LMFDB - Embedded newform 507.2.j.h.316.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(316,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("507.316");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.j (of order $6$, degree $2$, not 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			316.3
Root			$-0.385418 - 0.222521i$ of defining polynomial
Character	$\chi$	$=$	507.316
Dual form			507.2.j.h.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.385418 - 0.222521i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.900969 - 1.56052i) q^{4} -0.246980i q^{5} +(0.385418 - 0.222521i) q^{6} +(-1.51816 + 0.876510i) q^{7} +1.69202i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.385418 - 0.222521i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.900969 - 1.56052i) q^{4} -0.246980i q^{5} +(0.385418 - 0.222521i) q^{6} +(-1.51816 + 0.876510i) q^{7} +1.69202i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.0549581 + 0.0951903i) q^{10} +(4.89546 + 2.82640i) q^{11} +1.80194 q^{12} +0.780167 q^{14} +(0.213891 + 0.123490i) q^{15} +(-1.42543 + 2.46891i) q^{16} +(-1.90097 - 3.29257i) q^{17} +0.445042i q^{18} +(4.83424 - 2.79105i) q^{19} +(-0.385418 + 0.222521i) q^{20} -1.75302i q^{21} +(-1.25786 - 2.17869i) q^{22} +(4.17241 - 7.22682i) q^{23} +(-1.46533 - 0.846011i) q^{24} +4.93900 q^{25} +1.00000 q^{27} +(2.73563 + 1.57942i) q^{28} +(2.96950 - 5.14333i) q^{29} +(-0.0549581 - 0.0951903i) q^{30} +5.26875i q^{31} +(4.02944 - 2.32640i) q^{32} +(-4.89546 + 2.82640i) q^{33} +1.69202i q^{34} +(0.216480 + 0.374955i) q^{35} +(-0.900969 + 1.56052i) q^{36} +(2.76960 + 1.59903i) q^{37} -2.48427 q^{38} +0.417895 q^{40} +(-0.385418 - 0.222521i) q^{41} +(-0.390084 + 0.675645i) q^{42} +(0.856896 + 1.48419i) q^{43} -10.1860i q^{44} +(-0.213891 + 0.123490i) q^{45} +(-3.21624 + 1.85690i) q^{46} +6.73556i q^{47} +(-1.42543 - 2.46891i) q^{48} +(-1.96346 + 3.40081i) q^{49} +(-1.90358 - 1.09903i) q^{50} +3.80194 q^{51} -1.06100 q^{53} +(-0.385418 - 0.222521i) q^{54} +(0.698062 - 1.20908i) q^{55} +(-1.48307 - 2.56876i) q^{56} +5.58211i q^{57} +(-2.28900 + 1.32155i) q^{58} +(11.8660 - 6.85086i) q^{59} -0.445042i q^{60} +(4.25786 + 7.37484i) q^{61} +(1.17241 - 2.03067i) q^{62} +(1.51816 + 0.876510i) q^{63} +3.63102 q^{64} +2.51573 q^{66} +(-5.16218 - 2.98039i) q^{67} +(-3.42543 + 5.93301i) q^{68} +(4.17241 + 7.22682i) q^{69} -0.192685i q^{70} +(-4.95295 + 2.85958i) q^{71} +(1.46533 - 0.846011i) q^{72} -7.35690i q^{73} +(-0.711636 - 1.23259i) q^{74} +(-2.46950 + 4.27730i) q^{75} +(-8.71101 - 5.02930i) q^{76} -9.90946 q^{77} +4.45473 q^{79} +(0.609771 + 0.352052i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0990311 + 0.171527i) q^{82} -10.1860i q^{83} +(-2.73563 + 1.57942i) q^{84} +(-0.813199 + 0.469501i) q^{85} -0.762709i q^{86} +(2.96950 + 5.14333i) q^{87} +(-4.78232 + 8.28323i) q^{88} +(0.118700 + 0.0685317i) q^{89} +0.109916 q^{90} -15.0368 q^{92} +(-4.56287 - 2.63437i) q^{93} +(1.49880 - 2.59600i) q^{94} +(-0.689333 - 1.19396i) q^{95} +4.65279i q^{96} +(-11.8556 + 6.84481i) q^{97} +(1.51350 - 0.873822i) q^{98} -5.65279i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9	$ 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9} - 2 q^{10} + 4 q^{12} + 4 q^{14} + 10 q^{16} - 14 q^{17} + 10 q^{22} + 4 q^{23} + 20 q^{25} + 12 q^{27} + 16 q^{29} - 2 q^{30} - 36 q^{35} - 2 q^{36} - 80 q^{38} + 28 q^{40} - 2 q^{42} - 6 q^{43} + 10 q^{48} + 34 q^{49} + 28 q^{51} - 52 q^{53} + 26 q^{55} + 14 q^{56} + 26 q^{61} - 32 q^{62} - 16 q^{64} - 20 q^{66} - 14 q^{68} + 4 q^{69} - 14 q^{74} - 10 q^{75} + 60 q^{77} - 36 q^{79} - 6 q^{81} + 10 q^{82} + 16 q^{87} - 14 q^{88} + 4 q^{90} - 68 q^{92} - 64 q^{94} + 6 q^{95}+O(q^{100}) $ 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9 - 2 * q^10 + 4 * q^12 + 4 * q^14 + 10 * q^16 - 14 * q^17 + 10 * q^22 + 4 * q^23 + 20 * q^25 + 12 * q^27 + 16 * q^29 - 2 * q^30 - 36 * q^35 - 2 * q^36 - 80 * q^38 + 28 * q^40 - 2 * q^42 - 6 * q^43 + 10 * q^48 + 34 * q^49 + 28 * q^51 - 52 * q^53 + 26 * q^55 + 14 * q^56 + 26 * q^61 - 32 * q^62 - 16 * q^64 - 20 * q^66 - 14 * q^68 + 4 * q^69 - 14 * q^74 - 10 * q^75 + 60 * q^77 - 36 * q^79 - 6 * q^81 + 10 * q^82 + 16 * q^87 - 14 * q^88 + 4 * q^90 - 68 * q^92 - 64 * q^94 + 6 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−0.385418	−	0.222521i	−0.272531	−	0.157346i	0.357506	−	0.933911i	$-0.383627\pi$
$2$	−0.385418	−	0.222521i	−0.272531	−	0.157346i	−0.630037	+	0.776565i	$0.716960\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.900969	−	1.56052i	−0.450484	−	0.780262i
$5$		−	0.246980i		−	0.110453i	−0.998474	−	0.0552263i	$-0.982412\pi$
$5$		−	0.246980i		−	0.110453i	0.998474	−	0.0552263i	$-0.0175880\pi$
$6$	0.385418	−	0.222521i	0.157346	−	0.0908438i
$7$	−1.51816	+	0.876510i	−0.573811	+	0.331290i	−0.758670	−	0.651475i	$-0.774150\pi$
$7$	−1.51816	+	0.876510i	−0.573811	+	0.331290i	0.184859	+	0.982765i	$0.440817\pi$
$8$			1.69202i			0.598220i
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.0549581	+	0.0951903i	−0.0173793	+	0.0301018i
$11$	4.89546	+	2.82640i	1.47604	+	0.852191i	0.999634	−	0.0270365i	$-0.00860703\pi$
$11$	4.89546	+	2.82640i	1.47604	+	0.852191i	0.476403	+	0.879227i	$0.341940\pi$
$12$	1.80194			0.520175
$13$		0			0
$13$		0			0
$14$	0.780167			0.208509
$15$	0.213891	+	0.123490i	0.0552263	+	0.0318849i
$16$	−1.42543	+	2.46891i	−0.356357	+	0.617228i
$17$	−1.90097	−	3.29257i	−0.461053	−	0.798567i	0.537961	−	0.842970i	$-0.319195\pi$
$17$	−1.90097	−	3.29257i	−0.461053	−	0.798567i	−0.999014	+	0.0444031i	$0.985861\pi$
$18$			0.445042i			0.104897i
$19$	4.83424	−	2.79105i	1.10905	−	0.640311i	0.170468	−	0.985363i	$-0.445472\pi$
$19$	4.83424	−	2.79105i	1.10905	−	0.640311i	0.938584	+	0.345052i	$0.112139\pi$
$20$	−0.385418	+	0.222521i	−0.0861820	+	0.0497572i
$21$		−	1.75302i		−	0.382540i
$22$	−1.25786	−	2.17869i	−0.268178	−	0.464497i
$23$	4.17241	−	7.22682i	0.870007	−	1.50690i	0.00801894	−	0.999968i	$-0.497447\pi$
$23$	4.17241	−	7.22682i	0.870007	−	1.50690i	0.861988	−	0.506929i	$-0.169219\pi$
$24$	−1.46533	−	0.846011i	−0.299110	−	0.172691i
$25$	4.93900			0.987800
$26$		0			0
$27$	1.00000			0.192450
$28$	2.73563	+	1.57942i	0.516986	+	0.298482i
$29$	2.96950	−	5.14333i	0.551422	−	0.955092i	−0.446750	−	0.894659i	$-0.647419\pi$
$29$	2.96950	−	5.14333i	0.551422	−	0.955092i	0.998172	−	0.0604327i	$-0.0192481\pi$
$30$	−0.0549581	−	0.0951903i	−0.0100339	−	0.0173793i
$31$			5.26875i			0.946295i	0.880983	+	0.473148i	$0.156882\pi$
$31$			5.26875i			0.946295i	−0.880983	+	0.473148i	$0.843118\pi$
$32$	4.02944	−	2.32640i	0.712311	−	0.411253i
$33$	−4.89546	+	2.82640i	−0.852191	+	0.492012i
$34$			1.69202i			0.290179i
$35$	0.216480	+	0.374955i	0.0365918	+	0.0633789i
$36$	−0.900969	+	1.56052i	−0.150161	+	0.260087i
$37$	2.76960	+	1.59903i	0.455320	+	0.262879i	0.710074	−	0.704127i	$-0.248661\pi$
$37$	2.76960	+	1.59903i	0.455320	+	0.262879i	−0.254754	+	0.967006i	$0.581995\pi$
$38$	−2.48427			−0.403002
$39$		0			0
$40$	0.417895			0.0660750
$41$	−0.385418	−	0.222521i	−0.0601921	−	0.0347519i	0.469602	−	0.882878i	$-0.344397\pi$
$41$	−0.385418	−	0.222521i	−0.0601921	−	0.0347519i	−0.529794	+	0.848126i	$0.677731\pi$
$42$	−0.390084	+	0.675645i	−0.0601912	+	0.104254i
$43$	0.856896	+	1.48419i	0.130675	+	0.226336i	0.923937	−	0.382544i	$-0.124952\pi$
$43$	0.856896	+	1.48419i	0.130675	+	0.226336i	−0.793262	+	0.608881i	$0.791619\pi$
$44$		−	10.1860i		−	1.53559i
$45$	−0.213891	+	0.123490i	−0.0318849	+	0.0184088i
$46$	−3.21624	+	1.85690i	−0.474208	+	0.273784i
$47$			6.73556i			0.982483i	0.871024	+	0.491241i	$0.163457\pi$
$47$			6.73556i			0.982483i	−0.871024	+	0.491241i	$0.836543\pi$
$48$	−1.42543	−	2.46891i	−0.205743	−	0.356357i
$49$	−1.96346	+	3.40081i	−0.280494	+	0.485830i
$50$	−1.90358	−	1.09903i	−0.269207	−	0.155426i
$51$	3.80194			0.532378
$52$		0			0
$53$	−1.06100			−0.145739			−0.0728697	−	0.997341i	$-0.523216\pi$
$53$	−1.06100			−0.145739			−0.0728697	+	0.997341i	$0.523216\pi$
$54$	−0.385418	−	0.222521i	−0.0524487	−	0.0302813i
$55$	0.698062	−	1.20908i	0.0941267	−	0.163032i
$56$	−1.48307	−	2.56876i	−0.198184	−	0.343265i
$57$			5.58211i			0.739368i
$58$	−2.28900	+	1.32155i	−0.300560	+	0.173528i
$59$	11.8660	−	6.85086i	1.54483	−	0.891905i	0.546302	−	0.837589i	$-0.316035\pi$
$59$	11.8660	−	6.85086i	1.54483	−	0.891905i	0.998524	−	0.0543169i	$-0.0172981\pi$
$60$		−	0.445042i		−	0.0574547i
$61$	4.25786	+	7.37484i	0.545164	+	0.944251i	0.998597	+	0.0529608i	$0.0168658\pi$
$61$	4.25786	+	7.37484i	0.545164	+	0.944251i	−0.453433	+	0.891290i	$0.649801\pi$
$62$	1.17241	−	2.03067i	0.148896	−	0.257895i
$63$	1.51816	+	0.876510i	0.191270	+	0.110430i
$64$	3.63102			0.453878
$65$		0			0
$66$	2.51573			0.309665
$67$	−5.16218	−	2.98039i	−0.630661	−	0.364112i	0.150347	−	0.988633i	$-0.451961\pi$
$67$	−5.16218	−	2.98039i	−0.630661	−	0.364112i	−0.781008	+	0.624521i	$0.785294\pi$
$68$	−3.42543	+	5.93301i	−0.415394	+	0.719484i
$69$	4.17241	+	7.22682i	0.502299	+	0.870007i
$70$		−	0.192685i		−	0.0230303i
$71$	−4.95295	+	2.85958i	−0.587806	+	0.339370i	−0.764230	−	0.644944i	$-0.776881\pi$
$71$	−4.95295	+	2.85958i	−0.587806	+	0.339370i	0.176423	+	0.984314i	$0.443547\pi$
$72$	1.46533	−	0.846011i	0.172691	−	0.0997033i
$73$		−	7.35690i		−	0.861060i	−0.902576	−	0.430530i	$-0.858327\pi$
$73$		−	7.35690i		−	0.861060i	0.902576	−	0.430530i	$-0.141673\pi$
$74$	−0.711636	−	1.23259i	−0.0827260	−	0.143286i
$75$	−2.46950	+	4.27730i	−0.285153	+	0.493900i
$76$	−8.71101	−	5.02930i	−0.999221	−	0.576901i
$77$	−9.90946			−1.12929
$78$		0			0
$79$	4.45473			0.501196			0.250598	−	0.968091i	$-0.419373\pi$
$79$	4.45473			0.501196			0.250598	+	0.968091i	$0.419373\pi$
$80$	0.609771	+	0.352052i	0.0681745	+	0.0393606i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	0.0990311	+	0.171527i	0.0109362	+	0.0189420i
$83$		−	10.1860i		−	1.11806i	−0.829149	−	0.559028i	$-0.811174\pi$
$83$		−	10.1860i		−	1.11806i	0.829149	−	0.559028i	$-0.188826\pi$
$84$	−2.73563	+	1.57942i	−0.298482	+	0.172329i
$85$	−0.813199	+	0.469501i	−0.0882038	+	0.0509245i
$86$		−	0.762709i		−	0.0822450i
$87$	2.96950	+	5.14333i	0.318364	+	0.551422i
$88$	−4.78232	+	8.28323i	−0.509797	+	0.882995i
$89$	0.118700	+	0.0685317i	0.0125822	+	0.00726434i	0.506278	−	0.862370i	$-0.331021\pi$
$89$	0.118700	+	0.0685317i	0.0125822	+	0.00726434i	−0.493696	+	0.869635i	$0.664354\pi$
$90$	0.109916			0.0115862
$91$		0			0
$92$	−15.0368			−1.56770
$93$	−4.56287	−	2.63437i	−0.473148	−	0.273172i
$94$	1.49880	−	2.59600i	0.154590	−	0.267757i
$95$	−0.689333	−	1.19396i	−0.0707241	−	0.122498i
$96$			4.65279i			0.474874i
$97$	−11.8556	+	6.84481i	−1.20375	+	0.694986i	−0.961387	−	0.275200i	$-0.911256\pi$
$97$	−11.8556	+	6.84481i	−1.20375	+	0.694986i	−0.242363	+	0.970186i	$0.577923\pi$
$98$	1.51350	−	0.873822i	0.152887	−	0.0882693i
$99$		−	5.65279i		−	0.568127i
$100$	−4.44989	−	7.70743i	−0.444989	−	0.770743i
$101$	−2.70560	+	4.68623i	−0.269217	+	0.466297i	−0.968660	−	0.248391i	$-0.920098\pi$
$101$	−2.70560	+	4.68623i	−0.269217	+	0.466297i	0.699443	+	0.714688i	$0.253431\pi$
$102$	−1.46533	−	0.846011i	−0.145090	−	0.0837675i
$103$	−13.7560			−1.35542			−0.677710	−	0.735330i	$-0.737027\pi$
$103$	−13.7560			−1.35542			−0.677710	+	0.735330i	$0.737027\pi$
$104$		0			0
$105$	−0.432960			−0.0422526
$106$	0.408928	+	0.236094i	0.0397186	+	0.0229315i
$107$	6.40850	−	11.0999i	0.619533	−	1.07306i	−0.370038	−	0.929017i	$-0.620655\pi$
$107$	6.40850	−	11.0999i	0.619533	−	1.07306i	0.989571	−	0.144046i	$-0.0460114\pi$
$108$	−0.900969	−	1.56052i	−0.0866958	−	0.150161i
$109$			12.1468i			1.16345i	0.813386	+	0.581724i	$0.197622\pi$
$109$			12.1468i			1.16345i	−0.813386	+	0.581724i	$0.802378\pi$
$110$	−0.538091	+	0.310667i	−0.0513050	+	0.0296209i
$111$	−2.76960	+	1.59903i	−0.262879	+	0.151773i
$112$		−	4.99761i		−	0.472229i
$113$	0.818864	+	1.41831i	0.0770322	+	0.133424i	0.901968	−	0.431802i	$-0.142122\pi$
$113$	0.818864	+	1.41831i	0.0770322	+	0.133424i	−0.824936	+	0.565226i	$0.808789\pi$
$114$	1.24214	−	2.15144i	0.116337	−	0.201501i
$115$	−1.78488	−	1.03050i	−0.166441	−	0.0960946i
$116$	−10.7017			−0.993629
$117$		0			0
$118$	−6.09783			−0.561351
$119$	5.77195	+	3.33244i	0.529114	+	0.305484i
$120$	−0.208947	+	0.361908i	−0.0190742	+	0.0330375i
$121$	10.4770	+	18.1468i	0.952458	+	1.64970i
$122$		−	3.78986i		−	0.343117i
$123$	0.385418	−	0.222521i	0.0347519	−	0.0200640i
$124$	8.22201	−	4.74698i	0.738358	−	0.426291i
$125$		−	2.45473i		−	0.219558i
$126$	−0.390084	−	0.675645i	−0.0347514	−	0.0601912i
$127$	5.39977	−	9.35268i	0.479152	−	0.829916i	−0.520562	−	0.853824i	$-0.674277\pi$
$127$	5.39977	−	9.35268i	0.479152	−	0.829916i	0.999714	+	0.0239078i	$0.00761081\pi$
$128$	−9.45833	−	5.46077i	−0.836006	−	0.482669i
$129$	−1.71379			−0.150891
$130$		0			0
$131$	0.907542			0.0792923			0.0396462	−	0.999214i	$-0.487377\pi$
$131$	0.907542			0.0792923			0.0396462	+	0.999214i	$0.487377\pi$
$132$	8.82132	+	5.09299i	0.767797	+	0.443288i
$133$	−4.89277	+	8.47453i	−0.424257	+	0.734835i
$134$	1.32640	+	2.29739i	0.114583	+	0.198464i
$135$		−	0.246980i		−	0.0212566i
$136$	5.57111	−	3.21648i	0.477718	−	0.275811i
$137$	8.26903	−	4.77413i	0.706471	−	0.407881i	−0.103282	−	0.994652i	$-0.532934\pi$
$137$	8.26903	−	4.77413i	0.706471	−	0.407881i	0.809753	+	0.586771i	$0.199601\pi$
$138$		−	3.71379i		−	0.316139i
$139$	2.04623	+	3.54417i	0.173559	+	0.300613i	0.939662	−	0.342105i	$-0.111140\pi$
$139$	2.04623	+	3.54417i	0.173559	+	0.300613i	−0.766103	+	0.642718i	$0.777807\pi$
$140$	0.390084	−	0.675645i	0.0329681	−	0.0571024i
$141$	−5.83317	−	3.36778i	−0.491241	−	0.283618i
$142$	2.54527			0.213594
$143$		0			0
$144$	2.85086			0.237571
$145$	−1.27030	−	0.733406i	−0.105492	−	0.0609061i
$146$	−1.63706	+	2.83548i	−0.135484	+	0.234666i
$147$	−1.96346	−	3.40081i	−0.161943	−	0.280494i
$148$		−	5.76271i		−	0.473692i
$149$	−13.3267	+	7.69418i	−1.09177	+	0.630332i	−0.934046	−	0.357152i	$-0.883748\pi$
$149$	−13.3267	+	7.69418i	−1.09177	+	0.630332i	−0.157720	+	0.987484i	$0.550414\pi$
$150$	1.90358	−	1.09903i	0.155426	−	0.0897355i
$151$			3.67456i			0.299032i	0.988759	+	0.149516i	$0.0477715\pi$
$151$			3.67456i			0.299032i	−0.988759	+	0.149516i	$0.952228\pi$
$152$	4.72252	+	8.17965i	0.383047	+	0.663457i
$153$	−1.90097	+	3.29257i	−0.153684	+	0.266189i
$154$	3.81928	+	2.20506i	0.307766	+	0.177689i
$155$	1.30127			0.104521
$156$		0			0
$157$	−4.87800			−0.389307			−0.194653	−	0.980872i	$-0.562358\pi$
$157$	−4.87800			−0.389307			−0.194653	+	0.980872i	$0.562358\pi$
$158$	−1.71693	−	0.991271i	−0.136592	−	0.0788613i
$159$	0.530499	−	0.918852i	0.0420713	−	0.0728697i
$160$	−0.574572	−	0.995189i	−0.0454239	−	0.0786766i
$161$			14.6286i			1.15290i
$162$	0.385418	−	0.222521i	0.0302813	−	0.0174829i
$163$	−7.47468	+	4.31551i	−0.585462	+	0.338017i	−0.763301	−	0.646043i	$-0.776423\pi$
$163$	−7.47468	+	4.31551i	−0.585462	+	0.338017i	0.177839	+	0.984060i	$0.443089\pi$
$164$			0.801938i			0.0626208i
$165$	0.698062	+	1.20908i	0.0543441	+	0.0941267i
$166$	−2.26659	+	3.92586i	−0.175922	+	0.304706i
$167$	8.20108	+	4.73490i	0.634619	+	0.366397i	0.782539	−	0.622602i	$-0.213924\pi$
$167$	8.20108	+	4.73490i	0.634619	+	0.366397i	−0.147920	+	0.988999i	$0.547258\pi$
$168$	2.96615			0.228843
$169$		0			0
$170$	0.417895			0.0320511
$171$	−4.83424	−	2.79105i	−0.369684	−	0.213437i
$172$	1.54407	−	2.67441i	0.117734	−	0.203922i
$173$	2.38740	+	4.13509i	0.181510	+	0.314385i	0.942395	−	0.334502i	$-0.108568\pi$
$173$	2.38740	+	4.13509i	0.181510	+	0.314385i	−0.760885	+	0.648887i	$0.775235\pi$
$174$		−	2.64310i		−	0.200373i
$175$	−7.49819	+	4.32908i	−0.566810	+	0.327248i
$176$	−13.9563	+	8.05765i	−1.05199	+	0.607368i
$177$			13.7017i			1.02988i
$178$	−0.0304995	−	0.0528266i	−0.00228603	−	0.00395952i
$179$	1.71768	−	2.97510i	0.128385	−	0.222370i	−0.794666	−	0.607047i	$-0.792354\pi$
$179$	1.71768	−	2.97510i	0.128385	−	0.222370i	0.923051	+	0.384677i	$0.125687\pi$
$180$	0.385418	+	0.222521i	0.0287273	+	0.0165857i
$181$	13.4862			1.00242			0.501210	−	0.865326i	$-0.332888\pi$
$181$	13.4862			1.00242			0.501210	+	0.865326i	$0.332888\pi$
$182$		0			0
$183$	−8.51573			−0.629501
$184$	12.2279	+	7.05980i	0.901455	+	0.520456i
$185$	0.394928	−	0.684035i	0.0290357	−	0.0502913i
$186$	1.17241	+	2.03067i	0.0859651	+	0.148896i
$187$		−	21.4916i		−	1.57162i
$188$	10.5110	−	6.06853i	0.766594	−	0.442593i
$189$	−1.51816	+	0.876510i	−0.110430	+	0.0637567i
$190$			0.613564i			0.0445126i
$191$	0.650637	+	1.12694i	0.0470784	+	0.0815422i	0.888604	−	0.458674i	$-0.151676\pi$
$191$	0.650637	+	1.12694i	0.0470784	+	0.0815422i	−0.841526	+	0.540217i	$0.818342\pi$
$192$	−1.81551	+	3.14456i	−0.131023	+	0.226939i
$193$	−7.96368	−	4.59783i	−0.573238	−	0.330959i	0.185203	−	0.982700i	$-0.440706\pi$
$193$	−7.96368	−	4.59783i	−0.573238	−	0.330959i	−0.758442	+	0.651741i	$0.774039\pi$
$194$	6.09246			0.437413
$195$		0			0
$196$	7.07606			0.505433
$197$	−3.56136	−	2.05615i	−0.253737	−	0.146495i	0.367737	−	0.929930i	$-0.380133\pi$
$197$	−3.56136	−	2.05615i	−0.253737	−	0.146495i	−0.621474	+	0.783435i	$0.713466\pi$
$198$	−1.25786	+	2.17869i	−0.0893926	+	0.154832i
$199$	−12.3862	−	21.4535i	−0.878034	−	1.52080i	−0.853495	−	0.521101i	$-0.825521\pi$
$199$	−12.3862	−	21.4535i	−0.878034	−	1.52080i	−0.0245395	−	0.999699i	$-0.507812\pi$
$200$			8.35690i			0.590922i
$201$	5.16218	−	2.98039i	0.364112	−	0.210220i
$202$	2.08557	−	1.20410i	0.146740	−	0.0847204i
$203$			10.4112i			0.730722i
$204$	−3.42543	−	5.93301i	−0.239828	−	0.415394i
$205$	−0.0549581	+	0.0951903i	−0.00383844	+	0.00664838i
$206$	5.30181	+	3.06100i	0.369394	+	0.213270i
$207$	−8.34481			−0.580005
$208$		0			0
$209$	31.5545			2.18267
$210$	0.166870	+	0.0963427i	0.0115152	+	0.00664828i
$211$	2.96950	−	5.14333i	0.204429	−	0.354081i	−0.745522	−	0.666481i	$-0.767800\pi$
$211$	2.96950	−	5.14333i	0.204429	−	0.354081i	0.949951	+	0.312400i	$0.101133\pi$
$212$	0.955927	+	1.65571i	0.0656533	+	0.113715i
$213$		−	5.71917i		−	0.391871i
$214$	−4.93990	+	2.85205i	−0.337684	+	0.194962i
$215$	0.366564	−	0.211636i	0.0249995	−	0.0144334i
$216$			1.69202i			0.115127i
$217$	−4.61811	−	7.99881i	−0.313498	−	0.542994i
$218$	2.70291	−	4.68157i	0.183064	−	0.317076i
$219$	6.37126	+	3.67845i	0.430530	+	0.248566i
$220$	−2.51573			−0.169610
$221$		0			0
$222$	1.42327			0.0955237
$223$	−12.2985	−	7.10052i	−0.823566	−	0.475486i	0.0280785	−	0.999606i	$-0.491061\pi$
$223$	−12.2985	−	7.10052i	−0.823566	−	0.475486i	−0.851645	+	0.524120i	$0.824395\pi$
$224$	−4.07822	+	7.06368i	−0.272488	+	0.471962i
$225$	−2.46950	−	4.27730i	−0.164633	−	0.285153i
$226$		−	0.728857i		−	0.0484829i
$227$	13.8627	−	8.00365i	0.920101	−	0.531221i	0.0364340	−	0.999336i	$-0.488400\pi$
$227$	13.8627	−	8.00365i	0.920101	−	0.531221i	0.883667	+	0.468115i	$0.155067\pi$
$228$	8.71101	−	5.02930i	0.576901	−	0.333074i
$229$		−	1.84117i		−	0.121668i	−0.998148	−	0.0608339i	$-0.980624\pi$
$229$		−	1.84117i		−	0.121668i	0.998148	−	0.0608339i	$-0.0193760\pi$
$230$	0.458615	+	0.794345i	0.0302402	+	0.0523776i
$231$	4.95473	−	8.58185i	0.325997	−	0.564644i
$232$	8.70262	+	5.02446i	0.571355	+	0.329872i
$233$	23.4252			1.53464			0.767318	−	0.641267i	$-0.221591\pi$
$233$	23.4252			1.53464			0.767318	+	0.641267i	$0.221591\pi$
$234$		0			0
$235$	1.66355			0.108518
$236$	−21.3818	−	12.3448i	−1.39184	−	0.803579i
$237$	−2.22737	+	3.85791i	−0.144683	+	0.250598i
$238$	−1.48307	−	2.56876i	−0.0961334	−	0.166508i
$239$			14.6015i			0.944491i	0.881467	+	0.472246i	$0.156556\pi$
$239$			14.6015i			0.944491i	−0.881467	+	0.472246i	$0.843444\pi$
$240$	−0.609771	+	0.352052i	−0.0393606	+	0.0227248i
$241$	−7.47468	+	4.31551i	−0.481487	+	0.277987i	−0.721036	−	0.692898i	$-0.756334\pi$
$241$	−7.47468	+	4.31551i	−0.481487	+	0.277987i	0.239549	+	0.970884i	$0.423000\pi$
$242$		−	9.32544i		−	0.599462i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	7.67241	−	13.2890i	0.491176	−	0.850741i
$245$	0.839931	+	0.484935i	0.0536612	+	0.0309813i
$246$	−0.198062			−0.0126280
$247$		0			0
$248$	−8.91484			−0.566093
$249$	8.82132	+	5.09299i	0.559028	+	0.322755i
$250$	−0.546229	+	0.946096i	−0.0345466	+	0.0598364i
$251$	−1.90097	−	3.29257i	−0.119988	−	0.207825i	0.799775	−	0.600300i	$-0.204952\pi$
$251$	−1.90097	−	3.29257i	−0.119988	−	0.207825i	−0.919763	+	0.392475i	$0.871619\pi$
$252$		−	3.15883i		−	0.198988i
$253$	40.8517	−	23.5858i	2.56833	−	1.48282i
$254$	−4.16233	+	2.40312i	−0.261168	+	0.150785i
$255$		−	0.939001i		−	0.0588025i
$256$	−1.20075	−	2.07976i	−0.0750469	−	0.129985i
$257$	−10.2981	+	17.8368i	−0.642375	+	1.11263i	0.342526	+	0.939508i	$0.388717\pi$
$257$	−10.2981	+	17.8368i	−0.642375	+	1.11263i	−0.984901	+	0.173118i	$0.944616\pi$
$258$	0.660525	+	0.381355i	0.0411225	+	0.0237421i
$259$	−5.60627			−0.348357
$260$		0			0
$261$	−5.93900			−0.367615
$262$	−0.349783	−	0.201947i	−0.0216096	−	0.0124763i
$263$	−0.166366	+	0.288155i	−0.0102586	+	0.0177684i	−0.871109	−	0.491089i	$-0.836599\pi$
$263$	−0.166366	+	0.288155i	−0.0102586	+	0.0177684i	0.860851	+	0.508858i	$0.169932\pi$
$264$	−4.78232	−	8.28323i	−0.294332	−	0.509797i
$265$			0.262045i			0.0160973i
$266$	3.77152	−	2.17749i	0.231247	−	0.133510i
$267$	−0.118700	+	0.0685317i	−0.00726434	+	0.00419407i
$268$			10.7409i			0.656107i
$269$	−13.6516	−	23.6453i	−0.832353	−	1.44168i	−0.896168	−	0.443715i	$-0.853660\pi$
$269$	−13.6516	−	23.6453i	−0.832353	−	1.44168i	0.0638154	−	0.997962i	$-0.479673\pi$
$270$	−0.0549581	+	0.0951903i	−0.00334465	+	0.00579310i
$271$	24.2362	+	13.9928i	1.47224	+	0.850000i	0.999513	−	0.0312076i	$-0.00993529\pi$
$271$	24.2362	+	13.9928i	1.47224	+	0.850000i	0.472730	+	0.881207i	$0.343269\pi$
$272$	10.8388			0.657197
$273$		0			0
$274$	−4.24937			−0.256714
$275$	24.1787	+	13.9596i	1.45803	+	0.841794i
$276$	7.51842	−	13.0223i	0.452556	−	0.783849i
$277$	−1.05161	−	1.82143i	−0.0631849	−	0.109439i	0.832703	−	0.553721i	$-0.186792\pi$
$277$	−1.05161	−	1.82143i	−0.0631849	−	0.109439i	−0.895887	+	0.444281i	$0.853459\pi$
$278$		−	1.82132i		−	0.109235i
$279$	4.56287	−	2.63437i	0.273172	−	0.157716i
$280$	−0.634431	+	0.366289i	−0.0379145	+	0.0218900i
$281$		−	27.2349i		−	1.62470i	−0.583172	−	0.812349i	$-0.698189\pi$
$281$		−	27.2349i		−	1.62470i	0.583172	−	0.812349i	$-0.301811\pi$
$282$	1.49880	+	2.59600i	0.0892525	+	0.154590i
$283$	2.64191	−	4.57592i	0.157045	−	0.272010i	−0.776757	−	0.629801i	$-0.783137\pi$
$283$	2.64191	−	4.57592i	0.157045	−	0.272010i	0.933802	+	0.357791i	$0.116470\pi$
$284$	8.92490	+	5.15279i	0.529595	+	0.305762i
$285$	1.37867			0.0816651
$286$		0			0
$287$	0.780167			0.0460518
$288$	−4.02944	−	2.32640i	−0.237437	−	0.137084i
$289$	1.27263	−	2.20427i	0.0748609	−	0.129663i
$290$	0.326396	+	0.565335i	0.0191667	+	0.0331976i
$291$		−	13.6896i		−	0.802500i
$292$	−11.4806	+	6.62833i	−0.671852	+	0.387894i
$293$	−28.2865	+	16.3312i	−1.65252	+	0.954081i	−0.676485	+	0.736457i	$0.736498\pi$
$293$	−28.2865	+	16.3312i	−1.65252	+	0.954081i	−0.976033	+	0.217625i	$0.930169\pi$
$294$			1.74764i			0.101925i
$295$	−1.69202	−	2.93067i	−0.0985133	−	0.170630i
$296$	−2.70560	+	4.68623i	−0.157260	+	0.272381i
$297$	4.89546	+	2.82640i	0.284064	+	0.164004i
$298$	6.84846			0.396721
$299$		0			0
$300$	8.89977			0.513829
$301$	−2.60181	−	1.50216i	−0.149966	−	0.0865828i
$302$	0.817667	−	1.41624i	0.0470515	−	0.0814955i
$303$	−2.70560	−	4.68623i	−0.155432	−	0.269217i
$304$			15.9138i			0.912717i
$305$	1.82143	−	1.05161i	0.104295	−	0.0602148i
$306$	1.46533	−	0.846011i	0.0837675	−	0.0483632i
$307$			20.7614i			1.18491i	0.805602	+	0.592457i	$0.201842\pi$
$307$			20.7614i			1.18491i	−0.805602	+	0.592457i	$0.798158\pi$
$308$	8.92812	+	15.4640i	0.508727	+	0.881140i
$309$	6.87800	−	11.9130i	0.391276	−	0.677710i
$310$	−0.501534	−	0.289561i	−0.0284852	−	0.0164459i
$311$	11.3013			0.640836			0.320418	−	0.947276i	$-0.396177\pi$
$311$	11.3013			0.640836			0.320418	+	0.947276i	$0.396177\pi$
$312$		0			0
$313$	−4.27173			−0.241453			−0.120726	−	0.992686i	$-0.538522\pi$
$313$	−4.27173			−0.241453			−0.120726	+	0.992686i	$0.538522\pi$
$314$	1.88007	+	1.08546i	0.106098	+	0.0612559i
$315$	0.216480	−	0.374955i	0.0121973	−	0.0211263i
$316$	−4.01357	−	6.95171i	−0.225781	−	0.391064i
$317$			15.4776i			0.869307i	0.900598	+	0.434653i	$0.143129\pi$
$317$			15.4776i			0.869307i	−0.900598	+	0.434653i	$0.856871\pi$
$318$	−0.408928	+	0.236094i	−0.0229315	+	0.0132395i
$319$	29.0742	−	16.7860i	1.62784	−	0.939834i
$320$		−	0.896789i		−	0.0501320i
$321$	6.40850	+	11.0999i	0.357688	+	0.619533i
$322$	3.25518	−	5.63813i	0.181404	−	0.314201i
$323$	−18.3795	−	10.6114i	−1.02266	−	0.590435i
$324$	1.80194			0.100108
$325$		0			0
$326$	3.84117			0.212743
$327$	−10.5194	−	6.07338i	−0.581724	−	0.335858i
$328$	0.376510	−	0.652135i	0.0207893	−	0.0360081i
$329$	−5.90379	−	10.2257i	−0.325486	−	0.563759i
$330$		−	0.621334i		−	0.0342033i
$331$	5.25530	−	3.03415i	0.288857	−	0.166772i	−0.348569	−	0.937283i	$-0.613332\pi$
$331$	5.25530	−	3.03415i	0.288857	−	0.166772i	0.637426	+	0.770511i	$0.279999\pi$
$332$	−15.8955	+	9.17725i	−0.872377	+	0.503667i
$333$		−	3.19806i		−	0.175253i
$334$	−2.10723	−	3.64983i	−0.115302	−	0.199710i
$335$	−0.736094	+	1.27495i	−0.0402171	+	0.0696581i
$336$	4.32805	+	2.49880i	0.236115	+	0.136321i
$337$	−12.1239			−0.660432			−0.330216	−	0.943905i	$-0.607122\pi$
$337$	−12.1239			−0.660432			−0.330216	+	0.943905i	$0.607122\pi$
$338$		0			0
$339$	−1.63773			−0.0889491
$340$	1.46533	+	0.846011i	0.0794689	+	0.0458814i
$341$	−14.8916	+	25.7930i	−0.806424	+	1.39677i
$342$	1.24214	+	2.15144i	0.0671670	+	0.116337i
$343$		−	19.1551i		−	1.03428i
$344$	−2.51128	+	1.44989i	−0.135399	+	0.0781726i
$345$	1.78488	−	1.03050i	0.0960946	−	0.0554802i
$346$		−	2.12498i		−	0.114240i
$347$	−11.5749	−	20.0483i	−0.621371	−	1.07625i	−0.989231	−	0.146365i	$-0.953242\pi$
$347$	−11.5749	−	20.0483i	−0.621371	−	1.07625i	0.367859	−	0.929882i	$-0.380091\pi$
$348$	5.35086	−	9.26795i	0.286836	−	0.496814i
$349$	−19.2220	−	11.0978i	−1.02893	−	0.594053i	−0.112253	−	0.993680i	$-0.535807\pi$
$349$	−19.2220	−	11.0978i	−1.02893	−	0.594053i	−0.916678	+	0.399626i	$0.869140\pi$
$350$	3.85325			0.205965
$351$		0			0
$352$	26.3013			1.40186
$353$	4.39134	+	2.53534i	0.233728	+	0.134943i	0.612291	−	0.790633i	$-0.290248\pi$
$353$	4.39134	+	2.53534i	0.233728	+	0.134943i	−0.378563	+	0.925576i	$0.623582\pi$
$354$	3.04892	−	5.28088i	0.162048	−	0.280676i
$355$	0.706259	+	1.22328i	0.0374843	+	0.0649248i
$356$		−	0.246980i		−	0.0130899i
$357$	−5.77195	+	3.33244i	−0.305484	+	0.176371i
$358$	−1.32405	+	0.764438i	−0.0699780	+	0.0404018i
$359$			16.6746i			0.880050i	0.897986	+	0.440025i	$0.145030\pi$
$359$			16.6746i			0.880050i	−0.897986	+	0.440025i	$0.854970\pi$
$360$	−0.208947	−	0.361908i	−0.0110125	−	0.0190742i
$361$	6.07995	−	10.5308i	0.319997	−	0.554252i
$362$	−5.19781	−	3.00096i	−0.273191	−	0.157727i
$363$	−20.9541			−1.09980
$364$		0			0
$365$	−1.81700			−0.0951063
$366$	3.28211	+	1.89493i	0.171559	+	0.0990495i
$367$	0.589638	−	1.02128i	0.0307789	−	0.0533105i	−0.850226	−	0.526418i	$-0.823535\pi$
$367$	0.589638	−	1.02128i	0.0307789	−	0.0533105i	0.881005	+	0.473108i	$0.156868\pi$
$368$	11.8949	+	20.6026i	0.620066	+	1.07399i
$369$			0.445042i			0.0231680i
$370$	−0.304424	+	0.175760i	−0.0158263	+	0.00913730i
$371$	1.61077	−	0.929976i	0.0836268	−	0.0482820i
$372$			9.49396i			0.492239i
$373$	15.0462	+	26.0608i	0.779064	+	1.34938i	0.932482	+	0.361217i	$0.117639\pi$
$373$	15.0462	+	26.0608i	0.779064	+	1.34938i	−0.153417	+	0.988161i	$0.549028\pi$
$374$	−4.78232	+	8.28323i	−0.247288	+	0.428315i
$375$	2.12586	+	1.22737i	0.109779	+	0.0633809i
$376$	−11.3967			−0.587741
$377$		0			0
$378$	0.780167			0.0401275
$379$	16.5958	+	9.58157i	0.852467	+	0.492172i	0.861483	−	0.507787i	$-0.169536\pi$
$379$	16.5958	+	9.58157i	0.852467	+	0.492172i	−0.00901515	+	0.999959i	$0.502870\pi$
$380$	−1.24214	+	2.15144i	−0.0637202	+	0.110367i
$381$	5.39977	+	9.35268i	0.276639	+	0.479152i
$382$		−	0.579121i		−	0.0296304i
$383$	−13.3267	+	7.69418i	−0.680963	+	0.393154i	−0.800218	−	0.599710i	$-0.795283\pi$
$383$	−13.3267	+	7.69418i	−0.680963	+	0.393154i	0.119255	+	0.992864i	$0.461949\pi$
$384$	9.45833	−	5.46077i	0.482669	−	0.278669i
$385$			2.44743i			0.124733i
$386$	2.04623	+	3.54417i	0.104150	+	0.180394i
$387$	0.856896	−	1.48419i	0.0435585	−	0.0754455i
$388$	21.3630	+	12.3339i	1.08454	+	0.626160i
$389$	24.0315			1.21844			0.609222	−	0.793000i	$-0.291482\pi$
$389$	24.0315			1.21844			0.609222	+	0.793000i	$0.291482\pi$
$390$		0			0
$391$	−31.7265			−1.60448
$392$	−5.75425	−	3.32222i	−0.290633	−	0.167797i
$393$	−0.453771	+	0.785955i	−0.0228897	+	0.0396462i
$394$	0.915075	+	1.58496i	0.0461008	+	0.0798489i
$395$		−	1.10023i		−	0.0553585i
$396$	−8.82132	+	5.09299i	−0.443288	+	0.255932i
$397$	−25.6356	+	14.8007i	−1.28662	+	0.742828i	−0.978049	−	0.208375i	$-0.933183\pi$
$397$	−25.6356	+	14.8007i	−1.28662	+	0.742828i	−0.308567	+	0.951203i	$0.599849\pi$
$398$			11.0248i			0.552621i
$399$	−4.89277	−	8.47453i	−0.244945	−	0.424257i
$400$	−7.04019	+	12.1940i	−0.352009	+	0.609698i
$401$	−18.2759	−	10.5516i	−0.912656	−	0.526922i	−0.0313711	−	0.999508i	$-0.509987\pi$
$401$	−18.2759	−	10.5516i	−0.912656	−	0.526922i	−0.881285	+	0.472586i	$0.843321\pi$
$402$	−2.65279			−0.132309
$403$		0			0
$404$	9.75063			0.485112
$405$	0.213891	+	0.123490i	0.0106283	+	0.00613626i
$406$	2.31671	−	4.01266i	0.114976	−	0.199145i
$407$	9.03899	+	15.6560i	0.448046	+	0.776039i
$408$			6.43296i			0.318479i
$409$	−31.1963	+	18.0112i	−1.54256	+	0.890596i	−0.543880	+	0.839163i	$0.683045\pi$
$409$	−31.1963	+	18.0112i	−1.54256	+	0.890596i	−0.998676	+	0.0514328i	$0.983621\pi$
$410$	0.0423637	−	0.0244587i	0.00209219	−	0.00120793i
$411$			9.54825i			0.470981i
$412$	12.3937	+	21.4666i	0.610595	+	1.05758i
$413$	−12.0097	+	20.8014i	−0.590958	+	1.02357i
$414$	3.21624	+	1.85690i	0.158069	+	0.0912615i
$415$	−2.51573			−0.123492
$416$		0			0
$417$	−4.09246			−0.200409
$418$	−12.1617	−	7.02153i	−0.594846	−	0.343434i
$419$	−2.98427	+	5.16891i	−0.145791	+	0.252518i	−0.929668	−	0.368399i	$-0.879906\pi$
$419$	−2.98427	+	5.16891i	−0.145791	+	0.252518i	0.783877	+	0.620917i	$0.213239\pi$
$420$	0.390084	+	0.675645i	0.0190341	+	0.0329681i
$421$		−	2.09544i		−	0.102126i	−0.998695	−	0.0510628i	$-0.983739\pi$
$421$		−	2.09544i		−	0.102126i	0.998695	−	0.0510628i	$-0.0162609\pi$
$422$	−2.28900	+	1.32155i	−0.111427	+	0.0643321i
$423$	5.83317	−	3.36778i	0.283618	−	0.163747i
$424$		−	1.79523i		−	0.0871842i
$425$	−9.38889	−	16.2620i	−0.455428	−	0.788824i
$426$	−1.27263	+	2.20427i	−0.0616594	+	0.106797i
$427$	−12.9282	−	7.46412i	−0.625641	−	0.361214i
$428$	−23.0954			−1.11636
$429$		0			0
$430$	−0.188374			−0.00908418
$431$	2.49915	+	1.44289i	0.120380	+	0.0695014i	0.558981	−	0.829181i	$-0.311193\pi$
$431$	2.49915	+	1.44289i	0.120380	+	0.0695014i	−0.438601	+	0.898682i	$0.644526\pi$
$432$	−1.42543	+	2.46891i	−0.0685809	+	0.118786i
$433$	−6.32424	−	10.9539i	−0.303924	−	0.526411i	0.673097	−	0.739554i	$-0.264963\pi$
$433$	−6.32424	−	10.9539i	−0.303924	−	0.526411i	−0.977021	+	0.213143i	$0.931630\pi$
$434$			4.11051i			0.197311i
$435$	1.27030	−	0.733406i	0.0609061	−	0.0351641i
$436$	18.9553	−	10.9438i	0.907794	−	0.524115i
$437$		−	46.5816i		−	2.22830i
$438$	−1.63706	−	2.83548i	−0.0782219	−	0.135484i
$439$	−5.46346	+	9.46299i	−0.260757	+	0.451644i	−0.966443	−	0.256880i	$-0.917305\pi$
$439$	−5.46346	+	9.46299i	−0.260757	+	0.451644i	0.705687	+	0.708524i	$0.250639\pi$
$440$	2.04579	+	1.18114i	0.0975291	+	0.0563085i
$441$	3.92692			0.186996
$442$		0			0
$443$	−19.2403			−0.914133			−0.457067	−	0.889433i	$-0.651100\pi$
$443$	−19.2403			−0.914133			−0.457067	+	0.889433i	$0.651100\pi$
$444$	4.99065	+	2.88135i	0.236846	+	0.136743i
$445$	0.0169259	−	0.0293166i	0.000802366	−	0.00138974i
$446$	3.16003	+	5.47333i	0.149632	+	0.259170i
$447$		−	15.3884i		−	0.727844i
$448$	−5.51247	+	3.18263i	−0.260440	+	0.150365i
$449$	24.9588	−	14.4100i	1.17788	−	0.680050i	0.222357	−	0.974965i	$-0.428625\pi$
$449$	24.9588	−	14.4100i	1.17788	−	0.680050i	0.955523	+	0.294916i	$0.0952915\pi$
$450$			2.19806i			0.103618i
$451$	−1.25786	−	2.17869i	−0.0592305	−	0.102590i
$452$	1.47554	−	2.55571i	0.0694036	−	0.120211i
$453$	−3.18226	−	1.83728i	−0.149516	−	0.0863230i
$454$	−7.12392			−0.334342
$455$		0			0
$456$	−9.44504			−0.442305
$457$	15.6497	+	9.03534i	0.732061	+	0.422656i	0.819176	−	0.573543i	$-0.194431\pi$
$457$	15.6497	+	9.03534i	0.732061	+	0.422656i	−0.0871147	+	0.996198i	$0.527765\pi$
$458$	−0.409698	+	0.709618i	−0.0191439	+	0.0331583i
$459$	−1.90097	−	3.29257i	−0.0887296	−	0.153684i
$460$			3.71379i			0.173156i
$461$	−6.55376	+	3.78382i	−0.305239	+	0.176230i	−0.644794	−	0.764356i	$-0.723057\pi$
$461$	−6.55376	+	3.78382i	−0.305239	+	0.176230i	0.339555	+	0.940586i	$0.389724\pi$
$462$	−3.81928	+	2.20506i	−0.177689	+	0.102589i
$463$		−	35.3551i		−	1.64309i	−0.570143	−	0.821545i	$-0.693112\pi$
$463$		−	35.3551i		−	1.64309i	0.570143	−	0.821545i	$-0.306888\pi$
$464$	8.46562	+	14.6629i	0.393006	+	0.680707i
$465$	−0.650637	+	1.12694i	−0.0301726	+	0.0522604i
$466$	−9.02848	−	5.21260i	−0.418236	−	0.241469i
$467$	−13.0000			−0.601568			−0.300784	−	0.953692i	$-0.597248\pi$
$467$	−13.0000			−0.601568			−0.300784	+	0.953692i	$0.597248\pi$
$468$		0			0
$469$	10.4494			0.482506
$470$	−0.641160	−	0.370174i	−0.0295745	−	0.0170748i
$471$	2.43900	−	4.22447i	0.112383	−	0.194653i
$472$	11.5918	+	20.0776i	0.533556	+	0.924145i
$473$			9.68771i			0.445441i
$474$	1.71693	−	0.991271i	0.0788613	−	0.0455306i
$475$	23.8763	−	13.7850i	1.09552	−	0.632500i
$476$		−	12.0097i		−	0.550463i
$477$	0.530499	+	0.918852i	0.0242899	+	0.0420713i
$478$	3.24914	−	5.62767i	0.148612	−	0.257404i
$479$	−22.1066	−	12.7632i	−1.01008	−	0.583167i	−0.0988618	−	0.995101i	$-0.531520\pi$
$479$	−22.1066	−	12.7632i	−1.01008	−	0.583167i	−0.911214	+	0.411934i	$0.864853\pi$
$480$	1.14914			0.0524510
$481$		0			0
$482$	3.84117			0.174960
$483$	−12.6688	−	7.31431i	−0.576449	−	0.332813i
$484$	18.8790	−	32.6993i	0.858135	−	1.48633i
$485$	1.69053	+	2.92808i	0.0767630	+	0.132957i
$486$			0.445042i			0.0201875i
$487$	13.8627	−	8.00365i	0.628180	−	0.362680i	−0.151867	−	0.988401i	$-0.548529\pi$
$487$	13.8627	−	8.00365i	0.628180	−	0.362680i	0.780047	+	0.625721i	$0.215195\pi$
$488$	−12.4784	+	7.20440i	−0.564870	+	0.326128i
$489$		−	8.63102i		−	0.390308i
$490$	−0.215816	−	0.373805i	−0.00974958	−	0.0168868i
$491$	10.3693	−	17.9601i	0.467959	−	0.810528i	−0.531371	−	0.847139i	$-0.678323\pi$
$491$	10.3693	−	17.9601i	0.467959	−	0.810528i	0.999330	+	0.0366110i	$0.0116562\pi$
$492$	−0.694498	−	0.400969i	−0.0313104	−	0.0180771i
$493$	−22.5797			−1.01694
$494$		0			0
$495$	−1.39612			−0.0627511
$496$	−13.0081	−	7.51022i	−0.584080	−	0.337219i
$497$	5.01291	−	8.68261i	0.224860	−	0.389468i
$498$	−2.26659	−	3.92586i	−0.101569	−	0.175922i
$499$		−	8.06770i		−	0.361160i	−0.983560	−	0.180580i	$-0.942203\pi$
$499$		−	8.06770i		−	0.361160i	0.983560	−	0.180580i	$-0.0577975\pi$
$500$	−3.83067	+	2.21164i	−0.171313	+	0.0989074i
$501$	−8.20108	+	4.73490i	−0.366397	+	0.211540i
$502$			1.69202i			0.0755186i
$503$	15.1211	+	26.1905i	0.674216	+	1.16778i	0.976697	+	0.214622i	$0.0688518\pi$
$503$	15.1211	+	26.1905i	0.674216	+	1.16778i	−0.302481	+	0.953155i	$0.597815\pi$
$504$	−1.48307	+	2.56876i	−0.0660614	+	0.114422i
$505$	1.15740	+	0.668227i	0.0515037	+	0.0297357i
$506$	−20.9933			−0.933266
$507$		0			0
$508$	−19.4601			−0.863403
$509$	−13.8993	−	8.02475i	−0.616075	−	0.355691i	0.159264	−	0.987236i	$-0.449088\pi$
$509$	−13.8993	−	8.02475i	−0.616075	−	0.355691i	−0.775339	+	0.631545i	$0.782421\pi$
$510$	−0.208947	+	0.361908i	−0.00925235	+	0.0160255i
$511$	6.44839	+	11.1689i	0.285260	+	0.494085i
$512$			22.9119i			1.01257i
$513$	4.83424	−	2.79105i	0.213437	−	0.123228i
$514$	7.93810	−	4.58306i	0.350135	−	0.202150i
$515$			3.39745i			0.149710i
$516$	1.54407	+	2.67441i	0.0679740	+	0.117734i
$517$	−19.0374	+	32.9737i	−0.837262	+	1.45018i
$518$	2.16075	+	1.24751i	0.0949381	+	0.0548125i
$519$	−4.77479			−0.209590
$520$		0			0
$521$	−2.69309			−0.117986			−0.0589931	−	0.998258i	$-0.518789\pi$
$521$	−2.69309			−0.117986			−0.0589931	+	0.998258i	$0.518789\pi$
$522$	2.28900	+	1.32155i	0.100187	+	0.0578428i
$523$	−17.6978	+	30.6535i	−0.773872	+	1.34039i	0.161554	+	0.986864i	$0.448349\pi$
$523$	−17.6978	+	30.6535i	−0.773872	+	1.34039i	−0.935426	+	0.353522i	$0.884984\pi$
$524$	−0.817667	−	1.41624i	−0.0357200	−	0.0618688i
$525$		−	8.65817i		−	0.377874i
$526$	0.128241	−	0.0740400i	0.00559157	−	0.00322830i
$527$	17.3478	−	10.0157i	0.755680	−	0.436292i
$528$		−	16.1153i		−	0.701328i
$529$	−23.3180	−	40.3879i	−1.01382	−	1.75600i
$530$	0.0583105	−	0.100997i	0.00253285	−	0.00438702i
$531$	−11.8660	−	6.85086i	−0.514942	−	0.297302i
$532$	17.6329			0.764485
$533$		0			0
$534$	0.0609989			0.00263968
$535$	−2.74144	−	1.58277i	−0.118523	−	0.0684291i
$536$	5.04288	−	8.73452i	0.217819	−	0.377274i
$537$	1.71768	+	2.97510i	0.0741232	+	0.128385i
$538$			12.1511i			0.523870i
$539$	−19.2241	+	11.0990i	−0.828040	+	0.478069i
$540$	−0.385418	+	0.222521i	−0.0165857	+	0.00957578i
$541$			34.7338i			1.49332i	0.665205	+	0.746660i	$0.268344\pi$
$541$			34.7338i			1.49332i	−0.665205	+	0.746660i	$0.731656\pi$
$542$	−6.22737	−	10.7861i	−0.267488	−	0.463303i
$543$	−6.74309	+	11.6794i	−0.289374	+	0.501210i
$544$	−15.3197	−	8.84481i	−0.656825	−	0.379218i
$545$	3.00000			0.128506
$546$		0			0
$547$	−26.1183			−1.11674			−0.558368	−	0.829593i	$-0.688572\pi$
$547$	−26.1183			−1.11674			−0.558368	+	0.829593i	$0.688572\pi$
$548$	−14.9003	−	8.60268i	−0.636508	−	0.367488i
$549$	4.25786	−	7.37484i	0.181721	−	0.314750i
$550$	−6.21260	−	10.7605i	−0.264906	−	0.458831i
$551$		−	33.1521i		−	1.41233i
$552$	−12.2279	+	7.05980i	−0.520456	+	0.300485i
$553$	−6.76299	+	3.90462i	−0.287592	+	0.166041i
$554$			0.936017i			0.0397676i
$555$	0.394928	+	0.684035i	0.0167638	+	0.0290357i
$556$	3.68718	−	6.38638i	0.156371	−	0.270843i
$557$	21.4556	+	12.3874i	0.909103	+	0.524871i	0.880142	−	0.474710i	$-0.157447\pi$
$557$	21.4556	+	12.3874i	0.909103	+	0.524871i	0.0289605	+	0.999581i	$0.490780\pi$
$558$	−2.34481			−0.0992639
$559$		0			0
$560$	−1.23431			−0.0521590
$561$	18.6122	+	10.7458i	0.785809	+	0.453687i
$562$	−6.06033	+	10.4968i	−0.255640	+	0.442781i
$563$	2.63049	+	4.55614i	0.110862	+	0.192019i	0.916118	−	0.400909i	$-0.131306\pi$
$563$	2.63049	+	4.55614i	0.110862	+	0.192019i	−0.805256	+	0.592927i	$0.797972\pi$
$564$			12.1371i			0.511063i
$565$	0.350294	−	0.202243i	0.0147370	−	0.00850841i
$566$	−2.03648	+	1.17576i	−0.0855994	+	0.0494209i
$567$		−	1.75302i		−	0.0736199i
$568$	−4.83848	−	8.38049i	−0.203018	−	0.351638i
$569$	−16.8729	+	29.2248i	−0.707350	+	1.22517i	0.258487	+	0.966015i	$0.416776\pi$
$569$	−16.8729	+	29.2248i	−0.707350	+	1.22517i	−0.965837	+	0.259151i	$0.916557\pi$
$570$	−0.531362	−	0.306782i	−0.0222563	−	0.0128497i
$571$	−23.0887			−0.966234			−0.483117	−	0.875556i	$-0.660495\pi$
$571$	−23.0887			−0.966234			−0.483117	+	0.875556i	$0.660495\pi$
$572$		0			0
$573$	−1.30127			−0.0543615
$574$	−0.300690	−	0.173604i	−0.0125506	−	0.00724607i
$575$	20.6075	−	35.6933i	0.859393	−	1.48851i
$576$	−1.81551	−	3.14456i	−0.0756463	−	0.131023i
$577$			3.57002i			0.148622i	0.997235	+	0.0743110i	$0.0236758\pi$
$577$			3.57002i			0.148622i	−0.997235	+	0.0743110i	$0.976324\pi$
$578$	−0.980992	+	0.566376i	−0.0408039	+	0.0235581i
$579$	7.96368	−	4.59783i	0.330959	−	0.191079i
$580$			2.64310i			0.109749i
$581$	8.92812	+	15.4640i	0.370401	+	0.641553i
$582$	−3.04623	+	5.27622i	−0.126270	+	0.218706i
$583$	−5.19408	−	2.99880i	−0.215117	−	0.124198i
$584$	12.4480			0.515103
$585$		0			0
$586$	14.5362			0.600484
$587$	9.92682	+	5.73125i	0.409724	+	0.236554i	0.690671	−	0.723169i	$-0.257315\pi$
$587$	9.92682	+	5.73125i	0.409724	+	0.236554i	−0.280947	+	0.959723i	$0.590649\pi$
$588$	−3.53803	+	6.12805i	−0.145906	+	0.252717i
$589$	14.7054	+	25.4704i	0.605924	+	1.04949i
$590$			1.50604i			0.0620027i
$591$	3.56136	−	2.05615i	0.146495	−	0.0845789i
$592$	−7.89574	+	4.55861i	−0.324513	+	0.187358i
$593$			21.8538i			0.897430i	0.893675	+	0.448715i	$0.148118\pi$
$593$			21.8538i			0.897430i	−0.893675	+	0.448715i	$0.851882\pi$
$594$	−1.25786	−	2.17869i	−0.0516108	−	0.0893926i
$595$	0.823044	−	1.42555i	0.0337415	−	0.0584420i
$596$	24.0139	+	13.8644i	0.983647	+	0.567909i
$597$	24.7724			1.01387
$598$		0			0
$599$	27.0573			1.10553			0.552765	−	0.833337i	$-0.313573\pi$
$599$	27.0573			1.10553			0.552765	+	0.833337i	$0.313573\pi$
$600$	−7.23728	−	4.17845i	−0.295461	−	0.170584i
$601$	−5.43900	+	9.42063i	−0.221861	+	0.384275i	−0.955373	−	0.295401i	$-0.904547\pi$
$601$	−5.43900	+	9.42063i	−0.221861	+	0.384275i	0.733512	+	0.679677i	$0.237880\pi$
$602$	0.668522	+	1.15791i	0.0272469	+	0.0471931i
$603$			5.96077i			0.242741i
$604$	5.73424	−	3.31067i	0.233323	−	0.134709i
$605$	4.48188	−	2.58761i	0.182214	−	0.105201i
$606$			2.40821i			0.0978267i
$607$	14.8180	+	25.6655i	0.601443	+	1.04173i	0.992603	+	0.121407i	$0.0387405\pi$
$607$	14.8180	+	25.6655i	0.601443	+	1.04173i	−0.391160	+	0.920323i	$0.627926\pi$
$608$	12.9862	−	22.4927i	0.526660	−	0.912201i
$609$	−9.01636	−	5.20560i	−0.365361	−	0.210941i
$610$	−0.936017			−0.0378982
$611$		0			0
$612$	6.85086			0.276929
$613$	−8.86317	−	5.11715i	−0.357980	−	0.206680i	0.310214	−	0.950667i	$-0.399599\pi$
$613$	−8.86317	−	5.11715i	−0.357980	−	0.206680i	−0.668194	+	0.743987i	$0.732933\pi$
$614$	4.61984	−	8.00180i	0.186442	−	0.322926i
$615$	−0.0549581	−	0.0951903i	−0.00221613	−	0.00383844i
$616$		−	16.7670i		−	0.675563i
$617$	22.7615	−	13.1414i	0.916345	−	0.529052i	0.0338776	−	0.999426i	$-0.489214\pi$
$617$	22.7615	−	13.1414i	0.916345	−	0.529052i	0.882467	+	0.470374i	$0.155881\pi$
$618$	−5.30181	+	3.06100i	−0.213270	+	0.123131i
$619$		−	29.0834i		−	1.16896i	−0.811408	−	0.584479i	$-0.801299\pi$
$619$		−	29.0834i		−	1.16896i	0.811408	−	0.584479i	$-0.198701\pi$
$620$	−1.17241	−	2.03067i	−0.0470850	−	0.0815536i
$621$	4.17241	−	7.22682i	0.167433	−	0.290002i
$622$	−4.35571	−	2.51477i	−0.174648	−	0.100833i
$623$	−0.240275			−0.00962641
$624$		0			0
$625$	24.0887			0.963549
$626$	1.64640	+	0.950550i	0.0658034	+	0.0379916i
$627$	−15.7772	+	27.3270i	−0.630082	+	1.09133i
$628$	4.39493	+	7.61224i	0.175377	+	0.303761i
$629$		−	12.1588i		−	0.484804i
$630$	−0.166870	+	0.0963427i	−0.00664828	+	0.00383839i
$631$	−22.0386	+	12.7240i	−0.877344	+	0.506535i	−0.869782	−	0.493436i	$-0.835741\pi$
$631$	−22.0386	+	12.7240i	−0.877344	+	0.506535i	−0.00756243	+	0.999971i	$0.502407\pi$
$632$			7.53750i			0.299826i
$633$	2.96950	+	5.14333i	0.118027	+	0.204429i
$634$	3.44408	−	5.96533i	0.136782	−	0.236913i
$635$	−2.30992	−	1.33363i	−0.0916664	−	0.0529236i
$636$	−1.91185			−0.0758099
$637$		0			0
$638$	−14.9409			−0.591517
$639$	4.95295	+	2.85958i	0.195935	+	0.113123i
$640$	−1.34870	+	2.33602i	−0.0533120	+	0.0923391i
$641$	−13.3705	−	23.1583i	−0.528102	−	0.914699i	−0.999463	−	0.0327590i	$-0.989571\pi$
$641$	−13.3705	−	23.1583i	−0.528102	−	0.914699i	0.471361	−	0.881940i	$-0.343763\pi$
$642$		−	5.70410i		−	0.225123i
$643$	−28.5454	+	16.4807i	−1.12572	+	0.649935i	−0.942855	−	0.333203i	$-0.891870\pi$
$643$	−28.5454	+	16.4807i	−1.12572	+	0.649935i	−0.182865	+	0.983138i	$0.558537\pi$
$644$	22.8283	−	13.1799i	0.899562	−	0.519362i
$645$			0.423272i			0.0166663i
$646$	4.72252	+	8.17965i	0.185805	+	0.321824i
$647$	17.2473	−	29.8732i	0.678060	−	1.17443i	−0.297504	−	0.954721i	$-0.596154\pi$
$647$	17.2473	−	29.8732i	0.678060	−	1.17443i	0.975564	−	0.219714i	$-0.0705125\pi$
$648$	−1.46533	−	0.846011i	−0.0575637	−	0.0332344i
$649$	77.4529			3.04029
$650$		0			0
$651$	9.23623			0.361996
$652$	13.4689	+	7.77628i	0.527483	+	0.304543i
$653$	−18.0758	+	31.3083i	−0.707362	+	1.22519i	0.258471	+	0.966019i	$0.416781\pi$
$653$	−18.0758	+	31.3083i	−0.707362	+	1.22519i	−0.965832	+	0.259167i	$0.916552\pi$
$654$	2.70291	+	4.68157i	0.105692	+	0.183064i
$655$		−	0.224144i		−	0.00875805i
$656$	1.09877	−	0.634375i	0.0428997	−	0.0247682i
$657$	−6.37126	+	3.67845i	−0.248566	+	0.143510i
$658$			5.25487i			0.204856i
$659$	3.40850	+	5.90370i	0.132776	+	0.229975i	0.924746	−	0.380585i	$-0.124277\pi$
$659$	3.40850	+	5.90370i	0.132776	+	0.229975i	−0.791969	+	0.610561i	$0.790944\pi$
$660$	1.25786	−	2.17869i	0.0489623	−	0.0848052i
$661$	−9.43482	−	5.44720i	−0.366972	−	0.211871i	0.305163	−	0.952300i	$-0.401289\pi$
$661$	−9.43482	−	5.44720i	−0.366972	−	0.211871i	−0.672135	+	0.740429i	$0.734622\pi$
$662$	−2.70065			−0.104964
$663$		0			0
$664$	17.2349			0.668844
$665$	2.09304	+	1.20841i	0.0811645	+	0.0468603i
$666$	−0.711636	+	1.23259i	−0.0275753	+	0.0477619i
$667$	−24.7799	−	42.9201i	−0.959483	−	1.66187i
$668$		−	17.0640i		−	0.660225i
$669$	12.2985	−	7.10052i	0.475486	−	0.274522i
$670$	0.567407	−	0.327593i	0.0219209	−	0.0126560i
$671$			48.1377i			1.85833i
$672$	−4.07822	−	7.06368i	−0.157321	−	0.272488i
$673$	10.3693	−	17.9601i	0.399706	−	0.692311i	−0.593983	−	0.804477i	$-0.702446\pi$
$673$	10.3693	−	17.9601i	0.399706	−	0.692311i	0.993689	+	0.112166i	$0.0357789\pi$
$674$	4.67277	+	2.69783i	0.179988	+	0.103916i
$675$	4.93900			0.190102
$676$		0			0
$677$	−25.5786			−0.983067			−0.491534	−	0.870859i	$-0.663564\pi$
$677$	−25.5786			−0.983067			−0.491534	+	0.870859i	$0.663564\pi$
$678$	0.631209	+	0.364429i	0.0242414	+	0.0139958i
$679$	11.9991	−	20.7830i	0.460483	−	0.797580i
$680$	−0.794405	−	1.37595i	−0.0304640	−	0.0527653i
$681$			16.0073i			0.613401i
$682$	11.4789	−	6.62737i	0.439552	−	0.253775i
$683$	−18.7330	+	10.8155i	−0.716799	+	0.413844i	−0.813573	−	0.581462i	$-0.802481\pi$
$683$	−18.7330	+	10.8155i	−0.716799	+	0.413844i	0.0967744	+	0.995306i	$0.469147\pi$
$684$			10.0586i			0.384600i
$685$	−1.17911	−	2.04228i	−0.0450516	−	0.0780316i
$686$	−4.26241	+	7.38272i	−0.162740	+	0.281873i
$687$	1.59450	+	0.920583i	0.0608339	+	0.0351224i
$688$	−4.88577			−0.186268
$689$		0			0
$690$	−0.917231			−0.0349184
$691$	−2.27761	−	1.31498i	−0.0866444	−	0.0500242i	0.456052	−	0.889953i	$-0.349263\pi$
$691$	−2.27761	−	1.31498i	−0.0866444	−	0.0500242i	−0.542696	+	0.839929i	$0.682596\pi$
$692$	4.30194	−	7.45117i	0.163535	−	0.283251i
$693$	4.95473	+	8.58185i	0.188215	+	0.325997i
$694$			10.3026i			0.391081i
$695$	0.875338	−	0.505377i	0.0332035	−	0.0191700i
$696$	−8.70262	+	5.02446i	−0.329872	+	0.190452i
$697$			1.69202i			0.0640899i
$698$	4.93900	+	8.55460i	0.186944	+	0.323796i
$699$	−11.7126	+	20.2868i	−0.443011	+	0.767318i
$700$	13.5113	+	7.80074i	0.510678	+	0.294840i
$701$	−40.0925			−1.51427			−0.757136	−	0.653258i	$-0.773402\pi$
$701$	−40.0925			−1.51427			−0.757136	+	0.653258i	$0.773402\pi$
$702$		0			0
$703$	17.8519			0.673298
$704$	17.7755	+	10.2627i	0.669941	+	0.386790i
$705$	−0.831773	+	1.44067i	−0.0313264	+	0.0542589i
$706$	−1.12833	−	1.95433i	−0.0424654	−	0.0735523i
$707$		−	9.48593i		−	0.356755i
$708$	21.3818	−	12.3448i	0.803579	−	0.463947i
$709$	−20.1002	+	11.6048i	−0.754877	+	0.435829i	−0.827454	−	0.561534i	$-0.810211\pi$
$709$	−20.1002	+	11.6048i	−0.754877	+	0.435829i	0.0725761	+	0.997363i	$0.476878\pi$
$710$		−	0.628630i		−	0.0235921i
$711$	−2.22737	−	3.85791i	−0.0835327	−	0.144683i
$712$	−0.115957	+	0.200844i	−0.00434567	+	0.00752693i
$713$	38.0763	+	21.9834i	1.42597	+	0.823284i
$714$	2.96615			0.111005
$715$		0			0
$716$	−6.19029			−0.231342
$717$	−12.6453	−	7.30074i	−0.472246	−	0.272651i
$718$	3.71044	−	6.42667i	0.138472	−	0.239841i
$719$	−13.0073	−	22.5293i	−0.485090	−	0.840201i	0.514763	−	0.857333i	$-0.327880\pi$
$719$	−13.0073	−	22.5293i	−0.485090	−	0.840201i	−0.999853	+	0.0171315i	$0.994547\pi$
$720$		−	0.704103i		−	0.0262404i
$721$	20.8838	−	12.0573i	0.777754	−	0.449036i
$722$	−4.68664	+	2.70583i	−0.174419	+	0.100701i
$723$		−	8.63102i		−	0.320991i
$724$	−12.1506	−	21.0455i	−0.451575	−	0.782151i
$725$	14.6664	−	25.4029i	0.544695	−	0.943440i
$726$	8.07607	+	4.66272i	0.299731	+	0.173050i
$727$	16.5472			0.613701			0.306851	−	0.951758i	$-0.400725\pi$
$727$	16.5472			0.613701			0.306851	+	0.951758i	$0.400725\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	0.700305	+	0.404321i	0.0259194	+	0.0149646i
$731$	3.25786	−	5.64279i	0.120496	−	0.208706i
$732$	7.67241	+	13.2890i	0.283580	+	0.491176i
$733$			18.8750i			0.697165i	0.937278	+	0.348582i	$0.113337\pi$
$733$			18.8750i			0.697165i	−0.937278	+	0.348582i	$0.886663\pi$
$734$	−0.454514	+	0.262414i	−0.0167764	+	0.00968586i
$735$	−0.839931	+	0.484935i	−0.0309813	+	0.0178871i
$736$		−	38.8267i		−	1.43117i
$737$	−16.8475	−	29.1807i	−0.620586	−	1.07489i
$738$	0.0990311	−	0.171527i	0.00364539	−	0.00631399i
$739$	40.9837	+	23.6619i	1.50761	+	0.870419i	0.999961	+	0.00885483i	$0.00281862\pi$
$739$	40.9837	+	23.6619i	1.50761	+	0.870419i	0.507649	+	0.861564i	$0.330515\pi$
$740$	−1.42327			−0.0523205
$741$		0			0
$742$	−0.827757			−0.0303879
$743$	7.69697	+	4.44385i	0.282374	+	0.163029i	0.634498	−	0.772925i	$-0.281207\pi$
$743$	7.69697	+	4.44385i	0.282374	+	0.163029i	−0.352124	+	0.935954i	$0.614540\pi$
$744$	4.45742	−	7.72048i	0.163417	−	0.283046i
$745$	1.90030	+	3.29142i	0.0696218	+	0.120588i
$746$		−	13.3924i		−	0.490331i
$747$	−8.82132	+	5.09299i	−0.322755	+	0.186343i
$748$	−33.5381	+	19.3632i	−1.22627	+	0.707990i
$749$			22.4685i			0.820980i
$750$	−0.546229	−	0.946096i	−0.0199455	−	0.0345466i
$751$	0.355404	−	0.615578i	0.0129689	−	0.0224627i	−0.859468	−	0.511189i	$-0.829205\pi$
$751$	0.355404	−	0.615578i	0.0129689	−	0.0224627i	0.872437	+	0.488727i	$0.162538\pi$
$752$	−16.6295	−	9.60106i	−0.606416	−	0.350114i
$753$	3.80194			0.138550
$754$		0			0
$755$	0.907542			0.0330288
$756$	2.73563	+	1.57942i	0.0994939	+	0.0574428i
$757$	−4.89277	+	8.47453i	−0.177831	+	0.308012i	−0.941137	−	0.338025i	$-0.890241\pi$
$757$	−4.89277	+	8.47453i	−0.177831	+	0.308012i	0.763306	+	0.646037i	$0.223575\pi$
$758$	−4.26420	−	7.38581i	−0.154883	−	0.268265i
$759$			47.1715i			1.71222i
$760$	2.02021	−	1.16637i	0.0732806	−	0.0423086i
$761$	16.3514	−	9.44049i	0.592738	−	0.342218i	−0.173441	−	0.984844i	$-0.555489\pi$
$761$	16.3514	−	9.44049i	0.592738	−	0.342218i	0.766180	+	0.642627i	$0.222155\pi$
$762$		−	4.80625i		−	0.174112i
$763$	−10.6468	−	18.4407i	−0.385438	−	0.667599i
$764$	1.17241	−	2.03067i	0.0424162	−	0.0734670i
$765$	0.813199	+	0.469501i	0.0294013	+	0.0169748i
$766$	6.84846			0.247445
$767$		0			0
$768$	2.40150			0.0866567
$769$	10.7689	+	6.21744i	0.388337	+	0.224207i	0.681439	−	0.731875i	$-0.261354\pi$
$769$	10.7689	+	6.21744i	0.388337	+	0.224207i	−0.293102	+	0.956081i	$0.594688\pi$
$770$	0.544605	−	0.943284i	0.0196262	−	0.0339936i
$771$	−10.2981	−	17.8368i	−0.370875	−	0.642375i
$772$			16.5700i			0.596368i
$773$	39.5553	−	22.8373i	1.42271	−	0.821400i	0.426177	−	0.904640i	$-0.359860\pi$
$773$	39.5553	−	22.8373i	1.42271	−	0.821400i	0.996530	+	0.0832399i	$0.0265268\pi$
$774$	−0.660525	+	0.381355i	−0.0237421	+	0.0137075i
$775$			26.0224i			0.934751i
$776$	−11.5816	−	20.0599i	−0.415754	−	0.720107i
$777$	2.80313	−	4.85517i	0.100562	−	0.174178i
$778$	−9.26215	−	5.34750i	−0.332064	−	0.191717i
$779$	−2.48427			−0.0890082
$780$		0			0
$781$	−32.3293			−1.15683
$782$	12.2279	+	7.05980i	0.437270	+	0.252458i
$783$	2.96950	−	5.14333i	0.106121	−	0.183807i
$784$	−5.59754	−	9.69522i	−0.199912	−	0.346258i
$785$			1.20477i			0.0430000i
$786$	0.349783	−	0.201947i	0.0124763	−	0.00720322i
$787$	3.91332	−	2.25936i	0.139495	−	0.0805374i	−0.428628	−	0.903481i	$-0.641003\pi$
$787$	3.91332	−	2.25936i	0.139495	−	0.0805374i	0.568123	+	0.822944i	$0.307670\pi$
$788$			7.41013i			0.263975i
$789$	−0.166366	−	0.288155i	−0.00592280	−	0.0102586i
$790$	−0.244824	+	0.424047i	−0.00871044	+	0.0150869i
$791$	−2.48633	−	1.43548i	−0.0884038	−	0.0510400i
$792$	9.56465			0.339865
$793$		0			0
$794$	13.1739			0.467524
$795$	−0.226938	−	0.131023i	−0.00804865	−	0.00464689i
$796$	−22.3192	+	38.6579i	−0.791082	+	1.37019i
$797$	−14.3696	−	24.8888i	−0.508996	−	0.881607i	−0.999946	−	0.0104193i	$-0.996683\pi$
$797$	−14.3696	−	24.8888i	−0.508996	−	0.881607i	0.490949	−	0.871188i	$-0.336650\pi$
$798$			4.35498i			0.154165i
$799$	22.1773	−	12.8041i	0.784578	−	0.452976i
$800$	19.9014	−	11.4901i	0.703620	−	0.406235i
$801$		−	0.137063i		−	0.00484289i
$802$	4.69591	+	8.13355i	0.165818	+	0.287206i
$803$	20.7935	−	36.0154i	0.733787	−	1.27096i
$804$	−9.30193	−	5.37047i	−0.328054	−	0.189402i
$805$	3.61297			0.127341
$806$		0			0
$807$	27.3032			0.961118
$808$	−7.92920	−	4.57792i	−0.278948	−	0.161051i
$809$	−2.71446	+	4.70158i	−0.0954352	+	0.165299i	−0.909790	−	0.415069i	$-0.863758\pi$
$809$	−2.71446	+	4.70158i	−0.0954352	+	0.165299i	0.814355	+	0.580367i	$0.197091\pi$
$810$	−0.0549581	−	0.0951903i	−0.00193103	−	0.00334465i
$811$			0.629104i			0.0220908i	0.999939	+	0.0110454i	$0.00351593\pi$
$811$			0.629104i			0.0220908i	−0.999939	+	0.0110454i	$0.996484\pi$
$812$	16.2469	−	9.38016i	0.570155	−	0.329179i
$813$	−24.2362	+	13.9928i	−0.850000	+	0.490748i
$814$		−	8.04546i		−	0.281993i
$815$	1.06584	+	1.84609i	0.0373349	+	0.0646659i
$816$	−5.41939	+	9.38665i	−0.189716	+	0.328599i
$817$	8.28489	+	4.78328i	0.289852	+	0.167346i
$818$	16.0315			0.560527
$819$		0			0
$820$	0.198062			0.00691663
$821$	−31.4055	−	18.1320i	−1.09606	−	0.632811i	−0.160877	−	0.986975i	$-0.551432\pi$
$821$	−31.4055	−	18.1320i	−1.09606	−	0.632811i	−0.935183	+	0.354164i	$0.884765\pi$
$822$	2.12469	−	3.68006i	0.0741069	−	0.128357i
$823$	20.8698	+	36.1476i	0.727476	+	1.26002i	0.957947	+	0.286946i	$0.0926399\pi$
$823$	20.8698	+	36.1476i	0.727476	+	1.26002i	−0.230471	+	0.973079i	$0.574027\pi$
$824$		−	23.2755i		−	0.810839i
$825$	−24.1787	+	13.9596i	−0.841794	+	0.486010i
$826$	9.25749	−	5.34481i	0.322109	−	0.185970i
$827$		−	38.1997i		−	1.32833i	−0.747584	−	0.664167i	$-0.768786\pi$
$827$		−	38.1997i		−	1.32833i	0.747584	−	0.664167i	$-0.231214\pi$
$828$	7.51842	+	13.0223i	0.261283	+	0.452556i
$829$	7.98941	−	13.8381i	0.277484	−	0.480616i	−0.693275	−	0.720673i	$-0.743833\pi$
$829$	7.98941	−	13.8381i	0.277484	−	0.480616i	0.970759	+	0.240057i	$0.0771662\pi$
$830$	0.969606	+	0.559802i	0.0336555	+	0.0194310i
$831$	2.10321			0.0729596
$832$		0			0
$833$	14.9299			0.517290
$834$	1.57731	+	0.910658i	0.0546176	+	0.0315335i
$835$	1.16942	−	2.02550i	0.0404696	−	0.0700953i
$836$	−28.4296	−	49.2415i	−0.983259	−	1.70305i
$837$			5.26875i			0.182115i
$838$	2.30038	−	1.32813i	0.0794653	−	0.0458793i
$839$	4.01731	−	2.31940i	0.138693	−	0.0800744i	−0.429048	−	0.903282i	$-0.641151\pi$
$839$	4.01731	−	2.31940i	0.138693	−	0.0800744i	0.567741	+	0.823207i	$0.307818\pi$
$840$		−	0.732578i		−	0.0252763i
$841$	−3.13587	−	5.43148i	−0.108133	−	0.187292i
$842$	−0.466280	+	0.807620i	−0.0160691	+	0.0278324i
$843$	23.5861	+	13.6174i	0.812349	+	0.469010i
$844$	−10.7017			−0.368368
$845$		0			0
$846$	−2.99761			−0.103060
$847$	−31.8116	−	18.3665i	−1.09306	−	0.631079i
$848$	1.51238	−	2.61951i	0.0519352	−	0.0899545i
$849$	2.64191	+	4.57592i	0.0906700	+	0.157045i
$850$			8.35690i			0.286639i
$851$	23.1118	−	13.3436i	0.792263	−	0.457413i
$852$	−8.92490	+	5.15279i	−0.305762	+	0.176532i
$853$		−	18.3884i		−	0.629605i	−0.949157	−	0.314803i	$-0.898062\pi$
$853$		−	18.3884i		−	0.629605i	0.949157	−	0.314803i	$-0.101938\pi$
$854$	3.32185	+	5.75361i	0.113671	+	0.196884i
$855$	−0.689333	+	1.19396i	−0.0235747	+	0.0408326i
$856$	18.7812	+	10.8433i	0.641928	+	0.370617i
$857$	−28.1849			−0.962778			−0.481389	−	0.876507i	$-0.659868\pi$
$857$	−28.1849			−0.962778			−0.481389	+	0.876507i	$0.659868\pi$
$858$		0			0
$859$	33.3957			1.13944			0.569722	−	0.821837i	$-0.307051\pi$
$859$	33.3957			1.13944			0.569722	+	0.821837i	$0.307051\pi$
$860$	−0.660525	−	0.381355i	−0.0225237	−	0.0130041i
$861$	−0.390084	+	0.675645i	−0.0132940	+	0.0230259i
$862$	−0.642145	−	1.11223i	−0.0218715	−	0.0378826i
$863$		−	43.0640i		−	1.46592i	−0.680274	−	0.732958i	$-0.738139\pi$
$863$		−	43.0640i		−	1.46592i	0.680274	−	0.732958i	$-0.261861\pi$
$864$	4.02944	−	2.32640i	0.137084	−	0.0791456i
$865$	1.02128	−	0.589638i	0.0347247	−	0.0200483i
$866$			5.62910i			0.191285i
$867$	1.27263	+	2.20427i	0.0432209	+	0.0748609i
$868$	−8.32155	+	14.4134i	−0.282452	+	0.489221i
$869$	21.8080	+	12.5908i	0.739785	+	0.427115i
$870$	−0.652793			−0.0221317
$871$		0			0
$872$	−20.5526			−0.695998
$873$	11.8556	+	6.84481i	0.401250	+	0.231662i
$874$	−10.3654	+	17.9534i	−0.350614	+	0.607282i
$875$	2.15160	+	3.72667i	0.0727372	+	0.125985i
$876$		−	13.2567i		−	0.447901i
$877$	−26.1281	+	15.0851i	−0.882285	+	0.509387i	−0.871411	−	0.490554i	$-0.836795\pi$
$877$	−26.1281	+	15.0851i	−0.882285	+	0.509387i	−0.0108736	+	0.999941i	$0.503461\pi$
$878$	4.21143	−	2.43147i	0.142129	−	0.0820581i
$879$		−	32.6625i		−	1.10168i
$880$	1.99007	+	3.44691i	0.0670854	+	0.116195i
$881$	−1.78136	+	3.08541i	−0.0600157	+	0.103950i	−0.894472	−	0.447124i	$-0.852448\pi$
$881$	−1.78136	+	3.08541i	−0.0600157	+	0.103950i	0.834456	+	0.551074i	$0.185782\pi$
$882$	−1.51350	−	0.873822i	−0.0509623	−	0.0294231i
$883$	10.2088			0.343554			0.171777	−	0.985136i	$-0.445049\pi$
$883$	10.2088			0.343554			0.171777	+	0.985136i	$0.445049\pi$
$884$		0			0
$885$	3.38404			0.113753
$886$	7.41554	+	4.28136i	0.249130	+	0.143835i
$887$	4.66823	−	8.08561i	0.156744	−	0.271488i	−0.776949	−	0.629564i	$-0.783234\pi$
$887$	4.66823	−	8.08561i	0.156744	−	0.271488i	0.933693	+	0.358076i	$0.116567\pi$
$888$	−2.70560	−	4.68623i	−0.0907938	−	0.157260i
$889$			18.9318i			0.634953i
$890$	−0.0130471	+	0.00753275i	−0.000437340	+	0.000252498i
$891$	−4.89546	+	2.82640i	−0.164004	+	0.0946878i
$892$			25.5894i			0.856797i
$893$	18.7993	+	32.5614i	0.629095	+	1.08962i
$894$	−3.42423	+	5.93094i	−0.114523	+	0.198360i
$895$	−0.734790	−	0.424231i	−0.0245613	−	0.0141805i
$896$	19.1457			0.639613
$897$		0			0
$898$	−12.8261			−0.428013
$899$	27.0989	+	15.6456i	0.903799	+	0.521808i
$900$	−4.44989	+	7.70743i	−0.148330	+	0.256914i
$901$	2.01693	+	3.49342i	0.0671935	+	0.116383i
$902$			1.11960i			0.0372788i
$903$	2.60181	−	1.50216i	0.0865828	−	0.0499886i
$904$	−2.39982	+	1.38553i	−0.0798167	+	0.0460822i
$905$		−	3.33081i		−	0.110720i
$906$	0.817667	+	1.41624i	0.0271652	+	0.0470515i
$907$	−20.5402	+	35.5766i	−0.682026	+	1.18130i	0.292336	+	0.956316i	$0.405567\pi$
$907$	−20.5402	+	35.5766i	−0.682026	+	1.18130i	−0.974362	+	0.224988i	$0.927766\pi$
$908$	−24.9798	−	14.4221i	−0.828983	−	0.478613i
$909$	5.41119			0.179478
$910$		0			0
$911$	−18.9705			−0.628519			−0.314260	−	0.949337i	$-0.601756\pi$
$911$	−18.9705			−0.628519			−0.314260	+	0.949337i	$0.601756\pi$
$912$	−13.7817	−	7.95689i	−0.456359	−	0.263479i
$913$	28.7896	−	49.8651i	0.952797	−	1.65029i
$914$	−4.02111	−	6.96476i	−0.133006	−	0.230374i
$915$			2.10321i			0.0695300i
$916$	−2.87318	+	1.65883i	−0.0949327	+	0.0548094i
$917$	−1.37779	+	0.795470i	−0.0454988	+	0.0262687i
$918$			1.69202i			0.0558450i
$919$	−14.5010	−	25.1164i	−0.478343	−	0.828514i	0.521349	−	0.853343i	$-0.325429\pi$
$919$	−14.5010	−	25.1164i	−0.478343	−	0.828514i	−0.999692	+	0.0248299i	$0.992096\pi$
$920$	1.74363	−	3.02005i	0.0574857	−	0.0995681i
$921$	−17.9799	−	10.3807i	−0.592457	−	0.342055i
$922$	3.36791			0.110916
$923$		0			0
$924$	−17.8562			−0.587427
$925$	13.6791	+	7.89762i	0.449765	+	0.259672i
$926$	−7.86725	+	13.6265i	−0.258534	+	0.447794i
$927$	6.87800	+	11.9130i	0.225903	+	0.391276i
$928$		−	27.6329i		−	0.907096i
$929$	−43.9258	+	25.3605i	−1.44116	+	0.832052i	−0.997927	−	0.0643554i	$-0.979501\pi$
$929$	−43.9258	+	25.3605i	−1.44116	+	0.832052i	−0.443230	+	0.896408i	$0.646168\pi$
$930$	0.501534	−	0.289561i	0.0164459	−	0.00949507i
$931$			21.9205i			0.718415i
$932$	−21.1054	−	36.5556i	−0.691329	−	1.19742i
$933$	−5.65064	+	9.78719i	−0.184994	+	0.320418i
$934$	5.01043	+	2.89277i	0.163946	+	0.0946544i
$935$	−5.30798			−0.173589
$936$		0			0
$937$	51.3051			1.67606			0.838032	−	0.545620i	$-0.183706\pi$
$937$	51.3051			1.67606			0.838032	+	0.545620i	$0.183706\pi$
$938$	−4.02736	−	2.32520i	−0.131498	−	0.0759205i
$939$	2.13587	−	3.69943i	0.0697014	−	0.120726i
$940$	−1.49880	−	2.59600i	−0.0488856	−	0.0846723i
$941$		−	34.7036i		−	1.13131i	−0.824643	−	0.565653i	$-0.808624\pi$
$941$		−	34.7036i		−	1.13131i	0.824643	−	0.565653i	$-0.191376\pi$
$942$	−1.88007	+	1.08546i	−0.0612559	+	0.0353661i
$943$	−3.21624	+	1.85690i	−0.104735	+	0.0604688i
$944$			39.0616i			1.27135i
$945$	0.216480	+	0.374955i	0.00704210	+	0.0121973i
$946$	2.15572	−	3.73381i	0.0700884	−	0.121397i
$947$	−11.2693	−	6.50634i	−0.366203	−	0.211428i	0.305595	−	0.952162i	$-0.401145\pi$
$947$	−11.2693	−	6.50634i	−0.366203	−	0.211428i	−0.671798	+	0.740734i	$0.734478\pi$
$948$	8.02715			0.260710
$949$		0			0
$950$	−12.2698			−0.398085
$951$	−13.4040	−	7.73878i	−0.434653	−	0.250947i
$952$	−5.63856	+	9.76626i	−0.182747	+	0.316526i
$953$	13.0075	+	22.5297i	0.421355	+	0.729809i	0.996072	−	0.0885434i	$-0.0282212\pi$
$953$	13.0075	+	22.5297i	0.421355	+	0.729809i	−0.574717	+	0.818352i	$0.694888\pi$
$954$		−	0.472189i		−	0.0152877i
$955$	0.278330	−	0.160694i	0.00900656	−	0.00519994i
$956$	22.7860	−	13.1555i	0.736951	−	0.425479i
$957$			33.5719i			1.08523i
$958$	5.68018	+	9.83835i	0.183518	+	0.317863i
$959$	−8.36914	+	14.4958i	−0.270254	+	0.468093i
$960$	0.776642	+	0.448394i	0.0250660	+	0.0144719i
$961$	3.24027			0.104525
$962$		0			0
$963$	−12.8170			−0.413022
$964$	13.4689	+	7.77628i	0.433805	+	0.250457i
$965$	−1.13557	+	1.96687i	−0.0365553	+	0.0633157i
$966$	3.25518	+	5.63813i	0.104734	+	0.181404i
$967$			36.6644i			1.17905i	0.807751	+	0.589524i	$0.200685\pi$
$967$			36.6644i			1.17905i	−0.807751	+	0.589524i	$0.799315\pi$
$968$	−30.7047	+	17.7274i	−0.986886	+	0.569779i
$969$	18.3795	−	10.6114i	0.590435	−	0.340888i
$970$		−	1.50471i		−	0.0483134i
$971$	18.9233	+	32.7761i	0.607277	+	1.05183i	0.991687	+	0.128672i	$0.0410714\pi$
$971$	18.9233	+	32.7761i	0.607277	+	1.05183i	−0.384411	+	0.923162i	$0.625595\pi$
$972$	−0.900969	+	1.56052i	−0.0288986	+	0.0500538i
$973$	−6.21301	−	3.58708i	−0.199180	−	0.114997i
$974$	−7.12392			−0.228265
$975$		0			0
$976$	−24.2771			−0.777091
$977$	−25.0279	−	14.4499i	−0.800715	−	0.462293i	0.0430063	−	0.999075i	$-0.486306\pi$
$977$	−25.0279	−	14.4499i	−0.800715	−	0.462293i	−0.843721	+	0.536782i	$0.819640\pi$
$978$	−1.92058	+	3.32655i	−0.0614135	+	0.106371i
$979$	0.387395	+	0.670988i	0.0123812	+	0.0214449i
$980$		−	1.74764i		−	0.0558264i
$981$	10.5194	−	6.07338i	0.335858	−	0.193908i
$982$	−7.99300	+	4.61476i	−0.255067	+	0.147263i
$983$			19.3991i			0.618735i	0.950942	+	0.309368i	$0.100117\pi$
$983$			19.3991i			0.618735i	−0.950942	+	0.309368i	$0.899883\pi$
$984$	0.376510	+	0.652135i	0.0120027	+	0.0207893i
$985$	−0.507828	+	0.879584i	−0.0161808	+	0.0280259i
$986$	8.70262	+	5.02446i	0.277148	+	0.160011i
$987$	11.8076			0.375839
$988$		0			0
$989$	14.3013			0.454754
$990$	0.538091	+	0.310667i	0.0171017	+	0.00987364i
$991$	2.59150	−	4.48861i	0.0823217	−	0.142585i	−0.821925	−	0.569596i	$-0.807100\pi$
$991$	2.59150	−	4.48861i	0.0823217	−	0.142585i	0.904247	+	0.427010i	$0.140433\pi$
$992$	12.2572	+	21.2301i	0.389167	+	0.674056i
$993$			6.06829i			0.192572i
$994$	−3.86413	+	2.23095i	−0.122563	+	0.0707616i
$995$	−5.29858	+	3.05914i	−0.167976	+	0.0969812i
$996$		−	18.3545i		−	0.581585i
$997$	24.6821	+	42.7506i	0.781690	+	1.35393i	0.930957	+	0.365130i	$0.118975\pi$
$997$	24.6821	+	42.7506i	0.781690	+	1.35393i	−0.149267	+	0.988797i	$0.547691\pi$
$998$	−1.79523	+	3.10943i	−0.0568271	+	0.0984274i
$999$	2.76960	+	1.59903i	0.0876264	+	0.0505911i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.j.h.316.3		12
13.2	odd	12		507.2.e.j.484.2		6
13.3	even	3	inner	507.2.j.h.361.4		12
13.4	even	6		507.2.b.g.337.3		6
13.5	odd	4		507.2.e.j.22.2		6
13.6	odd	12		507.2.a.k.1.2	yes	3
13.7	odd	12		507.2.a.j.1.2	✓	3
13.8	odd	4		507.2.e.k.22.2		6
13.9	even	3		507.2.b.g.337.4		6
13.10	even	6	inner	507.2.j.h.361.3		12
13.11	odd	12		507.2.e.k.484.2		6
13.12	even	2	inner	507.2.j.h.316.4		12
39.17	odd	6		1521.2.b.m.1351.4		6
39.20	even	12		1521.2.a.q.1.2		3
39.32	even	12		1521.2.a.p.1.2		3
39.35	odd	6		1521.2.b.m.1351.3		6
52.7	even	12		8112.2.a.by.1.3		3
52.19	even	12		8112.2.a.cf.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.a.j.1.2	✓	3	13.7	odd	12
507.2.a.k.1.2	yes	3	13.6	odd	12
507.2.b.g.337.3		6	13.4	even	6
507.2.b.g.337.4		6	13.9	even	3
507.2.e.j.22.2		6	13.5	odd	4
507.2.e.j.484.2		6	13.2	odd	12
507.2.e.k.22.2		6	13.8	odd	4
507.2.e.k.484.2		6	13.11	odd	12
507.2.j.h.316.3		12	1.1	even	1	trivial
507.2.j.h.316.4		12	13.12	even	2	inner
507.2.j.h.361.3		12	13.10	even	6	inner
507.2.j.h.361.4		12	13.3	even	3	inner
1521.2.a.p.1.2		3	39.32	even	12
1521.2.a.q.1.2		3	39.20	even	12
1521.2.b.m.1351.3		6	39.35	odd	6
1521.2.b.m.1351.4		6	39.17	odd	6
8112.2.a.by.1.3		3	52.7	even	12
8112.2.a.cf.1.1		3	52.19	even	12

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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.j (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.385418 - 0.222521i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.900969 - 1.56052i) q^{4} -0.246980i q^{5} +(0.385418 - 0.222521i) q^{6} +(-1.51816 + 0.876510i) q^{7} +1.69202i q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.385418 - 0.222521i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.900969 - 1.56052i) q^{4} -0.246980i q^{5} +(0.385418 - 0.222521i) q^{6} +(-1.51816 + 0.876510i) q^{7} +1.69202i q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.0549581 + 0.0951903i) q^{10} +(4.89546 + 2.82640i) q^{11} +1.80194 q^{12} +0.780167 q^{14} +(0.213891 + 0.123490i) q^{15} +(-1.42543 + 2.46891i) q^{16} +(-1.90097 - 3.29257i) q^{17} +0.445042i q^{18} +(4.83424 - 2.79105i) q^{19} +(-0.385418 + 0.222521i) q^{20} -1.75302i q^{21} +(-1.25786 - 2.17869i) q^{22} +(4.17241 - 7.22682i) q^{23} +(-1.46533 - 0.846011i) q^{24} +4.93900 q^{25} +1.00000 q^{27} +(2.73563 + 1.57942i) q^{28} +(2.96950 - 5.14333i) q^{29} +(-0.0549581 - 0.0951903i) q^{30} +5.26875i q^{31} +(4.02944 - 2.32640i) q^{32} +(-4.89546 + 2.82640i) q^{33} +1.69202i q^{34} +(0.216480 + 0.374955i) q^{35} +(-0.900969 + 1.56052i) q^{36} +(2.76960 + 1.59903i) q^{37} -2.48427 q^{38} +0.417895 q^{40} +(-0.385418 - 0.222521i) q^{41} +(-0.390084 + 0.675645i) q^{42} +(0.856896 + 1.48419i) q^{43} -10.1860i q^{44} +(-0.213891 + 0.123490i) q^{45} +(-3.21624 + 1.85690i) q^{46} +6.73556i q^{47} +(-1.42543 - 2.46891i) q^{48} +(-1.96346 + 3.40081i) q^{49} +(-1.90358 - 1.09903i) q^{50} +3.80194 q^{51} -1.06100 q^{53} +(-0.385418 - 0.222521i) q^{54} +(0.698062 - 1.20908i) q^{55} +(-1.48307 - 2.56876i) q^{56} +5.58211i q^{57} +(-2.28900 + 1.32155i) q^{58} +(11.8660 - 6.85086i) q^{59} -0.445042i q^{60} +(4.25786 + 7.37484i) q^{61} +(1.17241 - 2.03067i) q^{62} +(1.51816 + 0.876510i) q^{63} +3.63102 q^{64} +2.51573 q^{66} +(-5.16218 - 2.98039i) q^{67} +(-3.42543 + 5.93301i) q^{68} +(4.17241 + 7.22682i) q^{69} -0.192685i q^{70} +(-4.95295 + 2.85958i) q^{71} +(1.46533 - 0.846011i) q^{72} -7.35690i q^{73} +(-0.711636 - 1.23259i) q^{74} +(-2.46950 + 4.27730i) q^{75} +(-8.71101 - 5.02930i) q^{76} -9.90946 q^{77} +4.45473 q^{79} +(0.609771 + 0.352052i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(0.0990311 + 0.171527i) q^{82} -10.1860i q^{83} +(-2.73563 + 1.57942i) q^{84} +(-0.813199 + 0.469501i) q^{85} -0.762709i q^{86} +(2.96950 + 5.14333i) q^{87} +(-4.78232 + 8.28323i) q^{88} +(0.118700 + 0.0685317i) q^{89} +0.109916 q^{90} -15.0368 q^{92} +(-4.56287 - 2.63437i) q^{93} +(1.49880 - 2.59600i) q^{94} +(-0.689333 - 1.19396i) q^{95} +4.65279i q^{96} +(-11.8556 + 6.84481i) q^{97} +(1.51350 - 0.873822i) q^{98} -5.65279i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9	\( 12 q - 6 q^{3} - 2 q^{4} - 6 q^{9} - 2 q^{10} + 4 q^{12} + 4 q^{14} + 10 q^{16} - 14 q^{17} + 10 q^{22} + 4 q^{23} + 20 q^{25} + 12 q^{27} + 16 q^{29} - 2 q^{30} - 36 q^{35} - 2 q^{36} - 80 q^{38} + 28 q^{40} - 2 q^{42} - 6 q^{43} + 10 q^{48} + 34 q^{49} + 28 q^{51} - 52 q^{53} + 26 q^{55} + 14 q^{56} + 26 q^{61} - 32 q^{62} - 16 q^{64} - 20 q^{66} - 14 q^{68} + 4 q^{69} - 14 q^{74} - 10 q^{75} + 60 q^{77} - 36 q^{79} - 6 q^{81} + 10 q^{82} + 16 q^{87} - 14 q^{88} + 4 q^{90} - 68 q^{92} - 64 q^{94} + 6 q^{95}+O(q^{100}) \) 12 * q - 6 * q^3 - 2 * q^4 - 6 * q^9 - 2 * q^10 + 4 * q^12 + 4 * q^14 + 10 * q^16 - 14 * q^17 + 10 * q^22 + 4 * q^23 + 20 * q^25 + 12 * q^27 + 16 * q^29 - 2 * q^30 - 36 * q^35 - 2 * q^36 - 80 * q^38 + 28 * q^40 - 2 * q^42 - 6 * q^43 + 10 * q^48 + 34 * q^49 + 28 * q^51 - 52 * q^53 + 26 * q^55 + 14 * q^56 + 26 * q^61 - 32 * q^62 - 16 * q^64 - 20 * q^66 - 14 * q^68 + 4 * q^69 - 14 * q^74 - 10 * q^75 + 60 * q^77 - 36 * q^79 - 6 * q^81 + 10 * q^82 + 16 * q^87 - 14 * q^88 + 4 * q^90 - 68 * q^92 - 64 * q^94 + 6 * q^95

Introduction

L-functions

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