LMFDB - Embedded newform 105.4.m.a.13.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(13,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

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

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

chi := DirichletCharacter("105.13");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.m (of order $4$, degree $2$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			13.11
Character	$\chi$	$=$	105.13
Dual form			105.4.m.a.97.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.811442 + 0.811442i) q^{2} +(-2.12132 + 2.12132i) q^{3} +6.68312i q^{4} +(-4.54645 + 10.2142i) q^{5} -3.44266i q^{6} +(-15.2496 - 10.5095i) q^{7} +(-11.9145 - 11.9145i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(-0.811442 + 0.811442i) q^{2} +(-2.12132 + 2.12132i) q^{3} +6.68312i q^{4} +(-4.54645 + 10.2142i) q^{5} -3.44266i q^{6} +(-15.2496 - 10.5095i) q^{7} +(-11.9145 - 11.9145i) q^{8} -9.00000i q^{9} +(-4.59905 - 11.9774i) q^{10} +47.0616 q^{11} +(-14.1770 - 14.1770i) q^{12} +(6.35598 - 6.35598i) q^{13} +(20.9020 - 3.84634i) q^{14} +(-12.0231 - 31.3121i) q^{15} -34.1292 q^{16} +(-48.7908 - 48.7908i) q^{17} +(7.30297 + 7.30297i) q^{18} -122.702 q^{19} +(-68.2628 - 30.3845i) q^{20} +(54.6433 - 10.0553i) q^{21} +(-38.1877 + 38.1877i) q^{22} +(32.8029 + 32.8029i) q^{23} +50.5489 q^{24} +(-83.6597 - 92.8766i) q^{25} +10.3150i q^{26} +(19.0919 + 19.0919i) q^{27} +(70.2362 - 101.915i) q^{28} +111.792i q^{29} +(35.1640 + 15.6518i) q^{30} +69.1953i q^{31} +(123.010 - 123.010i) q^{32} +(-99.8327 + 99.8327i) q^{33} +79.1817 q^{34} +(176.677 - 107.982i) q^{35} +60.1481 q^{36} +(-227.678 + 227.678i) q^{37} +(99.5657 - 99.5657i) q^{38} +26.9661i q^{39} +(175.866 - 67.5284i) q^{40} +258.481i q^{41} +(-36.1805 + 52.4992i) q^{42} +(-331.574 - 331.574i) q^{43} +314.518i q^{44} +(91.9278 + 40.9180i) q^{45} -53.2353 q^{46} +(332.722 + 332.722i) q^{47} +(72.3989 - 72.3989i) q^{48} +(122.101 + 320.531i) q^{49} +(143.249 + 7.47901i) q^{50} +207.002 q^{51} +(42.4778 + 42.4778i) q^{52} +(-397.103 - 397.103i) q^{53} -30.9839 q^{54} +(-213.963 + 480.696i) q^{55} +(56.4763 + 306.907i) q^{56} +(260.291 - 260.291i) q^{57} +(-90.7126 - 90.7126i) q^{58} +124.410 q^{59} +(209.262 - 80.3520i) q^{60} -390.333i q^{61} +(-56.1479 - 56.1479i) q^{62} +(-94.5854 + 137.247i) q^{63} -73.4027i q^{64} +(36.0241 + 93.8183i) q^{65} -162.017i q^{66} +(-172.872 + 172.872i) q^{67} +(326.075 - 326.075i) q^{68} -139.171 q^{69} +(-55.7426 + 230.984i) q^{70} +146.934 q^{71} +(-107.230 + 107.230i) q^{72} +(-360.078 + 360.078i) q^{73} -369.495i q^{74} +(374.490 + 19.5521i) q^{75} -820.034i q^{76} +(-717.671 - 494.593i) q^{77} +(-21.8814 - 21.8814i) q^{78} +1191.77i q^{79} +(155.166 - 348.602i) q^{80} -81.0000 q^{81} +(-209.743 - 209.743i) q^{82} +(-33.8129 + 33.8129i) q^{83} +(67.2011 + 365.188i) q^{84} +(720.183 - 276.534i) q^{85} +538.106 q^{86} +(-237.147 - 237.147i) q^{87} +(-560.715 - 560.715i) q^{88} -1283.38 q^{89} +(-107.797 + 41.3914i) q^{90} +(-163.724 + 30.1282i) q^{91} +(-219.226 + 219.226i) q^{92} +(-146.785 - 146.785i) q^{93} -539.968 q^{94} +(557.859 - 1253.30i) q^{95} +521.886i q^{96} +(212.490 + 212.490i) q^{97} +(-359.171 - 161.014i) q^{98} -423.554i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) $ 48 * q + 4 * q^7 - 168 * q^8	$ 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) $ 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.811442	+	0.811442i	−0.286888	+	0.286888i	−0.835848	−	0.548960i	$-0.815024\pi$
$2$	−0.811442	+	0.811442i	−0.286888	+	0.286888i	0.548960	+	0.835848i	$0.315024\pi$
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$3$	−2.12132	+	2.12132i	−0.408248	+	0.408248i
$4$			6.68312i			0.835391i
$5$	−4.54645	+	10.2142i	−0.406647	+	0.913586i
$5$	−4.54645	+	10.2142i	−0.406647	+	0.913586i
$6$		−	3.44266i		−	0.234243i
$7$	−15.2496	−	10.5095i	−0.823402	−	0.567459i
$7$	−15.2496	−	10.5095i	−0.823402	−	0.567459i
$8$	−11.9145	−	11.9145i	−0.526551	−	0.526551i
$9$		−	9.00000i		−	0.333333i
$10$	−4.59905	−	11.9774i	−0.145435	−	0.378759i
$11$	47.0616			1.28996			0.644982	−	0.764198i	$-0.276865\pi$
$11$	47.0616			1.28996			0.644982	+	0.764198i	$0.276865\pi$
$12$	−14.1770	−	14.1770i	−0.341047	−	0.341047i
$13$	6.35598	−	6.35598i	0.135602	−	0.135602i	−0.636048	−	0.771650i	$-0.719432\pi$
$13$	6.35598	−	6.35598i	0.135602	−	0.135602i	0.771650	+	0.636048i	$0.219432\pi$
$14$	20.9020	−	3.84634i	0.399021	−	0.0734270i
$15$	−12.0231	−	31.3121i	−0.206957	−	0.538982i
$16$	−34.1292			−0.533268
$17$	−48.7908	−	48.7908i	−0.696088	−	0.696088i	0.267476	−	0.963564i	$-0.413810\pi$
$17$	−48.7908	−	48.7908i	−0.696088	−	0.696088i	−0.963564	+	0.267476i	$0.913810\pi$
$18$	7.30297	+	7.30297i	0.0956293	+	0.0956293i
$19$	−122.702			−1.48157			−0.740785	−	0.671743i	$-0.765546\pi$
$19$	−122.702			−1.48157			−0.740785	+	0.671743i	$0.765546\pi$
$20$	−68.2628	−	30.3845i	−0.763201	−	0.339709i
$21$	54.6433	−	10.0553i	0.567816	−	0.104488i
$22$	−38.1877	+	38.1877i	−0.370075	+	0.370075i
$23$	32.8029	+	32.8029i	0.297386	+	0.297386i	0.839989	−	0.542603i	$-0.182561\pi$
$23$	32.8029	+	32.8029i	0.297386	+	0.297386i	−0.542603	+	0.839989i	$0.682561\pi$
$24$	50.5489			0.429927
$25$	−83.6597	−	92.8766i	−0.669277	−	0.743013i
$26$			10.3150i			0.0778054i
$27$	19.0919	+	19.0919i	0.136083	+	0.136083i
$28$	70.2362	−	101.915i	0.474050	−	0.687862i
$29$			111.792i			0.715836i	0.933753	+	0.357918i	$0.116513\pi$
$29$			111.792i			0.715836i	−0.933753	+	0.357918i	$0.883487\pi$
$30$	35.1640	+	15.6518i	0.214001	+	0.0952541i
$31$			69.1953i			0.400898i	0.979704	+	0.200449i	$0.0642401\pi$
$31$			69.1953i			0.400898i	−0.979704	+	0.200449i	$0.935760\pi$
$32$	123.010	−	123.010i	0.679540	−	0.679540i
$33$	−99.8327	+	99.8327i	−0.526626	+	0.526626i
$34$	79.1817			0.399399
$35$	176.677	−	107.982i	0.853256	−	0.521493i
$36$	60.1481			0.278464
$37$	−227.678	+	227.678i	−1.01162	+	1.01162i	−0.0116924	+	0.999932i	$0.503722\pi$
$37$	−227.678	+	227.678i	−1.01162	+	1.01162i	−0.999932	+	0.0116924i	$0.996278\pi$
$38$	99.5657	−	99.5657i	0.425044	−	0.425044i
$39$			26.9661i			0.110719i
$40$	175.866	−	67.5284i	0.695170	−	0.266929i
$41$			258.481i			0.984586i	0.870430	+	0.492293i	$0.163841\pi$
$41$			258.481i			0.984586i	−0.870430	+	0.492293i	$0.836159\pi$
$42$	−36.1805	+	52.4992i	−0.132923	+	0.192876i
$43$	−331.574	−	331.574i	−1.17592	−	1.17592i	−0.980774	−	0.195147i	$-0.937481\pi$
$43$	−331.574	−	331.574i	−1.17592	−	1.17592i	−0.195147	−	0.980774i	$-0.562519\pi$
$44$			314.518i			1.07762i
$45$	91.9278	+	40.9180i	0.304529	+	0.135549i
$46$	−53.2353			−0.170633
$47$	332.722	+	332.722i	1.03261	+	1.03261i	0.999450	+	0.0331550i	$0.0105555\pi$
$47$	332.722	+	332.722i	1.03261	+	1.03261i	0.0331550	+	0.999450i	$0.489444\pi$
$48$	72.3989	−	72.3989i	0.217706	−	0.217706i
$49$	122.101	+	320.531i	0.355981	+	0.934493i
$50$	143.249	+	7.47901i	0.405169	+	0.0211538i
$51$	207.002			0.568354
$52$	42.4778	+	42.4778i	0.113281	+	0.113281i
$53$	−397.103	−	397.103i	−1.02917	−	1.02917i	−0.999561	−	0.0296135i	$-0.990572\pi$
$53$	−397.103	−	397.103i	−1.02917	−	1.02917i	−0.0296135	−	0.999561i	$-0.509428\pi$
$54$	−30.9839			−0.0780810
$55$	−213.963	+	480.696i	−0.524559	+	1.17849i
$56$	56.4763	+	306.907i	0.134767	+	0.732360i
$57$	260.291	−	260.291i	0.604848	−	0.604848i
$58$	−90.7126	−	90.7126i	−0.205365	−	0.205365i
$59$	124.410			0.274522			0.137261	−	0.990535i	$-0.456170\pi$
$59$	124.410			0.274522			0.137261	+	0.990535i	$0.456170\pi$
$60$	209.262	−	80.3520i	0.450261	−	0.172890i
$61$		−	390.333i		−	0.819296i	−0.912244	−	0.409648i	$-0.865651\pi$
$61$		−	390.333i		−	0.819296i	0.912244	−	0.409648i	$-0.134349\pi$
$62$	−56.1479	−	56.1479i	−0.115013	−	0.115013i
$63$	−94.5854	+	137.247i	−0.189153	+	0.274467i
$64$		−	73.4027i		−	0.143365i
$65$	36.0241	+	93.8183i	0.0687421	+	0.179027i
$66$		−	162.017i		−	0.302165i
$67$	−172.872	+	172.872i	−0.315219	+	0.315219i	−0.846928	−	0.531708i	$-0.821550\pi$
$67$	−172.872	+	172.872i	−0.315219	+	0.315219i	0.531708	+	0.846928i	$0.321550\pi$
$68$	326.075	−	326.075i	0.581506	−	0.581506i
$69$	−139.171			−0.242815
$70$	−55.7426	+	230.984i	−0.0951787	+	0.394399i
$71$	146.934			0.245604			0.122802	−	0.992431i	$-0.460812\pi$
$71$	146.934			0.245604			0.122802	+	0.992431i	$0.460812\pi$
$72$	−107.230	+	107.230i	−0.175517	+	0.175517i
$73$	−360.078	+	360.078i	−0.577314	+	0.577314i	−0.934162	−	0.356849i	$-0.883851\pi$
$73$	−360.078	+	360.078i	−0.577314	+	0.577314i	0.356849	+	0.934162i	$0.383851\pi$
$74$		−	369.495i		−	0.580445i
$75$	374.490	+	19.5521i	0.576565	+	0.0301024i
$76$		−	820.034i		−	1.23769i
$77$	−717.671	−	494.593i	−1.06216	−	0.732001i
$78$	−21.8814	−	21.8814i	−0.0317639	−	0.0317639i
$79$			1191.77i			1.69728i	0.528973	+	0.848639i	$0.322577\pi$
$79$			1191.77i			1.69728i	−0.528973	+	0.848639i	$0.677423\pi$
$80$	155.166	−	348.602i	0.216852	−	0.487186i
$81$	−81.0000			−0.111111
$82$	−209.743	−	209.743i	−0.282466	−	0.282466i
$83$	−33.8129	+	33.8129i	−0.0447163	+	0.0447163i	−0.729111	−	0.684395i	$-0.760066\pi$
$83$	−33.8129	+	33.8129i	−0.0447163	+	0.0447163i	0.684395	+	0.729111i	$0.260066\pi$
$84$	67.2011	+	365.188i	0.0872885	+	0.474349i
$85$	720.183	−	276.534i	0.918998	−	0.352874i
$86$	538.106			0.674715
$87$	−237.147	−	237.147i	−0.292239	−	0.292239i
$88$	−560.715	−	560.715i	−0.679232	−	0.679232i
$89$	−1283.38			−1.52852			−0.764261	−	0.644908i	$-0.776896\pi$
$89$	−1283.38			−1.52852			−0.764261	+	0.644908i	$0.776896\pi$
$90$	−107.797	+	41.3914i	−0.126253	+	0.0484782i
$91$	−163.724	+	30.1282i	−0.188604	+	0.0347065i
$92$	−219.226	+	219.226i	−0.248434	+	0.248434i
$93$	−146.785	−	146.785i	−0.163666	−	0.163666i
$94$	−539.968			−0.592484
$95$	557.859	−	1253.30i	0.602475	−	1.35354i
$96$			521.886i			0.554842i
$97$	212.490	+	212.490i	0.222423	+	0.222423i	0.809518	−	0.587095i	$-0.199728\pi$
$97$	212.490	+	212.490i	0.222423	+	0.222423i	−0.587095	+	0.809518i	$0.699728\pi$
$98$	−359.171	−	161.014i	−0.370221	−	0.165968i
$99$		−	423.554i		−	0.429988i
$100$	620.706	−	559.108i	0.620706	−	0.559108i
$101$			111.213i			0.109566i	0.998498	+	0.0547828i	$0.0174466\pi$
$101$			111.213i			0.109566i	−0.998498	+	0.0547828i	$0.982553\pi$
$102$	−167.970	+	167.970i	−0.163054	+	0.163054i
$103$	345.690	−	345.690i	0.330698	−	0.330698i	−0.522154	−	0.852851i	$-0.674871\pi$
$103$	345.690	−	345.690i	0.330698	−	0.330698i	0.852851	+	0.522154i	$0.174871\pi$
$104$	−151.457			−0.142803
$105$	−145.726	+	603.853i	−0.135442	+	0.561239i
$106$	644.452			0.590516
$107$	−1377.95	+	1377.95i	−1.24496	+	1.24496i	−0.287046	+	0.957917i	$0.592673\pi$
$107$	−1377.95	+	1377.95i	−1.24496	+	1.24496i	−0.957917	+	0.287046i	$0.907327\pi$
$108$	−127.593	+	127.593i	−0.113682	+	0.113682i
$109$		−	1711.62i		−	1.50407i	−0.659124	−	0.752034i	$-0.729073\pi$
$109$		−	1711.62i		−	1.50407i	0.659124	−	0.752034i	$-0.270927\pi$
$110$	−216.439	−	563.675i	−0.187606	−	0.488585i
$111$		−	965.957i		−	0.825988i
$112$	520.457	+	358.680i	0.439094	+	0.302608i
$113$	−227.921	−	227.921i	−0.189743	−	0.189743i	0.605842	−	0.795585i	$-0.292836\pi$
$113$	−227.921	−	227.921i	−0.189743	−	0.189743i	−0.795585	+	0.605842i	$0.792836\pi$
$114$			422.421i			0.347047i
$115$	−484.192	+	185.919i	−0.392619	+	0.150757i
$116$	−747.120			−0.598003
$117$	−57.2038	−	57.2038i	−0.0452008	−	0.0452008i
$118$	−100.952	+	100.952i	−0.0787572	+	0.0787572i
$119$	231.275	+	1256.81i	0.178159	+	0.968162i
$120$	−229.818	+	516.317i	−0.174828	+	0.392776i
$121$	883.793			0.664007
$122$	316.733	+	316.733i	0.235046	+	0.235046i
$123$	−548.322	−	548.322i	−0.401955	−	0.401955i
$124$	−462.441			−0.334906
$125$	1329.01	−	432.258i	0.950965	−	0.309298i
$126$	−34.6171	−	188.118i	−0.0244757	−	0.133007i
$127$	−67.2228	+	67.2228i	−0.0469689	+	0.0469689i	−0.730201	−	0.683232i	$-0.760574\pi$
$127$	−67.2228	+	67.2228i	−0.0469689	+	0.0469689i	0.683232	+	0.730201i	$0.260574\pi$
$128$	1043.64	+	1043.64i	0.720669	+	0.720669i
$129$	1406.75			0.960136
$130$	−105.360	−	46.8966i	−0.0710818	−	0.0316393i
$131$			2233.09i			1.48936i	0.667424	+	0.744678i	$0.267397\pi$
$131$			2233.09i			1.48936i	−0.667424	+	0.744678i	$0.732603\pi$
$132$	−667.194	−	667.194i	−0.439938	−	0.439938i
$133$	1871.16	+	1289.54i	1.21993	+	0.840729i
$134$		−	280.551i		−	0.180865i
$135$	−281.808	+	108.208i	−0.179661	+	0.0689857i
$136$			1162.64i			0.733052i
$137$	221.734	−	221.734i	0.138277	−	0.138277i	−0.634580	−	0.772857i	$-0.718827\pi$
$137$	221.734	−	221.734i	0.138277	−	0.138277i	0.772857	+	0.634580i	$0.218827\pi$
$138$	112.929	−	112.929i	0.0696606	−	0.0696606i
$139$	1884.04			1.14966			0.574829	−	0.818274i	$-0.305069\pi$
$139$	1884.04			1.14966			0.574829	+	0.818274i	$0.305069\pi$
$140$	721.656	+	1180.76i	0.435650	+	0.712802i
$141$	−1411.62			−0.843119
$142$	−119.229	+	119.229i	−0.0704609	+	0.0704609i
$143$	299.122	−	299.122i	0.174922	−	0.174922i
$144$			307.162i			0.177756i
$145$	−1141.86	−	508.256i	−0.653977	−	0.291092i
$146$		−	584.364i		−	0.331249i
$147$	−938.966	−	420.933i	−0.526834	−	0.236177i
$148$	−1521.60	−	1521.60i	−0.845101	−	0.845101i
$149$		−	1940.65i		−	1.06701i	−0.845798	−	0.533504i	$-0.820875\pi$
$149$		−	1940.65i		−	1.06701i	0.845798	−	0.533504i	$-0.179125\pi$
$150$	−319.742	+	288.011i	−0.174046	+	0.156774i
$151$	1479.51			0.797358			0.398679	−	0.917091i	$-0.369469\pi$
$151$	1479.51			0.797358			0.398679	+	0.917091i	$0.369469\pi$
$152$	1461.94	+	1461.94i	0.780122	+	0.780122i
$153$	−439.117	+	439.117i	−0.232029	+	0.232029i
$154$	983.682	−	181.015i	0.514723	−	0.0947181i
$155$	−706.774	−	314.593i	−0.366255	−	0.163024i
$156$	−180.218			−0.0924935
$157$	151.871	+	151.871i	0.0772017	+	0.0772017i	0.744653	−	0.667452i	$-0.232615\pi$
$157$	151.871	+	151.871i	0.0772017	+	0.0772017i	−0.667452	+	0.744653i	$0.732615\pi$
$158$	−967.054	−	967.054i	−0.486929	−	0.486929i
$159$	1684.76			0.840318
$160$	697.189	+	1815.70i	0.344485	+	0.897150i
$161$	−155.490	−	844.974i	−0.0761139	−	0.413623i
$162$	65.7268	−	65.7268i	0.0318764	−	0.0318764i
$163$	1578.51	+	1578.51i	0.758516	+	0.758516i	0.976052	−	0.217536i	$-0.0698020\pi$
$163$	1578.51	+	1578.51i	0.758516	+	0.758516i	−0.217536	+	0.976052i	$0.569802\pi$
$164$	−1727.46			−0.822514
$165$	−565.827	−	1473.59i	−0.266967	−	0.695268i
$166$		−	54.8744i		−	0.0256571i
$167$	995.566	+	995.566i	0.461312	+	0.461312i	0.899085	−	0.437773i	$-0.144233\pi$
$167$	995.566	+	995.566i	0.461312	+	0.461312i	−0.437773	+	0.899085i	$0.644233\pi$
$168$	−770.852	−	531.243i	−0.354003	−	0.243966i
$169$			2116.20i			0.963224i
$170$	−359.995	+	808.778i	−0.162414	+	0.364885i
$171$			1104.32i			0.493856i
$172$	2215.95	−	2215.95i	0.982354	−	0.982354i
$173$	1095.42	−	1095.42i	0.481407	−	0.481407i	−0.424174	−	0.905581i	$-0.639435\pi$
$173$	1095.42	−	1095.42i	0.481407	−	0.481407i	0.905581	+	0.424174i	$0.139435\pi$
$174$	384.861			0.167680
$175$	299.692	+	2295.55i	0.129455	+	0.991585i
$176$	−1606.17			−0.687897
$177$	−263.914	+	263.914i	−0.112073	+	0.112073i
$178$	1041.39	−	1041.39i	0.438514	−	0.438514i
$179$			579.722i			0.242070i	0.992648	+	0.121035i	$0.0386213\pi$
$179$			579.722i			0.242070i	−0.992648	+	0.121035i	$0.961379\pi$
$180$	−273.460	+	614.365i	−0.113236	+	0.254400i
$181$		−	1187.74i		−	0.487755i	−0.969806	−	0.243878i	$-0.921580\pi$
$181$		−	1187.74i		−	0.487755i	0.969806	−	0.243878i	$-0.0784195\pi$
$182$	108.405	−	157.300i	0.0441513	−	0.0640651i
$183$	828.022	+	828.022i	0.334476	+	0.334476i
$184$		−	781.661i		−	0.313178i
$185$	−1290.42	−	3360.68i	−0.512832	−	1.33558i
$186$	238.216			0.0939076
$187$	−2296.17	−	2296.17i	−0.897929	−	0.897929i
$188$	−2223.62	+	2223.62i	−0.862629	+	0.862629i
$189$	−90.4980	−	491.790i	−0.0348294	−	0.189272i
$190$	564.313	+	1469.65i	0.215472	+	0.561157i
$191$	−972.125			−0.368275			−0.184137	−	0.982900i	$-0.558949\pi$
$191$	−972.125			−0.368275			−0.184137	+	0.982900i	$0.558949\pi$
$192$	155.711	+	155.711i	0.0585284	+	0.0585284i
$193$	1277.75	+	1277.75i	0.476552	+	0.476552i	0.904027	−	0.427475i	$-0.140597\pi$
$193$	1277.75	+	1277.75i	0.476552	+	0.476552i	−0.427475	+	0.904027i	$0.640597\pi$
$194$	−344.846			−0.127621
$195$	−275.437	−	122.600i	−0.101151	−	0.0450234i
$196$	−2142.15	+	816.020i	−0.780667	+	0.297383i
$197$	959.936	−	959.936i	0.347170	−	0.347170i	−0.511884	−	0.859055i	$-0.671052\pi$
$197$	959.936	−	959.936i	0.347170	−	0.347170i	0.859055	+	0.511884i	$0.171052\pi$
$198$	343.690	+	343.690i	0.123358	+	0.123358i
$199$	3154.27			1.12362			0.561809	−	0.827267i	$-0.310106\pi$
$199$	3154.27			1.12362			0.561809	+	0.827267i	$0.310106\pi$
$200$	−109.815	+	2103.34i	−0.0388256	+	0.743643i
$201$		−	733.434i		−	0.257375i
$202$	−90.2430	−	90.2430i	−0.0314330	−	0.0314330i
$203$	1174.88	−	1704.78i	0.406207	−	0.589421i
$204$			1383.42i			0.474797i
$205$	−2640.18	−	1175.17i	−0.899503	−	0.400378i
$206$			561.015i			0.189746i
$207$	295.226	−	295.226i	0.0991287	−	0.0991287i
$208$	−216.924	+	216.924i	−0.0723124	+	0.0723124i
$209$	−5774.56			−1.91117
$210$	−371.744	−	608.240i	−0.122156	−	0.199869i
$211$	−991.755			−0.323579			−0.161790	−	0.986825i	$-0.551727\pi$
$211$	−991.755			−0.323579			−0.161790	+	0.986825i	$0.551727\pi$
$212$	2653.89	−	2653.89i	0.859763	−	0.859763i
$213$	−311.695	+	311.695i	−0.100268	+	0.100268i
$214$		−	2236.24i		−	0.714329i
$215$	4894.25	−	1879.28i	1.55249	−	0.596120i
$216$		−	454.940i		−	0.143309i
$217$	727.207	−	1055.20i	0.227493	−	0.330100i
$218$	1388.88	+	1388.88i	0.431499	+	0.431499i
$219$		−	1527.68i		−	0.471375i
$220$	−3212.55	−	1429.94i	−0.984501	−	0.438212i
$221$	−620.226			−0.188782
$222$	783.818	+	783.818i	0.236966	+	0.236966i
$223$	−2748.98	+	2748.98i	−0.825496	+	0.825496i	−0.986890	−	0.161394i	$-0.948401\pi$
$223$	−2748.98	+	2748.98i	−0.825496	+	0.825496i	0.161394	+	0.986890i	$0.448401\pi$
$224$	−3168.62	+	583.083i	−0.945145	+	0.173923i
$225$	−835.889	+	752.937i	−0.247671	+	0.223092i
$226$	369.889			0.108870
$227$	2447.76	+	2447.76i	0.715699	+	0.715699i	0.967721	−	0.252022i	$-0.0810957\pi$
$227$	2447.76	+	2447.76i	0.715699	+	0.715699i	−0.252022	+	0.967721i	$0.581096\pi$
$228$	1739.55	+	1739.55i	0.505284	+	0.505284i
$229$	−6394.63			−1.84528			−0.922639	−	0.385664i	$-0.873972\pi$
$229$	−6394.63			−1.84528			−0.922639	+	0.385664i	$0.873972\pi$
$230$	242.032	−	543.756i	0.0693873	−	0.155888i
$231$	2571.60	−	473.220i	0.732463	−	0.134786i
$232$	1331.94	−	1331.94i	0.376924	−	0.376924i
$233$	641.078	+	641.078i	0.180251	+	0.180251i	0.791465	−	0.611214i	$-0.209319\pi$
$233$	641.078	+	641.078i	0.180251	+	0.180251i	−0.611214	+	0.791465i	$0.709319\pi$
$234$	92.8351			0.0259351
$235$	−4911.19	+	1885.78i	−1.36328	+	0.523468i
$236$			831.448i			0.229333i
$237$	−2528.13	−	2528.13i	−0.692911	−	0.692911i
$238$	−1207.49	−	832.159i	−0.328866	−	0.226642i
$239$		−	5704.10i		−	1.54380i	−0.635745	−	0.771899i	$-0.719307\pi$
$239$		−	5704.10i		−	1.54380i	0.635745	−	0.771899i	$-0.280693\pi$
$240$	410.339	+	1068.65i	0.110364	+	0.287422i
$241$		−	4745.28i		−	1.26834i	−0.773193	−	0.634171i	$-0.781342\pi$
$241$		−	4745.28i		−	1.26834i	0.773193	−	0.634171i	$-0.218658\pi$
$242$	−717.146	+	717.146i	−0.190496	+	0.190496i
$243$	171.827	−	171.827i	0.0453609	−	0.0453609i
$244$	2608.65			0.684432
$245$	−3829.10	−	210.109i	−0.998498	−	0.0547893i
$246$	889.862			0.230632
$247$	−779.892	+	779.892i	−0.200904	+	0.200904i
$248$	824.427	−	824.427i	0.211093	−	0.211093i
$249$		−	143.456i		−	0.0365107i
$250$	−727.665	+	1429.17i	−0.184086	+	0.361554i
$251$		−	100.815i		−	0.0253521i	−0.999920	−	0.0126760i	$-0.995965\pi$
$251$		−	100.815i		−	0.0253521i	0.999920	−	0.0126760i	$-0.00403502\pi$
$252$	−917.236	−	632.126i	−0.229287	−	0.158017i
$253$	1543.76	+	1543.76i	0.383617	+	0.383617i
$254$		−	109.095i		−	0.0269496i
$255$	−941.122	+	2114.36i	−0.231119	+	0.519240i
$256$	−1106.48			−0.270138
$257$	1554.62	+	1554.62i	0.377332	+	0.377332i	0.870139	−	0.492807i	$-0.164029\pi$
$257$	1554.62	+	1554.62i	0.377332	+	0.377332i	−0.492807	+	0.870139i	$0.664029\pi$
$258$	−1141.50	+	1141.50i	−0.275451	+	0.275451i
$259$	5864.79	−	1079.23i	1.40703	−	0.258918i
$260$	−626.999	+	240.753i	−0.149557	+	0.0574265i
$261$	1006.13			0.238612
$262$	−1812.02	−	1812.02i	−0.427278	−	0.427278i
$263$	3703.36	+	3703.36i	0.868285	+	0.868285i	0.992282	−	0.123998i	$-0.0395716\pi$
$263$	3703.36	+	3703.36i	0.868285	+	0.868285i	−0.123998	+	0.992282i	$0.539572\pi$
$264$	2378.91			0.554591
$265$	5861.49	−	2250.68i	1.35875	−	0.521729i
$266$	−2564.72	+	471.954i	−0.591177	+	0.108787i
$267$	2722.47	−	2722.47i	0.624016	−	0.624016i
$268$	−1155.33	−	1155.33i	−0.263331	−	0.263331i
$269$	730.510			0.165576			0.0827881	−	0.996567i	$-0.473618\pi$
$269$	730.510			0.165576			0.0827881	+	0.996567i	$0.473618\pi$
$270$	140.867	−	316.476i	0.0317514	−	0.0713337i
$271$		−	5669.88i		−	1.27092i	−0.772132	−	0.635462i	$-0.780810\pi$
$271$		−	5669.88i		−	1.27092i	0.772132	−	0.635462i	$-0.219190\pi$
$272$	1665.19	+	1665.19i	0.371202	+	0.371202i
$273$	283.400	−	411.223i	0.0628284	−	0.0911661i
$274$			359.848i			0.0793401i
$275$	−3937.16	−	4370.92i	−0.863343	−	0.958460i
$276$		−	930.097i		−	0.202845i
$277$	−5980.25	+	5980.25i	−1.29718	+	1.29718i	−0.366931	+	0.930248i	$0.619591\pi$
$277$	−5980.25	+	5980.25i	−1.29718	+	1.29718i	−0.930248	+	0.366931i	$0.880409\pi$
$278$	−1528.79	+	1528.79i	−0.329823	+	0.329823i
$279$	622.758			0.133633
$280$	−3391.57	−	818.475i	−0.723876	−	0.174690i
$281$	4582.79			0.972905			0.486452	−	0.873707i	$-0.338291\pi$
$281$	4582.79			0.972905			0.486452	+	0.873707i	$0.338291\pi$
$282$	1145.45	−	1145.45i	0.241881	−	0.241881i
$283$	−1702.34	+	1702.34i	−0.357574	+	0.357574i	−0.862918	−	0.505344i	$-0.831366\pi$
$283$	−1702.34	+	1702.34i	−0.357574	+	0.357574i	0.505344	+	0.862918i	$0.331366\pi$
$284$			981.981i			0.205176i
$285$	1475.26	+	3842.06i	0.306621	+	0.798540i
$286$			485.441i			0.100366i
$287$	2716.51	−	3941.74i	0.558712	−	0.810710i
$288$	−1107.09	−	1107.09i	−0.226513	−	0.226513i
$289$		−	151.922i		−	0.0309224i
$290$	1338.98	−	514.137i	0.271129	−	0.104107i
$291$	−901.518			−0.181608
$292$	−2406.44	−	2406.44i	−0.482282	−	0.482282i
$293$	1568.34	−	1568.34i	0.312708	−	0.312708i	−0.533250	−	0.845958i	$-0.679029\pi$
$293$	1568.34	−	1568.34i	0.312708	−	0.312708i	0.845958	+	0.533250i	$0.179029\pi$
$294$	1103.48	−	420.353i	0.218899	−	0.0833861i
$295$	−565.624	+	1270.75i	−0.111634	+	0.250800i
$296$	5425.35			1.06534
$297$	898.494	+	898.494i	0.175542	+	0.175542i
$298$	1574.72	+	1574.72i	0.306111	+	0.306111i
$299$	416.989			0.0806525
$300$	−130.669	+	2502.76i	−0.0251473	+	0.481657i
$301$	1571.71	+	8541.06i	0.300969	+	1.63554i
$302$	−1200.54	+	1200.54i	−0.228752	+	0.228752i
$303$	−235.919	−	235.919i	−0.0447300	−	0.0447300i
$304$	4187.72			0.790074
$305$	3986.94	+	1774.63i	0.748497	+	0.333164i
$306$		−	712.635i		−	0.133133i
$307$	6468.95	+	6468.95i	1.20261	+	1.20261i	0.973368	+	0.229246i	$0.0736261\pi$
$307$	6468.95	+	6468.95i	1.20261	+	1.20261i	0.229246	+	0.973368i	$0.426374\pi$
$308$	3305.43	−	4796.29i	0.611507	−	0.887317i
$309$			1466.64i			0.270013i
$310$	828.780	−	318.233i	0.151844	−	0.0583045i
$311$			10432.5i			1.90217i	0.308936	+	0.951083i	$0.400027\pi$
$311$			10432.5i			1.90217i	−0.308936	+	0.951083i	$0.599973\pi$
$312$	321.288	−	321.288i	0.0582992	−	0.0582992i
$313$	−5223.03	+	5223.03i	−0.943206	+	0.943206i	−0.998472	−	0.0552660i	$-0.982399\pi$
$313$	−5223.03	+	5223.03i	−0.943206	+	0.943206i	0.0552660	+	0.998472i	$0.482399\pi$
$314$	−246.470			−0.0442965
$315$	−971.836	−	1590.10i	−0.173831	−	0.284419i
$316$	−7964.77			−1.41789
$317$	−5323.08	+	5323.08i	−0.943136	+	0.943136i	−0.998468	−	0.0553322i	$-0.982378\pi$
$317$	−5323.08	+	5323.08i	−0.943136	+	0.943136i	0.0553322	+	0.998468i	$0.482378\pi$
$318$	−1367.09	+	1367.09i	−0.241077	+	0.241077i
$319$			5261.11i			0.923403i
$320$	749.750	+	333.721i	0.130976	+	0.0582987i
$321$		−	5846.13i		−	1.01651i
$322$	811.818	+	559.476i	0.140500	+	0.0968272i
$323$	5986.73	+	5986.73i	1.03130	+	1.03130i
$324$		−	541.333i		−	0.0928212i
$325$	−1122.06	−	58.5827i	−0.191510	−	0.00999872i
$326$	−2561.73			−0.435218
$327$	3630.89	+	3630.89i	0.614033	+	0.614033i
$328$	3079.68	−	3079.68i	0.518435	−	0.518435i
$329$	−1577.14	−	8570.61i	−0.264288	−	1.43621i
$330$	1654.87	+	736.601i	0.276054	+	0.122874i
$331$	−8385.42			−1.39246			−0.696230	−	0.717818i	$-0.745141\pi$
$331$	−8385.42			−1.39246			−0.696230	+	0.717818i	$0.745141\pi$
$332$	−225.976	−	225.976i	−0.0373556	−	0.0373556i
$333$	2049.11	+	2049.11i	0.337208	+	0.337208i
$334$	−1615.69			−0.264690
$335$	−979.796	−	2551.70i	−0.159797	−	0.416163i
$336$	−1864.93	+	343.180i	−0.302798	+	0.0557203i
$337$	593.913	−	593.913i	0.0960015	−	0.0960015i	−0.657475	−	0.753476i	$-0.728375\pi$
$337$	593.913	−	593.913i	0.0960015	−	0.0960015i	0.753476	+	0.657475i	$0.228375\pi$
$338$	−1717.18	−	1717.18i	−0.276337	−	0.276337i
$339$	966.987			0.154925
$340$	1848.11	+	4813.07i	0.294788	+	0.767722i
$341$			3256.44i			0.517144i
$342$	−896.091	−	896.091i	−0.141681	−	0.141681i
$343$	1506.62	−	6171.20i	0.237171	−	0.971468i
$344$			7901.08i			1.23837i
$345$	632.734	−	1421.52i	0.0987398	−	0.221832i
$346$			1777.74i			0.276220i
$347$	1216.59	−	1216.59i	0.188213	−	0.188213i	−0.606710	−	0.794923i	$-0.707511\pi$
$347$	1216.59	−	1216.59i	0.188213	−	0.188213i	0.794923	+	0.606710i	$0.207511\pi$
$348$	1584.88	−	1584.88i	0.244134	−	0.244134i
$349$	−3420.88			−0.524687			−0.262343	−	0.964975i	$-0.584495\pi$
$349$	−3420.88			−0.524687			−0.262343	+	0.964975i	$0.584495\pi$
$350$	−2105.89	−	1619.52i	−0.321613	−	0.247335i
$351$	242.695			0.0369063
$352$	5789.04	−	5789.04i	0.876582	−	0.876582i
$353$	67.8564	−	67.8564i	0.0102313	−	0.0102313i	−0.701973	−	0.712204i	$-0.747697\pi$
$353$	67.8564	−	67.8564i	0.0102313	−	0.0102313i	0.712204	+	0.701973i	$0.247697\pi$
$354$		−	428.301i		−	0.0643049i
$355$	−668.029	+	1500.82i	−0.0998741	+	0.224381i
$356$		−	8577.01i		−	1.27691i
$357$	−3156.70	−	2175.48i	−0.467983	−	0.322517i
$358$	−470.411	−	470.411i	−0.0694469	−	0.0694469i
$359$		−	6854.98i		−	1.00778i	−0.863768	−	0.503889i	$-0.831902\pi$
$359$		−	6854.98i		−	1.00778i	0.863768	−	0.503889i	$-0.168098\pi$
$360$	−607.756	−	1582.79i	−0.0889765	−	0.231723i
$361$	8196.83			1.19505
$362$	963.778	+	963.778i	0.139931	+	0.139931i
$363$	−1874.81	+	1874.81i	−0.271080	+	0.271080i
$364$	−201.350	−	1094.19i	−0.0289935	−	0.157558i
$365$	−2040.83	−	5314.98i	−0.292663	−	0.762188i
$366$	−1343.78			−0.191914
$367$	−5841.95	−	5841.95i	−0.830920	−	0.830920i	0.156723	−	0.987643i	$-0.449907\pi$
$367$	−5841.95	−	5841.95i	−0.830920	−	0.830920i	−0.987643	+	0.156723i	$0.949907\pi$
$368$	−1119.54	−	1119.54i	−0.158587	−	0.158587i
$369$	2326.33			0.328195
$370$	3774.10	+	1679.89i	0.530287	+	0.236036i
$371$	1882.32	+	10229.0i	0.263410	+	1.43144i
$372$	980.985	−	980.985i	0.136725	−	0.136725i
$373$	−5333.16	−	5333.16i	−0.740323	−	0.740323i	0.232317	−	0.972640i	$-0.425369\pi$
$373$	−5333.16	−	5333.16i	−0.740323	−	0.740323i	−0.972640	+	0.232317i	$0.925369\pi$
$374$	3726.42			0.515210
$375$	−1902.31	+	3736.22i	−0.261959	+	0.514500i
$376$		−	7928.42i		−	1.08744i
$377$	710.547	+	710.547i	0.0970690	+	0.0970690i
$378$	472.492	+	325.625i	0.0642920	+	0.0443078i
$379$		−	8939.57i		−	1.21160i	−0.795618	−	0.605798i	$-0.792854\pi$
$379$		−	8939.57i		−	1.21160i	0.795618	−	0.605798i	$-0.207146\pi$
$380$	8375.99	+	3728.24i	1.13073	+	0.503302i
$381$		−	285.202i		−	0.0383500i
$382$	788.823	−	788.823i	0.105654	−	0.105654i
$383$	4901.85	−	4901.85i	0.653976	−	0.653976i	−0.299972	−	0.953948i	$-0.596977\pi$
$383$	4901.85	−	4901.85i	0.653976	−	0.653976i	0.953948	+	0.299972i	$0.0969773\pi$
$384$	−4427.79			−0.588424
$385$	8314.72	−	5081.79i	1.10067	−	0.672707i
$386$	−2073.64			−0.273434
$387$	−2984.17	+	2984.17i	−0.391974	+	0.391974i
$388$	−1420.10	+	1420.10i	−0.185810	+	0.185810i
$389$			11003.6i			1.43420i	0.696969	+	0.717101i	$0.254532\pi$
$389$			11003.6i			1.43420i	−0.696969	+	0.717101i	$0.745468\pi$
$390$	322.984	−	124.019i	0.0419357	−	0.0161024i
$391$		−	3200.96i		−	0.414014i
$392$	2364.19	−	5273.75i	0.304616	−	0.679501i
$393$	−4737.09	−	4737.09i	−0.608027	−	0.608027i
$394$			1557.86i			0.199198i
$395$	−12173.0	−	5418.33i	−1.55061	−	0.690192i
$396$	2830.67			0.359208
$397$	−10543.3	−	10543.3i	−1.33289	−	1.33289i	−0.902778	−	0.430107i	$-0.858476\pi$
$397$	−10543.3	−	10543.3i	−1.33289	−	1.33289i	−0.430107	−	0.902778i	$-0.641524\pi$
$398$	−2559.50	+	2559.50i	−0.322352	+	0.322352i
$399$	−6704.85	+	1233.81i	−0.841259	+	0.154807i
$400$	2855.23	+	3169.80i	0.356904	+	0.396225i
$401$	−9885.66			−1.23109			−0.615544	−	0.788102i	$-0.711064\pi$
$401$	−9885.66			−1.23109			−0.615544	+	0.788102i	$0.711064\pi$
$402$	595.139	+	595.139i	0.0738379	+	0.0738379i
$403$	439.804	+	439.804i	0.0543627	+	0.0543627i
$404$	−743.251			−0.0915300
$405$	368.262	−	827.350i	0.0451829	−	0.101510i
$406$	429.990	+	2336.68i	0.0525617	+	0.285634i
$407$	−10714.9	+	10714.9i	−1.30496	+	1.30496i
$408$	−2466.32	−	2466.32i	−0.299267	−	0.299267i
$409$	1778.29			0.214989			0.107495	−	0.994206i	$-0.465717\pi$
$409$	1778.29			0.214989			0.107495	+	0.994206i	$0.465717\pi$
$410$	3095.94	−	1188.77i	0.372920	−	0.143193i
$411$			940.736i			0.112903i
$412$	2310.29	+	2310.29i	0.276262	+	0.276262i
$413$	−1897.21	−	1307.49i	−0.226042	−	0.155780i
$414$			479.118i			0.0568777i
$415$	−191.643	−	499.101i	−0.0226684	−	0.0590359i
$416$		−	1563.69i		−	0.184294i
$417$	−3996.66	+	3996.66i	−0.469346	+	0.469346i
$418$	4685.72	−	4685.72i	0.548292	−	0.548292i
$419$	−12780.7			−1.49016			−0.745079	−	0.666976i	$-0.767588\pi$
$419$	−12780.7			−1.49016			−0.745079	+	0.666976i	$0.767588\pi$
$420$	−4035.63	−	973.903i	−0.468854	−	0.113147i
$421$	11972.9			1.38605			0.693023	−	0.720916i	$-0.256279\pi$
$421$	11972.9			1.38605			0.693023	+	0.720916i	$0.256279\pi$
$422$	804.751	−	804.751i	0.0928310	−	0.0928310i
$423$	2994.50	−	2994.50i	0.344202	−	0.344202i
$424$			9462.56i			1.08383i
$425$	−449.702	+	8613.34i	−0.0513265	+	0.983078i
$426$		−	505.844i		−	0.0575311i
$427$	−4102.20	+	5952.43i	−0.464917	+	0.674610i
$428$	−9208.98	−	9208.98i	−1.04003	−	1.04003i
$429$			1269.07i			0.142823i
$430$	−2446.47	+	5496.33i	−0.274371	+	0.616410i
$431$	1294.36			0.144657			0.0723287	−	0.997381i	$-0.476957\pi$
$431$	1294.36			0.144657			0.0723287	+	0.997381i	$0.476957\pi$
$432$	−651.590	−	651.590i	−0.0725686	−	0.0725686i
$433$	−9248.52	+	9248.52i	−1.02646	+	1.02646i	−0.0268152	+	0.999640i	$0.508537\pi$
$433$	−9248.52	+	9248.52i	−1.02646	+	1.02646i	−0.999640	+	0.0268152i	$0.991463\pi$
$434$	266.149	+	1446.32i	0.0294367	+	0.159967i
$435$	3500.44	−	1344.09i	0.385823	−	0.148147i
$436$	11439.0			1.25648
$437$	−4024.99	−	4024.99i	−0.440598	−	0.440598i
$438$	1239.62	+	1239.62i	0.135232	+	0.135232i
$439$	3709.27			0.403267			0.201633	−	0.979461i	$-0.435375\pi$
$439$	3709.27			0.403267			0.201633	+	0.979461i	$0.435375\pi$
$440$	8276.52	−	3177.99i	0.896744	−	0.344329i
$441$	2884.78	−	1098.91i	0.311498	−	0.118660i
$442$	503.277	−	503.277i	0.0541594	−	0.0541594i
$443$	441.078	+	441.078i	0.0473054	+	0.0473054i	0.730364	−	0.683058i	$-0.239351\pi$
$443$	441.078	+	441.078i	0.0473054	+	0.0473054i	−0.683058	+	0.730364i	$0.739351\pi$
$444$	6455.61			0.690022
$445$	5834.83	−	13108.7i	0.621568	−	1.39643i
$446$		−	4461.28i		−	0.473650i
$447$	4116.74	+	4116.74i	0.435604	+	0.435604i
$448$	−771.425	+	1119.36i	−0.0813535	+	0.118047i
$449$			7375.06i			0.775168i	0.921834	+	0.387584i	$0.126690\pi$
$449$			7375.06i			0.775168i	−0.921834	+	0.387584i	$0.873310\pi$
$450$	67.3111	−	1289.24i	0.00705128	−	0.135056i
$451$			12164.5i			1.27008i
$452$	1523.22	−	1523.22i	0.158510	−	0.158510i
$453$	−3138.52	+	3138.52i	−0.325520	+	0.325520i
$454$	−3972.43			−0.410651
$455$	436.628	−	1809.29i	0.0449878	−	0.186419i
$456$	−6202.46			−0.636967
$457$	2880.31	−	2880.31i	0.294826	−	0.294826i	−0.544157	−	0.838983i	$-0.683151\pi$
$457$	2880.31	−	2880.31i	0.294826	−	0.294826i	0.838983	+	0.544157i	$0.183151\pi$
$458$	5188.87	−	5188.87i	0.529388	−	0.529388i
$459$		−	1863.02i		−	0.189451i
$460$	−1242.52	−	3235.92i	−0.125941	−	0.327990i
$461$		−	13598.8i		−	1.37389i	−0.726711	−	0.686943i	$-0.758952\pi$
$461$		−	13598.8i		−	1.37389i	0.726711	−	0.686943i	$-0.241048\pi$
$462$	−1702.71	+	2470.69i	−0.171466	+	0.248803i
$463$	3784.31	+	3784.31i	0.379853	+	0.379853i	0.871049	−	0.491196i	$-0.163440\pi$
$463$	3784.31	+	3784.31i	0.379853	+	0.379853i	−0.491196	+	0.871049i	$0.663440\pi$
$464$		−	3815.37i		−	0.381732i
$465$	2166.65	−	831.943i	0.216077	−	0.0829687i
$466$	−1040.39			−0.103424
$467$	2918.56	+	2918.56i	0.289197	+	0.289197i	0.836763	−	0.547566i	$-0.184445\pi$
$467$	2918.56	+	2918.56i	0.289197	+	0.289197i	−0.547566	+	0.836763i	$0.684445\pi$
$468$	382.300	−	382.300i	0.0377603	−	0.0377603i
$469$	4453.03	−	819.436i	0.438426	−	0.0806782i
$470$	2454.94	−	5515.34i	0.240932	−	0.541285i
$471$	−644.336			−0.0630349
$472$	−1482.28	−	1482.28i	−0.144550	−	0.144550i
$473$	−15604.4	−	15604.4i	−1.51690	−	1.51690i
$474$	4102.86			0.397575
$475$	10265.2	+	11396.2i	0.991580	+	1.10082i
$476$	−8399.39	+	1545.64i	−0.808793	+	0.148832i
$477$	−3573.93	+	3573.93i	−0.343058	+	0.343058i
$478$	4628.55	+	4628.55i	0.442897	+	0.442897i
$479$	10671.2			1.01791			0.508957	−	0.860792i	$-0.330031\pi$
$479$	10671.2			1.01791			0.508957	+	0.860792i	$0.330031\pi$
$480$	−5330.65	−	2372.73i	−0.506895	−	0.225624i
$481$			2894.24i			0.274357i
$482$	3850.52	+	3850.52i	0.363872	+	0.363872i
$483$	2122.30	+	1462.62i	0.199934	+	0.137787i
$484$			5906.50i			0.554705i
$485$	−3136.49	+	1204.34i	−0.293651	+	0.112755i
$486$			278.855i			0.0260270i
$487$	−1867.09	+	1867.09i	−0.173728	+	0.173728i	−0.788615	−	0.614887i	$-0.789202\pi$
$487$	−1867.09	+	1867.09i	−0.173728	+	0.173728i	0.614887	+	0.788615i	$0.289202\pi$
$488$	−4650.63	+	4650.63i	−0.431402	+	0.431402i
$489$	−6697.03			−0.619326
$490$	3277.58	−	2936.60i	0.302175	−	0.270739i
$491$	15349.2			1.41079			0.705396	−	0.708813i	$-0.250769\pi$
$491$	15349.2			1.41079			0.705396	+	0.708813i	$0.250769\pi$
$492$	3664.50	−	3664.50i	0.335790	−	0.335790i
$493$	5454.41	−	5454.41i	0.498285	−	0.498285i
$494$		−	1265.67i		−	0.115274i
$495$	4326.27	+	1925.67i	0.392831	+	0.174853i
$496$		−	2361.58i		−	0.213786i
$497$	−2240.69	−	1544.20i	−0.202231	−	0.139370i
$498$	116.406	+	116.406i	0.0104745	+	0.0104745i
$499$			7059.56i			0.633325i	0.948538	+	0.316663i	$0.102562\pi$
$499$			7059.56i			0.633325i	−0.948538	+	0.316663i	$0.897438\pi$
$500$	2888.83	+	8881.97i	0.258385	+	0.794427i
$501$	−4223.83			−0.376660
$502$	81.8053	+	81.8053i	0.00727321	+	0.00727321i
$503$	−2440.13	+	2440.13i	−0.216302	+	0.216302i	−0.806938	−	0.590636i	$-0.798877\pi$
$503$	−2440.13	+	2440.13i	−0.216302	+	0.216302i	0.590636	+	0.806938i	$0.298877\pi$
$504$	2762.16	−	508.287i	0.244120	−	0.0449224i
$505$	−1135.95	−	505.625i	−0.100098	−	0.0445545i
$506$	−2505.34			−0.220110
$507$	−4489.14	−	4489.14i	−0.393235	−	0.393235i
$508$	−449.258	−	449.258i	−0.0392374	−	0.0392374i
$509$	11565.4			1.00713			0.503564	−	0.863958i	$-0.332022\pi$
$509$	11565.4			1.00713			0.503564	+	0.863958i	$0.332022\pi$
$510$	−952.011	−	2479.34i	−0.0826583	−	0.215269i
$511$	9275.27	−	1706.81i	0.802963	−	0.147759i
$512$	−7451.28	+	7451.28i	−0.643170	+	0.643170i
$513$	−2342.62	−	2342.62i	−0.201616	−	0.201616i
$514$	−2522.96			−0.216504
$515$	1959.29	+	5102.61i	0.167644	+	0.436598i
$516$			9401.49i			0.802088i
$517$	15658.4	+	15658.4i	1.33202	+	1.33202i
$518$	−3883.21	+	5634.66i	−0.329379	+	0.477940i
$519$			4647.48i			0.393067i
$520$	688.589	−	1547.01i	0.0580704	−	0.130463i
$521$			6288.19i			0.528773i	0.964417	+	0.264387i	$0.0851695\pi$
$521$			6288.19i			0.528773i	−0.964417	+	0.264387i	$0.914831\pi$
$522$	−816.414	+	816.414i	−0.0684549	+	0.0684549i
$523$	−3302.60	+	3302.60i	−0.276124	+	0.276124i	−0.831559	−	0.555436i	$-0.812551\pi$
$523$	−3302.60	+	3302.60i	−0.276124	+	0.276124i	0.555436	+	0.831559i	$0.312551\pi$
$524$	−14924.0			−1.24419
$525$	−5505.34	−	4233.86i	−0.457663	−	0.351963i
$526$	−6010.12			−0.498201
$527$	3376.09	−	3376.09i	0.279060	−	0.279060i
$528$	3407.21	−	3407.21i	0.280833	−	0.280833i
$529$		−	10014.9i		−	0.823123i
$530$	−2929.96	+	6582.56i	−0.240131	+	0.539487i
$531$		−	1119.69i		−	0.0915075i
$532$	−8618.13	+	12505.2i	−0.702337	+	1.01912i
$533$	1642.90	+	1642.90i	0.133512	+	0.133512i
$534$			4418.25i			0.358045i
$535$	−7809.85	−	20339.4i	−0.631120	−	1.64364i
$536$	4119.37			0.331958
$537$	−1229.78	−	1229.78i	−0.0988245	−	0.0988245i
$538$	−592.767	+	592.767i	−0.0475018	+	0.0475018i
$539$	5746.29	+	15084.7i	0.459203	+	1.20546i
$540$	−723.168	−	1883.36i	−0.0576300	−	0.150087i
$541$	11630.6			0.924289			0.462145	−	0.886805i	$-0.347080\pi$
$541$	11630.6			0.924289			0.462145	+	0.886805i	$0.347080\pi$
$542$	4600.77	+	4600.77i	0.364613	+	0.364613i
$543$	2519.57	+	2519.57i	0.199125	+	0.199125i
$544$	−12003.5			−0.946039
$545$	17482.8	+	7781.79i	1.37409	+	0.611624i
$546$	103.721	+	563.646i	0.00812975	+	0.0441792i
$547$	6512.62	−	6512.62i	0.509066	−	0.509066i	−0.405173	−	0.914240i	$-0.632789\pi$
$547$	6512.62	−	6512.62i	0.509066	−	0.509066i	0.914240	+	0.405173i	$0.132789\pi$
$548$	1481.87	+	1481.87i	0.115515	+	0.115515i
$549$	−3513.00			−0.273099
$550$	6741.52	+	351.974i	0.522653	+	0.0272877i
$551$		−	13717.1i		−	1.06056i
$552$	1658.15	+	1658.15i	0.127854	+	0.127854i
$553$	12524.9	−	18174.1i	0.963135	−	1.39754i
$554$		−	9705.25i		−	0.744290i
$555$	9866.48	+	4391.67i	0.754610	+	0.335885i
$556$			12591.3i			0.960413i
$557$	−3672.75	+	3672.75i	−0.279389	+	0.279389i	−0.832865	−	0.553476i	$-0.813301\pi$
$557$	−3672.75	+	3672.75i	−0.279389	+	0.279389i	0.553476	+	0.832865i	$0.313301\pi$
$558$	−505.331	+	505.331i	−0.0383376	+	0.0383376i
$559$	−4214.96			−0.318915
$560$	−6029.85	+	3685.33i	−0.455014	+	0.278096i
$561$	9741.83			0.733156
$562$	−3718.66	+	3718.66i	−0.279115	+	0.279115i
$563$	3765.85	−	3765.85i	0.281903	−	0.281903i	−0.551964	−	0.833868i	$-0.686122\pi$
$563$	3765.85	−	3765.85i	0.281903	−	0.281903i	0.833868	+	0.551964i	$0.186122\pi$
$564$		−	9434.02i		−	0.704333i
$565$	3364.26	−	1291.80i	0.250505	−	0.0961883i
$566$		−	2762.69i		−	0.205167i
$567$	1235.22	+	851.268i	0.0914891	+	0.0630510i
$568$	−1750.65	−	1750.65i	−0.129323	−	0.129323i
$569$			14873.6i			1.09584i	0.836529	+	0.547922i	$0.184581\pi$
$569$			14873.6i			1.09584i	−0.836529	+	0.547922i	$0.815419\pi$
$570$	−4314.69	−	1920.52i	−0.317057	−	0.141126i
$571$	−13602.3			−0.996916			−0.498458	−	0.866914i	$-0.666100\pi$
$571$	−13602.3			−0.996916			−0.498458	+	0.866914i	$0.666100\pi$
$572$	1999.07	+	1999.07i	0.146128	+	0.146128i
$573$	2062.19	−	2062.19i	0.150348	−	0.150348i
$574$	994.207	+	5402.78i	0.0722951	+	0.392870i
$575$	302.343	−	5790.91i	0.0219279	−	0.419996i
$576$	−660.624			−0.0477882
$577$	4519.16	+	4519.16i	0.326057	+	0.326057i	0.851085	−	0.525028i	$-0.175945\pi$
$577$	4519.16	+	4519.16i	0.326057	+	0.326057i	−0.525028	+	0.851085i	$0.675945\pi$
$578$	123.276	+	123.276i	0.00887126	+	0.00887126i
$579$	−5421.04			−0.389103
$580$	3396.74	−	7631.23i	0.243176	−	0.546327i
$581$	870.990	−	160.278i	0.0621941	−	0.0114448i
$582$	731.529	−	731.529i	0.0521011	−	0.0521011i
$583$	−18688.3	−	18688.3i	−1.32760	−	1.32760i
$584$	8580.29			0.607971
$585$	844.365	−	324.217i	0.0596755	−	0.0229140i
$586$			2545.23i			0.179424i
$587$	−17037.9	−	17037.9i	−1.19800	−	1.19800i	−0.974763	−	0.223241i	$-0.928336\pi$
$587$	−17037.9	−	17037.9i	−1.19800	−	1.19800i	−0.223241	−	0.974763i	$-0.571664\pi$
$588$	2813.15	−	6275.22i	0.197300	−	0.440112i
$589$		−	8490.41i		−	0.593958i
$590$	−572.168	−	1490.11i	−0.0399251	−	0.103978i
$591$			4072.66i			0.283463i
$592$	7770.47	−	7770.47i	0.539467	−	0.539467i
$593$	−5362.06	+	5362.06i	−0.371321	+	0.371321i	−0.867958	−	0.496637i	$-0.834568\pi$
$593$	−5362.06	+	5362.06i	−0.371321	+	0.371321i	0.496637	+	0.867958i	$0.334568\pi$
$594$	−1458.15			−0.100722
$595$	−13888.7	−	3351.72i	−0.956946	−	0.230936i
$596$	12969.6			0.891368
$597$	−6691.21	+	6691.21i	−0.458715	+	0.458715i
$598$	−338.362	+	338.362i	−0.0231382	+	0.0231382i
$599$		−	5584.54i		−	0.380932i	−0.981694	−	0.190466i	$-0.939000\pi$
$599$		−	5584.54i		−	0.380932i	0.981694	−	0.190466i	$-0.0609998\pi$
$600$	−4228.91	−	4694.81i	−0.287741	−	0.319442i
$601$		−	19025.6i		−	1.29130i	−0.763634	−	0.645649i	$-0.776587\pi$
$601$		−	19025.6i		−	1.29130i	0.763634	−	0.645649i	$-0.223413\pi$
$602$	−8205.92	−	5655.22i	−0.555562	−	0.382873i
$603$	1555.85	+	1555.85i	0.105073	+	0.105073i
$604$			9887.76i			0.666105i
$605$	−4018.12	+	9027.24i	−0.270016	+	0.606627i
$606$	382.869			0.0256650
$607$	1636.42	+	1636.42i	0.109424	+	0.109424i	0.759699	−	0.650275i	$-0.225346\pi$
$607$	1636.42	+	1636.42i	0.109424	+	0.109424i	−0.650275	+	0.759699i	$0.725346\pi$
$608$	−15093.6	+	15093.6i	−1.00678	+	1.00678i
$609$	1124.11	+	6108.68i	0.0747965	+	0.406463i
$610$	−4675.18	+	1795.16i	−0.310316	+	0.119154i
$611$	4229.54			0.280047
$612$	−2934.67	−	2934.67i	−0.193835	−	0.193835i
$613$	−6492.66	−	6492.66i	−0.427791	−	0.427791i	0.460084	−	0.887875i	$-0.347819\pi$
$613$	−6492.66	−	6492.66i	−0.427791	−	0.427791i	−0.887875	+	0.460084i	$0.847819\pi$
$614$	−10498.4			−0.690031
$615$	8093.58	−	3107.75i	0.530674	−	0.203767i
$616$	2657.86	+	14443.5i	0.173845	+	0.944717i
$617$	10437.9	−	10437.9i	0.681060	−	0.681060i	−0.279179	−	0.960239i	$-0.590062\pi$
$617$	10437.9	−	10437.9i	0.681060	−	0.681060i	0.960239	+	0.279179i	$0.0900622\pi$
$618$	−1190.09	−	1190.09i	−0.0774636	−	0.0774636i
$619$	−11190.6			−0.726636			−0.363318	−	0.931665i	$-0.618356\pi$
$619$	−11190.6			−0.726636			−0.363318	+	0.931665i	$0.618356\pi$
$620$	2102.46	−	4723.46i	0.136189	−	0.305966i
$621$			1252.54i			0.0809383i
$622$	−8465.38	−	8465.38i	−0.545708	−	0.545708i
$623$	19571.1	+	13487.7i	1.25859	+	0.867373i
$624$		−	920.331i		−	0.0590428i
$625$	−1627.13	+	15540.0i	−0.104136	+	0.994563i
$626$		−	8476.38i		−	0.541189i
$627$	12249.7	−	12249.7i	0.780232	−	0.780232i
$628$	−1014.98	+	1014.98i	−0.0644935	+	0.0644935i
$629$	22217.2			1.40836
$630$	2078.86	+	501.683i	0.131466	+	0.0317262i
$631$	−27632.2			−1.74329			−0.871647	−	0.490133i	$-0.836948\pi$
$631$	−27632.2			−1.74329			−0.871647	+	0.490133i	$0.836948\pi$
$632$	14199.4	−	14199.4i	0.893704	−	0.893704i
$633$	2103.83	−	2103.83i	0.132101	−	0.132101i
$634$		−	8638.74i		−	0.541149i
$635$	−381.002	−	992.251i	−0.0238104	−	0.0620099i
$636$			11259.5i			0.701994i
$637$	2813.36	+	1261.21i	0.174991	+	0.0784476i
$638$	−4269.08	−	4269.08i	−0.264913	−	0.264913i
$639$		−	1322.41i		−	0.0818681i
$640$	−15404.8	+	5915.09i	−0.951451	+	0.365335i
$641$	−2161.05			−0.133161			−0.0665806	−	0.997781i	$-0.521209\pi$
$641$	−2161.05			−0.133161			−0.0665806	+	0.997781i	$0.521209\pi$
$642$	4743.79	+	4743.79i	0.291624	+	0.291624i
$643$	−10891.0	+	10891.0i	−0.667959	+	0.667959i	−0.957243	−	0.289284i	$-0.906583\pi$
$643$	−10891.0	+	10891.0i	−0.667959	+	0.667959i	0.289284	+	0.957243i	$0.406583\pi$
$644$	5647.07	−	1039.16i	0.345537	−	0.0635849i
$645$	−6395.72	+	14368.8i	−0.390436	+	0.877166i
$646$	−9715.77			−0.591737
$647$	−9796.19	−	9796.19i	−0.595252	−	0.595252i	0.343794	−	0.939045i	$-0.388288\pi$
$647$	−9796.19	−	9796.19i	−0.595252	−	0.595252i	−0.939045	+	0.343794i	$0.888288\pi$
$648$	965.074	+	965.074i	0.0585057	+	0.0585057i
$649$	5854.94			0.354124
$650$	958.023	−	862.950i	0.0578104	−	0.0520733i
$651$	695.782	+	3781.06i	0.0418892	+	0.227637i
$652$	−10549.4	+	10549.4i	−0.633657	+	0.633657i
$653$	16668.7	+	16668.7i	0.998925	+	0.998925i	0.999999	−	0.00107454i	$-0.000342037\pi$
$653$	16668.7	+	16668.7i	0.998925	+	0.998925i	−0.00107454	+	0.999999i	$0.500342\pi$
$654$	−5892.52			−0.352317
$655$	−22809.2	−	10152.6i	−1.36065	−	0.605641i
$656$		−	8821.75i		−	0.525048i
$657$	3240.70	+	3240.70i	0.192438	+	0.192438i
$658$	8234.31	+	5674.79i	0.487852	+	0.336210i
$659$		−	13534.7i		−	0.800056i	−0.916503	−	0.400028i	$-0.869000\pi$
$659$		−	13534.7i		−	0.800056i	0.916503	−	0.400028i	$-0.131000\pi$
$660$	9848.22	−	3781.49i	0.580820	−	0.223022i
$661$		−	4401.31i		−	0.258988i	−0.991580	−	0.129494i	$-0.958665\pi$
$661$		−	4401.31i		−	0.258988i	0.991580	−	0.129494i	$-0.0413353\pi$
$662$	6804.28	−	6804.28i	0.399480	−	0.399480i
$663$	1315.70	−	1315.70i	0.0770701	−	0.0770701i
$664$	805.728			0.0470908
$665$	−21678.7	+	13249.6i	−1.26416	+	0.772628i
$666$	−3325.46			−0.193482
$667$	−3667.10	+	3667.10i	−0.212880	+	0.212880i
$668$	−6653.49	+	6653.49i	−0.385376	+	0.385376i
$669$		−	11663.0i		−	0.674015i
$670$	2865.61	+	1275.51i	0.165236	+	0.0735482i
$671$		−	18369.7i		−	1.05686i
$672$	5484.76	−	7958.57i	0.314850	−	0.456858i
$673$	13974.6	+	13974.6i	0.800420	+	0.800420i	0.983161	−	0.182741i	$-0.0584971\pi$
$673$	13974.6	+	13974.6i	0.800420	+	0.800420i	−0.182741	+	0.983161i	$0.558497\pi$
$674$			963.851i			0.0550833i
$675$	175.969	−	3370.41i	0.0100341	−	0.192188i
$676$	−14142.9			−0.804668
$677$	−9910.40	−	9910.40i	−0.562611	−	0.562611i	0.367437	−	0.930048i	$-0.380235\pi$
$677$	−9910.40	−	9910.40i	−0.562611	−	0.562611i	−0.930048	+	0.367437i	$0.880235\pi$
$678$	−784.653	+	784.653i	−0.0444461	+	0.0444461i
$679$	−1007.23	−	5473.55i	−0.0569277	−	0.309360i
$680$	−11875.4	−	5285.86i	−0.669706	−	0.298093i
$681$	−10385.0			−0.584366
$682$	−2642.41	−	2642.41i	−0.148362	−	0.148362i
$683$	−11316.5	−	11316.5i	−0.633986	−	0.633986i	0.315079	−	0.949065i	$-0.397969\pi$
$683$	−11316.5	−	11316.5i	−0.633986	−	0.633986i	−0.949065	+	0.315079i	$0.897969\pi$
$684$	−7380.31			−0.412563
$685$	1256.73	+	3272.93i	0.0700981	+	0.182558i
$686$	3785.04	+	6230.10i	0.210661	+	0.346744i
$687$	13565.1	−	13565.1i	0.753332	−	0.753332i
$688$	11316.4	+	11316.4i	0.627081	+	0.627081i
$689$	−5047.95			−0.279117
$690$	640.054	+	1666.91i	0.0353137	+	0.0919682i
$691$		−	18547.8i		−	1.02111i	−0.859844	−	0.510557i	$-0.829439\pi$
$691$		−	18547.8i		−	1.02111i	0.859844	−	0.510557i	$-0.170561\pi$
$692$	7320.84	+	7320.84i	0.402163	+	0.402163i
$693$	−4451.34	+	6459.04i	−0.244000	+	0.354053i
$694$			1974.38i			0.107992i
$695$	−8565.70	+	19244.0i	−0.467504	+	1.05031i
$696$			5650.96i			0.307758i
$697$	12611.5	−	12611.5i	0.685358	−	0.685358i
$698$	2775.85	−	2775.85i	0.150526	−	0.150526i
$699$	−2719.86			−0.147174
$700$	−15341.5	+	2002.88i	−0.828361	+	0.108145i
$701$	−9679.24			−0.521512			−0.260756	−	0.965405i	$-0.583972\pi$
$701$	−9679.24			−0.521512			−0.260756	+	0.965405i	$0.583972\pi$
$702$	−196.933	+	196.933i	−0.0105880	+	0.0105880i
$703$	27936.6	−	27936.6i	1.49879	−	1.49879i
$704$		−	3454.45i		−	0.184935i
$705$	6417.85	−	14418.6i	0.342851	−	0.770261i
$706$			110.123i			0.00587045i
$707$	1168.79	−	1695.96i	0.0621739	−	0.0902165i
$708$	−1763.77	−	1763.77i	−0.0936250	−	0.0936250i
$709$			15134.7i			0.801686i	0.916147	+	0.400843i	$0.131283\pi$
$709$			15134.7i			0.801686i	−0.916147	+	0.400843i	$0.868717\pi$
$710$	−675.758	−	1759.89i	−0.0357194	−	0.0930247i
$711$	10726.0			0.565759
$712$	15290.9	+	15290.9i	0.804845	+	0.804845i
$713$	−2269.81	+	2269.81i	−0.119222	+	0.119222i
$714$	4326.75	−	796.199i	0.226785	−	0.0417325i
$715$	1695.35	+	4415.24i	0.0886749	+	0.230938i
$716$	−3874.36			−0.202223
$717$	12100.2	+	12100.2i	0.630253	+	0.630253i
$718$	5562.42	+	5562.42i	0.289119	+	0.289119i
$719$	16820.2			0.872445			0.436222	−	0.899839i	$-0.356316\pi$
$719$	16820.2			0.872445			0.436222	+	0.899839i	$0.356316\pi$
$720$	−3137.42	−	1396.50i	−0.162395	−	0.0722839i
$721$	−8904.66	+	1638.62i	−0.459954	+	0.0846397i
$722$	−6651.25	+	6651.25i	−0.342844	+	0.342844i
$723$	10066.3	+	10066.3i	0.517798	+	0.517798i
$724$	7937.78			0.407466
$725$	10382.9	−	9352.48i	0.531875	−	0.479093i
$726$		−	3042.59i		−	0.155539i
$727$	−6865.13	−	6865.13i	−0.350225	−	0.350225i	0.509968	−	0.860193i	$-0.329657\pi$
$727$	−6865.13	−	6865.13i	−0.350225	−	0.350225i	−0.860193	+	0.509968i	$0.829657\pi$
$728$	2309.65	+	1591.73i	0.117584	+	0.0810349i
$729$			729.000i			0.0370370i
$730$	5968.81	+	2656.78i	0.302624	+	0.134701i
$731$			32355.5i			1.63709i
$732$	−5533.78	+	5533.78i	−0.279418	+	0.279418i
$733$	−5472.36	+	5472.36i	−0.275752	+	0.275752i	−0.831411	−	0.555659i	$-0.812466\pi$
$733$	−5472.36	+	5472.36i	−0.275752	+	0.275752i	0.555659	+	0.831411i	$0.312466\pi$
$734$	9480.81			0.476762
$735$	8568.45	−	7677.03i	0.430003	−	0.385267i
$736$	8070.16			0.404171
$737$	−8135.64	+	8135.64i	−0.406621	+	0.406621i
$738$	−1887.68	+	1887.68i	−0.0941552	+	0.0941552i
$739$		−	13345.3i		−	0.664295i	−0.943227	−	0.332147i	$-0.892227\pi$
$739$		−	13345.3i		−	0.664295i	0.943227	−	0.332147i	$-0.107773\pi$
$740$	22459.8	−	8624.07i	1.11573	−	0.428415i
$741$		−	3308.80i		−	0.164038i
$742$	−9827.64	−	6772.85i	−0.486232	−	0.335093i
$743$	1331.63	+	1331.63i	0.0657505	+	0.0657505i	0.739217	−	0.673467i	$-0.235196\pi$
$743$	1331.63	+	1331.63i	0.0657505	+	0.0657505i	−0.673467	+	0.739217i	$0.735196\pi$
$744$			3497.75i			0.172357i
$745$	19822.2	+	8823.05i	0.974802	+	0.433895i
$746$	8655.10			0.424780
$747$	304.316	+	304.316i	0.0149054	+	0.0149054i
$748$	15345.6	−	15345.6i	0.750121	−	0.750121i
$749$	35494.6	−	6531.64i	1.73157	−	0.318639i
$750$	−1488.11	−	4575.34i	−0.0724510	−	0.222757i
$751$	−10872.5			−0.528287			−0.264144	−	0.964483i	$-0.585089\pi$
$751$	−10872.5			−0.528287			−0.264144	+	0.964483i	$0.585089\pi$
$752$	−11355.5	−	11355.5i	−0.550655	−	0.550655i
$753$	213.861	+	213.861i	0.0103499	+	0.0103499i
$754$	−1153.13			−0.0556959
$755$	−6726.52	+	15112.0i	−0.324243	+	0.728454i
$756$	3286.69	−	604.810i	0.158116	−	0.0290962i
$757$	−6114.57	+	6114.57i	−0.293577	+	0.293577i	−0.838492	−	0.544915i	$-0.816562\pi$
$757$	−6114.57	+	6114.57i	−0.293577	+	0.293577i	0.544915	+	0.838492i	$0.316562\pi$
$758$	7253.94	+	7253.94i	0.347592	+	0.347592i
$759$	−6549.61			−0.313222
$760$	−21579.1	+	8285.88i	−1.02994	+	0.395474i
$761$			12938.4i			0.616318i	0.951335	+	0.308159i	$0.0997129\pi$
$761$			12938.4i			0.616318i	−0.951335	+	0.308159i	$0.900287\pi$
$762$	231.425	+	231.425i	0.0110021	+	0.0110021i
$763$	−17988.2	+	26101.5i	−0.853497	+	1.23845i
$764$		−	6496.84i		−	0.307653i
$765$	−2488.81	−	6481.65i	−0.117625	−	0.306333i
$766$			7955.13i			0.375236i
$767$	790.748	−	790.748i	0.0372259	−	0.0372259i
$768$	2347.21	−	2347.21i	0.110283	−	0.110283i
$769$	−30980.7			−1.45278			−0.726392	−	0.687281i	$-0.758804\pi$
$769$	−30980.7			−1.45278			−0.726392	+	0.687281i	$0.758804\pi$
$770$	−2623.33	+	10870.5i	−0.122777	+	0.508760i
$771$	−6595.67			−0.308090
$772$	−8539.38	+	8539.38i	−0.398107	+	0.398107i
$773$	2711.05	−	2711.05i	0.126144	−	0.126144i	−0.641216	−	0.767360i	$-0.721570\pi$
$773$	2711.05	−	2711.05i	0.126144	−	0.126144i	0.767360	+	0.641216i	$0.221570\pi$
$774$		−	4842.96i		−	0.224905i
$775$	6426.62	−	5788.85i	0.297872	−	0.268312i
$776$		−	5063.42i		−	0.234235i
$777$	−10151.7	+	14730.5i	−0.468714	+	0.680120i
$778$	−8928.78	−	8928.78i	−0.411456	−	0.411456i
$779$		−	31716.2i		−	1.45873i
$780$	819.351	−	1840.78i	0.0376122	−	0.0845007i
$781$	6914.97			0.316821
$782$	2597.39	+	2597.39i	0.118776	+	0.118776i
$783$	−2134.32	+	2134.32i	−0.0974129	+	0.0974129i
$784$	−4167.22	−	10939.5i	−0.189833	−	0.498335i
$785$	−2241.72	+	860.770i	−0.101924	+	0.0391365i
$786$	7687.74			0.348871
$787$	17187.2	+	17187.2i	0.778473	+	0.778473i	0.979571	−	0.201098i	$-0.0644510\pi$
$787$	17187.2	+	17187.2i	0.778473	+	0.778473i	−0.201098	+	0.979571i	$0.564451\pi$
$788$	6415.37	+	6415.37i	0.290023	+	0.290023i
$789$	−15712.0			−0.708951
$790$	14274.3	−	5481.02i	0.642859	−	0.246843i
$791$	1080.38	+	5871.04i	0.0485635	+	0.263907i
$792$	−5046.44	+	5046.44i	−0.226411	+	0.226411i
$793$	−2480.95	−	2480.95i	−0.111099	−	0.111099i
$794$	17110.6			0.764777
$795$	−7659.69	+	17208.5i	−0.341712	+	0.767702i
$796$			21080.3i			0.938660i
$797$	9725.84	+	9725.84i	0.432254	+	0.432254i	0.889395	−	0.457140i	$-0.151126\pi$
$797$	9725.84	+	9725.84i	0.432254	+	0.432254i	−0.457140	+	0.889395i	$0.651126\pi$
$798$	4439.43	−	6441.76i	0.196935	−	0.285759i
$799$		−	32467.5i		−	1.43757i
$800$	−21715.7	−	1133.77i	−0.959707	−	0.0501062i
$801$			11550.5i			0.509507i
$802$	8021.64	−	8021.64i	0.353184	−	0.353184i
$803$	−16945.8	+	16945.8i	−0.744714	+	0.744714i
$804$	4901.63			0.215009
$805$	9337.66	+	2253.42i	0.408831	+	0.0986617i
$806$	−713.750			−0.0311920
$807$	−1549.65	+	1549.65i	−0.0675962	+	0.0675962i
$808$	1325.05	−	1325.05i	0.0576919	−	0.0576919i
$809$			13840.9i			0.601507i	0.953702	+	0.300754i	$0.0972382\pi$
$809$			13840.9i			0.601507i	−0.953702	+	0.300754i	$0.902762\pi$
$810$	372.523	+	970.169i	0.0161594	+	0.0420843i
$811$		−	6459.17i		−	0.279670i	−0.990175	−	0.139835i	$-0.955343\pi$
$811$		−	6459.17i		−	0.279670i	0.990175	−	0.139835i	$-0.0446571\pi$
$812$	11393.3	+	7851.84i	0.492396	+	0.339342i
$813$	12027.6	+	12027.6i	0.518853	+	0.518853i
$814$		−	17389.0i		−	0.748754i
$815$	−23299.8	+	8946.58i	−1.00142	+	0.384521i
$816$	−7064.79			−0.303085
$817$	40684.9	+	40684.9i	1.74221	+	1.74221i
$818$	−1442.98	+	1442.98i	−0.0616779	+	0.0616779i
$819$	271.153	+	1473.52i	0.0115688	+	0.0628680i
$820$	7853.82	−	17644.7i	0.334472	−	0.751437i
$821$	−29095.0			−1.23681			−0.618407	−	0.785858i	$-0.712222\pi$
$821$	−29095.0			−1.23681			−0.618407	+	0.785858i	$0.712222\pi$
$822$	−763.352	−	763.352i	−0.0323905	−	0.0323905i
$823$	28670.5	+	28670.5i	1.21433	+	1.21433i	0.969589	+	0.244737i	$0.0787018\pi$
$823$	28670.5	+	28670.5i	1.21433	+	1.21433i	0.244737	+	0.969589i	$0.421298\pi$
$824$	−8237.45			−0.348259
$825$	17624.1	+	920.153i	0.743748	+	0.0388310i
$826$	2600.42	−	478.524i	0.109540	−	0.0201573i
$827$	26904.3	−	26904.3i	1.13126	−	1.13126i	0.141293	−	0.989968i	$-0.454874\pi$
$827$	26904.3	−	26904.3i	1.13126	−	1.13126i	0.989968	−	0.141293i	$-0.0451260\pi$
$828$	1973.03	+	1973.03i	0.0828112	+	0.0828112i
$829$	5672.16			0.237638			0.118819	−	0.992916i	$-0.462089\pi$
$829$	5672.16			0.237638			0.118819	+	0.992916i	$0.462089\pi$
$830$	560.498	+	249.484i	0.0234400	+	0.0104334i
$831$		−	25372.1i		−	1.05914i
$832$	−466.546	−	466.546i	−0.0194406	−	0.0194406i
$833$	9681.54	−	21596.4i	0.402695	−	0.898284i
$834$		−	6486.11i		−	0.269299i
$835$	−14695.2	+	5642.62i	−0.609039	+	0.233857i
$836$		−	38592.1i		−	1.59657i
$837$	−1321.07	+	1321.07i	−0.0545553	+	0.0545553i
$838$	10370.8	−	10370.8i	0.427508	−	0.427508i
$839$	17815.9			0.733102			0.366551	−	0.930398i	$-0.380539\pi$
$839$	17815.9			0.733102			0.366551	+	0.930398i	$0.380539\pi$
$840$	8930.86	−	5458.36i	0.366838	−	0.224204i
$841$	11891.6			0.487579
$842$	−9715.34	+	9715.34i	−0.397640	+	0.397640i
$843$	−9721.56	+	9721.56i	−0.397187	+	0.397187i
$844$		−	6628.02i		−	0.270315i
$845$	−21615.3	−	9621.20i	−0.879988	−	0.391692i
$846$			4859.72i			0.197495i
$847$	−13477.5	−	9288.21i	−0.546744	−	0.376796i
$848$	13552.8	+	13552.8i	0.548826	+	0.548826i
$849$		−	7222.40i		−	0.291958i
$850$	−6624.32	−	7354.13i	−0.267308	−	0.296758i
$851$	−14937.0			−0.601686
$852$	−2083.10	−	2083.10i	−0.0837625	−	0.0837625i
$853$	−14900.6	+	14900.6i	−0.598110	+	0.598110i	−0.939809	−	0.341699i	$-0.888998\pi$
$853$	−14900.6	+	14900.6i	−0.598110	+	0.598110i	0.341699	+	0.939809i	$0.388998\pi$
$854$	−1501.35	−	8158.75i	−0.0601584	−	0.326917i
$855$	−11279.7	−	5020.73i	−0.451180	−	0.200825i
$856$	32835.1			1.31107
$857$	−15227.9	−	15227.9i	−0.606973	−	0.606973i	0.335181	−	0.942154i	$-0.391203\pi$
$857$	−15227.9	−	15227.9i	−0.606973	−	0.606973i	−0.942154	+	0.335181i	$0.891203\pi$
$858$	−1029.77	−	1029.77i	−0.0409743	−	0.0409743i
$859$	−28883.5			−1.14726			−0.573628	−	0.819116i	$-0.694464\pi$
$859$	−28883.5			−1.14726			−0.573628	+	0.819116i	$0.694464\pi$
$860$	12559.5	+	32708.9i	0.497993	+	1.29693i
$861$	2599.12	+	14124.3i	0.102878	+	0.559064i
$862$	−1050.30	+	1050.30i	−0.0415005	+	0.0415005i
$863$	23740.1	+	23740.1i	0.936410	+	0.936410i	0.998096	−	0.0616857i	$-0.0196476\pi$
$863$	23740.1	+	23740.1i	0.936410	+	0.936410i	−0.0616857	+	0.998096i	$0.519648\pi$
$864$	4696.98			0.184947
$865$	6208.58	+	16169.1i	0.244044	+	0.635569i
$866$		−	15009.3i		−	0.588955i
$867$	322.275	+	322.275i	0.0126240	+	0.0126240i
$868$	7052.04	+	4860.01i	0.275763	+	0.190046i
$869$			56086.7i			2.18943i
$870$	−1749.75	+	3931.05i	−0.0681863	+	0.153190i
$871$			2197.54i			0.0854889i
$872$	−20393.1	+	20393.1i	−0.791969	+	0.791969i
$873$	1912.41	−	1912.41i	0.0741411	−	0.0741411i
$874$	6532.09			0.252805
$875$	−24809.8	−	7375.49i	−0.958540	−	0.284957i
$876$	10209.7			0.393782
$877$	26994.5	−	26994.5i	1.03939	−	1.03939i	0.0401931	−	0.999192i	$-0.487203\pi$
$877$	26994.5	−	26994.5i	1.03939	−	1.03939i	0.999192	−	0.0401931i	$-0.0127973\pi$
$878$	−3009.86	+	3009.86i	−0.115692	+	0.115692i
$879$			6653.91i			0.255325i
$880$	7302.38	−	16405.8i	0.279731	−	0.628452i
$881$		−	14885.5i		−	0.569244i	−0.958640	−	0.284622i	$-0.908132\pi$
$881$		−	14885.5i		−	0.569244i	0.958640	−	0.284622i	$-0.0918681\pi$
$882$	−1449.13	+	3232.54i	−0.0553227	+	0.123407i
$883$	−1000.38	−	1000.38i	−0.0381264	−	0.0381264i	0.687787	−	0.725913i	$-0.258582\pi$
$883$	−1000.38	−	1000.38i	−0.0381264	−	0.0381264i	−0.725913	+	0.687787i	$0.758582\pi$
$884$		−	4145.05i		−	0.157707i
$885$	−1495.80	−	3895.54i	−0.0568143	−	0.147963i
$886$	−715.819			−0.0271427
$887$	−32848.8	−	32848.8i	−1.24347	−	1.24347i	−0.958553	−	0.284915i	$-0.908034\pi$
$887$	−32848.8	−	32848.8i	−1.24347	−	1.24347i	−0.284915	−	0.958553i	$-0.591966\pi$
$888$	−11508.9	+	11508.9i	−0.434925	+	0.434925i
$889$	1731.60	−	318.645i	0.0653272	−	0.0120214i
$890$	5902.34	+	15371.6i	0.222300	+	0.578941i
$891$	−3811.99			−0.143329
$892$	−18371.8	−	18371.8i	−0.689612	−	0.689612i
$893$	−40825.7	−	40825.7i	−1.52988	−	1.52988i
$894$	−6680.98			−0.249939
$895$	−5921.40	−	2635.68i	−0.221151	−	0.0984368i
$896$	−4946.99	−	26883.2i	−0.184450	−	1.00235i
$897$	−884.568	+	884.568i	−0.0329263	+	0.0329263i
$898$	−5984.43	−	5984.43i	−0.222386	−	0.222386i
$899$	−7735.48			−0.286977
$900$	−5031.97	−	5586.35i	−0.186369	−	0.206902i
$901$			38749.9i			1.43279i
$902$	−9870.82	−	9870.82i	−0.364371	−	0.364371i
$903$	−21452.4	−	14784.2i	−0.790577	−	0.544837i
$904$			5431.13i			0.199819i
$905$	12131.8	+	5399.98i	0.445606	+	0.198344i
$906$		−	5093.45i		−	0.186775i
$907$	−3132.55	+	3132.55i	−0.114680	+	0.114680i	−0.762118	−	0.647438i	$-0.775840\pi$
$907$	−3132.55	+	3132.55i	−0.114680	+	0.114680i	0.647438	+	0.762118i	$0.275840\pi$
$908$	−16358.7	+	16358.7i	−0.597888	+	0.597888i
$909$	1000.92			0.0365219
$910$	1113.83	+	1822.43i	0.0405749	+	0.0663879i
$911$	−18810.6			−0.684108			−0.342054	−	0.939680i	$-0.611123\pi$
$911$	−18810.6			−0.684108			−0.342054	+	0.939680i	$0.611123\pi$
$912$	−8883.50	+	8883.50i	−0.322546	+	0.322546i
$913$	−1591.29	+	1591.29i	−0.0576824	+	0.0576824i
$914$			4674.41i			0.169164i
$915$	−12222.1	+	4693.02i	−0.441586	+	0.169559i
$916$		−	42736.1i		−	1.54153i
$917$	23468.6	−	34053.7i	0.845148	−	1.22634i
$918$	1511.73	+	1511.73i	0.0543513	+	0.0543513i
$919$			30657.2i			1.10042i	0.835025	+	0.550212i	$0.185453\pi$
$919$			30657.2i			1.10042i	−0.835025	+	0.550212i	$0.814547\pi$
$920$	7984.04	+	3553.78i	0.286115	+	0.127353i
$921$	−27445.4			−0.981931
$922$	11034.7	+	11034.7i	0.394151	+	0.394151i
$923$	933.911	−	933.911i	0.0333045	−	0.0333045i
$924$	3162.59	+	17186.3i	0.112599	+	0.611892i
$925$	40193.5	+	2098.50i	1.42871	+	0.0745927i
$926$	−6141.50			−0.217951
$927$	−3111.21	−	3111.21i	−0.110233	−	0.110233i
$928$	13751.5	+	13751.5i	0.486439	+	0.486439i
$929$	1690.64			0.0597072			0.0298536	−	0.999554i	$-0.490496\pi$
$929$	1690.64			0.0597072			0.0298536	+	0.999554i	$0.490496\pi$
$930$	−1083.03	+	2433.18i	−0.0381872	+	0.0857926i
$931$	−14982.1	−	39329.9i	−0.527410	−	1.38452i
$932$	−4284.40	+	4284.40i	−0.150580	+	0.150580i
$933$	−22130.7	−	22130.7i	−0.776556	−	0.776556i
$934$	−4736.49			−0.165934
$935$	33893.0	−	13014.1i	1.18547	−	0.455195i
$936$			1363.11i			0.0476011i
$937$	−9415.33	−	9415.33i	−0.328266	−	0.328266i	0.523661	−	0.851927i	$-0.324566\pi$
$937$	−9415.33	−	9415.33i	−0.328266	−	0.328266i	−0.851927	+	0.523661i	$0.824566\pi$
$938$	−2948.45	+	4278.30i	−0.102634	+	0.148925i
$939$		−	22159.5i		−	0.770124i
$940$	−12602.9	−	32822.1i	−0.437300	−	1.13887i
$941$			40817.7i			1.41405i	0.707190	+	0.707024i	$0.249963\pi$
$941$			40817.7i			1.41405i	−0.707190	+	0.707024i	$0.750037\pi$
$942$	522.841	−	522.841i	0.0180840	−	0.0180840i
$943$	−8478.95	+	8478.95i	−0.292802	+	0.292802i
$944$	−4246.01			−0.146394
$945$	5434.68	+	1311.53i	0.187080	+	0.0451472i
$946$	25324.1			0.870358
$947$	36885.1	−	36885.1i	1.26569	−	1.26569i	0.317394	−	0.948294i	$-0.397192\pi$
$947$	36885.1	−	36885.1i	1.26569	−	1.26569i	0.948294	−	0.317394i	$-0.102808\pi$
$948$	16895.8	−	16895.8i	0.578851	−	0.578851i
$949$			4577.29i			0.156570i
$950$	−17576.9	−	917.691i	−0.600286	−	0.0313409i
$951$		−	22583.9i		−	0.770067i
$952$	12218.7	−	17729.7i	0.415977	−	0.603597i
$953$	−19383.6	−	19383.6i	−0.658864	−	0.658864i	0.296247	−	0.955111i	$-0.404265\pi$
$953$	−19383.6	−	19383.6i	−0.658864	−	0.658864i	−0.955111	+	0.296247i	$0.904265\pi$
$954$		−	5800.06i		−	0.196839i
$955$	4419.72	−	9929.48i	0.149758	−	0.336451i
$956$	38121.2			1.28967
$957$	−11160.5	−	11160.5i	−0.376977	−	0.376977i
$958$	−8659.07	+	8659.07i	−0.292027	+	0.292027i
$959$	−5711.66	+	1051.05i	−0.192324	+	0.0353911i
$960$	−2298.39	+	882.529i	−0.0772710	+	0.0296703i
$961$	25003.0			0.839281
$962$	−2348.50	−	2348.50i	−0.0787098	−	0.0787098i
$963$	12401.5	+	12401.5i	0.414988	+	0.414988i
$964$	31713.3			1.05956
$965$	−18860.4	+	7241.98i	−0.629160	+	0.241583i
$966$	−2908.95	+	535.299i	−0.0968882	+	0.0178292i
$967$	10511.9	−	10511.9i	0.349578	−	0.349578i	−0.510375	−	0.859952i	$-0.670493\pi$
$967$	10511.9	−	10511.9i	0.349578	−	0.349578i	0.859952	+	0.510375i	$0.170493\pi$
$968$	−10530.0	−	10530.0i	−0.349634	−	0.349634i
$969$	−25399.6			−0.842055
$970$	1567.82	−	3522.33i	0.0518967	−	0.116593i
$971$			11937.1i			0.394520i	0.980351	+	0.197260i	$0.0632042\pi$
$971$			11937.1i			0.394520i	−0.980351	+	0.197260i	$0.936796\pi$
$972$	1148.34	+	1148.34i	0.0378941	+	0.0378941i
$973$	−28730.9	−	19800.3i	−0.946630	−	0.652383i
$974$		−	3030.06i		−	0.0996811i
$975$	2504.52	−	2255.98i	0.0822655	−	0.0741016i
$976$			13321.8i			0.436905i
$977$	−35517.3	+	35517.3i	−1.16305	+	1.16305i	−0.179244	+	0.983805i	$0.557365\pi$
$977$	−35517.3	+	35517.3i	−1.16305	+	1.16305i	−0.983805	+	0.179244i	$0.942635\pi$
$978$	5434.25	−	5434.25i	0.177677	−	0.177677i
$979$	−60398.1			−1.97174
$980$	1404.18	−	25590.3i	0.0457704	−	0.834136i
$981$	−15404.6			−0.501356
$982$	−12455.0	+	12455.0i	−0.404739	+	0.404739i
$983$	32641.2	−	32641.2i	1.05910	−	1.05910i	0.0609579	−	0.998140i	$-0.480584\pi$
$983$	32641.2	−	32641.2i	1.05910	−	1.05910i	0.998140	−	0.0609579i	$-0.0194155\pi$
$984$			13066.0i			0.423300i
$985$	5440.68	+	14169.3i	0.175994	+	0.458346i
$986$			8851.88i			0.285904i
$987$	21526.6	+	14835.4i	0.694225	+	0.478435i
$988$	−5212.12	−	5212.12i	−0.167834	−	0.167834i
$989$		−	21753.2i		−	0.699406i
$990$	−5073.08	+	1947.95i	−0.162862	+	0.0625352i
$991$	2297.54			0.0736465			0.0368232	−	0.999322i	$-0.488276\pi$
$991$	2297.54			0.0736465			0.0368232	+	0.999322i	$0.488276\pi$
$992$	8511.70	+	8511.70i	0.272426	+	0.272426i
$993$	17788.2	−	17788.2i	0.568470	−	0.568470i
$994$	3071.22	−	565.160i	0.0980013	−	0.0180340i
$995$	−14340.7	+	32218.3i	−0.456915	+	1.02652i
$996$	958.735			0.0305007
$997$	−4284.98	−	4284.98i	−0.136115	−	0.136115i	0.635766	−	0.771882i	$-0.280684\pi$
$997$	−4284.98	−	4284.98i	−0.136115	−	0.136115i	−0.771882	+	0.635766i	$0.780684\pi$
$998$	−5728.42	−	5728.42i	−0.181693	−	0.181693i
$999$	−8693.62			−0.275329

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.m.a.13.11	✓	48
5.2	odd	4	inner	105.4.m.a.97.12	yes	48
7.6	odd	2	inner	105.4.m.a.13.12	yes	48
35.27	even	4	inner	105.4.m.a.97.11	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.m.a.13.11	✓	48	1.1	even	1	trivial
105.4.m.a.13.12	yes	48	7.6	odd	2	inner
105.4.m.a.97.11	yes	48	35.27	even	4	inner
105.4.m.a.97.12	yes	48	5.2	odd	4	inner

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.811442 + 0.811442i) q^{2} +(-2.12132 + 2.12132i) q^{3} +6.68312i q^{4} +(-4.54645 + 10.2142i) q^{5} -3.44266i q^{6} +(-15.2496 - 10.5095i) q^{7} +(-11.9145 - 11.9145i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(-0.811442 + 0.811442i) q^{2} +(-2.12132 + 2.12132i) q^{3} +6.68312i q^{4} +(-4.54645 + 10.2142i) q^{5} -3.44266i q^{6} +(-15.2496 - 10.5095i) q^{7} +(-11.9145 - 11.9145i) q^{8} -9.00000i q^{9} +(-4.59905 - 11.9774i) q^{10} +47.0616 q^{11} +(-14.1770 - 14.1770i) q^{12} +(6.35598 - 6.35598i) q^{13} +(20.9020 - 3.84634i) q^{14} +(-12.0231 - 31.3121i) q^{15} -34.1292 q^{16} +(-48.7908 - 48.7908i) q^{17} +(7.30297 + 7.30297i) q^{18} -122.702 q^{19} +(-68.2628 - 30.3845i) q^{20} +(54.6433 - 10.0553i) q^{21} +(-38.1877 + 38.1877i) q^{22} +(32.8029 + 32.8029i) q^{23} +50.5489 q^{24} +(-83.6597 - 92.8766i) q^{25} +10.3150i q^{26} +(19.0919 + 19.0919i) q^{27} +(70.2362 - 101.915i) q^{28} +111.792i q^{29} +(35.1640 + 15.6518i) q^{30} +69.1953i q^{31} +(123.010 - 123.010i) q^{32} +(-99.8327 + 99.8327i) q^{33} +79.1817 q^{34} +(176.677 - 107.982i) q^{35} +60.1481 q^{36} +(-227.678 + 227.678i) q^{37} +(99.5657 - 99.5657i) q^{38} +26.9661i q^{39} +(175.866 - 67.5284i) q^{40} +258.481i q^{41} +(-36.1805 + 52.4992i) q^{42} +(-331.574 - 331.574i) q^{43} +314.518i q^{44} +(91.9278 + 40.9180i) q^{45} -53.2353 q^{46} +(332.722 + 332.722i) q^{47} +(72.3989 - 72.3989i) q^{48} +(122.101 + 320.531i) q^{49} +(143.249 + 7.47901i) q^{50} +207.002 q^{51} +(42.4778 + 42.4778i) q^{52} +(-397.103 - 397.103i) q^{53} -30.9839 q^{54} +(-213.963 + 480.696i) q^{55} +(56.4763 + 306.907i) q^{56} +(260.291 - 260.291i) q^{57} +(-90.7126 - 90.7126i) q^{58} +124.410 q^{59} +(209.262 - 80.3520i) q^{60} -390.333i q^{61} +(-56.1479 - 56.1479i) q^{62} +(-94.5854 + 137.247i) q^{63} -73.4027i q^{64} +(36.0241 + 93.8183i) q^{65} -162.017i q^{66} +(-172.872 + 172.872i) q^{67} +(326.075 - 326.075i) q^{68} -139.171 q^{69} +(-55.7426 + 230.984i) q^{70} +146.934 q^{71} +(-107.230 + 107.230i) q^{72} +(-360.078 + 360.078i) q^{73} -369.495i q^{74} +(374.490 + 19.5521i) q^{75} -820.034i q^{76} +(-717.671 - 494.593i) q^{77} +(-21.8814 - 21.8814i) q^{78} +1191.77i q^{79} +(155.166 - 348.602i) q^{80} -81.0000 q^{81} +(-209.743 - 209.743i) q^{82} +(-33.8129 + 33.8129i) q^{83} +(67.2011 + 365.188i) q^{84} +(720.183 - 276.534i) q^{85} +538.106 q^{86} +(-237.147 - 237.147i) q^{87} +(-560.715 - 560.715i) q^{88} -1283.38 q^{89} +(-107.797 + 41.3914i) q^{90} +(-163.724 + 30.1282i) q^{91} +(-219.226 + 219.226i) q^{92} +(-146.785 - 146.785i) q^{93} -539.968 q^{94} +(557.859 - 1253.30i) q^{95} +521.886i q^{96} +(212.490 + 212.490i) q^{97} +(-359.171 - 161.014i) q^{98} -423.554i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 4 q^{7} - 168 q^{8}+O(q^{10}) \) 48 * q + 4 * q^7 - 168 * q^8	\( 48 q + 4 q^{7} - 168 q^{8} + 112 q^{11} + 168 q^{15} - 544 q^{16} - 96 q^{21} - 192 q^{22} + 400 q^{23} + 520 q^{25} + 1052 q^{28} - 48 q^{30} - 1344 q^{32} + 392 q^{35} - 1728 q^{36} - 456 q^{37} + 1068 q^{42} + 192 q^{43} - 208 q^{46} + 3528 q^{50} + 672 q^{51} - 1728 q^{53} - 48 q^{56} + 696 q^{57} + 3016 q^{58} + 840 q^{60} - 36 q^{63} - 4720 q^{65} - 4784 q^{67} + 2220 q^{70} - 3088 q^{71} - 1512 q^{72} + 2352 q^{77} + 1416 q^{78} - 3888 q^{81} - 472 q^{85} + 10832 q^{86} + 2128 q^{88} - 5664 q^{91} + 10600 q^{92} - 1368 q^{93} - 6912 q^{95} - 3888 q^{98}+O(q^{100}) \) 48 * q + 4 * q^7 - 168 * q^8 + 112 * q^11 + 168 * q^15 - 544 * q^16 - 96 * q^21 - 192 * q^22 + 400 * q^23 + 520 * q^25 + 1052 * q^28 - 48 * q^30 - 1344 * q^32 + 392 * q^35 - 1728 * q^36 - 456 * q^37 + 1068 * q^42 + 192 * q^43 - 208 * q^46 + 3528 * q^50 + 672 * q^51 - 1728 * q^53 - 48 * q^56 + 696 * q^57 + 3016 * q^58 + 840 * q^60 - 36 * q^63 - 4720 * q^65 - 4784 * q^67 + 2220 * q^70 - 3088 * q^71 - 1512 * q^72 + 2352 * q^77 + 1416 * q^78 - 3888 * q^81 - 472 * q^85 + 10832 * q^86 + 2128 * q^88 - 5664 * q^91 + 10600 * q^92 - 1368 * q^93 - 6912 * q^95 - 3888 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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