LMFDB - Embedded newform 75.3.j.a.11.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(11,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 8]))

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

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

chi := DirichletCharacter("75.11");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.j (of order $10$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			11.14
Character	$\chi$	$=$	75.11
Dual form			75.3.j.a.41.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.37909 + 1.89816i) q^{2} +(2.88640 - 0.817724i) q^{3} +(-0.465043 + 1.43126i) q^{4} +(-3.05671 + 3.95684i) q^{5} +(5.53279 + 4.35114i) q^{6} -3.37306 q^{7} +(5.56759 - 1.80902i) q^{8} +(7.66265 - 4.72056i) q^{9} +O(q^{10})$	\(q+(1.37909 + 1.89816i) q^{2} +(2.88640 - 0.817724i) q^{3} +(-0.465043 + 1.43126i) q^{4} +(-3.05671 + 3.95684i) q^{5} +(5.53279 + 4.35114i) q^{6} -3.37306 q^{7} +(5.56759 - 1.80902i) q^{8} +(7.66265 - 4.72056i) q^{9} +(-11.7262 - 0.345267i) q^{10} +(-2.62002 - 3.60615i) q^{11} +(-0.171930 + 4.51146i) q^{12} +(-8.09526 - 5.88155i) q^{13} +(-4.65176 - 6.40260i) q^{14} +(-5.58729 + 13.9206i) q^{15} +(15.9820 + 11.6116i) q^{16} +(-20.2558 + 6.58152i) q^{17} +(19.5279 + 8.03484i) q^{18} +(-7.07267 - 21.7674i) q^{19} +(-4.24174 - 6.21503i) q^{20} +(-9.73600 + 2.75823i) q^{21} +(3.23179 - 9.94643i) q^{22} +(13.1257 + 18.0660i) q^{23} +(14.5910 - 9.77432i) q^{24} +(-6.31310 - 24.1898i) q^{25} -23.4773i q^{26} +(18.2574 - 19.8914i) q^{27} +(1.56862 - 4.82771i) q^{28} +(4.71042 + 1.53051i) q^{29} +(-34.1289 + 8.59221i) q^{30} +(0.396417 + 1.22005i) q^{31} +22.9335i q^{32} +(-10.5113 - 8.26634i) q^{33} +(-40.4275 - 29.3723i) q^{34} +(10.3104 - 13.3466i) q^{35} +(3.19287 + 13.1625i) q^{36} +(57.1413 + 41.5156i) q^{37} +(31.5642 - 43.4444i) q^{38} +(-28.1757 - 10.3568i) q^{39} +(-9.86049 + 27.5597i) q^{40} +(-36.9062 + 50.7970i) q^{41} +(-18.6624 - 14.6766i) q^{42} -21.4915 q^{43} +(6.37974 - 2.07290i) q^{44} +(-4.74398 + 44.7492i) q^{45} +(-16.1905 + 49.8293i) q^{46} +(72.7717 + 23.6450i) q^{47} +(55.6257 + 20.4470i) q^{48} -37.6225 q^{49} +(37.2097 - 45.3432i) q^{50} +(-53.0846 + 35.5606i) q^{51} +(12.1826 - 8.85121i) q^{52} +(-40.2473 - 13.0771i) q^{53} +(62.9357 + 7.22337i) q^{54} +(22.2776 + 0.655943i) q^{55} +(-18.7798 + 6.10193i) q^{56} +(-38.2143 - 57.0461i) q^{57} +(3.59096 + 11.0518i) q^{58} +(-7.52052 + 10.3511i) q^{59} +(-17.3256 - 14.4705i) q^{60} +(50.1822 - 36.4595i) q^{61} +(-1.76915 + 2.43502i) q^{62} +(-25.8466 + 15.9227i) q^{63} +(20.3966 - 14.8190i) q^{64} +(48.0171 - 14.0534i) q^{65} +(1.19482 - 31.3521i) q^{66} +(35.8442 + 110.317i) q^{67} -32.0520i q^{68} +(52.6590 + 41.4125i) q^{69} +(39.5531 + 1.16461i) q^{70} +(-52.8656 - 17.1771i) q^{71} +(34.1229 - 40.1441i) q^{72} +(39.0233 - 28.3521i) q^{73} +165.717i q^{74} +(-38.0027 - 64.6591i) q^{75} +34.4439 q^{76} +(8.83747 + 12.1637i) q^{77} +(-19.1979 - 67.7650i) q^{78} +(6.65697 - 20.4881i) q^{79} +(-94.7977 + 27.7450i) q^{80} +(36.4326 - 72.3441i) q^{81} -147.318 q^{82} +(-69.8488 + 22.6953i) q^{83} +(0.579930 - 15.2174i) q^{84} +(35.8741 - 100.267i) q^{85} +(-29.6387 - 40.7942i) q^{86} +(14.8477 + 0.565841i) q^{87} +(-21.1108 - 15.3379i) q^{88} +(-76.7412 - 105.625i) q^{89} +(-91.4836 + 52.7086i) q^{90} +(27.3057 + 19.8388i) q^{91} +(-31.9610 + 10.3848i) q^{92} +(2.14188 + 3.19739i) q^{93} +(55.4771 + 170.741i) q^{94} +(107.749 + 38.5512i) q^{95} +(18.7533 + 66.1955i) q^{96} +(19.5073 - 60.0372i) q^{97} +(-51.8850 - 71.4135i) q^{98} +(-37.0993 - 15.2647i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9}+O(q^{10}) $ 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9	$ 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9} - 20 q^{10} + 31 q^{12} - 42 q^{13} + 45 q^{15} - 130 q^{16} + 30 q^{18} - 36 q^{19} - 60 q^{21} - 70 q^{22} - 72 q^{24} + 100 q^{25} - 154 q^{27} - 62 q^{28} + 15 q^{30} + 114 q^{31} - 10 q^{33} + 178 q^{34} + 271 q^{36} - 98 q^{37} - 155 q^{39} - 120 q^{40} - 475 q^{42} - 52 q^{43} + 35 q^{45} + 198 q^{46} - 326 q^{48} + 112 q^{49} + 44 q^{51} + 412 q^{52} + 304 q^{54} + 10 q^{55} + 622 q^{57} + 190 q^{58} + 360 q^{60} - 306 q^{61} + 293 q^{63} + 474 q^{64} + 320 q^{66} + 472 q^{67} + 269 q^{69} - 840 q^{70} + 175 q^{72} + 318 q^{73} - 310 q^{75} + 112 q^{76} + 815 q^{78} - 346 q^{79} - 373 q^{81} - 1620 q^{82} - 730 q^{84} - 530 q^{85} - 370 q^{87} - 810 q^{88} - 230 q^{90} - 550 q^{91} - 272 q^{93} - 612 q^{94} - 698 q^{96} + 182 q^{97} - 160 q^{99}+O(q^{100}) $ 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9 - 20 * q^10 + 31 * q^12 - 42 * q^13 + 45 * q^15 - 130 * q^16 + 30 * q^18 - 36 * q^19 - 60 * q^21 - 70 * q^22 - 72 * q^24 + 100 * q^25 - 154 * q^27 - 62 * q^28 + 15 * q^30 + 114 * q^31 - 10 * q^33 + 178 * q^34 + 271 * q^36 - 98 * q^37 - 155 * q^39 - 120 * q^40 - 475 * q^42 - 52 * q^43 + 35 * q^45 + 198 * q^46 - 326 * q^48 + 112 * q^49 + 44 * q^51 + 412 * q^52 + 304 * q^54 + 10 * q^55 + 622 * q^57 + 190 * q^58 + 360 * q^60 - 306 * q^61 + 293 * q^63 + 474 * q^64 + 320 * q^66 + 472 * q^67 + 269 * q^69 - 840 * q^70 + 175 * q^72 + 318 * q^73 - 310 * q^75 + 112 * q^76 + 815 * q^78 - 346 * q^79 - 373 * q^81 - 1620 * q^82 - 730 * q^84 - 530 * q^85 - 370 * q^87 - 810 * q^88 - 230 * q^90 - 550 * q^91 - 272 * q^93 - 612 * q^94 - 698 * q^96 + 182 * q^97 - 160 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{4}{5}\right)$

Coefficient data

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

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

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

$2$	1.37909	+	1.89816i	0.689547	+	0.949080i	0.999999	−	0.00150912i	$-0.000480369\pi$
$2$	1.37909	+	1.89816i	0.689547	+	0.949080i	−0.310452	+	0.950589i	$0.600480\pi$
$3$	2.88640	−	0.817724i	0.962135	−	0.272575i
$3$	2.88640	−	0.817724i	0.962135	−	0.272575i
$4$	−0.465043	+	1.43126i	−0.116261	+	0.357814i
$5$	−3.05671	+	3.95684i	−0.611341	+	0.791367i
$5$	−3.05671	+	3.95684i	−0.611341	+	0.791367i
$6$	5.53279	+	4.35114i	0.922132	+	0.725190i
$7$	−3.37306			−0.481865			−0.240933	−	0.970542i	$-0.577453\pi$
$7$	−3.37306			−0.481865			−0.240933	+	0.970542i	$0.577453\pi$
$8$	5.56759	−	1.80902i	0.695949	−	0.226128i
$9$	7.66265	−	4.72056i	0.851406	−	0.524507i
$10$	−11.7262	−	0.345267i	−1.17262	−	0.0345267i
$11$	−2.62002	−	3.60615i	−0.238184	−	0.327832i	0.673146	−	0.739510i	$-0.264943\pi$
$11$	−2.62002	−	3.60615i	−0.238184	−	0.327832i	−0.911329	+	0.411678i	$0.864943\pi$
$12$	−0.171930	+	4.51146i	−0.0143275	+	0.375955i
$13$	−8.09526	−	5.88155i	−0.622712	−	0.452427i	0.231156	−	0.972917i	$-0.425749\pi$
$13$	−8.09526	−	5.88155i	−0.622712	−	0.452427i	−0.853868	+	0.520490i	$0.825749\pi$
$14$	−4.65176	−	6.40260i	−0.332269	−	0.457329i
$15$	−5.58729	+	13.9206i	−0.372486	+	0.928038i
$16$	15.9820	+	11.6116i	0.998877	+	0.725727i
$17$	−20.2558	+	6.58152i	−1.19152	+	0.387148i	−0.836634	−	0.547762i	$-0.815480\pi$
$17$	−20.2558	+	6.58152i	−1.19152	+	0.387148i	−0.354885	+	0.934910i	$0.615480\pi$
$18$	19.5279	+	8.03484i	1.08488	+	0.446380i
$19$	−7.07267	−	21.7674i	−0.372246	−	1.14565i	−0.945318	−	0.326150i	$-0.894249\pi$
$19$	−7.07267	−	21.7674i	−0.372246	−	1.14565i	0.573072	−	0.819505i	$-0.305751\pi$
$20$	−4.24174	−	6.21503i	−0.212087	−	0.310751i
$21$	−9.73600	+	2.75823i	−0.463619	+	0.131344i
$22$	3.23179	−	9.94643i	0.146900	−	0.452110i
$23$	13.1257	+	18.0660i	0.570682	+	0.785477i	0.992635	−	0.121141i	$-0.0386553\pi$
$23$	13.1257	+	18.0660i	0.570682	+	0.785477i	−0.421953	+	0.906618i	$0.638655\pi$
$24$	14.5910	−	9.77432i	0.607960	−	0.407263i
$25$	−6.31310	−	24.1898i	−0.252524	−	0.967591i
$26$		−	23.4773i		−	0.902973i
$27$	18.2574	−	19.8914i	0.676200	−	0.736718i
$28$	1.56862	−	4.82771i	0.0560220	−	0.172418i
$29$	4.71042	+	1.53051i	0.162428	+	0.0527761i	0.389102	−	0.921195i	$-0.372785\pi$
$29$	4.71042	+	1.53051i	0.162428	+	0.0527761i	−0.226674	+	0.973971i	$0.572785\pi$
$30$	−34.1289	+	8.59221i	−1.13763	+	0.286407i
$31$	0.396417	+	1.22005i	0.0127877	+	0.0393564i	0.957247	−	0.289273i	$-0.0934134\pi$
$31$	0.396417	+	1.22005i	0.0127877	+	0.0393564i	−0.944459	+	0.328629i	$0.893413\pi$
$32$			22.9335i			0.716673i
$33$	−10.5113	−	8.26634i	−0.318523	−	0.250495i
$34$	−40.4275	−	29.3723i	−1.18904	−	0.863890i
$35$	10.3104	−	13.3466i	0.294584	−	0.381332i
$36$	3.19287	+	13.1625i	0.0886908	+	0.365625i
$37$	57.1413	+	41.5156i	1.54436	+	1.12204i	0.947526	+	0.319679i	$0.103575\pi$
$37$	57.1413	+	41.5156i	1.54436	+	1.12204i	0.596834	+	0.802365i	$0.296425\pi$
$38$	31.5642	−	43.4444i	0.830637	−	1.14327i
$39$	−28.1757	−	10.3568i	−0.722453	−	0.265560i
$40$	−9.86049	+	27.5597i	−0.246512	+	0.688992i
$41$	−36.9062	+	50.7970i	−0.900150	+	1.23895i	0.0702696	+	0.997528i	$0.477614\pi$
$41$	−36.9062	+	50.7970i	−0.900150	+	1.23895i	−0.970420	+	0.241423i	$0.922386\pi$
$42$	−18.6624	−	14.6766i	−0.444343	−	0.349444i
$43$	−21.4915			−0.499801			−0.249901	−	0.968271i	$-0.580398\pi$
$43$	−21.4915			−0.499801			−0.249901	+	0.968271i	$0.580398\pi$
$44$	6.37974	−	2.07290i	0.144994	−	0.0471114i
$45$	−4.74398	+	44.7492i	−0.105422	+	0.994428i
$46$	−16.1905	+	49.8293i	−0.351968	+	1.08325i
$47$	72.7717	+	23.6450i	1.54833	+	0.503084i	0.953661	−	0.300884i	$-0.0972816\pi$
$47$	72.7717	+	23.6450i	1.54833	+	0.503084i	0.594673	+	0.803968i	$0.297282\pi$
$48$	55.6257	+	20.4470i	1.15887	+	0.425978i
$49$	−37.6225			−0.767806
$50$	37.2097	−	45.3432i	0.744194	−	0.906865i
$51$	−53.0846	+	35.5606i	−1.04088	+	0.697267i
$52$	12.1826	−	8.85121i	0.234282	−	0.170215i
$53$	−40.2473	−	13.0771i	−0.759383	−	0.246739i	−0.0963693	−	0.995346i	$-0.530723\pi$
$53$	−40.2473	−	13.0771i	−0.759383	−	0.246739i	−0.663014	+	0.748607i	$0.730723\pi$
$54$	62.9357	+	7.22337i	1.16548	+	0.133766i
$55$	22.2776	+	0.655943i	0.405047	+	0.0119262i
$56$	−18.7798	+	6.10193i	−0.335354	+	0.108963i
$57$	−38.2143	−	57.0461i	−0.670427	−	1.00081i
$58$	3.59096	+	11.0518i	0.0619131	+	0.190549i
$59$	−7.52052	+	10.3511i	−0.127466	+	0.175442i	−0.867980	−	0.496599i	$-0.834582\pi$
$59$	−7.52052	+	10.3511i	−0.127466	+	0.175442i	0.740514	+	0.672041i	$0.234582\pi$
$60$	−17.3256	−	14.4705i	−0.288759	−	0.241175i
$61$	50.1822	−	36.4595i	0.822658	−	0.597696i	−0.0948143	−	0.995495i	$-0.530226\pi$
$61$	50.1822	−	36.4595i	0.822658	−	0.597696i	0.917473	+	0.397799i	$0.130226\pi$
$62$	−1.76915	+	2.43502i	−0.0285347	+	0.0392746i
$63$	−25.8466	+	15.9227i	−0.410263	+	0.252742i
$64$	20.3966	−	14.8190i	0.318697	−	0.231547i
$65$	48.0171	−	14.0534i	0.738725	−	0.216207i
$66$	1.19482	−	31.3521i	0.0181033	−	0.475032i
$67$	35.8442	+	110.317i	0.534989	+	1.64653i	0.743674	+	0.668543i	$0.233082\pi$
$67$	35.8442	+	110.317i	0.534989	+	1.64653i	−0.208685	+	0.977983i	$0.566918\pi$
$68$		−	32.0520i		−	0.471352i
$69$	52.6590	+	41.4125i	0.763174	+	0.600181i
$70$	39.5531	+	1.16461i	0.565044	+	0.0166372i
$71$	−52.8656	−	17.1771i	−0.744585	−	0.241930i	−0.0879357	−	0.996126i	$-0.528027\pi$
$71$	−52.8656	−	17.1771i	−0.744585	−	0.241930i	−0.656650	+	0.754196i	$0.728027\pi$
$72$	34.1229	−	40.1441i	0.473930	−	0.557557i
$73$	39.0233	−	28.3521i	0.534566	−	0.388385i	−0.287497	−	0.957782i	$-0.592823\pi$
$73$	39.0233	−	28.3521i	0.534566	−	0.388385i	0.822063	+	0.569397i	$0.192823\pi$
$74$			165.717i			2.23942i
$75$	−38.0027	−	64.6591i	−0.506703	−	0.862121i
$76$	34.4439			0.453209
$77$	8.83747	+	12.1637i	0.114772	+	0.157971i
$78$	−19.1979	−	67.7650i	−0.246128	−	0.868781i
$79$	6.65697	−	20.4881i	0.0842655	−	0.259342i	−0.900042	−	0.435802i	$-0.856465\pi$
$79$	6.65697	−	20.4881i	0.0842655	−	0.259342i	0.984308	+	0.176460i	$0.0564646\pi$
$80$	−94.7977	+	27.7450i	−1.18497	+	0.346812i
$81$	36.4326	−	72.3441i	0.449785	−	0.893137i
$82$	−147.318			−1.79656
$83$	−69.8488	+	22.6953i	−0.841552	+	0.273437i	−0.697903	−	0.716192i	$-0.745883\pi$
$83$	−69.8488	+	22.6953i	−0.841552	+	0.273437i	−0.143649	+	0.989629i	$0.545883\pi$
$84$	0.579930	−	15.2174i	0.00690393	−	0.181160i
$85$	35.8741	−	100.267i	0.422048	−	1.17961i
$86$	−29.6387	−	40.7942i	−0.344636	−	0.474351i
$87$	14.8477	+	0.565841i	0.170663	+	0.00650392i
$88$	−21.1108	−	15.3379i	−0.239895	−	0.174294i
$89$	−76.7412	−	105.625i	−0.862260	−	1.18680i	−0.981026	−	0.193877i	$-0.937894\pi$
$89$	−76.7412	−	105.625i	−0.862260	−	1.18680i	0.118765	−	0.992922i	$-0.462106\pi$
$90$	−91.4836	+	52.7086i	−1.01648	+	0.585651i
$91$	27.3057	+	19.8388i	0.300063	+	0.218009i
$92$	−31.9610	+	10.3848i	−0.347403	+	0.112878i
$93$	2.14188	+	3.19739i	0.0230310	+	0.0343805i
$94$	55.4771	+	170.741i	0.590182	+	1.81639i
$95$	107.749	+	38.5512i	1.13420	+	0.405803i
$96$	18.7533	+	66.1955i	0.195347	+	0.689536i
$97$	19.5073	−	60.0372i	0.201106	−	0.618940i	−0.798745	−	0.601670i	$-0.794502\pi$
$97$	19.5073	−	60.0372i	0.201106	−	0.618940i	0.999851	−	0.0172705i	$-0.00549764\pi$
$98$	−51.8850	−	71.4135i	−0.529438	−	0.728709i
$99$	−37.0993	−	15.2647i	−0.374741	−	0.154189i
$100$	37.5576	+	2.21362i	0.375576	+	0.0221362i
$101$		−	84.4028i		−	0.835672i	−0.908523	−	0.417836i	$-0.862789\pi$
$101$		−	84.4028i		−	0.835672i	0.908523	−	0.417836i	$-0.137211\pi$
$102$	−140.708	−	51.7217i	−1.37949	−	0.507076i
$103$	−45.7671	+	140.857i	−0.444341	+	1.36754i	0.438864	+	0.898554i	$0.355381\pi$
$103$	−45.7671	+	140.857i	−0.444341	+	1.36754i	−0.883205	+	0.468987i	$0.844619\pi$
$104$	−55.7109	−	18.1016i	−0.535682	−	0.174054i
$105$	18.8462	−	46.9549i	0.179488	−	0.447189i
$106$	−30.6823	−	94.4304i	−0.289456	−	0.890853i
$107$			14.2682i			0.133348i	0.997775	+	0.0666739i	$0.0212387\pi$
$107$			14.2682i			0.133348i	−0.997775	+	0.0666739i	$0.978761\pi$
$108$	19.9792	+	35.3814i	0.184992	+	0.327605i
$109$	16.9125	+	12.2877i	0.155161	+	0.112731i	0.662657	−	0.748923i	$-0.269429\pi$
$109$	16.9125	+	12.2877i	0.155161	+	0.112731i	−0.507496	+	0.861654i	$0.669429\pi$
$110$	29.4778	+	43.1910i	0.267980	+	0.392645i
$111$	198.881	+	73.1050i	1.79172	+	0.658603i
$112$	−53.9083	−	39.1667i	−0.481324	−	0.349703i
$113$	64.9659	−	89.4178i	0.574919	−	0.791308i	−0.418208	−	0.908351i	$-0.637342\pi$
$113$	64.9659	−	89.4178i	0.574919	−	0.791308i	0.993127	+	0.117043i	$0.0373416\pi$
$114$	55.5815	−	151.209i	0.487557	−	1.32639i
$115$	−111.605	−	3.28612i	−0.970482	−	0.0285750i
$116$	−4.38109	+	6.03006i	−0.0377680	+	0.0519833i
$117$	−89.7954	−	6.85410i	−0.767482	−	0.0585820i
$118$	−30.0196			−0.254403
$119$	68.3240	−	22.1998i	0.574152	−	0.186553i
$120$	−5.92514	+	87.6116i	−0.0493762	+	0.730097i
$121$	31.2513	−	96.1815i	0.258275	−	0.794888i
$122$	138.412	+	44.9727i	1.13452	+	0.368629i
$123$	−64.9882	+	176.800i	−0.528359	+	1.43740i
$124$	−1.93055			−0.0155690
$125$	115.012	+	48.9611i	0.920098	+	0.391689i
$126$	−65.8687	−	27.1020i	−0.522768	−	0.215095i
$127$	76.4769	−	55.5638i	0.602181	−	0.437510i	−0.244472	−	0.969656i	$-0.578614\pi$
$127$	76.4769	−	55.5638i	0.602181	−	0.437510i	0.846652	+	0.532147i	$0.178614\pi$
$128$	143.502	+	46.6267i	1.12111	+	0.364271i
$129$	−62.0330	+	17.5741i	−0.480876	+	0.136233i
$130$	92.8958	+	71.7632i	0.714583	+	0.552024i
$131$	91.8557	−	29.8457i	0.701189	−	0.227830i	0.0633404	−	0.997992i	$-0.479825\pi$
$131$	91.8557	−	29.8457i	0.701189	−	0.227830i	0.637848	+	0.770162i	$0.279825\pi$
$132$	16.7194	−	11.2001i	0.126662	−	0.0848493i
$133$	23.8565	+	73.4228i	0.179372	+	0.552051i
$134$	−159.967	+	220.176i	−1.19378	+	1.64310i
$135$	22.8995	+	133.044i	0.169626	+	0.985509i
$136$	−100.870	+	73.2864i	−0.741692	+	0.538871i
$137$	28.5517	−	39.2981i	0.208407	−	0.286847i	−0.691999	−	0.721899i	$-0.743270\pi$
$137$	28.5517	−	39.2981i	0.208407	−	0.286847i	0.900406	+	0.435051i	$0.143270\pi$
$138$	−5.98577	+	157.067i	−0.0433751	+	1.13817i
$139$	160.333	−	116.489i	1.15348	−	0.838049i	0.164536	−	0.986371i	$-0.447387\pi$
$139$	160.333	−	116.489i	1.15348	−	0.838049i	0.988939	+	0.148322i	$0.0473873\pi$
$140$	14.3076	+	20.9636i	0.102197	+	0.149740i
$141$	229.384	+	8.74173i	1.62683	+	0.0619981i
$142$	−40.3018	−	124.036i	−0.283815	−	0.873494i
$143$			44.6024i			0.311905i
$144$	177.278	+	13.5317i	1.23110	+	0.0939701i
$145$	−20.4543	+	13.9600i	−0.141064	+	0.0962761i
$146$	107.634	+	34.9723i	0.737217	+	0.239536i
$147$	−108.594	+	30.7648i	−0.738733	+	0.209284i
$148$	−85.9926	+	62.4773i	−0.581031	+	0.422144i
$149$			3.03795i			0.0203889i	0.999948	+	0.0101945i	$0.00324506\pi$
$149$			3.03795i			0.0203889i	−0.999948	+	0.0101945i	$0.996755\pi$
$150$	70.3239	−	161.306i	0.468826	−	1.07537i
$151$	−152.499			−1.00992			−0.504962	−	0.863142i	$-0.668494\pi$
$151$	−152.499			−1.00992			−0.504962	+	0.863142i	$0.668494\pi$
$152$	−78.7555	−	108.398i	−0.518128	−	0.713142i
$153$	−124.145	+	146.051i	−0.811405	+	0.954581i
$154$	−10.9010	+	33.5499i	−0.0707858	+	0.217856i
$155$	−6.03926	−	2.16077i	−0.0389630	−	0.0139404i
$156$	27.9262	−	35.5102i	0.179014	−	0.227629i
$157$	−234.303			−1.49238			−0.746189	−	0.665734i	$-0.768119\pi$
$157$	−234.303			−1.49238			−0.746189	+	0.665734i	$0.768119\pi$
$158$	48.0702	−	15.6190i	0.304242	−	0.0988541i
$159$	−126.863	−	4.83473i	−0.797884	−	0.0304071i
$160$	−90.7443	−	70.1011i	−0.567152	−	0.438132i
$161$	−44.2737	−	60.9375i	−0.274992	−	0.378494i
$162$	187.565	−	30.6145i	1.15781	−	0.188978i
$163$	36.5672	+	26.5676i	0.224339	+	0.162991i	0.694277	−	0.719707i	$-0.255724\pi$
$163$	36.5672	+	26.5676i	0.224339	+	0.162991i	−0.469939	+	0.882699i	$0.655724\pi$
$164$	−55.5405	−	76.4449i	−0.338662	−	0.466128i
$165$	64.8384	−	16.3236i	0.392960	−	0.0989308i
$166$	−139.407	−	101.285i	−0.839803	−	0.610152i
$167$	−200.457	+	65.1324i	−1.20034	+	0.390014i	−0.839886	−	0.542762i	$-0.817378\pi$
$167$	−200.457	+	65.1324i	−1.20034	+	0.390014i	−0.360455	+	0.932777i	$0.617378\pi$
$168$	−49.2164	+	32.9693i	−0.292955	+	0.196246i
$169$	−21.2833	−	65.5033i	−0.125937	−	0.387593i
$170$	239.796	−	70.1825i	1.41057	−	0.412838i
$171$	−156.950	−	133.409i	−0.917836	−	0.780172i
$172$	9.99445	−	30.7598i	0.0581073	−	0.178836i
$173$	−166.893	−	229.709i	−0.964701	−	1.32780i	−0.944678	−	0.327998i	$-0.893626\pi$
$173$	−166.893	−	229.709i	−0.964701	−	1.32780i	−0.0200230	−	0.999800i	$-0.506374\pi$
$174$	19.4023	+	28.9636i	0.111508	+	0.166458i
$175$	21.2945	+	81.5934i	0.121683	+	0.466248i
$176$		−	88.0563i		−	0.500320i
$177$	−13.2429	+	36.0272i	−0.0748187	+	0.203543i
$178$	94.6602	−	291.334i	0.531799	−	1.63671i
$179$	11.0047	+	3.57565i	0.0614788	+	0.0199757i	0.339595	−	0.940572i	$-0.389710\pi$
$179$	11.0047	+	3.57565i	0.0614788	+	0.0199757i	−0.278116	+	0.960547i	$0.589710\pi$
$180$	−61.8414	−	27.6002i	−0.343564	−	0.153334i
$181$	31.0511	+	95.5654i	0.171553	+	0.527985i	0.999459	−	0.0328808i	$-0.0104682\pi$
$181$	31.0511	+	95.5654i	0.171553	+	0.527985i	−0.827906	+	0.560866i	$0.810468\pi$
$182$			79.1902i			0.435111i
$183$	115.032	−	146.272i	0.628591	−	0.799300i
$184$	105.760	+	76.8393i	0.574784	+	0.417605i
$185$	−338.935	+	99.1979i	−1.83208	+	0.536205i
$186$	−3.11530	+	8.47514i	−0.0167489	+	0.0455653i
$187$	76.8046	+	55.8018i	0.410720	+	0.298405i
$188$	−67.6839	+	93.1589i	−0.360021	+	0.495526i
$189$	−61.5832	+	67.0948i	−0.325837	+	0.354999i
$190$	75.4199	+	257.691i	0.396947	+	1.35627i
$191$	−124.768	+	171.728i	−0.653233	+	0.899098i	−0.999234	−	0.0391359i	$-0.987539\pi$
$191$	−124.768	+	171.728i	−0.653233	+	0.899098i	0.346001	+	0.938234i	$0.387539\pi$
$192$	46.7550	−	59.4525i	0.243516	−	0.309648i
$193$	142.877			0.740293			0.370147	−	0.928973i	$-0.379307\pi$
$193$	142.877			0.740293			0.370147	+	0.928973i	$0.379307\pi$
$194$	140.863	−	45.7690i	0.726096	−	0.235923i
$195$	127.105	−	79.8287i	0.651820	−	0.409378i
$196$	17.4961	−	53.8474i	0.0892657	−	0.274732i
$197$	109.468	+	35.5685i	0.555677	+	0.180551i	0.573375	−	0.819293i	$-0.305634\pi$
$197$	109.468	+	35.5685i	0.555677	+	0.180551i	−0.0176979	+	0.999843i	$0.505634\pi$
$198$	−22.1887	−	91.4719i	−0.112064	−	0.461979i
$199$	−134.807			−0.677422			−0.338711	−	0.940890i	$-0.609991\pi$
$199$	−134.807			−0.677422			−0.338711	+	0.940890i	$0.609991\pi$
$200$	−78.9086	−	123.258i	−0.394543	−	0.616291i
$201$	193.670	+	289.109i	0.963532	+	1.43835i
$202$	160.210	−	116.399i	0.793119	−	0.576235i
$203$	−15.8885	−	5.16249i	−0.0782685	−	0.0254310i
$204$	−26.2097	−	92.5149i	−0.128479	−	0.453504i
$205$	−88.1840	−	301.303i	−0.430166	−	1.46977i
$206$	−330.486	+	107.381i	−1.60430	+	0.521269i
$207$	185.859	+	76.4726i	0.897871	+	0.369433i
$208$	−61.0843	−	187.998i	−0.293675	−	0.903838i
$209$	−59.9660	+	82.5362i	−0.286919	+	0.394910i
$210$	115.119	−	28.9820i	0.548184	−	0.138010i
$211$	−79.9128	+	58.0601i	−0.378734	+	0.275166i	−0.760823	−	0.648959i	$-0.775205\pi$
$211$	−79.9128	+	58.0601i	−0.378734	+	0.275166i	0.382090	+	0.924125i	$0.375205\pi$
$212$	37.4335	−	51.5228i	0.176573	−	0.243032i
$213$	−166.637	−	6.35050i	−0.782336	−	0.0298146i
$214$	−27.0834	+	19.6772i	−0.126558	+	0.0919496i
$215$	65.6930	−	85.0382i	0.305549	−	0.395526i
$216$	65.6658	−	143.775i	0.304008	−	0.665626i
$217$	−1.33714	−	4.11529i	−0.00616193	−	0.0189645i
$218$			49.0486i			0.224994i
$219$	89.4528	−	113.746i	0.408460	−	0.519388i
$220$	−11.2988	+	31.5798i	−0.0513584	+	0.143545i
$221$	202.686	+	65.8566i	0.917130	+	0.297993i
$222$	135.511	+	478.327i	0.610410	+	2.15463i
$223$	210.320	−	152.807i	0.943140	−	0.685231i	−0.00603439	−	0.999982i	$-0.501921\pi$
$223$	210.320	−	152.807i	0.943140	−	0.685231i	0.949174	+	0.314750i	$0.101921\pi$
$224$		−	77.3561i		−	0.345340i
$225$	−162.564	−	155.556i	−0.722509	−	0.691362i
$226$	259.323			1.14745
$227$	79.7849	+	109.815i	0.351475	+	0.483764i	0.947749	−	0.319017i	$-0.103353\pi$
$227$	79.7849	+	109.815i	0.351475	+	0.483764i	−0.596274	+	0.802781i	$0.703353\pi$
$228$	99.4189	−	28.1656i	0.436048	−	0.123533i
$229$	−96.8245	+	297.995i	−0.422814	+	1.30129i	0.482257	+	0.876030i	$0.339817\pi$
$229$	−96.8245	+	297.995i	−0.422814	+	1.30129i	−0.905072	+	0.425259i	$0.860183\pi$
$230$	−147.677	−	216.377i	−0.642073	−	0.940769i
$231$	35.4551	+	27.8828i	0.153485	+	0.120705i
$232$	28.9944			0.124976
$233$	−61.2816	+	19.9116i	−0.263011	+	0.0854576i	−0.437554	−	0.899192i	$-0.644155\pi$
$233$	−61.2816	+	19.9116i	−0.263011	+	0.0854576i	0.174543	+	0.984650i	$0.444155\pi$
$234$	−110.826	−	179.898i	−0.473616	−	0.768797i
$235$	−316.001	+	215.670i	−1.34468	+	0.917744i
$236$	−11.3177	−	15.5775i	−0.0479564	−	0.0660063i
$237$	2.46114	−	64.5804i	0.0103845	−	0.272491i
$238$	136.364	+	99.0743i	0.572958	+	0.416279i
$239$	77.7490	+	107.012i	0.325310	+	0.447750i	0.940079	−	0.340957i	$-0.110751\pi$
$239$	77.7490	+	107.012i	0.325310	+	0.447750i	−0.614769	+	0.788707i	$0.710751\pi$
$240$	−250.937	+	157.602i	−1.04557	+	0.656673i
$241$	−85.3756	−	62.0290i	−0.354256	−	0.257382i	0.396396	−	0.918079i	$-0.370261\pi$
$241$	−85.3756	−	62.0290i	−0.354256	−	0.257382i	−0.750652	+	0.660698i	$0.770261\pi$
$242$	225.666	−	73.3234i	0.932505	−	0.302989i
$243$	46.0016	−	238.606i	0.189307	−	0.981918i
$244$	28.8460	+	88.7787i	0.118221	+	0.363847i
$245$	115.001	−	148.866i	0.469391	−	0.607616i
$246$	−425.219	+	120.465i	−1.72853	+	0.489697i
$247$	−70.7711	+	217.811i	−0.286523	+	0.881827i
$248$	4.41418	+	6.07560i	0.0177991	+	0.0244984i
$249$	−183.053	+	122.625i	−0.735154	+	0.492469i
$250$	65.6767	+	285.834i	0.262707	+	1.14333i
$251$		−	72.5890i		−	0.289199i	−0.989490	−	0.144600i	$-0.953811\pi$
$251$		−	72.5890i		−	0.289199i	0.989490	−	0.144600i	$-0.0461894\pi$
$252$	−10.7697	−	44.3978i	−0.0427370	−	0.176182i
$253$	30.7590	−	94.6664i	0.121577	−	0.374175i
$254$	210.938	+	68.5378i	0.830464	+	0.269834i
$255$	21.5567	−	318.745i	0.0845359	−	1.24998i
$256$	78.2347	+	240.782i	0.305604	+	0.940554i
$257$			308.895i			1.20193i	0.799277	+	0.600963i	$0.205216\pi$
$257$			308.895i			1.20193i	−0.799277	+	0.600963i	$0.794784\pi$
$258$	−118.908	−	93.5123i	−0.460883	−	0.362451i
$259$	−192.741	−	140.034i	−0.744173	−	0.540674i
$260$	−2.21597	+	75.2602i	−0.00852296	+	0.289462i
$261$	43.3191	−	10.5081i	0.165974	−	0.0402608i
$262$	183.330	+	133.197i	0.699732	+	0.508385i
$263$	−9.02363	+	12.4200i	−0.0343104	+	0.0472242i	−0.825828	−	0.563923i	$-0.809292\pi$
$263$	−9.02363	+	12.4200i	−0.0343104	+	0.0472242i	0.791517	+	0.611147i	$0.209292\pi$
$264$	−73.4764	−	27.0085i	−0.278320	−	0.102305i
$265$	174.768	−	119.279i	0.659503	−	0.450110i
$266$	−106.468	+	146.540i	−0.400255	+	0.550904i
$267$	−307.878	−	242.124i	−1.15310	−	0.906831i
$268$	−174.561			−0.651348
$269$	325.915	−	105.896i	1.21158	−	0.393666i	0.367571	−	0.929995i	$-0.380189\pi$
$269$	325.915	−	105.896i	1.21158	−	0.393666i	0.844009	+	0.536329i	$0.180189\pi$
$270$	−220.958	+	226.947i	−0.818361	+	0.840543i
$271$	−39.2367	+	120.758i	−0.144785	+	0.445602i	−0.996983	−	0.0776169i	$-0.975269\pi$
$271$	−39.2367	+	120.758i	−0.144785	+	0.445602i	0.852198	+	0.523219i	$0.175269\pi$
$272$	−400.152	−	130.017i	−1.47115	−	0.478004i
$273$	95.0381	+	34.9342i	0.348125	+	0.127964i
$274$	113.970			0.415947
$275$	−70.6914	+	86.1436i	−0.257060	+	0.313250i
$276$	−83.7606	+	56.1099i	−0.303480	+	0.203297i
$277$	84.2329	−	61.1988i	0.304090	−	0.220934i	−0.425267	−	0.905068i	$-0.639820\pi$
$277$	84.2329	−	61.1988i	0.304090	−	0.220934i	0.729356	+	0.684134i	$0.239820\pi$
$278$	442.229	+	143.689i	1.59075	+	0.516866i
$279$	8.79692	+	7.47749i	0.0315302	+	0.0268010i
$280$	33.2600	−	92.9604i	0.118786	−	0.332001i
$281$	183.763	−	59.7084i	0.653962	−	0.212485i	0.0368020	−	0.999323i	$-0.488283\pi$
$281$	183.763	−	59.7084i	0.653962	−	0.212485i	0.617160	+	0.786837i	$0.288283\pi$
$282$	299.748	+	447.462i	1.06294	+	1.58675i
$283$	53.4361	+	164.459i	0.188820	+	0.581128i	0.999993	−	0.00367772i	$-0.00117066\pi$
$283$	53.4361	+	164.459i	0.188820	+	0.581128i	−0.811173	+	0.584806i	$0.801171\pi$
$284$	49.1695	−	67.6761i	0.173132	−	0.238296i
$285$	342.532	+	23.1653i	1.20187	+	0.0812819i
$286$	−84.6626	+	61.5110i	−0.296023	+	0.215073i
$287$	124.487	−	171.341i	0.433751	−	0.597007i
$288$	108.259	+	175.732i	0.375900	+	0.610180i
$289$	133.176	−	96.7583i	0.460818	−	0.334804i
$290$	−54.7068	−	19.5734i	−0.188644	−	0.0674944i
$291$	7.21199	−	189.243i	0.0247835	−	0.650320i
$292$	22.4316	+	69.0373i	0.0768204	+	0.236429i
$293$			207.823i			0.709295i	0.935000	+	0.354647i	$0.115399\pi$
$293$			207.823i			0.709295i	−0.935000	+	0.354647i	$0.884601\pi$
$294$	−208.157	−	163.701i	−0.708019	−	0.556805i
$295$	−17.9696	−	61.3977i	−0.0609140	−	0.208128i
$296$	393.242	+	127.772i	1.32852	+	0.431663i
$297$	−119.566	−	13.7230i	−0.402579	−	0.0462055i
$298$	−5.76652	+	4.18962i	−0.0193507	+	0.0140591i
$299$		−	223.448i		−	0.747318i
$300$	110.217	−	24.3224i	0.367388	−	0.0810745i
$301$	72.4919			0.240837
$302$	−210.310	−	289.467i	−0.696390	−	0.958499i
$303$	−69.0182	−	243.621i	−0.227783	−	0.804029i
$304$	139.720	−	430.013i	0.459604	−	1.41452i
$305$	−9.12792	+	310.008i	−0.0299276	+	1.01642i
$306$	−448.435	−	34.2292i	−1.46548	−	0.111860i
$307$	440.998			1.43648			0.718238	−	0.695797i	$-0.244949\pi$
$307$	440.998			1.43648			0.718238	+	0.695797i	$0.244949\pi$
$308$	−21.5192	+	6.99202i	−0.0698676	+	0.0227014i
$309$	−16.9205	+	443.994i	−0.0547588	+	1.43687i
$310$	−4.22722	−	14.4434i	−0.0136362	−	0.0465915i
$311$	−249.354	−	343.207i	−0.801782	−	1.10356i	−0.992540	−	0.121921i	$-0.961095\pi$
$311$	−249.354	−	343.207i	−0.801782	−	1.10356i	0.190758	−	0.981637i	$-0.438905\pi$
$312$	−175.606	−	6.69230i	−0.562841	−	0.0214497i
$313$	−289.069	−	210.021i	−0.923542	−	0.670993i	0.0208611	−	0.999782i	$-0.493359\pi$
$313$	−289.069	−	210.021i	−0.923542	−	0.670993i	−0.944403	+	0.328790i	$0.893359\pi$
$314$	−323.126	−	444.745i	−1.02907	−	1.41639i
$315$	16.0017	−	150.942i	0.0507991	−	0.479180i
$316$	26.2279	+	19.0557i	0.0829996	+	0.0603027i
$317$	44.8089	−	14.5593i	0.141353	−	0.0459284i	−0.237486	−	0.971391i	$-0.576323\pi$
$317$	44.8089	−	14.5593i	0.141353	−	0.0459284i	0.378839	+	0.925463i	$0.376323\pi$
$318$	−165.780	−	247.475i	−0.521319	−	0.778222i
$319$	−6.82215	−	20.9964i	−0.0213860	−	0.0658195i
$320$	−3.71006	+	126.003i	−0.0115939	+	0.393761i
$321$	11.6675	+	41.1839i	0.0363473	+	0.128299i
$322$	54.6116	−	168.077i	0.169601	−	0.521979i
$323$	286.526	+	394.369i	0.887076	+	1.22096i
$324$	86.6002	+	85.7874i	0.267285	+	0.264776i
$325$	−91.1671	+	232.953i	−0.280514	+	0.716779i
$326$			106.050i			0.325305i
$327$	58.8644	+	21.6374i	0.180013	+	0.0661695i
$328$	−113.586	+	349.581i	−0.346298	+	1.06580i
$329$	−245.463	−	79.7557i	−0.746088	−	0.242419i
$330$	120.403	+	100.562i	0.364858	+	0.304733i
$331$	181.011	+	557.095i	0.546862	+	1.68307i	0.716522	+	0.697564i	$0.245733\pi$
$331$	181.011	+	557.095i	0.546862	+	1.68307i	−0.169661	+	0.985503i	$0.554267\pi$
$332$		−	110.526i		−	0.332909i
$333$	633.831	+	48.3805i	1.90340	+	0.145287i
$334$	−400.081	−	290.676i	−1.19785	−	0.870286i
$335$	−546.072	−	195.377i	−1.63007	−	0.583216i
$336$	−187.629	−	68.9687i	−0.558419	−	0.205264i
$337$	−470.017	−	341.487i	−1.39471	−	1.01332i	−0.995330	−	0.0965292i	$-0.969226\pi$
$337$	−470.017	−	341.487i	−1.39471	−	1.01332i	−0.399379	−	0.916786i	$-0.630774\pi$
$338$	94.9841	−	130.734i	0.281018	−	0.386788i
$339$	114.399	−	311.220i	0.337459	−	0.918053i
$340$	126.824	+	97.9734i	0.373013	+	0.288157i
$341$	3.36105	−	4.62609i	0.00985645	−	0.0135662i
$342$	36.7835	−	481.900i	0.107554	−	1.40906i
$343$	292.183			0.851844
$344$	−119.656	+	38.8785i	−0.347836	+	0.113019i
$345$	−324.826	+	81.7774i	−0.941523	+	0.237036i
$346$	205.863	−	633.581i	0.594979	−	1.83116i
$347$	−162.741	−	52.8779i	−0.468995	−	0.152386i	0.0649787	−	0.997887i	$-0.479302\pi$
$347$	−162.741	−	52.8779i	−0.468995	−	0.152386i	−0.533974	+	0.845501i	$0.679302\pi$
$348$	−7.71468	+	20.9877i	−0.0221686	+	0.0603095i
$349$	−145.329			−0.416415			−0.208208	−	0.978085i	$-0.566763\pi$
$349$	−145.329			−0.416415			−0.208208	+	0.978085i	$0.566763\pi$
$350$	−125.510	+	152.945i	−0.358601	+	0.436987i
$351$	−264.790	+	53.6441i	−0.754389	+	0.152832i
$352$	82.7017	−	60.0863i	0.234948	−	0.170700i
$353$	−352.028	−	114.381i	−0.997248	−	0.324025i	−0.235482	−	0.971879i	$-0.575667\pi$
$353$	−352.028	−	114.381i	−0.997248	−	0.324025i	−0.761765	+	0.647853i	$0.775667\pi$
$354$	−86.6486	+	24.5477i	−0.244770	+	0.0693438i
$355$	229.561	−	156.675i	0.646652	−	0.441338i
$356$	186.865	−	60.7160i	0.524900	−	0.170550i
$357$	179.057	−	119.948i	0.501562	−	0.335988i
$358$	8.38937	+	25.8198i	0.0234340	+	0.0721225i
$359$	306.710	−	422.150i	0.854346	−	1.17591i	−0.128543	−	0.991704i	$-0.541030\pi$
$359$	306.710	−	422.150i	0.854346	−	1.17591i	0.982888	−	0.184202i	$-0.0589700\pi$
$360$	54.5397	+	257.728i	0.151499	+	0.715910i
$361$	−131.743	+	95.7172i	−0.364940	+	0.265145i
$362$	−138.576	+	190.734i	−0.382807	+	0.526888i
$363$	11.5538	−	303.174i	0.0318288	−	0.835189i
$364$	−41.0927	+	29.8556i	−0.112892	+	0.0820209i
$365$	−7.09818	+	241.073i	−0.0194471	+	0.660474i
$366$	436.288	+	16.6268i	1.19204	+	0.0454284i
$367$	176.644	+	543.654i	0.481318	+	1.48134i	0.837243	+	0.546830i	$0.184166\pi$
$367$	176.644	+	543.654i	0.481318	+	1.48134i	−0.355925	+	0.934514i	$0.615834\pi$
$368$			441.142i			1.19875i
$369$	−43.0088	+	563.458i	−0.116555	+	1.52699i
$370$	−655.716	−	506.549i	−1.77221	−	1.36905i
$371$	135.756	+	44.1099i	0.365920	+	0.118895i
$372$	−5.57235	+	1.57866i	−0.0149794	+	0.00424370i
$373$	−528.046	+	383.648i	−1.41567	+	1.02855i	−0.423206	+	0.906034i	$0.639095\pi$
$373$	−528.046	+	383.648i	−1.41567	+	1.02855i	−0.992467	+	0.122513i	$0.960905\pi$
$374$			222.743i			0.595570i
$375$	372.008	+	47.2732i	0.992022	+	0.126062i
$376$	447.937			1.19132
$377$	−29.1303	−	40.0944i	−0.0772686	−	0.106351i
$378$	−212.286	−	24.3648i	−0.561602	−	0.0644572i
$379$	54.8305	−	168.751i	0.144672	−	0.445253i	−0.852297	−	0.523058i	$-0.824791\pi$
$379$	54.8305	−	168.751i	0.144672	−	0.445253i	0.996969	+	0.0778047i	$0.0247911\pi$
$380$	−105.285	+	136.289i	−0.277065	+	0.358654i
$381$	175.308	−	222.916i	0.460125	−	0.585083i
$382$	−498.033			−1.30375
$383$	−297.376	+	96.6232i	−0.776437	+	0.252280i	−0.670318	−	0.742074i	$-0.733842\pi$
$383$	−297.376	+	96.6232i	−0.776437	+	0.252280i	−0.106119	+	0.994353i	$0.533842\pi$
$384$	452.333	+	17.2383i	1.17795	+	0.0448913i
$385$	−75.1435	−	2.21253i	−0.195178	−	0.00574684i
$386$	197.040	+	271.203i	0.510467	+	0.702598i
$387$	−164.682	+	101.452i	−0.425534	+	0.262149i
$388$	76.8569	+	55.8398i	0.198085	+	0.143917i
$389$	244.283	+	336.226i	0.627976	+	0.864335i	0.997903	−	0.0647257i	$-0.0206172\pi$
$389$	244.283	+	336.226i	0.627976	+	0.864335i	−0.369927	+	0.929061i	$0.620617\pi$
$390$	326.817	+	131.174i	0.837993	+	0.336345i
$391$	−384.773	−	279.554i	−0.984075	−	0.714972i
$392$	−209.467	+	68.0599i	−0.534354	+	0.173622i
$393$	240.727	−	161.260i	0.612537	−	0.410330i
$394$	83.4527	+	256.841i	0.211809	+	0.651880i
$395$	60.7195	+	88.9665i	0.153720	+	0.225232i
$396$	39.1005	−	45.9999i	0.0987386	−	0.116161i
$397$	−48.7772	+	150.121i	−0.122865	+	0.378138i	−0.993506	−	0.113780i	$-0.963704\pi$
$397$	−48.7772	+	150.121i	−0.122865	+	0.378138i	0.870641	+	0.491918i	$0.163704\pi$
$398$	−185.911	−	255.885i	−0.467114	−	0.642928i
$399$	128.899	+	192.420i	0.323055	+	0.482255i
$400$	179.986	−	459.907i	0.449966	−	1.14977i
$401$		−	4.30333i		−	0.0107315i	−0.999986	−	0.00536575i	$-0.998292\pi$
$401$		−	4.30333i		−	0.0107315i	0.999986	−	0.00536575i	$-0.00170798\pi$
$402$	−281.687	+	766.326i	−0.700713	+	1.90628i
$403$	3.96667	−	12.2081i	0.00984284	−	0.0302932i
$404$	120.802	+	39.2510i	0.299015	+	0.0971558i
$405$	174.890	+	365.292i	0.431828	+	0.901956i
$406$	−12.1125	−	37.2785i	−0.0298338	−	0.0918189i
$407$		−	314.832i		−	0.773542i
$408$	−231.224	+	294.018i	−0.566725	+	0.720633i
$409$	444.826	+	323.185i	1.08759	+	0.790183i	0.978991	−	0.203902i	$-0.0653625\pi$
$409$	444.826	+	323.185i	1.08759	+	0.790183i	0.108602	+	0.994085i	$0.465363\pi$
$410$	450.307	−	582.913i	1.09831	−	1.42174i
$411$	50.2768	−	136.778i	0.122328	−	0.332792i
$412$	−180.318	−	131.009i	−0.437666	−	0.317983i
$413$	25.3671	−	34.9149i	0.0614216	−	0.0845396i
$414$	111.160	+	458.253i	0.268503	+	1.10689i
$415$	123.706	−	345.753i	0.298086	−	0.833140i
$416$	134.885	−	185.653i	0.324242	−	0.446281i
$417$	367.530	−	467.342i	0.881367	−	1.12072i
$418$	−239.366			−0.572645
$419$	−85.5387	+	27.7932i	−0.204150	+	0.0663322i	−0.409307	−	0.912397i	$-0.634229\pi$
$419$	−85.5387	+	27.7932i	−0.204150	+	0.0663322i	0.205157	+	0.978729i	$0.434229\pi$
$420$	58.4401	+	48.8098i	0.139143	+	0.116214i
$421$	90.6646	−	279.037i	0.215355	−	0.662796i	−0.783773	−	0.621048i	$-0.786707\pi$
$421$	90.6646	−	279.037i	0.215355	−	0.662796i	0.999128	−	0.0417480i	$-0.0132927\pi$
$422$	−220.415	−	71.6170i	−0.522309	−	0.169709i
$423$	669.242	−	162.340i	1.58213	−	0.383783i
$424$	−247.737			−0.584287
$425$	287.083	+	448.434i	0.675488	+	1.05514i
$426$	−217.754	−	325.063i	−0.511161	−	0.763058i
$427$	−169.267	+	122.980i	−0.396410	+	0.288009i
$428$	−20.4215	−	6.63534i	−0.0477137	−	0.0155031i
$429$	36.4725	+	128.741i	0.0850175	+	0.300095i
$430$	252.013	+	7.42029i	0.586076	+	0.0172565i
$431$	−42.4635	+	13.7972i	−0.0985231	+	0.0320121i	−0.357864	−	0.933774i	$-0.616495\pi$
$431$	−42.4635	+	13.7972i	−0.0985231	+	0.0320121i	0.259341	+	0.965786i	$0.416495\pi$
$432$	522.762	−	105.907i	1.21010	−	0.245155i
$433$	−62.8414	−	193.406i	−0.145130	−	0.446665i	0.851898	−	0.523708i	$-0.175452\pi$
$433$	−62.8414	−	193.406i	−0.145130	−	0.446665i	−0.997028	+	0.0770437i	$0.975452\pi$
$434$	5.96744	−	8.21347i	0.0137499	−	0.0189250i
$435$	−47.6240	+	57.0203i	−0.109480	+	0.131081i
$436$	−25.4519	+	18.4919i	−0.0583759	+	0.0424126i
$437$	300.416	−	413.487i	0.687451	−	0.946195i
$438$	339.272	+	12.9295i	0.774593	+	0.0295195i
$439$	−232.609	+	169.000i	−0.529861	+	0.384966i	−0.820306	−	0.571925i	$-0.806197\pi$
$439$	−232.609	+	169.000i	−0.529861	+	0.384966i	0.290445	+	0.956892i	$0.406197\pi$
$440$	125.219	−	36.6485i	0.284589	−	0.0832921i
$441$	−288.288	+	177.599i	−0.653715	+	0.402720i
$442$	154.516	+	475.552i	0.349584	+	1.07591i
$443$			16.3231i			0.0368468i	0.999830	+	0.0184234i	$0.00586469\pi$
$443$			16.3231i			0.0368468i	−0.999830	+	0.0184234i	$0.994135\pi$
$444$	−197.120	+	250.653i	−0.443965	+	0.564534i
$445$	652.517	+	19.2128i	1.46633	+	0.0431748i
$446$	580.103	+	188.487i	1.30068	+	0.422616i
$447$	2.48421	+	8.76876i	0.00555751	+	0.0196169i
$448$	−68.7990	+	49.9854i	−0.153569	+	0.111575i
$449$		−	38.4769i		−	0.0856946i	−0.999082	−	0.0428473i	$-0.986357\pi$
$449$		−	38.4769i		−	0.0856946i	0.999082	−	0.0428473i	$-0.0136429\pi$
$450$	71.0793	−	523.100i	0.157954	−	1.16244i
$451$	279.876			0.620568
$452$	97.7678	+	134.566i	0.216301	+	0.297712i
$453$	−440.172	+	124.702i	−0.971683	+	0.275280i
$454$	−98.4146	+	302.889i	−0.216772	+	0.667157i
$455$	−161.964	+	47.4030i	−0.355966	+	0.104183i
$456$	−315.959	−	248.479i	−0.692894	−	0.544910i
$457$	−520.156			−1.13820			−0.569099	−	0.822269i	$-0.692708\pi$
$457$	−520.156			−1.13820			−0.569099	+	0.822269i	$0.692708\pi$
$458$	−699.173	+	227.175i	−1.52658	+	0.496015i
$459$	−238.903	+	523.078i	−0.520486	+	1.13960i
$460$	56.6046	−	158.208i	0.123054	−	0.343930i
$461$	26.9185	+	37.0502i	0.0583916	+	0.0803692i	0.837214	−	0.546875i	$-0.184183\pi$
$461$	26.9185	+	37.0502i	0.0583916	+	0.0803692i	−0.778823	+	0.627244i	$0.784183\pi$
$462$	−4.03019	+	105.752i	−0.00872336	+	0.228901i
$463$	−277.239	−	201.426i	−0.598789	−	0.435045i	0.246660	−	0.969102i	$-0.420667\pi$
$463$	−277.239	−	201.426i	−0.598789	−	0.435045i	−0.845449	+	0.534057i	$0.820667\pi$
$464$	57.5104	+	79.1562i	0.123945	+	0.170595i
$465$	−19.1987	−	1.29840i	−0.0412874	−	0.00279225i
$466$	−122.309	−	88.8624i	−0.262465	−	0.190692i
$467$	521.860	−	169.562i	1.11747	−	0.363089i	0.308670	−	0.951169i	$-0.400116\pi$
$467$	521.860	−	169.562i	1.11747	−	0.363089i	0.808803	+	0.588080i	$0.200116\pi$
$468$	51.5687	−	125.333i	0.110189	−	0.267805i
$469$	−120.905	−	372.106i	−0.257792	−	0.793403i
$470$	−845.171	−	302.391i	−1.79824	−	0.643385i
$471$	−676.294	+	191.596i	−1.43587	+	0.406785i
$472$	−23.1458	+	71.2355i	−0.0490378	+	0.150923i
$473$	56.3080	+	77.5013i	0.119044	+	0.163851i
$474$	125.978	−	84.3908i	0.265776	−	0.178040i
$475$	−481.899	+	308.506i	−1.01452	+	0.649487i
$476$			108.113i			0.227128i
$477$	−370.133	+	89.7844i	−0.775960	+	0.188227i
$478$	−95.9033	+	295.160i	−0.200635	+	0.617490i
$479$	325.428	+	105.738i	0.679389	+	0.220747i	0.628328	−	0.777948i	$-0.283740\pi$
$479$	325.428	+	105.738i	0.679389	+	0.220747i	0.0510614	+	0.998696i	$0.483740\pi$
$480$	−319.248	−	128.136i	−0.665100	−	0.266951i
$481$	−218.398	−	672.159i	−0.454049	−	1.39742i
$482$		−	247.600i		−	0.513694i
$483$	−177.622	−	139.687i	−0.367747	−	0.289206i
$484$	123.127	+	89.4571i	0.254395	+	0.184829i
$485$	177.929	+	260.703i	0.366865	+	0.537532i
$486$	516.353	−	241.742i	1.06245	−	0.497411i
$487$	104.270	+	75.7569i	0.214108	+	0.155558i	0.689670	−	0.724124i	$-0.257755\pi$
$487$	104.270	+	75.7569i	0.214108	+	0.155558i	−0.475563	+	0.879682i	$0.657755\pi$
$488$	213.438	−	293.772i	0.437373	−	0.601992i
$489$	127.273	+	46.7830i	0.260271	+	0.0956707i
$490$	441.169	+	12.9898i	0.900344	+	0.0265098i
$491$	−86.5002	+	119.057i	−0.176171	+	0.242479i	−0.887967	−	0.459908i	$-0.847882\pi$
$491$	−86.5002	+	119.057i	−0.176171	+	0.242479i	0.711795	+	0.702387i	$0.247882\pi$
$492$	−222.823	−	175.234i	−0.452893	−	0.356167i
$493$	−105.486			−0.213968
$494$	−511.040	+	166.047i	−1.03449	+	0.336128i
$495$	173.802	−	100.136i	0.351114	−	0.202296i
$496$	−7.83118	+	24.1019i	−0.0157887	+	0.0485925i
$497$	178.319	+	57.9392i	0.358790	+	0.116578i
$498$	−485.209	−	178.354i	−0.974315	−	0.358140i
$499$	799.679			1.60256			0.801282	−	0.598287i	$-0.204152\pi$
$499$	799.679			1.60256			0.801282	+	0.598287i	$0.204152\pi$
$500$	−123.561	+	141.843i	−0.247123	+	0.283686i
$501$	−525.339	+	351.917i	−1.04858	+	0.702429i
$502$	137.786	−	100.107i	0.274473	−	0.199417i
$503$	−194.978	−	63.3521i	−0.387630	−	0.125949i	0.108717	−	0.994073i	$-0.465326\pi$
$503$	−194.978	−	63.3521i	−0.387630	−	0.125949i	−0.496347	+	0.868124i	$0.665326\pi$
$504$	−115.099	+	135.408i	−0.228370	+	0.268667i
$505$	333.968	+	257.995i	0.661323	+	0.510880i
$506$	222.111	−	72.1684i	0.438955	−	0.142625i
$507$	−114.996	−	171.665i	−0.226816	−	0.338590i
$508$	43.9609	+	135.298i	0.0865371	+	0.266334i
$509$	134.410	−	184.999i	0.264067	−	0.363457i	−0.656309	−	0.754492i	$-0.727883\pi$
$509$	134.410	−	184.999i	0.264067	−	0.363457i	0.920375	+	0.391036i	$0.127883\pi$
$510$	634.759	−	398.662i	1.24462	−	0.781690i
$511$	−131.628	+	95.6332i	−0.257589	+	0.187149i
$512$	5.60744	−	7.71797i	0.0109520	−	0.0150742i
$513$	−562.113	−	256.731i	−1.09574	−	0.500451i
$514$	−586.332	+	425.995i	−1.14072	+	0.828784i
$515$	−417.450	−	611.650i	−0.810583	−	1.18767i
$516$	3.69503	−	96.9578i	0.00716091	−	0.187903i
$517$	−105.396	−	324.376i	−0.203861	−	0.627419i
$518$		−	558.974i		−	1.07910i
$519$	−669.560	−	526.560i	−1.29010	−	1.01457i
$520$	241.917	−	165.108i	0.465225	−	0.317515i
$521$	−910.957	−	295.988i	−1.74848	−	0.568115i	−0.752571	−	0.658511i	$-0.771187\pi$
$521$	−910.957	−	295.988i	−1.74848	−	0.568115i	−0.995906	+	0.0903961i	$0.971187\pi$
$522$	79.6872	+	67.7351i	0.152657	+	0.129761i
$523$	445.173	−	323.437i	0.851192	−	0.618427i	−0.0742825	−	0.997237i	$-0.523667\pi$
$523$	445.173	−	323.437i	0.851192	−	0.618427i	0.925474	+	0.378810i	$0.123667\pi$
$524$			145.349i			0.277383i
$525$	128.185	+	218.099i	0.244162	+	0.415426i
$526$	−36.0195			−0.0684782
$527$	−16.0595	−	22.1040i	−0.0304735	−	0.0419432i
$528$	−72.0057	−	254.166i	−0.136374	−	0.481375i
$529$	9.37463	−	28.8522i	0.0177214	−	0.0545409i
$530$	467.433	+	167.241i	0.881948	+	0.315549i
$531$	−8.76408	+	114.818i	−0.0165049	+	0.216230i
$532$	−116.181			−0.218385
$533$	597.530	−	194.149i	1.12107	−	0.364257i
$534$	34.9966	−	918.314i	0.0655368	−	1.71969i
$535$	−56.4570	−	43.6138i	−0.105527	−	0.0815210i
$536$	399.132	+	549.358i	0.744650	+	1.02492i
$537$	34.6879	+	1.32194i	0.0645957	+	0.00246172i
$538$	650.476	+	472.598i	1.20906	+	0.878435i
$539$	98.5716	+	135.672i	0.182879	+	0.251711i
$540$	−201.069	−	29.0960i	−0.372349	−	0.0538815i
$541$	82.6806	+	60.0710i	0.152829	+	0.111037i	0.661572	−	0.749882i	$-0.269890\pi$
$541$	82.6806	+	60.0710i	0.152829	+	0.111037i	−0.508743	+	0.860919i	$0.669890\pi$
$542$	−283.329	+	92.0592i	−0.522748	+	0.169851i
$543$	167.772	+	250.449i	0.308972	+	0.461232i
$544$	−150.938	−	464.538i	−0.277459	−	0.853930i
$545$	−100.317	+	29.3603i	−0.184068	+	0.0538722i
$546$	64.7558	+	228.575i	0.118600	+	0.418636i
$547$	304.596	−	937.449i	0.556847	−	1.71380i	−0.134166	−	0.990959i	$-0.542836\pi$
$547$	304.596	−	937.449i	0.556847	−	1.71380i	0.691014	−	0.722841i	$-0.257164\pi$
$548$	42.9678	+	59.1401i	0.0784084	+	0.107920i
$549$	212.419	−	516.265i	0.386920	−	0.940373i
$550$	−261.004	−	15.3834i	−0.474554	−	0.0279699i
$551$		−	113.358i		−	0.205732i
$552$	368.100	+	135.307i	0.666848	+	0.245121i
$553$	−22.4543	+	69.1074i	−0.0406046	+	0.124968i
$554$	232.330	+	75.4886i	0.419368	+	0.136261i
$555$	−897.186	+	563.480i	−1.61655	+	1.01528i
$556$	92.1634	+	283.650i	0.165762	+	0.510162i
$557$		−	348.660i		−	0.625961i	−0.949759	−	0.312981i	$-0.898672\pi$
$557$		−	348.660i		−	0.625961i	0.949759	−	0.312981i	$-0.101328\pi$
$558$	−2.06169	+	27.0101i	−0.00369478	+	0.0484052i
$559$	173.979	+	126.403i	0.311232	+	0.226123i
$560$	319.758	−	93.5853i	0.570996	−	0.167117i
$561$	267.320	+	98.2616i	0.476505	+	0.175154i
$562$	366.763	+	266.469i	0.652603	+	0.474144i
$563$	−332.220	+	457.261i	−0.590089	+	0.812187i	−0.994756	−	0.102277i	$-0.967387\pi$
$563$	−332.220	+	457.261i	−0.590089	+	0.812187i	0.404667	+	0.914464i	$0.367387\pi$
$564$	−119.185	+	324.241i	−0.211321	+	0.574896i
$565$	155.230	+	530.383i	0.274744	+	0.938731i
$566$	−238.477	+	328.235i	−0.421337	+	0.579920i
$567$	−122.889	+	244.021i	−0.216736	+	0.430372i
$568$	−325.408			−0.572901
$569$	−682.400	+	221.725i	−1.19930	+	0.389675i	−0.839502	−	0.543356i	$-0.817153\pi$
$569$	−682.400	+	221.725i	−1.19930	+	0.389675i	−0.359795	+	0.933032i	$0.617153\pi$
$570$	428.412	+	682.128i	0.751601	+	1.19672i
$571$	−34.4260	+	105.952i	−0.0602908	+	0.185556i	−0.976666	−	0.214765i	$-0.931101\pi$
$571$	−34.4260	+	105.952i	−0.0602908	+	0.185556i	0.916375	+	0.400321i	$0.131101\pi$
$572$	−63.8375	−	20.7421i	−0.111604	−	0.0362623i
$573$	−219.704	+	597.701i	−0.383427	+	1.04311i
$574$	496.911			0.865699
$575$	354.148	−	431.560i	0.615909	−	0.750539i
$576$	86.3382	−	209.837i	0.149893	−	0.364300i
$577$	525.110	−	381.515i	0.910070	−	0.661204i	−0.0309627	−	0.999521i	$-0.509857\pi$
$577$	525.110	−	381.515i	0.910070	−	0.661204i	0.941033	+	0.338316i	$0.109857\pi$
$578$	367.325	+	119.351i	0.635511	+	0.206490i
$579$	412.400	−	116.834i	0.712262	−	0.201785i
$580$	−10.4682	−	35.7674i	−0.0180487	−	0.0616679i
$581$	235.604	−	76.5524i	0.405514	−	0.131760i
$582$	369.160	−	247.295i	0.634295	−	0.424905i
$583$	58.2906	+	179.400i	0.0999839	+	0.307719i
$584$	165.976	−	228.447i	0.284206	−	0.391176i
$585$	301.599	−	334.355i	0.515553	−	0.571546i
$586$	−394.482	+	286.608i	−0.673178	+	0.489092i
$587$	−596.191	+	820.586i	−1.01566	+	1.39793i	−0.100453	+	0.994942i	$0.532029\pi$
$587$	−596.191	+	820.586i	−1.01566	+	1.39793i	−0.915204	+	0.402990i	$0.867971\pi$
$588$	6.46844	−	169.732i	0.0110008	−	0.288660i
$589$	23.7536	−	17.2580i	0.0403286	−	0.0293005i
$590$	91.7609	−	118.782i	0.155527	−	0.201326i
$591$	345.055	+	13.1499i	0.583850	+	0.0222503i
$592$	431.171	+	1327.01i	0.728329	+	2.24157i
$593$			329.734i			0.556044i	0.960575	+	0.278022i	$0.0896788\pi$
$593$			329.734i			0.556044i	−0.960575	+	0.278022i	$0.910321\pi$
$594$	−138.844	−	245.881i	−0.233744	−	0.413941i
$595$	−121.005	+	338.205i	−0.203370	+	0.568412i
$596$	−4.34809	−	1.41278i	−0.00729545	−	0.00237043i
$597$	−389.107	+	110.235i	−0.651771	+	0.184648i
$598$	424.140	−	308.156i	0.709264	−	0.515311i
$599$		−	156.310i		−	0.260952i	−0.991451	−	0.130476i	$-0.958349\pi$
$599$		−	156.310i		−	0.260952i	0.991451	−	0.130476i	$-0.0416506\pi$
$600$	−328.553	−	291.248i	−0.547589	−	0.485413i
$601$	−324.144			−0.539340			−0.269670	−	0.962953i	$-0.586915\pi$
$601$	−324.144			−0.539340			−0.269670	+	0.962953i	$0.586915\pi$
$602$	99.9731	+	137.601i	0.166068	+	0.228573i
$603$	795.421	+	676.118i	1.31911	+	1.12126i
$604$	70.9184	−	218.264i	0.117415	−	0.361365i
$605$	285.048	+	417.655i	0.471155	+	0.690338i
$606$	367.248	−	466.983i	0.606020	−	0.770600i
$607$	−966.327			−1.59197			−0.795986	−	0.605315i	$-0.793047\pi$
$607$	−966.327			−1.59197			−0.795986	+	0.605315i	$0.793047\pi$
$608$	499.204	−	162.201i	0.821060	−	0.266778i
$609$	−50.0821	−	1.90861i	−0.0822366	−	0.00313401i
$610$	−601.034	+	410.205i	−0.985302	+	0.672467i
$611$	−450.036	−	619.422i	−0.736557	−	1.01378i
$612$	−151.303	−	245.603i	−0.247228	−	0.401312i
$613$	183.532	+	133.344i	0.299400	+	0.217527i	0.727335	−	0.686283i	$-0.240759\pi$
$613$	183.532	+	133.344i	0.299400	+	0.217527i	−0.427935	+	0.903809i	$0.640759\pi$
$614$	608.178	+	837.085i	0.990518	+	1.36333i
$615$	−500.918	−	797.572i	−0.814500	−	1.29687i
$616$	71.2079	+	51.7356i	0.115597	+	0.0839863i
$617$	−191.858	+	62.3386i	−0.310954	+	0.101035i	−0.460337	−	0.887744i	$-0.652271\pi$
$617$	−191.858	+	62.3386i	−0.310954	+	0.101035i	0.149383	+	0.988779i	$0.452271\pi$
$618$	−866.107	+	580.192i	−1.40147	+	0.938822i
$619$	−57.1032	−	175.746i	−0.0922508	−	0.283919i	0.894277	−	0.447514i	$-0.147691\pi$
$619$	−57.1032	−	175.746i	−0.0922508	−	0.283919i	−0.986527	+	0.163596i	$0.947691\pi$
$620$	5.90113	−	7.63887i	0.00951794	−	0.0123208i
$621$	598.998	+	68.7493i	0.964570	+	0.110707i
$622$	307.578	−	946.628i	0.494499	−	1.52191i
$623$	258.852	+	356.280i	0.415493	+	0.571877i
$624$	−330.045	−	492.689i	−0.528918	−	0.789565i
$625$	−545.289	+	305.425i	−0.872463	+	0.488680i
$626$		−	838.337i		−	1.33920i
$627$	−105.594	+	287.268i	−0.168412	+	0.458163i
$628$	108.961	−	335.348i	0.173505	−	0.533994i
$629$	−1430.68	−	464.856i	−2.27453	−	0.739040i
$630$	308.579	−	177.789i	0.489808	−	0.282205i
$631$	207.738	+	639.352i	0.329220	+	1.01324i	0.969500	+	0.245093i	$0.0788186\pi$
$631$	207.738	+	639.352i	0.329220	+	1.01324i	−0.640279	+	0.768142i	$0.721181\pi$
$632$		−	126.112i		−	0.199544i
$633$	−183.184	+	232.931i	−0.289390	+	0.367980i
$634$	89.4316	+	64.9759i	0.141059	+	0.102486i
$635$	−13.9108	+	472.449i	−0.0219068	+	0.744014i
$636$	65.9167	−	179.326i	0.103643	−	0.281959i
$637$	304.564	+	221.278i	0.478122	+	0.347376i
$638$	30.4462	−	41.9055i	0.0477213	−	0.0656827i
$639$	−486.176	+	117.933i	−0.760839	+	0.184559i
$640$	−623.138	+	425.290i	−0.973653	+	0.664516i
$641$	468.123	−	644.316i	0.730301	−	1.00517i	−0.268817	−	0.963191i	$-0.586633\pi$
$641$	468.123	−	644.316i	0.730301	−	1.00517i	0.999118	−	0.0419820i	$-0.0133672\pi$
$642$	−62.0830	+	78.9431i	−0.0967025	+	0.122964i
$643$	365.802			0.568899			0.284449	−	0.958691i	$-0.408189\pi$
$643$	365.802			0.568899			0.284449	+	0.958691i	$0.408189\pi$
$644$	107.806	−	35.0284i	0.167401	−	0.0543919i
$645$	120.079	−	299.173i	0.186169	−	0.463834i
$646$	−353.429	+	1087.74i	−0.547104	+	1.68381i
$647$	611.528	+	198.698i	0.945175	+	0.307106i	0.740754	−	0.671777i	$-0.234469\pi$
$647$	611.528	+	198.698i	0.945175	+	0.307106i	0.204422	+	0.978883i	$0.434469\pi$
$648$	71.9697	−	468.690i	0.111064	−	0.723287i
$649$	57.0315			0.0878760
$650$	−567.910	+	148.215i	−0.873708	+	0.228022i
$651$	−7.22469	−	10.7850i	−0.0110978	−	0.0165668i
$652$	−55.0304	+	39.9819i	−0.0844024	+	0.0613219i
$653$	−188.649	−	61.2957i	−0.288895	−	0.0938678i	0.160984	−	0.986957i	$-0.448533\pi$
$653$	−188.649	−	61.2957i	−0.288895	−	0.0938678i	−0.449880	+	0.893089i	$0.648533\pi$
$654$	40.1082	+	141.574i	0.0613275	+	0.216474i
$655$	−162.681	+	454.688i	−0.248368	+	0.694180i
$656$	−1179.67	+	383.299i	−1.79828	+	0.584297i
$657$	165.184	−	401.464i	0.251422	−	0.611057i
$658$	−187.127	−	575.919i	−0.284388	−	0.875256i
$659$	573.854	−	789.842i	0.870795	−	1.19855i	−0.108092	−	0.994141i	$-0.534474\pi$
$659$	573.854	−	789.842i	0.870795	−	1.19855i	0.978886	−	0.204405i	$-0.0655260\pi$
$660$	−6.78944	+	100.392i	−0.0102870	+	0.152108i
$661$	601.856	−	437.274i	0.910524	−	0.661534i	−0.0306237	−	0.999531i	$-0.509749\pi$
$661$	601.856	−	437.274i	0.910524	−	0.661534i	0.941147	+	0.337997i	$0.109749\pi$
$662$	−807.824	+	1111.87i	−1.22028	+	1.67957i
$663$	638.885	+	24.3477i	0.963628	+	0.0367235i
$664$	−347.834	+	252.716i	−0.523846	+	0.380596i
$665$	−363.444	−	130.036i	−0.546533	−	0.195542i
$666$	782.279	+	1269.83i	1.17459	+	1.90666i
$667$	34.1774	+	105.187i	0.0512405	+	0.157702i
$668$		−	317.195i		−	0.474842i
$669$	482.116	−	613.045i	0.720651	−	0.916361i
$670$	−382.227	−	1305.98i	−0.570489	−	1.94922i
$671$	−262.956	−	85.4397i	−0.391887	−	0.127332i
$672$	−63.2560	−	223.281i	−0.0941309	−	0.332263i
$673$	−257.702	+	187.231i	−0.382915	+	0.278204i	−0.762546	−	0.646934i	$-0.776051\pi$
$673$	−257.702	+	187.231i	−0.382915	+	0.278204i	0.379631	+	0.925138i	$0.376051\pi$
$674$		−	1363.11i		−	2.02242i
$675$	−596.429	−	316.066i	−0.883598	−	0.468246i
$676$	103.650			0.153328
$677$	323.236	+	444.896i	0.477453	+	0.657158i	0.978013	−	0.208544i	$-0.0668725\pi$
$677$	323.236	+	444.896i	0.477453	+	0.657158i	−0.500560	+	0.865702i	$0.666873\pi$
$678$	748.512	−	212.055i	1.10400	−	0.312765i
$679$	−65.7991	+	202.509i	−0.0969059	+	0.298246i
$680$	18.3478	−	623.142i	0.0269821	−	0.916385i
$681$	320.089	+	251.727i	0.470029	+	0.369643i
$682$	13.4163			0.0196719
$683$	173.358	−	56.3274i	0.253818	−	0.0824705i	−0.179344	−	0.983786i	$-0.557398\pi$
$683$	173.358	−	56.3274i	0.253818	−	0.0824705i	0.433162	+	0.901316i	$0.357398\pi$
$684$	263.931	−	162.594i	0.385865	−	0.237711i
$685$	68.2218	+	233.097i	0.0995939	+	0.340288i
$686$	402.947	+	554.609i	0.587386	+	0.808468i
$687$	−35.7968	+	939.310i	−0.0521060	+	1.36726i
$688$	−343.477	−	249.551i	−0.499240	−	0.362719i
$689$	248.898	+	342.579i	0.361246	+	0.497212i
$690$	−603.192	−	503.792i	−0.874191	−	0.730134i
$691$	665.823	+	483.748i	0.963564	+	0.700070i	0.953976	−	0.299884i	$-0.0969480\pi$
$691$	665.823	+	483.748i	0.963564	+	0.700070i	0.00958808	+	0.999954i	$0.496948\pi$
$692$	406.385	−	132.042i	0.587261	−	0.190813i
$693$	125.138	+	51.4887i	0.180575	+	0.0742982i
$694$	−124.065	−	381.833i	−0.178768	−	0.550191i
$695$	−29.1639	+	990.483i	−0.0419624	+	1.42516i
$696$	83.6895	−	23.7094i	0.120244	−	0.0340653i
$697$	413.244	−	1271.83i	0.592889	−	1.82473i
$698$	−200.422	−	275.858i	−0.287138	−	0.395212i
$699$	−160.601	+	107.584i	−0.229759	+	0.153912i
$700$	−126.684	−	7.46666i	−0.180977	−	0.0106667i
$701$			985.600i			1.40599i	0.711194	+	0.702996i	$0.248155\pi$
$701$			985.600i			1.40599i	−0.711194	+	0.702996i	$0.751845\pi$
$702$	−466.996	−	428.634i	−0.665237	−	0.610590i
$703$	499.547	−	1537.45i	0.710593	−	2.18698i
$704$	−106.879	−	34.7271i	−0.151817	−	0.0493283i
$705$	−735.747	+	880.912i	−1.04361	+	1.24952i
$706$	−268.367	−	825.948i	−0.380123	−	1.16990i
$707$			284.696i			0.402681i
$708$	−45.4056	−	35.7082i	−0.0641322	−	0.0504353i
$709$	516.660	+	375.376i	0.728717	+	0.529444i	0.889157	−	0.457602i	$-0.151291\pi$
$709$	516.660	+	375.376i	0.728717	+	0.529444i	−0.160441	+	0.987046i	$0.551291\pi$
$710$	613.981	+	219.674i	0.864762	+	0.309400i
$711$	−45.7051	−	188.418i	−0.0642828	−	0.265004i
$712$	−618.342	−	449.252i	−0.868457	−	0.630971i
$713$	−16.8381	+	23.1756i	−0.0236158	+	0.0325044i
$714$	474.617	+	174.460i	0.664730	+	0.244342i
$715$	−176.485	−	136.337i	−0.246832	−	0.190680i
$716$	−10.2353	+	14.0877i	−0.0142951	+	0.0196756i
$717$	311.921	+	245.303i	0.435037	+	0.342125i
$718$	1224.29			1.70514
$719$	−69.1035	+	22.4531i	−0.0961106	+	0.0312282i	−0.356678	−	0.934228i	$-0.616091\pi$
$719$	−69.1035	+	22.4531i	−0.0961106	+	0.0312282i	0.260567	+	0.965456i	$0.416091\pi$
$720$	−595.430	+	660.099i	−0.826986	+	0.916804i
$721$	154.375	−	475.118i	0.214112	−	0.658970i
$722$	−363.373	−	118.067i	−0.503287	−	0.163528i
$723$	−297.151	−	109.227i	−0.410997	−	0.151075i
$724$	−151.219			−0.208865
$725$	7.28526	−	123.606i	0.0100486	−	0.170491i
$726$	591.406	−	396.174i	0.814608	−	0.545694i
$727$	−20.2988	+	14.7479i	−0.0279213	+	0.0202860i	−0.601658	−	0.798754i	$-0.705493\pi$
$727$	−20.2988	+	14.7479i	−0.0279213	+	0.0202860i	0.573737	+	0.819040i	$0.305493\pi$
$728$	187.916	+	61.0576i	0.258126	+	0.0838704i
$729$	−62.3348	−	726.330i	−0.0855073	−	0.996338i
$730$	−467.384	+	318.989i	−0.640252	+	0.436971i
$731$	435.327	−	141.446i	0.595523	−	0.193497i
$732$	155.858	+	232.663i	0.212920	+	0.317846i
$733$	−94.8689	−	291.977i	−0.129426	−	0.398331i	0.865256	−	0.501331i	$-0.167156\pi$
$733$	−94.8689	−	291.977i	−0.129426	−	0.398331i	−0.994681	+	0.103000i	$0.967156\pi$
$734$	−788.333	+	1085.05i	−1.07402	+	1.47827i
$735$	210.208	−	523.727i	0.285997	−	0.712553i
$736$	−414.317	+	301.019i	−0.562930	+	0.408993i
$737$	303.907	−	418.293i	0.412358	−	0.567561i
$738$	−1128.85	+	695.423i	−1.52960	+	0.942308i
$739$	253.991	−	184.536i	0.343696	−	0.249710i	−0.402524	−	0.915410i	$-0.631867\pi$
$739$	253.991	−	184.536i	0.343696	−	0.249710i	0.746220	+	0.665700i	$0.231867\pi$
$740$	15.6417	−	531.233i	0.0211374	−	0.717883i
$741$	−26.1647	+	686.562i	−0.0353099	+	0.926535i
$742$	103.493	+	318.519i	0.139479	+	0.429271i
$743$		−	1224.65i		−	1.64825i	−0.566411	−	0.824123i	$-0.691669\pi$
$743$		−	1224.65i		−	1.64825i	0.566411	−	0.824123i	$-0.308331\pi$
$744$	17.7093	+	13.9271i	0.0238028	+	0.0187192i
$745$	−12.0207	−	9.28613i	−0.0161351	−	0.0124646i
$746$	−1456.45	−	473.229i	−1.95235	−	0.634355i
$747$	−428.093	+	503.632i	−0.573083	+	0.674206i
$748$	−115.584	+	83.9767i	−0.154524	+	0.112268i
$749$		−	48.1275i		−	0.0642557i
$750$	423.303	+	771.326i	0.564403	+	1.02843i
$751$	−821.998			−1.09454			−0.547269	−	0.836957i	$-0.684332\pi$
$751$	−821.998			−1.09454			−0.547269	+	0.836957i	$0.684332\pi$
$752$	888.483	+	1222.89i	1.18149	+	1.62619i
$753$	−59.3578	−	209.521i	−0.0788284	−	0.278249i
$754$	35.9322	−	110.588i	0.0476554	−	0.146668i
$755$	466.143	−	603.412i	0.617408	−	0.799221i
$756$	−67.3909	−	119.343i	−0.0891414	−	0.157862i
$757$	−5.01883			−0.00662989			−0.00331495	−	0.999995i	$-0.501055\pi$
$757$	−5.01883			−0.00662989			−0.00331495	+	0.999995i	$0.501055\pi$
$758$	395.933	−	128.646i	0.522339	−	0.169718i
$759$	11.3718	−	298.398i	0.0149827	−	0.393146i
$760$	669.644	+	19.7171i	0.881110	+	0.0259435i
$761$	−421.246	−	579.796i	−0.553543	−	0.761887i	0.436945	−	0.899488i	$-0.356061\pi$
$761$	−421.246	−	579.796i	−0.553543	−	0.761887i	−0.990488	+	0.137602i	$0.956061\pi$
$762$	664.897	+	25.3390i	0.872568	+	0.0332533i
$763$	−57.0470	−	41.4470i	−0.0747667	−	0.0543212i
$764$	−187.764	−	258.435i	−0.245764	−	0.338266i
$765$	−198.425	−	937.656i	−0.259379	−	1.22569i
$766$	−593.515	−	431.214i	−0.774824	−	0.562942i
$767$	121.761	−	39.5626i	0.158750	−	0.0515809i
$768$	422.710	+	631.019i	0.550404	+	0.821639i
$769$	208.102	+	640.471i	0.270613	+	0.832862i	0.990347	+	0.138612i	$0.0442639\pi$
$769$	208.102	+	640.471i	0.270613	+	0.832862i	−0.719734	+	0.694250i	$0.755736\pi$
$770$	−99.4301	−	145.686i	−0.129130	−	0.189202i
$771$	252.591	+	891.595i	0.327614	+	1.15641i
$772$	−66.4438	+	204.493i	−0.0860671	+	0.264887i
$773$	−411.723	−	566.687i	−0.532629	−	0.733102i	0.454899	−	0.890543i	$-0.349675\pi$
$773$	−411.723	−	566.687i	−0.532629	−	0.733102i	−0.987528	+	0.157442i	$0.949675\pi$
$774$	−419.683	−	172.680i	−0.542226	−	0.223101i
$775$	27.0100	−	17.2915i	0.0348517	−	0.0223117i
$776$		−	369.552i		−	0.476226i
$777$	−670.838	−	246.587i	−0.863369	−	0.317358i
$778$	−301.323	+	927.376i	−0.387304	+	1.19200i
$779$	1366.74	+	444.082i	1.75449	+	0.570067i
$780$	55.1459	+	219.043i	0.0706999	+	0.280825i
$781$	76.5658	+	235.645i	0.0980356	+	0.301722i
$782$		−	1115.89i		−	1.42697i
$783$	116.444	−	65.7536i	0.148715	−	0.0839766i
$784$	−601.284	−	436.859i	−0.766944	−	0.557218i
$785$	716.197	−	927.100i	0.912352	−	1.18102i
$786$	638.082	+	234.547i	0.811809	+	0.298405i
$787$	−174.087	−	126.481i	−0.221203	−	0.160713i	0.471665	−	0.881778i	$-0.343653\pi$
$787$	−174.087	−	126.481i	−0.221203	−	0.160713i	−0.692868	+	0.721064i	$0.743653\pi$
$788$	−101.815	+	140.136i	−0.129207	+	0.177838i
$789$	−15.8897	+	43.2279i	−0.0201391	+	0.0547882i
$790$	−85.1348	+	237.948i	−0.107766	+	0.301201i
$791$	−219.133	+	301.611i	−0.277033	+	0.381304i
$792$	−234.168	−	17.8741i	−0.295667	−	0.0225683i
$793$	−620.676			−0.782693
$794$	−352.222	+	114.444i	−0.443604	+	0.144136i
$795$	406.915	−	487.200i	0.511842	−	0.612830i
$796$	62.6911	−	192.943i	0.0787576	−	0.242391i
$797$	528.025	+	171.566i	0.662516	+	0.215264i	0.620925	−	0.783870i	$-0.286757\pi$
$797$	528.025	+	171.566i	0.662516	+	0.215264i	0.0415911	+	0.999135i	$0.486757\pi$
$798$	−187.479	+	510.036i	−0.234937	+	0.639143i
$799$	−1629.67			−2.03964
$800$	554.757	−	144.782i	0.693446	−	0.180977i
$801$	−1086.65	−	447.108i	−1.35662	−	0.558187i
$802$	8.16841	−	5.93470i	0.0101850	−	0.00739987i
$803$	−204.484	−	66.4408i	−0.254650	−	0.0827407i
$804$	−503.854	+	142.743i	−0.626684	+	0.177541i
$805$	376.451	+	11.0843i	0.467642	+	0.0137693i
$806$	28.6434	−	9.30681i	0.0355377	−	0.0115469i
$807$	854.129	−	572.168i	1.05840	−	0.709006i
$808$	−152.686	−	469.921i	−0.188968	−	0.581585i
$809$	−515.346	+	709.314i	−0.637017	+	0.876778i	−0.998452	−	0.0556189i	$-0.982287\pi$
$809$	−515.346	+	709.314i	−0.637017	+	0.876778i	0.361435	+	0.932397i	$0.382287\pi$
$810$	−452.193	+	835.742i	−0.558263	+	1.03178i
$811$	−325.503	+	236.492i	−0.401360	+	0.291605i	−0.770095	−	0.637930i	$-0.779791\pi$
$811$	−325.503	+	236.492i	−0.401360	+	0.291605i	0.368735	+	0.929535i	$0.379791\pi$
$812$	14.7777	−	20.3397i	0.0181991	−	0.0250489i
$813$	−14.5061	+	380.641i	−0.0178427	+	0.468193i
$814$	597.601	−	434.182i	0.734153	−	0.533394i
$815$	−216.899	+	63.4810i	−0.266133	+	0.0778908i
$816$	−1261.32	−	48.0684i	−1.54573	−	0.0589073i
$817$	152.002	+	467.814i	0.186049	+	0.572599i
$818$			1290.05i			1.57708i
$819$	302.885	+	23.1193i	0.369823	+	0.0282286i
$820$	472.251	+	13.9050i	0.575916	+	0.0169573i
$821$	−371.437	−	120.687i	−0.452421	−	0.147000i	0.0739383	−	0.997263i	$-0.476443\pi$
$821$	−371.437	−	120.687i	−0.452421	−	0.147000i	−0.526359	+	0.850262i	$0.676443\pi$
$822$	328.962	−	93.1956i	0.400197	−	0.113377i
$823$	−107.117	+	77.8249i	−0.130154	+	0.0945625i	−0.650958	−	0.759114i	$-0.725632\pi$
$823$	−107.117	+	77.8249i	−0.130154	+	0.0945625i	0.520803	+	0.853677i	$0.325632\pi$
$824$			867.027i			1.05222i
$825$	−133.602	+	306.451i	−0.161942	+	0.371456i
$826$	101.258			0.122588
$827$	−368.501	−	507.199i	−0.445588	−	0.613300i	0.525854	−	0.850575i	$-0.323746\pi$
$827$	−368.501	−	507.199i	−0.445588	−	0.613300i	−0.971443	+	0.237275i	$0.923746\pi$
$828$	−195.884	+	230.449i	−0.236575	+	0.278320i
$829$	−177.309	+	545.700i	−0.213883	+	0.658264i	0.785348	+	0.619054i	$0.212484\pi$
$829$	−177.309	+	545.700i	−0.213883	+	0.658264i	−0.999231	+	0.0392093i	$0.987516\pi$
$830$	826.896	−	242.012i	0.996261	−	0.291581i
$831$	193.086	−	245.524i	0.232354	−	0.295456i
$832$	−252.275			−0.303215
$833$	762.075	−	247.613i	0.914856	−	0.297255i
$834$	1393.95	+	53.1229i	1.67140	+	0.0636965i
$835$	355.020	−	992.266i	0.425173	−	1.18834i
$836$	−90.2436	−	124.210i	−0.107947	−	0.148576i
$837$	31.5060	+	14.3896i	0.0376416	+	0.0171919i
$838$	−170.722	−	124.037i	−0.203725	−	0.148015i
$839$	810.725	+	1115.87i	0.966300	+	1.33000i	0.943894	+	0.330248i	$0.107133\pi$
$839$	810.725	+	1115.87i	0.966300	+	1.33000i	0.0224056	+	0.999749i	$0.492867\pi$
$840$	19.9858	−	295.519i	0.0237927	−	0.351808i
$841$	−660.538	−	479.909i	−0.785419	−	0.570641i
$842$	654.692	−	212.722i	0.777544	−	0.252639i
$843$	481.591	−	322.610i	0.571282	−	0.382693i
$844$	−45.9359	−	141.376i	−0.0544264	−	0.167507i
$845$	324.243	+	116.010i	0.383719	+	0.137290i
$846$	1231.09	+	1046.45i	1.45520	+	1.23693i
$847$	−105.412	+	324.426i	−0.124454	+	0.383029i
$848$	−491.387	−	676.336i	−0.579466	−	0.797566i
$849$	288.720	+	431.000i	0.340071	+	0.507656i
$850$	−455.286	+	1163.36i	−0.535630	+	1.36866i
$851$			1577.23i			1.85339i
$852$	86.5828	−	235.548i	0.101623	−	0.276464i
$853$	−247.404	+	761.432i	−0.290040	+	0.892651i	0.694803	+	0.719201i	$0.255492\pi$
$853$	−247.404	+	761.432i	−0.290040	+	0.892651i	−0.984843	+	0.173451i	$0.944508\pi$
$854$	−466.871	−	151.696i	−0.546687	−	0.177629i
$855$	1007.63	−	213.232i	1.17851	−	0.249394i
$856$	25.8115	+	79.4397i	0.0301536	+	0.0928033i
$857$			980.480i			1.14408i	0.820224	+	0.572042i	$0.193849\pi$
$857$			980.480i			1.14408i	−0.820224	+	0.572042i	$0.806151\pi$
$858$	−194.071	+	246.776i	−0.226190	+	0.287618i
$859$	−328.594	−	238.738i	−0.382531	−	0.277925i	0.379857	−	0.925045i	$-0.375973\pi$
$859$	−328.594	−	238.738i	−0.382531	−	0.277925i	−0.762388	+	0.647120i	$0.775973\pi$
$860$	91.1612	+	133.570i	0.106001	+	0.155314i
$861$	219.209	−	596.355i	0.254598	−	0.692631i
$862$	−84.7505	−	61.5748i	−0.0983184	−	0.0714325i
$863$	−714.791	+	983.826i	−0.828263	+	1.14001i	0.159980	+	0.987120i	$0.448857\pi$
$863$	−714.791	+	983.826i	−0.828263	+	1.14001i	−0.988244	+	0.152887i	$0.951143\pi$
$864$	456.180	+	418.707i	0.527986	+	0.484614i
$865$	1419.06	+	41.7831i	1.64054	+	0.0483042i
$866$	280.451	−	386.008i	0.323847	−	0.445736i
$867$	305.279	−	388.185i	0.352110	−	0.447734i
$868$	6.51186			0.00750214
$869$	−91.3243	+	29.6731i	−0.105091	+	0.0341462i
$870$	−173.912	−	11.7616i	−0.199898	−	0.0135191i
$871$	358.668	−	1103.87i	0.411788	−	1.26735i
$872$	116.391	+	37.8177i	0.133476	+	0.0433689i
$873$	−133.932	−	552.130i	−0.153416	−	0.632451i
$874$	1199.17			1.37204
$875$	−387.943	−	165.148i	−0.443363	−	0.188741i
$876$	121.200	+	180.927i	0.138356	+	0.206537i
$877$	−353.440	+	256.789i	−0.403010	+	0.292804i	−0.770766	−	0.637119i	$-0.780126\pi$
$877$	−353.440	+	256.789i	−0.403010	+	0.292804i	0.367756	+	0.929922i	$0.380126\pi$
$878$	−641.579	−	208.462i	−0.730728	−	0.237428i
$879$	169.942	+	599.862i	0.193336	+	0.682437i
$880$	348.424	+	269.162i	0.395937	+	0.305866i
$881$	340.537	−	110.647i	0.386534	−	0.125593i	−0.109302	−	0.994009i	$-0.534862\pi$
$881$	340.537	−	110.647i	0.386534	−	0.125593i	0.495836	+	0.868416i	$0.334862\pi$
$882$	−734.688	−	302.291i	−0.832980	−	0.342733i
$883$	356.579	+	1097.44i	0.403827	+	1.24285i	0.921871	+	0.387498i	$0.126661\pi$
$883$	356.579	+	1097.44i	0.403827	+	1.24285i	−0.518044	+	0.855354i	$0.673339\pi$
$884$	−188.515	+	259.469i	−0.213252	+	0.293517i
$885$	−102.074	−	162.524i	−0.115338	−	0.183643i
$886$	−30.9839	+	22.5111i	−0.0349706	+	0.0254076i
$887$	−61.1191	+	84.1233i	−0.0689055	+	0.0948402i	−0.842079	−	0.539355i	$-0.818668\pi$
$887$	−61.1191	+	84.1233i	−0.0689055	+	0.0948402i	0.773173	+	0.634195i	$0.218668\pi$
$888$	1239.54	+	47.2384i	1.39588	+	0.0531964i
$889$	−257.961	+	187.420i	−0.290170	+	0.210821i
$890$	863.413	+	1265.08i	0.970127	+	1.42143i
$891$	−356.337	+	58.1618i	−0.399930	+	0.0652770i
$892$	120.897	+	372.084i	0.135535	+	0.417134i
$893$		−	1751.29i		−	1.96113i
$894$	−13.2186	+	16.8084i	−0.0147859	+	0.0188013i
$895$	−47.7864	+	32.6141i	−0.0533926	+	0.0364404i
$896$	−484.041	−	157.274i	−0.540224	−	0.175529i
$897$	−182.719	−	644.961i	−0.203700	−	0.719020i
$898$	73.0353	−	53.0632i	0.0813310	−	0.0590905i
$899$			6.35365i			0.00706746i
$900$	298.240	−	160.331i	0.331378	−	0.178145i
$901$	901.310			1.00034
$902$	385.976	+	531.250i	0.427911	+	0.588969i
$903$	209.241	−	59.2783i	0.231717	−	0.0656460i
$904$	199.945	−	615.367i	0.221178	−	0.680715i
$905$	−473.050	−	169.251i	−0.522708	−	0.187018i
$906$	−843.743	−	663.542i	−0.931284	−	0.732387i
$907$	604.764			0.666773			0.333387	−	0.942790i	$-0.391809\pi$
$907$	604.764			0.666773			0.333387	+	0.942790i	$0.391809\pi$
$908$	−194.276	+	63.1241i	−0.213960	+	0.0695200i
$909$	−398.429	−	646.750i	−0.438316	−	0.711496i
$910$	−313.343	−	242.061i	−0.344333	−	0.266001i
$911$	758.296	+	1043.71i	0.832378	+	1.14567i	0.987476	+	0.157771i	$0.0504307\pi$
$911$	758.296	+	1043.71i	0.832378	+	1.14567i	−0.155098	+	0.987899i	$0.549569\pi$
$912$	51.6555	−	1355.44i	0.0566398	−	1.48623i
$913$	264.848	+	192.423i	0.290085	+	0.210759i
$914$	−717.345	−	987.340i	−0.784841	−	1.08024i
$915$	227.155	+	902.274i	0.248256	+	0.986092i
$916$	−381.480	−	277.161i	−0.416463	−	0.302578i
$917$	−309.835	+	100.671i	−0.337878	+	0.109783i
$918$	−1322.36	+	267.897i	−1.44047	+	0.291827i
$919$	−27.4712	−	84.5477i	−0.0298925	−	0.0919997i	0.934997	−	0.354655i	$-0.115402\pi$
$919$	−27.4712	−	84.5477i	−0.0298925	−	0.0919997i	−0.964890	+	0.262655i	$0.915402\pi$
$920$	−627.318	+	183.601i	−0.681868	+	0.199566i
$921$	1272.90	−	360.615i	1.38208	−	0.391547i
$922$	−33.2040	+	102.191i	−0.0360130	+	0.110837i
$923$	326.933	+	449.984i	0.354206	+	0.487523i
$924$	−56.3956	+	37.7786i	−0.0610342	+	0.0408859i
$925$	643.514	−	1644.33i	0.695690	−	1.77765i
$926$		−	804.030i		−	0.868283i
$927$	314.225	+	1295.38i	0.338970	+	1.39739i
$928$	−35.0999	+	108.027i	−0.0378232	+	0.116408i
$929$	−718.923	−	233.592i	−0.773868	−	0.251445i	−0.104648	−	0.994509i	$-0.533372\pi$
$929$	−718.923	−	233.592i	−0.773868	−	0.251445i	−0.669220	+	0.743065i	$0.733372\pi$
$930$	−24.0122	−	38.2327i	−0.0258195	−	0.0411105i
$931$	266.091	+	818.945i	0.285812	+	0.879640i
$932$		−	96.9694i		−	0.104044i
$933$	−1000.39	−	786.730i	−1.07222	−	0.843226i
$934$	1041.55	+	756.731i	1.11515	+	0.810204i
$935$	−455.568	+	133.333i	−0.487238	+	0.142603i
$936$	−512.343	+	124.281i	−0.547375	+	0.132779i
$937$	−343.788	−	249.777i	−0.366903	−	0.266571i	0.389022	−	0.921228i	$-0.372813\pi$
$937$	−343.788	−	249.777i	−0.366903	−	0.266571i	−0.755926	+	0.654657i	$0.772813\pi$
$938$	539.578	−	742.666i	0.575243	−	0.791754i
$939$	−1006.11	−	369.826i	−1.07147	−	0.393851i
$940$	−161.725	−	552.574i	−0.172048	−	0.587844i
$941$	591.938	−	814.733i	0.629052	−	0.865816i	−0.368921	−	0.929461i	$-0.620273\pi$
$941$	591.938	−	814.733i	0.629052	−	0.865816i	0.997973	+	0.0636452i	$0.0202726\pi$
$942$	−1296.35	−	1019.49i	−1.37617	−	1.08226i
$943$	−1402.12			−1.48687
$944$	−240.386	+	78.1063i	−0.254647	+	0.0827397i
$945$	−77.2412	−	448.764i	−0.0817368	−	0.474882i
$946$	−69.4559	+	213.763i	−0.0734206	+	0.225965i
$947$	−1268.08	−	412.025i	−1.33905	−	0.435084i	−0.450056	−	0.893000i	$-0.648596\pi$
$947$	−1268.08	−	412.025i	−1.33905	−	0.435084i	−0.888995	+	0.457916i	$0.848596\pi$
$948$	91.2865	+	33.5552i	0.0962937	+	0.0353957i
$949$	−482.658			−0.508596
$950$	−1250.18	−	489.262i	−1.31598	−	0.515012i
$951$	117.431	−	78.6654i	0.123482	−	0.0827186i
$952$	340.241	−	247.199i	0.357396	−	0.259663i
$953$	−538.203	−	174.873i	−0.564746	−	0.183497i	0.0127094	−	0.999919i	$-0.495954\pi$
$953$	−538.203	−	174.873i	−0.564746	−	0.183497i	−0.577456	+	0.816422i	$0.695954\pi$
$954$	−680.873	−	578.750i	−0.713703	−	0.606656i
$955$	−298.121	−	1018.61i	−0.312169	−	1.06660i
$956$	−189.319	+	61.5133i	−0.198032	+	0.0643445i
$957$	−36.8607	−	55.0255i	−0.0385170	−	0.0574979i
$958$	248.088	+	763.536i	0.258964	+	0.797010i
$959$	−96.3066	+	132.555i	−0.100424	+	0.138222i
$960$	92.3274	+	366.731i	0.0961743	+	0.382011i
$961$	776.134	−	563.894i	0.807632	−	0.586779i
$962$	974.674	−	1341.52i	1.01317	−	1.39452i
$963$	67.3541	+	109.332i	0.0699419	+	0.113533i
$964$	128.483	−	93.3482i	0.133281	−	0.0968342i
$965$	−436.732	+	565.339i	−0.452572	+	0.585844i
$966$	20.1903	−	529.796i	0.0209010	−	0.548443i
$967$	56.8845	+	175.073i	0.0588258	+	0.181047i	0.976151	−	0.217090i	$-0.0696567\pi$
$967$	56.8845	+	175.073i	0.0588258	+	0.181047i	−0.917326	+	0.398138i	$0.869657\pi$
$968$		−	592.034i		−	0.611605i
$969$	1149.51	+	904.008i	1.18629	+	0.932929i
$970$	−249.475	+	697.272i	−0.257191	+	0.718838i
$971$	−539.980	−	175.450i	−0.556107	−	0.180690i	0.0174617	−	0.999848i	$-0.494441\pi$
$971$	−539.980	−	175.450i	−0.556107	−	0.180690i	−0.573569	+	0.819157i	$0.694441\pi$
$972$	320.114	+	176.802i	0.329335	+	0.181895i
$973$	−540.812	+	392.923i	−0.555819	+	0.403826i
$974$			302.398i			0.310470i
$975$	−72.6536	+	746.946i	−0.0745165	+	0.766099i
$976$	1225.37			1.25550
$977$	−812.151	−	1117.83i	−0.831270	−	1.14415i	−0.987685	−	0.156454i	$-0.949994\pi$
$977$	−812.151	−	1117.83i	−0.831270	−	1.14415i	0.156415	−	0.987691i	$-0.450006\pi$
$978$	86.7193	+	306.102i	0.0886700	+	0.312988i
$979$	−179.837	+	553.480i	−0.183694	+	0.565352i
$980$	159.585	+	233.825i	0.162842	+	0.238597i
$981$	187.600	+	14.3195i	0.191233	+	0.0145969i
$982$	−345.282			−0.351611
$983$	−527.082	+	171.259i	−0.536197	+	0.174221i	−0.564583	−	0.825376i	$-0.690963\pi$
$983$	−527.082	+	171.259i	−0.536197	+	0.174221i	0.0283863	+	0.999597i	$0.490963\pi$
$984$	−41.9936	+	1101.91i	−0.0426764	+	1.11983i
$985$	−475.351	+	324.426i	−0.482590	+	0.329367i
$986$	−145.476	−	200.230i	−0.147541	−	0.203073i
$987$	−773.723	−	29.4863i	−0.783914	−	0.0298747i
$988$	−278.832	−	202.583i	−0.282218	−	0.205044i
$989$	−282.090	−	388.264i	−0.285228	−	0.392582i
$990$	429.764	+	191.806i	0.434105	+	0.193743i
$991$	−75.7914	−	55.0657i	−0.0764797	−	0.0555658i	0.548888	−	0.835896i	$-0.315051\pi$
$991$	−75.7914	−	55.0657i	−0.0764797	−	0.0555658i	−0.625368	+	0.780330i	$0.715051\pi$
$992$	−27.9800	+	9.09126i	−0.0282057	+	0.00916457i
$993$	978.021	+	1459.98i	0.984916	+	1.47028i
$994$	135.940	+	418.381i	0.136761	+	0.420906i
$995$	412.065	−	533.409i	0.414136	−	0.536090i
$996$	−90.3796	−	319.022i	−0.0907425	−	0.320303i
$997$	−585.322	+	1801.44i	−0.587083	+	1.80686i	0.00365476	+	0.999993i	$0.498837\pi$
$997$	−585.322	+	1801.44i	−0.587083	+	1.80686i	−0.590738	+	0.806863i	$0.701163\pi$
$998$	1102.83	+	1517.92i	1.10504	+	1.52096i
$999$	1869.06	−	378.654i	1.87093	−	0.379033i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.j.a.11.14	yes	72
3.2	odd	2	inner	75.3.j.a.11.5	✓	72
5.2	odd	4		375.3.h.b.74.9		144
5.3	odd	4		375.3.h.b.74.28		144
5.4	even	2		375.3.j.a.176.5		72
15.2	even	4		375.3.h.b.74.27		144
15.8	even	4		375.3.h.b.74.10		144
15.14	odd	2		375.3.j.a.176.14		72
25.9	even	10		375.3.j.a.326.14		72
25.12	odd	20		375.3.h.b.299.10		144
25.13	odd	20		375.3.h.b.299.27		144
25.16	even	5	inner	75.3.j.a.41.5	yes	72
75.38	even	20		375.3.h.b.299.9		144
75.41	odd	10	inner	75.3.j.a.41.14	yes	72
75.59	odd	10		375.3.j.a.326.5		72
75.62	even	20		375.3.h.b.299.28		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.j.a.11.5	✓	72	3.2	odd	2	inner
75.3.j.a.11.14	yes	72	1.1	even	1	trivial
75.3.j.a.41.5	yes	72	25.16	even	5	inner
75.3.j.a.41.14	yes	72	75.41	odd	10	inner
375.3.h.b.74.9		144	5.2	odd	4
375.3.h.b.74.10		144	15.8	even	4
375.3.h.b.74.27		144	15.2	even	4
375.3.h.b.74.28		144	5.3	odd	4
375.3.h.b.299.9		144	75.38	even	20
375.3.h.b.299.10		144	25.12	odd	20
375.3.h.b.299.27		144	25.13	odd	20
375.3.h.b.299.28		144	75.62	even	20
375.3.j.a.176.5		72	5.4	even	2
375.3.j.a.176.14		72	15.14	odd	2
375.3.j.a.326.5		72	75.59	odd	10
375.3.j.a.326.14		72	25.9	even	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.j (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37909 + 1.89816i) q^{2} +(2.88640 - 0.817724i) q^{3} +(-0.465043 + 1.43126i) q^{4} +(-3.05671 + 3.95684i) q^{5} +(5.53279 + 4.35114i) q^{6} -3.37306 q^{7} +(5.56759 - 1.80902i) q^{8} +(7.66265 - 4.72056i) q^{9} +O(q^{10})\)	\(q+(1.37909 + 1.89816i) q^{2} +(2.88640 - 0.817724i) q^{3} +(-0.465043 + 1.43126i) q^{4} +(-3.05671 + 3.95684i) q^{5} +(5.53279 + 4.35114i) q^{6} -3.37306 q^{7} +(5.56759 - 1.80902i) q^{8} +(7.66265 - 4.72056i) q^{9} +(-11.7262 - 0.345267i) q^{10} +(-2.62002 - 3.60615i) q^{11} +(-0.171930 + 4.51146i) q^{12} +(-8.09526 - 5.88155i) q^{13} +(-4.65176 - 6.40260i) q^{14} +(-5.58729 + 13.9206i) q^{15} +(15.9820 + 11.6116i) q^{16} +(-20.2558 + 6.58152i) q^{17} +(19.5279 + 8.03484i) q^{18} +(-7.07267 - 21.7674i) q^{19} +(-4.24174 - 6.21503i) q^{20} +(-9.73600 + 2.75823i) q^{21} +(3.23179 - 9.94643i) q^{22} +(13.1257 + 18.0660i) q^{23} +(14.5910 - 9.77432i) q^{24} +(-6.31310 - 24.1898i) q^{25} -23.4773i q^{26} +(18.2574 - 19.8914i) q^{27} +(1.56862 - 4.82771i) q^{28} +(4.71042 + 1.53051i) q^{29} +(-34.1289 + 8.59221i) q^{30} +(0.396417 + 1.22005i) q^{31} +22.9335i q^{32} +(-10.5113 - 8.26634i) q^{33} +(-40.4275 - 29.3723i) q^{34} +(10.3104 - 13.3466i) q^{35} +(3.19287 + 13.1625i) q^{36} +(57.1413 + 41.5156i) q^{37} +(31.5642 - 43.4444i) q^{38} +(-28.1757 - 10.3568i) q^{39} +(-9.86049 + 27.5597i) q^{40} +(-36.9062 + 50.7970i) q^{41} +(-18.6624 - 14.6766i) q^{42} -21.4915 q^{43} +(6.37974 - 2.07290i) q^{44} +(-4.74398 + 44.7492i) q^{45} +(-16.1905 + 49.8293i) q^{46} +(72.7717 + 23.6450i) q^{47} +(55.6257 + 20.4470i) q^{48} -37.6225 q^{49} +(37.2097 - 45.3432i) q^{50} +(-53.0846 + 35.5606i) q^{51} +(12.1826 - 8.85121i) q^{52} +(-40.2473 - 13.0771i) q^{53} +(62.9357 + 7.22337i) q^{54} +(22.2776 + 0.655943i) q^{55} +(-18.7798 + 6.10193i) q^{56} +(-38.2143 - 57.0461i) q^{57} +(3.59096 + 11.0518i) q^{58} +(-7.52052 + 10.3511i) q^{59} +(-17.3256 - 14.4705i) q^{60} +(50.1822 - 36.4595i) q^{61} +(-1.76915 + 2.43502i) q^{62} +(-25.8466 + 15.9227i) q^{63} +(20.3966 - 14.8190i) q^{64} +(48.0171 - 14.0534i) q^{65} +(1.19482 - 31.3521i) q^{66} +(35.8442 + 110.317i) q^{67} -32.0520i q^{68} +(52.6590 + 41.4125i) q^{69} +(39.5531 + 1.16461i) q^{70} +(-52.8656 - 17.1771i) q^{71} +(34.1229 - 40.1441i) q^{72} +(39.0233 - 28.3521i) q^{73} +165.717i q^{74} +(-38.0027 - 64.6591i) q^{75} +34.4439 q^{76} +(8.83747 + 12.1637i) q^{77} +(-19.1979 - 67.7650i) q^{78} +(6.65697 - 20.4881i) q^{79} +(-94.7977 + 27.7450i) q^{80} +(36.4326 - 72.3441i) q^{81} -147.318 q^{82} +(-69.8488 + 22.6953i) q^{83} +(0.579930 - 15.2174i) q^{84} +(35.8741 - 100.267i) q^{85} +(-29.6387 - 40.7942i) q^{86} +(14.8477 + 0.565841i) q^{87} +(-21.1108 - 15.3379i) q^{88} +(-76.7412 - 105.625i) q^{89} +(-91.4836 + 52.7086i) q^{90} +(27.3057 + 19.8388i) q^{91} +(-31.9610 + 10.3848i) q^{92} +(2.14188 + 3.19739i) q^{93} +(55.4771 + 170.741i) q^{94} +(107.749 + 38.5512i) q^{95} +(18.7533 + 66.1955i) q^{96} +(19.5073 - 60.0372i) q^{97} +(-51.8850 - 71.4135i) q^{98} +(-37.0993 - 15.2647i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9}+O(q^{10}) \) 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9	\( 72 q - q^{3} + 26 q^{4} - 11 q^{6} - 8 q^{7} - 13 q^{9} - 20 q^{10} + 31 q^{12} - 42 q^{13} + 45 q^{15} - 130 q^{16} + 30 q^{18} - 36 q^{19} - 60 q^{21} - 70 q^{22} - 72 q^{24} + 100 q^{25} - 154 q^{27} - 62 q^{28} + 15 q^{30} + 114 q^{31} - 10 q^{33} + 178 q^{34} + 271 q^{36} - 98 q^{37} - 155 q^{39} - 120 q^{40} - 475 q^{42} - 52 q^{43} + 35 q^{45} + 198 q^{46} - 326 q^{48} + 112 q^{49} + 44 q^{51} + 412 q^{52} + 304 q^{54} + 10 q^{55} + 622 q^{57} + 190 q^{58} + 360 q^{60} - 306 q^{61} + 293 q^{63} + 474 q^{64} + 320 q^{66} + 472 q^{67} + 269 q^{69} - 840 q^{70} + 175 q^{72} + 318 q^{73} - 310 q^{75} + 112 q^{76} + 815 q^{78} - 346 q^{79} - 373 q^{81} - 1620 q^{82} - 730 q^{84} - 530 q^{85} - 370 q^{87} - 810 q^{88} - 230 q^{90} - 550 q^{91} - 272 q^{93} - 612 q^{94} - 698 q^{96} + 182 q^{97} - 160 q^{99}+O(q^{100}) \) 72 * q - q^3 + 26 * q^4 - 11 * q^6 - 8 * q^7 - 13 * q^9 - 20 * q^10 + 31 * q^12 - 42 * q^13 + 45 * q^15 - 130 * q^16 + 30 * q^18 - 36 * q^19 - 60 * q^21 - 70 * q^22 - 72 * q^24 + 100 * q^25 - 154 * q^27 - 62 * q^28 + 15 * q^30 + 114 * q^31 - 10 * q^33 + 178 * q^34 + 271 * q^36 - 98 * q^37 - 155 * q^39 - 120 * q^40 - 475 * q^42 - 52 * q^43 + 35 * q^45 + 198 * q^46 - 326 * q^48 + 112 * q^49 + 44 * q^51 + 412 * q^52 + 304 * q^54 + 10 * q^55 + 622 * q^57 + 190 * q^58 + 360 * q^60 - 306 * q^61 + 293 * q^63 + 474 * q^64 + 320 * q^66 + 472 * q^67 + 269 * q^69 - 840 * q^70 + 175 * q^72 + 318 * q^73 - 310 * q^75 + 112 * q^76 + 815 * q^78 - 346 * q^79 - 373 * q^81 - 1620 * q^82 - 730 * q^84 - 530 * q^85 - 370 * q^87 - 810 * q^88 - 230 * q^90 - 550 * q^91 - 272 * q^93 - 612 * q^94 - 698 * q^96 + 182 * q^97 - 160 * q^99

Introduction

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