LMFDB - Embedded newform 231.2.i.e.67.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} + 8x^{6} + 21x^{4} - 4x^{3} + 28x^{2} + 12x + 9 $ x^8 - 2x^7 + 8x^6 + 21x^4 - 4x^3 + 28x^2 + 12x + 9
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.3
Root			$-0.276205 - 0.478401i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.e.100.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.276205 + 0.478401i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.847422 - 1.46778i) q^{4} +(-0.795012 - 1.37700i) q^{5} -0.552409 q^{6} +(0.886763 - 2.49272i) q^{7} +2.04107 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.276205 + 0.478401i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.847422 - 1.46778i) q^{4} +(-0.795012 - 1.37700i) q^{5} -0.552409 q^{6} +(0.886763 - 2.49272i) q^{7} +2.04107 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.439172 - 0.760669i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.847422 + 1.46778i) q^{12} +2.87834 q^{13} +(1.43745 - 0.264273i) q^{14} +1.59002 q^{15} +(-1.13109 - 1.95911i) q^{16} +(-2.41864 + 4.18921i) q^{17} +(0.276205 - 0.478401i) q^{18} +(0.572943 + 0.992366i) q^{19} -2.69484 q^{20} +(1.71538 + 2.01432i) q^{21} +0.552409 q^{22} +(1.82594 + 3.16261i) q^{23} +(-1.02053 + 1.76762i) q^{24} +(1.23591 - 2.14066i) q^{25} +(0.795012 + 1.37700i) q^{26} +1.00000 q^{27} +(-2.90730 - 3.41396i) q^{28} -0.325935 q^{29} +(0.439172 + 0.760669i) q^{30} +(-3.22577 + 5.58719i) q^{31} +(2.66589 - 4.61746i) q^{32} +(0.500000 + 0.866025i) q^{33} -2.67216 q^{34} +(-4.13747 + 0.760669i) q^{35} -1.69484 q^{36} +(-0.847422 - 1.46778i) q^{37} +(-0.316499 + 0.548192i) q^{38} +(-1.43917 + 2.49272i) q^{39} +(-1.62267 - 2.81055i) q^{40} -4.05839 q^{41} +(-0.489856 + 1.37700i) q^{42} +4.62764 q^{43} +(-0.847422 - 1.46778i) q^{44} +(-0.795012 + 1.37700i) q^{45} +(-1.00866 + 1.74706i) q^{46} +(-0.152578 - 0.264273i) q^{47} +2.26218 q^{48} +(-5.42730 - 4.42090i) q^{49} +1.36546 q^{50} +(-2.41864 - 4.18921i) q^{51} +(2.43917 - 4.22477i) q^{52} +(-2.85686 + 4.94822i) q^{53} +(0.276205 + 0.478401i) q^{54} -1.59002 q^{55} +(1.80994 - 5.08781i) q^{56} -1.14589 q^{57} +(-0.0900249 - 0.155928i) q^{58} +(-5.93075 + 10.2724i) q^{59} +(1.34742 - 2.33380i) q^{60} +(-0.886763 - 1.53592i) q^{61} -3.56389 q^{62} +(-2.60214 + 0.478401i) q^{63} -1.57904 q^{64} +(-2.28832 - 3.96349i) q^{65} +(-0.276205 + 0.478401i) q^{66} +(-7.63574 + 13.2255i) q^{67} +(4.09922 + 7.10005i) q^{68} -3.65187 q^{69} +(-1.50669 - 1.76927i) q^{70} +9.16666 q^{71} +(-1.02053 - 1.76762i) q^{72} +(5.86648 - 10.1610i) q^{73} +(0.468124 - 0.810814i) q^{74} +(1.23591 + 2.14066i) q^{75} +1.94210 q^{76} +(-1.71538 - 2.01432i) q^{77} -1.59002 q^{78} +(4.35513 + 7.54331i) q^{79} +(-1.79846 + 3.11503i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.12095 - 1.94154i) q^{82} +8.40856 q^{83} +(4.41022 - 0.810814i) q^{84} +7.69139 q^{85} +(1.27818 + 2.21387i) q^{86} +(0.162968 - 0.282268i) q^{87} +(1.02053 - 1.76762i) q^{88} +(2.87489 + 4.97946i) q^{89} -0.878345 q^{90} +(2.55241 - 7.17491i) q^{91} +6.18935 q^{92} +(-3.22577 - 5.58719i) q^{93} +(0.0842856 - 0.145987i) q^{94} +(0.910993 - 1.57789i) q^{95} +(2.66589 + 4.61746i) q^{96} -3.65329 q^{97} +(0.615916 - 3.81750i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9} - 10 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} + 8 q^{15} - 12 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{24} - 4 q^{25} + 4 q^{26} + 8 q^{27} - 22 q^{28} + 16 q^{29} - 10 q^{30} + 12 q^{31} - 26 q^{32} + 4 q^{33} - 32 q^{34} - 2 q^{35} + 8 q^{36} + 4 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} + 4 q^{41} + 20 q^{42} + 36 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} - 12 q^{47} + 24 q^{48} - 4 q^{49} + 4 q^{50} - 2 q^{51} + 6 q^{52} + 12 q^{53} - 2 q^{54} - 8 q^{55} + 48 q^{56} + 4 q^{58} - 12 q^{59} - 2 q^{61} - 52 q^{62} + 2 q^{63} + 112 q^{64} + 4 q^{65} + 2 q^{66} - 28 q^{67} + 48 q^{68} + 8 q^{69} - 32 q^{70} + 24 q^{71} - 12 q^{72} - 6 q^{73} + 16 q^{74} - 4 q^{75} - 36 q^{76} + 4 q^{77} - 8 q^{78} - 2 q^{79} - 16 q^{80} - 4 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{85} - 36 q^{86} - 8 q^{87} + 12 q^{88} - 8 q^{89} + 20 q^{90} + 12 q^{91} - 32 q^{92} + 12 q^{93} - 20 q^{94} - 34 q^{95} - 26 q^{96} - 88 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9 - 10 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 + 8 * q^15 - 12 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^24 - 4 * q^25 + 4 * q^26 + 8 * q^27 - 22 * q^28 + 16 * q^29 - 10 * q^30 + 12 * q^31 - 26 * q^32 + 4 * q^33 - 32 * q^34 - 2 * q^35 + 8 * q^36 + 4 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 + 4 * q^41 + 20 * q^42 + 36 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 - 12 * q^47 + 24 * q^48 - 4 * q^49 + 4 * q^50 - 2 * q^51 + 6 * q^52 + 12 * q^53 - 2 * q^54 - 8 * q^55 + 48 * q^56 + 4 * q^58 - 12 * q^59 - 2 * q^61 - 52 * q^62 + 2 * q^63 + 112 * q^64 + 4 * q^65 + 2 * q^66 - 28 * q^67 + 48 * q^68 + 8 * q^69 - 32 * q^70 + 24 * q^71 - 12 * q^72 - 6 * q^73 + 16 * q^74 - 4 * q^75 - 36 * q^76 + 4 * q^77 - 8 * q^78 - 2 * q^79 - 16 * q^80 - 4 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^85 - 36 * q^86 - 8 * q^87 + 12 * q^88 - 8 * q^89 + 20 * q^90 + 12 * q^91 - 32 * q^92 + 12 * q^93 - 20 * q^94 - 34 * q^95 - 26 * q^96 - 88 * q^97 + 16 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.276205	+	0.478401i	0.195306	+	0.338280i	0.947001	−	0.321231i	$-0.104097\pi$
$2$	0.276205	+	0.478401i	0.195306	+	0.338280i	−0.751695	+	0.659511i	$0.770763\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	0.847422	−	1.46778i	0.423711	−	0.733889i
$5$	−0.795012	−	1.37700i	−0.355540	−	0.615814i	0.631670	−	0.775237i	$-0.282370\pi$
$5$	−0.795012	−	1.37700i	−0.355540	−	0.615814i	−0.987210	+	0.159423i	$0.949036\pi$
$6$	−0.552409			−0.225520
$7$	0.886763	−	2.49272i	0.335165	−	0.942159i
$7$	0.886763	−	2.49272i	0.335165	−	0.942159i
$8$	2.04107			0.721626
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.439172	−	0.760669i	0.138879	−	0.240545i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	0.847422	+	1.46778i	0.244630	+	0.423711i
$13$	2.87834			0.798309			0.399155	−	0.916884i	$-0.369304\pi$
$13$	2.87834			0.798309			0.399155	+	0.916884i	$0.369304\pi$
$14$	1.43745	−	0.264273i	0.384174	−	0.0706299i
$15$	1.59002			0.410543
$16$	−1.13109	−	1.95911i	−0.282773	−	0.489777i
$17$	−2.41864	+	4.18921i	−0.586606	+	1.01603i	0.408067	+	0.912952i	$0.366203\pi$
$17$	−2.41864	+	4.18921i	−0.586606	+	1.01603i	−0.994673	+	0.103080i	$0.967130\pi$
$18$	0.276205	−	0.478401i	0.0651021	−	0.112760i
$19$	0.572943	+	0.992366i	0.131442	+	0.227664i	0.924233	−	0.381830i	$-0.124706\pi$
$19$	0.572943	+	0.992366i	0.131442	+	0.227664i	−0.792791	+	0.609494i	$0.791373\pi$
$20$	−2.69484			−0.602585
$21$	1.71538	+	2.01432i	0.374326	+	0.439560i
$22$	0.552409			0.117774
$23$	1.82594	+	3.16261i	0.380734	+	0.659450i	0.991167	−	0.132617i	$-0.0423381\pi$
$23$	1.82594	+	3.16261i	0.380734	+	0.659450i	−0.610434	+	0.792068i	$0.709005\pi$
$24$	−1.02053	+	1.76762i	−0.208315	+	0.360813i
$25$	1.23591	−	2.14066i	0.247182	−	0.428132i
$26$	0.795012	+	1.37700i	0.155915	+	0.270052i
$27$	1.00000			0.192450
$28$	−2.90730	−	3.41396i	−0.549427	−	0.645177i
$29$	−0.325935			−0.0605247			−0.0302623	−	0.999542i	$-0.509634\pi$
$29$	−0.325935			−0.0605247			−0.0302623	+	0.999542i	$0.509634\pi$
$30$	0.439172	+	0.760669i	0.0801815	+	0.138879i
$31$	−3.22577	+	5.58719i	−0.579365	+	1.00349i	0.416188	+	0.909279i	$0.363366\pi$
$31$	−3.22577	+	5.58719i	−0.579365	+	1.00349i	−0.995552	+	0.0942105i	$0.969967\pi$
$32$	2.66589	−	4.61746i	0.471268	−	0.816259i
$33$	0.500000	+	0.866025i	0.0870388	+	0.150756i
$34$	−2.67216			−0.458271
$35$	−4.13747	+	0.760669i	−0.699360	+	0.128577i
$36$	−1.69484			−0.282474
$37$	−0.847422	−	1.46778i	−0.139315	−	0.241301i	0.787922	−	0.615775i	$-0.211157\pi$
$37$	−0.847422	−	1.46778i	−0.139315	−	0.241301i	−0.927238	+	0.374473i	$0.877823\pi$
$38$	−0.316499	+	0.548192i	−0.0513429	+	0.0889285i
$39$	−1.43917	+	2.49272i	−0.230452	+	0.399155i
$40$	−1.62267	−	2.81055i	−0.256567	−	0.444387i
$41$	−4.05839			−0.633815			−0.316907	−	0.948456i	$-0.602644\pi$
$41$	−4.05839			−0.633815			−0.316907	+	0.948456i	$0.602644\pi$
$42$	−0.489856	+	1.37700i	−0.0755865	+	0.212476i
$43$	4.62764			0.705709			0.352854	−	0.935678i	$-0.385211\pi$
$43$	4.62764			0.705709			0.352854	+	0.935678i	$0.385211\pi$
$44$	−0.847422	−	1.46778i	−0.127754	−	0.221276i
$45$	−0.795012	+	1.37700i	−0.118513	+	0.205271i
$46$	−1.00866	+	1.74706i	−0.148719	+	0.257590i
$47$	−0.152578	−	0.264273i	−0.0222558	−	0.0385482i	0.854683	−	0.519150i	$-0.173751\pi$
$47$	−0.152578	−	0.264273i	−0.0222558	−	0.0385482i	−0.876939	+	0.480602i	$0.840418\pi$
$48$	2.26218			0.326518
$49$	−5.42730	−	4.42090i	−0.775329	−	0.631558i
$50$	1.36546			0.193105
$51$	−2.41864	−	4.18921i	−0.338677	−	0.586606i
$52$	2.43917	−	4.22477i	0.338252	−	0.585870i
$53$	−2.85686	+	4.94822i	−0.392420	+	0.679691i	−0.992768	−	0.120048i	$-0.961695\pi$
$53$	−2.85686	+	4.94822i	−0.392420	+	0.679691i	0.600348	+	0.799739i	$0.295029\pi$
$54$	0.276205	+	0.478401i	0.0375867	+	0.0651021i
$55$	−1.59002			−0.214399
$56$	1.80994	−	5.08781i	0.241864	−	0.679887i
$57$	−1.14589			−0.151776
$58$	−0.0900249	−	0.155928i	−0.0118208	−	0.0204743i
$59$	−5.93075	+	10.2724i	−0.772118	+	1.33735i	0.164281	+	0.986414i	$0.447469\pi$
$59$	−5.93075	+	10.2724i	−0.772118	+	1.33735i	−0.936400	+	0.350935i	$0.885864\pi$
$60$	1.34742	−	2.33380i	0.173951	−	0.301293i
$61$	−0.886763	−	1.53592i	−0.113538	−	0.196654i	0.803656	−	0.595094i	$-0.202885\pi$
$61$	−0.886763	−	1.53592i	−0.113538	−	0.196654i	−0.917195	+	0.398440i	$0.869552\pi$
$62$	−3.56389			−0.452614
$63$	−2.60214	+	0.478401i	−0.327839	+	0.0602728i
$64$	−1.57904			−0.197380
$65$	−2.28832	−	3.96349i	−0.283831	−	0.491610i
$66$	−0.276205	+	0.478401i	−0.0339985	+	0.0588870i
$67$	−7.63574	+	13.2255i	−0.932854	+	1.61575i	−0.154438	+	0.988002i	$0.549357\pi$
$67$	−7.63574	+	13.2255i	−0.932854	+	1.61575i	−0.778416	+	0.627749i	$0.783977\pi$
$68$	4.09922	+	7.10005i	0.497103	+	0.861007i
$69$	−3.65187			−0.439634
$70$	−1.50669	−	1.76927i	−0.180084	−	0.211468i
$71$	9.16666			1.08788			0.543941	−	0.839123i	$-0.316931\pi$
$71$	9.16666			1.08788			0.543941	+	0.839123i	$0.316931\pi$
$72$	−1.02053	−	1.76762i	−0.120271	−	0.208315i
$73$	5.86648	−	10.1610i	0.686619	−	1.18926i	−0.286306	−	0.958138i	$-0.592427\pi$
$73$	5.86648	−	10.1610i	0.686619	−	1.18926i	0.972925	−	0.231121i	$-0.0742393\pi$
$74$	0.468124	−	0.810814i	0.0544183	−	0.0942553i
$75$	1.23591	+	2.14066i	0.142711	+	0.247182i
$76$	1.94210			0.222774
$77$	−1.71538	−	2.01432i	−0.195485	−	0.229553i
$78$	−1.59002			−0.180035
$79$	4.35513	+	7.54331i	0.489991	+	0.848689i	0.999934	−	0.0115194i	$-0.00366683\pi$
$79$	4.35513	+	7.54331i	0.489991	+	0.848689i	−0.509943	+	0.860208i	$0.670333\pi$
$80$	−1.79846	+	3.11503i	−0.201074	+	0.348271i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.12095	−	1.94154i	−0.123788	−	0.214407i
$83$	8.40856			0.922959			0.461480	−	0.887151i	$-0.347319\pi$
$83$	8.40856			0.922959			0.461480	+	0.887151i	$0.347319\pi$
$84$	4.41022	−	0.810814i	0.481195	−	0.0884671i
$85$	7.69139			0.834249
$86$	1.27818	+	2.21387i	0.137829	+	0.238727i
$87$	0.162968	−	0.282268i	0.0174720	−	0.0302623i
$88$	1.02053	−	1.76762i	0.108789	−	0.188428i
$89$	2.87489	+	4.97946i	0.304738	+	0.527822i	0.977203	−	0.212307i	$-0.0680977\pi$
$89$	2.87489	+	4.97946i	0.304738	+	0.527822i	−0.672465	+	0.740129i	$0.734764\pi$
$90$	−0.878345			−0.0925857
$91$	2.55241	−	7.17491i	0.267565	−	0.752135i
$92$	6.18935			0.645284
$93$	−3.22577	−	5.58719i	−0.334496	−	0.579365i
$94$	0.0842856	−	0.145987i	0.00869339	−	0.0150574i
$95$	0.910993	−	1.57789i	0.0934659	−	0.161888i
$96$	2.66589	+	4.61746i	0.272086	+	0.471268i
$97$	−3.65329			−0.370935			−0.185467	−	0.982650i	$-0.559380\pi$
$97$	−3.65329			−0.370935			−0.185467	+	0.982650i	$0.559380\pi$
$98$	0.615916	−	3.81750i	0.0622169	−	0.385626i
$99$	−1.00000			−0.100504
$100$	−2.09468	−	3.62808i	−0.209468	−	0.362808i
$101$	−0.142189	+	0.246278i	−0.0141483	+	0.0245056i	−0.873013	−	0.487697i	$-0.837837\pi$
$101$	−0.142189	+	0.246278i	−0.0141483	+	0.0245056i	0.858865	+	0.512203i	$0.171170\pi$
$102$	1.33608	−	2.31416i	0.132292	−	0.229136i
$103$	8.34671	+	14.4569i	0.822426	+	1.42448i	0.903871	+	0.427806i	$0.140713\pi$
$103$	8.34671	+	14.4569i	0.822426	+	1.42448i	−0.0814443	+	0.996678i	$0.525953\pi$
$104$	5.87489			0.576081
$105$	1.40998	−	3.96349i	0.137599	−	0.386797i
$106$	−3.15631			−0.306568
$107$	−8.97475	−	15.5447i	−0.867621	−	1.50276i	−0.864421	−	0.502769i	$-0.832314\pi$
$107$	−8.97475	−	15.5447i	−0.867621	−	1.50276i	−0.00320086	−	0.999995i	$-0.501019\pi$
$108$	0.847422	−	1.46778i	0.0815432	−	0.141237i
$109$	−5.54399	+	9.60247i	−0.531018	+	0.919750i	0.468327	+	0.883555i	$0.344857\pi$
$109$	−5.54399	+	9.60247i	−0.531018	+	0.919750i	−0.999345	+	0.0361949i	$0.988476\pi$
$110$	−0.439172	−	0.760669i	−0.0418734	−	0.0725269i
$111$	1.69484			0.160867
$112$	−5.88652	+	1.08223i	−0.556224	+	0.102261i
$113$	1.72443			0.162221			0.0811105	−	0.996705i	$-0.474153\pi$
$113$	1.72443			0.162221			0.0811105	+	0.996705i	$0.474153\pi$
$114$	−0.316499	−	0.548192i	−0.0296428	−	0.0513429i
$115$	2.90328	−	5.02863i	0.270732	−	0.468922i
$116$	−0.276205	+	0.478401i	−0.0256450	+	0.0444184i
$117$	−1.43917	−	2.49272i	−0.133052	−	0.230452i
$118$	−6.55241			−0.603198
$119$	8.29776	+	9.74382i	0.760654	+	0.893215i
$120$	3.24535			0.296258
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	0.489856	−	0.848456i	0.0443495	−	0.0768156i
$123$	2.02920	−	3.51467i	0.182967	−	0.316907i
$124$	5.46717	+	9.46942i	0.490966	+	0.850379i
$125$	−11.8804			−1.06261
$126$	−0.947591	−	1.11273i	−0.0844181	−	0.0991298i
$127$	20.3675			1.80732			0.903661	−	0.428248i	$-0.140869\pi$
$127$	20.3675			1.80732			0.903661	+	0.428248i	$0.140869\pi$
$128$	−5.76792	−	9.99033i	−0.509817	−	0.883029i
$129$	−2.31382	+	4.00765i	−0.203721	+	0.352854i
$130$	1.26409	−	2.18947i	0.110868	−	0.192029i
$131$	−10.0910	−	17.4782i	−0.881659	−	1.52708i	−0.849496	−	0.527595i	$-0.823094\pi$
$131$	−10.0910	−	17.4782i	−0.881659	−	1.52708i	−0.0321623	−	0.999483i	$-0.510239\pi$
$132$	1.69484			0.147517
$133$	2.98175	−	0.548192i	0.258551	−	0.0475343i
$134$	−8.43611			−0.728769
$135$	−0.795012	−	1.37700i	−0.0684238	−	0.118513i
$136$	−4.93660	+	8.55045i	−0.423310	+	0.733195i
$137$	10.6316	−	18.4144i	0.908317	−	1.57325i	0.0919163	−	0.995767i	$-0.470701\pi$
$137$	10.6316	−	18.4144i	0.908317	−	1.57325i	0.816401	−	0.577485i	$-0.195966\pi$
$138$	−1.00866	−	1.74706i	−0.0858632	−	0.148719i
$139$	5.27951			0.447802			0.223901	−	0.974612i	$-0.428121\pi$
$139$	5.27951			0.447802			0.223901	+	0.974612i	$0.428121\pi$
$140$	−2.38969	+	6.71749i	−0.201965	+	0.567732i
$141$	0.305156			0.0256988
$142$	2.53188	+	4.38534i	0.212470	+	0.368009i
$143$	1.43917	−	2.49272i	0.120350	−	0.208452i
$144$	−1.13109	+	1.95911i	−0.0942576	+	0.163259i
$145$	0.259123	+	0.448814i	0.0215190	+	0.0372719i
$146$	6.48139			0.536404
$147$	6.54227	−	2.48973i	0.539597	−	0.205350i
$148$	−2.87250			−0.236118
$149$	−0.682729	−	1.18252i	−0.0559313	−	0.0968759i	0.836704	−	0.547655i	$-0.184479\pi$
$149$	−0.682729	−	1.18252i	−0.0559313	−	0.0968759i	−0.892635	+	0.450779i	$0.851146\pi$
$150$	−0.682729	+	1.18252i	−0.0557446	+	0.0965524i
$151$	−7.97450	+	13.8122i	−0.648956	+	1.12402i	0.334417	+	0.942425i	$0.391461\pi$
$151$	−7.97450	+	13.8122i	−0.648956	+	1.12402i	−0.983373	+	0.181599i	$0.941873\pi$
$152$	1.16941	+	2.02549i	0.0948520	+	0.164289i
$153$	4.83728			0.391071
$154$	0.489856	−	1.37700i	0.0394737	−	0.110962i
$155$	10.2581			0.823950
$156$	2.43917	+	4.22477i	0.195290	+	0.338252i
$157$	4.19830	−	7.27166i	0.335060	−	0.580342i	−0.648436	−	0.761269i	$-0.724577\pi$
$157$	4.19830	−	7.27166i	0.335060	−	0.580342i	0.983496	+	0.180927i	$0.0579099\pi$
$158$	−2.40582	+	4.16700i	−0.191396	+	0.331508i
$159$	−2.85686	−	4.94822i	−0.226564	−	0.392420i
$160$	−8.47767			−0.670219
$161$	9.50268	−	1.74706i	0.748916	−	0.137687i
$162$	−0.552409			−0.0434014
$163$	8.65652	+	14.9935i	0.678031	+	1.17438i	0.975573	+	0.219675i	$0.0704999\pi$
$163$	8.65652	+	14.9935i	0.678031	+	1.17438i	−0.297542	+	0.954709i	$0.596167\pi$
$164$	−3.43917	+	5.95682i	−0.268554	+	0.465150i
$165$	0.795012	−	1.37700i	0.0618916	−	0.107199i
$166$	2.32248	+	4.02266i	0.180260	+	0.312219i
$167$	18.4945			1.43115			0.715574	−	0.698537i	$-0.246165\pi$
$167$	18.4945			1.43115			0.715574	+	0.698537i	$0.246165\pi$
$168$	3.50120	+	4.11136i	0.270123	+	0.317198i
$169$	−4.71513			−0.362702
$170$	2.12440	+	3.67957i	0.162934	+	0.282210i
$171$	0.572943	−	0.992366i	0.0438140	−	0.0758881i
$172$	3.92156	−	6.79235i	0.299016	−	0.517912i
$173$	−6.13402	−	10.6244i	−0.466361	−	0.807760i	0.532901	−	0.846177i	$-0.321102\pi$
$173$	−6.13402	−	10.6244i	−0.466361	−	0.807760i	−0.999262	+	0.0384172i	$0.987768\pi$
$174$	0.180050			0.0136495
$175$	−4.24010	−	4.97904i	−0.320522	−	0.376380i
$176$	−2.26218			−0.170518
$177$	−5.93075	−	10.2724i	−0.445783	−	0.772118i
$178$	−1.58812	+	2.75070i	−0.119035	+	0.206174i
$179$	−6.90582	+	11.9612i	−0.516165	+	0.894024i	0.483659	+	0.875257i	$0.339308\pi$
$179$	−6.90582	+	11.9612i	−0.516165	+	0.894024i	−0.999824	+	0.0187674i	$0.994026\pi$
$180$	1.34742	+	2.33380i	0.100431	+	0.173951i
$181$	−18.7687			−1.39506			−0.697532	−	0.716554i	$-0.745718\pi$
$181$	−18.7687			−1.39506			−0.697532	+	0.716554i	$0.745718\pi$
$182$	4.13747	−	0.760669i	0.306689	−	0.0563845i
$183$	1.77353			0.131103
$184$	3.72686	+	6.45510i	0.274747	+	0.475877i
$185$	−1.34742	+	2.33380i	−0.0990644	+	0.171585i
$186$	1.78194	−	3.08642i	0.130658	−	0.226307i
$187$	2.41864	+	4.18921i	0.176868	+	0.306345i
$188$	−0.517192			−0.0377201
$189$	0.886763	−	2.49272i	0.0645025	−	0.181319i
$190$	1.00648			0.0730179
$191$	−4.05839	−	7.02935i	−0.293655	−	0.508626i	0.681016	−	0.732269i	$-0.261538\pi$
$191$	−4.05839	−	7.02935i	−0.293655	−	0.508626i	−0.974671	+	0.223643i	$0.928205\pi$
$192$	0.789519	−	1.36749i	0.0569786	−	0.0986899i
$193$	−0.595383	+	1.03123i	−0.0428566	+	0.0742298i	−0.886658	−	0.462426i	$-0.846979\pi$
$193$	−0.595383	+	1.03123i	−0.0428566	+	0.0742298i	0.843801	+	0.536656i	$0.180313\pi$
$194$	−1.00905	−	1.74773i	−0.0724459	−	0.125480i
$195$	4.57664			0.327740
$196$	−11.0881	+	4.21970i	−0.792008	+	0.301407i
$197$	−26.7523			−1.90602			−0.953012	−	0.302933i	$-0.902034\pi$
$197$	−26.7523			−1.90602			−0.953012	+	0.302933i	$0.902034\pi$
$198$	−0.276205	−	0.478401i	−0.0196290	−	0.0339985i
$199$	3.01684	−	5.22531i	0.213858	−	0.370413i	−0.739061	−	0.673639i	$-0.764730\pi$
$199$	3.01684	−	5.22531i	0.213858	−	0.370413i	0.952919	+	0.303226i	$0.0980637\pi$
$200$	2.52258	−	4.36923i	0.178373	−	0.308951i
$201$	−7.63574	−	13.2255i	−0.538584	−	0.932854i
$202$	−0.157093			−0.0110530
$203$	−0.289027	+	0.812465i	−0.0202857	+	0.0570239i
$204$	−8.19843			−0.574005
$205$	3.22647	+	5.58842i	0.225347	+	0.390312i
$206$	−4.61080	+	7.98615i	−0.321250	+	0.556421i
$207$	1.82594	−	3.16261i	0.126911	−	0.219817i
$208$	−3.25567	−	5.63899i	−0.225740	−	0.390993i
$209$	1.14589			0.0792626
$210$	2.28558	−	0.420201i	0.157720	−	0.0289966i
$211$	−20.4601			−1.40853			−0.704264	−	0.709938i	$-0.748723\pi$
$211$	−20.4601			−1.40853			−0.704264	+	0.709938i	$0.748723\pi$
$212$	4.84193	+	8.38647i	0.332545	+	0.575985i
$213$	−4.58333	+	7.93856i	−0.314045	+	0.543941i
$214$	4.95773	−	8.58705i	0.338904	−	0.586998i
$215$	−3.67903	−	6.37227i	−0.250908	−	0.434585i
$216$	2.04107			0.138877
$217$	11.0668	+	12.9954i	0.751264	+	0.882188i
$218$	−6.12511			−0.414845
$219$	5.86648	+	10.1610i	0.396420	+	0.686619i
$220$	−1.34742	+	2.33380i	−0.0908432	+	0.157345i
$221$	−6.96168	+	12.0580i	−0.468293	+	0.811107i
$222$	0.468124	+	0.810814i	0.0314184	+	0.0544183i
$223$	−29.6048			−1.98248			−0.991242	−	0.132055i	$-0.957843\pi$
$223$	−29.6048			−1.98248			−0.991242	+	0.132055i	$0.957843\pi$
$224$	−9.14602	−	10.7399i	−0.611094	−	0.717591i
$225$	−2.47182			−0.164788
$226$	0.476296	+	0.824969i	0.0316828	+	0.0548761i
$227$	12.0416	−	20.8566i	0.799226	−	1.38430i	−0.120894	−	0.992665i	$-0.538576\pi$
$227$	12.0416	−	20.8566i	0.799226	−	1.38430i	0.920121	−	0.391635i	$-0.128090\pi$
$228$	−0.971049	+	1.68191i	−0.0643093	+	0.111387i
$229$	2.60735	+	4.51607i	0.172299	+	0.298430i	0.939223	−	0.343307i	$-0.111547\pi$
$229$	2.60735	+	4.51607i	0.172299	+	0.298430i	−0.766924	+	0.641737i	$0.778214\pi$
$230$	3.20760			0.211503
$231$	2.60214	−	0.478401i	0.171208	−	0.0314765i
$232$	−0.665256			−0.0436762
$233$	−1.57294	−	2.72442i	−0.103047	−	0.178482i	0.809892	−	0.586579i	$-0.199526\pi$
$233$	−1.57294	−	2.72442i	−0.103047	−	0.178482i	−0.912939	+	0.408097i	$0.866193\pi$
$234$	0.795012	−	1.37700i	0.0519716	−	0.0900174i
$235$	−0.242603	+	0.420201i	−0.0158257	+	0.0274109i
$236$	10.0517	+	17.4101i	0.654310	+	1.13330i
$237$	−8.71027			−0.565793
$238$	−2.36957	+	6.66094i	−0.153596	+	0.431765i
$239$	2.75465			0.178184			0.0890919	−	0.996023i	$-0.471604\pi$
$239$	2.75465			0.178184			0.0890919	+	0.996023i	$0.471604\pi$
$240$	−1.79846	−	3.11503i	−0.116090	−	0.201074i
$241$	4.51479	−	7.81985i	0.290823	−	0.503721i	−0.683181	−	0.730249i	$-0.739404\pi$
$241$	4.51479	−	7.81985i	0.290823	−	0.503721i	0.974005	+	0.226528i	$0.0727374\pi$
$242$	0.276205	−	0.478401i	0.0177551	−	0.0307528i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	−3.00585			−0.192430
$245$	−1.77282	+	10.9881i	−0.113261	+	0.702003i
$246$	2.24190			0.142938
$247$	1.64913	+	2.85637i	0.104931	+	0.181747i
$248$	−6.58400	+	11.4038i	−0.418085	+	0.724144i
$249$	−4.20428	+	7.28203i	−0.266435	+	0.461480i
$250$	−3.28142	−	5.68358i	−0.207535	−	0.359461i
$251$	−6.73133			−0.424878			−0.212439	−	0.977174i	$-0.568141\pi$
$251$	−6.73133			−0.424878			−0.212439	+	0.977174i	$0.568141\pi$
$252$	−1.50292	+	4.22477i	−0.0946754	+	0.266136i
$253$	3.65187			0.229591
$254$	5.62560	+	9.74382i	0.352981	+	0.611382i
$255$	−3.84570	+	6.66094i	−0.240827	+	0.417124i
$256$	1.60722	−	2.78378i	0.100451	−	0.173986i
$257$	−13.8447	−	23.9797i	−0.863607	−	1.49581i	−0.868424	−	0.495823i	$-0.834867\pi$
$257$	−13.8447	−	23.9797i	−0.863607	−	1.49581i	0.00481687	−	0.999988i	$-0.498467\pi$
$258$	−2.55635			−0.159152
$259$	−4.41022	+	0.810814i	−0.274038	+	0.0503816i
$260$	−7.75669			−0.481049
$261$	0.162968	+	0.282268i	0.0100874	+	0.0174720i
$262$	5.57439	−	9.65512i	0.344387	−	0.596495i
$263$	−2.30170	+	3.98667i	−0.141929	+	0.245829i	−0.928223	−	0.372024i	$-0.878664\pi$
$263$	−2.30170	+	3.98667i	−0.141929	+	0.245829i	0.786294	+	0.617853i	$0.211997\pi$
$264$	1.02053	+	1.76762i	0.0628095	+	0.108789i
$265$	9.08495			0.558084
$266$	1.08583	+	1.27506i	0.0665765	+	0.0781789i
$267$	−5.74979			−0.351881
$268$	12.9414	+	22.4151i	0.790521	+	1.36922i
$269$	−9.55515	+	16.5500i	−0.582588	+	1.00907i	0.412583	+	0.910920i	$0.364627\pi$
$269$	−9.55515	+	16.5500i	−0.582588	+	1.00907i	−0.995171	+	0.0981522i	$0.968707\pi$
$270$	0.439172	−	0.760669i	0.0267272	−	0.0462928i
$271$	−7.68643	−	13.3133i	−0.466917	−	0.808724i	0.532369	−	0.846513i	$-0.321302\pi$
$271$	−7.68643	−	13.3133i	−0.466917	−	0.808724i	−0.999286	+	0.0377885i	$0.987969\pi$
$272$	10.9428			0.663505
$273$	4.93745	+	5.79790i	0.298828	+	0.350905i
$274$	11.7460			0.709600
$275$	−1.23591	−	2.14066i	−0.0745282	−	0.129087i
$276$	−3.09468	+	5.36013i	−0.186278	+	0.322642i
$277$	4.69484	−	8.13171i	0.282086	−	0.488587i	−0.689812	−	0.723988i	$-0.742307\pi$
$277$	4.69484	−	8.13171i	0.282086	−	0.488587i	0.971898	+	0.235401i	$0.0756404\pi$
$278$	1.45823	+	2.52572i	0.0874586	+	0.151483i
$279$	6.45153			0.386243
$280$	−8.44485	+	1.55258i	−0.504676	+	0.0927842i
$281$	26.9788			1.60942			0.804710	−	0.593668i	$-0.202321\pi$
$281$	26.9788			1.60942			0.804710	+	0.593668i	$0.202321\pi$
$282$	0.0842856	+	0.145987i	0.00501913	+	0.00869339i
$283$	11.7878	−	20.4171i	0.700712	−	1.21367i	−0.267505	−	0.963556i	$-0.586199\pi$
$283$	11.7878	−	20.4171i	0.700712	−	1.21367i	0.968217	−	0.250112i	$-0.0804673\pi$
$284$	7.76803	−	13.4546i	0.460948	−	0.798385i
$285$	0.910993	+	1.57789i	0.0539626	+	0.0934659i
$286$	1.59002			0.0940201
$287$	−3.59883	+	10.1164i	−0.212432	+	0.597155i
$288$	−5.33178			−0.314178
$289$	−3.19963	−	5.54192i	−0.188214	−	0.325995i
$290$	−0.143142	+	0.247929i	−0.00840558	+	0.0145589i
$291$	1.82664	−	3.16384i	0.107080	−	0.185467i
$292$	−9.94276	−	17.2214i	−0.581856	−	1.00780i
$293$	−11.8500			−0.692286			−0.346143	−	0.938182i	$-0.612509\pi$
$293$	−11.8500			−0.692286			−0.346143	+	0.938182i	$0.612509\pi$
$294$	2.99809	+	2.44215i	0.174852	+	0.142429i
$295$	18.8601			1.09808
$296$	−1.72964	−	2.99583i	−0.100534	−	0.174129i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	0.377146	−	0.653236i	0.0218475	−	0.0378409i
$299$	5.25567	+	9.10309i	0.303943	+	0.526445i
$300$	4.18935			0.241872
$301$	4.10362	−	11.5354i	0.236529	−	0.664890i
$302$	−8.81038			−0.506980
$303$	−0.142189	−	0.246278i	−0.00816852	−	0.0141483i
$304$	1.29610	−	2.24491i	0.0743365	−	0.128755i
$305$	−1.40998	+	2.44215i	−0.0807349	+	0.139837i
$306$	1.33608	+	2.31416i	0.0763786	+	0.132292i
$307$	19.5894			1.11803			0.559013	−	0.829159i	$-0.311180\pi$
$307$	19.5894			1.11803			0.559013	+	0.829159i	$0.311180\pi$
$308$	−4.41022	+	0.810814i	−0.251296	+	0.0462004i
$309$	−16.6934			−0.949656
$310$	2.83334	+	4.90748i	0.160923	+	0.278726i
$311$	10.7008	−	18.5344i	0.606788	−	1.05099i	−0.384978	−	0.922926i	$-0.625791\pi$
$311$	10.7008	−	18.5344i	0.606788	−	1.05099i	0.991766	−	0.128062i	$-0.0408758\pi$
$312$	−2.93745	+	5.08781i	−0.166300	+	0.288040i
$313$	6.66392	+	11.5422i	0.376667	+	0.652407i	0.990575	−	0.136971i	$-0.0437367\pi$
$313$	6.66392	+	11.5422i	0.376667	+	0.652407i	−0.613908	+	0.789378i	$0.710403\pi$
$314$	4.63836			0.261758
$315$	2.72749	+	3.20282i	0.153677	+	0.180458i
$316$	14.7625			0.830458
$317$	3.54776	+	6.14490i	0.199262	+	0.345132i	0.948289	−	0.317407i	$-0.102812\pi$
$317$	3.54776	+	6.14490i	0.199262	+	0.345132i	−0.749027	+	0.662539i	$0.769479\pi$
$318$	1.57816	−	2.73345i	0.0884986	−	0.153284i
$319$	−0.162968	+	0.282268i	−0.00912444	+	0.0158040i
$320$	1.25535	+	2.17434i	0.0701765	+	0.121549i
$321$	17.9495			1.00184
$322$	3.46048	+	4.06354i	0.192845	+	0.226452i
$323$	−5.54297			−0.308419
$324$	0.847422	+	1.46778i	0.0470790	+	0.0815432i
$325$	3.55738	−	6.16156i	0.197328	−	0.341782i
$326$	−4.78194	+	8.28257i	−0.264847	+	0.458729i
$327$	−5.54399	−	9.60247i	−0.306583	−	0.531018i
$328$	−8.28345			−0.457377
$329$	−0.794059	+	0.145987i	−0.0437779	+	0.00804852i
$330$	0.878345			0.0483513
$331$	−10.3675	−	17.9570i	−0.569849	−	0.987007i	−0.996580	−	0.0826290i	$-0.973668\pi$
$331$	−10.3675	−	17.9570i	−0.569849	−	0.987007i	0.426731	−	0.904378i	$-0.359665\pi$
$332$	7.12560	−	12.3419i	0.391068	−	0.677350i
$333$	−0.847422	+	1.46778i	−0.0464384	+	0.0804337i
$334$	5.10827	+	8.84778i	0.279512	+	0.484129i
$335$	24.2820			1.32667
$336$	2.00602	−	5.63899i	0.109437	−	0.307632i
$337$	−5.30755			−0.289121			−0.144560	−	0.989496i	$-0.546177\pi$
$337$	−5.30755			−0.289121			−0.144560	+	0.989496i	$0.546177\pi$
$338$	−1.30234	−	2.25572i	−0.0708380	−	0.122695i
$339$	−0.862216	+	1.49340i	−0.0468291	+	0.0811105i
$340$	6.51785	−	11.2893i	0.353480	−	0.612246i
$341$	3.22577	+	5.58719i	0.174685	+	0.302563i
$342$	0.632998			0.0342286
$343$	−15.8328	+	9.60845i	−0.854891	+	0.518808i
$344$	9.44532			0.509258
$345$	2.90328	+	5.02863i	0.156307	+	0.270732i
$346$	3.38849	−	5.86903i	0.182166	−	0.315521i
$347$	−8.40156	+	14.5519i	−0.451019	+	0.781188i	−0.998450	−	0.0556630i	$-0.982273\pi$
$347$	−8.40156	+	14.5519i	−0.451019	+	0.781188i	0.547430	+	0.836851i	$0.315606\pi$
$348$	−0.276205	−	0.478401i	−0.0148061	−	0.0256450i
$349$	−0.870459			−0.0465946			−0.0232973	−	0.999729i	$-0.507416\pi$
$349$	−0.870459			−0.0465946			−0.0232973	+	0.999729i	$0.507416\pi$
$350$	1.21084	−	3.40370i	0.0647220	−	0.181936i
$351$	2.87834			0.153635
$352$	−2.66589	−	4.61746i	−0.142093	−	0.246111i
$353$	0.469077	−	0.812465i	0.0249665	−	0.0432432i	−0.853272	−	0.521466i	$-0.825385\pi$
$353$	0.469077	−	0.812465i	0.0249665	−	0.0432432i	0.878239	+	0.478223i	$0.158719\pi$
$354$	3.27620	−	5.67455i	0.174128	−	0.301599i
$355$	−7.28761	−	12.6225i	−0.386786	−	0.669934i
$356$	9.74499			0.516483
$357$	−12.5873	+	2.31416i	−0.666189	+	0.122478i
$358$	−7.62968			−0.403241
$359$	13.5050	+	23.3913i	0.712765	+	1.23454i	0.963815	+	0.266571i	$0.0858905\pi$
$359$	13.5050	+	23.3913i	0.712765	+	1.23454i	−0.251051	+	0.967974i	$0.580776\pi$
$360$	−1.62267	+	2.81055i	−0.0855224	+	0.148129i
$361$	8.84347	−	15.3173i	0.465446	−	0.806176i
$362$	−5.18399	−	8.97894i	−0.272465	−	0.471923i
$363$	1.00000			0.0524864
$364$	−8.36820	−	9.82654i	−0.438613	−	0.515051i
$365$	−18.6557			−0.976483
$366$	0.489856	+	0.848456i	0.0256052	+	0.0443495i
$367$	14.2055	−	24.6046i	0.741520	−	1.28435i	−0.210283	−	0.977641i	$-0.567439\pi$
$367$	14.2055	−	24.6046i	0.741520	−	1.28435i	0.951803	−	0.306710i	$-0.0992281\pi$
$368$	4.13060	−	7.15441i	0.215322	−	0.372949i
$369$	2.02920	+	3.51467i	0.105636	+	0.182967i
$370$	−1.48866			−0.0773916
$371$	9.80118	+	11.5092i	0.508852	+	0.597530i
$372$	−10.9343			−0.566919
$373$	4.87338	+	8.44094i	0.252334	+	0.437055i	0.964168	−	0.265293i	$-0.0854685\pi$
$373$	4.87338	+	8.44094i	0.252334	+	0.437055i	−0.711834	+	0.702348i	$0.752135\pi$
$374$	−1.33608	+	2.31416i	−0.0690870	+	0.119662i
$375$	5.94019	−	10.2887i	0.306750	−	0.531307i
$376$	−0.311422	−	0.539399i	−0.0160604	−	0.0278174i
$377$	−0.938154			−0.0483174
$378$	1.43745	−	0.264273i	0.0739343	−	0.0135927i
$379$	−33.1034			−1.70041			−0.850204	−	0.526454i	$-0.823521\pi$
$379$	−33.1034			−1.70041			−0.850204	+	0.526454i	$0.823521\pi$
$380$	−1.54399	−	2.67427i	−0.0792051	−	0.137187i
$381$	−10.1837	+	17.6388i	−0.521729	+	0.903661i
$382$	2.24190	−	3.88308i	0.114705	−	0.198676i
$383$	5.34418	+	9.25639i	0.273075	+	0.472980i	0.969648	−	0.244507i	$-0.0786260\pi$
$383$	5.34418	+	9.25639i	0.273075	+	0.472980i	−0.696573	+	0.717486i	$0.745293\pi$
$384$	11.5358			0.588686
$385$	−1.40998	+	3.96349i	−0.0718590	+	0.201998i
$386$	−0.657790			−0.0334806
$387$	−2.31382	−	4.00765i	−0.117618	−	0.203721i
$388$	−3.09587	+	5.36221i	−0.157169	+	0.272225i
$389$	19.2942	−	33.4185i	0.978253	−	1.69438i	0.309501	−	0.950899i	$-0.399838\pi$
$389$	19.2942	−	33.4185i	0.978253	−	1.69438i	0.668753	−	0.743485i	$-0.266829\pi$
$390$	1.26409	+	2.18947i	0.0640097	+	0.110868i
$391$	−17.6651			−0.893363
$392$	−11.0775	−	9.02336i	−0.559498	−	0.455748i
$393$	20.1821			1.01805
$394$	−7.38912	−	12.7983i	−0.372258	−	0.644770i
$395$	6.92477	−	11.9941i	0.348423	−	0.603486i
$396$	−0.847422	+	1.46778i	−0.0425846	+	0.0737586i
$397$	−6.96957	−	12.0716i	−0.349793	−	0.605859i	0.636420	−	0.771343i	$-0.280415\pi$
$397$	−6.96957	−	12.0716i	−0.349793	−	0.605859i	−0.986212	+	0.165484i	$0.947081\pi$
$398$	3.33306			0.167071
$399$	−1.01613	+	2.85637i	−0.0508701	+	0.142997i
$400$	−5.59171			−0.279586
$401$	6.56854	+	11.3770i	0.328017	+	0.568142i	0.982118	−	0.188265i	$-0.0602863\pi$
$401$	6.56854	+	11.3770i	0.328017	+	0.568142i	−0.654101	+	0.756407i	$0.726953\pi$
$402$	4.21806	−	7.30589i	0.210378	−	0.364385i
$403$	−9.28487	+	16.0819i	−0.462512	+	0.801095i
$404$	0.240987	+	0.417402i	0.0119896	+	0.0207665i
$405$	1.59002			0.0790090
$406$	−0.468515	+	0.0861359i	−0.0232520	+	0.00427485i
$407$	−1.69484			−0.0840103
$408$	−4.93660	−	8.55045i	−0.244398	−	0.423310i
$409$	12.5164	−	21.6791i	0.618898	−	1.07196i	−0.370789	−	0.928717i	$-0.620913\pi$
$409$	12.5164	−	21.6791i	0.618898	−	1.07196i	0.989687	−	0.143246i	$-0.0457540\pi$
$410$	−1.78233	+	3.08709i	−0.0880232	+	0.152461i
$411$	10.6316	+	18.4144i	0.524417	+	0.908317i
$412$	28.2928			1.39388
$413$	20.3470	+	23.8929i	1.00121	+	1.17569i
$414$	2.01733			0.0991463
$415$	−6.68491	−	11.5786i	−0.328149	−	0.568371i
$416$	7.67336	−	13.2906i	0.376217	−	0.651627i
$417$	−2.63976	+	4.57219i	−0.129269	+	0.223901i
$418$	0.316499	+	0.548192i	0.0154805	+	0.0268130i
$419$	5.04297			0.246365			0.123183	−	0.992384i	$-0.460690\pi$
$419$	5.04297			0.246365			0.123183	+	0.992384i	$0.460690\pi$
$420$	−4.62267	−	5.42828i	−0.225563	−	0.264873i
$421$	9.94055			0.484473			0.242236	−	0.970217i	$-0.422119\pi$
$421$	9.94055			0.484473			0.242236	+	0.970217i	$0.422119\pi$
$422$	−5.65116	−	9.78810i	−0.275094	−	0.476477i
$423$	−0.152578	+	0.264273i	−0.00741860	+	0.0128494i
$424$	−5.83104	+	10.0997i	−0.283180	+	0.490483i
$425$	5.97844	+	10.3550i	0.289997	+	0.502290i
$426$	−5.06375			−0.245340
$427$	−4.61496	+	0.848456i	−0.223334	+	0.0410597i
$428$	−30.4216			−1.47048
$429$	1.43917	+	2.49272i	0.0694839	+	0.120350i
$430$	2.03233	−	3.52010i	0.0980077	−	0.169754i
$431$	−6.84379	+	11.8538i	−0.329654	+	0.570977i	−0.982443	−	0.186562i	$-0.940265\pi$
$431$	−6.84379	+	11.8538i	−0.329654	+	0.570977i	0.652789	+	0.757539i	$0.273599\pi$
$432$	−1.13109	−	1.95911i	−0.0544197	−	0.0942576i
$433$	−4.26360			−0.204895			−0.102448	−	0.994738i	$-0.532667\pi$
$433$	−4.26360			−0.204895			−0.102448	+	0.994738i	$0.532667\pi$
$434$	−3.16032	+	8.88377i	−0.151700	+	0.426435i
$435$	−0.518245			−0.0248480
$436$	9.39620	+	16.2747i	0.449996	+	0.779417i
$437$	−2.09231	+	3.62399i	−0.100089	+	0.173359i
$438$	−3.24070	+	5.61305i	−0.154846	+	0.268202i
$439$	11.7016	+	20.2678i	0.558487	+	0.967328i	0.997623	+	0.0689072i	$0.0219513\pi$
$439$	11.7016	+	20.2678i	0.558487	+	0.967328i	−0.439136	+	0.898421i	$0.644715\pi$
$440$	−3.24535			−0.154716
$441$	−1.11496	+	6.91063i	−0.0530935	+	0.329078i
$442$	−7.69139			−0.365842
$443$	7.35960	+	12.7472i	0.349665	+	0.605638i	0.986190	−	0.165618i	$-0.0529620\pi$
$443$	7.35960	+	12.7472i	0.349665	+	0.605638i	−0.636525	+	0.771256i	$0.719629\pi$
$444$	1.43625	−	2.48765i	0.0681613	−	0.118059i
$445$	4.57115	−	7.91747i	0.216693	−	0.375324i
$446$	−8.17699	−	14.1630i	−0.387192	−	0.670636i
$447$	1.36546			0.0645839
$448$	−1.40023	+	3.93610i	−0.0661548	+	0.185963i
$449$	−34.8625			−1.64526			−0.822631	−	0.568575i	$-0.807495\pi$
$449$	−34.8625			−1.64526			−0.822631	+	0.568575i	$0.807495\pi$
$450$	−0.682729	−	1.18252i	−0.0321841	−	0.0557446i
$451$	−2.02920	+	3.51467i	−0.0955512	+	0.165499i
$452$	1.46132	−	2.53108i	0.0687348	−	0.119052i
$453$	−7.97450	−	13.8122i	−0.374675	−	0.648956i
$454$	13.3037			0.624376
$455$	−11.9091	+	2.18947i	−0.558305	+	0.102644i
$456$	−2.33883			−0.109526
$457$	5.30068	+	9.18105i	0.247955	+	0.429471i	0.962958	−	0.269650i	$-0.0869080\pi$
$457$	5.30068	+	9.18105i	0.247955	+	0.429471i	−0.715003	+	0.699121i	$0.753575\pi$
$458$	−1.44033	+	2.49472i	−0.0673020	+	0.116571i
$459$	−2.41864	+	4.18921i	−0.112892	+	0.195535i
$460$	−4.92061	−	8.52275i	−0.229425	−	0.397375i
$461$	−6.84418			−0.318765			−0.159383	−	0.987217i	$-0.550950\pi$
$461$	−6.84418			−0.318765			−0.159383	+	0.987217i	$0.550950\pi$
$462$	0.947591	+	1.11273i	0.0440859	+	0.0517688i
$463$	−11.7299			−0.545136			−0.272568	−	0.962137i	$-0.587873\pi$
$463$	−11.7299			−0.545136			−0.272568	+	0.962137i	$0.587873\pi$
$464$	0.368663	+	0.638542i	0.0171147	+	0.0296436i
$465$	−5.12905	+	8.88377i	−0.237854	+	0.411975i
$466$	0.868908	−	1.50499i	0.0402514	−	0.0697175i
$467$	19.1443	+	33.1590i	0.885894	+	1.53441i	0.844685	+	0.535263i	$0.179788\pi$
$467$	19.1443	+	33.1590i	0.885894	+	1.53441i	0.0412088	+	0.999151i	$0.486879\pi$
$468$	−4.87834			−0.225502
$469$	26.1964	+	30.7616i	1.20964	+	1.42044i
$470$	−0.268032			−0.0123634
$471$	4.19830	+	7.27166i	0.193447	+	0.335060i
$472$	−12.1051	+	20.9666i	−0.557181	+	0.965065i
$473$	2.31382	−	4.00765i	0.106390	−	0.184272i
$474$	−2.40582	−	4.16700i	−0.110503	−	0.191396i
$475$	2.83242			0.129961
$476$	21.3335	−	3.92213i	0.977818	−	0.179771i
$477$	5.71372			0.261613
$478$	0.760848	+	1.31783i	0.0348004	+	0.0602760i
$479$	−6.31446	+	10.9370i	−0.288515	+	0.499722i	−0.973455	−	0.228876i	$-0.926495\pi$
$479$	−6.31446	+	10.9370i	−0.288515	+	0.499722i	0.684941	+	0.728599i	$0.259828\pi$
$480$	4.23884	−	7.34188i	0.193475	−	0.335109i
$481$	−2.43917	−	4.22477i	−0.111217	−	0.192633i
$482$	4.98803			0.227199
$483$	−3.23834	+	9.10309i	−0.147350	+	0.414205i
$484$	−1.69484			−0.0770384
$485$	2.90441	+	5.03058i	0.131882	+	0.228427i
$486$	0.276205	−	0.478401i	0.0125289	−	0.0217007i
$487$	−17.8070	+	30.8426i	−0.806911	+	1.39761i	0.108082	+	0.994142i	$0.465529\pi$
$487$	−17.8070	+	30.8426i	−0.806911	+	1.39761i	−0.914993	+	0.403470i	$0.867804\pi$
$488$	−1.80994	−	3.13491i	−0.0819322	−	0.141911i
$489$	−17.3130			−0.782923
$490$	−5.74636	+	2.18684i	−0.259594	+	0.0987915i
$491$	7.59854			0.342917			0.171459	−	0.985191i	$-0.445152\pi$
$491$	7.59854			0.342917			0.171459	+	0.985191i	$0.445152\pi$
$492$	−3.43917	−	5.95682i	−0.155050	−	0.268554i
$493$	0.788320	−	1.36541i	0.0355041	−	0.0614950i
$494$	−0.910993	+	1.57789i	−0.0409875	+	0.0709925i
$495$	0.795012	+	1.37700i	0.0357332	+	0.0618916i
$496$	14.5945			0.655315
$497$	8.12866	−	22.8499i	0.364620	−	1.02496i
$498$	−4.64497			−0.208146
$499$	−0.803040	−	1.39091i	−0.0359490	−	0.0622655i	0.847491	−	0.530810i	$-0.178112\pi$
$499$	−0.803040	−	1.39091i	−0.0359490	−	0.0622655i	−0.883440	+	0.468544i	$0.844779\pi$
$500$	−10.0677	+	17.4378i	−0.450241	+	0.779840i
$501$	−9.24725	+	16.0167i	−0.413137	+	0.715574i
$502$	−1.85923	−	3.22027i	−0.0829813	−	0.143728i
$503$	−38.6291			−1.72239			−0.861194	−	0.508277i	$-0.830283\pi$
$503$	−38.6291			−1.72239			−0.861194	+	0.508277i	$0.830283\pi$
$504$	−5.31114	+	0.976448i	−0.236577	+	0.0434944i
$505$	0.452167			0.0201212
$506$	1.00866	+	1.74706i	0.0448406	+	0.0776662i
$507$	2.35757	−	4.08342i	0.104703	−	0.181351i
$508$	17.2599	−	29.8950i	0.765782	−	1.32637i
$509$	−15.8991	−	27.5381i	−0.704716	−	1.22060i	−0.966794	−	0.255558i	$-0.917741\pi$
$509$	−15.8991	−	27.5381i	−0.704716	−	1.22060i	0.262078	−	0.965047i	$-0.415592\pi$
$510$	−4.24880			−0.188140
$511$	−20.1264	−	23.6339i	−0.890341	−	1.04550i
$512$	−21.2960			−0.941159
$513$	0.572943	+	0.992366i	0.0252960	+	0.0438140i
$514$	7.64793	−	13.2466i	0.337336	−	0.584282i
$515$	13.2715	−	22.9869i	0.584811	−	1.01292i
$516$	3.92156	+	6.79235i	0.172637	+	0.299016i
$517$	−0.305156			−0.0134208
$518$	−1.60602	−	1.88590i	−0.0705644	−	0.0828618i
$519$	12.2680			0.538507
$520$	−4.67061	−	8.08974i	−0.204820	−	0.354759i
$521$	−6.03416	+	10.4515i	−0.264362	+	0.457888i	−0.967396	−	0.253268i	$-0.918495\pi$
$521$	−6.03416	+	10.4515i	−0.264362	+	0.457888i	0.703035	+	0.711156i	$0.251828\pi$
$522$	−0.0900249	+	0.155928i	−0.00394028	+	0.00682477i
$523$	−0.142825	−	0.247380i	−0.00624531	−	0.0108172i	0.862886	−	0.505399i	$-0.168655\pi$
$523$	−0.142825	−	0.247380i	−0.00624531	−	0.0108172i	−0.869131	+	0.494582i	$0.835321\pi$
$524$	−34.2055			−1.49427
$525$	6.43202	−	1.18252i	0.280717	−	0.0516094i
$526$	−2.54297			−0.110879
$527$	−15.6039	−	27.0268i	−0.679718	−	1.17731i
$528$	1.13109	−	1.95911i	0.0492244	−	0.0852592i
$529$	4.83192	−	8.36913i	0.210083	−	0.363875i
$530$	2.50931	+	4.34625i	0.108997	+	0.188789i
$531$	11.8615			0.514746
$532$	1.72218	−	4.84110i	0.0746660	−	0.209888i
$533$	−11.6815			−0.505980
$534$	−1.58812	−	2.75070i	−0.0687246	−	0.119035i
$535$	−14.2701	+	24.7165i	−0.616949	+	1.06859i
$536$	−15.5851	+	26.9941i	−0.673172	+	1.16597i
$537$	−6.90582	−	11.9612i	−0.298008	−	0.516165i
$538$	−10.5567			−0.455132
$539$	−6.54227	+	2.48973i	−0.281795	+	0.107240i
$540$	−2.69484			−0.115968
$541$	−1.40501	−	2.43355i	−0.0604060	−	0.104626i	0.834241	−	0.551400i	$-0.185906\pi$
$541$	−1.40501	−	2.43355i	−0.0604060	−	0.104626i	−0.894647	+	0.446774i	$0.852573\pi$
$542$	4.24605	−	7.35438i	0.182384	−	0.315898i
$543$	9.38433	−	16.2541i	0.402720	−	0.697532i
$544$	12.8957	+	22.3359i	0.552897	+	0.957646i
$545$	17.6302			0.755193
$546$	−1.40998	+	3.96349i	−0.0603414	+	0.169622i
$547$	−20.8781			−0.892681			−0.446341	−	0.894863i	$-0.647273\pi$
$547$	−20.8781			−0.892681			−0.446341	+	0.894863i	$0.647273\pi$
$548$	−18.0189	−	31.2096i	−0.769728	−	1.33321i
$549$	−0.886763	+	1.53592i	−0.0378461	+	0.0655514i
$550$	0.682729	−	1.18252i	0.0291116	−	0.0504229i
$551$	−0.186742	−	0.323447i	−0.00795549	−	0.0137793i
$552$	−7.45371			−0.317251
$553$	22.6653	−	4.16700i	0.963828	−	0.177199i
$554$	5.18695			0.220372
$555$	−1.34742	−	2.33380i	−0.0571949	−	0.0990644i
$556$	4.47397	−	7.74915i	0.189739	−	0.328637i
$557$	−9.13771	+	15.8270i	−0.387177	+	0.670611i	−0.992069	−	0.125697i	$-0.959883\pi$
$557$	−9.13771	+	15.8270i	−0.387177	+	0.670611i	0.604891	+	0.796308i	$0.293217\pi$
$558$	1.78194	+	3.08642i	0.0754357	+	0.130658i
$559$	13.3199			0.563374
$560$	6.17009	+	7.24536i	0.260734	+	0.306172i
$561$	−4.83728			−0.204230
$562$	7.45167	+	12.9067i	0.314330	+	0.544435i
$563$	−8.14944	+	14.1152i	−0.343458	+	0.594886i	−0.985072	−	0.172141i	$-0.944932\pi$
$563$	−8.14944	+	14.1152i	−0.343458	+	0.594886i	0.641615	+	0.767027i	$0.278265\pi$
$564$	0.258596	−	0.447902i	0.0108889	−	0.0188601i
$565$	−1.37094	−	2.37455i	−0.0576761	−	0.0998979i
$566$	13.0234			0.547413
$567$	1.71538	+	2.01432i	0.0720391	+	0.0845934i
$568$	18.7098			0.785045
$569$	−8.37221	−	14.5011i	−0.350981	−	0.607918i	0.635440	−	0.772150i	$-0.280819\pi$
$569$	−8.37221	−	14.5011i	−0.350981	−	0.607918i	−0.986422	+	0.164232i	$0.947485\pi$
$570$	−0.503241	+	0.871640i	−0.0210785	+	0.0365090i
$571$	−12.1461	+	21.0377i	−0.508300	+	0.880401i	0.491654	+	0.870791i	$0.336392\pi$
$571$	−12.1461	+	21.0377i	−0.508300	+	0.880401i	−0.999954	+	0.00961042i	$0.996941\pi$
$572$	−2.43917	−	4.22477i	−0.101987	−	0.176647i
$573$	8.11679			0.339084
$574$	−5.83373	+	1.07252i	−0.243495	+	0.0447663i
$575$	9.02677			0.376442
$576$	0.789519	+	1.36749i	0.0328966	+	0.0569786i
$577$	−11.1586	+	19.3273i	−0.464540	+	0.804607i	−0.999181	−	0.0404725i	$-0.987114\pi$
$577$	−11.1586	+	19.3273i	−0.464540	+	0.804607i	0.534641	+	0.845080i	$0.320447\pi$
$578$	1.76751	−	3.06141i	0.0735185	−	0.127338i
$579$	−0.595383	−	1.03123i	−0.0247433	−	0.0428566i
$580$	0.878345			0.0364713
$581$	7.45640	−	20.9602i	0.309344	−	0.869575i
$582$	2.01811			0.0836533
$583$	2.85686	+	4.94822i	0.118319	+	0.204934i
$584$	11.9739	−	20.7393i	0.495482	−	0.858200i
$585$	−2.28832	+	3.96349i	−0.0946104	+	0.163870i
$586$	−3.27303	−	5.66906i	−0.135208	−	0.234187i
$587$	−26.6944			−1.10180			−0.550898	−	0.834572i	$-0.685715\pi$
$587$	−26.6944			−1.10180			−0.550898	+	0.834572i	$0.685715\pi$
$588$	1.88969	−	11.7124i	0.0779294	−	0.483013i
$589$	−7.39272			−0.304612
$590$	5.20925	+	9.02268i	0.214461	+	0.371458i
$591$	13.3762	−	23.1682i	0.550222	−	0.953012i
$592$	−1.91702	+	3.32038i	−0.0787892	+	0.136467i
$593$	11.4721	+	19.8702i	0.471101	+	0.815971i	0.999454	−	0.0330538i	$-0.0105233\pi$
$593$	11.4721	+	19.8702i	0.471101	+	0.815971i	−0.528352	+	0.849025i	$0.677190\pi$
$594$	0.552409			0.0226656
$595$	6.82044	−	19.1725i	0.279611	−	0.785995i
$596$	−2.31424			−0.0947948
$597$	3.01684	+	5.22531i	0.123471	+	0.213858i
$598$	−2.90328	+	5.02863i	−0.118724	+	0.205636i
$599$	10.3521	−	17.9303i	0.422974	−	0.732613i	−0.573255	−	0.819377i	$-0.694319\pi$
$599$	10.3521	−	17.9303i	0.422974	−	0.732613i	0.996229	+	0.0867645i	$0.0276528\pi$
$600$	2.52258	+	4.36923i	0.102984	+	0.178373i
$601$	−11.2354			−0.458302			−0.229151	−	0.973391i	$-0.573595\pi$
$601$	−11.2354			−0.458302			−0.229151	+	0.973391i	$0.573595\pi$
$602$	6.65199	−	1.22296i	0.271115	−	0.0498441i
$603$	15.2715			0.621903
$604$	13.5155	+	23.4096i	0.549939	+	0.952523i
$605$	−0.795012	+	1.37700i	−0.0323219	+	0.0559831i
$606$	0.0785463	−	0.136046i	0.00319073	−	0.00552650i
$607$	3.72700	+	6.45535i	0.151274	+	0.262015i	0.931696	−	0.363239i	$-0.118329\pi$
$607$	3.72700	+	6.45535i	0.151274	+	0.262015i	−0.780422	+	0.625253i	$0.784996\pi$
$608$	6.10962			0.247778
$609$	−0.559102	−	0.656538i	−0.0226560	−	0.0266043i
$610$	−1.55777			−0.0630721
$611$	−0.439172	−	0.760669i	−0.0177670	−	0.0307734i
$612$	4.09922	−	7.10005i	0.165701	−	0.287002i
$613$	−10.5940	+	18.3493i	−0.427886	+	0.741121i	−0.996685	−	0.0813559i	$-0.974075\pi$
$613$	−10.5940	+	18.3493i	−0.427886	+	0.741121i	0.568799	+	0.822477i	$0.307408\pi$
$614$	5.41068	+	9.37158i	0.218357	+	0.378206i
$615$	−6.45295			−0.260208
$616$	−3.50120	−	4.11136i	−0.141067	−	0.165651i
$617$	39.7670			1.60096			0.800479	−	0.599361i	$-0.204578\pi$
$617$	39.7670			1.60096			0.800479	+	0.599361i	$0.204578\pi$
$618$	−4.61080	−	7.98615i	−0.185474	−	0.321250i
$619$	−8.64771	+	14.9783i	−0.347581	+	0.602028i	−0.985819	−	0.167811i	$-0.946330\pi$
$619$	−8.64771	+	14.9783i	−0.347581	+	0.602028i	0.638238	+	0.769839i	$0.279663\pi$
$620$	8.69294	−	15.0566i	0.349117	−	0.604688i
$621$	1.82594	+	3.16261i	0.0732723	+	0.126911i
$622$	11.8225			0.474038
$623$	14.9618	−	2.75070i	0.599430	−	0.110205i
$624$	6.51134			0.260662
$625$	3.26550	+	5.65601i	0.130620	+	0.226240i
$626$	−3.68121	+	6.37605i	−0.147131	+	0.254838i
$627$	−0.572943	+	0.992366i	−0.0228811	+	0.0396313i
$628$	−7.11545	−	12.3243i	−0.283938	−	0.491794i
$629$	8.19843			0.326893
$630$	−0.778884	+	2.18947i	−0.0310315	+	0.0872305i
$631$	−22.8639			−0.910198			−0.455099	−	0.890441i	$-0.650396\pi$
$631$	−22.8639			−0.910198			−0.455099	+	0.890441i	$0.650396\pi$
$632$	8.88912	+	15.3964i	0.353590	+	0.612436i
$633$	10.2300	−	17.7189i	0.406607	−	0.704264i
$634$	−1.95982	+	3.39450i	−0.0778342	+	0.134813i
$635$	−16.1924	−	28.0461i	−0.642576	−	1.11297i
$636$	−9.68386			−0.383990
$637$	−15.6216	−	12.7249i	−0.618952	−	0.504178i
$638$	−0.180050			−0.00712824
$639$	−4.58333	−	7.93856i	−0.181314	−	0.314045i
$640$	−9.17114	+	15.8849i	−0.362521	+	0.627905i
$641$	3.36284	−	5.82462i	0.132824	−	0.230058i	−0.791940	−	0.610599i	$-0.790929\pi$
$641$	3.36284	−	5.82462i	0.132824	−	0.230058i	0.924764	+	0.380541i	$0.124262\pi$
$642$	4.95773	+	8.58705i	0.195666	+	0.338904i
$643$	8.16118			0.321845			0.160923	−	0.986967i	$-0.448553\pi$
$643$	8.16118			0.321845			0.160923	+	0.986967i	$0.448553\pi$
$644$	5.48849	−	15.4283i	0.216277	−	0.607961i
$645$	7.35806			0.289723
$646$	−1.53099	−	2.65176i	−0.0602361	−	0.104332i
$647$	9.83192	−	17.0294i	0.386533	−	0.669494i	−0.605448	−	0.795885i	$-0.707006\pi$
$647$	9.83192	−	17.0294i	0.386533	−	0.669494i	0.991981	+	0.126391i	$0.0403393\pi$
$648$	−1.02053	+	1.76762i	−0.0400903	+	0.0694385i
$649$	5.93075	+	10.2724i	0.232802	+	0.403226i
$650$	3.93026			0.154157
$651$	−16.7878	+	3.08642i	−0.657965	+	0.120966i
$652$	29.3429			1.14916
$653$	11.1517	+	19.3154i	0.436401	+	0.755869i	0.997409	−	0.0719417i	$-0.0229195\pi$
$653$	11.1517	+	19.3154i	0.436401	+	0.755869i	−0.561008	+	0.827811i	$0.689586\pi$
$654$	3.06255	−	5.30450i	0.119755	−	0.207422i
$655$	−16.0450	+	27.7908i	−0.626930	+	1.08588i
$656$	4.59042	+	7.95083i	0.179226	+	0.310428i
$657$	−11.7330			−0.457746
$658$	−0.289163	−	0.339556i	−0.0112728	−	0.0132373i
$659$	19.0497			0.742072			0.371036	−	0.928619i	$-0.379003\pi$
$659$	19.0497			0.742072			0.371036	+	0.928619i	$0.379003\pi$
$660$	−1.34742	−	2.33380i	−0.0524483	−	0.0908432i
$661$	−12.1612	+	21.0638i	−0.473015	+	0.819286i	−0.999523	−	0.0308845i	$-0.990168\pi$
$661$	−12.1612	+	21.0638i	−0.473015	+	0.819286i	0.526508	+	0.850170i	$0.323501\pi$
$662$	5.72710	−	9.91963i	0.222590	−	0.385537i
$663$	−6.96168	−	12.0580i	−0.270369	−	0.468293i
$664$	17.1624			0.666032
$665$	−3.12539	−	3.67006i	−0.121198	−	0.142319i
$666$	−0.936248			−0.0362789
$667$	−0.595137	−	1.03081i	−0.0230438	−	0.0399130i
$668$	15.6726	−	27.1458i	0.606393	−	1.05030i
$669$	14.8024	−	25.6385i	0.572294	−	0.991242i
$670$	6.70681	+	11.6165i	0.259107	+	0.448786i
$671$	−1.77353			−0.0684662
$672$	13.8741	−	2.55073i	0.535203	−	0.0983965i
$673$	42.6054			1.64232			0.821159	−	0.570699i	$-0.193328\pi$
$673$	42.6054			1.64232			0.821159	+	0.570699i	$0.193328\pi$
$674$	−1.46597	−	2.53914i	−0.0564671	−	0.0978039i
$675$	1.23591	−	2.14066i	0.0475702	−	0.0823940i
$676$	−3.99571	+	6.92076i	−0.153681	+	0.266183i
$677$	6.98302	+	12.0949i	0.268379	+	0.464846i	0.968443	−	0.249233i	$-0.0801786\pi$
$677$	6.98302	+	12.0949i	0.268379	+	0.464846i	−0.700064	+	0.714080i	$0.746845\pi$
$678$	−0.952592			−0.0365841
$679$	−3.23960	+	9.10662i	−0.124324	+	0.349480i
$680$	15.6986			0.602016
$681$	12.0416	+	20.8566i	0.461434	+	0.799226i
$682$	−1.78194	+	3.08642i	−0.0682342	+	0.118185i
$683$	2.64173	−	4.57561i	0.101083	−	0.175081i	−0.811048	−	0.584979i	$-0.801103\pi$
$683$	2.64173	−	4.57561i	0.101083	−	0.175081i	0.912131	+	0.409899i	$0.134436\pi$
$684$	−0.971049	−	1.68191i	−0.0371290	−	0.0643093i
$685$	−33.8090			−1.29177
$686$	−8.96978	−	4.92052i	−0.342468	−	0.187866i
$687$	−5.21471			−0.198953
$688$	−5.23428	−	9.06605i	−0.199555	−	0.345640i
$689$	−8.22302	+	14.2427i	−0.313272	+	0.542603i
$690$	−1.60380	+	2.77786i	−0.0610557	+	0.105751i
$691$	−14.0658	−	24.3627i	−0.535088	−	0.926799i	−0.999159	−	0.0410014i	$-0.986945\pi$
$691$	−14.0658	−	24.3627i	−0.535088	−	0.926799i	0.464071	−	0.885798i	$-0.346388\pi$
$692$	−20.7924			−0.790408
$693$	−0.886763	+	2.49272i	−0.0336853	+	0.0946906i
$694$	−9.28220			−0.352347
$695$	−4.19728	−	7.26990i	−0.159212	−	0.275763i
$696$	0.332628	−	0.576128i	0.0126082	−	0.0218381i
$697$	9.81579	−	17.0014i	0.371800	−	0.643976i
$698$	−0.240425	−	0.416428i	−0.00910022	−	0.0157620i
$699$	3.14589			0.118988
$700$	−10.9013	+	2.00419i	−0.412030	+	0.0757512i
$701$	29.9421			1.13090			0.565449	−	0.824783i	$-0.308703\pi$
$701$	29.9421			1.13090			0.565449	+	0.824783i	$0.308703\pi$
$702$	0.795012	+	1.37700i	0.0300058	+	0.0519716i
$703$	0.971049	−	1.68191i	0.0366238	−	0.0634343i
$704$	−0.789519	+	1.36749i	−0.0297561	+	0.0515391i
$705$	−0.242603	−	0.420201i	−0.00913696	−	0.0158257i
$706$	0.518245			0.0195044
$707$	0.487814	+	0.572826i	0.0183461	+	0.0215433i
$708$	−20.1034			−0.755532
$709$	8.35341	+	14.4685i	0.313719	+	0.543377i	0.979164	−	0.203070i	$-0.0650917\pi$
$709$	8.35341	+	14.4685i	0.313719	+	0.543377i	−0.665446	+	0.746446i	$0.731758\pi$
$710$	4.02575	−	6.97280i	0.151084	−	0.261684i
$711$	4.35513	−	7.54331i	0.163330	−	0.282896i
$712$	5.86785	+	10.1634i	0.219907	+	0.380890i
$713$	−23.5602			−0.882335
$714$	−4.58376	−	5.38258i	−0.171543	−	0.201438i
$715$	−4.57664			−0.171157
$716$	11.7043	+	20.2724i	0.437409	+	0.757615i
$717$	−1.37733	+	2.38560i	−0.0514372	+	0.0890919i
$718$	−7.46027	+	12.9216i	−0.278415	+	0.482228i
$719$	−11.6748	−	20.2213i	−0.435395	−	0.754127i	0.561933	−	0.827183i	$-0.310058\pi$
$719$	−11.6748	−	20.2213i	−0.435395	−	0.754127i	−0.997328	+	0.0730563i	$0.976725\pi$
$720$	3.59693			0.134050
$721$	43.4386	−	7.98615i	1.61774	−	0.297420i
$722$	9.77044			0.363618
$723$	4.51479	+	7.81985i	0.167907	+	0.290823i
$724$	−15.9050	+	27.5482i	−0.591104	+	1.02382i
$725$	−0.402827	+	0.697717i	−0.0149606	+	0.0259125i
$726$	0.276205	+	0.478401i	0.0102509	+	0.0177551i
$727$	14.4262			0.535037			0.267519	−	0.963553i	$-0.413796\pi$
$727$	14.4262			0.535037			0.267519	+	0.963553i	$0.413796\pi$
$728$	5.20964	−	14.6445i	0.193082	−	0.542760i
$729$	1.00000			0.0370370
$730$	−5.15279	−	8.92489i	−0.190713	−	0.330325i
$731$	−11.1926	+	19.3861i	−0.413973	+	0.717022i
$732$	1.50292	−	2.60314i	0.0555497	−	0.0962149i
$733$	−13.4733	−	23.3365i	−0.497649	−	0.861953i	0.502347	−	0.864666i	$-0.332470\pi$
$733$	−13.4733	−	23.3365i	−0.497649	−	0.861953i	−0.999996	+	0.00271253i	$0.999137\pi$
$734$	15.6945			0.579294
$735$	−8.62955	−	7.02935i	−0.318306	−	0.259281i
$736$	19.4710			0.717710
$737$	7.63574	+	13.2255i	0.281266	+	0.487167i
$738$	−1.12095	+	1.94154i	−0.0412627	+	0.0714690i
$739$	22.2858	−	38.6001i	0.819795	−	1.41993i	−0.0860388	−	0.996292i	$-0.527421\pi$
$739$	22.2858	−	38.6001i	0.819795	−	1.41993i	0.905833	−	0.423634i	$-0.139246\pi$
$740$	2.28367	+	3.95543i	0.0839494	+	0.145405i
$741$	−3.29825			−0.121164
$742$	−2.79890	+	7.86780i	−0.102751	+	0.288836i
$743$	44.7041			1.64004			0.820018	−	0.572338i	$-0.193963\pi$
$743$	44.7041			1.64004			0.820018	+	0.572338i	$0.193963\pi$
$744$	−6.58400	−	11.4038i	−0.241381	−	0.418085i
$745$	−1.08556	+	1.88024i	−0.0397717	+	0.0688866i
$746$	−2.69210	+	4.66285i	−0.0985648	+	0.170719i
$747$	−4.20428	−	7.28203i	−0.153827	−	0.266435i
$748$	8.19843			0.299764
$749$	−46.7071	+	8.58705i	−1.70664	+	0.313764i
$750$	6.56283			0.239641
$751$	−22.2962	−	38.6182i	−0.813600	−	1.40920i	−0.910329	−	0.413886i	$-0.864171\pi$
$751$	−22.2962	−	38.6182i	−0.813600	−	1.40920i	0.0967287	−	0.995311i	$-0.469162\pi$
$752$	−0.345160	+	0.597834i	−0.0125867	+	0.0218008i
$753$	3.36567	−	5.82951i	0.122652	−	0.212439i
$754$	−0.259123	−	0.448814i	−0.00943669	−	0.0163448i
$755$	25.3593			0.922920
$756$	−2.90730	−	3.41396i	−0.105737	−	0.124164i
$757$	5.85842			0.212928			0.106464	−	0.994317i	$-0.466047\pi$
$757$	5.85842			0.212928			0.106464	+	0.994317i	$0.466047\pi$
$758$	−9.14332	−	15.8367i	−0.332100	−	0.575214i
$759$	−1.82594	+	3.16261i	−0.0662773	+	0.114796i
$760$	1.85940	−	3.22057i	0.0674475	−	0.116822i
$761$	19.2017	+	33.2583i	0.696061	+	1.20561i	0.969822	+	0.243816i	$0.0783992\pi$
$761$	19.2017	+	33.2583i	0.696061	+	1.20561i	−0.273760	+	0.961798i	$0.588267\pi$
$762$	−11.2512			−0.407588
$763$	19.0201	+	22.3347i	0.688573	+	0.808572i
$764$	−13.7567			−0.497700
$765$	−3.84570	−	6.66094i	−0.139041	−	0.240827i
$766$	−2.95218	+	5.11332i	−0.106666	+	0.184752i
$767$	−17.0708	+	29.5674i	−0.616389	+	1.06762i
$768$	1.60722	+	2.78378i	0.0579954	+	0.100451i
$769$	−1.44505			−0.0521099			−0.0260549	−	0.999661i	$-0.508294\pi$
$769$	−1.44505			−0.0521099			−0.0260549	+	0.999661i	$0.508294\pi$
$770$	−2.28558	+	0.420201i	−0.0823664	+	0.0151430i
$771$	27.6893			0.997207
$772$	1.00908	+	1.74778i	0.0363176	+	0.0629039i
$773$	1.05839	−	1.83319i	0.0380678	−	0.0659354i	−0.846364	−	0.532605i	$-0.821213\pi$
$773$	1.05839	−	1.83319i	0.0380678	−	0.0659354i	0.884432	+	0.466670i	$0.154546\pi$
$774$	1.27818	−	2.21387i	0.0459431	−	0.0795758i
$775$	7.97352	+	13.8105i	0.286417	+	0.496089i
$776$	−7.45660			−0.267676
$777$	1.50292	−	4.22477i	0.0539171	−	0.151563i
$778$	21.3166			0.764236
$779$	−2.32523	−	4.02741i	−0.0833099	−	0.144297i
$780$	3.87834	−	6.71749i	0.138867	−	0.240525i
$781$	4.58333	−	7.93856i	0.164005	−	0.284064i
$782$	−4.87919	−	8.45100i	−0.174479	−	0.302207i
$783$	−0.325935			−0.0116480
$784$	−2.52225	+	15.6331i	−0.0900803	+	0.558326i
$785$	−13.3508			−0.476510
$786$	5.57439	+	9.65512i	0.198832	+	0.344387i
$787$	7.64321	−	13.2384i	0.272451	−	0.471899i	−0.697038	−	0.717034i	$-0.745499\pi$
$787$	7.64321	−	13.2384i	0.272451	−	0.471899i	0.969489	+	0.245135i	$0.0788324\pi$
$788$	−22.6705	+	39.2665i	−0.807603	+	1.39881i
$789$	−2.30170	−	3.98667i	−0.0819429	−	0.141929i
$790$	7.65062			0.272197
$791$	1.52916	−	4.29853i	0.0543708	−	0.152838i
$792$	−2.04107			−0.0725261
$793$	−2.55241	−	4.42090i	−0.0906387	−	0.156991i
$794$	3.85006	−	6.66849i	0.136633	−	0.236656i
$795$	−4.54248	+	7.86780i	−0.161105	+	0.279042i
$796$	−5.11307	−	8.85609i	−0.181228	−	0.313896i
$797$	15.1839			0.537840			0.268920	−	0.963163i	$-0.413333\pi$
$797$	15.1839			0.537840			0.268920	+	0.963163i	$0.413333\pi$
$798$	−1.64715	+	0.302827i	−0.0583085	+	0.0107199i
$799$	1.47613			0.0522216
$800$	−6.58961	−	11.4135i	−0.232978	−	0.403529i
$801$	2.87489	−	4.97946i	0.101579	−	0.175941i
$802$	−3.62852	+	6.28479i	−0.128128	+	0.221923i
$803$	−5.86648	−	10.1610i	−0.207023	−	0.358575i
$804$	−25.8828			−0.912815
$805$	−9.96045	−	11.6963i	−0.351060	−	0.412240i
$806$	−10.2581			−0.361326
$807$	−9.55515	−	16.5500i	−0.336357	−	0.582588i
$808$	−0.290216	+	0.502669i	−0.0102098	+	0.0176838i
$809$	5.94467	−	10.2965i	0.209003	−	0.362004i	−0.742398	−	0.669960i	$-0.766311\pi$
$809$	5.94467	−	10.2965i	0.209003	−	0.362004i	0.951401	+	0.307955i	$0.0996447\pi$
$810$	0.439172	+	0.760669i	0.0154309	+	0.0267272i
$811$	−3.83804			−0.134772			−0.0673859	−	0.997727i	$-0.521466\pi$
$811$	−3.83804			−0.134772			−0.0673859	+	0.997727i	$0.521466\pi$
$812$	0.947591	+	1.11273i	0.0332539	+	0.0390491i
$813$	15.3729			0.539149
$814$	−0.468124	−	0.810814i	−0.0164077	−	0.0284190i
$815$	13.7641	−	23.8401i	0.482135	−	0.835082i
$816$	−5.47140	+	9.47675i	−0.191537	+	0.331753i
$817$	2.65137	+	4.59231i	0.0927598	+	0.160665i
$818$	13.8284			0.483499
$819$	−7.48986	+	1.37700i	−0.261717	+	0.0481163i
$820$	10.9367			0.381928
$821$	−15.8873	−	27.5175i	−0.554469	−	0.960368i	−0.997945	−	0.0640821i	$-0.979588\pi$
$821$	−15.8873	−	27.5175i	−0.554469	−	0.960368i	0.443476	−	0.896286i	$-0.353745\pi$
$822$	−5.87299	+	10.1723i	−0.204844	+	0.354800i
$823$	−6.19160	+	10.7242i	−0.215826	+	0.373821i	−0.953528	−	0.301305i	$-0.902578\pi$
$823$	−6.19160	+	10.7242i	−0.215826	+	0.373821i	0.737702	+	0.675126i	$0.235911\pi$
$824$	17.0362	+	29.5076i	0.593484	+	1.02794i
$825$	2.47182			0.0860578
$826$	−5.81043	+	16.3333i	−0.202171	+	0.568309i
$827$	−28.7072			−0.998248			−0.499124	−	0.866530i	$-0.666345\pi$
$827$	−28.7072			−0.998248			−0.499124	+	0.866530i	$0.666345\pi$
$828$	−3.09468	−	5.36013i	−0.107547	−	0.186278i
$829$	−1.35827	+	2.35260i	−0.0471748	+	0.0817091i	−0.888649	−	0.458589i	$-0.848355\pi$
$829$	−1.35827	+	2.35260i	−0.0471748	+	0.0817091i	0.841474	+	0.540298i	$0.181688\pi$
$830$	3.69281	−	6.39613i	0.128179	−	0.222013i
$831$	4.69484	+	8.13171i	0.162862	+	0.282086i
$832$	−4.54502			−0.157570
$833$	31.6468	−	12.0435i	1.09650	−	0.417283i
$834$	−2.91645			−0.100988
$835$	−14.7034	−	25.4670i	−0.508831	−	0.881321i
$836$	0.971049	−	1.68191i	0.0335844	−	0.0581699i
$837$	−3.22577	+	5.58719i	−0.111499	+	0.193122i
$838$	1.39289	+	2.41256i	0.0481167	+	0.0833406i
$839$	−48.9487			−1.68990			−0.844948	−	0.534848i	$-0.820369\pi$
$839$	−48.9487			−1.68990			−0.844948	+	0.534848i	$0.820369\pi$
$840$	2.87785	−	8.08974i	0.0992954	−	0.279123i
$841$	−28.8938			−0.996337
$842$	2.74563	+	4.75557i	0.0946206	+	0.163888i
$843$	−13.4894	+	23.3643i	−0.464599	+	0.804710i
$844$	−17.3383	+	30.0308i	−0.596809	+	1.03370i
$845$	3.74859	+	6.49274i	0.128955	+	0.223357i
$846$	−0.168571			−0.00579560
$847$	−2.60214	+	0.478401i	−0.0894106	+	0.0164380i
$848$	12.9255			0.443863
$849$	11.7878	+	20.4171i	0.404556	+	0.700712i
$850$	−3.30255	+	5.72018i	−0.113276	+	0.196201i
$851$	3.09468	−	5.36013i	0.106084	−	0.183743i
$852$	7.76803	+	13.4546i	0.266128	+	0.460948i
$853$	−21.5962			−0.739441			−0.369721	−	0.929143i	$-0.620547\pi$
$853$	−21.5962			−0.739441			−0.369721	+	0.929143i	$0.620547\pi$
$854$	−1.68058	−	1.97345i	−0.0575081	−	0.0675302i
$855$	−1.82199			−0.0623106
$856$	−18.3181	−	31.7278i	−0.626098	−	1.08443i
$857$	4.72073	−	8.17655i	0.161257	−	0.279306i	−0.774063	−	0.633109i	$-0.781778\pi$
$857$	4.72073	−	8.17655i	0.161257	−	0.279306i	0.935320	+	0.353803i	$0.115112\pi$
$858$	−0.795012	+	1.37700i	−0.0271413	+	0.0470101i
$859$	1.75465	+	3.03915i	0.0598680	+	0.103694i	0.894406	−	0.447256i	$-0.147599\pi$
$859$	1.75465	+	3.03915i	0.0598680	+	0.103694i	−0.834538	+	0.550950i	$0.814265\pi$
$860$	−12.4708			−0.425250
$861$	−6.96168	−	8.17490i	−0.237253	−	0.278600i
$862$	−7.56115			−0.257534
$863$	−19.4393	−	33.6698i	−0.661721	−	1.14613i	−0.980163	−	0.198192i	$-0.936493\pi$
$863$	−19.4393	−	33.6698i	−0.661721	−	1.14613i	0.318443	−	0.947942i	$-0.396840\pi$
$864$	2.66589	−	4.61746i	0.0906955	−	0.157089i
$865$	−9.75324	+	16.8931i	−0.331620	+	0.574383i
$866$	−1.17763	−	2.03971i	−0.0400174	−	0.0693121i
$867$	6.39926			0.217330
$868$	28.4527	−	5.23100i	0.965747	−	0.177552i
$869$	8.71027			0.295476
$870$	−0.143142	−	0.247929i	−0.00485296	−	0.00840558i
$871$	−21.9783	+	38.0675i	−0.744706	+	1.28987i
$872$	−11.3157	+	19.5993i	−0.383196	+	0.663716i
$873$	1.82664	+	3.16384i	0.0618225	+	0.107080i
$874$	−2.31163			−0.0781919
$875$	−10.5351	+	29.6145i	−0.356151	+	1.00115i
$876$	19.8855			0.671869
$877$	−2.19728	−	3.80580i	−0.0741968	−	0.128513i	0.826540	−	0.562878i	$-0.190306\pi$
$877$	−2.19728	−	3.80580i	−0.0741968	−	0.128513i	−0.900737	+	0.434366i	$0.856973\pi$
$878$	−6.46408	+	11.1961i	−0.218152	+	0.377850i
$879$	5.92501	−	10.2624i	0.199846	−	0.346143i
$880$	1.79846	+	3.11503i	0.0606262	+	0.105008i
$881$	−29.9918			−1.01045			−0.505225	−	0.862988i	$-0.668591\pi$
$881$	−29.9918			−1.01045			−0.505225	+	0.862988i	$0.668591\pi$
$882$	−3.61401	+	1.37535i	−0.121690	+	0.0463105i
$883$	16.8653			0.567563			0.283782	−	0.958889i	$-0.408411\pi$
$883$	16.8653			0.567563			0.283782	+	0.958889i	$0.408411\pi$
$884$	11.7990	+	20.4364i	0.396842	+	0.687350i
$885$	−9.43005	+	16.3333i	−0.316988	+	0.549039i
$886$	−4.06551	+	7.04168i	−0.136584	+	0.236570i
$887$	−5.01391	−	8.68434i	−0.168350	−	0.291592i	0.769490	−	0.638659i	$-0.220511\pi$
$887$	−5.01391	−	8.68434i	−0.168350	−	0.291592i	−0.937840	+	0.347068i	$0.887177\pi$
$888$	3.45929			0.116086
$889$	18.0611	−	50.7705i	0.605751	−	1.70279i
$890$	5.05030			0.169286
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	−25.0878	+	43.4533i	−0.840001	+	1.45492i
$893$	0.174837	−	0.302827i	0.00585070	−	0.0101337i
$894$	0.377146	+	0.653236i	0.0126136	+	0.0218475i
$895$	21.9608			0.734070
$896$	−30.0179	+	5.51876i	−1.00283	+	0.184369i
$897$	−10.5113			−0.350964
$898$	−9.62919	−	16.6782i	−0.321330	−	0.556560i
$899$	1.05139	−	1.82106i	0.0350659	−	0.0607359i
$900$	−2.09468	+	3.62808i	−0.0698225	+	0.120936i
$901$	−13.8194	−	23.9359i	−0.460392	−	0.797422i
$902$	−2.24190			−0.0746470
$903$	7.93815	+	9.32154i	0.264165	+	0.310202i
$904$	3.51968			0.117063
$905$	14.9213	+	25.8445i	0.496001	+	0.859100i
$906$	4.40519	−	7.63001i	0.146353	−	0.253490i
$907$	25.2758	−	43.7790i	0.839271	−	1.45366i	−0.0512348	−	0.998687i	$-0.516316\pi$
$907$	25.2758	−	43.7790i	0.839271	−	1.45366i	0.890505	−	0.454973i	$-0.150351\pi$
$908$	−20.4086	−	35.3487i	−0.677282	−	1.17309i
$909$	0.284377			0.00943219
$910$	−4.33678	−	5.09256i	−0.143763	−	0.168817i
$911$	21.7956			0.722120			0.361060	−	0.932543i	$-0.382415\pi$
$911$	21.7956			0.722120			0.361060	+	0.932543i	$0.382415\pi$
$912$	1.29610	+	2.24491i	0.0429182	+	0.0743365i
$913$	4.20428	−	7.28203i	0.139141	−	0.241000i
$914$	−2.92815	+	5.07170i	−0.0968545	+	0.167757i
$915$	−1.40998	−	2.44215i	−0.0466123	−	0.0807349i
$916$	8.83811			0.292019
$917$	−52.5166	+	9.65512i	−1.73425	+	0.318840i
$918$	−2.67216			−0.0881944
$919$	−11.2489	−	19.4837i	−0.371067	−	0.642708i	0.618663	−	0.785657i	$-0.287675\pi$
$919$	−11.2489	−	19.4837i	−0.371067	−	0.642708i	−0.989730	+	0.142949i	$0.954341\pi$
$920$	5.92579	−	10.2638i	0.195368	−	0.338387i
$921$	−9.79470	+	16.9649i	−0.322746	+	0.559013i
$922$	−1.89040	−	3.27426i	−0.0622568	−	0.107832i
$923$	26.3848			0.868467
$924$	1.50292	−	4.22477i	0.0494426	−	0.138985i
$925$	−4.18935			−0.137745
$926$	−3.23986	−	5.61160i	−0.106468	−	0.184409i
$927$	8.34671	−	14.4569i	0.274142	−	0.474828i
$928$	−0.868908	+	1.50499i	−0.0285233	+	0.0494038i
$929$	2.83989	+	4.91884i	0.0931738	+	0.161382i	0.908845	−	0.417134i	$-0.136965\pi$
$929$	2.83989	+	4.91884i	0.0931738	+	0.161382i	−0.815671	+	0.578516i	$0.803632\pi$
$930$	−5.66667			−0.185817
$931$	1.27762	−	7.91880i	0.0418723	−	0.259528i
$932$	−5.33178			−0.174648
$933$	10.7008	+	18.5344i	0.350329	+	0.606788i
$934$	−10.5755	+	18.3173i	−0.346041	+	0.599361i
$935$	3.84570	−	6.66094i	0.125768	−	0.217836i
$936$	−2.93745	−	5.08781i	−0.0960135	−	0.166300i
$937$	40.6016			1.32640			0.663198	−	0.748444i	$-0.269199\pi$
$937$	40.6016			1.32640			0.663198	+	0.748444i	$0.269199\pi$
$938$	−7.48083	+	21.0289i	−0.244258	+	0.686617i
$939$	−13.3278			−0.434938
$940$	0.411174	+	0.712175i	0.0134110	+	0.0232286i
$941$	−8.82365	+	15.2830i	−0.287643	+	0.498212i	−0.973247	−	0.229763i	$-0.926205\pi$
$941$	−8.82365	+	15.2830i	−0.287643	+	0.498212i	0.685604	+	0.727975i	$0.259538\pi$
$942$	−2.31918	+	4.01693i	−0.0755629	+	0.130879i
$943$	−7.41037	−	12.8351i	−0.241315	−	0.417969i
$944$	26.8329			0.873337
$945$	−4.13747	+	0.760669i	−0.134592	+	0.0247446i
$946$	2.55635			0.0831142
$947$	−14.1472	−	24.5037i	−0.459723	−	0.796263i	0.539223	−	0.842163i	$-0.318718\pi$
$947$	−14.1472	−	24.5037i	−0.459723	−	0.796263i	−0.998946	+	0.0458995i	$0.985385\pi$
$948$	−7.38127	+	12.7847i	−0.239732	+	0.415229i
$949$	16.8857	−	29.2470i	0.548134	−	0.949396i
$950$	0.782329	+	1.35503i	0.0253821	+	0.0439631i
$951$	−7.09552			−0.230088
$952$	16.9363	+	19.8878i	0.548908	+	0.644567i
$953$	43.3325			1.40368			0.701839	−	0.712335i	$-0.252362\pi$
$953$	43.3325			1.40368			0.701839	+	0.712335i	$0.252362\pi$
$954$	1.57816	+	2.73345i	0.0510947	+	0.0884986i
$955$	−6.45295	+	11.1768i	−0.208813	+	0.361674i
$956$	2.33435	−	4.04322i	0.0754984	−	0.130767i
$957$	−0.162968	−	0.282268i	−0.00526800	−	0.00912444i
$958$	−6.97633			−0.225395
$959$	−36.4743	−	42.8308i	−1.17782	−	1.38308i
$960$	−2.51071			−0.0810328
$961$	−5.31114	−	9.19917i	−0.171327	−	0.296747i
$962$	1.34742	−	2.33380i	0.0434426	−	0.0752448i
$963$	−8.97475	+	15.5447i	−0.289207	+	0.500921i
$964$	−7.65187	−	13.2534i	−0.246450	−	0.426864i
$965$	1.89335			0.0609490
$966$	−5.24937	+	0.965091i	−0.168896	+	0.0310513i
$967$	−2.82833			−0.0909529			−0.0454764	−	0.998965i	$-0.514481\pi$
$967$	−2.82833			−0.0909529			−0.0454764	+	0.998965i	$0.514481\pi$
$968$	−1.02053	−	1.76762i	−0.0328012	−	0.0568133i
$969$	2.77148	−	4.80035i	0.0890329	−	0.154209i
$970$	−1.60442	+	2.77894i	−0.0515149	+	0.0892264i
$971$	14.4665	+	25.0566i	0.464251	+	0.804106i	0.999167	−	0.0407988i	$-0.0129903\pi$
$971$	14.4665	+	25.0566i	0.464251	+	0.804106i	−0.534916	+	0.844905i	$0.679657\pi$
$972$	−1.69484			−0.0543621
$973$	4.68167	−	13.1603i	0.150088	−	0.421901i
$974$	−19.6735			−0.630379
$975$	3.55738	+	6.16156i	0.113927	+	0.197328i
$976$	−2.00602	+	3.47453i	−0.0642111	+	0.111217i
$977$	−28.4958	+	49.3562i	−0.911663	+	1.57905i	−0.0999471	+	0.994993i	$0.531867\pi$
$977$	−28.4958	+	49.3562i	−0.911663	+	1.57905i	−0.811715	+	0.584053i	$0.801466\pi$
$978$	−4.78194	−	8.28257i	−0.152910	−	0.264847i
$979$	5.74979			0.183764
$980$	14.6257	+	11.9136i	0.467202	+	0.380567i
$981$	11.0880			0.354012
$982$	2.09875	+	3.63515i	0.0669739	+	0.116002i
$983$	−15.5618	+	26.9539i	−0.496346	+	0.859696i	−0.999991	−	0.00421438i	$-0.998659\pi$
$983$	−15.5618	+	26.9539i	−0.496346	+	0.859696i	0.503645	+	0.863911i	$0.331992\pi$
$984$	4.14173	−	7.17368i	0.132033	−	0.228689i
$985$	21.2684	+	36.8380i	0.677668	+	1.17376i
$986$	0.870951			0.0277367
$987$	0.270601	−	0.760669i	0.00861333	−	0.0242124i
$988$	5.59002			0.177842
$989$	8.44977	+	14.6354i	0.268687	+	0.465380i
$990$	−0.439172	+	0.760669i	−0.0139578	+	0.0241756i
$991$	−4.28438	+	7.42076i	−0.136098	+	0.235728i	−0.926016	−	0.377484i	$-0.876789\pi$
$991$	−4.28438	+	7.42076i	−0.136098	+	0.235728i	0.789919	+	0.613212i	$0.210123\pi$
$992$	17.1991	+	29.7897i	0.546072	+	0.945824i
$993$	20.7350			0.658005
$994$	13.1766	−	2.42250i	0.417936	−	0.0768371i
$995$	−9.59369			−0.304140
$996$	7.12560	+	12.3419i	0.225783	+	0.391068i
$997$	−7.29290	+	12.6317i	−0.230968	+	0.400049i	−0.958093	−	0.286456i	$-0.907523\pi$
$997$	−7.29290	+	12.6317i	−0.230968	+	0.400049i	0.727125	+	0.686505i	$0.240856\pi$
$998$	0.443607	−	0.768349i	0.0140421	−	0.0243217i
$999$	−0.847422	−	1.46778i	−0.0268112	−	0.0464384i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.e.67.3	✓	8
3.2	odd	2		693.2.i.i.298.2		8
7.2	even	3	inner	231.2.i.e.100.3	yes	8
7.3	odd	6		1617.2.a.x.1.2		4
7.4	even	3		1617.2.a.z.1.2		4
21.2	odd	6		693.2.i.i.100.2		8
21.11	odd	6		4851.2.a.bt.1.3		4
21.17	even	6		4851.2.a.bu.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.e.67.3	✓	8	1.1	even	1	trivial
231.2.i.e.100.3	yes	8	7.2	even	3	inner
693.2.i.i.100.2		8	21.2	odd	6
693.2.i.i.298.2		8	3.2	odd	2
1617.2.a.x.1.2		4	7.3	odd	6
1617.2.a.z.1.2		4	7.4	even	3
4851.2.a.bt.1.3		4	21.11	odd	6
4851.2.a.bu.1.3		4	21.17	even	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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.276205 + 0.478401i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.847422 - 1.46778i) q^{4} +(-0.795012 - 1.37700i) q^{5} -0.552409 q^{6} +(0.886763 - 2.49272i) q^{7} +2.04107 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.276205 + 0.478401i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(0.847422 - 1.46778i) q^{4} +(-0.795012 - 1.37700i) q^{5} -0.552409 q^{6} +(0.886763 - 2.49272i) q^{7} +2.04107 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.439172 - 0.760669i) q^{10} +(0.500000 - 0.866025i) q^{11} +(0.847422 + 1.46778i) q^{12} +2.87834 q^{13} +(1.43745 - 0.264273i) q^{14} +1.59002 q^{15} +(-1.13109 - 1.95911i) q^{16} +(-2.41864 + 4.18921i) q^{17} +(0.276205 - 0.478401i) q^{18} +(0.572943 + 0.992366i) q^{19} -2.69484 q^{20} +(1.71538 + 2.01432i) q^{21} +0.552409 q^{22} +(1.82594 + 3.16261i) q^{23} +(-1.02053 + 1.76762i) q^{24} +(1.23591 - 2.14066i) q^{25} +(0.795012 + 1.37700i) q^{26} +1.00000 q^{27} +(-2.90730 - 3.41396i) q^{28} -0.325935 q^{29} +(0.439172 + 0.760669i) q^{30} +(-3.22577 + 5.58719i) q^{31} +(2.66589 - 4.61746i) q^{32} +(0.500000 + 0.866025i) q^{33} -2.67216 q^{34} +(-4.13747 + 0.760669i) q^{35} -1.69484 q^{36} +(-0.847422 - 1.46778i) q^{37} +(-0.316499 + 0.548192i) q^{38} +(-1.43917 + 2.49272i) q^{39} +(-1.62267 - 2.81055i) q^{40} -4.05839 q^{41} +(-0.489856 + 1.37700i) q^{42} +4.62764 q^{43} +(-0.847422 - 1.46778i) q^{44} +(-0.795012 + 1.37700i) q^{45} +(-1.00866 + 1.74706i) q^{46} +(-0.152578 - 0.264273i) q^{47} +2.26218 q^{48} +(-5.42730 - 4.42090i) q^{49} +1.36546 q^{50} +(-2.41864 - 4.18921i) q^{51} +(2.43917 - 4.22477i) q^{52} +(-2.85686 + 4.94822i) q^{53} +(0.276205 + 0.478401i) q^{54} -1.59002 q^{55} +(1.80994 - 5.08781i) q^{56} -1.14589 q^{57} +(-0.0900249 - 0.155928i) q^{58} +(-5.93075 + 10.2724i) q^{59} +(1.34742 - 2.33380i) q^{60} +(-0.886763 - 1.53592i) q^{61} -3.56389 q^{62} +(-2.60214 + 0.478401i) q^{63} -1.57904 q^{64} +(-2.28832 - 3.96349i) q^{65} +(-0.276205 + 0.478401i) q^{66} +(-7.63574 + 13.2255i) q^{67} +(4.09922 + 7.10005i) q^{68} -3.65187 q^{69} +(-1.50669 - 1.76927i) q^{70} +9.16666 q^{71} +(-1.02053 - 1.76762i) q^{72} +(5.86648 - 10.1610i) q^{73} +(0.468124 - 0.810814i) q^{74} +(1.23591 + 2.14066i) q^{75} +1.94210 q^{76} +(-1.71538 - 2.01432i) q^{77} -1.59002 q^{78} +(4.35513 + 7.54331i) q^{79} +(-1.79846 + 3.11503i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.12095 - 1.94154i) q^{82} +8.40856 q^{83} +(4.41022 - 0.810814i) q^{84} +7.69139 q^{85} +(1.27818 + 2.21387i) q^{86} +(0.162968 - 0.282268i) q^{87} +(1.02053 - 1.76762i) q^{88} +(2.87489 + 4.97946i) q^{89} -0.878345 q^{90} +(2.55241 - 7.17491i) q^{91} +6.18935 q^{92} +(-3.22577 - 5.58719i) q^{93} +(0.0842856 - 0.145987i) q^{94} +(0.910993 - 1.57789i) q^{95} +(2.66589 + 4.61746i) q^{96} -3.65329 q^{97} +(0.615916 - 3.81750i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9	\( 8 q - 2 q^{2} - 4 q^{3} - 4 q^{4} - 4 q^{5} + 4 q^{6} + 2 q^{7} + 24 q^{8} - 4 q^{9} - 10 q^{10} + 4 q^{11} - 4 q^{12} - 4 q^{13} - 4 q^{14} + 8 q^{15} - 12 q^{16} - 2 q^{17} - 2 q^{18} - 4 q^{21} - 4 q^{22} - 4 q^{23} - 12 q^{24} - 4 q^{25} + 4 q^{26} + 8 q^{27} - 22 q^{28} + 16 q^{29} - 10 q^{30} + 12 q^{31} - 26 q^{32} + 4 q^{33} - 32 q^{34} - 2 q^{35} + 8 q^{36} + 4 q^{37} - 8 q^{38} + 2 q^{39} + 6 q^{40} + 4 q^{41} + 20 q^{42} + 36 q^{43} + 4 q^{44} - 4 q^{45} + 14 q^{46} - 12 q^{47} + 24 q^{48} - 4 q^{49} + 4 q^{50} - 2 q^{51} + 6 q^{52} + 12 q^{53} - 2 q^{54} - 8 q^{55} + 48 q^{56} + 4 q^{58} - 12 q^{59} - 2 q^{61} - 52 q^{62} + 2 q^{63} + 112 q^{64} + 4 q^{65} + 2 q^{66} - 28 q^{67} + 48 q^{68} + 8 q^{69} - 32 q^{70} + 24 q^{71} - 12 q^{72} - 6 q^{73} + 16 q^{74} - 4 q^{75} - 36 q^{76} + 4 q^{77} - 8 q^{78} - 2 q^{79} - 16 q^{80} - 4 q^{81} + 12 q^{82} - 24 q^{83} - 4 q^{84} + 36 q^{85} - 36 q^{86} - 8 q^{87} + 12 q^{88} - 8 q^{89} + 20 q^{90} + 12 q^{91} - 32 q^{92} + 12 q^{93} - 20 q^{94} - 34 q^{95} - 26 q^{96} - 88 q^{97} + 16 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q - 2 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 + 4 * q^6 + 2 * q^7 + 24 * q^8 - 4 * q^9 - 10 * q^10 + 4 * q^11 - 4 * q^12 - 4 * q^13 - 4 * q^14 + 8 * q^15 - 12 * q^16 - 2 * q^17 - 2 * q^18 - 4 * q^21 - 4 * q^22 - 4 * q^23 - 12 * q^24 - 4 * q^25 + 4 * q^26 + 8 * q^27 - 22 * q^28 + 16 * q^29 - 10 * q^30 + 12 * q^31 - 26 * q^32 + 4 * q^33 - 32 * q^34 - 2 * q^35 + 8 * q^36 + 4 * q^37 - 8 * q^38 + 2 * q^39 + 6 * q^40 + 4 * q^41 + 20 * q^42 + 36 * q^43 + 4 * q^44 - 4 * q^45 + 14 * q^46 - 12 * q^47 + 24 * q^48 - 4 * q^49 + 4 * q^50 - 2 * q^51 + 6 * q^52 + 12 * q^53 - 2 * q^54 - 8 * q^55 + 48 * q^56 + 4 * q^58 - 12 * q^59 - 2 * q^61 - 52 * q^62 + 2 * q^63 + 112 * q^64 + 4 * q^65 + 2 * q^66 - 28 * q^67 + 48 * q^68 + 8 * q^69 - 32 * q^70 + 24 * q^71 - 12 * q^72 - 6 * q^73 + 16 * q^74 - 4 * q^75 - 36 * q^76 + 4 * q^77 - 8 * q^78 - 2 * q^79 - 16 * q^80 - 4 * q^81 + 12 * q^82 - 24 * q^83 - 4 * q^84 + 36 * q^85 - 36 * q^86 - 8 * q^87 + 12 * q^88 - 8 * q^89 + 20 * q^90 + 12 * q^91 - 32 * q^92 + 12 * q^93 - 20 * q^94 - 34 * q^95 - 26 * q^96 - 88 * q^97 + 16 * q^98 - 8 * q^99

Introduction

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