LMFDB - Embedded newform 546.2.bd.a.121.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(121,546)]

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, 1]))

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

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

chi := DirichletCharacter("546.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bd (of order $6$, 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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26x^{14} + 249x^{12} + 1144x^{10} + 2766x^{8} + 3554x^{6} + 2260x^{4} + 564x^{2} + 9 $ x^16 + 26x^14 + 249x^12 + 1144x^10 + 2766x^8 + 3554x^6 + 2260x^4 + 564*x^2 + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			121.7
Root			$3.28902i$ of defining polynomial
Character	$\chi$	$=$	546.121
Dual form			546.2.bd.a.361.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.152918 - 0.0882870i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.623746 - 2.57117i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.152918 - 0.0882870i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.623746 - 2.57117i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -0.176574 q^{10} -2.92586i q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.87127 + 2.18078i) q^{13} +(-1.82577 - 1.91483i) q^{14} +(0.152918 + 0.0882870i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.536265 + 0.928838i) q^{17} +(0.866025 - 0.500000i) q^{18} -4.80348i q^{19} +(-0.152918 + 0.0882870i) q^{20} +(0.623746 + 2.57117i) q^{21} +(-1.46293 - 2.53387i) q^{22} +(-0.966059 - 1.67326i) q^{23} +1.00000i q^{24} +(-2.48441 - 4.30313i) q^{25} +(-1.39621 + 3.32424i) q^{26} -1.00000 q^{27} +(-2.53858 - 0.745408i) q^{28} +(0.880456 - 1.52499i) q^{29} +0.176574 q^{30} +(0.771896 - 0.445654i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.92586i q^{33} +1.07253i q^{34} +(-0.131620 + 0.448247i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.26164 - 3.61516i) q^{37} +(-2.40174 - 4.15994i) q^{38} +(2.87127 - 2.18078i) q^{39} +(-0.0882870 + 0.152918i) q^{40} +(-3.65298 - 2.10905i) q^{41} +(1.82577 + 1.91483i) q^{42} +(-2.42721 - 4.20406i) q^{43} +(-2.53387 - 1.46293i) q^{44} +(-0.152918 - 0.0882870i) q^{45} +(-1.67326 - 0.966059i) q^{46} +(6.56871 + 3.79245i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-6.22188 + 3.20752i) q^{49} +(-4.30313 - 2.48441i) q^{50} +(0.536265 - 0.928838i) q^{51} +(0.452970 + 3.57698i) q^{52} +(3.98604 + 6.90402i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.258315 + 0.447415i) q^{55} +(-2.57117 + 0.623746i) q^{56} +4.80348i q^{57} -1.76091i q^{58} +(12.3878 + 7.15207i) q^{59} +(0.152918 - 0.0882870i) q^{60} -6.40996 q^{61} +(0.445654 - 0.771896i) q^{62} +(-0.623746 - 2.57117i) q^{63} -1.00000 q^{64} +(0.631603 - 0.0799828i) q^{65} +(1.46293 + 2.53387i) q^{66} +11.2558i q^{67} +(0.536265 + 0.928838i) q^{68} +(0.966059 + 1.67326i) q^{69} +(0.110137 + 0.454003i) q^{70} +(11.6285 - 6.71374i) q^{71} -1.00000i q^{72} +(-9.20985 + 5.31731i) q^{73} +(3.61516 - 6.26164i) q^{74} +(2.48441 + 4.30313i) q^{75} +(-4.15994 - 2.40174i) q^{76} +(-7.52289 + 1.82499i) q^{77} +(1.39621 - 3.32424i) q^{78} +(3.86312 - 6.69111i) q^{79} +0.176574i q^{80} +1.00000 q^{81} -4.21809 q^{82} +9.49646i q^{83} +(2.53858 + 0.745408i) q^{84} +(0.164009 - 0.0946905i) q^{85} +(-4.20406 - 2.42721i) q^{86} +(-0.880456 + 1.52499i) q^{87} -2.92586 q^{88} +(4.92847 - 2.84545i) q^{89} -0.176574 q^{90} +(7.39810 + 6.02230i) q^{91} -1.93212 q^{92} +(-0.771896 + 0.445654i) q^{93} +7.58490 q^{94} +(-0.424085 + 0.734537i) q^{95} +(0.866025 + 0.500000i) q^{96} +(9.29173 - 5.36458i) q^{97} +(-3.78455 + 5.88874i) q^{98} -2.92586i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	$ 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) $ 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.152918	−	0.0882870i	−0.0683868	−	0.0394832i	0.465417	−	0.885092i	$-0.345904\pi$
$5$	−0.152918	−	0.0882870i	−0.0683868	−	0.0394832i	−0.533804	+	0.845609i	$0.679238\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−0.623746	−	2.57117i	−0.235754	−	0.971813i
$7$	−0.623746	−	2.57117i	−0.235754	−	0.971813i
$8$		−	1.00000i		−	0.353553i
$9$	1.00000			0.333333
$10$	−0.176574			−0.0558376
$11$		−	2.92586i		−	0.882179i	−0.897463	−	0.441090i	$-0.854592\pi$
$11$		−	2.92586i		−	0.882179i	0.897463	−	0.441090i	$-0.145408\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.87127	+	2.18078i	−0.796348	+	0.604838i
$13$	−2.87127	+	2.18078i	−0.796348	+	0.604838i
$14$	−1.82577	−	1.91483i	−0.487957	−	0.511760i
$15$	0.152918	+	0.0882870i	0.0394832	+	0.0227956i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.536265	+	0.928838i	−0.130063	+	0.225276i	−0.923701	−	0.383115i	$-0.874851\pi$
$17$	−0.536265	+	0.928838i	−0.130063	+	0.225276i	0.793637	+	0.608391i	$0.208185\pi$
$18$	0.866025	−	0.500000i	0.204124	−	0.117851i
$19$		−	4.80348i		−	1.10199i	−0.834507	−	0.550997i	$-0.814247\pi$
$19$		−	4.80348i		−	1.10199i	0.834507	−	0.550997i	$-0.185753\pi$
$20$	−0.152918	+	0.0882870i	−0.0341934	+	0.0197416i
$21$	0.623746	+	2.57117i	0.136113	+	0.561076i
$22$	−1.46293	−	2.53387i	−0.311897	−	0.540222i
$23$	−0.966059	−	1.67326i	−0.201437	−	0.348899i	0.747555	−	0.664200i	$-0.231228\pi$
$23$	−0.966059	−	1.67326i	−0.201437	−	0.348899i	−0.948992	+	0.315301i	$0.897895\pi$
$24$			1.00000i			0.204124i
$25$	−2.48441	−	4.30313i	−0.496882	−	0.860625i
$26$	−1.39621	+	3.32424i	−0.273819	+	0.651938i
$27$	−1.00000			−0.192450
$28$	−2.53858	−	0.745408i	−0.479746	−	0.140869i
$29$	0.880456	−	1.52499i	0.163497	−	0.283184i	−0.772624	−	0.634864i	$-0.781056\pi$
$29$	0.880456	−	1.52499i	0.163497	−	0.283184i	0.936120	+	0.351680i	$0.114389\pi$
$30$	0.176574			0.0322379
$31$	0.771896	−	0.445654i	0.138637	−	0.0800418i	−0.429077	−	0.903268i	$-0.641161\pi$
$31$	0.771896	−	0.445654i	0.138637	−	0.0800418i	0.567714	+	0.823226i	$0.307828\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$			2.92586i			0.509326i
$34$			1.07253i			0.183937i
$35$	−0.131620	+	0.448247i	−0.0222478	+	0.0757675i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	6.26164	−	3.61516i	1.02941	−	0.594328i	0.112592	−	0.993641i	$-0.464085\pi$
$37$	6.26164	−	3.61516i	1.02941	−	0.594328i	0.916815	+	0.399313i	$0.130751\pi$
$38$	−2.40174	−	4.15994i	−0.389614	−	0.674831i
$39$	2.87127	−	2.18078i	0.459772	−	0.349204i
$40$	−0.0882870	+	0.152918i	−0.0139594	+	0.0241784i
$41$	−3.65298	−	2.10905i	−0.570499	−	0.329378i	0.186850	−	0.982389i	$-0.440172\pi$
$41$	−3.65298	−	2.10905i	−0.570499	−	0.329378i	−0.757349	+	0.653011i	$0.773506\pi$
$42$	1.82577	+	1.91483i	0.281722	+	0.295465i
$43$	−2.42721	−	4.20406i	−0.370146	−	0.641112i	0.619441	−	0.785043i	$-0.287359\pi$
$43$	−2.42721	−	4.20406i	−0.370146	−	0.641112i	−0.989588	+	0.143930i	$0.954026\pi$
$44$	−2.53387	−	1.46293i	−0.381995	−	0.220545i
$45$	−0.152918	−	0.0882870i	−0.0227956	−	0.0131611i
$46$	−1.67326	−	0.966059i	−0.246709	−	0.142438i
$47$	6.56871	+	3.79245i	0.958145	+	0.553185i	0.895602	−	0.444857i	$-0.146745\pi$
$47$	6.56871	+	3.79245i	0.958145	+	0.553185i	0.0625435	+	0.998042i	$0.480079\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−6.22188	+	3.20752i	−0.888840	+	0.458217i
$50$	−4.30313	−	2.48441i	−0.608554	−	0.351349i
$51$	0.536265	−	0.928838i	0.0750921	−	0.130063i
$52$	0.452970	+	3.57698i	0.0628157	+	0.496038i
$53$	3.98604	+	6.90402i	0.547524	+	0.948339i	0.998443	+	0.0557748i	$0.0177629\pi$
$53$	3.98604	+	6.90402i	0.547524	+	0.948339i	−0.450919	+	0.892565i	$0.648904\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−0.258315	+	0.447415i	−0.0348312	+	0.0603294i
$56$	−2.57117	+	0.623746i	−0.343588	+	0.0833516i
$57$			4.80348i			0.636237i
$58$		−	1.76091i		−	0.231219i
$59$	12.3878	+	7.15207i	1.61275	+	0.931120i	0.988730	+	0.149710i	$0.0478341\pi$
$59$	12.3878	+	7.15207i	1.61275	+	0.931120i	0.624018	+	0.781410i	$0.285499\pi$
$60$	0.152918	−	0.0882870i	0.0197416	−	0.0113978i
$61$	−6.40996			−0.820711			−0.410356	−	0.911926i	$-0.634595\pi$
$61$	−6.40996			−0.820711			−0.410356	+	0.911926i	$0.634595\pi$
$62$	0.445654	−	0.771896i	0.0565981	−	0.0980308i
$63$	−0.623746	−	2.57117i	−0.0785846	−	0.323938i
$64$	−1.00000			−0.125000
$65$	0.631603	−	0.0799828i	0.0783407	−	0.00992065i
$66$	1.46293	+	2.53387i	0.180074	+	0.311897i
$67$			11.2558i			1.37512i	0.726129	+	0.687558i	$0.241317\pi$
$67$			11.2558i			1.37512i	−0.726129	+	0.687558i	$0.758683\pi$
$68$	0.536265	+	0.928838i	0.0650317	+	0.112638i
$69$	0.966059	+	1.67326i	0.116300	+	0.201437i
$70$	0.110137	+	0.454003i	0.0131639	+	0.0542637i
$71$	11.6285	−	6.71374i	1.38005	−	0.796774i	0.387888	−	0.921707i	$-0.373205\pi$
$71$	11.6285	−	6.71374i	1.38005	−	0.796774i	0.992165	+	0.124933i	$0.0398715\pi$
$72$		−	1.00000i		−	0.117851i
$73$	−9.20985	+	5.31731i	−1.07793	+	0.622344i	−0.930338	−	0.366704i	$-0.880486\pi$
$73$	−9.20985	+	5.31731i	−1.07793	+	0.622344i	−0.147594	+	0.989048i	$0.547153\pi$
$74$	3.61516	−	6.26164i	0.420254	−	0.727901i
$75$	2.48441	+	4.30313i	0.286875	+	0.496882i
$76$	−4.15994	−	2.40174i	−0.477178	−	0.275499i
$77$	−7.52289	+	1.82499i	−0.857313	+	0.207977i
$78$	1.39621	−	3.32424i	0.158089	−	0.376397i
$79$	3.86312	−	6.69111i	0.434635	−	0.752809i	−0.562631	−	0.826708i	$-0.690211\pi$
$79$	3.86312	−	6.69111i	0.434635	−	0.752809i	0.997266	+	0.0738989i	$0.0235442\pi$
$80$			0.176574i			0.0197416i
$81$	1.00000			0.111111
$82$	−4.21809			−0.465811
$83$			9.49646i			1.04237i	0.853443	+	0.521186i	$0.174510\pi$
$83$			9.49646i			1.04237i	−0.853443	+	0.521186i	$0.825490\pi$
$84$	2.53858	+	0.745408i	0.276981	+	0.0813306i
$85$	0.164009	−	0.0946905i	0.0177892	−	0.0102706i
$86$	−4.20406	−	2.42721i	−0.453335	−	0.261733i
$87$	−0.880456	+	1.52499i	−0.0943948	+	0.163497i
$88$	−2.92586			−0.311897
$89$	4.92847	−	2.84545i	0.522417	−	0.301618i	−0.215506	−	0.976502i	$-0.569140\pi$
$89$	4.92847	−	2.84545i	0.522417	−	0.301618i	0.737923	+	0.674885i	$0.235807\pi$
$90$	−0.176574			−0.0186125
$91$	7.39810	+	6.02230i	0.775532	+	0.631308i
$92$	−1.93212			−0.201437
$93$	−0.771896	+	0.445654i	−0.0800418	+	0.0462122i
$94$	7.58490			0.782322
$95$	−0.424085	+	0.734537i	−0.0435102	+	0.0753619i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	9.29173	−	5.36458i	0.943432	−	0.544691i	0.0523976	−	0.998626i	$-0.483314\pi$
$97$	9.29173	−	5.36458i	0.943432	−	0.544691i	0.891035	+	0.453935i	$0.149980\pi$
$98$	−3.78455	+	5.88874i	−0.382297	+	0.594852i
$99$		−	2.92586i		−	0.294060i
$100$	−4.96882			−0.496882
$101$	7.63322			0.759533			0.379767	−	0.925082i	$-0.376004\pi$
$101$	7.63322			0.759533			0.379767	+	0.925082i	$0.376004\pi$
$102$		−	1.07253i		−	0.106196i
$103$	4.70230	−	8.14463i	0.463332	−	0.802514i	−0.535793	−	0.844349i	$-0.679987\pi$
$103$	4.70230	−	8.14463i	0.463332	−	0.802514i	0.999125	+	0.0418355i	$0.0133206\pi$
$104$	2.18078	+	2.87127i	0.213843	+	0.281552i
$105$	0.131620	−	0.448247i	0.0128448	−	0.0437444i
$106$	6.90402	+	3.98604i	0.670577	+	0.387158i
$107$	0.957952	+	1.65922i	0.0926087	+	0.160403i	0.908608	−	0.417650i	$-0.137146\pi$
$107$	0.957952	+	1.65922i	0.0926087	+	0.160403i	−0.815999	+	0.578053i	$0.803813\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−10.1264	+	5.84647i	−0.969932	+	0.559991i	−0.899216	−	0.437506i	$-0.855862\pi$
$109$	−10.1264	+	5.84647i	−0.969932	+	0.559991i	−0.0707166	+	0.997496i	$0.522529\pi$
$110$			0.516630i			0.0492588i
$111$	−6.26164	+	3.61516i	−0.594328	+	0.343136i
$112$	−1.91483	+	1.82577i	−0.180934	+	0.172519i
$113$	5.97238	+	10.3445i	0.561834	+	0.973125i	0.997336	+	0.0729377i	$0.0232374\pi$
$113$	5.97238	+	10.3445i	0.561834	+	0.973125i	−0.435502	+	0.900188i	$0.643429\pi$
$114$	2.40174	+	4.15994i	0.224944	+	0.389614i
$115$			0.341162i			0.0318135i
$116$	−0.880456	−	1.52499i	−0.0817483	−	0.141592i
$117$	−2.87127	+	2.18078i	−0.265449	+	0.201613i
$118$	14.3041			1.31680
$119$	2.72270	+	0.799472i	0.249589	+	0.0732874i
$120$	0.0882870	−	0.152918i	0.00805947	−	0.0139594i
$121$	2.43936			0.221760
$122$	−5.55119	+	3.20498i	−0.502581	+	0.290165i
$123$	3.65298	+	2.10905i	0.329378	+	0.190166i
$124$		−	0.891308i		−	0.0800418i
$125$			1.76024i			0.157440i
$126$	−1.82577	−	1.91483i	−0.162652	−	0.170587i
$127$	7.99301	−	13.8443i	0.709265	−	1.22848i	−0.255866	−	0.966712i	$-0.582361\pi$
$127$	7.99301	−	13.8443i	0.709265	−	1.22848i	0.965130	−	0.261770i	$-0.0843061\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.42721	+	4.20406i	0.213704	+	0.370146i
$130$	0.506993	−	0.385069i	0.0444662	−	0.0337727i
$131$	−5.45578	+	9.44968i	−0.476673	+	0.825622i	−0.999643	−	0.0267291i	$-0.991491\pi$
$131$	−5.45578	+	9.44968i	−0.476673	+	0.825622i	0.522969	+	0.852351i	$0.324824\pi$
$132$	2.53387	+	1.46293i	0.220545	+	0.127332i
$133$	−12.3506	+	2.99615i	−1.07093	+	0.259799i
$134$	5.62791	+	9.74782i	0.486177	+	0.842083i
$135$	0.152918	+	0.0882870i	0.0131611	+	0.00759854i
$136$	0.928838	+	0.536265i	0.0796472	+	0.0459843i
$137$	2.12407	+	1.22633i	0.181471	+	0.104772i	0.587984	−	0.808873i	$-0.299922\pi$
$137$	2.12407	+	1.22633i	0.181471	+	0.104772i	−0.406513	+	0.913645i	$0.633255\pi$
$138$	1.67326	+	0.966059i	0.142438	+	0.0822364i
$139$	−5.25740	−	9.10609i	−0.445927	−	0.772368i	0.552189	−	0.833719i	$-0.313793\pi$
$139$	−5.25740	−	9.10609i	−0.445927	−	0.772368i	−0.998116	+	0.0613504i	$0.980459\pi$
$140$	0.322383	+	0.338109i	0.0272464	+	0.0285755i
$141$	−6.56871	−	3.79245i	−0.553185	−	0.319382i
$142$	6.71374	−	11.6285i	0.563404	−	0.975845i
$143$	6.38064	+	8.40094i	0.533576	+	0.702522i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−0.269274	+	0.155466i	−0.0223620	+	0.0129107i
$146$	−5.31731	+	9.20985i	−0.440064	+	0.762213i
$147$	6.22188	−	3.20752i	0.513172	−	0.264552i
$148$		−	7.23032i		−	0.594328i
$149$		−	16.5343i		−	1.35454i	−0.735735	−	0.677270i	$-0.763163\pi$
$149$		−	16.5343i		−	1.35454i	0.735735	−	0.677270i	$-0.236837\pi$
$150$	4.30313	+	2.48441i	0.351349	+	0.202851i
$151$	−3.33765	+	1.92699i	−0.271614	+	0.156816i	−0.629621	−	0.776903i	$-0.716790\pi$
$151$	−3.33765	+	1.92699i	−0.271614	+	0.156816i	0.358007	+	0.933719i	$0.383456\pi$
$152$	−4.80348			−0.389614
$153$	−0.536265	+	0.928838i	−0.0433544	+	0.0750921i
$154$	−5.60252	+	5.34193i	−0.451464	+	0.430465i
$155$	−0.157382			−0.0126412
$156$	−0.452970	−	3.57698i	−0.0362667	−	0.286388i
$157$	7.50411	+	12.9975i	0.598893	+	1.03731i	0.992985	+	0.118243i	$0.0377261\pi$
$157$	7.50411	+	12.9975i	0.598893	+	1.03731i	−0.394091	+	0.919071i	$0.628941\pi$
$158$		−	7.72623i		−	0.614666i
$159$	−3.98604	−	6.90402i	−0.316113	−	0.547524i
$160$	0.0882870	+	0.152918i	0.00697970	+	0.0120892i
$161$	−3.69968	+	3.52760i	−0.291575	+	0.278014i
$162$	0.866025	−	0.500000i	0.0680414	−	0.0392837i
$163$		−	5.47191i		−	0.428593i	−0.976769	−	0.214297i	$-0.931254\pi$
$163$		−	5.47191i		−	0.428593i	0.976769	−	0.214297i	$-0.0687459\pi$
$164$	−3.65298	+	2.10905i	−0.285250	+	0.164689i
$165$	0.258315	−	0.447415i	0.0201098	−	0.0348312i
$166$	4.74823	+	8.22417i	0.368534	+	0.638320i
$167$	−13.4219	−	7.74914i	−1.03862	−	0.599647i	−0.119177	−	0.992873i	$-0.538026\pi$
$167$	−13.4219	−	7.74914i	−1.03862	−	0.599647i	−0.919442	+	0.393226i	$0.871359\pi$
$168$	2.57117	−	0.623746i	0.198370	−	0.0481231i
$169$	3.48843	−	12.5232i	0.268341	−	0.963324i
$170$	0.0946905	−	0.164009i	0.00726243	−	0.0125789i
$171$		−	4.80348i		−	0.367332i
$172$	−4.85443			−0.370146
$173$	5.81699			0.442257			0.221129	−	0.975245i	$-0.429026\pi$
$173$	5.81699			0.442257			0.221129	+	0.975245i	$0.429026\pi$
$174$			1.76091i			0.133494i
$175$	−9.51445	+	9.07191i	−0.719225	+	0.685772i
$176$	−2.53387	+	1.46293i	−0.190997	+	0.110272i
$177$	−12.3878	−	7.15207i	−0.931120	−	0.537583i
$178$	2.84545	−	4.92847i	0.213276	−	0.369404i
$179$	9.58765			0.716614			0.358307	−	0.933604i	$-0.383354\pi$
$179$	9.58765			0.716614			0.358307	+	0.933604i	$0.383354\pi$
$180$	−0.152918	+	0.0882870i	−0.0113978	+	0.00658053i
$181$	−21.7904			−1.61967			−0.809833	−	0.586660i	$-0.800442\pi$
$181$	−21.7904			−1.61967			−0.809833	+	0.586660i	$0.800442\pi$
$182$	9.41809	+	1.51641i	0.698116	+	0.112404i
$183$	6.40996			0.473838
$184$	−1.67326	+	0.966059i	−0.123355	+	0.0712188i
$185$	−1.27669			−0.0938639
$186$	−0.445654	+	0.771896i	−0.0326769	+	0.0565981i
$187$	2.71765	+	1.56903i	0.198734	+	0.114739i
$188$	6.56871	−	3.79245i	0.479073	−	0.276593i
$189$	0.623746	+	2.57117i	0.0453709	+	0.187025i
$190$			0.848170i			0.0615328i
$191$	−16.0710			−1.16286			−0.581428	−	0.813598i	$-0.697506\pi$
$191$	−16.0710			−1.16286			−0.581428	+	0.813598i	$0.697506\pi$
$192$	1.00000			0.0721688
$193$			1.55462i			0.111904i	0.998433	+	0.0559519i	$0.0178194\pi$
$193$			1.55462i			0.111904i	−0.998433	+	0.0559519i	$0.982181\pi$
$194$	5.36458	−	9.29173i	0.385155	−	0.667107i
$195$	−0.631603	+	0.0799828i	−0.0452300	+	0.00572769i
$196$	−0.333147	+	6.99207i	−0.0237962	+	0.499433i
$197$	14.8579	+	8.57819i	1.05858	+	0.611171i	0.925039	−	0.379872i	$-0.124032\pi$
$197$	14.8579	+	8.57819i	1.05858	+	0.611171i	0.133540	+	0.991043i	$0.457365\pi$
$198$	−1.46293	−	2.53387i	−0.103966	−	0.180074i
$199$	9.82701	−	17.0209i	0.696619	−	1.20658i	−0.273013	−	0.962010i	$-0.588020\pi$
$199$	9.82701	−	17.0209i	0.696619	−	1.20658i	0.969632	−	0.244569i	$-0.0786463\pi$
$200$	−4.30313	+	2.48441i	−0.304277	+	0.175674i
$201$		−	11.2558i		−	0.793924i
$202$	6.61056	−	3.81661i	0.465117	−	0.268536i
$203$	−4.47021	−	1.31260i	−0.313747	−	0.0921262i
$204$	−0.536265	−	0.928838i	−0.0375460	−	0.0650317i
$205$	0.372403	+	0.645021i	0.0260098	+	0.0450502i
$206$		−	9.40460i		−	0.655250i
$207$	−0.966059	−	1.67326i	−0.0671457	−	0.116300i
$208$	3.32424	+	1.39621i	0.230495	+	0.0968096i
$209$	−14.0543			−0.972157
$210$	−0.110137	−	0.454003i	−0.00760020	−	0.0313292i
$211$	−1.40778	+	2.43835i	−0.0969157	+	0.167863i	−0.910407	−	0.413715i	$-0.864231\pi$
$211$	−1.40778	+	2.43835i	−0.0969157	+	0.167863i	0.813491	+	0.581578i	$0.197564\pi$
$212$	7.97207			0.547524
$213$	−11.6285	+	6.71374i	−0.796774	+	0.460018i
$214$	1.65922	+	0.957952i	0.113422	+	0.0654843i
$215$			0.857166i			0.0584582i
$216$			1.00000i			0.0680414i
$217$	−1.62732	−	1.70670i	−0.110470	−	0.115859i
$218$	−5.84647	+	10.1264i	−0.395973	+	0.685846i
$219$	9.20985	−	5.31731i	0.622344	−	0.359311i
$220$	0.258315	+	0.447415i	0.0174156	+	0.0301647i
$221$	−0.485824	−	3.83642i	−0.0326801	−	0.258066i
$222$	−3.61516	+	6.26164i	−0.242634	+	0.420254i
$223$	−10.9006	−	6.29348i	−0.729960	−	0.421442i	0.0884478	−	0.996081i	$-0.471809\pi$
$223$	−10.9006	−	6.29348i	−0.729960	−	0.421442i	−0.818407	+	0.574638i	$0.805143\pi$
$224$	−0.745408	+	2.53858i	−0.0498046	+	0.169616i
$225$	−2.48441	−	4.30313i	−0.165627	−	0.286875i
$226$	10.3445	+	5.97238i	0.688104	+	0.397277i
$227$	14.3351	+	8.27640i	0.951457	+	0.549324i	0.893533	−	0.448997i	$-0.148219\pi$
$227$	14.3351	+	8.27640i	0.951457	+	0.549324i	0.0579236	+	0.998321i	$0.481552\pi$
$228$	4.15994	+	2.40174i	0.275499	+	0.159059i
$229$	−6.18450	−	3.57062i	−0.408683	−	0.235953i	0.281541	−	0.959549i	$-0.409155\pi$
$229$	−6.18450	−	3.57062i	−0.408683	−	0.235953i	−0.690224	+	0.723596i	$0.742488\pi$
$230$	0.170581	+	0.295455i	0.0112478	+	0.0194817i
$231$	7.52289	−	1.82499i	0.494970	−	0.120076i
$232$	−1.52499	−	0.880456i	−0.100121	−	0.0578048i
$233$	0.423576	−	0.733656i	0.0277494	−	0.0480634i	−0.851817	−	0.523839i	$-0.824499\pi$
$233$	0.423576	−	0.733656i	0.0277494	−	0.0480634i	0.879567	+	0.475776i	$0.157833\pi$
$234$	−1.39621	+	3.32424i	−0.0912730	+	0.217313i
$235$	−0.669648	−	1.15986i	−0.0436830	−	0.0756612i
$236$	12.3878	−	7.15207i	0.806374	−	0.465560i
$237$	−3.86312	+	6.69111i	−0.250936	+	0.434635i
$238$	2.75766	−	0.668986i	0.178753	−	0.0433639i
$239$		−	3.61226i		−	0.233658i	−0.993152	−	0.116829i	$-0.962727\pi$
$239$		−	3.61226i		−	0.233658i	0.993152	−	0.116829i	$-0.0372729\pi$
$240$		−	0.176574i		−	0.0113978i
$241$	−4.16826	−	2.40655i	−0.268501	−	0.155019i	0.359705	−	0.933066i	$-0.382877\pi$
$241$	−4.16826	−	2.40655i	−0.268501	−	0.155019i	−0.628206	+	0.778047i	$0.716211\pi$
$242$	2.11255	−	1.21968i	0.135800	−	0.0784040i
$243$	−1.00000			−0.0641500
$244$	−3.20498	+	5.55119i	−0.205178	+	0.355378i
$245$	1.23462	+	0.0588250i	0.0788768	+	0.00375819i
$246$	4.21809			0.268936
$247$	10.4753	+	13.7921i	0.666529	+	0.877571i
$248$	−0.445654	−	0.771896i	−0.0282991	−	0.0490154i
$249$		−	9.49646i		−	0.601814i
$250$	0.880118	+	1.52441i	0.0556635	+	0.0964121i
$251$	−7.69851	−	13.3342i	−0.485926	−	0.841648i	0.513943	−	0.857824i	$-0.328184\pi$
$251$	−7.69851	−	13.3342i	−0.485926	−	0.841648i	−0.999869	+	0.0161758i	$0.994851\pi$
$252$	−2.53858	−	0.745408i	−0.159915	−	0.0469563i
$253$	−4.89573	+	2.82655i	−0.307792	+	0.177704i
$254$		−	15.9860i		−	1.00305i
$255$	−0.164009	+	0.0946905i	−0.0102706	+	0.00592975i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.02902	+	5.24641i	0.188945	+	0.327262i	0.944899	−	0.327363i	$-0.106160\pi$
$257$	3.02902	+	5.24641i	0.188945	+	0.327262i	−0.755954	+	0.654625i	$0.772827\pi$
$258$	4.20406	+	2.42721i	0.261733	+	0.151112i
$259$	−13.2009	−	13.8448i	−0.820263	−	0.860276i
$260$	0.246534	−	0.586975i	0.0152894	−	0.0364027i
$261$	0.880456	−	1.52499i	0.0544989	−	0.0943948i
$262$			10.9116i			0.674118i
$263$	−19.7128			−1.21554			−0.607772	−	0.794112i	$-0.707936\pi$
$263$	−19.7128			−1.21554			−0.607772	+	0.794112i	$0.707936\pi$
$264$	2.92586			0.180074
$265$		−	1.40766i		−	0.0864719i
$266$	−9.19785	+	8.77004i	−0.563956	+	0.537726i
$267$	−4.92847	+	2.84545i	−0.301618	+	0.174139i
$268$	9.74782	+	5.62791i	0.595443	+	0.343779i
$269$	2.28526	−	3.95818i	0.139335	−	0.241335i	−0.787910	−	0.615790i	$-0.788837\pi$
$269$	2.28526	−	3.95818i	0.139335	−	0.241335i	0.927245	+	0.374455i	$0.122170\pi$
$270$	0.176574			0.0107460
$271$	11.2482	−	6.49414i	0.683278	−	0.394491i	−0.117811	−	0.993036i	$-0.537588\pi$
$271$	11.2482	−	6.49414i	0.683278	−	0.394491i	0.801089	+	0.598545i	$0.204254\pi$
$272$	1.07253			0.0650317
$273$	−7.39810	−	6.02230i	−0.447754	−	0.364486i
$274$	2.45266			0.148171
$275$	−12.5903	+	7.26903i	−0.759226	+	0.438339i
$276$	1.93212			0.116300
$277$	−3.55100	+	6.15052i	−0.213359	+	0.369549i	−0.952764	−	0.303713i	$-0.901774\pi$
$277$	−3.55100	+	6.15052i	−0.213359	+	0.369549i	0.739405	+	0.673261i	$0.235107\pi$
$278$	−9.10609	−	5.25740i	−0.546147	−	0.315318i
$279$	0.771896	−	0.445654i	0.0462122	−	0.0266806i
$280$	0.448247	+	0.131620i	0.0267879	+	0.00786578i
$281$			22.4230i			1.33764i	0.743424	+	0.668821i	$0.233201\pi$
$281$			22.4230i			1.33764i	−0.743424	+	0.668821i	$0.766799\pi$
$282$	−7.58490			−0.451674
$283$	12.1153			0.720180			0.360090	−	0.932918i	$-0.382746\pi$
$283$	12.1153			0.720180			0.360090	+	0.932918i	$0.382746\pi$
$284$		−	13.4275i		−	0.796774i
$285$	0.424085	−	0.734537i	0.0251206	−	0.0435102i
$286$	9.72626	+	4.08511i	0.575126	+	0.241557i
$287$	−3.14420	+	10.7080i	−0.185596	+	0.632070i
$288$	−0.866025	−	0.500000i	−0.0510310	−	0.0294628i
$289$	7.92484	+	13.7262i	0.466167	+	0.807425i
$290$	−0.155466	+	0.269274i	−0.00912926	+	0.0158123i
$291$	−9.29173	+	5.36458i	−0.544691	+	0.314477i
$292$			10.6346i			0.622344i
$293$	−11.4120	+	6.58873i	−0.666697	+	0.384917i	−0.794824	−	0.606840i	$-0.792437\pi$
$293$	−11.4120	+	6.58873i	−0.666697	+	0.384917i	0.128127	+	0.991758i	$0.459103\pi$
$294$	3.78455	−	5.88874i	0.220719	−	0.343438i
$295$	−1.26287	−	2.18736i	−0.0735272	−	0.127353i
$296$	−3.61516	−	6.26164i	−0.210127	−	0.363950i
$297$			2.92586i			0.169775i
$298$	−8.26713	−	14.3191i	−0.478902	−	0.829483i
$299$	6.42283	+	2.69764i	0.371442	+	0.156008i
$300$	4.96882			0.286875
$301$	−9.29540	+	8.86305i	−0.535778	+	0.510858i
$302$	−1.92699	+	3.33765i	−0.110886	+	0.192060i
$303$	−7.63322			−0.438517
$304$	−4.15994	+	2.40174i	−0.238589	+	0.137749i
$305$	0.980196	+	0.565916i	0.0561259	+	0.0324043i
$306$			1.07253i			0.0613124i
$307$		−	7.47440i		−	0.426587i	−0.976988	−	0.213293i	$-0.931581\pi$
$307$		−	7.47440i		−	0.426587i	0.976988	−	0.213293i	$-0.0684190\pi$
$308$	−2.18096	+	7.42751i	−0.124271	+	0.423222i
$309$	−4.70230	+	8.14463i	−0.267505	+	0.463332i
$310$	−0.136297	+	0.0786910i	−0.00774113	+	0.00446935i
$311$	−12.7812	−	22.1376i	−0.724753	−	1.25531i	−0.959075	−	0.283150i	$-0.908620\pi$
$311$	−12.7812	−	22.1376i	−0.724753	−	1.25531i	0.234322	−	0.972159i	$-0.424713\pi$
$312$	−2.18078	−	2.87127i	−0.123462	−	0.162554i
$313$	4.39220	−	7.60752i	0.248262	−	0.430002i	−0.714782	−	0.699348i	$-0.753474\pi$
$313$	4.39220	−	7.60752i	0.248262	−	0.430002i	0.963044	+	0.269345i	$0.0868073\pi$
$314$	12.9975	+	7.50411i	0.733492	+	0.423482i
$315$	−0.131620	+	0.448247i	−0.00741593	+	0.0252558i
$316$	−3.86312	−	6.69111i	−0.217317	−	0.376405i
$317$	−18.7405	−	10.8198i	−1.05257	−	0.607702i	−0.129203	−	0.991618i	$-0.541242\pi$
$317$	−18.7405	−	10.8198i	−1.05257	−	0.607702i	−0.923368	+	0.383916i	$0.874575\pi$
$318$	−6.90402	−	3.98604i	−0.387158	−	0.223526i
$319$	−4.46192	−	2.57609i	−0.249819	−	0.144233i
$320$	0.152918	+	0.0882870i	0.00854836	+	0.00493540i
$321$	−0.957952	−	1.65922i	−0.0534677	−	0.0926087i
$322$	−1.44022	+	4.90483i	−0.0802600	+	0.273335i
$323$	4.46166	+	2.57594i	0.248253	+	0.143329i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	16.5176	+	6.93751i	0.916230	+	0.384824i
$326$	−2.73596	−	4.73882i	−0.151531	−	0.262459i
$327$	10.1264	−	5.84647i	0.559991	−	0.323311i
$328$	−2.10905	+	3.65298i	−0.116453	+	0.201702i
$329$	5.65384	−	19.2548i	0.311706	−	1.06155i
$330$		−	0.516630i		−	0.0284396i
$331$			22.2158i			1.22109i	0.791981	+	0.610546i	$0.209050\pi$
$331$			22.2158i			1.22109i	−0.791981	+	0.610546i	$0.790950\pi$
$332$	8.22417	+	4.74823i	0.451360	+	0.260593i
$333$	6.26164	−	3.61516i	0.343136	−	0.198109i
$334$	−15.4983			−0.848028
$335$	0.993742	−	1.72121i	0.0542939	−	0.0940399i
$336$	1.91483	−	1.82577i	0.104463	−	0.0996038i
$337$	−8.92796			−0.486337			−0.243169	−	0.969984i	$-0.578187\pi$
$337$	−8.92796			−0.486337			−0.243169	+	0.969984i	$0.578187\pi$
$338$	−3.24054	−	12.5896i	−0.176262	−	0.684786i
$339$	−5.97238	−	10.3445i	−0.324375	−	0.561834i
$340$		−	0.189381i		−	0.0102706i
$341$	−1.30392	−	2.25846i	−0.0706112	−	0.122302i
$342$	−2.40174	−	4.15994i	−0.129871	−	0.224944i
$343$	12.1280	+	13.9969i	0.654849	+	0.755760i
$344$	−4.20406	+	2.42721i	−0.226667	+	0.130867i
$345$		−	0.341162i		−	0.0183675i
$346$	5.03766	−	2.90849i	0.270826	−	0.156362i
$347$	13.8864	−	24.0520i	0.745461	−	1.29118i	−0.204518	−	0.978863i	$-0.565563\pi$
$347$	13.8864	−	24.0520i	0.745461	−	1.29118i	0.949979	−	0.312314i	$-0.101104\pi$
$348$	0.880456	+	1.52499i	0.0471974	+	0.0817483i
$349$	−4.50235	−	2.59943i	−0.241005	−	0.139144i	0.374634	−	0.927173i	$-0.377769\pi$
$349$	−4.50235	−	2.59943i	−0.241005	−	0.139144i	−0.615639	+	0.788029i	$0.711102\pi$
$350$	−3.70380	+	12.6137i	−0.197976	+	0.674232i
$351$	2.87127	−	2.18078i	0.153257	−	0.116401i
$352$	−1.46293	+	2.53387i	−0.0779744	+	0.135056i
$353$		−	11.6632i		−	0.620768i	−0.950611	−	0.310384i	$-0.899542\pi$
$353$		−	11.6632i		−	0.620768i	0.950611	−	0.310384i	$-0.100458\pi$
$354$	−14.3041			−0.760257
$355$	−2.37094			−0.125837
$356$		−	5.69091i		−	0.301618i
$357$	−2.72270	−	0.799472i	−0.144100	−	0.0423125i
$358$	8.30315	−	4.79382i	0.438835	−	0.253361i
$359$	−17.3765	−	10.0323i	−0.917094	−	0.529485i	−0.0343874	−	0.999409i	$-0.510948\pi$
$359$	−17.3765	−	10.0323i	−0.917094	−	0.529485i	−0.882707	+	0.469924i	$0.844281\pi$
$360$	−0.0882870	+	0.152918i	−0.00465314	+	0.00805947i
$361$	−4.07345			−0.214392
$362$	−18.8710	+	10.8952i	−0.991839	+	0.572639i
$363$	−2.43936			−0.128033
$364$	8.91451	−	3.39580i	0.467248	−	0.177988i
$365$	1.87780			0.0982885
$366$	5.55119	−	3.20498i	0.290165	−	0.167527i
$367$	18.3127			0.955914			0.477957	−	0.878383i	$-0.341378\pi$
$367$	18.3127			0.955914			0.477957	+	0.878383i	$0.341378\pi$
$368$	−0.966059	+	1.67326i	−0.0503593	+	0.0872249i
$369$	−3.65298	−	2.10905i	−0.190166	−	0.109793i
$370$	−1.10564	+	0.638343i	−0.0574796	+	0.0331859i
$371$	15.2652	−	14.5551i	0.792528	−	0.755666i
$372$			0.891308i			0.0462122i
$373$	16.1655			0.837019			0.418510	−	0.908212i	$-0.362553\pi$
$373$	16.1655			0.837019			0.418510	+	0.908212i	$0.362553\pi$
$374$	3.13807			0.162266
$375$		−	1.76024i		−	0.0908982i
$376$	3.79245	−	6.56871i	0.195581	−	0.338755i
$377$	0.797641	+	6.29875i	0.0410806	+	0.324402i
$378$	1.82577	+	1.91483i	0.0939073	+	0.0984882i
$379$	8.13999	+	4.69963i	0.418123	+	0.241404i	0.694274	−	0.719711i	$-0.255726\pi$
$379$	8.13999	+	4.69963i	0.418123	+	0.241404i	−0.276151	+	0.961114i	$0.589059\pi$
$380$	0.424085	+	0.734537i	0.0217551	+	0.0376810i
$381$	−7.99301	+	13.8443i	−0.409494	+	0.709265i
$382$	−13.9179	+	8.03549i	−0.712101	+	0.411132i
$383$		−	34.2898i		−	1.75213i	−0.482197	−	0.876063i	$-0.660161\pi$
$383$		−	34.2898i		−	1.75213i	0.482197	−	0.876063i	$-0.339839\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	1.31151	+	0.385100i	0.0668405	+	0.0196265i
$386$	0.777309	+	1.34634i	0.0395640	+	0.0685268i
$387$	−2.42721	−	4.20406i	−0.123382	−	0.213704i
$388$		−	10.7292i		−	0.544691i
$389$	−7.07233	−	12.2496i	−0.358581	−	0.621081i	0.629143	−	0.777290i	$-0.283406\pi$
$389$	−7.07233	−	12.2496i	−0.358581	−	0.621081i	−0.987724	+	0.156209i	$0.950073\pi$
$390$	−0.506993	+	0.385069i	−0.0256726	+	0.0194987i
$391$	2.07225			0.104798
$392$	3.20752	+	6.22188i	0.162004	+	0.314252i
$393$	5.45578	−	9.44968i	0.275207	−	0.476673i
$394$	17.1564			0.864326
$395$	−1.18148	+	0.682126i	−0.0594466	+	0.0343215i
$396$	−2.53387	−	1.46293i	−0.127332	−	0.0735149i
$397$		−	4.11439i		−	0.206495i	−0.994656	−	0.103248i	$-0.967077\pi$
$397$		−	4.11439i		−	0.206495i	0.994656	−	0.103248i	$-0.0329234\pi$
$398$		−	19.6540i		−	0.985167i
$399$	12.3506	−	2.99615i	0.618303	−	0.149995i
$400$	−2.48441	+	4.30313i	−0.124221	+	0.215156i
$401$	30.3471	−	17.5209i	1.51546	−	0.874953i	0.515628	−	0.856813i	$-0.327559\pi$
$401$	30.3471	−	17.5209i	1.51546	−	0.874953i	0.999835	−	0.0181405i	$-0.00577463\pi$
$402$	−5.62791	−	9.74782i	−0.280694	−	0.486177i
$403$	−1.24445	+	2.96293i	−0.0619906	+	0.147594i
$404$	3.81661	−	6.61056i	0.189883	−	0.328888i
$405$	−0.152918	−	0.0882870i	−0.00759854	−	0.00438702i
$406$	−4.52761	+	1.09836i	−0.224702	+	0.0545108i
$407$	−10.5774	−	18.3207i	−0.524304	−	0.908121i
$408$	−0.928838	−	0.536265i	−0.0459843	−	0.0265491i
$409$	18.1532	+	10.4808i	0.897618	+	0.518240i	0.876427	−	0.481535i	$-0.159921\pi$
$409$	18.1532	+	10.4808i	0.897618	+	0.518240i	0.0211914	+	0.999775i	$0.493254\pi$
$410$	0.645021	+	0.372403i	0.0318553	+	0.0183917i
$411$	−2.12407	−	1.22633i	−0.104772	−	0.0604904i
$412$	−4.70230	−	8.14463i	−0.231666	−	0.401257i
$413$	10.6624	−	36.3122i	0.524663	−	1.78680i
$414$	−1.67326	−	0.966059i	−0.0822364	−	0.0474792i
$415$	0.838414	−	1.45218i	0.0411561	−	0.0712845i
$416$	3.57698	−	0.452970i	0.175376	−	0.0222087i
$417$	5.25740	+	9.10609i	0.257456	+	0.445927i
$418$	−12.1714	+	7.02715i	−0.595322	+	0.343709i
$419$	−10.0352	+	17.3815i	−0.490253	+	0.849144i	−0.999937	−	0.0112180i	$-0.996429\pi$
$419$	−10.0352	+	17.3815i	−0.490253	+	0.849144i	0.509684	+	0.860362i	$0.329762\pi$
$420$	−0.322383	−	0.338109i	−0.0157307	−	0.0164980i
$421$			39.9991i			1.94944i	0.223437	+	0.974718i	$0.428272\pi$
$421$			39.9991i			1.94944i	−0.223437	+	0.974718i	$0.571728\pi$
$422$			2.81556i			0.137059i
$423$	6.56871	+	3.79245i	0.319382	+	0.184395i
$424$	6.90402	−	3.98604i	0.335289	−	0.193579i
$425$	5.32921			0.258505
$426$	−6.71374	+	11.6285i	−0.325282	+	0.563404i
$427$	3.99819	+	16.4811i	0.193486	+	0.797578i
$428$	1.91590			0.0926087
$429$	−6.38064	−	8.40094i	−0.308060	−	0.405601i
$430$	0.428583	+	0.742327i	0.0206681	+	0.0357982i
$431$			40.7992i			1.96523i	0.185660	+	0.982614i	$0.440558\pi$
$431$			40.7992i			1.96523i	−0.185660	+	0.982614i	$0.559442\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−4.47420	−	7.74954i	−0.215016	−	0.372419i	0.738261	−	0.674515i	$-0.235647\pi$
$433$	−4.47420	−	7.74954i	−0.215016	−	0.372419i	−0.953278	+	0.302096i	$0.902314\pi$
$434$	−2.26265	−	0.664388i	−0.108611	−	0.0318916i
$435$	0.269274	−	0.155466i	0.0129107	−	0.00745401i
$436$			11.6929i			0.559991i
$437$	−8.03749	+	4.64045i	−0.384485	+	0.221983i
$438$	5.31731	−	9.20985i	0.254071	−	0.440064i
$439$	−20.5262	−	35.5525i	−0.979663	−	1.69683i	−0.663600	−	0.748088i	$-0.730972\pi$
$439$	−20.5262	−	35.5525i	−0.979663	−	1.69683i	−0.316063	−	0.948738i	$-0.602361\pi$
$440$	0.447415	+	0.258315i	0.0213297	+	0.0123147i
$441$	−6.22188	+	3.20752i	−0.296280	+	0.152739i
$442$	−2.33895	−	3.07953i	−0.111252	−	0.146478i
$443$	−15.9629	+	27.6485i	−0.758420	+	1.31362i	0.185236	+	0.982694i	$0.440695\pi$
$443$	−15.9629	+	27.6485i	−0.758420	+	1.31362i	−0.943656	+	0.330928i	$0.892638\pi$
$444$			7.23032i			0.343136i
$445$	−1.00487			−0.0476353
$446$	−12.5870			−0.596009
$447$			16.5343i			0.782044i
$448$	0.623746	+	2.57117i	0.0294692	+	0.121477i
$449$	7.38864	−	4.26583i	0.348692	−	0.201317i	−0.315417	−	0.948953i	$-0.602144\pi$
$449$	7.38864	−	4.26583i	0.348692	−	0.201317i	0.664109	+	0.747636i	$0.268811\pi$
$450$	−4.30313	−	2.48441i	−0.202851	−	0.117116i
$451$	−6.17077	+	10.6881i	−0.290570	+	0.503282i
$452$	11.9448			0.561834
$453$	3.33765	−	1.92699i	0.156816	−	0.0905379i
$454$	16.5528			0.776861
$455$	−0.599610	−	1.57407i	−0.0281101	−	0.0737936i
$456$	4.80348			0.224944
$457$	−27.2830	+	15.7518i	−1.27624	+	0.736839i	−0.976155	−	0.217073i	$-0.930349\pi$
$457$	−27.2830	+	15.7518i	−1.27624	+	0.736839i	−0.300087	+	0.953912i	$0.597016\pi$
$458$	−7.14125			−0.333689
$459$	0.536265	−	0.928838i	0.0250307	−	0.0433544i
$460$	0.295455	+	0.170581i	0.0137757	+	0.00795338i
$461$	1.35012	−	0.779490i	0.0628812	−	0.0363045i	−0.468230	−	0.883607i	$-0.655108\pi$
$461$	1.35012	−	0.779490i	0.0628812	−	0.0363045i	0.531111	+	0.847302i	$0.321775\pi$
$462$	5.60252	−	5.34193i	0.260653	−	0.248529i
$463$			14.2290i			0.661278i	0.943757	+	0.330639i	$0.107264\pi$
$463$			14.2290i			0.661278i	−0.943757	+	0.330639i	$0.892736\pi$
$464$	−1.76091			−0.0817483
$465$	0.157382			0.00729841
$466$		−	0.847153i		−	0.0392436i
$467$	−12.4006	+	21.4785i	−0.573833	+	0.993907i	0.422335	+	0.906440i	$0.361211\pi$
$467$	−12.4006	+	21.4785i	−0.573833	+	0.993907i	−0.996167	+	0.0874674i	$0.972123\pi$
$468$	0.452970	+	3.57698i	0.0209386	+	0.165346i
$469$	28.9407	−	7.02077i	1.33636	−	0.324189i
$470$	−1.15986	−	0.669648i	−0.0535006	−	0.0308886i
$471$	−7.50411	−	12.9975i	−0.345771	−	0.598893i
$472$	7.15207	−	12.3878i	0.329201	−	0.570192i
$473$	−12.3005	+	7.10168i	−0.565576	+	0.326535i
$474$			7.72623i			0.354878i
$475$	−20.6700	+	11.9338i	−0.948404	+	0.547561i
$476$	2.05371	−	1.95819i	0.0941317	−	0.0897535i
$477$	3.98604	+	6.90402i	0.182508	+	0.316113i
$478$	−1.80613	−	3.12831i	−0.0826106	−	0.143086i
$479$		−	16.1610i		−	0.738415i	−0.929347	−	0.369208i	$-0.879629\pi$
$479$		−	16.1610i		−	0.738415i	0.929347	−	0.369208i	$-0.120371\pi$
$480$	−0.0882870	−	0.152918i	−0.00402973	−	0.00697970i
$481$	−10.0950	+	24.0353i	−0.460294	+	1.09592i
$482$	−4.81309			−0.219230
$483$	3.69968	−	3.52760i	0.168341	−	0.160511i
$484$	1.21968	−	2.11255i	0.0554400	−	0.0960249i
$485$	−1.89449			−0.0860245
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	21.9440	+	12.6694i	0.994379	+	0.574105i	0.906580	−	0.422033i	$-0.138683\pi$
$487$	21.9440	+	12.6694i	0.994379	+	0.574105i	0.0877989	+	0.996138i	$0.472017\pi$
$488$			6.40996i			0.290165i
$489$			5.47191i			0.247448i
$490$	1.09862	−	0.566365i	0.0496307	−	0.0255858i
$491$	11.9342	−	20.6706i	0.538583	−	0.932853i	−0.460398	−	0.887713i	$-0.652293\pi$
$491$	11.9342	−	20.6706i	0.538583	−	0.932853i	0.998981	−	0.0451402i	$-0.0143735\pi$
$492$	3.65298	−	2.10905i	0.164689	−	0.0950832i
$493$	0.944315	+	1.63560i	0.0425298	+	0.0736638i
$494$	15.9680	+	6.70666i	0.718432	+	0.301747i
$495$	−0.258315	+	0.447415i	−0.0116104	+	0.0201098i
$496$	−0.771896	−	0.445654i	−0.0346591	−	0.0200105i
$497$	−24.5154	−	25.7113i	−1.09967	−	1.15331i
$498$	−4.74823	−	8.22417i	−0.212773	−	0.368534i
$499$	26.9786	+	15.5761i	1.20773	+	0.697282i	0.962262	−	0.272123i	$-0.0877259\pi$
$499$	26.9786	+	15.5761i	1.20773	+	0.697282i	0.245465	+	0.969405i	$0.421059\pi$
$500$	1.52441	+	0.880118i	0.0681736	+	0.0393601i
$501$	13.4219	+	7.74914i	0.599647	+	0.346206i
$502$	−13.3342	−	7.69851i	−0.595135	−	0.343601i
$503$	20.5275	+	35.5547i	0.915276	+	1.58530i	0.806496	+	0.591239i	$0.201361\pi$
$503$	20.5275	+	35.5547i	0.915276	+	1.58530i	0.108780	+	0.994066i	$0.465306\pi$
$504$	−2.57117	+	0.623746i	−0.114529	+	0.0277839i
$505$	−1.16725	−	0.673914i	−0.0519421	−	0.0299888i
$506$	−2.82655	+	4.89573i	−0.125655	+	0.217642i
$507$	−3.48843	+	12.5232i	−0.154927	+	0.556175i
$508$	−7.99301	−	13.8443i	−0.354632	−	0.614241i
$509$	32.8840	−	18.9856i	1.45756	−	0.841522i	0.458669	−	0.888607i	$-0.348326\pi$
$509$	32.8840	−	18.9856i	1.45756	−	0.841522i	0.998891	+	0.0470849i	$0.0149931\pi$
$510$	−0.0946905	+	0.164009i	−0.00419296	+	0.00726243i
$511$	19.4163	+	20.3635i	0.858929	+	0.900828i
$512$			1.00000i			0.0441942i
$513$			4.80348i			0.212079i
$514$	5.24641	+	3.02902i	0.231409	+	0.133604i
$515$	−1.43813	+	0.830305i	−0.0633716	+	0.0365876i
$516$	4.85443			0.213704
$517$	11.0962	−	19.2191i	0.488009	−	0.845256i
$518$	−18.3547	−	5.38953i	−0.806460	−	0.236803i
$519$	−5.81699			−0.255337
$520$	−0.0799828	−	0.631603i	−0.00350748	−	0.0276976i
$521$	11.9534	+	20.7039i	0.523687	+	0.907053i	0.999620	+	0.0275709i	$0.00877720\pi$
$521$	11.9534	+	20.7039i	0.523687	+	0.907053i	−0.475933	+	0.879482i	$0.657889\pi$
$522$		−	1.76091i		−	0.0770730i
$523$	4.08485	+	7.07518i	0.178618	+	0.309376i	0.941407	−	0.337271i	$-0.109504\pi$
$523$	4.08485	+	7.07518i	0.178618	+	0.309376i	−0.762789	+	0.646647i	$0.776171\pi$
$524$	5.45578	+	9.44968i	0.238337	+	0.412811i
$525$	9.51445	−	9.07191i	0.415245	−	0.395931i
$526$	−17.0718	+	9.85640i	−0.744365	+	0.429759i
$527$			0.955955i			0.0416420i
$528$	2.53387	−	1.46293i	0.110272	−	0.0636658i
$529$	9.63346	−	16.6856i	0.418846	−	0.725463i
$530$	−0.703830	−	1.21907i	−0.0305724	−	0.0529530i
$531$	12.3878	+	7.15207i	0.537583	+	0.310373i
$532$	−3.58055	+	12.1940i	−0.155237	+	0.528677i
$533$	15.0881	−	1.91067i	0.653536	−	0.0827604i
$534$	−2.84545	+	4.92847i	−0.123135	+	0.213276i
$535$		−	0.338299i		−	0.0146259i
$536$	11.2558			0.486177
$537$	−9.58765			−0.413737
$538$		−	4.57052i		−	0.197049i
$539$	9.38475	+	18.2043i	0.404230	+	0.784116i
$540$	0.152918	−	0.0882870i	0.00658053	−	0.00379927i
$541$	20.0917	+	11.6000i	0.863811	+	0.498721i	0.865286	−	0.501278i	$-0.167136\pi$
$541$	20.0917	+	11.6000i	0.863811	+	0.498721i	−0.00147595	+	0.999999i	$0.500470\pi$
$542$	6.49414	−	11.2482i	0.278947	−	0.483151i
$543$	21.7904			0.935115
$544$	0.928838	−	0.536265i	0.0398236	−	0.0229922i
$545$	2.06467			0.0884408
$546$	−9.41809	−	1.51641i	−0.403057	−	0.0648964i
$547$	−17.1563			−0.733549			−0.366774	−	0.930310i	$-0.619538\pi$
$547$	−17.1563			−0.733549			−0.366774	+	0.930310i	$0.619538\pi$
$548$	2.12407	−	1.22633i	0.0907356	−	0.0523862i
$549$	−6.40996			−0.273570
$550$	−7.26903	+	12.5903i	−0.309953	+	0.536854i
$551$	−7.32528	−	4.22925i	−0.312068	−	0.180172i
$552$	1.67326	−	0.966059i	0.0712188	−	0.0411182i
$553$	−19.6136	−	5.75919i	−0.834056	−	0.244906i
$554$			7.10200i			0.301735i
$555$	1.27669			0.0541923
$556$	−10.5148			−0.445927
$557$			38.9663i			1.65106i	0.564360	+	0.825529i	$0.309123\pi$
$557$			38.9663i			1.65106i	−0.564360	+	0.825529i	$0.690877\pi$
$558$	0.445654	−	0.771896i	0.0188660	−	0.0326769i
$559$	16.1373	+	6.77779i	0.682535	+	0.286670i
$560$	0.454003	−	0.110137i	0.0191851	−	0.00465415i
$561$	−2.71765	−	1.56903i	−0.114739	−	0.0662447i
$562$	11.2115	+	19.4189i	0.472928	+	0.819135i
$563$	−11.1751	+	19.3559i	−0.470975	+	0.815752i	−0.999449	−	0.0331972i	$-0.989431\pi$
$563$	−11.1751	+	19.3559i	−0.470975	+	0.815752i	0.528474	+	0.848949i	$0.322764\pi$
$564$	−6.56871	+	3.79245i	−0.276593	+	0.159691i
$565$		−	2.10913i		−	0.0887320i
$566$	10.4922	−	6.05765i	0.441019	−	0.254622i
$567$	−0.623746	−	2.57117i	−0.0261949	−	0.107979i
$568$	−6.71374	−	11.6285i	−0.281702	−	0.487922i
$569$	11.1642	+	19.3370i	0.468029	+	0.810649i	0.999332	−	0.0365321i	$-0.0116311\pi$
$569$	11.1642	+	19.3370i	0.468029	+	0.810649i	−0.531304	+	0.847181i	$0.678298\pi$
$570$		−	0.848170i		−	0.0355260i
$571$	3.08495	+	5.34329i	0.129101	+	0.223610i	0.923329	−	0.384011i	$-0.125458\pi$
$571$	3.08495	+	5.34329i	0.129101	+	0.223610i	−0.794228	+	0.607620i	$0.792124\pi$
$572$	10.4657	−	1.32533i	0.437595	−	0.0554147i
$573$	16.0710			0.671375
$574$	2.63102	+	10.8455i	0.109817	+	0.452681i
$575$	−4.80017	+	8.31415i	−0.200181	+	0.346724i
$576$	−1.00000			−0.0416667
$577$	−24.2758	+	14.0157i	−1.01062	+	0.583480i	−0.911372	−	0.411583i	$-0.864976\pi$
$577$	−24.2758	+	14.0157i	−1.01062	+	0.583480i	−0.0992444	+	0.995063i	$0.531643\pi$
$578$	13.7262	+	7.92484i	0.570936	+	0.329630i
$579$		−	1.55462i		−	0.0646077i
$580$			0.310931i			0.0129107i
$581$	24.4171	−	5.92338i	1.01299	−	0.245743i
$582$	−5.36458	+	9.29173i	−0.222369	+	0.385155i
$583$	20.2002	−	11.6626i	0.836605	−	0.483014i
$584$	5.31731	+	9.20985i	0.220032	+	0.381106i
$585$	0.631603	−	0.0799828i	0.0261136	−	0.00330688i
$586$	−6.58873	+	11.4120i	−0.272178	+	0.471426i
$587$	7.07274	+	4.08345i	0.291923	+	0.168542i	0.638809	−	0.769365i	$-0.279427\pi$
$587$	7.07274	+	4.08345i	0.291923	+	0.168542i	−0.346886	+	0.937907i	$0.612761\pi$
$588$	0.333147	−	6.99207i	0.0137387	−	0.288348i
$589$	−2.14069	−	3.70779i	−0.0882057	−	0.152777i
$590$	−2.18736	−	1.26287i	−0.0900520	−	0.0519915i
$591$	−14.8579	−	8.57819i	−0.611171	−	0.352860i
$592$	−6.26164	−	3.61516i	−0.257352	−	0.148582i
$593$	20.5433	+	11.8607i	0.843614	+	0.487061i	0.858491	−	0.512828i	$-0.171402\pi$
$593$	20.5433	+	11.8607i	0.843614	+	0.487061i	−0.0148770	+	0.999889i	$0.504736\pi$
$594$	1.46293	+	2.53387i	0.0600247	+	0.103966i
$595$	−0.345766	−	0.362632i	−0.0141750	−	0.0148665i
$596$	−14.3191	−	8.26713i	−0.586533	−	0.338635i
$597$	−9.82701	+	17.0209i	−0.402193	+	0.696619i
$598$	6.91115	−	0.875192i	0.282618	−	0.0357893i
$599$	−18.4912	−	32.0277i	−0.755531	−	1.30862i	−0.945110	−	0.326753i	$-0.894046\pi$
$599$	−18.4912	−	32.0277i	−0.755531	−	1.30862i	0.189579	−	0.981866i	$-0.439288\pi$
$600$	4.30313	−	2.48441i	0.175674	−	0.101426i
$601$	13.6167	−	23.5847i	0.555435	−	0.962041i	−0.442435	−	0.896801i	$-0.645885\pi$
$601$	13.6167	−	23.5847i	0.555435	−	0.962041i	0.997870	−	0.0652406i	$-0.0207815\pi$
$602$	−3.61853	+	12.3233i	−0.147480	+	0.502261i
$603$			11.2558i			0.458372i
$604$			3.85398i			0.156816i
$605$	−0.373021	−	0.215364i	−0.0151655	−	0.00875579i
$606$	−6.61056	+	3.81661i	−0.268536	+	0.155039i
$607$	−23.0013			−0.933594			−0.466797	−	0.884364i	$-0.654592\pi$
$607$	−23.0013			−0.933594			−0.466797	+	0.884364i	$0.654592\pi$
$608$	−2.40174	+	4.15994i	−0.0974035	+	0.168708i
$609$	4.47021	+	1.31260i	0.181142	+	0.0531891i
$610$	1.13183			0.0458266
$611$	−27.1311	+	3.43573i	−1.09761	+	0.138995i
$612$	0.536265	+	0.928838i	0.0216772	+	0.0375460i
$613$			43.4644i			1.75551i	0.479109	+	0.877755i	$0.340960\pi$
$613$			43.4644i			1.75551i	−0.479109	+	0.877755i	$0.659040\pi$
$614$	−3.73720	−	6.47302i	−0.150821	−	0.261230i
$615$	−0.372403	−	0.645021i	−0.0150167	−	0.0260098i
$616$	1.82499	+	7.52289i	0.0735310	+	0.303106i
$617$	−27.8756	+	16.0940i	−1.12223	+	0.647920i	−0.941969	−	0.335699i	$-0.891028\pi$
$617$	−27.8756	+	16.0940i	−1.12223	+	0.647920i	−0.180261	+	0.983619i	$0.557694\pi$
$618$			9.40460i			0.378309i
$619$	17.1556	−	9.90481i	0.689543	−	0.398108i	−0.113898	−	0.993492i	$-0.536334\pi$
$619$	17.1556	−	9.90481i	0.689543	−	0.398108i	0.803441	+	0.595385i	$0.203000\pi$
$620$	−0.0786910	+	0.136297i	−0.00316031	+	0.00547381i
$621$	0.966059	+	1.67326i	0.0387666	+	0.0671457i
$622$	−22.1376	−	12.7812i	−0.887638	−	0.512478i
$623$	−10.3903	−	10.8971i	−0.416278	−	0.436584i
$624$	−3.32424	−	1.39621i	−0.133076	−	0.0558931i
$625$	−12.2666	+	21.2465i	−0.490666	+	0.849858i
$626$		−	8.78441i		−	0.351096i
$627$	14.0543			0.561275
$628$	15.0082			0.598893
$629$			7.75473i			0.309201i
$630$	0.110137	+	0.454003i	0.00438798	+	0.0180879i
$631$	9.34937	−	5.39786i	0.372192	−	0.214885i	−0.302223	−	0.953237i	$-0.597729\pi$
$631$	9.34937	−	5.39786i	0.372192	−	0.214885i	0.674416	+	0.738352i	$0.264396\pi$
$632$	−6.69111	−	3.86312i	−0.266158	−	0.153667i
$633$	1.40778	−	2.43835i	0.0559543	−	0.0969157i
$634$	−21.6396			−0.859420
$635$	−2.44454	+	1.41136i	−0.0970087	+	0.0560080i
$636$	−7.97207			−0.316113
$637$	10.8698	−	22.7782i	0.430679	−	0.902505i
$638$	−5.15218			−0.203977
$639$	11.6285	−	6.71374i	0.460018	−	0.265591i
$640$	0.176574			0.00697970
$641$	14.6776	−	25.4224i	0.579732	−	1.00413i	−0.415778	−	0.909466i	$-0.636491\pi$
$641$	14.6776	−	25.4224i	0.579732	−	1.00413i	0.995510	−	0.0946590i	$-0.0301761\pi$
$642$	−1.65922	−	0.957952i	−0.0654843	−	0.0378074i
$643$	33.3805	−	19.2723i	1.31640	−	0.760024i	0.333252	−	0.942838i	$-0.391854\pi$
$643$	33.3805	−	19.2723i	1.31640	−	0.760024i	0.983148	+	0.182814i	$0.0585206\pi$
$644$	1.20515	+	4.96781i	0.0474896	+	0.195759i
$645$		−	0.857166i		−	0.0337509i
$646$	5.15188			0.202698
$647$	−14.4676			−0.568779			−0.284390	−	0.958709i	$-0.591791\pi$
$647$	−14.4676			−0.568779			−0.284390	+	0.958709i	$0.591791\pi$
$648$		−	1.00000i		−	0.0392837i
$649$	20.9259	−	36.2448i	0.821415	−	1.42273i
$650$	17.7734	−	2.25073i	0.697130	−	0.0882809i
$651$	1.62732	+	1.70670i	0.0637798	+	0.0668910i
$652$	−4.73882	−	2.73596i	−0.185586	−	0.107148i
$653$	3.69217	+	6.39503i	0.144486	+	0.250257i	0.929181	−	0.369625i	$-0.120514\pi$
$653$	3.69217	+	6.39503i	0.144486	+	0.250257i	−0.784695	+	0.619882i	$0.787180\pi$
$654$	5.84647	−	10.1264i	0.228615	−	0.395973i
$655$	1.66857	−	0.963348i	0.0651964	−	0.0376411i
$656$			4.21809i			0.164689i
$657$	−9.20985	+	5.31731i	−0.359311	+	0.207448i
$658$	−4.73105	−	19.5021i	−0.184436	−	0.760271i
$659$	−0.566263	−	0.980796i	−0.0220585	−	0.0382064i	0.854785	−	0.518982i	$-0.173689\pi$
$659$	−0.566263	−	0.980796i	−0.0220585	−	0.0382064i	−0.876844	+	0.480775i	$0.840355\pi$
$660$	−0.258315	−	0.447415i	−0.0100549	−	0.0174156i
$661$		−	5.22358i		−	0.203174i	−0.994827	−	0.101587i	$-0.967608\pi$
$661$		−	5.22358i		−	0.203174i	0.994827	−	0.101587i	$-0.0323919\pi$
$662$	11.1079	+	19.2395i	0.431721	+	0.747763i
$663$	0.485824	+	3.83642i	0.0188678	+	0.148994i
$664$	9.49646			0.368534
$665$	2.15315	+	0.632233i	0.0834954	+	0.0245169i
$666$	3.61516	−	6.26164i	0.140085	−	0.242634i
$667$	−3.40229			−0.131737
$668$	−13.4219	+	7.74914i	−0.519309	+	0.299823i
$669$	10.9006	+	6.29348i	0.421442	+	0.243320i
$670$		−	1.98748i		−	0.0767832i
$671$			18.7546i			0.724014i
$672$	0.745408	−	2.53858i	0.0287547	−	0.0979277i
$673$	18.9348	−	32.7960i	0.729883	−	1.26419i	−0.227049	−	0.973883i	$-0.572908\pi$
$673$	18.9348	−	32.7960i	0.729883	−	1.26419i	0.956932	−	0.290311i	$-0.0937588\pi$
$674$	−7.73184	+	4.46398i	−0.297819	+	0.171946i
$675$	2.48441	+	4.30313i	0.0956250	+	0.165627i
$676$	−9.10120	−	9.28268i	−0.350046	−	0.357026i
$677$	−7.27659	+	12.6034i	−0.279662	+	0.484389i	−0.971301	−	0.237855i	$-0.923556\pi$
$677$	−7.27659	+	12.6034i	−0.279662	+	0.484389i	0.691639	+	0.722244i	$0.256889\pi$
$678$	−10.3445	−	5.97238i	−0.397277	−	0.229368i
$679$	−19.5890	−	20.5445i	−0.751755	−	0.788426i
$680$	−0.0946905	−	0.164009i	−0.00363121	−	0.00628945i
$681$	−14.3351	−	8.27640i	−0.549324	−	0.317152i
$682$	−2.25846	−	1.30392i	−0.0864808	−	0.0499297i
$683$	16.1671	+	9.33409i	0.618618	+	0.357159i	0.776331	−	0.630326i	$-0.217079\pi$
$683$	16.1671	+	9.33409i	0.618618	+	0.357159i	−0.157713	+	0.987485i	$0.550412\pi$
$684$	−4.15994	−	2.40174i	−0.159059	−	0.0918329i
$685$	−0.216538	−	0.375055i	−0.00827349	−	0.0143301i
$686$	17.5016	+	6.05766i	0.668213	+	0.231282i
$687$	6.18450	+	3.57062i	0.235953	+	0.136228i
$688$	−2.42721	+	4.20406i	−0.0925366	+	0.160278i
$689$	−26.5011	−	11.1307i	−1.00961	−	0.424045i
$690$	−0.170581	−	0.295455i	−0.00649391	−	0.0112478i
$691$	−33.7395	+	19.4795i	−1.28351	+	0.741035i	−0.977488	−	0.210990i	$-0.932331\pi$
$691$	−33.7395	+	19.4795i	−1.28351	+	0.741035i	−0.306021	+	0.952025i	$0.598998\pi$
$692$	2.90849	−	5.03766i	0.110564	−	0.191503i
$693$	−7.52289	+	1.82499i	−0.285771	+	0.0693257i
$694$		−	27.7728i		−	1.05424i
$695$			1.85664i			0.0704264i
$696$	1.52499	+	0.880456i	0.0578048	+	0.0333736i
$697$	3.91793	−	2.26202i	0.148402	−	0.0856800i
$698$	−5.19886			−0.196780
$699$	−0.423576	+	0.733656i	−0.0160211	+	0.0277494i
$700$	3.09928	+	12.7757i	0.117142	+	0.482876i
$701$	−25.7948			−0.974257			−0.487128	−	0.873330i	$-0.661956\pi$
$701$	−25.7948			−0.974257			−0.487128	+	0.873330i	$0.661956\pi$
$702$	1.39621	−	3.32424i	0.0526965	−	0.125466i
$703$	−17.3654	−	30.0777i	−0.654947	−	1.13440i
$704$			2.92586i			0.110272i
$705$	0.669648	+	1.15986i	0.0252204	+	0.0436830i
$706$	−5.83158	−	10.1006i	−0.219475	−	0.380141i
$707$	−4.76119	−	19.6263i	−0.179063	−	0.738124i
$708$	−12.3878	+	7.15207i	−0.465560	+	0.268791i
$709$		−	6.61973i		−	0.248609i	−0.992244	−	0.124305i	$-0.960330\pi$
$709$		−	6.61973i		−	0.248609i	0.992244	−	0.124305i	$-0.0396700\pi$
$710$	−2.05330	+	1.18547i	−0.0770589	+	0.0444900i
$711$	3.86312	−	6.69111i	0.144878	−	0.250936i
$712$	−2.84545	−	4.92847i	−0.106638	−	0.184702i
$713$	−1.49139	−	0.861056i	−0.0558531	−	0.0322468i
$714$	−2.75766	+	0.668986i	−0.103203	+	0.0250362i
$715$	−0.234018	−	1.84798i	−0.00875179	−	0.0691105i
$716$	4.79382	−	8.30315i	0.179154	−	0.310303i
$717$			3.61226i			0.134903i
$718$	−20.0646			−0.748804
$719$	16.7410			0.624334			0.312167	−	0.950027i	$-0.398945\pi$
$719$	16.7410			0.624334			0.312167	+	0.950027i	$0.398945\pi$
$720$			0.176574i			0.00658053i
$721$	−23.8743	−	7.01026i	−0.889125	−	0.261076i
$722$	−3.52771	+	2.03672i	−0.131288	+	0.0757990i
$723$	4.16826	+	2.40655i	0.155019	+	0.0895004i
$724$	−10.8952	+	18.8710i	−0.404917	+	0.701336i
$725$	−8.74966			−0.324954
$726$	−2.11255	+	1.21968i	−0.0784040	+	0.0452666i
$727$	32.5435			1.20697			0.603485	−	0.797374i	$-0.293778\pi$
$727$	32.5435			1.20697			0.603485	+	0.797374i	$0.293778\pi$
$728$	6.02230	−	7.39810i	0.223201	−	0.274192i
$729$	1.00000			0.0370370
$730$	1.62622	−	0.938899i	0.0601891	−	0.0347502i
$731$	5.20651			0.192570
$732$	3.20498	−	5.55119i	0.118459	−	0.205178i
$733$	21.4590	+	12.3894i	0.792608	+	0.457612i	0.840880	−	0.541222i	$-0.182038\pi$
$733$	21.4590	+	12.3894i	0.792608	+	0.457612i	−0.0482720	+	0.998834i	$0.515371\pi$
$734$	15.8592	−	9.15633i	0.585375	−	0.337966i
$735$	−1.23462	−	0.0588250i	−0.0455396	−	0.00216979i
$736$			1.93212i			0.0712188i
$737$	32.9329			1.21310
$738$	−4.21809			−0.155270
$739$			14.3591i			0.528207i	0.964494	+	0.264104i	$0.0850761\pi$
$739$			14.3591i			0.528207i	−0.964494	+	0.264104i	$0.914924\pi$
$740$	−0.638343	+	1.10564i	−0.0234660	+	0.0406442i
$741$	−10.4753	−	13.7921i	−0.384821	−	0.506666i
$742$	5.94244	−	20.2377i	0.218154	−	0.742950i
$743$	−25.5487	−	14.7505i	−0.937290	−	0.541145i	−0.0481805	−	0.998839i	$-0.515342\pi$
$743$	−25.5487	−	14.7505i	−0.937290	−	0.541145i	−0.889110	+	0.457694i	$0.848676\pi$
$744$	0.445654	+	0.771896i	0.0163385	+	0.0282991i
$745$	−1.45976	+	2.52838i	−0.0534815	+	0.0926327i
$746$	13.9998	−	8.08277i	0.512568	−	0.295931i
$747$			9.49646i			0.347457i
$748$	2.71765	−	1.56903i	0.0993670	−	0.0573696i
$749$	3.66863	−	3.49800i	0.134049	−	0.127814i
$750$	−0.880118	−	1.52441i	−0.0321374	−	0.0556635i
$751$	−15.4187	−	26.7059i	−0.562635	−	0.974513i	−0.997265	−	0.0739041i	$-0.976454\pi$
$751$	−15.4187	−	26.7059i	−0.562635	−	0.974513i	0.434630	−	0.900609i	$-0.356879\pi$
$752$		−	7.58490i		−	0.276593i
$753$	7.69851	+	13.3342i	0.280549	+	0.485926i
$754$	3.84015	+	5.05606i	0.139850	+	0.184131i
$755$	0.680513			0.0247664
$756$	2.53858	+	0.745408i	0.0923271	+	0.0271102i
$757$	4.61356	−	7.99092i	0.167683	−	0.290435i	−0.769922	−	0.638138i	$-0.779705\pi$
$757$	4.61356	−	7.99092i	0.167683	−	0.290435i	0.937605	+	0.347703i	$0.113038\pi$
$758$	9.39925			0.341396
$759$	4.89573	−	2.82655i	0.177704	−	0.102597i
$760$	0.734537	+	0.424085i	0.0266445	+	0.0153832i
$761$			26.5667i			0.963043i	0.876434	+	0.481521i	$0.159916\pi$
$761$			26.5667i			0.963043i	−0.876434	+	0.481521i	$0.840084\pi$
$762$			15.9860i			0.579112i
$763$	21.3486	+	22.3900i	0.772871	+	0.810573i
$764$	−8.03549	+	13.9179i	−0.290714	+	0.503531i
$765$	0.164009	−	0.0946905i	0.00592975	−	0.00342354i
$766$	−17.1449	−	29.6958i	−0.619470	−	1.07295i
$767$	−51.1657	+	6.47935i	−1.84749	+	0.233956i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−28.4925	−	16.4502i	−1.02747	−	0.593208i	−0.111209	−	0.993797i	$-0.535472\pi$
$769$	−28.4925	−	16.4502i	−1.02747	−	0.593208i	−0.916258	+	0.400589i	$0.868806\pi$
$770$	1.32835	−	0.322246i	0.0478703	−	0.0116129i
$771$	−3.02902	−	5.24641i	−0.109087	−	0.188945i
$772$	1.34634	+	0.777309i	0.0484558	+	0.0279760i
$773$	−19.5981	−	11.3150i	−0.704896	−	0.406972i	0.104272	−	0.994549i	$-0.466749\pi$
$773$	−19.5981	−	11.3150i	−0.704896	−	0.406972i	−0.809168	+	0.587577i	$0.800082\pi$
$774$	−4.20406	−	2.42721i	−0.151112	−	0.0872444i
$775$	−3.83541	−	2.21438i	−0.137772	−	0.0795427i
$776$	−5.36458	−	9.29173i	−0.192577	−	0.333554i
$777$	13.2009	+	13.8448i	0.473579	+	0.496680i
$778$	−12.2496	−	7.07233i	−0.439170	−	0.253555i
$779$	−10.1308	+	17.5470i	−0.362973	+	0.628687i
$780$	−0.246534	+	0.586975i	−0.00882734	+	0.0210171i
$781$	−19.6434	−	34.0234i	−0.702897	−	1.21745i
$782$	1.79462	−	1.03613i	0.0641756	−	0.0370518i
$783$	−0.880456	+	1.52499i	−0.0314649	+	0.0544989i
$784$	5.88874	+	3.78455i	0.210312	+	0.135162i
$785$		−	2.65006i		−	0.0945848i
$786$		−	10.9116i		−	0.389202i
$787$	−41.4749	−	23.9456i	−1.47842	−	0.853567i	−0.478719	−	0.877968i	$-0.658899\pi$
$787$	−41.4749	−	23.9456i	−1.47842	−	0.853567i	−0.999702	+	0.0244012i	$0.992232\pi$
$788$	14.8579	−	8.57819i	0.529290	−	0.305586i
$789$	19.7128			0.701794
$790$	−0.682126	+	1.18148i	−0.0242690	+	0.0420351i
$791$	22.8722	−	21.8084i	0.813241	−	0.775416i
$792$	−2.92586			−0.103966
$793$	18.4048	−	13.9787i	0.653572	−	0.496398i
$794$	−2.05719	−	3.56316i	−0.0730070	−	0.126452i
$795$			1.40766i			0.0499246i
$796$	−9.82701	−	17.0209i	−0.348309	−	0.603289i
$797$	−21.8283	−	37.8077i	−0.773198	−	1.33922i	−0.935802	−	0.352527i	$-0.885322\pi$
$797$	−21.8283	−	37.8077i	−0.773198	−	1.33922i	0.162604	−	0.986691i	$-0.448011\pi$
$798$	9.19785	−	8.77004i	0.325600	−	0.310456i
$799$	−7.04514	+	4.06751i	−0.249239	+	0.143898i
$800$			4.96882i			0.175674i
$801$	4.92847	−	2.84545i	0.174139	−	0.100539i
$802$	17.5209	−	30.3471i	0.618685	−	1.07159i
$803$	15.5577	+	26.9467i	0.549019	+	0.950929i
$804$	−9.74782	−	5.62791i	−0.343779	−	0.198481i
$805$	0.877187	−	0.212798i	0.0309168	−	0.00750016i
$806$	0.403736	+	3.18820i	0.0142210	+	0.112299i
$807$	−2.28526	+	3.95818i	−0.0804449	+	0.139335i
$808$		−	7.63322i		−	0.268536i
$809$	6.11416			0.214963			0.107481	−	0.994207i	$-0.465721\pi$
$809$	6.11416			0.214963			0.107481	+	0.994207i	$0.465721\pi$
$810$	−0.176574			−0.00620418
$811$			7.91394i			0.277896i	0.990300	+	0.138948i	$0.0443721\pi$
$811$			7.91394i			0.277896i	−0.990300	+	0.138948i	$0.955628\pi$
$812$	−3.37185	+	3.21502i	−0.118329	+	0.112825i
$813$	−11.2482	+	6.49414i	−0.394491	+	0.227759i
$814$	−18.3207	−	10.5774i	−0.642139	−	0.370739i
$815$	−0.483099	+	0.836752i	−0.0169222	+	0.0293101i
$816$	−1.07253			−0.0375460
$817$	−20.1941	+	11.6591i	−0.706502	+	0.407899i
$818$	20.9615			0.732902
$819$	7.39810	+	6.02230i	0.258511	+	0.210436i
$820$	0.744806			0.0260098
$821$	28.1689	−	16.2633i	0.983102	−	0.567594i	0.0798970	−	0.996803i	$-0.474541\pi$
$821$	28.1689	−	16.2633i	0.983102	−	0.567594i	0.903205	+	0.429209i	$0.141208\pi$
$822$	−2.45266			−0.0855463
$823$	0.687389	−	1.19059i	0.0239609	−	0.0415015i	−0.853796	−	0.520607i	$-0.825706\pi$
$823$	0.687389	−	1.19059i	0.0239609	−	0.0415015i	0.877757	+	0.479106i	$0.159039\pi$
$824$	−8.14463	−	4.70230i	−0.283732	−	0.163812i
$825$	12.5903	−	7.26903i	0.438339	−	0.253075i
$826$	−8.92215	−	36.7785i	−0.310441	−	1.27969i
$827$			35.9181i			1.24899i	0.781027	+	0.624497i	$0.214696\pi$
$827$			35.9181i			1.24899i	−0.781027	+	0.624497i	$0.785304\pi$
$828$	−1.93212			−0.0671457
$829$	−36.4571			−1.26621			−0.633104	−	0.774067i	$-0.718219\pi$
$829$	−36.4571			−1.26621			−0.633104	+	0.774067i	$0.718219\pi$
$830$		−	1.67683i		−	0.0582036i
$831$	3.55100	−	6.15052i	0.123183	−	0.213359i
$832$	2.87127	−	2.18078i	0.0995435	−	0.0756048i
$833$	0.357309	−	7.49920i	0.0123800	−	0.259832i
$834$	9.10609	+	5.25740i	0.315318	+	0.182049i
$835$	1.36830	+	2.36996i	0.0473519	+	0.0820159i
$836$	−7.02715	+	12.1714i	−0.243039	+	0.420956i
$837$	−0.771896	+	0.445654i	−0.0266806	+	0.0154041i
$838$			20.0705i			0.693323i
$839$	−1.65338	+	0.954579i	−0.0570810	+	0.0329557i	−0.528269	−	0.849077i	$-0.677159\pi$
$839$	−1.65338	+	0.954579i	−0.0570810	+	0.0329557i	0.471188	+	0.882033i	$0.343825\pi$
$840$	−0.448247	−	0.131620i	−0.0154660	−	0.00454131i
$841$	12.9496	+	22.4294i	0.446538	+	0.773426i
$842$	19.9995	+	34.6402i	0.689230	+	1.19378i
$843$		−	22.4230i		−	0.772288i
$844$	1.40778	+	2.43835i	0.0484578	+	0.0839314i
$845$	−1.63908	+	1.60704i	−0.0563861	+	0.0552837i
$846$	7.58490			0.260774
$847$	−1.52154	−	6.27202i	−0.0522808	−	0.215509i
$848$	3.98604	−	6.90402i	0.136881	−	0.237085i
$849$	−12.1153			−0.415796
$850$	4.61523	−	2.66460i	0.158301	−	0.0913952i
$851$	−12.0982	−	6.98491i	−0.414722	−	0.239440i
$852$			13.4275i			0.460018i
$853$		−	47.0459i		−	1.61082i	−0.592718	−	0.805410i	$-0.701945\pi$
$853$		−	47.0459i		−	1.61082i	0.592718	−	0.805410i	$-0.298055\pi$
$854$	11.7031	+	12.2740i	0.400472	+	0.420007i
$855$	−0.424085	+	0.734537i	−0.0145034	+	0.0251206i
$856$	1.65922	−	0.957952i	0.0567110	−	0.0327421i
$857$	−6.91687	−	11.9804i	−0.236276	−	0.409242i	0.723367	−	0.690464i	$-0.242594\pi$
$857$	−6.91687	−	11.9804i	−0.236276	−	0.409242i	−0.959643	+	0.281222i	$0.909260\pi$
$858$	−9.72626	−	4.08511i	−0.332049	−	0.139463i
$859$	19.1824	−	33.2248i	0.654493	−	1.13362i	−0.327527	−	0.944842i	$-0.606215\pi$
$859$	19.1824	−	33.2248i	0.654493	−	1.13362i	0.982021	−	0.188774i	$-0.0604514\pi$
$860$	0.742327	+	0.428583i	0.0253131	+	0.0146146i
$861$	3.14420	−	10.7080i	0.107154	−	0.364926i
$862$	20.3996	+	35.3331i	0.694813	+	1.20345i
$863$	−20.0002	−	11.5471i	−0.680813	−	0.393068i	0.119348	−	0.992852i	$-0.461919\pi$
$863$	−20.0002	−	11.5471i	−0.680813	−	0.393068i	−0.800161	+	0.599785i	$0.795253\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−0.889520	−	0.513565i	−0.0302446	−	0.0174617i
$866$	−7.74954	−	4.47420i	−0.263340	−	0.152039i
$867$	−7.92484	−	13.7262i	−0.269142	−	0.466167i
$868$	−2.29171	+	0.555950i	−0.0777857	+	0.0188702i
$869$	−19.5772	−	11.3029i	−0.664113	−	0.383426i
$870$	0.155466	−	0.269274i	0.00527078	−	0.00912926i
$871$	−24.5464	−	32.3185i	−0.831723	−	1.09507i
$872$	5.84647	+	10.1264i	0.197987	+	0.342923i
$873$	9.29173	−	5.36458i	0.314477	−	0.181564i
$874$	−4.64045	+	8.03749i	−0.156965	+	0.271872i
$875$	4.52587	−	1.09794i	0.153002	−	0.0371171i
$876$		−	10.6346i		−	0.359311i
$877$			34.7751i			1.17427i	0.809489	+	0.587135i	$0.199744\pi$
$877$			34.7751i			1.17427i	−0.809489	+	0.587135i	$0.800256\pi$
$878$	−35.5525	−	20.5262i	−1.19984	−	0.692726i
$879$	11.4120	−	6.58873i	0.384917	−	0.222232i
$880$	0.516630			0.0174156
$881$	−3.20704	+	5.55476i	−0.108048	+	0.187144i	−0.914979	−	0.403501i	$-0.867793\pi$
$881$	−3.20704	+	5.55476i	−0.108048	+	0.187144i	0.806931	+	0.590645i	$0.201127\pi$
$882$	−3.78455	+	5.88874i	−0.127432	+	0.198284i
$883$	14.4538			0.486410			0.243205	−	0.969975i	$-0.421801\pi$
$883$	14.4538			0.486410			0.243205	+	0.969975i	$0.421801\pi$
$884$	−3.56535	−	1.49747i	−0.119916	−	0.0503655i
$885$	1.26287	+	2.18736i	0.0424509	+	0.0735272i
$886$			31.9258i			1.07257i
$887$	4.44793	+	7.70404i	0.149347	+	0.258676i	0.930986	−	0.365054i	$-0.118950\pi$
$887$	4.44793	+	7.70404i	0.149347	+	0.258676i	−0.781639	+	0.623731i	$0.785616\pi$
$888$	3.61516	+	6.26164i	0.121317	+	0.210127i
$889$	−40.5817	−	11.9161i	−1.36107	−	0.399653i
$890$	−0.870240	+	0.502433i	−0.0291705	+	0.0168416i
$891$		−	2.92586i		−	0.0980199i
$892$	−10.9006	+	6.29348i	−0.364980	+	0.210721i
$893$	18.2170	−	31.5527i	0.609607	−	1.05587i
$894$	8.26713	+	14.3191i	0.276494	+	0.478902i
$895$	−1.46612	−	0.846465i	−0.0490070	−	0.0282942i
$896$	1.82577	+	1.91483i	0.0609946	+	0.0639700i
$897$	−6.42283	−	2.69764i	−0.214452	−	0.0900715i
$898$	4.26583	−	7.38864i	0.142353	−	0.246562i
$899$		−	1.56952i		−	0.0523463i
$900$	−4.96882			−0.165627
$901$	−8.55028			−0.284851
$902$			12.3415i			0.410928i
$903$	9.29540	−	8.86305i	0.309331	−	0.294944i
$904$	10.3445	−	5.97238i	0.344052	−	0.198638i
$905$	3.33213	+	1.92381i	0.110764	+	0.0639495i
$906$	1.92699	−	3.33765i	0.0640200	−	0.110886i
$907$	−16.8723			−0.560236			−0.280118	−	0.959966i	$-0.590374\pi$
$907$	−16.8723			−0.560236			−0.280118	+	0.959966i	$0.590374\pi$
$908$	14.3351	−	8.27640i	0.475728	−	0.274662i
$909$	7.63322			0.253178
$910$	−1.30631	−	1.06338i	−0.0433039	−	0.0352508i
$911$	34.2043			1.13324			0.566620	−	0.823979i	$-0.308251\pi$
$911$	34.2043			1.13324			0.566620	+	0.823979i	$0.308251\pi$
$912$	4.15994	−	2.40174i	0.137749	−	0.0795296i
$913$	27.7853			0.919558
$914$	−15.7518	+	27.2830i	−0.521024	+	0.902440i
$915$	−0.980196	−	0.565916i	−0.0324043	−	0.0187086i
$916$	−6.18450	+	3.57062i	−0.204342	+	0.117977i
$917$	27.6998	+	8.13355i	0.914728	+	0.268594i
$918$		−	1.07253i		−	0.0353988i
$919$	−30.9712			−1.02164			−0.510822	−	0.859686i	$-0.670659\pi$
$919$	−30.9712			−1.02164			−0.510822	+	0.859686i	$0.670659\pi$
$920$	0.341162			0.0112478
$921$			7.47440i			0.246290i
$922$	0.779490	−	1.35012i	0.0256711	−	0.0444637i
$923$	−18.7475	+	44.6362i	−0.617083	+	1.46922i
$924$	2.18096	−	7.42751i	0.0717482	−	0.244347i
$925$	−31.1130	−	17.9631i	−1.02299	−	0.590622i
$926$	7.11450	+	12.3227i	0.233797	+	0.404948i
$927$	4.70230	−	8.14463i	0.154444	−	0.267505i
$928$	−1.52499	+	0.880456i	−0.0500604	+	0.0289024i
$929$			11.3171i			0.371300i	0.982616	+	0.185650i	$0.0594391\pi$
$929$			11.3171i			0.371300i	−0.982616	+	0.185650i	$0.940561\pi$
$930$	0.136297	−	0.0786910i	0.00446935	−	0.00258038i
$931$	15.4073	+	29.8867i	0.504953	+	0.979497i
$932$	−0.423576	−	0.733656i	−0.0138747	−	0.0240317i
$933$	12.7812	+	22.1376i	0.418436	+	0.724753i
$934$			24.8013i			0.811522i
$935$	−0.277051	−	0.479866i	−0.00906053	−	0.0156933i
$936$	2.18078	+	2.87127i	0.0712809	+	0.0938505i
$937$	27.9371			0.912666			0.456333	−	0.889809i	$-0.349163\pi$
$937$	27.9371			0.912666			0.456333	+	0.889809i	$0.349163\pi$
$938$	21.5530	−	20.5505i	0.703729	−	0.670997i
$939$	−4.39220	+	7.60752i	−0.143334	+	0.248262i
$940$	−1.33930			−0.0436830
$941$	32.4430	−	18.7309i	1.05761	−	0.610611i	0.132840	−	0.991138i	$-0.457590\pi$
$941$	32.4430	−	18.7309i	1.05761	−	0.610611i	0.924770	+	0.380526i	$0.124257\pi$
$942$	−12.9975	−	7.50411i	−0.423482	−	0.244497i
$943$			8.14985i			0.265396i
$944$		−	14.3041i		−	0.465560i
$945$	0.131620	−	0.448247i	0.00428159	−	0.0145815i
$946$	−7.10168	+	12.3005i	−0.230895	+	0.399923i
$947$	−23.9430	+	13.8235i	−0.778044	+	0.449204i	−0.835737	−	0.549131i	$-0.814959\pi$
$947$	−23.9430	+	13.8235i	−0.778044	+	0.449204i	0.0576927	+	0.998334i	$0.481626\pi$
$948$	3.86312	+	6.69111i	0.125468	+	0.217317i
$949$	14.8481	−	35.3521i	0.481991	−	1.14758i
$950$	−11.9338	+	20.6700i	−0.387184	+	0.670623i
$951$	18.7405	+	10.8198i	0.607702	+	0.350857i
$952$	0.799472	−	2.72270i	0.0259110	−	0.0882431i
$953$	−0.581849	−	1.00779i	−0.0188479	−	0.0326456i	0.856448	−	0.516234i	$-0.172667\pi$
$953$	−0.581849	−	1.00779i	−0.0188479	−	0.0326456i	−0.875296	+	0.483588i	$0.839333\pi$
$954$	6.90402	+	3.98604i	0.223526	+	0.129053i
$955$	2.45754	+	1.41886i	0.0795241	+	0.0459132i
$956$	−3.12831	−	1.80613i	−0.101177	−	0.0584145i
$957$	4.46192	+	2.57609i	0.144233	+	0.0832731i
$958$	−8.08050	−	13.9958i	−0.261069	−	0.452185i
$959$	1.82823	−	6.22626i	0.0590367	−	0.201056i
$960$	−0.152918	−	0.0882870i	−0.00493540	−	0.00284945i
$961$	−15.1028	+	26.1588i	−0.487187	+	0.843832i
$962$	3.27512	+	25.8627i	0.105594	+	0.833848i
$963$	0.957952	+	1.65922i	0.0308696	+	0.0534677i
$964$	−4.16826	+	2.40655i	−0.134251	+	0.0775096i
$965$	0.137253	−	0.237728i	0.00441832	−	0.00765275i
$966$	1.44022	−	4.90483i	0.0463382	−	0.157810i
$967$		−	25.1147i		−	0.807633i	−0.914840	−	0.403817i	$-0.867683\pi$
$967$		−	25.1147i		−	0.807633i	0.914840	−	0.403817i	$-0.132317\pi$
$968$		−	2.43936i		−	0.0784040i
$969$	−4.46166	−	2.57594i	−0.143329	−	0.0827511i
$970$	−1.64068	+	0.947246i	−0.0526790	+	0.0304142i
$971$	−31.4932			−1.01066			−0.505332	−	0.862925i	$-0.668630\pi$
$971$	−31.4932			−1.01066			−0.505332	+	0.862925i	$0.668630\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−20.1341	+	19.1976i	−0.645468	+	0.615446i
$974$	25.3388			0.811907
$975$	−16.5176	−	6.93751i	−0.528986	−	0.222178i
$976$	3.20498	+	5.55119i	0.102589	+	0.177689i
$977$		−	32.8638i		−	1.05141i	−0.850668	−	0.525703i	$-0.823802\pi$
$977$		−	32.8638i		−	1.05141i	0.850668	−	0.525703i	$-0.176198\pi$
$978$	2.73596	+	4.73882i	0.0874862	+	0.151531i
$979$	−8.32539	−	14.4200i	−0.266081	−	0.460865i
$980$	0.668253	−	1.03980i	0.0213466	−	0.0332151i
$981$	−10.1264	+	5.84647i	−0.323311	+	0.186664i
$982$		−	23.8684i		−	0.761671i
$983$	−31.8893	+	18.4113i	−1.01711	+	0.587230i	−0.913266	−	0.407364i	$-0.866448\pi$
$983$	−31.8893	+	18.4113i	−1.01711	+	0.587230i	−0.103846	+	0.994593i	$0.533115\pi$
$984$	2.10905	−	3.65298i	0.0672340	−	0.116453i
$985$	−1.51469	−	2.62351i	−0.0482619	−	0.0835921i
$986$	1.63560	+	0.944315i	0.0520882	+	0.0300731i
$987$	−5.65384	+	19.2548i	−0.179964	+	0.612888i
$988$	17.1820	−	2.17584i	0.546632	−	0.0692225i
$989$	−4.68966	+	8.12273i	−0.149123	+	0.258288i
$990$			0.516630i			0.0164196i
$991$	−29.7104			−0.943783			−0.471892	−	0.881657i	$-0.656429\pi$
$991$	−29.7104			−0.943783			−0.471892	+	0.881657i	$0.656429\pi$
$992$	−0.891308			−0.0282991
$993$		−	22.2158i		−	0.704998i
$994$	−34.0867	−	10.0089i	−1.08116	−	0.317464i
$995$	−3.00545	+	1.73520i	−0.0952791	+	0.0550094i
$996$	−8.22417	−	4.74823i	−0.260593	−	0.150453i
$997$	−12.6402	+	21.8934i	−0.400318	+	0.693371i	−0.993764	−	0.111502i	$-0.964434\pi$
$997$	−12.6402	+	21.8934i	−0.400318	+	0.693371i	0.593446	+	0.804874i	$0.297767\pi$
$998$	31.1522			0.986106
$999$	−6.26164	+	3.61516i	−0.198109	+	0.114379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bd.a.121.7	✓	16
3.2	odd	2		1638.2.cr.a.667.2		16
7.4	even	3		546.2.bm.a.277.6	yes	16
13.10	even	6		546.2.bm.a.205.2	yes	16
21.11	odd	6		1638.2.dt.a.1369.3		16
39.23	odd	6		1638.2.dt.a.1297.7		16
91.88	even	6	inner	546.2.bd.a.361.7	yes	16
273.179	odd	6		1638.2.cr.a.361.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bd.a.121.7	✓	16	1.1	even	1	trivial
546.2.bd.a.361.7	yes	16	91.88	even	6	inner
546.2.bm.a.205.2	yes	16	13.10	even	6
546.2.bm.a.277.6	yes	16	7.4	even	3
1638.2.cr.a.361.2		16	273.179	odd	6
1638.2.cr.a.667.2		16	3.2	odd	2
1638.2.dt.a.1297.7		16	39.23	odd	6
1638.2.dt.a.1369.3		16	21.11	odd	6

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.bd (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.152918 - 0.0882870i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.623746 - 2.57117i) q^{7} -1.00000i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} -1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.152918 - 0.0882870i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-0.623746 - 2.57117i) q^{7} -1.00000i q^{8} +1.00000 q^{9} -0.176574 q^{10} -2.92586i q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.87127 + 2.18078i) q^{13} +(-1.82577 - 1.91483i) q^{14} +(0.152918 + 0.0882870i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.536265 + 0.928838i) q^{17} +(0.866025 - 0.500000i) q^{18} -4.80348i q^{19} +(-0.152918 + 0.0882870i) q^{20} +(0.623746 + 2.57117i) q^{21} +(-1.46293 - 2.53387i) q^{22} +(-0.966059 - 1.67326i) q^{23} +1.00000i q^{24} +(-2.48441 - 4.30313i) q^{25} +(-1.39621 + 3.32424i) q^{26} -1.00000 q^{27} +(-2.53858 - 0.745408i) q^{28} +(0.880456 - 1.52499i) q^{29} +0.176574 q^{30} +(0.771896 - 0.445654i) q^{31} +(-0.866025 - 0.500000i) q^{32} +2.92586i q^{33} +1.07253i q^{34} +(-0.131620 + 0.448247i) q^{35} +(0.500000 - 0.866025i) q^{36} +(6.26164 - 3.61516i) q^{37} +(-2.40174 - 4.15994i) q^{38} +(2.87127 - 2.18078i) q^{39} +(-0.0882870 + 0.152918i) q^{40} +(-3.65298 - 2.10905i) q^{41} +(1.82577 + 1.91483i) q^{42} +(-2.42721 - 4.20406i) q^{43} +(-2.53387 - 1.46293i) q^{44} +(-0.152918 - 0.0882870i) q^{45} +(-1.67326 - 0.966059i) q^{46} +(6.56871 + 3.79245i) q^{47} +(0.500000 + 0.866025i) q^{48} +(-6.22188 + 3.20752i) q^{49} +(-4.30313 - 2.48441i) q^{50} +(0.536265 - 0.928838i) q^{51} +(0.452970 + 3.57698i) q^{52} +(3.98604 + 6.90402i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-0.258315 + 0.447415i) q^{55} +(-2.57117 + 0.623746i) q^{56} +4.80348i q^{57} -1.76091i q^{58} +(12.3878 + 7.15207i) q^{59} +(0.152918 - 0.0882870i) q^{60} -6.40996 q^{61} +(0.445654 - 0.771896i) q^{62} +(-0.623746 - 2.57117i) q^{63} -1.00000 q^{64} +(0.631603 - 0.0799828i) q^{65} +(1.46293 + 2.53387i) q^{66} +11.2558i q^{67} +(0.536265 + 0.928838i) q^{68} +(0.966059 + 1.67326i) q^{69} +(0.110137 + 0.454003i) q^{70} +(11.6285 - 6.71374i) q^{71} -1.00000i q^{72} +(-9.20985 + 5.31731i) q^{73} +(3.61516 - 6.26164i) q^{74} +(2.48441 + 4.30313i) q^{75} +(-4.15994 - 2.40174i) q^{76} +(-7.52289 + 1.82499i) q^{77} +(1.39621 - 3.32424i) q^{78} +(3.86312 - 6.69111i) q^{79} +0.176574i q^{80} +1.00000 q^{81} -4.21809 q^{82} +9.49646i q^{83} +(2.53858 + 0.745408i) q^{84} +(0.164009 - 0.0946905i) q^{85} +(-4.20406 - 2.42721i) q^{86} +(-0.880456 + 1.52499i) q^{87} -2.92586 q^{88} +(4.92847 - 2.84545i) q^{89} -0.176574 q^{90} +(7.39810 + 6.02230i) q^{91} -1.93212 q^{92} +(-0.771896 + 0.445654i) q^{93} +7.58490 q^{94} +(-0.424085 + 0.734537i) q^{95} +(0.866025 + 0.500000i) q^{96} +(9.29173 - 5.36458i) q^{97} +(-3.78455 + 5.88874i) q^{98} -2.92586i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9}+O(q^{10}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9	\( 16 q - 16 q^{3} + 8 q^{4} + 8 q^{7} + 16 q^{9} - 8 q^{10} - 8 q^{12} - 10 q^{13} + 4 q^{14} - 8 q^{16} - 8 q^{21} + 6 q^{22} - 16 q^{23} + 2 q^{26} - 16 q^{27} + 10 q^{28} - 4 q^{29} + 8 q^{30} + 12 q^{31} + 16 q^{35} + 8 q^{36} + 30 q^{37} - 2 q^{38} + 10 q^{39} - 4 q^{40} - 18 q^{41} - 4 q^{42} - 32 q^{43} + 6 q^{44} + 12 q^{46} + 66 q^{47} + 8 q^{48} - 2 q^{49} + 36 q^{50} + 4 q^{52} + 2 q^{53} + 16 q^{55} + 2 q^{56} - 36 q^{59} - 8 q^{61} + 4 q^{62} + 8 q^{63} - 16 q^{64} - 28 q^{65} - 6 q^{66} + 16 q^{69} - 6 q^{70} - 30 q^{71} - 18 q^{73} + 6 q^{74} - 18 q^{76} - 34 q^{77} - 2 q^{78} - 24 q^{79} + 16 q^{81} - 12 q^{82} - 10 q^{84} + 72 q^{85} + 4 q^{87} + 12 q^{88} - 42 q^{89} - 8 q^{90} - 18 q^{91} - 32 q^{92} - 12 q^{93} + 48 q^{94} - 40 q^{95} - 6 q^{97} - 12 q^{98}+O(q^{100}) \) 16 * q - 16 * q^3 + 8 * q^4 + 8 * q^7 + 16 * q^9 - 8 * q^10 - 8 * q^12 - 10 * q^13 + 4 * q^14 - 8 * q^16 - 8 * q^21 + 6 * q^22 - 16 * q^23 + 2 * q^26 - 16 * q^27 + 10 * q^28 - 4 * q^29 + 8 * q^30 + 12 * q^31 + 16 * q^35 + 8 * q^36 + 30 * q^37 - 2 * q^38 + 10 * q^39 - 4 * q^40 - 18 * q^41 - 4 * q^42 - 32 * q^43 + 6 * q^44 + 12 * q^46 + 66 * q^47 + 8 * q^48 - 2 * q^49 + 36 * q^50 + 4 * q^52 + 2 * q^53 + 16 * q^55 + 2 * q^56 - 36 * q^59 - 8 * q^61 + 4 * q^62 + 8 * q^63 - 16 * q^64 - 28 * q^65 - 6 * q^66 + 16 * q^69 - 6 * q^70 - 30 * q^71 - 18 * q^73 + 6 * q^74 - 18 * q^76 - 34 * q^77 - 2 * q^78 - 24 * q^79 + 16 * q^81 - 12 * q^82 - 10 * q^84 + 72 * q^85 + 4 * q^87 + 12 * q^88 - 42 * q^89 - 8 * q^90 - 18 * q^91 - 32 * q^92 - 12 * q^93 + 48 * q^94 - 40 * q^95 - 6 * q^97 - 12 * q^98

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