LMFDB - Embedded newform 546.2.k.b.445.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (of order $3$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.447703281.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} - 2x^{6} + 2x^{5} + 3x^{4} + 4x^{3} - 8x^{2} - 8x + 16 $ x^8 - x^7 - 2x^6 + 2x^5 + 3x^4 + 4x^3 - 8x^2 - 8x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			445.1
Root			$1.26359 + 0.635098i$ of defining polynomial
Character	$\chi$	$=$	546.445
Dual form			546.2.k.b.373.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97513 - 3.42102i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.48662 + 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97513 - 3.42102i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.48662 + 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.95025 q^{10} +4.91377 q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.39335 - 1.21869i) q^{13} +(-1.15207 - 2.38175i) q^{14} +(1.97513 + 3.42102i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0702857 - 0.121738i) q^{17} +(-0.500000 + 0.866025i) q^{18} -0.776963 q^{19} +(-1.97513 + 3.42102i) q^{20} +(1.48662 - 2.18860i) q^{21} +(-2.45689 + 4.25545i) q^{22} +(-4.76845 + 8.25920i) q^{23} -1.00000 q^{24} +(-5.30226 + 9.18378i) q^{25} +(2.75209 - 2.32938i) q^{26} -1.00000 q^{27} +(2.63869 + 0.193156i) q^{28} +(-0.629759 - 1.09077i) q^{29} -3.95025 q^{30} +(-1.67992 + 2.90971i) q^{31} +(-0.500000 - 0.866025i) q^{32} -4.91377 q^{33} +0.140571 q^{34} +(10.4235 + 0.763015i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.56841 + 9.64476i) q^{37} +(0.388481 - 0.672870i) q^{38} +(3.39335 + 1.21869i) q^{39} +(-1.97513 - 3.42102i) q^{40} +(4.65505 + 8.06279i) q^{41} +(1.15207 + 2.38175i) q^{42} +(-0.541233 + 0.937443i) q^{43} +(-2.45689 - 4.25545i) q^{44} +(-1.97513 - 3.42102i) q^{45} +(-4.76845 - 8.25920i) q^{46} +(3.33199 + 5.77118i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.57990 - 6.50724i) q^{49} +(-5.30226 - 9.18378i) q^{50} +(0.0702857 + 0.121738i) q^{51} +(0.641255 + 3.54807i) q^{52} +(5.53204 - 9.58177i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-9.70533 - 16.8101i) q^{55} +(-1.48662 + 2.18860i) q^{56} +0.776963 q^{57} +1.25952 q^{58} +(-0.215609 - 0.373446i) q^{59} +(1.97513 - 3.42102i) q^{60} -8.28114 q^{61} +(-1.67992 - 2.90971i) q^{62} +(-1.48662 + 2.18860i) q^{63} +1.00000 q^{64} +(2.53312 + 14.0158i) q^{65} +(2.45689 - 4.25545i) q^{66} +8.19628 q^{67} +(-0.0702857 + 0.121738i) q^{68} +(4.76845 - 8.25920i) q^{69} +(-5.87254 + 8.64551i) q^{70} +(1.93865 - 3.35783i) q^{71} +1.00000 q^{72} +(-0.0817820 + 0.141650i) q^{73} +(-5.56841 - 9.64476i) q^{74} +(5.30226 - 9.18378i) q^{75} +(0.388481 + 0.672870i) q^{76} +(-7.30493 + 10.7543i) q^{77} +(-2.75209 + 2.32938i) q^{78} +(2.17517 + 3.76751i) q^{79} +3.95025 q^{80} +1.00000 q^{81} -9.31010 q^{82} -10.5220 q^{83} +(-2.63869 - 0.193156i) q^{84} +(-0.277647 + 0.480898i) q^{85} +(-0.541233 - 0.937443i) q^{86} +(0.629759 + 1.09077i) q^{87} +4.91377 q^{88} +(0.536369 - 0.929018i) q^{89} +3.95025 q^{90} +(7.71185 - 5.61493i) q^{91} +9.53690 q^{92} +(1.67992 - 2.90971i) q^{93} -6.66398 q^{94} +(1.53460 + 2.65801i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-6.54097 + 11.3293i) q^{97} +(6.92538 + 1.01936i) q^{98} +4.91377 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} - 10 q^{23} - 8 q^{24} - 18 q^{25} + 10 q^{26} - 8 q^{27} + 2 q^{29} + 4 q^{30} + 6 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{34} + 18 q^{35} - 4 q^{36} - 28 q^{37} + 6 q^{38} + 11 q^{39} + 2 q^{40} + 3 q^{42} - 6 q^{43} - 6 q^{44} + 2 q^{45} - 10 q^{46} + q^{47} + 4 q^{48} - 7 q^{49} - 18 q^{50} - 4 q^{51} + q^{52} + 7 q^{53} + 4 q^{54} + q^{55} + 3 q^{56} + 12 q^{57} - 4 q^{58} + 2 q^{59} - 2 q^{60} - 48 q^{61} + 6 q^{62} + 3 q^{63} + 8 q^{64} + 19 q^{65} + 6 q^{66} + 30 q^{67} + 4 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} + 8 q^{72} + q^{73} - 28 q^{74} + 18 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} - 4 q^{80} + 8 q^{81} - 32 q^{83} - 13 q^{85} - 6 q^{86} - 2 q^{87} + 12 q^{88} + 25 q^{89} - 4 q^{90} + 34 q^{91} + 20 q^{92} - 6 q^{93} - 2 q^{94} - 8 q^{95} + 4 q^{96} - q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 12 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 - 10 * q^23 - 8 * q^24 - 18 * q^25 + 10 * q^26 - 8 * q^27 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^34 + 18 * q^35 - 4 * q^36 - 28 * q^37 + 6 * q^38 + 11 * q^39 + 2 * q^40 + 3 * q^42 - 6 * q^43 - 6 * q^44 + 2 * q^45 - 10 * q^46 + q^47 + 4 * q^48 - 7 * q^49 - 18 * q^50 - 4 * q^51 + q^52 + 7 * q^53 + 4 * q^54 + q^55 + 3 * q^56 + 12 * q^57 - 4 * q^58 + 2 * q^59 - 2 * q^60 - 48 * q^61 + 6 * q^62 + 3 * q^63 + 8 * q^64 + 19 * q^65 + 6 * q^66 + 30 * q^67 + 4 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 + 8 * q^72 + q^73 - 28 * q^74 + 18 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 - 4 * q^80 + 8 * q^81 - 32 * q^83 - 13 * q^85 - 6 * q^86 - 2 * q^87 + 12 * q^88 + 25 * q^89 - 4 * q^90 + 34 * q^91 + 20 * q^92 - 6 * q^93 - 2 * q^94 - 8 * q^95 + 4 * q^96 - q^97 + 2 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.97513	−	3.42102i	−0.883304	−	1.52993i	−0.847646	−	0.530563i	$-0.821981\pi$
$5$	−1.97513	−	3.42102i	−0.883304	−	1.52993i	−0.0356582	−	0.999364i	$-0.511353\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	−1.48662	+	2.18860i	−0.561891	+	0.827211i
$7$	−1.48662	+	2.18860i	−0.561891	+	0.827211i
$8$	1.00000			0.353553
$9$	1.00000			0.333333
$10$	3.95025			1.24918
$11$	4.91377			1.48156			0.740779	−	0.671749i	$-0.234456\pi$
$11$	4.91377			1.48156			0.740779	+	0.671749i	$0.234456\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−3.39335	−	1.21869i	−0.941145	−	0.338004i
$13$	−3.39335	−	1.21869i	−0.941145	−	0.338004i
$14$	−1.15207	−	2.38175i	−0.307903	−	0.636550i
$15$	1.97513	+	3.42102i	0.509976	+	0.883304i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−0.0702857	−	0.121738i	−0.0170468	−	0.0295259i	0.857376	−	0.514690i	$-0.172093\pi$
$17$	−0.0702857	−	0.121738i	−0.0170468	−	0.0295259i	−0.874423	+	0.485164i	$0.838760\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.776963			−0.178248			−0.0891238	−	0.996021i	$-0.528407\pi$
$19$	−0.776963			−0.178248			−0.0891238	+	0.996021i	$0.528407\pi$
$20$	−1.97513	+	3.42102i	−0.441652	+	0.764963i
$21$	1.48662	−	2.18860i	0.324408	−	0.477591i
$22$	−2.45689	+	4.25545i	−0.523810	+	0.907266i
$23$	−4.76845	+	8.25920i	−0.994291	+	1.72216i	−0.404735	+	0.914434i	$0.632636\pi$
$23$	−4.76845	+	8.25920i	−0.994291	+	1.72216i	−0.589556	+	0.807728i	$0.700697\pi$
$24$	−1.00000			−0.204124
$25$	−5.30226	+	9.18378i	−1.06045	+	1.83676i
$26$	2.75209	−	2.32938i	0.539729	−	0.456829i
$27$	−1.00000			−0.192450
$28$	2.63869	+	0.193156i	0.498666	+	0.0365030i
$29$	−0.629759	−	1.09077i	−0.116943	−	0.202552i	0.801612	−	0.597845i	$-0.203976\pi$
$29$	−0.629759	−	1.09077i	−0.116943	−	0.202552i	−0.918555	+	0.395293i	$0.870643\pi$
$30$	−3.95025			−0.721214
$31$	−1.67992	+	2.90971i	−0.301723	+	0.522600i	−0.976526	−	0.215398i	$-0.930895\pi$
$31$	−1.67992	+	2.90971i	−0.301723	+	0.522600i	0.674803	+	0.737998i	$0.264229\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−4.91377			−0.855378
$34$	0.140571			0.0241078
$35$	10.4235	+	0.763015i	1.76189	+	0.128973i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.56841	+	9.64476i	−0.915440	+	1.58559i	−0.109185	+	0.994021i	$0.534824\pi$
$37$	−5.56841	+	9.64476i	−0.915440	+	1.58559i	−0.806256	+	0.591567i	$0.798509\pi$
$38$	0.388481	−	0.672870i	0.0630200	−	0.109154i
$39$	3.39335	+	1.21869i	0.543370	+	0.195147i
$40$	−1.97513	−	3.42102i	−0.312295	−	0.540911i
$41$	4.65505	+	8.06279i	0.726997	+	1.25920i	0.958147	+	0.286277i	$0.0924179\pi$
$41$	4.65505	+	8.06279i	0.726997	+	1.25920i	−0.231150	+	0.972918i	$0.574249\pi$
$42$	1.15207	+	2.38175i	0.177768	+	0.367512i
$43$	−0.541233	+	0.937443i	−0.0825372	+	0.142959i	−0.904339	−	0.426815i	$-0.859636\pi$
$43$	−0.541233	+	0.937443i	−0.0825372	+	0.142959i	0.821802	+	0.569773i	$0.192969\pi$
$44$	−2.45689	−	4.25545i	−0.370390	−	0.641534i
$45$	−1.97513	−	3.42102i	−0.294435	−	0.509976i
$46$	−4.76845	−	8.25920i	−0.703070	−	1.21775i
$47$	3.33199	+	5.77118i	0.486021	+	0.841813i	0.999871	−	0.0160671i	$-0.00511454\pi$
$47$	3.33199	+	5.77118i	0.486021	+	0.841813i	−0.513850	+	0.857880i	$0.671781\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−2.57990	−	6.50724i	−0.368557	−	0.929605i
$50$	−5.30226	−	9.18378i	−0.749852	−	1.29878i
$51$	0.0702857	+	0.121738i	0.00984197	+	0.0170468i
$52$	0.641255	+	3.54807i	0.0889261	+	0.492029i
$53$	5.53204	−	9.58177i	0.759884	−	1.31616i	−0.183026	−	0.983108i	$-0.558589\pi$
$53$	5.53204	−	9.58177i	0.759884	−	1.31616i	0.942910	−	0.333049i	$-0.108077\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−9.70533	−	16.8101i	−1.30867	−	2.26668i
$56$	−1.48662	+	2.18860i	−0.198658	+	0.292463i
$57$	0.776963			0.102911
$58$	1.25952			0.165383
$59$	−0.215609	−	0.373446i	−0.0280699	−	0.0486185i	0.851649	−	0.524112i	$-0.175603\pi$
$59$	−0.215609	−	0.373446i	−0.0280699	−	0.0486185i	−0.879719	+	0.475494i	$0.842269\pi$
$60$	1.97513	−	3.42102i	0.254988	−	0.441652i
$61$	−8.28114			−1.06029			−0.530146	−	0.847906i	$-0.677863\pi$
$61$	−8.28114			−1.06029			−0.530146	+	0.847906i	$0.677863\pi$
$62$	−1.67992	−	2.90971i	−0.213351	−	0.369534i
$63$	−1.48662	+	2.18860i	−0.187297	+	0.275737i
$64$	1.00000			0.125000
$65$	2.53312	+	14.0158i	0.314195	+	1.73844i
$66$	2.45689	−	4.25545i	0.302422	−	0.523810i
$67$	8.19628			1.00134			0.500668	−	0.865640i	$-0.333088\pi$
$67$	8.19628			1.00134			0.500668	+	0.865640i	$0.333088\pi$
$68$	−0.0702857	+	0.121738i	−0.00852340	+	0.0147630i
$69$	4.76845	−	8.25920i	0.574054	−	0.994291i
$70$	−5.87254	+	8.64551i	−0.701903	+	1.03334i
$71$	1.93865	−	3.35783i	0.230075	−	0.398502i	−0.727755	−	0.685837i	$-0.759436\pi$
$71$	1.93865	−	3.35783i	0.230075	−	0.398502i	0.957830	+	0.287336i	$0.0927695\pi$
$72$	1.00000			0.117851
$73$	−0.0817820	+	0.141650i	−0.00957185	+	0.0165789i	−0.870772	−	0.491688i	$-0.836380\pi$
$73$	−0.0817820	+	0.141650i	−0.00957185	+	0.0165789i	0.861200	+	0.508267i	$0.169714\pi$
$74$	−5.56841	−	9.64476i	−0.647314	−	1.12118i
$75$	5.30226	−	9.18378i	0.612252	−	1.06045i
$76$	0.388481	+	0.672870i	0.0445619	+	0.0771834i
$77$	−7.30493	+	10.7543i	−0.832474	+	1.22556i
$78$	−2.75209	+	2.32938i	−0.311613	+	0.263750i
$79$	2.17517	+	3.76751i	0.244726	+	0.423878i	0.962055	−	0.272857i	$-0.0879687\pi$
$79$	2.17517	+	3.76751i	0.244726	+	0.423878i	−0.717329	+	0.696735i	$0.754635\pi$
$80$	3.95025			0.441652
$81$	1.00000			0.111111
$82$	−9.31010			−1.02813
$83$	−10.5220			−1.15494			−0.577472	−	0.816410i	$-0.695961\pi$
$83$	−10.5220			−1.15494			−0.577472	+	0.816410i	$0.695961\pi$
$84$	−2.63869	−	0.193156i	−0.287905	−	0.0210750i
$85$	−0.277647	+	0.480898i	−0.0301150	+	0.0521607i
$86$	−0.541233	−	0.937443i	−0.0583626	−	0.101087i
$87$	0.629759	+	1.09077i	0.0675173	+	0.116943i
$88$	4.91377			0.523810
$89$	0.536369	−	0.929018i	0.0568550	−	0.0984757i	−0.836197	−	0.548429i	$-0.815226\pi$
$89$	0.536369	−	0.929018i	0.0568550	−	0.0984757i	0.893052	+	0.449953i	$0.148559\pi$
$90$	3.95025			0.416393
$91$	7.71185	−	5.61493i	0.808421	−	0.588604i
$92$	9.53690			0.994291
$93$	1.67992	−	2.90971i	0.174200	−	0.301723i
$94$	−6.66398			−0.687337
$95$	1.53460	+	2.65801i	0.157447	+	0.272706i
$96$	0.500000	+	0.866025i	0.0510310	+	0.0883883i
$97$	−6.54097	+	11.3293i	−0.664135	+	1.15032i	0.315384	+	0.948964i	$0.397867\pi$
$97$	−6.54097	+	11.3293i	−0.664135	+	1.15032i	−0.979519	+	0.201351i	$0.935467\pi$
$98$	6.92538	+	1.01936i	0.699569	+	0.102971i
$99$	4.91377			0.493853
$100$	10.6045			1.06045
$101$	7.38523			0.734858			0.367429	−	0.930052i	$-0.380238\pi$
$101$	7.38523			0.734858			0.367429	+	0.930052i	$0.380238\pi$
$102$	−0.140571			−0.0139187
$103$	−1.99107	−	3.44863i	−0.196186	−	0.339804i	0.751103	−	0.660185i	$-0.229522\pi$
$103$	−1.99107	−	3.44863i	−0.196186	−	0.339804i	−0.947289	+	0.320382i	$0.896189\pi$
$104$	−3.39335	−	1.21869i	−0.332745	−	0.119502i
$105$	−10.4235	−	0.763015i	−1.01723	−	0.0744626i
$106$	5.53204	+	9.58177i	0.537319	+	0.930664i
$107$	3.53679	−	6.12590i	0.341914	−	0.592213i	−0.642874	−	0.765972i	$-0.722258\pi$
$107$	3.53679	−	6.12590i	0.341914	−	0.592213i	0.984788	+	0.173759i	$0.0555914\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−7.42350	+	12.8579i	−0.711042	+	1.23156i	0.253424	+	0.967355i	$0.418443\pi$
$109$	−7.42350	+	12.8579i	−0.711042	+	1.23156i	−0.964466	+	0.264206i	$0.914890\pi$
$110$	19.4107			1.85073
$111$	5.56841	−	9.64476i	0.528530	−	0.915440i
$112$	−1.15207	−	2.38175i	−0.108860	−	0.225054i
$113$	−0.785895	+	1.36121i	−0.0739308	+	0.128052i	−0.900621	−	0.434606i	$-0.856888\pi$
$113$	−0.785895	+	1.36121i	−0.0739308	+	0.128052i	0.826690	+	0.562658i	$0.190221\pi$
$114$	−0.388481	+	0.672870i	−0.0363846	+	0.0630200i
$115$	37.6732			3.51304
$116$	−0.629759	+	1.09077i	−0.0584717	+	0.101276i
$117$	−3.39335	−	1.21869i	−0.313715	−	0.112668i
$118$	0.431218			0.0396969
$119$	0.370925	+	0.0271522i	0.0340026	+	0.00248904i
$120$	1.97513	+	3.42102i	0.180304	+	0.312295i
$121$	13.1452			1.19502
$122$	4.14057	−	7.17168i	0.374870	−	0.649293i
$123$	−4.65505	−	8.06279i	−0.419732	−	0.726997i
$124$	3.35985			0.301723
$125$	22.1392			1.98019
$126$	−1.15207	−	2.38175i	−0.102634	−	0.212183i
$127$	−5.42757	−	9.40083i	−0.481619	−	0.834188i	0.518159	−	0.855285i	$-0.326618\pi$
$127$	−5.42757	−	9.40083i	−0.481619	−	0.834188i	−0.999777	+	0.0210962i	$0.993284\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	0.541233	−	0.937443i	0.0476529	−	0.0825372i
$130$	−13.4046	−	4.81414i	−1.17566	−	0.422228i
$131$	−0.961751	−	1.66580i	−0.0840285	−	0.145542i	0.820948	−	0.571003i	$-0.193445\pi$
$131$	−0.961751	−	1.66580i	−0.0840285	−	0.145542i	−0.904977	+	0.425461i	$0.860112\pi$
$132$	2.45689	+	4.25545i	0.213845	+	0.370390i
$133$	1.15505	−	1.70046i	0.100156	−	0.147448i
$134$	−4.09814	+	7.09819i	−0.354026	+	0.613190i
$135$	1.97513	+	3.42102i	0.169992	+	0.294435i
$136$	−0.0702857	−	0.121738i	−0.00602695	−	0.0104390i
$137$	−7.94106	−	13.7543i	−0.678450	−	1.17511i	−0.975447	−	0.220232i	$-0.929319\pi$
$137$	−7.94106	−	13.7543i	−0.678450	−	1.17511i	0.296997	−	0.954878i	$-0.404015\pi$
$138$	4.76845	+	8.25920i	0.405917	+	0.703070i
$139$	2.94351	−	5.09831i	0.249665	−	0.432433i	−0.713768	−	0.700383i	$-0.753013\pi$
$139$	2.94351	−	5.09831i	0.249665	−	0.432433i	0.963433	+	0.267950i	$0.0863461\pi$
$140$	−4.55096	−	9.40852i	−0.384626	−	0.795165i
$141$	−3.33199	−	5.77118i	−0.280604	−	0.486021i
$142$	1.93865	+	3.35783i	0.162688	+	0.281783i
$143$	−16.6741	−	5.98837i	−1.39436	−	0.500773i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.48771	+	4.30884i	−0.206593	+	0.357829i
$146$	−0.0817820	−	0.141650i	−0.00676832	−	0.0117231i
$147$	2.57990	+	6.50724i	0.212787	+	0.536708i
$148$	11.1368			0.915440
$149$	−13.2701			−1.08713			−0.543564	−	0.839368i	$-0.682925\pi$
$149$	−13.2701			−1.08713			−0.543564	+	0.839368i	$0.682925\pi$
$150$	5.30226	+	9.18378i	0.432927	+	0.749852i
$151$	−8.06783	+	13.9739i	−0.656551	+	1.13718i	0.324952	+	0.945731i	$0.394652\pi$
$151$	−8.06783	+	13.9739i	−0.656551	+	1.13718i	−0.981503	+	0.191449i	$0.938681\pi$
$152$	−0.776963			−0.0630200
$153$	−0.0702857	−	0.121738i	−0.00568227	−	0.00984197i
$154$	−5.66100	−	11.7034i	−0.456176	−	0.943086i
$155$	13.2723			1.06605
$156$	−0.641255	−	3.54807i	−0.0513415	−	0.284073i
$157$	−8.85322	+	15.3342i	−0.706564	+	1.22380i	0.259561	+	0.965727i	$0.416422\pi$
$157$	−8.85322	+	15.3342i	−0.706564	+	1.22380i	−0.966124	+	0.258077i	$0.916911\pi$
$158$	−4.35034			−0.346095
$159$	−5.53204	+	9.58177i	−0.438719	+	0.759884i
$160$	−1.97513	+	3.42102i	−0.156148	+	0.270455i
$161$	−10.9872	−	22.7145i	−0.865909	−	1.79016i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	3.27142			0.256237			0.128119	−	0.991759i	$-0.459106\pi$
$163$	3.27142			0.256237			0.128119	+	0.991759i	$0.459106\pi$
$164$	4.65505	−	8.06279i	0.363498	−	0.629598i
$165$	9.70533	+	16.8101i	0.755559	+	1.30867i
$166$	5.26102	−	9.11236i	0.408335	−	0.707256i
$167$	−4.42914	−	7.67150i	−0.342737	−	0.593638i	0.642203	−	0.766535i	$-0.278021\pi$
$167$	−4.42914	−	7.67150i	−0.342737	−	0.593638i	−0.984940	+	0.172896i	$0.944687\pi$
$168$	1.48662	−	2.18860i	0.114695	−	0.168854i
$169$	10.0296	+	8.27088i	0.771506	+	0.636221i
$170$	−0.277647	−	0.480898i	−0.0212945	−	0.0368832i
$171$	−0.776963			−0.0594158
$172$	1.08247			0.0825372
$173$	−14.9497			−1.13661			−0.568303	−	0.822819i	$-0.692400\pi$
$173$	−14.9497			−1.13661			−0.568303	+	0.822819i	$0.692400\pi$
$174$	−1.25952			−0.0954838
$175$	−12.2171	−	25.2573i	−0.923527	−	1.90927i
$176$	−2.45689	+	4.25545i	−0.185195	+	0.320767i
$177$	0.215609	+	0.373446i	0.0162062	+	0.0280699i
$178$	0.536369	+	0.929018i	0.0402026	+	0.0696329i
$179$	−23.2069			−1.73456			−0.867281	−	0.497819i	$-0.834134\pi$
$179$	−23.2069			−1.73456			−0.867281	+	0.497819i	$0.834134\pi$
$180$	−1.97513	+	3.42102i	−0.147217	+	0.254988i
$181$	19.4618			1.44658			0.723291	−	0.690543i	$-0.242629\pi$
$181$	19.4618			1.44658			0.723291	+	0.690543i	$0.242629\pi$
$182$	1.00674	+	9.48612i	0.0746248	+	0.703158i
$183$	8.28114			0.612160
$184$	−4.76845	+	8.25920i	−0.351535	+	0.608876i
$185$	43.9932			3.23445
$186$	1.67992	+	2.90971i	0.123178	+	0.213351i
$187$	−0.345368	−	0.598195i	−0.0252558	−	0.0437444i
$188$	3.33199	−	5.77118i	0.243010	−	0.420906i
$189$	1.48662	−	2.18860i	0.108136	−	0.159197i
$190$	−3.06920			−0.222663
$191$	−14.5964			−1.05616			−0.528078	−	0.849196i	$-0.677087\pi$
$191$	−14.5964			−1.05616			−0.528078	+	0.849196i	$0.677087\pi$
$192$	−1.00000			−0.0721688
$193$	−1.76860			−0.127307			−0.0636534	−	0.997972i	$-0.520275\pi$
$193$	−1.76860			−0.127307			−0.0636534	+	0.997972i	$0.520275\pi$
$194$	−6.54097	−	11.3293i	−0.469614	−	0.813396i
$195$	−2.53312	−	14.0158i	−0.181401	−	1.00369i
$196$	−4.34548	+	5.48788i	−0.310391	+	0.391991i
$197$	2.92757	+	5.07070i	0.208581	+	0.361272i	0.951268	−	0.308366i	$-0.0997823\pi$
$197$	2.92757	+	5.07070i	0.208581	+	0.361272i	−0.742687	+	0.669639i	$0.766449\pi$
$198$	−2.45689	+	4.25545i	−0.174603	+	0.302422i
$199$	−6.96137	−	12.0575i	−0.493479	−	0.854730i	0.506493	−	0.862244i	$-0.330942\pi$
$199$	−6.96137	−	12.0575i	−0.493479	−	0.854730i	−0.999972	+	0.00751379i	$0.997608\pi$
$200$	−5.30226	+	9.18378i	−0.374926	+	0.649391i
$201$	−8.19628			−0.578121
$202$	−3.69262	+	6.39580i	−0.259812	+	0.450007i
$203$	3.32348	+	0.243283i	0.233262	+	0.0170751i
$204$	0.0702857	−	0.121738i	0.00492099	−	0.00852340i
$205$	18.3886	−	31.8501i	1.28432	−	2.22450i
$206$	3.98214			0.277449
$207$	−4.76845	+	8.25920i	−0.331430	+	0.574054i
$208$	2.75209	−	2.32938i	0.190823	−	0.161513i
$209$	−3.81782			−0.264084
$210$	5.87254	−	8.64551i	0.405244	−	0.596597i
$211$	3.35399	+	5.80929i	0.230898	+	0.399928i	0.958073	−	0.286525i	$-0.0925002\pi$
$211$	3.35399	+	5.80929i	0.230898	+	0.399928i	−0.727174	+	0.686453i	$0.759167\pi$
$212$	−11.0641			−0.759884
$213$	−1.93865	+	3.35783i	−0.132834	+	0.230075i
$214$	3.53679	+	6.12590i	0.241770	+	0.418758i
$215$	4.27601			0.291622
$216$	−1.00000			−0.0680414
$217$	−3.87077	−	8.00232i	−0.262765	−	0.543233i
$218$	−7.42350	−	12.8579i	−0.502783	−	0.870846i
$219$	0.0817820	−	0.141650i	0.00552631	−	0.00957185i
$220$	−9.70533	+	16.8101i	−0.654333	+	1.13334i
$221$	0.0901422	+	0.498757i	0.00606362	+	0.0335500i
$222$	5.56841	+	9.64476i	0.373727	+	0.647314i
$223$	−1.02744	−	1.77957i	−0.0688023	−	0.119169i	0.829572	−	0.558400i	$-0.188584\pi$
$223$	−1.02744	−	1.77957i	−0.0688023	−	0.119169i	−0.898374	+	0.439231i	$0.855251\pi$
$224$	2.63869	+	0.193156i	0.176305	+	0.0129058i
$225$	−5.30226	+	9.18378i	−0.353484	+	0.612252i
$226$	−0.785895	−	1.36121i	−0.0522770	−	0.0905463i
$227$	12.9149	+	22.3692i	0.857190	+	1.48470i	0.874598	+	0.484849i	$0.161125\pi$
$227$	12.9149	+	22.3692i	0.857190	+	1.48470i	−0.0174074	+	0.999848i	$0.505541\pi$
$228$	−0.388481	−	0.672870i	−0.0257278	−	0.0445619i
$229$	5.39496	+	9.34435i	0.356509	+	0.617492i	0.987375	−	0.158400i	$-0.0506336\pi$
$229$	5.39496	+	9.34435i	0.356509	+	0.617492i	−0.630866	+	0.775892i	$0.717300\pi$
$230$	−18.8366	+	32.6259i	−1.24205	+	2.15129i
$231$	7.30493	−	10.7543i	0.480629	−	0.707579i
$232$	−0.629759	−	1.09077i	−0.0413457	−	0.0716129i
$233$	−1.92109	−	3.32742i	−0.125855	−	0.217987i	0.796212	−	0.605018i	$-0.206834\pi$
$233$	−1.92109	−	3.32742i	−0.125855	−	0.217987i	−0.922067	+	0.387031i	$0.873501\pi$
$234$	2.75209	−	2.32938i	0.179910	−	0.152276i
$235$	13.1622	−	22.7976i	0.858608	−	1.48715i
$236$	−0.215609	+	0.373446i	−0.0140350	+	0.0243093i
$237$	−2.17517	−	3.76751i	−0.141293	−	0.244726i
$238$	−0.208977	+	0.307654i	−0.0135460	+	0.0199423i
$239$	10.2560			0.663404			0.331702	−	0.943384i	$-0.392377\pi$
$239$	10.2560			0.663404			0.331702	+	0.943384i	$0.392377\pi$
$240$	−3.95025			−0.254988
$241$	0.316427	+	0.548068i	0.0203829	+	0.0353042i	0.876037	−	0.482244i	$-0.160178\pi$
$241$	0.316427	+	0.548068i	0.0203829	+	0.0353042i	−0.855654	+	0.517548i	$0.826845\pi$
$242$	−6.57259	+	11.3841i	−0.422502	+	0.731795i
$243$	−1.00000			−0.0641500
$244$	4.14057	+	7.17168i	0.265073	+	0.459120i
$245$	−17.1658	+	21.6785i	−1.09668	+	1.38499i
$246$	9.31010			0.593590
$247$	2.63650	+	0.946878i	0.167757	+	0.0602484i
$248$	−1.67992	+	2.90971i	−0.106675	+	0.184767i
$249$	10.5220			0.666807
$250$	−11.0696	+	19.1731i	−0.700104	+	1.21262i
$251$	7.53648	−	13.0536i	0.475698	−	0.823934i	−0.523914	−	0.851771i	$-0.675529\pi$
$251$	7.53648	−	13.0536i	0.475698	−	0.823934i	0.999612	+	0.0278373i	$0.00886202\pi$
$252$	2.63869	+	0.193156i	0.166222	+	0.0121677i
$253$	−23.4311	+	40.5838i	−1.47310	+	2.55148i
$254$	10.8551			0.681112
$255$	0.277647	−	0.480898i	0.0173869	−	0.0301150i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.56909	+	9.64595i	−0.347390	+	0.601698i	−0.985785	−	0.168012i	$-0.946265\pi$
$257$	−5.56909	+	9.64595i	−0.347390	+	0.601698i	0.638395	+	0.769709i	$0.279599\pi$
$258$	0.541233	+	0.937443i	0.0336957	+	0.0583626i
$259$	−12.8304	−	26.5251i	−0.797240	−	1.64819i
$260$	10.8715	−	9.20163i	0.674219	−	0.570661i
$261$	−0.629759	−	1.09077i	−0.0389811	−	0.0675173i
$262$	1.92350			0.118834
$263$	17.1706			1.05878			0.529391	−	0.848378i	$-0.322420\pi$
$263$	17.1706			1.05878			0.529391	+	0.848378i	$0.322420\pi$
$264$	−4.91377			−0.302422
$265$	−43.7059			−2.68483
$266$	0.895114	+	1.85053i	0.0548829	+	0.113463i
$267$	−0.536369	+	0.929018i	−0.0328252	+	0.0568550i
$268$	−4.09814	−	7.09819i	−0.250334	−	0.433591i
$269$	−1.64355	−	2.84672i	−0.100209	−	0.173568i	0.811562	−	0.584267i	$-0.198618\pi$
$269$	−1.64355	−	2.84672i	−0.100209	−	0.173568i	−0.911771	+	0.410699i	$0.865285\pi$
$270$	−3.95025			−0.240405
$271$	−7.36304	+	12.7532i	−0.447273	+	0.774699i	−0.998207	−	0.0598494i	$-0.980938\pi$
$271$	−7.36304	+	12.7532i	−0.447273	+	0.774699i	0.550935	+	0.834548i	$0.314271\pi$
$272$	0.140571			0.00852340
$273$	−7.71185	+	5.61493i	−0.466742	+	0.339831i
$274$	15.8821			0.959474
$275$	−26.0541	+	45.1270i	−1.57112	+	2.72126i
$276$	−9.53690			−0.574054
$277$	−9.25021	−	16.0218i	−0.555791	−	0.962659i	−0.997842	−	0.0656684i	$-0.979082\pi$
$277$	−9.25021	−	16.0218i	−0.555791	−	0.962659i	0.442050	−	0.896990i	$-0.354251\pi$
$278$	2.94351	+	5.09831i	0.176540	+	0.305776i
$279$	−1.67992	+	2.90971i	−0.100574	+	0.174200i
$280$	10.4235	+	0.763015i	0.622923	+	0.0455989i
$281$	−31.3463			−1.86996			−0.934981	−	0.354698i	$-0.884584\pi$
$281$	−31.3463			−1.86996			−0.934981	+	0.354698i	$0.884584\pi$
$282$	6.66398			0.396834
$283$	−14.7197			−0.874995			−0.437498	−	0.899220i	$-0.644135\pi$
$283$	−14.7197			−0.874995			−0.437498	+	0.899220i	$0.644135\pi$
$284$	−3.87729			−0.230075
$285$	−1.53460	−	2.65801i	−0.0909019	−	0.157447i
$286$	13.5231	−	11.4460i	0.799640	−	0.676818i
$287$	−24.5665	−	1.79830i	−1.45011	−	0.106150i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	8.49012	−	14.7053i	0.499419	−	0.865019i
$290$	−2.48771	−	4.30884i	−0.146083	−	0.253024i
$291$	6.54097	−	11.3293i	0.383438	−	0.664135i
$292$	0.163564			0.00957185
$293$	8.39523	−	14.5410i	0.490454	−	0.849492i	−0.509485	−	0.860479i	$-0.670164\pi$
$293$	8.39523	−	14.5410i	0.490454	−	0.849492i	0.999940	+	0.0109876i	$0.00349752\pi$
$294$	−6.92538	−	1.01936i	−0.403896	−	0.0594501i
$295$	−0.851711	+	1.47521i	−0.0495886	+	0.0858899i
$296$	−5.56841	+	9.64476i	−0.323657	+	0.560590i
$297$	−4.91377			−0.285126
$298$	6.63504	−	11.4922i	0.384358	−	0.665727i
$299$	26.2464	−	22.2150i	1.51787	−	1.28473i
$300$	−10.6045			−0.612252
$301$	−1.24707	−	2.57816i	−0.0718801	−	0.148603i
$302$	−8.06783	−	13.9739i	−0.464252	−	0.804107i
$303$	−7.38523			−0.424271
$304$	0.388481	−	0.672870i	0.0222809	−	0.0385917i
$305$	16.3563	+	28.3300i	0.936560	+	1.62217i
$306$	0.140571			0.00803594
$307$	5.69511			0.325037			0.162519	−	0.986705i	$-0.448038\pi$
$307$	5.69511			0.325037			0.162519	+	0.986705i	$0.448038\pi$
$308$	12.9659	+	0.949124i	0.738802	+	0.0540814i
$309$	1.99107	+	3.44863i	0.113268	+	0.196186i
$310$	−6.63613	+	11.4941i	−0.376907	+	0.652822i
$311$	0.183797	−	0.318345i	0.0104221	−	0.0180517i	−0.860767	−	0.508999i	$-0.830016\pi$
$311$	0.183797	−	0.318345i	0.0104221	−	0.0180517i	0.871189	+	0.490947i	$0.163349\pi$
$312$	3.39335	+	1.21869i	0.192110	+	0.0689948i
$313$	−2.95742	−	5.12240i	−0.167163	−	0.289535i	0.770258	−	0.637732i	$-0.220127\pi$
$313$	−2.95742	−	5.12240i	−0.167163	−	0.289535i	−0.937421	+	0.348197i	$0.886794\pi$
$314$	−8.85322	−	15.3342i	−0.499616	−	0.865360i
$315$	10.4235	+	0.763015i	0.587298	+	0.0429910i
$316$	2.17517	−	3.76751i	0.122363	−	0.211939i
$317$	−4.28899	−	7.42875i	−0.240894	−	0.417240i	0.720075	−	0.693896i	$-0.244107\pi$
$317$	−4.28899	−	7.42875i	−0.240894	−	0.417240i	−0.960969	+	0.276656i	$0.910774\pi$
$318$	−5.53204	−	9.58177i	−0.310221	−	0.537319i
$319$	−3.09449	−	5.35982i	−0.173258	−	0.300092i
$320$	−1.97513	−	3.42102i	−0.110413	−	0.191241i
$321$	−3.53679	+	6.12590i	−0.197404	+	0.341914i
$322$	25.1649	+	1.84211i	1.40239	+	0.102657i
$323$	0.0546094	+	0.0945863i	0.00303855	+	0.00526292i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	29.1846	−	24.7019i	1.61887	−	1.37022i
$326$	−1.63571	+	2.83313i	−0.0905935	+	0.156912i
$327$	7.42350	−	12.8579i	0.410521	−	0.711042i
$328$	4.65505	+	8.06279i	0.257032	+	0.445193i
$329$	−17.5842	−	1.28719i	−0.969448	−	0.0709649i
$330$	−19.4107			−1.06852
$331$	−4.14977			−0.228092			−0.114046	−	0.993475i	$-0.536381\pi$
$331$	−4.14977			−0.228092			−0.114046	+	0.993475i	$0.536381\pi$
$332$	5.26102	+	9.11236i	0.288736	+	0.500106i
$333$	−5.56841	+	9.64476i	−0.305147	+	0.528530i
$334$	8.85828			0.484704
$335$	−16.1887	−	28.0397i	−0.884483	−	1.53197i
$336$	1.15207	+	2.38175i	0.0628504	+	0.129935i
$337$	18.5391			1.00989			0.504945	−	0.863152i	$-0.331513\pi$
$337$	18.5391			1.00989			0.504945	+	0.863152i	$0.331513\pi$
$338$	−12.1776	+	4.55044i	−0.662373	+	0.247511i
$339$	0.785895	−	1.36121i	0.0426840	−	0.0739308i
$340$	0.555293			0.0301150
$341$	−8.25477	+	14.2977i	−0.447021	+	0.774262i
$342$	0.388481	−	0.672870i	0.0210067	−	0.0363846i
$343$	18.0770	+	4.02745i	0.976069	+	0.217462i
$344$	−0.541233	+	0.937443i	−0.0291813	+	0.0505435i
$345$	−37.6732			−2.02826
$346$	7.47486	−	12.9468i	0.401851	−	0.696027i
$347$	11.4934	+	19.9072i	0.616999	+	1.06867i	0.990030	+	0.140854i	$0.0449849\pi$
$347$	11.4934	+	19.9072i	0.616999	+	1.06867i	−0.373032	+	0.927819i	$0.621682\pi$
$348$	0.629759	−	1.09077i	0.0337586	−	0.0584717i
$349$	7.29494	+	12.6352i	0.390489	+	0.676347i	0.992514	−	0.122130i	$-0.0389726\pi$
$349$	7.29494	+	12.6352i	0.390489	+	0.676347i	−0.602025	+	0.798477i	$0.705639\pi$
$350$	27.9820	+	2.04832i	1.49570	+	0.109487i
$351$	3.39335	+	1.21869i	0.181123	+	0.0650489i
$352$	−2.45689	−	4.25545i	−0.130953	−	0.226816i
$353$	−19.7304			−1.05015			−0.525073	−	0.851057i	$-0.675962\pi$
$353$	−19.7304			−1.05015			−0.525073	+	0.851057i	$0.675962\pi$
$354$	−0.431218			−0.0229190
$355$	−15.3163			−0.812904
$356$	−1.07274			−0.0568550
$357$	−0.370925	−	0.0271522i	−0.0196314	−	0.00143705i
$358$	11.6034	−	20.0977i	0.613260	−	1.06220i
$359$	18.8344	+	32.6222i	0.994044	+	1.72173i	0.591401	+	0.806378i	$0.298575\pi$
$359$	18.8344	+	32.6222i	0.994044	+	1.72173i	0.402644	+	0.915357i	$0.368091\pi$
$360$	−1.97513	−	3.42102i	−0.104098	−	0.180304i
$361$	−18.3963			−0.968228
$362$	−9.73088	+	16.8544i	−0.511444	+	0.885847i
$363$	−13.1452			−0.689943
$364$	−8.71859	−	3.87119i	−0.456978	−	0.202906i
$365$	0.646119			0.0338194
$366$	−4.14057	+	7.17168i	−0.216431	+	0.374870i
$367$	2.50281			0.130646			0.0653229	−	0.997864i	$-0.479192\pi$
$367$	2.50281			0.130646			0.0653229	+	0.997864i	$0.479192\pi$
$368$	−4.76845	−	8.25920i	−0.248573	−	0.430540i
$369$	4.65505	+	8.06279i	0.242332	+	0.419732i
$370$	−21.9966	+	38.0993i	−1.14355	+	1.98069i
$371$	12.7466	+	26.3519i	0.661768	+	1.36812i
$372$	−3.35985			−0.174200
$373$	−13.1674			−0.681783			−0.340891	−	0.940103i	$-0.610729\pi$
$373$	−13.1674			−0.681783			−0.340891	+	0.940103i	$0.610729\pi$
$374$	0.690736			0.0357171
$375$	−22.1392			−1.14327
$376$	3.33199	+	5.77118i	0.171834	+	0.297626i
$377$	0.807672	+	4.46886i	0.0415972	+	0.230158i
$378$	1.15207	+	2.38175i	0.0592560	+	0.122504i
$379$	−5.93228	−	10.2750i	−0.304721	−	0.527792i	0.672478	−	0.740117i	$-0.265230\pi$
$379$	−5.93228	−	10.2750i	−0.304721	−	0.527792i	−0.977199	+	0.212325i	$0.931896\pi$
$380$	1.53460	−	2.65801i	0.0787233	−	0.136353i
$381$	5.42757	+	9.40083i	0.278063	+	0.481619i
$382$	7.29819	−	12.6408i	0.373408	−	0.646761i
$383$	16.4228			0.839165			0.419582	−	0.907717i	$-0.362177\pi$
$383$	16.4228			0.839165			0.419582	+	0.907717i	$0.362177\pi$
$384$	0.500000	−	0.866025i	0.0255155	−	0.0441942i
$385$	51.2187	+	3.74928i	2.61035	+	0.191081i
$386$	0.884301	−	1.53165i	0.0450098	−	0.0779592i
$387$	−0.541233	+	0.937443i	−0.0275124	+	0.0476529i
$388$	13.0819			0.664135
$389$	9.03721	−	15.6529i	0.458205	−	0.793634i	−0.540662	−	0.841240i	$-0.681826\pi$
$389$	9.03721	−	15.6529i	0.458205	−	0.793634i	0.998866	+	0.0476065i	$0.0151594\pi$
$390$	13.4046	+	4.81414i	0.678767	+	0.243773i
$391$	1.34062			0.0677979
$392$	−2.57990	−	6.50724i	−0.130305	−	0.328665i
$393$	0.961751	+	1.66580i	0.0485139	+	0.0840285i
$394$	−5.85514			−0.294978
$395$	8.59248	−	14.8826i	0.432335	−	0.748826i
$396$	−2.45689	−	4.25545i	−0.123463	−	0.213845i
$397$	−2.40982			−0.120945			−0.0604726	−	0.998170i	$-0.519261\pi$
$397$	−2.40982			−0.120945			−0.0604726	+	0.998170i	$0.519261\pi$
$398$	13.9227			0.697884
$399$	−1.15505	+	1.70046i	−0.0578249	+	0.0851294i
$400$	−5.30226	−	9.18378i	−0.265113	−	0.459189i
$401$	12.4622	−	21.5851i	0.622331	−	1.07791i	−0.366719	−	0.930332i	$-0.619519\pi$
$401$	12.4622	−	21.5851i	0.622331	−	1.07791i	0.989051	−	0.147577i	$-0.0471476\pi$
$402$	4.09814	−	7.09819i	0.204397	−	0.354026i
$403$	9.24660	−	7.82635i	0.460606	−	0.389858i
$404$	−3.69262	−	6.39580i	−0.183715	−	0.318203i
$405$	−1.97513	−	3.42102i	−0.0981449	−	0.169992i
$406$	−1.87243	+	2.75658i	−0.0929271	+	0.136807i
$407$	−27.3619	+	47.3922i	−1.35628	+	2.34914i
$408$	0.0702857	+	0.121738i	0.00347966	+	0.00602695i
$409$	−13.7384	−	23.7957i	−0.679323	−	1.17662i	−0.975185	−	0.221391i	$-0.928940\pi$
$409$	−13.7384	−	23.7957i	−0.679323	−	1.17662i	0.295863	−	0.955231i	$-0.404393\pi$
$410$	18.3886	+	31.8501i	0.908150	+	1.57296i
$411$	7.94106	+	13.7543i	0.391704	+	0.678450i
$412$	−1.99107	+	3.44863i	−0.0980929	+	0.169902i
$413$	1.13785	+	0.0832924i	0.0559901	+	0.00409855i
$414$	−4.76845	−	8.25920i	−0.234357	−	0.405917i
$415$	20.7824	+	35.9961i	1.02017	+	1.76698i
$416$	0.641255	+	3.54807i	0.0314401	+	0.173958i
$417$	−2.94351	+	5.09831i	−0.144144	+	0.249665i
$418$	1.90891	−	3.30633i	0.0933678	−	0.161718i
$419$	−5.16655	−	8.94872i	−0.252402	−	0.437174i	0.711784	−	0.702398i	$-0.247887\pi$
$419$	−5.16655	−	8.94872i	−0.252402	−	0.437174i	−0.964187	+	0.265224i	$0.914554\pi$
$420$	4.55096	+	9.40852i	0.222064	+	0.459089i
$421$	−16.8702			−0.822204			−0.411102	−	0.911589i	$-0.634856\pi$
$421$	−16.8702			−0.822204			−0.411102	+	0.911589i	$0.634856\pi$
$422$	−6.70799			−0.326540
$423$	3.33199	+	5.77118i	0.162007	+	0.280604i
$424$	5.53204	−	9.58177i	0.268659	−	0.465332i
$425$	1.49069			0.0723092
$426$	−1.93865	−	3.35783i	−0.0939277	−	0.162688i
$427$	12.3109	−	18.1241i	0.595768	−	0.877085i
$428$	−7.07358			−0.341914
$429$	16.6741	+	5.98837i	0.805035	+	0.289121i
$430$	−2.13801	+	3.70314i	−0.103104	+	0.178581i
$431$	24.3436			1.17259			0.586294	−	0.810098i	$-0.300586\pi$
$431$	24.3436			1.17259			0.586294	+	0.810098i	$0.300586\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	0.984059	−	1.70444i	0.0472909	−	0.0819102i	−0.841411	−	0.540396i	$-0.818275\pi$
$433$	0.984059	−	1.70444i	0.0472909	−	0.0819102i	0.888702	+	0.458485i	$0.151608\pi$
$434$	8.86560	+	0.648974i	0.425562	+	0.0311518i
$435$	2.48771	−	4.30884i	0.119276	−	0.206593i
$436$	14.8470			0.711042
$437$	3.70491	−	6.41709i	0.177230	−	0.306971i
$438$	0.0817820	+	0.141650i	0.00390769	+	0.00676832i
$439$	−10.1318	+	17.5488i	−0.483564	+	0.837558i	−0.999822	−	0.0188756i	$-0.993991\pi$
$439$	−10.1318	+	17.5488i	−0.483564	+	0.837558i	0.516258	+	0.856433i	$0.327325\pi$
$440$	−9.70533	−	16.8101i	−0.462683	−	0.801391i
$441$	−2.57990	−	6.50724i	−0.122852	−	0.309868i
$442$	−0.477008	−	0.171313i	−0.0226889	−	0.00814854i
$443$	−14.2707	−	24.7177i	−0.678024	−	1.17437i	−0.975575	−	0.219666i	$-0.929503\pi$
$443$	−14.2707	−	24.7177i	−0.678024	−	1.17437i	0.297551	−	0.954706i	$-0.403830\pi$
$444$	−11.1368			−0.528530
$445$	−4.23759			−0.200881
$446$	2.05487			0.0973011
$447$	13.2701			0.627653
$448$	−1.48662	+	2.18860i	−0.0702364	+	0.103401i
$449$	12.1517	−	21.0474i	0.573475	−	0.993287i	−0.422731	−	0.906255i	$-0.638928\pi$
$449$	12.1517	−	21.0474i	0.573475	−	0.993287i	0.996206	−	0.0870320i	$-0.0277382\pi$
$450$	−5.30226	−	9.18378i	−0.249951	−	0.432927i
$451$	22.8739	+	39.6187i	1.07709	+	1.86557i
$452$	1.57179			0.0739308
$453$	8.06783	−	13.9739i	0.379060	−	0.656551i
$454$	−25.8298			−1.21225
$455$	−34.4407	−	15.2922i	−1.61460	−	0.716909i
$456$	0.776963			0.0363846
$457$	3.12651	−	5.41528i	0.146252	−	0.253316i	−0.783587	−	0.621282i	$-0.786612\pi$
$457$	3.12651	−	5.41528i	0.146252	−	0.253316i	0.929839	+	0.367966i	$0.119946\pi$
$458$	−10.7899			−0.504180
$459$	0.0702857	+	0.121738i	0.00328066	+	0.00568227i
$460$	−18.8366	−	32.6259i	−0.878261	−	1.52119i
$461$	9.65625	−	16.7251i	0.449736	−	0.778966i	−0.548632	−	0.836064i	$-0.684851\pi$
$461$	9.65625	−	16.7251i	0.449736	−	0.778966i	0.998369	+	0.0570976i	$0.0181846\pi$
$462$	5.66100	+	11.7034i	0.263374	+	0.544491i
$463$	21.4480			0.996772			0.498386	−	0.866955i	$-0.333926\pi$
$463$	21.4480			0.996772			0.498386	+	0.866955i	$0.333926\pi$
$464$	1.25952			0.0584717
$465$	−13.2723			−0.615486
$466$	3.84218			0.177986
$467$	2.39255	+	4.14402i	0.110714	+	0.191762i	0.916058	−	0.401045i	$-0.131353\pi$
$467$	2.39255	+	4.14402i	0.110714	+	0.191762i	−0.805344	+	0.592807i	$0.798020\pi$
$468$	0.641255	+	3.54807i	0.0296420	+	0.164010i
$469$	−12.1848	+	17.9384i	−0.562641	+	0.828316i
$470$	13.1622	+	22.7976i	0.607128	+	1.05158i
$471$	8.85322	−	15.3342i	0.407935	−	0.706564i
$472$	−0.215609	−	0.373446i	−0.00992422	−	0.0171893i
$473$	−2.65950	+	4.60638i	−0.122284	+	0.211802i
$474$	4.35034			0.199818
$475$	4.11966	−	7.13545i	0.189023	−	0.327397i
$476$	−0.161948	−	0.334806i	−0.00742287	−	0.0153458i
$477$	5.53204	−	9.58177i	0.253295	−	0.438719i
$478$	−5.12799	+	8.88194i	−0.234549	+	0.406250i
$479$	−11.7132			−0.535190			−0.267595	−	0.963532i	$-0.586229\pi$
$479$	−11.7132			−0.535190			−0.267595	+	0.963532i	$0.586229\pi$
$480$	1.97513	−	3.42102i	0.0901518	−	0.156148i
$481$	30.6495	−	25.9418i	1.39750	−	1.18285i
$482$	−0.632854			−0.0288257
$483$	10.9872	+	22.7145i	0.499933	+	1.03355i
$484$	−6.57259	−	11.3841i	−0.298754	−	0.517457i
$485$	51.6770			2.34653
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	12.8785	+	22.3062i	0.583581	+	1.01079i	0.995051	+	0.0993684i	$0.0316822\pi$
$487$	12.8785	+	22.3062i	0.583581	+	1.01079i	−0.411470	+	0.911423i	$0.634984\pi$
$488$	−8.28114			−0.374870
$489$	−3.27142			−0.147939
$490$	−10.1913	−	25.7052i	−0.460395	−	1.16124i
$491$	2.35012	+	4.07053i	0.106059	+	0.183700i	0.914171	−	0.405330i	$-0.132843\pi$
$491$	2.35012	+	4.07053i	0.106059	+	0.183700i	−0.808111	+	0.589030i	$0.799510\pi$
$492$	−4.65505	+	8.06279i	−0.209866	+	0.363498i
$493$	−0.0885262	+	0.153332i	−0.00398702	+	0.00690572i
$494$	−2.13827	+	1.80984i	−0.0962054	+	0.0814285i
$495$	−9.70533	−	16.8101i	−0.436222	−	0.755559i
$496$	−1.67992	−	2.90971i	−0.0754308	−	0.130650i
$497$	4.46690	+	9.23475i	0.200368	+	0.414235i
$498$	−5.26102	+	9.11236i	−0.235752	+	0.408335i
$499$	16.3247	+	28.2752i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941832\pi$
$499$	16.3247	+	28.2752i	0.730794	+	1.26577i	−0.225751	+	0.974185i	$0.572483\pi$
$500$	−11.0696	−	19.1731i	−0.495048	−	0.857449i
$501$	4.42914	+	7.67150i	0.197879	+	0.342737i
$502$	7.53648	+	13.0536i	0.336370	+	0.582609i
$503$	7.49164	−	12.9759i	0.334036	−	0.578567i	−0.649263	−	0.760564i	$-0.724923\pi$
$503$	7.49164	−	12.9759i	0.334036	−	0.578567i	0.983299	+	0.181997i	$0.0582560\pi$
$504$	−1.48662	+	2.18860i	−0.0662195	+	0.0974878i
$505$	−14.5868	−	25.2650i	−0.649103	−	1.12428i
$506$	−23.4311	−	40.5838i	−1.04164	−	1.80417i
$507$	−10.0296	−	8.27088i	−0.445429	−	0.367323i
$508$	−5.42757	+	9.40083i	−0.240809	+	0.417094i
$509$	0.210438	−	0.364489i	0.00932749	−	0.0161557i	−0.861324	−	0.508056i	$-0.830364\pi$
$509$	0.210438	−	0.364489i	0.00932749	−	0.0161557i	0.870651	+	0.491900i	$0.163698\pi$
$510$	0.277647	+	0.480898i	0.0122944	+	0.0212945i
$511$	−0.188437	−	0.389569i	−0.00833595	−	0.0172335i
$512$	1.00000			0.0441942
$513$	0.776963			0.0343037
$514$	−5.56909	−	9.64595i	−0.245642	−	0.425464i
$515$	−7.86522	+	13.6230i	−0.346583	+	0.600300i
$516$	−1.08247			−0.0476529
$517$	16.3727	+	28.3583i	0.720068	+	1.24720i
$518$	29.3866	+	2.15114i	1.29117	+	0.0945157i
$519$	14.9497			0.656220
$520$	2.53312	+	14.0158i	0.111085	+	0.614632i
$521$	−15.5914	+	27.0050i	−0.683070	+	1.18311i	0.290969	+	0.956732i	$0.406022\pi$
$521$	−15.5914	+	27.0050i	−0.683070	+	1.18311i	−0.974039	+	0.226379i	$0.927311\pi$
$522$	1.25952			0.0551276
$523$	−7.18192	+	12.4394i	−0.314043	+	0.543939i	−0.979234	−	0.202735i	$-0.935017\pi$
$523$	−7.18192	+	12.4394i	−0.314043	+	0.543939i	0.665190	+	0.746674i	$0.268350\pi$
$524$	−0.961751	+	1.66580i	−0.0420143	+	0.0727709i
$525$	12.2171	+	25.2573i	0.533199	+	1.10232i
$526$	−8.58528	+	14.8701i	−0.374336	+	0.648369i
$527$	0.472299			0.0205737
$528$	2.45689	−	4.25545i	0.106922	−	0.185195i
$529$	−33.9762	−	58.8486i	−1.47723	−	2.55863i
$530$	21.8530	−	37.8504i	0.949232	−	1.64412i
$531$	−0.215609	−	0.373446i	−0.00935664	−	0.0162062i
$532$	−2.05016	−	0.150075i	−0.0888859	−	0.00650657i
$533$	−5.97015	−	33.0329i	−0.258596	−	1.43081i
$534$	−0.536369	−	0.929018i	−0.0232110	−	0.0402026i
$535$	−27.9424			−1.20806
$536$	8.19628			0.354026
$537$	23.2069			1.00145
$538$	3.28711			0.141717
$539$	−12.6771	−	31.9751i	−0.546039	−	1.37726i
$540$	1.97513	−	3.42102i	0.0849959	−	0.147217i
$541$	4.68698	+	8.11808i	0.201509	+	0.349024i	0.949015	−	0.315232i	$-0.102082\pi$
$541$	4.68698	+	8.11808i	0.201509	+	0.349024i	−0.747506	+	0.664255i	$0.768749\pi$
$542$	−7.36304	−	12.7532i	−0.316270	−	0.547795i
$543$	−19.4618			−0.835184
$544$	−0.0702857	+	0.121738i	−0.00301348	+	0.00521949i
$545$	58.6494			2.51227
$546$	−1.00674	−	9.48612i	−0.0430847	−	0.405968i
$547$	17.7829			0.760343			0.380172	−	0.924916i	$-0.375865\pi$
$547$	17.7829			0.760343			0.380172	+	0.924916i	$0.375865\pi$
$548$	−7.94106	+	13.7543i	−0.339225	+	0.587555i
$549$	−8.28114			−0.353431
$550$	−26.0541	−	45.1270i	−1.11095	−	1.92422i
$551$	0.489299	+	0.847491i	0.0208449	+	0.0361043i
$552$	4.76845	−	8.25920i	0.202959	−	0.351535i
$553$	−11.4792	−	0.840294i	−0.488146	−	0.0357329i
$554$	18.5004			0.786008
$555$	−43.9932			−1.86741
$556$	−5.88702			−0.249665
$557$	13.3641			0.566257			0.283128	−	0.959082i	$-0.408628\pi$
$557$	13.3641			0.566257			0.283128	+	0.959082i	$0.408628\pi$
$558$	−1.67992	−	2.90971i	−0.0711169	−	0.123178i
$559$	2.97904	−	2.52147i	0.126000	−	0.106647i
$560$	−5.87254	+	8.64551i	−0.248160	+	0.365339i
$561$	0.345368	+	0.598195i	0.0145815	+	0.0252558i
$562$	15.6731	−	27.1467i	0.661131	−	1.14511i
$563$	13.6941	+	23.7189i	0.577139	+	0.999634i	0.995806	+	0.0914943i	$0.0291643\pi$
$563$	13.6941	+	23.7189i	0.577139	+	0.999634i	−0.418666	+	0.908140i	$0.637502\pi$
$564$	−3.33199	+	5.77118i	−0.140302	+	0.243010i
$565$	6.20897			0.261213
$566$	7.35985	−	12.7476i	0.309357	−	0.535823i
$567$	−1.48662	+	2.18860i	−0.0624323	+	0.0919124i
$568$	1.93865	−	3.35783i	0.0813438	−	0.140892i
$569$	5.48808	−	9.50564i	0.230072	−	0.398497i	−0.727757	−	0.685835i	$-0.759437\pi$
$569$	5.48808	−	9.50564i	0.230072	−	0.398497i	0.957829	+	0.287338i	$0.0927703\pi$
$570$	3.06920			0.128555
$571$	−14.5552	+	25.2103i	−0.609115	+	1.05502i	0.382271	+	0.924050i	$0.375142\pi$
$571$	−14.5552	+	25.2103i	−0.609115	+	1.05502i	−0.991387	+	0.130969i	$0.958191\pi$
$572$	3.15098	+	17.4344i	0.131749	+	0.728969i
$573$	14.5964			0.609772
$574$	13.8406	−	20.3760i	0.577696	−	0.850480i
$575$	−50.5671	−	87.5847i	−2.10879	−	3.65254i
$576$	1.00000			0.0416667
$577$	−10.0317	+	17.3753i	−0.417623	+	0.723345i	−0.995700	−	0.0926375i	$-0.970470\pi$
$577$	−10.0317	+	17.3753i	−0.417623	+	0.723345i	0.578076	+	0.815983i	$0.303804\pi$
$578$	8.49012	+	14.7053i	0.353142	+	0.611661i
$579$	1.76860			0.0735006
$580$	4.97542			0.206593
$581$	15.6423	−	23.0285i	0.648953	−	0.955383i
$582$	6.54097	+	11.3293i	0.271132	+	0.469614i
$583$	27.1832	−	47.0826i	1.12581	−	1.94996i
$584$	−0.0817820	+	0.141650i	−0.00338416	+	0.00586154i
$585$	2.53312	+	14.0158i	0.104732	+	0.579481i
$586$	8.39523	+	14.5410i	0.346804	+	0.600681i
$587$	16.0113	+	27.7323i	0.660855	+	1.14463i	0.980391	+	0.197060i	$0.0631395\pi$
$587$	16.0113	+	27.7323i	0.660855	+	1.14463i	−0.319536	+	0.947574i	$0.603527\pi$
$588$	4.34548	−	5.48788i	0.179205	−	0.226316i
$589$	1.30524	−	2.26074i	0.0537814	−	0.0931521i
$590$	−0.851711	−	1.47521i	−0.0350644	−	0.0607333i
$591$	−2.92757	−	5.07070i	−0.120424	−	0.208581i
$592$	−5.56841	−	9.64476i	−0.228860	−	0.396397i
$593$	12.2192	+	21.1643i	0.501784	+	0.869115i	0.999998	+	0.00206106i	$0.000656057\pi$
$593$	12.2192	+	21.1643i	0.501784	+	0.869115i	−0.498214	+	0.867054i	$0.666011\pi$
$594$	2.45689	−	4.25545i	0.100807	−	0.174603i
$595$	−0.639735	−	1.32257i	−0.0262266	−	0.0542201i
$596$	6.63504	+	11.4922i	0.271782	+	0.470740i
$597$	6.96137	+	12.0575i	0.284910	+	0.493479i
$598$	6.11559	+	33.8376i	0.250085	+	1.38372i
$599$	−7.93636	+	13.7462i	−0.324271	+	0.561654i	−0.981365	−	0.192155i	$-0.938452\pi$
$599$	−7.93636	+	13.7462i	−0.324271	+	0.561654i	0.657093	+	0.753809i	$0.271786\pi$
$600$	5.30226	−	9.18378i	0.216464	−	0.374926i
$601$	−0.0246085	−	0.0426231i	−0.00100380	−	0.00173863i	0.865523	−	0.500869i	$-0.166986\pi$
$601$	−0.0246085	−	0.0426231i	−0.00100380	−	0.00173863i	−0.866527	+	0.499130i	$0.833653\pi$
$602$	2.85629	+	0.209085i	0.116414	+	0.00852165i
$603$	8.19628			0.333778
$604$	16.1357			0.656551
$605$	−25.9634	−	44.9699i	−1.05556	−	1.82829i
$606$	3.69262	−	6.39580i	0.150002	−	0.259812i
$607$	13.2265			0.536847			0.268423	−	0.963301i	$-0.413497\pi$
$607$	13.2265			0.536847			0.268423	+	0.963301i	$0.413497\pi$
$608$	0.388481	+	0.672870i	0.0157550	+	0.0272885i
$609$	−3.32348	−	0.243283i	−0.134674	−	0.00985833i
$610$	−32.7126			−1.32450
$611$	−4.27331	−	23.6443i	−0.172880	−	0.956545i
$612$	−0.0702857	+	0.121738i	−0.00284113	+	0.00492099i
$613$	−2.35096			−0.0949543			−0.0474772	−	0.998872i	$-0.515118\pi$
$613$	−2.35096			−0.0949543			−0.0474772	+	0.998872i	$0.515118\pi$
$614$	−2.84756	+	4.93211i	−0.114918	+	0.199044i
$615$	−18.3886	+	31.8501i	−0.741501	+	1.28432i
$616$	−7.30493	+	10.7543i	−0.294324	+	0.433302i
$617$	−16.1133	+	27.9090i	−0.648697	+	1.12358i	0.334738	+	0.942311i	$0.391352\pi$
$617$	−16.1133	+	27.9090i	−0.648697	+	1.12358i	−0.983434	+	0.181264i	$0.941981\pi$
$618$	−3.98214			−0.160185
$619$	9.49745	−	16.4501i	0.381735	−	0.661184i	−0.609575	−	0.792728i	$-0.708660\pi$
$619$	9.49745	−	16.4501i	0.381735	−	0.661184i	0.991310	+	0.131544i	$0.0419934\pi$
$620$	−6.63613	−	11.4941i	−0.266513	−	0.461615i
$621$	4.76845	−	8.25920i	0.191351	−	0.331430i
$622$	0.183797	+	0.318345i	0.00736957	+	0.0127645i
$623$	1.23587	+	2.55500i	0.0495140	+	0.102364i
$624$	−2.75209	+	2.32938i	−0.110172	+	0.0932497i
$625$	−17.2165	−	29.8199i	−0.688662	−	1.19280i
$626$	5.91484			0.236404
$627$	3.81782			0.152469
$628$	17.7064			0.706564
$629$	1.56552			0.0624213
$630$	−5.87254	+	8.64551i	−0.233968	+	0.344445i
$631$	−11.7271	+	20.3119i	−0.466849	+	0.808606i	−0.999283	−	0.0378658i	$-0.987944\pi$
$631$	−11.7271	+	20.3119i	−0.466849	+	0.808606i	0.532434	+	0.846471i	$0.321277\pi$
$632$	2.17517	+	3.76751i	0.0865237	+	0.149863i
$633$	−3.35399	−	5.80929i	−0.133309	−	0.230898i
$634$	8.57798			0.340675
$635$	−21.4403	+	37.1357i	−0.850832	+	1.47368i
$636$	11.0641			0.438719
$637$	0.824188	+	25.2254i	0.0326555	+	0.999467i
$638$	6.18899			0.245024
$639$	1.93865	−	3.35783i	0.0766917	−	0.132834i
$640$	3.95025			0.156148
$641$	−2.80221	−	4.85357i	−0.110681	−	0.191705i	0.805364	−	0.592780i	$-0.201970\pi$
$641$	−2.80221	−	4.85357i	−0.110681	−	0.191705i	−0.916045	+	0.401076i	$0.868636\pi$
$642$	−3.53679	−	6.12590i	−0.139586	−	0.241770i
$643$	11.5626	−	20.0270i	0.455983	−	0.789786i	−0.542761	−	0.839887i	$-0.682621\pi$
$643$	11.5626	−	20.0270i	0.455983	−	0.789786i	0.998744	+	0.0501012i	$0.0159544\pi$
$644$	−14.1778	+	20.8724i	−0.558683	+	0.822488i
$645$	−4.27601			−0.168368
$646$	−0.109219			−0.00429716
$647$	17.7756			0.698832			0.349416	−	0.936968i	$-0.386380\pi$
$647$	17.7756			0.698832			0.349416	+	0.936968i	$0.386380\pi$
$648$	1.00000			0.0392837
$649$	−1.05945	−	1.83503i	−0.0415872	−	0.0720312i
$650$	6.80020	+	37.6255i	0.266726	+	1.47579i
$651$	3.87077	+	8.00232i	0.151708	+	0.313636i
$652$	−1.63571	−	2.83313i	−0.0640593	−	0.110954i
$653$	−1.25251	+	2.16941i	−0.0490145	+	0.0848956i	−0.889492	−	0.456951i	$-0.848941\pi$
$653$	−1.25251	+	2.16941i	−0.0490145	+	0.0848956i	0.840477	+	0.541847i	$0.182275\pi$
$654$	7.42350	+	12.8579i	0.290282	+	0.502783i
$655$	−3.79916	+	6.58034i	−0.148445	+	0.257115i
$656$	−9.31010			−0.363498
$657$	−0.0817820	+	0.141650i	−0.00319062	+	0.00552631i
$658$	9.90683	−	14.5848i	0.386209	−	0.568573i
$659$	−15.8598	+	27.4700i	−0.617810	+	1.07008i	0.372074	+	0.928203i	$0.378647\pi$
$659$	−15.8598	+	27.4700i	−0.617810	+	1.07008i	−0.989884	+	0.141876i	$0.954687\pi$
$660$	9.70533	−	16.8101i	0.377779	−	0.654333i
$661$	22.7146			0.883494			0.441747	−	0.897140i	$-0.354359\pi$
$661$	22.7146			0.883494			0.441747	+	0.897140i	$0.354359\pi$
$662$	2.07489	−	3.59381i	0.0806427	−	0.139677i
$663$	−0.0901422	−	0.498757i	−0.00350083	−	0.0193701i
$664$	−10.5220			−0.408335
$665$	−8.09867	−	0.592834i	−0.314053	−	0.0229891i
$666$	−5.56841	−	9.64476i	−0.215771	−	0.373727i
$667$	12.0119			0.465103
$668$	−4.42914	+	7.67150i	−0.171369	+	0.296819i
$669$	1.02744	+	1.77957i	0.0397230	+	0.0688023i
$670$	32.3774			1.25085
$671$	−40.6917			−1.57088
$672$	−2.63869	−	0.193156i	−0.101790	−	0.00745115i
$673$	−2.56027	−	4.43452i	−0.0986911	−	0.170938i	0.812452	−	0.583028i	$-0.198132\pi$
$673$	−2.56027	−	4.43452i	−0.0986911	−	0.170938i	−0.911143	+	0.412090i	$0.864799\pi$
$674$	−9.26955	+	16.0553i	−0.357050	+	0.618428i
$675$	5.30226	−	9.18378i	0.204084	−	0.353484i
$676$	2.14800	−	12.8213i	0.0826154	−	0.493127i
$677$	1.02921	+	1.78264i	0.0395556	+	0.0685123i	0.885125	−	0.465353i	$-0.154072\pi$
$677$	1.02921	+	1.78264i	0.0395556	+	0.0685123i	−0.845570	+	0.533865i	$0.820739\pi$
$678$	0.785895	+	1.36121i	0.0301821	+	0.0522770i
$679$	−15.0713	−	31.1579i	−0.578383	−	1.19573i
$680$	−0.277647	+	0.480898i	−0.0106473	+	0.0184416i
$681$	−12.9149	−	22.3692i	−0.494899	−	0.857190i
$682$	−8.25477	−	14.2977i	−0.316091	−	0.547486i
$683$	13.4644	+	23.3211i	0.515202	+	0.892356i	0.999844	+	0.0176436i	$0.00561642\pi$
$683$	13.4644	+	23.3211i	0.515202	+	0.892356i	−0.484642	+	0.874712i	$0.661050\pi$
$684$	0.388481	+	0.672870i	0.0148540	+	0.0257278i
$685$	−31.3692	+	54.3330i	−1.19856	+	2.07596i
$686$	−12.5264	+	13.6415i	−0.478260	+	0.520833i
$687$	−5.39496	−	9.34435i	−0.205831	−	0.356509i
$688$	−0.541233	−	0.937443i	−0.0206343	−	0.0357397i
$689$	−30.4493	+	25.7724i	−1.16003	+	0.981850i
$690$	18.8366	−	32.6259i	0.717097	−	1.24205i
$691$	−25.6380	+	44.4064i	−0.975316	+	1.68930i	−0.296430	+	0.955055i	$0.595796\pi$
$691$	−25.6380	+	44.4064i	−0.975316	+	1.68930i	−0.678887	+	0.734243i	$0.737537\pi$
$692$	7.47486	+	12.9468i	0.284152	+	0.492165i
$693$	−7.30493	+	10.7543i	−0.277491	+	0.408521i
$694$	−22.9868			−0.872568
$695$	−23.2552			−0.882121
$696$	0.629759	+	1.09077i	0.0238710	+	0.0413457i
$697$	0.654367	−	1.13340i	0.0247859	−	0.0429305i
$698$	−14.5899			−0.552235
$699$	1.92109	+	3.32742i	0.0726623	+	0.125855i
$700$	−15.7649	+	23.2090i	−0.595858	+	0.877217i
$701$	−26.2809			−0.992617			−0.496308	−	0.868146i	$-0.665311\pi$
$701$	−26.2809			−0.992617			−0.496308	+	0.868146i	$0.665311\pi$
$702$	−2.75209	+	2.32938i	−0.103871	+	0.0879167i
$703$	4.32644	−	7.49362i	0.163175	−	0.282627i
$704$	4.91377			0.185195
$705$	−13.1622	+	22.7976i	−0.495718	+	0.858608i
$706$	9.86522	−	17.0871i	0.371283	−	0.643080i
$707$	−10.9791	+	16.1633i	−0.412910	+	0.607883i
$708$	0.215609	−	0.373446i	0.00810309	−	0.0140350i
$709$	8.75932			0.328963			0.164482	−	0.986380i	$-0.447405\pi$
$709$	8.75932			0.328963			0.164482	+	0.986380i	$0.447405\pi$
$710$	7.65815	−	13.2643i	0.287405	−	0.497800i
$711$	2.17517	+	3.76751i	0.0815753	+	0.141293i
$712$	0.536369	−	0.929018i	0.0201013	−	0.0348164i
$713$	−16.0213	−	27.7496i	−0.600001	−	1.03923i
$714$	0.208977	−	0.307654i	0.00782076	−	0.0115137i
$715$	12.4472	+	68.8703i	0.465498	+	2.57560i
$716$	11.6034	+	20.0977i	0.433640	+	0.751087i
$717$	−10.2560			−0.383017
$718$	−37.6689			−1.40579
$719$	−2.27601			−0.0848810			−0.0424405	−	0.999099i	$-0.513513\pi$
$719$	−2.27601			−0.0848810			−0.0424405	+	0.999099i	$0.513513\pi$
$720$	3.95025			0.147217
$721$	10.5076	+	0.769173i	0.391324	+	0.0286455i
$722$	9.19816	−	15.9317i	0.342320	−	0.592916i
$723$	−0.316427	−	0.548068i	−0.0117681	−	0.0203829i
$724$	−9.73088	−	16.8544i	−0.361645	−	0.626388i
$725$	13.3566			0.496051
$726$	6.57259	−	11.3841i	0.243932	−	0.422502i
$727$	−39.8719			−1.47877			−0.739383	−	0.673285i	$-0.764883\pi$
$727$	−39.8719			−1.47877			−0.739383	+	0.673285i	$0.764883\pi$
$728$	7.71185	−	5.61493i	0.285820	−	0.208103i
$729$	1.00000			0.0370370
$730$	−0.323060	+	0.559556i	−0.0119570	+	0.0207101i
$731$	0.152164			0.00562798
$732$	−4.14057	−	7.17168i	−0.153040	−	0.265073i
$733$	−12.8845	−	22.3167i	−0.475901	−	0.824284i	0.523718	−	0.851892i	$-0.324545\pi$
$733$	−12.8845	−	22.3167i	−0.475901	−	0.824284i	−0.999619	+	0.0276073i	$0.991211\pi$
$734$	−1.25141	+	2.16750i	−0.0461903	+	0.0800039i
$735$	17.1658	−	21.6785i	0.633168	−	0.799624i
$736$	9.53690			0.351535
$737$	40.2747			1.48354
$738$	−9.31010			−0.342710
$739$	12.8179			0.471512			0.235756	−	0.971812i	$-0.424243\pi$
$739$	12.8179			0.471512			0.235756	+	0.971812i	$0.424243\pi$
$740$	−21.9966	−	38.0993i	−0.808612	−	1.40056i
$741$	−2.63650	−	0.946878i	−0.0968544	−	0.0347844i
$742$	−29.1947	−	2.13709i	−1.07177	−	0.0784551i
$743$	−10.1715	−	17.6176i	−0.373156	−	0.646326i	0.616893	−	0.787047i	$-0.288391\pi$
$743$	−10.1715	−	17.6176i	−0.373156	−	0.646326i	−0.990049	+	0.140721i	$0.955058\pi$
$744$	1.67992	−	2.90971i	0.0615890	−	0.106675i
$745$	26.2101	+	45.3972i	0.960264	+	1.66323i
$746$	6.58371	−	11.4033i	0.241047	−	0.417505i
$747$	−10.5220			−0.384981
$748$	−0.345368	+	0.598195i	−0.0126279	+	0.0218722i
$749$	8.14924	+	16.8475i	0.297767	+	0.615594i
$750$	11.0696	−	19.1731i	0.404205	−	0.700104i
$751$	15.2371	−	26.3914i	0.556008	−	0.963034i	−0.441816	−	0.897106i	$-0.645666\pi$
$751$	15.2371	−	26.3914i	0.556008	−	0.963034i	0.997824	−	0.0659287i	$-0.0210010\pi$
$752$	−6.66398			−0.243010
$753$	−7.53648	+	13.0536i	−0.274645	+	0.475698i
$754$	−4.27398	−	1.53496i	−0.155649	−	0.0559001i
$755$	63.7400			2.31974
$756$	−2.63869	−	0.193156i	−0.0959683	−	0.00702501i
$757$	10.7264	+	18.5787i	0.389859	+	0.675256i	0.992430	−	0.122809i	$-0.0391904\pi$
$757$	10.7264	+	18.5787i	0.389859	+	0.675256i	−0.602571	+	0.798065i	$0.705857\pi$
$758$	11.8646			0.430940
$759$	23.4311	−	40.5838i	0.850494	−	1.47310i
$760$	1.53460	+	2.65801i	0.0556658	+	0.0964160i
$761$	−50.0476			−1.81422			−0.907112	−	0.420890i	$-0.861718\pi$
$761$	−50.0476			−1.81422			−0.907112	+	0.420890i	$0.861718\pi$
$762$	−10.8551			−0.393240
$763$	−17.1048	−	35.3619i	−0.619234	−	1.28019i
$764$	7.29819	+	12.6408i	0.264039	+	0.457329i
$765$	−0.277647	+	0.480898i	−0.0100383	+	0.0173869i
$766$	−8.21139	+	14.2225i	−0.296690	+	0.513881i
$767$	0.276521	+	1.52999i	0.00998460	+	0.0552448i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	25.3820	+	43.9629i	0.915298	+	1.58534i	0.806465	+	0.591282i	$0.201378\pi$
$769$	25.3820	+	43.9629i	0.915298	+	1.58534i	0.108833	+	0.994060i	$0.465289\pi$
$770$	−28.8563	+	42.4821i	−1.03991	+	1.53095i
$771$	5.56909	−	9.64595i	0.200566	−	0.347390i
$772$	0.884301	+	1.53165i	0.0318267	+	0.0551255i
$773$	−7.14225	−	12.3707i	−0.256889	−	0.444944i	0.708518	−	0.705693i	$-0.249364\pi$
$773$	−7.14225	−	12.3707i	−0.256889	−	0.444944i	−0.965407	+	0.260748i	$0.916031\pi$
$774$	−0.541233	−	0.937443i	−0.0194542	−	0.0336957i
$775$	−17.8148	−	30.8561i	−0.639925	−	1.10838i
$776$	−6.54097	+	11.3293i	−0.234807	+	0.406698i
$777$	12.8304	+	26.5251i	0.460287	+	0.951583i
$778$	9.03721	+	15.6529i	0.324000	+	0.561184i
$779$	−3.61680	−	6.26448i	−0.129585	−	0.224448i
$780$	−10.8715	+	9.20163i	−0.389261	+	0.329471i
$781$	9.52607	−	16.4996i	0.340870	−	0.590403i
$782$	−0.670308	+	1.16101i	−0.0239702	+	0.0415176i
$783$	0.629759	+	1.09077i	0.0225058	+	0.0389811i
$784$	6.92538	+	1.01936i	0.247335	+	0.0364056i
$785$	69.9449			2.49644
$786$	−1.92350			−0.0686090
$787$	3.26997	+	5.66376i	0.116562	+	0.201891i	0.918403	−	0.395646i	$-0.129479\pi$
$787$	3.26997	+	5.66376i	0.116562	+	0.201891i	−0.801841	+	0.597537i	$0.796146\pi$
$788$	2.92757	−	5.07070i	0.104290	−	0.180636i
$789$	−17.1706			−0.611288
$790$	8.59248	+	14.8826i	0.305707	+	0.529500i
$791$	−1.81081	−	3.74361i	−0.0643849	−	0.133108i
$792$	4.91377			0.174603
$793$	28.1008	+	10.0922i	0.997888	+	0.358383i
$794$	1.20491	−	2.08696i	0.0427606	−	0.0740635i
$795$	43.7059			1.55009
$796$	−6.96137	+	12.0575i	−0.246739	+	0.427365i
$797$	−24.2958	+	42.0815i	−0.860601	+	1.49060i	0.0107495	+	0.999942i	$0.496578\pi$
$797$	−24.2958	+	42.0815i	−0.860601	+	1.49060i	−0.871350	+	0.490662i	$0.836755\pi$
$798$	−0.895114	−	1.85053i	−0.0316867	−	0.0655081i
$799$	0.468383	−	0.811263i	0.0165702	−	0.0287004i
$800$	10.6045			0.374926
$801$	0.536369	−	0.929018i	0.0189517	−	0.0328252i
$802$	12.4622	+	21.5851i	0.440055	+	0.762197i
$803$	−0.401858	+	0.696038i	−0.0141813	+	0.0245627i
$804$	4.09814	+	7.09819i	0.144530	+	0.250334i
$805$	−56.0058	+	82.4514i	−1.97395	+	2.90603i
$806$	2.15452	+	11.9210i	0.0758897	+	0.419898i
$807$	1.64355	+	2.84672i	0.0578559	+	0.100209i
$808$	7.38523			0.259812
$809$	41.7183			1.46674			0.733369	−	0.679831i	$-0.237947\pi$
$809$	41.7183			1.46674			0.733369	+	0.679831i	$0.237947\pi$
$810$	3.95025			0.138798
$811$	2.40508			0.0844538			0.0422269	−	0.999108i	$-0.486555\pi$
$811$	2.40508			0.0844538			0.0422269	+	0.999108i	$0.486555\pi$
$812$	−1.45105	−	2.99986i	−0.0509219	−	0.105274i
$813$	7.36304	−	12.7532i	0.258233	−	0.447273i
$814$	−27.3619	−	47.3922i	−0.959034	−	1.66109i
$815$	−6.46146	−	11.1916i	−0.226335	−	0.392024i
$816$	−0.140571			−0.00492099
$817$	0.420518	−	0.728358i	0.0147121	−	0.0254820i
$818$	27.4769			0.960707
$819$	7.71185	−	5.61493i	0.269474	−	0.196201i
$820$	−36.7773			−1.28432
$821$	0.226645	−	0.392561i	0.00790998	−	0.0137005i	−0.862043	−	0.506835i	$-0.830815\pi$
$821$	0.226645	−	0.392561i	0.00790998	−	0.0137005i	0.869953	+	0.493134i	$0.164149\pi$
$822$	−15.8821			−0.553952
$823$	2.09531	+	3.62919i	0.0730380	+	0.126506i	0.900231	−	0.435412i	$-0.143397\pi$
$823$	2.09531	+	3.62919i	0.0730380	+	0.126506i	−0.827193	+	0.561917i	$0.810064\pi$
$824$	−1.99107	−	3.44863i	−0.0693621	−	0.120139i
$825$	26.0541	−	45.1270i	0.907087	−	1.57112i
$826$	−0.641059	+	0.943763i	−0.0223053	+	0.0328377i
$827$	1.35282			0.0470421			0.0235211	−	0.999723i	$-0.492512\pi$
$827$	1.35282			0.0470421			0.0235211	+	0.999723i	$0.492512\pi$
$828$	9.53690			0.331430
$829$	−48.2162			−1.67462			−0.837309	−	0.546730i	$-0.815872\pi$
$829$	−48.2162			−1.67462			−0.837309	+	0.546730i	$0.815872\pi$
$830$	−41.5648			−1.44273
$831$	9.25021	+	16.0218i	0.320886	+	0.555791i
$832$	−3.39335	−	1.21869i	−0.117643	−	0.0422505i
$833$	−0.610851	+	0.771439i	−0.0211647	+	0.0267288i
$834$	−2.94351	−	5.09831i	−0.101925	−	0.176540i
$835$	−17.4962	+	30.3044i	−0.605482	+	1.04873i
$836$	1.90891	+	3.30633i	0.0660210	+	0.114352i
$837$	1.67992	−	2.90971i	0.0580667	−	0.100574i
$838$	10.3331			0.356951
$839$	14.1093	−	24.4380i	0.487107	−	0.843694i	−0.512783	−	0.858518i	$-0.671386\pi$
$839$	14.1093	−	24.4380i	0.487107	−	0.843694i	0.999890	+	0.0148244i	$0.00471891\pi$
$840$	−10.4235	−	0.763015i	−0.359645	−	0.0263265i
$841$	13.7068	−	23.7409i	0.472649	−	0.818651i
$842$	8.43511	−	14.6100i	0.290693	−	0.503495i
$843$	31.3463			1.07962
$844$	3.35399	−	5.80929i	0.115449	−	0.199964i
$845$	8.48514	−	50.6475i	0.291898	−	1.74233i
$846$	−6.66398			−0.229112
$847$	−19.5419	+	28.7695i	−0.671468	+	0.988530i
$848$	5.53204	+	9.58177i	0.189971	+	0.329039i
$849$	14.7197			0.505179
$850$	−0.745346	+	1.29098i	−0.0255652	+	0.0442801i
$851$	−53.1053	−	91.9811i	−1.82043	−	3.15307i
$852$	3.87729			0.132834
$853$	−3.29308			−0.112753			−0.0563764	−	0.998410i	$-0.517955\pi$
$853$	−3.29308			−0.112753			−0.0563764	+	0.998410i	$0.517955\pi$
$854$	9.54044	+	19.7236i	0.326467	+	0.674929i
$855$	1.53460	+	2.65801i	0.0524822	+	0.0909019i
$856$	3.53679	−	6.12590i	0.120885	−	0.209379i
$857$	16.7918	−	29.0842i	0.573596	−	0.993497i	−0.422597	−	0.906318i	$-0.638881\pi$
$857$	16.7918	−	29.0842i	0.573596	−	0.993497i	0.996193	−	0.0871794i	$-0.0277853\pi$
$858$	−13.5231	+	11.4460i	−0.461673	+	0.390761i
$859$	−13.6075	−	23.5688i	−0.464280	−	0.804157i	0.534888	−	0.844923i	$-0.320354\pi$
$859$	−13.6075	−	23.5688i	−0.464280	−	0.804157i	−0.999169	+	0.0407656i	$0.987020\pi$
$860$	−2.13801	−	3.70314i	−0.0729054	−	0.126276i
$861$	24.5665	+	1.79830i	0.837224	+	0.0612859i
$862$	−12.1718	+	21.0822i	−0.414573	+	0.718061i
$863$	−7.05959	−	12.2276i	−0.240311	−	0.416231i	0.720492	−	0.693463i	$-0.243916\pi$
$863$	−7.05959	−	12.2276i	−0.240311	−	0.416231i	−0.960803	+	0.277232i	$0.910583\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	29.5276	+	51.1433i	1.00397	+	1.73893i
$866$	0.984059	+	1.70444i	0.0334397	+	0.0579193i
$867$	−8.49012	+	14.7053i	−0.288340	+	0.499419i
$868$	−4.99483	+	7.35335i	−0.169536	+	0.249589i
$869$	10.6883	+	18.5127i	0.362576	+	0.628000i
$870$	2.48771	+	4.30884i	0.0843412	+	0.146083i
$871$	−27.8128	−	9.98874i	−0.942402	−	0.338455i
$872$	−7.42350	+	12.8579i	−0.251391	+	0.435423i
$873$	−6.54097	+	11.3293i	−0.221378	+	0.383438i
$874$	3.70491	+	6.41709i	0.125320	+	0.217061i
$875$	−32.9127	+	48.4538i	−1.11265	+	1.63804i
$876$	−0.163564			−0.00552631
$877$	−8.01911			−0.270786			−0.135393	−	0.990792i	$-0.543230\pi$
$877$	−8.01911			−0.270786			−0.135393	+	0.990792i	$0.543230\pi$
$878$	−10.1318	−	17.5488i	−0.341931	−	0.592243i
$879$	−8.39523	+	14.5410i	−0.283164	+	0.490454i
$880$	19.4107			0.654333
$881$	13.1358	+	22.7519i	0.442558	+	0.766532i	0.997878	−	0.0651039i	$-0.0207379\pi$
$881$	13.1358	+	22.7519i	0.442558	+	0.766532i	−0.555321	+	0.831636i	$0.687405\pi$
$882$	6.92538	+	1.01936i	0.233190	+	0.0343235i
$883$	−18.7341			−0.630452			−0.315226	−	0.949017i	$-0.602080\pi$
$883$	−18.7341			−0.630452			−0.315226	+	0.949017i	$0.602080\pi$
$884$	0.386865	−	0.327444i	0.0130117	−	0.0110131i
$885$	0.851711	−	1.47521i	0.0286300	−	0.0495886i
$886$	28.5415			0.958870
$887$	6.11884	−	10.5981i	0.205450	−	0.355851i	−0.744826	−	0.667259i	$-0.767467\pi$
$887$	6.11884	−	10.5981i	0.205450	−	0.355851i	0.950276	+	0.311408i	$0.100801\pi$
$888$	5.56841	−	9.64476i	0.186863	−	0.323657i
$889$	28.6434	+	2.09673i	0.960667	+	0.0703222i
$890$	2.11879	−	3.66986i	0.0710221	−	0.123014i
$891$	4.91377			0.164618
$892$	−1.02744	+	1.77957i	−0.0344011	+	0.0595845i
$893$	−2.58883	−	4.48399i	−0.0866320	−	0.150051i
$894$	−6.63504	+	11.4922i	−0.221909	+	0.384358i
$895$	45.8365	+	79.3911i	1.53214	+	2.65375i
$896$	−1.15207	−	2.38175i	−0.0384879	−	0.0795687i
$897$	−26.2464	+	22.2150i	−0.876342	+	0.741739i
$898$	12.1517	+	21.0474i	0.405508	+	0.702360i
$899$	4.23179			0.141138
$900$	10.6045			0.353484
$901$	−1.55529			−0.0518143
$902$	−45.7477			−1.52323
$903$	1.24707	+	2.57816i	0.0415000	+	0.0857959i
$904$	−0.785895	+	1.36121i	−0.0261385	+	0.0452732i
$905$	−38.4395	−	66.5791i	−1.27777	−	2.21316i
$906$	8.06783	+	13.9739i	0.268036	+	0.464252i
$907$	−22.8899			−0.760048			−0.380024	−	0.924977i	$-0.624084\pi$
$907$	−22.8899			−0.760048			−0.380024	+	0.924977i	$0.624084\pi$
$908$	12.9149	−	22.3692i	0.428595	−	0.742349i
$909$	7.38523			0.244953
$910$	30.4638	−	22.1804i	1.00986	−	0.735273i
$911$	22.0074			0.729139			0.364570	−	0.931176i	$-0.381216\pi$
$911$	22.0074			0.729139			0.364570	+	0.931176i	$0.381216\pi$
$912$	−0.388481	+	0.672870i	−0.0128639	+	0.0222809i
$913$	−51.7029			−1.71112
$914$	3.12651	+	5.41528i	0.103416	+	0.179121i
$915$	−16.3563	−	28.3300i	−0.540723	−	0.936560i
$916$	5.39496	−	9.34435i	0.178255	−	0.308746i
$917$	5.07553	+	0.371536i	0.167609	+	0.0122692i
$918$	−0.140571			−0.00463955
$919$	49.9202			1.64672			0.823358	−	0.567522i	$-0.192098\pi$
$919$	49.9202			1.64672			0.823358	+	0.567522i	$0.192098\pi$
$920$	37.6732			1.24205
$921$	−5.69511			−0.187660
$922$	9.65625	+	16.7251i	0.318012	+	0.550812i
$923$	−10.6707	+	9.03168i	−0.351229	+	0.297281i
$924$	−12.9659	−	0.949124i	−0.426548	−	0.0312239i
$925$	−59.0502	−	102.278i	−1.94156	−	3.36288i
$926$	−10.7240	+	18.5745i	−0.352412	+	0.610396i
$927$	−1.99107	−	3.44863i	−0.0653952	−	0.113268i
$928$	−0.629759	+	1.09077i	−0.0206729	+	0.0358064i
$929$	9.00296			0.295377			0.147689	−	0.989034i	$-0.452817\pi$
$929$	9.00296			0.295377			0.147689	+	0.989034i	$0.452817\pi$
$930$	6.63613	−	11.4941i	0.217607	−	0.376907i
$931$	2.00449	+	5.05588i	0.0656944	+	0.165700i
$932$	−1.92109	+	3.32742i	−0.0629274	+	0.108993i
$933$	−0.183797	+	0.318345i	−0.00601723	+	0.0104221i
$934$	−4.78510			−0.156573
$935$	−1.36429	+	2.36302i	−0.0446171	+	0.0772791i
$936$	−3.39335	−	1.21869i	−0.110915	−	0.0398342i
$937$	−42.4359			−1.38632			−0.693159	−	0.720784i	$-0.743782\pi$
$937$	−42.4359			−1.38632			−0.693159	+	0.720784i	$0.743782\pi$
$938$	−9.44267	−	19.5215i	−0.308314	−	0.637400i
$939$	2.95742	+	5.12240i	0.0965117	+	0.167163i
$940$	−26.3244			−0.858608
$941$	−4.68568	+	8.11583i	−0.152749	+	0.264569i	−0.932237	−	0.361848i	$-0.882146\pi$
$941$	−4.68568	+	8.11583i	−0.152749	+	0.264569i	0.779488	+	0.626417i	$0.215479\pi$
$942$	8.85322	+	15.3342i	0.288453	+	0.499616i
$943$	−88.7895			−2.89138
$944$	0.431218			0.0140350
$945$	−10.4235	−	0.763015i	−0.339077	−	0.0248209i
$946$	−2.65950	−	4.60638i	−0.0864677	−	0.149766i
$947$	18.1411	−	31.4213i	0.589507	−	1.02106i	−0.404790	−	0.914409i	$-0.632656\pi$
$947$	18.1411	−	31.4213i	0.589507	−	1.02106i	0.994297	−	0.106646i	$-0.0340111\pi$
$948$	−2.17517	+	3.76751i	−0.0706463	+	0.122363i
$949$	0.450143	−	0.381002i	0.0146122	−	0.0123679i
$950$	4.11966	+	7.13545i	0.133659	+	0.231505i
$951$	4.28899	+	7.42875i	0.139080	+	0.240894i
$952$	0.370925	+	0.0271522i	0.0120217	+	0.000880008i
$953$	9.41368	−	16.3050i	0.304939	−	0.528170i	−0.672309	−	0.740271i	$-0.734697\pi$
$953$	9.41368	−	16.3050i	0.304939	−	0.528170i	0.977248	+	0.212101i	$0.0680306\pi$
$954$	5.53204	+	9.58177i	0.179106	+	0.310221i
$955$	28.8297	+	49.9345i	0.932907	+	1.61584i
$956$	−5.12799	−	8.88194i	−0.165851	−	0.287262i
$957$	3.09449	+	5.35982i	0.100031	+	0.173258i
$958$	5.85660	−	10.1439i	0.189218	−	0.327735i
$959$	41.9080	+	3.06772i	1.35328	+	0.0990620i
$960$	1.97513	+	3.42102i	0.0637470	+	0.110413i
$961$	9.85571	+	17.0706i	0.317926	+	0.550664i
$962$	7.14154	+	39.5142i	0.230252	+	1.27399i
$963$	3.53679	−	6.12590i	0.113971	−	0.197404i
$964$	0.316427	−	0.548068i	0.0101914	−	0.0176521i
$965$	3.49322	+	6.05043i	0.112451	+	0.194770i
$966$	−25.1649	−	1.84211i	−0.809668	−	0.0592689i
$967$	−9.63971			−0.309992			−0.154996	−	0.987915i	$-0.549536\pi$
$967$	−9.63971			−0.309992			−0.154996	+	0.987915i	$0.549536\pi$
$968$	13.1452			0.422502
$969$	−0.0546094	−	0.0945863i	−0.00175431	−	0.00303855i
$970$	−25.8385	+	44.7536i	−0.829624	+	1.43695i
$971$	18.2733			0.586419			0.293209	−	0.956048i	$-0.405277\pi$
$971$	18.2733			0.586419			0.293209	+	0.956048i	$0.405277\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	6.78225	+	14.0214i	0.217429	+	0.449506i
$974$	−25.7570			−0.825308
$975$	−29.1846	+	24.7019i	−0.934654	+	0.791094i
$976$	4.14057	−	7.17168i	0.132536	−	0.229560i
$977$	32.0865			1.02654			0.513268	−	0.858228i	$-0.328435\pi$
$977$	32.0865			1.02654			0.513268	+	0.858228i	$0.328435\pi$
$978$	1.63571	−	2.83313i	0.0523042	−	0.0905935i
$979$	2.63560	−	4.56499i	0.0842340	−	0.145898i
$980$	27.3570	+	4.02672i	0.873888	+	0.128629i
$981$	−7.42350	+	12.8579i	−0.237014	+	0.410521i
$982$	−4.70024			−0.149991
$983$	−11.7559	+	20.3618i	−0.374955	+	0.649442i	−0.990320	−	0.138801i	$-0.955675\pi$
$983$	−11.7559	+	20.3618i	−0.374955	+	0.649442i	0.615365	+	0.788242i	$0.289009\pi$
$984$	−4.65505	−	8.06279i	−0.148398	−	0.257032i
$985$	11.5646	−	20.0306i	0.368480	−	0.638226i
$986$	−0.0885262	−	0.153332i	−0.00281925	−	0.00488308i
$987$	17.5842	+	1.28719i	0.559711	+	0.0409716i
$988$	−0.498231	−	2.75672i	−0.0158509	−	0.0877029i
$989$	−5.16168	−	8.94030i	−0.164132	−	0.284285i
$990$	19.4107			0.616911
$991$	25.1859			0.800058			0.400029	−	0.916503i	$-0.369000\pi$
$991$	25.1859			0.800058			0.400029	+	0.916503i	$0.369000\pi$
$992$	3.35985			0.106675
$993$	4.14977			0.131689
$994$	−10.2310	−	0.748922i	−0.324507	−	0.0237544i
$995$	−27.4992	+	47.6300i	−0.871783	+	1.50997i
$996$	−5.26102	−	9.11236i	−0.166702	−	0.288736i
$997$	−7.49790	−	12.9867i	−0.237461	−	0.411294i	0.722524	−	0.691346i	$-0.242982\pi$
$997$	−7.49790	−	12.9867i	−0.237461	−	0.411294i	−0.959985	+	0.280052i	$0.909648\pi$
$998$	−32.6494			−1.03350
$999$	5.56841	−	9.64476i	0.176177	−	0.305147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.b.445.1	yes	8
3.2	odd	2		1638.2.p.i.991.4		8
7.2	even	3		546.2.j.d.289.1	✓	8
13.9	even	3		546.2.j.d.529.1	yes	8
21.2	odd	6		1638.2.m.g.289.4		8
39.35	odd	6		1638.2.m.g.1621.4		8
91.9	even	3	inner	546.2.k.b.373.1	yes	8
273.191	odd	6		1638.2.p.i.919.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.d.289.1	✓	8	7.2	even	3
546.2.j.d.529.1	yes	8	13.9	even	3
546.2.k.b.373.1	yes	8	91.9	even	3	inner
546.2.k.b.445.1	yes	8	1.1	even	1	trivial
1638.2.m.g.289.4		8	21.2	odd	6
1638.2.m.g.1621.4		8	39.35	odd	6
1638.2.p.i.919.4		8	273.191	odd	6
1638.2.p.i.991.4		8	3.2	odd	2

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97513 - 3.42102i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.48662 + 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.97513 - 3.42102i) q^{5} +(0.500000 - 0.866025i) q^{6} +(-1.48662 + 2.18860i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +3.95025 q^{10} +4.91377 q^{11} +(0.500000 + 0.866025i) q^{12} +(-3.39335 - 1.21869i) q^{13} +(-1.15207 - 2.38175i) q^{14} +(1.97513 + 3.42102i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-0.0702857 - 0.121738i) q^{17} +(-0.500000 + 0.866025i) q^{18} -0.776963 q^{19} +(-1.97513 + 3.42102i) q^{20} +(1.48662 - 2.18860i) q^{21} +(-2.45689 + 4.25545i) q^{22} +(-4.76845 + 8.25920i) q^{23} -1.00000 q^{24} +(-5.30226 + 9.18378i) q^{25} +(2.75209 - 2.32938i) q^{26} -1.00000 q^{27} +(2.63869 + 0.193156i) q^{28} +(-0.629759 - 1.09077i) q^{29} -3.95025 q^{30} +(-1.67992 + 2.90971i) q^{31} +(-0.500000 - 0.866025i) q^{32} -4.91377 q^{33} +0.140571 q^{34} +(10.4235 + 0.763015i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.56841 + 9.64476i) q^{37} +(0.388481 - 0.672870i) q^{38} +(3.39335 + 1.21869i) q^{39} +(-1.97513 - 3.42102i) q^{40} +(4.65505 + 8.06279i) q^{41} +(1.15207 + 2.38175i) q^{42} +(-0.541233 + 0.937443i) q^{43} +(-2.45689 - 4.25545i) q^{44} +(-1.97513 - 3.42102i) q^{45} +(-4.76845 - 8.25920i) q^{46} +(3.33199 + 5.77118i) q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.57990 - 6.50724i) q^{49} +(-5.30226 - 9.18378i) q^{50} +(0.0702857 + 0.121738i) q^{51} +(0.641255 + 3.54807i) q^{52} +(5.53204 - 9.58177i) q^{53} +(0.500000 - 0.866025i) q^{54} +(-9.70533 - 16.8101i) q^{55} +(-1.48662 + 2.18860i) q^{56} +0.776963 q^{57} +1.25952 q^{58} +(-0.215609 - 0.373446i) q^{59} +(1.97513 - 3.42102i) q^{60} -8.28114 q^{61} +(-1.67992 - 2.90971i) q^{62} +(-1.48662 + 2.18860i) q^{63} +1.00000 q^{64} +(2.53312 + 14.0158i) q^{65} +(2.45689 - 4.25545i) q^{66} +8.19628 q^{67} +(-0.0702857 + 0.121738i) q^{68} +(4.76845 - 8.25920i) q^{69} +(-5.87254 + 8.64551i) q^{70} +(1.93865 - 3.35783i) q^{71} +1.00000 q^{72} +(-0.0817820 + 0.141650i) q^{73} +(-5.56841 - 9.64476i) q^{74} +(5.30226 - 9.18378i) q^{75} +(0.388481 + 0.672870i) q^{76} +(-7.30493 + 10.7543i) q^{77} +(-2.75209 + 2.32938i) q^{78} +(2.17517 + 3.76751i) q^{79} +3.95025 q^{80} +1.00000 q^{81} -9.31010 q^{82} -10.5220 q^{83} +(-2.63869 - 0.193156i) q^{84} +(-0.277647 + 0.480898i) q^{85} +(-0.541233 - 0.937443i) q^{86} +(0.629759 + 1.09077i) q^{87} +4.91377 q^{88} +(0.536369 - 0.929018i) q^{89} +3.95025 q^{90} +(7.71185 - 5.61493i) q^{91} +9.53690 q^{92} +(1.67992 - 2.90971i) q^{93} -6.66398 q^{94} +(1.53460 + 2.65801i) q^{95} +(0.500000 + 0.866025i) q^{96} +(-6.54097 + 11.3293i) q^{97} +(6.92538 + 1.01936i) q^{98} +4.91377 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9	\( 8 q - 4 q^{2} - 8 q^{3} - 4 q^{4} + 2 q^{5} + 4 q^{6} + 3 q^{7} + 8 q^{8} + 8 q^{9} - 4 q^{10} + 12 q^{11} + 4 q^{12} - 11 q^{13} - 3 q^{14} - 2 q^{15} - 4 q^{16} + 4 q^{17} - 4 q^{18} - 12 q^{19} + 2 q^{20} - 3 q^{21} - 6 q^{22} - 10 q^{23} - 8 q^{24} - 18 q^{25} + 10 q^{26} - 8 q^{27} + 2 q^{29} + 4 q^{30} + 6 q^{31} - 4 q^{32} - 12 q^{33} - 8 q^{34} + 18 q^{35} - 4 q^{36} - 28 q^{37} + 6 q^{38} + 11 q^{39} + 2 q^{40} + 3 q^{42} - 6 q^{43} - 6 q^{44} + 2 q^{45} - 10 q^{46} + q^{47} + 4 q^{48} - 7 q^{49} - 18 q^{50} - 4 q^{51} + q^{52} + 7 q^{53} + 4 q^{54} + q^{55} + 3 q^{56} + 12 q^{57} - 4 q^{58} + 2 q^{59} - 2 q^{60} - 48 q^{61} + 6 q^{62} + 3 q^{63} + 8 q^{64} + 19 q^{65} + 6 q^{66} + 30 q^{67} + 4 q^{68} + 10 q^{69} - 18 q^{70} + 6 q^{71} + 8 q^{72} + q^{73} - 28 q^{74} + 18 q^{75} + 6 q^{76} - 22 q^{77} - 10 q^{78} - 12 q^{79} - 4 q^{80} + 8 q^{81} - 32 q^{83} - 13 q^{85} - 6 q^{86} - 2 q^{87} + 12 q^{88} + 25 q^{89} - 4 q^{90} + 34 q^{91} + 20 q^{92} - 6 q^{93} - 2 q^{94} - 8 q^{95} + 4 q^{96} - q^{97} + 2 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 8 * q^3 - 4 * q^4 + 2 * q^5 + 4 * q^6 + 3 * q^7 + 8 * q^8 + 8 * q^9 - 4 * q^10 + 12 * q^11 + 4 * q^12 - 11 * q^13 - 3 * q^14 - 2 * q^15 - 4 * q^16 + 4 * q^17 - 4 * q^18 - 12 * q^19 + 2 * q^20 - 3 * q^21 - 6 * q^22 - 10 * q^23 - 8 * q^24 - 18 * q^25 + 10 * q^26 - 8 * q^27 + 2 * q^29 + 4 * q^30 + 6 * q^31 - 4 * q^32 - 12 * q^33 - 8 * q^34 + 18 * q^35 - 4 * q^36 - 28 * q^37 + 6 * q^38 + 11 * q^39 + 2 * q^40 + 3 * q^42 - 6 * q^43 - 6 * q^44 + 2 * q^45 - 10 * q^46 + q^47 + 4 * q^48 - 7 * q^49 - 18 * q^50 - 4 * q^51 + q^52 + 7 * q^53 + 4 * q^54 + q^55 + 3 * q^56 + 12 * q^57 - 4 * q^58 + 2 * q^59 - 2 * q^60 - 48 * q^61 + 6 * q^62 + 3 * q^63 + 8 * q^64 + 19 * q^65 + 6 * q^66 + 30 * q^67 + 4 * q^68 + 10 * q^69 - 18 * q^70 + 6 * q^71 + 8 * q^72 + q^73 - 28 * q^74 + 18 * q^75 + 6 * q^76 - 22 * q^77 - 10 * q^78 - 12 * q^79 - 4 * q^80 + 8 * q^81 - 32 * q^83 - 13 * q^85 - 6 * q^86 - 2 * q^87 + 12 * q^88 + 25 * q^89 - 4 * q^90 + 34 * q^91 + 20 * q^92 - 6 * q^93 - 2 * q^94 - 8 * q^95 + 4 * q^96 - q^97 + 2 * q^98 + 12 * q^99

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