	6.10593	+	16.9242i	0.0825125	+	0.228705i
$75$			0.167643i			0.00223524i
$76$	67.5417	+	81.4209i	0.888707	+	1.07133i
$77$	40.2194			0.522330
$78$	2.19892	−	0.793328i	0.0281912	−	0.0101709i
$79$		−	34.1723i		−	0.432561i	−0.976331	−	0.216281i	$-0.930607\pi$
$79$		−	34.1723i		−	0.432561i	0.976331	−	0.216281i	$-0.0693926\pi$
$80$	14.7506	−	78.4706i	0.184382	−	0.980883i
$81$	9.00000			0.111111
$82$	−6.24850	−	17.3194i	−0.0762012	−	0.211212i
$83$		−	91.0011i		−	1.09640i	−0.836348	−	0.548199i	$-0.815314\pi$
$83$		−	91.0011i		−	1.09640i	0.836348	−	0.548199i	$-0.184686\pi$
$84$	−11.1373	+	9.23882i	−0.132587	+	0.109986i
$85$	74.8275			0.880323
$86$	−127.336	+	45.9404i	−1.48065	+	0.534191i
$87$			31.0526i			0.356926i
$88$	78.1505	−	132.755i	0.888074	−	1.50858i
$89$	111.186			1.24928			0.624641	−	0.780912i	$-0.285245\pi$
$89$	111.186			1.24928			0.624641	+	0.780912i	$0.285245\pi$
$90$	10.1614	+	28.1649i	0.112904	+	0.312943i
$91$		−	1.40946i		−	0.0154885i
$92$	12.2478	+	14.7646i	0.133128	+	0.160484i
$93$	9.53423			0.102519
$94$	146.475	−	52.8454i	1.55824	−	0.562185i
$95$		−	131.980i		−	1.38926i
$96$	8.85437	+	54.7138i	0.0922330	+	0.569935i
$97$	16.5643			0.170766			0.0853828	−	0.996348i	$-0.472789\pi$
$97$	16.5643			0.170766			0.0853828	+	0.996348i	$0.472789\pi$
$98$	−30.2973	−	83.9770i	−0.309156	−	0.856908i
$99$			57.7689i			0.583524i
$100$	0.297976	−	0.247182i	0.00297976	−	0.00247182i
$101$	134.649			1.33316			0.666582	−	0.745432i	$-0.267757\pi$
$101$	134.649			1.33316			0.666582	+	0.745432i	$0.267757\pi$
$102$	−48.8600	+	17.6278i	−0.479020	+	0.172821i
$103$			125.591i			1.21933i	0.792658	+	0.609666i	$0.208696\pi$
$103$			125.591i			1.21933i	−0.792658	+	0.609666i	$0.791304\pi$
$104$	−4.65231	−	2.73872i	−0.0447337	−	0.0263339i
$105$	18.0531			0.171934
$106$	7.03863	+	19.5094i	0.0664021	+	0.184051i
$107$			188.450i			1.76122i	0.473844	+	0.880609i	$0.342866\pi$
$107$			188.450i			1.76122i	−0.473844	+	0.880609i	$0.657134\pi$
$108$	−13.2701	−	15.9970i	−0.122871	−	0.148120i
$109$	−182.041			−1.67011			−0.835053	−	0.550170i	$-0.814563\pi$
$109$	−182.041			−1.67011			−0.835053	+	0.550170i	$0.814563\pi$
$110$	−180.784	+	65.2235i	−1.64349	+	0.592941i
$111$			15.5815i			0.140374i
$112$	32.8430	+	6.17369i	0.293241	+	0.0551222i
$113$	151.109			1.33725			0.668624	−	0.743601i	$-0.266884\pi$
$113$	151.109			1.33725			0.668624	+	0.743601i	$0.266884\pi$
$114$	31.0916	+	86.1786i	0.272734	+	0.755952i
$115$		−	23.9327i		−	0.208110i
$116$	55.1942	−	45.7857i	0.475812	−	0.394704i
$117$	2.02446			0.0173031
$118$	−24.9307	+	8.99452i	−0.211277	+	0.0762247i
$119$			31.3182i			0.263178i
$120$	35.0790	−	59.5892i	0.292325	−	0.496577i
$121$	−249.805			−2.06450
$122$	11.6044	+	32.1646i	0.0951180	+	0.263644i
$123$		−	15.9453i		−	0.129637i
$124$	−14.0578	−	16.9466i	−0.113370	−	0.136666i
$125$	−125.241			−1.00193
$126$	−11.7881	+	4.25293i	−0.0935563	+	0.0337534i
$127$			1.94353i			0.0153034i	0.999971	+	0.00765168i	$0.00243563\pi$
$127$			1.94353i			0.0153034i	−0.999971	+	0.00765168i	$0.997564\pi$
$128$	84.1953	−	96.4113i	0.657776	−	0.753214i
$129$	−117.234			−0.908787
$130$	2.28570	+	6.33542i	0.0175823	+	0.0487340i
$131$			158.447i			1.20952i	0.796407	+	0.604761i	$0.206731\pi$
$131$			158.447i			1.20952i	−0.796407	+	0.604761i	$0.793269\pi$
$132$	102.681	−	85.1778i	0.777886	−	0.645286i
$133$	55.2386			0.415327
$134$	−73.4733	+	26.5078i	−0.548308	+	0.197819i
$135$			25.9304i			0.192077i
$136$	103.374	+	60.8545i	0.760106	+	0.447459i
$137$	40.2417			0.293735			0.146868	−	0.989156i	$-0.453081\pi$
$137$	40.2417			0.293735			0.146868	+	0.989156i	$0.453081\pi$
$138$	5.63804	+	15.6273i	0.0408554	+	0.113241i
$139$			191.528i			1.37790i	0.724808	+	0.688951i	$0.241929\pi$
$139$			191.528i			1.37790i	−0.724808	+	0.688951i	$0.758071\pi$
$140$	−26.6185	−	32.0883i	−0.190132	−	0.229202i
$141$	134.854			0.956411
$142$	80.4766	−	29.0345i	0.566737	−	0.204468i
$143$			12.9946i			0.0908710i
$144$	−8.86753	+	47.1738i	−0.0615801	+	0.327596i
$145$	−89.4674			−0.617016
$146$	−66.7960	−	185.143i	−0.457507	−	1.26810i
$147$		−	77.3146i		−	0.525950i
$148$	27.6952	−	22.9742i	0.187130	−	0.155231i
$149$	79.4490			0.533215			0.266607	−	0.963805i	$-0.414097\pi$
$149$	79.4490			0.533215			0.266607	+	0.963805i	$0.414097\pi$
$150$	0.315388	−	0.113786i	0.00210258	−	0.000758573i
$151$			121.347i			0.803619i	0.915723	+	0.401810i	$0.131619\pi$
$151$			121.347i			0.803619i	−0.915723	+	0.401810i	$0.868381\pi$
$152$	107.334	−	182.330i	0.706147	−	1.19954i
$153$	−44.9836			−0.294011
$154$	−27.2985	−	75.6650i	−0.177263	−	0.491331i
$155$			27.4696i			0.177223i
$156$	−2.98499	−	3.59837i	−0.0191345	−	0.0230665i
$157$	279.014			1.77716			0.888579	−	0.458723i	$-0.151693\pi$
$157$	279.014			1.77716			0.888579	+	0.458723i	$0.151693\pi$
$158$	−64.2886	+	23.1941i	−0.406890	+	0.146798i
$159$			17.9616i			0.112966i
$160$	−157.639	+	25.5108i	−0.985244	+	0.159443i
$161$	10.0168			0.0622159
$162$	−6.10866	−	16.9318i	−0.0377078	−	0.104517i
$163$		−	122.226i		−	0.749851i	−0.927055	−	0.374926i	$-0.877668\pi$
$163$		−	122.226i		−	0.749851i	0.927055	−	0.374926i	$-0.122332\pi$
$164$	−28.3419	+	23.5107i	−0.172816	+	0.143358i
$165$	−166.441			−1.00873
$166$	−171.201	+	61.7661i	−1.03133	+	0.372085i
$167$		−	33.1660i		−	0.198599i	−0.995058	−	0.0992994i	$-0.968340\pi$
$167$		−	33.1660i		−	0.198599i	0.995058	−	0.0992994i	$-0.0316602\pi$
$168$	24.9404	+	14.6819i	0.148455	+	0.0873924i
$169$	−168.545			−0.997305
$170$	−50.7884	−	140.773i	−0.298755	−	0.828079i
$171$			79.3415i			0.463985i
$172$	172.856	+	208.376i	1.00498	+	1.21149i
$173$	−267.678			−1.54727			−0.773637	−	0.633630i	$-0.781564\pi$
$173$	−267.678			−1.54727			−0.773637	+	0.633630i	$0.781564\pi$
$174$	58.4194	−	21.0766i	0.335744	−	0.121130i
$175$		−	0.202156i		−	0.00115518i
$176$	−302.797	−	56.9186i	−1.72044	−	0.323401i
$177$	−22.9528			−0.129677
$178$	−75.4665	−	209.175i	−0.423969	−	1.17514i
$179$		−	86.9713i		−	0.485873i	−0.970042	−	0.242937i	$-0.921889\pi$
$179$		−	86.9713i		−	0.485873i	0.970042	−	0.242937i	$-0.0781107\pi$
$180$	46.0899	−	38.2333i	0.256055	−	0.212407i
$181$	−86.9733			−0.480516			−0.240258	−	0.970709i	$-0.577232\pi$
$181$	−86.9733			−0.480516			−0.240258	+	0.970709i	$0.577232\pi$
$182$	−2.65162	+	0.956655i	−0.0145693	+	0.00525635i
$183$			29.6128i			0.161819i
$184$	19.4636	−	33.0631i	0.105780	−	0.179691i
$185$	−44.8927			−0.242663
$186$	−6.47126	−	17.9368i	−0.0347917	−	0.0964344i
$187$		−	288.739i		−	1.54406i
$188$	−198.837	−	239.695i	−1.05764	−	1.27498i
$189$	−10.8529			−0.0574226
$190$	−248.294	+	89.5799i	−1.30681	+	0.471473i
$191$			45.4377i			0.237894i	0.992901	+	0.118947i	$0.0379518\pi$
$191$			45.4377i			0.237894i	−0.992901	+	0.118947i	$0.962048\pi$
$192$	96.9236	−	53.7942i	0.504810	−	0.280178i
$193$	−310.888			−1.61082			−0.805409	−	0.592719i	$-0.798054\pi$
$193$	−310.888			−1.61082			−0.805409	+	0.592719i	$0.798054\pi$
$194$	−11.2428	−	31.1625i	−0.0579528	−	0.160631i
$195$			5.83280i			0.0299118i
$196$	−137.422	+	113.997i	−0.701134	+	0.581618i
$197$	361.476			1.83490			0.917451	−	0.397848i	$-0.130243\pi$
$197$	361.476			1.83490			0.917451	+	0.397848i	$0.130243\pi$
$198$	108.681	−	39.2101i	0.548894	−	0.198031i
$199$			159.586i			0.801938i	0.916092	+	0.400969i	$0.131326\pi$
$199$			159.586i			0.801938i	−0.916092	+	0.400969i	$0.868674\pi$
$200$	−0.667274	−	0.392811i	−0.00333637	−	0.00196406i
$201$	−67.6442			−0.336538
$202$	−91.3920	−	253.317i	−0.452436	−	1.25404i
$203$		−	37.4455i		−	0.184461i
$204$	66.3265	+	79.9559i	0.325130	+	0.391941i
$205$	45.9410			0.224102
$206$	236.275	−	85.2438i	1.14697	−	0.413805i
$207$			14.3875i			0.0695048i
$208$	−1.99467	+	10.6113i	−0.00958974	+	0.0510158i
$209$	−509.274			−2.43672
$210$	−12.2534	−	33.9634i	−0.0583493	−	0.161730i
$211$		−	117.414i		−	0.556462i	−0.960514	−	0.278231i	$-0.910252\pi$
$211$		−	117.414i		−	0.556462i	0.960514	−	0.278231i	$-0.0897481\pi$
$212$	31.9257	−	26.4836i	0.150593	−	0.124923i
$213$	74.0920			0.347850
$214$	354.533	−	127.909i	1.65669	−	0.597705i
$215$		−	337.768i		−	1.57102i
$216$	−21.0883	+	35.8230i	−0.0976309	+	0.165847i
$217$	−11.4971			−0.0529820
$218$	123.559	+	342.476i	0.566784	+	1.57099i
$219$		−	170.454i		−	0.778329i
$220$	245.411	+	295.840i	1.11550	+	1.34473i
$221$	−10.1186			−0.0457857
$222$	29.3135	−	10.5758i	0.132043	−	0.0476386i
$223$			129.094i			0.578898i	0.957193	+	0.289449i	$0.0934721\pi$
$223$			129.094i			0.578898i	−0.957193	+	0.289449i	$0.906528\pi$
$224$	−10.6773	−	65.9780i	−0.0476664	−	0.294545i
$225$	0.290366			0.00129052
$226$	−102.564	−	284.282i	−0.453822	−	1.25789i
$227$			407.639i			1.79577i	0.440234	+	0.897883i	$0.354895\pi$
$227$			407.639i			1.79577i	−0.440234	+	0.897883i	$0.645105\pi$
$228$	141.025	−	116.986i	0.618531	−	0.513095i
$229$	−64.4369			−0.281384			−0.140692	−	0.990053i	$-0.544933\pi$
$229$	−64.4369			−0.281384			−0.140692	+	0.990053i	$0.544933\pi$
$230$	−45.0247	+	16.2441i	−0.195760	+	0.0706264i
$231$		−	69.6621i		−	0.301567i
$232$	−123.599	−	72.7606i	−0.532756	−	0.313623i
$233$	210.500			0.903434			0.451717	−	0.892161i	$-0.350812\pi$
$233$	210.500			0.903434			0.451717	+	0.892161i	$0.350812\pi$
$234$	−1.37408	−	3.80863i	−0.00587216	−	0.0162762i
$235$			388.536i			1.65334i
$236$	33.8429	+	40.7972i	0.143402	+	0.172870i
$237$	−59.1882			−0.249739
$238$	58.9191	−	21.2569i	0.247559	−	0.0893147i
$239$			395.091i			1.65310i	0.562863	+	0.826550i	$0.309700\pi$
$239$			395.091i			1.65310i	−0.562863	+	0.826550i	$0.690300\pi$
$240$	−135.915	−	25.5488i	−0.566313	−	0.106453i
$241$	177.026			0.734548			0.367274	−	0.930113i	$-0.380291\pi$
$241$	177.026			0.734548			0.367274	+	0.930113i	$0.380291\pi$
$242$	169.553	+	469.959i	0.700630	+	1.94198i
$243$		−	15.5885i		−	0.0641500i
$244$	52.6351	−	43.6628i	0.215718	−	0.178946i
$245$	222.756			0.909206
$246$	−29.9980	+	10.8227i	−0.121943	+	0.0439948i
$247$			17.8471i			0.0722555i
$248$	−22.3401	+	37.9494i	−0.0900809	+	0.153022i
$249$	−157.618			−0.633006
$250$	85.0060	+	235.616i	0.340024	+	0.942465i
$251$			157.403i			0.627102i	0.949571	+	0.313551i	$0.101519\pi$
$251$			157.403i			0.627102i	−0.949571	+	0.313551i	$0.898481\pi$
$252$	16.0021	+	19.2904i	0.0635004	+	0.0765492i
$253$	−92.3499			−0.365020
$254$	3.65637	−	1.31915i	0.0143951	−	0.00519350i
$255$		−	129.605i		−	0.508255i
$256$	−238.526	−	92.9589i	−0.931742	−	0.363121i
$257$	103.852			0.404095			0.202048	−	0.979376i	$-0.435240\pi$
$257$	103.852			0.404095			0.202048	+	0.979376i	$0.435240\pi$
$258$	79.5711	+	220.552i	0.308415	+	0.854854i
$259$		−	18.7893i		−	0.0725457i
$260$	10.3675	−	8.60021i	0.0398749	−	0.0330777i
$261$	53.7846			0.206071
$262$	298.088	−	107.545i	1.13774	−	0.410476i
$263$		−	487.692i		−	1.85434i	−0.374638	−	0.927171i	$-0.622233\pi$
$263$		−	487.692i		−	1.85434i	0.374638	−	0.927171i	$-0.377767\pi$
$264$	−229.939	−	135.361i	−0.870982	−	0.512730i
$265$	−51.7502			−0.195284
$266$	−37.4926	−	103.921i	−0.140950	−	0.390679i
$267$		−	192.580i		−	0.721274i
$268$	99.7385	+	120.234i	0.372159	+	0.448634i
$269$	243.899			0.906689			0.453344	−	0.891335i	$-0.350231\pi$
$269$	243.899			0.906689			0.453344	+	0.891335i	$0.350231\pi$
$270$	48.7831	−	17.6000i	0.180678	−	0.0651853i
$271$			217.007i			0.800762i	0.916349	+	0.400381i	$0.131122\pi$
$271$			217.007i			0.800762i	−0.916349	+	0.400381i	$0.868878\pi$
$272$	44.3215	−	235.783i	0.162947	−	0.866850i
$273$	−2.44125			−0.00894231
$274$	−27.3137	−	75.7069i	−0.0996849	−	0.276303i
$275$			1.86379i			0.00677742i
$276$	25.5730	−	21.2138i	0.0926557	−	0.0768614i
$277$	224.196			0.809370			0.404685	−	0.914456i	$-0.367381\pi$
$277$	224.196			0.809370			0.404685	+	0.914456i	$0.367381\pi$
$278$	360.324	−	129.998i	1.29613	−	0.467619i
$279$		−	16.5138i		−	0.0591891i
$280$	−42.3009	+	71.8572i	−0.151075	+	0.256633i
$281$	−131.480			−0.467900			−0.233950	−	0.972249i	$-0.575165\pi$
$281$	−131.480			−0.467900			−0.233950	+	0.972249i	$0.575165\pi$
$282$	−91.5308	−	253.702i	−0.324577	−	0.899651i
$283$			65.1673i			0.230273i	0.993350	+	0.115137i	$0.0367306\pi$
$283$			65.1673i			0.230273i	−0.993350	+	0.115137i	$0.963269\pi$
$284$	−109.245	−	131.694i	−0.384667	−	0.463712i
$285$	−228.595			−0.802089
$286$	24.4467	−	8.81992i	0.0854781	−	0.0308389i
$287$			19.2281i			0.0669967i
$288$	94.7671	−	15.3362i	0.329052	−	0.0532507i
$289$	−64.1635			−0.222019
$290$	60.7251	+	168.315i	0.209397	+	0.580398i
$291$		−	28.6902i		−	0.0985916i
$292$	−302.973	+	251.327i	−1.03758	+	0.860710i
$293$	545.687			1.86241			0.931207	−	0.364490i	$-0.118757\pi$
$293$	545.687			1.86241			0.931207	+	0.364490i	$0.118757\pi$
$294$	−145.452	+	52.4765i	−0.494736	+	0.178492i
$295$		−	66.1305i		−	0.224171i
$296$	−62.0194	−	36.5096i	−0.209525	−	0.123343i
$297$	100.059			0.336898
$298$	−53.9252	−	149.468i	−0.180957	−	0.501570i
$299$			3.23633i			0.0108238i
$300$	−0.428132	−	0.516109i	−0.00142711	−	0.00172036i
$301$	141.369			0.469665
$302$	228.290	−	82.3628i	0.755927	−	0.272724i
$303$		−	233.220i		−	0.769702i
$304$	−415.871	−	78.1737i	−1.36800	−	0.257150i
$305$	−85.3192			−0.279735
$306$	30.5322	+	84.6280i	0.0997785	+	0.276562i
$307$		−	206.689i		−	0.673255i	−0.941638	−	0.336628i	$-0.890714\pi$
$307$		−	206.689i		−	0.673255i	0.941638	−	0.336628i	$-0.109286\pi$
$308$	−123.820	+	102.714i	−0.402014	+	0.333486i
$309$	217.530			0.703982
$310$	51.6788	−	18.6447i	0.166706	−	0.0601443i
$311$			378.823i			1.21808i	0.793139	+	0.609041i	$0.208445\pi$
$311$			378.823i			1.21808i	−0.793139	+	0.609041i	$0.791555\pi$
$312$	−4.74360	+	8.05803i	−0.0152039	+	0.0258270i
$313$	−475.039			−1.51770			−0.758848	−	0.651268i	$-0.774237\pi$
$313$	−475.039			−1.51770			−0.758848	+	0.651268i	$0.774237\pi$
$314$	−189.378	−	524.910i	−0.603114	−	1.67169i
$315$		−	31.2689i		−	0.0992662i
$316$	87.2705	+	105.204i	0.276173	+	0.332923i
$317$	−87.3361			−0.275508			−0.137754	−	0.990466i	$-0.543988\pi$
$317$	−87.3361			−0.275508			−0.137754	+	0.990466i	$0.543988\pi$
$318$	33.7913	−	12.1913i	0.106262	−	0.0383373i
$319$			345.231i			1.08223i
$320$	154.990	+	279.252i	0.484343	+	0.872663i
$321$	326.406			1.01684
$322$	−6.79877	−	18.8446i	−0.0211142	−	0.0585235i
$323$		−	396.563i		−	1.22775i
$324$	−27.7076	+	22.9845i	−0.0855173	+	0.0709399i
$325$	0.0653150			0.000200969
$326$	−229.944	+	82.9595i	−0.705350	+	0.254477i
$327$			315.305i			0.964236i
$328$	63.4676	+	37.3621i	0.193499	+	0.113909i
$329$	−162.617			−0.494277
$330$	112.970	+	313.127i	0.342334	+	0.948869i
$331$		−	302.792i		−	0.914779i	−0.889266	−	0.457389i	$-0.848785\pi$
$331$		−	302.792i		−	0.914779i	0.889266	−	0.457389i	$-0.151215\pi$
$332$	232.402	+	280.158i	0.700006	+	0.843850i
$333$	26.9879			0.0810448
$334$	−62.3954	+	22.5111i	−0.186813	+	0.0673985i
$335$		−	194.894i		−	0.581772i
$336$	10.6931	−	56.8857i	0.0318248	−	0.169303i
$337$	245.407			0.728211			0.364105	−	0.931358i	$-0.381375\pi$
$337$	245.407			0.728211			0.364105	+	0.931358i	$0.381375\pi$
$338$	114.398	+	317.084i	0.338456	+	0.938118i
$339$		−	261.728i		−	0.772060i
$340$	−230.366	+	191.097i	−0.677546	+	0.562050i
$341$	105.998			0.310845
$342$	149.266	−	53.8523i	0.436449	−	0.157463i
$343$			195.575i			0.570190i
$344$	274.695	−	466.628i	0.798532	−	1.35648i
$345$	−41.4526			−0.120153
$346$	181.684	+	503.585i	0.525098	+	1.45545i
$347$			208.864i			0.601914i	0.953638	+	0.300957i	$0.0973061\pi$
$347$			208.864i			0.601914i	−0.953638	+	0.300957i	$0.902694\pi$
$348$	−79.3032	−	95.5992i	−0.227883	−	0.274710i
$349$	488.684			1.40024			0.700121	−	0.714024i	$-0.253129\pi$
$349$	488.684			1.40024			0.700121	+	0.714024i	$0.253129\pi$
$350$	−0.380318	+	0.137212i	−0.00108662	+	0.000392034i
$351$		−	3.50647i		−	0.00998995i
$352$	98.4395	+	608.288i	0.279658	+	1.72809i
$353$	−195.703			−0.554399			−0.277200	−	0.960812i	$-0.589406\pi$
$353$	−195.703			−0.554399			−0.277200	+	0.960812i	$0.589406\pi$
$354$	15.5790	+	43.1812i	0.0440084	+	0.121981i
$355$			213.471i			0.601326i
$356$	−342.300	+	283.951i	−0.961518	+	0.797616i
$357$	54.2447			0.151946
$358$	−163.620	+	59.0309i	−0.457038	+	0.164891i
$359$		−	333.242i		−	0.928250i	−0.885770	−	0.464125i	$-0.846369\pi$
$359$		−	333.242i		−	0.928250i	0.885770	−	0.464125i	$-0.153631\pi$
$360$	−103.212	−	60.7587i	−0.286699	−	0.168774i
$361$	−338.453			−0.937542
$362$	59.0323	+	163.623i	0.163073	+	0.451999i
$363$			432.675i			1.19194i
$364$	3.59952	+	4.33919i	0.00988879	+	0.0119208i
$365$	491.105			1.34549
$366$	55.7108	−	20.0994i	0.152215	−	0.0549164i
$367$		−	217.361i		−	0.592265i	−0.955147	−	0.296132i	$-0.904303\pi$
$367$		−	217.361i		−	0.592265i	0.955147	−	0.296132i	$-0.0956970\pi$
$368$	−75.4125	−	14.1757i	−0.204925	−	0.0385210i
$369$	−27.6181			−0.0748458
$370$	30.4705	+	84.4569i	0.0823527	+	0.228262i
$371$		−	21.6594i		−	0.0583813i
$372$	−29.3523	+	24.3489i	−0.0789040	+	0.0654539i
$373$	−384.801			−1.03164			−0.515819	−	0.856698i	$-0.672512\pi$
$373$	−384.801			−1.03164			−0.515819	+	0.856698i	$0.672512\pi$
$374$	−543.207	+	195.979i	−1.45243	+	0.524008i
$375$			216.923i			0.578462i
$376$	−315.982	+	536.763i	−0.840378	+	1.42756i
$377$	12.0983			0.0320911
$378$	7.36629	+	20.4176i	0.0194875	+	0.0540148i
$379$		−	660.203i		−	1.74196i	−0.491319	−	0.870980i	$-0.663485\pi$
$379$		−	660.203i		−	1.74196i	0.491319	−	0.870980i	$-0.336515\pi$
$380$	337.054	+	406.316i	0.886985	+	1.06925i
$381$	3.36629			0.00883539
$382$	85.4822	−	30.8404i	0.223775	−	0.0807340i
$383$		−	241.541i		−	0.630655i	−0.948983	−	0.315327i	$-0.897886\pi$
$383$		−	241.541i		−	0.630655i	0.948983	−	0.315327i	$-0.102114\pi$
$384$	−166.989	−	145.831i	−0.434868	−	0.379767i
$385$	200.707			0.521318
$386$	211.012	+	584.875i	0.546664	+	1.51522i
$387$			203.055i			0.524689i
$388$	−50.9952	+	42.3024i	−0.131431	+	0.109027i
$389$	263.893			0.678389			0.339194	−	0.940716i	$-0.389846\pi$
$389$	263.893			0.678389			0.339194	+	0.940716i	$0.389846\pi$
$390$	10.9733	−	3.95895i	0.0281366	−	0.0101512i
$391$		−	71.9113i		−	0.183916i
$392$	307.737	+	181.159i	0.785045	+	0.462140i
$393$	274.439			0.698318
$394$	−245.348	−	680.047i	−0.622711	−	1.72601i
$395$		−	170.531i		−	0.431723i
$396$	−147.532	−	177.849i	−0.372556	−	0.449113i
$397$	15.2558			0.0384276			0.0192138	−	0.999815i	$-0.493884\pi$
$397$	15.2558			0.0384276			0.0192138	+	0.999815i	$0.493884\pi$
$398$	300.229	−	108.317i	0.754345	−	0.272154i
$399$		−	95.6760i		−	0.239789i
$400$	−0.286092	+	1.52196i	−0.000715231	+	0.00380491i
$401$	−243.402			−0.606987			−0.303493	−	0.952834i	$-0.598153\pi$
$401$	−243.402			−0.606987			−0.303493	+	0.952834i	$0.598153\pi$
$402$	45.9128	+	127.259i	0.114211	+	0.316566i
$403$		−	3.71461i		−	0.00921740i
$404$	−414.535	+	343.873i	−1.02608	+	0.851170i
$405$	44.9128			0.110896
$406$	−70.4465	+	25.4158i	−0.173514	+	0.0626005i
$407$			173.229i			0.425624i
$408$	105.403	−	179.050i	0.258341	−	0.438847i
$409$	146.837			0.359014			0.179507	−	0.983757i	$-0.442550\pi$
$409$	146.837			0.359014			0.179507	+	0.983757i	$0.442550\pi$
$410$	−31.1820	−	86.4290i	−0.0760536	−	0.210802i
$411$		−	69.7007i		−	0.169588i
$412$	−320.739	−	386.648i	−0.778494	−	0.938466i
$413$	27.6782			0.0670174
$414$	27.0673	−	9.76537i	0.0653799	−	0.0235879i
$415$		−	454.124i		−	1.09427i
$416$	21.3169	−	3.44973i	0.0512426	−	0.00829263i
$417$	331.737			0.795532
$418$	345.665	+	958.101i	0.826950	+	2.29211i
$419$			555.146i			1.32493i	0.749093	+	0.662465i	$0.230490\pi$
$419$			555.146i			1.32493i	−0.749093	+	0.662465i	$0.769510\pi$
$420$	−55.5786	+	46.1046i	−0.132330	+	0.109773i
$421$	−418.435			−0.993906			−0.496953	−	0.867777i	$-0.665548\pi$
$421$	−418.435			−0.993906			−0.496953	+	0.867777i	$0.665548\pi$
$422$	−220.891	+	79.6933i	−0.523438	+	0.188847i
$423$		−	233.574i		−	0.552184i
$424$	−71.4931	−	42.0866i	−0.168616	−	0.0992608i
$425$	−1.45130			−0.00341483
$426$	−50.2892	−	139.390i	−0.118050	−	0.327206i
$427$		−	35.7094i		−	0.0836285i
$428$	−481.271	−	580.168i	−1.12447	−	1.35553i
$429$	22.5072			0.0524644
$430$	−635.446	+	229.257i	−1.47778	+	0.533156i
$431$		−	438.415i		−	1.01720i	−0.861002	−	0.508602i	$-0.830163\pi$
$431$		−	438.415i		−	1.01720i	0.861002	−	0.508602i	$-0.169837\pi$
$432$	81.7074	+	15.3590i	0.189138	+	0.0355533i
$433$	84.8420			0.195940			0.0979700	−	0.995189i	$-0.468765\pi$
$433$	84.8420			0.195940			0.0979700	+	0.995189i	$0.468765\pi$
$434$	7.80354	+	21.6295i	0.0179805	+	0.0498377i
$435$			154.962i			0.356235i
$436$	560.437	−	464.904i	1.28541	−	1.06629i
$437$	−126.836			−0.290243
$438$	−320.676	+	115.694i	−0.732138	+	0.264142i
$439$			297.673i			0.678070i	0.940774	+	0.339035i	$0.110101\pi$
$439$			297.673i			0.678070i	−0.940774	+	0.339035i	$0.889899\pi$
$440$	389.995	−	662.491i	0.886353	−	1.50566i
$441$	−133.913			−0.303657
$442$	6.86793	+	19.0362i	0.0155383	+	0.0430684i
$443$		−	357.912i		−	0.807929i	−0.914775	−	0.403964i	$-0.867632\pi$
$443$		−	357.912i		−	0.807929i	0.914775	−	0.403964i	$-0.132368\pi$
$444$	−39.7925	−	47.9695i	−0.0896228	−	0.108039i
$445$	554.854			1.24686
$446$	242.866	−	87.6215i	0.544542	−	0.196461i
$447$		−	137.610i		−	0.307852i
$448$	−116.878	+	64.8691i	−0.260888	+	0.144797i
$449$	−636.511			−1.41762			−0.708810	−	0.705400i	$-0.750768\pi$
$449$	−636.511			−1.41762			−0.708810	+	0.705400i	$0.750768\pi$
$450$	−0.197083	−	0.546267i	−0.000437962	−	0.00121393i
$451$		−	177.274i		−	0.393069i
$452$	−465.208	+	385.908i	−1.02922	+	0.853778i
$453$	210.178			0.463970
$454$	766.893	−	276.681i	1.68919	−	0.609429i
$455$		−	7.03363i		−	0.0154585i
$456$	−315.805	−	185.908i	−0.692556	−	0.407694i
$457$	−333.595			−0.729966			−0.364983	−	0.931014i	$-0.618925\pi$
$457$	−333.595			−0.729966			−0.364983	+	0.931014i	$0.618925\pi$
$458$	43.7359	+	121.226i	0.0954933	+	0.264685i
$459$			77.9140i			0.169747i
$460$	61.1202	+	73.6798i	0.132870	+	0.160173i
$461$	−530.682			−1.15115			−0.575577	−	0.817748i	$-0.695222\pi$
$461$	−530.682			−1.15115			−0.575577	+	0.817748i	$0.695222\pi$
$462$	−131.056	+	47.2825i	−0.283670	+	0.102343i
$463$		−	610.806i		−	1.31924i	−0.751601	−	0.659618i	$-0.770718\pi$
$463$		−	610.806i		−	1.31924i	0.751601	−	0.659618i	$-0.229282\pi$
$464$	−52.9930	+	281.914i	−0.114209	+	0.607573i
$465$	47.5788			0.102320
$466$	−142.875	−	396.015i	−0.306598	−	0.849817i
$467$		−	157.833i		−	0.337972i	−0.985618	−	0.168986i	$-0.945951\pi$
$467$		−	157.833i		−	0.337972i	0.985618	−	0.168986i	$-0.0540492\pi$
$468$	−6.23256	+	5.17015i	−0.0133174	+	0.0110473i
$469$	81.5705			0.173924
$470$	730.954	−	263.715i	1.55522	−	0.561095i
$471$		−	483.266i		−	1.02604i
$472$	53.7816	−	91.3595i	0.113944	−	0.193558i
$473$	−1303.36			−2.75552
$474$	40.1734	+	111.351i	0.0847540	+	0.234918i
$475$			2.55979i			0.00538902i
$476$	−79.9815	−	96.4169i	−0.168028	−	0.202556i
$477$	31.1104			0.0652209
$478$	743.287	−	268.164i	1.55499	−	0.561013i
$479$		−	764.423i		−	1.59587i	−0.602742	−	0.797936i	$-0.705925\pi$
$479$		−	764.423i		−	1.59587i	0.602742	−	0.797936i	$-0.294075\pi$
$480$	44.1860	+	273.039i	0.0920543	+	0.568831i
$481$	6.07067			0.0126209
$482$	−120.155	−	333.040i	−0.249283	−	0.690954i
$483$		−	17.3495i		−	0.0359203i
$484$	769.055	−	637.960i	1.58896	−	1.31810i
$485$	82.6609			0.170435
$486$	−29.3267	+	10.5805i	−0.0603429	+	0.0217706i
$487$		−	167.028i		−	0.342973i	−0.985186	−	0.171487i	$-0.945143\pi$
$487$		−	167.028i		−	0.342973i	0.985186	−	0.171487i	$-0.0548570\pi$
$488$	−117.869	−	69.3870i	−0.241534	−	0.142187i
$489$	−211.701			−0.432927
$490$	−151.193	−	419.071i	−0.308557	−	0.855247i
$491$		−	128.950i		−	0.262628i	−0.991341	−	0.131314i	$-0.958080\pi$
$491$		−	128.950i		−	0.262628i	0.991341	−	0.131314i	$-0.0419196\pi$
$492$	40.7217	+	49.0896i	0.0827677	+	0.0997756i
$493$	−268.825			−0.545285
$494$	33.5759	−	12.1135i	0.0679673	−	0.0245214i
$495$			288.285i			0.582393i
$496$	86.5575	+	16.2707i	0.174511	+	0.0328038i
$497$	−89.3457			−0.179770
$498$	106.982	+	296.529i	0.214823	+	0.595439i
$499$			458.132i			0.918100i	0.888410	+	0.459050i	$0.151810\pi$
$499$			458.132i			0.918100i	−0.888410	+	0.459050i	$0.848190\pi$
$500$	385.569	−	319.844i	0.771139	−	0.639689i
$501$	−57.4452			−0.114661
$502$	296.123	−	106.836i	0.589886	−	0.212820i
$503$		−	591.001i		−	1.17495i	−0.809242	−	0.587476i	$-0.800122\pi$
$503$		−	591.001i		−	1.17495i	0.809242	−	0.587476i	$-0.199878\pi$
$504$	25.4298	−	43.1980i	0.0504560	−	0.0857104i
$505$	671.943			1.33058
$506$	62.6816	+	173.738i	0.123877	+	0.343357i
$507$			291.928i			0.575795i
$508$	−4.96345	−	5.98338i	−0.00977056	−	0.0117783i
$509$	−630.726			−1.23915			−0.619574	−	0.784938i	$-0.712695\pi$
$509$	−630.726			−1.23915			−0.619574	+	0.784938i	$0.712695\pi$
$510$	−243.827	+	87.9681i	−0.478091	+	0.172486i
$511$			205.546i			0.402243i
$512$	−12.9870	+	511.835i	−0.0253652	+	0.999678i
$513$	137.424			0.267882
$514$	−70.4889	−	195.378i	−0.137138	−	0.380113i
$515$			626.739i			1.21697i
$516$	360.918	−	299.395i	0.699454	−	0.580223i
$517$	1499.26			2.89992
$518$	−35.3485	+	12.7531i	−0.0682403	+	0.0246198i
$519$			463.632i			0.893319i
$520$	−23.2165	−	13.6671i	−0.0446470	−	0.0262828i
$521$	203.130			0.389884			0.194942	−	0.980815i	$-0.437548\pi$
$521$	203.130			0.389884			0.194942	+	0.980815i	$0.437548\pi$
$522$	−36.5058	−	101.185i	−0.0699345	−	0.193842i
$523$		−	520.529i		−	0.995276i	−0.867385	−	0.497638i	$-0.834201\pi$
$523$		−	520.529i		−	0.995276i	0.867385	−	0.497638i	$-0.165799\pi$
$524$	−404.649	−	487.800i	−0.772230	−	0.930916i
$525$	−0.350145			−0.000666943
$526$	−917.498	+	331.016i	−1.74429	+	0.629308i
$527$			82.5388i			0.156620i
$528$	−98.5859	+	524.461i	−0.186716	+	0.993297i
$529$	−23.0000			−0.0434783
$530$	35.1249	+	97.3579i	0.0662735	+	0.183694i
$531$			39.7553i			0.0748688i
$532$	−170.059	+	141.070i	−0.319659	+	0.265170i
$533$	−6.21242			−0.0116556
$534$	−362.302	+	130.712i	−0.678468	+	0.244779i
$535$			940.426i			1.75781i
$536$	158.500	−	269.246i	0.295709	−	0.502325i
$537$	−150.639			−0.280519
$538$	−165.544	−	458.849i	−0.307703	−	0.852879i
$539$		−	859.555i		−	1.59472i
$540$	−66.2220	−	79.8300i	−0.122633	−	0.147833i
$541$	−649.189			−1.19998			−0.599990	−	0.800007i	$-0.704829\pi$
$541$	−649.189			−1.19998			−0.599990	+	0.800007i	$0.704829\pi$
$542$	408.256	−	147.291i	0.753239	−	0.271755i
$543$			150.642i			0.277426i
$544$	−473.663	+	76.6532i	−0.870704	+	0.140907i
$545$	−908.444			−1.66687
$546$	1.65697	+	4.59274i	0.00303475	+	0.00841161i
$547$			807.856i			1.47688i	0.674317	+	0.738442i	$0.264438\pi$
$547$			807.856i			1.47688i	−0.674317	+	0.738442i	$0.735562\pi$
$548$	−123.889	+	102.771i	−0.226075	+	0.187538i
$549$	51.2909			0.0934260
$550$	3.50636	−	1.26503i	0.00637520	−	0.00230005i
$551$			474.150i			0.860527i
$552$	−57.2670	−	33.7119i	−0.103744	−	0.0610724i
$553$	71.3736			0.129066
$554$	−152.171	−	421.780i	−0.274676	−	0.761336i
$555$			77.7564i			0.140102i
$556$	−489.132	−	589.644i	−0.879734	−	1.06051i
$557$	187.300			0.336266			0.168133	−	0.985764i	$-0.446226\pi$
$557$	187.300			0.336266			0.168133	+	0.985764i	$0.446226\pi$
$558$	−31.0674	+	11.2086i	−0.0556764	+	0.0200870i
$559$			45.6751i			0.0817087i
$560$	163.897	+	30.8086i	0.292673	+	0.0550154i
$561$	−500.111			−0.891464
$562$	89.2406	+	247.354i	0.158791	+	0.440131i
$563$			455.565i			0.809174i	0.914500	+	0.404587i	$0.132585\pi$
$563$			455.565i			0.809174i	−0.914500	+	0.404587i	$0.867415\pi$
$564$	−415.165	+	344.395i	−0.736108	+	0.610629i
$565$	754.081			1.33466
$566$	122.600	−	44.2317i	0.216607	−	0.0781479i
$567$			18.7977i			0.0331530i
$568$	−173.608	+	294.910i	−0.305648	+	0.519208i
$569$	1043.09			1.83320			0.916600	−	0.399806i	$-0.130923\pi$
$569$	1043.09			1.83320			0.916600	+	0.399806i	$0.130923\pi$
$570$	155.157	+	430.058i	0.272205	+	0.754488i
$571$			148.571i			0.260194i	0.991501	+	0.130097i	$0.0415288\pi$
$571$			148.571i			0.260194i	−0.991501	+	0.130097i	$0.958471\pi$
$572$	−33.1860	−	40.0053i	−0.0580174	−	0.0699394i
$573$	78.7004			0.137348
$574$	36.1739	−	13.0509i	0.0630207	−	0.0227367i
$575$			0.464182i			0.000807273i
$576$	−93.1743	−	167.877i	−0.161761	−	0.291452i
$577$	314.979			0.545891			0.272946	−	0.962029i	$-0.412002\pi$
$577$	314.979			0.545891			0.272946	+	0.962029i	$0.412002\pi$
$578$	43.5504	+	120.711i	0.0753467	+	0.208843i
$579$			538.474i			0.930006i
$580$	275.436	−	228.485i	0.474890	−	0.393940i
$581$	190.068			0.327140
$582$	−53.9750	+	19.4732i	−0.0927405	+	0.0334590i
$583$			199.690i			0.342522i
$584$	678.463	+	399.398i	1.16175	+	0.683901i
$585$	10.1027			0.0172696
$586$	−370.380	−	1026.60i	−0.632048	−	1.75189i
$587$		−	12.0000i		−	0.0204429i	−0.999948	−	0.0102214i	$-0.996746\pi$
$587$		−	12.0000i		−	0.0204429i	0.999948	−	0.0102214i	$-0.00325364\pi$
$588$	197.449	+	238.022i	0.335797	+	0.404800i
$589$	145.581			0.247166
$590$	−124.412	+	44.8854i	−0.210867	+	0.0760770i
$591$		−	626.094i		−	1.05938i
$592$	−26.5907	+	141.458i	−0.0449167	+	0.238949i
$593$	−762.316			−1.28552			−0.642762	−	0.766066i	$-0.722212\pi$
$593$	−762.316			−1.28552			−0.642762	+	0.766066i	$0.722212\pi$
$594$	−67.9138	−	188.241i	−0.114333	−	0.316904i
$595$			156.287i			0.262668i
$596$	−244.594	+	202.900i	−0.410392	+	0.340436i
$597$	276.410			0.462999
$598$	6.08852	−	2.19663i	0.0101815	−	0.00367329i
$599$			112.991i			0.188632i	0.995542	+	0.0943161i	$0.0300664\pi$
$599$			112.991i			0.188632i	−0.995542	+	0.0943161i	$0.969934\pi$
$600$	−0.680369	+	1.15575i	−0.00113395	+	0.00192625i
$601$	609.920			1.01484			0.507421	−	0.861698i	$-0.330599\pi$
$601$	609.920			1.01484			0.507421	+	0.861698i	$0.330599\pi$
$602$	−95.9529	−	265.959i	−0.159390	−	0.441792i
$603$			117.163i			0.194300i
$604$	−309.899	−	373.580i	−0.513078	−	0.618510i
$605$	−1246.60			−2.06050
$606$	−438.758	+	158.296i	−0.724023	+	0.261214i
$607$		−	1079.22i		−	1.77795i	−0.457952	−	0.888977i	$-0.651417\pi$
$607$		−	1079.22i		−	1.77795i	0.457952	−	0.888977i	$-0.348583\pi$
$608$	135.200	+	835.440i	0.222368	+	1.37408i
$609$	−64.8576			−0.106498
$610$	57.9096	+	160.511i	0.0949337	+	0.263134i
$611$		−	52.5402i		−	0.0859905i
$612$	138.488	−	114.881i	0.226287	−	0.187714i
$613$	−407.000			−0.663948			−0.331974	−	0.943288i	$-0.607715\pi$
$613$	−407.000			−0.663948			−0.331974	+	0.943288i	$0.607715\pi$
$614$	−388.846	+	140.288i	−0.633299	+	0.228483i
$615$		−	79.5721i		−	0.129385i
$616$	277.278	+	163.228i	0.450127	+	0.264981i
$617$	−205.895			−0.333703			−0.166852	−	0.985982i	$-0.553360\pi$
$617$	−205.895			−0.333703			−0.166852	+	0.985982i	$0.553360\pi$
$618$	−147.647	−	409.241i	−0.238910	−	0.662203i
$619$		−	462.926i		−	0.747862i	−0.927457	−	0.373931i	$-0.878010\pi$
$619$		−	462.926i		−	0.747862i	0.927457	−	0.373931i	$-0.121990\pi$
$620$	−70.1529	−	84.5686i	−0.113150	−	0.136401i
$621$	24.9199			0.0401286
$622$	712.683	−	257.123i	1.14579	−	0.413380i
$623$			232.228i			0.372757i
$624$	18.3793	+	3.45486i	0.0294540	+	0.00553664i
$625$	−622.571			−0.996113
$626$	322.428	+	893.693i	0.515061	+	1.42762i
$627$			882.089i			1.40684i
$628$	−858.979	+	712.556i	−1.36780	+	1.13464i
$629$	−134.891			−0.214452
$630$	−58.8263	+	21.2234i	−0.0933751	+	0.0336880i
$631$		−	44.2517i		−	0.0701294i	−0.999385	−	0.0350647i	$-0.988836\pi$
$631$		−	44.2517i		−	0.0701294i	0.999385	−	0.0350647i	$-0.0111637\pi$
$632$	138.686	−	235.589i	0.219440	−	0.372767i
$633$	−203.366			−0.321274
$634$	59.2785	+	164.306i	0.0934993	+	0.259158i
$635$			9.69880i			0.0152737i
$636$	−45.8710	−	55.2970i	−0.0721242	−	0.0869449i
$637$	−30.1224			−0.0472879
$638$	649.485	−	234.322i	1.01800	−	0.367276i
$639$		−	128.331i		−	0.200831i
$640$	420.161	−	481.123i	0.656502	−	0.751754i
$641$	323.350			0.504446			0.252223	−	0.967669i	$-0.418838\pi$
$641$	323.350			0.504446			0.252223	+	0.967669i	$0.418838\pi$
$642$	−221.545	−	614.069i	−0.345085	−	0.956493i
$643$		−	26.9164i		−	0.0418607i	−0.999781	−	0.0209304i	$-0.993337\pi$
$643$		−	26.9164i		−	0.0418607i	0.999781	−	0.0209304i	$-0.00666283\pi$
$644$	−30.8378	+	25.5811i	−0.0478848	+	0.0397223i
$645$	−585.032			−0.907026
$646$	−746.057	+	269.163i	−1.15489	+	0.416662i
$647$		−	137.187i		−	0.212036i	−0.994364	−	0.106018i	$-0.966190\pi$
$647$		−	137.187i		−	0.212036i	0.994364	−	0.106018i	$-0.0338101\pi$
$648$	62.0472	+	36.5260i	0.0957518	+	0.0563672i
$649$	−255.180			−0.393190
$650$	−0.0443319	−	0.122878i	−6.82030e−5	−	0.000189042i
$651$			19.9135i			0.0305892i
$652$	312.145	+	376.287i	0.478749	+	0.577127i
$653$	−882.741			−1.35182			−0.675912	−	0.736982i	$-0.736250\pi$
$653$	−882.741			−1.35182			−0.675912	+	0.736982i	$0.736250\pi$
$654$	593.185	−	214.010i	0.907011	−	0.327233i
$655$			790.702i			1.20718i
$656$	27.2116	−	144.761i	0.0414811	−	0.220672i
$657$	−295.235			−0.449369
$658$	110.375	+	305.933i	0.167743	+	0.464943i
$659$			1139.27i			1.72878i	0.502822	+	0.864390i	$0.332295\pi$
$659$			1139.27i			1.72878i	−0.502822	+	0.864390i	$0.667705\pi$
$660$	512.410	−	425.064i	0.776379	−	0.644036i
$661$	−774.624			−1.17190			−0.585948	−	0.810348i	$-0.699278\pi$
$661$	−774.624			−1.17190			−0.585948	+	0.810348i	$0.699278\pi$
$662$	−569.644	+	205.517i	−0.860489	+	0.310449i
$663$			17.5260i			0.0264344i
$664$	369.323	−	627.373i	0.556209	−	0.944840i
$665$	275.658			0.414523
$666$	−18.3178	−	50.7725i	−0.0275042	−	0.0762350i
$667$			85.9807i			0.128907i
$668$	84.7005	+	102.106i	0.126797	+	0.152853i
$669$	223.598			0.334227
$670$	−366.654	+	132.282i	−0.547246	+	0.197436i
$671$			329.224i			0.490647i
$672$	−114.277	+	18.4936i	−0.170056	+	0.0275202i
$673$	1324.64			1.96826			0.984132	−	0.177440i	$-0.0567816\pi$
$673$	1324.64			1.96826			0.984132	+	0.177440i	$0.0567816\pi$
$674$	−166.568	−	461.686i	−0.247133	−	0.684994i
$675$		−	0.502929i		−	0.000745080i
$676$	518.885	−	430.435i	0.767582	−	0.636739i
$677$	531.553			0.785160			0.392580	−	0.919718i	$-0.371583\pi$
$677$	531.553			0.785160			0.392580	+	0.919718i	$0.371583\pi$
$678$	−492.391	+	177.646i	−0.726241	+	0.262014i
$679$			34.5968i			0.0509525i
$680$	515.870	+	303.683i	0.758633	+	0.446592i
$681$	706.051			1.03679
$682$	−71.9451	−	199.415i	−0.105491	−	0.292397i
$683$			1248.41i			1.82783i	0.405901	+	0.913917i	$0.366958\pi$
$683$			1248.41i			1.82783i	−0.405901	+	0.913917i	$0.633042\pi$
$684$	−202.625	−	244.263i	−0.296236	−	0.357109i
$685$	200.819			0.293166
$686$	367.936	−	132.745i	0.536350	−	0.193505i
$687$			111.608i			0.162457i
$688$	−1064.32	−	200.066i	−1.54697	−	0.290793i
$689$	6.99798			0.0101567
$690$	28.1356	+	77.9851i	0.0407762	+	0.113022i
$691$		−	951.553i		−	1.37707i	−0.725205	−	0.688533i	$-0.758255\pi$
$691$		−	951.553i		−	1.37707i	0.725205	−	0.688533i	$-0.241745\pi$
$692$	824.081	−	683.606i	1.19087	−	0.987870i
$693$	−120.658			−0.174110
$694$	392.938	−	141.765i	0.566193	−	0.204272i
$695$			955.787i			1.37523i
$696$	−126.025	+	214.081i	−0.181070	+	0.307587i
$697$	138.040			0.198049
$698$	−331.690	−	919.365i	−0.475200	−	1.31714i
$699$		−	364.597i		−	0.521598i
$700$	0.516274	+	0.622364i	0.000737535	+	0.000889091i
$701$	1037.32			1.47977			0.739884	−	0.672735i	$-0.234880\pi$
$701$	1037.32			1.47977			0.739884	+	0.672735i	$0.234880\pi$
$702$	−6.59675	+	2.37998i	−0.00939708	+	0.00339029i
$703$			237.918i			0.338432i
$704$	1077.56	−	598.064i	1.53063	−	0.849523i
$705$	672.964			0.954558
$706$	132.831	+	368.177i	0.188147	+	0.521497i
$707$			281.234i			0.397785i
$708$	70.6629	−	58.6176i	0.0998064	−	0.0827932i
$709$	602.919			0.850380			0.425190	−	0.905104i	$-0.360207\pi$
$709$	602.919			0.850380			0.425190	+	0.905104i	$0.360207\pi$
$710$	401.604	−	144.891i	0.565639	−	0.204072i
$711$			102.517i			0.144187i
$712$	766.532	+	451.243i	1.07659	+	0.633768i
$713$	26.3991			0.0370254
$714$	−36.8180	−	102.051i	−0.0515659	−	0.142928i
$715$			64.8469i			0.0906949i
$716$	222.111	+	267.752i	0.310210	+	0.373955i
$717$	684.318			0.954418
$718$	−626.929	+	226.185i	−0.873161	+	0.315020i
$719$			657.005i			0.913776i	0.889524	+	0.456888i	$0.151036\pi$
$719$			657.005i			0.913776i	−0.889524	+	0.456888i	$0.848964\pi$
$720$	−44.2518	+	235.412i	−0.0614608	+	0.326961i
$721$	−262.315			−0.363820
$722$	229.722	+	636.733i	0.318174	+	0.881902i
$723$		−	306.618i		−	0.424091i
$724$	267.758	−	222.116i	0.369832	−	0.306790i
$725$	1.73525			0.00239345
$726$	813.993	−	293.674i	1.12120	−	0.404509i
$727$			799.112i			1.09919i	0.835431	+	0.549596i	$0.185218\pi$
$727$			799.112i			1.09919i	−0.835431	+	0.549596i	$0.814782\pi$
$728$	5.72020	−	9.71698i	0.00785741	−	0.0133475i
$729$	−27.0000			−0.0370370
$730$	−333.333	−	923.919i	−0.456620	−	1.26564i
$731$		−	1014.90i		−	1.38838i
$732$	−75.6263	−	91.1667i	−0.103315	−	0.124545i
$733$	94.9997			0.129604			0.0648020	−	0.997898i	$-0.479358\pi$
$733$	94.9997			0.129604			0.0648020	+	0.997898i	$0.479358\pi$
$734$	−408.923	+	147.532i	−0.557116	+	0.200997i
$735$		−	385.824i		−	0.524930i
$736$	24.5166	+	151.496i	0.0333106	+	0.205836i
$737$	−752.043			−1.02041
$738$	18.7455	+	51.9581i	0.0254004	+	0.0704039i
$739$		−	430.276i		−	0.582241i	−0.956686	−	0.291120i	$-0.905972\pi$
$739$		−	430.276i		−	0.582241i	0.956686	−	0.291120i	$-0.0940281\pi$
$740$	138.208	−	114.649i	0.186767	−	0.154931i
$741$	30.9121			0.0417167
$742$	−40.7480	+	14.7011i	−0.0549165	+	0.0198129i
$743$			432.271i			0.581791i	0.956755	+	0.290896i	$0.0939532\pi$
$743$			432.271i			0.581791i	−0.956755	+	0.290896i	$0.906047\pi$
$744$	65.7302	+	38.6941i	0.0883471	+	0.0520082i
$745$	396.475			0.532181
$746$	261.180	+	723.928i	0.350107	+	0.970413i
$747$			273.003i			0.365466i
$748$	737.393	+	888.920i	0.985820	+	1.18840i
$749$	−393.604			−0.525507
$750$	408.099	−	147.235i	0.544132	−	0.196313i
$751$			1285.16i			1.71127i	0.517581	+	0.855634i	$0.326833\pi$
$751$			1285.16i			1.71127i	−0.517581	+	0.855634i	$0.673167\pi$
$752$	1224.29	+	230.136i	1.62804	+	0.306032i
$753$	272.629			0.362058
$754$	−8.21163	−	22.7607i	−0.0108907	−	0.0301866i
$755$			605.557i			0.802062i
$756$	33.4119	−	27.7165i	0.0441957	−	0.0366620i
$757$	308.267			0.407221			0.203611	−	0.979052i	$-0.434732\pi$
$757$	308.267			0.407221			0.203611	+	0.979052i	$0.434732\pi$
$758$	−1242.04	+	448.106i	−1.63858	+	0.591169i
$759$			159.955i			0.210744i
$760$	535.632	−	909.885i	0.704778	−	1.19722i
$761$	827.959			1.08799			0.543994	−	0.839089i	$-0.316911\pi$
$761$	827.959			1.08799			0.543994	+	0.839089i	$0.316911\pi$
$762$	−2.28483	−	6.33301i	−0.00299847	−	0.00831104i
$763$		−	380.219i		−	0.498321i
$764$	−116.040	−	139.886i	−0.151885	−	0.183096i
$765$	−224.482			−0.293441
$766$	−454.412	+	163.943i	−0.593227	+	0.214025i
$767$			8.94258i			0.0116592i
$768$	−161.010	+	413.139i	−0.209648	+	0.537942i
$769$	−1507.08			−1.95979			−0.979895	−	0.199513i	$-0.936064\pi$
$769$	−1507.08			−1.95979			−0.979895	+	0.199513i	$0.936064\pi$
$770$	−136.228	−	377.592i	−0.176920	−	0.490379i
$771$		−	179.878i		−	0.233305i
$772$	957.107	−	793.957i	1.23978	−	1.02844i
$773$	607.788			0.786272			0.393136	−	0.919480i	$-0.371390\pi$
$773$	607.788			0.786272			0.393136	+	0.919480i	$0.371390\pi$
$774$	382.008	−	137.821i	0.493550	−	0.178064i
$775$		−	0.532782i		−	0.000687461i
$776$	114.196	+	67.2251i	0.147160	+	0.0866303i
$777$	−32.5441			−0.0418843
$778$	−179.115	−	496.464i	−0.230225	−	0.638129i
$779$		−	243.473i		−	0.312546i
$780$	−14.8960	−	17.9570i	−0.0190974	−	0.0230218i
$781$	823.727			1.05471
$782$	−135.287	+	48.8091i	−0.173002	+	0.0624157i
$783$		−	93.1577i		−	0.118975i
$784$	131.942	−	701.908i	0.168293	−	0.895291i
$785$	1392.37			1.77371
$786$	−186.273	−	516.304i	−0.236988	−	0.656875i
$787$		−	960.229i		−	1.22011i	−0.792358	−	0.610057i	$-0.791147\pi$
$787$		−	960.229i		−	1.22011i	0.792358	−	0.610057i	$-0.208853\pi$
$788$	−1112.85	+	923.150i	−1.41224	+	1.17151i
$789$	−844.707			−1.07061
$790$	−320.820	+	115.746i	−0.406101	+	0.146514i
$791$			315.612i			0.399004i
$792$	−234.452	+	398.266i	−0.296025	+	0.502861i
$793$	11.5374			0.0145490
$794$	−10.3547	−	28.7007i	−0.0130412	−	0.0361470i
$795$			89.6340i			0.112747i
$796$	−407.556	−	491.304i	−0.512005	−	0.617216i
$797$	−1422.73			−1.78510			−0.892551	−	0.450946i	$-0.851087\pi$
$797$	−1422.73			−1.78510			−0.892551	+	0.450946i	$0.851087\pi$
$798$	−179.996	+	64.9391i	−0.225559	+	0.0813774i
$799$			1167.45i			1.46113i
$800$	3.05746	−	0.494791i	0.00382183	−	0.000618488i
$801$	−333.559			−0.416428
$802$	165.207	+	457.913i	0.205993	+	0.570964i
$803$		−	1895.04i		−	2.35996i
$804$	208.251	−	172.752i	0.259019	−	0.214866i
$805$	49.9867			0.0620953
$806$	−6.98832	+	2.52126i	−0.00867038	+	0.00312811i
$807$		−	422.446i		−	0.523477i
$808$	928.291	+	546.467i	1.14888	+	0.676321i
$809$	161.089			0.199121			0.0995603	−	0.995032i	$-0.468256\pi$
$809$	161.089			0.199121			0.0995603	+	0.995032i	$0.468256\pi$
$810$	−30.4841	−	84.4947i	−0.0376347	−	0.104314i
$811$			837.550i			1.03274i	0.856366	+	0.516369i	$0.172717\pi$
$811$			837.550i			1.03274i	−0.856366	+	0.516369i	$0.827283\pi$
$812$	95.6298	+	115.281i	0.117771	+	0.141971i
$813$	375.866			0.462320
$814$	325.897	−	117.578i	0.400365	−	0.144444i
$815$		−	609.945i		−	0.748398i
$816$	−408.389	−	76.7672i	−0.500476	−	0.0940774i
$817$	−1790.07			−2.19103
$818$	−99.6640	−	276.245i	−0.121839	−	0.337708i
$819$			4.22837i			0.00516284i
$820$	−141.435	+	117.326i	−0.172482	+	0.143080i
$821$	−196.002			−0.238735			−0.119368	−	0.992850i	$-0.538087\pi$
$821$	−196.002			−0.238735			−0.119368	+	0.992850i	$0.538087\pi$
$822$	−131.128	+	47.3086i	−0.159523	+	0.0575531i
$823$		−	824.575i		−	1.00191i	−0.865472	−	0.500957i	$-0.832982\pi$
$823$		−	824.575i		−	1.00191i	0.865472	−	0.500957i	$-0.167018\pi$
$824$	−509.705	+	865.842i	−0.618573	+	1.05078i
$825$	3.22818			0.00391295
$826$	−18.7863	−	52.0711i	−0.0227437	−	0.0630401i
$827$		−	1329.58i		−	1.60772i	−0.594818	−	0.803860i	$-0.702776\pi$
$827$		−	1329.58i		−	1.60772i	0.594818	−	0.803860i	$-0.297224\pi$
$828$	−36.7433	−	44.2937i	−0.0443760	−	0.0534948i
$829$	−1321.65			−1.59427			−0.797136	−	0.603799i	$-0.793653\pi$
$829$	−1321.65			−1.59427			−0.797136	+	0.603799i	$0.793653\pi$
$830$	−854.346	+	308.232i	−1.02933	+	0.371364i
$831$		−	388.318i		−	0.467290i
$832$	−20.9587	−	37.7622i	−0.0251907	−	0.0453873i
$833$	669.321			0.803506
$834$	−225.163	−	624.099i	−0.269980	−	0.748320i
$835$		−	165.509i		−	0.198214i
$836$	1567.86	−	1300.60i	1.87544	−	1.55575i
$837$	−28.6027			−0.0341729
$838$	1044.40	−	376.800i	1.24630	−	0.449642i
$839$			1041.21i			1.24102i	0.784200	+	0.620508i	$0.213073\pi$
$839$			1041.21i			1.24102i	−0.784200	+	0.620508i	$0.786927\pi$
$840$	124.460	+	73.2674i	0.148167	+	0.0872231i
$841$	−519.579			−0.617811
$842$	284.008	+	787.203i	0.337302	+	0.934921i
$843$			227.730i			0.270142i
$844$	299.855	+	361.472i	0.355278	+	0.428285i
$845$	−841.090			−0.995373
$846$	−439.424	+	158.536i	−0.519414	+	0.187395i
$847$		−	521.752i		−	0.616000i
$848$	−30.6525	+	163.066i	−0.0361468	+	0.192295i
$849$	112.873			0.132948
$850$	0.985057	+	2.73034i	0.00115889	+	0.00321217i
$851$			43.1432i			0.0506970i
$852$	−228.101	+	189.219i	−0.267724	+	0.222088i
$853$	1187.52			1.39216			0.696082	−	0.717963i	$-0.254925\pi$
$853$	1187.52			1.39216			0.696082	+	0.717963i	$0.254925\pi$
$854$	−67.1802	+	24.2374i	−0.0786654	+	0.0283810i
$855$			395.939i			0.463086i
$856$	−764.815	+	1299.20i	−0.893475	+	1.51776i
$857$	1210.00			1.41190			0.705952	−	0.708260i	$-0.250520\pi$
$857$	1210.00			1.41190			0.705952	+	0.708260i	$0.250520\pi$
$858$	−15.2766	−	42.3430i	−0.0178048	−	0.0493508i
$859$		−	164.933i		−	0.192006i	−0.995381	−	0.0960030i	$-0.969394\pi$
$859$		−	164.933i		−	0.192006i	0.995381	−	0.0960030i	$-0.0306058\pi$
$860$	862.605	+	1039.86i	1.00303	+	1.20914i
$861$	33.3040			0.0386806
$862$	−824.792	+	297.570i	−0.956835	+	0.345208i
$863$		−	48.6999i		−	0.0564309i	−0.999602	−	0.0282155i	$-0.991018\pi$
$863$		−	48.6999i		−	0.0564309i	0.999602	−	0.0282155i	$-0.00898245\pi$
$864$	−26.5631	−	164.141i	−0.0307443	−	0.189978i
$865$	−1335.80			−1.54428
$866$	−57.5857	−	159.614i	−0.0664962	−	0.184312i
$867$			111.135i			0.128183i
$868$	35.3952	−	29.3617i	0.0407779	−	0.0338268i
$869$	−658.032			−0.757229
$870$	291.531	−	105.179i	0.335093	−	0.120895i
$871$			26.3547i			0.0302580i
$872$	−1255.02	−	738.805i	−1.43924	−	0.847253i
$873$	−49.6928			−0.0569219
$874$	86.0888	+	238.618i	0.0984998	+	0.273018i
$875$		−	261.583i		−	0.298952i
$876$	435.312	+	524.764i	0.496931	+	0.599046i
$877$	−293.643			−0.334827			−0.167413	−	0.985887i	$-0.553541\pi$
$877$	−293.643			−0.334827			−0.167413	+	0.985887i	$0.553541\pi$
$878$	560.013	−	202.042i	0.637829	−	0.230117i
$879$		−	945.158i		−	1.07527i
$880$	−1511.05	−	284.042i	−1.71711	−	0.322774i
$881$	619.053			0.702671			0.351335	−	0.936250i	$-0.385728\pi$
$881$	619.053			0.702671			0.351335	+	0.936250i	$0.385728\pi$
$882$	90.8920	+	251.931i	0.103052	+	0.285636i
$883$			145.438i			0.164709i	0.996603	+	0.0823545i	$0.0262440\pi$
$883$			145.438i			0.164709i	−0.996603	+	0.0823545i	$0.973756\pi$
$884$	31.1515	−	25.8413i	0.0352392	−	0.0292323i
$885$	−114.541			−0.129425
$886$	−673.343	+	242.930i	−0.759980	+	0.274187i
$887$		−	1437.98i		−	1.62118i	−0.585617	−	0.810588i	$-0.699148\pi$
$887$		−	1437.98i		−	1.62118i	0.585617	−	0.810588i	$-0.300852\pi$
$888$	−63.2365	+	107.421i	−0.0712123	+	0.120969i
$889$	−4.05932			−0.00456617
$890$	−376.602	−	1043.85i	−0.423148	−	1.17286i
$891$		−	173.307i		−	0.194508i
$892$	−329.686	−	397.433i	−0.369603	−	0.445552i
$893$	2059.12			2.30585
$894$	−258.886	+	93.4012i	−0.289582	+	0.104476i
$895$		−	434.014i		−	0.484932i
$896$	201.368	+	175.854i	0.224741	+	0.196265i
$897$	5.60548			0.00624915
$898$	432.026	+	1197.47i	0.481098	+	1.33349i
$899$		−	98.6874i		−	0.109775i
$900$	−0.893928	+	0.741547i	−0.000993253	+	0.000823941i
$901$	−155.495			−0.172581
$902$	−333.507	+	120.323i	−0.369741	+	0.133396i
$903$		−	244.858i		−	0.271161i
$904$	1041.77	+	613.267i	1.15240	+	0.678393i
$905$	−434.024			−0.479585
$906$	−142.656	−	395.410i	−0.157457	−	0.436435i
$907$			1343.43i			1.48118i	0.671957	+	0.740590i	$0.265454\pi$
$907$			1343.43i			1.48118i	−0.671957	+	0.740590i	$0.734546\pi$
$908$	−1041.04	−	1254.97i	−1.14652	−	1.38212i
$909$	−403.948			−0.444388
$910$	−13.2324	+	4.77401i	−0.0145411	+	0.00524616i
$911$		−	458.672i		−	0.503482i	−0.967795	−	0.251741i	$-0.918997\pi$
$911$		−	458.672i		−	0.503482i	0.967795	−	0.251741i	$-0.0810031\pi$
$912$	−135.401	+	720.310i	−0.148466	+	0.789814i
$913$	−1752.34			−1.91932
$914$	226.424	+	627.593i	0.247729	+	0.686645i
$915$			147.777i			0.161505i
$916$	198.377	−	164.561i	0.216569	−	0.179652i
$917$	−330.939			−0.360893
$918$	146.580	−	52.8833i	0.159673	−	0.0576071i
$919$		−	591.909i		−	0.644079i	−0.946726	−	0.322039i	$-0.895632\pi$
$919$		−	591.909i		−	0.644079i	0.946726	−	0.322039i	$-0.104368\pi$
$920$	97.1294	−	164.995i	0.105575	−	0.179343i
$921$	−357.996			−0.388704
$922$	360.195	+	998.375i	0.390667	+	1.08284i
$923$		−	28.8668i		−	0.0312750i
$924$	177.906	+	214.463i	0.192538	+	0.232103i
$925$	0.870708			0.000941306
$926$	−1149.11	+	414.579i	−1.24094	+	0.447709i
$927$		−	376.774i		−	0.406444i
$928$	566.335	−	91.6503i	0.610275	−	0.0987611i
$929$	−1095.68			−1.17942			−0.589709	−	0.807616i	$-0.700758\pi$
$929$	−1095.68			−1.17942			−0.589709	+	0.807616i	$0.700758\pi$
$930$	−32.2936	−	89.5102i	−0.0347243	−	0.0962476i
$931$		−	1180.54i		−	1.26803i
$932$	−648.050	+	537.583i	−0.695333	+	0.576805i
$933$	656.141			0.703260
$934$	−296.932	+	107.127i	−0.317914	+	0.114698i
$935$		−	1440.90i		−	1.54107i
$936$	13.9569	+	8.21616i	0.0149112	+	0.00877795i
$937$	6.31450			0.00673906			0.00336953	−	0.999994i	$-0.498927\pi$
$937$	6.31450			0.00673906			0.00336953	+	0.999994i	$0.498927\pi$
$938$	−55.3652	−	153.459i	−0.0590247	−	0.163602i
$939$			822.791i			0.876242i
$940$	−992.256	−	1196.16i	−1.05559	−	1.27251i
$941$	1385.68			1.47256			0.736281	−	0.676676i	$-0.236580\pi$
$941$	1385.68			1.47256			0.736281	+	0.676676i	$0.236580\pi$
$942$	−909.172	+	328.012i	−0.965150	+	0.348208i
$943$		−	44.1506i		−	0.0468193i
$944$	−208.379	−	39.1702i	−0.220740	−	0.0414939i
$945$	−54.1593			−0.0573114
$946$	884.642	+	2452.02i	0.935140	+	2.59198i
$947$			1188.25i			1.25475i	0.778719	+	0.627373i	$0.215870\pi$
$947$			1188.25i			1.25475i	−0.778719	+	0.627373i	$0.784130\pi$
$948$	182.218	−	151.157i	0.192213	−	0.159448i
$949$	−66.4103			−0.0699792
$950$	4.81574	−	1.73743i	0.00506920	−	0.00182887i
$951$			151.271i			0.159065i
$952$	−127.103	+	215.912i	−0.133512	+	0.226798i
$953$	−300.811			−0.315647			−0.157823	−	0.987467i	$-0.550448\pi$
$953$	−300.811			−0.315647			−0.157823	+	0.987467i	$0.550448\pi$
$954$	−21.1159	−	58.5282i	−0.0221340	−	0.0613503i
$955$			226.748i			0.237433i
$956$	−1009.00	−	1216.34i	−1.05544	−	1.27232i
$957$	597.957			0.624825
$958$	−1438.11	+	518.845i	−1.50116	+	0.541591i
$959$			84.0503i			0.0876437i
$960$	483.679	−	268.450i	0.503832	−	0.279635i
$961$	930.699			0.968470
$962$	−4.12041	−	11.4208i	−0.00428317	−	0.0118719i
$963$		−	565.351i		−	0.587073i
$964$	−544.996	+	452.095i	−0.565349	+	0.468978i
$965$	−1551.43			−1.60770
$966$	−32.6398	+	11.7758i	−0.0337886	+	0.0121903i
$967$			1195.10i			1.23588i	0.786224	+	0.617941i	$0.212033\pi$
$967$			1195.10i			1.23588i	−0.786224	+	0.617941i	$0.787967\pi$
$968$	−1722.19	−	1013.82i	−1.77912	−	1.04733i
$969$	−686.868			−0.708842
$970$	−56.1053	−	155.510i	−0.0578405	−	0.160320i
$971$		−	330.658i		−	0.340533i	−0.985398	−	0.170267i	$-0.945537\pi$
$971$		−	330.658i		−	0.340533i	0.985398	−	0.170267i	$-0.0544629\pi$
$972$	39.8104	+	47.9910i	0.0409572	+	0.0493734i
$973$	−400.034			−0.411134
$974$	−314.231	+	113.369i	−0.322619	+	0.116395i
$975$		−	0.113129i		−	0.000116030i
$976$	−50.5360	+	268.843i	−0.0517786	+	0.275454i
$977$	1755.78			1.79711			0.898556	−	0.438859i	$-0.144617\pi$
$977$	1755.78			1.79711			0.898556	+	0.438859i	$0.144617\pi$
$978$	143.690	+	398.275i	0.146922	+	0.407234i
$979$		−	2141.03i		−	2.18696i
$980$	−685.780	+	568.881i	−0.699776	+	0.580491i
$981$	546.124			0.556702
$982$	−242.595	+	87.5238i	−0.247042	+	0.0891281i
$983$		−	1344.70i		−	1.36796i	−0.729503	−	0.683978i	$-0.760248\pi$
$983$		−	1344.70i		−	1.36796i	0.729503	−	0.683978i	$-0.239752\pi$
$984$	64.7131	−	109.929i	0.0657653	−	0.111717i
$985$	1803.88			1.83135
$986$	182.463	+	505.743i	0.185053	+	0.512924i
$987$			281.661i			0.285371i
$988$	−45.5786	−	54.9445i	−0.0461322	−	0.0556119i
$989$	−324.605			−0.328215
$990$	542.352	−	195.670i	0.547830	−	0.197647i
$991$		−	114.991i		−	0.116035i	−0.998316	−	0.0580175i	$-0.981522\pi$
$991$		−	114.991i		−	0.116035i	0.998316	−	0.0580175i	$-0.0184779\pi$
$992$	−28.1399	−	173.885i	−0.0283668	−	0.175287i
$993$	−524.451			−0.528148
$994$	60.6425	+	168.087i	0.0610086	+	0.169101i
$995$			796.382i			0.800384i
$996$	485.248	−	402.532i	0.487197	−	0.404148i
$997$	1581.80			1.58656			0.793282	−	0.608855i	$-0.208371\pi$
$997$	1581.80			1.58656			0.793282	+	0.608855i	$0.208371\pi$
$998$	861.886	−	310.953i	0.863614	−	0.311576i
$999$		−	46.7444i		−	0.0467912i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.3.f.b.139.13	✓	40
4.3	odd	2	inner	276.3.f.b.139.14	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.3.f.b.139.13	✓	40	1.1	even	1	trivial
276.3.f.b.139.14	yes	40	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	276.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.678740 - 1.88131i) q^{2} -1.73205i q^{3} +(-3.07862 + 2.55384i) q^{4} +4.99031 q^{5} +(-3.25852 + 1.17561i) q^{6} +2.08864i q^{7} +(6.89413 + 4.05844i) q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(-0.678740 - 1.88131i) q^{2} -1.73205i q^{3} +(-3.07862 + 2.55384i) q^{4} +4.99031 q^{5} +(-3.25852 + 1.17561i) q^{6} +2.08864i q^{7} +(6.89413 + 4.05844i) q^{8} -3.00000 q^{9} +(-3.38713 - 9.38830i) q^{10} -19.2563i q^{11} +(4.42337 + 5.33233i) q^{12} -0.674821 q^{13} +(3.92937 - 1.41764i) q^{14} -8.64347i q^{15} +(2.95584 - 15.7246i) q^{16} +14.9945 q^{17} +(2.03622 + 5.64392i) q^{18} -26.4472i q^{19} +(-15.3633 + 12.7444i) q^{20} +3.61763 q^{21} +(-36.2270 + 13.0700i) q^{22} -4.79583i q^{23} +(7.02943 - 11.9410i) q^{24} -0.0967887 q^{25} +(0.458028 + 1.26954i) q^{26} +5.19615i q^{27} +(-5.33404 - 6.43013i) q^{28} -17.9282 q^{29} +(-16.2610 + 5.86667i) q^{30} +5.50459i q^{31} +(-31.5890 + 5.11207i) q^{32} -33.3529 q^{33} +(-10.1774 - 28.2093i) q^{34} +10.4230i q^{35} +(9.23587 - 7.66151i) q^{36} -8.99597 q^{37} +(-49.7552 + 17.9508i) q^{38} +1.16882i q^{39} +(34.4039 + 20.2529i) q^{40} +9.20603 q^{41} +(-2.45543 - 6.80586i) q^{42} -67.6848i q^{43} +(49.1774 + 59.2829i) q^{44} -14.9709 q^{45} +(-9.02243 + 3.25512i) q^{46} +77.8580i q^{47} +(-27.2358 - 5.11967i) q^{48} +44.6376 q^{49} +(0.0656944 + 0.182089i) q^{50} -25.9713i q^{51} +(2.07752 - 1.72338i) q^{52} -10.3701 q^{53} +(9.77555 - 3.52684i) q^{54} -96.0949i q^{55} +(-8.47661 + 14.3993i) q^{56} -45.8078 q^{57} +(12.1686 + 33.7284i) q^{58} -13.2518i q^{59} +(22.0740 + 26.6100i) q^{60} -17.0970 q^{61} +(10.3558 - 3.73619i) q^{62} -6.26591i q^{63} +(31.0581 + 55.9589i) q^{64} -3.36757 q^{65} +(22.6379 + 62.7470i) q^{66} -39.0544i q^{67} +(-46.1626 + 38.2936i) q^{68} -8.30662 q^{69} +(19.6088 - 7.07448i) q^{70} +42.7770i q^{71} +(-20.6824 - 12.1753i) q^{72} +98.4117 q^{73} +(6.10593 + 16.9242i) q^{74} +0.167643i q^{75} +(67.5417 + 81.4209i) q^{76} +40.2194 q^{77} +(2.19892 - 0.793328i) q^{78} -34.1723i q^{79} +(14.7506 - 78.4706i) q^{80} +9.00000 q^{81} +(-6.24850 - 17.3194i) q^{82} -91.0011i q^{83} +(-11.1373 + 9.23882i) q^{84} +74.8275 q^{85} +(-127.336 + 45.9404i) q^{86} +31.0526i q^{87} +(78.1505 - 132.755i) q^{88} +111.186 q^{89} +(10.1614 + 28.1649i) q^{90} -1.40946i q^{91} +(12.2478 + 14.7646i) q^{92} +9.53423 q^{93} +(146.475 - 52.8454i) q^{94} -131.980i q^{95} +(8.85437 + 54.7138i) q^{96} +16.5643 q^{97} +(-30.2973 - 83.9770i) q^{98} +57.7689i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9}+O(q^{10}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9	\( 40 q + 4 q^{2} + 8 q^{4} + 4 q^{5} - 12 q^{6} - 44 q^{8} - 120 q^{9} - 24 q^{10} + 48 q^{12} + 8 q^{13} + 4 q^{14} + 40 q^{16} + 40 q^{17} - 12 q^{18} + 12 q^{20} + 24 q^{21} - 8 q^{22} + 36 q^{24} + 144 q^{25} - 128 q^{26} - 24 q^{28} - 72 q^{29} + 60 q^{30} + 44 q^{32} + 12 q^{33} - 80 q^{34} - 24 q^{36} + 68 q^{37} + 56 q^{38} + 140 q^{40} - 192 q^{41} + 36 q^{42} + 104 q^{44} - 12 q^{45} - 96 q^{48} - 200 q^{49} + 140 q^{50} - 184 q^{52} - 76 q^{53} + 36 q^{54} - 236 q^{56} + 84 q^{57} + 304 q^{58} + 96 q^{60} - 452 q^{61} + 40 q^{62} - 376 q^{64} + 744 q^{65} - 156 q^{66} + 300 q^{68} - 480 q^{70} + 132 q^{72} + 344 q^{73} + 500 q^{74} - 284 q^{76} - 56 q^{77} + 24 q^{78} - 228 q^{80} + 360 q^{81} + 144 q^{82} - 360 q^{84} + 96 q^{85} - 144 q^{86} + 300 q^{88} - 752 q^{89} + 72 q^{90} + 24 q^{93} - 200 q^{94} + 12 q^{96} - 40 q^{97} - 556 q^{98}+O(q^{100}) \) 40 * q + 4 * q^2 + 8 * q^4 + 4 * q^5 - 12 * q^6 - 44 * q^8 - 120 * q^9 - 24 * q^10 + 48 * q^12 + 8 * q^13 + 4 * q^14 + 40 * q^16 + 40 * q^17 - 12 * q^18 + 12 * q^20 + 24 * q^21 - 8 * q^22 + 36 * q^24 + 144 * q^25 - 128 * q^26 - 24 * q^28 - 72 * q^29 + 60 * q^30 + 44 * q^32 + 12 * q^33 - 80 * q^34 - 24 * q^36 + 68 * q^37 + 56 * q^38 + 140 * q^40 - 192 * q^41 + 36 * q^42 + 104 * q^44 - 12 * q^45 - 96 * q^48 - 200 * q^49 + 140 * q^50 - 184 * q^52 - 76 * q^53 + 36 * q^54 - 236 * q^56 + 84 * q^57 + 304 * q^58 + 96 * q^60 - 452 * q^61 + 40 * q^62 - 376 * q^64 + 744 * q^65 - 156 * q^66 + 300 * q^68 - 480 * q^70 + 132 * q^72 + 344 * q^73 + 500 * q^74 - 284 * q^76 - 56 * q^77 + 24 * q^78 - 228 * q^80 + 360 * q^81 + 144 * q^82 - 360 * q^84 + 96 * q^85 - 144 * q^86 + 300 * q^88 - 752 * q^89 + 72 * q^90 + 24 * q^93 - 200 * q^94 + 12 * q^96 - 40 * q^97 - 556 * q^98

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