LMFDB - Embedded newform 75.3.h.a.14.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(14,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("75.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			14.5
Character	$\chi$	$=$	75.14
Dual form			75.3.h.a.59.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.88806 + 1.37175i) q^{2} +(-2.96199 - 0.476037i) q^{3} +(0.446980 - 1.37566i) q^{4} +(-0.465978 + 4.97824i) q^{5} +(6.24541 - 3.16433i) q^{6} -12.5544i q^{7} +(-1.84155 - 5.66769i) q^{8} +(8.54678 + 2.82003i) q^{9} +(-5.94912 - 10.0384i) q^{10} +(-7.59880 - 10.4589i) q^{11} +(-1.97882 + 3.86192i) q^{12} +(-2.92256 + 4.02255i) q^{13} +(17.2215 + 23.7033i) q^{14} +(3.75005 - 14.5237i) q^{15} +(15.9325 + 11.5756i) q^{16} +(-3.32914 - 10.2460i) q^{17} +(-20.0052 + 6.39968i) q^{18} +(-1.29722 - 3.99244i) q^{19} +(6.64010 + 2.86620i) q^{20} +(-5.97634 + 37.1859i) q^{21} +(28.6939 + 9.32322i) q^{22} +(-17.6249 + 12.8053i) q^{23} +(2.75661 + 17.6643i) q^{24} +(-24.5657 - 4.63950i) q^{25} -11.6038i q^{26} +(-23.9730 - 12.4215i) q^{27} +(-17.2706 - 5.61156i) q^{28} +(-26.0760 - 8.47261i) q^{29} +(12.8426 + 32.5656i) q^{30} +(-8.64023 - 26.5919i) q^{31} -22.1228 q^{32} +(17.5288 + 34.5963i) q^{33} +(20.3406 + 14.7783i) q^{34} +(62.4987 + 5.85006i) q^{35} +(7.69966 - 10.4970i) q^{36} +(-0.0202976 + 0.0279372i) q^{37} +(7.92586 + 5.75848i) q^{38} +(10.5715 - 10.5235i) q^{39} +(29.0733 - 6.52663i) q^{40} +(44.4000 - 61.1113i) q^{41} +(-39.7262 - 78.4072i) q^{42} +43.3942i q^{43} +(-17.7844 + 5.77849i) q^{44} +(-18.0214 + 41.2338i) q^{45} +(15.7112 - 48.3541i) q^{46} +(1.52001 - 4.67812i) q^{47} +(-41.6814 - 41.8713i) q^{48} -108.612 q^{49} +(52.7457 - 24.9385i) q^{50} +(4.98338 + 31.9334i) q^{51} +(4.22736 + 5.81846i) q^{52} +(-0.528642 + 1.62699i) q^{53} +(62.3016 - 9.43260i) q^{54} +(55.6075 - 32.9550i) q^{55} +(-71.1543 + 23.1194i) q^{56} +(1.94181 + 12.4431i) q^{57} +(60.8553 - 19.7731i) q^{58} +(-28.0481 + 38.6049i) q^{59} +(-18.3035 - 11.6506i) q^{60} +(-5.28161 + 3.83732i) q^{61} +(52.7907 + 38.3547i) q^{62} +(35.4038 - 107.299i) q^{63} +(-21.9608 + 15.9555i) q^{64} +(-18.6634 - 16.4236i) q^{65} +(-80.5529 - 41.2746i) q^{66} +(-3.93744 + 1.27935i) q^{67} -15.5831 q^{68} +(58.3007 - 29.5390i) q^{69} +(-126.026 + 74.6874i) q^{70} +(51.8456 + 16.8457i) q^{71} +(0.243811 - 53.6337i) q^{72} +(21.0676 + 28.9970i) q^{73} -0.0805904i q^{74} +(70.5549 + 25.4364i) q^{75} -6.07208 q^{76} +(-131.304 + 95.3981i) q^{77} +(-5.52385 + 34.3704i) q^{78} +(5.27573 - 16.2370i) q^{79} +(-65.0503 + 73.9216i) q^{80} +(65.0948 + 48.2044i) q^{81} +176.287i q^{82} +(-17.6925 - 54.4519i) q^{83} +(48.4840 + 24.8428i) q^{84} +(52.5585 - 11.7988i) q^{85} +(-59.5261 - 81.9306i) q^{86} +(73.2036 + 37.5089i) q^{87} +(-45.2840 + 62.3281i) q^{88} +(-44.4639 - 61.1993i) q^{89} +(-22.5372 - 102.573i) q^{90} +(50.5006 + 36.6908i) q^{91} +(9.73774 + 29.9697i) q^{92} +(12.9335 + 82.8780i) q^{93} +(3.54736 + 10.9176i) q^{94} +(20.4798 - 4.59749i) q^{95} +(65.5274 + 10.5312i) q^{96} +(-28.4310 - 9.23778i) q^{97} +(205.066 - 148.989i) q^{98} +(-35.4509 - 110.818i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) $ 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

Character values

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

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

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

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

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

$2$	−1.88806	+	1.37175i	−0.944028	+	0.685876i	−0.949387	−	0.314109i	$-0.898294\pi$
$2$	−1.88806	+	1.37175i	−0.944028	+	0.685876i	0.00535908	+	0.999986i	$0.498294\pi$
$3$	−2.96199	−	0.476037i	−0.987330	−	0.158679i
$3$	−2.96199	−	0.476037i	−0.987330	−	0.158679i
$4$	0.446980	−	1.37566i	0.111745	−	0.343916i
$5$	−0.465978	+	4.97824i	−0.0931956	+	0.995648i
$5$	−0.465978	+	4.97824i	−0.0931956	+	0.995648i
$6$	6.24541	−	3.16433i	1.04090	−	0.527389i
$7$		−	12.5544i		−	1.79348i	−0.442556	−	0.896741i	$-0.645928\pi$
$7$		−	12.5544i		−	1.79348i	0.442556	−	0.896741i	$-0.354072\pi$
$8$	−1.84155	−	5.66769i	−0.230193	−	0.708462i
$9$	8.54678	+	2.82003i	0.949642	+	0.313337i
$10$	−5.94912	−	10.0384i	−0.594912	−	1.00384i
$11$	−7.59880	−	10.4589i	−0.690800	−	0.950805i	0.309200	−	0.950997i	$-0.399939\pi$
$11$	−7.59880	−	10.4589i	−0.690800	−	0.950805i	−1.00000		0.000192365i	$0.999939\pi$
$12$	−1.97882	+	3.86192i	−0.164902	+	0.321827i
$13$	−2.92256	+	4.02255i	−0.224812	+	0.309427i	−0.906492	−	0.422223i	$-0.861250\pi$
$13$	−2.92256	+	4.02255i	−0.224812	+	0.309427i	0.681680	+	0.731651i	$0.261250\pi$
$14$	17.2215	+	23.7033i	1.23011	+	1.69310i
$15$	3.75005	−	14.5237i	0.250003	−	0.968245i
$16$	15.9325	+	11.5756i	0.995778	+	0.723475i
$17$	−3.32914	−	10.2460i	−0.195831	−	0.602707i	−0.999966	−	0.00825983i	$-0.997371\pi$
$17$	−3.32914	−	10.2460i	−0.195831	−	0.602707i	0.804134	−	0.594448i	$-0.202629\pi$
$18$	−20.0052	+	6.39968i	−1.11140	+	0.355538i
$19$	−1.29722	−	3.99244i	−0.0682748	−	0.210128i	0.911098	−	0.412190i	$-0.135236\pi$
$19$	−1.29722	−	3.99244i	−0.0682748	−	0.210128i	−0.979373	+	0.202061i	$0.935236\pi$
$20$	6.64010	+	2.86620i	0.332005	+	0.143310i
$21$	−5.97634	+	37.1859i	−0.284588	+	1.77076i
$22$	28.6939	+	9.32322i	1.30427	+	0.423783i
$23$	−17.6249	+	12.8053i	−0.766301	+	0.556751i	−0.900837	−	0.434158i	$-0.857046\pi$
$23$	−17.6249	+	12.8053i	−0.766301	+	0.556751i	0.134535	+	0.990909i	$0.457046\pi$
$24$	2.75661	+	17.6643i	0.114859	+	0.736012i
$25$	−24.5657	−	4.63950i	−0.982629	−	0.185580i
$26$		−	11.6038i		−	0.446301i
$27$	−23.9730	−	12.4215i	−0.887890	−	0.460055i
$28$	−17.2706	−	5.61156i	−0.616807	−	0.200413i
$29$	−26.0760	−	8.47261i	−0.899172	−	0.292159i	−0.177277	−	0.984161i	$-0.556729\pi$
$29$	−26.0760	−	8.47261i	−0.899172	−	0.292159i	−0.721895	+	0.692002i	$0.756729\pi$
$30$	12.8426	+	32.5656i	0.428086	+	1.08552i
$31$	−8.64023	−	26.5919i	−0.278717	−	0.857803i	−0.988212	−	0.153092i	$-0.951077\pi$
$31$	−8.64023	−	26.5919i	−0.278717	−	0.857803i	0.709495	−	0.704711i	$-0.248923\pi$
$32$	−22.1228			−0.691336
$33$	17.5288	+	34.5963i	0.531175	+	1.04837i
$34$	20.3406	+	14.7783i	0.598253	+	0.434656i
$35$	62.4987	+	5.85006i	1.78568	+	0.167145i
$36$	7.69966	−	10.4970i	0.213879	−	0.291583i
$37$	−0.0202976	+	0.0279372i	−0.000548584	+	0.000755061i	−0.809291	−	0.587408i	$-0.800149\pi$
$37$	−0.0202976	+	0.0279372i	−0.000548584	+	0.000755061i	0.808743	+	0.588163i	$0.200149\pi$
$38$	7.92586	+	5.75848i	0.208575	+	0.151539i
$39$	10.5715	−	10.5235i	0.271063	−	0.269834i
$40$	29.0733	−	6.52663i	0.726831	−	0.163166i
$41$	44.4000	−	61.1113i	1.08293	−	1.49052i	0.226668	−	0.973972i	$-0.427217\pi$
$41$	44.4000	−	61.1113i	1.08293	−	1.49052i	0.856258	−	0.516548i	$-0.172783\pi$
$42$	−39.7262	−	78.4072i	−0.945862	−	1.86684i
$43$			43.3942i			1.00917i	0.863363	+	0.504583i	$0.168354\pi$
$43$			43.3942i			1.00917i	−0.863363	+	0.504583i	$0.831646\pi$
$44$	−17.7844	+	5.77849i	−0.404190	+	0.131329i
$45$	−18.0214	+	41.2338i	−0.400476	+	0.916307i
$46$	15.7112	−	48.3541i	0.341548	−	1.05118i
$47$	1.52001	−	4.67812i	0.0323407	−	0.0995346i	−0.933583	−	0.358361i	$-0.883336\pi$
$47$	1.52001	−	4.67812i	0.0323407	−	0.0995346i	0.965924	+	0.258826i	$0.0833357\pi$
$48$	−41.6814	−	41.8713i	−0.868362	−	0.872318i
$49$	−108.612			−2.21658
$50$	52.7457	−	24.9385i	1.05491	−	0.498769i
$51$	4.98338	+	31.9334i	0.0977134	+	0.626146i
$52$	4.22736	+	5.81846i	0.0812953	+	0.111893i
$53$	−0.528642	+	1.62699i	−0.00997438	+	0.0306980i	−0.955920	−	0.293628i	$-0.905137\pi$
$53$	−0.528642	+	1.62699i	−0.00997438	+	0.0306980i	0.945945	+	0.324326i	$0.105137\pi$
$54$	62.3016	−	9.43260i	1.15373	−	0.174678i
$55$	55.6075	−	32.9550i	1.01105	−	0.599183i
$56$	−71.1543	+	23.1194i	−1.27061	+	0.412847i
$57$	1.94181	+	12.4431i	0.0340668	+	0.218300i
$58$	60.8553	−	19.7731i	1.04923	−	0.340915i
$59$	−28.0481	+	38.6049i	−0.475392	+	0.654321i	−0.977611	−	0.210420i	$-0.932517\pi$
$59$	−28.0481	+	38.6049i	−0.475392	+	0.654321i	0.502219	+	0.864740i	$0.332517\pi$
$60$	−18.3035	−	11.6506i	−0.305058	−	0.194177i
$61$	−5.28161	+	3.83732i	−0.0865838	+	0.0629068i	−0.630235	−	0.776404i	$-0.717041\pi$
$61$	−5.28161	+	3.83732i	−0.0865838	+	0.0629068i	0.543651	+	0.839311i	$0.317041\pi$
$62$	52.7907	+	38.3547i	0.851463	+	0.618624i
$63$	35.4038	−	107.299i	0.561964	−	1.70317i
$64$	−21.9608	+	15.9555i	−0.343138	+	0.249304i
$65$	−18.6634	−	16.4236i	−0.287129	−	0.252671i
$66$	−80.5529	−	41.2746i	−1.22050	−	0.625373i
$67$	−3.93744	+	1.27935i	−0.0587677	+	0.0190948i	−0.338253	−	0.941055i	$-0.609836\pi$
$67$	−3.93744	+	1.27935i	−0.0587677	+	0.0190948i	0.279486	+	0.960150i	$0.409836\pi$
$68$	−15.5831			−0.229164
$69$	58.3007	−	29.5390i	0.844937	−	0.428101i
$70$	−126.026	+	74.6874i	−1.80037	+	1.06696i
$71$	51.8456	+	16.8457i	0.730220	+	0.237263i	0.650449	−	0.759550i	$-0.274581\pi$
$71$	51.8456	+	16.8457i	0.730220	+	0.237263i	0.0797717	+	0.996813i	$0.474581\pi$
$72$	0.243811	−	53.6337i	0.00338627	−	0.744913i
$73$	21.0676	+	28.9970i	0.288597	+	0.397220i	0.928558	−	0.371188i	$-0.121049\pi$
$73$	21.0676	+	28.9970i	0.288597	+	0.397220i	−0.639961	+	0.768408i	$0.721049\pi$
$74$		−	0.0805904i		−	0.00108906i
$75$	70.5549	+	25.4364i	0.940732	+	0.339151i
$76$	−6.07208			−0.0798958
$77$	−131.304	+	95.3981i	−1.70525	+	1.23894i
$78$	−5.52385	+	34.3704i	−0.0708186	+	0.440647i
$79$	5.27573	−	16.2370i	0.0667813	−	0.205532i	−0.912097	−	0.409974i	$-0.865538\pi$
$79$	5.27573	−	16.2370i	0.0667813	−	0.205532i	0.978879	+	0.204442i	$0.0655379\pi$
$80$	−65.0503	+	73.9216i	−0.813129	+	0.924020i
$81$	65.0948	+	48.2044i	0.803640	+	0.595116i
$82$			176.287i			2.14985i
$83$	−17.6925	−	54.4519i	−0.213162	−	0.656046i	−0.999279	−	0.0379682i	$-0.987911\pi$
$83$	−17.6925	−	54.4519i	−0.213162	−	0.656046i	0.786117	−	0.618078i	$-0.212089\pi$
$84$	48.4840	+	24.8428i	0.577191	+	0.295748i
$85$	52.5585	−	11.7988i	0.618335	−	0.138810i
$86$	−59.5261	−	81.9306i	−0.692164	−	0.952682i
$87$	73.2036	+	37.5089i	0.841421	+	0.431137i
$88$	−45.2840	+	62.3281i	−0.514591	+	0.708274i
$89$	−44.4639	−	61.1993i	−0.499595	−	0.687633i	0.482527	−	0.875881i	$-0.339719\pi$
$89$	−44.4639	−	61.1993i	−0.499595	−	0.687633i	−0.982121	+	0.188248i	$0.939719\pi$
$90$	−22.5372	−	102.573i	−0.250413	−	1.13970i
$91$	50.5006	+	36.6908i	0.554952	+	0.403196i
$92$	9.73774	+	29.9697i	0.105845	+	0.325757i
$93$	12.9335	+	82.8780i	0.139070	+	0.891161i
$94$	3.54736	+	10.9176i	0.0377378	+	0.116145i
$95$	20.4798	−	4.59749i	0.215577	−	0.0483946i
$96$	65.5274	+	10.5312i	0.682577	+	0.109701i
$97$	−28.4310	−	9.23778i	−0.293103	−	0.0952349i	0.158775	−	0.987315i	$-0.449246\pi$
$97$	−28.4310	−	9.23778i	−0.293103	−	0.0952349i	−0.451878	+	0.892080i	$0.649246\pi$
$98$	205.066	−	148.989i	2.09251	−	1.52030i
$99$	−35.4509	−	110.818i	−0.358090	−	1.11938i
$100$	−17.3628	+	31.7204i	−0.173628	+	0.317204i
$101$			26.0891i			0.258308i	0.991625	+	0.129154i	$0.0412261\pi$
$101$			26.0891i			0.258308i	−0.991625	+	0.129154i	$0.958774\pi$
$102$	−53.2137	−	53.4561i	−0.521703	−	0.524079i
$103$	−44.7560	−	14.5421i	−0.434524	−	0.141185i	0.0835838	−	0.996501i	$-0.473363\pi$
$103$	−44.7560	−	14.5421i	−0.434524	−	0.141185i	−0.518108	+	0.855315i	$0.673363\pi$
$104$	28.1806	+	9.15644i	0.270967	+	0.0880427i
$105$	−182.336	−	47.0795i	−1.73653	−	0.448376i
$106$	−1.23373	−	3.79702i	−0.0116389	−	0.0358209i
$107$	149.068			1.39316			0.696581	−	0.717478i	$-0.254704\pi$
$107$	149.068			1.39316			0.696581	+	0.717478i	$0.254704\pi$
$108$	−27.8033	+	27.4267i	−0.257438	+	0.253951i
$109$	120.472	+	87.5279i	1.10525	+	0.803008i	0.981908	−	0.189357i	$-0.0606402\pi$
$109$	120.472	+	87.5279i	1.10525	+	0.803008i	0.123338	+	0.992365i	$0.460640\pi$
$110$	−59.7839	+	138.501i	−0.543490	+	1.25910i
$111$	0.0734205	−	0.0730875i	0.000661446	−	0.000658446i
$112$	145.324	−	200.022i	1.29754	−	1.78591i
$113$	47.3048	+	34.3689i	0.418626	+	0.304150i	0.777085	−	0.629396i	$-0.216698\pi$
$113$	47.3048	+	34.3689i	0.418626	+	0.304150i	−0.358458	+	0.933546i	$0.616698\pi$
$114$	−20.7351	−	20.8296i	−0.181887	−	0.182715i
$115$	−55.5348	−	93.7081i	−0.482912	−	0.814853i
$116$	−23.3109	+	32.0847i	−0.200956	+	0.276592i
$117$	−36.3222	+	26.1382i	−0.310446	+	0.223403i
$118$		−	111.363i		−	0.943757i
$119$	−128.632	+	41.7952i	−1.08094	+	0.351220i
$120$	−89.2216	+	5.49188i	−0.743513	+	0.0457656i
$121$	−14.2548	+	43.8716i	−0.117808	+	0.362575i
$122$	4.70813	−	14.4901i	0.0385912	−	0.118772i
$123$	−160.604	+	159.875i	−1.30572	+	1.29980i
$124$	−40.4435			−0.326157
$125$	34.5436	−	120.132i	0.276349	−	0.961057i
$126$	80.3440	+	251.152i	0.637651	+	1.99327i
$127$	−78.3016	−	107.773i	−0.616548	−	0.848605i	0.380548	−	0.924761i	$-0.375735\pi$
$127$	−78.3016	−	107.773i	−0.616548	−	0.848605i	−0.997096	+	0.0761557i	$0.975735\pi$
$128$	46.9215	−	144.410i	0.366574	−	1.12820i
$129$	20.6572	−	128.533i	0.160134	−	0.996381i
$130$	57.7666	+	5.40713i	0.444359	+	0.0415933i
$131$	−201.121	+	65.3482i	−1.53528	+	0.498841i	−0.950068	−	0.312042i	$-0.898987\pi$
$131$	−201.121	+	65.3482i	−1.53528	+	0.498841i	−0.585208	+	0.810883i	$0.698987\pi$
$132$	55.4279	−	8.64983i	0.419909	−	0.0655290i
$133$	−50.1225	+	16.2858i	−0.376861	+	0.122450i
$134$	5.67915	−	7.81668i	0.0423817	−	0.0583334i
$135$	73.0081	−	113.555i	0.540801	−	0.841151i
$136$	−51.9406	+	37.7370i	−0.381916	+	0.277478i
$137$	155.247	+	112.794i	1.13319	+	0.823312i	0.986156	−	0.165819i	$-0.0530267\pi$
$137$	155.247	+	112.794i	1.13319	+	0.823312i	0.147036	+	0.989131i	$0.453027\pi$
$138$	−69.5548	+	135.745i	−0.504020	+	0.983661i
$139$	82.6077	−	60.0180i	0.594300	−	0.431784i	−0.249551	−	0.968362i	$-0.580283\pi$
$139$	82.6077	−	60.0180i	0.594300	−	0.431784i	0.843851	+	0.536577i	$0.180283\pi$
$140$	35.9834	−	83.3623i	0.257024	−	0.595445i
$141$	−6.72923	+	13.1330i	−0.0477250	+	0.0931417i
$142$	−120.996	+	39.3138i	−0.852081	+	0.276858i
$143$	64.2792			0.449505
$144$	103.528	+	143.864i	0.718941	+	0.999057i
$145$	54.3295	−	125.865i	0.374686	−	0.868031i
$146$	−79.5535	−	25.8485i	−0.544887	−	0.177045i
$147$	321.708	+	51.7034i	2.18849	+	0.351724i
$148$	0.0293596	+	0.0404101i	0.000198376	+	0.000273041i
$149$		−	114.565i		−	0.768892i	−0.923148	−	0.384446i	$-0.874393\pi$
$149$		−	114.565i		−	0.768892i	0.923148	−	0.384446i	$-0.125607\pi$
$150$	−168.104	+	48.7586i	−1.12069	+	0.325057i
$151$	−163.992			−1.08604			−0.543019	−	0.839720i	$-0.682719\pi$
$151$	−163.992			−1.08604			−0.543019	+	0.839720i	$0.682719\pi$
$152$	−20.2390	+	14.7045i	−0.133151	+	0.0967402i
$153$	0.440761	−	96.9588i	0.00288079	−	0.633717i
$154$	117.047	−	360.234i	0.760046	−	2.33918i
$155$	136.407	−	30.6219i	0.880044	−	0.197560i
$156$	−9.75159	−	19.2466i	−0.0625102	−	0.123376i
$157$		−	73.2155i		−	0.466341i	−0.972436	−	0.233170i	$-0.925090\pi$
$157$		−	73.2155i		−	0.466341i	0.972436	−	0.233170i	$-0.0749100\pi$
$158$	12.3123	+	37.8934i	0.0779260	+	0.239831i
$159$	2.34034	−	4.56748i	0.0147191	−	0.0287263i
$160$	10.3087	−	110.132i	0.0644295	−	0.688327i
$161$	160.762	+	221.270i	0.998522	+	1.37435i
$162$	−189.027	−	1.71862i	−1.16683	−	0.0106087i
$163$	11.4612	−	15.7750i	0.0703141	−	0.0967790i	−0.772412	−	0.635122i	$-0.780950\pi$
$163$	11.4612	−	15.7750i	0.0703141	−	0.0967790i	0.842726	+	0.538343i	$0.180950\pi$
$164$	−64.2227	−	88.3950i	−0.391602	−	0.538994i
$165$	−180.397	+	71.1413i	−1.09331	+	0.431159i
$166$	108.099	+	78.5384i	0.651198	+	0.473123i
$167$	−28.1359	−	86.5934i	−0.168478	−	0.518523i	0.830797	−	0.556575i	$-0.187885\pi$
$167$	−28.1359	−	86.5934i	−0.168478	−	0.518523i	−0.999276	+	0.0380519i	$0.987885\pi$
$168$	221.764	−	34.6075i	1.32002	−	0.205997i
$169$	44.5843	+	137.216i	0.263812	+	0.811931i
$170$	−83.0483	+	94.3740i	−0.488519	+	0.555141i
$171$	0.171746	−	37.7807i	0.00100436	−	0.220940i
$172$	59.6958	+	19.3963i	0.347069	+	0.112769i
$173$	−35.0251	+	25.4472i	−0.202457	+	0.147094i	−0.684394	−	0.729112i	$-0.739933\pi$
$173$	−35.0251	+	25.4472i	−0.202457	+	0.147094i	0.481937	+	0.876206i	$0.339933\pi$
$174$	−189.665	+	29.5983i	−1.09003	+	0.170105i
$175$	−58.2460	+	308.407i	−0.332834	+	1.76233i
$176$		−	254.596i		−	1.44657i
$177$	101.456	−	100.995i	0.573196	−	0.570596i
$178$	167.901	+	54.5542i	0.943262	+	0.306485i
$179$	−86.3556	−	28.0587i	−0.482434	−	0.156752i	0.0576956	−	0.998334i	$-0.481625\pi$
$179$	−86.3556	−	28.0587i	−0.482434	−	0.156752i	−0.540129	+	0.841582i	$0.681625\pi$
$180$	48.6687	+	43.2221i	0.270382	+	0.240123i
$181$	−34.0023	−	104.648i	−0.187858	−	0.578168i	0.812128	−	0.583480i	$-0.198309\pi$
$181$	−34.0023	−	104.648i	−0.187858	−	0.578168i	−0.999986	+	0.00531154i	$0.998309\pi$
$182$	−145.679			−0.800433
$183$	17.4708	−	8.85186i	0.0954688	−	0.0483708i
$184$	105.033	+	76.3112i	0.570834	+	0.414735i
$185$	−0.129620	−	0.114064i	−0.000700649	−	0.000616565i
$186$	−138.107	−	138.737i	−0.742513	−	0.745896i
$187$	−81.8642	+	112.676i	−0.437777	+	0.602548i
$188$	−5.75611	−	4.18206i	−0.0306176	−	0.0222450i
$189$	−155.944	+	300.966i	−0.825101	+	1.59241i
$190$	−32.3603	+	36.7735i	−0.170318	+	0.193545i
$191$	57.8437	−	79.6151i	0.302847	−	0.416833i	−0.630287	−	0.776362i	$-0.717063\pi$
$191$	57.8437	−	79.6151i	0.302847	−	0.416833i	0.933134	+	0.359529i	$0.117063\pi$
$192$	72.6431	−	36.8058i	0.378350	−	0.191697i
$193$		−	183.115i		−	0.948784i	−0.880314	−	0.474392i	$-0.842668\pi$
$193$		−	183.115i		−	0.948784i	0.880314	−	0.474392i	$-0.157332\pi$
$194$	66.3512	−	21.5588i	0.342017	−	0.111128i
$195$	47.4625	+	57.5310i	0.243398	+	0.295031i
$196$	−48.5475	+	149.414i	−0.247691	+	0.762316i
$197$	−104.482	+	321.562i	−0.530365	+	1.63229i	0.223092	+	0.974797i	$0.428385\pi$
$197$	−104.482	+	321.562i	−0.530365	+	1.63229i	−0.753457	+	0.657497i	$0.771615\pi$
$198$	218.949	+	160.601i	1.10580	+	0.811118i
$199$	−12.6514			−0.0635749			−0.0317875	−	0.999495i	$-0.510120\pi$
$199$	−12.6514			−0.0635749			−0.0317875	+	0.999495i	$0.510120\pi$
$200$	18.9436	+	147.775i	0.0947182	+	0.738874i
$201$	12.2717	−	1.91506i	0.0610531	−	0.00952767i
$202$	−35.7878	−	49.2577i	−0.177167	−	0.243850i
$203$	−106.368	+	327.368i	−0.523981	+	1.61265i
$204$	46.1571	+	7.41815i	0.226260	+	0.0363635i
$205$	283.537	+	249.510i	1.38311	+	1.21712i
$206$	104.450	−	33.9378i	0.507038	−	0.164747i
$207$	−186.748	+	59.7408i	−0.902163	+	0.288603i
$208$	−93.1270	+	30.2588i	−0.447726	+	0.145475i
$209$	−31.8990	+	43.9052i	−0.152627	+	0.210073i
$210$	408.841	−	161.231i	1.94686	−	0.767765i
$211$	293.037	−	212.904i	1.38880	−	1.00902i	0.392808	−	0.919621i	$-0.371504\pi$
$211$	293.037	−	212.904i	1.38880	−	1.00902i	0.995995	−	0.0894038i	$-0.0284962\pi$
$212$	2.00190	+	1.45447i	0.00944294	+	0.00686069i
$213$	−145.547	−	74.5772i	−0.683320	−	0.350128i
$214$	−281.449	+	204.485i	−1.31518	+	0.955537i
$215$	−216.027	−	20.2207i	−1.00477	−	0.0940499i
$216$	−26.2538	+	158.747i	−0.121545	+	0.734938i
$217$	−333.844	+	108.473i	−1.53845	+	0.499874i
$218$	−347.524			−1.59415
$219$	−48.5983	−	95.9179i	−0.221910	−	0.437981i
$220$	−20.4796	−	91.2275i	−0.0930891	−	0.414671i
$221$	50.9448	+	16.5530i	0.230519	+	0.0749003i
$222$	−0.0383640	+	0.238708i	−0.000172811	+	0.00107526i
$223$	−134.126	−	184.609i	−0.601462	−	0.827842i	0.394379	−	0.918948i	$-0.370960\pi$
$223$	−134.126	−	184.609i	−0.601462	−	0.827842i	−0.995841	+	0.0911062i	$0.970960\pi$
$224$			277.737i			1.23990i
$225$	−196.874	−	108.929i	−0.874997	−	0.484129i
$226$	−136.460			−0.603804
$227$	251.371	−	182.632i	1.10736	−	0.804545i	0.125115	−	0.992142i	$-0.460070\pi$
$227$	251.371	−	182.632i	1.10736	−	0.804545i	0.982246	+	0.187598i	$0.0600701\pi$
$228$	17.9855	+	2.89054i	0.0788836	+	0.0126778i
$229$	37.5038	−	115.425i	0.163772	−	0.504039i	−0.835172	−	0.549989i	$-0.814632\pi$
$229$	37.5038	−	115.425i	0.163772	−	0.504039i	0.998944	+	0.0459508i	$0.0146317\pi$
$230$	233.397	+	100.746i	1.01477	+	0.438026i
$231$	434.335	−	220.063i	1.88024	−	0.952653i
$232$			163.393i			0.704282i
$233$	−124.270	−	382.465i	−0.533350	−	1.64148i	−0.747188	−	0.664612i	$-0.768597\pi$
$233$	−124.270	−	382.465i	−0.533350	−	1.64148i	0.213839	−	0.976869i	$-0.431403\pi$
$234$	32.7232	−	99.1753i	0.139843	−	0.423826i
$235$	22.5805	+	9.74690i	0.0960873	+	0.0414762i
$236$	40.5704	+	55.8404i	0.171909	+	0.236612i
$237$	−23.3561	+	45.5824i	−0.0985488	+	0.192331i
$238$	185.532	−	255.363i	0.779548	−	1.07296i
$239$	115.387	+	158.817i	0.482792	+	0.664507i	0.979038	−	0.203675i	$-0.0652887\pi$
$239$	115.387	+	158.817i	0.482792	+	0.664507i	−0.496246	+	0.868182i	$0.665289\pi$
$240$	227.868	−	187.989i	0.949449	−	0.783286i
$241$	−291.933	−	212.102i	−1.21134	−	0.880091i	−0.215989	−	0.976396i	$-0.569298\pi$
$241$	−291.933	−	212.102i	−1.21134	−	0.880091i	−0.995352	+	0.0963050i	$0.969298\pi$
$242$	−33.2672	−	102.386i	−0.137468	−	0.423083i
$243$	−169.863	−	173.769i	−0.699025	−	0.715097i
$244$	2.91808	+	8.98093i	0.0119594	+	0.0368071i
$245$	50.6109	−	540.697i	0.206575	−	2.20693i
$246$	83.9193	−	522.161i	0.341135	−	2.12261i
$247$	19.8510	+	6.44998i	0.0803684	+	0.0261133i
$248$	−134.803	+	97.9403i	−0.543562	+	0.394921i
$249$	26.4839	+	169.708i	0.106361	+	0.681559i
$250$	99.5713	+	274.202i	0.398285	+	1.09681i
$251$		−	337.441i		−	1.34439i	−0.740376	−	0.672193i	$-0.765353\pi$
$251$		−	337.441i		−	1.34439i	0.740376	−	0.672193i	$-0.234647\pi$
$252$	−131.783	−	96.6644i	−0.522949	−	0.383589i
$253$	267.857	+	87.0319i	1.05872	+	0.344000i
$254$	295.676	+	96.0708i	1.16408	+	0.378231i
$255$	−161.294	+	9.92819i	−0.632527	+	0.0389341i
$256$	75.9506	+	233.752i	0.296682	+	0.913094i
$257$	−190.928			−0.742911			−0.371455	−	0.928451i	$-0.621141\pi$
$257$	−190.928			−0.742911			−0.371455	+	0.928451i	$0.621141\pi$
$258$	137.314	+	271.014i	0.532224	+	1.05044i
$259$	0.350735	+	0.254824i	0.00135419	+	0.000983875i
$260$	−30.9355	+	18.3335i	−0.118983	+	0.0705135i
$261$	−198.973	−	145.949i	−0.762348	−	0.559190i
$262$	290.086	−	399.270i	1.10720	−	1.52393i
$263$	221.916	+	161.231i	0.843787	+	0.613047i	0.923426	−	0.383776i	$-0.125377\pi$
$263$	221.916	+	161.231i	0.843787	+	0.613047i	−0.0796388	+	0.996824i	$0.525377\pi$
$264$	163.801	−	163.058i	0.620460	−	0.617646i
$265$	−7.85322	−	3.38985i	−0.0296348	−	0.0127919i
$266$	72.2940	−	99.5042i	0.271782	−	0.374076i
$267$	102.569	+	202.438i	0.384152	+	0.758196i
$268$			5.98844i			0.0223449i
$269$	132.545	−	43.0665i	0.492733	−	0.160099i	−0.0521023	−	0.998642i	$-0.516592\pi$
$269$	132.545	−	43.0665i	0.492733	−	0.160099i	0.544835	+	0.838543i	$0.316592\pi$
$270$	17.9265	+	314.548i	0.0663945	+	1.16499i
$271$	−108.618	+	334.292i	−0.400805	+	1.23355i	0.523543	+	0.851999i	$0.324610\pi$
$271$	−108.618	+	334.292i	−0.400805	+	1.23355i	−0.924348	+	0.381551i	$0.875390\pi$
$272$	65.5626	−	201.781i	0.241039	−	0.741842i
$273$	−132.116	−	132.718i	−0.483942	−	0.486147i
$274$	−447.841			−1.63446
$275$	138.146	+	292.184i	0.502350	+	1.06249i
$276$	−14.5764	−	93.4054i	−0.0528131	−	0.338426i
$277$	234.264	+	322.437i	0.845719	+	1.16403i	0.984790	+	0.173750i	$0.0555884\pi$
$277$	234.264	+	322.437i	0.845719	+	1.16403i	−0.139071	+	0.990282i	$0.544412\pi$
$278$	−73.6381	+	226.635i	−0.264885	+	0.815233i
$279$	1.14392	−	251.641i	0.00410008	−	0.901938i
$280$	−81.9377	−	364.996i	−0.292635	−	1.30356i
$281$	−167.897	+	54.5530i	−0.597498	+	0.194139i	−0.592124	−	0.805847i	$-0.701710\pi$
$281$	−167.897	+	54.5530i	−0.597498	+	0.194139i	−0.00537353	+	0.999986i	$0.501710\pi$
$282$	−5.31004	−	34.0266i	−0.0188299	−	0.120662i
$283$	−306.568	+	99.6099i	−1.08328	+	0.351979i	−0.795646	−	0.605762i	$-0.792868\pi$
$283$	−306.568	+	99.6099i	−1.08328	+	0.351979i	−0.287633	+	0.957741i	$0.592868\pi$
$284$	46.3480	−	63.7925i	0.163197	−	0.224621i
$285$	−62.8495	+	3.86859i	−0.220525	+	0.0135740i
$286$	−121.363	+	88.1752i	−0.424345	+	0.308305i
$287$	−767.214	−	557.414i	−2.67322	−	1.94221i
$288$	−189.078	−	62.3869i	−0.656522	−	0.216621i
$289$	139.908	−	101.649i	0.484111	−	0.351727i
$290$	70.0779	+	312.166i	0.241648	+	1.07643i
$291$	79.8147	+	40.8964i	0.274277	+	0.140538i
$292$	49.3070	−	16.0208i	0.168860	−	0.0548658i
$293$	330.675			1.12858			0.564292	−	0.825575i	$-0.309149\pi$
$293$	330.675			1.12858			0.564292	+	0.825575i	$0.309149\pi$
$294$	−678.327	+	343.685i	−2.30724	+	1.16900i
$295$	−179.115	−	157.619i	−0.607169	−	0.534303i
$296$	0.195719	+	0.0635929i	0.000661212	+	0.000214841i
$297$	52.2517	+	345.119i	0.175932	+	1.16202i
$298$	157.155	+	216.305i	0.527365	+	0.725855i
$299$		−	108.321i		−	0.362279i
$300$	66.5285	−	85.6903i	0.221762	−	0.285634i
$301$	544.787			1.80992
$302$	309.626	−	224.956i	1.02525	−	0.744888i
$303$	12.4194	−	77.2757i	0.0409880	−	0.255035i
$304$	25.5470	−	78.6254i	0.0840360	−	0.258636i
$305$	−16.6420	−	28.0812i	−0.0545638	−	0.0920697i
$306$	132.171	+	183.668i	0.431932	+	0.600223i
$307$			169.985i			0.553697i	0.960914	+	0.276849i	$0.0892901\pi$
$307$			169.985i			0.553697i	−0.960914	+	0.276849i	$0.910710\pi$
$308$	72.5454	+	223.272i	0.235537	+	0.724908i
$309$	125.644	+	64.3790i	0.406615	+	0.208346i
$310$	−215.538	+	244.932i	−0.695284	+	0.790104i
$311$	269.449	+	370.864i	0.866394	+	1.19249i	0.980007	+	0.198964i	$0.0637577\pi$
$311$	269.449	+	370.864i	0.866394	+	1.19249i	−0.113613	+	0.993525i	$0.536242\pi$
$312$	−79.1119	−	40.5363i	−0.253564	−	0.129924i
$313$	−187.842	+	258.542i	−0.600133	+	0.826012i	−0.995720	−	0.0924161i	$-0.970541\pi$
$313$	−187.842	+	258.542i	−0.600133	+	0.826012i	0.395587	+	0.918428i	$0.370541\pi$
$314$	100.434	+	138.235i	0.319852	+	0.440239i
$315$	517.665	+	226.248i	1.64338	+	0.718246i
$316$	−19.9785	−	14.5153i	−0.0632232	−	0.0459343i
$317$	75.8505	+	233.444i	0.239276	+	0.736415i	0.996525	+	0.0832897i	$0.0265427\pi$
$317$	75.8505	+	233.444i	0.239276	+	0.736415i	−0.757249	+	0.653126i	$0.773457\pi$
$318$	1.84676	+	11.8340i	0.00580743	+	0.0372139i
$319$	109.533	+	337.107i	0.343362	+	1.05676i
$320$	−69.1969	−	116.761i	−0.216240	−	0.364878i
$321$	−441.539	−	70.9620i	−1.37551	−	0.221066i
$322$	−607.055	−	197.244i	−1.88526	−	0.612560i
$323$	−36.5880	+	26.5827i	−0.113276	+	0.0822995i
$324$	95.4092	−	68.0022i	0.294473	−	0.209883i
$325$	90.4574	−	85.2578i	0.278330	−	0.262332i
$326$			45.5060i			0.139589i
$327$	−315.170	−	316.606i	−0.963822	−	0.968214i
$328$	−428.125	−	139.106i	−1.30526	−	0.424104i
$329$	−58.7309	−	19.0828i	−0.178513	−	0.0580025i
$330$	243.011	−	381.779i	0.736397	−	1.15690i
$331$	−46.4064	−	142.824i	−0.140200	−	0.431493i	0.856162	−	0.516707i	$-0.172842\pi$
$331$	−46.4064	−	142.824i	−0.140200	−	0.431493i	−0.996363	+	0.0852145i	$0.972842\pi$
$332$	−82.8156			−0.249445
$333$	−0.252263	+	0.181534i	−0.000757547	+	0.000545146i
$334$	171.907	+	124.898i	0.514691	+	0.373945i
$335$	−4.53416	−	20.1977i	−0.0135348	−	0.0602915i
$336$	−525.667	+	523.283i	−1.56449	+	1.55739i
$337$	371.305	−	511.058i	1.10180	−	1.51649i	0.268816	−	0.963192i	$-0.413368\pi$
$337$	371.305	−	511.058i	1.10180	−	1.51649i	0.832981	−	0.553301i	$-0.186632\pi$
$338$	−272.404	−	197.913i	−0.805930	−	0.585542i
$339$	−123.755	−	124.319i	−0.365060	−	0.366724i
$340$	7.26140	−	77.5766i	0.0213571	−	0.228167i
$341$	−212.465	+	292.433i	−0.623065	+	0.857575i
$342$	51.5015	+	71.5676i	0.150589	+	0.209262i
$343$			748.394i			2.18191i
$344$	245.945	−	79.9123i	0.714956	−	0.232303i
$345$	119.885	+	303.999i	0.347493	+	0.881157i
$346$	31.2221	−	96.0916i	0.0902371	−	0.277721i
$347$	177.557	−	546.463i	0.511690	−	1.57482i	−0.277534	−	0.960716i	$-0.589517\pi$
$347$	177.557	−	546.463i	0.511690	−	1.57482i	0.789224	−	0.614105i	$-0.210483\pi$
$348$	84.3202	−	83.9378i	0.242300	−	0.241201i
$349$	461.206			1.32151			0.660754	−	0.750603i	$-0.270237\pi$
$349$	461.206			1.32151			0.660754	+	0.750603i	$0.270237\pi$
$350$	−313.087	−	662.189i	−0.894534	−	1.89197i
$351$	120.029	−	60.1303i	0.341962	−	0.171311i
$352$	168.106	+	231.379i	0.477575	+	0.657326i
$353$	−54.2919	+	167.093i	−0.153801	+	0.473352i	−0.998037	−	0.0626196i	$-0.980055\pi$
$353$	−54.2919	+	167.093i	−0.153801	+	0.473352i	0.844236	+	0.535971i	$0.180055\pi$
$354$	−53.0131	+	329.857i	−0.149754	+	0.931800i
$355$	−108.021	+	250.250i	−0.304284	+	0.704930i
$356$	−104.064	+	33.8125i	−0.292315	+	0.0949790i
$357$	400.904	−	62.5632i	1.12298	−	0.175247i
$358$	201.534	−	65.4823i	0.562944	−	0.182911i
$359$	−271.386	+	373.531i	−0.755950	+	1.04048i	0.241590	+	0.970379i	$0.422331\pi$
$359$	−271.386	+	373.531i	−0.755950	+	1.04048i	−0.997540	+	0.0700981i	$0.977669\pi$
$360$	266.888	+	26.2059i	0.741355	+	0.0727942i
$361$	277.798	−	201.832i	0.769525	−	0.559092i
$362$	207.750	+	150.939i	0.573895	+	0.416959i
$363$	63.1070	−	123.162i	0.173848	−	0.339288i
$364$	73.0471	−	53.0718i	0.200679	−	0.145802i
$365$	−154.171	+	91.3675i	−0.422387	+	0.250322i
$366$	−20.8433	+	40.6784i	−0.0569489	+	0.111143i
$367$	375.313	−	121.946i	1.02265	−	0.332279i	0.250770	−	0.968047i	$-0.419316\pi$
$367$	375.313	−	121.946i	1.02265	−	0.332279i	0.771881	+	0.635768i	$0.219316\pi$
$368$	−429.037			−1.16586
$369$	551.813	−	397.095i	1.49543	−	1.07614i
$370$	0.401198	+	0.0375533i	0.00108432	+	0.000101496i
$371$	20.4259	+	6.63677i	0.0550562	+	0.0178889i
$372$	119.793	+	19.2526i	0.322025	+	0.0517543i
$373$	−203.237	−	279.732i	−0.544871	−	0.749951i	0.444434	−	0.895812i	$-0.353405\pi$
$373$	−203.237	−	279.732i	−0.544871	−	0.749951i	−0.989305	+	0.145861i	$0.953405\pi$
$374$		−	325.037i		−	0.869082i
$375$	−159.505	+	339.386i	−0.425347	+	0.905030i
$376$	−29.3133			−0.0779610
$377$	110.290	−	80.1304i	0.292547	−	0.212548i
$378$	−118.420	−	782.158i	−0.313281	−	2.06920i
$379$	−115.909	+	356.732i	−0.305829	+	0.941245i	0.673537	+	0.739153i	$0.264774\pi$
$379$	−115.909	+	356.732i	−0.305829	+	0.941245i	−0.979367	+	0.202092i	$0.935226\pi$
$380$	2.82946	−	30.2283i	0.00744594	−	0.0795481i
$381$	180.625	+	356.497i	0.474081	+	0.935687i
$382$			229.665i			0.601217i
$383$	−39.2793	−	120.889i	−0.102557	−	0.315638i	0.886592	−	0.462552i	$-0.153066\pi$
$383$	−39.2793	−	120.889i	−0.102557	−	0.315638i	−0.989149	+	0.146914i	$0.953066\pi$
$384$	−207.725	+	405.403i	−0.540952	+	1.05574i
$385$	−413.730	−	698.118i	−1.07462	−	1.81329i
$386$	251.189	+	345.732i	0.650748	+	0.895678i
$387$	−122.373	+	370.880i	−0.316209	+	0.958347i
$388$	−25.4162	+	34.9824i	−0.0655056	+	0.0901607i
$389$	−157.269	−	216.462i	−0.404291	−	0.556458i	0.557524	−	0.830161i	$-0.311752\pi$
$389$	−157.269	−	216.462i	−0.404291	−	0.556458i	−0.961814	+	0.273703i	$0.911752\pi$
$390$	−168.530	−	43.5149i	−0.432129	−	0.111577i
$391$	189.879	+	137.955i	0.485624	+	0.352826i
$392$	200.014	+	615.581i	0.510240	+	1.57036i
$393$	626.827	−	97.8197i	1.59498	−	0.248905i
$394$	−243.836	−	750.450i	−0.618873	−	1.90470i
$395$	78.3734	+	33.8299i	0.198414	+	0.0856454i
$396$	−168.295	−	0.765044i	−0.424987	−	0.00193193i
$397$	−68.6142	−	22.2941i	−0.172832	−	0.0561564i	0.221323	−	0.975201i	$-0.428963\pi$
$397$	−68.6142	−	22.2941i	−0.172832	−	0.0561564i	−0.394155	+	0.919044i	$0.628963\pi$
$398$	23.8866	−	17.3546i	0.0600165	−	0.0436045i
$399$	156.215	−	24.3782i	0.391517	−	0.0610983i
$400$	−337.687	−	358.282i	−0.844218	−	0.895704i
$401$			255.533i			0.637239i	0.947883	+	0.318620i	$0.103219\pi$
$401$			255.533i			0.637239i	−0.947883	+	0.318620i	$0.896781\pi$
$402$	−20.5426	+	20.4494i	−0.0511010	+	0.0508693i
$403$	132.219	+	42.9605i	0.328086	+	0.106602i
$404$	35.8898	+	11.6613i	0.0888362	+	0.0288646i
$405$	−270.306	+	301.595i	−0.667422	+	0.744680i
$406$	−248.238	−	763.999i	−0.611425	−	1.88177i
$407$	0.446429			0.00109688
$408$	171.812	−	87.0511i	0.421107	−	0.213361i
$409$	−577.930	−	419.891i	−1.41303	−	1.02663i	−0.992873	−	0.119178i	$-0.961974\pi$
$409$	−577.930	−	419.891i	−1.41303	−	1.02663i	−0.420160	−	0.907450i	$-0.638026\pi$
$410$	−877.600	−	82.1460i	−2.14049	−	0.200356i
$411$	−406.147	−	407.998i	−0.988193	−	0.992695i
$412$	−40.0101	+	55.0691i	−0.0971118	+	0.133663i
$413$	484.660	+	352.126i	1.17351	+	0.852606i
$414$	270.640	−	368.966i	0.653721	−	0.891221i
$415$	279.319	−	62.7040i	0.673057	−	0.151094i
$416$	64.6550	−	88.9900i	0.155421	−	0.213918i
$417$	−273.254	+	138.449i	−0.655286	+	0.332011i
$418$		−	126.653i		−	0.302997i
$419$	−4.75627	+	1.54540i	−0.0113515	+	0.00368832i	−0.314687	−	0.949195i	$-0.601900\pi$
$419$	−4.75627	+	1.54540i	−0.0113515	+	0.00368832i	0.303336	+	0.952884i	$0.401900\pi$
$420$	−146.266	+	229.789i	−0.348252	+	0.547116i
$421$	−34.6754	+	106.720i	−0.0823643	+	0.253491i	−0.983755	−	0.179515i	$-0.942547\pi$
$421$	−34.6754	+	106.720i	−0.0823643	+	0.253491i	0.901391	+	0.433006i	$0.142547\pi$
$422$	−261.219	+	803.950i	−0.619003	+	1.90509i
$423$	26.1837	−	35.6964i	0.0619000	−	0.0843886i
$424$	10.1948			0.0240444
$425$	34.2462	+	267.147i	0.0805793	+	0.628580i
$426$	377.103	−	58.8489i	0.885217	−	0.138143i
$427$	48.1751	+	66.3073i	0.112822	+	0.155287i
$428$	66.6306	−	205.068i	0.155679	−	0.479131i
$429$	−190.394	−	30.5993i	−0.443810	−	0.0713270i
$430$	435.608	−	258.157i	1.01304	−	0.600366i
$431$	418.838	−	136.089i	0.971783	−	0.315751i	0.220247	−	0.975444i	$-0.429314\pi$
$431$	418.838	−	136.089i	0.971783	−	0.315751i	0.751535	+	0.659693i	$0.229314\pi$
$432$	−238.163	−	475.407i	−0.551303	−	1.10048i
$433$	701.374	−	227.890i	1.61980	−	0.526305i	0.647906	−	0.761720i	$-0.275645\pi$
$433$	701.374	−	227.890i	1.61980	−	0.526305i	0.971895	+	0.235415i	$0.0756449\pi$
$434$	481.519	−	662.754i	1.10949	−	1.52708i
$435$	−220.840	+	346.947i	−0.507677	+	0.797579i
$436$	174.257	−	126.605i	0.399673	−	0.290380i
$437$	73.9877	+	53.7552i	0.169308	+	0.123010i
$438$	223.332	+	114.433i	0.509890	+	0.261264i
$439$	−150.664	+	109.464i	−0.343199	+	0.249349i	−0.746010	−	0.665934i	$-0.768033\pi$
$439$	−150.664	+	109.464i	−0.343199	+	0.249349i	0.402811	+	0.915283i	$0.368033\pi$
$440$	−289.183	−	254.478i	−0.657234	−	0.578360i
$441$	−928.284	−	306.290i	−2.10495	−	0.694535i
$442$	−118.893	+	38.6307i	−0.268989	+	0.0873998i
$443$	−474.687			−1.07153			−0.535764	−	0.844368i	$-0.679976\pi$
$443$	−474.687			−1.07153			−0.535764	+	0.844368i	$0.679976\pi$
$444$	−0.0677263	−	0.133671i	−0.000152537	−	0.000301060i
$445$	325.384	−	192.834i	0.731200	−	0.433336i
$446$	506.475	+	164.564i	1.13559	+	0.368977i
$447$	−54.5371	+	339.340i	−0.122007	+	0.759150i
$448$	200.311	+	275.704i	0.447122	+	0.615411i
$449$		−	211.075i		−	0.470100i	−0.971983	−	0.235050i	$-0.924475\pi$
$449$		−	211.075i		−	0.470100i	0.971983	−	0.235050i	$-0.0755254\pi$
$450$	521.133	−	64.3988i	1.15807	−	0.143109i
$451$	−976.541			−2.16528
$452$	68.4244	−	49.7133i	0.151381	−	0.109985i
$453$	485.742	+	78.0662i	1.07228	+	0.172332i
$454$	−224.077	+	689.637i	−0.493561	+	1.51902i
$455$	−206.188	+	234.307i	−0.453160	+	0.514961i
$456$	66.9477	−	33.9201i	0.146815	−	0.0743862i
$457$		−	353.601i		−	0.773743i	−0.922134	−	0.386872i	$-0.873556\pi$
$457$		−	353.601i		−	0.773743i	0.922134	−	0.386872i	$-0.126444\pi$
$458$	87.5251	+	269.374i	0.191103	+	0.588154i
$459$	−47.4615	+	286.981i	−0.103402	+	0.625231i
$460$	−153.734	+	34.5116i	−0.334204	+	0.0750252i
$461$	−175.509	−	241.567i	−0.380713	−	0.524007i	0.575060	−	0.818111i	$-0.304979\pi$
$461$	−175.509	−	241.567i	−0.380713	−	0.524007i	−0.955773	+	0.294104i	$0.904979\pi$
$462$	−518.177	+	1011.29i	−1.12160	+	2.18894i
$463$	305.117	−	419.957i	0.659000	−	0.907035i	−0.340448	−	0.940263i	$-0.610579\pi$
$463$	305.117	−	419.957i	0.659000	−	0.907035i	0.999448	+	0.0332279i	$0.0105787\pi$
$464$	−317.379	−	436.835i	−0.684007	−	0.941454i
$465$	−418.613	+	25.7670i	−0.900243	+	0.0554129i
$466$	759.277	+	551.647i	1.62935	+	1.18379i
$467$	−131.808	−	405.664i	−0.282244	−	0.868659i	−0.987211	−	0.159419i	$-0.949038\pi$
$467$	−131.808	−	405.664i	−0.282244	−	0.868659i	0.704967	−	0.709240i	$-0.250962\pi$
$468$	19.7220	+	61.6503i	0.0421411	+	0.131732i
$469$	16.0615	+	49.4321i	0.0342462	+	0.105399i
$470$	−56.0036	+	12.5722i	−0.119157	+	0.0267494i
$471$	−34.8533	+	216.864i	−0.0739985	+	0.460433i
$472$	270.453	+	87.8754i	0.572993	+	0.186177i
$473$	453.853	−	329.744i	0.959521	−	0.697133i
$474$	−18.4303	−	118.101i	−0.0388824	−	0.249158i
$475$	13.3443	+	104.096i	0.0280932	+	0.219149i
$476$			195.637i			0.411001i
$477$	−9.10636	+	12.4148i	−0.0190909	+	0.0260267i
$478$	−435.715	−	141.573i	−0.911539	−	0.296177i
$479$	280.502	+	91.1407i	0.585600	+	0.190273i	0.586808	−	0.809726i	$-0.300384\pi$
$479$	280.502	+	91.1407i	0.585600	+	0.190273i	−0.00120777	+	0.999999i	$0.500384\pi$
$480$	−82.9614	+	321.304i	−0.172836	+	0.669383i
$481$	−0.0530582	−	0.163296i	−0.000110308	−	0.000339493i
$482$	842.137			1.74717
$483$	−370.843	−	731.928i	−0.767791	−	1.51538i
$484$	53.9810	+	39.2195i	0.111531	+	0.0810320i
$485$	59.2361	−	137.232i	0.122136	−	0.282952i
$486$	559.079	+	95.0744i	1.15037	+	0.195626i
$487$	−389.881	+	536.625i	−0.800576	+	1.10190i	0.192133	+	0.981369i	$0.438459\pi$
$487$	−389.881	+	536.625i	−0.800576	+	1.10190i	−0.992710	+	0.120530i	$0.961541\pi$
$488$	31.4751	+	22.8680i	0.0644981	+	0.0468606i
$489$	−41.4574	+	41.2694i	−0.0847800	+	0.0843955i
$490$	646.147	+	1090.29i	1.31867	+	2.22509i
$491$	−315.408	+	434.122i	−0.642379	+	0.884158i	−0.998740	−	0.0501900i	$-0.984017\pi$
$491$	−315.408	+	434.122i	−0.642379	+	0.884158i	0.356361	+	0.934348i	$0.384017\pi$
$492$	148.148	+	292.398i	0.301113	+	0.594304i
$493$			295.382i			0.599152i
$494$	−46.3276	+	15.0527i	−0.0937805	+	0.0304711i
$495$	568.200	−	124.844i	1.14788	−	0.252211i
$496$	170.157	−	523.690i	0.343059	−	1.05583i
$497$	211.487	−	650.889i	0.425527	−	1.30964i
$498$	−282.801	−	284.089i	−0.567873	−	0.570460i
$499$	−791.222			−1.58562			−0.792808	−	0.609472i	$-0.791382\pi$
$499$	−791.222			−1.58562			−0.792808	+	0.609472i	$0.791382\pi$
$500$	−149.821	−	101.217i	−0.299642	−	0.202434i
$501$	42.1166	+	269.882i	0.0840651	+	0.538688i
$502$	462.885	+	637.107i	0.922082	+	1.26914i
$503$	135.778	−	417.883i	0.269937	−	0.830781i	−0.720578	−	0.693374i	$-0.756123\pi$
$503$	135.778	−	417.883i	0.269937	−	0.830781i	0.990515	−	0.137407i	$-0.0438767\pi$
$504$	−673.338	−	3.06090i	−1.33599	−	0.00607321i
$505$	−129.878	−	12.1570i	−0.257184	−	0.0240732i
$506$	−625.115	+	203.112i	−1.23540	+	0.401407i
$507$	−66.7382	−	427.657i	−0.131633	−	0.843505i
$508$	−183.259	+	59.5443i	−0.360745	+	0.117213i
$509$	311.605	−	428.888i	0.612191	−	0.842609i	−0.384564	−	0.923098i	$-0.625648\pi$
$509$	311.605	−	428.888i	0.612191	−	0.842609i	0.996755	+	0.0804893i	$0.0256483\pi$
$510$	290.914	−	240.001i	0.570419	−	0.470590i
$511$	364.040	−	264.490i	0.712406	−	0.517593i
$512$	27.3195	+	19.8488i	0.0533584	+	0.0387671i
$513$	−18.4937	+	111.824i	−0.0360501	+	0.217981i
$514$	360.483	−	261.906i	0.701328	−	0.509545i
$515$	93.2493	−	216.030i	0.181067	−	0.419475i
$516$	−167.585	−	85.8692i	−0.324777	−	0.166413i
$517$	−60.4781	+	19.6505i	−0.116979	+	0.0380088i
$518$	−1.01176			−0.00195321
$519$	115.858	−	58.7012i	0.223233	−	0.113104i
$520$	−58.7145	+	136.023i	−0.112912	+	0.261583i
$521$	−363.355	−	118.061i	−0.697419	−	0.226605i	−0.0612134	−	0.998125i	$-0.519497\pi$
$521$	−363.355	−	118.061i	−0.697419	−	0.226605i	−0.636206	+	0.771519i	$0.719497\pi$
$522$	575.877	+	2.61786i	1.10321	+	0.00501505i
$523$	66.4150	+	91.4124i	0.126988	+	0.174785i	0.867777	−	0.496953i	$-0.165548\pi$
$523$	66.4150	+	91.4124i	0.126988	+	0.174785i	−0.740789	+	0.671738i	$0.765548\pi$
$524$			305.885i			0.583749i
$525$	319.337	−	885.772i	0.608262	−	1.68718i
$526$	−640.159			−1.21703
$527$	−243.697	+	177.056i	−0.462422	+	0.335970i
$528$	−121.197	+	754.110i	−0.229540	+	1.42824i
$529$	−16.8065	+	51.7251i	−0.0317703	+	0.0977790i
$530$	19.4774	−	4.37246i	0.0367497	−	0.00824992i
$531$	−348.588	+	250.851i	−0.656475	+	0.472413i
$532$			76.2312i			0.143292i
$533$	116.062	+	357.202i	0.217753	+	0.670174i
$534$	−471.350	−	241.516i	−0.882679	−	0.452277i
$535$	−69.4626	+	742.098i	−0.129837	+	1.38710i
$536$	14.5019	+	19.9602i	0.0270559	+	0.0372392i
$537$	242.428	+	124.218i	0.451448	+	0.231318i
$538$	−191.176	+	263.131i	−0.355346	+	0.489091i
$539$	825.322	+	1135.96i	1.53121	+	2.10753i
$540$	−123.581	−	151.192i	−0.228853	−	0.279984i
$541$	−53.3470	−	38.7589i	−0.0986082	−	0.0716431i	0.537389	−	0.843335i	$-0.319411\pi$
$541$	−53.3470	−	38.7589i	−0.0986082	−	0.0716431i	−0.635997	+	0.771692i	$0.719411\pi$
$542$	−253.489	−	780.160i	−0.467692	−	1.43941i
$543$	50.8981	+	326.154i	0.0937350	+	0.600652i
$544$	73.6496	+	226.670i	0.135385	+	0.416673i
$545$	−491.872	+	558.951i	−0.902517	+	1.02560i
$546$	431.499	+	69.3485i	0.790291	+	0.127012i
$547$	−807.148	−	262.258i	−1.47559	−	0.479448i	−0.542798	−	0.839863i	$-0.682635\pi$
$547$	−807.148	−	262.258i	−1.47559	−	0.479448i	−0.932792	+	0.360415i	$0.882635\pi$
$548$	224.559	−	163.152i	0.409779	−	0.297722i
$549$	−55.9622	+	17.9024i	−0.101935	+	0.0326090i
$550$	−661.632	−	362.157i	−1.20297	−	0.658467i
$551$			115.098i			0.208889i
$552$	−274.781	−	276.033i	−0.497792	−	0.500060i
$553$	−203.845	−	66.2334i	−0.368617	−	0.119771i
$554$	−884.607	−	287.426i	−1.59676	−	0.518820i
$555$	0.329635	+	0.399562i	0.000593936	+	0.000719931i
$556$	−45.6406	−	140.467i	−0.0820874	−	0.252639i
$557$	−309.269			−0.555241			−0.277621	−	0.960691i	$-0.589546\pi$
$557$	−309.269			−0.555241			−0.277621	+	0.960691i	$0.589546\pi$
$558$	343.029	+	476.681i	0.614747	+	0.854266i
$559$	−174.555	−	126.822i	−0.312264	−	0.226873i
$560$	928.039	+	816.665i	1.65721	+	1.45833i
$561$	296.119	−	294.776i	0.527842	−	0.525448i
$562$	242.165	−	333.312i	0.430899	−	0.593082i
$563$	−426.536	−	309.897i	−0.757614	−	0.550438i	0.140564	−	0.990072i	$-0.455108\pi$
$563$	−426.536	−	309.897i	−0.757614	−	0.550438i	−0.898177	+	0.439633i	$0.855108\pi$
$564$	15.0587	+	15.1273i	0.0266999	+	0.0268215i
$565$	−193.140	+	219.479i	−0.341840	+	0.388459i
$566$	442.177	−	608.604i	0.781231	−	1.07527i
$567$	605.176	−	817.224i	1.06733	−	1.44131i
$568$		−	324.867i		−	0.571949i
$569$	−619.336	+	201.235i	−1.08846	+	0.353663i	−0.797653	−	0.603117i	$-0.793925\pi$
$569$	−619.336	+	201.235i	−1.08846	+	0.353663i	−0.290811	+	0.956780i	$0.593925\pi$
$570$	113.357	−	93.5181i	0.198871	−	0.164067i
$571$	−179.914	+	553.718i	−0.315086	+	0.969734i	0.660634	+	0.750708i	$0.270288\pi$
$571$	−179.914	+	553.718i	−0.315086	+	0.969734i	−0.975719	+	0.219025i	$0.929712\pi$
$572$	28.7315	−	88.4266i	0.0502300	−	0.154592i
$573$	−209.232	+	208.283i	−0.365152	+	0.363496i
$574$	2213.18			3.85571
$575$	492.379	−	232.800i	0.856312	−	0.404869i
$576$	−232.689	+	74.4376i	−0.403974	+	0.129232i
$577$	135.871	+	187.010i	0.235478	+	0.324107i	0.910359	−	0.413819i	$-0.135805\pi$
$577$	135.871	+	187.010i	0.235478	+	0.324107i	−0.674881	+	0.737926i	$0.735805\pi$
$578$	−124.717	+	383.838i	−0.215773	+	0.664080i
$579$	−87.1696	+	542.386i	−0.150552	+	0.936763i
$580$	−148.863	−	130.998i	−0.256660	−	0.225859i
$581$	−683.609	+	222.118i	−1.17661	+	0.382303i
$582$	−206.794	+	32.2714i	−0.355317	+	0.0554491i
$583$	21.0335	−	6.83420i	0.0360781	−	0.0117225i
$584$	125.549	−	172.804i	0.214982	−	0.295897i
$585$	−113.197	−	193.000i	−0.193499	−	0.329915i
$586$	−624.333	+	453.604i	−1.06541	+	0.774069i
$587$	443.896	+	322.509i	0.756212	+	0.549420i	0.897746	−	0.440513i	$-0.145204\pi$
$587$	443.896	+	322.509i	0.756212	+	0.549420i	−0.141534	+	0.989933i	$0.545204\pi$
$588$	214.924	−	419.452i	0.365517	−	0.713354i
$589$	−94.9581	+	68.9911i	−0.161219	+	0.117133i
$590$	554.393	+	51.8929i	0.939650	+	0.0879540i
$591$	462.550	−	902.726i	0.782656	−	1.52746i
$592$	−0.646781	+	0.210152i	−0.00109254	+	0.000354986i
$593$	1005.47			1.69557			0.847783	−	0.530343i	$-0.177937\pi$
$593$	1005.47			1.69557			0.847783	+	0.530343i	$0.177937\pi$
$594$	−572.072	−	579.927i	−0.963084	−	0.976308i
$595$	−148.127	−	659.838i	−0.248952	−	1.10897i
$596$	−157.603	−	51.2082i	−0.264434	−	0.0859199i
$597$	37.4734	+	6.02254i	0.0627695	+	0.0100880i
$598$	148.590	+	204.517i	0.248478	+	0.342001i
$599$			288.607i			0.481814i	0.970548	+	0.240907i	$0.0774449\pi$
$599$			288.607i			0.481814i	−0.970548	+	0.240907i	$0.922555\pi$
$600$	14.2354	−	446.726i	0.0237257	−	0.744543i
$601$	265.405			0.441605			0.220802	−	0.975319i	$-0.429132\pi$
$601$	265.405			0.441605			0.220802	+	0.975319i	$0.429132\pi$
$602$	−1028.59	+	747.312i	−1.70862	+	1.24138i
$603$	−37.2602	−	0.169380i	−0.0617914	−	0.000280895i
$604$	−73.3011	+	225.598i	−0.121359	+	0.373506i
$605$	−211.761	−	91.4068i	−0.350018	−	0.151086i
$606$	82.5546	+	162.937i	0.136229	+	0.268873i
$607$		−	357.546i		−	0.589038i	−0.955646	−	0.294519i	$-0.904841\pi$
$607$		−	357.546i		−	0.589038i	0.955646	−	0.294519i	$-0.0951595\pi$
$608$	28.6981	+	88.3237i	0.0472008	+	0.145269i
$609$	470.901	−	919.025i	0.773236	−	1.50907i
$610$	69.9415	+	30.1903i	0.114658	+	0.0494923i
$611$	14.3757	+	19.7864i	0.0235281	+	0.0323837i
$612$	−133.186	−	43.9450i	−0.217624	−	0.0718056i
$613$	−201.824	+	277.787i	−0.329240	+	0.453160i	−0.941260	−	0.337682i	$-0.890357\pi$
$613$	−201.824	+	277.787i	−0.329240	+	0.453160i	0.612020	+	0.790842i	$0.290357\pi$
$614$	−233.178	−	320.941i	−0.379768	−	0.522706i
$615$	−721.059	−	874.021i	−1.17245	−	1.42117i
$616$	782.490	+	568.512i	1.27028	+	0.922910i
$617$	−47.6139	−	146.541i	−0.0771701	−	0.237505i	0.905028	−	0.425351i	$-0.139849\pi$
$617$	−47.6139	−	146.541i	−0.0771701	−	0.237505i	−0.982198	+	0.187846i	$0.939849\pi$
$618$	−325.535	+	50.8015i	−0.526756	+	0.0822031i
$619$	−321.394	−	989.150i	−0.519216	−	1.59798i	−0.775479	−	0.631374i	$-0.782491\pi$
$619$	−321.394	−	989.150i	−0.519216	−	1.59798i	0.256263	−	0.966607i	$-0.417509\pi$
$620$	18.8458	−	201.337i	0.0303964	−	0.324738i
$621$	581.584	−	88.0530i	0.936528	−	0.141792i
$622$	−1017.47	−	330.595i	−1.63580	−	0.531504i
$623$	−768.319	+	558.216i	−1.23326	+	0.896014i
$624$	290.245	−	45.2944i	0.465137	−	0.0725871i
$625$	581.950	+	227.945i	0.931120	+	0.364713i
$626$		−	745.814i		−	1.19140i
$627$	115.385	−	114.862i	0.184027	−	0.183192i
$628$	−100.720	−	32.7259i	−0.160382	−	0.0521113i
$629$	0.353819	+	0.114963i	0.000562511	+	0.000182771i
$630$	−1287.74	+	282.940i	−2.04402	+	0.449111i
$631$	271.623	+	835.969i	0.430464	+	1.32483i	0.897664	+	0.440681i	$0.145263\pi$
$631$	271.623	+	835.969i	0.430464	+	1.32483i	−0.467200	+	0.884152i	$0.654737\pi$
$632$	−101.742			−0.160984
$633$	−969.324	+	491.123i	−1.53132	+	0.775866i
$634$	−463.437	−	336.707i	−0.730973	−	0.531083i
$635$	573.006	−	339.584i	0.902372	−	0.534778i
$636$	−5.23724	−	5.26110i	−0.00823465	−	0.00827217i
$637$	317.425	−	436.898i	0.498313	−	0.685869i
$638$	−669.231	−	486.224i	−1.04895	−	0.762107i
$639$	395.608	+	290.183i	0.619105	+	0.454120i
$640$	697.041	+	300.878i	1.08913	+	0.470122i
$641$	305.155	−	420.009i	0.476060	−	0.655241i	−0.501682	−	0.865052i	$-0.667285\pi$
$641$	305.155	−	420.009i	0.476060	−	0.655241i	0.977742	+	0.209812i	$0.0672851\pi$
$642$	930.992	−	471.702i	1.45014	−	0.734738i
$643$		−	702.045i		−	1.09183i	−0.837842	−	0.545914i	$-0.816183\pi$
$643$		−	702.045i		−	1.09183i	0.837842	−	0.545914i	$-0.183817\pi$
$644$	376.250	−	122.251i	0.584240	−	0.189831i
$645$	630.243	+	162.730i	0.977121	+	0.252295i
$646$	32.6152	−	100.379i	0.0504880	−	0.155386i
$647$	95.5712	−	294.138i	0.147714	−	0.454618i	−0.849636	−	0.527370i	$-0.823178\pi$
$647$	95.5712	−	294.138i	0.147714	−	0.454618i	0.997350	+	0.0727520i	$0.0231782\pi$
$648$	153.333	−	457.708i	0.236625	−	0.706340i
$649$	616.895			0.950532
$650$	−53.8360	+	285.056i	−0.0828246	+	0.438548i
$651$	1040.48	−	162.373i	1.59828	−	0.249420i
$652$	−16.5781	−	22.8179i	−0.0254266	−	0.0349967i
$653$	−40.3685	+	124.241i	−0.0618200	+	0.190263i	−0.977197	−	0.212336i	$-0.931893\pi$
$653$	−40.3685	+	124.241i	−0.0618200	+	0.190263i	0.915377	+	0.402598i	$0.131893\pi$
$654$	1029.36	+	165.434i	1.57395	+	0.252958i
$655$	−231.601	−	1031.68i	−0.353589	−	1.57508i
$656$	1414.80	−	459.697i	2.15671	−	0.700757i
$657$	98.2873	+	307.243i	0.149600	+	0.467645i
$658$	137.064	−	44.5348i	0.208304	−	0.0676821i
$659$	−543.472	+	748.024i	−0.824691	+	1.13509i	0.164197	+	0.986428i	$0.447497\pi$
$659$	−543.472	+	748.024i	−0.824691	+	1.13509i	−0.988888	+	0.148663i	$0.952503\pi$
$660$	17.2327	+	279.964i	0.0261101	+	0.424188i
$661$	−723.767	+	525.847i	−1.09496	+	0.795533i	−0.980230	−	0.197864i	$-0.936600\pi$
$661$	−723.767	+	525.847i	−1.09496	+	0.795533i	−0.114728	+	0.993397i	$0.536600\pi$
$662$	283.537	+	206.002i	0.428304	+	0.311181i
$663$	−143.018	−	73.2813i	−0.215714	−	0.110530i
$664$	−276.035	+	200.551i	−0.415715	+	0.302035i
$665$	−57.7186	−	257.111i	−0.0867949	−	0.386633i
$666$	0.227268	−	0.688788i	0.000341243	−	0.00103422i
$667$	568.082	−	184.581i	0.851697	−	0.276733i
$668$	−131.700			−0.197155
$669$	309.400	+	610.658i	0.462481	+	0.912793i
$670$	36.2669	+	31.9146i	0.0541298	+	0.0476337i
$671$	80.2679	+	26.0806i	0.119624	+	0.0388683i
$672$	132.213	−	822.655i	0.196746	−	1.22419i
$673$	−157.836	−	217.242i	−0.234526	−	0.322797i	0.675491	−	0.737368i	$-0.263932\pi$
$673$	−157.836	−	217.242i	−0.234526	−	0.322797i	−0.910017	+	0.414571i	$0.863932\pi$
$674$			1474.25i			2.18731i
$675$	531.286	+	416.366i	0.787090	+	0.616839i
$676$	208.692			0.308716
$677$	−674.872	+	490.323i	−0.996857	+	0.724259i	−0.961412	−	0.275113i	$-0.911285\pi$
$677$	−674.872	+	490.323i	−0.996857	+	0.724259i	−0.0354451	+	0.999372i	$0.511285\pi$
$678$	404.193	+	64.9599i	0.596154	+	0.0958110i
$679$	−115.975	+	356.933i	−0.170802	+	0.525674i
$680$	−163.661	−	276.157i	−0.240678	−	0.406114i
$681$	−831.498	+	421.291i	−1.22100	+	0.618636i
$682$		−	843.580i		−	1.23692i
$683$	−244.142	−	751.391i	−0.357455	−	1.10013i	−0.954572	−	0.297980i	$-0.903687\pi$
$683$	−244.142	−	751.391i	−0.357455	−	1.10013i	0.597117	−	0.802154i	$-0.296313\pi$
$684$	−51.8968	−	17.1235i	−0.0758724	−	0.0250343i
$685$	−633.856	+	720.299i	−0.925338	+	1.05153i
$686$	−1026.61	−	1413.01i	−1.49652	−	2.05978i
$687$	−166.032	+	324.034i	−0.241677	+	0.471665i
$688$	−502.314	+	691.376i	−0.730107	+	1.00491i
$689$	−4.99968	−	6.88147i	−0.00725643	−	0.00998762i
$690$	−643.361	−	409.515i	−0.932408	−	0.593499i
$691$	−760.429	−	552.484i	−1.10048	−	0.799543i	−0.119339	−	0.992854i	$-0.538078\pi$
$691$	−760.429	−	552.484i	−1.10048	−	0.799543i	−0.981138	+	0.193310i	$0.938078\pi$
$692$	19.3513	+	59.5572i	0.0279643	+	0.0860653i
$693$	−1391.25	+	445.064i	−2.00758	+	0.642228i
$694$	414.375	+	1275.32i	0.597082	+	1.83763i
$695$	260.291	+	439.208i	0.374519	+	0.631954i
$696$	77.7813	−	483.970i	0.111755	−	0.695359i
$697$	−773.962	−	251.475i	−1.11042	−	0.360797i
$698$	−870.783	+	632.661i	−1.24754	+	0.906390i
$699$	186.020	+	1192.02i	0.266124	+	1.70532i
$700$	398.230	+	217.979i	0.568900	+	0.311398i
$701$			959.479i			1.36873i	0.729140	+	0.684365i	$0.239920\pi$
$701$			959.479i			1.36873i	−0.729140	+	0.684365i	$0.760080\pi$
$702$	−144.137	+	278.179i	−0.205323	+	0.396266i
$703$	0.137868	+	0.0447961i	0.000196114	+	6.37213e-5i
$704$	333.752	+	108.443i	0.474079	+	0.154038i
$705$	−62.2434	−	39.6194i	−0.0882885	−	0.0561977i
$706$	−126.704	−	389.956i	−0.179468	−	0.552346i
$707$	327.532			0.463271
$708$	−93.5872	−	184.712i	−0.132185	−	0.260892i
$709$	394.579	+	286.678i	0.556529	+	0.404342i	0.830187	−	0.557485i	$-0.188234\pi$
$709$	394.579	+	286.678i	0.556529	+	0.404342i	−0.273658	+	0.961827i	$0.588234\pi$
$710$	−139.332	−	620.664i	−0.196243	−	0.874175i
$711$	90.8794	−	123.896i	0.127819	−	0.174257i
$712$	−264.977	+	364.709i	−0.372158	+	0.512232i
$713$	492.799	+	358.040i	0.691163	+	0.502160i
$714$	−671.108	+	668.064i	−0.939927	+	0.935664i
$715$	−29.9527	+	319.997i	−0.0418919	+	0.447549i
$716$	−77.1985	+	106.255i	−0.107819	+	0.148400i
$717$	−266.173	−	525.343i	−0.371232	−	0.732696i
$718$		−	1077.52i		−	1.50073i
$719$	9.24954	−	3.00536i	0.0128644	−	0.00417991i	−0.302578	−	0.953125i	$-0.597847\pi$
$719$	9.24954	−	3.00536i	0.0128644	−	0.00417991i	0.315442	+	0.948945i	$0.397847\pi$
$720$	−764.432	+	448.347i	−1.06171	+	0.622704i
$721$	−182.567	+	561.883i	−0.253213	+	0.779311i
$722$	−247.635	+	762.141i	−0.342984	+	1.05560i
$723$	763.735	+	767.215i	1.05634	+	1.06115i
$724$	−159.159			−0.219834
$725$	601.267	+	329.115i	0.829334	+	0.453952i
$726$	49.7977	+	319.103i	0.0685919	+	0.439536i
$727$	542.782	+	747.076i	0.746606	+	1.02761i	0.998211	+	0.0597846i	$0.0190414\pi$
$727$	542.782	+	747.076i	0.746606	+	1.02761i	−0.251606	+	0.967830i	$0.580959\pi$
$728$	114.953	−	353.790i	0.157903	−	0.485975i
$729$	420.413	+	595.562i	0.576698	+	0.816957i
$730$	165.750	−	383.992i	0.227055	−	0.526016i
$731$	444.618	−	144.465i	0.608232	−	0.197627i
$732$	−4.36808	−	27.9906i	−0.00596732	−	0.0382385i
$733$	−527.602	+	171.428i	−0.719784	+	0.233872i	−0.645929	−	0.763397i	$-0.723530\pi$
$733$	−527.602	+	171.428i	−0.719784	+	0.233872i	−0.0738544	+	0.997269i	$0.523530\pi$
$734$	−541.331	+	745.078i	−0.737508	+	1.01509i
$735$	−407.301	+	1577.45i	−0.554151	+	2.14619i
$736$	389.912	−	283.288i	0.529772	−	0.384902i
$737$	43.3004	+	31.4596i	0.0587522	+	0.0426860i
$738$	−497.136	+	1506.69i	−0.673626	+	2.04158i
$739$	1100.89	−	799.845i	1.48970	−	1.08233i	0.515440	−	0.856925i	$-0.327628\pi$
$739$	1100.89	−	799.845i	1.48970	−	1.08233i	0.974264	−	0.225408i	$-0.0723717\pi$
$740$	−0.214852	+	0.127329i	−0.000290340	+	0.000172066i
$741$	−55.7280	−	28.5546i	−0.0752065	−	0.0385352i
$742$	−47.6692	+	15.4887i	−0.0642442	+	0.0208742i
$743$	−124.104			−0.167031			−0.0835155	−	0.996506i	$-0.526615\pi$
$743$	−124.104			−0.167031			−0.0835155	+	0.996506i	$0.526615\pi$
$744$	445.909	−	225.927i	0.599340	−	0.303665i
$745$	570.331	+	53.3847i	0.765545	+	0.0716573i
$746$	767.445	+	249.358i	1.02875	+	0.334260i
$747$	2.34240	−	515.281i	0.00313574	−	0.689801i
$748$	118.413	+	162.982i	0.158306	+	0.217890i
$749$		−	1871.46i		−	2.49861i
$750$	−164.399	−	859.582i	−0.219199	−	1.14611i
$751$	632.917			0.842766			0.421383	−	0.906883i	$-0.361545\pi$
$751$	632.917			0.842766			0.421383	+	0.906883i	$0.361545\pi$
$752$	78.3697	−	56.9389i	0.104215	−	0.0757166i
$753$	−160.634	+	999.497i	−0.213326	+	1.32735i
$754$	−98.3147	+	302.581i	−0.130391	+	0.401302i
$755$	76.4166	−	816.390i	0.101214	−	1.08131i
$756$	344.325	+	349.053i	0.455456	+	0.461710i
$757$			1271.62i			1.67981i	0.542734	+	0.839904i	$0.317389\pi$
$757$			1271.62i			1.67981i	−0.542734	+	0.839904i	$0.682611\pi$
$758$	−270.505	−	832.529i	−0.356867	−	1.09832i
$759$	−751.959	−	385.297i	−0.990723	−	0.507638i
$760$	−63.7716	−	107.607i	−0.0839100	−	0.141588i
$761$	−706.088	−	971.847i	−0.927843	−	1.27707i	−0.960695	−	0.277606i	$-0.910459\pi$
$761$	−706.088	−	971.847i	−0.927843	−	1.27707i	0.0328525	−	0.999460i	$-0.489541\pi$
$762$	−830.055	−	425.313i	−1.08931	−	0.558154i
$763$	1098.86	−	1512.45i	1.44018	−	1.98224i
$764$	−83.6686	−	115.160i	−0.109514	−	0.150733i
$765$	482.479	+	47.3749i	0.630691	+	0.0619279i
$766$	239.992	+	174.364i	0.313305	+	0.227629i
$767$	−73.3182	−	225.650i	−0.0955908	−	0.294198i
$768$	−113.690	−	728.527i	−0.148034	−	0.948602i
$769$	−164.777	−	507.132i	−0.214275	−	0.659469i	−0.999204	−	0.0398846i	$-0.987301\pi$
$769$	−164.777	−	507.132i	−0.214275	−	0.659469i	0.784930	−	0.619585i	$-0.212699\pi$
$770$	1738.79	+	750.550i	2.25817	+	0.974740i
$771$	565.527	+	90.8888i	0.733498	+	0.117884i
$772$	−251.905	−	81.8489i	−0.326302	−	0.106022i
$773$	816.217	−	593.017i	1.05591	−	0.767163i	0.0825815	−	0.996584i	$-0.473684\pi$
$773$	816.217	−	593.017i	1.05591	−	0.767163i	0.973327	+	0.229422i	$0.0736835\pi$
$774$	−277.709	−	868.108i	−0.358797	−	1.12159i
$775$	88.8804	+	693.335i	0.114684	+	0.894626i
$776$			178.150i			0.229575i
$777$	−0.917567	−	0.921748i	−0.00118091	−	0.00118629i
$778$	593.865	+	192.959i	0.763323	+	0.248019i
$779$	−301.580	−	97.9892i	−0.387137	−	0.125788i
$780$	100.358	−	39.5773i	0.128664	−	0.0507401i
$781$	−217.778	−	670.253i	−0.278846	−	0.858198i
$782$	−547.742			−0.700437
$783$	519.878	+	527.017i	0.663957	+	0.673074i
$784$	−1730.46	−	1257.25i	−2.20722	−	1.60364i
$785$	364.484	+	34.1168i	0.464311	+	0.0434609i
$786$	−1049.30	+	1044.54i	−1.33499	+	1.32893i
$787$	527.782	−	726.430i	0.670625	−	0.923037i	−0.329149	−	0.944278i	$-0.606762\pi$
$787$	527.782	−	726.430i	0.670625	−	0.923037i	0.999774	+	0.0212413i	$0.00676184\pi$
$788$	395.660	+	287.464i	0.502107	+	0.364802i
$789$	−580.561	−	583.206i	−0.735819	−	0.739171i
$790$	−194.380	+	43.6361i	−0.246050	+	0.0552356i
$791$	431.480	−	593.882i	0.545487	−	0.750799i
$792$	−562.800	+	405.002i	−0.710606	+	0.511366i
$793$		−	32.4604i		−	0.0409336i
$794$	160.129	−	52.0292i	0.201674	−	0.0655279i
$795$	21.6475	+	13.7791i	0.0272295	+	0.0173322i
$796$	−5.65493	+	17.4041i	−0.00710419	+	0.0218644i
$797$	−24.0490	+	74.0152i	−0.0301744	+	0.0928673i	−0.965010	−	0.262215i	$-0.915547\pi$
$797$	−24.0490	+	74.0152i	−0.0301744	+	0.0928673i	0.934835	+	0.355082i	$0.115547\pi$
$798$	−261.502	+	260.316i	−0.327697	+	0.326210i
$799$	−52.9925			−0.0663235
$800$	543.462	+	102.639i	0.679327	+	0.128298i
$801$	−207.439	−	648.447i	−0.258975	−	0.809547i
$802$	−350.528	−	482.460i	−0.437067	−	0.601572i
$803$	143.187	−	440.685i	0.178316	−	0.548799i
$804$	2.85072	−	17.7377i	0.00354567	−	0.0220618i
$805$	−1176.45	+	697.205i	−1.46142	+	0.866093i
$806$	−308.568	+	100.260i	−0.382838	+	0.124392i
$807$	−413.099	+	64.4663i	−0.511894	+	0.0798839i
$808$	147.865	−	48.0443i	0.183001	−	0.0594607i
$809$	−503.318	+	692.758i	−0.622148	+	0.856314i	−0.997507	−	0.0705660i	$-0.977519\pi$
$809$	−503.318	+	692.758i	−0.622148	+	0.856314i	0.375359	+	0.926880i	$0.377519\pi$
$810$	96.6382	−	940.221i	0.119306	−	1.16077i
$811$	859.986	−	624.817i	1.06040	−	0.770427i	0.0862396	−	0.996274i	$-0.472515\pi$
$811$	859.986	−	624.817i	1.06040	−	0.770427i	0.974163	+	0.225847i	$0.0725149\pi$
$812$	402.803	+	292.654i	0.496063	+	0.360411i
$813$	480.861	−	938.464i	0.591465	−	1.15432i
$814$	−0.842883	+	0.612390i	−0.00103548	+	0.000752322i
$815$	73.1910	+	64.4074i	0.0898049	+	0.0790274i
$816$	−290.251	+	566.463i	−0.355700	+	0.694195i
$817$	173.249	−	56.2919i	0.212055	−	0.0689007i
$818$	1667.15			2.03808
$819$	328.148	+	456.002i	0.400669	+	0.556779i
$820$	469.978	−	278.526i	0.573144	−	0.339666i
$821$	−711.389	−	231.144i	−0.866491	−	0.281540i	−0.158154	−	0.987414i	$-0.550554\pi$
$821$	−711.389	−	231.144i	−0.866491	−	0.281540i	−0.708337	+	0.705874i	$0.750554\pi$
$822$	1326.50	+	213.189i	1.61375	+	0.259354i
$823$	−458.192	−	630.647i	−0.556733	−	0.766278i	0.434173	−	0.900829i	$-0.357041\pi$
$823$	−458.192	−	630.647i	−0.556733	−	0.766278i	−0.990907	+	0.134552i	$0.957041\pi$
$824$			280.443i			0.340343i
$825$	−270.097	−	931.209i	−0.327391	−	1.12874i
$826$	−1398.10			−1.69261
$827$	−551.236	+	400.497i	−0.666549	+	0.484276i	−0.868868	−	0.495043i	$-0.835152\pi$
$827$	−551.236	+	400.497i	−0.666549	+	0.484276i	0.202319	+	0.979320i	$0.435152\pi$
$828$	−1.28923	+	283.605i	−0.00155704	+	0.342518i
$829$	131.487	−	404.674i	0.158609	−	0.488147i	−0.839900	−	0.542741i	$-0.817386\pi$
$829$	131.487	−	404.674i	0.158609	−	0.488147i	0.998509	+	0.0545941i	$0.0173865\pi$
$830$	−441.355	+	501.545i	−0.531753	+	0.604271i
$831$	−540.396	−	1066.57i	−0.650296	−	1.28348i
$832$		−	134.969i		−	0.162223i
$833$	361.585	+	1112.84i	0.434075	+	1.33595i
$834$	326.002	−	636.236i	0.390890	−	0.762872i
$835$	444.193	−	99.7166i	0.531968	−	0.119421i
$836$	46.1406	+	63.5070i	0.0551921	+	0.0759653i
$837$	−123.179	+	744.813i	−0.147167	+	0.889860i
$838$	6.86018	−	9.44223i	0.00818637	−	0.0112676i
$839$	−795.202	−	1094.50i	−0.947797	−	1.30453i	−0.952499	−	0.304542i	$-0.901497\pi$
$839$	−795.202	−	1094.50i	−0.947797	−	1.30453i	0.00470187	−	0.999989i	$-0.498503\pi$
$840$	68.9471	+	1120.12i	0.0820798	+	1.33348i
$841$	−72.2106	−	52.4640i	−0.0858627	−	0.0623829i
$842$	−80.9242	−	249.059i	−0.0961095	−	0.295795i
$843$	523.278	−	81.6603i	0.620733	−	0.0968687i
$844$	−161.903	−	498.285i	−0.191828	−	0.590385i
$845$	−703.871	+	158.011i	−0.832983	+	0.186996i
$846$	−0.469652	+	103.314i	−0.000555145	+	0.122121i
$847$	550.780	+	178.959i	0.650272	+	0.211286i
$848$	−27.2560	+	19.8026i	−0.0321415	+	0.0233522i
$849$	955.469	−	149.106i	1.12541	−	0.175626i
$850$	−431.118	−	457.410i	−0.507197	−	0.538130i
$851$		−	0.752308i		−	0.000884028i
$852$	−167.650	+	166.889i	−0.196772	+	0.195880i
$853$	1153.47	+	374.784i	1.35225	+	0.439372i	0.893448	−	0.449167i	$-0.148279\pi$
$853$	1153.47	+	374.784i	1.35225	+	0.439372i	0.458800	+	0.888539i	$0.348279\pi$
$854$	−181.915	−	59.1076i	−0.213015	−	0.0692127i
$855$	188.001	+	18.4600i	0.219884	+	0.0215906i
$856$	−274.516	−	844.873i	−0.320696	−	0.987002i
$857$	549.363			0.641031			0.320515	−	0.947243i	$-0.396144\pi$
$857$	549.363			0.641031			0.320515	+	0.947243i	$0.396144\pi$
$858$	401.450	−	203.401i	0.467890	−	0.237064i
$859$	414.050	+	300.825i	0.482013	+	0.350203i	0.802105	−	0.597183i	$-0.203714\pi$
$859$	414.050	+	300.825i	0.482013	+	0.350203i	−0.320091	+	0.947387i	$0.603714\pi$
$860$	−124.377	+	288.142i	−0.144624	+	0.335049i
$861$	2007.13	+	2016.28i	2.33116	+	2.34178i
$862$	−604.110	+	831.486i	−0.700823	+	0.964601i
$863$	−342.771	−	249.038i	−0.397185	−	0.288572i	0.371208	−	0.928550i	$-0.378944\pi$
$863$	−342.771	−	249.038i	−0.397185	−	0.288572i	−0.768394	+	0.639978i	$0.778944\pi$
$864$	530.350	+	274.798i	0.613830	+	0.318053i
$865$	−110.362	−	186.221i	−0.127586	−	0.215285i
$866$	−1011.62	+	1392.38i	−1.16816	+	1.60783i
$867$	−462.795	+	234.482i	−0.533789	+	0.270453i
$868$			507.743i			0.584957i
$869$	−209.910	+	68.2038i	−0.241553	+	0.0784854i
$870$	−58.9675	−	957.992i	−0.0677787	−	1.10114i
$871$	6.36113	−	19.5775i	0.00730325	−	0.0224771i
$872$	274.227	−	843.984i	0.314480	−	0.967871i
$873$	−216.942	−	159.130i	−0.248502	−	0.182279i
$874$	−213.432			−0.244201
$875$	−1508.18	−	433.674i	−1.72364	−	0.495627i
$876$	−153.673	+	23.9815i	−0.175426	+	0.0273762i
$877$	−65.6432	−	90.3501i	−0.0748497	−	0.103022i	0.769951	−	0.638103i	$-0.220281\pi$
$877$	−65.6432	−	90.3501i	−0.0748497	−	0.103022i	−0.844800	+	0.535082i	$0.820281\pi$
$878$	134.305	−	413.349i	0.152967	−	0.470784i
$879$	−979.457	−	157.414i	−1.11429	−	0.179083i
$880$	1267.44	+	118.636i	1.44027	+	0.134814i
$881$	−264.217	+	85.8494i	−0.299906	+	0.0974454i	−0.455105	−	0.890438i	$-0.650398\pi$
$881$	−264.217	+	85.8494i	−0.299906	+	0.0974454i	0.155199	+	0.987883i	$0.450398\pi$
$882$	2172.81	−	695.084i	2.46350	−	0.788077i
$883$	−998.750	+	324.514i	−1.13109	+	0.367513i	−0.813989	−	0.580880i	$-0.802709\pi$
$883$	−998.750	+	324.514i	−1.13109	+	0.367513i	−0.317098	+	0.948393i	$0.602709\pi$
$884$	45.5426	−	62.6840i	0.0515188	−	0.0709095i
$885$	455.504	+	552.132i	0.514693	+	0.623878i
$886$	896.236	−	651.153i	1.01155	−	0.734936i
$887$	−527.586	−	383.313i	−0.594798	−	0.432146i	0.249231	−	0.968444i	$-0.419822\pi$
$887$	−527.586	−	383.313i	−0.594798	−	0.432146i	−0.844029	+	0.536298i	$0.819822\pi$
$888$	−0.549444	−	0.281531i	−0.000618744	−	0.000317039i
$889$	−1353.02	+	983.027i	−1.52196	+	1.10577i
$890$	−349.822	+	810.429i	−0.393059	+	0.910594i
$891$	9.52025	−	1047.11i	0.0106849	−	1.17521i
$892$	−313.911	+	101.996i	−0.351918	+	0.114345i
$893$	−20.6489			−0.0231231
$894$	−362.521	−	715.504i	−0.405505	−	0.800340i
$895$	179.923	−	416.824i	0.201031	−	0.465726i
$896$	−1812.97	−	589.070i	−2.02341	−	0.657444i
$897$	−51.5650	+	320.847i	−0.0574860	+	0.357689i
$898$	289.543	+	398.521i	0.322431	+	0.443788i
$899$			766.615i			0.852742i
$900$	−237.849	+	222.144i	−0.264276	+	0.246826i
$901$	18.4301			0.0204552
$902$	1843.76	−	1339.57i	2.04408	−	1.48511i
$903$	−1613.65	−	259.339i	−1.78699	−	0.287197i
$904$	107.679	−	331.401i	0.119114	−	0.366594i
$905$	536.809	−	120.508i	0.593160	−	0.133158i
$906$	−1024.20	+	518.925i	−1.13046	+	0.572765i
$907$			1.34888i			0.00148718i	1.00000		0.000743592i	$0.000236693\pi$
$907$			1.34888i			0.00148718i	−1.00000		0.000743592i	$0.999763\pi$
$908$	−138.882	−	427.435i	−0.152954	−	0.470743i
$909$	−73.5722	+	222.978i	−0.0809375	+	0.245300i
$910$	67.8831	−	725.224i	0.0745968	−	0.796949i
$911$	460.782	+	634.213i	0.505798	+	0.696172i	0.983204	−	0.182511i	$-0.0584226\pi$
$911$	460.782	+	634.213i	0.505798	+	0.696172i	−0.477405	+	0.878683i	$0.658423\pi$
$912$	−113.098	+	220.727i	−0.124011	+	0.242025i
$913$	−435.062	+	598.812i	−0.476519	+	0.655873i
$914$	485.052	+	667.617i	0.530692	+	0.730435i
$915$	35.9256	+	91.0986i	0.0392630	+	0.0995613i
$916$	−142.022	−	103.185i	−0.155046	−	0.112648i
$917$	820.406	+	2524.95i	0.894663	+	2.75349i
$918$	−304.057	−	606.942i	−0.331217	−	0.661157i
$919$	10.8003	+	33.2399i	0.0117522	+	0.0361697i	0.956761	−	0.290876i	$-0.0939468\pi$
$919$	10.8003	+	33.2399i	0.0117522	+	0.0361697i	−0.945008	+	0.327046i	$0.893947\pi$
$920$	−428.839	+	487.322i	−0.466129	+	0.529698i
$921$	80.9192	−	503.494i	0.0878602	−	0.546682i
$922$	662.740	+	215.337i	0.718807	+	0.233555i
$923$	−219.284	+	159.319i	−0.237578	+	0.172610i
$924$	−108.593	−	695.863i	−0.117525	−	0.753098i
$925$	0.628240	−	0.592128i	0.000679179	−	0.000640139i
$926$			1211.45i			1.30826i
$927$	−341.510	−	250.501i	−0.368403	−	0.270228i
$928$	576.873	+	187.437i	0.621630	+	0.201980i
$929$	317.359	+	103.116i	0.341613	+	0.110997i	0.474799	−	0.880094i	$-0.342521\pi$
$929$	317.359	+	103.116i	0.341613	+	0.110997i	−0.133186	+	0.991091i	$0.542521\pi$
$930$	755.019	−	622.883i	0.811848	−	0.669767i
$931$	140.894	+	433.627i	0.151336	+	0.465765i
$932$	−581.690			−0.624131
$933$	−621.559	−	1226.76i	−0.666194	−	1.31486i
$934$	805.331	+	585.108i	0.862239	+	0.626453i
$935$	−522.783	−	460.044i	−0.559127	−	0.492026i
$936$	215.032	+	157.728i	0.229735	+	0.168513i
$937$	−156.678	+	215.649i	−0.167213	+	0.230148i	−0.884397	−	0.466735i	$-0.845430\pi$
$937$	−156.678	+	215.649i	−0.167213	+	0.230148i	0.717185	+	0.696883i	$0.245430\pi$
$938$	−98.1335	−	71.2981i	−0.104620	−	0.0760108i
$939$	679.461	−	676.379i	0.723600	−	0.720318i
$940$	23.5015	−	26.7065i	0.0250016	−	0.0284112i
$941$	53.2570	−	73.3019i	0.0565961	−	0.0778979i	−0.779781	−	0.626053i	$-0.784670\pi$
$941$	53.2570	−	73.3019i	0.0565961	−	0.0778979i	0.836377	+	0.548155i	$0.184670\pi$
$942$	−231.678	−	457.261i	−0.245943	−	0.485415i
$943$			1645.64i			1.74511i
$944$	−893.751	+	290.397i	−0.946770	+	0.307624i
$945$	−1425.62	−	916.571i	−1.50859	−	0.969916i
$946$	−404.573	+	1245.15i	−0.427667	+	1.31622i
$947$	−406.796	+	1251.99i	−0.429562	+	1.32206i	0.468995	+	0.883201i	$0.344616\pi$
$947$	−406.796	+	1251.99i	−0.429562	+	1.32206i	−0.898557	+	0.438856i	$0.855384\pi$
$948$	52.2664	+	52.5046i	0.0551334	+	0.0553846i
$949$	−178.213			−0.187791
$950$	−167.988	−	178.233i	−0.176830	−	0.187614i
$951$	−113.541	−	727.566i	−0.119391	−	0.765053i
$952$	473.765	+	652.081i	0.497652	+	0.684959i
$953$	533.396	−	1641.62i	0.559702	−	1.72259i	−0.123488	−	0.992346i	$-0.539408\pi$
$953$	533.396	−	1641.62i	0.559702	−	1.72259i	0.683190	−	0.730240i	$-0.260592\pi$
$954$	0.163339	−	35.9314i	0.000171215	−	0.0376640i
$955$	369.389	+	325.059i	0.386795	+	0.340376i
$956$	270.055	−	87.7461i	0.282484	−	0.0917846i
$957$	−163.959	−	1050.65i	−0.171326	−	1.09786i
$958$	−654.627	+	212.701i	−0.683326	+	0.222026i
$959$	1416.05	−	1949.03i	1.47660	−	2.03236i
$960$	149.378	+	378.786i	0.155602	+	0.394568i
$961$	144.991	−	105.342i	0.150875	−	0.109617i
$962$	0.324179	+	0.235530i	0.000336984	+	0.000244834i
$963$	1274.05	+	420.378i	1.32300	+	0.436529i
$964$	−422.269	+	306.797i	−0.438039	+	0.318254i
$965$	911.591	+	85.3277i	0.944654	+	0.0884225i
$966$	1704.20	+	873.216i	1.76418	+	0.903950i
$967$	−692.020	+	224.851i	−0.715636	+	0.232524i	−0.644130	−	0.764916i	$-0.722780\pi$
$967$	−692.020	+	224.851i	−0.715636	+	0.232524i	−0.0715060	+	0.997440i	$0.522780\pi$
$968$	274.902			0.283989
$969$	121.028	−	61.3206i	0.124900	−	0.0632823i
$970$	76.4067	+	340.358i	0.0787698	+	0.350885i
$971$	1094.40	+	355.593i	1.12709	+	0.366213i	0.812468	−	0.583005i	$-0.198123\pi$
$971$	1094.40	+	355.593i	1.12709	+	0.366213i	0.314619	+	0.949218i	$0.398123\pi$
$972$	−314.973	+	156.003i	−0.324046	+	0.160497i
$973$	−753.489	−	1037.09i	−0.774397	−	1.06587i
$974$		−	1548.00i		−	1.58932i
$975$	−308.520	+	209.472i	−0.316430	+	0.214843i
$976$	−128.568			−0.131730
$977$	214.381	−	155.757i	0.219428	−	0.159424i	−0.472641	−	0.881255i	$-0.656699\pi$
$977$	214.381	−	155.757i	0.219428	−	0.159424i	0.692069	+	0.721831i	$0.256699\pi$
$978$	21.6625	−	134.788i	0.0221498	−	0.137820i
$979$	−302.202	+	930.083i	−0.308685	+	0.950034i
$980$	−721.196	−	311.305i	−0.735914	−	0.317658i
$981$	782.814	+	1087.82i	0.797976	+	1.10888i
$982$		−	1252.31i		−	1.27526i
$983$	500.620	+	1540.75i	0.509277	+	1.56739i	0.793459	+	0.608624i	$0.208278\pi$
$983$	500.620	+	1540.75i	0.509277	+	1.56739i	−0.284181	+	0.958771i	$0.591722\pi$
$984$	1201.88	+	615.834i	1.22142	+	0.625848i
$985$	−1552.13	−	669.976i	−1.57576	−	0.680179i
$986$	−405.191	−	557.697i	−0.410944	−	0.565616i
$987$	164.876	+	84.4812i	0.167048	+	0.0855940i
$988$	17.7460	−	24.4253i	0.0179615	−	0.0247219i
$989$	−555.674	−	764.819i	−0.561854	−	0.773326i
$990$	−901.537	+	1015.14i	−0.910643	+	1.02540i
$991$	−262.932	−	191.031i	−0.265320	−	0.192766i	0.447169	−	0.894449i	$-0.352432\pi$
$991$	−262.932	−	191.031i	−0.265320	−	0.192766i	−0.712489	+	0.701683i	$0.752432\pi$
$992$	191.146	+	588.286i	0.192687	+	0.593030i
$993$	69.4657	+	445.135i	0.0699554	+	0.448273i
$994$	493.560	+	1519.02i	0.496540	+	1.52819i
$995$	5.89528	−	62.9818i	0.00592491	−	0.0632982i
$996$	245.299	+	39.4233i	0.246284	+	0.0395816i
$997$	779.958	+	253.424i	0.782305	+	0.254186i	0.672824	−	0.739803i	$-0.265081\pi$
$997$	779.958	+	253.424i	0.782305	+	0.254186i	0.109481	+	0.993989i	$0.465081\pi$
$998$	1493.87	−	1085.36i	1.49687	−	1.08754i
$999$	0.833618	−	0.417614i	0.000834452	−	0.000418032i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.h.a.14.5	✓	72
3.2	odd	2	inner	75.3.h.a.14.14	yes	72
5.2	odd	4		375.3.j.b.176.9		144
5.3	odd	4		375.3.j.b.176.28		144
5.4	even	2		375.3.h.a.74.14		72
15.2	even	4		375.3.j.b.176.27		144
15.8	even	4		375.3.j.b.176.10		144
15.14	odd	2		375.3.h.a.74.5		72
25.9	even	10	inner	75.3.h.a.59.14	yes	72
25.12	odd	20		375.3.j.b.326.27		144
25.13	odd	20		375.3.j.b.326.10		144
25.16	even	5		375.3.h.a.299.5		72
75.38	even	20		375.3.j.b.326.28		144
75.41	odd	10		375.3.h.a.299.14		72
75.59	odd	10	inner	75.3.h.a.59.5	yes	72
75.62	even	20		375.3.j.b.326.9		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.h.a.14.5	✓	72	1.1	even	1	trivial
75.3.h.a.14.14	yes	72	3.2	odd	2	inner
75.3.h.a.59.5	yes	72	75.59	odd	10	inner
75.3.h.a.59.14	yes	72	25.9	even	10	inner
375.3.h.a.74.5		72	15.14	odd	2
375.3.h.a.74.14		72	5.4	even	2
375.3.h.a.299.5		72	25.16	even	5
375.3.h.a.299.14		72	75.41	odd	10
375.3.j.b.176.9		144	5.2	odd	4
375.3.j.b.176.10		144	15.8	even	4
375.3.j.b.176.27		144	15.2	even	4
375.3.j.b.176.28		144	5.3	odd	4
375.3.j.b.326.9		144	75.62	even	20
375.3.j.b.326.10		144	25.13	odd	20
375.3.j.b.326.27		144	25.12	odd	20
375.3.j.b.326.28		144	75.38	even	20

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.88806 + 1.37175i) q^{2} +(-2.96199 - 0.476037i) q^{3} +(0.446980 - 1.37566i) q^{4} +(-0.465978 + 4.97824i) q^{5} +(6.24541 - 3.16433i) q^{6} -12.5544i q^{7} +(-1.84155 - 5.66769i) q^{8} +(8.54678 + 2.82003i) q^{9} +(-5.94912 - 10.0384i) q^{10} +(-7.59880 - 10.4589i) q^{11} +(-1.97882 + 3.86192i) q^{12} +(-2.92256 + 4.02255i) q^{13} +(17.2215 + 23.7033i) q^{14} +(3.75005 - 14.5237i) q^{15} +(15.9325 + 11.5756i) q^{16} +(-3.32914 - 10.2460i) q^{17} +(-20.0052 + 6.39968i) q^{18} +(-1.29722 - 3.99244i) q^{19} +(6.64010 + 2.86620i) q^{20} +(-5.97634 + 37.1859i) q^{21} +(28.6939 + 9.32322i) q^{22} +(-17.6249 + 12.8053i) q^{23} +(2.75661 + 17.6643i) q^{24} +(-24.5657 - 4.63950i) q^{25} -11.6038i q^{26} +(-23.9730 - 12.4215i) q^{27} +(-17.2706 - 5.61156i) q^{28} +(-26.0760 - 8.47261i) q^{29} +(12.8426 + 32.5656i) q^{30} +(-8.64023 - 26.5919i) q^{31} -22.1228 q^{32} +(17.5288 + 34.5963i) q^{33} +(20.3406 + 14.7783i) q^{34} +(62.4987 + 5.85006i) q^{35} +(7.69966 - 10.4970i) q^{36} +(-0.0202976 + 0.0279372i) q^{37} +(7.92586 + 5.75848i) q^{38} +(10.5715 - 10.5235i) q^{39} +(29.0733 - 6.52663i) q^{40} +(44.4000 - 61.1113i) q^{41} +(-39.7262 - 78.4072i) q^{42} +43.3942i q^{43} +(-17.7844 + 5.77849i) q^{44} +(-18.0214 + 41.2338i) q^{45} +(15.7112 - 48.3541i) q^{46} +(1.52001 - 4.67812i) q^{47} +(-41.6814 - 41.8713i) q^{48} -108.612 q^{49} +(52.7457 - 24.9385i) q^{50} +(4.98338 + 31.9334i) q^{51} +(4.22736 + 5.81846i) q^{52} +(-0.528642 + 1.62699i) q^{53} +(62.3016 - 9.43260i) q^{54} +(55.6075 - 32.9550i) q^{55} +(-71.1543 + 23.1194i) q^{56} +(1.94181 + 12.4431i) q^{57} +(60.8553 - 19.7731i) q^{58} +(-28.0481 + 38.6049i) q^{59} +(-18.3035 - 11.6506i) q^{60} +(-5.28161 + 3.83732i) q^{61} +(52.7907 + 38.3547i) q^{62} +(35.4038 - 107.299i) q^{63} +(-21.9608 + 15.9555i) q^{64} +(-18.6634 - 16.4236i) q^{65} +(-80.5529 - 41.2746i) q^{66} +(-3.93744 + 1.27935i) q^{67} -15.5831 q^{68} +(58.3007 - 29.5390i) q^{69} +(-126.026 + 74.6874i) q^{70} +(51.8456 + 16.8457i) q^{71} +(0.243811 - 53.6337i) q^{72} +(21.0676 + 28.9970i) q^{73} -0.0805904i q^{74} +(70.5549 + 25.4364i) q^{75} -6.07208 q^{76} +(-131.304 + 95.3981i) q^{77} +(-5.52385 + 34.3704i) q^{78} +(5.27573 - 16.2370i) q^{79} +(-65.0503 + 73.9216i) q^{80} +(65.0948 + 48.2044i) q^{81} +176.287i q^{82} +(-17.6925 - 54.4519i) q^{83} +(48.4840 + 24.8428i) q^{84} +(52.5585 - 11.7988i) q^{85} +(-59.5261 - 81.9306i) q^{86} +(73.2036 + 37.5089i) q^{87} +(-45.2840 + 62.3281i) q^{88} +(-44.4639 - 61.1993i) q^{89} +(-22.5372 - 102.573i) q^{90} +(50.5006 + 36.6908i) q^{91} +(9.73774 + 29.9697i) q^{92} +(12.9335 + 82.8780i) q^{93} +(3.54736 + 10.9176i) q^{94} +(20.4798 - 4.59749i) q^{95} +(65.5274 + 10.5312i) q^{96} +(-28.4310 - 9.23778i) q^{97} +(205.066 - 148.989i) q^{98} +(-35.4509 - 110.818i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 5 q^{3} - 38 q^{4} + 5 q^{6} - 13 q^{9} - 20 q^{10} - 45 q^{12} - 10 q^{13} - 15 q^{15} + 22 q^{16} - 36 q^{19} + 54 q^{21} - 50 q^{22} - 20 q^{24} - 100 q^{25} + 100 q^{27} + 270 q^{28} - 5 q^{30}+ \cdots + 60 q^{99}+O(q^{100}) \) 72 * q - 5 * q^3 - 38 * q^4 + 5 * q^6 - 13 * q^9 - 20 * q^10 - 45 * q^12 - 10 * q^13 - 15 * q^15 + 22 * q^16 - 36 * q^19 + 54 * q^21 - 50 * q^22 - 20 * q^24 - 100 * q^25 + 100 * q^27 + 270 * q^28 - 5 * q^30 - 126 * q^31 + 20 * q^33 + 210 * q^34 - 213 * q^36 + 110 * q^37 - 191 * q^39 + 140 * q^40 - 175 * q^42 - 405 * q^45 - 210 * q^46 + 150 * q^48 - 224 * q^49 - 60 * q^51 - 320 * q^52 + 320 * q^54 - 10 * q^55 - 70 * q^58 + 1190 * q^60 + 294 * q^61 + 795 * q^63 + 362 * q^64 - 470 * q^66 - 260 * q^67 + 335 * q^69 + 1200 * q^70 + 215 * q^72 - 150 * q^73 + 200 * q^75 - 16 * q^76 - 1295 * q^78 - 346 * q^79 + 507 * q^81 - 456 * q^84 - 1450 * q^85 - 430 * q^87 - 1710 * q^88 - 820 * q^90 + 538 * q^91 - 560 * q^94 + 740 * q^96 - 150 * q^97 + 60 * q^99

Introduction

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