LMFDB - Embedded newform 231.2.w.a.13.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(13,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 1]))

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

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

chi := DirichletCharacter("231.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.w (of order $10$, degree $4$, 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:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			13.11
Character	$\chi$	$=$	231.13
Dual form			231.2.w.a.160.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819861 + 0.266389i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.01682 - 0.738766i) q^{4} +(-2.84938 + 0.925820i) q^{5} +(-0.266389 - 0.819861i) q^{6} +(0.656605 - 2.56298i) q^{7} +(-1.65026 - 2.27139i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})$	\(q+(0.819861 + 0.266389i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.01682 - 0.738766i) q^{4} +(-2.84938 + 0.925820i) q^{5} +(-0.266389 - 0.819861i) q^{6} +(0.656605 - 2.56298i) q^{7} +(-1.65026 - 2.27139i) q^{8} +(-0.309017 + 0.951057i) q^{9} -2.58273 q^{10} +(-3.28730 + 0.440063i) q^{11} +1.25686i q^{12} +(0.817616 - 2.51636i) q^{13} +(1.22107 - 1.92638i) q^{14} +(2.42383 + 1.76102i) q^{15} +(0.0288735 + 0.0888635i) q^{16} +(-1.16828 - 3.59560i) q^{17} +(-0.506702 + 0.697416i) q^{18} +(-0.962538 + 0.699325i) q^{19} +(3.58129 + 1.16363i) q^{20} +(-2.45944 + 0.975278i) q^{21} +(-2.81236 - 0.514911i) q^{22} +3.78972 q^{23} +(-0.867593 + 2.67018i) q^{24} +(3.21675 - 2.33711i) q^{25} +(1.34066 - 1.84526i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.56110 + 2.12102i) q^{28} +(-2.48679 + 3.42278i) q^{29} +(1.51809 + 2.08947i) q^{30} +(9.48536 + 3.08198i) q^{31} +5.69573i q^{32} +(2.28824 + 2.40082i) q^{33} -3.25911i q^{34} +(0.501942 + 7.91081i) q^{35} +(1.01682 - 0.738766i) q^{36} +(-6.34170 - 4.60751i) q^{37} +(-0.975440 + 0.316940i) q^{38} +(-2.51636 + 0.817616i) q^{39} +(6.80512 + 4.94421i) q^{40} +(8.15422 - 5.92439i) q^{41} +(-2.27620 + 0.144425i) q^{42} -8.56532i q^{43} +(3.66771 + 1.98108i) q^{44} -2.99602i q^{45} +(3.10704 + 1.00954i) q^{46} +(-4.26457 - 5.86968i) q^{47} +(0.0549206 - 0.0755918i) q^{48} +(-6.13774 - 3.36573i) q^{49} +(3.25987 - 1.05920i) q^{50} +(-2.22220 + 3.05860i) q^{51} +(-2.69038 + 1.95467i) q^{52} +(0.361533 - 1.11268i) q^{53} +0.862053 q^{54} +(8.95936 - 4.29736i) q^{55} +(-6.90509 + 2.73818i) q^{56} +(1.13153 + 0.367657i) q^{57} +(-2.95061 + 2.14375i) q^{58} +(-7.74072 + 10.6542i) q^{59} +(-1.16363 - 3.58129i) q^{60} +(-1.03090 - 3.17279i) q^{61} +(6.95567 + 5.05359i) q^{62} +(2.23464 + 1.41647i) q^{63} +(-1.45953 + 4.49198i) q^{64} +7.92704i q^{65} +(1.23649 + 2.57790i) q^{66} +11.2990 q^{67} +(-1.46837 + 4.51918i) q^{68} +(-2.22754 - 3.06595i) q^{69} +(-1.69583 + 6.61948i) q^{70} +(0.805527 + 2.47916i) q^{71} +(2.67018 - 0.867593i) q^{72} +(-7.86260 - 5.71251i) q^{73} +(-3.97192 - 5.46688i) q^{74} +(-3.78152 - 1.22869i) q^{75} +1.49537 q^{76} +(-1.03059 + 8.71424i) q^{77} -2.28087 q^{78} +(-12.7373 - 4.13859i) q^{79} +(-0.164543 - 0.226474i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(8.26352 - 2.68498i) q^{82} +(-0.867141 - 2.66879i) q^{83} +(3.22132 + 0.825263i) q^{84} +(6.65776 + 9.16362i) q^{85} +(2.28171 - 7.02237i) q^{86} +4.23078 q^{87} +(6.42445 + 6.74052i) q^{88} -6.28176i q^{89} +(0.798106 - 2.45632i) q^{90} +(-5.91254 - 3.74779i) q^{91} +(-3.85348 - 2.79972i) q^{92} +(-3.08198 - 9.48536i) q^{93} +(-1.93274 - 5.94836i) q^{94} +(2.09519 - 2.88378i) q^{95} +(4.60794 - 3.34786i) q^{96} +(8.72441 + 2.83473i) q^{97} +(-4.13550 - 4.39446i) q^{98} +(0.597307 - 3.26240i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	$ 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) $ 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{10}\right)$

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 $

$2$	0.819861	+	0.266389i	0.579729	+	0.188366i	0.584179	−	0.811625i	$-0.301416\pi$
$2$	0.819861	+	0.266389i	0.579729	+	0.188366i	−0.00444991	+	0.999990i	$0.501416\pi$
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$3$	−0.587785	−	0.809017i	−0.339358	−	0.467086i
$4$	−1.01682	−	0.738766i	−0.508412	−	0.369383i
$5$	−2.84938	+	0.925820i	−1.27428	+	0.414039i	−0.866563	−	0.499068i	$-0.833676\pi$
$5$	−2.84938	+	0.925820i	−1.27428	+	0.414039i	−0.407720	+	0.913107i	$0.633676\pi$
$6$	−0.266389	−	0.819861i	−0.108753	−	0.334707i
$7$	0.656605	−	2.56298i	0.248173	−	0.968716i
$7$	0.656605	−	2.56298i	0.248173	−	0.968716i
$8$	−1.65026	−	2.27139i	−0.583455	−	0.803057i
$9$	−0.309017	+	0.951057i	−0.103006	+	0.317019i
$10$	−2.58273			−0.816730
$11$	−3.28730	+	0.440063i	−0.991158	+	0.132684i
$11$	−3.28730	+	0.440063i	−0.991158	+	0.132684i
$12$			1.25686i			0.362825i
$13$	0.817616	−	2.51636i	0.226766	−	0.697913i	−0.771342	−	0.636421i	$-0.780414\pi$
$13$	0.817616	−	2.51636i	0.226766	−	0.697913i	0.998108	−	0.0614923i	$-0.0195859\pi$
$14$	1.22107	−	1.92638i	0.326346	−	0.514846i
$15$	2.42383	+	1.76102i	0.625830	+	0.454692i
$16$	0.0288735	+	0.0888635i	0.00721837	+	0.0222159i
$17$	−1.16828	−	3.59560i	−0.283350	−	0.872061i	−0.986888	−	0.161404i	$-0.948398\pi$
$17$	−1.16828	−	3.59560i	−0.283350	−	0.872061i	0.703539	−	0.710657i	$-0.251602\pi$
$18$	−0.506702	+	0.697416i	−0.119431	+	0.164382i
$19$	−0.962538	+	0.699325i	−0.220821	+	0.160436i	−0.692696	−	0.721229i	$-0.743577\pi$
$19$	−0.962538	+	0.699325i	−0.220821	+	0.160436i	0.471875	+	0.881665i	$0.343577\pi$
$20$	3.58129	+	1.16363i	0.800800	+	0.260196i
$21$	−2.45944	+	0.975278i	−0.536693	+	0.212823i
$22$	−2.81236	−	0.514911i	−0.599597	−	0.109779i
$23$	3.78972			0.790211			0.395105	−	0.918636i	$-0.370708\pi$
$23$	3.78972			0.790211			0.395105	+	0.918636i	$0.370708\pi$
$24$	−0.867593	+	2.67018i	−0.177097	+	0.545048i
$25$	3.21675	−	2.33711i	0.643350	−	0.467421i
$26$	1.34066	−	1.84526i	0.262926	−	0.361886i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	−2.56110	+	2.12102i	−0.484002	+	0.400836i
$29$	−2.48679	+	3.42278i	−0.461786	+	0.635593i	−0.974878	−	0.222740i	$-0.928500\pi$
$29$	−2.48679	+	3.42278i	−0.461786	+	0.635593i	0.513092	+	0.858333i	$0.328500\pi$
$30$	1.51809	+	2.08947i	0.277164	+	0.381483i
$31$	9.48536	+	3.08198i	1.70362	+	0.553540i	0.989251	−	0.146229i	$-0.0467137\pi$
$31$	9.48536	+	3.08198i	1.70362	+	0.553540i	0.714369	+	0.699769i	$0.246714\pi$
$32$			5.69573i			1.00687i
$33$	2.28824	+	2.40082i	0.398332	+	0.417929i
$34$		−	3.25911i		−	0.558933i
$35$	0.501942	+	7.91081i	0.0848436	+	1.33717i
$36$	1.01682	−	0.738766i	0.169471	−	0.123128i
$37$	−6.34170	−	4.60751i	−1.04257	−	0.757470i	−0.0717833	−	0.997420i	$-0.522869\pi$
$37$	−6.34170	−	4.60751i	−1.04257	−	0.757470i	−0.970785	+	0.239950i	$0.922869\pi$
$38$	−0.975440	+	0.316940i	−0.158237	+	0.0514144i
$39$	−2.51636	+	0.817616i	−0.402941	+	0.130923i
$40$	6.80512	+	4.94421i	1.07598	+	0.781748i
$41$	8.15422	−	5.92439i	1.27348	−	0.925234i	0.274140	−	0.961690i	$-0.411607\pi$
$41$	8.15422	−	5.92439i	1.27348	−	0.925234i	0.999335	+	0.0364559i	$0.0116068\pi$
$42$	−2.27620	+	0.144425i	−0.351225	+	0.0222853i
$43$		−	8.56532i		−	1.30620i	−0.757272	−	0.653099i	$-0.773468\pi$
$43$		−	8.56532i		−	1.30620i	0.757272	−	0.653099i	$-0.226532\pi$
$44$	3.66771	+	1.98108i	0.552928	+	0.298659i
$45$		−	2.99602i		−	0.446620i
$46$	3.10704	+	1.00954i	0.458109	+	0.148848i
$47$	−4.26457	−	5.86968i	−0.622052	−	0.856181i	0.375448	−	0.926843i	$-0.377489\pi$
$47$	−4.26457	−	5.86968i	−0.622052	−	0.856181i	−0.997500	+	0.0706624i	$0.977489\pi$
$48$	0.0549206	−	0.0755918i	0.00792711	−	0.0109107i
$49$	−6.13774	−	3.36573i	−0.876820	−	0.480819i
$50$	3.25987	−	1.05920i	0.461015	−	0.149793i
$51$	−2.22220	+	3.05860i	−0.311170	+	0.428289i
$52$	−2.69038	+	1.95467i	−0.373088	+	0.271064i
$53$	0.361533	−	1.11268i	0.0496603	−	0.152839i	−0.923151	−	0.384437i	$-0.874396\pi$
$53$	0.361533	−	1.11268i	0.0496603	−	0.152839i	0.972811	+	0.231598i	$0.0743955\pi$
$54$	0.862053			0.117311
$55$	8.95936	−	4.29736i	1.20808	−	0.579455i
$56$	−6.90509	+	2.73818i	−0.922732	+	0.365905i
$57$	1.13153	+	0.367657i	0.149875	+	0.0486973i
$58$	−2.95061	+	2.14375i	−0.387435	+	0.281488i
$59$	−7.74072	+	10.6542i	−1.00776	+	1.38706i	−0.0873127	+	0.996181i	$0.527828\pi$
$59$	−7.74072	+	10.6542i	−1.00776	+	1.38706i	−0.920443	+	0.390876i	$0.872172\pi$
$60$	−1.16363	−	3.58129i	−0.150224	−	0.462342i
$61$	−1.03090	−	3.17279i	−0.131993	−	0.406234i	0.863117	−	0.505004i	$-0.168509\pi$
$61$	−1.03090	−	3.17279i	−0.131993	−	0.406234i	−0.995110	+	0.0987702i	$0.968509\pi$
$62$	6.95567	+	5.05359i	0.883371	+	0.641807i
$63$	2.23464	+	1.41647i	0.281538	+	0.178459i
$64$	−1.45953	+	4.49198i	−0.182442	+	0.561497i
$65$			7.92704i			0.983229i
$66$	1.23649	+	2.57790i	0.152202	+	0.317318i
$67$	11.2990			1.38040			0.690199	−	0.723620i	$-0.257523\pi$
$67$	11.2990			1.38040			0.690199	+	0.723620i	$0.257523\pi$
$68$	−1.46837	+	4.51918i	−0.178066	+	0.548031i
$69$	−2.22754	−	3.06595i	−0.268164	−	0.369097i
$70$	−1.69583	+	6.61948i	−0.202691	+	0.791179i
$71$	0.805527	+	2.47916i	0.0955985	+	0.294222i	0.987409	−	0.158187i	$-0.0505648\pi$
$71$	0.805527	+	2.47916i	0.0955985	+	0.294222i	−0.891811	+	0.452409i	$0.850565\pi$
$72$	2.67018	−	0.867593i	0.314683	−	0.102247i
$73$	−7.86260	−	5.71251i	−0.920248	−	0.668599i	0.0233378	−	0.999728i	$-0.492571\pi$
$73$	−7.86260	−	5.71251i	−0.920248	−	0.668599i	−0.943586	+	0.331128i	$0.892571\pi$
$74$	−3.97192	−	5.46688i	−0.461726	−	0.635512i
$75$	−3.78152	−	1.22869i	−0.436652	−	0.141877i
$76$	1.49537			0.171531
$77$	−1.03059	+	8.71424i	−0.117446	+	0.993079i
$78$	−2.28087			−0.258258
$79$	−12.7373	−	4.13859i	−1.43306	−	0.465628i	−0.513330	−	0.858191i	$-0.671588\pi$
$79$	−12.7373	−	4.13859i	−1.43306	−	0.465628i	−0.919725	+	0.392563i	$0.871588\pi$
$80$	−0.164543	−	0.226474i	−0.0183965	−	0.0253206i
$81$	−0.809017	−	0.587785i	−0.0898908	−	0.0653095i
$82$	8.26352	−	2.68498i	0.912553	−	0.296507i
$83$	−0.867141	−	2.66879i	−0.0951811	−	0.292937i	0.892120	−	0.451799i	$-0.149218\pi$
$83$	−0.867141	−	2.66879i	−0.0951811	−	0.292937i	−0.987301	+	0.158862i	$0.949218\pi$
$84$	3.22132	+	0.825263i	0.351475	+	0.0900436i
$85$	6.65776	+	9.16362i	0.722135	+	0.993934i
$86$	2.28171	−	7.02237i	0.246043	−	0.757242i
$87$	4.23078			0.453588
$88$	6.42445	+	6.74052i	0.684849	+	0.718542i
$89$		−	6.28176i		−	0.665866i	−0.942951	−	0.332933i	$-0.891962\pi$
$89$		−	6.28176i		−	0.665866i	0.942951	−	0.332933i	$-0.108038\pi$
$90$	0.798106	−	2.45632i	0.0841278	−	0.258919i
$91$	−5.91254	−	3.74779i	−0.619802	−	0.392875i
$92$	−3.85348	−	2.79972i	−0.401753	−	0.291891i
$93$	−3.08198	−	9.48536i	−0.319586	−	0.983586i
$94$	−1.93274	−	5.94836i	−0.199347	−	0.613526i
$95$	2.09519	−	2.88378i	0.214962	−	0.295870i
$96$	4.60794	−	3.34786i	0.470296	−	0.341690i
$97$	8.72441	+	2.83473i	0.885830	+	0.287824i	0.716376	−	0.697714i	$-0.245800\pi$
$97$	8.72441	+	2.83473i	0.885830	+	0.287824i	0.169454	+	0.985538i	$0.445800\pi$
$98$	−4.13550	−	4.39446i	−0.417749	−	0.443907i
$99$	0.597307	−	3.26240i	0.0600316	−	0.327883i
$100$	−4.99745			−0.499745
$101$	2.66599	−	8.20508i	0.265276	−	0.816436i	−0.726353	−	0.687321i	$-0.758786\pi$
$101$	2.66599	−	8.20508i	0.265276	−	0.816436i	0.991630	−	0.129115i	$-0.0412136\pi$
$102$	−2.63667	+	1.91566i	−0.261070	+	0.189678i
$103$	−7.52111	+	10.3519i	−0.741077	+	1.02001i	0.257479	+	0.966284i	$0.417108\pi$
$103$	−7.52111	+	10.3519i	−0.741077	+	1.02001i	−0.998556	+	0.0537213i	$0.982892\pi$
$104$	−7.06492	+	2.29553i	−0.692772	+	0.225095i
$105$	6.10495	−	5.05594i	0.595782	−	0.493409i
$106$	0.592813	−	0.815937i	0.0575791	−	0.0792508i
$107$	2.74624	+	3.77988i	0.265489	+	0.365414i	0.920860	−	0.389892i	$-0.127488\pi$
$107$	2.74624	+	3.77988i	0.265489	+	0.365414i	−0.655371	+	0.755307i	$0.727488\pi$
$108$	−1.19535	−	0.388392i	−0.115023	−	0.0373731i
$109$		−	2.37589i		−	0.227569i	−0.993505	−	0.113784i	$-0.963703\pi$
$109$		−	2.37589i		−	0.227569i	0.993505	−	0.113784i	$-0.0362973\pi$
$110$	8.49020	−	1.13656i	0.809509	−	0.108367i
$111$			7.83877i			0.744023i
$112$	0.246714	−	0.0156540i	0.0233123	−	0.00147917i
$113$	3.78006	−	2.74637i	0.355598	−	0.258357i	−0.395616	−	0.918416i	$-0.629469\pi$
$113$	3.78006	−	2.74637i	0.355598	−	0.258357i	0.751214	+	0.660059i	$0.229469\pi$
$114$	0.829759	+	0.602855i	0.0777141	+	0.0564626i
$115$	−10.7984	+	3.50860i	−1.00695	+	0.327179i
$116$	5.05726	−	1.64320i	0.469555	−	0.152568i
$117$	2.14055	+	1.55520i	0.197894	+	0.143778i
$118$	−9.18448	+	6.67291i	−0.845500	+	0.614291i
$119$	−9.98255	+	0.633394i	−0.915099	+	0.0580631i
$120$		−	8.41159i		−	0.767870i
$121$	10.6127	−	2.89324i	0.964790	−	0.263021i
$122$		−	2.87587i		−	0.260369i
$123$	−9.58586	−	3.11463i	−0.864328	−	0.280837i
$124$	−7.36808	−	10.1413i	−0.661673	−	0.910715i
$125$	1.80306	−	2.48170i	0.161271	−	0.221970i
$126$	1.45476	+	1.75659i	0.129600	+	0.156490i
$127$	−5.02167	+	1.63164i	−0.445601	+	0.144785i	−0.523218	−	0.852199i	$-0.675269\pi$
$127$	−5.02167	+	1.63164i	−0.445601	+	0.144785i	0.0776173	+	0.996983i	$0.475269\pi$
$128$	4.30250	−	5.92188i	0.380291	−	0.523426i
$129$	−6.92949	+	5.03457i	−0.610107	+	0.443269i
$130$	−2.11168	+	6.49908i	−0.185206	+	0.570007i
$131$	−0.575585			−0.0502891			−0.0251445	−	0.999684i	$-0.508005\pi$
$131$	−0.575585			−0.0502891			−0.0251445	+	0.999684i	$0.508005\pi$
$132$	−0.553099	−	4.13169i	−0.0481411	−	0.359618i
$133$	1.16035	+	2.92615i	0.100615	+	0.253729i
$134$	9.26365	+	3.00994i	0.800257	+	0.260019i
$135$	−2.42383	+	1.76102i	−0.208610	+	0.151564i
$136$	−6.23903	+	8.58729i	−0.534993	+	0.736354i
$137$	−2.53650	−	7.80654i	−0.216708	−	0.666958i	−0.999028	−	0.0440812i	$-0.985964\pi$
$137$	−2.53650	−	7.80654i	−0.216708	−	0.666958i	0.782320	−	0.622876i	$-0.214036\pi$
$138$	−1.00954	−	3.10704i	−0.0859377	−	0.264489i
$139$	5.53262	+	4.01968i	0.469271	+	0.340945i	0.797157	−	0.603772i	$-0.206336\pi$
$139$	5.53262	+	4.01968i	0.469271	+	0.340945i	−0.327886	+	0.944717i	$0.606336\pi$
$140$	5.33385	−	8.41472i	0.450793	−	0.711174i
$141$	−2.24202	+	6.90022i	−0.188812	+	0.581104i
$142$			2.24715i			0.188577i
$143$	−1.58039	+	8.63184i	−0.132159	+	0.721831i
$144$	−0.0934366			−0.00778638
$145$	3.91695	−	12.0551i	0.325285	−	1.00112i
$146$	−4.92449	−	6.77798i	−0.407554	−	0.560950i
$147$	0.884740	+	6.94386i	0.0729721	+	0.572720i
$148$	3.04452	+	9.37006i	0.250258	+	0.770215i
$149$	15.1413	−	4.91971i	1.24042	−	0.403038i	0.385943	−	0.922522i	$-0.373876\pi$
$149$	15.1413	−	4.91971i	1.24042	−	0.403038i	0.854480	+	0.519484i	$0.173876\pi$
$150$	−2.77301	−	2.01471i	−0.226415	−	0.164500i
$151$	8.28511	+	11.4035i	0.674232	+	0.928001i	0.999847	−	0.0175013i	$-0.00557111\pi$
$151$	8.28511	+	11.4035i	0.674232	+	0.928001i	−0.325614	+	0.945503i	$0.605571\pi$
$152$	3.17688	+	1.03223i	0.257679	+	0.0837249i
$153$	3.78064			0.305646
$154$	−3.16631	+	6.86993i	−0.255149	+	0.553595i
$155$	−29.8808			−2.40008
$156$	3.16273	+	1.02763i	0.253221	+	0.0822764i
$157$	3.80885	+	5.24243i	0.303979	+	0.418392i	0.933492	−	0.358599i	$-0.116745\pi$
$157$	3.80885	+	5.24243i	0.303979	+	0.418392i	−0.629512	+	0.776990i	$0.716745\pi$
$158$	−9.34032	−	6.78614i	−0.743076	−	0.539876i
$159$	−1.11268	+	0.361533i	−0.0882415	+	0.0286714i
$160$	−5.27322	−	16.2293i	−0.416885	−	1.28304i
$161$	2.48835	−	9.71297i	0.196109	−	0.765490i
$162$	−0.506702	−	0.697416i	−0.0398103	−	0.0547941i
$163$	2.24149	−	6.89860i	0.175567	−	0.540340i	−0.824092	−	0.566456i	$-0.808314\pi$
$163$	2.24149	−	6.89860i	0.175567	−	0.540340i	0.999659	+	0.0261161i	$0.00831395\pi$
$164$	−12.6681			−0.989216
$165$	−8.74281	−	4.72235i	−0.680627	−	0.367634i
$166$		−	2.41903i		−	0.187753i
$167$	2.39636	−	7.37525i	0.185436	−	0.570714i	−0.814519	−	0.580136i	$-0.802999\pi$
$167$	2.39636	−	7.37525i	0.185436	−	0.570714i	0.999956	+	0.00942243i	$0.00299930\pi$
$168$	6.27395	+	3.97688i	0.484045	+	0.306823i
$169$	4.85364	+	3.52637i	0.373357	+	0.271259i
$170$	3.01735	+	9.28645i	0.231420	+	0.712238i
$171$	−0.367657	−	1.13153i	−0.0281154	−	0.0865304i
$172$	−6.32777	+	8.70943i	−0.482488	+	0.664088i
$173$	0.381264	−	0.277004i	0.0289869	−	0.0210602i	−0.573197	−	0.819417i	$-0.694297\pi$
$173$	0.381264	−	0.277004i	0.0289869	−	0.0210602i	0.602184	+	0.798357i	$0.294297\pi$
$174$	3.46866	+	1.12703i	0.262958	+	0.0854403i
$175$	−3.87782	−	9.77903i	−0.293136	−	0.739225i
$176$	−0.134021	−	0.279415i	−0.0101022	−	0.0210617i
$177$	13.1693			0.989865
$178$	1.67339	−	5.15017i	0.125426	−	0.386022i
$179$	−0.00219819	+	0.00159708i	−0.000164300	+	0.000119371i	−0.587867	−	0.808957i	$-0.700032\pi$
$179$	−0.00219819	+	0.00159708i	−0.000164300	+	0.000119371i	0.587703	+	0.809077i	$0.300032\pi$
$180$	−2.21336	+	3.04642i	−0.164974	+	0.227067i
$181$	−10.2553	+	3.33215i	−0.762270	+	0.247677i	−0.664253	−	0.747508i	$-0.731250\pi$
$181$	−10.2553	+	3.33215i	−0.762270	+	0.247677i	−0.0980175	+	0.995185i	$0.531250\pi$
$182$	−3.84909	−	4.64770i	−0.285314	−	0.344511i
$183$	−1.96089	+	2.69894i	−0.144953	+	0.199511i
$184$	−6.25402	−	8.60792i	−0.461053	−	0.634584i
$185$	22.3357	+	7.25729i	1.64215	+	0.533567i
$186$		−	8.59768i		−	0.630413i
$187$	5.42278	+	11.3057i	0.396553	+	0.826754i
$188$			9.11896i			0.665068i
$189$	−0.167536	−	2.64044i	−0.0121865	−	0.192064i
$190$	2.48597	−	1.80617i	0.180351	−	0.131033i
$191$	−15.8060	−	11.4837i	−1.14368	−	0.830933i	−0.156053	−	0.987749i	$-0.549877\pi$
$191$	−15.8060	−	11.4837i	−1.14368	−	0.830933i	−0.987628	+	0.156816i	$0.949877\pi$
$192$	4.49198	−	1.45953i	0.324181	−	0.105333i
$193$	−0.243485	+	0.0791131i	−0.0175264	+	0.00569469i	−0.317767	−	0.948169i	$-0.602933\pi$
$193$	−0.243485	+	0.0791131i	−0.0175264	+	0.00569469i	0.300241	+	0.953863i	$0.402933\pi$
$194$	6.39767	+	4.64818i	0.459326	+	0.333720i
$195$	6.41311	−	4.65940i	0.459253	−	0.333667i
$196$	3.75452	+	7.95671i	0.268180	+	0.568337i
$197$		−	3.45226i		−	0.245964i	−0.992409	−	0.122982i	$-0.960754\pi$
$197$		−	3.45226i		−	0.245964i	0.992409	−	0.122982i	$-0.0392457\pi$
$198$	1.35878	−	2.51560i	0.0965640	−	0.178776i
$199$			17.3382i			1.22908i	0.788887	+	0.614538i	$0.210657\pi$
$199$			17.3382i			1.22908i	−0.788887	+	0.614538i	$0.789343\pi$
$200$	−10.6170	−	3.44966i	−0.750732	−	0.243928i
$201$	−6.64141	−	9.14112i	−0.468449	−	0.644765i
$202$	4.37149	−	6.01684i	0.307577	−	0.423343i
$203$	7.13967	+	8.62101i	0.501106	+	0.605076i
$204$	4.51918	−	1.46837i	0.316406	−	0.102806i
$205$	−17.7496	+	24.4302i	−1.23968	+	1.70628i
$206$	−8.92391	+	6.48360i	−0.621758	+	0.451734i
$207$	−1.17109	+	3.60424i	−0.0813962	+	0.250512i
$208$	0.247220			0.0171416
$209$	2.85641	−	2.72247i	0.197582	−	0.188317i
$210$	6.35206	−	2.51888i	0.438333	−	0.173819i
$211$	16.8837	+	5.48586i	1.16232	+	0.377662i	0.825773	−	0.564003i	$-0.190739\pi$
$211$	16.8837	+	5.48586i	1.16232	+	0.377662i	0.336552	+	0.941665i	$0.390739\pi$
$212$	−1.18963	+	0.864315i	−0.0817040	+	0.0593614i
$213$	1.53220	−	2.10890i	0.104985	−	0.144499i
$214$	1.24462	+	3.83054i	0.0850804	+	0.261851i
$215$	7.92995	+	24.4059i	0.540818	+	1.66447i
$216$	−2.27139	−	1.65026i	−0.154548	−	0.112286i
$217$	14.1272	−	22.2871i	0.959016	−	1.51295i
$218$	0.632911	−	1.94790i	0.0428661	−	0.131928i
$219$			9.71871i			0.656730i
$220$	−12.2848	−	2.24921i	−0.828244	−	0.151642i
$221$	−10.0030			−0.672877
$222$	−2.08816	+	6.42670i	−0.140148	+	0.431332i
$223$	11.3962	+	15.6855i	0.763143	+	1.05038i	0.996946	+	0.0780921i	$0.0248828\pi$
$223$	11.3962	+	15.6855i	0.763143	+	1.05038i	−0.233803	+	0.972284i	$0.575117\pi$
$224$	14.5980	+	3.73984i	0.975373	+	0.249879i
$225$	1.22869	+	3.78152i	0.0819126	+	0.252101i
$226$	3.83073	−	1.24468i	0.254816	−	0.0827948i
$227$	17.3993	+	12.6413i	1.15483	+	0.839032i	0.989115	−	0.147141i	$-0.0470073\pi$
$227$	17.3993	+	12.6413i	1.15483	+	0.839032i	0.165714	+	0.986174i	$0.447007\pi$
$228$	−0.878956	−	1.20978i	−0.0582103	−	0.0801196i
$229$	−24.9466	−	8.10564i	−1.64852	−	0.535635i	−0.670099	−	0.742272i	$-0.733748\pi$
$229$	−24.9466	−	8.10564i	−1.64852	−	0.535635i	−0.978418	+	0.206637i	$0.933748\pi$
$230$	−9.78781			−0.645389
$231$	7.65573	−	4.28834i	0.503710	−	0.282152i
$232$	11.8783			0.779849
$233$	18.8597	+	6.12790i	1.23554	+	0.401452i	0.852719	−	0.522370i	$-0.174952\pi$
$233$	18.8597	+	6.12790i	1.23554	+	0.401452i	0.382823	+	0.923822i	$0.374952\pi$
$234$	1.34066	+	1.84526i	0.0876419	+	0.120629i
$235$	17.5857	+	12.7767i	1.14716	+	0.833462i
$236$	15.7419	−	5.11486i	1.02471	−	0.332949i
$237$	4.13859	+	12.7373i	0.268830	+	0.827375i
$238$	−8.35303	−	2.13995i	−0.541447	−	0.138712i
$239$	−10.7037	−	14.7323i	−0.692363	−	0.952956i	−0.999999	−	0.00145187i	$-0.999538\pi$
$239$	−10.7037	−	14.7323i	−0.692363	−	0.952956i	0.307636	−	0.951504i	$-0.400462\pi$
$240$	−0.0865055	+	0.266237i	−0.00558391	+	0.0171855i
$241$	21.0955			1.35888			0.679442	−	0.733730i	$-0.262222\pi$
$241$	21.0955			1.35888			0.679442	+	0.733730i	$0.262222\pi$
$242$	9.47166	+	0.455053i	0.608861	+	0.0292519i
$243$			1.00000i			0.0641500i
$244$	−1.29570	+	3.98777i	−0.0829490	+	0.255291i
$245$	20.6048	+	3.90781i	1.31639	+	0.249661i
$246$	−7.02937	−	5.10714i	−0.448176	−	0.325619i
$247$	0.972769	+	2.99387i	0.0618958	+	0.190496i
$248$	−8.65293	−	26.6310i	−0.549462	−	1.69107i
$249$	−1.64940	+	2.27020i	−0.104526	+	0.143868i
$250$	2.13936	−	1.55434i	0.135305	−	0.0983048i
$251$	−8.27185	−	2.68769i	−0.522115	−	0.169645i	0.0360901	−	0.999349i	$-0.488510\pi$
$251$	−8.27185	−	2.68769i	−0.522115	−	0.169645i	−0.558205	+	0.829703i	$0.688510\pi$
$252$	−1.22579	−	3.09118i	−0.0772176	−	0.194726i
$253$	−12.4579	+	1.66771i	−0.783224	+	0.104848i
$254$	−4.55172			−0.285600
$255$	3.50019	−	10.7725i	0.219190	−	0.674599i
$256$	12.7472	−	9.26138i	0.796699	−	0.578836i
$257$	−8.53672	+	11.7498i	−0.532506	+	0.732932i	−0.987510	−	0.157558i	$-0.949638\pi$
$257$	−8.53672	+	11.7498i	−0.532506	+	0.732932i	0.455004	+	0.890490i	$0.349638\pi$
$258$	−7.02237	+	2.28171i	−0.437194	+	0.142053i
$259$	−15.9730	+	13.2283i	−0.992511	+	0.821969i
$260$	5.85623	−	8.06041i	0.363188	−	0.499886i
$261$	−2.48679	−	3.42278i	−0.153929	−	0.211864i
$262$	−0.471900	−	0.153329i	−0.0291541	−	0.00947273i
$263$			22.6802i			1.39852i	0.714868	+	0.699260i	$0.246487\pi$
$263$			22.6802i			1.39852i	−0.714868	+	0.699260i	$0.753513\pi$
$264$	1.67699	−	9.15947i	0.103212	−	0.563726i
$265$			3.50517i			0.215321i
$266$	0.171832	+	2.70814i	0.0105357	+	0.166047i
$267$	−5.08205	+	3.69233i	−0.311017	+	0.225967i
$268$	−11.4891	−	8.34735i	−0.701811	−	0.509896i
$269$	−8.30524	+	2.69854i	−0.506380	+	0.164533i	−0.551055	−	0.834469i	$-0.685775\pi$
$269$	−8.30524	+	2.69854i	−0.506380	+	0.164533i	0.0446755	+	0.999002i	$0.485775\pi$
$270$	−2.45632	+	0.798106i	−0.149487	+	0.0485712i
$271$	3.29393	+	2.39318i	0.200092	+	0.145376i	0.683320	−	0.730119i	$-0.260536\pi$
$271$	3.29393	+	2.39318i	0.200092	+	0.145376i	−0.483227	+	0.875495i	$0.660536\pi$
$272$	0.285785	−	0.207635i	0.0173283	−	0.0125897i
$273$	0.443278	+	6.98624i	0.0268284	+	0.422826i
$274$		−	7.07597i		−	0.427475i
$275$	−9.54596	+	9.09834i	−0.575643	+	0.548651i
$276$			4.76316i			0.286709i
$277$	−4.51319	−	1.46642i	−0.271171	−	0.0881088i	0.170275	−	0.985397i	$-0.445534\pi$
$277$	−4.51319	−	1.46642i	−0.271171	−	0.0881088i	−0.441446	+	0.897288i	$0.645534\pi$
$278$	3.46518	+	4.76941i	0.207828	+	0.286050i
$279$	−5.86227	+	8.06873i	−0.350965	+	0.483062i
$280$	17.1402	−	14.1950i	1.02432	−	0.848313i
$281$	−7.45102	+	2.42098i	−0.444491	+	0.144424i	−0.522707	−	0.852513i	$-0.675078\pi$
$281$	−7.45102	+	2.42098i	−0.444491	+	0.144424i	0.0782159	+	0.996936i	$0.475078\pi$
$282$	−3.67629	+	5.05998i	−0.218920	+	0.301317i
$283$	24.0380	−	17.4646i	1.42891	−	1.03816i	0.438689	−	0.898639i	$-0.355443\pi$
$283$	24.0380	−	17.4646i	1.42891	−	1.03816i	0.990219	−	0.139524i	$-0.0445571\pi$
$284$	1.01244	−	3.11597i	0.0600772	−	0.184899i
$285$	−3.56455			−0.211146
$286$	−3.59513	+	6.65591i	−0.212585	+	0.393572i
$287$	−9.82999	−	24.7891i	−0.580246	−	1.46325i
$288$	−5.41696	−	1.76008i	−0.319197	−	0.103714i
$289$	2.18984	−	1.59101i	0.128814	−	0.0935891i
$290$	6.42270	−	8.84009i	0.377154	−	0.519108i
$291$	−2.83473	−	8.72441i	−0.166175	−	0.511434i
$292$	3.77467	+	11.6173i	0.220896	+	0.679848i
$293$	−4.04846	−	2.94138i	−0.236514	−	0.171837i	0.463215	−	0.886246i	$-0.346696\pi$
$293$	−4.04846	−	2.94138i	−0.236514	−	0.171837i	−0.699729	+	0.714409i	$0.746696\pi$
$294$	−1.12441	+	5.92869i	−0.0655767	+	0.345768i
$295$	12.1924	−	37.5244i	0.709869	−	2.18475i
$296$			22.0081i			1.27919i
$297$	−2.99042	+	1.43436i	−0.173522	+	0.0832298i
$298$	13.7243			0.795028
$299$	3.09853	−	9.53631i	0.179193	−	0.551499i
$300$	2.93743	+	4.04302i	0.169592	+	0.233424i
$301$	−21.9527	−	5.62403i	−1.26534	−	0.324164i
$302$	3.75488	+	11.5563i	0.216069	+	0.664992i
$303$	−8.20508	+	2.66599i	−0.471370	+	0.153157i
$304$	−0.0899363	−	0.0653425i	−0.00515820	−	0.00374765i
$305$	5.87487	+	8.08606i	0.336394	+	0.463007i
$306$	3.09960	+	1.00712i	0.177192	+	0.0575732i
$307$	−22.5386			−1.28635			−0.643173	−	0.765721i	$-0.722382\pi$
$307$	−22.5386			−1.28635			−0.643173	+	0.765721i	$0.722382\pi$
$308$	7.48571	−	8.09949i	0.426538	−	0.461511i
$309$	12.7957			0.727921
$310$	−24.4981	−	7.95991i	−1.39140	−	0.452092i
$311$	−0.453140	−	0.623694i	−0.0256952	−	0.0353664i	0.795976	−	0.605328i	$-0.206958\pi$
$311$	−0.453140	−	0.623694i	−0.0256952	−	0.0353664i	−0.821671	+	0.569962i	$0.806958\pi$
$312$	6.00978	+	4.36636i	0.340237	+	0.247196i
$313$	−0.0361381	+	0.0117420i	−0.00204264	+	0.000663695i	−0.310038	−	0.950724i	$-0.600342\pi$
$313$	−0.0361381	+	0.0117420i	−0.00204264	+	0.000663695i	0.307995	+	0.951388i	$0.400342\pi$
$314$	1.72620	+	5.31270i	0.0974152	+	0.299813i
$315$	−7.67874	−	1.96720i	−0.432648	−	0.110839i
$316$	9.89412	+	13.6181i	0.556588	+	0.766077i
$317$	−0.546837	+	1.68299i	−0.0307134	+	0.0945263i	−0.965238	−	0.261372i	$-0.915825\pi$
$317$	−0.546837	+	1.68299i	−0.0307134	+	0.0945263i	0.934525	+	0.355898i	$0.115825\pi$
$318$	−1.00855			−0.0565569
$319$	6.66860	−	12.3460i	0.373370	−	0.691245i
$320$		−	14.1506i		−	0.791044i
$321$	1.44378	−	4.44351i	0.0805842	−	0.248013i
$322$	4.62753	−	7.30042i	0.257882	−	0.406837i
$323$	3.63901	+	2.64389i	0.202480	+	0.147110i
$324$	0.388392	+	1.19535i	0.0215774	+	0.0664083i
$325$	−3.25094	−	10.0054i	−0.180330	−	0.554998i
$326$	3.67543	−	5.05879i	0.203563	−	0.280180i
$327$	−1.92213	+	1.39651i	−0.106294	+	0.0772273i
$328$	−26.9132	−	8.74462i	−1.48603	−	0.482841i
$329$	−17.8440	+	7.07596i	−0.983772	+	0.390110i
$330$	−5.90991	−	6.20066i	−0.325330	−	0.341335i
$331$	9.22180			0.506876			0.253438	−	0.967352i	$-0.418439\pi$
$331$	9.22180			0.506876			0.253438	+	0.967352i	$0.418439\pi$
$332$	−1.08988	+	3.35430i	−0.0598149	+	0.184091i
$333$	6.34170	−	4.60751i	0.347523	−	0.252490i
$334$	3.92937	−	5.40832i	0.215006	−	0.295930i
$335$	−32.1953	+	10.4609i	−1.75902	+	0.571539i
$336$	−0.157679	−	0.190394i	−0.00860210	−	0.0103869i
$337$	−4.81470	+	6.62687i	−0.262274	+	0.360989i	−0.919762	−	0.392476i	$-0.871619\pi$
$337$	−4.81470	+	6.62687i	−0.262274	+	0.360989i	0.657489	+	0.753464i	$0.271619\pi$
$338$	3.03992	+	4.18409i	0.165350	+	0.227585i
$339$	−4.44373	−	1.44385i	−0.241350	−	0.0784194i
$340$		−	14.2363i		−	0.772073i
$341$	−32.5375	−	5.95724i	−1.76200	−	0.322603i
$342$		−	1.02564i		−	0.0554602i
$343$	−12.6564	+	13.5210i	−0.683380	+	0.730063i
$344$	−19.4552	+	14.1350i	−1.04895	+	0.762108i
$345$	9.18563	+	6.67375i	0.494538	+	0.359303i
$346$	0.386374	−	0.125541i	0.0207716	−	0.00674910i
$347$	10.8624	−	3.52940i	0.583124	−	0.189468i	−0.00257587	−	0.999997i	$-0.500820\pi$
$347$	10.8624	−	3.52940i	0.583124	−	0.189468i	0.585699	+	0.810528i	$0.300820\pi$
$348$	−4.30196	−	3.12556i	−0.230609	−	0.167548i
$349$	−21.5509	+	15.6576i	−1.15359	+	0.838134i	−0.988954	−	0.148221i	$-0.952645\pi$
$349$	−21.5509	+	15.6576i	−1.15359	+	0.838134i	−0.164637	+	0.986354i	$0.552645\pi$
$350$	−0.574252	−	9.05046i	−0.0306951	−	0.483767i
$351$		−	2.64586i		−	0.141226i
$352$	−2.50648	−	18.7236i	−0.133596	−	0.997970i
$353$		−	21.0731i		−	1.12161i	−0.827949	−	0.560804i	$-0.810492\pi$
$353$		−	21.0731i		−	1.12161i	0.827949	−	0.560804i	$-0.189508\pi$
$354$	10.7970	+	3.50816i	0.573854	+	0.186456i
$355$	−4.59051	−	6.31830i	−0.243639	−	0.335340i
$356$	−4.64076	+	6.38745i	−0.245960	+	0.338534i
$357$	6.38002	+	7.70375i	0.337666	+	0.407726i
$358$	−0.00222765		0.000723808i	−0.000117735		3.82544e-5i
$359$	20.2540	−	27.8773i	1.06897	−	1.47131i	0.197847	−	0.980233i	$-0.436605\pi$
$359$	20.2540	−	27.8773i	1.06897	−	1.47131i	0.871119	−	0.491073i	$-0.163395\pi$
$360$	−6.80512	+	4.94421i	−0.358661	+	0.260583i
$361$	−5.43390	+	16.7238i	−0.285995	+	0.880201i
$362$	−9.29557			−0.488564
$363$	−8.57866	−	6.88525i	−0.450263	−	0.361382i
$364$	3.24327	+	8.17883i	0.169994	+	0.428687i
$365$	27.6923	+	8.99778i	1.44948	+	0.470965i
$366$	−2.32663	+	1.69039i	−0.121615	+	0.0883583i
$367$	21.0525	−	28.9762i	1.09893	−	1.51255i	0.262133	−	0.965032i	$-0.415574\pi$
$367$	21.0525	−	28.9762i	1.09893	−	1.51255i	0.836796	−	0.547514i	$-0.184426\pi$
$368$	0.109422	+	0.336768i	0.00570404	+	0.0175552i
$369$	3.11463	+	9.58586i	0.162141	+	0.499020i
$370$	16.3789	+	11.8999i	0.851497	+	0.618649i
$371$	−2.61440	−	1.65719i	−0.135733	−	0.0860372i
$372$	−3.87363	+	11.9218i	−0.200838	+	0.618117i
$373$		−	9.00849i		−	0.466442i	−0.972424	−	0.233221i	$-0.925073\pi$
$373$		−	9.00849i		−	0.466442i	0.972424	−	0.233221i	$-0.0749266\pi$
$374$	1.43421	+	10.7137i	0.0741613	+	0.553991i
$375$	−3.06755			−0.158408
$376$	−6.29467	+	19.3730i	−0.324623	+	0.999086i
$377$	6.57970	+	9.05619i	0.338872	+	0.466417i
$378$	0.566028	−	2.20943i	0.0291134	−	0.113641i
$379$	−8.88313	−	27.3395i	−0.456296	−	1.40433i	−0.869607	−	0.493744i	$-0.835628\pi$
$379$	−8.88313	−	27.3395i	−0.456296	−	1.40433i	0.413312	−	0.910590i	$-0.364372\pi$
$380$	−4.26088	+	1.38444i	−0.218579	+	0.0710205i
$381$	4.27169	+	3.10356i	0.218845	+	0.159000i
$382$	−9.89958	−	13.6256i	−0.506506	−	0.697146i
$383$	−10.2192	−	3.32042i	−0.522176	−	0.169665i	0.0360566	−	0.999350i	$-0.488520\pi$
$383$	−10.2192	−	3.32042i	−0.522176	−	0.169665i	−0.558233	+	0.829684i	$0.688520\pi$
$384$	−7.31985			−0.373540
$385$	−5.13128	−	25.7843i	−0.261514	−	1.31409i
$386$	−0.220699			−0.0112333
$387$	8.14610	+	2.64683i	0.414090	+	0.134546i
$388$	−6.77699	−	9.32773i	−0.344050	−	0.473544i
$389$	−23.4860	−	17.0636i	−1.19079	−	0.865159i	−0.197441	−	0.980315i	$-0.563263\pi$
$389$	−23.4860	−	17.0636i	−1.19079	−	0.865159i	−0.993347	+	0.115156i	$0.963263\pi$
$390$	6.49908	−	2.11168i	0.329094	−	0.106929i
$391$	−4.42745	−	13.6263i	−0.223906	−	0.689112i
$392$	2.48399	+	19.4955i	0.125460	+	0.984673i
$393$	0.338320	+	0.465658i	0.0170660	+	0.0234893i
$394$	0.919645	−	2.83038i	0.0463310	−	0.142592i
$395$	40.1250			2.01891
$396$	−3.01750	+	2.87601i	−0.151635	+	0.144525i
$397$		−	13.8724i		−	0.696234i	−0.937451	−	0.348117i	$-0.886821\pi$
$397$		−	13.8724i		−	0.696234i	0.937451	−	0.348117i	$-0.113179\pi$
$398$	−4.61872	+	14.2150i	−0.231515	+	0.712531i
$399$	1.68527	−	2.65869i	0.0843688	−	0.133101i
$400$	0.300562	+	0.218371i	0.0150281	+	0.0109186i
$401$	−1.64750	−	5.07048i	−0.0822722	−	0.253208i	0.901456	−	0.432871i	$-0.142499\pi$
$401$	−1.64750	−	5.07048i	−0.0822722	−	0.253208i	−0.983728	+	0.179663i	$0.942499\pi$
$402$	−3.00994	−	9.26365i	−0.150122	−	0.462029i
$403$	15.5108	−	21.3487i	0.772646	−	1.06346i
$404$	−8.77249	+	6.37358i	−0.436448	+	0.317098i
$405$	2.84938	+	0.925820i	0.141587	+	0.0460044i
$406$	3.55699	+	8.96996i	0.176531	+	0.445172i
$407$	22.8747	+	12.3555i	1.13385	+	0.612441i
$408$	10.6145			0.525495
$409$	5.09034	−	15.6664i	0.251701	−	0.774656i	−0.742761	−	0.669557i	$-0.766484\pi$
$409$	5.09034	−	15.6664i	0.251701	−	0.774656i	0.994462	−	0.105099i	$-0.0335159\pi$
$410$	−21.0601	+	15.3011i	−1.04009	+	0.755666i
$411$	−4.82471	+	6.64064i	−0.237985	+	0.327559i
$412$	15.2953	−	4.96975i	0.753546	−	0.244842i
$413$	22.2239	+	26.8349i	1.09357	+	1.32046i
$414$	−1.92026	+	2.64301i	−0.0943755	+	0.129897i
$415$	4.94163	+	6.80157i	0.242575	+	0.333876i
$416$	14.3325	+	4.65692i	0.702709	+	0.228324i
$417$		−	6.83869i		−	0.334892i
$418$	3.06709	−	1.47113i	0.150016	−	0.0719554i
$419$			12.4420i			0.607834i	0.952699	+	0.303917i	$0.0982945\pi$
$419$			12.4420i			0.607834i	−0.952699	+	0.303917i	$0.901706\pi$
$420$	−9.94282	+	0.630873i	−0.485160	+	0.0307834i
$421$	−9.56788	+	6.95147i	−0.466310	+	0.338794i	−0.796001	−	0.605295i	$-0.793055\pi$
$421$	−9.56788	+	6.95147i	−0.466310	+	0.338794i	0.329691	+	0.944089i	$0.393055\pi$
$422$	12.3809	+	8.99529i	0.602695	+	0.437884i
$423$	6.90022	−	2.24202i	0.335500	−	0.109011i
$424$	−3.12396	+	1.01504i	−0.151713	+	0.0492945i
$425$	−12.1614	−	8.83575i	−0.589913	−	0.428597i
$426$	1.81798	−	1.32084i	0.0880815	−	0.0639950i
$427$	−8.80870	+	0.558913i	−0.426283	+	0.0270477i
$428$		−	5.87230i		−	0.283848i
$429$	7.91224	−	3.79511i	0.382006	−	0.183229i
$430$			22.1219i			1.06681i
$431$	−18.0545	−	5.86627i	−0.869655	−	0.282568i	−0.160000	−	0.987117i	$-0.551149\pi$
$431$	−18.0545	−	5.86627i	−0.869655	−	0.282568i	−0.709655	+	0.704549i	$0.751149\pi$
$432$	0.0549206	+	0.0755918i	0.00264237	+	0.00363691i
$433$	17.3589	−	23.8925i	0.834218	−	1.14820i	−0.152906	−	0.988241i	$-0.548863\pi$
$433$	17.3589	−	23.8925i	0.834218	−	1.14820i	0.987123	−	0.159961i	$-0.0511370\pi$
$434$	17.5194	−	14.5090i	0.840957	−	0.696456i
$435$	−12.0551	+	3.91695i	−0.577999	+	0.187803i
$436$	−1.75523	+	2.41586i	−0.0840601	+	0.115699i
$437$	−3.64775	+	2.65024i	−0.174495	+	0.126778i
$438$	−2.58896	+	7.96799i	−0.123705	+	0.380726i
$439$	11.1851			0.533833			0.266917	−	0.963720i	$-0.413995\pi$
$439$	11.1851			0.533833			0.266917	+	0.963720i	$0.413995\pi$
$440$	−24.5462	−	13.2584i	−1.17020	−	0.632070i
$441$	5.09767	−	4.79727i	0.242746	−	0.228441i
$442$	−8.20110	−	2.66470i	−0.390087	−	0.126747i
$443$	−21.6884	+	15.7576i	−1.03045	+	0.748665i	−0.968399	−	0.249408i	$-0.919764\pi$
$443$	−21.6884	+	15.7576i	−1.03045	+	0.748665i	−0.0620506	+	0.998073i	$0.519764\pi$
$444$	5.79102	−	7.97065i	0.274830	−	0.378270i
$445$	5.81579	+	17.8991i	0.275695	+	0.848501i
$446$	5.16483	+	15.8957i	0.244562	+	0.752684i
$447$	−12.8800	−	9.35784i	−0.609201	−	0.442610i
$448$	10.5545	+	6.69021i	0.498654	+	0.316083i
$449$	3.45815	−	10.6431i	0.163200	−	0.502279i	−0.835699	−	0.549188i	$-0.814937\pi$
$449$	3.45815	−	10.6431i	0.163200	−	0.502279i	0.998899	+	0.0469089i	$0.0149370\pi$
$450$			3.42763i			0.161580i
$451$	−24.1983	+	23.0636i	−1.13945	+	1.08602i
$452$	−5.87258			−0.276223
$453$	4.35574	−	13.4056i	0.204650	−	0.629849i
$454$	10.8975	+	14.9991i	0.511444	+	0.703942i
$455$	20.3169	+	5.20494i	0.952469	+	0.244011i
$456$	−1.03223	−	3.17688i	−0.0483386	−	0.148771i
$457$	−6.96444	+	2.26288i	−0.325783	+	0.105853i	−0.467342	−	0.884077i	$-0.654788\pi$
$457$	−6.96444	+	2.26288i	−0.325783	+	0.105853i	0.141559	+	0.989930i	$0.454788\pi$
$458$	−18.2935	−	13.2910i	−0.854798	−	0.621047i
$459$	−2.22220	−	3.05860i	−0.103723	−	0.142763i
$460$	13.5721	+	4.40983i	0.632801	+	0.205609i
$461$	16.1665			0.752950			0.376475	−	0.926427i	$-0.377136\pi$
$461$	16.1665			0.752950			0.376475	+	0.926427i	$0.377136\pi$
$462$	7.41900	−	1.47644i	0.345163	−	0.0686902i
$463$	−7.36642			−0.342347			−0.171173	−	0.985241i	$-0.554756\pi$
$463$	−7.36642			−0.342347			−0.171173	+	0.985241i	$0.554756\pi$
$464$	−0.375962	−	0.122157i	−0.0174536	−	0.00567102i
$465$	17.5635	+	24.1740i	0.814486	+	1.12104i
$466$	13.8300	+	10.0480i	0.640660	+	0.465467i
$467$	22.8474	−	7.42358i	1.05725	−	0.343522i	0.271742	−	0.962370i	$-0.412400\pi$
$467$	22.8474	−	7.42358i	1.05725	−	0.343522i	0.785511	+	0.618848i	$0.212400\pi$
$468$	−1.02763	−	3.16273i	−0.0475023	−	0.146197i
$469$	7.41901	−	28.9592i	0.342578	−	1.33721i
$470$	11.0142	+	15.1598i	0.508048	+	0.699269i
$471$	2.00243	−	6.16285i	0.0922671	−	0.283969i
$472$	36.9740			1.70187
$473$	3.76928	+	28.1568i	0.173311	+	1.29465i
$474$			11.5453i			0.530292i
$475$	−1.46185	+	4.49911i	−0.0670742	+	0.206433i
$476$	10.6184	+	6.73072i	0.486695	+	0.308502i
$477$	0.946505	+	0.687676i	0.0433375	+	0.0314865i
$478$	−4.85099	−	14.9298i	−0.221879	−	0.682874i
$479$	−4.29021	−	13.2039i	−0.196025	−	0.603302i	−0.999963	−	0.00858942i	$-0.997266\pi$
$479$	−4.29021	−	13.2039i	−0.196025	−	0.603302i	0.803938	−	0.594713i	$-0.202734\pi$
$480$	−10.0303	+	13.8055i	−0.457817	+	0.630131i
$481$	−16.7792	+	12.1908i	−0.765068	+	0.555854i
$482$	17.2954	+	5.61962i	0.787785	+	0.255967i
$483$	−9.32058	+	3.69603i	−0.424101	+	0.168175i
$484$	−12.9287	−	4.89838i	−0.587667	−	0.222654i
$485$	−27.4836			−1.24797
$486$	−0.266389	+	0.819861i	−0.0120837	+	0.0371897i
$487$	−20.2885	+	14.7404i	−0.919358	+	0.667953i	−0.943364	−	0.331759i	$-0.892358\pi$
$487$	−20.2885	+	14.7404i	−0.919358	+	0.667953i	0.0240060	+	0.999712i	$0.492358\pi$
$488$	−5.50538	+	7.57751i	−0.249217	+	0.343018i
$489$	−6.89860	+	2.24149i	−0.311966	+	0.101364i
$490$	15.8521	+	8.69276i	0.716125	+	0.392699i
$491$	−4.34723	+	5.98345i	−0.196188	+	0.270029i	−0.895765	−	0.444527i	$-0.853372\pi$
$491$	−4.34723	+	5.98345i	−0.196188	+	0.270029i	0.699577	+	0.714557i	$0.253372\pi$
$492$	7.44615	+	10.2487i	0.335698	+	0.462049i
$493$	15.2122	+	4.94274i	0.685123	+	0.222610i
$494$			2.71370i			0.122095i
$495$	1.31844	+	9.84881i	0.0592593	+	0.442671i
$496$			0.931889i			0.0418431i
$497$	6.88295	−	0.436724i	0.308742	−	0.0195897i
$498$	−1.95704	+	1.42187i	−0.0876969	+	0.0637156i
$499$	27.1582	+	19.7316i	1.21577	+	0.883307i	0.995742	−	0.0921866i	$-0.0293856\pi$
$499$	27.1582	+	19.7316i	1.21577	+	0.883307i	0.220026	+	0.975494i	$0.429386\pi$
$500$	−3.66680	+	1.19141i	−0.163984	+	0.0532817i
$501$	−7.37525	+	2.39636i	−0.329502	+	0.107062i
$502$	−6.06580	−	4.40706i	−0.270730	−	0.196697i
$503$	2.68512	−	1.95085i	0.119723	−	0.0869841i	−0.526312	−	0.850291i	$-0.676426\pi$
$503$	2.68512	−	1.95085i	0.119723	−	0.0869841i	0.646036	+	0.763307i	$0.276426\pi$
$504$	−0.470373	−	7.41328i	−0.0209521	−	0.330214i
$505$			25.8477i			1.15021i
$506$	−10.6580	−	1.95137i	−0.473808	−	0.0867488i
$507$		−	5.99942i		−	0.266444i
$508$	6.31155	+	2.05075i	0.280030	+	0.0909873i
$509$	−14.2324	−	19.5892i	−0.630839	−	0.868276i	0.367246	−	0.930124i	$-0.380301\pi$
$509$	−14.2324	−	19.5892i	−0.630839	−	0.868276i	−0.998086	+	0.0618480i	$0.980301\pi$
$510$	5.73934	−	7.89952i	0.254142	−	0.349797i
$511$	−19.8037	+	16.4008i	−0.876064	+	0.725530i
$512$	−1.00513	+	0.326585i	−0.0444207	+	0.0144332i
$513$	−0.699325	+	0.962538i	−0.0308759	+	0.0424971i
$514$	−10.1289	+	7.35911i	−0.446768	+	0.324596i
$515$	11.8465	−	36.4598i	0.522019	−	1.60661i
$516$	10.7654			0.473922
$517$	16.6020	+	17.4187i	0.730153	+	0.766075i
$518$	−16.6195	+	6.59038i	−0.730219	+	0.289565i
$519$	−0.448202	−	0.145630i	−0.0196739	−	0.00639244i
$520$	18.0054	−	13.0817i	0.789589	−	0.573670i
$521$	23.7040	−	32.6257i	1.03849	−	1.42936i	0.140113	−	0.990136i	$-0.455253\pi$
$521$	23.7040	−	32.6257i	1.03849	−	1.42936i	0.898378	−	0.439224i	$-0.144747\pi$
$522$	−1.12703	−	3.46866i	−0.0493290	−	0.151819i
$523$	11.1479	+	34.3098i	0.487465	+	1.50026i	0.828379	+	0.560168i	$0.189264\pi$
$523$	11.1479	+	34.3098i	0.487465	+	1.50026i	−0.340914	+	0.940095i	$0.610736\pi$
$524$	0.585269	+	0.425223i	0.0255676	+	0.0185759i
$525$	−5.63207	+	8.88519i	−0.245804	+	0.387782i
$526$	−6.04175	+	18.5946i	−0.263433	+	0.810763i
$527$		−	37.7061i		−	1.64251i
$528$	−0.147276	+	0.272661i	−0.00640935	+	0.0118661i
$529$	−8.63804			−0.375567
$530$	−0.933740	+	2.87376i	−0.0405591	+	0.124828i
$531$	−7.74072	−	10.6542i	−0.335919	−	0.462352i
$532$	0.981867	−	3.83260i	0.0425693	−	0.166164i
$533$	−8.24089	−	25.3628i	−0.356953	−	1.09859i
$534$	−5.15017	+	1.67339i	−0.222870	+	0.0724148i
$535$	−11.3246	−	8.22779i	−0.489604	−	0.355718i
$536$	−18.6464	−	25.6645i	−0.805400	−	1.10854i
$537$	0.00258412		0.000839632i	0.000111513		3.62328e-5i
$538$	−7.52801			−0.324556
$539$	21.6577	+	8.36318i	0.932864	+	0.360228i
$540$	3.76559			0.162045
$541$	27.9264	+	9.07384i	1.20065	+	0.390115i	0.840000	−	0.542586i	$-0.182555\pi$
$541$	27.9264	+	9.07384i	1.20065	+	0.390115i	0.360650	+	0.932701i	$0.382555\pi$
$542$	2.06305	+	2.83955i	0.0886156	+	0.121969i
$543$	8.72368	+	6.33812i	0.374369	+	0.271995i
$544$	20.4795	−	6.65421i	0.878053	−	0.285297i
$545$	2.19965	+	6.76981i	0.0942225	+	0.289987i
$546$	−1.49763	+	5.84583i	−0.0640927	+	0.250178i
$547$	7.94517	+	10.9356i	0.339711	+	0.467572i	0.944357	−	0.328922i	$-0.106685\pi$
$547$	7.94517	+	10.9356i	0.339711	+	0.467572i	−0.604646	+	0.796494i	$0.706685\pi$
$548$	−3.18803	+	9.81176i	−0.136186	+	0.419138i
$549$	3.33607			0.142380
$550$	−10.2501	+	4.91644i	−0.437064	+	0.209638i
$551$		−	5.03363i		−	0.214440i
$552$	−3.28793	+	10.1192i	−0.139944	+	0.430703i
$553$	−18.9705	+	29.9280i	−0.806707	+	1.27267i
$554$	−3.30955	−	2.40453i	−0.140609	−	0.102159i
$555$	−7.25729	−	22.3357i	−0.308055	−	0.948096i
$556$	−2.65610	−	8.17462i	−0.112644	−	0.346681i
$557$	7.76535	−	10.6881i	0.329028	−	0.452869i	−0.612169	−	0.790727i	$-0.709703\pi$
$557$	7.76535	−	10.6881i	0.329028	−	0.452869i	0.941197	+	0.337859i	$0.109703\pi$
$558$	−6.95567	+	5.05359i	−0.294457	+	0.213936i
$559$	−21.5534	−	7.00314i	−0.911614	−	0.296201i
$560$	−0.688489	+	0.273017i	−0.0290940	+	0.0115371i
$561$	5.95907	−	11.0324i	0.251592	−	0.465790i
$562$	−6.75373			−0.284889
$563$	−1.24199	+	3.82245i	−0.0523436	+	0.161097i	−0.973811	−	0.227358i	$-0.926991\pi$
$563$	−1.24199	+	3.82245i	−0.0523436	+	0.161097i	0.921468	+	0.388455i	$0.126991\pi$
$564$	7.37739	−	5.35999i	0.310644	−	0.225696i
$565$	−8.22818	+	11.3251i	−0.346162	+	0.476452i
$566$	24.3602	−	7.91510i	1.02393	−	0.332696i
$567$	−2.03769	+	1.68755i	−0.0855748	+	0.0708705i
$568$	4.30180	−	5.92092i	0.180500	−	0.248436i
$569$	−9.75724	−	13.4297i	−0.409045	−	0.563002i	0.553940	−	0.832556i	$-0.313124\pi$
$569$	−9.75724	−	13.4297i	−0.409045	−	0.563002i	−0.962985	+	0.269555i	$0.913124\pi$
$570$	−2.92244	−	0.949557i	−0.122407	−	0.0397726i
$571$			9.29300i			0.388900i	0.980912	+	0.194450i	$0.0622922\pi$
$571$			9.29300i			0.388900i	−0.980912	+	0.194450i	$0.937708\pi$
$572$	7.98390	−	7.60953i	0.333823	−	0.318170i
$573$			19.5373i			0.816181i
$574$	−1.45569	−	22.9422i	−0.0607592	−	0.957590i
$575$	12.1906	−	8.85698i	0.508382	−	0.369361i
$576$	−3.82111	−	2.77620i	−0.159213	−	0.115675i
$577$	−11.6183	+	3.77502i	−0.483677	+	0.157156i	−0.540698	−	0.841217i	$-0.681840\pi$
$577$	−11.6183	+	3.77502i	−0.483677	+	0.157156i	0.0570207	+	0.998373i	$0.481840\pi$
$578$	2.21920	−	0.721061i	0.0923064	−	0.0299922i
$579$	0.207121	+	0.150482i	0.00860765	+	0.00625382i
$580$	−12.8888	+	9.36423i	−0.535177	+	0.388829i
$581$	−7.40942	+	0.470128i	−0.307394	+	0.0195042i
$582$		−	7.90795i		−	0.327795i
$583$	−0.698816	+	3.81682i	−0.0289420	+	0.158077i
$584$			27.2862i			1.12911i
$585$	−7.53907	−	2.44959i	−0.311702	−	0.101278i
$586$	−2.53562	−	3.48999i	−0.104746	−	0.144170i
$587$	19.5316	−	26.8830i	0.806157	−	1.10958i	−0.185748	−	0.982597i	$-0.559471\pi$
$587$	19.5316	−	26.8830i	0.806157	−	1.10958i	0.991905	−	0.126983i	$-0.0405292\pi$
$588$	4.23027	−	7.71431i	0.174453	−	0.318133i
$589$	−11.2853	+	3.66682i	−0.465004	+	0.151089i
$590$	19.9922	−	27.5169i	0.823064	−	1.13285i
$591$	−2.79294	+	2.02919i	−0.114886	+	0.0834697i
$592$	0.226333	−	0.696580i	0.00930221	−	0.0286293i
$593$	−0.109154			−0.00448241			−0.00224121	−	0.999997i	$-0.500713\pi$
$593$	−0.109154			−0.00448241			−0.00224121	+	0.999997i	$0.500713\pi$
$594$	−2.83383	+	0.379357i	−0.116273	+	0.0155652i
$595$	27.8577	−	11.0468i	1.14205	−	0.452876i
$596$	−19.0306	−	6.18340i	−0.779522	−	0.253282i
$597$	14.0269	−	10.1912i	0.574084	−	0.417097i
$598$	5.08074	−	6.99303i	0.207767	−	0.285966i
$599$	7.62725	+	23.4743i	0.311641	+	0.959133i	0.977115	+	0.212712i	$0.0682295\pi$
$599$	7.62725	+	23.4743i	0.311641	+	0.959133i	−0.665474	+	0.746421i	$0.731770\pi$
$600$	3.44966	+	10.6170i	0.140832	+	0.433435i
$601$	−33.7068	−	24.4894i	−1.37493	−	0.998943i	−0.997334	−	0.0729714i	$-0.976752\pi$
$601$	−33.7068	−	24.4894i	−1.37493	−	0.998943i	−0.377593	−	0.925972i	$-0.623248\pi$
$602$	−16.5000	−	10.4589i	−0.672491	−	0.426273i
$603$	−3.49160	+	10.7460i	−0.142189	+	0.437612i
$604$		−	17.7161i		−	0.720857i
$605$	−27.5610	+	18.0694i	−1.12051	+	0.734625i
$606$	−7.43722			−0.302116
$607$	−3.29822	+	10.1509i	−0.133871	+	0.412011i	−0.995413	−	0.0956751i	$-0.969499\pi$
$607$	−3.29822	+	10.1509i	−0.133871	+	0.412011i	0.861542	+	0.507686i	$0.169499\pi$
$608$	−3.98316	−	5.48235i	−0.161539	−	0.222339i
$609$	2.77795	−	10.8434i	0.112568	−	0.439397i
$610$	2.66254	+	8.19445i	0.107803	+	0.331784i
$611$	−18.2570	+	5.93207i	−0.738600	+	0.239986i
$612$	−3.84424	−	2.79301i	−0.155394	−	0.112901i
$613$	−4.92149	−	6.77385i	−0.198777	−	0.273593i	0.697979	−	0.716118i	$-0.254083\pi$
$613$	−4.92149	−	6.77385i	−0.198777	−	0.273593i	−0.896756	+	0.442525i	$0.854083\pi$
$614$	−18.4785	−	6.00404i	−0.745733	−	0.242303i
$615$	30.1974			1.21768
$616$	21.4941	−	12.0399i	0.866024	−	0.485101i
$617$	22.0617			0.888169			0.444084	−	0.895985i	$-0.353529\pi$
$617$	22.0617			0.888169			0.444084	+	0.895985i	$0.353529\pi$
$618$	10.4907	+	3.40863i	0.421997	+	0.137115i
$619$	−2.52233	−	3.47168i	−0.101381	−	0.139539i	0.755313	−	0.655365i	$-0.227485\pi$
$619$	−2.52233	−	3.47168i	−0.101381	−	0.139539i	−0.856693	+	0.515826i	$0.827485\pi$
$620$	30.3835	+	22.0749i	1.22023	+	0.886549i
$621$	3.60424	−	1.17109i	0.144633	−	0.0469941i
$622$	−0.205367	−	0.632054i	−0.00823446	−	0.0253431i
$623$	−16.1000	−	4.12464i	−0.645034	−	0.165250i
$624$	−0.145312	−	0.200005i	−0.00581715	−	0.00800662i
$625$	−8.98345	+	27.6482i	−0.359338	+	1.10593i
$626$	−0.0327561			−0.00130920
$627$	−3.88148	−	0.710654i	−0.155011	−	0.0283808i
$628$		−	8.14448i		−	0.325000i
$629$	−9.15788	+	28.1851i	−0.365149	+	1.12381i
$630$	−5.77146	−	3.65836i	−0.229940	−	0.145753i
$631$	12.9300	+	9.39417i	0.514734	+	0.373976i	0.814616	−	0.580000i	$-0.196947\pi$
$631$	12.9300	+	9.39417i	0.514734	+	0.373976i	−0.299882	+	0.953976i	$0.596947\pi$
$632$	11.6195	+	35.7610i	0.462198	+	1.42250i
$633$	−5.48586	−	16.8837i	−0.218043	−	0.671068i
$634$	−0.896662	+	1.23415i	−0.0356110	+	0.0490143i
$635$	12.7980	−	9.29833i	0.507875	−	0.368993i
$636$	1.39849	+	0.454397i	0.0554538	+	0.0180180i
$637$	−13.4877	+	12.6929i	−0.534403	+	0.502911i
$638$	8.75617	−	8.34560i	0.346660	−	0.330405i
$639$	−2.60674			−0.103121
$640$	−6.77687	+	20.8571i	−0.267879	+	0.824448i
$641$	24.0055	−	17.4410i	0.948162	−	0.688880i	−0.00220944	−	0.999998i	$-0.500703\pi$
$641$	24.0055	−	17.4410i	0.948162	−	0.688880i	0.950371	+	0.311118i	$0.100703\pi$
$642$	2.36741	−	3.25845i	0.0934340	−	0.128601i
$643$	9.83338	−	3.19506i	0.387791	−	0.126001i	−0.108632	−	0.994082i	$-0.534647\pi$
$643$	9.83338	−	3.19506i	0.387791	−	0.126001i	0.496422	+	0.868081i	$0.334647\pi$
$644$	−9.70583	+	8.03808i	−0.382463	+	0.316745i
$645$	15.0837	−	20.7609i	0.593918	−	0.817458i
$646$	2.27918	+	3.13702i	0.0896730	+	0.123424i
$647$	−25.0062	−	8.12501i	−0.983096	−	0.319427i	−0.227005	−	0.973894i	$-0.572893\pi$
$647$	−25.0062	−	8.12501i	−0.983096	−	0.319427i	−0.756091	+	0.654467i	$0.772893\pi$
$648$			2.80759i			0.110293i
$649$	20.7576	−	38.4299i	0.814806	−	1.50851i
$650$		−	9.06903i		−	0.355717i
$651$	−26.3344	+	1.67092i	−1.03213	+	0.0654886i
$652$	−7.37566	+	5.35873i	−0.288853	+	0.209864i
$653$	−10.7111	−	7.78210i	−0.419159	−	0.304537i	0.358140	−	0.933668i	$-0.383411\pi$
$653$	−10.7111	−	7.78210i	−0.419159	−	0.304537i	−0.777300	+	0.629131i	$0.783411\pi$
$654$	−1.94790	+	0.632911i	−0.0761689	+	0.0247488i
$655$	1.64006	−	0.532888i	0.0640825	−	0.0208217i
$656$	0.761902	+	0.553555i	0.0297473	+	0.0216127i
$657$	7.86260	−	5.71251i	0.306749	−	0.222866i
$658$	−16.5146	+	1.04785i	−0.643805	+	0.0408495i
$659$			45.3499i			1.76658i	0.468826	+	0.883291i	$0.344677\pi$
$659$			45.3499i			1.76658i	−0.468826	+	0.883291i	$0.655323\pi$
$660$	5.40119	+	11.2607i	0.210241	+	0.438322i
$661$			17.7296i			0.689600i	0.938676	+	0.344800i	$0.112053\pi$
$661$			17.7296i			0.689600i	−0.938676	+	0.344800i	$0.887947\pi$
$662$	7.56059	+	2.45659i	0.293851	+	0.0954779i
$663$	5.87964	+	8.09262i	0.228346	+	0.314291i
$664$	−4.63084	+	6.37380i	−0.179711	+	0.247352i
$665$	−6.01536	−	7.26344i	−0.233266	−	0.281664i
$666$	6.42670	−	2.08816i	0.249030	−	0.0809147i
$667$	−9.42424	+	12.9714i	−0.364908	+	0.502253i
$668$	−7.88527	+	5.72898i	−0.305090	+	0.221661i
$669$	5.99131	−	18.4394i	0.231638	−	0.712907i
$670$	−29.1823			−1.12741
$671$	4.78511	+	9.97625i	0.184727	+	0.385129i
$672$	−5.55492	−	14.0083i	−0.214286	−	0.540381i
$673$	−31.5131	−	10.2392i	−1.21474	−	0.394693i	−0.369576	−	0.929201i	$-0.620497\pi$
$673$	−31.5131	−	10.2392i	−1.21474	−	0.394693i	−0.845163	+	0.534508i	$0.820497\pi$
$674$	−5.71271	+	4.15053i	−0.220046	+	0.159872i
$675$	2.33711	−	3.21675i	0.0899553	−	0.123813i
$676$	−2.33013	−	7.17140i	−0.0896204	−	0.275823i
$677$	15.3335	+	47.1918i	0.589316	+	1.81373i	0.581199	+	0.813762i	$0.302584\pi$
$677$	15.3335	+	47.1918i	0.589316	+	1.81373i	0.00811736	+	0.999967i	$0.497416\pi$
$678$	−3.25861	−	2.36752i	−0.125146	−	0.0909241i
$679$	12.9939	−	20.4992i	0.498659	−	0.786687i
$680$	9.82710	−	30.2447i	0.376852	−	1.15983i
$681$		−	21.5067i		−	0.824137i
$682$	−25.0893	−	13.5517i	−0.960718	−	0.518923i
$683$	1.87225			0.0716395			0.0358197	−	0.999358i	$-0.488596\pi$
$683$	1.87225			0.0716395			0.0358197	+	0.999358i	$0.488596\pi$
$684$	−0.462095	+	1.42218i	−0.0176686	+	0.0543785i
$685$	14.4549	+	19.8955i	0.552294	+	0.760167i
$686$	−13.9783	+	7.71379i	−0.533694	+	0.294514i
$687$	8.10564	+	24.9466i	0.309249	+	0.951771i
$688$	0.761144	−	0.247311i	0.0290183	−	0.00942863i
$689$	−2.50432	−	1.81949i	−0.0954069	−	0.0693172i
$690$	5.75313	+	7.91850i	0.219018	+	0.301452i
$691$	−18.3312	−	5.95617i	−0.697352	−	0.226583i	−0.0611754	−	0.998127i	$-0.519485\pi$
$691$	−18.3312	−	5.95617i	−0.697352	−	0.226583i	−0.636176	+	0.771544i	$0.719485\pi$
$692$	−0.592320			−0.0225166
$693$	−7.96926	−	3.67299i	−0.302727	−	0.139525i
$694$	9.84585			0.373743
$695$	−19.4860	−	6.33140i	−0.739148	−	0.240164i
$696$	−6.98189	−	9.60975i	−0.264648	−	0.364257i
$697$	−30.8281	−	22.3980i	−1.16770	−	0.848383i
$698$	−21.8397	+	7.09616i	−0.826647	+	0.268594i
$699$	−6.12790	−	18.8597i	−0.231778	−	0.713340i
$700$	−3.28135	+	12.8084i	−0.124023	+	0.484111i
$701$	−23.4187	−	32.2331i	−0.884514	−	1.21743i	−0.975150	−	0.221545i	$-0.928890\pi$
$701$	−23.4187	−	32.2331i	−0.884514	−	1.21743i	0.0906365	−	0.995884i	$-0.471110\pi$
$702$	0.704828	−	2.16924i	0.0266020	−	0.0818726i
$703$	9.32627			0.351747
$704$	2.82117	−	15.4088i	0.106327	−	0.580740i
$705$		−	21.7371i		−	0.818666i
$706$	5.61364	−	17.2770i	0.211272	−	0.650229i
$707$	−19.2790	−	12.2204i	−0.725060	−	0.459595i
$708$	−13.3909	−	9.72904i	−0.503260	−	0.365640i
$709$	6.77403	+	20.8483i	0.254404	+	0.782975i	0.993947	+	0.109865i	$0.0350418\pi$
$709$	6.77403	+	20.8483i	0.254404	+	0.782975i	−0.739543	+	0.673110i	$0.764958\pi$
$710$	−2.08046	−	6.40299i	−0.0780782	−	0.240300i
$711$	7.87207	−	10.8350i	0.295226	−	0.406343i
$712$	−14.2683	+	10.3665i	−0.534728	+	0.388503i
$713$	35.9468	+	11.6798i	1.34622	+	0.437413i
$714$	3.17854	+	8.01557i	0.118954	+	0.299975i
$715$	−3.48840	−	26.0586i	−0.130459	−	0.974536i
$716$	0.00341504			0.000127626
$717$	−5.62725	+	17.3189i	−0.210154	+	0.646786i
$718$	24.0317	−	17.4600i	0.896854	−	0.651603i
$719$	15.4612	−	21.2806i	0.576607	−	0.793631i	−0.416712	−	0.909039i	$-0.636818\pi$
$719$	15.4612	−	21.2806i	0.576607	−	0.793631i	0.993318	+	0.115408i	$0.0368175\pi$
$720$	0.266237	−	0.0865055i	0.00992205	−	0.00322387i
$721$	21.5934	+	26.0736i	0.804180	+	0.971031i
$722$	−8.91009	+	12.2637i	−0.331599	+	0.456407i
$723$	−12.3996	−	17.0667i	−0.461148	−	0.634716i
$724$	12.8895	+	4.18806i	0.479035	+	0.155648i
$725$			16.8221i			0.624758i
$726$	−5.19916	−	7.93021i	−0.192959	−	0.294318i
$727$		−	43.6298i		−	1.61814i	−0.587711	−	0.809071i	$-0.699971\pi$
$727$		−	43.6298i		−	1.61814i	0.587711	−	0.809071i	$-0.300029\pi$
$728$	1.24454	+	19.6145i	0.0461258	+	0.726962i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	20.3070	+	14.7539i	0.751594	+	0.546065i
$731$	−30.7974	+	10.0067i	−1.13908	+	0.370111i
$732$	3.98777	−	1.29570i	0.147392	−	0.0478906i
$733$	−10.4616	−	7.60080i	−0.386408	−	0.280742i	0.377574	−	0.925979i	$-0.376758\pi$
$733$	−10.4616	−	7.60080i	−0.386408	−	0.280742i	−0.763982	+	0.645237i	$0.776758\pi$
$734$	24.9790	−	18.1483i	0.921993	−	0.669867i
$735$	−8.94973	−	18.9666i	−0.330116	−	0.699594i
$736$			21.5852i			0.795641i
$737$	−37.1434	+	4.97229i	−1.36819	+	0.183157i
$738$			8.68878i			0.319838i
$739$	32.7230	+	10.6324i	1.20374	+	0.391118i	0.841134	−	0.540826i	$-0.181888\pi$
$739$	32.7230	+	10.6324i	1.20374	+	0.391118i	0.362602	+	0.931944i	$0.381888\pi$
$740$	−17.3500	−	23.8802i	−0.637799	−	0.877854i
$741$	1.85032	−	2.54674i	0.0679731	−	0.0935569i
$742$	−1.70199	−	2.05512i	−0.0624819	−	0.0754457i
$743$	26.2959	−	8.54406i	0.964704	−	0.313451i	0.216028	−	0.976387i	$-0.430690\pi$
$743$	26.2959	−	8.54406i	0.964704	−	0.313451i	0.748676	+	0.662936i	$0.230690\pi$
$744$	−16.4589	+	22.6537i	−0.603411	+	0.830524i
$745$	−38.5886	+	28.0362i	−1.41378	+	1.02717i
$746$	2.39976	−	7.38571i	0.0878616	−	0.270410i
$747$	2.80613			0.102671
$748$	2.83825	−	15.5021i	0.103777	−	0.566812i
$749$	11.4909	−	4.55668i	0.419870	−	0.166497i
$750$	−2.51497	−	0.817162i	−0.0918336	−	0.0298386i
$751$	4.38865	−	3.18854i	0.160144	−	0.116351i	−0.504827	−	0.863220i	$-0.668444\pi$
$751$	4.38865	−	3.18854i	0.160144	−	0.116351i	0.664971	+	0.746869i	$0.268444\pi$
$752$	0.398467	−	0.548443i	0.0145306	−	0.0199997i
$753$	2.68769	+	8.27185i	0.0979448	+	0.301443i
$754$	2.98198	+	9.17758i	0.108597	+	0.334228i
$755$	−34.1650	−	24.8223i	−1.24339	−	0.903377i
$756$	−1.78031	+	2.80864i	−0.0647494	+	0.102149i
$757$	4.02463	−	12.3865i	0.146278	−	0.450196i	−0.850895	−	0.525335i	$-0.823940\pi$
$757$	4.02463	−	12.3865i	0.146278	−	0.450196i	0.997173	+	0.0751387i	$0.0239400\pi$
$758$		−	24.7809i		−	0.900084i
$759$	8.67180	+	9.09843i	0.314767	+	0.330252i
$760$	−10.0078			−0.363021
$761$	−1.70210	+	5.23852i	−0.0617010	+	0.189896i	−0.977156	−	0.212525i	$-0.931831\pi$
$761$	−1.70210	+	5.23852i	−0.0617010	+	0.189896i	0.915455	+	0.402421i	$0.131831\pi$
$762$	2.67543	+	3.68242i	0.0969208	+	0.133400i
$763$	−6.08935	−	1.56002i	−0.220449	−	0.0564765i
$764$	7.58813	+	23.3539i	0.274529	+	0.844913i
$765$	−10.7725	+	3.50019i	−0.389480	+	0.126550i
$766$	−7.49379	−	5.44456i	−0.270762	−	0.196720i
$767$	20.4809	+	28.1895i	0.739521	+	1.01786i
$768$	−14.9852	−	4.86899i	−0.540733	−	0.175695i
$769$	34.4500			1.24230			0.621150	−	0.783692i	$-0.286666\pi$
$769$	34.4500			1.24230			0.621150	+	0.783692i	$0.286666\pi$
$770$	2.66172	−	22.5065i	0.0959218	−	0.811078i
$771$	14.5235			0.523052
$772$	0.306028	+	0.0994345i	0.0110142	+	0.00357872i
$773$	28.4544	+	39.1642i	1.02344	+	1.40864i	0.909767	+	0.415119i	$0.136260\pi$
$773$	28.4544	+	39.1642i	1.02344	+	1.40864i	0.113668	+	0.993519i	$0.463740\pi$
$774$	5.97359	+	4.34007i	0.214716	+	0.156000i
$775$	37.7149	−	12.2543i	1.35476	−	0.440188i
$776$	−7.95877	−	24.4946i	−0.285703	−	0.879304i
$777$	20.0906	+	5.14697i	0.720747	+	0.184647i
$778$	−14.7097	−	20.2462i	−0.527369	−	0.725861i
$779$	−3.70568	+	11.4049i	−0.132770	+	0.408623i
$780$	−9.96322			−0.356741
$781$	−3.73900	−	7.79526i	−0.133792	−	0.278936i
$782$		−	12.3511i		−	0.441675i
$783$	−1.30738	+	4.02371i	−0.0467221	+	0.143796i
$784$	0.121873	−	0.642601i	0.00435259	−	0.0229500i
$785$	−15.7064	−	11.4114i	−0.560586	−	0.407290i
$786$	0.153329	+	0.471900i	0.00546908	+	0.0168321i
$787$	−0.232316	−	0.714995i	−0.00828117	−	0.0254868i	0.946831	−	0.321733i	$-0.104265\pi$
$787$	−0.232316	−	0.714995i	−0.00828117	−	0.0254868i	−0.955112	+	0.296246i	$0.904265\pi$
$788$	−2.55042	+	3.51035i	−0.0908548	+	0.125051i
$789$	18.3486	−	13.3311i	0.653229	−	0.474599i
$790$	32.8969	+	10.6888i	1.17042	+	0.380292i
$791$	−4.55690	−	11.4915i	−0.162025	−	0.408591i
$792$	−8.39588	+	4.02708i	−0.298335	+	0.143096i
$793$	−8.82677			−0.313448
$794$	3.69544	−	11.3734i	0.131146	−	0.403627i
$795$	2.83574	−	2.06029i	0.100573	−	0.0730709i
$796$	12.8089	−	17.6300i	0.454000	−	0.624877i
$797$	−14.2594	+	4.63317i	−0.505094	+	0.164115i	−0.550470	−	0.834855i	$-0.685552\pi$
$797$	−14.2594	+	4.63317i	−0.505094	+	0.164115i	0.0453757	+	0.998970i	$0.485552\pi$
$798$	2.08993	−	1.73082i	0.0739827	−	0.0612703i
$799$	−16.1228	+	22.1911i	−0.570383	+	0.785065i
$800$	13.3115	+	18.3217i	0.470633	+	0.647771i
$801$	5.97431	+	1.94117i	0.211092	+	0.0685879i
$802$		−	4.59597i		−	0.162289i
$803$	28.3606	+	15.3187i	1.00082	+	0.540586i
$804$			14.2014i			0.500844i
$805$	1.90222	+	29.9797i	0.0670444	+	1.05665i
$806$	18.4037	−	13.3711i	0.648244	−	0.470977i
$807$	7.06486	+	5.13292i	0.248695	+	0.180687i
$808$	−23.0365	+	7.48502i	−0.810422	+	0.263322i
$809$	−17.4307	+	5.66356i	−0.612829	+	0.199120i	−0.598954	−	0.800783i	$-0.704417\pi$
$809$	−17.4307	+	5.66356i	−0.612829	+	0.199120i	−0.0138752	+	0.999904i	$0.504417\pi$
$810$	2.08947	+	1.51809i	0.0734165	+	0.0533402i
$811$	−2.03313	+	1.47716i	−0.0713929	+	0.0518700i	−0.622909	−	0.782294i	$-0.714049\pi$
$811$	−2.03313	+	1.47716i	−0.0713929	+	0.0518700i	0.551516	+	0.834164i	$0.314049\pi$
$812$	−0.890878	−	14.0406i	−0.0312637	−	0.492729i
$813$		−	4.07153i		−	0.142795i
$814$	15.4627	+	16.2234i	0.541966	+	0.568629i
$815$			21.7320i			0.761238i
$816$	−0.335960	−	0.109160i	−0.0117610	−	0.00382137i
$817$	5.98994	+	8.24445i	0.209561	+	0.288437i
$818$	8.34674	−	11.4883i	0.291837	−	0.401679i
$819$	5.39143	−	4.46503i	0.188392	−	0.156021i
$820$	36.0964	−	11.7284i	1.26054	−	0.409575i
$821$	9.68958	−	13.3366i	0.338169	−	0.465449i	−0.605737	−	0.795665i	$-0.707122\pi$
$821$	9.68958	−	13.3366i	0.338169	−	0.465449i	0.943905	+	0.330216i	$0.107122\pi$
$822$	−5.72458	+	4.15915i	−0.199668	+	0.145067i
$823$	−16.9924	+	52.2971i	−0.592317	+	1.82296i	−0.0246623	+	0.999696i	$0.507851\pi$
$823$	−16.9924	+	52.2971i	−0.592317	+	1.82296i	−0.567654	+	0.823267i	$0.692149\pi$
$824$	35.9250			1.25151
$825$	12.9717	+	2.37497i	0.451616	+	0.0826858i
$826$	11.0720	+	27.9211i	0.385243	+	0.971499i
$827$	2.82926	+	0.919284i	0.0983832	+	0.0319666i	0.357795	−	0.933800i	$-0.383529\pi$
$827$	2.82926	+	0.919284i	0.0983832	+	0.0319666i	−0.259412	+	0.965767i	$0.583529\pi$
$828$	3.85348	−	2.79972i	0.133918	−	0.0972969i
$829$	−26.6112	+	36.6272i	−0.924247	+	1.27212i	0.0378149	+	0.999285i	$0.487960\pi$
$829$	−26.6112	+	36.6272i	−0.924247	+	1.27212i	−0.962062	+	0.272832i	$0.912040\pi$
$830$	2.23959	+	6.89274i	0.0777372	+	0.239251i
$831$	1.46642	+	4.51319i	0.0508697	+	0.156561i
$832$	10.1101	+	7.34543i	0.350505	+	0.254657i
$833$	−4.93121	+	26.0010i	−0.170856	+	0.900880i
$834$	1.82175	−	5.60678i	0.0630821	−	0.194147i
$835$			23.2335i			0.804029i
$836$	−4.91573	+	0.658056i	−0.170014	+	0.0227594i
$837$	9.97349			0.344734
$838$	−3.31442	+	10.2007i	−0.114495	+	0.352379i
$839$	13.3387	+	18.3592i	0.460503	+	0.633829i	0.974613	−	0.223896i	$-0.0718776\pi$
$839$	13.3387	+	18.3592i	0.460503	+	0.633829i	−0.514110	+	0.857724i	$0.671878\pi$
$840$	−21.5587	−	5.52309i	−0.743847	−	0.190565i
$841$	3.43024	+	10.5572i	0.118284	+	0.364041i
$842$	−9.69613	+	3.15046i	−0.334151	+	0.108572i
$843$	6.33822	+	4.60498i	0.218300	+	0.158604i
$844$	−13.1150	−	18.0513i	−0.451438	−	0.621351i
$845$	−17.0947	−	5.55439i	−0.588074	−	0.191077i
$846$	6.25448			0.215033
$847$	−0.446964	−	29.0998i	−0.0153579	−	0.999882i
$848$	0.109316			0.00375391
$849$	−28.2583	−	9.18168i	−0.969823	−	0.315114i
$850$	−7.61689	−	10.4837i	−0.261257	−	0.359589i
$851$	−24.0332	−	17.4612i	−0.823849	−	0.598561i
$852$	−3.11597	+	1.01244i	−0.106751	+	0.0346856i
$853$	−2.69473	−	8.29354i	−0.0922659	−	0.283965i	0.894266	−	0.447537i	$-0.147699\pi$
$853$	−2.69473	−	8.29354i	−0.0922659	−	0.283965i	−0.986531	+	0.163571i	$0.947699\pi$
$854$	−7.37080	−	1.88831i	−0.252223	−	0.0646166i
$855$	2.09519	+	2.88378i	0.0716540	+	0.0986232i
$856$	4.05355	−	12.4756i	0.138548	−	0.426406i
$857$	−13.8189			−0.472044			−0.236022	−	0.971748i	$-0.575844\pi$
$857$	−13.8189			−0.472044			−0.236022	+	0.971748i	$0.575844\pi$
$858$	7.49791	−	1.00373i	0.255975	−	0.0342667i
$859$		−	25.8858i		−	0.883212i	−0.897209	−	0.441606i	$-0.854409\pi$
$859$		−	25.8858i		−	0.883212i	0.897209	−	0.441606i	$-0.145591\pi$
$860$	9.96687	−	30.6749i	0.339867	−	1.04600i
$861$	−14.2769	+	22.5233i	−0.486554	+	0.767592i
$862$	−13.2395	−	9.61905i	−0.450939	−	0.327626i
$863$	11.5815	+	35.6443i	0.394241	+	1.21335i	0.929551	+	0.368692i	$0.120194\pi$
$863$	11.5815	+	35.6443i	0.394241	+	1.21335i	−0.535311	+	0.844655i	$0.679806\pi$
$864$	1.76008	+	5.41696i	0.0598790	+	0.184289i
$865$	−0.829910	+	1.14227i	−0.0282178	+	0.0388384i
$866$	20.5966	−	14.9643i	0.699902	−	0.508509i
$867$	−2.57431	−	0.836446i	−0.0874283	−	0.0284072i
$868$	−30.8299	+	12.2254i	−1.04643	+	0.414958i
$869$	43.6925	+	7.99960i	1.48217	+	0.271368i
$870$	−10.9270			−0.370459
$871$	9.23828	−	28.4325i	0.313027	−	0.963398i
$872$	−5.39656	+	3.92083i	−0.182751	+	0.132776i
$873$	−5.39198	+	7.42143i	−0.182491	+	0.251177i
$874$	−3.69664	+	1.20111i	−0.125041	+	0.0406282i
$875$	−5.17666	−	6.25071i	−0.175003	−	0.211313i
$876$	7.17986	−	9.88222i	0.242585	−	0.333889i
$877$	−16.1653	−	22.2496i	−0.545862	−	0.751315i	0.443581	−	0.896234i	$-0.353708\pi$
$877$	−16.1653	−	22.2496i	−0.545862	−	0.751315i	−0.989443	+	0.144920i	$0.953708\pi$
$878$	9.17019	+	2.97958i	0.309479	+	0.100556i
$879$			5.00417i			0.168786i
$880$	0.640566	+	0.672080i	0.0215935	+	0.0226558i
$881$			4.35647i			0.146773i	0.997304	+	0.0733865i	$0.0233807\pi$
$881$			4.35647i			0.146773i	−0.997304	+	0.0733865i	$0.976619\pi$
$882$	5.45732	−	2.57513i	0.183758	−	0.0867092i
$883$	13.1072	−	9.52295i	0.441093	−	0.320473i	−0.344976	−	0.938612i	$-0.612113\pi$
$883$	13.1072	−	9.52295i	0.441093	−	0.320473i	0.786069	+	0.618139i	$0.212113\pi$
$884$	10.1713	+	7.38990i	0.342099	+	0.248549i
$885$	−37.5244	+	12.1924i	−1.26137	+	0.409843i
$886$	−21.9792	+	7.14146i	−0.738404	+	0.239922i
$887$	40.3592	+	29.3227i	1.35513	+	0.984560i	0.998738	+	0.0502236i	$0.0159934\pi$
$887$	40.3592	+	29.3227i	1.35513	+	0.984560i	0.356393	+	0.934336i	$0.384007\pi$
$888$	17.8049	−	12.9360i	0.597493	−	0.434104i
$889$	0.884607	+	13.9418i	0.0296688	+	0.467592i
$890$			16.2241i			0.543832i
$891$	2.91814	+	1.57621i	0.0977615	+	0.0528050i
$892$		−	24.3685i		−	0.815916i
$893$	8.20963	+	2.66747i	0.274725	+	0.0892635i
$894$	−8.06695	−	11.1032i	−0.269799	−	0.371347i
$895$	0.00478487	−	0.00658580i	0.000159940	−	0.000220139i
$896$	−12.3526	−	14.9156i	−0.412672	−	0.498294i
$897$	−9.53631	+	3.09853i	−0.318408	+	0.103457i
$898$	5.67041	−	7.80466i	0.189224	−	0.260445i
$899$	−34.1370	+	24.8020i	−1.13853	+	0.827193i
$900$	1.54430	−	4.75286i	0.0514765	−	0.158429i
$901$	−4.42313			−0.147356
$902$	−25.9831	+	12.4628i	−0.865143	+	0.414966i
$903$	8.35356	+	21.0659i	0.277989	+	0.701028i
$904$	−12.4762	−	4.05375i	−0.414951	−	0.134826i
$905$	26.1363	−	18.9891i	0.868800	−	0.631220i
$906$	7.14220	−	9.83040i	0.237284	−	0.326593i
$907$	−16.5312	−	50.8779i	−0.548911	−	1.68937i	−0.711505	−	0.702681i	$-0.751986\pi$
$907$	−16.5312	−	50.8779i	−0.548911	−	1.68937i	0.162594	−	0.986693i	$-0.448014\pi$
$908$	−8.35302	−	25.7080i	−0.277205	−	0.853149i
$909$	6.97966	+	5.07102i	0.231501	+	0.168195i
$910$	15.2705	+	9.67952i	0.506211	+	0.320873i
$911$	−14.9123	+	45.8952i	−0.494065	+	1.52058i	0.324344	+	0.945939i	$0.394857\pi$
$911$	−14.9123	+	45.8952i	−0.494065	+	1.52058i	−0.818409	+	0.574636i	$0.805143\pi$
$912$			0.111167i			0.00368112i
$913$	4.02499	+	8.39150i	0.133208	+	0.277718i
$914$	−6.31268			−0.208805
$915$	3.08860	−	9.50574i	0.102106	−	0.314250i
$916$	19.3781	+	26.6717i	0.640271	+	0.881258i
$917$	−0.377932	+	1.47521i	−0.0124804	+	0.0487158i
$918$	−1.00712	−	3.09960i	−0.0332399	−	0.102302i
$919$	1.41831	−	0.460837i	0.0467857	−	0.0152016i	−0.285531	−	0.958370i	$-0.592170\pi$
$919$	1.41831	−	0.460837i	0.0467857	−	0.0152016i	0.332316	+	0.943168i	$0.392170\pi$
$920$	25.7895	+	18.7372i	0.850254	+	0.617746i
$921$	13.2479	+	18.2341i	0.436532	+	0.600834i
$922$	13.2543	+	4.30658i	0.436507	+	0.141830i
$923$	6.89707			0.227020
$924$	−10.9526	−	1.29531i	−0.360314	−	0.0426124i
$925$	−31.1679			−1.02479
$926$	−6.03945	−	1.96233i	−0.198469	−	0.0644863i
$927$	−7.52111	−	10.3519i	−0.247026	−	0.340002i
$928$	−19.4952	−	14.1641i	−0.639961	−	0.464959i
$929$	46.5000	−	15.1088i	1.52561	−	0.495702i	0.578250	−	0.815859i	$-0.303736\pi$
$929$	46.5000	−	15.1088i	1.52561	−	0.495702i	0.947364	+	0.320157i	$0.103736\pi$
$930$	7.95991	+	24.4981i	0.261016	+	0.803324i
$931$	8.26155	−	1.05263i	0.270761	−	0.0344986i
$932$	−14.6499	−	20.1639i	−0.479875	−	0.660491i
$933$	−0.238230	+	0.733196i	−0.00779930	+	0.0240038i
$934$	20.7093			0.677628
$935$	−25.9186	−	27.1937i	−0.847629	−	0.889330i
$936$		−	7.42849i		−	0.242808i
$937$	−1.40111	+	4.31217i	−0.0457722	+	0.140872i	−0.971331	−	0.237732i	$-0.923596\pi$
$937$	−1.40111	+	4.31217i	−0.0457722	+	0.140872i	0.925559	+	0.378605i	$0.123596\pi$
$938$	13.7970	−	21.7662i	0.450487	−	0.710692i
$939$	0.0307409	+	0.0223346i	0.00100319	+	0.000728861i
$940$	−8.44252	−	25.9834i	−0.275365	−	0.847485i
$941$	−14.1706	−	43.6126i	−0.461948	−	1.42173i	−0.862780	−	0.505579i	$-0.831279\pi$
$941$	−14.1706	−	43.6126i	−0.461948	−	1.42173i	0.400832	−	0.916151i	$-0.368721\pi$
$942$	3.28343	−	4.51926i	0.106980	−	0.147245i
$943$	30.9022	−	22.4518i	1.00631	−	0.731130i
$944$	−1.17027	−	0.380244i	−0.0380890	−	0.0123759i
$945$	2.92195	+	7.36852i	0.0950510	+	0.239698i
$946$	−4.41037	+	24.0887i	−0.143394	+	0.783193i
$947$	35.1289			1.14154			0.570768	−	0.821111i	$-0.306645\pi$
$947$	35.1289			1.14154			0.570768	+	0.821111i	$0.306645\pi$
$948$	5.20165	−	16.0090i	0.168942	−	0.519949i
$949$	−20.8033	+	15.1145i	−0.675305	+	0.490638i
$950$	−2.39703	+	3.29922i	−0.0777698	+	0.107041i
$951$	1.68299	−	0.546837i	0.0545748	−	0.0177324i
$952$	17.9125	+	21.6290i	0.580547	+	0.700999i
$953$	−29.1011	+	40.0542i	−0.942677	+	1.29748i	0.0120276	+	0.999928i	$0.496171\pi$
$953$	−29.1011	+	40.0542i	−0.942677	+	1.29748i	−0.954704	+	0.297556i	$0.903829\pi$
$954$	0.592813	+	0.815937i	0.0191930	+	0.0264169i
$955$	55.6692	+	18.0880i	1.80141	+	0.585314i
$956$			22.8877i			0.740242i
$957$	−13.9079	+	1.86181i	−0.449577	+	0.0601837i
$958$		−	11.9682i		−	0.386676i
$959$	−21.6735	+	1.37518i	−0.699873	+	0.0444070i
$960$	−11.4481	+	8.31753i	−0.369486	+	0.268447i
$961$	55.3938	+	40.2460i	1.78690	+	1.29826i
$962$	−17.0042	+	5.52499i	−0.548236	+	0.178133i
$963$	−4.44351	+	1.44378i	−0.143190	+	0.0465253i
$964$	−21.4505	−	15.5847i	−0.690873	−	0.501949i
$965$	0.620538	−	0.450847i	0.0199758	−	0.0145133i
$966$	−8.62616	+	0.547331i	−0.277542	+	0.0176101i
$967$		−	29.6816i		−	0.954497i	−0.878769	−	0.477248i	$-0.841634\pi$
$967$		−	29.6816i		−	0.954497i	0.878769	−	0.477248i	$-0.158366\pi$
$968$	−24.0854	−	19.3309i	−0.774133	−	0.621320i
$969$		−	4.49806i		−	0.144498i
$970$	−22.5328	−	7.32134i	−0.723484	−	0.235074i
$971$	15.8667	+	21.8386i	0.509186	+	0.700834i	0.983782	−	0.179370i	$-0.0574059\pi$
$971$	15.8667	+	21.8386i	0.509186	+	0.700834i	−0.474596	+	0.880204i	$0.657406\pi$
$972$	0.738766	−	1.01682i	0.0236959	−	0.0326147i
$973$	13.9351	−	11.5407i	0.446739	−	0.369976i
$974$	−20.5604	+	6.68049i	−0.658798	+	0.214057i
$975$	−6.18366	+	8.51107i	−0.198036	+	0.272573i
$976$	0.252179	−	0.183219i	0.00807207	−	0.00586470i
$977$	−11.7363	+	36.1206i	−0.375477	+	1.15560i	0.567679	+	0.823250i	$0.307842\pi$
$977$	−11.7363	+	36.1206i	−0.375477	+	1.15560i	−0.943156	+	0.332350i	$0.892158\pi$
$978$	−6.25301			−0.199949
$979$	2.76437	+	20.6500i	0.0883496	+	0.659978i
$980$	−18.0645	−	19.1957i	−0.577051	−	0.613185i
$981$	2.25960	+	0.734190i	0.0721436	+	0.0234409i
$982$	−5.15805	+	3.74754i	−0.164600	+	0.119589i
$983$	14.7992	−	20.3693i	0.472020	−	0.649680i	−0.504927	−	0.863162i	$-0.668480\pi$
$983$	14.7992	−	20.3693i	0.472020	−	0.649680i	0.976947	+	0.213482i	$0.0684805\pi$
$984$	8.74462	+	26.9132i	0.278768	+	0.857960i
$985$	3.19618	+	9.83682i	0.101839	+	0.313427i
$986$	11.1552	+	8.10473i	0.355254	+	0.258107i
$987$	16.2130	+	10.2770i	0.516066	+	0.327120i
$988$	1.22264	−	3.76289i	0.0388973	−	0.119714i
$989$		−	32.4601i		−	1.03217i
$990$	−1.54268	+	8.42588i	−0.0490296	+	0.267792i
$991$	−38.3480			−1.21816			−0.609082	−	0.793108i	$-0.708462\pi$
$991$	−38.3480			−1.21816			−0.609082	+	0.793108i	$0.708462\pi$
$992$	−17.5541	+	54.0260i	−0.557344	+	1.71533i
$993$	−5.42044	−	7.46059i	−0.172012	−	0.236755i
$994$	5.75940	+	1.47549i	0.182677	+	0.0467997i
$995$	−16.0521	−	49.4033i	−0.508886	−	1.56619i
$996$	3.35430	−	1.08988i	0.106285	−	0.0345341i
$997$	10.1493	+	7.37388i	0.321431	+	0.233533i	0.736786	−	0.676126i	$-0.236343\pi$
$997$	10.1493	+	7.37388i	0.321431	+	0.233533i	−0.415355	+	0.909659i	$0.636343\pi$
$998$	17.0097	+	23.4118i	0.538432	+	0.741088i
$999$	−7.45511	−	2.42231i	−0.235869	−	0.0766386i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.w.a.13.11	✓	64
3.2	odd	2		693.2.bu.f.244.6		64
7.6	odd	2	inner	231.2.w.a.13.12	yes	64
11.6	odd	10	inner	231.2.w.a.160.12	yes	64
21.20	even	2		693.2.bu.f.244.5		64
33.17	even	10		693.2.bu.f.622.5		64
77.6	even	10	inner	231.2.w.a.160.11	yes	64
231.83	odd	10		693.2.bu.f.622.6		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.w.a.13.11	✓	64	1.1	even	1	trivial
231.2.w.a.13.12	yes	64	7.6	odd	2	inner
231.2.w.a.160.11	yes	64	77.6	even	10	inner
231.2.w.a.160.12	yes	64	11.6	odd	10	inner
693.2.bu.f.244.5		64	21.20	even	2
693.2.bu.f.244.6		64	3.2	odd	2
693.2.bu.f.622.5		64	33.17	even	10
693.2.bu.f.622.6		64	231.83	odd	10

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.819861 + 0.266389i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.01682 - 0.738766i) q^{4} +(-2.84938 + 0.925820i) q^{5} +(-0.266389 - 0.819861i) q^{6} +(0.656605 - 2.56298i) q^{7} +(-1.65026 - 2.27139i) q^{8} +(-0.309017 + 0.951057i) q^{9} +O(q^{10})\)	\(q+(0.819861 + 0.266389i) q^{2} +(-0.587785 - 0.809017i) q^{3} +(-1.01682 - 0.738766i) q^{4} +(-2.84938 + 0.925820i) q^{5} +(-0.266389 - 0.819861i) q^{6} +(0.656605 - 2.56298i) q^{7} +(-1.65026 - 2.27139i) q^{8} +(-0.309017 + 0.951057i) q^{9} -2.58273 q^{10} +(-3.28730 + 0.440063i) q^{11} +1.25686i q^{12} +(0.817616 - 2.51636i) q^{13} +(1.22107 - 1.92638i) q^{14} +(2.42383 + 1.76102i) q^{15} +(0.0288735 + 0.0888635i) q^{16} +(-1.16828 - 3.59560i) q^{17} +(-0.506702 + 0.697416i) q^{18} +(-0.962538 + 0.699325i) q^{19} +(3.58129 + 1.16363i) q^{20} +(-2.45944 + 0.975278i) q^{21} +(-2.81236 - 0.514911i) q^{22} +3.78972 q^{23} +(-0.867593 + 2.67018i) q^{24} +(3.21675 - 2.33711i) q^{25} +(1.34066 - 1.84526i) q^{26} +(0.951057 - 0.309017i) q^{27} +(-2.56110 + 2.12102i) q^{28} +(-2.48679 + 3.42278i) q^{29} +(1.51809 + 2.08947i) q^{30} +(9.48536 + 3.08198i) q^{31} +5.69573i q^{32} +(2.28824 + 2.40082i) q^{33} -3.25911i q^{34} +(0.501942 + 7.91081i) q^{35} +(1.01682 - 0.738766i) q^{36} +(-6.34170 - 4.60751i) q^{37} +(-0.975440 + 0.316940i) q^{38} +(-2.51636 + 0.817616i) q^{39} +(6.80512 + 4.94421i) q^{40} +(8.15422 - 5.92439i) q^{41} +(-2.27620 + 0.144425i) q^{42} -8.56532i q^{43} +(3.66771 + 1.98108i) q^{44} -2.99602i q^{45} +(3.10704 + 1.00954i) q^{46} +(-4.26457 - 5.86968i) q^{47} +(0.0549206 - 0.0755918i) q^{48} +(-6.13774 - 3.36573i) q^{49} +(3.25987 - 1.05920i) q^{50} +(-2.22220 + 3.05860i) q^{51} +(-2.69038 + 1.95467i) q^{52} +(0.361533 - 1.11268i) q^{53} +0.862053 q^{54} +(8.95936 - 4.29736i) q^{55} +(-6.90509 + 2.73818i) q^{56} +(1.13153 + 0.367657i) q^{57} +(-2.95061 + 2.14375i) q^{58} +(-7.74072 + 10.6542i) q^{59} +(-1.16363 - 3.58129i) q^{60} +(-1.03090 - 3.17279i) q^{61} +(6.95567 + 5.05359i) q^{62} +(2.23464 + 1.41647i) q^{63} +(-1.45953 + 4.49198i) q^{64} +7.92704i q^{65} +(1.23649 + 2.57790i) q^{66} +11.2990 q^{67} +(-1.46837 + 4.51918i) q^{68} +(-2.22754 - 3.06595i) q^{69} +(-1.69583 + 6.61948i) q^{70} +(0.805527 + 2.47916i) q^{71} +(2.67018 - 0.867593i) q^{72} +(-7.86260 - 5.71251i) q^{73} +(-3.97192 - 5.46688i) q^{74} +(-3.78152 - 1.22869i) q^{75} +1.49537 q^{76} +(-1.03059 + 8.71424i) q^{77} -2.28087 q^{78} +(-12.7373 - 4.13859i) q^{79} +(-0.164543 - 0.226474i) q^{80} +(-0.809017 - 0.587785i) q^{81} +(8.26352 - 2.68498i) q^{82} +(-0.867141 - 2.66879i) q^{83} +(3.22132 + 0.825263i) q^{84} +(6.65776 + 9.16362i) q^{85} +(2.28171 - 7.02237i) q^{86} +4.23078 q^{87} +(6.42445 + 6.74052i) q^{88} -6.28176i q^{89} +(0.798106 - 2.45632i) q^{90} +(-5.91254 - 3.74779i) q^{91} +(-3.85348 - 2.79972i) q^{92} +(-3.08198 - 9.48536i) q^{93} +(-1.93274 - 5.94836i) q^{94} +(2.09519 - 2.88378i) q^{95} +(4.60794 - 3.34786i) q^{96} +(8.72441 + 2.83473i) q^{97} +(-4.13550 - 4.39446i) q^{98} +(0.597307 - 3.26240i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9}+O(q^{10}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9	\( 64 q + 12 q^{4} + 10 q^{7} - 20 q^{8} + 16 q^{9} - 16 q^{11} + 12 q^{14} - 12 q^{15} - 16 q^{16} + 10 q^{18} - 40 q^{22} - 24 q^{23} + 44 q^{25} - 30 q^{28} - 40 q^{29} - 40 q^{35} - 12 q^{36} + 32 q^{37} - 2 q^{42} + 22 q^{44} - 70 q^{46} - 50 q^{49} - 40 q^{51} - 64 q^{53} + 80 q^{56} + 2 q^{58} - 36 q^{60} + 10 q^{63} + 72 q^{64} - 8 q^{67} - 26 q^{70} + 68 q^{71} - 10 q^{72} + 80 q^{74} + 90 q^{77} - 72 q^{78} + 40 q^{79} - 16 q^{81} + 60 q^{84} - 40 q^{85} - 62 q^{86} + 140 q^{88} + 54 q^{91} + 18 q^{92} - 20 q^{93} + 20 q^{95} - 4 q^{99}+O(q^{100}) \) 64 * q + 12 * q^4 + 10 * q^7 - 20 * q^8 + 16 * q^9 - 16 * q^11 + 12 * q^14 - 12 * q^15 - 16 * q^16 + 10 * q^18 - 40 * q^22 - 24 * q^23 + 44 * q^25 - 30 * q^28 - 40 * q^29 - 40 * q^35 - 12 * q^36 + 32 * q^37 - 2 * q^42 + 22 * q^44 - 70 * q^46 - 50 * q^49 - 40 * q^51 - 64 * q^53 + 80 * q^56 + 2 * q^58 - 36 * q^60 + 10 * q^63 + 72 * q^64 - 8 * q^67 - 26 * q^70 + 68 * q^71 - 10 * q^72 + 80 * q^74 + 90 * q^77 - 72 * q^78 + 40 * q^79 - 16 * q^81 + 60 * q^84 - 40 * q^85 - 62 * q^86 + 140 * q^88 + 54 * q^91 + 18 * q^92 - 20 * q^93 + 20 * q^95 - 4 * q^99

Introduction

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