LMFDB - Embedded newform 75.3.k.a.58.1

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			58.1
Character	$\chi$	$=$	75.58
Dual form			75.3.k.a.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.41817 - 1.74164i) q^{2} +(-1.71073 - 0.270952i) q^{3} +(6.29941 + 8.67040i) q^{4} +(4.97139 - 0.534117i) q^{5} +(5.37565 + 3.90564i) q^{6} +(-0.908106 + 0.908106i) q^{7} +(-4.03119 - 25.4519i) q^{8} +(2.85317 + 0.927051i) q^{9} +O(q^{10})$	\(q+(-3.41817 - 1.74164i) q^{2} +(-1.71073 - 0.270952i) q^{3} +(6.29941 + 8.67040i) q^{4} +(4.97139 - 0.534117i) q^{5} +(5.37565 + 3.90564i) q^{6} +(-0.908106 + 0.908106i) q^{7} +(-4.03119 - 25.4519i) q^{8} +(2.85317 + 0.927051i) q^{9} +(-17.9233 - 6.83269i) q^{10} +(-3.13702 - 9.65474i) q^{11} +(-8.42731 - 16.5395i) q^{12} +(12.1077 - 6.16920i) q^{13} +(4.68566 - 1.52246i) q^{14} +(-8.64941 - 0.433282i) q^{15} +(-17.3017 + 53.2493i) q^{16} +(4.75437 - 0.753019i) q^{17} +(-8.13802 - 8.13802i) q^{18} +(21.9112 - 30.1582i) q^{19} +(35.9478 + 39.7393i) q^{20} +(1.79957 - 1.30747i) q^{21} +(-6.09227 + 38.4651i) q^{22} +(-4.14703 + 8.13900i) q^{23} +44.6336i q^{24} +(24.4294 - 5.31061i) q^{25} -52.1309 q^{26} +(-4.62981 - 2.35900i) q^{27} +(-13.5942 - 2.15311i) q^{28} +(14.7569 + 20.3112i) q^{29} +(28.8105 + 16.5452i) q^{30} +(-25.2119 - 18.3175i) q^{31} +(78.9952 - 78.9952i) q^{32} +(2.75060 + 17.3666i) q^{33} +(-17.5627 - 5.70648i) q^{34} +(-4.02951 + 4.99958i) q^{35} +(9.93539 + 30.5780i) q^{36} +(-12.6778 - 24.8816i) q^{37} +(-127.421 + 64.9243i) q^{38} +(-22.3846 + 7.27320i) q^{39} +(-33.6349 - 124.378i) q^{40} +(1.61742 - 4.97790i) q^{41} +(-8.42839 + 1.33493i) q^{42} +(44.2149 + 44.2149i) q^{43} +(63.9491 - 88.0184i) q^{44} +(14.6794 + 3.08480i) q^{45} +(28.3505 - 20.5978i) q^{46} +(-0.220758 + 1.39381i) q^{47} +(44.0266 - 86.4070i) q^{48} +47.3507i q^{49} +(-92.7531 - 24.3948i) q^{50} -8.33747 q^{51} +(129.761 + 66.1166i) q^{52} +(28.1049 + 4.45138i) q^{53} +(11.7169 + 16.1269i) q^{54} +(-20.7521 - 46.3220i) q^{55} +(26.7738 + 19.4523i) q^{56} +(-45.6556 + 45.6556i) q^{57} +(-15.0669 - 95.1284i) q^{58} +(-10.4466 - 3.39432i) q^{59} +(-50.7295 - 77.7232i) q^{60} +(-4.02338 - 12.3827i) q^{61} +(54.2760 + 106.523i) q^{62} +(-3.43284 + 1.74912i) q^{63} +(-194.603 + 63.2305i) q^{64} +(56.8972 - 37.1365i) q^{65} +(20.8444 - 64.1525i) q^{66} +(-109.312 + 17.3133i) q^{67} +(36.4787 + 36.4787i) q^{68} +(9.29972 - 12.8000i) q^{69} +(22.4811 - 10.0714i) q^{70} +(-40.2692 + 29.2573i) q^{71} +(12.0936 - 76.3558i) q^{72} +(-33.5940 + 65.9319i) q^{73} +107.130i q^{74} +(-43.2310 + 2.46579i) q^{75} +399.512 q^{76} +(11.6163 + 5.91879i) q^{77} +(89.1816 + 14.1250i) q^{78} +(16.0318 + 22.0658i) q^{79} +(-57.5723 + 273.964i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-14.1983 + 14.1983i) q^{82} +(5.17154 + 32.6518i) q^{83} +(22.6725 + 7.36675i) q^{84} +(23.2336 - 6.28294i) q^{85} +(-74.1274 - 228.141i) q^{86} +(-19.7417 - 38.7453i) q^{87} +(-233.086 + 118.763i) q^{88} +(9.58919 - 3.11572i) q^{89} +(-44.8039 - 36.1106i) q^{90} +(-5.39282 + 16.5974i) q^{91} +(-96.6923 + 15.3145i) q^{92} +(38.1675 + 38.1675i) q^{93} +(3.18211 - 4.37980i) q^{94} +(92.8212 - 161.631i) q^{95} +(-156.543 + 113.735i) q^{96} +(19.1131 - 120.675i) q^{97} +(82.4680 - 161.853i) q^{98} -30.4548i 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 $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	−3.41817	−	1.74164i	−1.70908	−	0.870822i	−0.983090	−	0.183121i	$-0.941380\pi$
$2$	−3.41817	−	1.74164i	−1.70908	−	0.870822i	−0.725994	−	0.687701i	$-0.758620\pi$
$3$	−1.71073	−	0.270952i	−0.570242	−	0.0903175i
$3$	−1.71073	−	0.270952i	−0.570242	−	0.0903175i
$4$	6.29941	+	8.67040i	1.57485	+	2.16760i
$5$	4.97139	−	0.534117i	0.994278	−	0.106823i
$5$	4.97139	−	0.534117i	0.994278	−	0.106823i
$6$	5.37565	+	3.90564i	0.895941	+	0.650940i
$7$	−0.908106	+	0.908106i	−0.129729	+	0.129729i	−0.768990	−	0.639261i	$-0.779240\pi$
$7$	−0.908106	+	0.908106i	−0.129729	+	0.129729i	0.639261	+	0.768990i	$0.279240\pi$
$8$	−4.03119	−	25.4519i	−0.503899	−	3.18149i
$9$	2.85317	+	0.927051i	0.317019	+	0.103006i
$10$	−17.9233	−	6.83269i	−1.79233	−	0.683269i
$11$	−3.13702	−	9.65474i	−0.285183	−	0.877704i	−0.986344	−	0.164700i	$-0.947334\pi$
$11$	−3.13702	−	9.65474i	−0.285183	−	0.877704i	0.701160	−	0.713004i	$-0.252666\pi$
$12$	−8.42731	−	16.5395i	−0.702275	−	1.37829i
$13$	12.1077	−	6.16920i	0.931365	−	0.474554i	0.0786334	−	0.996904i	$-0.474944\pi$
$13$	12.1077	−	6.16920i	0.931365	−	0.474554i	0.852731	+	0.522350i	$0.174944\pi$
$14$	4.68566	−	1.52246i	0.334690	−	0.108747i
$15$	−8.64941	−	0.433282i	−0.576627	−	0.0288854i
$16$	−17.3017	+	53.2493i	−1.08136	+	3.32808i
$17$	4.75437	−	0.753019i	0.279669	−	0.0442952i	−0.0150242	−	0.999887i	$-0.504783\pi$
$17$	4.75437	−	0.753019i	0.279669	−	0.0442952i	0.294693	+	0.955592i	$0.404783\pi$
$18$	−8.13802	−	8.13802i	−0.452112	−	0.452112i
$19$	21.9112	−	30.1582i	1.15322	−	1.58727i	0.419613	−	0.907703i	$-0.362166\pi$
$19$	21.9112	−	30.1582i	1.15322	−	1.58727i	0.733610	−	0.679571i	$-0.237834\pi$
$20$	35.9478	+	39.7393i	1.79739	+	1.98697i
$21$	1.79957	−	1.30747i	0.0856940	−	0.0622603i
$22$	−6.09227	+	38.4651i	−0.276922	+	1.74841i
$23$	−4.14703	+	8.13900i	−0.180306	+	0.353870i	−0.963415	−	0.268014i	$-0.913633\pi$
$23$	−4.14703	+	8.13900i	−0.180306	+	0.353870i	0.783109	+	0.621884i	$0.213633\pi$
$24$			44.6336i			1.85973i
$25$	24.4294	−	5.31061i	0.977177	−	0.212424i
$26$	−52.1309			−2.00503
$27$	−4.62981	−	2.35900i	−0.171474	−	0.0873705i
$28$	−13.5942	−	2.15311i	−0.485506	−	0.0768966i
$29$	14.7569	+	20.3112i	0.508860	+	0.700386i	0.983727	−	0.179672i	$-0.0575037\pi$
$29$	14.7569	+	20.3112i	0.508860	+	0.700386i	−0.474867	+	0.880058i	$0.657504\pi$
$30$	28.8105	+	16.5452i	0.960350	+	0.551507i
$31$	−25.2119	−	18.3175i	−0.813288	−	0.590888i	0.101494	−	0.994836i	$-0.467638\pi$
$31$	−25.2119	−	18.3175i	−0.813288	−	0.590888i	−0.914782	+	0.403948i	$0.867638\pi$
$32$	78.9952	−	78.9952i	2.46860	−	2.46860i
$33$	2.75060	+	17.3666i	0.0833515	+	0.526261i
$34$	−17.5627	−	5.70648i	−0.516551	−	0.167838i
$35$	−4.02951	+	4.99958i	−0.115129	+	0.142845i
$36$	9.93539	+	30.5780i	0.275983	+	0.849389i
$37$	−12.6778	−	24.8816i	−0.342644	−	0.672476i	0.653806	−	0.756662i	$-0.273171\pi$
$37$	−12.6778	−	24.8816i	−0.342644	−	0.672476i	−0.996450	+	0.0841857i	$0.973171\pi$
$38$	−127.421	+	64.9243i	−3.35319	+	1.70853i
$39$	−22.3846	+	7.27320i	−0.573964	+	0.186492i
$40$	−33.6349	−	124.378i	−0.840874	−	3.10946i
$41$	1.61742	−	4.97790i	0.0394492	−	0.121412i	−0.929392	−	0.369093i	$-0.879668\pi$
$41$	1.61742	−	4.97790i	0.0394492	−	0.121412i	0.968842	+	0.247681i	$0.0796684\pi$
$42$	−8.42839	+	1.33493i	−0.200676	+	0.0317839i
$43$	44.2149	+	44.2149i	1.02825	+	1.02825i	0.999589	+	0.0286641i	$0.00912530\pi$
$43$	44.2149	+	44.2149i	1.02825	+	1.02825i	0.0286641	+	0.999589i	$0.490875\pi$
$44$	63.9491	−	88.0184i	1.45339	−	2.00042i
$45$	14.6794	+	3.08480i	0.326208	+	0.0685512i
$46$	28.3505	−	20.5978i	0.616315	−	0.447779i
$47$	−0.220758	+	1.39381i	−0.00469697	+	0.0296555i	−0.989926	−	0.141589i	$-0.954779\pi$
$47$	−0.220758	+	1.39381i	−0.00469697	+	0.0296555i	0.985229	+	0.171245i	$0.0547788\pi$
$48$	44.0266	−	86.4070i	0.917220	−	1.80015i
$49$			47.3507i			0.966341i
$50$	−92.7531	−	24.3948i	−1.85506	−	0.487896i
$51$	−8.33747			−0.163480
$52$	129.761	+	66.1166i	2.49541	+	1.27147i
$53$	28.1049	+	4.45138i	0.530282	+	0.0839884i	0.415833	−	0.909441i	$-0.363490\pi$
$53$	28.1049	+	4.45138i	0.530282	+	0.0839884i	0.114448	+	0.993429i	$0.463490\pi$
$54$	11.7169	+	16.1269i	0.216980	+	0.298647i
$55$	−20.7521	−	46.3220i	−0.377311	−	0.842217i
$56$	26.7738	+	19.4523i	0.478104	+	0.347363i
$57$	−45.6556	+	45.6556i	−0.800975	+	0.800975i
$58$	−15.0669	−	95.1284i	−0.259773	−	1.64014i
$59$	−10.4466	−	3.39432i	−0.177061	−	0.0575308i	0.219145	−	0.975692i	$-0.429673\pi$
$59$	−10.4466	−	3.39432i	−0.177061	−	0.0575308i	−0.396206	+	0.918162i	$0.629673\pi$
$60$	−50.7295	−	77.7232i	−0.845491	−	1.29539i
$61$	−4.02338	−	12.3827i	−0.0659571	−	0.202995i	0.912646	−	0.408750i	$-0.134035\pi$
$61$	−4.02338	−	12.3827i	−0.0659571	−	0.202995i	−0.978604	+	0.205755i	$0.934035\pi$
$62$	54.2760	+	106.523i	0.875419	+	1.71811i
$63$	−3.43284	+	1.74912i	−0.0544895	+	0.0277638i
$64$	−194.603	+	63.2305i	−3.04068	+	0.987976i
$65$	56.8972	−	37.1365i	0.875342	−	0.571330i
$66$	20.8444	−	64.1525i	0.315825	−	0.972008i
$67$	−109.312	+	17.3133i	−1.63152	+	0.258407i	−0.903953	−	0.427633i	$-0.859348\pi$
$67$	−109.312	+	17.3133i	−1.63152	+	0.258407i	−0.727564	+	0.686039i	$0.759348\pi$
$68$	36.4787	+	36.4787i	0.536452	+	0.536452i
$69$	9.29972	−	12.8000i	0.134778	−	0.185507i
$70$	22.4811	−	10.0714i	0.321158	−	0.143878i
$71$	−40.2692	+	29.2573i	−0.567172	+	0.412075i	−0.834077	−	0.551648i	$-0.813999\pi$
$71$	−40.2692	+	29.2573i	−0.567172	+	0.412075i	0.266905	+	0.963723i	$0.413999\pi$
$72$	12.0936	−	76.3558i	0.167966	−	1.06050i
$73$	−33.5940	+	65.9319i	−0.460192	+	0.903177i	0.537993	+	0.842949i	$0.319183\pi$
$73$	−33.5940	+	65.9319i	−0.460192	+	0.903177i	−0.998185	+	0.0602278i	$0.980817\pi$
$74$			107.130i			1.44770i
$75$	−43.2310	+	2.46579i	−0.576413	+	0.0328772i
$76$	399.512			5.25673
$77$	11.6163	+	5.91879i	0.150861	+	0.0768673i
$78$	89.1816	+	14.1250i	1.14335	+	0.181090i
$79$	16.0318	+	22.0658i	0.202934	+	0.279314i	0.898338	−	0.439304i	$-0.144775\pi$
$79$	16.0318	+	22.0658i	0.202934	+	0.279314i	−0.695405	+	0.718618i	$0.744775\pi$
$80$	−57.5723	+	273.964i	−0.719654	+	3.42455i
$81$	7.28115	+	5.29007i	0.0898908	+	0.0653095i
$82$	−14.1983	+	14.1983i	−0.173150	+	0.173150i
$83$	5.17154	+	32.6518i	0.0623077	+	0.393395i	0.999058	+	0.0433967i	$0.0138179\pi$
$83$	5.17154	+	32.6518i	0.0623077	+	0.393395i	−0.936750	+	0.349999i	$0.886182\pi$
$84$	22.6725	+	7.36675i	0.269911	+	0.0876994i
$85$	23.2336	−	6.28294i	0.273337	−	0.0739170i
$86$	−74.1274	−	228.141i	−0.861946	−	2.65280i
$87$	−19.7417	−	38.7453i	−0.226916	−	0.445348i
$88$	−233.086	+	118.763i	−2.64870	+	1.34958i
$89$	9.58919	−	3.11572i	0.107744	−	0.0350080i	−0.254649	−	0.967034i	$-0.581960\pi$
$89$	9.58919	−	3.11572i	0.107744	−	0.0350080i	0.362393	+	0.932026i	$0.381960\pi$
$90$	−44.8039	−	36.1106i	−0.497822	−	0.401229i
$91$	−5.39282	+	16.5974i	−0.0592618	+	0.182389i
$92$	−96.6923	+	15.3145i	−1.05100	+	0.166462i
$93$	38.1675	+	38.1675i	0.410403	+	0.410403i
$94$	3.18211	−	4.37980i	0.0338522	−	0.0465936i
$95$	92.8212	−	161.631i	0.977065	−	1.70138i
$96$	−156.543	+	113.735i	−1.63066	+	1.18474i
$97$	19.1131	−	120.675i	0.197042	−	1.24407i	−0.668681	−	0.743550i	$-0.733141\pi$
$97$	19.1131	−	120.675i	0.197042	−	1.24407i	0.865723	−	0.500524i	$-0.166859\pi$
$98$	82.4680	−	161.853i	0.841511	−	1.65156i
$99$		−	30.4548i		−	0.307624i
$100$	199.936	+	178.359i	1.99936	+	1.78359i
$101$	−165.769			−1.64128			−0.820640	−	0.571445i	$-0.806383\pi$
$101$	−165.769			−1.64128			−0.820640	+	0.571445i	$0.806383\pi$
$102$	28.4989	+	14.5209i	0.279401	+	0.142362i
$103$	18.4972	+	2.92968i	0.179585	+	0.0284435i	0.245579	−	0.969377i	$-0.421022\pi$
$103$	18.4972	+	2.92968i	0.179585	+	0.0284435i	−0.0659942	+	0.997820i	$0.521022\pi$
$104$	−205.827	−	283.296i	−1.97910	−	2.72400i
$105$	8.24804	−	7.46111i	0.0785528	−	0.0710582i
$106$	−88.3147	−	64.1644i	−0.833157	−	0.605324i
$107$	25.5390	−	25.5390i	0.238683	−	0.238683i	−0.577622	−	0.816304i	$-0.696019\pi$
$107$	25.5390	−	25.5390i	0.238683	−	0.238683i	0.816304	+	0.577622i	$0.196019\pi$
$108$	−8.71156	−	55.0026i	−0.0806625	−	0.509283i
$109$	11.1380	+	3.61896i	0.102184	+	0.0332015i	0.359663	−	0.933082i	$-0.382892\pi$
$109$	11.1380	+	3.61896i	0.102184	+	0.0332015i	−0.257479	+	0.966284i	$0.582892\pi$
$110$	−9.74219	+	194.479i	−0.0885654	+	1.76799i
$111$	14.9465	+	46.0007i	0.134654	+	0.414421i
$112$	−32.6442	−	64.0678i	−0.291466	−	0.572034i
$113$	35.9329	−	18.3087i	0.317990	−	0.162024i	−0.287709	−	0.957718i	$-0.592893\pi$
$113$	35.9329	−	18.3087i	0.317990	−	0.162024i	0.605699	+	0.795694i	$0.292893\pi$
$114$	235.574	−	76.5427i	2.06644	−	0.671427i
$115$	−16.2693	+	42.6772i	−0.141472	+	0.371106i
$116$	−83.1460	+	255.897i	−0.716776	+	2.20601i
$117$	40.2646	−	6.37729i	0.344142	−	0.0545067i
$118$	29.7966	+	29.7966i	0.252514	+	0.252514i
$119$	−3.63365	+	5.00130i	−0.0305349	+	0.0420277i
$120$	23.8396	+	221.891i	0.198663	+	1.84909i
$121$	14.5179	−	10.5479i	0.119982	−	0.0871724i
$122$	−7.81366	+	49.3335i	−0.0640464	+	0.404373i
$123$	−4.11573	+	8.07758i	−0.0334612	+	0.0656714i
$124$		−	333.987i		−	2.69344i
$125$	118.612	−	39.4493i	0.948894	−	0.315594i
$126$	14.7804			0.117305
$127$	−61.6992	−	31.4373i	−0.485821	−	0.247538i	0.193883	−	0.981025i	$-0.437892\pi$
$127$	−61.6992	−	31.4373i	−0.485821	−	0.247538i	−0.679704	+	0.733487i	$0.737892\pi$
$128$	333.949	+	52.8924i	2.60898	+	0.413222i
$129$	−63.6594	−	87.6197i	−0.493484	−	0.679223i
$130$	−259.163	+	27.8440i	−1.99356	+	0.214185i
$131$	106.990	+	77.7326i	0.816716	+	0.593379i	0.915770	−	0.401703i	$-0.131582\pi$
$131$	106.990	+	77.7326i	0.816716	+	0.593379i	−0.0990542	+	0.995082i	$0.531582\pi$
$132$	−133.248	+	133.248i	−1.00946	+	1.00946i
$133$	7.48914	+	47.2846i	0.0563093	+	0.355523i
$134$	403.799	+	131.202i	3.01343	+	0.979122i
$135$	−24.2766	−	9.25467i	−0.179826	−	0.0685531i
$136$	−38.3316	−	117.972i	−0.281850	−	0.867445i
$137$	49.4350	+	97.0216i	0.360839	+	0.708187i	0.998045	−	0.0625074i	$-0.0199097\pi$
$137$	49.4350	+	97.0216i	0.360839	+	0.708187i	−0.637205	+	0.770694i	$0.719910\pi$
$138$	−54.0810	+	27.5556i	−0.391891	+	0.199678i
$139$	−102.441	+	33.2852i	−0.736989	+	0.239462i	−0.653373	−	0.757036i	$-0.726647\pi$
$139$	−102.441	+	33.2852i	−0.736989	+	0.239462i	−0.0836155	+	0.996498i	$0.526647\pi$
$140$	−68.7319	−	3.44304i	−0.490942	−	0.0245932i
$141$	0.755312	−	2.32461i	0.00535682	−	0.0164866i
$142$	188.603	−	29.8718i	1.32819	−	0.210365i
$143$	−97.5442	−	97.5442i	−0.682128	−	0.682128i
$144$	−98.7296	+	135.890i	−0.685622	+	0.943678i
$145$	84.2111	+	93.0929i	0.580766	+	0.642020i
$146$	229.660	−	166.858i	1.57301	−	1.14286i
$147$	12.8298	−	81.0041i	0.0872774	−	0.551048i
$148$	135.871	−	266.661i	0.918045	−	1.80177i
$149$			183.635i			1.23245i	0.787571	+	0.616223i	$0.211338\pi$
$149$			183.635i			1.23245i	−0.787571	+	0.616223i	$0.788662\pi$
$150$	152.065	+	66.8645i	1.01377	+	0.445764i
$151$	−170.291			−1.12775			−0.563877	−	0.825858i	$-0.690691\pi$
$151$	−170.291			−1.12775			−0.563877	+	0.825858i	$0.690691\pi$
$152$	−855.913	−	436.110i	−5.63101	−	2.86914i
$153$	14.2631	+	2.25906i	0.0932230	+	0.0147651i
$154$	−29.3980	−	40.4628i	−0.190896	−	0.262746i
$155$	−135.122	−	77.5975i	−0.871755	−	0.500629i
$156$	−204.071	−	148.266i	−1.30815	−	0.950426i
$157$	−183.396	+	183.396i	−1.16813	+	1.16813i	−0.185483	+	0.982648i	$0.559385\pi$
$157$	−183.396	+	183.396i	−1.16813	+	1.16813i	−0.982648	+	0.185483i	$0.940615\pi$
$158$	−16.3685	−	103.346i	−0.103598	−	0.654091i
$159$	−46.8737	−	15.2302i	−0.294803	−	0.0957874i
$160$	350.523	−	434.909i	2.19077	−	2.71818i
$161$	−3.62514	−	11.1570i	−0.0225164	−	0.0692983i
$162$	−15.6748	−	30.7635i	−0.0967580	−	0.189898i
$163$	−28.1861	+	14.3615i	−0.172921	+	0.0881074i	−0.538308	−	0.842748i	$-0.680936\pi$
$163$	−28.1861	+	14.3615i	−0.172921	+	0.0881074i	0.365388	+	0.930855i	$0.380936\pi$
$164$	53.3491	−	17.3342i	0.325300	−	0.105696i
$165$	22.9501	+	84.8670i	0.139092	+	0.514346i
$166$	39.1906	−	120.616i	0.236088	−	0.726605i
$167$	174.554	−	27.6467i	1.04524	−	0.165549i	0.389877	−	0.920867i	$-0.372518\pi$
$167$	174.554	−	27.6467i	1.04524	−	0.165549i	0.655359	+	0.755318i	$0.272518\pi$
$168$	−40.5320	−	40.5320i	−0.241262	−	0.241262i
$169$	9.20266	−	12.6664i	0.0544536	−	0.0749490i
$170$	−90.3592	−	18.9886i	−0.531525	−	0.111698i
$171$	90.4746	−	65.7337i	0.529091	−	0.384407i
$172$	−104.833	+	661.888i	−0.609493	+	3.84819i
$173$	29.5413	−	57.9781i	0.170759	−	0.335133i	−0.789729	−	0.613456i	$-0.789779\pi$
$173$	29.5413	−	57.9781i	0.170759	−	0.335133i	0.960487	+	0.278323i	$0.0897786\pi$
$174$			166.821i			0.958742i
$175$	−17.3619	+	27.0071i	−0.0992110	+	0.154326i
$176$	568.384			3.22945
$177$	16.9516	+	8.63728i	0.0957719	+	0.0487982i
$178$	−38.2039	−	6.05091i	−0.214629	−	0.0339939i
$179$	16.9777	+	23.3679i	0.0948477	+	0.130547i	0.853803	−	0.520596i	$-0.174290\pi$
$179$	16.9777	+	23.3679i	0.0948477	+	0.130547i	−0.758956	+	0.651142i	$0.774290\pi$
$180$	65.7249	+	146.708i	0.365139	+	0.815047i
$181$	207.136	+	150.493i	1.14440	+	0.831455i	0.987726	−	0.156195i	$-0.0499228\pi$
$181$	207.136	+	150.493i	1.14440	+	0.831455i	0.156674	+	0.987650i	$0.449923\pi$
$182$	47.3403	−	47.3403i	0.260112	−	0.260112i
$183$	3.52779	+	22.2736i	0.0192775	+	0.121713i
$184$	223.871	+	72.7401i	1.21669	+	0.395326i
$185$	−76.3161	−	116.925i	−0.412519	−	0.632026i
$186$	−63.9888	−	196.937i	−0.344026	−	1.05880i
$187$	−22.1848	−	43.5400i	−0.118635	−	0.232834i
$188$	−13.4755	+	6.86612i	−0.0716783	+	0.0365219i
$189$	6.34658	−	2.06213i	0.0335798	−	0.0109107i
$190$	−598.783	+	390.822i	−3.15149	+	2.05696i
$191$	−106.510	+	327.805i	−0.557645	+	1.71625i	0.131209	+	0.991355i	$0.458114\pi$
$191$	−106.510	+	327.805i	−0.557645	+	1.71625i	−0.688854	+	0.724900i	$0.741886\pi$
$192$	350.046	−	55.4418i	1.82315	−	0.288759i
$193$	70.5567	+	70.5567i	0.365579	+	0.365579i	0.865862	−	0.500283i	$-0.166771\pi$
$193$	70.5567	+	70.5567i	0.365579	+	0.365579i	−0.500283	+	0.865862i	$0.666771\pi$
$194$	−275.505	+	379.200i	−1.42013	+	1.95464i
$195$	−107.398	+	48.1139i	−0.550758	+	0.246738i
$196$	−410.549	+	298.282i	−2.09464	+	1.52184i
$197$	38.6724	−	244.168i	0.196307	−	1.23943i	−0.670925	−	0.741526i	$-0.734103\pi$
$197$	38.6724	−	244.168i	0.196307	−	1.23943i	0.867231	−	0.497906i	$-0.165897\pi$
$198$	−53.0414	+	104.100i	−0.267886	+	0.525756i
$199$		−	263.966i		−	1.32646i	−0.748414	−	0.663232i	$-0.769184\pi$
$199$		−	263.966i		−	1.32646i	0.748414	−	0.663232i	$-0.230816\pi$
$200$	−233.645	−	600.368i	−1.16823	−	3.00184i
$201$	191.693			0.953698
$202$	566.628	+	288.711i	2.80509	+	1.42926i
$203$	−31.8456	−	5.04384i	−0.156875	−	0.0248465i
$204$	−52.5211	−	72.2891i	−0.257457	−	0.354359i
$205$	5.38203	−	25.6110i	0.0262538	−	0.124932i
$206$	−58.1242	−	42.2297i	−0.282157	−	0.204999i
$207$	−19.3775	+	19.3775i	−0.0936109	+	0.0936109i
$208$	119.021	+	751.466i	0.572214	+	3.61282i
$209$	−359.906	−	116.940i	−1.72204	−	0.559524i
$210$	−41.1878	+	11.1382i	−0.196132	+	0.0530390i
$211$	6.79285	+	20.9062i	0.0321936	+	0.0990817i	0.965862	−	0.259057i	$-0.0834116\pi$
$211$	6.79285	+	20.9062i	0.0321936	+	0.0990817i	−0.933669	+	0.358138i	$0.883412\pi$
$212$	138.449	+	271.722i	0.653063	+	1.28171i
$213$	76.8170	−	39.1402i	0.360643	−	0.183757i
$214$	−131.777	+	42.8168i	−0.615779	+	0.200079i
$215$	243.425	+	196.194i	1.13221	+	0.912528i
$216$	−41.3776	+	127.347i	−0.191563	+	0.589570i
$217$	39.5293	−	6.26083i	0.182163	−	0.0288518i
$218$	−31.7687	−	31.7687i	−0.145728	−	0.145728i
$219$	75.3346	−	103.689i	0.343993	−	0.473466i
$220$	270.904	−	471.730i	1.23138	−	2.14423i
$221$	52.9192	−	38.4481i	0.239453	−	0.173973i
$222$	29.0271	−	183.270i	0.130753	−	0.825540i
$223$	−59.8004	+	117.365i	−0.268163	+	0.526300i	−0.985342	−	0.170589i	$-0.945433\pi$
$223$	−59.8004	+	117.365i	−0.268163	+	0.526300i	0.717179	+	0.696889i	$0.245433\pi$
$224$			143.472i			0.640500i
$225$	74.6245	+	7.49526i	0.331665	+	0.0333123i
$226$	−154.712			−0.684567
$227$	330.788	+	168.545i	1.45721	+	0.742488i	0.989922	−	0.141615i	$-0.0452297\pi$
$227$	330.788	+	168.545i	1.45721	+	0.742488i	0.467292	+	0.884103i	$0.345230\pi$
$228$	−683.455	−	108.249i	−2.99761	−	0.474775i
$229$	23.8773	+	32.8642i	0.104267	+	0.143512i	0.857962	−	0.513713i	$-0.171730\pi$
$229$	23.8773	+	32.8642i	0.104267	+	0.143512i	−0.753695	+	0.657225i	$0.771730\pi$
$230$	129.940	−	117.542i	0.564955	−	0.511054i
$231$	−18.2686	−	13.2729i	−0.0790846	−	0.0574584i
$232$	457.471	−	457.471i	1.97186	−	1.97186i
$233$	−59.2784	−	374.269i	−0.254414	−	1.60630i	−0.702076	−	0.712102i	$-0.747743\pi$
$233$	−59.2784	−	374.269i	−0.254414	−	1.60630i	0.447662	−	0.894203i	$-0.352257\pi$
$234$	−148.738	−	48.3280i	−0.635633	−	0.206530i
$235$	−0.353015	+	7.04708i	−0.00150219	+	0.0299876i
$236$	−36.3776	−	111.959i	−0.154142	−	0.474401i
$237$	−21.4472	−	42.0924i	−0.0904944	−	0.177605i
$238$	21.1309	−	10.7667i	0.0887854	−	0.0452384i
$239$	−104.422	+	33.9288i	−0.436913	+	0.141962i	−0.519211	−	0.854646i	$-0.673774\pi$
$239$	−104.422	+	33.9288i	−0.436913	+	0.141962i	0.0822979	+	0.996608i	$0.473774\pi$
$240$	172.722	−	453.078i	0.719674	−	1.88783i
$241$	70.1908	−	216.025i	0.291248	−	0.896369i	−0.693208	−	0.720738i	$-0.743803\pi$
$241$	70.1908	−	216.025i	0.291248	−	0.896369i	0.984456	−	0.175632i	$-0.0561968\pi$
$242$	−67.9952	+	10.7694i	−0.280972	+	0.0445016i
$243$	−11.0227	−	11.0227i	−0.0453609	−	0.0453609i
$244$	82.0180	−	112.888i	0.336139	−	0.462656i
$245$	25.2908	+	235.399i	0.103228	+	0.960811i
$246$	28.1365	−	20.4424i	0.114376	−	0.0830991i
$247$	79.2433	−	500.323i	0.320823	−	2.02560i
$248$	−364.583	+	715.534i	−1.47009	+	2.88522i
$249$		−	57.2596i		−	0.229958i
$250$	−474.142	−	71.7351i	−1.89657	−	0.286940i
$251$	20.9076			0.0832973			0.0416486	−	0.999132i	$-0.486739\pi$
$251$	20.9076			0.0832973			0.0416486	+	0.999132i	$0.486739\pi$
$252$	−36.7904	−	18.7457i	−0.145994	−	0.0743876i
$253$	91.5893	+	14.5063i	0.362013	+	0.0573372i
$254$	156.146	+	214.916i	0.614747	+	0.846127i
$255$	−41.4488	+	4.45318i	−0.162544	+	0.0174635i
$256$	−387.218	−	281.330i	−1.51257	−	1.09895i
$257$	−59.0918	+	59.0918i	−0.229929	+	0.229929i	−0.812663	−	0.582734i	$-0.801983\pi$
$257$	−59.0918	+	59.0918i	−0.229929	+	0.229929i	0.582734	+	0.812663i	$0.301983\pi$
$258$	64.9964	+	410.371i	0.251924	+	1.59059i
$259$	34.1079	+	11.0823i	0.131691	+	0.0427890i
$260$	680.407	+	259.384i	2.61695	+	0.997630i
$261$	23.2745	+	71.6317i	0.0891745	+	0.274451i
$262$	−230.326	−	452.041i	−0.879109	−	1.72535i
$263$	107.136	−	54.5884i	0.407360	−	0.207560i	−0.238289	−	0.971194i	$-0.576587\pi$
$263$	107.136	−	54.5884i	0.407360	−	0.207560i	0.645650	+	0.763634i	$0.276587\pi$
$264$	430.926	−	140.016i	1.63229	−	0.530364i
$265$	142.098	+	7.11823i	0.536219	+	0.0268613i
$266$	56.7537	−	174.670i	0.213360	−	0.656654i
$267$	−17.2487	+	2.73192i	−0.0646018	+	0.0102319i
$268$	−838.712	−	838.712i	−3.12952	−	3.12952i
$269$	−124.432	+	171.265i	−0.462571	+	0.636674i	−0.975039	−	0.222032i	$-0.928731\pi$
$269$	−124.432	+	171.265i	−0.462571	+	0.636674i	0.512469	+	0.858706i	$0.328731\pi$
$270$	66.8630	+	73.9151i	0.247641	+	0.273760i
$271$	259.546	−	188.571i	0.957734	−	0.695835i	0.00511084	−	0.999987i	$-0.498373\pi$
$271$	259.546	−	188.571i	0.957734	−	0.695835i	0.952623	+	0.304152i	$0.0983732\pi$
$272$	−42.1612	+	266.195i	−0.155004	+	0.978660i
$273$	13.7228	−	26.9324i	0.0502665	−	0.0986535i
$274$		−	417.734i		−	1.52458i
$275$	−127.908	−	219.200i	−0.465120	−	0.797093i
$276$	169.564			0.614361
$277$	241.153	+	122.874i	0.870590	+	0.443588i	0.831420	−	0.555645i	$-0.187529\pi$
$277$	241.153	+	122.874i	0.870590	+	0.443588i	0.0391702	+	0.999233i	$0.487529\pi$
$278$	408.133	+	64.6419i	1.46810	+	0.232525i
$279$	−54.9526	−	75.6358i	−0.196963	−	0.271096i
$280$	143.493	+	82.4047i	0.512474	+	0.294302i
$281$	−244.131	−	177.372i	−0.868795	−	0.631217i	0.0614681	−	0.998109i	$-0.480422\pi$
$281$	−244.131	−	177.372i	−0.868795	−	0.631217i	−0.930263	+	0.366892i	$0.880422\pi$
$282$	−6.63043	+	6.63043i	−0.0235122	+	0.0235122i
$283$	3.69327	+	23.3184i	0.0130504	+	0.0823971i	0.993354	−	0.115100i	$-0.0367188\pi$
$283$	3.69327	+	23.3184i	0.0130504	+	0.0823971i	−0.980304	+	0.197497i	$0.936719\pi$
$284$	−507.345	−	164.846i	−1.78643	−	0.580445i
$285$	−202.586	+	251.357i	−0.710829	+	0.881954i
$286$	163.535	+	503.310i	0.571802	+	1.75983i
$287$	3.05167	+	5.98924i	0.0106330	+	0.0208684i
$288$	298.619	−	152.154i	1.03687	−	0.528313i
$289$	−252.818	+	82.1456i	−0.874804	+	0.284241i
$290$	−125.713	−	464.873i	−0.433493	−	1.60301i
$291$	−65.3945	+	201.263i	−0.224723	+	0.691627i
$292$	−783.279	+	124.059i	−2.68246	+	0.424860i
$293$	−149.257	−	149.257i	−0.509409	−	0.509409i	0.404936	−	0.914345i	$-0.367294\pi$
$293$	−149.257	−	149.257i	−0.509409	−	0.509409i	−0.914345	+	0.404936i	$0.867294\pi$
$294$	−184.935	+	254.541i	−0.629029	+	0.865785i
$295$	−53.7472	−	11.2947i	−0.182194	−	0.0382873i
$296$	−582.179	+	422.978i	−1.96682	+	1.42898i
$297$	−8.25180	+	52.0998i	−0.0277838	+	0.175420i
$298$	319.826	−	627.694i	1.07324	−	2.10636i
$299$			124.129i			0.415147i
$300$	−293.709	−	359.297i	−0.979031	−	1.19766i
$301$	−80.3036			−0.266789
$302$	582.083	+	296.586i	1.92743	+	0.982074i
$303$	283.586	+	44.9156i	0.935927	+	0.148236i
$304$	1226.80	+	1688.55i	4.03553	+	5.55443i
$305$	−26.6156	−	59.4103i	−0.0872644	−	0.194788i
$306$	−44.8193	−	32.5631i	−0.146468	−	0.106415i
$307$	−83.4350	+	83.4350i	−0.271775	+	0.271775i	−0.829815	−	0.558039i	$-0.811554\pi$
$307$	−83.4350	+	83.4350i	−0.271775	+	0.271775i	0.558039	+	0.829815i	$0.311554\pi$
$308$	21.8575	+	138.003i	0.0709658	+	0.448060i
$309$	−30.8499	−	10.0237i	−0.0998379	−	0.0324393i
$310$	326.723	+	500.576i	1.05394	+	1.61476i
$311$	103.858	+	319.642i	0.333949	+	1.02779i	0.967238	+	0.253873i	$0.0817044\pi$
$311$	103.858	+	319.642i	0.333949	+	1.02779i	−0.633289	+	0.773915i	$0.718296\pi$
$312$	275.354	+	540.412i	0.882543	+	1.73209i
$313$	278.606	−	141.957i	0.890116	−	0.453537i	0.0517597	−	0.998660i	$-0.483517\pi$
$313$	278.606	−	141.957i	0.890116	−	0.453537i	0.838356	+	0.545123i	$0.183517\pi$
$314$	946.291	−	307.469i	3.01367	−	0.979200i
$315$	−16.1318	+	10.5291i	−0.0512119	+	0.0334257i
$316$	−90.3288	+	278.004i	−0.285851	+	0.879758i
$317$	−213.755	+	33.8554i	−0.674305	+	0.106799i	−0.484191	−	0.874963i	$-0.660886\pi$
$317$	−213.755	+	33.8554i	−0.674305	+	0.106799i	−0.190114	+	0.981762i	$0.560886\pi$
$318$	133.697	+	133.697i	0.420430	+	0.420430i
$319$	149.806	−	206.191i	0.469613	−	0.646367i
$320$	−933.677	+	418.284i	−2.91774	+	1.30714i
$321$	−50.6102	+	36.7704i	−0.157664	+	0.114550i
$322$	−7.04023	+	44.4503i	−0.0218641	+	0.138044i
$323$	81.4645	−	159.883i	0.252212	−	0.494994i
$324$			96.4548i			0.297700i
$325$	263.023	−	215.010i	0.809302	−	0.661568i
$326$	121.357			0.372262
$327$	−18.0735	−	9.20892i	−0.0552707	−	0.0281618i
$328$	−133.217	−	21.0995i	−0.406150	−	0.0643279i
$329$	−1.06526	−	1.46620i	−0.00323786	−	0.00445653i
$330$	69.3608	−	330.061i	0.210184	−	1.00018i
$331$	493.588	+	358.613i	1.49120	+	1.08342i	0.973725	+	0.227726i	$0.0731292\pi$
$331$	493.588	+	358.613i	1.49120	+	1.08342i	0.517478	+	0.855696i	$0.326871\pi$
$332$	−250.527	+	250.527i	−0.754598	+	0.754598i
$333$	−13.1054	−	82.7445i	−0.0393557	−	0.248482i
$334$	−644.807	−	209.510i	−1.93056	−	0.627277i
$335$	−534.183	+	144.456i	−1.59458	+	0.431213i
$336$	38.4859	+	118.447i	0.114541	+	0.352522i
$337$	−171.644	−	336.871i	−0.509330	−	0.999616i	−0.992286	−	0.123971i	$-0.960437\pi$
$337$	−171.644	−	336.871i	−0.509330	−	0.999616i	0.482956	−	0.875645i	$-0.339563\pi$
$338$	−53.5166	+	27.2681i	−0.158333	+	0.0806747i
$339$	−66.4322	+	21.5851i	−0.195965	+	0.0636729i
$340$	200.834	+	161.866i	0.590688	+	0.476077i
$341$	−97.7608	+	300.877i	−0.286689	+	0.882337i
$342$	−423.742	+	67.1142i	−1.23901	+	0.196240i
$343$	−87.4966	−	87.4966i	−0.255092	−	0.255092i
$344$	947.116	−	1303.59i	2.75324	−	3.78952i
$345$	39.3958	−	68.6007i	0.114191	−	0.198843i
$346$	−201.954	+	146.728i	−0.583683	+	0.424070i
$347$	33.3584	−	210.616i	0.0961336	−	0.606964i	−0.891841	−	0.452349i	$-0.850586\pi$
$347$	33.3584	−	210.616i	0.0961336	−	0.606964i	0.987975	−	0.154615i	$-0.0494138\pi$
$348$	211.576	−	415.241i	0.607977	−	1.19322i
$349$			269.868i			0.773262i	0.922235	+	0.386631i	$0.126361\pi$
$349$			269.868i			0.773262i	−0.922235	+	0.386631i	$0.873639\pi$
$350$	106.383	−	62.0766i	0.303951	−	0.177362i
$351$	−70.6097			−0.201167
$352$	−1010.49	−	514.869i	−2.87070	−	1.46270i
$353$	−564.377	−	89.3886i	−1.59880	−	0.253225i	−0.707527	−	0.706687i	$-0.750189\pi$
$353$	−564.377	−	89.3886i	−1.59880	−	0.253225i	−0.891276	+	0.453461i	$0.850189\pi$
$354$	−42.9004	−	59.0474i	−0.121188	−	0.166801i
$355$	−184.567	+	166.958i	−0.519908	+	0.470304i
$356$	87.4208	+	63.5149i	0.245564	+	0.178413i
$357$	7.57130	−	7.57130i	0.0212081	−	0.0212081i
$358$	−17.3343	−	109.444i	−0.0484198	−	0.305711i
$359$	431.296	+	140.137i	1.20138	+	0.390353i	0.840269	−	0.542170i	$-0.182397\pi$
$359$	431.296	+	140.137i	1.20138	+	0.390353i	0.361113	+	0.932522i	$0.382397\pi$
$360$	19.3389	−	386.054i	0.0537192	−	1.07237i
$361$	−317.861	−	978.275i	−0.880501	−	2.70990i
$362$	−445.921	−	875.170i	−1.23183	−	2.41760i
$363$	−27.6941	+	14.1108i	−0.0762922	+	0.0388728i
$364$	−177.878	+	57.7960i	−0.488675	+	0.158780i
$365$	−131.793	+	345.717i	−0.361078	+	0.947169i
$366$	26.7341	−	82.2790i	0.0730439	−	0.224806i
$367$	−343.962	+	54.4783i	−0.937227	+	0.148442i	−0.606320	−	0.795221i	$-0.707355\pi$
$367$	−343.962	+	54.4783i	−0.937227	+	0.148442i	−0.330907	+	0.943663i	$0.607355\pi$
$368$	−361.645	−	361.645i	−0.982731	−	0.982731i
$369$	9.22953	−	12.7034i	0.0250123	−	0.0344264i
$370$	57.2199	+	532.584i	0.154648	+	1.43942i
$371$	−29.5646	+	21.4799i	−0.0796889	+	0.0578974i
$372$	−90.4946	+	571.360i	−0.243265	+	1.53592i
$373$	−173.420	+	340.355i	−0.464932	+	0.912481i	0.532869	+	0.846198i	$0.321114\pi$
$373$	−173.420	+	340.355i	−0.464932	+	0.912481i	−0.997801	+	0.0662829i	$0.978886\pi$
$374$			187.465i			0.501244i
$375$	−213.601	+	35.3488i	−0.569603	+	0.0942635i
$376$	36.3651			0.0967156
$377$	303.977	+	154.884i	0.806305	+	0.410833i
$378$	−25.2852	−	4.00478i	−0.0668920	−	0.0105946i
$379$	258.810	+	356.221i	0.682875	+	0.939896i	0.999964	−	0.00849932i	$-0.00270545\pi$
$379$	258.810	+	356.221i	0.682875	+	0.939896i	−0.317089	+	0.948396i	$0.602705\pi$
$380$	1986.13	−	213.386i	5.22665	−	0.561542i
$381$	97.0325	+	70.4982i	0.254678	+	0.185035i
$382$	934.989	−	934.989i	2.44761	−	2.44761i
$383$	108.126	+	682.680i	0.282313	+	1.78245i	0.566882	+	0.823799i	$0.308149\pi$
$383$	108.126	+	682.680i	0.282313	+	1.78245i	−0.284569	+	0.958656i	$0.591851\pi$
$384$	−556.965	−	180.969i	−1.45043	−	0.471273i
$385$	60.9103	+	23.2201i	0.158209	+	0.0603121i
$386$	−118.290	−	364.059i	−0.306451	−	0.943159i
$387$	85.1631	+	167.142i	0.220060	+	0.431892i
$388$	1166.70	−	594.465i	3.00697	−	1.53213i
$389$	−485.229	+	157.661i	−1.24738	+	0.405297i	−0.856980	−	0.515350i	$-0.827662\pi$
$389$	−485.229	+	157.661i	−1.24738	+	0.405297i	−0.390396	+	0.920647i	$0.627662\pi$
$390$	450.901	+	22.5873i	1.15616	+	0.0579163i
$391$	−13.5877	+	41.8187i	−0.0347512	+	0.106953i
$392$	1205.17	−	190.880i	3.07441	−	0.486938i
$393$	−161.968	−	161.968i	−0.412133	−	0.412133i
$394$	−557.442	+	767.254i	−1.41483	+	1.94734i
$395$	91.4859	+	101.135i	0.231610	+	0.256038i
$396$	264.055	−	191.847i	0.666806	−	0.484463i
$397$	−108.022	+	682.023i	−0.272095	+	1.71794i	0.351493	+	0.936190i	$0.385674\pi$
$397$	−108.022	+	682.023i	−0.272095	+	1.71794i	−0.623589	+	0.781752i	$0.714326\pi$
$398$	−459.736	+	902.282i	−1.15511	+	2.26704i
$399$		−	82.9201i		−	0.207820i
$400$	−139.886	+	1392.73i	−0.349714	+	3.48183i
$401$	−543.726			−1.35592			−0.677962	−	0.735097i	$-0.737137\pi$
$401$	−543.726			−1.35592			−0.677962	+	0.735097i	$0.737137\pi$
$402$	−655.240	−	333.862i	−1.62995	−	0.830502i
$403$	−418.264	−	66.2465i	−1.03788	−	0.164383i
$404$	−1044.25	−	1437.29i	−2.58478	−	3.55764i
$405$	39.0230	+	22.4100i	0.0963530	+	0.0553333i
$406$	100.069	+	72.7043i	0.246475	+	0.179075i
$407$	−200.455	+	200.455i	−0.492519	+	0.492519i
$408$	33.6099	+	212.205i	0.0823772	+	0.520109i
$409$	73.4788	+	23.8747i	0.179655	+	0.0583734i	0.397463	−	0.917618i	$-0.369891\pi$
$409$	73.4788	+	23.8747i	0.179655	+	0.0583734i	−0.217808	+	0.975992i	$0.569891\pi$
$410$	−63.0019	+	78.1690i	−0.153663	+	0.190656i
$411$	−58.2815	−	179.372i	−0.141804	−	0.436428i
$412$	91.1203	+	178.834i	0.221166	+	0.434062i
$413$	12.5690	−	6.40425i	0.0304335	−	0.0155066i
$414$	99.9840	−	32.4868i	0.241507	−	0.0784705i
$415$	43.1496	+	159.563i	0.103975	+	0.384488i
$416$	469.116	−	1443.79i	1.12768	−	3.47065i
$417$	184.268	−	29.1852i	0.441890	−	0.0699885i
$418$	1026.55	+	1026.55i	2.45586	+	2.45586i
$419$	252.463	−	347.485i	0.602537	−	0.829321i	−0.393401	−	0.919367i	$-0.628702\pi$
$419$	252.463	−	347.485i	0.602537	−	0.829321i	0.995938	+	0.0900464i	$0.0287015\pi$
$420$	116.649	+	24.5132i	0.277735	+	0.0583647i
$421$	−5.32494	+	3.86879i	−0.0126483	+	0.00918954i	−0.594091	−	0.804398i	$-0.702488\pi$
$421$	−5.32494	+	3.86879i	−0.0126483	+	0.00918954i	0.581443	+	0.813587i	$0.302488\pi$
$422$	13.1921	−	83.2918i	0.0312610	−	0.197374i
$423$	−1.92199	+	3.77212i	−0.00454372	+	0.00891754i
$424$		−	733.269i		−	1.72941i
$425$	112.148	−	43.6445i	0.263877	−	0.102693i
$426$	−330.742			−0.776389
$427$	14.8985	+	7.59115i	0.0348910	+	0.0177779i
$428$	382.315	+	60.5527i	0.893258	+	0.141478i
$429$	140.442	+	193.301i	0.327370	+	0.450586i
$430$	−490.370	−	1094.58i	−1.14039	−	2.54554i
$431$	−50.0608	−	36.3713i	−0.116150	−	0.0843881i	0.528194	−	0.849124i	$-0.322869\pi$
$431$	−50.0608	−	36.3713i	−0.116150	−	0.0843881i	−0.644344	+	0.764736i	$0.722869\pi$
$432$	205.719	−	205.719i	0.476201	−	0.476201i
$433$	−11.9351	−	75.3552i	−0.0275637	−	0.174031i	0.970066	−	0.242841i	$-0.0780795\pi$
$433$	−11.9351	−	75.3552i	−0.0275637	−	0.174031i	−0.997630	+	0.0688109i	$0.978079\pi$
$434$	−146.022	−	47.4455i	−0.336456	−	0.109321i
$435$	−118.838	−	182.074i	−0.273192	−	0.418560i
$436$	38.7851	+	119.368i	0.0889567	+	0.273781i
$437$	154.591	+	303.403i	0.353756	+	0.694285i
$438$	−438.096	+	223.221i	−1.00022	+	0.509637i
$439$	667.652	−	216.933i	1.52085	−	0.494154i	0.574832	−	0.818272i	$-0.305067\pi$
$439$	667.652	−	216.933i	1.52085	−	0.494154i	0.946017	+	0.324118i	$0.105067\pi$
$440$	−1095.33	+	714.914i	−2.48938	+	1.62480i
$441$	−43.8965	+	135.100i	−0.0995386	+	0.306348i
$442$	−247.850	+	39.2555i	−0.560746	+	0.0888134i
$443$	33.0475	+	33.0475i	0.0745992	+	0.0745992i	0.743422	−	0.668823i	$-0.233201\pi$
$443$	33.0475	+	33.0475i	0.0745992	+	0.0745992i	−0.668823	+	0.743422i	$0.733201\pi$
$444$	−304.690	+	419.370i	−0.686239	+	0.944527i
$445$	46.0074	−	20.6112i	0.103388	−	0.0463173i
$446$	408.816	−	297.022i	0.916627	−	0.665969i
$447$	49.7562	−	314.148i	0.111311	−	0.702793i
$448$	119.301	−	234.140i	0.266296	−	0.522635i
$449$		−	866.360i		−	1.92953i	−0.263110	−	0.964766i	$-0.584748\pi$
$449$		−	866.360i		−	1.92953i	0.263110	−	0.964766i	$-0.415252\pi$
$450$	−242.025	−	155.589i	−0.537834	−	0.345754i
$451$	−53.1342			−0.117814
$452$	385.100	+	196.218i	0.851992	+	0.434112i
$453$	291.321	+	46.1408i	0.643093	+	0.101856i
$454$	−837.143	−	1152.23i	−1.84393	−	2.53795i
$455$	−17.9449	+	85.3926i	−0.0394393	+	0.187676i
$456$	1346.07	+	977.976i	2.95190	+	2.14468i
$457$	−264.460	+	264.460i	−0.578686	+	0.578686i	−0.934541	−	0.355855i	$-0.884190\pi$
$457$	−264.460	+	264.460i	−0.578686	+	0.578686i	0.355855	+	0.934541i	$0.384190\pi$
$458$	−24.3787	−	153.921i	−0.0532286	−	0.336072i
$459$	−23.7882	−	7.72926i	−0.0518262	−	0.0168393i
$460$	−472.515	+	127.780i	−1.02721	+	0.277782i
$461$	−119.674	−	368.320i	−0.259597	−	0.798959i	−0.992889	−	0.119044i	$-0.962017\pi$
$461$	−119.674	−	368.320i	−0.259597	−	0.798959i	0.733291	−	0.679914i	$-0.237983\pi$
$462$	39.3284	+	77.1863i	0.0851263	+	0.167070i
$463$	−487.456	+	248.371i	−1.05282	+	0.536439i	−0.892697	−	0.450658i	$-0.851190\pi$
$463$	−487.456	+	248.371i	−1.05282	+	0.536439i	−0.160124	+	0.987097i	$0.551190\pi$
$464$	−1336.88	+	434.377i	−2.88120	+	0.936158i
$465$	210.132	+	169.360i	0.451896	+	0.364214i
$466$	−449.220	+	1382.56i	−0.963991	+	2.96686i
$467$	388.108	−	61.4702i	0.831066	−	0.131628i	0.273616	−	0.961839i	$-0.411780\pi$
$467$	388.108	−	61.4702i	0.831066	−	0.131628i	0.557449	+	0.830211i	$0.311780\pi$
$468$	308.937	+	308.937i	0.660122	+	0.660122i
$469$	83.5443	−	114.989i	0.178133	−	0.245179i
$470$	13.4802	−	23.4733i	0.0286812	−	0.0499432i
$471$	363.433	−	264.049i	0.771620	−	0.560615i
$472$	−44.2795	+	279.570i	−0.0938126	+	0.592309i
$473$	288.181	−	565.586i	0.609261	−	1.19574i
$474$			181.232i			0.382347i
$475$	375.120	−	853.110i	0.789727	−	1.79602i
$476$	−66.2531			−0.139187
$477$	76.0615	+	38.7553i	0.159458	+	0.0812479i
$478$	416.025	+	65.8918i	0.870345	+	0.137849i
$479$	431.041	+	593.277i	0.899877	+	1.23857i	0.970507	+	0.241072i	$0.0774991\pi$
$479$	431.041	+	593.277i	0.899877	+	1.23857i	−0.0706298	+	0.997503i	$0.522501\pi$
$480$	−717.489	+	649.035i	−1.49477	+	1.35216i
$481$	−307.000	−	223.048i	−0.638253	−	0.463718i
$482$	−616.163	+	616.163i	−1.27835	+	1.27835i
$483$	3.17859	+	20.0688i	0.00658094	+	0.0415504i
$484$	182.908	+	59.4305i	0.377910	+	0.122790i
$485$	30.5638	−	610.132i	0.0630182	−	1.25800i
$486$	18.4798	+	56.8751i	0.0380244	+	0.117027i
$487$	124.926	+	245.181i	0.256522	+	0.503452i	0.982969	−	0.183770i	$-0.0588300\pi$
$487$	124.926	+	245.181i	0.256522	+	0.503452i	−0.726448	+	0.687222i	$0.758830\pi$
$488$	−298.945	+	152.320i	−0.612592	+	0.312131i
$489$	52.1099	−	16.9315i	0.106564	−	0.0346248i
$490$	323.532	−	848.680i	0.660270	−	1.73200i
$491$	275.506	−	847.921i	0.561112	−	1.72693i	−0.118117	−	0.993000i	$-0.537686\pi$
$491$	275.506	−	847.921i	0.561112	−	1.72693i	0.679229	−	0.733926i	$-0.262314\pi$
$492$	−95.9625	+	15.1990i	−0.195046	+	0.0308922i
$493$	85.4547	+	85.4547i	0.173336	+	0.173336i
$494$	−1142.25	+	1572.17i	−2.31225	+	3.18254i
$495$	−16.2664	−	151.403i	−0.0328615	−	0.305864i
$496$	1411.60	−	1025.59i	2.84598	−	2.06772i
$497$	9.99999	−	63.1375i	0.0201207	−	0.127037i
$498$	−99.7258	+	195.723i	−0.200253	+	0.393018i
$499$			97.2778i			0.194946i	0.995238	+	0.0974728i	$0.0310759\pi$
$499$			97.2778i			0.194946i	−0.995238	+	0.0974728i	$0.968924\pi$
$500$	1089.23	+	779.904i	2.17845	+	1.55981i
$501$	−306.106			−0.610989
$502$	−71.4658	−	36.4136i	−0.142362	−	0.0725371i
$503$	429.301	+	67.9946i	0.853481	+	0.135178i	0.567820	−	0.823153i	$-0.307787\pi$
$503$	429.301	+	67.9946i	0.853481	+	0.135178i	0.285661	+	0.958331i	$0.407787\pi$
$504$	58.3569	+	80.3214i	0.115788	+	0.159368i
$505$	−824.104	+	88.5403i	−1.63189	+	0.175327i
$506$	−287.803	−	209.101i	−0.568780	−	0.413243i
$507$	−19.1752	+	19.1752i	−0.0378210	+	0.0378210i
$508$	−116.095	−	732.993i	−0.228533	−	1.44290i
$509$	371.361	+	120.663i	0.729590	+	0.237058i	0.650176	−	0.759783i	$-0.274695\pi$
$509$	371.361	+	120.663i	0.729590	+	0.237058i	0.0794141	+	0.996842i	$0.474695\pi$
$510$	149.435	+	56.9673i	0.293009	+	0.111701i
$511$	−29.3663	−	90.3801i	−0.0574682	−	0.176869i
$512$	219.600	+	430.989i	0.428906	+	0.841775i
$513$	−172.588	+	87.9380i	−0.336429	+	0.171419i
$514$	304.903	−	99.0689i	0.593196	−	0.192741i
$515$	93.5218	+	4.68486i	0.181596	+	0.00909682i
$516$	358.681	−	1103.91i	0.695117	−	2.13935i
$517$	14.1494	−	2.24104i	0.0273683	−	0.00433471i
$518$	−97.2852	−	97.2852i	−0.187809	−	0.187809i
$519$	−66.2464	+	91.1803i	−0.127642	+	0.175685i
$520$	−1174.56	−	1298.44i	−2.25877	−	2.49700i
$521$	529.499	−	384.703i	1.01631	−	0.738394i	0.0507886	−	0.998709i	$-0.483827\pi$
$521$	529.499	−	384.703i	1.01631	−	0.738394i	0.965524	+	0.260315i	$0.0838265\pi$
$522$	45.2006	−	285.385i	0.0865911	−	0.546715i
$523$	−343.324	+	673.811i	−0.656451	+	1.28836i	0.287345	+	0.957827i	$0.407227\pi$
$523$	−343.324	+	673.811i	−0.656451	+	1.28836i	−0.943796	+	0.330530i	$0.892773\pi$
$524$			1417.31i			2.70480i
$525$	37.0191	−	41.4975i	0.0705126	−	0.0790429i
$526$	−461.282			−0.876962
$527$	−133.660	−	68.1033i	−0.253625	−	0.129228i
$528$	−972.349	−	154.005i	−1.84157	−	0.291676i
$529$	261.893	+	360.465i	0.495072	+	0.681408i
$530$	−473.318	−	271.816i	−0.893053	−	0.512860i
$531$	−26.6593	−	19.3691i	−0.0502058	−	0.0364767i
$532$	−362.799	+	362.799i	−0.681953	+	0.681953i
$533$	−11.1264	−	70.2493i	−0.0208750	−	0.131800i
$534$	63.7170	+	20.7029i	0.119320	+	0.0387695i
$535$	113.324	−	140.605i	0.211820	−	0.262814i
$536$	881.312	+	2712.40i	1.64424	+	5.06045i
$537$	−22.7127	−	44.5762i	−0.0422955	−	0.0830096i
$538$	723.611	−	368.698i	1.34500	−	0.685313i
$539$	457.159	−	148.540i	0.848161	−	0.275584i
$540$	−72.6864	−	268.786i	−0.134604	−	0.497753i
$541$	130.100	−	400.408i	0.240481	−	0.740125i	−0.755866	−	0.654727i	$-0.772784\pi$
$541$	130.100	−	400.408i	0.240481	−	0.740125i	0.996347	−	0.0853983i	$-0.0272163\pi$
$542$	−1215.60	+	192.531i	−2.24280	+	0.355224i
$543$	−313.577	−	313.577i	−0.577490	−	0.577490i
$544$	316.088	−	435.058i	0.581044	−	0.799738i
$545$	57.3044	+	12.0423i	0.105146	+	0.0220959i
$546$	−93.8134	+	68.1594i	−0.171819	+	0.124834i
$547$	89.0873	−	562.475i	0.162865	−	1.02829i	−0.761884	−	0.647714i	$-0.775725\pi$
$547$	89.0873	−	562.475i	0.162865	−	1.02829i	0.924749	−	0.380577i	$-0.124275\pi$
$548$	−529.804	+	1039.80i	−0.966796	+	1.89744i
$549$		−	39.0598i		−	0.0711472i
$550$	55.4424	+	972.035i	0.100804	+	1.76734i
$551$	935.892			1.69853
$552$	−363.273	−	185.097i	−0.658103	−	0.335320i
$553$	−34.5967	−	5.47957i	−0.0625618	−	0.00990881i
$554$	−610.301	−	840.007i	−1.10163	−	1.51626i
$555$	98.8749	+	220.704i	0.178153	+	0.397665i
$556$	−933.917	−	678.531i	−1.67971	−	1.22038i
$557$	−618.517	+	618.517i	−1.11044	+	1.11044i	−0.117353	+	0.993090i	$0.537441\pi$
$557$	−618.517	+	618.517i	−1.11044	+	1.11044i	−0.993090	+	0.117353i	$0.962559\pi$
$558$	56.1067	+	354.244i	0.100550	+	0.634845i
$559$	808.113	+	262.572i	1.44564	+	0.469717i
$560$	−196.507	−	301.070i	−0.350905	−	0.537625i
$561$	26.1548	+	80.4961i	0.0466217	+	0.143487i
$562$	525.564	+	1031.48i	0.935167	+	1.83537i
$563$	−548.413	+	279.430i	−0.974090	+	0.496324i	−0.867207	−	0.497948i	$-0.834087\pi$
$563$	−548.413	+	279.430i	−0.974090	+	0.496324i	−0.106883	+	0.994272i	$0.534087\pi$
$564$	24.9133	−	8.09483i	0.0441726	−	0.0143525i
$565$	168.858	−	110.212i	0.298863	−	0.195066i
$566$	27.9881	−	86.1385i	0.0494489	−	0.152188i
$567$	−11.4160	+	1.80812i	−0.0201340	+	0.00318892i
$568$	906.988	+	906.988i	1.59681	+	1.59681i
$569$	311.038	−	428.106i	0.546639	−	0.752384i	−0.442912	−	0.896565i	$-0.646055\pi$
$569$	311.038	−	428.106i	0.546639	−	0.752384i	0.989551	+	0.144181i	$0.0460547\pi$
$570$	1130.25	−	506.348i	1.98289	−	0.888329i
$571$	−655.845	+	476.500i	−1.14859	+	0.834500i	−0.988293	−	0.152568i	$-0.951246\pi$
$571$	−655.845	+	476.500i	−1.14859	+	0.834500i	−0.160298	+	0.987069i	$0.551246\pi$
$572$	231.276	−	1460.22i	0.404329	−	2.55283i
$573$	271.029	−	531.925i	0.473000	−	0.928316i
$574$		−	25.7872i		−	0.0449254i
$575$	−58.0865	+	220.855i	−0.101020	+	0.384095i
$576$	−613.854			−1.06572
$577$	2.72643	+	1.38919i	0.00472518	+	0.00240760i	0.456351	−	0.889800i	$-0.349156\pi$
$577$	2.72643	+	1.38919i	0.00472518	+	0.00240760i	−0.451626	+	0.892207i	$0.649156\pi$
$578$	1007.24	+	159.532i	1.74264	+	0.276007i
$579$	−101.586	−	139.821i	−0.175450	−	0.241486i
$580$	−276.672	+	1316.57i	−0.477021	+	2.26995i
$581$	−34.3476	−	24.9550i	−0.0591181	−	0.0429518i
$582$	574.059	−	574.059i	0.986355	−	0.986355i
$583$	−45.1886	−	285.310i	−0.0775105	−	0.489382i
$584$	1813.52	+	589.248i	3.10534	+	1.00899i
$585$	196.765	−	53.2100i	0.336350	−	0.0909573i
$586$	250.233	+	770.137i	0.427018	+	1.31423i
$587$	−138.928	−	272.661i	−0.236674	−	0.464500i	0.741868	−	0.670546i	$-0.233940\pi$
$587$	−138.928	−	272.661i	−0.236674	−	0.464500i	−0.978542	+	0.206046i	$0.933940\pi$
$588$	783.158	−	399.039i	1.33190	−	0.678637i
$589$	−1104.85	+	358.987i	−1.87580	+	0.609485i
$590$	164.046	+	132.216i	0.278043	+	0.224095i
$591$	−132.316	+	407.226i	−0.223885	+	0.689046i
$592$	1544.28	−	244.589i	2.60857	−	0.413158i
$593$	445.026	+	445.026i	0.750466	+	0.750466i	0.974566	−	0.224100i	$-0.0719443\pi$
$593$	445.026	+	445.026i	0.750466	+	0.750466i	−0.224100	+	0.974566i	$0.571944\pi$
$594$	118.945	−	163.714i	0.200245	−	0.275613i
$595$	−15.3930	+	26.8042i	−0.0258706	+	0.0450491i
$596$	−1592.18	+	1156.79i	−2.67145	+	1.94092i
$597$	−71.5224	+	451.574i	−0.119803	+	0.756406i
$598$	216.188	−	424.293i	0.361519	−	0.709521i
$599$		−	416.676i		−	0.695619i	−0.937565	−	0.347810i	$-0.886926\pi$
$599$		−	416.676i		−	0.695619i	0.937565	−	0.347810i	$-0.113074\pi$
$600$	237.031	+	1090.37i	0.395052	+	1.81729i
$601$	−341.539			−0.568284			−0.284142	−	0.958782i	$-0.591709\pi$
$601$	−341.539			−0.568284			−0.284142	+	0.958782i	$0.591709\pi$
$602$	274.491	+	139.860i	0.455965	+	0.232326i
$603$	−327.935	−	51.9398i	−0.543839	−	0.0861356i
$604$	−1072.73	−	1476.49i	−1.77605	−	2.44452i
$605$	66.5402	−	60.1918i	0.109984	−	0.0994905i
$606$	−891.118	−	647.435i	−1.47049	−	1.06837i
$607$	−596.304	+	596.304i	−0.982378	+	0.982378i	−0.999847	−	0.0174693i	$-0.994439\pi$
$607$	−596.304	+	596.304i	−0.982378	+	0.982378i	0.0174693	+	0.999847i	$0.494439\pi$
$608$	−651.473	−	4113.24i	−1.07150	−	6.76519i
$609$	53.1124	+	17.2573i	0.0872125	+	0.0283371i
$610$	−12.4949	+	249.429i	−0.0204834	+	0.408901i
$611$	5.92582	+	18.2378i	0.00969855	+	0.0298491i
$612$	70.2624	+	137.898i	0.114808	+	0.225323i
$613$	316.032	−	161.027i	0.515550	−	0.262686i	−0.176801	−	0.984247i	$-0.556575\pi$
$613$	316.032	−	161.027i	0.515550	−	0.262686i	0.692351	+	0.721561i	$0.256575\pi$
$614$	430.509	−	139.881i	0.701155	−	0.227819i
$615$	−16.1465	+	42.3551i	−0.0262545	+	0.0688700i
$616$	103.817	−	319.516i	0.168534	−	0.518695i
$617$	−560.242	+	88.7336i	−0.908009	+	0.143815i	−0.592933	−	0.805252i	$-0.702030\pi$
$617$	−560.242	+	88.7336i	−0.908009	+	0.143815i	−0.315076	+	0.949066i	$0.602030\pi$
$618$	87.9924	+	87.9924i	0.142383	+	0.142383i
$619$	26.0328	−	35.8310i	0.0420562	−	0.0578853i	−0.787471	−	0.616352i	$-0.788610\pi$
$619$	26.0328	−	35.8310i	0.0420562	−	0.0578853i	0.829527	+	0.558466i	$0.188610\pi$
$620$	−178.388	−	1660.38i	−0.287723	−	2.67803i
$621$	38.3999	−	27.8991i	0.0618356	−	0.0449262i
$622$	201.698	−	1273.47i	0.324274	−	2.04739i
$623$	−5.87860	+	11.5374i	−0.00943595	+	0.0185191i
$624$		−	1317.80i		−	2.11186i
$625$	568.595	−	259.470i	0.909752	−	0.415153i
$626$	−1199.56			−1.91623
$627$	584.015	+	297.570i	0.931443	+	0.474594i
$628$	−2745.41	−	434.830i	−4.37167	−	0.692405i
$629$	−79.0114	−	108.750i	−0.125614	−	0.172893i
$630$	73.4790	−	7.89445i	0.116633	−	0.0125309i
$631$	164.100	+	119.226i	0.260064	+	0.188947i	0.710175	−	0.704025i	$-0.248616\pi$
$631$	164.100	+	119.226i	0.260064	+	0.188947i	−0.450111	+	0.892972i	$0.648616\pi$
$632$	496.991	−	496.991i	0.786378	−	0.786378i
$633$	−5.95611	−	37.6054i	−0.00940934	−	0.0594082i
$634$	789.613	+	256.561i	1.24545	+	0.404670i
$635$	−323.522	−	123.333i	−0.509484	−	0.194225i
$636$	−163.225	−	502.355i	−0.256643	−	0.789867i
$637$	292.116	+	573.310i	0.458581	+	0.900016i
$638$	−871.175	+	443.886i	−1.36548	+	0.695746i
$639$	−142.018	+	46.1444i	−0.222250	+	0.0722135i
$640$	1688.44	+	84.5806i	2.63819	+	0.132157i
$641$	−242.522	+	746.406i	−0.378349	+	1.16444i	0.562842	+	0.826565i	$0.309708\pi$
$641$	−242.522	+	746.406i	−0.378349	+	1.16444i	−0.941191	+	0.337875i	$0.890292\pi$
$642$	237.035	−	37.5427i	0.369214	−	0.0584777i
$643$	464.369	+	464.369i	0.722192	+	0.722192i	0.969051	−	0.246860i	$-0.0793987\pi$
$643$	464.369	+	464.369i	0.722192	+	0.722192i	−0.246860	+	0.969051i	$0.579399\pi$
$644$	73.8996	−	101.714i	0.114751	−	0.157941i
$645$	−363.275	−	401.590i	−0.563217	−	0.622620i
$646$	−556.919	+	404.625i	−0.862103	+	0.626354i
$647$	117.380	−	741.107i	0.181422	−	1.14545i	−0.713971	−	0.700175i	$-0.753105\pi$
$647$	117.380	−	741.107i	0.181422	−	1.14545i	0.895393	−	0.445277i	$-0.146895\pi$
$648$	105.291	−	206.645i	0.162486	−	0.318896i
$649$			111.508i			0.171814i
$650$	−1273.53	+	276.847i	−1.95927	+	0.425918i
$651$	−69.3203			−0.106483
$652$	−302.076	−	153.915i	−0.463306	−	0.236066i
$653$	600.278	+	95.0747i	0.919262	+	0.145597i	0.598094	−	0.801426i	$-0.295925\pi$
$653$	600.278	+	95.0747i	0.919262	+	0.145597i	0.321167	+	0.947022i	$0.395925\pi$
$654$	45.7397	+	62.9553i	0.0699384	+	0.0962619i
$655$	573.406	+	329.294i	0.875429	+	0.502739i
$656$	237.085	+	172.253i	0.361411	+	0.262580i
$657$	−156.972	+	156.972i	−0.238922	+	0.238922i
$658$	1.08763	+	6.86701i	0.00165293	+	0.0104362i
$659$	−834.555	−	271.163i	−1.26640	−	0.411477i	−0.402627	−	0.915364i	$-0.631903\pi$
$659$	−834.555	−	271.163i	−1.26640	−	0.411477i	−0.863770	+	0.503887i	$0.831903\pi$
$660$	−591.259	+	733.599i	−0.895846	+	1.11151i
$661$	−100.534	−	309.412i	−0.152094	−	0.468097i	0.845761	−	0.533562i	$-0.179147\pi$
$661$	−100.534	−	309.412i	−0.152094	−	0.468097i	−0.997855	+	0.0654650i	$0.979147\pi$
$662$	−1062.59	−	2085.45i	−1.60512	−	3.15023i
$663$	−100.948	+	51.4355i	−0.152259	+	0.0775800i
$664$	810.204	−	263.251i	1.22019	−	0.396463i
$665$	62.4869	+	231.070i	0.0939653	+	0.347474i
$666$	−99.3148	+	305.660i	−0.149121	+	0.458948i
$667$	−226.510	+	35.8757i	−0.339596	+	0.0537867i
$668$	1339.30	+	1339.30i	2.00494	+	2.00494i
$669$	134.102	−	184.576i	0.200452	−	0.275899i
$670$	2077.52	+	436.582i	3.10078	+	0.651614i
$671$	−106.930	+	77.6895i	−0.159360	+	0.115782i
$672$	38.8741	−	245.441i	0.0578484	−	0.365240i
$673$	−56.2794	+	110.455i	−0.0836247	+	0.164123i	−0.929032	−	0.370000i	$-0.879358\pi$
$673$	−56.2794	+	110.455i	−0.0836247	+	0.164123i	0.845407	+	0.534122i	$0.179358\pi$
$674$			1450.42i			2.15196i
$675$	−125.631	−	33.0420i	−0.186120	−	0.0489512i
$676$	167.794			0.248216
$677$	−472.731	−	240.869i	−0.698274	−	0.355788i	0.0685486	−	0.997648i	$-0.478163\pi$
$677$	−472.731	−	240.869i	−0.698274	−	0.355788i	−0.766822	+	0.641860i	$0.778163\pi$
$678$	264.670	+	41.9196i	0.390369	+	0.0618283i
$679$	92.2291	+	126.943i	0.135831	+	0.186955i
$680$	−253.572	−	566.014i	−0.372901	−	0.832373i
$681$	−520.219	−	377.961i	−0.763905	−	0.555010i
$682$	858.184	−	858.184i	1.25833	−	1.25833i
$683$	71.2918	+	450.118i	0.104380	+	0.659031i	0.983290	+	0.182044i	$0.0582713\pi$
$683$	71.2918	+	450.118i	0.104380	+	0.659031i	−0.878910	+	0.476988i	$0.841729\pi$
$684$	1139.87	+	370.368i	1.66648	+	0.541473i
$685$	297.581	+	455.928i	0.434425	+	0.665588i
$686$	146.690	+	451.466i	0.213834	+	0.658114i
$687$	−31.9428	−	62.6913i	−0.0464961	−	0.0912537i
$688$	−3119.40	+	1589.42i	−4.53402	+	2.31020i
$689$	367.749	−	119.489i	0.533743	−	0.173424i
$690$	−254.140	+	165.875i	−0.368318	+	0.240399i
$691$	219.479	−	675.486i	0.317625	−	0.977549i	−0.657036	−	0.753860i	$-0.728190\pi$
$691$	219.479	−	675.486i	0.317625	−	0.977549i	0.974660	−	0.223689i	$-0.0718101\pi$
$692$	688.786	−	109.093i	0.995355	−	0.157649i
$693$	27.6562	+	27.6562i	0.0399079	+	0.0399079i
$694$	−480.843	+	661.824i	−0.692858	+	0.953637i
$695$	−491.498	+	220.190i	−0.707192	+	0.316820i
$696$	−906.560	+	658.655i	−1.30253	+	0.946343i
$697$	3.94136	−	24.8847i	0.00565474	−	0.0357026i
$698$	470.015	−	922.456i	0.673374	−	1.32157i
$699$			656.333i			0.938961i
$700$	−343.532	+	19.5942i	−0.490760	+	0.0279917i
$701$	1196.82			1.70731			0.853653	−	0.520842i	$-0.174382\pi$
$701$	1196.82			1.70731			0.853653	+	0.520842i	$0.174382\pi$
$702$	241.356	+	122.977i	0.343812	+	0.175181i
$703$	−1028.17	−	162.846i	−1.46255	−	0.231645i
$704$	1220.95	+	1680.49i	1.73430	+	2.38706i
$705$	2.51334	−	11.9600i	0.00356502	−	0.0169645i
$706$	1773.45	+	1288.49i	2.51197	+	1.82506i
$707$	150.536	−	150.536i	0.212922	−	0.212922i
$708$	31.8966	+	201.387i	0.0450517	+	0.284445i
$709$	−488.417	−	158.696i	−0.688882	−	0.223831i	−0.0564020	−	0.998408i	$-0.517963\pi$
$709$	−488.417	−	158.696i	−0.688882	−	0.223831i	−0.632480	+	0.774577i	$0.717963\pi$
$710$	921.663	−	249.240i	1.29812	−	0.351043i
$711$	25.2852	+	77.8198i	0.0355629	+	0.109451i
$712$	−117.957	−	231.503i	−0.165670	−	0.325145i
$713$	253.641	−	129.237i	0.355738	−	0.181257i
$714$	−39.0665	+	12.6935i	−0.0547150	+	0.0177780i
$715$	−537.031	−	432.830i	−0.751092	−	0.605357i
$716$	−95.6588	+	294.408i	−0.133602	+	0.411184i
$717$	187.831	−	29.7495i	0.261968	−	0.0414916i
$718$	−1230.17	−	1230.17i	−1.71334	−	1.71334i
$719$	−22.5681	+	31.0624i	−0.0313882	+	0.0432022i	−0.824423	−	0.565975i	$-0.808500\pi$
$719$	−22.5681	+	31.0624i	−0.0313882	+	0.0432022i	0.793034	+	0.609177i	$0.208500\pi$
$720$	−418.242	+	728.293i	−0.580892	+	1.01152i
$721$	−19.4579	+	14.1370i	−0.0269874	+	0.0196075i
$722$	−617.305	+	3897.51i	−0.854993	+	5.39821i
$723$	−178.610	+	350.541i	−0.247040	+	0.484843i
$724$			2743.98i			3.79002i
$725$	468.368	+	417.822i	0.646026	+	0.576307i
$726$	119.239			0.164241
$727$	−513.724	−	261.756i	−0.706636	−	0.360049i	0.0634537	−	0.997985i	$-0.479788\pi$
$727$	−513.724	−	261.756i	−0.706636	−	0.360049i	−0.770089	+	0.637936i	$0.779788\pi$
$728$	444.176	+	70.3505i	0.610131	+	0.0966353i
$729$	15.8702	+	21.8435i	0.0217698	+	0.0299636i
$730$	1052.61	−	952.180i	1.44193	−	1.30436i
$731$	243.509	+	176.919i	0.333117	+	0.242024i
$732$	−170.898	+	170.898i	−0.233467	+	0.233467i
$733$	−105.900	−	668.625i	−0.144475	−	0.912177i	−0.948315	−	0.317331i	$-0.897213\pi$
$733$	−105.900	−	668.625i	−0.144475	−	0.912177i	0.803840	−	0.594845i	$-0.202787\pi$
$734$	1270.60	+	412.844i	1.73107	+	0.562458i
$735$	20.5162	−	409.555i	0.0279132	−	0.557218i
$736$	315.347	+	970.538i	0.428460	+	1.31867i
$737$	510.067	+	1001.06i	0.692086	+	1.35830i
$738$	−53.6728	+	27.3477i	−0.0727274	+	0.0370565i
$739$	323.253	−	105.031i	0.437420	−	0.142126i	−0.0820250	−	0.996630i	$-0.526139\pi$
$739$	323.253	−	105.031i	0.437420	−	0.142126i	0.519445	+	0.854504i	$0.326139\pi$
$740$	533.038	−	1398.25i	0.720322	−	1.88952i
$741$	−271.127	+	834.444i	−0.365894	+	1.12611i
$742$	138.467	−	21.9310i	0.186613	−	0.0295566i
$743$	−434.284	−	434.284i	−0.584500	−	0.584500i	0.351636	−	0.936137i	$-0.385625\pi$
$743$	−434.284	−	434.284i	−0.584500	−	0.584500i	−0.936137	+	0.351636i	$0.885625\pi$
$744$	817.577	−	1125.30i	1.09889	−	1.51250i
$745$	98.0824	+	912.919i	0.131654	+	1.22539i
$746$	1185.56	−	861.357i	1.58922	−	1.15463i
$747$	−15.5146	+	97.9554i	−0.0207692	+	0.131132i
$748$	237.758	−	466.627i	0.317859	−	0.623833i
$749$			46.3843i			0.0619283i
$750$	791.690	+	251.189i	1.05559	+	0.334919i
$751$	−642.946			−0.856119			−0.428060	−	0.903750i	$-0.640803\pi$
$751$	−642.946			−0.856119			−0.428060	+	0.903750i	$0.640803\pi$
$752$	−70.3998	−	35.8705i	−0.0936168	−	0.0477002i
$753$	−35.7672	−	5.66497i	−0.0474996	−	0.00752320i
$754$	−769.292	−	1058.84i	−1.02028	−	1.40430i
$755$	−846.583	+	90.9554i	−1.12130	+	0.120471i
$756$	57.8592	+	42.0372i	0.0765333	+	0.0556047i
$757$	532.967	−	532.967i	0.704051	−	0.704051i	−0.261227	−	0.965278i	$-0.584127\pi$
$757$	532.967	−	532.967i	0.704051	−	0.704051i	0.965278	+	0.261227i	$0.0841270\pi$
$758$	−264.245	−	1668.38i	−0.348608	−	2.20102i
$759$	−152.754	−	49.6327i	−0.201257	−	0.0653922i
$760$	−4488.01	−	1710.91i	−5.90528	−	2.25120i
$761$	−17.4603	−	53.7374i	−0.0229439	−	0.0706142i	0.938929	−	0.344111i	$-0.111820\pi$
$761$	−17.4603	−	53.7374i	−0.0229439	−	0.0706142i	−0.961873	+	0.273497i	$0.911820\pi$
$762$	−208.891	−	409.971i	−0.274135	−	0.538019i
$763$	−13.4009	+	6.82810i	−0.0175634	+	0.00894901i
$764$	−3513.15	+	1141.49i	−4.59836	+	1.49410i
$765$	72.1141	+	3.61247i	0.0942669	+	0.00472218i
$766$	819.393	−	2521.83i	1.06970	−	3.29221i
$767$	−147.425	+	23.3499i	−0.192210	+	0.0304431i
$768$	586.197	+	586.197i	0.763277	+	0.763277i
$769$	20.1659	−	27.7560i	0.0262235	−	0.0360936i	−0.795704	−	0.605686i	$-0.792899\pi$
$769$	20.1659	−	27.7560i	0.0262235	−	0.0360936i	0.821927	+	0.569592i	$0.192899\pi$
$770$	−167.761	−	185.454i	−0.217871	−	0.240850i
$771$	117.101	−	85.0789i	0.151882	−	0.110349i
$772$	−167.289	+	1056.22i	−0.216695	+	1.36816i
$773$	32.6778	−	64.1339i	0.0422740	−	0.0829675i	−0.868903	−	0.494982i	$-0.835175\pi$
$773$	32.6778	−	64.1339i	0.0422740	−	0.0829675i	0.911177	+	0.412014i	$0.135175\pi$
$774$		−	719.643i		−	0.929772i
$775$	−713.190	−	313.596i	−0.920245	−	0.404640i
$776$	−3148.47			−4.05730
$777$	−55.3466	−	28.2005i	−0.0712311	−	0.0362941i
$778$	1933.18	+	306.186i	2.48481	+	0.393556i
$779$	−114.685	−	157.850i	−0.147221	−	0.202632i
$780$	−1093.71	−	628.092i	−1.40219	−	0.805247i
$781$	408.797	+	297.008i	0.523428	+	0.380292i
$782$	119.278	−	119.278i	0.152530	−	0.152530i
$783$	−20.4076	−	128.849i	−0.0260633	−	0.164557i
$784$	−2521.39	−	819.249i	−3.21606	−	1.04496i
$785$	−813.780	+	1009.69i	−1.03666	+	1.28623i
$786$	271.544	+	835.726i	0.345476	+	1.06327i
$787$	−464.136	−	910.917i	−0.589753	−	1.15746i	−0.972347	−	0.233539i	$-0.924969\pi$
$787$	−464.136	−	910.917i	−0.589753	−	1.15746i	0.382595	−	0.923916i	$-0.375031\pi$
$788$	2360.65	−	1202.81i	2.99574	−	1.52641i
$789$	−198.071	+	64.3571i	−0.251040	+	0.0815680i
$790$	−136.573	−	505.032i	−0.172877	−	0.639282i
$791$	−16.0046	+	49.2572i	−0.0202334	+	0.0622720i
$792$	−775.133	+	122.769i	−0.978704	+	0.155011i
$793$	−125.106	−	125.106i	−0.157762	−	0.157762i
$794$	1557.08	−	2143.14i	1.96106	−	2.69916i
$795$	−241.162	−	50.6792i	−0.303349	−	0.0637474i
$796$	2288.69	−	1662.83i	2.87524	−	2.08899i
$797$	−44.7823	+	282.744i	−0.0561886	+	0.354761i	0.943535	+	0.331271i	$0.107478\pi$
$797$	−44.7823	+	282.744i	−0.0561886	+	0.354761i	−0.999724	+	0.0234894i	$0.992522\pi$
$798$	−144.417	+	283.435i	−0.180974	+	0.355182i
$799$			6.79293i			0.00850179i
$800$	1510.30	−	2349.32i	1.88787	−	2.93665i
$801$	30.2480			0.0377628
$802$	1858.55	+	946.977i	2.31739	+	1.18077i
$803$	741.941	+	117.512i	0.923961	+	0.146341i
$804$	1207.56	+	1662.06i	1.50193	+	2.06724i
$805$	−23.9811	−	53.5296i	−0.0297902	−	0.0664965i
$806$	1314.32	+	954.909i	1.63067	+	1.18475i
$807$	259.273	−	259.273i	0.321280	−	0.321280i
$808$	668.248	+	4219.15i	0.827039	+	5.22172i
$809$	−1277.45	−	415.070i	−1.57905	−	0.513065i	−0.617241	−	0.786774i	$-0.711749\pi$
$809$	−1277.45	−	415.070i	−1.57905	−	0.513065i	−0.961813	+	0.273709i	$0.911749\pi$
$810$	−94.3568	−	144.565i	−0.116490	−	0.178476i
$811$	175.799	+	541.053i	0.216768	+	0.667143i	0.999023	+	0.0441855i	$0.0140693\pi$
$811$	175.799	+	541.053i	0.216768	+	0.667143i	−0.782255	+	0.622958i	$0.785931\pi$
$812$	−156.876	−	307.887i	−0.193197	−	0.379171i
$813$	−495.106	+	252.269i	−0.608986	+	0.310294i
$814$	1034.31	−	336.068i	1.27065	−	0.412860i
$815$	−132.453	+	86.4514i	−0.162519	+	0.106075i
$816$	144.253	−	443.964i	0.176780	−	0.544073i
$817$	2302.24	−	364.640i	2.81792	−	0.446315i
$818$	−209.582	−	209.582i	−0.256212	−	0.256212i
$819$	−30.7733	+	42.3558i	−0.0375742	+	0.0517165i
$820$	255.961	−	114.670i	0.312147	−	0.139841i
$821$	697.733	−	506.933i	0.849857	−	0.617458i	−0.0752493	−	0.997165i	$-0.523975\pi$
$821$	697.733	−	506.933i	0.849857	−	0.617458i	0.925107	+	0.379707i	$0.123975\pi$
$822$	−113.186	+	714.629i	−0.137696	+	0.869378i
$823$	581.981	−	1142.20i	0.707146	−	1.38785i	−0.205319	−	0.978695i	$-0.565823\pi$
$823$	581.981	−	1142.20i	0.707146	−	1.38785i	0.912464	−	0.409156i	$-0.134177\pi$
$824$		−	482.601i		−	0.585681i
$825$	159.423	+	409.649i	0.193240	+	0.496544i
$826$	−54.1170			−0.0655170
$827$	−810.049	−	412.740i	−0.979502	−	0.499081i	−0.110493	−	0.993877i	$-0.535243\pi$
$827$	−810.049	−	412.740i	−0.979502	−	0.499081i	−0.869009	+	0.494795i	$0.835243\pi$
$828$	−290.077	−	45.9436i	−0.350334	−	0.0554875i
$829$	463.220	+	637.567i	0.558769	+	0.769080i	0.991169	−	0.132602i	$-0.0423332\pi$
$829$	463.220	+	637.567i	0.558769	+	0.769080i	−0.432400	+	0.901682i	$0.642333\pi$
$830$	130.409	−	620.563i	0.157119	−	0.747667i
$831$	−379.255	−	275.545i	−0.456383	−	0.331582i
$832$	−1966.13	+	1966.13i	−2.36313	+	2.36313i
$833$	35.6560	+	225.123i	0.0428043	+	0.270256i
$834$	−680.689	−	221.169i	−0.816174	−	0.265191i
$835$	853.011	−	230.675i	1.02157	−	0.276257i
$836$	−1253.27	−	3857.18i	−1.49913	−	4.61385i
$837$	73.5152	+	144.282i	0.0878317	+	0.172379i
$838$	−1468.16	+	748.063i	−1.75198	+	0.892677i
$839$	−833.993	+	270.981i	−0.994032	+	0.322981i	−0.760478	−	0.649363i	$-0.775035\pi$
$839$	−833.993	+	270.981i	−0.994032	+	0.322981i	−0.233554	+	0.972344i	$0.575035\pi$
$840$	−223.149	−	179.852i	−0.265654	−	0.214109i
$841$	65.1064	−	200.377i	0.0774154	−	0.238260i
$842$	24.9396	−	3.95004i	0.0296195	−	0.00469126i
$843$	369.583	+	369.583i	0.438414	+	0.438414i
$844$	−138.474	+	190.594i	−0.164069	+	0.225822i
$845$	38.9847	−	67.8848i	0.0461357	−	0.0803371i
$846$	13.1394	−	9.54632i	0.0155312	−	0.0112841i
$847$	−3.60520	+	22.7623i	−0.00425643	+	0.0268741i
$848$	−723.297	+	1419.55i	−0.852944	+	1.67400i
$849$		−	40.8921i		−	0.0481650i
$850$	−459.353	−	46.1372i	−0.540415	−	0.0542791i
$851$	255.087			0.299750
$852$	823.263	+	419.473i	0.966271	+	0.492340i
$853$	595.371	+	94.2976i	0.697974	+	0.110548i	0.495331	−	0.868705i	$-0.335047\pi$
$853$	595.371	+	94.2976i	0.697974	+	0.110548i	0.202643	+	0.979253i	$0.435047\pi$
$854$	−37.7044	−	51.8956i	−0.0441503	−	0.0607677i
$855$	414.675	−	375.112i	0.485000	−	0.438727i
$856$	−752.971	−	547.065i	−0.879639	−	0.639095i
$857$	1089.99	−	1089.99i	1.27186	−	1.27186i	0.326756	−	0.945109i	$-0.394044\pi$
$857$	1089.99	−	1089.99i	1.27186	−	1.27186i	0.945109	−	0.326756i	$-0.105956\pi$
$858$	−143.391	−	905.336i	−0.167123	−	1.05517i
$859$	−990.040	−	321.684i	−1.15255	−	0.374486i	−0.330447	−	0.943825i	$-0.607199\pi$
$859$	−990.040	−	321.684i	−1.15255	−	0.374486i	−0.822103	+	0.569338i	$0.807199\pi$
$860$	−167.639	+	3346.50i	−0.194929	+	3.89128i
$861$	−3.59778	−	11.0728i	−0.00417860	−	0.0128604i
$862$	107.770	+	211.511i	0.125024	+	0.245373i
$863$	−608.476	+	310.034i	−0.705070	+	0.359251i	−0.769479	−	0.638672i	$-0.779484\pi$
$863$	−608.476	+	310.034i	−0.705070	+	0.359251i	0.0644086	+	0.997924i	$0.479484\pi$
$864$	−552.082	+	179.382i	−0.638984	+	0.207619i
$865$	115.894	−	304.010i	0.133982	−	0.351457i
$866$	−90.4458	+	278.364i	−0.104441	+	0.321436i
$867$	454.760	−	72.0270i	0.524522	−	0.0830761i
$868$	303.296	+	303.296i	0.349419	+	0.349419i
$869$	162.748	−	224.003i	0.187282	−	0.257772i
$870$	89.1020	+	829.332i	0.102416	+	0.953256i
$871$	−1216.71	+	883.990i	−1.39691	+	1.01491i
$872$	47.2101	−	298.073i	0.0541400	−	0.341827i
$873$	166.405	−	326.588i	0.190613	−	0.374098i
$874$		−	1306.32i		−	1.49465i
$875$	−71.8879	+	143.536i	−0.0821576	+	0.164041i
$876$	1373.59			1.56802
$877$	−456.767	−	232.734i	−0.520829	−	0.265376i	0.173753	−	0.984789i	$-0.444411\pi$
$877$	−456.767	−	232.734i	−0.520829	−	0.265376i	−0.694582	+	0.719414i	$0.744411\pi$
$878$	−2659.97	−	421.298i	−3.02958	−	0.479838i
$879$	214.896	+	295.779i	0.244478	+	0.336495i
$880$	2825.66	−	303.584i	3.21097	−	0.344981i
$881$	−561.504	−	407.957i	−0.637348	−	0.463061i	0.221590	−	0.975140i	$-0.428875\pi$
$881$	−561.504	−	407.957i	−0.637348	−	0.463061i	−0.858938	+	0.512079i	$0.828875\pi$
$882$	385.341	−	385.341i	0.436894	−	0.436894i
$883$	−188.666	−	1191.19i	−0.213665	−	1.34903i	−0.828330	−	0.560241i	$-0.810709\pi$
$883$	−188.666	−	1191.19i	−0.213665	−	1.34903i	0.614665	−	0.788789i	$-0.289291\pi$
$884$	666.720	+	216.630i	0.754208	+	0.245057i
$885$	88.8865	+	33.8852i	0.100437	+	0.0382883i
$886$	−55.4049	−	170.519i	−0.0625337	−	0.192459i
$887$	172.711	+	338.965i	0.194714	+	0.382148i	0.967635	−	0.252355i	$-0.0812050\pi$
$887$	172.711	+	338.965i	0.194714	+	0.382148i	−0.772921	+	0.634502i	$0.781205\pi$
$888$	1110.56	−	565.856i	1.25063	−	0.637225i
$889$	84.5778	−	27.4810i	0.0951382	−	0.0309123i
$890$	−193.159	−	9.67604i	−0.217032	−	0.0108720i
$891$	28.2331	−	86.8927i	0.0316870	−	0.0975226i
$892$	−1394.31	+	220.837i	−1.56313	+	0.247575i
$893$	37.1977	+	37.1977i	0.0416548	+	0.0416548i
$894$	−717.210	+	987.155i	−0.802248	+	1.10420i
$895$	96.8842	+	107.103i	0.108250	+	0.119668i
$896$	−351.293	+	255.230i	−0.392068	+	0.284854i
$897$	33.6330	−	212.350i	0.0374950	−	0.236734i
$898$	−1508.89	+	2961.36i	−1.68028	+	3.29773i
$899$		−	782.395i		−	0.870294i
$900$	405.104	+	694.240i	0.450115	+	0.771378i
$901$	136.973			0.152024
$902$	181.622	+	92.5408i	0.201354	+	0.102595i
$903$	137.377	+	21.7585i	0.152135	+	0.0240957i
$904$	−610.845	−	840.757i	−0.675714	−	0.930040i
$905$	1110.14	+	637.526i	1.22667	+	0.704449i
$906$	−915.424	−	665.095i	−1.01040	−	0.734100i
$907$	−153.381	+	153.381i	−0.169108	+	0.169108i	−0.786587	−	0.617479i	$-0.788154\pi$
$907$	−153.381	+	153.381i	−0.169108	+	0.169108i	0.617479	+	0.786587i	$0.288154\pi$
$908$	622.418	+	3929.79i	0.685482	+	4.32796i
$909$	−472.968	−	153.677i	−0.520317	−	0.169061i
$910$	210.062	−	260.633i	0.230837	−	0.286409i
$911$	222.949	+	686.166i	0.244730	+	0.753201i	0.995681	+	0.0928429i	$0.0295954\pi$
$911$	222.949	+	686.166i	0.244730	+	0.753201i	−0.750951	+	0.660358i	$0.770405\pi$
$912$	−1641.20	−	3221.04i	−1.79957	−	3.53185i
$913$	299.022	−	152.359i	0.327515	−	0.166877i
$914$	1364.56	−	443.373i	1.49296	−	0.485091i
$915$	29.4347	+	108.846i	0.0321691	+	0.118958i
$916$	−134.533	+	414.051i	−0.146870	+	0.452020i
$917$	−167.747	+	26.5686i	−0.182931	+	0.0289734i
$918$	67.8505	+	67.8505i	0.0739112	+	0.0739112i
$919$	634.369	−	873.134i	0.690282	−	0.950092i	−0.309718	−	0.950829i	$-0.600235\pi$
$919$	634.369	−	873.134i	0.690282	−	0.950092i	1.00000		0.000736845i	$0.000234545\pi$
$920$	1151.80	+	242.046i	1.25196	+	0.263093i
$921$	165.341	−	120.128i	0.179524	−	0.130432i
$922$	−232.415	+	1467.41i	−0.252077	+	1.59155i
$923$	−307.075	+	602.669i	−0.332693	+	0.652946i
$924$		−	242.007i		−	0.261912i
$925$	−441.849	−	540.517i	−0.477674	−	0.584343i
$926$	2098.78			2.26650
$927$	50.0598	+	25.5067i	0.0540020	+	0.0275154i
$928$	2770.21	+	438.759i	2.98514	+	0.472800i
$929$	335.119	+	461.252i	0.360731	+	0.496503i	0.950352	−	0.311176i	$-0.100723\pi$
$929$	335.119	+	461.252i	0.360731	+	0.496503i	−0.589621	+	0.807680i	$0.700723\pi$
$930$	−423.301	−	944.874i	−0.455162	−	1.01599i
$931$	1428.01	+	1037.51i	1.53385	+	1.11441i
$932$	2871.64	−	2871.64i	3.08116	−	3.08116i
$933$	−91.0648	−	574.961i	−0.0976043	−	0.616249i
$934$	−1433.68	−	465.830i	−1.53499	−	0.498747i
$935$	−133.545	−	204.605i	−0.142828	−	0.218829i
$936$	−324.629	−	999.104i	−0.346825	−	1.06742i
$937$	454.693	+	892.385i	0.485265	+	0.952386i	0.995715	+	0.0924782i	$0.0294788\pi$
$937$	454.693	+	892.385i	0.485265	+	0.952386i	−0.510450	+	0.859907i	$0.670521\pi$
$938$	−485.838	+	247.547i	−0.517951	+	0.263909i
$939$	−515.083	+	167.361i	−0.548544	+	0.178233i
$940$	−63.3248	+	41.3317i	−0.0673668	+	0.0439699i
$941$	−288.747	+	888.673i	−0.306852	+	0.944392i	0.672128	+	0.740435i	$0.265380\pi$
$941$	−288.747	+	888.673i	−0.306852	+	0.944392i	−0.978980	+	0.203957i	$0.934620\pi$
$942$	−1702.16	+	269.595i	−1.80696	+	0.286194i
$943$	33.8077	+	33.8077i	0.0358512	+	0.0358512i
$944$	361.490	−	497.548i	0.382934	−	0.527063i
$945$	30.4499	−	13.6415i	0.0322221	−	0.0144354i
$946$	−1970.10	+	1431.36i	−2.08256	+	1.51307i
$947$	141.661	−	894.411i	0.149589	−	0.944468i	−0.792687	−	0.609629i	$-0.791318\pi$
$947$	141.661	−	894.411i	0.149589	−	0.944468i	0.942276	−	0.334838i	$-0.108682\pi$
$948$	229.854	−	451.113i	0.242462	−	0.475858i
$949$			1005.54i			1.05957i
$950$	−2768.04	+	2262.75i	−2.91373	+	2.38184i
$951$	374.849			0.394163
$952$	141.941	+	72.3224i	0.149097	+	0.0759689i
$953$	−616.425	−	97.6321i	−0.646825	−	0.102447i	−0.175602	−	0.984461i	$-0.556187\pi$
$953$	−616.425	−	97.6321i	−0.646825	−	0.102447i	−0.471223	+	0.882014i	$0.656187\pi$
$954$	−192.493	−	264.944i	−0.201775	−	0.277719i
$955$	−354.418	+	1686.53i	−0.371118	+	1.76600i
$956$	−951.975	−	691.650i	−0.995790	−	0.723484i
$957$	−312.146	+	312.146i	−0.326171	+	0.326171i
$958$	−440.094	−	2778.64i	−0.459388	−	2.90046i
$959$	−132.998	−	43.2137i	−0.138684	−	0.0450612i
$960$	1710.60	−	462.588i	1.78188	−	0.481863i
$961$	3.14355	+	9.67484i	0.00327112	+	0.0100675i
$962$	660.906	+	1297.10i	0.687012	+	1.34834i
$963$	96.5432	−	49.1912i	0.100253	−	0.0510812i
$964$	2315.18	−	752.249i	2.40164	−	0.780341i
$965$	388.450	+	313.079i	0.402539	+	0.324434i
$966$	24.0878	−	74.1347i	0.0249356	−	0.0767440i
$967$	934.624	−	148.030i	0.966519	−	0.153082i	0.346829	−	0.937928i	$-0.387258\pi$
$967$	934.624	−	148.030i	0.966519	−	0.153082i	0.619690	+	0.784847i	$0.287258\pi$
$968$	−326.988	−	326.988i	−0.337797	−	0.337797i
$969$	−182.684	+	251.443i	−0.188528	+	0.259487i
$970$	−1167.10	+	2032.30i	−1.20320	+	2.09516i
$971$	−546.462	+	397.028i	−0.562783	+	0.408886i	−0.832476	−	0.554060i	$-0.813078\pi$
$971$	−546.462	+	397.028i	−0.562783	+	0.408886i	0.269693	+	0.962946i	$0.413078\pi$
$972$	26.1347	−	165.008i	0.0268875	−	0.169761i
$973$	62.8012	−	123.254i	0.0645438	−	0.126674i
$974$		−	1055.65i		−	1.08383i
$975$	−508.218	+	296.556i	−0.521249	+	0.304160i
$976$	728.981			0.746907
$977$	−1273.66	−	648.962i	−1.30364	−	0.664240i	−0.342300	−	0.939591i	$-0.611206\pi$
$977$	−1273.66	−	648.962i	−1.30364	−	0.664240i	−0.961344	+	0.275351i	$0.911206\pi$
$978$	−207.609	−	32.8821i	−0.212279	−	0.0336217i
$979$	−60.1629	−	82.8071i	−0.0614534	−	0.0845833i
$980$	−1881.68	+	1702.16i	−1.92009	+	1.73689i
$981$	28.4237	+	20.6510i	0.0289742	+	0.0210510i
$982$	−2418.50	+	2418.50i	−2.46283	+	2.46283i
$983$	130.928	+	826.647i	0.133192	+	0.840943i	0.960314	+	0.278921i	$0.0899766\pi$
$983$	130.928	+	826.647i	0.133192	+	0.840943i	−0.827122	+	0.562023i	$0.810023\pi$
$984$	222.181	+	72.1911i	0.225794	+	0.0733649i
$985$	61.8413	−	1234.51i	0.0627830	−	1.25331i
$986$	−143.267	−	440.930i	−0.145301	−	0.447191i
$987$	1.42509	+	2.79690i	0.00144386	+	0.00283374i
$988$	4837.18	−	2464.67i	4.89593	−	2.49460i
$989$	−543.226	+	176.505i	−0.549268	+	0.178468i
$990$	−208.088	+	545.850i	−0.210190	+	0.551364i
$991$	238.138	−	732.912i	0.240300	−	0.739569i	−0.756074	−	0.654487i	$-0.772885\pi$
$991$	238.138	−	732.912i	0.240300	−	0.739569i	0.996374	−	0.0850819i	$-0.0271152\pi$
$992$	−3438.62	+	544.624i	−3.46635	+	0.549016i
$993$	−747.228	−	747.228i	−0.752495	−	0.752495i
$994$	−144.145	+	198.398i	−0.145015	+	0.199596i
$995$	−140.989	−	1312.28i	−0.141698	−	1.31887i
$996$	496.463	−	360.702i	0.498457	−	0.362150i
$997$	95.6367	−	603.826i	0.0959244	−	0.605643i	−0.892159	−	0.451722i	$-0.850810\pi$
$997$	95.6367	−	603.826i	0.0959244	−	0.605643i	0.988083	−	0.153921i	$-0.0491901\pi$
$998$	169.423	−	332.512i	0.169763	−	0.333178i
$999$			145.104i			0.145249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.58.1	yes	80
3.2	odd	2		225.3.r.b.208.10		80
5.2	odd	4		375.3.k.c.232.10		80
5.3	odd	4		375.3.k.b.232.1		80
5.4	even	2		375.3.k.a.268.10		80
25.3	odd	20		375.3.k.a.7.10		80
25.4	even	10		375.3.k.b.118.1		80
25.21	even	5		375.3.k.c.118.10		80
25.22	odd	20	inner	75.3.k.a.22.1	✓	80
75.47	even	20		225.3.r.b.172.10		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.1	✓	80	25.22	odd	20	inner
75.3.k.a.58.1	yes	80	1.1	even	1	trivial
225.3.r.b.172.10		80	75.47	even	20
225.3.r.b.208.10		80	3.2	odd	2
375.3.k.a.7.10		80	25.3	odd	20
375.3.k.a.268.10		80	5.4	even	2
375.3.k.b.118.1		80	25.4	even	10
375.3.k.b.232.1		80	5.3	odd	4
375.3.k.c.118.10		80	25.21	even	5
375.3.k.c.232.10		80	5.2	odd	4

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)

\(f(q)\)	\(=\)	\(q+(-3.41817 - 1.74164i) q^{2} +(-1.71073 - 0.270952i) q^{3} +(6.29941 + 8.67040i) q^{4} +(4.97139 - 0.534117i) q^{5} +(5.37565 + 3.90564i) q^{6} +(-0.908106 + 0.908106i) q^{7} +(-4.03119 - 25.4519i) q^{8} +(2.85317 + 0.927051i) q^{9} +O(q^{10})\)	\(q+(-3.41817 - 1.74164i) q^{2} +(-1.71073 - 0.270952i) q^{3} +(6.29941 + 8.67040i) q^{4} +(4.97139 - 0.534117i) q^{5} +(5.37565 + 3.90564i) q^{6} +(-0.908106 + 0.908106i) q^{7} +(-4.03119 - 25.4519i) q^{8} +(2.85317 + 0.927051i) q^{9} +(-17.9233 - 6.83269i) q^{10} +(-3.13702 - 9.65474i) q^{11} +(-8.42731 - 16.5395i) q^{12} +(12.1077 - 6.16920i) q^{13} +(4.68566 - 1.52246i) q^{14} +(-8.64941 - 0.433282i) q^{15} +(-17.3017 + 53.2493i) q^{16} +(4.75437 - 0.753019i) q^{17} +(-8.13802 - 8.13802i) q^{18} +(21.9112 - 30.1582i) q^{19} +(35.9478 + 39.7393i) q^{20} +(1.79957 - 1.30747i) q^{21} +(-6.09227 + 38.4651i) q^{22} +(-4.14703 + 8.13900i) q^{23} +44.6336i q^{24} +(24.4294 - 5.31061i) q^{25} -52.1309 q^{26} +(-4.62981 - 2.35900i) q^{27} +(-13.5942 - 2.15311i) q^{28} +(14.7569 + 20.3112i) q^{29} +(28.8105 + 16.5452i) q^{30} +(-25.2119 - 18.3175i) q^{31} +(78.9952 - 78.9952i) q^{32} +(2.75060 + 17.3666i) q^{33} +(-17.5627 - 5.70648i) q^{34} +(-4.02951 + 4.99958i) q^{35} +(9.93539 + 30.5780i) q^{36} +(-12.6778 - 24.8816i) q^{37} +(-127.421 + 64.9243i) q^{38} +(-22.3846 + 7.27320i) q^{39} +(-33.6349 - 124.378i) q^{40} +(1.61742 - 4.97790i) q^{41} +(-8.42839 + 1.33493i) q^{42} +(44.2149 + 44.2149i) q^{43} +(63.9491 - 88.0184i) q^{44} +(14.6794 + 3.08480i) q^{45} +(28.3505 - 20.5978i) q^{46} +(-0.220758 + 1.39381i) q^{47} +(44.0266 - 86.4070i) q^{48} +47.3507i q^{49} +(-92.7531 - 24.3948i) q^{50} -8.33747 q^{51} +(129.761 + 66.1166i) q^{52} +(28.1049 + 4.45138i) q^{53} +(11.7169 + 16.1269i) q^{54} +(-20.7521 - 46.3220i) q^{55} +(26.7738 + 19.4523i) q^{56} +(-45.6556 + 45.6556i) q^{57} +(-15.0669 - 95.1284i) q^{58} +(-10.4466 - 3.39432i) q^{59} +(-50.7295 - 77.7232i) q^{60} +(-4.02338 - 12.3827i) q^{61} +(54.2760 + 106.523i) q^{62} +(-3.43284 + 1.74912i) q^{63} +(-194.603 + 63.2305i) q^{64} +(56.8972 - 37.1365i) q^{65} +(20.8444 - 64.1525i) q^{66} +(-109.312 + 17.3133i) q^{67} +(36.4787 + 36.4787i) q^{68} +(9.29972 - 12.8000i) q^{69} +(22.4811 - 10.0714i) q^{70} +(-40.2692 + 29.2573i) q^{71} +(12.0936 - 76.3558i) q^{72} +(-33.5940 + 65.9319i) q^{73} +107.130i q^{74} +(-43.2310 + 2.46579i) q^{75} +399.512 q^{76} +(11.6163 + 5.91879i) q^{77} +(89.1816 + 14.1250i) q^{78} +(16.0318 + 22.0658i) q^{79} +(-57.5723 + 273.964i) q^{80} +(7.28115 + 5.29007i) q^{81} +(-14.1983 + 14.1983i) q^{82} +(5.17154 + 32.6518i) q^{83} +(22.6725 + 7.36675i) q^{84} +(23.2336 - 6.28294i) q^{85} +(-74.1274 - 228.141i) q^{86} +(-19.7417 - 38.7453i) q^{87} +(-233.086 + 118.763i) q^{88} +(9.58919 - 3.11572i) q^{89} +(-44.8039 - 36.1106i) q^{90} +(-5.39282 + 16.5974i) q^{91} +(-96.6923 + 15.3145i) q^{92} +(38.1675 + 38.1675i) q^{93} +(3.18211 - 4.37980i) q^{94} +(92.8212 - 161.631i) q^{95} +(-156.543 + 113.735i) q^{96} +(19.1131 - 120.675i) q^{97} +(82.4680 - 161.853i) q^{98} -30.4548i 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

Introduction

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