LMFDB - Embedded newform 105.3.w.a.17.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(17,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 2]))

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

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

chi := DirichletCharacter("105.17");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			17.7
Character	$\chi$	$=$	105.17
Dual form			105.3.w.a.68.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.40293 - 0.643864i) q^{2} +(2.79517 - 1.08950i) q^{3} +(1.89543 + 1.09433i) q^{4} +(-1.28155 - 4.83297i) q^{5} +(-7.41810 + 0.818277i) q^{6} +(-6.92060 - 1.05130i) q^{7} +(3.18629 + 3.18629i) q^{8} +(6.62599 - 6.09067i) q^{9} +(-0.0322977 + 12.4385i) q^{10} +(-0.372125 - 0.214846i) q^{11} +(6.49031 + 0.993767i) q^{12} +(-10.4973 - 10.4973i) q^{13} +(15.9529 + 6.98214i) q^{14} +(-8.84767 - 12.1128i) q^{15} +(-9.98221 - 17.2897i) q^{16} +(-19.0543 + 5.10559i) q^{17} +(-19.8434 + 10.3692i) q^{18} +(-0.341650 - 0.591755i) q^{19} +(2.85976 - 10.5630i) q^{20} +(-20.4897 + 4.60141i) q^{21} +(0.755860 + 0.755860i) q^{22} +(9.41953 - 35.1542i) q^{23} +(12.3777 + 5.43478i) q^{24} +(-21.7153 + 12.3874i) q^{25} +(18.4655 + 31.9832i) q^{26} +(11.8850 - 24.2435i) q^{27} +(-11.9670 - 9.56606i) q^{28} +29.5987 q^{29} +(13.4614 + 34.8028i) q^{30} +(45.1246 + 26.0527i) q^{31} +(8.18932 + 30.5629i) q^{32} +(-1.27423 - 0.195104i) q^{33} +49.0736 q^{34} +(3.78819 + 34.7944i) q^{35} +(19.2243 - 4.29342i) q^{36} +(4.11887 - 15.3718i) q^{37} +(0.439953 + 1.64193i) q^{38} +(-40.7786 - 17.9050i) q^{39} +(11.3159 - 19.4826i) q^{40} +23.3438 q^{41} +(52.1980 + 2.13570i) q^{42} +(-3.53920 + 3.53920i) q^{43} +(-0.470224 - 0.814452i) q^{44} +(-37.9276 - 24.2177i) q^{45} +(-45.2690 + 78.4082i) q^{46} +(-5.58075 + 20.8276i) q^{47} +(-46.7391 - 37.4521i) q^{48} +(46.7895 + 14.5513i) q^{49} +(60.1561 - 15.7844i) q^{50} +(-47.6977 + 35.0307i) q^{51} +(-8.40942 - 31.3844i) q^{52} +(47.1211 - 12.6261i) q^{53} +(-44.1684 + 50.6031i) q^{54} +(-0.561450 + 2.07381i) q^{55} +(-18.7013 - 25.4008i) q^{56} +(-1.59969 - 1.28183i) q^{57} +(-71.1237 - 19.0575i) q^{58} +(-20.7598 - 11.9857i) q^{59} +(-3.51481 - 32.6411i) q^{60} +(33.3740 - 19.2685i) q^{61} +(-91.6571 - 91.6571i) q^{62} +(-52.2590 + 35.1852i) q^{63} +1.14413i q^{64} +(-37.2804 + 64.1861i) q^{65} +(2.93627 + 1.28925i) q^{66} +(68.3440 - 18.3127i) q^{67} +(-41.7033 - 11.1744i) q^{68} +(-11.9711 - 108.525i) q^{69} +(13.3001 - 86.0477i) q^{70} -121.143i q^{71} +(40.5190 + 1.70570i) q^{72} +(-35.3107 + 9.46146i) q^{73} +(-19.7947 + 34.2855i) q^{74} +(-47.2019 + 58.2836i) q^{75} -1.49551i q^{76} +(2.34946 + 1.87808i) q^{77} +(86.4600 + 69.2805i) q^{78} +(24.3623 - 14.0656i) q^{79} +(-70.7679 + 70.4013i) q^{80} +(6.80754 - 80.7134i) q^{81} +(-56.0936 - 15.0302i) q^{82} +(-48.6396 + 48.6396i) q^{83} +(-43.8721 - 13.7007i) q^{84} +(49.0943 + 85.5460i) q^{85} +(10.7832 - 6.22569i) q^{86} +(82.7335 - 32.2477i) q^{87} +(-0.501135 - 1.87026i) q^{88} +(-91.8429 + 53.0255i) q^{89} +(75.5445 + 82.6138i) q^{90} +(61.6120 + 83.6837i) q^{91} +(56.3241 - 56.3241i) q^{92} +(154.516 + 23.6587i) q^{93} +(26.8203 - 46.4542i) q^{94} +(-2.42210 + 2.40955i) q^{95} +(56.1888 + 76.5065i) q^{96} +(-87.0772 + 87.0772i) q^{97} +(-103.063 - 65.0919i) q^{98} +(-3.77426 + 0.842919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) $ 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Character values

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

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−2.40293	−	0.643864i	−1.20147	−	0.321932i	−0.398058	−	0.917360i	$-0.630316\pi$
$2$	−2.40293	−	0.643864i	−1.20147	−	0.321932i	−0.803409	+	0.595428i	$0.796982\pi$
$3$	2.79517	−	1.08950i	0.931725	−	0.363166i
$3$	2.79517	−	1.08950i	0.931725	−	0.363166i
$4$	1.89543	+	1.09433i	0.473857	+	0.273581i
$5$	−1.28155	−	4.83297i	−0.256310	−	0.966595i
$5$	−1.28155	−	4.83297i	−0.256310	−	0.966595i
$6$	−7.41810	+	0.818277i	−1.23635	+	0.136380i
$7$	−6.92060	−	1.05130i	−0.988658	−	0.150186i
$7$	−6.92060	−	1.05130i	−0.988658	−	0.150186i
$8$	3.18629	+	3.18629i	0.398286	+	0.398286i
$9$	6.62599	−	6.09067i	0.736221	−	0.676741i
$10$	−0.0322977	+	12.4385i	−0.00322977	+	1.24385i
$11$	−0.372125	−	0.214846i	−0.0338295	−	0.0195315i	0.482990	−	0.875626i	$-0.339551\pi$
$11$	−0.372125	−	0.214846i	−0.0338295	−	0.0195315i	−0.516819	+	0.856094i	$0.672884\pi$
$12$	6.49031	+	0.993767i	0.540859	+	0.0828139i
$13$	−10.4973	−	10.4973i	−0.807486	−	0.807486i	0.176766	−	0.984253i	$-0.443436\pi$
$13$	−10.4973	−	10.4973i	−0.807486	−	0.807486i	−0.984253	+	0.176766i	$0.943436\pi$
$14$	15.9529	+	6.98214i	1.13949	+	0.498724i
$15$	−8.84767	−	12.1128i	−0.589844	−	0.807517i
$16$	−9.98221	−	17.2897i	−0.623888	−	1.08061i
$17$	−19.0543	+	5.10559i	−1.12084	+	0.300329i	−0.771225	−	0.636563i	$-0.780356\pi$
$17$	−19.0543	+	5.10559i	−1.12084	+	0.300329i	−0.349619	+	0.936892i	$0.613689\pi$
$18$	−19.8434	+	10.3692i	−1.10241	+	0.576068i
$19$	−0.341650	−	0.591755i	−0.0179816	−	0.0311450i	0.856895	−	0.515492i	$-0.172391\pi$
$19$	−0.341650	−	0.591755i	−0.0179816	−	0.0311450i	−0.874876	+	0.484347i	$0.839057\pi$
$20$	2.85976	−	10.5630i	0.142988	−	0.528149i
$21$	−20.4897	+	4.60141i	−0.975699	+	0.219115i
$22$	0.755860	+	0.755860i	0.0343573	+	0.0343573i
$23$	9.41953	−	35.1542i	0.409545	−	1.52844i	−0.385972	−	0.922510i	$-0.626134\pi$
$23$	9.41953	−	35.1542i	0.409545	−	1.52844i	0.795517	−	0.605931i	$-0.207199\pi$
$24$	12.3777	+	5.43478i	0.515737	+	0.226449i
$25$	−21.7153	+	12.3874i	−0.868610	+	0.495496i
$26$	18.4655	+	31.9832i	0.710212	+	1.23012i
$27$	11.8850	−	24.2435i	0.440186	−	0.897906i
$28$	−11.9670	−	9.56606i	−0.427394	−	0.341645i
$29$	29.5987			1.02064			0.510322	−	0.859983i	$-0.329526\pi$
$29$	29.5987			1.02064			0.510322	+	0.859983i	$0.329526\pi$
$30$	13.4614	+	34.8028i	0.448713	+	1.16009i
$31$	45.1246	+	26.0527i	1.45563	+	0.840410i	0.998792	−	0.0491377i	$-0.0156473\pi$
$31$	45.1246	+	26.0527i	1.45563	+	0.840410i	0.456842	+	0.889548i	$0.348981\pi$
$32$	8.18932	+	30.5629i	0.255916	+	0.955092i
$33$	−1.27423	−	0.195104i	−0.0386130	−	0.00591225i
$34$	49.0736			1.44334
$35$	3.78819	+	34.7944i	0.108234	+	0.994125i
$36$	19.2243	−	4.29342i	0.534007	−	0.119262i
$37$	4.11887	−	15.3718i	0.111321	−	0.415455i	−0.887665	−	0.460490i	$-0.847674\pi$
$37$	4.11887	−	15.3718i	0.111321	−	0.415455i	0.998985	+	0.0450359i	$0.0143402\pi$
$38$	0.439953	+	1.64193i	0.0115777	+	0.0432086i
$39$	−40.7786	−	17.9050i	−1.04561	−	0.459104i
$40$	11.3159	−	19.4826i	0.282897	−	0.487066i
$41$	23.3438			0.569360			0.284680	−	0.958623i	$-0.408113\pi$
$41$	23.3438			0.569360			0.284680	+	0.958623i	$0.408113\pi$
$42$	52.1980	+	2.13570i	1.24281	+	0.0508499i
$43$	−3.53920	+	3.53920i	−0.0823069	+	0.0823069i	−0.747062	−	0.664755i	$-0.768536\pi$
$43$	−3.53920	+	3.53920i	−0.0823069	+	0.0823069i	0.664755	+	0.747062i	$0.268536\pi$
$44$	−0.470224	−	0.814452i	−0.0106869	−	0.0185103i
$45$	−37.9276	−	24.2177i	−0.842835	−	0.538172i
$46$	−45.2690	+	78.4082i	−0.984109	+	1.70453i
$47$	−5.58075	+	20.8276i	−0.118739	+	0.443141i	−0.999539	−	0.0303472i	$-0.990339\pi$
$47$	−5.58075	+	20.8276i	−0.118739	+	0.443141i	0.880800	+	0.473488i	$0.157005\pi$
$48$	−46.7391	−	37.4521i	−0.973730	−	0.780252i
$49$	46.7895	+	14.5513i	0.954888	+	0.296965i
$50$	60.1561	−	15.7844i	1.20312	−	0.315688i
$51$	−47.6977	+	35.0307i	−0.935248	+	0.686876i
$52$	−8.40942	−	31.3844i	−0.161720	−	0.603546i
$53$	47.1211	−	12.6261i	0.889078	−	0.238228i	0.214758	−	0.976667i	$-0.431104\pi$
$53$	47.1211	−	12.6261i	0.889078	−	0.238228i	0.674320	+	0.738439i	$0.264437\pi$
$54$	−44.1684	+	50.6031i	−0.817934	+	0.937095i
$55$	−0.561450	+	2.07381i	−0.0102082	+	0.0377056i
$56$	−18.7013	−	25.4008i	−0.333952	−	0.453586i
$57$	−1.59969	−	1.28183i	−0.0280647	−	0.0224883i
$58$	−71.1237	−	19.0575i	−1.22627	−	0.328578i
$59$	−20.7598	−	11.9857i	−0.351862	−	0.203147i	0.313643	−	0.949541i	$-0.398450\pi$
$59$	−20.7598	−	11.9857i	−0.351862	−	0.203147i	−0.665505	+	0.746394i	$0.731784\pi$
$60$	−3.51481	−	32.6411i	−0.0585802	−	0.544018i
$61$	33.3740	−	19.2685i	0.547115	−	0.315877i	−0.200842	−	0.979624i	$-0.564368\pi$
$61$	33.3740	−	19.2685i	0.547115	−	0.315877i	0.747958	+	0.663746i	$0.231035\pi$
$62$	−91.6571	−	91.6571i	−1.47834	−	1.47834i
$63$	−52.2590	+	35.1852i	−0.829508	+	0.558495i
$64$			1.14413i			0.0178770i
$65$	−37.2804	+	64.1861i	−0.573545	+	0.987479i
$66$	2.93627	+	1.28925i	0.0444889	+	0.0195341i
$67$	68.3440	−	18.3127i	1.02006	−	0.273324i	0.290233	−	0.956956i	$-0.406267\pi$
$67$	68.3440	−	18.3127i	1.02006	−	0.273324i	0.729827	+	0.683632i	$0.239601\pi$
$68$	−41.7033	−	11.1744i	−0.613284	−	0.164329i
$69$	−11.9711	−	108.525i	−0.173495	−	1.57282i
$70$	13.3001	−	86.0477i	0.190001	−	1.22925i
$71$		−	121.143i		−	1.70625i	−0.521711	−	0.853123i	$-0.674706\pi$
$71$		−	121.143i		−	1.70625i	0.521711	−	0.853123i	$-0.325294\pi$
$72$	40.5190	+	1.70570i	0.562763	+	0.0236903i
$73$	−35.3107	+	9.46146i	−0.483708	+	0.129609i	−0.492429	−	0.870353i	$-0.663891\pi$
$73$	−35.3107	+	9.46146i	−0.483708	+	0.129609i	0.00872079	+	0.999962i	$0.497224\pi$
$74$	−19.7947	+	34.2855i	−0.267496	+	0.463317i
$75$	−47.2019	+	58.2836i	−0.629358	+	0.777115i
$76$		−	1.49551i		−	0.0196777i
$77$	2.34946	+	1.87808i	0.0305125	+	0.0243907i
$78$	86.4600	+	69.2805i	1.10846	+	0.888212i
$79$	24.3623	−	14.0656i	0.308383	−	0.178045i	−0.337820	−	0.941211i	$-0.609689\pi$
$79$	24.3623	−	14.0656i	0.308383	−	0.178045i	0.646203	+	0.763166i	$0.276356\pi$
$80$	−70.7679	+	70.4013i	−0.884599	+	0.880017i
$81$	6.80754	−	80.7134i	0.0840437	−	0.996462i
$82$	−56.0936	−	15.0302i	−0.684068	−	0.183295i
$83$	−48.6396	+	48.6396i	−0.586019	+	0.586019i	−0.936551	−	0.350532i	$-0.886001\pi$
$83$	−48.6396	+	48.6396i	−0.586019	+	0.586019i	0.350532	+	0.936551i	$0.386001\pi$
$84$	−43.8721	−	13.7007i	−0.522287	−	0.163104i
$85$	49.0943	+	85.5460i	0.577580	+	1.00642i
$86$	10.7832	−	6.22569i	0.125386	−	0.0723918i
$87$	82.7335	−	32.2477i	0.950960	−	0.370663i
$88$	−0.501135	−	1.87026i	−0.00569472	−	0.0212530i
$89$	−91.8429	+	53.0255i	−1.03194	+	0.595793i	−0.917541	−	0.397642i	$-0.869829\pi$
$89$	−91.8429	+	53.0255i	−1.03194	+	0.595793i	−0.114402	+	0.993434i	$0.536495\pi$
$90$	75.5445	+	82.6138i	0.839383	+	0.917931i
$91$	61.6120	+	83.6837i	0.677055	+	0.919601i
$92$	56.3241	−	56.3241i	0.612219	−	0.612219i
$93$	154.516	+	23.6587i	1.66146	+	0.254395i
$94$	26.8203	−	46.4542i	0.285323	−	0.494193i
$95$	−2.42210	+	2.40955i	−0.0254957	+	0.0253637i
$96$	56.1888	+	76.5065i	0.585300	+	0.796943i
$97$	−87.0772	+	87.0772i	−0.897703	+	0.897703i	−0.995233	−	0.0975294i	$-0.968906\pi$
$97$	−87.0772	+	87.0772i	−0.897703	+	0.897703i	0.0975294	+	0.995233i	$0.468906\pi$
$98$	−103.063	−	65.0919i	−1.05166	−	0.664203i
$99$	−3.77426	+	0.842919i	−0.0381238	+	0.00851433i
$100$	−54.7155	−	0.284151i	−0.547155	−	0.00284151i
$101$	−2.33073	+	4.03694i	−0.0230765	+	0.0399697i	−0.877333	−	0.479882i	$-0.840679\pi$
$101$	−2.33073	+	4.03694i	−0.0230765	+	0.0399697i	0.854257	+	0.519852i	$0.174013\pi$
$102$	137.169	−	53.4656i	1.34480	−	0.524172i
$103$	32.2761	−	120.456i	0.313360	−	1.16948i	−0.612147	−	0.790744i	$-0.709694\pi$
$103$	32.2761	−	120.456i	0.313360	−	1.16948i	0.925507	−	0.378731i	$-0.123639\pi$
$104$		−	66.8950i		−	0.643222i
$105$	48.4970	+	93.1291i	0.461877	+	0.886944i
$106$	−121.358			−1.14489
$107$	45.9887	+	12.3226i	0.429801	+	0.115165i	0.467233	−	0.884134i	$-0.345251\pi$
$107$	45.9887	+	12.3226i	0.429801	+	0.115165i	−0.0374319	+	0.999299i	$0.511918\pi$
$108$	49.0575	−	32.9456i	0.454236	−	0.305052i
$109$	4.67775	+	2.70070i	0.0429152	+	0.0247771i	0.521304	−	0.853371i	$-0.325446\pi$
$109$	4.67775	+	2.70070i	0.0429152	+	0.0247771i	−0.478389	+	0.878148i	$0.658779\pi$
$110$	2.68438	−	4.62172i	0.0244034	−	0.0420157i
$111$	−5.23461	−	47.4544i	−0.0471586	−	0.427517i
$112$	50.9062	+	130.149i	0.454520	+	1.16205i
$113$	81.5799	+	81.5799i	0.721946	+	0.721946i	0.969001	−	0.247055i	$-0.0794629\pi$
$113$	81.5799	+	81.5799i	0.721946	+	0.721946i	−0.247055	+	0.969001i	$0.579463\pi$
$114$	3.01862	+	4.11014i	0.0264791	+	0.0360539i
$115$	−181.971	−	0.472505i	−1.58235	−	0.00410874i
$116$	56.1022	+	32.3906i	0.483639	+	0.279229i
$117$	−133.491	−	5.61947i	−1.14095	−	0.0480297i
$118$	42.1673	+	42.1673i	0.357350	+	0.357350i
$119$	137.235	−	15.3019i	1.15324	−	0.128588i
$120$	10.4035	−	66.7860i	0.0866960	−	0.556550i
$121$	−60.4077	−	104.629i	−0.499237	−	0.864704i
$122$	−92.6019	+	24.8126i	−0.759032	+	0.203382i
$123$	65.2499	−	25.4330i	0.530487	−	0.206772i
$124$	57.0203	+	98.7621i	0.459841	+	0.796468i
$125$	87.6971	+	89.0742i	0.701577	+	0.712593i
$126$	148.229	−	50.9000i	1.17642	−	0.403968i
$127$	−90.7970	−	90.7970i	−0.714937	−	0.714937i	0.252627	−	0.967564i	$-0.418705\pi$
$127$	−90.7970	−	90.7970i	−0.714937	−	0.714937i	−0.967564	+	0.252627i	$0.918705\pi$
$128$	33.4939	−	125.001i	0.261671	−	0.976570i
$129$	−6.03673	+	13.7486i	−0.0467963	+	0.106578i
$130$	130.910	−	130.231i	1.00700	−	1.00178i
$131$	−93.4605	−	161.878i	−0.713439	−	1.23571i	−0.963559	−	0.267497i	$-0.913803\pi$
$131$	−93.4605	−	161.878i	−0.713439	−	1.23571i	0.250120	−	0.968215i	$-0.419530\pi$
$132$	−2.20170	−	1.76423i	−0.0166795	−	0.0133653i
$133$	1.74231	+	4.45448i	0.0131001	+	0.0334924i
$134$	−176.017			−1.31356
$135$	−132.399	−	26.3708i	−0.980736	−	0.195339i
$136$	−76.9806	−	44.4447i	−0.566033	−	0.326800i
$137$	43.7217	+	163.172i	0.319137	+	1.19103i	0.920076	+	0.391740i	$0.128127\pi$
$137$	43.7217	+	163.172i	0.319137	+	1.19103i	−0.600939	+	0.799295i	$0.705207\pi$
$138$	−41.1092	+	268.485i	−0.297893	+	1.94554i
$139$	−36.2803			−0.261009			−0.130505	−	0.991448i	$-0.541660\pi$
$139$	−36.2803			−0.261009			−0.130505	+	0.991448i	$0.541660\pi$
$140$	−30.8961	+	70.0957i	−0.220687	+	0.500684i
$141$	7.09249	+	64.2970i	0.0503013	+	0.456007i
$142$	−77.9999	+	291.100i	−0.549295	+	2.05000i
$143$	1.65100	+	6.16163i	0.0115455	+	0.0430883i
$144$	−171.448	−	53.7630i	−1.19061	−	0.373354i
$145$	−37.9322	−	143.050i	−0.261602	−	0.986550i
$146$	90.9411			0.622884
$147$	146.638	−	10.3037i	0.997540	−	0.0700930i
$148$	24.6288	−	24.6288i	0.166411	−	0.166411i
$149$	93.3573	+	161.700i	0.626559	+	1.08523i	0.988237	+	0.152929i	$0.0488706\pi$
$149$	93.3573	+	161.700i	0.626559	+	1.08523i	−0.361678	+	0.932303i	$0.617796\pi$
$150$	150.950	−	109.660i	1.00633	−	0.731067i
$151$	−70.5808	+	122.249i	−0.467422	+	0.809599i	−0.999307	−	0.0372175i	$-0.988151\pi$
$151$	−70.5808	+	122.249i	−0.467422	+	0.809599i	0.531885	+	0.846817i	$0.321484\pi$
$152$	0.796908	−	2.97410i	0.00524282	−	0.0195665i
$153$	−95.1574	+	149.883i	−0.621944	+	0.979629i
$154$	−4.43637	−	6.02564i	−0.0288076	−	0.0391276i
$155$	68.0826	−	251.474i	0.439243	−	1.62241i
$156$	−57.6990	−	78.5628i	−0.369865	−	0.503608i
$157$	−29.6170	−	110.532i	−0.188644	−	0.704028i	−0.993821	−	0.110994i	$-0.964597\pi$
$157$	−29.6170	−	110.532i	−0.188644	−	0.704028i	0.805178	−	0.593034i	$-0.202070\pi$
$158$	−67.5972	+	18.1126i	−0.427830	+	0.114637i
$159$	117.956	−	86.6304i	0.741860	−	0.544845i
$160$	137.215	−	78.7467i	0.857593	−	0.492167i
$161$	−102.146	+	233.385i	−0.634450	+	1.44960i
$162$	−68.3265	+	189.566i	−0.421769	+	1.17016i
$163$	155.164	+	41.5762i	0.951929	+	0.255069i	0.701181	−	0.712984i	$-0.252657\pi$
$163$	155.164	+	41.5762i	0.951929	+	0.255069i	0.250749	+	0.968052i	$0.419323\pi$
$164$	44.2464	+	25.5457i	0.269795	+	0.155766i
$165$	0.690055	+	6.40835i	0.00418215	+	0.0388385i
$166$	148.195	−	85.5604i	0.892741	−	0.515424i
$167$	−41.5542	−	41.5542i	−0.248827	−	0.248827i	0.571662	−	0.820489i	$-0.306299\pi$
$167$	−41.5542	−	41.5542i	−0.248827	−	0.248827i	−0.820489	+	0.571662i	$0.806299\pi$
$168$	−79.9475	−	50.6246i	−0.475878	−	0.301337i
$169$			51.3876i			0.304069i
$170$	−62.8903	−	237.171i	−0.369943	−	1.39513i
$171$	−5.86796	−	1.84009i	−0.0343155	−	0.0107608i
$172$	−10.5813	+	2.83526i	−0.0615193	+	0.0164841i
$173$	190.957	+	51.1669i	1.10380	+	0.295762i	0.764311	−	0.644848i	$-0.223079\pi$
$173$	190.957	+	51.1669i	1.10380	+	0.295762i	0.339489	+	0.940610i	$0.389746\pi$
$174$	−219.566	+	24.2199i	−1.26188	+	0.139195i
$175$	163.306	−	62.8990i	0.933175	−	0.359423i
$176$			8.57857i			0.0487419i
$177$	−71.0857	−	10.8843i	−0.401614	−	0.0614933i
$178$	254.834	−	68.2825i	1.43165	−	0.383609i
$179$	42.3323	−	73.3217i	0.236493	−	0.409619i	−0.723212	−	0.690626i	$-0.757335\pi$
$179$	42.3323	−	73.3217i	0.236493	−	0.409619i	0.959706	+	0.281007i	$0.0906685\pi$
$180$	−45.3869	−	87.4081i	−0.252149	−	0.485600i
$181$			118.195i			0.653009i	0.945196	+	0.326504i	$0.105871\pi$
$181$			118.195i			0.653009i	−0.945196	+	0.326504i	$0.894129\pi$
$182$	−94.1685	−	240.756i	−0.517410	−	1.32284i
$183$	72.2933	−	90.2198i	0.395045	−	0.493004i
$184$	142.025	−	81.9980i	0.771873	−	0.445641i
$185$	−79.5701	−	0.206612i	−0.430109	−	0.00111682i
$186$	−356.058	−	156.337i	−1.91429	−	0.840523i
$187$	8.18752	+	2.19384i	0.0437835	+	0.0117318i
$188$	−33.3701	+	33.3701i	−0.177500	+	0.177500i
$189$	−107.739	+	155.285i	−0.570047	+	0.821612i
$190$	7.37156	−	4.23049i	0.0387977	−	0.0222657i
$191$	−9.72387	+	5.61408i	−0.0509103	+	0.0293931i	−0.525239	−	0.850955i	$-0.676024\pi$
$191$	−9.72387	+	5.61408i	−0.0509103	+	0.0293931i	0.474329	+	0.880348i	$0.342691\pi$
$192$	1.24652	+	3.19804i	0.00649231	+	0.0166564i
$193$	21.8590	+	81.5788i	0.113259	+	0.422688i	0.999151	−	0.0412037i	$-0.0131193\pi$
$193$	21.8590	+	81.5788i	0.113259	+	0.422688i	−0.885892	+	0.463892i	$0.846453\pi$
$194$	265.307	−	153.175i	1.36756	−	0.789561i
$195$	−34.2747	+	220.028i	−0.175768	+	1.12835i
$196$	72.7623	+	78.7839i	0.371236	+	0.401958i
$197$	−205.913	+	205.913i	−1.04524	+	1.04524i	−0.0463167	+	0.998927i	$0.514748\pi$
$197$	−205.913	+	205.913i	−1.04524	+	1.04524i	−0.998927	+	0.0463167i	$0.985252\pi$
$198$	9.61201	+	0.404630i	0.0485455	+	0.00204359i
$199$	−108.730	+	188.326i	−0.546384	+	0.946364i	0.452135	+	0.891950i	$0.350663\pi$
$199$	−108.730	+	188.326i	−0.546384	+	0.946364i	−0.998518	+	0.0544147i	$0.982671\pi$
$200$	−108.661	−	29.7213i	−0.543305	−	0.148606i
$201$	171.082	−	125.648i	0.851153	−	0.625114i
$202$	8.19983	−	8.19983i	0.0405932	−	0.0405932i
$203$	−204.841	−	31.1172i	−1.00907	−	0.153287i
$204$	−128.742	+	14.2013i	−0.631090	+	0.0696144i
$205$	−29.9162	−	112.820i	−0.145933	−	0.550341i
$206$	−155.114	+	268.666i	−0.752983	+	1.30420i
$207$	−151.699	−	290.302i	−0.732843	−	1.40243i
$208$	−76.7090	+	286.282i	−0.368793	+	1.37636i
$209$			0.293609i			0.00140483i
$210$	−56.5726	−	255.009i	−0.269393	−	1.21433i
$211$	80.4077			0.381079			0.190540	−	0.981680i	$-0.438976\pi$
$211$	80.4077			0.381079			0.190540	+	0.981680i	$0.438976\pi$
$212$	103.132	+	27.6341i	0.486470	+	0.130349i
$213$	−131.985	−	338.617i	−0.619650	−	1.58975i
$214$	−102.574	−	59.2209i	−0.479316	−	0.276733i
$215$	21.6405	+	12.5692i	0.100654	+	0.0584613i
$216$	115.116	−	39.3776i	0.532944	−	0.182304i
$217$	−284.900	−	227.740i	−1.31291	−	1.04949i
$218$	−9.50145	−	9.50145i	−0.0435846	−	0.0435846i
$219$	−88.3912	+	64.9173i	−0.403613	+	0.296426i
$220$	−3.33361	+	3.31634i	−0.0151528	+	0.0150743i
$221$	253.615	+	146.424i	1.14758	+	0.662554i
$222$	−17.9758	+	117.400i	−0.0809719	+	0.528829i
$223$	−166.034	−	166.034i	−0.744548	−	0.744548i	0.228901	−	0.973450i	$-0.426487\pi$
$223$	−166.034	−	166.034i	−0.744548	−	0.744548i	−0.973450	+	0.228901i	$0.926487\pi$
$224$	−24.5441	−	220.123i	−0.109572	−	0.982694i
$225$	−68.4376	+	214.339i	−0.304167	+	0.952619i
$226$	−143.505	−	248.558i	−0.634977	−	1.09981i
$227$	379.641	−	101.725i	1.67243	−	0.448126i	0.706665	−	0.707549i	$-0.250199\pi$
$227$	379.641	−	101.725i	1.67243	−	0.448126i	0.965764	+	0.259423i	$0.0835323\pi$
$228$	−1.62935	−	4.18020i	−0.00714627	−	0.0183342i
$229$	100.970	+	174.885i	0.440917	+	0.763691i	0.997758	−	0.0669285i	$-0.0213199\pi$
$229$	100.970	+	174.885i	0.440917	+	0.763691i	−0.556841	+	0.830619i	$0.687987\pi$
$230$	436.959	+	118.300i	1.89982	+	0.514347i
$231$	8.61332	+	2.68984i	0.0372871	+	0.0116443i
$232$	94.3100	+	94.3100i	0.406509	+	0.406509i
$233$	−20.3909	+	76.0997i	−0.0875144	+	0.326608i	−0.995778	−	0.0917892i	$-0.970741\pi$
$233$	−20.3909	+	76.0997i	−0.0875144	+	0.326608i	0.908264	+	0.418397i	$0.137408\pi$
$234$	317.152	+	99.4532i	1.35535	+	0.425014i
$235$	107.811	+	0.279943i	0.458772	+	0.00119125i
$236$	−26.2325	−	45.4360i	−0.111155	−	0.192525i
$237$	52.7724	−	65.8583i	0.222668	−	0.277883i
$238$	−339.619	−	51.5912i	−1.42697	−	0.216770i
$239$	−189.100			−0.791215			−0.395608	−	0.918420i	$-0.629466\pi$
$239$	−189.100			−0.791215			−0.395608	+	0.918420i	$0.629466\pi$
$240$	−121.107	+	273.885i	−0.504610	+	1.14119i
$241$	150.226	+	86.7329i	0.623343	+	0.359887i	0.778169	−	0.628054i	$-0.216148\pi$
$241$	150.226	+	86.7329i	0.623343	+	0.359887i	−0.154826	+	0.987942i	$0.549482\pi$
$242$	77.7887	+	290.311i	0.321441	+	1.19963i
$243$	−68.9088	−	233.025i	−0.283575	−	0.958950i
$244$	84.3441			0.345672
$245$	10.3629	−	244.781i	0.0422974	−	0.999105i
$246$	−173.167	+	19.1017i	−0.703929	+	0.0776491i
$247$	−2.62544	+	9.79826i	−0.0106293	+	0.0396691i
$248$	60.7687	+	226.792i	0.245035	+	0.914483i
$249$	−82.9634	+	188.949i	−0.333186	+	0.758830i
$250$	−153.379	−	270.504i	−0.613515	−	1.08202i
$251$	−6.94076			−0.0276524			−0.0138262	−	0.999904i	$-0.504401\pi$
$251$	−6.94076			−0.0276524			−0.0138262	+	0.999904i	$0.504401\pi$
$252$	−137.557	+	9.50260i	−0.545862	+	0.0377087i
$253$	−11.0580	+	11.0580i	−0.0437075	+	0.0437075i
$254$	159.718	+	276.640i	0.628812	+	1.08913i
$255$	230.429	+	185.628i	0.903644	+	0.727953i
$256$	−158.679	+	274.840i	−0.619840	+	1.07359i
$257$	85.7798	−	320.135i	0.333774	−	1.24566i	−0.571419	−	0.820659i	$-0.693607\pi$
$257$	85.7798	−	320.135i	0.333774	−	1.24566i	0.905193	−	0.425002i	$-0.139727\pi$
$258$	23.3581	−	29.1502i	0.0905353	−	0.112985i
$259$	−44.6655	+	102.052i	−0.172454	+	0.394024i
$260$	−140.903	+	80.8632i	−0.541934	+	0.311012i
$261$	196.121	−	180.276i	0.751421	−	0.690712i
$262$	120.352	+	449.159i	0.459358	+	1.71435i
$263$	497.456	−	133.293i	1.89147	−	0.506817i	0.893090	−	0.449877i	$-0.148532\pi$
$263$	497.456	−	133.293i	1.89147	−	0.506817i	0.998378	−	0.0569402i	$-0.0181344\pi$
$264$	−3.43840	−	4.68172i	−0.0130243	−	0.0177338i
$265$	−121.410	−	211.554i	−0.458149	−	0.798318i
$266$	−1.31858	−	11.8256i	−0.00495706	−	0.0444573i
$267$	−198.946	+	248.278i	−0.745115	+	0.929881i
$268$	149.581	+	40.0802i	0.558139	+	0.149553i
$269$	−411.981	−	237.857i	−1.53153	−	0.884227i	−0.999292	−	0.0376305i	$-0.988019\pi$
$269$	−411.981	−	237.857i	−1.53153	−	0.884227i	−0.532235	−	0.846597i	$-0.678648\pi$
$270$	301.168	+	148.614i	1.11544	+	0.550424i
$271$	79.8194	−	46.0837i	0.294536	−	0.170051i	−0.345449	−	0.938437i	$-0.612274\pi$
$271$	79.8194	−	46.0837i	0.294536	−	0.170051i	0.639986	+	0.768387i	$0.278940\pi$
$272$	278.478	+	278.478i	1.02382	+	1.02382i
$273$	263.389	+	166.784i	0.964796	+	0.610932i
$274$		−	420.242i		−	1.53373i
$275$	10.7422	+	0.0557867i	0.0390625	+	0.000202861i
$276$	96.0707	−	218.801i	0.348082	−	0.792756i
$277$	−88.2899	+	23.6572i	−0.318736	+	0.0854050i	−0.414640	−	0.909986i	$-0.636092\pi$
$277$	−88.2899	+	23.6572i	−0.318736	+	0.0854050i	0.0959040	+	0.995391i	$0.469426\pi$
$278$	87.1791	+	23.3596i	0.313594	+	0.0840273i
$279$	457.674	−	102.214i	1.64041	−	0.366359i
$280$	−98.7948	+	122.935i	−0.352838	+	0.439055i
$281$		−	54.9966i		−	0.195718i	−0.995200	−	0.0978588i	$-0.968801\pi$
$281$		−	54.9966i		−	0.195718i	0.995200	−	0.0978588i	$-0.0311994\pi$
$282$	24.3558	−	159.068i	0.0863680	−	0.564071i
$283$	155.174	−	41.5788i	0.548319	−	0.146922i	0.0259846	−	0.999662i	$-0.491728\pi$
$283$	155.174	−	41.5788i	0.548319	−	0.146922i	0.522334	+	0.852741i	$0.325061\pi$
$284$	132.570	−	229.618i	0.466797	−	0.808516i
$285$	−4.14498	+	9.37398i	−0.0145438	+	0.0328912i
$286$		−	15.8690i		−	0.0554861i
$287$	−161.553	−	24.5414i	−0.562903	−	0.0855100i
$288$	240.411	+	152.631i	0.834761	+	0.529970i
$289$	86.7194	−	50.0675i	0.300067	−	0.173244i
$290$	−0.955970	+	368.162i	−0.00329645	+	1.26952i
$291$	−148.526	+	338.266i	−0.510397	+	1.16243i
$292$	−77.2827	−	20.7078i	−0.264667	−	0.0709173i
$293$	−222.801	+	222.801i	−0.760413	+	0.760413i	−0.976397	−	0.215984i	$-0.930704\pi$
$293$	−222.801	+	222.801i	−0.760413	+	0.760413i	0.215984	+	0.976397i	$0.430704\pi$
$294$	−358.997	−	69.6562i	−1.22108	−	0.236926i
$295$	−31.3218	+	115.692i	−0.106176	+	0.392176i
$296$	62.1030	−	35.8552i	0.209807	−	0.121132i
$297$	−9.63134	+	6.46815i	−0.0324288	+	0.0217783i
$298$	−120.219	−	448.663i	−0.403419	−	1.50558i
$299$	−467.905	+	270.145i	−1.56490	+	0.903494i
$300$	−153.249	+	58.8181i	−0.510830	+	0.196060i
$301$	28.2142	−	20.7726i	0.0937347	−	0.0690120i
$302$	248.313	−	248.313i	0.822228	−	0.822228i
$303$	−2.11656	+	13.8233i	−0.00698533	+	0.0456214i
$304$	−6.82084	+	11.8140i	−0.0224370	+	0.0388620i
$305$	−135.895	−	136.602i	−0.445556	−	0.447876i
$306$	325.161	−	298.891i	1.06262	−	0.976768i
$307$	134.188	−	134.188i	0.437095	−	0.437095i	−0.453938	−	0.891033i	$-0.649981\pi$
$307$	134.188	−	134.188i	0.437095	−	0.437095i	0.891033	+	0.453938i	$0.149981\pi$
$308$	2.39800	+	6.13084i	0.00778571	+	0.0199053i
$309$	−41.0192	−	371.860i	−0.132748	−	1.20343i
$310$	−325.513	+	560.439i	−1.05004	+	1.80787i
$311$	97.8621	−	169.502i	0.314669	−	0.545023i	−0.664698	−	0.747112i	$-0.731440\pi$
$311$	97.8621	−	169.502i	0.314669	−	0.545023i	0.979367	+	0.202089i	$0.0647731\pi$
$312$	−72.8820	−	186.983i	−0.233596	−	0.599305i
$313$	−94.5260	+	352.776i	−0.302000	+	1.12708i	0.633497	+	0.773745i	$0.281619\pi$
$313$	−94.5260	+	352.776i	−0.302000	+	1.12708i	−0.935497	+	0.353334i	$0.885048\pi$
$314$			284.671i			0.906596i
$315$	237.022	+	207.475i	0.752449	+	0.658650i
$316$	61.5692			0.194839
$317$	165.211	+	44.2683i	0.521172	+	0.139648i	0.509808	−	0.860288i	$-0.329716\pi$
$317$	165.211	+	44.2683i	0.521172	+	0.139648i	0.0113631	+	0.999935i	$0.496383\pi$
$318$	−339.218	+	132.220i	−1.06672	+	0.415785i
$319$	−11.0144	−	6.35918i	−0.0345280	−	0.0199347i
$320$	5.52954	−	1.46626i	0.0172798	−	0.00458205i
$321$	141.972	−	15.6606i	0.442280	−	0.0487870i
$322$	395.720	−	495.041i	1.22894	−	1.53739i
$323$	9.53118	+	9.53118i	0.0295083	+	0.0295083i
$324$	101.230	−	145.537i	0.312438	−	0.449187i
$325$	357.987	+	97.9176i	1.10150	+	0.301285i
$326$	−346.080	−	199.810i	−1.06160	−	0.612913i
$327$	16.0175	+	2.45253i	0.0489833	+	0.00750010i
$328$	74.3801	+	74.3801i	0.226768	+	0.226768i
$329$	60.5183	−	138.273i	0.183946	−	0.420282i
$330$	2.46795	−	15.8431i	0.00747863	−	0.0480095i
$331$	−61.7449	−	106.945i	−0.186541	−	0.323098i	0.757554	−	0.652773i	$-0.226394\pi$
$331$	−61.7449	−	106.945i	−0.186541	−	0.323098i	−0.944095	+	0.329675i	$0.893061\pi$
$332$	−145.420	+	38.9652i	−0.438013	+	0.117365i
$333$	−66.3331	−	126.940i	−0.199198	−	0.381202i
$334$	73.0967	+	126.607i	0.218852	+	0.379063i
$335$	−176.091	−	306.836i	−0.525645	−	0.915929i
$336$	284.089	+	308.328i	0.845503	+	0.917643i
$337$	101.660	+	101.660i	0.301663	+	0.301663i	0.841664	−	0.540001i	$-0.181576\pi$
$337$	101.660	+	101.660i	0.301663	+	0.301663i	−0.540001	+	0.841664i	$0.681576\pi$
$338$	33.0867	−	123.481i	0.0978895	−	0.365329i
$339$	316.911	+	139.149i	0.934841	+	0.410469i
$340$	−0.560532	+	215.871i	−0.00164862	+	0.634916i
$341$	−11.1947	−	19.3897i	−0.0328290	−	0.0568614i
$342$	12.9155	+	8.19978i	0.0377647	+	0.0239760i
$343$	−308.514	−	149.894i	−0.899458	−	0.437008i
$344$	−22.5538			−0.0655634
$345$	−509.155	+	196.936i	−1.47581	+	0.570829i
$346$	−425.913	−	245.901i	−1.23096	−	0.710697i
$347$	2.59230	+	9.67460i	0.00747061	+	0.0278807i	0.969561	−	0.244852i	$-0.0787393\pi$
$347$	2.59230	+	9.67460i	0.00747061	+	0.0278807i	−0.962090	+	0.272732i	$0.912073\pi$
$348$	192.105	+	29.4142i	0.552025	+	0.0845236i
$349$	−321.605			−0.921506			−0.460753	−	0.887529i	$-0.652421\pi$
$349$	−321.605			−0.921506			−0.460753	+	0.887529i	$0.652421\pi$
$350$	−432.911	+	45.9954i	−1.23689	+	0.131416i
$351$	−379.253	+	129.731i	−1.08049	+	0.369603i
$352$	3.51889	−	13.1327i	0.00999685	−	0.0373088i
$353$	47.4018	+	176.906i	0.134283	+	0.501150i	1.00000		0.000616544i	$0.000196252\pi$
$353$	47.4018	+	176.906i	0.134283	+	0.501150i	−0.865717	+	0.500534i	$0.833137\pi$
$354$	163.806	+	71.9238i	0.462729	+	0.203175i
$355$	−585.483	+	155.251i	−1.64925	+	0.437328i
$356$	−232.109			−0.651991
$357$	366.924	−	192.289i	1.02780	−	0.538624i
$358$	−148.931	+	148.931i	−0.416008	+	0.416008i
$359$	−166.010	−	287.538i	−0.462424	−	0.800941i	0.536657	−	0.843800i	$-0.319687\pi$
$359$	−166.010	−	287.538i	−0.462424	−	0.800941i	−0.999081	+	0.0428588i	$0.986353\pi$
$360$	−43.6835	−	198.013i	−0.121343	−	0.550036i
$361$	180.267	−	312.231i	0.499353	−	0.864905i
$362$	76.1012	−	284.014i	0.210224	−	0.784568i
$363$	−282.843	−	226.643i	−0.779182	−	0.624360i
$364$	25.2038	+	226.040i	0.0692413	+	0.620989i
$365$	90.9794	+	158.530i	0.249259	+	0.434329i
$366$	−231.805	+	170.245i	−0.633347	+	0.465150i
$367$	−90.1348	−	336.388i	−0.245599	−	0.916588i	−0.973081	−	0.230462i	$-0.925976\pi$
$367$	−90.1348	−	336.388i	−0.245599	−	0.916588i	0.727482	−	0.686126i	$-0.240690\pi$
$368$	−701.832	+	188.055i	−1.90715	+	0.511020i
$369$	154.676	−	142.179i	0.419175	−	0.385309i
$370$	191.069	+	51.7288i	0.516402	+	0.139808i
$371$	−339.381	+	37.8415i	−0.914772	+	0.101999i
$372$	266.983	+	213.934i	0.717695	+	0.575090i
$373$	312.260	+	83.6699i	0.837159	+	0.224316i	0.651834	−	0.758361i	$-0.274000\pi$
$373$	312.260	+	83.6699i	0.837159	+	0.224316i	0.185325	+	0.982677i	$0.440666\pi$
$374$	−18.2615	−	10.5433i	−0.0488276	−	0.0281906i
$375$	342.175	+	153.432i	0.912466	+	0.409152i
$376$	−84.1447	+	48.5810i	−0.223789	+	0.129205i
$377$	−310.707	−	310.707i	−0.824157	−	0.824157i
$378$	358.871	−	303.770i	0.949395	−	0.803624i
$379$		−	104.552i		−	0.275864i	−0.990442	−	0.137932i	$-0.955955\pi$
$379$		−	104.552i		−	0.275864i	0.990442	−	0.137932i	$-0.0440455\pi$
$380$	−7.22774	+	1.91657i	−0.0190204	+	0.00504359i
$381$	−352.716	−	154.870i	−0.925765	−	0.406484i
$382$	26.9805	−	7.22941i	0.0706296	−	0.0189252i
$383$	−534.857	−	143.314i	−1.39649	−	0.374189i	−0.519409	−	0.854526i	$-0.673848\pi$
$383$	−534.857	−	143.314i	−1.39649	−	0.374189i	−0.877084	+	0.480337i	$0.840514\pi$
$384$	−42.5669	−	385.891i	−0.110851	−	1.00492i
$385$	6.06577	−	13.7617i	0.0157553	−	0.0357448i
$386$		−	210.103i		−	0.544307i
$387$	−1.89462	+	45.0068i	−0.00489566	+	0.116297i
$388$	−260.339	+	69.7577i	−0.670978	+	0.179788i
$389$	28.3514	−	49.1061i	0.0728829	−	0.126237i	−0.827281	−	0.561789i	$-0.810113\pi$
$389$	28.3514	−	49.1061i	0.0728829	−	0.126237i	0.900164	+	0.435552i	$0.143447\pi$
$390$	224.028	−	506.645i	0.574431	−	1.29909i
$391$			717.932i			1.83614i
$392$	102.720	+	195.450i	0.262042	+	0.498596i
$393$	−437.604	−	350.653i	−1.11350	−	0.892247i
$394$	627.375	−	362.215i	1.59232	−	0.919328i
$395$	−99.2000	−	99.7165i	−0.251139	−	0.252447i
$396$	−8.07625	−	2.53257i	−0.0203946	−	0.00639539i
$397$	248.624	+	66.6185i	0.626256	+	0.167805i	0.557970	−	0.829861i	$-0.311580\pi$
$397$	248.624	+	66.6185i	0.626256	+	0.167805i	0.0682861	+	0.997666i	$0.478247\pi$
$398$	382.528	−	382.528i	0.961127	−	0.961127i
$399$	9.72321	+	10.5528i	0.0243689	+	0.0264481i
$400$	430.940	+	251.796i	1.07735	+	0.629491i
$401$	−205.140	+	118.438i	−0.511572	+	0.295356i	−0.733479	−	0.679712i	$-0.762105\pi$
$401$	−205.140	+	118.438i	−0.511572	+	0.295356i	0.221908	+	0.975068i	$0.428772\pi$
$402$	−491.998	+	191.770i	−1.22388	+	0.477040i
$403$	−200.204	−	747.172i	−0.496784	−	1.85402i
$404$	−8.83545	+	5.10115i	−0.0218699	+	0.0126266i
$405$	−398.810	+	70.5377i	−0.984716	+	0.174167i
$406$	472.184	+	206.662i	1.16301	+	0.509020i
$407$	−4.83531	+	4.83531i	−0.0118804	+	0.0118804i
$408$	−263.596	−	40.3607i	−0.646070	−	0.0989232i
$409$	342.216	−	592.735i	0.836714	−	1.44923i	−0.0559134	−	0.998436i	$-0.517807\pi$
$409$	342.216	−	592.735i	0.836714	−	1.44923i	0.892627	−	0.450795i	$-0.148860\pi$
$410$	−0.753951	+	290.361i	−0.00183890	+	0.708197i
$411$	299.985	+	408.459i	0.729891	+	0.993817i
$412$	192.995	−	192.995i	0.468434	−	0.468434i
$413$	131.070	+	104.773i	0.317361	+	0.253688i
$414$	177.606	+	795.251i	0.429001	+	1.92090i
$415$	297.408	+	172.740i	0.716645	+	0.416240i
$416$	234.863	−	406.795i	0.564575	−	0.977873i
$417$	−101.410	+	39.5273i	−0.243189	+	0.0947896i
$418$	0.189045	−	0.705524i	0.000452260	−	0.00168786i
$419$			492.247i			1.17481i	0.809292	+	0.587407i	$0.199851\pi$
$419$			492.247i			1.17481i	−0.809292	+	0.587407i	$0.800149\pi$
$420$	−9.99099	+	229.591i	−0.0237881	+	0.546645i
$421$	493.063			1.17117			0.585586	−	0.810611i	$-0.300865\pi$
$421$	493.063			1.17117			0.585586	+	0.810611i	$0.300865\pi$
$422$	−193.214	−	51.7716i	−0.457854	−	0.122682i
$423$	89.8762	+	171.994i	0.212473	+	0.406606i
$424$	190.372	+	109.911i	0.448990	+	0.259225i
$425$	350.525	−	346.903i	0.824764	−	0.816242i
$426$	99.1289	+	898.654i	0.232697	+	2.10952i
$427$	−251.226	+	98.2636i	−0.588350	+	0.230125i
$428$	73.6832	+	73.6832i	0.172157	+	0.172157i
$429$	11.3279	+	15.4241i	0.0264054	+	0.0359535i
$430$	−43.9079	−	44.1365i	−0.102111	−	0.102643i
$431$	597.343	+	344.876i	1.38595	+	0.800177i	0.992855	−	0.119323i	$-0.0380724\pi$
$431$	597.343	+	344.876i	1.38595	+	0.800177i	0.393091	+	0.919500i	$0.371406\pi$
$432$	−537.801	+	36.5148i	−1.24491	+	0.0845250i
$433$	160.524	+	160.524i	0.370725	+	0.370725i	0.867741	−	0.497016i	$-0.165571\pi$
$433$	160.524	+	160.524i	0.370725	+	0.370725i	−0.497016	+	0.867741i	$0.665571\pi$
$434$	537.963	+	730.682i	1.23955	+	1.68360i
$435$	−261.879	−	358.522i	−0.602022	−	0.824188i
$436$	5.91089	+	10.2380i	0.0135571	+	0.0234816i
$437$	−24.0209	+	6.43637i	−0.0549676	+	0.0147285i
$438$	254.196	−	99.0800i	0.580356	−	0.226210i
$439$	222.946	+	386.155i	0.507851	+	0.879623i	0.999959	+	0.00908897i	$0.00289315\pi$
$439$	222.946	+	386.155i	0.507851	+	0.879623i	−0.492108	+	0.870534i	$0.663774\pi$
$440$	−8.39669	+	4.81881i	−0.0190834	+	0.0109518i
$441$	398.654	−	188.563i	0.903978	−	0.427580i
$442$	−515.142	−	515.142i	−1.16548	−	1.16548i
$443$	18.1482	−	67.7301i	0.0409666	−	0.152890i	−0.942413	−	0.334452i	$-0.891449\pi$
$443$	18.1482	−	67.7301i	0.0409666	−	0.152890i	0.983379	+	0.181562i	$0.0581154\pi$
$444$	42.0087	−	95.6747i	0.0946142	−	0.215484i
$445$	373.972	+	375.920i	0.840387	+	0.844763i
$446$	292.066	+	505.873i	0.654856	+	1.13424i
$447$	437.121	+	350.266i	0.977899	+	0.783593i
$448$	1.20282	−	7.91806i	0.00268487	−	0.0176742i
$449$	825.166			1.83779			0.918893	−	0.394507i	$-0.129084\pi$
$449$	825.166			1.83779			0.918893	+	0.394507i	$0.129084\pi$
$450$	302.456	−	470.978i	0.672125	−	1.04662i
$451$	−8.68681	−	5.01533i	−0.0192612	−	0.0111205i
$452$	65.3538	+	243.904i	0.144588	+	0.539610i
$453$	−64.0950	+	418.606i	−0.141490	+	0.924075i
$454$	−977.750			−2.15363
$455$	325.482	−	405.014i	0.715345	−	0.890140i
$456$	−1.01278	−	9.18136i	−0.00222101	−	0.0201346i
$457$	−81.8006	+	305.284i	−0.178995	+	0.668017i	0.816842	+	0.576861i	$0.195723\pi$
$457$	−81.8006	+	305.284i	−0.178995	+	0.668017i	−0.995837	+	0.0911557i	$0.970944\pi$
$458$	−130.022	−	485.248i	−0.283891	−	1.05949i
$459$	−102.684	+	522.624i	−0.223713	+	1.13861i
$460$	−344.395	−	200.031i	−0.748685	−	0.434849i
$461$	−428.348			−0.929172			−0.464586	−	0.885528i	$-0.653797\pi$
$461$	−428.348			−0.929172			−0.464586	+	0.885528i	$0.653797\pi$
$462$	−18.9653	−	12.0093i	−0.0410505	−	0.0259942i
$463$	−103.264	+	103.264i	−0.223033	+	0.223033i	−0.809774	−	0.586742i	$-0.800410\pi$
$463$	−103.264	+	103.264i	−0.223033	+	0.223033i	0.586742	+	0.809774i	$0.300410\pi$
$464$	−295.460	−	511.752i	−0.636768	−	1.10291i
$465$	−83.6775	−	777.089i	−0.179952	−	1.67116i
$466$	97.9957	−	169.734i	0.210291	−	0.364235i
$467$	−198.750	+	741.745i	−0.425589	+	1.58832i	0.337045	+	0.941489i	$0.390573\pi$
$467$	−198.750	+	741.745i	−0.425589	+	1.58832i	−0.762634	+	0.646831i	$0.776094\pi$
$468$	−246.873	−	156.734i	−0.527506	−	0.334901i
$469$	−492.234	+	54.8849i	−1.04954	+	0.117025i
$470$	−258.883	−	70.0886i	−0.550816	−	0.149125i
$471$	−203.209	−	276.689i	−0.431443	−	0.587451i
$472$	−27.9569	−	104.337i	−0.0592308	−	0.221052i
$473$	2.07741	−	0.556640i	0.00439198	−	0.00117683i
$474$	−169.212	+	124.275i	−0.356988	+	0.262183i
$475$	14.7493	+	8.61797i	0.0310512	+	0.0181431i
$476$	276.864	+	121.176i	0.581648	+	0.254572i
$477$	235.323	−	370.659i	0.493340	−	0.777064i
$478$	454.396	+	121.755i	0.950619	+	0.254718i
$479$	−74.2841	−	42.8879i	−0.155082	−	0.0895364i	0.420451	−	0.907315i	$-0.361872\pi$
$479$	−74.2841	−	42.8879i	−0.155082	−	0.0895364i	−0.575533	+	0.817779i	$0.695205\pi$
$480$	297.745	−	369.606i	0.620302	−	0.770012i
$481$	−204.600	+	118.126i	−0.425364	+	0.245584i
$482$	−305.138	−	305.138i	−0.633067	−	0.633067i
$483$	−31.2445	+	763.641i	−0.0646885	+	1.58104i
$484$		−	264.423i		−	0.546328i
$485$	532.436	+	309.248i	1.09781	+	0.637625i
$486$	15.5469	+	604.311i	0.0319895	+	1.24344i
$487$	902.831	−	241.913i	1.85386	−	0.496741i	0.854135	−	0.520051i	$-0.174087\pi$
$487$	902.831	−	241.913i	1.85386	−	0.496741i	0.999728	+	0.0233103i	$0.00742058\pi$
$488$	167.734	+	44.9443i	0.343718	+	0.0920990i
$489$	479.009	−	52.8386i	0.979568	−	0.108054i
$490$	−182.507	+	581.520i	−0.372463	+	1.18677i
$491$		−	145.083i		−	0.295484i	−0.989026	−	0.147742i	$-0.952800\pi$
$491$		−	145.083i		−	0.295484i	0.989026	−	0.147742i	$-0.0472005\pi$
$492$	151.508	+	23.1983i	0.307944	+	0.0471510i
$493$	−563.984	+	151.119i	−1.14398	+	0.306529i
$494$	12.6175	−	21.8541i	0.0255415	−	0.0442392i
$495$	8.91070	+	17.1606i	0.0180014	+	0.0346680i
$496$		−	1040.25i		−	2.09729i
$497$	−127.358	+	838.386i	−0.256254	+	1.68689i
$498$	321.013	−	400.614i	0.644604	−	0.804446i
$499$	−587.469	+	339.175i	−1.17729	+	0.679710i	−0.955387	−	0.295358i	$-0.904561\pi$
$499$	−587.469	+	339.175i	−1.17729	+	0.679710i	−0.221906	+	0.975068i	$0.571228\pi$
$500$	68.7474	+	264.803i	0.137495	+	0.529606i
$501$	−161.424	−	70.8780i	−0.322204	−	0.141473i
$502$	16.6782	+	4.46891i	0.0332235	+	0.00890220i
$503$	534.628	−	534.628i	1.06288	−	1.06288i	0.0649938	−	0.997886i	$-0.479297\pi$
$503$	534.628	−	534.628i	1.06288	−	1.06288i	0.997886	−	0.0649938i	$-0.0207028\pi$
$504$	−278.623	−	54.4021i	−0.552822	−	0.107941i
$505$	22.4974	+	6.09081i	0.0445492	+	0.0120610i
$506$	33.6915	−	19.4518i	0.0665839	−	0.0384422i
$507$	55.9867	+	143.637i	0.110427	+	0.283308i
$508$	−72.7376	−	271.460i	−0.143184	−	0.534371i
$509$	52.2460	−	30.1643i	0.102644	−	0.0592618i	−0.447799	−	0.894134i	$-0.647792\pi$
$509$	52.2460	−	30.1643i	0.102644	−	0.0592618i	0.550443	+	0.834872i	$0.314459\pi$
$510$	−434.187	−	594.417i	−0.851347	−	1.16552i
$511$	254.318	−	28.3569i	0.497687	−	0.0554929i
$512$	192.227	−	192.227i	0.375443	−	0.375443i
$513$	−18.4067	+	1.24975i	−0.0358806	+	0.00243617i
$514$	−412.246	+	714.032i	−0.802036	+	1.38917i
$515$	−623.524	−	1.61904i	−1.21073	−	0.00314377i
$516$	−26.4876	+	19.4534i	−0.0513326	+	0.0377003i
$517$	6.55148	−	6.55148i	0.0126721	−	0.0126721i
$518$	173.036	−	216.466i	0.334046	−	0.417888i
$519$	589.505	−	65.0272i	1.13585	−	0.125293i
$520$	−323.302	+	85.7294i	−0.621734	+	0.164864i
$521$	73.8519	−	127.915i	0.141750	−	0.245519i	−0.786406	−	0.617711i	$-0.788060\pi$
$521$	73.8519	−	127.915i	0.141750	−	0.245519i	0.928156	+	0.372192i	$0.121394\pi$
$522$	−587.338	+	306.916i	−1.12517	+	0.587961i
$523$	−24.9678	+	93.1810i	−0.0477395	+	0.178166i	−0.985679	−	0.168633i	$-0.946065\pi$
$523$	−24.9678	+	93.1810i	−0.0477395	+	0.178166i	0.937939	+	0.346799i	$0.112731\pi$
$524$		−	409.105i		−	0.780734i
$525$	387.939	−	353.735i	0.738932	−	0.673780i
$526$	−1281.18			−2.43570
$527$	−992.835	−	266.029i	−1.88394	−	0.504799i
$528$	9.34632	+	23.9786i	0.0177014	+	0.0454140i
$529$	−688.960	−	397.771i	−1.30238	−	0.751931i
$530$	155.527	+	586.522i	0.293447	+	1.10665i
$531$	−210.555	+	47.0241i	−0.396526	+	0.0885577i
$532$	−1.57223	+	10.3498i	−0.00295532	+	0.0194545i
$533$	−245.047	−	245.047i	−0.459751	−	0.459751i
$534$	637.911	−	468.502i	1.19459	−	0.877345i
$535$	0.618132	−	238.054i	0.00115539	−	0.444961i
$536$	276.114	+	159.414i	0.515137	+	0.297415i
$537$	38.4424	−	251.068i	0.0715873	−	0.467538i
$538$	836.814	+	836.814i	1.55542	+	1.55542i
$539$	−14.2853	−	15.4675i	−0.0265033	−	0.0286966i
$540$	−222.095	−	194.872i	−0.411287	−	0.360874i
$541$	−158.829	−	275.100i	−0.293584	−	0.508503i	0.681070	−	0.732218i	$-0.261515\pi$
$541$	−158.829	−	275.100i	−0.293584	−	0.508503i	−0.974655	+	0.223715i	$0.928181\pi$
$542$	−221.472	+	59.3433i	−0.408620	+	0.109490i
$543$	128.773	+	330.374i	0.237150	+	0.608424i
$544$	−312.084	−	540.545i	−0.573684	−	0.993649i
$545$	7.05765	−	26.0685i	0.0129498	−	0.0478322i
$546$	−525.520	−	570.359i	−0.962492	−	1.04461i
$547$	453.201	+	453.201i	0.828520	+	0.828520i	0.987312	−	0.158792i	$-0.0507598\pi$
$547$	453.201	+	453.201i	0.828520	+	0.828520i	−0.158792	+	0.987312i	$0.550760\pi$
$548$	−95.6916	+	357.126i	−0.174620	+	0.651690i
$549$	103.778	−	330.943i	0.189031	−	0.602811i
$550$	−25.7768	−	7.05056i	−0.0468670	−	0.0128192i
$551$	−10.1124	−	17.5152i	−0.0183528	−	0.0317880i
$552$	307.647	−	383.934i	0.557332	−	0.695533i
$553$	−183.389	+	71.7301i	−0.331625	+	0.129711i
$554$	227.387			0.410445
$555$	−222.637	+	86.1139i	−0.401148	+	0.155160i
$556$	−68.7666	−	39.7024i	−0.123681	−	0.0714073i
$557$	−242.494	−	905.000i	−0.435358	−	1.62478i	−0.740209	−	0.672377i	$-0.765274\pi$
$557$	−242.494	−	905.000i	−0.435358	−	1.62478i	0.304852	−	0.952400i	$-0.401393\pi$
$558$	−1165.57	−	49.0663i	−2.08884	−	0.0879324i
$559$	74.3042			0.132923
$560$	563.770	−	412.821i	1.00673	−	0.737181i
$561$	25.2757	−	2.78812i	0.0450547	−	0.00496990i
$562$	−35.4104	+	132.153i	−0.0630078	+	0.235148i
$563$	156.051	+	582.391i	0.277178	+	1.03444i	0.954368	+	0.298634i	$0.0965308\pi$
$563$	156.051	+	582.391i	0.277178	+	1.03444i	−0.677190	+	0.735808i	$0.736803\pi$
$564$	−56.9186	+	129.632i	−0.100919	+	0.229844i
$565$	289.725	−	498.822i	0.512787	−	0.882871i
$566$	−399.645			−0.706086
$567$	−131.966	+	551.429i	−0.232745	+	0.972538i
$568$	385.998	−	385.998i	0.679574	−	0.679574i
$569$	366.366	+	634.564i	0.643876	+	1.11523i	0.984560	+	0.175049i	$0.0560083\pi$
$569$	366.366	+	634.564i	0.643876	+	1.11523i	−0.340683	+	0.940178i	$0.610658\pi$
$570$	15.9957	−	19.8562i	0.0280626	−	0.0348355i
$571$	−320.119	+	554.462i	−0.560629	+	0.971037i	0.436813	+	0.899552i	$0.356107\pi$
$571$	−320.119	+	554.462i	−0.560629	+	0.971037i	−0.997442	+	0.0714851i	$0.977226\pi$
$572$	−3.61347	+	13.4857i	−0.00631726	+	0.0235763i
$573$	−21.0634	+	26.2865i	−0.0367598	+	0.0458751i
$574$	372.400	+	162.989i	0.648780	+	0.283954i
$575$	230.921	+	880.065i	0.401602	+	1.53055i
$576$	6.96850	+	7.58098i	0.0120981	+	0.0131614i
$577$	202.752	+	756.679i	0.351389	+	1.31140i	0.884968	+	0.465652i	$0.154180\pi$
$577$	202.752	+	756.679i	0.351389	+	1.31140i	−0.533579	+	0.845750i	$0.679153\pi$
$578$	−240.618	+	64.4733i	−0.416293	+	0.111545i
$579$	149.980	+	204.212i	0.259032	+	0.352697i
$580$	84.6452	−	312.650i	0.145940	−	0.539052i
$581$	387.750	−	285.480i	0.667384	−	0.491360i
$582$	574.695	−	717.201i	0.987448	−	1.23230i
$583$	−20.2476	−	5.42533i	−0.0347301	−	0.00930589i
$584$	−142.657	−	82.3631i	−0.244276	−	0.141033i
$585$	143.917	+	652.360i	0.246011	+	1.11514i
$586$	678.829	−	391.922i	1.15841	−	0.668809i
$587$	−26.5985	−	26.5985i	−0.0453126	−	0.0453126i	0.684087	−	0.729400i	$-0.260201\pi$
$587$	−26.5985	−	26.5985i	−0.0453126	−	0.0453126i	−0.729400	+	0.684087i	$0.760201\pi$
$588$	289.218	+	140.940i	0.491867	+	0.239694i
$589$		−	35.6037i		−	0.0604477i
$590$	149.754	−	257.833i	0.253820	−	0.437005i
$591$	−351.221	+	799.904i	−0.594282	+	1.35348i
$592$	−306.889	+	82.2307i	−0.518394	+	0.138903i
$593$	−329.845	−	88.3817i	−0.556231	−	0.149042i	−0.0302569	−	0.999542i	$-0.509633\pi$
$593$	−329.845	−	88.3817i	−0.556231	−	0.149042i	−0.525974	+	0.850500i	$0.676299\pi$
$594$	27.3081	−	9.34125i	0.0459732	−	0.0157260i
$595$	−249.827	−	643.643i	−0.419878	−	1.08175i
$596$			408.653i			0.685659i
$597$	−98.7390	+	644.867i	−0.165392	+	1.08018i
$598$	1298.28	−	347.873i	2.17104	−	0.581728i
$599$	494.868	−	857.136i	0.826156	−	1.43094i	−0.0748758	−	0.997193i	$-0.523856\pi$
$599$	494.868	−	857.136i	0.826156	−	1.43094i	0.901032	−	0.433752i	$-0.142811\pi$
$600$	−336.107	+	35.3097i	−0.560179	+	0.0588494i
$601$		−	621.566i		−	1.03422i	−0.855919	−	0.517110i	$-0.827008\pi$
$601$		−	621.566i		−	1.03422i	0.855919	−	0.517110i	$-0.172992\pi$
$602$	−81.1715	+	31.7491i	−0.134836	+	0.0527395i
$603$	341.310	−	537.601i	0.566020	−	0.891544i
$604$	−267.561	+	154.477i	−0.442982	+	0.255756i
$605$	−428.255	+	426.036i	−0.707859	+	0.704192i
$606$	13.9863	−	31.8536i	0.0230796	−	0.0525637i
$607$	412.620	+	110.561i	0.679769	+	0.182144i	0.582152	−	0.813080i	$-0.302211\pi$
$607$	412.620	+	110.561i	0.679769	+	0.182144i	0.0976179	+	0.995224i	$0.468878\pi$
$608$	15.2879	−	15.2879i	0.0251446	−	0.0251446i
$609$	−606.468	+	136.196i	−0.995842	+	0.223638i
$610$	238.593	+	415.744i	0.391135	+	0.681547i
$611$	277.217	−	160.051i	0.453711	−	0.261950i
$612$	−344.385	+	179.960i	−0.562720	+	0.294052i
$613$	285.788	+	1066.57i	0.466212	+	1.73993i	0.652841	+	0.757495i	$0.273577\pi$
$613$	285.788	+	1066.57i	0.466212	+	1.73993i	−0.186629	+	0.982430i	$0.559756\pi$
$614$	−408.844	+	236.046i	−0.665870	+	0.384440i
$615$	−206.538	−	282.757i	−0.335834	−	0.459768i
$616$	1.50195	+	13.4702i	0.00243823	+	0.0218672i
$617$	289.703	−	289.703i	0.469534	−	0.469534i	−0.432229	−	0.901764i	$-0.642273\pi$
$617$	289.703	−	289.703i	0.469534	−	0.469534i	0.901764	+	0.432229i	$0.142273\pi$
$618$	−140.861	+	919.965i	−0.227930	+	1.48862i
$619$	181.699	−	314.712i	0.293536	−	0.508419i	−0.681107	−	0.732184i	$-0.738501\pi$
$619$	181.699	−	314.712i	0.293536	−	0.508419i	0.974643	+	0.223764i	$0.0718346\pi$
$620$	404.240	−	402.146i	0.652000	−	0.648623i
$621$	−740.308	−	646.171i	−1.19212	−	1.04053i
$622$	−344.292	+	344.292i	−0.553525	+	0.553525i
$623$	691.354	−	270.414i	1.10972	−	0.434052i
$624$	97.4883	+	883.782i	0.156231	+	1.41632i
$625$	318.105	−	537.991i	0.508968	−	0.860786i
$626$	454.279	−	786.835i	0.725686	−	1.25693i
$627$	0.319887	+	0.820689i	0.000510186	+	0.00130891i
$628$	64.8214	−	241.917i	0.103219	−	0.385218i
$629$			313.929i			0.499092i
$630$	−435.962	−	651.158i	−0.692002	−	1.03358i
$631$	202.054			0.320213			0.160106	−	0.987100i	$-0.448816\pi$
$631$	202.054			0.320213			0.160106	+	0.987100i	$0.448816\pi$
$632$	122.442	+	32.8083i	0.193738	+	0.0519119i
$633$	224.753	−	87.6040i	0.355061	−	0.138395i
$634$	−368.489	−	212.747i	−0.581213	−	0.335564i
$635$	−322.458	+	555.180i	−0.507808	+	0.874299i
$636$	318.378	−	35.1197i	0.500595	−	0.0552197i
$637$	−338.415	−	643.914i	−0.531264	−	1.01085i
$638$	22.3725	+	22.3725i	0.0350666	+	0.0350666i
$639$	−737.844	−	802.695i	−1.15469	−	1.25617i
$640$	−647.051	−	1.68013i	−1.01102	−	0.00262521i
$641$	−100.665	−	58.1187i	−0.157043	−	0.0906688i	0.419419	−	0.907793i	$-0.362234\pi$
$641$	−100.665	−	58.1187i	−0.157043	−	0.0906688i	−0.576462	+	0.817124i	$0.695567\pi$
$642$	−351.232	−	53.7791i	−0.547091	−	0.0837680i
$643$	98.7534	+	98.7534i	0.153582	+	0.153582i	0.779716	−	0.626134i	$-0.215364\pi$
$643$	98.7534	+	98.7534i	0.153582	+	0.153582i	−0.626134	+	0.779716i	$0.715364\pi$
$644$	−449.011	+	330.583i	−0.697221	+	0.513328i
$645$	74.1831	+	11.5558i	0.115013	+	0.0179160i
$646$	−16.7660	−	29.0396i	−0.0259536	−	0.0449529i
$647$	856.891	−	229.603i	1.32441	−	0.354874i	0.473780	−	0.880643i	$-0.342889\pi$
$647$	856.891	−	229.603i	1.32441	−	0.354874i	0.850627	+	0.525770i	$0.176223\pi$
$648$	278.867	−	235.486i	0.430351	−	0.363404i
$649$	5.15017	+	8.92035i	0.00793555	+	0.0137448i
$650$	−797.172	−	465.784i	−1.22642	−	0.716591i
$651$	−1044.47	−	326.175i	−1.60441	−	0.501037i
$652$	248.605	+	248.605i	0.381296	+	0.381296i
$653$	−197.585	+	737.397i	−0.302580	+	1.12925i	0.632428	+	0.774619i	$0.282059\pi$
$653$	−197.585	+	737.397i	−0.302580	+	1.12925i	−0.935008	+	0.354626i	$0.884608\pi$
$654$	−36.9100	−	16.2064i	−0.0564373	−	0.0247804i
$655$	−662.579	+	659.147i	−1.01157	+	1.00633i
$656$	−233.022	−	403.607i	−0.355217	−	0.615254i
$657$	−176.342	+	277.757i	−0.268404	+	0.422766i
$658$	−234.450	+	293.295i	−0.356307	+	0.445737i
$659$	−399.413			−0.606089			−0.303045	−	0.952976i	$-0.598003\pi$
$659$	−399.413			−0.606089			−0.303045	+	0.952976i	$0.598003\pi$
$660$	−5.70487	+	12.9017i	−0.00864374	+	0.0195480i
$661$	−214.961	−	124.108i	−0.325206	−	0.187758i	0.328505	−	0.944502i	$-0.393455\pi$
$661$	−214.961	−	124.108i	−0.325206	−	0.187758i	−0.653711	+	0.756744i	$0.726789\pi$
$662$	79.5107	+	296.738i	0.120107	+	0.448245i
$663$	868.426	+	132.969i	1.30984	+	0.200557i
$664$	−309.960			−0.466807
$665$	19.2955	−	14.1292i	0.0290158	−	0.0212469i
$666$	77.6617	+	347.738i	0.116609	+	0.522130i
$667$	278.806	−	1040.52i	0.418000	−	1.56000i
$668$	−33.2891	−	124.237i	−0.0498340	−	0.185983i
$669$	−644.989	−	283.201i	−0.964108	−	0.423320i
$670$	225.575	+	850.686i	0.336679	+	1.26968i
$671$	−16.5591			−0.0246782
$672$	−308.429	−	588.543i	−0.458972	−	0.875807i
$673$	−745.439	+	745.439i	−1.10764	+	1.10764i	−0.114176	+	0.993461i	$0.536423\pi$
$673$	−745.439	+	745.439i	−1.10764	+	1.10764i	−0.993461	+	0.114176i	$0.963577\pi$
$674$	−178.828	−	309.738i	−0.265323	−	0.459553i
$675$	42.2269	+	673.678i	0.0625584	+	0.998041i
$676$	−56.2348	+	97.4015i	−0.0831875	+	0.144085i
$677$	−70.3733	+	262.637i	−0.103949	+	0.387942i	−0.998224	−	0.0595758i	$-0.981025\pi$
$677$	−70.3733	+	262.637i	−0.103949	+	0.387942i	0.894275	+	0.447518i	$0.147692\pi$
$678$	−671.923	−	538.413i	−0.991037	−	0.794120i
$679$	694.171	−	511.083i	1.02234	−	0.752699i
$680$	−116.146	+	429.003i	−0.170803	+	0.630887i
$681$	950.335	−	697.956i	1.39550	−	1.02490i
$682$	14.4157	+	53.8001i	0.0211374	+	0.0788858i
$683$	−629.078	+	168.561i	−0.921051	+	0.246795i	−0.688035	−	0.725678i	$-0.741526\pi$
$683$	−629.078	+	168.561i	−0.921051	+	0.246795i	−0.233017	+	0.972473i	$0.574860\pi$
$684$	−9.10863	−	9.90921i	−0.0133167	−	0.0144871i
$685$	732.573	−	420.419i	1.06945	−	0.613750i
$686$	644.828	+	558.826i	0.939982	+	0.814614i
$687$	472.766	+	378.828i	0.688160	+	0.551424i
$688$	96.5206	+	25.8626i	0.140292	+	0.0375910i
$689$	−627.186	−	362.106i	−0.910284	−	0.525553i
$690$	1350.26	−	145.397i	1.95691	−	0.210721i
$691$	565.572	−	326.533i	0.818484	−	0.472552i	−0.0314095	−	0.999507i	$-0.510000\pi$
$691$	565.572	−	326.533i	0.818484	−	0.472552i	0.849893	+	0.526955i	$0.176666\pi$
$692$	305.952	+	305.952i	0.442128	+	0.442128i
$693$	27.0063	−	1.86562i	0.0389701	−	0.00269210i
$694$		−	24.9165i		−	0.0359028i
$695$	46.4950	+	175.342i	0.0668993	+	0.252290i
$696$	366.363	+	160.862i	0.526384	+	0.231124i
$697$	−444.800	+	119.184i	−0.638164	+	0.170996i
$698$	772.796	+	207.070i	1.10716	+	0.296662i
$699$	25.9144	+	234.928i	0.0370736	+	0.336091i
$700$	378.366	+	59.4890i	0.540522	+	0.0849843i
$701$		−	71.3794i		−	0.101825i	−0.998703	−	0.0509125i	$-0.983787\pi$
$701$		−	71.3794i		−	0.101825i	0.998703	−	0.0509125i	$-0.0162130\pi$
$702$	994.848	−	67.5467i	1.41716	−	0.0962204i
$703$	−10.5036	+	2.81442i	−0.0149411	+	0.00400345i
$704$	0.245812	−	0.425759i	0.000349165	−	0.000604771i
$705$	301.657	−	116.678i	0.427882	−	0.165500i
$706$		−	455.614i		−	0.645345i
$707$	20.3741	−	25.4878i	0.0288177	−	0.0360506i
$708$	−122.827	−	98.4213i	−0.173484	−	0.139013i
$709$	−944.290	+	545.186i	−1.33186	+	0.768951i	−0.985585	−	0.169182i	$-0.945888\pi$
$709$	−944.290	+	545.186i	−1.33186	+	0.768951i	−0.346277	+	0.938132i	$0.612554\pi$
$710$	1506.84	+	3.91266i	2.12231	+	0.00551078i
$711$	75.7555	−	241.581i	0.106548	−	0.339776i
$712$	−461.593	−	123.683i	−0.648305	−	0.173713i
$713$	1340.91	−	1340.91i	1.88067	−	1.88067i
$714$	−1005.50	+	225.808i	−1.40827	+	0.316257i
$715$	27.6632	−	15.8757i	0.0386897	−	0.0222038i
$716$	160.476	−	92.6506i	0.224128	−	0.129400i
$717$	−528.569	+	206.024i	−0.737195	+	0.287342i
$718$	213.776	+	797.823i	0.297738	+	1.11117i
$719$	−38.2047	+	22.0575i	−0.0531359	+	0.0306780i	−0.526333	−	0.850279i	$-0.676433\pi$
$719$	−38.2047	+	22.0575i	−0.0531359	+	0.0306780i	0.473197	+	0.880957i	$0.343100\pi$
$720$	−40.1164	+	897.502i	−0.0557172	+	1.24653i
$721$	−350.005	+	799.696i	−0.485444	+	1.10915i
$722$	−634.203	+	634.203i	−0.878397	+	0.878397i
$723$	514.402	+	78.7629i	0.711483	+	0.108939i
$724$	−129.343	+	224.029i	−0.178651	+	0.309432i
$725$	−642.743	+	366.651i	−0.886543	+	0.505725i
$726$	533.726	+	726.720i	0.735160	+	1.00099i
$727$	−641.791	+	641.791i	−0.882794	+	0.882794i	−0.993818	−	0.111024i	$-0.964587\pi$
$727$	−641.791	+	641.791i	−0.882794	+	0.882794i	0.111024	+	0.993818i	$0.464587\pi$
$728$	−70.3269	+	462.954i	−0.0966029	+	0.635926i
$729$	−446.492	−	576.269i	−0.612472	−	0.790492i
$730$	−116.546	−	439.516i	−0.159651	−	0.602076i
$731$	49.3674	−	85.5068i	0.0675340	−	0.116972i
$732$	235.756	−	91.8926i	0.322071	−	0.125536i
$733$	325.490	−	1214.74i	0.444051	−	1.65722i	−0.274378	−	0.961622i	$-0.588472\pi$
$733$	325.490	−	1214.74i	0.444051	−	1.65722i	0.718429	−	0.695600i	$-0.244861\pi$
$734$			866.352i			1.18032i
$735$	−237.722	−	695.495i	−0.323431	−	0.946252i
$736$	1151.55			1.56461
$737$	−29.3670	−	7.86885i	−0.0398466	−	0.0106769i
$738$	−463.220	+	242.057i	−0.627669	+	0.327991i
$739$	592.533	+	342.099i	0.801803	+	0.462921i	0.844101	−	0.536184i	$-0.180135\pi$
$739$	592.533	+	342.099i	0.801803	+	0.462921i	−0.0422981	+	0.999105i	$0.513468\pi$
$740$	−150.593	−	87.4672i	−0.203504	−	0.118199i
$741$	3.33663	+	30.2482i	0.00450287	+	0.0408208i
$742$	839.874	+	127.584i	1.13191	+	0.171947i
$743$	−515.101	−	515.101i	−0.693273	−	0.693273i	0.269678	−	0.962951i	$-0.413083\pi$
$743$	−515.101	−	515.101i	−0.693273	−	0.693273i	−0.962951	+	0.269678i	$0.913083\pi$
$744$	416.948	+	567.715i	0.560414	+	0.763058i
$745$	661.848	−	658.419i	0.888386	−	0.883784i
$746$	−696.469	−	402.106i	−0.933604	−	0.539017i
$747$	−26.0380	+	618.533i	−0.0348567	+	0.828023i
$748$	13.1181	+	13.1181i	0.0175375	+	0.0175375i
$749$	−305.315	−	133.628i	−0.407630	−	0.178409i
$750$	−723.434	−	589.001i	−0.964579	−	0.785335i
$751$	−359.815	−	623.218i	−0.479114	−	0.829850i	0.520599	−	0.853801i	$-0.325709\pi$
$751$	−359.815	−	623.218i	−0.479114	−	0.829850i	−0.999713	+	0.0239511i	$0.992375\pi$
$752$	415.811	−	111.416i	0.552941	−	0.148160i
$753$	−19.4006	+	7.56194i	−0.0257644	+	0.0100424i
$754$	546.555	+	946.662i	0.724875	+	1.25552i
$755$	681.281	+	184.446i	0.902359	+	0.244299i
$756$	−374.143	+	176.430i	−0.494898	+	0.233372i
$757$	−720.617	−	720.617i	−0.951937	−	0.951937i	0.0469594	−	0.998897i	$-0.485047\pi$
$757$	−720.617	−	720.617i	−0.951937	−	0.951937i	−0.998897	+	0.0469594i	$0.985047\pi$
$758$	−67.3175	+	251.232i	−0.0888093	+	0.331441i
$759$	−18.8614	+	42.9567i	−0.0248503	+	0.0565964i
$760$	−15.3950	−	0.0399747i	−0.0202566	−	5.25984e-5i
$761$	−148.918	−	257.934i	−0.195688	−	0.338941i	0.751438	−	0.659804i	$-0.229361\pi$
$761$	−148.918	−	257.934i	−0.195688	−	0.338941i	−0.947126	+	0.320863i	$0.896027\pi$
$762$	747.838	+	599.244i	0.981415	+	0.786410i
$763$	−29.5336	−	23.6082i	−0.0387072	−	0.0309413i
$764$	−24.5745			−0.0321656
$765$	846.331	+	267.810i	1.10631	+	0.350079i
$766$	1192.95	+	688.750i	1.55738	+	0.899152i
$767$	92.1050	+	343.740i	0.120085	+	0.448162i
$768$	−144.098	+	941.107i	−0.187628	+	1.22540i
$769$	479.003			0.622890			0.311445	−	0.950264i	$-0.399187\pi$
$769$	479.003			0.622890			0.311445	+	0.950264i	$0.399187\pi$
$770$	−23.4363	+	29.1630i	−0.0304368	+	0.0378741i
$771$	−109.016	−	988.289i	−0.141396	−	1.28183i
$772$	−47.8417	+	178.547i	−0.0619711	+	0.231279i
$773$	105.667	+	394.353i	0.136697	+	0.510160i	0.999985	+	0.00544852i	$0.00173433\pi$
$773$	105.667	+	394.353i	0.136697	+	0.510160i	−0.863288	+	0.504711i	$0.831599\pi$
$774$	33.5309	−	106.928i	0.0433216	−	0.138150i
$775$	−1302.62	−	6.76481i	−1.68080	−	0.00872878i
$776$	−554.907			−0.715086
$777$	−13.6623	+	333.916i	−0.0175834	+	0.429751i
$778$	−99.7443	+	99.7443i	−0.128206	+	0.128206i
$779$	−7.97541	−	13.8138i	−0.0102380	−	0.0177327i
$780$	−305.748	+	379.540i	−0.391984	+	0.486590i
$781$	−26.0272	+	45.0805i	−0.0333255	+	0.0577215i
$782$	462.250	−	1725.14i	0.591113	−	2.20606i
$783$	351.782	−	717.575i	0.449274	−	0.916444i
$784$	−215.475	−	954.230i	−0.274841	−	1.21713i
$785$	−496.244	+	284.791i	−0.632158	+	0.362791i
$786$	825.761	+	1124.35i	1.05059	+	1.43048i
$787$	36.1405	+	134.878i	0.0459219	+	0.171383i	0.985078	−	0.172107i	$-0.0550575\pi$
$787$	36.1405	+	134.878i	0.0459219	+	0.171383i	−0.939156	+	0.343490i	$0.888391\pi$
$788$	−615.629	+	164.957i	−0.781255	+	0.209337i
$789$	1245.25	−	914.554i	1.57827	−	1.15913i
$790$	174.167	+	303.483i	0.220465	+	0.384156i
$791$	−478.817	−	650.348i	−0.605332	−	0.822184i
$792$	−14.7117	−	9.34009i	−0.0185753	−	0.0117930i
$793$	−552.606	−	148.070i	−0.696855	−	0.186722i
$794$	−554.533	−	320.160i	−0.698404	−	0.403224i
$795$	−569.849	−	459.056i	−0.716791	−	0.577428i
$796$	−412.181	+	237.973i	−0.517815	+	0.298961i
$797$	305.773	+	305.773i	0.383655	+	0.383655i	0.872417	−	0.488762i	$-0.162551\pi$
$797$	305.773	+	305.773i	0.383655	+	0.383655i	−0.488762	+	0.872417i	$0.662551\pi$
$798$	−16.5697	−	31.6181i	−0.0207640	−	0.0396217i
$799$		−	425.350i		−	0.532353i
$800$	−556.428	−	562.238i	−0.695535	−	0.702797i
$801$	−285.590	+	910.732i	−0.356541	+	1.13699i
$802$	569.196	−	152.516i	0.709721	−	0.190169i
$803$	15.1727	+	4.06553i	0.0188951	+	0.00506292i
$804$	461.773	−	50.9373i	0.574344	−	0.0633548i
$805$	1258.85	+	194.576i	1.56379	+	0.241710i
$806$			1924.31i			2.38748i
$807$	−1410.70	−	216.000i	−1.74808	−	0.267658i
$808$	−20.2892	+	5.43648i	−0.0251104	+	0.00672832i
$809$	331.049	−	573.394i	0.409208	−	0.708769i	−0.585593	−	0.810605i	$-0.699138\pi$
$809$	331.049	−	573.394i	0.409208	−	0.708769i	0.994801	+	0.101836i	$0.0324717\pi$
$810$	1003.73	+	87.2821i	1.23917	+	0.107756i
$811$			666.372i			0.821667i	0.911710	+	0.410834i	$0.134762\pi$
$811$			666.372i			0.821667i	−0.911710	+	0.410834i	$0.865238\pi$
$812$	−354.209	−	283.143i	−0.436217	−	0.348698i
$813$	172.901	−	215.775i	0.212670	−	0.265406i
$814$	14.7322	−	8.50565i	0.0180986	−	0.0104492i
$815$	2.08556	−	803.188i	0.00255897	−	0.985506i
$816$	1081.80	+	474.994i	1.32573	+	0.582101i
$817$	3.30351	+	0.885172i	0.00404346	+	0.00108344i
$818$	−1203.96	+	1203.96i	−1.47184	+	1.47184i
$819$	917.930	+	179.229i	1.12079	+	0.218839i
$820$	66.7576	−	246.580i	0.0814117	−	0.300707i
$821$	−561.249	+	324.037i	−0.683616	+	0.394686i	−0.801216	−	0.598375i	$-0.795813\pi$
$821$	−561.249	+	324.037i	−0.683616	+	0.394686i	0.117600	+	0.993061i	$0.462480\pi$
$822$	−457.852	−	1174.65i	−0.556998	−	1.42901i
$823$	−217.723	−	812.554i	−0.264548	−	0.987307i	−0.962526	−	0.271188i	$-0.912583\pi$
$823$	−217.723	−	812.554i	−0.264548	−	0.987307i	0.697978	−	0.716119i	$-0.254083\pi$
$824$	486.648	−	280.967i	0.590593	−	0.340979i
$825$	30.0870	−	11.5476i	0.0364691	−	0.0139971i
$826$	−247.493	−	336.154i	−0.299628	−	0.406966i
$827$	−72.7609	+	72.7609i	−0.0879818	+	0.0879818i	−0.749728	−	0.661746i	$-0.769816\pi$
$827$	−72.7609	+	72.7609i	−0.0879818	+	0.0879818i	0.661746	+	0.749728i	$0.269816\pi$
$828$	30.1517	−	716.255i	0.0364151	−	0.865042i
$829$	−713.103	+	1235.13i	−0.860197	+	1.48991i	0.0115413	+	0.999933i	$0.496326\pi$
$829$	−713.103	+	1235.13i	−0.860197	+	1.48991i	−0.871738	+	0.489972i	$0.837007\pi$
$830$	−603.430	−	606.572i	−0.727025	−	0.730810i
$831$	−221.011	+	162.318i	−0.265958	+	0.195328i
$832$	12.0103	−	12.0103i	0.0144354	−	0.0144354i
$833$	−965.837	−	38.3768i	−1.15947	−	0.0460706i
$834$	269.131	−	29.6873i	0.322699	−	0.0355963i
$835$	−147.576	+	254.084i	−0.176738	+	0.304292i
$836$	−0.321304	+	0.556515i	−0.000384335	+	0.000665688i
$837$	1167.92	−	784.340i	1.39536	−	0.937085i
$838$	316.940	−	1182.84i	0.378210	−	1.41150i
$839$			554.001i			0.660311i	0.943927	+	0.330156i	$0.107101\pi$
$839$			554.001i			0.660311i	−0.943927	+	0.330156i	$0.892899\pi$
$840$	−142.211	+	451.262i	−0.169299	+	0.537217i
$841$	35.0831			0.0417159
$842$	−1184.80	−	317.466i	−1.40712	−	0.377038i
$843$	−59.9187	−	153.725i	−0.0710779	−	0.182355i
$844$	152.407	+	87.9922i	0.180577	+	0.104256i
$845$	248.355	−	65.8558i	0.293911	−	0.0779359i
$846$	−105.226	−	471.159i	−0.124380	−	0.556925i
$847$	308.061	+	787.604i	0.363708	+	0.929875i
$848$	−688.674	−	688.674i	−0.812115	−	0.812115i
$849$	388.439	−	285.282i	0.457525	−	0.336021i
$850$	−1065.65	+	607.894i	−1.25370	+	0.715170i
$851$	−501.586	−	289.591i	−0.589407	−	0.340294i
$852$	120.388	−	786.258i	0.141301	−	0.922838i
$853$	−104.095	−	104.095i	−0.122034	−	0.122034i	0.643452	−	0.765486i	$-0.277502\pi$
$853$	−104.095	−	104.095i	−0.122034	−	0.122034i	−0.765486	+	0.643452i	$0.777502\pi$
$854$	666.947	−	74.3657i	0.780968	−	0.0870792i
$855$	−1.37302	+	30.7178i	−0.00160587	+	0.0359273i
$856$	107.270	+	185.797i	0.125315	+	0.217052i
$857$	750.052	−	200.976i	0.875207	−	0.234511i	0.206869	−	0.978369i	$-0.433673\pi$
$857$	750.052	−	200.976i	0.875207	−	0.234511i	0.668338	+	0.743858i	$0.267006\pi$
$858$	−17.2892	−	44.3566i	−0.0201506	−	0.0516977i
$859$	−131.576	−	227.897i	−0.153174	−	0.265305i	0.779219	−	0.626752i	$-0.215616\pi$
$859$	−131.576	−	227.897i	−0.153174	−	0.265305i	−0.932393	+	0.361447i	$0.882283\pi$
$860$	27.2632	+	47.5057i	0.0317014	+	0.0552392i
$861$	−478.307	+	107.414i	−0.555525	+	0.124755i
$862$	−1213.32	−	1213.32i	−1.40757	−	1.40757i
$863$	78.1523	−	291.668i	0.0905588	−	0.337970i	−0.905750	−	0.423813i	$-0.860692\pi$
$863$	78.1523	−	291.668i	0.0905588	−	0.337970i	0.996309	+	0.0858425i	$0.0273582\pi$
$864$	838.282	+	164.704i	0.970234	+	0.190630i
$865$	2.56665	−	988.464i	0.00296722	−	1.14273i
$866$	−282.373	−	489.084i	−0.326065	−	0.564762i
$867$	187.847	−	234.428i	0.216664	−	0.270390i
$868$	−290.786	−	743.439i	−0.335007	−	0.856496i
$869$	−12.0877			−0.0139100
$870$	398.440	+	1030.12i	0.457976	+	1.18404i
$871$	−909.664	−	525.195i	−1.04439	−	0.602979i
$872$	6.29946	+	23.5099i	0.00722415	+	0.0269609i
$873$	−46.6146	+	1107.33i	−0.0533958	+	1.26842i
$874$	61.8647			0.0707834
$875$	−513.273	−	708.643i	−0.586598	−	0.809878i
$876$	−238.580	+	26.3173i	−0.272351	+	0.0300426i
$877$	88.0311	−	328.537i	0.100378	−	0.374614i	−0.897402	−	0.441213i	$-0.854548\pi$
$877$	88.0311	−	328.537i	0.100378	−	0.374614i	0.997780	+	0.0665992i	$0.0212149\pi$
$878$	−287.094	−	1071.45i	−0.326987	−	1.22033i
$879$	−380.026	+	865.508i	−0.432339	+	0.984651i
$880$	41.4600	−	10.9939i	0.0471136	−	0.0124930i
$881$	222.583			0.252648			0.126324	−	0.991989i	$-0.459682\pi$
$881$	222.583			0.252648			0.126324	+	0.991989i	$0.459682\pi$
$882$	−1079.35	+	196.425i	−1.22375	+	0.222704i
$883$	−1079.63	+	1079.63i	−1.22269	+	1.22269i	−0.256013	+	0.966673i	$0.582409\pi$
$883$	−1079.63	+	1079.63i	−1.22269	+	1.22269i	−0.966673	+	0.256013i	$0.917591\pi$
$884$	320.472	+	555.074i	0.362525	+	0.627912i
$885$	38.4963	+	357.504i	0.0434986	+	0.403960i
$886$	−87.2180	+	151.066i	−0.0984401	+	0.170503i
$887$	40.8634	−	152.504i	0.0460692	−	0.171932i	−0.939058	−	0.343758i	$-0.888300\pi$
$887$	40.8634	−	152.504i	0.0460692	−	0.171932i	0.985127	+	0.171826i	$0.0549666\pi$
$888$	134.524	−	167.882i	0.151492	−	0.189057i
$889$	532.915	+	723.825i	0.599454	+	0.814201i
$890$	−656.590	−	1144.10i	−0.737741	−	1.28550i
$891$	−19.8743	+	28.5729i	−0.0223056	+	0.0320684i
$892$	−133.010	−	496.401i	−0.149115	−	0.556504i
$893$	14.2315	−	3.81333i	0.0159368	−	0.00427024i
$894$	−824.849	−	1123.11i	−0.922650	−	1.25628i
$895$	−408.613	−	110.625i	−0.456551	−	0.123604i
$896$	−363.212	+	829.870i	−0.405371	+	0.926195i
$897$	−1013.55	+	1264.88i	−1.12994	+	1.41013i
$898$	−1982.82	−	531.295i	−2.20804	−	0.591642i
$899$	1335.63	+	771.127i	1.48568	+	0.857761i
$900$	−364.275	+	331.371i	−0.404750	+	0.368190i
$901$	−833.399	+	481.163i	−0.924971	+	0.534032i
$902$	17.6446	+	17.6446i	0.0195617	+	0.0195617i
$903$	56.2317	−	88.8023i	0.0622721	−	0.0983414i
$904$			519.875i			0.575083i
$905$	571.231	−	151.472i	0.631195	−	0.167373i
$906$	423.542	−	964.614i	0.467485	−	1.06470i
$907$	512.284	−	137.266i	0.564811	−	0.151341i	0.0348954	−	0.999391i	$-0.488890\pi$
$907$	512.284	−	137.266i	0.564811	−	0.151341i	0.529916	+	0.848050i	$0.322224\pi$
$908$	830.902	+	222.640i	0.915090	+	0.245198i
$909$	9.14427	+	40.9444i	0.0100597	+	0.0450434i
$910$	−1042.89	+	763.655i	−1.14603	+	0.839181i
$911$			224.716i			0.246670i	0.992365	+	0.123335i	$0.0393589\pi$
$911$			224.716i			0.246670i	−0.992365	+	0.123335i	$0.960641\pi$
$912$	−6.19407	+	40.4536i	−0.00679175	+	0.0443570i
$913$	28.5500	−	7.64996i	0.0312706	−	0.00837893i
$914$	393.123	−	680.908i	0.430112	−	0.744976i
$915$	−528.677	−	233.770i	−0.577789	−	0.255487i
$916$			441.976i			0.482507i
$917$	476.620	+	1218.55i	0.519760	+	1.32884i
$918$	583.242	−	1189.71i	0.635339	−	1.29599i
$919$	1021.02	−	589.486i	1.11101	−	0.641442i	0.171920	−	0.985111i	$-0.445003\pi$
$919$	1021.02	−	589.486i	1.11101	−	0.641442i	0.939091	+	0.343669i	$0.111670\pi$
$920$	−578.306	−	581.317i	−0.628593	−	0.631866i
$921$	228.882	−	521.277i	0.248514	−	0.565990i
$922$	1029.29	+	275.798i	1.11637	+	0.299130i
$923$	−1271.68	+	1271.68i	−1.37777	+	1.37777i
$924$	13.3824	+	14.5242i	0.0144831	+	0.0157188i
$925$	100.975	+	384.825i	0.109162	+	0.416027i
$926$	314.625	−	181.649i	0.339768	−	0.196165i
$927$	−519.796	−	994.723i	−0.560729	−	1.07306i
$928$	242.393	+	904.623i	0.261199	+	0.974810i
$929$	474.227	−	273.795i	0.510470	−	0.294720i	−0.222557	−	0.974920i	$-0.571440\pi$
$929$	474.227	−	273.795i	0.510470	−	0.294720i	0.733027	+	0.680200i	$0.238107\pi$
$930$	−299.268	+	1921.17i	−0.321794	+	2.06578i
$931$	−7.37485	−	32.6594i	−0.00792142	−	0.0350799i
$932$	−121.927	+	121.927i	−0.130823	+	0.130823i
$933$	88.8695	−	580.408i	0.0952513	−	0.622088i
$934$	955.166	−	1654.40i	1.02266	−	1.77130i
$935$	0.110048	−	42.3816i	0.000117698	−	0.0453279i
$936$	−407.435	−	443.246i	−0.435294	−	0.473553i
$937$	−917.481	+	917.481i	−0.979169	+	0.979169i	−0.999787	−	0.0206186i	$-0.993436\pi$
$937$	−917.481	+	917.481i	−0.979169	+	0.979169i	0.0206186	+	0.999787i	$0.493436\pi$
$938$	1218.14	+	185.047i	1.29866	+	0.197278i
$939$	120.132	+	1089.06i	0.127936	+	1.15980i
$940$	204.042	+	118.511i	0.217066	+	0.126076i
$941$	−410.974	+	711.829i	−0.436742	+	0.756460i	−0.997436	−	0.0715634i	$-0.977201\pi$
$941$	−410.974	+	711.829i	−0.436742	+	0.756460i	0.560694	+	0.828023i	$0.310534\pi$
$942$	310.148	+	795.705i	0.329245	+	0.844698i
$943$	219.887	−	820.631i	0.233179	−	0.870234i
$944$			478.575i			0.506965i
$945$	888.560	+	321.694i	0.940275	+	0.340417i
$946$	−5.35027			−0.00565568
$947$	1065.97	+	285.625i	1.12563	+	0.301610i	0.773158	−	0.634214i	$-0.218676\pi$
$947$	1065.97	+	285.625i	1.12563	+	0.301610i	0.352467	+	0.935824i	$0.385343\pi$
$948$	172.097	−	67.0795i	0.181536	−	0.0707589i
$949$	469.988	+	271.347i	0.495245	+	0.285930i
$950$	−29.8929	−	30.2050i	−0.0314662	−	0.0317947i
$951$	510.025	−	56.2599i	0.536304	−	0.0591586i
$952$	486.027	+	388.514i	0.510533	+	0.408103i
$953$	864.642	+	864.642i	0.907284	+	0.907284i	0.996052	−	0.0887684i	$-0.0282931\pi$
$953$	864.642	+	864.642i	0.907284	+	0.907284i	−0.0887684	+	0.996052i	$0.528293\pi$
$954$	−804.120	+	739.154i	−0.842893	+	0.774794i
$955$	39.5943	+	39.8005i	0.0414600	+	0.0416759i
$956$	−358.426	−	206.937i	−0.374923	−	0.216462i
$957$	−37.7155	−	5.77483i	−0.0394102	−	0.00603430i
$958$	150.886	+	150.886i	0.157501	+	0.157501i
$959$	−131.038	−	1175.21i	−0.136640	−	1.22546i
$960$	13.8585	−	10.1229i	0.0144360	−	0.0105446i
$961$	876.989	+	1518.99i	0.912579	+	1.58063i
$962$	567.697	−	152.114i	0.590122	−	0.158123i
$963$	379.774	−	198.452i	0.394365	−	0.206077i
$964$	189.828	+	328.792i	0.196917	+	0.341070i
$965$	366.255	−	210.191i	0.379539	−	0.217815i
$966$	566.759	−	1814.86i	0.586707	−	1.87874i
$967$	990.382	+	990.382i	1.02418	+	1.02418i	0.999700	+	0.0244798i	$0.00779293\pi$
$967$	990.382	+	990.382i	1.02418	+	1.02418i	0.0244798	+	0.999700i	$0.492207\pi$
$968$	140.902	−	525.855i	0.145560	−	0.543239i
$969$	37.0255	+	16.2571i	0.0382100	+	0.0167772i
$970$	−1080.29	−	1085.92i	−1.11370	−	1.11950i
$971$	711.691	+	1232.68i	0.732946	+	1.26950i	0.955619	+	0.294607i	$0.0951887\pi$
$971$	711.691	+	1232.68i	0.732946	+	1.26950i	−0.222672	+	0.974893i	$0.571478\pi$
$972$	124.393	−	517.090i	0.127977	−	0.531986i
$973$	251.082	+	38.1415i	0.258049	+	0.0391999i
$974$	−2325.20			−2.38727
$975$	1107.32	−	116.329i	1.13571	−	0.119312i
$976$	−666.293	−	384.684i	−0.682677	−	0.394144i
$977$	−191.006	−	712.844i	−0.195503	−	0.729626i	−0.992136	−	0.125163i	$-0.960055\pi$
$977$	−191.006	−	712.844i	−0.195503	−	0.729626i	0.796634	−	0.604463i	$-0.206612\pi$
$978$	−1185.05	−	181.449i	−1.21170	−	0.185531i
$979$	45.5694			0.0465469
$980$	287.512	−	452.624i	0.293379	−	0.461861i
$981$	47.4438	−	10.5958i	0.0483627	−	0.0108010i
$982$	−93.4134	+	348.624i	−0.0951257	+	0.355014i
$983$	231.552	+	864.163i	0.235556	+	0.879108i	0.977897	+	0.209085i	$0.0670487\pi$
$983$	231.552	+	864.163i	0.235556	+	0.879108i	−0.742341	+	0.670022i	$0.766285\pi$
$984$	288.942	+	126.868i	0.293640	+	0.128931i
$985$	1259.06	+	731.284i	1.27823	+	0.742420i
$986$	1452.52			1.47314
$987$	18.5113	−	452.431i	0.0187551	−	0.458390i
$988$	−15.6988	+	15.6988i	−0.0158895	+	0.0158895i
$989$	91.0800	+	157.755i	0.0920930	+	0.159510i
$990$	−10.3627	−	46.9731i	−0.0104674	−	0.0474476i
$991$	523.474	−	906.684i	0.528228	−	0.914918i	−0.471230	−	0.882010i	$-0.656190\pi$
$991$	523.474	−	906.684i	0.528228	−	0.914918i	0.999458	−	0.0329077i	$-0.0104767\pi$
$992$	−426.708	+	1592.50i	−0.430149	+	1.60534i
$993$	−289.105	−	231.660i	−0.291143	−	0.233293i
$994$	845.840	−	1932.58i	0.850946	−	1.94425i
$995$	1049.52	+	284.141i	1.05479	+	0.285569i
$996$	−364.022	+	267.350i	−0.365484	+	0.268423i
$997$	−334.838	−	1249.63i	−0.335845	−	1.25339i	−0.902950	−	0.429746i	$-0.858603\pi$
$997$	−334.838	−	1249.63i	−0.335845	−	1.25339i	0.567104	−	0.823646i	$-0.308064\pi$
$998$	1630.03	−	436.766i	1.63330	−	0.437641i
$999$	−323.713	−	282.550i	−0.324037	−	0.282833i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.w.a.17.7	✓	112
3.2	odd	2	inner	105.3.w.a.17.22	yes	112
5.3	odd	4	inner	105.3.w.a.38.7	yes	112
7.5	odd	6	inner	105.3.w.a.47.22	yes	112
15.8	even	4	inner	105.3.w.a.38.22	yes	112
21.5	even	6	inner	105.3.w.a.47.7	yes	112
35.33	even	12	inner	105.3.w.a.68.22	yes	112
105.68	odd	12	inner	105.3.w.a.68.7	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.w.a.17.7	✓	112	1.1	even	1	trivial
105.3.w.a.17.22	yes	112	3.2	odd	2	inner
105.3.w.a.38.7	yes	112	5.3	odd	4	inner
105.3.w.a.38.22	yes	112	15.8	even	4	inner
105.3.w.a.47.7	yes	112	21.5	even	6	inner
105.3.w.a.47.22	yes	112	7.5	odd	6	inner
105.3.w.a.68.7	yes	112	105.68	odd	12	inner
105.3.w.a.68.22	yes	112	35.33	even	12	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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.40293 - 0.643864i) q^{2} +(2.79517 - 1.08950i) q^{3} +(1.89543 + 1.09433i) q^{4} +(-1.28155 - 4.83297i) q^{5} +(-7.41810 + 0.818277i) q^{6} +(-6.92060 - 1.05130i) q^{7} +(3.18629 + 3.18629i) q^{8} +(6.62599 - 6.09067i) q^{9} +(-0.0322977 + 12.4385i) q^{10} +(-0.372125 - 0.214846i) q^{11} +(6.49031 + 0.993767i) q^{12} +(-10.4973 - 10.4973i) q^{13} +(15.9529 + 6.98214i) q^{14} +(-8.84767 - 12.1128i) q^{15} +(-9.98221 - 17.2897i) q^{16} +(-19.0543 + 5.10559i) q^{17} +(-19.8434 + 10.3692i) q^{18} +(-0.341650 - 0.591755i) q^{19} +(2.85976 - 10.5630i) q^{20} +(-20.4897 + 4.60141i) q^{21} +(0.755860 + 0.755860i) q^{22} +(9.41953 - 35.1542i) q^{23} +(12.3777 + 5.43478i) q^{24} +(-21.7153 + 12.3874i) q^{25} +(18.4655 + 31.9832i) q^{26} +(11.8850 - 24.2435i) q^{27} +(-11.9670 - 9.56606i) q^{28} +29.5987 q^{29} +(13.4614 + 34.8028i) q^{30} +(45.1246 + 26.0527i) q^{31} +(8.18932 + 30.5629i) q^{32} +(-1.27423 - 0.195104i) q^{33} +49.0736 q^{34} +(3.78819 + 34.7944i) q^{35} +(19.2243 - 4.29342i) q^{36} +(4.11887 - 15.3718i) q^{37} +(0.439953 + 1.64193i) q^{38} +(-40.7786 - 17.9050i) q^{39} +(11.3159 - 19.4826i) q^{40} +23.3438 q^{41} +(52.1980 + 2.13570i) q^{42} +(-3.53920 + 3.53920i) q^{43} +(-0.470224 - 0.814452i) q^{44} +(-37.9276 - 24.2177i) q^{45} +(-45.2690 + 78.4082i) q^{46} +(-5.58075 + 20.8276i) q^{47} +(-46.7391 - 37.4521i) q^{48} +(46.7895 + 14.5513i) q^{49} +(60.1561 - 15.7844i) q^{50} +(-47.6977 + 35.0307i) q^{51} +(-8.40942 - 31.3844i) q^{52} +(47.1211 - 12.6261i) q^{53} +(-44.1684 + 50.6031i) q^{54} +(-0.561450 + 2.07381i) q^{55} +(-18.7013 - 25.4008i) q^{56} +(-1.59969 - 1.28183i) q^{57} +(-71.1237 - 19.0575i) q^{58} +(-20.7598 - 11.9857i) q^{59} +(-3.51481 - 32.6411i) q^{60} +(33.3740 - 19.2685i) q^{61} +(-91.6571 - 91.6571i) q^{62} +(-52.2590 + 35.1852i) q^{63} +1.14413i q^{64} +(-37.2804 + 64.1861i) q^{65} +(2.93627 + 1.28925i) q^{66} +(68.3440 - 18.3127i) q^{67} +(-41.7033 - 11.1744i) q^{68} +(-11.9711 - 108.525i) q^{69} +(13.3001 - 86.0477i) q^{70} -121.143i q^{71} +(40.5190 + 1.70570i) q^{72} +(-35.3107 + 9.46146i) q^{73} +(-19.7947 + 34.2855i) q^{74} +(-47.2019 + 58.2836i) q^{75} -1.49551i q^{76} +(2.34946 + 1.87808i) q^{77} +(86.4600 + 69.2805i) q^{78} +(24.3623 - 14.0656i) q^{79} +(-70.7679 + 70.4013i) q^{80} +(6.80754 - 80.7134i) q^{81} +(-56.0936 - 15.0302i) q^{82} +(-48.6396 + 48.6396i) q^{83} +(-43.8721 - 13.7007i) q^{84} +(49.0943 + 85.5460i) q^{85} +(10.7832 - 6.22569i) q^{86} +(82.7335 - 32.2477i) q^{87} +(-0.501135 - 1.87026i) q^{88} +(-91.8429 + 53.0255i) q^{89} +(75.5445 + 82.6138i) q^{90} +(61.6120 + 83.6837i) q^{91} +(56.3241 - 56.3241i) q^{92} +(154.516 + 23.6587i) q^{93} +(26.8203 - 46.4542i) q^{94} +(-2.42210 + 2.40955i) q^{95} +(56.1888 + 76.5065i) q^{96} +(-87.0772 + 87.0772i) q^{97} +(-103.063 - 65.0919i) q^{98} +(-3.77426 + 0.842919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q - 6 q^{3} - 16 q^{7} - 60 q^{10} - 30 q^{12} - 20 q^{15} + 120 q^{16} + 46 q^{18} - 96 q^{21} - 80 q^{22} + 28 q^{25} - 136 q^{28} - 80 q^{30} - 24 q^{31} - 36 q^{33} - 272 q^{36} + 60 q^{37} - 72 q^{40}+ \cdots + 2184 q^{96}+O(q^{100}) \) 112 * q - 6 * q^3 - 16 * q^7 - 60 * q^10 - 30 * q^12 - 20 * q^15 + 120 * q^16 + 46 * q^18 - 96 * q^21 - 80 * q^22 + 28 * q^25 - 136 * q^28 - 80 * q^30 - 24 * q^31 - 36 * q^33 - 272 * q^36 + 60 * q^37 - 72 * q^40 + 338 * q^42 - 48 * q^43 + 384 * q^45 + 40 * q^46 + 176 * q^51 - 204 * q^52 + 344 * q^57 - 284 * q^58 - 214 * q^60 - 912 * q^61 + 132 * q^63 - 444 * q^66 - 36 * q^67 + 208 * q^70 - 638 * q^72 + 708 * q^73 + 42 * q^75 + 664 * q^78 + 8 * q^81 + 1104 * q^82 + 264 * q^85 + 246 * q^87 + 180 * q^88 + 632 * q^91 + 196 * q^93 + 2184 * q^96

Introduction

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