LMFDB - Embedded newform 429.2.i.e.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(100,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("429.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 10x^{8} - 6x^{7} + 46x^{6} - 31x^{5} + 111x^{4} - 36x^{3} + 145x^{2} - 72x + 81 $ x^10 - 2x^9 + 10x^8 - 6x^7 + 46x^6 - 31x^5 + 111x^4 - 36x^3 + 145x^2 - 72*x + 81
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			100.1
Root			$-0.922622 + 1.59803i$ of defining polynomial
Character	$\chi$	$=$	429.100
Dual form			429.2.i.e.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.922622 + 1.59803i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.702461 - 1.21670i) q^{4} +3.96195 q^{5} +(0.922622 + 1.59803i) q^{6} +(1.80081 + 3.11910i) q^{7} -1.09806 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.922622 + 1.59803i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.702461 - 1.21670i) q^{4} +3.96195 q^{5} +(0.922622 + 1.59803i) q^{6} +(1.80081 + 3.11910i) q^{7} -1.09806 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.65538 + 6.33130i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.40492 q^{12} +(-0.170838 - 3.60150i) q^{13} -6.64588 q^{14} +(1.98097 - 3.43115i) q^{15} +(2.41802 - 4.18813i) q^{16} +(3.43522 + 5.94997i) q^{17} +1.84524 q^{18} +(-2.96705 - 5.13908i) q^{19} +(-2.78312 - 4.82050i) q^{20} +3.60163 q^{21} +(0.922622 + 1.59803i) q^{22} +(-0.390998 + 0.677229i) q^{23} +(-0.549031 + 0.950950i) q^{24} +10.6970 q^{25} +(5.91292 + 3.04982i) q^{26} -1.00000 q^{27} +(2.53001 - 4.38210i) q^{28} +(-1.65343 + 2.86382i) q^{29} +(3.65538 + 6.33130i) q^{30} -8.98526 q^{31} +(3.36377 + 5.82622i) q^{32} +(-0.500000 - 0.866025i) q^{33} -12.6776 q^{34} +(7.13474 + 12.3577i) q^{35} +(-0.702461 + 1.21670i) q^{36} +(2.46357 - 4.26702i) q^{37} +10.9499 q^{38} +(-3.20441 - 1.65280i) q^{39} -4.35047 q^{40} +(-2.43327 + 4.21455i) q^{41} +(-3.32294 + 5.75550i) q^{42} +(1.06788 + 1.84963i) q^{43} -1.40492 q^{44} +(-1.98097 - 3.43115i) q^{45} +(-0.721487 - 1.24965i) q^{46} -0.148204 q^{47} +(-2.41802 - 4.18813i) q^{48} +(-2.98587 + 5.17168i) q^{49} +(-9.86932 + 17.0942i) q^{50} +6.87044 q^{51} +(-4.26194 + 2.73777i) q^{52} -6.01599 q^{53} +(0.922622 - 1.59803i) q^{54} +(1.98097 - 3.43115i) q^{55} +(-1.97741 - 3.42497i) q^{56} -5.93410 q^{57} +(-3.05098 - 5.28445i) q^{58} +(-1.36244 - 2.35982i) q^{59} -5.56623 q^{60} +(3.45735 + 5.98830i) q^{61} +(8.28999 - 14.3587i) q^{62} +(1.80081 - 3.11910i) q^{63} -2.74187 q^{64} +(-0.676851 - 14.2690i) q^{65} +1.84524 q^{66} +(3.22591 - 5.58745i) q^{67} +(4.82622 - 8.35925i) q^{68} +(0.390998 + 0.677229i) q^{69} -26.3306 q^{70} +(5.26902 + 9.12620i) q^{71} +(0.549031 + 0.950950i) q^{72} -8.04060 q^{73} +(4.54588 + 7.87369i) q^{74} +(5.34852 - 9.26391i) q^{75} +(-4.16848 + 7.22001i) q^{76} +3.60163 q^{77} +(5.59768 - 3.59583i) q^{78} -8.13311 q^{79} +(9.58007 - 16.5932i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.48997 - 7.77686i) q^{82} -2.32038 q^{83} +(-2.53001 - 4.38210i) q^{84} +(13.6102 + 23.5735i) q^{85} -3.94100 q^{86} +(1.65343 + 2.86382i) q^{87} +(-0.549031 + 0.950950i) q^{88} +(2.17883 - 3.77385i) q^{89} +7.31076 q^{90} +(10.9258 - 7.01850i) q^{91} +1.09864 q^{92} +(-4.49263 + 7.78146i) q^{93} +(0.136737 - 0.236835i) q^{94} +(-11.7553 - 20.3608i) q^{95} +6.72754 q^{96} +(-2.08260 - 3.60718i) q^{97} +(-5.50965 - 9.54300i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.922622	+	1.59803i	−0.652392	+	1.12998i	0.330149	+	0.943929i	$0.392901\pi$
$2$	−0.922622	+	1.59803i	−0.652392	+	1.12998i	−0.982541	+	0.186047i	$0.940432\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.702461	−	1.21670i	−0.351231	−	0.608349i
$5$	3.96195			1.77184			0.885919	−	0.463841i	$-0.153529\pi$
$5$	3.96195			1.77184			0.885919	+	0.463841i	$0.153529\pi$
$6$	0.922622	+	1.59803i	0.376659	+	0.652392i
$7$	1.80081	+	3.11910i	0.680644	+	1.17891i	0.974785	+	0.223148i	$0.0716333\pi$
$7$	1.80081	+	3.11910i	0.680644	+	1.17891i	−0.294141	+	0.955762i	$0.595033\pi$
$8$	−1.09806			−0.388224
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−3.65538	+	6.33130i	−1.15593	+	2.00213i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.40492			−0.405566
$13$	−0.170838	−	3.60150i	−0.0473819	−	0.998877i
$13$	−0.170838	−	3.60150i	−0.0473819	−	0.998877i
$14$	−6.64588			−1.77619
$15$	1.98097	−	3.43115i	0.511485	−	0.885919i
$16$	2.41802	−	4.18813i	0.604505	−	1.04703i
$17$	3.43522	+	5.94997i	0.833163	+	1.44308i	0.895517	+	0.445027i	$0.146806\pi$
$17$	3.43522	+	5.94997i	0.833163	+	1.44308i	−0.0623542	+	0.998054i	$0.519861\pi$
$18$	1.84524			0.434928
$19$	−2.96705	−	5.13908i	−0.680688	−	1.17899i	−0.974771	−	0.223206i	$-0.928348\pi$
$19$	−2.96705	−	5.13908i	−0.680688	−	1.17899i	0.294083	−	0.955780i	$-0.404986\pi$
$20$	−2.78312	−	4.82050i	−0.622324	−	1.07790i
$21$	3.60163			0.785940
$22$	0.922622	+	1.59803i	0.196704	+	0.340701i
$23$	−0.390998	+	0.677229i	−0.0815288	+	0.141212i	−0.903907	−	0.427730i	$-0.859314\pi$
$23$	−0.390998	+	0.677229i	−0.0815288	+	0.141212i	0.822378	+	0.568941i	$0.192647\pi$
$24$	−0.549031	+	0.950950i	−0.112071	+	0.194112i
$25$	10.6970			2.13941
$26$	5.91292	+	3.04982i	1.15962	+	0.598119i
$27$	−1.00000			−0.192450
$28$	2.53001	−	4.38210i	0.478126	−	0.828139i
$29$	−1.65343	+	2.86382i	−0.307034	+	0.531799i	−0.977712	−	0.209950i	$-0.932670\pi$
$29$	−1.65343	+	2.86382i	−0.307034	+	0.531799i	0.670678	+	0.741749i	$0.266003\pi$
$30$	3.65538	+	6.33130i	0.667378	+	1.15593i
$31$	−8.98526			−1.61380			−0.806900	−	0.590688i	$-0.798856\pi$
$31$	−8.98526			−1.61380			−0.806900	+	0.590688i	$0.798856\pi$
$32$	3.36377	+	5.82622i	0.594636	+	1.02994i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	−12.6776			−2.17420
$35$	7.13474	+	12.3577i	1.20599	+	2.08884i
$36$	−0.702461	+	1.21670i	−0.117077	+	0.202783i
$37$	2.46357	−	4.26702i	0.405008	−	0.701494i	−0.589315	−	0.807904i	$-0.700602\pi$
$37$	2.46357	−	4.26702i	0.405008	−	0.701494i	0.994322	+	0.106410i	$0.0339354\pi$
$38$	10.9499			1.77630
$39$	−3.20441	−	1.65280i	−0.513116	−	0.264660i
$40$	−4.35047			−0.687869
$41$	−2.43327	+	4.21455i	−0.380013	+	0.658202i	−0.991064	−	0.133390i	$-0.957414\pi$
$41$	−2.43327	+	4.21455i	−0.380013	+	0.658202i	0.611051	+	0.791591i	$0.290747\pi$
$42$	−3.32294	+	5.75550i	−0.512741	+	0.888093i
$43$	1.06788	+	1.84963i	0.162850	+	0.282065i	0.935890	−	0.352293i	$-0.114598\pi$
$43$	1.06788	+	1.84963i	0.162850	+	0.282065i	−0.773039	+	0.634358i	$0.781265\pi$
$44$	−1.40492			−0.211800
$45$	−1.98097	−	3.43115i	−0.295306	−	0.511485i
$46$	−0.721487	−	1.24965i	−0.106377	−	0.184251i
$47$	−0.148204			−0.0216178			−0.0108089	−	0.999942i	$-0.503441\pi$
$47$	−0.148204			−0.0216178			−0.0108089	+	0.999942i	$0.503441\pi$
$48$	−2.41802	−	4.18813i	−0.349011	−	0.604505i
$49$	−2.98587	+	5.17168i	−0.426553	+	0.738811i
$50$	−9.86932	+	17.0942i	−1.39573	+	2.41748i
$51$	6.87044			0.962054
$52$	−4.26194	+	2.73777i	−0.591024	+	0.379661i
$53$	−6.01599			−0.826360			−0.413180	−	0.910649i	$-0.635582\pi$
$53$	−6.01599			−0.826360			−0.413180	+	0.910649i	$0.635582\pi$
$54$	0.922622	−	1.59803i	0.125553	−	0.217464i
$55$	1.98097	−	3.43115i	0.267115	−	0.462656i
$56$	−1.97741	−	3.42497i	−0.264242	−	0.457681i
$57$	−5.93410			−0.785991
$58$	−3.05098	−	5.28445i	−0.400613	−	0.693883i
$59$	−1.36244	−	2.35982i	−0.177375	−	0.307223i	0.763606	−	0.645683i	$-0.223427\pi$
$59$	−1.36244	−	2.35982i	−0.177375	−	0.307223i	−0.940981	+	0.338460i	$0.890094\pi$
$60$	−5.56623			−0.718597
$61$	3.45735	+	5.98830i	0.442668	+	0.766723i	0.997886	−	0.0649813i	$-0.0206988\pi$
$61$	3.45735	+	5.98830i	0.442668	+	0.766723i	−0.555219	+	0.831704i	$0.687365\pi$
$62$	8.28999	−	14.3587i	1.05283	−	1.82356i
$63$	1.80081	−	3.11910i	0.226881	−	0.392970i
$64$	−2.74187			−0.342734
$65$	−0.676851	−	14.2690i	−0.0839531	−	1.76985i
$66$	1.84524			0.227134
$67$	3.22591	−	5.58745i	0.394108	−	0.682615i	−0.598879	−	0.800840i	$-0.704387\pi$
$67$	3.22591	−	5.58745i	0.394108	−	0.682615i	0.992987	+	0.118224i	$0.0377202\pi$
$68$	4.82622	−	8.35925i	0.585265	−	1.01371i
$69$	0.390998	+	0.677229i	0.0470707	+	0.0815288i
$70$	−26.3306			−3.14711
$71$	5.26902	+	9.12620i	0.625317	+	1.08308i	0.988479	+	0.151355i	$0.0483637\pi$
$71$	5.26902	+	9.12620i	0.625317	+	1.08308i	−0.363162	+	0.931726i	$0.618303\pi$
$72$	0.549031	+	0.950950i	0.0647039	+	0.112071i
$73$	−8.04060			−0.941081			−0.470541	−	0.882378i	$-0.655941\pi$
$73$	−8.04060			−0.941081			−0.470541	+	0.882378i	$0.655941\pi$
$74$	4.54588	+	7.87369i	0.528448	+	0.915298i
$75$	5.34852	−	9.26391i	0.617594	−	1.06970i
$76$	−4.16848	+	7.22001i	−0.478157	+	0.828192i
$77$	3.60163			0.410444
$78$	5.59768	−	3.59583i	0.633812	−	0.407147i
$79$	−8.13311			−0.915046			−0.457523	−	0.889198i	$-0.651263\pi$
$79$	−8.13311			−0.915046			−0.457523	+	0.889198i	$0.651263\pi$
$80$	9.58007	−	16.5932i	1.07108	−	1.85517i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−4.48997	−	7.77686i	−0.495835	−	0.858811i
$83$	−2.32038			−0.254695			−0.127347	−	0.991858i	$-0.540646\pi$
$83$	−2.32038			−0.254695			−0.127347	+	0.991858i	$0.540646\pi$
$84$	−2.53001	−	4.38210i	−0.276046	−	0.478126i
$85$	13.6102	+	23.5735i	1.47623	+	2.55690i
$86$	−3.94100			−0.424969
$87$	1.65343	+	2.86382i	0.177266	+	0.307034i
$88$	−0.549031	+	0.950950i	−0.0585269	+	0.101372i
$89$	2.17883	−	3.77385i	0.230956	−	0.400027i	−0.727134	−	0.686496i	$-0.759148\pi$
$89$	2.17883	−	3.77385i	0.230956	−	0.400027i	0.958090	+	0.286468i	$0.0924814\pi$
$90$	7.31076			0.770622
$91$	10.9258	−	7.01850i	1.14534	−	0.735739i
$92$	1.09864			0.114542
$93$	−4.49263	+	7.78146i	−0.465864	+	0.806900i
$94$	0.136737	−	0.236835i	0.0141033	−	0.0244276i
$95$	−11.7553	−	20.3608i	−1.20607	−	2.08897i
$96$	6.72754			0.686627
$97$	−2.08260	−	3.60718i	−0.211456	−	0.366253i	0.740714	−	0.671820i	$-0.234487\pi$
$97$	−2.08260	−	3.60718i	−0.211456	−	0.366253i	−0.952171	+	0.305567i	$0.901154\pi$
$98$	−5.50965	−	9.54300i	−0.556559	−	0.963989i
$99$	−1.00000			−0.100504
$100$	−7.51426	−	13.0151i	−0.751426	−	1.30151i
$101$	6.82141	−	11.8150i	0.678755	−	1.17564i	−0.296601	−	0.955002i	$-0.595853\pi$
$101$	6.82141	−	11.8150i	0.678755	−	1.17564i	0.975356	−	0.220637i	$-0.0708137\pi$
$102$	−6.33882	+	10.9792i	−0.627636	+	1.08710i
$103$	−2.33241			−0.229819			−0.114909	−	0.993376i	$-0.536658\pi$
$103$	−2.33241			−0.229819			−0.114909	+	0.993376i	$0.536658\pi$
$104$	0.187591	+	3.95467i	0.0183948	+	0.387788i
$105$	14.2695			1.39256
$106$	5.55048	−	9.61372i	0.539111	−	0.933767i
$107$	1.43982	−	2.49385i	0.139193	−	0.241089i	−0.787998	−	0.615677i	$-0.788883\pi$
$107$	1.43982	−	2.49385i	0.139193	−	0.241089i	0.927191	+	0.374588i	$0.122216\pi$
$108$	0.702461	+	1.21670i	0.0675944	+	0.117077i
$109$	4.18615			0.400961			0.200480	−	0.979698i	$-0.435750\pi$
$109$	4.18615			0.400961			0.200480	+	0.979698i	$0.435750\pi$
$110$	3.65538	+	6.33130i	0.348527	+	0.603666i
$111$	−2.46357	−	4.26702i	−0.233831	−	0.405008i
$112$	17.4176			1.64581
$113$	−0.804703	−	1.39379i	−0.0757001	−	0.131116i	0.825690	−	0.564124i	$-0.190786\pi$
$113$	−0.804703	−	1.39379i	−0.0757001	−	0.131116i	−0.901391	+	0.433007i	$0.857453\pi$
$114$	5.47493	−	9.48286i	0.512774	−	0.888151i
$115$	−1.54912	+	2.68315i	−0.144456	+	0.250205i
$116$	4.64588			0.431359
$117$	−3.03357	+	1.94870i	−0.280454	+	0.180157i
$118$	5.02808			0.462872
$119$	−12.3724	+	21.4296i	−1.13417	+	1.96445i
$120$	−2.17523	+	3.76762i	−0.198571	+	0.343935i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−12.7593			−1.15517
$123$	2.43327	+	4.21455i	0.219401	+	0.380013i
$124$	6.31179	+	10.9323i	0.566816	+	0.981754i
$125$	22.5714			2.01885
$126$	3.32294	+	5.75550i	0.296031	+	0.512741i
$127$	10.3739	−	17.9682i	0.920537	−	1.59442i	0.121950	−	0.992536i	$-0.461085\pi$
$127$	10.3739	−	17.9682i	0.920537	−	1.59442i	0.798586	−	0.601880i	$-0.205582\pi$
$128$	−4.19783	+	7.27085i	−0.371039	+	0.642659i
$129$	2.13576			0.188043
$130$	23.4267	+	12.0832i	2.05466	+	1.05977i
$131$	−13.0928			−1.14392			−0.571960	−	0.820282i	$-0.693817\pi$
$131$	−13.0928			−1.14392			−0.571960	+	0.820282i	$0.693817\pi$
$132$	−0.702461	+	1.21670i	−0.0611414	+	0.105900i
$133$	10.6862	−	18.5091i	0.926612	−	1.60494i
$134$	5.95260	+	10.3102i	0.514226	+	0.890666i
$135$	−3.96195			−0.340990
$136$	−3.77209	−	6.53344i	−0.323454	−	0.560238i
$137$	−3.02080	−	5.23218i	−0.258084	−	0.447015i	0.707644	−	0.706569i	$-0.249758\pi$
$137$	−3.02080	−	5.23218i	−0.258084	−	0.447015i	−0.965729	+	0.259554i	$0.916425\pi$
$138$	−1.44297			−0.122834
$139$	−9.25650	−	16.0327i	−0.785126	−	1.35988i	−0.928924	−	0.370271i	$-0.879265\pi$
$139$	−9.25650	−	16.0327i	−0.785126	−	1.35988i	0.143797	−	0.989607i	$-0.454069\pi$
$140$	10.0238	−	17.3616i	0.847162	−	1.46733i
$141$	−0.0741022	+	0.128349i	−0.00624053	+	0.0108089i
$142$	−19.4452			−1.63181
$143$	−3.20441	−	1.65280i	−0.267966	−	0.138214i
$144$	−4.83604			−0.403003
$145$	−6.55081	+	11.3463i	−0.544015	+	0.942261i
$146$	7.41843	−	12.8491i	0.613954	−	1.06340i
$147$	2.98587	+	5.17168i	0.246270	+	0.426553i
$148$	−6.92224			−0.569005
$149$	−8.66243	−	15.0038i	−0.709654	−	1.22916i	−0.964986	−	0.262303i	$-0.915518\pi$
$149$	−8.66243	−	15.0038i	−0.709654	−	1.22916i	0.255332	−	0.966854i	$-0.417815\pi$
$150$	9.86932	+	17.0942i	0.805827	+	1.39573i
$151$	−23.0566			−1.87632			−0.938159	−	0.346203i	$-0.887471\pi$
$151$	−23.0566			−1.87632			−0.938159	+	0.346203i	$0.887471\pi$
$152$	3.25801	+	5.64303i	0.264259	+	0.457710i
$153$	3.43522	−	5.94997i	0.277721	−	0.481027i
$154$	−3.32294	+	5.75550i	−0.267770	+	0.463792i
$155$	−35.5991			−2.85939
$156$	0.240014	+	5.05983i	0.0192165	+	0.405111i
$157$	3.09464			0.246980			0.123490	−	0.992346i	$-0.460591\pi$
$157$	3.09464			0.246980			0.123490	+	0.992346i	$0.460591\pi$
$158$	7.50378	−	12.9969i	0.596969	−	1.03398i
$159$	−3.00799	+	5.21000i	−0.238550	+	0.413180i
$160$	13.3271	+	23.0832i	1.05360	+	1.82489i
$161$	−2.81646			−0.221968
$162$	−0.922622	−	1.59803i	−0.0724880	−	0.125553i
$163$	−8.59851	−	14.8931i	−0.673487	−	1.16651i	−0.976909	−	0.213658i	$-0.931462\pi$
$163$	−8.59851	−	14.8931i	−0.673487	−	1.16651i	0.303421	−	0.952857i	$-0.401871\pi$
$164$	6.83711			0.533889
$165$	−1.98097	−	3.43115i	−0.154219	−	0.267115i
$166$	2.14083	−	3.70803i	0.166161	−	0.287799i
$167$	6.07638	−	10.5246i	0.470205	−	0.814418i	−0.529215	−	0.848488i	$-0.677513\pi$
$167$	6.07638	−	10.5246i	0.470205	−	0.814418i	0.999419	+	0.0340695i	$0.0108468\pi$
$168$	−3.95481			−0.305121
$169$	−12.9416	+	1.23055i	−0.995510	+	0.0946574i
$170$	−50.2281			−3.85232
$171$	−2.96705	+	5.13908i	−0.226896	+	0.392995i
$172$	1.50029	−	2.59858i	0.114396	−	0.198140i
$173$	4.21017	+	7.29222i	0.320093	+	0.554417i	0.980507	−	0.196484i	$-0.0629525\pi$
$173$	4.21017	+	7.29222i	0.320093	+	0.554417i	−0.660414	+	0.750902i	$0.729619\pi$
$174$	−6.10196			−0.462589
$175$	19.2634	+	33.3652i	1.45618	+	2.52217i
$176$	−2.41802	−	4.18813i	−0.182265	−	0.315692i
$177$	−2.72489			−0.204815
$178$	4.02048	+	6.96367i	0.301347	+	0.521949i
$179$	−3.85062	+	6.66946i	−0.287808	+	0.498499i	−0.973286	−	0.229595i	$-0.926260\pi$
$179$	−3.85062	+	6.66946i	−0.287808	+	0.498499i	0.685478	+	0.728093i	$0.259593\pi$
$180$	−2.78312	+	4.82050i	−0.207441	+	0.359299i
$181$	24.7965			1.84311			0.921555	−	0.388247i	$-0.126919\pi$
$181$	24.7965			1.84311			0.921555	+	0.388247i	$0.126919\pi$
$182$	1.13537	+	23.9352i	0.0841592	+	1.77419i
$183$	6.91469			0.511149
$184$	0.429340	−	0.743640i	0.0316514	−	0.0548218i
$185$	9.76052	−	16.9057i	0.717608	−	1.24293i
$186$	−8.28999	−	14.3587i	−0.607852	−	1.05283i
$187$	6.87044			0.502416
$188$	0.104108	+	0.180320i	0.00759284	+	0.0131512i
$189$	−1.80081	−	3.11910i	−0.130990	−	0.226881i
$190$	43.3828			3.14732
$191$	8.37915	+	14.5131i	0.606294	+	1.05013i	0.991846	+	0.127446i	$0.0406778\pi$
$191$	8.37915	+	14.5131i	0.606294	+	1.05013i	−0.385552	+	0.922686i	$0.625989\pi$
$192$	−1.37094	+	2.37453i	−0.0989389	+	0.171367i
$193$	−4.42478	+	7.66394i	−0.318503	+	0.551663i	−0.980176	−	0.198130i	$-0.936513\pi$
$193$	−4.42478	+	7.66394i	−0.318503	+	0.551663i	0.661673	+	0.749792i	$0.269847\pi$
$194$	7.68582			0.551810
$195$	−12.6957	−	6.54831i	−0.909159	−	0.468934i
$196$	8.38983			0.599273
$197$	1.95492	−	3.38602i	0.139282	−	0.241244i	−0.787943	−	0.615748i	$-0.788854\pi$
$197$	1.95492	−	3.38602i	0.139282	−	0.241244i	0.927225	+	0.374504i	$0.122187\pi$
$198$	0.922622	−	1.59803i	0.0655679	−	0.113567i
$199$	7.26948	+	12.5911i	0.515320	+	0.892560i	0.999842	+	0.0177812i	$0.00566024\pi$
$199$	7.26948	+	12.5911i	0.515320	+	0.892560i	−0.484522	+	0.874779i	$0.661006\pi$
$200$	−11.7460			−0.830569
$201$	−3.22591	−	5.58745i	−0.227538	−	0.394108i
$202$	12.5872	+	21.8016i	0.885629	+	1.53395i
$203$	−11.9101			−0.835924
$204$	−4.82622	−	8.35925i	−0.337903	−	0.585265i
$205$	−9.64049	+	16.6978i	−0.673321	+	1.16623i
$206$	2.15193	−	3.72725i	0.149932	−	0.259690i
$207$	0.781997			0.0543525
$208$	−15.4967	−	7.99301i	−1.07450	−	0.554215i
$209$	−5.93410			−0.410470
$210$	−13.1653	+	22.8030i	−0.908494	+	1.57356i
$211$	−7.02113	+	12.1610i	−0.483355	+	0.837195i	−0.999817	−	0.0191149i	$-0.993915\pi$
$211$	−7.02113	+	12.1610i	−0.483355	+	0.837195i	0.516463	+	0.856310i	$0.327248\pi$
$212$	4.22600	+	7.31965i	0.290243	+	0.502715i
$213$	10.5380			0.722054
$214$	2.65682	+	4.60175i	0.181617	+	0.314569i
$215$	4.23089	+	7.32812i	0.288544	+	0.499774i
$216$	1.09806			0.0747137
$217$	−16.1808	−	28.0259i	−1.09842	−	1.90252i
$218$	−3.86224	+	6.68959i	−0.261584	+	0.453076i
$219$	−4.02030	+	6.96337i	−0.271667	+	0.470541i
$220$	−5.56623			−0.375275
$221$	20.8420	−	13.3884i	1.40198	−	0.900603i
$222$	9.09176			0.610199
$223$	−8.86145	+	15.3485i	−0.593407	+	1.02781i	0.400363	+	0.916357i	$0.368884\pi$
$223$	−8.86145	+	15.3485i	−0.593407	+	1.02781i	−0.993770	+	0.111454i	$0.964449\pi$
$224$	−12.1151	+	20.9839i	−0.809471	+	1.40205i
$225$	−5.34852	−	9.26391i	−0.356568	−	0.617594i
$226$	2.96975			0.197545
$227$	−0.756127	−	1.30965i	−0.0501859	−	0.0869246i	0.839841	−	0.542832i	$-0.182648\pi$
$227$	−0.756127	−	1.30965i	−0.0501859	−	0.0869246i	−0.890027	+	0.455908i	$0.849315\pi$
$228$	4.16848	+	7.22001i	0.276064	+	0.478157i
$229$	17.8874			1.18204			0.591018	−	0.806659i	$-0.298726\pi$
$229$	17.8874			1.18204			0.591018	+	0.806659i	$0.298726\pi$
$230$	−2.85849	−	4.95106i	−0.188484	−	0.326463i
$231$	1.80081	−	3.11910i	0.118485	−	0.205222i
$232$	1.81557	−	3.14466i	0.119198	−	0.206457i
$233$	13.5108			0.885121			0.442560	−	0.896739i	$-0.354070\pi$
$233$	13.5108			0.885121			0.442560	+	0.896739i	$0.354070\pi$
$234$	−0.315238	−	6.64565i	−0.0206077	−	0.434440i
$235$	−0.587178			−0.0383033
$236$	−1.91413	+	3.31537i	−0.124599	+	0.215812i
$237$	−4.06656	+	7.04348i	−0.264151	+	0.457523i
$238$	−22.8301	−	39.5428i	−1.47985	−	2.56318i
$239$	−0.706163			−0.0456779			−0.0228389	−	0.999739i	$-0.507270\pi$
$239$	−0.706163			−0.0456779			−0.0228389	+	0.999739i	$0.507270\pi$
$240$	−9.58007	−	16.5932i	−0.618391	−	1.07108i
$241$	9.68262	+	16.7708i	0.623712	+	1.08030i	0.988788	+	0.149323i	$0.0477096\pi$
$241$	9.68262	+	16.7708i	0.623712	+	1.08030i	−0.365076	+	0.930978i	$0.618957\pi$
$242$	1.84524			0.118617
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	4.85730	−	8.41310i	0.310957	−	0.538593i
$245$	−11.8299	+	20.4899i	−0.755782	+	1.30905i
$246$	−8.97995			−0.572541
$247$	−18.0015	+	11.5638i	−1.14541	+	0.735786i
$248$	9.86637			0.626515
$249$	−1.16019	+	2.00951i	−0.0735240	+	0.127347i
$250$	−20.8248	+	36.0697i	−1.31708	+	2.28125i
$251$	9.44484	+	16.3589i	0.596153	+	1.03257i	0.993383	+	0.114848i	$0.0366382\pi$
$251$	9.44484	+	16.3589i	0.596153	+	1.03257i	−0.397230	+	0.917719i	$0.630028\pi$
$252$	−5.06001			−0.318751
$253$	0.390998	+	0.677229i	0.0245818	+	0.0425770i
$254$	19.1424	+	33.1556i	1.20110	+	2.08037i
$255$	27.2203			1.70460
$256$	−10.4879	−	18.1656i	−0.655493	−	1.13535i
$257$	−12.3657	+	21.4180i	−0.771351	+	1.33602i	0.165472	+	0.986214i	$0.447085\pi$
$257$	−12.3657	+	21.4180i	−0.771351	+	1.33602i	−0.936823	+	0.349804i	$0.886248\pi$
$258$	−1.97050	+	3.41301i	−0.122678	+	0.212485i
$259$	17.7457			1.10266
$260$	−16.8856	+	10.8469i	−1.04720	+	0.672697i
$261$	3.30686			0.204690
$262$	12.0797	−	20.9226i	0.746284	−	1.29260i
$263$	3.87835	−	6.71750i	0.239149	−	0.414219i	−0.721321	−	0.692601i	$-0.756465\pi$
$263$	3.87835	−	6.71750i	0.239149	−	0.414219i	0.960470	+	0.278382i	$0.0897981\pi$
$264$	0.549031	+	0.950950i	0.0337905	+	0.0585269i
$265$	−23.8350			−1.46418
$266$	19.7187	+	34.1537i	1.20903	+	2.09410i
$267$	−2.17883	−	3.77385i	−0.133342	−	0.230956i
$268$	−9.06432			−0.553692
$269$	−11.2729	−	19.5252i	−0.687320	−	1.19047i	−0.972702	−	0.232059i	$-0.925454\pi$
$269$	−11.2729	−	19.5252i	−0.687320	−	1.19047i	0.285382	−	0.958414i	$-0.407880\pi$
$270$	3.65538	−	6.33130i	0.222459	−	0.385311i
$271$	−8.28353	+	14.3475i	−0.503189	+	0.871548i	0.496804	+	0.867862i	$0.334507\pi$
$271$	−8.28353	+	14.3475i	−0.503189	+	0.871548i	−0.999993	+	0.00368593i	$0.998827\pi$
$272$	33.2257			2.01460
$273$	−0.615295	−	12.9713i	−0.0372394	−	0.785057i
$274$	11.1482			0.673489
$275$	5.34852	−	9.26391i	0.322528	−	0.558635i
$276$	0.549322	−	0.951454i	0.0330653	−	0.0572708i
$277$	15.1781	+	26.2893i	0.911966	+	1.57957i	0.811284	+	0.584653i	$0.198769\pi$
$277$	15.1781	+	26.2893i	0.911966	+	1.57957i	0.100682	+	0.994919i	$0.467897\pi$
$278$	34.1610			2.04884
$279$	4.49263	+	7.78146i	0.268967	+	0.465864i
$280$	−7.83439	−	13.5696i	−0.468194	−	0.810936i
$281$	−2.63875			−0.157415			−0.0787073	−	0.996898i	$-0.525079\pi$
$281$	−2.63875			−0.157415			−0.0787073	+	0.996898i	$0.525079\pi$
$282$	−0.136737	−	0.236835i	−0.00814254	−	0.0141033i
$283$	10.7385	−	18.5996i	0.638335	−	1.10563i	−0.347463	−	0.937694i	$-0.612957\pi$
$283$	10.7385	−	18.5996i	0.638335	−	1.10563i	0.985798	−	0.167935i	$-0.0537100\pi$
$284$	7.40256	−	12.8216i	0.439261	−	0.760823i
$285$	−23.5106			−1.39265
$286$	5.59768	−	3.59583i	0.330998	−	0.212626i
$287$	−17.5275			−1.03461
$288$	3.36377	−	5.82622i	0.198212	−	0.343313i
$289$	−15.1015	+	26.1565i	−0.888321	+	1.53862i
$290$	−12.0878	−	20.9367i	−0.709822	−	1.22945i
$291$	−4.16521			−0.244169
$292$	5.64821	+	9.78299i	0.330537	+	0.572506i
$293$	−3.26548	−	5.65597i	−0.190771	−	0.330426i	0.754735	−	0.656030i	$-0.227766\pi$
$293$	−3.26548	−	5.65597i	−0.190771	−	0.330426i	−0.945506	+	0.325604i	$0.894432\pi$
$294$	−11.0193			−0.642659
$295$	−5.39793	−	9.34949i	−0.314280	−	0.544349i
$296$	−2.70515	+	4.68546i	−0.157234	+	0.272337i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	31.9686			1.85189
$299$	2.50584	+	1.29248i	0.144916	+	0.0747463i
$300$	−15.0285			−0.867672
$301$	−3.84611	+	6.66167i	−0.221686	+	0.383972i
$302$	21.2725	−	36.8451i	1.22410	−	2.12020i
$303$	−6.82141	−	11.8150i	−0.391880	−	0.678755i
$304$	−28.6975			−1.64592
$305$	13.6978	+	23.7253i	0.784335	+	1.35851i
$306$	6.33882	+	10.9792i	0.362366	+	0.627636i
$307$	−4.92236			−0.280934			−0.140467	−	0.990085i	$-0.544860\pi$
$307$	−4.92236			−0.280934			−0.140467	+	0.990085i	$0.544860\pi$
$308$	−2.53001	−	4.38210i	−0.144160	−	0.249693i
$309$	−1.16620	+	2.01992i	−0.0663430	+	0.114909i
$310$	32.8445	−	56.8884i	1.86544	−	3.23104i
$311$	−5.80253			−0.329031			−0.164516	−	0.986374i	$-0.552606\pi$
$311$	−5.80253			−0.329031			−0.164516	+	0.986374i	$0.552606\pi$
$312$	3.51864	+	1.81488i	0.199204	+	0.102747i
$313$	15.3403			0.867083			0.433542	−	0.901134i	$-0.357264\pi$
$313$	15.3403			0.867083			0.433542	+	0.901134i	$0.357264\pi$
$314$	−2.85519	+	4.94533i	−0.161127	+	0.279081i
$315$	7.13474	−	12.3577i	0.401997	−	0.696279i
$316$	5.71320	+	9.89554i	0.321392	+	0.556668i
$317$	−28.5880			−1.60566			−0.802832	−	0.596205i	$-0.796674\pi$
$317$	−28.5880			−1.60566			−0.802832	+	0.596205i	$0.796674\pi$
$318$	−5.55048	−	9.61372i	−0.311256	−	0.539111i
$319$	1.65343	+	2.86382i	0.0925743	+	0.160343i
$320$	−10.8632			−0.607269
$321$	−1.43982	−	2.49385i	−0.0803630	−	0.139193i
$322$	2.59853	−	4.50078i	0.144810	−	0.250819i
$323$	20.3849	−	35.3077i	1.13425	−	1.96458i
$324$	1.40492			0.0780513
$325$	−1.82746	−	38.5254i	−0.101369	−	2.13700i
$326$	31.7327			1.75751
$327$	2.09308	−	3.62532i	0.115747	−	0.200480i
$328$	2.67188	−	4.62784i	0.147530	−	0.255529i
$329$	−0.266889	−	0.462265i	−0.0147140	−	0.0254855i
$330$	7.31076			0.402444
$331$	−7.14423	−	12.3742i	−0.392683	−	0.680146i	0.600120	−	0.799910i	$-0.295120\pi$
$331$	−7.14423	−	12.3742i	−0.392683	−	0.680146i	−0.992802	+	0.119764i	$0.961786\pi$
$332$	1.62998	+	2.82320i	0.0894566	+	0.154943i
$333$	−4.92713			−0.270005
$334$	11.2124	+	19.4205i	0.613516	+	1.06264i
$335$	12.7809	−	22.1372i	0.698296	−	1.20948i
$336$	8.70881	−	15.0841i	0.475104	−	0.822905i
$337$	30.9516			1.68604			0.843020	−	0.537882i	$-0.180775\pi$
$337$	30.9516			1.68604			0.843020	+	0.537882i	$0.180775\pi$
$338$	9.97378	−	21.8164i	0.542502	−	1.18666i
$339$	−1.60941			−0.0874110
$340$	19.1212	−	33.1189i	1.03699	−	1.79613i
$341$	−4.49263	+	7.78146i	−0.243289	+	0.421390i
$342$	−5.47493	−	9.48286i	−0.296050	−	0.512774i
$343$	3.70342			0.199966
$344$	−1.17260	−	2.03100i	−0.0632224	−	0.109504i
$345$	1.54912	+	2.68315i	0.0834016	+	0.144456i
$346$	−15.5376			−0.835304
$347$	−7.52278	−	13.0298i	−0.403844	−	0.699478i	0.590342	−	0.807153i	$-0.298993\pi$
$347$	−7.52278	−	13.0298i	−0.403844	−	0.699478i	−0.994186	+	0.107675i	$0.965659\pi$
$348$	2.32294	−	4.02345i	0.124523	−	0.215680i
$349$	7.85769	−	13.6099i	0.420613	−	0.728523i	−0.575387	−	0.817881i	$-0.695148\pi$
$349$	7.85769	−	13.6099i	0.420613	−	0.728523i	0.996000	+	0.0893588i	$0.0284818\pi$
$350$	−71.0913			−3.79999
$351$	0.170838	+	3.60150i	0.00911866	+	0.192234i
$352$	6.72754			0.358579
$353$	10.7807	−	18.6727i	0.573799	−	0.993850i	−0.422372	−	0.906423i	$-0.638802\pi$
$353$	10.7807	−	18.6727i	0.573799	−	0.993850i	0.996171	−	0.0874268i	$-0.0278644\pi$
$354$	2.51404	−	4.35445i	0.133620	−	0.231436i
$355$	20.8756	+	36.1576i	1.10796	+	1.91904i
$356$	−6.12218			−0.324475
$357$	12.3724	+	21.4296i	0.654816	+	1.13417i
$358$	−7.10532	−	12.3068i	−0.375528	−	0.650433i
$359$	−6.08415			−0.321109			−0.160555	−	0.987027i	$-0.551328\pi$
$359$	−6.08415			−0.321109			−0.160555	+	0.987027i	$0.551328\pi$
$360$	2.17523	+	3.76762i	0.114645	+	0.198571i
$361$	−8.10677	+	14.0413i	−0.426672	+	0.739018i
$362$	−22.8778	+	39.6255i	−1.20243	+	2.08267i
$363$	−1.00000			−0.0524864
$364$	−16.2144	−	8.36319i	−0.849863	−	0.438350i
$365$	−31.8565			−1.66744
$366$	−6.37964	+	11.0499i	−0.333469	+	0.577586i
$367$	−0.518497	+	0.898063i	−0.0270653	+	0.0468785i	−0.879241	−	0.476378i	$-0.841950\pi$
$367$	−0.518497	+	0.898063i	−0.0270653	+	0.0468785i	0.852175	+	0.523256i	$0.175283\pi$
$368$	1.89088	+	3.27510i	0.0985691	+	0.170727i
$369$	4.86654			0.253342
$370$	18.0105	+	31.1952i	0.936324	+	1.62176i
$371$	−10.8337	−	18.7645i	−0.562457	−	0.974204i
$372$	12.6236			0.654503
$373$	−12.9394	−	22.4117i	−0.669978	−	1.16044i	−0.977910	−	0.209027i	$-0.932970\pi$
$373$	−12.9394	−	22.4117i	−0.669978	−	1.16044i	0.307932	−	0.951408i	$-0.400363\pi$
$374$	−6.33882	+	10.9792i	−0.327772	+	0.567718i
$375$	11.2857	−	19.5474i	0.582790	−	1.00942i
$376$	0.162738			0.00839255
$377$	10.5965	+	5.46558i	0.545750	+	0.281492i
$378$	6.64588			0.341827
$379$	−6.68946	+	11.5865i	−0.343614	+	0.595158i	−0.985101	−	0.171977i	$-0.944985\pi$
$379$	−6.68946	+	11.5865i	−0.343614	+	0.595158i	0.641487	+	0.767134i	$0.278318\pi$
$380$	−16.5153	+	28.6053i	−0.847216	+	1.46742i
$381$	−10.3739	−	17.9682i	−0.531472	−	0.920537i
$382$	−30.9231			−1.58217
$383$	16.0510	+	27.8012i	0.820168	+	1.42057i	0.905557	+	0.424226i	$0.139454\pi$
$383$	16.0510	+	27.8012i	0.820168	+	1.42057i	−0.0853881	+	0.996348i	$0.527213\pi$
$384$	4.19783	+	7.27085i	0.214220	+	0.371039i
$385$	14.2695			0.727240
$386$	−8.16479	−	14.1418i	−0.415577	−	0.719800i
$387$	1.06788	−	1.84963i	0.0542835	−	0.0940217i
$388$	−2.92590	+	5.06780i	−0.148540	+	0.257279i
$389$	−1.28575			−0.0651899			−0.0325950	−	0.999469i	$-0.510377\pi$
$389$	−1.28575			−0.0651899			−0.0325950	+	0.999469i	$0.510377\pi$
$390$	22.1777	−	14.2465i	1.12301	−	0.721399i
$391$	−5.37266			−0.271707
$392$	3.27867	−	5.67882i	0.165598	−	0.286824i
$393$	−6.54638	+	11.3387i	−0.330221	+	0.571960i
$394$	3.60730	+	6.24803i	0.181733	+	0.314771i
$395$	−32.2230			−1.62131
$396$	0.702461	+	1.21670i	0.0353000	+	0.0611414i
$397$	13.3021	+	23.0400i	0.667614	+	1.15634i	0.978569	+	0.205917i	$0.0660178\pi$
$397$	13.3021	+	23.0400i	0.667614	+	1.15634i	−0.310955	+	0.950425i	$0.600649\pi$
$398$	−26.8279			−1.34476
$399$	−10.6862	−	18.5091i	−0.534980	−	0.926612i
$400$	25.8656	−	44.8006i	1.29328	−	2.24003i
$401$	−10.7170	+	18.5624i	−0.535182	+	0.926962i	0.463973	+	0.885850i	$0.346424\pi$
$401$	−10.7170	+	18.5624i	−0.535182	+	0.926962i	−0.999155	+	0.0411127i	$0.986910\pi$
$402$	11.9052			0.593777
$403$	1.53502	+	32.3604i	0.0764649	+	1.61199i
$404$	−19.1671			−0.953599
$405$	−1.98097	+	3.43115i	−0.0984354	+	0.170495i
$406$	10.9885	−	19.0326i	0.545350	−	0.944574i
$407$	−2.46357	−	4.26702i	−0.122114	−	0.211508i
$408$	−7.54417			−0.373492
$409$	−12.0768	−	20.9176i	−0.597158	−	1.03431i	−0.993238	−	0.116092i	$-0.962963\pi$
$409$	−12.0768	−	20.9176i	−0.597158	−	1.03431i	0.396081	−	0.918216i	$-0.370370\pi$
$410$	−17.7891	−	30.8115i	−0.878539	−	1.52167i
$411$	−6.04160			−0.298010
$412$	1.63843	+	2.83784i	0.0807194	+	0.139810i
$413$	4.90702	−	8.49921i	0.241459	−	0.418219i
$414$	−0.721487	+	1.24965i	−0.0354591	+	0.0614170i
$415$	−9.19322			−0.451278
$416$	20.4085	−	13.1100i	1.00061	−	0.642769i
$417$	−18.5130			−0.906586
$418$	5.47493	−	9.48286i	0.267788	−	0.463822i
$419$	−3.25289	+	5.63418i	−0.158914	+	0.275248i	−0.934477	−	0.356022i	$-0.884133\pi$
$419$	−3.25289	+	5.63418i	−0.158914	+	0.275248i	0.775563	+	0.631270i	$0.217466\pi$
$420$	−10.0238	−	17.3616i	−0.489109	−	0.847162i
$421$	6.47037			0.315347			0.157673	−	0.987491i	$-0.449601\pi$
$421$	6.47037			0.315347			0.157673	+	0.987491i	$0.449601\pi$
$422$	−12.9557	−	22.4399i	−0.630673	−	1.09236i
$423$	0.0741022	+	0.128349i	0.00360297	+	0.00624053i
$424$	6.60593			0.320812
$425$	36.7467	+	63.6471i	1.78248	+	3.08734i
$426$	−9.72262	+	16.8401i	−0.471062	+	0.815904i
$427$	−12.4521	+	21.5676i	−0.602598	+	1.04373i
$428$	−4.04568			−0.195555
$429$	−3.03357	+	1.94870i	−0.146462	+	0.0940842i
$430$	−15.6141			−0.752976
$431$	8.81985	−	15.2764i	0.424837	−	0.735840i	−0.571568	−	0.820555i	$-0.693665\pi$
$431$	8.81985	−	15.2764i	0.424837	−	0.735840i	0.996405	+	0.0847150i	$0.0269980\pi$
$432$	−2.41802	+	4.18813i	−0.116337	+	0.201502i
$433$	2.00191	+	3.46741i	0.0962056	+	0.166633i	0.910111	−	0.414364i	$-0.135996\pi$
$433$	2.00191	+	3.46741i	0.0962056	+	0.166633i	−0.813906	+	0.580997i	$0.802663\pi$
$434$	59.7150			2.86641
$435$	6.55081	+	11.3463i	0.314087	+	0.544015i
$436$	−2.94061	−	5.09329i	−0.140830	−	0.243924i
$437$	4.64045			0.221983
$438$	−7.41843	−	12.8491i	−0.354467	−	0.613954i
$439$	1.88985	−	3.27331i	0.0901975	−	0.156227i	−0.817397	−	0.576075i	$-0.804584\pi$
$439$	1.88985	−	3.27331i	0.0901975	−	0.156227i	0.907594	+	0.419849i	$0.137917\pi$
$440$	−2.17523	+	3.76762i	−0.103700	+	0.179614i
$441$	5.97174			0.284368
$442$	2.16582	+	45.6585i	0.103018	+	2.17175i
$443$	28.0840			1.33431			0.667155	−	0.744919i	$-0.267512\pi$
$443$	28.0840			1.33431			0.667155	+	0.744919i	$0.267512\pi$
$444$	−3.46112	+	5.99484i	−0.164258	+	0.284502i
$445$	8.63242	−	14.9518i	0.409216	−	0.708783i
$446$	−16.3515	−	28.3217i	−0.774267	−	1.34107i
$447$	−17.3249			−0.819438
$448$	−4.93761	−	8.55219i	−0.233280	−	0.404053i
$449$	9.70126	+	16.8031i	0.457831	+	0.792986i	0.998846	−	0.0480266i	$-0.0152932\pi$
$449$	9.70126	+	16.8031i	0.457831	+	0.792986i	−0.541015	+	0.841013i	$0.681960\pi$
$450$	19.7386			0.930488
$451$	2.43327	+	4.21455i	0.114578	+	0.198455i
$452$	−1.13055	+	1.95816i	−0.0531764	+	0.0921043i
$453$	−11.5283	+	19.9676i	−0.541647	+	0.938159i
$454$	2.79048			0.130964
$455$	43.2875	−	27.8069i	2.02935	−	1.30361i
$456$	6.51601			0.305140
$457$	5.09606	−	8.82664i	0.238384	−	0.412893i	−0.721867	−	0.692032i	$-0.756716\pi$
$457$	5.09606	−	8.82664i	0.238384	−	0.412893i	0.960251	+	0.279139i	$0.0900491\pi$
$458$	−16.5033	+	28.5846i	−0.771151	+	1.33567i
$459$	−3.43522	−	5.94997i	−0.160342	−	0.277721i
$460$	4.35277			0.202949
$461$	10.1170	+	17.5231i	0.471195	+	0.816133i	0.999457	−	0.0329482i	$-0.0104896\pi$
$461$	10.1170	+	17.5231i	0.471195	+	0.816133i	−0.528263	+	0.849081i	$0.677156\pi$
$462$	3.32294	+	5.75550i	0.154597	+	0.267770i
$463$	−4.30791			−0.200206			−0.100103	−	0.994977i	$-0.531917\pi$
$463$	−4.30791			−0.200206			−0.100103	+	0.994977i	$0.531917\pi$
$464$	7.99605	+	13.8496i	0.371207	+	0.642950i
$465$	−17.7996	+	30.8297i	−0.825435	+	1.42970i
$466$	−12.4653	+	21.5906i	−0.577446	+	1.00017i
$467$	−13.4379			−0.621833			−0.310916	−	0.950437i	$-0.600636\pi$
$467$	−13.4379			−0.621833			−0.310916	+	0.950437i	$0.600636\pi$
$468$	4.50195	+	2.32206i	0.208103	+	0.107337i
$469$	23.2371			1.07299
$470$	0.541743	−	0.938327i	0.0249887	−	0.0432818i
$471$	1.54732	−	2.68004i	0.0712968	−	0.123490i
$472$	1.49605	+	2.59123i	0.0688612	+	0.119271i
$473$	2.13576			0.0982025
$474$	−7.50378	−	12.9969i	−0.344660	−	0.596969i
$475$	−31.7386	−	54.9730i	−1.45627	−	2.52233i
$476$	34.7645			1.59343
$477$	3.00799	+	5.21000i	0.137727	+	0.238550i
$478$	0.651521	−	1.12847i	0.0297999	−	0.0516149i
$479$	−11.6264	+	20.1375i	−0.531223	+	0.920105i	0.468113	+	0.883669i	$0.344934\pi$
$479$	−11.6264	+	20.1375i	−0.531223	+	0.920105i	−0.999336	+	0.0364365i	$0.988399\pi$
$480$	26.6542			1.21659
$481$	−15.7886	−	8.14357i	−0.719896	−	0.371315i
$482$	−35.7336			−1.62762
$483$	−1.40823	+	2.43913i	−0.0640767	+	0.110984i
$484$	−0.702461	+	1.21670i	−0.0319301	+	0.0553045i
$485$	−8.25117	−	14.2914i	−0.374666	−	0.648941i
$486$	−1.84524			−0.0837019
$487$	18.3896	+	31.8517i	0.833312	+	1.44334i	0.895398	+	0.445268i	$0.146891\pi$
$487$	18.3896	+	31.8517i	0.833312	+	1.44334i	−0.0620857	+	0.998071i	$0.519775\pi$
$488$	−3.79638	−	6.57553i	−0.171854	−	0.297660i
$489$	−17.1970			−0.777676
$490$	−21.8290	−	37.8089i	−0.986132	−	1.70803i
$491$	−20.0978	+	34.8104i	−0.907000	+	1.57097i	−0.0887899	+	0.996050i	$0.528300\pi$
$491$	−20.0978	+	34.8104i	−0.907000	+	1.57097i	−0.818210	+	0.574919i	$0.805033\pi$
$492$	3.41856	−	5.92111i	0.154120	−	0.266944i
$493$	−22.7196			−1.02324
$494$	−1.87065	−	39.4359i	−0.0841646	−	1.77431i
$495$	−3.96195			−0.178076
$496$	−21.7265	+	37.6314i	−0.975549	+	1.68970i
$497$	−18.9770	+	32.8692i	−0.851237	+	1.47439i
$498$	−2.14083	−	3.70803i	−0.0959330	−	0.166161i
$499$	1.57065			0.0703119			0.0351560	−	0.999382i	$-0.488807\pi$
$499$	1.57065			0.0703119			0.0351560	+	0.999382i	$0.488807\pi$
$500$	−15.8555	−	27.4626i	−0.709080	−	1.22816i
$501$	−6.07638	−	10.5246i	−0.271473	−	0.470205i
$502$	−34.8561			−1.55570
$503$	0.0338424	+	0.0586168i	0.00150896	+	0.00261359i	0.866779	−	0.498693i	$-0.166186\pi$
$503$	0.0338424	+	0.0586168i	0.00150896	+	0.00261359i	−0.865270	+	0.501306i	$0.832853\pi$
$504$	−1.97741	+	3.42497i	−0.0880807	+	0.152560i
$505$	27.0261	−	46.8105i	1.20264	−	2.08304i
$506$	−1.44297			−0.0641480
$507$	−5.40513	+	11.8231i	−0.240050	+	0.525080i
$508$	−29.1491			−1.29328
$509$	0.530130	−	0.918213i	0.0234976	−	0.0406991i	−0.854037	−	0.520211i	$-0.825853\pi$
$509$	0.530130	−	0.918213i	0.0234976	−	0.0406991i	0.877535	+	0.479512i	$0.159186\pi$
$510$	−25.1141	+	43.4988i	−1.11207	+	1.92616i
$511$	−14.4796	−	25.0795i	−0.640541	−	1.10945i
$512$	21.9141			0.968476
$513$	2.96705	+	5.13908i	0.130998	+	0.226896i
$514$	−22.8177	−	39.5214i	−1.00645	−	1.74322i
$515$	−9.24087			−0.407202
$516$	−1.50029	−	2.59858i	−0.0660466	−	0.114396i
$517$	−0.0741022	+	0.128349i	−0.00325901	+	0.00564477i
$518$	−16.3726	+	28.3581i	−0.719370	+	1.24598i
$519$	8.42033			0.369611
$520$	0.743225	+	15.6682i	0.0325926	+	0.687097i
$521$	23.7143			1.03894			0.519471	−	0.854488i	$-0.326129\pi$
$521$	23.7143			1.03894			0.519471	+	0.854488i	$0.326129\pi$
$522$	−3.05098	+	5.28445i	−0.133538	+	0.231294i
$523$	12.5693	−	21.7706i	0.549616	−	0.951963i	−0.448685	−	0.893690i	$-0.648107\pi$
$523$	12.5693	−	21.7706i	0.549616	−	0.951963i	0.998301	−	0.0582727i	$-0.0185593\pi$
$524$	9.19715	+	15.9299i	0.401780	+	0.695903i
$525$	38.5268			1.68145
$526$	7.15650	+	12.3954i	0.312038	+	0.540466i
$527$	−30.8663	−	53.4620i	−1.34456	−	2.32884i
$528$	−4.83604			−0.210462
$529$	11.1942	+	19.3890i	0.486706	+	0.843000i
$530$	21.9907	−	38.0891i	0.955216	−	1.65448i
$531$	−1.36244	+	2.35982i	−0.0591250	+	0.102408i
$532$	−30.0266			−1.30182
$533$	15.5944	+	8.04342i	0.675468	+	0.348399i
$534$	8.04095			0.347966
$535$	5.70450	−	9.88049i	0.246627	−	0.427171i
$536$	−3.54226	+	6.13537i	−0.153002	+	0.265007i
$537$	3.85062	+	6.66946i	0.166166	+	0.287808i
$538$	41.6024			1.79361
$539$	2.98587	+	5.17168i	0.128610	+	0.222760i
$540$	2.78312	+	4.82050i	0.119766	+	0.207441i
$541$	−22.6694			−0.974633			−0.487316	−	0.873225i	$-0.662024\pi$
$541$	−22.6694			−0.974633			−0.487316	+	0.873225i	$0.662024\pi$
$542$	−15.2851	−	26.4746i	−0.656553	−	1.13718i
$543$	12.3983	−	21.4744i	0.532060	−	0.921555i
$544$	−23.1106	+	40.0287i	−0.990858	+	1.71622i
$545$	16.5853			0.710437
$546$	21.2961	+	10.9843i	0.911391	+	0.470086i
$547$	30.0747			1.28590			0.642951	−	0.765908i	$-0.277710\pi$
$547$	30.0747			1.28590			0.642951	+	0.765908i	$0.277710\pi$
$548$	−4.24399	+	7.35081i	−0.181294	+	0.314011i
$549$	3.45735	−	5.98830i	0.147556	−	0.255574i
$550$	9.86932	+	17.0942i	0.420829	+	0.728898i
$551$	19.6232			0.835978
$552$	−0.429340	−	0.743640i	−0.0182739	−	0.0316514i
$553$	−14.6462	−	25.3680i	−0.622821	−	1.07876i
$554$	−56.0147			−2.37984
$555$	−9.76052	−	16.9057i	−0.414311	−	0.717608i
$556$	−13.0047	+	22.5247i	−0.551521	+	0.955262i
$557$	13.4301	−	23.2616i	0.569052	−	0.985628i	−0.427608	−	0.903964i	$-0.640643\pi$
$557$	13.4301	−	23.2616i	0.569052	−	0.985628i	0.996660	−	0.0816632i	$-0.0260232\pi$
$558$	−16.5800			−0.701887
$559$	6.47899	−	4.16196i	0.274032	−	0.176032i
$560$	69.0077			2.91611
$561$	3.43522	−	5.94997i	0.145035	−	0.251208i
$562$	2.43457	−	4.21679i	0.102696	−	0.177875i
$563$	13.3502	+	23.1232i	0.562643	+	0.974526i	0.997265	+	0.0739130i	$0.0235487\pi$
$563$	13.3502	+	23.1232i	0.562643	+	0.974526i	−0.434622	+	0.900613i	$0.643118\pi$
$564$	0.208216			0.00876746
$565$	−3.18819	−	5.52211i	−0.134128	−	0.232317i
$566$	19.8151	+	34.3207i	0.832890	+	1.44261i
$567$	−3.60163			−0.151254
$568$	−5.78571	−	10.0211i	−0.242763	−	0.420478i
$569$	0.361821	−	0.626692i	0.0151683	−	0.0262723i	−0.858342	−	0.513079i	$-0.828505\pi$
$569$	0.361821	−	0.626692i	0.0151683	−	0.0262723i	0.873510	+	0.486806i	$0.161838\pi$
$570$	21.6914	−	37.5706i	0.908552	−	1.57366i
$571$	−18.3499			−0.767919			−0.383959	−	0.923350i	$-0.625440\pi$
$571$	−18.3499			−0.767919			−0.383959	+	0.923350i	$0.625440\pi$
$572$	0.240014	+	5.05983i	0.0100355	+	0.211562i
$573$	16.7583			0.700088
$574$	16.1712	−	28.0094i	0.674974	−	1.16909i
$575$	−4.18252	+	7.24434i	−0.174423	+	0.302110i
$576$	1.37094	+	2.37453i	0.0571224	+	0.0989389i
$577$	3.87120			0.161160			0.0805802	−	0.996748i	$-0.474323\pi$
$577$	3.87120			0.161160			0.0805802	+	0.996748i	$0.474323\pi$
$578$	−27.8659	−	48.2651i	−1.15907	−	2.00756i
$579$	4.42478	+	7.66394i	0.183888	+	0.318503i
$580$	18.4068			0.764299
$581$	−4.17857	−	7.23750i	−0.173356	−	0.300262i
$582$	3.84291	−	6.65612i	0.159294	−	0.275905i
$583$	−3.00799	+	5.21000i	−0.124578	+	0.215776i
$584$	8.82908			0.365350
$585$	−12.0189	+	7.72065i	−0.496919	+	0.319210i
$586$	12.0512			0.497831
$587$	6.94280	−	12.0253i	0.286560	−	0.496336i	−0.686426	−	0.727199i	$-0.740822\pi$
$587$	6.94280	−	12.0253i	0.286560	−	0.496336i	0.972986	+	0.230863i	$0.0741549\pi$
$588$	4.19491	−	7.26580i	0.172995	−	0.299637i
$589$	26.6597	+	46.1760i	1.09849	+	1.90265i
$590$	19.9210			0.820135
$591$	−1.95492	−	3.38602i	−0.0804146	−	0.139282i
$592$	−11.9139	−	20.6355i	−0.489658	−	0.848113i
$593$	−20.7962			−0.853997			−0.426998	−	0.904252i	$-0.640429\pi$
$593$	−20.7962			−0.853997			−0.426998	+	0.904252i	$0.640429\pi$
$594$	−0.922622	−	1.59803i	−0.0378556	−	0.0655679i
$595$	−49.0188	+	84.9030i	−2.00957	+	3.48068i
$596$	−12.1700	+	21.0791i	−0.498504	+	0.863435i
$597$	14.5390			0.595040
$598$	−4.37737	+	2.81192i	−0.179004	+	0.114988i
$599$	11.7286			0.479218			0.239609	−	0.970869i	$-0.422981\pi$
$599$	11.7286			0.479218			0.239609	+	0.970869i	$0.422981\pi$
$600$	−5.87301	+	10.1723i	−0.239765	+	0.415284i
$601$	−6.34755	+	10.9943i	−0.258922	+	0.448466i	−0.965953	−	0.258716i	$-0.916701\pi$
$601$	−6.34755	+	10.9943i	−0.258922	+	0.448466i	0.707031	+	0.707182i	$0.250034\pi$
$602$	−7.09702	−	12.2924i	−0.289253	−	0.501001i
$603$	−6.45183			−0.262739
$604$	16.1964	+	28.0529i	0.659021	+	1.14146i
$605$	−1.98097	−	3.43115i	−0.0805381	−	0.139496i
$606$	25.1743			1.02264
$607$	−2.74731	−	4.75849i	−0.111510	−	0.193141i	0.804869	−	0.593452i	$-0.202235\pi$
$607$	−2.74731	−	4.75849i	−0.111510	−	0.193141i	−0.916379	+	0.400311i	$0.868902\pi$
$608$	19.9610	−	34.5734i	0.809523	−	1.40214i
$609$	−5.95504	+	10.3144i	−0.241311	+	0.417962i
$610$	−50.5517			−2.04678
$611$	0.0253189	+	0.533758i	0.00102429	+	0.0215935i
$612$	−9.65244			−0.390177
$613$	4.11405	−	7.12575i	0.166165	−	0.287806i	−0.770903	−	0.636952i	$-0.780195\pi$
$613$	4.11405	−	7.12575i	0.166165	−	0.287806i	0.937068	+	0.349146i	$0.113528\pi$
$614$	4.54148	−	7.86607i	0.183279	−	0.317449i
$615$	9.64049	+	16.6978i	0.388742	+	0.673321i
$616$	−3.95481			−0.159344
$617$	−16.7381	−	28.9912i	−0.673850	−	1.16714i	−0.976804	−	0.214137i	$-0.931306\pi$
$617$	−16.7381	−	28.9912i	−0.673850	−	1.16714i	0.302954	−	0.953005i	$-0.402027\pi$
$618$	−2.15193	−	3.72725i	−0.0865633	−	0.149932i
$619$	−0.440546			−0.0177071			−0.00885353	−	0.999961i	$-0.502818\pi$
$619$	−0.440546			−0.0177071			−0.00885353	+	0.999961i	$0.502818\pi$
$620$	25.0070	+	43.3134i	1.00431	+	1.73951i
$621$	0.390998	−	0.677229i	0.0156902	−	0.0271763i
$622$	5.35354	−	9.27260i	0.214657	−	0.371797i
$623$	15.6947			0.628795
$624$	−14.6705	+	9.42399i	−0.587289	+	0.377262i
$625$	35.9414			1.43766
$626$	−14.1533	+	24.5142i	−0.565678	+	0.979783i
$627$	−2.96705	+	5.13908i	−0.118493	+	0.205235i
$628$	−2.17387	−	3.76525i	−0.0867468	−	0.150250i
$629$	33.8516			1.34975
$630$	13.1653	+	22.8030i	0.524519	+	0.908494i
$631$	−2.42163	−	4.19438i	−0.0964034	−	0.166976i	0.813790	−	0.581159i	$-0.197401\pi$
$631$	−2.42163	−	4.19438i	−0.0964034	−	0.166976i	−0.910193	+	0.414183i	$0.864067\pi$
$632$	8.93066			0.355243
$633$	7.02113	+	12.1610i	0.279065	+	0.483355i
$634$	26.3759	−	45.6845i	1.04752	−	1.81436i
$635$	41.1009	−	71.1889i	1.63104	−	2.82505i
$636$	8.45200			0.335144
$637$	19.1359	+	9.87009i	0.758192	+	0.391067i
$638$	−6.10196			−0.241579
$639$	5.26902	−	9.12620i	0.208439	−	0.361027i
$640$	−16.6316	+	28.8067i	−0.657421	+	1.13869i
$641$	−19.1568	−	33.1806i	−0.756649	−	1.31055i	−0.944550	−	0.328367i	$-0.893502\pi$
$641$	−19.1568	−	33.1806i	−0.756649	−	1.31055i	0.187901	−	0.982188i	$-0.439831\pi$
$642$	5.31364			0.209713
$643$	5.62430	+	9.74157i	0.221801	+	0.384170i	0.955355	−	0.295461i	$-0.0954733\pi$
$643$	5.62430	+	9.74157i	0.221801	+	0.384170i	−0.733554	+	0.679631i	$0.762140\pi$
$644$	1.97846	+	3.42679i	0.0779621	+	0.135034i
$645$	8.46178			0.333182
$646$	37.6152	+	65.1514i	1.47995	+	2.56335i
$647$	−15.3054	+	26.5097i	−0.601718	+	1.04221i	0.390843	+	0.920457i	$0.372183\pi$
$647$	−15.3054	+	26.5097i	−0.601718	+	1.04221i	−0.992561	+	0.121748i	$0.961150\pi$
$648$	0.549031	−	0.950950i	0.0215680	−	0.0373568i
$649$	−2.72489			−0.106961
$650$	63.2507	+	32.6240i	2.48090	+	1.27962i
$651$	−32.3616			−1.26835
$652$	−12.0802	+	20.9236i	−0.473099	+	0.819431i
$653$	−17.3302	+	30.0168i	−0.678182	+	1.17465i	0.297345	+	0.954770i	$0.403899\pi$
$653$	−17.3302	+	30.0168i	−0.678182	+	1.17465i	−0.975528	+	0.219876i	$0.929435\pi$
$654$	3.86224	+	6.68959i	0.151025	+	0.261584i
$655$	−51.8728			−2.02684
$656$	11.7674	+	20.3817i	0.459439	+	0.795772i
$657$	4.02030	+	6.96337i	0.156847	+	0.271667i
$658$	0.984949			0.0383973
$659$	18.6519	+	32.3061i	0.726575	+	1.25847i	0.958322	+	0.285689i	$0.0922224\pi$
$659$	18.6519	+	32.3061i	0.726575	+	1.25847i	−0.231747	+	0.972776i	$0.574444\pi$
$660$	−2.78312	+	4.82050i	−0.108333	+	0.187638i
$661$	6.17221	−	10.6906i	0.240071	−	0.415815i	−0.720663	−	0.693285i	$-0.756163\pi$
$661$	6.17221	−	10.6906i	0.240071	−	0.415815i	0.960734	+	0.277470i	$0.0894959\pi$
$662$	26.3657			1.02473
$663$	−1.17373	−	24.7439i	−0.0455840	−	0.960973i
$664$	2.54792			0.0988785
$665$	42.3382	−	73.3320i	1.64181	−	2.84369i
$666$	4.54588	−	7.87369i	0.176149	−	0.305099i
$667$	−1.29298	−	2.23950i	−0.0500643	−	0.0867138i
$668$	−17.0737			−0.660601
$669$	8.86145	+	15.3485i	0.342603	+	0.593407i
$670$	23.5839	+	40.8485i	0.911125	+	1.57811i
$671$	6.91469			0.266939
$672$	12.1151	+	20.9839i	0.467348	+	0.809471i
$673$	−25.4766	+	44.1268i	−0.982051	+	1.70096i	−0.327681	+	0.944788i	$0.606267\pi$
$673$	−25.4766	+	44.1268i	−0.982051	+	1.70096i	−0.654370	+	0.756174i	$0.727066\pi$
$674$	−28.5566	+	49.4615i	−1.09996	+	1.90519i
$675$	−10.6970			−0.411729
$676$	10.5882	+	14.8817i	0.407238	+	0.572371i
$677$	−29.6621			−1.14001			−0.570003	−	0.821643i	$-0.693058\pi$
$677$	−29.6621			−1.14001			−0.570003	+	0.821643i	$0.693058\pi$
$678$	1.48487	−	2.57188i	0.0570262	−	0.0987723i
$679$	7.50077	−	12.9917i	0.287853	−	0.498576i
$680$	−14.9448	−	25.8852i	−0.573107	−	0.992651i
$681$	−1.51225			−0.0579497
$682$	−8.28999	−	14.3587i	−0.317440	−	0.549823i
$683$	12.4324	+	21.5336i	0.475713	+	0.823960i	0.999613	−	0.0278204i	$-0.00885664\pi$
$683$	12.4324	+	21.5336i	0.475713	+	0.823960i	−0.523900	+	0.851780i	$0.675523\pi$
$684$	8.33695			0.318771
$685$	−11.9683	−	20.7296i	−0.457284	−	0.792038i
$686$	−3.41686	+	5.91817i	−0.130456	+	0.225957i
$687$	8.94372	−	15.4910i	0.341224	−	0.591018i
$688$	10.3286			0.393775
$689$	1.02776	+	21.6666i	0.0391545	+	0.825432i
$690$	−5.71699			−0.217642
$691$	−16.5301	+	28.6309i	−0.628833	+	1.08917i	0.358953	+	0.933356i	$0.383134\pi$
$691$	−16.5301	+	28.6309i	−0.628833	+	1.08917i	−0.987786	+	0.155815i	$0.950200\pi$
$692$	5.91496	−	10.2450i	0.224853	−	0.389457i
$693$	−1.80081	−	3.11910i	−0.0684073	−	0.118485i
$694$	27.7627			1.05386
$695$	−36.6738	−	63.5209i	−1.39112	−	2.40948i
$696$	−1.81557	−	3.14466i	−0.0688190	−	0.119198i
$697$	−33.4353			−1.26645
$698$	14.4994	+	25.1136i	0.548809	+	0.950565i
$699$	6.75539	−	11.7007i	0.255512	−	0.442560i
$700$	27.0636	−	46.8755i	1.02291	−	1.77173i
$701$	−0.0470074			−0.00177545			−0.000887723	−	1.00000i	$-0.500283\pi$
$701$	−0.0470074			−0.00177545			−0.000887723		1.00000i	$0.500283\pi$
$702$	−5.91292	−	3.04982i	−0.223169	−	0.115108i
$703$	−29.2381			−1.10274
$704$	−1.37094	+	2.37453i	−0.0516691	+	0.0894936i
$705$	−0.293589	+	0.508511i	−0.0110572	+	0.0191516i
$706$	19.8930	+	34.4557i	0.748684	+	1.29676i
$707$	49.1364			1.84796
$708$	1.91413	+	3.31537i	0.0719373	+	0.124599i
$709$	−7.55348	−	13.0830i	−0.283677	−	0.491343i	0.688610	−	0.725131i	$-0.258221\pi$
$709$	−7.55348	−	13.0830i	−0.283677	−	0.491343i	−0.972287	+	0.233788i	$0.924888\pi$
$710$	−77.0410			−2.89130
$711$	4.06656	+	7.04348i	0.152508	+	0.264151i
$712$	−2.39249	+	4.14392i	−0.0896625	+	0.155300i
$713$	3.51322	−	6.08507i	0.131571	−	0.227888i
$714$	−45.6601			−1.70879
$715$	−12.6957	−	6.54831i	−0.474793	−	0.244893i
$716$	10.8196			0.404349
$717$	−0.353082	+	0.611555i	−0.0131861	+	0.0228389i
$718$	5.61337	−	9.72264i	0.209489	−	0.362846i
$719$	−5.61016	−	9.71709i	−0.209224	−	0.362386i	0.742246	−	0.670127i	$-0.233760\pi$
$719$	−5.61016	−	9.71709i	−0.209224	−	0.362386i	−0.951470	+	0.307741i	$0.900427\pi$
$720$	−19.1601			−0.714056
$721$	−4.20023	−	7.27501i	−0.156425	−	0.270936i
$722$	−14.9590	−	25.9097i	−0.556715	−	0.964259i
$723$	19.3652			0.720201
$724$	−17.4186	−	30.1699i	−0.647357	−	1.12126i
$725$	−17.6868	+	30.6344i	−0.656872	+	1.13773i
$726$	0.922622	−	1.59803i	0.0342417	−	0.0593084i
$727$	12.8992			0.478404			0.239202	−	0.970970i	$-0.423114\pi$
$727$	12.8992			0.478404			0.239202	+	0.970970i	$0.423114\pi$
$728$	−11.9972	+	7.70675i	−0.444646	+	0.285631i
$729$	1.00000			0.0370370
$730$	29.3915	−	50.9075i	1.08783	−	1.88417i
$731$	−7.33682	+	12.7077i	−0.271362	+	0.470013i
$732$	−4.85730	−	8.41310i	−0.179531	−	0.310957i
$733$	−0.479304			−0.0177035			−0.00885175	−	0.999961i	$-0.502818\pi$
$733$	−0.479304			−0.0177035			−0.00885175	+	0.999961i	$0.502818\pi$
$734$	−0.956753	−	1.65715i	−0.0353144	−	0.0611663i
$735$	11.8299	+	20.4899i	0.436351	+	0.755782i
$736$	−5.26091			−0.193920
$737$	−3.22591	−	5.58745i	−0.118828	−	0.205816i
$738$	−4.48997	+	7.77686i	−0.165278	+	0.286270i
$739$	4.67682	−	8.10050i	0.172040	−	0.297982i	−0.767093	−	0.641536i	$-0.778298\pi$
$739$	4.67682	−	8.10050i	0.172040	−	0.297982i	0.939133	+	0.343554i	$0.111631\pi$
$740$	−27.4256			−1.00818
$741$	1.01377	+	21.3717i	0.0372418	+	0.785108i
$742$	39.9816			1.46777
$743$	−0.634787	+	1.09948i	−0.0232881	+	0.0403361i	−0.877435	−	0.479696i	$-0.840747\pi$
$743$	−0.634787	+	1.09948i	−0.0232881	+	0.0403361i	0.854146	+	0.520032i	$0.174080\pi$
$744$	4.93319	−	8.54453i	0.180859	−	0.313258i
$745$	−34.3201	−	59.4442i	−1.25739	−	2.17787i
$746$	47.7528			1.74835
$747$	1.16019	+	2.00951i	0.0424491	+	0.0735240i
$748$	−4.82622	−	8.35925i	−0.176464	−	0.305645i
$749$	10.3714			0.378963
$750$	20.8248	+	36.0697i	0.760416	+	1.31708i
$751$	8.91898	−	15.4481i	0.325458	−	0.563710i	−0.656147	−	0.754633i	$-0.727815\pi$
$751$	8.91898	−	15.4481i	0.325458	−	0.563710i	0.981605	+	0.190923i	$0.0611481\pi$
$752$	−0.358361	+	0.620699i	−0.0130681	+	0.0226346i
$753$	18.8897			0.688378
$754$	−18.5107	+	11.8909i	−0.674122	+	0.433041i
$755$	−91.3490			−3.32453
$756$	−2.53001	+	4.38210i	−0.0920154	+	0.159375i
$757$	3.96670	−	6.87052i	0.144172	−	0.249713i	−0.784892	−	0.619633i	$-0.787281\pi$
$757$	3.96670	−	6.87052i	0.144172	−	0.249713i	0.929064	+	0.369920i	$0.120615\pi$
$758$	−12.3437	−	21.3799i	−0.448343	−	0.776552i
$759$	0.781997			0.0283847
$760$	12.9081	+	22.3574i	0.468224	+	0.810988i
$761$	12.2119	+	21.1516i	0.442680	+	0.766745i	0.997887	−	0.0649674i	$-0.0206943\pi$
$761$	12.2119	+	21.1516i	0.442680	+	0.766745i	−0.555207	+	0.831712i	$0.687361\pi$
$762$	38.2848			1.38691
$763$	7.53849	+	13.0570i	0.272912	+	0.472697i
$764$	11.7721	−	20.3898i	0.425898	−	0.737677i
$765$	13.6102	−	23.5735i	0.492077	−	0.852302i
$766$	−59.2360			−2.14029
$767$	−8.26615	+	5.30999i	−0.298473	+	0.191733i
$768$	−20.9758			−0.756898
$769$	−10.5714	+	18.3103i	−0.381216	+	0.660285i	−0.991236	−	0.132101i	$-0.957828\pi$
$769$	−10.5714	+	18.3103i	−0.381216	+	0.660285i	0.610021	+	0.792385i	$0.291161\pi$
$770$	−13.1653	+	22.8030i	−0.474445	+	0.821763i
$771$	12.3657	+	21.4180i	0.445339	+	0.771351i
$772$	12.4329			0.447471
$773$	−14.3930	−	24.9295i	−0.517682	−	0.896651i	−0.999789	−	0.0205388i	$-0.993462\pi$
$773$	−14.3930	−	24.9295i	−0.517682	−	0.896651i	0.482107	−	0.876112i	$-0.339872\pi$
$774$	1.97050	+	3.41301i	0.0708282	+	0.122678i
$775$	−96.1156			−3.45258
$776$	2.28683	+	3.96090i	0.0820924	+	0.142188i
$777$	8.87285	−	15.3682i	0.318312	−	0.551332i
$778$	1.18626	−	2.05466i	0.0425294	−	0.0736631i
$779$	28.8785			1.03468
$780$	0.950924	+	20.0468i	0.0340485	+	0.717790i
$781$	10.5380			0.377080
$782$	4.95693	−	8.58566i	0.177260	−	0.307022i
$783$	1.65343	−	2.86382i	0.0590888	−	0.102345i
$784$	14.4398	+	25.0104i	0.515706	+	0.893229i
$785$	12.2608			0.437608
$786$	−12.0797	−	20.9226i	−0.430867	−	0.746284i
$787$	7.81778	+	13.5408i	0.278674	+	0.482677i	0.971055	−	0.238854i	$-0.0767718\pi$
$787$	7.81778	+	13.5408i	0.278674	+	0.482677i	−0.692382	+	0.721531i	$0.743439\pi$
$788$	−5.49302			−0.195681
$789$	−3.87835	−	6.71750i	−0.138073	−	0.239149i
$790$	29.7296	−	51.4932i	1.05773	−	1.83205i
$791$	2.89824	−	5.01991i	0.103050	−	0.178487i
$792$	1.09806			0.0390179
$793$	20.9762	−	13.4747i	0.744888	−	0.478499i
$794$	−49.0913			−1.74219
$795$	−11.9175	+	20.6418i	−0.422671	+	0.732088i
$796$	10.2131	−	17.6895i	0.361992	−	0.626989i
$797$	26.0265	+	45.0791i	0.921904	+	1.59679i	0.796466	+	0.604684i	$0.206700\pi$
$797$	26.0265	+	45.0791i	0.921904	+	1.59679i	0.125439	+	0.992101i	$0.459966\pi$
$798$	39.4373			1.39607
$799$	−0.509114	−	0.881812i	−0.0180112	−	0.0311963i
$800$	35.9824	+	62.3233i	1.27217	+	2.20346i
$801$	−4.35767			−0.153971
$802$	−19.7755	−	34.2522i	−0.698297	−	1.20949i
$803$	−4.02030	+	6.96337i	−0.141873	+	0.245732i
$804$	−4.53216	+	7.84993i	−0.159837	+	0.276846i
$805$	−11.1587			−0.393292
$806$	−53.1291	−	27.4034i	−1.87139	−	0.965244i
$807$	−22.5458			−0.793649
$808$	−7.49033	+	12.9736i	−0.263509	+	0.456411i
$809$	−9.03738	+	15.6532i	−0.317737	+	0.550337i	−0.980016	−	0.198921i	$-0.936256\pi$
$809$	−9.03738	+	15.6532i	−0.317737	+	0.550337i	0.662278	+	0.749258i	$0.269590\pi$
$810$	−3.65538	−	6.33130i	−0.128437	−	0.222459i
$811$	−10.8267			−0.380178			−0.190089	−	0.981767i	$-0.560878\pi$
$811$	−10.8267			−0.380178			−0.190089	+	0.981767i	$0.560878\pi$
$812$	8.36638	+	14.4910i	0.293602	+	0.508534i
$813$	8.28353	+	14.3475i	0.290516	+	0.503189i
$814$	9.09176			0.318666
$815$	−34.0669	−	59.0055i	−1.19331	−	2.06687i
$816$	16.6129	−	28.7743i	0.581566	−	1.00730i
$817$	6.33692	−	10.9759i	0.221701	−	0.383997i
$818$	44.5691			1.55832
$819$	−11.5411	−	5.95278i	−0.403279	−	0.208007i
$820$	27.0883			0.945964
$821$	−15.6797	+	27.1580i	−0.547224	+	0.947820i	0.451239	+	0.892403i	$0.350982\pi$
$821$	−15.6797	+	27.1580i	−0.547224	+	0.947820i	−0.998463	+	0.0554172i	$0.982351\pi$
$822$	5.57411	−	9.65464i	0.194419	−	0.336744i
$823$	−17.9512	−	31.0924i	−0.625739	−	1.08381i	−0.988397	−	0.151890i	$-0.951464\pi$
$823$	−17.9512	−	31.0924i	−0.625739	−	1.08381i	0.362658	−	0.931922i	$-0.381869\pi$
$824$	2.56113			0.0892211
$825$	−5.34852	−	9.26391i	−0.186212	−	0.322528i
$826$	9.05464	+	15.6831i	0.315051	+	0.545685i
$827$	38.0375			1.32269			0.661347	−	0.750080i	$-0.269985\pi$
$827$	38.0375			1.32269			0.661347	+	0.750080i	$0.269985\pi$
$828$	−0.549322	−	0.951454i	−0.0190903	−	0.0330653i
$829$	12.8952	−	22.3352i	0.447870	−	0.775733i	−0.550377	−	0.834916i	$-0.685516\pi$
$829$	12.8952	−	22.3352i	0.447870	−	0.775733i	0.998247	+	0.0591827i	$0.0188495\pi$
$830$	8.48187	−	14.6910i	0.294410	−	0.509933i
$831$	30.3563			1.05305
$832$	0.468416	+	9.87487i	0.0162394	+	0.342349i
$833$	−41.0285			−1.42155
$834$	17.0805	−	29.5843i	0.591449	−	1.02442i
$835$	24.0743	−	41.6979i	0.833126	−	1.44302i
$836$	4.16848	+	7.22001i	0.144170	+	0.249709i
$837$	8.98526			0.310576
$838$	−6.00238	−	10.3964i	−0.207349	−	0.359139i
$839$	−8.35372	−	14.4691i	−0.288403	−	0.499528i	0.685026	−	0.728519i	$-0.259791\pi$
$839$	−8.35372	−	14.4691i	−0.288403	−	0.499528i	−0.973429	+	0.228991i	$0.926457\pi$
$840$	−15.6688			−0.540624
$841$	9.03234	+	15.6445i	0.311460	+	0.539464i
$842$	−5.96970	+	10.3398i	−0.205730	+	0.356334i
$843$	−1.31937	+	2.28522i	−0.0454417	+	0.0787073i
$844$	19.7283			0.679076
$845$	−51.2741	+	4.87536i	−1.76388	+	0.167718i
$846$	−0.273473			−0.00940220
$847$	1.80081	−	3.11910i	0.0618767	−	0.107174i
$848$	−14.5468	+	25.1958i	−0.499538	+	0.865226i
$849$	−10.7385	−	18.5996i	−0.368543	−	0.638335i
$850$	−135.613			−4.65149
$851$	1.92650	+	3.33680i	0.0660396	+	0.114384i
$852$	−7.40256	−	12.8216i	−0.253608	−	0.439261i
$853$	1.88846			0.0646596			0.0323298	−	0.999477i	$-0.489707\pi$
$853$	1.88846			0.0646596			0.0323298	+	0.999477i	$0.489707\pi$
$854$	−22.9771	−	39.7975i	−0.786261	−	1.36184i
$855$	−11.7553	+	20.3608i	−0.402023	+	0.696324i
$856$	−1.58101	+	2.73840i	−0.0540380	+	0.0935965i
$857$	42.6619			1.45730			0.728651	−	0.684885i	$-0.240148\pi$
$857$	42.6619			1.45730			0.728651	+	0.684885i	$0.240148\pi$
$858$	−0.315238	−	6.64565i	−0.0107620	−	0.226879i
$859$	10.5950			0.361498			0.180749	−	0.983529i	$-0.442148\pi$
$859$	10.5950			0.361498			0.180749	+	0.983529i	$0.442148\pi$
$860$	5.94408	−	10.2954i	0.202691	−	0.351072i
$861$	−8.76374	+	15.1792i	−0.298667	+	0.517307i
$862$	16.2748	+	28.1887i	0.554321	+	0.960112i
$863$	−0.425823			−0.0144952			−0.00724759	−	0.999974i	$-0.502307\pi$
$863$	−0.425823			−0.0144952			−0.00724759	+	0.999974i	$0.502307\pi$
$864$	−3.36377	−	5.82622i	−0.114438	−	0.198212i
$865$	16.6805	+	28.8914i	0.567153	+	0.982337i
$866$	−7.38802			−0.251055
$867$	15.1015	+	26.1565i	0.512873	+	0.888321i
$868$	−22.7327	+	39.3743i	−0.771600	+	1.33645i
$869$	−4.06656	+	7.04348i	−0.137948	+	0.238934i
$870$	−24.1757			−0.819632
$871$	−20.6743	−	10.6636i	−0.700522	−	0.361322i
$872$	−4.59666			−0.155663
$873$	−2.08260	+	3.60718i	−0.0704855	+	0.122084i
$874$	−4.28138	+	7.41556i	−0.144820	+	0.250835i
$875$	40.6469	+	70.4024i	1.37412	+	2.38004i
$876$	11.2964			0.381671
$877$	12.1272	+	21.0049i	0.409507	+	0.709287i	0.994834	−	0.101510i	$-0.0323675\pi$
$877$	12.1272	+	21.0049i	0.409507	+	0.709287i	−0.585328	+	0.810797i	$0.699034\pi$
$878$	3.48723	+	6.04005i	0.117688	+	0.203842i
$879$	−6.53096			−0.220284
$880$	−9.58007	−	16.5932i	−0.322944	−	0.559355i
$881$	−16.4748	+	28.5352i	−0.555051	+	0.961377i	0.442849	+	0.896596i	$0.353968\pi$
$881$	−16.4748	+	28.5352i	−0.555051	+	0.961377i	−0.997900	+	0.0647801i	$0.979365\pi$
$882$	−5.50965	+	9.54300i	−0.185520	+	0.321330i
$883$	−12.8270			−0.431664			−0.215832	−	0.976431i	$-0.569246\pi$
$883$	−12.8270			−0.431664			−0.215832	+	0.976431i	$0.569246\pi$
$884$	−30.9304	−	15.9536i	−1.04030	−	0.536576i
$885$	−10.7959			−0.362899
$886$	−25.9109	+	44.8790i	−0.870493	+	1.50774i
$887$	10.4450	−	18.0913i	0.350710	−	0.607448i	−0.635664	−	0.771966i	$-0.719274\pi$
$887$	10.4450	−	18.0913i	0.350710	−	0.607448i	0.986374	+	0.164518i	$0.0526069\pi$
$888$	2.70515	+	4.68546i	0.0907789	+	0.157234i
$889$	74.7261			2.50623
$890$	15.9289	+	27.5897i	0.533939	+	0.924809i
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$	24.8993			0.833690
$893$	0.439730	+	0.761634i	0.0147150	+	0.0254871i
$894$	15.9843	−	27.6856i	0.534595	−	0.925945i
$895$	−15.2559	+	26.4241i	−0.509950	+	0.883259i
$896$	−30.2380			−1.01018
$897$	2.37224	−	1.52388i	0.0792069	−	0.0508808i
$898$	−35.8024			−1.19474
$899$	14.8565	−	25.7322i	0.495492	−	0.858217i
$900$	−7.51426	+	13.0151i	−0.250475	+	0.433836i
$901$	−20.6662	−	35.7950i	−0.688492	−	1.19250i
$902$	−8.97995			−0.299000
$903$	3.84611	+	6.66167i	0.127991	+	0.221686i
$904$	0.883615	+	1.53047i	0.0293886	+	0.0509025i
$905$	98.2425			3.26569
$906$	−21.2725	−	36.8451i	−0.706732	−	1.22410i
$907$	−20.5385	+	35.5737i	−0.681969	+	1.18120i	0.292410	+	0.956293i	$0.405543\pi$
$907$	−20.5385	+	35.5737i	−0.681969	+	1.18120i	−0.974379	+	0.224912i	$0.927791\pi$
$908$	−1.06230	+	1.83996i	−0.0352537	+	0.0610612i
$909$	−13.6428			−0.452504
$910$	4.49827	+	94.8299i	0.149116	+	3.14358i
$911$	9.00958			0.298501			0.149250	−	0.988799i	$-0.452314\pi$
$911$	9.00958			0.298501			0.149250	+	0.988799i	$0.452314\pi$
$912$	−14.3488	+	24.8528i	−0.475135	+	0.822958i
$913$	−1.16019	+	2.00951i	−0.0383967	+	0.0665050i
$914$	9.40347	+	16.2873i	0.311039	+	0.538736i
$915$	27.3957			0.905672
$916$	−12.5652	−	21.7636i	−0.415167	−	0.719091i
$917$	−23.5776	−	40.8377i	−0.778602	−	1.34858i
$918$	12.6776			0.418424
$919$	−17.1674	−	29.7348i	−0.566300	−	0.980861i	−0.996927	−	0.0783312i	$-0.975041\pi$
$919$	−17.1674	−	29.7348i	−0.566300	−	0.980861i	0.430627	−	0.902530i	$-0.358292\pi$
$920$	1.70103	−	2.94626i	0.0560811	−	0.0971354i
$921$	−2.46118	+	4.26289i	−0.0810986	+	0.140467i
$922$	−37.3366			−1.22961
$923$	31.9679	−	20.5355i	1.05224	−	0.675933i
$924$	−5.06001			−0.166462
$925$	26.3529	−	45.6445i	0.866477	−	1.50078i
$926$	3.97458	−	6.88417i	0.130613	−	0.226228i
$927$	1.16620	+	2.01992i	0.0383031	+	0.0663430i
$928$	−22.2470			−0.730295
$929$	−14.8732	−	25.7611i	−0.487973	−	0.845194i	0.511931	−	0.859026i	$-0.328930\pi$
$929$	−14.8732	−	25.7611i	−0.487973	−	0.845194i	−0.999904	+	0.0138323i	$0.995597\pi$
$930$	−32.8445	−	56.8884i	−1.07701	−	1.86544i
$931$	35.4369			1.16140
$932$	−9.49080	−	16.4386i	−0.310882	−	0.538463i
$933$	−2.90126	+	5.02514i	−0.0949831	+	0.164516i
$934$	12.3981	−	21.4742i	0.405679	−	0.702656i
$935$	27.2203			0.890200
$936$	3.33105	−	2.13980i	0.108879	−	0.0699414i
$937$	−31.4090			−1.02609			−0.513044	−	0.858362i	$-0.671482\pi$
$937$	−31.4090			−1.02609			−0.513044	+	0.858362i	$0.671482\pi$
$938$	−21.4391	+	37.1335i	−0.700010	+	1.21245i
$939$	7.67013	−	13.2851i	0.250305	−	0.433542i
$940$	0.412470	+	0.714419i	0.0134533	+	0.0233018i
$941$	−15.6552			−0.510346			−0.255173	−	0.966895i	$-0.582132\pi$
$941$	−15.6552			−0.510346			−0.255173	+	0.966895i	$0.582132\pi$
$942$	2.85519	+	4.94533i	0.0930270	+	0.161127i
$943$	−1.90281	−	3.29576i	−0.0619640	−	0.107325i
$944$	−13.1777			−0.428896
$945$	−7.13474	−	12.3577i	−0.232093	−	0.401997i
$946$	−1.97050	+	3.41301i	−0.0640665	+	0.110966i
$947$	18.7705	−	32.5115i	0.609961	−	1.05648i	−0.381286	−	0.924457i	$-0.624519\pi$
$947$	18.7705	−	32.5115i	0.609961	−	1.05648i	0.991246	−	0.132026i	$-0.0421481\pi$
$948$	11.4264			0.371112
$949$	1.37364	+	28.9582i	0.0445903	+	0.940024i
$950$	117.131			3.80023
$951$	−14.2940	+	24.7580i	−0.463515	+	0.802832i
$952$	13.5857	−	23.5310i	0.440314	−	0.762646i
$953$	23.0498	+	39.9234i	0.746657	+	1.29325i	0.949417	+	0.314019i	$0.101676\pi$
$953$	23.0498	+	39.9234i	0.746657	+	1.29325i	−0.202760	+	0.979228i	$0.564991\pi$
$954$	−11.1010			−0.359407
$955$	33.1978	+	57.5002i	1.07425	+	1.86066i
$956$	0.496052	+	0.859188i	0.0160435	+	0.0277881i
$957$	3.30686			0.106896
$958$	−21.4535	−	37.1586i	−0.693131	−	1.20054i
$959$	10.8798	−	18.8444i	0.351327	−	0.608517i
$960$	−5.43158	+	9.40778i	−0.175304	+	0.303635i
$961$	49.7348			1.60435
$962$	27.5805	−	17.7171i	0.889232	−	0.571223i
$963$	−2.87964			−0.0927952
$964$	13.6033	−	23.5617i	0.438134	−	0.758870i
$965$	−17.5307	+	30.3641i	−0.564335	+	0.977456i
$966$	−2.59853	−	4.50078i	−0.0836063	−	0.144810i
$967$	33.2498			1.06924			0.534621	−	0.845092i	$-0.320454\pi$
$967$	33.2498			1.06924			0.534621	+	0.845092i	$0.320454\pi$
$968$	0.549031	+	0.950950i	0.0176465	+	0.0305647i
$969$	−20.3849	−	35.3077i	−0.654858	−	1.13425i
$970$	30.4508			0.977717
$971$	−27.4668	−	47.5739i	−0.881451	−	1.52672i	−0.849728	−	0.527221i	$-0.823234\pi$
$971$	−27.4668	−	47.5739i	−0.881451	−	1.52672i	−0.0317231	−	0.999497i	$-0.510099\pi$
$972$	0.702461	−	1.21670i	0.0225315	−	0.0390256i
$973$	33.3385	−	57.7440i	1.06878	−	1.85119i
$974$	−67.8665			−2.17458
$975$	−34.2777	−	17.6801i	−1.09777	−	0.566216i
$976$	33.4397			1.07038
$977$	−0.790210	+	1.36868i	−0.0252811	+	0.0437881i	−0.878389	−	0.477946i	$-0.841381\pi$
$977$	−0.790210	+	1.36868i	−0.0252811	+	0.0437881i	0.853108	+	0.521734i	$0.174715\pi$
$978$	15.8663	−	27.4813i	0.507350	−	0.878755i
$979$	−2.17883	−	3.77385i	−0.0696358	−	0.120613i
$980$	33.2401			1.06182
$981$	−2.09308	−	3.62532i	−0.0668268	−	0.115747i
$982$	−37.0853	−	64.2336i	−1.18344	−	2.04978i
$983$	6.65652			0.212310			0.106155	−	0.994350i	$-0.466146\pi$
$983$	6.65652			0.212310			0.106155	+	0.994350i	$0.466146\pi$
$984$	−2.67188	−	4.62784i	−0.0851765	−	0.147530i
$985$	7.74529	−	13.4152i	0.246785	−	0.427445i
$986$	20.9616	−	36.3065i	0.667553	−	1.15624i
$987$	−0.533777			−0.0169903
$988$	26.7150	+	13.7793i	0.849918	+	0.438379i
$989$	−1.67016			−0.0531080
$990$	3.65538	−	6.33130i	0.116176	−	0.201222i
$991$	22.0574	−	38.2045i	0.700676	−	1.21361i	−0.267553	−	0.963543i	$-0.586215\pi$
$991$	22.0574	−	38.2045i	0.700676	−	1.21361i	0.968229	−	0.250063i	$-0.0804515\pi$
$992$	−30.2243	−	52.3501i	−0.959624	−	1.66212i
$993$	−14.2885			−0.453431
$994$	−35.0173	−	60.6517i	−1.11068	−	1.92375i
$995$	28.8013	+	49.8853i	0.913063	+	1.58147i
$996$	3.25995			0.103296
$997$	24.5815	+	42.5764i	0.778504	+	1.34841i	0.932804	+	0.360385i	$0.117355\pi$
$997$	24.5815	+	42.5764i	0.778504	+	1.34841i	−0.154299	+	0.988024i	$0.549312\pi$
$998$	−1.44911	+	2.50994i	−0.0458709	+	0.0794508i
$999$	−2.46357	+	4.26702i	−0.0779438	+	0.135003i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.e.100.1	✓	10
13.3	even	3	inner	429.2.i.e.133.1	yes	10
13.4	even	6		5577.2.a.u.1.1		5
13.9	even	3		5577.2.a.o.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.e.100.1	✓	10	1.1	even	1	trivial
429.2.i.e.133.1	yes	10	13.3	even	3	inner
5577.2.a.o.1.5		5	13.9	even	3
5577.2.a.u.1.1		5	13.4	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.922622 + 1.59803i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.702461 - 1.21670i) q^{4} +3.96195 q^{5} +(0.922622 + 1.59803i) q^{6} +(1.80081 + 3.11910i) q^{7} -1.09806 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.922622 + 1.59803i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.702461 - 1.21670i) q^{4} +3.96195 q^{5} +(0.922622 + 1.59803i) q^{6} +(1.80081 + 3.11910i) q^{7} -1.09806 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-3.65538 + 6.33130i) q^{10} +(0.500000 - 0.866025i) q^{11} -1.40492 q^{12} +(-0.170838 - 3.60150i) q^{13} -6.64588 q^{14} +(1.98097 - 3.43115i) q^{15} +(2.41802 - 4.18813i) q^{16} +(3.43522 + 5.94997i) q^{17} +1.84524 q^{18} +(-2.96705 - 5.13908i) q^{19} +(-2.78312 - 4.82050i) q^{20} +3.60163 q^{21} +(0.922622 + 1.59803i) q^{22} +(-0.390998 + 0.677229i) q^{23} +(-0.549031 + 0.950950i) q^{24} +10.6970 q^{25} +(5.91292 + 3.04982i) q^{26} -1.00000 q^{27} +(2.53001 - 4.38210i) q^{28} +(-1.65343 + 2.86382i) q^{29} +(3.65538 + 6.33130i) q^{30} -8.98526 q^{31} +(3.36377 + 5.82622i) q^{32} +(-0.500000 - 0.866025i) q^{33} -12.6776 q^{34} +(7.13474 + 12.3577i) q^{35} +(-0.702461 + 1.21670i) q^{36} +(2.46357 - 4.26702i) q^{37} +10.9499 q^{38} +(-3.20441 - 1.65280i) q^{39} -4.35047 q^{40} +(-2.43327 + 4.21455i) q^{41} +(-3.32294 + 5.75550i) q^{42} +(1.06788 + 1.84963i) q^{43} -1.40492 q^{44} +(-1.98097 - 3.43115i) q^{45} +(-0.721487 - 1.24965i) q^{46} -0.148204 q^{47} +(-2.41802 - 4.18813i) q^{48} +(-2.98587 + 5.17168i) q^{49} +(-9.86932 + 17.0942i) q^{50} +6.87044 q^{51} +(-4.26194 + 2.73777i) q^{52} -6.01599 q^{53} +(0.922622 - 1.59803i) q^{54} +(1.98097 - 3.43115i) q^{55} +(-1.97741 - 3.42497i) q^{56} -5.93410 q^{57} +(-3.05098 - 5.28445i) q^{58} +(-1.36244 - 2.35982i) q^{59} -5.56623 q^{60} +(3.45735 + 5.98830i) q^{61} +(8.28999 - 14.3587i) q^{62} +(1.80081 - 3.11910i) q^{63} -2.74187 q^{64} +(-0.676851 - 14.2690i) q^{65} +1.84524 q^{66} +(3.22591 - 5.58745i) q^{67} +(4.82622 - 8.35925i) q^{68} +(0.390998 + 0.677229i) q^{69} -26.3306 q^{70} +(5.26902 + 9.12620i) q^{71} +(0.549031 + 0.950950i) q^{72} -8.04060 q^{73} +(4.54588 + 7.87369i) q^{74} +(5.34852 - 9.26391i) q^{75} +(-4.16848 + 7.22001i) q^{76} +3.60163 q^{77} +(5.59768 - 3.59583i) q^{78} -8.13311 q^{79} +(9.58007 - 16.5932i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-4.48997 - 7.77686i) q^{82} -2.32038 q^{83} +(-2.53001 - 4.38210i) q^{84} +(13.6102 + 23.5735i) q^{85} -3.94100 q^{86} +(1.65343 + 2.86382i) q^{87} +(-0.549031 + 0.950950i) q^{88} +(2.17883 - 3.77385i) q^{89} +7.31076 q^{90} +(10.9258 - 7.01850i) q^{91} +1.09864 q^{92} +(-4.49263 + 7.78146i) q^{93} +(0.136737 - 0.236835i) q^{94} +(-11.7553 - 20.3608i) q^{95} +6.72754 q^{96} +(-2.08260 - 3.60718i) q^{97} +(-5.50965 - 9.54300i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9	\( 10 q + 2 q^{2} + 5 q^{3} - 6 q^{4} + 4 q^{5} - 2 q^{6} + 9 q^{7} - 18 q^{8} - 5 q^{9} + 5 q^{10} + 5 q^{11} - 12 q^{12} - 3 q^{13} - 6 q^{14} + 2 q^{15} - 4 q^{16} + 3 q^{17} - 4 q^{18} - 5 q^{19} - 28 q^{20} + 18 q^{21} - 2 q^{22} + 5 q^{23} - 9 q^{24} + 42 q^{25} + 20 q^{26} - 10 q^{27} + 11 q^{28} - 12 q^{29} - 5 q^{30} - 36 q^{31} + 35 q^{32} - 5 q^{33} - 6 q^{34} - 6 q^{36} + q^{37} + 74 q^{38} + 6 q^{39} - 62 q^{40} - 30 q^{41} - 3 q^{42} + 3 q^{43} - 12 q^{44} - 2 q^{45} - 24 q^{46} - 44 q^{47} + 4 q^{48} - 14 q^{49} - 18 q^{50} + 6 q^{51} + 35 q^{52} + 14 q^{53} - 2 q^{54} + 2 q^{55} - 27 q^{56} - 10 q^{57} + 3 q^{58} + 12 q^{59} - 56 q^{60} - 18 q^{61} + 28 q^{62} + 9 q^{63} + 110 q^{64} - 28 q^{65} - 4 q^{66} + 37 q^{67} + 8 q^{68} - 5 q^{69} - 32 q^{70} + 17 q^{71} + 9 q^{72} + 4 q^{73} + q^{74} + 21 q^{75} + 26 q^{76} + 18 q^{77} + 25 q^{78} - 12 q^{79} - 38 q^{80} - 5 q^{81} + 36 q^{82} + 8 q^{83} - 11 q^{84} + 41 q^{85} - 28 q^{86} + 12 q^{87} - 9 q^{88} - 14 q^{89} - 10 q^{90} + 35 q^{91} - 12 q^{92} - 18 q^{93} - 20 q^{94} + 7 q^{95} + 70 q^{96} + 15 q^{97} + 4 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q + 2 * q^2 + 5 * q^3 - 6 * q^4 + 4 * q^5 - 2 * q^6 + 9 * q^7 - 18 * q^8 - 5 * q^9 + 5 * q^10 + 5 * q^11 - 12 * q^12 - 3 * q^13 - 6 * q^14 + 2 * q^15 - 4 * q^16 + 3 * q^17 - 4 * q^18 - 5 * q^19 - 28 * q^20 + 18 * q^21 - 2 * q^22 + 5 * q^23 - 9 * q^24 + 42 * q^25 + 20 * q^26 - 10 * q^27 + 11 * q^28 - 12 * q^29 - 5 * q^30 - 36 * q^31 + 35 * q^32 - 5 * q^33 - 6 * q^34 - 6 * q^36 + q^37 + 74 * q^38 + 6 * q^39 - 62 * q^40 - 30 * q^41 - 3 * q^42 + 3 * q^43 - 12 * q^44 - 2 * q^45 - 24 * q^46 - 44 * q^47 + 4 * q^48 - 14 * q^49 - 18 * q^50 + 6 * q^51 + 35 * q^52 + 14 * q^53 - 2 * q^54 + 2 * q^55 - 27 * q^56 - 10 * q^57 + 3 * q^58 + 12 * q^59 - 56 * q^60 - 18 * q^61 + 28 * q^62 + 9 * q^63 + 110 * q^64 - 28 * q^65 - 4 * q^66 + 37 * q^67 + 8 * q^68 - 5 * q^69 - 32 * q^70 + 17 * q^71 + 9 * q^72 + 4 * q^73 + q^74 + 21 * q^75 + 26 * q^76 + 18 * q^77 + 25 * q^78 - 12 * q^79 - 38 * q^80 - 5 * q^81 + 36 * q^82 + 8 * q^83 - 11 * q^84 + 41 * q^85 - 28 * q^86 + 12 * q^87 - 9 * q^88 - 14 * q^89 - 10 * q^90 + 35 * q^91 - 12 * q^92 - 18 * q^93 - 20 * q^94 + 7 * q^95 + 70 * q^96 + 15 * q^97 + 4 * q^98 - 10 * q^99

Introduction

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