LMFDB - Embedded newform 429.2.i.c.133.1

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:	10.0.7965937851507.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} + 8x^{8} - 6x^{7} + 28x^{6} - 23x^{5} + 51x^{4} - 10x^{3} + 25x^{2} - 6x + 9 $ x^10 - 2x^9 + 8x^8 - 6x^7 + 28x^6 - 23x^5 + 51x^4 - 10x^3 + 25x^2 - 6*x + 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			133.1
Root			$1.19780 - 2.07464i$ of defining polynomial
Character	$\chi$	$=$	429.133
Dual form			429.2.i.c.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19780 - 2.07464i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.86943 + 3.23795i) q^{4} +3.82235 q^{5} +(-1.19780 + 2.07464i) q^{6} +(-2.02991 + 3.51590i) q^{7} +4.16562 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.19780 - 2.07464i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.86943 + 3.23795i) q^{4} +3.82235 q^{5} +(-1.19780 + 2.07464i) q^{6} +(-2.02991 + 3.51590i) q^{7} +4.16562 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.57839 - 7.93001i) q^{10} +(0.500000 + 0.866025i) q^{11} +3.73887 q^{12} +(1.95068 - 3.03230i) q^{13} +9.72567 q^{14} +(-1.91117 - 3.31025i) q^{15} +(-1.25070 - 2.16628i) q^{16} +(2.90676 - 5.03465i) q^{17} +2.39559 q^{18} +(2.85444 - 4.94403i) q^{19} +(-7.14563 + 12.3766i) q^{20} +4.05982 q^{21} +(1.19780 - 2.07464i) q^{22} +(2.62232 + 4.54199i) q^{23} +(-2.08281 - 3.60753i) q^{24} +9.61033 q^{25} +(-8.62747 - 0.414889i) q^{26} +1.00000 q^{27} +(-7.58956 - 13.1455i) q^{28} +(-1.68222 - 2.91369i) q^{29} +(-4.57839 + 7.93001i) q^{30} -1.05349 q^{31} +(1.16945 - 2.02555i) q^{32} +(0.500000 - 0.866025i) q^{33} -13.9268 q^{34} +(-7.75901 + 13.4390i) q^{35} +(-1.86943 - 3.23795i) q^{36} +(-0.752883 - 1.30403i) q^{37} -13.6761 q^{38} +(-3.60139 - 0.173188i) q^{39} +15.9224 q^{40} +(2.74945 + 4.76218i) q^{41} +(-4.86283 - 8.42268i) q^{42} +(1.55825 - 2.69897i) q^{43} -3.73887 q^{44} +(-1.91117 + 3.31025i) q^{45} +(6.28201 - 10.8808i) q^{46} +4.97001 q^{47} +(-1.25070 + 2.16628i) q^{48} +(-4.74105 - 8.21174i) q^{49} +(-11.5112 - 19.9380i) q^{50} -5.81351 q^{51} +(6.17178 + 11.9849i) q^{52} +4.56558 q^{53} +(-1.19780 - 2.07464i) q^{54} +(1.91117 + 3.31025i) q^{55} +(-8.45583 + 14.6459i) q^{56} -5.70888 q^{57} +(-4.02991 + 6.98001i) q^{58} +(-2.01276 + 3.48621i) q^{59} +14.2913 q^{60} +(-7.27717 + 12.6044i) q^{61} +(1.26186 + 2.18561i) q^{62} +(-2.02991 - 3.51590i) q^{63} -10.6059 q^{64} +(7.45618 - 11.5905i) q^{65} -2.39559 q^{66} +(1.68264 + 2.91441i) q^{67} +(10.8680 + 18.8239i) q^{68} +(2.62232 - 4.54199i) q^{69} +37.1749 q^{70} +(-1.82895 + 3.16783i) q^{71} +(-2.08281 + 3.60753i) q^{72} -0.00632885 q^{73} +(-1.80360 + 3.12393i) q^{74} +(-4.80517 - 8.32279i) q^{75} +(10.6724 + 18.4851i) q^{76} -4.05982 q^{77} +(3.95443 + 7.67905i) q^{78} -3.36756 q^{79} +(-4.78061 - 8.28026i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.58656 - 11.4083i) q^{82} +8.92689 q^{83} +(-7.58956 + 13.1455i) q^{84} +(11.1106 - 19.2442i) q^{85} -7.46587 q^{86} +(-1.68222 + 2.91369i) q^{87} +(2.08281 + 3.60753i) q^{88} +(6.51256 + 11.2801i) q^{89} +9.15679 q^{90} +(6.70158 + 13.0137i) q^{91} -19.6090 q^{92} +(0.526743 + 0.912346i) q^{93} +(-5.95306 - 10.3110i) q^{94} +(10.9107 - 18.8978i) q^{95} -2.33891 q^{96} +(9.68010 - 16.7664i) q^{97} +(-11.3576 + 19.6720i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−1.19780	−	2.07464i	−0.846970	−	1.46700i	−0.883899	−	0.467678i	$-0.845091\pi$
$2$	−1.19780	−	2.07464i	−0.846970	−	1.46700i	0.0369290	−	0.999318i	$-0.488242\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.86943	+	3.23795i	−0.934717	+	1.61898i
$5$	3.82235			1.70941			0.854703	−	0.519118i	$-0.173739\pi$
$5$	3.82235			1.70941			0.854703	+	0.519118i	$0.173739\pi$
$6$	−1.19780	+	2.07464i	−0.488998	+	0.846970i
$7$	−2.02991	+	3.51590i	−0.767233	+	1.32889i	0.171825	+	0.985128i	$0.445034\pi$
$7$	−2.02991	+	3.51590i	−0.767233	+	1.32889i	−0.939058	+	0.343759i	$0.888300\pi$
$8$	4.16562			1.47277
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−4.57839	−	7.93001i	−1.44782	−	2.50769i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$	3.73887			1.07932
$13$	1.95068	−	3.03230i	0.541021	−	0.841009i
$13$	1.95068	−	3.03230i	0.541021	−	0.841009i
$14$	9.72567			2.59929
$15$	−1.91117	−	3.31025i	−0.493463	−	0.854703i
$16$	−1.25070	−	2.16628i	−0.312675	−	0.541569i
$17$	2.90676	−	5.03465i	0.704992	−	1.22108i	−0.261702	−	0.965149i	$-0.584284\pi$
$17$	2.90676	−	5.03465i	0.704992	−	1.22108i	0.966694	−	0.255934i	$-0.0823828\pi$
$18$	2.39559			0.564647
$19$	2.85444	−	4.94403i	0.654853	−	1.13424i	−0.327078	−	0.944997i	$-0.606064\pi$
$19$	2.85444	−	4.94403i	0.654853	−	1.13424i	0.981931	−	0.189241i	$-0.0606028\pi$
$20$	−7.14563	+	12.3766i	−1.59781	+	2.76749i
$21$	4.05982			0.885924
$22$	1.19780	−	2.07464i	0.255371	−	0.442316i
$23$	2.62232	+	4.54199i	0.546791	+	0.947070i	0.998492	+	0.0549003i	$0.0174841\pi$
$23$	2.62232	+	4.54199i	0.546791	+	0.947070i	−0.451701	+	0.892169i	$0.649183\pi$
$24$	−2.08281	−	3.60753i	−0.425152	−	0.736385i
$25$	9.61033			1.92207
$26$	−8.62747	−	0.414889i	−1.69199	−	0.0813663i
$27$	1.00000			0.192450
$28$	−7.58956	−	13.1455i	−1.43429	−	2.48427i
$29$	−1.68222	−	2.91369i	−0.312380	−	0.541058i	0.666497	−	0.745508i	$-0.267793\pi$
$29$	−1.68222	−	2.91369i	−0.312380	−	0.541058i	−0.978877	+	0.204450i	$0.934459\pi$
$30$	−4.57839	+	7.93001i	−0.835897	+	1.44782i
$31$	−1.05349			−0.189212			−0.0946059	−	0.995515i	$-0.530159\pi$
$31$	−1.05349			−0.189212			−0.0946059	+	0.995515i	$0.530159\pi$
$32$	1.16945	−	2.02555i	0.206732	−	0.358071i
$33$	0.500000	−	0.866025i	0.0870388	−	0.150756i
$34$	−13.9268			−2.38843
$35$	−7.75901	+	13.4390i	−1.31151	+	2.27161i
$36$	−1.86943	−	3.23795i	−0.311572	−	0.539659i
$37$	−0.752883	−	1.30403i	−0.123773	−	0.214382i	0.797479	−	0.603346i	$-0.206166\pi$
$37$	−0.752883	−	1.30403i	−0.123773	−	0.214382i	−0.921253	+	0.388964i	$0.872833\pi$
$38$	−13.6761			−2.21856
$39$	−3.60139	−	0.173188i	−0.576684	−	0.0277323i
$40$	15.9224			2.51756
$41$	2.74945	+	4.76218i	0.429392	+	0.743728i	0.996819	−	0.0796952i	$-0.0253947\pi$
$41$	2.74945	+	4.76218i	0.429392	+	0.743728i	−0.567428	+	0.823423i	$0.692061\pi$
$42$	−4.86283	−	8.42268i	−0.750352	−	1.29965i
$43$	1.55825	−	2.69897i	0.237631	−	0.411589i	−0.722403	−	0.691472i	$-0.756962\pi$
$43$	1.55825	−	2.69897i	0.237631	−	0.411589i	0.960034	+	0.279883i	$0.0902957\pi$
$44$	−3.73887			−0.563656
$45$	−1.91117	+	3.31025i	−0.284901	+	0.493463i
$46$	6.28201	−	10.8808i	0.926231	−	1.60428i
$47$	4.97001			0.724950			0.362475	−	0.931993i	$-0.381932\pi$
$47$	4.97001			0.724950			0.362475	+	0.931993i	$0.381932\pi$
$48$	−1.25070	+	2.16628i	−0.180523	+	0.312675i
$49$	−4.74105	−	8.21174i	−0.677293	−	1.17311i
$50$	−11.5112	−	19.9380i	−1.62793	−	2.81966i
$51$	−5.81351			−0.814055
$52$	6.17178	+	11.9849i	0.855873	+	1.66201i
$53$	4.56558			0.627131			0.313565	−	0.949567i	$-0.398476\pi$
$53$	4.56558			0.627131			0.313565	+	0.949567i	$0.398476\pi$
$54$	−1.19780	−	2.07464i	−0.162999	−	0.282323i
$55$	1.91117	+	3.31025i	0.257703	+	0.446354i
$56$	−8.45583	+	14.6459i	−1.12996	+	1.95714i
$57$	−5.70888			−0.756159
$58$	−4.02991	+	6.98001i	−0.529153	+	0.916520i
$59$	−2.01276	+	3.48621i	−0.262039	+	0.453866i	−0.966784	−	0.255596i	$-0.917728\pi$
$59$	−2.01276	+	3.48621i	−0.262039	+	0.453866i	0.704744	+	0.709461i	$0.251062\pi$
$60$	14.2913			1.84499
$61$	−7.27717	+	12.6044i	−0.931746	+	1.61383i	−0.151411	+	0.988471i	$0.548382\pi$
$61$	−7.27717	+	12.6044i	−0.931746	+	1.61383i	−0.780335	+	0.625361i	$0.784952\pi$
$62$	1.26186	+	2.18561i	0.160257	+	0.277573i
$63$	−2.02991	−	3.51590i	−0.255744	−	0.442962i
$64$	−10.6059			−1.32573
$65$	7.45618	−	11.5905i	0.924825	−	1.43763i
$66$	−2.39559			−0.294877
$67$	1.68264	+	2.91441i	0.205567	+	0.356052i	0.950313	−	0.311296i	$-0.100763\pi$
$67$	1.68264	+	2.91441i	0.205567	+	0.356052i	−0.744746	+	0.667347i	$0.767430\pi$
$68$	10.8680	+	18.8239i	1.31794	+	2.28273i
$69$	2.62232	−	4.54199i	0.315690	−	0.546791i
$70$	37.1749			4.44325
$71$	−1.82895	+	3.16783i	−0.217056	+	0.375952i	−0.953907	−	0.300104i	$-0.902979\pi$
$71$	−1.82895	+	3.16783i	−0.217056	+	0.375952i	0.736851	+	0.676056i	$0.236312\pi$
$72$	−2.08281	+	3.60753i	−0.245462	+	0.425152i
$73$	−0.00632885			−0.000740735			−0.000370368	−	1.00000i	$-0.500118\pi$
$73$	−0.00632885			−0.000740735			−0.000370368		1.00000i	$0.500118\pi$
$74$	−1.80360	+	3.12393i	−0.209665	+	0.363150i
$75$	−4.80517	−	8.32279i	−0.554853	−	0.961033i
$76$	10.6724	+	18.4851i	1.22420	+	2.12038i
$77$	−4.05982			−0.462659
$78$	3.95443	+	7.67905i	0.447751	+	0.869481i
$79$	−3.36756			−0.378880			−0.189440	−	0.981892i	$-0.560667\pi$
$79$	−3.36756			−0.378880			−0.189440	+	0.981892i	$0.560667\pi$
$80$	−4.78061	−	8.28026i	−0.534488	−	0.925761i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.58656	−	11.4083i	0.727364	−	1.25983i
$83$	8.92689			0.979853			0.489927	−	0.871764i	$-0.337024\pi$
$83$	8.92689			0.979853			0.489927	+	0.871764i	$0.337024\pi$
$84$	−7.58956	+	13.1455i	−0.828089	+	1.43429i
$85$	11.1106	−	19.2442i	1.20512	−	2.08732i
$86$	−7.46587			−0.805066
$87$	−1.68222	+	2.91369i	−0.180353	+	0.312380i
$88$	2.08281	+	3.60753i	0.222028	+	0.384564i
$89$	6.51256	+	11.2801i	0.690330	+	1.19569i	0.971730	+	0.236096i	$0.0758681\pi$
$89$	6.51256	+	11.2801i	0.690330	+	1.19569i	−0.281399	+	0.959591i	$0.590799\pi$
$90$	9.15679			0.965210
$91$	6.70158	+	13.0137i	0.702516	+	1.36421i
$92$	−19.6090			−2.04438
$93$	0.526743	+	0.912346i	0.0546208	+	0.0946059i
$94$	−5.95306	−	10.3110i	−0.614011	−	1.06350i
$95$	10.9107	−	18.8978i	1.11941	−	1.93887i
$96$	−2.33891			−0.238714
$97$	9.68010	−	16.7664i	0.982865	−	1.70237i	0.331800	−	0.943350i	$-0.392344\pi$
$97$	9.68010	−	16.7664i	0.982865	−	1.70237i	0.651065	−	0.759022i	$-0.274323\pi$
$98$	−11.3576	+	19.6720i	−1.14729	+	1.98717i
$99$	−1.00000			−0.100504
$100$	−17.9659	+	31.1178i	−1.79659	+	3.11178i
$101$	−1.19042	−	2.06186i	−0.118451	−	0.205163i	0.800703	−	0.599061i	$-0.204459\pi$
$101$	−1.19042	−	2.06186i	−0.118451	−	0.205163i	−0.919154	+	0.393898i	$0.871126\pi$
$102$	6.96341	+	12.0610i	0.689480	+	1.19421i
$103$	−10.6841			−1.05274			−0.526370	−	0.850256i	$-0.676447\pi$
$103$	−10.6841			−1.05274			−0.526370	+	0.850256i	$0.676447\pi$
$104$	8.12579	−	12.6314i	0.796800	−	1.23861i
$105$	15.5180			1.51440
$106$	−5.46864	−	9.47196i	−0.531161	−	0.919998i
$107$	−6.71509	−	11.6309i	−0.649172	−	1.12440i	−0.983321	−	0.181879i	$-0.941782\pi$
$107$	−6.71509	−	11.6309i	−0.649172	−	1.12440i	0.334149	−	0.942520i	$-0.391551\pi$
$108$	−1.86943	+	3.23795i	−0.179886	+	0.311572i
$109$	−13.0924			−1.25403			−0.627014	−	0.779008i	$-0.715723\pi$
$109$	−13.0924			−1.25403			−0.627014	+	0.779008i	$0.715723\pi$
$110$	4.57839	−	7.93001i	0.436533	−	0.756097i
$111$	−0.752883	+	1.30403i	−0.0714605	+	0.123773i
$112$	10.1552			0.959578
$113$	4.86232	−	8.42179i	0.457409	−	0.792255i	−0.541414	−	0.840756i	$-0.682111\pi$
$113$	4.86232	−	8.42179i	0.457409	−	0.792255i	0.998823	+	0.0485008i	$0.0154443\pi$
$114$	6.83807	+	11.8439i	0.640444	+	1.10928i
$115$	10.0234	+	17.3610i	0.934687	+	1.61893i
$116$	12.5792			1.16795
$117$	1.65071	+	3.20549i	0.152608	+	0.296348i
$118$	9.64353			0.887758
$119$	11.8009	+	20.4398i	1.08179	+	1.87371i
$120$	−7.96122	−	13.7892i	−0.726757	−	1.25878i
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$	34.8663			3.15665
$123$	2.74945	−	4.76218i	0.247909	−	0.429392i
$124$	1.96942	−	3.41114i	0.176860	−	0.306330i
$125$	17.6223			1.57619
$126$	−4.86283	+	8.42268i	−0.433216	+	0.750352i
$127$	−6.45966	−	11.1885i	−0.573202	−	0.992815i	−0.996234	−	0.0867006i	$-0.972368\pi$
$127$	−6.45966	−	11.1885i	−0.573202	−	0.992815i	0.423032	−	0.906115i	$-0.360966\pi$
$128$	10.3648	+	17.9523i	0.916125	+	1.58677i
$129$	−3.11650			−0.274393
$130$	−32.9772	−	1.58585i	−2.89229	−	0.139088i
$131$	−4.98647			−0.435670			−0.217835	−	0.975986i	$-0.569899\pi$
$131$	−4.98647			−0.435670			−0.217835	+	0.975986i	$0.569899\pi$
$132$	1.86943	+	3.23795i	0.162713	+	0.281828i
$133$	11.5885	+	20.0719i	1.00485	+	1.74045i
$134$	4.03091	−	6.98174i	0.348218	−	0.603131i
$135$	3.82235			0.328975
$136$	12.1084	−	20.9725i	1.03829	−	1.79837i
$137$	4.80727	−	8.32643i	0.410713	−	0.711375i	−0.584255	−	0.811570i	$-0.698613\pi$
$137$	4.80727	−	8.32643i	0.410713	−	0.711375i	0.994968	+	0.100195i	$0.0319466\pi$
$138$	−12.5640			−1.06952
$139$	−8.29759	+	14.3718i	−0.703792	+	1.21900i	0.263334	+	0.964705i	$0.415178\pi$
$139$	−8.29759	+	14.3718i	−0.703792	+	1.21900i	−0.967126	+	0.254299i	$0.918155\pi$
$140$	−29.0099	−	50.2467i	−2.45179	−	4.24662i
$141$	−2.48500	−	4.30415i	−0.209275	−	0.362475i
$142$	8.76283			0.735360
$143$	3.60139	+	0.173188i	0.301163	+	0.0144827i
$144$	2.50140			0.208450
$145$	−6.43002	−	11.1371i	−0.533984	−	0.924887i
$146$	0.00758067	+	0.0131301i	0.000627381	+	0.00108666i
$147$	−4.74105	+	8.21174i	−0.391035	+	0.677293i
$148$	5.62986			0.462772
$149$	−8.09070	+	14.0135i	−0.662816	+	1.14803i	0.317056	+	0.948407i	$0.397306\pi$
$149$	−8.09070	+	14.0135i	−0.662816	+	1.14803i	−0.979872	+	0.199625i	$0.936028\pi$
$150$	−11.5112	+	19.9380i	−0.939888	+	1.62793i
$151$	−2.02312			−0.164639			−0.0823196	−	0.996606i	$-0.526233\pi$
$151$	−2.02312			−0.164639			−0.0823196	+	0.996606i	$0.526233\pi$
$152$	11.8905	−	20.5950i	0.964448	−	1.67047i
$153$	2.90676	+	5.03465i	0.234997	+	0.407027i
$154$	4.86283	+	8.42268i	0.391858	+	0.678719i
$155$	−4.02679			−0.323440
$156$	7.29334	−	11.3374i	0.583934	−	0.907716i
$157$	−18.3521			−1.46465			−0.732327	−	0.680953i	$-0.761566\pi$
$157$	−18.3521			−1.46465			−0.732327	+	0.680953i	$0.761566\pi$
$158$	4.03366	+	6.98650i	0.320900	+	0.555816i
$159$	−2.28279	−	3.95391i	−0.181037	−	0.313565i
$160$	4.47006	−	7.74237i	0.353389	−	0.612088i
$161$	−21.2923			−1.67806
$162$	−1.19780	+	2.07464i	−0.0941078	+	0.162999i
$163$	−10.0722	+	17.4456i	−0.788917	+	1.36644i	0.137715	+	0.990472i	$0.456024\pi$
$163$	−10.0722	+	17.4456i	−0.788917	+	1.36644i	−0.926631	+	0.375972i	$0.877309\pi$
$164$	−20.5596			−1.60544
$165$	1.91117	−	3.31025i	0.148785	−	0.257703i
$166$	−10.6926	−	18.5201i	−0.829906	−	1.43744i
$167$	−0.519947	−	0.900575i	−0.0402347	−	0.0696886i	0.845207	−	0.534439i	$-0.179477\pi$
$167$	−0.519947	−	0.900575i	−0.0402347	−	0.0696886i	−0.885442	+	0.464751i	$0.846144\pi$
$168$	16.9117			1.30476
$169$	−5.38969	−	11.8301i	−0.414592	−	0.910007i
$170$	−53.2331			−4.08279
$171$	2.85444	+	4.94403i	0.218284	+	0.378080i
$172$	5.82610	+	10.0911i	0.444236	+	0.769439i
$173$	−8.03064	+	13.9095i	−0.610558	+	1.05752i	0.380588	+	0.924745i	$0.375722\pi$
$173$	−8.03064	+	13.9095i	−0.610558	+	1.05752i	−0.991146	+	0.132773i	$0.957612\pi$
$174$	8.05982			0.611013
$175$	−19.5081	+	33.7890i	−1.47467	+	2.55421i
$176$	1.25070	−	2.16628i	0.0942750	−	0.163289i
$177$	4.02553			0.302577
$178$	15.6015	−	27.0225i	1.16938	−	2.02542i
$179$	−0.473091	−	0.819418i	−0.0353605	−	0.0612461i	0.847804	−	0.530310i	$-0.177925\pi$
$179$	−0.473091	−	0.819418i	−0.0353605	−	0.0612461i	−0.883164	+	0.469064i	$0.844591\pi$
$180$	−7.14563	−	12.3766i	−0.532603	−	0.922496i
$181$	−11.7118			−0.870534			−0.435267	−	0.900301i	$-0.643346\pi$
$181$	−11.7118			−0.870534			−0.435267	+	0.900301i	$0.643346\pi$
$182$	18.9717	−	29.4912i	1.40627	−	2.18603i
$183$	14.5543			1.07589
$184$	10.9236	+	18.9202i	0.805297	+	1.39482i
$185$	−2.87778	−	4.98446i	−0.211579	−	0.366465i
$186$	1.26186	−	2.18561i	0.0925243	−	0.160257i
$187$	5.81351			0.425126
$188$	−9.29110	+	16.0927i	−0.677623	+	1.17368i
$189$	−2.02991	+	3.51590i	−0.147654	+	0.255744i
$190$	−52.2750			−3.79243
$191$	5.31376	−	9.20371i	0.384490	−	0.665957i	−0.607208	−	0.794543i	$-0.707711\pi$
$191$	5.31376	−	9.20371i	0.384490	−	0.665957i	0.991698	+	0.128586i	$0.0410438\pi$
$192$	5.30293	+	9.18495i	0.382706	+	0.662867i
$193$	11.9830	+	20.7551i	0.862553	+	1.49399i	0.869457	+	0.494009i	$0.164469\pi$
$193$	11.9830	+	20.7551i	0.862553	+	1.49399i	−0.00690373	+	0.999976i	$0.502198\pi$
$194$	−46.3792			−3.32983
$195$	−13.7658	−	0.661985i	−0.985786	−	0.0474058i
$196$	35.4523			2.53231
$197$	−7.80117	−	13.5120i	−0.555810	−	0.962692i	−0.997840	−	0.0656913i	$-0.979075\pi$
$197$	−7.80117	−	13.5120i	−0.555810	−	0.962692i	0.442030	−	0.897000i	$-0.354259\pi$
$198$	1.19780	+	2.07464i	0.0851237	+	0.147439i
$199$	3.39892	−	5.88711i	0.240943	−	0.417326i	−0.720040	−	0.693933i	$-0.755877\pi$
$199$	3.39892	−	5.88711i	0.240943	−	0.417326i	0.960983	+	0.276607i	$0.0892099\pi$
$200$	40.0330			2.83076
$201$	1.68264	−	2.91441i	0.118684	−	0.205567i
$202$	−2.85175	+	4.93938i	−0.200649	+	0.347534i
$203$	13.6590			0.958673
$204$	10.8680	−	18.8239i	0.760911	−	1.31794i
$205$	10.5093	+	18.2027i	0.734004	+	1.27133i
$206$	12.7974	+	22.1658i	0.891639	+	1.54436i
$207$	−5.24463			−0.364527
$208$	−9.00851	−	0.433213i	−0.624628	−	0.0300379i
$209$	5.70888			0.394891
$210$	−18.5874	−	32.1944i	−1.28266	−	2.22162i
$211$	7.62151	+	13.2008i	0.524686	+	0.908784i	0.999587	+	0.0287440i	$0.00915077\pi$
$211$	7.62151	+	13.2008i	0.524686	+	0.908784i	−0.474900	+	0.880040i	$0.657516\pi$
$212$	−8.53506	+	14.7831i	−0.586190	+	1.01531i
$213$	3.65789			0.250635
$214$	−16.0866	+	27.8628i	−1.09966	+	1.90467i
$215$	5.95618	−	10.3164i	0.406208	−	0.703573i
$216$	4.16562			0.283435
$217$	2.13848	−	3.70396i	0.145170	−	0.251441i
$218$	15.6821	+	27.1622i	1.06212	+	1.83965i
$219$	0.00316442	+	0.00548094i	0.000213832	+	0.000370368i
$220$	−14.2913			−0.963516
$221$	−9.59642	−	18.6352i	−0.645525	−	1.25354i
$222$	3.60720			0.242100
$223$	−1.70108	−	2.94635i	−0.113913	−	0.197302i	0.803432	−	0.595397i	$-0.203005\pi$
$223$	−1.70108	−	2.94635i	−0.113913	−	0.197302i	−0.917345	+	0.398094i	$0.869672\pi$
$224$	4.74777	+	8.22337i	0.317223	+	0.549447i
$225$	−4.80517	+	8.32279i	−0.320344	+	0.554853i
$226$	−23.2963			−1.54965
$227$	1.98497	−	3.43807i	0.131747	−	0.228193i	−0.792603	−	0.609738i	$-0.791275\pi$
$227$	1.98497	−	3.43807i	0.131747	−	0.228193i	0.924350	+	0.381545i	$0.124608\pi$
$228$	10.6724	−	18.4851i	0.706795	−	1.22420i
$229$	0.989162			0.0653657			0.0326828	−	0.999466i	$-0.489595\pi$
$229$	0.989162			0.0653657			0.0326828	+	0.999466i	$0.489595\pi$
$230$	24.0120	−	41.5900i	1.58330	−	2.74236i
$231$	2.02991	+	3.51590i	0.133558	+	0.231329i
$232$	−7.00748	−	12.1373i	−0.460064	−	0.796853i
$233$	−14.9645			−0.980355			−0.490178	−	0.871623i	$-0.663068\pi$
$233$	−14.9645			−0.980355			−0.490178	+	0.871623i	$0.663068\pi$
$234$	4.67304	−	7.26416i	0.305486	−	0.474873i
$235$	18.9971			1.23923
$236$	−7.52546	−	13.0345i	−0.489866	−	0.848472i
$237$	1.68378	+	2.91640i	0.109373	+	0.189440i
$238$	28.2702	−	48.9653i	1.83248	−	3.17395i
$239$	19.6498			1.27104			0.635519	−	0.772085i	$-0.280786\pi$
$239$	19.6498			1.27104			0.635519	+	0.772085i	$0.280786\pi$
$240$	−4.78061	+	8.28026i	−0.308587	+	0.534488i
$241$	4.60933	−	7.98360i	0.296913	−	0.514269i	−0.678515	−	0.734587i	$-0.737376\pi$
$241$	4.60933	−	7.98360i	0.296913	−	0.514269i	0.975428	+	0.220318i	$0.0707095\pi$
$242$	2.39559			0.153995
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−27.2084	−	47.1263i	−1.74184	−	3.01695i
$245$	−18.1219	−	31.3881i	−1.15777	−	2.00531i
$246$	−13.1731			−0.839887
$247$	−9.42370	−	18.2997i	−0.599615	−	1.16438i
$248$	−4.38843			−0.278665
$249$	−4.46344	−	7.73091i	−0.282859	−	0.489927i
$250$	−21.1079	−	36.5600i	−1.33498	−	2.31226i
$251$	−10.6460	+	18.4394i	−0.671968	+	1.16388i	0.305377	+	0.952231i	$0.401217\pi$
$251$	−10.6460	+	18.4394i	−0.671968	+	1.16388i	−0.977345	+	0.211651i	$0.932116\pi$
$252$	15.1791			0.956194
$253$	−2.62232	+	4.54199i	−0.164864	+	0.285552i
$254$	−15.4747	+	26.8030i	−0.970970	+	1.68177i
$255$	−22.2213			−1.39155
$256$	14.2239	−	24.6365i	0.888994	−	1.53978i
$257$	4.28045	+	7.41396i	0.267007	+	0.462470i	0.968088	−	0.250612i	$-0.0806319\pi$
$257$	4.28045	+	7.41396i	0.267007	+	0.462470i	−0.701080	+	0.713082i	$0.747299\pi$
$258$	3.73294	+	6.46563i	0.232402	+	0.402533i
$259$	6.11314			0.379852
$260$	23.5907	+	45.8104i	1.46303	+	2.84104i
$261$	3.36443			0.208253
$262$	5.97278	+	10.3452i	0.368999	+	0.639126i
$263$	−14.0654	−	24.3619i	−0.867307	−	1.50222i	−0.864738	−	0.502224i	$-0.832515\pi$
$263$	−14.0654	−	24.3619i	−0.867307	−	1.50222i	−0.00256942	−	0.999997i	$-0.500818\pi$
$264$	2.08281	−	3.60753i	0.128188	−	0.222028i
$265$	17.4512			1.07202
$266$	27.7613	−	48.0840i	1.70216	−	2.94822i
$267$	6.51256	−	11.2801i	0.398562	−	0.690330i
$268$	−12.5823			−0.768587
$269$	8.88225	−	15.3845i	0.541560	−	0.938010i	−0.457255	−	0.889336i	$-0.651167\pi$
$269$	8.88225	−	15.3845i	0.541560	−	0.938010i	0.998815	−	0.0486738i	$-0.0154995\pi$
$270$	−4.57839	−	7.93001i	−0.278632	−	0.482605i
$271$	−1.21986	−	2.11286i	−0.0741012	−	0.128347i	0.826594	−	0.562799i	$-0.190275\pi$
$271$	−1.21986	−	2.11286i	−0.0741012	−	0.128347i	−0.900695	+	0.434452i	$0.856942\pi$
$272$	−14.5419			−0.881733
$273$	7.91940	−	12.3106i	0.479304	−	0.745070i
$274$	−23.0325			−1.39145
$275$	4.80517	+	8.32279i	0.289762	+	0.501883i
$276$	9.80450	+	16.9819i	0.590162	+	1.02219i
$277$	−7.85092	+	13.5982i	−0.471716	+	0.817036i	−0.999476	−	0.0323572i	$-0.989699\pi$
$277$	−7.85092	+	13.5982i	−0.471716	+	0.817036i	0.527760	+	0.849393i	$0.323032\pi$
$278$	39.7553			2.38436
$279$	0.526743	−	0.912346i	0.0315353	−	0.0546208i
$280$	−32.3211	+	55.9818i	−1.93156	+	3.34555i
$281$	30.5093			1.82003			0.910017	−	0.414571i	$-0.136068\pi$
$281$	30.5093			1.82003			0.910017	+	0.414571i	$0.136068\pi$
$282$	−5.95306	+	10.3110i	−0.354500	+	0.614011i
$283$	7.98355	+	13.8279i	0.474573	+	0.821984i	0.999576	−	0.0291159i	$-0.00926919\pi$
$283$	7.98355	+	13.8279i	0.474573	+	0.821984i	−0.525003	+	0.851100i	$0.675936\pi$
$284$	−6.83819	−	11.8441i	−0.405772	−	0.702818i
$285$	−21.8213			−1.29258
$286$	−3.95443	−	7.67905i	−0.233830	−	0.454072i
$287$	−22.3245			−1.31777
$288$	1.16945	+	2.02555i	0.0689107	+	0.119357i
$289$	−8.39847	−	14.5466i	−0.494028	−	0.855681i
$290$	−15.4037	+	26.6800i	−0.904537	+	1.56670i
$291$	−19.3602			−1.13491
$292$	0.0118314	−	0.0204925i	0.000692378	−	0.00119923i
$293$	−9.94864	+	17.2316i	−0.581206	+	1.00668i	0.414131	+	0.910217i	$0.364086\pi$
$293$	−9.94864	+	17.2316i	−0.581206	+	1.00668i	−0.995337	+	0.0964609i	$0.969248\pi$
$294$	22.7153			1.32478
$295$	−7.69348	+	13.3255i	−0.447932	+	0.775840i
$296$	−3.13623	−	5.43210i	−0.182289	−	0.315735i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	38.7641			2.24554
$299$	18.8880	+	0.908309i	1.09232	+	0.0525289i
$300$	35.9318			2.07452
$301$	6.32621	+	10.9573i	0.364637	+	0.631569i
$302$	2.42329	+	4.19726i	0.139445	+	0.241525i
$303$	−1.19042	+	2.06186i	−0.0683876	+	0.118451i
$304$	−14.2802			−0.819024
$305$	−27.8159	+	48.1785i	−1.59273	+	2.75869i
$306$	6.96341	−	12.0610i	0.398072	−	0.689480i
$307$	10.3458			0.590464			0.295232	−	0.955426i	$-0.404603\pi$
$307$	10.3458			0.590464			0.295232	+	0.955426i	$0.404603\pi$
$308$	7.58956	−	13.1455i	0.432455	−	0.749034i
$309$	5.34207	+	9.25274i	0.303900	+	0.526370i
$310$	4.82328	+	8.35416i	0.273944	+	0.474485i
$311$	−19.6627			−1.11497			−0.557484	−	0.830187i	$-0.688233\pi$
$311$	−19.6627			−1.11497			−0.557484	+	0.830187i	$0.688233\pi$
$312$	−15.0020	−	0.721436i	−0.849322	−	0.0408433i
$313$	−17.2708			−0.976204			−0.488102	−	0.872787i	$-0.662311\pi$
$313$	−17.2708			−0.976204			−0.488102	+	0.872787i	$0.662311\pi$
$314$	21.9820	+	38.0740i	1.24052	+	2.14864i
$315$	−7.75901	−	13.4390i	−0.437171	−	0.757202i
$316$	6.29544	−	10.9040i	0.354146	−	0.613399i
$317$	8.93735			0.501972			0.250986	−	0.967991i	$-0.419245\pi$
$317$	8.93735			0.501972			0.250986	+	0.967991i	$0.419245\pi$
$318$	−5.46864	+	9.47196i	−0.306666	+	0.531161i
$319$	1.68222	−	2.91369i	0.0941861	−	0.163135i
$320$	−40.5393			−2.26622
$321$	−6.71509	+	11.6309i	−0.374800	+	0.649172i
$322$	25.5038	+	44.1739i	1.42127	+	2.46171i
$323$	−16.5943	−	28.7422i	−0.923333	−	1.59926i
$324$	3.73887			0.207715
$325$	18.7467	−	29.1414i	1.03988	−	1.61648i
$326$	48.2579			2.67276
$327$	6.54622	+	11.3384i	0.362007	+	0.627014i
$328$	11.4532	+	19.8375i	0.632395	+	1.09534i
$329$	−10.0887	+	17.4741i	−0.556206	+	0.963377i
$330$	−9.15679			−0.504065
$331$	6.90466	−	11.9592i	0.379514	−	0.657338i	−0.611477	−	0.791262i	$-0.709424\pi$
$331$	6.90466	−	11.9592i	0.379514	−	0.657338i	0.990992	+	0.133924i	$0.0427578\pi$
$332$	−16.6882	+	28.9049i	−0.915885	+	1.58636i
$333$	1.50577			0.0825155
$334$	−1.24558	+	2.15741i	−0.0681552	+	0.118048i
$335$	6.43162	+	11.1399i	0.351397	+	0.608637i
$336$	−5.07761	−	8.79468i	−0.277006	−	0.479789i
$337$	10.7973			0.588165			0.294083	−	0.955780i	$-0.404986\pi$
$337$	10.7973			0.588165			0.294083	+	0.955780i	$0.404986\pi$
$338$	−18.0875	+	25.3518i	−0.983830	+	1.37895i
$339$	−9.72464			−0.528170
$340$	41.5412	+	71.9515i	2.25289	+	3.90212i
$341$	−0.526743	−	0.912346i	−0.0285248	−	0.0494063i
$342$	6.83807	−	11.8439i	0.369761	−	0.640444i
$343$	10.0769			0.544101
$344$	6.49108	−	11.2429i	0.349976	−	0.606176i
$345$	10.0234	−	17.3610i	0.539642	−	0.934687i
$346$	38.4763			2.06850
$347$	−5.02081	+	8.69630i	−0.269531	+	0.466842i	−0.968741	−	0.248075i	$-0.920202\pi$
$347$	−5.02081	+	8.69630i	−0.269531	+	0.466842i	0.699210	+	0.714917i	$0.253535\pi$
$348$	−6.28959	−	10.8939i	−0.337157	−	0.583974i
$349$	−14.7807	−	25.6010i	−0.791194	−	1.37039i	−0.925228	−	0.379411i	$-0.876127\pi$
$349$	−14.7807	−	25.6010i	−0.791194	−	1.37039i	0.134034	−	0.990977i	$-0.457207\pi$
$350$	93.4669			4.99602
$351$	1.95068	−	3.03230i	0.104120	−	0.161852i
$352$	2.33891			0.124664
$353$	13.0890	+	22.6707i	0.696655	+	1.20664i	0.969620	+	0.244618i	$0.0786624\pi$
$353$	13.0890	+	22.6707i	0.696655	+	1.20664i	−0.272965	+	0.962024i	$0.588004\pi$
$354$	−4.82176	−	8.35154i	−0.256274	−	0.443879i
$355$	−6.99087	+	12.1085i	−0.371037	+	0.642655i
$356$	−48.6992			−2.58105
$357$	11.8009	−	20.4398i	0.624570	−	1.08179i
$358$	−1.13333	+	1.96299i	−0.0598985	+	0.103747i
$359$	−33.2680			−1.75582			−0.877910	−	0.478825i	$-0.841063\pi$
$359$	−33.2680			−1.75582			−0.877910	+	0.478825i	$0.841063\pi$
$360$	−7.96122	+	13.7892i	−0.419593	+	0.726757i
$361$	−6.79564	−	11.7704i	−0.357665	−	0.619494i
$362$	14.0284	+	24.2979i	0.737317	+	1.27707i
$363$	1.00000			0.0524864
$364$	−54.6659	−	2.62884i	−2.86527	−	0.137789i
$365$	−0.0241910			−0.00126622
$366$	−17.4331	−	30.1951i	−0.911245	−	1.57832i
$367$	−1.69733	−	2.93985i	−0.0885996	−	0.153459i	0.818320	−	0.574763i	$-0.194906\pi$
$367$	−1.69733	−	2.93985i	−0.0885996	−	0.153459i	−0.906919	+	0.421304i	$0.861573\pi$
$368$	6.55946	−	11.3613i	0.341936	−	0.592250i
$369$	−5.49890			−0.286261
$370$	−6.89399	+	11.9407i	−0.358402	+	0.620770i
$371$	−9.26771	+	16.0521i	−0.481156	+	0.833386i
$372$	−3.93885			−0.204220
$373$	−4.44352	+	7.69640i	−0.230077	+	0.398504i	−0.957830	−	0.287334i	$-0.907231\pi$
$373$	−4.44352	+	7.69640i	−0.230077	+	0.398504i	0.727754	+	0.685838i	$0.240564\pi$
$374$	−6.96341	−	12.0610i	−0.360069	−	0.623658i
$375$	−8.81115	−	15.2614i	−0.455006	−	0.788093i
$376$	20.7032			1.06768
$377$	−12.1166	−	0.582680i	−0.624039	−	0.0300096i
$378$	9.72567			0.500234
$379$	−16.1501	−	27.9727i	−0.829573	−	1.43686i	−0.898373	−	0.439233i	$-0.855250\pi$
$379$	−16.1501	−	27.9727i	−0.829573	−	1.43686i	0.0687999	−	0.997630i	$-0.478083\pi$
$380$	40.7935	+	70.6564i	2.09266	+	3.62460i
$381$	−6.45966	+	11.1885i	−0.330938	+	0.573202i
$382$	−25.4592			−1.30261
$383$	6.17721	−	10.6992i	0.315641	−	0.546706i	−0.663933	−	0.747792i	$-0.731114\pi$
$383$	6.17721	−	10.6992i	0.315641	−	0.546706i	0.979574	+	0.201086i	$0.0644472\pi$
$384$	10.3648	−	17.9523i	0.528925	−	0.916125i
$385$	−15.5180			−0.790872
$386$	28.7063	−	49.7208i	1.46111	−	2.53072i
$387$	1.55825	+	2.69897i	0.0792104	+	0.137196i
$388$	36.1926	+	62.6874i	1.83740	+	3.18247i
$389$	−5.42849			−0.275235			−0.137618	−	0.990485i	$-0.543945\pi$
$389$	−5.42849			−0.275235			−0.137618	+	0.990485i	$0.543945\pi$
$390$	15.1152	+	29.3520i	0.765388	+	1.48630i
$391$	30.4898			1.54193
$392$	−19.7494	−	34.2070i	−0.997497	−	1.72772i
$393$	2.49323	+	4.31841i	0.125767	+	0.217835i
$394$	−18.6884	+	32.3693i	−0.941510	+	1.63074i
$395$	−12.8720			−0.647660
$396$	1.86943	−	3.23795i	0.0939426	−	0.162713i
$397$	−5.63771	+	9.76480i	−0.282949	+	0.490081i	−0.972110	−	0.234527i	$-0.924646\pi$
$397$	−5.63771	+	9.76480i	−0.282949	+	0.490081i	0.689161	+	0.724608i	$0.257979\pi$
$398$	−16.2849			−0.816287
$399$	11.5885	−	20.0719i	0.580150	−	1.00485i
$400$	−12.0196	−	20.8186i	−0.600982	−	1.04093i
$401$	1.23687	+	2.14233i	0.0617664	+	0.106983i	0.895255	−	0.445554i	$-0.146993\pi$
$401$	1.23687	+	2.14233i	0.0617664	+	0.106983i	−0.833489	+	0.552537i	$0.813660\pi$
$402$	−8.06182			−0.402087
$403$	−2.05502	+	3.19449i	−0.102368	+	0.159129i
$404$	8.90162			0.442872
$405$	−1.91117	−	3.31025i	−0.0949670	−	0.164488i
$406$	−16.3607	−	28.3375i	−0.811967	−	1.40637i
$407$	0.752883	−	1.30403i	0.0373190	−	0.0646385i
$408$	−24.2169			−1.19892
$409$	−5.67503	+	9.82945i	−0.280612	+	0.486035i	−0.971536	−	0.236893i	$-0.923871\pi$
$409$	−5.67503	+	9.82945i	−0.280612	+	0.486035i	0.690923	+	0.722928i	$0.257204\pi$
$410$	25.1761	−	43.6063i	1.24336	−	2.15356i
$411$	−9.61453			−0.474250
$412$	19.9733	−	34.5948i	0.984014	−	1.70436i
$413$	−8.17145	−	14.1534i	−0.402091	−	0.696441i
$414$	6.28201	+	10.8808i	0.308744	+	0.534760i
$415$	34.1217			1.67497
$416$	−3.86086	−	7.49734i	−0.189294	−	0.367587i
$417$	16.5952			0.812669
$418$	−6.83807	−	11.8439i	−0.334461	−	0.579304i
$419$	−3.71606	−	6.43641i	−0.181542	−	0.314439i	0.760864	−	0.648911i	$-0.224775\pi$
$419$	−3.71606	−	6.43641i	−0.181542	−	0.314439i	−0.942406	+	0.334472i	$0.891442\pi$
$420$	−29.0099	+	50.2467i	−1.41554	+	2.45179i
$421$	−17.6143			−0.858468			−0.429234	−	0.903193i	$-0.641217\pi$
$421$	−17.6143			−0.858468			−0.429234	+	0.903193i	$0.641217\pi$
$422$	18.2580	−	31.6239i	0.888788	−	1.53943i
$423$	−2.48500	+	4.30415i	−0.120825	+	0.209275i
$424$	19.0185			0.923619
$425$	27.9349	−	48.3847i	1.35504	−	2.34700i
$426$	−4.38141	−	7.58883i	−0.212280	−	0.367680i
$427$	−29.5440	−	51.1717i	−1.42973	−	2.47637i
$428$	50.2137			2.42717
$429$	−1.65071	−	3.20549i	−0.0796970	−	0.154762i
$430$	−28.5372			−1.37618
$431$	−7.76179	−	13.4438i	−0.373872	−	0.647566i	0.616285	−	0.787523i	$-0.288637\pi$
$431$	−7.76179	−	13.4438i	−0.373872	−	0.647566i	−0.990158	+	0.139957i	$0.955304\pi$
$432$	−1.25070	−	2.16628i	−0.0601743	−	0.104225i
$433$	−1.70511	+	2.95333i	−0.0819422	+	0.141928i	−0.904084	−	0.427355i	$-0.859446\pi$
$433$	−1.70511	+	2.95333i	−0.0819422	+	0.141928i	0.822142	+	0.569283i	$0.192779\pi$
$434$	−10.2459			−0.491817
$435$	−6.43002	+	11.1371i	−0.308296	+	0.533984i
$436$	24.4755	−	42.3927i	1.17216	−	2.03024i
$437$	29.9410			1.43227
$438$	0.00758067	−	0.0131301i	0.000362219	−	0.000627381i
$439$	4.83467	+	8.37390i	0.230746	+	0.399664i	0.958028	−	0.286675i	$-0.0925499\pi$
$439$	4.83467	+	8.37390i	0.230746	+	0.399664i	−0.727282	+	0.686339i	$0.759217\pi$
$440$	7.96122	+	13.7892i	0.379536	+	0.657376i
$441$	9.48210			0.451529
$442$	−27.1668	+	42.2303i	−1.29219	+	2.00869i
$443$	−1.23707			−0.0587749			−0.0293874	−	0.999568i	$-0.509356\pi$
$443$	−1.23707			−0.0587749			−0.0293874	+	0.999568i	$0.509356\pi$
$444$	−2.81493	−	4.87560i	−0.133591	−	0.231386i
$445$	24.8933	+	43.1164i	1.18005	+	2.04391i
$446$	−4.07509	+	7.05827i	−0.192961	+	0.334219i
$447$	16.1814			0.765354
$448$	21.5289	−	37.2892i	1.01715	−	1.76175i
$449$	1.08768	−	1.88392i	0.0513308	−	0.0889076i	−0.839218	−	0.543795i	$-0.816987\pi$
$449$	1.08768	−	1.88392i	0.0513308	−	0.0889076i	0.890549	+	0.454887i	$0.150320\pi$
$450$	23.0225			1.08529
$451$	−2.74945	+	4.76218i	−0.129466	+	0.224242i
$452$	18.1796	+	31.4880i	0.855095	+	1.48107i
$453$	1.01156	+	1.75207i	0.0475272	+	0.0823196i
$454$	−9.51036			−0.446343
$455$	25.6157	+	49.7429i	1.20088	+	2.33198i
$456$	−23.7810			−1.11365
$457$	11.7328	+	20.3218i	0.548836	+	0.950611i	0.998355	+	0.0573406i	$0.0182621\pi$
$457$	11.7328	+	20.3218i	0.548836	+	0.950611i	−0.449519	+	0.893271i	$0.648405\pi$
$458$	−1.18482	−	2.05216i	−0.0553628	−	0.0958912i
$459$	2.90676	−	5.03465i	0.135676	−	0.234997i
$460$	−74.9524			−3.49467
$461$	−5.75680	+	9.97107i	−0.268121	+	0.464399i	−0.968377	−	0.249493i	$-0.919736\pi$
$461$	−5.75680	+	9.97107i	−0.268121	+	0.464399i	0.700256	+	0.713892i	$0.253069\pi$
$462$	4.86283	−	8.42268i	0.226240	−	0.391858i
$463$	−11.5553			−0.537022			−0.268511	−	0.963277i	$-0.586532\pi$
$463$	−11.5553			−0.537022			−0.268511	+	0.963277i	$0.586532\pi$
$464$	−4.20790	+	7.28829i	−0.195347	+	0.338350i
$465$	2.01340	+	3.48730i	0.0933690	+	0.161720i
$466$	17.9244	+	31.0460i	0.830332	+	1.43818i
$467$	−0.875475			−0.0405121			−0.0202561	−	0.999795i	$-0.506448\pi$
$467$	−0.875475			−0.0405121			−0.0202561	+	0.999795i	$0.506448\pi$
$468$	−13.4651	−	0.647528i	−0.622425	−	0.0299320i
$469$	−13.6624			−0.630870
$470$	−22.7547	−	39.4122i	−1.04959	−	1.81795i
$471$	9.17603	+	15.8934i	0.422809	+	0.732327i
$472$	−8.38441	+	14.5222i	−0.385924	+	0.668440i
$473$	3.11650			0.143297
$474$	4.03366	−	6.98650i	0.185272	−	0.320900i
$475$	27.4321	−	47.5138i	1.25867	−	2.18008i
$476$	−88.2440			−4.04466
$477$	−2.28279	+	3.95391i	−0.104522	+	0.181037i
$478$	−23.5364	−	40.7663i	−1.07653	−	1.86461i
$479$	11.6197	+	20.1259i	0.530917	+	0.919575i	0.999349	+	0.0360756i	$0.0114857\pi$
$479$	11.6197	+	20.1259i	0.530917	+	0.919575i	−0.468432	+	0.883499i	$0.655181\pi$
$480$	−8.94011			−0.408059
$481$	−5.42285	−	0.260781i	−0.247261	−	0.0118906i
$482$	−22.0842			−1.00591
$483$	10.6461	+	18.4396i	0.484415	+	0.839032i
$484$	−1.86943	−	3.23795i	−0.0849743	−	0.147180i
$485$	37.0007	−	64.0871i	1.68011	−	2.91004i
$486$	2.39559			0.108666
$487$	−15.7535	+	27.2859i	−0.713861	+	1.23644i	0.249536	+	0.968366i	$0.419722\pi$
$487$	−15.7535	+	27.2859i	−0.713861	+	1.23644i	−0.963397	+	0.268078i	$0.913611\pi$
$488$	−30.3139	+	52.5053i	−1.37225	+	2.37680i
$489$	20.1444			0.910962
$490$	−43.4128	+	75.1932i	−1.96119	+	3.39688i
$491$	3.70134	+	6.41091i	0.167039	+	0.289320i	0.937378	−	0.348315i	$-0.113246\pi$
$491$	3.70134	+	6.41091i	0.167039	+	0.289320i	−0.770338	+	0.637635i	$0.779913\pi$
$492$	10.2798	+	17.8052i	0.463450	+	0.802719i
$493$	−19.5592			−0.880901
$494$	−26.6778	+	41.4702i	−1.20029	+	1.86583i
$495$	−3.82235			−0.171802
$496$	1.31760	+	2.28214i	0.0591618	+	0.102471i
$497$	−7.42519	−	12.8608i	−0.333065	−	0.576886i
$498$	−10.6926	+	18.5201i	−0.479147	+	0.829906i
$499$	39.9472			1.78828			0.894140	−	0.447787i	$-0.147788\pi$
$499$	39.9472			1.78828			0.894140	+	0.447787i	$0.147788\pi$
$500$	−32.9437	+	57.0602i	−1.47329	+	2.55181i
$501$	−0.519947	+	0.900575i	−0.0232295	+	0.0402347i
$502$	51.0068			2.27655
$503$	0.995247	−	1.72382i	0.0443759	−	0.0768613i	−0.842984	−	0.537938i	$-0.819203\pi$
$503$	0.995247	−	1.72382i	0.0443759	−	0.0768613i	0.887360	+	0.461077i	$0.152537\pi$
$504$	−8.45583	−	14.6459i	−0.376653	−	0.652381i
$505$	−4.55018	−	7.88115i	−0.202481	−	0.350707i
$506$	12.5640			0.558539
$507$	−7.55032	+	10.5827i	−0.335321	+	0.469992i
$508$	48.3036			2.14313
$509$	−8.10896	−	14.0451i	−0.359423	−	0.622539i	0.628441	−	0.777857i	$-0.283693\pi$
$509$	−8.10896	−	14.0451i	−0.359423	−	0.622539i	−0.987865	+	0.155318i	$0.950360\pi$
$510$	26.6166	+	46.1012i	1.17860	+	2.04140i
$511$	0.0128470	−	0.0222516i	0.000568317	−	0.000984353i
$512$	−26.6903			−1.17956
$513$	2.85444	−	4.94403i	0.126027	−	0.218284i
$514$	10.2542	−	17.7608i	0.452295	−	0.783397i
$515$	−40.8385			−1.79956
$516$	5.82610	−	10.0911i	0.256480	−	0.444236i
$517$	2.48500	+	4.30415i	0.109290	+	0.189296i
$518$	−7.32229	−	12.6826i	−0.321723	−	0.557241i
$519$	16.0613			0.705012
$520$	31.0596	−	48.2817i	1.36205	−	2.11729i
$521$	17.9249			0.785306			0.392653	−	0.919687i	$-0.371557\pi$
$521$	17.9249			0.785306			0.392653	+	0.919687i	$0.371557\pi$
$522$	−4.02991	−	6.98001i	−0.176384	−	0.305507i
$523$	−15.1137	−	26.1778i	−0.660878	−	1.14467i	−0.980385	−	0.197090i	$-0.936851\pi$
$523$	−15.1137	−	26.1778i	−0.660878	−	1.14467i	0.319507	−	0.947584i	$-0.396483\pi$
$524$	9.32188	−	16.1460i	0.407228	−	0.705340i
$525$	39.0162			1.70281
$526$	−33.6949	+	58.3613i	−1.46917	+	2.54467i
$527$	−3.06223	+	5.30394i	−0.133393	+	0.231043i
$528$	−2.50140			−0.108859
$529$	−2.25310	+	3.90248i	−0.0979608	+	0.169673i
$530$	−20.9030	−	36.2051i	−0.907970	−	1.57265i
$531$	−2.01276	−	3.48621i	−0.0873465	−	0.151289i
$532$	−86.6557			−3.75700
$533$	19.8037	+	0.952344i	0.857792	+	0.0412506i
$534$	−31.2029			−1.35028
$535$	−25.6674	−	44.4572i	−1.10970	−	1.92205i
$536$	7.00922	+	12.1403i	0.302752	+	0.524382i
$537$	−0.473091	+	0.819418i	−0.0204154	+	0.0353605i
$538$	−42.5565			−1.83474
$539$	4.74105	−	8.21174i	0.204212	−	0.353705i
$540$	−7.14563	+	12.3766i	−0.307499	+	0.532603i
$541$	16.5223			0.710347			0.355174	−	0.934800i	$-0.384422\pi$
$541$	16.5223			0.710347			0.355174	+	0.934800i	$0.384422\pi$
$542$	−2.92229	+	5.06155i	−0.125523	+	0.217412i
$543$	5.85592	+	10.1428i	0.251302	+	0.435267i
$544$	−6.79864	−	11.7756i	−0.291489	−	0.504874i
$545$	−50.0438			−2.14364
$546$	−35.0259	−	1.68437i	−1.49897	−	0.0720844i
$547$	−28.2565			−1.20816			−0.604080	−	0.796924i	$-0.706459\pi$
$547$	−28.2565			−1.20816			−0.604080	+	0.796924i	$0.706459\pi$
$548$	17.9737	+	31.1314i	0.767800	+	1.32987i
$549$	−7.27717	−	12.6044i	−0.310582	−	0.537944i
$550$	11.5112	−	19.9380i	0.490840	−	0.850160i
$551$	−19.2071			−0.818252
$552$	10.9236	−	18.9202i	0.464939	−	0.805297i
$553$	6.83584	−	11.8400i	0.290690	−	0.503489i
$554$	37.6152			1.59812
$555$	−2.87778	+	4.98446i	−0.122155	+	0.211579i
$556$	−31.0236	−	53.7344i	−1.31569	−	2.27885i
$557$	0.873661	+	1.51323i	0.0370182	+	0.0641174i	0.883941	−	0.467599i	$-0.154881\pi$
$557$	0.873661	+	1.51323i	0.0370182	+	0.0641174i	−0.846923	+	0.531716i	$0.821547\pi$
$558$	−2.52373			−0.106838
$559$	−5.14444	−	9.98991i	−0.217587	−	0.422528i
$560$	38.8168			1.64031
$561$	−2.90676	−	5.03465i	−0.122723	−	0.212563i
$562$	−36.5440	−	63.2960i	−1.54151	−	2.66998i
$563$	−1.57810	+	2.73335i	−0.0665089	+	0.115197i	−0.897362	−	0.441295i	$-0.854519\pi$
$563$	−1.57810	+	2.73335i	−0.0665089	+	0.115197i	0.830853	+	0.556491i	$0.187853\pi$
$564$	18.5822			0.782452
$565$	18.5855	−	32.1910i	0.781897	−	1.35429i
$566$	19.1253	−	33.1261i	0.803898	−	1.39239i
$567$	4.05982			0.170496
$568$	−7.61870	+	13.1960i	−0.319674	+	0.553691i
$569$	3.92754	+	6.80270i	0.164651	+	0.285184i	0.936531	−	0.350584i	$-0.114017\pi$
$569$	3.92754	+	6.80270i	0.164651	+	0.285184i	−0.771880	+	0.635768i	$0.780684\pi$
$570$	26.1375	+	45.2715i	1.09478	+	1.89621i
$571$	−23.8772			−0.999231			−0.499615	−	0.866247i	$-0.666525\pi$
$571$	−23.8772			−0.999231			−0.499615	+	0.866247i	$0.666525\pi$
$572$	−7.29334	+	11.3374i	−0.304950	+	0.474039i
$573$	−10.6275			−0.443971
$574$	26.7402	+	46.3154i	1.11612	+	1.93317i
$575$	25.2013	+	43.6500i	1.05097	+	1.82033i
$576$	5.30293	−	9.18495i	0.220956	−	0.382706i
$577$	28.9230			1.20408			0.602041	−	0.798465i	$-0.294354\pi$
$577$	28.9230			1.20408			0.602041	+	0.798465i	$0.294354\pi$
$578$	−20.1193	+	34.8477i	−0.836854	+	1.44947i
$579$	11.9830	−	20.7551i	0.497995	−	0.862553i
$580$	48.0820			1.99650
$581$	−18.1208	+	31.3861i	−0.751776	+	1.30211i
$582$	23.1896	+	40.1655i	0.961239	+	1.66491i
$583$	2.28279	+	3.95391i	0.0945436	+	0.163754i
$584$	−0.0263636			−0.00109093
$585$	6.30958	+	12.2525i	0.260869	+	0.506578i
$586$	47.6658			1.96906
$587$	−15.1861	−	26.3032i	−0.626799	−	1.08565i	−0.988190	−	0.153233i	$-0.951031\pi$
$587$	−15.1861	−	26.3032i	−0.626799	−	1.08565i	0.361391	−	0.932414i	$-0.382302\pi$
$588$	−17.7262	−	30.7026i	−0.731015	−	1.26615i
$589$	−3.00711	+	5.20847i	−0.123906	+	0.214611i
$590$	36.8609			1.51754
$591$	−7.80117	+	13.5120i	−0.320897	+	0.555810i
$592$	−1.88326	+	3.26191i	−0.0774016	+	0.134063i
$593$	41.8447			1.71836			0.859178	−	0.511676i	$-0.170975\pi$
$593$	41.8447			1.71836			0.859178	+	0.511676i	$0.170975\pi$
$594$	1.19780	−	2.07464i	0.0491462	−	0.0851237i
$595$	45.1071	+	78.1278i	1.84921	+	3.20293i
$596$	−30.2501	−	52.3947i	−1.23909	−	2.14617i
$597$	−6.79785			−0.278217
$598$	−20.7395	−	40.2738i	−0.848103	−	1.64692i
$599$	−10.2426			−0.418501			−0.209251	−	0.977862i	$-0.567102\pi$
$599$	−10.2426			−0.418501			−0.209251	+	0.977862i	$0.567102\pi$
$600$	−20.0165	−	34.6696i	−0.817170	−	1.41538i
$601$	9.29155	+	16.0934i	0.379010	+	0.656465i	0.990919	−	0.134464i	$-0.0429312\pi$
$601$	9.29155	+	16.0934i	0.379010	+	0.656465i	−0.611908	+	0.790929i	$0.709598\pi$
$602$	15.1550	−	26.2493i	0.617673	−	1.06984i
$603$	−3.36527			−0.137044
$604$	3.78209	−	6.55077i	0.153891	−	0.266547i
$605$	−1.91117	+	3.31025i	−0.0777002	+	0.134581i
$606$	5.70351			0.231689
$607$	−0.539012	+	0.933595i	−0.0218778	+	0.0378935i	−0.876757	−	0.480934i	$-0.840298\pi$
$607$	−0.539012	+	0.933595i	−0.0218778	+	0.0378935i	0.854879	+	0.518827i	$0.173631\pi$
$608$	−6.67627	−	11.5636i	−0.270758	−	0.468967i
$609$	−6.82949	−	11.8290i	−0.276745	−	0.479336i
$610$	133.271			5.39599
$611$	9.69490	−	15.0706i	0.392214	−	0.609690i
$612$	−21.7360			−0.878624
$613$	5.97314	+	10.3458i	0.241253	+	0.417862i	0.961071	−	0.276300i	$-0.0891084\pi$
$613$	5.97314	+	10.3458i	0.241253	+	0.417862i	−0.719819	+	0.694162i	$0.755775\pi$
$614$	−12.3921	−	21.4638i	−0.500105	−	0.866208i
$615$	10.5093	−	18.2027i	0.423778	−	0.734004i
$616$	−16.9117			−0.681390
$617$	12.6732	−	21.9506i	0.510202	−	0.883696i	−0.489728	−	0.871875i	$-0.662904\pi$
$617$	12.6732	−	21.9506i	0.510202	−	0.883696i	0.999930	−	0.0118207i	$-0.00376273\pi$
$618$	12.7974	−	22.1658i	0.514788	−	0.891639i
$619$	12.6835			0.509792			0.254896	−	0.966968i	$-0.417959\pi$
$619$	12.6835			0.509792			0.254896	+	0.966968i	$0.417959\pi$
$620$	7.52782	−	13.0386i	0.302325	−	0.523642i
$621$	2.62232	+	4.54199i	0.105230	+	0.182264i
$622$	23.5519	+	40.7931i	0.944345	+	1.63565i
$623$	−52.8796			−2.11858
$624$	4.12908	+	8.01821i	0.165296	+	0.320985i
$625$	19.3069			0.772274
$626$	20.6869	+	35.8308i	0.826816	+	1.43209i
$627$	−2.85444	−	4.94403i	−0.113995	−	0.197446i
$628$	34.3080	−	59.4232i	1.36904	−	2.37124i
$629$	−8.75380			−0.349037
$630$	−18.5874	+	32.1944i	−0.740541	+	1.28266i
$631$	1.09739	−	1.90074i	0.0436865	−	0.0756672i	−0.843355	−	0.537356i	$-0.819423\pi$
$631$	1.09739	−	1.90074i	0.0436865	−	0.0756672i	0.887042	+	0.461689i	$0.152756\pi$
$632$	−14.0280			−0.558004
$633$	7.62151	−	13.2008i	0.302928	−	0.524686i
$634$	−10.7051	−	18.5418i	−0.425155	−	0.736390i
$635$	−24.6911	−	42.7662i	−0.979835	−	1.69712i
$636$	17.0701			0.676874
$637$	−34.1487	−	1.64219i	−1.35302	−	0.0650659i
$638$	−8.05982			−0.319091
$639$	−1.82895	−	3.16783i	−0.0723520	−	0.125317i
$640$	39.6177	+	68.6199i	1.56603	+	2.71244i
$641$	−9.94043	+	17.2173i	−0.392623	+	0.680044i	−0.992795	−	0.119828i	$-0.961766\pi$
$641$	−9.94043	+	17.2173i	−0.392623	+	0.680044i	0.600171	+	0.799871i	$0.295099\pi$
$642$	32.1732			1.26978
$643$	−16.5287	+	28.6285i	−0.651827	+	1.12900i	0.330852	+	0.943683i	$0.392664\pi$
$643$	−16.5287	+	28.6285i	−0.651827	+	1.12900i	−0.982679	+	0.185315i	$0.940670\pi$
$644$	39.8045	−	68.9433i	1.56852	−	2.71675i
$645$	−11.9124			−0.469048
$646$	−39.7532	+	68.8546i	−1.56407	+	2.70905i
$647$	−22.0707	−	38.2276i	−0.867690	−	1.50288i	−0.864351	−	0.502889i	$-0.832270\pi$
$647$	−22.0707	−	38.2276i	−0.867690	−	1.50288i	−0.00333955	−	0.999994i	$-0.501063\pi$
$648$	−2.08281	−	3.60753i	−0.0818205	−	0.141717i
$649$	−4.02553			−0.158016
$650$	−82.9128	−	3.98722i	−3.25211	−	0.156392i
$651$	−4.27696			−0.167627
$652$	−37.6587	−	65.2267i	−1.47483	−	2.55448i
$653$	−9.36032	−	16.2125i	−0.366298	−	0.634446i	0.622686	−	0.782472i	$-0.286041\pi$
$653$	−9.36032	−	16.2125i	−0.366298	−	0.634446i	−0.988983	+	0.148026i	$0.952708\pi$
$654$	15.6821	−	27.1622i	0.613218	−	1.06212i
$655$	−19.0600			−0.744736
$656$	6.87747	−	11.9121i	0.268520	−	0.465090i
$657$	0.00316442	−	0.00548094i	0.000123456	−	0.000213832i
$658$	48.3367			1.88436
$659$	18.4498	−	31.9560i	0.718703	−	1.24483i	−0.242811	−	0.970074i	$-0.578070\pi$
$659$	18.4498	−	31.9560i	0.718703	−	1.24483i	0.961514	−	0.274756i	$-0.0885971\pi$
$660$	7.14563	+	12.3766i	0.278143	+	0.481758i
$661$	9.36752	+	16.2250i	0.364354	+	0.631080i	0.988672	−	0.150090i	$-0.0479564\pi$
$661$	9.36752	+	16.2250i	0.364354	+	0.631080i	−0.624318	+	0.781170i	$0.714623\pi$
$662$	−33.0815			−1.28575
$663$	−11.3403	+	17.6283i	−0.440421	+	0.684627i
$664$	37.1860			1.44310
$665$	44.2952	+	76.7216i	1.71770	+	2.97514i
$666$	−1.80360	−	3.12393i	−0.0698882	−	0.121050i
$667$	8.82261	−	15.2812i	0.341613	−	0.591691i
$668$	3.88803			0.150432
$669$	−1.70108	+	2.94635i	−0.0657675	+	0.113913i
$670$	15.4075	−	26.6866i	0.595245	−	1.03099i
$671$	−14.5543			−0.561864
$672$	4.74777	−	8.22337i	0.183149	−	0.317223i
$673$	−17.9325	−	31.0600i	−0.691246	−	1.19727i	−0.971430	−	0.237328i	$-0.923729\pi$
$673$	−17.9325	−	31.0600i	−0.691246	−	1.19727i	0.280183	−	0.959947i	$-0.409605\pi$
$674$	−12.9329	−	22.4005i	−0.498158	−	0.862836i
$675$	9.61033			0.369902
$676$	48.3810	+	4.66400i	1.86081	+	0.179385i
$677$	−9.94933			−0.382384			−0.191192	−	0.981553i	$-0.561235\pi$
$677$	−9.94933			−0.382384			−0.191192	+	0.981553i	$0.561235\pi$
$678$	11.6481	+	20.1752i	0.447344	+	0.774823i
$679$	39.2994	+	68.0686i	1.50817	+	2.61223i
$680$	46.2827	−	80.1640i	1.77486	−	3.07415i
$681$	−3.96994			−0.152128
$682$	−1.26186	+	2.18561i	−0.0483192	+	0.0836914i
$683$	4.98562	−	8.63535i	0.190769	−	0.330422i	−0.754736	−	0.656029i	$-0.772235\pi$
$683$	4.98562	−	8.63535i	0.190769	−	0.330422i	0.945505	+	0.325606i	$0.105568\pi$
$684$	−21.3447			−0.816136
$685$	18.3750	−	31.8265i	0.702074	−	1.21603i
$686$	−12.0701	−	20.9060i	−0.460837	−	0.798193i
$687$	−0.494581	−	0.856640i	−0.0188694	−	0.0326828i
$688$	−7.79562			−0.297205
$689$	8.90599	−	13.8442i	0.339291	−	0.527423i
$690$	−48.0240			−1.82824
$691$	5.83127	+	10.1001i	0.221832	+	0.384224i	0.955364	−	0.295430i	$-0.0954630\pi$
$691$	5.83127	+	10.1001i	0.221832	+	0.384224i	−0.733532	+	0.679655i	$0.762130\pi$
$692$	−30.0255	−	52.0057i	−1.14140	−	1.97696i
$693$	2.02991	−	3.51590i	0.0771098	−	0.133558i
$694$	24.0556			0.913139
$695$	−31.7163	+	54.9342i	−1.20307	+	2.08377i
$696$	−7.00748	+	12.1373i	−0.265618	+	0.460064i
$697$	31.9679			1.21087
$698$	−35.4086	+	61.3295i	−1.34024	+	2.32136i
$699$	7.48224	+	12.9596i	0.283004	+	0.490178i
$700$	−72.9382	−	126.333i	−2.75680	−	4.77493i
$701$	10.7213			0.404937			0.202468	−	0.979289i	$-0.435104\pi$
$701$	10.7213			0.404937			0.202468	+	0.979289i	$0.435104\pi$
$702$	−8.62747	−	0.414889i	−0.325623	−	0.0156590i
$703$	−8.59624			−0.324213
$704$	−5.30293	−	9.18495i	−0.199862	−	0.346171i
$705$	−9.49855	−	16.4520i	−0.357736	−	0.619617i
$706$	31.3558	−	54.3099i	1.18009	−	2.04398i
$707$	9.66574			0.363518
$708$	−7.52546	+	13.0345i	−0.282824	+	0.489866i
$709$	−11.8838	+	20.5834i	−0.446307	+	0.773026i	−0.998142	−	0.0609271i	$-0.980594\pi$
$709$	−11.8838	+	20.5834i	−0.446307	+	0.773026i	0.551836	+	0.833953i	$0.313928\pi$
$710$	33.4946			1.25703
$711$	1.68378	−	2.91640i	0.0631467	−	0.109373i
$712$	27.1289	+	46.9886i	1.01670	+	1.76097i
$713$	−2.76258	−	4.78492i	−0.103459	−	0.179197i
$714$	−56.5403			−2.11597
$715$	13.7658	+	0.661985i	0.514810	+	0.0247568i
$716$	3.53765			0.132208
$717$	−9.82489	−	17.0172i	−0.366917	−	0.635519i
$718$	39.8484	+	69.0194i	1.48713	+	2.57578i
$719$	3.20607	−	5.55308i	0.119566	−	0.207095i	−0.800030	−	0.599961i	$-0.795183\pi$
$719$	3.20607	−	5.55308i	0.119566	−	0.207095i	0.919596	+	0.392866i	$0.128516\pi$
$720$	9.56121			0.356325
$721$	21.6878	−	37.5644i	0.807697	−	1.39897i
$722$	−16.2796	+	28.1971i	−0.605863	+	1.04939i
$723$	−9.21866			−0.342846
$724$	21.8945	−	37.9224i	0.813703	−	1.40938i
$725$	−16.1667	−	28.0015i	−0.600415	−	1.03995i
$726$	−1.19780	−	2.07464i	−0.0444544	−	0.0769973i
$727$	−42.2092			−1.56545			−0.782727	−	0.622365i	$-0.786172\pi$
$727$	−42.2092			−1.56545			−0.782727	+	0.622365i	$0.786172\pi$
$728$	27.9162	+	54.2101i	1.03464	+	2.00916i
$729$	1.00000			0.0370370
$730$	0.0289760	+	0.0501878i	0.00107245	+	0.00185753i
$731$	−9.05891	−	15.6905i	−0.335056	−	0.580334i
$732$	−27.2084	+	47.1263i	−1.00565	+	1.74184i
$733$	−7.41443			−0.273858			−0.136929	−	0.990581i	$-0.543723\pi$
$733$	−7.41443			−0.273858			−0.136929	+	0.990581i	$0.543723\pi$
$734$	−4.06610	+	7.04269i	−0.150083	+	0.259951i
$735$	−18.1219	+	31.3881i	−0.668438	+	1.15777i
$736$	12.2667			0.452157
$737$	−1.68264	+	2.91441i	−0.0619807	+	0.107354i
$738$	6.58656	+	11.4083i	0.242455	+	0.419944i
$739$	−5.65482	−	9.79444i	−0.208016	−	0.360294i	0.743073	−	0.669210i	$-0.233367\pi$
$739$	−5.65482	−	9.79444i	−0.208016	−	0.360294i	−0.951089	+	0.308916i	$0.900034\pi$
$740$	21.5193			0.791065
$741$	−11.1362	+	17.3110i	−0.409098	+	0.635937i
$742$	44.4033			1.63010
$743$	10.5167	+	18.2155i	0.385821	+	0.668262i	0.991883	−	0.127156i	$-0.0405848\pi$
$743$	10.5167	+	18.2155i	0.385821	+	0.668262i	−0.606062	+	0.795418i	$0.707252\pi$
$744$	2.19421	+	3.80049i	0.0804438	+	0.139333i
$745$	−30.9255	+	53.5645i	−1.13302	+	1.96245i
$746$	21.2897			0.779472
$747$	−4.46344	+	7.73091i	−0.163309	+	0.282859i
$748$	−10.8680	+	18.8239i	−0.397373	+	0.688270i
$749$	54.5240			1.99227
$750$	−21.1079	+	36.5600i	−0.770753	+	1.33498i
$751$	21.9857	+	38.0804i	0.802271	+	1.38957i	0.918118	+	0.396307i	$0.129708\pi$
$751$	21.9857	+	38.0804i	0.802271	+	1.38957i	−0.115847	+	0.993267i	$0.536958\pi$
$752$	−6.21599	−	10.7664i	−0.226674	−	0.392610i
$753$	21.2919			0.775922
$754$	13.3044	+	25.8356i	0.484518	+	0.940879i
$755$	−7.73307			−0.281435
$756$	−7.58956	−	13.1455i	−0.276030	−	0.478097i
$757$	1.00491	+	1.74056i	0.0365242	+	0.0632617i	0.883710	−	0.468036i	$-0.155038\pi$
$757$	1.00491	+	1.74056i	0.0365242	+	0.0632617i	−0.847185	+	0.531297i	$0.821705\pi$
$758$	−38.6890	+	67.0113i	−1.40525	+	2.43396i
$759$	5.24463			0.190368
$760$	45.4496	−	78.7211i	1.64863	−	2.85551i
$761$	1.62429	−	2.81336i	0.0588805	−	0.101984i	−0.835083	−	0.550125i	$-0.814580\pi$
$761$	1.62429	−	2.81336i	0.0588805	−	0.101984i	0.893963	+	0.448140i	$0.147914\pi$
$762$	30.9494			1.12118
$763$	26.5764	−	46.0318i	0.962132	−	1.66646i
$764$	19.8675	+	34.4115i	0.718780	+	1.24496i
$765$	11.1106	+	19.2442i	0.401706	+	0.695775i
$766$	−29.5962			−1.06935
$767$	6.64497	+	12.9038i	0.239936	+	0.465929i
$768$	−28.4478			−1.02652
$769$	−23.3040	−	40.3638i	−0.840365	−	1.45556i	−0.889586	−	0.456768i	$-0.849007\pi$
$769$	−23.3040	−	40.3638i	−0.840365	−	1.45556i	0.0492207	−	0.998788i	$-0.484326\pi$
$770$	18.5874	+	32.1944i	0.669845	+	1.16021i
$771$	4.28045	−	7.41396i	0.154157	−	0.267007i
$772$	−89.6055			−3.22497
$773$	13.0854	−	22.6647i	0.470651	−	0.815191i	−0.528786	−	0.848755i	$-0.677353\pi$
$773$	13.0854	−	22.6647i	0.470651	−	0.815191i	0.999437	+	0.0335642i	$0.0106858\pi$
$774$	3.73294	−	6.46563i	0.134178	−	0.232402i
$775$	−10.1244			−0.363678
$776$	40.3236	−	69.8426i	1.44753	−	2.50720i
$777$	−3.05657	−	5.29413i	−0.109654	−	0.189926i
$778$	6.50223	+	11.2622i	0.233116	+	0.403769i
$779$	31.3925			1.12475
$780$	27.8777	−	43.3354i	0.998180	−	1.55166i
$781$	−3.65789			−0.130890
$782$	−36.5205	−	63.2554i	−1.30597	−	2.26201i
$783$	−1.68222	−	2.91369i	−0.0601175	−	0.104127i
$784$	−11.8593	+	20.5408i	−0.423545	+	0.733602i
$785$	−70.1480			−2.50369
$786$	5.97278	−	10.3452i	0.213042	−	0.368999i
$787$	1.47889	−	2.56151i	0.0527167	−	0.0913080i	−0.838463	−	0.544959i	$-0.816545\pi$
$787$	1.47889	−	2.56151i	0.0527167	−	0.0913080i	0.891180	+	0.453651i	$0.149879\pi$
$788$	58.3351			2.07810
$789$	−14.0654	+	24.3619i	−0.500740	+	0.867307i
$790$	15.4180	+	26.7048i	0.548549	+	0.950115i
$791$	19.7401	+	34.1909i	0.701878	+	1.21569i
$792$	−4.16562			−0.148019
$793$	24.0250	+	46.6538i	0.853152	+	1.65672i
$794$	27.0113			0.958596
$795$	−8.72562	−	15.1132i	−0.309466	−	0.536011i
$796$	12.7081	+	22.0111i	0.450428	+	0.780164i
$797$	3.77378	−	6.53638i	0.133674	−	0.231530i	−0.791416	−	0.611278i	$-0.790656\pi$
$797$	3.77378	−	6.53638i	0.133674	−	0.231530i	0.925090	+	0.379748i	$0.123989\pi$
$798$	−55.5226			−1.96548
$799$	14.4466	−	25.0223i	0.511084	−	0.885224i
$800$	11.2388	−	19.4662i	0.397353	−	0.688236i
$801$	−13.0251			−0.460220
$802$	2.96304	−	5.13214i	0.104629	−	0.181222i
$803$	−0.00316442	−	0.00548094i	−0.000111670	−	0.000193418i
$804$	6.29115	+	10.8966i	0.221872	+	0.384293i
$805$	−81.3864			−2.86849
$806$	9.08892	+	0.437080i	0.320144	+	0.0153955i
$807$	−17.7645			−0.625340
$808$	−4.95882	−	8.58894i	−0.174451	−	0.302158i
$809$	2.99247	+	5.18311i	0.105210	+	0.182228i	0.913824	−	0.406111i	$-0.133115\pi$
$809$	2.99247	+	5.18311i	0.105210	+	0.182228i	−0.808614	+	0.588339i	$0.799782\pi$
$810$	−4.57839	+	7.93001i	−0.160868	+	0.278632i
$811$	−16.7015			−0.586471			−0.293235	−	0.956040i	$-0.594732\pi$
$811$	−16.7015			−0.586471			−0.293235	+	0.956040i	$0.594732\pi$
$812$	−25.5346	+	44.2272i	−0.896088	+	1.55207i
$813$	−1.21986	+	2.11286i	−0.0427824	+	0.0741012i
$814$	−3.60720			−0.126432
$815$	−38.4995	+	66.6831i	−1.34858	+	2.33581i
$816$	7.27096	+	12.5937i	0.254535	+	0.440867i
$817$	−8.89586	−	15.4081i	−0.311227	−	0.539061i
$818$	27.1901			0.950681
$819$	−14.6210	−	0.703112i	−0.510898	−	0.0245687i
$820$	−78.5861			−2.74435
$821$	24.1740	+	41.8706i	0.843679	+	1.46130i	0.886763	+	0.462224i	$0.152948\pi$
$821$	24.1740	+	41.8706i	0.843679	+	1.46130i	−0.0430838	+	0.999071i	$0.513718\pi$
$822$	11.5163	+	19.9467i	0.401676	+	0.695723i
$823$	9.21767	−	15.9655i	0.321308	−	0.556522i	−0.659450	−	0.751748i	$-0.729211\pi$
$823$	9.21767	−	15.9655i	0.321308	−	0.556522i	0.980758	+	0.195227i	$0.0625442\pi$
$824$	−44.5061			−1.55044
$825$	4.80517	−	8.32279i	0.167294	−	0.289762i
$826$	−19.5755	+	33.9057i	−0.681118	+	1.17973i
$827$	−44.1498			−1.53524			−0.767620	−	0.640906i	$-0.778559\pi$
$827$	−44.1498			−1.53524			−0.767620	+	0.640906i	$0.778559\pi$
$828$	9.80450	−	16.9819i	0.340730	−	0.590162i
$829$	6.33886	+	10.9792i	0.220158	+	0.381324i	0.954856	−	0.297070i	$-0.0960095\pi$
$829$	6.33886	+	10.9792i	0.220158	+	0.381324i	−0.734698	+	0.678394i	$0.762676\pi$
$830$	−40.8708	−	70.7903i	−1.41865	−	2.45717i
$831$	15.7018			0.544691
$832$	−20.6887	+	32.1602i	−0.717250	+	1.11495i
$833$	−55.1243			−1.90995
$834$	−19.8776	−	34.4291i	−0.688307	−	1.19218i
$835$	−1.98742	−	3.44231i	−0.0687775	−	0.119126i
$836$	−10.6724	+	18.4851i	−0.369112	+	0.639320i
$837$	−1.05349			−0.0364138
$838$	−8.90218	+	15.4190i	−0.307521	+	0.532641i
$839$	9.68136	−	16.7686i	0.334238	−	0.578917i	−0.649100	−	0.760703i	$-0.724854\pi$
$839$	9.68136	−	16.7686i	0.334238	−	0.578917i	0.983338	+	0.181786i	$0.0581878\pi$
$840$	64.6422			2.23037
$841$	8.84029	−	15.3118i	0.304838	−	0.527994i
$842$	21.0984	+	36.5434i	0.727097	+	1.25937i
$843$	−15.2547	−	26.4219i	−0.525399	−	0.910017i
$844$	−56.9917			−1.96173
$845$	−20.6013	−	45.2187i	−0.708706	−	1.55557i
$846$	11.9061			0.409341
$847$	−2.02991	−	3.51590i	−0.0697485	−	0.120808i
$848$	−5.71017	−	9.89031i	−0.196088	−	0.339635i
$849$	7.98355	−	13.8279i	0.273995	−	0.474573i
$850$	−133.841			−4.59072
$851$	3.94860	−	6.83917i	0.135356	−	0.234444i
$852$	−6.83819	+	11.8441i	−0.234273	+	0.405772i
$853$	−13.8312			−0.473572			−0.236786	−	0.971562i	$-0.576094\pi$
$853$	−13.8312			−0.473572			−0.236786	+	0.971562i	$0.576094\pi$
$854$	−70.7754	+	122.587i	−2.42188	+	4.19482i
$855$	10.9107	+	18.8978i	0.373136	+	0.646291i
$856$	−27.9725	−	48.4498i	−0.956081	−	1.65598i
$857$	43.9275			1.50054			0.750268	−	0.661134i	$-0.229924\pi$
$857$	43.9275			1.50054			0.750268	+	0.661134i	$0.229924\pi$
$858$	−4.67304	+	7.26416i	−0.159535	+	0.247994i
$859$	34.0142			1.16055			0.580275	−	0.814421i	$-0.302945\pi$
$859$	34.0142			1.16055			0.580275	+	0.814421i	$0.302945\pi$
$860$	22.2694	+	38.5717i	0.759379	+	1.31528i
$861$	11.1623	+	19.3336i	0.380409	+	0.658887i
$862$	−18.5941	+	32.2059i	−0.633318	+	1.09694i
$863$	−11.8884			−0.404686			−0.202343	−	0.979315i	$-0.564856\pi$
$863$	−11.8884			−0.404686			−0.202343	+	0.979315i	$0.564856\pi$
$864$	1.16945	−	2.02555i	0.0397856	−	0.0689107i
$865$	−30.6959	+	53.1668i	−1.04369	+	1.80773i
$866$	8.16948			0.277610
$867$	−8.39847	+	14.5466i	−0.285227	+	0.494028i
$868$	7.99550	+	13.8486i	0.271385	+	0.470053i
$869$	−1.68378	−	2.91640i	−0.0571184	−	0.0989319i
$870$	30.8074			1.04447
$871$	12.1197	+	0.582825i	0.410659	+	0.0197483i
$872$	−54.5381			−1.84689
$873$	9.68010	+	16.7664i	0.327622	+	0.567457i
$874$	−35.8632	−	62.1169i	−1.21309	−	2.10114i
$875$	−35.7716	+	61.9583i	−1.20930	+	2.09457i
$876$	−0.0236627			−0.000799489
$877$	16.4261	−	28.4509i	0.554672	−	0.960719i	−0.443257	−	0.896394i	$-0.646177\pi$
$877$	16.4261	−	28.4509i	0.554672	−	0.960719i	0.997929	−	0.0643249i	$-0.0204894\pi$
$878$	11.5819	−	20.0605i	0.390871	−	0.677008i
$879$	19.8973			0.671119
$880$	4.78061	−	8.28026i	0.161154	−	0.279127i
$881$	7.75408	+	13.4305i	0.261242	+	0.452484i	0.966572	−	0.256395i	$-0.0825347\pi$
$881$	7.75408	+	13.4305i	0.261242	+	0.452484i	−0.705330	+	0.708879i	$0.749201\pi$
$882$	−11.3576	−	19.6720i	−0.382431	−	0.662391i
$883$	18.1363			0.610336			0.305168	−	0.952299i	$-0.401287\pi$
$883$	18.1363			0.610336			0.305168	+	0.952299i	$0.401287\pi$
$884$	78.2797	+	3.76441i	2.63283	+	0.126611i
$885$	15.3870			0.517227
$886$	1.48176	+	2.56648i	0.0497806	+	0.0862225i
$887$	−14.3402	−	24.8379i	−0.481497	−	0.833977i	0.518278	−	0.855212i	$-0.326573\pi$
$887$	−14.3402	−	24.8379i	−0.481497	−	0.833977i	−0.999774	+	0.0212357i	$0.993240\pi$
$888$	−3.13623	+	5.43210i	−0.105245	+	0.182289i
$889$	52.4501			1.75912
$890$	59.6342	−	103.289i	1.99894	−	3.46227i
$891$	0.500000	−	0.866025i	0.0167506	−	0.0290129i
$892$	12.7202			0.425904
$893$	14.1866	−	24.5719i	0.474736	−	0.822267i
$894$	−19.3820	−	33.5707i	−0.648232	−	1.12277i
$895$	−1.80832	−	3.13210i	−0.0604454	−	0.104694i
$896$	−84.1581			−2.81152
$897$	−8.65737	−	16.8116i	−0.289061	−	0.561324i
$898$	−5.21128			−0.173903
$899$	1.77219	+	3.06953i	0.0591060	+	0.102375i
$900$	−17.9659	−	31.1178i	−0.598863	−	1.03726i
$901$	13.2710	−	22.9861i	0.442122	−	0.765778i
$902$	13.1731			0.438617
$903$	6.32621	−	10.9573i	0.210523	−	0.364637i
$904$	20.2546	−	35.0820i	0.673658	−	1.16681i
$905$	−44.7667			−1.48810
$906$	2.42329	−	4.19726i	0.0805083	−	0.139445i
$907$	5.43056	+	9.40601i	0.180319	+	0.312321i	0.941989	−	0.335643i	$-0.108954\pi$
$907$	5.43056	+	9.40601i	0.180319	+	0.312321i	−0.761670	+	0.647965i	$0.775620\pi$
$908$	7.42154	+	12.8545i	0.246292	+	0.426591i
$909$	2.38083			0.0789673
$910$	72.5163	−	112.725i	2.40389	−	3.73681i
$911$	20.5377			0.680445			0.340223	−	0.940345i	$-0.389498\pi$
$911$	20.5377			0.680445			0.340223	+	0.940345i	$0.389498\pi$
$912$	7.14009	+	12.3670i	0.236432	+	0.409512i
$913$	4.46344	+	7.73091i	0.147718	+	0.255856i
$914$	28.1069	−	48.6827i	0.929695	−	1.61028i
$915$	55.6317			1.83913
$916$	−1.84917	+	3.20286i	−0.0610984	+	0.105826i
$917$	10.1221	−	17.5319i	0.334260	−	0.578956i
$918$	−13.9268			−0.459653
$919$	−0.543417	+	0.941227i	−0.0179257	+	0.0310482i	−0.874849	−	0.484396i	$-0.839040\pi$
$919$	−0.543417	+	0.941227i	−0.0179257	+	0.0310482i	0.856923	+	0.515444i	$0.172373\pi$
$920$	41.7537	+	72.3196i	1.37658	+	2.38431i
$921$	−5.17288	−	8.95969i	−0.170452	−	0.295232i
$922$	27.5819			0.908362
$923$	6.03812	+	11.7253i	0.198747	+	0.385944i
$924$	−15.1791			−0.499356
$925$	−7.23546	−	12.5322i	−0.237900	−	0.412056i
$926$	13.8410	+	23.9732i	0.454842	+	0.787809i
$927$	5.34207	−	9.25274i	0.175457	−	0.303900i
$928$	−7.86910			−0.258316
$929$	−24.7157	+	42.8089i	−0.810896	+	1.40451i	0.101341	+	0.994852i	$0.467687\pi$
$929$	−24.7157	+	42.8089i	−0.810896	+	1.40451i	−0.912237	+	0.409662i	$0.865647\pi$
$930$	4.82328	−	8.35416i	0.158162	−	0.273944i
$931$	−54.1322			−1.77411
$932$	27.9751	−	48.4543i	0.916355	−	1.58717i
$933$	9.83134	+	17.0284i	0.321864	+	0.557484i
$934$	1.04864	+	1.81630i	0.0343126	+	0.0594311i
$935$	22.2213			0.726713
$936$	6.87623	+	13.3529i	0.224757	+	0.436452i
$937$	27.6967			0.904811			0.452405	−	0.891812i	$-0.350566\pi$
$937$	27.6967			0.904811			0.452405	+	0.891812i	$0.350566\pi$
$938$	16.3648	+	28.3446i	0.534328	+	0.925484i
$939$	8.63541	+	14.9570i	0.281806	+	0.488102i
$940$	−35.5138	+	61.5117i	−1.15833	+	2.00629i
$941$	35.6961			1.16366			0.581829	−	0.813311i	$-0.302337\pi$
$941$	35.6961			1.16366			0.581829	+	0.813311i	$0.302337\pi$
$942$	21.9820	−	38.0740i	0.716214	−	1.24052i
$943$	−14.4198	+	24.9759i	−0.469575	+	0.813328i
$944$	10.0694			0.327733
$945$	−7.75901	+	13.4390i	−0.252401	+	0.437171i
$946$	−3.73294	−	6.46563i	−0.121368	−	0.210216i
$947$	−7.71754	−	13.3672i	−0.250786	−	0.434375i	0.712956	−	0.701209i	$-0.247356\pi$
$947$	−7.71754	−	13.3672i	−0.250786	−	0.434375i	−0.963743	+	0.266834i	$0.914023\pi$
$948$	−12.5909			−0.408933
$949$	−0.0123456	+	0.0191910i	−0.000400754	+	0.000622965i
$950$	−131.432			−4.26423
$951$	−4.46867	−	7.73997i	−0.144907	−	0.250986i
$952$	49.1581	+	85.1443i	1.59322	+	2.75954i
$953$	8.11602	−	14.0574i	0.262904	−	0.455363i	−0.704109	−	0.710092i	$-0.748653\pi$
$953$	8.11602	−	14.0574i	0.262904	−	0.455363i	0.967012	+	0.254730i	$0.0819865\pi$
$954$	10.9373			0.354108
$955$	20.3110	−	35.1798i	0.657250	−	1.13839i
$956$	−36.7340	+	63.6251i	−1.18806	+	2.05778i
$957$	−3.36443			−0.108757
$958$	27.8360	−	48.2134i	0.899342	−	1.55771i
$959$	19.5166	+	33.8038i	0.630225	+	1.09158i
$960$	20.2697	+	35.1081i	0.654200	+	1.13311i
$961$	−29.8902			−0.964199
$962$	5.95445	+	11.5629i	0.191979	+	0.372801i
$963$	13.4302			0.432781
$964$	17.2337	+	29.8496i	0.555060	+	0.961391i
$965$	45.8031	+	79.3332i	1.47445	+	2.55383i
$966$	25.5038	−	44.1739i	0.820571	−	1.42127i
$967$	49.6654			1.59713			0.798567	−	0.601907i	$-0.205592\pi$
$967$	49.6654			1.59713			0.798567	+	0.601907i	$0.205592\pi$
$968$	−2.08281	+	3.60753i	−0.0669441	+	0.115951i
$969$	−16.5943	+	28.7422i	−0.533086	+	0.923333i
$970$	−177.277			−5.69203
$971$	−22.3511	+	38.7133i	−0.717282	+	1.24237i	0.244791	+	0.969576i	$0.421281\pi$
$971$	−22.3511	+	38.7133i	−0.717282	+	1.24237i	−0.962073	+	0.272792i	$0.912053\pi$
$972$	−1.86943	−	3.23795i	−0.0599621	−	0.103857i
$973$	−33.6867	−	58.3470i	−1.07995	−	1.87052i
$974$	75.4782			2.41848
$975$	−34.6106	−	1.66440i	−1.10842	−	0.0533033i
$976$	36.4062			1.16533
$977$	−17.5389	−	30.3783i	−0.561120	−	0.971889i	−0.997399	−	0.0720772i	$-0.977037\pi$
$977$	−17.5389	−	30.3783i	−0.561120	−	0.971889i	0.436279	−	0.899812i	$-0.356296\pi$
$978$	−24.1289	−	41.7925i	−0.771558	−	1.33638i
$979$	−6.51256	+	11.2801i	−0.208142	+	0.360513i
$980$	135.511			4.32874
$981$	6.54622	−	11.3384i	0.209005	−	0.362007i
$982$	8.86691	−	15.3579i	0.282954	−	0.490091i
$983$	24.6519			0.786272			0.393136	−	0.919480i	$-0.371390\pi$
$983$	24.6519			0.786272			0.393136	+	0.919480i	$0.371390\pi$
$984$	11.4532	−	19.8375i	0.365113	−	0.632395i
$985$	−29.8188	−	51.6476i	−0.950105	−	1.64563i
$986$	23.4279	+	40.5784i	0.746097	+	1.29228i
$987$	20.1773			0.642251
$988$	76.8707	+	3.69666i	2.44558	+	0.117606i
$989$	16.3449			0.519738
$990$	4.57839	+	7.93001i	0.145511	+	0.252032i
$991$	−0.481199	−	0.833461i	−0.0152858	−	0.0264758i	0.858281	−	0.513179i	$-0.171532\pi$
$991$	−0.481199	−	0.833461i	−0.0152858	−	0.0264758i	−0.873567	+	0.486704i	$0.838199\pi$
$992$	−1.23200	+	2.13389i	−0.0391162	+	0.0677512i
$993$	−13.8093			−0.438225
$994$	−17.7877	+	30.8093i	−0.564192	+	0.977210i
$995$	12.9919	−	22.5026i	0.411870	−	0.713379i
$996$	33.3765			1.05757
$997$	−21.7284	+	37.6347i	−0.688145	+	1.19190i	0.284292	+	0.958738i	$0.408241\pi$
$997$	−21.7284	+	37.6347i	−0.688145	+	1.19190i	−0.972437	+	0.233165i	$0.925092\pi$
$998$	−47.8486	−	82.8762i	−1.51462	−	2.62340i
$999$	−0.752883	−	1.30403i	−0.0238202	−	0.0412578i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.i.c.133.1	yes	10
13.3	even	3		5577.2.a.v.1.5		5
13.9	even	3	inner	429.2.i.c.100.1	✓	10
13.10	even	6		5577.2.a.p.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.i.c.100.1	✓	10	13.9	even	3	inner
429.2.i.c.133.1	yes	10	1.1	even	1	trivial
5577.2.a.p.1.1		5	13.10	even	6
5577.2.a.v.1.5		5	13.3	even	3

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)

\(f(q)\)	\(=\)	\(q+(-1.19780 - 2.07464i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.86943 + 3.23795i) q^{4} +3.82235 q^{5} +(-1.19780 + 2.07464i) q^{6} +(-2.02991 + 3.51590i) q^{7} +4.16562 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.19780 - 2.07464i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.86943 + 3.23795i) q^{4} +3.82235 q^{5} +(-1.19780 + 2.07464i) q^{6} +(-2.02991 + 3.51590i) q^{7} +4.16562 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.57839 - 7.93001i) q^{10} +(0.500000 + 0.866025i) q^{11} +3.73887 q^{12} +(1.95068 - 3.03230i) q^{13} +9.72567 q^{14} +(-1.91117 - 3.31025i) q^{15} +(-1.25070 - 2.16628i) q^{16} +(2.90676 - 5.03465i) q^{17} +2.39559 q^{18} +(2.85444 - 4.94403i) q^{19} +(-7.14563 + 12.3766i) q^{20} +4.05982 q^{21} +(1.19780 - 2.07464i) q^{22} +(2.62232 + 4.54199i) q^{23} +(-2.08281 - 3.60753i) q^{24} +9.61033 q^{25} +(-8.62747 - 0.414889i) q^{26} +1.00000 q^{27} +(-7.58956 - 13.1455i) q^{28} +(-1.68222 - 2.91369i) q^{29} +(-4.57839 + 7.93001i) q^{30} -1.05349 q^{31} +(1.16945 - 2.02555i) q^{32} +(0.500000 - 0.866025i) q^{33} -13.9268 q^{34} +(-7.75901 + 13.4390i) q^{35} +(-1.86943 - 3.23795i) q^{36} +(-0.752883 - 1.30403i) q^{37} -13.6761 q^{38} +(-3.60139 - 0.173188i) q^{39} +15.9224 q^{40} +(2.74945 + 4.76218i) q^{41} +(-4.86283 - 8.42268i) q^{42} +(1.55825 - 2.69897i) q^{43} -3.73887 q^{44} +(-1.91117 + 3.31025i) q^{45} +(6.28201 - 10.8808i) q^{46} +4.97001 q^{47} +(-1.25070 + 2.16628i) q^{48} +(-4.74105 - 8.21174i) q^{49} +(-11.5112 - 19.9380i) q^{50} -5.81351 q^{51} +(6.17178 + 11.9849i) q^{52} +4.56558 q^{53} +(-1.19780 - 2.07464i) q^{54} +(1.91117 + 3.31025i) q^{55} +(-8.45583 + 14.6459i) q^{56} -5.70888 q^{57} +(-4.02991 + 6.98001i) q^{58} +(-2.01276 + 3.48621i) q^{59} +14.2913 q^{60} +(-7.27717 + 12.6044i) q^{61} +(1.26186 + 2.18561i) q^{62} +(-2.02991 - 3.51590i) q^{63} -10.6059 q^{64} +(7.45618 - 11.5905i) q^{65} -2.39559 q^{66} +(1.68264 + 2.91441i) q^{67} +(10.8680 + 18.8239i) q^{68} +(2.62232 - 4.54199i) q^{69} +37.1749 q^{70} +(-1.82895 + 3.16783i) q^{71} +(-2.08281 + 3.60753i) q^{72} -0.00632885 q^{73} +(-1.80360 + 3.12393i) q^{74} +(-4.80517 - 8.32279i) q^{75} +(10.6724 + 18.4851i) q^{76} -4.05982 q^{77} +(3.95443 + 7.67905i) q^{78} -3.36756 q^{79} +(-4.78061 - 8.28026i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(6.58656 - 11.4083i) q^{82} +8.92689 q^{83} +(-7.58956 + 13.1455i) q^{84} +(11.1106 - 19.2442i) q^{85} -7.46587 q^{86} +(-1.68222 + 2.91369i) q^{87} +(2.08281 + 3.60753i) q^{88} +(6.51256 + 11.2801i) q^{89} +9.15679 q^{90} +(6.70158 + 13.0137i) q^{91} -19.6090 q^{92} +(0.526743 + 0.912346i) q^{93} +(-5.95306 - 10.3110i) q^{94} +(10.9107 - 18.8978i) q^{95} -2.33891 q^{96} +(9.68010 - 16.7664i) q^{97} +(-11.3576 + 19.6720i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q - 2 q^{2} - 5 q^{3} - 2 q^{4} + 16 q^{5} - 2 q^{6} - 9 q^{7} + 6 q^{8} - 5 q^{9} - 7 q^{10} + 5 q^{11} + 4 q^{12} + q^{13} + 6 q^{14} - 8 q^{15} + 4 q^{16} - 3 q^{17} + 4 q^{18} + 3 q^{19} - 6 q^{20} + 18 q^{21} + 2 q^{22} + q^{23} - 3 q^{24} + 18 q^{25} - 20 q^{26} + 10 q^{27} - 25 q^{28} + 2 q^{29} - 7 q^{30} - 4 q^{31} - 3 q^{32} + 5 q^{33} - 46 q^{34} - 12 q^{35} - 2 q^{36} + q^{37} + 14 q^{38} - 2 q^{39} + 50 q^{40} - 18 q^{41} - 3 q^{42} + 9 q^{43} - 4 q^{44} - 8 q^{45} + 2 q^{46} + 32 q^{47} + 4 q^{48} - 22 q^{49} - 12 q^{50} + 6 q^{51} - 7 q^{52} + 6 q^{53} - 2 q^{54} + 8 q^{55} - 25 q^{56} - 6 q^{57} - 29 q^{58} - 16 q^{59} + 12 q^{60} - 8 q^{61} - 16 q^{62} - 9 q^{63} - 2 q^{64} - 6 q^{65} - 4 q^{66} - 19 q^{67} + 22 q^{68} + q^{69} + 72 q^{70} - 25 q^{71} - 3 q^{72} + 16 q^{73} + 5 q^{74} - 9 q^{75} + 38 q^{76} - 18 q^{77} + 13 q^{78} + 36 q^{79} - 20 q^{80} - 5 q^{81} + 40 q^{82} + 44 q^{83} - 25 q^{84} + 7 q^{85} - 8 q^{86} + 2 q^{87} + 3 q^{88} + 20 q^{89} + 14 q^{90} - 25 q^{91} - 60 q^{92} + 2 q^{93} + 8 q^{94} + 7 q^{95} + 6 q^{96} - 21 q^{97} - 6 q^{98} - 10 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 - 5 * q^3 - 2 * q^4 + 16 * q^5 - 2 * q^6 - 9 * q^7 + 6 * q^8 - 5 * q^9 - 7 * q^10 + 5 * q^11 + 4 * q^12 + q^13 + 6 * q^14 - 8 * q^15 + 4 * q^16 - 3 * q^17 + 4 * q^18 + 3 * q^19 - 6 * q^20 + 18 * q^21 + 2 * q^22 + q^23 - 3 * q^24 + 18 * q^25 - 20 * q^26 + 10 * q^27 - 25 * q^28 + 2 * q^29 - 7 * q^30 - 4 * q^31 - 3 * q^32 + 5 * q^33 - 46 * q^34 - 12 * q^35 - 2 * q^36 + q^37 + 14 * q^38 - 2 * q^39 + 50 * q^40 - 18 * q^41 - 3 * q^42 + 9 * q^43 - 4 * q^44 - 8 * q^45 + 2 * q^46 + 32 * q^47 + 4 * q^48 - 22 * q^49 - 12 * q^50 + 6 * q^51 - 7 * q^52 + 6 * q^53 - 2 * q^54 + 8 * q^55 - 25 * q^56 - 6 * q^57 - 29 * q^58 - 16 * q^59 + 12 * q^60 - 8 * q^61 - 16 * q^62 - 9 * q^63 - 2 * q^64 - 6 * q^65 - 4 * q^66 - 19 * q^67 + 22 * q^68 + q^69 + 72 * q^70 - 25 * q^71 - 3 * q^72 + 16 * q^73 + 5 * q^74 - 9 * q^75 + 38 * q^76 - 18 * q^77 + 13 * q^78 + 36 * q^79 - 20 * q^80 - 5 * q^81 + 40 * q^82 + 44 * q^83 - 25 * q^84 + 7 * q^85 - 8 * q^86 + 2 * q^87 + 3 * q^88 + 20 * q^89 + 14 * q^90 - 25 * q^91 - 60 * q^92 + 2 * q^93 + 8 * q^94 + 7 * q^95 + 6 * q^96 - 21 * q^97 - 6 * q^98 - 10 * q^99

Introduction

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