LMFDB - Embedded newform 273.2.p.a.34.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(34,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 1]))

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

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

chi := DirichletCharacter("273.34");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.p (of order $4$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(i, \sqrt{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 9 $ x^4 + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			34.2
Root			$1.22474 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	273.34
Dual form			273.2.p.a.265.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 1.22474i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(1.00000 + 2.44949i) q^{7} +(1.22474 - 1.22474i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(1.22474 + 1.22474i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(1.00000 + 2.44949i) q^{7} +(1.22474 - 1.22474i) q^{8} -1.00000 q^{9} -4.89898 q^{10} +(-0.449490 + 0.449490i) q^{11} -1.00000 q^{12} +(-2.00000 - 3.00000i) q^{13} +(-1.77526 + 4.22474i) q^{14} +(-2.00000 - 2.00000i) q^{15} +5.00000 q^{16} +2.00000 q^{17} +(-1.22474 - 1.22474i) q^{18} +(0.550510 - 0.550510i) q^{19} +(-2.00000 - 2.00000i) q^{20} +(-2.44949 + 1.00000i) q^{21} -1.10102 q^{22} +8.89898i q^{23} +(1.22474 + 1.22474i) q^{24} -3.00000i q^{25} +(1.22474 - 6.12372i) q^{26} -1.00000i q^{27} +(-2.44949 + 1.00000i) q^{28} +2.89898 q^{29} -4.89898i q^{30} +(5.44949 - 5.44949i) q^{31} +(3.67423 + 3.67423i) q^{32} +(-0.449490 - 0.449490i) q^{33} +(2.44949 + 2.44949i) q^{34} +(-6.89898 - 2.89898i) q^{35} -1.00000i q^{36} +(7.89898 - 7.89898i) q^{37} +1.34847 q^{38} +(3.00000 - 2.00000i) q^{39} +4.89898i q^{40} +(4.00000 - 4.00000i) q^{41} +(-4.22474 - 1.77526i) q^{42} -6.89898i q^{43} +(-0.449490 - 0.449490i) q^{44} +(2.00000 - 2.00000i) q^{45} +(-10.8990 + 10.8990i) q^{46} +(-1.55051 - 1.55051i) q^{47} +5.00000i q^{48} +(-5.00000 + 4.89898i) q^{49} +(3.67423 - 3.67423i) q^{50} +2.00000i q^{51} +(3.00000 - 2.00000i) q^{52} -11.7980 q^{53} +(1.22474 - 1.22474i) q^{54} -1.79796i q^{55} +(4.22474 + 1.77526i) q^{56} +(0.550510 + 0.550510i) q^{57} +(3.55051 + 3.55051i) q^{58} +(4.44949 + 4.44949i) q^{59} +(2.00000 - 2.00000i) q^{60} +10.0000i q^{61} +13.3485 q^{62} +(-1.00000 - 2.44949i) q^{63} -1.00000i q^{64} +(10.0000 + 2.00000i) q^{65} -1.10102i q^{66} +(-6.34847 - 6.34847i) q^{67} +2.00000i q^{68} -8.89898 q^{69} +(-4.89898 - 12.0000i) q^{70} +(2.44949 + 2.44949i) q^{71} +(-1.22474 + 1.22474i) q^{72} +(-7.89898 - 7.89898i) q^{73} +19.3485 q^{74} +3.00000 q^{75} +(0.550510 + 0.550510i) q^{76} +(-1.55051 - 0.651531i) q^{77} +(6.12372 + 1.22474i) q^{78} -2.89898 q^{79} +(-10.0000 + 10.0000i) q^{80} +1.00000 q^{81} +9.79796 q^{82} +(-0.449490 + 0.449490i) q^{83} +(-1.00000 - 2.44949i) q^{84} +(-4.00000 + 4.00000i) q^{85} +(8.44949 - 8.44949i) q^{86} +2.89898i q^{87} +1.10102i q^{88} +(-2.00000 - 2.00000i) q^{89} +4.89898 q^{90} +(5.34847 - 7.89898i) q^{91} -8.89898 q^{92} +(5.44949 + 5.44949i) q^{93} -3.79796i q^{94} +2.20204i q^{95} +(-3.67423 + 3.67423i) q^{96} +(-7.89898 + 7.89898i) q^{97} +(-12.1237 - 0.123724i) q^{98} +(0.449490 - 0.449490i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 4 * q - 8 * q^5 + 4 * q^7 - 4 * q^9	$ 4 q - 8 q^{5} + 4 q^{7} - 4 q^{9} + 8 q^{11} - 4 q^{12} - 8 q^{13} - 12 q^{14} - 8 q^{15} + 20 q^{16} + 8 q^{17} + 12 q^{19} - 8 q^{20} - 24 q^{22} - 8 q^{29} + 12 q^{31} + 8 q^{33} - 8 q^{35} + 12 q^{37} - 24 q^{38} + 12 q^{39} + 16 q^{41} - 12 q^{42} + 8 q^{44} + 8 q^{45} - 24 q^{46} - 16 q^{47} - 20 q^{49} + 12 q^{52} - 8 q^{53} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 8 q^{59} + 8 q^{60} + 24 q^{62} - 4 q^{63} + 40 q^{65} + 4 q^{67} - 16 q^{69} - 12 q^{73} + 48 q^{74} + 12 q^{75} + 12 q^{76} - 16 q^{77} + 8 q^{79} - 40 q^{80} + 4 q^{81} + 8 q^{83} - 4 q^{84} - 16 q^{85} + 24 q^{86} - 8 q^{89} - 8 q^{91} - 16 q^{92} + 12 q^{93} - 12 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) $ 4 * q - 8 * q^5 + 4 * q^7 - 4 * q^9 + 8 * q^11 - 4 * q^12 - 8 * q^13 - 12 * q^14 - 8 * q^15 + 20 * q^16 + 8 * q^17 + 12 * q^19 - 8 * q^20 - 24 * q^22 - 8 * q^29 + 12 * q^31 + 8 * q^33 - 8 * q^35 + 12 * q^37 - 24 * q^38 + 12 * q^39 + 16 * q^41 - 12 * q^42 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 16 * q^47 - 20 * q^49 + 12 * q^52 - 8 * q^53 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 8 * q^59 + 8 * q^60 + 24 * q^62 - 4 * q^63 + 40 * q^65 + 4 * q^67 - 16 * q^69 - 12 * q^73 + 48 * q^74 + 12 * q^75 + 12 * q^76 - 16 * q^77 + 8 * q^79 - 40 * q^80 + 4 * q^81 + 8 * q^83 - 4 * q^84 - 16 * q^85 + 24 * q^86 - 8 * q^89 - 8 * q^91 - 16 * q^92 + 12 * q^93 - 12 * q^97 - 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$-1$

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 $

$2$	1.22474	+	1.22474i	0.866025	+	0.866025i	0.992030	−	0.126004i	$-0.0402153\pi$
$2$	1.22474	+	1.22474i	0.866025	+	0.866025i	−0.126004	+	0.992030i	$0.540215\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$			1.00000i			0.500000i
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	−0.994936	−	0.100509i	$-0.967953\pi$
$5$	−2.00000	+	2.00000i	−0.894427	+	0.894427i	0.100509	+	0.994936i	$0.467953\pi$
$6$	−1.22474	+	1.22474i	−0.500000	+	0.500000i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$7$	1.00000	+	2.44949i	0.377964	+	0.925820i
$8$	1.22474	−	1.22474i	0.433013	−	0.433013i
$9$	−1.00000			−0.333333
$10$	−4.89898			−1.54919
$11$	−0.449490	+	0.449490i	−0.135526	+	0.135526i	−0.771615	−	0.636089i	$-0.780551\pi$
$11$	−0.449490	+	0.449490i	−0.135526	+	0.135526i	0.636089	+	0.771615i	$0.280551\pi$
$12$	−1.00000			−0.288675
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$13$	−2.00000	−	3.00000i	−0.554700	−	0.832050i
$14$	−1.77526	+	4.22474i	−0.474457	+	1.12911i
$15$	−2.00000	−	2.00000i	−0.516398	−	0.516398i
$16$	5.00000			1.25000
$17$	2.00000			0.485071			0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000			0.485071			0.242536	+	0.970143i	$0.422021\pi$
$18$	−1.22474	−	1.22474i	−0.288675	−	0.288675i
$19$	0.550510	−	0.550510i	0.126296	−	0.126296i	−0.641134	−	0.767429i	$-0.721536\pi$
$19$	0.550510	−	0.550510i	0.126296	−	0.126296i	0.767429	+	0.641134i	$0.221536\pi$
$20$	−2.00000	−	2.00000i	−0.447214	−	0.447214i
$21$	−2.44949	+	1.00000i	−0.534522	+	0.218218i
$22$	−1.10102			−0.234738
$23$			8.89898i			1.85557i	0.373121	+	0.927783i	$0.378288\pi$
$23$			8.89898i			1.85557i	−0.373121	+	0.927783i	$0.621712\pi$
$24$	1.22474	+	1.22474i	0.250000	+	0.250000i
$25$		−	3.00000i		−	0.600000i
$26$	1.22474	−	6.12372i	0.240192	−	1.20096i
$27$		−	1.00000i		−	0.192450i
$28$	−2.44949	+	1.00000i	−0.462910	+	0.188982i
$29$	2.89898			0.538327			0.269163	−	0.963095i	$-0.413253\pi$
$29$	2.89898			0.538327			0.269163	+	0.963095i	$0.413253\pi$
$30$		−	4.89898i		−	0.894427i
$31$	5.44949	−	5.44949i	0.978757	−	0.978757i	−0.0210218	−	0.999779i	$-0.506692\pi$
$31$	5.44949	−	5.44949i	0.978757	−	0.978757i	0.999779	+	0.0210218i	$0.00669193\pi$
$32$	3.67423	+	3.67423i	0.649519	+	0.649519i
$33$	−0.449490	−	0.449490i	−0.0782461	−	0.0782461i
$34$	2.44949	+	2.44949i	0.420084	+	0.420084i
$35$	−6.89898	−	2.89898i	−1.16614	−	0.490017i
$36$		−	1.00000i		−	0.166667i
$37$	7.89898	−	7.89898i	1.29858	−	1.29858i	0.369257	−	0.929327i	$-0.379612\pi$
$37$	7.89898	−	7.89898i	1.29858	−	1.29858i	0.929327	−	0.369257i	$-0.120388\pi$
$38$	1.34847			0.218751
$39$	3.00000	−	2.00000i	0.480384	−	0.320256i
$40$			4.89898i			0.774597i
$41$	4.00000	−	4.00000i	0.624695	−	0.624695i	−0.322033	−	0.946728i	$-0.604366\pi$
$41$	4.00000	−	4.00000i	0.624695	−	0.624695i	0.946728	+	0.322033i	$0.104366\pi$
$42$	−4.22474	−	1.77526i	−0.651892	−	0.273928i
$43$		−	6.89898i		−	1.05208i	−0.850458	−	0.526042i	$-0.823675\pi$
$43$		−	6.89898i		−	1.05208i	0.850458	−	0.526042i	$-0.176325\pi$
$44$	−0.449490	−	0.449490i	−0.0677631	−	0.0677631i
$45$	2.00000	−	2.00000i	0.298142	−	0.298142i
$46$	−10.8990	+	10.8990i	−1.60697	+	1.60697i
$47$	−1.55051	−	1.55051i	−0.226165	−	0.226165i	0.584923	−	0.811089i	$-0.301125\pi$
$47$	−1.55051	−	1.55051i	−0.226165	−	0.226165i	−0.811089	+	0.584923i	$0.801125\pi$
$48$			5.00000i			0.721688i
$49$	−5.00000	+	4.89898i	−0.714286	+	0.699854i
$50$	3.67423	−	3.67423i	0.519615	−	0.519615i
$51$			2.00000i			0.280056i
$52$	3.00000	−	2.00000i	0.416025	−	0.277350i
$53$	−11.7980			−1.62057			−0.810287	−	0.586033i	$-0.800689\pi$
$53$	−11.7980			−1.62057			−0.810287	+	0.586033i	$0.800689\pi$
$54$	1.22474	−	1.22474i	0.166667	−	0.166667i
$55$		−	1.79796i		−	0.242437i
$56$	4.22474	+	1.77526i	0.564555	+	0.237228i
$57$	0.550510	+	0.550510i	0.0729169	+	0.0729169i
$58$	3.55051	+	3.55051i	0.466205	+	0.466205i
$59$	4.44949	+	4.44949i	0.579274	+	0.579274i	0.934703	−	0.355429i	$-0.115665\pi$
$59$	4.44949	+	4.44949i	0.579274	+	0.579274i	−0.355429	+	0.934703i	$0.615665\pi$
$60$	2.00000	−	2.00000i	0.258199	−	0.258199i
$61$			10.0000i			1.28037i	0.768221	+	0.640184i	$0.221142\pi$
$61$			10.0000i			1.28037i	−0.768221	+	0.640184i	$0.778858\pi$
$62$	13.3485			1.69526
$63$	−1.00000	−	2.44949i	−0.125988	−	0.308607i
$64$		−	1.00000i		−	0.125000i
$65$	10.0000	+	2.00000i	1.24035	+	0.248069i
$66$		−	1.10102i		−	0.135526i
$67$	−6.34847	−	6.34847i	−0.775589	−	0.775589i	0.203488	−	0.979077i	$-0.434772\pi$
$67$	−6.34847	−	6.34847i	−0.775589	−	0.775589i	−0.979077	+	0.203488i	$0.934772\pi$
$68$			2.00000i			0.242536i
$69$	−8.89898			−1.07131
$70$	−4.89898	−	12.0000i	−0.585540	−	1.43427i
$71$	2.44949	+	2.44949i	0.290701	+	0.290701i	0.837357	−	0.546656i	$-0.184100\pi$
$71$	2.44949	+	2.44949i	0.290701	+	0.290701i	−0.546656	+	0.837357i	$0.684100\pi$
$72$	−1.22474	+	1.22474i	−0.144338	+	0.144338i
$73$	−7.89898	−	7.89898i	−0.924506	−	0.924506i	0.0728382	−	0.997344i	$-0.476794\pi$
$73$	−7.89898	−	7.89898i	−0.924506	−	0.924506i	−0.997344	+	0.0728382i	$0.976794\pi$
$74$	19.3485			2.24921
$75$	3.00000			0.346410
$76$	0.550510	+	0.550510i	0.0631479	+	0.0631479i
$77$	−1.55051	−	0.651531i	−0.176697	−	0.0742488i
$78$	6.12372	+	1.22474i	0.693375	+	0.138675i
$79$	−2.89898			−0.326161			−0.163080	−	0.986613i	$-0.552143\pi$
$79$	−2.89898			−0.326161			−0.163080	+	0.986613i	$0.552143\pi$
$80$	−10.0000	+	10.0000i	−1.11803	+	1.11803i
$81$	1.00000			0.111111
$82$	9.79796			1.08200
$83$	−0.449490	+	0.449490i	−0.0493379	+	0.0493379i	−0.731345	−	0.682007i	$-0.761107\pi$
$83$	−0.449490	+	0.449490i	−0.0493379	+	0.0493379i	0.682007	+	0.731345i	$0.261107\pi$
$84$	−1.00000	−	2.44949i	−0.109109	−	0.267261i
$85$	−4.00000	+	4.00000i	−0.433861	+	0.433861i
$86$	8.44949	−	8.44949i	0.911132	−	0.911132i
$87$			2.89898i			0.310803i
$88$			1.10102i			0.117369i
$89$	−2.00000	−	2.00000i	−0.212000	−	0.212000i	0.593117	−	0.805116i	$-0.297897\pi$
$89$	−2.00000	−	2.00000i	−0.212000	−	0.212000i	−0.805116	+	0.593117i	$0.797897\pi$
$90$	4.89898			0.516398
$91$	5.34847	−	7.89898i	0.560672	−	0.828038i
$92$	−8.89898			−0.927783
$93$	5.44949	+	5.44949i	0.565086	+	0.565086i
$94$		−	3.79796i		−	0.391730i
$95$			2.20204i			0.225925i
$96$	−3.67423	+	3.67423i	−0.375000	+	0.375000i
$97$	−7.89898	+	7.89898i	−0.802020	+	0.802020i	−0.983411	−	0.181391i	$-0.941940\pi$
$97$	−7.89898	+	7.89898i	−0.802020	+	0.802020i	0.181391	+	0.983411i	$0.441940\pi$
$98$	−12.1237	−	0.123724i	−1.22468	−	0.0124980i
$99$	0.449490	−	0.449490i	0.0451754	−	0.0451754i
$100$	3.00000			0.300000
$101$	5.10102			0.507571			0.253785	−	0.967261i	$-0.418324\pi$
$101$	5.10102			0.507571			0.253785	+	0.967261i	$0.418324\pi$
$102$	−2.44949	+	2.44949i	−0.242536	+	0.242536i
$103$	1.79796			0.177158			0.0885791	−	0.996069i	$-0.471767\pi$
$103$	1.79796			0.177158			0.0885791	+	0.996069i	$0.471767\pi$
$104$	−6.12372	−	1.22474i	−0.600481	−	0.120096i
$105$	2.89898	−	6.89898i	0.282911	−	0.673271i
$106$	−14.4495	−	14.4495i	−1.40346	−	1.40346i
$107$	0.898979			0.0869076			0.0434538	−	0.999055i	$-0.486164\pi$
$107$	0.898979			0.0869076			0.0434538	+	0.999055i	$0.486164\pi$
$108$	1.00000			0.0962250
$109$	−0.101021	−	0.101021i	−0.00967601	−	0.00967601i	0.702252	−	0.711928i	$-0.252178\pi$
$109$	−0.101021	−	0.101021i	−0.00967601	−	0.00967601i	−0.711928	+	0.702252i	$0.752178\pi$
$110$	2.20204	−	2.20204i	0.209956	−	0.209956i
$111$	7.89898	+	7.89898i	0.749738	+	0.749738i
$112$	5.00000	+	12.2474i	0.472456	+	1.15728i
$113$	−18.8990			−1.77787			−0.888933	−	0.458037i	$-0.848553\pi$
$113$	−18.8990			−1.77787			−0.888933	+	0.458037i	$0.848553\pi$
$114$			1.34847i			0.126296i
$115$	−17.7980	−	17.7980i	−1.65967	−	1.65967i
$116$			2.89898i			0.269163i
$117$	2.00000	+	3.00000i	0.184900	+	0.277350i
$118$			10.8990i			1.00333i
$119$	2.00000	+	4.89898i	0.183340	+	0.449089i
$120$	−4.89898			−0.447214
$121$			10.5959i			0.963265i
$122$	−12.2474	+	12.2474i	−1.10883	+	1.10883i
$123$	4.00000	+	4.00000i	0.360668	+	0.360668i
$124$	5.44949	+	5.44949i	0.489379	+	0.489379i
$125$	−4.00000	−	4.00000i	−0.357771	−	0.357771i
$126$	1.77526	−	4.22474i	0.158152	−	0.376370i
$127$			8.00000i			0.709885i	0.934888	+	0.354943i	$0.115500\pi$
$127$			8.00000i			0.709885i	−0.934888	+	0.354943i	$0.884500\pi$
$128$	8.57321	−	8.57321i	0.757772	−	0.757772i
$129$	6.89898			0.607421
$130$	9.79796	+	14.6969i	0.859338	+	1.28901i
$131$		−	18.6969i		−	1.63356i	−0.576950	−	0.816780i	$-0.695757\pi$
$131$		−	18.6969i		−	1.63356i	0.576950	−	0.816780i	$-0.304243\pi$
$132$	0.449490	−	0.449490i	0.0391231	−	0.0391231i
$133$	1.89898	+	0.797959i	0.164662	+	0.0691918i
$134$		−	15.5505i		−	1.34336i
$135$	2.00000	+	2.00000i	0.172133	+	0.172133i
$136$	2.44949	−	2.44949i	0.210042	−	0.210042i
$137$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$137$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$138$	−10.8990	−	10.8990i	−0.927783	−	0.927783i
$139$		−	6.89898i		−	0.585164i	−0.956240	−	0.292582i	$-0.905486\pi$
$139$		−	6.89898i		−	0.585164i	0.956240	−	0.292582i	$-0.0945144\pi$
$140$	2.89898	−	6.89898i	0.245008	−	0.583070i
$141$	1.55051	−	1.55051i	0.130577	−	0.130577i
$142$			6.00000i			0.503509i
$143$	2.24745	+	0.449490i	0.187941	+	0.0375882i
$144$	−5.00000			−0.416667
$145$	−5.79796	+	5.79796i	−0.481494	+	0.481494i
$146$		−	19.3485i		−	1.60129i
$147$	−4.89898	−	5.00000i	−0.404061	−	0.412393i
$148$	7.89898	+	7.89898i	0.649292	+	0.649292i
$149$	−0.898979	−	0.898979i	−0.0736473	−	0.0736473i	0.669324	−	0.742971i	$-0.266584\pi$
$149$	−0.898979	−	0.898979i	−0.0736473	−	0.0736473i	−0.742971	+	0.669324i	$0.766584\pi$
$150$	3.67423	+	3.67423i	0.300000	+	0.300000i
$151$	7.44949	−	7.44949i	0.606231	−	0.606231i	−0.335728	−	0.941959i	$-0.608982\pi$
$151$	7.44949	−	7.44949i	0.606231	−	0.606231i	0.941959	+	0.335728i	$0.108982\pi$
$152$		−	1.34847i		−	0.109375i
$153$	−2.00000			−0.161690
$154$	−1.10102	−	2.69694i	−0.0887228	−	0.217325i
$155$			21.7980i			1.75085i
$156$	2.00000	+	3.00000i	0.160128	+	0.240192i
$157$			12.0000i			0.957704i	0.877896	+	0.478852i	$0.158947\pi$
$157$			12.0000i			0.957704i	−0.877896	+	0.478852i	$0.841053\pi$
$158$	−3.55051	−	3.55051i	−0.282463	−	0.282463i
$159$		−	11.7980i		−	0.935639i
$160$	−14.6969			−1.16190
$161$	−21.7980	+	8.89898i	−1.71792	+	0.701338i
$162$	1.22474	+	1.22474i	0.0962250	+	0.0962250i
$163$	5.44949	−	5.44949i	0.426837	−	0.426837i	−0.460712	−	0.887549i	$-0.652406\pi$
$163$	5.44949	−	5.44949i	0.426837	−	0.426837i	0.887549	+	0.460712i	$0.152406\pi$
$164$	4.00000	+	4.00000i	0.312348	+	0.312348i
$165$	1.79796			0.139971
$166$	−1.10102			−0.0854558
$167$	11.3485	+	11.3485i	0.878171	+	0.878171i	0.993345	−	0.115174i	$-0.0367427\pi$
$167$	11.3485	+	11.3485i	0.878171	+	0.878171i	−0.115174	+	0.993345i	$0.536743\pi$
$168$	−1.77526	+	4.22474i	−0.136964	+	0.325946i
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	−9.79796			−0.751469
$171$	−0.550510	+	0.550510i	−0.0420986	+	0.0420986i
$172$	6.89898			0.526042
$173$	−12.6969			−0.965330			−0.482665	−	0.875805i	$-0.660331\pi$
$173$	−12.6969			−0.965330			−0.482665	+	0.875805i	$0.660331\pi$
$174$	−3.55051	+	3.55051i	−0.269163	+	0.269163i
$175$	7.34847	−	3.00000i	0.555492	−	0.226779i
$176$	−2.24745	+	2.24745i	−0.169408	+	0.169408i
$177$	−4.44949	+	4.44949i	−0.334444	+	0.334444i
$178$		−	4.89898i		−	0.367194i
$179$		−	21.7980i		−	1.62926i	−0.579984	−	0.814628i	$-0.696941\pi$
$179$		−	21.7980i		−	1.62926i	0.579984	−	0.814628i	$-0.303059\pi$
$180$	2.00000	+	2.00000i	0.149071	+	0.149071i
$181$	−2.00000			−0.148659			−0.0743294	−	0.997234i	$-0.523682\pi$
$181$	−2.00000			−0.148659			−0.0743294	+	0.997234i	$0.523682\pi$
$182$	16.2247	−	3.12372i	1.20266	−	0.231546i
$183$	−10.0000			−0.739221
$184$	10.8990	+	10.8990i	0.803483	+	0.803483i
$185$			31.5959i			2.32298i
$186$			13.3485i			0.978757i
$187$	−0.898979	+	0.898979i	−0.0657399	+	0.0657399i
$188$	1.55051	−	1.55051i	0.113083	−	0.113083i
$189$	2.44949	−	1.00000i	0.178174	−	0.0727393i
$190$	−2.69694	+	2.69694i	−0.195656	+	0.195656i
$191$	−13.7980			−0.998385			−0.499193	−	0.866491i	$-0.666370\pi$
$191$	−13.7980			−0.998385			−0.499193	+	0.866491i	$0.666370\pi$
$192$	1.00000			0.0721688
$193$	14.7980	−	14.7980i	1.06518	−	1.06518i	0.0674583	−	0.997722i	$-0.478511\pi$
$193$	14.7980	−	14.7980i	1.06518	−	1.06518i	0.997722	−	0.0674583i	$-0.0214890\pi$
$194$	−19.3485			−1.38914
$195$	−2.00000	+	10.0000i	−0.143223	+	0.716115i
$196$	−4.89898	−	5.00000i	−0.349927	−	0.357143i
$197$	−7.79796	−	7.79796i	−0.555582	−	0.555582i	0.372465	−	0.928046i	$-0.378513\pi$
$197$	−7.79796	−	7.79796i	−0.555582	−	0.555582i	−0.928046	+	0.372465i	$0.878513\pi$
$198$	1.10102			0.0782461
$199$	22.8990			1.62327			0.811633	−	0.584168i	$-0.198579\pi$
$199$	22.8990			1.62327			0.811633	+	0.584168i	$0.198579\pi$
$200$	−3.67423	−	3.67423i	−0.259808	−	0.259808i
$201$	6.34847	−	6.34847i	0.447786	−	0.447786i
$202$	6.24745	+	6.24745i	0.439569	+	0.439569i
$203$	2.89898	+	7.10102i	0.203468	+	0.498394i
$204$	−2.00000			−0.140028
$205$			16.0000i			1.11749i
$206$	2.20204	+	2.20204i	0.153423	+	0.153423i
$207$		−	8.89898i		−	0.618522i
$208$	−10.0000	−	15.0000i	−0.693375	−	1.04006i
$209$			0.494897i			0.0342328i
$210$	12.0000	−	4.89898i	0.828079	−	0.338062i
$211$	9.10102			0.626540			0.313270	−	0.949664i	$-0.398576\pi$
$211$	9.10102			0.626540			0.313270	+	0.949664i	$0.398576\pi$
$212$		−	11.7980i		−	0.810287i
$213$	−2.44949	+	2.44949i	−0.167836	+	0.167836i
$214$	1.10102	+	1.10102i	0.0752642	+	0.0752642i
$215$	13.7980	+	13.7980i	0.941013	+	0.941013i
$216$	−1.22474	−	1.22474i	−0.0833333	−	0.0833333i
$217$	18.7980	+	7.89898i	1.27609	+	0.536218i
$218$		−	0.247449i		−	0.0167593i
$219$	7.89898	−	7.89898i	0.533764	−	0.533764i
$220$	1.79796			0.121218
$221$	−4.00000	−	6.00000i	−0.269069	−	0.403604i
$222$			19.3485i			1.29858i
$223$	−2.55051	+	2.55051i	−0.170795	+	0.170795i	−0.787329	−	0.616534i	$-0.788536\pi$
$223$	−2.55051	+	2.55051i	−0.170795	+	0.170795i	0.616534	+	0.787329i	$0.288536\pi$
$224$	−5.32577	+	12.6742i	−0.355843	+	0.846833i
$225$			3.00000i			0.200000i
$226$	−23.1464	−	23.1464i	−1.53968	−	1.53968i
$227$	−0.651531	+	0.651531i	−0.0432436	+	0.0432436i	−0.728398	−	0.685154i	$-0.759735\pi$
$227$	−0.651531	+	0.651531i	−0.0432436	+	0.0432436i	0.685154	+	0.728398i	$0.259735\pi$
$228$	−0.550510	+	0.550510i	−0.0364584	+	0.0364584i
$229$	13.0000	+	13.0000i	0.859064	+	0.859064i	0.991228	−	0.132164i	$-0.0421925\pi$
$229$	13.0000	+	13.0000i	0.859064	+	0.859064i	−0.132164	+	0.991228i	$0.542192\pi$
$230$		−	43.5959i		−	2.87463i
$231$	0.651531	−	1.55051i	0.0428676	−	0.102016i
$232$	3.55051	−	3.55051i	0.233102	−	0.233102i
$233$			11.7980i			0.772910i	0.922308	+	0.386455i	$0.126301\pi$
$233$			11.7980i			0.772910i	−0.922308	+	0.386455i	$0.873699\pi$
$234$	−1.22474	+	6.12372i	−0.0800641	+	0.400320i
$235$	6.20204			0.404577
$236$	−4.44949	+	4.44949i	−0.289637	+	0.289637i
$237$		−	2.89898i		−	0.188309i
$238$	−3.55051	+	8.44949i	−0.230145	+	0.547699i
$239$	−7.34847	−	7.34847i	−0.475333	−	0.475333i	0.428302	−	0.903635i	$-0.359112\pi$
$239$	−7.34847	−	7.34847i	−0.475333	−	0.475333i	−0.903635	+	0.428302i	$0.859112\pi$
$240$	−10.0000	−	10.0000i	−0.645497	−	0.645497i
$241$	−13.8990	−	13.8990i	−0.895312	−	0.895312i	0.0997051	−	0.995017i	$-0.468210\pi$
$241$	−13.8990	−	13.8990i	−0.895312	−	0.895312i	−0.995017	+	0.0997051i	$0.968210\pi$
$242$	−12.9773	+	12.9773i	−0.834212	+	0.834212i
$243$			1.00000i			0.0641500i
$244$	−10.0000			−0.640184
$245$	0.202041	−	19.7980i	0.0129079	−	1.26485i
$246$			9.79796i			0.624695i
$247$	−2.75255	−	0.550510i	−0.175141	−	0.0350281i
$248$		−	13.3485i		−	0.847629i
$249$	−0.449490	−	0.449490i	−0.0284853	−	0.0284853i
$250$		−	9.79796i		−	0.619677i
$251$	−4.89898			−0.309221			−0.154610	−	0.987976i	$-0.549412\pi$
$251$	−4.89898			−0.309221			−0.154610	+	0.987976i	$0.549412\pi$
$252$	2.44949	−	1.00000i	0.154303	−	0.0629941i
$253$	−4.00000	−	4.00000i	−0.251478	−	0.251478i
$254$	−9.79796	+	9.79796i	−0.614779	+	0.614779i
$255$	−4.00000	−	4.00000i	−0.250490	−	0.250490i
$256$	19.0000			1.18750
$257$	20.6969			1.29104			0.645520	−	0.763744i	$-0.276641\pi$
$257$	20.6969			1.29104			0.645520	+	0.763744i	$0.276641\pi$
$258$	8.44949	+	8.44949i	0.526042	+	0.526042i
$259$	27.2474	+	11.4495i	1.69307	+	0.711437i
$260$	−2.00000	+	10.0000i	−0.124035	+	0.620174i
$261$	−2.89898			−0.179442
$262$	22.8990	−	22.8990i	1.41470	−	1.41470i
$263$	16.8990			1.04204			0.521018	−	0.853546i	$-0.325552\pi$
$263$	16.8990			1.04204			0.521018	+	0.853546i	$0.325552\pi$
$264$	−1.10102			−0.0677631
$265$	23.5959	−	23.5959i	1.44949	−	1.44949i
$266$	1.34847	+	3.30306i	0.0826800	+	0.202524i
$267$	2.00000	−	2.00000i	0.122398	−	0.122398i
$268$	6.34847	−	6.34847i	0.387794	−	0.387794i
$269$			6.00000i			0.365826i	0.983129	+	0.182913i	$0.0585527\pi$
$269$			6.00000i			0.365826i	−0.983129	+	0.182913i	$0.941447\pi$
$270$			4.89898i			0.298142i
$271$	−4.55051	−	4.55051i	−0.276424	−	0.276424i	0.555256	−	0.831680i	$-0.312620\pi$
$271$	−4.55051	−	4.55051i	−0.276424	−	0.276424i	−0.831680	+	0.555256i	$0.812620\pi$
$272$	10.0000			0.606339
$273$	7.89898	+	5.34847i	0.478068	+	0.323704i
$274$		0			0
$275$	1.34847	+	1.34847i	0.0813158	+	0.0813158i
$276$		−	8.89898i		−	0.535656i
$277$		−	17.7980i		−	1.06938i	−0.845050	−	0.534688i	$-0.820429\pi$
$277$		−	17.7980i		−	1.06938i	0.845050	−	0.534688i	$-0.179571\pi$
$278$	8.44949	−	8.44949i	0.506767	−	0.506767i
$279$	−5.44949	+	5.44949i	−0.326252	+	0.326252i
$280$	−12.0000	+	4.89898i	−0.717137	+	0.292770i
$281$	−4.00000	+	4.00000i	−0.238620	+	0.238620i	−0.816279	−	0.577659i	$-0.803967\pi$
$281$	−4.00000	+	4.00000i	−0.238620	+	0.238620i	0.577659	+	0.816279i	$0.303967\pi$
$282$	3.79796			0.226165
$283$	−12.6969			−0.754755			−0.377377	−	0.926060i	$-0.623174\pi$
$283$	−12.6969			−0.754755			−0.377377	+	0.926060i	$0.623174\pi$
$284$	−2.44949	+	2.44949i	−0.145350	+	0.145350i
$285$	−2.20204			−0.130438
$286$	2.20204	+	3.30306i	0.130209	+	0.195314i
$287$	13.7980	+	5.79796i	0.814468	+	0.342243i
$288$	−3.67423	−	3.67423i	−0.216506	−	0.216506i
$289$	−13.0000			−0.764706
$290$	−14.2020			−0.833973
$291$	−7.89898	−	7.89898i	−0.463046	−	0.463046i
$292$	7.89898	−	7.89898i	0.462253	−	0.462253i
$293$	−18.6969	−	18.6969i	−1.09229	−	1.09229i	−0.995284	−	0.0970027i	$-0.969074\pi$
$293$	−18.6969	−	18.6969i	−1.09229	−	1.09229i	−0.0970027	−	0.995284i	$-0.530926\pi$
$294$	0.123724	−	12.1237i	0.00721575	−	0.707070i
$295$	−17.7980			−1.03624
$296$		−	19.3485i		−	1.12461i
$297$	0.449490	+	0.449490i	0.0260820	+	0.0260820i
$298$		−	2.20204i		−	0.127561i
$299$	26.6969	−	17.7980i	1.54392	−	1.02928i
$300$			3.00000i			0.173205i
$301$	16.8990	−	6.89898i	0.974041	−	0.397651i
$302$	18.2474			1.05002
$303$			5.10102i			0.293046i
$304$	2.75255	−	2.75255i	0.157870	−	0.157870i
$305$	−20.0000	−	20.0000i	−1.14520	−	1.14520i
$306$	−2.44949	−	2.44949i	−0.140028	−	0.140028i
$307$	13.4495	+	13.4495i	0.767603	+	0.767603i	0.977684	−	0.210081i	$-0.0673728\pi$
$307$	13.4495	+	13.4495i	0.767603	+	0.767603i	−0.210081	+	0.977684i	$0.567373\pi$
$308$	0.651531	−	1.55051i	0.0371244	−	0.0883485i
$309$			1.79796i			0.102282i
$310$	−26.6969	+	26.6969i	−1.51628	+	1.51628i
$311$	15.1010			0.856300			0.428150	−	0.903708i	$-0.359165\pi$
$311$	15.1010			0.856300			0.428150	+	0.903708i	$0.359165\pi$
$312$	1.22474	−	6.12372i	0.0693375	−	0.346688i
$313$			25.5959i			1.44677i	0.690447	+	0.723383i	$0.257414\pi$
$313$			25.5959i			1.44677i	−0.690447	+	0.723383i	$0.742586\pi$
$314$	−14.6969	+	14.6969i	−0.829396	+	0.829396i
$315$	6.89898	+	2.89898i	0.388713	+	0.163339i
$316$		−	2.89898i		−	0.163080i
$317$	16.6969	+	16.6969i	0.937793	+	0.937793i	0.998175	−	0.0603819i	$-0.0192318\pi$
$317$	16.6969	+	16.6969i	0.937793	+	0.937793i	−0.0603819	+	0.998175i	$0.519232\pi$
$318$	14.4495	−	14.4495i	0.810287	−	0.810287i
$319$	−1.30306	+	1.30306i	−0.0729574	+	0.0729574i
$320$	2.00000	+	2.00000i	0.111803	+	0.111803i
$321$			0.898979i			0.0501761i
$322$	−37.5959	−	15.7980i	−2.09514	−	0.880386i
$323$	1.10102	−	1.10102i	0.0612624	−	0.0612624i
$324$			1.00000i			0.0555556i
$325$	−9.00000	+	6.00000i	−0.499230	+	0.332820i
$326$	13.3485			0.739303
$327$	0.101021	−	0.101021i	0.00558645	−	0.00558645i
$328$		−	9.79796i		−	0.541002i
$329$	2.24745	−	5.34847i	0.123906	−	0.294871i
$330$	2.20204	+	2.20204i	0.121218	+	0.121218i
$331$	−21.2474	−	21.2474i	−1.16787	−	1.16787i	−0.982709	−	0.185156i	$-0.940721\pi$
$331$	−21.2474	−	21.2474i	−1.16787	−	1.16787i	−0.185156	−	0.982709i	$-0.559279\pi$
$332$	−0.449490	−	0.449490i	−0.0246690	−	0.0246690i
$333$	−7.89898	+	7.89898i	−0.432861	+	0.432861i
$334$			27.7980i			1.52104i
$335$	25.3939			1.38742
$336$	−12.2474	+	5.00000i	−0.668153	+	0.272772i
$337$			23.7980i			1.29636i	0.761488	+	0.648179i	$0.224469\pi$
$337$			23.7980i			1.29636i	−0.761488	+	0.648179i	$0.775531\pi$
$338$	−20.8207	+	8.57321i	−1.13249	+	0.466321i
$339$		−	18.8990i		−	1.02645i
$340$	−4.00000	−	4.00000i	−0.216930	−	0.216930i
$341$			4.89898i			0.265295i
$342$	−1.34847			−0.0729169
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	−8.44949	−	8.44949i	−0.455566	−	0.455566i
$345$	17.7980	−	17.7980i	0.958210	−	0.958210i
$346$	−15.5505	−	15.5505i	−0.836001	−	0.836001i
$347$	2.20204			0.118212			0.0591059	−	0.998252i	$-0.481175\pi$
$347$	2.20204			0.118212			0.0591059	+	0.998252i	$0.481175\pi$
$348$	−2.89898			−0.155402
$349$	8.79796	+	8.79796i	0.470944	+	0.470944i	0.902220	−	0.431276i	$-0.141936\pi$
$349$	8.79796	+	8.79796i	0.470944	+	0.470944i	−0.431276	+	0.902220i	$0.641936\pi$
$350$	12.6742	+	5.32577i	0.677466	+	0.284674i
$351$	−3.00000	+	2.00000i	−0.160128	+	0.106752i
$352$	−3.30306			−0.176054
$353$	−9.79796	+	9.79796i	−0.521493	+	0.521493i	−0.918022	−	0.396529i	$-0.870215\pi$
$353$	−9.79796	+	9.79796i	−0.521493	+	0.521493i	0.396529	+	0.918022i	$0.370215\pi$
$354$	−10.8990			−0.579274
$355$	−9.79796			−0.520022
$356$	2.00000	−	2.00000i	0.106000	−	0.106000i
$357$	−4.89898	+	2.00000i	−0.259281	+	0.105851i
$358$	26.6969	−	26.6969i	1.41098	−	1.41098i
$359$	4.44949	−	4.44949i	0.234835	−	0.234835i	−0.579872	−	0.814707i	$-0.696898\pi$
$359$	4.44949	−	4.44949i	0.234835	−	0.234835i	0.814707	+	0.579872i	$0.196898\pi$
$360$		−	4.89898i		−	0.258199i
$361$			18.3939i			0.968099i
$362$	−2.44949	−	2.44949i	−0.128742	−	0.128742i
$363$	−10.5959			−0.556141
$364$	7.89898	+	5.34847i	0.414019	+	0.280336i
$365$	31.5959			1.65381
$366$	−12.2474	−	12.2474i	−0.640184	−	0.640184i
$367$			26.4949i			1.38302i	0.722366	+	0.691511i	$0.243055\pi$
$367$			26.4949i			1.38302i	−0.722366	+	0.691511i	$0.756945\pi$
$368$			44.4949i			2.31946i
$369$	−4.00000	+	4.00000i	−0.208232	+	0.208232i
$370$	−38.6969	+	38.6969i	−2.01176	+	2.01176i
$371$	−11.7980	−	28.8990i	−0.612520	−	1.50036i
$372$	−5.44949	+	5.44949i	−0.282543	+	0.282543i
$373$	9.79796			0.507319			0.253660	−	0.967294i	$-0.418366\pi$
$373$	9.79796			0.507319			0.253660	+	0.967294i	$0.418366\pi$
$374$	−2.20204			−0.113865
$375$	4.00000	−	4.00000i	0.206559	−	0.206559i
$376$	−3.79796			−0.195865
$377$	−5.79796	−	8.69694i	−0.298610	−	0.447915i
$378$	4.22474	+	1.77526i	0.217297	+	0.0913093i
$379$	13.4495	+	13.4495i	0.690854	+	0.690854i	0.962420	−	0.271566i	$-0.0875415\pi$
$379$	13.4495	+	13.4495i	0.690854	+	0.690854i	−0.271566	+	0.962420i	$0.587542\pi$
$380$	−2.20204			−0.112962
$381$	−8.00000			−0.409852
$382$	−16.8990	−	16.8990i	−0.864627	−	0.864627i
$383$	−16.2474	+	16.2474i	−0.830206	+	0.830206i	−0.987545	−	0.157339i	$-0.949709\pi$
$383$	−16.2474	+	16.2474i	−0.830206	+	0.830206i	0.157339	+	0.987545i	$0.449709\pi$
$384$	8.57321	+	8.57321i	0.437500	+	0.437500i
$385$	4.40408	−	1.79796i	0.224453	−	0.0916325i
$386$	36.2474			1.84495
$387$			6.89898i			0.350695i
$388$	−7.89898	−	7.89898i	−0.401010	−	0.401010i
$389$			1.10102i			0.0558240i	0.999610	+	0.0279120i	$0.00888581\pi$
$389$			1.10102i			0.0558240i	−0.999610	+	0.0279120i	$0.991114\pi$
$390$	−14.6969	+	9.79796i	−0.744208	+	0.496139i
$391$			17.7980i			0.900081i
$392$	−0.123724	+	12.1237i	−0.00624902	+	0.612341i
$393$	18.6969			0.943136
$394$		−	19.1010i		−	0.962296i
$395$	5.79796	−	5.79796i	0.291727	−	0.291727i
$396$	0.449490	+	0.449490i	0.0225877	+	0.0225877i
$397$	−8.79796	−	8.79796i	−0.441557	−	0.441557i	0.450978	−	0.892535i	$-0.351075\pi$
$397$	−8.79796	−	8.79796i	−0.441557	−	0.441557i	−0.892535	+	0.450978i	$0.851075\pi$
$398$	28.0454	+	28.0454i	1.40579	+	1.40579i
$399$	−0.797959	+	1.89898i	−0.0399479	+	0.0950679i
$400$		−	15.0000i		−	0.750000i
$401$	−14.0000	+	14.0000i	−0.699127	+	0.699127i	−0.964222	−	0.265096i	$-0.914597\pi$
$401$	−14.0000	+	14.0000i	−0.699127	+	0.699127i	0.265096	+	0.964222i	$0.414597\pi$
$402$	15.5505			0.775589
$403$	−27.2474	−	5.44949i	−1.35729	−	0.271458i
$404$			5.10102i			0.253785i
$405$	−2.00000	+	2.00000i	−0.0993808	+	0.0993808i
$406$	−5.14643	+	12.2474i	−0.255413	+	0.607831i
$407$			7.10102i			0.351985i
$408$	2.44949	+	2.44949i	0.121268	+	0.121268i
$409$	5.69694	−	5.69694i	0.281695	−	0.281695i	−0.552089	−	0.833785i	$-0.686169\pi$
$409$	5.69694	−	5.69694i	0.281695	−	0.281695i	0.833785	+	0.552089i	$0.186169\pi$
$410$	−19.5959	+	19.5959i	−0.967773	+	0.967773i
$411$		0			0
$412$			1.79796i			0.0885791i
$413$	−6.44949	+	15.3485i	−0.317359	+	0.755249i
$414$	10.8990	−	10.8990i	0.535656	−	0.535656i
$415$		−	1.79796i		−	0.0882583i
$416$	3.67423	−	18.3712i	0.180144	−	0.900721i
$417$	6.89898			0.337844
$418$	−0.606123	+	0.606123i	−0.0296464	+	0.0296464i
$419$		−	34.2929i		−	1.67532i	−0.546195	−	0.837658i	$-0.683924\pi$
$419$		−	34.2929i		−	1.67532i	0.546195	−	0.837658i	$-0.316076\pi$
$420$	6.89898	+	2.89898i	0.336636	+	0.141456i
$421$	13.8990	+	13.8990i	0.677395	+	0.677395i	0.959410	−	0.282015i	$-0.0910028\pi$
$421$	13.8990	+	13.8990i	0.677395	+	0.677395i	−0.282015	+	0.959410i	$0.591003\pi$
$422$	11.1464	+	11.1464i	0.542600	+	0.542600i
$423$	1.55051	+	1.55051i	0.0753884	+	0.0753884i
$424$	−14.4495	+	14.4495i	−0.701729	+	0.701729i
$425$		−	6.00000i		−	0.291043i
$426$	−6.00000			−0.290701
$427$	−24.4949	+	10.0000i	−1.18539	+	0.483934i
$428$			0.898979i			0.0434538i
$429$	−0.449490	+	2.24745i	−0.0217016	+	0.108508i
$430$			33.7980i			1.62988i
$431$	24.0454	+	24.0454i	1.15823	+	1.15823i	0.984857	+	0.173370i	$0.0554656\pi$
$431$	24.0454	+	24.0454i	1.15823	+	1.15823i	0.173370	+	0.984857i	$0.444534\pi$
$432$		−	5.00000i		−	0.240563i
$433$	10.2020			0.490279			0.245139	−	0.969488i	$-0.421166\pi$
$433$	10.2020			0.490279			0.245139	+	0.969488i	$0.421166\pi$
$434$	13.3485	+	32.6969i	0.640747	+	1.56950i
$435$	−5.79796	−	5.79796i	−0.277991	−	0.277991i
$436$	0.101021	−	0.101021i	0.00483801	−	0.00483801i
$437$	4.89898	+	4.89898i	0.234350	+	0.234350i
$438$	19.3485			0.924506
$439$	−11.5959			−0.553443			−0.276721	−	0.960950i	$-0.589248\pi$
$439$	−11.5959			−0.553443			−0.276721	+	0.960950i	$0.589248\pi$
$440$	−2.20204	−	2.20204i	−0.104978	−	0.104978i
$441$	5.00000	−	4.89898i	0.238095	−	0.233285i
$442$	2.44949	−	12.2474i	0.116510	−	0.582552i
$443$	−34.6969			−1.64850			−0.824251	−	0.566225i	$-0.808403\pi$
$443$	−34.6969			−1.64850			−0.824251	+	0.566225i	$0.808403\pi$
$444$	−7.89898	+	7.89898i	−0.374869	+	0.374869i
$445$	8.00000			0.379236
$446$	−6.24745			−0.295825
$447$	0.898979	−	0.898979i	0.0425203	−	0.0425203i
$448$	2.44949	−	1.00000i	0.115728	−	0.0472456i
$449$	5.10102	−	5.10102i	0.240732	−	0.240732i	−0.576421	−	0.817153i	$-0.695551\pi$
$449$	5.10102	−	5.10102i	0.240732	−	0.240732i	0.817153	+	0.576421i	$0.195551\pi$
$450$	−3.67423	+	3.67423i	−0.173205	+	0.173205i
$451$			3.59592i			0.169325i
$452$		−	18.8990i		−	0.888933i
$453$	7.44949	+	7.44949i	0.350008	+	0.350008i
$454$	−1.59592			−0.0749001
$455$	5.10102	+	26.4949i	0.239140	+	1.24210i
$456$	1.34847			0.0631479
$457$	−12.7980	−	12.7980i	−0.598663	−	0.598663i	0.341294	−	0.939957i	$-0.389135\pi$
$457$	−12.7980	−	12.7980i	−0.598663	−	0.598663i	−0.939957	+	0.341294i	$0.889135\pi$
$458$			31.8434i			1.48794i
$459$		−	2.00000i		−	0.0933520i
$460$	17.7980	−	17.7980i	0.829834	−	0.829834i
$461$	−24.6969	+	24.6969i	−1.15025	+	1.15025i	−0.163749	+	0.986502i	$0.552359\pi$
$461$	−24.6969	+	24.6969i	−1.15025	+	1.15025i	−0.986502	+	0.163749i	$0.947641\pi$
$462$	2.69694	−	1.10102i	0.125473	−	0.0512241i
$463$	14.1464	−	14.1464i	0.657440	−	0.657440i	−0.297333	−	0.954774i	$-0.596097\pi$
$463$	14.1464	−	14.1464i	0.657440	−	0.657440i	0.954774	+	0.297333i	$0.0960973\pi$
$464$	14.4949			0.672909
$465$	−21.7980			−1.01086
$466$	−14.4495	+	14.4495i	−0.669360	+	0.669360i
$467$	−40.8990			−1.89258			−0.946290	−	0.323320i	$-0.895201\pi$
$467$	−40.8990			−1.89258			−0.946290	+	0.323320i	$0.895201\pi$
$468$	−3.00000	+	2.00000i	−0.138675	+	0.0924500i
$469$	9.20204	−	21.8990i	0.424911	−	1.01120i
$470$	7.59592	+	7.59592i	0.350374	+	0.350374i
$471$	−12.0000			−0.552931
$472$	10.8990			0.501666
$473$	3.10102	+	3.10102i	0.142585	+	0.142585i
$474$	3.55051	−	3.55051i	0.163080	−	0.163080i
$475$	−1.65153	−	1.65153i	−0.0757774	−	0.0757774i
$476$	−4.89898	+	2.00000i	−0.224544	+	0.0916698i
$477$	11.7980			0.540191
$478$		−	18.0000i		−	0.823301i
$479$	−14.2474	−	14.2474i	−0.650983	−	0.650983i	0.302247	−	0.953230i	$-0.402263\pi$
$479$	−14.2474	−	14.2474i	−0.650983	−	0.650983i	−0.953230	+	0.302247i	$0.902263\pi$
$480$		−	14.6969i		−	0.670820i
$481$	−39.4949	−	7.89898i	−1.80081	−	0.360162i
$482$		−	34.0454i		−	1.55073i
$483$	−8.89898	−	21.7980i	−0.404918	−	0.991841i
$484$	−10.5959			−0.481633
$485$		−	31.5959i		−	1.43470i
$486$	−1.22474	+	1.22474i	−0.0555556	+	0.0555556i
$487$	−9.24745	−	9.24745i	−0.419042	−	0.419042i	0.465832	−	0.884873i	$-0.345755\pi$
$487$	−9.24745	−	9.24745i	−0.419042	−	0.419042i	−0.884873	+	0.465832i	$0.845755\pi$
$488$	12.2474	+	12.2474i	0.554416	+	0.554416i
$489$	5.44949	+	5.44949i	0.246434	+	0.246434i
$490$	24.4949	−	24.0000i	1.10657	−	1.08421i
$491$			27.1010i			1.22305i	0.791224	+	0.611526i	$0.209444\pi$
$491$			27.1010i			1.22305i	−0.791224	+	0.611526i	$0.790556\pi$
$492$	−4.00000	+	4.00000i	−0.180334	+	0.180334i
$493$	5.79796			0.261127
$494$	−2.69694	−	4.04541i	−0.121341	−	0.182011i
$495$			1.79796i			0.0808122i
$496$	27.2474	−	27.2474i	1.22345	−	1.22345i
$497$	−3.55051	+	8.44949i	−0.159262	+	0.379011i
$498$		−	1.10102i		−	0.0493379i
$499$	9.24745	+	9.24745i	0.413973	+	0.413973i	0.883120	−	0.469147i	$-0.155439\pi$
$499$	9.24745	+	9.24745i	0.413973	+	0.413973i	−0.469147	+	0.883120i	$0.655439\pi$
$500$	4.00000	−	4.00000i	0.178885	−	0.178885i
$501$	−11.3485	+	11.3485i	−0.507012	+	0.507012i
$502$	−6.00000	−	6.00000i	−0.267793	−	0.267793i
$503$			2.69694i			0.120251i	0.998191	+	0.0601253i	$0.0191500\pi$
$503$			2.69694i			0.120251i	−0.998191	+	0.0601253i	$0.980850\pi$
$504$	−4.22474	−	1.77526i	−0.188185	−	0.0790761i
$505$	−10.2020	+	10.2020i	−0.453985	+	0.453985i
$506$		−	9.79796i		−	0.435572i
$507$	−12.0000	−	5.00000i	−0.532939	−	0.222058i
$508$	−8.00000			−0.354943
$509$	14.8990	−	14.8990i	0.660386	−	0.660386i	−0.295085	−	0.955471i	$-0.595348\pi$
$509$	14.8990	−	14.8990i	0.660386	−	0.660386i	0.955471	+	0.295085i	$0.0953481\pi$
$510$		−	9.79796i		−	0.433861i
$511$	11.4495	−	27.2474i	0.506496	−	1.20536i
$512$	6.12372	+	6.12372i	0.270633	+	0.270633i
$513$	−0.550510	−	0.550510i	−0.0243056	−	0.0243056i
$514$	25.3485	+	25.3485i	1.11807	+	1.11807i
$515$	−3.59592	+	3.59592i	−0.158455	+	0.158455i
$516$			6.89898i			0.303711i
$517$	1.39388			0.0613026
$518$	19.3485	+	47.3939i	0.850123	+	2.08237i
$519$		−	12.6969i		−	0.557334i
$520$	14.6969	−	9.79796i	0.644503	−	0.429669i
$521$		−	27.3939i		−	1.20015i	−0.799945	−	0.600074i	$-0.795138\pi$
$521$		−	27.3939i		−	1.20015i	0.799945	−	0.600074i	$-0.204862\pi$
$522$	−3.55051	−	3.55051i	−0.155402	−	0.155402i
$523$		−	30.4949i		−	1.33345i	−0.745304	−	0.666724i	$-0.767696\pi$
$523$		−	30.4949i		−	1.33345i	0.745304	−	0.666724i	$-0.232304\pi$
$524$	18.6969			0.816780
$525$	3.00000	+	7.34847i	0.130931	+	0.320713i
$526$	20.6969	+	20.6969i	0.902429	+	0.902429i
$527$	10.8990	−	10.8990i	0.474767	−	0.474767i
$528$	−2.24745	−	2.24745i	−0.0978077	−	0.0978077i
$529$	−56.1918			−2.44312
$530$	57.7980			2.51058
$531$	−4.44949	−	4.44949i	−0.193091	−	0.193091i
$532$	−0.797959	+	1.89898i	−0.0345959	+	0.0823312i
$533$	−20.0000	−	4.00000i	−0.866296	−	0.173259i
$534$	4.89898			0.212000
$535$	−1.79796	+	1.79796i	−0.0777325	+	0.0777325i
$536$	−15.5505			−0.671680
$537$	21.7980			0.940651
$538$	−7.34847	+	7.34847i	−0.316815	+	0.316815i
$539$	0.0454077	−	4.44949i	0.00195585	−	0.191653i
$540$	−2.00000	+	2.00000i	−0.0860663	+	0.0860663i
$541$	−11.8990	+	11.8990i	−0.511577	+	0.511577i	−0.915009	−	0.403432i	$-0.867817\pi$
$541$	−11.8990	+	11.8990i	−0.511577	+	0.511577i	0.403432	+	0.915009i	$0.367817\pi$
$542$		−	11.1464i		−	0.478780i
$543$		−	2.00000i		−	0.0858282i
$544$	7.34847	+	7.34847i	0.315063	+	0.315063i
$545$	0.404082			0.0173090
$546$	3.12372	+	16.2247i	0.133683	+	0.694355i
$547$	13.7980			0.589958			0.294979	−	0.955504i	$-0.404687\pi$
$547$	13.7980			0.589958			0.294979	+	0.955504i	$0.404687\pi$
$548$		0			0
$549$		−	10.0000i		−	0.426790i
$550$			3.30306i			0.140843i
$551$	1.59592	−	1.59592i	0.0679884	−	0.0679884i
$552$	−10.8990	+	10.8990i	−0.463891	+	0.463891i
$553$	−2.89898	−	7.10102i	−0.123277	−	0.301966i
$554$	21.7980	−	21.7980i	0.926107	−	0.926107i
$555$	−31.5959			−1.34117
$556$	6.89898			0.292582
$557$	18.6969	−	18.6969i	0.792215	−	0.792215i	−0.189639	−	0.981854i	$-0.560732\pi$
$557$	18.6969	−	18.6969i	0.792215	−	0.792215i	0.981854	+	0.189639i	$0.0607318\pi$
$558$	−13.3485			−0.565086
$559$	−20.6969	+	13.7980i	−0.875387	+	0.583591i
$560$	−34.4949	−	14.4949i	−1.45768	−	0.612521i
$561$	−0.898979	−	0.898979i	−0.0379549	−	0.0379549i
$562$	−9.79796			−0.413302
$563$	21.7980			0.918674			0.459337	−	0.888262i	$-0.348087\pi$
$563$	21.7980			0.918674			0.459337	+	0.888262i	$0.348087\pi$
$564$	1.55051	+	1.55051i	0.0652883	+	0.0652883i
$565$	37.7980	−	37.7980i	1.59017	−	1.59017i
$566$	−15.5505	−	15.5505i	−0.653637	−	0.653637i
$567$	1.00000	+	2.44949i	0.0419961	+	0.102869i
$568$	6.00000			0.251754
$569$		−	23.3939i		−	0.980722i	−0.871519	−	0.490361i	$-0.836865\pi$
$569$		−	23.3939i		−	0.980722i	0.871519	−	0.490361i	$-0.163135\pi$
$570$	−2.69694	−	2.69694i	−0.112962	−	0.112962i
$571$			43.1918i			1.80752i	0.428037	+	0.903761i	$0.359205\pi$
$571$			43.1918i			1.80752i	−0.428037	+	0.903761i	$0.640795\pi$
$572$	−0.449490	+	2.24745i	−0.0187941	+	0.0939706i
$573$		−	13.7980i		−	0.576418i
$574$	9.79796	+	24.0000i	0.408959	+	1.00174i
$575$	26.6969			1.11334
$576$			1.00000i			0.0416667i
$577$	−17.8990	+	17.8990i	−0.745144	+	0.745144i	−0.973563	−	0.228419i	$-0.926644\pi$
$577$	−17.8990	+	17.8990i	−0.745144	+	0.745144i	0.228419	+	0.973563i	$0.426644\pi$
$578$	−15.9217	−	15.9217i	−0.662255	−	0.662255i
$579$	14.7980	+	14.7980i	0.614982	+	0.614982i
$580$	−5.79796	−	5.79796i	−0.240747	−	0.240747i
$581$	−1.55051	−	0.651531i	−0.0643260	−	0.0270301i
$582$		−	19.3485i		−	0.802020i
$583$	5.30306	−	5.30306i	0.219630	−	0.219630i
$584$	−19.3485			−0.800645
$585$	−10.0000	−	2.00000i	−0.413449	−	0.0826898i
$586$		−	45.7980i		−	1.89190i
$587$	3.55051	−	3.55051i	0.146545	−	0.146545i	−0.630028	−	0.776573i	$-0.716956\pi$
$587$	3.55051	−	3.55051i	0.146545	−	0.146545i	0.776573	+	0.630028i	$0.216956\pi$
$588$	5.00000	−	4.89898i	0.206197	−	0.202031i
$589$		−	6.00000i		−	0.247226i
$590$	−21.7980	−	21.7980i	−0.897408	−	0.897408i
$591$	7.79796	−	7.79796i	0.320765	−	0.320765i
$592$	39.4949	−	39.4949i	1.62323	−	1.62323i
$593$	−17.1010	−	17.1010i	−0.702255	−	0.702255i	0.262639	−	0.964894i	$-0.415407\pi$
$593$	−17.1010	−	17.1010i	−0.702255	−	0.702255i	−0.964894	+	0.262639i	$0.915407\pi$
$594$			1.10102i			0.0451754i
$595$	−13.7980	−	5.79796i	−0.565661	−	0.237693i
$596$	0.898979	−	0.898979i	0.0368236	−	0.0368236i
$597$			22.8990i			0.937193i
$598$	54.4949	+	10.8990i	2.22846	+	0.445692i
$599$	4.49490			0.183657			0.0918283	−	0.995775i	$-0.470729\pi$
$599$	4.49490			0.183657			0.0918283	+	0.995775i	$0.470729\pi$
$600$	3.67423	−	3.67423i	0.150000	−	0.150000i
$601$		−	41.5959i		−	1.69673i	−0.529409	−	0.848366i	$-0.677586\pi$
$601$		−	41.5959i		−	1.69673i	0.529409	−	0.848366i	$-0.322414\pi$
$602$	29.1464	+	12.2474i	1.18792	+	0.499169i
$603$	6.34847	+	6.34847i	0.258530	+	0.258530i
$604$	7.44949	+	7.44949i	0.303115	+	0.303115i
$605$	−21.1918	−	21.1918i	−0.861571	−	0.861571i
$606$	−6.24745	+	6.24745i	−0.253785	+	0.253785i
$607$			14.8990i			0.604731i	0.953192	+	0.302365i	$0.0977763\pi$
$607$			14.8990i			0.604731i	−0.953192	+	0.302365i	$0.902224\pi$
$608$	4.04541			0.164063
$609$	−7.10102	+	2.89898i	−0.287748	+	0.117473i
$610$		−	48.9898i		−	1.98354i
$611$	−1.55051	+	7.75255i	−0.0627269	+	0.313635i
$612$		−	2.00000i		−	0.0808452i
$613$	−7.89898	−	7.89898i	−0.319037	−	0.319037i	0.529360	−	0.848397i	$-0.322432\pi$
$613$	−7.89898	−	7.89898i	−0.319037	−	0.319037i	−0.848397	+	0.529360i	$0.822432\pi$
$614$			32.9444i			1.32953i
$615$	−16.0000			−0.645182
$616$	−2.69694	+	1.10102i	−0.108663	+	0.0443614i
$617$	2.20204	+	2.20204i	0.0886508	+	0.0886508i	0.750042	−	0.661391i	$-0.230033\pi$
$617$	2.20204	+	2.20204i	0.0886508	+	0.0886508i	−0.661391	+	0.750042i	$0.730033\pi$
$618$	−2.20204	+	2.20204i	−0.0885791	+	0.0885791i
$619$	−10.5505	−	10.5505i	−0.424061	−	0.424061i	0.462538	−	0.886599i	$-0.346939\pi$
$619$	−10.5505	−	10.5505i	−0.424061	−	0.424061i	−0.886599	+	0.462538i	$0.846939\pi$
$620$	−21.7980			−0.875427
$621$	8.89898			0.357104
$622$	18.4949	+	18.4949i	0.741578	+	0.741578i
$623$	2.89898	−	6.89898i	0.116145	−	0.276402i
$624$	15.0000	−	10.0000i	0.600481	−	0.400320i
$625$	31.0000			1.24000
$626$	−31.3485	+	31.3485i	−1.25294	+	1.25294i
$627$	−0.494897			−0.0197643
$628$	−12.0000			−0.478852
$629$	15.7980	−	15.7980i	0.629906	−	0.629906i
$630$	4.89898	+	12.0000i	0.195180	+	0.478091i
$631$	13.2474	−	13.2474i	0.527373	−	0.527373i	−0.392415	−	0.919788i	$-0.628360\pi$
$631$	13.2474	−	13.2474i	0.527373	−	0.527373i	0.919788	+	0.392415i	$0.128360\pi$
$632$	−3.55051	+	3.55051i	−0.141232	+	0.141232i
$633$			9.10102i			0.361733i
$634$			40.8990i			1.62431i
$635$	−16.0000	−	16.0000i	−0.634941	−	0.634941i
$636$	11.7980			0.467820
$637$	24.6969	+	5.20204i	0.978528	+	0.206112i
$638$	−3.19184			−0.126366
$639$	−2.44949	−	2.44949i	−0.0969003	−	0.0969003i
$640$			34.2929i			1.35554i
$641$			8.69694i			0.343508i	0.985140	+	0.171754i	$0.0549435\pi$
$641$			8.69694i			0.343508i	−0.985140	+	0.171754i	$0.945057\pi$
$642$	−1.10102	+	1.10102i	−0.0434538	+	0.0434538i
$643$	−14.1464	+	14.1464i	−0.557881	+	0.557881i	−0.928704	−	0.370823i	$-0.879076\pi$
$643$	−14.1464	+	14.1464i	−0.557881	+	0.557881i	0.370823	+	0.928704i	$0.379076\pi$
$644$	−8.89898	−	21.7980i	−0.350669	−	0.858960i
$645$	−13.7980	+	13.7980i	−0.543294	+	0.543294i
$646$	2.69694			0.106110
$647$	12.0000			0.471769			0.235884	−	0.971781i	$-0.424201\pi$
$647$	12.0000			0.471769			0.235884	+	0.971781i	$0.424201\pi$
$648$	1.22474	−	1.22474i	0.0481125	−	0.0481125i
$649$	−4.00000			−0.157014
$650$	−18.3712	−	3.67423i	−0.720577	−	0.144115i
$651$	−7.89898	+	18.7980i	−0.309585	+	0.736750i
$652$	5.44949	+	5.44949i	0.213418	+	0.213418i
$653$	1.10102			0.0430863			0.0215431	−	0.999768i	$-0.493142\pi$
$653$	1.10102			0.0430863			0.0215431	+	0.999768i	$0.493142\pi$
$654$	0.247449			0.00967601
$655$	37.3939	+	37.3939i	1.46110	+	1.46110i
$656$	20.0000	−	20.0000i	0.780869	−	0.780869i
$657$	7.89898	+	7.89898i	0.308169	+	0.308169i
$658$	9.30306	−	3.79796i	0.362671	−	0.148060i
$659$	−31.5959			−1.23080			−0.615401	−	0.788214i	$-0.711006\pi$
$659$	−31.5959			−1.23080			−0.615401	+	0.788214i	$0.711006\pi$
$660$			1.79796i			0.0699855i
$661$	26.3939	+	26.3939i	1.02660	+	1.02660i	0.999636	+	0.0269665i	$0.00858474\pi$
$661$	26.3939	+	26.3939i	1.02660	+	1.02660i	0.0269665	+	0.999636i	$0.491415\pi$
$662$		−	52.0454i		−	2.02280i
$663$	6.00000	−	4.00000i	0.233021	−	0.155347i
$664$			1.10102i			0.0427279i
$665$	−5.39388	+	2.20204i	−0.209166	+	0.0853915i
$666$	−19.3485			−0.749738
$667$			25.7980i			0.998901i
$668$	−11.3485	+	11.3485i	−0.439085	+	0.439085i
$669$	−2.55051	−	2.55051i	−0.0986084	−	0.0986084i
$670$	31.1010	+	31.1010i	1.20154	+	1.20154i
$671$	−4.49490	−	4.49490i	−0.173524	−	0.173524i
$672$	−12.6742	−	5.32577i	−0.488919	−	0.205446i
$673$			13.3939i			0.516296i	0.966105	+	0.258148i	$0.0831122\pi$
$673$			13.3939i			0.516296i	−0.966105	+	0.258148i	$0.916888\pi$
$674$	−29.1464	+	29.1464i	−1.12268	+	1.12268i
$675$	−3.00000			−0.115470
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$			34.8990i			1.34128i	0.741784	+	0.670638i	$0.233980\pi$
$677$			34.8990i			1.34128i	−0.741784	+	0.670638i	$0.766020\pi$
$678$	23.1464	−	23.1464i	0.888933	−	0.888933i
$679$	−27.2474	−	11.4495i	−1.04566	−	0.439391i
$680$			9.79796i			0.375735i
$681$	−0.651531	−	0.651531i	−0.0249667	−	0.0249667i
$682$	−6.00000	+	6.00000i	−0.229752	+	0.229752i
$683$	1.75255	−	1.75255i	0.0670595	−	0.0670595i	−0.672782	−	0.739841i	$-0.734901\pi$
$683$	1.75255	−	1.75255i	0.0670595	−	0.0670595i	0.739841	+	0.672782i	$0.234901\pi$
$684$	−0.550510	−	0.550510i	−0.0210493	−	0.0210493i
$685$		0			0
$686$	−11.8207	−	29.8207i	−0.451315	−	1.13856i
$687$	−13.0000	+	13.0000i	−0.495981	+	0.495981i
$688$		−	34.4949i		−	1.31511i
$689$	23.5959	+	35.3939i	0.898933	+	1.34840i
$690$	43.5959			1.65967
$691$	−26.1464	+	26.1464i	−0.994657	+	0.994657i	−0.999986	−	0.00532880i	$-0.998304\pi$
$691$	−26.1464	+	26.1464i	−0.994657	+	0.994657i	0.00532880	+	0.999986i	$0.498304\pi$
$692$		−	12.6969i		−	0.482665i
$693$	1.55051	+	0.651531i	0.0588990	+	0.0247496i
$694$	2.69694	+	2.69694i	0.102374	+	0.102374i
$695$	13.7980	+	13.7980i	0.523386	+	0.523386i
$696$	3.55051	+	3.55051i	0.134582	+	0.134582i
$697$	8.00000	−	8.00000i	0.303022	−	0.303022i
$698$			21.5505i			0.815699i
$699$	−11.7980			−0.446240
$700$	3.00000	+	7.34847i	0.113389	+	0.277746i
$701$		−	28.6969i		−	1.08387i	−0.840421	−	0.541934i	$-0.817692\pi$
$701$		−	28.6969i		−	1.08387i	0.840421	−	0.541934i	$-0.182308\pi$
$702$	−6.12372	−	1.22474i	−0.231125	−	0.0462250i
$703$		−	8.69694i		−	0.328011i
$704$	0.449490	+	0.449490i	0.0169408	+	0.0169408i
$705$			6.20204i			0.233582i
$706$	−24.0000			−0.903252
$707$	5.10102	+	12.4949i	0.191844	+	0.469919i
$708$	−4.44949	−	4.44949i	−0.167222	−	0.167222i
$709$	−19.8990	+	19.8990i	−0.747322	+	0.747322i	−0.973975	−	0.226654i	$-0.927221\pi$
$709$	−19.8990	+	19.8990i	−0.747322	+	0.747322i	0.226654	+	0.973975i	$0.427221\pi$
$710$	−12.0000	−	12.0000i	−0.450352	−	0.450352i
$711$	2.89898			0.108720
$712$	−4.89898			−0.183597
$713$	48.4949	+	48.4949i	1.81615	+	1.81615i
$714$	−8.44949	−	3.55051i	−0.316214	−	0.132875i
$715$	−5.39388	+	3.59592i	−0.201720	+	0.134480i
$716$	21.7980			0.814628
$717$	7.34847	−	7.34847i	0.274434	−	0.274434i
$718$	10.8990			0.406746
$719$	−7.10102			−0.264823			−0.132412	−	0.991195i	$-0.542272\pi$
$719$	−7.10102			−0.264823			−0.132412	+	0.991195i	$0.542272\pi$
$720$	10.0000	−	10.0000i	0.372678	−	0.372678i
$721$	1.79796	+	4.40408i	0.0669595	+	0.164017i
$722$	−22.5278	+	22.5278i	−0.838398	+	0.838398i
$723$	13.8990	−	13.8990i	0.516909	−	0.516909i
$724$		−	2.00000i		−	0.0743294i
$725$		−	8.69694i		−	0.322996i
$726$	−12.9773	−	12.9773i	−0.481633	−	0.481633i
$727$	14.8990			0.552573			0.276286	−	0.961075i	$-0.410896\pi$
$727$	14.8990			0.552573			0.276286	+	0.961075i	$0.410896\pi$
$728$	−3.12372	−	16.2247i	−0.115773	−	0.601329i
$729$	−1.00000			−0.0370370
$730$	38.6969	+	38.6969i	1.43224	+	1.43224i
$731$		−	13.7980i		−	0.510336i
$732$		−	10.0000i		−	0.369611i
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	−0.853506	−	0.521083i	$-0.825528\pi$
$733$	−9.00000	+	9.00000i	−0.332423	+	0.332423i	0.521083	+	0.853506i	$0.325528\pi$
$734$	−32.4495	+	32.4495i	−1.19773	+	1.19773i
$735$	19.7980	+	0.202041i	0.730259	+	0.00745240i
$736$	−32.6969	+	32.6969i	−1.20523	+	1.20523i
$737$	5.70714			0.210225
$738$	−9.79796			−0.360668
$739$	22.3485	−	22.3485i	0.822102	−	0.822102i	−0.164307	−	0.986409i	$-0.552539\pi$
$739$	22.3485	−	22.3485i	0.822102	−	0.822102i	0.986409	+	0.164307i	$0.0525389\pi$
$740$	−31.5959			−1.16149
$741$	0.550510	−	2.75255i	0.0202235	−	0.101117i
$742$	20.9444	−	49.8434i	0.768893	−	1.82981i
$743$	18.0454	+	18.0454i	0.662022	+	0.662022i	0.955856	−	0.293835i	$-0.0949315\pi$
$743$	18.0454	+	18.0454i	0.662022	+	0.662022i	−0.293835	+	0.955856i	$0.594931\pi$
$744$	13.3485			0.489379
$745$	3.59592			0.131744
$746$	12.0000	+	12.0000i	0.439351	+	0.439351i
$747$	0.449490	−	0.449490i	0.0164460	−	0.0164460i
$748$	−0.898979	−	0.898979i	−0.0328699	−	0.0328699i
$749$	0.898979	+	2.20204i	0.0328480	+	0.0804608i
$750$	9.79796			0.357771
$751$		−	20.2929i		−	0.740497i	−0.928933	−	0.370248i	$-0.879273\pi$
$751$		−	20.2929i		−	0.740497i	0.928933	−	0.370248i	$-0.120727\pi$
$752$	−7.75255	−	7.75255i	−0.282706	−	0.282706i
$753$		−	4.89898i		−	0.178529i
$754$	3.55051	−	17.7526i	0.129302	−	0.646510i
$755$			29.7980i			1.08446i
$756$	1.00000	+	2.44949i	0.0363696	+	0.0890871i
$757$	−37.7980			−1.37379			−0.686895	−	0.726757i	$-0.741027\pi$
$757$	−37.7980			−1.37379			−0.686895	+	0.726757i	$0.741027\pi$
$758$			32.9444i			1.19659i
$759$	4.00000	−	4.00000i	0.145191	−	0.145191i
$760$	2.69694	+	2.69694i	0.0978282	+	0.0978282i
$761$	−14.6969	−	14.6969i	−0.532764	−	0.532764i	0.388630	−	0.921394i	$-0.372948\pi$
$761$	−14.6969	−	14.6969i	−0.532764	−	0.532764i	−0.921394	+	0.388630i	$0.872948\pi$
$762$	−9.79796	−	9.79796i	−0.354943	−	0.354943i
$763$	0.146428	−	0.348469i	0.00530106	−	0.0126154i
$764$		−	13.7980i		−	0.499193i
$765$	4.00000	−	4.00000i	0.144620	−	0.144620i
$766$	−39.7980			−1.43796
$767$	4.44949	−	22.2474i	0.160662	−	0.803309i
$768$			19.0000i			0.685603i
$769$	4.10102	−	4.10102i	0.147887	−	0.147887i	−0.629287	−	0.777173i	$-0.716653\pi$
$769$	4.10102	−	4.10102i	0.147887	−	0.147887i	0.777173	+	0.629287i	$0.216653\pi$
$770$	7.59592	+	3.19184i	0.273738	+	0.115026i
$771$			20.6969i			0.745382i
$772$	14.7980	+	14.7980i	0.532590	+	0.532590i
$773$	36.0000	−	36.0000i	1.29483	−	1.29483i	0.363067	−	0.931763i	$-0.381730\pi$
$773$	36.0000	−	36.0000i	1.29483	−	1.29483i	0.931763	−	0.363067i	$-0.118270\pi$
$774$	−8.44949	+	8.44949i	−0.303711	+	0.303711i
$775$	−16.3485	−	16.3485i	−0.587254	−	0.587254i
$776$			19.3485i			0.694570i
$777$	−11.4495	+	27.2474i	−0.410748	+	0.977497i
$778$	−1.34847	+	1.34847i	−0.0483450	+	0.0483450i
$779$		−	4.40408i		−	0.157793i
$780$	−10.0000	−	2.00000i	−0.358057	−	0.0716115i
$781$	−2.20204			−0.0787952
$782$	−21.7980	+	21.7980i	−0.779493	+	0.779493i
$783$		−	2.89898i		−	0.103601i
$784$	−25.0000	+	24.4949i	−0.892857	+	0.874818i
$785$	−24.0000	−	24.0000i	−0.856597	−	0.856597i
$786$	22.8990	+	22.8990i	0.816780	+	0.816780i
$787$	−15.2474	−	15.2474i	−0.543513	−	0.543513i	0.381044	−	0.924557i	$-0.375565\pi$
$787$	−15.2474	−	15.2474i	−0.543513	−	0.543513i	−0.924557	+	0.381044i	$0.875565\pi$
$788$	7.79796	−	7.79796i	0.277791	−	0.277791i
$789$			16.8990i			0.601620i
$790$	14.2020			0.505286
$791$	−18.8990	−	46.2929i	−0.671970	−	1.64598i
$792$		−	1.10102i		−	0.0391231i
$793$	30.0000	−	20.0000i	1.06533	−	0.710221i
$794$		−	21.5505i		−	0.764799i
$795$	23.5959	+	23.5959i	0.836861	+	0.836861i
$796$			22.8990i			0.811633i
$797$	−41.1918			−1.45909			−0.729545	−	0.683933i	$-0.760268\pi$
$797$	−41.1918			−1.45909			−0.729545	+	0.683933i	$0.760268\pi$
$798$	−3.30306	+	1.34847i	−0.116927	+	0.0477353i
$799$	−3.10102	−	3.10102i	−0.109706	−	0.109706i
$800$	11.0227	−	11.0227i	0.389711	−	0.389711i
$801$	2.00000	+	2.00000i	0.0706665	+	0.0706665i
$802$	−34.2929			−1.21092
$803$	7.10102			0.250590
$804$	6.34847	+	6.34847i	0.223893	+	0.223893i
$805$	25.7980	−	61.3939i	0.909259	−	2.16385i
$806$	−26.6969	−	40.0454i	−0.940360	−	1.41054i
$807$	−6.00000			−0.211210
$808$	6.24745	−	6.24745i	0.219784	−	0.219784i
$809$	−22.8990			−0.805085			−0.402543	−	0.915401i	$-0.631873\pi$
$809$	−22.8990			−0.805085			−0.402543	+	0.915401i	$0.631873\pi$
$810$	−4.89898			−0.172133
$811$	7.04541	−	7.04541i	0.247398	−	0.247398i	−0.572504	−	0.819902i	$-0.694028\pi$
$811$	7.04541	−	7.04541i	0.247398	−	0.247398i	0.819902	+	0.572504i	$0.194028\pi$
$812$	−7.10102	+	2.89898i	−0.249197	+	0.101734i
$813$	4.55051	−	4.55051i	0.159593	−	0.159593i
$814$	−8.69694	+	8.69694i	−0.304828	+	0.304828i
$815$			21.7980i			0.763549i
$816$			10.0000i			0.350070i
$817$	−3.79796	−	3.79796i	−0.132874	−	0.132874i
$818$	13.9546			0.487911
$819$	−5.34847	+	7.89898i	−0.186891	+	0.276013i
$820$	−16.0000			−0.558744
$821$	−35.5959	−	35.5959i	−1.24231	−	1.24231i	−0.959042	−	0.283264i	$-0.908583\pi$
$821$	−35.5959	−	35.5959i	−1.24231	−	1.24231i	−0.283264	−	0.959042i	$-0.591417\pi$
$822$		0			0
$823$		−	12.6969i		−	0.442587i	−0.975207	−	0.221294i	$-0.928972\pi$
$823$		−	12.6969i		−	0.442587i	0.975207	−	0.221294i	$-0.0710280\pi$
$824$	2.20204	−	2.20204i	0.0767117	−	0.0767117i
$825$	−1.34847	+	1.34847i	−0.0469477	+	0.0469477i
$826$	−26.6969	+	10.8990i	−0.928905	+	0.379224i
$827$	9.34847	−	9.34847i	0.325078	−	0.325078i	−0.525633	−	0.850711i	$-0.676172\pi$
$827$	9.34847	−	9.34847i	0.325078	−	0.325078i	0.850711	+	0.525633i	$0.176172\pi$
$828$	8.89898			0.309261
$829$	34.2020			1.18789			0.593943	−	0.804507i	$-0.297570\pi$
$829$	34.2020			1.18789			0.593943	+	0.804507i	$0.297570\pi$
$830$	2.20204	−	2.20204i	0.0764340	−	0.0764340i
$831$	17.7980			0.617404
$832$	−3.00000	+	2.00000i	−0.104006	+	0.0693375i
$833$	−10.0000	+	9.79796i	−0.346479	+	0.339479i
$834$	8.44949	+	8.44949i	0.292582	+	0.292582i
$835$	−45.3939			−1.57092
$836$	−0.494897			−0.0171164
$837$	−5.44949	−	5.44949i	−0.188362	−	0.188362i
$838$	42.0000	−	42.0000i	1.45087	−	1.45087i
$839$	−8.44949	−	8.44949i	−0.291709	−	0.291709i	0.546046	−	0.837755i	$-0.316132\pi$
$839$	−8.44949	−	8.44949i	−0.291709	−	0.291709i	−0.837755	+	0.546046i	$0.816132\pi$
$840$	−4.89898	−	12.0000i	−0.169031	−	0.414039i
$841$	−20.5959			−0.710204
$842$			34.0454i			1.17328i
$843$	−4.00000	−	4.00000i	−0.137767	−	0.137767i
$844$			9.10102i			0.313270i
$845$	−14.0000	−	34.0000i	−0.481615	−	1.16964i
$846$			3.79796i			0.130577i
$847$	−25.9546	+	10.5959i	−0.891810	+	0.364080i
$848$	−58.9898			−2.02572
$849$		−	12.6969i		−	0.435758i
$850$	7.34847	−	7.34847i	0.252050	−	0.252050i
$851$	70.2929	+	70.2929i	2.40961	+	2.40961i
$852$	−2.44949	−	2.44949i	−0.0839181	−	0.0839181i
$853$	−19.2020	−	19.2020i	−0.657465	−	0.657465i	0.297314	−	0.954780i	$-0.403909\pi$
$853$	−19.2020	−	19.2020i	−0.657465	−	0.657465i	−0.954780	+	0.297314i	$0.903909\pi$
$854$	−42.2474	−	17.7526i	−1.44568	−	0.607480i
$855$		−	2.20204i		−	0.0753082i
$856$	1.10102	−	1.10102i	0.0376321	−	0.0376321i
$857$	−22.4949			−0.768411			−0.384206	−	0.923248i	$-0.625525\pi$
$857$	−22.4949			−0.768411			−0.384206	+	0.923248i	$0.625525\pi$
$858$	−3.30306	+	2.20204i	−0.112765	+	0.0751764i
$859$			10.2020i			0.348089i	0.984738	+	0.174045i	$0.0556837\pi$
$859$			10.2020i			0.348089i	−0.984738	+	0.174045i	$0.944316\pi$
$860$	−13.7980	+	13.7980i	−0.470506	+	0.470506i
$861$	−5.79796	+	13.7980i	−0.197594	+	0.470233i
$862$			58.8990i			2.00611i
$863$	15.1464	+	15.1464i	0.515590	+	0.515590i	0.916234	−	0.400644i	$-0.131213\pi$
$863$	15.1464	+	15.1464i	0.515590	+	0.515590i	−0.400644	+	0.916234i	$0.631213\pi$
$864$	3.67423	−	3.67423i	0.125000	−	0.125000i
$865$	25.3939	−	25.3939i	0.863418	−	0.863418i
$866$	12.4949	+	12.4949i	0.424594	+	0.424594i
$867$		−	13.0000i		−	0.441503i
$868$	−7.89898	+	18.7980i	−0.268109	+	0.638044i
$869$	1.30306	−	1.30306i	0.0442033	−	0.0442033i
$870$		−	14.2020i		−	0.481494i
$871$	−6.34847	+	31.7423i	−0.215110	+	1.07555i
$872$	−0.247449			−0.00837967
$873$	7.89898	−	7.89898i	0.267340	−	0.267340i
$874$			12.0000i			0.405906i
$875$	5.79796	−	13.7980i	0.196007	−	0.466456i
$876$	7.89898	+	7.89898i	0.266882	+	0.266882i
$877$	11.6969	+	11.6969i	0.394978	+	0.394978i	0.876457	−	0.481480i	$-0.159900\pi$
$877$	11.6969	+	11.6969i	0.394978	+	0.394978i	−0.481480	+	0.876457i	$0.659900\pi$
$878$	−14.2020	−	14.2020i	−0.479296	−	0.479296i
$879$	18.6969	−	18.6969i	0.630632	−	0.630632i
$880$		−	8.98979i		−	0.303046i
$881$	16.6969			0.562534			0.281267	−	0.959630i	$-0.409245\pi$
$881$	16.6969			0.562534			0.281267	+	0.959630i	$0.409245\pi$
$882$	12.1237	+	0.123724i	0.408227	+	0.00416602i
$883$		−	18.2020i		−	0.612547i	−0.951943	−	0.306274i	$-0.900918\pi$
$883$		−	18.2020i		−	0.612547i	0.951943	−	0.306274i	$-0.0990823\pi$
$884$	6.00000	−	4.00000i	0.201802	−	0.134535i
$885$		−	17.7980i		−	0.598272i
$886$	−42.4949	−	42.4949i	−1.42764	−	1.42764i
$887$			12.0000i			0.402921i	0.979497	+	0.201460i	$0.0645687\pi$
$887$			12.0000i			0.402921i	−0.979497	+	0.201460i	$0.935431\pi$
$888$	19.3485			0.649292
$889$	−19.5959	+	8.00000i	−0.657226	+	0.268311i
$890$	9.79796	+	9.79796i	0.328428	+	0.328428i
$891$	−0.449490	+	0.449490i	−0.0150585	+	0.0150585i
$892$	−2.55051	−	2.55051i	−0.0853974	−	0.0853974i
$893$	−1.70714			−0.0571274
$894$	2.20204			0.0736473
$895$	43.5959	+	43.5959i	1.45725	+	1.45725i
$896$	29.5732	+	12.4268i	0.987972	+	0.415150i
$897$	17.7980	+	26.6969i	0.594257	+	0.891385i
$898$	12.4949			0.416960
$899$	15.7980	−	15.7980i	0.526891	−	0.526891i
$900$	−3.00000			−0.100000
$901$	−23.5959			−0.786094
$902$	−4.40408	+	4.40408i	−0.146640	+	0.146640i
$903$	6.89898	+	16.8990i	0.229584	+	0.562363i
$904$	−23.1464	+	23.1464i	−0.769839	+	0.769839i
$905$	4.00000	−	4.00000i	0.132964	−	0.132964i
$906$			18.2474i			0.606231i
$907$		−	0.404082i		−	0.0134173i	−0.999977	−	0.00670866i	$-0.997865\pi$
$907$		−	0.404082i		−	0.0134173i	0.999977	−	0.00670866i	$-0.00213545\pi$
$908$	−0.651531	−	0.651531i	−0.0216218	−	0.0216218i
$909$	−5.10102			−0.169190
$910$	−26.2020	+	38.6969i	−0.868589	+	1.28279i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	2.75255	+	2.75255i	0.0911461	+	0.0911461i
$913$		−	0.404082i		−	0.0133732i
$914$		−	31.3485i		−	1.03692i
$915$	20.0000	−	20.0000i	0.661180	−	0.661180i
$916$	−13.0000	+	13.0000i	−0.429532	+	0.429532i
$917$	45.7980	−	18.6969i	1.51238	−	0.617427i
$918$	2.44949	−	2.44949i	0.0808452	−	0.0808452i
$919$	14.4949			0.478143			0.239071	−	0.971002i	$-0.423157\pi$
$919$	14.4949			0.478143			0.239071	+	0.971002i	$0.423157\pi$
$920$	−43.5959			−1.43731
$921$	−13.4495	+	13.4495i	−0.443176	+	0.443176i
$922$	−60.4949			−1.99229
$923$	2.44949	−	12.2474i	0.0806259	−	0.403130i
$924$	1.55051	+	0.651531i	0.0510080	+	0.0214338i
$925$	−23.6969	−	23.6969i	−0.779151	−	0.779151i
$926$	34.6515			1.13872
$927$	−1.79796			−0.0590527
$928$	10.6515	+	10.6515i	0.349654	+	0.349654i
$929$	4.89898	−	4.89898i	0.160730	−	0.160730i	−0.622160	−	0.782890i	$-0.713745\pi$
$929$	4.89898	−	4.89898i	0.160730	−	0.160730i	0.782890	+	0.622160i	$0.213745\pi$
$930$	−26.6969	−	26.6969i	−0.875427	−	0.875427i
$931$	−0.0556128	+	5.44949i	−0.00182264	+	0.178600i
$932$	−11.7980			−0.386455
$933$			15.1010i			0.494385i
$934$	−50.0908	−	50.0908i	−1.63902	−	1.63902i
$935$		−	3.59592i		−	0.117599i
$936$	6.12372	+	1.22474i	0.200160	+	0.0400320i
$937$		−	9.59592i		−	0.313485i	−0.987640	−	0.156742i	$-0.949901\pi$
$937$		−	9.59592i		−	0.313485i	0.987640	−	0.156742i	$-0.0500993\pi$
$938$	38.0908	−	15.5505i	1.24371	−	0.507742i
$939$	−25.5959			−0.835291
$940$			6.20204i			0.202288i
$941$	16.8990	−	16.8990i	0.550891	−	0.550891i	−0.375807	−	0.926698i	$-0.622634\pi$
$941$	16.8990	−	16.8990i	0.550891	−	0.550891i	0.926698	+	0.375807i	$0.122634\pi$
$942$	−14.6969	−	14.6969i	−0.478852	−	0.478852i
$943$	35.5959	+	35.5959i	1.15916	+	1.15916i
$944$	22.2474	+	22.2474i	0.724093	+	0.724093i
$945$	−2.89898	+	6.89898i	−0.0943038	+	0.224424i
$946$			7.59592i			0.246965i
$947$	−13.5505	+	13.5505i	−0.440332	+	0.440332i	−0.892124	−	0.451791i	$-0.850785\pi$
$947$	−13.5505	+	13.5505i	−0.440332	+	0.440332i	0.451791	+	0.892124i	$0.350785\pi$
$948$	2.89898			0.0941545
$949$	−7.89898	+	39.4949i	−0.256412	+	1.28206i
$950$		−	4.04541i		−	0.131250i
$951$	−16.6969	+	16.6969i	−0.541435	+	0.541435i
$952$	8.44949	+	3.55051i	0.273850	+	0.115073i
$953$			6.00000i			0.194359i	0.995267	+	0.0971795i	$0.0309821\pi$
$953$			6.00000i			0.194359i	−0.995267	+	0.0971795i	$0.969018\pi$
$954$	14.4495	+	14.4495i	0.467820	+	0.467820i
$955$	27.5959	−	27.5959i	0.892983	−	0.892983i
$956$	7.34847	−	7.34847i	0.237666	−	0.237666i
$957$	−1.30306	−	1.30306i	−0.0421220	−	0.0421220i
$958$		−	34.8990i		−	1.12753i
$959$		0			0
$960$	−2.00000	+	2.00000i	−0.0645497	+	0.0645497i
$961$		−	28.3939i		−	0.915932i
$962$	−38.6969	−	58.0454i	−1.24764	−	1.87146i
$963$	−0.898979			−0.0289692
$964$	13.8990	−	13.8990i	0.447656	−	0.447656i
$965$			59.1918i			1.90545i
$966$	15.7980	−	37.5959i	0.508291	−	1.20963i
$967$	10.7526	+	10.7526i	0.345779	+	0.345779i	0.858535	−	0.512756i	$-0.171375\pi$
$967$	10.7526	+	10.7526i	0.345779	+	0.345779i	−0.512756	+	0.858535i	$0.671375\pi$
$968$	12.9773	+	12.9773i	0.417106	+	0.417106i
$969$	1.10102	+	1.10102i	0.0353699	+	0.0353699i
$970$	38.6969	−	38.6969i	1.24248	−	1.24248i
$971$			45.7980i			1.46973i	0.678215	+	0.734863i	$0.262754\pi$
$971$			45.7980i			1.46973i	−0.678215	+	0.734863i	$0.737246\pi$
$972$	−1.00000			−0.0320750
$973$	16.8990	−	6.89898i	0.541756	−	0.221171i
$974$		−	22.6515i		−	0.725802i
$975$	−6.00000	−	9.00000i	−0.192154	−	0.288231i
$976$			50.0000i			1.60046i
$977$	−33.5959	−	33.5959i	−1.07483	−	1.07483i	−0.996964	−	0.0778647i	$-0.975190\pi$
$977$	−33.5959	−	33.5959i	−1.07483	−	1.07483i	−0.0778647	−	0.996964i	$-0.524810\pi$
$978$			13.3485i			0.426837i
$979$	1.79796			0.0574630
$980$	19.7980	+	0.202041i	0.632423	+	0.00645396i
$981$	0.101021	+	0.101021i	0.00322534	+	0.00322534i
$982$	−33.1918	+	33.1918i	−1.05919	+	1.05919i
$983$	17.7526	+	17.7526i	0.566218	+	0.566218i	0.931067	−	0.364848i	$-0.118879\pi$
$983$	17.7526	+	17.7526i	0.566218	+	0.566218i	−0.364848	+	0.931067i	$0.618879\pi$
$984$	9.79796			0.312348
$985$	31.1918			0.993855
$986$	7.10102	+	7.10102i	0.226143	+	0.226143i
$987$	5.34847	+	2.24745i	0.170244	+	0.0715371i
$988$	0.550510	−	2.75255i	0.0175141	−	0.0875703i
$989$	61.3939			1.95221
$990$	−2.20204	+	2.20204i	−0.0699855	+	0.0699855i
$991$	55.1918			1.75323			0.876613	−	0.481196i	$-0.159797\pi$
$991$	55.1918			1.75323			0.876613	+	0.481196i	$0.159797\pi$
$992$	40.0454			1.27144
$993$	21.2474	−	21.2474i	0.674267	−	0.674267i
$994$	−14.6969	+	6.00000i	−0.466159	+	0.190308i
$995$	−45.7980	+	45.7980i	−1.45189	+	1.45189i
$996$	0.449490	−	0.449490i	0.0142426	−	0.0142426i
$997$			49.3939i			1.56432i	0.623078	+	0.782160i	$0.285882\pi$
$997$			49.3939i			1.56432i	−0.623078	+	0.782160i	$0.714118\pi$
$998$			22.6515i			0.717022i
$999$	−7.89898	−	7.89898i	−0.249913	−	0.249913i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.p.a.34.2	✓	4
3.2	odd	2		819.2.y.d.307.1		4
7.6	odd	2		273.2.p.d.34.2	yes	4
13.5	odd	4		273.2.p.d.265.2	yes	4
21.20	even	2		819.2.y.a.307.1		4
39.5	even	4		819.2.y.a.811.1		4
91.83	even	4	inner	273.2.p.a.265.2	yes	4
273.83	odd	4		819.2.y.d.811.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.p.a.34.2	✓	4	1.1	even	1	trivial
273.2.p.a.265.2	yes	4	91.83	even	4	inner
273.2.p.d.34.2	yes	4	7.6	odd	2
273.2.p.d.265.2	yes	4	13.5	odd	4
819.2.y.a.307.1		4	21.20	even	2
819.2.y.a.811.1		4	39.5	even	4
819.2.y.d.307.1		4	3.2	odd	2
819.2.y.d.811.1		4	273.83	odd	4

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.p (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 + 1.22474i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(1.00000 + 2.44949i) q^{7} +(1.22474 - 1.22474i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(1.22474 + 1.22474i) q^{2} +1.00000i q^{3} +1.00000i q^{4} +(-2.00000 + 2.00000i) q^{5} +(-1.22474 + 1.22474i) q^{6} +(1.00000 + 2.44949i) q^{7} +(1.22474 - 1.22474i) q^{8} -1.00000 q^{9} -4.89898 q^{10} +(-0.449490 + 0.449490i) q^{11} -1.00000 q^{12} +(-2.00000 - 3.00000i) q^{13} +(-1.77526 + 4.22474i) q^{14} +(-2.00000 - 2.00000i) q^{15} +5.00000 q^{16} +2.00000 q^{17} +(-1.22474 - 1.22474i) q^{18} +(0.550510 - 0.550510i) q^{19} +(-2.00000 - 2.00000i) q^{20} +(-2.44949 + 1.00000i) q^{21} -1.10102 q^{22} +8.89898i q^{23} +(1.22474 + 1.22474i) q^{24} -3.00000i q^{25} +(1.22474 - 6.12372i) q^{26} -1.00000i q^{27} +(-2.44949 + 1.00000i) q^{28} +2.89898 q^{29} -4.89898i q^{30} +(5.44949 - 5.44949i) q^{31} +(3.67423 + 3.67423i) q^{32} +(-0.449490 - 0.449490i) q^{33} +(2.44949 + 2.44949i) q^{34} +(-6.89898 - 2.89898i) q^{35} -1.00000i q^{36} +(7.89898 - 7.89898i) q^{37} +1.34847 q^{38} +(3.00000 - 2.00000i) q^{39} +4.89898i q^{40} +(4.00000 - 4.00000i) q^{41} +(-4.22474 - 1.77526i) q^{42} -6.89898i q^{43} +(-0.449490 - 0.449490i) q^{44} +(2.00000 - 2.00000i) q^{45} +(-10.8990 + 10.8990i) q^{46} +(-1.55051 - 1.55051i) q^{47} +5.00000i q^{48} +(-5.00000 + 4.89898i) q^{49} +(3.67423 - 3.67423i) q^{50} +2.00000i q^{51} +(3.00000 - 2.00000i) q^{52} -11.7980 q^{53} +(1.22474 - 1.22474i) q^{54} -1.79796i q^{55} +(4.22474 + 1.77526i) q^{56} +(0.550510 + 0.550510i) q^{57} +(3.55051 + 3.55051i) q^{58} +(4.44949 + 4.44949i) q^{59} +(2.00000 - 2.00000i) q^{60} +10.0000i q^{61} +13.3485 q^{62} +(-1.00000 - 2.44949i) q^{63} -1.00000i q^{64} +(10.0000 + 2.00000i) q^{65} -1.10102i q^{66} +(-6.34847 - 6.34847i) q^{67} +2.00000i q^{68} -8.89898 q^{69} +(-4.89898 - 12.0000i) q^{70} +(2.44949 + 2.44949i) q^{71} +(-1.22474 + 1.22474i) q^{72} +(-7.89898 - 7.89898i) q^{73} +19.3485 q^{74} +3.00000 q^{75} +(0.550510 + 0.550510i) q^{76} +(-1.55051 - 0.651531i) q^{77} +(6.12372 + 1.22474i) q^{78} -2.89898 q^{79} +(-10.0000 + 10.0000i) q^{80} +1.00000 q^{81} +9.79796 q^{82} +(-0.449490 + 0.449490i) q^{83} +(-1.00000 - 2.44949i) q^{84} +(-4.00000 + 4.00000i) q^{85} +(8.44949 - 8.44949i) q^{86} +2.89898i q^{87} +1.10102i q^{88} +(-2.00000 - 2.00000i) q^{89} +4.89898 q^{90} +(5.34847 - 7.89898i) q^{91} -8.89898 q^{92} +(5.44949 + 5.44949i) q^{93} -3.79796i q^{94} +2.20204i q^{95} +(-3.67423 + 3.67423i) q^{96} +(-7.89898 + 7.89898i) q^{97} +(-12.1237 - 0.123724i) q^{98} +(0.449490 - 0.449490i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 4 * q - 8 * q^5 + 4 * q^7 - 4 * q^9	\( 4 q - 8 q^{5} + 4 q^{7} - 4 q^{9} + 8 q^{11} - 4 q^{12} - 8 q^{13} - 12 q^{14} - 8 q^{15} + 20 q^{16} + 8 q^{17} + 12 q^{19} - 8 q^{20} - 24 q^{22} - 8 q^{29} + 12 q^{31} + 8 q^{33} - 8 q^{35} + 12 q^{37} - 24 q^{38} + 12 q^{39} + 16 q^{41} - 12 q^{42} + 8 q^{44} + 8 q^{45} - 24 q^{46} - 16 q^{47} - 20 q^{49} + 12 q^{52} - 8 q^{53} + 12 q^{56} + 12 q^{57} + 24 q^{58} + 8 q^{59} + 8 q^{60} + 24 q^{62} - 4 q^{63} + 40 q^{65} + 4 q^{67} - 16 q^{69} - 12 q^{73} + 48 q^{74} + 12 q^{75} + 12 q^{76} - 16 q^{77} + 8 q^{79} - 40 q^{80} + 4 q^{81} + 8 q^{83} - 4 q^{84} - 16 q^{85} + 24 q^{86} - 8 q^{89} - 8 q^{91} - 16 q^{92} + 12 q^{93} - 12 q^{97} - 24 q^{98} - 8 q^{99}+O(q^{100}) \) 4 * q - 8 * q^5 + 4 * q^7 - 4 * q^9 + 8 * q^11 - 4 * q^12 - 8 * q^13 - 12 * q^14 - 8 * q^15 + 20 * q^16 + 8 * q^17 + 12 * q^19 - 8 * q^20 - 24 * q^22 - 8 * q^29 + 12 * q^31 + 8 * q^33 - 8 * q^35 + 12 * q^37 - 24 * q^38 + 12 * q^39 + 16 * q^41 - 12 * q^42 + 8 * q^44 + 8 * q^45 - 24 * q^46 - 16 * q^47 - 20 * q^49 + 12 * q^52 - 8 * q^53 + 12 * q^56 + 12 * q^57 + 24 * q^58 + 8 * q^59 + 8 * q^60 + 24 * q^62 - 4 * q^63 + 40 * q^65 + 4 * q^67 - 16 * q^69 - 12 * q^73 + 48 * q^74 + 12 * q^75 + 12 * q^76 - 16 * q^77 + 8 * q^79 - 40 * q^80 + 4 * q^81 + 8 * q^83 - 4 * q^84 - 16 * q^85 + 24 * q^86 - 8 * q^89 - 8 * q^91 - 16 * q^92 + 12 * q^93 - 12 * q^97 - 24 * q^98 - 8 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more