LMFDB - Embedded newform 231.2.j.g.169.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(64,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 0, 6]))

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

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

chi := DirichletCharacter("231.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.j (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.84454428669$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 12 x^{18} - 3 x^{17} + 94 x^{16} - 10 x^{15} + 662 x^{14} - 153 x^{13} + 4638 x^{12} + \cdots + 121 $ x^20 + 12x^18 - 3x^17 + 94x^16 - 10x^15 + 662x^14 - 153x^13 + 4638x^12 - 1174x^11 + 15808x^10 - 3393x^9 + 26062x^8 - 15494x^7 + 11660x^6 - 33295x^5 + 67756x^4 - 43696x^3 + 13084x^2 - 1155x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			169.5
Root			$-2.14548 + 1.55878i$ of defining polynomial
Character	$\chi$	$=$	231.169
Dual form			231.2.j.g.190.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.14548 + 1.55878i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.55524 + 4.78653i) q^{4} +(-1.38593 + 1.00694i) q^{5} +(2.14548 - 1.55878i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.48543 + 7.64935i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(2.14548 + 1.55878i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.55524 + 4.78653i) q^{4} +(-1.38593 + 1.00694i) q^{5} +(2.14548 - 1.55878i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.48543 + 7.64935i) q^{8} +(-0.809017 - 0.587785i) q^{9} -4.54308 q^{10} +(2.49598 - 2.18405i) q^{11} +5.03286 q^{12} +(-1.22292 - 0.888505i) q^{13} +(0.819499 - 2.52216i) q^{14} +(0.529379 + 1.62926i) q^{15} +(-9.11274 + 6.62079i) q^{16} +(1.93668 - 1.40708i) q^{17} +(-0.819499 - 2.52216i) q^{18} +(1.95646 - 6.02136i) q^{19} +(-6.97521 - 5.06779i) q^{20} -1.00000 q^{21} +(8.75952 - 0.795152i) q^{22} -5.05885 q^{23} +(6.50693 + 4.72756i) q^{24} +(-0.638201 + 1.96418i) q^{25} +(-1.23877 - 3.81253i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(4.07167 - 2.95824i) q^{28} +(2.57892 + 7.93708i) q^{29} +(-1.40389 + 4.32073i) q^{30} +(-4.88551 - 3.54953i) q^{31} -13.7855 q^{32} +(-1.30586 - 3.04873i) q^{33} +6.34841 q^{34} +(1.38593 + 1.00694i) q^{35} +(1.55524 - 4.78653i) q^{36} +(-2.30953 - 7.10802i) q^{37} +(13.5835 - 9.86900i) q^{38} +(-1.22292 + 0.888505i) q^{39} +(-4.25780 - 13.1042i) q^{40} +(-1.55577 + 4.78817i) q^{41} +(-2.14548 - 1.55878i) q^{42} +2.02506 q^{43} +(14.3359 + 8.55037i) q^{44} +1.71311 q^{45} +(-10.8536 - 7.88563i) q^{46} +(-1.70895 + 5.25959i) q^{47} +(3.48076 + 10.7127i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-4.43097 + 3.21929i) q^{50} +(-0.739744 - 2.27670i) q^{51} +(2.35092 - 7.23540i) q^{52} +(-5.04607 - 3.66618i) q^{53} -2.65195 q^{54} +(-1.26005 + 5.54025i) q^{55} +8.04301 q^{56} +(-5.12208 - 3.72141i) q^{57} +(-6.83916 + 21.0488i) q^{58} +(3.45303 + 10.6273i) q^{59} +(-6.97521 + 5.06779i) q^{60} +(-11.1722 + 8.11711i) q^{61} +(-4.94881 - 15.2309i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-11.3510 - 8.24697i) q^{64} +2.58956 q^{65} +(1.95061 - 8.57651i) q^{66} +13.6173 q^{67} +(9.74702 + 7.08162i) q^{68} +(-1.56327 + 4.81125i) q^{69} +(1.40389 + 4.32073i) q^{70} +(11.5956 - 8.42466i) q^{71} +(6.50693 - 4.72756i) q^{72} +(-0.441988 - 1.36030i) q^{73} +(6.12478 - 18.8501i) q^{74} +(1.67083 + 1.21393i) q^{75} +31.8642 q^{76} +(-2.84846 - 1.69891i) q^{77} -4.00873 q^{78} +(-5.43444 - 3.94835i) q^{79} +(5.96291 - 18.3520i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-10.8016 + 7.84779i) q^{82} +(-4.74874 + 3.45016i) q^{83} +(-1.55524 - 4.78653i) q^{84} +(-1.26726 + 3.90023i) q^{85} +(4.34471 + 3.15662i) q^{86} +8.34554 q^{87} +(10.5030 + 24.5209i) q^{88} +16.4241 q^{89} +(3.67543 + 2.67036i) q^{90} +(-0.467115 + 1.43763i) q^{91} +(-7.86773 - 24.2144i) q^{92} +(-4.88551 + 3.54953i) q^{93} +(-11.8650 + 8.62046i) q^{94} +(3.35163 + 10.3152i) q^{95} +(-4.25995 + 13.1108i) q^{96} +(-9.74994 - 7.08375i) q^{97} -2.65195 q^{98} +(-3.30304 + 0.299836i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) $ 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	2.14548	+	1.55878i	1.51708	+	1.10222i	0.962911	+	0.269820i	$0.0869642\pi$
$2$	2.14548	+	1.55878i	1.51708	+	1.10222i	0.554170	+	0.832404i	$0.313036\pi$
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$3$	0.309017	−	0.951057i	0.178411	−	0.549093i
$4$	1.55524	+	4.78653i	0.777620	+	2.39327i
$5$	−1.38593	+	1.00694i	−0.619808	+	0.450317i	−0.852855	−	0.522149i	$-0.825131\pi$
$5$	−1.38593	+	1.00694i	−0.619808	+	0.450317i	0.233046	+	0.972466i	$0.425131\pi$
$6$	2.14548	−	1.55878i	0.875887	−	0.636369i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$7$	−0.309017	−	0.951057i	−0.116797	−	0.359466i
$8$	−2.48543	+	7.64935i	−0.878731	+	2.70446i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$	−4.54308			−1.43665
$11$	2.49598	−	2.18405i	0.752566	−	0.658517i
$11$	2.49598	−	2.18405i	0.752566	−	0.658517i
$12$	5.03286			1.45286
$13$	−1.22292	−	0.888505i	−0.339178	−	0.246427i	0.405137	−	0.914256i	$-0.367224\pi$
$13$	−1.22292	−	0.888505i	−0.339178	−	0.246427i	−0.744315	+	0.667829i	$0.767224\pi$
$14$	0.819499	−	2.52216i	0.219020	−	0.674075i
$15$	0.529379	+	1.62926i	0.136685	+	0.420674i
$16$	−9.11274	+	6.62079i	−2.27818	+	1.65520i
$17$	1.93668	−	1.40708i	0.469713	−	0.341266i	−0.327617	−	0.944811i	$-0.606245\pi$
$17$	1.93668	−	1.40708i	0.469713	−	0.341266i	0.797329	+	0.603544i	$0.206245\pi$
$18$	−0.819499	−	2.52216i	−0.193158	−	0.594478i
$19$	1.95646	−	6.02136i	0.448842	−	1.38140i	−0.429372	−	0.903128i	$-0.641265\pi$
$19$	1.95646	−	6.02136i	0.448842	−	1.38140i	0.878214	−	0.478267i	$-0.158735\pi$
$20$	−6.97521	−	5.06779i	−1.55970	−	1.13319i
$21$	−1.00000			−0.218218
$22$	8.75952	−	0.795152i	1.86754	−	0.169527i
$23$	−5.05885			−1.05484			−0.527422	−	0.849604i	$-0.676841\pi$
$23$	−5.05885			−1.05484			−0.527422	+	0.849604i	$0.676841\pi$
$24$	6.50693	+	4.72756i	1.32822	+	0.965009i
$25$	−0.638201	+	1.96418i	−0.127640	+	0.392836i
$26$	−1.23877	−	3.81253i	−0.242942	−	0.747699i
$27$	−0.809017	+	0.587785i	−0.155695	+	0.113119i
$28$	4.07167	−	2.95824i	0.769473	−	0.559055i
$29$	2.57892	+	7.93708i	0.478893	+	1.47388i	0.840635	+	0.541602i	$0.182182\pi$
$29$	2.57892	+	7.93708i	0.478893	+	1.47388i	−0.361743	+	0.932278i	$0.617818\pi$
$30$	−1.40389	+	4.32073i	−0.256314	+	0.788854i
$31$	−4.88551	−	3.54953i	−0.877463	−	0.637514i	0.0551159	−	0.998480i	$-0.482447\pi$
$31$	−4.88551	−	3.54953i	−0.877463	−	0.637514i	−0.932579	+	0.360966i	$0.882447\pi$
$32$	−13.7855			−2.43696
$33$	−1.30586	−	3.04873i	−0.227321	−	0.530715i
$34$	6.34841			1.08874
$35$	1.38593	+	1.00694i	0.234265	+	0.170204i
$36$	1.55524	−	4.78653i	0.259207	−	0.797756i
$37$	−2.30953	−	7.10802i	−0.379685	−	1.16855i	−0.940263	−	0.340449i	$-0.889421\pi$
$37$	−2.30953	−	7.10802i	−0.379685	−	1.16855i	0.560578	−	0.828102i	$-0.310579\pi$
$38$	13.5835	−	9.86900i	2.20354	−	1.60096i
$39$	−1.22292	+	0.888505i	−0.195824	+	0.142275i
$40$	−4.25780	−	13.1042i	−0.673218	−	2.07195i
$41$	−1.55577	+	4.78817i	−0.242970	+	0.747786i	0.752993	+	0.658028i	$0.228609\pi$
$41$	−1.55577	+	4.78817i	−0.242970	+	0.747786i	−0.995964	+	0.0897576i	$0.971391\pi$
$42$	−2.14548	−	1.55878i	−0.331054	−	0.240525i
$43$	2.02506			0.308818			0.154409	−	0.988007i	$-0.450653\pi$
$43$	2.02506			0.308818			0.154409	+	0.988007i	$0.450653\pi$
$44$	14.3359	+	8.55037i	2.16122	+	1.28902i
$45$	1.71311			0.255375
$46$	−10.8536	−	7.88563i	−1.60028	−	1.16267i
$47$	−1.70895	+	5.25959i	−0.249275	+	0.767190i	0.745629	+	0.666362i	$0.232149\pi$
$47$	−1.70895	+	5.25959i	−0.249275	+	0.767190i	−0.994904	+	0.100829i	$0.967851\pi$
$48$	3.48076	+	10.7127i	0.502404	+	1.54624i
$49$	−0.809017	+	0.587785i	−0.115574	+	0.0839693i
$50$	−4.43097	+	3.21929i	−0.626634	+	0.455276i
$51$	−0.739744	−	2.27670i	−0.103585	−	0.318802i
$52$	2.35092	−	7.23540i	0.326014	−	1.00337i
$53$	−5.04607	−	3.66618i	−0.693131	−	0.503589i	0.184557	−	0.982822i	$-0.440915\pi$
$53$	−5.04607	−	3.66618i	−0.693131	−	0.503589i	−0.877688	+	0.479233i	$0.840915\pi$
$54$	−2.65195			−0.360885
$55$	−1.26005	+	5.54025i	−0.169905	+	0.747047i
$56$	8.04301			1.07479
$57$	−5.12208	−	3.72141i	−0.678436	−	0.492912i
$58$	−6.83916	+	21.0488i	−0.898026	+	2.76384i
$59$	3.45303	+	10.6273i	0.449546	+	1.38356i	0.877420	+	0.479723i	$0.159263\pi$
$59$	3.45303	+	10.6273i	0.449546	+	1.38356i	−0.427874	+	0.903838i	$0.640737\pi$
$60$	−6.97521	+	5.06779i	−0.900496	+	0.654248i
$61$	−11.1722	+	8.11711i	−1.43046	+	1.03929i	−0.440527	+	0.897739i	$0.645209\pi$
$61$	−11.1722	+	8.11711i	−1.43046	+	1.03929i	−0.989931	+	0.141550i	$0.954791\pi$
$62$	−4.94881	−	15.2309i	−0.628499	−	1.93432i
$63$	−0.309017	+	0.951057i	−0.0389325	+	0.119822i
$64$	−11.3510	−	8.24697i	−1.41887	−	1.03087i
$65$	2.58956			0.321195
$66$	1.95061	−	8.57651i	0.240103	−	1.05570i
$67$	13.6173			1.66362			0.831811	−	0.555059i	$-0.187304\pi$
$67$	13.6173			1.66362			0.831811	+	0.555059i	$0.187304\pi$
$68$	9.74702	+	7.08162i	1.18200	+	0.858773i
$69$	−1.56327	+	4.81125i	−0.188196	+	0.579207i
$70$	1.40389	+	4.32073i	0.167797	+	0.516426i
$71$	11.5956	−	8.42466i	1.37614	−	0.999823i	0.378910	−	0.925434i	$-0.376299\pi$
$71$	11.5956	−	8.42466i	1.37614	−	0.999823i	0.997229	−	0.0743897i	$-0.0237009\pi$
$72$	6.50693	−	4.72756i	0.766849	−	0.557148i
$73$	−0.441988	−	1.36030i	−0.0517308	−	0.159211i	0.921854	−	0.387538i	$-0.126674\pi$
$73$	−0.441988	−	1.36030i	−0.0517308	−	0.159211i	−0.973584	+	0.228327i	$0.926674\pi$
$74$	6.12478	−	18.8501i	0.711991	−	2.19128i
$75$	1.67083	+	1.21393i	0.192931	+	0.140173i
$76$	31.8642			3.65508
$77$	−2.84846	−	1.69891i	−0.324612	−	0.193609i
$78$	−4.00873			−0.453900
$79$	−5.43444	−	3.94835i	−0.611423	−	0.444225i	0.238492	−	0.971144i	$-0.423347\pi$
$79$	−5.43444	−	3.94835i	−0.611423	−	0.444225i	−0.849915	+	0.526920i	$0.823347\pi$
$80$	5.96291	−	18.3520i	0.666674	−	2.05181i
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	−10.8016	+	7.84779i	−1.19283	+	0.866644i
$83$	−4.74874	+	3.45016i	−0.521242	+	0.378705i	−0.817072	−	0.576536i	$-0.804404\pi$
$83$	−4.74874	+	3.45016i	−0.521242	+	0.378705i	0.295829	+	0.955241i	$0.404404\pi$
$84$	−1.55524	−	4.78653i	−0.169691	−	0.522254i
$85$	−1.26726	+	3.90023i	−0.137454	+	0.423039i
$86$	4.34471	+	3.15662i	0.468502	+	0.340387i
$87$	8.34554			0.894736
$88$	10.5030	+	24.5209i	1.11963	+	2.61394i
$89$	16.4241			1.74095			0.870473	−	0.492215i	$-0.163813\pi$
$89$	16.4241			1.74095			0.870473	+	0.492215i	$0.163813\pi$
$90$	3.67543	+	2.67036i	0.387424	+	0.281480i
$91$	−0.467115	+	1.43763i	−0.0489669	+	0.150705i
$92$	−7.86773	−	24.2144i	−0.820267	−	2.52452i
$93$	−4.88551	+	3.54953i	−0.506604	+	0.368069i
$94$	−11.8650	+	8.62046i	−1.22379	+	0.889133i
$95$	3.35163	+	10.3152i	0.343869	+	1.05832i
$96$	−4.25995	+	13.1108i	−0.434780	+	1.33811i
$97$	−9.74994	−	7.08375i	−0.989957	−	0.719246i	−0.0300450	−	0.999549i	$-0.509565\pi$
$97$	−9.74994	−	7.08375i	−0.989957	−	0.719246i	−0.959912	+	0.280303i	$0.909565\pi$
$98$	−2.65195			−0.267888
$99$	−3.30304	+	0.299836i	−0.331968	+	0.0301347i
$100$	−10.3942			−1.03942
$101$	4.32699	+	3.14374i	0.430551	+	0.312814i	0.781869	−	0.623442i	$-0.214266\pi$
$101$	4.32699	+	3.14374i	0.430551	+	0.312814i	−0.351318	+	0.936256i	$0.614266\pi$
$102$	1.96177	−	6.03770i	0.194244	−	0.597821i
$103$	2.89788	+	8.91875i	0.285536	+	0.878791i	0.986237	+	0.165336i	$0.0528707\pi$
$103$	2.89788	+	8.91875i	0.285536	+	0.878791i	−0.700701	+	0.713455i	$0.747129\pi$
$104$	9.83597	−	7.14625i	0.964496	−	0.700748i
$105$	1.38593	−	1.00694i	0.135253	−	0.0982672i
$106$	−5.11145	−	15.7314i	−0.496468	−	1.52797i
$107$	−3.76107	+	11.5754i	−0.363596	+	1.11903i	0.587259	+	0.809399i	$0.300207\pi$
$107$	−3.76107	+	11.5754i	−0.363596	+	1.11903i	−0.950856	+	0.309635i	$0.899793\pi$
$108$	−4.07167	−	2.95824i	−0.391797	−	0.284657i
$109$	−6.31429			−0.604799			−0.302399	−	0.953181i	$-0.597788\pi$
$109$	−6.31429			−0.604799			−0.302399	+	0.953181i	$0.597788\pi$
$110$	−11.3394	+	9.92233i	−1.08117	+	0.946057i
$111$	−7.47381			−0.709383
$112$	9.11274	+	6.62079i	0.861073	+	0.625606i
$113$	1.04067	−	3.20285i	0.0978978	−	0.301298i	−0.890100	−	0.455765i	$-0.849366\pi$
$113$	1.04067	−	3.20285i	0.0978978	−	0.301298i	0.987998	+	0.154466i	$0.0493658\pi$
$114$	−5.18844	−	15.9684i	−0.485942	−	1.49558i
$115$	7.01123	−	5.09396i	0.653801	−	0.475014i
$116$	−33.9803	+	24.6881i	−3.15499	+	2.29224i
$117$	0.467115	+	1.43763i	0.0431848	+	0.132909i
$118$	−9.15728	+	28.1832i	−0.842996	+	2.59447i
$119$	−1.93668	−	1.40708i	−0.177535	−	0.128987i
$120$	−13.7785			−1.25780
$121$	1.45982	−	10.9027i	0.132711	−	0.991155i
$122$	−36.6225			−3.31565
$123$	4.07306	+	2.95925i	0.367255	+	0.266826i
$124$	9.39181	−	28.9050i	0.843410	−	2.59575i
$125$	−3.74020	−	11.5112i	−0.334534	−	1.02959i
$126$	−2.14548	+	1.55878i	−0.191134	+	0.138867i
$127$	0.901033	−	0.654639i	0.0799537	−	0.0580898i	−0.547090	−	0.837074i	$-0.684265\pi$
$127$	0.901033	−	0.654639i	0.0799537	−	0.0580898i	0.627044	+	0.778984i	$0.284265\pi$
$128$	−2.97814	−	9.16578i	−0.263233	−	0.810149i
$129$	0.625777	−	1.92594i	0.0550966	−	0.169570i
$130$	5.55584	+	4.03655i	0.487279	+	0.354029i
$131$	−14.3843			−1.25676			−0.628379	−	0.777907i	$-0.716281\pi$
$131$	−14.3843			−1.25676			−0.628379	+	0.777907i	$0.716281\pi$
$132$	12.5619	−	10.9920i	1.09337	−	0.956734i
$133$	−6.33123			−0.548988
$134$	29.2157	+	21.2264i	2.52385	+	1.83368i
$135$	0.529379	−	1.62926i	0.0455617	−	0.140225i
$136$	5.94977	+	18.3115i	0.510188	+	1.57020i
$137$	−2.20692	+	1.60342i	−0.188550	+	0.136990i	−0.678056	−	0.735010i	$-0.737177\pi$
$137$	−2.20692	+	1.60342i	−0.188550	+	0.136990i	0.489506	+	0.872000i	$0.337177\pi$
$138$	−10.8536	+	7.88563i	−0.923924	+	0.671270i
$139$	0.109127	+	0.335860i	0.00925607	+	0.0284872i	0.955578	−	0.294739i	$-0.0952326\pi$
$139$	0.109127	+	0.335860i	0.00925607	+	0.0284872i	−0.946322	+	0.323226i	$0.895233\pi$
$140$	−2.66429	+	8.19985i	−0.225174	+	0.693014i
$141$	4.47408	+	3.25061i	0.376785	+	0.273751i
$142$	38.0102			3.18974
$143$	−4.99293	+	0.453237i	−0.417530	+	0.0379016i
$144$	11.2640			0.938664
$145$	−11.5664	−	8.40346i	−0.960535	−	0.697869i
$146$	1.17213	−	3.60745i	0.0970064	−	0.298555i
$147$	0.309017	+	0.951057i	0.0254873	+	0.0784418i
$148$	30.4309	−	22.1093i	2.50140	−	1.81738i
$149$	0.413730	−	0.300593i	0.0338941	−	0.0246255i	−0.570709	−	0.821152i	$-0.693332\pi$
$149$	0.413730	−	0.300593i	0.0338941	−	0.0246255i	0.604603	+	0.796527i	$0.293332\pi$
$150$	1.69248	+	5.20892i	0.138190	+	0.425306i
$151$	0.302146	−	0.929908i	0.0245883	−	0.0756749i	−0.938009	−	0.346610i	$-0.887333\pi$
$151$	0.302146	−	0.929908i	0.0245883	−	0.0756749i	0.962598	+	0.270935i	$0.0873328\pi$
$152$	41.1969	+	29.9313i	3.34151	+	2.42775i
$153$	−2.39386			−0.193532
$154$	−3.46308	−	8.08508i	−0.279063	−	0.651515i
$155$	10.3452			0.830942
$156$	−6.15480	−	4.47172i	−0.492778	−	0.358024i
$157$	−1.01655	+	3.12862i	−0.0811296	+	0.249691i	−0.983391	−	0.181497i	$-0.941906\pi$
$157$	−1.01655	+	3.12862i	−0.0811296	+	0.249691i	0.902262	+	0.431189i	$0.141906\pi$
$158$	−5.50485	−	16.9422i	−0.437943	−	1.34785i
$159$	−5.04607	+	3.66618i	−0.400179	+	0.290747i
$160$	19.1058	−	13.8812i	1.51044	−	1.09740i
$161$	1.56327	+	4.81125i	0.123203	+	0.379180i
$162$	−0.819499	+	2.52216i	−0.0643859	+	0.198159i
$163$	−2.81720	−	2.04682i	−0.220660	−	0.160319i	0.471964	−	0.881618i	$-0.343545\pi$
$163$	−2.81720	−	2.04682i	−0.220660	−	0.160319i	−0.692624	+	0.721299i	$0.743545\pi$
$164$	−25.3383			−1.97859
$165$	4.87972	+	2.91041i	0.379885	+	0.226575i
$166$	−15.5664			−1.20818
$167$	3.70106	+	2.68898i	0.286397	+	0.208080i	0.721703	−	0.692203i	$-0.243360\pi$
$167$	3.70106	+	2.68898i	0.286397	+	0.208080i	−0.435306	+	0.900283i	$0.643360\pi$
$168$	2.48543	−	7.64935i	0.191755	−	0.590160i
$169$	−3.31112	−	10.1906i	−0.254702	−	0.783892i
$170$	−8.79848	+	6.39247i	−0.674812	+	0.490280i
$171$	−5.12208	+	3.72141i	−0.391695	+	0.284583i
$172$	3.14945	+	9.69301i	0.240143	+	0.739085i
$173$	1.76904	−	5.44456i	0.134498	−	0.413942i	−0.861014	−	0.508582i	$-0.830170\pi$
$173$	1.76904	−	5.44456i	0.134498	−	0.413942i	0.995512	+	0.0946399i	$0.0301700\pi$
$174$	17.9052	+	13.0089i	1.35739	+	0.986199i
$175$	2.06526			0.156119
$176$	−8.28505	+	36.4281i	−0.624509	+	2.74587i
$177$	11.1742			0.839907
$178$	35.2374	+	25.6015i	2.64116	+	1.91891i
$179$	0.913765	−	2.81228i	0.0682980	−	0.210200i	−0.911082	−	0.412224i	$-0.864752\pi$
$179$	0.913765	−	2.81228i	0.0682980	−	0.210200i	0.979380	+	0.202024i	$0.0647520\pi$
$180$	2.66429	+	8.19985i	0.198585	+	0.611181i
$181$	7.60479	−	5.52520i	0.565260	−	0.410685i	−0.268121	−	0.963385i	$-0.586403\pi$
$181$	7.60479	−	5.52520i	0.565260	−	0.410685i	0.833380	+	0.552700i	$0.186403\pi$
$182$	−3.24313	+	2.35627i	−0.240397	+	0.174659i
$183$	4.26742	+	13.1338i	0.315456	+	0.970875i
$184$	12.5734	−	38.6969i	0.926923	−	2.85278i
$185$	10.3582	+	7.52567i	0.761550	+	0.553299i
$186$	−16.0147			−1.17425
$187$	1.76077	−	7.74184i	0.128760	−	0.566139i
$188$	−27.8330			−2.02993
$189$	0.809017	+	0.587785i	0.0588473	+	0.0427551i
$190$	−8.88836	+	27.3555i	−0.644829	+	1.98458i
$191$	−2.84577	−	8.75838i	−0.205913	−	0.633734i	−0.999675	−	0.0255056i	$-0.991880\pi$
$191$	−2.84577	−	8.75838i	−0.205913	−	0.633734i	0.793762	−	0.608229i	$-0.208120\pi$
$192$	−11.3510	+	8.24697i	−0.819187	+	0.595174i
$193$	1.20723	−	0.877101i	0.0868980	−	0.0631351i	−0.543488	−	0.839417i	$-0.682897\pi$
$193$	1.20723	−	0.877101i	0.0868980	−	0.0631351i	0.630386	+	0.776282i	$0.282897\pi$
$194$	−9.87627	−	30.3960i	−0.709075	−	2.18231i
$195$	0.800218	−	2.46282i	0.0573048	−	0.176366i
$196$	−4.07167	−	2.95824i	−0.290834	−	0.211303i
$197$	3.37718			0.240614			0.120307	−	0.992737i	$-0.461612\pi$
$197$	3.37718			0.240614			0.120307	+	0.992737i	$0.461612\pi$
$198$	−7.55398	−	4.50543i	−0.536838	−	0.320187i
$199$	27.8114			1.97150			0.985750	−	0.168215i	$-0.0538002\pi$
$199$	27.8114			1.97150			0.985750	+	0.168215i	$0.0538002\pi$
$200$	−13.4385	−	9.76365i	−0.950246	−	0.690394i
$201$	4.20799	−	12.9509i	0.296809	−	0.913483i
$202$	4.38305	+	13.4896i	0.308390	+	0.949127i
$203$	6.75169	−	4.90539i	0.473876	−	0.344291i
$204$	9.74702	−	7.08162i	0.682428	−	0.495813i
$205$	−2.66520	−	8.20264i	−0.186146	−	0.572897i
$206$	−7.68504	+	23.6521i	−0.535442	+	1.64792i
$207$	4.09270	+	2.97352i	0.284462	+	0.206674i
$208$	17.0268			1.18059
$209$	−8.26769	−	19.3022i	−0.571888	−	1.33516i
$210$	4.54308			0.313503
$211$	19.4219	+	14.1109i	1.33706	+	0.971432i	0.999547	+	0.0301125i	$0.00958657\pi$
$211$	19.4219	+	14.1109i	1.33706	+	0.971432i	0.337516	+	0.941320i	$0.390413\pi$
$212$	9.70047	−	29.8550i	0.666231	−	2.05045i
$213$	−4.42911	−	13.6314i	−0.303477	−	0.934007i
$214$	−26.1127	+	18.9720i	−1.78503	+	1.29690i
$215$	−2.80659	+	2.03911i	−0.191408	+	0.139066i
$216$	−2.48543	−	7.64935i	−0.169112	−	0.520473i
$217$	−1.86610	+	5.74326i	−0.126679	+	0.389878i
$218$	−13.5471	−	9.84258i	−0.917529	−	0.666624i
$219$	−1.43030			−0.0966510
$220$	−28.4783	+	2.58514i	−1.92001	+	0.174290i
$221$	−3.61860			−0.243413
$222$	−16.0349	−	11.6500i	−1.07619	−	0.781898i
$223$	7.05109	−	21.7010i	0.472176	−	1.45321i	−0.377553	−	0.925988i	$-0.623234\pi$
$223$	7.05109	−	21.7010i	0.472176	−	1.45321i	0.849729	−	0.527220i	$-0.176766\pi$
$224$	4.25995	+	13.1108i	0.284630	+	0.876002i
$225$	1.67083	−	1.21393i	0.111389	−	0.0809287i
$226$	7.22526	−	5.24946i	0.480617	−	0.349189i
$227$	4.45128	+	13.6996i	0.295442	+	0.909277i	0.983073	+	0.183217i	$0.0586509\pi$
$227$	4.45128	+	13.6996i	0.295442	+	0.909277i	−0.687630	+	0.726061i	$0.741349\pi$
$228$	9.84659	−	30.3047i	0.652106	−	2.00698i
$229$	3.06915	+	2.22986i	0.202815	+	0.147354i	0.684557	−	0.728959i	$-0.259996\pi$
$229$	3.06915	+	2.22986i	0.202815	+	0.147354i	−0.481742	+	0.876313i	$0.659996\pi$
$230$	22.9828			1.51544
$231$	−2.49598	+	2.18405i	−0.164223	+	0.143700i
$232$	−67.1233			−4.40686
$233$	−22.2354	−	16.1549i	−1.45669	−	1.05834i	−0.984211	−	0.177001i	$-0.943360\pi$
$233$	−22.2354	−	16.1549i	−1.45669	−	1.05834i	−0.472476	−	0.881343i	$-0.656640\pi$
$234$	−1.23877	+	3.81253i	−0.0809807	+	0.249233i
$235$	−2.92761	−	9.01025i	−0.190976	−	0.587764i
$236$	−45.4978	+	33.0561i	−2.96166	+	2.15177i
$237$	−5.43444	+	3.94835i	−0.353005	+	0.256473i
$238$	−1.96177	−	6.03770i	−0.127163	−	0.391366i
$239$	3.47135	−	10.6837i	0.224543	−	0.691072i	−0.773795	−	0.633436i	$-0.781644\pi$
$239$	3.47135	−	10.6837i	0.224543	−	0.691072i	0.998338	−	0.0576354i	$-0.0183561\pi$
$240$	−15.6111	−	11.3421i	−1.00769	−	0.732131i
$241$	14.7496			0.950105			0.475052	−	0.879958i	$-0.342429\pi$
$241$	14.7496			0.950105			0.475052	+	0.879958i	$0.342429\pi$
$242$	20.1269	−	21.1159i	1.29381	−	1.35738i
$243$	1.00000			0.0641500
$244$	−56.2283	−	40.8523i	−3.59965	−	2.61530i
$245$	0.529379	−	1.62926i	0.0338208	−	0.104090i
$246$	4.12583	+	12.6980i	0.263053	+	0.809595i
$247$	−7.74261	+	5.62533i	−0.492650	+	0.357931i
$248$	39.2942	−	28.5489i	2.49518	−	1.81286i
$249$	1.81386	+	5.58248i	0.114949	+	0.353775i
$250$	9.91885	−	30.5271i	0.627323	−	1.93070i
$251$	−6.16417	−	4.47853i	−0.389079	−	0.282682i	0.375999	−	0.926620i	$-0.377300\pi$
$251$	−6.16417	−	4.47853i	−0.389079	−	0.282682i	−0.765078	+	0.643938i	$0.777300\pi$
$252$	−5.03286			−0.317040
$253$	−12.6268	+	11.0488i	−0.793839	+	0.694632i
$254$	2.95358			0.185324
$255$	3.31773	+	2.41047i	0.207765	+	0.150950i
$256$	−0.773480	+	2.38053i	−0.0483425	+	0.148783i
$257$	−0.0894241	−	0.275219i	−0.00557812	−	0.0171677i	0.948229	−	0.317588i	$-0.102873\pi$
$257$	−0.0894241	−	0.275219i	−0.00557812	−	0.0171677i	−0.953807	+	0.300421i	$0.902873\pi$
$258$	4.34471	−	3.15662i	0.270490	−	0.196522i
$259$	−6.04644	+	4.39299i	−0.375707	+	0.272967i
$260$	4.02738	+	12.3950i	0.249768	+	0.768706i
$261$	2.57892	−	7.93708i	0.159631	−	0.491293i
$262$	−30.8611	−	22.4219i	−1.90660	−	1.38523i
$263$	12.3251			0.759998			0.379999	−	0.924987i	$-0.375924\pi$
$263$	12.3251			0.759998			0.379999	+	0.924987i	$0.375924\pi$
$264$	26.5664	−	2.41158i	1.63505	−	0.148423i
$265$	10.6851			0.656383
$266$	−13.5835	−	9.86900i	−0.832858	−	0.605107i
$267$	5.07531	−	15.6202i	0.310604	−	0.955941i
$268$	21.1782	+	65.1798i	1.29367	+	3.98149i
$269$	−10.2349	+	7.43611i	−0.624034	+	0.453388i	−0.854328	−	0.519734i	$-0.826031\pi$
$269$	−10.2349	+	7.43611i	−0.624034	+	0.453388i	0.230294	+	0.973121i	$0.426031\pi$
$270$	3.67543	−	2.67036i	0.223680	−	0.162513i
$271$	3.32200	+	10.2241i	0.201797	+	0.621068i	0.999830	+	0.0184533i	$0.00587420\pi$
$271$	3.32200	+	10.2241i	0.201797	+	0.621068i	−0.798033	+	0.602614i	$0.794126\pi$
$272$	−8.33245	+	25.6447i	−0.505229	+	1.55494i
$273$	1.22292	+	0.888505i	0.0740146	+	0.0537748i
$274$	−7.23428			−0.437039
$275$	2.69694	+	6.29642i	0.162632	+	0.379688i
$276$	−25.4605			−1.53254
$277$	4.92607	+	3.57900i	0.295979	+	0.215041i	0.725857	−	0.687846i	$-0.241443\pi$
$277$	4.92607	+	3.57900i	0.295979	+	0.215041i	−0.429878	+	0.902887i	$0.641443\pi$
$278$	−0.289401	+	0.890685i	−0.0173571	+	0.0534197i
$279$	1.86610	+	5.74326i	0.111720	+	0.343840i
$280$	−11.1471	+	8.09882i	−0.666165	+	0.483997i
$281$	6.96666	−	5.06158i	0.415596	−	0.301948i	−0.360267	−	0.932849i	$-0.617314\pi$
$281$	6.96666	−	5.06158i	0.415596	−	0.301948i	0.775864	+	0.630901i	$0.217314\pi$
$282$	4.53204	+	13.9482i	0.269879	+	0.830603i
$283$	0.987485	−	3.03917i	0.0586999	−	0.180660i	−0.917407	−	0.397950i	$-0.869722\pi$
$283$	0.987485	−	3.03917i	0.0586999	−	0.180660i	0.976107	+	0.217290i	$0.0697218\pi$
$284$	58.3588	+	42.4001i	3.46296	+	2.51599i
$285$	10.8461			0.642467
$286$	−11.4187	−	6.81047i	−0.675202	−	0.402711i
$287$	5.03457			0.297182
$288$	11.1527	+	8.10291i	0.657179	+	0.477469i
$289$	−3.48244	+	10.7179i	−0.204850	+	0.630462i
$290$	−11.7162	−	36.0588i	−0.688000	−	2.11745i
$291$	−9.74994	+	7.08375i	−0.571552	+	0.415257i
$292$	5.82373	−	4.23119i	0.340808	−	0.247611i
$293$	−2.64263	−	8.13317i	−0.154384	−	0.475145i	0.843714	−	0.536793i	$-0.180364\pi$
$293$	−2.64263	−	8.13317i	−0.154384	−	0.475145i	−0.998098	+	0.0616479i	$0.980364\pi$
$294$	−0.819499	+	2.52216i	−0.0477941	+	0.147095i
$295$	−15.4868	−	11.2518i	−0.901673	−	0.655104i
$296$	60.1119			3.49393
$297$	−0.735535	+	3.23404i	−0.0426801	+	0.187658i
$298$	1.35621			0.0785629
$299$	6.18658	+	4.49481i	0.357779	+	0.259942i
$300$	−3.21198	+	9.88545i	−0.185444	+	0.570737i
$301$	−0.625777	−	1.92594i	−0.0360692	−	0.111010i
$302$	2.09777	−	1.52412i	0.120713	−	0.0877031i
$303$	4.32699	−	3.14374i	0.248579	−	0.180603i
$304$	22.0375	+	67.8244i	1.26394	+	3.89000i
$305$	7.31054	−	22.4995i	0.418600	−	1.28832i
$306$	−5.13597	−	3.73150i	−0.293604	−	0.213316i
$307$	−3.49789			−0.199635			−0.0998176	−	0.995006i	$-0.531826\pi$
$307$	−3.49789			−0.199635			−0.0998176	+	0.995006i	$0.531826\pi$
$308$	3.70185	−	16.2765i	0.210932	−	0.927437i
$309$	9.37773			0.533480
$310$	22.1953	+	16.1258i	1.26061	+	0.915884i
$311$	−1.14039	+	3.50976i	−0.0646656	+	0.199020i	−0.978169	−	0.207811i	$-0.933366\pi$
$311$	−1.14039	+	3.50976i	−0.0646656	+	0.199020i	0.913503	+	0.406831i	$0.133366\pi$
$312$	−3.75701	−	11.5629i	−0.212699	−	0.654619i
$313$	21.2482	−	15.4377i	1.20102	−	0.872590i	0.206633	−	0.978419i	$-0.433749\pi$
$313$	21.2482	−	15.4377i	1.20102	−	0.872590i	0.994384	+	0.105828i	$0.0337494\pi$
$314$	−7.05782	+	5.12780i	−0.398296	+	0.289379i
$315$	−0.529379	−	1.62926i	−0.0298272	−	0.0917985i
$316$	10.4471	−	32.1528i	0.587694	−	1.80874i
$317$	−10.5821	−	7.68834i	−0.594350	−	0.431820i	0.249519	−	0.968370i	$-0.419727\pi$
$317$	−10.5821	−	7.68834i	−0.594350	−	0.431820i	−0.843869	+	0.536550i	$0.819727\pi$
$318$	−16.5410			−0.927572
$319$	23.7719	+	14.1783i	1.33097	+	0.793833i
$320$	24.0359			1.34365
$321$	9.84660	+	7.15397i	0.549584	+	0.399296i
$322$	−4.14572	+	12.7592i	−0.231032	+	0.711044i
$323$	−4.68349	−	14.4143i	−0.260597	−	0.802034i
$324$	−4.07167	+	2.95824i	−0.226204	+	0.164347i
$325$	2.52565	−	1.83500i	0.140098	−	0.101787i
$326$	−2.85370	−	8.78278i	−0.158052	−	0.486433i
$327$	−1.95122	+	6.00524i	−0.107903	+	0.332091i
$328$	−32.7596	−	23.8013i	−1.80885	−	1.31420i
$329$	5.53026			0.304893
$330$	5.93262	+	13.8506i	0.326580	+	0.762452i
$331$	7.93676			0.436244			0.218122	−	0.975922i	$-0.430007\pi$
$331$	7.93676			0.436244			0.218122	+	0.975922i	$0.430007\pi$
$332$	−23.8998	−	17.3642i	−1.31167	−	0.952984i
$333$	−2.30953	+	7.10802i	−0.126562	+	0.389517i
$334$	3.74902	+	11.5383i	0.205137	+	0.631347i
$335$	−18.8727	+	13.7118i	−1.03113	+	0.749157i
$336$	9.11274	−	6.62079i	0.497141	−	0.361194i
$337$	3.09034	+	9.51109i	0.168342	+	0.518102i	0.999267	−	0.0382818i	$-0.0121884\pi$
$337$	3.09034	+	9.51109i	0.168342	+	0.518102i	−0.830925	+	0.556384i	$0.812188\pi$
$338$	8.78095	−	27.0250i	0.477621	−	1.46997i
$339$	−2.72450	−	1.97947i	−0.147975	−	0.107510i
$340$	−20.6395			−1.11933
$341$	−19.9465	+	1.81066i	−1.08016	+	0.0980526i
$342$	−16.7901			−0.907907
$343$	0.809017	+	0.587785i	0.0436828	+	0.0317374i
$344$	−5.03313	+	15.4904i	−0.271368	+	0.835185i
$345$	−2.67805	−	8.24220i	−0.144181	−	0.443745i
$346$	12.2823	−	8.92361i	0.660301	−	0.479736i
$347$	4.37559	−	3.17905i	0.234894	−	0.170661i	−0.464111	−	0.885777i	$-0.653626\pi$
$347$	4.37559	−	3.17905i	0.234894	−	0.170661i	0.699006	+	0.715116i	$0.253626\pi$
$348$	12.9793	+	39.9462i	0.695765	+	2.14134i
$349$	−8.81659	+	27.1347i	−0.471941	+	1.45249i	0.378098	+	0.925766i	$0.376578\pi$
$349$	−8.81659	+	27.1347i	−0.471941	+	1.45249i	−0.850039	+	0.526720i	$0.823422\pi$
$350$	4.43097	+	3.21929i	0.236845	+	0.172078i
$351$	1.51161			0.0806840
$352$	−34.4083	+	30.1083i	−1.83397	+	1.60478i
$353$	−19.2226			−1.02312			−0.511559	−	0.859248i	$-0.670932\pi$
$353$	−19.2226			−1.02312			−0.511559	+	0.859248i	$0.670932\pi$
$354$	23.9741	+	17.4182i	1.27421	+	0.925766i
$355$	−7.58754	+	23.3520i	−0.402705	+	1.23940i
$356$	25.5433	+	78.6143i	1.35379	+	4.16655i
$357$	−1.93668	+	1.40708i	−0.102500	+	0.0744704i
$358$	6.34419	−	4.60932i	0.335301	−	0.243610i
$359$	6.90739	+	21.2588i	0.364558	+	1.12199i	0.950257	+	0.311466i	$0.100820\pi$
$359$	6.90739	+	21.2588i	0.364558	+	1.12199i	−0.585699	+	0.810529i	$0.699180\pi$
$360$	−4.25780	+	13.1042i	−0.224406	+	0.690650i
$361$	−17.0577	−	12.3932i	−0.897776	−	0.652272i
$362$	24.9285			1.31021
$363$	−9.91798	−	4.75750i	−0.520559	−	0.249704i
$364$	−7.60775			−0.398754
$365$	1.98231	+	1.44023i	0.103759	+	0.0753851i
$366$	−11.3170	+	34.8301i	−0.591549	+	1.82060i
$367$	−7.24485	−	22.2974i	−0.378178	−	1.16391i	−0.941309	−	0.337545i	$-0.890403\pi$
$367$	−7.24485	−	22.2974i	−0.378178	−	1.16391i	0.563131	−	0.826368i	$-0.309597\pi$
$368$	46.1000	−	33.4936i	2.40313	−	1.74597i
$369$	4.07306	−	2.95925i	0.212035	−	0.154052i
$370$	10.4924	+	32.2923i	0.545474	+	1.67880i
$371$	−1.92743	+	5.93201i	−0.100067	+	0.307975i
$372$	−24.5881	−	17.8643i	−1.27483	−	0.926220i
$373$	−33.4536			−1.73216			−0.866082	−	0.499903i	$-0.833369\pi$
$373$	−33.4536			−1.73216			−0.866082	+	0.499903i	$0.833369\pi$
$374$	15.8455	−	13.8653i	0.819352	−	0.716956i
$375$	−12.1036			−0.625025
$376$	−35.9850	−	26.1447i	−1.85579	−	1.34831i
$377$	3.89833	−	11.9978i	0.200774	−	0.617919i
$378$	0.819499	+	2.52216i	0.0421505	+	0.129726i
$379$	14.8694	−	10.8032i	0.763788	−	0.554925i	−0.136282	−	0.990670i	$-0.543515\pi$
$379$	14.8694	−	10.8032i	0.763788	−	0.554925i	0.900070	+	0.435745i	$0.143515\pi$
$380$	−44.1617	+	32.0853i	−2.26545	+	1.64594i
$381$	−0.344164	−	1.05923i	−0.0176320	−	0.0542659i
$382$	7.54685	−	23.2268i	0.386131	−	1.18839i
$383$	−17.2647	−	12.5435i	−0.882185	−	0.640945i	0.0516438	−	0.998666i	$-0.483554\pi$
$383$	−17.2647	−	12.5435i	−0.882185	−	0.640945i	−0.933829	+	0.357721i	$0.883554\pi$
$384$	−9.63748			−0.491810
$385$	5.65847	−	0.513652i	0.288382	−	0.0261781i
$386$	3.95728			0.201420
$387$	−1.63831	−	1.19030i	−0.0832798	−	0.0605063i
$388$	18.7431	−	57.6854i	0.951537	−	2.92853i
$389$	4.79639	+	14.7618i	0.243187	+	0.748452i	0.995929	+	0.0901368i	$0.0287304\pi$
$389$	4.79639	+	14.7618i	0.243187	+	0.748452i	−0.752743	+	0.658315i	$0.771270\pi$
$390$	5.55584	−	4.03655i	0.281331	−	0.204399i
$391$	−9.79735	+	7.11819i	−0.495474	+	0.359983i
$392$	−2.48543	−	7.64935i	−0.125533	−	0.386351i
$393$	−4.44498	+	13.6802i	−0.224220	+	0.690077i
$394$	7.24567	+	5.26429i	0.365031	+	0.265211i
$395$	11.5075			0.579007
$396$	−6.57220	−	15.3438i	−0.330265	−	0.771056i
$397$	21.4777			1.07794			0.538968	−	0.842326i	$-0.318815\pi$
$397$	21.4777			1.07794			0.538968	+	0.842326i	$0.318815\pi$
$398$	59.6688	+	43.3519i	2.99093	+	2.17303i
$399$	−1.95646	+	6.02136i	−0.0979455	+	0.301445i
$400$	−7.18867	−	22.1245i	−0.359434	−	1.10622i
$401$	−7.18493	+	5.22015i	−0.358798	+	0.260682i	−0.752551	−	0.658534i	$-0.771177\pi$
$401$	−7.18493	+	5.22015i	−0.358798	+	0.260682i	0.393753	+	0.919216i	$0.371177\pi$
$402$	29.2157	−	21.2264i	1.45714	−	1.05868i
$403$	2.82082	+	8.68160i	0.140515	+	0.432461i
$404$	−8.31812	+	25.6005i	−0.413842	+	1.27367i
$405$	−1.38593	−	1.00694i	−0.0688676	−	0.0500352i
$406$	22.1320			1.09839
$407$	−21.2888	−	12.6973i	−1.05525	−	0.629382i
$408$	19.2539			0.953208
$409$	−4.41542	−	3.20799i	−0.218329	−	0.158625i	0.473245	−	0.880931i	$-0.343082\pi$
$409$	−4.41542	−	3.20799i	−0.218329	−	0.158625i	−0.691574	+	0.722306i	$0.743082\pi$
$410$	7.06799	−	21.7530i	0.349063	−	1.07431i
$411$	0.842969	+	2.59439i	0.0415806	+	0.127972i
$412$	−38.1830	+	27.7416i	−1.88114	+	1.36673i
$413$	9.04015	−	6.56805i	0.444837	−	0.323193i
$414$	4.14572	+	12.7592i	0.203751	+	0.627082i
$415$	3.10733	−	9.56339i	0.152533	−	0.469448i
$416$	16.8586	+	12.2485i	0.826561	+	0.600531i
$417$	0.353144			0.0172935
$418$	12.3497	−	54.2999i	0.604046	−	2.65590i
$419$	19.9805			0.976114			0.488057	−	0.872812i	$-0.337706\pi$
$419$	19.9805			0.976114			0.488057	+	0.872812i	$0.337706\pi$
$420$	6.97521	+	5.06779i	0.340355	+	0.247283i
$421$	−8.74895	+	26.9265i	−0.426398	+	1.31232i	0.475252	+	0.879850i	$0.342357\pi$
$421$	−8.74895	+	26.9265i	−0.426398	+	1.31232i	−0.901649	+	0.432468i	$0.857643\pi$
$422$	19.6736	+	60.5491i	0.957695	+	2.94748i
$423$	4.47408	−	3.25061i	0.217537	−	0.158050i
$424$	40.5856	−	29.4871i	1.97101	−	1.43202i
$425$	1.52777	+	4.70198i	0.0741075	+	0.228079i
$426$	11.7458	−	36.1498i	0.569085	−	1.75146i
$427$	11.1722	+	8.11711i	0.540663	+	0.392814i
$428$	−61.2553			−2.96089
$429$	−1.11185	+	4.88862i	−0.0536804	+	0.236025i
$430$	−9.20000			−0.443664
$431$	−25.6982	−	18.6708i	−1.23784	−	0.899342i	−0.240386	−	0.970677i	$-0.577274\pi$
$431$	−25.6982	−	18.6708i	−1.23784	−	0.899342i	−0.997452	+	0.0713351i	$0.977274\pi$
$432$	3.48076	−	10.7127i	0.167468	−	0.515413i
$433$	−4.06856	−	12.5217i	−0.195523	−	0.601757i	−0.999970	−	0.00773305i	$-0.997538\pi$
$433$	−4.06856	−	12.5217i	−0.195523	−	0.601757i	0.804447	−	0.594024i	$-0.202462\pi$
$434$	−12.9561	+	9.41319i	−0.621915	+	0.451848i
$435$	−11.5664	+	8.40346i	−0.554565	+	0.402915i
$436$	−9.82023	−	30.2235i	−0.470304	−	1.44745i
$437$	−9.89744	+	30.4612i	−0.473459	+	1.45716i
$438$	−3.06868	−	2.22953i	−0.146627	−	0.106531i
$439$	−9.81161			−0.468283			−0.234141	−	0.972203i	$-0.575228\pi$
$439$	−9.81161			−0.468283			−0.234141	+	0.972203i	$0.575228\pi$
$440$	−39.2476	−	23.4085i	−1.87106	−	1.11595i
$441$	1.00000			0.0476190
$442$	−7.76362	−	5.64060i	−0.369278	−	0.268296i
$443$	0.767950	−	2.36351i	0.0364864	−	0.112294i	−0.931155	−	0.364625i	$-0.881197\pi$
$443$	0.767950	−	2.36351i	0.0364864	−	0.112294i	0.967641	+	0.252331i	$0.0811972\pi$
$444$	−11.6236	−	35.7736i	−0.551630	−	1.69774i
$445$	−22.7627	+	16.5380i	−1.07905	+	0.783978i
$446$	48.9551	−	35.5679i	2.31809	−	1.68419i
$447$	−0.158031	−	0.486369i	−0.00747460	−	0.0230045i
$448$	−4.33569	+	13.3439i	−0.204842	+	0.630439i
$449$	12.6285	+	9.17515i	0.595976	+	0.433002i	0.844448	−	0.535637i	$-0.179928\pi$
$449$	12.6285	+	9.17515i	0.595976	+	0.433002i	−0.248472	+	0.968639i	$0.579928\pi$
$450$	5.47698			0.258187
$451$	6.57444	+	15.3490i	0.309578	+	0.722758i
$452$	16.9490			0.797215
$453$	−0.791027	−	0.574715i	−0.0371657	−	0.0270025i
$454$	−11.8046	+	36.3308i	−0.554017	+	1.70509i
$455$	−0.800218	−	2.46282i	−0.0375148	−	0.115459i
$456$	41.1969	−	29.9313i	1.92922	−	1.40166i
$457$	−11.0554	+	8.03223i	−0.517150	+	0.375732i	−0.815529	−	0.578716i	$-0.803554\pi$
$457$	−11.0554	+	8.03223i	−0.517150	+	0.375732i	0.298379	+	0.954447i	$0.403554\pi$
$458$	3.10891	+	9.56824i	0.145270	+	0.447095i
$459$	−0.739744	+	2.27670i	−0.0345283	+	0.106267i
$460$	35.2865	+	25.6372i	1.64524	+	1.19534i
$461$	18.6545			0.868825			0.434412	−	0.900714i	$-0.356956\pi$
$461$	18.6545			0.868825			0.434412	+	0.900714i	$0.356956\pi$
$462$	−8.75952	+	0.795152i	−0.407530	+	0.0369938i
$463$	−18.5697			−0.863006			−0.431503	−	0.902111i	$-0.642017\pi$
$463$	−18.5697			−0.863006			−0.431503	+	0.902111i	$0.642017\pi$
$464$	−76.0508	−	55.2541i	−3.53057	−	2.56511i
$465$	3.19683	−	9.83882i	0.148249	−	0.456264i
$466$	−22.5234	−	69.3200i	−1.04338	−	3.21119i
$467$	−28.2815	+	20.5477i	−1.30871	+	0.950835i	−1.00000		0.000321071i	$-0.999898\pi$
$467$	−28.2815	+	20.5477i	−1.30871	+	0.950835i	−0.308712	+	0.951156i	$0.599898\pi$
$468$	−6.15480	+	4.47172i	−0.284506	+	0.206705i
$469$	−4.20799	−	12.9509i	−0.194307	−	0.598015i
$470$	7.76388	−	23.8948i	0.358121	−	1.10218i
$471$	2.66136	+	1.93359i	0.122629	+	0.0890953i
$472$	−89.8745			−4.13681
$473$	5.05450	−	4.42283i	0.232406	−	0.203362i
$474$	−17.8141			−0.818228
$475$	10.5784	+	7.68568i	0.485372	+	0.352643i
$476$	3.72303	−	11.4583i	0.170645	−	0.525191i
$477$	1.92743	+	5.93201i	0.0882508	+	0.271608i
$478$	24.1012	−	17.5106i	1.10236	−	0.800915i
$479$	−32.8011	+	23.8314i	−1.49872	+	1.08888i	−0.527830	+	0.849350i	$0.676994\pi$
$479$	−32.8011	+	23.8314i	−1.49872	+	1.08888i	−0.970888	+	0.239532i	$0.923006\pi$
$480$	−7.29776	−	22.4602i	−0.333096	−	1.02516i
$481$	−3.49113	+	10.7446i	−0.159182	+	0.489911i
$482$	31.6449	+	22.9914i	1.44139	+	1.04723i
$483$	5.05885			0.230186
$484$	54.4565	−	9.96881i	2.47530	−	0.453128i
$485$	20.6457			0.937472
$486$	2.14548	+	1.55878i	0.0973208	+	0.0707077i
$487$	4.18930	−	12.8933i	0.189835	−	0.584253i	−0.810163	−	0.586205i	$-0.800621\pi$
$487$	4.18930	−	12.8933i	0.189835	−	0.584253i	0.999998	+	0.00195204i	$0.000621354\pi$
$488$	−34.3229	−	105.635i	−1.55372	−	4.78187i
$489$	−2.81720	+	2.04682i	−0.127398	+	0.0925602i
$490$	3.67543	−	2.67036i	0.166039	−	0.120634i
$491$	−7.24935	−	22.3112i	−0.327158	−	1.00689i	−0.970457	−	0.241275i	$-0.922435\pi$
$491$	−7.24935	−	22.3112i	−0.327158	−	1.00689i	0.643298	−	0.765616i	$-0.277565\pi$
$492$	−7.82997	+	24.0982i	−0.353002	+	1.08643i
$493$	16.1626	+	11.7428i	0.727927	+	0.528870i
$494$	−25.3802			−1.14191
$495$	4.27588	−	3.74152i	0.192187	−	0.168169i
$496$	68.0211			3.05424
$497$	−11.5956	−	8.42466i	−0.520132	−	0.377898i
$498$	−4.81027	+	14.8045i	−0.215553	+	0.663405i
$499$	5.34216	+	16.4415i	0.239148	+	0.736021i	0.996544	+	0.0830658i	$0.0264712\pi$
$499$	5.34216	+	16.4415i	0.239148	+	0.736021i	−0.757396	+	0.652956i	$0.773529\pi$
$500$	49.2817	−	35.8052i	2.20394	−	1.60126i
$501$	3.70106	−	2.68898i	0.165351	−	0.120135i
$502$	−6.24403	−	19.2172i	−0.278685	−	0.857704i
$503$	1.00304	−	3.08705i	0.0447235	−	0.137645i	−0.926201	−	0.377029i	$-0.876946\pi$
$503$	1.00304	−	3.08705i	0.0447235	−	0.137645i	0.970925	+	0.239384i	$0.0769456\pi$
$504$	−6.50693	−	4.72756i	−0.289842	−	0.210582i
$505$	−9.16247			−0.407724
$506$	−44.3131	+	4.02255i	−1.96996	+	0.178824i
$507$	−10.7150			−0.475871
$508$	4.53477	+	3.29470i	0.201198	+	0.146179i
$509$	−4.82082	+	14.8370i	−0.213679	+	0.657636i	0.785566	+	0.618778i	$0.212372\pi$
$509$	−4.82082	+	14.8370i	−0.213679	+	0.657636i	−0.999245	+	0.0388581i	$0.987628\pi$
$510$	3.36072	+	10.3432i	0.148815	+	0.458006i
$511$	−1.15714	+	0.840712i	−0.0511889	+	0.0371909i
$512$	−20.9640	+	15.2312i	−0.926485	+	0.673131i
$513$	1.95646	+	6.02136i	0.0863798	+	0.265850i
$514$	0.237148	−	0.729868i	0.0104602	−	0.0321931i
$515$	−12.9969	−	9.44281i	−0.572712	−	0.416100i
$516$	10.1918			0.448670
$517$	7.22174	+	16.8603i	0.317612	+	0.741513i
$518$	−19.8202			−0.870850
$519$	−4.63142	−	3.36492i	−0.203297	−	0.147704i
$520$	−6.43616	+	19.8085i	−0.282244	+	0.868658i
$521$	−1.34232	−	4.13123i	−0.0588080	−	0.180993i	0.917337	−	0.398111i	$-0.130334\pi$
$521$	−1.34232	−	4.13123i	−0.0588080	−	0.180993i	−0.976145	+	0.217119i	$0.930334\pi$
$522$	17.9052	−	13.0089i	0.783688	−	0.569382i
$523$	−10.0849	+	7.32713i	−0.440983	+	0.320393i	−0.786026	−	0.618194i	$-0.787865\pi$
$523$	−10.0849	+	7.32713i	−0.440983	+	0.320393i	0.345042	+	0.938587i	$0.387865\pi$
$524$	−22.3710	−	68.8507i	−0.977280	−	3.00776i
$525$	0.638201	−	1.96418i	0.0278534	−	0.0857239i
$526$	26.4432	+	19.2121i	1.15298	+	0.837687i
$527$	−14.4561			−0.629718
$528$	32.0849	+	19.1364i	1.39632	+	0.832807i
$529$	2.59198			0.112695
$530$	22.9247	+	16.6558i	0.995785	+	0.723480i
$531$	3.45303	−	10.6273i	0.149849	−	0.461187i
$532$	−9.84659	−	30.3047i	−0.426904	−	1.31387i
$533$	6.15689	−	4.47324i	0.266685	−	0.193758i
$534$	35.2374	−	25.6015i	1.52487	−	1.10788i
$535$	−6.44311	−	19.8299i	−0.278560	−	0.857320i
$536$	−33.8449	+	104.164i	−1.46188	+	4.49919i
$537$	−2.39227	−	1.73809i	−0.103234	−	0.0750039i
$538$	−33.5500			−1.44644
$539$	−0.735535	+	3.23404i	−0.0316818	+	0.139300i
$540$	8.62183			0.371025
$541$	10.1738	+	7.39173i	0.437408	+	0.317795i	0.784604	−	0.619997i	$-0.212866\pi$
$541$	10.1738	+	7.39173i	0.437408	+	0.317795i	−0.347196	+	0.937792i	$0.612866\pi$
$542$	−8.80979	+	27.1137i	−0.378413	+	1.16463i
$543$	−2.90477	−	8.93997i	−0.124656	−	0.383651i
$544$	−26.6980	+	19.3973i	−1.14467	+	0.831651i
$545$	8.75118	−	6.35810i	0.374859	−	0.272351i
$546$	1.23877	+	3.81253i	0.0530143	+	0.163161i
$547$	−0.0775023	+	0.238528i	−0.00331376	+	0.0101987i	−0.952700	−	0.303913i	$-0.901707\pi$
$547$	−0.0775023	+	0.238528i	−0.00331376	+	0.0101987i	0.949386	+	0.314112i	$0.101707\pi$
$548$	−11.1071	−	8.06981i	−0.474473	−	0.344725i
$549$	13.8096			0.589381
$550$	−4.02851	+	17.7127i	−0.171776	+	0.755274i
$551$	52.8376			2.25096
$552$	−32.9176	−	23.9160i	−1.40107	−	1.01793i
$553$	−2.07577	+	6.38857i	−0.0882708	+	0.271670i
$554$	4.98989	+	15.3573i	0.212000	+	0.652470i
$555$	10.3582	−	7.52567i	0.439681	−	0.319447i
$556$	−1.43788	+	1.04468i	−0.0609799	+	0.0443045i
$557$	8.75028	+	26.9306i	0.370761	+	1.14109i	0.946294	+	0.323307i	$0.104795\pi$
$557$	8.75028	+	26.9306i	0.370761	+	1.14109i	−0.575533	+	0.817779i	$0.695205\pi$
$558$	−4.94881	+	15.2309i	−0.209500	+	0.644774i
$559$	−2.47649	−	1.79927i	−0.104744	−	0.0761012i
$560$	−19.2964			−0.815421
$561$	−6.81882	−	4.06695i	−0.287891	−	0.171707i
$562$	22.8367			0.963308
$563$	−13.1091	−	9.52433i	−0.552483	−	0.401403i	0.276217	−	0.961095i	$-0.410919\pi$
$563$	−13.1091	−	9.52433i	−0.552483	−	0.401403i	−0.828700	+	0.559693i	$0.810919\pi$
$564$	−8.60088	+	26.4708i	−0.362163	+	1.11462i
$565$	1.78278	+	5.48682i	0.0750019	+	0.230832i
$566$	6.85602	−	4.98119i	0.288180	−	0.209375i
$567$	0.809017	−	0.587785i	0.0339755	−	0.0246847i
$568$	35.6233	+	109.637i	1.49472	+	4.60028i
$569$	−1.97953	+	6.09236i	−0.0829862	+	0.255405i	−0.983937	−	0.178516i	$-0.942870\pi$
$569$	−1.97953	+	6.09236i	−0.0829862	+	0.255405i	0.900951	+	0.433921i	$0.142870\pi$
$570$	23.2700	+	16.9067i	0.974674	+	0.708142i
$571$	25.9443			1.08574			0.542868	−	0.839818i	$-0.317338\pi$
$571$	25.9443			1.08574			0.542868	+	0.839818i	$0.317338\pi$
$572$	−9.93463	−	23.1939i	−0.415388	−	0.969787i
$573$	−9.20911			−0.384716
$574$	10.8016	+	7.84779i	0.450848	+	0.327561i
$575$	3.22856	−	9.93650i	0.134640	−	0.414381i
$576$	4.33569	+	13.3439i	0.180654	+	0.555995i
$577$	−7.25058	+	5.26785i	−0.301845	+	0.219304i	−0.728390	−	0.685163i	$-0.759731\pi$
$577$	−7.25058	+	5.26785i	−0.301845	+	0.219304i	0.426544	+	0.904467i	$0.359731\pi$
$578$	−24.1783	+	17.5665i	−1.00568	+	0.730672i
$579$	−0.461119	−	1.41918i	−0.0191635	−	0.0589791i
$580$	22.2350	−	68.4322i	0.923257	−	2.84149i
$581$	4.74874	+	3.45016i	0.197011	+	0.143137i
$582$	−31.9603			−1.32480
$583$	−20.6020	+	1.87016i	−0.853248	+	0.0774542i
$584$	11.5039			0.476037
$585$	−2.09500	−	1.52210i	−0.0866175	−	0.0629313i
$586$	7.00813	−	21.5688i	0.289503	−	0.890999i
$587$	1.53315	+	4.71854i	0.0632798	+	0.194755i	0.977698	−	0.210015i	$-0.0673514\pi$
$587$	1.53315	+	4.71854i	0.0632798	+	0.194755i	−0.914418	+	0.404771i	$0.867351\pi$
$588$	−4.07167	+	2.95824i	−0.167913	+	0.121996i
$589$	−30.9313	+	22.4729i	−1.27450	+	0.925980i
$590$	−15.6874	−	48.2809i	−0.645840	−	1.98769i
$591$	1.04361	−	3.21189i	0.0429283	−	0.132120i
$592$	68.1069	+	49.4825i	2.79918	+	2.03372i
$593$	30.7179			1.26143			0.630716	−	0.776013i	$-0.282761\pi$
$593$	30.7179			1.26143			0.630716	+	0.776013i	$0.282761\pi$
$594$	−6.61922	+	5.79201i	−0.271590	+	0.237649i
$595$	4.10094			0.168122
$596$	2.08225	+	1.51284i	0.0852921	+	0.0619684i
$597$	8.59421	−	26.4503i	0.351738	−	1.08254i
$598$	6.26674	+	19.2870i	0.256266	+	0.788705i
$599$	26.4690	−	19.2309i	1.08149	−	0.785752i	0.103552	−	0.994624i	$-0.466979\pi$
$599$	26.4690	−	19.2309i	1.08149	−	0.785752i	0.977943	+	0.208872i	$0.0669792\pi$
$600$	−13.4385	+	9.76365i	−0.548625	+	0.398599i
$601$	−12.5977	−	38.7716i	−0.513869	−	1.58153i	−0.785330	−	0.619078i	$-0.787507\pi$
$601$	−12.5977	−	38.7716i	−0.513869	−	1.58153i	0.271460	−	0.962450i	$-0.412493\pi$
$602$	1.65953	−	5.10752i	0.0676375	−	0.208167i
$603$	−11.0167	−	8.00407i	−0.448633	−	0.325951i
$604$	4.92095			0.200230
$605$	8.95514	+	16.5804i	0.364078	+	0.674088i
$606$	14.1838			0.576179
$607$	20.6513	+	15.0041i	0.838212	+	0.608997i	0.921871	−	0.387498i	$-0.126661\pi$
$607$	20.6513	+	15.0041i	0.838212	+	0.608997i	−0.0836587	+	0.996494i	$0.526661\pi$
$608$	−26.9708	+	83.0075i	−1.09381	+	3.36640i
$609$	−2.57892	−	7.93708i	−0.104503	−	0.321627i
$610$	50.7564	−	36.8767i	2.05507	−	1.49309i
$611$	6.76308	−	4.91367i	0.273605	−	0.198786i
$612$	−3.72303	−	11.4583i	−0.150495	−	0.463175i
$613$	−11.4336	+	35.1891i	−0.461800	+	1.42127i	0.401163	+	0.916007i	$0.368606\pi$
$613$	−11.4336	+	35.1891i	−0.461800	+	1.42127i	−0.862963	+	0.505267i	$0.831394\pi$
$614$	−7.50464	−	5.45244i	−0.302863	−	0.220043i
$615$	−8.62477			−0.347784
$616$	20.0752	−	17.5664i	0.808852	−	0.707769i
$617$	−43.0676			−1.73384			−0.866918	−	0.498452i	$-0.833902\pi$
$617$	−43.0676			−1.73384			−0.866918	+	0.498452i	$0.833902\pi$
$618$	20.1197	+	14.6178i	0.809333	+	0.588015i
$619$	4.49645	−	13.8387i	0.180728	−	0.556223i	−0.819121	−	0.573621i	$-0.805538\pi$
$619$	4.49645	−	13.8387i	0.180728	−	0.556223i	0.999849	+	0.0173982i	$0.00553830\pi$
$620$	16.0892	+	49.5174i	0.646157	+	1.98867i
$621$	4.09270	−	2.97352i	0.164234	−	0.119323i
$622$	−7.91762	+	5.75249i	−0.317468	+	0.230654i
$623$	−5.07531	−	15.6202i	−0.203338	−	0.625810i
$624$	5.26156	−	16.1934i	0.210631	−	0.648256i
$625$	8.42056	+	6.11789i	0.336822	+	0.244716i
$626$	69.6514			2.78383
$627$	−20.9123	+	1.89833i	−0.835159	+	0.0758121i
$628$	−16.5562			−0.660666
$629$	−14.4743	−	10.5162i	−0.577130	−	0.419309i
$630$	1.40389	−	4.32073i	0.0559323	−	0.172142i
$631$	2.11020	+	6.49452i	0.0840057	+	0.258543i	0.984233	−	0.176878i	$-0.0565997\pi$
$631$	2.11020	+	6.49452i	0.0840057	+	0.258543i	−0.900227	+	0.435421i	$0.856600\pi$
$632$	43.7093	−	31.7566i	1.73866	−	1.26321i
$633$	19.4219	−	14.1109i	0.771953	−	0.560857i
$634$	−10.7192	−	32.9903i	−0.425714	−	1.31021i
$635$	−0.589590	+	1.81457i	−0.0233972	+	0.0720090i
$636$	−25.3962	−	18.4514i	−1.00702	−	0.731645i
$637$	1.51161			0.0598924
$638$	28.9012	+	67.4744i	1.14421	+	2.67134i
$639$	−14.3329			−0.567000
$640$	13.3569	+	9.70436i	0.527978	+	0.383598i
$641$	−3.52797	+	10.8580i	−0.139346	+	0.428864i	−0.996241	−	0.0866281i	$-0.972391\pi$
$641$	−3.52797	+	10.8580i	−0.139346	+	0.428864i	0.856894	+	0.515492i	$0.172391\pi$
$642$	9.97418	+	30.6974i	0.393649	+	1.21153i
$643$	29.3099	−	21.2949i	1.15587	−	0.839790i	0.166621	−	0.986021i	$-0.446714\pi$
$643$	29.3099	−	21.2949i	1.15587	−	0.839790i	0.989250	+	0.146231i	$0.0467143\pi$
$644$	−20.5980	+	14.9653i	−0.811674	+	0.589716i
$645$	1.07202	+	3.29935i	0.0422109	+	0.129912i
$646$	12.4204	−	38.2261i	0.488675	−	1.50399i
$647$	19.5403	+	14.1968i	0.768208	+	0.558136i	0.901417	−	0.432952i	$-0.142528\pi$
$647$	19.5403	+	14.1968i	0.768208	+	0.558136i	−0.133209	+	0.991088i	$0.542528\pi$
$648$	−8.04301			−0.315959
$649$	31.8294	+	18.9840i	1.24941	+	0.745187i
$650$	8.27908			0.324732
$651$	4.88551	+	3.54953i	0.191478	+	0.139117i
$652$	5.41573	−	16.6679i	0.212096	−	0.652766i
$653$	−5.66913	−	17.4478i	−0.221850	−	0.682784i	−0.998596	−	0.0529703i	$-0.983131\pi$
$653$	−5.66913	−	17.4478i	−0.221850	−	0.682784i	0.776746	−	0.629814i	$-0.216869\pi$
$654$	−13.5471	+	9.84258i	−0.529735	+	0.384875i
$655$	19.9356	−	14.4841i	0.778949	−	0.565940i
$656$	−17.5241	−	53.9337i	−0.684202	−	2.10576i
$657$	−0.441988	+	1.36030i	−0.0172436	+	0.0530704i
$658$	11.8650	+	8.62046i	0.462548	+	0.336061i
$659$	−9.32284			−0.363166			−0.181583	−	0.983376i	$-0.558122\pi$
$659$	−9.32284			−0.363166			−0.181583	+	0.983376i	$0.558122\pi$
$660$	−6.34166	+	27.8833i	−0.246849	+	1.08536i
$661$	−9.30120			−0.361775			−0.180887	−	0.983504i	$-0.557897\pi$
$661$	−9.30120			−0.361775			−0.180887	+	0.983504i	$0.557897\pi$
$662$	17.0281	+	12.3717i	0.661817	+	0.480838i
$663$	−1.11821	+	3.44149i	−0.0434276	+	0.133656i
$664$	−14.5889	−	44.8999i	−0.566158	−	1.74246i
$665$	8.77467	−	6.37517i	0.340267	−	0.247218i
$666$	−16.0349	+	11.6500i	−0.621339	+	0.451429i
$667$	−13.0463	−	40.1525i	−0.505157	−	1.55471i
$668$	−7.11486	+	21.8973i	−0.275282	+	0.847231i
$669$	−18.4600	−	13.4120i	−0.713705	−	0.518537i
$670$	−61.8647			−2.39004
$671$	−10.1575	+	44.6609i	−0.392125	+	1.72411i
$672$	13.7855			0.531787
$673$	−29.0694	−	21.1202i	−1.12054	−	0.814123i	−0.136253	−	0.990674i	$-0.543506\pi$
$673$	−29.0694	−	21.1202i	−1.12054	−	0.814123i	−0.984292	+	0.176551i	$0.943506\pi$
$674$	−8.19544	+	25.2230i	−0.315677	+	0.971553i
$675$	−0.638201	−	1.96418i	−0.0245644	−	0.0756014i
$676$	43.6280	−	31.6976i	1.67800	−	1.21914i
$677$	38.4071	−	27.9044i	1.47610	−	1.07245i	0.497318	−	0.867568i	$-0.334318\pi$
$677$	38.4071	−	27.9044i	1.47610	−	1.07245i	0.978786	−	0.204884i	$-0.0656817\pi$
$678$	−2.75980	−	8.49380i	−0.105990	−	0.326202i
$679$	−3.72415	+	11.4617i	−0.142920	+	0.439861i
$680$	−26.6846	−	19.3875i	−1.02331	−	0.743475i
$681$	14.4047			0.551988
$682$	−45.6171	−	27.2075i	−1.74677	−	1.04183i
$683$	−30.1415			−1.15333			−0.576667	−	0.816980i	$-0.695647\pi$
$683$	−30.1415			−1.15333			−0.576667	+	0.816980i	$0.695647\pi$
$684$	−25.7787	−	18.7293i	−0.985673	−	0.716133i
$685$	1.44410	−	4.44448i	0.0551761	−	0.169815i
$686$	0.819499	+	2.52216i	0.0312886	+	0.0962964i
$687$	3.06915	−	2.22986i	0.117095	−	0.0850746i
$688$	−18.4538	+	13.4075i	−0.703545	+	0.511156i
$689$	2.91353	+	8.96691i	0.110996	+	0.341612i
$690$	7.10207	−	21.8579i	0.270371	−	0.832117i
$691$	−37.0354	−	26.9078i	−1.40889	−	1.02362i	−0.993482	−	0.113985i	$-0.963638\pi$
$691$	−37.0354	−	26.9078i	−1.40889	−	1.02362i	−0.415409	−	0.909635i	$-0.636362\pi$
$692$	28.8118			1.09526
$693$	1.30586	+	3.04873i	0.0496054	+	0.115812i
$694$	14.3432			0.544459
$695$	−0.489434	−	0.355594i	−0.0185653	−	0.0134885i
$696$	−20.7422	+	63.8380i	−0.786232	+	2.41977i
$697$	3.72430	+	11.4622i	0.141068	+	0.434162i
$698$	−61.2127	+	44.4737i	−2.31694	+	1.68335i
$699$	−22.2354	+	16.1549i	−0.841018	+	0.611036i
$700$	3.21198	+	9.88545i	0.121401	+	0.373635i
$701$	3.83930	−	11.8162i	0.145008	−	0.446290i	−0.852004	−	0.523536i	$-0.824613\pi$
$701$	3.83930	−	11.8162i	0.145008	−	0.446290i	0.997012	+	0.0772457i	$0.0246126\pi$
$702$	3.24313	+	2.35627i	0.122404	+	0.0889318i
$703$	−47.3184			−1.78465
$704$	−46.3437	+	4.20688i	−1.74664	+	0.158553i
$705$	−9.47394			−0.356809
$706$	−41.2417	−	29.9639i	−1.55215	−	1.12771i
$707$	1.65276	−	5.08668i	0.0621585	−	0.191304i
$708$	17.3786	+	53.4859i	0.653128	+	2.01012i
$709$	3.65899	−	2.65841i	0.137416	−	0.0998388i	−0.516953	−	0.856013i	$-0.672934\pi$
$709$	3.65899	−	2.65841i	0.137416	−	0.0998388i	0.654370	+	0.756175i	$0.272934\pi$
$710$	−52.6796	+	38.2739i	−1.97703	+	1.43640i
$711$	2.07577	+	6.38857i	0.0778476	+	0.239590i
$712$	−40.8208	+	125.633i	−1.52982	+	4.70831i
$713$	24.7151	+	17.9565i	0.925586	+	0.672478i
$714$	−6.34841			−0.237583
$715$	6.46349	−	5.65573i	0.241721	−	0.211512i
$716$	14.8822			0.556174
$717$	−9.08810	−	6.60289i	−0.339401	−	0.246590i
$718$	−18.3181	+	56.3773i	−0.683625	+	2.10398i
$719$	−2.57112	−	7.91310i	−0.0958867	−	0.295109i	0.891597	−	0.452830i	$-0.149585\pi$
$719$	−2.57112	−	7.91310i	−0.0958867	−	0.295109i	−0.987484	+	0.157721i	$0.949585\pi$
$720$	−15.6111	+	11.3421i	−0.581791	+	0.422696i
$721$	7.58674	−	5.51209i	0.282545	−	0.205281i
$722$	−17.2787	−	53.1785i	−0.643048	−	1.97910i
$723$	4.55787	−	14.0277i	0.169509	−	0.521695i
$724$	38.2738	+	27.8076i	1.42244	+	1.03346i
$725$	−17.2357			−0.640119
$726$	−13.8629	−	25.6670i	−0.514500	−	0.952593i
$727$	39.9612			1.48208			0.741040	−	0.671461i	$-0.234333\pi$
$727$	39.9612			1.48208			0.741040	+	0.671461i	$0.234333\pi$
$728$	−9.83597	−	7.14625i	−0.364545	−	0.264858i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$	2.00799	+	6.17996i	0.0743190	+	0.228731i
$731$	3.92188	−	2.84941i	0.145056	−	0.105389i
$732$	−56.2283	+	40.8523i	−2.07826	+	1.50994i
$733$	−4.10613	−	12.6374i	−0.151663	−	0.466772i	0.846144	−	0.532954i	$-0.178918\pi$
$733$	−4.10613	−	12.6374i	−0.151663	−	0.466772i	−0.997808	+	0.0661822i	$0.978918\pi$
$734$	19.2130	−	59.1316i	0.709165	−	2.18259i
$735$	−1.38593	−	1.00694i	−0.0511209	−	0.0371415i
$736$	69.7388			2.57061
$737$	33.9886	−	29.7410i	1.25199	−	1.09552i
$738$	13.3515			0.491474
$739$	5.29565	+	3.84752i	0.194804	+	0.141533i	0.680912	−	0.732366i	$-0.261584\pi$
$739$	5.29565	+	3.84752i	0.194804	+	0.141533i	−0.486108	+	0.873899i	$0.661584\pi$
$740$	−19.9124	+	61.2841i	−0.731995	+	2.25285i
$741$	2.95741	+	9.10198i	0.108643	+	0.334370i
$742$	−13.3819	+	9.72255i	−0.491266	+	0.356926i
$743$	26.9014	−	19.5450i	0.986915	−	0.717036i	0.0276716	−	0.999617i	$-0.491191\pi$
$743$	26.9014	−	19.5450i	0.986915	−	0.717036i	0.959243	+	0.282581i	$0.0911907\pi$
$744$	−15.0090	−	46.1931i	−0.550258	−	1.69352i
$745$	−0.270724	+	0.833203i	−0.00991856	+	0.0305262i
$746$	−71.7740	−	52.1468i	−2.62783	−	1.90923i
$747$	5.86977			0.214764
$748$	39.7950	−	3.61242i	1.45505	−	0.132083i
$749$	12.1711			0.444721
$750$	−25.9679	−	18.8668i	−0.948213	−	0.688917i
$751$	−0.237730	+	0.731659i	−0.00867490	+	0.0266986i	−0.955300	−	0.295637i	$-0.904468\pi$
$751$	−0.237730	+	0.731659i	−0.00867490	+	0.0266986i	0.946625	+	0.322336i	$0.104468\pi$
$752$	−19.2495	−	59.2439i	−0.701957	−	2.16040i
$753$	−6.16417	+	4.47853i	−0.224635	+	0.163207i
$754$	27.0657	−	19.6644i	0.985675	−	0.716135i
$755$	0.517608	+	1.59303i	0.0188377	+	0.0579764i
$756$	−1.55524	+	4.78653i	−0.0565635	+	0.174085i
$757$	1.85608	+	1.34852i	0.0674602	+	0.0490127i	0.621004	−	0.783807i	$-0.286725\pi$
$757$	1.85608	+	1.34852i	0.0674602	+	0.0490127i	−0.553544	+	0.832820i	$0.686725\pi$
$758$	48.7417			1.77038
$759$	6.60614	+	15.4231i	0.239788	+	0.559821i
$760$	−87.2351			−3.16435
$761$	3.23539	+	2.35065i	0.117283	+	0.0852109i	0.644880	−	0.764283i	$-0.276907\pi$
$761$	3.23539	+	2.35065i	0.117283	+	0.0852109i	−0.527598	+	0.849494i	$0.676907\pi$
$762$	0.912707	−	2.80902i	0.0330639	−	0.101760i
$763$	1.95122	+	6.00524i	0.0706390	+	0.217404i
$764$	37.4964	−	27.2428i	1.35657	−	0.985608i
$765$	3.31773	−	2.41047i	0.119953	−	0.0871509i
$766$	−17.4884	−	53.8237i	−0.631881	−	1.94473i
$767$	5.21965	−	16.0644i	0.188471	−	0.580053i
$768$	2.02500	+	1.47125i	0.0730708	+	0.0530891i
$769$	48.3136			1.74223			0.871116	−	0.491077i	$-0.163396\pi$
$769$	48.3136			1.74223			0.871116	+	0.491077i	$0.163396\pi$
$770$	12.9408	+	7.71828i	0.466353	+	0.278147i
$771$	−0.289382			−0.0104218
$772$	6.07580	+	4.41433i	0.218673	+	0.158875i
$773$	−4.15257	+	12.7803i	−0.149358	+	0.459675i	−0.997546	−	0.0700199i	$-0.977694\pi$
$773$	−4.15257	+	12.7803i	−0.149358	+	0.459675i	0.848188	+	0.529695i	$0.177694\pi$
$774$	−1.65953	−	5.10752i	−0.0596507	−	0.183586i
$775$	10.0899	−	7.33071i	0.362438	−	0.263327i
$776$	78.4188	−	56.9746i	2.81507	−	2.04527i
$777$	2.30953	+	7.10802i	0.0828541	+	0.254999i
$778$	−12.7198	+	39.1475i	−0.456027	+	1.40351i
$779$	25.7875	+	18.7357i	0.923932	+	0.671276i
$780$	13.0329			0.466652
$781$	10.5423	−	46.3531i	0.377235	−	1.65864i
$782$	−32.1157			−1.14845
$783$	−6.75169	−	4.90539i	−0.241286	−	0.175304i
$784$	3.48076	−	10.7127i	0.124313	−	0.382595i
$785$	−1.74146	−	5.35967i	−0.0621554	−	0.191295i
$786$	−30.8611	+	22.4219i	−1.10078	+	0.799762i
$787$	5.95242	−	4.32469i	0.212181	−	0.154158i	−0.476619	−	0.879110i	$-0.658138\pi$
$787$	5.95242	−	4.32469i	0.212181	−	0.154158i	0.688800	+	0.724952i	$0.258138\pi$
$788$	5.25233	+	16.1650i	0.187106	+	0.575855i
$789$	3.80866	−	11.7219i	0.135592	−	0.417309i
$790$	24.6891	+	17.9377i	0.878400	+	0.638195i
$791$	−3.36767			−0.119741
$792$	5.91592	−	26.0114i	0.210213	−	0.924274i
$793$	20.8749			0.741288
$794$	46.0799	+	33.4790i	1.63531	+	1.18813i
$795$	3.30189	−	10.1622i	0.117106	−	0.360415i
$796$	43.2534	+	133.120i	1.53308	+	4.71833i
$797$	3.90464	−	2.83689i	0.138309	−	0.100488i	−0.516479	−	0.856300i	$-0.672758\pi$
$797$	3.90464	−	2.83689i	0.138309	−	0.100488i	0.654789	+	0.755812i	$0.272758\pi$
$798$	−13.5835	+	9.86900i	−0.480851	+	0.349359i
$799$	4.09098	+	12.5907i	0.144728	+	0.445428i
$800$	8.79792	−	27.0772i	0.311053	−	0.957324i
$801$	−13.2873	−	9.65382i	−0.469485	−	0.341101i
$802$	−23.5522			−0.831655
$803$	−4.07416	−	2.42996i	−0.143774	−	0.0857513i
$804$	68.5341			2.41701
$805$	−7.01123	−	5.09396i	−0.247113	−	0.179538i
$806$	−7.48069	+	23.0232i	−0.263496	+	0.810957i
$807$	3.90939	+	12.0319i	0.137617	+	0.423542i
$808$	−34.8020	+	25.2851i	−1.22433	+	0.889527i
$809$	42.2996	−	30.7325i	1.48718	−	1.08050i	0.512021	−	0.858973i	$-0.328897\pi$
$809$	42.2996	−	30.7325i	1.48718	−	1.08050i	0.975155	−	0.221524i	$-0.0711030\pi$
$810$	−1.40389	−	4.32073i	−0.0493277	−	0.151815i
$811$	−10.9156	+	33.5947i	−0.383298	+	1.17967i	0.554410	+	0.832244i	$0.312944\pi$
$811$	−10.9156	+	33.5947i	−0.383298	+	1.17967i	−0.937708	+	0.347426i	$0.887056\pi$
$812$	33.9803	+	24.6881i	1.19247	+	0.866384i
$813$	10.7502			0.377026
$814$	−25.8824	−	60.4264i	−0.907176	−	2.11794i
$815$	5.96547			0.208961
$816$	21.8146	+	15.8493i	0.763665	+	0.554835i
$817$	3.96194	−	12.1936i	0.138611	−	0.426600i
$818$	−4.47263	−	13.7653i	−0.156382	−	0.481294i
$819$	1.22292	−	0.888505i	0.0427324	−	0.0310469i
$820$	35.1172	−	25.5141i	1.22635	−	0.890993i
$821$	9.40526	+	28.9464i	0.328246	+	1.01024i	0.969954	+	0.243288i	$0.0782261\pi$
$821$	9.40526	+	28.9464i	0.328246	+	1.01024i	−0.641708	+	0.766949i	$0.721774\pi$
$822$	−2.23552	+	6.88021i	−0.0779726	+	0.239975i
$823$	−37.1206	−	26.9697i	−1.29394	−	0.940104i	−0.294065	−	0.955786i	$-0.595008\pi$
$823$	−37.1206	−	26.9697i	−1.29394	−	0.940104i	−0.999877	+	0.0156819i	$0.995008\pi$
$824$	−75.4251			−2.62756
$825$	6.82165	−	0.619240i	0.237499	−	0.0215592i
$826$	29.6336			1.03108
$827$	−9.89408	−	7.18847i	−0.344051	−	0.249968i	0.402318	−	0.915500i	$-0.368205\pi$
$827$	−9.89408	−	7.18847i	−0.344051	−	0.249968i	−0.746369	+	0.665532i	$0.768205\pi$
$828$	−7.86773	+	24.2144i	−0.273422	+	0.841507i
$829$	6.10050	+	18.7754i	0.211879	+	0.652097i	0.999360	+	0.0357585i	$0.0113847\pi$
$829$	6.10050	+	18.7754i	0.211879	+	0.652097i	−0.787481	+	0.616339i	$0.788615\pi$
$830$	21.5739	−	15.6744i	0.748842	−	0.544066i
$831$	4.92607	−	3.57900i	0.170883	−	0.124154i
$832$	6.55389	+	20.1708i	0.227215	+	0.699297i
$833$	−0.739744	+	2.27670i	−0.0256306	+	0.0788829i
$834$	0.757661	+	0.550473i	0.0262357	+	0.0190613i
$835$	−7.83707			−0.271213
$836$	79.5324	−	69.5931i	2.75069	−	2.40693i
$837$	6.03882			0.208732
$838$	42.8678	+	31.1453i	1.48084	+	1.07590i
$839$	3.08217	−	9.48594i	0.106408	−	0.327491i	−0.883650	−	0.468148i	$-0.844921\pi$
$839$	3.08217	−	9.48594i	0.106408	−	0.327491i	0.990058	+	0.140657i	$0.0449214\pi$
$840$	4.25780	+	13.1042i	0.146908	+	0.452137i
$841$	−32.8850	+	23.8924i	−1.13397	+	0.823875i
$842$	−60.7431	+	44.1325i	−2.09335	+	1.52091i
$843$	−2.66103	−	8.18980i	−0.0916507	−	0.282072i
$844$	−37.3364	+	114.910i	−1.28517	+	3.95535i
$845$	14.8503	+	10.7894i	0.510866	+	0.371166i
$846$	14.6660			0.504228
$847$	−10.8202	+	1.98074i	−0.371786	+	0.0680592i
$848$	70.2565			2.41262
$849$	−2.58527	−	1.87831i	−0.0887262	−	0.0644634i
$850$	−4.05156	+	12.4694i	−0.138968	+	0.427698i
$851$	11.6836	+	35.9584i	0.400508	+	1.23264i
$852$	58.3588	−	42.4001i	1.99934	−	1.45261i
$853$	0.565471	−	0.410839i	0.0193614	−	0.0140669i	−0.578062	−	0.815993i	$-0.696191\pi$
$853$	0.565471	−	0.410839i	0.0193614	−	0.0140669i	0.597424	+	0.801926i	$0.296191\pi$
$854$	11.3170	+	34.8301i	0.387259	+	1.19186i
$855$	3.35163	−	10.3152i	0.114623	−	0.352774i
$856$	−79.1963	−	57.5395i	−2.70687	−	1.96666i
$857$	−40.0835			−1.36922			−0.684612	−	0.728907i	$-0.740028\pi$
$857$	−40.0835			−1.36922			−0.684612	+	0.728907i	$0.740028\pi$
$858$	−10.0057	+	8.75529i	−0.341589	+	0.298901i
$859$	−28.0045			−0.955503			−0.477751	−	0.878495i	$-0.658548\pi$
$859$	−28.0045			−0.955503			−0.477751	+	0.878495i	$0.658548\pi$
$860$	−14.1252	−	10.2626i	−0.481665	−	0.349950i
$861$	1.55577	−	4.78817i	0.0530205	−	0.163180i
$862$	−26.0311	−	80.1156i	−0.886624	−	2.72875i
$863$	21.0736	−	15.3109i	0.717354	−	0.521188i	−0.168184	−	0.985756i	$-0.553790\pi$
$863$	21.0736	−	15.3109i	0.717354	−	0.521188i	0.885538	+	0.464567i	$0.153790\pi$
$864$	11.1527	−	8.10291i	0.379423	−	0.275667i
$865$	3.03056	+	9.32711i	0.103042	+	0.317131i
$866$	10.7896	−	33.2071i	0.366647	−	1.12842i
$867$	9.11715	+	6.62400i	0.309635	+	0.224963i
$868$	−30.3925			−1.03159
$869$	−22.1877	+	2.01410i	−0.752665	+	0.0683237i
$870$	−37.9145			−1.28542
$871$	−16.6529	−	12.0991i	−0.564263	−	0.409961i
$872$	15.6937	−	48.3002i	0.531455	−	1.63565i
$873$	3.72415	+	11.4617i	0.126043	+	0.387921i
$874$	−68.7170	+	49.9258i	−2.32439	+	1.68877i
$875$	−9.79198	+	7.11429i	−0.331029	+	0.240507i
$876$	−2.22447	−	6.84620i	−0.0751577	−	0.231312i
$877$	−13.1771	+	40.5550i	−0.444960	+	1.36945i	0.437567	+	0.899186i	$0.355840\pi$
$877$	−13.1771	+	40.5550i	−0.444960	+	1.36945i	−0.882527	+	0.470261i	$0.844160\pi$
$878$	−21.0506	−	15.2941i	−0.710422	−	0.516152i
$879$	−8.55173			−0.288443
$880$	−25.1983	−	58.8294i	−0.849436	−	1.98314i
$881$	−5.07985			−0.171144			−0.0855722	−	0.996332i	$-0.527272\pi$
$881$	−5.07985			−0.171144			−0.0855722	+	0.996332i	$0.527272\pi$
$882$	2.14548	+	1.55878i	0.0722419	+	0.0524868i
$883$	15.1568	−	46.6478i	0.510066	−	1.56982i	−0.282016	−	0.959410i	$-0.591003\pi$
$883$	15.1568	−	46.6478i	0.510066	−	1.56982i	0.792083	−	0.610414i	$-0.208997\pi$
$884$	−5.62779	−	17.3205i	−0.189283	−	0.582553i
$885$	−15.4868	+	11.2518i	−0.520581	+	0.378225i
$886$	5.33180	−	3.87378i	0.179125	−	0.130142i
$887$	16.6644	+	51.2876i	0.559534	+	1.72207i	0.683657	+	0.729803i	$0.260388\pi$
$887$	16.6644	+	51.2876i	0.559534	+	1.72207i	−0.124123	+	0.992267i	$0.539612\pi$
$888$	18.5756	−	57.1698i	0.623356	−	1.91849i
$889$	−0.901033	−	0.654639i	−0.0302197	−	0.0219559i
$890$	−74.6159			−2.50113
$891$	2.84846	+	1.69891i	0.0954269	+	0.0569156i
$892$	114.839			3.84509
$893$	28.3264	+	20.5804i	0.947908	+	0.688695i
$894$	0.419091	−	1.28983i	0.0140165	−	0.0431383i
$895$	1.56538	+	4.81774i	0.0523248	+	0.161039i
$896$	−7.79688	+	5.66477i	−0.260476	+	0.189247i
$897$	6.18658	−	4.49481i	0.206564	−	0.150077i
$898$	12.7921	+	39.3701i	0.426879	+	1.31380i
$899$	15.5736	−	47.9306i	0.519409	−	1.59858i
$900$	8.40906	+	6.10954i	0.280302	+	0.203651i
$901$	−14.9312			−0.497430
$902$	−9.82047	+	43.1791i	−0.326986	+	1.43771i
$903$	−2.02506			−0.0673897
$904$	21.9132	+	15.9209i	0.728822	+	0.529520i
$905$	−4.97619	+	15.3151i	−0.165414	+	0.509092i
$906$	−0.801276	−	2.46607i	−0.0266206	−	0.0819298i
$907$	−20.8424	+	15.1429i	−0.692061	+	0.502812i	−0.877337	−	0.479875i	$-0.840682\pi$
$907$	−20.8424	+	15.1429i	−0.692061	+	0.502812i	0.185276	+	0.982687i	$0.440682\pi$
$908$	−58.6510	+	42.6125i	−1.94640	+	1.41414i
$909$	−1.65276	−	5.08668i	−0.0548186	−	0.168714i
$910$	2.12214	−	6.53128i	0.0703483	−	0.216510i
$911$	23.6129	+	17.1558i	0.782331	+	0.568397i	0.905678	−	0.423967i	$-0.139363\pi$
$911$	23.6129	+	17.1558i	0.782331	+	0.568397i	−0.123346	+	0.992364i	$0.539363\pi$
$912$	71.3148			2.36147
$913$	−4.31742	+	18.9830i	−0.142886	+	0.628247i
$914$	−36.2396			−1.19870
$915$	−19.1392	−	13.9055i	−0.632724	−	0.459701i
$916$	−5.90007	+	18.1585i	−0.194944	+	0.599975i
$917$	4.44498	+	13.6802i	0.146786	+	0.451761i
$918$	−5.13597	+	3.73150i	−0.169512	+	0.123158i
$919$	32.7816	−	23.8172i	1.08136	−	0.785657i	0.103444	−	0.994635i	$-0.467014\pi$
$919$	32.7816	−	23.8172i	1.08136	−	0.785657i	0.977920	+	0.208978i	$0.0670138\pi$
$920$	21.5396	+	66.2920i	0.710139	+	2.18558i
$921$	−1.08091	+	3.32669i	−0.0356171	+	0.109618i
$922$	40.0227	+	29.0782i	1.31808	+	0.957639i
$923$	−21.6658			−0.713139
$924$	−14.3359	−	8.55037i	−0.471616	−	0.281286i
$925$	15.4354			0.507512
$926$	−39.8408	−	28.9460i	−1.30925	−	0.951226i
$927$	2.89788	−	8.91875i	0.0951788	−	0.292930i
$928$	−35.5516	−	109.417i	−1.16704	−	3.59178i
$929$	−4.15304	+	3.01736i	−0.136257	+	0.0989963i	−0.653826	−	0.756645i	$-0.726837\pi$
$929$	−4.15304	+	3.01736i	−0.136257	+	0.0989963i	0.517569	+	0.855641i	$0.326837\pi$
$930$	22.1953	−	16.1258i	0.727812	−	0.528786i
$931$	1.95646	+	6.02136i	0.0641204	+	0.197342i
$932$	42.7448	−	131.555i	1.40015	−	4.30923i
$933$	2.98558	+	2.16915i	0.0977435	+	0.0710148i
$934$	−92.7066			−3.03345
$935$	5.35525	+	12.5027i	0.175135	+	0.408881i
$936$	−12.1579			−0.397394
$937$	20.4911	+	14.8877i	0.669416	+	0.486359i	0.869830	−	0.493352i	$-0.164229\pi$
$937$	20.4911	+	14.8877i	0.669416	+	0.486359i	−0.200414	+	0.979711i	$0.564229\pi$
$938$	11.1594	−	34.3451i	0.364367	−	1.12141i
$939$	−8.11608	−	24.9787i	−0.264858	−	0.815150i
$940$	38.5747	−	28.0262i	1.25817	−	0.914114i
$941$	−17.2117	+	12.5051i	−0.561086	+	0.407653i	−0.831856	−	0.554991i	$-0.812722\pi$
$941$	−17.2117	+	12.5051i	−0.561086	+	0.407653i	0.270770	+	0.962644i	$0.412722\pi$
$942$	2.69585	+	8.29696i	0.0878354	+	0.270330i
$943$	7.87041	−	24.2226i	0.256296	−	0.788797i
$944$	−101.828	−	73.9823i	−3.31422	−	2.40792i
$945$	−1.71311			−0.0557274
$946$	17.7385	−	1.61023i	0.576729	−	0.0523530i
$947$	−30.1418			−0.979476			−0.489738	−	0.871870i	$-0.662908\pi$
$947$	−30.1418			−0.979476			−0.489738	+	0.871870i	$0.662908\pi$
$948$	−27.3508	−	19.8715i	−0.888313	−	0.645397i
$949$	−0.668116	+	2.05625i	−0.0216880	+	0.0667487i
$950$	10.7155	+	32.9789i	0.347656	+	1.06998i
$951$	−10.5821	+	7.68834i	−0.343148	+	0.249312i
$952$	15.5767	−	11.3171i	0.504844	−	0.366790i
$953$	2.75961	+	8.49320i	0.0893925	+	0.275122i	0.985752	−	0.168207i	$-0.0537976\pi$
$953$	2.75961	+	8.49320i	0.0893925	+	0.275122i	−0.896359	+	0.443328i	$0.853798\pi$
$954$	−5.11145	+	15.7314i	−0.165489	+	0.509323i
$955$	12.7632	+	9.27301i	0.413008	+	0.300068i
$956$	56.5367			1.82853
$957$	20.8303	−	18.2271i	0.673348	−	0.589199i
$958$	−107.522			−3.47387
$959$	2.20692	+	1.60342i	0.0712653	+	0.0517772i
$960$	7.42751	−	22.8595i	0.239722	−	0.737788i
$961$	1.68951	+	5.19976i	0.0545002	+	0.167734i
$962$	−24.2386	+	17.6103i	−0.781482	+	0.567780i
$963$	9.84660	−	7.15397i	0.317302	−	0.230534i
$964$	22.9391	+	70.5994i	0.738820	+	2.27385i
$965$	−0.789947	+	2.43121i	−0.0254293	+	0.0782633i
$966$	10.8536	+	7.88563i	0.349210	+	0.253716i
$967$	−38.3461			−1.23313			−0.616564	−	0.787305i	$-0.711476\pi$
$967$	−38.3461			−1.23313			−0.616564	+	0.787305i	$0.711476\pi$
$968$	79.7703	+	38.2646i	2.56392	+	1.22987i
$969$	−15.1561			−0.486884
$970$	44.2948	+	32.1821i	1.42222	+	1.03330i
$971$	9.62612	−	29.6262i	0.308917	−	0.950749i	−0.669269	−	0.743020i	$-0.733393\pi$
$971$	9.62612	−	29.6262i	0.308917	−	0.950749i	0.978186	−	0.207729i	$-0.0666072\pi$
$972$	1.55524	+	4.78653i	0.0498843	+	0.153528i
$973$	0.285699	−	0.207573i	0.00915910	−	0.00665448i
$974$	29.0859	−	21.1322i	0.931973	−	0.677118i
$975$	−0.964714	−	2.96908i	−0.0308956	−	0.0950868i
$976$	48.0680	−	147.938i	1.53862	−	4.73538i
$977$	−24.0815	−	17.4962i	−0.770435	−	0.559754i	0.131658	−	0.991295i	$-0.457970\pi$
$977$	−24.0815	−	17.4962i	−0.770435	−	0.559754i	−0.902093	+	0.431542i	$0.857970\pi$
$978$	−9.23477			−0.295295
$979$	40.9941	−	35.8710i	1.31018	−	1.14644i
$980$	8.62183			0.275414
$981$	5.10836	+	3.71144i	0.163098	+	0.118497i
$982$	19.2249	−	59.1683i	0.613492	−	1.88814i
$983$	−12.3319	−	37.9537i	−0.393326	−	1.21053i	−0.930257	−	0.366908i	$-0.880417\pi$
$983$	−12.3319	−	37.9537i	−0.393326	−	1.21053i	0.536931	−	0.843626i	$-0.319583\pi$
$984$	−32.7596	+	23.8013i	−1.04434	+	0.758756i
$985$	−4.68055	+	3.40062i	−0.149135	+	0.108353i
$986$	16.3720	+	50.3879i	0.521391	+	1.60468i
$987$	1.70895	−	5.25959i	0.0543963	−	0.167415i
$988$	−38.9675	−	28.3115i	−1.23972	−	0.900709i
$989$	−10.2445			−0.325755
$990$	15.0060	−	1.36218i	0.476922	−	0.0432929i
$991$	−10.7771			−0.342345			−0.171173	−	0.985241i	$-0.554756\pi$
$991$	−10.7771			−0.342345			−0.171173	+	0.985241i	$0.554756\pi$
$992$	67.3492	+	48.9320i	2.13834	+	1.55359i
$993$	2.45259	−	7.54831i	0.0778307	−	0.239538i
$994$	−11.7458	−	36.1498i	−0.372554	−	1.14660i
$995$	−38.5448	+	28.0044i	−1.22195	+	0.887800i
$996$	−23.8998	+	17.3642i	−0.757293	+	0.550205i
$997$	0.352040	+	1.08347i	0.0111492	+	0.0343137i	0.956476	−	0.291810i	$-0.0942574\pi$
$997$	0.352040	+	1.08347i	0.0111492	+	0.0343137i	−0.945327	+	0.326124i	$0.894257\pi$
$998$	−14.1672	+	43.6020i	−0.448454	+	1.38020i
$999$	6.04644	+	4.39299i	0.191301	+	0.138988i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.j.g.169.5	✓	20
3.2	odd	2		693.2.m.j.631.1		20
11.3	even	5	inner	231.2.j.g.190.5	yes	20
11.5	even	5		2541.2.a.bq.1.1		10
11.6	odd	10		2541.2.a.br.1.10		10
33.5	odd	10		7623.2.a.cx.1.10		10
33.14	odd	10		693.2.m.j.190.1		20
33.17	even	10		7623.2.a.cy.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.j.g.169.5	✓	20	1.1	even	1	trivial
231.2.j.g.190.5	yes	20	11.3	even	5	inner
693.2.m.j.190.1		20	33.14	odd	10
693.2.m.j.631.1		20	3.2	odd	2
2541.2.a.bq.1.1		10	11.5	even	5
2541.2.a.br.1.10		10	11.6	odd	10
7623.2.a.cx.1.10		10	33.5	odd	10
7623.2.a.cy.1.1		10	33.17	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.j (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.14548 + 1.55878i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.55524 + 4.78653i) q^{4} +(-1.38593 + 1.00694i) q^{5} +(2.14548 - 1.55878i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.48543 + 7.64935i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(2.14548 + 1.55878i) q^{2} +(0.309017 - 0.951057i) q^{3} +(1.55524 + 4.78653i) q^{4} +(-1.38593 + 1.00694i) q^{5} +(2.14548 - 1.55878i) q^{6} +(-0.309017 - 0.951057i) q^{7} +(-2.48543 + 7.64935i) q^{8} +(-0.809017 - 0.587785i) q^{9} -4.54308 q^{10} +(2.49598 - 2.18405i) q^{11} +5.03286 q^{12} +(-1.22292 - 0.888505i) q^{13} +(0.819499 - 2.52216i) q^{14} +(0.529379 + 1.62926i) q^{15} +(-9.11274 + 6.62079i) q^{16} +(1.93668 - 1.40708i) q^{17} +(-0.819499 - 2.52216i) q^{18} +(1.95646 - 6.02136i) q^{19} +(-6.97521 - 5.06779i) q^{20} -1.00000 q^{21} +(8.75952 - 0.795152i) q^{22} -5.05885 q^{23} +(6.50693 + 4.72756i) q^{24} +(-0.638201 + 1.96418i) q^{25} +(-1.23877 - 3.81253i) q^{26} +(-0.809017 + 0.587785i) q^{27} +(4.07167 - 2.95824i) q^{28} +(2.57892 + 7.93708i) q^{29} +(-1.40389 + 4.32073i) q^{30} +(-4.88551 - 3.54953i) q^{31} -13.7855 q^{32} +(-1.30586 - 3.04873i) q^{33} +6.34841 q^{34} +(1.38593 + 1.00694i) q^{35} +(1.55524 - 4.78653i) q^{36} +(-2.30953 - 7.10802i) q^{37} +(13.5835 - 9.86900i) q^{38} +(-1.22292 + 0.888505i) q^{39} +(-4.25780 - 13.1042i) q^{40} +(-1.55577 + 4.78817i) q^{41} +(-2.14548 - 1.55878i) q^{42} +2.02506 q^{43} +(14.3359 + 8.55037i) q^{44} +1.71311 q^{45} +(-10.8536 - 7.88563i) q^{46} +(-1.70895 + 5.25959i) q^{47} +(3.48076 + 10.7127i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-4.43097 + 3.21929i) q^{50} +(-0.739744 - 2.27670i) q^{51} +(2.35092 - 7.23540i) q^{52} +(-5.04607 - 3.66618i) q^{53} -2.65195 q^{54} +(-1.26005 + 5.54025i) q^{55} +8.04301 q^{56} +(-5.12208 - 3.72141i) q^{57} +(-6.83916 + 21.0488i) q^{58} +(3.45303 + 10.6273i) q^{59} +(-6.97521 + 5.06779i) q^{60} +(-11.1722 + 8.11711i) q^{61} +(-4.94881 - 15.2309i) q^{62} +(-0.309017 + 0.951057i) q^{63} +(-11.3510 - 8.24697i) q^{64} +2.58956 q^{65} +(1.95061 - 8.57651i) q^{66} +13.6173 q^{67} +(9.74702 + 7.08162i) q^{68} +(-1.56327 + 4.81125i) q^{69} +(1.40389 + 4.32073i) q^{70} +(11.5956 - 8.42466i) q^{71} +(6.50693 - 4.72756i) q^{72} +(-0.441988 - 1.36030i) q^{73} +(6.12478 - 18.8501i) q^{74} +(1.67083 + 1.21393i) q^{75} +31.8642 q^{76} +(-2.84846 - 1.69891i) q^{77} -4.00873 q^{78} +(-5.43444 - 3.94835i) q^{79} +(5.96291 - 18.3520i) q^{80} +(0.309017 + 0.951057i) q^{81} +(-10.8016 + 7.84779i) q^{82} +(-4.74874 + 3.45016i) q^{83} +(-1.55524 - 4.78653i) q^{84} +(-1.26726 + 3.90023i) q^{85} +(4.34471 + 3.15662i) q^{86} +8.34554 q^{87} +(10.5030 + 24.5209i) q^{88} +16.4241 q^{89} +(3.67543 + 2.67036i) q^{90} +(-0.467115 + 1.43763i) q^{91} +(-7.86773 - 24.2144i) q^{92} +(-4.88551 + 3.54953i) q^{93} +(-11.8650 + 8.62046i) q^{94} +(3.35163 + 10.3152i) q^{95} +(-4.25995 + 13.1108i) q^{96} +(-9.74994 - 7.08375i) q^{97} -2.65195 q^{98} +(-3.30304 + 0.299836i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9}+O(q^{10}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9	\( 20 q - 5 q^{3} - 14 q^{4} - 5 q^{5} + 5 q^{7} - 9 q^{8} - 5 q^{9} + 12 q^{10} - q^{11} + 36 q^{12} + 13 q^{13} - 24 q^{16} - q^{17} + 10 q^{19} - 46 q^{20} - 20 q^{21} + 26 q^{22} + 6 q^{24} - 8 q^{25} - 53 q^{26} - 5 q^{27} + 4 q^{28} + 3 q^{29} - 3 q^{30} - 13 q^{31} + 82 q^{32} + 9 q^{33} + 42 q^{34} + 5 q^{35} - 14 q^{36} - 32 q^{37} + 16 q^{38} + 13 q^{39} + 20 q^{40} - 3 q^{41} + 12 q^{43} + 25 q^{44} + 10 q^{45} - 13 q^{46} + 20 q^{47} - 14 q^{48} - 5 q^{49} - 83 q^{50} + 9 q^{51} - 80 q^{52} + 3 q^{53} - 28 q^{55} - 6 q^{56} - 10 q^{57} + 2 q^{58} - 9 q^{59} - 46 q^{60} - 15 q^{61} - 37 q^{62} + 5 q^{63} - 49 q^{64} + 58 q^{65} - 4 q^{66} + 76 q^{67} + 51 q^{68} + 3 q^{70} + 37 q^{71} + 6 q^{72} + 27 q^{73} - 32 q^{74} - 23 q^{75} + 4 q^{76} + 6 q^{77} + 2 q^{78} + 5 q^{79} + 137 q^{80} - 5 q^{81} - 55 q^{82} - 42 q^{83} + 14 q^{84} - 48 q^{85} + 3 q^{86} + 28 q^{87} + 151 q^{88} - 18 q^{89} - 3 q^{90} + 7 q^{91} + 39 q^{92} - 13 q^{93} - 35 q^{94} - 96 q^{95} - 48 q^{96} - 27 q^{97} - q^{99}+O(q^{100}) \) 20 * q - 5 * q^3 - 14 * q^4 - 5 * q^5 + 5 * q^7 - 9 * q^8 - 5 * q^9 + 12 * q^10 - q^11 + 36 * q^12 + 13 * q^13 - 24 * q^16 - q^17 + 10 * q^19 - 46 * q^20 - 20 * q^21 + 26 * q^22 + 6 * q^24 - 8 * q^25 - 53 * q^26 - 5 * q^27 + 4 * q^28 + 3 * q^29 - 3 * q^30 - 13 * q^31 + 82 * q^32 + 9 * q^33 + 42 * q^34 + 5 * q^35 - 14 * q^36 - 32 * q^37 + 16 * q^38 + 13 * q^39 + 20 * q^40 - 3 * q^41 + 12 * q^43 + 25 * q^44 + 10 * q^45 - 13 * q^46 + 20 * q^47 - 14 * q^48 - 5 * q^49 - 83 * q^50 + 9 * q^51 - 80 * q^52 + 3 * q^53 - 28 * q^55 - 6 * q^56 - 10 * q^57 + 2 * q^58 - 9 * q^59 - 46 * q^60 - 15 * q^61 - 37 * q^62 + 5 * q^63 - 49 * q^64 + 58 * q^65 - 4 * q^66 + 76 * q^67 + 51 * q^68 + 3 * q^70 + 37 * q^71 + 6 * q^72 + 27 * q^73 - 32 * q^74 - 23 * q^75 + 4 * q^76 + 6 * q^77 + 2 * q^78 + 5 * q^79 + 137 * q^80 - 5 * q^81 - 55 * q^82 - 42 * q^83 + 14 * q^84 - 48 * q^85 + 3 * q^86 + 28 * q^87 + 151 * q^88 - 18 * q^89 - 3 * q^90 + 7 * q^91 + 39 * q^92 - 13 * q^93 - 35 * q^94 - 96 * q^95 - 48 * q^96 - 27 * q^97 - q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more