LMFDB - Embedded newform 25.4.e.a.9.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,4,Mod(4,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("25.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	25.e (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:	$1.47504775014$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			9.3
Character	$\chi$	$=$	25.9
Dual form			25.4.e.a.14.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.442260 + 0.608718i) q^{2} +(-6.75579 + 2.19509i) q^{3} +(2.29719 + 7.07003i) q^{4} +(1.00498 + 11.1351i) q^{5} +(1.65162 - 5.08317i) q^{6} -18.3105i q^{7} +(-11.0443 - 3.58852i) q^{8} +(18.9788 - 13.7889i) q^{9} +O(q^{10})$	\(q+(-0.442260 + 0.608718i) q^{2} +(-6.75579 + 2.19509i) q^{3} +(2.29719 + 7.07003i) q^{4} +(1.00498 + 11.1351i) q^{5} +(1.65162 - 5.08317i) q^{6} -18.3105i q^{7} +(-11.0443 - 3.58852i) q^{8} +(18.9788 - 13.7889i) q^{9} +(-7.22259 - 4.31284i) q^{10} +(34.1808 + 24.8338i) q^{11} +(-31.0387 - 42.7211i) q^{12} +(20.6196 + 28.3805i) q^{13} +(11.1459 + 8.09800i) q^{14} +(-31.2319 - 73.0202i) q^{15} +(-41.0441 + 29.8203i) q^{16} +(62.4001 + 20.2750i) q^{17} +17.6510i q^{18} +(29.2980 - 90.1699i) q^{19} +(-76.4167 + 32.6847i) q^{20} +(40.1932 + 123.702i) q^{21} +(-30.2336 + 9.82348i) q^{22} +(-84.6849 + 116.559i) q^{23} +82.4903 q^{24} +(-122.980 + 22.3811i) q^{25} -26.3950 q^{26} +(14.7844 - 20.3490i) q^{27} +(129.456 - 42.0628i) q^{28} +(28.1756 + 86.7157i) q^{29} +(58.2613 + 13.2824i) q^{30} +(99.7311 - 306.941i) q^{31} -131.074i q^{32} +(-285.431 - 92.7420i) q^{33} +(-39.9388 + 29.0172i) q^{34} +(203.889 - 18.4017i) q^{35} +(141.086 + 102.505i) q^{36} +(27.3325 + 37.6199i) q^{37} +(41.9307 + 57.7127i) q^{38} +(-201.600 - 146.471i) q^{39} +(28.8591 - 126.586i) q^{40} +(-68.8543 + 50.0256i) q^{41} +(-93.0754 - 30.2420i) q^{42} +84.2967i q^{43} +(-97.0559 + 298.707i) q^{44} +(172.614 + 197.473i) q^{45} +(-33.4987 - 103.098i) q^{46} +(50.4632 - 16.3965i) q^{47} +(211.827 - 291.555i) q^{48} +7.72504 q^{49} +(40.7653 - 84.7584i) q^{50} -466.067 q^{51} +(-153.284 + 210.977i) q^{52} +(552.862 - 179.636i) q^{53} +(5.84825 + 17.9991i) q^{54} +(-242.175 + 405.563i) q^{55} +(-65.7077 + 202.227i) q^{56} +673.480i q^{57} +(-65.2463 - 21.1998i) q^{58} +(-156.348 + 113.594i) q^{59} +(444.509 - 388.552i) q^{60} +(-297.367 - 216.050i) q^{61} +(142.733 + 196.456i) q^{62} +(-252.482 - 347.512i) q^{63} +(-248.566 - 180.594i) q^{64} +(-295.297 + 258.123i) q^{65} +(182.688 - 132.731i) q^{66} +(277.789 + 90.2592i) q^{67} +487.746i q^{68} +(316.256 - 973.337i) q^{69} +(-78.9704 + 132.249i) q^{70} +(-239.879 - 738.272i) q^{71} +(-259.090 + 84.1835i) q^{72} +(297.958 - 410.103i) q^{73} -34.9880 q^{74} +(781.698 - 421.154i) q^{75} +704.807 q^{76} +(454.720 - 625.868i) q^{77} +(178.319 - 57.9393i) q^{78} +(383.131 + 1179.16i) q^{79} +(-373.300 - 427.061i) q^{80} +(-250.942 + 772.321i) q^{81} -64.0371i q^{82} +(-715.915 - 232.615i) q^{83} +(-782.245 + 568.334i) q^{84} +(-163.053 + 715.206i) q^{85} +(-51.3129 - 37.2810i) q^{86} +(-380.697 - 523.985i) q^{87} +(-288.388 - 396.931i) q^{88} +(-204.768 - 148.772i) q^{89} +(-196.545 + 17.7389i) q^{90} +(519.662 - 377.556i) q^{91} +(-1018.61 - 330.967i) q^{92} +2292.54i q^{93} +(-12.3370 + 37.9694i) q^{94} +(1033.49 + 235.616i) q^{95} +(287.720 + 885.510i) q^{96} +(354.095 - 115.053i) q^{97} +(-3.41647 + 4.70237i) q^{98} +991.141 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) $ 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	−0.442260	+	0.608718i	−0.156362	+	0.215214i	−0.880010	−	0.474955i	$-0.842464\pi$
$2$	−0.442260	+	0.608718i	−0.156362	+	0.215214i	0.723647	+	0.690170i	$0.242464\pi$
$3$	−6.75579	+	2.19509i	−1.30015	+	0.422445i	−0.875634	−	0.482975i	$-0.839556\pi$
$3$	−6.75579	+	2.19509i	−1.30015	+	0.422445i	−0.424518	+	0.905420i	$0.639556\pi$
$4$	2.29719	+	7.07003i	0.287149	+	0.883754i
$5$	1.00498	+	11.1351i	0.0898883	+	0.995952i
$5$	1.00498	+	11.1351i	0.0898883	+	0.995952i
$6$	1.65162	−	5.08317i	0.112379	−	0.345866i
$7$		−	18.3105i		−	0.988675i	−0.869270	−	0.494337i	$-0.835411\pi$
$7$		−	18.3105i		−	0.988675i	0.869270	−	0.494337i	$-0.164589\pi$
$8$	−11.0443	−	3.58852i	−0.488095	−	0.158592i
$9$	18.9788	−	13.7889i	0.702919	−	0.510700i
$10$	−7.22259	−	4.31284i	−0.228398	−	0.136384i
$11$	34.1808	+	24.8338i	0.936900	+	0.680698i	0.947672	−	0.319244i	$-0.103429\pi$
$11$	34.1808	+	24.8338i	0.936900	+	0.680698i	−0.0107726	+	0.999942i	$0.503429\pi$
$12$	−31.0387	−	42.7211i	−0.746675	−	1.02771i
$13$	20.6196	+	28.3805i	0.439912	+	0.605487i	0.970193	−	0.242335i	$-0.0779133\pi$
$13$	20.6196	+	28.3805i	0.439912	+	0.605487i	−0.530280	+	0.847822i	$0.677913\pi$
$14$	11.1459	+	8.09800i	0.212777	+	0.154592i
$15$	−31.2319	−	73.0202i	−0.537603	−	1.25692i
$16$	−41.0441	+	29.8203i	−0.641315	+	0.465943i
$17$	62.4001	+	20.2750i	0.890249	+	0.289260i	0.718207	−	0.695830i	$-0.244963\pi$
$17$	62.4001	+	20.2750i	0.890249	+	0.289260i	0.172043	+	0.985089i	$0.444963\pi$
$18$			17.6510i			0.231132i
$19$	29.2980	−	90.1699i	0.353759	−	1.08876i	−0.602967	−	0.797766i	$-0.706015\pi$
$19$	29.2980	−	90.1699i	0.353759	−	1.08876i	0.956726	−	0.290991i	$-0.0939850\pi$
$20$	−76.4167	+	32.6847i	−0.854365	+	0.365426i
$21$	40.1932	+	123.702i	0.417661	+	1.28543i
$22$	−30.2336	+	9.82348i	−0.292992	+	0.0951988i
$23$	−84.6849	+	116.559i	−0.767740	+	1.05670i	0.228791	+	0.973476i	$0.426523\pi$
$23$	−84.6849	+	116.559i	−0.767740	+	1.05670i	−0.996531	+	0.0832276i	$0.973477\pi$
$24$	82.4903			0.701594
$25$	−122.980	+	22.3811i	−0.983840	+	0.179049i
$26$	−26.3950			−0.199095
$27$	14.7844	−	20.3490i	0.105380	−	0.145043i
$28$	129.456	−	42.0628i	0.873745	−	0.283897i
$29$	28.1756	+	86.7157i	0.180417	+	0.555265i	0.999839	−	0.0179244i	$-0.00570583\pi$
$29$	28.1756	+	86.7157i	0.180417	+	0.555265i	−0.819423	+	0.573190i	$0.805706\pi$
$30$	58.2613	+	13.2824i	0.354567	+	0.0808344i
$31$	99.7311	−	306.941i	0.577814	−	1.77833i	−0.0485778	−	0.998819i	$-0.515469\pi$
$31$	99.7311	−	306.941i	0.577814	−	1.77833i	0.626392	−	0.779509i	$-0.284531\pi$
$32$		−	131.074i		−	0.724090i
$33$	−285.431	−	92.7420i	−1.50567	−	0.489222i
$34$	−39.9388	+	29.0172i	−0.201454	+	0.146365i
$35$	203.889	−	18.4017i	0.984673	−	0.0888703i
$36$	141.086	+	102.505i	0.653176	+	0.474560i
$37$	27.3325	+	37.6199i	0.121444	+	0.167154i	0.865410	−	0.501064i	$-0.167058\pi$
$37$	27.3325	+	37.6199i	0.121444	+	0.167154i	−0.743966	+	0.668217i	$0.767058\pi$
$38$	41.9307	+	57.7127i	0.179002	+	0.246375i
$39$	−201.600	−	146.471i	−0.827738	−	0.601387i
$40$	28.8591	−	126.586i	0.114076	−	0.500375i
$41$	−68.8543	+	50.0256i	−0.262274	+	0.190553i	−0.711149	−	0.703041i	$-0.751825\pi$
$41$	−68.8543	+	50.0256i	−0.262274	+	0.190553i	0.448875	+	0.893595i	$0.351825\pi$
$42$	−93.0754	−	30.2420i	−0.341949	−	0.111106i
$43$			84.2967i			0.298956i	0.988765	+	0.149478i	$0.0477594\pi$
$43$			84.2967i			0.298956i	−0.988765	+	0.149478i	$0.952241\pi$
$44$	−97.0559	+	298.707i	−0.332539	+	1.02345i
$45$	172.614	+	197.473i	0.571817	+	0.654167i
$46$	−33.4987	−	103.098i	−0.107372	−	0.330457i
$47$	50.4632	−	16.3965i	0.156613	−	0.0508867i	−0.229661	−	0.973271i	$-0.573762\pi$
$47$	50.4632	−	16.3965i	0.156613	−	0.0508867i	0.386274	+	0.922384i	$0.373762\pi$
$48$	211.827	−	291.555i	0.636972	−	0.876716i
$49$	7.72504			0.0225220
$50$	40.7653	−	84.7584i	0.115302	−	0.239733i
$51$	−466.067			−1.27966
$52$	−153.284	+	210.977i	−0.408781	+	0.562639i
$53$	552.862	−	179.636i	1.43286	−	0.465563i	0.513194	−	0.858273i	$-0.328462\pi$
$53$	552.862	−	179.636i	1.43286	−	0.465563i	0.919663	+	0.392709i	$0.128462\pi$
$54$	5.84825	+	17.9991i	0.0147379	+	0.0453586i
$55$	−242.175	+	405.563i	−0.593726	+	0.994294i
$56$	−65.7077	+	202.227i	−0.156796	+	0.482568i
$57$			673.480i			1.56499i
$58$	−65.2463	−	21.1998i	−0.147711	−	0.0479943i
$59$	−156.348	+	113.594i	−0.344997	+	0.250655i	−0.746767	−	0.665085i	$-0.768395\pi$
$59$	−156.348	+	113.594i	−0.344997	+	0.250655i	0.401770	+	0.915741i	$0.368395\pi$
$60$	444.509	−	388.552i	0.956432	−	0.836031i
$61$	−297.367	−	216.050i	−0.624164	−	0.453481i	0.230210	−	0.973141i	$-0.426059\pi$
$61$	−297.367	−	216.050i	−0.624164	−	0.453481i	−0.854373	+	0.519660i	$0.826059\pi$
$62$	142.733	+	196.456i	0.292373	+	0.402417i
$63$	−252.482	−	347.512i	−0.504916	−	0.694958i
$64$	−248.566	−	180.594i	−0.485480	−	0.352722i
$65$	−295.297	+	258.123i	−0.563493	+	0.492558i
$66$	182.688	−	132.731i	0.340718	−	0.247546i
$67$	277.789	+	90.2592i	0.506528	+	0.164581i	0.551123	−	0.834424i	$-0.314200\pi$
$67$	277.789	+	90.2592i	0.506528	+	0.164581i	−0.0445947	+	0.999005i	$0.514200\pi$
$68$			487.746i			0.869822i
$69$	316.256	−	973.337i	0.551779	−	1.69820i
$70$	−78.9704	+	132.249i	−0.134840	+	0.225812i
$71$	−239.879	−	738.272i	−0.400963	−	1.23404i	−0.924219	−	0.381863i	$-0.875283\pi$
$71$	−239.879	−	738.272i	−0.400963	−	1.23404i	0.523256	−	0.852176i	$-0.324717\pi$
$72$	−259.090	+	84.1835i	−0.424084	+	0.137793i
$73$	297.958	−	410.103i	0.477716	−	0.657520i	−0.500348	−	0.865825i	$-0.666794\pi$
$73$	297.958	−	410.103i	0.477716	−	0.657520i	0.978064	+	0.208304i	$0.0667945\pi$
$74$	−34.9880			−0.0549631
$75$	781.698	−	421.154i	1.20350	−	0.648409i
$76$	704.807			1.06377
$77$	454.720	−	625.868i	0.672989	−	0.926289i
$78$	178.319	−	57.9393i	0.258854	−	0.0841068i
$79$	383.131	+	1179.16i	0.545640	+	1.67931i	0.719463	+	0.694531i	$0.244388\pi$
$79$	383.131	+	1179.16i	0.545640	+	1.67931i	−0.173823	+	0.984777i	$0.555612\pi$
$80$	−373.300	−	427.061i	−0.521703	−	0.596836i
$81$	−250.942	+	772.321i	−0.344228	+	1.05943i
$82$		−	64.0371i		−	0.0862405i
$83$	−715.915	−	232.615i	−0.946770	−	0.307624i	−0.205368	−	0.978685i	$-0.565839\pi$
$83$	−715.915	−	232.615i	−0.946770	−	0.307624i	−0.741403	+	0.671061i	$0.765839\pi$
$84$	−782.245	+	568.334i	−1.01607	+	0.738218i
$85$	−163.053	+	715.206i	−0.208066	+	0.912646i
$86$	−51.3129	−	37.2810i	−0.0643397	−	0.0467455i
$87$	−380.697	−	523.985i	−0.469138	−	0.645713i
$88$	−288.388	−	396.931i	−0.349343	−	0.480830i
$89$	−204.768	−	148.772i	−0.243880	−	0.177189i	0.459130	−	0.888369i	$-0.348161\pi$
$89$	−204.768	−	148.772i	−0.243880	−	0.177189i	−0.703010	+	0.711180i	$0.748161\pi$
$90$	−196.545	+	17.7389i	−0.230197	+	0.0207761i
$91$	519.662	−	377.556i	0.598630	−	0.434930i
$92$	−1018.61	−	330.967i	−1.15432	−	0.375062i
$93$			2292.54i			2.55619i
$94$	−12.3370	+	37.9694i	−0.0135368	+	0.0416621i
$95$	1033.49	+	235.616i	1.11615	+	0.254460i
$96$	287.720	+	885.510i	0.305888	+	0.941427i
$97$	354.095	−	115.053i	0.370649	−	0.120431i	−0.117769	−	0.993041i	$-0.537574\pi$
$97$	354.095	−	115.053i	0.370649	−	0.120431i	0.488418	+	0.872610i	$0.337574\pi$
$98$	−3.41647	+	4.70237i	−0.00352159	+	0.00484705i
$99$	991.141			1.00620
$100$	−440.744	−	818.059i	−0.440744	−	0.818059i
$101$	738.741			0.727797			0.363898	−	0.931439i	$-0.381446\pi$
$101$	738.741			0.727797			0.363898	+	0.931439i	$0.381446\pi$
$102$	206.123	−	283.703i	0.200090	−	0.275400i
$103$	−638.472	+	207.452i	−0.610781	+	0.198455i	−0.598043	−	0.801464i	$-0.704055\pi$
$103$	−638.472	+	207.452i	−0.610781	+	0.198455i	−0.0127383	+	0.999919i	$0.504055\pi$
$104$	−125.886	−	387.438i	−0.118694	−	0.365302i
$105$	−1337.04	+	571.873i	−1.24268	+	0.531515i
$106$	−135.161	+	415.982i	−0.123849	+	0.381168i
$107$		−	614.878i		−	0.555537i	−0.960648	−	0.277769i	$-0.910405\pi$
$107$		−	614.878i		−	0.555537i	0.960648	−	0.277769i	$-0.0895948\pi$
$108$	177.830	+	57.7806i	0.158442	+	0.0514810i
$109$	778.845	−	565.864i	0.684402	−	0.497247i	−0.190413	−	0.981704i	$-0.560983\pi$
$109$	778.845	−	565.864i	0.684402	−	0.497247i	0.874815	+	0.484457i	$0.160983\pi$
$110$	−139.769	−	326.781i	−0.121150	−	0.283248i
$111$	−267.232	−	194.155i	−0.228509	−	0.166022i
$112$	546.025	+	751.540i	0.460666	+	0.634052i
$113$	−32.1527	−	44.2544i	−0.0267670	−	0.0368416i	0.795424	−	0.606054i	$-0.207248\pi$
$113$	−32.1527	−	44.2544i	−0.0267670	−	0.0368416i	−0.822191	+	0.569212i	$0.807248\pi$
$114$	−409.959	−	297.853i	−0.336809	−	0.244706i
$115$	−1383.00	−	825.833i	−1.12144	−	0.669647i
$116$	−548.357	+	398.405i	−0.438911	+	0.318888i
$117$	782.672	+	254.306i	0.618445	+	0.200945i
$118$		−	145.410i		−	0.113441i
$119$	371.246	−	1142.58i	0.285984	−	0.880167i
$120$	82.9013	+	918.536i	0.0630651	+	0.698754i
$121$	140.308	+	431.822i	0.105415	+	0.324434i
$122$	263.027	−	85.4627i	0.195191	−	0.0634215i
$123$	355.355	−	489.104i	0.260498	−	0.358545i
$124$	2399.18			1.73752
$125$	−372.808	−	1346.90i	−0.266760	−	0.963763i
$126$	323.199			0.228515
$127$	−997.511	+	1372.96i	−0.696967	+	0.959292i	0.303013	+	0.952986i	$0.402007\pi$
$127$	−997.511	+	1372.96i	−0.696967	+	0.959292i	−0.999980	+	0.00630602i	$0.997993\pi$
$128$	1217.13	−	395.471i	0.840472	−	0.273086i
$129$	−185.039	−	569.490i	−0.126293	−	0.388689i
$130$	−26.5265	−	293.910i	−0.0178963	−	0.198289i
$131$	−78.9843	+	243.089i	−0.0526786	+	0.162128i	−0.973935	−	0.226828i	$-0.927164\pi$
$131$	−78.9843	+	243.089i	−0.0526786	+	0.162128i	0.921256	+	0.388956i	$0.127164\pi$
$132$		−	2231.05i		−	1.47112i
$133$	−1651.06	−	536.461i	−1.07643	−	0.349752i
$134$	−177.797	+	129.177i	−0.114622	+	0.0832778i
$135$	241.446	+	144.175i	0.153928	+	0.0919157i
$136$	−616.410	−	447.848i	−0.388652	−	0.282372i
$137$	−703.396	−	968.142i	−0.438651	−	0.603751i	0.531261	−	0.847208i	$-0.321718\pi$
$137$	−703.396	−	968.142i	−0.438651	−	0.603751i	−0.969912	+	0.243457i	$0.921718\pi$
$138$	452.620	+	622.978i	0.279200	+	0.384286i
$139$	695.004	+	504.950i	0.424097	+	0.308124i	0.779284	−	0.626671i	$-0.215583\pi$
$139$	695.004	+	504.950i	0.424097	+	0.308124i	−0.355187	+	0.934795i	$0.615583\pi$
$140$	598.473	+	1399.23i	0.361287	+	0.844689i
$141$	−304.927	+	221.542i	−0.182124	+	0.132321i
$142$	555.488	+	180.489i	0.328278	+	0.106664i
$143$			1482.13i			0.866728i
$144$	−367.779	+	1131.91i	−0.212835	+	0.655039i
$145$	−937.270	+	400.885i	−0.536800	+	0.229598i
$146$	117.863	+	362.744i	0.0668109	+	0.205623i
$147$	−52.1887	+	16.9571i	−0.0292820	+	0.00951430i
$148$	−203.186	+	279.662i	−0.112850	+	0.155325i
$149$	−2601.16			−1.43017			−0.715085	−	0.699037i	$-0.753612\pi$
$149$	−2601.16			−1.43017			−0.715085	+	0.699037i	$0.753612\pi$
$150$	−89.3495	+	662.093i	−0.0486357	+	0.360398i
$151$	−641.233			−0.345581			−0.172791	−	0.984959i	$-0.555278\pi$
$151$	−641.233			−0.345581			−0.172791	+	0.984959i	$0.555278\pi$
$152$	−647.153	+	890.730i	−0.345336	+	0.475314i
$153$	1463.85	−	475.633i	0.773498	−	0.251325i
$154$	179.873	+	553.592i	0.0941206	+	0.289674i
$155$	3518.04	+	802.044i	1.82307	+	0.415624i
$156$	572.439	−	1761.79i	0.293794	−	0.904204i
$157$			2002.84i			1.01812i	0.860732	+	0.509058i	$0.170006\pi$
$157$			2002.84i			1.01812i	−0.860732	+	0.509058i	$0.829994\pi$
$158$	−887.216	−	288.274i	−0.446729	−	0.145151i
$159$	−3340.70	+	2427.16i	−1.66626	+	1.21061i
$160$	1459.52	−	131.727i	0.721159	−	0.0650872i
$161$	2134.25	+	1550.62i	1.04474	+	0.759045i
$162$	−359.144	−	494.320i	−0.174179	−	0.239737i
$163$	−1027.35	−	1414.03i	−0.493672	−	0.679481i	0.487388	−	0.873185i	$-0.337950\pi$
$163$	−1027.35	−	1414.03i	−0.493672	−	0.679481i	−0.981060	+	0.193705i	$0.937950\pi$
$164$	−511.854	−	371.884i	−0.243714	−	0.177068i
$165$	745.837	−	3271.50i	0.351899	−	1.54355i
$166$	458.217	−	332.914i	0.214244	−	0.155658i
$167$	−128.596	−	41.7834i	−0.0595871	−	0.0193610i	0.279072	−	0.960270i	$-0.409973\pi$
$167$	−128.596	−	41.7834i	−0.0595871	−	0.0193610i	−0.338659	+	0.940909i	$0.609973\pi$
$168$		−	1510.44i		−	0.693649i
$169$	298.627	−	919.079i	0.135925	−	0.418334i
$170$	−363.247	−	415.560i	−0.163881	−	0.187482i
$171$	−687.303	−	2115.30i	−0.307365	−	0.945972i
$172$	−595.980	+	193.646i	−0.264204	+	0.0858450i
$173$	−228.994	+	315.183i	−0.100636	+	0.138514i	−0.856365	−	0.516370i	$-0.827283\pi$
$173$	−228.994	+	315.183i	−0.100636	+	0.138514i	0.755729	+	0.654885i	$0.227283\pi$
$174$	487.326			0.212322
$175$	409.810	+	2251.83i	0.177021	+	0.972698i
$176$	−2143.47			−0.918014
$177$	806.908	−	1110.61i	0.342661	−	0.471632i
$178$	181.121	−	58.8498i	0.0762673	−	0.0247808i
$179$	411.728	+	1267.17i	0.171922	+	0.529120i	0.999480	−	0.0322600i	$-0.0102705\pi$
$179$	411.728	+	1267.17i	0.171922	+	0.529120i	−0.827558	+	0.561380i	$0.810270\pi$
$180$	−999.612	+	1674.02i	−0.413926	+	0.693189i
$181$	1191.92	−	3668.35i	0.489473	−	1.50644i	−0.335923	−	0.941889i	$-0.609048\pi$
$181$	1191.92	−	3668.35i	0.489473	−	1.50644i	0.825396	−	0.564554i	$-0.190952\pi$
$182$			483.305i			0.196841i
$183$	2483.20	+	806.840i	1.00308	+	0.325920i
$184$	1353.56	−	983.420i	0.542315	−	0.394015i
$185$	−391.432	+	342.157i	−0.155560	+	0.135978i
$186$	−1395.51	−	1013.90i	−0.550129	−	0.399692i
$187$	1629.38	+	2242.65i	0.637176	+	0.876998i
$188$	231.847	+	319.110i	0.0899426	+	0.123795i
$189$	−372.600	−	270.710i	−0.143400	−	0.104187i
$190$	−600.496	+	524.902i	−0.229287	+	0.200423i
$191$	−2131.59	+	1548.69i	−0.807522	+	0.586699i	−0.913111	−	0.407711i	$-0.866327\pi$
$191$	−2131.59	+	1548.69i	−0.807522	+	0.586699i	0.105589	+	0.994410i	$0.466327\pi$
$192$	2075.68	+	674.429i	0.780204	+	0.253504i
$193$		−	4884.45i		−	1.82171i	−0.412724	−	0.910856i	$-0.635423\pi$
$193$		−	4884.45i		−	1.82171i	0.412724	−	0.910856i	$-0.364577\pi$
$194$	−86.5675	+	266.427i	−0.0320370	+	0.0985999i
$195$	1428.36	−	2392.03i	0.524548	−	0.878445i
$196$	17.7459	+	54.6162i	0.00646716	+	0.0199039i
$197$	−447.635	+	145.445i	−0.161892	+	0.0526018i	−0.388841	−	0.921305i	$-0.627125\pi$
$197$	−447.635	+	145.445i	−0.161892	+	0.0526018i	0.226950	+	0.973906i	$0.427125\pi$
$198$	−438.342	+	603.326i	−0.157331	+	0.216548i
$199$	−2673.92			−0.952508			−0.476254	−	0.879308i	$-0.658006\pi$
$199$	−2673.92			−0.952508			−0.476254	+	0.879308i	$0.658006\pi$
$200$	1438.55	+	194.132i	0.508603	+	0.0686361i
$201$	−2074.81			−0.728090
$202$	−326.715	+	449.685i	−0.113800	+	0.156632i
$203$	1587.81	−	515.910i	0.548977	−	0.178373i
$204$	−1070.65	−	3295.11i	−0.367452	−	1.13090i
$205$	−626.236	−	716.423i	−0.213357	−	0.244084i
$206$	156.090	−	480.397i	0.0527929	−	0.162480i
$207$			3379.86i			1.13486i
$208$	−1692.63	−	549.969i	−0.564245	−	0.183334i
$209$	3240.69	−	2354.50i	1.07255	−	0.779254i
$210$	243.208	−	1066.80i	0.0799189	−	0.350552i
$211$	2713.32	+	1971.34i	0.885274	+	0.643189i	0.934641	−	0.355592i	$-0.115721\pi$
$211$	2713.32	+	1971.34i	0.885274	+	0.643189i	−0.0493675	+	0.998781i	$0.515721\pi$
$212$	2540.06	+	3496.09i	0.822887	+	1.13261i
$213$	3241.14	+	4461.05i	1.04263	+	1.43505i
$214$	374.287	+	271.935i	0.119560	+	0.0868651i
$215$	−938.650	+	84.7166i	−0.297746	+	0.0268727i
$216$	−236.307	+	171.687i	−0.0744381	+	0.0540825i
$217$	−5620.24	−	1826.13i	−1.75819	−	0.571270i
$218$			724.356i			0.225044i
$219$	−1112.72	+	3424.62i	−0.343338	+	1.05669i
$220$	−3423.67	−	780.530i	−1.04920	−	0.239197i
$221$	711.252	+	2189.01i	0.216489	+	0.666284i
$222$	236.371	−	76.8017i	0.0714604	−	0.0232189i
$223$	707.795	−	974.196i	0.212545	−	0.292542i	−0.689412	−	0.724370i	$-0.742131\pi$
$223$	707.795	−	974.196i	0.212545	−	0.292542i	0.901956	+	0.431827i	$0.142131\pi$
$224$	−2400.04			−0.715889
$225$	−2025.40	+	2120.53i	−0.600119	+	0.628304i
$226$	41.1583			0.0121142
$227$	1485.06	−	2044.01i	0.434216	−	0.597647i	−0.534698	−	0.845043i	$-0.679575\pi$
$227$	1485.06	−	2044.01i	0.434216	−	0.597647i	0.968915	+	0.247396i	$0.0795747\pi$
$228$	−4761.52	+	1547.11i	−1.38307	+	0.449386i
$229$	646.904	+	1990.97i	0.186675	+	0.574527i	0.999973	−	0.00732009i	$-0.00233008\pi$
$229$	646.904	+	1990.97i	0.186675	+	0.574527i	−0.813298	+	0.581847i	$0.802330\pi$
$230$	1114.34	−	476.623i	0.319468	−	0.136642i
$231$	−1698.15	+	5226.38i	−0.483681	+	1.48862i
$232$		−	1058.83i		−	0.299635i
$233$	3179.48	+	1033.07i	0.893967	+	0.290468i	0.719745	−	0.694239i	$-0.244259\pi$
$233$	3179.48	+	1033.07i	0.893967	+	0.290468i	0.174223	+	0.984706i	$0.444259\pi$
$234$	−500.945	+	363.958i	−0.139948	+	0.101678i
$235$	233.291	+	545.434i	0.0647584	+	0.151405i
$236$	−1162.27	−	844.441i	−0.320583	−	0.232917i
$237$	−5176.70	−	7125.12i	−1.41883	−	1.95285i
$238$	531.320	+	731.300i	0.144707	+	0.199173i
$239$	1987.31	+	1443.87i	0.537860	+	0.390778i	0.823290	−	0.567621i	$-0.192136\pi$
$239$	1987.31	+	1443.87i	0.537860	+	0.390778i	−0.285430	+	0.958400i	$0.592136\pi$
$240$	3459.37	+	2065.71i	0.930424	+	0.555587i
$241$	4538.00	−	3297.05i	1.21294	−	0.881251i	0.217444	−	0.976073i	$-0.430228\pi$
$241$	4538.00	−	3297.05i	1.21294	−	0.881251i	0.995494	+	0.0948218i	$0.0302281\pi$
$242$	−324.910	−	105.570i	−0.0863059	−	0.0280425i
$243$		−	5089.36i		−	1.34355i
$244$	844.370	−	2598.70i	0.221538	−	0.681824i
$245$	7.76352	+	86.0189i	0.00202446	+	0.0224308i
$246$	140.567	+	432.621i	0.0364319	+	0.112126i
$247$	3163.18	−	1027.78i	0.814852	−	0.264761i
$248$	−2202.93	+	3032.07i	−0.564056	+	0.776357i
$249$	5347.18			1.36090
$250$	984.760	+	368.744i	0.249127	+	0.0932857i
$251$	97.9305			0.0246268			0.0123134	−	0.999924i	$-0.496080\pi$
$251$	97.9305			0.0246268			0.0123134	+	0.999924i	$0.496080\pi$
$252$	1876.92	−	2583.36i	0.469185	−	0.645778i
$253$	−5789.19	+	1881.02i	−1.43859	+	0.467426i
$254$	−394.584	−	1214.41i	−0.0974741	−	0.299994i
$255$	−468.389	−	5189.69i	−0.115026	−	1.27448i
$256$	461.991	−	1421.86i	0.112791	−	0.347134i
$257$		−	4693.45i		−	1.13918i	−0.821929	−	0.569590i	$-0.807102\pi$
$257$		−	4693.45i		−	1.13918i	0.821929	−	0.569590i	$-0.192898\pi$
$258$	428.494	+	139.226i	0.103399	+	0.0335963i
$259$	688.841	−	500.472i	0.165261	−	0.120069i
$260$	−2503.29	−	1494.80i	−0.597106	−	0.356552i
$261$	1730.45	+	1257.25i	0.410392	+	0.298167i
$262$	−113.041	−	155.587i	−0.0266553	−	0.0366879i
$263$	−3071.74	−	4227.89i	−0.720197	−	0.991266i	−0.999517	−	0.0310682i	$-0.990109\pi$
$263$	−3071.74	−	4227.89i	−0.720197	−	0.991266i	0.279320	−	0.960198i	$-0.409891\pi$
$264$	2819.58	+	2048.55i	0.657324	+	0.477574i
$265$	2555.87	+	5975.63i	0.592476	+	1.38521i
$266$	1056.75	−	767.773i	0.243584	−	0.176974i
$267$	1709.94	+	555.592i	0.391934	+	0.127347i
$268$			2171.32i			0.494905i
$269$	−1320.45	+	4063.94i	−0.299292	+	0.921125i	0.682454	+	0.730928i	$0.260913\pi$
$269$	−1320.45	+	4063.94i	−0.299292	+	0.921125i	−0.981746	+	0.190197i	$0.939087\pi$
$270$	−194.544	+	83.2094i	−0.0438502	+	0.0187554i
$271$	−853.936	−	2628.14i	−0.191413	−	0.589108i	−1.00000		0.000731472i	$-0.999767\pi$
$271$	−853.936	−	2628.14i	−0.191413	−	0.589108i	0.808587	−	0.588377i	$-0.200233\pi$
$272$	−3165.76	+	1028.62i	−0.705708	+	0.229299i
$273$	−2681.95	+	3691.39i	−0.594576	+	0.818364i
$274$	900.409			0.198524
$275$	−4759.36	−	2289.06i	−1.04364	−	0.501947i
$276$	7608.02			1.65924
$277$	−1874.63	+	2580.21i	−0.406627	+	0.559674i	−0.962392	−	0.271665i	$-0.912426\pi$
$277$	−1874.63	+	2580.21i	−0.406627	+	0.559674i	0.555764	+	0.831340i	$0.312426\pi$
$278$	−614.744	+	199.742i	−0.132626	+	0.0430926i
$279$	−2339.60	−	7200.55i	−0.502036	−	1.54511i
$280$	−2317.85	−	528.426i	−0.494708	−	0.112784i
$281$	−2133.26	+	6565.51i	−0.452882	+	1.39383i	0.420721	+	0.907190i	$0.361777\pi$
$281$	−2133.26	+	6565.51i	−0.452882	+	1.39383i	−0.873604	+	0.486638i	$0.838223\pi$
$282$		−	283.594i		−	0.0598857i
$283$	7263.77	+	2360.14i	1.52575	+	0.495745i	0.947402	−	0.320047i	$-0.103699\pi$
$283$	7263.77	+	2360.14i	1.52575	+	0.495745i	0.578345	+	0.815792i	$0.303699\pi$
$284$	4668.55	−	3391.90i	0.975450	−	0.708706i
$285$	−7499.25	+	676.835i	−1.55866	+	0.140675i
$286$	−902.201	−	655.487i	−0.186532	−	0.135524i
$287$	915.994	+	1260.76i	0.188395	+	0.259304i
$288$	−1807.37	−	2487.63i	−0.369793	−	0.508976i
$289$	−492.009	−	357.466i	−0.100144	−	0.0727591i
$290$	170.490	−	747.828i	0.0345225	−	0.151428i
$291$	−2139.64	+	1554.54i	−0.431024	+	0.313158i
$292$	3583.91	+	1164.48i	0.718262	+	0.233377i
$293$			3024.68i			0.603085i	0.953453	+	0.301542i	$0.0975015\pi$
$293$			3024.68i			0.603085i	−0.953453	+	0.301542i	$0.902499\pi$
$294$	12.7588	−	39.2677i	0.00253099	−	0.00778958i
$295$	−1422.00	−	1626.79i	−0.280652	−	0.321070i
$296$	−166.869	−	513.571i	−0.0327671	−	0.100847i
$297$	1010.69	−	328.392i	0.197461	−	0.0641590i
$298$	1150.39	−	1583.37i	0.223625	−	0.307793i
$299$	−5054.17			−0.977559
$300$	4773.28	+	4559.16i	0.918619	+	0.877411i
$301$	1543.52			0.295571
$302$	283.591	−	390.330i	0.0540359	−	0.0743740i
$303$	−4990.78	+	1621.60i	−0.946247	+	0.307454i
$304$	1486.38	+	4574.62i	0.280428	+	0.863067i
$305$	2106.89	−	3528.33i	0.395541	−	0.662400i
$306$	−357.874	+	1101.42i	−0.0668572	+	0.205765i
$307$			3456.26i			0.642538i	0.946988	+	0.321269i	$0.104109\pi$
$307$			3456.26i			0.642538i	−0.946988	+	0.321269i	$0.895891\pi$
$308$	5469.48	+	1777.14i	1.01186	+	0.328773i
$309$	3858.00	−	2803.00i	0.710272	−	0.516043i
$310$	−2044.10	+	1786.78i	−0.374507	+	0.327362i
$311$	−5224.69	−	3795.96i	−0.952620	−	0.692119i	−0.00119529	−	0.999999i	$-0.500380\pi$
$311$	−5224.69	−	3795.96i	−0.952620	−	0.692119i	−0.951425	+	0.307880i	$0.900380\pi$
$312$	1700.92	+	2341.12i	0.308640	+	0.424807i
$313$	2704.59	+	3722.55i	0.488410	+	0.672239i	0.980094	−	0.198535i	$-0.0636182\pi$
$313$	2704.59	+	3722.55i	0.488410	+	0.672239i	−0.491683	+	0.870774i	$0.663618\pi$
$314$	−1219.17	−	885.776i	−0.219113	−	0.159195i
$315$	3615.83	−	3160.65i	0.646759	−	0.565341i
$316$	−7456.54	+	5417.49i	−1.32741	+	0.964423i
$317$	−594.894	−	193.293i	−0.105403	−	0.0342474i	0.255841	−	0.966719i	$-0.417648\pi$
$317$	−594.894	−	193.293i	−0.105403	−	0.0342474i	−0.361243	+	0.932472i	$0.617648\pi$
$318$		−	3106.98i		−	0.547895i
$319$	−1190.41	+	3663.72i	−0.208935	+	0.643037i
$320$	1761.12	−	2949.30i	0.307655	−	0.515221i
$321$	1349.71	+	4153.98i	0.234684	+	0.722283i
$322$	−1887.78	+	613.378i	−0.326715	+	0.106156i
$323$	3656.39	−	5032.59i	0.629867	−	0.866937i
$324$	−6036.80			−1.03512
$325$	−3170.99	−	3028.75i	−0.541215	−	0.516937i
$326$	1315.10			0.223426
$327$	−4019.59	+	5532.49i	−0.679767	+	0.935620i
$328$	939.968	−	305.414i	0.158235	−	0.0514136i
$329$	−300.228	−	924.007i	−0.0503104	−	0.154839i
$330$	1661.57	+	1900.86i	0.277170	+	0.317087i
$331$	311.330	−	958.176i	0.0516987	−	0.159112i	−0.921874	−	0.387490i	$-0.873342\pi$
$331$	311.330	−	958.176i	0.0516987	−	0.159112i	0.973573	+	0.228378i	$0.0733422\pi$
$332$		−	5595.90i		−	0.925046i
$333$	1037.48	+	337.096i	0.170731	+	0.0554738i
$334$	82.3071	−	59.7996i	0.0134840	−	0.00979667i
$335$	−725.871	+	3183.92i	−0.118384	+	0.519271i
$336$	−5338.53	−	3878.67i	−0.866787	−	0.629758i
$337$	−2755.10	−	3792.07i	−0.445340	−	0.612958i	0.526048	−	0.850455i	$-0.323673\pi$
$337$	−2755.10	−	3792.07i	−0.445340	−	0.612958i	−0.971388	+	0.237496i	$0.923673\pi$
$338$	427.389	+	588.251i	0.0687779	+	0.0946646i
$339$	314.359	+	228.395i	0.0503647	+	0.0365921i
$340$	−5431.09	+	490.176i	−0.866300	+	0.0781868i
$341$	11031.4	−	8014.77i	1.75186	−	1.27280i
$342$	1591.59	+	517.139i	0.251647	+	0.0817651i
$343$		−	6421.96i		−	1.01094i
$344$	302.500	−	931.001i	0.0474120	−	0.145919i
$345$	11156.0	+	2543.35i	1.74093	+	0.396897i
$346$	−90.5829	−	278.786i	−0.0140745	−	0.0433168i
$347$	4782.55	−	1553.94i	0.739886	−	0.240404i	0.0852625	−	0.996359i	$-0.472827\pi$
$347$	4782.55	−	1553.94i	0.739886	−	0.240404i	0.654624	+	0.755955i	$0.272827\pi$
$348$	2830.05	−	3895.23i	0.435939	−	0.600018i
$349$	−5501.17			−0.843756			−0.421878	−	0.906653i	$-0.638629\pi$
$349$	−5501.17			−0.843756			−0.421878	+	0.906653i	$0.638629\pi$
$350$	−1551.97	−	746.434i	−0.237018	−	0.113996i
$351$	882.364			0.134180
$352$	3255.07	−	4480.22i	0.492886	−	0.678400i
$353$	−3449.60	+	1120.84i	−0.520124	+	0.168998i	−0.557301	−	0.830310i	$-0.688163\pi$
$353$	−3449.60	+	1120.84i	−0.520124	+	0.168998i	0.0371778	+	0.999309i	$0.488163\pi$
$354$	319.188	+	982.359i	0.0479227	+	0.147491i
$355$	7979.64	−	3413.02i	1.19300	−	0.510266i
$356$	581.435	−	1789.47i	0.0865618	−	0.266410i
$357$			8533.93i			1.26516i
$358$	−953.438	−	309.791i	−0.140756	−	0.0457345i
$359$	−3963.25	+	2879.47i	−0.582653	+	0.423322i	−0.839680	−	0.543082i	$-0.817257\pi$
$359$	−3963.25	+	2879.47i	−0.582653	+	0.423322i	0.257026	+	0.966404i	$0.417257\pi$
$360$	−1197.77	−	2800.39i	−0.175356	−	0.409981i
$361$	−1723.18	−	1251.97i	−0.251230	−	0.182529i
$362$	1705.85	+	2347.90i	0.247673	+	0.340893i
$363$	−1895.78	−	2609.31i	−0.274111	−	0.377282i
$364$	3863.10	+	2806.70i	0.556267	+	0.404152i
$365$	4865.98	+	2905.64i	0.697800	+	0.416679i
$366$	−1589.36	+	1154.74i	−0.226986	+	0.164915i
$367$	4114.12	+	1336.76i	0.585165	+	0.190132i	0.586613	−	0.809867i	$-0.300461\pi$
$367$	4114.12	+	1336.76i	0.585165	+	0.190132i	−0.00144820	+	0.999999i	$0.500461\pi$
$368$		−	7309.38i		−	1.03540i
$369$	−616.974	+	1898.85i	−0.0870417	+	0.267887i
$370$	−35.1623	−	389.594i	−0.00494054	−	0.0547406i
$371$	−3289.22	−	10123.2i	−0.460291	−	1.41663i
$372$	−16208.4	+	5266.41i	−2.25904	+	0.734008i
$373$	−5957.57	+	8199.89i	−0.827001	+	1.13827i	0.161473	+	0.986877i	$0.448376\pi$
$373$	−5957.57	+	8199.89i	−0.827001	+	1.13827i	−0.988474	+	0.151392i	$0.951624\pi$
$374$	−2085.75			−0.288373
$375$	5475.18	+	8281.02i	0.753965	+	1.14035i
$376$	−616.172			−0.0845123
$377$	−1880.06	+	2587.68i	−0.256839	+	0.353508i
$378$	329.572	−	107.084i	0.0448449	−	0.0145710i
$379$	−1076.43	−	3312.91i	−0.145891	−	0.449005i	0.851234	−	0.524787i	$-0.175855\pi$
$379$	−1076.43	−	3312.91i	−0.145891	−	0.449005i	−0.997124	+	0.0757815i	$0.975855\pi$
$380$	708.318	+	7848.08i	0.0956209	+	1.05947i
$381$	3725.21	−	11465.0i	0.500914	−	1.54166i
$382$		−	1982.46i		−	0.265528i
$383$	−6791.52	−	2206.70i	−0.906085	−	0.294405i	−0.181339	−	0.983421i	$-0.558043\pi$
$383$	−6791.52	−	2206.70i	−0.906085	−	0.294405i	−0.724746	+	0.689016i	$0.758043\pi$
$384$	−7354.60	+	5343.43i	−0.977378	+	0.710106i
$385$	7426.08	+	4434.35i	0.983033	+	0.587002i
$386$	2973.25	+	2160.19i	0.392058	+	0.284847i
$387$	1162.36	+	1599.85i	0.152677	+	0.210142i
$388$	1626.85	+	2239.17i	0.212863	+	0.292981i
$389$	1446.50	+	1050.94i	0.188536	+	0.136979i	0.678049	−	0.735017i	$-0.262826\pi$
$389$	1446.50	+	1050.94i	0.188536	+	0.136979i	−0.489514	+	0.871996i	$0.662826\pi$
$390$	824.366	+	1927.37i	0.107034	+	0.250246i
$391$	−7647.57	+	5556.28i	−0.989141	+	0.718653i
$392$	−85.3179	−	27.7215i	−0.0109929	−	0.00357180i
$393$		−	1815.63i		−	0.233045i
$394$	109.435	−	336.808i	0.0139931	−	0.0430663i
$395$	−12744.9	+	5451.22i	−1.62346	+	0.694381i
$396$	2276.84	+	7007.40i	0.288928	+	0.889230i
$397$	10620.3	−	3450.75i	1.34261	−	0.436242i	0.452412	−	0.891809i	$-0.350564\pi$
$397$	10620.3	−	3450.75i	1.34261	−	0.436242i	0.890201	+	0.455567i	$0.150564\pi$
$398$	1182.57	−	1627.66i	0.148936	−	0.204993i
$399$	12331.8			1.54727
$400$	4380.20	−	4585.92i	0.547525	−	0.573240i
$401$	−14629.3			−1.82183			−0.910914	−	0.412596i	$-0.864622\pi$
$401$	−14629.3			−1.82183			−0.910914	+	0.412596i	$0.864622\pi$
$402$	917.606	−	1262.98i	0.113846	−	0.156695i
$403$	10767.6	−	3498.59i	1.33094	−	0.432450i
$404$	1697.03	+	5222.92i	0.208986	+	0.643193i
$405$	−8852.05	−	2018.09i	−1.08608	−	0.247605i
$406$	−388.179	+	1194.69i	−0.0474508	+	0.146039i
$407$			1964.65i			0.239273i
$408$	5147.40	+	1672.49i	0.624594	+	0.202943i
$409$	−345.764	+	251.212i	−0.0418017	+	0.0303707i	−0.608490	−	0.793562i	$-0.708224\pi$
$409$	−345.764	+	251.212i	−0.0418017	+	0.0303707i	0.566688	+	0.823932i	$0.308224\pi$
$410$	713.059	−	64.3562i	0.0858914	−	0.00775201i
$411$	6877.15	+	4996.54i	0.825365	+	0.599663i
$412$	−2933.38	−	4037.46i	−0.350770	−	0.482794i
$413$	2079.96	+	2862.82i	0.247816	+	0.341090i
$414$	−2057.38	−	1494.77i	−0.244238	−	0.177450i
$415$	1870.71	−	8205.55i	0.221275	−	0.970589i
$416$	3719.95	−	2702.70i	0.438427	−	0.318536i
$417$	−5803.71	−	1885.74i	−0.681556	−	0.221451i
$418$			3013.96i			0.352674i
$419$	882.901	−	2717.29i	0.102942	−	0.316822i	−0.886300	−	0.463111i	$-0.846733\pi$
$419$	882.901	−	2717.29i	0.102942	−	0.316822i	0.989242	+	0.146289i	$0.0467331\pi$
$420$	−7114.59	−	8139.20i	−0.826563	−	0.945600i
$421$	1128.11	+	3471.97i	0.130596	+	0.401932i	0.994879	−	0.101073i	$-0.0322276\pi$
$421$	1128.11	+	3471.97i	0.130596	+	0.401932i	−0.864283	+	0.503005i	$0.832228\pi$
$422$	−2399.99	+	779.802i	−0.276847	+	0.0899531i
$423$	731.641	−	1007.02i	0.0840984	−	0.115752i
$424$	−6750.62			−0.773205
$425$	−8127.74	−	1096.84i	−0.927655	−	0.125187i
$426$	−4148.95			−0.471871
$427$	−3955.99	+	5444.95i	−0.448346	+	0.617095i
$428$	4347.20	−	1412.49i	0.490958	−	0.159522i
$429$	−3253.41	−	10013.0i	−0.366145	−	1.12688i
$430$	363.558	−	608.840i	0.0407729	−	0.0682811i
$431$	−2042.89	+	6287.37i	−0.228312	+	0.702672i	0.769626	+	0.638495i	$0.220443\pi$
$431$	−2042.89	+	6287.37i	−0.228312	+	0.702672i	−0.997938	+	0.0641779i	$0.979557\pi$
$432$			1276.08i			0.142119i
$433$	−5494.49	−	1785.27i	−0.609811	−	0.198140i	−0.0121996	−	0.999926i	$-0.503883\pi$
$433$	−5494.49	−	1785.27i	−0.609811	−	0.198140i	−0.597611	+	0.801786i	$0.703883\pi$
$434$	3597.20	−	2613.52i	0.397860	−	0.289062i
$435$	5452.02	−	4765.69i	0.600929	−	0.525281i
$436$	5789.83	+	4206.56i	0.635970	+	0.462059i
$437$	8028.99	+	11051.0i	0.878898	+	1.20970i
$438$	−1592.51	−	2191.90i	−0.173729	−	0.239117i
$439$	−8575.73	−	6230.63i	−0.932340	−	0.677384i	0.0142249	−	0.999899i	$-0.495472\pi$
$439$	−8575.73	−	6230.63i	−0.932340	−	0.677384i	−0.946565	+	0.322514i	$0.895472\pi$
$440$	4130.04	−	3610.13i	0.447482	−	0.391150i
$441$	146.612	−	106.520i	0.0158311	−	0.0115020i
$442$	−1647.05	−	535.158i	−0.177244	−	0.0575902i
$443$			8710.52i			0.934198i	0.884205	+	0.467099i	$0.154701\pi$
$443$			8710.52i			0.934198i	−0.884205	+	0.467099i	$0.845299\pi$
$444$	758.800	−	2335.35i	0.0811060	−	0.249619i
$445$	1450.81	−	2429.62i	0.154550	−	0.258820i
$446$	279.982	+	861.695i	0.0297254	+	0.0914853i
$447$	17572.9	−	5709.78i	1.85944	−	0.604168i
$448$	−3306.76	+	4551.37i	−0.348728	+	0.479982i
$449$	16762.7			1.76188			0.880938	−	0.473231i	$-0.156912\pi$
$449$	16762.7			1.76188			0.880938	+	0.473231i	$0.156912\pi$
$450$	−395.049	−	2170.72i	−0.0413840	−	0.227397i
$451$	−3595.82			−0.375434
$452$	239.019	−	328.981i	0.0248728	−	0.0342345i
$453$	4332.03	−	1407.56i	0.449308	−	0.145989i
$454$	587.445	+	1807.97i	0.0607272	+	0.186899i
$455$	4726.37	+	5407.04i	0.486980	+	0.557112i
$456$	2416.80	−	7438.14i	0.248195	−	0.763866i
$457$		−	13257.8i		−	1.35706i	−0.734574	−	0.678529i	$-0.762618\pi$
$457$		−	13257.8i		−	1.35706i	0.734574	−	0.678529i	$-0.237382\pi$
$458$	−1498.04	−	486.742i	−0.152835	−	0.0496593i
$459$	1335.12	−	970.024i	0.135770	−	0.0986423i
$460$	2661.66	−	11674.9i	0.269783	−	1.18336i
$461$	11729.4	+	8521.91i	1.18502	+	0.860965i	0.992729	−	0.120374i	$-0.0384092\pi$
$461$	11729.4	+	8521.91i	1.18502	+	0.860965i	0.192288	+	0.981339i	$0.438409\pi$
$462$	−2430.37	−	3345.11i	−0.244742	−	0.336859i
$463$	2587.63	+	3561.56i	0.259735	+	0.357494i	0.918891	−	0.394512i	$-0.129086\pi$
$463$	2587.63	+	3561.56i	0.259735	+	0.357494i	−0.659156	+	0.752006i	$0.729086\pi$
$464$	−3742.33	−	2718.96i	−0.374426	−	0.272036i
$465$	−25527.7	+	2303.97i	−2.54584	+	0.229772i
$466$	−2035.00	+	1478.52i	−0.202296	+	0.146976i
$467$	−16249.4	−	5279.74i	−1.61013	−	0.523163i	−0.640546	−	0.767920i	$-0.721292\pi$
$467$	−16249.4	−	5279.74i	−1.61013	−	0.523163i	−0.969584	+	0.244757i	$0.921292\pi$
$468$			6117.71i			0.604254i
$469$	1652.69	−	5086.47i	0.162717	−	0.500791i
$470$	−435.190	−	99.2149i	−0.0427103	−	0.00973711i
$471$	−4396.42	−	13530.8i	−0.430098	−	1.32371i
$472$	2134.40	−	693.508i	0.208143	−	0.0676299i
$473$	−2093.41	+	2881.33i	−0.203499	+	0.280092i
$474$	6626.63			0.642133
$475$	−1584.96	+	11744.8i	−0.153101	+	1.13450i
$476$	8930.88			0.859971
$477$	8015.67	−	11032.6i	0.769418	−	1.05901i
$478$	−1757.82	+	571.149i	−0.168202	+	0.0546522i
$479$	3360.08	+	10341.3i	0.320514	+	0.986439i	0.973425	+	0.229005i	$0.0735473\pi$
$479$	3360.08	+	10341.3i	0.320514	+	0.986439i	−0.652912	+	0.757434i	$0.726453\pi$
$480$	−9571.07	+	4093.70i	−0.910120	+	0.389273i
$481$	−504.087	+	1551.42i	−0.0477846	+	0.147066i
$482$			4220.51i			0.398836i
$483$	−17822.3	−	5790.82i	−1.67897	−	0.545531i
$484$	−2730.68	+	1983.96i	−0.256450	+	0.186322i
$485$	1636.98	+	3827.26i	0.153261	+	0.358323i
$486$	3097.98	+	2250.82i	0.289151	+	0.210080i
$487$	−6590.77	−	9071.42i	−0.613258	−	0.844077i	0.383583	−	0.923507i	$-0.374690\pi$
$487$	−6590.77	−	9071.42i	−0.613258	−	0.844077i	−0.996840	+	0.0794297i	$0.974690\pi$
$488$	2508.92	+	3453.24i	0.232733	+	0.320329i
$489$	10044.5	+	7297.76i	0.928891	+	0.674879i
$490$	−55.7947	−	33.3169i	−0.00514398	−	0.00307164i
$491$	878.183	−	638.038i	0.0807166	−	0.0586441i	−0.546695	−	0.837332i	$-0.684114\pi$
$491$	878.183	−	638.038i	0.0807166	−	0.0586441i	0.627412	+	0.778688i	$0.284114\pi$
$492$	4274.29	+	1388.80i	0.391667	+	0.127260i
$493$			5982.32i			0.546512i
$494$	−773.319	+	2380.03i	−0.0704317	+	0.216766i
$495$	996.079	+	11036.4i	0.0904453	+	1.00212i
$496$	5059.69	+	15572.1i	0.458038	+	1.40970i
$497$	−13518.1	+	4392.31i	−1.22006	+	0.396422i
$498$	−2364.84	+	3254.93i	−0.212793	+	0.292885i
$499$	637.826			0.0572205			0.0286102	−	0.999591i	$-0.490892\pi$
$499$	637.826			0.0572205			0.0286102	+	0.999591i	$0.490892\pi$
$500$	8666.21	−	5729.85i	0.775129	−	0.512493i
$501$	960.485			0.0856513
$502$	−43.3107	+	59.6120i	−0.00385070	+	0.00530003i
$503$	−12809.0	+	4161.89i	−1.13544	+	0.368926i	−0.815639	−	0.578561i	$-0.803615\pi$
$503$	−12809.0	+	4161.89i	−1.13544	+	0.368926i	−0.319797	+	0.947486i	$0.603615\pi$
$504$	1541.44	+	4744.07i	0.136233	+	0.419281i
$505$	742.421	+	8225.94i	0.0654204	+	0.724851i
$506$	1415.31	−	4355.89i	0.124345	−	0.382693i
$507$			6864.62i			0.601318i
$508$	−11998.3	−	3898.49i	−1.04791	−	0.340487i
$509$	−3580.02	+	2601.04i	−0.311752	+	0.226501i	−0.732648	−	0.680608i	$-0.761716\pi$
$509$	−3580.02	+	2601.04i	−0.311752	+	0.226501i	0.420896	+	0.907109i	$0.361716\pi$
$510$	3366.21	+	2010.07i	0.292271	+	0.174525i
$511$	−7509.21	−	5455.76i	−0.650074	−	0.472306i
$512$	6679.03	+	9192.90i	0.576512	+	0.793501i
$513$	−1401.71	−	1929.29i	−0.120638	−	0.166043i
$514$	2856.99	+	2075.72i	0.245168	+	0.178125i
$515$	−2951.65	−	6900.95i	−0.252554	−	0.590470i
$516$	3601.24	−	2616.46i	0.307240	−	0.223223i
$517$	2132.06	+	692.748i	0.181369	+	0.0589304i
$518$			640.648i			0.0543407i
$519$	855.180	−	2631.97i	0.0723280	−	0.222603i
$520$	4187.64	−	1791.12i	0.353154	−	0.151050i
$521$	1803.47	+	5550.52i	0.151654	+	0.466742i	0.997806	−	0.0661984i	$-0.0210870\pi$
$521$	1803.47	+	5550.52i	0.151654	+	0.466742i	−0.846153	+	0.532940i	$0.821087\pi$
$522$	−1530.62	+	497.328i	−0.128340	+	0.0417001i
$523$	4013.98	−	5524.77i	0.335601	−	0.461915i	−0.607549	−	0.794282i	$-0.707847\pi$
$523$	4013.98	−	5524.77i	0.335601	−	0.461915i	0.943150	+	0.332367i	$0.107847\pi$
$524$	−1900.09			−0.158408
$525$	−7711.55	−	14313.3i	−0.641066	−	1.18987i
$526$	3932.10			0.325946
$527$	12446.4	−	17131.1i	1.02880	−	1.41602i
$528$	14480.9	−	4705.11i	1.19356	−	0.387810i
$529$	−2654.60	−	8170.01i	−0.218180	−	0.671490i
$530$	−4767.83	−	1086.97i	−0.390757	−	0.0890851i
$531$	−1400.97	+	4311.75i	−0.114495	+	0.352380i
$532$		−	12905.4i		−	1.05173i
$533$	−2839.50	−	922.610i	−0.230755	−	0.0749769i
$534$	−1094.43	+	795.153i	−0.0886906	+	0.0644375i
$535$	6846.71	−	617.941i	0.553288	−	0.0499363i
$536$	−2744.10	−	1993.71i	−0.221133	−	0.160662i
$537$	−5563.09	−	7656.94i	−0.447049	−	0.615310i
$538$	−1889.81	−	2601.10i	−0.151441	−	0.208441i
$539$	264.048	+	191.842i	0.0211008	+	0.0153307i
$540$	−464.676	+	2038.23i	−0.0370305	+	0.162428i
$541$	−967.976	+	703.276i	−0.0769252	+	0.0558895i	−0.625583	−	0.780157i	$-0.715139\pi$
$541$	−967.976	+	703.276i	−0.0769252	+	0.0558895i	0.548658	+	0.836047i	$0.315139\pi$
$542$	1977.46	+	642.516i	0.156714	+	0.0509196i
$543$			27398.9i			2.16538i
$544$	2657.53	−	8179.04i	0.209450	−	0.644620i
$545$	7083.67	+	8103.82i	0.556754	+	0.636935i
$546$	−1060.90	−	3265.11i	−0.0831543	−	0.255923i
$547$	−3230.05	+	1049.51i	−0.252481	+	0.0820360i	−0.432523	−	0.901623i	$-0.642377\pi$
$547$	−3230.05	+	1049.51i	−0.252481	+	0.0820360i	0.180042	+	0.983659i	$0.442377\pi$
$548$	5228.96	−	7197.04i	0.407609	−	0.561026i
$549$	−8622.77			−0.670329
$550$	3498.26	−	1884.75i	0.271212	−	0.146120i
$551$	8644.63			0.668373
$552$	−6985.68	+	9614.97i	−0.538642	+	0.741377i
$553$	21590.9	−	7015.32i	1.66029	−	0.539461i
$554$	−741.546	−	2282.25i	−0.0568688	−	0.175024i
$555$	1893.37	−	3170.77i	0.144809	−	0.242507i
$556$	−1973.45	+	6073.66i	−0.150527	+	0.463275i
$557$			10683.8i			0.812727i	0.913712	+	0.406363i	$0.133203\pi$
$557$			10683.8i			0.812727i	−0.913712	+	0.406363i	$0.866797\pi$
$558$	5417.81	+	1760.35i	0.411029	+	0.133551i
$559$	−2392.38	+	1738.17i	−0.181014	+	0.131515i
$560$	−7819.71	+	6835.32i	−0.590077	+	0.515795i
$561$	−15930.5	−	11574.2i	−1.19891	−	0.871058i
$562$	−3053.09	−	4202.22i	−0.229158	−	0.315409i
$563$	−14464.4	−	19908.5i	−1.08277	−	1.49031i	−0.856433	−	0.516258i	$-0.827325\pi$
$563$	−14464.4	−	19908.5i	−1.08277	−	1.49031i	−0.226338	−	0.974049i	$-0.572675\pi$
$564$	−2266.79	−	1646.92i	−0.169236	−	0.122957i
$565$	460.463	−	402.498i	0.0342864	−	0.0299703i
$566$	−4649.13	+	3377.79i	−0.345261	+	0.250847i
$567$	14141.6	+	4594.88i	1.04743	+	0.340330i
$568$			9014.53i			0.665918i
$569$	6908.81	−	21263.1i	0.509020	−	1.56660i	−0.284886	−	0.958561i	$-0.591956\pi$
$569$	6908.81	−	21263.1i	0.509020	−	1.56660i	0.793906	−	0.608040i	$-0.208044\pi$
$570$	2904.61	−	4864.27i	0.213440	−	0.357442i
$571$	−159.190	−	489.935i	−0.0116670	−	0.0359074i	0.945054	−	0.326916i	$-0.106009\pi$
$571$	−159.190	−	489.935i	−0.0116670	−	0.0359074i	−0.956721	+	0.291008i	$0.906009\pi$
$572$	−10478.7	+	3404.74i	−0.765974	+	0.248880i
$573$	11001.1	−	15141.7i	0.802053	−	1.10393i
$574$	−1172.55			−0.0852638
$575$	7805.83	−	16229.7i	0.566132	−	1.17709i
$576$	−7207.67			−0.521388
$577$	−14590.6	+	20082.2i	−1.05271	+	1.44893i	−0.166277	+	0.986079i	$0.553175\pi$
$577$	−14590.6	+	20082.2i	−1.05271	+	1.44893i	−0.886435	+	0.462854i	$0.846825\pi$
$578$	435.191	−	141.402i	0.0313176	−	0.0101757i
$579$	10721.8	+	32998.3i	0.769573	+	2.36850i
$580$	−4987.36	−	5705.61i	−0.357050	−	0.408470i
$581$	−4259.30	+	13108.8i	−0.304140	+	0.936048i
$582$		−	1989.95i		−	0.141729i
$583$	23358.3	+	7589.57i	1.65935	+	0.539156i
$584$	−4762.41	+	3460.09i	−0.337448	+	0.245171i
$585$	−2045.14	+	8970.69i	−0.144541	+	0.634004i
$586$	−1841.18	−	1337.69i	−0.129792	−	0.0942998i
$587$	1714.50	+	2359.81i	0.120554	+	0.165928i	0.865029	−	0.501723i	$-0.167300\pi$
$587$	1714.50	+	2359.81i	0.120554	+	0.165928i	−0.744475	+	0.667650i	$0.767300\pi$
$588$	−239.775	−	330.022i	−0.0168166	−	0.0231460i
$589$	−24754.9	−	17985.5i	−1.73176	−	1.25820i
$590$	1619.15	−	146.134i	0.112982	−	0.0101970i
$591$	2704.86	−	1965.19i	0.188262	−	0.136781i
$592$	−2243.68	−	729.015i	−0.155768	−	0.0506121i
$593$		−	20216.9i		−	1.40002i	−0.714135	−	0.700008i	$-0.753180\pi$
$593$		−	20216.9i		−	1.40002i	0.714135	−	0.700008i	$-0.246820\pi$
$594$	−247.087	+	760.456i	−0.0170675	+	0.0525285i
$595$	13095.8	+	2985.58i	0.902311	+	0.205709i
$596$	−5975.37	−	18390.3i	−0.410672	−	1.26392i
$597$	18064.4	−	5869.49i	1.23840	−	0.402382i
$598$	2235.25	−	3076.56i	0.152853	−	0.210385i
$599$	9846.60			0.671655			0.335827	−	0.941924i	$-0.390984\pi$
$599$	9846.60			0.671655			0.335827	+	0.941924i	$0.390984\pi$
$600$	−10144.7	+	1846.22i	−0.690257	+	0.125620i
$601$	−3897.54			−0.264532			−0.132266	−	0.991214i	$-0.542225\pi$
$601$	−3897.54			−0.264532			−0.132266	+	0.991214i	$0.542225\pi$
$602$	−682.634	+	939.565i	−0.0462161	+	0.0636110i
$603$	6516.68	−	2117.40i	0.440099	−	0.142997i
$604$	−1473.03	−	4533.53i	−0.0992333	−	0.305409i
$605$	−4667.37	+	1996.31i	−0.313645	+	0.134151i
$606$	1220.12	−	3755.15i	0.0817888	−	0.251720i
$607$			15944.1i			1.06615i	0.846069	+	0.533073i	$0.178963\pi$
$607$			15944.1i			1.06615i	−0.846069	+	0.533073i	$0.821037\pi$
$608$	−11818.9	−	3840.21i	−0.788358	−	0.256153i
$609$	−9594.43	+	6970.76i	−0.638400	+	0.463825i
$610$	1215.97	+	2842.94i	0.0807102	+	0.188700i
$611$	1505.87	+	1094.08i	0.0997073	+	0.0724416i
$612$	6725.48	+	9256.83i	0.444218	+	0.611414i
$613$	4148.25	+	5709.58i	0.273322	+	0.376195i	0.923508	−	0.383580i	$-0.125309\pi$
$613$	4148.25	+	5709.58i	0.273322	+	0.376195i	−0.650186	+	0.759775i	$0.725309\pi$
$614$	−2103.89	−	1528.56i	−0.138283	−	0.100469i
$615$	5803.33	+	3465.36i	0.380509	+	0.227214i
$616$	−7268.02	+	5280.52i	−0.475384	+	0.345387i
$617$	21616.4	+	7023.59i	1.41044	+	0.458280i	0.912552	−	0.408960i	$-0.134108\pi$
$617$	21616.4	+	7023.59i	1.41044	+	0.458280i	0.497890	+	0.867240i	$0.334108\pi$
$618$			3588.09i			0.233550i
$619$	−4529.81	+	13941.3i	−0.294133	+	0.905248i	0.689378	+	0.724402i	$0.257884\pi$
$619$	−4529.81	+	13941.3i	−0.294133	+	0.905248i	−0.983511	+	0.180847i	$0.942116\pi$
$620$	2411.13	+	26715.1i	0.156183	+	1.73049i
$621$	1119.84	+	3446.50i	0.0723631	+	0.222711i
$622$	4621.34	−	1501.56i	0.297908	−	0.0967962i
$623$	−2724.10	+	3749.40i	−0.175183	+	0.241118i
$624$	12642.3			0.811052
$625$	14623.2	−	5504.86i	0.935883	−	0.352311i
$626$	−3462.11			−0.221045
$627$	−16725.1	+	23020.1i	−1.06529	+	1.46624i
$628$	−14160.2	+	4600.91i	−0.899764	+	0.292351i
$629$	942.804	+	2901.65i	0.0597648	+	0.183937i
$630$	324.809	+	3598.85i	0.0205408	+	0.227590i
$631$	1901.26	−	5851.48i	0.119949	−	0.369166i	−0.872998	−	0.487724i	$-0.837827\pi$
$631$	1901.26	−	5851.48i	0.119949	−	0.369166i	0.992947	+	0.118558i	$0.0378271\pi$
$632$		−	14397.9i		−	0.906196i
$633$	−22657.9	−	7362.00i	−1.42270	−	0.462264i
$634$	380.759	−	276.637i	0.0238515	−	0.0173291i
$635$	−16290.5	−	9727.57i	−1.01806	−	0.607916i
$636$	−24834.3	−	18043.2i	−1.54834	−	1.12494i
$637$	159.288	+	219.240i	0.00990770	+	0.0136368i
$638$	−1703.70	−	2344.94i	−0.105721	−	0.145513i
$639$	−14732.6	−	10703.8i	−0.912068	−	0.662656i
$640$	5626.79	+	13155.4i	0.347529	+	0.812522i
$641$	20427.4	−	14841.4i	1.25871	−	0.914508i	0.260018	−	0.965604i	$-0.416272\pi$
$641$	20427.4	−	14841.4i	1.25871	−	0.914508i	0.998694	+	0.0510962i	$0.0162715\pi$
$642$	−3125.53	−	1015.55i	−0.192141	−	0.0624305i
$643$			28655.2i			1.75747i	0.477313	+	0.878733i	$0.341611\pi$
$643$			28655.2i			1.75747i	−0.477313	+	0.878733i	$0.658389\pi$
$644$	−6060.17	+	18651.3i	−0.370814	+	1.14125i
$645$	6155.36	−	2632.75i	0.375763	−	0.160720i
$646$	1446.35	+	4451.42i	0.0880898	+	0.271113i
$647$	−23552.4	+	7652.65i	−1.43113	+	0.465002i	−0.919120	−	0.393977i	$-0.871099\pi$
$647$	−23552.4	+	7652.65i	−1.43113	+	0.465002i	−0.512010	+	0.858979i	$0.671099\pi$
$648$	5542.98	−	7629.26i	0.336032	−	0.462509i
$649$	−8165.08			−0.493848
$650$	3246.05	−	590.748i	0.195878	−	0.0356478i
$651$	41977.7			2.52724
$652$	7637.21	−	10511.7i	0.458736	−	0.631396i
$653$	−5882.70	+	1911.40i	−0.352539	+	0.114547i	−0.479932	−	0.877305i	$-0.659339\pi$
$653$	−5882.70	+	1911.40i	−0.352539	+	0.114547i	0.127394	+	0.991852i	$0.459339\pi$
$654$	−1590.03	−	4893.60i	−0.0950687	−	0.292591i
$655$	−2786.19	−	635.197i	−0.166207	−	0.0378919i
$656$	1334.29	−	4106.52i	0.0794134	−	0.244409i
$657$		−	11891.8i		−	0.706153i
$658$	695.239	+	225.897i	0.0411903	+	0.0133835i
$659$	−7255.82	+	5271.66i	−0.428902	+	0.311616i	−0.781210	−	0.624269i	$-0.785397\pi$
$659$	−7255.82	+	5271.66i	−0.428902	+	0.311616i	0.352308	+	0.935884i	$0.385397\pi$
$660$	24842.9	−	2242.16i	1.46517	−	0.132237i
$661$	−5391.92	−	3917.46i	−0.317279	−	0.230517i	0.417735	−	0.908569i	$-0.362824\pi$
$661$	−5391.92	−	3917.46i	−0.317279	−	0.230517i	−0.735013	+	0.678053i	$0.762824\pi$
$662$	445.570	+	613.275i	0.0261595	+	0.0360055i
$663$	−9610.14	−	13227.2i	−0.562936	−	0.774815i
$664$	7072.07	+	5138.16i	0.413327	+	0.300300i
$665$	4314.25	−	18923.8i	0.251578	−	1.10351i
$666$	−664.030	+	482.446i	−0.0386346	+	0.0280697i
$667$	−12493.5	−	4059.39i	−0.725264	−	0.235652i
$668$		−	1005.16i		−	0.0582199i
$669$	−2643.26	+	8135.13i	−0.152757	+	0.470138i
$670$	−1617.08	−	1849.97i	−0.0932439	−	0.106672i
$671$	−4798.91	−	14769.5i	−0.276095	−	0.849733i
$672$	16214.1	−	5268.29i	0.930765	−	0.302424i
$673$	9934.39	−	13673.5i	0.569008	−	0.783173i	−0.423429	−	0.905930i	$-0.639174\pi$
$673$	9934.39	−	13673.5i	0.569008	−	0.783173i	0.992437	+	0.122757i	$0.0391735\pi$
$674$	3526.77			0.201552
$675$	−1362.75	+	2833.41i	−0.0777073	+	0.161567i
$676$	7183.92			0.408735
$677$	11439.1	−	15744.5i	0.649393	−	0.893813i	−0.349680	−	0.936869i	$-0.613710\pi$
$677$	11439.1	−	15744.5i	0.649393	−	0.893813i	0.999073	+	0.0430565i	$0.0137095\pi$
$678$	−278.057	+	90.3461i	−0.0157503	+	0.00511758i
$679$	−2106.67	−	6483.67i	−0.119067	−	0.366451i
$680$	4367.34	−	7313.85i	0.246294	−	0.412461i
$681$	−5545.98	+	17068.8i	−0.312074	+	0.960465i
$682$			10259.6i			0.576043i
$683$	17268.9	+	5611.00i	0.967460	+	0.314347i	0.749790	−	0.661676i	$-0.230154\pi$
$683$	17268.9	+	5611.00i	0.967460	+	0.314347i	0.217670	+	0.976022i	$0.430154\pi$
$684$	13376.4	−	9718.51i	0.747747	−	0.543270i
$685$	10073.4	−	8805.34i	0.561878	−	0.491145i
$686$	3909.16	+	2840.17i	0.217569	+	0.158073i
$687$	−8740.70	−	12030.5i	−0.485412	−	0.668113i
$688$	−2513.75	−	3459.88i	−0.139296	−	0.191725i
$689$	16498.0	+	11986.5i	0.912224	+	0.662770i
$690$	−6482.04	+	5666.04i	−0.357633	+	0.312613i
$691$	−149.160	+	108.371i	−0.00821176	+	0.00596619i	−0.591884	−	0.806023i	$-0.701615\pi$
$691$	−149.160	+	108.371i	−0.00821176	+	0.00596619i	0.583672	+	0.811990i	$0.301615\pi$
$692$	−2754.40	−	894.958i	−0.151310	−	0.0491636i
$693$		−	18148.3i		−	0.994801i
$694$	−1169.21	+	3598.47i	−0.0639520	+	0.196824i
$695$	−4924.19	+	8246.39i	−0.268756	+	0.450077i
$696$	2324.22	+	7153.20i	0.126579	+	0.389571i
$697$	−5310.78	+	1725.58i	−0.288609	+	0.0937746i
$698$	2432.94	−	3348.66i	0.131932	−	0.181588i
$699$	−23747.6			−1.28500
$700$	−14979.1	+	8070.25i	−0.808794	+	0.435752i
$701$	−32806.2			−1.76758			−0.883790	−	0.467883i	$-0.845017\pi$
$701$	−32806.2			−1.76758			−0.883790	+	0.467883i	$0.845017\pi$
$702$	−390.234	+	537.111i	−0.0209807	+	0.0288774i
$703$	4192.97	−	1362.38i	0.224952	−	0.0730912i
$704$	−4011.35	−	12345.7i	−0.214749	−	0.660931i
$705$	−2773.34	−	3172.74i	−0.148156	−	0.169493i
$706$	843.341	−	2595.54i	0.0449569	−	0.138363i
$707$		−	13526.7i		−	0.719555i
$708$	9705.70	+	3153.57i	0.515201	+	0.167399i
$709$	1742.52	−	1266.01i	0.0923012	−	0.0670608i	−0.540677	−	0.841230i	$-0.681832\pi$
$709$	1742.52	−	1266.01i	0.0923012	−	0.0670608i	0.632979	+	0.774169i	$0.281832\pi$
$710$	−1451.50	+	6366.79i	−0.0767239	+	0.336537i
$711$	23530.6	+	17096.0i	1.24116	+	0.901758i
$712$	1727.65	+	2377.91i	0.0909360	+	0.125163i
$713$	27330.9	+	37617.8i	1.43555	+	1.97587i
$714$	−5194.75	−	3774.21i	−0.272281	−	0.197824i
$715$	−16503.7	+	1489.52i	−0.863220	+	0.0779087i
$716$	−8013.10	+	5821.85i	−0.418245	+	0.303873i
$717$	−16595.3	−	5392.13i	−0.864382	−	0.280855i
$718$		−	3685.98i		−	0.191587i
$719$	9692.29	−	29829.8i	0.502728	−	1.54724i	−0.301829	−	0.953362i	$-0.597597\pi$
$719$	9692.29	−	29829.8i	0.502728	−	1.54724i	0.804557	−	0.593876i	$-0.202403\pi$
$720$	−12973.5	−	2957.70i	−0.671519	−	0.153093i
$721$	3798.55	+	11690.7i	0.196207	+	0.603864i
$722$	1524.19	−	495.239i	0.0785657	−	0.0255276i
$723$	−23420.4	+	32235.5i	−1.20472	+	1.65816i
$724$	28673.4			1.47188
$725$	−5405.83	−	10033.7i	−0.276921	−	0.513989i
$726$	2426.76			0.124057
$727$	18850.2	−	25945.0i	0.961642	−	1.32359i	0.0154839	−	0.999880i	$-0.495071\pi$
$727$	18850.2	−	25945.0i	0.961642	−	1.32359i	0.946158	−	0.323706i	$-0.104929\pi$
$728$	−7094.19	+	2305.04i	−0.361165	+	0.117350i
$729$	4396.14	+	13529.9i	0.223347	+	0.687392i
$730$	−3920.74	+	1676.96i	−0.198785	+	0.0850235i
$731$	−1709.12	+	5260.12i	−0.0864759	+	0.266146i
$732$			19409.8i			0.980062i
$733$	−13196.2	−	4287.69i	−0.664954	−	0.216057i	−0.0429576	−	0.999077i	$-0.513678\pi$
$733$	−13196.2	−	4287.69i	−0.664954	−	0.216057i	−0.621996	+	0.783020i	$0.713678\pi$
$734$	−2633.22	+	1913.15i	−0.132417	+	0.0962064i
$735$	−241.268	−	564.084i	−0.0121079	−	0.0283082i
$736$	15277.8	+	11100.0i	0.765148	+	0.555913i
$737$	7253.58	+	9983.70i	0.362536	+	0.498988i
$738$	−883.002	−	1215.35i	−0.0440430	−	0.0606200i
$739$	18028.8	+	13098.7i	0.897429	+	0.652020i	0.937804	−	0.347164i	$-0.112855\pi$
$739$	18028.8	+	13098.7i	0.897429	+	0.652020i	−0.0403756	+	0.999185i	$0.512855\pi$
$740$	−3318.25	−	1981.44i	−0.164840	−	0.0984313i
$741$	−19113.7	+	13886.9i	−0.947584	+	0.688460i
$742$	7616.85	+	2474.87i	0.376851	+	0.122446i
$743$		−	8470.08i		−	0.418219i	−0.977892	−	0.209110i	$-0.932943\pi$
$743$		−	8470.08i		−	0.418219i	0.977892	−	0.209110i	$-0.0670566\pi$
$744$	8226.85	−	25319.6i	0.405391	−	1.24766i
$745$	−2614.12	−	28964.1i	−0.128556	−	1.42438i
$746$	−2356.63	−	7252.96i	−0.115660	−	0.355965i
$747$	−16794.7	+	5456.94i	−0.822606	+	0.267281i
$748$	−12112.6	+	16671.5i	−0.592085	+	0.814936i
$749$	−11258.7			−0.549246
$750$	−7462.26	−	329.523i	−0.363311	−	0.0160433i
$751$	−20007.5			−0.972150			−0.486075	−	0.873917i	$-0.661572\pi$
$751$	−20007.5			−0.972150			−0.486075	+	0.873917i	$0.661572\pi$
$752$	−1582.27	+	2177.81i	−0.0767280	+	0.105607i
$753$	−661.598	+	214.966i	−0.0320185	+	0.0104035i
$754$	−743.694	−	2288.86i	−0.0359201	−	0.110551i
$755$	−644.427	−	7140.18i	−0.0310637	−	0.344182i
$756$	1057.99	−	3256.17i	0.0508979	−	0.156648i
$757$			26804.5i			1.28696i	0.765465	+	0.643478i	$0.222509\pi$
$757$			26804.5i			1.28696i	−0.765465	+	0.643478i	$0.777491\pi$
$758$	2492.69	+	809.924i	0.119444	+	0.0388097i
$759$	34981.5	−	25415.6i	1.67292	−	1.21545i
$760$	−10568.7	−	6310.93i	−0.504432	−	0.301213i
$761$	19751.1	+	14350.0i	0.940834	+	0.683556i	0.948621	−	0.316413i	$-0.102479\pi$
$761$	19751.1	+	14350.0i	0.940834	+	0.683556i	−0.00778690	+	0.999970i	$0.502479\pi$
$762$	5331.46	+	7338.12i	0.253462	+	0.348861i
$763$	−10361.3	−	14261.1i	−0.491616	−	0.676651i
$764$	−15846.0	−	11512.8i	−0.750377	−	0.545180i
$765$	6767.35	+	15822.1i	0.319836	+	0.747775i
$766$	4346.87	−	3158.19i	0.205038	−	0.148969i
$767$	−6447.70	−	2094.98i	−0.303537	−	0.0986251i
$768$			10619.9i			0.498975i
$769$	−7128.06	+	21937.9i	−0.334258	+	1.02874i	0.632828	+	0.774292i	$0.281894\pi$
$769$	−7128.06	+	21937.9i	−0.334258	+	1.02874i	−0.967086	+	0.254449i	$0.918106\pi$
$770$	−5983.52	+	2559.25i	−0.280041	+	0.119778i
$771$	10302.5	+	31708.0i	0.481241	+	1.48111i
$772$	34533.2	−	11220.5i	1.60994	−	0.523103i
$773$	−69.7773	+	96.0402i	−0.00324672	+	0.00446873i	−0.810637	−	0.585549i	$-0.800879\pi$
$773$	−69.7773	+	96.0402i	−0.00324672	+	0.00446873i	0.807391	+	0.590017i	$0.200879\pi$
$774$	−1487.92			−0.0690985
$775$	−5395.26	+	39979.7i	−0.250069	+	1.85305i
$776$	−4323.62			−0.200011
$777$	−3555.08	+	4893.15i	−0.164141	+	0.225921i
$778$	−1279.46	+	415.720i	−0.0589597	+	0.0191572i
$779$	2493.51	+	7674.23i	0.114684	+	0.352963i
$780$	20192.9	+	4603.59i	0.926953	+	0.211327i
$781$	10134.8	−	31191.8i	0.464344	−	1.42911i
$782$		−	7112.53i		−	0.325248i
$783$	2181.13	+	708.694i	0.0995497	+	0.0323457i
$784$	−317.068	+	230.363i	−0.0144437	+	0.0104939i
$785$	−22301.8	+	2012.82i	−1.01399	+	0.0915167i
$786$	1105.21	+	802.981i	0.0501546	+	0.0364394i
$787$	−24986.5	−	34390.9i	−1.13173	−	1.55769i	−0.784742	−	0.619822i	$-0.787205\pi$
$787$	−24986.5	−	34390.9i	−1.13173	−	1.55769i	−0.346987	−	0.937870i	$-0.612795\pi$
$788$	−2056.60	−	2830.67i	−0.0929740	−	0.127968i
$789$	30032.6	+	21820.0i	1.35512	+	0.984553i
$790$	2318.32	−	10168.9i	0.104408	−	0.457968i
$791$	−810.321	+	588.733i	−0.0364244	+	0.0264639i
$792$	−10946.5	−	3556.73i	−0.491120	−	0.159575i
$793$		−	12894.3i		−	0.577415i
$794$	−2596.40	+	7990.89i	−0.116049	+	0.357161i
$795$	−30384.0	−	34759.7i	−1.35548	−	1.55069i
$796$	−6142.50	−	18904.7i	−0.273512	−	0.841782i
$797$	−13119.7	+	4262.86i	−0.583093	+	0.189458i	−0.585686	−	0.810538i	$-0.699175\pi$
$797$	−13119.7	+	4262.86i	−0.583093	+	0.189458i	0.00259271	+	0.999997i	$0.499175\pi$
$798$	−5453.84	+	7506.57i	−0.241935	+	0.332995i
$799$	3481.35			0.154144
$800$	2933.59	+	16119.5i	0.129647	+	0.712389i
$801$	−5937.65			−0.261918
$802$	6469.95	−	8905.13i	0.284865	−	0.392084i
$803$	20368.9	−	6618.24i	0.895145	−	0.290850i
$804$	−4766.24	−	14669.0i	−0.209070	−	0.643452i
$805$	−15121.4	+	25323.4i	−0.662063	+	1.10874i
$806$	−2632.40	+	8101.69i	−0.115040	+	0.354057i
$807$		−	30353.6i		−	1.32404i
$808$	−8158.91	−	2650.99i	−0.355234	−	0.115423i
$809$	2512.86	−	1825.70i	0.109206	−	0.0793425i	−0.531842	−	0.846843i	$-0.678500\pi$
$809$	2512.86	−	1825.70i	0.109206	−	0.0793425i	0.641048	+	0.767501i	$0.278500\pi$
$810$	5143.35	−	4495.88i	0.223110	−	0.195024i
$811$	−4229.43	−	3072.86i	−0.183126	−	0.133049i	0.492446	−	0.870343i	$-0.336103\pi$
$811$	−4229.43	−	3072.86i	−0.183126	−	0.133049i	−0.675572	+	0.737294i	$0.736103\pi$
$812$	7295.00	+	10040.7i	0.315276	+	0.433941i
$813$	11538.0	+	15880.7i	0.497732	+	0.685069i
$814$	−1195.92	−	868.885i	−0.0514949	−	0.0374133i
$815$	14712.9	−	12860.7i	0.632355	−	0.552751i
$816$	19129.3	−	13898.3i	0.820662	−	0.596246i
$817$	7601.02	+	2469.72i	0.325491	+	0.105758i
$818$		−	321.573i		−	0.0137452i
$819$	4656.47	−	14331.1i	0.198669	−	0.611441i
$820$	3626.55	−	6073.27i	0.154445	−	0.258644i
$821$	1705.29	+	5248.33i	0.0724907	+	0.223104i	0.980737	−	0.195332i	$-0.0625785\pi$
$821$	1705.29	+	5248.33i	0.0724907	+	0.223104i	−0.908246	+	0.418436i	$0.862579\pi$
$822$	−6082.97	+	1976.48i	−0.258112	+	0.0838657i
$823$	−2526.09	+	3476.86i	−0.106991	+	0.147261i	−0.859155	−	0.511715i	$-0.829010\pi$
$823$	−2526.09	+	3476.86i	−0.106991	+	0.147261i	0.752164	+	0.658976i	$0.229010\pi$
$824$	7795.94			0.329593
$825$	37177.9	+	5017.16i	1.56893	+	0.211728i
$826$	−2662.53			−0.112157
$827$	20188.0	−	27786.4i	0.848858	−	1.16835i	−0.135255	−	0.990811i	$-0.543185\pi$
$827$	20188.0	−	27786.4i	0.848858	−	1.16835i	0.984113	−	0.177542i	$-0.0568145\pi$
$828$	−23895.7	+	7764.18i	−1.00294	+	0.325874i
$829$	−376.816	−	1159.72i	−0.0157869	−	0.0485871i	0.942853	−	0.333210i	$-0.108132\pi$
$829$	−376.816	−	1159.72i	−0.0157869	−	0.0485871i	−0.958640	+	0.284623i	$0.908132\pi$
$830$	4167.53	+	4767.71i	0.174286	+	0.199385i
$831$	7000.83	−	21546.3i	0.292246	−	0.899440i
$832$		−	10778.2i		−	0.449119i
$833$	482.043	+	156.625i	0.0200502	+	0.00651470i
$834$	3714.63	−	2698.83i	0.154229	−	0.112054i
$835$	336.024	−	1473.92i	0.0139265	−	0.0610863i
$836$	24090.9	+	17503.0i	0.996650	+	0.724109i
$837$	−4771.47	−	6567.36i	−0.197044	−	0.271208i
$838$	1263.59	+	1739.18i	0.0520884	+	0.0716935i
$839$	−8336.99	−	6057.18i	−0.343057	−	0.249246i	0.402893	−	0.915247i	$-0.368005\pi$
$839$	−8336.99	−	6057.18i	−0.343057	−	0.249246i	−0.745951	+	0.666001i	$0.768005\pi$
$840$	16818.9	−	1517.96i	0.690841	−	0.0623509i
$841$	13005.4	−	9448.96i	0.533248	−	0.387427i
$842$	−2612.37	−	848.810i	−0.106922	−	0.0347410i
$843$		−	49037.9i		−	2.00351i
$844$	−7704.44	+	23711.8i	−0.314215	+	0.967055i
$845$	10534.1	+	2401.58i	0.428858	+	0.0977713i
$846$	289.415	+	890.726i	0.0117616	+	0.0361984i
$847$	7906.89	−	2569.10i	0.320760	−	0.104221i
$848$	−17334.9	+	23859.5i	−0.701986	+	0.966202i
$849$	−54253.2			−2.19313
$850$	4262.23	−	4462.41i	0.171992	−	0.180070i
$851$	−6699.58			−0.269869
$852$	−24094.2	+	33162.9i	−0.968844	+	1.33350i
$853$	−24879.1	+	8083.71i	−0.998645	+	0.324479i	−0.762324	−	0.647196i	$-0.775942\pi$
$853$	−24879.1	+	8083.71i	−0.998645	+	0.324479i	−0.236321	+	0.971675i	$0.575942\pi$
$854$	−1564.87	−	4816.16i	−0.0627033	−	0.192981i
$855$	22863.3	−	9779.02i	0.914514	−	0.391153i
$856$	−2206.50	+	6790.92i	−0.0881036	+	0.271155i
$857$			4458.12i			0.177697i	0.996045	+	0.0888485i	$0.0283187\pi$
$857$			4458.12i			0.177697i	−0.996045	+	0.0888485i	$0.971681\pi$
$858$	7533.93	+	2447.92i	0.299772	+	0.0974017i
$859$	−16051.9	+	11662.4i	−0.637585	+	0.463232i	−0.859020	−	0.511943i	$-0.828926\pi$
$859$	−16051.9	+	11662.4i	−0.637585	+	0.463232i	0.221435	+	0.975175i	$0.428926\pi$
$860$	−2755.21	−	6441.67i	−0.109246	−	0.255418i
$861$	−8955.74	−	6506.72i	−0.354484	−	0.257548i
$862$	−2923.75	−	4024.19i	−0.115526	−	0.159008i
$863$	23067.7	+	31750.0i	0.909889	+	1.25235i	0.967205	+	0.253999i	$0.0817459\pi$
$863$	23067.7	+	31750.0i	0.909889	+	1.25235i	−0.0573157	+	0.998356i	$0.518254\pi$
$864$	−2667.23	−	1937.85i	−0.105024	−	0.0763046i
$865$	−3739.73	−	2233.11i	−0.146999	−	0.0877782i
$866$	3516.71	−	2555.04i	0.137994	−	0.100258i
$867$	4108.58	+	1334.96i	0.160940	+	0.0522924i
$868$		−	43930.2i		−	1.71784i
$869$	−16187.2	+	49819.1i	−0.631891	+	1.94476i
$870$	489.753	+	5426.41i	0.0190853	+	0.211463i
$871$	3166.32	+	9744.92i	0.123176	+	0.379097i
$872$	−10632.4	+	3454.69i	−0.412913	+	0.134164i
$873$	5133.86	−	7066.15i	0.199032	−	0.273944i
$874$	−10277.8			−0.397771
$875$	−24662.4	+	6826.31i	−0.952848	+	0.263739i
$876$	−26768.3			−1.03244
$877$	−25884.7	+	35627.2i	−0.996651	+	1.37177i	−0.0692927	+	0.997596i	$0.522074\pi$
$877$	−25884.7	+	35627.2i	−0.996651	+	1.37177i	−0.927358	+	0.374175i	$0.877926\pi$
$878$	7585.39	−	2464.64i	0.291566	−	0.0947354i
$879$	−6639.45	−	20434.1i	−0.254770	−	0.784102i
$880$	−2154.15	−	23867.8i	−0.0825187	−	0.914297i
$881$	2085.16	−	6417.46i	0.0797398	−	0.245414i	−0.903237	−	0.429141i	$-0.858816\pi$
$881$	2085.16	−	6417.46i	0.0797398	−	0.245414i	0.982977	+	0.183727i	$0.0588163\pi$
$882$			136.355i			0.00520556i
$883$	28775.9	+	9349.85i	1.09670	+	0.356339i	0.800832	−	0.598889i	$-0.204391\pi$
$883$	28775.9	+	9349.85i	1.09670	+	0.356339i	0.295868	+	0.955229i	$0.404391\pi$
$884$	−13842.5	+	10057.1i	−0.526666	+	0.382645i
$885$	13177.7	+	7868.84i	0.500524	+	0.298879i
$886$	−5302.25	−	3852.31i	−0.201053	−	0.146073i
$887$	30226.5	+	41603.3i	1.14420	+	1.57486i	0.757742	+	0.652554i	$0.226302\pi$
$887$	30226.5	+	41603.3i	1.14420	+	1.57486i	0.386460	+	0.922306i	$0.373698\pi$
$888$	2254.67	+	3103.28i	0.0852045	+	0.117274i
$889$	25139.5	+	18264.9i	0.948428	+	0.689073i
$890$	837.320	+	1957.65i	0.0315360	+	0.0737311i
$891$	−27757.1	+	20166.7i	−1.04366	+	0.758260i
$892$	8513.53	+	2766.21i	0.319567	+	0.103834i
$893$		−	5030.64i		−	0.188515i
$894$	−4296.13	+	13222.1i	−0.160721	+	0.494647i
$895$	−13696.2	+	5858.10i	−0.511525	+	0.218787i
$896$	−7241.27	−	22286.3i	−0.269993	−	0.830954i
$897$	34144.9	−	11094.3i	1.27098	−	0.412965i
$898$	−7413.48	+	10203.8i	−0.275491	+	0.379181i
$899$	29426.5			1.09169
$900$	−19644.9	−	9448.40i	−0.727590	−	0.349941i
$901$	38140.7			1.41027
$902$	1590.29	−	2188.84i	0.0587037	−	0.0807987i
$903$	−10427.7	+	3388.15i	−0.384287	+	0.124862i
$904$	196.297	+	604.141i	0.00722207	+	0.0222273i
$905$	42045.2	+	9585.49i	1.54434	+	0.352080i
$906$	−1059.07	+	3259.49i	−0.0388359	+	0.119525i
$907$			24020.1i			0.879353i	0.898156	+	0.439676i	$0.144907\pi$
$907$			24020.1i			0.879353i	−0.898156	+	0.439676i	$0.855093\pi$
$908$	17862.7	+	5803.95i	0.652858	+	0.212126i
$909$	14020.4	−	10186.4i	0.511582	−	0.371686i
$910$	−5381.64	+	485.713i	−0.196044	+	0.0176937i
$911$	−19068.7	−	13854.2i	−0.693495	−	0.503854i	0.184312	−	0.982868i	$-0.440994\pi$
$911$	−19068.7	−	13854.2i	−0.693495	−	0.503854i	−0.877807	+	0.479014i	$0.840994\pi$
$912$	−20083.4	−	27642.4i	−0.729197	−	1.00365i
$913$	−18693.8	−	25729.9i	−0.677630	−	0.932677i
$914$	8070.28	+	5863.40i	0.292058	+	0.212193i
$915$	−6488.66	+	28461.5i	−0.234436	+	1.02831i
$916$	−12590.1	+	9147.26i	−0.454137	+	0.329950i
$917$	4451.08	+	1446.24i	0.160292	+	0.0520820i
$918$			1241.72i			0.0446435i
$919$	13725.0	−	42241.3i	0.492651	−	1.51622i	−0.327934	−	0.944701i	$-0.606352\pi$
$919$	13725.0	−	42241.3i	0.492651	−	1.51622i	0.820585	−	0.571524i	$-0.193648\pi$
$920$	12310.8	+	14083.7i	0.441167	+	0.504702i
$921$	−7586.79	−	23349.7i	−0.271437	−	0.835397i
$922$	−10374.9	+	3371.00i	−0.370584	+	0.120410i
$923$	16006.3	−	22030.8i	0.570806	−	0.785647i
$924$	−40851.7			−1.45446
$925$	−4203.33	−	4014.77i	−0.149410	−	0.142708i
$926$	−3312.39			−0.117551
$927$	−9256.89	+	12741.0i	−0.327979	+	0.451424i
$928$	11366.2	−	3693.10i	0.402062	−	0.130638i
$929$	−16568.4	−	50992.1i	−0.585135	−	1.80086i	−0.598729	−	0.800952i	$-0.704327\pi$
$929$	−16568.4	−	50992.1i	−0.585135	−	1.80086i	0.0135946	−	0.999908i	$-0.495673\pi$
$930$	9887.39	−	16558.1i	0.348624	−	0.583830i
$931$	226.328	−	696.565i	0.00796734	−	0.0245210i
$932$			24852.2i			0.873454i
$933$	43629.4	+	14176.0i	1.53093	+	0.497431i
$934$	10400.3	−	7556.26i	0.364356	−	0.264720i
$935$	−23334.6	+	20397.1i	−0.816173	+	0.713429i
$936$	−7731.51	−	5617.27i	−0.269992	−	0.196161i
$937$	31902.6	+	43910.1i	1.11229	+	1.53093i	0.818006	+	0.575210i	$0.195079\pi$
$937$	31902.6	+	43910.1i	1.11229	+	1.53093i	0.294279	+	0.955720i	$0.404921\pi$
$938$	2365.30	+	3255.56i	0.0823347	+	0.113324i
$939$	−26443.0	−	19211.9i	−0.918992	−	0.667687i
$940$	−3320.32	+	2902.34i	−0.115209	+	0.100706i
$941$	−21662.4	+	15738.6i	−0.750450	+	0.545234i	−0.895966	−	0.444122i	$-0.853516\pi$
$941$	−21662.4	+	15738.6i	−0.750450	+	0.545234i	0.145516	+	0.989356i	$0.453516\pi$
$942$	10180.8	+	3307.94i	0.352132	+	0.114414i
$943$		−	12262.0i		−	0.423441i
$944$	3029.78	−	9324.72i	0.104461	−	0.321498i
$945$	2639.92	−	4420.99i	0.0908747	−	0.152185i
$946$	−828.087	−	2548.59i	−0.0284603	−	0.0875917i
$947$	−40283.4	+	13088.9i	−1.38230	+	0.449135i	−0.903424	−	0.428749i	$-0.858954\pi$
$947$	−40283.4	+	13088.9i	−1.38230	+	0.449135i	−0.478873	+	0.877884i	$0.658954\pi$
$948$	38482.9	−	52967.2i	1.31842	−	1.81466i
$949$	17782.7			0.608274
$950$	−6448.31	−	6159.05i	−0.220222	−	0.210343i
$951$	4443.28			0.151507
$952$	−8200.33	+	11286.8i	−0.279175	+	0.384251i
$953$	−46945.5	+	15253.5i	−1.59571	+	0.518478i	−0.966042	−	0.258385i	$-0.916810\pi$
$953$	−46945.5	+	15253.5i	−1.59571	+	0.518478i	−0.629669	+	0.776863i	$0.716810\pi$
$954$	3170.75	+	9758.57i	0.107607	+	0.331180i
$955$	−19387.0	−	22179.1i	−0.656911	−	0.751516i
$956$	−5642.94	+	17367.2i	−0.190906	+	0.587547i
$957$		−	27364.4i		−	0.924310i
$958$	−7780.94	−	2528.18i	−0.262412	−	0.0852629i
$959$	−17727.2	+	12879.5i	−0.596914	+	0.433683i
$960$	−5423.80	+	23790.6i	−0.182346	+	0.799833i
$961$	−60164.8	−	43712.3i	−2.01956	−	1.46730i
$962$	−721.440	−	992.977i	−0.0241790	−	0.0332795i
$963$	−8478.49	−	11669.6i	−0.283713	−	0.390497i
$964$	33734.9	+	24509.8i	1.12710	+	0.818888i
$965$	54388.7	−	4908.78i	1.81434	−	0.163751i
$966$	11407.1	−	8287.71i	0.379934	−	0.276038i
$967$	31518.0	+	10240.8i	1.04814	+	0.340561i	0.781938	−	0.623356i	$-0.214231\pi$
$967$	31518.0	+	10240.8i	1.04814	+	0.340561i	0.266201	+	0.963917i	$0.414231\pi$
$968$		−	5272.69i		−	0.175073i
$969$	−13654.8	+	42025.2i	−0.452689	+	1.39323i
$970$	−3053.69	−	696.182i	−0.101080	−	0.0230444i
$971$	2576.27	+	7928.95i	0.0851457	+	0.262051i	0.984561	−	0.175045i	$-0.0560070\pi$
$971$	2576.27	+	7928.95i	0.0851457	+	0.262051i	−0.899415	+	0.437096i	$0.856007\pi$
$972$	35981.9	−	11691.2i	1.18737	−	0.385799i
$973$	9245.89	−	12725.9i	0.304635	−	0.419294i
$974$	8436.77			0.277548
$975$	28070.9	+	13501.0i	0.922040	+	0.443463i
$976$	18647.9			0.611582
$977$	20463.5	−	28165.6i	0.670098	−	0.922311i	−0.329665	−	0.944098i	$-0.606936\pi$
$977$	20463.5	−	28165.6i	0.670098	−	0.922311i	0.999763	+	0.0217874i	$0.00693569\pi$
$978$	−8884.55	+	2886.77i	−0.290487	+	0.0943850i
$979$	−3304.54	−	10170.3i	−0.107879	−	0.332017i
$980$	−590.322	+	252.490i	−0.0192420	+	0.00823011i
$981$	6978.90	−	21478.8i	0.227135	−	0.699049i
$982$			816.744i			0.0265411i
$983$	5327.61	+	1731.05i	0.172863	+	0.0561666i	0.394170	−	0.919038i	$-0.371032\pi$
$983$	5327.61	+	1731.05i	0.172863	+	0.0561666i	−0.221307	+	0.975204i	$0.571032\pi$
$984$	−5679.81	+	4126.63i	−0.184010	+	0.133691i
$985$	−2069.41	−	4838.28i	−0.0669410	−	0.156508i
$986$	−3641.55	−	2645.74i	−0.117617	−	0.0854539i
$987$	4056.56	+	5583.37i	0.130822	+	0.180061i
$988$	14532.9	+	20002.8i	0.467968	+	0.644102i
$989$	−9825.51	−	7138.65i	−0.315908	−	0.229521i
$990$	−7158.60	−	4274.64i	−0.229814	−	0.137229i
$991$	22251.0	−	16166.3i	0.713245	−	0.518203i	−0.170974	−	0.985276i	$-0.554691\pi$
$991$	22251.0	−	16166.3i	0.713245	−	0.518203i	0.884219	+	0.467073i	$0.154691\pi$
$992$	−40232.0	−	13072.2i	−1.28767	−	0.418389i
$993$			7156.63i			0.228710i
$994$	3304.85	−	10171.3i	0.105456	−	0.324561i
$995$	−2687.24	−	29774.3i	−0.0856193	−	0.948652i
$996$	12283.5	+	37804.7i	0.390781	+	1.20270i
$997$	−41715.9	+	13554.3i	−1.32513	+	0.430561i	−0.884254	−	0.467007i	$-0.845332\pi$
$997$	−41715.9	+	13554.3i	−1.32513	+	0.430561i	−0.440876	+	0.897568i	$0.645332\pi$
$998$	−282.085	+	388.256i	−0.00894713	+	0.0123147i
$999$	1169.62			0.0370422

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.4.e.a.9.3	✓	24
3.2	odd	2		225.4.m.a.109.4		24
5.2	odd	4		125.4.d.b.76.5		48
5.3	odd	4		125.4.d.b.76.8		48
5.4	even	2		125.4.e.a.49.4		24
25.2	odd	20		125.4.d.b.51.5		48
25.8	odd	20		625.4.a.g.1.10		24
25.11	even	5		125.4.e.a.74.4		24
25.14	even	10	inner	25.4.e.a.14.3	yes	24
25.17	odd	20		625.4.a.g.1.15		24
25.23	odd	20		125.4.d.b.51.8		48
75.14	odd	10		225.4.m.a.64.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.4.e.a.9.3	✓	24	1.1	even	1	trivial
25.4.e.a.14.3	yes	24	25.14	even	10	inner
125.4.d.b.51.5		48	25.2	odd	20
125.4.d.b.51.8		48	25.23	odd	20
125.4.d.b.76.5		48	5.2	odd	4
125.4.d.b.76.8		48	5.3	odd	4
125.4.e.a.49.4		24	5.4	even	2
125.4.e.a.74.4		24	25.11	even	5
225.4.m.a.64.4		24	75.14	odd	10
225.4.m.a.109.4		24	3.2	odd	2
625.4.a.g.1.10		24	25.8	odd	20
625.4.a.g.1.15		24	25.17	odd	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	25.e (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.442260 + 0.608718i) q^{2} +(-6.75579 + 2.19509i) q^{3} +(2.29719 + 7.07003i) q^{4} +(1.00498 + 11.1351i) q^{5} +(1.65162 - 5.08317i) q^{6} -18.3105i q^{7} +(-11.0443 - 3.58852i) q^{8} +(18.9788 - 13.7889i) q^{9} +O(q^{10})\)	\(q+(-0.442260 + 0.608718i) q^{2} +(-6.75579 + 2.19509i) q^{3} +(2.29719 + 7.07003i) q^{4} +(1.00498 + 11.1351i) q^{5} +(1.65162 - 5.08317i) q^{6} -18.3105i q^{7} +(-11.0443 - 3.58852i) q^{8} +(18.9788 - 13.7889i) q^{9} +(-7.22259 - 4.31284i) q^{10} +(34.1808 + 24.8338i) q^{11} +(-31.0387 - 42.7211i) q^{12} +(20.6196 + 28.3805i) q^{13} +(11.1459 + 8.09800i) q^{14} +(-31.2319 - 73.0202i) q^{15} +(-41.0441 + 29.8203i) q^{16} +(62.4001 + 20.2750i) q^{17} +17.6510i q^{18} +(29.2980 - 90.1699i) q^{19} +(-76.4167 + 32.6847i) q^{20} +(40.1932 + 123.702i) q^{21} +(-30.2336 + 9.82348i) q^{22} +(-84.6849 + 116.559i) q^{23} +82.4903 q^{24} +(-122.980 + 22.3811i) q^{25} -26.3950 q^{26} +(14.7844 - 20.3490i) q^{27} +(129.456 - 42.0628i) q^{28} +(28.1756 + 86.7157i) q^{29} +(58.2613 + 13.2824i) q^{30} +(99.7311 - 306.941i) q^{31} -131.074i q^{32} +(-285.431 - 92.7420i) q^{33} +(-39.9388 + 29.0172i) q^{34} +(203.889 - 18.4017i) q^{35} +(141.086 + 102.505i) q^{36} +(27.3325 + 37.6199i) q^{37} +(41.9307 + 57.7127i) q^{38} +(-201.600 - 146.471i) q^{39} +(28.8591 - 126.586i) q^{40} +(-68.8543 + 50.0256i) q^{41} +(-93.0754 - 30.2420i) q^{42} +84.2967i q^{43} +(-97.0559 + 298.707i) q^{44} +(172.614 + 197.473i) q^{45} +(-33.4987 - 103.098i) q^{46} +(50.4632 - 16.3965i) q^{47} +(211.827 - 291.555i) q^{48} +7.72504 q^{49} +(40.7653 - 84.7584i) q^{50} -466.067 q^{51} +(-153.284 + 210.977i) q^{52} +(552.862 - 179.636i) q^{53} +(5.84825 + 17.9991i) q^{54} +(-242.175 + 405.563i) q^{55} +(-65.7077 + 202.227i) q^{56} +673.480i q^{57} +(-65.2463 - 21.1998i) q^{58} +(-156.348 + 113.594i) q^{59} +(444.509 - 388.552i) q^{60} +(-297.367 - 216.050i) q^{61} +(142.733 + 196.456i) q^{62} +(-252.482 - 347.512i) q^{63} +(-248.566 - 180.594i) q^{64} +(-295.297 + 258.123i) q^{65} +(182.688 - 132.731i) q^{66} +(277.789 + 90.2592i) q^{67} +487.746i q^{68} +(316.256 - 973.337i) q^{69} +(-78.9704 + 132.249i) q^{70} +(-239.879 - 738.272i) q^{71} +(-259.090 + 84.1835i) q^{72} +(297.958 - 410.103i) q^{73} -34.9880 q^{74} +(781.698 - 421.154i) q^{75} +704.807 q^{76} +(454.720 - 625.868i) q^{77} +(178.319 - 57.9393i) q^{78} +(383.131 + 1179.16i) q^{79} +(-373.300 - 427.061i) q^{80} +(-250.942 + 772.321i) q^{81} -64.0371i q^{82} +(-715.915 - 232.615i) q^{83} +(-782.245 + 568.334i) q^{84} +(-163.053 + 715.206i) q^{85} +(-51.3129 - 37.2810i) q^{86} +(-380.697 - 523.985i) q^{87} +(-288.388 - 396.931i) q^{88} +(-204.768 - 148.772i) q^{89} +(-196.545 + 17.7389i) q^{90} +(519.662 - 377.556i) q^{91} +(-1018.61 - 330.967i) q^{92} +2292.54i q^{93} +(-12.3370 + 37.9694i) q^{94} +(1033.49 + 235.616i) q^{95} +(287.720 + 885.510i) q^{96} +(354.095 - 115.053i) q^{97} +(-3.41647 + 4.70237i) q^{98} +991.141 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9}+O(q^{10}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9	\( 24 q - 5 q^{2} - 5 q^{3} + 13 q^{4} + 15 q^{5} - 7 q^{6} - 110 q^{8} + 47 q^{9} - 5 q^{10} + 83 q^{11} - 165 q^{12} - 5 q^{13} + 31 q^{14} - 225 q^{15} + 89 q^{16} - 165 q^{17} - 115 q^{19} + 395 q^{20} + 138 q^{21} + 30 q^{22} + 75 q^{23} + 640 q^{24} + 595 q^{25} - 822 q^{26} + 595 q^{27} + 675 q^{28} + 125 q^{29} - 965 q^{30} + 633 q^{31} - 1285 q^{33} - 779 q^{34} + 190 q^{35} - 531 q^{36} - 1510 q^{37} + 255 q^{38} - 1241 q^{39} - 2470 q^{40} - 117 q^{41} + 1745 q^{42} + 516 q^{44} + 1725 q^{45} + 1233 q^{46} - 95 q^{47} + 1410 q^{48} + 1148 q^{49} + 2165 q^{50} - 2022 q^{51} + 1740 q^{52} + 2580 q^{53} + 1745 q^{54} - 315 q^{55} + 3160 q^{56} - 4230 q^{58} - 1905 q^{59} + 560 q^{60} - 567 q^{61} - 6880 q^{62} - 1950 q^{63} - 3612 q^{64} - 3170 q^{65} - 2774 q^{66} + 4195 q^{67} + 539 q^{69} + 3630 q^{70} + 2473 q^{71} + 215 q^{72} - 845 q^{73} + 3596 q^{74} + 2045 q^{75} - 3280 q^{76} + 3870 q^{77} + 9295 q^{78} + 775 q^{79} - 3670 q^{80} + 3309 q^{81} - 4625 q^{83} - 5694 q^{84} - 1460 q^{85} - 3897 q^{86} - 8485 q^{87} - 1650 q^{88} - 2410 q^{89} - 8845 q^{90} - 382 q^{91} + 4090 q^{92} + 5401 q^{94} + 3545 q^{95} + 6488 q^{96} + 5185 q^{97} + 5180 q^{98} + 6024 q^{99}+O(q^{100}) \) 24 * q - 5 * q^2 - 5 * q^3 + 13 * q^4 + 15 * q^5 - 7 * q^6 - 110 * q^8 + 47 * q^9 - 5 * q^10 + 83 * q^11 - 165 * q^12 - 5 * q^13 + 31 * q^14 - 225 * q^15 + 89 * q^16 - 165 * q^17 - 115 * q^19 + 395 * q^20 + 138 * q^21 + 30 * q^22 + 75 * q^23 + 640 * q^24 + 595 * q^25 - 822 * q^26 + 595 * q^27 + 675 * q^28 + 125 * q^29 - 965 * q^30 + 633 * q^31 - 1285 * q^33 - 779 * q^34 + 190 * q^35 - 531 * q^36 - 1510 * q^37 + 255 * q^38 - 1241 * q^39 - 2470 * q^40 - 117 * q^41 + 1745 * q^42 + 516 * q^44 + 1725 * q^45 + 1233 * q^46 - 95 * q^47 + 1410 * q^48 + 1148 * q^49 + 2165 * q^50 - 2022 * q^51 + 1740 * q^52 + 2580 * q^53 + 1745 * q^54 - 315 * q^55 + 3160 * q^56 - 4230 * q^58 - 1905 * q^59 + 560 * q^60 - 567 * q^61 - 6880 * q^62 - 1950 * q^63 - 3612 * q^64 - 3170 * q^65 - 2774 * q^66 + 4195 * q^67 + 539 * q^69 + 3630 * q^70 + 2473 * q^71 + 215 * q^72 - 845 * q^73 + 3596 * q^74 + 2045 * q^75 - 3280 * q^76 + 3870 * q^77 + 9295 * q^78 + 775 * q^79 - 3670 * q^80 + 3309 * q^81 - 4625 * q^83 - 5694 * q^84 - 1460 * q^85 - 3897 * q^86 - 8485 * q^87 - 1650 * q^88 - 2410 * q^89 - 8845 * q^90 - 382 * q^91 + 4090 * q^92 + 5401 * q^94 + 3545 * q^95 + 6488 * q^96 + 5185 * q^97 + 5180 * q^98 + 6024 * q^99

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