LMFDB - Embedded newform 75.3.k.a.13.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([0, 19]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (of order $20$, degree $8$, 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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.9
Character	$\chi$	$=$	75.13
Dual form			75.3.k.a.52.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.92729 - 0.463638i) q^{2} +(0.786335 - 1.54327i) q^{3} +(4.54985 - 1.47834i) q^{4} +(-2.61452 + 4.26196i) q^{5} +(1.58631 - 4.88217i) q^{6} +(2.66748 - 2.66748i) q^{7} +(2.07035 - 1.05489i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})$	\(q+(2.92729 - 0.463638i) q^{2} +(0.786335 - 1.54327i) q^{3} +(4.54985 - 1.47834i) q^{4} +(-2.61452 + 4.26196i) q^{5} +(1.58631 - 4.88217i) q^{6} +(2.66748 - 2.66748i) q^{7} +(2.07035 - 1.05489i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-5.67746 + 13.6882i) q^{10} +(-2.59311 - 1.88400i) q^{11} +(1.29624 - 8.18412i) q^{12} +(-14.9551 - 2.36865i) q^{13} +(6.57174 - 9.04523i) q^{14} +(4.52146 + 7.38623i) q^{15} +(-9.90993 + 7.19998i) q^{16} +(5.47793 + 10.7510i) q^{17} +(-6.28713 - 6.28713i) q^{18} +(22.7308 + 7.38568i) q^{19} +(-5.59508 + 23.2564i) q^{20} +(-2.01910 - 6.21416i) q^{21} +(-8.46427 - 4.31276i) q^{22} +(1.40503 + 8.87104i) q^{23} -4.02460i q^{24} +(-11.3286 - 22.2860i) q^{25} -44.8761 q^{26} +(-5.13218 + 0.812857i) q^{27} +(8.19320 - 16.0801i) q^{28} +(30.5703 - 9.93290i) q^{29} +(16.6602 + 19.5253i) q^{30} +(11.6600 - 35.8856i) q^{31} +(-32.2432 + 32.2432i) q^{32} +(-4.94657 + 2.52040i) q^{33} +(21.0201 + 28.9317i) q^{34} +(4.39450 + 18.3429i) q^{35} +(-11.6110 - 8.43589i) q^{36} +(10.4793 - 66.1635i) q^{37} +(69.9639 + 11.0812i) q^{38} +(-15.4152 + 21.2172i) q^{39} +(-0.917050 + 11.5818i) q^{40} +(-55.8597 + 40.5844i) q^{41} +(-8.79163 - 17.2545i) q^{42} +(-34.9751 - 34.9751i) q^{43} +(-14.5834 - 4.73845i) q^{44} +(14.9543 - 1.16977i) q^{45} +(8.22589 + 25.3167i) q^{46} +(35.6128 + 18.1456i) q^{47} +(3.31899 + 20.9553i) q^{48} +34.7691i q^{49} +(-43.4946 - 59.9851i) q^{50} +20.8992 q^{51} +(-71.5452 + 11.3316i) q^{52} +(33.9753 - 66.6802i) q^{53} +(-14.6465 + 4.75894i) q^{54} +(14.8093 - 6.12594i) q^{55} +(2.70870 - 8.33651i) q^{56} +(29.2721 - 29.2721i) q^{57} +(84.8830 - 43.2501i) q^{58} +(6.33807 + 8.72361i) q^{59} +(31.4913 + 26.9220i) q^{60} +(65.9802 + 47.9374i) q^{61} +(17.4942 - 110.454i) q^{62} +(-11.1778 - 1.77039i) q^{63} +(-50.6362 + 69.6948i) q^{64} +(49.1955 - 57.5451i) q^{65} +(-13.3115 + 9.67137i) q^{66} +(3.44626 + 6.76367i) q^{67} +(40.8174 + 40.8174i) q^{68} +(14.7952 + 4.80726i) q^{69} +(21.3684 + 51.6574i) q^{70} +(30.8556 + 94.9637i) q^{71} +(-6.21104 - 3.16468i) q^{72} +(-3.29433 - 20.7996i) q^{73} -198.539i q^{74} +(-43.3013 - 0.0411995i) q^{75} +114.340 q^{76} +(-11.9426 + 1.89152i) q^{77} +(-35.2877 + 69.2559i) q^{78} +(-116.946 + 37.9981i) q^{79} +(-4.77631 - 61.0602i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-144.701 + 144.701i) q^{82} +(-69.6419 + 35.4843i) q^{83} +(-18.3733 - 25.2886i) q^{84} +(-60.1426 - 4.76212i) q^{85} +(-118.598 - 86.1665i) q^{86} +(8.70937 - 54.9888i) q^{87} +(-7.35605 - 1.16508i) q^{88} +(-29.4736 + 40.5670i) q^{89} +(43.2333 - 10.3576i) q^{90} +(-46.2107 + 33.5740i) q^{91} +(19.5071 + 38.2848i) q^{92} +(-46.2126 - 46.2126i) q^{93} +(112.662 + 36.6061i) q^{94} +(-90.9076 + 77.5676i) q^{95} +(24.4060 + 75.1139i) q^{96} +(53.7184 + 27.3709i) q^{97} +(16.1203 + 101.779i) q^{98} +9.61576i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{19}{20}\right)$

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 $

$2$	2.92729	−	0.463638i	1.46365	−	0.231819i	0.626767	−	0.779207i	$-0.284378\pi$
$2$	2.92729	−	0.463638i	1.46365	−	0.231819i	0.836879	+	0.547388i	$0.184378\pi$
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$3$	0.786335	−	1.54327i	0.262112	−	0.514423i
$4$	4.54985	−	1.47834i	1.13746	−	0.369584i
$5$	−2.61452	+	4.26196i	−0.522904	+	0.852391i
$5$	−2.61452	+	4.26196i	−0.522904	+	0.852391i
$6$	1.58631	−	4.88217i	0.264386	−	0.813695i
$7$	2.66748	−	2.66748i	0.381068	−	0.381068i	−0.490419	−	0.871487i	$-0.663156\pi$
$7$	2.66748	−	2.66748i	0.381068	−	0.381068i	0.871487	+	0.490419i	$0.163156\pi$
$8$	2.07035	−	1.05489i	0.258793	−	0.131862i
$9$	−1.76336	−	2.42705i	−0.195928	−	0.269672i
$10$	−5.67746	+	13.6882i	−0.567746	+	1.36882i
$11$	−2.59311	−	1.88400i	−0.235737	−	0.171273i	0.463645	−	0.886021i	$-0.346541\pi$
$11$	−2.59311	−	1.88400i	−0.235737	−	0.171273i	−0.699382	+	0.714748i	$0.746541\pi$
$12$	1.29624	−	8.18412i	0.108020	−	0.682010i
$13$	−14.9551	−	2.36865i	−1.15039	−	0.182204i	−0.448026	−	0.894020i	$-0.647873\pi$
$13$	−14.9551	−	2.36865i	−1.15039	−	0.182204i	−0.702366	+	0.711816i	$0.747873\pi$
$14$	6.57174	−	9.04523i	0.469410	−	0.646088i
$15$	4.52146	+	7.38623i	0.301430	+	0.492415i
$16$	−9.90993	+	7.19998i	−0.619370	+	0.449999i
$17$	5.47793	+	10.7510i	0.322231	+	0.632414i	0.994126	−	0.108233i	$-0.0345192\pi$
$17$	5.47793	+	10.7510i	0.322231	+	0.632414i	−0.671894	+	0.740647i	$0.734519\pi$
$18$	−6.28713	−	6.28713i	−0.349285	−	0.349285i
$19$	22.7308	+	7.38568i	1.19636	+	0.388720i	0.838420	−	0.545025i	$-0.183480\pi$
$19$	22.7308	+	7.38568i	1.19636	+	0.388720i	0.357938	+	0.933745i	$0.383480\pi$
$20$	−5.59508	+	23.2564i	−0.279754	+	1.16282i
$21$	−2.01910	−	6.21416i	−0.0961478	−	0.295913i
$22$	−8.46427	−	4.31276i	−0.384740	−	0.196035i
$23$	1.40503	+	8.87104i	0.0610884	+	0.385697i	0.999223	+	0.0394251i	$0.0125526\pi$
$23$	1.40503	+	8.87104i	0.0610884	+	0.385697i	−0.938134	+	0.346272i	$0.887447\pi$
$24$		−	4.02460i		−	0.167692i
$25$	−11.3286	−	22.2860i	−0.453143	−	0.891438i
$26$	−44.8761			−1.72600
$27$	−5.13218	+	0.812857i	−0.190081	+	0.0301058i
$28$	8.19320	−	16.0801i	0.292614	−	0.574288i
$29$	30.5703	−	9.93290i	1.05415	−	0.342514i	0.269854	−	0.962901i	$-0.413025\pi$
$29$	30.5703	−	9.93290i	1.05415	−	0.342514i	0.784295	+	0.620388i	$0.213025\pi$
$30$	16.6602	+	19.5253i	0.555339	+	0.650845i
$31$	11.6600	−	35.8856i	0.376128	−	1.15760i	−0.566587	−	0.824002i	$-0.691737\pi$
$31$	11.6600	−	35.8856i	0.376128	−	1.15760i	0.942715	−	0.333600i	$-0.108263\pi$
$32$	−32.2432	+	32.2432i	−1.00760	+	1.00760i
$33$	−4.94657	+	2.52040i	−0.149896	+	0.0763758i
$34$	21.0201	+	28.9317i	0.618238	+	0.850931i
$35$	4.39450	+	18.3429i	0.125557	+	0.524082i
$36$	−11.6110	−	8.43589i	−0.322528	−	0.234330i
$37$	10.4793	−	66.1635i	0.283224	−	1.78820i	−0.278043	−	0.960569i	$-0.589686\pi$
$37$	10.4793	−	66.1635i	0.283224	−	1.78820i	0.561267	−	0.827635i	$-0.310314\pi$
$38$	69.9639	+	11.0812i	1.84116	+	0.291611i
$39$	−15.4152	+	21.2172i	−0.395261	+	0.544030i
$40$	−0.917050	+	11.5818i	−0.0229262	+	0.289544i
$41$	−55.8597	+	40.5844i	−1.36243	+	0.989864i	−0.364144	+	0.931343i	$0.618639\pi$
$41$	−55.8597	+	40.5844i	−1.36243	+	0.989864i	−0.998286	+	0.0585212i	$0.981361\pi$
$42$	−8.79163	−	17.2545i	−0.209325	−	0.410822i
$43$	−34.9751	−	34.9751i	−0.813374	−	0.813374i	0.171764	−	0.985138i	$-0.445053\pi$
$43$	−34.9751	−	34.9751i	−0.813374	−	0.813374i	−0.985138	+	0.171764i	$0.945053\pi$
$44$	−14.5834	−	4.73845i	−0.331442	−	0.107692i
$45$	14.9543	−	1.16977i	0.332318	−	0.0259949i
$46$	8.22589	+	25.3167i	0.178824	+	0.550363i
$47$	35.6128	+	18.1456i	0.757718	+	0.386077i	0.789765	−	0.613410i	$-0.210202\pi$
$47$	35.6128	+	18.1456i	0.757718	+	0.386077i	−0.0320466	+	0.999486i	$0.510202\pi$
$48$	3.31899	+	20.9553i	0.0691456	+	0.436568i
$49$			34.7691i			0.709574i
$50$	−43.4946	−	59.9851i	−0.869892	−	1.19970i
$51$	20.8992			0.409789
$52$	−71.5452	+	11.3316i	−1.37587	+	0.217916i
$53$	33.9753	−	66.6802i	0.641043	−	1.25812i	−0.310491	−	0.950576i	$-0.600494\pi$
$53$	33.9753	−	66.6802i	0.641043	−	1.25812i	0.951535	−	0.307542i	$-0.0995064\pi$
$54$	−14.6465	+	4.75894i	−0.271232	+	0.0881286i
$55$	14.8093	−	6.12594i	0.269259	−	0.111381i
$56$	2.70870	−	8.33651i	0.0483696	−	0.148866i
$57$	29.2721	−	29.2721i	0.513546	−	0.513546i
$58$	84.8830	−	43.2501i	1.46350	−	0.745691i
$59$	6.33807	+	8.72361i	0.107425	+	0.147858i	0.859345	−	0.511397i	$-0.170872\pi$
$59$	6.33807	+	8.72361i	0.107425	+	0.147858i	−0.751920	+	0.659255i	$0.770872\pi$
$60$	31.4913	+	26.9220i	0.524855	+	0.448701i
$61$	65.9802	+	47.9374i	1.08164	+	0.785860i	0.977969	−	0.208752i	$-0.0669400\pi$
$61$	65.9802	+	47.9374i	1.08164	+	0.785860i	0.103674	+	0.994611i	$0.466940\pi$
$62$	17.4942	−	110.454i	0.282164	−	1.78151i
$63$	−11.1778	−	1.77039i	−0.177426	−	0.0281015i
$64$	−50.6362	+	69.6948i	−0.791191	+	1.08898i
$65$	49.1955	−	57.5451i	0.756854	−	0.885309i
$66$	−13.3115	+	9.67137i	−0.201689	+	0.146536i
$67$	3.44626	+	6.76367i	0.0514368	+	0.100950i	0.915294	−	0.402786i	$-0.131958\pi$
$67$	3.44626	+	6.76367i	0.0514368	+	0.100950i	−0.863857	+	0.503737i	$0.831958\pi$
$68$	40.8174	+	40.8174i	0.600256	+	0.600256i
$69$	14.7952	+	4.80726i	0.214423	+	0.0696704i
$70$	21.3684	+	51.6574i	0.305263	+	0.737963i
$71$	30.8556	+	94.9637i	0.434586	+	1.33752i	0.893511	+	0.449042i	$0.148235\pi$
$71$	30.8556	+	94.9637i	0.434586	+	1.33752i	−0.458925	+	0.888475i	$0.651765\pi$
$72$	−6.21104	−	3.16468i	−0.0862645	−	0.0439539i
$73$	−3.29433	−	20.7996i	−0.0451278	−	0.284926i	0.954796	−	0.297262i	$-0.0960733\pi$
$73$	−3.29433	−	20.7996i	−0.0451278	−	0.284926i	−0.999924	+	0.0123357i	$0.996073\pi$
$74$		−	198.539i		−	2.68295i
$75$	−43.3013	−	0.0411995i	−0.577350	−	0.000549326i
$76$	114.340			1.50448
$77$	−11.9426	+	1.89152i	−0.155098	+	0.0245652i
$78$	−35.2877	+	69.2559i	−0.452406	+	0.887896i
$79$	−116.946	+	37.9981i	−1.48033	+	0.480988i	−0.934211	−	0.356720i	$-0.883895\pi$
$79$	−116.946	+	37.9981i	−1.48033	+	0.480988i	−0.546118	+	0.837708i	$0.683895\pi$
$80$	−4.77631	−	61.0602i	−0.0597039	−	0.763252i
$81$	−2.78115	+	8.55951i	−0.0343352	+	0.105673i
$82$	−144.701	+	144.701i	−1.76465	+	1.76465i
$83$	−69.6419	+	35.4843i	−0.839059	+	0.427522i	−0.820046	−	0.572298i	$-0.806052\pi$
$83$	−69.6419	+	35.4843i	−0.839059	+	0.427522i	−0.0190125	+	0.999819i	$0.506052\pi$
$84$	−18.3733	−	25.2886i	−0.218729	−	0.301055i
$85$	−60.1426	−	4.76212i	−0.707560	−	0.0560249i
$86$	−118.598	−	86.1665i	−1.37905	−	1.00194i
$87$	8.70937	−	54.9888i	0.100108	−	0.632055i
$88$	−7.35605	−	1.16508i	−0.0835915	−	0.0132396i
$89$	−29.4736	+	40.5670i	−0.331165	+	0.455809i	−0.941835	−	0.336076i	$-0.890900\pi$
$89$	−29.4736	+	40.5670i	−0.331165	+	0.455809i	0.610670	+	0.791885i	$0.290900\pi$
$90$	43.2333	−	10.3576i	0.480370	−	0.115085i
$91$	−46.2107	+	33.5740i	−0.507810	+	0.368946i
$92$	19.5071	+	38.2848i	0.212034	+	0.416139i
$93$	−46.2126	−	46.2126i	−0.496909	−	0.496909i
$94$	112.662	+	36.6061i	1.19853	+	0.389426i
$95$	−90.9076	+	77.5676i	−0.956922	+	0.816501i
$96$	24.4060	+	75.1139i	0.254229	+	0.782436i
$97$	53.7184	+	27.3709i	0.553798	+	0.282174i	0.708410	−	0.705801i	$-0.249413\pi$
$97$	53.7184	+	27.3709i	0.553798	+	0.282174i	−0.154612	+	0.987975i	$0.549413\pi$
$98$	16.1203	+	101.779i	0.164493	+	1.03857i
$99$			9.61576i			0.0971289i
$100$	−84.4895	−	84.6504i	−0.844895	−	0.846504i
$101$	51.5051			0.509952			0.254976	−	0.966947i	$-0.417932\pi$
$101$	51.5051			0.509952			0.254976	+	0.966947i	$0.417932\pi$
$102$	61.1781	−	9.68967i	0.599786	−	0.0949967i
$103$	−36.4251	+	71.4882i	−0.353641	+	0.694061i	−0.997468	−	0.0711106i	$-0.977346\pi$
$103$	−36.4251	+	71.4882i	−0.353641	+	0.694061i	0.643827	+	0.765171i	$0.277346\pi$
$104$	−33.4609	+	10.8721i	−0.321740	+	0.104540i
$105$	31.7635	+	7.64172i	0.302509	+	0.0727783i
$106$	68.5401	−	210.945i	0.646605	−	1.99005i
$107$	−30.1998	+	30.1998i	−0.282241	+	0.282241i	−0.834002	−	0.551761i	$-0.813956\pi$
$107$	−30.1998	+	30.1998i	−0.282241	+	0.282241i	0.551761	+	0.834002i	$0.313956\pi$
$108$	−22.1490	+	11.2855i	−0.205083	+	0.104495i
$109$	15.3903	+	21.1830i	0.141196	+	0.194339i	0.873758	−	0.486361i	$-0.161676\pi$
$109$	15.3903	+	21.1830i	0.141196	+	0.194339i	−0.732563	+	0.680700i	$0.761676\pi$
$110$	40.5108	−	24.7986i	0.368280	−	0.225441i
$111$	−93.8679	−	68.1990i	−0.845657	−	0.614406i
$112$	−7.22871	+	45.6403i	−0.0645421	+	0.407503i
$113$	−186.893	−	29.6010i	−1.65392	−	0.261956i	−0.741424	−	0.671037i	$-0.765849\pi$
$113$	−186.893	−	29.6010i	−1.65392	−	0.261956i	−0.912498	+	0.409081i	$0.865849\pi$
$114$	72.1163	−	99.2596i	0.632599	−	0.870698i
$115$	−41.4815	−	17.2053i	−0.360708	−	0.149611i
$116$	124.406	−	90.3865i	1.07247	−	0.779194i
$117$	20.6223	+	40.4736i	0.176259	+	0.345928i
$118$	22.5980	+	22.5980i	0.191508	+	0.191508i
$119$	43.2904	+	14.0659i	0.363785	+	0.118201i
$120$	17.1527	+	10.5224i	0.142939	+	0.0876867i
$121$	−34.2163	−	105.307i	−0.282780	−	0.870306i
$122$	215.369	+	109.736i	1.76532	+	0.899475i
$123$	18.7083	+	118.119i	0.152100	+	0.960320i
$124$		−	180.512i		−	1.45574i
$125$	124.601	+	9.98523i	0.996804	+	0.0798818i
$126$	−33.5416			−0.266203
$127$	26.9140	−	4.26276i	0.211921	−	0.0335650i	−0.0495711	−	0.998771i	$-0.515785\pi$
$127$	26.9140	−	4.26276i	0.211921	−	0.0335650i	0.261492	+	0.965206i	$0.415785\pi$
$128$	−33.1082	+	64.9786i	−0.258658	+	0.507645i
$129$	−81.4780	+	26.4738i	−0.631613	+	0.205223i
$130$	117.330	−	191.260i	0.902535	−	1.47123i
$131$	−18.0898	+	55.6746i	−0.138090	+	0.424997i	−0.996058	−	0.0887064i	$-0.971727\pi$
$131$	−18.0898	+	55.6746i	−0.138090	+	0.424997i	0.857968	+	0.513703i	$0.171727\pi$
$132$	−18.7802	+	18.7802i	−0.142274	+	0.142274i
$133$	80.3350	−	40.9327i	0.604023	−	0.307765i
$134$	13.2241	+	18.2014i	0.0986874	+	0.135832i
$135$	9.95383	−	23.9984i	0.0737320	−	0.177766i
$136$	22.6824	+	16.4797i	0.166783	+	0.121175i
$137$	18.9766	−	119.813i	0.138515	−	0.874549i	−0.816360	−	0.577543i	$-0.804012\pi$
$137$	18.9766	−	119.813i	0.138515	−	0.874549i	0.954875	−	0.297007i	$-0.0959883\pi$
$138$	45.5388	+	7.21263i	0.329991	+	0.0522654i
$139$	44.1543	−	60.7732i	0.317657	−	0.437217i	−0.620093	−	0.784528i	$-0.712905\pi$
$139$	44.1543	−	60.7732i	0.317657	−	0.437217i	0.937750	+	0.347311i	$0.112905\pi$
$140$	47.1113	+	76.9608i	0.336509	+	0.549720i
$141$	56.0071	−	40.6915i	0.397213	−	0.288592i
$142$	134.352	+	263.681i	0.946141	+	1.85691i
$143$	34.3176	+	34.3176i	0.239983	+	0.239983i
$144$	34.9495	+	11.3558i	0.242705	+	0.0788595i
$145$	−37.5931	+	156.259i	−0.259263	+	1.07765i
$146$	−19.2869	−	59.3591i	−0.132102	−	0.406569i
$147$	53.6581	+	27.3402i	0.365021	+	0.185988i
$148$	−50.1329	−	316.526i	−0.338735	−	2.13869i
$149$		−	106.919i		−	0.717579i	−0.933418	−	0.358790i	$-0.883190\pi$
$149$		−	106.919i		−	0.717579i	0.933418	−	0.358790i	$-0.116810\pi$
$150$	−126.775	+	19.9555i	−0.845163	+	0.133037i
$151$	234.915			1.55573			0.777864	−	0.628432i	$-0.216303\pi$
$151$	234.915			1.55573			0.777864	+	0.628432i	$0.216303\pi$
$152$	54.8517	−	8.68766i	0.360867	−	0.0571557i
$153$	16.4338	−	32.2531i	0.107410	−	0.210805i
$154$	−34.0825	+	11.0741i	−0.221315	+	0.0719095i
$155$	122.458	+	143.518i	0.790051	+	0.925922i
$156$	−38.7707	+	119.324i	−0.248530	+	0.764897i
$157$	45.9560	−	45.9560i	0.292713	−	0.292713i	−0.545438	−	0.838151i	$-0.683637\pi$
$157$	45.9560	−	45.9560i	0.292713	−	0.292713i	0.838151	+	0.545438i	$0.183637\pi$
$158$	−324.718	+	165.452i	−2.05518	+	1.04716i
$159$	−76.1896	−	104.866i	−0.479180	−	0.659534i
$160$	−53.1187	−	221.720i	−0.331992	−	1.38575i
$161$	27.4112	+	19.9154i	0.170256	+	0.123698i
$162$	−4.17274	+	26.3456i	−0.0257576	+	0.162627i
$163$	−165.714	−	26.2466i	−1.01665	−	0.161022i	−0.374200	−	0.927348i	$-0.622083\pi$
$163$	−165.714	−	26.2466i	−1.01665	−	0.161022i	−0.642452	+	0.766326i	$0.722083\pi$
$164$	−194.156	+	267.233i	−1.18388	+	1.62947i
$165$	2.19106	−	27.6717i	0.0132791	−	0.167707i
$166$	−187.410	+	136.162i	−1.12898	+	0.820250i
$167$	−10.2158	−	20.0497i	−0.0611726	−	0.120058i	0.858396	−	0.512988i	$-0.171461\pi$
$167$	−10.2158	−	20.0497i	−0.0611726	−	0.120058i	−0.919568	+	0.392930i	$0.871461\pi$
$168$	−10.7355	−	10.7355i	−0.0639020	−	0.0639020i
$169$	57.3158	+	18.6230i	0.339147	+	0.110195i
$170$	−178.263	+	13.9443i	−1.04861	+	0.0820251i
$171$	−22.1570	−	68.1924i	−0.129573	−	0.398786i
$172$	−210.836	−	107.427i	−1.22579	−	0.624573i
$173$	−33.2739	−	210.083i	−0.192335	−	1.21435i	−0.875182	−	0.483793i	$-0.839259\pi$
$173$	−33.2739	−	210.083i	−0.192335	−	1.21435i	0.682847	−	0.730561i	$-0.260741\pi$
$174$		−	165.006i		−	0.948312i
$175$	−89.6660	−	29.2286i	−0.512377	−	0.167021i
$176$	39.2623			0.223081
$177$	18.4467	−	2.92167i	0.104219	−	0.0165066i
$178$	−67.4696	+	132.417i	−0.379043	+	0.743913i
$179$	−243.955	+	79.2659i	−1.36288	+	0.442826i	−0.897003	−	0.442024i	$-0.854261\pi$
$179$	−243.955	+	79.2659i	−1.36288	+	0.442826i	−0.465876	+	0.884850i	$0.654261\pi$
$180$	66.3107	−	27.4298i	0.368393	−	0.152388i
$181$	−37.1986	+	114.486i	−0.205517	+	0.632517i	0.794174	+	0.607690i	$0.207904\pi$
$181$	−37.1986	+	114.486i	−0.205517	+	0.632517i	−0.999692	+	0.0248275i	$0.992096\pi$
$182$	−119.706	+	119.706i	−0.657726	+	0.657726i
$183$	125.863	−	64.1303i	0.687775	−	0.350439i
$184$	12.2669	+	16.8840i	0.0666680	+	0.0917607i
$185$	254.588	+	217.648i	1.37615	+	1.17648i
$186$	−156.704	−	113.852i	−0.842492	−	0.612106i
$187$	6.05013	−	38.1990i	0.0323536	−	0.204273i
$188$	188.858	+	29.9122i	1.00456	+	0.159107i
$189$	−11.5217	+	15.8583i	−0.0609614	+	0.0839061i
$190$	−230.150	+	269.211i	−1.21131	+	1.41690i
$191$	229.742	−	166.917i	1.20284	−	0.873912i	0.208276	−	0.978070i	$-0.433215\pi$
$191$	229.742	−	166.917i	1.20284	−	0.873912i	0.994561	+	0.104158i	$0.0332149\pi$
$192$	67.7408	+	132.949i	0.352816	+	0.692441i
$193$	158.631	+	158.631i	0.821924	+	0.821924i	0.986384	−	0.164460i	$-0.0525882\pi$
$193$	158.631	+	158.631i	0.821924	+	0.821924i	−0.164460	+	0.986384i	$0.552588\pi$
$194$	169.940	+	55.2167i	0.875977	+	0.284622i
$195$	−50.1234	−	121.172i	−0.257043	−	0.621393i
$196$	51.4005	+	158.194i	0.262247	+	0.807115i
$197$	−299.748	−	152.729i	−1.52156	−	0.775274i	−0.524466	−	0.851431i	$-0.675735\pi$
$197$	−299.748	−	152.729i	−1.52156	−	0.775274i	−0.997096	+	0.0761570i	$0.975735\pi$
$198$	4.45823	+	28.1482i	0.0225163	+	0.142162i
$199$			174.588i			0.877327i	0.898651	+	0.438663i	$0.144548\pi$
$199$			174.588i			0.877327i	−0.898651	+	0.438663i	$0.855452\pi$
$200$	−46.9634	−	34.1892i	−0.234817	−	0.170946i
$201$	13.1481			0.0654134
$202$	150.771	−	23.8797i	0.746389	−	0.118216i
$203$	55.0499	−	108.041i	0.271182	−	0.532224i
$204$	95.0884	−	30.8961i	0.466120	−	0.151452i
$205$	−26.9228	−	344.180i	−0.131331	−	1.67893i
$206$	−73.4822	+	226.155i	−0.356710	+	1.09784i
$207$	19.0529	−	19.0529i	0.0920429	−	0.0920429i
$208$	165.258	−	84.2032i	0.794510	−	0.404823i
$209$	−45.0287	−	61.9767i	−0.215448	−	0.296539i
$210$	96.5240	+	7.64281i	0.459638	+	0.0363943i
$211$	257.285	+	186.929i	1.21936	+	0.885917i	0.996047	−	0.0888292i	$-0.0283125\pi$
$211$	257.285	+	186.929i	1.21936	+	0.885917i	0.223314	+	0.974747i	$0.428313\pi$
$212$	56.0067	−	353.612i	0.264183	−	1.66798i
$213$	170.817	+	27.0548i	0.801959	+	0.127018i
$214$	−74.4020	+	102.406i	−0.347673	+	0.478530i
$215$	240.505	−	57.6192i	1.11863	−	0.267996i
$216$	−9.76791	+	7.09680i	−0.0452218	+	0.0328556i
$217$	−64.6215	−	126.827i	−0.297795	−	0.584455i
$218$	54.8732	+	54.8732i	0.251712	+	0.251712i
$219$	−34.6898	−	11.2714i	−0.158401	−	0.0514676i
$220$	58.3238	−	49.7652i	0.265108	−	0.226206i
$221$	−56.4574	−	173.758i	−0.255464	−	0.786236i
$222$	−306.398	−	156.118i	−1.38017	−	0.703233i
$223$	38.5866	+	243.626i	0.173034	+	1.09249i	0.909404	+	0.415915i	$0.136539\pi$
$223$	38.5866	+	243.626i	0.173034	+	1.09249i	−0.736369	+	0.676580i	$0.763461\pi$
$224$			172.016i			0.767929i
$225$	−34.1129	+	66.7931i	−0.151613	+	0.296858i
$226$	−560.815			−2.48148
$227$	−27.5940	+	4.37046i	−0.121559	+	0.0192531i	−0.216918	−	0.976190i	$-0.569600\pi$
$227$	−27.5940	+	4.37046i	−0.121559	+	0.0192531i	0.0953583	+	0.995443i	$0.469600\pi$
$228$	89.9097	−	176.458i	0.394341	−	0.773938i
$229$	94.0683	−	30.5646i	0.410779	−	0.133470i	−0.0963357	−	0.995349i	$-0.530712\pi$
$229$	94.0683	−	30.5646i	0.410779	−	0.133470i	0.507114	+	0.861879i	$0.330712\pi$
$230$	−129.405	−	31.1326i	−0.562632	−	0.135359i
$231$	−6.47174	+	19.9180i	−0.0280162	+	0.0862250i
$232$	52.8130	−	52.8130i	0.227642	−	0.227642i
$233$	173.156	−	88.2272i	0.743158	−	0.378658i	−0.0410493	−	0.999157i	$-0.513070\pi$
$233$	173.156	−	88.2272i	0.743158	−	0.378658i	0.784207	+	0.620499i	$0.213070\pi$
$234$	79.1326	+	108.917i	0.338173	+	0.465456i
$235$	−170.446	+	104.338i	−0.725303	+	0.443992i
$236$	41.7337	+	30.3213i	0.176838	+	0.128480i
$237$	−33.3175	+	210.358i	−0.140580	+	0.887588i
$238$	133.245	+	21.1040i	0.559854	+	0.0886721i
$239$	72.7549	−	100.138i	0.304414	−	0.418989i	−0.629215	−	0.777231i	$-0.716624\pi$
$239$	72.7549	−	100.138i	0.304414	−	0.418989i	0.933629	+	0.358242i	$0.116624\pi$
$240$	−97.9881	−	40.6426i	−0.408284	−	0.169344i
$241$	−136.086	+	98.8722i	−0.564672	+	0.410258i	−0.833166	−	0.553023i	$-0.813474\pi$
$241$	−136.086	+	98.8722i	−0.564672	+	0.410258i	0.268494	+	0.963281i	$0.413474\pi$
$242$	−148.985	−	292.400i	−0.615642	−	1.20827i
$243$	11.0227	+	11.0227i	0.0453609	+	0.0453609i
$244$	371.068	+	120.567i	1.52077	+	0.494129i
$245$	−148.185	−	90.9046i	−0.604835	−	0.371039i
$246$	109.529	+	337.096i	0.445240	+	1.37031i
$247$	−322.447	−	164.295i	−1.30545	−	0.665162i
$248$	−13.7154	−	86.5958i	−0.0553041	−	0.349176i
$249$			135.379i			0.543689i
$250$	369.372	−	28.5398i	1.47749	−	0.114159i
$251$	−107.500			−0.428287			−0.214144	−	0.976802i	$-0.568696\pi$
$251$	−107.500			−0.428287			−0.214144	+	0.976802i	$0.568696\pi$
$252$	−53.4747	+	8.46956i	−0.212201	+	0.0336094i
$253$	13.0696	−	25.6506i	0.0516587	−	0.101386i
$254$	76.8087	−	24.9567i	0.302397	−	0.0982546i
$255$	−54.6415	+	89.0716i	−0.214280	+	0.349300i
$256$	39.6932	−	122.163i	0.155052	−	0.477200i
$257$	−87.6024	+	87.6024i	−0.340865	+	0.340865i	−0.856693	−	0.515827i	$-0.827485\pi$
$257$	−87.6024	+	87.6024i	−0.340865	+	0.340865i	0.515827	+	0.856693i	$0.327485\pi$
$258$	−226.236	+	115.273i	−0.876883	+	0.446794i
$259$	−148.537	−	204.443i	−0.573500	−	0.789355i
$260$	138.761	−	334.549i	0.533698	−	1.28673i
$261$	−78.0140	−	56.6805i	−0.298904	−	0.217167i
$262$	−27.1412	+	171.363i	−0.103592	+	0.654057i
$263$	54.9321	+	8.70039i	0.208867	+	0.0330813i	0.259991	−	0.965611i	$-0.416280\pi$
$263$	54.9321	+	8.70039i	0.208867	+	0.0330813i	−0.0511239	+	0.998692i	$0.516280\pi$
$264$	−7.58235	+	10.4362i	−0.0287210	+	0.0395311i
$265$	195.359	+	319.138i	0.737205	+	1.20429i
$266$	216.186	−	157.068i	0.812730	−	0.590483i
$267$	39.4296	+	77.3850i	0.147676	+	0.289831i
$268$	25.6790	+	25.6790i	0.0958171	+	0.0958171i
$269$	27.6442	+	8.98216i	0.102767	+	0.0333909i	0.359949	−	0.932972i	$-0.382794\pi$
$269$	27.6442	+	8.98216i	0.102767	+	0.0333909i	−0.257182	+	0.966363i	$0.582794\pi$
$270$	18.0112	−	74.8652i	0.0667082	−	0.277278i
$271$	−95.3779	−	293.543i	−0.351948	−	1.08318i	−0.957758	−	0.287575i	$-0.907151\pi$
$271$	−95.3779	−	293.543i	−0.351948	−	1.08318i	0.605810	−	0.795609i	$-0.292849\pi$
$272$	−131.693	−	67.1010i	−0.484166	−	0.246695i
$273$	15.4767	+	97.7160i	0.0566912	+	0.357934i
$274$		−	359.527i		−	1.31214i
$275$	−12.6106	+	79.1329i	−0.0458567	+	0.287756i
$276$	74.4228			0.269648
$277$	194.312	−	30.7760i	0.701488	−	0.111105i	0.204506	−	0.978865i	$-0.434441\pi$
$277$	194.312	−	30.7760i	0.701488	−	0.111105i	0.496982	+	0.867761i	$0.334441\pi$
$278$	101.076	−	198.372i	0.363582	−	0.713570i
$279$	−107.657	+	34.9799i	−0.385867	+	0.125376i
$280$	28.4479	+	33.3403i	0.101600	+	0.119073i
$281$	−83.9149	+	258.264i	−0.298630	+	0.919088i	0.683348	+	0.730092i	$0.260523\pi$
$281$	−83.9149	+	258.264i	−0.298630	+	0.919088i	−0.981978	+	0.188995i	$0.939477\pi$
$282$	145.083	−	145.083i	0.514479	−	0.514479i
$283$	222.387	−	113.312i	0.785818	−	0.400394i	−0.0145569	−	0.999894i	$-0.504634\pi$
$283$	222.387	−	113.312i	0.785818	−	0.400394i	0.800375	+	0.599500i	$0.204634\pi$
$284$	280.777	+	386.456i	0.988651	+	1.36076i
$285$	48.2239	+	201.289i	0.169207	+	0.706277i
$286$	116.369	+	84.5467i	0.406883	+	0.295618i
$287$	−40.7464	+	257.262i	−0.141973	+	0.896385i
$288$	135.112	+	21.3997i	0.469140	+	0.0743044i
$289$	84.2928	−	116.019i	0.291671	−	0.401450i
$290$	−37.5985	+	474.846i	−0.129650	+	1.63740i
$291$	84.4813	−	61.3792i	0.290314	−	0.210925i
$292$	−45.7375	−	89.7650i	−0.156635	−	0.307414i
$293$	−355.357	−	355.357i	−1.21282	−	1.21282i	−0.970094	−	0.242728i	$-0.921958\pi$
$293$	−355.357	−	355.357i	−1.21282	−	1.21282i	−0.242728	−	0.970094i	$-0.578042\pi$
$294$	169.749	+	55.1547i	0.577377	+	0.187601i
$295$	−53.7507	+	4.20454i	−0.182206	+	0.0142527i
$296$	−48.0998	−	148.036i	−0.162499	−	0.500122i
$297$	14.8397	+	7.56121i	0.0499653	+	0.0254586i
$298$	−49.5718	−	312.984i	−0.166348	−	1.05028i
$299$		−	135.995i		−	0.454834i
$300$	−197.075	+	63.8264i	−0.656918	+	0.212755i
$301$	−186.590			−0.619902
$302$	687.665	−	108.915i	2.27704	−	0.360647i
$303$	40.5003	−	79.4862i	0.133664	−	0.262331i
$304$	−278.437	+	90.4697i	−0.915912	+	0.297598i
$305$	−376.814	+	155.872i	−1.23546	+	0.511054i
$306$	33.1527	−	102.034i	0.108342	−	0.333443i
$307$	227.454	−	227.454i	0.740893	−	0.740893i	−0.231857	−	0.972750i	$-0.574480\pi$
$307$	227.454	−	227.454i	0.740893	−	0.740893i	0.972750	+	0.231857i	$0.0744800\pi$
$308$	−51.5407	+	26.2613i	−0.167340	+	0.0852640i
$309$	81.6832	+	112.427i	0.264347	+	0.363843i
$310$	425.010	+	363.343i	1.37100	+	1.17207i
$311$	67.6661	+	49.1623i	0.217576	+	0.158078i	0.691235	−	0.722630i	$-0.257067\pi$
$311$	67.6661	+	49.1623i	0.217576	+	0.158078i	−0.473659	+	0.880708i	$0.657067\pi$
$312$	−9.53289	+	60.1883i	−0.0305541	+	0.192911i
$313$	−443.561	−	70.2532i	−1.41713	−	0.224451i	−0.599582	−	0.800313i	$-0.704667\pi$
$313$	−443.561	−	70.2532i	−1.41713	−	0.224451i	−0.817547	+	0.575862i	$0.804667\pi$
$314$	113.220	−	155.834i	0.360572	−	0.496285i
$315$	36.7700	−	43.0107i	0.116730	−	0.136542i
$316$	−475.913	+	345.771i	−1.50605	+	1.09421i
$317$	51.5638	+	101.200i	0.162662	+	0.319242i	0.957923	−	0.287025i	$-0.0926664\pi$
$317$	51.5638	+	101.200i	0.162662	+	0.319242i	−0.795261	+	0.606267i	$0.792666\pi$
$318$	−271.649	−	271.649i	−0.854242	−	0.854242i
$319$	−97.9857	−	31.8375i	−0.307165	−	0.0998040i
$320$	−164.647	−	398.028i	−0.514521	−	1.24384i
$321$	22.8593	+	70.3536i	0.0712127	+	0.219170i
$322$	89.4741	+	45.5893i	0.277870	+	0.141582i
$323$	45.1139	+	284.838i	0.139671	+	0.881851i
$324$			43.0560i			0.132889i
$325$	116.632	+	360.122i	0.358868	+	1.10807i
$326$	−497.263			−1.52535
$327$	44.7930	−	7.09451i	0.136982	−	0.0216957i
$328$	−72.8366	+	142.950i	−0.222063	+	0.435823i
$329$	143.399	−	46.5932i	0.435864	−	0.141621i
$330$	−6.41578	−	82.0190i	−0.0194418	−	0.248543i
$331$	177.857	−	547.387i	0.537332	−	1.65374i	−0.201224	−	0.979545i	$-0.564492\pi$
$331$	177.857	−	547.387i	0.537332	−	1.65374i	0.738556	−	0.674193i	$-0.235508\pi$
$332$	−264.403	+	264.403i	−0.796393	+	0.796393i
$333$	−179.061	+	91.2361i	−0.537721	+	0.273982i
$334$	−39.2005	−	53.9548i	−0.117367	−	0.161541i
$335$	−37.8368	−	2.99593i	−0.112946	−	0.00894309i
$336$	64.7511	+	47.0444i	0.192712	+	0.140013i
$337$	−29.5779	+	186.748i	−0.0877683	+	0.554147i	0.904145	+	0.427227i	$0.140509\pi$
$337$	−29.5779	+	186.748i	−0.0877683	+	0.554147i	−0.991913	+	0.126921i	$0.959491\pi$
$338$	176.414	+	27.9413i	0.521936	+	0.0826665i
$339$	−192.643	+	265.150i	−0.568268	+	0.782154i
$340$	−280.680	+	67.2442i	−0.825530	+	0.197777i
$341$	−97.8441	+	71.0879i	−0.286933	+	0.208469i
$342$	−96.4767	−	189.346i	−0.282096	−	0.553644i
$343$	223.452	+	223.452i	0.651464	+	0.651464i
$344$	−109.306	−	35.5155i	−0.317749	−	0.103243i
$345$	−59.1707	+	50.4879i	−0.171509	+	0.146342i
$346$	−194.805	−	599.548i	−0.563020	−	1.73280i
$347$	333.286	+	169.818i	0.960480	+	0.489389i	0.862643	−	0.505814i	$-0.168808\pi$
$347$	333.286	+	169.818i	0.960480	+	0.489389i	0.0978368	+	0.995202i	$0.468808\pi$
$348$	−41.6656	−	263.066i	−0.119729	−	0.755938i
$349$		−	156.078i		−	0.447215i	−0.974679	−	0.223607i	$-0.928217\pi$
$349$		−	156.078i		−	0.447215i	0.974679	−	0.223607i	$-0.0717833\pi$
$350$	−276.030	−	43.9881i	−0.788657	−	0.125680i
$351$	78.6776			0.224153
$352$	144.356	−	22.8638i	0.410103	−	0.0649540i
$353$	43.4608	−	85.2966i	0.123118	−	0.241633i	−0.821218	−	0.570614i	$-0.806705\pi$
$353$	43.4608	−	85.2966i	0.123118	−	0.241633i	0.944337	+	0.328981i	$0.106705\pi$
$354$	52.6443	−	17.1052i	0.148713	−	0.0483197i
$355$	−485.404	−	116.779i	−1.36733	−	0.328956i
$356$	−74.1291	+	228.146i	−0.208228	+	0.640859i
$357$	55.7482	−	55.7482i	0.156157	−	0.156157i
$358$	−677.378	+	345.141i	−1.89212	+	0.964082i
$359$	−129.426	−	178.139i	−0.360517	−	0.496209i	0.589776	−	0.807567i	$-0.299216\pi$
$359$	−129.426	−	178.139i	−0.360517	−	0.496209i	−0.950293	+	0.311358i	$0.899216\pi$
$360$	29.7266	−	18.1971i	0.0825740	−	0.0505474i
$361$	170.085	+	123.574i	0.471151	+	0.342311i
$362$	−55.8115	+	352.380i	−0.154175	+	0.973424i
$363$	−189.422	−	30.0016i	−0.521825	−	0.0826490i
$364$	−160.618	+	221.072i	−0.441259	+	0.607341i
$365$	97.2600	+	40.3407i	0.266466	+	0.110522i
$366$	338.704	−	246.083i	0.925421	−	0.672358i
$367$	198.031	+	388.657i	0.539593	+	1.05901i	0.986397	+	0.164379i	$0.0525621\pi$
$367$	198.031	+	388.657i	0.539593	+	1.05901i	−0.446804	+	0.894632i	$0.647438\pi$
$368$	−77.7951	−	77.7951i	−0.211400	−	0.211400i
$369$	197.001	+	64.0095i	0.533878	+	0.173467i
$370$	846.163	+	519.083i	2.28693	+	1.40293i
$371$	−87.2398	−	268.496i	−0.235148	−	0.723710i
$372$	−278.578	−	141.943i	−0.748866	−	0.381566i
$373$	33.7994	+	213.401i	0.0906150	+	0.572120i	0.990663	+	0.136330i	$0.0435309\pi$
$373$	33.7994	+	213.401i	0.0906150	+	0.572120i	−0.900048	+	0.435790i	$0.856469\pi$
$374$		−	114.625i		−	0.306483i
$375$	113.388	−	184.440i	0.302367	−	0.491841i
$376$	92.8725			0.247001
$377$	−480.710	+	76.1369i	−1.27509	+	0.201955i
$378$	−26.3749	+	51.7636i	−0.0697748	+	0.136941i
$379$	181.518	−	58.9787i	0.478938	−	0.155617i	−0.0595916	−	0.998223i	$-0.518980\pi$
$379$	181.518	−	58.9787i	0.478938	−	0.155617i	0.538530	+	0.842606i	$0.318980\pi$
$380$	−298.945	+	487.314i	−0.786698	+	1.28240i
$381$	14.5848	−	44.8875i	0.0382804	−	0.117815i
$382$	595.132	−	595.132i	1.55794	−	1.55794i
$383$	372.337	−	189.715i	0.972159	−	0.495340i	0.105597	−	0.994409i	$-0.466325\pi$
$383$	372.337	−	189.715i	0.972159	−	0.495340i	0.866562	+	0.499069i	$0.166325\pi$
$384$	74.2452	+	102.190i	0.193347	+	0.266119i
$385$	23.1626	−	55.8442i	0.0601625	−	0.145050i
$386$	537.907	+	390.813i	1.39354	+	1.01247i
$387$	−23.2128	+	146.560i	−0.0599814	+	0.378707i
$388$	284.874	+	45.1197i	0.734212	+	0.116288i
$389$	238.891	−	328.805i	0.614116	−	0.845258i	−0.382792	−	0.923834i	$-0.625038\pi$
$389$	238.891	−	328.805i	0.614116	−	0.845258i	0.996908	+	0.0785766i	$0.0250375\pi$
$390$	−202.905	−	331.466i	−0.520270	−	0.849912i
$391$	−87.6762	+	63.7005i	−0.224236	+	0.162917i
$392$	36.6778	+	71.9841i	0.0935657	+	0.183633i
$393$	71.6962	+	71.6962i	0.182433	+	0.182433i
$394$	−948.260	−	308.108i	−2.40675	−	0.782001i
$395$	143.812	−	597.766i	0.364080	−	1.51333i
$396$	14.2153	+	43.7503i	0.0358973	+	0.110481i
$397$	−476.549	−	242.814i	−1.20038	−	0.611622i	−0.264648	−	0.964345i	$-0.585256\pi$
$397$	−476.549	−	242.814i	−1.20038	−	0.611622i	−0.935728	+	0.352723i	$0.885256\pi$
$398$	80.9456	+	511.070i	0.203381	+	1.28410i
$399$		−	156.165i		−	0.391392i
$400$	272.724	+	139.287i	0.681809	+	0.348217i
$401$	−283.049			−0.705859			−0.352929	−	0.935650i	$-0.614814\pi$
$401$	−283.049			−0.705859			−0.352929	+	0.935650i	$0.614814\pi$
$402$	38.4883	−	6.09595i	0.0957420	−	0.0151640i
$403$	−259.376	+	509.055i	−0.643614	+	1.26316i
$404$	234.341	−	76.1419i	0.580051	−	0.188470i
$405$	−29.2089	−	34.2322i	−0.0721207	−	0.0845239i
$406$	111.055	−	341.792i	0.273534	−	0.841853i
$407$	−151.826	+	151.826i	−0.373037	+	0.373037i
$408$	43.2687	−	22.0465i	0.106051	−	0.0540355i
$409$	187.227	+	257.695i	0.457767	+	0.630062i	0.974044	−	0.226360i	$-0.0726825\pi$
$409$	187.227	+	257.695i	0.457767	+	0.630062i	−0.516277	+	0.856422i	$0.672682\pi$
$410$	−238.386	−	995.034i	−0.581429	−	2.42691i
$411$	−169.982	−	123.499i	−0.413582	−	0.300485i
$412$	−60.0451	+	379.110i	−0.145740	+	0.920169i
$413$	40.1767	+	6.36336i	0.0972801	+	0.0154077i
$414$	46.9397	−	64.6070i	0.113381	−	0.156056i
$415$	30.8475	−	389.585i	0.0743313	−	0.938759i
$416$	558.573	−	405.827i	1.34272	−	0.975546i
$417$	−59.0693	−	115.930i	−0.141653	−	0.278010i
$418$	−160.547	−	160.547i	−0.384083	−	0.384083i
$419$	585.104	+	190.112i	1.39643	+	0.453728i	0.908035	−	0.418895i	$-0.137582\pi$
$419$	585.104	+	190.112i	1.39643	+	0.453728i	0.488395	+	0.872622i	$0.337582\pi$
$420$	155.816	−	12.1884i	0.370991	−	0.0290201i
$421$	109.343	+	336.522i	0.259721	+	0.799341i	0.992863	+	0.119264i	$0.0380535\pi$
$421$	109.343	+	336.522i	0.259721	+	0.799341i	−0.733141	+	0.680077i	$0.761947\pi$
$422$	839.816	+	427.908i	1.99008	+	1.01400i
$423$	−18.7577	−	118.431i	−0.0443443	−	0.279979i
$424$		−	173.892i		−	0.410122i
$425$	177.540	−	243.875i	0.417741	−	0.573823i
$426$	512.576			1.20323
$427$	303.873	−	48.1287i	0.711646	−	0.112714i
$428$	−92.7593	+	182.050i	−0.216727	+	0.425351i
$429$	79.9464	−	25.9761i	0.186355	−	0.0605505i
$430$	677.315	−	280.176i	1.57515	−	0.651571i
$431$	−98.1469	+	302.065i	−0.227719	+	0.700847i	0.770285	+	0.637700i	$0.220114\pi$
$431$	−98.1469	+	302.065i	−0.227719	+	0.700847i	−0.998004	+	0.0631474i	$0.979886\pi$
$432$	45.0070	−	45.0070i	0.104183	−	0.104183i
$433$	50.0527	−	25.5031i	0.115595	−	0.0588986i	−0.395237	−	0.918579i	$-0.629337\pi$
$433$	50.0527	−	25.5031i	0.115595	−	0.0588986i	0.510832	+	0.859681i	$0.329337\pi$
$434$	−247.968	−	341.298i	−0.571354	−	0.786401i
$435$	211.589	+	180.888i	0.486412	+	0.415835i
$436$	101.339	+	73.6274i	0.232430	+	0.168870i
$437$	−33.5811	+	212.023i	−0.0768447	+	0.485178i
$438$	−106.773	−	16.9112i	−0.243774	−	0.0386100i
$439$	206.646	−	284.423i	0.470719	−	0.647889i	−0.505969	−	0.862551i	$-0.668865\pi$
$439$	206.646	−	284.423i	0.470719	−	0.647889i	0.976688	+	0.214662i	$0.0688651\pi$
$440$	24.1981	−	28.3050i	0.0549956	−	0.0643296i
$441$	84.3864	−	61.3103i	0.191352	−	0.139026i
$442$	−245.828	−	482.465i	−0.556172	−	1.09155i
$443$	236.089	+	236.089i	0.532932	+	0.532932i	0.921444	−	0.388512i	$-0.127011\pi$
$443$	236.089	+	236.089i	0.532932	+	0.532932i	−0.388512	+	0.921444i	$0.627011\pi$
$444$	−527.906	−	171.527i	−1.18898	−	0.386322i
$445$	−95.8354	−	231.679i	−0.215360	−	0.520626i
$446$	225.909	+	695.275i	0.506521	+	1.55891i
$447$	−165.005	−	84.0743i	−0.369139	−	0.188086i
$448$	50.8383	+	320.980i	0.113478	+	0.716474i
$449$			548.645i			1.22193i	0.791659	+	0.610963i	$0.209218\pi$
$449$			548.645i			1.22193i	−0.791659	+	0.610963i	$0.790782\pi$
$450$	−68.8905	+	211.339i	−0.153090	+	0.469642i
$451$	221.311			0.490712
$452$	−894.097	+	141.611i	−1.97809	+	0.313299i
$453$	184.722	−	362.537i	0.407774	−	0.800302i
$454$	−78.7493	+	25.5872i	−0.173457	+	0.0563595i
$455$	−22.2723	−	284.728i	−0.0489501	−	0.625776i
$456$	29.7244	−	91.4824i	0.0651851	−	0.200619i
$457$	−51.8314	+	51.8314i	−0.113417	+	0.113417i	−0.761537	−	0.648121i	$-0.775555\pi$
$457$	−51.8314	+	51.8314i	−0.113417	+	0.113417i	0.648121	+	0.761537i	$0.275555\pi$
$458$	261.194	−	133.085i	0.570294	−	0.290579i
$459$	−36.8528	−	50.7235i	−0.0802893	−	0.110509i
$460$	−214.170	−	16.9581i	−0.465587	−	0.0368654i
$461$	−282.819	−	205.480i	−0.613491	−	0.445727i	0.237151	−	0.971473i	$-0.423786\pi$
$461$	−282.819	−	205.480i	−0.613491	−	0.445727i	−0.850642	+	0.525746i	$0.823786\pi$
$462$	−9.70996	+	61.3063i	−0.0210172	+	0.132698i
$463$	−711.727	−	112.726i	−1.53721	−	0.243470i	−0.670357	−	0.742039i	$-0.733859\pi$
$463$	−711.727	−	112.726i	−1.53721	−	0.243470i	−0.866850	+	0.498569i	$0.833859\pi$
$464$	−231.433	+	318.540i	−0.498778	+	0.686509i
$465$	317.780	−	76.1323i	0.683397	−	0.163725i
$466$	465.972	−	338.548i	0.999940	−	0.726499i
$467$	53.2132	+	104.437i	0.113947	+	0.223633i	0.940936	−	0.338585i	$-0.109948\pi$
$467$	53.2132	+	104.437i	0.113947	+	0.223633i	−0.826989	+	0.562218i	$0.809948\pi$
$468$	153.662	+	153.662i	0.328338	+	0.328338i
$469$	27.2348	+	8.84912i	0.0580699	+	0.0188681i
$470$	−450.571	+	384.453i	−0.958661	+	0.817985i
$471$	−34.7857	−	107.059i	−0.0738549	−	0.227302i
$472$	22.3245	+	11.3749i	0.0472977	+	0.0240994i
$473$	24.8010	+	156.587i	0.0524333	+	0.331051i
$474$			631.227i			1.33170i
$475$	−92.9103	−	590.246i	−0.195601	−	1.24262i
$476$	217.759			0.457477
$477$	−221.747	+	35.1213i	−0.464878	+	0.0736295i
$478$	166.547	−	326.866i	0.348424	−	0.683821i
$479$	−846.762	+	275.130i	−1.76777	+	0.574383i	−0.997957	−	0.0638859i	$-0.979651\pi$
$479$	−846.762	+	275.130i	−1.76777	+	0.574383i	−0.769813	+	0.638269i	$0.779651\pi$
$480$	−383.942	−	92.3696i	−0.799880	−	0.192437i
$481$	−313.437	+	964.660i	−0.651636	+	2.00553i
$482$	−352.522	+	352.522i	−0.731374	+	0.731374i
$483$	52.2892	−	26.6427i	0.108259	−	0.0551608i
$484$	−311.359	−	428.548i	−0.643303	−	0.885430i
$485$	−257.101	+	157.384i	−0.530106	+	0.324503i
$486$	37.3772	+	27.1561i	0.0769079	+	0.0558768i
$487$	124.029	−	783.086i	0.254679	−	1.60798i	−0.446359	−	0.894854i	$-0.647279\pi$
$487$	124.029	−	783.086i	0.254679	−	1.60798i	0.701037	−	0.713125i	$-0.252721\pi$
$488$	187.171	+	29.6450i	0.383547	+	0.0607479i
$489$	−170.812	+	235.103i	−0.349309	+	0.480783i
$490$	−475.926	−	197.400i	−0.971278	−	0.402858i
$491$	−159.270	+	115.717i	−0.324380	+	0.235676i	−0.738042	−	0.674755i	$-0.764249\pi$
$491$	−159.270	+	115.717i	−0.324380	+	0.235676i	0.413662	+	0.910430i	$0.364249\pi$
$492$	259.740	+	509.769i	0.527927	+	1.03612i
$493$	274.251	+	274.251i	0.556290	+	0.556290i
$494$	−1020.07	−	331.441i	−2.06492	−	0.670933i
$495$	−40.9820	−	25.1406i	−0.0827919	−	0.0507891i
$496$	142.827	+	439.576i	0.287957	+	0.886241i
$497$	335.620	+	171.007i	0.675292	+	0.344078i
$498$	62.7666	+	396.293i	0.126037	+	0.795769i
$499$			384.731i			0.771004i	0.922707	+	0.385502i	$0.125972\pi$
$499$			384.731i			0.771004i	−0.922707	+	0.385502i	$0.874028\pi$
$500$	581.676	−	138.770i	1.16335	−	0.277541i
$501$	−38.9751			−0.0777946
$502$	−314.684	+	49.8411i	−0.626861	+	0.0992850i
$503$	−273.130	+	536.048i	−0.543002	+	1.06570i	0.442616	+	0.896711i	$0.354051\pi$
$503$	−273.130	+	536.048i	−0.543002	+	1.06570i	−0.985618	+	0.168990i	$0.945949\pi$
$504$	−25.0095	+	8.12609i	−0.0496221	+	0.0161232i
$505$	−134.661	+	219.513i	−0.266656	+	0.434678i
$506$	26.3661	−	81.1464i	0.0521069	−	0.160368i
$507$	73.8097	−	73.8097i	0.145581	−	0.145581i
$508$	116.153	−	59.1829i	0.228647	−	0.116502i
$509$	−229.621	−	316.046i	−0.451122	−	0.620916i	0.521516	−	0.853241i	$-0.325367\pi$
$509$	−229.621	−	316.046i	−0.451122	−	0.620916i	−0.972638	+	0.232325i	$0.925367\pi$
$510$	−118.655	+	286.072i	−0.232656	+	0.560926i
$511$	−64.2700	−	46.6949i	−0.125773	−	0.0913794i
$512$	105.187	−	664.127i	0.205444	−	1.29712i
$513$	−122.662	−	19.4278i	−0.239107	−	0.0378709i
$514$	−215.822	+	297.053i	−0.419887	+	0.577925i
$515$	−209.446	−	342.150i	−0.406691	−	0.664368i
$516$	−331.576	+	240.904i	−0.642589	+	0.466868i
$517$	−58.1613	−	114.148i	−0.112498	−	0.220789i
$518$	−529.597	−	529.597i	−1.02239	−	1.02239i
$519$	−350.379	−	113.845i	−0.675105	−	0.219355i
$520$	41.1478	−	171.034i	0.0791303	−	0.328912i
$521$	−155.041	−	477.166i	−0.297583	−	0.915865i	−0.982342	−	0.187096i	$-0.940093\pi$
$521$	−155.041	−	477.166i	−0.297583	−	0.915865i	0.684759	−	0.728769i	$-0.259907\pi$
$522$	−254.649	−	129.750i	−0.487833	−	0.248564i
$523$	−52.7905	−	333.306i	−0.100938	−	0.637297i	−0.985344	−	0.170579i	$-0.945436\pi$
$523$	−52.7905	−	333.306i	−0.100938	−	0.637297i	0.884406	−	0.466718i	$-0.154564\pi$
$524$			280.054i			0.534454i
$525$	−115.615	+	115.395i	−0.220219	+	0.219800i
$526$	164.836			0.313377
$527$	449.680	−	71.2224i	0.853283	−	0.135147i
$528$	30.8733	−	60.5922i	0.0584721	−	0.114758i
$529$	426.388	−	138.542i	0.806026	−	0.261894i
$530$	719.838	+	843.635i	1.35819	+	1.59176i
$531$	9.99637	−	30.7656i	0.0188255	−	0.0579391i
$532$	305.000	−	305.000i	0.573309	−	0.573309i
$533$	931.517	−	474.632i	1.74769	−	0.890491i
$534$	151.301	+	208.247i	0.283334	+	0.389976i
$535$	−49.7523	−	207.668i	−0.0929950	−	0.388165i
$536$	14.2699	+	10.3677i	0.0266230	+	0.0193427i
$537$	−69.5020	+	438.818i	−0.129426	+	0.817166i
$538$	85.0872	+	13.4765i	0.158155	+	0.0250492i
$539$	65.5051	−	90.1600i	0.121531	−	0.167273i
$540$	9.81078	−	123.904i	0.0181681	−	0.229452i
$541$	−700.747	+	509.123i	−1.29528	+	0.941077i	−0.999898	−	0.0143018i	$-0.995447\pi$
$541$	−700.747	+	509.123i	−1.29528	+	0.941077i	−0.295384	+	0.955379i	$0.595447\pi$
$542$	−415.296	−	815.065i	−0.766230	−	1.50381i
$543$	147.432	+	147.432i	0.271513	+	0.271513i
$544$	−523.274	−	170.022i	−0.961901	−	0.312541i
$545$	−130.519	+	10.2096i	−0.239485	+	0.0187332i
$546$	90.6096	+	278.868i	0.165952	+	0.510747i
$547$	780.975	+	397.927i	1.42774	+	0.727471i	0.985540	−	0.169444i	$-0.0541971\pi$
$547$	780.975	+	397.927i	1.42774	+	0.727471i	0.442203	+	0.896915i	$0.354197\pi$
$548$	−90.7838	−	573.187i	−0.165664	−	1.04596i
$549$		−	244.668i		−	0.445661i
$550$	−0.225964	+	237.492i	−0.000410844	+	0.431803i
$551$	768.249			1.39428
$552$	35.7024	−	5.65470i	0.0646782	−	0.0102440i
$553$	−210.592	+	413.310i	−0.380817	+	0.747396i
$554$	554.540	−	180.181i	1.00097	−	0.325236i
$555$	536.081	−	221.753i	0.965911	−	0.399555i
$556$	111.052	−	341.784i	0.199734	−	0.614719i
$557$	107.969	−	107.969i	0.193841	−	0.193841i	−0.603513	−	0.797353i	$-0.706233\pi$
$557$	107.969	−	107.969i	0.193841	−	0.193841i	0.797353	+	0.603513i	$0.206233\pi$
$558$	−298.925	+	152.310i	−0.535708	+	0.272957i
$559$	440.212	+	605.899i	0.787498	+	1.08390i
$560$	−175.617	−	150.136i	−0.313603	−	0.268100i
$561$	−54.1939	−	39.3742i	−0.0966023	−	0.0701857i
$562$	−125.903	+	794.919i	−0.224026	+	1.41445i
$563$	−347.620	−	55.0577i	−0.617443	−	0.0977934i	−0.160125	−	0.987097i	$-0.551190\pi$
$563$	−347.620	−	55.0577i	−0.617443	−	0.0977934i	−0.457318	+	0.889303i	$0.651190\pi$
$564$	194.668	−	267.938i	0.345157	−	0.475067i
$565$	614.794	−	719.138i	1.08813	−	1.27281i
$566$	598.455	−	434.803i	1.05734	−	0.768203i
$567$	15.4136	+	30.2510i	0.0271845	+	0.0533527i
$568$	164.058	+	164.058i	0.288835	+	0.288835i
$569$	263.942	+	85.7600i	0.463870	+	0.150721i	0.531622	−	0.846982i	$-0.321583\pi$
$569$	263.942	+	85.7600i	0.463870	+	0.150721i	−0.0677518	+	0.997702i	$0.521583\pi$
$570$	234.491	+	566.873i	0.411387	+	0.994514i
$571$	−15.1133	−	46.5140i	−0.0264682	−	0.0814607i	0.936950	−	0.349464i	$-0.113636\pi$
$571$	−15.1133	−	46.5140i	−0.0264682	−	0.0814607i	−0.963418	+	0.268003i	$0.913636\pi$
$572$	206.873	+	105.407i	0.361666	+	0.184278i
$573$	−76.9441	−	485.806i	−0.134283	−	0.847829i
$574$			771.974i			1.34490i
$575$	181.782	−	131.809i	0.316143	−	0.229232i
$576$	258.442			0.448685
$577$	−334.695	+	53.0106i	−0.580061	+	0.0918727i	−0.439569	−	0.898209i	$-0.644869\pi$
$577$	−334.695	+	53.0106i	−0.580061	+	0.0918727i	−0.140493	+	0.990082i	$0.544869\pi$
$578$	192.959	−	378.703i	0.333839	−	0.655195i
$579$	369.548	−	120.073i	0.638252	−	0.207381i
$580$	59.9605	+	766.532i	0.103380	+	1.32161i
$581$	−91.1145	+	280.422i	−0.156824	+	0.482654i
$582$	218.844	−	218.844i	0.376020	−	0.376020i
$583$	−213.727	+	108.899i	−0.366599	+	0.186791i
$584$	−28.7618	−	39.5872i	−0.0492496	−	0.0677863i
$585$	−226.414	−	17.9276i	−0.387033	−	0.0306454i
$586$	−1204.99	−	875.477i	−2.05630	−	1.49399i
$587$	58.1663	−	367.247i	0.0990907	−	0.625634i	−0.887297	−	0.461198i	$-0.847420\pi$
$587$	58.1663	−	367.247i	0.0990907	−	0.625634i	0.986388	−	0.164436i	$-0.0525804\pi$
$588$	284.555	+	45.0690i	0.483936	+	0.0766480i
$589$	530.080	−	729.592i	0.899966	−	1.23870i
$590$	−155.395	+	37.2287i	−0.263381	+	0.0630996i
$591$	−471.404	+	342.495i	−0.797638	+	0.579518i
$592$	372.528	+	731.126i	0.629270	+	1.23501i
$593$	−357.080	−	357.080i	−0.602158	−	0.602158i	0.338727	−	0.940885i	$-0.390004\pi$
$593$	−357.080	−	357.080i	−0.602158	−	0.602158i	−0.940885	+	0.338727i	$0.890004\pi$
$594$	46.9458	+	15.2536i	0.0790334	+	0.0256795i
$595$	−173.132	+	147.726i	−0.290978	+	0.248279i
$596$	−158.063	−	486.467i	−0.265206	−	0.816220i
$597$	269.436	+	137.285i	0.451317	+	0.229958i
$598$	−63.0525	−	398.098i	−0.105439	−	0.665715i
$599$			618.437i			1.03245i	0.856453	+	0.516225i	$0.172663\pi$
$599$			618.437i			1.03245i	−0.856453	+	0.516225i	$0.827337\pi$
$600$	−89.6921	+	45.5930i	−0.149487	+	0.0759883i
$601$	801.428			1.33349			0.666745	−	0.745286i	$-0.267687\pi$
$601$	801.428			1.33349			0.666745	+	0.745286i	$0.267687\pi$
$602$	−546.205	+	86.5103i	−0.907317	+	0.143705i
$603$	10.3388	−	20.2910i	0.0171456	−	0.0336501i
$604$	1068.83	−	347.284i	1.76958	−	0.574973i
$605$	538.273	+	129.499i	0.889708	+	0.214048i
$606$	81.7033	−	251.457i	0.134824	−	0.414945i
$607$	−541.619	+	541.619i	−0.892288	+	0.892288i	−0.994738	−	0.102450i	$-0.967332\pi$
$607$	−541.619	+	541.619i	−0.892288	+	0.892288i	0.102450	+	0.994738i	$0.467332\pi$
$608$	−971.052	+	494.776i	−1.59712	+	0.813776i
$609$	−123.449	−	169.913i	−0.202708	−	0.279004i
$610$	−1030.78	+	630.987i	−1.68980	+	1.03440i
$611$	−489.612	−	355.724i	−0.801328	−	0.582199i
$612$	27.0903	−	171.042i	0.0442653	−	0.279480i
$613$	409.251	+	64.8189i	0.667619	+	0.105740i	0.481039	−	0.876699i	$-0.340260\pi$
$613$	409.251	+	64.8189i	0.667619	+	0.105740i	0.186580	+	0.982440i	$0.440260\pi$
$614$	560.369	−	771.281i	0.912653	−	1.25616i
$615$	−552.333	−	229.092i	−0.898102	−	0.372507i
$616$	−22.7299	+	16.5143i	−0.0368992	+	0.0268089i
$617$	−334.883	−	657.246i	−0.542761	−	1.06523i	−0.985674	−	0.168664i	$-0.946055\pi$
$617$	−334.883	−	657.246i	−0.542761	−	1.06523i	0.442913	−	0.896565i	$-0.353945\pi$
$618$	291.236	+	291.236i	0.471256	+	0.471256i
$619$	−282.209	−	91.6951i	−0.455910	−	0.148134i	0.0720540	−	0.997401i	$-0.477045\pi$
$619$	−282.209	−	91.6951i	−0.455910	−	0.148134i	−0.527965	+	0.849266i	$0.677045\pi$
$620$	769.334	+	471.952i	1.24086	+	0.761213i
$621$	−14.4218	−	44.3857i	−0.0232235	−	0.0714745i
$622$	220.872	+	112.540i	0.355100	+	0.180932i
$623$	29.5913	+	186.832i	0.0474980	+	0.299891i
$624$		−	321.250i		−	0.514823i
$625$	−368.327	+	504.936i	−0.589324	+	0.807897i
$626$	−1331.01			−2.12621
$627$	−131.054	+	20.7570i	−0.209018	+	0.0331052i
$628$	141.155	−	277.032i	0.224769	−	0.441133i
$629$	768.732	−	249.776i	1.22215	−	0.397100i
$630$	87.6951	−	142.953i	0.139199	−	0.226909i
$631$	−5.38412	+	16.5706i	−0.00853267	+	0.0262609i	−0.955232	−	0.295857i	$-0.904395\pi$
$631$	−5.38412	+	16.5706i	−0.00853267	+	0.0262609i	0.946700	+	0.322118i	$0.104395\pi$
$632$	−202.035	+	202.035i	−0.319675	+	0.319675i
$633$	490.793	−	250.072i	0.775345	−	0.395058i
$634$	197.862	+	272.334i	0.312085	+	0.429549i
$635$	−52.1995	+	125.851i	−0.0822039	+	0.198191i
$636$	−501.679	−	364.491i	−0.788803	−	0.573099i
$637$	82.3560	−	519.976i	0.129287	−	0.816288i
$638$	−301.594	−	47.7678i	−0.472718	−	0.0748711i
$639$	176.072	−	242.343i	0.275544	−	0.379253i
$640$	−190.374	−	310.994i	−0.297459	−	0.485928i
$641$	52.2009	−	37.9262i	0.0814367	−	0.0591672i	−0.546322	−	0.837575i	$-0.683972\pi$
$641$	52.2009	−	37.9262i	0.0814367	−	0.0591672i	0.627759	+	0.778408i	$0.283972\pi$
$642$	99.5344	+	195.347i	0.155038	+	0.304279i
$643$	133.819	+	133.819i	0.208117	+	0.208117i	0.803467	−	0.595350i	$-0.202987\pi$
$643$	133.819	+	133.819i	0.208117	+	0.208117i	−0.595350	+	0.803467i	$0.702987\pi$
$644$	154.159	+	50.0892i	0.239377	+	0.0777782i
$645$	100.196	−	416.472i	0.155342	−	0.645693i
$646$	264.123	+	812.887i	0.408859	+	1.25834i
$647$	1116.71	+	568.992i	1.72598	+	0.879431i	0.975940	+	0.218041i	$0.0699666\pi$
$647$	1116.71	+	568.992i	1.72598	+	0.879431i	0.750042	+	0.661391i	$0.230033\pi$
$648$	3.27143	+	20.6550i	0.00504850	+	0.0318750i
$649$		−	34.5622i		−	0.0532545i
$650$	508.382	+	1000.11i	0.782126	+	1.53863i
$651$	−246.542			−0.378713
$652$	−792.777	+	125.564i	−1.21592	+	0.192582i
$653$	−240.812	+	472.620i	−0.368778	+	0.723768i	−0.998596	−	0.0529751i	$-0.983130\pi$
$653$	−240.812	+	472.620i	−0.368778	+	0.723768i	0.629818	+	0.776743i	$0.283130\pi$
$654$	127.833	−	41.5354i	0.195463	−	0.0635098i
$655$	−189.987	−	222.660i	−0.290056	−	0.339939i
$656$	261.358	−	804.377i	0.398412	−	1.22618i
$657$	−44.6726	+	44.6726i	−0.0679948	+	0.0679948i
$658$	398.169	−	202.877i	0.605120	−	0.308324i
$659$	22.4848	+	30.9477i	0.0341196	+	0.0469615i	0.825736	−	0.564057i	$-0.190760\pi$
$659$	22.4848	+	30.9477i	0.0341196	+	0.0469615i	−0.791616	+	0.611018i	$0.790760\pi$
$660$	−30.9391	−	129.141i	−0.0468775	−	0.195669i
$661$	−756.059	−	549.309i	−1.14381	−	0.831027i	−0.156165	−	0.987731i	$-0.549913\pi$
$661$	−756.059	−	549.309i	−1.14381	−	0.831027i	−0.987646	+	0.156704i	$0.949913\pi$
$662$	266.850	−	1684.82i	0.403096	−	2.54505i
$663$	−312.550	−	49.5030i	−0.471418	−	0.0746652i
$664$	−106.751	+	146.930i	−0.160769	+	0.221280i
$665$	−35.5840	+	449.404i	−0.0535097	+	0.675795i
$666$	−481.863	+	350.094i	−0.723518	+	0.525667i
$667$	131.067	+	257.234i	0.196503	+	0.385659i
$668$	−76.1207	−	76.1207i	−0.113953	−	0.113953i
$669$	406.323	+	132.022i	0.607358	+	0.197343i
$670$	−112.148	+	8.77260i	−0.167386	+	0.0130934i
$671$	−80.7795	−	248.614i	−0.120387	−	0.370512i
$672$	265.467	+	135.262i	0.395040	+	0.201283i
$673$	−8.22955	−	51.9593i	−0.0122282	−	0.0772055i	0.980820	−	0.194918i	$-0.0624440\pi$
$673$	−8.22955	−	51.9593i	−0.0122282	−	0.0772055i	−0.993048	+	0.117712i	$0.962444\pi$
$674$			560.378i			0.831422i
$675$	76.2555	+	105.167i	0.112971	+	0.155803i
$676$	288.309			0.426493
$677$	−180.544	+	28.5953i	−0.266682	+	0.0422383i	−0.288343	−	0.957527i	$-0.593104\pi$
$677$	−180.544	+	28.5953i	−0.266682	+	0.0422383i	0.0216614	+	0.999765i	$0.493104\pi$
$678$	−440.988	+	865.488i	−0.650425	+	1.27653i
$679$	216.304	−	70.2814i	0.318562	−	0.103507i
$680$	−129.540	+	53.5849i	−0.190499	+	0.0788013i
$681$	−14.9533	+	46.0216i	−0.0219579	+	0.0675794i
$682$	−253.459	+	253.459i	−0.371641	+	0.371641i
$683$	−907.556	+	462.423i	−1.32878	+	0.677047i	−0.966895	−	0.255176i	$-0.917866\pi$
$683$	−907.556	+	462.423i	−1.32878	+	0.677047i	−0.361884	+	0.932223i	$0.617866\pi$
$684$	−201.623	−	277.510i	−0.294770	−	0.405716i
$685$	461.024	+	394.132i	0.673028	+	0.575375i
$686$	757.711	+	550.509i	1.10454	+	0.802492i
$687$	26.7997	−	169.207i	0.0390098	−	0.246298i
$688$	598.420	+	94.7805i	0.869797	+	0.137762i
$689$	−666.046	+	916.734i	−0.966685	+	1.33053i
$690$	−149.802	+	175.227i	−0.217104	+	0.253952i
$691$	154.293	−	112.101i	0.223290	−	0.162230i	−0.470516	−	0.882391i	$-0.655932\pi$
$691$	154.293	−	112.101i	0.223290	−	0.162230i	0.693806	+	0.720162i	$0.255932\pi$
$692$	−461.966	−	906.659i	−0.667580	−	1.31020i
$693$	25.6498	+	25.6498i	0.0370128	+	0.0370128i
$694$	1054.36	+	342.583i	1.51925	+	0.493635i
$695$	143.570	+	347.076i	0.206576	+	0.499390i
$696$	−39.9760	−	123.033i	−0.0574367	−	0.176772i
$697$	−742.320	−	378.231i	−1.06502	−	0.542655i
$698$	−72.3636	−	456.886i	−0.103673	−	0.654564i
$699$		−	336.602i		−	0.481548i
$700$	−451.177	−	0.429277i	−0.644538	−	0.000613253i
$701$	171.400			0.244508			0.122254	−	0.992499i	$-0.460988\pi$
$701$	171.400			0.244508			0.122254	+	0.992499i	$0.460988\pi$
$702$	230.312	−	36.4779i	0.328080	−	0.0519628i
$703$	726.865	−	1426.55i	1.03395	−	2.02924i
$704$	262.610	−	85.3272i	0.373026	−	0.121203i
$705$	26.9939	+	345.089i	0.0382892	+	0.489488i
$706$	87.6757	−	269.838i	0.124187	−	0.382207i
$707$	137.389	−	137.389i	0.194326	−	0.194326i
$708$	79.6107	−	40.5637i	0.112444	−	0.0572933i
$709$	−451.404	−	621.304i	−0.636677	−	0.876311i	0.361756	−	0.932273i	$-0.382177\pi$
$709$	−451.404	−	621.304i	−0.636677	−	0.876311i	−0.998433	+	0.0559622i	$0.982177\pi$
$710$	−1475.06	−	116.796i	−2.07755	−	0.164501i
$711$	298.441	+	216.830i	0.419748	+	0.304965i
$712$	−18.2268	+	115.079i	−0.0255994	+	0.161628i
$713$	334.726	+	53.0153i	0.469461	+	0.0743553i
$714$	137.344	−	189.038i	0.192359	−	0.264760i
$715$	−235.984	+	56.5361i	−0.330048	+	0.0790714i
$716$	−992.780	+	721.297i	−1.38656	+	1.00740i
$717$	−97.3309	−	191.023i	−0.135747	−	0.266419i
$718$	−461.459	−	461.459i	−0.642700	−	0.642700i
$719$	−417.040	−	135.505i	−0.580028	−	0.188463i	0.00428501	−	0.999991i	$-0.498636\pi$
$719$	−417.040	−	135.505i	−0.580028	−	0.188463i	−0.584313	+	0.811528i	$0.698636\pi$
$720$	−139.774	+	119.263i	−0.194130	+	0.165643i
$721$	93.5302	+	287.856i	0.129723	+	0.399246i
$722$	555.183	+	282.880i	0.768952	+	0.391801i
$723$	45.5773	+	287.764i	0.0630391	+	0.398013i
$724$			575.885i			0.795422i
$725$	−567.682	−	568.763i	−0.783010	−	0.784501i
$726$	−568.405			−0.782927
$727$	−633.104	+	100.274i	−0.870845	+	0.137928i	−0.575835	−	0.817566i	$-0.695323\pi$
$727$	−633.104	+	100.274i	−0.870845	+	0.137928i	−0.295010	+	0.955494i	$0.595323\pi$
$728$	−60.2551	+	118.257i	−0.0827680	+	0.162441i
$729$	25.6785	−	8.34346i	0.0352243	−	0.0114451i
$730$	303.412	+	72.9955i	0.415633	+	0.0999938i
$731$	184.427	−	567.609i	0.252295	−	0.776483i
$732$	477.852	−	477.852i	0.652803	−	0.652803i
$733$	312.714	−	159.336i	0.426621	−	0.217374i	−0.227478	−	0.973783i	$-0.573048\pi$
$733$	312.714	−	159.336i	0.426621	−	0.217374i	0.654099	+	0.756409i	$0.273048\pi$
$734$	759.890	+	1045.90i	1.03527	+	1.42493i
$735$	−256.813	+	157.207i	−0.349405	+	0.213887i
$736$	−331.334	−	240.728i	−0.450182	−	0.327076i
$737$	3.80625	−	24.0317i	0.00516451	−	0.0326074i
$738$	606.356	+	96.0374i	0.821621	+	0.130132i
$739$	280.598	−	386.210i	0.379699	−	0.522611i	−0.575806	−	0.817587i	$-0.695311\pi$
$739$	280.598	−	386.210i	0.379699	−	0.522611i	0.955505	+	0.294975i	$0.0953115\pi$
$740$	1480.10	+	613.901i	2.00013	+	0.829595i
$741$	−507.102	+	368.431i	−0.684349	+	0.497208i
$742$	−379.861	−	745.520i	−0.511942	−	1.00474i
$743$	955.391	+	955.391i	1.28586	+	1.28586i	0.937281	+	0.348574i	$0.113334\pi$
$743$	955.391	+	955.391i	1.28586	+	1.28586i	0.348574	+	0.937281i	$0.386666\pi$
$744$	−144.425	−	46.9267i	−0.194120	−	0.0630735i
$745$	455.685	+	279.543i	0.611658	+	0.375225i
$746$	197.881	+	609.016i	0.265256	+	0.816375i
$747$	208.926	+	106.453i	0.279686	+	0.142507i
$748$	−28.9438	−	182.744i	−0.0386949	−	0.244310i
$749$			161.115i			0.215106i
$750$	246.405	−	592.482i	0.328540	−	0.789976i
$751$	−170.736			−0.227344			−0.113672	−	0.993518i	$-0.536261\pi$
$751$	−170.736			−0.227344			−0.113672	+	0.993518i	$0.536261\pi$
$752$	−483.568	+	76.5896i	−0.643043	+	0.101848i
$753$	−84.5310	+	165.901i	−0.112259	+	0.220321i
$754$	−1371.88	+	445.750i	−1.81947	+	0.591181i
$755$	−614.190	+	1001.20i	−0.813497	+	1.32609i
$756$	−28.9782	+	89.1857i	−0.0383309	+	0.117970i
$757$	188.024	−	188.024i	0.248381	−	0.248381i	−0.571925	−	0.820306i	$-0.693803\pi$
$757$	188.024	−	188.024i	0.248381	−	0.248381i	0.820306	+	0.571925i	$0.193803\pi$
$758$	504.010	−	256.806i	0.664921	−	0.338794i
$759$	−29.3087	−	40.3399i	−0.0386149	−	0.0531488i
$760$	−106.385	+	256.490i	−0.139980	+	0.337487i
$761$	839.386	+	609.850i	1.10300	+	0.801379i	0.981548	−	0.191217i	$-0.0612436\pi$
$761$	839.386	+	609.850i	1.10300	+	0.801379i	0.121456	+	0.992597i	$0.461244\pi$
$762$	21.8825	−	138.161i	0.0287172	−	0.181313i
$763$	97.5585	+	15.4517i	0.127862	+	0.0202513i
$764$	798.532	−	1099.08i	1.04520	−	1.43859i
$765$	94.4950	+	154.367i	0.123523	+	0.201786i
$766$	1001.98	−	727.981i	1.30807	−	0.950367i
$767$	−74.1233	−	145.475i	−0.0966405	−	0.189668i
$768$	−157.318	−	157.318i	−0.204842	−	0.204842i
$769$	−507.845	−	165.009i	−0.660397	−	0.214576i	−0.0404041	−	0.999183i	$-0.512865\pi$
$769$	−507.845	−	165.009i	−0.660397	−	0.214576i	−0.619993	+	0.784607i	$0.712865\pi$
$770$	41.9121	−	174.211i	0.0544313	−	0.226248i
$771$	66.3092	+	204.079i	0.0860041	+	0.264694i
$772$	956.260	+	487.239i	1.23868	+	0.631138i
$773$	−55.7537	−	352.015i	−0.0721264	−	0.455388i	−0.997148	−	0.0754733i	$-0.975953\pi$
$773$	−55.7537	−	352.015i	−0.0721264	−	0.455388i	0.925021	−	0.379915i	$-0.124047\pi$
$774$			439.786i			0.568198i
$775$	−931.836	+	146.680i	−1.20237	+	0.189264i
$776$	140.089			0.180527
$777$	−432.310	+	68.4712i	−0.556383	+	0.0881225i
$778$	546.857	−	1073.27i	0.702901	−	1.37952i
$779$	−1569.48	+	509.954i	−2.01473	+	0.654627i
$780$	−407.187	−	477.214i	−0.522034	−	0.611812i
$781$	98.9000	−	304.383i	0.126632	−	0.389735i
$782$	−227.120	+	227.120i	−0.290435	+	0.290435i
$783$	−148.818	+	75.8267i	−0.190062	+	0.0968413i
$784$	−250.337	−	344.559i	−0.319308	−	0.439489i
$785$	75.7096	+	316.015i	0.0964454	+	0.402567i
$786$	243.117	+	176.635i	0.309309	+	0.224726i
$787$	−225.398	+	1423.11i	−0.286402	+	1.80827i	0.254379	+	0.967104i	$0.418129\pi$
$787$	−225.398	+	1423.11i	−0.286402	+	1.80827i	−0.540781	+	0.841163i	$0.681871\pi$
$788$	−1589.59	−	251.767i	−2.01725	−	0.319501i
$789$	56.6221	−	77.9336i	0.0717643	−	0.0987751i
$790$	143.832	−	1816.51i	0.182066	−	2.29938i
$791$	−577.493	+	419.574i	−0.730080	+	0.530434i
$792$	10.1436	+	19.9080i	0.0128076	+	0.0251363i
$793$	−873.193	−	873.193i	−1.10113	−	1.10113i
$794$	−1507.58	−	489.841i	−1.89871	−	0.616928i
$795$	646.134	−	50.5425i	0.812747	−	0.0635755i
$796$	258.100	+	794.350i	0.324246	+	0.997927i
$797$	92.9463	+	47.3585i	0.116620	+	0.0594209i	0.511327	−	0.859386i	$-0.329154\pi$
$797$	92.9463	+	47.3585i	0.116620	+	0.0594209i	−0.394707	+	0.918807i	$0.629154\pi$
$798$	−72.4041	−	457.142i	−0.0907320	−	0.572859i
$799$			482.275i			0.603598i
$800$	1083.84	+	353.301i	1.35480	+	0.441627i
$801$	150.431			0.187804
$802$	−828.568	+	131.232i	−1.03313	+	0.163631i
$803$	−30.6439	+	60.1420i	−0.0381618	+	0.0748967i
$804$	59.8219	−	19.4373i	0.0744053	−	0.0241757i
$805$	−156.546	+	64.7561i	−0.194467	+	0.0804424i
$806$	−523.254	+	1610.41i	−0.649198	+	1.99803i
$807$	35.5995	−	35.5995i	0.0441134	−	0.0441134i
$808$	106.633	−	54.3325i	0.131972	−	0.0672431i
$809$	37.0600	+	51.0088i	0.0458097	+	0.0630516i	0.831307	−	0.555813i	$-0.187593\pi$
$809$	37.0600	+	51.0088i	0.0458097	+	0.0630516i	−0.785498	+	0.618865i	$0.787593\pi$
$810$	−101.374	−	86.6652i	−0.125153	−	0.106994i
$811$	432.662	+	314.348i	0.533492	+	0.387605i	0.821662	−	0.569974i	$-0.193047\pi$
$811$	432.662	+	314.348i	0.533492	+	0.387605i	−0.288170	+	0.957579i	$0.593047\pi$
$812$	90.7472	−	572.955i	0.111758	−	0.705610i
$813$	−528.014	−	83.6293i	−0.649464	−	0.102865i
$814$	−374.047	+	514.832i	−0.459517	+	0.632471i
$815$	545.125	−	637.645i	0.668865	−	0.782386i
$816$	−207.110	+	150.474i	−0.253811	+	0.184405i
$817$	−536.696	−	1053.33i	−0.656911	−	1.28926i
$818$	667.544	+	667.544i	0.816069	+	0.816069i
$819$	162.972	+	52.9528i	0.198989	+	0.0646554i
$820$	−631.309	−	1526.17i	−0.769890	−	1.86118i
$821$	−161.216	−	496.172i	−0.196365	−	0.604351i	−0.999958	−	0.00917082i	$-0.997081\pi$
$821$	−161.216	−	496.172i	−0.196365	−	0.604351i	0.803592	−	0.595180i	$-0.202919\pi$
$822$	−554.846	−	282.708i	−0.674995	−	0.343927i
$823$	109.552	+	691.687i	0.133114	+	0.840446i	0.960392	+	0.278653i	$0.0898880\pi$
$823$	109.552	+	691.687i	0.133114	+	0.840446i	−0.827278	+	0.561792i	$0.810112\pi$
$824$			186.430i			0.226250i
$825$	112.207	+	81.6864i	0.136009	+	0.0990139i
$826$	120.559			0.145955
$827$	103.550	−	16.4007i	0.125212	−	0.0198316i	−0.0935141	−	0.995618i	$-0.529810\pi$
$827$	103.550	−	16.4007i	0.125212	−	0.0198316i	0.218726	+	0.975786i	$0.429810\pi$
$828$	58.5213	−	114.854i	0.0706779	−	0.138713i
$829$	186.783	−	60.6896i	0.225312	−	0.0732082i	−0.194186	−	0.980965i	$-0.562206\pi$
$829$	186.783	−	60.6896i	0.225312	−	0.0732082i	0.419497	+	0.907757i	$0.362206\pi$
$830$	−90.3266	−	1154.73i	−0.108827	−	1.39124i
$831$	105.299	−	324.076i	0.126713	−	0.389983i
$832$	922.352	−	922.352i	1.10860	−	1.10860i
$833$	−373.804	+	190.463i	−0.448745	+	0.228647i
$834$	−226.662	−	311.974i	−0.271778	−	0.374070i
$835$	112.160	+	8.88090i	0.134324	+	0.0106358i
$836$	−296.496	−	215.417i	−0.354661	−	0.257676i
$837$	−30.6711	+	193.649i	−0.0366440	+	0.231361i
$838$	1800.91	+	285.237i	2.14906	+	0.340378i
$839$	−479.806	+	660.396i	−0.571878	+	0.787122i	−0.992776	−	0.119986i	$-0.961715\pi$
$839$	−479.806	+	660.396i	−0.571878	+	0.787122i	0.420898	+	0.907108i	$0.361715\pi$
$840$	73.8227	−	17.6861i	0.0878841	−	0.0210549i
$841$	155.499	−	112.977i	0.184898	−	0.134336i
$842$	476.103	+	934.404i	0.565443	+	1.10974i
$843$	332.585	+	332.585i	0.394525	+	0.394525i
$844$	1446.95	+	470.144i	1.71440	+	0.557042i
$845$	−229.224	+	195.587i	−0.271271	+	0.231464i
$846$	−109.818	−	337.986i	−0.129809	−	0.399510i
$847$	−372.175	−	189.633i	−0.439404	−	0.223888i
$848$	143.404	+	905.418i	0.169109	+	1.06771i
$849$		−	432.303i		−	0.509191i
$850$	406.642	−	796.207i	0.478403	−	0.936714i
$851$	601.663			0.707007
$852$	817.190	−	129.430i	0.959143	−	0.151913i
$853$	130.878	−	256.862i	0.153432	−	0.301128i	−0.801477	−	0.598026i	$-0.795952\pi$
$853$	130.878	−	256.862i	0.153432	−	0.301128i	0.954909	+	0.296898i	$0.0959521\pi$
$854$	867.210	−	281.774i	1.01547	−	0.329946i
$855$	348.563	+	83.8580i	0.407676	+	0.0980795i
$856$	−30.6665	+	94.3818i	−0.0358253	+	0.110259i
$857$	−697.530	+	697.530i	−0.813921	+	0.813921i	−0.985219	−	0.171298i	$-0.945204\pi$
$857$	−697.530	+	697.530i	−0.813921	+	0.813921i	0.171298	+	0.985219i	$0.445204\pi$
$858$	221.983	−	113.106i	0.258721	−	0.131825i
$859$	441.134	+	607.170i	0.513544	+	0.706833i	0.984512	−	0.175317i	$-0.0560952\pi$
$859$	441.134	+	607.170i	0.513544	+	0.706833i	−0.470968	+	0.882150i	$0.656095\pi$
$860$	1009.08	−	617.707i	1.17335	−	0.718264i
$861$	364.985	+	265.177i	0.423908	+	0.307987i
$862$	−147.256	+	929.737i	−0.170831	+	1.07858i
$863$	1105.28	+	175.059i	1.28074	+	0.202849i	0.759469	−	0.650544i	$-0.225459\pi$
$863$	1105.28	+	175.059i	1.28074	+	0.202849i	0.521268	+	0.853393i	$0.325459\pi$
$864$	139.269	−	191.687i	0.161191	−	0.221860i
$865$	982.362	+	407.455i	1.13568	+	0.471046i
$866$	134.695	−	97.8614i	0.155537	−	0.113004i
$867$	−112.766	−	221.316i	−0.130065	−	0.255267i
$868$	−481.511	−	481.511i	−0.554736	−	0.554736i
$869$	374.842	+	121.793i	0.431348	+	0.140154i
$870$	703.250	+	431.412i	0.808333	+	0.495876i
$871$	−35.5184	−	109.314i	−0.0407789	−	0.125504i
$872$	54.2091	+	27.6209i	0.0621664	+	0.0316754i
$873$	−28.2941	−	178.642i	−0.0324102	−	0.204630i
$874$			636.222i			0.727943i
$875$	359.005	−	305.734i	0.410291	−	0.349410i
$876$	−174.496			−0.199197
$877$	249.430	−	39.5058i	0.284412	−	0.0450465i	−0.0125983	−	0.999921i	$-0.504010\pi$
$877$	249.430	−	39.5058i	0.284412	−	0.0450465i	0.297011	+	0.954874i	$0.404010\pi$
$878$	473.043	−	928.399i	0.538773	−	1.05740i
$879$	−827.841	+	268.982i	−0.941798	+	0.306009i
$880$	−102.652	+	167.334i	−0.116650	+	0.190152i
$881$	477.436	−	1469.40i	0.541925	−	1.66787i	−0.186265	−	0.982500i	$-0.559638\pi$
$881$	477.436	−	1469.40i	0.541925	−	1.66787i	0.728190	−	0.685375i	$-0.240362\pi$
$882$	218.598	−	218.598i	0.247844	−	0.247844i
$883$	−745.643	+	379.924i	−0.844443	+	0.430265i	−0.822003	−	0.569483i	$-0.807143\pi$
$883$	−745.643	+	379.924i	−0.844443	+	0.430265i	−0.0224398	+	0.999748i	$0.507143\pi$
$884$	−513.746	−	707.111i	−0.581161	−	0.799899i
$885$	−35.7773	+	86.2579i	−0.0404263	+	0.0974665i
$886$	800.560	+	581.641i	0.903567	+	0.656480i
$887$	23.9378	−	151.137i	0.0269874	−	0.170392i	−0.970513	−	0.241047i	$-0.922509\pi$
$887$	23.9378	−	151.137i	0.0269874	−	0.170392i	0.997501	+	0.0706556i	$0.0225091\pi$
$888$	−266.282	−	42.1749i	−0.299867	−	0.0474943i
$889$	60.4216	−	83.1633i	0.0679659	−	0.0935470i
$890$	−387.953	−	633.758i	−0.435902	−	0.712088i
$891$	23.3379	−	16.9560i	0.0261930	−	0.0190303i
$892$	535.725	+	1051.42i	0.600589	+	1.17872i
$893$	675.489	+	675.489i	0.756426	+	0.756426i
$894$	−521.998	−	169.608i	−0.583891	−	0.189718i
$895$	299.998	−	1246.97i	0.335194	−	1.39326i
$896$	85.0134	+	261.644i	0.0948810	+	0.292014i
$897$	−209.877	−	106.938i	−0.233977	−	0.119217i
$898$	254.372	+	1606.04i	0.283266	+	1.78847i
$899$		−	1212.85i		−	1.34911i
$900$	−56.4658	+	354.329i	−0.0627398	+	0.393699i
$901$	902.996			1.00222
$902$	647.842	−	102.608i	0.718229	−	0.113756i
$903$	−146.723	+	287.959i	−0.162483	+	0.318892i
$904$	−418.160	+	135.868i	−0.462566	+	0.150297i
$905$	−390.676	−	457.864i	−0.431687	−	0.505927i
$906$	372.649	−	1146.90i	0.411312	−	1.26589i
$907$	−858.411	+	858.411i	−0.946429	+	0.946429i	−0.998636	−	0.0522074i	$-0.983374\pi$
$907$	−858.411	+	858.411i	−0.946429	+	0.946429i	0.0522074	+	0.998636i	$0.483374\pi$
$908$	−119.088	+	60.6781i	−0.131154	+	0.0668262i
$909$	−90.8218	−	125.006i	−0.0999140	−	0.137520i
$910$	−197.208	−	823.156i	−0.216712	−	0.904567i
$911$	124.673	+	90.5802i	0.136853	+	0.0994295i	0.654106	−	0.756403i	$-0.273045\pi$
$911$	124.673	+	90.5802i	0.136853	+	0.0994295i	−0.517253	+	0.855833i	$0.673045\pi$
$912$	−79.3257	+	500.843i	−0.0869800	+	0.549170i
$913$	247.441	+	39.1908i	0.271020	+	0.0429253i
$914$	−127.695	+	175.757i	−0.139710	+	0.192294i
$915$	−55.7503	+	704.092i	−0.0609293	+	0.769500i
$916$	382.812	−	278.129i	0.417917	−	0.303635i
$917$	100.257	+	196.765i	0.109331	+	0.214574i
$918$	−131.396	−	131.396i	−0.143133	−	0.143133i
$919$	−1262.85	−	410.326i	−1.37416	−	0.446492i	−0.473416	−	0.880839i	$-0.656979\pi$
$919$	−1262.85	−	410.326i	−1.37416	−	0.446492i	−0.900746	+	0.434347i	$0.856979\pi$
$920$	−104.031	+	8.13761i	−0.113077	+	0.00884523i
$921$	−172.168	−	529.878i	−0.186936	−	0.575329i
$922$	−923.163	−	470.375i	−1.00126	−	0.510168i
$923$	−236.512	−	1493.28i	−0.256243	−	1.61785i
$924$			100.191i			0.108432i
$925$	−1593.23	+	515.997i	−1.72241	+	0.557835i
$926$	−2135.70			−2.30637
$927$	237.736	−	37.6537i	0.256457	−	0.0406189i
$928$	−665.417	+	1305.95i	−0.717044	+	1.40728i
$929$	778.256	−	252.871i	0.837736	−	0.272197i	0.141435	−	0.989947i	$-0.454828\pi$
$929$	778.256	−	252.871i	0.837736	−	0.272197i	0.696300	+	0.717751i	$0.254828\pi$
$930$	894.936	−	370.196i	0.962297	−	0.398060i
$931$	−256.794	+	790.330i	−0.275826	+	0.848904i
$932$	657.404	−	657.404i	0.705369	−	0.705369i
$933$	129.079	−	65.7690i	0.138348	−	0.0704919i
$934$	204.191	+	281.045i	0.218620	+	0.300905i
$935$	146.984	+	125.657i	0.157203	+	0.134393i
$936$	85.3907	+	62.0399i	0.0912293	+	0.0662820i
$937$	205.540	−	1297.73i	0.219359	−	1.38498i	−0.594582	−	0.804035i	$-0.702683\pi$
$937$	205.540	−	1297.73i	0.219359	−	1.38498i	0.813942	−	0.580946i	$-0.197317\pi$
$938$	83.8270	+	13.2769i	0.0893678	+	0.0141545i
$939$	−457.207	+	629.292i	−0.486909	+	0.670172i
$940$	−621.258	+	726.700i	−0.660913	+	0.773085i
$941$	−402.969	+	292.774i	−0.428235	+	0.311131i	−0.780943	−	0.624602i	$-0.785261\pi$
$941$	−402.969	+	292.774i	−0.428235	+	0.311131i	0.352708	+	0.935734i	$0.385261\pi$
$942$	−151.464	−	297.266i	−0.160790	−	0.315569i
$943$	−438.511	−	438.511i	−0.465016	−	0.465016i
$944$	−125.620	−	40.8163i	−0.133072	−	0.0432376i
$945$	−37.4635	−	90.5667i	−0.0396439	−	0.0958378i
$946$	145.199	+	446.878i	0.153488	+	0.472386i
$947$	−1170.22	−	596.258i	−1.23572	−	0.629629i	−0.290750	−	0.956799i	$-0.593905\pi$
$947$	−1170.22	−	596.258i	−1.23572	−	0.629629i	−0.944965	+	0.327170i	$0.893905\pi$
$948$	159.391	+	1006.35i	0.168134	+	1.06155i
$949$			318.863i			0.335999i
$950$	−545.636	−	1684.75i	−0.574354	−	1.77342i
$951$	196.725			0.206861
$952$	104.464	−	16.5455i	0.109731	−	0.0173797i
$953$	−244.779	+	480.405i	−0.256851	+	0.504098i	−0.983039	−	0.183398i	$-0.941290\pi$
$953$	−244.779	+	480.405i	−0.256851	+	0.504098i	0.726188	+	0.687496i	$0.241290\pi$
$954$	−632.834	+	205.620i	−0.663348	+	0.215535i
$955$	110.729	+	1415.56i	0.115947	+	1.48226i
$956$	182.986	−	563.172i	0.191408	−	0.589092i
$957$	−126.183	+	126.183i	−0.131853	+	0.131853i
$958$	−2351.16	+	1197.98i	−2.45424	+	1.25050i
$959$	−268.980	−	370.219i	−0.280479	−	0.386047i
$960$	−743.731	−	58.8889i	−0.774720	−	0.0613427i
$961$	−374.360	−	271.988i	−0.389552	−	0.283026i
$962$	−470.269	+	2969.16i	−0.488845	+	3.08645i
$963$	126.550	+	20.0435i	0.131412	+	0.0208136i
$964$	−473.004	+	651.035i	−0.490668	+	0.675347i
$965$	−1090.82	+	261.335i	−1.13039	+	0.270813i
$966$	140.713	−	102.234i	0.145666	−	0.105832i
$967$	751.595	+	1475.09i	0.777244	+	1.52543i	0.849231	+	0.528021i	$0.177066\pi$
$967$	751.595	+	1475.09i	0.777244	+	1.52543i	−0.0719874	+	0.997406i	$0.522934\pi$
$968$	−181.927	−	181.927i	−0.187942	−	0.187942i
$969$	475.056	+	154.355i	0.490254	+	0.159293i
$970$	−679.642	+	579.910i	−0.700662	+	0.597846i
$971$	−496.664	−	1528.58i	−0.511498	−	1.57423i	−0.789565	−	0.613666i	$-0.789694\pi$
$971$	−496.664	−	1528.58i	−0.511498	−	1.57423i	0.278068	−	0.960561i	$-0.410306\pi$
$972$	66.4470	+	33.8564i	0.0683611	+	0.0348317i
$973$	−44.3305	−	279.892i	−0.0455606	−	0.287658i
$974$		−	2349.82i		−	2.41255i
$975$	647.477	+	103.182i	0.664079	+	0.105828i
$976$	−999.008			−1.02357
$977$	914.524	−	144.846i	0.936054	−	0.148256i	0.330271	−	0.943886i	$-0.392860\pi$
$977$	914.524	−	144.846i	0.936054	−	0.148256i	0.605783	+	0.795630i	$0.292860\pi$
$978$	−391.015	+	767.410i	−0.399811	+	0.784673i
$979$	152.857	−	49.6661i	0.156135	−	0.0507315i
$980$	−808.606	−	194.536i	−0.825108	−	0.198506i
$981$	24.2735	−	74.7062i	0.0247437	−	0.0761532i
$982$	−412.580	+	412.580i	−0.420143	+	0.420143i
$983$	−375.845	+	191.503i	−0.382345	+	0.194814i	−0.634590	−	0.772849i	$-0.718831\pi$
$983$	−375.845	+	191.503i	−0.382345	+	0.194814i	0.252245	+	0.967663i	$0.418831\pi$
$984$	163.336	+	224.813i	0.165992	+	0.228468i
$985$	1434.62	−	878.198i	1.45647	−	0.891572i
$986$	929.966	+	675.660i	0.943171	+	0.685254i
$987$	40.8539	−	257.941i	0.0413920	−	0.261339i
$988$	−1709.97	−	270.833i	−1.73074	−	0.274122i
$989$	261.124	−	359.406i	0.264028	−	0.363404i
$990$	−131.622	−	54.5931i	−0.132952	−	0.0551446i
$991$	1493.14	−	1084.83i	1.50670	−	1.09468i	0.539080	−	0.842255i	$-0.318772\pi$
$991$	1493.14	−	1084.83i	1.50670	−	1.09468i	0.967617	−	0.252424i	$-0.0812278\pi$
$992$	781.114	+	1533.02i	0.787414	+	1.54539i
$993$	−704.910	−	704.910i	−0.709880	−	0.709880i
$994$	1061.74	+	344.981i	1.06815	+	0.347064i
$995$	−744.087	−	456.464i	−0.747826	−	0.458758i
$996$	200.135	+	615.953i	0.200939	+	0.618427i
$997$	451.791	+	230.199i	0.453150	+	0.230892i	0.665642	−	0.746271i	$-0.268158\pi$
$997$	451.791	+	230.199i	0.453150	+	0.230892i	−0.212492	+	0.977163i	$0.568158\pi$
$998$	178.376	+	1126.22i	0.178733	+	1.12848i
$999$			348.081i			0.348430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.13.9	✓	80
3.2	odd	2		225.3.r.b.163.2		80
5.2	odd	4		375.3.k.c.82.9		80
5.3	odd	4		375.3.k.b.82.2		80
5.4	even	2		375.3.k.a.43.2		80
25.2	odd	20	inner	75.3.k.a.52.9	yes	80
25.11	even	5		375.3.k.c.343.9		80
25.14	even	10		375.3.k.b.343.2		80
25.23	odd	20		375.3.k.a.157.2		80
75.2	even	20		225.3.r.b.127.2		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.13.9	✓	80	1.1	even	1	trivial
75.3.k.a.52.9	yes	80	25.2	odd	20	inner
225.3.r.b.127.2		80	75.2	even	20
225.3.r.b.163.2		80	3.2	odd	2
375.3.k.a.43.2		80	5.4	even	2
375.3.k.a.157.2		80	25.23	odd	20
375.3.k.b.82.2		80	5.3	odd	4
375.3.k.b.343.2		80	25.14	even	10
375.3.k.c.82.9		80	5.2	odd	4
375.3.k.c.343.9		80	25.11	even	5

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(2.92729 - 0.463638i) q^{2} +(0.786335 - 1.54327i) q^{3} +(4.54985 - 1.47834i) q^{4} +(-2.61452 + 4.26196i) q^{5} +(1.58631 - 4.88217i) q^{6} +(2.66748 - 2.66748i) q^{7} +(2.07035 - 1.05489i) q^{8} +(-1.76336 - 2.42705i) q^{9} +O(q^{10})\)	\(q+(2.92729 - 0.463638i) q^{2} +(0.786335 - 1.54327i) q^{3} +(4.54985 - 1.47834i) q^{4} +(-2.61452 + 4.26196i) q^{5} +(1.58631 - 4.88217i) q^{6} +(2.66748 - 2.66748i) q^{7} +(2.07035 - 1.05489i) q^{8} +(-1.76336 - 2.42705i) q^{9} +(-5.67746 + 13.6882i) q^{10} +(-2.59311 - 1.88400i) q^{11} +(1.29624 - 8.18412i) q^{12} +(-14.9551 - 2.36865i) q^{13} +(6.57174 - 9.04523i) q^{14} +(4.52146 + 7.38623i) q^{15} +(-9.90993 + 7.19998i) q^{16} +(5.47793 + 10.7510i) q^{17} +(-6.28713 - 6.28713i) q^{18} +(22.7308 + 7.38568i) q^{19} +(-5.59508 + 23.2564i) q^{20} +(-2.01910 - 6.21416i) q^{21} +(-8.46427 - 4.31276i) q^{22} +(1.40503 + 8.87104i) q^{23} -4.02460i q^{24} +(-11.3286 - 22.2860i) q^{25} -44.8761 q^{26} +(-5.13218 + 0.812857i) q^{27} +(8.19320 - 16.0801i) q^{28} +(30.5703 - 9.93290i) q^{29} +(16.6602 + 19.5253i) q^{30} +(11.6600 - 35.8856i) q^{31} +(-32.2432 + 32.2432i) q^{32} +(-4.94657 + 2.52040i) q^{33} +(21.0201 + 28.9317i) q^{34} +(4.39450 + 18.3429i) q^{35} +(-11.6110 - 8.43589i) q^{36} +(10.4793 - 66.1635i) q^{37} +(69.9639 + 11.0812i) q^{38} +(-15.4152 + 21.2172i) q^{39} +(-0.917050 + 11.5818i) q^{40} +(-55.8597 + 40.5844i) q^{41} +(-8.79163 - 17.2545i) q^{42} +(-34.9751 - 34.9751i) q^{43} +(-14.5834 - 4.73845i) q^{44} +(14.9543 - 1.16977i) q^{45} +(8.22589 + 25.3167i) q^{46} +(35.6128 + 18.1456i) q^{47} +(3.31899 + 20.9553i) q^{48} +34.7691i q^{49} +(-43.4946 - 59.9851i) q^{50} +20.8992 q^{51} +(-71.5452 + 11.3316i) q^{52} +(33.9753 - 66.6802i) q^{53} +(-14.6465 + 4.75894i) q^{54} +(14.8093 - 6.12594i) q^{55} +(2.70870 - 8.33651i) q^{56} +(29.2721 - 29.2721i) q^{57} +(84.8830 - 43.2501i) q^{58} +(6.33807 + 8.72361i) q^{59} +(31.4913 + 26.9220i) q^{60} +(65.9802 + 47.9374i) q^{61} +(17.4942 - 110.454i) q^{62} +(-11.1778 - 1.77039i) q^{63} +(-50.6362 + 69.6948i) q^{64} +(49.1955 - 57.5451i) q^{65} +(-13.3115 + 9.67137i) q^{66} +(3.44626 + 6.76367i) q^{67} +(40.8174 + 40.8174i) q^{68} +(14.7952 + 4.80726i) q^{69} +(21.3684 + 51.6574i) q^{70} +(30.8556 + 94.9637i) q^{71} +(-6.21104 - 3.16468i) q^{72} +(-3.29433 - 20.7996i) q^{73} -198.539i q^{74} +(-43.3013 - 0.0411995i) q^{75} +114.340 q^{76} +(-11.9426 + 1.89152i) q^{77} +(-35.2877 + 69.2559i) q^{78} +(-116.946 + 37.9981i) q^{79} +(-4.77631 - 61.0602i) q^{80} +(-2.78115 + 8.55951i) q^{81} +(-144.701 + 144.701i) q^{82} +(-69.6419 + 35.4843i) q^{83} +(-18.3733 - 25.2886i) q^{84} +(-60.1426 - 4.76212i) q^{85} +(-118.598 - 86.1665i) q^{86} +(8.70937 - 54.9888i) q^{87} +(-7.35605 - 1.16508i) q^{88} +(-29.4736 + 40.5670i) q^{89} +(43.2333 - 10.3576i) q^{90} +(-46.2107 + 33.5740i) q^{91} +(19.5071 + 38.2848i) q^{92} +(-46.2126 - 46.2126i) q^{93} +(112.662 + 36.6061i) q^{94} +(-90.9076 + 77.5676i) q^{95} +(24.4060 + 75.1139i) q^{96} +(53.7184 + 27.3709i) q^{97} +(16.1203 + 101.779i) q^{98} +9.61576i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

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